Subgroups — D₄₇×C₂₅₇ #37563576

Order 24158.

8 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₇×C₂₅₇	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₂×C₂₅₇	—	47	1	no	maximal, Hall
3	C₂₅₇	D₄₇	1	1	yes	characteristic, direct product factor, Sylow
4	D₄₇	C₂₅₇	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₄₇	C₂×C₂₅₇	1	1	yes	characteristic, complemented, Sylow
6	C₂	—	47	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₂₅₇	D₄₇
commutator, cosocle, hypocenter	C₄₇	C₂×C₂₅₇
Frattini	C₁	G
Fitting, socle	C₄₇×C₂₅₇	C₂
LCS	G ▷ C₄₇
UCS	C₁ ◁ C₂₅₇

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.