Subgroups — C₃×D₃×C₃₇×C₄₇ #44531081

Order 31302.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₃₇×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₃×C₃₇×C₄₇	C₃	1	1	yes	maximal, characteristic, direct product factor
3	C₂×C₃×C₃₇×C₄₇	—	3	1	no	maximal
4	C₃×C₃₇×C₄₇	—	2	1	no	—
5	C₃×C₃₇×C₄₇	D₃	1	1	yes	characteristic, direct product factor
6	C₃×C₃₇×C₄₇	C₂×C₃	1	1	yes	characteristic, complemented
7	C₂×C₃₇×C₄₇	—	3	1	no	Hall
8	C₃₇×C₄₇	C₃×D₃	1	1	yes	characteristic, direct product factor, Hall
9	C₃×D₃×C₄₇	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₃×D₃×C₃₇	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Hall
11	C₃²×C₄₇	C₂×C₃₇	1	1	yes	characteristic, complemented, Hall
12	C₃²×C₃₇	C₂×C₄₇	1	1	yes	characteristic, complemented, Hall
13	C₂×C₃×C₄₇	—	3	1	no	—
14	D₃×C₄₇	C₃×C₃₇	1	1	yes	characteristic, direct product factor
15	C₂×C₃×C₃₇	—	3	1	no	—
16	D₃×C₃₇	C₃×C₄₇	1	1	yes	characteristic, direct product factor
17	C₃×C₄₇	—	2	1	no	—
18	C₃×C₄₇	D₃×C₃₇	1	1	yes	characteristic, direct product factor
19	C₃×C₄₇	C₂×C₃×C₃₇	1	1	yes	characteristic, complemented
20	C₃×C₃₇	—	2	1	no	—
21	C₃×C₃₇	D₃×C₄₇	1	1	yes	characteristic, direct product factor
22	C₃×C₃₇	C₂×C₃×C₄₇	1	1	yes	characteristic, complemented
23	C₂×C₄₇	—	3	1	no	Hall
24	C₂×C₃₇	—	3	1	no	Hall
25	C₄₇	C₃×D₃×C₃₇	1	1	yes	characteristic, direct product factor, Sylow
26	C₃₇	C₃×D₃×C₄₇	1	1	yes	characteristic, direct product factor, Sylow
27	C₃×D₃	C₃₇×C₄₇	1	1	yes	characteristic, direct product factor, Hall
28	C₃²	C₂×C₃₇×C₄₇	1	1	yes	characteristic, complemented, Sylow
29	C₂×C₃	—	3	1	no	—
30	D₃	C₃×C₃₇×C₄₇	1	1	yes	characteristic, direct product factor
31	C₃	—	2	1	no	—
32	C₃	C₂×C₃×C₃₇×C₄₇	1	1	yes	characteristic, complemented
33	C₃	D₃×C₃₇×C₄₇	1	1	yes	characteristic, direct product factor
34	C₂	—	3	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃×C₃₇×C₄₇	D₃
commutator, cosocle, hypocenter	C₃	C₂×C₃×C₃₇×C₄₇
Frattini	C₁	G
Fitting, socle	C₃²×C₃₇×C₄₇	C₂
LCS	G ▷ C₃
UCS	C₁ ◁ C₃×C₃₇×C₄₇

Complements

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

N	H ≅ G/N	type
1. C₃²×C₃₇×C₄₇	C₂	semidirect
2. D₃×C₃₇×C₄₇	C₃	direct (N × H)
5. C₃×C₃₇×C₄₇	D₃	direct (N × H)
6. C₃×C₃₇×C₄₇	C₂×C₃	semidirect
8. C₃₇×C₄₇	C₃×D₃	direct (N × H)
9. C₃×D₃×C₄₇	C₃₇	direct (N × H)
10. C₃×D₃×C₃₇	C₄₇	direct (N × H)
11. C₃²×C₄₇	C₂×C₃₇	semidirect
12. C₃²×C₃₇	C₂×C₄₇	semidirect
14. D₃×C₄₇	C₃×C₃₇	direct (N × H)
16. D₃×C₃₇	C₃×C₄₇	direct (N × H)
18. C₃×C₄₇	D₃×C₃₇	direct (N × H)
19. C₃×C₄₇	C₂×C₃×C₃₇	semidirect
21. C₃×C₃₇	D₃×C₄₇	direct (N × H)
22. C₃×C₃₇	C₂×C₃×C₄₇	semidirect
25. C₄₇	C₃×D₃×C₃₇	direct (N × H)
26. C₃₇	C₃×D₃×C₄₇	direct (N × H)
27. C₃×D₃	C₃₇×C₄₇	direct (N × H)
28. C₃²	C₂×C₃₇×C₄₇	semidirect
30. D₃	C₃×C₃₇×C₄₇	direct (N × H)
32. C₃	C₂×C₃×C₃₇×C₄₇	semidirect
33. C₃	D₃×C₃₇×C₄₇	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃²×C₃₇×C₄₇	2
D₃×C₃₇×C₄₇	3
C₂×C₃×C₃₇×C₄₇	3
C₃×D₃×C₄₇	37
C₃×D₃×C₃₇	47

Subgroups — C3×D3×C37×C47 #44531081

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×D₃×C₃₇×C₄₇ #44531081