Finite Group Databasebeta

← C₄₁×C₆₁⋊C₃ #21418901

Subgroups — C₄₁×C₆₁⋊C₃ #21418901

Order 7503.

8 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₁×C₆₁	C₃	1	1	yes	maximal, characteristic, complemented, Hall
2	C₆₁⋊C₃	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₃×C₄₁	—	61	1	no	maximal, Hall
4	C₆₁	C₃×C₄₁	1	1	yes	characteristic, complemented, Sylow
5	C₄₁	C₆₁⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
6	C₃	—	61	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₄₁	C₆₁⋊C₃
commutator, hypocenter	C₆₁	C₃×C₄₁
Frattini	C₁	G
Fitting, socle	C₄₁×C₆₁	C₃
LCS	G ▷ C₆₁
UCS	C₁ ◁ C₄₁

Complements

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

N	H ≅ G/N	type
1. C₄₁×C₆₁	C₃	semidirect
2. C₆₁⋊C₃	C₄₁	direct (N × H)
4. C₆₁	C₃×C₄₁	semidirect
5. C₄₁	C₆₁⋊C₃	direct (N × H)