Subgroups — C₂×D₉ #152

Order 36.

15 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₉	C₂	1	1	yes	maximal, characteristic, complemented
2	D₉	C₂	1	2	yes	maximal, direct product factor
3	C₂×D₃	—	3	1	no	maximal
4	C₉	C₂²	1	1	yes	characteristic, complemented, Sylow
5	C₂×C₃	D₃	1	1	yes	characteristic
6	D₃	—	3	2	no	—
7	C₂²	—	9	1	no	Sylow
8	C₃	C₂×D₃	1	1	yes	characteristic
9	C₂	—	9	2	no	—
10	C₂	D₉	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂	D₉
commutator, cosocle, hypocenter	C₉	C₂²
Frattini	C₃	C₂×D₃
Fitting	C₂×C₉	C₂
socle	C₂×C₃	D₃
LCS	G ▷ C₉
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.