Subgroups — C₄×C₈² #7838

Order 256.

375 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄²×C₈	C₂	1	3	yes	maximal
2	C₂×C₈²	C₂	1	4	yes	maximal
3	C₂×C₄×C₈	C₄	1	12	yes	—
4	C₂×C₄×C₈	C₂²	1	6	yes	—
5	C₄³	C₂²	1	1	yes	characteristic
6	C₈²	C₄	1	16	yes	direct product factor
7	C₂²×C₈	C₂×C₄	1	12	yes	—
8	C₂×C₄²	C₂×C₄	1	6	yes	—
9	C₂×C₄²	C₂³	1	1	yes	characteristic
10	C₄×C₈	C₈	1	48	yes	direct product factor
11	C₄×C₈	C₂×C₄	1	24	yes	—
12	C₂²×C₄	C₄²	1	4	yes	—
13	C₂²×C₄	C₂²×C₄	1	3	yes	—
14	C₂×C₈	C₄²	1	24	yes	—
15	C₂×C₈	C₂×C₈	1	48	yes	—
16	C₄²	C₂×C₈	1	24	yes	—
17	C₄²	C₂²×C₄	1	4	yes	—
18	C₂³	C₂×C₄²	1	1	yes	characteristic
19	C₂×C₄	C₄×C₈	1	24	yes	—
20	C₂×C₄	C₂×C₄²	1	6	yes	—
21	C₂×C₄	C₂²×C₈	1	12	yes	—
22	C₈	C₄×C₈	1	48	yes	direct product factor
23	C₂²	C₄³	1	1	yes	characteristic
24	C₂²	C₂×C₄×C₈	1	6	yes	—
25	C₄	C₈²	1	16	yes	direct product factor
26	C₄	C₂×C₄×C₈	1	12	yes	—
27	C₂	C₂×C₈²	1	4	yes	—
28	C₂	C₄²×C₈	1	3	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
C₄²×C₈	2
C₂×C₈²	2