Subgroups — D₂₃×C₃₄₉ #30631069

Order 16054.

8 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×C₃₄₉	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₂×C₃₄₉	—	23	1	no	maximal, Hall
3	C₃₄₉	D₂₃	1	1	yes	characteristic, direct product factor, Sylow
4	D₂₃	C₃₄₉	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₂₃	C₂×C₃₄₉	1	1	yes	characteristic, complemented, Sylow
6	C₂	—	23	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃₄₉	D₂₃
commutator, cosocle, hypocenter	C₂₃	C₂×C₃₄₉
Frattini	C₁	G
Fitting, socle	C₂₃×C₃₄₉	C₂
LCS	G ▷ C₂₃
UCS	C₁ ◁ C₃₄₉

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.