Subgroups — #407

Order 64.

95 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₄	C₂	1	1	yes	maximal, characteristic
2	C₂×M₁₆	C₂	1	2	yes	maximal, complemented
3	C₂²⋊C₈	C₂	1	4	yes	maximal, complemented
4	C₂⁴	C₄	1	1	yes	characteristic
5	C₂²×C₄	—	2	4	no	—
6	C₂²×C₄	C₄	1	1	yes	characteristic
7	C₂²×C₄	C₄	1	2	yes	—
8	C₂²×C₄	C₂²	1	2	yes	—
9	C₂²×C₄	C₂²	1	1	yes	characteristic
10	M₁₆	—	2	4	no	—
11	C₂×C₈	C₂²	1	4	yes	complemented
12	C₂³	—	2	2	no	—
13	C₂³	—	2	4	no	—
14	C₂³	C₂×C₄	1	1	yes	characteristic
15	C₂³	C₂×C₄	1	2	yes	—
16	C₂×C₄	—	2	2	no	—
17	C₂×C₄	—	2	4	no	—
18	C₂×C₄	—	2	4	no	—
19	C₂×C₄	C₂×C₄	1	2	yes	—
20	C₂×C₄	C₂×C₄	1	1	yes	characteristic
21	C₂×C₄	D₄	1	4	yes	—
22	C₂×C₄	C₂³	1	1	yes	characteristic
23	C₈	—	2	4	no	—
24	C₂²	—	2	8	no	—
25	C₂²	—	2	2	no	—
26	C₂²	—	2	2	no	—
27	C₂²	—	2	2	no	—
28	C₂²	C₂²⋊C₄	1	2	yes	—
29	C₂²	M₁₆	1	4	yes	complemented
30	C₂²	C₂²×C₄	1	1	yes	characteristic
31	C₄	—	2	2	no	—
32	C₄	C₂²⋊C₄	1	2	yes	—
33	C₄	C₂×D₄	1	2	yes	—
34	C₂	—	2	2	no	—
35	C₂	—	2	4	no	—
36	C₂	C₂×C₂²⋊C₄	1	1	yes	characteristic
37	C₂	C₂×M₁₆	1	2	yes	—

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.