Subgroups — D₃₃×C₁₅₇⋊C₃ #44527273

Order 31086.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₁₁×C₁₅₇⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₁₁×C₁₅₇⋊C₃	—	3	1	no	maximal
3	D₃₃×C₁₅₇	C₃	1	1	yes	maximal, characteristic, complemented
4	C₃×C₁₁×C₁₅₇	C₂×C₃	1	1	yes	characteristic, complemented
5	C₁₁×C₁₅₇⋊C₃	—	2	1	no	—
6	C₁₁×C₁₅₇⋊C₃	D₃	1	1	yes	characteristic, complemented
7	D₁₁×C₁₅₇	—	3	1	no	Hall
8	D₃×C₁₅₇⋊C₃	—	11	1	no	maximal, Hall
9	C₁₁×C₁₅₇	C₃×D₃	1	1	yes	characteristic, complemented, Hall
10	C₃×C₁₅₇⋊C₃	D₁₁	1	1	yes	characteristic, complemented, Hall
11	D₃×C₁₅₇	—	11	1	no	—
12	C₂×C₁₅₇⋊C₃	—	33	1	no	—
13	C₃×C₁₅₇	C₃×D₁₁	1	1	yes	characteristic, complemented
14	C₁₅₇⋊C₃	—	2	1	no	—
15	C₁₅₇⋊C₃	D₃₃	1	1	yes	characteristic, direct product factor
16	C₂×C₁₅₇	—	33	1	no	Hall
17	C₃×D₃₃	—	157	1	no	maximal, Hall
18	C₁₅₇	C₃×D₃₃	1	1	yes	characteristic, complemented, Sylow
19	C₃²×C₁₁	—	157	1	no	Hall
20	D₃₃	C₁₅₇⋊C₃	1	1	yes	characteristic, direct product factor
21	C₃×D₁₁	—	471	1	no	—
22	C₃×C₁₁	—	314	1	no	—
23	C₃×C₁₁	—	157	1	no	—
24	C₃×C₁₁	C₂×C₁₅₇⋊C₃	1	1	yes	characteristic, complemented
25	D₁₁	—	3	1	no	Hall
26	C₃×D₃	—	1727	1	no	Hall
27	C₁₁	D₃×C₁₅₇⋊C₃	1	1	yes	characteristic, complemented, Sylow
28	C₃²	—	157	1	no	Sylow
29	C₂×C₃	—	5181	1	no	—
30	D₃	—	11	1	no	—
31	C₃	—	314	1	no	—
32	C₃	—	157	1	no	—
33	C₃	D₁₁×C₁₅₇⋊C₃	1	1	yes	characteristic, complemented
34	C₂	—	33	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃×C₁₁×C₁₅₇	C₂×C₃
LCS	G ▷ C₃×C₁₁×C₁₅₇
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. C₃×C₁₁×C₁₅₇⋊C₃	C₂	semidirect
3. D₃₃×C₁₅₇	C₃	semidirect
4. C₃×C₁₁×C₁₅₇	C₂×C₃	semidirect
6. C₁₁×C₁₅₇⋊C₃	D₃	semidirect
9. C₁₁×C₁₅₇	C₃×D₃	semidirect
10. C₃×C₁₅₇⋊C₃	D₁₁	semidirect
13. C₃×C₁₅₇	C₃×D₁₁	semidirect
15. C₁₅₇⋊C₃	D₃₃	direct (N × H)
18. C₁₅₇	C₃×D₃₃	semidirect
20. D₃₃	C₁₅₇⋊C₃	direct (N × H)
24. C₃×C₁₁	C₂×C₁₅₇⋊C₃	semidirect
27. C₁₁	D₃×C₁₅₇⋊C₃	semidirect
33. C₃	D₁₁×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×C₁₁×C₁₅₇⋊C₃	2
D₁₁×C₁₅₇⋊C₃	3
D₃₃×C₁₅₇	3
D₃×C₁₅₇⋊C₃	11
C₃×D₃₃	157

Subgroups — D33×C157⋊C3 #44527273

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₃₃×C₁₅₇⋊C₃ #44527273