Subgroups — C₂×#4324 #66986

Order 352.

68 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₄×C₁₁	C₂	1	1	yes	maximal, characteristic
2	C₂×Dic₂₂	C₂	1	1	yes	maximal, characteristic, complemented
3	#4324	C₂	1	4	yes	maximal, direct product factor
4	C₂×C₁₁⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂³×C₁₁	—	2	1	no	—
6	D₄×C₁₁	—	2	1	no	—
7	D₄×C₁₁	C₂²	1	2	yes	—
8	C₂×C₄×C₁₁	C₂²	1	1	yes	characteristic
9	C₂×Dic₁₁	—	2	1	no	—
10	Dic₂₂	—	2	1	no	—
11	Dic₂₂	C₂²	1	2	yes	complemented
12	C₁₁⋊C₈	C₂²	1	2	yes	complemented
13	C₂²×C₁₁	—	2	2	no	—
14	C₂²×C₁₁	—	4	2	no	—
15	C₂²×C₁₁	D₄	1	1	yes	characteristic
16	C₄×C₁₁	D₄	1	1	yes	characteristic
17	C₄×C₁₁	C₂³	1	1	yes	characteristic
18	Dic₁₁	—	2	2	no	—
19	C₂×SD₁₆	—	11	1	no	maximal, Sylow
20	C₂×C₁₁	—	4	2	no	—
21	C₂×C₁₁	SD₁₆	1	2	yes	complemented
22	C₂×C₁₁	C₂×D₄	1	1	yes	characteristic
23	C₂×Q₈	—	11	1	no	—
24	C₂×D₄	D₁₁	1	1	yes	characteristic
25	SD₁₆	—	11	4	no	—
26	C₂×C₈	—	11	1	no	—
27	C₁₁	C₂×SD₁₆	1	1	yes	characteristic, complemented, Sylow
28	C₂³	—	2	1	no	—
29	Q₈	—	11	2	no	—
30	Q₈	—	22	1	no	—
31	D₄	—	2	1	no	—
32	D₄	C₂×D₁₁	1	2	yes	—
33	C₂×C₄	—	22	1	no	—
34	C₂×C₄	C₂×D₁₁	1	1	yes	characteristic
35	C₈	—	11	2	no	—
36	C₂²	—	2	2	no	—
37	C₂²	—	4	2	no	—
38	C₂²	C₂²⋊D₁₁	1	1	yes	characteristic
39	C₄	—	22	2	no	—
40	C₄	C₂²⋊D₁₁	1	1	yes	characteristic
41	C₄	C₂²×D₁₁	1	1	yes	characteristic
42	C₂	—	4	2	no	—
43	C₂	#4324	1	2	yes	direct product factor
44	C₂	C₂×C₂²⋊D₁₁	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.