Subgroups — D₁₃₆₀₇ #41030331

Order 27214.

8 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×C₁₂₃₇	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₁₂₃₇	—	11	1	no	maximal, Hall
3	C₁₂₃₇	D₁₁	1	1	yes	characteristic, complemented, Sylow
4	D₁₁	—	1237	1	no	maximal, Hall
5	C₁₁	D₁₂₃₇	1	1	yes	characteristic, complemented, Sylow
6	C₂	—	13607	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₁₁×C₁₂₃₇	C₂
LCS	G ▷ C₁₁×C₁₂₃₇
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.