Subgroups — D₃×C₇×C₁₅₇⋊C₃ #34089972

Order 19782.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₇×C₁₅₇⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₃×C₇×C₁₅₇	C₃	1	1	yes	maximal, characteristic, complemented
3	C₂×C₇×C₁₅₇⋊C₃	—	3	1	no	maximal
4	C₃×C₇×C₁₅₇	C₂×C₃	1	1	yes	characteristic, complemented
5	C₇×C₁₅₇⋊C₃	—	2	1	no	—
6	C₇×C₁₅₇⋊C₃	D₃	1	1	yes	characteristic, direct product factor
7	D₃×C₁₅₇⋊C₃	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₂×C₇×C₁₅₇	—	3	1	no	Hall
9	C₃×C₁₅₇⋊C₃	C₂×C₇	1	1	yes	characteristic, complemented, Hall
10	C₇×C₁₅₇	C₃×D₃	1	1	yes	characteristic, complemented, Hall
11	D₃×C₁₅₇	C₃×C₇	1	1	yes	characteristic, complemented
12	C₂×C₁₅₇⋊C₃	—	3	1	no	—
13	C₃×C₁₅₇	C₂×C₃×C₇	1	1	yes	characteristic, complemented
14	C₁₅₇⋊C₃	—	2	1	no	—
15	C₁₅₇⋊C₃	D₃×C₇	1	1	yes	characteristic, direct product factor
16	C₂×C₁₅₇	—	3	1	no	Hall
17	C₁₅₇	C₃×D₃×C₇	1	1	yes	characteristic, complemented, Sylow
18	C₃×D₃×C₇	—	157	1	no	maximal, Hall
19	C₃²×C₇	—	157	1	no	Hall
20	C₂×C₃×C₇	—	471	1	no	—
21	D₃×C₇	C₁₅₇⋊C₃	1	1	yes	characteristic, direct product factor
22	C₃×C₇	—	314	1	no	—
23	C₃×C₇	—	157	1	no	—
24	C₃×C₇	C₂×C₁₅₇⋊C₃	1	1	yes	characteristic, complemented
25	C₃×D₃	—	157	1	no	Hall
26	C₂×C₇	—	3	1	no	Hall
27	C₃²	—	157	1	no	Sylow
28	C₇	D₃×C₁₅₇⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
29	C₂×C₃	—	471	1	no	—
30	D₃	C₇×C₁₅₇⋊C₃	1	1	yes	characteristic, direct product factor
31	C₃	—	314	1	no	—
32	C₃	—	157	1	no	—
33	C₃	C₂×C₇×C₁₅₇⋊C₃	1	1	yes	characteristic, complemented
34	C₂	—	3	1	no	Sylow

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

Complements

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

N	H ≅ G/N	type
1. C₃×C₇×C₁₅₇⋊C₃	C₂	semidirect
2. D₃×C₇×C₁₅₇	C₃	semidirect
4. C₃×C₇×C₁₅₇	C₂×C₃	semidirect
6. C₇×C₁₅₇⋊C₃	D₃	direct (N × H)
7. D₃×C₁₅₇⋊C₃	C₇	direct (N × H)
9. C₃×C₁₅₇⋊C₃	C₂×C₇	semidirect
10. C₇×C₁₅₇	C₃×D₃	semidirect
11. D₃×C₁₅₇	C₃×C₇	semidirect
13. C₃×C₁₅₇	C₂×C₃×C₇	semidirect
15. C₁₅₇⋊C₃	D₃×C₇	direct (N × H)
17. C₁₅₇	C₃×D₃×C₇	semidirect
21. D₃×C₇	C₁₅₇⋊C₃	direct (N × H)
24. C₃×C₇	C₂×C₁₅₇⋊C₃	semidirect
28. C₇	D₃×C₁₅₇⋊C₃	direct (N × H)
30. D₃	C₇×C₁₅₇⋊C₃	direct (N × H)
33. C₃	C₂×C₇×C₁₅₇⋊C₃	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₇×C₁₅₇⋊C₃	2
D₃×C₇×C₁₅₇	3
C₂×C₇×C₁₅₇⋊C₃	3
D₃×C₁₅₇⋊C₃	7
C₃×D₃×C₇	157

Subgroups — D3×C7×C157⋊C3 #34089972

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₃×C₇×C₁₅₇⋊C₃ #34089972