Subgroups — C₂×C₃×C₇₃×D₃₇ #44569492

Order 32412.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₇₃×D₃₇	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₃×C₃₇×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₇₃×D₃₇	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₃×C₃₇×C₇₃	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₃₇×C₇₃	C₂×C₃	1	1	yes	characteristic, complemented
6	C₇₃×D₃₇	C₂×C₃	1	2	yes	direct product factor
7	C₃₇×C₇₃	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
8	C₂²×C₃×C₇₃	—	37	1	no	maximal, Hall
9	C₂×C₃×D₃₇	C₇₃	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₂×C₃×C₇₃	—	37	2	no	—
11	C₂×C₃×C₇₃	D₃₇	1	1	yes	characteristic, direct product factor
12	C₂²×C₇₃	—	37	1	no	Hall
13	C₂×C₃×C₃₇	C₂×C₇₃	1	1	yes	characteristic, complemented
14	C₃×D₃₇	C₂×C₇₃	1	2	yes	direct product factor
15	C₃×C₇₃	C₂×D₃₇	1	1	yes	characteristic, direct product factor, Hall
16	C₂×D₃₇	C₃×C₇₃	1	1	yes	characteristic, direct product factor, Hall
17	C₂×C₇₃	—	37	2	no	—
18	C₂×C₇₃	C₃×D₃₇	1	1	yes	characteristic, direct product factor
19	C₃×C₃₇	C₂²×C₇₃	1	1	yes	characteristic, complemented, Hall
20	C₂×C₃₇	C₂×C₃×C₇₃	1	1	yes	characteristic, complemented
21	D₃₇	C₂×C₃×C₇₃	1	2	yes	direct product factor
22	C₇₃	C₂×C₃×D₃₇	1	1	yes	characteristic, direct product factor, Sylow
23	C₃₇	C₂²×C₃×C₇₃	1	1	yes	characteristic, complemented, Sylow
24	C₂²×C₃	—	37	1	no	Hall
25	C₂×C₃	—	37	2	no	—
26	C₂×C₃	C₇₃×D₃₇	1	1	yes	characteristic, direct product factor
27	C₂²	—	37	1	no	Sylow
28	C₃	C₂×C₇₃×D₃₇	1	1	yes	characteristic, direct product factor, Sylow
29	C₂	—	37	2	no	—
30	C₂	C₃×C₇₃×D₃₇	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₃×C₇₃	D₃₇
commutator, cosocle, hypocenter	C₃₇	C₂²×C₃×C₇₃
Frattini	C₁	G
Fitting, socle	C₂×C₃×C₃₇×C₇₃	C₂
LCS	G ▷ C₃₇
UCS	C₁ ◁ C₂×C₃×C₇₃

Complements

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

N	H ≅ G/N	type
1. C₃×C₇₃×D₃₇	C₂	direct (N × H)
2. C₂×C₃×C₃₇×C₇₃	C₂	semidirect
3. C₂×C₇₃×D₃₇	C₃	direct (N × H)
4. C₃×C₃₇×C₇₃	C₂²	semidirect
5. C₂×C₃₇×C₇₃	C₂×C₃	semidirect
6. C₇₃×D₃₇	C₂×C₃	direct (N × H)
7. C₃₇×C₇₃	C₂²×C₃	semidirect
9. C₂×C₃×D₃₇	C₇₃	direct (N × H)
11. C₂×C₃×C₇₃	D₃₇	direct (N × H)
13. C₂×C₃×C₃₇	C₂×C₇₃	semidirect
14. C₃×D₃₇	C₂×C₇₃	direct (N × H)
15. C₃×C₇₃	C₂×D₃₇	direct (N × H)
16. C₂×D₃₇	C₃×C₇₃	direct (N × H)
18. C₂×C₇₃	C₃×D₃₇	direct (N × H)
19. C₃×C₃₇	C₂²×C₇₃	semidirect
20. C₂×C₃₇	C₂×C₃×C₇₃	semidirect
21. D₃₇	C₂×C₃×C₇₃	direct (N × H)
22. C₇₃	C₂×C₃×D₃₇	direct (N × H)
23. C₃₇	C₂²×C₃×C₇₃	semidirect
26. C₂×C₃	C₇₃×D₃₇	direct (N × H)
28. C₃	C₂×C₇₃×D₃₇	direct (N × H)
30. C₂	C₃×C₇₃×D₃₇	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×C₇₃×D₃₇	2
C₂×C₃×C₃₇×C₇₃	2
C₂×C₇₃×D₃₇	3
C₂²×C₃×C₇₃	37
C₂×C₃×D₃₇	73

Subgroups — C2×C3×C73×D37 #44569492

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×C₇₃×D₃₇ #44569492