Subgroups — Dic₁₄₅₀₇ #72291249

Order 58028.

12 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₈₉×C₁₆₃	C₂	1	1	yes	maximal, characteristic
2	C₈₉×C₁₆₃	C₄	1	1	yes	characteristic, complemented, Hall
3	Dic₁₆₃	—	89	1	no	maximal, Hall
4	Dic₈₉	—	163	1	no	maximal, Hall
5	C₂×C₁₆₃	D₈₉	1	1	yes	characteristic
6	C₂×C₈₉	D₁₆₃	1	1	yes	characteristic
7	C₁₆₃	Dic₈₉	1	1	yes	characteristic, complemented, Sylow
8	C₈₉	Dic₁₆₃	1	1	yes	characteristic, complemented, Sylow
9	C₄	—	14507	1	no	Sylow
10	C₂	D₁₄₅₀₇	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂	D₁₄₅₀₇
commutator, hypocenter	C₈₉×C₁₆₃	C₄
Fitting, socle, prime radical, cosocle	C₂×C₈₉×C₁₆₃	C₂
LCS	G ▷ C₈₉×C₁₆₃
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.