Subgroups — D₁₁₇₆₃ #37555167

Order 23526.

12 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₉×C₁₃₀₇	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₃₉₂₁	—	3	1	no	maximal
3	C₃×C₁₃₀₇	D₃	1	1	yes	characteristic
4	D₁₃₀₇	—	9	1	no	Hall
5	C₁₃₀₇	D₉	1	1	yes	characteristic, complemented, Sylow
6	D₉	—	1307	1	no	maximal, Hall
7	C₉	D₁₃₀₇	1	1	yes	characteristic, complemented, Sylow
8	D₃	—	3921	1	no	—
9	C₃	D₃₉₂₁	1	1	yes	characteristic
10	C₂	—	11763	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁	G
commutator, Fitting, cosocle, hypocenter	C₉×C₁₃₀₇	C₂
Frattini	C₃	D₃₉₂₁
socle	C₃×C₁₃₀₇	D₃
LCS	G ▷ C₉×C₁₃₀₇
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.