Subgroups — C₃×D₇×C₁₅₇⋊C₃ #34089970

Order 19782.

48 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	D₇×C₁₅₇⋊C₃	C₃	1	3	yes	maximal, direct product factor
3	C₃×D₇×C₁₅₇	C₃	1	1	yes	maximal, characteristic, complemented
4	C₃×C₇×C₁₅₇	C₂×C₃	1	1	yes	characteristic, complemented
5	C₇×C₁₅₇⋊C₃	C₂×C₃	1	3	yes	complemented
6	C₂×C₃×C₁₅₇⋊C₃	—	7	1	no	maximal, Hall
7	D₇×C₁₅₇	C₃²	1	1	yes	characteristic, complemented, Hall
8	C₃×C₁₅₇⋊C₃	D₇	1	1	yes	characteristic, direct product factor, Hall
9	C₇×C₁₅₇	C₂×C₃²	1	1	yes	characteristic, complemented, Hall
10	C₂×C₃×C₁₅₇	—	7	1	no	—
11	C₂×C₁₅₇⋊C₃	—	7	3	no	—
12	C₃×C₁₅₇	C₃×D₇	1	1	yes	characteristic, complemented
13	C₁₅₇⋊C₃	C₃×D₇	1	3	yes	direct product factor
14	C₂×C₁₅₇	—	7	1	no	Hall
15	C₁₅₇	C₃²×D₇	1	1	yes	characteristic, complemented, Sylow
16	C₃²×D₇	—	157	1	no	maximal, Hall
17	C₃²×C₇	—	157	1	no	Hall
18	C₃×D₇	—	157	3	no	—
19	C₃×D₇	C₁₅₇⋊C₃	1	1	yes	characteristic, direct product factor
20	C₃×C₇	—	157	3	no	—
21	C₃×C₇	C₂×C₁₅₇⋊C₃	1	1	yes	characteristic, complemented
22	C₂×C₃²	—	1099	1	no	Hall
23	D₇	C₃×C₁₅₇⋊C₃	1	1	yes	characteristic, direct product factor, Hall
24	C₃²	—	157	1	no	Sylow
25	C₇	C₂×C₃×C₁₅₇⋊C₃	1	1	yes	characteristic, complemented, Sylow
26	C₂×C₃	—	7	1	no	—
27	C₂×C₃	—	1099	3	no	—
28	C₃	—	157	3	no	—
29	C₃	D₇×C₁₅₇⋊C₃	1	1	yes	characteristic, direct product factor
30	C₂	—	7	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃	D₇×C₁₅₇⋊C₃
commutator, cosocle, hypocenter	C₇×C₁₅₇	C₂×C₃²
Frattini	C₁	G
Fitting, socle	C₃×C₇×C₁₅₇	C₂×C₃
LCS	G ▷ C₇×C₁₅₇
UCS	C₁ ◁ C₃

Complements

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

N	H ≅ G/N	type
1. C₃×C₇×C₁₅₇⋊C₃	C₂	semidirect
2. D₇×C₁₅₇⋊C₃	C₃	direct (N × H)
3. C₃×D₇×C₁₅₇	C₃	semidirect
4. C₃×C₇×C₁₅₇	C₂×C₃	semidirect
5. C₇×C₁₅₇⋊C₃	C₂×C₃	semidirect
7. D₇×C₁₅₇	C₃²	semidirect
8. C₃×C₁₅₇⋊C₃	D₇	direct (N × H)
9. C₇×C₁₅₇	C₂×C₃²	semidirect
12. C₃×C₁₅₇	C₃×D₇	semidirect
13. C₁₅₇⋊C₃	C₃×D₇	direct (N × H)
15. C₁₅₇	C₃²×D₇	semidirect
19. C₃×D₇	C₁₅₇⋊C₃	direct (N × H)
21. C₃×C₇	C₂×C₁₅₇⋊C₃	semidirect
23. D₇	C₃×C₁₅₇⋊C₃	direct (N × H)
25. C₇	C₂×C₃×C₁₅₇⋊C₃	semidirect
29. C₃	D₇×C₁₅₇⋊C₃	direct (N × H)

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
D₇×C₁₅₇⋊C₃	3
C₃×D₇×C₁₅₇	3
C₂×C₃×C₁₅₇⋊C₃	7
C₃²×D₇	157

Subgroups — C3×D7×C157⋊C3 #34089970

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×D₇×C₁₅₇⋊C₃ #34089970