Finite Group Databasebeta

← C₂₃×C₃₁⋊C₉ #20264382

Subgroups — C₂₃×C₃₁⋊C₉ #20264382

Order 6417.

12 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₂₃×C₃₁	C₃	1	1	yes	maximal, characteristic
2	C₂₃×C₃₁	C₉	1	1	yes	characteristic, complemented, Hall
3	C₃₁⋊C₉	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₉×C₂₃	—	31	1	no	maximal, Hall
5	C₃×C₃₁	C₃×C₂₃	1	1	yes	characteristic
6	C₃×C₂₃	C₃₁⋊C₃	1	1	yes	characteristic
7	C₃₁	C₉×C₂₃	1	1	yes	characteristic, complemented, Sylow
8	C₂₃	C₃₁⋊C₉	1	1	yes	characteristic, direct product factor, Sylow
9	C₉	—	31	1	no	Sylow
10	C₃	C₂₃×C₃₁⋊C₃	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₃×C₂₃	C₃₁⋊C₃
commutator, hypocenter	C₃₁	C₉×C₂₃
Frattini	C₃	C₂₃×C₃₁⋊C₃
Fitting, socle	C₃×C₂₃×C₃₁	C₃
LCS	G ▷ C₃₁
UCS	C₁ ◁ C₃×C₂₃

Complements

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

N	H ≅ G/N	type
2. C₂₃×C₃₁	C₉	semidirect
3. C₃₁⋊C₉	C₂₃	direct (N × H)
7. C₃₁	C₉×C₂₃	semidirect
8. C₂₃	C₃₁⋊C₉	direct (N × H)