Subgroups — C₂₈₃⋊C₈₁ #37523943

Order 22923.

10 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₇×C₂₈₃	C₃	1	1	yes	maximal, characteristic
2	C₉×C₂₈₃	C₉	1	1	yes	characteristic
3	C₃×C₂₈₃	C₂₇	1	1	yes	characteristic
4	C₂₈₃	C₈₁	1	1	yes	characteristic, complemented, Sylow
5	C₈₁	—	283	1	no	maximal, Sylow
6	C₂₇	C₂₈₃⋊C₃	1	1	yes	characteristic
7	C₉	C₂₈₃⋊C₉	1	1	yes	characteristic
8	C₃	C₂₈₃⋊C₂₇	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂₇	C₂₈₃⋊C₃
commutator, hypocenter	C₂₈₃	C₈₁
Fitting, cosocle	C₂₇×C₂₈₃	C₃
socle, prime radical	C₃×C₂₈₃	C₂₇
LCS	G ▷ C₂₈₃
UCS	C₁ ◁ C₂₇

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

N	H ≅ G/N	type
4. C₂₈₃	C₈₁	semidirect

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

subgroup	index
C₂₇×C₂₈₃	3
C₈₁	283