Subgroups — C₂²×D₃² #3849

Order 144.

284 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃⋊D₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₃×D₃	C₂	1	2	yes	maximal, complemented
3	C₂×D₃²	C₂	1	12	yes	maximal, direct product factor
4	C₂³×D₃	—	3	2	no	maximal
5	C₂²×C₃²	C₂²	1	1	yes	characteristic, complemented
6	C₂×C₃⋊D₃	C₂²	1	6	yes	complemented
7	C₂×C₃×D₃	C₂²	1	12	yes	complemented
8	D₃²	C₂²	1	16	yes	direct product factor
9	C₂³×C₃	—	3	2	no	—
10	C₂²×D₃	—	3	2	no	—
11	C₂²×D₃	—	3	24	no	—
12	C₂²×D₃	—	6	1	no	—
13	C₂²×D₃	D₃	1	2	yes	direct product factor
14	C₂×C₃²	C₂³	1	3	yes	complemented
15	C₃⋊D₃	C₂³	1	4	yes	complemented
16	C₃×D₃	C₂³	1	8	yes	complemented
17	C₂⁴	—	9	1	no	Sylow
18	C₂²×C₃	—	2	1	no	—
19	C₂²×C₃	—	3	12	no	—
20	C₂²×C₃	C₂×D₃	1	2	yes	complemented
21	C₂×D₃	—	3	12	no	—
22	C₂×D₃	—	3	32	no	—
23	C₂×D₃	—	6	6	no	—
24	C₂×D₃	C₂×D₃	1	12	yes	direct product factor
25	C₃²	C₂⁴	1	1	yes	characteristic, complemented, Sylow
26	C₂³	—	3	2	no	—
27	C₂³	—	9	12	no	—
28	C₂³	—	9	1	no	—
29	C₂×C₃	—	2	3	no	—
30	C₂×C₃	—	3	8	no	—
31	C₂×C₃	C₂²×D₃	1	6	yes	complemented
32	D₃	—	3	8	no	—
33	D₃	—	6	4	no	—
34	D₃	C₂²×D₃	1	8	yes	direct product factor
35	C₂²	—	3	12	no	—
36	C₂²	—	9	16	no	—
37	C₂²	—	9	6	no	—
38	C₂²	D₃²	1	1	yes	characteristic, direct product factor
39	C₃	—	2	1	no	—
40	C₃	C₂³×D₃	1	2	yes	complemented
41	C₂	—	3	8	no	—
42	C₂	—	9	4	no	—
43	C₂	C₂×D₃²	1	3	yes	direct product factor

	subgroup	G/H
center, hypercenter	C₂²	D₃²
commutator, cosocle, hypocenter	C₃²	C₂⁴
Frattini	C₁	G
Fitting, socle	C₂²×C₃²	C₂²
LCS	G ▷ C₃²
UCS	C₁ ◁ C₂²

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.