Subgroups — D₉×C₇⋊(C₁₁⋊D₁₁) #44478972

Order 30492.

420 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇⋊(C₉⋊(C₁₁⋊D₁₁))	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇×C₁₁²×D₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₉×C₇⋊(C₁₁⋊D₁₁)	C₂	1	1	yes	maximal, characteristic, complemented
4	D₃×C₇⋊(C₁₁⋊D₁₁)	—	3	1	no	maximal
5	C₇×C₉×C₁₁²	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₃⋊(C₇⋊(C₁₁⋊D₁₁))	—	3	1	no	—
7	D₃×C₇×C₁₁²	—	3	1	no	—
8	C₃×C₇⋊(C₁₁⋊D₁₁)	D₃	1	1	yes	characteristic
9	D₉×C₁₁⋊D₁₁	—	7	1	no	maximal, Hall
10	C₂×C₇⋊(C₁₁⋊D₁₁)	—	9	1	no	Hall
11	D₉×D₇₇	—	11	12	no	maximal
12	C₃×C₇×C₁₁²	C₂×D₃	1	1	yes	characteristic
13	C₉⋊(C₁₁⋊D₁₁)	—	7	1	no	—
14	C₁₁²×D₉	D₇	1	1	yes	characteristic, complemented
15	C₉×C₁₁⋊D₁₁	—	7	1	no	—
16	C₂×C₇×C₁₁²	—	9	1	no	—
17	C₇⋊(C₁₁⋊D₁₁)	—	9	1	no	—
18	C₇⋊(C₁₁⋊D₁₁)	D₉	1	1	yes	characteristic, direct product factor
19	D₃×C₁₁⋊D₁₁	—	21	1	no	—
20	D₆₉₃	—	11	12	no	—
21	C₇×C₁₁×D₉	D₁₁	1	12	yes	complemented
22	C₉×D₇₇	—	11	12	no	—
23	C₉×C₁₁²	C₂×D₇	1	1	yes	characteristic, complemented, Hall
24	D₃×D₇₇	—	33	12	no	—
25	C₇×C₁₁²	C₂×D₉	1	1	yes	characteristic, complemented, Hall
26	C₃⋊(C₁₁⋊D₁₁)	—	21	1	no	—
27	D₃×C₁₁²	—	3	1	no	—
28	C₃×C₁₁⋊D₁₁	—	7	1	no	—
29	C₇×C₉×C₁₁	C₂×D₁₁	1	12	yes	complemented
30	C₂×C₁₁⋊D₁₁	—	63	1	no	Hall
31	D₂₃₁	—	33	12	no	—
32	D₃×C₇×C₁₁	—	3	12	no	—
33	C₃×D₇₇	—	11	12	no	—
34	D₉×D₁₁	—	77	12	no	—
35	C₃×C₁₁²	D₃×D₇	1	1	yes	characteristic
36	C₂×D₇₇	—	99	12	no	—
37	D₇×D₉	—	121	1	no	Hall
38	C₂×C₁₁²	—	9	1	no	—
39	C₁₁⋊D₁₁	—	7	1	no	—
40	C₁₁⋊D₁₁	—	63	1	no	—
41	C₃×C₇×C₁₁	D₃×D₁₁	1	12	yes	—
42	D₉₉	—	77	12	no	—
43	C₉×D₁₁	—	77	12	no	—
44	C₁₁×D₉	D₇₇	1	12	yes	complemented
45	C₂×C₇×C₁₁	—	9	12	no	—
46	D₇₇	—	11	12	no	—
47	D₇₇	—	99	12	no	—
48	D₃×D₁₁	—	231	12	no	—
49	D₆₃	—	121	1	no	—
50	C₉×D₇	—	121	1	no	—
51	C₇×D₉	C₁₁⋊D₁₁	1	1	yes	characteristic, complemented
52	C₁₁²	D₇×D₉	1	1	yes	characteristic, complemented, Sylow
53	C₉×C₁₁	C₂×D₇₇	1	12	yes	complemented
54	D₃×D₇	—	363	1	no	—
55	C₇×C₁₁	D₉×D₁₁	1	12	yes	complemented
56	D₃₃	—	231	12	no	—
57	C₃×D₁₁	—	77	12	no	—
58	D₃×C₁₁	—	3	12	no	—
59	C₇×C₉	C₂×C₁₁⋊D₁₁	1	1	yes	characteristic, complemented, Hall
60	C₂×D₁₁	—	693	12	no	—
61	D₂₁	—	363	1	no	—
62	C₃×D₇	—	121	1	no	—
63	D₃×C₇	—	3	1	no	—
64	C₂×D₉	—	847	1	no	Hall
65	C₃×C₁₁	D₃×D₇₇	1	12	yes	—
66	C₂×D₇	—	1089	1	no	Hall
67	C₂×C₁₁	—	9	12	no	—
68	D₁₁	—	77	12	no	—
69	D₁₁	—	693	12	no	—
70	C₃×C₇	D₃×C₁₁⋊D₁₁	1	1	yes	characteristic
71	C₂×C₉	—	847	1	no	—
72	D₉	—	847	1	no	—
73	D₉	C₇⋊(C₁₁⋊D₁₁)	1	1	yes	characteristic, direct product factor
74	C₂×C₇	—	9	1	no	—
75	D₇	—	1089	1	no	—
76	D₇	—	121	1	no	—
77	C₂×D₃	—	2541	1	no	—
78	C₁₁	D₉×D₇₇	1	12	yes	complemented
79	C₉	C₂×C₇⋊(C₁₁⋊D₁₁)	1	1	yes	characteristic, complemented, Sylow
80	C₇	D₉×C₁₁⋊D₁₁	1	1	yes	characteristic, complemented, Sylow
81	C₂×C₃	—	847	1	no	—
82	D₃	—	3	1	no	—
83	D₃	—	2541	1	no	—
84	C₂²	—	7623	1	no	Sylow
85	C₃	D₃×C₇⋊(C₁₁⋊D₁₁)	1	1	yes	characteristic
86	C₂	—	9	1	no	—
87	C₂	—	847	1	no	—
88	C₂	—	7623	1	no	—

	subgroup	G/H
center, hypercenter	C₁	G
commutator, Fitting, cosocle, hypocenter	C₇×C₉×C₁₁²	C₂²
Frattini	C₃	D₃×C₇⋊(C₁₁⋊D₁₁)
socle	C₃×C₇×C₁₁²	C₂×D₃
LCS	G ▷ C₇×C₉×C₁₁²
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. C₇⋊(C₉⋊(C₁₁⋊D₁₁))	C₂	semidirect
2. C₇×C₁₁²×D₉	C₂	semidirect
3. C₉×C₇⋊(C₁₁⋊D₁₁)	C₂	semidirect
5. C₇×C₉×C₁₁²	C₂²	semidirect
14. C₁₁²×D₉	D₇	semidirect
18. C₇⋊(C₁₁⋊D₁₁)	D₉	direct (N × H)
21. C₇×C₁₁×D₉	D₁₁	semidirect
23. C₉×C₁₁²	C₂×D₇	semidirect
25. C₇×C₁₁²	C₂×D₉	semidirect
29. C₇×C₉×C₁₁	C₂×D₁₁	semidirect
44. C₁₁×D₉	D₇₇	semidirect
51. C₇×D₉	C₁₁⋊D₁₁	semidirect
52. C₁₁²	D₇×D₉	semidirect
53. C₉×C₁₁	C₂×D₇₇	semidirect
55. C₇×C₁₁	D₉×D₁₁	semidirect
59. C₇×C₉	C₂×C₁₁⋊D₁₁	semidirect
73. D₉	C₇⋊(C₁₁⋊D₁₁)	direct (N × H)
78. C₁₁	D₉×D₇₇	semidirect
79. C₉	C₂×C₇⋊(C₁₁⋊D₁₁)	semidirect
80. C₇	D₉×C₁₁⋊D₁₁	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⋊D₁₁))	2
C₇×C₁₁²×D₉	2
C₉×C₇⋊(C₁₁⋊D₁₁)	2
D₃×C₇⋊(C₁₁⋊D₁₁)	3
D₉×C₁₁⋊D₁₁	7
D₉×D₇₇	11

Subgroups — D9×C7⋊(C11⋊D11) #44478972

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₉×C₇⋊(C₁₁⋊D₁₁) #44478972