Subgroups — C₈₉×#62617 #36440465

Order 22784.

1766 conjugacy classes of subgroups.

The subgroup lattice has 1154 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈₉×#3546	C₂	1	1	yes	maximal, characteristic, complemented
2	C₈₉×#3544	C₂	1	1	yes	maximal, characteristic, complemented
3	C₈₉×#3369	C₂	1	1	yes	maximal, characteristic, complemented
4	C₈₉×#3366	C₂	1	1	yes	maximal, characteristic, complemented
5	C₈₉×#3362	C₂	1	1	yes	maximal, characteristic, complemented
6	C₈₉×#3360	C₂	1	1	yes	maximal, characteristic, complemented
7	C₈₉×#3332	C₂	1	2	yes	maximal, complemented
8	C₈₉×#3331	C₂	1	1	yes	maximal, characteristic, complemented
9	C₈₉×#3325	C₂	1	1	yes	maximal, characteristic, complemented
10	C₈₉×#3323	C₂	1	2	yes	maximal, complemented
11	C₈₉×#3317	C₂	1	2	yes	maximal, complemented
12	C₈₉×#3306	C₂	1	2	yes	maximal, complemented
13	C₈₉×#3303	C₂	1	1	yes	maximal, characteristic, complemented
14	C₈₉×#3295	C₂	1	1	yes	maximal, characteristic, complemented
15	C₈₉×#3244	C₂	1	2	yes	maximal, complemented
16	C₈₉×#3227	C₂	1	1	yes	maximal, characteristic, complemented
17	C₈₉×#3224	C₂	1	2	yes	maximal, complemented
18	C₈₉×#3212	C₂	1	1	yes	maximal, characteristic, complemented
19	C₈₉×#3173	C₂	1	2	yes	maximal, complemented
20	C₈₉×#3171	C₂	1	1	yes	maximal, characteristic, complemented
21	C₈₉×#3141	C₂	1	1	yes	maximal, characteristic, complemented
22	C₈₉×#3136	C₂	1	2	yes	maximal, complemented
23	C₈₉×#2969	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	#556×C₈₉	C₂²	1	1	yes	characteristic
28	#555×C₈₉	C₂²	1	1	yes	characteristic
29	#554×C₈₉	C₂²	1	1	yes	characteristic
30	#554×C₈₉	C₂²	1	1	yes	characteristic, complemented
31	#553×C₈₉	—	2	1	no	—
32	#552×C₈₉	—	2	1	no	—
33	#552×C₈₉	C₂²	1	2	yes	complemented
34	#550×C₈₉	C₂²	1	2	yes	—
35	#550×C₈₉	C₂²	1	1	yes	characteristic
36	#547×C₈₉	—	2	1	no	—
37	#547×C₈₉	C₂²	1	1	yes	characteristic
38	#547×C₈₉	C₂²	1	2	yes	complemented
39	#546×C₈₉	—	2	1	no	—
40	#546×C₈₉	C₂²	1	2	yes	—
41	D₄²×C₈₉	C₂²	1	1	yes	characteristic
42	#544×C₈₉	—	2	1	no	—
43	#544×C₈₉	C₂²	1	2	yes	complemented
44	#542×C₈₉	—	2	1	no	—
45	#542×C₈₉	C₂²	1	2	yes	—
46	#542×C₈₉	C₂²	1	2	yes	complemented
47	#538×C₈₉	—	2	2	no	—
48	#537×C₈₉	—	2	1	no	—
49	#536×C₈₉	—	2	2	no	—
50	#535×C₈₉	—	2	1	no	—
51	#535×C₈₉	C₂²	1	2	yes	—
52	#532×C₈₉	C₂²	1	1	yes	characteristic
53	#532×C₈₉	C₂²	1	1	yes	characteristic
54	C₂×C₄⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic, complemented
55	#529×C₈₉	C₂²	1	1	yes	characteristic
56	#529×C₈₉	C₂²	1	1	yes	characteristic, complemented
57	#501×C₈₉	C₂²	1	1	yes	characteristic, complemented
58	#498×C₈₉	C₂²	1	2	yes	complemented
59	#496×C₈₉	C₂²	1	1	yes	characteristic
60	#495×C₈₉	C₂²	1	2	yes	complemented
61	#490×C₈₉	C₂²	1	1	yes	characteristic
62	#490×C₈₉	C₂²	1	2	yes	complemented
63	#489×C₈₉	C₂²	1	2	yes	—
64	#489×C₈₉	C₂²	1	2	yes	complemented
65	#489×C₈₉	C₂²	1	2	yes	complemented
66	#489×C₈₉	C₂²	1	1	yes	characteristic, complemented
67	#488×C₈₉	C₂²	1	2	yes	—
68	#488×C₈₉	C₂²	1	2	yes	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	2	yes	—
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	#481×C₈₉	C₂²	1	2	yes	—
79	#481×C₈₉	C₂²	1	2	yes	—
80	#481×C₈₉	C₂²	1	2	yes	complemented
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
85	#476×C₈₉	C₂²	1	1	yes	characteristic, complemented
86	#476×C₈₉	C₂²	1	1	yes	characteristic, complemented
87	#476×C₈₉	C₂²	1	2	yes	complemented
88	#475×C₈₉	C₂²	1	2	yes	complemented
89	#470×C₈₉	C₂²	1	2	yes	complemented
90	#469×C₈₉	C₂²	1	2	yes	—
91	#469×C₈₉	C₂²	1	1	yes	characteristic
92	#469×C₈₉	C₂²	1	1	yes	characteristic, complemented
93	#468×C₈₉	C₂²	1	1	yes	characteristic
94	#468×C₈₉	C₂²	1	1	yes	characteristic, complemented
95	#465×C₈₉	C₂²	1	2	yes	—
96	#465×C₈₉	C₂²	1	2	yes	complemented
97	#464×C₈₉	C₂²	1	2	yes	—
98	#463×C₈₉	C₂²	1	2	yes	—
99	#462×C₈₉	C₂²	1	1	yes	characteristic, complemented
100	#461×C₈₉	C₂²	1	1	yes	characteristic, complemented
101	#460×C₈₉	C₂²	1	1	yes	characteristic
102	#460×C₈₉	C₂²	1	2	yes	complemented
103	#459×C₈₉	C₂²	1	1	yes	characteristic
104	#459×C₈₉	C₂²	1	2	yes	complemented
105	#452×C₈₉	C₂²	1	2	yes	complemented
106	#452×C₈₉	C₂²	1	2	yes	complemented
107	#450×C₈₉	C₂²	1	2	yes	—
108	#449×C₈₉	C₂²	1	2	yes	complemented
109	#449×C₈₉	C₂²	1	2	yes	complemented
110	#447×C₈₉	C₂²	1	2	yes	—
111	#446×C₈₉	C₂²	1	1	yes	characteristic, complemented
112	C₈×Q₈×C₈₉	C₂²	1	1	yes	characteristic, complemented
113	#442×C₈₉	C₂²	1	2	yes	complemented
114	#441×C₈₉	C₂²	1	2	yes	complemented
115	C₄×SD₁₆×C₈₉	C₂²	1	1	yes	characteristic
116	C₄×SD₁₆×C₈₉	C₂²	1	2	yes	complemented
117	C₄×SD₁₆×C₈₉	C₂²	1	1	yes	characteristic, complemented
118	C₄×SD₁₆×C₈₉	C₂²	1	2	yes	complemented
119	C₄×D₈×C₈₉	C₂²	1	1	yes	characteristic
120	C₄×D₈×C₈₉	C₂²	1	1	yes	characteristic, complemented
121	#436×C₈₉	C₂²	1	1	yes	characteristic
122	#436×C₈₉	C₂²	1	2	yes	complemented
123	#435×C₈₉	C₂²	1	2	yes	complemented
124	C₈×D₄×C₈₉	C₂²	1	1	yes	characteristic
125	#433×C₈₉	C₂²	1	2	yes	complemented
126	#431×C₈₉	C₂²	1	1	yes	characteristic, complemented
127	#418×C₈₉	C₂²	1	2	yes	—
128	#417×C₈₉	C₂²	1	2	yes	complemented
129	#417×C₈₉	C₂²	1	2	yes	complemented
130	#417×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	C₄×M₁₆×C₈₉	C₂²	1	1	yes	characteristic, complemented
135	C₂×#41×C₈₉	—	2	1	no	—
136	C₂×#41×C₈₉	—	2	2	no	—
137	C₂×#41×C₈₉	—	2	1	no	—
138	C₂×#41×C₈₉	C₂³	1	2	yes	—
139	C₂×#41×C₈₉	C₂³	1	2	yes	—
140	C₂²×Q₈×C₈₉	—	2	1	no	—
141	C₂²×D₄×C₈₉	—	2	1	no	—
142	C₂²×D₄×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	2	yes	—
146	C₂×SD₁₆×C₈₉	C₂³	1	2	yes	—
147	C₂×SD₁₆×C₈₉	C₂³	1	1	yes	characteristic
148	C₂×D₈×C₈₉	C₂³	1	1	yes	characteristic
149	C₂×D₈×C₈₉	C₂³	1	1	yes	characteristic
150	C₂×D₈×C₈₉	C₂³	1	2	yes	—
151	C₂×M₁₆×C₈₉	C₂³	1	1	yes	characteristic
152	C₂×M₁₆×C₈₉	C₂³	1	1	yes	characteristic
153	C₂×M₁₆×C₈₉	C₂³	1	2	yes	—
154	C₂²×C₈×C₈₉	C₂³	1	2	yes	—
155	C₄⋊Q₈×C₈₉	—	2	2	no	—
156	C₄⋊Q₈×C₈₉	—	2	2	no	—
157	C₄⋊Q₈×C₈₉	—	2	1	no	—
158	C₄⋊Q₈×C₈₉	—	2	1	no	—
159	C₄⋊Q₈×C₈₉	—	2	1	no	—
160	C₄⋊Q₈×C₈₉	C₂³	1	1	yes	characteristic
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	#127×C₈₉	—	2	2	no	—
167	#127×C₈₉	C₂³	1	1	yes	characteristic
168	#127×C₈₉	C₂³	1	2	yes	—
169	#127×C₈₉	C₂³	1	1	yes	characteristic
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	1	no	—
175	#126×C₈₉	D₄	1	2	yes	—
176	#125×C₈₉	—	2	1	no	—
177	#125×C₈₉	—	2	2	no	—
178	#125×C₈₉	—	2	2	no	—
179	#125×C₈₉	D₄	1	1	yes	characteristic
180	#125×C₈₉	C₂³	1	2	yes	—
181	#125×C₈₉	C₂³	1	1	yes	characteristic
182	#124×C₈₉	—	2	2	no	—
183	#124×C₈₉	—	2	2	no	—
184	#124×C₈₉	—	2	2	no	—
185	#124×C₈₉	—	2	1	no	—
186	#124×C₈₉	D₄	1	1	yes	characteristic
187	#124×C₈₉	C₂³	1	2	yes	—
188	#124×C₈₉	C₂³	1	2	yes	—
189	#124×C₈₉	C₂³	1	1	yes	characteristic
190	#123×C₈₉	—	2	2	no	—
191	#123×C₈₉	—	2	1	no	—
192	#123×C₈₉	—	2	2	no	—
193	#123×C₈₉	—	2	2	no	—
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	2	no	—
202	C₂²⋊Q₈×C₈₉	—	2	2	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	—	2	2	no	—
208	C₂²⋊Q₈×C₈₉	D₄	1	1	yes	characteristic
209	C₂²⋊Q₈×C₈₉	C₂³	1	2	yes	—
210	C₂²⋊Q₈×C₈₉	C₂³	1	1	yes	characteristic
211	C₂²⋊Q₈×C₈₉	C₂³	1	2	yes	—
212	#121×C₈₉	—	2	1	no	—
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	2	yes	—
227	#121×C₈₉	C₂³	1	1	yes	characteristic
228	#121×C₈₉	C₂³	1	2	yes	—
229	#121×C₈₉	C₂³	1	1	yes	characteristic
230	#121×C₈₉	C₂³	1	1	yes	characteristic
231	#120×C₈₉	—	2	2	no	—
232	#120×C₈₉	—	2	2	no	—
233	#120×C₈₉	—	2	2	no	—
234	#120×C₈₉	—	2	2	no	—
235	C₄×Q₈×C₈₉	—	2	1	no	—
236	C₄×Q₈×C₈₉	C₂³	1	1	yes	characteristic
237	C₄×Q₈×C₈₉	C₂³	1	2	yes	—
238	C₄×Q₈×C₈₉	C₂³	1	2	yes	—
239	C₄×Q₈×C₈₉	C₂³	1	1	yes	characteristic
240	C₄×D₄×C₈₉	—	2	1	no	—
241	C₄×D₄×C₈₉	—	2	1	no	—
242	C₄×D₄×C₈₉	—	2	2	no	—
243	C₄×D₄×C₈₉	—	2	1	no	—
244	C₄×D₄×C₈₉	—	2	1	no	—
245	C₄×D₄×C₈₉	—	2	1	no	—
246	C₄×D₄×C₈₉	C₂³	1	1	yes	characteristic
247	C₄×D₄×C₈₉	C₂³	1	1	yes	characteristic
248	C₄×D₄×C₈₉	C₂³	1	1	yes	characteristic
249	C₄×D₄×C₈₉	C₂³	1	2	yes	—
250	C₄×D₄×C₈₉	C₂³	1	2	yes	—
251	C₄×D₄×C₈₉	C₂³	1	1	yes	characteristic
252	C₄×D₄×C₈₉	C₂³	1	2	yes	—
253	#117×C₈₉	—	2	1	no	—
254	#117×C₈₉	—	2	1	no	—
255	#117×C₈₉	—	2	2	no	—
256	#117×C₈₉	—	2	1	no	—
257	#117×C₈₉	C₂³	1	2	yes	—
258	#117×C₈₉	C₂³	1	2	yes	—
259	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
260	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
261	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
262	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
263	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
264	C₂×C₂²⋊C₄×C₈₉	—	2	2	no	—
265	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
266	#107×C₈₉	C₂³	1	1	yes	characteristic
267	#107×C₈₉	C₂³	1	1	yes	characteristic
268	#106×C₈₉	C₂³	1	1	yes	characteristic
269	#106×C₈₉	C₂³	1	2	yes	—
270	#106×C₈₉	C₂³	1	2	yes	—
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	#102×C₈₉	C₂³	1	1	yes	characteristic
287	#102×C₈₉	C₂³	1	2	yes	—
288	#102×C₈₉	C₂³	1	2	yes	—
289	#102×C₈₉	C₂³	1	2	yes	—
290	#102×C₈₉	C₂³	1	1	yes	characteristic
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	2	yes	—
300	#102×C₈₉	C₂³	1	1	yes	characteristic
301	#102×C₈₉	C₂³	1	1	yes	characteristic
302	C₂²⋊C₈×C₈₉	C₂³	1	2	yes	—
303	C₂²⋊C₈×C₈₉	C₂³	1	2	yes	—
304	C₂²⋊C₈×C₈₉	C₂³	1	2	yes	—
305	#97×C₈₉	C₂³	1	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	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	4	no	—
319	#41×C₈₉	—	8	2	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	2	no	—
324	C₂×Q₈×C₈₉	—	2	1	no	—
325	C₂×Q₈×C₈₉	—	8	2	no	—
326	C₂×Q₈×C₈₉	C₂×D₄	1	1	yes	characteristic
327	C₂×Q₈×C₈₉	C₂⁴	1	2	yes	—
328	C₂×Q₈×C₈₉	C₂⁴	1	1	yes	characteristic
329	C₂×D₄×C₈₉	—	2	1	no	—
330	C₂×D₄×C₈₉	—	2	1	no	—
331	C₂×D₄×C₈₉	—	2	2	no	—
332	C₂×D₄×C₈₉	—	2	2	no	—
333	C₂×D₄×C₈₉	—	2	2	no	—
334	C₂×D₄×C₈₉	—	2	1	no	—
335	C₂×D₄×C₈₉	—	2	2	no	—
336	C₂×D₄×C₈₉	—	2	1	no	—
337	C₂×D₄×C₈₉	—	2	1	no	—
338	C₂×D₄×C₈₉	—	2	1	no	—
339	C₂×D₄×C₈₉	—	2	2	no	—
340	C₂×D₄×C₈₉	—	2	1	no	—
341	C₂×D₄×C₈₉	—	2	2	no	—
342	C₂×D₄×C₈₉	—	2	2	no	—
343	C₂×D₄×C₈₉	—	4	2	no	—
344	C₂×D₄×C₈₉	—	4	2	no	—
345	C₂×D₄×C₈₉	—	8	2	no	—
346	C₂×D₄×C₈₉	C₂×D₄	1	1	yes	characteristic
347	C₂×D₄×C₈₉	C₂×D₄	1	2	yes	—
348	C₂×D₄×C₈₉	C₂⁴	1	1	yes	characteristic
349	C₂×D₄×C₈₉	C₂⁴	1	2	yes	—
350	C₂×D₄×C₈₉	C₂⁴	1	1	yes	characteristic
351	C₂×D₄×C₈₉	C₂⁴	1	1	yes	characteristic
352	C₂²×C₄×C₈₉	—	2	2	no	—
353	C₂²×C₄×C₈₉	—	2	2	no	—
354	C₂²×C₄×C₈₉	—	2	1	no	—
355	C₂²×C₄×C₈₉	—	2	1	no	—
356	C₂²×C₄×C₈₉	—	2	1	no	—
357	C₂²×C₄×C₈₉	—	2	2	no	—
358	C₂²×C₄×C₈₉	—	2	2	no	—
359	C₂²×C₄×C₈₉	—	2	2	no	—
360	C₂²×C₄×C₈₉	—	2	2	no	—
361	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
362	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
363	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
364	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
365	Q₁₆×C₈₉	—	4	2	no	—
366	SD₁₆×C₈₉	—	4	2	no	—
367	SD₁₆×C₈₉	—	4	2	no	—
368	SD₁₆×C₈₉	—	4	1	no	—
369	SD₁₆×C₈₉	—	4	1	no	—
370	D₈×C₈₉	—	4	1	no	—
371	D₈×C₈₉	—	4	1	no	—
372	D₈×C₈₉	—	4	2	no	—
373	M₁₆×C₈₉	—	4	1	no	—
374	M₁₆×C₈₉	—	4	1	no	—
375	M₁₆×C₈₉	—	4	2	no	—
376	C₂×C₈×C₈₉	—	4	2	no	—
377	C₂×C₈×C₈₉	C₂⁴	1	1	yes	characteristic
378	C₂×C₈×C₈₉	C₂⁴	1	2	yes	—
379	C₂×C₈×C₈₉	C₂⁴	1	1	yes	characteristic
380	C₂×C₈×C₈₉	C₂⁴	1	2	yes	—
381	C₂×C₈×C₈₉	C₂⁴	1	1	yes	characteristic
382	C₂×C₈×C₈₉	C₂⁴	1	1	yes	characteristic
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	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	2	no	—
391	C₄⋊C₄×C₈₉	—	2	2	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	1	no	—
396	C₄⋊C₄×C₈₉	—	2	1	no	—
397	C₄⋊C₄×C₈₉	—	2	1	no	—
398	C₄⋊C₄×C₈₉	—	2	2	no	—
399	C₄⋊C₄×C₈₉	—	2	2	no	—
400	C₄⋊C₄×C₈₉	—	2	1	no	—
401	C₄⋊C₄×C₈₉	—	2	2	no	—
402	C₄⋊C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
403	C₄⋊C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
404	C₄⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
405	C₄⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
406	C₄⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
407	C₄⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
408	C₄⋊C₄×C₈₉	C₂⁴	1	2	yes	—
409	C₄⋊C₄×C₈₉	C₂⁴	1	1	yes	characteristic
410	C₄⋊C₄×C₈₉	C₂⁴	1	2	yes	—
411	C₄⋊C₄×C₈₉	C₂⁴	1	1	yes	characteristic
412	C₄⋊C₄×C₈₉	C₂⁴	1	1	yes	characteristic
413	C₄⋊C₄×C₈₉	C₂⁴	1	1	yes	characteristic
414	C₂²⋊C₄×C₈₉	—	2	2	no	—
415	C₂²⋊C₄×C₈₉	—	2	1	no	—
416	C₂²⋊C₄×C₈₉	—	2	2	no	—
417	C₂²⋊C₄×C₈₉	—	2	2	no	—
418	C₂²⋊C₄×C₈₉	—	2	1	no	—
419	C₂²⋊C₄×C₈₉	—	2	2	no	—
420	C₂²⋊C₄×C₈₉	—	2	2	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	—	2	1	no	—
425	C₂²⋊C₄×C₈₉	—	2	2	no	—
426	C₂²⋊C₄×C₈₉	—	2	2	no	—
427	C₂²⋊C₄×C₈₉	—	2	2	no	—
428	C₂²⋊C₄×C₈₉	—	2	1	no	—
429	C₂²⋊C₄×C₈₉	—	2	1	no	—
430	C₂²⋊C₄×C₈₉	—	2	2	no	—
431	C₂²⋊C₄×C₈₉	—	2	1	no	—
432	C₂²⋊C₄×C₈₉	—	2	2	no	—
433	C₂²⋊C₄×C₈₉	—	2	1	no	—
434	C₂²⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
435	C₂²⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
436	C₂²⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
437	C₂²⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
438	C₂²⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
439	C₄²×C₈₉	—	2	2	no	—
440	C₄²×C₈₉	—	2	1	no	—
441	C₄²×C₈₉	—	2	2	no	—
442	C₄²×C₈₉	—	2	2	no	—
443	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
444	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
445	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
446	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
447	C₄²×C₈₉	C₂⁴	1	2	yes	—
448	C₂³×C₈₉	—	2	1	no	—
449	C₂³×C₈₉	—	2	1	no	—
450	C₂³×C₈₉	—	2	2	no	—
451	C₂³×C₈₉	—	2	1	no	—
452	C₂³×C₈₉	—	8	2	no	—
453	C₂³×C₈₉	—	8	2	no	—
454	C₂³×C₈₉	—	8	2	no	—
455	C₂³×C₈₉	C₂²×D₄	1	2	yes	—
456	C₂³×C₈₉	C₂²×D₄	1	1	yes	characteristic
457	Q₈×C₈₉	—	2	2	no	—
458	Q₈×C₈₉	—	2	1	no	—
459	Q₈×C₈₉	—	2	1	no	—
460	Q₈×C₈₉	—	2	2	no	—
461	Q₈×C₈₉	—	2	2	no	—
462	Q₈×C₈₉	—	8	1	no	—
463	Q₈×C₈₉	—	8	2	no	—
464	Q₈×C₈₉	—	8	1	no	—
465	Q₈×C₈₉	—	8	2	no	—
466	Q₈×C₈₉	—	8	1	no	—
467	D₄×C₈₉	—	2	2	no	—
468	D₄×C₈₉	—	2	1	no	—
469	D₄×C₈₉	—	2	1	no	—
470	D₄×C₈₉	—	2	1	no	—
471	D₄×C₈₉	—	2	2	no	—
472	D₄×C₈₉	—	2	1	no	—
473	D₄×C₈₉	—	2	1	no	—
474	D₄×C₈₉	—	2	2	no	—
475	D₄×C₈₉	—	2	1	no	—
476	D₄×C₈₉	—	4	2	no	—
477	D₄×C₈₉	—	4	2	no	—
478	D₄×C₈₉	—	4	2	no	—
479	D₄×C₈₉	—	8	1	no	—
480	D₄×C₈₉	—	8	1	no	—
481	D₄×C₈₉	—	8	2	no	—
482	D₄×C₈₉	—	8	2	no	—
483	D₄×C₈₉	—	8	1	no	—
484	D₄×C₈₉	—	8	2	no	—
485	D₄×C₈₉	—	8	2	no	—
486	D₄×C₈₉	—	8	2	no	—
487	D₄×C₈₉	—	8	2	no	—
488	D₄×C₈₉	—	8	2	no	—
489	D₄×C₈₉	—	8	1	no	—
490	D₄×C₈₉	—	8	1	no	—
491	C₂×C₄×C₈₉	—	2	2	no	—
492	C₂×C₄×C₈₉	—	2	2	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	1	no	—
497	C₂×C₄×C₈₉	—	2	1	no	—
498	C₂×C₄×C₈₉	—	2	1	no	—
499	C₂×C₄×C₈₉	—	2	2	no	—
500	C₂×C₄×C₈₉	—	2	2	no	—
501	C₂×C₄×C₈₉	—	2	1	no	—
502	C₂×C₄×C₈₉	—	2	1	no	—
503	C₂×C₄×C₈₉	—	2	2	no	—
504	C₂×C₄×C₈₉	—	4	1	no	—
505	C₂×C₄×C₈₉	—	4	4	no	—
506	C₂×C₄×C₈₉	—	4	2	no	—
507	C₂×C₄×C₈₉	—	4	2	no	—
508	C₂×C₄×C₈₉	—	4	2	no	—
509	C₂×C₄×C₈₉	—	8	2	no	—
510	C₂×C₄×C₈₉	—	8	2	no	—
511	C₂×C₄×C₈₉	—	8	2	no	—
512	C₂×C₄×C₈₉	—	8	2	no	—
513	C₂×C₄×C₈₉	—	8	2	no	—
514	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
515	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
516	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
517	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
518	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
519	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
520	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
521	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
522	C₂×C₄×C₈₉	C₂⁵	1	1	yes	characteristic
523	C₈×C₈₉	—	2	1	no	—
524	C₈×C₈₉	—	2	2	no	—
525	C₈×C₈₉	—	2	1	no	—
526	C₈×C₈₉	—	2	1	no	—
527	C₈×C₈₉	—	2	1	no	—
528	C₈×C₈₉	—	2	2	no	—
529	C₂²×C₈₉	—	2	1	no	—
530	C₂²×C₈₉	—	2	2	no	—
531	C₂²×C₈₉	—	2	1	no	—
532	C₂²×C₈₉	—	2	2	no	—
533	C₂²×C₈₉	—	2	1	no	—
534	C₂²×C₈₉	—	2	2	no	—
535	C₂²×C₈₉	—	4	1	no	—
536	C₂²×C₈₉	—	4	1	no	—
537	C₂²×C₈₉	—	4	2	no	—
538	C₂²×C₈₉	—	4	1	no	—
539	C₂²×C₈₉	—	4	1	no	—
540	C₂²×C₈₉	—	4	2	no	—
541	C₂²×C₈₉	—	4	1	no	—
542	C₂²×C₈₉	—	4	1	no	—
543	C₂²×C₈₉	—	4	1	no	—
544	C₂²×C₈₉	—	4	1	no	—
545	C₂²×C₈₉	—	4	1	no	—
546	C₂²×C₈₉	—	4	2	no	—
547	C₂²×C₈₉	—	16	4	no	—
548	C₂²×C₈₉	C₂³×D₄	1	1	yes	characteristic
549	C₄×C₈₉	—	2	1	no	—
550	C₄×C₈₉	—	2	1	no	—
551	C₄×C₈₉	—	2	2	no	—
552	C₄×C₈₉	—	2	1	no	—
553	C₄×C₈₉	—	2	2	no	—
554	C₄×C₈₉	—	2	1	no	—
555	C₄×C₈₉	—	2	2	no	—
556	C₄×C₈₉	—	4	2	no	—
557	C₄×C₈₉	—	4	2	no	—
558	C₄×C₈₉	—	4	1	no	—
559	C₄×C₈₉	—	4	2	no	—
560	C₄×C₈₉	—	4	1	no	—
561	C₄×C₈₉	—	4	1	no	—
562	C₄×C₈₉	—	4	1	no	—
563	C₄×C₈₉	—	4	1	no	—
564	C₄×C₈₉	#577	1	2	yes	—
565	C₄×C₈₉	#585	1	1	yes	characteristic
566	C₄×C₈₉	#585	1	1	yes	characteristic
567	#62617	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
568	C₂×C₈₉	—	4	1	no	—
569	C₂×C₈₉	—	4	2	no	—
570	C₂×C₈₉	—	8	1	no	—
571	C₂×C₈₉	—	8	1	no	—
572	C₂×C₈₉	—	8	2	no	—
573	C₂×C₈₉	—	8	1	no	—
574	C₂×C₈₉	#3500	1	1	yes	characteristic
575	C₂×C₈₉	C₂×#577	1	1	yes	characteristic
576	C₂×C₈₉	#3585	1	1	yes	characteristic
577	#3546	C₂×C₈₉	1	1	yes	characteristic, complemented
578	#3544	C₂×C₈₉	1	1	yes	characteristic, complemented
579	#3369	C₂×C₈₉	1	1	yes	characteristic, complemented
580	#3366	C₂×C₈₉	1	1	yes	characteristic, complemented
581	#3362	C₂×C₈₉	1	1	yes	characteristic, complemented
582	#3360	C₂×C₈₉	1	1	yes	characteristic, complemented
583	#3332	C₂×C₈₉	1	2	yes	complemented
584	#3331	C₂×C₈₉	1	1	yes	characteristic, complemented
585	#3325	C₂×C₈₉	1	1	yes	characteristic, complemented
586	#3323	C₂×C₈₉	1	2	yes	complemented
587	#3317	C₂×C₈₉	1	2	yes	complemented
588	#3306	C₂×C₈₉	1	2	yes	complemented
589	#3303	C₂×C₈₉	1	1	yes	characteristic, complemented
590	#3295	C₂×C₈₉	1	1	yes	characteristic, complemented
591	#3244	C₂×C₈₉	1	2	yes	complemented
592	#3227	C₂×C₈₉	1	1	yes	characteristic, complemented
593	#3224	C₂×C₈₉	1	2	yes	complemented
594	#3212	C₂×C₈₉	1	1	yes	characteristic, complemented
595	#3173	C₂×C₈₉	1	2	yes	complemented
596	#3171	C₂×C₈₉	1	1	yes	characteristic, complemented
597	#3141	C₂×C₈₉	1	1	yes	characteristic, complemented
598	#3136	C₂×C₈₉	1	2	yes	complemented
599	#2969	C₂×C₈₉	1	1	yes	characteristic, complemented
600	C₈₉	#62617	1	1	yes	characteristic, direct product factor, Sylow
601	#563	—	2	2	no	—
602	#560	—	2	2	no	—
603	Q₈²	C₂²×C₈₉	1	1	yes	characteristic, complemented
604	#556	C₂²×C₈₉	1	1	yes	characteristic
605	#555	C₂²×C₈₉	1	1	yes	characteristic
606	#554	C₂²×C₈₉	1	1	yes	characteristic
607	#554	C₂²×C₈₉	1	1	yes	characteristic, complemented
608	#553	—	2	1	no	—
609	#552	—	2	1	no	—
610	#552	C₂²×C₈₉	1	2	yes	complemented
611	#550	C₂²×C₈₉	1	2	yes	—
612	#550	C₂²×C₈₉	1	1	yes	characteristic
613	#547	—	2	1	no	—
614	#547	C₂²×C₈₉	1	1	yes	characteristic
615	#547	C₂²×C₈₉	1	2	yes	complemented
616	#546	—	2	1	no	—
617	#546	C₂²×C₈₉	1	2	yes	—
618	D₄²	C₂²×C₈₉	1	1	yes	characteristic
619	#544	—	2	1	no	—
620	#544	C₂²×C₈₉	1	2	yes	complemented
621	#542	—	2	1	no	—
622	#542	C₂²×C₈₉	1	2	yes	—
623	#542	C₂²×C₈₉	1	2	yes	complemented
624	#538	—	2	2	no	—
625	#537	—	2	1	no	—
626	#536	—	2	2	no	—
627	#535	—	2	1	no	—
628	#535	C₂²×C₈₉	1	2	yes	—
629	#532	C₂²×C₈₉	1	1	yes	characteristic
630	#532	C₂²×C₈₉	1	1	yes	characteristic
631	C₂×C₄⋊Q₈	C₂²×C₈₉	1	1	yes	characteristic, complemented
632	#529	C₂²×C₈₉	1	1	yes	characteristic
633	#529	C₂²×C₈₉	1	1	yes	characteristic, complemented
634	#501	C₂²×C₈₉	1	1	yes	characteristic, complemented
635	#498	C₂²×C₈₉	1	2	yes	complemented
636	#496	C₂²×C₈₉	1	1	yes	characteristic
637	#495	C₂²×C₈₉	1	2	yes	complemented
638	#490	C₂²×C₈₉	1	1	yes	characteristic
639	#490	C₂²×C₈₉	1	2	yes	complemented
640	#489	C₂²×C₈₉	1	2	yes	—
641	#489	C₂²×C₈₉	1	2	yes	complemented
642	#489	C₂²×C₈₉	1	2	yes	complemented
643	#489	C₂²×C₈₉	1	1	yes	characteristic, complemented
644	#488	C₂²×C₈₉	1	2	yes	—
645	#488	C₂²×C₈₉	1	2	yes	complemented
646	#487	C₂²×C₈₉	1	1	yes	characteristic, complemented
647	#487	C₂²×C₈₉	1	1	yes	characteristic, complemented
648	#486	C₂²×C₈₉	1	1	yes	characteristic
649	#486	C₂²×C₈₉	1	1	yes	characteristic
650	#486	C₂²×C₈₉	1	2	yes	—
651	#486	C₂²×C₈₉	1	2	yes	complemented
652	#485	C₂²×C₈₉	1	2	yes	complemented
653	#483	C₂²×C₈₉	1	2	yes	complemented
654	#482	C₂²×C₈₉	1	2	yes	—
655	#481	C₂²×C₈₉	1	2	yes	—
656	#481	C₂²×C₈₉	1	2	yes	—
657	#481	C₂²×C₈₉	1	2	yes	complemented
658	#479	C₂²×C₈₉	1	2	yes	complemented
659	#478	C₂²×C₈₉	1	2	yes	complemented
660	#476	C₂²×C₈₉	1	1	yes	characteristic
661	#476	C₂²×C₈₉	1	1	yes	characteristic
662	#476	C₂²×C₈₉	1	1	yes	characteristic, complemented
663	#476	C₂²×C₈₉	1	1	yes	characteristic, complemented
664	#476	C₂²×C₈₉	1	2	yes	complemented
665	#475	C₂²×C₈₉	1	2	yes	complemented
666	#470	C₂²×C₈₉	1	2	yes	complemented
667	#469	C₂²×C₈₉	1	2	yes	—
668	#469	C₂²×C₈₉	1	1	yes	characteristic
669	#469	C₂²×C₈₉	1	1	yes	characteristic, complemented
670	#468	C₂²×C₈₉	1	1	yes	characteristic
671	#468	C₂²×C₈₉	1	1	yes	characteristic, complemented
672	#465	C₂²×C₈₉	1	2	yes	—
673	#465	C₂²×C₈₉	1	2	yes	complemented
674	#464	C₂²×C₈₉	1	2	yes	—
675	#463	C₂²×C₈₉	1	2	yes	—
676	#462	C₂²×C₈₉	1	1	yes	characteristic, complemented
677	#461	C₂²×C₈₉	1	1	yes	characteristic, complemented
678	#460	C₂²×C₈₉	1	1	yes	characteristic
679	#460	C₂²×C₈₉	1	2	yes	complemented
680	#459	C₂²×C₈₉	1	1	yes	characteristic
681	#459	C₂²×C₈₉	1	2	yes	complemented
682	#452	C₂²×C₈₉	1	2	yes	complemented
683	#452	C₂²×C₈₉	1	2	yes	complemented
684	#450	C₂²×C₈₉	1	2	yes	—
685	#449	C₂²×C₈₉	1	2	yes	complemented
686	#449	C₂²×C₈₉	1	2	yes	complemented
687	#447	C₂²×C₈₉	1	2	yes	—
688	#446	C₂²×C₈₉	1	1	yes	characteristic, complemented
689	C₈×Q₈	C₂²×C₈₉	1	1	yes	characteristic, complemented
690	#442	C₂²×C₈₉	1	2	yes	complemented
691	#441	C₂²×C₈₉	1	2	yes	complemented
692	C₄×SD₁₆	C₂²×C₈₉	1	1	yes	characteristic
693	C₄×SD₁₆	C₂²×C₈₉	1	1	yes	characteristic, complemented
694	C₄×SD₁₆	C₂²×C₈₉	1	2	yes	complemented
695	C₄×SD₁₆	C₂²×C₈₉	1	2	yes	complemented
696	C₄×D₈	C₂²×C₈₉	1	1	yes	characteristic
697	C₄×D₈	C₂²×C₈₉	1	1	yes	characteristic, complemented
698	#436	C₂²×C₈₉	1	1	yes	characteristic
699	#436	C₂²×C₈₉	1	2	yes	complemented
700	#435	C₂²×C₈₉	1	2	yes	complemented
701	C₈×D₄	C₂²×C₈₉	1	1	yes	characteristic
702	#433	C₂²×C₈₉	1	2	yes	complemented
703	#431	C₂²×C₈₉	1	1	yes	characteristic, complemented
704	#418	C₂²×C₈₉	1	2	yes	—
705	#417	C₂²×C₈₉	1	2	yes	complemented
706	#417	C₂²×C₈₉	1	2	yes	complemented
707	#417	C₂²×C₈₉	1	2	yes	complemented
708	#416	C₂²×C₈₉	1	2	yes	complemented
709	C₂×#102	C₂²×C₈₉	1	2	yes	—
710	#405	C₂²×C₈₉	1	2	yes	complemented
711	C₄×M₁₆	C₂²×C₈₉	1	1	yes	characteristic, complemented
712	C₂×#41	—	2	1	no	—
713	C₂×#41	—	2	2	no	—
714	C₂×#41	—	2	1	no	—
715	C₂×#41	C₂³×C₈₉	1	2	yes	—
716	C₂×#41	C₂³×C₈₉	1	2	yes	—
717	C₂²×Q₈	—	2	1	no	—
718	C₂²×D₄	—	2	1	no	—
719	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
720	C₂×Q₁₆	C₂³×C₈₉	1	2	yes	—
721	C₂×SD₁₆	C₂³×C₈₉	1	1	yes	characteristic
722	C₂×SD₁₆	C₂³×C₈₉	1	2	yes	—
723	C₂×SD₁₆	C₂³×C₈₉	1	2	yes	—
724	C₂×SD₁₆	C₂³×C₈₉	1	1	yes	characteristic
725	C₂×D₈	C₂³×C₈₉	1	1	yes	characteristic
726	C₂×D₈	C₂³×C₈₉	1	1	yes	characteristic
727	C₂×D₈	C₂³×C₈₉	1	2	yes	—
728	C₂×M₁₆	C₂³×C₈₉	1	1	yes	characteristic
729	C₂×M₁₆	C₂³×C₈₉	1	1	yes	characteristic
730	C₂×M₁₆	C₂³×C₈₉	1	2	yes	—
731	C₂²×C₈	C₂³×C₈₉	1	2	yes	—
732	C₄⋊Q₈	—	2	2	no	—
733	C₄⋊Q₈	—	2	2	no	—
734	C₄⋊Q₈	—	2	1	no	—
735	C₄⋊Q₈	—	2	1	no	—
736	C₄⋊Q₈	—	2	1	no	—
737	C₄⋊Q₈	C₂³×C₈₉	1	1	yes	characteristic
738	C₄⋊Q₈	C₂³×C₈₉	1	2	yes	—
739	C₄⋊Q₈	C₂³×C₈₉	1	1	yes	characteristic
740	C₄⋊Q₈	C₂³×C₈₉	1	1	yes	characteristic
741	C₄⋊Q₈	C₂³×C₈₉	1	1	yes	characteristic
742	C₄⋊Q₈	C₂³×C₈₉	1	2	yes	—
743	#127	—	2	2	no	—
744	#127	C₂³×C₈₉	1	1	yes	characteristic
745	#127	C₂³×C₈₉	1	1	yes	characteristic
746	#127	C₂³×C₈₉	1	2	yes	—
747	#126	—	2	2	no	—
748	#126	—	2	2	no	—
749	#126	—	2	2	no	—
750	#126	—	2	2	no	—
751	#126	—	2	1	no	—
752	#126	D₄×C₈₉	1	2	yes	—
753	#125	—	2	1	no	—
754	#125	—	2	2	no	—
755	#125	—	2	2	no	—
756	#125	D₄×C₈₉	1	1	yes	characteristic
757	#125	C₂³×C₈₉	1	1	yes	characteristic
758	#125	C₂³×C₈₉	1	2	yes	—
759	#124	—	2	2	no	—
760	#124	—	2	2	no	—
761	#124	—	2	2	no	—
762	#124	—	2	1	no	—
763	#124	D₄×C₈₉	1	1	yes	characteristic
764	#124	C₂³×C₈₉	1	1	yes	characteristic
765	#124	C₂³×C₈₉	1	2	yes	—
766	#124	C₂³×C₈₉	1	2	yes	—
767	#123	—	2	2	no	—
768	#123	—	2	1	no	—
769	#123	—	2	2	no	—
770	#123	—	2	2	no	—
771	#123	—	2	2	no	—
772	#123	—	2	2	no	—
773	#123	—	2	2	no	—
774	#123	—	2	2	no	—
775	#123	D₄×C₈₉	1	2	yes	—
776	C₂²⋊Q₈	—	2	1	no	—
777	C₂²⋊Q₈	—	2	1	no	—
778	C₂²⋊Q₈	—	2	2	no	—
779	C₂²⋊Q₈	—	2	2	no	—
780	C₂²⋊Q₈	—	2	2	no	—
781	C₂²⋊Q₈	—	2	2	no	—
782	C₂²⋊Q₈	—	2	2	no	—
783	C₂²⋊Q₈	—	2	2	no	—
784	C₂²⋊Q₈	—	2	2	no	—
785	C₂²⋊Q₈	D₄×C₈₉	1	1	yes	characteristic
786	C₂²⋊Q₈	C₂³×C₈₉	1	1	yes	characteristic
787	C₂²⋊Q₈	C₂³×C₈₉	1	2	yes	—
788	C₂²⋊Q₈	C₂³×C₈₉	1	2	yes	—
789	#121	—	2	1	no	—
790	#121	—	2	1	no	—
791	#121	—	2	1	no	—
792	#121	—	2	1	no	—
793	#121	—	2	1	no	—
794	#121	—	2	1	no	—
795	#121	—	2	2	no	—
796	#121	—	2	2	no	—
797	#121	—	2	1	no	—
798	#121	—	2	2	no	—
799	#121	—	2	2	no	—
800	#121	—	2	2	no	—
801	#121	—	2	2	no	—
802	#121	D₄×C₈₉	1	1	yes	characteristic
803	#121	C₂³×C₈₉	1	1	yes	characteristic
804	#121	C₂³×C₈₉	1	1	yes	characteristic
805	#121	C₂³×C₈₉	1	1	yes	characteristic
806	#121	C₂³×C₈₉	1	2	yes	—
807	#121	C₂³×C₈₉	1	2	yes	—
808	#120	—	2	2	no	—
809	#120	—	2	2	no	—
810	#120	—	2	2	no	—
811	#120	—	2	2	no	—
812	C₄×Q₈	—	2	1	no	—
813	C₄×Q₈	C₂³×C₈₉	1	1	yes	characteristic
814	C₄×Q₈	C₂³×C₈₉	1	2	yes	—
815	C₄×Q₈	C₂³×C₈₉	1	2	yes	—
816	C₄×Q₈	C₂³×C₈₉	1	1	yes	characteristic
817	C₄×D₄	—	2	1	no	—
818	C₄×D₄	—	2	1	no	—
819	C₄×D₄	—	2	2	no	—
820	C₄×D₄	—	2	1	no	—
821	C₄×D₄	—	2	1	no	—
822	C₄×D₄	—	2	1	no	—
823	C₄×D₄	C₂³×C₈₉	1	1	yes	characteristic
824	C₄×D₄	C₂³×C₈₉	1	1	yes	characteristic
825	C₄×D₄	C₂³×C₈₉	1	1	yes	characteristic
826	C₄×D₄	C₂³×C₈₉	1	2	yes	—
827	C₄×D₄	C₂³×C₈₉	1	2	yes	—
828	C₄×D₄	C₂³×C₈₉	1	1	yes	characteristic
829	C₄×D₄	C₂³×C₈₉	1	2	yes	—
830	#117	—	2	1	no	—
831	#117	—	2	1	no	—
832	#117	—	2	2	no	—
833	#117	—	2	1	no	—
834	#117	C₂³×C₈₉	1	2	yes	—
835	#117	C₂³×C₈₉	1	2	yes	—
836	C₂×C₄⋊C₄	—	2	1	no	—
837	C₂×C₄⋊C₄	—	2	1	no	—
838	C₂×C₄⋊C₄	—	2	1	no	—
839	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
840	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
841	C₂×C₂²⋊C₄	—	2	2	no	—
842	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
843	#107	C₂³×C₈₉	1	1	yes	characteristic
844	#107	C₂³×C₈₉	1	1	yes	characteristic
845	#106	C₂³×C₈₉	1	1	yes	characteristic
846	#106	C₂³×C₈₉	1	2	yes	—
847	#106	C₂³×C₈₉	1	2	yes	—
848	#106	C₂³×C₈₉	1	1	yes	characteristic
849	#106	C₂³×C₈₉	1	2	yes	—
850	#106	C₂³×C₈₉	1	2	yes	—
851	C₄⋊C₈	C₂³×C₈₉	1	1	yes	characteristic
852	C₄⋊C₈	C₂³×C₈₉	1	1	yes	characteristic
853	C₄⋊C₈	C₂³×C₈₉	1	2	yes	—
854	C₄⋊C₈	C₂³×C₈₉	1	2	yes	—
855	#103	C₂³×C₈₉	1	2	yes	—
856	#103	C₂³×C₈₉	1	2	yes	—
857	#103	C₂³×C₈₉	1	2	yes	—
858	#103	C₂³×C₈₉	1	2	yes	—
859	#103	C₂³×C₈₉	1	2	yes	—
860	#103	C₂³×C₈₉	1	2	yes	—
861	#103	C₂³×C₈₉	1	1	yes	characteristic
862	#103	C₂³×C₈₉	1	1	yes	characteristic
863	#102	C₂³×C₈₉	1	1	yes	characteristic
864	#102	C₂³×C₈₉	1	2	yes	—
865	#102	C₂³×C₈₉	1	2	yes	—
866	#102	C₂³×C₈₉	1	2	yes	—
867	#102	C₂³×C₈₉	1	1	yes	characteristic
868	#102	C₂³×C₈₉	1	2	yes	—
869	#102	C₂³×C₈₉	1	1	yes	characteristic
870	#102	C₂³×C₈₉	1	2	yes	—
871	#102	C₂³×C₈₉	1	2	yes	—
872	#102	C₂³×C₈₉	1	2	yes	—
873	#102	C₂³×C₈₉	1	2	yes	—
874	#102	C₂³×C₈₉	1	1	yes	characteristic
875	#102	C₂³×C₈₉	1	2	yes	—
876	#102	C₂³×C₈₉	1	2	yes	—
877	#102	C₂³×C₈₉	1	1	yes	characteristic
878	#102	C₂³×C₈₉	1	1	yes	characteristic
879	C₂²⋊C₈	C₂³×C₈₉	1	2	yes	—
880	C₂²⋊C₈	C₂³×C₈₉	1	2	yes	—
881	C₂²⋊C₈	C₂³×C₈₉	1	2	yes	—
882	#97	C₂³×C₈₉	1	1	yes	characteristic
883	#97	C₂³×C₈₉	1	1	yes	characteristic
884	#97	C₂³×C₈₉	1	2	yes	—
885	C₄×C₈	C₂³×C₈₉	1	1	yes	characteristic
886	C₄×C₈	C₂³×C₈₉	1	1	yes	characteristic
887	C₄×C₈	C₂³×C₈₉	1	2	yes	—
888	C₄×C₈	C₂³×C₈₉	1	2	yes	—
889	C₂⁴	—	2	2	no	—
890	#41	—	4	2	no	—
891	#41	—	4	2	no	—
892	#41	—	4	2	no	—
893	#41	—	4	2	no	—
894	#41	—	8	2	no	—
895	#41	—	8	4	no	—
896	#41	—	8	2	no	—
897	C₂×Q₈	—	2	1	no	—
898	C₂×Q₈	—	2	1	no	—
899	C₂×Q₈	—	2	2	no	—
900	C₂×Q₈	—	2	2	no	—
901	C₂×Q₈	—	2	1	no	—
902	C₂×Q₈	—	8	2	no	—
903	C₂×Q₈	C₂×D₄×C₈₉	1	1	yes	characteristic
904	C₂×Q₈	C₂⁴×C₈₉	1	2	yes	—
905	C₂×Q₈	C₂⁴×C₈₉	1	1	yes	characteristic
906	C₂×D₄	—	2	1	no	—
907	C₂×D₄	—	2	1	no	—
908	C₂×D₄	—	2	2	no	—
909	C₂×D₄	—	2	2	no	—
910	C₂×D₄	—	2	2	no	—
911	C₂×D₄	—	2	1	no	—
912	C₂×D₄	—	2	2	no	—
913	C₂×D₄	—	2	1	no	—
914	C₂×D₄	—	2	1	no	—
915	C₂×D₄	—	2	1	no	—
916	C₂×D₄	—	2	2	no	—
917	C₂×D₄	—	2	1	no	—
918	C₂×D₄	—	2	2	no	—
919	C₂×D₄	—	2	2	no	—
920	C₂×D₄	—	4	2	no	—
921	C₂×D₄	—	4	2	no	—
922	C₂×D₄	—	8	2	no	—
923	C₂×D₄	C₂×D₄×C₈₉	1	1	yes	characteristic
924	C₂×D₄	C₂×D₄×C₈₉	1	2	yes	—
925	C₂×D₄	C₂⁴×C₈₉	1	1	yes	characteristic
926	C₂×D₄	C₂⁴×C₈₉	1	2	yes	—
927	C₂×D₄	C₂⁴×C₈₉	1	1	yes	characteristic
928	C₂×D₄	C₂⁴×C₈₉	1	1	yes	characteristic
929	C₂²×C₄	—	2	2	no	—
930	C₂²×C₄	—	2	2	no	—
931	C₂²×C₄	—	2	1	no	—
932	C₂²×C₄	—	2	1	no	—
933	C₂²×C₄	—	2	1	no	—
934	C₂²×C₄	—	2	2	no	—
935	C₂²×C₄	—	2	2	no	—
936	C₂²×C₄	—	2	2	no	—
937	C₂²×C₄	—	2	2	no	—
938	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
939	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
940	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
941	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
942	Q₁₆	—	4	2	no	—
943	SD₁₆	—	4	2	no	—
944	SD₁₆	—	4	2	no	—
945	SD₁₆	—	4	1	no	—
946	SD₁₆	—	4	1	no	—
947	D₈	—	4	1	no	—
948	D₈	—	4	1	no	—
949	D₈	—	4	2	no	—
950	M₁₆	—	4	1	no	—
951	M₁₆	—	4	1	no	—
952	M₁₆	—	4	2	no	—
953	C₂×C₈	—	4	2	no	—
954	C₂×C₈	C₂⁴×C₈₉	1	1	yes	characteristic
955	C₂×C₈	C₂⁴×C₈₉	1	2	yes	—
956	C₂×C₈	C₂⁴×C₈₉	1	1	yes	characteristic
957	C₂×C₈	C₂⁴×C₈₉	1	2	yes	—
958	C₂×C₈	C₂⁴×C₈₉	1	1	yes	characteristic
959	C₂×C₈	C₂⁴×C₈₉	1	1	yes	characteristic
960	C₄⋊C₄	—	2	1	no	—
961	C₄⋊C₄	—	2	1	no	—
962	C₄⋊C₄	—	2	1	no	—
963	C₄⋊C₄	—	2	2	no	—
964	C₄⋊C₄	—	2	2	no	—
965	C₄⋊C₄	—	2	2	no	—
966	C₄⋊C₄	—	2	2	no	—
967	C₄⋊C₄	—	2	2	no	—
968	C₄⋊C₄	—	2	2	no	—
969	C₄⋊C₄	—	2	2	no	—
970	C₄⋊C₄	—	2	1	no	—
971	C₄⋊C₄	—	2	1	no	—
972	C₄⋊C₄	—	2	1	no	—
973	C₄⋊C₄	—	2	1	no	—
974	C₄⋊C₄	—	2	1	no	—
975	C₄⋊C₄	—	2	2	no	—
976	C₄⋊C₄	—	2	2	no	—
977	C₄⋊C₄	—	2	1	no	—
978	C₄⋊C₄	—	2	2	no	—
979	C₄⋊C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
980	C₄⋊C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
981	C₄⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
982	C₄⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
983	C₄⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
984	C₄⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
985	C₄⋊C₄	C₂⁴×C₈₉	1	2	yes	—
986	C₄⋊C₄	C₂⁴×C₈₉	1	1	yes	characteristic
987	C₄⋊C₄	C₂⁴×C₈₉	1	2	yes	—
988	C₄⋊C₄	C₂⁴×C₈₉	1	1	yes	characteristic
989	C₄⋊C₄	C₂⁴×C₈₉	1	1	yes	characteristic
990	C₄⋊C₄	C₂⁴×C₈₉	1	1	yes	characteristic
991	C₂²⋊C₄	—	2	2	no	—
992	C₂²⋊C₄	—	2	1	no	—
993	C₂²⋊C₄	—	2	2	no	—
994	C₂²⋊C₄	—	2	2	no	—
995	C₂²⋊C₄	—	2	1	no	—
996	C₂²⋊C₄	—	2	2	no	—
997	C₂²⋊C₄	—	2	2	no	—
998	C₂²⋊C₄	—	2	1	no	—
999	C₂²⋊C₄	—	2	2	no	—
1000	C₂²⋊C₄	—	2	1	no	—
1001	C₂²⋊C₄	—	2	1	no	—
1002	C₂²⋊C₄	—	2	2	no	—
1003	C₂²⋊C₄	—	2	2	no	—
1004	C₂²⋊C₄	—	2	2	no	—
1005	C₂²⋊C₄	—	2	1	no	—
1006	C₂²⋊C₄	—	2	1	no	—
1007	C₂²⋊C₄	—	2	2	no	—
1008	C₂²⋊C₄	—	2	1	no	—
1009	C₂²⋊C₄	—	2	2	no	—
1010	C₂²⋊C₄	—	2	1	no	—
1011	C₂²⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
1012	C₂²⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
1013	C₂²⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
1014	C₂²⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
1015	C₂²⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
1016	C₄²	—	2	2	no	—
1017	C₄²	—	2	1	no	—
1018	C₄²	—	2	2	no	—
1019	C₄²	—	2	2	no	—
1020	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
1021	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
1022	C₄²	C₂⁴×C₈₉	1	1	yes	characteristic
1023	C₄²	C₂⁴×C₈₉	1	1	yes	characteristic
1024	C₄²	C₂⁴×C₈₉	1	2	yes	—
1025	C₂³	—	2	1	no	—
1026	C₂³	—	2	1	no	—
1027	C₂³	—	2	2	no	—
1028	C₂³	—	2	1	no	—
1029	C₂³	—	8	2	no	—
1030	C₂³	—	8	2	no	—
1031	C₂³	—	8	2	no	—
1032	C₂³	C₂²×D₄×C₈₉	1	2	yes	—
1033	C₂³	C₂²×D₄×C₈₉	1	1	yes	characteristic
1034	Q₈	—	2	2	no	—
1035	Q₈	—	2	1	no	—
1036	Q₈	—	2	1	no	—
1037	Q₈	—	2	2	no	—
1038	Q₈	—	2	2	no	—
1039	Q₈	—	8	1	no	—
1040	Q₈	—	8	2	no	—
1041	Q₈	—	8	1	no	—
1042	Q₈	—	8	1	no	—
1043	Q₈	—	8	2	no	—
1044	D₄	—	2	2	no	—
1045	D₄	—	2	1	no	—
1046	D₄	—	2	1	no	—
1047	D₄	—	2	1	no	—
1048	D₄	—	2	2	no	—
1049	D₄	—	2	1	no	—
1050	D₄	—	2	1	no	—
1051	D₄	—	2	2	no	—
1052	D₄	—	2	1	no	—
1053	D₄	—	4	2	no	—
1054	D₄	—	4	2	no	—
1055	D₄	—	4	2	no	—
1056	D₄	—	8	1	no	—
1057	D₄	—	8	1	no	—
1058	D₄	—	8	2	no	—
1059	D₄	—	8	2	no	—
1060	D₄	—	8	1	no	—
1061	D₄	—	8	2	no	—
1062	D₄	—	8	2	no	—
1063	D₄	—	8	2	no	—
1064	D₄	—	8	2	no	—
1065	D₄	—	8	1	no	—
1066	D₄	—	8	1	no	—
1067	D₄	—	8	2	no	—
1068	C₂×C₄	—	2	2	no	—
1069	C₂×C₄	—	2	2	no	—
1070	C₂×C₄	—	2	2	no	—
1071	C₂×C₄	—	2	1	no	—
1072	C₂×C₄	—	2	1	no	—
1073	C₂×C₄	—	2	1	no	—
1074	C₂×C₄	—	2	1	no	—
1075	C₂×C₄	—	2	1	no	—
1076	C₂×C₄	—	2	2	no	—
1077	C₂×C₄	—	2	2	no	—
1078	C₂×C₄	—	2	1	no	—
1079	C₂×C₄	—	2	1	no	—
1080	C₂×C₄	—	2	2	no	—
1081	C₂×C₄	—	4	1	no	—
1082	C₂×C₄	—	4	4	no	—
1083	C₂×C₄	—	4	2	no	—
1084	C₂×C₄	—	4	2	no	—
1085	C₂×C₄	—	4	2	no	—
1086	C₂×C₄	—	8	2	no	—
1087	C₂×C₄	—	8	2	no	—
1088	C₂×C₄	—	8	2	no	—
1089	C₂×C₄	—	8	2	no	—
1090	C₂×C₄	—	8	2	no	—
1091	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
1092	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
1093	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
1094	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
1095	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
1096	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
1097	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
1098	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
1099	C₂×C₄	C₂⁵×C₈₉	1	1	yes	characteristic
1100	C₈	—	2	1	no	—
1101	C₈	—	2	2	no	—
1102	C₈	—	2	1	no	—
1103	C₈	—	2	1	no	—
1104	C₈	—	2	1	no	—
1105	C₈	—	2	2	no	—
1106	C₂²	—	2	1	no	—
1107	C₂²	—	2	2	no	—
1108	C₂²	—	2	1	no	—
1109	C₂²	—	2	2	no	—
1110	C₂²	—	2	1	no	—
1111	C₂²	—	2	2	no	—
1112	C₂²	—	4	1	no	—
1113	C₂²	—	4	1	no	—
1114	C₂²	—	4	1	no	—
1115	C₂²	—	4	2	no	—
1116	C₂²	—	4	1	no	—
1117	C₂²	—	4	1	no	—
1118	C₂²	—	4	2	no	—
1119	C₂²	—	4	1	no	—
1120	C₂²	—	4	1	no	—
1121	C₂²	—	4	2	no	—
1122	C₂²	—	4	1	no	—
1123	C₂²	—	4	1	no	—
1124	C₂²	—	16	4	no	—
1125	C₂²	C₂³×D₄×C₈₉	1	1	yes	characteristic
1126	C₄	—	2	1	no	—
1127	C₄	—	2	2	no	—
1128	C₄	—	2	1	no	—
1129	C₄	—	2	1	no	—
1130	C₄	—	2	2	no	—
1131	C₄	—	2	1	no	—
1132	C₄	—	2	2	no	—
1133	C₄	—	4	1	no	—
1134	C₄	—	4	1	no	—
1135	C₄	—	4	1	no	—
1136	C₄	—	4	2	no	—
1137	C₄	—	4	2	no	—
1138	C₄	—	4	1	no	—
1139	C₄	—	4	2	no	—
1140	C₄	—	4	1	no	—
1141	C₄	#577×C₈₉	1	2	yes	—
1142	C₄	#585×C₈₉	1	1	yes	characteristic
1143	C₄	#585×C₈₉	1	1	yes	characteristic
1144	C₂	—	4	1	no	—
1145	C₂	—	4	2	no	—
1146	C₂	—	8	1	no	—
1147	C₂	—	8	1	no	—
1148	C₂	—	8	2	no	—
1149	C₂	—	8	1	no	—
1150	C₂	C₈₉×#3500	1	1	yes	characteristic
1151	C₂	C₂×#577×C₈₉	1	1	yes	characteristic
1152	C₂	C₈₉×#3585	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. C₈₉×#3546	C₂	semidirect
2. C₈₉×#3544	C₂	semidirect
3. C₈₉×#3369	C₂	semidirect
4. C₈₉×#3366	C₂	semidirect
5. C₈₉×#3362	C₂	semidirect
6. C₈₉×#3360	C₂	semidirect
7. C₈₉×#3332	C₂	semidirect
8. C₈₉×#3331	C₂	semidirect
9. C₈₉×#3325	C₂	semidirect
10. C₈₉×#3323	C₂	semidirect
11. C₈₉×#3317	C₂	semidirect
12. C₈₉×#3306	C₂	semidirect
13. C₈₉×#3303	C₂	semidirect
14. C₈₉×#3295	C₂	semidirect
15. C₈₉×#3244	C₂	semidirect
16. C₈₉×#3227	C₂	semidirect
17. C₈₉×#3224	C₂	semidirect
18. C₈₉×#3212	C₂	semidirect
19. C₈₉×#3173	C₂	semidirect
20. C₈₉×#3171	C₂	semidirect
21. C₈₉×#3141	C₂	semidirect
22. C₈₉×#3136	C₂	semidirect
23. C₈₉×#2969	C₂	semidirect
26. Q₈²×C₈₉	C₂²	semidirect
30. #554×C₈₉	C₂²	semidirect
33. #552×C₈₉	C₂²	semidirect
38. #547×C₈₉	C₂²	semidirect
43. #544×C₈₉	C₂²	semidirect
46. #542×C₈₉	C₂²	semidirect
54. C₂×C₄⋊Q₈×C₈₉	C₂²	semidirect
56. #529×C₈₉	C₂²	semidirect
57. #501×C₈₉	C₂²	semidirect
58. #498×C₈₉	C₂²	semidirect
60. #495×C₈₉	C₂²	semidirect
62. #490×C₈₉	C₂²	semidirect
64. #489×C₈₉	C₂²	semidirect
65. #489×C₈₉	C₂²	semidirect
66. #489×C₈₉	C₂²	semidirect
68. #488×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
80. #481×C₈₉	C₂²	semidirect
81. #479×C₈₉	C₂²	semidirect
82. #478×C₈₉	C₂²	semidirect
85. #476×C₈₉	C₂²	semidirect
86. #476×C₈₉	C₂²	semidirect
87. #476×C₈₉	C₂²	semidirect
88. #475×C₈₉	C₂²	semidirect
89. #470×C₈₉	C₂²	semidirect
92. #469×C₈₉	C₂²	semidirect
94. #468×C₈₉	C₂²	semidirect
96. #465×C₈₉	C₂²	semidirect
99. #462×C₈₉	C₂²	semidirect
100. #461×C₈₉	C₂²	semidirect
102. #460×C₈₉	C₂²	semidirect
104. #459×C₈₉	C₂²	semidirect
105. #452×C₈₉	C₂²	semidirect
106. #452×C₈₉	C₂²	semidirect
108. #449×C₈₉	C₂²	semidirect
109. #449×C₈₉	C₂²	semidirect
111. #446×C₈₉	C₂²	semidirect
112. C₈×Q₈×C₈₉	C₂²	semidirect
113. #442×C₈₉	C₂²	semidirect
114. #441×C₈₉	C₂²	semidirect
116. C₄×SD₁₆×C₈₉	C₂²	semidirect
117. C₄×SD₁₆×C₈₉	C₂²	semidirect
118. C₄×SD₁₆×C₈₉	C₂²	semidirect
120. C₄×D₈×C₈₉	C₂²	semidirect
122. #436×C₈₉	C₂²	semidirect
123. #435×C₈₉	C₂²	semidirect
125. #433×C₈₉	C₂²	semidirect
126. #431×C₈₉	C₂²	semidirect
128. #417×C₈₉	C₂²	semidirect
129. #417×C₈₉	C₂²	semidirect
130. #417×C₈₉	C₂²	semidirect
131. #416×C₈₉	C₂²	semidirect
133. #405×C₈₉	C₂²	semidirect
134. C₄×M₁₆×C₈₉	C₂²	semidirect
567. #62617	C₈₉	direct (N × H)
577. #3546	C₂×C₈₉	semidirect
578. #3544	C₂×C₈₉	semidirect
579. #3369	C₂×C₈₉	semidirect
580. #3366	C₂×C₈₉	semidirect
581. #3362	C₂×C₈₉	semidirect
582. #3360	C₂×C₈₉	semidirect
583. #3332	C₂×C₈₉	semidirect
584. #3331	C₂×C₈₉	semidirect
585. #3325	C₂×C₈₉	semidirect
586. #3323	C₂×C₈₉	semidirect
587. #3317	C₂×C₈₉	semidirect
588. #3306	C₂×C₈₉	semidirect
589. #3303	C₂×C₈₉	semidirect
590. #3295	C₂×C₈₉	semidirect
591. #3244	C₂×C₈₉	semidirect
592. #3227	C₂×C₈₉	semidirect
593. #3224	C₂×C₈₉	semidirect
594. #3212	C₂×C₈₉	semidirect
595. #3173	C₂×C₈₉	semidirect
596. #3171	C₂×C₈₉	semidirect
597. #3141	C₂×C₈₉	semidirect
598. #3136	C₂×C₈₉	semidirect
599. #2969	C₂×C₈₉	semidirect
600. C₈₉	#62617	direct (N × H)
603. Q₈²	C₂²×C₈₉	semidirect
607. #554	C₂²×C₈₉	semidirect
610. #552	C₂²×C₈₉	semidirect
615. #547	C₂²×C₈₉	semidirect
620. #544	C₂²×C₈₉	semidirect
623. #542	C₂²×C₈₉	semidirect
631. C₂×C₄⋊Q₈	C₂²×C₈₉	semidirect
633. #529	C₂²×C₈₉	semidirect
634. #501	C₂²×C₈₉	semidirect
635. #498	C₂²×C₈₉	semidirect
637. #495	C₂²×C₈₉	semidirect
639. #490	C₂²×C₈₉	semidirect
641. #489	C₂²×C₈₉	semidirect
642. #489	C₂²×C₈₉	semidirect
643. #489	C₂²×C₈₉	semidirect
645. #488	C₂²×C₈₉	semidirect
646. #487	C₂²×C₈₉	semidirect
647. #487	C₂²×C₈₉	semidirect
651. #486	C₂²×C₈₉	semidirect
652. #485	C₂²×C₈₉	semidirect
653. #483	C₂²×C₈₉	semidirect
657. #481	C₂²×C₈₉	semidirect
658. #479	C₂²×C₈₉	semidirect
659. #478	C₂²×C₈₉	semidirect
662. #476	C₂²×C₈₉	semidirect
663. #476	C₂²×C₈₉	semidirect
664. #476	C₂²×C₈₉	semidirect
665. #475	C₂²×C₈₉	semidirect
666. #470	C₂²×C₈₉	semidirect
669. #469	C₂²×C₈₉	semidirect
671. #468	C₂²×C₈₉	semidirect
673. #465	C₂²×C₈₉	semidirect
676. #462	C₂²×C₈₉	semidirect
677. #461	C₂²×C₈₉	semidirect
679. #460	C₂²×C₈₉	semidirect
681. #459	C₂²×C₈₉	semidirect
682. #452	C₂²×C₈₉	semidirect
683. #452	C₂²×C₈₉	semidirect
685. #449	C₂²×C₈₉	semidirect
686. #449	C₂²×C₈₉	semidirect
688. #446	C₂²×C₈₉	semidirect
689. C₈×Q₈	C₂²×C₈₉	semidirect
690. #442	C₂²×C₈₉	semidirect
691. #441	C₂²×C₈₉	semidirect
693. C₄×SD₁₆	C₂²×C₈₉	semidirect
694. C₄×SD₁₆	C₂²×C₈₉	semidirect
695. C₄×SD₁₆	C₂²×C₈₉	semidirect
697. C₄×D₈	C₂²×C₈₉	semidirect
699. #436	C₂²×C₈₉	semidirect
700. #435	C₂²×C₈₉	semidirect
702. #433	C₂²×C₈₉	semidirect
703. #431	C₂²×C₈₉	semidirect
705. #417	C₂²×C₈₉	semidirect
706. #417	C₂²×C₈₉	semidirect
707. #417	C₂²×C₈₉	semidirect
708. #416	C₂²×C₈₉	semidirect
710. #405	C₂²×C₈₉	semidirect
711. C₄×M₁₆	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×#3546	2
C₈₉×#3544	2
C₈₉×#3369	2
C₈₉×#3366	2
C₈₉×#3362	2
C₈₉×#3360	2
C₈₉×#3332	2
C₈₉×#3331	2
C₈₉×#3325	2
C₈₉×#3323	2
C₈₉×#3317	2
C₈₉×#3306	2
C₈₉×#3303	2
C₈₉×#3295	2
C₈₉×#3244	2
C₈₉×#3227	2
C₈₉×#3224	2
C₈₉×#3212	2
C₈₉×#3173	2
C₈₉×#3171	2
C₈₉×#3141	2
C₈₉×#3136	2
C₈₉×#2969	2
#62617	89

Subgroups — C89×#62617 #36440465

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#62617 #36440465