Subgroups — Dic₄₂₈₆ #30686239

Order 17144.

12 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₂₁₄₃	C₂	1	1	yes	maximal, characteristic
2	Dic₂₁₄₃	C₂	1	2	yes	maximal
3	C₂×C₂₁₄₃	C₂²	1	1	yes	characteristic
4	C₂₁₄₃	Q₈	1	1	yes	characteristic, complemented, Sylow
5	Q₈	—	2143	1	no	maximal, Sylow
6	C₄	—	2143	2	no	—
7	C₄	D₂₁₄₃	1	1	yes	characteristic
8	C₂	C₂×D₂₁₄₃	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂	C₂×D₂₁₄₃
commutator, socle, prime radical, cosocle	C₂×C₂₁₄₃	C₂²
Fitting	C₄×C₂₁₄₃	C₂
hypercenter	C₄	D₂₁₄₃
hypocenter	C₂₁₄₃	Q₈
LCS	G ▷ C₂×C₂₁₄₃ ▷ C₂₁₄₃
UCS	C₁ ◁ C₂ ◁ C₄

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
4. C₂₁₄₃	Q₈	semidirect

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.