Subgroups — #564×Dic₈₉ #36717150

Order 22784.

1800 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26023438	C₂	1	15	yes	maximal
2	#125×Dic₈₉	C₂	1	15	yes	maximal
3	C₂×#564×C₈₉	C₂	1	1	yes	maximal, characteristic
4	#19151497	C₂²	1	30	yes	—
5	#19151484	C₂²	1	60	yes	—
6	#19151464	C₂²	1	15	yes	—
7	C₄⋊C₄×Dic₈₉	C₂²	1	30	yes	—
8	C₄²×Dic₈₉	C₂²	1	5	yes	—
9	#564×C₈₉	C₄	1	16	yes	complemented
10	C₂×#125×C₈₉	C₂²	1	15	yes	—
11	C₂×C₄⋊Dic₈₉	C₂³	1	30	yes	—
12	C₂×C₄×Dic₈₉	C₂³	1	15	yes	—
13	C₂×C₄×Dic₈₉	C₂³	1	15	yes	—
14	#15667919	C₂³	1	60	yes	—
15	#125×C₈₉	C₂×C₄	1	120	yes	—
16	C₂×C₄⋊C₄×C₈₉	C₂³	1	30	yes	—
17	C₂×C₄²×C₈₉	C₂³	1	5	yes	—
18	C₂²×Dic₈₉	C₂⁴	1	15	yes	—
19	C₂²×Dic₈₉	C₂⁴	1	1	yes	characteristic
20	C₄⋊Dic₈₉	—	4	30	no	—
21	C₄×Dic₈₉	—	2	30	no	—
22	C₄×Dic₈₉	—	4	15	no	—
23	C₂²×C₄×C₈₉	C₂⁴	1	15	yes	—
24	C₄⋊C₄×C₈₉	C₂²×C₄	1	120	yes	—
25	C₄²×C₈₉	C₂²×C₄	1	20	yes	—
26	C₂³×C₈₉	C₂⁵	1	1	yes	characteristic
27	C₂×C₄×C₈₉	—	2	15	no	—
28	C₂×C₄×C₈₉	—	2	15	no	—
29	C₂×C₄×C₈₉	C₂³×C₄	1	30	yes	—
30	C₂×Dic₈₉	—	2	15	no	—
31	C₂×Dic₈₉	—	2	30	no	—
32	C₂×Dic₈₉	2₋¹⁺⁴	1	6	yes	—
33	C₂²×C₈₉	C₂⁴×C₄	1	1	yes	characteristic
34	C₂²×C₈₉	C₂×2₋¹⁺⁴	1	3	yes	—
35	C₂²×C₈₉	#585	1	3	yes	—
36	C₄×C₈₉	—	2	30	no	—
37	Dic₈₉	—	4	15	no	—
38	Dic₈₉	#564	1	4	yes	direct product factor
39	C₄×#564	—	89	1	no	maximal, Sylow
40	C₂×C₈₉	C₄×2₋¹⁺⁴	1	3	yes	—
41	C₂×C₈₉	C₂×#564	1	1	yes	characteristic
42	C₂×C₈₉	#3531	1	3	yes	—
43	C₂×#564	D₈₉	1	1	yes	characteristic
44	#2382	—	89	15	no	—
45	C₄×#125	—	89	15	no	—
46	C₈₉	C₄×#564	1	1	yes	characteristic, complemented, Sylow
47	#564	Dic₈₉	1	16	yes	direct product factor
48	C₂×#125	C₂×D₈₉	1	15	yes	—
49	#389	—	89	30	no	—
50	#387	—	89	60	no	—
51	#382	—	89	15	no	—
52	C₄×C₄⋊C₄	—	89	30	no	—
53	C₄³	—	89	5	no	—
54	#125	C₂×Dic₈₉	1	120	yes	—
55	C₂×C₄⋊C₄	—	89	30	no	—
56	C₂×C₄⋊C₄	C₂²×D₈₉	1	30	yes	—
57	C₂×C₄²	—	89	15	no	—
58	C₂×C₄²	—	89	15	no	—
59	C₂×C₄²	C₂²×D₈₉	1	5	yes	—
60	#95	—	89	60	no	—
61	C₂²×C₄	—	89	1	no	—
62	C₂²×C₄	—	89	15	no	—
63	C₂²×C₄	C₂³×D₈₉	1	15	yes	—
64	C₄⋊C₄	—	356	30	no	—
65	C₄⋊C₄	C₂²×Dic₈₉	1	120	yes	—
66	C₄²	—	356	15	no	—
67	C₄²	—	178	30	no	—
68	C₄²	C₂²×Dic₈₉	1	20	yes	—
69	C₂³	C₂⁴×D₈₉	1	1	yes	characteristic
70	C₂×C₄	—	2	15	no	—
71	C₂×C₄	—	2	15	no	—
72	C₂×C₄	—	89	6	no	—
73	C₂×C₄	—	178	15	no	—
74	C₂×C₄	—	178	30	no	—
75	C₂×C₄	C₂³×Dic₈₉	1	30	yes	—
76	C₂²	C₂⁴×Dic₈₉	1	1	yes	characteristic
77	C₂²	2₋¹⁺⁴×D₈₉	1	3	yes	—
78	C₂²	#19152435	1	3	yes	—
79	C₄	—	2	30	no	—
80	C₄	—	89	4	no	—
81	C₄	—	356	15	no	—
82	C₂	2₋¹⁺⁴×Dic₈₉	1	3	yes	—
83	C₂	#564×D₈₉	1	1	yes	characteristic
84	C₂	#26034400	1	3	yes	—

	subgroup	G/H
center, Frattini	C₂³	C₂⁴×D₈₉
commutator	C₂²×C₈₉	C₂⁴×C₄
Fitting	C₂×#564×C₈₉	C₂
socle, prime radical, cosocle	C₂³×C₈₉	C₂⁵
hypercenter	C₂×#564	D₈₉
hypocenter	C₈₉	C₄×#564
LCS	G ▷ C₂²×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂³ ◁ C₂×#564

Complements

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

N	H ≅ G/N	type
9. #564×C₈₉	C₄	semidirect
38. Dic₈₉	#564	direct (N × H)
46. C₈₉	C₄×#564	semidirect
47. #564	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
#26023438	2
#125×Dic₈₉	2
C₂×#564×C₈₉	2
C₄×#564	89

Subgroups — #564×Dic89 #36717150

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #564×Dic₈₉ #36717150