Subgroups — C₁₁×#4034 #13183102

Order 1760.

136 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₁×Dic₁₀	C₂	1	2	yes	maximal
2	C₅×C₁₁×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic
3	C₁₁×C₄⋊Dic₅	C₂	1	1	yes	maximal, characteristic
4	C₁₁×#683	C₂	1	2	yes	maximal
5	C₄×C₁₁×Dic₅	C₂	1	1	yes	maximal, characteristic
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	1	yes	characteristic
10	C₂×C₁₁×Dic₅	C₂²	1	1	yes	characteristic
11	C₁₁×Dic₁₀	—	2	4	no	—
12	C₁₁×C₄⋊Q₈	—	5	1	no	maximal, Hall
13	C₂²×C₅×C₁₁	C₂³	1	1	yes	characteristic
14	C₄×C₅×C₁₁	—	2	2	no	—
15	C₄×C₅×C₁₁	Q₈	1	2	yes	complemented
16	C₁₁×Dic₅	—	2	2	no	—
17	C₁₁×Dic₅	D₄	1	2	yes	—
18	C₁₁×Dic₅	Q₈	1	2	yes	complemented
19	C₂×Q₈×C₁₁	—	5	2	no	—
20	C₁₁×C₄⋊C₄	—	5	2	no	—
21	C₁₁×C₄⋊C₄	—	5	1	no	—
22	C₁₁×C₄⋊C₄	D₅	1	1	yes	characteristic
23	C₄²×C₁₁	—	5	1	no	—
24	#4034	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
25	C₂×C₅×C₁₁	C₂×D₄	1	1	yes	characteristic
26	C₂×C₅×C₁₁	C₂×Q₈	1	1	yes	characteristic
27	C₂×C₅×C₁₁	C₂×Q₈	1	1	yes	characteristic
28	Q₈×C₁₁	—	10	4	no	—
29	C₂×C₄×C₁₁	—	5	1	no	—
30	C₂×C₄×C₁₁	—	5	1	no	—
31	C₂×C₄×C₁₁	—	5	2	no	—
32	C₂×C₄×C₁₁	C₂×D₅	1	2	yes	—
33	C₂×C₄×C₁₁	C₂×D₅	1	1	yes	characteristic
34	C₂×Dic₁₀	C₂×C₁₁	1	2	yes	—
35	C₅×C₄⋊C₄	C₂×C₁₁	1	1	yes	characteristic
36	C₄⋊Dic₅	C₂×C₁₁	1	1	yes	characteristic
37	#683	C₂×C₁₁	1	2	yes	—
38	C₄×Dic₅	C₂×C₁₁	1	1	yes	characteristic
39	C₅×C₁₁	C₄⋊Q₈	1	1	yes	characteristic, complemented, Hall
40	C₂²×C₁₁	C₂²×D₅	1	1	yes	characteristic
41	C₄×C₁₁	—	2	2	no	—
42	C₄×C₁₁	—	5	2	no	—
43	C₄×C₁₁	—	5	2	no	—
44	C₄×C₁₁	—	10	2	no	—
45	C₄×C₁₁	Dic₁₀	1	2	yes	complemented
46	C₂×C₄×C₅	C₂²×C₁₁	1	2	yes	—
47	C₂×C₄×C₅	C₂²×C₁₁	1	1	yes	characteristic
48	C₂×Dic₅	C₂²×C₁₁	1	2	yes	—
49	C₂×Dic₅	C₂²×C₁₁	1	1	yes	characteristic
50	C₂×Dic₅	C₂²×C₁₁	1	1	yes	characteristic
51	Dic₁₀	—	2	4	no	—
52	C₄⋊Q₈	—	5	1	no	Sylow
53	C₂×C₁₁	C₂×Dic₁₀	1	1	yes	characteristic
54	C₂×C₁₁	D₄×D₅	1	1	yes	characteristic
55	C₂×C₁₁	Q₈×D₅	1	1	yes	characteristic
56	C₂²×C₅	C₂³×C₁₁	1	1	yes	characteristic
57	C₄×C₅	—	2	2	no	—
58	C₄×C₅	Q₈×C₁₁	1	2	yes	complemented
59	Dic₅	—	2	2	no	—
60	Dic₅	D₄×C₁₁	1	2	yes	—
61	Dic₅	Q₈×C₁₁	1	2	yes	complemented
62	C₂×Q₈	—	5	2	no	—
63	C₄⋊C₄	—	5	2	no	—
64	C₄⋊C₄	—	5	1	no	—
65	C₄⋊C₄	D₅×C₁₁	1	1	yes	characteristic
66	C₄²	—	5	1	no	—
67	C₁₁	#4034	1	1	yes	characteristic, direct product factor, Sylow
68	C₂×C₅	C₂×D₄×C₁₁	1	1	yes	characteristic
69	C₂×C₅	C₂×Q₈×C₁₁	1	1	yes	characteristic
70	C₂×C₅	C₂×Q₈×C₁₁	1	1	yes	characteristic
71	Q₈	—	10	4	no	—
72	C₂×C₄	—	5	1	no	—
73	C₂×C₄	—	5	1	no	—
74	C₂×C₄	—	5	2	no	—
75	C₂×C₄	C₂×D₅×C₁₁	1	2	yes	—
76	C₂×C₄	C₂×D₅×C₁₁	1	1	yes	characteristic
77	C₅	C₁₁×C₄⋊Q₈	1	1	yes	characteristic, complemented, Sylow
78	C₂²	C₂²×D₅×C₁₁	1	1	yes	characteristic
79	C₄	—	2	2	no	—
80	C₄	—	5	2	no	—
81	C₄	—	5	2	no	—
82	C₄	—	10	2	no	—
83	C₄	C₁₁×Dic₁₀	1	2	yes	complemented
84	C₂	C₂×C₁₁×Dic₁₀	1	1	yes	characteristic
85	C₂	D₄×D₅×C₁₁	1	1	yes	characteristic
86	C₂	Q₈×D₅×C₁₁	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
15. C₄×C₅×C₁₁	Q₈	semidirect
18. C₁₁×Dic₅	Q₈	semidirect
24. #4034	C₁₁	direct (N × H)
39. C₅×C₁₁	C₄⋊Q₈	semidirect
45. C₄×C₁₁	Dic₁₀	semidirect
58. C₄×C₅	Q₈×C₁₁	semidirect
61. Dic₅	Q₈×C₁₁	semidirect
67. C₁₁	#4034	direct (N × H)
77. C₅	C₁₁×C₄⋊Q₈	semidirect
83. C₄	C₁₁×Dic₁₀	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₁₁×Dic₁₀	2
C₅×C₁₁×C₄⋊C₄	2
C₁₁×C₄⋊Dic₅	2
C₁₁×#683	2
C₄×C₁₁×Dic₅	2
C₁₁×C₄⋊Q₈	5
#4034	11

Subgroups — C11×#4034 #13183102

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#4034 #13183102