Subgroups — #37557778

Order 23772.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#20238433	C₂	1	1	yes	maximal, characteristic
2	C₇×Dic₂₈₃	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	#20238433	C₄	1	1	yes	characteristic, complemented, Hall
4	C₂×C₇×C₂₈₃	C₂×C₃	1	1	yes	characteristic
5	(C₂₈₃⋊C₃)⋊C₄	—	7	1	no	maximal, Hall
6	C₇×C₂₈₃	C₃×C₄	1	1	yes	characteristic, complemented, Hall
7	C₂×C₂₈₃⋊C₃	—	7	1	no	—
8	Dic₂₈₃	ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented, Hall
9	C₂₈₃⋊C₃	—	7	1	no	Hall
10	C₂×C₂₈₃	C₂×ΓL(1,𝔽₈)	1	1	yes	characteristic
11	C₂₈₃	C₄×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented, Sylow
12	C₄×ΓL(1,𝔽₈)	—	283	1	no	maximal, Hall
13	C₂×ΓL(1,𝔽₈)	—	566	1	no	—
14	C₄×C₇	—	283	1	no	Hall
15	ΓL(1,𝔽₈)	—	566	1	no	Hall
16	C₂×C₇	D₂₈₃⋊C₃	1	1	yes	characteristic
17	C₃×C₄	—	1981	1	no	Hall
18	C₇	(C₂₈₃⋊C₃)⋊C₄	1	1	yes	characteristic, complemented, Sylow
19	C₂×C₃	—	3962	1	no	—
20	C₄	—	283	1	no	Sylow
21	C₃	—	3962	1	no	Sylow
22	C₂	#26045220	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂	#26045220
commutator, hypocenter	C₇×C₂₈₃	C₃×C₄
Fitting, socle, cosocle	C₂×C₇×C₂₈₃	C₂×C₃
prime radical	C₂×#20238433	C₂
LCS	G ▷ C₇×C₂₈₃
UCS	C₁ ◁ C₂

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.