Finite Group Databasebeta

← C₁₇×D₃₁₇ #24924684

Subgroups — C₁₇×D₃₁₇ #24924684

Order 10778.

8 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₇×C₃₁₇	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₃₁₇	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₃₁₇	C₂×C₁₇	1	1	yes	characteristic, complemented, Sylow
4	C₂×C₁₇	—	317	1	no	maximal, Hall
5	C₁₇	D₃₁₇	1	1	yes	characteristic, direct product factor, Sylow
6	C₂	—	317	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁₇	D₃₁₇
commutator, cosocle, hypocenter	C₃₁₇	C₂×C₁₇
Frattini	C₁	G
Fitting, socle	C₁₇×C₃₁₇	C₂
LCS	G ▷ C₃₁₇
UCS	C₁ ◁ C₁₇

Complements

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

N	H ≅ G/N	type
1. C₁₇×C₃₁₇	C₂	semidirect
2. D₃₁₇	C₁₇	direct (N × H)
3. C₃₁₇	C₂×C₁₇	semidirect
5. C₁₇	D₃₁₇	direct (N × H)