Subgroups — D₇₁×C₂₂₃ #44539701

Order 31666.

8 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇₁×C₂₂₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₂×C₂₂₃	—	71	1	no	maximal, Hall
3	C₂₂₃	D₇₁	1	1	yes	characteristic, direct product factor, Sylow
4	D₇₁	C₂₂₃	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₇₁	C₂×C₂₂₃	1	1	yes	characteristic, complemented, Sylow
6	C₂	—	71	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₂₂₃	D₇₁
commutator, cosocle, hypocenter	C₇₁	C₂×C₂₂₃
Frattini	C₁	G
Fitting, socle	C₇₁×C₂₂₃	C₂
LCS	G ▷ C₇₁
UCS	C₁ ◁ C₂₂₃

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.