Subgroups — Dic₁₄₈₀₉ #72292017

Order 59236.

12 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅₉×C₂₅₁	C₂	1	1	yes	maximal, characteristic
2	C₅₉×C₂₅₁	C₄	1	1	yes	characteristic, complemented, Hall
3	Dic₂₅₁	—	59	1	no	maximal, Hall
4	C₂×C₂₅₁	D₅₉	1	1	yes	characteristic
5	C₂₅₁	Dic₅₉	1	1	yes	characteristic, complemented, Sylow
6	Dic₅₉	—	251	1	no	maximal, Hall
7	C₂×C₅₉	D₂₅₁	1	1	yes	characteristic
8	C₅₉	Dic₂₅₁	1	1	yes	characteristic, complemented, Sylow
9	C₄	—	14809	1	no	Sylow
10	C₂	D₁₄₈₀₉	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂	D₁₄₈₀₉
commutator, hypocenter	C₅₉×C₂₅₁	C₄
Fitting, socle, prime radical, cosocle	C₂×C₅₉×C₂₅₁	C₂
LCS	G ▷ C₅₉×C₂₅₁
UCS	C₁ ◁ C₂

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.