Subgroups — C₁₁×C₉⋊#63118 #38787896

Order 25740.

72 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₉×C₁₁×D₁₃	C₂	1	1	yes	maximal, characteristic
2	C₁₁×C₃⋊#63118	—	3	1	no	maximal
3	C₅×C₉×C₁₁×C₁₃	C₄	1	1	yes	characteristic, complemented, Hall
4	C₁₁×C₉⋊#261	—	5	1	no	maximal, Hall
5	C₃×C₅×C₁₁×D₁₃	D₃	1	1	yes	characteristic
6	C₁₁×#63118	—	9	1	no	Hall
7	C₉×C₁₁×D₁₃	D₅	1	1	yes	characteristic
8	C₉⋊#63118	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₃×C₅×C₁₁×C₁₃	Dic₃	1	1	yes	characteristic
10	C₁₁×Dic₄₅	—	13	1	no	maximal, Hall
11	C₁₁×C₃⋊#261	—	15	1	no	—
12	C₅×C₁₁×D₁₃	D₉	1	1	yes	characteristic
13	C₉×C₁₁×C₁₃	Dic₅	1	1	yes	characteristic, complemented, Hall
14	C₅×C₉×D₁₃	C₂×C₁₁	1	1	yes	characteristic
15	C₂×C₅×C₉×C₁₁	—	13	1	no	—
16	C₃×C₁₁×D₁₃	D₁₅	1	1	yes	characteristic
17	C₃⋊#63118	—	3	1	no	—
18	C₅×C₁₁×C₁₃	Dic₉	1	1	yes	characteristic, complemented, Hall
19	C₁₁×Dic₁₅	—	39	1	no	—
20	C₅×C₉×C₁₃	C₄×C₁₁	1	1	yes	characteristic, complemented, Hall
21	C₁₁×#261	—	45	1	no	Hall
22	C₅×C₉×C₁₁	#261	1	1	yes	characteristic, complemented, Hall
23	C₉⋊#261	—	5	1	no	Hall
24	C₃×C₁₁×C₁₃	Dic₁₅	1	1	yes	characteristic
25	C₁₁×Dic₉	—	65	1	no	Hall
26	C₃×C₅×D₁₃	D₃×C₁₁	1	1	yes	characteristic
27	C₂×C₃×C₅×C₁₁	—	13	1	no	—
28	C₁₁×D₁₃	D₄₅	1	1	yes	characteristic
29	#63118	—	9	1	no	Hall
30	C₉×D₁₃	D₅×C₁₁	1	1	yes	characteristic
31	C₁₁×Dic₅	—	117	1	no	Hall
32	C₂×C₉×C₁₁	—	13	1	no	—
33	C₃×C₅×C₁₃	C₁₁×Dic₃	1	1	yes	characteristic
34	Dic₄₅	—	13	1	no	Hall
35	C₃×C₅×C₁₁	C₃⋊#261	1	1	yes	characteristic
36	C₃⋊#261	—	15	1	no	—
37	C₁₁×C₁₃	Dic₄₅	1	1	yes	characteristic, complemented, Hall
38	C₁₁×Dic₃	—	195	1	no	—
39	C₅×D₁₃	C₁₁×D₉	1	1	yes	characteristic
40	C₉×C₁₃	C₁₁×Dic₅	1	1	yes	characteristic, complemented, Hall
41	C₂×C₅×C₁₁	—	13	1	no	—
42	C₉×C₁₁	#63118	1	1	yes	characteristic, complemented, Hall
43	C₂×C₅×C₉	—	13	1	no	—
44	C₃×D₁₃	C₁₁×D₁₅	1	1	yes	characteristic
45	C₂×C₃×C₁₁	—	13	1	no	—
46	C₅×C₁₃	C₁₁×Dic₉	1	1	yes	characteristic, complemented, Hall
47	Dic₁₅	—	39	1	no	—
48	C₅×C₁₁	C₉⋊#261	1	1	yes	characteristic, complemented, Hall
49	#261	—	45	1	no	Hall
50	C₅×C₉	C₁₁×#261	1	1	yes	characteristic, complemented, Hall
51	C₄×C₁₁	—	585	1	no	Hall
52	C₃×C₁₃	C₁₁×Dic₁₅	1	1	yes	characteristic
53	Dic₉	—	65	1	no	Hall
54	C₃×C₁₁	C₃⋊#63118	1	1	yes	characteristic
55	C₂×C₃×C₅	—	13	1	no	—
56	D₁₃	C₁₁×D₄₅	1	1	yes	characteristic
57	C₂×C₁₁	—	13	1	no	—
58	Dic₅	—	117	1	no	Hall
59	C₂×C₉	—	13	1	no	—
60	C₃×C₅	C₁₁×C₃⋊#261	1	1	yes	characteristic
61	C₁₃	C₁₁×Dic₄₅	1	1	yes	characteristic, complemented, Sylow
62	Dic₃	—	195	1	no	—
63	C₁₁	C₉⋊#63118	1	1	yes	characteristic, direct product factor, Sylow
64	C₂×C₅	—	13	1	no	—
65	C₉	C₁₁×#63118	1	1	yes	characteristic, complemented, Sylow
66	C₂×C₃	—	13	1	no	—
67	C₅	C₁₁×C₉⋊#261	1	1	yes	characteristic, complemented, Sylow
68	C₄	—	585	1	no	Sylow
69	C₃	C₁₁×C₃⋊#63118	1	1	yes	characteristic
70	C₂	—	13	1	no	—

	subgroup	G/H
center, hypercenter	C₁₁	C₉⋊#63118
commutator, hypocenter	C₅×C₉×C₁₃	C₄×C₁₁
Frattini	C₃	C₁₁×C₃⋊#63118
Fitting	C₅×C₉×C₁₁×C₁₃	C₄
socle	C₃×C₅×C₁₁×C₁₃	Dic₃
prime radical	C₃×C₅×C₁₁×D₁₃	D₃
cosocle	C₅×C₉×D₁₃	C₂×C₁₁
LCS	G ▷ C₅×C₉×C₁₃
UCS	C₁ ◁ C₁₁

Complements

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

N	H ≅ G/N	type
3. C₅×C₉×C₁₁×C₁₃	C₄	semidirect
8. C₉⋊#63118	C₁₁	direct (N × H)
13. C₉×C₁₁×C₁₃	Dic₅	semidirect
18. C₅×C₁₁×C₁₃	Dic₉	semidirect
20. C₅×C₉×C₁₃	C₄×C₁₁	semidirect
22. C₅×C₉×C₁₁	#261	semidirect
37. C₁₁×C₁₃	Dic₄₅	semidirect
40. C₉×C₁₃	C₁₁×Dic₅	semidirect
42. C₉×C₁₁	#63118	semidirect
46. C₅×C₁₃	C₁₁×Dic₉	semidirect
48. C₅×C₁₁	C₉⋊#261	semidirect
50. C₅×C₉	C₁₁×#261	semidirect
61. C₁₃	C₁₁×Dic₄₅	semidirect
63. C₁₁	C₉⋊#63118	direct (N × H)
65. C₉	C₁₁×#63118	semidirect
67. C₅	C₁₁×C₉⋊#261	semidirect

Maximal subgroups

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

subgroup	index
C₅×C₉×C₁₁×D₁₃	2
C₁₁×C₃⋊#63118	3
C₁₁×C₉⋊#261	5
C₉⋊#63118	11
C₁₁×Dic₄₅	13

Subgroups — C11×C9⋊#63118 #38787896

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×C₉⋊#63118 #38787896