Subgroups — C₂³×C₄² #3418

Order 128.

1500 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁴×C₄	C₂	1	3	yes	maximal
2	C₂²×C₄²	C₂	1	28	yes	maximal, direct product factor
3	C₂⁵	C₂²	1	1	yes	characteristic
4	C₂³×C₄	C₄	1	48	yes	direct product factor
5	C₂³×C₄	C₂²	1	42	yes	—
6	C₂×C₄²	C₂²	1	112	yes	direct product factor
7	C₂⁴	C₂×C₄	1	24	yes	—
8	C₂⁴	C₂³	1	7	yes	—
9	C₂²×C₄	C₂×C₄	1	336	yes	direct product factor
10	C₂²×C₄	C₂³	1	84	yes	—
11	C₄²	C₂³	1	64	yes	direct product factor
12	C₂³	C₄²	1	64	yes	direct product factor
13	C₂³	C₂²×C₄	1	84	yes	—
14	C₂³	C₂⁴	1	7	yes	—
15	C₂×C₄	C₂²×C₄	1	336	yes	direct product factor
16	C₂×C₄	C₂⁴	1	24	yes	—
17	C₂²	C₂×C₄²	1	112	yes	direct product factor
18	C₂²	C₂³×C₄	1	42	yes	—
19	C₂²	C₂⁵	1	1	yes	characteristic
20	C₄	C₂³×C₄	1	48	yes	direct product factor
21	C₂	C₂²×C₄²	1	28	yes	direct product factor
22	C₂	C₂⁴×C₄	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
C₂⁴×C₄	2
C₂²×C₄²	2