Subgroups — C₈₉×#29516 #36407364

Order 22784.

682 conjugacy classes of subgroups.

The subgroup lattice has 576 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈₉×#2860	C₂	1	1	yes	maximal, characteristic
2	C₄×#125×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₈₉×#2101	C₂	1	1	yes	maximal, characteristic, complemented
4	C₈₉×#2092	C₂	1	1	yes	maximal, characteristic
5	C₈₉×#2059	C₂	1	1	yes	maximal, characteristic, complemented
6	C₈₉×#2025	C₂	1	1	yes	maximal, characteristic
7	C₈₉×#1942	C₂	1	1	yes	maximal, characteristic, complemented
8	C₈₉×#1941	C₂	1	1	yes	maximal, characteristic, complemented
9	C₈₉×#1934	C₂	1	1	yes	maximal, characteristic
10	C₈₉×#1934	C₂	1	1	yes	maximal, characteristic
11	C₈₉×#1926	C₂	1	1	yes	maximal, characteristic
12	C₈₉×#1925	C₂	1	1	yes	maximal, characteristic
13	C₈₉×#1921	C₂	1	1	yes	maximal, characteristic, complemented
14	C₈₉×#1920	C₂	1	1	yes	maximal, characteristic, complemented
15	C₈₉×#1744	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#126×C₈₉	—	2	1	no	—
17	C₂×#125×C₈₉	C₂²	1	1	yes	characteristic
18	C₂×#107×C₈₉	C₂²	1	1	yes	characteristic
19	C₂×#107×C₈₉	C₂²	1	1	yes	characteristic
20	C₂×#106×C₈₉	C₂²	1	1	yes	characteristic
21	C₂×#106×C₈₉	C₂²	1	1	yes	characteristic
22	C₂×#102×C₈₉	C₂²	1	1	yes	characteristic
23	C₂×#102×C₈₉	C₂²	1	1	yes	characteristic
24	C₂×#102×C₈₉	C₂²	1	1	yes	characteristic
25	C₂×#102×C₈₉	C₂²	1	1	yes	characteristic
26	C₂×C₄×C₈×C₈₉	C₂²	1	1	yes	characteristic
27	C₂×C₄×C₈×C₈₉	C₂²	1	1	yes	characteristic
28	#390×C₈₉	C₂²	1	1	yes	characteristic
29	#390×C₈₉	C₂²	1	1	yes	characteristic
30	#390×C₈₉	C₂²	1	1	yes	characteristic
31	#389×C₈₉	C₂²	1	1	yes	characteristic
32	#389×C₈₉	C₂²	1	1	yes	characteristic
33	#389×C₈₉	C₂²	1	1	yes	characteristic
34	#389×C₈₉	C₂²	1	1	yes	characteristic
35	#389×C₈₉	C₂²	1	1	yes	characteristic
36	#388×C₈₉	—	2	1	no	—
37	#388×C₈₉	—	2	1	no	—
38	#388×C₈₉	—	2	1	no	—
39	#387×C₈₉	—	2	1	no	—
40	#387×C₈₉	—	2	1	no	—
41	#382×C₈₉	C₂²	1	1	yes	characteristic
42	C₄×C₄⋊C₄×C₈₉	—	2	1	no	—
43	C₄×C₄⋊C₄×C₈₉	—	2	1	no	—
44	C₄×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
45	C₄×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
46	C₄³×C₈₉	C₂²	1	1	yes	characteristic
47	#340×C₈₉	C₂²	1	1	yes	characteristic
48	#340×C₈₉	C₂²	1	1	yes	characteristic
49	#340×C₈₉	C₂²	1	1	yes	characteristic
50	#340×C₈₉	C₂²	1	1	yes	characteristic
51	#340×C₈₉	C₂²	1	1	yes	characteristic
52	#340×C₈₉	C₂²	1	1	yes	characteristic
53	#340×C₈₉	C₂²	1	1	yes	characteristic
54	#340×C₈₉	C₂²	1	1	yes	characteristic
55	#336×C₈₉	C₂²	1	1	yes	characteristic
56	#336×C₈₉	C₂²	1	1	yes	characteristic
57	#336×C₈₉	C₂²	1	1	yes	characteristic
58	#336×C₈₉	C₂²	1	1	yes	characteristic
59	C₂²×D₄×C₈₉	C₂³	1	1	yes	characteristic
60	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
61	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
62	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
63	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
64	#126×C₈₉	—	4	4	no	—
65	#125×C₈₉	—	2	2	no	—
66	#125×C₈₉	—	2	2	no	—
67	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
68	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
69	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
70	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
71	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
72	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
73	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
74	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
75	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
76	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
77	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
78	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
79	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
80	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
81	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
82	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
83	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
84	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
85	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
86	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
87	C₂×C₄²×C₈₉	—	2	1	no	—
88	C₂×C₄²×C₈₉	—	2	1	no	—
89	C₂×C₄²×C₈₉	D₄	1	1	yes	characteristic
90	C₂×C₄²×C₈₉	D₄	1	1	yes	characteristic
91	C₂×C₄²×C₈₉	D₄	1	1	yes	characteristic
92	C₂×C₄²×C₈₉	D₄	1	1	yes	characteristic
93	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
94	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
95	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
96	#107×C₈₉	—	2	2	no	—
97	#107×C₈₉	—	2	2	no	—
98	#106×C₈₉	—	2	2	no	—
99	#106×C₈₉	—	2	2	no	—
100	#102×C₈₉	—	2	2	no	—
101	#102×C₈₉	—	2	2	no	—
102	#102×C₈₉	—	2	2	no	—
103	#102×C₈₉	—	2	2	no	—
104	C₄×C₈×C₈₉	—	2	2	no	—
105	C₄×C₈×C₈₉	—	2	2	no	—
106	#95×C₈₉	—	2	1	no	—
107	#95×C₈₉	—	2	1	no	—
108	#95×C₈₉	—	2	1	no	—
109	#95×C₈₉	—	2	1	no	—
110	#95×C₈₉	—	2	1	no	—
111	#95×C₈₉	—	2	1	no	—
112	#95×C₈₉	—	2	1	no	—
113	#95×C₈₉	—	2	1	no	—
114	#95×C₈₉	—	2	1	no	—
115	C₂⁴×C₈₉	—	2	1	no	—
116	C₂×D₄×C₈₉	—	2	1	no	—
117	C₂×D₄×C₈₉	—	2	1	no	—
118	C₂×D₄×C₈₉	—	2	1	no	—
119	C₂×D₄×C₈₉	—	2	1	no	—
120	C₂×D₄×C₈₉	—	2	1	no	—
121	C₂×D₄×C₈₉	—	2	1	no	—
122	C₂²×C₄×C₈₉	—	2	1	no	—
123	C₂²×C₄×C₈₉	—	2	1	no	—
124	C₂²×C₄×C₈₉	—	2	1	no	—
125	C₂²×C₄×C₈₉	—	2	1	no	—
126	C₂²×C₄×C₈₉	—	2	1	no	—
127	C₂²×C₄×C₈₉	—	2	1	no	—
128	C₂²×C₄×C₈₉	—	2	1	no	—
129	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
130	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
131	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
132	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
133	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
134	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
135	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
136	C₂×C₈×C₈₉	—	2	1	no	—
137	C₂×C₈×C₈₉	—	2	1	no	—
138	C₂×C₈×C₈₉	—	2	1	no	—
139	C₂×C₈×C₈₉	—	2	1	no	—
140	C₂×C₈×C₈₉	—	2	1	no	—
141	C₂×C₈×C₈₉	—	2	1	no	—
142	C₂×C₈×C₈₉	—	2	1	no	—
143	C₂×C₈×C₈₉	—	2	1	no	—
144	C₂×C₈×C₈₉	—	2	1	no	—
145	C₂×C₈×C₈₉	—	2	1	no	—
146	C₂×C₈×C₈₉	#41	1	2	yes	—
147	C₂×C₈×C₈₉	#41	1	2	yes	—
148	C₄⋊C₄×C₈₉	—	2	4	no	—
149	C₄⋊C₄×C₈₉	—	2	4	no	—
150	C₄⋊C₄×C₈₉	—	2	1	no	—
151	C₄⋊C₄×C₈₉	—	2	1	no	—
152	C₄⋊C₄×C₈₉	—	2	1	no	—
153	C₄⋊C₄×C₈₉	—	2	1	no	—
154	C₄⋊C₄×C₈₉	—	2	1	no	—
155	C₄⋊C₄×C₈₉	—	2	1	no	—
156	C₄⋊C₄×C₈₉	—	2	1	no	—
157	C₄⋊C₄×C₈₉	—	2	1	no	—
158	C₄⋊C₄×C₈₉	—	2	1	no	—
159	C₄⋊C₄×C₈₉	—	2	1	no	—
160	C₄⋊C₄×C₈₉	—	2	1	no	—
161	C₄⋊C₄×C₈₉	—	2	1	no	—
162	C₄⋊C₄×C₈₉	—	4	2	no	—
163	C₄⋊C₄×C₈₉	—	4	2	no	—
164	C₄⋊C₄×C₈₉	—	4	2	no	—
165	C₄⋊C₄×C₈₉	—	4	2	no	—
166	C₄⋊C₄×C₈₉	—	4	2	no	—
167	C₄⋊C₄×C₈₉	#41	1	2	yes	—
168	C₄⋊C₄×C₈₉	#41	1	2	yes	—
169	C₂²⋊C₄×C₈₉	—	4	2	no	—
170	C₂²⋊C₄×C₈₉	—	4	2	no	—
171	C₂²⋊C₄×C₈₉	—	4	2	no	—
172	C₂²⋊C₄×C₈₉	—	4	2	no	—
173	C₂²⋊C₄×C₈₉	—	4	2	no	—
174	C₂²⋊C₄×C₈₉	—	4	2	no	—
175	C₄²×C₈₉	—	2	2	no	—
176	C₄²×C₈₉	—	2	2	no	—
177	C₄²×C₈₉	—	2	2	no	—
178	C₄²×C₈₉	—	2	1	no	—
179	C₄²×C₈₉	—	2	1	no	—
180	C₄²×C₈₉	—	2	1	no	—
181	C₄²×C₈₉	—	2	1	no	—
182	C₄²×C₈₉	—	2	1	no	—
183	C₄²×C₈₉	—	2	1	no	—
184	C₄²×C₈₉	—	4	1	no	—
185	C₄²×C₈₉	—	4	2	no	—
186	C₄²×C₈₉	—	4	2	no	—
187	C₂³×C₈₉	—	4	1	no	—
188	C₂³×C₈₉	—	4	1	no	—
189	C₂³×C₈₉	—	4	1	no	—
190	C₂³×C₈₉	—	4	1	no	—
191	C₂³×C₈₉	—	4	1	no	—
192	C₂³×C₈₉	—	4	1	no	—
193	C₂³×C₈₉	—	4	1	no	—
194	C₂³×C₈₉	C₂²×D₄	1	1	yes	characteristic
195	D₄×C₈₉	—	4	1	no	—
196	D₄×C₈₉	—	4	1	no	—
197	D₄×C₈₉	—	4	1	no	—
198	D₄×C₈₉	—	4	1	no	—
199	C₂×C₄×C₈₉	—	2	1	no	—
200	C₂×C₄×C₈₉	—	2	1	no	—
201	C₂×C₄×C₈₉	—	2	1	no	—
202	C₂×C₄×C₈₉	—	2	1	no	—
203	C₂×C₄×C₈₉	—	2	1	no	—
204	C₂×C₄×C₈₉	—	2	1	no	—
205	C₂×C₄×C₈₉	—	2	1	no	—
206	C₂×C₄×C₈₉	—	2	1	no	—
207	C₂×C₄×C₈₉	—	2	2	no	—
208	C₂×C₄×C₈₉	—	2	2	no	—
209	C₂×C₄×C₈₉	—	2	1	no	—
210	C₂×C₄×C₈₉	—	2	1	no	—
211	C₂×C₄×C₈₉	—	2	1	no	—
212	C₂×C₄×C₈₉	—	2	1	no	—
213	C₂×C₄×C₈₉	—	2	1	no	—
214	C₂×C₄×C₈₉	—	2	1	no	—
215	C₂×C₄×C₈₉	—	2	1	no	—
216	C₂×C₄×C₈₉	—	4	1	no	—
217	C₂×C₄×C₈₉	—	4	1	no	—
218	C₂×C₄×C₈₉	—	4	1	no	—
219	C₂×C₄×C₈₉	—	4	1	no	—
220	C₂×C₄×C₈₉	—	4	1	no	—
221	C₂×C₄×C₈₉	—	4	1	no	—
222	C₂×C₄×C₈₉	—	4	1	no	—
223	C₂×C₄×C₈₉	—	4	1	no	—
224	C₂×C₄×C₈₉	—	4	1	no	—
225	C₂×C₄×C₈₉	—	4	1	no	—
226	C₂×C₄×C₈₉	—	4	1	no	—
227	C₂×C₄×C₈₉	—	4	1	no	—
228	C₂×C₄×C₈₉	—	4	1	no	—
229	C₂×C₄×C₈₉	—	4	1	no	—
230	C₂×C₄×C₈₉	—	4	1	no	—
231	C₂×C₄×C₈₉	—	4	1	no	—
232	C₂×C₄×C₈₉	—	4	1	no	—
233	C₂×C₄×C₈₉	—	4	1	no	—
234	C₂×C₄×C₈₉	—	4	1	no	—
235	C₂×C₄×C₈₉	#135	1	2	yes	—
236	C₂×C₄×C₈₉	#135	1	2	yes	—
237	C₂×C₄×C₈₉	AGL(1,ℤ/8)	1	2	yes	—
238	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
239	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
240	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
241	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
242	C₂×C₄×C₈₉	2₋¹⁺⁴	1	1	yes	characteristic
243	C₂×C₄×C₈₉	2₋¹⁺⁴	1	1	yes	characteristic
244	C₈×C₈₉	—	2	2	no	—
245	C₈×C₈₉	—	2	2	no	—
246	C₈×C₈₉	—	4	1	no	—
247	C₈×C₈₉	—	4	1	no	—
248	C₂²×C₈₉	—	8	1	no	—
249	C₂²×C₈₉	—	8	1	no	—
250	C₂²×C₈₉	—	8	1	no	—
251	C₂²×C₈₉	—	8	1	no	—
252	C₂²×C₈₉	—	8	1	no	—
253	C₂²×C₈₉	—	8	1	no	—
254	C₂²×C₈₉	—	8	1	no	—
255	C₂²×C₈₉	#525	1	1	yes	characteristic
256	C₂²×C₈₉	#532	1	1	yes	characteristic
257	C₂²×C₈₉	#536	1	1	yes	characteristic
258	C₂²×C₈₉	C₂×#135	1	1	yes	characteristic
259	C₂²×C₈₉	C₂×#135	1	1	yes	characteristic
260	C₂²×C₈₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
261	C₂²×C₈₉	#575	1	1	yes	characteristic
262	C₄×C₈₉	—	2	2	no	—
263	C₄×C₈₉	—	2	2	no	—
264	C₄×C₈₉	—	2	2	no	—
265	C₄×C₈₉	—	4	1	no	—
266	C₄×C₈₉	—	4	2	no	—
267	C₄×C₈₉	—	4	1	no	—
268	C₄×C₈₉	—	4	2	no	—
269	C₄×C₈₉	—	4	1	no	—
270	C₄×C₈₉	—	8	1	no	—
271	C₄×C₈₉	—	8	1	no	—
272	C₄×C₈₉	—	8	1	no	—
273	C₄×C₈₉	—	8	1	no	—
274	C₄×C₈₉	—	8	1	no	—
275	C₄×C₈₉	#552	1	1	yes	characteristic
276	C₄×C₈₉	#552	1	1	yes	characteristic
277	C₄×C₈₉	#556	1	1	yes	characteristic
278	C₄×C₈₉	#556	1	1	yes	characteristic
279	#29516	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
280	C₂×C₈₉	—	16	1	no	—
281	C₂×C₈₉	#2604	1	1	yes	characteristic
282	C₂×C₈₉	#3102	1	1	yes	characteristic
283	C₂×C₈₉	#3106	1	1	yes	characteristic
284	C₂×C₈₉	#3168	1	1	yes	characteristic
285	C₂×C₈₉	#3180	1	1	yes	characteristic
286	C₂×C₈₉	#3228	1	1	yes	characteristic
287	C₂×C₈₉	#3232	1	1	yes	characteristic
288	#2860	C₂×C₈₉	1	1	yes	characteristic
289	C₄×#125	C₂×C₈₉	1	1	yes	characteristic, complemented
290	#2101	C₂×C₈₉	1	1	yes	characteristic, complemented
291	#2092	C₂×C₈₉	1	1	yes	characteristic
292	#2059	C₂×C₈₉	1	1	yes	characteristic, complemented
293	#2025	C₂×C₈₉	1	1	yes	characteristic
294	#1942	C₂×C₈₉	1	1	yes	characteristic, complemented
295	#1941	C₂×C₈₉	1	1	yes	characteristic, complemented
296	#1934	C₂×C₈₉	1	1	yes	characteristic
297	#1934	C₂×C₈₉	1	1	yes	characteristic
298	#1926	C₂×C₈₉	1	1	yes	characteristic
299	#1925	C₂×C₈₉	1	1	yes	characteristic
300	#1921	C₂×C₈₉	1	1	yes	characteristic, complemented
301	#1920	C₂×C₈₉	1	1	yes	characteristic, complemented
302	#1744	C₂×C₈₉	1	1	yes	characteristic, complemented
303	C₈₉	#29516	1	1	yes	characteristic, direct product factor, Sylow
304	C₂×#126	—	2	1	no	—
305	C₂×#125	C₂²×C₈₉	1	1	yes	characteristic
306	C₂×#107	C₂²×C₈₉	1	1	yes	characteristic
307	C₂×#107	C₂²×C₈₉	1	1	yes	characteristic
308	C₂×#106	C₂²×C₈₉	1	1	yes	characteristic
309	C₂×#106	C₂²×C₈₉	1	1	yes	characteristic
310	C₂×#102	C₂²×C₈₉	1	1	yes	characteristic
311	C₂×#102	C₂²×C₈₉	1	1	yes	characteristic
312	C₂×#102	C₂²×C₈₉	1	1	yes	characteristic
313	C₂×#102	C₂²×C₈₉	1	1	yes	characteristic
314	C₂×C₄×C₈	C₂²×C₈₉	1	1	yes	characteristic
315	C₂×C₄×C₈	C₂²×C₈₉	1	1	yes	characteristic
316	#390	C₂²×C₈₉	1	1	yes	characteristic
317	#390	C₂²×C₈₉	1	1	yes	characteristic
318	#390	C₂²×C₈₉	1	1	yes	characteristic
319	#389	C₂²×C₈₉	1	1	yes	characteristic
320	#389	C₂²×C₈₉	1	1	yes	characteristic
321	#389	C₂²×C₈₉	1	1	yes	characteristic
322	#389	C₂²×C₈₉	1	1	yes	characteristic
323	#389	C₂²×C₈₉	1	1	yes	characteristic
324	#388	—	2	1	no	—
325	#388	—	2	1	no	—
326	#388	—	2	1	no	—
327	#387	—	2	1	no	—
328	#387	—	2	1	no	—
329	#382	C₂²×C₈₉	1	1	yes	characteristic
330	C₄×C₄⋊C₄	—	2	1	no	—
331	C₄×C₄⋊C₄	—	2	1	no	—
332	C₄×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
333	C₄×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
334	C₄³	C₂²×C₈₉	1	1	yes	characteristic
335	#340	C₂²×C₈₉	1	1	yes	characteristic
336	#340	C₂²×C₈₉	1	1	yes	characteristic
337	#340	C₂²×C₈₉	1	1	yes	characteristic
338	#340	C₂²×C₈₉	1	1	yes	characteristic
339	#340	C₂²×C₈₉	1	1	yes	characteristic
340	#340	C₂²×C₈₉	1	1	yes	characteristic
341	#340	C₂²×C₈₉	1	1	yes	characteristic
342	#340	C₂²×C₈₉	1	1	yes	characteristic
343	#336	C₂²×C₈₉	1	1	yes	characteristic
344	#336	C₂²×C₈₉	1	1	yes	characteristic
345	#336	C₂²×C₈₉	1	1	yes	characteristic
346	#336	C₂²×C₈₉	1	1	yes	characteristic
347	C₂²×D₄	C₂³×C₈₉	1	1	yes	characteristic
348	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
349	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
350	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
351	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
352	#126	—	4	4	no	—
353	#125	—	2	2	no	—
354	#125	—	2	2	no	—
355	C₂×C₄⋊C₄	—	2	1	no	—
356	C₂×C₄⋊C₄	—	2	1	no	—
357	C₂×C₄⋊C₄	—	2	1	no	—
358	C₂×C₄⋊C₄	—	2	1	no	—
359	C₂×C₄⋊C₄	—	2	1	no	—
360	C₂×C₄⋊C₄	—	2	1	no	—
361	C₂×C₄⋊C₄	—	2	1	no	—
362	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
363	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
364	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
365	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
366	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
367	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
368	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
369	C₂×C₂²⋊C₄	—	2	1	no	—
370	C₂×C₂²⋊C₄	—	2	1	no	—
371	C₂×C₂²⋊C₄	—	2	1	no	—
372	C₂×C₂²⋊C₄	—	2	1	no	—
373	C₂×C₂²⋊C₄	—	2	1	no	—
374	C₂×C₂²⋊C₄	—	2	1	no	—
375	C₂×C₄²	—	2	1	no	—
376	C₂×C₄²	—	2	1	no	—
377	C₂×C₄²	D₄×C₈₉	1	1	yes	characteristic
378	C₂×C₄²	D₄×C₈₉	1	1	yes	characteristic
379	C₂×C₄²	D₄×C₈₉	1	1	yes	characteristic
380	C₂×C₄²	D₄×C₈₉	1	1	yes	characteristic
381	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
382	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
383	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
384	#107	—	2	2	no	—
385	#107	—	2	2	no	—
386	#106	—	2	2	no	—
387	#106	—	2	2	no	—
388	#102	—	2	2	no	—
389	#102	—	2	2	no	—
390	#102	—	2	2	no	—
391	#102	—	2	2	no	—
392	C₄×C₈	—	2	2	no	—
393	C₄×C₈	—	2	2	no	—
394	#95	—	2	1	no	—
395	#95	—	2	1	no	—
396	#95	—	2	1	no	—
397	#95	—	2	1	no	—
398	#95	—	2	1	no	—
399	#95	—	2	1	no	—
400	#95	—	2	1	no	—
401	#95	—	2	1	no	—
402	#95	—	2	1	no	—
403	C₂⁴	—	2	1	no	—
404	C₂×D₄	—	2	1	no	—
405	C₂×D₄	—	2	1	no	—
406	C₂×D₄	—	2	1	no	—
407	C₂×D₄	—	2	1	no	—
408	C₂×D₄	—	2	1	no	—
409	C₂×D₄	—	2	1	no	—
410	C₂²×C₄	—	2	1	no	—
411	C₂²×C₄	—	2	1	no	—
412	C₂²×C₄	—	2	1	no	—
413	C₂²×C₄	—	2	1	no	—
414	C₂²×C₄	—	2	1	no	—
415	C₂²×C₄	—	2	1	no	—
416	C₂²×C₄	—	2	1	no	—
417	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
418	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
419	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
420	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
421	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
422	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
423	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
424	C₂×C₈	—	2	1	no	—
425	C₂×C₈	—	2	1	no	—
426	C₂×C₈	—	2	1	no	—
427	C₂×C₈	—	2	1	no	—
428	C₂×C₈	—	2	1	no	—
429	C₂×C₈	—	2	1	no	—
430	C₂×C₈	—	2	1	no	—
431	C₂×C₈	—	2	1	no	—
432	C₂×C₈	—	2	1	no	—
433	C₂×C₈	—	2	1	no	—
434	C₂×C₈	#41×C₈₉	1	2	yes	—
435	C₂×C₈	#41×C₈₉	1	2	yes	—
436	C₄⋊C₄	—	2	4	no	—
437	C₄⋊C₄	—	2	4	no	—
438	C₄⋊C₄	—	2	1	no	—
439	C₄⋊C₄	—	2	1	no	—
440	C₄⋊C₄	—	2	1	no	—
441	C₄⋊C₄	—	2	1	no	—
442	C₄⋊C₄	—	2	1	no	—
443	C₄⋊C₄	—	2	1	no	—
444	C₄⋊C₄	—	2	1	no	—
445	C₄⋊C₄	—	2	1	no	—
446	C₄⋊C₄	—	2	1	no	—
447	C₄⋊C₄	—	2	1	no	—
448	C₄⋊C₄	—	2	1	no	—
449	C₄⋊C₄	—	2	1	no	—
450	C₄⋊C₄	—	4	2	no	—
451	C₄⋊C₄	—	4	2	no	—
452	C₄⋊C₄	—	4	2	no	—
453	C₄⋊C₄	—	4	2	no	—
454	C₄⋊C₄	—	4	2	no	—
455	C₄⋊C₄	#41×C₈₉	1	2	yes	—
456	C₄⋊C₄	#41×C₈₉	1	2	yes	—
457	C₂²⋊C₄	—	4	2	no	—
458	C₂²⋊C₄	—	4	2	no	—
459	C₂²⋊C₄	—	4	2	no	—
460	C₂²⋊C₄	—	4	2	no	—
461	C₂²⋊C₄	—	4	2	no	—
462	C₂²⋊C₄	—	4	2	no	—
463	C₄²	—	2	2	no	—
464	C₄²	—	2	2	no	—
465	C₄²	—	2	2	no	—
466	C₄²	—	2	1	no	—
467	C₄²	—	2	1	no	—
468	C₄²	—	2	1	no	—
469	C₄²	—	2	1	no	—
470	C₄²	—	2	1	no	—
471	C₄²	—	2	1	no	—
472	C₄²	—	4	1	no	—
473	C₄²	—	4	2	no	—
474	C₄²	—	4	2	no	—
475	C₂³	—	4	1	no	—
476	C₂³	—	4	1	no	—
477	C₂³	—	4	1	no	—
478	C₂³	—	4	1	no	—
479	C₂³	—	4	1	no	—
480	C₂³	—	4	1	no	—
481	C₂³	—	4	1	no	—
482	C₂³	C₂²×D₄×C₈₉	1	1	yes	characteristic
483	D₄	—	4	1	no	—
484	D₄	—	4	1	no	—
485	D₄	—	4	1	no	—
486	D₄	—	4	1	no	—
487	C₂×C₄	—	2	1	no	—
488	C₂×C₄	—	2	1	no	—
489	C₂×C₄	—	2	1	no	—
490	C₂×C₄	—	2	1	no	—
491	C₂×C₄	—	2	1	no	—
492	C₂×C₄	—	2	1	no	—
493	C₂×C₄	—	2	1	no	—
494	C₂×C₄	—	2	1	no	—
495	C₂×C₄	—	2	2	no	—
496	C₂×C₄	—	2	2	no	—
497	C₂×C₄	—	2	1	no	—
498	C₂×C₄	—	2	1	no	—
499	C₂×C₄	—	2	1	no	—
500	C₂×C₄	—	2	1	no	—
501	C₂×C₄	—	2	1	no	—
502	C₂×C₄	—	2	1	no	—
503	C₂×C₄	—	2	1	no	—
504	C₂×C₄	—	4	1	no	—
505	C₂×C₄	—	4	1	no	—
506	C₂×C₄	—	4	1	no	—
507	C₂×C₄	—	4	1	no	—
508	C₂×C₄	—	4	1	no	—
509	C₂×C₄	—	4	1	no	—
510	C₂×C₄	—	4	1	no	—
511	C₂×C₄	—	4	1	no	—
512	C₂×C₄	—	4	1	no	—
513	C₂×C₄	—	4	1	no	—
514	C₂×C₄	—	4	1	no	—
515	C₂×C₄	—	4	1	no	—
516	C₂×C₄	—	4	1	no	—
517	C₂×C₄	—	4	1	no	—
518	C₂×C₄	—	4	1	no	—
519	C₂×C₄	—	4	1	no	—
520	C₂×C₄	—	4	1	no	—
521	C₂×C₄	—	4	1	no	—
522	C₂×C₄	—	4	1	no	—
523	C₂×C₄	#135×C₈₉	1	2	yes	—
524	C₂×C₄	#135×C₈₉	1	2	yes	—
525	C₂×C₄	AGL(1,ℤ/8)×C₈₉	1	2	yes	—
526	C₂×C₄	C₂×#41×C₈₉	1	1	yes	characteristic
527	C₂×C₄	C₂×#41×C₈₉	1	1	yes	characteristic
528	C₂×C₄	C₂×#41×C₈₉	1	1	yes	characteristic
529	C₂×C₄	C₂×#41×C₈₉	1	1	yes	characteristic
530	C₂×C₄	2₋¹⁺⁴×C₈₉	1	1	yes	characteristic
531	C₂×C₄	2₋¹⁺⁴×C₈₉	1	1	yes	characteristic
532	C₈	—	2	2	no	—
533	C₈	—	2	2	no	—
534	C₈	—	4	1	no	—
535	C₈	—	4	1	no	—
536	C₂²	—	8	1	no	—
537	C₂²	—	8	1	no	—
538	C₂²	—	8	1	no	—
539	C₂²	—	8	1	no	—
540	C₂²	—	8	1	no	—
541	C₂²	—	8	1	no	—
542	C₂²	—	8	1	no	—
543	C₂²	#525×C₈₉	1	1	yes	characteristic
544	C₂²	#532×C₈₉	1	1	yes	characteristic
545	C₂²	#536×C₈₉	1	1	yes	characteristic
546	C₂²	C₂×#135×C₈₉	1	1	yes	characteristic
547	C₂²	C₂×#135×C₈₉	1	1	yes	characteristic
548	C₂²	C₂×AGL(1,ℤ/8)×C₈₉	1	1	yes	characteristic
549	C₂²	#575×C₈₉	1	1	yes	characteristic
550	C₄	—	2	2	no	—
551	C₄	—	2	2	no	—
552	C₄	—	2	2	no	—
553	C₄	—	4	1	no	—
554	C₄	—	4	2	no	—
555	C₄	—	4	1	no	—
556	C₄	—	4	2	no	—
557	C₄	—	4	1	no	—
558	C₄	—	8	1	no	—
559	C₄	—	8	1	no	—
560	C₄	—	8	1	no	—
561	C₄	—	8	1	no	—
562	C₄	—	8	1	no	—
563	C₄	#552×C₈₉	1	1	yes	characteristic
564	C₄	#552×C₈₉	1	1	yes	characteristic
565	C₄	#556×C₈₉	1	1	yes	characteristic
566	C₄	#556×C₈₉	1	1	yes	characteristic
567	C₂	—	16	1	no	—
568	C₂	C₈₉×#2604	1	1	yes	characteristic
569	C₂	C₈₉×#3102	1	1	yes	characteristic
570	C₂	C₈₉×#3106	1	1	yes	characteristic
571	C₂	C₈₉×#3168	1	1	yes	characteristic
572	C₂	C₈₉×#3180	1	1	yes	characteristic
573	C₂	C₈₉×#3228	1	1	yes	characteristic
574	C₂	C₈₉×#3232	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₈₉	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₈₉
prime radical	C₂²×D₄×C₈₉	C₂³
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₈₉ ◁ C₄³×C₈₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₄×#125×C₈₉	C₂	semidirect
3. C₈₉×#2101	C₂	semidirect
5. C₈₉×#2059	C₂	semidirect
7. C₈₉×#1942	C₂	semidirect
8. C₈₉×#1941	C₂	semidirect
13. C₈₉×#1921	C₂	semidirect
14. C₈₉×#1920	C₂	semidirect
15. C₈₉×#1744	C₂	semidirect
279. #29516	C₈₉	direct (N × H)
289. C₄×#125	C₂×C₈₉	semidirect
290. #2101	C₂×C₈₉	semidirect
292. #2059	C₂×C₈₉	semidirect
294. #1942	C₂×C₈₉	semidirect
295. #1941	C₂×C₈₉	semidirect
300. #1921	C₂×C₈₉	semidirect
301. #1920	C₂×C₈₉	semidirect
302. #1744	C₂×C₈₉	semidirect
303. C₈₉	#29516	direct (N × H)

Maximal subgroups

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

subgroup	index
C₈₉×#2860	2
C₄×#125×C₈₉	2
C₈₉×#2101	2
C₈₉×#2092	2
C₈₉×#2059	2
C₈₉×#2025	2
C₈₉×#1942	2
C₈₉×#1941	2
C₈₉×#1934	2
C₈₉×#1926	2
C₈₉×#1925	2
C₈₉×#1921	2
C₈₉×#1920	2
C₈₉×#1744	2
#29516	89

Subgroups — C89×#29516 #36407364

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#29516 #36407364