Subgroups — C₉×C₁₁×D₁₁₉ #37555613

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	C₃×C₁₁×D₁₁₉	C₃	1	1	yes	maximal, characteristic
3	C₃×C₇×C₁₁×C₁₇	C₂×C₃	1	1	yes	characteristic
4	C₉×C₁₁×D₁₇	—	7	1	no	maximal, Hall
5	C₁₁×D₁₁₉	C₉	1	1	yes	characteristic, direct product factor, Hall
6	C₉×D₁₁₉	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₉×C₁₁×C₁₇	D₇	1	1	yes	characteristic, complemented, Hall
8	C₉×C₁₁×D₇	—	17	1	no	maximal, Hall
9	C₇×C₁₁×C₁₇	C₂×C₉	1	1	yes	characteristic, complemented, Hall
10	C₃×C₁₁×D₁₇	—	7	1	no	—
11	C₇×C₉×C₁₇	C₂×C₁₁	1	1	yes	characteristic, complemented, Hall
12	C₃×D₁₁₉	C₃×C₁₁	1	1	yes	characteristic
13	C₇×C₉×C₁₁	D₁₇	1	1	yes	characteristic, complemented, Hall
14	C₃×C₁₁×C₁₇	C₃×D₇	1	1	yes	characteristic
15	C₃×C₁₁×D₇	—	17	1	no	—
16	C₁₁×D₁₇	—	7	1	no	Hall
17	C₃×C₇×C₁₇	C₂×C₃×C₁₁	1	1	yes	characteristic
18	C₉×D₁₇	—	7	1	no	Hall
19	D₁₁₉	C₉×C₁₁	1	1	yes	characteristic, direct product factor, Hall
20	C₃×C₇×C₁₁	C₃×D₁₇	1	1	yes	characteristic
21	C₂×C₉×C₁₁	—	119	1	no	Hall
22	C₁₁×C₁₇	C₉×D₇	1	1	yes	characteristic, complemented, Hall
23	C₁₁×D₇	—	17	1	no	Hall
24	C₉×C₁₇	C₁₁×D₇	1	1	yes	characteristic, complemented, Hall
25	C₉×D₇	—	17	1	no	Hall
26	C₇×C₁₇	C₂×C₉×C₁₁	1	1	yes	characteristic, complemented, Hall
27	C₃×D₁₇	—	7	1	no	—
28	C₉×C₁₁	D₁₁₉	1	1	yes	characteristic, direct product factor, Hall
29	C₇×C₁₁	C₉×D₁₇	1	1	yes	characteristic, complemented, Hall
30	C₂×C₃×C₁₁	—	119	1	no	—
31	C₇×C₉	C₁₁×D₁₇	1	1	yes	characteristic, complemented, Hall
32	C₃×C₁₇	C₃×C₁₁×D₇	1	1	yes	characteristic
33	C₃×D₇	—	17	1	no	—
34	D₁₇	—	7	1	no	Hall
35	C₃×C₁₁	C₃×D₁₁₉	1	1	yes	characteristic
36	C₂×C₁₁	—	119	1	no	Hall
37	C₃×C₇	C₃×C₁₁×D₁₇	1	1	yes	characteristic
38	C₂×C₉	—	119	1	no	Hall
39	C₁₇	C₉×C₁₁×D₇	1	1	yes	characteristic, complemented, Sylow
40	D₇	—	17	1	no	Hall
41	C₁₁	C₉×D₁₁₉	1	1	yes	characteristic, direct product factor, Sylow
42	C₉	C₁₁×D₁₁₉	1	1	yes	characteristic, direct product factor, Sylow
43	C₇	C₉×C₁₁×D₁₇	1	1	yes	characteristic, complemented, Sylow
44	C₂×C₃	—	119	1	no	—
45	C₃	C₃×C₁₁×D₁₁₉	1	1	yes	characteristic
46	C₂	—	119	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₉×C₁₁	D₁₁₉
commutator, hypocenter	C₇×C₁₇	C₂×C₉×C₁₁
Frattini	C₃	C₃×C₁₁×D₁₁₉
Fitting	C₇×C₉×C₁₁×C₁₇	C₂
socle	C₃×C₇×C₁₁×C₁₇	C₂×C₃
prime radical	C₃×C₁₁×D₁₁₉	C₃
cosocle	C₃×C₇×C₁₇	C₂×C₃×C₁₁
LCS	G ▷ C₇×C₁₇
UCS	C₁ ◁ C₉×C₁₁

Complements

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

N	H ≅ G/N	type
1. C₇×C₉×C₁₁×C₁₇	C₂	semidirect
5. C₁₁×D₁₁₉	C₉	direct (N × H)
6. C₉×D₁₁₉	C₁₁	direct (N × H)
7. C₉×C₁₁×C₁₇	D₇	semidirect
9. C₇×C₁₁×C₁₇	C₂×C₉	semidirect
11. C₇×C₉×C₁₇	C₂×C₁₁	semidirect
13. C₇×C₉×C₁₁	D₁₇	semidirect
19. D₁₁₉	C₉×C₁₁	direct (N × H)
22. C₁₁×C₁₇	C₉×D₇	semidirect
24. C₉×C₁₇	C₁₁×D₇	semidirect
26. C₇×C₁₇	C₂×C₉×C₁₁	semidirect
28. C₉×C₁₁	D₁₁₉	direct (N × H)
29. C₇×C₁₁	C₉×D₁₇	semidirect
31. C₇×C₉	C₁₁×D₁₇	semidirect
39. C₁₇	C₉×C₁₁×D₇	semidirect
41. C₁₁	C₉×D₁₁₉	direct (N × H)
42. C₉	C₁₁×D₁₁₉	direct (N × H)
43. C₇	C₉×C₁₁×D₁₇	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
C₃×C₁₁×D₁₁₉	3
C₉×C₁₁×D₁₇	7
C₉×D₁₁₉	11
C₉×C₁₁×D₇	17

Subgroups — C9×C11×D119 #37555613

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×C₁₁×D₁₁₉ #37555613