Subgroups — C₉×D₇×C₁₁⋊D₁₁ #44478953

Order 30492.

420 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₉×C₇⋊(C₁₁⋊D₁₁)	C₂	1	1	yes	maximal, characteristic, complemented
2	C₉×C₁₁²×D₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×C₉×C₁₁⋊D₁₁	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×D₇×C₁₁⋊D₁₁	C₃	1	1	yes	maximal, characteristic
5	C₇×C₉×C₁₁²	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₃×C₇⋊(C₁₁⋊D₁₁)	C₂×C₃	1	1	yes	characteristic
7	C₃×C₁₁²×D₇	C₂×C₃	1	1	yes	characteristic
8	C₃×C₇×C₁₁⋊D₁₁	C₂×C₃	1	1	yes	characteristic
9	C₂×C₉×C₁₁⋊D₁₁	—	7	1	no	maximal, Hall
10	D₇×C₁₁⋊D₁₁	C₉	1	1	yes	characteristic, direct product factor, Hall
11	C₉×D₇×D₁₁	—	11	12	no	maximal
12	C₃×C₇×C₁₁²	C₂²×C₃	1	1	yes	characteristic
13	C₉×C₁₁⋊D₁₁	—	7	1	no	—
14	C₉×C₁₁⋊D₁₁	D₇	1	1	yes	characteristic, direct product factor
15	C₂×C₉×C₁₁²	—	7	1	no	—
16	C₇⋊(C₁₁⋊D₁₁)	C₂×C₉	1	1	yes	characteristic, complemented
17	C₁₁²×D₇	C₂×C₉	1	1	yes	characteristic, complemented
18	C₇×C₁₁⋊D₁₁	C₂×C₉	1	1	yes	characteristic, complemented
19	C₂×C₃×C₁₁⋊D₁₁	—	7	1	no	—
20	C₉×D₇₇	—	11	12	no	—
21	C₉×C₁₁×D₇	D₁₁	1	12	yes	complemented
22	C₇×C₉×D₁₁	—	11	12	no	—
23	C₉×C₁₁²	C₂×D₇	1	1	yes	characteristic, complemented, Hall
24	C₃×D₇×D₁₁	—	11	12	no	—
25	C₇×C₁₁²	C₂²×C₉	1	1	yes	characteristic, complemented, Hall
26	C₂×C₃×C₁₁²	—	7	1	no	—
27	C₃×C₁₁⋊D₁₁	—	7	1	no	—
28	C₃×C₁₁⋊D₁₁	C₃×D₇	1	1	yes	characteristic
29	C₇×C₉×C₁₁	C₂×D₁₁	1	12	yes	complemented
30	C₂×C₁₁⋊D₁₁	—	7	1	no	Hall
31	C₃×D₇₇	—	11	12	no	—
32	C₃×C₁₁×D₇	C₃×D₁₁	1	12	yes	—
33	C₃×C₇×D₁₁	—	11	12	no	—
34	C₂×C₉×D₁₁	—	77	12	no	—
35	C₃×C₁₁²	C₂×C₃×D₇	1	1	yes	characteristic
36	D₇×D₁₁	—	11	12	no	—
37	C₂×C₉×D₇	—	121	1	no	Hall
38	C₂×C₁₁²	—	7	1	no	—
39	C₁₁⋊D₁₁	—	7	1	no	—
40	C₁₁⋊D₁₁	C₉×D₇	1	1	yes	characteristic, direct product factor
41	C₃×C₇×C₁₁	C₂×C₃×D₁₁	1	12	yes	—
42	C₂×C₉×C₁₁	—	7	12	no	—
43	C₉×D₁₁	—	11	12	no	—
44	C₉×D₁₁	—	77	12	no	—
45	D₇₇	—	11	12	no	—
46	C₇×D₁₁	—	11	12	no	—
47	C₁₁×D₇	C₉×D₁₁	1	12	yes	complemented
48	C₂×C₃×D₁₁	—	77	12	no	—
49	C₂×C₇×C₉	—	121	1	no	—
50	C₉×D₇	—	121	1	no	—
51	C₉×D₇	C₁₁⋊D₁₁	1	1	yes	characteristic, direct product factor
52	C₁₁²	C₂×C₉×D₇	1	1	yes	characteristic, complemented, Sylow
53	C₉×C₁₁	D₇×D₁₁	1	12	yes	complemented
54	C₂×C₃×D₇	—	121	1	no	—
55	C₇×C₁₁	C₂×C₉×D₁₁	1	12	yes	complemented
56	C₂×C₃×C₁₁	—	7	12	no	—
57	C₃×D₁₁	—	11	12	no	—
58	C₃×D₁₁	—	77	12	no	—
59	C₇×C₉	C₂×C₁₁⋊D₁₁	1	1	yes	characteristic, complemented, Hall
60	C₂×D₁₁	—	77	12	no	—
61	C₂×C₃×C₇	—	121	1	no	—
62	C₃×D₇	—	121	1	no	—
63	C₃×D₇	C₃×C₁₁⋊D₁₁	1	1	yes	characteristic
64	C₂²×C₉	—	847	1	no	Hall
65	C₃×C₁₁	C₃×D₇×D₁₁	1	12	yes	—
66	C₂×D₇	—	121	1	no	Hall
67	C₂×C₁₁	—	7	12	no	—
68	D₁₁	—	11	12	no	—
69	D₁₁	—	77	12	no	—
70	C₃×C₇	C₂×C₃×C₁₁⋊D₁₁	1	1	yes	characteristic
71	C₂×C₉	—	7	1	no	—
72	C₂×C₉	—	847	1	no	—
73	C₂×C₉	—	121	1	no	—
74	C₂×C₇	—	121	1	no	—
75	D₇	—	121	1	no	—
76	D₇	C₉×C₁₁⋊D₁₁	1	1	yes	characteristic, direct product factor
77	C₂²×C₃	—	847	1	no	—
78	C₁₁	C₉×D₇×D₁₁	1	12	yes	complemented
79	C₉	D₇×C₁₁⋊D₁₁	1	1	yes	characteristic, direct product factor, Sylow
80	C₇	C₂×C₉×C₁₁⋊D₁₁	1	1	yes	characteristic, complemented, Sylow
81	C₂×C₃	—	7	1	no	—
82	C₂×C₃	—	847	1	no	—
83	C₂×C₃	—	121	1	no	—
84	C₂²	—	847	1	no	Sylow
85	C₃	C₃×D₇×C₁₁⋊D₁₁	1	1	yes	characteristic
86	C₂	—	7	1	no	—
87	C₂	—	847	1	no	—
88	C₂	—	121	1	no	—

	subgroup	G/H
center, hypercenter	C₉	D₇×C₁₁⋊D₁₁
commutator, hypocenter	C₇×C₁₁²	C₂²×C₉
Frattini	C₃	C₃×D₇×C₁₁⋊D₁₁
Fitting	C₇×C₉×C₁₁²	C₂²
socle, cosocle	C₃×C₇×C₁₁²	C₂²×C₃
prime radical	C₃×D₇×C₁₁⋊D₁₁	C₃
LCS	G ▷ C₇×C₁₁²
UCS	C₁ ◁ C₉

Complements

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

N	H ≅ G/N	type
1. C₉×C₇⋊(C₁₁⋊D₁₁)	C₂	semidirect
2. C₉×C₁₁²×D₇	C₂	semidirect
3. C₇×C₉×C₁₁⋊D₁₁	C₂	semidirect
5. C₇×C₉×C₁₁²	C₂²	semidirect
10. D₇×C₁₁⋊D₁₁	C₉	direct (N × H)
14. C₉×C₁₁⋊D₁₁	D₇	direct (N × H)
16. C₇⋊(C₁₁⋊D₁₁)	C₂×C₉	semidirect
17. C₁₁²×D₇	C₂×C₉	semidirect
18. C₇×C₁₁⋊D₁₁	C₂×C₉	semidirect
21. C₉×C₁₁×D₇	D₁₁	semidirect
23. C₉×C₁₁²	C₂×D₇	semidirect
25. C₇×C₁₁²	C₂²×C₉	semidirect
29. C₇×C₉×C₁₁	C₂×D₁₁	semidirect
40. C₁₁⋊D₁₁	C₉×D₇	direct (N × H)
47. C₁₁×D₇	C₉×D₁₁	semidirect
51. C₉×D₇	C₁₁⋊D₁₁	direct (N × H)
52. C₁₁²	C₂×C₉×D₇	semidirect
53. C₉×C₁₁	D₇×D₁₁	semidirect
55. C₇×C₁₁	C₂×C₉×D₁₁	semidirect
59. C₇×C₉	C₂×C₁₁⋊D₁₁	semidirect
76. D₇	C₉×C₁₁⋊D₁₁	direct (N × H)
78. C₁₁	C₉×D₇×D₁₁	semidirect
79. C₉	D₇×C₁₁⋊D₁₁	direct (N × H)
80. C₇	C₂×C₉×C₁₁⋊D₁₁	semidirect

Maximal subgroups

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

subgroup	index
C₉×C₇⋊(C₁₁⋊D₁₁)	2
C₉×C₁₁²×D₇	2
C₇×C₉×C₁₁⋊D₁₁	2
C₃×D₇×C₁₁⋊D₁₁	3
C₂×C₉×C₁₁⋊D₁₁	7
C₉×D₇×D₁₁	11

Subgroups — C9×D7×C11⋊D11 #44478953

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×D₇×C₁₁⋊D₁₁ #44478953