Subgroups — C₄³×C₈ #353104

Order 512.

3330 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄²×C₈	C₂	1	14	yes	maximal
2	C₄⁴	C₂	1	1	yes	maximal, characteristic
3	C₂²×C₄×C₈	C₂²	1	28	yes	—
4	C₂×C₄³	C₄	1	8	yes	—
5	C₂×C₄³	C₂²	1	7	yes	—
6	C₄²×C₈	C₄	1	112	yes	direct product factor
7	C₂³×C₈	C₂³	1	8	yes	—
8	C₂²×C₄²	C₂×C₄	1	28	yes	—
9	C₂²×C₄²	C₂³	1	7	yes	—
10	C₂×C₄×C₈	C₂×C₄	1	336	yes	—
11	C₄³	C₈	1	64	yes	direct product factor
12	C₄³	C₂×C₄	1	56	yes	—
13	C₂³×C₄	C₂²×C₄	1	14	yes	—
14	C₂³×C₄	C₂⁴	1	1	yes	characteristic
15	C₂²×C₈	C₂²×C₄	1	112	yes	—
16	C₂×C₄²	C₄²	1	112	yes	—
17	C₂×C₄²	C₂×C₈	1	224	yes	—
18	C₂×C₄²	C₂²×C₄	1	84	yes	—
19	C₄×C₈	C₄²	1	448	yes	direct product factor
20	C₂⁴	C₂³×C₄	1	1	yes	characteristic
21	C₂²×C₄	C₂×C₄²	1	84	yes	—
22	C₂²×C₄	C₂²×C₈	1	112	yes	—
23	C₂²×C₄	C₂³×C₄	1	14	yes	—
24	C₂×C₈	C₂×C₄²	1	224	yes	—
25	C₄²	C₄×C₈	1	448	yes	direct product factor
26	C₄²	C₂×C₄²	1	112	yes	—
27	C₂³	C₂²×C₄²	1	7	yes	—
28	C₂³	C₂³×C₈	1	8	yes	—
29	C₂×C₄	C₄³	1	56	yes	—
30	C₂×C₄	C₂×C₄×C₈	1	336	yes	—
31	C₂×C₄	C₂²×C₄²	1	28	yes	—
32	C₈	C₄³	1	64	yes	direct product factor
33	C₂²	C₂×C₄³	1	7	yes	—
34	C₂²	C₂²×C₄×C₈	1	28	yes	—
35	C₄	C₄²×C₈	1	112	yes	direct product factor
36	C₄	C₂×C₄³	1	8	yes	—
37	C₂	C₄⁴	1	1	yes	characteristic
38	C₂	C₂×C₄²×C₈	1	14	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.

subgroup	index
C₂×C₄²×C₈	2
C₄⁴	2