Subgroups — D₄₁×C₁₄₉ #27132000

Order 12218.

8 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₁×C₁₄₉	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₂×C₁₄₉	—	41	1	no	maximal, Hall
3	C₁₄₉	D₄₁	1	1	yes	characteristic, direct product factor, Sylow
4	D₄₁	C₁₄₉	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₄₁	C₂×C₁₄₉	1	1	yes	characteristic, complemented, Sylow
6	C₂	—	41	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁₄₉	D₄₁
commutator, cosocle, hypocenter	C₄₁	C₂×C₁₄₉
Frattini	C₁	G
Fitting, socle	C₄₁×C₁₄₉	C₂
LCS	G ▷ C₄₁
UCS	C₁ ◁ C₁₄₉

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.