Subgroups — C₉×C₇⋊(C₁₁⋊#261) #49114459

Order 36036.

72 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×C₉×C₁₁×D₁₃	C₂	1	1	yes	maximal, characteristic
2	C₃×C₇⋊(C₁₁⋊#261)	C₃	1	1	yes	maximal, characteristic
3	C₇×C₉×C₁₁×C₁₃	C₄	1	1	yes	characteristic, complemented, Hall
4	C₃×C₇×C₁₁×D₁₃	C₂×C₃	1	1	yes	characteristic
5	C₉×C₁₁⋊#261	—	7	1	no	maximal, Hall
6	C₇⋊(C₁₁⋊#261)	C₉	1	1	yes	characteristic, direct product factor, Hall
7	C₉×C₇⋊#261	—	11	1	no	maximal, Hall
8	C₃×C₇×C₁₁×C₁₃	C₃×C₄	1	1	yes	characteristic
9	C₉×Dic₇₇	—	13	1	no	maximal, Hall
10	C₉×C₁₁×D₁₃	D₇	1	1	yes	characteristic
11	C₇×C₁₁×D₁₃	C₂×C₉	1	1	yes	characteristic
12	C₃×C₁₁⋊#261	—	7	1	no	—
13	C₇×C₉×D₁₃	D₁₁	1	1	yes	characteristic
14	C₂×C₇×C₉×C₁₁	—	13	1	no	—
15	C₉×C₁₁×C₁₃	Dic₇	1	1	yes	characteristic, complemented, Hall
16	C₃×C₇⋊#261	—	11	1	no	—
17	C₇×C₁₁×C₁₃	C₄×C₉	1	1	yes	characteristic, complemented, Hall
18	C₃×Dic₇₇	—	13	1	no	—
19	C₃×C₁₁×D₁₃	C₃×D₇	1	1	yes	characteristic
20	C₇×C₉×C₁₃	Dic₁₁	1	1	yes	characteristic, complemented, Hall
21	C₇×C₉×C₁₁	#261	1	1	yes	characteristic, complemented, Hall
22	C₁₁⋊#261	—	7	1	no	Hall
23	C₃×C₇×D₁₃	C₃×D₁₁	1	1	yes	characteristic
24	C₉×#261	—	77	1	no	Hall
25	C₂×C₃×C₇×C₁₁	—	13	1	no	—
26	C₃×C₁₁×C₁₃	C₃×Dic₇	1	1	yes	characteristic
27	C₉×Dic₁₁	—	91	1	no	Hall
28	C₇⋊#261	—	11	1	no	Hall
29	Dic₇₇	—	13	1	no	Hall
30	C₁₁×D₁₃	C₉×D₇	1	1	yes	characteristic
31	C₃×C₇×C₁₃	C₃×Dic₁₁	1	1	yes	characteristic
32	C₉×Dic₇	—	143	1	no	Hall
33	C₉×D₁₃	D₇₇	1	1	yes	characteristic
34	C₃×C₇×C₁₁	C₃×#261	1	1	yes	characteristic
35	C₂×C₉×C₁₁	—	13	1	no	—
36	C₇×D₁₃	C₉×D₁₁	1	1	yes	characteristic
37	C₃×#261	—	77	1	no	—
38	C₂×C₇×C₁₁	—	13	1	no	—
39	C₁₁×C₁₃	C₉×Dic₇	1	1	yes	characteristic, complemented, Hall
40	C₃×Dic₁₁	—	91	1	no	—
41	C₂×C₇×C₉	—	13	1	no	—
42	C₉×C₁₃	Dic₇₇	1	1	yes	characteristic, complemented, Hall
43	C₉×C₁₁	C₇⋊#261	1	1	yes	characteristic, complemented, Hall
44	C₇×C₁₃	C₉×Dic₁₁	1	1	yes	characteristic, complemented, Hall
45	C₃×Dic₇	—	143	1	no	—
46	C₃×D₁₃	C₃×D₇₇	1	1	yes	characteristic
47	C₇×C₁₁	C₉×#261	1	1	yes	characteristic, complemented, Hall
48	C₂×C₃×C₁₁	—	13	1	no	—
49	C₇×C₉	C₁₁⋊#261	1	1	yes	characteristic, complemented, Hall
50	#261	—	77	1	no	Hall
51	Dic₁₁	—	91	1	no	Hall
52	C₂×C₃×C₇	—	13	1	no	—
53	C₃×C₁₃	C₃×Dic₇₇	1	1	yes	characteristic
54	C₄×C₉	—	1001	1	no	Hall
55	C₃×C₁₁	C₃×C₇⋊#261	1	1	yes	characteristic
56	Dic₇	—	143	1	no	Hall
57	D₁₃	C₉×D₇₇	1	1	yes	characteristic
58	C₂×C₁₁	—	13	1	no	—
59	C₃×C₇	C₃×C₁₁⋊#261	1	1	yes	characteristic
60	C₂×C₉	—	13	1	no	—
61	C₂×C₇	—	13	1	no	—
62	C₁₃	C₉×Dic₇₇	1	1	yes	characteristic, complemented, Sylow
63	C₃×C₄	—	1001	1	no	—
64	C₁₁	C₉×C₇⋊#261	1	1	yes	characteristic, complemented, Sylow
65	C₉	C₇⋊(C₁₁⋊#261)	1	1	yes	characteristic, direct product factor, Sylow
66	C₇	C₉×C₁₁⋊#261	1	1	yes	characteristic, complemented, Sylow
67	C₂×C₃	—	13	1	no	—
68	C₄	—	1001	1	no	Sylow
69	C₃	C₃×C₇⋊(C₁₁⋊#261)	1	1	yes	characteristic
70	C₂	—	13	1	no	—

	subgroup	G/H
center, hypercenter	C₉	C₇⋊(C₁₁⋊#261)
commutator, hypocenter	C₇×C₁₁×C₁₃	C₄×C₉
Frattini	C₃	C₃×C₇⋊(C₁₁⋊#261)
Fitting	C₇×C₉×C₁₁×C₁₃	C₄
socle	C₃×C₇×C₁₁×C₁₃	C₃×C₄
prime radical, cosocle	C₃×C₇×C₁₁×D₁₃	C₂×C₃
LCS	G ▷ C₇×C₁₁×C₁₃
UCS	C₁ ◁ C₉

Complements

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

N	H ≅ G/N	type
3. C₇×C₉×C₁₁×C₁₃	C₄	semidirect
6. C₇⋊(C₁₁⋊#261)	C₉	direct (N × H)
15. C₉×C₁₁×C₁₃	Dic₇	semidirect
17. C₇×C₁₁×C₁₃	C₄×C₉	semidirect
20. C₇×C₉×C₁₃	Dic₁₁	semidirect
21. C₇×C₉×C₁₁	#261	semidirect
39. C₁₁×C₁₃	C₉×Dic₇	semidirect
42. C₉×C₁₃	Dic₇₇	semidirect
43. C₉×C₁₁	C₇⋊#261	semidirect
44. C₇×C₁₃	C₉×Dic₁₁	semidirect
47. C₇×C₁₁	C₉×#261	semidirect
49. C₇×C₉	C₁₁⋊#261	semidirect
62. C₁₃	C₉×Dic₇₇	semidirect
64. C₁₁	C₉×C₇⋊#261	semidirect
65. C₉	C₇⋊(C₁₁⋊#261)	direct (N × H)
66. C₇	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
C₇×C₉×C₁₁×D₁₃	2
C₃×C₇⋊(C₁₁⋊#261)	3
C₉×C₁₁⋊#261	7
C₉×C₇⋊#261	11
C₉×Dic₇₇	13

Subgroups — C9×C7⋊(C11⋊#261) #49114459

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×C₇⋊(C₁₁⋊#261) #49114459