Subgroups — C₂³×C₂²⋊C₄ #3419

Order 128.

2316 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁶	C₂	1	1	yes	maximal, characteristic
2	C₂⁴×C₄	C₂	1	2	yes	maximal, complemented
3	C₂²×C₂²⋊C₄	C₂	1	28	yes	maximal, direct product factor
4	C₂⁵	—	2	16	no	—
5	C₂⁵	C₄	1	16	yes	complemented
6	C₂⁵	C₂²	1	14	yes	—
7	C₂⁵	C₂²	1	1	yes	characteristic
8	C₂³×C₄	—	2	16	no	—
9	C₂³×C₄	C₂²	1	28	yes	complemented
10	C₂×C₂²⋊C₄	C₂²	1	112	yes	direct product factor
11	C₂⁴	—	2	128	no	—
12	C₂⁴	—	2	112	no	—
13	C₂⁴	C₂×C₄	1	8	yes	—
14	C₂⁴	C₂×C₄	1	112	yes	complemented
15	C₂⁴	D₄	1	16	yes	—
16	C₂⁴	C₂³	1	28	yes	—
17	C₂⁴	C₂³	1	7	yes	—
18	C₂²×C₄	—	2	112	no	—
19	C₂²×C₄	C₂³	1	56	yes	complemented
20	C₂²⋊C₄	C₂³	1	64	yes	direct product factor
21	C₂³	—	2	448	no	—
22	C₂³	—	2	112	no	—
23	C₂³	C₂²⋊C₄	1	64	yes	direct product factor
24	C₂³	C₂²×C₄	1	28	yes	—
25	C₂³	C₂²×C₄	1	112	yes	complemented
26	C₂³	C₂×D₄	1	56	yes	—
27	C₂³	C₂⁴	1	8	yes	—
28	C₂³	C₂⁴	1	7	yes	—
29	C₂×C₄	—	2	112	no	—
30	C₂×C₄	C₂⁴	1	16	yes	complemented
31	C₂²	—	2	224	no	—
32	C₂²	—	2	16	no	—
33	C₂²	C₂×C₂²⋊C₄	1	112	yes	direct product factor
34	C₂²	C₂³×C₄	1	14	yes	—
35	C₂²	C₂³×C₄	1	16	yes	complemented
36	C₂²	C₂²×D₄	1	28	yes	—
37	C₂²	C₂⁵	1	1	yes	characteristic
38	C₄	—	2	16	no	—
39	C₂	—	2	16	no	—
40	C₂	C₂²×C₂²⋊C₄	1	28	yes	direct product factor
41	C₂	C₂⁴×C₄	1	1	yes	characteristic
42	C₂	C₂³×D₄	1	2	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.