Subgroups — #44478965

Order 30492.

180 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×D₆₉₃	C₂	1	2	yes	maximal, complemented
2	C₇×C₉×C₁₁⋊D₁₁	C₂	1	1	yes	maximal, characteristic, complemented
3	#23779059	—	3	1	no	maximal
4	C₇×C₉×C₁₁²	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₁₁×D₂₃₁	—	3	2	no	—
6	C₃×C₇×C₁₁⋊D₁₁	D₃	1	1	yes	characteristic
7	D₉₉⋊D₁₁	—	7	1	no	maximal, Hall
8	D₇₇⋊D₁₁	—	9	1	no	Hall
9	D₁₁×D₆₃	—	11	2	no	maximal
10	C₃×C₇×C₁₁²	C₂×D₃	1	1	yes	characteristic
11	C₁₁×D₉₉	—	7	2	no	—
12	C₉×C₁₁⋊D₁₁	D₇	1	1	yes	characteristic, complemented
13	C₁₁×D₇₇	—	9	2	no	—
14	C₇×C₁₁⋊D₁₁	D₉	1	1	yes	characteristic, complemented
15	D₃₃⋊D₁₁	—	21	1	no	—
16	D₆₉₃	D₁₁	1	2	yes	complemented
17	C₁₁×D₆₃	—	11	2	no	—
18	C₇×C₉×D₁₁	—	11	2	no	—
19	C₇×C₉×D₁₁	—	22	5	no	—
20	C₉×C₁₁²	C₂×D₇	1	1	yes	characteristic, complemented, Hall
21	D₁₁×D₂₁	—	33	2	no	—
22	C₇×C₁₁²	C₂×D₉	1	1	yes	characteristic, complemented, Hall
23	C₁₁×D₃₃	—	21	2	no	—
24	C₃×C₁₁⋊D₁₁	D₂₁	1	1	yes	characteristic
25	C₇×C₉×C₁₁	—	2	5	no	—
26	C₇×C₉×C₁₁	C₂×D₁₁	1	2	yes	complemented
27	D₁₁²	—	63	1	no	Hall
28	D₂₃₁	—	3	2	no	—
29	C₁₁×D₂₁	—	33	2	no	—
30	C₃×C₇×D₁₁	—	11	2	no	—
31	C₃×C₇×D₁₁	—	22	5	no	—
32	D₉×D₁₁	—	77	2	no	—
33	C₃×C₁₁²	C₂×D₂₁	1	1	yes	characteristic
34	D₇×D₁₁	—	99	2	no	—
35	C₂×D₆₃	—	121	1	no	Hall
36	C₁₁⋊D₁₁	D₆₃	1	1	yes	characteristic, complemented
37	C₁₁×D₁₁	—	63	2	no	—
38	C₃×C₇×C₁₁	—	2	5	no	—
39	C₃×C₇×C₁₁	D₃×D₁₁	1	2	yes	—
40	D₉₉	—	7	2	no	—
41	C₉×D₁₁	—	11	2	no	—
42	C₉×D₁₁	—	22	5	no	—
43	C₁₁×D₉	—	77	2	no	—
44	D₇₇	—	9	2	no	—
45	C₇×D₁₁	—	11	2	no	—
46	C₇×D₁₁	—	22	5	no	—
47	C₁₁×D₇	—	99	2	no	—
48	D₃×D₁₁	—	231	2	no	—
49	C₂×C₇×C₉	—	121	1	no	—
50	D₆₃	—	11	2	no	—
51	C₁₁²	C₂×D₆₃	1	1	yes	characteristic, complemented, Sylow
52	C₉×C₁₁	—	2	5	no	—
53	C₉×C₁₁	D₇×D₁₁	1	2	yes	complemented
54	C₂×D₂₁	—	363	1	no	—
55	C₇×C₁₁	—	2	5	no	—
56	C₇×C₁₁	D₉×D₁₁	1	2	yes	complemented
57	D₃₃	—	21	2	no	—
58	C₃×D₁₁	—	11	2	no	—
59	C₃×D₁₁	—	22	5	no	—
60	D₃×C₁₁	—	231	2	no	—
61	C₇×C₉	D₁₁²	1	1	yes	characteristic, complemented, Hall
62	C₂×D₁₁	—	693	2	no	—
63	C₂×C₃×C₇	—	121	1	no	—
64	D₂₁	—	33	2	no	—
65	C₂×D₉	—	847	1	no	Hall
66	C₃×C₁₁	—	2	5	no	—
67	C₃×C₁₁	D₁₁×D₂₁	1	2	yes	—
68	C₂×D₇	—	1089	1	no	Hall
69	C₂×C₁₁	—	693	2	no	—
70	D₁₁	—	11	2	no	—
71	D₁₁	—	22	5	no	—
72	D₁₁	—	63	2	no	—
73	C₃×C₇	D₃₃⋊D₁₁	1	1	yes	characteristic
74	C₂×C₉	—	121	1	no	—
75	D₉	—	77	2	no	—
76	C₂×C₇	—	121	1	no	—
77	D₇	—	99	2	no	—
78	C₂×D₃	—	2541	1	no	—
79	C₁₁	—	2	5	no	—
80	C₁₁	D₁₁×D₆₃	1	2	yes	complemented
81	C₉	D₇₇⋊D₁₁	1	1	yes	characteristic, complemented, Sylow
82	C₇	D₉₉⋊D₁₁	1	1	yes	characteristic, complemented, Sylow
83	C₂×C₃	—	121	1	no	—
84	D₃	—	231	2	no	—
85	C₂²	—	7623	1	no	Sylow
86	C₃	#23779059	1	1	yes	characteristic
87	C₂	—	121	1	no	—
88	C₂	—	693	2	no	—

	subgroup	G/H
center, hypercenter	C₁	G
commutator, Fitting, cosocle, hypocenter	C₇×C₉×C₁₁²	C₂²
Frattini	C₃	#23779059
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. C₁₁×D₆₉₃	C₂	semidirect
2. C₇×C₉×C₁₁⋊D₁₁	C₂	semidirect
4. C₇×C₉×C₁₁²	C₂²	semidirect
12. C₉×C₁₁⋊D₁₁	D₇	semidirect
14. C₇×C₁₁⋊D₁₁	D₉	semidirect
16. D₆₉₃	D₁₁	semidirect
20. C₉×C₁₁²	C₂×D₇	semidirect
22. C₇×C₁₁²	C₂×D₉	semidirect
26. C₇×C₉×C₁₁	C₂×D₁₁	semidirect
36. C₁₁⋊D₁₁	D₆₃	semidirect
51. C₁₁²	C₂×D₆₃	semidirect
53. C₉×C₁₁	D₇×D₁₁	semidirect
56. C₇×C₁₁	D₉×D₁₁	semidirect
61. C₇×C₉	D₁₁²	semidirect
80. C₁₁	D₁₁×D₆₃	semidirect
81. C₉	D₇₇⋊D₁₁	semidirect
82. C₇	D₉₉⋊D₁₁	semidirect

Maximal subgroups

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

subgroup	index
C₁₁×D₆₉₃	2
C₇×C₉×C₁₁⋊D₁₁	2
#23779059	3
D₉₉⋊D₁₁	7
D₁₁×D₆₃	11