Subgroups — C₇×C₃₇×D₆₉ #49088352

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	C₇×C₃₇×D₂₃	—	3	1	no	maximal, Hall
3	C₇×C₂₃×C₃₇	D₃	1	1	yes	characteristic, complemented, Hall
4	C₃₇×D₆₉	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₃×C₂₃×C₃₇	C₂×C₇	1	1	yes	characteristic, complemented, Hall
6	C₃₇×D₂₃	—	3	1	no	Hall
7	D₃×C₇×C₃₇	—	23	1	no	maximal, Hall
8	C₇×D₆₉	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₂₃×C₃₇	D₃×C₇	1	1	yes	characteristic, complemented, Hall
10	C₃×C₇×C₃₇	D₂₃	1	1	yes	characteristic, complemented, Hall
11	C₂×C₇×C₃₇	—	69	1	no	Hall
12	C₃×C₇×C₂₃	C₂×C₃₇	1	1	yes	characteristic, complemented, Hall
13	C₇×D₂₃	—	3	1	no	Hall
14	C₇×C₃₇	D₆₉	1	1	yes	characteristic, direct product factor, Hall
15	D₃×C₃₇	—	23	1	no	Hall
16	C₇×C₂₃	D₃×C₃₇	1	1	yes	characteristic, complemented, Hall
17	D₆₉	C₇×C₃₇	1	1	yes	characteristic, direct product factor, Hall
18	C₃×C₃₇	C₇×D₂₃	1	1	yes	characteristic, complemented, Hall
19	C₂×C₃₇	—	69	1	no	Hall
20	C₃×C₂₃	C₂×C₇×C₃₇	1	1	yes	characteristic, complemented, Hall
21	D₂₃	—	3	1	no	Hall
22	D₃×C₇	—	23	1	no	Hall
23	C₃₇	C₇×D₆₉	1	1	yes	characteristic, direct product factor, Sylow
24	C₂₃	D₃×C₇×C₃₇	1	1	yes	characteristic, complemented, Sylow
25	C₃×C₇	C₃₇×D₂₃	1	1	yes	characteristic, complemented, Hall
26	C₂×C₇	—	69	1	no	Hall
27	C₇	C₃₇×D₆₉	1	1	yes	characteristic, direct product factor, Sylow
28	D₃	—	23	1	no	Hall
29	C₃	C₇×C₃₇×D₂₃	1	1	yes	characteristic, complemented, Sylow
30	C₂	—	69	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₇×C₃₇	D₆₉
commutator, cosocle, hypocenter	C₃×C₂₃	C₂×C₇×C₃₇
Frattini	C₁	G
Fitting, socle	C₃×C₇×C₂₃×C₃₇	C₂
LCS	G ▷ C₃×C₂₃
UCS	C₁ ◁ C₇×C₃₇

Complements

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

N	H ≅ G/N	type
1. C₃×C₇×C₂₃×C₃₇	C₂	semidirect
3. C₇×C₂₃×C₃₇	D₃	semidirect
4. C₃₇×D₆₉	C₇	direct (N × H)
5. C₃×C₂₃×C₃₇	C₂×C₇	semidirect
8. C₇×D₆₉	C₃₇	direct (N × H)
9. C₂₃×C₃₇	D₃×C₇	semidirect
10. C₃×C₇×C₃₇	D₂₃	semidirect
12. C₃×C₇×C₂₃	C₂×C₃₇	semidirect
14. C₇×C₃₇	D₆₉	direct (N × H)
16. C₇×C₂₃	D₃×C₃₇	semidirect
17. D₆₉	C₇×C₃₇	direct (N × H)
18. C₃×C₃₇	C₇×D₂₃	semidirect
20. C₃×C₂₃	C₂×C₇×C₃₇	semidirect
23. C₃₇	C₇×D₆₉	direct (N × H)
24. C₂₃	D₃×C₇×C₃₇	semidirect
25. C₃×C₇	C₃₇×D₂₃	semidirect
27. C₇	C₃₇×D₆₉	direct (N × H)
29. C₃	C₇×C₃₇×D₂₃	semidirect

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
C₇×C₃₇×D₂₃	3
C₃₇×D₆₉	7
D₃×C₇×C₃₇	23
C₇×D₆₉	37

Subgroups — C7×C37×D69 #49088352

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×C₃₇×D₆₉ #49088352