Subgroups — C₈₉×#62563 #36440411

Order 22784.

1724 conjugacy classes of subgroups.

The subgroup lattice has 1134 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈₉×#3555	C₂	1	1	yes	maximal, characteristic, complemented
2	C₈₉×#3546	C₂	1	1	yes	maximal, characteristic
3	C₈₉×#3369	C₂	1	1	yes	maximal, characteristic, complemented
4	C₈₉×#3368	C₂	1	1	yes	maximal, characteristic, complemented
5	C₈₉×#3364	C₂	1	1	yes	maximal, characteristic, complemented
6	C₈₉×#3362	C₂	1	1	yes	maximal, characteristic, complemented
7	C₈₉×#3331	C₂	1	1	yes	maximal, characteristic, complemented
8	C₈₉×#3324	C₂	1	1	yes	maximal, characteristic, complemented
9	C₈₉×#3317	C₂	1	2	yes	maximal, complemented
10	C₈₉×#3311	C₂	1	2	yes	maximal, complemented
11	C₈₉×#3304	C₂	1	2	yes	maximal, complemented
12	C₈₉×#3302	C₂	1	1	yes	maximal, characteristic, complemented
13	C₈₉×#3296	C₂	1	2	yes	maximal, complemented
14	C₈₉×#3295	C₂	1	1	yes	maximal, characteristic, complemented
15	C₈₉×#3244	C₂	1	2	yes	maximal, complemented
16	C₈₉×#3235	C₂	1	1	yes	maximal, characteristic, complemented
17	C₈₉×#3222	C₂	1	2	yes	maximal, complemented
18	C₈₉×#3216	C₂	1	1	yes	maximal, characteristic, complemented
19	C₈₉×#3178	C₂	1	2	yes	maximal, complemented
20	C₈₉×#3167	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	#563×C₈₉	—	2	2	no	—
25	#560×C₈₉	—	2	2	no	—
26	Q₈²×C₈₉	C₂²	1	1	yes	characteristic, complemented
27	#557×C₈₉	—	2	1	no	—
28	#557×C₈₉	C₂²	1	1	yes	characteristic, complemented
29	#556×C₈₉	—	2	1	no	—
30	#556×C₈₉	C₂²	1	1	yes	characteristic
31	#556×C₈₉	C₂²	1	1	yes	characteristic
32	#556×C₈₉	C₂²	1	2	yes	complemented
33	#554×C₈₉	C₂²	1	1	yes	characteristic
34	#553×C₈₉	—	2	1	no	—
35	#552×C₈₉	C₂²	1	2	yes	complemented
36	#550×C₈₉	C₂²	1	2	yes	—
37	#550×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	1	no	—
44	#542×C₈₉	C₂²	1	2	yes	—
45	#541×C₈₉	—	2	2	no	—
46	#541×C₈₉	—	2	1	no	—
47	#541×C₈₉	C₂²	1	2	yes	complemented
48	#538×C₈₉	—	2	2	no	—
49	#537×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	#533×C₈₉	C₂²	1	1	yes	characteristic, complemented
54	#532×C₈₉	C₂²	1	1	yes	characteristic
55	#532×C₈₉	C₂²	1	1	yes	characteristic
56	#529×C₈₉	C₂²	1	1	yes	characteristic
57	#501×C₈₉	C₂²	1	2	yes	complemented
58	#498×C₈₉	C₂²	1	1	yes	characteristic, complemented
59	#497×C₈₉	C₂²	1	2	yes	complemented
60	#492×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	#487×C₈₉	C₂²	1	1	yes	characteristic, complemented
71	#486×C₈₉	C₂²	1	1	yes	characteristic
72	#486×C₈₉	C₂²	1	1	yes	characteristic
73	#486×C₈₉	C₂²	1	1	yes	characteristic
74	#486×C₈₉	C₂²	1	2	yes	complemented
75	#485×C₈₉	C₂²	1	2	yes	complemented
76	#483×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	#481×C₈₉	C₂²	1	2	yes	—
81	#479×C₈₉	C₂²	1	2	yes	complemented
82	#478×C₈₉	C₂²	1	2	yes	complemented
83	#476×C₈₉	C₂²	1	1	yes	characteristic
84	#476×C₈₉	C₂²	1	1	yes	characteristic, complemented
85	#476×C₈₉	C₂²	1	2	yes	complemented
86	#475×C₈₉	C₂²	1	2	yes	complemented
87	#474×C₈₉	C₂²	1	1	yes	characteristic
88	#474×C₈₉	C₂²	1	1	yes	characteristic, complemented
89	#470×C₈₉	C₂²	1	2	yes	complemented
90	#468×C₈₉	C₂²	1	2	yes	—
91	#467×C₈₉	C₂²	1	2	yes	complemented
92	#465×C₈₉	C₂²	1	1	yes	characteristic
93	#465×C₈₉	C₂²	1	1	yes	characteristic
94	#465×C₈₉	C₂²	1	2	yes	—
95	#465×C₈₉	C₂²	1	1	yes	characteristic, complemented
96	#465×C₈₉	C₂²	1	1	yes	characteristic, complemented
97	#464×C₈₉	C₂²	1	2	yes	—
98	#464×C₈₉	C₂²	1	2	yes	—
99	#462×C₈₉	C₂²	1	1	yes	characteristic, complemented
100	#462×C₈₉	C₂²	1	1	yes	characteristic, complemented
101	#460×C₈₉	C₂²	1	1	yes	characteristic
102	#460×C₈₉	C₂²	1	1	yes	characteristic
103	#460×C₈₉	C₂²	1	2	yes	complemented
104	#460×C₈₉	C₂²	1	2	yes	complemented
105	#452×C₈₉	C₂²	1	2	yes	complemented
106	#452×C₈₉	C₂²	1	2	yes	complemented
107	#452×C₈₉	C₂²	1	2	yes	complemented
108	#452×C₈₉	C₂²	1	2	yes	complemented
109	#450×C₈₉	C₂²	1	2	yes	—
110	#450×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	#441×C₈₉	C₂²	1	2	yes	complemented
114	#440×C₈₉	C₂²	1	2	yes	complemented
115	C₄×Q₁₆×C₈₉	C₂²	1	2	yes	complemented
116	C₄×SD₁₆×C₈₉	C₂²	1	1	yes	characteristic
117	C₄×SD₁₆×C₈₉	C₂²	1	1	yes	characteristic
118	C₄×SD₁₆×C₈₉	C₂²	1	1	yes	characteristic, complemented
119	C₄×SD₁₆×C₈₉	C₂²	1	1	yes	characteristic, complemented
120	C₄×SD₁₆×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	C₂³	1	2	yes	—
138	C₂×#41×C₈₉	C₂³	1	2	yes	—
139	C₂²×D₄×C₈₉	—	2	1	no	—
140	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
141	C₂×Q₁₆×C₈₉	C₂³	1	2	yes	—
142	C₂×Q₁₆×C₈₉	C₂³	1	2	yes	—
143	C₂×SD₁₆×C₈₉	C₂³	1	1	yes	characteristic
144	C₂×SD₁₆×C₈₉	C₂³	1	1	yes	characteristic
145	C₂×SD₁₆×C₈₉	C₂³	1	2	yes	—
146	C₂×SD₁₆×C₈₉	C₂³	1	1	yes	characteristic
147	C₂×SD₁₆×C₈₉	C₂³	1	1	yes	characteristic
148	C₂×SD₁₆×C₈₉	C₂³	1	2	yes	—
149	C₂×M₁₆×C₈₉	C₂³	1	2	yes	—
150	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
151	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
152	C₂²×C₈×C₈₉	C₂³	1	2	yes	—
153	C₄⋊Q₈×C₈₉	—	2	1	no	—
154	C₄⋊Q₈×C₈₉	—	2	2	no	—
155	C₄⋊Q₈×C₈₉	—	2	1	no	—
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	1	yes	characteristic
160	C₄⋊Q₈×C₈₉	C₂³	1	2	yes	—
161	C₄⋊Q₈×C₈₉	C₂³	1	1	yes	characteristic
162	C₄⋊Q₈×C₈₉	C₂³	1	1	yes	characteristic
163	C₄⋊Q₈×C₈₉	C₂³	1	1	yes	characteristic
164	#127×C₈₉	—	2	2	no	—
165	#127×C₈₉	C₂³	1	1	yes	characteristic
166	#127×C₈₉	C₂³	1	2	yes	—
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	—	2	2	no	—
172	#126×C₈₉	—	2	2	no	—
173	#126×C₈₉	—	2	2	no	—
174	#126×C₈₉	—	2	2	no	—
175	#126×C₈₉	—	2	2	no	—
176	#126×C₈₉	D₄	1	2	yes	—
177	#125×C₈₉	—	2	2	no	—
178	#125×C₈₉	—	2	2	no	—
179	#125×C₈₉	—	2	2	no	—
180	#125×C₈₉	—	2	1	no	—
181	#125×C₈₉	—	2	2	no	—
182	#125×C₈₉	—	2	2	no	—
183	#125×C₈₉	—	2	1	no	—
184	#125×C₈₉	D₄	1	1	yes	characteristic
185	#125×C₈₉	C₂³	1	2	yes	—
186	#125×C₈₉	C₂³	1	2	yes	—
187	#124×C₈₉	—	2	1	no	—
188	#124×C₈₉	—	2	2	no	—
189	#124×C₈₉	—	2	2	no	—
190	#124×C₈₉	—	2	1	no	—
191	#124×C₈₉	D₄	1	1	yes	characteristic
192	#124×C₈₉	C₂³	1	2	yes	—
193	#124×C₈₉	C₂³	1	2	yes	—
194	#123×C₈₉	—	2	2	no	—
195	#123×C₈₉	—	2	2	no	—
196	#123×C₈₉	—	2	2	no	—
197	#123×C₈₉	—	2	2	no	—
198	#123×C₈₉	D₄	1	2	yes	—
199	C₂²⋊Q₈×C₈₉	—	2	1	no	—
200	C₂²⋊Q₈×C₈₉	—	2	1	no	—
201	C₂²⋊Q₈×C₈₉	—	2	1	no	—
202	C₂²⋊Q₈×C₈₉	—	2	1	no	—
203	C₂²⋊Q₈×C₈₉	—	2	2	no	—
204	C₂²⋊Q₈×C₈₉	—	2	2	no	—
205	C₂²⋊Q₈×C₈₉	—	2	2	no	—
206	C₂²⋊Q₈×C₈₉	—	2	2	no	—
207	C₂²⋊Q₈×C₈₉	D₄	1	1	yes	characteristic
208	C₂²⋊Q₈×C₈₉	C₂³	1	2	yes	—
209	C₂²⋊Q₈×C₈₉	C₂³	1	2	yes	—
210	C₂²⋊Q₈×C₈₉	C₂³	1	1	yes	characteristic
211	C₂²⋊Q₈×C₈₉	C₂³	1	1	yes	characteristic
212	C₂²⋊Q₈×C₈₉	C₂³	1	2	yes	—
213	#121×C₈₉	—	2	1	no	—
214	#121×C₈₉	—	2	1	no	—
215	#121×C₈₉	—	2	1	no	—
216	#121×C₈₉	—	2	1	no	—
217	#121×C₈₉	—	2	1	no	—
218	#121×C₈₉	—	2	2	no	—
219	#121×C₈₉	—	2	2	no	—
220	#121×C₈₉	—	2	1	no	—
221	#121×C₈₉	—	2	2	no	—
222	#121×C₈₉	—	2	2	no	—
223	#121×C₈₉	—	2	2	no	—
224	#121×C₈₉	—	2	2	no	—
225	#121×C₈₉	D₄	1	1	yes	characteristic
226	#121×C₈₉	C₂³	1	1	yes	characteristic
227	#121×C₈₉	C₂³	1	2	yes	—
228	#121×C₈₉	C₂³	1	1	yes	characteristic
229	#120×C₈₉	—	2	2	no	—
230	#120×C₈₉	—	2	2	no	—
231	#120×C₈₉	—	2	2	no	—
232	#120×C₈₉	—	2	2	no	—
233	C₄×Q₈×C₈₉	—	2	1	no	—
234	C₄×Q₈×C₈₉	—	2	1	no	—
235	C₄×Q₈×C₈₉	—	2	2	no	—
236	C₄×Q₈×C₈₉	—	2	1	no	—
237	C₄×Q₈×C₈₉	—	2	1	no	—
238	C₄×Q₈×C₈₉	—	2	1	no	—
239	C₄×Q₈×C₈₉	—	2	1	no	—
240	C₄×Q₈×C₈₉	C₂³	1	1	yes	characteristic
241	C₄×Q₈×C₈₉	C₂³	1	1	yes	characteristic
242	C₄×Q₈×C₈₉	C₂³	1	2	yes	—
243	C₄×Q₈×C₈₉	C₂³	1	2	yes	—
244	C₄×Q₈×C₈₉	C₂³	1	2	yes	—
245	C₄×Q₈×C₈₉	C₂³	1	1	yes	characteristic
246	C₄×D₄×C₈₉	—	2	1	no	—
247	C₄×D₄×C₈₉	—	2	2	no	—
248	C₄×D₄×C₈₉	—	2	1	no	—
249	C₄×D₄×C₈₉	—	2	1	no	—
250	C₄×D₄×C₈₉	—	2	1	no	—
251	C₄×D₄×C₈₉	C₂³	1	1	yes	characteristic
252	C₄×D₄×C₈₉	C₂³	1	1	yes	characteristic
253	C₄×D₄×C₈₉	C₂³	1	2	yes	—
254	C₄×D₄×C₈₉	C₂³	1	1	yes	characteristic
255	C₄×D₄×C₈₉	C₂³	1	2	yes	—
256	#117×C₈₉	—	2	1	no	—
257	#117×C₈₉	—	2	1	no	—
258	#117×C₈₉	—	2	2	no	—
259	#117×C₈₉	C₂³	1	2	yes	—
260	#117×C₈₉	C₂³	1	2	yes	—
261	#117×C₈₉	C₂³	1	2	yes	—
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	2	yes	—
267	#107×C₈₉	C₂³	1	2	yes	—
268	#106×C₈₉	C₂³	1	1	yes	characteristic
269	#106×C₈₉	C₂³	1	1	yes	characteristic
270	#106×C₈₉	C₂³	1	1	yes	characteristic
271	#106×C₈₉	C₂³	1	1	yes	characteristic
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	#103×C₈₉	C₂³	1	1	yes	characteristic
285	#103×C₈₉	C₂³	1	1	yes	characteristic
286	#103×C₈₉	C₂³	1	1	yes	characteristic
287	#103×C₈₉	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
293	#102×C₈₉	C₂³	1	2	yes	—
294	#102×C₈₉	C₂³	1	2	yes	—
295	#102×C₈₉	C₂³	1	2	yes	—
296	#102×C₈₉	C₂³	1	2	yes	—
297	#102×C₈₉	C₂³	1	1	yes	characteristic
298	#102×C₈₉	C₂³	1	2	yes	—
299	#102×C₈₉	C₂³	1	1	yes	characteristic
300	#102×C₈₉	C₂³	1	2	yes	—
301	#102×C₈₉	C₂³	1	2	yes	—
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	C₂×Q₈×C₈₉	—	2	1	no	—
320	C₂×Q₈×C₈₉	—	2	1	no	—
321	C₂×Q₈×C₈₉	—	2	1	no	—
322	C₂×Q₈×C₈₉	—	2	2	no	—
323	C₂×Q₈×C₈₉	—	2	1	no	—
324	C₂×Q₈×C₈₉	C₂×D₄	1	1	yes	characteristic
325	C₂×Q₈×C₈₉	C₂⁴	1	2	yes	—
326	C₂×Q₈×C₈₉	C₂⁴	1	1	yes	characteristic
327	C₂×Q₈×C₈₉	C₂⁴	1	1	yes	characteristic
328	C₂×D₄×C₈₉	—	2	1	no	—
329	C₂×D₄×C₈₉	—	2	2	no	—
330	C₂×D₄×C₈₉	—	2	2	no	—
331	C₂×D₄×C₈₉	—	2	2	no	—
332	C₂×D₄×C₈₉	—	2	1	no	—
333	C₂×D₄×C₈₉	—	2	1	no	—
334	C₂×D₄×C₈₉	—	2	1	no	—
335	C₂×D₄×C₈₉	—	2	1	no	—
336	C₂×D₄×C₈₉	—	2	2	no	—
337	C₂×D₄×C₈₉	—	2	1	no	—
338	C₂×D₄×C₈₉	—	2	2	no	—
339	C₂×D₄×C₈₉	—	2	2	no	—
340	C₂×D₄×C₈₉	—	4	2	no	—
341	C₂×D₄×C₈₉	—	4	2	no	—
342	C₂×D₄×C₈₉	—	8	2	no	—
343	C₂×D₄×C₈₉	C₂×D₄	1	1	yes	characteristic
344	C₂×D₄×C₈₉	C₂×D₄	1	2	yes	—
345	C₂×D₄×C₈₉	C₂⁴	1	1	yes	characteristic
346	C₂×D₄×C₈₉	C₂⁴	1	2	yes	—
347	C₂×D₄×C₈₉	C₂⁴	1	1	yes	characteristic
348	C₂²×C₄×C₈₉	—	2	2	no	—
349	C₂²×C₄×C₈₉	—	2	1	no	—
350	C₂²×C₄×C₈₉	—	2	1	no	—
351	C₂²×C₄×C₈₉	—	2	2	no	—
352	C₂²×C₄×C₈₉	—	2	2	no	—
353	C₂²×C₄×C₈₉	—	2	2	no	—
354	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
355	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
356	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
357	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
358	Q₁₆×C₈₉	—	4	2	no	—
359	Q₁₆×C₈₉	—	4	2	no	—
360	SD₁₆×C₈₉	—	4	1	no	—
361	SD₁₆×C₈₉	—	4	1	no	—
362	SD₁₆×C₈₉	—	4	1	no	—
363	SD₁₆×C₈₉	—	4	1	no	—
364	SD₁₆×C₈₉	—	4	2	no	—
365	SD₁₆×C₈₉	—	4	2	no	—
366	M₁₆×C₈₉	—	4	2	no	—
367	C₂×C₈×C₈₉	—	4	1	no	—
368	C₂×C₈×C₈₉	—	4	2	no	—
369	C₂×C₈×C₈₉	—	4	1	no	—
370	C₂×C₈×C₈₉	C₂⁴	1	1	yes	characteristic
371	C₂×C₈×C₈₉	C₂⁴	1	1	yes	characteristic
372	C₂×C₈×C₈₉	C₂⁴	1	1	yes	characteristic
373	C₂×C₈×C₈₉	C₂⁴	1	1	yes	characteristic
374	C₂×C₈×C₈₉	C₂⁴	1	2	yes	—
375	C₂×C₈×C₈₉	C₂⁴	1	2	yes	—
376	C₄⋊C₄×C₈₉	—	2	1	no	—
377	C₄⋊C₄×C₈₉	—	2	2	no	—
378	C₄⋊C₄×C₈₉	—	2	2	no	—
379	C₄⋊C₄×C₈₉	—	2	1	no	—
380	C₄⋊C₄×C₈₉	—	2	1	no	—
381	C₄⋊C₄×C₈₉	—	2	2	no	—
382	C₄⋊C₄×C₈₉	—	2	1	no	—
383	C₄⋊C₄×C₈₉	—	2	1	no	—
384	C₄⋊C₄×C₈₉	—	2	1	no	—
385	C₄⋊C₄×C₈₉	—	2	1	no	—
386	C₄⋊C₄×C₈₉	—	2	1	no	—
387	C₄⋊C₄×C₈₉	—	2	2	no	—
388	C₄⋊C₄×C₈₉	—	2	2	no	—
389	C₄⋊C₄×C₈₉	—	2	2	no	—
390	C₄⋊C₄×C₈₉	—	2	2	no	—
391	C₄⋊C₄×C₈₉	—	2	1	no	—
392	C₄⋊C₄×C₈₉	—	2	1	no	—
393	C₄⋊C₄×C₈₉	—	2	2	no	—
394	C₄⋊C₄×C₈₉	—	2	2	no	—
395	C₄⋊C₄×C₈₉	—	2	2	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	C₂×D₄	1	1	yes	characteristic
401	C₄⋊C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
402	C₄⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
403	C₄⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
404	C₄⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
405	C₄⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
406	C₄⋊C₄×C₈₉	C₂⁴	1	1	yes	characteristic
407	C₄⋊C₄×C₈₉	C₂⁴	1	2	yes	—
408	C₄⋊C₄×C₈₉	C₂⁴	1	1	yes	characteristic
409	C₄⋊C₄×C₈₉	C₂⁴	1	2	yes	—
410	C₄⋊C₄×C₈₉	C₂⁴	1	1	yes	characteristic
411	C₄⋊C₄×C₈₉	C₂⁴	1	1	yes	characteristic
412	C₂²⋊C₄×C₈₉	—	2	2	no	—
413	C₂²⋊C₄×C₈₉	—	2	1	no	—
414	C₂²⋊C₄×C₈₉	—	2	1	no	—
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	2	no	—
419	C₂²⋊C₄×C₈₉	—	2	1	no	—
420	C₂²⋊C₄×C₈₉	—	2	2	no	—
421	C₂²⋊C₄×C₈₉	—	2	2	no	—
422	C₂²⋊C₄×C₈₉	—	2	1	no	—
423	C₂²⋊C₄×C₈₉	—	2	2	no	—
424	C₂²⋊C₄×C₈₉	—	2	2	no	—
425	C₂²⋊C₄×C₈₉	—	2	2	no	—
426	C₂²⋊C₄×C₈₉	—	2	1	no	—
427	C₂²⋊C₄×C₈₉	—	2	2	no	—
428	C₂²⋊C₄×C₈₉	—	2	1	no	—
429	C₂²⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
430	C₂²⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
431	C₂²⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
432	C₂²⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
433	C₂²⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
434	C₄²×C₈₉	—	2	2	no	—
435	C₄²×C₈₉	—	2	1	no	—
436	C₄²×C₈₉	—	2	2	no	—
437	C₄²×C₈₉	—	2	1	no	—
438	C₄²×C₈₉	—	2	2	no	—
439	C₄²×C₈₉	—	2	2	no	—
440	C₄²×C₈₉	—	2	2	no	—
441	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
442	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
443	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
444	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
445	C₄²×C₈₉	C₂⁴	1	2	yes	—
446	C₂³×C₈₉	—	2	1	no	—
447	C₂³×C₈₉	—	2	2	no	—
448	C₂³×C₈₉	—	2	1	no	—
449	C₂³×C₈₉	—	8	2	no	—
450	C₂³×C₈₉	—	8	2	no	—
451	C₂³×C₈₉	—	8	2	no	—
452	C₂³×C₈₉	C₂²×D₄	1	2	yes	—
453	C₂³×C₈₉	C₂²×D₄	1	1	yes	characteristic
454	Q₈×C₈₉	—	2	2	no	—
455	Q₈×C₈₉	—	2	1	no	—
456	Q₈×C₈₉	—	2	1	no	—
457	Q₈×C₈₉	—	2	1	no	—
458	Q₈×C₈₉	—	2	1	no	—
459	Q₈×C₈₉	—	2	2	no	—
460	Q₈×C₈₉	—	2	2	no	—
461	Q₈×C₈₉	—	4	2	no	—
462	Q₈×C₈₉	—	8	1	no	—
463	Q₈×C₈₉	—	8	1	no	—
464	Q₈×C₈₉	—	8	2	no	—
465	Q₈×C₈₉	—	8	1	no	—
466	D₄×C₈₉	—	2	2	no	—
467	D₄×C₈₉	—	2	1	no	—
468	D₄×C₈₉	—	2	1	no	—
469	D₄×C₈₉	—	2	2	no	—
470	D₄×C₈₉	—	2	2	no	—
471	D₄×C₈₉	—	2	1	no	—
472	D₄×C₈₉	—	2	1	no	—
473	D₄×C₈₉	—	4	2	no	—
474	D₄×C₈₉	—	4	2	no	—
475	D₄×C₈₉	—	8	1	no	—
476	D₄×C₈₉	—	8	1	no	—
477	D₄×C₈₉	—	8	2	no	—
478	D₄×C₈₉	—	8	2	no	—
479	D₄×C₈₉	—	8	1	no	—
480	D₄×C₈₉	—	8	2	no	—
481	D₄×C₈₉	—	8	2	no	—
482	D₄×C₈₉	—	8	2	no	—
483	D₄×C₈₉	—	8	2	no	—
484	D₄×C₈₉	—	8	1	no	—
485	D₄×C₈₉	—	8	1	no	—
486	C₂×C₄×C₈₉	—	2	2	no	—
487	C₂×C₄×C₈₉	—	2	2	no	—
488	C₂×C₄×C₈₉	—	2	1	no	—
489	C₂×C₄×C₈₉	—	2	1	no	—
490	C₂×C₄×C₈₉	—	2	2	no	—
491	C₂×C₄×C₈₉	—	2	1	no	—
492	C₂×C₄×C₈₉	—	2	1	no	—
493	C₂×C₄×C₈₉	—	2	2	no	—
494	C₂×C₄×C₈₉	—	2	1	no	—
495	C₂×C₄×C₈₉	—	2	1	no	—
496	C₂×C₄×C₈₉	—	2	2	no	—
497	C₂×C₄×C₈₉	—	2	2	no	—
498	C₂×C₄×C₈₉	—	2	1	no	—
499	C₂×C₄×C₈₉	—	2	1	no	—
500	C₂×C₄×C₈₉	—	4	1	no	—
501	C₂×C₄×C₈₉	—	4	2	no	—
502	C₂×C₄×C₈₉	—	4	2	no	—
503	C₂×C₄×C₈₉	—	8	2	no	—
504	C₂×C₄×C₈₉	—	8	2	no	—
505	C₂×C₄×C₈₉	—	8	2	no	—
506	C₂×C₄×C₈₉	—	8	2	no	—
507	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
508	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
509	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
510	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
511	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
512	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
513	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
514	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
515	C₂×C₄×C₈₉	C₂⁵	1	1	yes	characteristic
516	C₈×C₈₉	—	2	1	no	—
517	C₈×C₈₉	—	2	1	no	—
518	C₈×C₈₉	—	2	1	no	—
519	C₈×C₈₉	—	2	1	no	—
520	C₈×C₈₉	—	2	2	no	—
521	C₈×C₈₉	—	2	2	no	—
522	C₂²×C₈₉	—	2	1	no	—
523	C₂²×C₈₉	—	2	2	no	—
524	C₂²×C₈₉	—	2	1	no	—
525	C₂²×C₈₉	—	2	2	no	—
526	C₂²×C₈₉	—	2	1	no	—
527	C₂²×C₈₉	—	2	2	no	—
528	C₂²×C₈₉	—	4	1	no	—
529	C₂²×C₈₉	—	4	2	no	—
530	C₂²×C₈₉	—	4	1	no	—
531	C₂²×C₈₉	—	4	1	no	—
532	C₂²×C₈₉	—	4	2	no	—
533	C₂²×C₈₉	—	4	1	no	—
534	C₂²×C₈₉	—	4	1	no	—
535	C₂²×C₈₉	—	4	1	no	—
536	C₂²×C₈₉	—	4	2	no	—
537	C₂²×C₈₉	—	16	4	no	—
538	C₂²×C₈₉	C₂³×D₄	1	1	yes	characteristic
539	C₄×C₈₉	—	2	1	no	—
540	C₄×C₈₉	—	2	1	no	—
541	C₄×C₈₉	—	2	2	no	—
542	C₄×C₈₉	—	2	1	no	—
543	C₄×C₈₉	—	2	2	no	—
544	C₄×C₈₉	—	2	1	no	—
545	C₄×C₈₉	—	2	2	no	—
546	C₄×C₈₉	—	4	1	no	—
547	C₄×C₈₉	—	4	2	no	—
548	C₄×C₈₉	—	4	1	no	—
549	C₄×C₈₉	—	4	2	no	—
550	C₄×C₈₉	—	4	1	no	—
551	C₄×C₈₉	—	4	1	no	—
552	C₄×C₈₉	—	4	1	no	—
553	C₄×C₈₉	—	4	1	no	—
554	C₄×C₈₉	—	4	2	no	—
555	C₄×C₈₉	#577	1	2	yes	—
556	C₄×C₈₉	#585	1	1	yes	characteristic
557	C₄×C₈₉	#585	1	1	yes	characteristic
558	#62563	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
559	C₂×C₈₉	—	4	1	no	—
560	C₂×C₈₉	—	4	2	no	—
561	C₂×C₈₉	—	8	1	no	—
562	C₂×C₈₉	—	8	2	no	—
563	C₂×C₈₉	—	8	1	no	—
564	C₂×C₈₉	#3500	1	1	yes	characteristic
565	C₂×C₈₉	C₂×#577	1	1	yes	characteristic
566	C₂×C₈₉	#3584	1	1	yes	characteristic
567	#3555	C₂×C₈₉	1	1	yes	characteristic, complemented
568	#3546	C₂×C₈₉	1	1	yes	characteristic
569	#3369	C₂×C₈₉	1	1	yes	characteristic, complemented
570	#3368	C₂×C₈₉	1	1	yes	characteristic, complemented
571	#3364	C₂×C₈₉	1	1	yes	characteristic, complemented
572	#3362	C₂×C₈₉	1	1	yes	characteristic, complemented
573	#3331	C₂×C₈₉	1	1	yes	characteristic, complemented
574	#3324	C₂×C₈₉	1	1	yes	characteristic, complemented
575	#3317	C₂×C₈₉	1	2	yes	complemented
576	#3311	C₂×C₈₉	1	2	yes	complemented
577	#3304	C₂×C₈₉	1	2	yes	complemented
578	#3302	C₂×C₈₉	1	1	yes	characteristic, complemented
579	#3296	C₂×C₈₉	1	2	yes	complemented
580	#3295	C₂×C₈₉	1	1	yes	characteristic, complemented
581	#3244	C₂×C₈₉	1	2	yes	complemented
582	#3235	C₂×C₈₉	1	1	yes	characteristic, complemented
583	#3222	C₂×C₈₉	1	2	yes	complemented
584	#3216	C₂×C₈₉	1	1	yes	characteristic, complemented
585	#3178	C₂×C₈₉	1	2	yes	complemented
586	#3167	C₂×C₈₉	1	1	yes	characteristic, complemented
587	#3136	C₂×C₈₉	1	2	yes	complemented
588	#3131	C₂×C₈₉	1	1	yes	characteristic, complemented
589	#2966	C₂×C₈₉	1	1	yes	characteristic, complemented
590	C₈₉	#62563	1	1	yes	characteristic, direct product factor, Sylow
591	#563	—	2	2	no	—
592	#560	—	2	2	no	—
593	Q₈²	C₂²×C₈₉	1	1	yes	characteristic, complemented
594	#557	—	2	1	no	—
595	#557	C₂²×C₈₉	1	1	yes	characteristic, complemented
596	#556	—	2	1	no	—
597	#556	C₂²×C₈₉	1	1	yes	characteristic
598	#556	C₂²×C₈₉	1	1	yes	characteristic
599	#556	C₂²×C₈₉	1	2	yes	complemented
600	#554	C₂²×C₈₉	1	1	yes	characteristic
601	#553	—	2	1	no	—
602	#552	C₂²×C₈₉	1	2	yes	complemented
603	#550	C₂²×C₈₉	1	2	yes	—
604	#550	C₂²×C₈₉	1	1	yes	characteristic
605	#547	C₂²×C₈₉	1	1	yes	characteristic
606	#546	—	2	1	no	—
607	#546	C₂²×C₈₉	1	2	yes	—
608	D₄²	C₂²×C₈₉	1	1	yes	characteristic
609	#544	C₂²×C₈₉	1	2	yes	complemented
610	#542	—	2	1	no	—
611	#542	C₂²×C₈₉	1	2	yes	—
612	#541	—	2	2	no	—
613	#541	—	2	1	no	—
614	#541	C₂²×C₈₉	1	2	yes	complemented
615	#538	—	2	2	no	—
616	#537	—	2	1	no	—
617	#535	—	2	1	no	—
618	#535	C₂²×C₈₉	1	2	yes	—
619	#533	C₂²×C₈₉	1	1	yes	characteristic, complemented
620	#533	C₂²×C₈₉	1	1	yes	characteristic, complemented
621	#532	C₂²×C₈₉	1	1	yes	characteristic
622	#532	C₂²×C₈₉	1	1	yes	characteristic
623	#529	C₂²×C₈₉	1	1	yes	characteristic
624	#501	C₂²×C₈₉	1	2	yes	complemented
625	#498	C₂²×C₈₉	1	1	yes	characteristic, complemented
626	#497	C₂²×C₈₉	1	2	yes	complemented
627	#492	C₂²×C₈₉	1	1	yes	characteristic
628	#490	C₂²×C₈₉	1	2	yes	—
629	#490	C₂²×C₈₉	1	2	yes	complemented
630	#489	C₂²×C₈₉	1	2	yes	—
631	#489	C₂²×C₈₉	1	2	yes	complemented
632	#488	C₂²×C₈₉	1	2	yes	—
633	#488	C₂²×C₈₉	1	2	yes	complemented
634	#488	C₂²×C₈₉	1	2	yes	complemented
635	#487	C₂²×C₈₉	1	1	yes	characteristic, complemented
636	#487	C₂²×C₈₉	1	1	yes	characteristic, complemented
637	#487	C₂²×C₈₉	1	1	yes	characteristic, complemented
638	#486	C₂²×C₈₉	1	1	yes	characteristic
639	#486	C₂²×C₈₉	1	1	yes	characteristic
640	#486	C₂²×C₈₉	1	1	yes	characteristic
641	#486	C₂²×C₈₉	1	2	yes	complemented
642	#485	C₂²×C₈₉	1	2	yes	complemented
643	#483	C₂²×C₈₉	1	2	yes	complemented
644	#482	C₂²×C₈₉	1	2	yes	—
645	#482	C₂²×C₈₉	1	2	yes	—
646	#482	C₂²×C₈₉	1	2	yes	complemented
647	#481	C₂²×C₈₉	1	2	yes	—
648	#479	C₂²×C₈₉	1	2	yes	complemented
649	#478	C₂²×C₈₉	1	2	yes	complemented
650	#476	C₂²×C₈₉	1	1	yes	characteristic
651	#476	C₂²×C₈₉	1	1	yes	characteristic, complemented
652	#476	C₂²×C₈₉	1	2	yes	complemented
653	#475	C₂²×C₈₉	1	2	yes	complemented
654	#474	C₂²×C₈₉	1	1	yes	characteristic
655	#474	C₂²×C₈₉	1	1	yes	characteristic, complemented
656	#470	C₂²×C₈₉	1	2	yes	complemented
657	#468	C₂²×C₈₉	1	2	yes	—
658	#467	C₂²×C₈₉	1	2	yes	complemented
659	#465	C₂²×C₈₉	1	1	yes	characteristic
660	#465	C₂²×C₈₉	1	1	yes	characteristic
661	#465	C₂²×C₈₉	1	2	yes	—
662	#465	C₂²×C₈₉	1	1	yes	characteristic, complemented
663	#465	C₂²×C₈₉	1	1	yes	characteristic, complemented
664	#464	C₂²×C₈₉	1	2	yes	—
665	#464	C₂²×C₈₉	1	2	yes	—
666	#462	C₂²×C₈₉	1	1	yes	characteristic, complemented
667	#462	C₂²×C₈₉	1	1	yes	characteristic, complemented
668	#460	C₂²×C₈₉	1	1	yes	characteristic
669	#460	C₂²×C₈₉	1	1	yes	characteristic
670	#460	C₂²×C₈₉	1	2	yes	complemented
671	#460	C₂²×C₈₉	1	2	yes	complemented
672	#452	C₂²×C₈₉	1	2	yes	complemented
673	#452	C₂²×C₈₉	1	2	yes	complemented
674	#452	C₂²×C₈₉	1	2	yes	complemented
675	#452	C₂²×C₈₉	1	2	yes	complemented
676	#450	C₂²×C₈₉	1	2	yes	—
677	#450	C₂²×C₈₉	1	2	yes	—
678	#446	C₂²×C₈₉	1	1	yes	characteristic, complemented
679	C₈×Q₈	C₂²×C₈₉	1	1	yes	characteristic, complemented
680	#441	C₂²×C₈₉	1	2	yes	complemented
681	#440	C₂²×C₈₉	1	2	yes	complemented
682	C₄×Q₁₆	C₂²×C₈₉	1	2	yes	complemented
683	C₄×SD₁₆	C₂²×C₈₉	1	1	yes	characteristic
684	C₄×SD₁₆	C₂²×C₈₉	1	1	yes	characteristic
685	C₄×SD₁₆	C₂²×C₈₉	1	1	yes	characteristic, complemented
686	C₄×SD₁₆	C₂²×C₈₉	1	1	yes	characteristic, complemented
687	C₄×SD₁₆	C₂²×C₈₉	1	2	yes	complemented
688	#436	C₂²×C₈₉	1	1	yes	characteristic
689	#435	C₂²×C₈₉	1	2	yes	complemented
690	C₈×D₄	C₂²×C₈₉	1	1	yes	characteristic
691	C₈×D₄	C₂²×C₈₉	1	2	yes	complemented
692	#433	C₂²×C₈₉	1	2	yes	complemented
693	#432	C₂²×C₈₉	1	1	yes	characteristic, complemented
694	#418	C₂²×C₈₉	1	2	yes	—
695	#417	C₂²×C₈₉	1	2	yes	complemented
696	#416	C₂²×C₈₉	1	2	yes	complemented
697	#416	C₂²×C₈₉	1	2	yes	complemented
698	#416	C₂²×C₈₉	1	2	yes	complemented
699	C₂×#102	C₂²×C₈₉	1	2	yes	—
700	#405	C₂²×C₈₉	1	2	yes	complemented
701	C₂×C₄×C₈	C₂²×C₈₉	1	1	yes	characteristic, complemented
702	C₂×#41	—	2	1	no	—
703	C₂×#41	—	2	1	no	—
704	C₂×#41	C₂³×C₈₉	1	2	yes	—
705	C₂×#41	C₂³×C₈₉	1	2	yes	—
706	C₂²×D₄	—	2	1	no	—
707	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
708	C₂×Q₁₆	C₂³×C₈₉	1	2	yes	—
709	C₂×Q₁₆	C₂³×C₈₉	1	2	yes	—
710	C₂×SD₁₆	C₂³×C₈₉	1	1	yes	characteristic
711	C₂×SD₁₆	C₂³×C₈₉	1	1	yes	characteristic
712	C₂×SD₁₆	C₂³×C₈₉	1	2	yes	—
713	C₂×SD₁₆	C₂³×C₈₉	1	1	yes	characteristic
714	C₂×SD₁₆	C₂³×C₈₉	1	1	yes	characteristic
715	C₂×SD₁₆	C₂³×C₈₉	1	2	yes	—
716	C₂×M₁₆	C₂³×C₈₉	1	2	yes	—
717	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
718	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
719	C₂²×C₈	C₂³×C₈₉	1	2	yes	—
720	C₄⋊Q₈	—	2	1	no	—
721	C₄⋊Q₈	—	2	2	no	—
722	C₄⋊Q₈	—	2	1	no	—
723	C₄⋊Q₈	—	2	2	no	—
724	C₄⋊Q₈	C₂³×C₈₉	1	1	yes	characteristic
725	C₄⋊Q₈	C₂³×C₈₉	1	1	yes	characteristic
726	C₄⋊Q₈	C₂³×C₈₉	1	1	yes	characteristic
727	C₄⋊Q₈	C₂³×C₈₉	1	1	yes	characteristic
728	C₄⋊Q₈	C₂³×C₈₉	1	1	yes	characteristic
729	C₄⋊Q₈	C₂³×C₈₉	1	1	yes	characteristic
730	C₄⋊Q₈	C₂³×C₈₉	1	2	yes	—
731	#127	—	2	2	no	—
732	#127	C₂³×C₈₉	1	1	yes	characteristic
733	#127	C₂³×C₈₉	1	1	yes	characteristic
734	#127	C₂³×C₈₉	1	2	yes	—
735	#126	—	2	2	no	—
736	#126	—	2	2	no	—
737	#126	—	2	2	no	—
738	#126	—	2	2	no	—
739	#126	—	2	2	no	—
740	#126	—	2	2	no	—
741	#126	—	2	2	no	—
742	#126	—	2	2	no	—
743	#126	D₄×C₈₉	1	2	yes	—
744	#125	—	2	2	no	—
745	#125	—	2	2	no	—
746	#125	—	2	2	no	—
747	#125	—	2	1	no	—
748	#125	—	2	2	no	—
749	#125	—	2	2	no	—
750	#125	—	2	1	no	—
751	#125	D₄×C₈₉	1	1	yes	characteristic
752	#125	C₂³×C₈₉	1	2	yes	—
753	#125	C₂³×C₈₉	1	2	yes	—
754	#124	—	2	1	no	—
755	#124	—	2	2	no	—
756	#124	—	2	2	no	—
757	#124	—	2	1	no	—
758	#124	D₄×C₈₉	1	1	yes	characteristic
759	#124	C₂³×C₈₉	1	2	yes	—
760	#124	C₂³×C₈₉	1	2	yes	—
761	#123	—	2	2	no	—
762	#123	—	2	2	no	—
763	#123	—	2	2	no	—
764	#123	—	2	2	no	—
765	#123	D₄×C₈₉	1	2	yes	—
766	C₂²⋊Q₈	—	2	1	no	—
767	C₂²⋊Q₈	—	2	1	no	—
768	C₂²⋊Q₈	—	2	1	no	—
769	C₂²⋊Q₈	—	2	1	no	—
770	C₂²⋊Q₈	—	2	2	no	—
771	C₂²⋊Q₈	—	2	2	no	—
772	C₂²⋊Q₈	—	2	2	no	—
773	C₂²⋊Q₈	—	2	2	no	—
774	C₂²⋊Q₈	D₄×C₈₉	1	1	yes	characteristic
775	C₂²⋊Q₈	C₂³×C₈₉	1	1	yes	characteristic
776	C₂²⋊Q₈	C₂³×C₈₉	1	1	yes	characteristic
777	C₂²⋊Q₈	C₂³×C₈₉	1	2	yes	—
778	C₂²⋊Q₈	C₂³×C₈₉	1	2	yes	—
779	C₂²⋊Q₈	C₂³×C₈₉	1	2	yes	—
780	#121	—	2	1	no	—
781	#121	—	2	1	no	—
782	#121	—	2	1	no	—
783	#121	—	2	1	no	—
784	#121	—	2	1	no	—
785	#121	—	2	2	no	—
786	#121	—	2	2	no	—
787	#121	—	2	1	no	—
788	#121	—	2	2	no	—
789	#121	—	2	2	no	—
790	#121	—	2	2	no	—
791	#121	—	2	2	no	—
792	#121	D₄×C₈₉	1	1	yes	characteristic
793	#121	C₂³×C₈₉	1	1	yes	characteristic
794	#121	C₂³×C₈₉	1	1	yes	characteristic
795	#121	C₂³×C₈₉	1	2	yes	—
796	#120	—	2	2	no	—
797	#120	—	2	2	no	—
798	#120	—	2	2	no	—
799	#120	—	2	2	no	—
800	C₄×Q₈	—	2	1	no	—
801	C₄×Q₈	—	2	1	no	—
802	C₄×Q₈	—	2	2	no	—
803	C₄×Q₈	—	2	1	no	—
804	C₄×Q₈	—	2	1	no	—
805	C₄×Q₈	—	2	1	no	—
806	C₄×Q₈	—	2	1	no	—
807	C₄×Q₈	C₂³×C₈₉	1	1	yes	characteristic
808	C₄×Q₈	C₂³×C₈₉	1	1	yes	characteristic
809	C₄×Q₈	C₂³×C₈₉	1	2	yes	—
810	C₄×Q₈	C₂³×C₈₉	1	2	yes	—
811	C₄×Q₈	C₂³×C₈₉	1	2	yes	—
812	C₄×Q₈	C₂³×C₈₉	1	1	yes	characteristic
813	C₄×D₄	—	2	1	no	—
814	C₄×D₄	—	2	2	no	—
815	C₄×D₄	—	2	1	no	—
816	C₄×D₄	—	2	1	no	—
817	C₄×D₄	—	2	1	no	—
818	C₄×D₄	C₂³×C₈₉	1	1	yes	characteristic
819	C₄×D₄	C₂³×C₈₉	1	1	yes	characteristic
820	C₄×D₄	C₂³×C₈₉	1	2	yes	—
821	C₄×D₄	C₂³×C₈₉	1	1	yes	characteristic
822	C₄×D₄	C₂³×C₈₉	1	2	yes	—
823	#117	—	2	1	no	—
824	#117	—	2	1	no	—
825	#117	—	2	2	no	—
826	#117	C₂³×C₈₉	1	2	yes	—
827	#117	C₂³×C₈₉	1	2	yes	—
828	#117	C₂³×C₈₉	1	2	yes	—
829	C₂×C₄⋊C₄	—	2	1	no	—
830	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
831	C₂×C₂²⋊C₄	—	2	2	no	—
832	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
833	#107	C₂³×C₈₉	1	2	yes	—
834	#107	C₂³×C₈₉	1	2	yes	—
835	#106	C₂³×C₈₉	1	1	yes	characteristic
836	#106	C₂³×C₈₉	1	1	yes	characteristic
837	#106	C₂³×C₈₉	1	1	yes	characteristic
838	#106	C₂³×C₈₉	1	1	yes	characteristic
839	#106	C₂³×C₈₉	1	2	yes	—
840	#106	C₂³×C₈₉	1	2	yes	—
841	C₄⋊C₈	C₂³×C₈₉	1	1	yes	characteristic
842	C₄⋊C₈	C₂³×C₈₉	1	1	yes	characteristic
843	C₄⋊C₈	C₂³×C₈₉	1	2	yes	—
844	C₄⋊C₈	C₂³×C₈₉	1	2	yes	—
845	#103	C₂³×C₈₉	1	2	yes	—
846	#103	C₂³×C₈₉	1	2	yes	—
847	#103	C₂³×C₈₉	1	2	yes	—
848	#103	C₂³×C₈₉	1	2	yes	—
849	#103	C₂³×C₈₉	1	2	yes	—
850	#103	C₂³×C₈₉	1	2	yes	—
851	#103	C₂³×C₈₉	1	1	yes	characteristic
852	#103	C₂³×C₈₉	1	1	yes	characteristic
853	#103	C₂³×C₈₉	1	1	yes	characteristic
854	#103	C₂³×C₈₉	1	1	yes	characteristic
855	#102	C₂³×C₈₉	1	1	yes	characteristic
856	#102	C₂³×C₈₉	1	2	yes	—
857	#102	C₂³×C₈₉	1	2	yes	—
858	#102	C₂³×C₈₉	1	2	yes	—
859	#102	C₂³×C₈₉	1	1	yes	characteristic
860	#102	C₂³×C₈₉	1	2	yes	—
861	#102	C₂³×C₈₉	1	2	yes	—
862	#102	C₂³×C₈₉	1	2	yes	—
863	#102	C₂³×C₈₉	1	2	yes	—
864	#102	C₂³×C₈₉	1	1	yes	characteristic
865	#102	C₂³×C₈₉	1	2	yes	—
866	#102	C₂³×C₈₉	1	1	yes	characteristic
867	#102	C₂³×C₈₉	1	2	yes	—
868	#102	C₂³×C₈₉	1	2	yes	—
869	C₂²⋊C₈	C₂³×C₈₉	1	2	yes	—
870	C₂²⋊C₈	C₂³×C₈₉	1	2	yes	—
871	C₂²⋊C₈	C₂³×C₈₉	1	2	yes	—
872	#97	C₂³×C₈₉	1	2	yes	—
873	#97	C₂³×C₈₉	1	2	yes	—
874	C₄×C₈	C₂³×C₈₉	1	1	yes	characteristic
875	C₄×C₈	C₂³×C₈₉	1	1	yes	characteristic
876	C₄×C₈	C₂³×C₈₉	1	1	yes	characteristic
877	C₄×C₈	C₂³×C₈₉	1	1	yes	characteristic
878	C₄×C₈	C₂³×C₈₉	1	2	yes	—
879	C₂⁴	—	2	2	no	—
880	#41	—	4	2	no	—
881	#41	—	4	2	no	—
882	#41	—	4	2	no	—
883	#41	—	4	2	no	—
884	#41	—	8	2	no	—
885	#41	—	8	2	no	—
886	C₂×Q₈	—	2	1	no	—
887	C₂×Q₈	—	2	1	no	—
888	C₂×Q₈	—	2	1	no	—
889	C₂×Q₈	—	2	2	no	—
890	C₂×Q₈	—	2	1	no	—
891	C₂×Q₈	C₂×D₄×C₈₉	1	1	yes	characteristic
892	C₂×Q₈	C₂⁴×C₈₉	1	2	yes	—
893	C₂×Q₈	C₂⁴×C₈₉	1	1	yes	characteristic
894	C₂×Q₈	C₂⁴×C₈₉	1	1	yes	characteristic
895	C₂×D₄	—	2	1	no	—
896	C₂×D₄	—	2	2	no	—
897	C₂×D₄	—	2	2	no	—
898	C₂×D₄	—	2	2	no	—
899	C₂×D₄	—	2	1	no	—
900	C₂×D₄	—	2	1	no	—
901	C₂×D₄	—	2	1	no	—
902	C₂×D₄	—	2	1	no	—
903	C₂×D₄	—	2	2	no	—
904	C₂×D₄	—	2	1	no	—
905	C₂×D₄	—	2	2	no	—
906	C₂×D₄	—	2	2	no	—
907	C₂×D₄	—	4	2	no	—
908	C₂×D₄	—	4	2	no	—
909	C₂×D₄	—	8	2	no	—
910	C₂×D₄	C₂×D₄×C₈₉	1	1	yes	characteristic
911	C₂×D₄	C₂×D₄×C₈₉	1	2	yes	—
912	C₂×D₄	C₂⁴×C₈₉	1	1	yes	characteristic
913	C₂×D₄	C₂⁴×C₈₉	1	2	yes	—
914	C₂×D₄	C₂⁴×C₈₉	1	1	yes	characteristic
915	C₂²×C₄	—	2	2	no	—
916	C₂²×C₄	—	2	1	no	—
917	C₂²×C₄	—	2	1	no	—
918	C₂²×C₄	—	2	2	no	—
919	C₂²×C₄	—	2	2	no	—
920	C₂²×C₄	—	2	2	no	—
921	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
922	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
923	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
924	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
925	Q₁₆	—	4	2	no	—
926	Q₁₆	—	4	2	no	—
927	SD₁₆	—	4	1	no	—
928	SD₁₆	—	4	1	no	—
929	SD₁₆	—	4	1	no	—
930	SD₁₆	—	4	1	no	—
931	SD₁₆	—	4	2	no	—
932	SD₁₆	—	4	2	no	—
933	M₁₆	—	4	2	no	—
934	C₂×C₈	—	4	1	no	—
935	C₂×C₈	—	4	2	no	—
936	C₂×C₈	—	4	1	no	—
937	C₂×C₈	C₂⁴×C₈₉	1	1	yes	characteristic
938	C₂×C₈	C₂⁴×C₈₉	1	1	yes	characteristic
939	C₂×C₈	C₂⁴×C₈₉	1	1	yes	characteristic
940	C₂×C₈	C₂⁴×C₈₉	1	1	yes	characteristic
941	C₂×C₈	C₂⁴×C₈₉	1	2	yes	—
942	C₂×C₈	C₂⁴×C₈₉	1	2	yes	—
943	C₄⋊C₄	—	2	1	no	—
944	C₄⋊C₄	—	2	2	no	—
945	C₄⋊C₄	—	2	2	no	—
946	C₄⋊C₄	—	2	1	no	—
947	C₄⋊C₄	—	2	1	no	—
948	C₄⋊C₄	—	2	2	no	—
949	C₄⋊C₄	—	2	1	no	—
950	C₄⋊C₄	—	2	1	no	—
951	C₄⋊C₄	—	2	1	no	—
952	C₄⋊C₄	—	2	1	no	—
953	C₄⋊C₄	—	2	1	no	—
954	C₄⋊C₄	—	2	2	no	—
955	C₄⋊C₄	—	2	2	no	—
956	C₄⋊C₄	—	2	2	no	—
957	C₄⋊C₄	—	2	2	no	—
958	C₄⋊C₄	—	2	1	no	—
959	C₄⋊C₄	—	2	1	no	—
960	C₄⋊C₄	—	2	2	no	—
961	C₄⋊C₄	—	2	2	no	—
962	C₄⋊C₄	—	2	2	no	—
963	C₄⋊C₄	—	2	1	no	—
964	C₄⋊C₄	—	2	1	no	—
965	C₄⋊C₄	—	2	2	no	—
966	C₄⋊C₄	—	2	2	no	—
967	C₄⋊C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
968	C₄⋊C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
969	C₄⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
970	C₄⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
971	C₄⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
972	C₄⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
973	C₄⋊C₄	C₂⁴×C₈₉	1	1	yes	characteristic
974	C₄⋊C₄	C₂⁴×C₈₉	1	2	yes	—
975	C₄⋊C₄	C₂⁴×C₈₉	1	1	yes	characteristic
976	C₄⋊C₄	C₂⁴×C₈₉	1	2	yes	—
977	C₄⋊C₄	C₂⁴×C₈₉	1	1	yes	characteristic
978	C₄⋊C₄	C₂⁴×C₈₉	1	1	yes	characteristic
979	C₂²⋊C₄	—	2	2	no	—
980	C₂²⋊C₄	—	2	1	no	—
981	C₂²⋊C₄	—	2	1	no	—
982	C₂²⋊C₄	—	2	2	no	—
983	C₂²⋊C₄	—	2	2	no	—
984	C₂²⋊C₄	—	2	2	no	—
985	C₂²⋊C₄	—	2	2	no	—
986	C₂²⋊C₄	—	2	1	no	—
987	C₂²⋊C₄	—	2	2	no	—
988	C₂²⋊C₄	—	2	2	no	—
989	C₂²⋊C₄	—	2	1	no	—
990	C₂²⋊C₄	—	2	2	no	—
991	C₂²⋊C₄	—	2	2	no	—
992	C₂²⋊C₄	—	2	2	no	—
993	C₂²⋊C₄	—	2	1	no	—
994	C₂²⋊C₄	—	2	2	no	—
995	C₂²⋊C₄	—	2	1	no	—
996	C₂²⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
997	C₂²⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
998	C₂²⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
999	C₂²⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
1000	C₂²⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
1001	C₄²	—	2	2	no	—
1002	C₄²	—	2	1	no	—
1003	C₄²	—	2	2	no	—
1004	C₄²	—	2	1	no	—
1005	C₄²	—	2	2	no	—
1006	C₄²	—	2	2	no	—
1007	C₄²	—	2	2	no	—
1008	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
1009	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
1010	C₄²	C₂⁴×C₈₉	1	1	yes	characteristic
1011	C₄²	C₂⁴×C₈₉	1	1	yes	characteristic
1012	C₄²	C₂⁴×C₈₉	1	2	yes	—
1013	C₂³	—	2	1	no	—
1014	C₂³	—	2	2	no	—
1015	C₂³	—	2	1	no	—
1016	C₂³	—	8	2	no	—
1017	C₂³	—	8	2	no	—
1018	C₂³	—	8	2	no	—
1019	C₂³	C₂²×D₄×C₈₉	1	2	yes	—
1020	C₂³	C₂²×D₄×C₈₉	1	1	yes	characteristic
1021	Q₈	—	2	2	no	—
1022	Q₈	—	2	1	no	—
1023	Q₈	—	2	1	no	—
1024	Q₈	—	2	1	no	—
1025	Q₈	—	2	1	no	—
1026	Q₈	—	2	2	no	—
1027	Q₈	—	2	2	no	—
1028	Q₈	—	4	2	no	—
1029	Q₈	—	8	1	no	—
1030	Q₈	—	8	1	no	—
1031	Q₈	—	8	2	no	—
1032	Q₈	—	8	1	no	—
1033	D₄	—	2	2	no	—
1034	D₄	—	2	1	no	—
1035	D₄	—	2	1	no	—
1036	D₄	—	2	2	no	—
1037	D₄	—	2	2	no	—
1038	D₄	—	2	1	no	—
1039	D₄	—	2	1	no	—
1040	D₄	—	4	2	no	—
1041	D₄	—	4	2	no	—
1042	D₄	—	8	1	no	—
1043	D₄	—	8	1	no	—
1044	D₄	—	8	2	no	—
1045	D₄	—	8	2	no	—
1046	D₄	—	8	1	no	—
1047	D₄	—	8	2	no	—
1048	D₄	—	8	2	no	—
1049	D₄	—	8	2	no	—
1050	D₄	—	8	2	no	—
1051	D₄	—	8	1	no	—
1052	D₄	—	8	1	no	—
1053	C₂×C₄	—	2	2	no	—
1054	C₂×C₄	—	2	2	no	—
1055	C₂×C₄	—	2	1	no	—
1056	C₂×C₄	—	2	1	no	—
1057	C₂×C₄	—	2	2	no	—
1058	C₂×C₄	—	2	1	no	—
1059	C₂×C₄	—	2	1	no	—
1060	C₂×C₄	—	2	2	no	—
1061	C₂×C₄	—	2	1	no	—
1062	C₂×C₄	—	2	1	no	—
1063	C₂×C₄	—	2	2	no	—
1064	C₂×C₄	—	2	2	no	—
1065	C₂×C₄	—	2	1	no	—
1066	C₂×C₄	—	2	1	no	—
1067	C₂×C₄	—	4	1	no	—
1068	C₂×C₄	—	4	2	no	—
1069	C₂×C₄	—	4	2	no	—
1070	C₂×C₄	—	8	2	no	—
1071	C₂×C₄	—	8	2	no	—
1072	C₂×C₄	—	8	2	no	—
1073	C₂×C₄	—	8	2	no	—
1074	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
1075	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
1076	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
1077	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
1078	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
1079	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
1080	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
1081	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
1082	C₂×C₄	C₂⁵×C₈₉	1	1	yes	characteristic
1083	C₈	—	2	1	no	—
1084	C₈	—	2	1	no	—
1085	C₈	—	2	1	no	—
1086	C₈	—	2	1	no	—
1087	C₈	—	2	2	no	—
1088	C₈	—	2	2	no	—
1089	C₂²	—	2	1	no	—
1090	C₂²	—	2	2	no	—
1091	C₂²	—	2	1	no	—
1092	C₂²	—	2	2	no	—
1093	C₂²	—	2	1	no	—
1094	C₂²	—	2	2	no	—
1095	C₂²	—	4	1	no	—
1096	C₂²	—	4	1	no	—
1097	C₂²	—	4	2	no	—
1098	C₂²	—	4	1	no	—
1099	C₂²	—	4	2	no	—
1100	C₂²	—	4	1	no	—
1101	C₂²	—	4	1	no	—
1102	C₂²	—	4	2	no	—
1103	C₂²	—	4	1	no	—
1104	C₂²	—	16	4	no	—
1105	C₂²	C₂³×D₄×C₈₉	1	1	yes	characteristic
1106	C₄	—	2	1	no	—
1107	C₄	—	2	2	no	—
1108	C₄	—	2	1	no	—
1109	C₄	—	2	1	no	—
1110	C₄	—	2	2	no	—
1111	C₄	—	2	1	no	—
1112	C₄	—	2	2	no	—
1113	C₄	—	4	1	no	—
1114	C₄	—	4	1	no	—
1115	C₄	—	4	2	no	—
1116	C₄	—	4	1	no	—
1117	C₄	—	4	2	no	—
1118	C₄	—	4	1	no	—
1119	C₄	—	4	2	no	—
1120	C₄	—	4	1	no	—
1121	C₄	—	4	1	no	—
1122	C₄	#577×C₈₉	1	2	yes	—
1123	C₄	#585×C₈₉	1	1	yes	characteristic
1124	C₄	#585×C₈₉	1	1	yes	characteristic
1125	C₂	—	4	1	no	—
1126	C₂	—	4	2	no	—
1127	C₂	—	8	1	no	—
1128	C₂	—	8	2	no	—
1129	C₂	—	8	1	no	—
1130	C₂	C₈₉×#3500	1	1	yes	characteristic
1131	C₂	C₂×#577×C₈₉	1	1	yes	characteristic
1132	C₂	C₈₉×#3584	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₈₉	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₈₉
prime radical	C₈₉×#3546	C₂
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×#3555	C₂	semidirect
3. C₈₉×#3369	C₂	semidirect
4. C₈₉×#3368	C₂	semidirect
5. C₈₉×#3364	C₂	semidirect
6. C₈₉×#3362	C₂	semidirect
7. C₈₉×#3331	C₂	semidirect
8. C₈₉×#3324	C₂	semidirect
9. C₈₉×#3317	C₂	semidirect
10. C₈₉×#3311	C₂	semidirect
11. C₈₉×#3304	C₂	semidirect
12. C₈₉×#3302	C₂	semidirect
13. C₈₉×#3296	C₂	semidirect
14. C₈₉×#3295	C₂	semidirect
15. C₈₉×#3244	C₂	semidirect
16. C₈₉×#3235	C₂	semidirect
17. C₈₉×#3222	C₂	semidirect
18. C₈₉×#3216	C₂	semidirect
19. C₈₉×#3178	C₂	semidirect
20. C₈₉×#3167	C₂	semidirect
21. C₈₉×#3136	C₂	semidirect
22. C₈₉×#3131	C₂	semidirect
23. C₈₉×#2966	C₂	semidirect
26. Q₈²×C₈₉	C₂²	semidirect
28. #557×C₈₉	C₂²	semidirect
32. #556×C₈₉	C₂²	semidirect
35. #552×C₈₉	C₂²	semidirect
42. #544×C₈₉	C₂²	semidirect
47. #541×C₈₉	C₂²	semidirect
52. #533×C₈₉	C₂²	semidirect
53. #533×C₈₉	C₂²	semidirect
57. #501×C₈₉	C₂²	semidirect
58. #498×C₈₉	C₂²	semidirect
59. #497×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
70. #487×C₈₉	C₂²	semidirect
74. #486×C₈₉	C₂²	semidirect
75. #485×C₈₉	C₂²	semidirect
76. #483×C₈₉	C₂²	semidirect
79. #482×C₈₉	C₂²	semidirect
81. #479×C₈₉	C₂²	semidirect
82. #478×C₈₉	C₂²	semidirect
84. #476×C₈₉	C₂²	semidirect
85. #476×C₈₉	C₂²	semidirect
86. #475×C₈₉	C₂²	semidirect
88. #474×C₈₉	C₂²	semidirect
89. #470×C₈₉	C₂²	semidirect
91. #467×C₈₉	C₂²	semidirect
95. #465×C₈₉	C₂²	semidirect
96. #465×C₈₉	C₂²	semidirect
99. #462×C₈₉	C₂²	semidirect
100. #462×C₈₉	C₂²	semidirect
103. #460×C₈₉	C₂²	semidirect
104. #460×C₈₉	C₂²	semidirect
105. #452×C₈₉	C₂²	semidirect
106. #452×C₈₉	C₂²	semidirect
107. #452×C₈₉	C₂²	semidirect
108. #452×C₈₉	C₂²	semidirect
111. #446×C₈₉	C₂²	semidirect
112. C₈×Q₈×C₈₉	C₂²	semidirect
113. #441×C₈₉	C₂²	semidirect
114. #440×C₈₉	C₂²	semidirect
115. C₄×Q₁₆×C₈₉	C₂²	semidirect
118. C₄×SD₁₆×C₈₉	C₂²	semidirect
119. C₄×SD₁₆×C₈₉	C₂²	semidirect
120. C₄×SD₁₆×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
558. #62563	C₈₉	direct (N × H)
567. #3555	C₂×C₈₉	semidirect
569. #3369	C₂×C₈₉	semidirect
570. #3368	C₂×C₈₉	semidirect
571. #3364	C₂×C₈₉	semidirect
572. #3362	C₂×C₈₉	semidirect
573. #3331	C₂×C₈₉	semidirect
574. #3324	C₂×C₈₉	semidirect
575. #3317	C₂×C₈₉	semidirect
576. #3311	C₂×C₈₉	semidirect
577. #3304	C₂×C₈₉	semidirect
578. #3302	C₂×C₈₉	semidirect
579. #3296	C₂×C₈₉	semidirect
580. #3295	C₂×C₈₉	semidirect
581. #3244	C₂×C₈₉	semidirect
582. #3235	C₂×C₈₉	semidirect
583. #3222	C₂×C₈₉	semidirect
584. #3216	C₂×C₈₉	semidirect
585. #3178	C₂×C₈₉	semidirect
586. #3167	C₂×C₈₉	semidirect
587. #3136	C₂×C₈₉	semidirect
588. #3131	C₂×C₈₉	semidirect
589. #2966	C₂×C₈₉	semidirect
590. C₈₉	#62563	direct (N × H)
593. Q₈²	C₂²×C₈₉	semidirect
595. #557	C₂²×C₈₉	semidirect
599. #556	C₂²×C₈₉	semidirect
602. #552	C₂²×C₈₉	semidirect
609. #544	C₂²×C₈₉	semidirect
614. #541	C₂²×C₈₉	semidirect
619. #533	C₂²×C₈₉	semidirect
620. #533	C₂²×C₈₉	semidirect
624. #501	C₂²×C₈₉	semidirect
625. #498	C₂²×C₈₉	semidirect
626. #497	C₂²×C₈₉	semidirect
629. #490	C₂²×C₈₉	semidirect
631. #489	C₂²×C₈₉	semidirect
633. #488	C₂²×C₈₉	semidirect
634. #488	C₂²×C₈₉	semidirect
635. #487	C₂²×C₈₉	semidirect
636. #487	C₂²×C₈₉	semidirect
637. #487	C₂²×C₈₉	semidirect
641. #486	C₂²×C₈₉	semidirect
642. #485	C₂²×C₈₉	semidirect
643. #483	C₂²×C₈₉	semidirect
646. #482	C₂²×C₈₉	semidirect
648. #479	C₂²×C₈₉	semidirect
649. #478	C₂²×C₈₉	semidirect
651. #476	C₂²×C₈₉	semidirect
652. #476	C₂²×C₈₉	semidirect
653. #475	C₂²×C₈₉	semidirect
655. #474	C₂²×C₈₉	semidirect
656. #470	C₂²×C₈₉	semidirect
658. #467	C₂²×C₈₉	semidirect
662. #465	C₂²×C₈₉	semidirect
663. #465	C₂²×C₈₉	semidirect
666. #462	C₂²×C₈₉	semidirect
667. #462	C₂²×C₈₉	semidirect
670. #460	C₂²×C₈₉	semidirect
671. #460	C₂²×C₈₉	semidirect
672. #452	C₂²×C₈₉	semidirect
673. #452	C₂²×C₈₉	semidirect
674. #452	C₂²×C₈₉	semidirect
675. #452	C₂²×C₈₉	semidirect
678. #446	C₂²×C₈₉	semidirect
679. C₈×Q₈	C₂²×C₈₉	semidirect
680. #441	C₂²×C₈₉	semidirect
681. #440	C₂²×C₈₉	semidirect
682. C₄×Q₁₆	C₂²×C₈₉	semidirect
685. C₄×SD₁₆	C₂²×C₈₉	semidirect
686. C₄×SD₁₆	C₂²×C₈₉	semidirect
687. C₄×SD₁₆	C₂²×C₈₉	semidirect
689. #435	C₂²×C₈₉	semidirect
691. C₈×D₄	C₂²×C₈₉	semidirect
692. #433	C₂²×C₈₉	semidirect
693. #432	C₂²×C₈₉	semidirect
695. #417	C₂²×C₈₉	semidirect
696. #416	C₂²×C₈₉	semidirect
697. #416	C₂²×C₈₉	semidirect
698. #416	C₂²×C₈₉	semidirect
700. #405	C₂²×C₈₉	semidirect
701. 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×#3555	2
C₈₉×#3546	2
C₈₉×#3369	2
C₈₉×#3368	2
C₈₉×#3364	2
C₈₉×#3362	2
C₈₉×#3331	2
C₈₉×#3324	2
C₈₉×#3317	2
C₈₉×#3311	2
C₈₉×#3304	2
C₈₉×#3302	2
C₈₉×#3296	2
C₈₉×#3295	2
C₈₉×#3244	2
C₈₉×#3235	2
C₈₉×#3222	2
C₈₉×#3216	2
C₈₉×#3178	2
C₈₉×#3167	2
C₈₉×#3136	2
C₈₉×#3131	2
C₈₉×#2966	2
#62563	89

Subgroups — C89×#62563 #36440411

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#62563 #36440411