Subgroups — #66972

Order 352.

62 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#4343	C₂	1	2	yes	maximal, complemented
2	C₁₁×Q₁₆	C₂	1	1	yes	maximal, characteristic, complemented
3	#4325	C₂	1	2	yes	maximal, complemented
4	D₈₈	C₂	1	1	yes	maximal, characteristic, complemented
5	C₈×D₁₁	C₂	1	1	yes	maximal, characteristic, complemented
6	Q₈×C₁₁	C₂²	1	2	yes	—
7	D₄₄	—	2	2	no	—
8	D₄₄	C₂²	1	2	yes	—
9	C₄×D₁₁	—	2	2	no	—
10	C₄×D₁₁	C₂²	1	1	yes	characteristic
11	C₈×C₁₁	C₂²	1	1	yes	characteristic
12	C₁₁⋊C₈	C₂²	1	1	yes	characteristic
13	C₂×D₁₁	—	2	2	no	—
14	C₂×D₁₁	D₄	1	1	yes	characteristic
15	C₄×C₁₁	—	2	2	no	—
16	C₄×C₁₁	C₂³	1	1	yes	characteristic
17	Dic₁₁	D₄	1	1	yes	characteristic
18	#135	—	11	1	no	maximal, Sylow
19	C₂×C₁₁	C₂×D₄	1	1	yes	characteristic
20	D₁₁	—	2	1	no	—
21	D₁₁	—	4	2	no	—
22	#41	—	11	2	no	—
23	Q₁₆	D₁₁	1	1	yes	characteristic, complemented
24	SD₁₆	—	11	2	no	—
25	D₈	—	11	1	no	—
26	C₂×C₈	—	11	1	no	—
27	C₁₁	#135	1	1	yes	characteristic, complemented, Sylow
28	Q₈	C₂×D₁₁	1	2	yes	—
29	D₄	—	11	2	no	—
30	D₄	—	22	2	no	—
31	C₂×C₄	—	11	1	no	—
32	C₂×C₄	—	22	2	no	—
33	C₈	—	11	1	no	—
34	C₈	C₂×D₁₁	1	1	yes	characteristic
35	C₂²	—	11	1	no	—
36	C₂²	—	22	2	no	—
37	C₄	—	2	2	no	—
38	C₄	—	11	1	no	—
39	C₄	C₂²×D₁₁	1	1	yes	characteristic
40	C₂	—	22	1	no	—
41	C₂	—	44	2	no	—
42	C₂	D₄×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.