Subgroups — #64231

Order 288.

162 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×GO⁺(4,𝔽₂)	C₂	1	4	yes	maximal, complemented
2	#3802	C₂	1	2	yes	maximal, complemented
3	C₄×#157	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×D₃²	C₂²	1	4	yes	—
5	C₂×#157	C₂²	1	2	yes	—
6	GO⁺(4,𝔽₂)	—	2	8	no	—
7	C₄×C₃⋊D₃	C₂²	1	1	yes	characteristic
8	C₃×D₁₂	—	2	2	no	—
9	#625	—	2	2	no	—
10	D₃×D₄	—	6	2	no	—
11	C₂×C₃⋊D₃	C₂³	1	1	yes	characteristic
12	C₂×C₃×D₃	—	2	4	no	—
13	D₃²	—	2	8	no	—
14	#157	D₄	1	4	yes	complemented
15	C₃²×C₄	D₄	1	1	yes	characteristic, complemented
16	C₃⋊Dic₃	D₄	1	1	yes	characteristic, complemented
17	#127	—	9	1	no	maximal, Sylow
18	C₂²×D₃	—	6	4	no	—
19	C₃×D₄	—	6	2	no	—
20	#67	—	6	4	no	—
21	D₁₂	—	2	2	no	—
22	C₄×D₃	—	6	2	no	—
23	C₂×C₃²	C₂×D₄	1	1	yes	characteristic
24	C₃⋊D₃	C₂×D₄	1	2	yes	—
25	C₃×D₃	—	4	4	no	—
26	C₂×D₄	—	9	2	no	—
27	C₂×D₄	—	9	4	no	—
28	C₄²	—	9	1	no	—
29	C₂²×C₃	—	6	4	no	—
30	C₂×D₃	—	2	4	no	—
31	C₂×D₃	—	6	2	no	—
32	C₂×D₃	—	12	8	no	—
33	C₃×C₄	—	2	2	no	—
34	Dic₃	—	6	2	no	—
35	C₃²	#127	1	1	yes	characteristic, complemented, Sylow
36	C₂³	—	9	4	no	—
37	D₄	—	6	2	no	—
38	D₄	—	18	2	no	—
39	D₄	—	18	8	no	—
40	C₂×C₄	—	9	2	no	—
41	C₂×C₄	—	9	1	no	—
42	C₂×C₃	—	2	2	no	—
43	C₂×C₃	—	12	4	no	—
44	D₃	—	4	4	no	—
45	D₃	—	6	4	no	—
46	C₂²	—	6	4	no	—
47	C₂²	—	9	1	no	—
48	C₂²	—	18	8	no	—
49	C₄	—	9	4	no	—
50	C₄	—	9	1	no	—
51	C₄	GO⁺(4,𝔽₂)	1	1	yes	characteristic, complemented
52	C₃	—	2	2	no	—
53	C₂	—	9	2	no	—
54	C₂	—	12	4	no	—
55	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.