Subgroups — C₈₃×D₁₄₉ #37612840

Order 24734.

8 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈₃×C₁₄₉	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₁₄₉	C₈₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₂×C₈₃	—	149	1	no	maximal, Hall
4	C₁₄₉	C₂×C₈₃	1	1	yes	characteristic, complemented, Sylow
5	C₈₃	D₁₄₉	1	1	yes	characteristic, direct product factor, Sylow
6	C₂	—	149	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₈₃	D₁₄₉
commutator, cosocle, hypocenter	C₁₄₉	C₂×C₈₃
Frattini	C₁	G
Fitting, socle	C₈₃×C₁₄₉	C₂
LCS	G ▷ C₁₄₉
UCS	C₁ ◁ C₈₃

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.