Subgroups — C₂⁴×C₈ #3569

Order 128.

988 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁴×C₄	C₂	1	1	yes	maximal, characteristic
2	C₂³×C₈	C₂	1	30	yes	maximal, direct product factor
3	C₂⁵	C₄	1	1	yes	characteristic
4	C₂³×C₄	C₄	1	15	yes	—
5	C₂³×C₄	C₂²	1	15	yes	—
6	C₂²×C₈	C₂²	1	140	yes	direct product factor
7	C₂⁴	C₈	1	16	yes	direct product factor
8	C₂⁴	C₂×C₄	1	15	yes	—
9	C₂²×C₄	C₂×C₄	1	105	yes	—
10	C₂²×C₄	C₂³	1	35	yes	—
11	C₂×C₈	C₂³	1	120	yes	direct product factor
12	C₂³	C₂×C₈	1	120	yes	direct product factor
13	C₂³	C₂²×C₄	1	35	yes	—
14	C₂×C₄	C₂²×C₄	1	105	yes	—
15	C₂×C₄	C₂⁴	1	15	yes	—
16	C₈	C₂⁴	1	16	yes	direct product factor
17	C₂²	C₂²×C₈	1	140	yes	direct product factor
18	C₂²	C₂³×C₄	1	15	yes	—
19	C₄	C₂³×C₄	1	15	yes	—
20	C₄	C₂⁵	1	1	yes	characteristic
21	C₂	C₂³×C₈	1	30	yes	direct product factor
22	C₂	C₂⁴×C₄	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.

subgroup	index
C₂⁴×C₄	2
C₂³×C₈	2