Subgroups — C₂×D₇×C₃₁×C₃₇ #44545809

Order 32116.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₇×C₃₁×C₃₇	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₇×C₃₁×C₃₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×C₃₁×C₃₇	C₂²	1	1	yes	characteristic, complemented, Hall
4	C₂²×C₃₁×C₃₇	—	7	1	no	maximal, Hall
5	C₂×C₃₁×C₃₇	—	7	2	no	—
6	C₂×C₃₁×C₃₇	D₇	1	1	yes	characteristic, direct product factor
7	C₃₁×C₃₇	C₂×D₇	1	1	yes	characteristic, direct product factor, Hall
8	C₂×D₇×C₃₇	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₂×D₇×C₃₁	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₂×C₇×C₃₇	C₂×C₃₁	1	1	yes	characteristic, complemented
11	D₇×C₃₇	C₂×C₃₁	1	2	yes	direct product factor
12	C₂×C₇×C₃₁	C₂×C₃₇	1	1	yes	characteristic, complemented
13	D₇×C₃₁	C₂×C₃₇	1	2	yes	direct product factor
14	C₇×C₃₇	C₂²×C₃₁	1	1	yes	characteristic, complemented, Hall
15	C₇×C₃₁	C₂²×C₃₇	1	1	yes	characteristic, complemented, Hall
16	C₂²×C₃₇	—	7	1	no	Hall
17	C₂²×C₃₁	—	7	1	no	Hall
18	C₂×C₃₇	—	7	2	no	—
19	C₂×C₃₇	D₇×C₃₁	1	1	yes	characteristic, direct product factor
20	C₂×C₃₁	—	7	2	no	—
21	C₂×C₃₁	D₇×C₃₇	1	1	yes	characteristic, direct product factor
22	C₃₇	C₂×D₇×C₃₁	1	1	yes	characteristic, direct product factor, Sylow
23	C₃₁	C₂×D₇×C₃₇	1	1	yes	characteristic, direct product factor, Sylow
24	C₂×D₇	C₃₁×C₃₇	1	1	yes	characteristic, direct product factor, Hall
25	C₂×C₇	C₂×C₃₁×C₃₇	1	1	yes	characteristic, complemented
26	D₇	C₂×C₃₁×C₃₇	1	2	yes	direct product factor
27	C₇	C₂²×C₃₁×C₃₇	1	1	yes	characteristic, complemented, Sylow
28	C₂²	—	7	1	no	Sylow
29	C₂	—	7	2	no	—
30	C₂	D₇×C₃₁×C₃₇	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₃₁×C₃₇	D₇
commutator, cosocle, hypocenter	C₇	C₂²×C₃₁×C₃₇
Frattini	C₁	G
Fitting, socle	C₂×C₇×C₃₁×C₃₇	C₂
LCS	G ▷ C₇
UCS	C₁ ◁ C₂×C₃₁×C₃₇

Complements

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

N	H ≅ G/N	type
1. D₇×C₃₁×C₃₇	C₂	direct (N × H)
2. C₂×C₇×C₃₁×C₃₇	C₂	semidirect
3. C₇×C₃₁×C₃₇	C₂²	semidirect
6. C₂×C₃₁×C₃₇	D₇	direct (N × H)
7. C₃₁×C₃₇	C₂×D₇	direct (N × H)
8. C₂×D₇×C₃₇	C₃₁	direct (N × H)
9. C₂×D₇×C₃₁	C₃₇	direct (N × H)
10. C₂×C₇×C₃₇	C₂×C₃₁	semidirect
11. D₇×C₃₇	C₂×C₃₁	direct (N × H)
12. C₂×C₇×C₃₁	C₂×C₃₇	semidirect
13. D₇×C₃₁	C₂×C₃₇	direct (N × H)
14. C₇×C₃₇	C₂²×C₃₁	semidirect
15. C₇×C₃₁	C₂²×C₃₇	semidirect
19. C₂×C₃₇	D₇×C₃₁	direct (N × H)
21. C₂×C₃₁	D₇×C₃₇	direct (N × H)
22. C₃₇	C₂×D₇×C₃₁	direct (N × H)
23. C₃₁	C₂×D₇×C₃₇	direct (N × H)
24. C₂×D₇	C₃₁×C₃₇	direct (N × H)
25. C₂×C₇	C₂×C₃₁×C₃₇	semidirect
26. D₇	C₂×C₃₁×C₃₇	direct (N × H)
27. C₇	C₂²×C₃₁×C₃₇	semidirect
30. C₂	D₇×C₃₁×C₃₇	direct (N × H)

Maximal subgroups

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

subgroup	index
D₇×C₃₁×C₃₇	2
C₂×C₇×C₃₁×C₃₇	2
C₂²×C₃₁×C₃₇	7
C₂×D₇×C₃₇	31
C₂×D₇×C₃₁	37

Subgroups — C2×D7×C31×C37 #44545809

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×D₇×C₃₁×C₃₇ #44545809