Subgroups — C₂³×D₉ #3769

Order 144.

201 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×D₉	C₂	1	14	yes	maximal, direct product factor
3	C₂³×D₃	—	3	1	no	maximal
4	C₂²×C₉	C₂²	1	7	yes	complemented
5	C₂×D₉	C₂²	1	28	yes	direct product factor
6	C₂³×C₃	D₃	1	1	yes	characteristic
7	C₂²×D₃	—	3	14	no	—
8	C₂×C₉	C₂³	1	7	yes	complemented
9	D₉	C₂³	1	8	yes	direct product factor
10	C₂⁴	—	9	1	no	Sylow
11	C₂²×C₃	C₂×D₃	1	7	yes	—
12	C₂×D₃	—	3	28	no	—
13	C₉	C₂⁴	1	1	yes	characteristic, complemented, Sylow
14	C₂³	—	9	14	no	—
15	C₂³	D₉	1	1	yes	characteristic, direct product factor
16	C₂×C₃	C₂²×D₃	1	7	yes	—
17	D₃	—	3	8	no	—
18	C₂²	—	9	28	no	—
19	C₂²	C₂×D₉	1	7	yes	direct product factor
20	C₃	C₂³×D₃	1	1	yes	characteristic
21	C₂	—	9	8	no	—
22	C₂	C₂²×D₉	1	7	yes	direct product factor

	subgroup	G/H
center, hypercenter	C₂³	D₉
commutator, cosocle, hypocenter	C₉	C₂⁴
Frattini	C₃	C₂³×D₃
Fitting	C₂³×C₉	C₂
socle	C₂³×C₃	D₃
LCS	G ▷ C₉
UCS	C₁ ◁ C₂³

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.