Subgroups — D₆₄×D₈₉ #36475469

Order 22784.

142 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₃₂×D₈₉	C₂	1	2	yes	maximal, complemented
2	D₅₆₉₆	C₂	1	1	yes	maximal, characteristic, complemented
3	#26018464	C₂	1	2	yes	maximal, complemented
4	C₆₄×D₈₉	C₂	1	1	yes	maximal, characteristic, complemented
5	C₈₉×D₆₄	C₂	1	1	yes	maximal, characteristic, complemented
6	D₁₆×D₈₉	—	2	2	no	—
7	D₂₈₄₈	C₂²	1	2	yes	complemented
8	#19151433	—	2	2	no	—
9	C₃₂×D₈₉	C₂²	1	1	yes	characteristic
10	#19151317	C₂²	1	1	yes	characteristic, complemented
11	D₃₂×C₈₉	C₂²	1	2	yes	complemented
12	C₆₄×C₈₉	C₂²	1	1	yes	characteristic, complemented
13	D₈×D₈₉	—	4	2	no	—
14	D₁₄₂₄	—	2	2	no	—
15	#15667953	—	4	2	no	—
16	C₁₆×D₈₉	D₄	1	1	yes	characteristic
17	#15667918	D₄	1	1	yes	characteristic
18	D₁₆×C₈₉	—	2	2	no	—
19	C₃₂×C₈₉	C₂³	1	1	yes	characteristic
20	D₄×D₈₉	—	8	2	no	—
21	D₇₁₂	—	4	2	no	—
22	#13083559	—	8	2	no	—
23	C₈×D₈₉	D₈	1	1	yes	characteristic
24	#13083549	D₈	1	1	yes	characteristic
25	D₈×C₈₉	—	4	2	no	—
26	C₁₆×C₈₉	C₂×D₄	1	1	yes	characteristic
27	C₂²×D₈₉	—	16	2	no	—
28	D₄×C₈₉	—	8	2	no	—
29	C₂²⋊D₈₉	—	16	2	no	—
30	D₃₅₆	—	8	2	no	—
31	C₄×D₈₉	D₁₆	1	1	yes	characteristic
32	C₈×C₈₉	C₂×D₈	1	1	yes	characteristic
33	#10623494	D₁₆	1	1	yes	characteristic
34	C₂²×C₈₉	—	16	2	no	—
35	C₂×D₈₉	—	16	2	no	—
36	C₂×D₈₉	—	32	4	no	—
37	C₂×D₈₉	D₃₂	1	1	yes	characteristic
38	C₄×C₈₉	C₂×D₁₆	1	1	yes	characteristic
39	Dic₈₉	D₃₂	1	1	yes	characteristic
40	C₂×D₆₄	—	89	1	no	maximal, Sylow
41	C₂×C₈₉	—	32	2	no	—
42	C₂×C₈₉	C₂×D₃₂	1	1	yes	characteristic
43	D₈₉	—	32	2	no	—
44	D₈₉	D₆₄	1	2	yes	direct product factor
45	C₂×D₃₂	—	89	2	no	—
46	D₆₄	—	89	2	no	—
47	D₆₄	—	89	1	no	—
48	D₆₄	D₈₉	1	1	yes	characteristic, direct product factor
49	C₂×C₆₄	—	89	1	no	—
50	C₈₉	C₂×D₆₄	1	1	yes	characteristic, complemented, Sylow
51	C₂×D₁₆	—	178	2	no	—
52	D₃₂	—	89	2	no	—
53	D₃₂	—	178	2	no	—
54	D₃₂	C₂×D₈₉	1	2	yes	complemented
55	C₂×C₃₂	—	89	1	no	—
56	C₆₄	—	89	1	no	—
57	C₆₄	C₂×D₈₉	1	1	yes	characteristic, complemented
58	C₂×D₈	—	356	2	no	—
59	D₁₆	—	2	2	no	—
60	D₁₆	—	356	2	no	—
61	D₁₆	—	178	2	no	—
62	C₂×C₁₆	—	89	1	no	—
63	C₃₂	—	89	1	no	—
64	C₃₂	C₂²×D₈₉	1	1	yes	characteristic
65	C₂×D₄	—	712	2	no	—
66	D₈	—	4	2	no	—
67	D₈	—	356	2	no	—
68	D₈	—	712	2	no	—
69	C₂×C₈	—	89	1	no	—
70	C₁₆	—	89	1	no	—
71	C₁₆	D₄×D₈₉	1	1	yes	characteristic
72	C₂³	—	1424	2	no	—
73	D₄	—	8	2	no	—
74	D₄	—	1424	2	no	—
75	D₄	—	712	2	no	—
76	C₂×C₄	—	89	1	no	—
77	C₈	—	89	1	no	—
78	C₈	D₈×D₈₉	1	1	yes	characteristic
79	C₂²	—	16	2	no	—
80	C₂²	—	2848	4	no	—
81	C₂²	—	89	1	no	—
82	C₂²	—	1424	2	no	—
83	C₄	—	89	1	no	—
84	C₄	D₁₆×D₈₉	1	1	yes	characteristic
85	C₂	—	32	2	no	—
86	C₂	—	2848	2	no	—
87	C₂	—	89	2	no	—
88	C₂	D₃₂×D₈₉	1	1	yes	characteristic

	subgroup	G/H
center	C₂	D₃₂×D₈₉
commutator, cosocle	C₃₂×C₈₉	C₂³
Frattini	C₃₂	C₂²×D₈₉
Fitting	C₈₉×D₆₄	C₂
socle	C₂×C₈₉	C₂×D₃₂
hypercenter	D₆₄	D₈₉
hypocenter	C₈₉	C₂×D₆₄
LCS	G ▷ C₃₂×C₈₉ ▷ C₁₆×C₈₉ ▷ C₈×C₈₉ ▷ C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈ ◁ C₁₆ ◁ C₃₂ ◁ D₆₄

Complements

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

N	H ≅ G/N	type
1. D₃₂×D₈₉	C₂	semidirect
2. D₅₆₉₆	C₂	semidirect
3. #26018464	C₂	semidirect
4. C₆₄×D₈₉	C₂	semidirect
5. C₈₉×D₆₄	C₂	semidirect
7. D₂₈₄₈	C₂²	semidirect
10. #19151317	C₂²	semidirect
11. D₃₂×C₈₉	C₂²	semidirect
12. C₆₄×C₈₉	C₂²	semidirect
44. D₈₉	D₆₄	direct (N × H)
48. D₆₄	D₈₉	direct (N × H)
50. C₈₉	C₂×D₆₄	semidirect
54. D₃₂	C₂×D₈₉	semidirect
57. C₆₄	C₂×D₈₉	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
D₃₂×D₈₉	2
D₅₆₉₆	2
#26018464	2
C₆₄×D₈₉	2
C₈₉×D₆₄	2
C₂×D₆₄	89

Subgroups — D64×D89 #36475469

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₆₄×D₈₉ #36475469