Subgroups — D₃₇×C₄₂₁ #44528283

Order 31154.

8 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₇×C₄₂₁	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₂×C₄₂₁	—	37	1	no	maximal, Hall
3	C₄₂₁	D₃₇	1	1	yes	characteristic, direct product factor, Sylow
4	D₃₇	C₄₂₁	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₃₇	C₂×C₄₂₁	1	1	yes	characteristic, complemented, Sylow
6	C₂	—	37	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₄₂₁	D₃₇
commutator, cosocle, hypocenter	C₃₇	C₂×C₄₂₁
Frattini	C₁	G
Fitting, socle	C₃₇×C₄₂₁	C₂
LCS	G ▷ C₃₇
UCS	C₁ ◁ C₄₂₁

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.