Subgroups — C₅₃×D₂₁₁ #36375367

Order 22366.

8 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₃×C₂₁₁	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₂₁₁	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₂₁₁	C₂×C₅₃	1	1	yes	characteristic, complemented, Sylow
4	C₂×C₅₃	—	211	1	no	maximal, Hall
5	C₅₃	D₂₁₁	1	1	yes	characteristic, direct product factor, Sylow
6	C₂	—	211	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₅₃	D₂₁₁
commutator, cosocle, hypocenter	C₂₁₁	C₂×C₅₃
Frattini	C₁	G
Fitting, socle	C₅₃×C₂₁₁	C₂
LCS	G ▷ C₂₁₁
UCS	C₁ ◁ C₅₃

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.