Subgroups — C₈₉×#62152 #36440000

Order 22784.

1730 conjugacy classes of subgroups.

The subgroup lattice has 1116 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈₉×#3515	C₂	1	1	yes	maximal, characteristic, complemented
2	C₈₉×#3475	C₂	1	1	yes	maximal, characteristic, complemented
3	C₈₉×#3381	C₂	1	1	yes	maximal, characteristic, complemented
4	C₈₉×#3380	C₂	1	1	yes	maximal, characteristic, complemented
5	C₈₉×#3364	C₂	1	1	yes	maximal, characteristic, complemented
6	C₈₉×#3360	C₂	1	1	yes	maximal, characteristic, complemented
7	C₈₉×#3357	C₂	1	1	yes	maximal, characteristic, complemented
8	C₈₉×#3354	C₂	1	1	yes	maximal, characteristic, complemented
9	C₈₉×#3352	C₂	1	2	yes	maximal, complemented
10	C₈₉×#3351	C₂	1	2	yes	maximal, complemented
11	C₈₉×#3331	C₂	1	1	yes	maximal, characteristic, complemented
12	C₈₉×#3330	C₂	1	1	yes	maximal, characteristic, complemented
13	C₈₉×#3323	C₂	1	2	yes	maximal, complemented
14	C₈₉×#3322	C₂	1	2	yes	maximal, complemented
15	C₈₉×#3256	C₂	1	2	yes	maximal, complemented
16	C₈₉×#3252	C₂	1	1	yes	maximal, characteristic, complemented
17	C₈₉×#3232	C₂	1	2	yes	maximal, complemented
18	C₈₉×#3231	C₂	1	1	yes	maximal, characteristic, complemented
19	C₈₉×#3105	C₂	1	1	yes	maximal, characteristic, complemented
20	C₈₉×#3102	C₂	1	2	yes	maximal, complemented
21	C₈₉×#3080	C₂	1	2	yes	maximal, complemented
22	C₈₉×#3077	C₂	1	1	yes	maximal, characteristic, complemented
23	C₈₉×#2991	C₂	1	1	yes	maximal, characteristic, complemented
24	#557×C₈₉	C₂²	1	1	yes	characteristic, complemented
25	#556×C₈₉	C₂²	1	1	yes	characteristic
26	#555×C₈₉	C₂²	1	1	yes	characteristic
27	#554×C₈₉	C₂²	1	1	yes	characteristic
28	#554×C₈₉	C₂²	1	1	yes	characteristic, complemented
29	#554×C₈₉	C₂²	1	1	yes	characteristic, complemented
30	#553×C₈₉	—	2	1	no	—
31	#553×C₈₉	C₂²	1	2	yes	—
32	#552×C₈₉	—	2	1	no	—
33	#552×C₈₉	—	2	2	no	—
34	#552×C₈₉	—	2	1	no	—
35	#552×C₈₉	C₂²	1	2	yes	—
36	#552×C₈₉	C₂²	1	2	yes	—
37	#551×C₈₉	—	2	2	no	—
38	#547×C₈₉	—	2	1	no	—
39	#547×C₈₉	C₂²	1	1	yes	characteristic
40	#547×C₈₉	C₂²	1	1	yes	characteristic, complemented
41	#546×C₈₉	C₂²	1	2	yes	—
42	#541×C₈₉	—	2	1	no	—
43	#539×C₈₉	—	2	2	no	—
44	#533×C₈₉	C₂²	1	1	yes	characteristic
45	#533×C₈₉	C₂²	1	1	yes	characteristic
46	#529×C₈₉	—	2	2	no	—
47	#529×C₈₉	C₂²	1	1	yes	characteristic
48	#529×C₈₉	C₂²	1	2	yes	—
49	#529×C₈₉	C₂²	1	2	yes	complemented
50	C₂×#125×C₈₉	C₂²	1	2	yes	complemented
51	#525×C₈₉	—	2	1	no	—
52	#520×C₈₉	—	2	1	no	—
53	C₄×#41×C₈₉	C₂²	1	2	yes	—
54	C₄×#41×C₈₉	C₂²	1	1	yes	characteristic
55	C₂×C₄×D₄×C₈₉	C₂²	1	1	yes	characteristic
56	C₂×#117×C₈₉	—	2	1	no	—
57	#500×C₈₉	C₂²	1	1	yes	characteristic, complemented
58	#499×C₈₉	C₂²	1	2	yes	complemented
59	#499×C₈₉	C₂²	1	2	yes	complemented
60	#498×C₈₉	C₂²	1	1	yes	characteristic, complemented
61	#488×C₈₉	C₂²	1	2	yes	—
62	#488×C₈₉	C₂²	1	2	yes	—
63	#487×C₈₉	C₂²	1	1	yes	characteristic, complemented
64	#487×C₈₉	C₂²	1	1	yes	characteristic, complemented
65	#485×C₈₉	C₂²	1	2	yes	—
66	#485×C₈₉	C₂²	1	2	yes	—
67	#485×C₈₉	C₂²	1	2	yes	complemented
68	#484×C₈₉	C₂²	1	1	yes	characteristic
69	#484×C₈₉	C₂²	1	2	yes	complemented
70	#483×C₈₉	C₂²	1	2	yes	complemented
71	#482×C₈₉	C₂²	1	2	yes	complemented
72	#481×C₈₉	C₂²	1	2	yes	—
73	#481×C₈₉	C₂²	1	1	yes	characteristic
74	#480×C₈₉	C₂²	1	2	yes	—
75	#479×C₈₉	C₂²	1	2	yes	complemented
76	#479×C₈₉	C₂²	1	2	yes	complemented
77	#479×C₈₉	C₂²	1	2	yes	complemented
78	#479×C₈₉	C₂²	1	2	yes	complemented
79	#479×C₈₉	C₂²	1	2	yes	complemented
80	#479×C₈₉	C₂²	1	2	yes	complemented
81	#478×C₈₉	C₂²	1	2	yes	—
82	#478×C₈₉	C₂²	1	2	yes	—
83	#478×C₈₉	C₂²	1	2	yes	—
84	#478×C₈₉	C₂²	1	2	yes	—
85	#478×C₈₉	C₂²	1	1	yes	characteristic
86	#478×C₈₉	C₂²	1	1	yes	characteristic
87	#478×C₈₉	C₂²	1	2	yes	complemented
88	#477×C₈₉	C₂²	1	1	yes	characteristic, complemented
89	#476×C₈₉	C₂²	1	1	yes	characteristic
90	#476×C₈₉	C₂²	1	1	yes	characteristic
91	#476×C₈₉	C₂²	1	1	yes	characteristic, complemented
92	#474×C₈₉	C₂²	1	1	yes	characteristic
93	#474×C₈₉	C₂²	1	1	yes	characteristic
94	#470×C₈₉	C₂²	1	2	yes	—
95	#470×C₈₉	C₂²	1	2	yes	complemented
96	#469×C₈₉	C₂²	1	2	yes	—
97	#468×C₈₉	C₂²	1	2	yes	—
98	#468×C₈₉	C₂²	1	2	yes	—
99	#468×C₈₉	C₂²	1	2	yes	complemented
100	#464×C₈₉	C₂²	1	2	yes	—
101	#464×C₈₉	C₂²	1	2	yes	complemented
102	#463×C₈₉	C₂²	1	2	yes	—
103	#463×C₈₉	C₂²	1	1	yes	characteristic
104	#463×C₈₉	C₂²	1	1	yes	characteristic
105	#462×C₈₉	C₂²	1	1	yes	characteristic, complemented
106	#461×C₈₉	C₂²	1	1	yes	characteristic, complemented
107	#452×C₈₉	C₂²	1	2	yes	—
108	#450×C₈₉	C₂²	1	1	yes	characteristic
109	#449×C₈₉	C₂²	1	2	yes	—
110	#447×C₈₉	C₂²	1	1	yes	characteristic
111	C₈×Q₈×C₈₉	C₂²	1	1	yes	characteristic, complemented
112	C₈×Q₈×C₈₉	C₂²	1	1	yes	characteristic, complemented
113	C₄×Q₁₆×C₈₉	C₂²	1	2	yes	complemented
114	C₄×SD₁₆×C₈₉	C₂²	1	2	yes	—
115	C₄×SD₁₆×C₈₉	C₂²	1	1	yes	characteristic
116	C₄×SD₁₆×C₈₉	C₂²	1	1	yes	characteristic
117	C₄×SD₁₆×C₈₉	C₂²	1	2	yes	complemented
118	C₄×D₈×C₈₉	C₂²	1	2	yes	—
119	C₄×D₈×C₈₉	C₂²	1	1	yes	characteristic
120	C₄×D₈×C₈₉	C₂²	1	1	yes	characteristic
121	#436×C₈₉	C₂²	1	2	yes	—
122	#436×C₈₉	C₂²	1	2	yes	—
123	#436×C₈₉	C₂²	1	1	yes	characteristic, complemented
124	#436×C₈₉	C₂²	1	1	yes	characteristic, complemented
125	#431×C₈₉	C₂²	1	1	yes	characteristic
126	#431×C₈₉	C₂²	1	2	yes	complemented
127	#428×C₈₉	C₂²	1	2	yes	—
128	#428×C₈₉	C₂²	1	2	yes	complemented
129	#428×C₈₉	C₂²	1	2	yes	complemented
130	#423×C₈₉	C₂²	1	1	yes	characteristic
131	#423×C₈₉	C₂²	1	2	yes	complemented
132	#418×C₈₉	C₂²	1	2	yes	—
133	#417×C₈₉	C₂²	1	2	yes	—
134	#417×C₈₉	C₂²	1	2	yes	—
135	C₂×#41×C₈₉	—	2	1	no	—
136	C₂×#41×C₈₉	D₄	1	1	yes	characteristic
137	C₂×#41×C₈₉	C₂³	1	2	yes	—
138	C₂²×D₄×C₈₉	C₂³	1	1	yes	characteristic
139	C₂³×C₄×C₈₉	—	2	1	no	—
140	C₂×Q₁₆×C₈₉	C₂³	1	2	yes	—
141	C₂×SD₁₆×C₈₉	C₂³	1	1	yes	characteristic
142	C₂×SD₁₆×C₈₉	C₂³	1	1	yes	characteristic
143	C₂×SD₁₆×C₈₉	C₂³	1	2	yes	—
144	C₂×D₈×C₈₉	C₂³	1	1	yes	characteristic
145	C₂×D₈×C₈₉	C₂³	1	1	yes	characteristic
146	C₂×M₁₆×C₈₉	C₂³	1	2	yes	—
147	C₂×M₁₆×C₈₉	C₂³	1	2	yes	—
148	C₂×M₁₆×C₈₉	C₂³	1	2	yes	—
149	C₄⋊Q₈×C₈₉	—	2	1	no	—
150	C₄⋊Q₈×C₈₉	C₂³	1	1	yes	characteristic
151	C₄⋊Q₈×C₈₉	C₂³	1	1	yes	characteristic
152	C₄⋊Q₈×C₈₉	C₂³	1	1	yes	characteristic
153	C₄⋊Q₈×C₈₉	C₂³	1	1	yes	characteristic
154	#126×C₈₉	—	2	2	no	—
155	#126×C₈₉	—	2	2	no	—
156	#126×C₈₉	—	2	2	no	—
157	#126×C₈₉	—	2	2	no	—
158	#126×C₈₉	—	2	2	no	—
159	#126×C₈₉	—	2	1	no	—
160	#126×C₈₉	—	2	2	no	—
161	#125×C₈₉	—	2	2	no	—
162	#125×C₈₉	—	2	2	no	—
163	#125×C₈₉	—	2	2	no	—
164	#125×C₈₉	—	2	1	no	—
165	#125×C₈₉	—	2	2	no	—
166	#125×C₈₉	—	2	2	no	—
167	#125×C₈₉	—	2	1	no	—
168	#125×C₈₉	C₂³	1	1	yes	characteristic
169	#125×C₈₉	C₂³	1	2	yes	—
170	#125×C₈₉	C₂³	1	2	yes	—
171	#125×C₈₉	C₂³	1	2	yes	—
172	#125×C₈₉	C₂³	1	2	yes	—
173	#124×C₈₉	—	2	2	no	—
174	#124×C₈₉	C₂³	1	1	yes	characteristic
175	#124×C₈₉	C₂³	1	2	yes	—
176	#123×C₈₉	—	2	2	no	—
177	#123×C₈₉	—	2	2	no	—
178	#123×C₈₉	—	2	1	no	—
179	#123×C₈₉	—	2	2	no	—
180	#123×C₈₉	—	2	2	no	—
181	#123×C₈₉	—	2	2	no	—
182	#123×C₈₉	—	2	2	no	—
183	#123×C₈₉	—	2	2	no	—
184	#123×C₈₉	—	2	2	no	—
185	C₂²⋊Q₈×C₈₉	—	2	1	no	—
186	C₂²⋊Q₈×C₈₉	—	2	1	no	—
187	C₂²⋊Q₈×C₈₉	—	2	1	no	—
188	C₂²⋊Q₈×C₈₉	—	2	1	no	—
189	C₂²⋊Q₈×C₈₉	—	2	1	no	—
190	C₂²⋊Q₈×C₈₉	—	2	1	no	—
191	C₂²⋊Q₈×C₈₉	—	2	2	no	—
192	C₂²⋊Q₈×C₈₉	—	2	2	no	—
193	C₂²⋊Q₈×C₈₉	—	2	1	no	—
194	C₂²⋊Q₈×C₈₉	—	2	2	no	—
195	C₂²⋊Q₈×C₈₉	C₂³	1	1	yes	characteristic
196	C₂²⋊Q₈×C₈₉	C₂³	1	2	yes	—
197	C₂²⋊Q₈×C₈₉	C₂³	1	2	yes	—
198	C₂²⋊Q₈×C₈₉	C₂³	1	2	yes	—
199	#121×C₈₉	—	2	1	no	—
200	#121×C₈₉	—	2	1	no	—
201	#121×C₈₉	—	2	2	no	—
202	#121×C₈₉	—	2	2	no	—
203	#121×C₈₉	C₂³	1	1	yes	characteristic
204	#121×C₈₉	C₂³	1	2	yes	—
205	#121×C₈₉	C₂³	1	2	yes	—
206	#120×C₈₉	—	2	2	no	—
207	C₄×Q₈×C₈₉	—	2	1	no	—
208	C₄×Q₈×C₈₉	—	2	1	no	—
209	C₄×Q₈×C₈₉	—	2	1	no	—
210	C₄×Q₈×C₈₉	—	2	1	no	—
211	C₄×Q₈×C₈₉	D₄	1	1	yes	characteristic
212	C₄×Q₈×C₈₉	C₂³	1	1	yes	characteristic
213	C₄×Q₈×C₈₉	C₂³	1	2	yes	—
214	C₄×Q₈×C₈₉	C₂³	1	2	yes	—
215	C₄×Q₈×C₈₉	C₂³	1	2	yes	—
216	C₄×Q₈×C₈₉	C₂³	1	1	yes	characteristic
217	C₄×D₄×C₈₉	—	2	1	no	—
218	C₄×D₄×C₈₉	—	2	2	no	—
219	C₄×D₄×C₈₉	—	2	2	no	—
220	C₄×D₄×C₈₉	—	2	2	no	—
221	C₄×D₄×C₈₉	—	2	2	no	—
222	C₄×D₄×C₈₉	—	2	1	no	—
223	C₄×D₄×C₈₉	—	2	2	no	—
224	C₄×D₄×C₈₉	—	2	1	no	—
225	C₄×D₄×C₈₉	—	2	1	no	—
226	C₄×D₄×C₈₉	D₄	1	1	yes	characteristic
227	C₄×D₄×C₈₉	D₄	1	2	yes	—
228	C₄×D₄×C₈₉	C₂³	1	1	yes	characteristic
229	C₄×D₄×C₈₉	C₂³	1	1	yes	characteristic
230	C₄×D₄×C₈₉	C₂³	1	1	yes	characteristic
231	C₄×D₄×C₈₉	C₂³	1	2	yes	—
232	C₄×D₄×C₈₉	C₂³	1	2	yes	—
233	C₄×D₄×C₈₉	C₂³	1	1	yes	characteristic
234	C₄×D₄×C₈₉	C₂³	1	1	yes	characteristic
235	C₄×D₄×C₈₉	C₂³	1	2	yes	—
236	C₄×D₄×C₈₉	C₂³	1	1	yes	characteristic
237	#117×C₈₉	—	2	1	no	—
238	#117×C₈₉	—	2	1	no	—
239	#117×C₈₉	—	2	1	no	—
240	#117×C₈₉	—	2	2	no	—
241	#117×C₈₉	—	2	2	no	—
242	#117×C₈₉	—	2	2	no	—
243	#117×C₈₉	—	2	2	no	—
244	#117×C₈₉	—	2	1	no	—
245	#117×C₈₉	—	2	2	no	—
246	#117×C₈₉	D₄	1	1	yes	characteristic
247	#117×C₈₉	D₄	1	2	yes	—
248	#117×C₈₉	C₂³	1	2	yes	—
249	#117×C₈₉	C₂³	1	2	yes	—
250	C₂×C₄⋊C₄×C₈₉	—	2	2	no	—
251	C₂×C₄⋊C₄×C₈₉	—	2	2	no	—
252	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
253	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
254	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
255	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
256	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
257	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
258	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
259	C₂×C₂²⋊C₄×C₈₉	—	2	2	no	—
260	C₂×C₄²×C₈₉	—	2	2	no	—
261	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
262	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
263	#107×C₈₉	C₂³	1	2	yes	—
264	#107×C₈₉	C₂³	1	2	yes	—
265	#107×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	2	yes	—
270	#106×C₈₉	C₂³	1	2	yes	—
271	#106×C₈₉	C₂³	1	2	yes	—
272	#106×C₈₉	C₂³	1	1	yes	characteristic
273	#106×C₈₉	C₂³	1	2	yes	—
274	#106×C₈₉	C₂³	1	2	yes	—
275	#106×C₈₉	C₂³	1	1	yes	characteristic
276	#106×C₈₉	C₂³	1	2	yes	—
277	C₄⋊C₈×C₈₉	C₂³	1	2	yes	—
278	C₄⋊C₈×C₈₉	C₂³	1	1	yes	characteristic
279	C₄⋊C₈×C₈₉	C₂³	1	1	yes	characteristic
280	C₄⋊C₈×C₈₉	C₂³	1	1	yes	characteristic
281	C₄⋊C₈×C₈₉	C₂³	1	2	yes	—
282	C₄⋊C₈×C₈₉	C₂³	1	2	yes	—
283	C₄⋊C₈×C₈₉	C₂³	1	1	yes	characteristic
284	#103×C₈₉	C₂³	1	2	yes	—
285	#103×C₈₉	C₂³	1	2	yes	—
286	#103×C₈₉	C₂³	1	2	yes	—
287	#103×C₈₉	C₂³	1	2	yes	—
288	#103×C₈₉	C₂³	1	1	yes	characteristic
289	#103×C₈₉	C₂³	1	1	yes	characteristic
290	#103×C₈₉	C₂³	1	2	yes	—
291	#103×C₈₉	C₂³	1	2	yes	—
292	#103×C₈₉	C₂³	1	2	yes	—
293	#102×C₈₉	C₂³	1	1	yes	characteristic
294	#102×C₈₉	C₂³	1	1	yes	characteristic
295	#102×C₈₉	C₂³	1	2	yes	—
296	#102×C₈₉	C₂³	1	2	yes	—
297	#102×C₈₉	C₂³	1	2	yes	—
298	#102×C₈₉	C₂³	1	2	yes	—
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	#102×C₈₉	C₂³	1	2	yes	—
303	#102×C₈₉	C₂³	1	1	yes	characteristic
304	C₂²⋊C₈×C₈₉	C₂³	1	1	yes	characteristic
305	C₂²⋊C₈×C₈₉	C₂³	1	1	yes	characteristic
306	C₂²⋊C₈×C₈₉	C₂³	1	2	yes	—
307	C₂²⋊C₈×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	C₂⁴×C₈₉	—	2	1	no	—
313	#41×C₈₉	—	2	4	no	—
314	#41×C₈₉	—	4	2	no	—
315	#41×C₈₉	—	4	2	no	—
316	#41×C₈₉	—	4	4	no	—
317	C₂×Q₈×C₈₉	—	2	1	no	—
318	C₂×Q₈×C₈₉	—	2	1	no	—
319	C₂×Q₈×C₈₉	—	2	1	no	—
320	C₂×Q₈×C₈₉	C₂×D₄	1	1	yes	characteristic
321	C₂×Q₈×C₈₉	C₂⁴	1	2	yes	—
322	C₂×Q₈×C₈₉	C₂⁴	1	1	yes	characteristic
323	C₂×D₄×C₈₉	—	2	2	no	—
324	C₂×D₄×C₈₉	—	2	2	no	—
325	C₂×D₄×C₈₉	—	2	2	no	—
326	C₂×D₄×C₈₉	—	2	2	no	—
327	C₂×D₄×C₈₉	—	2	1	no	—
328	C₂×D₄×C₈₉	—	2	1	no	—
329	C₂×D₄×C₈₉	—	4	1	no	—
330	C₂×D₄×C₈₉	C₂×D₄	1	1	yes	characteristic
331	C₂×D₄×C₈₉	C₂×D₄	1	2	yes	—
332	C₂×D₄×C₈₉	C₂⁴	1	1	yes	characteristic
333	C₂×D₄×C₈₉	C₂⁴	1	1	yes	characteristic
334	C₂×D₄×C₈₉	C₂⁴	1	1	yes	characteristic
335	C₂²×C₄×C₈₉	—	2	1	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	—	2	1	no	—
341	C₂²×C₄×C₈₉	—	2	1	no	—
342	C₂²×C₄×C₈₉	—	2	1	no	—
343	C₂²×C₄×C₈₉	—	2	1	no	—
344	C₂²×C₄×C₈₉	—	2	2	no	—
345	C₂²×C₄×C₈₉	—	2	2	no	—
346	C₂²×C₄×C₈₉	—	4	4	no	—
347	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
348	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
349	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
350	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
351	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
352	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
353	Q₁₆×C₈₉	—	4	2	no	—
354	SD₁₆×C₈₉	—	2	2	no	—
355	SD₁₆×C₈₉	—	4	2	no	—
356	SD₁₆×C₈₉	—	4	1	no	—
357	D₈×C₈₉	—	2	2	no	—
358	D₈×C₈₉	—	4	1	no	—
359	M₁₆×C₈₉	—	4	2	no	—
360	M₁₆×C₈₉	—	4	2	no	—
361	M₁₆×C₈₉	—	4	2	no	—
362	C₂×C₈×C₈₉	C₂⁴	1	1	yes	characteristic
363	C₂×C₈×C₈₉	C₂⁴	1	1	yes	characteristic
364	C₂×C₈×C₈₉	C₂⁴	1	2	yes	—
365	C₂×C₈×C₈₉	C₂⁴	1	1	yes	characteristic
366	C₂×C₈×C₈₉	C₂⁴	1	2	yes	—
367	C₂×C₈×C₈₉	C₂⁴	1	1	yes	characteristic
368	C₄⋊C₄×C₈₉	—	2	2	no	—
369	C₄⋊C₄×C₈₉	—	2	1	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	2	no	—
375	C₄⋊C₄×C₈₉	—	2	2	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	2	no	—
380	C₄⋊C₄×C₈₉	—	2	2	no	—
381	C₄⋊C₄×C₈₉	—	2	1	no	—
382	C₄⋊C₄×C₈₉	—	2	2	no	—
383	C₄⋊C₄×C₈₉	—	2	2	no	—
384	C₄⋊C₄×C₈₉	—	2	1	no	—
385	C₄⋊C₄×C₈₉	—	2	2	no	—
386	C₄⋊C₄×C₈₉	—	2	2	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	1	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	C₂×D₄	1	1	yes	characteristic
395	C₄⋊C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
396	C₄⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
397	C₄⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
398	C₄⋊C₄×C₈₉	C₂⁴	1	1	yes	characteristic
399	C₄⋊C₄×C₈₉	C₂⁴	1	1	yes	characteristic
400	C₄⋊C₄×C₈₉	C₂⁴	1	2	yes	—
401	C₄⋊C₄×C₈₉	C₂⁴	1	2	yes	—
402	C₄⋊C₄×C₈₉	C₂⁴	1	1	yes	characteristic
403	C₄⋊C₄×C₈₉	C₂⁴	1	1	yes	characteristic
404	C₄⋊C₄×C₈₉	C₂⁴	1	2	yes	—
405	C₂²⋊C₄×C₈₉	—	2	2	no	—
406	C₂²⋊C₄×C₈₉	—	2	2	no	—
407	C₂²⋊C₄×C₈₉	—	2	2	no	—
408	C₂²⋊C₄×C₈₉	—	2	2	no	—
409	C₂²⋊C₄×C₈₉	—	2	2	no	—
410	C₂²⋊C₄×C₈₉	—	2	1	no	—
411	C₂²⋊C₄×C₈₉	—	2	1	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	1	no	—
416	C₂²⋊C₄×C₈₉	—	2	1	no	—
417	C₂²⋊C₄×C₈₉	—	2	1	no	—
418	C₂²⋊C₄×C₈₉	—	2	1	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	2	no	—
423	C₂²⋊C₄×C₈₉	—	2	2	no	—
424	C₂²⋊C₄×C₈₉	—	2	1	no	—
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	C₄²×C₈₉	—	2	2	no	—
429	C₄²×C₈₉	—	2	2	no	—
430	C₄²×C₈₉	—	2	2	no	—
431	C₄²×C₈₉	—	2	2	no	—
432	C₄²×C₈₉	—	2	2	no	—
433	C₄²×C₈₉	—	2	1	no	—
434	C₄²×C₈₉	C₂×D₄	1	2	yes	—
435	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
436	C₄²×C₈₉	C₂×D₄	1	2	yes	—
437	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
438	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
439	C₄²×C₈₉	C₂⁴	1	2	yes	—
440	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
441	C₂³×C₈₉	—	2	1	no	—
442	C₂³×C₈₉	—	2	1	no	—
443	C₂³×C₈₉	—	2	1	no	—
444	C₂³×C₈₉	—	4	2	no	—
445	C₂³×C₈₉	—	4	2	no	—
446	C₂³×C₈₉	—	8	1	no	—
447	C₂³×C₈₉	C₂²×D₄	1	1	yes	characteristic
448	C₂³×C₈₉	C₂²×D₄	1	2	yes	—
449	Q₈×C₈₉	—	2	2	no	—
450	Q₈×C₈₉	—	2	1	no	—
451	Q₈×C₈₉	—	2	2	no	—
452	Q₈×C₈₉	—	2	1	no	—
453	Q₈×C₈₉	—	2	2	no	—
454	Q₈×C₈₉	—	4	2	no	—
455	Q₈×C₈₉	—	8	1	no	—
456	Q₈×C₈₉	—	8	1	no	—
457	D₄×C₈₉	—	2	2	no	—
458	D₄×C₈₉	—	2	1	no	—
459	D₄×C₈₉	—	2	1	no	—
460	D₄×C₈₉	—	2	1	no	—
461	D₄×C₈₉	—	2	1	no	—
462	D₄×C₈₉	—	2	1	no	—
463	D₄×C₈₉	—	4	2	no	—
464	D₄×C₈₉	—	4	2	no	—
465	D₄×C₈₉	—	4	4	no	—
466	D₄×C₈₉	—	4	4	no	—
467	D₄×C₈₉	—	8	1	no	—
468	D₄×C₈₉	—	8	2	no	—
469	D₄×C₈₉	2₋¹⁺⁴	1	2	yes	—
470	C₂×C₄×C₈₉	—	2	2	no	—
471	C₂×C₄×C₈₉	—	2	1	no	—
472	C₂×C₄×C₈₉	—	2	2	no	—
473	C₂×C₄×C₈₉	—	2	1	no	—
474	C₂×C₄×C₈₉	—	2	2	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	2	no	—
479	C₂×C₄×C₈₉	—	2	2	no	—
480	C₂×C₄×C₈₉	—	2	2	no	—
481	C₂×C₄×C₈₉	—	2	1	no	—
482	C₂×C₄×C₈₉	—	2	1	no	—
483	C₂×C₄×C₈₉	—	2	1	no	—
484	C₂×C₄×C₈₉	—	4	2	no	—
485	C₂×C₄×C₈₉	—	4	1	no	—
486	C₂×C₄×C₈₉	—	4	2	no	—
487	C₂×C₄×C₈₉	—	4	4	no	—
488	C₂×C₄×C₈₉	—	4	2	no	—
489	C₂×C₄×C₈₉	—	4	2	no	—
490	C₂×C₄×C₈₉	—	4	2	no	—
491	C₂×C₄×C₈₉	—	4	4	no	—
492	C₂×C₄×C₈₉	—	4	2	no	—
493	C₂×C₄×C₈₉	—	4	2	no	—
494	C₂×C₄×C₈₉	—	4	2	no	—
495	C₂×C₄×C₈₉	—	8	2	no	—
496	C₂×C₄×C₈₉	—	8	2	no	—
497	C₂×C₄×C₈₉	—	8	2	no	—
498	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
499	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
500	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
501	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
502	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
503	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
504	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
505	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
506	C₂×C₄×C₈₉	C₂⁵	1	1	yes	characteristic
507	C₈×C₈₉	—	2	1	no	—
508	C₈×C₈₉	—	2	1	no	—
509	C₈×C₈₉	—	2	1	no	—
510	C₈×C₈₉	—	2	1	no	—
511	C₈×C₈₉	—	2	2	no	—
512	C₈×C₈₉	—	2	2	no	—
513	C₂²×C₈₉	—	2	2	no	—
514	C₂²×C₈₉	—	2	1	no	—
515	C₂²×C₈₉	—	2	2	no	—
516	C₂²×C₈₉	—	2	1	no	—
517	C₂²×C₈₉	—	2	2	no	—
518	C₂²×C₈₉	—	2	1	no	—
519	C₂²×C₈₉	—	2	2	no	—
520	C₂²×C₈₉	—	4	1	no	—
521	C₂²×C₈₉	—	4	1	no	—
522	C₂²×C₈₉	—	4	1	no	—
523	C₂²×C₈₉	—	4	1	no	—
524	C₂²×C₈₉	—	4	1	no	—
525	C₂²×C₈₉	—	4	1	no	—
526	C₂²×C₈₉	—	4	1	no	—
527	C₂²×C₈₉	—	4	1	no	—
528	C₂²×C₈₉	—	8	4	no	—
529	C₂²×C₈₉	C₂³×D₄	1	1	yes	characteristic
530	C₄×C₈₉	—	2	1	no	—
531	C₄×C₈₉	—	2	2	no	—
532	C₄×C₈₉	—	2	1	no	—
533	C₄×C₈₉	—	2	2	no	—
534	C₄×C₈₉	—	2	1	no	—
535	C₄×C₈₉	—	2	1	no	—
536	C₄×C₈₉	—	2	2	no	—
537	C₄×C₈₉	—	4	1	no	—
538	C₄×C₈₉	—	4	2	no	—
539	C₄×C₈₉	—	4	2	no	—
540	C₄×C₈₉	—	4	2	no	—
541	C₄×C₈₉	—	4	1	no	—
542	C₄×C₈₉	—	4	1	no	—
543	C₄×C₈₉	—	4	1	no	—
544	C₄×C₈₉	—	4	1	no	—
545	C₄×C₈₉	—	4	2	no	—
546	C₄×C₈₉	#575	1	2	yes	—
547	C₄×C₈₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
548	C₄×C₈₉	#585	1	1	yes	characteristic
549	#62152	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
550	C₂×C₈₉	—	4	2	no	—
551	C₂×C₈₉	—	4	1	no	—
552	C₂×C₈₉	—	4	2	no	—
553	C₂×C₈₉	—	8	1	no	—
554	C₂×C₈₉	—	8	1	no	—
555	C₂×C₈₉	#3489	1	1	yes	characteristic
556	C₂×C₈₉	C₂×#575	1	1	yes	characteristic
557	C₂×C₈₉	#3584	1	1	yes	characteristic
558	#3515	C₂×C₈₉	1	1	yes	characteristic, complemented
559	#3475	C₂×C₈₉	1	1	yes	characteristic, complemented
560	#3381	C₂×C₈₉	1	1	yes	characteristic, complemented
561	#3380	C₂×C₈₉	1	1	yes	characteristic, complemented
562	#3364	C₂×C₈₉	1	1	yes	characteristic, complemented
563	#3360	C₂×C₈₉	1	1	yes	characteristic, complemented
564	#3357	C₂×C₈₉	1	1	yes	characteristic, complemented
565	#3354	C₂×C₈₉	1	1	yes	characteristic, complemented
566	#3352	C₂×C₈₉	1	2	yes	complemented
567	#3351	C₂×C₈₉	1	2	yes	complemented
568	#3331	C₂×C₈₉	1	1	yes	characteristic, complemented
569	#3330	C₂×C₈₉	1	1	yes	characteristic, complemented
570	#3323	C₂×C₈₉	1	2	yes	complemented
571	#3322	C₂×C₈₉	1	2	yes	complemented
572	#3256	C₂×C₈₉	1	2	yes	complemented
573	#3252	C₂×C₈₉	1	1	yes	characteristic, complemented
574	#3232	C₂×C₈₉	1	2	yes	complemented
575	#3231	C₂×C₈₉	1	1	yes	characteristic, complemented
576	#3105	C₂×C₈₉	1	1	yes	characteristic, complemented
577	#3102	C₂×C₈₉	1	2	yes	complemented
578	#3080	C₂×C₈₉	1	2	yes	complemented
579	#3077	C₂×C₈₉	1	1	yes	characteristic, complemented
580	#2991	C₂×C₈₉	1	1	yes	characteristic, complemented
581	C₈₉	#62152	1	1	yes	characteristic, direct product factor, Sylow
582	#557	C₂²×C₈₉	1	1	yes	characteristic, complemented
583	#556	C₂²×C₈₉	1	1	yes	characteristic
584	#555	C₂²×C₈₉	1	1	yes	characteristic
585	#554	C₂²×C₈₉	1	1	yes	characteristic
586	#554	C₂²×C₈₉	1	1	yes	characteristic, complemented
587	#554	C₂²×C₈₉	1	1	yes	characteristic, complemented
588	#553	—	2	1	no	—
589	#553	C₂²×C₈₉	1	2	yes	—
590	#552	—	2	1	no	—
591	#552	—	2	2	no	—
592	#552	—	2	1	no	—
593	#552	C₂²×C₈₉	1	2	yes	—
594	#552	C₂²×C₈₉	1	2	yes	—
595	#551	—	2	2	no	—
596	#547	—	2	1	no	—
597	#547	C₂²×C₈₉	1	1	yes	characteristic
598	#547	C₂²×C₈₉	1	1	yes	characteristic, complemented
599	#546	C₂²×C₈₉	1	2	yes	—
600	#541	—	2	1	no	—
601	#539	—	2	2	no	—
602	#533	C₂²×C₈₉	1	1	yes	characteristic
603	#533	C₂²×C₈₉	1	1	yes	characteristic
604	#529	—	2	2	no	—
605	#529	C₂²×C₈₉	1	1	yes	characteristic
606	#529	C₂²×C₈₉	1	2	yes	—
607	#529	C₂²×C₈₉	1	2	yes	complemented
608	C₂×#125	C₂²×C₈₉	1	2	yes	complemented
609	#525	—	2	1	no	—
610	#520	—	2	1	no	—
611	C₄×#41	C₂²×C₈₉	1	2	yes	—
612	C₄×#41	C₂²×C₈₉	1	1	yes	characteristic
613	C₂×C₄×D₄	C₂²×C₈₉	1	1	yes	characteristic
614	C₂×#117	—	2	1	no	—
615	#500	C₂²×C₈₉	1	1	yes	characteristic, complemented
616	#499	C₂²×C₈₉	1	2	yes	complemented
617	#499	C₂²×C₈₉	1	2	yes	complemented
618	#498	C₂²×C₈₉	1	1	yes	characteristic, complemented
619	#488	C₂²×C₈₉	1	2	yes	—
620	#488	C₂²×C₈₉	1	2	yes	—
621	#487	C₂²×C₈₉	1	1	yes	characteristic, complemented
622	#487	C₂²×C₈₉	1	1	yes	characteristic, complemented
623	#485	C₂²×C₈₉	1	2	yes	—
624	#485	C₂²×C₈₉	1	2	yes	—
625	#485	C₂²×C₈₉	1	2	yes	complemented
626	#484	C₂²×C₈₉	1	1	yes	characteristic
627	#484	C₂²×C₈₉	1	2	yes	complemented
628	#483	C₂²×C₈₉	1	2	yes	complemented
629	#482	C₂²×C₈₉	1	2	yes	complemented
630	#481	C₂²×C₈₉	1	1	yes	characteristic
631	#481	C₂²×C₈₉	1	2	yes	—
632	#480	C₂²×C₈₉	1	2	yes	—
633	#479	C₂²×C₈₉	1	2	yes	complemented
634	#479	C₂²×C₈₉	1	2	yes	complemented
635	#479	C₂²×C₈₉	1	2	yes	complemented
636	#479	C₂²×C₈₉	1	2	yes	complemented
637	#479	C₂²×C₈₉	1	2	yes	complemented
638	#479	C₂²×C₈₉	1	2	yes	complemented
639	#478	C₂²×C₈₉	1	2	yes	—
640	#478	C₂²×C₈₉	1	2	yes	—
641	#478	C₂²×C₈₉	1	1	yes	characteristic
642	#478	C₂²×C₈₉	1	2	yes	—
643	#478	C₂²×C₈₉	1	2	yes	—
644	#478	C₂²×C₈₉	1	1	yes	characteristic
645	#478	C₂²×C₈₉	1	2	yes	complemented
646	#477	C₂²×C₈₉	1	1	yes	characteristic, complemented
647	#476	C₂²×C₈₉	1	1	yes	characteristic
648	#476	C₂²×C₈₉	1	1	yes	characteristic
649	#476	C₂²×C₈₉	1	1	yes	characteristic, complemented
650	#474	C₂²×C₈₉	1	1	yes	characteristic
651	#474	C₂²×C₈₉	1	1	yes	characteristic
652	#470	C₂²×C₈₉	1	2	yes	—
653	#470	C₂²×C₈₉	1	2	yes	complemented
654	#469	C₂²×C₈₉	1	2	yes	—
655	#468	C₂²×C₈₉	1	2	yes	—
656	#468	C₂²×C₈₉	1	2	yes	—
657	#468	C₂²×C₈₉	1	2	yes	complemented
658	#464	C₂²×C₈₉	1	2	yes	—
659	#464	C₂²×C₈₉	1	2	yes	complemented
660	#463	C₂²×C₈₉	1	1	yes	characteristic
661	#463	C₂²×C₈₉	1	2	yes	—
662	#463	C₂²×C₈₉	1	1	yes	characteristic
663	#462	C₂²×C₈₉	1	1	yes	characteristic, complemented
664	#461	C₂²×C₈₉	1	1	yes	characteristic, complemented
665	#452	C₂²×C₈₉	1	2	yes	—
666	#450	C₂²×C₈₉	1	1	yes	characteristic
667	#449	C₂²×C₈₉	1	2	yes	—
668	#447	C₂²×C₈₉	1	1	yes	characteristic
669	C₈×Q₈	C₂²×C₈₉	1	1	yes	characteristic, complemented
670	C₈×Q₈	C₂²×C₈₉	1	1	yes	characteristic, complemented
671	C₄×Q₁₆	C₂²×C₈₉	1	2	yes	complemented
672	C₄×SD₁₆	C₂²×C₈₉	1	1	yes	characteristic
673	C₄×SD₁₆	C₂²×C₈₉	1	1	yes	characteristic
674	C₄×SD₁₆	C₂²×C₈₉	1	2	yes	—
675	C₄×SD₁₆	C₂²×C₈₉	1	2	yes	complemented
676	C₄×D₈	C₂²×C₈₉	1	1	yes	characteristic
677	C₄×D₈	C₂²×C₈₉	1	1	yes	characteristic
678	C₄×D₈	C₂²×C₈₉	1	2	yes	—
679	#436	C₂²×C₈₉	1	2	yes	—
680	#436	C₂²×C₈₉	1	2	yes	—
681	#436	C₂²×C₈₉	1	1	yes	characteristic, complemented
682	#436	C₂²×C₈₉	1	1	yes	characteristic, complemented
683	#431	C₂²×C₈₉	1	1	yes	characteristic
684	#431	C₂²×C₈₉	1	2	yes	complemented
685	#428	C₂²×C₈₉	1	2	yes	—
686	#428	C₂²×C₈₉	1	2	yes	complemented
687	#428	C₂²×C₈₉	1	2	yes	complemented
688	#423	C₂²×C₈₉	1	1	yes	characteristic
689	#423	C₂²×C₈₉	1	2	yes	complemented
690	#418	C₂²×C₈₉	1	2	yes	—
691	#417	C₂²×C₈₉	1	2	yes	—
692	#417	C₂²×C₈₉	1	2	yes	—
693	C₂×#41	—	2	1	no	—
694	C₂×#41	D₄×C₈₉	1	1	yes	characteristic
695	C₂×#41	C₂³×C₈₉	1	2	yes	—
696	C₂²×D₄	C₂³×C₈₉	1	1	yes	characteristic
697	C₂³×C₄	—	2	1	no	—
698	C₂×Q₁₆	C₂³×C₈₉	1	2	yes	—
699	C₂×SD₁₆	C₂³×C₈₉	1	1	yes	characteristic
700	C₂×SD₁₆	C₂³×C₈₉	1	1	yes	characteristic
701	C₂×SD₁₆	C₂³×C₈₉	1	2	yes	—
702	C₂×D₈	C₂³×C₈₉	1	1	yes	characteristic
703	C₂×D₈	C₂³×C₈₉	1	1	yes	characteristic
704	C₂×M₁₆	C₂³×C₈₉	1	2	yes	—
705	C₂×M₁₆	C₂³×C₈₉	1	2	yes	—
706	C₂×M₁₆	C₂³×C₈₉	1	2	yes	—
707	C₄⋊Q₈	—	2	1	no	—
708	C₄⋊Q₈	C₂³×C₈₉	1	1	yes	characteristic
709	C₄⋊Q₈	C₂³×C₈₉	1	1	yes	characteristic
710	C₄⋊Q₈	C₂³×C₈₉	1	1	yes	characteristic
711	C₄⋊Q₈	C₂³×C₈₉	1	1	yes	characteristic
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	1	no	—
718	#126	—	2	2	no	—
719	#125	—	2	2	no	—
720	#125	—	2	2	no	—
721	#125	—	2	2	no	—
722	#125	—	2	1	no	—
723	#125	—	2	2	no	—
724	#125	—	2	2	no	—
725	#125	—	2	1	no	—
726	#125	C₂³×C₈₉	1	1	yes	characteristic
727	#125	C₂³×C₈₉	1	2	yes	—
728	#125	C₂³×C₈₉	1	2	yes	—
729	#125	C₂³×C₈₉	1	2	yes	—
730	#125	C₂³×C₈₉	1	2	yes	—
731	#124	—	2	2	no	—
732	#124	C₂³×C₈₉	1	1	yes	characteristic
733	#124	C₂³×C₈₉	1	2	yes	—
734	#123	—	2	2	no	—
735	#123	—	2	2	no	—
736	#123	—	2	1	no	—
737	#123	—	2	2	no	—
738	#123	—	2	2	no	—
739	#123	—	2	2	no	—
740	#123	—	2	2	no	—
741	#123	—	2	2	no	—
742	#123	—	2	2	no	—
743	C₂²⋊Q₈	—	2	1	no	—
744	C₂²⋊Q₈	—	2	1	no	—
745	C₂²⋊Q₈	—	2	1	no	—
746	C₂²⋊Q₈	—	2	1	no	—
747	C₂²⋊Q₈	—	2	1	no	—
748	C₂²⋊Q₈	—	2	1	no	—
749	C₂²⋊Q₈	—	2	2	no	—
750	C₂²⋊Q₈	—	2	2	no	—
751	C₂²⋊Q₈	—	2	1	no	—
752	C₂²⋊Q₈	—	2	2	no	—
753	C₂²⋊Q₈	C₂³×C₈₉	1	2	yes	—
754	C₂²⋊Q₈	C₂³×C₈₉	1	1	yes	characteristic
755	C₂²⋊Q₈	C₂³×C₈₉	1	2	yes	—
756	C₂²⋊Q₈	C₂³×C₈₉	1	2	yes	—
757	#121	—	2	1	no	—
758	#121	—	2	1	no	—
759	#121	—	2	2	no	—
760	#121	—	2	2	no	—
761	#121	C₂³×C₈₉	1	2	yes	—
762	#121	C₂³×C₈₉	1	1	yes	characteristic
763	#121	C₂³×C₈₉	1	2	yes	—
764	#120	—	2	2	no	—
765	C₄×Q₈	—	2	1	no	—
766	C₄×Q₈	—	2	1	no	—
767	C₄×Q₈	—	2	1	no	—
768	C₄×Q₈	—	2	1	no	—
769	C₄×Q₈	D₄×C₈₉	1	1	yes	characteristic
770	C₄×Q₈	C₂³×C₈₉	1	2	yes	—
771	C₄×Q₈	C₂³×C₈₉	1	2	yes	—
772	C₄×Q₈	C₂³×C₈₉	1	1	yes	characteristic
773	C₄×Q₈	C₂³×C₈₉	1	2	yes	—
774	C₄×Q₈	C₂³×C₈₉	1	1	yes	characteristic
775	C₄×D₄	—	2	1	no	—
776	C₄×D₄	—	2	2	no	—
777	C₄×D₄	—	2	2	no	—
778	C₄×D₄	—	2	2	no	—
779	C₄×D₄	—	2	2	no	—
780	C₄×D₄	—	2	1	no	—
781	C₄×D₄	—	2	2	no	—
782	C₄×D₄	—	2	1	no	—
783	C₄×D₄	—	2	1	no	—
784	C₄×D₄	D₄×C₈₉	1	1	yes	characteristic
785	C₄×D₄	D₄×C₈₉	1	2	yes	—
786	C₄×D₄	C₂³×C₈₉	1	1	yes	characteristic
787	C₄×D₄	C₂³×C₈₉	1	1	yes	characteristic
788	C₄×D₄	C₂³×C₈₉	1	1	yes	characteristic
789	C₄×D₄	C₂³×C₈₉	1	1	yes	characteristic
790	C₄×D₄	C₂³×C₈₉	1	2	yes	—
791	C₄×D₄	C₂³×C₈₉	1	1	yes	characteristic
792	C₄×D₄	C₂³×C₈₉	1	2	yes	—
793	C₄×D₄	C₂³×C₈₉	1	2	yes	—
794	C₄×D₄	C₂³×C₈₉	1	1	yes	characteristic
795	#117	—	2	1	no	—
796	#117	—	2	1	no	—
797	#117	—	2	1	no	—
798	#117	—	2	2	no	—
799	#117	—	2	2	no	—
800	#117	—	2	2	no	—
801	#117	—	2	2	no	—
802	#117	—	2	1	no	—
803	#117	—	2	2	no	—
804	#117	D₄×C₈₉	1	1	yes	characteristic
805	#117	D₄×C₈₉	1	2	yes	—
806	#117	C₂³×C₈₉	1	2	yes	—
807	#117	C₂³×C₈₉	1	2	yes	—
808	C₂×C₄⋊C₄	—	2	2	no	—
809	C₂×C₄⋊C₄	—	2	2	no	—
810	C₂×C₄⋊C₄	—	2	1	no	—
811	C₂×C₄⋊C₄	—	2	1	no	—
812	C₂×C₄⋊C₄	—	2	1	no	—
813	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
814	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
815	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
816	C₂×C₂²⋊C₄	—	2	1	no	—
817	C₂×C₂²⋊C₄	—	2	2	no	—
818	C₂×C₄²	—	2	2	no	—
819	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
820	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
821	#107	C₂³×C₈₉	1	2	yes	—
822	#107	C₂³×C₈₉	1	2	yes	—
823	#107	C₂³×C₈₉	1	1	yes	characteristic
824	#107	C₂³×C₈₉	1	2	yes	—
825	#107	C₂³×C₈₉	1	2	yes	—
826	#107	C₂³×C₈₉	1	1	yes	characteristic
827	#107	C₂³×C₈₉	1	2	yes	—
828	#106	C₂³×C₈₉	1	2	yes	—
829	#106	C₂³×C₈₉	1	2	yes	—
830	#106	C₂³×C₈₉	1	1	yes	characteristic
831	#106	C₂³×C₈₉	1	2	yes	—
832	#106	C₂³×C₈₉	1	2	yes	—
833	#106	C₂³×C₈₉	1	1	yes	characteristic
834	#106	C₂³×C₈₉	1	2	yes	—
835	C₄⋊C₈	C₂³×C₈₉	1	2	yes	—
836	C₄⋊C₈	C₂³×C₈₉	1	1	yes	characteristic
837	C₄⋊C₈	C₂³×C₈₉	1	1	yes	characteristic
838	C₄⋊C₈	C₂³×C₈₉	1	1	yes	characteristic
839	C₄⋊C₈	C₂³×C₈₉	1	2	yes	—
840	C₄⋊C₈	C₂³×C₈₉	1	2	yes	—
841	C₄⋊C₈	C₂³×C₈₉	1	1	yes	characteristic
842	#103	C₂³×C₈₉	1	2	yes	—
843	#103	C₂³×C₈₉	1	2	yes	—
844	#103	C₂³×C₈₉	1	2	yes	—
845	#103	C₂³×C₈₉	1	2	yes	—
846	#103	C₂³×C₈₉	1	1	yes	characteristic
847	#103	C₂³×C₈₉	1	1	yes	characteristic
848	#103	C₂³×C₈₉	1	2	yes	—
849	#103	C₂³×C₈₉	1	2	yes	—
850	#103	C₂³×C₈₉	1	2	yes	—
851	#102	C₂³×C₈₉	1	1	yes	characteristic
852	#102	C₂³×C₈₉	1	1	yes	characteristic
853	#102	C₂³×C₈₉	1	2	yes	—
854	#102	C₂³×C₈₉	1	2	yes	—
855	#102	C₂³×C₈₉	1	2	yes	—
856	#102	C₂³×C₈₉	1	2	yes	—
857	#102	C₂³×C₈₉	1	1	yes	characteristic
858	#102	C₂³×C₈₉	1	1	yes	characteristic
859	#102	C₂³×C₈₉	1	1	yes	characteristic
860	#102	C₂³×C₈₉	1	2	yes	—
861	#102	C₂³×C₈₉	1	1	yes	characteristic
862	C₂²⋊C₈	C₂³×C₈₉	1	1	yes	characteristic
863	C₂²⋊C₈	C₂³×C₈₉	1	1	yes	characteristic
864	C₂²⋊C₈	C₂³×C₈₉	1	2	yes	—
865	C₂²⋊C₈	C₂³×C₈₉	1	2	yes	—
866	C₄×C₈	C₂³×C₈₉	1	1	yes	characteristic
867	C₄×C₈	C₂³×C₈₉	1	1	yes	characteristic
868	C₄×C₈	C₂³×C₈₉	1	2	yes	—
869	C₄×C₈	C₂³×C₈₉	1	2	yes	—
870	C₂⁴	—	2	1	no	—
871	#41	—	2	4	no	—
872	#41	—	4	2	no	—
873	#41	—	4	2	no	—
874	#41	—	4	4	no	—
875	C₂×Q₈	—	2	1	no	—
876	C₂×Q₈	—	2	1	no	—
877	C₂×Q₈	—	2	1	no	—
878	C₂×Q₈	C₂×D₄×C₈₉	1	1	yes	characteristic
879	C₂×Q₈	C₂⁴×C₈₉	1	2	yes	—
880	C₂×Q₈	C₂⁴×C₈₉	1	1	yes	characteristic
881	C₂×D₄	—	2	2	no	—
882	C₂×D₄	—	2	2	no	—
883	C₂×D₄	—	2	2	no	—
884	C₂×D₄	—	2	2	no	—
885	C₂×D₄	—	2	1	no	—
886	C₂×D₄	—	2	1	no	—
887	C₂×D₄	—	4	1	no	—
888	C₂×D₄	C₂×D₄×C₈₉	1	1	yes	characteristic
889	C₂×D₄	C₂×D₄×C₈₉	1	2	yes	—
890	C₂×D₄	C₂⁴×C₈₉	1	1	yes	characteristic
891	C₂×D₄	C₂⁴×C₈₉	1	1	yes	characteristic
892	C₂×D₄	C₂⁴×C₈₉	1	1	yes	characteristic
893	C₂²×C₄	—	2	1	no	—
894	C₂²×C₄	—	2	2	no	—
895	C₂²×C₄	—	2	2	no	—
896	C₂²×C₄	—	2	1	no	—
897	C₂²×C₄	—	2	2	no	—
898	C₂²×C₄	—	2	1	no	—
899	C₂²×C₄	—	2	1	no	—
900	C₂²×C₄	—	2	1	no	—
901	C₂²×C₄	—	2	1	no	—
902	C₂²×C₄	—	2	2	no	—
903	C₂²×C₄	—	2	2	no	—
904	C₂²×C₄	—	4	4	no	—
905	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
906	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
907	C₂²×C₄	C₂×D₄×C₈₉	1	2	yes	—
908	C₂²×C₄	C₂×D₄×C₈₉	1	2	yes	—
909	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
910	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
911	Q₁₆	—	4	2	no	—
912	SD₁₆	—	2	2	no	—
913	SD₁₆	—	4	2	no	—
914	SD₁₆	—	4	1	no	—
915	D₈	—	2	2	no	—
916	D₈	—	4	1	no	—
917	M₁₆	—	4	2	no	—
918	M₁₆	—	4	2	no	—
919	M₁₆	—	4	2	no	—
920	C₂×C₈	C₂⁴×C₈₉	1	1	yes	characteristic
921	C₂×C₈	C₂⁴×C₈₉	1	1	yes	characteristic
922	C₂×C₈	C₂⁴×C₈₉	1	2	yes	—
923	C₂×C₈	C₂⁴×C₈₉	1	1	yes	characteristic
924	C₂×C₈	C₂⁴×C₈₉	1	2	yes	—
925	C₂×C₈	C₂⁴×C₈₉	1	1	yes	characteristic
926	C₄⋊C₄	—	2	2	no	—
927	C₄⋊C₄	—	2	1	no	—
928	C₄⋊C₄	—	2	1	no	—
929	C₄⋊C₄	—	2	1	no	—
930	C₄⋊C₄	—	2	1	no	—
931	C₄⋊C₄	—	2	2	no	—
932	C₄⋊C₄	—	2	2	no	—
933	C₄⋊C₄	—	2	2	no	—
934	C₄⋊C₄	—	2	1	no	—
935	C₄⋊C₄	—	2	2	no	—
936	C₄⋊C₄	—	2	2	no	—
937	C₄⋊C₄	—	2	2	no	—
938	C₄⋊C₄	—	2	2	no	—
939	C₄⋊C₄	—	2	1	no	—
940	C₄⋊C₄	—	2	2	no	—
941	C₄⋊C₄	—	2	2	no	—
942	C₄⋊C₄	—	2	1	no	—
943	C₄⋊C₄	—	2	2	no	—
944	C₄⋊C₄	—	2	2	no	—
945	C₄⋊C₄	—	2	2	no	—
946	C₄⋊C₄	—	2	2	no	—
947	C₄⋊C₄	—	2	2	no	—
948	C₄⋊C₄	—	2	1	no	—
949	C₄⋊C₄	—	2	1	no	—
950	C₄⋊C₄	—	2	1	no	—
951	C₄⋊C₄	—	2	2	no	—
952	C₄⋊C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
953	C₄⋊C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
954	C₄⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
955	C₄⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
956	C₄⋊C₄	C₂⁴×C₈₉	1	1	yes	characteristic
957	C₄⋊C₄	C₂⁴×C₈₉	1	1	yes	characteristic
958	C₄⋊C₄	C₂⁴×C₈₉	1	2	yes	—
959	C₄⋊C₄	C₂⁴×C₈₉	1	2	yes	—
960	C₄⋊C₄	C₂⁴×C₈₉	1	1	yes	characteristic
961	C₄⋊C₄	C₂⁴×C₈₉	1	1	yes	characteristic
962	C₄⋊C₄	C₂⁴×C₈₉	1	2	yes	—
963	C₂²⋊C₄	—	2	2	no	—
964	C₂²⋊C₄	—	2	2	no	—
965	C₂²⋊C₄	—	2	2	no	—
966	C₂²⋊C₄	—	2	2	no	—
967	C₂²⋊C₄	—	2	2	no	—
968	C₂²⋊C₄	—	2	1	no	—
969	C₂²⋊C₄	—	2	1	no	—
970	C₂²⋊C₄	—	2	2	no	—
971	C₂²⋊C₄	—	2	2	no	—
972	C₂²⋊C₄	—	2	1	no	—
973	C₂²⋊C₄	—	2	1	no	—
974	C₂²⋊C₄	—	2	1	no	—
975	C₂²⋊C₄	—	2	1	no	—
976	C₂²⋊C₄	—	2	1	no	—
977	C₂²⋊C₄	—	2	1	no	—
978	C₂²⋊C₄	—	2	2	no	—
979	C₂²⋊C₄	—	2	2	no	—
980	C₂²⋊C₄	—	2	2	no	—
981	C₂²⋊C₄	—	2	2	no	—
982	C₂²⋊C₄	—	2	1	no	—
983	C₂²⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
984	C₂²⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
985	C₂²⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
986	C₄²	—	2	2	no	—
987	C₄²	—	2	2	no	—
988	C₄²	—	2	2	no	—
989	C₄²	—	2	2	no	—
990	C₄²	—	2	2	no	—
991	C₄²	—	2	1	no	—
992	C₄²	C₂×D₄×C₈₉	1	2	yes	—
993	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
994	C₄²	C₂×D₄×C₈₉	1	2	yes	—
995	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
996	C₄²	C₂⁴×C₈₉	1	1	yes	characteristic
997	C₄²	C₂⁴×C₈₉	1	2	yes	—
998	C₄²	C₂⁴×C₈₉	1	1	yes	characteristic
999	C₂³	—	2	1	no	—
1000	C₂³	—	2	1	no	—
1001	C₂³	—	2	1	no	—
1002	C₂³	—	4	2	no	—
1003	C₂³	—	4	2	no	—
1004	C₂³	—	8	1	no	—
1005	C₂³	C₂²×D₄×C₈₉	1	1	yes	characteristic
1006	C₂³	C₂²×D₄×C₈₉	1	2	yes	—
1007	Q₈	—	2	2	no	—
1008	Q₈	—	2	1	no	—
1009	Q₈	—	2	2	no	—
1010	Q₈	—	2	1	no	—
1011	Q₈	—	2	2	no	—
1012	Q₈	—	4	2	no	—
1013	Q₈	—	8	1	no	—
1014	Q₈	—	8	1	no	—
1015	D₄	—	2	2	no	—
1016	D₄	—	2	1	no	—
1017	D₄	—	2	1	no	—
1018	D₄	—	2	1	no	—
1019	D₄	—	2	1	no	—
1020	D₄	—	2	1	no	—
1021	D₄	—	4	2	no	—
1022	D₄	—	4	2	no	—
1023	D₄	—	4	4	no	—
1024	D₄	—	4	4	no	—
1025	D₄	—	8	1	no	—
1026	D₄	—	8	2	no	—
1027	D₄	2₋¹⁺⁴×C₈₉	1	2	yes	—
1028	C₂×C₄	—	2	2	no	—
1029	C₂×C₄	—	2	1	no	—
1030	C₂×C₄	—	2	2	no	—
1031	C₂×C₄	—	2	1	no	—
1032	C₂×C₄	—	2	2	no	—
1033	C₂×C₄	—	2	1	no	—
1034	C₂×C₄	—	2	1	no	—
1035	C₂×C₄	—	2	2	no	—
1036	C₂×C₄	—	2	2	no	—
1037	C₂×C₄	—	2	2	no	—
1038	C₂×C₄	—	2	2	no	—
1039	C₂×C₄	—	2	1	no	—
1040	C₂×C₄	—	2	1	no	—
1041	C₂×C₄	—	2	1	no	—
1042	C₂×C₄	—	4	2	no	—
1043	C₂×C₄	—	4	1	no	—
1044	C₂×C₄	—	4	2	no	—
1045	C₂×C₄	—	4	4	no	—
1046	C₂×C₄	—	4	2	no	—
1047	C₂×C₄	—	4	2	no	—
1048	C₂×C₄	—	4	2	no	—
1049	C₂×C₄	—	4	4	no	—
1050	C₂×C₄	—	4	2	no	—
1051	C₂×C₄	—	4	2	no	—
1052	C₂×C₄	—	4	2	no	—
1053	C₂×C₄	—	8	2	no	—
1054	C₂×C₄	—	8	2	no	—
1055	C₂×C₄	—	8	2	no	—
1056	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
1057	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
1058	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
1059	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
1060	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
1061	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
1062	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
1063	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
1064	C₂×C₄	C₂⁵×C₈₉	1	1	yes	characteristic
1065	C₈	—	2	1	no	—
1066	C₈	—	2	1	no	—
1067	C₈	—	2	1	no	—
1068	C₈	—	2	1	no	—
1069	C₈	—	2	2	no	—
1070	C₈	—	2	2	no	—
1071	C₂²	—	2	1	no	—
1072	C₂²	—	2	2	no	—
1073	C₂²	—	2	2	no	—
1074	C₂²	—	2	1	no	—
1075	C₂²	—	2	2	no	—
1076	C₂²	—	2	1	no	—
1077	C₂²	—	2	2	no	—
1078	C₂²	—	4	1	no	—
1079	C₂²	—	4	1	no	—
1080	C₂²	—	4	1	no	—
1081	C₂²	—	4	1	no	—
1082	C₂²	—	4	1	no	—
1083	C₂²	—	4	1	no	—
1084	C₂²	—	4	1	no	—
1085	C₂²	—	4	1	no	—
1086	C₂²	—	8	4	no	—
1087	C₂²	C₂³×D₄×C₈₉	1	1	yes	characteristic
1088	C₄	—	2	1	no	—
1089	C₄	—	2	2	no	—
1090	C₄	—	2	1	no	—
1091	C₄	—	2	2	no	—
1092	C₄	—	2	1	no	—
1093	C₄	—	2	2	no	—
1094	C₄	—	2	1	no	—
1095	C₄	—	4	1	no	—
1096	C₄	—	4	1	no	—
1097	C₄	—	4	1	no	—
1098	C₄	—	4	2	no	—
1099	C₄	—	4	1	no	—
1100	C₄	—	4	2	no	—
1101	C₄	—	4	2	no	—
1102	C₄	—	4	2	no	—
1103	C₄	—	4	1	no	—
1104	C₄	#575×C₈₉	1	2	yes	—
1105	C₄	C₂×2₋¹⁺⁴×C₈₉	1	1	yes	characteristic
1106	C₄	#585×C₈₉	1	1	yes	characteristic
1107	C₂	—	4	2	no	—
1108	C₂	—	4	1	no	—
1109	C₂	—	4	2	no	—
1110	C₂	—	8	1	no	—
1111	C₂	—	8	1	no	—
1112	C₂	C₈₉×#3489	1	1	yes	characteristic
1113	C₂	C₂×#575×C₈₉	1	1	yes	characteristic
1114	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 ◁ C₄×#41×C₈₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₈₉×#3515	C₂	semidirect
2. C₈₉×#3475	C₂	semidirect
3. C₈₉×#3381	C₂	semidirect
4. C₈₉×#3380	C₂	semidirect
5. C₈₉×#3364	C₂	semidirect
6. C₈₉×#3360	C₂	semidirect
7. C₈₉×#3357	C₂	semidirect
8. C₈₉×#3354	C₂	semidirect
9. C₈₉×#3352	C₂	semidirect
10. C₈₉×#3351	C₂	semidirect
11. C₈₉×#3331	C₂	semidirect
12. C₈₉×#3330	C₂	semidirect
13. C₈₉×#3323	C₂	semidirect
14. C₈₉×#3322	C₂	semidirect
15. C₈₉×#3256	C₂	semidirect
16. C₈₉×#3252	C₂	semidirect
17. C₈₉×#3232	C₂	semidirect
18. C₈₉×#3231	C₂	semidirect
19. C₈₉×#3105	C₂	semidirect
20. C₈₉×#3102	C₂	semidirect
21. C₈₉×#3080	C₂	semidirect
22. C₈₉×#3077	C₂	semidirect
23. C₈₉×#2991	C₂	semidirect
24. #557×C₈₉	C₂²	semidirect
28. #554×C₈₉	C₂²	semidirect
29. #554×C₈₉	C₂²	semidirect
40. #547×C₈₉	C₂²	semidirect
49. #529×C₈₉	C₂²	semidirect
50. C₂×#125×C₈₉	C₂²	semidirect
57. #500×C₈₉	C₂²	semidirect
58. #499×C₈₉	C₂²	semidirect
59. #499×C₈₉	C₂²	semidirect
60. #498×C₈₉	C₂²	semidirect
63. #487×C₈₉	C₂²	semidirect
64. #487×C₈₉	C₂²	semidirect
67. #485×C₈₉	C₂²	semidirect
69. #484×C₈₉	C₂²	semidirect
70. #483×C₈₉	C₂²	semidirect
71. #482×C₈₉	C₂²	semidirect
75. #479×C₈₉	C₂²	semidirect
76. #479×C₈₉	C₂²	semidirect
77. #479×C₈₉	C₂²	semidirect
78. #479×C₈₉	C₂²	semidirect
79. #479×C₈₉	C₂²	semidirect
80. #479×C₈₉	C₂²	semidirect
87. #478×C₈₉	C₂²	semidirect
88. #477×C₈₉	C₂²	semidirect
91. #476×C₈₉	C₂²	semidirect
95. #470×C₈₉	C₂²	semidirect
99. #468×C₈₉	C₂²	semidirect
101. #464×C₈₉	C₂²	semidirect
105. #462×C₈₉	C₂²	semidirect
106. #461×C₈₉	C₂²	semidirect
111. C₈×Q₈×C₈₉	C₂²	semidirect
112. C₈×Q₈×C₈₉	C₂²	semidirect
113. C₄×Q₁₆×C₈₉	C₂²	semidirect
117. C₄×SD₁₆×C₈₉	C₂²	semidirect
123. #436×C₈₉	C₂²	semidirect
124. #436×C₈₉	C₂²	semidirect
126. #431×C₈₉	C₂²	semidirect
128. #428×C₈₉	C₂²	semidirect
129. #428×C₈₉	C₂²	semidirect
131. #423×C₈₉	C₂²	semidirect
549. #62152	C₈₉	direct (N × H)
558. #3515	C₂×C₈₉	semidirect
559. #3475	C₂×C₈₉	semidirect
560. #3381	C₂×C₈₉	semidirect
561. #3380	C₂×C₈₉	semidirect
562. #3364	C₂×C₈₉	semidirect
563. #3360	C₂×C₈₉	semidirect
564. #3357	C₂×C₈₉	semidirect
565. #3354	C₂×C₈₉	semidirect
566. #3352	C₂×C₈₉	semidirect
567. #3351	C₂×C₈₉	semidirect
568. #3331	C₂×C₈₉	semidirect
569. #3330	C₂×C₈₉	semidirect
570. #3323	C₂×C₈₉	semidirect
571. #3322	C₂×C₈₉	semidirect
572. #3256	C₂×C₈₉	semidirect
573. #3252	C₂×C₈₉	semidirect
574. #3232	C₂×C₈₉	semidirect
575. #3231	C₂×C₈₉	semidirect
576. #3105	C₂×C₈₉	semidirect
577. #3102	C₂×C₈₉	semidirect
578. #3080	C₂×C₈₉	semidirect
579. #3077	C₂×C₈₉	semidirect
580. #2991	C₂×C₈₉	semidirect
581. C₈₉	#62152	direct (N × H)
582. #557	C₂²×C₈₉	semidirect
586. #554	C₂²×C₈₉	semidirect
587. #554	C₂²×C₈₉	semidirect
598. #547	C₂²×C₈₉	semidirect
607. #529	C₂²×C₈₉	semidirect
608. C₂×#125	C₂²×C₈₉	semidirect
615. #500	C₂²×C₈₉	semidirect
616. #499	C₂²×C₈₉	semidirect
617. #499	C₂²×C₈₉	semidirect
618. #498	C₂²×C₈₉	semidirect
621. #487	C₂²×C₈₉	semidirect
622. #487	C₂²×C₈₉	semidirect
625. #485	C₂²×C₈₉	semidirect
627. #484	C₂²×C₈₉	semidirect
628. #483	C₂²×C₈₉	semidirect
629. #482	C₂²×C₈₉	semidirect
633. #479	C₂²×C₈₉	semidirect
634. #479	C₂²×C₈₉	semidirect
635. #479	C₂²×C₈₉	semidirect
636. #479	C₂²×C₈₉	semidirect
637. #479	C₂²×C₈₉	semidirect
638. #479	C₂²×C₈₉	semidirect
645. #478	C₂²×C₈₉	semidirect
646. #477	C₂²×C₈₉	semidirect
649. #476	C₂²×C₈₉	semidirect
653. #470	C₂²×C₈₉	semidirect
657. #468	C₂²×C₈₉	semidirect
659. #464	C₂²×C₈₉	semidirect
663. #462	C₂²×C₈₉	semidirect
664. #461	C₂²×C₈₉	semidirect
669. C₈×Q₈	C₂²×C₈₉	semidirect
670. C₈×Q₈	C₂²×C₈₉	semidirect
671. C₄×Q₁₆	C₂²×C₈₉	semidirect
675. C₄×SD₁₆	C₂²×C₈₉	semidirect
681. #436	C₂²×C₈₉	semidirect
682. #436	C₂²×C₈₉	semidirect
684. #431	C₂²×C₈₉	semidirect
686. #428	C₂²×C₈₉	semidirect
687. #428	C₂²×C₈₉	semidirect
689. #423	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×#3515	2
C₈₉×#3475	2
C₈₉×#3381	2
C₈₉×#3380	2
C₈₉×#3364	2
C₈₉×#3360	2
C₈₉×#3357	2
C₈₉×#3354	2
C₈₉×#3352	2
C₈₉×#3351	2
C₈₉×#3331	2
C₈₉×#3330	2
C₈₉×#3323	2
C₈₉×#3322	2
C₈₉×#3256	2
C₈₉×#3252	2
C₈₉×#3232	2
C₈₉×#3231	2
C₈₉×#3105	2
C₈₉×#3102	2
C₈₉×#3080	2
C₈₉×#3077	2
C₈₉×#2991	2
#62152	89

Subgroups — C89×#62152 #36440000

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#62152 #36440000