Subgroups — C₃×D₃₂₉₇ #34089995

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	D₃₂₉₇	C₃	1	1	yes	maximal, characteristic, direct product factor
3	C₃×D₁₀₉₉	—	3	1	no	maximal
4	C₃×C₇×C₁₅₇	—	2	1	no	—
5	C₃×C₇×C₁₅₇	D₃	1	1	yes	characteristic, complemented
6	C₃×C₇×C₁₅₇	C₂×C₃	1	1	yes	characteristic, complemented
7	C₃×D₄₇₁	—	7	1	no	maximal, Hall
8	D₁₀₉₉	—	3	1	no	Hall
9	C₃²×C₁₅₇	D₇	1	1	yes	characteristic, complemented, Hall
10	C₇×C₁₅₇	C₃×D₃	1	1	yes	characteristic, complemented, Hall
11	D₄₇₁	—	7	1	no	—
12	C₃×D₁₅₇	—	21	1	no	—
13	C₃×C₁₅₇	—	2	1	no	—
14	C₃×C₁₅₇	C₃×D₇	1	1	yes	characteristic, complemented
15	C₃×C₁₅₇	D₂₁	1	1	yes	characteristic, complemented
16	D₁₅₇	—	21	1	no	Hall
17	C₁₅₇	C₃×D₂₁	1	1	yes	characteristic, complemented, Sylow
18	C₃×D₂₁	—	157	1	no	maximal, Hall
19	C₃²×C₇	D₁₅₇	1	1	yes	characteristic, complemented, Hall
20	D₂₁	—	157	1	no	—
21	C₃×D₇	—	471	1	no	—
22	C₃×C₇	—	2	1	no	—
23	C₃×C₇	C₃×D₁₅₇	1	1	yes	characteristic, complemented
24	C₃×C₇	D₄₇₁	1	1	yes	characteristic, complemented
25	C₃×D₃	—	1099	1	no	Hall
26	D₇	—	471	1	no	Hall
27	C₃²	D₁₀₉₉	1	1	yes	characteristic, complemented, Sylow
28	C₇	C₃×D₄₇₁	1	1	yes	characteristic, complemented, Sylow
29	C₂×C₃	—	3297	1	no	—
30	D₃	—	1099	1	no	—
31	C₃	—	2	1	no	—
32	C₃	C₃×D₁₀₉₉	1	1	yes	characteristic, complemented
33	C₃	D₃₂₉₇	1	1	yes	characteristic, direct product factor
34	C₂	—	3297	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃	D₃₂₉₇
commutator, cosocle, hypocenter	C₃×C₇×C₁₅₇	C₂×C₃
Frattini	C₁	G
Fitting, socle	C₃²×C₇×C₁₅₇	C₂
LCS	G ▷ C₃×C₇×C₁₅₇
UCS	C₁ ◁ C₃

Complements

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

N	H ≅ G/N	type
1. C₃²×C₇×C₁₅₇	C₂	semidirect
2. D₃₂₉₇	C₃	direct (N × H)
5. C₃×C₇×C₁₅₇	D₃	semidirect
6. C₃×C₇×C₁₅₇	C₂×C₃	semidirect
9. C₃²×C₁₅₇	D₇	semidirect
10. C₇×C₁₅₇	C₃×D₃	semidirect
14. C₃×C₁₅₇	C₃×D₇	semidirect
15. C₃×C₁₅₇	D₂₁	semidirect
17. C₁₅₇	C₃×D₂₁	semidirect
19. C₃²×C₇	D₁₅₇	semidirect
23. C₃×C₇	C₃×D₁₅₇	semidirect
24. C₃×C₇	D₄₇₁	semidirect
27. C₃²	D₁₀₉₉	semidirect
28. C₇	C₃×D₄₇₁	semidirect
32. C₃	C₃×D₁₀₉₉	semidirect
33. C₃	D₃₂₉₇	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
D₃₂₉₇	3
C₃×D₁₀₉₉	3
C₃×D₄₇₁	7
C₃×D₂₁	157

Subgroups — C3×D3297 #34089995

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×D₃₂₉₇ #34089995