Subgroups — C₂×D₁₆₄₈ #20268212

Order 6592.

98 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₈₂₄	C₂	1	2	yes	maximal, complemented
2	D₁₆₄₈	C₂	1	4	yes	maximal, direct product factor
3	C₂×C₁₆×C₁₀₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×D₄₁₂	—	2	2	no	—
5	D₈₂₄	—	2	2	no	—
6	D₈₂₄	C₂²	1	4	yes	complemented
7	C₂×C₈×C₁₀₃	C₂²	1	1	yes	characteristic
8	C₁₆×C₁₀₃	C₂²	1	2	yes	complemented
9	C₂²×D₁₀₃	—	4	2	no	—
10	C₂×C₄×C₁₀₃	D₄	1	1	yes	characteristic
11	D₄₁₂	—	2	4	no	—
12	D₄₁₂	—	4	2	no	—
13	C₈×C₁₀₃	D₄	1	1	yes	characteristic
14	C₈×C₁₀₃	C₂³	1	1	yes	characteristic
15	C₂²×C₁₀₃	D₈	1	1	yes	characteristic
16	C₂×D₁₀₃	—	4	4	no	—
17	C₂×D₁₀₃	—	8	4	no	—
18	C₄×C₁₀₃	D₈	1	1	yes	characteristic
19	C₄×C₁₀₃	C₂×D₄	1	1	yes	characteristic
20	C₂×C₁₀₃	D₁₆	1	2	yes	complemented
21	C₂×C₁₀₃	C₂×D₈	1	1	yes	characteristic
22	D₁₀₃	—	8	4	no	—
23	C₁₀₃	C₂×D₁₆	1	1	yes	characteristic, complemented, Sylow
24	C₂×D₁₆	—	103	1	no	maximal, Sylow
25	C₂×D₈	—	103	2	no	—
26	D₁₆	—	103	4	no	—
27	C₂×C₁₆	D₁₀₃	1	1	yes	characteristic, complemented
28	C₂×D₄	—	206	2	no	—
29	D₈	—	103	4	no	—
30	D₈	—	206	2	no	—
31	C₂×C₈	C₂×D₁₀₃	1	1	yes	characteristic
32	C₁₆	C₂×D₁₀₃	1	2	yes	complemented
33	C₂³	—	412	2	no	—
34	D₄	—	412	2	no	—
35	D₄	—	206	4	no	—
36	C₂×C₄	D₄₁₂	1	1	yes	characteristic
37	C₈	D₄₁₂	1	1	yes	characteristic
38	C₈	C₂²×D₁₀₃	1	1	yes	characteristic
39	C₂²	—	824	4	no	—
40	C₂²	—	412	4	no	—
41	C₂²	D₈₂₄	1	1	yes	characteristic
42	C₄	D₈₂₄	1	1	yes	characteristic
43	C₄	C₂×D₄₁₂	1	1	yes	characteristic
44	C₂	—	824	4	no	—
45	C₂	D₁₆₄₈	1	2	yes	direct product factor
46	C₂	C₂×D₈₂₄	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₈₂₄
commutator	C₈×C₁₀₃	C₂³
Frattini	C₈	C₂²×D₁₀₃
Fitting	C₂×C₁₆×C₁₀₃	C₂
socle	C₂²×C₁₀₃	D₈
hypercenter	C₂×C₁₆	D₁₀₃
hypocenter	C₁₀₃	C₂×D₁₆
LCS	G ▷ C₈×C₁₀₃ ▷ C₄×C₁₀₃ ▷ C₂×C₁₀₃ ▷ C₁₀₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆

Complements

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

N	H ≅ G/N	type
1. C₂×D₈₂₄	C₂	semidirect
2. D₁₆₄₈	C₂	direct (N × H)
3. C₂×C₁₆×C₁₀₃	C₂	semidirect
6. D₈₂₄	C₂²	semidirect
8. C₁₆×C₁₀₃	C₂²	semidirect
20. C₂×C₁₀₃	D₁₆	semidirect
23. C₁₀₃	C₂×D₁₆	semidirect
27. C₂×C₁₆	D₁₀₃	semidirect
32. C₁₆	C₂×D₁₀₃	semidirect
45. C₂	D₁₆₄₈	direct (N × H)

Subgroups — C2×D1648 #20268212

Conjugacy classes of subgroups

Complements

Subgroups — C₂×D₁₆₄₈ #20268212