Subgroups — C₇×D₁₇ #6636

Order 238.

8 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×C₁₇	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₁₇	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₁₇	C₂×C₇	1	1	yes	characteristic, complemented, Sylow
4	C₂×C₇	—	17	1	no	maximal, Hall
5	C₇	D₁₇	1	1	yes	characteristic, direct product factor, Sylow
6	C₂	—	17	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₇	D₁₇
commutator, cosocle, hypocenter	C₁₇	C₂×C₇
Frattini	C₁	G
Fitting, socle	C₇×C₁₇	C₂
LCS	G ▷ C₁₇
UCS	C₁ ◁ C₇

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

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.