Subgroups — D₁₆₁₇₇ #44568989

Order 32354.

8 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×C₂₃₁₁	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₂₃₁₁	—	7	1	no	maximal, Hall
3	C₂₃₁₁	D₇	1	1	yes	characteristic, complemented, Sylow
4	D₇	—	2311	1	no	maximal, Hall
5	C₇	D₂₃₁₁	1	1	yes	characteristic, complemented, Sylow
6	C₂	—	16177	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₇×C₂₃₁₁	C₂
LCS	G ▷ C₇×C₂₃₁₁
UCS	C₁

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.