Subgroups — Q₆₄×D₇₃ #22612234

Order 9344.

104 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Q₃₂×D₇₃	C₂	1	2	yes	maximal
2	Dic₁₁₆₈	C₂	1	1	yes	maximal, characteristic, complemented
3	#17988427	C₂	1	2	yes	maximal, complemented
4	C₃₂×D₇₃	C₂	1	1	yes	maximal, characteristic
5	Q₆₄×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
6	Q₁₆×D₇₃	—	2	2	no	—
7	Dic₅₈₄	C₂²	1	2	yes	—
8	#14556537	—	2	2	no	—
9	C₁₆×D₇₃	C₂²	1	1	yes	characteristic
10	#14556497	C₂²	1	1	yes	characteristic
11	Q₃₂×C₇₃	C₂²	1	2	yes	—
12	C₃₂×C₇₃	C₂²	1	1	yes	characteristic
13	Q₈×D₇₃	—	4	2	no	—
14	Dic₂₉₂	—	2	2	no	—
15	#11924018	—	4	2	no	—
16	C₈×D₇₃	D₄	1	1	yes	characteristic
17	#11924003	D₄	1	1	yes	characteristic
18	Q₁₆×C₇₃	—	2	2	no	—
19	C₁₆×C₇₃	C₂³	1	1	yes	characteristic
20	Q₈×C₇₃	—	4	2	no	—
21	C₄×D₇₃	—	8	2	no	—
22	C₄×D₇₃	D₈	1	1	yes	characteristic
23	Dic₁₄₆	—	4	2	no	—
24	Dic₁₄₆	—	8	2	no	—
25	C₈×C₇₃	C₂×D₄	1	1	yes	characteristic
26	#10596831	D₈	1	1	yes	characteristic
27	C₂×D₇₃	D₁₆	1	1	yes	characteristic
28	C₄×C₇₃	—	8	2	no	—
29	C₄×C₇₃	C₂×D₈	1	1	yes	characteristic
30	Dic₇₃	—	8	2	no	—
31	Dic₇₃	D₁₆	1	1	yes	characteristic
32	C₂×C₇₃	C₂×D₁₆	1	1	yes	characteristic
33	D₇₃	Q₆₄	1	2	yes	direct product factor
34	C₂×Q₆₄	—	73	1	no	maximal, Sylow
35	C₇₃	C₂×Q₆₄	1	1	yes	characteristic, complemented, Sylow
36	C₂×Q₃₂	—	73	2	no	—
37	Q₆₄	—	73	2	no	—
38	Q₆₄	—	73	1	no	—
39	Q₆₄	D₇₃	1	1	yes	characteristic, direct product factor
40	C₂×C₃₂	—	73	1	no	—
41	C₂×Q₁₆	—	146	2	no	—
42	Q₃₂	—	73	2	no	—
43	Q₃₂	—	146	2	no	—
44	Q₃₂	C₂×D₇₃	1	2	yes	—
45	C₂×C₁₆	—	73	1	no	—
46	C₃₂	—	73	1	no	—
47	C₃₂	C₂×D₇₃	1	1	yes	characteristic
48	C₂×Q₈	—	292	2	no	—
49	Q₁₆	—	2	2	no	—
50	Q₁₆	—	292	2	no	—
51	Q₁₆	—	146	2	no	—
52	C₂×C₈	—	73	1	no	—
53	C₁₆	—	73	1	no	—
54	C₁₆	C₂²×D₇₃	1	1	yes	characteristic
55	Q₈	—	4	2	no	—
56	Q₈	—	292	2	no	—
57	Q₈	—	584	2	no	—
58	C₂×C₄	—	584	2	no	—
59	C₂×C₄	—	73	1	no	—
60	C₈	—	73	1	no	—
61	C₈	D₄×D₇₃	1	1	yes	characteristic
62	C₂²	—	73	1	no	—
63	C₄	—	8	2	no	—
64	C₄	—	584	2	no	—
65	C₄	—	73	1	no	—
66	C₄	D₈×D₇₃	1	1	yes	characteristic
67	C₂	—	73	2	no	—
68	C₂	D₁₆×D₇₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂	D₁₆×D₇₃
commutator	C₁₆×C₇₃	C₂³
Frattini	C₁₆	C₂²×D₇₃
Fitting	Q₆₄×C₇₃	C₂
socle	C₂×C₇₃	C₂×D₁₆
hypercenter	Q₆₄	D₇₃
hypocenter	C₇₃	C₂×Q₆₄
LCS	G ▷ C₁₆×C₇₃ ▷ C₈×C₇₃ ▷ C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈ ◁ C₁₆ ◁ Q₆₄

Complements

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

N	H ≅ G/N	type
2. Dic₁₁₆₈	C₂	semidirect
3. #17988427	C₂	semidirect
5. Q₆₄×C₇₃	C₂	semidirect
33. D₇₃	Q₆₄	direct (N × H)
35. C₇₃	C₂×Q₆₄	semidirect
39. Q₆₄	D₇₃	direct (N × H)

Subgroups — Q64×D73 #22612234

Conjugacy classes of subgroups

Complements

Subgroups — Q₆₄×D₇₃ #22612234