Subgroups — C₄⋊S₄ #980

Order 96.

56 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×S₄	C₂	1	2	yes	maximal, complemented
2	C₄×A₄	C₂	1	1	yes	maximal, characteristic, complemented
3	#121	—	3	1	no	maximal, Sylow
4	C₂×A₄	C₂²	1	1	yes	characteristic
5	S₄	—	2	2	no	—
6	D₁₂	—	4	1	no	maximal
7	C₂×D₄	—	3	1	no	—
8	C₂×D₄	—	3	2	no	—
9	C₂²×C₄	D₃	1	1	yes	characteristic, complemented
10	C₄⋊C₄	—	3	1	no	—
11	C₂²⋊C₄	—	3	2	no	—
12	C₂×D₃	—	4	2	no	—
13	A₄	D₄	1	1	yes	characteristic, complemented
14	C₃×C₄	—	4	1	no	—
15	C₂³	—	3	2	no	—
16	C₂³	C₂×D₃	1	1	yes	characteristic
17	D₄	—	6	1	no	—
18	D₄	—	6	2	no	—
19	D₄	—	6	2	no	—
20	D₄	—	6	1	no	—
21	C₂×C₄	—	3	1	no	—
22	C₂×C₄	—	3	1	no	—
23	C₂×C₄	—	3	2	no	—
24	C₂×C₃	—	4	1	no	—
25	D₃	—	8	2	no	—
26	C₂²	—	3	1	no	—
27	C₂²	—	3	1	no	—
28	C₂²	—	6	2	no	—
29	C₂²	—	6	2	no	—
30	C₂²	—	6	2	no	—
31	C₂²	D₁₂	1	1	yes	characteristic, complemented
32	C₄	—	3	1	no	—
33	C₄	—	6	2	no	—
34	C₄	S₄	1	1	yes	characteristic, complemented
35	C₃	—	4	1	no	Sylow
36	C₂	—	3	1	no	—
37	C₂	—	3	1	no	—
38	C₂	—	12	2	no	—
39	C₂	C₂×S₄	1	1	yes	characteristic

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.