Subgroups — C₂³×C₄⋊C₈ #60094

Order 256.

1935 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	1	yes	characteristic
5	C₂⁴×C₄	C₄	1	1	yes	characteristic
6	C₂⁴×C₄	C₂²	1	1	yes	characteristic
7	C₂³×C₈	—	2	16	no	—
8	C₂³×C₈	C₂²	1	28	yes	—
9	C₂²×C₄²	C₄	1	14	yes	—
10	C₂²×C₄²	C₂²	1	14	yes	—
11	C₂×C₄⋊C₈	C₂²	1	112	yes	direct product factor
12	C₂⁵	C₂×C₄	1	1	yes	characteristic
13	C₂³×C₄	—	2	8	no	—
14	C₂³×C₄	C₈	1	16	yes	complemented
15	C₂³×C₄	C₂×C₄	1	14	yes	—
16	C₂³×C₄	C₂×C₄	1	7	yes	—
17	C₂³×C₄	C₂×C₄	1	14	yes	—
18	C₂³×C₄	D₄	1	8	yes	—
19	C₂³×C₄	Q₈	1	8	yes	—
20	C₂³×C₄	C₂³	1	7	yes	—
21	C₂²×C₈	—	2	112	no	—
22	C₂²×C₈	C₂³	1	56	yes	—
23	C₂×C₄²	C₂×C₄	1	84	yes	—
24	C₂×C₄²	C₂³	1	28	yes	—
25	C₄⋊C₈	C₂³	1	64	yes	direct product factor
26	C₂⁴	C₄⋊C₄	1	8	yes	—
27	C₂⁴	C₂×C₈	1	8	yes	—
28	C₂⁴	M₁₆	1	8	yes	—
29	C₂⁴	C₂²×C₄	1	7	yes	—
30	C₂²×C₄	—	2	56	no	—
31	C₂²×C₄	C₄⋊C₄	1	56	yes	—
32	C₂²×C₄	C₂×C₈	1	112	yes	complemented
33	C₂²×C₄	C₂²×C₄	1	28	yes	—
34	C₂²×C₄	C₂²×C₄	1	21	yes	—
35	C₂²×C₄	C₂²×C₄	1	28	yes	—
36	C₂²×C₄	C₂×D₄	1	28	yes	—
37	C₂²×C₄	C₂×Q₈	1	28	yes	—
38	C₂²×C₄	C₂⁴	1	7	yes	—
39	C₂×C₈	—	2	112	no	—
40	C₂×C₈	C₂⁴	1	16	yes	—
41	C₄²	C₂²×C₄	1	56	yes	—
42	C₄²	C₂⁴	1	8	yes	—
43	C₂³	C₄⋊C₈	1	64	yes	direct product factor
44	C₂³	C₂×C₄⋊C₄	1	28	yes	—
45	C₂³	C₂²×C₈	1	28	yes	—
46	C₂³	C₂×M₁₆	1	28	yes	—
47	C₂³	C₂³×C₄	1	7	yes	—
48	C₂×C₄	—	2	56	no	—
49	C₂×C₄	C₂×C₄⋊C₄	1	84	yes	—
50	C₂×C₄	C₂²×C₈	1	112	yes	complemented
51	C₂×C₄	C₂³×C₄	1	8	yes	—
52	C₂×C₄	C₂³×C₄	1	7	yes	—
53	C₂×C₄	C₂³×C₄	1	8	yes	—
54	C₂×C₄	C₂²×D₄	1	14	yes	—
55	C₂×C₄	C₂²×Q₈	1	14	yes	—
56	C₂×C₄	C₂⁵	1	1	yes	characteristic
57	C₈	—	2	16	no	—
58	C₂²	C₂×C₄⋊C₈	1	112	yes	direct product factor
59	C₂²	C₂²×C₄⋊C₄	1	14	yes	—
60	C₂²	C₂³×C₈	1	14	yes	—
61	C₂²	C₂²×M₁₆	1	14	yes	—
62	C₂²	C₂⁴×C₄	1	1	yes	characteristic
63	C₄	—	2	8	no	—
64	C₄	C₂²×C₄⋊C₄	1	14	yes	—
65	C₄	C₂³×C₈	1	16	yes	complemented
66	C₄	C₂³×D₄	1	1	yes	characteristic
67	C₄	C₂³×Q₈	1	1	yes	characteristic
68	C₂	C₂²×C₄⋊C₈	1	28	yes	direct product factor
69	C₂	C₂³×C₄⋊C₄	1	1	yes	characteristic
70	C₂	C₂⁴×C₈	1	1	yes	characteristic
71	C₂	C₂³×M₁₆	1	1	yes	characteristic

	subgroup	G/H
center	C₂⁴×C₄	C₂²
commutator	C₂	C₂⁴×C₈
Frattini, cosocle	C₂×C₄	C₂⁵
socle, prime radical	C₂⁵	C₂×C₄
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₄ ◁ 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)
11. C₂×C₄⋊C₈	C₂²	direct (N × H)
14. C₂³×C₄	C₈	semidirect
25. C₄⋊C₈	C₂³	direct (N × H)
32. C₂²×C₄	C₂×C₈	semidirect
43. C₂³	C₄⋊C₈	direct (N × H)
50. C₂×C₄	C₂²×C₈	semidirect
58. C₂²	C₂×C₄⋊C₈	direct (N × H)
65. C₄	C₂³×C₈	semidirect
68. 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 #60094

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂³×C₄⋊C₈ #60094