Subgroups — #3724

Order 144.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃⋊Dic₃	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×Dic₃	C₂	1	2	yes	maximal
3	Dic₃⋊C₄	—	3	2	no	maximal
4	C₂²×C₃²	C₂²	1	1	yes	characteristic
5	C₃⋊Dic₃	C₄	1	2	yes	complemented
6	C₃×Dic₃	—	2	2	no	—
7	C₂×C₃×C₄	—	3	2	no	—
8	C₂×Dic₃	—	3	2	no	—
9	C₂×Dic₃	—	6	1	no	—
10	C₂×Dic₃	D₃	1	2	yes	—
11	C₂×C₃²	C₂×C₄	1	1	yes	characteristic
12	C₂×C₃²	D₄	1	1	yes	characteristic
13	C₂×C₃²	Q₈	1	1	yes	characteristic
14	C₄⋊C₄	—	9	1	no	Sylow
15	C₂²×C₃	—	2	1	no	—
16	C₂²×C₃	C₂×D₃	1	2	yes	—
17	C₃×C₄	—	6	2	no	—
18	Dic₃	—	2	2	no	—
19	Dic₃	—	3	4	no	—
20	Dic₃	—	6	2	no	—
21	C₃²	C₄⋊C₄	1	1	yes	characteristic, complemented, Sylow
22	C₂×C₄	—	3	2	no	—
23	C₂×C₄	—	9	1	no	—
24	C₂×C₃	—	2	1	no	—
25	C₂×C₃	—	2	1	no	—
26	C₂×C₃	—	2	1	no	—
27	C₂×C₃	Dic₆	1	2	yes	—
28	C₂×C₃	C₄×D₃	1	2	yes	—
29	C₂×C₃	#67	1	2	yes	—
30	C₂²	D₃²	1	1	yes	characteristic
31	C₄	—	6	2	no	—
32	C₄	—	9	2	no	—
33	C₃	—	2	1	no	—
34	C₃	Dic₃⋊C₄	1	2	yes	complemented
35	C₂	#624	1	1	yes	characteristic
36	C₂	#625	1	1	yes	characteristic
37	C₂	#627	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂²	D₃²
commutator	C₂×C₃²	C₂×C₄
Fitting, socle, prime radical, cosocle	C₂²×C₃²	C₂²
hypocenter	C₃²	C₄⋊C₄
LCS	G ▷ C₂×C₃² ▷ 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.