Subgroups — #3722

Order 144.

84 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
2	C₂×C₃×Dic₃	C₂	1	2	yes	maximal, complemented
3	(C₂×D₃)⋊C₄	—	3	2	no	maximal
4	C₂²×C₃²	C₂²	1	1	yes	characteristic
5	C₂×C₃⋊D₃	—	2	2	no	—
6	C₂×C₃⋊D₃	C₄	1	2	yes	complemented
7	C₃×Dic₃	—	2	2	no	—
8	C₂²×D₃	—	3	2	no	—
9	C₂²×D₃	—	6	1	no	—
10	C₂×C₃×C₄	—	3	2	no	—
11	C₂×Dic₃	D₃	1	2	yes	complemented
12	C₂×C₃²	C₂×C₄	1	1	yes	characteristic
13	C₂×C₃²	D₄	1	2	yes	—
14	C₃⋊D₃	—	2	2	no	—
15	C₂²⋊C₄	—	9	1	no	Sylow
16	C₂²×C₃	—	2	1	no	—
17	C₂²×C₃	C₂×D₃	1	2	yes	—
18	C₂×D₃	—	3	4	no	—
19	C₂×D₃	—	6	2	no	—
20	C₂×D₃	—	6	4	no	—
21	C₂×D₃	—	6	2	no	—
22	C₂×D₃	—	6	2	no	—
23	C₃×C₄	—	6	2	no	—
24	Dic₃	—	2	2	no	—
25	C₃²	C₂²⋊C₄	1	1	yes	characteristic, complemented, Sylow
26	C₂³	—	9	1	no	—
27	C₂×C₄	—	3	2	no	—
28	C₂×C₃	—	2	1	no	—
29	C₂×C₃	—	2	2	no	—
30	C₂×C₃	C₄×D₃	1	2	yes	—
31	C₂×C₃	D₁₂	1	2	yes	—
32	C₂×C₃	#67	1	2	yes	—
33	D₃	—	6	4	no	—
34	D₃	—	6	4	no	—
35	C₂²	—	9	2	no	—
36	C₂²	—	18	2	no	—
37	C₂²	D₃²	1	1	yes	characteristic
38	C₄	—	6	2	no	—
39	C₃	—	2	1	no	—
40	C₃	(C₂×D₃)⋊C₄	1	2	yes	complemented
41	C₂	—	18	2	no	—
42	C₂	#624	1	1	yes	characteristic
43	C₂	#626	1	2	yes	—

	subgroup	G/H
center, Frattini, hypercenter	C₂²	D₃²
commutator	C₂×C₃²	C₂×C₄
Fitting, socle, cosocle	C₂²×C₃²	C₂²
prime radical	C₂²×C₃⋊D₃	C₂
hypocenter	C₃²	C₂²⋊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.