Subgroups — C₁₆₇×D₈₉ #44446176

Order 29726.

8 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈₉×C₁₆₇	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₂×C₁₆₇	—	89	1	no	maximal, Hall
3	D₈₉	C₁₆₇	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₁₆₇	D₈₉	1	1	yes	characteristic, direct product factor, Sylow
5	C₈₉	C₂×C₁₆₇	1	1	yes	characteristic, complemented, Sylow
6	C₂	—	89	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁₆₇	D₈₉
commutator, cosocle, hypocenter	C₈₉	C₂×C₁₆₇
Frattini	C₁	G
Fitting, socle	C₈₉×C₁₆₇	C₂
LCS	G ▷ C₈₉
UCS	C₁ ◁ C₁₆₇

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.