Subgroups — D₁₅₈₅₁ #44540199

Order 31702.

12 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₂₁×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₁₄₄₁	—	11	1	no	maximal
3	C₁₁×C₁₃₁	D₁₁	1	1	yes	characteristic
4	D₁₃₁	—	121	1	no	Hall
5	D₁₂₁	—	131	1	no	maximal, Hall
6	C₁₃₁	D₁₂₁	1	1	yes	characteristic, complemented, Sylow
7	C₁₂₁	D₁₃₁	1	1	yes	characteristic, complemented, Sylow
8	D₁₁	—	1441	1	no	—
9	C₁₁	D₁₄₄₁	1	1	yes	characteristic
10	C₂	—	15851	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁	G
commutator, Fitting, cosocle, hypocenter	C₁₂₁×C₁₃₁	C₂
Frattini	C₁₁	D₁₄₄₁
socle	C₁₁×C₁₃₁	D₁₁
LCS	G ▷ C₁₂₁×C₁₃₁
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.