Subgroups — Dic₆₁₀₉ #37567708

Order 24436.

12 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₁×C₁₄₉	C₂	1	1	yes	maximal, characteristic
2	C₄₁×C₁₄₉	C₄	1	1	yes	characteristic, complemented, Hall
3	Dic₁₄₉	—	41	1	no	maximal, Hall
4	C₂×C₁₄₉	D₄₁	1	1	yes	characteristic
5	Dic₄₁	—	149	1	no	maximal, Hall
6	C₁₄₉	Dic₄₁	1	1	yes	characteristic, complemented, Sylow
7	C₂×C₄₁	D₁₄₉	1	1	yes	characteristic
8	C₄₁	Dic₁₄₉	1	1	yes	characteristic, complemented, Sylow
9	C₄	—	6109	1	no	Sylow
10	C₂	D₆₁₀₉	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂	D₆₁₀₉
commutator, hypocenter	C₄₁×C₁₄₉	C₄
Fitting, socle, prime radical, cosocle	C₂×C₄₁×C₁₄₉	C₂
LCS	G ▷ C₄₁×C₁₄₉
UCS	C₁ ◁ C₂

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.