Subgroups — #66997

Order 352.

68 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Q₈×C₁₁	C₂	1	1	yes	maximal, characteristic
2	C₂×Dic₂₂	C₂	1	1	yes	maximal, characteristic
3	Dic₁₁⋊C₄	C₂	1	4	yes	maximal
4	C₄×Dic₁₁	C₂	1	1	yes	maximal, characteristic
5	Q₈×C₁₁	—	2	2	no	—
6	C₂×C₄×C₁₁	C₂²	1	2	yes	—
7	C₂×C₄×C₁₁	C₂²	1	1	yes	characteristic
8	C₂×Dic₁₁	C₂²	1	2	yes	—
9	C₂×Dic₁₁	C₂²	1	2	yes	—
10	Dic₂₂	—	2	2	no	—
11	C₂²×C₁₁	C₂³	1	1	yes	characteristic
12	C₄×C₁₁	—	2	2	no	—
13	C₄×C₁₁	D₄	1	2	yes	—
14	Dic₁₁	—	2	2	no	—
15	Dic₁₁	Q₈	1	4	yes	complemented
16	C₄⋊Q₈	—	11	1	no	maximal, Sylow
17	C₂×C₁₁	C₂×D₄	1	1	yes	characteristic
18	C₂×C₁₁	C₂×Q₈	1	2	yes	—
19	C₂×Q₈	—	11	1	no	—
20	C₂×Q₈	D₁₁	1	1	yes	characteristic
21	C₄⋊C₄	—	11	4	no	—
22	C₄²	—	11	1	no	—
23	C₁₁	C₄⋊Q₈	1	1	yes	characteristic, complemented, Sylow
24	Q₈	—	2	2	no	—
25	Q₈	—	22	2	no	—
26	C₂×C₄	—	11	2	no	—
27	C₂×C₄	—	11	2	no	—
28	C₂×C₄	C₂×D₁₁	1	2	yes	—
29	C₂×C₄	C₂×D₁₁	1	1	yes	characteristic
30	C₂²	C₂²×D₁₁	1	1	yes	characteristic
31	C₄	—	2	2	no	—
32	C₄	—	11	4	no	—
33	C₄	—	22	2	no	—
34	C₄	C₂²⋊D₁₁	1	2	yes	—
35	C₂	Q₈×D₁₁	1	2	yes	—
36	C₂	C₂×C₂²⋊D₁₁	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂²×D₁₁
commutator, socle, prime radical, cosocle	C₂²×C₁₁	C₂³
Fitting	C₂×Q₈×C₁₁	C₂
hypercenter	C₂×Q₈	D₁₁
hypocenter	C₁₁	C₄⋊Q₈
LCS	G ▷ C₂²×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂² ◁ C₂×Q₈

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

N	H ≅ G/N	type
15. Dic₁₁	Q₈	semidirect
23. C₁₁	C₄⋊Q₈	semidirect

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