Subgroups — C₂³×C₃⋊D₃ #3853

Order 144.

402 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₃²	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₃⋊D₃	C₂	1	14	yes	maximal, direct product factor
3	C₂³×D₃	—	3	4	no	maximal
4	C₂²×C₃²	C₂²	1	7	yes	complemented
5	C₂×C₃⋊D₃	C₂²	1	28	yes	direct product factor
6	C₂³×C₃	D₃	1	4	yes	complemented
7	C₂²×D₃	—	3	56	no	—
8	C₂×C₃²	C₂³	1	7	yes	complemented
9	C₃⋊D₃	C₂³	1	8	yes	direct product factor
10	C₂⁴	—	9	1	no	Sylow
11	C₂²×C₃	C₂×D₃	1	28	yes	complemented
12	C₂×D₃	—	3	112	no	—
13	C₃²	C₂⁴	1	1	yes	characteristic, complemented, Sylow
14	C₂³	—	9	14	no	—
15	C₂³	C₃⋊D₃	1	1	yes	characteristic, direct product factor
16	C₂×C₃	C₂²×D₃	1	28	yes	complemented
17	D₃	—	3	32	no	—
18	C₂²	—	9	28	no	—
19	C₂²	C₂×C₃⋊D₃	1	7	yes	direct product factor
20	C₃	C₂³×D₃	1	4	yes	complemented
21	C₂	—	9	8	no	—
22	C₂	C₂²×C₃⋊D₃	1	7	yes	direct product factor

	subgroup	G/H
center, hypercenter	C₂³	C₃⋊D₃
commutator, cosocle, hypocenter	C₃²	C₂⁴
Frattini	C₁	G
Fitting, socle	C₂³×C₃²	C₂
LCS	G ▷ C₃²
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.