Subgroups — C₉×C₁₁⋊#63118 #38787874

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	C₃×C₁₁⋊#63118	C₃	1	1	yes	maximal, characteristic
3	C₅×C₉×C₁₁×C₁₃	C₄	1	1	yes	characteristic, complemented, Hall
4	C₉×C₁₁⋊#261	—	5	1	no	maximal, Hall
5	C₃×C₅×C₁₁×D₁₃	C₂×C₃	1	1	yes	characteristic
6	C₁₁⋊#63118	C₉	1	1	yes	characteristic, direct product factor, Hall
7	C₉×C₁₁×D₁₃	D₅	1	1	yes	characteristic
8	C₉×#63118	—	11	1	no	maximal, Hall
9	C₃×C₅×C₁₁×C₁₃	C₃×C₄	1	1	yes	characteristic
10	C₉×Dic₅₅	—	13	1	no	maximal, Hall
11	C₃×C₁₁⋊#261	—	5	1	no	—
12	C₅×C₁₁×D₁₃	C₂×C₉	1	1	yes	characteristic
13	C₉×C₁₁×C₁₃	Dic₅	1	1	yes	characteristic, complemented, Hall
14	C₅×C₉×D₁₃	D₁₁	1	1	yes	characteristic
15	C₂×C₅×C₉×C₁₁	—	13	1	no	—
16	C₃×C₁₁×D₁₃	C₃×D₅	1	1	yes	characteristic
17	C₃×#63118	—	11	1	no	—
18	C₅×C₁₁×C₁₃	C₄×C₉	1	1	yes	characteristic, complemented, Hall
19	C₃×Dic₅₅	—	13	1	no	—
20	C₅×C₉×C₁₃	Dic₁₁	1	1	yes	characteristic, complemented, Hall
21	C₁₁⋊#261	—	5	1	no	Hall
22	C₅×C₉×C₁₁	#261	1	1	yes	characteristic, complemented, Hall
23	C₉×#261	—	55	1	no	Hall
24	C₃×C₁₁×C₁₃	C₃×Dic₅	1	1	yes	characteristic
25	C₉×Dic₁₁	—	65	1	no	Hall
26	C₃×C₅×D₁₃	C₃×D₁₁	1	1	yes	characteristic
27	C₂×C₃×C₅×C₁₁	—	13	1	no	—
28	C₁₁×D₁₃	C₉×D₅	1	1	yes	characteristic
29	#63118	—	11	1	no	Hall
30	C₉×D₁₃	D₅₅	1	1	yes	characteristic
31	Dic₅₅	—	13	1	no	Hall
32	C₂×C₉×C₁₁	—	13	1	no	—
33	C₃×C₅×C₁₃	C₃×Dic₁₁	1	1	yes	characteristic
34	C₉×Dic₅	—	143	1	no	Hall
35	C₃×C₅×C₁₁	C₃×#261	1	1	yes	characteristic
36	C₃×#261	—	55	1	no	—
37	C₁₁×C₁₃	C₉×Dic₅	1	1	yes	characteristic, complemented, Hall
38	C₃×Dic₁₁	—	65	1	no	—
39	C₅×D₁₃	C₉×D₁₁	1	1	yes	characteristic
40	C₉×C₁₃	Dic₅₅	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	C₃×D₅₅	1	1	yes	characteristic
45	C₂×C₃×C₁₁	—	13	1	no	—
46	C₅×C₁₃	C₉×Dic₁₁	1	1	yes	characteristic, complemented, Hall
47	C₃×Dic₅	—	143	1	no	—
48	C₅×C₁₁	C₉×#261	1	1	yes	characteristic, complemented, Hall
49	#261	—	55	1	no	Hall
50	C₅×C₉	C₁₁⋊#261	1	1	yes	characteristic, complemented, Hall
51	Dic₁₁	—	65	1	no	Hall
52	C₃×C₁₃	C₃×Dic₅₅	1	1	yes	characteristic
53	C₄×C₉	—	715	1	no	Hall
54	C₃×C₁₁	C₃×#63118	1	1	yes	characteristic
55	C₂×C₃×C₅	—	13	1	no	—
56	D₁₃	C₉×D₅₅	1	1	yes	characteristic
57	C₂×C₁₁	—	13	1	no	—
58	Dic₅	—	143	1	no	Hall
59	C₂×C₉	—	13	1	no	—
60	C₃×C₅	C₃×C₁₁⋊#261	1	1	yes	characteristic
61	C₁₃	C₉×Dic₅₅	1	1	yes	characteristic, complemented, Sylow
62	C₃×C₄	—	715	1	no	—
63	C₁₁	C₉×#63118	1	1	yes	characteristic, complemented, Sylow
64	C₂×C₅	—	13	1	no	—
65	C₉	C₁₁⋊#63118	1	1	yes	characteristic, direct product factor, Sylow
66	C₂×C₃	—	13	1	no	—
67	C₅	C₉×C₁₁⋊#261	1	1	yes	characteristic, complemented, Sylow
68	C₄	—	715	1	no	Sylow
69	C₃	C₃×C₁₁⋊#63118	1	1	yes	characteristic
70	C₂	—	13	1	no	—

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

Complements

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

N	H ≅ G/N	type
3. C₅×C₉×C₁₁×C₁₃	C₄	semidirect
6. C₁₁⋊#63118	C₉	direct (N × H)
13. C₉×C₁₁×C₁₃	Dic₅	semidirect
18. C₅×C₁₁×C₁₃	C₄×C₉	semidirect
20. C₅×C₉×C₁₃	Dic₁₁	semidirect
22. C₅×C₉×C₁₁	#261	semidirect
37. C₁₁×C₁₃	C₉×Dic₅	semidirect
40. C₉×C₁₃	Dic₅₅	semidirect
42. C₉×C₁₁	#63118	semidirect
46. C₅×C₁₃	C₉×Dic₁₁	semidirect
48. C₅×C₁₁	C₉×#261	semidirect
50. C₅×C₉	C₁₁⋊#261	semidirect
61. C₁₃	C₉×Dic₅₅	semidirect
63. C₁₁	C₉×#63118	semidirect
65. C₉	C₁₁⋊#63118	direct (N × H)
67. C₅	C₉×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×C₉×C₁₁×D₁₃	2
C₃×C₁₁⋊#63118	3
C₉×C₁₁⋊#261	5
C₉×#63118	11
C₉×Dic₅₅	13

Subgroups — C9×C11⋊#63118 #38787874

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×C₁₁⋊#63118 #38787874