Subgroups — D₁₁₇₂₇ #37553016

Order 23454.

12 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₉×C₁₃₀₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₃₉₀₉	—	3	1	no	maximal
3	C₃×C₁₃₀₃	D₃	1	1	yes	characteristic
4	D₁₃₀₃	—	9	1	no	Hall
5	C₁₃₀₃	D₉	1	1	yes	characteristic, complemented, Sylow
6	D₉	—	1303	1	no	maximal, Hall
7	C₉	D₁₃₀₃	1	1	yes	characteristic, complemented, Sylow
8	D₃	—	3909	1	no	—
9	C₃	D₃₉₀₉	1	1	yes	characteristic
10	C₂	—	11727	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁	G
commutator, Fitting, cosocle, hypocenter	C₉×C₁₃₀₃	C₂
Frattini	C₃	D₃₉₀₉
socle	C₃×C₁₃₀₃	D₃
LCS	G ▷ C₉×C₁₃₀₃
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.