Subgroups — #64225

Order 288.

130 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#3802	C₂	1	2	yes	maximal, complemented
2	#3787	C₂	1	1	yes	maximal, characteristic, complemented
3	#3774	C₂	1	4	yes	maximal, complemented
4	C₂×D₃²	—	2	2	no	—
5	C₄×C₃⋊D₃	C₂²	1	1	yes	characteristic
6	C₃×D₁₂	—	2	2	no	—
7	#625	C₂²	1	4	yes	complemented
8	#622	C₂²	1	2	yes	complemented
9	D₃×D₄	—	6	2	no	—
10	C₂×C₃⋊D₃	D₄	1	1	yes	characteristic
11	C₂×C₃×D₃	—	2	4	no	—
12	D₃²	—	4	4	no	—
13	C₃²×C₄	D₄	1	1	yes	characteristic
14	C₃⋊Dic₃	C₂³	1	1	yes	characteristic
15	C₂×D₈	—	9	1	no	maximal, Sylow
16	C₂²×D₃	—	6	4	no	—
17	C₃×D₄	—	6	2	no	—
18	#67	—	6	4	no	—
19	D₁₂	—	2	2	no	—
20	C₄×D₃	—	6	2	no	—
21	C₂×C₃²	C₂×D₄	1	1	yes	characteristic
22	C₃⋊D₃	D₈	1	2	yes	complemented
23	C₃×D₃	—	4	4	no	—
24	C₂×D₄	—	9	2	no	—
25	D₈	—	9	4	no	—
26	C₂×C₈	—	9	1	no	—
27	C₂²×C₃	—	6	4	no	—
28	C₂×D₃	—	2	4	no	—
29	C₂×D₃	—	6	2	no	—
30	C₂×D₃	—	12	8	no	—
31	C₃×C₄	—	2	2	no	—
32	Dic₃	—	6	2	no	—
33	C₃²	C₂×D₈	1	1	yes	characteristic, complemented, Sylow
34	C₂³	—	18	2	no	—
35	D₄	—	6	2	no	—
36	D₄	—	9	4	no	—
37	C₂×C₄	—	9	1	no	—
38	C₈	—	9	2	no	—
39	C₂×C₃	—	2	2	no	—
40	C₂×C₃	—	12	4	no	—
41	D₃	—	4	4	no	—
42	D₃	—	6	4	no	—
43	C₂²	—	6	4	no	—
44	C₂²	—	9	1	no	—
45	C₂²	—	36	4	no	—
46	C₄	—	9	1	no	—
47	C₄	GO⁺(4,𝔽₂)	1	1	yes	characteristic
48	C₃	—	2	2	no	—
49	C₂	—	9	2	no	—
50	C₂	—	12	4	no	—
51	C₂	C₂×GO⁺(4,𝔽₂)	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.