Subgroups — #66876

Order 352.

26 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₈×C₁₁	C₂	1	1	yes	maximal, characteristic
2	C₁₁⋊C₁₆	C₂	1	2	yes	maximal, complemented
3	C₂×C₄×C₁₁	C₄	1	1	yes	characteristic
4	C₈×C₁₁	C₄	1	1	yes	characteristic
5	C₈×C₁₁	C₂²	1	1	yes	characteristic
6	C₂²×C₁₁	C₈	1	1	yes	characteristic
7	C₄×C₁₁	C₈	1	1	yes	characteristic
8	C₄×C₁₁	C₂×C₄	1	1	yes	characteristic
9	M₃₂	—	11	1	no	maximal, Sylow
10	C₂×C₁₁	—	2	1	no	—
11	C₂×C₁₁	C₂×C₈	1	1	yes	characteristic
12	C₂×C₈	D₁₁	1	1	yes	characteristic
13	C₁₆	—	11	2	no	—
14	C₁₁	M₃₂	1	1	yes	characteristic, complemented, Sylow
15	C₂×C₄	Dic₁₁	1	1	yes	characteristic
16	C₈	Dic₁₁	1	1	yes	characteristic
17	C₈	C₂×D₁₁	1	1	yes	characteristic
18	C₂²	C₁₁⋊C₈	1	1	yes	characteristic
19	C₄	C₁₁⋊C₈	1	1	yes	characteristic
20	C₄	C₂×Dic₁₁	1	1	yes	characteristic
21	C₂	—	2	1	no	—
22	C₂	C₂×C₁₁⋊C₈	1	1	yes	characteristic

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

N	H ≅ G/N	type
2. C₁₁⋊C₁₆	C₂	semidirect
14. C₁₁	M₃₂	semidirect

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