Subgroups — C₂×D₄₂₈₉ #31769751

Order 17156.

10 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₂₈₉	C₂	1	1	yes	maximal, characteristic, complemented
2	D₄₂₈₉	C₂	1	2	yes	maximal, direct product factor
3	C₄₂₈₉	C₂²	1	1	yes	characteristic, complemented, Sylow
4	C₂²	—	4289	1	no	maximal, Sylow
5	C₂	—	4289	2	no	—
6	C₂	D₄₂₈₉	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂	D₄₂₈₉
commutator, cosocle, hypocenter	C₄₂₈₉	C₂²
Frattini	C₁	G
Fitting, socle	C₂×C₄₂₈₉	C₂
LCS	G ▷ C₄₂₈₉
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.