Subgroups — D₁₆₂₀₉ #44569749

Order 32418.

12 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₉×C₁₈₀₁	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₅₄₀₃	—	3	1	no	maximal
3	C₃×C₁₈₀₁	D₃	1	1	yes	characteristic
4	D₁₈₀₁	—	9	1	no	Hall
5	C₁₈₀₁	D₉	1	1	yes	characteristic, complemented, Sylow
6	D₉	—	1801	1	no	maximal, Hall
7	C₉	D₁₈₀₁	1	1	yes	characteristic, complemented, Sylow
8	D₃	—	5403	1	no	—
9	C₃	D₅₄₀₃	1	1	yes	characteristic
10	C₂	—	16209	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁	G
commutator, Fitting, cosocle, hypocenter	C₉×C₁₈₀₁	C₂
Frattini	C₃	D₅₄₀₃
socle	C₃×C₁₈₀₁	D₃
LCS	G ▷ C₉×C₁₈₀₁
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.