Subgroups — Dic₂₇₄₇ #24926913

Order 10988.

12 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₁×C₆₇	C₂	1	1	yes	maximal, characteristic
2	C₄₁×C₆₇	C₄	1	1	yes	characteristic, complemented, Hall
3	Dic₆₇	—	41	1	no	maximal, Hall
4	Dic₄₁	—	67	1	no	maximal, Hall
5	C₂×C₆₇	D₄₁	1	1	yes	characteristic
6	C₂×C₄₁	D₆₇	1	1	yes	characteristic
7	C₆₇	Dic₄₁	1	1	yes	characteristic, complemented, Sylow
8	C₄₁	Dic₆₇	1	1	yes	characteristic, complemented, Sylow
9	C₄	—	2747	1	no	Sylow
10	C₂	D₂₇₄₇	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂	D₂₇₄₇
commutator, hypocenter	C₄₁×C₆₇	C₄
Fitting, socle, prime radical, cosocle	C₂×C₄₁×C₆₇	C₂
LCS	G ▷ C₄₁×C₆₇
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.