Subgroups — D₆₇×C₁₈₁ #37564666

Order 24254.

8 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₇×C₁₈₁	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₂×C₁₈₁	—	67	1	no	maximal, Hall
3	C₁₈₁	D₆₇	1	1	yes	characteristic, direct product factor, Sylow
4	D₆₇	C₁₈₁	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₆₇	C₂×C₁₈₁	1	1	yes	characteristic, complemented, Sylow
6	C₂	—	67	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁₈₁	D₆₇
commutator, cosocle, hypocenter	C₆₇	C₂×C₁₈₁
Frattini	C₁	G
Fitting, socle	C₆₇×C₁₈₁	C₂
LCS	G ▷ C₆₇
UCS	C₁ ◁ C₁₈₁

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.