Subgroups — C₃×D₃×C₇×C₁₅₇ #34089998

Order 19782.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₇×C₁₅₇	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₃×C₇×C₁₅₇	C₃	1	1	yes	maximal, characteristic, direct product factor
3	C₂×C₃×C₇×C₁₅₇	—	3	1	no	maximal
4	C₃×C₇×C₁₅₇	—	2	1	no	—
5	C₃×C₇×C₁₅₇	D₃	1	1	yes	characteristic, direct product factor
6	C₃×C₇×C₁₅₇	C₂×C₃	1	1	yes	characteristic, complemented
7	C₃×D₃×C₁₅₇	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₂×C₇×C₁₅₇	—	3	1	no	Hall
9	C₃²×C₁₅₇	C₂×C₇	1	1	yes	characteristic, complemented, Hall
10	C₇×C₁₅₇	C₃×D₃	1	1	yes	characteristic, direct product factor, Hall
11	C₂×C₃×C₁₅₇	—	3	1	no	—
12	D₃×C₁₅₇	C₃×C₇	1	1	yes	characteristic, direct product factor
13	C₃×C₁₅₇	—	2	1	no	—
14	C₃×C₁₅₇	D₃×C₇	1	1	yes	characteristic, direct product factor
15	C₃×C₁₅₇	C₂×C₃×C₇	1	1	yes	characteristic, complemented
16	C₂×C₁₅₇	—	3	1	no	Hall
17	C₁₅₇	C₃×D₃×C₇	1	1	yes	characteristic, direct product factor, Sylow
18	C₃×D₃×C₇	C₁₅₇	1	1	yes	maximal, characteristic, direct product factor, Hall
19	C₃²×C₇	C₂×C₁₅₇	1	1	yes	characteristic, complemented, Hall
20	C₂×C₃×C₇	—	3	1	no	—
21	D₃×C₇	C₃×C₁₅₇	1	1	yes	characteristic, direct product factor
22	C₃×C₇	—	2	1	no	—
23	C₃×C₇	D₃×C₁₅₇	1	1	yes	characteristic, direct product factor
24	C₃×C₇	C₂×C₃×C₁₅₇	1	1	yes	characteristic, complemented
25	C₃×D₃	C₇×C₁₅₇	1	1	yes	characteristic, direct product factor, Hall
26	C₂×C₇	—	3	1	no	Hall
27	C₃²	C₂×C₇×C₁₅₇	1	1	yes	characteristic, complemented, Sylow
28	C₇	C₃×D₃×C₁₅₇	1	1	yes	characteristic, direct product factor, Sylow
29	C₂×C₃	—	3	1	no	—
30	D₃	C₃×C₇×C₁₅₇	1	1	yes	characteristic, direct product factor
31	C₃	—	2	1	no	—
32	C₃	C₂×C₃×C₇×C₁₅₇	1	1	yes	characteristic, complemented
33	C₃	D₃×C₇×C₁₅₇	1	1	yes	characteristic, direct product factor
34	C₂	—	3	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃×C₇×C₁₅₇	D₃
commutator, cosocle, hypocenter	C₃	C₂×C₃×C₇×C₁₅₇
Frattini	C₁	G
Fitting, socle	C₃²×C₇×C₁₅₇	C₂
LCS	G ▷ C₃
UCS	C₁ ◁ C₃×C₇×C₁₅₇

Complements

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

N	H ≅ G/N	type
1. C₃²×C₇×C₁₅₇	C₂	semidirect
2. D₃×C₇×C₁₅₇	C₃	direct (N × H)
5. C₃×C₇×C₁₅₇	D₃	direct (N × H)
6. C₃×C₇×C₁₅₇	C₂×C₃	semidirect
7. C₃×D₃×C₁₅₇	C₇	direct (N × H)
9. C₃²×C₁₅₇	C₂×C₇	semidirect
10. C₇×C₁₅₇	C₃×D₃	direct (N × H)
12. D₃×C₁₅₇	C₃×C₇	direct (N × H)
14. C₃×C₁₅₇	D₃×C₇	direct (N × H)
15. C₃×C₁₅₇	C₂×C₃×C₇	semidirect
17. C₁₅₇	C₃×D₃×C₇	direct (N × H)
18. C₃×D₃×C₇	C₁₅₇	direct (N × H)
19. C₃²×C₇	C₂×C₁₅₇	semidirect
21. D₃×C₇	C₃×C₁₅₇	direct (N × H)
23. C₃×C₇	D₃×C₁₅₇	direct (N × H)
24. C₃×C₇	C₂×C₃×C₁₅₇	semidirect
25. C₃×D₃	C₇×C₁₅₇	direct (N × H)
27. C₃²	C₂×C₇×C₁₅₇	semidirect
28. C₇	C₃×D₃×C₁₅₇	direct (N × H)
30. D₃	C₃×C₇×C₁₅₇	direct (N × H)
32. C₃	C₂×C₃×C₇×C₁₅₇	semidirect
33. C₃	D₃×C₇×C₁₅₇	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×C₁₅₇	2
D₃×C₇×C₁₅₇	3
C₂×C₃×C₇×C₁₅₇	3
C₃×D₃×C₁₅₇	7
C₃×D₃×C₇	157

Subgroups — C3×D3×C7×C157 #34089998

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×D₃×C₇×C₁₅₇ #34089998