Subgroups — C₈₉×#62561 #36440409

Order 22784.

1780 conjugacy classes of subgroups.

The subgroup lattice has 1172 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈₉×#3547	C₂	1	1	yes	maximal, characteristic, complemented
2	C₈₉×#3546	C₂	1	1	yes	maximal, characteristic, complemented
3	C₈₉×#3367	C₂	1	1	yes	maximal, characteristic, complemented
4	C₈₉×#3366	C₂	1	1	yes	maximal, characteristic, complemented
5	C₈₉×#3360	C₂	1	1	yes	maximal, characteristic, complemented
6	C₈₉×#3358	C₂	1	1	yes	maximal, characteristic, complemented
7	C₈₉×#3330	C₂	1	1	yes	maximal, characteristic, complemented
8	C₈₉×#3325	C₂	1	1	yes	maximal, characteristic, complemented
9	C₈₉×#3319	C₂	1	2	yes	maximal, complemented
10	C₈₉×#3309	C₂	1	2	yes	maximal, complemented
11	C₈₉×#3305	C₂	1	2	yes	maximal, complemented
12	C₈₉×#3303	C₂	1	1	yes	maximal, characteristic, complemented
13	C₈₉×#3297	C₂	1	2	yes	maximal, complemented
14	C₈₉×#3294	C₂	1	1	yes	maximal, characteristic, complemented
15	C₈₉×#3243	C₂	1	2	yes	maximal, complemented
16	C₈₉×#3235	C₂	1	1	yes	maximal, characteristic, complemented
17	C₈₉×#3220	C₂	1	2	yes	maximal, complemented
18	C₈₉×#3214	C₂	1	1	yes	maximal, characteristic, complemented
19	C₈₉×#3179	C₂	1	2	yes	maximal, complemented
20	C₈₉×#3169	C₂	1	1	yes	maximal, characteristic, complemented
21	C₈₉×#3136	C₂	1	2	yes	maximal, complemented
22	C₈₉×#3131	C₂	1	1	yes	maximal, characteristic, complemented
23	C₈₉×#2966	C₂	1	1	yes	maximal, characteristic, complemented
24	#562×C₈₉	—	2	2	no	—
25	#560×C₈₉	—	2	2	no	—
26	#556×C₈₉	C₂²	1	1	yes	characteristic
27	#555×C₈₉	C₂²	1	1	yes	characteristic
28	#555×C₈₉	C₂²	1	2	yes	complemented
29	#554×C₈₉	C₂²	1	1	yes	characteristic, complemented
30	#553×C₈₉	—	2	1	no	—
31	#553×C₈₉	C₂²	1	2	yes	complemented
32	#552×C₈₉	—	2	1	no	—
33	#550×C₈₉	C₂²	1	2	yes	—
34	#550×C₈₉	C₂²	1	1	yes	characteristic
35	D₄×Q₈×C₈₉	C₂²	1	1	yes	characteristic, complemented
36	#548×C₈₉	—	2	1	no	—
37	#547×C₈₉	C₂²	1	1	yes	characteristic
38	#547×C₈₉	C₂²	1	1	yes	characteristic
39	#546×C₈₉	—	2	1	no	—
40	#546×C₈₉	C₂²	1	2	yes	—
41	D₄²×C₈₉	C₂²	1	1	yes	characteristic
42	#544×C₈₉	C₂²	1	2	yes	complemented
43	#542×C₈₉	—	2	2	no	—
44	#542×C₈₉	C₂²	1	2	yes	—
45	#540×C₈₉	C₂²	1	2	yes	complemented
46	#538×C₈₉	—	2	2	no	—
47	#537×C₈₉	—	2	1	no	—
48	#537×C₈₉	—	2	1	no	—
49	#536×C₈₉	—	2	1	no	—
50	#535×C₈₉	—	2	1	no	—
51	#535×C₈₉	C₂²	1	2	yes	—
52	#533×C₈₉	C₂²	1	1	yes	characteristic, complemented
53	#532×C₈₉	C₂²	1	1	yes	characteristic
54	#532×C₈₉	C₂²	1	1	yes	characteristic
55	#532×C₈₉	C₂²	1	1	yes	characteristic, complemented
56	#529×C₈₉	C₂²	1	1	yes	characteristic
57	#501×C₈₉	C₂²	1	2	yes	complemented
58	#500×C₈₉	C₂²	1	1	yes	characteristic, complemented
59	#496×C₈₉	C₂²	1	2	yes	complemented
60	#493×C₈₉	C₂²	1	1	yes	characteristic
61	#490×C₈₉	C₂²	1	2	yes	—
62	#490×C₈₉	C₂²	1	2	yes	complemented
63	#489×C₈₉	C₂²	1	2	yes	—
64	#489×C₈₉	C₂²	1	2	yes	complemented
65	#488×C₈₉	C₂²	1	2	yes	—
66	#488×C₈₉	C₂²	1	2	yes	complemented
67	#488×C₈₉	C₂²	1	2	yes	complemented
68	#487×C₈₉	C₂²	1	1	yes	characteristic, complemented
69	#487×C₈₉	C₂²	1	1	yes	characteristic, complemented
70	#486×C₈₉	C₂²	1	1	yes	characteristic
71	#486×C₈₉	C₂²	1	1	yes	characteristic
72	#486×C₈₉	C₂²	1	1	yes	characteristic
73	#486×C₈₉	C₂²	1	2	yes	complemented
74	#486×C₈₉	C₂²	1	1	yes	characteristic, complemented
75	#485×C₈₉	C₂²	1	2	yes	complemented
76	#484×C₈₉	C₂²	1	2	yes	complemented
77	#482×C₈₉	C₂²	1	2	yes	—
78	#482×C₈₉	C₂²	1	2	yes	—
79	#482×C₈₉	C₂²	1	2	yes	complemented
80	#480×C₈₉	C₂²	1	2	yes	—
81	#479×C₈₉	C₂²	1	2	yes	complemented
82	#478×C₈₉	C₂²	1	2	yes	complemented
83	#477×C₈₉	C₂²	1	2	yes	complemented
84	#476×C₈₉	C₂²	1	1	yes	characteristic
85	#476×C₈₉	C₂²	1	1	yes	characteristic, complemented
86	#474×C₈₉	C₂²	1	1	yes	characteristic
87	#474×C₈₉	C₂²	1	2	yes	complemented
88	#474×C₈₉	C₂²	1	1	yes	characteristic, complemented
89	#469×C₈₉	C₂²	1	2	yes	—
90	#468×C₈₉	C₂²	1	2	yes	complemented
91	#466×C₈₉	C₂²	1	1	yes	characteristic
92	#466×C₈₉	C₂²	1	1	yes	characteristic
93	#466×C₈₉	C₂²	1	2	yes	—
94	#466×C₈₉	C₂²	1	1	yes	characteristic, complemented
95	#466×C₈₉	C₂²	1	1	yes	characteristic, complemented
96	#465×C₈₉	C₂²	1	2	yes	complemented
97	#463×C₈₉	C₂²	1	2	yes	—
98	#463×C₈₉	C₂²	1	2	yes	—
99	#461×C₈₉	C₂²	1	1	yes	characteristic, complemented
100	#461×C₈₉	C₂²	1	1	yes	characteristic, complemented
101	#459×C₈₉	C₂²	1	1	yes	characteristic
102	#459×C₈₉	C₂²	1	1	yes	characteristic
103	#459×C₈₉	C₂²	1	2	yes	complemented
104	#459×C₈₉	C₂²	1	2	yes	complemented
105	#449×C₈₉	C₂²	1	2	yes	complemented
106	#449×C₈₉	C₂²	1	2	yes	complemented
107	#449×C₈₉	C₂²	1	2	yes	complemented
108	#449×C₈₉	C₂²	1	2	yes	complemented
109	#447×C₈₉	C₂²	1	2	yes	—
110	#447×C₈₉	C₂²	1	2	yes	—
111	#446×C₈₉	C₂²	1	1	yes	characteristic, complemented
112	C₈×Q₈×C₈₉	C₂²	1	1	yes	characteristic, complemented
113	#442×C₈₉	C₂²	1	2	yes	complemented
114	#440×C₈₉	C₂²	1	2	yes	complemented
115	C₄×SD₁₆×C₈₉	C₂²	1	2	yes	complemented
116	C₄×D₈×C₈₉	C₂²	1	1	yes	characteristic
117	C₄×D₈×C₈₉	C₂²	1	1	yes	characteristic
118	C₄×D₈×C₈₉	C₂²	1	1	yes	characteristic, complemented
119	C₄×D₈×C₈₉	C₂²	1	1	yes	characteristic, complemented
120	C₄×D₈×C₈₉	C₂²	1	2	yes	complemented
121	#436×C₈₉	C₂²	1	1	yes	characteristic
122	#435×C₈₉	C₂²	1	2	yes	complemented
123	C₈×D₄×C₈₉	C₂²	1	1	yes	characteristic
124	C₈×D₄×C₈₉	C₂²	1	2	yes	complemented
125	#433×C₈₉	C₂²	1	2	yes	complemented
126	#432×C₈₉	C₂²	1	1	yes	characteristic, complemented
127	#418×C₈₉	C₂²	1	2	yes	—
128	#417×C₈₉	C₂²	1	2	yes	complemented
129	#416×C₈₉	C₂²	1	2	yes	complemented
130	#416×C₈₉	C₂²	1	2	yes	complemented
131	#416×C₈₉	C₂²	1	2	yes	complemented
132	C₂×#102×C₈₉	C₂²	1	2	yes	—
133	#405×C₈₉	C₂²	1	2	yes	complemented
134	C₂×C₄×C₈×C₈₉	C₂²	1	1	yes	characteristic, complemented
135	C₂×#41×C₈₉	—	2	1	no	—
136	C₂×#41×C₈₉	—	2	1	no	—
137	C₂×#41×C₈₉	—	2	1	no	—
138	C₂×#41×C₈₉	—	2	1	no	—
139	C₂×#41×C₈₉	C₂³	1	2	yes	—
140	C₂×#41×C₈₉	C₂³	1	2	yes	—
141	C₂²×Q₈×C₈₉	—	2	1	no	—
142	C₂²×D₄×C₈₉	—	2	1	no	—
143	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
144	C₂×SD₁₆×C₈₉	C₂³	1	2	yes	—
145	C₂×SD₁₆×C₈₉	C₂³	1	2	yes	—
146	C₂×D₈×C₈₉	C₂³	1	1	yes	characteristic
147	C₂×D₈×C₈₉	C₂³	1	1	yes	characteristic
148	C₂×D₈×C₈₉	C₂³	1	2	yes	—
149	C₂×D₈×C₈₉	C₂³	1	1	yes	characteristic
150	C₂×D₈×C₈₉	C₂³	1	1	yes	characteristic
151	C₂×D₈×C₈₉	C₂³	1	2	yes	—
152	C₂×M₁₆×C₈₉	C₂³	1	2	yes	—
153	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
154	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
155	C₂²×C₈×C₈₉	C₂³	1	2	yes	—
156	C₄⋊Q₈×C₈₉	—	2	2	no	—
157	C₄⋊Q₈×C₈₉	C₂³	1	1	yes	characteristic
158	C₄⋊Q₈×C₈₉	C₂³	1	1	yes	characteristic
159	C₄⋊Q₈×C₈₉	C₂³	1	2	yes	—
160	C₄⋊Q₈×C₈₉	C₂³	1	1	yes	characteristic
161	C₄⋊Q₈×C₈₉	C₂³	1	1	yes	characteristic
162	C₄⋊Q₈×C₈₉	C₂³	1	1	yes	characteristic
163	#127×C₈₉	—	2	2	no	—
164	#127×C₈₉	C₂³	1	1	yes	characteristic
165	#127×C₈₉	C₂³	1	2	yes	—
166	#127×C₈₉	C₂³	1	1	yes	characteristic
167	#127×C₈₉	C₂³	1	1	yes	characteristic
168	#126×C₈₉	—	2	2	no	—
169	#126×C₈₉	—	2	2	no	—
170	#126×C₈₉	—	2	2	no	—
171	#126×C₈₉	D₄	1	2	yes	—
172	#125×C₈₉	—	2	2	no	—
173	#125×C₈₉	D₄	1	1	yes	characteristic
174	#125×C₈₉	C₂³	1	2	yes	—
175	#125×C₈₉	C₂³	1	2	yes	—
176	#124×C₈₉	—	2	2	no	—
177	#124×C₈₉	—	2	2	no	—
178	#124×C₈₉	—	2	2	no	—
179	#124×C₈₉	—	2	2	no	—
180	#124×C₈₉	—	2	1	no	—
181	#124×C₈₉	—	2	1	no	—
182	#124×C₈₉	D₄	1	1	yes	characteristic
183	#124×C₈₉	C₂³	1	2	yes	—
184	#124×C₈₉	C₂³	1	2	yes	—
185	#123×C₈₉	—	2	2	no	—
186	#123×C₈₉	—	2	2	no	—
187	#123×C₈₉	—	2	2	no	—
188	#123×C₈₉	—	2	2	no	—
189	#123×C₈₉	—	2	2	no	—
190	#123×C₈₉	—	2	2	no	—
191	#123×C₈₉	—	2	2	no	—
192	#123×C₈₉	D₄	1	2	yes	—
193	C₂²⋊Q₈×C₈₉	—	2	1	no	—
194	C₂²⋊Q₈×C₈₉	—	2	1	no	—
195	C₂²⋊Q₈×C₈₉	—	2	1	no	—
196	C₂²⋊Q₈×C₈₉	—	2	1	no	—
197	C₂²⋊Q₈×C₈₉	—	2	1	no	—
198	C₂²⋊Q₈×C₈₉	—	2	2	no	—
199	C₂²⋊Q₈×C₈₉	—	2	1	no	—
200	C₂²⋊Q₈×C₈₉	—	2	2	no	—
201	C₂²⋊Q₈×C₈₉	—	2	2	no	—
202	C₂²⋊Q₈×C₈₉	—	2	2	no	—
203	C₂²⋊Q₈×C₈₉	—	2	2	no	—
204	C₂²⋊Q₈×C₈₉	D₄	1	1	yes	characteristic
205	C₂²⋊Q₈×C₈₉	C₂³	1	2	yes	—
206	#121×C₈₉	—	2	1	no	—
207	#121×C₈₉	—	2	1	no	—
208	#121×C₈₉	—	2	2	no	—
209	#121×C₈₉	—	2	2	no	—
210	#121×C₈₉	—	2	1	no	—
211	#121×C₈₉	—	2	1	no	—
212	#121×C₈₉	—	2	1	no	—
213	#121×C₈₉	—	2	1	no	—
214	#121×C₈₉	—	2	1	no	—
215	#121×C₈₉	—	2	2	no	—
216	#121×C₈₉	—	2	2	no	—
217	#121×C₈₉	—	2	1	no	—
218	#121×C₈₉	—	2	2	no	—
219	#121×C₈₉	—	2	2	no	—
220	#121×C₈₉	—	2	2	no	—
221	#121×C₈₉	—	2	2	no	—
222	#121×C₈₉	—	2	2	no	—
223	#121×C₈₉	—	2	2	no	—
224	#121×C₈₉	D₄	1	1	yes	characteristic
225	#121×C₈₉	C₂³	1	2	yes	—
226	#121×C₈₉	C₂³	1	2	yes	—
227	#121×C₈₉	C₂³	1	1	yes	characteristic
228	#121×C₈₉	C₂³	1	1	yes	characteristic
229	#121×C₈₉	C₂³	1	1	yes	characteristic
230	#121×C₈₉	C₂³	1	2	yes	—
231	#121×C₈₉	C₂³	1	1	yes	characteristic
232	#120×C₈₉	—	2	2	no	—
233	#120×C₈₉	—	2	2	no	—
234	#120×C₈₉	—	2	2	no	—
235	#120×C₈₉	—	2	2	no	—
236	C₄×Q₈×C₈₉	—	2	1	no	—
237	C₄×Q₈×C₈₉	—	2	1	no	—
238	C₄×Q₈×C₈₉	C₂³	1	2	yes	—
239	C₄×Q₈×C₈₉	C₂³	1	1	yes	characteristic
240	C₄×D₄×C₈₉	—	2	2	no	—
241	C₄×D₄×C₈₉	—	2	2	no	—
242	C₄×D₄×C₈₉	—	2	1	no	—
243	C₄×D₄×C₈₉	—	2	1	no	—
244	C₄×D₄×C₈₉	—	2	1	no	—
245	C₄×D₄×C₈₉	—	2	1	no	—
246	C₄×D₄×C₈₉	C₂³	1	1	yes	characteristic
247	C₄×D₄×C₈₉	C₂³	1	1	yes	characteristic
248	C₄×D₄×C₈₉	C₂³	1	1	yes	characteristic
249	C₄×D₄×C₈₉	C₂³	1	1	yes	characteristic
250	C₄×D₄×C₈₉	C₂³	1	2	yes	—
251	C₄×D₄×C₈₉	C₂³	1	2	yes	—
252	C₄×D₄×C₈₉	C₂³	1	2	yes	—
253	C₄×D₄×C₈₉	C₂³	1	1	yes	characteristic
254	C₄×D₄×C₈₉	C₂³	1	2	yes	—
255	#117×C₈₉	—	2	1	no	—
256	#117×C₈₉	—	2	1	no	—
257	#117×C₈₉	—	2	2	no	—
258	#117×C₈₉	C₂³	1	2	yes	—
259	#117×C₈₉	C₂³	1	2	yes	—
260	#117×C₈₉	C₂³	1	2	yes	—
261	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
262	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
263	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
264	C₂×C₂²⋊C₄×C₈₉	—	2	2	no	—
265	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
266	#107×C₈₉	C₂³	1	1	yes	characteristic
267	#107×C₈₉	C₂³	1	1	yes	characteristic
268	#107×C₈₉	C₂³	1	1	yes	characteristic
269	#107×C₈₉	C₂³	1	1	yes	characteristic
270	#107×C₈₉	C₂³	1	2	yes	—
271	#107×C₈₉	C₂³	1	2	yes	—
272	#106×C₈₉	C₂³	1	2	yes	—
273	#106×C₈₉	C₂³	1	2	yes	—
274	C₄⋊C₈×C₈₉	C₂³	1	1	yes	characteristic
275	C₄⋊C₈×C₈₉	C₂³	1	1	yes	characteristic
276	C₄⋊C₈×C₈₉	C₂³	1	2	yes	—
277	C₄⋊C₈×C₈₉	C₂³	1	2	yes	—
278	#103×C₈₉	C₂³	1	2	yes	—
279	#103×C₈₉	C₂³	1	2	yes	—
280	#103×C₈₉	C₂³	1	2	yes	—
281	#103×C₈₉	C₂³	1	2	yes	—
282	#103×C₈₉	C₂³	1	2	yes	—
283	#103×C₈₉	C₂³	1	2	yes	—
284	#102×C₈₉	C₂³	1	1	yes	characteristic
285	#102×C₈₉	C₂³	1	2	yes	—
286	#102×C₈₉	C₂³	1	2	yes	—
287	#102×C₈₉	C₂³	1	2	yes	—
288	#102×C₈₉	C₂³	1	1	yes	characteristic
289	#102×C₈₉	C₂³	1	2	yes	—
290	#102×C₈₉	C₂³	1	2	yes	—
291	#102×C₈₉	C₂³	1	2	yes	—
292	#102×C₈₉	C₂³	1	2	yes	—
293	#102×C₈₉	C₂³	1	1	yes	characteristic
294	#102×C₈₉	C₂³	1	2	yes	—
295	#102×C₈₉	C₂³	1	1	yes	characteristic
296	#102×C₈₉	C₂³	1	2	yes	—
297	#102×C₈₉	C₂³	1	2	yes	—
298	#102×C₈₉	C₂³	1	1	yes	characteristic
299	#102×C₈₉	C₂³	1	1	yes	characteristic
300	#102×C₈₉	C₂³	1	1	yes	characteristic
301	#102×C₈₉	C₂³	1	1	yes	characteristic
302	C₂²⋊C₈×C₈₉	C₂³	1	2	yes	—
303	C₂²⋊C₈×C₈₉	C₂³	1	2	yes	—
304	C₂²⋊C₈×C₈₉	C₂³	1	2	yes	—
305	#97×C₈₉	C₂³	1	2	yes	—
306	#97×C₈₉	C₂³	1	2	yes	—
307	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
308	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
309	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
310	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
311	C₄×C₈×C₈₉	C₂³	1	2	yes	—
312	C₂⁴×C₈₉	—	2	2	no	—
313	#41×C₈₉	—	4	2	no	—
314	#41×C₈₉	—	4	2	no	—
315	#41×C₈₉	—	4	2	no	—
316	#41×C₈₉	—	4	2	no	—
317	#41×C₈₉	—	8	2	no	—
318	#41×C₈₉	—	8	2	no	—
319	#41×C₈₉	—	8	2	no	—
320	#41×C₈₉	—	8	2	no	—
321	C₂×Q₈×C₈₉	—	2	1	no	—
322	C₂×Q₈×C₈₉	—	2	1	no	—
323	C₂×Q₈×C₈₉	—	2	1	no	—
324	C₂×Q₈×C₈₉	—	2	2	no	—
325	C₂×Q₈×C₈₉	—	2	1	no	—
326	C₂×Q₈×C₈₉	—	8	2	no	—
327	C₂×Q₈×C₈₉	C₂×D₄	1	1	yes	characteristic
328	C₂×Q₈×C₈₉	C₂⁴	1	2	yes	—
329	C₂×D₄×C₈₉	—	2	2	no	—
330	C₂×D₄×C₈₉	—	2	1	no	—
331	C₂×D₄×C₈₉	—	2	2	no	—
332	C₂×D₄×C₈₉	—	2	2	no	—
333	C₂×D₄×C₈₉	—	2	2	no	—
334	C₂×D₄×C₈₉	—	2	1	no	—
335	C₂×D₄×C₈₉	—	2	2	no	—
336	C₂×D₄×C₈₉	—	2	1	no	—
337	C₂×D₄×C₈₉	—	2	1	no	—
338	C₂×D₄×C₈₉	—	2	1	no	—
339	C₂×D₄×C₈₉	—	2	1	no	—
340	C₂×D₄×C₈₉	—	2	1	no	—
341	C₂×D₄×C₈₉	—	2	2	no	—
342	C₂×D₄×C₈₉	—	2	1	no	—
343	C₂×D₄×C₈₉	—	2	1	no	—
344	C₂×D₄×C₈₉	—	2	2	no	—
345	C₂×D₄×C₈₉	—	2	2	no	—
346	C₂×D₄×C₈₉	—	2	1	no	—
347	C₂×D₄×C₈₉	—	4	2	no	—
348	C₂×D₄×C₈₉	—	4	2	no	—
349	C₂×D₄×C₈₉	—	8	2	no	—
350	C₂×D₄×C₈₉	C₂×D₄	1	1	yes	characteristic
351	C₂×D₄×C₈₉	C₂×D₄	1	2	yes	—
352	C₂×D₄×C₈₉	C₂⁴	1	1	yes	characteristic
353	C₂×D₄×C₈₉	C₂⁴	1	2	yes	—
354	C₂×D₄×C₈₉	C₂⁴	1	1	yes	characteristic
355	C₂×D₄×C₈₉	C₂⁴	1	1	yes	characteristic
356	C₂×D₄×C₈₉	C₂⁴	1	1	yes	characteristic
357	C₂²×C₄×C₈₉	—	2	2	no	—
358	C₂²×C₄×C₈₉	—	2	1	no	—
359	C₂²×C₄×C₈₉	—	2	1	no	—
360	C₂²×C₄×C₈₉	—	2	1	no	—
361	C₂²×C₄×C₈₉	—	2	1	no	—
362	C₂²×C₄×C₈₉	—	2	2	no	—
363	C₂²×C₄×C₈₉	—	2	2	no	—
364	C₂²×C₄×C₈₉	—	2	2	no	—
365	C₂²×C₄×C₈₉	—	2	2	no	—
366	C₂²×C₄×C₈₉	—	2	2	no	—
367	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
368	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
369	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
370	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
371	SD₁₆×C₈₉	—	4	2	no	—
372	SD₁₆×C₈₉	—	4	2	no	—
373	D₈×C₈₉	—	4	1	no	—
374	D₈×C₈₉	—	4	1	no	—
375	D₈×C₈₉	—	4	1	no	—
376	D₈×C₈₉	—	4	1	no	—
377	D₈×C₈₉	—	4	2	no	—
378	D₈×C₈₉	—	4	2	no	—
379	M₁₆×C₈₉	—	4	2	no	—
380	C₂×C₈×C₈₉	—	4	1	no	—
381	C₂×C₈×C₈₉	—	4	2	no	—
382	C₂×C₈×C₈₉	—	4	1	no	—
383	C₂×C₈×C₈₉	C₂⁴	1	1	yes	characteristic
384	C₂×C₈×C₈₉	C₂⁴	1	1	yes	characteristic
385	C₂×C₈×C₈₉	C₂⁴	1	1	yes	characteristic
386	C₂×C₈×C₈₉	C₂⁴	1	1	yes	characteristic
387	C₂×C₈×C₈₉	C₂⁴	1	2	yes	—
388	C₂×C₈×C₈₉	C₂⁴	1	2	yes	—
389	C₄⋊C₄×C₈₉	—	2	1	no	—
390	C₄⋊C₄×C₈₉	—	2	1	no	—
391	C₄⋊C₄×C₈₉	—	2	2	no	—
392	C₄⋊C₄×C₈₉	—	2	2	no	—
393	C₄⋊C₄×C₈₉	—	2	2	no	—
394	C₄⋊C₄×C₈₉	—	2	2	no	—
395	C₄⋊C₄×C₈₉	—	2	1	no	—
396	C₄⋊C₄×C₈₉	—	2	1	no	—
397	C₄⋊C₄×C₈₉	—	2	1	no	—
398	C₄⋊C₄×C₈₉	—	2	2	no	—
399	C₄⋊C₄×C₈₉	—	2	2	no	—
400	C₄⋊C₄×C₈₉	—	2	2	no	—
401	C₄⋊C₄×C₈₉	—	2	1	no	—
402	C₄⋊C₄×C₈₉	—	2	2	no	—
403	C₄⋊C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
404	C₄⋊C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
405	C₄⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
406	C₄⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
407	C₄⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
408	C₄⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
409	C₄⋊C₄×C₈₉	C₂⁴	1	2	yes	—
410	C₄⋊C₄×C₈₉	C₂⁴	1	1	yes	characteristic
411	C₄⋊C₄×C₈₉	C₂⁴	1	2	yes	—
412	C₄⋊C₄×C₈₉	C₂⁴	1	1	yes	characteristic
413	C₄⋊C₄×C₈₉	C₂⁴	1	1	yes	characteristic
414	C₄⋊C₄×C₈₉	C₂⁴	1	1	yes	characteristic
415	C₂²⋊C₄×C₈₉	—	2	2	no	—
416	C₂²⋊C₄×C₈₉	—	2	2	no	—
417	C₂²⋊C₄×C₈₉	—	2	2	no	—
418	C₂²⋊C₄×C₈₉	—	2	1	no	—
419	C₂²⋊C₄×C₈₉	—	2	2	no	—
420	C₂²⋊C₄×C₈₉	—	2	1	no	—
421	C₂²⋊C₄×C₈₉	—	2	2	no	—
422	C₂²⋊C₄×C₈₉	—	2	2	no	—
423	C₂²⋊C₄×C₈₉	—	2	2	no	—
424	C₂²⋊C₄×C₈₉	—	2	1	no	—
425	C₂²⋊C₄×C₈₉	—	2	1	no	—
426	C₂²⋊C₄×C₈₉	—	2	2	no	—
427	C₂²⋊C₄×C₈₉	—	2	2	no	—
428	C₂²⋊C₄×C₈₉	—	2	2	no	—
429	C₂²⋊C₄×C₈₉	—	2	1	no	—
430	C₂²⋊C₄×C₈₉	—	2	2	no	—
431	C₂²⋊C₄×C₈₉	—	2	1	no	—
432	C₂²⋊C₄×C₈₉	—	2	2	no	—
433	C₂²⋊C₄×C₈₉	—	2	1	no	—
434	C₂²⋊C₄×C₈₉	—	2	2	no	—
435	C₂²⋊C₄×C₈₉	—	2	1	no	—
436	C₂²⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
437	C₂²⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
438	C₂²⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
439	C₂²⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
440	C₂²⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
441	C₄²×C₈₉	—	2	2	no	—
442	C₄²×C₈₉	—	2	2	no	—
443	C₄²×C₈₉	—	2	2	no	—
444	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
445	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
446	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
447	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
448	C₄²×C₈₉	C₂⁴	1	2	yes	—
449	C₂³×C₈₉	—	2	1	no	—
450	C₂³×C₈₉	—	2	1	no	—
451	C₂³×C₈₉	—	2	1	no	—
452	C₂³×C₈₉	—	2	2	no	—
453	C₂³×C₈₉	—	2	1	no	—
454	C₂³×C₈₉	—	8	2	no	—
455	C₂³×C₈₉	—	8	2	no	—
456	C₂³×C₈₉	—	8	2	no	—
457	C₂³×C₈₉	C₂²×D₄	1	2	yes	—
458	C₂³×C₈₉	C₂²×D₄	1	1	yes	characteristic
459	Q₈×C₈₉	—	2	2	no	—
460	Q₈×C₈₉	—	2	2	no	—
461	Q₈×C₈₉	—	2	2	no	—
462	Q₈×C₈₉	—	4	2	no	—
463	Q₈×C₈₉	—	8	1	no	—
464	Q₈×C₈₉	—	8	2	no	—
465	Q₈×C₈₉	—	8	1	no	—
466	Q₈×C₈₉	—	8	1	no	—
467	D₄×C₈₉	—	2	2	no	—
468	D₄×C₈₉	—	2	1	no	—
469	D₄×C₈₉	—	2	1	no	—
470	D₄×C₈₉	—	2	1	no	—
471	D₄×C₈₉	—	2	1	no	—
472	D₄×C₈₉	—	2	1	no	—
473	D₄×C₈₉	—	2	1	no	—
474	D₄×C₈₉	—	2	2	no	—
475	D₄×C₈₉	—	2	2	no	—
476	D₄×C₈₉	—	2	1	no	—
477	D₄×C₈₉	—	2	1	no	—
478	D₄×C₈₉	—	4	2	no	—
479	D₄×C₈₉	—	4	2	no	—
480	D₄×C₈₉	—	8	1	no	—
481	D₄×C₈₉	—	8	1	no	—
482	D₄×C₈₉	—	8	1	no	—
483	D₄×C₈₉	—	8	2	no	—
484	D₄×C₈₉	—	8	2	no	—
485	D₄×C₈₉	—	8	1	no	—
486	D₄×C₈₉	—	8	1	no	—
487	D₄×C₈₉	—	8	2	no	—
488	D₄×C₈₉	—	8	2	no	—
489	D₄×C₈₉	—	8	2	no	—
490	D₄×C₈₉	—	8	2	no	—
491	D₄×C₈₉	—	8	2	no	—
492	D₄×C₈₉	—	8	1	no	—
493	D₄×C₈₉	—	8	1	no	—
494	D₄×C₈₉	—	8	1	no	—
495	D₄×C₈₉	—	8	1	no	—
496	D₄×C₈₉	—	8	2	no	—
497	C₂×C₄×C₈₉	—	2	2	no	—
498	C₂×C₄×C₈₉	—	2	2	no	—
499	C₂×C₄×C₈₉	—	2	1	no	—
500	C₂×C₄×C₈₉	—	2	1	no	—
501	C₂×C₄×C₈₉	—	2	2	no	—
502	C₂×C₄×C₈₉	—	2	2	no	—
503	C₂×C₄×C₈₉	—	2	1	no	—
504	C₂×C₄×C₈₉	—	2	1	no	—
505	C₂×C₄×C₈₉	—	2	2	no	—
506	C₂×C₄×C₈₉	—	2	2	no	—
507	C₂×C₄×C₈₉	—	2	1	no	—
508	C₂×C₄×C₈₉	—	2	1	no	—
509	C₂×C₄×C₈₉	—	4	1	no	—
510	C₂×C₄×C₈₉	—	4	2	no	—
511	C₂×C₄×C₈₉	—	4	2	no	—
512	C₂×C₄×C₈₉	—	4	2	no	—
513	C₂×C₄×C₈₉	—	4	2	no	—
514	C₂×C₄×C₈₉	—	8	2	no	—
515	C₂×C₄×C₈₉	—	8	2	no	—
516	C₂×C₄×C₈₉	—	8	2	no	—
517	C₂×C₄×C₈₉	—	8	2	no	—
518	C₂×C₄×C₈₉	—	8	2	no	—
519	C₂×C₄×C₈₉	—	8	2	no	—
520	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
521	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
522	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
523	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
524	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
525	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
526	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
527	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
528	C₂×C₄×C₈₉	C₂⁵	1	1	yes	characteristic
529	C₈×C₈₉	—	2	1	no	—
530	C₈×C₈₉	—	2	1	no	—
531	C₈×C₈₉	—	2	1	no	—
532	C₈×C₈₉	—	2	1	no	—
533	C₈×C₈₉	—	2	2	no	—
534	C₈×C₈₉	—	2	2	no	—
535	C₂²×C₈₉	—	2	1	no	—
536	C₂²×C₈₉	—	2	2	no	—
537	C₂²×C₈₉	—	2	1	no	—
538	C₂²×C₈₉	—	2	2	no	—
539	C₂²×C₈₉	—	2	1	no	—
540	C₂²×C₈₉	—	2	2	no	—
541	C₂²×C₈₉	—	4	1	no	—
542	C₂²×C₈₉	—	4	1	no	—
543	C₂²×C₈₉	—	4	1	no	—
544	C₂²×C₈₉	—	4	2	no	—
545	C₂²×C₈₉	—	4	1	no	—
546	C₂²×C₈₉	—	4	1	no	—
547	C₂²×C₈₉	—	4	2	no	—
548	C₂²×C₈₉	—	4	1	no	—
549	C₂²×C₈₉	—	4	1	no	—
550	C₂²×C₈₉	—	4	1	no	—
551	C₂²×C₈₉	—	4	1	no	—
552	C₂²×C₈₉	—	4	1	no	—
553	C₂²×C₈₉	—	4	1	no	—
554	C₂²×C₈₉	—	4	1	no	—
555	C₂²×C₈₉	—	4	2	no	—
556	C₂²×C₈₉	—	16	4	no	—
557	C₂²×C₈₉	C₂³×D₄	1	1	yes	characteristic
558	C₄×C₈₉	—	2	1	no	—
559	C₄×C₈₉	—	2	1	no	—
560	C₄×C₈₉	—	2	2	no	—
561	C₄×C₈₉	—	2	1	no	—
562	C₄×C₈₉	—	2	2	no	—
563	C₄×C₈₉	—	2	1	no	—
564	C₄×C₈₉	—	2	2	no	—
565	C₄×C₈₉	—	4	2	no	—
566	C₄×C₈₉	—	4	2	no	—
567	C₄×C₈₉	—	4	1	no	—
568	C₄×C₈₉	—	4	1	no	—
569	C₄×C₈₉	—	4	1	no	—
570	C₄×C₈₉	—	4	1	no	—
571	C₄×C₈₉	—	4	2	no	—
572	C₄×C₈₉	#576	1	2	yes	—
573	C₄×C₈₉	#585	1	1	yes	characteristic
574	C₄×C₈₉	#585	1	1	yes	characteristic
575	#62561	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
576	C₂×C₈₉	—	4	1	no	—
577	C₂×C₈₉	—	4	2	no	—
578	C₂×C₈₉	—	8	1	no	—
579	C₂×C₈₉	—	8	1	no	—
580	C₂×C₈₉	—	8	1	no	—
581	C₂×C₈₉	—	8	2	no	—
582	C₂×C₈₉	—	8	1	no	—
583	C₂×C₈₉	#3500	1	1	yes	characteristic
584	C₂×C₈₉	C₂×#576	1	1	yes	characteristic
585	C₂×C₈₉	#3584	1	1	yes	characteristic
586	#3547	C₂×C₈₉	1	1	yes	characteristic, complemented
587	#3546	C₂×C₈₉	1	1	yes	characteristic, complemented
588	#3367	C₂×C₈₉	1	1	yes	characteristic, complemented
589	#3366	C₂×C₈₉	1	1	yes	characteristic, complemented
590	#3360	C₂×C₈₉	1	1	yes	characteristic, complemented
591	#3358	C₂×C₈₉	1	1	yes	characteristic, complemented
592	#3330	C₂×C₈₉	1	1	yes	characteristic, complemented
593	#3325	C₂×C₈₉	1	1	yes	characteristic, complemented
594	#3319	C₂×C₈₉	1	2	yes	complemented
595	#3309	C₂×C₈₉	1	2	yes	complemented
596	#3305	C₂×C₈₉	1	2	yes	complemented
597	#3303	C₂×C₈₉	1	1	yes	characteristic, complemented
598	#3297	C₂×C₈₉	1	2	yes	complemented
599	#3294	C₂×C₈₉	1	1	yes	characteristic, complemented
600	#3243	C₂×C₈₉	1	2	yes	complemented
601	#3235	C₂×C₈₉	1	1	yes	characteristic, complemented
602	#3220	C₂×C₈₉	1	2	yes	complemented
603	#3214	C₂×C₈₉	1	1	yes	characteristic, complemented
604	#3179	C₂×C₈₉	1	2	yes	complemented
605	#3169	C₂×C₈₉	1	1	yes	characteristic, complemented
606	#3136	C₂×C₈₉	1	2	yes	complemented
607	#3131	C₂×C₈₉	1	1	yes	characteristic, complemented
608	#2966	C₂×C₈₉	1	1	yes	characteristic, complemented
609	C₈₉	#62561	1	1	yes	characteristic, direct product factor, Sylow
610	#562	—	2	2	no	—
611	#560	—	2	2	no	—
612	#556	C₂²×C₈₉	1	1	yes	characteristic
613	#555	C₂²×C₈₉	1	1	yes	characteristic
614	#555	C₂²×C₈₉	1	2	yes	complemented
615	#554	C₂²×C₈₉	1	1	yes	characteristic, complemented
616	#553	—	2	1	no	—
617	#553	C₂²×C₈₉	1	2	yes	complemented
618	#552	—	2	1	no	—
619	#550	C₂²×C₈₉	1	2	yes	—
620	#550	C₂²×C₈₉	1	1	yes	characteristic
621	D₄×Q₈	C₂²×C₈₉	1	1	yes	characteristic, complemented
622	#548	—	2	1	no	—
623	#547	C₂²×C₈₉	1	1	yes	characteristic
624	#547	C₂²×C₈₉	1	1	yes	characteristic
625	#546	—	2	1	no	—
626	#546	C₂²×C₈₉	1	2	yes	—
627	D₄²	C₂²×C₈₉	1	1	yes	characteristic
628	#544	C₂²×C₈₉	1	2	yes	complemented
629	#542	—	2	2	no	—
630	#542	C₂²×C₈₉	1	2	yes	—
631	#540	C₂²×C₈₉	1	2	yes	complemented
632	#538	—	2	2	no	—
633	#537	—	2	1	no	—
634	#537	—	2	1	no	—
635	#536	—	2	1	no	—
636	#535	—	2	1	no	—
637	#535	C₂²×C₈₉	1	2	yes	—
638	#533	C₂²×C₈₉	1	1	yes	characteristic, complemented
639	#532	C₂²×C₈₉	1	1	yes	characteristic
640	#532	C₂²×C₈₉	1	1	yes	characteristic
641	#532	C₂²×C₈₉	1	1	yes	characteristic, complemented
642	#529	C₂²×C₈₉	1	1	yes	characteristic
643	#501	C₂²×C₈₉	1	2	yes	complemented
644	#500	C₂²×C₈₉	1	1	yes	characteristic, complemented
645	#496	C₂²×C₈₉	1	2	yes	complemented
646	#493	C₂²×C₈₉	1	1	yes	characteristic
647	#490	C₂²×C₈₉	1	2	yes	—
648	#490	C₂²×C₈₉	1	2	yes	complemented
649	#489	C₂²×C₈₉	1	2	yes	—
650	#489	C₂²×C₈₉	1	2	yes	complemented
651	#488	C₂²×C₈₉	1	2	yes	—
652	#488	C₂²×C₈₉	1	2	yes	complemented
653	#488	C₂²×C₈₉	1	2	yes	complemented
654	#487	C₂²×C₈₉	1	1	yes	characteristic, complemented
655	#487	C₂²×C₈₉	1	1	yes	characteristic, complemented
656	#486	C₂²×C₈₉	1	1	yes	characteristic
657	#486	C₂²×C₈₉	1	1	yes	characteristic
658	#486	C₂²×C₈₉	1	1	yes	characteristic
659	#486	C₂²×C₈₉	1	2	yes	complemented
660	#486	C₂²×C₈₉	1	1	yes	characteristic, complemented
661	#485	C₂²×C₈₉	1	2	yes	complemented
662	#484	C₂²×C₈₉	1	2	yes	complemented
663	#482	C₂²×C₈₉	1	2	yes	—
664	#482	C₂²×C₈₉	1	2	yes	—
665	#482	C₂²×C₈₉	1	2	yes	complemented
666	#480	C₂²×C₈₉	1	2	yes	—
667	#479	C₂²×C₈₉	1	2	yes	complemented
668	#478	C₂²×C₈₉	1	2	yes	complemented
669	#477	C₂²×C₈₉	1	2	yes	complemented
670	#476	C₂²×C₈₉	1	1	yes	characteristic
671	#476	C₂²×C₈₉	1	1	yes	characteristic, complemented
672	#474	C₂²×C₈₉	1	1	yes	characteristic
673	#474	C₂²×C₈₉	1	1	yes	characteristic, complemented
674	#474	C₂²×C₈₉	1	2	yes	complemented
675	#469	C₂²×C₈₉	1	2	yes	—
676	#468	C₂²×C₈₉	1	2	yes	complemented
677	#466	C₂²×C₈₉	1	1	yes	characteristic
678	#466	C₂²×C₈₉	1	1	yes	characteristic
679	#466	C₂²×C₈₉	1	2	yes	—
680	#466	C₂²×C₈₉	1	1	yes	characteristic, complemented
681	#466	C₂²×C₈₉	1	1	yes	characteristic, complemented
682	#465	C₂²×C₈₉	1	2	yes	complemented
683	#463	C₂²×C₈₉	1	2	yes	—
684	#463	C₂²×C₈₉	1	2	yes	—
685	#461	C₂²×C₈₉	1	1	yes	characteristic, complemented
686	#461	C₂²×C₈₉	1	1	yes	characteristic, complemented
687	#459	C₂²×C₈₉	1	1	yes	characteristic
688	#459	C₂²×C₈₉	1	1	yes	characteristic
689	#459	C₂²×C₈₉	1	2	yes	complemented
690	#459	C₂²×C₈₉	1	2	yes	complemented
691	#449	C₂²×C₈₉	1	2	yes	complemented
692	#449	C₂²×C₈₉	1	2	yes	complemented
693	#449	C₂²×C₈₉	1	2	yes	complemented
694	#449	C₂²×C₈₉	1	2	yes	complemented
695	#447	C₂²×C₈₉	1	2	yes	—
696	#447	C₂²×C₈₉	1	2	yes	—
697	#446	C₂²×C₈₉	1	1	yes	characteristic, complemented
698	C₈×Q₈	C₂²×C₈₉	1	1	yes	characteristic, complemented
699	#442	C₂²×C₈₉	1	2	yes	complemented
700	#440	C₂²×C₈₉	1	2	yes	complemented
701	C₄×SD₁₆	C₂²×C₈₉	1	2	yes	complemented
702	C₄×D₈	C₂²×C₈₉	1	1	yes	characteristic
703	C₄×D₈	C₂²×C₈₉	1	1	yes	characteristic
704	C₄×D₈	C₂²×C₈₉	1	1	yes	characteristic, complemented
705	C₄×D₈	C₂²×C₈₉	1	1	yes	characteristic, complemented
706	C₄×D₈	C₂²×C₈₉	1	2	yes	complemented
707	#436	C₂²×C₈₉	1	1	yes	characteristic
708	#435	C₂²×C₈₉	1	2	yes	complemented
709	C₈×D₄	C₂²×C₈₉	1	1	yes	characteristic
710	C₈×D₄	C₂²×C₈₉	1	2	yes	complemented
711	#433	C₂²×C₈₉	1	2	yes	complemented
712	#432	C₂²×C₈₉	1	1	yes	characteristic, complemented
713	#418	C₂²×C₈₉	1	2	yes	—
714	#417	C₂²×C₈₉	1	2	yes	complemented
715	#416	C₂²×C₈₉	1	2	yes	complemented
716	#416	C₂²×C₈₉	1	2	yes	complemented
717	#416	C₂²×C₈₉	1	2	yes	complemented
718	C₂×#102	C₂²×C₈₉	1	2	yes	—
719	#405	C₂²×C₈₉	1	2	yes	complemented
720	C₂×C₄×C₈	C₂²×C₈₉	1	1	yes	characteristic, complemented
721	C₂×#41	—	2	1	no	—
722	C₂×#41	—	2	1	no	—
723	C₂×#41	—	2	1	no	—
724	C₂×#41	—	2	1	no	—
725	C₂×#41	C₂³×C₈₉	1	2	yes	—
726	C₂×#41	C₂³×C₈₉	1	2	yes	—
727	C₂²×Q₈	—	2	1	no	—
728	C₂²×D₄	—	2	1	no	—
729	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
730	C₂×SD₁₆	C₂³×C₈₉	1	2	yes	—
731	C₂×SD₁₆	C₂³×C₈₉	1	2	yes	—
732	C₂×D₈	C₂³×C₈₉	1	1	yes	characteristic
733	C₂×D₈	C₂³×C₈₉	1	1	yes	characteristic
734	C₂×D₈	C₂³×C₈₉	1	2	yes	—
735	C₂×D₈	C₂³×C₈₉	1	1	yes	characteristic
736	C₂×D₈	C₂³×C₈₉	1	1	yes	characteristic
737	C₂×D₈	C₂³×C₈₉	1	2	yes	—
738	C₂×M₁₆	C₂³×C₈₉	1	2	yes	—
739	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
740	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
741	C₂²×C₈	C₂³×C₈₉	1	2	yes	—
742	C₄⋊Q₈	—	2	2	no	—
743	C₄⋊Q₈	C₂³×C₈₉	1	1	yes	characteristic
744	C₄⋊Q₈	C₂³×C₈₉	1	1	yes	characteristic
745	C₄⋊Q₈	C₂³×C₈₉	1	1	yes	characteristic
746	C₄⋊Q₈	C₂³×C₈₉	1	1	yes	characteristic
747	C₄⋊Q₈	C₂³×C₈₉	1	1	yes	characteristic
748	C₄⋊Q₈	C₂³×C₈₉	1	2	yes	—
749	#127	—	2	2	no	—
750	#127	C₂³×C₈₉	1	1	yes	characteristic
751	#127	C₂³×C₈₉	1	1	yes	characteristic
752	#127	C₂³×C₈₉	1	1	yes	characteristic
753	#127	C₂³×C₈₉	1	2	yes	—
754	#126	—	2	2	no	—
755	#126	—	2	2	no	—
756	#126	—	2	2	no	—
757	#126	D₄×C₈₉	1	2	yes	—
758	#125	—	2	2	no	—
759	#125	D₄×C₈₉	1	1	yes	characteristic
760	#125	C₂³×C₈₉	1	2	yes	—
761	#125	C₂³×C₈₉	1	2	yes	—
762	#124	—	2	2	no	—
763	#124	—	2	2	no	—
764	#124	—	2	2	no	—
765	#124	—	2	2	no	—
766	#124	—	2	1	no	—
767	#124	—	2	1	no	—
768	#124	D₄×C₈₉	1	1	yes	characteristic
769	#124	C₂³×C₈₉	1	2	yes	—
770	#124	C₂³×C₈₉	1	2	yes	—
771	#123	—	2	2	no	—
772	#123	—	2	2	no	—
773	#123	—	2	2	no	—
774	#123	—	2	2	no	—
775	#123	—	2	2	no	—
776	#123	—	2	2	no	—
777	#123	—	2	2	no	—
778	#123	D₄×C₈₉	1	2	yes	—
779	C₂²⋊Q₈	—	2	1	no	—
780	C₂²⋊Q₈	—	2	1	no	—
781	C₂²⋊Q₈	—	2	1	no	—
782	C₂²⋊Q₈	—	2	1	no	—
783	C₂²⋊Q₈	—	2	1	no	—
784	C₂²⋊Q₈	—	2	2	no	—
785	C₂²⋊Q₈	—	2	1	no	—
786	C₂²⋊Q₈	—	2	2	no	—
787	C₂²⋊Q₈	—	2	2	no	—
788	C₂²⋊Q₈	—	2	2	no	—
789	C₂²⋊Q₈	—	2	2	no	—
790	C₂²⋊Q₈	D₄×C₈₉	1	1	yes	characteristic
791	C₂²⋊Q₈	C₂³×C₈₉	1	2	yes	—
792	#121	—	2	1	no	—
793	#121	—	2	1	no	—
794	#121	—	2	2	no	—
795	#121	—	2	2	no	—
796	#121	—	2	1	no	—
797	#121	—	2	1	no	—
798	#121	—	2	1	no	—
799	#121	—	2	1	no	—
800	#121	—	2	1	no	—
801	#121	—	2	2	no	—
802	#121	—	2	2	no	—
803	#121	—	2	1	no	—
804	#121	—	2	2	no	—
805	#121	—	2	2	no	—
806	#121	—	2	2	no	—
807	#121	—	2	2	no	—
808	#121	—	2	2	no	—
809	#121	—	2	2	no	—
810	#121	D₄×C₈₉	1	1	yes	characteristic
811	#121	C₂³×C₈₉	1	1	yes	characteristic
812	#121	C₂³×C₈₉	1	1	yes	characteristic
813	#121	C₂³×C₈₉	1	1	yes	characteristic
814	#121	C₂³×C₈₉	1	1	yes	characteristic
815	#121	C₂³×C₈₉	1	2	yes	—
816	#121	C₂³×C₈₉	1	2	yes	—
817	#121	C₂³×C₈₉	1	2	yes	—
818	#120	—	2	2	no	—
819	#120	—	2	2	no	—
820	#120	—	2	2	no	—
821	#120	—	2	2	no	—
822	C₄×Q₈	—	2	1	no	—
823	C₄×Q₈	—	2	1	no	—
824	C₄×Q₈	C₂³×C₈₉	1	2	yes	—
825	C₄×Q₈	C₂³×C₈₉	1	1	yes	characteristic
826	C₄×D₄	—	2	2	no	—
827	C₄×D₄	—	2	2	no	—
828	C₄×D₄	—	2	1	no	—
829	C₄×D₄	—	2	1	no	—
830	C₄×D₄	—	2	1	no	—
831	C₄×D₄	—	2	1	no	—
832	C₄×D₄	C₂³×C₈₉	1	1	yes	characteristic
833	C₄×D₄	C₂³×C₈₉	1	1	yes	characteristic
834	C₄×D₄	C₂³×C₈₉	1	1	yes	characteristic
835	C₄×D₄	C₂³×C₈₉	1	1	yes	characteristic
836	C₄×D₄	C₂³×C₈₉	1	2	yes	—
837	C₄×D₄	C₂³×C₈₉	1	2	yes	—
838	C₄×D₄	C₂³×C₈₉	1	2	yes	—
839	C₄×D₄	C₂³×C₈₉	1	1	yes	characteristic
840	C₄×D₄	C₂³×C₈₉	1	2	yes	—
841	#117	—	2	1	no	—
842	#117	—	2	1	no	—
843	#117	—	2	2	no	—
844	#117	C₂³×C₈₉	1	2	yes	—
845	#117	C₂³×C₈₉	1	2	yes	—
846	#117	C₂³×C₈₉	1	2	yes	—
847	C₂×C₄⋊C₄	—	2	1	no	—
848	C₂×C₄⋊C₄	—	2	1	no	—
849	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
850	C₂×C₂²⋊C₄	—	2	2	no	—
851	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
852	#107	C₂³×C₈₉	1	1	yes	characteristic
853	#107	C₂³×C₈₉	1	1	yes	characteristic
854	#107	C₂³×C₈₉	1	1	yes	characteristic
855	#107	C₂³×C₈₉	1	1	yes	characteristic
856	#107	C₂³×C₈₉	1	2	yes	—
857	#107	C₂³×C₈₉	1	2	yes	—
858	#106	C₂³×C₈₉	1	2	yes	—
859	#106	C₂³×C₈₉	1	2	yes	—
860	C₄⋊C₈	C₂³×C₈₉	1	1	yes	characteristic
861	C₄⋊C₈	C₂³×C₈₉	1	1	yes	characteristic
862	C₄⋊C₈	C₂³×C₈₉	1	2	yes	—
863	C₄⋊C₈	C₂³×C₈₉	1	2	yes	—
864	#103	C₂³×C₈₉	1	2	yes	—
865	#103	C₂³×C₈₉	1	2	yes	—
866	#103	C₂³×C₈₉	1	2	yes	—
867	#103	C₂³×C₈₉	1	2	yes	—
868	#103	C₂³×C₈₉	1	2	yes	—
869	#103	C₂³×C₈₉	1	2	yes	—
870	#102	C₂³×C₈₉	1	1	yes	characteristic
871	#102	C₂³×C₈₉	1	2	yes	—
872	#102	C₂³×C₈₉	1	2	yes	—
873	#102	C₂³×C₈₉	1	2	yes	—
874	#102	C₂³×C₈₉	1	1	yes	characteristic
875	#102	C₂³×C₈₉	1	2	yes	—
876	#102	C₂³×C₈₉	1	2	yes	—
877	#102	C₂³×C₈₉	1	2	yes	—
878	#102	C₂³×C₈₉	1	2	yes	—
879	#102	C₂³×C₈₉	1	1	yes	characteristic
880	#102	C₂³×C₈₉	1	2	yes	—
881	#102	C₂³×C₈₉	1	1	yes	characteristic
882	#102	C₂³×C₈₉	1	2	yes	—
883	#102	C₂³×C₈₉	1	2	yes	—
884	#102	C₂³×C₈₉	1	1	yes	characteristic
885	#102	C₂³×C₈₉	1	1	yes	characteristic
886	#102	C₂³×C₈₉	1	1	yes	characteristic
887	#102	C₂³×C₈₉	1	1	yes	characteristic
888	C₂²⋊C₈	C₂³×C₈₉	1	2	yes	—
889	C₂²⋊C₈	C₂³×C₈₉	1	2	yes	—
890	C₂²⋊C₈	C₂³×C₈₉	1	2	yes	—
891	#97	C₂³×C₈₉	1	2	yes	—
892	#97	C₂³×C₈₉	1	2	yes	—
893	C₄×C₈	C₂³×C₈₉	1	1	yes	characteristic
894	C₄×C₈	C₂³×C₈₉	1	1	yes	characteristic
895	C₄×C₈	C₂³×C₈₉	1	1	yes	characteristic
896	C₄×C₈	C₂³×C₈₉	1	1	yes	characteristic
897	C₄×C₈	C₂³×C₈₉	1	2	yes	—
898	C₂⁴	—	2	2	no	—
899	#41	—	4	2	no	—
900	#41	—	4	2	no	—
901	#41	—	4	2	no	—
902	#41	—	4	2	no	—
903	#41	—	8	2	no	—
904	#41	—	8	2	no	—
905	#41	—	8	2	no	—
906	#41	—	8	2	no	—
907	C₂×Q₈	—	2	1	no	—
908	C₂×Q₈	—	2	1	no	—
909	C₂×Q₈	—	2	1	no	—
910	C₂×Q₈	—	2	2	no	—
911	C₂×Q₈	—	2	1	no	—
912	C₂×Q₈	—	8	2	no	—
913	C₂×Q₈	C₂×D₄×C₈₉	1	1	yes	characteristic
914	C₂×Q₈	C₂⁴×C₈₉	1	2	yes	—
915	C₂×D₄	—	2	2	no	—
916	C₂×D₄	—	2	1	no	—
917	C₂×D₄	—	2	2	no	—
918	C₂×D₄	—	2	2	no	—
919	C₂×D₄	—	2	2	no	—
920	C₂×D₄	—	2	1	no	—
921	C₂×D₄	—	2	2	no	—
922	C₂×D₄	—	2	1	no	—
923	C₂×D₄	—	2	1	no	—
924	C₂×D₄	—	2	1	no	—
925	C₂×D₄	—	2	1	no	—
926	C₂×D₄	—	2	1	no	—
927	C₂×D₄	—	2	2	no	—
928	C₂×D₄	—	2	1	no	—
929	C₂×D₄	—	2	1	no	—
930	C₂×D₄	—	2	2	no	—
931	C₂×D₄	—	2	2	no	—
932	C₂×D₄	—	2	1	no	—
933	C₂×D₄	—	4	2	no	—
934	C₂×D₄	—	4	2	no	—
935	C₂×D₄	—	8	2	no	—
936	C₂×D₄	C₂×D₄×C₈₉	1	1	yes	characteristic
937	C₂×D₄	C₂×D₄×C₈₉	1	2	yes	—
938	C₂×D₄	C₂⁴×C₈₉	1	1	yes	characteristic
939	C₂×D₄	C₂⁴×C₈₉	1	2	yes	—
940	C₂×D₄	C₂⁴×C₈₉	1	1	yes	characteristic
941	C₂×D₄	C₂⁴×C₈₉	1	1	yes	characteristic
942	C₂×D₄	C₂⁴×C₈₉	1	1	yes	characteristic
943	C₂²×C₄	—	2	2	no	—
944	C₂²×C₄	—	2	1	no	—
945	C₂²×C₄	—	2	1	no	—
946	C₂²×C₄	—	2	1	no	—
947	C₂²×C₄	—	2	1	no	—
948	C₂²×C₄	—	2	2	no	—
949	C₂²×C₄	—	2	2	no	—
950	C₂²×C₄	—	2	2	no	—
951	C₂²×C₄	—	2	2	no	—
952	C₂²×C₄	—	2	2	no	—
953	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
954	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
955	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
956	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
957	SD₁₆	—	4	2	no	—
958	SD₁₆	—	4	2	no	—
959	D₈	—	4	1	no	—
960	D₈	—	4	1	no	—
961	D₈	—	4	1	no	—
962	D₈	—	4	1	no	—
963	D₈	—	4	2	no	—
964	D₈	—	4	2	no	—
965	M₁₆	—	4	2	no	—
966	C₂×C₈	—	4	1	no	—
967	C₂×C₈	—	4	2	no	—
968	C₂×C₈	—	4	1	no	—
969	C₂×C₈	C₂⁴×C₈₉	1	1	yes	characteristic
970	C₂×C₈	C₂⁴×C₈₉	1	1	yes	characteristic
971	C₂×C₈	C₂⁴×C₈₉	1	1	yes	characteristic
972	C₂×C₈	C₂⁴×C₈₉	1	1	yes	characteristic
973	C₂×C₈	C₂⁴×C₈₉	1	2	yes	—
974	C₂×C₈	C₂⁴×C₈₉	1	2	yes	—
975	C₄⋊C₄	—	2	1	no	—
976	C₄⋊C₄	—	2	1	no	—
977	C₄⋊C₄	—	2	2	no	—
978	C₄⋊C₄	—	2	2	no	—
979	C₄⋊C₄	—	2	2	no	—
980	C₄⋊C₄	—	2	2	no	—
981	C₄⋊C₄	—	2	1	no	—
982	C₄⋊C₄	—	2	1	no	—
983	C₄⋊C₄	—	2	1	no	—
984	C₄⋊C₄	—	2	2	no	—
985	C₄⋊C₄	—	2	2	no	—
986	C₄⋊C₄	—	2	2	no	—
987	C₄⋊C₄	—	2	1	no	—
988	C₄⋊C₄	—	2	2	no	—
989	C₄⋊C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
990	C₄⋊C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
991	C₄⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
992	C₄⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
993	C₄⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
994	C₄⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
995	C₄⋊C₄	C₂⁴×C₈₉	1	2	yes	—
996	C₄⋊C₄	C₂⁴×C₈₉	1	1	yes	characteristic
997	C₄⋊C₄	C₂⁴×C₈₉	1	2	yes	—
998	C₄⋊C₄	C₂⁴×C₈₉	1	1	yes	characteristic
999	C₄⋊C₄	C₂⁴×C₈₉	1	1	yes	characteristic
1000	C₄⋊C₄	C₂⁴×C₈₉	1	1	yes	characteristic
1001	C₂²⋊C₄	—	2	2	no	—
1002	C₂²⋊C₄	—	2	2	no	—
1003	C₂²⋊C₄	—	2	2	no	—
1004	C₂²⋊C₄	—	2	1	no	—
1005	C₂²⋊C₄	—	2	2	no	—
1006	C₂²⋊C₄	—	2	1	no	—
1007	C₂²⋊C₄	—	2	2	no	—
1008	C₂²⋊C₄	—	2	2	no	—
1009	C₂²⋊C₄	—	2	2	no	—
1010	C₂²⋊C₄	—	2	1	no	—
1011	C₂²⋊C₄	—	2	1	no	—
1012	C₂²⋊C₄	—	2	2	no	—
1013	C₂²⋊C₄	—	2	2	no	—
1014	C₂²⋊C₄	—	2	2	no	—
1015	C₂²⋊C₄	—	2	1	no	—
1016	C₂²⋊C₄	—	2	2	no	—
1017	C₂²⋊C₄	—	2	1	no	—
1018	C₂²⋊C₄	—	2	2	no	—
1019	C₂²⋊C₄	—	2	1	no	—
1020	C₂²⋊C₄	—	2	2	no	—
1021	C₂²⋊C₄	—	2	1	no	—
1022	C₂²⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
1023	C₂²⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
1024	C₂²⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
1025	C₂²⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
1026	C₂²⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
1027	C₄²	—	2	2	no	—
1028	C₄²	—	2	2	no	—
1029	C₄²	—	2	2	no	—
1030	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
1031	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
1032	C₄²	C₂⁴×C₈₉	1	1	yes	characteristic
1033	C₄²	C₂⁴×C₈₉	1	1	yes	characteristic
1034	C₄²	C₂⁴×C₈₉	1	2	yes	—
1035	C₂³	—	2	1	no	—
1036	C₂³	—	2	1	no	—
1037	C₂³	—	2	1	no	—
1038	C₂³	—	2	2	no	—
1039	C₂³	—	2	1	no	—
1040	C₂³	—	8	2	no	—
1041	C₂³	—	8	2	no	—
1042	C₂³	—	8	2	no	—
1043	C₂³	C₂²×D₄×C₈₉	1	2	yes	—
1044	C₂³	C₂²×D₄×C₈₉	1	1	yes	characteristic
1045	Q₈	—	2	2	no	—
1046	Q₈	—	2	2	no	—
1047	Q₈	—	2	2	no	—
1048	Q₈	—	4	2	no	—
1049	Q₈	—	8	1	no	—
1050	Q₈	—	8	2	no	—
1051	Q₈	—	8	1	no	—
1052	Q₈	—	8	1	no	—
1053	D₄	—	2	2	no	—
1054	D₄	—	2	1	no	—
1055	D₄	—	2	1	no	—
1056	D₄	—	2	1	no	—
1057	D₄	—	2	1	no	—
1058	D₄	—	2	1	no	—
1059	D₄	—	2	1	no	—
1060	D₄	—	2	2	no	—
1061	D₄	—	2	2	no	—
1062	D₄	—	2	1	no	—
1063	D₄	—	2	1	no	—
1064	D₄	—	4	2	no	—
1065	D₄	—	4	2	no	—
1066	D₄	—	8	1	no	—
1067	D₄	—	8	1	no	—
1068	D₄	—	8	1	no	—
1069	D₄	—	8	2	no	—
1070	D₄	—	8	2	no	—
1071	D₄	—	8	1	no	—
1072	D₄	—	8	1	no	—
1073	D₄	—	8	2	no	—
1074	D₄	—	8	2	no	—
1075	D₄	—	8	2	no	—
1076	D₄	—	8	2	no	—
1077	D₄	—	8	2	no	—
1078	D₄	—	8	1	no	—
1079	D₄	—	8	1	no	—
1080	D₄	—	8	1	no	—
1081	D₄	—	8	1	no	—
1082	D₄	—	8	2	no	—
1083	C₂×C₄	—	2	2	no	—
1084	C₂×C₄	—	2	2	no	—
1085	C₂×C₄	—	2	1	no	—
1086	C₂×C₄	—	2	1	no	—
1087	C₂×C₄	—	2	2	no	—
1088	C₂×C₄	—	2	2	no	—
1089	C₂×C₄	—	2	1	no	—
1090	C₂×C₄	—	2	1	no	—
1091	C₂×C₄	—	2	2	no	—
1092	C₂×C₄	—	2	2	no	—
1093	C₂×C₄	—	2	1	no	—
1094	C₂×C₄	—	2	1	no	—
1095	C₂×C₄	—	4	1	no	—
1096	C₂×C₄	—	4	2	no	—
1097	C₂×C₄	—	4	2	no	—
1098	C₂×C₄	—	4	2	no	—
1099	C₂×C₄	—	4	2	no	—
1100	C₂×C₄	—	8	2	no	—
1101	C₂×C₄	—	8	2	no	—
1102	C₂×C₄	—	8	2	no	—
1103	C₂×C₄	—	8	2	no	—
1104	C₂×C₄	—	8	2	no	—
1105	C₂×C₄	—	8	2	no	—
1106	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
1107	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
1108	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
1109	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
1110	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
1111	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
1112	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
1113	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
1114	C₂×C₄	C₂⁵×C₈₉	1	1	yes	characteristic
1115	C₈	—	2	1	no	—
1116	C₈	—	2	1	no	—
1117	C₈	—	2	1	no	—
1118	C₈	—	2	1	no	—
1119	C₈	—	2	2	no	—
1120	C₈	—	2	2	no	—
1121	C₂²	—	2	1	no	—
1122	C₂²	—	2	2	no	—
1123	C₂²	—	2	1	no	—
1124	C₂²	—	2	2	no	—
1125	C₂²	—	2	1	no	—
1126	C₂²	—	2	2	no	—
1127	C₂²	—	4	1	no	—
1128	C₂²	—	4	1	no	—
1129	C₂²	—	4	1	no	—
1130	C₂²	—	4	1	no	—
1131	C₂²	—	4	2	no	—
1132	C₂²	—	4	1	no	—
1133	C₂²	—	4	1	no	—
1134	C₂²	—	4	1	no	—
1135	C₂²	—	4	2	no	—
1136	C₂²	—	4	1	no	—
1137	C₂²	—	4	1	no	—
1138	C₂²	—	4	2	no	—
1139	C₂²	—	4	1	no	—
1140	C₂²	—	4	1	no	—
1141	C₂²	—	4	1	no	—
1142	C₂²	—	16	4	no	—
1143	C₂²	C₂³×D₄×C₈₉	1	1	yes	characteristic
1144	C₄	—	2	1	no	—
1145	C₄	—	2	2	no	—
1146	C₄	—	2	1	no	—
1147	C₄	—	2	1	no	—
1148	C₄	—	2	2	no	—
1149	C₄	—	2	1	no	—
1150	C₄	—	2	2	no	—
1151	C₄	—	4	1	no	—
1152	C₄	—	4	1	no	—
1153	C₄	—	4	1	no	—
1154	C₄	—	4	1	no	—
1155	C₄	—	4	2	no	—
1156	C₄	—	4	2	no	—
1157	C₄	—	4	2	no	—
1158	C₄	#576×C₈₉	1	2	yes	—
1159	C₄	#585×C₈₉	1	1	yes	characteristic
1160	C₄	#585×C₈₉	1	1	yes	characteristic
1161	C₂	—	4	1	no	—
1162	C₂	—	4	2	no	—
1163	C₂	—	8	1	no	—
1164	C₂	—	8	1	no	—
1165	C₂	—	8	1	no	—
1166	C₂	—	8	2	no	—
1167	C₂	—	8	1	no	—
1168	C₂	C₈₉×#3500	1	1	yes	characteristic
1169	C₂	C₂×#576×C₈₉	1	1	yes	characteristic
1170	C₂	C₈₉×#3584	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×#3547	C₂	semidirect
2. C₈₉×#3546	C₂	semidirect
3. C₈₉×#3367	C₂	semidirect
4. C₈₉×#3366	C₂	semidirect
5. C₈₉×#3360	C₂	semidirect
6. C₈₉×#3358	C₂	semidirect
7. C₈₉×#3330	C₂	semidirect
8. C₈₉×#3325	C₂	semidirect
9. C₈₉×#3319	C₂	semidirect
10. C₈₉×#3309	C₂	semidirect
11. C₈₉×#3305	C₂	semidirect
12. C₈₉×#3303	C₂	semidirect
13. C₈₉×#3297	C₂	semidirect
14. C₈₉×#3294	C₂	semidirect
15. C₈₉×#3243	C₂	semidirect
16. C₈₉×#3235	C₂	semidirect
17. C₈₉×#3220	C₂	semidirect
18. C₈₉×#3214	C₂	semidirect
19. C₈₉×#3179	C₂	semidirect
20. C₈₉×#3169	C₂	semidirect
21. C₈₉×#3136	C₂	semidirect
22. C₈₉×#3131	C₂	semidirect
23. C₈₉×#2966	C₂	semidirect
28. #555×C₈₉	C₂²	semidirect
29. #554×C₈₉	C₂²	semidirect
31. #553×C₈₉	C₂²	semidirect
35. D₄×Q₈×C₈₉	C₂²	semidirect
42. #544×C₈₉	C₂²	semidirect
45. #540×C₈₉	C₂²	semidirect
52. #533×C₈₉	C₂²	semidirect
55. #532×C₈₉	C₂²	semidirect
57. #501×C₈₉	C₂²	semidirect
58. #500×C₈₉	C₂²	semidirect
59. #496×C₈₉	C₂²	semidirect
62. #490×C₈₉	C₂²	semidirect
64. #489×C₈₉	C₂²	semidirect
66. #488×C₈₉	C₂²	semidirect
67. #488×C₈₉	C₂²	semidirect
68. #487×C₈₉	C₂²	semidirect
69. #487×C₈₉	C₂²	semidirect
73. #486×C₈₉	C₂²	semidirect
74. #486×C₈₉	C₂²	semidirect
75. #485×C₈₉	C₂²	semidirect
76. #484×C₈₉	C₂²	semidirect
79. #482×C₈₉	C₂²	semidirect
81. #479×C₈₉	C₂²	semidirect
82. #478×C₈₉	C₂²	semidirect
83. #477×C₈₉	C₂²	semidirect
85. #476×C₈₉	C₂²	semidirect
87. #474×C₈₉	C₂²	semidirect
88. #474×C₈₉	C₂²	semidirect
90. #468×C₈₉	C₂²	semidirect
94. #466×C₈₉	C₂²	semidirect
95. #466×C₈₉	C₂²	semidirect
96. #465×C₈₉	C₂²	semidirect
99. #461×C₈₉	C₂²	semidirect
100. #461×C₈₉	C₂²	semidirect
103. #459×C₈₉	C₂²	semidirect
104. #459×C₈₉	C₂²	semidirect
105. #449×C₈₉	C₂²	semidirect
106. #449×C₈₉	C₂²	semidirect
107. #449×C₈₉	C₂²	semidirect
108. #449×C₈₉	C₂²	semidirect
111. #446×C₈₉	C₂²	semidirect
112. C₈×Q₈×C₈₉	C₂²	semidirect
113. #442×C₈₉	C₂²	semidirect
114. #440×C₈₉	C₂²	semidirect
115. C₄×SD₁₆×C₈₉	C₂²	semidirect
118. C₄×D₈×C₈₉	C₂²	semidirect
119. C₄×D₈×C₈₉	C₂²	semidirect
120. C₄×D₈×C₈₉	C₂²	semidirect
122. #435×C₈₉	C₂²	semidirect
124. C₈×D₄×C₈₉	C₂²	semidirect
125. #433×C₈₉	C₂²	semidirect
126. #432×C₈₉	C₂²	semidirect
128. #417×C₈₉	C₂²	semidirect
129. #416×C₈₉	C₂²	semidirect
130. #416×C₈₉	C₂²	semidirect
131. #416×C₈₉	C₂²	semidirect
133. #405×C₈₉	C₂²	semidirect
134. C₂×C₄×C₈×C₈₉	C₂²	semidirect
575. #62561	C₈₉	direct (N × H)
586. #3547	C₂×C₈₉	semidirect
587. #3546	C₂×C₈₉	semidirect
588. #3367	C₂×C₈₉	semidirect
589. #3366	C₂×C₈₉	semidirect
590. #3360	C₂×C₈₉	semidirect
591. #3358	C₂×C₈₉	semidirect
592. #3330	C₂×C₈₉	semidirect
593. #3325	C₂×C₈₉	semidirect
594. #3319	C₂×C₈₉	semidirect
595. #3309	C₂×C₈₉	semidirect
596. #3305	C₂×C₈₉	semidirect
597. #3303	C₂×C₈₉	semidirect
598. #3297	C₂×C₈₉	semidirect
599. #3294	C₂×C₈₉	semidirect
600. #3243	C₂×C₈₉	semidirect
601. #3235	C₂×C₈₉	semidirect
602. #3220	C₂×C₈₉	semidirect
603. #3214	C₂×C₈₉	semidirect
604. #3179	C₂×C₈₉	semidirect
605. #3169	C₂×C₈₉	semidirect
606. #3136	C₂×C₈₉	semidirect
607. #3131	C₂×C₈₉	semidirect
608. #2966	C₂×C₈₉	semidirect
609. C₈₉	#62561	direct (N × H)
614. #555	C₂²×C₈₉	semidirect
615. #554	C₂²×C₈₉	semidirect
617. #553	C₂²×C₈₉	semidirect
621. D₄×Q₈	C₂²×C₈₉	semidirect
628. #544	C₂²×C₈₉	semidirect
631. #540	C₂²×C₈₉	semidirect
638. #533	C₂²×C₈₉	semidirect
641. #532	C₂²×C₈₉	semidirect
643. #501	C₂²×C₈₉	semidirect
644. #500	C₂²×C₈₉	semidirect
645. #496	C₂²×C₈₉	semidirect
648. #490	C₂²×C₈₉	semidirect
650. #489	C₂²×C₈₉	semidirect
652. #488	C₂²×C₈₉	semidirect
653. #488	C₂²×C₈₉	semidirect
654. #487	C₂²×C₈₉	semidirect
655. #487	C₂²×C₈₉	semidirect
659. #486	C₂²×C₈₉	semidirect
660. #486	C₂²×C₈₉	semidirect
661. #485	C₂²×C₈₉	semidirect
662. #484	C₂²×C₈₉	semidirect
665. #482	C₂²×C₈₉	semidirect
667. #479	C₂²×C₈₉	semidirect
668. #478	C₂²×C₈₉	semidirect
669. #477	C₂²×C₈₉	semidirect
671. #476	C₂²×C₈₉	semidirect
673. #474	C₂²×C₈₉	semidirect
674. #474	C₂²×C₈₉	semidirect
676. #468	C₂²×C₈₉	semidirect
680. #466	C₂²×C₈₉	semidirect
681. #466	C₂²×C₈₉	semidirect
682. #465	C₂²×C₈₉	semidirect
685. #461	C₂²×C₈₉	semidirect
686. #461	C₂²×C₈₉	semidirect
689. #459	C₂²×C₈₉	semidirect
690. #459	C₂²×C₈₉	semidirect
691. #449	C₂²×C₈₉	semidirect
692. #449	C₂²×C₈₉	semidirect
693. #449	C₂²×C₈₉	semidirect
694. #449	C₂²×C₈₉	semidirect
697. #446	C₂²×C₈₉	semidirect
698. C₈×Q₈	C₂²×C₈₉	semidirect
699. #442	C₂²×C₈₉	semidirect
700. #440	C₂²×C₈₉	semidirect
701. C₄×SD₁₆	C₂²×C₈₉	semidirect
704. C₄×D₈	C₂²×C₈₉	semidirect
705. C₄×D₈	C₂²×C₈₉	semidirect
706. C₄×D₈	C₂²×C₈₉	semidirect
708. #435	C₂²×C₈₉	semidirect
710. C₈×D₄	C₂²×C₈₉	semidirect
711. #433	C₂²×C₈₉	semidirect
712. #432	C₂²×C₈₉	semidirect
714. #417	C₂²×C₈₉	semidirect
715. #416	C₂²×C₈₉	semidirect
716. #416	C₂²×C₈₉	semidirect
717. #416	C₂²×C₈₉	semidirect
719. #405	C₂²×C₈₉	semidirect
720. C₂×C₄×C₈	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×#3547	2
C₈₉×#3546	2
C₈₉×#3367	2
C₈₉×#3366	2
C₈₉×#3360	2
C₈₉×#3358	2
C₈₉×#3330	2
C₈₉×#3325	2
C₈₉×#3319	2
C₈₉×#3309	2
C₈₉×#3305	2
C₈₉×#3303	2
C₈₉×#3297	2
C₈₉×#3294	2
C₈₉×#3243	2
C₈₉×#3235	2
C₈₉×#3220	2
C₈₉×#3214	2
C₈₉×#3179	2
C₈₉×#3169	2
C₈₉×#3136	2
C₈₉×#3131	2
C₈₉×#2966	2
#62561	89

Subgroups — C89×#62561 #36440409

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#62561 #36440409