Subgroups — C₁₁×C₁₁⋊#63118 #44538261

Order 31460.

88 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₁₁²×D₁₃	C₂	1	1	yes	maximal, characteristic
2	C₅×C₁₁²×C₁₃	C₄	1	1	yes	characteristic, complemented, Hall
3	C₁₁×C₁₁⋊#261	—	5	1	no	maximal, Hall
4	C₁₁²×D₁₃	D₅	1	1	yes	characteristic
5	C₁₁⋊#63118	C₁₁	1	1	yes	maximal, characteristic, direct product factor
6	C₁₁×#63118	—	11	1	no	maximal
7	C₁₁×Dic₅₅	—	13	1	no	maximal, Hall
8	C₁₁²×C₁₃	Dic₅	1	1	yes	characteristic, complemented, Hall
9	C₅×C₁₁×D₁₃	—	2	5	no	—
10	C₅×C₁₁×D₁₃	D₁₁	1	1	yes	characteristic
11	C₅×C₁₁×D₁₃	C₂×C₁₁	1	1	yes	characteristic
12	C₂×C₅×C₁₁²	—	13	1	no	—
13	C₅×C₁₁×C₁₃	—	2	5	no	—
14	C₅×C₁₁×C₁₃	Dic₁₁	1	1	yes	characteristic, complemented
15	C₅×C₁₁×C₁₃	C₄×C₁₁	1	1	yes	characteristic, complemented
16	C₅×C₁₁²	#261	1	1	yes	characteristic, complemented, Hall
17	C₁₁⋊#261	—	5	1	no	—
18	C₁₁×#261	—	55	1	no	—
19	C₁₁×Dic₁₁	—	65	1	no	Hall
20	C₁₁×D₁₃	—	2	5	no	—
21	C₁₁×D₁₃	D₅×C₁₁	1	1	yes	characteristic
22	C₁₁×D₁₃	D₅₅	1	1	yes	characteristic
23	#63118	—	11	1	no	Hall
24	C₂×C₁₁²	—	13	1	no	—
25	Dic₅₅	—	13	1	no	—
26	C₁₁×Dic₅	—	143	1	no	—
27	C₁₁×C₁₃	—	2	5	no	—
28	C₁₁×C₁₃	C₁₁×Dic₅	1	1	yes	characteristic, complemented
29	C₁₁×C₁₃	Dic₅₅	1	1	yes	characteristic, complemented
30	C₅×D₁₃	C₁₁×D₁₁	1	1	yes	characteristic
31	C₁₁²	#63118	1	1	yes	characteristic, complemented, Sylow
32	C₂×C₅×C₁₁	—	13	1	no	—
33	C₂×C₅×C₁₁	—	13	1	no	—
34	C₂×C₅×C₁₁	—	26	5	no	—
35	C₅×C₁₃	C₁₁×Dic₁₁	1	1	yes	characteristic, complemented, Hall
36	C₅×C₁₁	—	2	5	no	—
37	C₅×C₁₁	C₁₁×#261	1	1	yes	characteristic, complemented
38	C₅×C₁₁	C₁₁⋊#261	1	1	yes	characteristic, complemented
39	#261	—	55	1	no	Hall
40	C₄×C₁₁	—	715	1	no	—
41	Dic₁₁	—	65	1	no	—
42	D₁₃	C₁₁×D₅₅	1	1	yes	characteristic
43	C₂×C₁₁	—	13	1	no	—
44	C₂×C₁₁	—	13	1	no	—
45	C₂×C₁₁	—	26	5	no	—
46	Dic₅	—	143	1	no	Hall
47	C₁₃	C₁₁×Dic₅₅	1	1	yes	characteristic, complemented, Sylow
48	C₁₁	—	2	5	no	—
49	C₁₁	C₁₁×#63118	1	1	yes	characteristic, complemented
50	C₁₁	C₁₁⋊#63118	1	1	yes	characteristic, direct product factor
51	C₂×C₅	—	13	1	no	—
52	C₅	C₁₁×C₁₁⋊#261	1	1	yes	characteristic, complemented, Sylow
53	C₄	—	715	1	no	Sylow
54	C₂	—	13	1	no	—

	subgroup	G/H
center, hypercenter	C₁₁	C₁₁⋊#63118
commutator, hypocenter	C₅×C₁₁×C₁₃	C₄×C₁₁
Frattini	C₁	G
Fitting, socle	C₅×C₁₁²×C₁₃	C₄
prime radical	C₅×C₁₁²×D₁₃	C₂
cosocle	C₅×C₁₁×D₁₃	C₂×C₁₁
LCS	G ▷ C₅×C₁₁×C₁₃
UCS	C₁ ◁ C₁₁

Complements

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

N	H ≅ G/N	type
2. C₅×C₁₁²×C₁₃	C₄	semidirect
5. C₁₁⋊#63118	C₁₁	direct (N × H)
8. C₁₁²×C₁₃	Dic₅	semidirect
14. C₅×C₁₁×C₁₃	Dic₁₁	semidirect
15. C₅×C₁₁×C₁₃	C₄×C₁₁	semidirect
16. C₅×C₁₁²	#261	semidirect
28. C₁₁×C₁₃	C₁₁×Dic₅	semidirect
29. C₁₁×C₁₃	Dic₅₅	semidirect
31. C₁₁²	#63118	semidirect
35. C₅×C₁₃	C₁₁×Dic₁₁	semidirect
37. C₅×C₁₁	C₁₁×#261	semidirect
38. C₅×C₁₁	C₁₁⋊#261	semidirect
47. C₁₃	C₁₁×Dic₅₅	semidirect
49. C₁₁	C₁₁×#63118	semidirect
50. C₁₁	C₁₁⋊#63118	direct (N × H)
52. C₅	C₁₁×C₁₁⋊#261	semidirect

Maximal subgroups

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

subgroup	index
C₅×C₁₁²×D₁₃	2
C₁₁×C₁₁⋊#261	5
C₁₁⋊#63118	11
C₁₁×#63118	11
C₁₁×Dic₅₅	13

Subgroups — C11×C11⋊#63118 #44538261

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×C₁₁⋊#63118 #44538261