Subgroups — #66997⋊C₅ #13182542

Order 1760.

136 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Q₈×C₁₁⋊C₅	C₂	1	1	yes	maximal, characteristic
2	C₂×(C₁₁⋊C₅)⋊Q₈	C₂	1	1	yes	maximal, characteristic
3	(Dic₁₁⋊C₄)⋊C₅	C₂	1	4	yes	maximal
4	C₄×Dic₁₁⋊C₅	C₂	1	1	yes	maximal, characteristic
5	Q₈×C₁₁⋊C₅	—	2	2	no	—
6	C₂×C₄×C₁₁⋊C₅	C₂²	1	2	yes	—
7	C₂×C₄×C₁₁⋊C₅	C₂²	1	1	yes	characteristic
8	C₂×Dic₁₁⋊C₅	C₂²	1	2	yes	—
9	C₂×Dic₁₁⋊C₅	C₂²	1	2	yes	—
10	(C₁₁⋊C₅)⋊Q₈	—	2	2	no	—
11	#66997	C₅	1	1	yes	maximal, characteristic, complemented, Hall
12	C₂²×C₁₁⋊C₅	C₂³	1	1	yes	characteristic
13	C₄×C₁₁⋊C₅	—	2	2	no	—
14	C₄×C₁₁⋊C₅	D₄	1	2	yes	—
15	Dic₁₁⋊C₅	—	2	2	no	—
16	Dic₁₁⋊C₅	Q₈	1	4	yes	complemented
17	C₂×Q₈×C₁₁	C₂×C₅	1	1	yes	characteristic
18	C₂×Dic₂₂	C₂×C₅	1	1	yes	characteristic
19	Dic₁₁⋊C₄	C₂×C₅	1	4	yes	—
20	C₄×Dic₁₁	C₂×C₅	1	1	yes	characteristic
21	C₅×C₄⋊Q₈	—	11	1	no	maximal, Hall
22	C₂×C₁₁⋊C₅	C₂×D₄	1	1	yes	characteristic
23	C₂×C₁₁⋊C₅	C₂×Q₈	1	2	yes	—
24	Q₈×C₁₁	—	2	2	no	—
25	C₂×C₄×C₁₁	C₂²×C₅	1	2	yes	—
26	C₂×C₄×C₁₁	C₂²×C₅	1	1	yes	characteristic
27	C₂×Dic₁₁	C₂²×C₅	1	2	yes	—
28	C₂×Dic₁₁	C₂²×C₅	1	2	yes	—
29	Dic₂₂	—	2	2	no	—
30	C₂×C₅×Q₈	—	11	1	no	—
31	C₂×C₅×Q₈	—	11	1	no	—
32	C₅×C₄⋊C₄	—	11	4	no	—
33	C₄²×C₅	—	11	1	no	—
34	C₁₁⋊C₅	C₄⋊Q₈	1	1	yes	characteristic, complemented, Hall
35	C₂²×C₁₁	C₂³×C₅	1	1	yes	characteristic
36	C₄×C₁₁	—	2	2	no	—
37	C₄×C₁₁	C₅×D₄	1	2	yes	—
38	Dic₁₁	—	2	2	no	—
39	Dic₁₁	C₅×Q₈	1	4	yes	complemented
40	C₅×Q₈	—	22	2	no	—
41	C₅×Q₈	—	22	2	no	—
42	C₂×C₄×C₅	—	11	2	no	—
43	C₂×C₄×C₅	—	11	2	no	—
44	C₂×C₄×C₅	—	11	1	no	—
45	C₂×C₄×C₅	—	11	2	no	—
46	C₄⋊Q₈	—	11	1	no	Sylow
47	C₂×C₁₁	C₂×C₅×D₄	1	1	yes	characteristic
48	C₂×C₁₁	C₂×C₅×Q₈	1	2	yes	—
49	C₂²×C₅	—	11	1	no	—
50	C₄×C₅	—	11	4	no	—
51	C₄×C₅	—	11	2	no	—
52	C₄×C₅	—	22	2	no	—
53	C₄×C₅	—	22	2	no	—
54	C₂×Q₈	—	11	1	no	—
55	C₂×Q₈	AGL(1,𝔽₁₁)	1	1	yes	characteristic
56	C₄⋊C₄	—	11	4	no	—
57	C₄²	—	11	1	no	—
58	C₁₁	C₅×C₄⋊Q₈	1	1	yes	characteristic, complemented, Sylow
59	C₂×C₅	—	11	2	no	—
60	C₂×C₅	—	11	1	no	—
61	Q₈	—	2	2	no	—
62	Q₈	—	22	2	no	—
63	C₂×C₄	—	11	2	no	—
64	C₂×C₄	—	11	2	no	—
65	C₂×C₄	C₂×AGL(1,𝔽₁₁)	1	2	yes	—
66	C₂×C₄	C₂×AGL(1,𝔽₁₁)	1	1	yes	characteristic
67	C₅	—	11	1	no	Sylow
68	C₂²	C₂²×AGL(1,𝔽₁₁)	1	1	yes	characteristic
69	C₄	—	2	2	no	—
70	C₄	—	11	4	no	—
71	C₄	—	22	2	no	—
72	C₄	C₂²⋊AGL(1,𝔽₁₁)	1	2	yes	—
73	C₂	Q₈×AGL(1,𝔽₁₁)	1	2	yes	—
74	C₂	C₂×C₂²⋊AGL(1,𝔽₁₁)	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂²×AGL(1,𝔽₁₁)
commutator, socle, cosocle	C₂²×C₁₁	C₂³×C₅
Fitting	C₂×Q₈×C₁₁	C₂×C₅
prime radical	C₂²×C₁₁⋊C₅	C₂³
hypercenter	C₂×Q₈	AGL(1,𝔽₁₁)
hypocenter	C₁₁	C₅×C₄⋊Q₈
LCS	G ▷ C₂²×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂² ◁ C₂×Q₈

Complements

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

N	H ≅ G/N	type
11. #66997	C₅	semidirect
16. Dic₁₁⋊C₅	Q₈	semidirect
34. C₁₁⋊C₅	C₄⋊Q₈	semidirect
39. Dic₁₁	C₅×Q₈	semidirect
58. C₁₁	C₅×C₄⋊Q₈	semidirect

Maximal subgroups

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

subgroup	index
C₂×Q₈×C₁₁⋊C₅	2
C₂×(C₁₁⋊C₅)⋊Q₈	2
(Dic₁₁⋊C₄)⋊C₅	2
C₄×Dic₁₁⋊C₅	2
#66997	5
C₅×C₄⋊Q₈	11

Subgroups — #66997⋊C5 #13182542

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #66997⋊C₅ #13182542