Subgroups — #427

Order 64.

57 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₈	C₂	1	1	yes	maximal, characteristic
2	#117	C₂	1	2	yes	maximal
3	#107	C₂	1	2	yes	maximal, complemented
4	#106	C₂	1	2	yes	maximal, complemented
5	C₂²×C₄	C₂²	1	1	yes	characteristic
6	C₂×C₈	C₄	1	4	yes	complemented
7	C₂×C₈	C₂²	1	1	yes	characteristic
8	C₂×C₈	C₂²	1	1	yes	characteristic
9	C₄⋊C₄	C₂²	1	4	yes	—
10	C₂²⋊C₄	—	2	2	no	—
11	C₄²	—	2	2	no	—
12	C₂³	D₄	1	1	yes	characteristic
13	C₂×C₄	—	2	4	no	—
14	C₂×C₄	C₂×C₄	1	2	yes	—
15	C₂×C₄	D₄	1	1	yes	characteristic
16	C₂×C₄	Q₈	1	2	yes	—
17	C₂×C₄	C₂³	1	1	yes	characteristic
18	C₈	C₂×C₄	1	2	yes	—
19	C₈	C₂×C₄	1	2	yes	—
20	C₂²	—	2	2	no	—
21	C₂²	C₄⋊C₄	1	2	yes	—
22	C₂²	C₂×D₄	1	1	yes	characteristic
23	C₄	—	4	4	no	—
24	C₄	C₄⋊C₄	1	2	yes	—
25	C₄	C₂²×C₄	1	1	yes	characteristic
26	C₄	C₂×Q₈	1	1	yes	characteristic
27	C₂	—	2	2	no	—
28	C₂	C₂×C₄⋊C₄	1	1	yes	characteristic
29	C₂	#135	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.