Subgroups — C₇×D₉×C₁₁⋊D₁₁ #44478958

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	C₇×C₉×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	C₇×C₃⋊(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	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₂×C₇×C₁₁⋊D₁₁	—	9	1	no	Hall
11	C₇×D₉×D₁₁	—	11	12	no	maximal
12	C₃×C₇×C₁₁²	C₂×D₃	1	1	yes	characteristic
13	C₉⋊(C₁₁⋊D₁₁)	C₂×C₇	1	1	yes	characteristic, complemented
14	C₁₁²×D₉	C₂×C₇	1	1	yes	characteristic, complemented
15	C₉×C₁₁⋊D₁₁	C₂×C₇	1	1	yes	characteristic, complemented
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	—	3	1	no	—
20	C₇×D₉₉	—	11	12	no	—
21	C₇×C₁₁×D₉	D₁₁	1	12	yes	complemented
22	C₇×C₉×D₁₁	—	11	12	no	—
23	C₉×C₁₁²	C₂²×C₇	1	1	yes	characteristic, complemented, Hall
24	D₃×C₇×D₁₁	—	33	12	no	—
25	C₇×C₁₁²	C₂×D₉	1	1	yes	characteristic, complemented, Hall
26	C₃⋊(C₁₁⋊D₁₁)	—	3	1	no	—
27	D₃×C₁₁²	—	3	1	no	—
28	C₃×C₁₁⋊D₁₁	D₃×C₇	1	1	yes	characteristic
29	C₇×C₉×C₁₁	C₂×D₁₁	1	12	yes	complemented
30	C₂×C₁₁⋊D₁₁	—	9	1	no	Hall
31	C₇×D₃₃	—	33	12	no	—
32	D₃×C₇×C₁₁	—	3	12	no	—
33	C₃×C₇×D₁₁	—	11	12	no	—
34	D₉×D₁₁	—	11	12	no	—
35	C₃×C₁₁²	C₂×D₃×C₇	1	1	yes	characteristic
36	C₂×C₇×D₁₁	—	99	12	no	—
37	C₂×C₇×D₉	—	121	1	no	Hall
38	C₂×C₁₁²	—	9	1	no	—
39	C₁₁⋊D₁₁	—	9	1	no	—
40	C₁₁⋊D₁₁	C₇×D₉	1	1	yes	characteristic, direct product factor
41	C₃×C₇×C₁₁	D₃×D₁₁	1	12	yes	—
42	D₉₉	—	11	12	no	—
43	C₉×D₁₁	—	11	12	no	—
44	C₁₁×D₉	C₇×D₁₁	1	12	yes	complemented
45	C₂×C₇×C₁₁	—	9	12	no	—
46	C₇×D₁₁	—	11	12	no	—
47	C₇×D₁₁	—	99	12	no	—
48	D₃×D₁₁	—	33	12	no	—
49	C₂×C₇×C₉	—	121	1	no	—
50	C₇×D₉	—	121	1	no	—
51	C₇×D₉	C₁₁⋊D₁₁	1	1	yes	characteristic, direct product factor
52	C₁₁²	C₂×C₇×D₉	1	1	yes	characteristic, complemented, Sylow
53	C₉×C₁₁	C₂×C₇×D₁₁	1	12	yes	complemented
54	C₂×D₃×C₇	—	363	1	no	—
55	C₇×C₁₁	D₉×D₁₁	1	12	yes	complemented
56	D₃₃	—	33	12	no	—
57	C₃×D₁₁	—	11	12	no	—
58	D₃×C₁₁	—	3	12	no	—
59	C₇×C₉	C₂×C₁₁⋊D₁₁	1	1	yes	characteristic, complemented, Hall
60	C₂×D₁₁	—	99	12	no	—
61	C₂×C₃×C₇	—	121	1	no	—
62	D₃×C₇	—	3	1	no	—
63	D₃×C₇	—	363	1	no	—
64	C₂×D₉	—	121	1	no	Hall
65	C₃×C₁₁	D₃×C₇×D₁₁	1	12	yes	—
66	C₂²×C₇	—	1089	1	no	Hall
67	C₂×C₁₁	—	9	12	no	—
68	D₁₁	—	11	12	no	—
69	D₁₁	—	99	12	no	—
70	C₃×C₇	D₃×C₁₁⋊D₁₁	1	1	yes	characteristic
71	C₂×C₉	—	121	1	no	—
72	D₉	—	121	1	no	—
73	D₉	C₇×C₁₁⋊D₁₁	1	1	yes	characteristic, direct product factor
74	C₂×C₇	—	9	1	no	—
75	C₂×C₇	—	1089	1	no	—
76	C₂×C₇	—	121	1	no	—
77	C₂×D₃	—	363	1	no	—
78	C₁₁	C₇×D₉×D₁₁	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, direct product factor, Sylow
81	C₂×C₃	—	121	1	no	—
82	D₃	—	3	1	no	—
83	D₃	—	363	1	no	—
84	C₂²	—	1089	1	no	Sylow
85	C₃	D₃×C₇×C₁₁⋊D₁₁	1	1	yes	characteristic
86	C₂	—	9	1	no	—
87	C₂	—	1089	1	no	—
88	C₂	—	121	1	no	—

	subgroup	G/H
center, hypercenter	C₇	D₉×C₁₁⋊D₁₁
commutator, cosocle, hypocenter	C₉×C₁₁²	C₂²×C₇
Frattini	C₃	D₃×C₇×C₁₁⋊D₁₁
Fitting	C₇×C₉×C₁₁²	C₂²
socle	C₃×C₇×C₁₁²	C₂×D₃
LCS	G ▷ C₉×C₁₁²
UCS	C₁ ◁ C₇

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. C₇×C₉×C₁₁⋊D₁₁	C₂	semidirect
5. C₇×C₉×C₁₁²	C₂²	semidirect
9. D₉×C₁₁⋊D₁₁	C₇	direct (N × H)
13. C₉⋊(C₁₁⋊D₁₁)	C₂×C₇	semidirect
14. C₁₁²×D₉	C₂×C₇	semidirect
15. C₉×C₁₁⋊D₁₁	C₂×C₇	semidirect
18. C₇×C₁₁⋊D₁₁	D₉	direct (N × H)
21. C₇×C₁₁×D₉	D₁₁	semidirect
23. C₉×C₁₁²	C₂²×C₇	semidirect
25. C₇×C₁₁²	C₂×D₉	semidirect
29. C₇×C₉×C₁₁	C₂×D₁₁	semidirect
40. C₁₁⋊D₁₁	C₇×D₉	direct (N × H)
44. C₁₁×D₉	C₇×D₁₁	semidirect
51. C₇×D₉	C₁₁⋊D₁₁	direct (N × H)
52. C₁₁²	C₂×C₇×D₉	semidirect
53. C₉×C₁₁	C₂×C₇×D₁₁	semidirect
55. C₇×C₁₁	D₉×D₁₁	semidirect
59. C₇×C₉	C₂×C₁₁⋊D₁₁	semidirect
73. D₉	C₇×C₁₁⋊D₁₁	direct (N × H)
78. C₁₁	C₇×D₉×D₁₁	semidirect
79. C₉	C₂×C₇×C₁₁⋊D₁₁	semidirect
80. C₇	D₉×C₁₁⋊D₁₁	direct (N × H)

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
C₇×C₉×C₁₁⋊D₁₁	2
D₃×C₇×C₁₁⋊D₁₁	3
D₉×C₁₁⋊D₁₁	7
C₇×D₉×D₁₁	11

Subgroups — C7×D9×C11⋊D11 #44478958

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×D₉×C₁₁⋊D₁₁ #44478958