Subgroups — C₈₉×#61459 #36439307

Order 22784.

1900 conjugacy classes of subgroups.

The subgroup lattice has 1170 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈₉×#3483	C₂	1	1	yes	maximal, characteristic, complemented
2	C₈₉×#3475	C₂	1	1	yes	maximal, characteristic, complemented
3	C₈₉×#3397	C₂	1	1	yes	maximal, characteristic, complemented
4	C₈₉×#3385	C₂	1	1	yes	maximal, characteristic, complemented
5	C₈₉×#3369	C₂	1	1	yes	maximal, characteristic, complemented
6	C₈₉×#3366	C₂	1	1	yes	maximal, characteristic, complemented
7	C₈₉×#3348	C₂	1	2	yes	maximal, complemented
8	C₈₉×#3341	C₂	1	1	yes	maximal, characteristic, complemented
9	C₈₉×#3319	C₂	1	2	yes	maximal, complemented
10	C₈₉×#3317	C₂	1	2	yes	maximal, complemented
11	C₈₉×#3305	C₂	1	1	yes	maximal, characteristic, complemented
12	C₈₉×#3303	C₂	1	1	yes	maximal, characteristic, complemented
13	C₈₉×#3284	C₂	1	1	yes	maximal, characteristic, complemented
14	C₈₉×#3268	C₂	1	2	yes	maximal, complemented
15	C₈₉×#3182	C₂	1	1	yes	maximal, characteristic, complemented
16	C₈₉×#3180	C₂	1	2	yes	maximal, complemented
17	C₈₉×#3116	C₂	1	1	yes	maximal, characteristic, complemented
18	C₈₉×#3115	C₂	1	2	yes	maximal, complemented
19	C₈₉×#3111	C₂	1	2	yes	maximal, complemented
20	C₈₉×#3109	C₂	1	1	yes	maximal, characteristic, complemented
21	C₈₉×#2970	C₂	1	1	yes	maximal, characteristic, complemented
22	C₄×AGL(1,ℤ/8)×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
23	C₈₉×#2943	C₂	1	2	yes	maximal, complemented
24	C₂×AGL(1,ℤ/8)×C₈₉	C₂²	1	1	yes	characteristic
25	C₂×#135×C₈₉	C₂²	1	2	yes	—
26	Q₈²×C₈₉	C₂²	1	1	yes	characteristic, complemented
27	#556×C₈₉	C₂²	1	1	yes	characteristic
28	#555×C₈₉	—	2	2	no	—
29	#555×C₈₉	—	2	1	no	—
30	#555×C₈₉	C₂²	1	2	yes	—
31	#555×C₈₉	C₂²	1	1	yes	characteristic
32	#555×C₈₉	C₂²	1	1	yes	characteristic, complemented
33	#554×C₈₉	C₂²	1	1	yes	characteristic
34	#553×C₈₉	—	2	1	no	—
35	#552×C₈₉	—	2	1	no	—
36	#552×C₈₉	C₂²	1	2	yes	—
37	#551×C₈₉	—	2	2	no	—
38	#550×C₈₉	—	2	1	no	—
39	#550×C₈₉	C₂²	1	2	yes	—
40	#550×C₈₉	C₂²	1	1	yes	characteristic, complemented
41	#550×C₈₉	C₂²	1	1	yes	characteristic, complemented
42	#547×C₈₉	C₂²	1	1	yes	characteristic
43	#546×C₈₉	C₂²	1	2	yes	—
44	#533×C₈₉	C₂²	1	1	yes	characteristic
45	#532×C₈₉	—	2	1	no	—
46	#532×C₈₉	—	2	2	no	—
47	#532×C₈₉	C₂²	1	1	yes	characteristic
48	#532×C₈₉	C₂²	1	2	yes	complemented
49	#529×C₈₉	—	2	2	no	—
50	#529×C₈₉	C₂²	1	2	yes	—
51	#525×C₈₉	—	2	1	no	—
52	C₄×#41×C₈₉	—	2	1	no	—
53	C₄×#41×C₈₉	C₂²	1	2	yes	—
54	C₄×#41×C₈₉	C₂²	1	1	yes	characteristic
55	C₄×#41×C₈₉	C₂²	1	1	yes	characteristic
56	C₄×#41×C₈₉	C₂²	1	2	yes	complemented
57	C₂×C₄×D₄×C₈₉	C₂²	1	1	yes	characteristic
58	C₂×#117×C₈₉	—	2	1	no	—
59	#501×C₈₉	C₂²	1	2	yes	complemented
60	#500×C₈₉	C₂²	1	1	yes	characteristic, complemented
61	#496×C₈₉	C₂²	1	2	yes	—
62	#492×C₈₉	C₂²	1	1	yes	characteristic, complemented
63	#490×C₈₉	C₂²	1	2	yes	complemented
64	#489×C₈₉	C₂²	1	2	yes	—
65	#487×C₈₉	C₂²	1	1	yes	characteristic, complemented
66	#486×C₈₉	C₂²	1	1	yes	characteristic, complemented
67	#485×C₈₉	C₂²	1	2	yes	—
68	#485×C₈₉	C₂²	1	2	yes	complemented
69	#482×C₈₉	C₂²	1	2	yes	—
70	#482×C₈₉	C₂²	1	2	yes	complemented
71	#482×C₈₉	C₂²	1	2	yes	complemented
72	#481×C₈₉	C₂²	1	2	yes	—
73	#479×C₈₉	C₂²	1	2	yes	complemented
74	#478×C₈₉	C₂²	1	2	yes	complemented
75	#477×C₈₉	C₂²	1	1	yes	characteristic, complemented
76	#476×C₈₉	C₂²	1	1	yes	characteristic
77	#476×C₈₉	C₂²	1	1	yes	characteristic
78	#476×C₈₉	C₂²	1	1	yes	characteristic, complemented
79	#475×C₈₉	C₂²	1	2	yes	complemented
80	#474×C₈₉	C₂²	1	2	yes	—
81	#468×C₈₉	C₂²	1	2	yes	—
82	#468×C₈₉	C₂²	1	2	yes	—
83	#466×C₈₉	C₂²	1	2	yes	—
84	#466×C₈₉	C₂²	1	2	yes	—
85	#465×C₈₉	C₂²	1	2	yes	complemented
86	#465×C₈₉	C₂²	1	2	yes	complemented
87	#464×C₈₉	C₂²	1	2	yes	—
88	#463×C₈₉	C₂²	1	2	yes	—
89	#462×C₈₉	C₂²	1	1	yes	characteristic, complemented
90	#461×C₈₉	C₂²	1	1	yes	characteristic, complemented
91	#460×C₈₉	C₂²	1	2	yes	complemented
92	#459×C₈₉	C₂²	1	1	yes	characteristic
93	#459×C₈₉	C₂²	1	1	yes	characteristic
94	#459×C₈₉	C₂²	1	2	yes	—
95	#452×C₈₉	C₂²	1	2	yes	—
96	#452×C₈₉	C₂²	1	2	yes	complemented
97	#449×C₈₉	C₂²	1	2	yes	—
98	#449×C₈₉	C₂²	1	2	yes	—
99	#449×C₈₉	C₂²	1	2	yes	—
100	#447×C₈₉	C₂²	1	2	yes	—
101	#446×C₈₉	C₂²	1	1	yes	characteristic, complemented
102	#446×C₈₉	C₂²	1	1	yes	characteristic, complemented
103	#442×C₈₉	C₂²	1	2	yes	—
104	#442×C₈₉	C₂²	1	2	yes	—
105	#442×C₈₉	C₂²	1	2	yes	—
106	#442×C₈₉	C₂²	1	1	yes	characteristic
107	#442×C₈₉	C₂²	1	1	yes	characteristic
108	#441×C₈₉	C₂²	1	2	yes	complemented
109	#441×C₈₉	C₂²	1	2	yes	complemented
110	#440×C₈₉	C₂²	1	1	yes	characteristic
111	#440×C₈₉	C₂²	1	2	yes	—
112	#440×C₈₉	C₂²	1	1	yes	characteristic
113	#440×C₈₉	C₂²	1	2	yes	complemented
114	#440×C₈₉	C₂²	1	2	yes	complemented
115	#440×C₈₉	C₂²	1	2	yes	complemented
116	#440×C₈₉	C₂²	1	2	yes	complemented
117	C₄×SD₁₆×C₈₉	C₂²	1	1	yes	characteristic
118	C₄×SD₁₆×C₈₉	C₂²	1	1	yes	characteristic
119	C₄×D₈×C₈₉	C₂²	1	1	yes	characteristic
120	C₄×D₈×C₈₉	C₂²	1	1	yes	characteristic
121	#435×C₈₉	C₂²	1	2	yes	—
122	#435×C₈₉	C₂²	1	2	yes	—
123	C₈×D₄×C₈₉	C₂²	1	1	yes	characteristic, complemented
124	C₈×D₄×C₈₉	C₂²	1	1	yes	characteristic, complemented
125	#432×C₈₉	C₂²	1	1	yes	characteristic
126	#432×C₈₉	C₂²	1	2	yes	complemented
127	#428×C₈₉	C₂²	1	1	yes	characteristic
128	#427×C₈₉	C₂²	1	2	yes	complemented
129	#418×C₈₉	C₂²	1	1	yes	characteristic
130	#417×C₈₉	C₂²	1	1	yes	characteristic
131	#416×C₈₉	C₂²	1	2	yes	—
132	#416×C₈₉	C₂²	1	2	yes	complemented
133	C₄×M₁₆×C₈₉	C₂²	1	1	yes	characteristic
134	C₂×#97×C₈₉	C₂²	1	2	yes	complemented
135	C₂×#41×C₈₉	—	2	1	no	—
136	C₂×#41×C₈₉	—	2	1	no	—
137	C₂×#41×C₈₉	—	2	2	no	—
138	C₂×#41×C₈₉	D₄	1	1	yes	characteristic
139	C₂×#41×C₈₉	C₂³	1	2	yes	—
140	C₂×#41×C₈₉	C₂³	1	2	yes	—
141	C₂×#41×C₈₉	C₂³	1	1	yes	characteristic
142	C₂²×D₄×C₈₉	C₂³	1	1	yes	characteristic
143	C₂³×C₄×C₈₉	—	2	1	no	—
144	AGL(1,ℤ/8)×C₈₉	—	2	4	no	—
145	#135×C₈₉	—	2	8	no	—
146	C₂×Q₁₆×C₈₉	C₂³	1	2	yes	—
147	C₂×SD₁₆×C₈₉	C₂³	1	1	yes	characteristic
148	C₂×SD₁₆×C₈₉	C₂³	1	2	yes	—
149	C₂×SD₁₆×C₈₉	C₂³	1	2	yes	—
150	C₂×SD₁₆×C₈₉	C₂³	1	2	yes	—
151	C₂×SD₁₆×C₈₉	C₂³	1	1	yes	characteristic
152	C₂×D₈×C₈₉	C₂³	1	1	yes	characteristic
153	C₂×D₈×C₈₉	C₂³	1	1	yes	characteristic
154	C₂×D₈×C₈₉	C₂³	1	2	yes	—
155	C₂×D₈×C₈₉	C₂³	1	2	yes	—
156	C₂×M₁₆×C₈₉	C₂³	1	1	yes	characteristic
157	C₂×M₁₆×C₈₉	C₂³	1	1	yes	characteristic
158	C₂²×C₈×C₈₉	C₂³	1	2	yes	—
159	C₂²×C₈×C₈₉	C₂³	1	2	yes	—
160	C₄⋊Q₈×C₈₉	—	2	1	no	—
161	C₄⋊Q₈×C₈₉	—	2	2	no	—
162	C₄⋊Q₈×C₈₉	C₂³	1	1	yes	characteristic
163	C₄⋊Q₈×C₈₉	C₂³	1	2	yes	—
164	C₄⋊Q₈×C₈₉	C₂³	1	1	yes	characteristic
165	C₄⋊Q₈×C₈₉	C₂³	1	1	yes	characteristic
166	#127×C₈₉	—	2	2	no	—
167	#127×C₈₉	—	2	1	no	—
168	#127×C₈₉	C₂³	1	1	yes	characteristic
169	#127×C₈₉	C₂³	1	2	yes	—
170	#126×C₈₉	—	2	2	no	—
171	#126×C₈₉	—	2	2	no	—
172	#126×C₈₉	—	2	2	no	—
173	#125×C₈₉	—	2	2	no	—
174	#125×C₈₉	—	2	1	no	—
175	#125×C₈₉	C₂³	1	2	yes	—
176	#124×C₈₉	—	2	2	no	—
177	#124×C₈₉	—	2	2	no	—
178	#124×C₈₉	—	2	2	no	—
179	#124×C₈₉	—	2	2	no	—
180	#124×C₈₉	—	2	1	no	—
181	#124×C₈₉	—	2	2	no	—
182	#124×C₈₉	C₂³	1	2	yes	—
183	#123×C₈₉	—	2	2	no	—
184	#123×C₈₉	—	2	2	no	—
185	#123×C₈₉	—	2	2	no	—
186	#123×C₈₉	—	2	2	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	2	no	—
191	C₂²⋊Q₈×C₈₉	C₂³	1	2	yes	—
192	C₂²⋊Q₈×C₈₉	C₂³	1	2	yes	—
193	#121×C₈₉	—	2	1	no	—
194	#121×C₈₉	—	2	1	no	—
195	#121×C₈₉	—	2	2	no	—
196	#121×C₈₉	—	2	1	no	—
197	#121×C₈₉	—	2	1	no	—
198	#121×C₈₉	—	2	2	no	—
199	#121×C₈₉	—	2	1	no	—
200	#121×C₈₉	—	2	2	no	—
201	#121×C₈₉	—	2	2	no	—
202	#121×C₈₉	—	2	2	no	—
203	#121×C₈₉	—	2	2	no	—
204	#121×C₈₉	—	2	2	no	—
205	#121×C₈₉	C₂³	1	2	yes	—
206	#121×C₈₉	C₂³	1	2	yes	—
207	#121×C₈₉	C₂³	1	2	yes	—
208	#121×C₈₉	C₂³	1	2	yes	—
209	#120×C₈₉	—	2	2	no	—
210	C₄×Q₈×C₈₉	—	2	1	no	—
211	C₄×Q₈×C₈₉	—	2	1	no	—
212	C₄×Q₈×C₈₉	D₄	1	1	yes	characteristic
213	C₄×Q₈×C₈₉	C₂³	1	1	yes	characteristic
214	C₄×Q₈×C₈₉	C₂³	1	1	yes	characteristic
215	C₄×Q₈×C₈₉	C₂³	1	2	yes	—
216	C₄×Q₈×C₈₉	C₂³	1	2	yes	—
217	C₄×Q₈×C₈₉	C₂³	1	2	yes	—
218	C₄×Q₈×C₈₉	C₂³	1	1	yes	characteristic
219	C₄×D₄×C₈₉	—	2	2	no	—
220	C₄×D₄×C₈₉	—	2	1	no	—
221	C₄×D₄×C₈₉	—	2	1	no	—
222	C₄×D₄×C₈₉	—	2	2	no	—
223	C₄×D₄×C₈₉	—	2	2	no	—
224	C₄×D₄×C₈₉	—	2	2	no	—
225	C₄×D₄×C₈₉	—	2	2	no	—
226	C₄×D₄×C₈₉	—	2	2	no	—
227	C₄×D₄×C₈₉	—	2	1	no	—
228	C₄×D₄×C₈₉	—	2	1	no	—
229	C₄×D₄×C₈₉	—	2	1	no	—
230	C₄×D₄×C₈₉	—	2	1	no	—
231	C₄×D₄×C₈₉	—	2	2	no	—
232	C₄×D₄×C₈₉	D₄	1	2	yes	—
233	C₄×D₄×C₈₉	D₄	1	1	yes	characteristic
234	C₄×D₄×C₈₉	C₂³	1	1	yes	characteristic
235	C₄×D₄×C₈₉	C₂³	1	1	yes	characteristic
236	C₄×D₄×C₈₉	C₂³	1	1	yes	characteristic
237	C₄×D₄×C₈₉	C₂³	1	1	yes	characteristic
238	C₄×D₄×C₈₉	C₂³	1	1	yes	characteristic
239	C₄×D₄×C₈₉	C₂³	1	2	yes	—
240	C₄×D₄×C₈₉	C₂³	1	1	yes	characteristic
241	C₄×D₄×C₈₉	C₂³	1	2	yes	—
242	C₄×D₄×C₈₉	C₂³	1	2	yes	—
243	C₄×D₄×C₈₉	C₂³	1	1	yes	characteristic
244	C₄×D₄×C₈₉	C₂³	1	2	yes	—
245	#117×C₈₉	—	2	1	no	—
246	#117×C₈₉	—	2	1	no	—
247	#117×C₈₉	—	2	1	no	—
248	#117×C₈₉	—	2	2	no	—
249	#117×C₈₉	—	2	1	no	—
250	#117×C₈₉	—	2	2	no	—
251	#117×C₈₉	—	2	2	no	—
252	#117×C₈₉	—	2	2	no	—
253	#117×C₈₉	—	2	1	no	—
254	#117×C₈₉	—	2	2	no	—
255	#117×C₈₉	D₄	1	1	yes	characteristic
256	#117×C₈₉	D₄	1	2	yes	—
257	#117×C₈₉	C₂³	1	2	yes	—
258	#117×C₈₉	C₂³	1	2	yes	—
259	#117×C₈₉	C₂³	1	1	yes	characteristic
260	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
261	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
262	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
263	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
264	C₂×C₂²⋊C₄×C₈₉	—	2	2	no	—
265	C₂×C₄²×C₈₉	—	2	2	no	—
266	C₂×C₄²×C₈₉	—	2	1	no	—
267	C₂×C₄²×C₈₉	—	2	2	no	—
268	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
269	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
270	#107×C₈₉	C₂³	1	1	yes	characteristic
271	#107×C₈₉	C₂³	1	2	yes	—
272	#107×C₈₉	C₂³	1	1	yes	characteristic
273	#107×C₈₉	C₂³	1	2	yes	—
274	#107×C₈₉	C₂³	1	2	yes	—
275	#106×C₈₉	C₂³	1	2	yes	—
276	#106×C₈₉	C₂³	1	2	yes	—
277	#106×C₈₉	C₂³	1	1	yes	characteristic
278	#106×C₈₉	C₂³	1	1	yes	characteristic
279	#106×C₈₉	C₂³	1	2	yes	—
280	C₄⋊C₈×C₈₉	C₂³	1	1	yes	characteristic
281	C₄⋊C₈×C₈₉	C₂³	1	1	yes	characteristic
282	C₄⋊C₈×C₈₉	C₂³	1	2	yes	—
283	C₄⋊C₈×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	1	yes	characteristic
289	#103×C₈₉	C₂³	1	2	yes	—
290	#103×C₈₉	C₂³	1	2	yes	—
291	#102×C₈₉	C₂³	1	1	yes	characteristic
292	#102×C₈₉	C₂³	1	2	yes	—
293	#102×C₈₉	C₂³	1	2	yes	—
294	#102×C₈₉	C₂³	1	2	yes	—
295	#102×C₈₉	C₂³	1	1	yes	characteristic
296	#102×C₈₉	C₂³	1	1	yes	characteristic
297	#102×C₈₉	C₂³	1	1	yes	characteristic
298	#102×C₈₉	C₂³	1	1	yes	characteristic
299	#102×C₈₉	C₂³	1	1	yes	characteristic
300	#102×C₈₉	C₂³	1	2	yes	—
301	#102×C₈₉	C₂³	1	2	yes	—
302	#102×C₈₉	C₂³	1	2	yes	—
303	#102×C₈₉	C₂³	1	2	yes	—
304	C₂²⋊C₈×C₈₉	C₂³	1	2	yes	—
305	C₂²⋊C₈×C₈₉	C₂³	1	2	yes	—
306	C₂²⋊C₈×C₈₉	C₂³	1	2	yes	—
307	#97×C₈₉	C₂³	1	1	yes	characteristic
308	#97×C₈₉	C₂³	1	2	yes	—
309	#97×C₈₉	C₂³	1	2	yes	—
310	#97×C₈₉	C₂³	1	2	yes	—
311	#97×C₈₉	C₂³	1	1	yes	characteristic
312	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
313	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
314	C₂⁴×C₈₉	—	2	1	no	—
315	#41×C₈₉	—	2	4	no	—
316	#41×C₈₉	—	2	2	no	—
317	#41×C₈₉	—	2	4	no	—
318	#41×C₈₉	—	4	2	no	—
319	#41×C₈₉	—	4	2	no	—
320	#41×C₈₉	—	4	2	no	—
321	#41×C₈₉	—	4	1	no	—
322	#41×C₈₉	—	4	4	no	—
323	#41×C₈₉	—	8	2	no	—
324	#41×C₈₉	—	8	4	no	—
325	C₂×Q₈×C₈₉	—	2	1	no	—
326	C₂×Q₈×C₈₉	—	2	2	no	—
327	C₂×Q₈×C₈₉	—	2	1	no	—
328	C₂×Q₈×C₈₉	C₂×D₄	1	1	yes	characteristic
329	C₂×Q₈×C₈₉	C₂⁴	1	2	yes	—
330	C₂×Q₈×C₈₉	C₂⁴	1	1	yes	characteristic
331	C₂×D₄×C₈₉	—	2	2	no	—
332	C₂×D₄×C₈₉	—	2	2	no	—
333	C₂×D₄×C₈₉	—	2	1	no	—
334	C₂×D₄×C₈₉	—	2	2	no	—
335	C₂×D₄×C₈₉	—	2	2	no	—
336	C₂×D₄×C₈₉	—	2	2	no	—
337	C₂×D₄×C₈₉	—	2	2	no	—
338	C₂×D₄×C₈₉	—	2	2	no	—
339	C₂×D₄×C₈₉	—	2	1	no	—
340	C₂×D₄×C₈₉	—	2	2	no	—
341	C₂×D₄×C₈₉	—	2	1	no	—
342	C₂×D₄×C₈₉	—	2	2	no	—
343	C₂×D₄×C₈₉	—	2	1	no	—
344	C₂×D₄×C₈₉	—	4	1	no	—
345	C₂×D₄×C₈₉	C₂×D₄	1	1	yes	characteristic
346	C₂×D₄×C₈₉	C₂×D₄	1	2	yes	—
347	C₂×D₄×C₈₉	C₂⁴	1	1	yes	characteristic
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	C₂²×C₄×C₈₉	—	2	1	no	—
352	C₂²×C₄×C₈₉	—	2	1	no	—
353	C₂²×C₄×C₈₉	—	2	2	no	—
354	C₂²×C₄×C₈₉	—	2	2	no	—
355	C₂²×C₄×C₈₉	—	2	1	no	—
356	C₂²×C₄×C₈₉	—	2	2	no	—
357	C₂²×C₄×C₈₉	—	2	1	no	—
358	C₂²×C₄×C₈₉	—	2	1	no	—
359	C₂²×C₄×C₈₉	—	2	2	no	—
360	C₂²×C₄×C₈₉	—	2	1	no	—
361	C₂²×C₄×C₈₉	—	2	1	no	—
362	C₂²×C₄×C₈₉	—	2	1	no	—
363	C₂²×C₄×C₈₉	—	2	2	no	—
364	C₂²×C₄×C₈₉	—	4	4	no	—
365	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
366	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
367	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
368	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
369	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
370	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
371	Q₁₆×C₈₉	—	2	4	no	—
372	SD₁₆×C₈₉	—	2	2	no	—
373	SD₁₆×C₈₉	—	2	4	no	—
374	SD₁₆×C₈₉	—	4	2	no	—
375	SD₁₆×C₈₉	—	4	2	no	—
376	SD₁₆×C₈₉	#41	1	4	yes	complemented
377	D₈×C₈₉	—	2	4	no	—
378	D₈×C₈₉	—	2	2	no	—
379	D₈×C₈₉	—	2	2	no	—
380	D₈×C₈₉	—	4	2	no	—
381	M₁₆×C₈₉	—	2	2	no	—
382	M₁₆×C₈₉	—	4	1	no	—
383	C₂×C₈×C₈₉	—	2	4	no	—
384	C₂×C₈×C₈₉	—	4	2	no	—
385	C₂×C₈×C₈₉	C₂⁴	1	1	yes	characteristic
386	C₂×C₈×C₈₉	C₂⁴	1	1	yes	characteristic
387	C₂×C₈×C₈₉	C₂⁴	1	1	yes	characteristic
388	C₂×C₈×C₈₉	C₂⁴	1	2	yes	—
389	C₂×C₈×C₈₉	C₂⁴	1	2	yes	—
390	C₂×C₈×C₈₉	C₂⁴	1	1	yes	characteristic
391	C₄⋊C₄×C₈₉	—	2	1	no	—
392	C₄⋊C₄×C₈₉	—	2	1	no	—
393	C₄⋊C₄×C₈₉	—	2	2	no	—
394	C₄⋊C₄×C₈₉	—	2	2	no	—
395	C₄⋊C₄×C₈₉	—	2	1	no	—
396	C₄⋊C₄×C₈₉	—	2	1	no	—
397	C₄⋊C₄×C₈₉	—	2	2	no	—
398	C₄⋊C₄×C₈₉	—	2	1	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	—	2	2	no	—
403	C₄⋊C₄×C₈₉	—	2	2	no	—
404	C₄⋊C₄×C₈₉	—	2	2	no	—
405	C₄⋊C₄×C₈₉	—	2	1	no	—
406	C₄⋊C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
407	C₄⋊C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
408	C₄⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
409	C₄⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
410	C₄⋊C₄×C₈₉	C₂⁴	1	1	yes	characteristic
411	C₄⋊C₄×C₈₉	C₂⁴	1	1	yes	characteristic
412	C₄⋊C₄×C₈₉	C₂⁴	1	2	yes	—
413	C₄⋊C₄×C₈₉	C₂⁴	1	1	yes	characteristic
414	C₄⋊C₄×C₈₉	C₂⁴	1	2	yes	—
415	C₄⋊C₄×C₈₉	C₂⁴	1	1	yes	characteristic
416	C₂²⋊C₄×C₈₉	—	2	2	no	—
417	C₂²⋊C₄×C₈₉	—	2	1	no	—
418	C₂²⋊C₄×C₈₉	—	2	2	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	2	no	—
424	C₂²⋊C₄×C₈₉	—	2	1	no	—
425	C₂²⋊C₄×C₈₉	—	2	1	no	—
426	C₂²⋊C₄×C₈₉	—	2	1	no	—
427	C₂²⋊C₄×C₈₉	—	2	2	no	—
428	C₂²⋊C₄×C₈₉	—	2	2	no	—
429	C₂²⋊C₄×C₈₉	—	2	2	no	—
430	C₂²⋊C₄×C₈₉	—	2	2	no	—
431	C₂²⋊C₄×C₈₉	—	2	2	no	—
432	C₂²⋊C₄×C₈₉	—	2	1	no	—
433	C₂²⋊C₄×C₈₉	—	2	1	no	—
434	C₂²⋊C₄×C₈₉	—	2	2	no	—
435	C₂²⋊C₄×C₈₉	—	2	2	no	—
436	C₂²⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
437	C₂²⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
438	C₂²⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
439	C₄²×C₈₉	—	2	1	no	—
440	C₄²×C₈₉	—	2	2	no	—
441	C₄²×C₈₉	—	2	1	no	—
442	C₄²×C₈₉	—	2	2	no	—
443	C₄²×C₈₉	—	2	2	no	—
444	C₄²×C₈₉	—	2	2	no	—
445	C₄²×C₈₉	—	2	2	no	—
446	C₄²×C₈₉	—	2	1	no	—
447	C₄²×C₈₉	C₂×D₄	1	2	yes	—
448	C₄²×C₈₉	C₂×D₄	1	2	yes	—
449	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
450	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
451	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
452	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
453	C₄²×C₈₉	C₂⁴	1	2	yes	—
454	C₂³×C₈₉	—	2	1	no	—
455	C₂³×C₈₉	—	2	1	no	—
456	C₂³×C₈₉	—	2	1	no	—
457	C₂³×C₈₉	—	2	2	no	—
458	C₂³×C₈₉	—	4	2	no	—
459	C₂³×C₈₉	—	4	2	no	—
460	C₂³×C₈₉	—	8	1	no	—
461	C₂³×C₈₉	C₂²×D₄	1	1	yes	characteristic
462	C₂³×C₈₉	C₂²×D₄	1	2	yes	—
463	Q₈×C₈₉	—	2	2	no	—
464	Q₈×C₈₉	—	2	1	no	—
465	Q₈×C₈₉	—	2	2	no	—
466	Q₈×C₈₉	—	2	2	no	—
467	Q₈×C₈₉	—	8	1	no	—
468	Q₈×C₈₉	—	8	2	no	—
469	Q₈×C₈₉	—	8	1	no	—
470	Q₈×C₈₉	C₂×#41	1	2	yes	—
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	—	2	1	no	—
477	D₄×C₈₉	—	2	2	no	—
478	D₄×C₈₉	—	2	1	no	—
479	D₄×C₈₉	—	4	2	no	—
480	D₄×C₈₉	—	4	2	no	—
481	D₄×C₈₉	—	4	4	no	—
482	D₄×C₈₉	—	4	2	no	—
483	D₄×C₈₉	—	4	4	no	—
484	D₄×C₈₉	—	4	4	no	—
485	D₄×C₈₉	—	4	2	no	—
486	D₄×C₈₉	—	8	2	no	—
487	D₄×C₈₉	—	8	1	no	—
488	D₄×C₈₉	—	8	2	no	—
489	D₄×C₈₉	—	8	2	no	—
490	D₄×C₈₉	—	8	2	no	—
491	D₄×C₈₉	—	8	2	no	—
492	D₄×C₈₉	C₂×#41	1	2	yes	—
493	C₂×C₄×C₈₉	—	2	1	no	—
494	C₂×C₄×C₈₉	—	2	2	no	—
495	C₂×C₄×C₈₉	—	2	2	no	—
496	C₂×C₄×C₈₉	—	2	1	no	—
497	C₂×C₄×C₈₉	—	2	2	no	—
498	C₂×C₄×C₈₉	—	2	1	no	—
499	C₂×C₄×C₈₉	—	2	1	no	—
500	C₂×C₄×C₈₉	—	2	1	no	—
501	C₂×C₄×C₈₉	—	2	2	no	—
502	C₂×C₄×C₈₉	—	2	2	no	—
503	C₂×C₄×C₈₉	—	2	2	no	—
504	C₂×C₄×C₈₉	—	2	1	no	—
505	C₂×C₄×C₈₉	—	2	1	no	—
506	C₂×C₄×C₈₉	—	4	2	no	—
507	C₂×C₄×C₈₉	—	4	2	no	—
508	C₂×C₄×C₈₉	—	4	1	no	—
509	C₂×C₄×C₈₉	—	4	4	no	—
510	C₂×C₄×C₈₉	—	4	2	no	—
511	C₂×C₄×C₈₉	—	4	4	no	—
512	C₂×C₄×C₈₉	—	4	2	no	—
513	C₂×C₄×C₈₉	—	4	2	no	—
514	C₂×C₄×C₈₉	—	4	4	no	—
515	C₂×C₄×C₈₉	—	4	2	no	—
516	C₂×C₄×C₈₉	—	4	4	no	—
517	C₂×C₄×C₈₉	—	4	2	no	—
518	C₂×C₄×C₈₉	—	4	2	no	—
519	C₂×C₄×C₈₉	—	4	2	no	—
520	C₂×C₄×C₈₉	—	4	2	no	—
521	C₂×C₄×C₈₉	—	8	2	no	—
522	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
523	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
524	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
525	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
526	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
527	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
528	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
529	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
530	C₂×C₄×C₈₉	C₂⁵	1	1	yes	characteristic
531	C₈×C₈₉	—	2	2	no	—
532	C₈×C₈₉	—	2	1	no	—
533	C₈×C₈₉	—	2	1	no	—
534	C₈×C₈₉	—	2	2	no	—
535	C₈×C₈₉	—	2	1	no	—
536	C₈×C₈₉	C₂×#41	1	2	yes	—
537	C₂²×C₈₉	—	2	2	no	—
538	C₂²×C₈₉	—	2	1	no	—
539	C₂²×C₈₉	—	2	2	no	—
540	C₂²×C₈₉	—	2	1	no	—
541	C₂²×C₈₉	—	2	2	no	—
542	C₂²×C₈₉	—	2	1	no	—
543	C₂²×C₈₉	—	2	2	no	—
544	C₂²×C₈₉	—	4	1	no	—
545	C₂²×C₈₉	—	4	1	no	—
546	C₂²×C₈₉	—	4	1	no	—
547	C₂²×C₈₉	—	4	2	no	—
548	C₂²×C₈₉	—	4	1	no	—
549	C₂²×C₈₉	—	4	1	no	—
550	C₂²×C₈₉	—	4	2	no	—
551	C₂²×C₈₉	—	4	1	no	—
552	C₂²×C₈₉	—	4	1	no	—
553	C₂²×C₈₉	—	4	2	no	—
554	C₂²×C₈₉	—	4	1	no	—
555	C₂²×C₈₉	—	8	4	no	—
556	C₂²×C₈₉	C₂³×D₄	1	1	yes	characteristic
557	C₄×C₈₉	—	2	1	no	—
558	C₄×C₈₉	—	2	2	no	—
559	C₄×C₈₉	—	2	1	no	—
560	C₄×C₈₉	—	2	2	no	—
561	C₄×C₈₉	—	2	1	no	—
562	C₄×C₈₉	—	2	2	no	—
563	C₄×C₈₉	—	2	1	no	—
564	C₄×C₈₉	—	2	2	no	—
565	C₄×C₈₉	—	4	1	no	—
566	C₄×C₈₉	—	4	2	no	—
567	C₄×C₈₉	—	4	2	no	—
568	C₄×C₈₉	—	4	2	no	—
569	C₄×C₈₉	—	4	1	no	—
570	C₄×C₈₉	—	4	1	no	—
571	C₄×C₈₉	—	4	1	no	—
572	C₄×C₈₉	#575	1	2	yes	—
573	C₄×C₈₉	C₂²×#41	1	1	yes	characteristic
574	C₄×C₈₉	#585	1	1	yes	characteristic
575	#61459	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
576	C₂×C₈₉	—	4	2	no	—
577	C₂×C₈₉	—	4	1	no	—
578	C₂×C₈₉	—	4	2	no	—
579	C₂×C₈₉	—	8	1	no	—
580	C₂×C₈₉	—	8	2	no	—
581	C₂×C₈₉	—	8	1	no	—
582	C₂×C₈₉	D₄×#41	1	1	yes	characteristic
583	C₂×C₈₉	C₂×#575	1	1	yes	characteristic
584	C₂×C₈₉	#3585	1	1	yes	characteristic
585	#3483	C₂×C₈₉	1	1	yes	characteristic, complemented
586	#3475	C₂×C₈₉	1	1	yes	characteristic, complemented
587	#3397	C₂×C₈₉	1	1	yes	characteristic, complemented
588	#3385	C₂×C₈₉	1	1	yes	characteristic, complemented
589	#3369	C₂×C₈₉	1	1	yes	characteristic, complemented
590	#3366	C₂×C₈₉	1	1	yes	characteristic, complemented
591	#3348	C₂×C₈₉	1	2	yes	complemented
592	#3341	C₂×C₈₉	1	1	yes	characteristic, complemented
593	#3319	C₂×C₈₉	1	2	yes	complemented
594	#3317	C₂×C₈₉	1	2	yes	complemented
595	#3305	C₂×C₈₉	1	1	yes	characteristic, complemented
596	#3303	C₂×C₈₉	1	1	yes	characteristic, complemented
597	#3284	C₂×C₈₉	1	1	yes	characteristic, complemented
598	#3268	C₂×C₈₉	1	2	yes	complemented
599	#3182	C₂×C₈₉	1	1	yes	characteristic, complemented
600	#3180	C₂×C₈₉	1	2	yes	complemented
601	#3116	C₂×C₈₉	1	1	yes	characteristic, complemented
602	#3115	C₂×C₈₉	1	2	yes	complemented
603	#3111	C₂×C₈₉	1	2	yes	complemented
604	#3109	C₂×C₈₉	1	1	yes	characteristic, complemented
605	#2970	C₂×C₈₉	1	1	yes	characteristic, complemented
606	C₄×AGL(1,ℤ/8)	C₂×C₈₉	1	1	yes	characteristic, complemented
607	#2943	C₂×C₈₉	1	2	yes	complemented
608	C₈₉	#61459	1	1	yes	characteristic, direct product factor, Sylow
609	C₂×AGL(1,ℤ/8)	C₂²×C₈₉	1	1	yes	characteristic
610	C₂×#135	C₂²×C₈₉	1	2	yes	—
611	Q₈²	C₂²×C₈₉	1	1	yes	characteristic, complemented
612	#556	C₂²×C₈₉	1	1	yes	characteristic
613	#555	—	2	2	no	—
614	#555	—	2	1	no	—
615	#555	C₂²×C₈₉	1	1	yes	characteristic
616	#555	C₂²×C₈₉	1	2	yes	—
617	#555	C₂²×C₈₉	1	1	yes	characteristic, complemented
618	#554	C₂²×C₈₉	1	1	yes	characteristic
619	#553	—	2	1	no	—
620	#552	—	2	1	no	—
621	#552	C₂²×C₈₉	1	2	yes	—
622	#551	—	2	2	no	—
623	#550	—	2	1	no	—
624	#550	C₂²×C₈₉	1	2	yes	—
625	#550	C₂²×C₈₉	1	1	yes	characteristic, complemented
626	#550	C₂²×C₈₉	1	1	yes	characteristic, complemented
627	#547	C₂²×C₈₉	1	1	yes	characteristic
628	#546	C₂²×C₈₉	1	2	yes	—
629	#533	C₂²×C₈₉	1	1	yes	characteristic
630	#532	—	2	1	no	—
631	#532	—	2	2	no	—
632	#532	C₂²×C₈₉	1	1	yes	characteristic
633	#532	C₂²×C₈₉	1	2	yes	complemented
634	#529	—	2	2	no	—
635	#529	C₂²×C₈₉	1	2	yes	—
636	#525	—	2	1	no	—
637	C₄×#41	—	2	1	no	—
638	C₄×#41	C₂²×C₈₉	1	2	yes	—
639	C₄×#41	C₂²×C₈₉	1	1	yes	characteristic
640	C₄×#41	C₂²×C₈₉	1	1	yes	characteristic
641	C₄×#41	C₂²×C₈₉	1	2	yes	complemented
642	C₂×C₄×D₄	C₂²×C₈₉	1	1	yes	characteristic
643	C₂×#117	—	2	1	no	—
644	#501	C₂²×C₈₉	1	2	yes	complemented
645	#500	C₂²×C₈₉	1	1	yes	characteristic, complemented
646	#496	C₂²×C₈₉	1	2	yes	—
647	#492	C₂²×C₈₉	1	1	yes	characteristic, complemented
648	#490	C₂²×C₈₉	1	2	yes	complemented
649	#489	C₂²×C₈₉	1	2	yes	—
650	#487	C₂²×C₈₉	1	1	yes	characteristic, complemented
651	#486	C₂²×C₈₉	1	1	yes	characteristic, complemented
652	#485	C₂²×C₈₉	1	2	yes	—
653	#485	C₂²×C₈₉	1	2	yes	complemented
654	#482	C₂²×C₈₉	1	2	yes	—
655	#482	C₂²×C₈₉	1	2	yes	complemented
656	#482	C₂²×C₈₉	1	2	yes	complemented
657	#481	C₂²×C₈₉	1	2	yes	—
658	#479	C₂²×C₈₉	1	2	yes	complemented
659	#478	C₂²×C₈₉	1	2	yes	complemented
660	#477	C₂²×C₈₉	1	1	yes	characteristic, complemented
661	#476	C₂²×C₈₉	1	1	yes	characteristic
662	#476	C₂²×C₈₉	1	1	yes	characteristic
663	#476	C₂²×C₈₉	1	1	yes	characteristic, complemented
664	#475	C₂²×C₈₉	1	2	yes	complemented
665	#474	C₂²×C₈₉	1	2	yes	—
666	#468	C₂²×C₈₉	1	2	yes	—
667	#468	C₂²×C₈₉	1	2	yes	—
668	#466	C₂²×C₈₉	1	2	yes	—
669	#466	C₂²×C₈₉	1	2	yes	—
670	#465	C₂²×C₈₉	1	2	yes	complemented
671	#465	C₂²×C₈₉	1	2	yes	complemented
672	#464	C₂²×C₈₉	1	2	yes	—
673	#463	C₂²×C₈₉	1	2	yes	—
674	#462	C₂²×C₈₉	1	1	yes	characteristic, complemented
675	#461	C₂²×C₈₉	1	1	yes	characteristic, complemented
676	#460	C₂²×C₈₉	1	2	yes	complemented
677	#459	C₂²×C₈₉	1	1	yes	characteristic
678	#459	C₂²×C₈₉	1	1	yes	characteristic
679	#459	C₂²×C₈₉	1	2	yes	—
680	#452	C₂²×C₈₉	1	2	yes	—
681	#452	C₂²×C₈₉	1	2	yes	complemented
682	#449	C₂²×C₈₉	1	2	yes	—
683	#449	C₂²×C₈₉	1	2	yes	—
684	#449	C₂²×C₈₉	1	2	yes	—
685	#447	C₂²×C₈₉	1	2	yes	—
686	#446	C₂²×C₈₉	1	1	yes	characteristic, complemented
687	#446	C₂²×C₈₉	1	1	yes	characteristic, complemented
688	#442	C₂²×C₈₉	1	2	yes	—
689	#442	C₂²×C₈₉	1	2	yes	—
690	#442	C₂²×C₈₉	1	2	yes	—
691	#442	C₂²×C₈₉	1	1	yes	characteristic
692	#442	C₂²×C₈₉	1	1	yes	characteristic
693	#441	C₂²×C₈₉	1	2	yes	complemented
694	#441	C₂²×C₈₉	1	2	yes	complemented
695	#440	C₂²×C₈₉	1	1	yes	characteristic
696	#440	C₂²×C₈₉	1	2	yes	—
697	#440	C₂²×C₈₉	1	1	yes	characteristic
698	#440	C₂²×C₈₉	1	2	yes	complemented
699	#440	C₂²×C₈₉	1	2	yes	complemented
700	#440	C₂²×C₈₉	1	2	yes	complemented
701	#440	C₂²×C₈₉	1	2	yes	complemented
702	C₄×SD₁₆	C₂²×C₈₉	1	1	yes	characteristic
703	C₄×SD₁₆	C₂²×C₈₉	1	1	yes	characteristic
704	C₄×D₈	C₂²×C₈₉	1	1	yes	characteristic
705	C₄×D₈	C₂²×C₈₉	1	1	yes	characteristic
706	#435	C₂²×C₈₉	1	2	yes	—
707	#435	C₂²×C₈₉	1	2	yes	—
708	C₈×D₄	C₂²×C₈₉	1	1	yes	characteristic, complemented
709	C₈×D₄	C₂²×C₈₉	1	1	yes	characteristic, complemented
710	#432	C₂²×C₈₉	1	1	yes	characteristic
711	#432	C₂²×C₈₉	1	2	yes	complemented
712	#428	C₂²×C₈₉	1	1	yes	characteristic
713	#427	C₂²×C₈₉	1	2	yes	complemented
714	#418	C₂²×C₈₉	1	1	yes	characteristic
715	#417	C₂²×C₈₉	1	1	yes	characteristic
716	#416	C₂²×C₈₉	1	2	yes	—
717	#416	C₂²×C₈₉	1	2	yes	complemented
718	C₄×M₁₆	C₂²×C₈₉	1	1	yes	characteristic
719	C₂×#97	C₂²×C₈₉	1	2	yes	complemented
720	C₂×#41	—	2	1	no	—
721	C₂×#41	—	2	1	no	—
722	C₂×#41	—	2	2	no	—
723	C₂×#41	D₄×C₈₉	1	1	yes	characteristic
724	C₂×#41	C₂³×C₈₉	1	2	yes	—
725	C₂×#41	C₂³×C₈₉	1	1	yes	characteristic
726	C₂×#41	C₂³×C₈₉	1	2	yes	—
727	C₂²×D₄	C₂³×C₈₉	1	1	yes	characteristic
728	C₂³×C₄	—	2	1	no	—
729	AGL(1,ℤ/8)	—	2	4	no	—
730	#135	—	2	8	no	—
731	C₂×Q₁₆	C₂³×C₈₉	1	2	yes	—
732	C₂×SD₁₆	C₂³×C₈₉	1	2	yes	—
733	C₂×SD₁₆	C₂³×C₈₉	1	1	yes	characteristic
734	C₂×SD₁₆	C₂³×C₈₉	1	2	yes	—
735	C₂×SD₁₆	C₂³×C₈₉	1	2	yes	—
736	C₂×SD₁₆	C₂³×C₈₉	1	1	yes	characteristic
737	C₂×D₈	C₂³×C₈₉	1	2	yes	—
738	C₂×D₈	C₂³×C₈₉	1	1	yes	characteristic
739	C₂×D₈	C₂³×C₈₉	1	1	yes	characteristic
740	C₂×D₈	C₂³×C₈₉	1	2	yes	—
741	C₂×M₁₆	C₂³×C₈₉	1	1	yes	characteristic
742	C₂×M₁₆	C₂³×C₈₉	1	1	yes	characteristic
743	C₂²×C₈	C₂³×C₈₉	1	2	yes	—
744	C₂²×C₈	C₂³×C₈₉	1	2	yes	—
745	C₄⋊Q₈	—	2	1	no	—
746	C₄⋊Q₈	—	2	2	no	—
747	C₄⋊Q₈	C₂³×C₈₉	1	1	yes	characteristic
748	C₄⋊Q₈	C₂³×C₈₉	1	1	yes	characteristic
749	C₄⋊Q₈	C₂³×C₈₉	1	2	yes	—
750	C₄⋊Q₈	C₂³×C₈₉	1	1	yes	characteristic
751	#127	—	2	2	no	—
752	#127	—	2	1	no	—
753	#127	C₂³×C₈₉	1	1	yes	characteristic
754	#127	C₂³×C₈₉	1	2	yes	—
755	#126	—	2	2	no	—
756	#126	—	2	2	no	—
757	#126	—	2	2	no	—
758	#125	—	2	2	no	—
759	#125	—	2	1	no	—
760	#125	C₂³×C₈₉	1	2	yes	—
761	#124	—	2	2	no	—
762	#124	—	2	2	no	—
763	#124	—	2	2	no	—
764	#124	—	2	2	no	—
765	#124	—	2	1	no	—
766	#124	—	2	2	no	—
767	#124	C₂³×C₈₉	1	2	yes	—
768	#123	—	2	2	no	—
769	#123	—	2	2	no	—
770	#123	—	2	2	no	—
771	#123	—	2	2	no	—
772	C₂²⋊Q₈	—	2	1	no	—
773	C₂²⋊Q₈	—	2	1	no	—
774	C₂²⋊Q₈	—	2	1	no	—
775	C₂²⋊Q₈	—	2	2	no	—
776	C₂²⋊Q₈	C₂³×C₈₉	1	2	yes	—
777	C₂²⋊Q₈	C₂³×C₈₉	1	2	yes	—
778	#121	—	2	1	no	—
779	#121	—	2	1	no	—
780	#121	—	2	2	no	—
781	#121	—	2	1	no	—
782	#121	—	2	1	no	—
783	#121	—	2	2	no	—
784	#121	—	2	1	no	—
785	#121	—	2	2	no	—
786	#121	—	2	2	no	—
787	#121	—	2	2	no	—
788	#121	—	2	2	no	—
789	#121	—	2	2	no	—
790	#121	C₂³×C₈₉	1	2	yes	—
791	#121	C₂³×C₈₉	1	2	yes	—
792	#121	C₂³×C₈₉	1	2	yes	—
793	#121	C₂³×C₈₉	1	2	yes	—
794	#120	—	2	2	no	—
795	C₄×Q₈	—	2	1	no	—
796	C₄×Q₈	—	2	1	no	—
797	C₄×Q₈	D₄×C₈₉	1	1	yes	characteristic
798	C₄×Q₈	C₂³×C₈₉	1	1	yes	characteristic
799	C₄×Q₈	C₂³×C₈₉	1	2	yes	—
800	C₄×Q₈	C₂³×C₈₉	1	1	yes	characteristic
801	C₄×Q₈	C₂³×C₈₉	1	2	yes	—
802	C₄×Q₈	C₂³×C₈₉	1	2	yes	—
803	C₄×Q₈	C₂³×C₈₉	1	1	yes	characteristic
804	C₄×D₄	—	2	2	no	—
805	C₄×D₄	—	2	1	no	—
806	C₄×D₄	—	2	1	no	—
807	C₄×D₄	—	2	2	no	—
808	C₄×D₄	—	2	2	no	—
809	C₄×D₄	—	2	2	no	—
810	C₄×D₄	—	2	2	no	—
811	C₄×D₄	—	2	2	no	—
812	C₄×D₄	—	2	1	no	—
813	C₄×D₄	—	2	1	no	—
814	C₄×D₄	—	2	1	no	—
815	C₄×D₄	—	2	1	no	—
816	C₄×D₄	—	2	2	no	—
817	C₄×D₄	D₄×C₈₉	1	2	yes	—
818	C₄×D₄	D₄×C₈₉	1	1	yes	characteristic
819	C₄×D₄	C₂³×C₈₉	1	1	yes	characteristic
820	C₄×D₄	C₂³×C₈₉	1	1	yes	characteristic
821	C₄×D₄	C₂³×C₈₉	1	1	yes	characteristic
822	C₄×D₄	C₂³×C₈₉	1	1	yes	characteristic
823	C₄×D₄	C₂³×C₈₉	1	1	yes	characteristic
824	C₄×D₄	C₂³×C₈₉	1	2	yes	—
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	2	yes	—
829	C₄×D₄	C₂³×C₈₉	1	1	yes	characteristic
830	#117	—	2	1	no	—
831	#117	—	2	1	no	—
832	#117	—	2	1	no	—
833	#117	—	2	2	no	—
834	#117	—	2	1	no	—
835	#117	—	2	2	no	—
836	#117	—	2	2	no	—
837	#117	—	2	2	no	—
838	#117	—	2	1	no	—
839	#117	—	2	2	no	—
840	#117	D₄×C₈₉	1	1	yes	characteristic
841	#117	D₄×C₈₉	1	2	yes	—
842	#117	C₂³×C₈₉	1	2	yes	—
843	#117	C₂³×C₈₉	1	1	yes	characteristic
844	#117	C₂³×C₈₉	1	2	yes	—
845	C₂×C₄⋊C₄	—	2	1	no	—
846	C₂×C₄⋊C₄	—	2	1	no	—
847	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
848	C₂×C₂²⋊C₄	—	2	1	no	—
849	C₂×C₂²⋊C₄	—	2	2	no	—
850	C₂×C₄²	—	2	2	no	—
851	C₂×C₄²	—	2	1	no	—
852	C₂×C₄²	—	2	2	no	—
853	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
854	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
855	#107	C₂³×C₈₉	1	1	yes	characteristic
856	#107	C₂³×C₈₉	1	2	yes	—
857	#107	C₂³×C₈₉	1	1	yes	characteristic
858	#107	C₂³×C₈₉	1	2	yes	—
859	#107	C₂³×C₈₉	1	2	yes	—
860	#106	C₂³×C₈₉	1	2	yes	—
861	#106	C₂³×C₈₉	1	2	yes	—
862	#106	C₂³×C₈₉	1	1	yes	characteristic
863	#106	C₂³×C₈₉	1	1	yes	characteristic
864	#106	C₂³×C₈₉	1	2	yes	—
865	C₄⋊C₈	C₂³×C₈₉	1	1	yes	characteristic
866	C₄⋊C₈	C₂³×C₈₉	1	1	yes	characteristic
867	C₄⋊C₈	C₂³×C₈₉	1	2	yes	—
868	C₄⋊C₈	C₂³×C₈₉	1	2	yes	—
869	#103	C₂³×C₈₉	1	2	yes	—
870	#103	C₂³×C₈₉	1	2	yes	—
871	#103	C₂³×C₈₉	1	1	yes	characteristic
872	#103	C₂³×C₈₉	1	2	yes	—
873	#103	C₂³×C₈₉	1	1	yes	characteristic
874	#103	C₂³×C₈₉	1	2	yes	—
875	#103	C₂³×C₈₉	1	2	yes	—
876	#102	C₂³×C₈₉	1	1	yes	characteristic
877	#102	C₂³×C₈₉	1	2	yes	—
878	#102	C₂³×C₈₉	1	2	yes	—
879	#102	C₂³×C₈₉	1	2	yes	—
880	#102	C₂³×C₈₉	1	1	yes	characteristic
881	#102	C₂³×C₈₉	1	1	yes	characteristic
882	#102	C₂³×C₈₉	1	1	yes	characteristic
883	#102	C₂³×C₈₉	1	1	yes	characteristic
884	#102	C₂³×C₈₉	1	1	yes	characteristic
885	#102	C₂³×C₈₉	1	2	yes	—
886	#102	C₂³×C₈₉	1	2	yes	—
887	#102	C₂³×C₈₉	1	2	yes	—
888	#102	C₂³×C₈₉	1	2	yes	—
889	C₂²⋊C₈	C₂³×C₈₉	1	2	yes	—
890	C₂²⋊C₈	C₂³×C₈₉	1	2	yes	—
891	C₂²⋊C₈	C₂³×C₈₉	1	2	yes	—
892	#97	C₂³×C₈₉	1	1	yes	characteristic
893	#97	C₂³×C₈₉	1	2	yes	—
894	#97	C₂³×C₈₉	1	2	yes	—
895	#97	C₂³×C₈₉	1	2	yes	—
896	#97	C₂³×C₈₉	1	1	yes	characteristic
897	C₄×C₈	C₂³×C₈₉	1	1	yes	characteristic
898	C₄×C₈	C₂³×C₈₉	1	1	yes	characteristic
899	C₂⁴	—	2	1	no	—
900	#41	—	2	4	no	—
901	#41	—	2	2	no	—
902	#41	—	2	4	no	—
903	#41	—	4	2	no	—
904	#41	—	4	2	no	—
905	#41	—	4	2	no	—
906	#41	—	4	1	no	—
907	#41	—	4	4	no	—
908	#41	—	8	2	no	—
909	#41	—	8	4	no	—
910	C₂×Q₈	—	2	1	no	—
911	C₂×Q₈	—	2	2	no	—
912	C₂×Q₈	—	2	1	no	—
913	C₂×Q₈	C₂×D₄×C₈₉	1	1	yes	characteristic
914	C₂×Q₈	C₂⁴×C₈₉	1	2	yes	—
915	C₂×Q₈	C₂⁴×C₈₉	1	1	yes	characteristic
916	C₂×D₄	—	2	2	no	—
917	C₂×D₄	—	2	2	no	—
918	C₂×D₄	—	2	1	no	—
919	C₂×D₄	—	2	2	no	—
920	C₂×D₄	—	2	2	no	—
921	C₂×D₄	—	2	2	no	—
922	C₂×D₄	—	2	2	no	—
923	C₂×D₄	—	2	2	no	—
924	C₂×D₄	—	2	1	no	—
925	C₂×D₄	—	2	2	no	—
926	C₂×D₄	—	2	1	no	—
927	C₂×D₄	—	2	2	no	—
928	C₂×D₄	—	2	1	no	—
929	C₂×D₄	—	4	1	no	—
930	C₂×D₄	C₂×D₄×C₈₉	1	1	yes	characteristic
931	C₂×D₄	C₂×D₄×C₈₉	1	2	yes	—
932	C₂×D₄	C₂⁴×C₈₉	1	1	yes	characteristic
933	C₂×D₄	C₂⁴×C₈₉	1	1	yes	characteristic
934	C₂×D₄	C₂⁴×C₈₉	1	2	yes	—
935	C₂×D₄	C₂⁴×C₈₉	1	1	yes	characteristic
936	C₂²×C₄	—	2	1	no	—
937	C₂²×C₄	—	2	1	no	—
938	C₂²×C₄	—	2	2	no	—
939	C₂²×C₄	—	2	2	no	—
940	C₂²×C₄	—	2	1	no	—
941	C₂²×C₄	—	2	2	no	—
942	C₂²×C₄	—	2	1	no	—
943	C₂²×C₄	—	2	1	no	—
944	C₂²×C₄	—	2	2	no	—
945	C₂²×C₄	—	2	1	no	—
946	C₂²×C₄	—	2	1	no	—
947	C₂²×C₄	—	2	1	no	—
948	C₂²×C₄	—	2	2	no	—
949	C₂²×C₄	—	4	4	no	—
950	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
951	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
952	C₂²×C₄	C₂×D₄×C₈₉	1	2	yes	—
953	C₂²×C₄	C₂×D₄×C₈₉	1	2	yes	—
954	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
955	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
956	Q₁₆	—	2	4	no	—
957	SD₁₆	—	2	2	no	—
958	SD₁₆	—	2	4	no	—
959	SD₁₆	—	4	2	no	—
960	SD₁₆	—	4	2	no	—
961	SD₁₆	#41×C₈₉	1	4	yes	complemented
962	D₈	—	2	4	no	—
963	D₈	—	2	2	no	—
964	D₈	—	2	2	no	—
965	D₈	—	4	2	no	—
966	M₁₆	—	2	2	no	—
967	M₁₆	—	4	1	no	—
968	C₂×C₈	—	2	4	no	—
969	C₂×C₈	—	4	2	no	—
970	C₂×C₈	C₂⁴×C₈₉	1	1	yes	characteristic
971	C₂×C₈	C₂⁴×C₈₉	1	1	yes	characteristic
972	C₂×C₈	C₂⁴×C₈₉	1	1	yes	characteristic
973	C₂×C₈	C₂⁴×C₈₉	1	2	yes	—
974	C₂×C₈	C₂⁴×C₈₉	1	2	yes	—
975	C₂×C₈	C₂⁴×C₈₉	1	1	yes	characteristic
976	C₄⋊C₄	—	2	1	no	—
977	C₄⋊C₄	—	2	1	no	—
978	C₄⋊C₄	—	2	2	no	—
979	C₄⋊C₄	—	2	2	no	—
980	C₄⋊C₄	—	2	1	no	—
981	C₄⋊C₄	—	2	1	no	—
982	C₄⋊C₄	—	2	2	no	—
983	C₄⋊C₄	—	2	1	no	—
984	C₄⋊C₄	—	2	2	no	—
985	C₄⋊C₄	—	2	1	no	—
986	C₄⋊C₄	—	2	2	no	—
987	C₄⋊C₄	—	2	2	no	—
988	C₄⋊C₄	—	2	2	no	—
989	C₄⋊C₄	—	2	2	no	—
990	C₄⋊C₄	—	2	1	no	—
991	C₄⋊C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
992	C₄⋊C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
993	C₄⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
994	C₄⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
995	C₄⋊C₄	C₂⁴×C₈₉	1	1	yes	characteristic
996	C₄⋊C₄	C₂⁴×C₈₉	1	1	yes	characteristic
997	C₄⋊C₄	C₂⁴×C₈₉	1	2	yes	—
998	C₄⋊C₄	C₂⁴×C₈₉	1	1	yes	characteristic
999	C₄⋊C₄	C₂⁴×C₈₉	1	2	yes	—
1000	C₄⋊C₄	C₂⁴×C₈₉	1	1	yes	characteristic
1001	C₂²⋊C₄	—	2	2	no	—
1002	C₂²⋊C₄	—	2	1	no	—
1003	C₂²⋊C₄	—	2	2	no	—
1004	C₂²⋊C₄	—	2	2	no	—
1005	C₂²⋊C₄	—	2	2	no	—
1006	C₂²⋊C₄	—	2	1	no	—
1007	C₂²⋊C₄	—	2	2	no	—
1008	C₂²⋊C₄	—	2	2	no	—
1009	C₂²⋊C₄	—	2	1	no	—
1010	C₂²⋊C₄	—	2	1	no	—
1011	C₂²⋊C₄	—	2	1	no	—
1012	C₂²⋊C₄	—	2	2	no	—
1013	C₂²⋊C₄	—	2	2	no	—
1014	C₂²⋊C₄	—	2	2	no	—
1015	C₂²⋊C₄	—	2	2	no	—
1016	C₂²⋊C₄	—	2	2	no	—
1017	C₂²⋊C₄	—	2	1	no	—
1018	C₂²⋊C₄	—	2	1	no	—
1019	C₂²⋊C₄	—	2	2	no	—
1020	C₂²⋊C₄	—	2	2	no	—
1021	C₂²⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
1022	C₂²⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
1023	C₂²⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
1024	C₄²	—	2	1	no	—
1025	C₄²	—	2	2	no	—
1026	C₄²	—	2	1	no	—
1027	C₄²	—	2	2	no	—
1028	C₄²	—	2	2	no	—
1029	C₄²	—	2	2	no	—
1030	C₄²	—	2	2	no	—
1031	C₄²	—	2	1	no	—
1032	C₄²	C₂×D₄×C₈₉	1	2	yes	—
1033	C₄²	C₂×D₄×C₈₉	1	2	yes	—
1034	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
1035	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
1036	C₄²	C₂⁴×C₈₉	1	1	yes	characteristic
1037	C₄²	C₂⁴×C₈₉	1	1	yes	characteristic
1038	C₄²	C₂⁴×C₈₉	1	2	yes	—
1039	C₂³	—	2	1	no	—
1040	C₂³	—	2	1	no	—
1041	C₂³	—	2	2	no	—
1042	C₂³	—	2	1	no	—
1043	C₂³	—	4	2	no	—
1044	C₂³	—	4	2	no	—
1045	C₂³	—	8	1	no	—
1046	C₂³	C₂²×D₄×C₈₉	1	1	yes	characteristic
1047	C₂³	C₂²×D₄×C₈₉	1	2	yes	—
1048	Q₈	—	2	2	no	—
1049	Q₈	—	2	1	no	—
1050	Q₈	—	2	2	no	—
1051	Q₈	—	2	2	no	—
1052	Q₈	—	8	1	no	—
1053	Q₈	—	8	2	no	—
1054	Q₈	—	8	1	no	—
1055	Q₈	C₂×#41×C₈₉	1	2	yes	—
1056	D₄	—	2	2	no	—
1057	D₄	—	2	1	no	—
1058	D₄	—	2	1	no	—
1059	D₄	—	2	2	no	—
1060	D₄	—	2	1	no	—
1061	D₄	—	2	1	no	—
1062	D₄	—	2	2	no	—
1063	D₄	—	2	1	no	—
1064	D₄	—	4	2	no	—
1065	D₄	—	4	2	no	—
1066	D₄	—	4	4	no	—
1067	D₄	—	4	2	no	—
1068	D₄	—	4	4	no	—
1069	D₄	—	4	4	no	—
1070	D₄	—	4	2	no	—
1071	D₄	—	8	2	no	—
1072	D₄	—	8	1	no	—
1073	D₄	—	8	2	no	—
1074	D₄	—	8	2	no	—
1075	D₄	—	8	2	no	—
1076	D₄	—	8	2	no	—
1077	D₄	C₂×#41×C₈₉	1	2	yes	—
1078	C₂×C₄	—	2	1	no	—
1079	C₂×C₄	—	2	2	no	—
1080	C₂×C₄	—	2	2	no	—
1081	C₂×C₄	—	2	1	no	—
1082	C₂×C₄	—	2	2	no	—
1083	C₂×C₄	—	2	1	no	—
1084	C₂×C₄	—	2	1	no	—
1085	C₂×C₄	—	2	1	no	—
1086	C₂×C₄	—	2	2	no	—
1087	C₂×C₄	—	2	2	no	—
1088	C₂×C₄	—	2	2	no	—
1089	C₂×C₄	—	2	1	no	—
1090	C₂×C₄	—	2	1	no	—
1091	C₂×C₄	—	4	2	no	—
1092	C₂×C₄	—	4	2	no	—
1093	C₂×C₄	—	4	1	no	—
1094	C₂×C₄	—	4	4	no	—
1095	C₂×C₄	—	4	2	no	—
1096	C₂×C₄	—	4	4	no	—
1097	C₂×C₄	—	4	2	no	—
1098	C₂×C₄	—	4	2	no	—
1099	C₂×C₄	—	4	4	no	—
1100	C₂×C₄	—	4	2	no	—
1101	C₂×C₄	—	4	4	no	—
1102	C₂×C₄	—	4	2	no	—
1103	C₂×C₄	—	4	2	no	—
1104	C₂×C₄	—	4	2	no	—
1105	C₂×C₄	—	4	2	no	—
1106	C₂×C₄	—	8	2	no	—
1107	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
1108	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
1109	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
1110	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
1111	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
1112	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
1113	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
1114	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
1115	C₂×C₄	C₂⁵×C₈₉	1	1	yes	characteristic
1116	C₈	—	2	2	no	—
1117	C₈	—	2	1	no	—
1118	C₈	—	2	1	no	—
1119	C₈	—	2	2	no	—
1120	C₈	—	2	1	no	—
1121	C₈	C₂×#41×C₈₉	1	2	yes	—
1122	C₂²	—	2	1	no	—
1123	C₂²	—	2	2	no	—
1124	C₂²	—	2	2	no	—
1125	C₂²	—	2	1	no	—
1126	C₂²	—	2	2	no	—
1127	C₂²	—	2	1	no	—
1128	C₂²	—	2	2	no	—
1129	C₂²	—	4	1	no	—
1130	C₂²	—	4	1	no	—
1131	C₂²	—	4	1	no	—
1132	C₂²	—	4	2	no	—
1133	C₂²	—	4	1	no	—
1134	C₂²	—	4	1	no	—
1135	C₂²	—	4	2	no	—
1136	C₂²	—	4	1	no	—
1137	C₂²	—	4	1	no	—
1138	C₂²	—	4	2	no	—
1139	C₂²	—	4	1	no	—
1140	C₂²	—	8	4	no	—
1141	C₂²	C₂³×D₄×C₈₉	1	1	yes	characteristic
1142	C₄	—	2	1	no	—
1143	C₄	—	2	2	no	—
1144	C₄	—	2	1	no	—
1145	C₄	—	2	2	no	—
1146	C₄	—	2	1	no	—
1147	C₄	—	2	2	no	—
1148	C₄	—	2	1	no	—
1149	C₄	—	2	2	no	—
1150	C₄	—	4	1	no	—
1151	C₄	—	4	1	no	—
1152	C₄	—	4	1	no	—
1153	C₄	—	4	1	no	—
1154	C₄	—	4	2	no	—
1155	C₄	—	4	2	no	—
1156	C₄	—	4	2	no	—
1157	C₄	#575×C₈₉	1	2	yes	—
1158	C₄	C₂²×#41×C₈₉	1	1	yes	characteristic
1159	C₄	#585×C₈₉	1	1	yes	characteristic
1160	C₂	—	4	2	no	—
1161	C₂	—	4	1	no	—
1162	C₂	—	4	2	no	—
1163	C₂	—	8	2	no	—
1164	C₂	—	8	1	no	—
1165	C₂	—	8	1	no	—
1166	C₂	D₄×#41×C₈₉	1	1	yes	characteristic
1167	C₂	C₂×#575×C₈₉	1	1	yes	characteristic
1168	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 ◁ C₄×#41×C₈₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₈₉×#3483	C₂	semidirect
2. C₈₉×#3475	C₂	semidirect
3. C₈₉×#3397	C₂	semidirect
4. C₈₉×#3385	C₂	semidirect
5. C₈₉×#3369	C₂	semidirect
6. C₈₉×#3366	C₂	semidirect
7. C₈₉×#3348	C₂	semidirect
8. C₈₉×#3341	C₂	semidirect
9. C₈₉×#3319	C₂	semidirect
10. C₈₉×#3317	C₂	semidirect
11. C₈₉×#3305	C₂	semidirect
12. C₈₉×#3303	C₂	semidirect
13. C₈₉×#3284	C₂	semidirect
14. C₈₉×#3268	C₂	semidirect
15. C₈₉×#3182	C₂	semidirect
16. C₈₉×#3180	C₂	semidirect
17. C₈₉×#3116	C₂	semidirect
18. C₈₉×#3115	C₂	semidirect
19. C₈₉×#3111	C₂	semidirect
20. C₈₉×#3109	C₂	semidirect
21. C₈₉×#2970	C₂	semidirect
22. C₄×AGL(1,ℤ/8)×C₈₉	C₂	semidirect
23. C₈₉×#2943	C₂	semidirect
26. Q₈²×C₈₉	C₂²	semidirect
32. #555×C₈₉	C₂²	semidirect
40. #550×C₈₉	C₂²	semidirect
41. #550×C₈₉	C₂²	semidirect
48. #532×C₈₉	C₂²	semidirect
56. C₄×#41×C₈₉	C₂²	semidirect
59. #501×C₈₉	C₂²	semidirect
60. #500×C₈₉	C₂²	semidirect
62. #492×C₈₉	C₂²	semidirect
63. #490×C₈₉	C₂²	semidirect
65. #487×C₈₉	C₂²	semidirect
66. #486×C₈₉	C₂²	semidirect
68. #485×C₈₉	C₂²	semidirect
70. #482×C₈₉	C₂²	semidirect
71. #482×C₈₉	C₂²	semidirect
73. #479×C₈₉	C₂²	semidirect
74. #478×C₈₉	C₂²	semidirect
75. #477×C₈₉	C₂²	semidirect
78. #476×C₈₉	C₂²	semidirect
79. #475×C₈₉	C₂²	semidirect
85. #465×C₈₉	C₂²	semidirect
86. #465×C₈₉	C₂²	semidirect
89. #462×C₈₉	C₂²	semidirect
90. #461×C₈₉	C₂²	semidirect
91. #460×C₈₉	C₂²	semidirect
96. #452×C₈₉	C₂²	semidirect
101. #446×C₈₉	C₂²	semidirect
102. #446×C₈₉	C₂²	semidirect
108. #441×C₈₉	C₂²	semidirect
109. #441×C₈₉	C₂²	semidirect
113. #440×C₈₉	C₂²	semidirect
114. #440×C₈₉	C₂²	semidirect
115. #440×C₈₉	C₂²	semidirect
116. #440×C₈₉	C₂²	semidirect
123. C₈×D₄×C₈₉	C₂²	semidirect
124. C₈×D₄×C₈₉	C₂²	semidirect
126. #432×C₈₉	C₂²	semidirect
128. #427×C₈₉	C₂²	semidirect
132. #416×C₈₉	C₂²	semidirect
134. C₂×#97×C₈₉	C₂²	semidirect
376. SD₁₆×C₈₉	#41	semidirect
575. #61459	C₈₉	direct (N × H)
585. #3483	C₂×C₈₉	semidirect
586. #3475	C₂×C₈₉	semidirect
587. #3397	C₂×C₈₉	semidirect
588. #3385	C₂×C₈₉	semidirect
589. #3369	C₂×C₈₉	semidirect
590. #3366	C₂×C₈₉	semidirect
591. #3348	C₂×C₈₉	semidirect
592. #3341	C₂×C₈₉	semidirect
593. #3319	C₂×C₈₉	semidirect
594. #3317	C₂×C₈₉	semidirect
595. #3305	C₂×C₈₉	semidirect
596. #3303	C₂×C₈₉	semidirect
597. #3284	C₂×C₈₉	semidirect
598. #3268	C₂×C₈₉	semidirect
599. #3182	C₂×C₈₉	semidirect
600. #3180	C₂×C₈₉	semidirect
601. #3116	C₂×C₈₉	semidirect
602. #3115	C₂×C₈₉	semidirect
603. #3111	C₂×C₈₉	semidirect
604. #3109	C₂×C₈₉	semidirect
605. #2970	C₂×C₈₉	semidirect
606. C₄×AGL(1,ℤ/8)	C₂×C₈₉	semidirect
607. #2943	C₂×C₈₉	semidirect
608. C₈₉	#61459	direct (N × H)
611. Q₈²	C₂²×C₈₉	semidirect
617. #555	C₂²×C₈₉	semidirect
625. #550	C₂²×C₈₉	semidirect
626. #550	C₂²×C₈₉	semidirect
633. #532	C₂²×C₈₉	semidirect
641. C₄×#41	C₂²×C₈₉	semidirect
644. #501	C₂²×C₈₉	semidirect
645. #500	C₂²×C₈₉	semidirect
647. #492	C₂²×C₈₉	semidirect
648. #490	C₂²×C₈₉	semidirect
650. #487	C₂²×C₈₉	semidirect
651. #486	C₂²×C₈₉	semidirect
653. #485	C₂²×C₈₉	semidirect
655. #482	C₂²×C₈₉	semidirect
656. #482	C₂²×C₈₉	semidirect
658. #479	C₂²×C₈₉	semidirect
659. #478	C₂²×C₈₉	semidirect
660. #477	C₂²×C₈₉	semidirect
663. #476	C₂²×C₈₉	semidirect
664. #475	C₂²×C₈₉	semidirect
670. #465	C₂²×C₈₉	semidirect
671. #465	C₂²×C₈₉	semidirect
674. #462	C₂²×C₈₉	semidirect
675. #461	C₂²×C₈₉	semidirect
676. #460	C₂²×C₈₉	semidirect
681. #452	C₂²×C₈₉	semidirect
686. #446	C₂²×C₈₉	semidirect
687. #446	C₂²×C₈₉	semidirect
693. #441	C₂²×C₈₉	semidirect
694. #441	C₂²×C₈₉	semidirect
698. #440	C₂²×C₈₉	semidirect
699. #440	C₂²×C₈₉	semidirect
700. #440	C₂²×C₈₉	semidirect
701. #440	C₂²×C₈₉	semidirect
708. C₈×D₄	C₂²×C₈₉	semidirect
709. C₈×D₄	C₂²×C₈₉	semidirect
711. #432	C₂²×C₈₉	semidirect
713. #427	C₂²×C₈₉	semidirect
717. #416	C₂²×C₈₉	semidirect
719. C₂×#97	C₂²×C₈₉	semidirect
961. SD₁₆	#41×C₈₉	semidirect

Maximal subgroups

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

subgroup	index
C₈₉×#3483	2
C₈₉×#3475	2
C₈₉×#3397	2
C₈₉×#3385	2
C₈₉×#3369	2
C₈₉×#3366	2
C₈₉×#3348	2
C₈₉×#3341	2
C₈₉×#3319	2
C₈₉×#3317	2
C₈₉×#3305	2
C₈₉×#3303	2
C₈₉×#3284	2
C₈₉×#3268	2
C₈₉×#3182	2
C₈₉×#3180	2
C₈₉×#3116	2
C₈₉×#3115	2
C₈₉×#3111	2
C₈₉×#3109	2
C₈₉×#2970	2
C₄×AGL(1,ℤ/8)×C₈₉	2
C₈₉×#2943	2
#61459	89

Subgroups — C89×#61459 #36439307

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#61459 #36439307