Subgroups — Q₆₄×D₅₃ #20277018

Order 6784.

104 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Q₃₂×D₅₃	C₂	1	2	yes	maximal
2	Dic₈₄₈	C₂	1	1	yes	maximal, characteristic, complemented
3	#16810463	C₂	1	2	yes	maximal, complemented
4	C₃₂×D₅₃	C₂	1	1	yes	maximal, characteristic
5	C₅₃×Q₆₄	C₂	1	1	yes	maximal, characteristic, complemented
6	Q₁₆×D₅₃	—	2	2	no	—
7	Dic₄₂₄	C₂²	1	2	yes	—
8	#13133163	—	2	2	no	—
9	C₁₆×D₅₃	C₂²	1	1	yes	characteristic
10	#13133123	C₂²	1	1	yes	characteristic
11	Q₃₂×C₅₃	C₂²	1	2	yes	—
12	C₃₂×C₅₃	C₂²	1	1	yes	characteristic
13	Q₈×D₅₃	—	4	2	no	—
14	Q₁₆×C₅₃	—	2	2	no	—
15	#11719925	—	4	2	no	—
16	Dic₂₁₂	—	2	2	no	—
17	C₈×D₅₃	D₄	1	1	yes	characteristic
18	C₁₆×C₅₃	C₂³	1	1	yes	characteristic
19	#11719908	D₄	1	1	yes	characteristic
20	Q₈×C₅₃	—	4	2	no	—
21	C₄×D₅₃	—	8	2	no	—
22	C₄×D₅₃	D₈	1	1	yes	characteristic
23	Dic₁₀₆	—	4	2	no	—
24	Dic₁₀₆	—	8	2	no	—
25	C₈×C₅₃	C₂×D₄	1	1	yes	characteristic
26	#88322	D₈	1	1	yes	characteristic
27	C₂×D₅₃	D₁₆	1	1	yes	characteristic
28	C₄×C₅₃	—	8	2	no	—
29	C₄×C₅₃	C₂×D₈	1	1	yes	characteristic
30	Dic₅₃	—	8	2	no	—
31	Dic₅₃	D₁₆	1	1	yes	characteristic
32	C₂×Q₆₄	—	53	1	no	maximal, Sylow
33	C₂×C₅₃	C₂×D₁₆	1	1	yes	characteristic
34	D₅₃	Q₆₄	1	2	yes	direct product factor
35	C₂×Q₃₂	—	53	2	no	—
36	Q₆₄	—	53	2	no	—
37	Q₆₄	—	53	1	no	—
38	Q₆₄	D₅₃	1	1	yes	characteristic, direct product factor
39	C₂×C₃₂	—	53	1	no	—
40	C₅₃	C₂×Q₆₄	1	1	yes	characteristic, complemented, Sylow
41	C₂×Q₁₆	—	106	2	no	—
42	Q₃₂	—	53	2	no	—
43	Q₃₂	—	106	2	no	—
44	Q₃₂	C₂×D₅₃	1	2	yes	—
45	C₂×C₁₆	—	53	1	no	—
46	C₃₂	—	53	1	no	—
47	C₃₂	C₂×D₅₃	1	1	yes	characteristic
48	C₂×Q₈	—	212	2	no	—
49	Q₁₆	—	2	2	no	—
50	Q₁₆	—	106	2	no	—
51	Q₁₆	—	212	2	no	—
52	C₂×C₈	—	53	1	no	—
53	C₁₆	—	53	1	no	—
54	C₁₆	C₂²×D₅₃	1	1	yes	characteristic
55	Q₈	—	4	2	no	—
56	Q₈	—	424	2	no	—
57	Q₈	—	212	2	no	—
58	C₂×C₄	—	53	1	no	—
59	C₂×C₄	—	424	2	no	—
60	C₈	—	53	1	no	—
61	C₈	D₄×D₅₃	1	1	yes	characteristic
62	C₂²	—	53	1	no	—
63	C₄	—	8	2	no	—
64	C₄	—	53	1	no	—
65	C₄	—	424	2	no	—
66	C₄	D₈×D₅₃	1	1	yes	characteristic
67	C₂	—	53	2	no	—
68	C₂	D₁₆×D₅₃	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
2. Dic₈₄₈	C₂	semidirect
3. #16810463	C₂	semidirect
5. C₅₃×Q₆₄	C₂	semidirect
34. D₅₃	Q₆₄	direct (N × H)
38. Q₆₄	D₅₃	direct (N × H)
40. C₅₃	C₂×Q₆₄	semidirect

Subgroups — Q64×D53 #20277018

Conjugacy classes of subgroups

Complements

Subgroups — Q₆₄×D₅₃ #20277018