Subgroups — C₂×C₄×C₈ #402

Order 64.

81 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₈	C₂	1	2	yes	maximal
2	C₂×C₄²	C₂	1	1	yes	maximal, characteristic
3	C₄×C₈	C₂	1	4	yes	maximal, direct product factor
4	C₂²×C₄	C₄	1	2	yes	—
5	C₂²×C₄	C₂²	1	1	yes	characteristic
6	C₂×C₈	C₄	1	8	yes	direct product factor
7	C₂×C₈	C₂²	1	4	yes	—
8	C₄²	C₄	1	2	yes	—
9	C₄²	C₂²	1	2	yes	—
10	C₂³	C₂×C₄	1	1	yes	characteristic
11	C₂×C₄	C₈	1	8	yes	direct product factor
12	C₂×C₄	C₂×C₄	1	1	yes	characteristic
13	C₂×C₄	C₂×C₄	1	4	yes	—
14	C₂×C₄	C₂×C₄	1	4	yes	—
15	C₂×C₄	C₂³	1	1	yes	characteristic
16	C₈	C₂×C₄	1	8	yes	direct product factor
17	C₂²	C₄²	1	2	yes	—
18	C₂²	C₂×C₈	1	4	yes	—
19	C₂²	C₂²×C₄	1	1	yes	characteristic
20	C₄	C₄²	1	2	yes	—
21	C₄	C₂×C₈	1	8	yes	direct product factor
22	C₄	C₂²×C₄	1	2	yes	—
23	C₂	C₄×C₈	1	4	yes	direct product factor
24	C₂	C₂×C₄²	1	1	yes	characteristic
25	C₂	C₂²×C₈	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.