Subgroups — C₂×Dic₈₄₈ #20277020

Order 6784.

104 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Dic₄₂₄	C₂	1	2	yes	maximal
2	Dic₈₄₈	C₂	1	4	yes	maximal, direct product factor
3	C₂×C₃₂×C₅₃	C₂	1	1	yes	maximal, characteristic
4	C₂×Dic₂₁₂	—	2	2	no	—
5	Dic₄₂₄	—	2	2	no	—
6	Dic₄₂₄	C₂²	1	4	yes	—
7	C₂×C₁₆×C₅₃	C₂²	1	1	yes	characteristic
8	C₃₂×C₅₃	C₂²	1	2	yes	—
9	C₂×Dic₁₀₆	—	4	2	no	—
10	C₂×C₈×C₅₃	D₄	1	1	yes	characteristic
11	Dic₂₁₂	—	2	4	no	—
12	Dic₂₁₂	—	4	2	no	—
13	C₁₆×C₅₃	D₄	1	1	yes	characteristic
14	C₁₆×C₅₃	C₂³	1	1	yes	characteristic
15	C₂×C₄×C₅₃	D₈	1	1	yes	characteristic
16	C₂×Dic₅₃	—	8	2	no	—
17	Dic₁₀₆	—	4	4	no	—
18	Dic₁₀₆	—	8	2	no	—
19	C₈×C₅₃	D₈	1	1	yes	characteristic
20	C₈×C₅₃	C₂×D₄	1	1	yes	characteristic
21	C₂²×C₅₃	D₁₆	1	1	yes	characteristic
22	C₄×C₅₃	D₁₆	1	1	yes	characteristic
23	C₄×C₅₃	C₂×D₈	1	1	yes	characteristic
24	Dic₅₃	—	8	4	no	—
25	C₂×Q₆₄	—	53	1	no	maximal, Sylow
26	C₂×C₅₃	Q₆₄	1	2	yes	complemented
27	C₂×C₅₃	C₂×D₁₆	1	1	yes	characteristic
28	C₂×Q₃₂	—	53	2	no	—
29	Q₆₄	—	53	4	no	—
30	C₂×C₃₂	D₅₃	1	1	yes	characteristic
31	C₅₃	C₂×Q₆₄	1	1	yes	characteristic, complemented, Sylow
32	C₂×Q₁₆	—	106	2	no	—
33	Q₃₂	—	53	4	no	—
34	Q₃₂	—	106	2	no	—
35	C₂×C₁₆	C₂×D₅₃	1	1	yes	characteristic
36	C₃₂	C₂×D₅₃	1	2	yes	—
37	C₂×Q₈	—	212	2	no	—
38	Q₁₆	—	106	4	no	—
39	Q₁₆	—	212	2	no	—
40	C₂×C₈	D₂₁₂	1	1	yes	characteristic
41	C₁₆	D₂₁₂	1	1	yes	characteristic
42	C₁₆	C₂²×D₅₃	1	1	yes	characteristic
43	Q₈	—	424	2	no	—
44	Q₈	—	212	4	no	—
45	C₂×C₄	—	424	2	no	—
46	C₂×C₄	D₄₂₄	1	1	yes	characteristic
47	C₈	D₄₂₄	1	1	yes	characteristic
48	C₈	C₂×D₂₁₂	1	1	yes	characteristic
49	C₂²	D₈₄₈	1	1	yes	characteristic
50	C₄	—	424	4	no	—
51	C₄	D₈₄₈	1	1	yes	characteristic
52	C₄	C₂×D₄₂₄	1	1	yes	characteristic
53	C₂	Dic₈₄₈	1	2	yes	direct product factor
54	C₂	C₂×D₈₄₈	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₈₄₈
commutator	C₁₆×C₅₃	C₂³
Frattini	C₁₆	C₂²×D₅₃
Fitting	C₂×C₃₂×C₅₃	C₂
socle	C₂²×C₅₃	D₁₆
hypercenter	C₂×C₃₂	D₅₃
hypocenter	C₅₃	C₂×Q₆₄
LCS	G ▷ C₁₆×C₅₃ ▷ C₈×C₅₃ ▷ C₄×C₅₃ ▷ C₂×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆ ◁ C₂×C₃₂

Complements

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

N	H ≅ G/N	type
2. Dic₈₄₈	C₂	direct (N × H)
26. C₂×C₅₃	Q₆₄	semidirect
31. C₅₃	C₂×Q₆₄	semidirect
53. C₂	Dic₈₄₈	direct (N × H)

Subgroups — C2×Dic848 #20277020

Conjugacy classes of subgroups

Complements

Subgroups — C₂×Dic₈₄₈ #20277020