Subgroups — C₂³×D₁₆ #62625

Order 256.

1295 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×D₈	C₂	1	2	yes	maximal, complemented
2	C₂²×D₁₆	C₂	1	28	yes	maximal, direct product factor
3	C₂³×C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂³×D₄	—	2	2	no	—
5	C₂²×D₈	—	2	14	no	—
6	C₂²×D₈	C₂²	1	28	yes	complemented
7	C₂³×C₈	C₂²	1	1	yes	characteristic
8	C₂×D₁₆	C₂²	1	112	yes	direct product factor
9	C₂²×C₁₆	C₂²	1	14	yes	complemented
10	C₂⁵	—	4	2	no	—
11	C₂²×D₄	—	2	28	no	—
12	C₂²×D₄	—	4	14	no	—
13	C₂³×C₄	D₄	1	1	yes	characteristic
14	C₂×D₈	—	2	84	no	—
15	C₂×D₈	C₂³	1	56	yes	complemented
16	C₂²×C₈	D₄	1	7	yes	—
17	C₂²×C₈	C₂³	1	7	yes	—
18	D₁₆	C₂³	1	64	yes	direct product factor
19	C₂×C₁₆	C₂³	1	28	yes	complemented
20	C₂⁴	—	4	28	no	—
21	C₂⁴	—	8	16	no	—
22	C₂⁴	D₈	1	1	yes	characteristic
23	C₂×D₄	—	2	56	no	—
24	C₂×D₄	—	4	84	no	—
25	C₂²×C₄	D₈	1	7	yes	—
26	C₂²×C₄	C₂×D₄	1	7	yes	—
27	D₈	—	2	56	no	—
28	D₈	C₂⁴	1	16	yes	complemented
29	C₂×C₈	C₂×D₄	1	21	yes	—
30	C₂×C₈	C₂⁴	1	7	yes	—
31	C₁₆	C₂⁴	1	8	yes	complemented
32	C₂³	—	4	56	no	—
33	C₂³	—	8	112	no	—
34	C₂³	D₁₆	1	8	yes	direct product factor
35	C₂³	C₂×D₈	1	7	yes	—
36	D₄	—	2	16	no	—
37	D₄	—	4	56	no	—
38	C₂×C₄	C₂×D₈	1	21	yes	—
39	C₂×C₄	C₂²×D₄	1	7	yes	—
40	C₈	C₂²×D₄	1	7	yes	—
41	C₈	C₂⁵	1	1	yes	characteristic
42	C₂²	—	4	16	no	—
43	C₂²	—	8	112	no	—
44	C₂²	C₂×D₁₆	1	28	yes	direct product factor
45	C₂²	C₂²×D₈	1	7	yes	—
46	C₄	C₂²×D₈	1	7	yes	—
47	C₄	C₂³×D₄	1	1	yes	characteristic
48	C₂	—	8	16	no	—
49	C₂	C₂²×D₁₆	1	14	yes	direct product factor
50	C₂	C₂³×D₈	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂⁴	D₈
commutator, Frattini, cosocle	C₈	C₂⁵
LCS	G ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂⁴ ◁ C₂³×C₄ ◁ C₂³×C₈ ◁ G
LECS	G ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
1. C₂³×D₈	C₂	semidirect
2. C₂²×D₁₆	C₂	direct (N × H)
3. C₂³×C₁₆	C₂	semidirect
6. C₂²×D₈	C₂²	semidirect
8. C₂×D₁₆	C₂²	direct (N × H)
9. C₂²×C₁₆	C₂²	semidirect
15. C₂×D₈	C₂³	semidirect
18. D₁₆	C₂³	direct (N × H)
19. C₂×C₁₆	C₂³	semidirect
28. D₈	C₂⁴	semidirect
31. C₁₆	C₂⁴	semidirect
34. C₂³	D₁₆	direct (N × H)
44. C₂²	C₂×D₁₆	direct (N × H)
49. C₂	C₂²×D₁₆	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×D₈	2
C₂²×D₁₆	2
C₂³×C₁₆	2

Subgroups — C23×D16 #62625

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂³×D₁₆ #62625