Subgroups — C₄₃×D₄₃₁ #49150448

Order 37066.

8 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₃×C₄₃₁	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₄₃₁	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₄₃₁	C₂×C₄₃	1	1	yes	characteristic, complemented, Sylow
4	C₂×C₄₃	—	431	1	no	maximal, Hall
5	C₄₃	D₄₃₁	1	1	yes	characteristic, direct product factor, Sylow
6	C₂	—	431	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₄₃	D₄₃₁
commutator, cosocle, hypocenter	C₄₃₁	C₂×C₄₃
Frattini	C₁	G
Fitting, socle	C₄₃×C₄₃₁	C₂
LCS	G ▷ C₄₃₁
UCS	C₁ ◁ C₄₃

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.