Subgroups — C₂×C₃²×D₄ #3836

Order 144.

162 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₃²	C₂	1	2	yes	maximal, complemented
2	C₃²×D₄	C₂	1	4	yes	maximal, direct product factor
3	C₂×C₃²×C₄	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₃×D₄	C₃	1	4	yes	maximal, direct product factor
5	C₂²×C₃²	—	2	4	no	—
6	C₂²×C₃²	C₂²	1	1	yes	characteristic
7	C₂²×C₃²	C₂²	1	4	yes	complemented
8	C₃²×C₄	C₂²	1	2	yes	complemented
9	C₂³×C₃	C₂×C₃	1	8	yes	complemented
10	C₃×D₄	C₂×C₃	1	16	yes	direct product factor
11	C₂×C₃×C₄	C₂×C₃	1	4	yes	complemented
12	C₂×C₃²	—	2	4	no	—
13	C₂×C₃²	D₄	1	2	yes	direct product factor
14	C₂×C₃²	C₂³	1	1	yes	characteristic
15	C₂×D₄	C₃²	1	1	yes	characteristic, direct product factor, Sylow
16	C₂²×C₃	—	2	16	no	—
17	C₂²×C₃	C₂²×C₃	1	4	yes	—
18	C₂²×C₃	C₂²×C₃	1	16	yes	complemented
19	C₃×C₄	C₂²×C₃	1	8	yes	complemented
20	C₃²	C₂×D₄	1	1	yes	characteristic, direct product factor, Sylow
21	C₂³	C₂×C₃²	1	2	yes	complemented
22	D₄	C₂×C₃²	1	4	yes	direct product factor
23	C₂×C₄	C₂×C₃²	1	1	yes	characteristic, complemented
24	C₂×C₃	—	2	16	no	—
25	C₂×C₃	C₃×D₄	1	8	yes	direct product factor
26	C₂×C₃	C₂³×C₃	1	4	yes	—
27	C₂²	—	2	4	no	—
28	C₂²	C₂²×C₃²	1	1	yes	characteristic
29	C₂²	C₂²×C₃²	1	4	yes	complemented
30	C₄	C₂²×C₃²	1	2	yes	complemented
31	C₃	C₂×C₃×D₄	1	4	yes	direct product factor
32	C₂	—	2	4	no	—
33	C₂	C₃²×D₄	1	2	yes	direct product factor
34	C₂	C₂³×C₃²	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃²	C₂²
commutator, Frattini, cosocle	C₂	C₂³×C₃²
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃² ◁ G

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.