Finite Group Databasebeta

← C₂₃⋊(D₆₁⋊C₃) #22554532

Subgroups — C₂₃⋊(D₆₁⋊C₃) #22554532

Order 8418.

16 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×C₆₁⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₁₄₀₃	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₂₃×C₆₁	C₂×C₃	1	1	yes	characteristic, complemented, Hall
4	D₆₁⋊C₃	—	23	1	no	maximal, Hall
5	C₆₁⋊C₃	D₂₃	1	1	yes	characteristic, complemented, Hall
6	C₃×D₂₃	—	61	1	no	maximal, Hall
7	D₆₁	—	23	1	no	Hall
8	C₃×C₂₃	—	61	1	no	Hall
9	C₆₁	C₃×D₂₃	1	1	yes	characteristic, complemented, Sylow
10	D₂₃	—	61	1	no	Hall
11	C₂₃	D₆₁⋊C₃	1	1	yes	characteristic, complemented, Sylow
12	C₂×C₃	—	1403	1	no	Hall
13	C₃	—	61	1	no	Sylow
14	C₂	—	1403	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₂₃×C₆₁	C₂×C₃
LCS	G ▷ C₂₃×C₆₁
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. C₂₃×C₆₁⋊C₃	C₂	semidirect
2. D₁₄₀₃	C₃	semidirect
3. C₂₃×C₆₁	C₂×C₃	semidirect
5. C₆₁⋊C₃	D₂₃	semidirect
9. C₆₁	C₃×D₂₃	semidirect
11. C₂₃	D₆₁⋊C₃	semidirect