Subgroups — Dic₈₁₁₉ #44570345

Order 32476.

12 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₃×C₃₅₃	C₂	1	1	yes	maximal, characteristic
2	C₂₃×C₃₅₃	C₄	1	1	yes	characteristic, complemented, Hall
3	Dic₃₅₃	—	23	1	no	maximal, Hall
4	C₂×C₃₅₃	D₂₃	1	1	yes	characteristic
5	C₃₅₃	Dic₂₃	1	1	yes	characteristic, complemented, Sylow
6	Dic₂₃	—	353	1	no	maximal, Hall
7	C₂×C₂₃	D₃₅₃	1	1	yes	characteristic
8	C₂₃	Dic₃₅₃	1	1	yes	characteristic, complemented, Sylow
9	C₄	—	8119	1	no	Sylow
10	C₂	D₈₁₁₉	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂	D₈₁₁₉
commutator, hypocenter	C₂₃×C₃₅₃	C₄
Fitting, socle, prime radical, cosocle	C₂×C₂₃×C₃₅₃	C₂
LCS	G ▷ C₂₃×C₃₅₃
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.