Subgroups — C₈₉×#62611 #36440459

Order 22784.

1646 conjugacy classes of subgroups.

The subgroup lattice has 1088 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×#3552	C₂	1	1	yes	maximal, characteristic
3	C₈₉×#3374	C₂	1	1	yes	maximal, characteristic, complemented
4	C₈₉×#3369	C₂	1	1	yes	maximal, characteristic, complemented
5	C₈₉×#3364	C₂	1	1	yes	maximal, characteristic, complemented
6	C₈₉×#3363	C₂	1	1	yes	maximal, characteristic, complemented
7	C₈₉×#3331	C₂	1	1	yes	maximal, characteristic, complemented
8	C₈₉×#3328	C₂	1	2	yes	maximal, complemented
9	C₈₉×#3328	C₂	1	1	yes	maximal, characteristic, complemented
10	C₈₉×#3327	C₂	1	2	yes	maximal, complemented
11	C₈₉×#3313	C₂	1	2	yes	maximal, complemented
12	C₈₉×#3312	C₂	1	2	yes	maximal, complemented
13	C₈₉×#3302	C₂	1	1	yes	maximal, characteristic, complemented
14	C₈₉×#3299	C₂	1	1	yes	maximal, characteristic, complemented
15	C₈₉×#3242	C₂	1	2	yes	maximal, complemented
16	C₈₉×#3233	C₂	1	1	yes	maximal, characteristic, complemented
17	C₈₉×#3223	C₂	1	2	yes	maximal, complemented
18	C₈₉×#3209	C₂	1	1	yes	maximal, characteristic, complemented
19	C₈₉×#3177	C₂	1	2	yes	maximal, complemented
20	C₈₉×#3172	C₂	1	1	yes	maximal, characteristic, complemented
21	C₈₉×#3139	C₂	1	1	yes	maximal, characteristic, complemented
22	C₈₉×#3137	C₂	1	2	yes	maximal, complemented
23	C₈₉×#2969	C₂	1	1	yes	maximal, characteristic, complemented
24	#563×C₈₉	—	2	2	no	—
25	#563×C₈₉	—	2	2	no	—
26	Q₈²×C₈₉	C₂²	1	1	yes	characteristic
27	#557×C₈₉	—	2	1	no	—
28	#557×C₈₉	C₂²	1	1	yes	characteristic
29	#557×C₈₉	C₂²	1	1	yes	characteristic
30	#556×C₈₉	—	2	1	no	—
31	#556×C₈₉	C₂²	1	1	yes	characteristic
32	#556×C₈₉	C₂²	1	1	yes	characteristic
33	#556×C₈₉	C₂²	1	2	yes	—
34	#554×C₈₉	—	2	1	no	—
35	#554×C₈₉	C₂²	1	1	yes	characteristic
36	#553×C₈₉	—	2	1	no	—
37	#552×C₈₉	C₂²	1	2	yes	—
38	D₄×Q₈×C₈₉	C₂²	1	1	yes	characteristic
39	D₄×Q₈×C₈₉	C₂²	1	2	yes	—
40	#548×C₈₉	C₂²	1	2	yes	—
41	#547×C₈₉	C₂²	1	1	yes	characteristic
42	#544×C₈₉	—	2	1	no	—
43	#544×C₈₉	C₂²	1	2	yes	—
44	#542×C₈₉	—	2	1	no	—
45	#542×C₈₉	—	2	1	no	—
46	#541×C₈₉	—	2	2	no	—
47	#541×C₈₉	—	2	1	no	—
48	#541×C₈₉	C₂²	1	2	yes	—
49	#541×C₈₉	C₂²	1	2	yes	—
50	#539×C₈₉	—	2	2	no	—
51	#536×C₈₉	C₂²	1	2	yes	—
52	#533×C₈₉	C₂²	1	1	yes	characteristic
53	#533×C₈₉	C₂²	1	1	yes	characteristic
54	C₂×C₄⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic
55	#529×C₈₉	C₂²	1	1	yes	characteristic
56	#529×C₈₉	C₂²	1	1	yes	characteristic
57	#501×C₈₉	C₂²	1	1	yes	characteristic
58	#499×C₈₉	C₂²	1	2	yes	—
59	#497×C₈₉	C₂²	1	1	yes	characteristic
60	#494×C₈₉	C₂²	1	2	yes	—
61	#491×C₈₉	C₂²	1	2	yes	—
62	#491×C₈₉	C₂²	1	2	yes	—
63	#491×C₈₉	C₂²	1	2	yes	—
64	#491×C₈₉	C₂²	1	1	yes	characteristic
65	#489×C₈₉	C₂²	1	2	yes	—
66	#489×C₈₉	C₂²	1	1	yes	characteristic
67	#488×C₈₉	C₂²	1	2	yes	—
68	#488×C₈₉	C₂²	1	2	yes	—
69	#487×C₈₉	C₂²	1	2	yes	—
70	#487×C₈₉	C₂²	1	1	yes	characteristic
71	#487×C₈₉	C₂²	1	1	yes	characteristic
72	#487×C₈₉	C₂²	1	1	yes	characteristic
73	#487×C₈₉	C₂²	1	1	yes	characteristic
74	#487×C₈₉	C₂²	1	2	yes	—
75	#485×C₈₉	C₂²	1	2	yes	—
76	#485×C₈₉	C₂²	1	2	yes	—
77	#485×C₈₉	C₂²	1	2	yes	—
78	#484×C₈₉	C₂²	1	2	yes	—
79	#483×C₈₉	C₂²	1	2	yes	—
80	#482×C₈₉	C₂²	1	2	yes	—
81	#479×C₈₉	C₂²	1	2	yes	—
82	#479×C₈₉	C₂²	1	2	yes	—
83	#477×C₈₉	C₂²	1	1	yes	characteristic
84	#477×C₈₉	C₂²	1	2	yes	—
85	#476×C₈₉	C₂²	1	1	yes	characteristic
86	#475×C₈₉	C₂²	1	2	yes	—
87	#475×C₈₉	C₂²	1	1	yes	characteristic
88	#474×C₈₉	C₂²	1	1	yes	characteristic
89	#470×C₈₉	C₂²	1	2	yes	—
90	#470×C₈₉	C₂²	1	1	yes	characteristic
91	#470×C₈₉	C₂²	1	2	yes	—
92	#470×C₈₉	C₂²	1	1	yes	characteristic
93	#468×C₈₉	C₂²	1	1	yes	characteristic
94	#468×C₈₉	C₂²	1	1	yes	characteristic
95	#467×C₈₉	C₂²	1	2	yes	—
96	#467×C₈₉	C₂²	1	2	yes	—
97	#464×C₈₉	C₂²	1	2	yes	—
98	#464×C₈₉	C₂²	1	2	yes	—
99	#462×C₈₉	C₂²	1	1	yes	characteristic
100	#462×C₈₉	C₂²	1	2	yes	—
101	#462×C₈₉	C₂²	1	1	yes	characteristic
102	#462×C₈₉	C₂²	1	1	yes	characteristic
103	#462×C₈₉	C₂²	1	2	yes	—
104	#462×C₈₉	C₂²	1	1	yes	characteristic
105	#452×C₈₉	C₂²	1	2	yes	—
106	#452×C₈₉	C₂²	1	2	yes	—
107	#451×C₈₉	C₂²	1	2	yes	—
108	#451×C₈₉	C₂²	1	2	yes	—
109	#451×C₈₉	C₂²	1	2	yes	—
110	#451×C₈₉	C₂²	1	2	yes	—
111	#446×C₈₉	C₂²	1	1	yes	characteristic
112	C₈×Q₈×C₈₉	C₂²	1	1	yes	characteristic
113	#441×C₈₉	C₂²	1	2	yes	—
114	#441×C₈₉	C₂²	1	2	yes	—
115	C₄×Q₁₆×C₈₉	C₂²	1	2	yes	—
116	C₄×Q₁₆×C₈₉	C₂²	1	1	yes	characteristic
117	C₄×Q₁₆×C₈₉	C₂²	1	2	yes	—
118	C₄×Q₁₆×C₈₉	C₂²	1	1	yes	characteristic
119	C₄×SD₁₆×C₈₉	C₂²	1	1	yes	characteristic
120	C₄×SD₁₆×C₈₉	C₂²	1	1	yes	characteristic
121	#436×C₈₉	C₂²	1	2	yes	—
122	#436×C₈₉	C₂²	1	1	yes	characteristic
123	#435×C₈₉	C₂²	1	2	yes	—
124	C₈×D₄×C₈₉	C₂²	1	1	yes	characteristic
125	#433×C₈₉	C₂²	1	2	yes	—
126	#431×C₈₉	C₂²	1	1	yes	characteristic
127	#419×C₈₉	C₂²	1	2	yes	—
128	#419×C₈₉	C₂²	1	2	yes	—
129	#419×C₈₉	C₂²	1	2	yes	—
130	#417×C₈₉	C₂²	1	2	yes	—
131	#416×C₈₉	C₂²	1	2	yes	—
132	C₂×#103×C₈₉	C₂²	1	2	yes	—
133	#405×C₈₉	C₂²	1	2	yes	—
134	C₄×M₁₆×C₈₉	C₂²	1	1	yes	characteristic
135	C₂×#41×C₈₉	C₂³	1	2	yes	—
136	C₂²×Q₈×C₈₉	C₂³	1	2	yes	—
137	C₂²×Q₈×C₈₉	C₂³	1	2	yes	—
138	C₂×Q₁₆×C₈₉	C₂³	1	1	yes	characteristic
139	C₂×Q₁₆×C₈₉	C₂³	1	1	yes	characteristic
140	C₂×Q₁₆×C₈₉	C₂³	1	2	yes	—
141	C₂×Q₁₆×C₈₉	C₂³	1	2	yes	—
142	C₂×Q₁₆×C₈₉	C₂³	1	2	yes	—
143	C₂×Q₁₆×C₈₉	C₂³	1	2	yes	—
144	C₂×SD₁₆×C₈₉	C₂³	1	1	yes	characteristic
145	C₂×SD₁₆×C₈₉	C₂³	1	1	yes	characteristic
146	C₂×M₁₆×C₈₉	C₂³	1	1	yes	characteristic
147	C₂×M₁₆×C₈₉	C₂³	1	1	yes	characteristic
148	C₂×M₁₆×C₈₉	C₂³	1	2	yes	—
149	C₂²×C₈×C₈₉	C₂³	1	2	yes	—
150	C₄⋊Q₈×C₈₉	—	2	1	no	—
151	C₄⋊Q₈×C₈₉	—	2	2	no	—
152	C₄⋊Q₈×C₈₉	—	2	1	no	—
153	C₄⋊Q₈×C₈₉	—	2	1	no	—
154	C₄⋊Q₈×C₈₉	—	2	2	no	—
155	C₄⋊Q₈×C₈₉	—	2	2	no	—
156	C₄⋊Q₈×C₈₉	—	2	1	no	—
157	C₄⋊Q₈×C₈₉	—	2	1	no	—
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	2	yes	—
162	C₄⋊Q₈×C₈₉	C₂³	1	1	yes	characteristic
163	C₄⋊Q₈×C₈₉	C₂³	1	1	yes	characteristic
164	C₄⋊Q₈×C₈₉	C₂³	1	2	yes	—
165	C₄⋊Q₈×C₈₉	C₂³	1	1	yes	characteristic
166	C₄⋊Q₈×C₈₉	C₂³	1	1	yes	characteristic
167	#126×C₈₉	—	2	2	no	—
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	—	2	1	no	—
177	#126×C₈₉	D₄	1	2	yes	—
178	#125×C₈₉	—	2	2	no	—
179	#125×C₈₉	—	2	2	no	—
180	#125×C₈₉	—	2	2	no	—
181	#125×C₈₉	—	2	2	no	—
182	#125×C₈₉	—	2	2	no	—
183	#125×C₈₉	—	2	1	no	—
184	#125×C₈₉	—	2	2	no	—
185	#125×C₈₉	—	2	2	no	—
186	#125×C₈₉	—	2	2	no	—
187	#125×C₈₉	—	2	1	no	—
188	#125×C₈₉	—	2	1	no	—
189	#125×C₈₉	D₄	1	1	yes	characteristic
190	#125×C₈₉	C₂³	1	2	yes	—
191	#125×C₈₉	C₂³	1	2	yes	—
192	#125×C₈₉	C₂³	1	1	yes	characteristic
193	#124×C₈₉	—	2	1	no	—
194	#124×C₈₉	—	2	2	no	—
195	#124×C₈₉	—	2	2	no	—
196	#124×C₈₉	D₄	1	1	yes	characteristic
197	#124×C₈₉	C₂³	1	2	yes	—
198	#124×C₈₉	C₂³	1	1	yes	characteristic
199	#123×C₈₉	—	2	2	no	—
200	#123×C₈₉	—	2	1	no	—
201	#123×C₈₉	—	2	2	no	—
202	#123×C₈₉	—	2	2	no	—
203	#123×C₈₉	—	2	2	no	—
204	#123×C₈₉	D₄	1	2	yes	—
205	C₂²⋊Q₈×C₈₉	—	2	1	no	—
206	C₂²⋊Q₈×C₈₉	—	2	1	no	—
207	C₂²⋊Q₈×C₈₉	—	2	1	no	—
208	C₂²⋊Q₈×C₈₉	—	2	1	no	—
209	C₂²⋊Q₈×C₈₉	—	2	2	no	—
210	C₂²⋊Q₈×C₈₉	—	2	2	no	—
211	C₂²⋊Q₈×C₈₉	—	2	2	no	—
212	C₂²⋊Q₈×C₈₉	—	2	2	no	—
213	C₂²⋊Q₈×C₈₉	—	2	2	no	—
214	C₂²⋊Q₈×C₈₉	—	2	2	no	—
215	C₂²⋊Q₈×C₈₉	—	2	2	no	—
216	C₂²⋊Q₈×C₈₉	—	2	2	no	—
217	C₂²⋊Q₈×C₈₉	—	2	2	no	—
218	C₂²⋊Q₈×C₈₉	D₄	1	1	yes	characteristic
219	C₂²⋊Q₈×C₈₉	C₂³	1	1	yes	characteristic
220	C₂²⋊Q₈×C₈₉	C₂³	1	1	yes	characteristic
221	C₂²⋊Q₈×C₈₉	C₂³	1	2	yes	—
222	C₂²⋊Q₈×C₈₉	C₂³	1	2	yes	—
223	C₂²⋊Q₈×C₈₉	C₂³	1	2	yes	—
224	C₂²⋊Q₈×C₈₉	C₂³	1	2	yes	—
225	C₂²⋊Q₈×C₈₉	C₂³	1	1	yes	characteristic
226	#121×C₈₉	—	2	2	no	—
227	#121×C₈₉	—	2	1	no	—
228	#121×C₈₉	D₄	1	1	yes	characteristic
229	#121×C₈₉	C₂³	1	1	yes	characteristic
230	C₄×Q₈×C₈₉	—	2	1	no	—
231	C₄×Q₈×C₈₉	—	2	1	no	—
232	C₄×Q₈×C₈₉	—	2	2	no	—
233	C₄×Q₈×C₈₉	—	2	1	no	—
234	C₄×Q₈×C₈₉	—	2	1	no	—
235	C₄×Q₈×C₈₉	—	2	1	no	—
236	C₄×Q₈×C₈₉	—	2	1	no	—
237	C₄×Q₈×C₈₉	—	2	1	no	—
238	C₄×Q₈×C₈₉	C₂³	1	1	yes	characteristic
239	C₄×Q₈×C₈₉	C₂³	1	1	yes	characteristic
240	C₄×Q₈×C₈₉	C₂³	1	1	yes	characteristic
241	C₄×Q₈×C₈₉	C₂³	1	2	yes	—
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	2	no	—
247	C₄×D₄×C₈₉	—	2	1	no	—
248	C₄×D₄×C₈₉	—	2	1	no	—
249	C₄×D₄×C₈₉	—	2	1	no	—
250	C₄×D₄×C₈₉	—	2	2	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	#117×C₈₉	—	2	1	no	—
255	#117×C₈₉	—	2	1	no	—
256	#117×C₈₉	—	2	2	no	—
257	#117×C₈₉	—	2	1	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	—	2	1	no	—
264	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
265	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
266	#107×C₈₉	C₂³	1	2	yes	—
267	#107×C₈₉	C₂³	1	2	yes	—
268	#107×C₈₉	C₂³	1	1	yes	characteristic
269	#107×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	1	yes	characteristic
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	2	yes	—
285	#103×C₈₉	C₂³	1	2	yes	—
286	#103×C₈₉	C₂³	1	1	yes	characteristic
287	#103×C₈₉	C₂³	1	2	yes	—
288	#103×C₈₉	C₂³	1	2	yes	—
289	#103×C₈₉	C₂³	1	2	yes	—
290	#103×C₈₉	C₂³	1	2	yes	—
291	#103×C₈₉	C₂³	1	2	yes	—
292	#103×C₈₉	C₂³	1	2	yes	—
293	#103×C₈₉	C₂³	1	2	yes	—
294	#103×C₈₉	C₂³	1	1	yes	characteristic
295	#103×C₈₉	C₂³	1	1	yes	characteristic
296	#103×C₈₉	C₂³	1	1	yes	characteristic
297	#103×C₈₉	C₂³	1	1	yes	characteristic
298	#102×C₈₉	C₂³	1	1	yes	characteristic
299	#102×C₈₉	C₂³	1	2	yes	—
300	#102×C₈₉	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
306	#97×C₈₉	C₂³	1	1	yes	characteristic
307	#97×C₈₉	C₂³	1	2	yes	—
308	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
309	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
310	C₄×C₈×C₈₉	C₂³	1	2	yes	—
311	C₄×C₈×C₈₉	C₂³	1	2	yes	—
312	#41×C₈₉	—	4	2	no	—
313	#41×C₈₉	—	4	2	no	—
314	C₂×Q₈×C₈₉	—	2	1	no	—
315	C₂×Q₈×C₈₉	—	2	1	no	—
316	C₂×Q₈×C₈₉	—	2	1	no	—
317	C₂×Q₈×C₈₉	—	2	2	no	—
318	C₂×Q₈×C₈₉	—	2	2	no	—
319	C₂×Q₈×C₈₉	—	2	2	no	—
320	C₂×Q₈×C₈₉	—	4	2	no	—
321	C₂×Q₈×C₈₉	—	4	2	no	—
322	C₂×Q₈×C₈₉	—	4	2	no	—
323	C₂×Q₈×C₈₉	—	4	2	no	—
324	C₂×Q₈×C₈₉	C₂×D₄	1	1	yes	characteristic
325	C₂×Q₈×C₈₉	C₂⁴	1	1	yes	characteristic
326	C₂×Q₈×C₈₉	C₂⁴	1	2	yes	—
327	C₂×Q₈×C₈₉	C₂⁴	1	2	yes	—
328	C₂×Q₈×C₈₉	C₂⁴	1	1	yes	characteristic
329	C₂×Q₈×C₈₉	C₂⁴	1	1	yes	characteristic
330	C₂×D₄×C₈₉	—	2	1	no	—
331	C₂×D₄×C₈₉	—	2	2	no	—
332	C₂×D₄×C₈₉	C₂×D₄	1	1	yes	characteristic
333	C₂×D₄×C₈₉	C₂×D₄	1	2	yes	—
334	C₂×D₄×C₈₉	C₂⁴	1	1	yes	characteristic
335	C₂²×C₄×C₈₉	—	2	2	no	—
336	C₂²×C₄×C₈₉	—	2	2	no	—
337	C₂²×C₄×C₈₉	—	2	2	no	—
338	C₂²×C₄×C₈₉	—	2	1	no	—
339	C₂²×C₄×C₈₉	—	2	2	no	—
340	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
341	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
342	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
343	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
344	Q₁₆×C₈₉	—	4	2	no	—
345	Q₁₆×C₈₉	—	4	2	no	—
346	Q₁₆×C₈₉	—	4	1	no	—
347	Q₁₆×C₈₉	—	4	1	no	—
348	Q₁₆×C₈₉	—	4	2	no	—
349	Q₁₆×C₈₉	—	4	2	no	—
350	SD₁₆×C₈₉	—	4	1	no	—
351	SD₁₆×C₈₉	—	4	1	no	—
352	M₁₆×C₈₉	—	4	1	no	—
353	M₁₆×C₈₉	—	4	1	no	—
354	M₁₆×C₈₉	—	4	2	no	—
355	C₂×C₈×C₈₉	—	4	2	no	—
356	C₂×C₈×C₈₉	C₂⁴	1	1	yes	characteristic
357	C₂×C₈×C₈₉	C₂⁴	1	2	yes	—
358	C₂×C₈×C₈₉	C₂⁴	1	1	yes	characteristic
359	C₂×C₈×C₈₉	C₂⁴	1	2	yes	—
360	C₂×C₈×C₈₉	C₂⁴	1	1	yes	characteristic
361	C₂×C₈×C₈₉	C₂⁴	1	1	yes	characteristic
362	C₄⋊C₄×C₈₉	—	2	1	no	—
363	C₄⋊C₄×C₈₉	—	2	1	no	—
364	C₄⋊C₄×C₈₉	—	2	1	no	—
365	C₄⋊C₄×C₈₉	—	2	2	no	—
366	C₄⋊C₄×C₈₉	—	2	2	no	—
367	C₄⋊C₄×C₈₉	—	2	2	no	—
368	C₄⋊C₄×C₈₉	—	2	1	no	—
369	C₄⋊C₄×C₈₉	—	2	2	no	—
370	C₄⋊C₄×C₈₉	—	2	1	no	—
371	C₄⋊C₄×C₈₉	—	2	1	no	—
372	C₄⋊C₄×C₈₉	—	2	1	no	—
373	C₄⋊C₄×C₈₉	—	2	2	no	—
374	C₄⋊C₄×C₈₉	—	2	1	no	—
375	C₄⋊C₄×C₈₉	—	2	1	no	—
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	2	no	—
383	C₄⋊C₄×C₈₉	—	2	2	no	—
384	C₄⋊C₄×C₈₉	—	2	2	no	—
385	C₄⋊C₄×C₈₉	—	2	2	no	—
386	C₄⋊C₄×C₈₉	—	2	1	no	—
387	C₄⋊C₄×C₈₉	—	2	1	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	2	no	—
393	C₄⋊C₄×C₈₉	—	2	1	no	—
394	C₄⋊C₄×C₈₉	—	2	1	no	—
395	C₄⋊C₄×C₈₉	—	2	2	no	—
396	C₄⋊C₄×C₈₉	—	2	2	no	—
397	C₄⋊C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
398	C₄⋊C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
399	C₄⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
400	C₄⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
401	C₄⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
402	C₄⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
403	C₄⋊C₄×C₈₉	C₂⁴	1	1	yes	characteristic
404	C₄⋊C₄×C₈₉	C₂⁴	1	2	yes	—
405	C₄⋊C₄×C₈₉	C₂⁴	1	2	yes	—
406	C₄⋊C₄×C₈₉	C₂⁴	1	1	yes	characteristic
407	C₄⋊C₄×C₈₉	C₂⁴	1	1	yes	characteristic
408	C₄⋊C₄×C₈₉	C₂⁴	1	1	yes	characteristic
409	C₂²⋊C₄×C₈₉	—	2	1	no	—
410	C₂²⋊C₄×C₈₉	—	2	1	no	—
411	C₂²⋊C₄×C₈₉	—	2	2	no	—
412	C₂²⋊C₄×C₈₉	—	2	2	no	—
413	C₂²⋊C₄×C₈₉	—	2	2	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	1	no	—
421	C₂²⋊C₄×C₈₉	—	2	1	no	—
422	C₂²⋊C₄×C₈₉	—	2	2	no	—
423	C₂²⋊C₄×C₈₉	—	2	1	no	—
424	C₂²⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
425	C₂²⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
426	C₂²⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
427	C₂²⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
428	C₂²⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
429	C₄²×C₈₉	—	2	2	no	—
430	C₄²×C₈₉	—	2	1	no	—
431	C₄²×C₈₉	—	2	1	no	—
432	C₄²×C₈₉	—	2	2	no	—
433	C₄²×C₈₉	—	2	1	no	—
434	C₄²×C₈₉	—	2	2	no	—
435	C₄²×C₈₉	—	2	2	no	—
436	C₄²×C₈₉	—	2	2	no	—
437	C₄²×C₈₉	—	2	2	no	—
438	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
439	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
440	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
441	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
442	C₄²×C₈₉	C₂⁴	1	2	yes	—
443	C₂³×C₈₉	—	2	1	no	—
444	C₂³×C₈₉	C₂²×D₄	1	2	yes	—
445	C₂³×C₈₉	C₂²×D₄	1	1	yes	characteristic
446	Q₈×C₈₉	—	2	2	no	—
447	Q₈×C₈₉	—	2	1	no	—
448	Q₈×C₈₉	—	2	1	no	—
449	Q₈×C₈₉	—	2	1	no	—
450	Q₈×C₈₉	—	2	1	no	—
451	Q₈×C₈₉	—	2	2	no	—
452	Q₈×C₈₉	—	2	1	no	—
453	Q₈×C₈₉	—	2	1	no	—
454	Q₈×C₈₉	—	2	2	no	—
455	Q₈×C₈₉	—	2	2	no	—
456	Q₈×C₈₉	—	2	2	no	—
457	Q₈×C₈₉	—	4	2	no	—
458	Q₈×C₈₉	—	8	1	no	—
459	Q₈×C₈₉	—	8	1	no	—
460	Q₈×C₈₉	—	8	2	no	—
461	Q₈×C₈₉	—	8	2	no	—
462	Q₈×C₈₉	—	8	2	no	—
463	D₄×C₈₉	—	2	2	no	—
464	D₄×C₈₉	—	2	1	no	—
465	D₄×C₈₉	—	2	1	no	—
466	D₄×C₈₉	—	4	2	no	—
467	D₄×C₈₉	—	4	2	no	—
468	D₄×C₈₉	—	8	2	no	—
469	C₂×C₄×C₈₉	—	2	2	no	—
470	C₂×C₄×C₈₉	—	2	2	no	—
471	C₂×C₄×C₈₉	—	2	1	no	—
472	C₂×C₄×C₈₉	—	2	1	no	—
473	C₂×C₄×C₈₉	—	2	2	no	—
474	C₂×C₄×C₈₉	—	2	1	no	—
475	C₂×C₄×C₈₉	—	2	1	no	—
476	C₂×C₄×C₈₉	—	2	1	no	—
477	C₂×C₄×C₈₉	—	2	2	no	—
478	C₂×C₄×C₈₉	—	2	1	no	—
479	C₂×C₄×C₈₉	—	2	1	no	—
480	C₂×C₄×C₈₉	—	2	2	no	—
481	C₂×C₄×C₈₉	—	2	1	no	—
482	C₂×C₄×C₈₉	—	2	2	no	—
483	C₂×C₄×C₈₉	—	2	1	no	—
484	C₂×C₄×C₈₉	—	2	2	no	—
485	C₂×C₄×C₈₉	—	4	1	no	—
486	C₂×C₄×C₈₉	—	4	2	no	—
487	C₂×C₄×C₈₉	—	8	2	no	—
488	C₂×C₄×C₈₉	—	8	2	no	—
489	C₂×C₄×C₈₉	—	8	2	no	—
490	C₂×C₄×C₈₉	—	8	2	no	—
491	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
492	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
493	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
494	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
495	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
496	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
497	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
498	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
499	C₂×C₄×C₈₉	C₂⁵	1	1	yes	characteristic
500	C₈×C₈₉	—	2	1	no	—
501	C₈×C₈₉	—	2	2	no	—
502	C₈×C₈₉	—	2	1	no	—
503	C₈×C₈₉	—	2	1	no	—
504	C₈×C₈₉	—	2	1	no	—
505	C₈×C₈₉	—	2	2	no	—
506	C₂²×C₈₉	—	2	1	no	—
507	C₂²×C₈₉	—	2	2	no	—
508	C₂²×C₈₉	—	2	1	no	—
509	C₂²×C₈₉	—	2	2	no	—
510	C₂²×C₈₉	—	2	1	no	—
511	C₂²×C₈₉	—	2	2	no	—
512	C₂²×C₈₉	—	4	1	no	—
513	C₂²×C₈₉	—	4	1	no	—
514	C₂²×C₈₉	—	4	1	no	—
515	C₂²×C₈₉	C₂³×D₄	1	1	yes	characteristic
516	C₄×C₈₉	—	2	1	no	—
517	C₄×C₈₉	—	2	1	no	—
518	C₄×C₈₉	—	2	2	no	—
519	C₄×C₈₉	—	2	2	no	—
520	C₄×C₈₉	—	2	1	no	—
521	C₄×C₈₉	—	2	1	no	—
522	C₄×C₈₉	—	2	2	no	—
523	C₄×C₈₉	—	4	1	no	—
524	C₄×C₈₉	—	4	2	no	—
525	C₄×C₈₉	—	4	1	no	—
526	C₄×C₈₉	—	4	1	no	—
527	C₄×C₈₉	—	4	2	no	—
528	C₄×C₈₉	—	4	1	no	—
529	C₄×C₈₉	—	4	2	no	—
530	C₄×C₈₉	—	4	1	no	—
531	C₄×C₈₉	—	4	1	no	—
532	C₄×C₈₉	—	4	1	no	—
533	C₄×C₈₉	—	4	2	no	—
534	C₄×C₈₉	#578	1	2	yes	—
535	C₄×C₈₉	#585	1	1	yes	characteristic
536	C₄×C₈₉	#585	1	1	yes	characteristic
537	#62611	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
538	C₂×C₈₉	—	4	1	no	—
539	C₂×C₈₉	—	4	2	no	—
540	C₂×C₈₉	—	8	1	no	—
541	C₂×C₈₉	#3500	1	1	yes	characteristic
542	C₂×C₈₉	C₂×#578	1	1	yes	characteristic
543	C₂×C₈₉	#3586	1	1	yes	characteristic
544	#3555	C₂×C₈₉	1	1	yes	characteristic, complemented
545	#3552	C₂×C₈₉	1	1	yes	characteristic
546	#3374	C₂×C₈₉	1	1	yes	characteristic, complemented
547	#3369	C₂×C₈₉	1	1	yes	characteristic, complemented
548	#3364	C₂×C₈₉	1	1	yes	characteristic, complemented
549	#3363	C₂×C₈₉	1	1	yes	characteristic, complemented
550	#3331	C₂×C₈₉	1	1	yes	characteristic, complemented
551	#3328	C₂×C₈₉	1	1	yes	characteristic, complemented
552	#3328	C₂×C₈₉	1	2	yes	complemented
553	#3327	C₂×C₈₉	1	2	yes	complemented
554	#3313	C₂×C₈₉	1	2	yes	complemented
555	#3312	C₂×C₈₉	1	2	yes	complemented
556	#3302	C₂×C₈₉	1	1	yes	characteristic, complemented
557	#3299	C₂×C₈₉	1	1	yes	characteristic, complemented
558	#3242	C₂×C₈₉	1	2	yes	complemented
559	#3233	C₂×C₈₉	1	1	yes	characteristic, complemented
560	#3223	C₂×C₈₉	1	2	yes	complemented
561	#3209	C₂×C₈₉	1	1	yes	characteristic, complemented
562	#3177	C₂×C₈₉	1	2	yes	complemented
563	#3172	C₂×C₈₉	1	1	yes	characteristic, complemented
564	#3139	C₂×C₈₉	1	1	yes	characteristic, complemented
565	#3137	C₂×C₈₉	1	2	yes	complemented
566	#2969	C₂×C₈₉	1	1	yes	characteristic, complemented
567	C₈₉	#62611	1	1	yes	characteristic, direct product factor, Sylow
568	#563	—	2	2	no	—
569	#563	—	2	2	no	—
570	Q₈²	C₂²×C₈₉	1	1	yes	characteristic
571	#557	—	2	1	no	—
572	#557	C₂²×C₈₉	1	1	yes	characteristic
573	#557	C₂²×C₈₉	1	1	yes	characteristic
574	#556	—	2	1	no	—
575	#556	C₂²×C₈₉	1	1	yes	characteristic
576	#556	C₂²×C₈₉	1	1	yes	characteristic
577	#556	C₂²×C₈₉	1	2	yes	—
578	#554	—	2	1	no	—
579	#554	C₂²×C₈₉	1	1	yes	characteristic
580	#553	—	2	1	no	—
581	#552	C₂²×C₈₉	1	2	yes	—
582	D₄×Q₈	C₂²×C₈₉	1	1	yes	characteristic
583	D₄×Q₈	C₂²×C₈₉	1	2	yes	—
584	#548	C₂²×C₈₉	1	2	yes	—
585	#547	C₂²×C₈₉	1	1	yes	characteristic
586	#544	—	2	1	no	—
587	#544	C₂²×C₈₉	1	2	yes	—
588	#542	—	2	1	no	—
589	#542	—	2	1	no	—
590	#541	—	2	2	no	—
591	#541	—	2	1	no	—
592	#541	C₂²×C₈₉	1	2	yes	—
593	#541	C₂²×C₈₉	1	2	yes	—
594	#539	—	2	2	no	—
595	#536	C₂²×C₈₉	1	2	yes	—
596	#533	C₂²×C₈₉	1	1	yes	characteristic
597	#533	C₂²×C₈₉	1	1	yes	characteristic
598	C₂×C₄⋊Q₈	C₂²×C₈₉	1	1	yes	characteristic
599	#529	C₂²×C₈₉	1	1	yes	characteristic
600	#529	C₂²×C₈₉	1	1	yes	characteristic
601	#501	C₂²×C₈₉	1	1	yes	characteristic
602	#499	C₂²×C₈₉	1	2	yes	—
603	#497	C₂²×C₈₉	1	1	yes	characteristic
604	#494	C₂²×C₈₉	1	2	yes	—
605	#491	C₂²×C₈₉	1	2	yes	—
606	#491	C₂²×C₈₉	1	2	yes	—
607	#491	C₂²×C₈₉	1	2	yes	—
608	#491	C₂²×C₈₉	1	1	yes	characteristic
609	#489	C₂²×C₈₉	1	2	yes	—
610	#489	C₂²×C₈₉	1	1	yes	characteristic
611	#488	C₂²×C₈₉	1	2	yes	—
612	#488	C₂²×C₈₉	1	2	yes	—
613	#487	C₂²×C₈₉	1	2	yes	—
614	#487	C₂²×C₈₉	1	1	yes	characteristic
615	#487	C₂²×C₈₉	1	1	yes	characteristic
616	#487	C₂²×C₈₉	1	1	yes	characteristic
617	#487	C₂²×C₈₉	1	1	yes	characteristic
618	#487	C₂²×C₈₉	1	2	yes	—
619	#485	C₂²×C₈₉	1	2	yes	—
620	#485	C₂²×C₈₉	1	2	yes	—
621	#485	C₂²×C₈₉	1	2	yes	—
622	#484	C₂²×C₈₉	1	2	yes	—
623	#483	C₂²×C₈₉	1	2	yes	—
624	#482	C₂²×C₈₉	1	2	yes	—
625	#479	C₂²×C₈₉	1	2	yes	—
626	#479	C₂²×C₈₉	1	2	yes	—
627	#477	C₂²×C₈₉	1	1	yes	characteristic
628	#477	C₂²×C₈₉	1	2	yes	—
629	#476	C₂²×C₈₉	1	1	yes	characteristic
630	#475	C₂²×C₈₉	1	2	yes	—
631	#475	C₂²×C₈₉	1	1	yes	characteristic
632	#474	C₂²×C₈₉	1	1	yes	characteristic
633	#470	C₂²×C₈₉	1	1	yes	characteristic
634	#470	C₂²×C₈₉	1	2	yes	—
635	#470	C₂²×C₈₉	1	2	yes	—
636	#470	C₂²×C₈₉	1	1	yes	characteristic
637	#468	C₂²×C₈₉	1	1	yes	characteristic
638	#468	C₂²×C₈₉	1	1	yes	characteristic
639	#467	C₂²×C₈₉	1	2	yes	—
640	#467	C₂²×C₈₉	1	2	yes	—
641	#464	C₂²×C₈₉	1	2	yes	—
642	#464	C₂²×C₈₉	1	2	yes	—
643	#462	C₂²×C₈₉	1	1	yes	characteristic
644	#462	C₂²×C₈₉	1	2	yes	—
645	#462	C₂²×C₈₉	1	1	yes	characteristic
646	#462	C₂²×C₈₉	1	1	yes	characteristic
647	#462	C₂²×C₈₉	1	2	yes	—
648	#462	C₂²×C₈₉	1	1	yes	characteristic
649	#452	C₂²×C₈₉	1	2	yes	—
650	#452	C₂²×C₈₉	1	2	yes	—
651	#451	C₂²×C₈₉	1	2	yes	—
652	#451	C₂²×C₈₉	1	2	yes	—
653	#451	C₂²×C₈₉	1	2	yes	—
654	#451	C₂²×C₈₉	1	2	yes	—
655	#446	C₂²×C₈₉	1	1	yes	characteristic
656	C₈×Q₈	C₂²×C₈₉	1	1	yes	characteristic
657	#441	C₂²×C₈₉	1	2	yes	—
658	#441	C₂²×C₈₉	1	2	yes	—
659	C₄×Q₁₆	C₂²×C₈₉	1	1	yes	characteristic
660	C₄×Q₁₆	C₂²×C₈₉	1	2	yes	—
661	C₄×Q₁₆	C₂²×C₈₉	1	2	yes	—
662	C₄×Q₁₆	C₂²×C₈₉	1	1	yes	characteristic
663	C₄×SD₁₆	C₂²×C₈₉	1	1	yes	characteristic
664	C₄×SD₁₆	C₂²×C₈₉	1	1	yes	characteristic
665	#436	C₂²×C₈₉	1	1	yes	characteristic
666	#436	C₂²×C₈₉	1	2	yes	—
667	#435	C₂²×C₈₉	1	2	yes	—
668	C₈×D₄	C₂²×C₈₉	1	1	yes	characteristic
669	#433	C₂²×C₈₉	1	2	yes	—
670	#431	C₂²×C₈₉	1	1	yes	characteristic
671	#419	C₂²×C₈₉	1	2	yes	—
672	#419	C₂²×C₈₉	1	2	yes	—
673	#419	C₂²×C₈₉	1	2	yes	—
674	#417	C₂²×C₈₉	1	2	yes	—
675	#416	C₂²×C₈₉	1	2	yes	—
676	C₂×#103	C₂²×C₈₉	1	2	yes	—
677	#405	C₂²×C₈₉	1	2	yes	—
678	C₄×M₁₆	C₂²×C₈₉	1	1	yes	characteristic
679	C₂×#41	C₂³×C₈₉	1	2	yes	—
680	C₂²×Q₈	C₂³×C₈₉	1	2	yes	—
681	C₂²×Q₈	C₂³×C₈₉	1	2	yes	—
682	C₂×Q₁₆	C₂³×C₈₉	1	1	yes	characteristic
683	C₂×Q₁₆	C₂³×C₈₉	1	1	yes	characteristic
684	C₂×Q₁₆	C₂³×C₈₉	1	2	yes	—
685	C₂×Q₁₆	C₂³×C₈₉	1	2	yes	—
686	C₂×Q₁₆	C₂³×C₈₉	1	2	yes	—
687	C₂×Q₁₆	C₂³×C₈₉	1	2	yes	—
688	C₂×SD₁₆	C₂³×C₈₉	1	1	yes	characteristic
689	C₂×SD₁₆	C₂³×C₈₉	1	1	yes	characteristic
690	C₂×M₁₆	C₂³×C₈₉	1	1	yes	characteristic
691	C₂×M₁₆	C₂³×C₈₉	1	1	yes	characteristic
692	C₂×M₁₆	C₂³×C₈₉	1	2	yes	—
693	C₂²×C₈	C₂³×C₈₉	1	2	yes	—
694	C₄⋊Q₈	—	2	1	no	—
695	C₄⋊Q₈	—	2	2	no	—
696	C₄⋊Q₈	—	2	1	no	—
697	C₄⋊Q₈	—	2	1	no	—
698	C₄⋊Q₈	—	2	2	no	—
699	C₄⋊Q₈	—	2	2	no	—
700	C₄⋊Q₈	—	2	1	no	—
701	C₄⋊Q₈	—	2	1	no	—
702	C₄⋊Q₈	C₂³×C₈₉	1	2	yes	—
703	C₄⋊Q₈	C₂³×C₈₉	1	1	yes	characteristic
704	C₄⋊Q₈	C₂³×C₈₉	1	1	yes	characteristic
705	C₄⋊Q₈	C₂³×C₈₉	1	1	yes	characteristic
706	C₄⋊Q₈	C₂³×C₈₉	1	2	yes	—
707	C₄⋊Q₈	C₂³×C₈₉	1	1	yes	characteristic
708	C₄⋊Q₈	C₂³×C₈₉	1	1	yes	characteristic
709	C₄⋊Q₈	C₂³×C₈₉	1	1	yes	characteristic
710	C₄⋊Q₈	C₂³×C₈₉	1	2	yes	—
711	#126	—	2	2	no	—
712	#126	—	2	2	no	—
713	#126	—	2	2	no	—
714	#126	—	2	2	no	—
715	#126	—	2	2	no	—
716	#126	—	2	2	no	—
717	#126	—	2	2	no	—
718	#126	—	2	2	no	—
719	#126	—	2	2	no	—
720	#126	—	2	1	no	—
721	#126	D₄×C₈₉	1	2	yes	—
722	#125	—	2	2	no	—
723	#125	—	2	2	no	—
724	#125	—	2	2	no	—
725	#125	—	2	2	no	—
726	#125	—	2	2	no	—
727	#125	—	2	1	no	—
728	#125	—	2	2	no	—
729	#125	—	2	2	no	—
730	#125	—	2	2	no	—
731	#125	—	2	1	no	—
732	#125	—	2	1	no	—
733	#125	D₄×C₈₉	1	1	yes	characteristic
734	#125	C₂³×C₈₉	1	1	yes	characteristic
735	#125	C₂³×C₈₉	1	2	yes	—
736	#125	C₂³×C₈₉	1	2	yes	—
737	#124	—	2	1	no	—
738	#124	—	2	2	no	—
739	#124	—	2	2	no	—
740	#124	D₄×C₈₉	1	1	yes	characteristic
741	#124	C₂³×C₈₉	1	1	yes	characteristic
742	#124	C₂³×C₈₉	1	2	yes	—
743	#123	—	2	2	no	—
744	#123	—	2	1	no	—
745	#123	—	2	2	no	—
746	#123	—	2	2	no	—
747	#123	—	2	2	no	—
748	#123	D₄×C₈₉	1	2	yes	—
749	C₂²⋊Q₈	—	2	1	no	—
750	C₂²⋊Q₈	—	2	1	no	—
751	C₂²⋊Q₈	—	2	1	no	—
752	C₂²⋊Q₈	—	2	1	no	—
753	C₂²⋊Q₈	—	2	2	no	—
754	C₂²⋊Q₈	—	2	2	no	—
755	C₂²⋊Q₈	—	2	2	no	—
756	C₂²⋊Q₈	—	2	2	no	—
757	C₂²⋊Q₈	—	2	2	no	—
758	C₂²⋊Q₈	—	2	2	no	—
759	C₂²⋊Q₈	—	2	2	no	—
760	C₂²⋊Q₈	—	2	2	no	—
761	C₂²⋊Q₈	—	2	2	no	—
762	C₂²⋊Q₈	D₄×C₈₉	1	1	yes	characteristic
763	C₂²⋊Q₈	C₂³×C₈₉	1	1	yes	characteristic
764	C₂²⋊Q₈	C₂³×C₈₉	1	1	yes	characteristic
765	C₂²⋊Q₈	C₂³×C₈₉	1	1	yes	characteristic
766	C₂²⋊Q₈	C₂³×C₈₉	1	2	yes	—
767	C₂²⋊Q₈	C₂³×C₈₉	1	2	yes	—
768	C₂²⋊Q₈	C₂³×C₈₉	1	2	yes	—
769	C₂²⋊Q₈	C₂³×C₈₉	1	2	yes	—
770	#121	—	2	2	no	—
771	#121	—	2	1	no	—
772	#121	D₄×C₈₉	1	1	yes	characteristic
773	#121	C₂³×C₈₉	1	1	yes	characteristic
774	C₄×Q₈	—	2	1	no	—
775	C₄×Q₈	—	2	1	no	—
776	C₄×Q₈	—	2	2	no	—
777	C₄×Q₈	—	2	1	no	—
778	C₄×Q₈	—	2	1	no	—
779	C₄×Q₈	—	2	1	no	—
780	C₄×Q₈	—	2	1	no	—
781	C₄×Q₈	—	2	1	no	—
782	C₄×Q₈	C₂³×C₈₉	1	1	yes	characteristic
783	C₄×Q₈	C₂³×C₈₉	1	1	yes	characteristic
784	C₄×Q₈	C₂³×C₈₉	1	1	yes	characteristic
785	C₄×Q₈	C₂³×C₈₉	1	2	yes	—
786	C₄×Q₈	C₂³×C₈₉	1	2	yes	—
787	C₄×Q₈	C₂³×C₈₉	1	2	yes	—
788	C₄×Q₈	C₂³×C₈₉	1	2	yes	—
789	C₄×Q₈	C₂³×C₈₉	1	1	yes	characteristic
790	C₄×D₄	—	2	2	no	—
791	C₄×D₄	—	2	1	no	—
792	C₄×D₄	—	2	1	no	—
793	C₄×D₄	—	2	1	no	—
794	C₄×D₄	—	2	2	no	—
795	C₄×D₄	C₂³×C₈₉	1	1	yes	characteristic
796	C₄×D₄	C₂³×C₈₉	1	1	yes	characteristic
797	C₄×D₄	C₂³×C₈₉	1	2	yes	—
798	#117	—	2	1	no	—
799	#117	—	2	1	no	—
800	#117	—	2	2	no	—
801	#117	—	2	1	no	—
802	#117	C₂³×C₈₉	1	2	yes	—
803	#117	C₂³×C₈₉	1	2	yes	—
804	#117	C₂³×C₈₉	1	2	yes	—
805	C₂×C₄⋊C₄	—	2	1	no	—
806	C₂×C₄⋊C₄	—	2	1	no	—
807	C₂×C₄⋊C₄	—	2	1	no	—
808	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
809	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
810	#107	C₂³×C₈₉	1	2	yes	—
811	#107	C₂³×C₈₉	1	2	yes	—
812	#107	C₂³×C₈₉	1	1	yes	characteristic
813	#107	C₂³×C₈₉	1	1	yes	characteristic
814	#106	C₂³×C₈₉	1	1	yes	characteristic
815	#106	C₂³×C₈₉	1	1	yes	characteristic
816	#106	C₂³×C₈₉	1	2	yes	—
817	#106	C₂³×C₈₉	1	2	yes	—
818	C₄⋊C₈	C₂³×C₈₉	1	1	yes	characteristic
819	C₄⋊C₈	C₂³×C₈₉	1	1	yes	characteristic
820	C₄⋊C₈	C₂³×C₈₉	1	2	yes	—
821	C₄⋊C₈	C₂³×C₈₉	1	2	yes	—
822	#103	C₂³×C₈₉	1	1	yes	characteristic
823	#103	C₂³×C₈₉	1	2	yes	—
824	#103	C₂³×C₈₉	1	2	yes	—
825	#103	C₂³×C₈₉	1	2	yes	—
826	#103	C₂³×C₈₉	1	2	yes	—
827	#103	C₂³×C₈₉	1	2	yes	—
828	#103	C₂³×C₈₉	1	2	yes	—
829	#103	C₂³×C₈₉	1	2	yes	—
830	#103	C₂³×C₈₉	1	1	yes	characteristic
831	#103	C₂³×C₈₉	1	2	yes	—
832	#103	C₂³×C₈₉	1	2	yes	—
833	#103	C₂³×C₈₉	1	2	yes	—
834	#103	C₂³×C₈₉	1	2	yes	—
835	#103	C₂³×C₈₉	1	2	yes	—
836	#103	C₂³×C₈₉	1	2	yes	—
837	#103	C₂³×C₈₉	1	2	yes	—
838	#103	C₂³×C₈₉	1	1	yes	characteristic
839	#103	C₂³×C₈₉	1	1	yes	characteristic
840	#103	C₂³×C₈₉	1	1	yes	characteristic
841	#103	C₂³×C₈₉	1	1	yes	characteristic
842	#102	C₂³×C₈₉	1	1	yes	characteristic
843	#102	C₂³×C₈₉	1	2	yes	—
844	#102	C₂³×C₈₉	1	1	yes	characteristic
845	#102	C₂³×C₈₉	1	2	yes	—
846	C₂²⋊C₈	C₂³×C₈₉	1	2	yes	—
847	C₂²⋊C₈	C₂³×C₈₉	1	2	yes	—
848	C₂²⋊C₈	C₂³×C₈₉	1	2	yes	—
849	#97	C₂³×C₈₉	1	1	yes	characteristic
850	#97	C₂³×C₈₉	1	1	yes	characteristic
851	#97	C₂³×C₈₉	1	2	yes	—
852	C₄×C₈	C₂³×C₈₉	1	1	yes	characteristic
853	C₄×C₈	C₂³×C₈₉	1	1	yes	characteristic
854	C₄×C₈	C₂³×C₈₉	1	2	yes	—
855	C₄×C₈	C₂³×C₈₉	1	2	yes	—
856	#41	—	4	2	no	—
857	#41	—	4	2	no	—
858	C₂×Q₈	—	2	1	no	—
859	C₂×Q₈	—	2	1	no	—
860	C₂×Q₈	—	2	1	no	—
861	C₂×Q₈	—	2	2	no	—
862	C₂×Q₈	—	2	2	no	—
863	C₂×Q₈	—	2	2	no	—
864	C₂×Q₈	—	4	2	no	—
865	C₂×Q₈	—	4	2	no	—
866	C₂×Q₈	—	4	2	no	—
867	C₂×Q₈	—	4	2	no	—
868	C₂×Q₈	C₂×D₄×C₈₉	1	1	yes	characteristic
869	C₂×Q₈	C₂⁴×C₈₉	1	1	yes	characteristic
870	C₂×Q₈	C₂⁴×C₈₉	1	2	yes	—
871	C₂×Q₈	C₂⁴×C₈₉	1	2	yes	—
872	C₂×Q₈	C₂⁴×C₈₉	1	1	yes	characteristic
873	C₂×Q₈	C₂⁴×C₈₉	1	1	yes	characteristic
874	C₂×D₄	—	2	1	no	—
875	C₂×D₄	—	2	2	no	—
876	C₂×D₄	C₂×D₄×C₈₉	1	1	yes	characteristic
877	C₂×D₄	C₂×D₄×C₈₉	1	2	yes	—
878	C₂×D₄	C₂⁴×C₈₉	1	1	yes	characteristic
879	C₂²×C₄	—	2	2	no	—
880	C₂²×C₄	—	2	2	no	—
881	C₂²×C₄	—	2	2	no	—
882	C₂²×C₄	—	2	1	no	—
883	C₂²×C₄	—	2	2	no	—
884	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
885	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
886	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
887	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
888	Q₁₆	—	4	2	no	—
889	Q₁₆	—	4	2	no	—
890	Q₁₆	—	4	1	no	—
891	Q₁₆	—	4	1	no	—
892	Q₁₆	—	4	2	no	—
893	Q₁₆	—	4	2	no	—
894	SD₁₆	—	4	1	no	—
895	SD₁₆	—	4	1	no	—
896	M₁₆	—	4	1	no	—
897	M₁₆	—	4	1	no	—
898	M₁₆	—	4	2	no	—
899	C₂×C₈	—	4	2	no	—
900	C₂×C₈	C₂⁴×C₈₉	1	1	yes	characteristic
901	C₂×C₈	C₂⁴×C₈₉	1	2	yes	—
902	C₂×C₈	C₂⁴×C₈₉	1	1	yes	characteristic
903	C₂×C₈	C₂⁴×C₈₉	1	2	yes	—
904	C₂×C₈	C₂⁴×C₈₉	1	1	yes	characteristic
905	C₂×C₈	C₂⁴×C₈₉	1	1	yes	characteristic
906	C₄⋊C₄	—	2	1	no	—
907	C₄⋊C₄	—	2	1	no	—
908	C₄⋊C₄	—	2	1	no	—
909	C₄⋊C₄	—	2	2	no	—
910	C₄⋊C₄	—	2	2	no	—
911	C₄⋊C₄	—	2	2	no	—
912	C₄⋊C₄	—	2	1	no	—
913	C₄⋊C₄	—	2	2	no	—
914	C₄⋊C₄	—	2	1	no	—
915	C₄⋊C₄	—	2	1	no	—
916	C₄⋊C₄	—	2	1	no	—
917	C₄⋊C₄	—	2	2	no	—
918	C₄⋊C₄	—	2	1	no	—
919	C₄⋊C₄	—	2	1	no	—
920	C₄⋊C₄	—	2	1	no	—
921	C₄⋊C₄	—	2	2	no	—
922	C₄⋊C₄	—	2	2	no	—
923	C₄⋊C₄	—	2	1	no	—
924	C₄⋊C₄	—	2	1	no	—
925	C₄⋊C₄	—	2	2	no	—
926	C₄⋊C₄	—	2	2	no	—
927	C₄⋊C₄	—	2	2	no	—
928	C₄⋊C₄	—	2	2	no	—
929	C₄⋊C₄	—	2	2	no	—
930	C₄⋊C₄	—	2	1	no	—
931	C₄⋊C₄	—	2	1	no	—
932	C₄⋊C₄	—	2	2	no	—
933	C₄⋊C₄	—	2	2	no	—
934	C₄⋊C₄	—	2	2	no	—
935	C₄⋊C₄	—	2	1	no	—
936	C₄⋊C₄	—	2	2	no	—
937	C₄⋊C₄	—	2	1	no	—
938	C₄⋊C₄	—	2	1	no	—
939	C₄⋊C₄	—	2	2	no	—
940	C₄⋊C₄	—	2	2	no	—
941	C₄⋊C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
942	C₄⋊C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
943	C₄⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
944	C₄⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
945	C₄⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
946	C₄⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
947	C₄⋊C₄	C₂⁴×C₈₉	1	1	yes	characteristic
948	C₄⋊C₄	C₂⁴×C₈₉	1	2	yes	—
949	C₄⋊C₄	C₂⁴×C₈₉	1	2	yes	—
950	C₄⋊C₄	C₂⁴×C₈₉	1	1	yes	characteristic
951	C₄⋊C₄	C₂⁴×C₈₉	1	1	yes	characteristic
952	C₄⋊C₄	C₂⁴×C₈₉	1	1	yes	characteristic
953	C₂²⋊C₄	—	2	1	no	—
954	C₂²⋊C₄	—	2	1	no	—
955	C₂²⋊C₄	—	2	2	no	—
956	C₂²⋊C₄	—	2	2	no	—
957	C₂²⋊C₄	—	2	2	no	—
958	C₂²⋊C₄	—	2	1	no	—
959	C₂²⋊C₄	—	2	2	no	—
960	C₂²⋊C₄	—	2	2	no	—
961	C₂²⋊C₄	—	2	2	no	—
962	C₂²⋊C₄	—	2	2	no	—
963	C₂²⋊C₄	—	2	1	no	—
964	C₂²⋊C₄	—	2	1	no	—
965	C₂²⋊C₄	—	2	1	no	—
966	C₂²⋊C₄	—	2	2	no	—
967	C₂²⋊C₄	—	2	1	no	—
968	C₂²⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
969	C₂²⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
970	C₂²⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
971	C₂²⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
972	C₂²⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
973	C₄²	—	2	2	no	—
974	C₄²	—	2	1	no	—
975	C₄²	—	2	1	no	—
976	C₄²	—	2	2	no	—
977	C₄²	—	2	1	no	—
978	C₄²	—	2	2	no	—
979	C₄²	—	2	2	no	—
980	C₄²	—	2	2	no	—
981	C₄²	—	2	2	no	—
982	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
983	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
984	C₄²	C₂⁴×C₈₉	1	1	yes	characteristic
985	C₄²	C₂⁴×C₈₉	1	1	yes	characteristic
986	C₄²	C₂⁴×C₈₉	1	2	yes	—
987	C₂³	—	2	1	no	—
988	C₂³	C₂²×D₄×C₈₉	1	2	yes	—
989	C₂³	C₂²×D₄×C₈₉	1	1	yes	characteristic
990	Q₈	—	2	2	no	—
991	Q₈	—	2	1	no	—
992	Q₈	—	2	1	no	—
993	Q₈	—	2	1	no	—
994	Q₈	—	2	1	no	—
995	Q₈	—	2	2	no	—
996	Q₈	—	2	1	no	—
997	Q₈	—	2	1	no	—
998	Q₈	—	2	2	no	—
999	Q₈	—	2	2	no	—
1000	Q₈	—	2	2	no	—
1001	Q₈	—	4	2	no	—
1002	Q₈	—	8	1	no	—
1003	Q₈	—	8	1	no	—
1004	Q₈	—	8	2	no	—
1005	Q₈	—	8	2	no	—
1006	Q₈	—	8	2	no	—
1007	D₄	—	2	2	no	—
1008	D₄	—	2	1	no	—
1009	D₄	—	2	1	no	—
1010	D₄	—	4	2	no	—
1011	D₄	—	4	2	no	—
1012	D₄	—	8	2	no	—
1013	C₂×C₄	—	2	2	no	—
1014	C₂×C₄	—	2	2	no	—
1015	C₂×C₄	—	2	1	no	—
1016	C₂×C₄	—	2	1	no	—
1017	C₂×C₄	—	2	2	no	—
1018	C₂×C₄	—	2	1	no	—
1019	C₂×C₄	—	2	1	no	—
1020	C₂×C₄	—	2	1	no	—
1021	C₂×C₄	—	2	2	no	—
1022	C₂×C₄	—	2	1	no	—
1023	C₂×C₄	—	2	1	no	—
1024	C₂×C₄	—	2	2	no	—
1025	C₂×C₄	—	2	1	no	—
1026	C₂×C₄	—	2	2	no	—
1027	C₂×C₄	—	2	1	no	—
1028	C₂×C₄	—	2	2	no	—
1029	C₂×C₄	—	4	1	no	—
1030	C₂×C₄	—	4	2	no	—
1031	C₂×C₄	—	8	2	no	—
1032	C₂×C₄	—	8	2	no	—
1033	C₂×C₄	—	8	2	no	—
1034	C₂×C₄	—	8	2	no	—
1035	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
1036	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
1037	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
1038	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
1039	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
1040	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
1041	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
1042	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
1043	C₂×C₄	C₂⁵×C₈₉	1	1	yes	characteristic
1044	C₈	—	2	1	no	—
1045	C₈	—	2	2	no	—
1046	C₈	—	2	1	no	—
1047	C₈	—	2	1	no	—
1048	C₈	—	2	1	no	—
1049	C₈	—	2	2	no	—
1050	C₂²	—	2	1	no	—
1051	C₂²	—	2	2	no	—
1052	C₂²	—	2	1	no	—
1053	C₂²	—	2	2	no	—
1054	C₂²	—	2	1	no	—
1055	C₂²	—	2	2	no	—
1056	C₂²	—	4	1	no	—
1057	C₂²	—	4	1	no	—
1058	C₂²	—	4	1	no	—
1059	C₂²	C₂³×D₄×C₈₉	1	1	yes	characteristic
1060	C₄	—	2	1	no	—
1061	C₄	—	2	2	no	—
1062	C₄	—	2	1	no	—
1063	C₄	—	2	1	no	—
1064	C₄	—	2	2	no	—
1065	C₄	—	2	2	no	—
1066	C₄	—	2	1	no	—
1067	C₄	—	4	1	no	—
1068	C₄	—	4	2	no	—
1069	C₄	—	4	1	no	—
1070	C₄	—	4	2	no	—
1071	C₄	—	4	1	no	—
1072	C₄	—	4	1	no	—
1073	C₄	—	4	2	no	—
1074	C₄	—	4	1	no	—
1075	C₄	—	4	2	no	—
1076	C₄	—	4	1	no	—
1077	C₄	—	4	1	no	—
1078	C₄	#578×C₈₉	1	2	yes	—
1079	C₄	#585×C₈₉	1	1	yes	characteristic
1080	C₄	#585×C₈₉	1	1	yes	characteristic
1081	C₂	—	4	1	no	—
1082	C₂	—	4	2	no	—
1083	C₂	—	8	1	no	—
1084	C₂	C₈₉×#3500	1	1	yes	characteristic
1085	C₂	C₂×#578×C₈₉	1	1	yes	characteristic
1086	C₂	C₈₉×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₈₉	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₈₉
prime radical	C₈₉×#3552	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×#3374	C₂	semidirect
4. C₈₉×#3369	C₂	semidirect
5. C₈₉×#3364	C₂	semidirect
6. C₈₉×#3363	C₂	semidirect
7. C₈₉×#3331	C₂	semidirect
8. C₈₉×#3328	C₂	semidirect
9. C₈₉×#3328	C₂	semidirect
10. C₈₉×#3327	C₂	semidirect
11. C₈₉×#3313	C₂	semidirect
12. C₈₉×#3312	C₂	semidirect
13. C₈₉×#3302	C₂	semidirect
14. C₈₉×#3299	C₂	semidirect
15. C₈₉×#3242	C₂	semidirect
16. C₈₉×#3233	C₂	semidirect
17. C₈₉×#3223	C₂	semidirect
18. C₈₉×#3209	C₂	semidirect
19. C₈₉×#3177	C₂	semidirect
20. C₈₉×#3172	C₂	semidirect
21. C₈₉×#3139	C₂	semidirect
22. C₈₉×#3137	C₂	semidirect
23. C₈₉×#2969	C₂	semidirect
537. #62611	C₈₉	direct (N × H)
544. #3555	C₂×C₈₉	semidirect
546. #3374	C₂×C₈₉	semidirect
547. #3369	C₂×C₈₉	semidirect
548. #3364	C₂×C₈₉	semidirect
549. #3363	C₂×C₈₉	semidirect
550. #3331	C₂×C₈₉	semidirect
551. #3328	C₂×C₈₉	semidirect
552. #3328	C₂×C₈₉	semidirect
553. #3327	C₂×C₈₉	semidirect
554. #3313	C₂×C₈₉	semidirect
555. #3312	C₂×C₈₉	semidirect
556. #3302	C₂×C₈₉	semidirect
557. #3299	C₂×C₈₉	semidirect
558. #3242	C₂×C₈₉	semidirect
559. #3233	C₂×C₈₉	semidirect
560. #3223	C₂×C₈₉	semidirect
561. #3209	C₂×C₈₉	semidirect
562. #3177	C₂×C₈₉	semidirect
563. #3172	C₂×C₈₉	semidirect
564. #3139	C₂×C₈₉	semidirect
565. #3137	C₂×C₈₉	semidirect
566. #2969	C₂×C₈₉	semidirect
567. C₈₉	#62611	direct (N × H)

Maximal subgroups

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

subgroup	index
C₈₉×#3555	2
C₈₉×#3552	2
C₈₉×#3374	2
C₈₉×#3369	2
C₈₉×#3364	2
C₈₉×#3363	2
C₈₉×#3331	2
C₈₉×#3328	2
C₈₉×#3327	2
C₈₉×#3313	2
C₈₉×#3312	2
C₈₉×#3302	2
C₈₉×#3299	2
C₈₉×#3242	2
C₈₉×#3233	2
C₈₉×#3223	2
C₈₉×#3209	2
C₈₉×#3177	2
C₈₉×#3172	2
C₈₉×#3139	2
C₈₉×#3137	2
C₈₉×#2969	2
#62611	89

Subgroups — C89×#62611 #36440459

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#62611 #36440459