Subgroups — C₂×C₃₁×D₁₈₇ #37550865

Order 23188.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×D₁₈₇	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₁₁×C₁₇×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₁×C₁₇×C₃₁	C₂²	1	1	yes	characteristic, complemented, Hall
4	C₂×C₃₁×D₁₇	—	11	1	no	maximal, Hall
5	C₂×D₁₁×C₃₁	—	17	1	no	maximal, Hall
6	C₂×C₁₇×C₃₁	D₁₁	1	1	yes	characteristic, complemented
7	C₃₁×D₁₇	—	11	2	no	—
8	C₂×D₁₈₇	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₂×C₁₁×C₃₁	D₁₇	1	1	yes	characteristic, complemented
10	D₁₁×C₃₁	—	17	2	no	—
11	C₁₇×C₃₁	C₂×D₁₁	1	1	yes	characteristic, complemented, Hall
12	C₂×C₁₁×C₁₇	C₂×C₃₁	1	1	yes	characteristic, complemented
13	D₁₈₇	C₂×C₃₁	1	2	yes	direct product factor
14	C₁₁×C₃₁	C₂×D₁₇	1	1	yes	characteristic, complemented, Hall
15	C₁₁×C₁₇	C₂²×C₃₁	1	1	yes	characteristic, complemented, Hall
16	C₂²×C₃₁	—	187	1	no	Hall
17	C₂×D₁₇	—	11	1	no	Hall
18	C₂×C₃₁	—	187	2	no	—
19	C₂×C₃₁	D₁₈₇	1	1	yes	characteristic, direct product factor
20	C₂×D₁₁	—	17	1	no	Hall
21	C₂×C₁₇	D₁₁×C₃₁	1	1	yes	characteristic, complemented
22	D₁₇	—	11	2	no	—
23	C₃₁	C₂×D₁₈₇	1	1	yes	characteristic, direct product factor, Sylow
24	C₂×C₁₁	C₃₁×D₁₇	1	1	yes	characteristic, complemented
25	D₁₁	—	17	2	no	—
26	C₁₇	C₂×D₁₁×C₃₁	1	1	yes	characteristic, complemented, Sylow
27	C₁₁	C₂×C₃₁×D₁₇	1	1	yes	characteristic, complemented, Sylow
28	C₂²	—	187	1	no	Sylow
29	C₂	—	187	2	no	—
30	C₂	C₃₁×D₁₈₇	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₃₁	D₁₈₇
commutator, cosocle, hypocenter	C₁₁×C₁₇	C₂²×C₃₁
Frattini	C₁	G
Fitting, socle	C₂×C₁₁×C₁₇×C₃₁	C₂
LCS	G ▷ C₁₁×C₁₇
UCS	C₁ ◁ C₂×C₃₁

Complements

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

N	H ≅ G/N	type
1. C₃₁×D₁₈₇	C₂	direct (N × H)
2. C₂×C₁₁×C₁₇×C₃₁	C₂	semidirect
3. C₁₁×C₁₇×C₃₁	C₂²	semidirect
6. C₂×C₁₇×C₃₁	D₁₁	semidirect
8. C₂×D₁₈₇	C₃₁	direct (N × H)
9. C₂×C₁₁×C₃₁	D₁₇	semidirect
11. C₁₇×C₃₁	C₂×D₁₁	semidirect
12. C₂×C₁₁×C₁₇	C₂×C₃₁	semidirect
13. D₁₈₇	C₂×C₃₁	direct (N × H)
14. C₁₁×C₃₁	C₂×D₁₇	semidirect
15. C₁₁×C₁₇	C₂²×C₃₁	semidirect
19. C₂×C₃₁	D₁₈₇	direct (N × H)
21. C₂×C₁₇	D₁₁×C₃₁	semidirect
23. C₃₁	C₂×D₁₈₇	direct (N × H)
24. C₂×C₁₁	C₃₁×D₁₇	semidirect
26. C₁₇	C₂×D₁₁×C₃₁	semidirect
27. C₁₁	C₂×C₃₁×D₁₇	semidirect
30. C₂	C₃₁×D₁₈₇	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃₁×D₁₈₇	2
C₂×C₁₁×C₁₇×C₃₁	2
C₂×C₃₁×D₁₇	11
C₂×D₁₁×C₃₁	17
C₂×D₁₈₇	31

Subgroups — C2×C31×D187 #37550865

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃₁×D₁₈₇ #37550865