Subgroups — Q₆₄×D₆₁ #21448122

Order 7808.

104 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Q₃₂×D₆₁	C₂	1	2	yes	maximal
2	Dic₉₇₆	C₂	1	1	yes	maximal, characteristic, complemented
3	#16839602	C₂	1	2	yes	maximal, complemented
4	C₃₂×D₆₁	C₂	1	1	yes	maximal, characteristic
5	C₆₁×Q₆₄	C₂	1	1	yes	maximal, characteristic, complemented
6	Q₁₆×D₆₁	—	2	2	no	—
7	Dic₄₈₈	C₂²	1	2	yes	—
8	#14519723	—	2	2	no	—
9	C₁₆×D₆₁	C₂²	1	1	yes	characteristic
10	#14519683	C₂²	1	1	yes	characteristic
11	Q₃₂×C₆₁	C₂²	1	2	yes	—
12	C₃₂×C₆₁	C₂²	1	1	yes	characteristic
13	Q₈×D₆₁	—	4	2	no	—
14	Q₁₆×C₆₁	—	2	2	no	—
15	#11758202	—	4	2	no	—
16	Dic₂₄₄	—	2	2	no	—
17	C₈×D₆₁	D₄	1	1	yes	characteristic
18	C₁₆×C₆₁	C₂³	1	1	yes	characteristic
19	#11758185	D₄	1	1	yes	characteristic
20	Q₈×C₆₁	—	4	2	no	—
21	C₄×D₆₁	—	8	2	no	—
22	C₄×D₆₁	D₈	1	1	yes	characteristic
23	Dic₁₂₂	—	4	2	no	—
24	Dic₁₂₂	—	8	2	no	—
25	C₈×C₆₁	C₂×D₄	1	1	yes	characteristic
26	#92418	D₈	1	1	yes	characteristic
27	C₂×D₆₁	D₁₆	1	1	yes	characteristic
28	C₄×C₆₁	—	8	2	no	—
29	C₄×C₆₁	C₂×D₈	1	1	yes	characteristic
30	Dic₆₁	—	8	2	no	—
31	Dic₆₁	D₁₆	1	1	yes	characteristic
32	C₂×Q₆₄	—	61	1	no	maximal, Sylow
33	C₂×C₆₁	C₂×D₁₆	1	1	yes	characteristic
34	D₆₁	Q₆₄	1	2	yes	direct product factor
35	C₂×Q₃₂	—	61	2	no	—
36	Q₆₄	—	61	2	no	—
37	Q₆₄	—	61	1	no	—
38	Q₆₄	D₆₁	1	1	yes	characteristic, direct product factor
39	C₂×C₃₂	—	61	1	no	—
40	C₆₁	C₂×Q₆₄	1	1	yes	characteristic, complemented, Sylow
41	C₂×Q₁₆	—	122	2	no	—
42	Q₃₂	—	61	2	no	—
43	Q₃₂	—	122	2	no	—
44	Q₃₂	C₂×D₆₁	1	2	yes	—
45	C₂×C₁₆	—	61	1	no	—
46	C₃₂	—	61	1	no	—
47	C₃₂	C₂×D₆₁	1	1	yes	characteristic
48	C₂×Q₈	—	244	2	no	—
49	Q₁₆	—	2	2	no	—
50	Q₁₆	—	122	2	no	—
51	Q₁₆	—	244	2	no	—
52	C₂×C₈	—	61	1	no	—
53	C₁₆	—	61	1	no	—
54	C₁₆	C₂²×D₆₁	1	1	yes	characteristic
55	Q₈	—	4	2	no	—
56	Q₈	—	488	2	no	—
57	Q₈	—	244	2	no	—
58	C₂×C₄	—	61	1	no	—
59	C₂×C₄	—	488	2	no	—
60	C₈	—	61	1	no	—
61	C₈	D₄×D₆₁	1	1	yes	characteristic
62	C₂²	—	61	1	no	—
63	C₄	—	8	2	no	—
64	C₄	—	61	1	no	—
65	C₄	—	488	2	no	—
66	C₄	D₈×D₆₁	1	1	yes	characteristic
67	C₂	—	61	2	no	—
68	C₂	D₁₆×D₆₁	1	1	yes	characteristic

	subgroup	G/H
center	C₂	D₁₆×D₆₁
commutator	C₁₆×C₆₁	C₂³
Frattini	C₁₆	C₂²×D₆₁
Fitting	C₆₁×Q₆₄	C₂
socle	C₂×C₆₁	C₂×D₁₆
hypercenter	Q₆₄	D₆₁
hypocenter	C₆₁	C₂×Q₆₄
LCS	G ▷ C₁₆×C₆₁ ▷ C₈×C₆₁ ▷ C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈ ◁ C₁₆ ◁ Q₆₄

Complements

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

N	H ≅ G/N	type
2. Dic₉₇₆	C₂	semidirect
3. #16839602	C₂	semidirect
5. C₆₁×Q₆₄	C₂	semidirect
34. D₆₁	Q₆₄	direct (N × H)
38. Q₆₄	D₆₁	direct (N × H)
40. C₆₁	C₂×Q₆₄	semidirect

Subgroups — Q64×D61 #21448122

Conjugacy classes of subgroups

Complements

Subgroups — Q₆₄×D₆₁ #21448122