Subgroups — C₃×C₃₇×D₁₆₁ #49088348

Order 35742.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₇×C₂₃×C₃₇	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₃₇×D₁₆₁	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₇×C₂₃×C₃₇	C₂×C₃	1	1	yes	characteristic, complemented, Hall
4	C₃×C₃₇×D₂₃	—	7	1	no	maximal, Hall
5	C₃×C₂₃×C₃₇	D₇	1	1	yes	characteristic, complemented, Hall
6	C₃₇×D₂₃	—	7	1	no	Hall
7	C₃×D₇×C₃₇	—	23	1	no	maximal, Hall
8	C₃×D₁₆₁	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₂₃×C₃₇	C₃×D₇	1	1	yes	characteristic, complemented, Hall
10	C₃×C₇×C₃₇	D₂₃	1	1	yes	characteristic, complemented, Hall
11	D₇×C₃₇	—	23	1	no	Hall
12	C₃×C₇×C₂₃	C₂×C₃₇	1	1	yes	characteristic, complemented, Hall
13	D₁₆₁	C₃×C₃₇	1	1	yes	characteristic, direct product factor, Hall
14	C₇×C₃₇	C₃×D₂₃	1	1	yes	characteristic, complemented, Hall
15	C₂×C₃×C₃₇	—	161	1	no	Hall
16	C₇×C₂₃	C₂×C₃×C₃₇	1	1	yes	characteristic, complemented, Hall
17	C₃×D₂₃	—	7	1	no	Hall
18	C₃×C₃₇	D₁₆₁	1	1	yes	characteristic, direct product factor, Hall
19	C₂×C₃₇	—	161	1	no	Hall
20	C₃×C₂₃	D₇×C₃₇	1	1	yes	characteristic, complemented, Hall
21	D₂₃	—	7	1	no	Hall
22	C₃×D₇	—	23	1	no	Hall
23	C₃₇	C₃×D₁₆₁	1	1	yes	characteristic, direct product factor, Sylow
24	C₂₃	C₃×D₇×C₃₇	1	1	yes	characteristic, complemented, Sylow
25	C₃×C₇	C₃₇×D₂₃	1	1	yes	characteristic, complemented, Hall
26	D₇	—	23	1	no	Hall
27	C₇	C₃×C₃₇×D₂₃	1	1	yes	characteristic, complemented, Sylow
28	C₂×C₃	—	161	1	no	Hall
29	C₃	C₃₇×D₁₆₁	1	1	yes	characteristic, direct product factor, Sylow
30	C₂	—	161	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃×C₃₇	D₁₆₁
commutator, cosocle, hypocenter	C₇×C₂₃	C₂×C₃×C₃₇
Frattini	C₁	G
Fitting, socle	C₃×C₇×C₂₃×C₃₇	C₂
LCS	G ▷ C₇×C₂₃
UCS	C₁ ◁ C₃×C₃₇

Complements

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

N	H ≅ G/N	type
1. C₃×C₇×C₂₃×C₃₇	C₂	semidirect
2. C₃₇×D₁₆₁	C₃	direct (N × H)
3. C₇×C₂₃×C₃₇	C₂×C₃	semidirect
5. C₃×C₂₃×C₃₇	D₇	semidirect
8. C₃×D₁₆₁	C₃₇	direct (N × H)
9. C₂₃×C₃₇	C₃×D₇	semidirect
10. C₃×C₇×C₃₇	D₂₃	semidirect
12. C₃×C₇×C₂₃	C₂×C₃₇	semidirect
13. D₁₆₁	C₃×C₃₇	direct (N × H)
14. C₇×C₃₇	C₃×D₂₃	semidirect
16. C₇×C₂₃	C₂×C₃×C₃₇	semidirect
18. C₃×C₃₇	D₁₆₁	direct (N × H)
20. C₃×C₂₃	D₇×C₃₇	semidirect
23. C₃₇	C₃×D₁₆₁	direct (N × H)
24. C₂₃	C₃×D₇×C₃₇	semidirect
25. C₃×C₇	C₃₇×D₂₃	semidirect
27. C₇	C₃×C₃₇×D₂₃	semidirect
29. C₃	C₃₇×D₁₆₁	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×C₇×C₂₃×C₃₇	2
C₃₇×D₁₆₁	3
C₃×C₃₇×D₂₃	7
C₃×D₇×C₃₇	23
C₃×D₁₆₁	37

Subgroups — C3×C37×D161 #49088348

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₃₇×D₁₆₁ #49088348