Transitive Subgroups of S₄

T	Name(s)	\|G\|	Parity	\|C_S₄(G)\|	Subfields	Other Representations	Resolvents
1	C(4) = 4	4 = 2²	-1	4	2T1		2: 2T1
2	E(4) = 2[x]2	4 = 2²	1	4	2T1, 2T1, 2T1		2: 2T1, 2T1, 2T1
3	D(4)	8 = 2³	-1	2	2T1	4T3, 8T4	2: 2T1, 2T1, 2T1 4: 4T2
4	A4	12 = 2² · 3	1	1		6T4, 12T4	3: 3T1
5	S4	24 = 2³ · 3	-1	1		6T7, 6T8, 8T14, 12T8, 12T9	2: 2T1 6: 3T2