Subgroups — C₂²×C₄×C₈ #2869

Order 128.

380 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₈	C₂	1	2	yes	maximal
2	C₂²×C₄²	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄×C₈	C₂	1	12	yes	maximal, direct product factor
4	C₂³×C₄	C₄	1	2	yes	—
5	C₂³×C₄	C₂²	1	1	yes	characteristic
6	C₂²×C₈	C₄	1	16	yes	direct product factor
7	C₂²×C₈	C₂²	1	12	yes	—
8	C₂×C₄²	C₄	1	6	yes	—
9	C₂×C₄²	C₂²	1	6	yes	—
10	C₄×C₈	C₂²	1	16	yes	direct product factor
11	C₂⁴	C₂×C₄	1	1	yes	characteristic
12	C₂²×C₄	C₈	1	16	yes	direct product factor
13	C₂²×C₄	C₂×C₄	1	3	yes	—
14	C₂²×C₄	C₂×C₄	1	8	yes	—
15	C₂²×C₄	C₂×C₄	1	12	yes	—
16	C₂²×C₄	C₂³	1	3	yes	—
17	C₂×C₈	C₂×C₄	1	48	yes	direct product factor
18	C₂×C₈	C₂³	1	8	yes	—
19	C₄²	C₂×C₄	1	12	yes	—
20	C₄²	C₂³	1	4	yes	—
21	C₂³	C₄²	1	4	yes	—
22	C₂³	C₂×C₈	1	8	yes	—
23	C₂³	C₂²×C₄	1	3	yes	—
24	C₂×C₄	C₄²	1	12	yes	—
25	C₂×C₄	C₂×C₈	1	48	yes	direct product factor
26	C₂×C₄	C₂²×C₄	1	3	yes	—
27	C₂×C₄	C₂²×C₄	1	8	yes	—
28	C₂×C₄	C₂²×C₄	1	12	yes	—
29	C₂×C₄	C₂⁴	1	1	yes	characteristic
30	C₈	C₂²×C₄	1	16	yes	direct product factor
31	C₂²	C₄×C₈	1	16	yes	direct product factor
32	C₂²	C₂×C₄²	1	6	yes	—
33	C₂²	C₂²×C₈	1	12	yes	—
34	C₂²	C₂³×C₄	1	1	yes	characteristic
35	C₄	C₂×C₄²	1	6	yes	—
36	C₄	C₂²×C₈	1	16	yes	direct product factor
37	C₄	C₂³×C₄	1	2	yes	—
38	C₂	C₂×C₄×C₈	1	12	yes	direct product factor
39	C₂	C₂²×C₄²	1	1	yes	characteristic
40	C₂	C₂³×C₈	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.