Subgroups — #431

Order 64.

59 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄²	C₂	1	1	yes	maximal, characteristic
2	C₄⋊C₈	C₂	1	2	yes	maximal, complemented
3	C₂²⋊C₈	C₂	1	2	yes	maximal
4	C₄×C₈	C₂	1	2	yes	maximal, complemented
5	C₂²×C₄	C₄	1	1	yes	characteristic
6	C₂²×C₄	C₄	1	1	yes	characteristic
7	C₂²×C₄	C₂²	1	1	yes	characteristic
8	C₂×C₈	C₂²	1	4	yes	—
9	C₄²	C₄	1	1	yes	characteristic
10	C₄²	C₄	1	1	yes	characteristic
11	C₄²	C₂²	1	1	yes	characteristic
12	C₄²	C₂²	1	1	yes	characteristic
13	C₂³	C₂×C₄	1	1	yes	characteristic
14	C₂×C₄	—	2	2	no	—
15	C₂×C₄	—	2	2	no	—
16	C₂×C₄	C₈	1	4	yes	complemented
17	C₂×C₄	C₂×C₄	1	1	yes	characteristic
18	C₂×C₄	C₂×C₄	1	1	yes	characteristic
19	C₂×C₄	C₂×C₄	1	1	yes	characteristic
20	C₂×C₄	C₂×C₄	1	1	yes	characteristic
21	C₂×C₄	C₂×C₄	1	1	yes	characteristic
22	C₂×C₄	C₂³	1	1	yes	characteristic
23	C₈	—	2	4	no	—
24	C₂²	—	2	1	no	—
25	C₂²	—	2	1	no	—
26	C₂²	C₂×C₈	1	2	yes	—
27	C₂²	C₂²×C₄	1	1	yes	characteristic
28	C₄	—	2	1	no	—
29	C₄	—	2	1	no	—
30	C₄	C₂×C₈	1	2	yes	—
31	C₄	C₂×C₈	1	2	yes	—
32	C₄	M₁₆	1	2	yes	—
33	C₄	#41	1	2	yes	—
34	C₂	—	2	2	no	—
35	C₂	#117	1	1	yes	characteristic
36	C₂	C₂²×C₈	1	1	yes	characteristic
37	C₂	C₂×M₁₆	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.