Subgroups — D₁₇₁₇₉ #46805331

Order 34358.

8 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₁×C₄₁₉	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₄₁₉	—	41	1	no	maximal, Hall
3	C₄₁₉	D₄₁	1	1	yes	characteristic, complemented, Sylow
4	D₄₁	—	419	1	no	maximal, Hall
5	C₄₁	D₄₁₉	1	1	yes	characteristic, complemented, Sylow
6	C₂	—	17179	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₄₁×C₄₁₉	C₂
LCS	G ▷ C₄₁×C₄₁₉
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.