Subgroups — C₆₄×Dic₈₉ #36442230

Order 22784.

86 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#19151317	C₂	1	1	yes	maximal, characteristic
2	C₃₂×Dic₈₉	C₂	1	1	yes	maximal, characteristic
3	C₂×C₆₄×C₈₉	C₂	1	1	yes	maximal, characteristic
4	C₂×#15667918	C₄	1	1	yes	characteristic
5	C₁₆×Dic₈₉	C₄	1	1	yes	characteristic
6	#19151317	C₄	1	2	yes	complemented
7	C₂×C₃₂×C₈₉	C₂²	1	1	yes	characteristic
8	C₆₄×C₈₉	C₄	1	2	yes	complemented
9	C₂×#13083549	C₈	1	1	yes	characteristic
10	C₈×Dic₈₉	C₈	1	1	yes	characteristic
11	#15667918	C₈	1	2	yes	—
12	C₂×C₁₆×C₈₉	C₂×C₄	1	1	yes	characteristic
13	C₃₂×C₈₉	C₂×C₄	1	1	yes	characteristic
14	C₃₂×C₈₉	C₂×C₄	1	1	yes	characteristic
15	C₂×#10623494	C₁₆	1	1	yes	characteristic
16	C₄×Dic₈₉	C₁₆	1	1	yes	characteristic
17	#13083549	C₁₆	1	2	yes	—
18	C₂×C₈×C₈₉	C₂×C₈	1	1	yes	characteristic
19	C₁₆×C₈₉	C₄²	1	1	yes	characteristic
20	C₁₆×C₈₉	C₂×C₈	1	1	yes	characteristic
21	C₂×C₄×C₈₉	C₂×C₁₆	1	1	yes	characteristic
22	C₂×Dic₈₉	C₃₂	1	2	yes	—
23	C₈×C₈₉	C₄×C₈	1	1	yes	characteristic
24	C₈×C₈₉	C₂×C₁₆	1	1	yes	characteristic
25	#10623494	C₃₂	1	2	yes	—
26	C₂²×C₈₉	C₂×C₃₂	1	1	yes	characteristic
27	C₄×C₈₉	C₄×C₁₆	1	1	yes	characteristic
28	C₄×C₈₉	C₂×C₃₂	1	1	yes	characteristic
29	Dic₈₉	C₆₄	1	4	yes	direct product factor
30	C₄×C₆₄	—	89	1	no	maximal, Sylow
31	C₂×C₈₉	C₄×C₃₂	1	1	yes	characteristic
32	C₂×C₈₉	C₂×C₆₄	1	2	yes	—
33	C₂×C₆₄	—	89	1	no	—
34	C₂×C₆₄	D₈₉	1	1	yes	characteristic
35	C₄×C₃₂	—	89	1	no	—
36	C₈₉	C₄×C₆₄	1	1	yes	characteristic, complemented, Sylow
37	C₂×C₃₂	—	89	1	no	—
38	C₂×C₃₂	C₂×D₈₉	1	1	yes	characteristic
39	C₄×C₁₆	—	89	1	no	—
40	C₆₄	—	89	2	no	—
41	C₆₄	Dic₈₉	1	2	yes	direct product factor
42	C₂×C₁₆	—	89	1	no	—
43	C₂×C₁₆	C₄×D₈₉	1	1	yes	characteristic
44	C₄×C₈	—	89	1	no	—
45	C₃₂	—	89	2	no	—
46	C₃₂	C₄×D₈₉	1	1	yes	characteristic
47	C₃₂	C₂×Dic₈₉	1	1	yes	characteristic
48	C₂×C₈	—	89	1	no	—
49	C₂×C₈	C₈×D₈₉	1	1	yes	characteristic
50	C₄²	—	89	1	no	—
51	C₁₆	—	89	2	no	—
52	C₁₆	C₄×Dic₈₉	1	1	yes	characteristic
53	C₁₆	C₈×D₈₉	1	1	yes	characteristic
54	C₂×C₄	—	89	2	no	—
55	C₂×C₄	C₁₆×D₈₉	1	1	yes	characteristic
56	C₈	—	89	2	no	—
57	C₈	C₈×Dic₈₉	1	1	yes	characteristic
58	C₈	C₁₆×D₈₉	1	1	yes	characteristic
59	C₂²	C₃₂×D₈₉	1	1	yes	characteristic
60	C₄	—	89	4	no	—
61	C₄	C₁₆×Dic₈₉	1	1	yes	characteristic
62	C₄	C₃₂×D₈₉	1	1	yes	characteristic
63	C₂	C₃₂×Dic₈₉	1	1	yes	characteristic
64	C₂	C₆₄×D₈₉	1	2	yes	—

	subgroup	G/H
center, hypercenter	C₂×C₆₄	D₈₉
commutator, hypocenter	C₈₉	C₄×C₆₄
Frattini	C₂×C₃₂	C₂×D₈₉
Fitting	C₂×C₆₄×C₈₉	C₂
socle, prime radical	C₂²×C₈₉	C₂×C₃₂
cosocle	C₂×C₃₂×C₈₉	C₂²
LCS	G ▷ C₈₉
UCS	C₁ ◁ C₂×C₆₄

Complements

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

N	H ≅ G/N	type
6. #19151317	C₄	semidirect
8. C₆₄×C₈₉	C₄	semidirect
29. Dic₈₉	C₆₄	direct (N × H)
36. C₈₉	C₄×C₆₄	semidirect
41. C₆₄	Dic₈₉	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×#19151317	2
C₃₂×Dic₈₉	2
C₂×C₆₄×C₈₉	2
C₄×C₆₄	89

Subgroups — C64×Dic89 #36442230

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₄×Dic₈₉ #36442230