Subgroups — C₂³×C₃×D₃ #3852

Order 144.

284 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	C₂⁴×C₃	—	3	1	no	maximal
4	C₂³×D₃	C₃	1	1	yes	maximal, characteristic, direct product factor
5	C₂²×C₃²	C₂²	1	7	yes	complemented
6	C₂×C₃×D₃	C₂²	1	28	yes	direct product factor
7	C₂³×C₃	—	2	1	no	—
8	C₂³×C₃	—	3	14	no	—
9	C₂³×C₃	D₃	1	1	yes	characteristic, direct product factor
10	C₂³×C₃	C₂×C₃	1	1	yes	characteristic, complemented
11	C₂²×D₃	C₂×C₃	1	14	yes	direct product factor
12	C₂×C₃²	C₂³	1	7	yes	complemented
13	C₃×D₃	C₂³	1	8	yes	direct product factor
14	C₂⁴	—	3	1	no	Sylow
15	C₂²×C₃	—	2	7	no	—
16	C₂²×C₃	—	3	28	no	—
17	C₂²×C₃	C₂×D₃	1	7	yes	direct product factor
18	C₂²×C₃	C₂²×C₃	1	7	yes	complemented
19	C₂×D₃	C₂²×C₃	1	28	yes	direct product factor
20	C₃²	C₂⁴	1	1	yes	characteristic, complemented, Sylow
21	C₂³	—	3	14	no	—
22	C₂³	C₃×D₃	1	1	yes	characteristic, direct product factor
23	C₂×C₃	—	2	7	no	—
24	C₂×C₃	—	3	8	no	—
25	C₂×C₃	C₂²×D₃	1	7	yes	direct product factor
26	C₂×C₃	C₂³×C₃	1	7	yes	complemented
27	D₃	C₂³×C₃	1	8	yes	direct product factor
28	C₂²	—	3	28	no	—
29	C₂²	C₂×C₃×D₃	1	7	yes	direct product factor
30	C₃	—	2	1	no	—
31	C₃	C₂³×D₃	1	1	yes	characteristic, direct product factor
32	C₃	C₂⁴×C₃	1	1	yes	characteristic, complemented
33	C₂	—	3	8	no	—
34	C₂	C₂²×C₃×D₃	1	7	yes	direct product factor

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

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.