Subgroups — D₅₃×C₂₁₁ #36375366

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	C₂×C₂₁₁	—	53	1	no	maximal, Hall
3	C₂₁₁	D₅₃	1	1	yes	characteristic, direct product factor, Sylow
4	D₅₃	C₂₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₅₃	C₂×C₂₁₁	1	1	yes	characteristic, complemented, Sylow
6	C₂	—	53	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₂₁₁	D₅₃
commutator, cosocle, hypocenter	C₅₃	C₂×C₂₁₁
Frattini	C₁	G
Fitting, socle	C₅₃×C₂₁₁	C₂
LCS	G ▷ C₅₃
UCS	C₁ ◁ C₂₁₁

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.