Subgroups — C₁₁×#4090 #13183154

Order 1760.

136 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×Q₈×C₁₁	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₁×Dic₁₀	C₂	1	1	yes	maximal, characteristic
3	C₁₁×#683	C₂	1	4	yes	maximal
4	C₄×C₁₁×Dic₅	C₂	1	1	yes	maximal, characteristic
5	C₅×Q₈×C₁₁	—	2	2	no	—
6	C₂×C₄×C₅×C₁₁	C₂²	1	2	yes	—
7	C₂×C₄×C₅×C₁₁	C₂²	1	1	yes	characteristic
8	C₂×C₁₁×Dic₅	C₂²	1	2	yes	—
9	C₂×C₁₁×Dic₅	C₂²	1	2	yes	—
10	C₁₁×Dic₁₀	—	2	2	no	—
11	C₁₁×C₄⋊Q₈	—	5	1	no	maximal, Hall
12	C₂²×C₅×C₁₁	C₂³	1	1	yes	characteristic
13	C₄×C₅×C₁₁	—	2	2	no	—
14	C₄×C₅×C₁₁	D₄	1	2	yes	—
15	C₁₁×Dic₅	—	2	2	no	—
16	C₁₁×Dic₅	Q₈	1	4	yes	complemented
17	C₂×Q₈×C₁₁	—	5	1	no	—
18	C₂×Q₈×C₁₁	D₅	1	1	yes	characteristic
19	C₁₁×C₄⋊C₄	—	5	4	no	—
20	C₄²×C₁₁	—	5	1	no	—
21	#4090	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
22	C₂×C₅×C₁₁	C₂×D₄	1	1	yes	characteristic
23	C₂×C₅×C₁₁	C₂×Q₈	1	2	yes	—
24	Q₈×C₁₁	—	2	2	no	—
25	Q₈×C₁₁	—	10	2	no	—
26	C₂×C₄×C₁₁	—	5	2	no	—
27	C₂×C₄×C₁₁	—	5	2	no	—
28	C₂×C₄×C₁₁	C₂×D₅	1	2	yes	—
29	C₂×C₄×C₁₁	C₂×D₅	1	1	yes	characteristic
30	C₂×C₅×Q₈	C₂×C₁₁	1	1	yes	characteristic
31	C₂×Dic₁₀	C₂×C₁₁	1	1	yes	characteristic
32	#683	C₂×C₁₁	1	4	yes	—
33	C₄×Dic₅	C₂×C₁₁	1	1	yes	characteristic
34	C₅×C₁₁	C₄⋊Q₈	1	1	yes	characteristic, complemented, Hall
35	C₂²×C₁₁	C₂²×D₅	1	1	yes	characteristic
36	C₄×C₁₁	—	2	2	no	—
37	C₄×C₁₁	—	5	4	no	—
38	C₄×C₁₁	—	10	2	no	—
39	C₄×C₁₁	C₂²⋊D₅	1	2	yes	—
40	C₅×Q₈	—	2	2	no	—
41	C₂×C₄×C₅	C₂²×C₁₁	1	2	yes	—
42	C₂×C₄×C₅	C₂²×C₁₁	1	1	yes	characteristic
43	C₂×Dic₅	C₂²×C₁₁	1	2	yes	—
44	C₂×Dic₅	C₂²×C₁₁	1	2	yes	—
45	Dic₁₀	—	2	2	no	—
46	C₄⋊Q₈	—	5	1	no	Sylow
47	C₂×C₁₁	Q₈×D₅	1	2	yes	—
48	C₂×C₁₁	C₂×C₂²⋊D₅	1	1	yes	characteristic
49	C₂²×C₅	C₂³×C₁₁	1	1	yes	characteristic
50	C₄×C₅	—	2	2	no	—
51	C₄×C₅	D₄×C₁₁	1	2	yes	—
52	Dic₅	—	2	2	no	—
53	Dic₅	Q₈×C₁₁	1	4	yes	complemented
54	C₂×Q₈	—	5	1	no	—
55	C₂×Q₈	D₅×C₁₁	1	1	yes	characteristic
56	C₄⋊C₄	—	5	4	no	—
57	C₄²	—	5	1	no	—
58	C₁₁	#4090	1	1	yes	characteristic, direct product factor, Sylow
59	C₂×C₅	C₂×D₄×C₁₁	1	1	yes	characteristic
60	C₂×C₅	C₂×Q₈×C₁₁	1	2	yes	—
61	Q₈	—	2	2	no	—
62	Q₈	—	10	2	no	—
63	C₂×C₄	—	5	2	no	—
64	C₂×C₄	—	5	2	no	—
65	C₂×C₄	C₂×D₅×C₁₁	1	2	yes	—
66	C₂×C₄	C₂×D₅×C₁₁	1	1	yes	characteristic
67	C₅	C₁₁×C₄⋊Q₈	1	1	yes	characteristic, complemented, Sylow
68	C₂²	C₂²×D₅×C₁₁	1	1	yes	characteristic
69	C₄	—	2	2	no	—
70	C₄	—	5	4	no	—
71	C₄	—	10	2	no	—
72	C₄	C₁₁×C₂²⋊D₅	1	2	yes	—
73	C₂	Q₈×D₅×C₁₁	1	2	yes	—
74	C₂	C₂×C₁₁×C₂²⋊D₅	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₁₁	C₂²×D₅
commutator, cosocle	C₂²×C₅	C₂³×C₁₁
Frattini	C₂²	C₂²×D₅×C₁₁
Fitting	C₂×C₅×Q₈×C₁₁	C₂
socle, prime radical	C₂²×C₅×C₁₁	C₂³
hypercenter	C₂×Q₈×C₁₁	D₅
hypocenter	C₅	C₁₁×C₄⋊Q₈
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂²×C₁₁ ◁ C₂×Q₈×C₁₁

Complements

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

N	H ≅ G/N	type
16. C₁₁×Dic₅	Q₈	semidirect
21. #4090	C₁₁	direct (N × H)
34. C₅×C₁₁	C₄⋊Q₈	semidirect
53. Dic₅	Q₈×C₁₁	semidirect
58. C₁₁	#4090	direct (N × H)
67. C₅	C₁₁×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×C₅×Q₈×C₁₁	2
C₂×C₁₁×Dic₁₀	2
C₁₁×#683	2
C₄×C₁₁×Dic₅	2
C₁₁×C₄⋊Q₈	5
#4090	11

Subgroups — C11×#4090 #13183154

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#4090 #13183154