Subgroups — C₂³×C₄⋊Q₈ #62665

Order 256.

6095 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁴×Q₈	C₂	1	2	yes	maximal
2	C₂²×C₄⋊Q₈	C₂	1	56	yes	maximal, direct product factor
3	C₂³×C₄⋊C₄	C₂	1	4	yes	maximal
4	C₂³×C₄²	C₂	1	1	yes	maximal, characteristic
5	C₂³×Q₈	—	2	32	no	—
6	C₂³×Q₈	C₂²	1	56	yes	—
7	C₂⁴×C₄	C₂²	1	4	yes	—
8	C₂⁴×C₄	C₂²	1	1	yes	characteristic
9	C₂⁴×C₄	C₂²	1	2	yes	—
10	C₂×C₄⋊Q₈	C₂²	1	448	yes	direct product factor
11	C₂²×C₄⋊C₄	C₂²	1	112	yes	—
12	C₂²×C₄²	C₂²	1	28	yes	—
13	C₂⁵	C₂³	1	1	yes	characteristic
14	C₂²×Q₈	—	2	448	no	—
15	C₂²×Q₈	C₂³	1	224	yes	—
16	C₂³×C₄	—	2	32	no	—
17	C₂³×C₄	D₄	1	16	yes	—
18	C₂³×C₄	Q₈	1	32	yes	complemented
19	C₂³×C₄	C₂³	1	56	yes	—
20	C₂³×C₄	C₂³	1	14	yes	—
21	C₂³×C₄	C₂³	1	28	yes	—
22	C₄⋊Q₈	C₂³	1	512	yes	direct product factor
23	C₂×C₄⋊C₄	C₂³	1	448	yes	—
24	C₂×C₄²	C₂³	1	112	yes	—
25	C₂⁴	C₂×D₄	1	8	yes	—
26	C₂⁴	C₂×Q₈	1	16	yes	—
27	C₂⁴	C₂⁴	1	7	yes	—
28	C₂×Q₈	—	2	896	no	—
29	C₂×Q₈	C₂⁴	1	128	yes	—
30	C₂²×C₄	—	2	224	no	—
31	C₂²×C₄	C₂×D₄	1	112	yes	—
32	C₂²×C₄	C₂×Q₈	1	224	yes	complemented
33	C₂²×C₄	C₂⁴	1	112	yes	—
34	C₂²×C₄	C₂⁴	1	28	yes	—
35	C₂²×C₄	C₂⁴	1	56	yes	—
36	C₄⋊C₄	C₂⁴	1	256	yes	—
37	C₄²	C₂⁴	1	64	yes	—
38	C₂³	C₄⋊Q₈	1	64	yes	direct product factor
39	C₂³	C₂²×D₄	1	28	yes	—
40	C₂³	C₂²×Q₈	1	56	yes	—
41	C₂³	C₂⁵	1	7	yes	—
42	Q₈	—	2	256	no	—
43	C₂×C₄	—	2	224	no	—
44	C₂×C₄	C₂²×D₄	1	112	yes	—
45	C₂×C₄	C₂²×Q₈	1	224	yes	complemented
46	C₂×C₄	C₂⁵	1	32	yes	—
47	C₂×C₄	C₂⁵	1	8	yes	—
48	C₂×C₄	C₂⁵	1	16	yes	—
49	C₂²	C₂×C₄⋊Q₈	1	112	yes	direct product factor
50	C₂²	C₂³×D₄	1	14	yes	—
51	C₂²	C₂³×Q₈	1	28	yes	—
52	C₂²	C₂⁶	1	1	yes	characteristic
53	C₄	—	2	32	no	—
54	C₄	C₂³×D₄	1	16	yes	—
55	C₄	C₂³×Q₈	1	32	yes	complemented
56	C₂	C₂²×C₄⋊Q₈	1	28	yes	direct product factor
57	C₂	C₂⁴×D₄	1	1	yes	characteristic
58	C₂	C₂⁴×Q₈	1	2	yes	—

	subgroup	G/H
center, socle, prime radical	C₂⁵	C₂³
commutator, Frattini, cosocle	C₂²	C₂⁶
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂⁵ ◁ G
LECS	G ▷ C₂² ▷ C₁

Complements

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

N	H ≅ G/N	type
2. C₂²×C₄⋊Q₈	C₂	direct (N × H)
10. C₂×C₄⋊Q₈	C₂²	direct (N × H)
18. C₂³×C₄	Q₈	semidirect
22. C₄⋊Q₈	C₂³	direct (N × H)
32. C₂²×C₄	C₂×Q₈	semidirect
38. C₂³	C₄⋊Q₈	direct (N × H)
45. C₂×C₄	C₂²×Q₈	semidirect
49. C₂²	C₂×C₄⋊Q₈	direct (N × H)
55. C₄	C₂³×Q₈	semidirect
56. C₂	C₂²×C₄⋊Q₈	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×Q₈	2
C₂²×C₄⋊Q₈	2
C₂³×C₄⋊C₄	2
C₂³×C₄²	2

Subgroups — C23×C4⋊Q8 #62665

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂³×C₄⋊Q₈ #62665