Subgroups — C₂²×D₈₀₈ #20265947

Order 6464.

338 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×D₄₀₄	C₂	1	2	yes	maximal, complemented
2	C₂×D₈₀₈	C₂	1	12	yes	maximal, direct product factor
3	C₂²×C₈×C₁₀₁	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂³×D₁₀₁	—	2	2	no	—
5	C₂×D₄₀₄	—	2	6	no	—
6	C₂×D₄₀₄	C₂²	1	12	yes	complemented
7	D₈₀₈	C₂²	1	16	yes	direct product factor
8	C₂²×C₄×C₁₀₁	C₂²	1	1	yes	characteristic
9	C₂×C₈×C₁₀₁	C₂²	1	6	yes	complemented
10	C₂³×C₁₀₁	D₄	1	1	yes	characteristic
11	C₂²×D₁₀₁	—	2	12	no	—
12	C₂²×D₁₀₁	—	4	8	no	—
13	C₂×C₄×C₁₀₁	D₄	1	3	yes	—
14	C₂×C₄×C₁₀₁	C₂³	1	3	yes	—
15	D₄₀₄	—	2	12	no	—
16	D₄₀₄	C₂³	1	8	yes	complemented
17	C₈×C₁₀₁	C₂³	1	4	yes	complemented
18	C₂²×C₁₀₁	D₈	1	4	yes	complemented
19	C₂²×C₁₀₁	C₂×D₄	1	3	yes	—
20	C₂×D₁₀₁	—	2	8	no	—
21	C₂×D₁₀₁	—	4	24	no	—
22	C₄×C₁₀₁	C₂×D₄	1	3	yes	—
23	C₄×C₁₀₁	C₂⁴	1	1	yes	characteristic
24	C₂×C₁₀₁	C₂×D₈	1	6	yes	complemented
25	C₂×C₁₀₁	C₂²×D₄	1	1	yes	characteristic
26	D₁₀₁	—	4	8	no	—
27	C₁₀₁	C₂²×D₈	1	1	yes	characteristic, complemented, Sylow
28	C₂²×D₈	—	101	1	no	maximal, Sylow
29	C₂²×D₄	—	101	2	no	—
30	C₂×D₈	—	101	12	no	—
31	C₂²×C₈	D₁₀₁	1	1	yes	characteristic, complemented
32	C₂⁴	—	202	2	no	—
33	C₂×D₄	—	101	12	no	—
34	C₂×D₄	—	202	6	no	—
35	C₂²×C₄	C₂×D₁₀₁	1	1	yes	characteristic
36	D₈	—	101	16	no	—
37	C₂×C₈	C₂×D₁₀₁	1	6	yes	complemented
38	C₂³	—	404	8	no	—
39	C₂³	—	202	12	no	—
40	C₂³	D₄₀₄	1	1	yes	characteristic
41	D₄	—	101	8	no	—
42	D₄	—	202	12	no	—
43	C₂×C₄	D₄₀₄	1	3	yes	—
44	C₂×C₄	C₂²×D₁₀₁	1	3	yes	—
45	C₈	C₂²×D₁₀₁	1	4	yes	complemented
46	C₂²	—	404	24	no	—
47	C₂²	—	202	8	no	—
48	C₂²	D₈₀₈	1	4	yes	direct product factor
49	C₂²	C₂×D₄₀₄	1	3	yes	—
50	C₄	C₂×D₄₀₄	1	3	yes	—
51	C₄	C₂³×D₁₀₁	1	1	yes	characteristic
52	C₂	—	404	8	no	—
53	C₂	C₂×D₈₀₈	1	6	yes	direct product factor
54	C₂	C₂²×D₄₀₄	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	D₄₀₄
commutator	C₄×C₁₀₁	C₂⁴
Frattini	C₄	C₂³×D₁₀₁
Fitting	C₂²×C₈×C₁₀₁	C₂
socle	C₂³×C₁₀₁	D₄
hypercenter	C₂²×C₈	D₁₀₁
hypocenter	C₁₀₁	C₂²×D₈
LCS	G ▷ C₄×C₁₀₁ ▷ C₂×C₁₀₁ ▷ C₁₀₁
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂²×C₈

Complements

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

N	H ≅ G/N	type
1. C₂²×D₄₀₄	C₂	semidirect
2. C₂×D₈₀₈	C₂	direct (N × H)
3. C₂²×C₈×C₁₀₁	C₂	semidirect
6. C₂×D₄₀₄	C₂²	semidirect
7. D₈₀₈	C₂²	direct (N × H)
9. C₂×C₈×C₁₀₁	C₂²	semidirect
16. D₄₀₄	C₂³	semidirect
17. C₈×C₁₀₁	C₂³	semidirect
18. C₂²×C₁₀₁	D₈	semidirect
24. C₂×C₁₀₁	C₂×D₈	semidirect
27. C₁₀₁	C₂²×D₈	semidirect
31. C₂²×C₈	D₁₀₁	semidirect
37. C₂×C₈	C₂×D₁₀₁	semidirect
45. C₈	C₂²×D₁₀₁	semidirect
48. C₂²	D₈₀₈	direct (N × H)
53. C₂	C₂×D₈₀₈	direct (N × H)

Subgroups — C22×D808 #20265947

Conjugacy classes of subgroups

Complements

Subgroups — C₂²×D₈₀₈ #20265947