Subgroups — C₈₉×#62166 #36440014

Order 22784.

1750 conjugacy classes of subgroups.

The subgroup lattice has 1032 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈₉×#3559	C₂	1	1	yes	maximal, characteristic, complemented
2	C₈₉×#3520	C₂	1	1	yes	maximal, characteristic, complemented
3	C₈₉×#3384	C₂	1	2	yes	maximal, complemented
4	C₈₉×#3376	C₂	1	2	yes	maximal, complemented
5	C₈₉×#3346	C₂	1	2	yes	maximal, complemented
6	C₈₉×#3345	C₂	1	2	yes	maximal, complemented
7	C₈₉×#3335	C₂	1	2	yes	maximal, complemented
8	C₈₉×#3307	C₂	1	2	yes	maximal, complemented
9	C₈₉×#3306	C₂	1	2	yes	maximal, complemented
10	C₈₉×#3297	C₂	1	2	yes	maximal, complemented
11	C₈₉×#3257	C₂	1	2	yes	maximal, complemented
12	C₈₉×#3246	C₂	1	1	yes	maximal, characteristic, complemented
13	C₈₉×#3244	C₂	1	2	yes	maximal, complemented
14	C₈₉×#3236	C₂	1	1	yes	maximal, characteristic, complemented
15	C₈₉×#3119	C₂	1	2	yes	maximal, complemented
16	C₈₉×#3109	C₂	1	1	yes	maximal, characteristic, complemented
17	C₈₉×#3084	C₂	1	2	yes	maximal, complemented
18	C₂×#478×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
19	C₈₉×#2992	C₂	1	1	yes	maximal, characteristic, complemented
20	#563×C₈₉	—	2	1	no	—
21	#562×C₈₉	—	2	1	no	—
22	#556×C₈₉	C₂²	1	1	yes	characteristic
23	#554×C₈₉	C₂²	1	2	yes	—
24	#554×C₈₉	C₂²	1	2	yes	complemented
25	#553×C₈₉	C₂²	1	2	yes	—
26	#553×C₈₉	C₂²	1	2	yes	complemented
27	#552×C₈₉	—	2	1	no	—
28	#551×C₈₉	—	2	2	no	—
29	D₄×Q₈×C₈₉	C₂²	1	1	yes	characteristic
30	#548×C₈₉	—	2	1	no	—
31	#547×C₈₉	—	2	2	no	—
32	#547×C₈₉	C₂²	1	1	yes	characteristic
33	#547×C₈₉	C₂²	1	2	yes	—
34	#547×C₈₉	C₂²	1	1	yes	characteristic
35	#546×C₈₉	C₂²	1	2	yes	—
36	#544×C₈₉	C₂²	1	2	yes	complemented
37	#542×C₈₉	C₂²	1	2	yes	—
38	#540×C₈₉	C₂²	1	2	yes	complemented
39	#539×C₈₉	—	2	2	no	—
40	#539×C₈₉	—	2	2	no	—
41	#539×C₈₉	—	2	1	no	—
42	#537×C₈₉	—	2	1	no	—
43	#533×C₈₉	C₂²	1	1	yes	characteristic
44	#532×C₈₉	C₂²	1	1	yes	characteristic
45	#529×C₈₉	C₂²	1	1	yes	characteristic
46	C₂×#125×C₈₉	C₂²	1	1	yes	characteristic
47	#525×C₈₉	—	2	1	no	—
48	C₂×C₂²⋊Q₈×C₈₉	—	2	1	no	—
49	#520×C₈₉	C₂²	1	2	yes	—
50	C₂×C₄×D₄×C₈₉	C₂²	1	1	yes	characteristic
51	#501×C₈₉	C₂²	1	2	yes	complemented
52	#501×C₈₉	C₂²	1	2	yes	complemented
53	#498×C₈₉	C₂²	1	2	yes	complemented
54	#491×C₈₉	C₂²	1	2	yes	complemented
55	#489×C₈₉	C₂²	1	2	yes	—
56	#488×C₈₉	C₂²	1	2	yes	—
57	#485×C₈₉	C₂²	1	2	yes	complemented
58	#484×C₈₉	C₂²	1	2	yes	—
59	#483×C₈₉	C₂²	1	2	yes	—
60	#483×C₈₉	C₂²	1	2	yes	complemented
61	#482×C₈₉	C₂²	1	2	yes	—
62	#481×C₈₉	C₂²	1	2	yes	—
63	#481×C₈₉	C₂²	1	2	yes	—
64	#481×C₈₉	C₂²	1	2	yes	complemented
65	#480×C₈₉	C₂²	1	2	yes	complemented
66	#479×C₈₉	C₂²	1	2	yes	complemented
67	#479×C₈₉	C₂²	1	2	yes	complemented
68	#479×C₈₉	C₂²	1	2	yes	complemented
69	#478×C₈₉	C₂²	1	2	yes	—
70	#478×C₈₉	C₂²	1	2	yes	—
71	#478×C₈₉	C₂²	1	2	yes	—
72	#478×C₈₉	C₂²	1	2	yes	—
73	#478×C₈₉	C₂²	1	2	yes	—
74	#476×C₈₉	C₂²	1	1	yes	characteristic
75	#476×C₈₉	C₂²	1	2	yes	—
76	#476×C₈₉	C₂²	1	1	yes	characteristic
77	#476×C₈₉	C₂²	1	2	yes	complemented
78	#476×C₈₉	C₂²	1	2	yes	complemented
79	#475×C₈₉	C₂²	1	2	yes	complemented
80	#475×C₈₉	C₂²	1	2	yes	complemented
81	#474×C₈₉	C₂²	1	2	yes	complemented
82	#469×C₈₉	C₂²	1	2	yes	—
83	#468×C₈₉	C₂²	1	2	yes	complemented
84	#466×C₈₉	C₂²	1	2	yes	—
85	#465×C₈₉	C₂²	1	2	yes	—
86	#465×C₈₉	C₂²	1	2	yes	—
87	#465×C₈₉	C₂²	1	2	yes	complemented
88	#463×C₈₉	C₂²	1	2	yes	—
89	#463×C₈₉	C₂²	1	2	yes	—
90	#461×C₈₉	C₂²	1	2	yes	complemented
91	#460×C₈₉	C₂²	1	2	yes	complemented
92	#459×C₈₉	C₂²	1	1	yes	characteristic
93	#459×C₈₉	C₂²	1	1	yes	characteristic
94	#449×C₈₉	C₂²	1	2	yes	—
95	#449×C₈₉	C₂²	1	2	yes	—
96	#447×C₈₉	C₂²	1	2	yes	—
97	#446×C₈₉	C₂²	1	2	yes	complemented
98	#442×C₈₉	C₂²	1	2	yes	—
99	#442×C₈₉	C₂²	1	2	yes	—
100	#442×C₈₉	C₂²	1	2	yes	—
101	#440×C₈₉	C₂²	1	2	yes	complemented
102	C₄×SD₁₆×C₈₉	C₂²	1	2	yes	complemented
103	C₄×D₈×C₈₉	C₂²	1	2	yes	—
104	#435×C₈₉	C₂²	1	2	yes	—
105	#435×C₈₉	C₂²	1	2	yes	complemented
106	C₈×D₄×C₈₉	C₂²	1	2	yes	—
107	#433×C₈₉	C₂²	1	2	yes	complemented
108	#432×C₈₉	C₂²	1	1	yes	characteristic
109	#428×C₈₉	C₂²	1	2	yes	complemented
110	C₂×#107×C₈₉	C₂²	1	1	yes	characteristic
111	C₂×#106×C₈₉	C₂²	1	1	yes	characteristic
112	C₂×#106×C₈₉	C₂²	1	2	yes	complemented
113	#424×C₈₉	C₂²	1	2	yes	complemented
114	C₂×C₄⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
115	#417×C₈₉	C₂²	1	2	yes	—
116	#416×C₈₉	C₂²	1	2	yes	—
117	C₂×#102×C₈₉	C₂²	1	1	yes	characteristic
118	C₂×#102×C₈₉	C₂²	1	1	yes	characteristic
119	C₂×#41×C₈₉	—	2	1	no	—
120	C₂×#41×C₈₉	—	2	2	no	—
121	C₂×#41×C₈₉	—	2	1	no	—
122	C₂×#41×C₈₉	C₂³	1	2	yes	—
123	C₂²×Q₈×C₈₉	—	2	1	no	—
124	C₂²×D₄×C₈₉	C₂³	1	1	yes	characteristic
125	C₂³×C₄×C₈₉	—	2	1	no	—
126	C₂×SD₁₆×C₈₉	C₂³	1	2	yes	—
127	C₂×SD₁₆×C₈₉	C₂³	1	2	yes	—
128	C₂×D₈×C₈₉	C₂³	1	2	yes	—
129	C₂×D₈×C₈₉	C₂³	1	2	yes	—
130	C₂×M₁₆×C₈₉	C₂³	1	2	yes	—
131	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
132	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
133	C₂²×C₈×C₈₉	C₂³	1	2	yes	—
134	C₄⋊Q₈×C₈₉	—	2	2	no	—
135	C₄⋊Q₈×C₈₉	C₂³	1	1	yes	characteristic
136	C₄⋊Q₈×C₈₉	C₂³	1	2	yes	—
137	C₄⋊Q₈×C₈₉	C₂³	1	1	yes	characteristic
138	C₄⋊Q₈×C₈₉	C₂³	1	2	yes	—
139	C₄⋊Q₈×C₈₉	C₂³	1	1	yes	characteristic
140	#127×C₈₉	C₂³	1	1	yes	characteristic
141	#126×C₈₉	—	2	2	no	—
142	#126×C₈₉	—	2	2	no	—
143	#126×C₈₉	—	2	2	no	—
144	#126×C₈₉	—	2	2	no	—
145	#126×C₈₉	D₄	1	2	yes	—
146	#125×C₈₉	—	2	2	no	—
147	#125×C₈₉	—	2	2	no	—
148	#125×C₈₉	—	2	1	no	—
149	#125×C₈₉	—	2	1	no	—
150	#125×C₈₉	—	2	1	no	—
151	#125×C₈₉	D₄	1	1	yes	characteristic
152	#125×C₈₉	C₂³	1	2	yes	—
153	#125×C₈₉	C₂³	1	2	yes	—
154	#125×C₈₉	C₂³	1	2	yes	—
155	#124×C₈₉	—	2	2	no	—
156	#124×C₈₉	—	2	1	no	—
157	#124×C₈₉	D₄	1	1	yes	characteristic
158	#124×C₈₉	C₂³	1	2	yes	—
159	#123×C₈₉	—	2	2	no	—
160	#123×C₈₉	—	2	2	no	—
161	#123×C₈₉	—	2	2	no	—
162	#123×C₈₉	—	2	2	no	—
163	#123×C₈₉	—	2	2	no	—
164	#123×C₈₉	—	2	2	no	—
165	#123×C₈₉	—	2	2	no	—
166	#123×C₈₉	—	2	2	no	—
167	#123×C₈₉	—	2	2	no	—
168	#123×C₈₉	—	2	2	no	—
169	#123×C₈₉	D₄	1	2	yes	—
170	C₂²⋊Q₈×C₈₉	—	2	1	no	—
171	C₂²⋊Q₈×C₈₉	—	2	2	no	—
172	C₂²⋊Q₈×C₈₉	—	2	1	no	—
173	C₂²⋊Q₈×C₈₉	—	2	2	no	—
174	C₂²⋊Q₈×C₈₉	—	2	1	no	—
175	C₂²⋊Q₈×C₈₉	—	2	1	no	—
176	C₂²⋊Q₈×C₈₉	—	2	2	no	—
177	C₂²⋊Q₈×C₈₉	—	2	2	no	—
178	C₂²⋊Q₈×C₈₉	—	2	2	no	—
179	C₂²⋊Q₈×C₈₉	—	2	2	no	—
180	C₂²⋊Q₈×C₈₉	—	2	2	no	—
181	C₂²⋊Q₈×C₈₉	—	2	2	no	—
182	C₂²⋊Q₈×C₈₉	—	2	2	no	—
183	C₂²⋊Q₈×C₈₉	—	2	2	no	—
184	C₂²⋊Q₈×C₈₉	D₄	1	1	yes	characteristic
185	C₂²⋊Q₈×C₈₉	C₂³	1	2	yes	—
186	C₂²⋊Q₈×C₈₉	C₂³	1	2	yes	—
187	#121×C₈₉	—	2	1	no	—
188	#121×C₈₉	—	2	2	no	—
189	#121×C₈₉	—	2	2	no	—
190	#121×C₈₉	—	2	1	no	—
191	#121×C₈₉	—	2	2	no	—
192	#121×C₈₉	—	2	2	no	—
193	#121×C₈₉	—	2	2	no	—
194	#121×C₈₉	D₄	1	1	yes	characteristic
195	#121×C₈₉	C₂³	1	2	yes	—
196	#121×C₈₉	C₂³	1	2	yes	—
197	#121×C₈₉	C₂³	1	2	yes	—
198	#121×C₈₉	C₂³	1	2	yes	—
199	#120×C₈₉	—	2	2	no	—
200	C₄×Q₈×C₈₉	—	2	1	no	—
201	C₄×Q₈×C₈₉	C₂³	1	2	yes	—
202	C₄×Q₈×C₈₉	C₂³	1	2	yes	—
203	C₄×Q₈×C₈₉	C₂³	1	1	yes	characteristic
204	C₄×D₄×C₈₉	—	2	2	no	—
205	C₄×D₄×C₈₉	—	2	2	no	—
206	C₄×D₄×C₈₉	—	2	2	no	—
207	C₄×D₄×C₈₉	—	2	2	no	—
208	C₄×D₄×C₈₉	—	2	2	no	—
209	C₄×D₄×C₈₉	—	2	1	no	—
210	C₄×D₄×C₈₉	—	2	1	no	—
211	C₄×D₄×C₈₉	—	2	1	no	—
212	C₄×D₄×C₈₉	C₂³	1	2	yes	—
213	C₄×D₄×C₈₉	C₂³	1	2	yes	—
214	C₄×D₄×C₈₉	C₂³	1	2	yes	—
215	C₄×D₄×C₈₉	C₂³	1	2	yes	—
216	C₄×D₄×C₈₉	C₂³	1	1	yes	characteristic
217	C₄×D₄×C₈₉	C₂³	1	1	yes	characteristic
218	C₄×D₄×C₈₉	C₂³	1	1	yes	characteristic
219	C₄×D₄×C₈₉	C₂³	1	1	yes	characteristic
220	C₄×D₄×C₈₉	C₂³	1	2	yes	—
221	C₄×D₄×C₈₉	C₂³	1	1	yes	characteristic
222	#117×C₈₉	—	2	1	no	—
223	#117×C₈₉	—	2	2	no	—
224	#117×C₈₉	—	2	1	no	—
225	#117×C₈₉	C₂³	1	2	yes	—
226	#117×C₈₉	C₂³	1	2	yes	—
227	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
228	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
229	C₂×C₄⋊C₄×C₈₉	—	2	2	no	—
230	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
231	C₂×C₄⋊C₄×C₈₉	—	2	2	no	—
232	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
233	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
234	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
235	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
236	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
237	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
238	C₂×C₂²⋊C₄×C₈₉	—	2	2	no	—
239	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
240	#107×C₈₉	C₂³	1	2	yes	—
241	#107×C₈₉	C₂³	1	2	yes	—
242	#107×C₈₉	C₂³	1	2	yes	—
243	#107×C₈₉	C₂³	1	2	yes	—
244	#106×C₈₉	C₂³	1	2	yes	—
245	#106×C₈₉	C₂³	1	2	yes	—
246	#106×C₈₉	C₂³	1	2	yes	—
247	#106×C₈₉	C₂³	1	2	yes	—
248	#106×C₈₉	C₂³	1	2	yes	—
249	#106×C₈₉	C₂³	1	2	yes	—
250	#106×C₈₉	C₂³	1	2	yes	—
251	#106×C₈₉	C₂³	1	2	yes	—
252	C₄⋊C₈×C₈₉	C₂³	1	2	yes	—
253	C₄⋊C₈×C₈₉	C₂³	1	2	yes	—
254	C₄⋊C₈×C₈₉	C₂³	1	1	yes	characteristic
255	C₄⋊C₈×C₈₉	C₂³	1	2	yes	—
256	C₄⋊C₈×C₈₉	C₂³	1	2	yes	—
257	C₄⋊C₈×C₈₉	C₂³	1	1	yes	characteristic
258	#103×C₈₉	C₂³	1	2	yes	—
259	#103×C₈₉	C₂³	1	2	yes	—
260	#103×C₈₉	C₂³	1	2	yes	—
261	#103×C₈₉	C₂³	1	2	yes	—
262	#103×C₈₉	C₂³	1	2	yes	—
263	#103×C₈₉	C₂³	1	2	yes	—
264	#102×C₈₉	C₂³	1	2	yes	—
265	#102×C₈₉	C₂³	1	2	yes	—
266	#102×C₈₉	C₂³	1	2	yes	—
267	#102×C₈₉	C₂³	1	2	yes	—
268	#102×C₈₉	C₂³	1	2	yes	—
269	#102×C₈₉	C₂³	1	2	yes	—
270	#102×C₈₉	C₂³	1	2	yes	—
271	#102×C₈₉	C₂³	1	2	yes	—
272	#102×C₈₉	C₂³	1	2	yes	—
273	#102×C₈₉	C₂³	1	2	yes	—
274	C₂²⋊C₈×C₈₉	C₂³	1	2	yes	—
275	C₂²⋊C₈×C₈₉	C₂³	1	2	yes	—
276	C₂²⋊C₈×C₈₉	C₂³	1	2	yes	—
277	#97×C₈₉	C₂³	1	2	yes	—
278	#97×C₈₉	C₂³	1	2	yes	—
279	C₄×C₈×C₈₉	C₂³	1	2	yes	—
280	C₂⁴×C₈₉	—	2	1	no	—
281	#41×C₈₉	—	2	4	no	—
282	#41×C₈₉	—	4	2	no	—
283	#41×C₈₉	—	8	2	no	—
284	#41×C₈₉	—	8	4	no	—
285	#41×C₈₉	—	8	2	no	—
286	C₂×Q₈×C₈₉	—	2	1	no	—
287	C₂×Q₈×C₈₉	—	2	2	no	—
288	C₂×Q₈×C₈₉	—	2	2	no	—
289	C₂×Q₈×C₈₉	—	2	1	no	—
290	C₂×Q₈×C₈₉	—	8	2	no	—
291	C₂×Q₈×C₈₉	C₂×D₄	1	1	yes	characteristic
292	C₂×Q₈×C₈₉	C₂⁴	1	2	yes	—
293	C₂×D₄×C₈₉	—	2	2	no	—
294	C₂×D₄×C₈₉	—	2	2	no	—
295	C₂×D₄×C₈₉	—	2	2	no	—
296	C₂×D₄×C₈₉	—	2	2	no	—
297	C₂×D₄×C₈₉	—	2	2	no	—
298	C₂×D₄×C₈₉	—	2	2	no	—
299	C₂×D₄×C₈₉	—	2	1	no	—
300	C₂×D₄×C₈₉	—	2	1	no	—
301	C₂×D₄×C₈₉	—	2	1	no	—
302	C₂×D₄×C₈₉	—	4	1	no	—
303	C₂×D₄×C₈₉	C₂×D₄	1	2	yes	—
304	C₂×D₄×C₈₉	C₂×D₄	1	1	yes	characteristic
305	C₂×D₄×C₈₉	C₂⁴	1	1	yes	characteristic
306	C₂×D₄×C₈₉	C₂⁴	1	2	yes	—
307	C₂×D₄×C₈₉	C₂⁴	1	1	yes	characteristic
308	C₂²×C₄×C₈₉	—	2	1	no	—
309	C₂²×C₄×C₈₉	—	2	1	no	—
310	C₂²×C₄×C₈₉	—	2	1	no	—
311	C₂²×C₄×C₈₉	—	2	2	no	—
312	C₂²×C₄×C₈₉	—	2	2	no	—
313	C₂²×C₄×C₈₉	—	2	2	no	—
314	C₂²×C₄×C₈₉	—	2	1	no	—
315	C₂²×C₄×C₈₉	—	2	1	no	—
316	C₂²×C₄×C₈₉	—	2	2	no	—
317	C₂²×C₄×C₈₉	—	2	1	no	—
318	C₂²×C₄×C₈₉	—	2	2	no	—
319	C₂²×C₄×C₈₉	—	2	2	no	—
320	C₂²×C₄×C₈₉	—	2	2	no	—
321	C₂²×C₄×C₈₉	—	2	1	no	—
322	C₂²×C₄×C₈₉	—	8	2	no	—
323	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
324	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
325	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
326	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
327	SD₁₆×C₈₉	—	4	2	no	—
328	SD₁₆×C₈₉	—	4	2	no	—
329	D₈×C₈₉	—	2	4	no	—
330	D₈×C₈₉	—	4	2	no	—
331	M₁₆×C₈₉	—	4	2	no	—
332	C₂×C₈×C₈₉	—	4	1	no	—
333	C₂×C₈×C₈₉	—	4	2	no	—
334	C₂×C₈×C₈₉	—	4	1	no	—
335	C₂×C₈×C₈₉	C₂⁴	1	2	yes	—
336	C₂×C₈×C₈₉	C₂⁴	1	2	yes	—
337	C₂×C₈×C₈₉	C₂⁴	1	2	yes	—
338	C₂×C₈×C₈₉	C₂⁴	1	2	yes	—
339	C₄⋊C₄×C₈₉	—	2	2	no	—
340	C₄⋊C₄×C₈₉	—	2	2	no	—
341	C₄⋊C₄×C₈₉	—	2	1	no	—
342	C₄⋊C₄×C₈₉	—	2	2	no	—
343	C₄⋊C₄×C₈₉	—	2	2	no	—
344	C₄⋊C₄×C₈₉	—	2	2	no	—
345	C₄⋊C₄×C₈₉	—	2	2	no	—
346	C₄⋊C₄×C₈₉	—	2	2	no	—
347	C₄⋊C₄×C₈₉	—	2	2	no	—
348	C₄⋊C₄×C₈₉	—	2	2	no	—
349	C₄⋊C₄×C₈₉	—	2	2	no	—
350	C₄⋊C₄×C₈₉	—	2	1	no	—
351	C₄⋊C₄×C₈₉	—	2	1	no	—
352	C₄⋊C₄×C₈₉	—	2	2	no	—
353	C₄⋊C₄×C₈₉	—	2	1	no	—
354	C₄⋊C₄×C₈₉	—	2	1	no	—
355	C₄⋊C₄×C₈₉	—	2	1	no	—
356	C₄⋊C₄×C₈₉	—	2	1	no	—
357	C₄⋊C₄×C₈₉	—	2	2	no	—
358	C₄⋊C₄×C₈₉	—	2	2	no	—
359	C₄⋊C₄×C₈₉	—	2	2	no	—
360	C₄⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
361	C₄⋊C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
362	C₄⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
363	C₄⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
364	C₄⋊C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
365	C₄⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
366	C₄⋊C₄×C₈₉	C₂⁴	1	2	yes	—
367	C₄⋊C₄×C₈₉	C₂⁴	1	2	yes	—
368	C₄⋊C₄×C₈₉	C₂⁴	1	2	yes	—
369	C₄⋊C₄×C₈₉	C₂⁴	1	1	yes	characteristic
370	C₄⋊C₄×C₈₉	C₂⁴	1	1	yes	characteristic
371	C₄⋊C₄×C₈₉	C₂⁴	1	2	yes	—
372	C₂²⋊C₄×C₈₉	—	2	2	no	—
373	C₂²⋊C₄×C₈₉	—	2	2	no	—
374	C₂²⋊C₄×C₈₉	—	2	2	no	—
375	C₂²⋊C₄×C₈₉	—	2	1	no	—
376	C₂²⋊C₄×C₈₉	—	2	1	no	—
377	C₂²⋊C₄×C₈₉	—	2	1	no	—
378	C₂²⋊C₄×C₈₉	—	2	1	no	—
379	C₂²⋊C₄×C₈₉	—	2	2	no	—
380	C₂²⋊C₄×C₈₉	—	2	2	no	—
381	C₂²⋊C₄×C₈₉	—	2	2	no	—
382	C₂²⋊C₄×C₈₉	—	2	2	no	—
383	C₂²⋊C₄×C₈₉	—	2	2	no	—
384	C₂²⋊C₄×C₈₉	—	2	2	no	—
385	C₂²⋊C₄×C₈₉	—	2	2	no	—
386	C₂²⋊C₄×C₈₉	—	2	2	no	—
387	C₂²⋊C₄×C₈₉	—	2	2	no	—
388	C₂²⋊C₄×C₈₉	—	2	2	no	—
389	C₂²⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
390	C₂²⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
391	C₂²⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
392	C₂²⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
393	C₂²⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
394	C₄²×C₈₉	—	2	2	no	—
395	C₄²×C₈₉	—	2	2	no	—
396	C₄²×C₈₉	—	2	2	no	—
397	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
398	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
399	C₄²×C₈₉	C₂⁴	1	2	yes	—
400	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
401	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
402	C₂³×C₈₉	—	2	1	no	—
403	C₂³×C₈₉	—	2	1	no	—
404	C₂³×C₈₉	—	2	2	no	—
405	C₂³×C₈₉	—	4	2	no	—
406	C₂³×C₈₉	—	4	2	no	—
407	C₂³×C₈₉	—	8	1	no	—
408	C₂³×C₈₉	C₂²×D₄	1	2	yes	—
409	C₂³×C₈₉	C₂²×D₄	1	1	yes	characteristic
410	Q₈×C₈₉	—	2	2	no	—
411	Q₈×C₈₉	—	2	2	no	—
412	Q₈×C₈₉	—	4	1	no	—
413	Q₈×C₈₉	—	4	2	no	—
414	Q₈×C₈₉	—	8	2	no	—
415	Q₈×C₈₉	—	8	1	no	—
416	Q₈×C₈₉	—	8	2	no	—
417	D₄×C₈₉	—	2	4	no	—
418	D₄×C₈₉	—	2	2	no	—
419	D₄×C₈₉	—	2	1	no	—
420	D₄×C₈₉	—	2	1	no	—
421	D₄×C₈₉	—	2	1	no	—
422	D₄×C₈₉	—	2	2	no	—
423	D₄×C₈₉	—	4	1	no	—
424	D₄×C₈₉	—	4	2	no	—
425	D₄×C₈₉	—	4	4	no	—
426	D₄×C₈₉	—	4	4	no	—
427	D₄×C₈₉	—	8	1	no	—
428	D₄×C₈₉	—	8	1	no	—
429	D₄×C₈₉	—	8	2	no	—
430	D₄×C₈₉	—	8	2	no	—
431	D₄×C₈₉	—	8	2	no	—
432	D₄×C₈₉	2₋¹⁺⁴	1	2	yes	—
433	C₂×C₄×C₈₉	—	2	2	no	—
434	C₂×C₄×C₈₉	—	2	1	no	—
435	C₂×C₄×C₈₉	—	2	2	no	—
436	C₂×C₄×C₈₉	—	2	1	no	—
437	C₂×C₄×C₈₉	—	2	2	no	—
438	C₂×C₄×C₈₉	—	2	2	no	—
439	C₂×C₄×C₈₉	—	2	1	no	—
440	C₂×C₄×C₈₉	—	2	2	no	—
441	C₂×C₄×C₈₉	—	2	2	no	—
442	C₂×C₄×C₈₉	—	2	2	no	—
443	C₂×C₄×C₈₉	—	2	1	no	—
444	C₂×C₄×C₈₉	—	2	2	no	—
445	C₂×C₄×C₈₉	—	4	1	no	—
446	C₂×C₄×C₈₉	—	4	4	no	—
447	C₂×C₄×C₈₉	—	4	2	no	—
448	C₂×C₄×C₈₉	—	4	2	no	—
449	C₂×C₄×C₈₉	—	4	2	no	—
450	C₂×C₄×C₈₉	—	8	2	no	—
451	C₂×C₄×C₈₉	—	8	1	no	—
452	C₂×C₄×C₈₉	—	8	1	no	—
453	C₂×C₄×C₈₉	—	8	2	no	—
454	C₂×C₄×C₈₉	—	8	2	no	—
455	C₂×C₄×C₈₉	—	8	2	no	—
456	C₂×C₄×C₈₉	—	8	1	no	—
457	C₂×C₄×C₈₉	—	8	1	no	—
458	C₂×C₄×C₈₉	—	8	2	no	—
459	C₂×C₄×C₈₉	—	8	2	no	—
460	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
461	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
462	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
463	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
464	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
465	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
466	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
467	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
468	C₂×C₄×C₈₉	C₂⁵	1	1	yes	characteristic
469	C₈×C₈₉	—	2	2	no	—
470	C₈×C₈₉	—	2	2	no	—
471	C₈×C₈₉	—	2	2	no	—
472	C₈×C₈₉	—	2	2	no	—
473	C₂²×C₈₉	—	2	1	no	—
474	C₂²×C₈₉	—	2	1	no	—
475	C₂²×C₈₉	—	2	2	no	—
476	C₂²×C₈₉	—	2	2	no	—
477	C₂²×C₈₉	—	2	2	no	—
478	C₂²×C₈₉	—	2	2	no	—
479	C₂²×C₈₉	—	4	1	no	—
480	C₂²×C₈₉	—	4	1	no	—
481	C₂²×C₈₉	—	4	1	no	—
482	C₂²×C₈₉	—	4	2	no	—
483	C₂²×C₈₉	—	4	1	no	—
484	C₂²×C₈₉	—	4	2	no	—
485	C₂²×C₈₉	—	4	2	no	—
486	C₂²×C₈₉	—	4	1	no	—
487	C₂²×C₈₉	—	8	4	no	—
488	C₂²×C₈₉	#577	1	2	yes	—
489	C₂²×C₈₉	C₂³×D₄	1	1	yes	characteristic
490	C₄×C₈₉	—	2	1	no	—
491	C₄×C₈₉	—	2	1	no	—
492	C₄×C₈₉	—	2	2	no	—
493	C₄×C₈₉	—	2	2	no	—
494	C₄×C₈₉	—	2	1	no	—
495	C₄×C₈₉	—	2	1	no	—
496	C₄×C₈₉	—	2	1	no	—
497	C₄×C₈₉	—	2	2	no	—
498	C₄×C₈₉	—	4	1	no	—
499	C₄×C₈₉	—	4	1	no	—
500	C₄×C₈₉	—	4	2	no	—
501	C₄×C₈₉	—	4	2	no	—
502	C₄×C₈₉	—	4	2	no	—
503	C₄×C₈₉	—	4	2	no	—
504	C₄×C₈₉	—	4	2	no	—
505	C₄×C₈₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
506	C₄×C₈₉	#585	1	1	yes	characteristic
507	#62166	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
508	C₂×C₈₉	—	2	2	no	—
509	C₂×C₈₉	—	4	2	no	—
510	C₂×C₈₉	—	4	2	no	—
511	C₂×C₈₉	—	8	2	no	—
512	C₂×C₈₉	—	8	1	no	—
513	C₂×C₈₉	#3489	1	1	yes	characteristic
514	C₂×C₈₉	C₂×#577	1	1	yes	characteristic
515	C₂×C₈₉	#3585	1	1	yes	characteristic
516	#3559	C₂×C₈₉	1	1	yes	characteristic, complemented
517	#3520	C₂×C₈₉	1	1	yes	characteristic, complemented
518	#3384	C₂×C₈₉	1	2	yes	complemented
519	#3376	C₂×C₈₉	1	2	yes	complemented
520	#3346	C₂×C₈₉	1	2	yes	complemented
521	#3345	C₂×C₈₉	1	2	yes	complemented
522	#3335	C₂×C₈₉	1	2	yes	complemented
523	#3307	C₂×C₈₉	1	2	yes	complemented
524	#3306	C₂×C₈₉	1	2	yes	complemented
525	#3297	C₂×C₈₉	1	2	yes	complemented
526	#3257	C₂×C₈₉	1	2	yes	complemented
527	#3246	C₂×C₈₉	1	1	yes	characteristic, complemented
528	#3244	C₂×C₈₉	1	2	yes	complemented
529	#3236	C₂×C₈₉	1	1	yes	characteristic, complemented
530	#3119	C₂×C₈₉	1	2	yes	complemented
531	#3109	C₂×C₈₉	1	1	yes	characteristic, complemented
532	#3084	C₂×C₈₉	1	2	yes	complemented
533	C₂×#478	C₂×C₈₉	1	1	yes	characteristic, complemented
534	#2992	C₂×C₈₉	1	1	yes	characteristic, complemented
535	C₈₉	#62166	1	1	yes	characteristic, direct product factor, Sylow
536	#563	—	2	1	no	—
537	#562	—	2	1	no	—
538	#556	C₂²×C₈₉	1	1	yes	characteristic
539	#554	C₂²×C₈₉	1	2	yes	—
540	#554	C₂²×C₈₉	1	2	yes	complemented
541	#553	C₂²×C₈₉	1	2	yes	—
542	#553	C₂²×C₈₉	1	2	yes	complemented
543	#552	—	2	1	no	—
544	#551	—	2	2	no	—
545	D₄×Q₈	C₂²×C₈₉	1	1	yes	characteristic
546	#548	—	2	1	no	—
547	#547	—	2	2	no	—
548	#547	C₂²×C₈₉	1	1	yes	characteristic
549	#547	C₂²×C₈₉	1	2	yes	—
550	#547	C₂²×C₈₉	1	1	yes	characteristic
551	#546	C₂²×C₈₉	1	2	yes	—
552	#544	C₂²×C₈₉	1	2	yes	complemented
553	#542	C₂²×C₈₉	1	2	yes	—
554	#540	C₂²×C₈₉	1	2	yes	complemented
555	#539	—	2	2	no	—
556	#539	—	2	2	no	—
557	#539	—	2	1	no	—
558	#537	—	2	1	no	—
559	#533	C₂²×C₈₉	1	1	yes	characteristic
560	#532	C₂²×C₈₉	1	1	yes	characteristic
561	#529	C₂²×C₈₉	1	1	yes	characteristic
562	C₂×#125	C₂²×C₈₉	1	1	yes	characteristic
563	#525	—	2	1	no	—
564	C₂×C₂²⋊Q₈	—	2	1	no	—
565	#520	C₂²×C₈₉	1	2	yes	—
566	C₂×C₄×D₄	C₂²×C₈₉	1	1	yes	characteristic
567	#501	C₂²×C₈₉	1	2	yes	complemented
568	#501	C₂²×C₈₉	1	2	yes	complemented
569	#498	C₂²×C₈₉	1	2	yes	complemented
570	#491	C₂²×C₈₉	1	2	yes	complemented
571	#489	C₂²×C₈₉	1	2	yes	—
572	#488	C₂²×C₈₉	1	2	yes	—
573	#485	C₂²×C₈₉	1	2	yes	complemented
574	#484	C₂²×C₈₉	1	2	yes	—
575	#483	C₂²×C₈₉	1	2	yes	—
576	#483	C₂²×C₈₉	1	2	yes	complemented
577	#482	C₂²×C₈₉	1	2	yes	—
578	#481	C₂²×C₈₉	1	2	yes	—
579	#481	C₂²×C₈₉	1	2	yes	—
580	#481	C₂²×C₈₉	1	2	yes	complemented
581	#480	C₂²×C₈₉	1	2	yes	complemented
582	#479	C₂²×C₈₉	1	2	yes	complemented
583	#479	C₂²×C₈₉	1	2	yes	complemented
584	#479	C₂²×C₈₉	1	2	yes	complemented
585	#478	C₂²×C₈₉	1	2	yes	—
586	#478	C₂²×C₈₉	1	2	yes	—
587	#478	C₂²×C₈₉	1	2	yes	—
588	#478	C₂²×C₈₉	1	2	yes	—
589	#478	C₂²×C₈₉	1	2	yes	—
590	#476	C₂²×C₈₉	1	1	yes	characteristic
591	#476	C₂²×C₈₉	1	2	yes	—
592	#476	C₂²×C₈₉	1	1	yes	characteristic
593	#476	C₂²×C₈₉	1	2	yes	complemented
594	#476	C₂²×C₈₉	1	2	yes	complemented
595	#475	C₂²×C₈₉	1	2	yes	complemented
596	#475	C₂²×C₈₉	1	2	yes	complemented
597	#474	C₂²×C₈₉	1	2	yes	complemented
598	#469	C₂²×C₈₉	1	2	yes	—
599	#468	C₂²×C₈₉	1	2	yes	complemented
600	#466	C₂²×C₈₉	1	2	yes	—
601	#465	C₂²×C₈₉	1	2	yes	—
602	#465	C₂²×C₈₉	1	2	yes	—
603	#465	C₂²×C₈₉	1	2	yes	complemented
604	#463	C₂²×C₈₉	1	2	yes	—
605	#463	C₂²×C₈₉	1	2	yes	—
606	#461	C₂²×C₈₉	1	2	yes	complemented
607	#460	C₂²×C₈₉	1	2	yes	complemented
608	#459	C₂²×C₈₉	1	1	yes	characteristic
609	#459	C₂²×C₈₉	1	1	yes	characteristic
610	#449	C₂²×C₈₉	1	2	yes	—
611	#449	C₂²×C₈₉	1	2	yes	—
612	#447	C₂²×C₈₉	1	2	yes	—
613	#446	C₂²×C₈₉	1	2	yes	complemented
614	#442	C₂²×C₈₉	1	2	yes	—
615	#442	C₂²×C₈₉	1	2	yes	—
616	#442	C₂²×C₈₉	1	2	yes	—
617	#440	C₂²×C₈₉	1	2	yes	complemented
618	C₄×SD₁₆	C₂²×C₈₉	1	2	yes	complemented
619	C₄×D₈	C₂²×C₈₉	1	2	yes	—
620	#435	C₂²×C₈₉	1	2	yes	—
621	#435	C₂²×C₈₉	1	2	yes	complemented
622	C₈×D₄	C₂²×C₈₉	1	2	yes	—
623	#433	C₂²×C₈₉	1	2	yes	complemented
624	#432	C₂²×C₈₉	1	1	yes	characteristic
625	#428	C₂²×C₈₉	1	2	yes	complemented
626	C₂×#107	C₂²×C₈₉	1	1	yes	characteristic
627	C₂×#106	C₂²×C₈₉	1	1	yes	characteristic
628	C₂×#106	C₂²×C₈₉	1	2	yes	complemented
629	#424	C₂²×C₈₉	1	2	yes	complemented
630	C₂×C₄⋊C₈	C₂²×C₈₉	1	1	yes	characteristic
631	#417	C₂²×C₈₉	1	2	yes	—
632	#416	C₂²×C₈₉	1	2	yes	—
633	C₂×#102	C₂²×C₈₉	1	1	yes	characteristic
634	C₂×#102	C₂²×C₈₉	1	1	yes	characteristic
635	C₂×#41	—	2	1	no	—
636	C₂×#41	—	2	2	no	—
637	C₂×#41	—	2	1	no	—
638	C₂×#41	C₂³×C₈₉	1	2	yes	—
639	C₂²×Q₈	—	2	1	no	—
640	C₂²×D₄	C₂³×C₈₉	1	1	yes	characteristic
641	C₂³×C₄	—	2	1	no	—
642	C₂×SD₁₆	C₂³×C₈₉	1	2	yes	—
643	C₂×SD₁₆	C₂³×C₈₉	1	2	yes	—
644	C₂×D₈	C₂³×C₈₉	1	2	yes	—
645	C₂×D₈	C₂³×C₈₉	1	2	yes	—
646	C₂×M₁₆	C₂³×C₈₉	1	2	yes	—
647	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
648	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
649	C₂²×C₈	C₂³×C₈₉	1	2	yes	—
650	C₄⋊Q₈	—	2	2	no	—
651	C₄⋊Q₈	C₂³×C₈₉	1	1	yes	characteristic
652	C₄⋊Q₈	C₂³×C₈₉	1	1	yes	characteristic
653	C₄⋊Q₈	C₂³×C₈₉	1	1	yes	characteristic
654	C₄⋊Q₈	C₂³×C₈₉	1	2	yes	—
655	C₄⋊Q₈	C₂³×C₈₉	1	2	yes	—
656	#127	C₂³×C₈₉	1	1	yes	characteristic
657	#126	—	2	2	no	—
658	#126	—	2	2	no	—
659	#126	—	2	2	no	—
660	#126	—	2	2	no	—
661	#126	D₄×C₈₉	1	2	yes	—
662	#125	—	2	2	no	—
663	#125	—	2	2	no	—
664	#125	—	2	1	no	—
665	#125	—	2	1	no	—
666	#125	—	2	1	no	—
667	#125	D₄×C₈₉	1	1	yes	characteristic
668	#125	C₂³×C₈₉	1	2	yes	—
669	#125	C₂³×C₈₉	1	2	yes	—
670	#125	C₂³×C₈₉	1	2	yes	—
671	#124	—	2	2	no	—
672	#124	—	2	1	no	—
673	#124	D₄×C₈₉	1	1	yes	characteristic
674	#124	C₂³×C₈₉	1	2	yes	—
675	#123	—	2	2	no	—
676	#123	—	2	2	no	—
677	#123	—	2	2	no	—
678	#123	—	2	2	no	—
679	#123	—	2	2	no	—
680	#123	—	2	2	no	—
681	#123	—	2	2	no	—
682	#123	—	2	2	no	—
683	#123	—	2	2	no	—
684	#123	—	2	2	no	—
685	#123	D₄×C₈₉	1	2	yes	—
686	C₂²⋊Q₈	—	2	1	no	—
687	C₂²⋊Q₈	—	2	2	no	—
688	C₂²⋊Q₈	—	2	1	no	—
689	C₂²⋊Q₈	—	2	2	no	—
690	C₂²⋊Q₈	—	2	1	no	—
691	C₂²⋊Q₈	—	2	1	no	—
692	C₂²⋊Q₈	—	2	2	no	—
693	C₂²⋊Q₈	—	2	2	no	—
694	C₂²⋊Q₈	—	2	2	no	—
695	C₂²⋊Q₈	—	2	2	no	—
696	C₂²⋊Q₈	—	2	2	no	—
697	C₂²⋊Q₈	—	2	2	no	—
698	C₂²⋊Q₈	—	2	2	no	—
699	C₂²⋊Q₈	—	2	2	no	—
700	C₂²⋊Q₈	D₄×C₈₉	1	1	yes	characteristic
701	C₂²⋊Q₈	C₂³×C₈₉	1	2	yes	—
702	C₂²⋊Q₈	C₂³×C₈₉	1	2	yes	—
703	#121	—	2	1	no	—
704	#121	—	2	2	no	—
705	#121	—	2	2	no	—
706	#121	—	2	1	no	—
707	#121	—	2	2	no	—
708	#121	—	2	2	no	—
709	#121	—	2	2	no	—
710	#121	D₄×C₈₉	1	1	yes	characteristic
711	#121	C₂³×C₈₉	1	2	yes	—
712	#121	C₂³×C₈₉	1	2	yes	—
713	#121	C₂³×C₈₉	1	2	yes	—
714	#121	C₂³×C₈₉	1	2	yes	—
715	#120	—	2	2	no	—
716	C₄×Q₈	—	2	1	no	—
717	C₄×Q₈	C₂³×C₈₉	1	2	yes	—
718	C₄×Q₈	C₂³×C₈₉	1	2	yes	—
719	C₄×Q₈	C₂³×C₈₉	1	1	yes	characteristic
720	C₄×D₄	—	2	2	no	—
721	C₄×D₄	—	2	2	no	—
722	C₄×D₄	—	2	2	no	—
723	C₄×D₄	—	2	2	no	—
724	C₄×D₄	—	2	2	no	—
725	C₄×D₄	—	2	1	no	—
726	C₄×D₄	—	2	1	no	—
727	C₄×D₄	—	2	1	no	—
728	C₄×D₄	C₂³×C₈₉	1	1	yes	characteristic
729	C₄×D₄	C₂³×C₈₉	1	1	yes	characteristic
730	C₄×D₄	C₂³×C₈₉	1	1	yes	characteristic
731	C₄×D₄	C₂³×C₈₉	1	1	yes	characteristic
732	C₄×D₄	C₂³×C₈₉	1	2	yes	—
733	C₄×D₄	C₂³×C₈₉	1	2	yes	—
734	C₄×D₄	C₂³×C₈₉	1	2	yes	—
735	C₄×D₄	C₂³×C₈₉	1	2	yes	—
736	C₄×D₄	C₂³×C₈₉	1	2	yes	—
737	C₄×D₄	C₂³×C₈₉	1	1	yes	characteristic
738	#117	—	2	1	no	—
739	#117	—	2	2	no	—
740	#117	—	2	1	no	—
741	#117	C₂³×C₈₉	1	2	yes	—
742	#117	C₂³×C₈₉	1	2	yes	—
743	C₂×C₄⋊C₄	—	2	1	no	—
744	C₂×C₄⋊C₄	—	2	1	no	—
745	C₂×C₄⋊C₄	—	2	2	no	—
746	C₂×C₄⋊C₄	—	2	1	no	—
747	C₂×C₄⋊C₄	—	2	2	no	—
748	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
749	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
750	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
751	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
752	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
753	C₂×C₂²⋊C₄	—	2	1	no	—
754	C₂×C₂²⋊C₄	—	2	2	no	—
755	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
756	#107	C₂³×C₈₉	1	2	yes	—
757	#107	C₂³×C₈₉	1	2	yes	—
758	#107	C₂³×C₈₉	1	2	yes	—
759	#107	C₂³×C₈₉	1	2	yes	—
760	#106	C₂³×C₈₉	1	2	yes	—
761	#106	C₂³×C₈₉	1	2	yes	—
762	#106	C₂³×C₈₉	1	2	yes	—
763	#106	C₂³×C₈₉	1	2	yes	—
764	#106	C₂³×C₈₉	1	2	yes	—
765	#106	C₂³×C₈₉	1	2	yes	—
766	#106	C₂³×C₈₉	1	2	yes	—
767	#106	C₂³×C₈₉	1	2	yes	—
768	C₄⋊C₈	C₂³×C₈₉	1	2	yes	—
769	C₄⋊C₈	C₂³×C₈₉	1	2	yes	—
770	C₄⋊C₈	C₂³×C₈₉	1	1	yes	characteristic
771	C₄⋊C₈	C₂³×C₈₉	1	2	yes	—
772	C₄⋊C₈	C₂³×C₈₉	1	2	yes	—
773	C₄⋊C₈	C₂³×C₈₉	1	1	yes	characteristic
774	#103	C₂³×C₈₉	1	2	yes	—
775	#103	C₂³×C₈₉	1	2	yes	—
776	#103	C₂³×C₈₉	1	2	yes	—
777	#103	C₂³×C₈₉	1	2	yes	—
778	#103	C₂³×C₈₉	1	2	yes	—
779	#103	C₂³×C₈₉	1	2	yes	—
780	#102	C₂³×C₈₉	1	2	yes	—
781	#102	C₂³×C₈₉	1	2	yes	—
782	#102	C₂³×C₈₉	1	2	yes	—
783	#102	C₂³×C₈₉	1	2	yes	—
784	#102	C₂³×C₈₉	1	2	yes	—
785	#102	C₂³×C₈₉	1	2	yes	—
786	#102	C₂³×C₈₉	1	2	yes	—
787	#102	C₂³×C₈₉	1	2	yes	—
788	#102	C₂³×C₈₉	1	2	yes	—
789	#102	C₂³×C₈₉	1	2	yes	—
790	C₂²⋊C₈	C₂³×C₈₉	1	2	yes	—
791	C₂²⋊C₈	C₂³×C₈₉	1	2	yes	—
792	C₂²⋊C₈	C₂³×C₈₉	1	2	yes	—
793	#97	C₂³×C₈₉	1	2	yes	—
794	#97	C₂³×C₈₉	1	2	yes	—
795	C₄×C₈	C₂³×C₈₉	1	2	yes	—
796	C₂⁴	—	2	1	no	—
797	#41	—	2	4	no	—
798	#41	—	4	2	no	—
799	#41	—	8	2	no	—
800	#41	—	8	4	no	—
801	#41	—	8	2	no	—
802	C₂×Q₈	—	2	1	no	—
803	C₂×Q₈	—	2	2	no	—
804	C₂×Q₈	—	2	2	no	—
805	C₂×Q₈	—	2	1	no	—
806	C₂×Q₈	—	8	2	no	—
807	C₂×Q₈	C₂×D₄×C₈₉	1	1	yes	characteristic
808	C₂×Q₈	C₂⁴×C₈₉	1	2	yes	—
809	C₂×D₄	—	2	2	no	—
810	C₂×D₄	—	2	2	no	—
811	C₂×D₄	—	2	2	no	—
812	C₂×D₄	—	2	2	no	—
813	C₂×D₄	—	2	2	no	—
814	C₂×D₄	—	2	2	no	—
815	C₂×D₄	—	2	1	no	—
816	C₂×D₄	—	2	1	no	—
817	C₂×D₄	—	2	1	no	—
818	C₂×D₄	—	4	1	no	—
819	C₂×D₄	C₂×D₄×C₈₉	1	2	yes	—
820	C₂×D₄	C₂×D₄×C₈₉	1	1	yes	characteristic
821	C₂×D₄	C₂⁴×C₈₉	1	1	yes	characteristic
822	C₂×D₄	C₂⁴×C₈₉	1	2	yes	—
823	C₂×D₄	C₂⁴×C₈₉	1	1	yes	characteristic
824	C₂²×C₄	—	2	1	no	—
825	C₂²×C₄	—	2	1	no	—
826	C₂²×C₄	—	2	1	no	—
827	C₂²×C₄	—	2	2	no	—
828	C₂²×C₄	—	2	2	no	—
829	C₂²×C₄	—	2	2	no	—
830	C₂²×C₄	—	2	1	no	—
831	C₂²×C₄	—	2	1	no	—
832	C₂²×C₄	—	2	2	no	—
833	C₂²×C₄	—	2	1	no	—
834	C₂²×C₄	—	2	2	no	—
835	C₂²×C₄	—	2	2	no	—
836	C₂²×C₄	—	2	2	no	—
837	C₂²×C₄	—	2	1	no	—
838	C₂²×C₄	—	8	2	no	—
839	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
840	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
841	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
842	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
843	SD₁₆	—	4	2	no	—
844	SD₁₆	—	4	2	no	—
845	D₈	—	2	4	no	—
846	D₈	—	4	2	no	—
847	M₁₆	—	4	2	no	—
848	C₂×C₈	—	4	1	no	—
849	C₂×C₈	—	4	2	no	—
850	C₂×C₈	—	4	1	no	—
851	C₂×C₈	C₂⁴×C₈₉	1	2	yes	—
852	C₂×C₈	C₂⁴×C₈₉	1	2	yes	—
853	C₂×C₈	C₂⁴×C₈₉	1	2	yes	—
854	C₂×C₈	C₂⁴×C₈₉	1	2	yes	—
855	C₄⋊C₄	—	2	2	no	—
856	C₄⋊C₄	—	2	2	no	—
857	C₄⋊C₄	—	2	1	no	—
858	C₄⋊C₄	—	2	2	no	—
859	C₄⋊C₄	—	2	2	no	—
860	C₄⋊C₄	—	2	2	no	—
861	C₄⋊C₄	—	2	2	no	—
862	C₄⋊C₄	—	2	2	no	—
863	C₄⋊C₄	—	2	2	no	—
864	C₄⋊C₄	—	2	2	no	—
865	C₄⋊C₄	—	2	2	no	—
866	C₄⋊C₄	—	2	1	no	—
867	C₄⋊C₄	—	2	1	no	—
868	C₄⋊C₄	—	2	2	no	—
869	C₄⋊C₄	—	2	1	no	—
870	C₄⋊C₄	—	2	1	no	—
871	C₄⋊C₄	—	2	1	no	—
872	C₄⋊C₄	—	2	1	no	—
873	C₄⋊C₄	—	2	2	no	—
874	C₄⋊C₄	—	2	2	no	—
875	C₄⋊C₄	—	2	2	no	—
876	C₄⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
877	C₄⋊C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
878	C₄⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
879	C₄⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
880	C₄⋊C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
881	C₄⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
882	C₄⋊C₄	C₂⁴×C₈₉	1	2	yes	—
883	C₄⋊C₄	C₂⁴×C₈₉	1	2	yes	—
884	C₄⋊C₄	C₂⁴×C₈₉	1	2	yes	—
885	C₄⋊C₄	C₂⁴×C₈₉	1	1	yes	characteristic
886	C₄⋊C₄	C₂⁴×C₈₉	1	1	yes	characteristic
887	C₄⋊C₄	C₂⁴×C₈₉	1	2	yes	—
888	C₂²⋊C₄	—	2	2	no	—
889	C₂²⋊C₄	—	2	2	no	—
890	C₂²⋊C₄	—	2	2	no	—
891	C₂²⋊C₄	—	2	1	no	—
892	C₂²⋊C₄	—	2	1	no	—
893	C₂²⋊C₄	—	2	1	no	—
894	C₂²⋊C₄	—	2	1	no	—
895	C₂²⋊C₄	—	2	2	no	—
896	C₂²⋊C₄	—	2	2	no	—
897	C₂²⋊C₄	—	2	2	no	—
898	C₂²⋊C₄	—	2	2	no	—
899	C₂²⋊C₄	—	2	2	no	—
900	C₂²⋊C₄	—	2	2	no	—
901	C₂²⋊C₄	—	2	2	no	—
902	C₂²⋊C₄	—	2	2	no	—
903	C₂²⋊C₄	—	2	2	no	—
904	C₂²⋊C₄	—	2	2	no	—
905	C₂²⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
906	C₂²⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
907	C₂²⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
908	C₂²⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
909	C₂²⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
910	C₄²	—	2	2	no	—
911	C₄²	—	2	2	no	—
912	C₄²	—	2	2	no	—
913	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
914	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
915	C₄²	C₂⁴×C₈₉	1	2	yes	—
916	C₄²	C₂⁴×C₈₉	1	1	yes	characteristic
917	C₄²	C₂⁴×C₈₉	1	1	yes	characteristic
918	C₂³	—	2	1	no	—
919	C₂³	—	2	1	no	—
920	C₂³	—	2	2	no	—
921	C₂³	—	4	2	no	—
922	C₂³	—	4	2	no	—
923	C₂³	—	8	1	no	—
924	C₂³	C₂²×D₄×C₈₉	1	2	yes	—
925	C₂³	C₂²×D₄×C₈₉	1	1	yes	characteristic
926	Q₈	—	2	2	no	—
927	Q₈	—	2	2	no	—
928	Q₈	—	4	1	no	—
929	Q₈	—	4	2	no	—
930	Q₈	—	8	2	no	—
931	Q₈	—	8	1	no	—
932	Q₈	—	8	2	no	—
933	D₄	—	2	4	no	—
934	D₄	—	2	2	no	—
935	D₄	—	2	1	no	—
936	D₄	—	2	1	no	—
937	D₄	—	2	1	no	—
938	D₄	—	2	2	no	—
939	D₄	—	4	1	no	—
940	D₄	—	4	2	no	—
941	D₄	—	4	4	no	—
942	D₄	—	4	4	no	—
943	D₄	—	8	1	no	—
944	D₄	—	8	1	no	—
945	D₄	—	8	2	no	—
946	D₄	—	8	2	no	—
947	D₄	—	8	2	no	—
948	D₄	2₋¹⁺⁴×C₈₉	1	2	yes	—
949	C₂×C₄	—	2	2	no	—
950	C₂×C₄	—	2	1	no	—
951	C₂×C₄	—	2	2	no	—
952	C₂×C₄	—	2	1	no	—
953	C₂×C₄	—	2	2	no	—
954	C₂×C₄	—	2	2	no	—
955	C₂×C₄	—	2	1	no	—
956	C₂×C₄	—	2	2	no	—
957	C₂×C₄	—	2	2	no	—
958	C₂×C₄	—	2	2	no	—
959	C₂×C₄	—	2	1	no	—
960	C₂×C₄	—	2	2	no	—
961	C₂×C₄	—	4	1	no	—
962	C₂×C₄	—	4	4	no	—
963	C₂×C₄	—	4	2	no	—
964	C₂×C₄	—	4	2	no	—
965	C₂×C₄	—	4	2	no	—
966	C₂×C₄	—	8	2	no	—
967	C₂×C₄	—	8	1	no	—
968	C₂×C₄	—	8	1	no	—
969	C₂×C₄	—	8	2	no	—
970	C₂×C₄	—	8	2	no	—
971	C₂×C₄	—	8	2	no	—
972	C₂×C₄	—	8	1	no	—
973	C₂×C₄	—	8	1	no	—
974	C₂×C₄	—	8	2	no	—
975	C₂×C₄	—	8	2	no	—
976	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
977	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
978	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
979	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
980	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
981	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
982	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
983	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
984	C₂×C₄	C₂⁵×C₈₉	1	1	yes	characteristic
985	C₈	—	2	2	no	—
986	C₈	—	2	2	no	—
987	C₈	—	2	2	no	—
988	C₈	—	2	2	no	—
989	C₂²	—	2	1	no	—
990	C₂²	—	2	1	no	—
991	C₂²	—	2	2	no	—
992	C₂²	—	2	2	no	—
993	C₂²	—	2	2	no	—
994	C₂²	—	2	2	no	—
995	C₂²	—	4	1	no	—
996	C₂²	—	4	1	no	—
997	C₂²	—	4	2	no	—
998	C₂²	—	4	1	no	—
999	C₂²	—	4	1	no	—
1000	C₂²	—	4	2	no	—
1001	C₂²	—	4	1	no	—
1002	C₂²	—	4	2	no	—
1003	C₂²	—	8	4	no	—
1004	C₂²	#577×C₈₉	1	2	yes	—
1005	C₂²	C₂³×D₄×C₈₉	1	1	yes	characteristic
1006	C₄	—	2	1	no	—
1007	C₄	—	2	1	no	—
1008	C₄	—	2	2	no	—
1009	C₄	—	2	1	no	—
1010	C₄	—	2	1	no	—
1011	C₄	—	2	2	no	—
1012	C₄	—	2	2	no	—
1013	C₄	—	2	1	no	—
1014	C₄	—	4	2	no	—
1015	C₄	—	4	2	no	—
1016	C₄	—	4	1	no	—
1017	C₄	—	4	1	no	—
1018	C₄	—	4	2	no	—
1019	C₄	—	4	2	no	—
1020	C₄	—	4	2	no	—
1021	C₄	C₂×2₋¹⁺⁴×C₈₉	1	1	yes	characteristic
1022	C₄	#585×C₈₉	1	1	yes	characteristic
1023	C₂	—	2	2	no	—
1024	C₂	—	4	2	no	—
1025	C₂	—	4	2	no	—
1026	C₂	—	8	2	no	—
1027	C₂	—	8	1	no	—
1028	C₂	C₈₉×#3489	1	1	yes	characteristic
1029	C₂	C₂×#577×C₈₉	1	1	yes	characteristic
1030	C₂	C₈₉×#3585	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₈₉	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₈₉
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₈₉ ◁ #529×C₈₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₈₉×#3559	C₂	semidirect
2. C₈₉×#3520	C₂	semidirect
3. C₈₉×#3384	C₂	semidirect
4. C₈₉×#3376	C₂	semidirect
5. C₈₉×#3346	C₂	semidirect
6. C₈₉×#3345	C₂	semidirect
7. C₈₉×#3335	C₂	semidirect
8. C₈₉×#3307	C₂	semidirect
9. C₈₉×#3306	C₂	semidirect
10. C₈₉×#3297	C₂	semidirect
11. C₈₉×#3257	C₂	semidirect
12. C₈₉×#3246	C₂	semidirect
13. C₈₉×#3244	C₂	semidirect
14. C₈₉×#3236	C₂	semidirect
15. C₈₉×#3119	C₂	semidirect
16. C₈₉×#3109	C₂	semidirect
17. C₈₉×#3084	C₂	semidirect
18. C₂×#478×C₈₉	C₂	semidirect
19. C₈₉×#2992	C₂	semidirect
24. #554×C₈₉	C₂²	semidirect
26. #553×C₈₉	C₂²	semidirect
36. #544×C₈₉	C₂²	semidirect
38. #540×C₈₉	C₂²	semidirect
51. #501×C₈₉	C₂²	semidirect
52. #501×C₈₉	C₂²	semidirect
53. #498×C₈₉	C₂²	semidirect
54. #491×C₈₉	C₂²	semidirect
57. #485×C₈₉	C₂²	semidirect
60. #483×C₈₉	C₂²	semidirect
64. #481×C₈₉	C₂²	semidirect
65. #480×C₈₉	C₂²	semidirect
66. #479×C₈₉	C₂²	semidirect
67. #479×C₈₉	C₂²	semidirect
68. #479×C₈₉	C₂²	semidirect
77. #476×C₈₉	C₂²	semidirect
78. #476×C₈₉	C₂²	semidirect
79. #475×C₈₉	C₂²	semidirect
80. #475×C₈₉	C₂²	semidirect
81. #474×C₈₉	C₂²	semidirect
83. #468×C₈₉	C₂²	semidirect
87. #465×C₈₉	C₂²	semidirect
90. #461×C₈₉	C₂²	semidirect
91. #460×C₈₉	C₂²	semidirect
97. #446×C₈₉	C₂²	semidirect
101. #440×C₈₉	C₂²	semidirect
102. C₄×SD₁₆×C₈₉	C₂²	semidirect
105. #435×C₈₉	C₂²	semidirect
107. #433×C₈₉	C₂²	semidirect
109. #428×C₈₉	C₂²	semidirect
112. C₂×#106×C₈₉	C₂²	semidirect
113. #424×C₈₉	C₂²	semidirect
507. #62166	C₈₉	direct (N × H)
516. #3559	C₂×C₈₉	semidirect
517. #3520	C₂×C₈₉	semidirect
518. #3384	C₂×C₈₉	semidirect
519. #3376	C₂×C₈₉	semidirect
520. #3346	C₂×C₈₉	semidirect
521. #3345	C₂×C₈₉	semidirect
522. #3335	C₂×C₈₉	semidirect
523. #3307	C₂×C₈₉	semidirect
524. #3306	C₂×C₈₉	semidirect
525. #3297	C₂×C₈₉	semidirect
526. #3257	C₂×C₈₉	semidirect
527. #3246	C₂×C₈₉	semidirect
528. #3244	C₂×C₈₉	semidirect
529. #3236	C₂×C₈₉	semidirect
530. #3119	C₂×C₈₉	semidirect
531. #3109	C₂×C₈₉	semidirect
532. #3084	C₂×C₈₉	semidirect
533. C₂×#478	C₂×C₈₉	semidirect
534. #2992	C₂×C₈₉	semidirect
535. C₈₉	#62166	direct (N × H)
540. #554	C₂²×C₈₉	semidirect
542. #553	C₂²×C₈₉	semidirect
552. #544	C₂²×C₈₉	semidirect
554. #540	C₂²×C₈₉	semidirect
567. #501	C₂²×C₈₉	semidirect
568. #501	C₂²×C₈₉	semidirect
569. #498	C₂²×C₈₉	semidirect
570. #491	C₂²×C₈₉	semidirect
573. #485	C₂²×C₈₉	semidirect
576. #483	C₂²×C₈₉	semidirect
580. #481	C₂²×C₈₉	semidirect
581. #480	C₂²×C₈₉	semidirect
582. #479	C₂²×C₈₉	semidirect
583. #479	C₂²×C₈₉	semidirect
584. #479	C₂²×C₈₉	semidirect
593. #476	C₂²×C₈₉	semidirect
594. #476	C₂²×C₈₉	semidirect
595. #475	C₂²×C₈₉	semidirect
596. #475	C₂²×C₈₉	semidirect
597. #474	C₂²×C₈₉	semidirect
599. #468	C₂²×C₈₉	semidirect
603. #465	C₂²×C₈₉	semidirect
606. #461	C₂²×C₈₉	semidirect
607. #460	C₂²×C₈₉	semidirect
613. #446	C₂²×C₈₉	semidirect
617. #440	C₂²×C₈₉	semidirect
618. C₄×SD₁₆	C₂²×C₈₉	semidirect
621. #435	C₂²×C₈₉	semidirect
623. #433	C₂²×C₈₉	semidirect
625. #428	C₂²×C₈₉	semidirect
628. C₂×#106	C₂²×C₈₉	semidirect
629. #424	C₂²×C₈₉	semidirect

Maximal subgroups

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

subgroup	index
C₈₉×#3559	2
C₈₉×#3520	2
C₈₉×#3384	2
C₈₉×#3376	2
C₈₉×#3346	2
C₈₉×#3345	2
C₈₉×#3335	2
C₈₉×#3307	2
C₈₉×#3306	2
C₈₉×#3297	2
C₈₉×#3257	2
C₈₉×#3246	2
C₈₉×#3244	2
C₈₉×#3236	2
C₈₉×#3119	2
C₈₉×#3109	2
C₈₉×#3084	2
C₂×#478×C₈₉	2
C₈₉×#2992	2
#62166	89

Subgroups — C89×#62166 #36440014

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#62166 #36440014