T	Name(s)	\|G\|	Parity	\|C_S₂₂(G)\|	Subfields	Other Representations	Resolvents
1	t22n1	22 = 2 · 11	-1	22	2T1, 11T1		2: 2T1 11: 11T1
2	t22n2	22 = 2 · 11	-1	22	2T1, 11T2	11T2	2: 2T1
3	t22n3	44 = 2² · 11	-1	2	2T1, 11T2	22T3	2: 2T1, 2T1, 2T1 4: 4T2 22: 11T2
4	t22n4	110 = 2 · 5 · 11	-1	2	2T1, 11T4	11T4	2: 2T1 5: 5T1 10: 10T1
5	t22n5	110 = 2 · 5 · 11	-1	2	2T1, 11T3		2: 2T1 5: 5T1 10: 10T1 55: 11T3
6	t22n6	220 = 2² · 5 · 11	-1	2	2T1, 11T4	22T6	2: 2T1, 2T1, 2T1 4: 4T2 5: 5T1 10: 10T1, 10T1, 10T1 20: 20T3 110: 11T4
7	t22n7	242 = 2 · 11²	-1	11	2T1	22T7, 22T7, 22T7, 22T7	2: 2T1 11: 11T1 22: 11T2, 22T1
8	t22n8	484 = 2² · 11²	1	1	2T1	22T8, 22T8, 22T8, 22T8, 22T8	2: 2T1 4: 4T1
9	t22n9	484 = 2² · 11²	-1	1	2T1	22T9, 22T9, 22T9, 22T9	2: 2T1, 2T1, 2T1 4: 4T2 22: 11T2, 11T2 44: 22T3, 22T3
10	t22n10	968 = 2³ · 11²	-1	1	2T1	22T10	2: 2T1, 2T1, 2T1 4: 4T2 8: 4T3
11	t22n11	1210 = 2 · 5 · 11²	-1	1	2T1	22T11, 22T11, 22T11, 22T11	2: 2T1 5: 5T1 10: 10T1 55: 11T3 110: 11T4, 22T5
12	t22n12	1210 = 2 · 5 · 11²	-1	1	2T1		2: 2T1 10: 5T2
13	t22n13	1320 = 2³ · 3 · 5 · 11	-1	2	2T1, 11T5	22T13	2: 2T1 660: 11T5
14	t22n14	1320 = 2³ · 3 · 5 · 11	-1	1	2T1	12T218	2: 2T1
15	t22n15	2420 = 2² · 5 · 11²	-1	1	2T1	22T15, 22T15, 22T15, 22T15	2: 2T1, 2T1, 2T1 4: 4T2 5: 5T1 10: 10T1, 10T1, 10T1 20: 20T3 110: 11T4, 11T4 220: 22T6, 22T6
16	t22n16	2420 = 2² · 5 · 11²	1	1	2T1		2: 2T1 4: 4T1 10: 5T2 20: 20T2
17	t22n17	2420 = 2² · 5 · 11²	-1	1	2T1		2: 2T1, 2T1, 2T1 4: 4T2 10: 5T2 20: 10T3
18	t22n18	2420 = 2² · 5 · 11²	1	1	2T1	22T18, 22T18, 22T18, 22T18, 22T18	2: 2T1 4: 4T1 5: 5T1 10: 10T1 20: 20T1
19	t22n19	4840 = 2³ · 5 · 11²	-1	1	2T1		2: 2T1, 2T1, 2T1 4: 4T2 8: 4T3 10: 5T2 20: 10T3 40: 20T7
20	t22n20	4840 = 2³ · 5 · 11²	-1	1	2T1	22T20	2: 2T1, 2T1, 2T1 4: 4T2 5: 5T1 8: 4T3 10: 10T1, 10T1, 10T1 20: 20T3 40: 20T12
21	t22n21	6050 = 2 · 5² · 11²	-1	1	2T1		2: 2T1 5: 5T1 10: 5T2, 10T1 50: 10T6
22	t22n22	7920 = 2⁴ · 3² · 5 · 11	1	2	11T6	11T6, 12T272
23	t22n23	11264 = 2¹⁰ · 11	1	2	11T1	22T23, 22T23, 22T23, 22T23, 22T23, 22T23, 22T23, 22T23, 22T23, 22T23, 22T23, 22T23, 22T23, 22T23, 22T23, 22T23, 22T23, 22T23, 22T23, 22T23, 22T23, 22T23, 22T23, 22T23, 22T23, 22T23, 22T23, 22T23, 22T23, 22T23, 22T23, 22T23, 22T23, 22T23, 22T23, 22T23, 22T23, 22T23, 22T23, 22T23, 22T23, 22T23, 22T23, 22T23, 22T23, 22T23, 22T23, 22T23, 22T23, 22T23, 22T23, 22T23, 22T23, 22T23, 22T23, 22T23, 22T23, 22T23, 22T23, 22T23, 22T23, 22T23, 22T23, 22T23, 22T23, 22T23, 22T23, 22T23, 22T23, 22T23, 22T23, 22T23, 22T23, 22T23, 22T23, 22T23, 22T23, 22T23, 22T23, 22T23, 22T23, 22T23, 22T23, 22T23, 22T23, 22T23, 22T23, 22T23, 22T23, 22T23, 22T23, 22T23	11: 11T1
24	t22n24	12100 = 2² · 5² · 11²	1	1	2T1		2: 2T1 4: 4T1 5: 5T1 10: 5T2, 10T1 20: 20T1, 20T2 50: 10T6 100: 20T25
25	t22n25	12100 = 2² · 5² · 11²	-1	1	2T1		2: 2T1, 2T1, 2T1 4: 4T2 5: 5T1 10: 5T2, 10T1, 10T1, 10T1 20: 10T3, 20T3 50: 10T6 100: 20T24
26	t22n26	15840 = 2⁵ · 3² · 5 · 11	-1	2	11T6	22T27	2: 2T1 7920: 11T6
27	t22n27	15840 = 2⁵ · 3² · 5 · 11	-1	2	2T1, 11T6	22T26	2: 2T1 7920: 11T6
28	t22n28	22528 = 2¹¹ · 11	-1	2	11T1	22T28, 22T28, 22T28, 22T28, 22T28, 22T28, 22T28, 22T28, 22T28, 22T28, 22T28, 22T28, 22T28, 22T28, 22T28, 22T28, 22T28, 22T28, 22T28, 22T28, 22T28, 22T28, 22T28, 22T28, 22T28, 22T28, 22T28, 22T28, 22T28, 22T28, 22T28, 22T28, 22T28, 22T28, 22T28, 22T28, 22T28, 22T28, 22T28, 22T28, 22T28, 22T28, 22T28, 22T28, 22T28, 22T28, 22T28, 22T28, 22T28, 22T28, 22T28, 22T28, 22T28, 22T28, 22T28, 22T28, 22T28, 22T28, 22T28, 22T28, 22T28, 22T28, 22T28, 22T28, 22T28, 22T28, 22T28, 22T28, 22T28, 22T28, 22T28, 22T28, 22T28, 22T28, 22T28, 22T28, 22T28, 22T28, 22T28, 22T28, 22T28, 22T28, 22T28, 22T28, 22T28, 22T28, 22T28, 22T28, 22T28, 22T28, 22T28, 22T28	2: 2T1 11: 11T1 22: 22T1 11264: 22T23
29	t22n29	22528 = 2¹¹ · 11	-1	2	11T2	22T30, 22T29, 22T30, 22T30, 22T29, 22T29, 22T30, 22T29, 22T30, 22T29, 22T30, 22T29, 22T29, 22T30, 22T30, 22T29, 22T29, 22T30, 22T30, 22T29, 22T30, 22T30, 22T30, 22T29, 22T29, 22T30, 22T29, 22T30, 22T29, 22T30, 22T29, 22T30, 22T30, 22T29, 22T29, 22T30, 22T29, 22T30, 22T29, 22T30, 22T30, 22T29, 22T30, 22T29, 22T30, 22T29, 22T30, 22T29, 22T29, 22T30, 22T30, 22T29, 22T29, 22T30, 22T30, 22T29, 22T29, 22T30, 22T29, 22T30, 22T29	2: 2T1 22: 11T2
30	t22n30	22528 = 2¹¹ · 11	1	2	11T2	22T29, 22T29, 22T30, 22T29, 22T30, 22T29, 22T30, 22T30, 22T29, 22T29, 22T29, 22T30, 22T30, 22T29, 22T29, 22T30, 22T29, 22T30, 22T30, 22T29, 22T29, 22T30, 22T30, 22T29, 22T30, 22T29, 22T29, 22T30, 22T30, 22T29, 22T29, 22T30, 22T29, 22T30, 22T30, 22T29, 22T29, 22T30, 22T30, 22T29, 22T30, 22T29, 22T29, 22T30, 22T29, 22T30, 22T29, 22T30, 22T29, 22T30, 22T30, 22T29, 22T30, 22T29, 22T30, 22T29, 22T30, 22T29, 22T29, 22T30, 22T30	2: 2T1 22: 11T2
31	t22n31	24200 = 2³ · 5² · 11²	-1	1	2T1		2: 2T1, 2T1, 2T1 4: 4T2 5: 5T1 8: 4T3 10: 5T2, 10T1, 10T1, 10T1 20: 10T3, 20T3 40: 20T7, 20T12 50: 10T6 100: 20T24 200: 20T53
32	t22n32	45056 = 2¹² · 11	-1	2	11T2	22T32, 22T32, 22T32, 22T32, 22T32, 22T32, 22T32, 22T32, 22T32, 22T32, 22T32, 22T32, 22T32, 22T32, 22T32, 22T32, 22T32, 22T32, 22T32, 22T32, 22T32, 22T32, 22T32, 22T32, 22T32, 22T32, 22T32, 22T32, 22T32, 22T32, 22T32, 22T32, 22T32, 22T32, 22T32, 22T32, 22T32, 22T32, 22T32, 22T32, 22T32, 22T32, 22T32, 22T32, 22T32, 22T32, 22T32, 22T32, 22T32, 22T32, 22T32, 22T32, 22T32, 22T32, 22T32, 22T32, 22T32, 22T32, 22T32, 22T32, 22T32	2: 2T1, 2T1, 2T1 4: 4T2 22: 11T2 44: 22T3 22528: 22T29
33	t22n33	56320 = 2¹⁰ · 5 · 11	1	2	11T3	22T33, 22T33	5: 5T1 55: 11T3
34	t22n34	112640 = 2¹¹ · 5 · 11	1	2	11T4	22T35	2: 2T1 5: 5T1 10: 10T1 110: 11T4
35	t22n35	112640 = 2¹¹ · 5 · 11	-1	2	11T4	22T34	2: 2T1 5: 5T1 10: 10T1 110: 11T4
36	t22n36	112640 = 2¹¹ · 5 · 11	-1	2	11T3	22T36, 22T36	2: 2T1 5: 5T1 10: 10T1 55: 11T3 110: 22T5 56320: 22T33
37	t22n37	225280 = 2¹² · 5 · 11	-1	2	11T4	22T37	2: 2T1, 2T1, 2T1 4: 4T2 5: 5T1 10: 10T1, 10T1, 10T1 20: 20T3 110: 11T4 220: 22T6 112640: 22T34
38	t22n38	443520 = 2⁷ · 3² · 5 · 7 · 11	1	1
39	t22n39	675840 = 2¹² · 3 · 5 · 11	1	2	11T5	22T39	660: 11T5
40	t22n40	871200 = 2⁵ · 3² · 5² · 11²	-1	1	2T1	22T40	2: 2T1
41	t22n41	887040 = 2⁸ · 3² · 5 · 7 · 11	-1	1			2: 2T1
42	t22n42	1351680 = 2¹³ · 3 · 5 · 11	-1	2	11T5	22T42	2: 2T1 660: 11T5 1320: 22T13 675840: 22T39
43	t22n43	8110080 = 2¹⁴ · 3² · 5 · 11	1	2	11T6	22T43	7920: 11T6
44	t22n44	16220160 = 2¹⁵ · 3² · 5 · 11	-1	2	11T6	22T44	2: 2T1 7920: 11T6 15840: 22T26 8110080: 22T43
45	t22n45	39916800 = 2⁸ · 3⁴ · 5² · 7 · 11	-1	2	2T1, 11T8	11T8	2: 2T1
46	t22n46	39916800 = 2⁸ · 3⁴ · 5² · 7 · 11	-1	2	2T1, 11T7		2: 2T1 19958400: 11T7
47	t22n47	79833600 = 2⁹ · 3⁴ · 5² · 7 · 11	-1	2	2T1, 11T8	22T47	2: 2T1, 2T1, 2T1 4: 4T2 39916800: 11T8
48	t22n48	125452800 = 2⁹ · 3⁴ · 5² · 11²	-1	1	2T1		2: 2T1
49	t22n49	20437401600 = 2¹⁷ · 3⁴ · 5² · 7 · 11	1	2	11T7		19958400: 11T7
50	t22n50	40874803200 = 2¹⁸ · 3⁴ · 5² · 7 · 11	-1	2	11T8	22T51	2: 2T1 39916800: 11T8
51	t22n51	40874803200 = 2¹⁸ · 3⁴ · 5² · 7 · 11	1	2	11T8	22T50	2: 2T1 39916800: 11T8
52	t22n52	40874803200 = 2¹⁸ · 3⁴ · 5² · 7 · 11	-1	2	11T7		2: 2T1 19958400: 11T7 39916800: 22T46 20437401600: 22T49
53	t22n53	81749606400 = 2¹⁹ · 3⁴ · 5² · 7 · 11	-1	2	11T8	22T53	2: 2T1, 2T1, 2T1 4: 4T2 39916800: 11T8 79833600: 22T47 40874803200: 22T50
54	t22n54	796675461120000 = 2¹⁵ · 3⁸ · 5⁴ · 7² · 11²	-1	1	2T1		2: 2T1
55	t22n55	1593350922240000 = 2¹⁶ · 3⁸ · 5⁴ · 7² · 11²	1	1	2T1		2: 2T1 4: 4T1
56	t22n56	1593350922240000 = 2¹⁶ · 3⁸ · 5⁴ · 7² · 11²	-1	1	2T1		2: 2T1, 2T1, 2T1 4: 4T2
57	t22n57	3186701844480000 = 2¹⁷ · 3⁸ · 5⁴ · 7² · 11²	-1	1	2T1		2: 2T1, 2T1, 2T1 4: 4T2 8: 4T3
58	A22	562000363888803840000 = 2¹⁸ · 3⁹ · 5⁴ · 7³ · 11² · 13 · 17 · 19	1	1
59	S22	1124000727777607680000 = 2¹⁹ · 3⁹ · 5⁴ · 7³ · 11² · 13 · 17 · 19	-1	1			2: 2T1

Transitive Subgroups of S22

Transitive Subgroups of S₂₂