Subgroups — D₁₇×C₆₇₇ #37527690

Order 23018.

8 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₇×C₆₇₇	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₂×C₆₇₇	—	17	1	no	maximal, Hall
3	C₆₇₇	D₁₇	1	1	yes	characteristic, direct product factor, Sylow
4	D₁₇	C₆₇₇	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₁₇	C₂×C₆₇₇	1	1	yes	characteristic, complemented, Sylow
6	C₂	—	17	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₆₇₇	D₁₇
commutator, cosocle, hypocenter	C₁₇	C₂×C₆₇₇
Frattini	C₁	G
Fitting, socle	C₁₇×C₆₇₇	C₂
LCS	G ▷ C₁₇
UCS	C₁ ◁ C₆₇₇

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.