Subgroups — C₂²×C₄³ #33985

Order 256.

4047 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₄²	C₂	1	7	yes	maximal
2	C₂×C₄³	C₂	1	24	yes	maximal, direct product factor
3	C₂⁴×C₄	C₂²	1	7	yes	—
4	C₂²×C₄²	C₄	1	112	yes	direct product factor
5	C₂²×C₄²	C₂²	1	84	yes	—
6	C₄³	C₂²	1	64	yes	direct product factor
7	C₂⁵	C₂³	1	1	yes	characteristic
8	C₂³×C₄	C₂×C₄	1	168	yes	—
9	C₂³×C₄	C₂³	1	42	yes	—
10	C₂×C₄²	C₂×C₄	1	672	yes	direct product factor
11	C₂×C₄²	C₂³	1	112	yes	—
12	C₂⁴	C₂²×C₄	1	28	yes	—
13	C₂⁴	C₂⁴	1	3	yes	—
14	C₂²×C₄	C₄²	1	448	yes	direct product factor
15	C₂²×C₄	C₂²×C₄	1	504	yes	—
16	C₂²×C₄	C₂⁴	1	28	yes	—
17	C₄²	C₂²×C₄	1	448	yes	direct product factor
18	C₂³	C₂×C₄²	1	112	yes	—
19	C₂³	C₂³×C₄	1	42	yes	—
20	C₂³	C₂⁵	1	1	yes	characteristic
21	C₂×C₄	C₂×C₄²	1	672	yes	direct product factor
22	C₂×C₄	C₂³×C₄	1	168	yes	—
23	C₂²	C₄³	1	64	yes	direct product factor
24	C₂²	C₂²×C₄²	1	84	yes	—
25	C₂²	C₂⁴×C₄	1	7	yes	—
26	C₄	C₂²×C₄²	1	112	yes	direct product factor
27	C₂	C₂×C₄³	1	24	yes	direct product factor
28	C₂	C₂³×C₄²	1	7	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
C₂³×C₄²	2
C₂×C₄³	2