Subgroups — C₂³×C₄×C₈ #60050

Order 256.

2319 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁴×C₈	C₂	1	2	yes	maximal
2	C₂³×C₄²	C₂	1	1	yes	maximal, characteristic
3	C₂²×C₄×C₈	C₂	1	28	yes	maximal, direct product factor
4	C₂⁴×C₄	C₄	1	2	yes	—
5	C₂⁴×C₄	C₂²	1	1	yes	characteristic
6	C₂³×C₈	C₄	1	32	yes	direct product factor
7	C₂³×C₈	C₂²	1	28	yes	—
8	C₂²×C₄²	C₄	1	14	yes	—
9	C₂²×C₄²	C₂²	1	14	yes	—
10	C₂×C₄×C₈	C₂²	1	112	yes	direct product factor
11	C₂⁵	C₂×C₄	1	1	yes	characteristic
12	C₂³×C₄	C₈	1	32	yes	direct product factor
13	C₂³×C₄	C₂×C₄	1	7	yes	—
14	C₂³×C₄	C₂×C₄	1	16	yes	—
15	C₂³×C₄	C₂×C₄	1	28	yes	—
16	C₂³×C₄	C₂³	1	7	yes	—
17	C₂²×C₈	C₂×C₄	1	224	yes	direct product factor
18	C₂²×C₈	C₂³	1	56	yes	—
19	C₂×C₄²	C₂×C₄	1	84	yes	—
20	C₂×C₄²	C₂³	1	28	yes	—
21	C₄×C₈	C₂³	1	64	yes	direct product factor
22	C₂⁴	C₄²	1	8	yes	—
23	C₂⁴	C₂×C₈	1	16	yes	—
24	C₂⁴	C₂²×C₄	1	7	yes	—
25	C₂²×C₄	C₄²	1	56	yes	—
26	C₂²×C₄	C₂×C₈	1	224	yes	direct product factor
27	C₂²×C₄	C₂²×C₄	1	21	yes	—
28	C₂²×C₄	C₂²×C₄	1	56	yes	—
29	C₂²×C₄	C₂²×C₄	1	56	yes	—
30	C₂²×C₄	C₂⁴	1	7	yes	—
31	C₂×C₈	C₂²×C₄	1	224	yes	direct product factor
32	C₂×C₈	C₂⁴	1	16	yes	—
33	C₄²	C₂²×C₄	1	56	yes	—
34	C₄²	C₂⁴	1	8	yes	—
35	C₂³	C₄×C₈	1	64	yes	direct product factor
36	C₂³	C₂×C₄²	1	28	yes	—
37	C₂³	C₂²×C₈	1	56	yes	—
38	C₂³	C₂³×C₄	1	7	yes	—
39	C₂×C₄	C₂×C₄²	1	84	yes	—
40	C₂×C₄	C₂²×C₈	1	224	yes	direct product factor
41	C₂×C₄	C₂³×C₄	1	7	yes	—
42	C₂×C₄	C₂³×C₄	1	16	yes	—
43	C₂×C₄	C₂³×C₄	1	28	yes	—
44	C₂×C₄	C₂⁵	1	1	yes	characteristic
45	C₈	C₂³×C₄	1	32	yes	direct product factor
46	C₂²	C₂×C₄×C₈	1	112	yes	direct product factor
47	C₂²	C₂²×C₄²	1	14	yes	—
48	C₂²	C₂³×C₈	1	28	yes	—
49	C₂²	C₂⁴×C₄	1	1	yes	characteristic
50	C₄	C₂²×C₄²	1	14	yes	—
51	C₄	C₂³×C₈	1	32	yes	direct product factor
52	C₄	C₂⁴×C₄	1	2	yes	—
53	C₂	C₂²×C₄×C₈	1	28	yes	direct product factor
54	C₂	C₂³×C₄²	1	1	yes	characteristic
55	C₂	C₂⁴×C₈	1	2	yes	—

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂×C₄	C₂⁵
socle, prime radical	C₂⁵	C₂×C₄
LCS	G ▷ C₁
UCS	C₁ ◁ G
LECS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
3. C₂²×C₄×C₈	C₂	direct (N × H)
6. C₂³×C₈	C₄	direct (N × H)
10. C₂×C₄×C₈	C₂²	direct (N × H)
12. C₂³×C₄	C₈	direct (N × H)
17. C₂²×C₈	C₂×C₄	direct (N × H)
21. C₄×C₈	C₂³	direct (N × H)
26. C₂²×C₄	C₂×C₈	direct (N × H)
31. C₂×C₈	C₂²×C₄	direct (N × H)
35. C₂³	C₄×C₈	direct (N × H)
40. C₂×C₄	C₂²×C₈	direct (N × H)
45. C₈	C₂³×C₄	direct (N × H)
46. C₂²	C₂×C₄×C₈	direct (N × H)
51. C₄	C₂³×C₈	direct (N × H)
53. C₂	C₂²×C₄×C₈	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂⁴×C₈	2
C₂³×C₄²	2
C₂²×C₄×C₈	2

Subgroups — C23×C4×C8 #60050

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂³×C₄×C₈ #60050