Subgroups — #66871

Order 352.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic
2	C₄⋊Dic₁₁	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₁⋊C₈	C₂	1	1	yes	maximal, characteristic
4	C₂×C₄×C₁₁	—	2	1	no	—
5	C₂×C₄×C₁₁	C₂²	1	1	yes	characteristic
6	C₂×Dic₁₁	—	2	1	no	—
7	C₁₁⋊C₈	C₄	1	2	yes	complemented
8	C₂²×C₁₁	D₄	1	1	yes	characteristic
9	C₄×C₁₁	—	4	1	no	—
10	C₄×C₁₁	C₂×C₄	1	1	yes	characteristic
11	C₄×C₁₁	Q₈	1	1	yes	characteristic
12	Dic₁₁	—	4	1	no	—
13	#107	—	11	1	no	maximal, Sylow
14	C₂×C₁₁	C₄⋊C₄	1	1	yes	characteristic
15	C₂×C₁₁	D₈	1	1	yes	characteristic
16	C₂×C₁₁	Q₁₆	1	1	yes	characteristic
17	C₂×C₈	—	11	1	no	—
18	C₄⋊C₄	—	11	1	no	—
19	C₄⋊C₄	D₁₁	1	1	yes	characteristic
20	C₁₁	#107	1	1	yes	characteristic, complemented, Sylow
21	C₂×C₄	—	2	1	no	—
22	C₂×C₄	—	22	1	no	—
23	C₂×C₄	C₂×D₁₁	1	1	yes	characteristic
24	C₈	—	11	2	no	—
25	C₂²	C₂²⋊D₁₁	1	1	yes	characteristic
26	C₄	—	4	1	no	—
27	C₄	—	44	1	no	—
28	C₄	Dic₂₂	1	1	yes	characteristic
29	C₄	C₄×D₁₁	1	1	yes	characteristic
30	C₂	Dic₁₁⋊C₄	1	1	yes	characteristic
31	C₂	#4323	1	1	yes	characteristic
32	C₂	#4326	1	1	yes	characteristic

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

N	H ≅ G/N	type
7. C₁₁⋊C₈	C₄	semidirect
20. C₁₁	#107	semidirect

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