Subgroups — C₂³×D₄₀₄ #20265999

Order 6464.

1362 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁴×D₁₀₁	C₂	1	2	yes	maximal, complemented
2	C₂²×D₄₀₄	C₂	1	28	yes	maximal, direct product factor
3	C₂³×C₄×C₁₀₁	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂³×D₁₀₁	—	2	16	no	—
5	C₂³×D₁₀₁	C₂²	1	28	yes	complemented
6	C₂×D₄₀₄	C₂²	1	112	yes	direct product factor
7	C₂⁴×C₁₀₁	C₂²	1	1	yes	characteristic
8	C₂²×C₄×C₁₀₁	C₂²	1	14	yes	complemented
9	C₂³×C₁₀₁	D₄	1	8	yes	complemented
10	C₂³×C₁₀₁	C₂³	1	7	yes	—
11	C₂²×D₁₀₁	—	2	112	no	—
12	C₂²×D₁₀₁	C₂³	1	56	yes	complemented
13	C₂×C₄×C₁₀₁	C₂³	1	28	yes	complemented
14	D₄₀₄	C₂³	1	64	yes	direct product factor
15	C₂²×C₁₀₁	C₂×D₄	1	28	yes	complemented
16	C₂²×C₁₀₁	C₂⁴	1	7	yes	—
17	C₂×D₁₀₁	—	2	112	no	—
18	C₂×D₁₀₁	C₂⁴	1	16	yes	complemented
19	C₄×C₁₀₁	C₂⁴	1	8	yes	complemented
20	C₂×C₁₀₁	C₂²×D₄	1	14	yes	complemented
21	C₂×C₁₀₁	C₂⁵	1	1	yes	characteristic
22	D₁₀₁	—	2	16	no	—
23	C₁₀₁	C₂³×D₄	1	1	yes	characteristic, complemented, Sylow
24	C₂³×D₄	—	101	1	no	maximal, Sylow
25	C₂⁵	—	101	2	no	—
26	C₂²×D₄	—	101	28	no	—
27	C₂³×C₄	D₁₀₁	1	1	yes	characteristic, complemented
28	C₂⁴	—	101	28	no	—
29	C₂⁴	—	202	16	no	—
30	C₂⁴	C₂×D₁₀₁	1	1	yes	characteristic
31	C₂×D₄	—	101	112	no	—
32	C₂²×C₄	C₂×D₁₀₁	1	14	yes	complemented
33	C₂³	—	101	56	no	—
34	C₂³	—	202	112	no	—
35	C₂³	D₄₀₄	1	8	yes	direct product factor
36	C₂³	C₂²×D₁₀₁	1	7	yes	—
37	D₄	—	101	64	no	—
38	C₂×C₄	C₂²×D₁₀₁	1	28	yes	complemented
39	C₂²	—	101	16	no	—
40	C₂²	—	202	112	no	—
41	C₂²	C₂×D₄₀₄	1	28	yes	direct product factor
42	C₂²	C₂³×D₁₀₁	1	7	yes	—
43	C₄	C₂³×D₁₀₁	1	8	yes	complemented
44	C₂	—	202	16	no	—
45	C₂	C₂²×D₄₀₄	1	14	yes	direct product factor
46	C₂	C₂⁴×D₁₀₁	1	1	yes	characteristic

	subgroup	G/H
center	C₂⁴	C₂×D₁₀₁
commutator	C₂×C₁₀₁	C₂⁵
Frattini	C₂	C₂⁴×D₁₀₁
Fitting	C₂³×C₄×C₁₀₁	C₂
socle	C₂⁴×C₁₀₁	C₂²
hypercenter	C₂³×C₄	D₁₀₁
hypocenter	C₁₀₁	C₂³×D₄
LCS	G ▷ C₂×C₁₀₁ ▷ C₁₀₁
UCS	C₁ ◁ C₂⁴ ◁ C₂³×C₄

Complements

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

N	H ≅ G/N	type
1. C₂⁴×D₁₀₁	C₂	semidirect
2. C₂²×D₄₀₄	C₂	direct (N × H)
3. C₂³×C₄×C₁₀₁	C₂	semidirect
5. C₂³×D₁₀₁	C₂²	semidirect
6. C₂×D₄₀₄	C₂²	direct (N × H)
8. C₂²×C₄×C₁₀₁	C₂²	semidirect
9. C₂³×C₁₀₁	D₄	semidirect
12. C₂²×D₁₀₁	C₂³	semidirect
13. C₂×C₄×C₁₀₁	C₂³	semidirect
14. D₄₀₄	C₂³	direct (N × H)
15. C₂²×C₁₀₁	C₂×D₄	semidirect
18. C₂×D₁₀₁	C₂⁴	semidirect
19. C₄×C₁₀₁	C₂⁴	semidirect
20. C₂×C₁₀₁	C₂²×D₄	semidirect
23. C₁₀₁	C₂³×D₄	semidirect
27. C₂³×C₄	D₁₀₁	semidirect
32. C₂²×C₄	C₂×D₁₀₁	semidirect
35. C₂³	D₄₀₄	direct (N × H)
38. C₂×C₄	C₂²×D₁₀₁	semidirect
41. C₂²	C₂×D₄₀₄	direct (N × H)
43. C₄	C₂³×D₁₀₁	semidirect
45. C₂	C₂²×D₄₀₄	direct (N × H)

Subgroups — C23×D404 #20265999

Conjugacy classes of subgroups

Complements

Subgroups — C₂³×D₄₀₄ #20265999