Subgroups — #3802

Order 144.

116 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₃²	C₂	1	2	yes	maximal, complemented
2	C₄×C₃⋊D₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×D₁₂	C₂	1	2	yes	maximal, complemented
4	#625	C₂	1	2	yes	maximal, complemented
5	D₃×D₄	—	3	2	no	maximal
6	C₂×C₃⋊D₃	C₂²	1	1	yes	characteristic
7	C₂×C₃×D₃	C₂²	1	4	yes	complemented
8	D₃²	—	2	4	no	—
9	C₃²×C₄	C₂²	1	1	yes	characteristic, complemented
10	C₃⋊Dic₃	C₂²	1	1	yes	characteristic, complemented
11	C₂²×D₃	—	3	4	no	—
12	C₃×D₄	—	3	2	no	—
13	#67	—	3	4	no	—
14	D₁₂	D₃	1	2	yes	complemented
15	C₄×D₃	—	3	2	no	—
16	C₄×D₃	—	6	1	no	—
17	C₂×C₃²	C₂³	1	1	yes	characteristic
18	C₃⋊D₃	D₄	1	2	yes	complemented
19	C₃×D₃	—	2	4	no	—
20	C₂×D₄	—	9	1	no	Sylow
21	C₂²×C₃	—	3	4	no	—
22	C₂×D₃	—	3	2	no	—
23	C₂×D₃	—	6	1	no	—
24	C₂×D₃	—	6	8	no	—
25	C₂×D₃	C₂×D₃	1	4	yes	complemented
26	C₃×C₄	—	2	1	no	—
27	C₃×C₄	C₂×D₃	1	2	yes	complemented
28	Dic₃	—	3	2	no	—
29	Dic₃	—	6	1	no	—
30	C₃²	C₂×D₄	1	1	yes	characteristic, complemented, Sylow
31	C₂³	—	9	2	no	—
32	D₄	—	3	2	no	—
33	D₄	—	9	2	no	—
34	C₂×C₄	—	9	1	no	—
35	C₂×C₃	—	2	1	no	—
36	C₂×C₃	—	6	4	no	—
37	C₂×C₃	C₂²×D₃	1	2	yes	—
38	D₃	—	2	4	no	—
39	D₃	—	3	4	no	—
40	D₃	—	6	2	no	—
41	C₂²	—	3	4	no	—
42	C₂²	—	9	1	no	—
43	C₂²	—	18	4	no	—
44	C₄	—	9	1	no	—
45	C₄	D₃²	1	1	yes	characteristic, complemented
46	C₃	—	2	1	no	—
47	C₃	D₃×D₄	1	2	yes	complemented
48	C₂	—	6	4	no	—
49	C₂	—	9	2	no	—
50	C₂	C₂×D₃²	1	1	yes	characteristic

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.