Subgroups — C₂×C₆₄×D₈₉ #36475461

Order 22784.

142 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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

	subgroup	G/H
center, hypercenter	C₂×C₆₄	D₈₉
commutator, hypocenter	C₈₉	C₂²×C₆₄
Frattini	C₃₂	C₂²×D₈₉
Fitting	C₂×C₆₄×C₈₉	C₂
socle	C₂²×C₈₉	C₂×C₃₂
prime radical	C₂²×D₈₉	C₃₂
cosocle	C₃₂×C₈₉	C₂³
LCS	G ▷ C₈₉
UCS	C₁ ◁ C₂×C₆₄

Complements

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

N	H ≅ G/N	type
2. C₂×#19151317	C₂	semidirect
3. C₆₄×D₈₉	C₂	direct (N × H)
4. C₂×C₆₄×C₈₉	C₂	semidirect
9. #19151317	C₂²	semidirect
11. C₆₄×C₈₉	C₂²	semidirect
37. C₂×D₈₉	C₆₄	direct (N × H)
43. C₂×C₈₉	C₂×C₆₄	semidirect
45. D₈₉	C₂×C₆₄	direct (N × H)
49. C₂×C₆₄	D₈₉	direct (N × H)
50. C₈₉	C₂²×C₆₄	semidirect
57. C₆₄	C₂×D₈₉	direct (N × H)
89. C₂	C₆₄×D₈₉	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₃₂×D₈₉	2
C₂×#19151317	2
C₆₄×D₈₉	2
C₂×C₆₄×C₈₉	2
C₂²×C₆₄	89

Subgroups — C2×C64×D89 #36475461

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₆₄×D₈₉ #36475461