Subgroups — C₈₉×#61896 #36439744

Order 22784.

1776 conjugacy classes of subgroups.

The subgroup lattice has 1138 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈₉×#3522	C₂	1	1	yes	maximal, characteristic, complemented
2	C₈₉×#3480	C₂	1	1	yes	maximal, characteristic, complemented
3	C₈₉×#3403	C₂	1	2	yes	maximal, complemented
4	C₈₉×#3401	C₂	1	2	yes	maximal, complemented
5	C₈₉×#3400	C₂	1	1	yes	maximal, characteristic, complemented
6	C₈₉×#3399	C₂	1	1	yes	maximal, characteristic, complemented
7	C₈₉×#3399	C₂	1	1	yes	maximal, characteristic, complemented
8	C₈₉×#3397	C₂	1	1	yes	maximal, characteristic, complemented
9	C₈₉×#3376	C₂	1	2	yes	maximal, complemented
10	C₈₉×#3375	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈₉×#3372	C₂	1	1	yes	maximal, characteristic, complemented
12	C₈₉×#3370	C₂	1	2	yes	maximal, complemented
13	C₈₉×#3369	C₂	1	1	yes	maximal, characteristic, complemented
14	C₈₉×#3366	C₂	1	1	yes	maximal, characteristic, complemented
15	C₈₉×#3219	C₂	1	2	yes	maximal, complemented
16	C₈₉×#3214	C₂	1	2	yes	maximal, complemented
17	C₈₉×#3212	C₂	1	1	yes	maximal, characteristic, complemented
18	C₈₉×#3207	C₂	1	1	yes	maximal, characteristic, complemented
19	C₈₉×#3115	C₂	1	2	yes	maximal, complemented
20	C₈₉×#3111	C₂	1	2	yes	maximal, complemented
21	C₈₉×#3106	C₂	1	1	yes	maximal, characteristic, complemented
22	C₈₉×#3102	C₂	1	1	yes	maximal, characteristic, complemented
23	C₈₉×#2983	C₂	1	1	yes	maximal, characteristic, complemented
24	#559×C₈₉	C₂²	1	2	yes	—
25	#559×C₈₉	C₂²	1	1	yes	characteristic
26	#559×C₈₉	C₂²	1	1	yes	characteristic
27	#559×C₈₉	C₂²	1	2	yes	—
28	Q₈²×C₈₉	C₂²	1	1	yes	characteristic
29	#557×C₈₉	C₂²	1	1	yes	characteristic
30	#556×C₈₉	C₂²	1	1	yes	characteristic
31	#556×C₈₉	C₂²	1	2	yes	—
32	#554×C₈₉	C₂²	1	1	yes	characteristic
33	#554×C₈₉	C₂²	1	2	yes	—
34	#553×C₈₉	—	2	1	no	—
35	#553×C₈₉	—	2	2	no	—
36	#550×C₈₉	C₂²	1	1	yes	characteristic
37	#550×C₈₉	C₂²	1	1	yes	characteristic
38	#548×C₈₉	—	2	1	no	—
39	#548×C₈₉	—	2	1	no	—
40	#547×C₈₉	—	2	1	no	—
41	#547×C₈₉	—	2	2	no	—
42	#542×C₈₉	—	2	1	no	—
43	#542×C₈₉	—	2	2	no	—
44	#532×C₈₉	C₂²	1	1	yes	characteristic
45	#532×C₈₉	C₂²	1	2	yes	—
46	#532×C₈₉	C₂²	1	1	yes	characteristic
47	#532×C₈₉	C₂²	1	2	yes	—
48	#529×C₈₉	—	2	1	no	—
49	#529×C₈₉	—	2	2	no	—
50	#529×C₈₉	C₂²	1	1	yes	characteristic
51	#529×C₈₉	C₂²	1	2	yes	—
52	#520×C₈₉	—	2	1	no	—
53	C₄×#41×C₈₉	—	2	1	no	—
54	C₄×#41×C₈₉	C₂²	1	1	yes	characteristic
55	C₄×#41×C₈₉	C₂²	1	2	yes	—
56	C₂×C₄×Q₈×C₈₉	C₂²	1	1	yes	characteristic
57	#497×C₈₉	C₂²	1	2	yes	—
58	#496×C₈₉	C₂²	1	2	yes	—
59	#496×C₈₉	C₂²	1	2	yes	—
60	#496×C₈₉	C₂²	1	2	yes	—
61	#495×C₈₉	C₂²	1	2	yes	—
62	#493×C₈₉	C₂²	1	1	yes	characteristic
63	#492×C₈₉	C₂²	1	1	yes	characteristic
64	#491×C₈₉	C₂²	1	2	yes	—
65	#490×C₈₉	C₂²	1	2	yes	—
66	#489×C₈₉	C₂²	1	2	yes	—
67	#489×C₈₉	C₂²	1	2	yes	—
68	#488×C₈₉	C₂²	1	2	yes	—
69	#487×C₈₉	C₂²	1	1	yes	characteristic
70	#486×C₈₉	C₂²	1	1	yes	characteristic
71	#485×C₈₉	C₂²	1	1	yes	characteristic
72	#482×C₈₉	C₂²	1	1	yes	characteristic
73	#482×C₈₉	C₂²	1	2	yes	—
74	#479×C₈₉	C₂²	1	1	yes	characteristic
75	#479×C₈₉	C₂²	1	2	yes	—
76	#478×C₈₉	C₂²	1	1	yes	characteristic
77	#478×C₈₉	C₂²	1	2	yes	—
78	#477×C₈₉	C₂²	1	1	yes	characteristic
79	#476×C₈₉	C₂²	1	1	yes	characteristic
80	#475×C₈₉	C₂²	1	2	yes	—
81	#474×C₈₉	C₂²	1	2	yes	—
82	#464×C₈₉	C₂²	1	1	yes	characteristic
83	#464×C₈₉	C₂²	1	2	yes	—
84	#464×C₈₉	C₂²	1	2	yes	—
85	#464×C₈₉	C₂²	1	2	yes	—
86	#463×C₈₉	C₂²	1	1	yes	characteristic
87	#463×C₈₉	C₂²	1	2	yes	—
88	#463×C₈₉	C₂²	1	2	yes	—
89	#463×C₈₉	C₂²	1	2	yes	—
90	#463×C₈₉	C₂²	1	2	yes	—
91	#463×C₈₉	C₂²	1	2	yes	—
92	#462×C₈₉	C₂²	1	1	yes	characteristic
93	#461×C₈₉	C₂²	1	1	yes	characteristic
94	#461×C₈₉	C₂²	1	2	yes	—
95	#461×C₈₉	C₂²	1	2	yes	—
96	#460×C₈₉	C₂²	1	1	yes	characteristic
97	#460×C₈₉	C₂²	1	2	yes	—
98	#460×C₈₉	C₂²	1	1	yes	characteristic
99	#459×C₈₉	C₂²	1	1	yes	characteristic
100	#459×C₈₉	C₂²	1	1	yes	characteristic
101	#459×C₈₉	C₂²	1	2	yes	—
102	#459×C₈₉	C₂²	1	2	yes	—
103	#459×C₈₉	C₂²	1	2	yes	—
104	#452×C₈₉	C₂²	1	1	yes	characteristic
105	#452×C₈₉	C₂²	1	2	yes	—
106	#449×C₈₉	C₂²	1	1	yes	characteristic
107	#449×C₈₉	C₂²	1	2	yes	—
108	#449×C₈₉	C₂²	1	2	yes	—
109	#449×C₈₉	C₂²	1	2	yes	—
110	#449×C₈₉	C₂²	1	2	yes	—
111	#446×C₈₉	C₂²	1	1	yes	characteristic
112	#446×C₈₉	C₂²	1	1	yes	characteristic
113	#446×C₈₉	C₂²	1	2	yes	—
114	#446×C₈₉	C₂²	1	1	yes	characteristic
115	#446×C₈₉	C₂²	1	1	yes	characteristic
116	#446×C₈₉	C₂²	1	2	yes	—
117	#442×C₈₉	C₂²	1	2	yes	—
118	#442×C₈₉	C₂²	1	2	yes	—
119	#442×C₈₉	C₂²	1	2	yes	—
120	#441×C₈₉	C₂²	1	2	yes	—
121	#440×C₈₉	C₂²	1	2	yes	—
122	#440×C₈₉	C₂²	1	2	yes	—
123	#440×C₈₉	C₂²	1	2	yes	—
124	#440×C₈₉	C₂²	1	2	yes	—
125	C₄×Q₁₆×C₈₉	C₂²	1	1	yes	characteristic
126	C₄×SD₁₆×C₈₉	C₂²	1	1	yes	characteristic
127	C₄×SD₁₆×C₈₉	C₂²	1	1	yes	characteristic
128	C₄×SD₁₆×C₈₉	C₂²	1	2	yes	—
129	C₄×D₈×C₈₉	C₂²	1	1	yes	characteristic
130	C₄×D₈×C₈₉	C₂²	1	2	yes	—
131	#432×C₈₉	C₂²	1	2	yes	—
132	#432×C₈₉	C₂²	1	2	yes	—
133	#431×C₈₉	C₂²	1	1	yes	characteristic
134	#431×C₈₉	C₂²	1	1	yes	characteristic
135	C₂×#41×C₈₉	—	2	1	no	—
136	C₂×#41×C₈₉	—	2	1	no	—
137	C₂×#41×C₈₉	—	2	1	no	—
138	C₂×#41×C₈₉	—	2	2	no	—
139	C₂×#41×C₈₉	C₂³	1	1	yes	characteristic
140	C₂×#41×C₈₉	C₂³	1	2	yes	—
141	C₂²×Q₈×C₈₉	D₄	1	1	yes	characteristic
142	C₂×Q₁₆×C₈₉	C₂³	1	1	yes	characteristic
143	C₂×Q₁₆×C₈₉	C₂³	1	2	yes	—
144	C₂×SD₁₆×C₈₉	C₂³	1	2	yes	—
145	C₂×SD₁₆×C₈₉	C₂³	1	1	yes	characteristic
146	C₂×SD₁₆×C₈₉	C₂³	1	1	yes	characteristic
147	C₂×SD₁₆×C₈₉	C₂³	1	2	yes	—
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×D₈×C₈₉	C₂³	1	1	yes	characteristic
152	C₂×D₈×C₈₉	C₂³	1	2	yes	—
153	C₂×D₈×C₈₉	C₂³	1	2	yes	—
154	C₂×D₈×C₈₉	C₂³	1	2	yes	—
155	C₂×D₈×C₈₉	C₂³	1	2	yes	—
156	C₄⋊Q₈×C₈₉	—	2	1	no	—
157	C₄⋊Q₈×C₈₉	—	2	2	no	—
158	C₄⋊Q₈×C₈₉	C₂³	1	2	yes	—
159	C₄⋊Q₈×C₈₉	C₂³	1	1	yes	characteristic
160	C₄⋊Q₈×C₈₉	C₂³	1	2	yes	—
161	C₄⋊Q₈×C₈₉	C₂³	1	1	yes	characteristic
162	#127×C₈₉	C₂³	1	2	yes	—
163	#127×C₈₉	C₂³	1	1	yes	characteristic
164	#127×C₈₉	C₂³	1	1	yes	characteristic
165	#127×C₈₉	C₂³	1	2	yes	—
166	#126×C₈₉	—	2	2	no	—
167	#126×C₈₉	—	2	2	no	—
168	#126×C₈₉	—	2	2	no	—
169	#126×C₈₉	—	2	2	no	—
170	#126×C₈₉	—	2	1	no	—
171	#125×C₈₉	—	2	1	no	—
172	#125×C₈₉	—	2	2	no	—
173	#125×C₈₉	C₂³	1	1	yes	characteristic
174	#125×C₈₉	C₂³	1	2	yes	—
175	#124×C₈₉	—	2	1	no	—
176	#124×C₈₉	—	2	2	no	—
177	#124×C₈₉	—	2	1	no	—
178	#124×C₈₉	—	2	2	no	—
179	#124×C₈₉	—	2	2	no	—
180	#124×C₈₉	—	2	1	no	—
181	#124×C₈₉	C₂³	1	2	yes	—
182	#124×C₈₉	C₂³	1	2	yes	—
183	#124×C₈₉	C₂³	1	2	yes	—
184	#124×C₈₉	C₂³	1	1	yes	characteristic
185	#124×C₈₉	C₂³	1	2	yes	—
186	#123×C₈₉	—	2	1	no	—
187	#123×C₈₉	—	2	2	no	—
188	#123×C₈₉	—	2	2	no	—
189	#123×C₈₉	—	2	2	no	—
190	#123×C₈₉	—	2	2	no	—
191	#123×C₈₉	—	2	2	no	—
192	#123×C₈₉	—	2	2	no	—
193	#123×C₈₉	—	2	2	no	—
194	C₂²⋊Q₈×C₈₉	—	2	1	no	—
195	C₂²⋊Q₈×C₈₉	—	2	2	no	—
196	C₂²⋊Q₈×C₈₉	—	2	1	no	—
197	C₂²⋊Q₈×C₈₉	—	2	2	no	—
198	C₂²⋊Q₈×C₈₉	—	2	2	no	—
199	C₂²⋊Q₈×C₈₉	—	2	2	no	—
200	C₂²⋊Q₈×C₈₉	—	2	2	no	—
201	C₂²⋊Q₈×C₈₉	C₂³	1	1	yes	characteristic
202	#121×C₈₉	—	2	1	no	—
203	#121×C₈₉	—	2	2	no	—
204	#121×C₈₉	—	2	1	no	—
205	#121×C₈₉	—	2	2	no	—
206	#121×C₈₉	—	2	1	no	—
207	#121×C₈₉	—	2	2	no	—
208	#121×C₈₉	—	2	1	no	—
209	#121×C₈₉	—	2	2	no	—
210	#121×C₈₉	—	2	1	no	—
211	#121×C₈₉	—	2	2	no	—
212	#121×C₈₉	C₂³	1	1	yes	characteristic
213	#121×C₈₉	C₂³	1	2	yes	—
214	C₄×Q₈×C₈₉	—	2	1	no	—
215	C₄×Q₈×C₈₉	—	2	1	no	—
216	C₄×Q₈×C₈₉	D₄	1	1	yes	characteristic
217	C₄×Q₈×C₈₉	D₄	1	1	yes	characteristic
218	C₄×Q₈×C₈₉	D₄	1	2	yes	—
219	C₄×Q₈×C₈₉	C₂³	1	1	yes	characteristic
220	C₄×Q₈×C₈₉	C₂³	1	1	yes	characteristic
221	C₄×Q₈×C₈₉	C₂³	1	1	yes	characteristic
222	C₄×Q₈×C₈₉	C₂³	1	2	yes	—
223	C₄×Q₈×C₈₉	C₂³	1	2	yes	—
224	C₄×Q₈×C₈₉	C₂³	1	2	yes	—
225	C₄×Q₈×C₈₉	C₂³	1	1	yes	characteristic
226	C₄×Q₈×C₈₉	C₂³	1	1	yes	characteristic
227	C₄×Q₈×C₈₉	C₂³	1	2	yes	—
228	C₄×D₄×C₈₉	—	2	1	no	—
229	C₄×D₄×C₈₉	—	2	2	no	—
230	C₄×D₄×C₈₉	—	2	1	no	—
231	C₄×D₄×C₈₉	—	2	2	no	—
232	C₄×D₄×C₈₉	—	2	1	no	—
233	C₄×D₄×C₈₉	—	2	2	no	—
234	C₄×D₄×C₈₉	—	2	1	no	—
235	C₄×D₄×C₈₉	—	2	2	no	—
236	C₄×D₄×C₈₉	—	2	1	no	—
237	C₄×D₄×C₈₉	—	2	2	no	—
238	C₄×D₄×C₈₉	—	2	1	no	—
239	C₄×D₄×C₈₉	—	2	2	no	—
240	C₄×D₄×C₈₉	—	2	1	no	—
241	C₄×D₄×C₈₉	—	2	2	no	—
242	C₄×D₄×C₈₉	—	2	2	no	—
243	C₄×D₄×C₈₉	—	2	1	no	—
244	C₄×D₄×C₈₉	C₂³	1	1	yes	characteristic
245	C₄×D₄×C₈₉	C₂³	1	1	yes	characteristic
246	C₄×D₄×C₈₉	C₂³	1	1	yes	characteristic
247	C₄×D₄×C₈₉	C₂³	1	2	yes	—
248	C₄×D₄×C₈₉	C₂³	1	2	yes	—
249	C₄×D₄×C₈₉	C₂³	1	2	yes	—
250	C₄×D₄×C₈₉	C₂³	1	2	yes	—
251	C₄×D₄×C₈₉	C₂³	1	2	yes	—
252	C₄×D₄×C₈₉	C₂³	1	2	yes	—
253	#117×C₈₉	—	2	1	no	—
254	#117×C₈₉	—	2	2	no	—
255	#117×C₈₉	—	2	2	no	—
256	#117×C₈₉	—	2	1	no	—
257	#117×C₈₉	—	2	1	no	—
258	#117×C₈₉	—	2	2	no	—
259	#117×C₈₉	C₂³	1	1	yes	characteristic
260	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
261	C₂×C₄⋊C₄×C₈₉	—	2	2	no	—
262	C₂×C₄⋊C₄×C₈₉	D₄	1	1	yes	characteristic
263	C₂×C₄⋊C₄×C₈₉	D₄	1	2	yes	—
264	C₂×C₄²×C₈₉	—	2	1	no	—
265	C₂×C₄²×C₈₉	—	2	2	no	—
266	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
267	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
268	#107×C₈₉	C₂³	1	2	yes	—
269	#107×C₈₉	C₂³	1	1	yes	characteristic
270	#107×C₈₉	C₂³	1	1	yes	characteristic
271	#106×C₈₉	C₂³	1	2	yes	—
272	#106×C₈₉	C₂³	1	1	yes	characteristic
273	#106×C₈₉	C₂³	1	1	yes	characteristic
274	C₄⋊C₈×C₈₉	C₂³	1	1	yes	characteristic
275	C₄⋊C₈×C₈₉	C₂³	1	1	yes	characteristic
276	C₄⋊C₈×C₈₉	C₂³	1	1	yes	characteristic
277	C₄⋊C₈×C₈₉	C₂³	1	1	yes	characteristic
278	C₄⋊C₈×C₈₉	C₂³	1	2	yes	—
279	C₄⋊C₈×C₈₉	C₂³	1	2	yes	—
280	C₄⋊C₈×C₈₉	C₂³	1	2	yes	—
281	C₄⋊C₈×C₈₉	C₂³	1	2	yes	—
282	#103×C₈₉	C₂³	1	1	yes	characteristic
283	#103×C₈₉	C₂³	1	2	yes	—
284	#103×C₈₉	C₂³	1	1	yes	characteristic
285	#103×C₈₉	C₂³	1	1	yes	characteristic
286	#103×C₈₉	C₂³	1	1	yes	characteristic
287	#103×C₈₉	C₂³	1	2	yes	—
288	#103×C₈₉	C₂³	1	2	yes	—
289	#103×C₈₉	C₂³	1	2	yes	—
290	#103×C₈₉	C₂³	1	2	yes	—
291	#102×C₈₉	C₂³	1	2	yes	—
292	#102×C₈₉	C₂³	1	1	yes	characteristic
293	#102×C₈₉	C₂³	1	2	yes	—
294	#102×C₈₉	C₂³	1	1	yes	characteristic
295	#102×C₈₉	C₂³	1	1	yes	characteristic
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	2	yes	—
301	#102×C₈₉	C₂³	1	2	yes	—
302	C₂²⋊C₈×C₈₉	C₂³	1	1	yes	characteristic
303	C₂²⋊C₈×C₈₉	C₂³	1	1	yes	characteristic
304	C₂²⋊C₈×C₈₉	C₂³	1	2	yes	—
305	#97×C₈₉	C₂³	1	2	yes	—
306	#97×C₈₉	C₂³	1	2	yes	—
307	#97×C₈₉	C₂³	1	2	yes	—
308	#97×C₈₉	C₂³	1	2	yes	—
309	C₄×C₈×C₈₉	C₂³	1	2	yes	—
310	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
311	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
312	#41×C₈₉	—	4	1	no	—
313	#41×C₈₉	—	4	2	no	—
314	#41×C₈₉	—	4	1	no	—
315	#41×C₈₉	—	4	2	no	—
316	#41×C₈₉	—	4	4	no	—
317	#41×C₈₉	—	4	4	no	—
318	#41×C₈₉	—	8	2	no	—
319	#41×C₈₉	—	8	4	no	—
320	C₂×Q₈×C₈₉	—	2	2	no	—
321	C₂×Q₈×C₈₉	—	2	1	no	—
322	C₂×Q₈×C₈₉	—	4	2	no	—
323	C₂×Q₈×C₈₉	C₂×D₄	1	1	yes	characteristic
324	C₂×Q₈×C₈₉	C₂×D₄	1	1	yes	characteristic
325	C₂×Q₈×C₈₉	C₂×D₄	1	2	yes	—
326	C₂×Q₈×C₈₉	C₂⁴	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	2	no	—
331	C₂×D₄×C₈₉	—	2	1	no	—
332	C₂×D₄×C₈₉	—	2	2	no	—
333	C₂×D₄×C₈₉	—	2	2	no	—
334	C₂×D₄×C₈₉	—	2	2	no	—
335	C₂×D₄×C₈₉	—	2	1	no	—
336	C₂×D₄×C₈₉	—	2	1	no	—
337	C₂×D₄×C₈₉	—	2	2	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	C₂⁴	1	1	yes	characteristic
342	C₂×D₄×C₈₉	C₂⁴	1	2	yes	—
343	C₂×D₄×C₈₉	C₂⁴	1	1	yes	characteristic
344	C₂×D₄×C₈₉	C₂⁴	1	2	yes	—
345	C₂²×C₄×C₈₉	—	2	1	no	—
346	C₂²×C₄×C₈₉	—	2	2	no	—
347	C₂²×C₄×C₈₉	—	2	2	no	—
348	C₂²×C₄×C₈₉	—	2	1	no	—
349	C₂²×C₄×C₈₉	—	2	2	no	—
350	C₂²×C₄×C₈₉	—	2	1	no	—
351	C₂²×C₄×C₈₉	—	2	1	no	—
352	C₂²×C₄×C₈₉	—	2	2	no	—
353	C₂²×C₄×C₈₉	—	2	2	no	—
354	C₂²×C₄×C₈₉	—	2	2	no	—
355	C₂²×C₄×C₈₉	—	2	2	no	—
356	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
357	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
358	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
359	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
360	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
361	Q₁₆×C₈₉	—	4	2	no	—
362	Q₁₆×C₈₉	—	4	1	no	—
363	SD₁₆×C₈₉	—	4	1	no	—
364	SD₁₆×C₈₉	—	4	1	no	—
365	SD₁₆×C₈₉	—	4	2	no	—
366	SD₁₆×C₈₉	—	4	2	no	—
367	SD₁₆×C₈₉	—	4	2	no	—
368	SD₁₆×C₈₉	—	4	2	no	—
369	SD₁₆×C₈₉	—	4	2	no	—
370	D₈×C₈₉	—	4	2	no	—
371	D₈×C₈₉	—	4	2	no	—
372	D₈×C₈₉	—	4	1	no	—
373	D₈×C₈₉	—	4	2	no	—
374	D₈×C₈₉	—	4	2	no	—
375	C₂×C₈×C₈₉	C₂⁴	1	1	yes	characteristic
376	C₂×C₈×C₈₉	C₂⁴	1	2	yes	—
377	C₂×C₈×C₈₉	C₂⁴	1	2	yes	—
378	C₂×C₈×C₈₉	C₂⁴	1	1	yes	characteristic
379	C₂×C₈×C₈₉	C₂⁴	1	1	yes	characteristic
380	C₂×C₈×C₈₉	C₂⁴	1	1	yes	characteristic
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	1	no	—
386	C₄⋊C₄×C₈₉	—	2	2	no	—
387	C₄⋊C₄×C₈₉	—	2	1	no	—
388	C₄⋊C₄×C₈₉	—	2	2	no	—
389	C₄⋊C₄×C₈₉	—	2	1	no	—
390	C₄⋊C₄×C₈₉	—	2	2	no	—
391	C₄⋊C₄×C₈₉	—	2	1	no	—
392	C₄⋊C₄×C₈₉	—	2	2	no	—
393	C₄⋊C₄×C₈₉	—	2	1	no	—
394	C₄⋊C₄×C₈₉	—	2	2	no	—
395	C₄⋊C₄×C₈₉	—	2	1	no	—
396	C₄⋊C₄×C₈₉	—	2	2	no	—
397	C₄⋊C₄×C₈₉	—	2	1	no	—
398	C₄⋊C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
399	C₄⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
400	C₄⋊C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
401	C₄⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
402	C₄⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
403	C₄⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
404	C₄⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
405	C₄⋊C₄×C₈₉	C₂⁴	1	1	yes	characteristic
406	C₄⋊C₄×C₈₉	C₂⁴	1	2	yes	—
407	C₄⋊C₄×C₈₉	C₂⁴	1	1	yes	characteristic
408	C₄⋊C₄×C₈₉	C₂⁴	1	1	yes	characteristic
409	C₄⋊C₄×C₈₉	C₂⁴	1	1	yes	characteristic
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	2	no	—
415	C₂²⋊C₄×C₈₉	—	2	1	no	—
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	1	no	—
421	C₂²⋊C₄×C₈₉	—	2	2	no	—
422	C₂²⋊C₄×C₈₉	—	2	1	no	—
423	C₂²⋊C₄×C₈₉	—	2	2	no	—
424	C₂²⋊C₄×C₈₉	—	2	2	no	—
425	C₂²⋊C₄×C₈₉	—	2	2	no	—
426	C₂²⋊C₄×C₈₉	—	2	2	no	—
427	C₂²⋊C₄×C₈₉	—	2	1	no	—
428	C₂²⋊C₄×C₈₉	—	2	2	no	—
429	C₂²⋊C₄×C₈₉	—	2	1	no	—
430	C₂²⋊C₄×C₈₉	—	2	2	no	—
431	C₂²⋊C₄×C₈₉	—	2	2	no	—
432	C₂²⋊C₄×C₈₉	—	2	2	no	—
433	C₄²×C₈₉	—	2	1	no	—
434	C₄²×C₈₉	—	2	1	no	—
435	C₄²×C₈₉	—	2	2	no	—
436	C₄²×C₈₉	—	2	2	no	—
437	C₄²×C₈₉	—	2	1	no	—
438	C₄²×C₈₉	—	2	2	no	—
439	C₄²×C₈₉	—	2	1	no	—
440	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
441	C₄²×C₈₉	C₂×D₄	1	2	yes	—
442	C₄²×C₈₉	C₂×D₄	1	2	yes	—
443	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
444	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
445	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
446	C₄²×C₈₉	C₂⁴	1	2	yes	—
447	C₄²×C₈₉	C₂⁴	1	2	yes	—
448	C₂³×C₈₉	—	2	1	no	—
449	C₂³×C₈₉	—	2	2	no	—
450	C₂³×C₈₉	—	2	2	no	—
451	C₂³×C₈₉	—	2	1	no	—
452	C₂³×C₈₉	C₂²×D₄	1	1	yes	characteristic
453	Q₈×C₈₉	—	2	2	no	—
454	Q₈×C₈₉	—	2	2	no	—
455	Q₈×C₈₉	—	2	1	no	—
456	Q₈×C₈₉	—	2	2	no	—
457	Q₈×C₈₉	—	2	1	no	—
458	Q₈×C₈₉	—	2	1	no	—
459	Q₈×C₈₉	—	2	1	no	—
460	Q₈×C₈₉	—	2	2	no	—
461	Q₈×C₈₉	—	4	2	no	—
462	Q₈×C₈₉	—	8	2	no	—
463	Q₈×C₈₉	—	8	1	no	—
464	D₄×C₈₉	—	2	1	no	—
465	D₄×C₈₉	—	2	2	no	—
466	D₄×C₈₉	—	2	1	no	—
467	D₄×C₈₉	—	2	2	no	—
468	D₄×C₈₉	—	2	2	no	—
469	D₄×C₈₉	—	2	2	no	—
470	D₄×C₈₉	—	2	1	no	—
471	D₄×C₈₉	—	2	1	no	—
472	D₄×C₈₉	—	4	4	no	—
473	D₄×C₈₉	—	4	4	no	—
474	D₄×C₈₉	—	4	2	no	—
475	D₄×C₈₉	—	4	4	no	—
476	D₄×C₈₉	—	4	4	no	—
477	D₄×C₈₉	—	4	2	no	—
478	D₄×C₈₉	—	4	2	no	—
479	D₄×C₈₉	—	4	2	no	—
480	D₄×C₈₉	—	8	2	no	—
481	D₄×C₈₉	—	8	1	no	—
482	D₄×C₈₉	—	8	2	no	—
483	D₄×C₈₉	—	8	1	no	—
484	C₂×C₄×C₈₉	—	2	2	no	—
485	C₂×C₄×C₈₉	—	2	1	no	—
486	C₂×C₄×C₈₉	—	2	1	no	—
487	C₂×C₄×C₈₉	—	2	1	no	—
488	C₂×C₄×C₈₉	—	2	1	no	—
489	C₂×C₄×C₈₉	—	2	1	no	—
490	C₂×C₄×C₈₉	—	2	1	no	—
491	C₂×C₄×C₈₉	—	2	2	no	—
492	C₂×C₄×C₈₉	—	2	2	no	—
493	C₂×C₄×C₈₉	—	2	1	no	—
494	C₂×C₄×C₈₉	—	2	1	no	—
495	C₂×C₄×C₈₉	—	4	2	no	—
496	C₂×C₄×C₈₉	—	4	1	no	—
497	C₂×C₄×C₈₉	—	4	2	no	—
498	C₂×C₄×C₈₉	—	4	2	no	—
499	C₂×C₄×C₈₉	—	4	4	no	—
500	C₂×C₄×C₈₉	—	4	4	no	—
501	C₂×C₄×C₈₉	—	4	4	no	—
502	C₂×C₄×C₈₉	—	4	2	no	—
503	C₂×C₄×C₈₉	—	4	2	no	—
504	C₂×C₄×C₈₉	—	8	1	no	—
505	C₂×C₄×C₈₉	—	8	2	no	—
506	C₂×C₄×C₈₉	—	8	2	no	—
507	C₂×C₄×C₈₉	—	8	2	no	—
508	C₂×C₄×C₈₉	—	8	2	no	—
509	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
510	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
511	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
512	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
513	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
514	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
515	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
516	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
517	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
518	C₂×C₄×C₈₉	C₂⁵	1	1	yes	characteristic
519	C₈×C₈₉	—	2	1	no	—
520	C₈×C₈₉	—	2	1	no	—
521	C₈×C₈₉	—	2	2	no	—
522	C₈×C₈₉	—	2	1	no	—
523	C₈×C₈₉	—	2	2	no	—
524	C₈×C₈₉	—	2	1	no	—
525	C₂²×C₈₉	—	2	1	no	—
526	C₂²×C₈₉	—	2	1	no	—
527	C₂²×C₈₉	—	2	1	no	—
528	C₂²×C₈₉	—	4	2	no	—
529	C₂²×C₈₉	—	4	1	no	—
530	C₂²×C₈₉	—	4	1	no	—
531	C₂²×C₈₉	—	4	2	no	—
532	C₂²×C₈₉	—	4	2	no	—
533	C₂²×C₈₉	—	4	1	no	—
534	C₂²×C₈₉	—	4	1	no	—
535	C₂²×C₈₉	—	4	2	no	—
536	C₂²×C₈₉	—	4	2	no	—
537	C₂²×C₈₉	—	4	2	no	—
538	C₂²×C₈₉	—	4	1	no	—
539	C₂²×C₈₉	—	4	1	no	—
540	C₂²×C₈₉	C₂³×D₄	1	1	yes	characteristic
541	C₄×C₈₉	—	2	1	no	—
542	C₄×C₈₉	—	2	2	no	—
543	C₄×C₈₉	—	2	2	no	—
544	C₄×C₈₉	—	2	1	no	—
545	C₄×C₈₉	—	2	1	no	—
546	C₄×C₈₉	—	2	1	no	—
547	C₄×C₈₉	—	2	2	no	—
548	C₄×C₈₉	—	2	2	no	—
549	C₄×C₈₉	—	4	1	no	—
550	C₄×C₈₉	—	4	2	no	—
551	C₄×C₈₉	—	4	1	no	—
552	C₄×C₈₉	—	4	1	no	—
553	C₄×C₈₉	—	4	2	no	—
554	C₄×C₈₉	—	4	1	no	—
555	C₄×C₈₉	—	4	1	no	—
556	C₄×C₈₉	—	4	1	no	—
557	C₄×C₈₉	#575	1	2	yes	—
558	C₄×C₈₉	#585	1	1	yes	characteristic
559	C₄×C₈₉	#585	1	1	yes	characteristic
560	#61896	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
561	C₂×C₈₉	—	4	1	no	—
562	C₂×C₈₉	—	8	1	no	—
563	C₂×C₈₉	—	8	2	no	—
564	C₂×C₈₉	—	8	2	no	—
565	C₂×C₈₉	—	8	1	no	—
566	C₂×C₈₉	#3487	1	1	yes	characteristic
567	C₂×C₈₉	C₂×#575	1	1	yes	characteristic
568	C₂×C₈₉	#3585	1	1	yes	characteristic
569	#3522	C₂×C₈₉	1	1	yes	characteristic, complemented
570	#3480	C₂×C₈₉	1	1	yes	characteristic, complemented
571	#3403	C₂×C₈₉	1	2	yes	complemented
572	#3401	C₂×C₈₉	1	2	yes	complemented
573	#3400	C₂×C₈₉	1	1	yes	characteristic, complemented
574	#3399	C₂×C₈₉	1	1	yes	characteristic, complemented
575	#3399	C₂×C₈₉	1	1	yes	characteristic, complemented
576	#3397	C₂×C₈₉	1	1	yes	characteristic, complemented
577	#3376	C₂×C₈₉	1	2	yes	complemented
578	#3375	C₂×C₈₉	1	1	yes	characteristic, complemented
579	#3372	C₂×C₈₉	1	1	yes	characteristic, complemented
580	#3370	C₂×C₈₉	1	2	yes	complemented
581	#3369	C₂×C₈₉	1	1	yes	characteristic, complemented
582	#3366	C₂×C₈₉	1	1	yes	characteristic, complemented
583	#3219	C₂×C₈₉	1	2	yes	complemented
584	#3214	C₂×C₈₉	1	2	yes	complemented
585	#3212	C₂×C₈₉	1	1	yes	characteristic, complemented
586	#3207	C₂×C₈₉	1	1	yes	characteristic, complemented
587	#3115	C₂×C₈₉	1	2	yes	complemented
588	#3111	C₂×C₈₉	1	2	yes	complemented
589	#3106	C₂×C₈₉	1	1	yes	characteristic, complemented
590	#3102	C₂×C₈₉	1	1	yes	characteristic, complemented
591	#2983	C₂×C₈₉	1	1	yes	characteristic, complemented
592	C₈₉	#61896	1	1	yes	characteristic, direct product factor, Sylow
593	#559	C₂²×C₈₉	1	2	yes	—
594	#559	C₂²×C₈₉	1	1	yes	characteristic
595	#559	C₂²×C₈₉	1	1	yes	characteristic
596	#559	C₂²×C₈₉	1	2	yes	—
597	Q₈²	C₂²×C₈₉	1	1	yes	characteristic
598	#557	C₂²×C₈₉	1	1	yes	characteristic
599	#556	C₂²×C₈₉	1	1	yes	characteristic
600	#556	C₂²×C₈₉	1	2	yes	—
601	#554	C₂²×C₈₉	1	1	yes	characteristic
602	#554	C₂²×C₈₉	1	2	yes	—
603	#553	—	2	1	no	—
604	#553	—	2	2	no	—
605	#550	C₂²×C₈₉	1	1	yes	characteristic
606	#550	C₂²×C₈₉	1	1	yes	characteristic
607	#548	—	2	1	no	—
608	#548	—	2	1	no	—
609	#547	—	2	1	no	—
610	#547	—	2	2	no	—
611	#542	—	2	1	no	—
612	#542	—	2	2	no	—
613	#532	C₂²×C₈₉	1	1	yes	characteristic
614	#532	C₂²×C₈₉	1	2	yes	—
615	#532	C₂²×C₈₉	1	1	yes	characteristic
616	#532	C₂²×C₈₉	1	2	yes	—
617	#529	—	2	1	no	—
618	#529	—	2	2	no	—
619	#529	C₂²×C₈₉	1	1	yes	characteristic
620	#529	C₂²×C₈₉	1	2	yes	—
621	#520	—	2	1	no	—
622	C₄×#41	—	2	1	no	—
623	C₄×#41	C₂²×C₈₉	1	1	yes	characteristic
624	C₄×#41	C₂²×C₈₉	1	2	yes	—
625	C₂×C₄×Q₈	C₂²×C₈₉	1	1	yes	characteristic
626	#497	C₂²×C₈₉	1	2	yes	—
627	#496	C₂²×C₈₉	1	2	yes	—
628	#496	C₂²×C₈₉	1	2	yes	—
629	#496	C₂²×C₈₉	1	2	yes	—
630	#495	C₂²×C₈₉	1	2	yes	—
631	#493	C₂²×C₈₉	1	1	yes	characteristic
632	#492	C₂²×C₈₉	1	1	yes	characteristic
633	#491	C₂²×C₈₉	1	2	yes	—
634	#490	C₂²×C₈₉	1	2	yes	—
635	#489	C₂²×C₈₉	1	2	yes	—
636	#489	C₂²×C₈₉	1	2	yes	—
637	#488	C₂²×C₈₉	1	2	yes	—
638	#487	C₂²×C₈₉	1	1	yes	characteristic
639	#486	C₂²×C₈₉	1	1	yes	characteristic
640	#485	C₂²×C₈₉	1	1	yes	characteristic
641	#482	C₂²×C₈₉	1	1	yes	characteristic
642	#482	C₂²×C₈₉	1	2	yes	—
643	#479	C₂²×C₈₉	1	1	yes	characteristic
644	#479	C₂²×C₈₉	1	2	yes	—
645	#478	C₂²×C₈₉	1	1	yes	characteristic
646	#478	C₂²×C₈₉	1	2	yes	—
647	#477	C₂²×C₈₉	1	1	yes	characteristic
648	#476	C₂²×C₈₉	1	1	yes	characteristic
649	#475	C₂²×C₈₉	1	2	yes	—
650	#474	C₂²×C₈₉	1	2	yes	—
651	#464	C₂²×C₈₉	1	1	yes	characteristic
652	#464	C₂²×C₈₉	1	2	yes	—
653	#464	C₂²×C₈₉	1	2	yes	—
654	#464	C₂²×C₈₉	1	2	yes	—
655	#463	C₂²×C₈₉	1	1	yes	characteristic
656	#463	C₂²×C₈₉	1	2	yes	—
657	#463	C₂²×C₈₉	1	2	yes	—
658	#463	C₂²×C₈₉	1	2	yes	—
659	#463	C₂²×C₈₉	1	2	yes	—
660	#463	C₂²×C₈₉	1	2	yes	—
661	#462	C₂²×C₈₉	1	1	yes	characteristic
662	#461	C₂²×C₈₉	1	1	yes	characteristic
663	#461	C₂²×C₈₉	1	2	yes	—
664	#461	C₂²×C₈₉	1	2	yes	—
665	#460	C₂²×C₈₉	1	1	yes	characteristic
666	#460	C₂²×C₈₉	1	2	yes	—
667	#460	C₂²×C₈₉	1	1	yes	characteristic
668	#459	C₂²×C₈₉	1	1	yes	characteristic
669	#459	C₂²×C₈₉	1	1	yes	characteristic
670	#459	C₂²×C₈₉	1	2	yes	—
671	#459	C₂²×C₈₉	1	2	yes	—
672	#459	C₂²×C₈₉	1	2	yes	—
673	#452	C₂²×C₈₉	1	1	yes	characteristic
674	#452	C₂²×C₈₉	1	2	yes	—
675	#449	C₂²×C₈₉	1	1	yes	characteristic
676	#449	C₂²×C₈₉	1	2	yes	—
677	#449	C₂²×C₈₉	1	2	yes	—
678	#449	C₂²×C₈₉	1	2	yes	—
679	#449	C₂²×C₈₉	1	2	yes	—
680	#446	C₂²×C₈₉	1	1	yes	characteristic
681	#446	C₂²×C₈₉	1	1	yes	characteristic
682	#446	C₂²×C₈₉	1	2	yes	—
683	#446	C₂²×C₈₉	1	1	yes	characteristic
684	#446	C₂²×C₈₉	1	1	yes	characteristic
685	#446	C₂²×C₈₉	1	2	yes	—
686	#442	C₂²×C₈₉	1	2	yes	—
687	#442	C₂²×C₈₉	1	2	yes	—
688	#442	C₂²×C₈₉	1	2	yes	—
689	#441	C₂²×C₈₉	1	2	yes	—
690	#440	C₂²×C₈₉	1	2	yes	—
691	#440	C₂²×C₈₉	1	2	yes	—
692	#440	C₂²×C₈₉	1	2	yes	—
693	#440	C₂²×C₈₉	1	2	yes	—
694	C₄×Q₁₆	C₂²×C₈₉	1	1	yes	characteristic
695	C₄×SD₁₆	C₂²×C₈₉	1	1	yes	characteristic
696	C₄×SD₁₆	C₂²×C₈₉	1	1	yes	characteristic
697	C₄×SD₁₆	C₂²×C₈₉	1	2	yes	—
698	C₄×D₈	C₂²×C₈₉	1	1	yes	characteristic
699	C₄×D₈	C₂²×C₈₉	1	2	yes	—
700	#432	C₂²×C₈₉	1	2	yes	—
701	#432	C₂²×C₈₉	1	2	yes	—
702	#431	C₂²×C₈₉	1	1	yes	characteristic
703	#431	C₂²×C₈₉	1	1	yes	characteristic
704	C₂×#41	—	2	1	no	—
705	C₂×#41	—	2	1	no	—
706	C₂×#41	—	2	1	no	—
707	C₂×#41	—	2	2	no	—
708	C₂×#41	C₂³×C₈₉	1	1	yes	characteristic
709	C₂×#41	C₂³×C₈₉	1	2	yes	—
710	C₂²×Q₈	D₄×C₈₉	1	1	yes	characteristic
711	C₂×Q₁₆	C₂³×C₈₉	1	1	yes	characteristic
712	C₂×Q₁₆	C₂³×C₈₉	1	2	yes	—
713	C₂×SD₁₆	C₂³×C₈₉	1	2	yes	—
714	C₂×SD₁₆	C₂³×C₈₉	1	1	yes	characteristic
715	C₂×SD₁₆	C₂³×C₈₉	1	1	yes	characteristic
716	C₂×SD₁₆	C₂³×C₈₉	1	2	yes	—
717	C₂×SD₁₆	C₂³×C₈₉	1	2	yes	—
718	C₂×SD₁₆	C₂³×C₈₉	1	2	yes	—
719	C₂×SD₁₆	C₂³×C₈₉	1	2	yes	—
720	C₂×D₈	C₂³×C₈₉	1	1	yes	characteristic
721	C₂×D₈	C₂³×C₈₉	1	2	yes	—
722	C₂×D₈	C₂³×C₈₉	1	2	yes	—
723	C₂×D₈	C₂³×C₈₉	1	2	yes	—
724	C₂×D₈	C₂³×C₈₉	1	2	yes	—
725	C₄⋊Q₈	—	2	1	no	—
726	C₄⋊Q₈	—	2	2	no	—
727	C₄⋊Q₈	C₂³×C₈₉	1	2	yes	—
728	C₄⋊Q₈	C₂³×C₈₉	1	1	yes	characteristic
729	C₄⋊Q₈	C₂³×C₈₉	1	2	yes	—
730	C₄⋊Q₈	C₂³×C₈₉	1	1	yes	characteristic
731	#127	C₂³×C₈₉	1	2	yes	—
732	#127	C₂³×C₈₉	1	1	yes	characteristic
733	#127	C₂³×C₈₉	1	1	yes	characteristic
734	#127	C₂³×C₈₉	1	2	yes	—
735	#126	—	2	2	no	—
736	#126	—	2	2	no	—
737	#126	—	2	2	no	—
738	#126	—	2	2	no	—
739	#126	—	2	1	no	—
740	#125	—	2	1	no	—
741	#125	—	2	2	no	—
742	#125	C₂³×C₈₉	1	1	yes	characteristic
743	#125	C₂³×C₈₉	1	2	yes	—
744	#124	—	2	1	no	—
745	#124	—	2	2	no	—
746	#124	—	2	1	no	—
747	#124	—	2	2	no	—
748	#124	—	2	2	no	—
749	#124	—	2	1	no	—
750	#124	C₂³×C₈₉	1	1	yes	characteristic
751	#124	C₂³×C₈₉	1	2	yes	—
752	#124	C₂³×C₈₉	1	2	yes	—
753	#124	C₂³×C₈₉	1	2	yes	—
754	#124	C₂³×C₈₉	1	2	yes	—
755	#123	—	2	1	no	—
756	#123	—	2	2	no	—
757	#123	—	2	2	no	—
758	#123	—	2	2	no	—
759	#123	—	2	2	no	—
760	#123	—	2	2	no	—
761	#123	—	2	2	no	—
762	#123	—	2	2	no	—
763	C₂²⋊Q₈	—	2	1	no	—
764	C₂²⋊Q₈	—	2	2	no	—
765	C₂²⋊Q₈	—	2	1	no	—
766	C₂²⋊Q₈	—	2	2	no	—
767	C₂²⋊Q₈	—	2	2	no	—
768	C₂²⋊Q₈	—	2	2	no	—
769	C₂²⋊Q₈	—	2	2	no	—
770	C₂²⋊Q₈	C₂³×C₈₉	1	1	yes	characteristic
771	#121	—	2	1	no	—
772	#121	—	2	2	no	—
773	#121	—	2	1	no	—
774	#121	—	2	2	no	—
775	#121	—	2	1	no	—
776	#121	—	2	2	no	—
777	#121	—	2	1	no	—
778	#121	—	2	2	no	—
779	#121	—	2	1	no	—
780	#121	—	2	2	no	—
781	#121	C₂³×C₈₉	1	1	yes	characteristic
782	#121	C₂³×C₈₉	1	2	yes	—
783	C₄×Q₈	—	2	1	no	—
784	C₄×Q₈	—	2	1	no	—
785	C₄×Q₈	D₄×C₈₉	1	1	yes	characteristic
786	C₄×Q₈	D₄×C₈₉	1	1	yes	characteristic
787	C₄×Q₈	D₄×C₈₉	1	2	yes	—
788	C₄×Q₈	C₂³×C₈₉	1	1	yes	characteristic
789	C₄×Q₈	C₂³×C₈₉	1	2	yes	—
790	C₄×Q₈	C₂³×C₈₉	1	1	yes	characteristic
791	C₄×Q₈	C₂³×C₈₉	1	2	yes	—
792	C₄×Q₈	C₂³×C₈₉	1	1	yes	characteristic
793	C₄×Q₈	C₂³×C₈₉	1	2	yes	—
794	C₄×Q₈	C₂³×C₈₉	1	1	yes	characteristic
795	C₄×Q₈	C₂³×C₈₉	1	1	yes	characteristic
796	C₄×Q₈	C₂³×C₈₉	1	2	yes	—
797	C₄×D₄	—	2	1	no	—
798	C₄×D₄	—	2	2	no	—
799	C₄×D₄	—	2	1	no	—
800	C₄×D₄	—	2	2	no	—
801	C₄×D₄	—	2	1	no	—
802	C₄×D₄	—	2	2	no	—
803	C₄×D₄	—	2	1	no	—
804	C₄×D₄	—	2	2	no	—
805	C₄×D₄	—	2	1	no	—
806	C₄×D₄	—	2	2	no	—
807	C₄×D₄	—	2	1	no	—
808	C₄×D₄	—	2	2	no	—
809	C₄×D₄	—	2	1	no	—
810	C₄×D₄	—	2	2	no	—
811	C₄×D₄	—	2	2	no	—
812	C₄×D₄	—	2	1	no	—
813	C₄×D₄	C₂³×C₈₉	1	1	yes	characteristic
814	C₄×D₄	C₂³×C₈₉	1	2	yes	—
815	C₄×D₄	C₂³×C₈₉	1	1	yes	characteristic
816	C₄×D₄	C₂³×C₈₉	1	2	yes	—
817	C₄×D₄	C₂³×C₈₉	1	1	yes	characteristic
818	C₄×D₄	C₂³×C₈₉	1	2	yes	—
819	C₄×D₄	C₂³×C₈₉	1	2	yes	—
820	C₄×D₄	C₂³×C₈₉	1	2	yes	—
821	C₄×D₄	C₂³×C₈₉	1	2	yes	—
822	#117	—	2	1	no	—
823	#117	—	2	2	no	—
824	#117	—	2	2	no	—
825	#117	—	2	1	no	—
826	#117	—	2	1	no	—
827	#117	—	2	2	no	—
828	#117	C₂³×C₈₉	1	1	yes	characteristic
829	C₂×C₄⋊C₄	—	2	1	no	—
830	C₂×C₄⋊C₄	—	2	2	no	—
831	C₂×C₄⋊C₄	D₄×C₈₉	1	1	yes	characteristic
832	C₂×C₄⋊C₄	D₄×C₈₉	1	2	yes	—
833	C₂×C₄²	—	2	1	no	—
834	C₂×C₄²	—	2	2	no	—
835	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
836	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
837	#107	C₂³×C₈₉	1	2	yes	—
838	#107	C₂³×C₈₉	1	1	yes	characteristic
839	#107	C₂³×C₈₉	1	1	yes	characteristic
840	#106	C₂³×C₈₉	1	2	yes	—
841	#106	C₂³×C₈₉	1	1	yes	characteristic
842	#106	C₂³×C₈₉	1	1	yes	characteristic
843	C₄⋊C₈	C₂³×C₈₉	1	1	yes	characteristic
844	C₄⋊C₈	C₂³×C₈₉	1	1	yes	characteristic
845	C₄⋊C₈	C₂³×C₈₉	1	1	yes	characteristic
846	C₄⋊C₈	C₂³×C₈₉	1	1	yes	characteristic
847	C₄⋊C₈	C₂³×C₈₉	1	2	yes	—
848	C₄⋊C₈	C₂³×C₈₉	1	2	yes	—
849	C₄⋊C₈	C₂³×C₈₉	1	2	yes	—
850	C₄⋊C₈	C₂³×C₈₉	1	2	yes	—
851	#103	C₂³×C₈₉	1	1	yes	characteristic
852	#103	C₂³×C₈₉	1	2	yes	—
853	#103	C₂³×C₈₉	1	1	yes	characteristic
854	#103	C₂³×C₈₉	1	1	yes	characteristic
855	#103	C₂³×C₈₉	1	1	yes	characteristic
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	#102	C₂³×C₈₉	1	2	yes	—
861	#102	C₂³×C₈₉	1	1	yes	characteristic
862	#102	C₂³×C₈₉	1	2	yes	—
863	#102	C₂³×C₈₉	1	1	yes	characteristic
864	#102	C₂³×C₈₉	1	1	yes	characteristic
865	#102	C₂³×C₈₉	1	2	yes	—
866	#102	C₂³×C₈₉	1	1	yes	characteristic
867	#102	C₂³×C₈₉	1	2	yes	—
868	#102	C₂³×C₈₉	1	2	yes	—
869	#102	C₂³×C₈₉	1	2	yes	—
870	#102	C₂³×C₈₉	1	2	yes	—
871	C₂²⋊C₈	C₂³×C₈₉	1	1	yes	characteristic
872	C₂²⋊C₈	C₂³×C₈₉	1	1	yes	characteristic
873	C₂²⋊C₈	C₂³×C₈₉	1	2	yes	—
874	#97	C₂³×C₈₉	1	2	yes	—
875	#97	C₂³×C₈₉	1	2	yes	—
876	#97	C₂³×C₈₉	1	2	yes	—
877	#97	C₂³×C₈₉	1	2	yes	—
878	C₄×C₈	C₂³×C₈₉	1	2	yes	—
879	C₄×C₈	C₂³×C₈₉	1	1	yes	characteristic
880	C₄×C₈	C₂³×C₈₉	1	1	yes	characteristic
881	#41	—	4	1	no	—
882	#41	—	4	2	no	—
883	#41	—	4	1	no	—
884	#41	—	4	2	no	—
885	#41	—	4	4	no	—
886	#41	—	4	4	no	—
887	#41	—	8	2	no	—
888	#41	—	8	4	no	—
889	C₂×Q₈	—	2	2	no	—
890	C₂×Q₈	—	2	1	no	—
891	C₂×Q₈	—	4	2	no	—
892	C₂×Q₈	C₂×D₄×C₈₉	1	1	yes	characteristic
893	C₂×Q₈	C₂×D₄×C₈₉	1	1	yes	characteristic
894	C₂×Q₈	C₂×D₄×C₈₉	1	2	yes	—
895	C₂×Q₈	C₂⁴×C₈₉	1	1	yes	characteristic
896	C₂×Q₈	C₂⁴×C₈₉	1	2	yes	—
897	C₂×Q₈	C₂⁴×C₈₉	1	1	yes	characteristic
898	C₂×D₄	—	2	1	no	—
899	C₂×D₄	—	2	2	no	—
900	C₂×D₄	—	2	1	no	—
901	C₂×D₄	—	2	2	no	—
902	C₂×D₄	—	2	2	no	—
903	C₂×D₄	—	2	2	no	—
904	C₂×D₄	—	2	1	no	—
905	C₂×D₄	—	2	1	no	—
906	C₂×D₄	—	2	2	no	—
907	C₂×D₄	—	2	1	no	—
908	C₂×D₄	—	2	2	no	—
909	C₂×D₄	—	2	1	no	—
910	C₂×D₄	C₂⁴×C₈₉	1	1	yes	characteristic
911	C₂×D₄	C₂⁴×C₈₉	1	2	yes	—
912	C₂×D₄	C₂⁴×C₈₉	1	1	yes	characteristic
913	C₂×D₄	C₂⁴×C₈₉	1	2	yes	—
914	C₂²×C₄	—	2	1	no	—
915	C₂²×C₄	—	2	2	no	—
916	C₂²×C₄	—	2	2	no	—
917	C₂²×C₄	—	2	1	no	—
918	C₂²×C₄	—	2	2	no	—
919	C₂²×C₄	—	2	1	no	—
920	C₂²×C₄	—	2	1	no	—
921	C₂²×C₄	—	2	2	no	—
922	C₂²×C₄	—	2	2	no	—
923	C₂²×C₄	—	2	2	no	—
924	C₂²×C₄	—	2	2	no	—
925	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
926	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
927	C₂²×C₄	C₂×D₄×C₈₉	1	2	yes	—
928	C₂²×C₄	C₂×D₄×C₈₉	1	2	yes	—
929	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
930	Q₁₆	—	4	2	no	—
931	Q₁₆	—	4	1	no	—
932	SD₁₆	—	4	1	no	—
933	SD₁₆	—	4	1	no	—
934	SD₁₆	—	4	2	no	—
935	SD₁₆	—	4	2	no	—
936	SD₁₆	—	4	2	no	—
937	SD₁₆	—	4	2	no	—
938	SD₁₆	—	4	2	no	—
939	D₈	—	4	2	no	—
940	D₈	—	4	2	no	—
941	D₈	—	4	1	no	—
942	D₈	—	4	2	no	—
943	D₈	—	4	2	no	—
944	C₂×C₈	C₂⁴×C₈₉	1	1	yes	characteristic
945	C₂×C₈	C₂⁴×C₈₉	1	2	yes	—
946	C₂×C₈	C₂⁴×C₈₉	1	2	yes	—
947	C₂×C₈	C₂⁴×C₈₉	1	1	yes	characteristic
948	C₂×C₈	C₂⁴×C₈₉	1	1	yes	characteristic
949	C₂×C₈	C₂⁴×C₈₉	1	1	yes	characteristic
950	C₄⋊C₄	—	2	1	no	—
951	C₄⋊C₄	—	2	2	no	—
952	C₄⋊C₄	—	2	2	no	—
953	C₄⋊C₄	—	2	1	no	—
954	C₄⋊C₄	—	2	1	no	—
955	C₄⋊C₄	—	2	2	no	—
956	C₄⋊C₄	—	2	1	no	—
957	C₄⋊C₄	—	2	2	no	—
958	C₄⋊C₄	—	2	1	no	—
959	C₄⋊C₄	—	2	2	no	—
960	C₄⋊C₄	—	2	1	no	—
961	C₄⋊C₄	—	2	2	no	—
962	C₄⋊C₄	—	2	1	no	—
963	C₄⋊C₄	—	2	2	no	—
964	C₄⋊C₄	—	2	1	no	—
965	C₄⋊C₄	—	2	2	no	—
966	C₄⋊C₄	—	2	1	no	—
967	C₄⋊C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
968	C₄⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
969	C₄⋊C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
970	C₄⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
971	C₄⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
972	C₄⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
973	C₄⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
974	C₄⋊C₄	C₂⁴×C₈₉	1	1	yes	characteristic
975	C₄⋊C₄	C₂⁴×C₈₉	1	2	yes	—
976	C₄⋊C₄	C₂⁴×C₈₉	1	1	yes	characteristic
977	C₄⋊C₄	C₂⁴×C₈₉	1	1	yes	characteristic
978	C₄⋊C₄	C₂⁴×C₈₉	1	1	yes	characteristic
979	C₂²⋊C₄	—	2	1	no	—
980	C₂²⋊C₄	—	2	1	no	—
981	C₂²⋊C₄	—	2	2	no	—
982	C₂²⋊C₄	—	2	2	no	—
983	C₂²⋊C₄	—	2	2	no	—
984	C₂²⋊C₄	—	2	1	no	—
985	C₂²⋊C₄	—	2	2	no	—
986	C₂²⋊C₄	—	2	1	no	—
987	C₂²⋊C₄	—	2	2	no	—
988	C₂²⋊C₄	—	2	2	no	—
989	C₂²⋊C₄	—	2	1	no	—
990	C₂²⋊C₄	—	2	2	no	—
991	C₂²⋊C₄	—	2	1	no	—
992	C₂²⋊C₄	—	2	2	no	—
993	C₂²⋊C₄	—	2	2	no	—
994	C₂²⋊C₄	—	2	2	no	—
995	C₂²⋊C₄	—	2	2	no	—
996	C₂²⋊C₄	—	2	1	no	—
997	C₂²⋊C₄	—	2	2	no	—
998	C₂²⋊C₄	—	2	1	no	—
999	C₂²⋊C₄	—	2	2	no	—
1000	C₂²⋊C₄	—	2	2	no	—
1001	C₂²⋊C₄	—	2	2	no	—
1002	C₄²	—	2	1	no	—
1003	C₄²	—	2	1	no	—
1004	C₄²	—	2	2	no	—
1005	C₄²	—	2	2	no	—
1006	C₄²	—	2	1	no	—
1007	C₄²	—	2	2	no	—
1008	C₄²	—	2	1	no	—
1009	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
1010	C₄²	C₂×D₄×C₈₉	1	2	yes	—
1011	C₄²	C₂×D₄×C₈₉	1	2	yes	—
1012	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
1013	C₄²	C₂⁴×C₈₉	1	1	yes	characteristic
1014	C₄²	C₂⁴×C₈₉	1	1	yes	characteristic
1015	C₄²	C₂⁴×C₈₉	1	2	yes	—
1016	C₄²	C₂⁴×C₈₉	1	2	yes	—
1017	C₂³	—	2	2	no	—
1018	C₂³	—	2	1	no	—
1019	C₂³	—	2	2	no	—
1020	C₂³	—	2	1	no	—
1021	C₂³	C₂²×D₄×C₈₉	1	1	yes	characteristic
1022	Q₈	—	2	2	no	—
1023	Q₈	—	2	2	no	—
1024	Q₈	—	2	1	no	—
1025	Q₈	—	2	2	no	—
1026	Q₈	—	2	1	no	—
1027	Q₈	—	2	1	no	—
1028	Q₈	—	2	1	no	—
1029	Q₈	—	2	2	no	—
1030	Q₈	—	4	2	no	—
1031	Q₈	—	8	2	no	—
1032	Q₈	—	8	1	no	—
1033	D₄	—	2	1	no	—
1034	D₄	—	2	2	no	—
1035	D₄	—	2	1	no	—
1036	D₄	—	2	2	no	—
1037	D₄	—	2	2	no	—
1038	D₄	—	2	2	no	—
1039	D₄	—	2	1	no	—
1040	D₄	—	2	1	no	—
1041	D₄	—	4	4	no	—
1042	D₄	—	4	4	no	—
1043	D₄	—	4	2	no	—
1044	D₄	—	4	4	no	—
1045	D₄	—	4	4	no	—
1046	D₄	—	4	2	no	—
1047	D₄	—	4	2	no	—
1048	D₄	—	4	2	no	—
1049	D₄	—	8	2	no	—
1050	D₄	—	8	1	no	—
1051	D₄	—	8	2	no	—
1052	D₄	—	8	1	no	—
1053	C₂×C₄	—	2	2	no	—
1054	C₂×C₄	—	2	1	no	—
1055	C₂×C₄	—	2	1	no	—
1056	C₂×C₄	—	2	1	no	—
1057	C₂×C₄	—	2	1	no	—
1058	C₂×C₄	—	2	1	no	—
1059	C₂×C₄	—	2	1	no	—
1060	C₂×C₄	—	2	2	no	—
1061	C₂×C₄	—	2	2	no	—
1062	C₂×C₄	—	2	1	no	—
1063	C₂×C₄	—	2	1	no	—
1064	C₂×C₄	—	4	2	no	—
1065	C₂×C₄	—	4	1	no	—
1066	C₂×C₄	—	4	2	no	—
1067	C₂×C₄	—	4	4	no	—
1068	C₂×C₄	—	4	4	no	—
1069	C₂×C₄	—	4	2	no	—
1070	C₂×C₄	—	4	4	no	—
1071	C₂×C₄	—	4	2	no	—
1072	C₂×C₄	—	4	2	no	—
1073	C₂×C₄	—	8	1	no	—
1074	C₂×C₄	—	8	2	no	—
1075	C₂×C₄	—	8	2	no	—
1076	C₂×C₄	—	8	2	no	—
1077	C₂×C₄	—	8	2	no	—
1078	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
1079	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
1080	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
1081	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
1082	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
1083	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
1084	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
1085	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
1086	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
1087	C₂×C₄	C₂⁵×C₈₉	1	1	yes	characteristic
1088	C₈	—	2	1	no	—
1089	C₈	—	2	1	no	—
1090	C₈	—	2	2	no	—
1091	C₈	—	2	1	no	—
1092	C₈	—	2	2	no	—
1093	C₈	—	2	1	no	—
1094	C₂²	—	2	1	no	—
1095	C₂²	—	2	1	no	—
1096	C₂²	—	2	1	no	—
1097	C₂²	—	4	2	no	—
1098	C₂²	—	4	2	no	—
1099	C₂²	—	4	1	no	—
1100	C₂²	—	4	1	no	—
1101	C₂²	—	4	2	no	—
1102	C₂²	—	4	1	no	—
1103	C₂²	—	4	1	no	—
1104	C₂²	—	4	2	no	—
1105	C₂²	—	4	2	no	—
1106	C₂²	—	4	1	no	—
1107	C₂²	—	4	1	no	—
1108	C₂²	—	4	2	no	—
1109	C₂²	C₂³×D₄×C₈₉	1	1	yes	characteristic
1110	C₄	—	2	1	no	—
1111	C₄	—	2	2	no	—
1112	C₄	—	2	2	no	—
1113	C₄	—	2	1	no	—
1114	C₄	—	2	2	no	—
1115	C₄	—	2	2	no	—
1116	C₄	—	2	1	no	—
1117	C₄	—	2	1	no	—
1118	C₄	—	4	1	no	—
1119	C₄	—	4	1	no	—
1120	C₄	—	4	1	no	—
1121	C₄	—	4	2	no	—
1122	C₄	—	4	1	no	—
1123	C₄	—	4	1	no	—
1124	C₄	—	4	2	no	—
1125	C₄	—	4	1	no	—
1126	C₄	#575×C₈₉	1	2	yes	—
1127	C₄	#585×C₈₉	1	1	yes	characteristic
1128	C₄	#585×C₈₉	1	1	yes	characteristic
1129	C₂	—	4	1	no	—
1130	C₂	—	8	2	no	—
1131	C₂	—	8	1	no	—
1132	C₂	—	8	2	no	—
1133	C₂	—	8	1	no	—
1134	C₂	C₈₉×#3487	1	1	yes	characteristic
1135	C₂	C₂×#575×C₈₉	1	1	yes	characteristic
1136	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 ◁ C₂×C₄×Q₈×C₈₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₈₉×#3522	C₂	semidirect
2. C₈₉×#3480	C₂	semidirect
3. C₈₉×#3403	C₂	semidirect
4. C₈₉×#3401	C₂	semidirect
5. C₈₉×#3400	C₂	semidirect
6. C₈₉×#3399	C₂	semidirect
7. C₈₉×#3399	C₂	semidirect
8. C₈₉×#3397	C₂	semidirect
9. C₈₉×#3376	C₂	semidirect
10. C₈₉×#3375	C₂	semidirect
11. C₈₉×#3372	C₂	semidirect
12. C₈₉×#3370	C₂	semidirect
13. C₈₉×#3369	C₂	semidirect
14. C₈₉×#3366	C₂	semidirect
15. C₈₉×#3219	C₂	semidirect
16. C₈₉×#3214	C₂	semidirect
17. C₈₉×#3212	C₂	semidirect
18. C₈₉×#3207	C₂	semidirect
19. C₈₉×#3115	C₂	semidirect
20. C₈₉×#3111	C₂	semidirect
21. C₈₉×#3106	C₂	semidirect
22. C₈₉×#3102	C₂	semidirect
23. C₈₉×#2983	C₂	semidirect
560. #61896	C₈₉	direct (N × H)
569. #3522	C₂×C₈₉	semidirect
570. #3480	C₂×C₈₉	semidirect
571. #3403	C₂×C₈₉	semidirect
572. #3401	C₂×C₈₉	semidirect
573. #3400	C₂×C₈₉	semidirect
574. #3399	C₂×C₈₉	semidirect
575. #3399	C₂×C₈₉	semidirect
576. #3397	C₂×C₈₉	semidirect
577. #3376	C₂×C₈₉	semidirect
578. #3375	C₂×C₈₉	semidirect
579. #3372	C₂×C₈₉	semidirect
580. #3370	C₂×C₈₉	semidirect
581. #3369	C₂×C₈₉	semidirect
582. #3366	C₂×C₈₉	semidirect
583. #3219	C₂×C₈₉	semidirect
584. #3214	C₂×C₈₉	semidirect
585. #3212	C₂×C₈₉	semidirect
586. #3207	C₂×C₈₉	semidirect
587. #3115	C₂×C₈₉	semidirect
588. #3111	C₂×C₈₉	semidirect
589. #3106	C₂×C₈₉	semidirect
590. #3102	C₂×C₈₉	semidirect
591. #2983	C₂×C₈₉	semidirect
592. C₈₉	#61896	direct (N × H)

Maximal subgroups

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

subgroup	index
C₈₉×#3522	2
C₈₉×#3480	2
C₈₉×#3403	2
C₈₉×#3401	2
C₈₉×#3400	2
C₈₉×#3399	2
C₈₉×#3397	2
C₈₉×#3376	2
C₈₉×#3375	2
C₈₉×#3372	2
C₈₉×#3370	2
C₈₉×#3369	2
C₈₉×#3366	2
C₈₉×#3219	2
C₈₉×#3214	2
C₈₉×#3212	2
C₈₉×#3207	2
C₈₉×#3115	2
C₈₉×#3111	2
C₈₉×#3106	2
C₈₉×#3102	2
C₈₉×#2983	2
#61896	89

Subgroups — C89×#61896 #36439744

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#61896 #36439744