Subgroups — D₃×C₃₇×C₃₁⋊C₃ #35207607

Order 20646.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₃₇×C₃₁⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₃×C₃₁×C₃₇	C₃	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃₇×C₃₁⋊C₃	—	3	1	no	maximal
4	C₃×C₃₁×C₃₇	C₂×C₃	1	1	yes	characteristic, complemented
5	C₃₇×C₃₁⋊C₃	—	2	1	no	—
6	C₃₇×C₃₁⋊C₃	D₃	1	1	yes	characteristic, direct product factor
7	C₂×C₃₁×C₃₇	—	3	1	no	Hall
8	C₃₁×C₃₇	C₃×D₃	1	1	yes	characteristic, complemented, Hall
9	C₃×D₃×C₃₇	—	31	1	no	maximal, Hall
10	D₃×C₃₁⋊C₃	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Hall
11	C₃²×C₃₇	—	31	1	no	Hall
12	C₃×C₃₁⋊C₃	C₂×C₃₇	1	1	yes	characteristic, complemented, Hall
13	C₂×C₃×C₃₇	—	93	1	no	—
14	D₃×C₃₇	C₃₁⋊C₃	1	1	yes	characteristic, direct product factor
15	D₃×C₃₁	C₃×C₃₇	1	1	yes	characteristic, complemented
16	C₂×C₃₁⋊C₃	—	3	1	no	—
17	C₃×C₃₇	—	31	1	no	—
18	C₃×C₃₇	—	62	1	no	—
19	C₃×C₃₇	C₂×C₃₁⋊C₃	1	1	yes	characteristic, complemented
20	C₃×C₃₁	C₂×C₃×C₃₇	1	1	yes	characteristic, complemented
21	C₃₁⋊C₃	—	2	1	no	—
22	C₃₁⋊C₃	D₃×C₃₇	1	1	yes	characteristic, direct product factor
23	C₂×C₃₇	—	3	1	no	Hall
24	C₂×C₃₁	—	3	1	no	Hall
25	C₃₇	D₃×C₃₁⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
26	C₃₁	C₃×D₃×C₃₇	1	1	yes	characteristic, complemented, Sylow
27	C₃×D₃	—	31	1	no	Hall
28	C₃²	—	31	1	no	Sylow
29	C₂×C₃	—	93	1	no	—
30	D₃	C₃₇×C₃₁⋊C₃	1	1	yes	characteristic, direct product factor
31	C₃	—	31	1	no	—
32	C₃	—	62	1	no	—
33	C₃	C₂×C₃₇×C₃₁⋊C₃	1	1	yes	characteristic, complemented
34	C₂	—	3	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃₇	D₃×C₃₁⋊C₃
commutator, cosocle, hypocenter	C₃×C₃₁	C₂×C₃×C₃₇
Frattini	C₁	G
Fitting, socle	C₃×C₃₁×C₃₇	C₂×C₃
LCS	G ▷ C₃×C₃₁
UCS	C₁ ◁ C₃₇

Complements

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

N	H ≅ G/N	type
1. C₃×C₃₇×C₃₁⋊C₃	C₂	semidirect
2. D₃×C₃₁×C₃₇	C₃	semidirect
4. C₃×C₃₁×C₃₇	C₂×C₃	semidirect
6. C₃₇×C₃₁⋊C₃	D₃	direct (N × H)
8. C₃₁×C₃₇	C₃×D₃	semidirect
10. D₃×C₃₁⋊C₃	C₃₇	direct (N × H)
12. C₃×C₃₁⋊C₃	C₂×C₃₇	semidirect
14. D₃×C₃₇	C₃₁⋊C₃	direct (N × H)
15. D₃×C₃₁	C₃×C₃₇	semidirect
19. C₃×C₃₇	C₂×C₃₁⋊C₃	semidirect
20. C₃×C₃₁	C₂×C₃×C₃₇	semidirect
22. C₃₁⋊C₃	D₃×C₃₇	direct (N × H)
25. C₃₇	D₃×C₃₁⋊C₃	direct (N × H)
26. C₃₁	C₃×D₃×C₃₇	semidirect
30. D₃	C₃₇×C₃₁⋊C₃	direct (N × H)
33. C₃	C₂×C₃₇×C₃₁⋊C₃	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₃₇×C₃₁⋊C₃	2
D₃×C₃₁×C₃₇	3
C₂×C₃₇×C₃₁⋊C₃	3
C₃×D₃×C₃₇	31
D₃×C₃₁⋊C₃	37

Subgroups — D3×C37×C31⋊C3 #35207607

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₃×C₃₇×C₃₁⋊C₃ #35207607