Subgroups — C₂×C₇⋊(C₉⋊(C₁₁⋊D₁₁)) #44478984

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

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

Complements

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

N	H ≅ G/N	type
1. C₇⋊(C₉⋊(C₁₁⋊D₁₁))	C₂	direct (N × H)
2. C₂×C₇×C₉×C₁₁²	C₂	semidirect
4. C₇×C₉×C₁₁²	C₂²	semidirect
12. C₂×C₉×C₁₁²	D₇	semidirect
13. C₂×C₇×C₁₁²	D₉	semidirect
16. C₂×C₇×C₉×C₁₁	D₁₁	semidirect
18. C₉×C₁₁²	C₂×D₇	semidirect
20. C₇×C₁₁²	C₂×D₉	semidirect
23. C₇×C₉×C₁₁	C₂×D₁₁	semidirect
31. C₂×C₁₁²	D₆₃	semidirect
34. C₂×C₉×C₁₁	D₇₇	semidirect
36. C₂×C₇×C₁₁	D₉₉	semidirect
39. C₂×C₇×C₉	C₁₁⋊D₁₁	semidirect
41. C₁₁²	C₂×D₆₃	semidirect
42. C₉×C₁₁	C₂×D₇₇	semidirect
44. C₇×C₁₁	C₂×D₉₉	semidirect
47. C₇×C₉	C₂×C₁₁⋊D₁₁	semidirect
54. C₂×C₁₁	D₆₉₃	semidirect
57. C₂×C₉	C₇⋊(C₁₁⋊D₁₁)	semidirect
59. C₂×C₇	C₉⋊(C₁₁⋊D₁₁)	semidirect
62. C₁₁	C₂×D₆₉₃	semidirect
63. C₉	C₂×C₇⋊(C₁₁⋊D₁₁)	semidirect
64. C₇	C₂×C₉⋊(C₁₁⋊D₁₁)	semidirect
70. C₂	C₇⋊(C₉⋊(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
C₂×C₇×C₉×C₁₁²	2
C₂×C₃⋊(C₇⋊(C₁₁⋊D₁₁))	3
C₂×C₉⋊(C₁₁⋊D₁₁)	7
C₂×D₆₉₃	11

Subgroups — C2×C7⋊(C9⋊(C11⋊D11)) #44478984

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₇⋊(C₉⋊(C₁₁⋊D₁₁)) #44478984