Subgroups — #66893

Order 352.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×Q₁₆	C₂	1	1	yes	maximal, characteristic
2	Dic₄₄	C₂	1	1	yes	maximal, characteristic
3	C₁₁⋊C₁₆	C₂	1	1	yes	maximal, characteristic
4	Q₈×C₁₁	—	2	1	no	—
5	Dic₂₂	—	2	1	no	—
6	C₈×C₁₁	C₂²	1	1	yes	characteristic
7	C₄×C₁₁	—	4	1	no	—
8	C₄×C₁₁	D₄	1	1	yes	characteristic
9	Dic₁₁	—	4	1	no	—
10	Q₃₂	—	11	1	no	maximal, Sylow
11	C₂×C₁₁	D₈	1	1	yes	characteristic
12	Q₁₆	—	11	1	no	—
13	Q₁₆	D₁₁	1	1	yes	characteristic
14	C₁₆	—	11	1	no	—
15	C₁₁	Q₃₂	1	1	yes	characteristic, complemented, Sylow
16	Q₈	—	2	1	no	—
17	Q₈	—	22	1	no	—
18	C₈	C₂×D₁₁	1	1	yes	characteristic
19	C₄	—	4	1	no	—
20	C₄	—	44	1	no	—
21	C₄	C₂²⋊D₁₁	1	1	yes	characteristic
22	C₂	#4323	1	1	yes	characteristic

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

N	H ≅ G/N	type
15. C₁₁	Q₃₂	semidirect

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