Subgroups — D₁₂₂₄₉ #37587721

Order 24498.

12 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₉×C₁₃₆₁	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₄₀₈₃	—	3	1	no	maximal
3	C₃×C₁₃₆₁	D₃	1	1	yes	characteristic
4	D₁₃₆₁	—	9	1	no	Hall
5	C₁₃₆₁	D₉	1	1	yes	characteristic, complemented, Sylow
6	D₉	—	1361	1	no	maximal, Hall
7	C₉	D₁₃₆₁	1	1	yes	characteristic, complemented, Sylow
8	D₃	—	4083	1	no	—
9	C₃	D₄₀₈₃	1	1	yes	characteristic
10	C₂	—	12249	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁	G
commutator, Fitting, cosocle, hypocenter	C₉×C₁₃₆₁	C₂
Frattini	C₃	D₄₀₈₃
socle	C₃×C₁₃₆₁	D₃
LCS	G ▷ C₉×C₁₃₆₁
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.