Finite Group Databasebeta

← C₂×C₆₁₇⋊C₇ #22575673

Subgroups — C₂×C₆₁₇⋊C₇ #22575673

Order 8638.

8 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₁₇⋊C₇	C₂	1	1	yes	maximal, characteristic, direct product factor, Hall
2	C₂×C₆₁₇	C₇	1	1	yes	maximal, characteristic, complemented, Hall
3	C₆₁₇	C₂×C₇	1	1	yes	characteristic, complemented, Sylow
4	C₂×C₇	—	617	1	no	maximal, Hall
5	C₇	—	617	1	no	Sylow
6	C₂	C₆₁₇⋊C₇	1	1	yes	characteristic, direct product factor, Sylow

	subgroup	G/H
center, hypercenter	C₂	C₆₁₇⋊C₇
commutator, hypocenter	C₆₁₇	C₂×C₇
Frattini	C₁	G
Fitting, socle	C₂×C₆₁₇	C₇
LCS	G ▷ C₆₁₇
UCS	C₁ ◁ C₂

Complements

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

N	H ≅ G/N	type
1. C₆₁₇⋊C₇	C₂	direct (N × H)
2. C₂×C₆₁₇	C₇	semidirect
3. C₆₁₇	C₂×C₇	semidirect
6. C₂	C₆₁₇⋊C₇	direct (N × H)