Subgroups — C₂²×#95×D₈₉ #36712594

Order 22784.

14334 conjugacy classes of subgroups.

The subgroup lattice has 186 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁴×C₄×D₈₉	C₂	1	3	yes	maximal
2	C₂²×#15667919	C₂	1	3	yes	maximal, complemented
3	C₂×#95×D₈₉	C₂	1	24	yes	maximal, direct product factor
4	C₂²×#95×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂⁵×D₈₉	C₂²	1	1	yes	characteristic
6	C₂⁴×Dic₈₉	C₂²	1	3	yes	—
7	C₂³×C₄×D₈₉	—	2	48	no	—
8	C₂³×C₄×D₈₉	C₄	1	48	yes	complemented
9	C₂³×C₄×D₈₉	C₂²	1	36	yes	—
10	C₂×#15667919	C₂²	1	36	yes	complemented
11	#95×D₈₉	C₂²	1	64	yes	direct product factor
12	C₂⁴×C₄×C₈₉	C₂²	1	3	yes	—
13	C₂×#95×C₈₉	C₂²	1	12	yes	complemented
14	C₂⁴×D₈₉	C₂×C₄	1	24	yes	—
15	C₂⁴×D₈₉	D₄	1	24	yes	—
16	C₂⁴×D₈₉	Q₈	1	8	yes	—
17	C₂⁴×D₈₉	C₂³	1	6	yes	—
18	C₂³×Dic₈₉	—	2	24	no	—
19	C₂³×Dic₈₉	C₂×C₄	1	24	yes	complemented
20	C₂³×Dic₈₉	C₂³	1	18	yes	—
21	C₂²×C₄×D₈₉	—	2	384	no	—
22	C₂²×C₄×D₈₉	—	2	288	no	—
23	C₂²×C₄×D₈₉	C₂×C₄	1	288	yes	complemented
24	C₂²×C₄×D₈₉	C₂³	1	48	yes	—
25	#15667919	C₂³	1	48	yes	complemented
26	C₂⁵×C₈₉	C₂³	1	1	yes	characteristic
27	C₂³×C₄×C₈₉	—	2	24	no	—
28	C₂³×C₄×C₈₉	C₂×C₄	1	24	yes	complemented
29	C₂³×C₄×C₈₉	C₂³	1	18	yes	—
30	#95×C₈₉	C₂³	1	16	yes	complemented
31	C₂³×D₈₉	C₄²	1	64	yes	—
32	C₂³×D₈₉	C₂²⋊C₄	1	192	yes	—
33	C₂³×D₈₉	C₄⋊C₄	1	192	yes	—
34	C₂³×D₈₉	C₂²×C₄	1	72	yes	—
35	C₂³×D₈₉	C₂×D₄	1	72	yes	—
36	C₂³×D₈₉	C₂×Q₈	1	24	yes	—
37	C₂³×D₈₉	C₂⁴	1	4	yes	—
38	C₂²×Dic₈₉	—	2	96	no	—
39	C₂²×Dic₈₉	—	2	72	no	—
40	C₂²×Dic₈₉	C₂²×C₄	1	72	yes	complemented
41	C₂²×Dic₈₉	C₂⁴	1	12	yes	—
42	C₂×C₄×D₈₉	—	2	1152	no	—
43	C₂×C₄×D₈₉	—	2	192	no	—
44	C₂×C₄×D₈₉	C₂²×C₄	1	192	yes	complemented
45	C₂⁴×C₈₉	C₂²×C₄	1	12	yes	—
46	C₂⁴×C₈₉	C₂×D₄	1	12	yes	—
47	C₂⁴×C₈₉	C₂×Q₈	1	4	yes	—
48	C₂⁴×C₈₉	C₂⁴	1	3	yes	—
49	C₂²×C₄×C₈₉	—	2	96	no	—
50	C₂²×C₄×C₈₉	—	2	72	no	—
51	C₂²×C₄×C₈₉	C₂²×C₄	1	72	yes	complemented
52	C₂²×C₄×C₈₉	C₂⁴	1	12	yes	—
53	C₂³×C₈₉	C₂×C₄²	1	16	yes	—
54	C₂³×C₈₉	C₂×C₂²⋊C₄	1	48	yes	—
55	C₂³×C₈₉	C₂×C₄⋊C₄	1	48	yes	—
56	C₂³×C₈₉	C₂³×C₄	1	18	yes	—
57	C₂³×C₈₉	C₂²×D₄	1	18	yes	—
58	C₂³×C₈₉	C₂²×Q₈	1	6	yes	—
59	C₂³×C₈₉	C₂⁵	1	1	yes	characteristic
60	C₂²×D₈₉	#95	1	512	yes	direct product factor
61	C₂²×D₈₉	C₂×C₄²	1	96	yes	—
62	C₂²×D₈₉	C₂×C₂²⋊C₄	1	288	yes	—
63	C₂²×D₈₉	C₂×C₄⋊C₄	1	288	yes	—
64	C₂²×D₈₉	C₂³×C₄	1	24	yes	—
65	C₂²×D₈₉	C₂²×D₄	1	24	yes	—
66	C₂²×D₈₉	C₂²×Q₈	1	8	yes	—
67	C₂×C₄×C₈₉	—	2	144	no	—
68	C₂×C₄×C₈₉	—	2	24	no	—
69	C₂×C₄×C₈₉	C₂³×C₄	1	24	yes	complemented
70	C₂×Dic₈₉	—	2	144	no	—
71	C₂×Dic₈₉	—	2	24	no	—
72	C₂×Dic₈₉	C₂³×C₄	1	24	yes	complemented
73	C₄×D₈₉	—	2	384	no	—
74	C₂²×C₈₉	C₂×#95	1	64	yes	complemented
75	C₂²×C₈₉	C₂²×C₄²	1	12	yes	—
76	C₂²×C₈₉	C₂²×C₂²⋊C₄	1	36	yes	—
77	C₂²×C₈₉	C₂²×C₄⋊C₄	1	36	yes	—
78	C₂²×C₈₉	C₂⁴×C₄	1	3	yes	—
79	C₂²×C₈₉	C₂³×D₄	1	3	yes	—
80	C₂²×C₈₉	C₂³×Q₈	1	1	yes	characteristic
81	C₂×D₈₉	C₂×#95	1	384	yes	direct product factor
82	C₂×D₈₉	C₂²×C₄²	1	16	yes	—
83	C₂×D₈₉	C₂²×C₂²⋊C₄	1	48	yes	—
84	C₂×D₈₉	C₂²×C₄⋊C₄	1	48	yes	—
85	C₄×C₈₉	—	2	24	no	—
86	Dic₈₉	—	2	24	no	—
87	C₂³×#95	—	89	1	no	maximal, Sylow
88	C₂×C₈₉	C₂²×#95	1	24	yes	complemented
89	C₂×C₈₉	C₂³×C₄²	1	1	yes	characteristic
90	C₂×C₈₉	C₂³×C₂²⋊C₄	1	3	yes	—
91	C₂×C₈₉	C₂³×C₄⋊C₄	1	3	yes	—
92	D₈₉	C₂²×#95	1	32	yes	direct product factor
93	C₂⁵×C₄	—	89	3	no	—
94	C₂²×#95	—	89	24	no	—
95	C₂²×#95	—	89	3	no	—
96	C₂²×#95	D₈₉	1	1	yes	characteristic, direct product factor
97	C₈₉	C₂³×#95	1	1	yes	characteristic, complemented, Sylow
98	C₂⁶	—	89	1	no	—
99	C₂⁴×C₄	—	89	3	no	—
100	C₂⁴×C₄	—	89	48	no	—
101	C₂⁴×C₄	—	89	36	no	—
102	C₂⁴×C₄	—	178	48	no	—
103	C₂⁴×C₄	C₂×D₈₉	1	3	yes	—
104	C₂×#95	—	89	36	no	—
105	C₂×#95	—	89	64	no	—
106	C₂×#95	C₂×D₈₉	1	12	yes	direct product factor
107	C₂⁵	—	89	24	no	—
108	C₂⁵	—	89	24	no	—
109	C₂⁵	—	89	8	no	—
110	C₂⁵	—	89	6	no	—
111	C₂⁵	C₂²×D₈₉	1	1	yes	characteristic
112	C₂³×C₄	—	2	24	no	—
113	C₂³×C₄	—	89	24	no	—
114	C₂³×C₄	—	89	18	no	—
115	C₂³×C₄	—	89	288	no	—
116	C₂³×C₄	—	89	48	no	—
117	C₂³×C₄	—	178	288	no	—
118	C₂³×C₄	—	178	384	no	—
119	C₂³×C₄	—	178	24	no	—
120	C₂³×C₄	C₄×D₈₉	1	24	yes	complemented
121	C₂³×C₄	C₂²×D₈₉	1	18	yes	—
122	#95	—	89	48	no	—
123	#95	C₂²×D₈₉	1	16	yes	direct product factor
124	C₂⁴	—	89	72	no	—
125	C₂⁴	—	89	72	no	—
126	C₂⁴	—	89	24	no	—
127	C₂⁴	—	89	4	no	—
128	C₂⁴	—	89	64	no	—
129	C₂⁴	—	89	192	no	—
130	C₂⁴	—	89	192	no	—
131	C₂⁴	C₂×C₄×D₈₉	1	12	yes	—
132	C₂⁴	D₄×D₈₉	1	12	yes	—
133	C₂⁴	Q₈×D₈₉	1	4	yes	—
134	C₂⁴	C₂³×D₈₉	1	3	yes	—
135	C₂²×C₄	—	2	72	no	—
136	C₂²×C₄	—	2	96	no	—
137	C₂²×C₄	—	89	72	no	—
138	C₂²×C₄	—	89	12	no	—
139	C₂²×C₄	—	89	192	no	—
140	C₂²×C₄	—	178	192	no	—
141	C₂²×C₄	—	178	1152	no	—
142	C₂²×C₄	—	178	72	no	—
143	C₂²×C₄	—	178	96	no	—
144	C₂²×C₄	C₂×C₄×D₈₉	1	72	yes	complemented
145	C₂²×C₄	C₂³×D₈₉	1	12	yes	—
146	C₂³	—	89	24	no	—
147	C₂³	—	89	24	no	—
148	C₂³	—	89	8	no	—
149	C₂³	—	89	512	no	—
150	C₂³	—	89	96	no	—
151	C₂³	—	89	288	no	—
152	C₂³	—	89	288	no	—
153	C₂³	C₄²×D₈₉	1	16	yes	—
154	C₂³	C₂²⋊C₄×D₈₉	1	48	yes	—
155	C₂³	C₄⋊C₄×D₈₉	1	48	yes	—
156	C₂³	C₂²×C₄×D₈₉	1	18	yes	—
157	C₂³	C₂×D₄×D₈₉	1	18	yes	—
158	C₂³	C₂×Q₈×D₈₉	1	6	yes	—
159	C₂³	C₂⁴×D₈₉	1	1	yes	characteristic
160	C₂×C₄	—	2	24	no	—
161	C₂×C₄	—	2	144	no	—
162	C₂×C₄	—	89	24	no	—
163	C₂×C₄	—	178	384	no	—
164	C₂×C₄	—	178	24	no	—
165	C₂×C₄	—	178	144	no	—
166	C₂×C₄	C₂²×C₄×D₈₉	1	24	yes	complemented
167	C₂²	—	89	48	no	—
168	C₂²	—	89	48	no	—
169	C₂²	—	89	384	no	—
170	C₂²	—	89	16	no	—
171	C₂²	#95×D₈₉	1	64	yes	direct product factor
172	C₂²	C₂×C₄²×D₈₉	1	12	yes	—
173	C₂²	C₂×C₂²⋊C₄×D₈₉	1	36	yes	—
174	C₂²	C₂×C₄⋊C₄×D₈₉	1	36	yes	—
175	C₂²	C₂³×C₄×D₈₉	1	3	yes	—
176	C₂²	C₂²×D₄×D₈₉	1	3	yes	—
177	C₂²	C₂²×Q₈×D₈₉	1	1	yes	characteristic
178	C₄	—	2	24	no	—
179	C₄	—	178	24	no	—
180	C₂	—	89	32	no	—
181	C₂	C₂×#95×D₈₉	1	24	yes	direct product factor
182	C₂	C₂²×C₄²×D₈₉	1	1	yes	characteristic
183	C₂	C₂²×C₂²⋊C₄×D₈₉	1	3	yes	—
184	C₂	C₂²×C₄⋊C₄×D₈₉	1	3	yes	—

	subgroup	G/H
center	C₂⁵	C₂²×D₈₉
commutator	C₂×C₈₉	C₂³×C₄²
Frattini	C₂³	C₂⁴×D₈₉
Fitting	C₂²×#95×C₈₉	C₂
socle	C₂⁵×C₈₉	C₂³
prime radical	C₂⁵×D₈₉	C₂²
cosocle	C₂³×C₈₉	C₂⁵
hypercenter	C₂²×#95	D₈₉
hypocenter	C₈₉	C₂³×#95
LCS	G ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂⁵ ◁ C₂²×#95

Complements

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

N	H ≅ G/N	type
2. C₂²×#15667919	C₂	semidirect
3. C₂×#95×D₈₉	C₂	direct (N × H)
4. C₂²×#95×C₈₉	C₂	semidirect
8. C₂³×C₄×D₈₉	C₄	semidirect
10. C₂×#15667919	C₂²	semidirect
11. #95×D₈₉	C₂²	direct (N × H)
13. C₂×#95×C₈₉	C₂²	semidirect
19. C₂³×Dic₈₉	C₂×C₄	semidirect
23. C₂²×C₄×D₈₉	C₂×C₄	semidirect
25. #15667919	C₂³	semidirect
28. C₂³×C₄×C₈₉	C₂×C₄	semidirect
30. #95×C₈₉	C₂³	semidirect
40. C₂²×Dic₈₉	C₂²×C₄	semidirect
44. C₂×C₄×D₈₉	C₂²×C₄	semidirect
51. C₂²×C₄×C₈₉	C₂²×C₄	semidirect
60. C₂²×D₈₉	#95	direct (N × H)
69. C₂×C₄×C₈₉	C₂³×C₄	semidirect
72. C₂×Dic₈₉	C₂³×C₄	semidirect
74. C₂²×C₈₉	C₂×#95	semidirect
81. C₂×D₈₉	C₂×#95	direct (N × H)
88. C₂×C₈₉	C₂²×#95	semidirect
92. D₈₉	C₂²×#95	direct (N × H)
96. C₂²×#95	D₈₉	direct (N × H)
97. C₈₉	C₂³×#95	semidirect
106. C₂×#95	C₂×D₈₉	direct (N × H)
120. C₂³×C₄	C₄×D₈₉	semidirect
123. #95	C₂²×D₈₉	direct (N × H)
144. C₂²×C₄	C₂×C₄×D₈₉	semidirect
166. C₂×C₄	C₂²×C₄×D₈₉	semidirect
171. C₂²	#95×D₈₉	direct (N × H)
181. C₂	C₂×#95×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
C₂⁴×C₄×D₈₉	2
C₂²×#15667919	2
C₂×#95×D₈₉	2
C₂²×#95×C₈₉	2
C₂³×#95	89

Subgroups — C22×#95×D89 #36712594

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×#95×D₈₉ #36712594