Subgroups — C₂²×S₄ #1019

Order 96.

131 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×A₄	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×S₄	C₂	1	6	yes	maximal, direct product factor
3	C₂²×D₄	—	3	1	no	maximal, Sylow
4	C₂²×D₃	—	4	1	no	maximal
5	C₂×A₄	C₂²	1	3	yes	complemented
6	S₄	C₂²	1	4	yes	direct product factor
7	C₂⁴	—	3	1	no	—
8	C₂⁴	D₃	1	1	yes	characteristic, complemented
9	C₂×D₄	—	3	6	no	—
10	C₂×D₄	—	3	6	no	—
11	C₂²×C₄	—	3	1	no	—
12	C₂²×C₃	—	4	1	no	—
13	C₂×D₃	—	4	6	no	—
14	A₄	C₂³	1	1	yes	characteristic, complemented
15	C₂³	—	3	1	no	—
16	C₂³	—	3	3	no	—
17	C₂³	—	3	6	no	—
18	C₂³	—	6	3	no	—
19	C₂³	—	6	1	no	—
20	C₂³	C₂×D₃	1	3	yes	complemented
21	D₄	—	3	12	no	—
22	D₄	—	3	4	no	—
23	C₂×C₄	—	3	6	no	—
24	C₂×C₃	—	4	3	no	—
25	D₃	—	4	4	no	—
26	C₂²	—	3	3	no	—
27	C₂²	—	3	3	no	—
28	C₂²	—	3	3	no	—
29	C₂²	—	3	4	no	—
30	C₂²	—	6	1	no	—
31	C₂²	—	6	6	no	—
32	C₂²	—	6	6	no	—
33	C₂²	S₄	1	1	yes	characteristic, direct product factor
34	C₂²	C₂²×D₃	1	1	yes	characteristic, complemented
35	C₄	—	3	4	no	—
36	C₃	—	4	1	no	Sylow
37	C₂	—	3	1	no	—
38	C₂	—	3	3	no	—
39	C₂	—	6	4	no	—
40	C₂	C₂×S₄	1	3	yes	direct product factor

	subgroup	G/H
center, hypercenter	C₂²	S₄
commutator, cosocle, hypocenter	A₄	C₂³
Frattini	C₁	G
Fitting, socle	C₂⁴	D₃
LCS	G ▷ A₄
UCS	C₁ ◁ C₂²

Splittings G = N ⋊ H with N normal; H ≅ G/N.

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.