Subgroups — C₃²×C₇×D₁₈₇ #37555650

Order 23562.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₇×C₁₁×C₁₇	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₃×C₇×D₁₈₇	C₃	1	4	yes	maximal, direct product factor
3	C₃×C₇×C₁₁×C₁₇	C₂×C₃	1	4	yes	complemented
4	C₃²×D₁₈₇	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₇×D₁₈₇	C₃²	1	1	yes	characteristic, direct product factor, Hall
6	C₃²×C₇×D₁₇	—	11	1	no	maximal, Hall
7	C₃²×C₁₁×C₁₇	C₂×C₇	1	1	yes	characteristic, complemented, Hall
8	C₃²×C₇×D₁₁	—	17	1	no	maximal, Hall
9	C₇×C₁₁×C₁₇	C₂×C₃²	1	1	yes	characteristic, complemented, Hall
10	C₃×D₁₈₇	C₃×C₇	1	4	yes	direct product factor
11	C₃²×C₇×C₁₇	D₁₁	1	1	yes	characteristic, complemented, Hall
12	C₃×C₇×D₁₇	—	11	4	no	—
13	C₃²×C₇×C₁₁	D₁₇	1	1	yes	characteristic, complemented, Hall
14	C₃×C₁₁×C₁₇	C₂×C₃×C₇	1	4	yes	complemented
15	C₃×C₇×D₁₁	—	17	4	no	—
16	D₁₈₇	C₃²×C₇	1	1	yes	characteristic, direct product factor, Hall
17	C₃×C₇×C₁₇	C₃×D₁₁	1	4	yes	complemented
18	C₃²×D₁₇	—	11	1	no	Hall
19	C₇×D₁₇	—	11	1	no	Hall
20	C₃×C₇×C₁₁	C₃×D₁₇	1	4	yes	complemented
21	C₃²×D₁₁	—	17	1	no	Hall
22	C₁₁×C₁₇	C₂×C₃²×C₇	1	1	yes	characteristic, complemented, Hall
23	C₇×D₁₁	—	17	1	no	Hall
24	C₃²×C₁₇	C₇×D₁₁	1	1	yes	characteristic, complemented, Hall
25	C₂×C₃²×C₇	—	187	1	no	Hall
26	C₇×C₁₇	C₃²×D₁₁	1	1	yes	characteristic, complemented, Hall
27	C₃×D₁₇	—	11	4	no	—
28	C₃²×C₁₁	C₇×D₁₇	1	1	yes	characteristic, complemented, Hall
29	C₇×C₁₁	C₃²×D₁₇	1	1	yes	characteristic, complemented, Hall
30	C₃×D₁₁	—	17	4	no	—
31	C₃²×C₇	D₁₈₇	1	1	yes	characteristic, direct product factor, Hall
32	C₃×C₁₇	C₃×C₇×D₁₁	1	4	yes	complemented
33	C₂×C₃×C₇	—	187	4	no	—
34	D₁₇	—	11	1	no	Hall
35	C₃×C₁₁	C₃×C₇×D₁₇	1	4	yes	complemented
36	D₁₁	—	17	1	no	Hall
37	C₃×C₇	C₃×D₁₈₇	1	4	yes	direct product factor
38	C₂×C₃²	—	187	1	no	Hall
39	C₁₇	C₃²×C₇×D₁₁	1	1	yes	characteristic, complemented, Sylow
40	C₂×C₇	—	187	1	no	Hall
41	C₁₁	C₃²×C₇×D₁₇	1	1	yes	characteristic, complemented, Sylow
42	C₃²	C₇×D₁₈₇	1	1	yes	characteristic, direct product factor, Sylow
43	C₇	C₃²×D₁₈₇	1	1	yes	characteristic, direct product factor, Sylow
44	C₂×C₃	—	187	4	no	—
45	C₃	C₃×C₇×D₁₈₇	1	4	yes	direct product factor
46	C₂	—	187	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃²×C₇	D₁₈₇
commutator, cosocle, hypocenter	C₁₁×C₁₇	C₂×C₃²×C₇
Frattini	C₁	G
Fitting, socle	C₃²×C₇×C₁₁×C₁₇	C₂
LCS	G ▷ C₁₁×C₁₇
UCS	C₁ ◁ C₃²×C₇

Complements

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

N	H ≅ G/N	type
1. C₃²×C₇×C₁₁×C₁₇	C₂	semidirect
2. C₃×C₇×D₁₈₇	C₃	direct (N × H)
3. C₃×C₇×C₁₁×C₁₇	C₂×C₃	semidirect
4. C₃²×D₁₈₇	C₇	direct (N × H)
5. C₇×D₁₈₇	C₃²	direct (N × H)
7. C₃²×C₁₁×C₁₇	C₂×C₇	semidirect
9. C₇×C₁₁×C₁₇	C₂×C₃²	semidirect
10. C₃×D₁₈₇	C₃×C₇	direct (N × H)
11. C₃²×C₇×C₁₇	D₁₁	semidirect
13. C₃²×C₇×C₁₁	D₁₇	semidirect
14. C₃×C₁₁×C₁₇	C₂×C₃×C₇	semidirect
16. D₁₈₇	C₃²×C₇	direct (N × H)
17. C₃×C₇×C₁₇	C₃×D₁₁	semidirect
20. C₃×C₇×C₁₁	C₃×D₁₇	semidirect
22. C₁₁×C₁₇	C₂×C₃²×C₇	semidirect
24. C₃²×C₁₇	C₇×D₁₁	semidirect
26. C₇×C₁₇	C₃²×D₁₁	semidirect
28. C₃²×C₁₁	C₇×D₁₇	semidirect
29. C₇×C₁₁	C₃²×D₁₇	semidirect
31. C₃²×C₇	D₁₈₇	direct (N × H)
32. C₃×C₁₇	C₃×C₇×D₁₁	semidirect
35. C₃×C₁₁	C₃×C₇×D₁₇	semidirect
37. C₃×C₇	C₃×D₁₈₇	direct (N × H)
39. C₁₇	C₃²×C₇×D₁₁	semidirect
41. C₁₁	C₃²×C₇×D₁₇	semidirect
42. C₃²	C₇×D₁₈₇	direct (N × H)
43. C₇	C₃²×D₁₈₇	direct (N × H)
45. C₃	C₃×C₇×D₁₈₇	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃²×C₇×C₁₁×C₁₇	2
C₃×C₇×D₁₈₇	3
C₃²×D₁₈₇	7
C₃²×C₇×D₁₇	11
C₃²×C₇×D₁₁	17

Subgroups — C32×C7×D187 #37555650

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃²×C₇×D₁₈₇ #37555650