Subgroups — C₇×C₂₃⋊(D₃₇⋊C₃) #49088366

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	C₇×D₈₅₁	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₇×C₂₃×C₃₇	C₂×C₃	1	1	yes	characteristic, complemented, Hall
4	C₂₃⋊(D₃₇⋊C₃)	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₂₃×C₃₇⋊C₃	C₂×C₇	1	1	yes	characteristic, complemented, Hall
6	D₈₅₁	C₃×C₇	1	1	yes	characteristic, complemented, Hall
7	C₇×D₃₇⋊C₃	—	23	1	no	maximal, Hall
8	C₃×C₇×D₂₃	—	37	1	no	maximal, Hall
9	C₂₃×C₃₇	C₂×C₃×C₇	1	1	yes	characteristic, complemented, Hall
10	C₇×C₃₇⋊C₃	D₂₃	1	1	yes	characteristic, complemented, Hall
11	C₇×D₃₇	—	23	1	no	Hall
12	C₃×C₇×C₂₃	—	37	1	no	Hall
13	C₇×D₂₃	—	37	1	no	Hall
14	C₇×C₃₇	C₃×D₂₃	1	1	yes	characteristic, complemented, Hall
15	D₃₇⋊C₃	—	23	1	no	Hall
16	C₇×C₂₃	D₃₇⋊C₃	1	1	yes	characteristic, complemented, Hall
17	C₃×D₂₃	—	37	1	no	Hall
18	C₃₇⋊C₃	C₇×D₂₃	1	1	yes	characteristic, complemented, Hall
19	D₃₇	—	23	1	no	Hall
20	C₃×C₂₃	—	37	1	no	Hall
21	D₂₃	—	37	1	no	Hall
22	C₂×C₃×C₇	—	851	1	no	Hall
23	C₃₇	C₃×C₇×D₂₃	1	1	yes	characteristic, complemented, Sylow
24	C₂₃	C₇×D₃₇⋊C₃	1	1	yes	characteristic, complemented, Sylow
25	C₃×C₇	—	37	1	no	Hall
26	C₂×C₇	—	851	1	no	Hall
27	C₇	C₂₃⋊(D₃₇⋊C₃)	1	1	yes	characteristic, direct product factor, Sylow
28	C₂×C₃	—	851	1	no	Hall
29	C₃	—	37	1	no	Sylow
30	C₂	—	851	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₇	C₂₃⋊(D₃₇⋊C₃)
commutator, cosocle, hypocenter	C₂₃×C₃₇	C₂×C₃×C₇
Frattini	C₁	G
Fitting, socle	C₇×C₂₃×C₃₇	C₂×C₃
LCS	G ▷ C₂₃×C₃₇
UCS	C₁ ◁ C₇

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

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