Subgroups — C₁₇×D₆₉₁ #37555039

Order 23494.

8 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₇×C₆₉₁	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₆₉₁	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₆₉₁	C₂×C₁₇	1	1	yes	characteristic, complemented, Sylow
4	C₂×C₁₇	—	691	1	no	maximal, Hall
5	C₁₇	D₆₉₁	1	1	yes	characteristic, direct product factor, Sylow
6	C₂	—	691	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁₇	D₆₉₁
commutator, cosocle, hypocenter	C₆₉₁	C₂×C₁₇
Frattini	C₁	G
Fitting, socle	C₁₇×C₆₉₁	C₂
LCS	G ▷ C₆₉₁
UCS	C₁ ◁ C₁₇

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.