Subgroups — C₁₁×D₁₀₇₁ #37555621

Order 23562.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×C₉×C₁₁×C₁₇	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₁₁×D₃₅₇	—	3	1	no	maximal
3	C₃×C₇×C₁₁×C₁₇	D₃	1	1	yes	characteristic
4	C₁₁×D₁₅₃	—	7	1	no	maximal, Hall
5	C₁₁×D₁₁₉	—	9	1	no	Hall
6	D₁₀₇₁	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₉×C₁₁×C₁₇	D₇	1	1	yes	characteristic, complemented, Hall
8	C₁₁×D₆₃	—	17	1	no	maximal, Hall
9	C₇×C₁₁×C₁₇	D₉	1	1	yes	characteristic, complemented, Hall
10	C₁₁×D₅₁	—	21	1	no	—
11	C₇×C₉×C₁₇	C₂×C₁₁	1	1	yes	characteristic, complemented, Hall
12	D₃₅₇	—	3	1	no	—
13	C₇×C₉×C₁₁	D₁₇	1	1	yes	characteristic, complemented, Hall
14	C₃×C₁₁×C₁₇	D₂₁	1	1	yes	characteristic
15	C₁₁×D₂₁	—	51	1	no	—
16	C₁₁×D₁₇	—	63	1	no	Hall
17	C₃×C₇×C₁₇	D₃×C₁₁	1	1	yes	characteristic
18	D₁₅₃	—	7	1	no	Hall
19	D₁₁₉	—	9	1	no	Hall
20	C₃×C₇×C₁₁	D₅₁	1	1	yes	characteristic
21	C₁₁×D₉	—	119	1	no	Hall
22	C₁₁×C₁₇	D₆₃	1	1	yes	characteristic, complemented, Hall
23	C₁₁×D₇	—	153	1	no	Hall
24	C₉×C₁₇	C₁₁×D₇	1	1	yes	characteristic, complemented, Hall
25	D₆₃	—	17	1	no	Hall
26	C₇×C₁₇	C₁₁×D₉	1	1	yes	characteristic, complemented, Hall
27	D₅₁	—	21	1	no	—
28	C₉×C₁₁	D₁₁₉	1	1	yes	characteristic, complemented, Hall
29	C₇×C₁₁	D₁₅₃	1	1	yes	characteristic, complemented, Hall
30	D₃×C₁₁	—	357	1	no	—
31	C₇×C₉	C₁₁×D₁₇	1	1	yes	characteristic, complemented, Hall
32	C₃×C₁₇	C₁₁×D₂₁	1	1	yes	characteristic
33	D₂₁	—	51	1	no	—
34	D₁₇	—	63	1	no	Hall
35	C₃×C₁₁	D₃₅₇	1	1	yes	characteristic
36	C₂×C₁₁	—	1071	1	no	Hall
37	C₃×C₇	C₁₁×D₅₁	1	1	yes	characteristic
38	D₉	—	119	1	no	Hall
39	C₁₇	C₁₁×D₆₃	1	1	yes	characteristic, complemented, Sylow
40	D₇	—	153	1	no	Hall
41	C₁₁	D₁₀₇₁	1	1	yes	characteristic, direct product factor, Sylow
42	C₉	C₁₁×D₁₁₉	1	1	yes	characteristic, complemented, Sylow
43	C₇	C₁₁×D₁₅₃	1	1	yes	characteristic, complemented, Sylow
44	D₃	—	357	1	no	—
45	C₃	C₁₁×D₃₅₇	1	1	yes	characteristic
46	C₂	—	1071	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁₁	D₁₀₇₁
commutator, cosocle, hypocenter	C₇×C₉×C₁₇	C₂×C₁₁
Frattini	C₃	C₁₁×D₃₅₇
Fitting	C₇×C₉×C₁₁×C₁₇	C₂
socle	C₃×C₇×C₁₁×C₁₇	D₃
LCS	G ▷ C₇×C₉×C₁₇
UCS	C₁ ◁ C₁₁

Complements

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

N	H ≅ G/N	type
1. C₇×C₉×C₁₁×C₁₇	C₂	semidirect
6. D₁₀₇₁	C₁₁	direct (N × H)
7. C₉×C₁₁×C₁₇	D₇	semidirect
9. C₇×C₁₁×C₁₇	D₉	semidirect
11. C₇×C₉×C₁₇	C₂×C₁₁	semidirect
13. C₇×C₉×C₁₁	D₁₇	semidirect
22. C₁₁×C₁₇	D₆₃	semidirect
24. C₉×C₁₇	C₁₁×D₇	semidirect
26. C₇×C₁₇	C₁₁×D₉	semidirect
28. C₉×C₁₁	D₁₁₉	semidirect
29. C₇×C₁₁	D₁₅₃	semidirect
31. C₇×C₉	C₁₁×D₁₇	semidirect
39. C₁₇	C₁₁×D₆₃	semidirect
41. C₁₁	D₁₀₇₁	direct (N × H)
42. C₉	C₁₁×D₁₁₉	semidirect
43. C₇	C₁₁×D₁₅₃	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×C₁₇	2
C₁₁×D₃₅₇	3
C₁₁×D₁₅₃	7
D₁₀₇₁	11
C₁₁×D₆₃	17

Subgroups — C11×D1071 #37555621

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×D₁₀₇₁ #37555621