Subgroups — D₂₄₉ #92512

Order 498.

8 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₈₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₈₃	—	3	1	no	maximal, Hall
3	C₈₃	D₃	1	1	yes	characteristic, complemented, Sylow
4	D₃	—	83	1	no	maximal, Hall
5	C₃	D₈₃	1	1	yes	characteristic, complemented, Sylow
6	C₂	—	249	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃×C₈₃	C₂
LCS	G ▷ C₃×C₈₃
UCS	C₁

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.