Subgroups — C₂₃×(C₃₇⋊C₃)⋊D₇ #49088374

Order 35742.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×C₂₃×C₃₇⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₂₃×D₂₅₉	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₇×C₂₃×C₃₇	C₂×C₃	1	1	yes	characteristic, complemented, Hall
4	C₂₃×D₃₇⋊C₃	—	7	1	no	maximal, Hall
5	C₂₃×C₃₇⋊C₃	D₇	1	1	yes	characteristic, complemented, Hall
6	C₂₃×D₃₇	—	7	1	no	Hall
7	(C₃₇⋊C₃)⋊D₇	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₃×D₇×C₂₃	—	37	1	no	maximal, Hall
9	C₂₃×C₃₇	C₃×D₇	1	1	yes	characteristic, complemented, Hall
10	C₇×C₃₇⋊C₃	C₂×C₂₃	1	1	yes	characteristic, complemented, Hall
11	D₂₅₉	C₃×C₂₃	1	1	yes	characteristic, complemented, Hall
12	C₃×C₇×C₂₃	—	37	1	no	Hall
13	D₇×C₂₃	—	37	1	no	Hall
14	C₇×C₃₇	C₂×C₃×C₂₃	1	1	yes	characteristic, complemented, Hall
15	D₃₇⋊C₃	—	7	1	no	Hall
16	C₇×C₂₃	D₃₇⋊C₃	1	1	yes	characteristic, complemented, Hall
17	C₂×C₃×C₂₃	—	259	1	no	Hall
18	C₃₇⋊C₃	D₇×C₂₃	1	1	yes	characteristic, complemented, Hall
19	D₃₇	—	7	1	no	Hall
20	C₃×C₂₃	—	37	1	no	Hall
21	C₂×C₂₃	—	259	1	no	Hall
22	C₃×D₇	—	37	1	no	Hall
23	C₃₇	C₃×D₇×C₂₃	1	1	yes	characteristic, complemented, Sylow
24	C₂₃	(C₃₇⋊C₃)⋊D₇	1	1	yes	characteristic, direct product factor, Sylow
25	C₃×C₇	—	37	1	no	Hall
26	D₇	—	37	1	no	Hall
27	C₇	C₂₃×D₃₇⋊C₃	1	1	yes	characteristic, complemented, Sylow
28	C₂×C₃	—	259	1	no	Hall
29	C₃	—	37	1	no	Sylow
30	C₂	—	259	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₂₃	(C₃₇⋊C₃)⋊D₇
commutator, cosocle, hypocenter	C₇×C₃₇	C₂×C₃×C₂₃
Frattini	C₁	G
Fitting, socle	C₇×C₂₃×C₃₇	C₂×C₃
LCS	G ▷ C₇×C₃₇
UCS	C₁ ◁ C₂₃

Complements

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

N	H ≅ G/N	type
1. C₇×C₂₃×C₃₇⋊C₃	C₂	semidirect
2. C₂₃×D₂₅₉	C₃	semidirect
3. C₇×C₂₃×C₃₇	C₂×C₃	semidirect
5. C₂₃×C₃₇⋊C₃	D₇	semidirect
7. (C₃₇⋊C₃)⋊D₇	C₂₃	direct (N × H)
9. C₂₃×C₃₇	C₃×D₇	semidirect
10. C₇×C₃₇⋊C₃	C₂×C₂₃	semidirect
11. D₂₅₉	C₃×C₂₃	semidirect
14. C₇×C₃₇	C₂×C₃×C₂₃	semidirect
16. C₇×C₂₃	D₃₇⋊C₃	semidirect
18. C₃₇⋊C₃	D₇×C₂₃	semidirect
23. C₃₇	C₃×D₇×C₂₃	semidirect
24. C₂₃	(C₃₇⋊C₃)⋊D₇	direct (N × H)
27. C₇	C₂₃×D₃₇⋊C₃	semidirect

Maximal subgroups

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

subgroup	index
C₇×C₂₃×C₃₇⋊C₃	2
C₂₃×D₂₅₉	3
C₂₃×D₃₇⋊C₃	7
(C₃₇⋊C₃)⋊D₇	23
C₃×D₇×C₂₃	37

Subgroups — C23×(C37⋊C3)⋊D7 #49088374

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×(C₃₇⋊C₃)⋊D₇ #49088374