Subgroups — C₄×Dic₂₂ #66921

Order 352.

70 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Dic₂₂	C₂	1	1	yes	maximal, characteristic
2	C₄²×C₁₁	C₂	1	1	yes	maximal, characteristic
3	C₄⋊Dic₁₁	C₂	1	1	yes	maximal, characteristic
4	Dic₁₁⋊C₄	C₂	1	2	yes	maximal
5	C₄×Dic₁₁	C₂	1	2	yes	maximal
6	C₂×C₄×C₁₁	C₂²	1	1	yes	characteristic
7	C₂×C₄×C₁₁	C₂²	1	1	yes	characteristic
8	C₂×C₄×C₁₁	C₂²	1	1	yes	characteristic
9	C₂×Dic₁₁	C₂²	1	2	yes	—
10	C₂×Dic₁₁	C₂²	1	2	yes	—
11	Dic₂₂	C₄	1	4	yes	direct product factor
12	C₂²×C₁₁	C₂³	1	1	yes	characteristic
13	C₄×C₁₁	—	2	1	no	—
14	C₄×C₁₁	C₂×C₄	1	2	yes	—
15	C₄×C₁₁	Q₈	1	2	yes	complemented
16	Dic₁₁	—	2	2	no	—
17	Dic₁₁	C₂×C₄	1	4	yes	—
18	C₄×Q₈	—	11	1	no	maximal, Sylow
19	C₂×C₁₁	C₂²×C₄	1	1	yes	characteristic
20	C₂×C₁₁	C₂×Q₈	1	1	yes	characteristic
21	C₂×C₁₁	#41	1	1	yes	characteristic
22	C₂×Q₈	—	11	1	no	—
23	C₄⋊C₄	—	11	2	no	—
24	C₄⋊C₄	—	11	1	no	—
25	C₄²	—	11	2	no	—
26	C₄²	D₁₁	1	1	yes	characteristic
27	C₁₁	C₄×Q₈	1	1	yes	characteristic, complemented, Sylow
28	Q₈	—	11	4	no	—
29	C₂×C₄	—	11	2	no	—
30	C₂×C₄	—	11	2	no	—
31	C₂×C₄	C₂×D₁₁	1	1	yes	characteristic
32	C₂×C₄	C₂×D₁₁	1	1	yes	characteristic
33	C₂×C₄	C₂×D₁₁	1	1	yes	characteristic
34	C₂²	C₂²×D₁₁	1	1	yes	characteristic
35	C₄	—	2	1	no	—
36	C₄	—	11	4	no	—
37	C₄	—	22	2	no	—
38	C₄	Dic₂₂	1	2	yes	direct product factor
39	C₄	C₄×D₁₁	1	2	yes	—
40	C₂	C₂×Dic₂₂	1	1	yes	characteristic
41	C₂	C₂×C₄×D₁₁	1	1	yes	characteristic
42	C₂	#4339	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.