Subgroups — C₈₉×#63026 #36440874

Order 22784.

6678 conjugacy classes of subgroups.

The subgroup lattice has 1278 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈₉×#3568	C₂	1	2	yes	maximal, complemented
2	C₈₉×#3566	C₂	1	6	yes	maximal, complemented
3	C₈₉×#3564	C₂	1	6	yes	maximal, complemented
4	C₈₉×#3545	C₂	1	3	yes	maximal, complemented
5	C₈₉×#3535	C₂	1	6	yes	maximal, complemented
6	C₈₉×#3533	C₂	1	3	yes	maximal, complemented
7	C₈₉×#3532	C₂	1	1	yes	maximal, characteristic, complemented
8	C₈₉×#3521	C₂	1	6	yes	maximal, complemented
9	C₈₉×#3513	C₂	1	6	yes	maximal, complemented
10	C₈₉×#3510	C₂	1	3	yes	maximal, complemented
11	C₈₉×#3495	C₂	1	6	yes	maximal, complemented
12	C₈₉×#3491	C₂	1	3	yes	maximal, complemented
13	C₈₉×#3490	C₂	1	3	yes	maximal, complemented
14	C₈₉×#3475	C₂	1	6	yes	maximal, complemented
15	C₂×#551×C₈₉	C₂	1	3	yes	maximal, complemented
16	#563×C₈₉	C₂²	1	3	yes	complemented
17	#563×C₈₉	C₂²	1	6	yes	complemented
18	#563×C₈₉	C₂²	1	6	yes	complemented
19	#563×C₈₉	C₂²	1	3	yes	complemented
20	#562×C₈₉	C₂²	1	6	yes	complemented
21	#562×C₈₉	C₂²	1	6	yes	complemented
22	H(3,𝔽₄)×C₈₉	C₂²	1	1	yes	characteristic, complemented
23	H(3,𝔽₄)×C₈₉	C₂²	1	1	yes	characteristic, complemented
24	#560×C₈₉	C₂²	1	3	yes	complemented
25	#560×C₈₉	C₂²	1	1	yes	characteristic, complemented
26	#559×C₈₉	C₂²	1	3	yes	complemented
27	#559×C₈₉	C₂²	1	6	yes	complemented
28	#556×C₈₉	C₂²	1	6	yes	complemented
29	#556×C₈₉	C₂²	1	6	yes	complemented
30	#556×C₈₉	C₂²	1	6	yes	complemented
31	#556×C₈₉	C₂²	1	6	yes	complemented
32	#555×C₈₉	C₂²	1	6	yes	complemented
33	#554×C₈₉	C₂²	1	6	yes	complemented
34	#554×C₈₉	C₂²	1	6	yes	complemented
35	#554×C₈₉	C₂²	1	6	yes	complemented
36	#553×C₈₉	C₂²	1	6	yes	complemented
37	#553×C₈₉	C₂²	1	6	yes	complemented
38	#553×C₈₉	C₂²	1	6	yes	complemented
39	#553×C₈₉	C₂²	1	6	yes	complemented
40	#552×C₈₉	C₂²	1	6	yes	complemented
41	#552×C₈₉	C₂²	1	6	yes	complemented
42	#552×C₈₉	C₂²	1	6	yes	complemented
43	#552×C₈₉	C₂²	1	6	yes	complemented
44	#552×C₈₉	C₂²	1	6	yes	complemented
45	#552×C₈₉	C₂²	1	6	yes	complemented
46	#552×C₈₉	C₂²	1	6	yes	complemented
47	#552×C₈₉	C₂²	1	6	yes	complemented
48	#552×C₈₉	C₂²	1	6	yes	complemented
49	#552×C₈₉	C₂²	1	6	yes	complemented
50	#551×C₈₉	C₂²	1	3	yes	complemented
51	#551×C₈₉	C₂²	1	6	yes	complemented
52	#551×C₈₉	C₂²	1	6	yes	complemented
53	#551×C₈₉	C₂²	1	6	yes	complemented
54	#551×C₈₉	C₂²	1	6	yes	complemented
55	#551×C₈₉	C₂²	1	3	yes	complemented
56	#551×C₈₉	C₂²	1	6	yes	complemented
57	#551×C₈₉	C₂²	1	3	yes	complemented
58	#551×C₈₉	C₂²	1	3	yes	complemented
59	#551×C₈₉	C₂²	1	6	yes	complemented
60	#551×C₈₉	C₂²	1	6	yes	complemented
61	#551×C₈₉	C₂²	1	6	yes	complemented
62	#551×C₈₉	C₂²	1	6	yes	complemented
63	#551×C₈₉	C₂²	1	6	yes	complemented
64	#551×C₈₉	C₂²	1	3	yes	complemented
65	#551×C₈₉	C₂²	1	6	yes	complemented
66	#551×C₈₉	C₂²	1	6	yes	complemented
67	#551×C₈₉	C₂²	1	6	yes	complemented
68	#551×C₈₉	C₂²	1	3	yes	complemented
69	#551×C₈₉	C₂²	1	3	yes	complemented
70	#551×C₈₉	C₂²	1	3	yes	complemented
71	#551×C₈₉	C₂²	1	6	yes	complemented
72	#547×C₈₉	C₂²	1	6	yes	complemented
73	#547×C₈₉	C₂²	1	6	yes	complemented
74	#546×C₈₉	C₂²	1	6	yes	complemented
75	#546×C₈₉	C₂²	1	6	yes	complemented
76	#546×C₈₉	C₂²	1	6	yes	complemented
77	#546×C₈₉	C₂²	1	6	yes	complemented
78	#546×C₈₉	C₂²	1	6	yes	complemented
79	#546×C₈₉	C₂²	1	6	yes	complemented
80	D₄²×C₈₉	C₂²	1	3	yes	complemented
81	#544×C₈₉	C₂²	1	6	yes	complemented
82	#543×C₈₉	C₂²	1	3	yes	complemented
83	#543×C₈₉	C₂²	1	3	yes	complemented
84	#542×C₈₉	C₂²	1	6	yes	complemented
85	#542×C₈₉	C₂²	1	6	yes	complemented
86	#542×C₈₉	C₂²	1	6	yes	complemented
87	#542×C₈₉	C₂²	1	6	yes	complemented
88	#542×C₈₉	C₂²	1	6	yes	complemented
89	#542×C₈₉	C₂²	1	6	yes	complemented
90	#541×C₈₉	C₂²	1	6	yes	complemented
91	#541×C₈₉	C₂²	1	6	yes	complemented
92	#541×C₈₉	C₂²	1	6	yes	complemented
93	#540×C₈₉	C₂²	1	6	yes	complemented
94	#539×C₈₉	C₂²	1	6	yes	complemented
95	#539×C₈₉	C₂²	1	6	yes	complemented
96	#539×C₈₉	C₂²	1	6	yes	complemented
97	#539×C₈₉	C₂²	1	6	yes	complemented
98	#539×C₈₉	C₂²	1	6	yes	complemented
99	#539×C₈₉	C₂²	1	6	yes	complemented
100	#538×C₈₉	C₂²	1	6	yes	—
101	#538×C₈₉	C₂²	1	6	yes	complemented
102	#538×C₈₉	C₂²	1	6	yes	complemented
103	#538×C₈₉	C₂²	1	6	yes	complemented
104	#538×C₈₉	C₂²	1	6	yes	complemented
105	#538×C₈₉	C₂²	1	6	yes	complemented
106	#536×C₈₉	C₂²	1	6	yes	complemented
107	#536×C₈₉	C₂²	1	3	yes	complemented
108	#535×C₈₉	C₂²	1	3	yes	—
109	#534×C₈₉	C₂²	1	3	yes	—
110	#534×C₈₉	C₂²	1	3	yes	complemented
111	#533×C₈₉	C₂²	1	6	yes	complemented
112	#533×C₈₉	C₂²	1	3	yes	complemented
113	#529×C₈₉	C₂²	1	6	yes	complemented
114	#529×C₈₉	C₂²	1	6	yes	complemented
115	#529×C₈₉	C₂²	1	6	yes	complemented
116	#529×C₈₉	C₂²	1	6	yes	complemented
117	#529×C₈₉	C₂²	1	6	yes	complemented
118	#529×C₈₉	C₂²	1	6	yes	complemented
119	#529×C₈₉	C₂²	1	6	yes	complemented
120	#529×C₈₉	C₂²	1	6	yes	complemented
121	C₂×#126×C₈₉	C₂²	1	6	yes	complemented
122	C₂×#126×C₈₉	C₂²	1	2	yes	complemented
123	C₂×#124×C₈₉	C₂²	1	3	yes	complemented
124	#525×C₈₉	C₂²	1	6	yes	—
125	#525×C₈₉	C₂²	1	6	yes	complemented
126	#525×C₈₉	C₂²	1	6	yes	complemented
127	C₂×#123×C₈₉	C₂²	1	3	yes	complemented
128	C₂×#123×C₈₉	C₂²	1	6	yes	complemented
129	C₂×#123×C₈₉	C₂²	1	3	yes	complemented
130	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	6	yes	complemented
131	C₂×#120×C₈₉	C₂²	1	3	yes	—
132	C₂×#120×C₈₉	C₂²	1	1	yes	characteristic, complemented
133	#520×C₈₉	C₂²	1	6	yes	complemented
134	#519×C₈₉	C₂²	1	3	yes	complemented
135	#518×C₈₉	C₂²	1	3	yes	complemented
136	#518×C₈₉	C₂²	1	3	yes	complemented
137	#518×C₈₉	C₂²	1	3	yes	complemented
138	C₄×#41×C₈₉	C₂²	1	3	yes	complemented
139	C₄×#41×C₈₉	C₂²	1	6	yes	complemented
140	C₂×C₄×D₄×C₈₉	C₂²	1	6	yes	complemented
141	C₂×#117×C₈₉	C₂²	1	6	yes	complemented
142	C₂×#117×C₈₉	C₂²	1	3	yes	complemented
143	C₂²×C₂²⋊C₄×C₈₉	C₂²	1	3	yes	complemented
144	C₂⁵×C₈₉	C₂³	1	1	yes	characteristic
145	C₂×#41×C₈₉	C₂³	1	6	yes	—
146	C₂×#41×C₈₉	C₂³	1	3	yes	—
147	C₂×#41×C₈₉	C₂³	1	6	yes	—
148	C₂²×Q₈×C₈₉	C₂³	1	3	yes	—
149	C₂²×D₄×C₈₉	C₂³	1	6	yes	—
150	C₂²×D₄×C₈₉	C₂³	1	3	yes	—
151	C₂²×D₄×C₈₉	C₂³	1	3	yes	—
152	C₂²×D₄×C₈₉	C₂³	1	3	yes	—
153	C₂³×C₄×C₈₉	C₂³	1	6	yes	—
154	C₂³×C₄×C₈₉	C₂³	1	3	yes	—
155	C₄⋊Q₈×C₈₉	C₂³	1	6	yes	complemented
156	C₄⋊Q₈×C₈₉	C₂³	1	6	yes	complemented
157	C₄⋊Q₈×C₈₉	C₂³	1	6	yes	complemented
158	C₄⋊Q₈×C₈₉	C₂³	1	6	yes	complemented
159	C₄⋊Q₈×C₈₉	C₂³	1	6	yes	complemented
160	#127×C₈₉	C₂³	1	1	yes	characteristic
161	#127×C₈₉	C₂³	1	3	yes	—
162	#126×C₈₉	C₂³	1	6	yes	—
163	#126×C₈₉	C₂³	1	6	yes	—
164	#126×C₈₉	C₂³	1	2	yes	—
165	#126×C₈₉	C₂³	1	6	yes	—
166	#126×C₈₉	C₂³	1	6	yes	—
167	#126×C₈₉	C₂³	1	6	yes	—
168	#126×C₈₉	C₂³	1	6	yes	—
169	#126×C₈₉	C₂³	1	6	yes	—
170	#126×C₈₉	C₂³	1	6	yes	—
171	#126×C₈₉	C₂³	1	6	yes	—
172	#126×C₈₉	C₂³	1	6	yes	—
173	#126×C₈₉	C₂³	1	6	yes	—
174	#126×C₈₉	C₂³	1	6	yes	—
175	#126×C₈₉	C₂³	1	6	yes	—
176	#126×C₈₉	C₂³	1	6	yes	complemented
177	#126×C₈₉	C₂³	1	2	yes	complemented
178	#126×C₈₉	C₂³	1	6	yes	complemented
179	#126×C₈₉	C₂³	1	6	yes	complemented
180	#126×C₈₉	C₂³	1	6	yes	complemented
181	#126×C₈₉	C₂³	1	6	yes	complemented
182	#126×C₈₉	C₂³	1	6	yes	complemented
183	#126×C₈₉	C₂³	1	6	yes	complemented
184	#126×C₈₉	C₂³	1	6	yes	complemented
185	#126×C₈₉	C₂³	1	6	yes	complemented
186	#126×C₈₉	C₂³	1	6	yes	complemented
187	#126×C₈₉	C₂³	1	2	yes	complemented
188	#125×C₈₉	C₂³	1	6	yes	complemented
189	#125×C₈₉	C₂³	1	6	yes	complemented
190	#125×C₈₉	C₂³	1	6	yes	complemented
191	#125×C₈₉	C₂³	1	6	yes	complemented
192	#125×C₈₉	C₂³	1	6	yes	complemented
193	#125×C₈₉	C₂³	1	6	yes	complemented
194	#125×C₈₉	C₂³	1	6	yes	complemented
195	#125×C₈₉	C₂³	1	6	yes	complemented
196	#125×C₈₉	C₂³	1	6	yes	complemented
197	#125×C₈₉	C₂³	1	6	yes	complemented
198	#125×C₈₉	C₂³	1	6	yes	complemented
199	#125×C₈₉	C₂³	1	6	yes	complemented
200	#125×C₈₉	C₂³	1	6	yes	complemented
201	#124×C₈₉	C₂³	1	3	yes	—
202	#124×C₈₉	C₂³	1	3	yes	—
203	#124×C₈₉	C₂³	1	6	yes	—
204	#124×C₈₉	C₂³	1	6	yes	—
205	#124×C₈₉	C₂³	1	3	yes	—
206	#124×C₈₉	C₂³	1	3	yes	—
207	#124×C₈₉	C₂³	1	6	yes	—
208	#124×C₈₉	C₂³	1	6	yes	—
209	#124×C₈₉	C₂³	1	6	yes	—
210	#124×C₈₉	C₂³	1	3	yes	—
211	#124×C₈₉	C₂³	1	3	yes	—
212	#124×C₈₉	C₂³	1	6	yes	—
213	#124×C₈₉	C₂³	1	6	yes	—
214	#124×C₈₉	C₂³	1	6	yes	complemented
215	#124×C₈₉	C₂³	1	6	yes	complemented
216	#124×C₈₉	C₂³	1	6	yes	complemented
217	#124×C₈₉	C₂³	1	6	yes	complemented
218	#123×C₈₉	C₂³	1	6	yes	—
219	#123×C₈₉	C₂³	1	6	yes	—
220	#123×C₈₉	C₂³	1	6	yes	—
221	#123×C₈₉	C₂³	1	3	yes	—
222	#123×C₈₉	C₂³	1	3	yes	—
223	#123×C₈₉	C₂³	1	6	yes	—
224	#123×C₈₉	C₂³	1	6	yes	—
225	#123×C₈₉	C₂³	1	6	yes	—
226	#123×C₈₉	C₂³	1	6	yes	—
227	#123×C₈₉	C₂³	1	3	yes	—
228	#123×C₈₉	C₂³	1	3	yes	—
229	#123×C₈₉	C₂³	1	6	yes	—
230	#123×C₈₉	C₂³	1	6	yes	—
231	#123×C₈₉	C₂³	1	6	yes	—
232	#123×C₈₉	C₂³	1	6	yes	—
233	#123×C₈₉	C₂³	1	6	yes	—
234	#123×C₈₉	C₂³	1	6	yes	—
235	#123×C₈₉	C₂³	1	6	yes	—
236	#123×C₈₉	C₂³	1	6	yes	—
237	#123×C₈₉	C₂³	1	6	yes	—
238	#123×C₈₉	C₂³	1	6	yes	—
239	#123×C₈₉	C₂³	1	6	yes	—
240	#123×C₈₉	C₂³	1	6	yes	—
241	#123×C₈₉	C₂³	1	3	yes	—
242	#123×C₈₉	C₂³	1	3	yes	—
243	#123×C₈₉	C₂³	1	3	yes	—
244	#123×C₈₉	C₂³	1	3	yes	—
245	#123×C₈₉	C₂³	1	6	yes	—
246	#123×C₈₉	C₂³	1	6	yes	—
247	#123×C₈₉	C₂³	1	6	yes	complemented
248	#123×C₈₉	C₂³	1	6	yes	complemented
249	#123×C₈₉	C₂³	1	6	yes	complemented
250	#123×C₈₉	C₂³	1	6	yes	complemented
251	#123×C₈₉	C₂³	1	6	yes	complemented
252	#123×C₈₉	C₂³	1	6	yes	complemented
253	#123×C₈₉	C₂³	1	6	yes	complemented
254	C₂²⋊Q₈×C₈₉	C₂³	1	6	yes	—
255	C₂²⋊Q₈×C₈₉	C₂³	1	6	yes	—
256	C₂²⋊Q₈×C₈₉	C₂³	1	6	yes	—
257	C₂²⋊Q₈×C₈₉	C₂³	1	6	yes	—
258	C₂²⋊Q₈×C₈₉	C₂³	1	6	yes	—
259	C₂²⋊Q₈×C₈₉	C₂³	1	6	yes	—
260	C₂²⋊Q₈×C₈₉	C₂³	1	6	yes	—
261	C₂²⋊Q₈×C₈₉	C₂³	1	6	yes	—
262	C₂²⋊Q₈×C₈₉	C₂³	1	6	yes	—
263	C₂²⋊Q₈×C₈₉	C₂³	1	6	yes	—
264	C₂²⋊Q₈×C₈₉	C₂³	1	6	yes	—
265	C₂²⋊Q₈×C₈₉	C₂³	1	6	yes	—
266	C₂²⋊Q₈×C₈₉	C₂³	1	6	yes	—
267	C₂²⋊Q₈×C₈₉	C₂³	1	6	yes	—
268	C₂²⋊Q₈×C₈₉	C₂³	1	6	yes	—
269	C₂²⋊Q₈×C₈₉	C₂³	1	6	yes	—
270	C₂²⋊Q₈×C₈₉	C₂³	1	6	yes	—
271	C₂²⋊Q₈×C₈₉	C₂³	1	6	yes	complemented
272	C₂²⋊Q₈×C₈₉	C₂³	1	6	yes	complemented
273	C₂²⋊Q₈×C₈₉	C₂³	1	6	yes	complemented
274	C₂²⋊Q₈×C₈₉	C₂³	1	6	yes	complemented
275	C₂²⋊Q₈×C₈₉	C₂³	1	6	yes	complemented
276	C₂²⋊Q₈×C₈₉	C₂³	1	6	yes	complemented
277	C₂²⋊Q₈×C₈₉	C₂³	1	6	yes	complemented
278	C₂²⋊Q₈×C₈₉	C₂³	1	6	yes	complemented
279	C₂²⋊Q₈×C₈₉	C₂³	1	6	yes	complemented
280	C₂²⋊Q₈×C₈₉	C₂³	1	6	yes	complemented
281	C₂²⋊Q₈×C₈₉	C₂³	1	6	yes	complemented
282	C₂²⋊Q₈×C₈₉	C₂³	1	6	yes	complemented
283	C₂²⋊Q₈×C₈₉	C₂³	1	6	yes	complemented
284	#121×C₈₉	C₂³	1	6	yes	—
285	#121×C₈₉	C₂³	1	6	yes	—
286	#121×C₈₉	C₂³	1	6	yes	—
287	#121×C₈₉	C₂³	1	6	yes	—
288	#121×C₈₉	C₂³	1	6	yes	—
289	#121×C₈₉	C₂³	1	6	yes	—
290	#121×C₈₉	C₂³	1	6	yes	—
291	#121×C₈₉	C₂³	1	6	yes	—
292	#121×C₈₉	C₂³	1	6	yes	—
293	#121×C₈₉	C₂³	1	6	yes	—
294	#121×C₈₉	C₂³	1	6	yes	—
295	#121×C₈₉	C₂³	1	6	yes	—
296	#121×C₈₉	C₂³	1	6	yes	—
297	#121×C₈₉	C₂³	1	6	yes	complemented
298	#121×C₈₉	C₂³	1	6	yes	complemented
299	#121×C₈₉	C₂³	1	6	yes	complemented
300	#120×C₈₉	C₂³	1	3	yes	—
301	#120×C₈₉	C₂³	1	3	yes	—
302	#120×C₈₉	C₂³	1	6	yes	—
303	#120×C₈₉	C₂³	1	6	yes	—
304	#120×C₈₉	C₂³	1	3	yes	—
305	#120×C₈₉	C₂³	1	3	yes	—
306	#120×C₈₉	C₂³	1	6	yes	—
307	#120×C₈₉	C₂³	1	2	yes	—
308	#120×C₈₉	C₂³	1	6	yes	—
309	#120×C₈₉	C₂³	1	6	yes	—
310	#120×C₈₉	C₂³	1	1	yes	characteristic
311	#120×C₈₉	C₂³	1	3	yes	—
312	#120×C₈₉	C₂³	1	3	yes	—
313	#120×C₈₉	C₂³	1	3	yes	—
314	#120×C₈₉	C₂³	1	2	yes	complemented
315	C₄×Q₈×C₈₉	C₂³	1	6	yes	complemented
316	C₄×Q₈×C₈₉	C₂³	1	6	yes	complemented
317	C₄×Q₈×C₈₉	C₂³	1	6	yes	complemented
318	C₄×Q₈×C₈₉	C₂³	1	6	yes	complemented
319	C₄×Q₈×C₈₉	C₂³	1	6	yes	complemented
320	C₄×Q₈×C₈₉	C₂³	1	6	yes	complemented
321	C₄×Q₈×C₈₉	C₂³	1	6	yes	complemented
322	C₄×Q₈×C₈₉	C₂³	1	6	yes	complemented
323	C₄×Q₈×C₈₉	C₂³	1	6	yes	complemented
324	C₄×D₄×C₈₉	C₂³	1	6	yes	—
325	C₄×D₄×C₈₉	C₂³	1	6	yes	—
326	C₄×D₄×C₈₉	C₂³	1	6	yes	—
327	C₄×D₄×C₈₉	C₂³	1	6	yes	—
328	C₄×D₄×C₈₉	C₂³	1	6	yes	—
329	C₄×D₄×C₈₉	C₂³	1	6	yes	—
330	C₄×D₄×C₈₉	C₂³	1	6	yes	—
331	C₄×D₄×C₈₉	C₂³	1	6	yes	—
332	C₄×D₄×C₈₉	C₂³	1	6	yes	—
333	C₄×D₄×C₈₉	C₂³	1	6	yes	—
334	C₄×D₄×C₈₉	C₂³	1	6	yes	—
335	C₄×D₄×C₈₉	C₂³	1	6	yes	—
336	C₄×D₄×C₈₉	C₂³	1	6	yes	—
337	C₄×D₄×C₈₉	C₂³	1	6	yes	—
338	C₄×D₄×C₈₉	C₂³	1	6	yes	—
339	C₄×D₄×C₈₉	C₂³	1	6	yes	—
340	C₄×D₄×C₈₉	C₂³	1	6	yes	—
341	C₄×D₄×C₈₉	C₂³	1	6	yes	—
342	C₄×D₄×C₈₉	C₂³	1	6	yes	—
343	C₄×D₄×C₈₉	C₂³	1	6	yes	—
344	C₄×D₄×C₈₉	C₂³	1	6	yes	—
345	C₄×D₄×C₈₉	C₂³	1	6	yes	—
346	C₄×D₄×C₈₉	C₂³	1	6	yes	complemented
347	C₄×D₄×C₈₉	C₂³	1	6	yes	complemented
348	C₄×D₄×C₈₉	C₂³	1	6	yes	complemented
349	C₄×D₄×C₈₉	C₂³	1	6	yes	complemented
350	C₄×D₄×C₈₉	C₂³	1	6	yes	complemented
351	C₄×D₄×C₈₉	C₂³	1	6	yes	complemented
352	C₄×D₄×C₈₉	C₂³	1	6	yes	complemented
353	#117×C₈₉	C₂³	1	6	yes	—
354	#117×C₈₉	C₂³	1	6	yes	—
355	#117×C₈₉	C₂³	1	6	yes	—
356	#117×C₈₉	C₂³	1	6	yes	—
357	#117×C₈₉	C₂³	1	6	yes	—
358	#117×C₈₉	C₂³	1	6	yes	—
359	#117×C₈₉	C₂³	1	6	yes	—
360	#117×C₈₉	C₂³	1	6	yes	—
361	#117×C₈₉	C₂³	1	6	yes	—
362	#117×C₈₉	C₂³	1	3	yes	—
363	#117×C₈₉	C₂³	1	6	yes	—
364	#117×C₈₉	C₂³	1	3	yes	—
365	#117×C₈₉	C₂³	1	6	yes	—
366	#117×C₈₉	C₂³	1	3	yes	—
367	#117×C₈₉	C₂³	1	6	yes	complemented
368	#117×C₈₉	C₂³	1	6	yes	complemented
369	#117×C₈₉	C₂³	1	6	yes	complemented
370	#117×C₈₉	C₂³	1	6	yes	complemented
371	#117×C₈₉	C₂³	1	6	yes	complemented
372	#117×C₈₉	C₂³	1	6	yes	complemented
373	#117×C₈₉	C₂³	1	6	yes	complemented
374	#117×C₈₉	C₂³	1	6	yes	complemented
375	C₂×C₄⋊C₄×C₈₉	C₂³	1	6	yes	—
376	C₂×C₄⋊C₄×C₈₉	C₂³	1	6	yes	—
377	C₂×C₄⋊C₄×C₈₉	C₂³	1	6	yes	—
378	C₂×C₄⋊C₄×C₈₉	C₂³	1	6	yes	—
379	C₂×C₄⋊C₄×C₈₉	C₂³	1	6	yes	complemented
380	C₂×C₄⋊C₄×C₈₉	C₂³	1	6	yes	complemented
381	C₂×C₄⋊C₄×C₈₉	C₂³	1	6	yes	complemented
382	C₂×C₂²⋊C₄×C₈₉	C₂³	1	6	yes	—
383	C₂×C₂²⋊C₄×C₈₉	C₂³	1	3	yes	—
384	C₂×C₂²⋊C₄×C₈₉	C₂³	1	6	yes	—
385	C₂×C₂²⋊C₄×C₈₉	C₂³	1	6	yes	—
386	C₂×C₂²⋊C₄×C₈₉	C₂³	1	6	yes	—
387	C₂×C₂²⋊C₄×C₈₉	C₂³	1	3	yes	—
388	C₂×C₂²⋊C₄×C₈₉	C₂³	1	6	yes	—
389	C₂×C₂²⋊C₄×C₈₉	C₂³	1	3	yes	—
390	C₂×C₂²⋊C₄×C₈₉	C₂³	1	6	yes	—
391	C₂×C₂²⋊C₄×C₈₉	C₂³	1	3	yes	—
392	C₂×C₂²⋊C₄×C₈₉	C₂³	1	6	yes	—
393	C₂×C₂²⋊C₄×C₈₉	C₂³	1	3	yes	—
394	C₂×C₂²⋊C₄×C₈₉	C₂³	1	3	yes	—
395	C₂×C₂²⋊C₄×C₈₉	C₂³	1	3	yes	—
396	C₂×C₂²⋊C₄×C₈₉	C₂³	1	3	yes	—
397	C₂×C₂²⋊C₄×C₈₉	C₂³	1	6	yes	—
398	C₂×C₂²⋊C₄×C₈₉	C₂³	1	6	yes	complemented
399	C₂×C₄²×C₈₉	C₂³	1	3	yes	—
400	C₂×C₄²×C₈₉	C₂³	1	6	yes	—
401	C₂×C₄²×C₈₉	C₂³	1	6	yes	complemented
402	C₂×C₄²×C₈₉	C₂³	1	2	yes	complemented
403	C₂⁴×C₈₉	—	4	6	no	—
404	C₂⁴×C₈₉	C₂⁴	1	3	yes	—
405	C₂⁴×C₈₉	C₂⁴	1	3	yes	—
406	C₂⁴×C₈₉	C₂⁴	1	3	yes	—
407	C₂⁴×C₈₉	C₂⁴	1	1	yes	characteristic
408	C₂⁴×C₈₉	C₂⁴	1	1	yes	characteristic
409	C₂⁴×C₈₉	C₂⁴	1	1	yes	characteristic
410	#41×C₈₉	—	4	12	no	—
411	#41×C₈₉	—	4	12	no	—
412	#41×C₈₉	—	4	6	no	—
413	C₂×Q₈×C₈₉	—	4	6	no	—
414	C₂×Q₈×C₈₉	C₂⁴	1	3	yes	—
415	C₂×Q₈×C₈₉	C₂⁴	1	6	yes	—
416	C₂×Q₈×C₈₉	C₂⁴	1	6	yes	—
417	C₂×Q₈×C₈₉	C₂⁴	1	3	yes	—
418	C₂×Q₈×C₈₉	C₂⁴	1	6	yes	—
419	C₂×Q₈×C₈₉	C₂⁴	1	3	yes	—
420	C₂×D₄×C₈₉	—	4	6	no	—
421	C₂×D₄×C₈₉	—	4	6	no	—
422	C₂×D₄×C₈₉	—	4	12	no	—
423	C₂×D₄×C₈₉	—	4	6	no	—
424	C₂×D₄×C₈₉	C₂⁴	1	6	yes	—
425	C₂×D₄×C₈₉	C₂⁴	1	6	yes	—
426	C₂×D₄×C₈₉	C₂⁴	1	6	yes	—
427	C₂×D₄×C₈₉	C₂⁴	1	3	yes	—
428	C₂×D₄×C₈₉	C₂⁴	1	6	yes	—
429	C₂×D₄×C₈₉	C₂⁴	1	3	yes	—
430	C₂×D₄×C₈₉	C₂⁴	1	3	yes	—
431	C₂×D₄×C₈₉	C₂⁴	1	6	yes	—
432	C₂×D₄×C₈₉	C₂⁴	1	3	yes	—
433	C₂×D₄×C₈₉	C₂⁴	1	6	yes	—
434	C₂×D₄×C₈₉	C₂⁴	1	6	yes	—
435	C₂×D₄×C₈₉	C₂⁴	1	6	yes	—
436	C₂×D₄×C₈₉	C₂⁴	1	3	yes	—
437	C₂×D₄×C₈₉	C₂⁴	1	6	yes	—
438	C₂²×C₄×C₈₉	—	4	6	no	—
439	C₂²×C₄×C₈₉	—	4	12	no	—
440	C₂²×C₄×C₈₉	C₂⁴	1	6	yes	—
441	C₂²×C₄×C₈₉	C₂⁴	1	3	yes	—
442	C₂²×C₄×C₈₉	C₂⁴	1	6	yes	—
443	C₂²×C₄×C₈₉	C₂⁴	1	6	yes	—
444	C₂²×C₄×C₈₉	C₂⁴	1	6	yes	—
445	C₂²×C₄×C₈₉	C₂⁴	1	3	yes	—
446	C₂²×C₄×C₈₉	C₂⁴	1	6	yes	—
447	C₂²×C₄×C₈₉	C₂⁴	1	6	yes	—
448	C₂²×C₄×C₈₉	C₂⁴	1	6	yes	—
449	C₂²×C₄×C₈₉	C₂⁴	1	6	yes	—
450	C₂²×C₄×C₈₉	C₂⁴	1	6	yes	—
451	C₂²×C₄×C₈₉	C₂⁴	1	3	yes	—
452	C₂²×C₄×C₈₉	C₂⁴	1	6	yes	—
453	C₂²×C₄×C₈₉	C₂⁴	1	6	yes	—
454	C₂²×C₄×C₈₉	C₂⁴	1	6	yes	—
455	C₂²×C₄×C₈₉	C₂⁴	1	6	yes	—
456	C₂²×C₄×C₈₉	C₂⁴	1	3	yes	—
457	C₂²×C₄×C₈₉	C₂⁴	1	3	yes	—
458	C₄⋊C₄×C₈₉	C₂⁴	1	6	yes	—
459	C₄⋊C₄×C₈₉	C₂⁴	1	6	yes	—
460	C₄⋊C₄×C₈₉	C₂⁴	1	6	yes	—
461	C₄⋊C₄×C₈₉	C₂⁴	1	6	yes	—
462	C₄⋊C₄×C₈₉	C₂⁴	1	6	yes	—
463	C₄⋊C₄×C₈₉	C₂⁴	1	6	yes	—
464	C₄⋊C₄×C₈₉	C₂⁴	1	6	yes	—
465	C₄⋊C₄×C₈₉	C₂⁴	1	6	yes	—
466	C₄⋊C₄×C₈₉	C₂⁴	1	6	yes	—
467	C₄⋊C₄×C₈₉	C₂⁴	1	6	yes	—
468	C₄⋊C₄×C₈₉	C₂⁴	1	6	yes	—
469	C₄⋊C₄×C₈₉	C₂⁴	1	6	yes	—
470	C₄⋊C₄×C₈₉	C₂⁴	1	6	yes	—
471	C₄⋊C₄×C₈₉	C₂⁴	1	6	yes	—
472	C₄⋊C₄×C₈₉	C₂⁴	1	6	yes	—
473	C₄⋊C₄×C₈₉	C₂⁴	1	6	yes	—
474	C₄⋊C₄×C₈₉	C₂⁴	1	6	yes	—
475	C₄⋊C₄×C₈₉	C₂⁴	1	6	yes	—
476	C₄⋊C₄×C₈₉	C₂⁴	1	6	yes	—
477	C₄⋊C₄×C₈₉	C₂⁴	1	6	yes	—
478	C₄⋊C₄×C₈₉	C₂⁴	1	6	yes	—
479	C₄⋊C₄×C₈₉	C₂⁴	1	6	yes	—
480	C₄⋊C₄×C₈₉	C₂⁴	1	6	yes	—
481	C₄⋊C₄×C₈₉	C₂⁴	1	6	yes	—
482	C₄⋊C₄×C₈₉	C₂⁴	1	6	yes	—
483	C₄⋊C₄×C₈₉	C₂⁴	1	6	yes	—
484	C₄⋊C₄×C₈₉	C₂⁴	1	6	yes	—
485	C₄⋊C₄×C₈₉	C₂⁴	1	6	yes	—
486	C₄⋊C₄×C₈₉	C₂⁴	1	6	yes	—
487	C₄⋊C₄×C₈₉	C₂⁴	1	6	yes	—
488	C₄⋊C₄×C₈₉	C₂⁴	1	6	yes	—
489	C₂²⋊C₄×C₈₉	C₂⁴	1	3	yes	—
490	C₂²⋊C₄×C₈₉	C₂⁴	1	3	yes	—
491	C₂²⋊C₄×C₈₉	C₂⁴	1	6	yes	—
492	C₂²⋊C₄×C₈₉	C₂⁴	1	6	yes	—
493	C₂²⋊C₄×C₈₉	C₂⁴	1	6	yes	—
494	C₂²⋊C₄×C₈₉	C₂⁴	1	6	yes	—
495	C₂²⋊C₄×C₈₉	C₂⁴	1	3	yes	—
496	C₂²⋊C₄×C₈₉	C₂⁴	1	3	yes	—
497	C₂²⋊C₄×C₈₉	C₂⁴	1	6	yes	—
498	C₂²⋊C₄×C₈₉	C₂⁴	1	6	yes	—
499	C₂²⋊C₄×C₈₉	C₂⁴	1	3	yes	—
500	C₂²⋊C₄×C₈₉	C₂⁴	1	6	yes	—
501	C₂²⋊C₄×C₈₉	C₂⁴	1	3	yes	—
502	C₂²⋊C₄×C₈₉	C₂⁴	1	6	yes	—
503	C₂²⋊C₄×C₈₉	C₂⁴	1	6	yes	—
504	C₂²⋊C₄×C₈₉	C₂⁴	1	6	yes	—
505	C₂²⋊C₄×C₈₉	C₂⁴	1	6	yes	—
506	C₂²⋊C₄×C₈₉	C₂⁴	1	6	yes	—
507	C₂²⋊C₄×C₈₉	C₂⁴	1	6	yes	—
508	C₂²⋊C₄×C₈₉	C₂⁴	1	6	yes	—
509	C₂²⋊C₄×C₈₉	C₂⁴	1	6	yes	—
510	C₂²⋊C₄×C₈₉	C₂⁴	1	6	yes	—
511	C₂²⋊C₄×C₈₉	C₂⁴	1	3	yes	—
512	C₂²⋊C₄×C₈₉	C₂⁴	1	3	yes	—
513	C₂²⋊C₄×C₈₉	C₂⁴	1	3	yes	—
514	C₂²⋊C₄×C₈₉	C₂⁴	1	3	yes	—
515	C₂²⋊C₄×C₈₉	C₂⁴	1	6	yes	—
516	C₂²⋊C₄×C₈₉	C₂⁴	1	6	yes	—
517	C₂²⋊C₄×C₈₉	C₂⁴	1	6	yes	—
518	C₂²⋊C₄×C₈₉	C₂⁴	1	6	yes	—
519	C₂²⋊C₄×C₈₉	C₂⁴	1	6	yes	—
520	C₂²⋊C₄×C₈₉	C₂⁴	1	3	yes	—
521	C₂²⋊C₄×C₈₉	C₂⁴	1	3	yes	—
522	C₂²⋊C₄×C₈₉	C₂⁴	1	6	yes	—
523	C₂²⋊C₄×C₈₉	C₂⁴	1	6	yes	—
524	C₂²⋊C₄×C₈₉	C₂⁴	1	6	yes	—
525	C₂²⋊C₄×C₈₉	C₂⁴	1	6	yes	—
526	C₂²⋊C₄×C₈₉	C₂⁴	1	6	yes	—
527	C₂²⋊C₄×C₈₉	C₂⁴	1	6	yes	—
528	C₄²×C₈₉	C₂⁴	1	3	yes	—
529	C₄²×C₈₉	C₂⁴	1	6	yes	—
530	C₄²×C₈₉	C₂⁴	1	3	yes	—
531	C₄²×C₈₉	C₂⁴	1	6	yes	—
532	C₄²×C₈₉	C₂⁴	1	6	yes	—
533	C₄²×C₈₉	C₂⁴	1	6	yes	—
534	C₄²×C₈₉	C₂⁴	1	6	yes	—
535	C₄²×C₈₉	C₂⁴	1	6	yes	—
536	C₄²×C₈₉	C₂⁴	1	6	yes	—
537	C₄²×C₈₉	C₂⁴	1	2	yes	—
538	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
539	C₄²×C₈₉	C₂⁴	1	6	yes	—
540	C₄²×C₈₉	C₂⁴	1	6	yes	—
541	C₄²×C₈₉	C₂⁴	1	3	yes	—
542	C₂³×C₈₉	—	2	12	no	—
543	C₂³×C₈₉	—	2	6	no	—
544	C₂³×C₈₉	—	2	6	no	—
545	C₂³×C₈₉	—	4	3	no	—
546	C₂³×C₈₉	—	4	6	no	—
547	C₂³×C₈₉	—	4	6	no	—
548	C₂³×C₈₉	—	4	3	no	—
549	C₂³×C₈₉	—	4	3	no	—
550	C₂³×C₈₉	—	4	3	no	—
551	C₂³×C₈₉	—	8	8	no	—
552	C₂³×C₈₉	C₂⁵	1	1	yes	characteristic
553	C₂³×C₈₉	C₂⁵	1	3	yes	—
554	C₂³×C₈₉	C₂⁵	1	3	yes	—
555	C₂³×C₈₉	C₂⁵	1	2	yes	—
556	C₂³×C₈₉	C₂⁵	1	3	yes	—
557	C₂³×C₈₉	C₂⁵	1	3	yes	—
558	Q₈×C₈₉	—	4	3	no	—
559	Q₈×C₈₉	—	4	6	no	—
560	Q₈×C₈₉	—	4	3	no	—
561	Q₈×C₈₉	—	4	6	no	—
562	Q₈×C₈₉	—	4	6	no	—
563	Q₈×C₈₉	—	4	3	no	—
564	D₄×C₈₉	—	2	12	no	—
565	D₄×C₈₉	—	2	12	no	—
566	D₄×C₈₉	—	2	12	no	—
567	D₄×C₈₉	—	4	3	no	—
568	D₄×C₈₉	—	4	3	no	—
569	D₄×C₈₉	—	4	3	no	—
570	D₄×C₈₉	—	4	3	no	—
571	D₄×C₈₉	—	4	6	no	—
572	D₄×C₈₉	—	4	6	no	—
573	D₄×C₈₉	—	4	6	no	—
574	D₄×C₈₉	—	4	6	no	—
575	D₄×C₈₉	—	4	6	no	—
576	D₄×C₈₉	—	4	6	no	—
577	D₄×C₈₉	—	4	3	no	—
578	C₂×C₄×C₈₉	—	2	12	no	—
579	C₂×C₄×C₈₉	—	2	12	no	—
580	C₂×C₄×C₈₉	—	2	6	no	—
581	C₂×C₄×C₈₉	—	4	3	no	—
582	C₂×C₄×C₈₉	—	4	6	no	—
583	C₂×C₄×C₈₉	—	4	6	no	—
584	C₂×C₄×C₈₉	—	4	6	no	—
585	C₂×C₄×C₈₉	—	4	3	no	—
586	C₂×C₄×C₈₉	—	4	6	no	—
587	C₂×C₄×C₈₉	—	4	6	no	—
588	C₂×C₄×C₈₉	—	4	3	no	—
589	C₂×C₄×C₈₉	—	4	6	no	—
590	C₂×C₄×C₈₉	—	4	3	no	—
591	C₂×C₄×C₈₉	—	4	6	no	—
592	C₂×C₄×C₈₉	—	4	6	no	—
593	C₂×C₄×C₈₉	—	4	6	no	—
594	C₂×C₄×C₈₉	—	4	6	no	—
595	C₂×C₄×C₈₉	—	4	6	no	—
596	C₂×C₄×C₈₉	C₂⁵	1	6	yes	—
597	C₂×C₄×C₈₉	C₂⁵	1	3	yes	—
598	C₂×C₄×C₈₉	C₂⁵	1	6	yes	—
599	C₂×C₄×C₈₉	C₂⁵	1	3	yes	—
600	C₂×C₄×C₈₉	C₂⁵	1	6	yes	—
601	C₂×C₄×C₈₉	C₂⁵	1	6	yes	—
602	C₂×C₄×C₈₉	C₂⁵	1	6	yes	—
603	C₂×C₄×C₈₉	C₂⁵	1	6	yes	—
604	C₂×C₄×C₈₉	C₂⁵	1	6	yes	—
605	C₂²×C₈₉	—	2	6	no	—
606	C₂²×C₈₉	—	2	3	no	—
607	C₂²×C₈₉	—	2	6	no	—
608	C₂²×C₈₉	—	2	6	no	—
609	C₂²×C₈₉	—	2	3	no	—
610	C₂²×C₈₉	—	2	6	no	—
611	C₂²×C₈₉	—	2	6	no	—
612	C₂²×C₈₉	—	2	3	no	—
613	C₂²×C₈₉	—	2	3	no	—
614	C₂²×C₈₉	—	4	12	no	—
615	C₂²×C₈₉	—	8	6	no	—
616	C₂²×C₈₉	—	8	6	no	—
617	C₂²×C₈₉	—	8	2	no	—
618	C₂²×C₈₉	—	16	1	no	—
619	C₂²×C₈₉	—	16	1	no	—
620	C₂²×C₈₉	#585	1	6	yes	—
621	C₂²×C₈₉	C₂⁶	1	1	yes	characteristic
622	C₄×C₈₉	—	2	6	no	—
623	C₄×C₈₉	—	2	6	no	—
624	C₄×C₈₉	—	2	6	no	—
625	C₄×C₈₉	—	2	3	no	—
626	C₄×C₈₉	—	2	6	no	—
627	C₄×C₈₉	—	2	3	no	—
628	C₄×C₈₉	—	2	6	no	—
629	C₄×C₈₉	—	2	6	no	—
630	C₄×C₈₉	—	2	6	no	—
631	#63026	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
632	C₂×C₈₉	—	2	6	no	—
633	C₂×C₈₉	—	4	3	no	—
634	C₂×C₈₉	—	4	3	no	—
635	C₂×C₈₉	—	4	1	no	—
636	C₂×C₈₉	—	4	3	no	—
637	C₂×C₈₉	—	4	2	no	—
638	C₂×C₈₉	C₂×#585	1	3	yes	—
639	#3568	C₂×C₈₉	1	2	yes	complemented
640	#3566	C₂×C₈₉	1	6	yes	complemented
641	#3564	C₂×C₈₉	1	6	yes	complemented
642	#3545	C₂×C₈₉	1	3	yes	complemented
643	#3535	C₂×C₈₉	1	6	yes	complemented
644	#3533	C₂×C₈₉	1	3	yes	complemented
645	#3532	C₂×C₈₉	1	1	yes	characteristic, complemented
646	#3521	C₂×C₈₉	1	6	yes	complemented
647	#3513	C₂×C₈₉	1	6	yes	complemented
648	#3510	C₂×C₈₉	1	3	yes	complemented
649	#3495	C₂×C₈₉	1	6	yes	complemented
650	#3491	C₂×C₈₉	1	3	yes	complemented
651	#3490	C₂×C₈₉	1	3	yes	complemented
652	#3475	C₂×C₈₉	1	6	yes	complemented
653	C₂×#551	C₂×C₈₉	1	3	yes	complemented
654	C₈₉	#63026	1	1	yes	characteristic, direct product factor, Sylow
655	#563	C₂²×C₈₉	1	3	yes	complemented
656	#563	C₂²×C₈₉	1	6	yes	complemented
657	#563	C₂²×C₈₉	1	6	yes	complemented
658	#563	C₂²×C₈₉	1	3	yes	complemented
659	#562	C₂²×C₈₉	1	6	yes	complemented
660	#562	C₂²×C₈₉	1	6	yes	complemented
661	H(3,𝔽₄)	C₂²×C₈₉	1	1	yes	characteristic, complemented
662	H(3,𝔽₄)	C₂²×C₈₉	1	1	yes	characteristic, complemented
663	#560	C₂²×C₈₉	1	3	yes	complemented
664	#560	C₂²×C₈₉	1	1	yes	characteristic, complemented
665	#559	C₂²×C₈₉	1	3	yes	complemented
666	#559	C₂²×C₈₉	1	6	yes	complemented
667	#556	C₂²×C₈₉	1	6	yes	complemented
668	#556	C₂²×C₈₉	1	6	yes	complemented
669	#556	C₂²×C₈₉	1	6	yes	complemented
670	#556	C₂²×C₈₉	1	6	yes	complemented
671	#555	C₂²×C₈₉	1	6	yes	complemented
672	#554	C₂²×C₈₉	1	6	yes	complemented
673	#554	C₂²×C₈₉	1	6	yes	complemented
674	#554	C₂²×C₈₉	1	6	yes	complemented
675	#553	C₂²×C₈₉	1	6	yes	complemented
676	#553	C₂²×C₈₉	1	6	yes	complemented
677	#553	C₂²×C₈₉	1	6	yes	complemented
678	#553	C₂²×C₈₉	1	6	yes	complemented
679	#552	C₂²×C₈₉	1	6	yes	complemented
680	#552	C₂²×C₈₉	1	6	yes	complemented
681	#552	C₂²×C₈₉	1	6	yes	complemented
682	#552	C₂²×C₈₉	1	6	yes	complemented
683	#552	C₂²×C₈₉	1	6	yes	complemented
684	#552	C₂²×C₈₉	1	6	yes	complemented
685	#552	C₂²×C₈₉	1	6	yes	complemented
686	#552	C₂²×C₈₉	1	6	yes	complemented
687	#552	C₂²×C₈₉	1	6	yes	complemented
688	#552	C₂²×C₈₉	1	6	yes	complemented
689	#551	C₂²×C₈₉	1	3	yes	complemented
690	#551	C₂²×C₈₉	1	6	yes	complemented
691	#551	C₂²×C₈₉	1	6	yes	complemented
692	#551	C₂²×C₈₉	1	6	yes	complemented
693	#551	C₂²×C₈₉	1	6	yes	complemented
694	#551	C₂²×C₈₉	1	3	yes	complemented
695	#551	C₂²×C₈₉	1	6	yes	complemented
696	#551	C₂²×C₈₉	1	3	yes	complemented
697	#551	C₂²×C₈₉	1	3	yes	complemented
698	#551	C₂²×C₈₉	1	6	yes	complemented
699	#551	C₂²×C₈₉	1	6	yes	complemented
700	#551	C₂²×C₈₉	1	6	yes	complemented
701	#551	C₂²×C₈₉	1	6	yes	complemented
702	#551	C₂²×C₈₉	1	6	yes	complemented
703	#551	C₂²×C₈₉	1	3	yes	complemented
704	#551	C₂²×C₈₉	1	6	yes	complemented
705	#551	C₂²×C₈₉	1	6	yes	complemented
706	#551	C₂²×C₈₉	1	6	yes	complemented
707	#551	C₂²×C₈₉	1	3	yes	complemented
708	#551	C₂²×C₈₉	1	3	yes	complemented
709	#551	C₂²×C₈₉	1	3	yes	complemented
710	#551	C₂²×C₈₉	1	6	yes	complemented
711	#547	C₂²×C₈₉	1	6	yes	complemented
712	#547	C₂²×C₈₉	1	6	yes	complemented
713	#546	C₂²×C₈₉	1	6	yes	complemented
714	#546	C₂²×C₈₉	1	6	yes	complemented
715	#546	C₂²×C₈₉	1	6	yes	complemented
716	#546	C₂²×C₈₉	1	6	yes	complemented
717	#546	C₂²×C₈₉	1	6	yes	complemented
718	#546	C₂²×C₈₉	1	6	yes	complemented
719	D₄²	C₂²×C₈₉	1	3	yes	complemented
720	#544	C₂²×C₈₉	1	6	yes	complemented
721	#543	C₂²×C₈₉	1	3	yes	complemented
722	#543	C₂²×C₈₉	1	3	yes	complemented
723	#542	C₂²×C₈₉	1	6	yes	complemented
724	#542	C₂²×C₈₉	1	6	yes	complemented
725	#542	C₂²×C₈₉	1	6	yes	complemented
726	#542	C₂²×C₈₉	1	6	yes	complemented
727	#542	C₂²×C₈₉	1	6	yes	complemented
728	#542	C₂²×C₈₉	1	6	yes	complemented
729	#541	C₂²×C₈₉	1	6	yes	complemented
730	#541	C₂²×C₈₉	1	6	yes	complemented
731	#541	C₂²×C₈₉	1	6	yes	complemented
732	#540	C₂²×C₈₉	1	6	yes	complemented
733	#539	C₂²×C₈₉	1	6	yes	complemented
734	#539	C₂²×C₈₉	1	6	yes	complemented
735	#539	C₂²×C₈₉	1	6	yes	complemented
736	#539	C₂²×C₈₉	1	6	yes	complemented
737	#539	C₂²×C₈₉	1	6	yes	complemented
738	#539	C₂²×C₈₉	1	6	yes	complemented
739	#538	C₂²×C₈₉	1	6	yes	—
740	#538	C₂²×C₈₉	1	6	yes	complemented
741	#538	C₂²×C₈₉	1	6	yes	complemented
742	#538	C₂²×C₈₉	1	6	yes	complemented
743	#538	C₂²×C₈₉	1	6	yes	complemented
744	#538	C₂²×C₈₉	1	6	yes	complemented
745	#536	C₂²×C₈₉	1	6	yes	complemented
746	#536	C₂²×C₈₉	1	3	yes	complemented
747	#535	C₂²×C₈₉	1	3	yes	—
748	#534	C₂²×C₈₉	1	3	yes	—
749	#534	C₂²×C₈₉	1	3	yes	complemented
750	#533	C₂²×C₈₉	1	6	yes	complemented
751	#533	C₂²×C₈₉	1	3	yes	complemented
752	#529	C₂²×C₈₉	1	6	yes	complemented
753	#529	C₂²×C₈₉	1	6	yes	complemented
754	#529	C₂²×C₈₉	1	6	yes	complemented
755	#529	C₂²×C₈₉	1	6	yes	complemented
756	#529	C₂²×C₈₉	1	6	yes	complemented
757	#529	C₂²×C₈₉	1	6	yes	complemented
758	#529	C₂²×C₈₉	1	6	yes	complemented
759	#529	C₂²×C₈₉	1	6	yes	complemented
760	C₂×#126	C₂²×C₈₉	1	6	yes	complemented
761	C₂×#126	C₂²×C₈₉	1	2	yes	complemented
762	C₂×#124	C₂²×C₈₉	1	3	yes	complemented
763	#525	C₂²×C₈₉	1	6	yes	—
764	#525	C₂²×C₈₉	1	6	yes	complemented
765	#525	C₂²×C₈₉	1	6	yes	complemented
766	C₂×#123	C₂²×C₈₉	1	3	yes	complemented
767	C₂×#123	C₂²×C₈₉	1	6	yes	complemented
768	C₂×#123	C₂²×C₈₉	1	3	yes	complemented
769	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	6	yes	complemented
770	C₂×#120	C₂²×C₈₉	1	3	yes	—
771	C₂×#120	C₂²×C₈₉	1	1	yes	characteristic, complemented
772	#520	C₂²×C₈₉	1	6	yes	complemented
773	#519	C₂²×C₈₉	1	3	yes	complemented
774	#518	C₂²×C₈₉	1	3	yes	complemented
775	#518	C₂²×C₈₉	1	3	yes	complemented
776	#518	C₂²×C₈₉	1	3	yes	complemented
777	C₄×#41	C₂²×C₈₉	1	3	yes	complemented
778	C₄×#41	C₂²×C₈₉	1	6	yes	complemented
779	C₂×C₄×D₄	C₂²×C₈₉	1	6	yes	complemented
780	C₂×#117	C₂²×C₈₉	1	6	yes	complemented
781	C₂×#117	C₂²×C₈₉	1	3	yes	complemented
782	C₂²×C₂²⋊C₄	C₂²×C₈₉	1	3	yes	complemented
783	C₂⁵	C₂³×C₈₉	1	1	yes	characteristic
784	C₂×#41	C₂³×C₈₉	1	6	yes	—
785	C₂×#41	C₂³×C₈₉	1	3	yes	—
786	C₂×#41	C₂³×C₈₉	1	6	yes	—
787	C₂²×Q₈	C₂³×C₈₉	1	3	yes	—
788	C₂²×D₄	C₂³×C₈₉	1	6	yes	—
789	C₂²×D₄	C₂³×C₈₉	1	3	yes	—
790	C₂²×D₄	C₂³×C₈₉	1	3	yes	—
791	C₂²×D₄	C₂³×C₈₉	1	3	yes	—
792	C₂³×C₄	C₂³×C₈₉	1	6	yes	—
793	C₂³×C₄	C₂³×C₈₉	1	3	yes	—
794	C₄⋊Q₈	C₂³×C₈₉	1	6	yes	complemented
795	C₄⋊Q₈	C₂³×C₈₉	1	6	yes	complemented
796	C₄⋊Q₈	C₂³×C₈₉	1	6	yes	complemented
797	C₄⋊Q₈	C₂³×C₈₉	1	6	yes	complemented
798	C₄⋊Q₈	C₂³×C₈₉	1	6	yes	complemented
799	#127	C₂³×C₈₉	1	1	yes	characteristic
800	#127	C₂³×C₈₉	1	3	yes	—
801	#126	C₂³×C₈₉	1	6	yes	—
802	#126	C₂³×C₈₉	1	6	yes	—
803	#126	C₂³×C₈₉	1	2	yes	—
804	#126	C₂³×C₈₉	1	6	yes	—
805	#126	C₂³×C₈₉	1	6	yes	—
806	#126	C₂³×C₈₉	1	6	yes	—
807	#126	C₂³×C₈₉	1	6	yes	—
808	#126	C₂³×C₈₉	1	6	yes	—
809	#126	C₂³×C₈₉	1	6	yes	—
810	#126	C₂³×C₈₉	1	6	yes	—
811	#126	C₂³×C₈₉	1	6	yes	—
812	#126	C₂³×C₈₉	1	6	yes	—
813	#126	C₂³×C₈₉	1	6	yes	—
814	#126	C₂³×C₈₉	1	6	yes	—
815	#126	C₂³×C₈₉	1	6	yes	complemented
816	#126	C₂³×C₈₉	1	2	yes	complemented
817	#126	C₂³×C₈₉	1	6	yes	complemented
818	#126	C₂³×C₈₉	1	6	yes	complemented
819	#126	C₂³×C₈₉	1	6	yes	complemented
820	#126	C₂³×C₈₉	1	6	yes	complemented
821	#126	C₂³×C₈₉	1	6	yes	complemented
822	#126	C₂³×C₈₉	1	6	yes	complemented
823	#126	C₂³×C₈₉	1	6	yes	complemented
824	#126	C₂³×C₈₉	1	6	yes	complemented
825	#126	C₂³×C₈₉	1	6	yes	complemented
826	#126	C₂³×C₈₉	1	2	yes	complemented
827	#125	C₂³×C₈₉	1	6	yes	complemented
828	#125	C₂³×C₈₉	1	6	yes	complemented
829	#125	C₂³×C₈₉	1	6	yes	complemented
830	#125	C₂³×C₈₉	1	6	yes	complemented
831	#125	C₂³×C₈₉	1	6	yes	complemented
832	#125	C₂³×C₈₉	1	6	yes	complemented
833	#125	C₂³×C₈₉	1	6	yes	complemented
834	#125	C₂³×C₈₉	1	6	yes	complemented
835	#125	C₂³×C₈₉	1	6	yes	complemented
836	#125	C₂³×C₈₉	1	6	yes	complemented
837	#125	C₂³×C₈₉	1	6	yes	complemented
838	#125	C₂³×C₈₉	1	6	yes	complemented
839	#125	C₂³×C₈₉	1	6	yes	complemented
840	#124	C₂³×C₈₉	1	3	yes	—
841	#124	C₂³×C₈₉	1	3	yes	—
842	#124	C₂³×C₈₉	1	6	yes	—
843	#124	C₂³×C₈₉	1	6	yes	—
844	#124	C₂³×C₈₉	1	3	yes	—
845	#124	C₂³×C₈₉	1	3	yes	—
846	#124	C₂³×C₈₉	1	6	yes	—
847	#124	C₂³×C₈₉	1	6	yes	—
848	#124	C₂³×C₈₉	1	6	yes	—
849	#124	C₂³×C₈₉	1	3	yes	—
850	#124	C₂³×C₈₉	1	3	yes	—
851	#124	C₂³×C₈₉	1	6	yes	—
852	#124	C₂³×C₈₉	1	6	yes	—
853	#124	C₂³×C₈₉	1	6	yes	complemented
854	#124	C₂³×C₈₉	1	6	yes	complemented
855	#124	C₂³×C₈₉	1	6	yes	complemented
856	#124	C₂³×C₈₉	1	6	yes	complemented
857	#123	C₂³×C₈₉	1	6	yes	—
858	#123	C₂³×C₈₉	1	6	yes	—
859	#123	C₂³×C₈₉	1	6	yes	—
860	#123	C₂³×C₈₉	1	3	yes	—
861	#123	C₂³×C₈₉	1	3	yes	—
862	#123	C₂³×C₈₉	1	6	yes	—
863	#123	C₂³×C₈₉	1	6	yes	—
864	#123	C₂³×C₈₉	1	6	yes	—
865	#123	C₂³×C₈₉	1	6	yes	—
866	#123	C₂³×C₈₉	1	3	yes	—
867	#123	C₂³×C₈₉	1	3	yes	—
868	#123	C₂³×C₈₉	1	6	yes	—
869	#123	C₂³×C₈₉	1	6	yes	—
870	#123	C₂³×C₈₉	1	6	yes	—
871	#123	C₂³×C₈₉	1	6	yes	—
872	#123	C₂³×C₈₉	1	6	yes	—
873	#123	C₂³×C₈₉	1	6	yes	—
874	#123	C₂³×C₈₉	1	6	yes	—
875	#123	C₂³×C₈₉	1	6	yes	—
876	#123	C₂³×C₈₉	1	6	yes	—
877	#123	C₂³×C₈₉	1	6	yes	—
878	#123	C₂³×C₈₉	1	6	yes	—
879	#123	C₂³×C₈₉	1	6	yes	—
880	#123	C₂³×C₈₉	1	3	yes	—
881	#123	C₂³×C₈₉	1	3	yes	—
882	#123	C₂³×C₈₉	1	3	yes	—
883	#123	C₂³×C₈₉	1	3	yes	—
884	#123	C₂³×C₈₉	1	6	yes	—
885	#123	C₂³×C₈₉	1	6	yes	—
886	#123	C₂³×C₈₉	1	6	yes	complemented
887	#123	C₂³×C₈₉	1	6	yes	complemented
888	#123	C₂³×C₈₉	1	6	yes	complemented
889	#123	C₂³×C₈₉	1	6	yes	complemented
890	#123	C₂³×C₈₉	1	6	yes	complemented
891	#123	C₂³×C₈₉	1	6	yes	complemented
892	#123	C₂³×C₈₉	1	6	yes	complemented
893	C₂²⋊Q₈	C₂³×C₈₉	1	6	yes	—
894	C₂²⋊Q₈	C₂³×C₈₉	1	6	yes	—
895	C₂²⋊Q₈	C₂³×C₈₉	1	6	yes	—
896	C₂²⋊Q₈	C₂³×C₈₉	1	6	yes	—
897	C₂²⋊Q₈	C₂³×C₈₉	1	6	yes	—
898	C₂²⋊Q₈	C₂³×C₈₉	1	6	yes	—
899	C₂²⋊Q₈	C₂³×C₈₉	1	6	yes	—
900	C₂²⋊Q₈	C₂³×C₈₉	1	6	yes	—
901	C₂²⋊Q₈	C₂³×C₈₉	1	6	yes	—
902	C₂²⋊Q₈	C₂³×C₈₉	1	6	yes	—
903	C₂²⋊Q₈	C₂³×C₈₉	1	6	yes	—
904	C₂²⋊Q₈	C₂³×C₈₉	1	6	yes	—
905	C₂²⋊Q₈	C₂³×C₈₉	1	6	yes	—
906	C₂²⋊Q₈	C₂³×C₈₉	1	6	yes	—
907	C₂²⋊Q₈	C₂³×C₈₉	1	6	yes	—
908	C₂²⋊Q₈	C₂³×C₈₉	1	6	yes	—
909	C₂²⋊Q₈	C₂³×C₈₉	1	6	yes	—
910	C₂²⋊Q₈	C₂³×C₈₉	1	6	yes	complemented
911	C₂²⋊Q₈	C₂³×C₈₉	1	6	yes	complemented
912	C₂²⋊Q₈	C₂³×C₈₉	1	6	yes	complemented
913	C₂²⋊Q₈	C₂³×C₈₉	1	6	yes	complemented
914	C₂²⋊Q₈	C₂³×C₈₉	1	6	yes	complemented
915	C₂²⋊Q₈	C₂³×C₈₉	1	6	yes	complemented
916	C₂²⋊Q₈	C₂³×C₈₉	1	6	yes	complemented
917	C₂²⋊Q₈	C₂³×C₈₉	1	6	yes	complemented
918	C₂²⋊Q₈	C₂³×C₈₉	1	6	yes	complemented
919	C₂²⋊Q₈	C₂³×C₈₉	1	6	yes	complemented
920	C₂²⋊Q₈	C₂³×C₈₉	1	6	yes	complemented
921	C₂²⋊Q₈	C₂³×C₈₉	1	6	yes	complemented
922	C₂²⋊Q₈	C₂³×C₈₉	1	6	yes	complemented
923	#121	C₂³×C₈₉	1	6	yes	—
924	#121	C₂³×C₈₉	1	6	yes	—
925	#121	C₂³×C₈₉	1	6	yes	—
926	#121	C₂³×C₈₉	1	6	yes	—
927	#121	C₂³×C₈₉	1	6	yes	—
928	#121	C₂³×C₈₉	1	6	yes	—
929	#121	C₂³×C₈₉	1	6	yes	—
930	#121	C₂³×C₈₉	1	6	yes	—
931	#121	C₂³×C₈₉	1	6	yes	—
932	#121	C₂³×C₈₉	1	6	yes	—
933	#121	C₂³×C₈₉	1	6	yes	—
934	#121	C₂³×C₈₉	1	6	yes	—
935	#121	C₂³×C₈₉	1	6	yes	—
936	#121	C₂³×C₈₉	1	6	yes	complemented
937	#121	C₂³×C₈₉	1	6	yes	complemented
938	#121	C₂³×C₈₉	1	6	yes	complemented
939	#120	C₂³×C₈₉	1	3	yes	—
940	#120	C₂³×C₈₉	1	3	yes	—
941	#120	C₂³×C₈₉	1	6	yes	—
942	#120	C₂³×C₈₉	1	6	yes	—
943	#120	C₂³×C₈₉	1	3	yes	—
944	#120	C₂³×C₈₉	1	3	yes	—
945	#120	C₂³×C₈₉	1	6	yes	—
946	#120	C₂³×C₈₉	1	2	yes	—
947	#120	C₂³×C₈₉	1	6	yes	—
948	#120	C₂³×C₈₉	1	6	yes	—
949	#120	C₂³×C₈₉	1	1	yes	characteristic
950	#120	C₂³×C₈₉	1	3	yes	—
951	#120	C₂³×C₈₉	1	3	yes	—
952	#120	C₂³×C₈₉	1	3	yes	—
953	#120	C₂³×C₈₉	1	2	yes	complemented
954	C₄×Q₈	C₂³×C₈₉	1	6	yes	complemented
955	C₄×Q₈	C₂³×C₈₉	1	6	yes	complemented
956	C₄×Q₈	C₂³×C₈₉	1	6	yes	complemented
957	C₄×Q₈	C₂³×C₈₉	1	6	yes	complemented
958	C₄×Q₈	C₂³×C₈₉	1	6	yes	complemented
959	C₄×Q₈	C₂³×C₈₉	1	6	yes	complemented
960	C₄×Q₈	C₂³×C₈₉	1	6	yes	complemented
961	C₄×Q₈	C₂³×C₈₉	1	6	yes	complemented
962	C₄×Q₈	C₂³×C₈₉	1	6	yes	complemented
963	C₄×D₄	C₂³×C₈₉	1	6	yes	—
964	C₄×D₄	C₂³×C₈₉	1	6	yes	—
965	C₄×D₄	C₂³×C₈₉	1	6	yes	—
966	C₄×D₄	C₂³×C₈₉	1	6	yes	—
967	C₄×D₄	C₂³×C₈₉	1	6	yes	—
968	C₄×D₄	C₂³×C₈₉	1	6	yes	—
969	C₄×D₄	C₂³×C₈₉	1	6	yes	—
970	C₄×D₄	C₂³×C₈₉	1	6	yes	—
971	C₄×D₄	C₂³×C₈₉	1	6	yes	—
972	C₄×D₄	C₂³×C₈₉	1	6	yes	—
973	C₄×D₄	C₂³×C₈₉	1	6	yes	—
974	C₄×D₄	C₂³×C₈₉	1	6	yes	—
975	C₄×D₄	C₂³×C₈₉	1	6	yes	—
976	C₄×D₄	C₂³×C₈₉	1	6	yes	—
977	C₄×D₄	C₂³×C₈₉	1	6	yes	—
978	C₄×D₄	C₂³×C₈₉	1	6	yes	—
979	C₄×D₄	C₂³×C₈₉	1	6	yes	—
980	C₄×D₄	C₂³×C₈₉	1	6	yes	—
981	C₄×D₄	C₂³×C₈₉	1	6	yes	—
982	C₄×D₄	C₂³×C₈₉	1	6	yes	—
983	C₄×D₄	C₂³×C₈₉	1	6	yes	—
984	C₄×D₄	C₂³×C₈₉	1	6	yes	—
985	C₄×D₄	C₂³×C₈₉	1	6	yes	complemented
986	C₄×D₄	C₂³×C₈₉	1	6	yes	complemented
987	C₄×D₄	C₂³×C₈₉	1	6	yes	complemented
988	C₄×D₄	C₂³×C₈₉	1	6	yes	complemented
989	C₄×D₄	C₂³×C₈₉	1	6	yes	complemented
990	C₄×D₄	C₂³×C₈₉	1	6	yes	complemented
991	C₄×D₄	C₂³×C₈₉	1	6	yes	complemented
992	#117	C₂³×C₈₉	1	6	yes	—
993	#117	C₂³×C₈₉	1	6	yes	—
994	#117	C₂³×C₈₉	1	6	yes	—
995	#117	C₂³×C₈₉	1	6	yes	—
996	#117	C₂³×C₈₉	1	6	yes	—
997	#117	C₂³×C₈₉	1	6	yes	—
998	#117	C₂³×C₈₉	1	6	yes	—
999	#117	C₂³×C₈₉	1	6	yes	—
1000	#117	C₂³×C₈₉	1	6	yes	—
1001	#117	C₂³×C₈₉	1	3	yes	—
1002	#117	C₂³×C₈₉	1	6	yes	—
1003	#117	C₂³×C₈₉	1	3	yes	—
1004	#117	C₂³×C₈₉	1	6	yes	—
1005	#117	C₂³×C₈₉	1	3	yes	—
1006	#117	C₂³×C₈₉	1	6	yes	complemented
1007	#117	C₂³×C₈₉	1	6	yes	complemented
1008	#117	C₂³×C₈₉	1	6	yes	complemented
1009	#117	C₂³×C₈₉	1	6	yes	complemented
1010	#117	C₂³×C₈₉	1	6	yes	complemented
1011	#117	C₂³×C₈₉	1	6	yes	complemented
1012	#117	C₂³×C₈₉	1	6	yes	complemented
1013	#117	C₂³×C₈₉	1	6	yes	complemented
1014	C₂×C₄⋊C₄	C₂³×C₈₉	1	6	yes	—
1015	C₂×C₄⋊C₄	C₂³×C₈₉	1	6	yes	—
1016	C₂×C₄⋊C₄	C₂³×C₈₉	1	6	yes	—
1017	C₂×C₄⋊C₄	C₂³×C₈₉	1	6	yes	—
1018	C₂×C₄⋊C₄	C₂³×C₈₉	1	6	yes	complemented
1019	C₂×C₄⋊C₄	C₂³×C₈₉	1	6	yes	complemented
1020	C₂×C₄⋊C₄	C₂³×C₈₉	1	6	yes	complemented
1021	C₂×C₂²⋊C₄	C₂³×C₈₉	1	6	yes	—
1022	C₂×C₂²⋊C₄	C₂³×C₈₉	1	3	yes	—
1023	C₂×C₂²⋊C₄	C₂³×C₈₉	1	6	yes	—
1024	C₂×C₂²⋊C₄	C₂³×C₈₉	1	6	yes	—
1025	C₂×C₂²⋊C₄	C₂³×C₈₉	1	6	yes	—
1026	C₂×C₂²⋊C₄	C₂³×C₈₉	1	3	yes	—
1027	C₂×C₂²⋊C₄	C₂³×C₈₉	1	6	yes	—
1028	C₂×C₂²⋊C₄	C₂³×C₈₉	1	3	yes	—
1029	C₂×C₂²⋊C₄	C₂³×C₈₉	1	6	yes	—
1030	C₂×C₂²⋊C₄	C₂³×C₈₉	1	3	yes	—
1031	C₂×C₂²⋊C₄	C₂³×C₈₉	1	6	yes	—
1032	C₂×C₂²⋊C₄	C₂³×C₈₉	1	3	yes	—
1033	C₂×C₂²⋊C₄	C₂³×C₈₉	1	3	yes	—
1034	C₂×C₂²⋊C₄	C₂³×C₈₉	1	3	yes	—
1035	C₂×C₂²⋊C₄	C₂³×C₈₉	1	3	yes	—
1036	C₂×C₂²⋊C₄	C₂³×C₈₉	1	6	yes	—
1037	C₂×C₂²⋊C₄	C₂³×C₈₉	1	6	yes	complemented
1038	C₂×C₄²	C₂³×C₈₉	1	3	yes	—
1039	C₂×C₄²	C₂³×C₈₉	1	6	yes	—
1040	C₂×C₄²	C₂³×C₈₉	1	6	yes	complemented
1041	C₂×C₄²	C₂³×C₈₉	1	2	yes	complemented
1042	C₂⁴	—	4	6	no	—
1043	C₂⁴	C₂⁴×C₈₉	1	3	yes	—
1044	C₂⁴	C₂⁴×C₈₉	1	3	yes	—
1045	C₂⁴	C₂⁴×C₈₉	1	3	yes	—
1046	C₂⁴	C₂⁴×C₈₉	1	1	yes	characteristic
1047	C₂⁴	C₂⁴×C₈₉	1	1	yes	characteristic
1048	C₂⁴	C₂⁴×C₈₉	1	1	yes	characteristic
1049	#41	—	4	12	no	—
1050	#41	—	4	12	no	—
1051	#41	—	4	6	no	—
1052	C₂×Q₈	—	4	6	no	—
1053	C₂×Q₈	C₂⁴×C₈₉	1	3	yes	—
1054	C₂×Q₈	C₂⁴×C₈₉	1	6	yes	—
1055	C₂×Q₈	C₂⁴×C₈₉	1	6	yes	—
1056	C₂×Q₈	C₂⁴×C₈₉	1	3	yes	—
1057	C₂×Q₈	C₂⁴×C₈₉	1	6	yes	—
1058	C₂×Q₈	C₂⁴×C₈₉	1	3	yes	—
1059	C₂×D₄	—	4	6	no	—
1060	C₂×D₄	—	4	6	no	—
1061	C₂×D₄	—	4	12	no	—
1062	C₂×D₄	—	4	6	no	—
1063	C₂×D₄	C₂⁴×C₈₉	1	6	yes	—
1064	C₂×D₄	C₂⁴×C₈₉	1	6	yes	—
1065	C₂×D₄	C₂⁴×C₈₉	1	6	yes	—
1066	C₂×D₄	C₂⁴×C₈₉	1	3	yes	—
1067	C₂×D₄	C₂⁴×C₈₉	1	6	yes	—
1068	C₂×D₄	C₂⁴×C₈₉	1	3	yes	—
1069	C₂×D₄	C₂⁴×C₈₉	1	3	yes	—
1070	C₂×D₄	C₂⁴×C₈₉	1	6	yes	—
1071	C₂×D₄	C₂⁴×C₈₉	1	3	yes	—
1072	C₂×D₄	C₂⁴×C₈₉	1	6	yes	—
1073	C₂×D₄	C₂⁴×C₈₉	1	6	yes	—
1074	C₂×D₄	C₂⁴×C₈₉	1	6	yes	—
1075	C₂×D₄	C₂⁴×C₈₉	1	3	yes	—
1076	C₂×D₄	C₂⁴×C₈₉	1	6	yes	—
1077	C₂²×C₄	—	4	6	no	—
1078	C₂²×C₄	—	4	12	no	—
1079	C₂²×C₄	C₂⁴×C₈₉	1	6	yes	—
1080	C₂²×C₄	C₂⁴×C₈₉	1	3	yes	—
1081	C₂²×C₄	C₂⁴×C₈₉	1	6	yes	—
1082	C₂²×C₄	C₂⁴×C₈₉	1	6	yes	—
1083	C₂²×C₄	C₂⁴×C₈₉	1	6	yes	—
1084	C₂²×C₄	C₂⁴×C₈₉	1	3	yes	—
1085	C₂²×C₄	C₂⁴×C₈₉	1	6	yes	—
1086	C₂²×C₄	C₂⁴×C₈₉	1	6	yes	—
1087	C₂²×C₄	C₂⁴×C₈₉	1	6	yes	—
1088	C₂²×C₄	C₂⁴×C₈₉	1	6	yes	—
1089	C₂²×C₄	C₂⁴×C₈₉	1	6	yes	—
1090	C₂²×C₄	C₂⁴×C₈₉	1	3	yes	—
1091	C₂²×C₄	C₂⁴×C₈₉	1	6	yes	—
1092	C₂²×C₄	C₂⁴×C₈₉	1	6	yes	—
1093	C₂²×C₄	C₂⁴×C₈₉	1	6	yes	—
1094	C₂²×C₄	C₂⁴×C₈₉	1	6	yes	—
1095	C₂²×C₄	C₂⁴×C₈₉	1	3	yes	—
1096	C₂²×C₄	C₂⁴×C₈₉	1	3	yes	—
1097	C₄⋊C₄	C₂⁴×C₈₉	1	6	yes	—
1098	C₄⋊C₄	C₂⁴×C₈₉	1	6	yes	—
1099	C₄⋊C₄	C₂⁴×C₈₉	1	6	yes	—
1100	C₄⋊C₄	C₂⁴×C₈₉	1	6	yes	—
1101	C₄⋊C₄	C₂⁴×C₈₉	1	6	yes	—
1102	C₄⋊C₄	C₂⁴×C₈₉	1	6	yes	—
1103	C₄⋊C₄	C₂⁴×C₈₉	1	6	yes	—
1104	C₄⋊C₄	C₂⁴×C₈₉	1	6	yes	—
1105	C₄⋊C₄	C₂⁴×C₈₉	1	6	yes	—
1106	C₄⋊C₄	C₂⁴×C₈₉	1	6	yes	—
1107	C₄⋊C₄	C₂⁴×C₈₉	1	6	yes	—
1108	C₄⋊C₄	C₂⁴×C₈₉	1	6	yes	—
1109	C₄⋊C₄	C₂⁴×C₈₉	1	6	yes	—
1110	C₄⋊C₄	C₂⁴×C₈₉	1	6	yes	—
1111	C₄⋊C₄	C₂⁴×C₈₉	1	6	yes	—
1112	C₄⋊C₄	C₂⁴×C₈₉	1	6	yes	—
1113	C₄⋊C₄	C₂⁴×C₈₉	1	6	yes	—
1114	C₄⋊C₄	C₂⁴×C₈₉	1	6	yes	—
1115	C₄⋊C₄	C₂⁴×C₈₉	1	6	yes	—
1116	C₄⋊C₄	C₂⁴×C₈₉	1	6	yes	—
1117	C₄⋊C₄	C₂⁴×C₈₉	1	6	yes	—
1118	C₄⋊C₄	C₂⁴×C₈₉	1	6	yes	—
1119	C₄⋊C₄	C₂⁴×C₈₉	1	6	yes	—
1120	C₄⋊C₄	C₂⁴×C₈₉	1	6	yes	—
1121	C₄⋊C₄	C₂⁴×C₈₉	1	6	yes	—
1122	C₄⋊C₄	C₂⁴×C₈₉	1	6	yes	—
1123	C₄⋊C₄	C₂⁴×C₈₉	1	6	yes	—
1124	C₄⋊C₄	C₂⁴×C₈₉	1	6	yes	—
1125	C₄⋊C₄	C₂⁴×C₈₉	1	6	yes	—
1126	C₄⋊C₄	C₂⁴×C₈₉	1	6	yes	—
1127	C₄⋊C₄	C₂⁴×C₈₉	1	6	yes	—
1128	C₂²⋊C₄	C₂⁴×C₈₉	1	3	yes	—
1129	C₂²⋊C₄	C₂⁴×C₈₉	1	3	yes	—
1130	C₂²⋊C₄	C₂⁴×C₈₉	1	6	yes	—
1131	C₂²⋊C₄	C₂⁴×C₈₉	1	6	yes	—
1132	C₂²⋊C₄	C₂⁴×C₈₉	1	6	yes	—
1133	C₂²⋊C₄	C₂⁴×C₈₉	1	6	yes	—
1134	C₂²⋊C₄	C₂⁴×C₈₉	1	3	yes	—
1135	C₂²⋊C₄	C₂⁴×C₈₉	1	3	yes	—
1136	C₂²⋊C₄	C₂⁴×C₈₉	1	6	yes	—
1137	C₂²⋊C₄	C₂⁴×C₈₉	1	6	yes	—
1138	C₂²⋊C₄	C₂⁴×C₈₉	1	3	yes	—
1139	C₂²⋊C₄	C₂⁴×C₈₉	1	6	yes	—
1140	C₂²⋊C₄	C₂⁴×C₈₉	1	3	yes	—
1141	C₂²⋊C₄	C₂⁴×C₈₉	1	6	yes	—
1142	C₂²⋊C₄	C₂⁴×C₈₉	1	6	yes	—
1143	C₂²⋊C₄	C₂⁴×C₈₉	1	6	yes	—
1144	C₂²⋊C₄	C₂⁴×C₈₉	1	6	yes	—
1145	C₂²⋊C₄	C₂⁴×C₈₉	1	6	yes	—
1146	C₂²⋊C₄	C₂⁴×C₈₉	1	6	yes	—
1147	C₂²⋊C₄	C₂⁴×C₈₉	1	6	yes	—
1148	C₂²⋊C₄	C₂⁴×C₈₉	1	6	yes	—
1149	C₂²⋊C₄	C₂⁴×C₈₉	1	6	yes	—
1150	C₂²⋊C₄	C₂⁴×C₈₉	1	3	yes	—
1151	C₂²⋊C₄	C₂⁴×C₈₉	1	3	yes	—
1152	C₂²⋊C₄	C₂⁴×C₈₉	1	3	yes	—
1153	C₂²⋊C₄	C₂⁴×C₈₉	1	3	yes	—
1154	C₂²⋊C₄	C₂⁴×C₈₉	1	6	yes	—
1155	C₂²⋊C₄	C₂⁴×C₈₉	1	6	yes	—
1156	C₂²⋊C₄	C₂⁴×C₈₉	1	6	yes	—
1157	C₂²⋊C₄	C₂⁴×C₈₉	1	6	yes	—
1158	C₂²⋊C₄	C₂⁴×C₈₉	1	6	yes	—
1159	C₂²⋊C₄	C₂⁴×C₈₉	1	3	yes	—
1160	C₂²⋊C₄	C₂⁴×C₈₉	1	3	yes	—
1161	C₂²⋊C₄	C₂⁴×C₈₉	1	6	yes	—
1162	C₂²⋊C₄	C₂⁴×C₈₉	1	6	yes	—
1163	C₂²⋊C₄	C₂⁴×C₈₉	1	6	yes	—
1164	C₂²⋊C₄	C₂⁴×C₈₉	1	6	yes	—
1165	C₂²⋊C₄	C₂⁴×C₈₉	1	6	yes	—
1166	C₂²⋊C₄	C₂⁴×C₈₉	1	6	yes	—
1167	C₄²	C₂⁴×C₈₉	1	3	yes	—
1168	C₄²	C₂⁴×C₈₉	1	6	yes	—
1169	C₄²	C₂⁴×C₈₉	1	3	yes	—
1170	C₄²	C₂⁴×C₈₉	1	6	yes	—
1171	C₄²	C₂⁴×C₈₉	1	6	yes	—
1172	C₄²	C₂⁴×C₈₉	1	6	yes	—
1173	C₄²	C₂⁴×C₈₉	1	6	yes	—
1174	C₄²	C₂⁴×C₈₉	1	6	yes	—
1175	C₄²	C₂⁴×C₈₉	1	6	yes	—
1176	C₄²	C₂⁴×C₈₉	1	2	yes	—
1177	C₄²	C₂⁴×C₈₉	1	1	yes	characteristic
1178	C₄²	C₂⁴×C₈₉	1	6	yes	—
1179	C₄²	C₂⁴×C₈₉	1	6	yes	—
1180	C₄²	C₂⁴×C₈₉	1	3	yes	—
1181	C₂³	—	2	12	no	—
1182	C₂³	—	2	6	no	—
1183	C₂³	—	2	6	no	—
1184	C₂³	—	4	3	no	—
1185	C₂³	—	4	6	no	—
1186	C₂³	—	4	6	no	—
1187	C₂³	—	4	3	no	—
1188	C₂³	—	4	3	no	—
1189	C₂³	—	4	3	no	—
1190	C₂³	—	8	8	no	—
1191	C₂³	C₂⁵×C₈₉	1	1	yes	characteristic
1192	C₂³	C₂⁵×C₈₉	1	3	yes	—
1193	C₂³	C₂⁵×C₈₉	1	3	yes	—
1194	C₂³	C₂⁵×C₈₉	1	2	yes	—
1195	C₂³	C₂⁵×C₈₉	1	3	yes	—
1196	C₂³	C₂⁵×C₈₉	1	3	yes	—
1197	Q₈	—	4	3	no	—
1198	Q₈	—	4	6	no	—
1199	Q₈	—	4	3	no	—
1200	Q₈	—	4	6	no	—
1201	Q₈	—	4	6	no	—
1202	Q₈	—	4	3	no	—
1203	D₄	—	2	12	no	—
1204	D₄	—	2	12	no	—
1205	D₄	—	2	12	no	—
1206	D₄	—	4	3	no	—
1207	D₄	—	4	3	no	—
1208	D₄	—	4	3	no	—
1209	D₄	—	4	3	no	—
1210	D₄	—	4	6	no	—
1211	D₄	—	4	6	no	—
1212	D₄	—	4	6	no	—
1213	D₄	—	4	6	no	—
1214	D₄	—	4	6	no	—
1215	D₄	—	4	6	no	—
1216	D₄	—	4	3	no	—
1217	C₂×C₄	—	2	12	no	—
1218	C₂×C₄	—	2	12	no	—
1219	C₂×C₄	—	2	6	no	—
1220	C₂×C₄	—	4	3	no	—
1221	C₂×C₄	—	4	6	no	—
1222	C₂×C₄	—	4	6	no	—
1223	C₂×C₄	—	4	6	no	—
1224	C₂×C₄	—	4	3	no	—
1225	C₂×C₄	—	4	6	no	—
1226	C₂×C₄	—	4	6	no	—
1227	C₂×C₄	—	4	3	no	—
1228	C₂×C₄	—	4	6	no	—
1229	C₂×C₄	—	4	3	no	—
1230	C₂×C₄	—	4	6	no	—
1231	C₂×C₄	—	4	6	no	—
1232	C₂×C₄	—	4	6	no	—
1233	C₂×C₄	—	4	6	no	—
1234	C₂×C₄	—	4	6	no	—
1235	C₂×C₄	C₂⁵×C₈₉	1	6	yes	—
1236	C₂×C₄	C₂⁵×C₈₉	1	3	yes	—
1237	C₂×C₄	C₂⁵×C₈₉	1	6	yes	—
1238	C₂×C₄	C₂⁵×C₈₉	1	3	yes	—
1239	C₂×C₄	C₂⁵×C₈₉	1	6	yes	—
1240	C₂×C₄	C₂⁵×C₈₉	1	6	yes	—
1241	C₂×C₄	C₂⁵×C₈₉	1	6	yes	—
1242	C₂×C₄	C₂⁵×C₈₉	1	6	yes	—
1243	C₂×C₄	C₂⁵×C₈₉	1	6	yes	—
1244	C₂²	—	2	6	no	—
1245	C₂²	—	2	3	no	—
1246	C₂²	—	2	6	no	—
1247	C₂²	—	2	6	no	—
1248	C₂²	—	2	3	no	—
1249	C₂²	—	2	6	no	—
1250	C₂²	—	2	6	no	—
1251	C₂²	—	2	3	no	—
1252	C₂²	—	2	3	no	—
1253	C₂²	—	4	12	no	—
1254	C₂²	—	8	6	no	—
1255	C₂²	—	8	6	no	—
1256	C₂²	—	8	2	no	—
1257	C₂²	—	16	1	no	—
1258	C₂²	—	16	1	no	—
1259	C₂²	#585×C₈₉	1	6	yes	—
1260	C₂²	C₂⁶×C₈₉	1	1	yes	characteristic
1261	C₄	—	2	6	no	—
1262	C₄	—	2	6	no	—
1263	C₄	—	2	6	no	—
1264	C₄	—	2	3	no	—
1265	C₄	—	2	6	no	—
1266	C₄	—	2	3	no	—
1267	C₄	—	2	6	no	—
1268	C₄	—	2	6	no	—
1269	C₄	—	2	6	no	—
1270	C₂	—	2	6	no	—
1271	C₂	—	4	3	no	—
1272	C₂	—	4	3	no	—
1273	C₂	—	4	1	no	—
1274	C₂	—	4	3	no	—
1275	C₂	—	4	2	no	—
1276	C₂	C₂×#585×C₈₉	1	3	yes	—

	subgroup	G/H
center, socle	C₂²×C₈₉	C₂⁶
commutator, Frattini, cosocle	C₂²	C₂⁶×C₈₉
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₈₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₈₉×#3568	C₂	semidirect
2. C₈₉×#3566	C₂	semidirect
3. C₈₉×#3564	C₂	semidirect
4. C₈₉×#3545	C₂	semidirect
5. C₈₉×#3535	C₂	semidirect
6. C₈₉×#3533	C₂	semidirect
7. C₈₉×#3532	C₂	semidirect
8. C₈₉×#3521	C₂	semidirect
9. C₈₉×#3513	C₂	semidirect
10. C₈₉×#3510	C₂	semidirect
11. C₈₉×#3495	C₂	semidirect
12. C₈₉×#3491	C₂	semidirect
13. C₈₉×#3490	C₂	semidirect
14. C₈₉×#3475	C₂	semidirect
15. C₂×#551×C₈₉	C₂	semidirect
16. #563×C₈₉	C₂²	semidirect
17. #563×C₈₉	C₂²	semidirect
18. #563×C₈₉	C₂²	semidirect
19. #563×C₈₉	C₂²	semidirect
20. #562×C₈₉	C₂²	semidirect
21. #562×C₈₉	C₂²	semidirect
22. H(3,𝔽₄)×C₈₉	C₂²	semidirect
23. H(3,𝔽₄)×C₈₉	C₂²	semidirect
24. #560×C₈₉	C₂²	semidirect
25. #560×C₈₉	C₂²	semidirect
26. #559×C₈₉	C₂²	semidirect
27. #559×C₈₉	C₂²	semidirect
28. #556×C₈₉	C₂²	semidirect
29. #556×C₈₉	C₂²	semidirect
30. #556×C₈₉	C₂²	semidirect
31. #556×C₈₉	C₂²	semidirect
32. #555×C₈₉	C₂²	semidirect
33. #554×C₈₉	C₂²	semidirect
34. #554×C₈₉	C₂²	semidirect
35. #554×C₈₉	C₂²	semidirect
36. #553×C₈₉	C₂²	semidirect
37. #553×C₈₉	C₂²	semidirect
38. #553×C₈₉	C₂²	semidirect
39. #553×C₈₉	C₂²	semidirect
40. #552×C₈₉	C₂²	semidirect
41. #552×C₈₉	C₂²	semidirect
42. #552×C₈₉	C₂²	semidirect
43. #552×C₈₉	C₂²	semidirect
44. #552×C₈₉	C₂²	semidirect
45. #552×C₈₉	C₂²	semidirect
46. #552×C₈₉	C₂²	semidirect
47. #552×C₈₉	C₂²	semidirect
48. #552×C₈₉	C₂²	semidirect
49. #552×C₈₉	C₂²	semidirect
50. #551×C₈₉	C₂²	semidirect
51. #551×C₈₉	C₂²	semidirect
52. #551×C₈₉	C₂²	semidirect
53. #551×C₈₉	C₂²	semidirect
54. #551×C₈₉	C₂²	semidirect
55. #551×C₈₉	C₂²	semidirect
56. #551×C₈₉	C₂²	semidirect
57. #551×C₈₉	C₂²	semidirect
58. #551×C₈₉	C₂²	semidirect
59. #551×C₈₉	C₂²	semidirect
60. #551×C₈₉	C₂²	semidirect
61. #551×C₈₉	C₂²	semidirect
62. #551×C₈₉	C₂²	semidirect
63. #551×C₈₉	C₂²	semidirect
64. #551×C₈₉	C₂²	semidirect
65. #551×C₈₉	C₂²	semidirect
66. #551×C₈₉	C₂²	semidirect
67. #551×C₈₉	C₂²	semidirect
68. #551×C₈₉	C₂²	semidirect
69. #551×C₈₉	C₂²	semidirect
70. #551×C₈₉	C₂²	semidirect
71. #551×C₈₉	C₂²	semidirect
72. #547×C₈₉	C₂²	semidirect
73. #547×C₈₉	C₂²	semidirect
74. #546×C₈₉	C₂²	semidirect
75. #546×C₈₉	C₂²	semidirect
76. #546×C₈₉	C₂²	semidirect
77. #546×C₈₉	C₂²	semidirect
78. #546×C₈₉	C₂²	semidirect
79. #546×C₈₉	C₂²	semidirect
80. D₄²×C₈₉	C₂²	semidirect
81. #544×C₈₉	C₂²	semidirect
82. #543×C₈₉	C₂²	semidirect
83. #543×C₈₉	C₂²	semidirect
84. #542×C₈₉	C₂²	semidirect
85. #542×C₈₉	C₂²	semidirect
86. #542×C₈₉	C₂²	semidirect
87. #542×C₈₉	C₂²	semidirect
88. #542×C₈₉	C₂²	semidirect
89. #542×C₈₉	C₂²	semidirect
90. #541×C₈₉	C₂²	semidirect
91. #541×C₈₉	C₂²	semidirect
92. #541×C₈₉	C₂²	semidirect
93. #540×C₈₉	C₂²	semidirect
94. #539×C₈₉	C₂²	semidirect
95. #539×C₈₉	C₂²	semidirect
96. #539×C₈₉	C₂²	semidirect
97. #539×C₈₉	C₂²	semidirect
98. #539×C₈₉	C₂²	semidirect
99. #539×C₈₉	C₂²	semidirect
101. #538×C₈₉	C₂²	semidirect
102. #538×C₈₉	C₂²	semidirect
103. #538×C₈₉	C₂²	semidirect
104. #538×C₈₉	C₂²	semidirect
105. #538×C₈₉	C₂²	semidirect
106. #536×C₈₉	C₂²	semidirect
107. #536×C₈₉	C₂²	semidirect
110. #534×C₈₉	C₂²	semidirect
111. #533×C₈₉	C₂²	semidirect
112. #533×C₈₉	C₂²	semidirect
113. #529×C₈₉	C₂²	semidirect
114. #529×C₈₉	C₂²	semidirect
115. #529×C₈₉	C₂²	semidirect
116. #529×C₈₉	C₂²	semidirect
117. #529×C₈₉	C₂²	semidirect
118. #529×C₈₉	C₂²	semidirect
119. #529×C₈₉	C₂²	semidirect
120. #529×C₈₉	C₂²	semidirect
121. C₂×#126×C₈₉	C₂²	semidirect
122. C₂×#126×C₈₉	C₂²	semidirect
123. C₂×#124×C₈₉	C₂²	semidirect
125. #525×C₈₉	C₂²	semidirect
126. #525×C₈₉	C₂²	semidirect
127. C₂×#123×C₈₉	C₂²	semidirect
128. C₂×#123×C₈₉	C₂²	semidirect
129. C₂×#123×C₈₉	C₂²	semidirect
130. C₂×C₂²⋊Q₈×C₈₉	C₂²	semidirect
132. C₂×#120×C₈₉	C₂²	semidirect
133. #520×C₈₉	C₂²	semidirect
134. #519×C₈₉	C₂²	semidirect
135. #518×C₈₉	C₂²	semidirect
136. #518×C₈₉	C₂²	semidirect
137. #518×C₈₉	C₂²	semidirect
138. C₄×#41×C₈₉	C₂²	semidirect
139. C₄×#41×C₈₉	C₂²	semidirect
140. C₂×C₄×D₄×C₈₉	C₂²	semidirect
141. C₂×#117×C₈₉	C₂²	semidirect
142. C₂×#117×C₈₉	C₂²	semidirect
143. C₂²×C₂²⋊C₄×C₈₉	C₂²	semidirect
155. C₄⋊Q₈×C₈₉	C₂³	semidirect
156. C₄⋊Q₈×C₈₉	C₂³	semidirect
157. C₄⋊Q₈×C₈₉	C₂³	semidirect
158. C₄⋊Q₈×C₈₉	C₂³	semidirect
159. C₄⋊Q₈×C₈₉	C₂³	semidirect
176. #126×C₈₉	C₂³	semidirect
177. #126×C₈₉	C₂³	semidirect
178. #126×C₈₉	C₂³	semidirect
179. #126×C₈₉	C₂³	semidirect
180. #126×C₈₉	C₂³	semidirect
181. #126×C₈₉	C₂³	semidirect
182. #126×C₈₉	C₂³	semidirect
183. #126×C₈₉	C₂³	semidirect
184. #126×C₈₉	C₂³	semidirect
185. #126×C₈₉	C₂³	semidirect
186. #126×C₈₉	C₂³	semidirect
187. #126×C₈₉	C₂³	semidirect
188. #125×C₈₉	C₂³	semidirect
189. #125×C₈₉	C₂³	semidirect
190. #125×C₈₉	C₂³	semidirect
191. #125×C₈₉	C₂³	semidirect
192. #125×C₈₉	C₂³	semidirect
193. #125×C₈₉	C₂³	semidirect
194. #125×C₈₉	C₂³	semidirect
195. #125×C₈₉	C₂³	semidirect
196. #125×C₈₉	C₂³	semidirect
197. #125×C₈₉	C₂³	semidirect
198. #125×C₈₉	C₂³	semidirect
199. #125×C₈₉	C₂³	semidirect
200. #125×C₈₉	C₂³	semidirect
214. #124×C₈₉	C₂³	semidirect
215. #124×C₈₉	C₂³	semidirect
216. #124×C₈₉	C₂³	semidirect
217. #124×C₈₉	C₂³	semidirect
247. #123×C₈₉	C₂³	semidirect
248. #123×C₈₉	C₂³	semidirect
249. #123×C₈₉	C₂³	semidirect
250. #123×C₈₉	C₂³	semidirect
251. #123×C₈₉	C₂³	semidirect
252. #123×C₈₉	C₂³	semidirect
253. #123×C₈₉	C₂³	semidirect
271. C₂²⋊Q₈×C₈₉	C₂³	semidirect
272. C₂²⋊Q₈×C₈₉	C₂³	semidirect
273. C₂²⋊Q₈×C₈₉	C₂³	semidirect
274. C₂²⋊Q₈×C₈₉	C₂³	semidirect
275. C₂²⋊Q₈×C₈₉	C₂³	semidirect
276. C₂²⋊Q₈×C₈₉	C₂³	semidirect
277. C₂²⋊Q₈×C₈₉	C₂³	semidirect
278. C₂²⋊Q₈×C₈₉	C₂³	semidirect
279. C₂²⋊Q₈×C₈₉	C₂³	semidirect
280. C₂²⋊Q₈×C₈₉	C₂³	semidirect
281. C₂²⋊Q₈×C₈₉	C₂³	semidirect
282. C₂²⋊Q₈×C₈₉	C₂³	semidirect
283. C₂²⋊Q₈×C₈₉	C₂³	semidirect
297. #121×C₈₉	C₂³	semidirect
298. #121×C₈₉	C₂³	semidirect
299. #121×C₈₉	C₂³	semidirect
314. #120×C₈₉	C₂³	semidirect
315. C₄×Q₈×C₈₉	C₂³	semidirect
316. C₄×Q₈×C₈₉	C₂³	semidirect
317. C₄×Q₈×C₈₉	C₂³	semidirect
318. C₄×Q₈×C₈₉	C₂³	semidirect
319. C₄×Q₈×C₈₉	C₂³	semidirect
320. C₄×Q₈×C₈₉	C₂³	semidirect
321. C₄×Q₈×C₈₉	C₂³	semidirect
322. C₄×Q₈×C₈₉	C₂³	semidirect
323. C₄×Q₈×C₈₉	C₂³	semidirect
346. C₄×D₄×C₈₉	C₂³	semidirect
347. C₄×D₄×C₈₉	C₂³	semidirect
348. C₄×D₄×C₈₉	C₂³	semidirect
349. C₄×D₄×C₈₉	C₂³	semidirect
350. C₄×D₄×C₈₉	C₂³	semidirect
351. C₄×D₄×C₈₉	C₂³	semidirect
352. C₄×D₄×C₈₉	C₂³	semidirect
367. #117×C₈₉	C₂³	semidirect
368. #117×C₈₉	C₂³	semidirect
369. #117×C₈₉	C₂³	semidirect
370. #117×C₈₉	C₂³	semidirect
371. #117×C₈₉	C₂³	semidirect
372. #117×C₈₉	C₂³	semidirect
373. #117×C₈₉	C₂³	semidirect
374. #117×C₈₉	C₂³	semidirect
379. C₂×C₄⋊C₄×C₈₉	C₂³	semidirect
380. C₂×C₄⋊C₄×C₈₉	C₂³	semidirect
381. C₂×C₄⋊C₄×C₈₉	C₂³	semidirect
398. C₂×C₂²⋊C₄×C₈₉	C₂³	semidirect
401. C₂×C₄²×C₈₉	C₂³	semidirect
402. C₂×C₄²×C₈₉	C₂³	semidirect
631. #63026	C₈₉	direct (N × H)
639. #3568	C₂×C₈₉	semidirect
640. #3566	C₂×C₈₉	semidirect
641. #3564	C₂×C₈₉	semidirect
642. #3545	C₂×C₈₉	semidirect
643. #3535	C₂×C₈₉	semidirect
644. #3533	C₂×C₈₉	semidirect
645. #3532	C₂×C₈₉	semidirect
646. #3521	C₂×C₈₉	semidirect
647. #3513	C₂×C₈₉	semidirect
648. #3510	C₂×C₈₉	semidirect
649. #3495	C₂×C₈₉	semidirect
650. #3491	C₂×C₈₉	semidirect
651. #3490	C₂×C₈₉	semidirect
652. #3475	C₂×C₈₉	semidirect
653. C₂×#551	C₂×C₈₉	semidirect
654. C₈₉	#63026	direct (N × H)
655. #563	C₂²×C₈₉	semidirect
656. #563	C₂²×C₈₉	semidirect
657. #563	C₂²×C₈₉	semidirect
658. #563	C₂²×C₈₉	semidirect
659. #562	C₂²×C₈₉	semidirect
660. #562	C₂²×C₈₉	semidirect
661. H(3,𝔽₄)	C₂²×C₈₉	semidirect
662. H(3,𝔽₄)	C₂²×C₈₉	semidirect
663. #560	C₂²×C₈₉	semidirect
664. #560	C₂²×C₈₉	semidirect
665. #559	C₂²×C₈₉	semidirect
666. #559	C₂²×C₈₉	semidirect
667. #556	C₂²×C₈₉	semidirect
668. #556	C₂²×C₈₉	semidirect
669. #556	C₂²×C₈₉	semidirect
670. #556	C₂²×C₈₉	semidirect
671. #555	C₂²×C₈₉	semidirect
672. #554	C₂²×C₈₉	semidirect
673. #554	C₂²×C₈₉	semidirect
674. #554	C₂²×C₈₉	semidirect
675. #553	C₂²×C₈₉	semidirect
676. #553	C₂²×C₈₉	semidirect
677. #553	C₂²×C₈₉	semidirect
678. #553	C₂²×C₈₉	semidirect
679. #552	C₂²×C₈₉	semidirect
680. #552	C₂²×C₈₉	semidirect
681. #552	C₂²×C₈₉	semidirect
682. #552	C₂²×C₈₉	semidirect
683. #552	C₂²×C₈₉	semidirect
684. #552	C₂²×C₈₉	semidirect
685. #552	C₂²×C₈₉	semidirect
686. #552	C₂²×C₈₉	semidirect
687. #552	C₂²×C₈₉	semidirect
688. #552	C₂²×C₈₉	semidirect
689. #551	C₂²×C₈₉	semidirect
690. #551	C₂²×C₈₉	semidirect
691. #551	C₂²×C₈₉	semidirect
692. #551	C₂²×C₈₉	semidirect
693. #551	C₂²×C₈₉	semidirect
694. #551	C₂²×C₈₉	semidirect
695. #551	C₂²×C₈₉	semidirect
696. #551	C₂²×C₈₉	semidirect
697. #551	C₂²×C₈₉	semidirect
698. #551	C₂²×C₈₉	semidirect
699. #551	C₂²×C₈₉	semidirect
700. #551	C₂²×C₈₉	semidirect
701. #551	C₂²×C₈₉	semidirect
702. #551	C₂²×C₈₉	semidirect
703. #551	C₂²×C₈₉	semidirect
704. #551	C₂²×C₈₉	semidirect
705. #551	C₂²×C₈₉	semidirect
706. #551	C₂²×C₈₉	semidirect
707. #551	C₂²×C₈₉	semidirect
708. #551	C₂²×C₈₉	semidirect
709. #551	C₂²×C₈₉	semidirect
710. #551	C₂²×C₈₉	semidirect
711. #547	C₂²×C₈₉	semidirect
712. #547	C₂²×C₈₉	semidirect
713. #546	C₂²×C₈₉	semidirect
714. #546	C₂²×C₈₉	semidirect
715. #546	C₂²×C₈₉	semidirect
716. #546	C₂²×C₈₉	semidirect
717. #546	C₂²×C₈₉	semidirect
718. #546	C₂²×C₈₉	semidirect
719. D₄²	C₂²×C₈₉	semidirect
720. #544	C₂²×C₈₉	semidirect
721. #543	C₂²×C₈₉	semidirect
722. #543	C₂²×C₈₉	semidirect
723. #542	C₂²×C₈₉	semidirect
724. #542	C₂²×C₈₉	semidirect
725. #542	C₂²×C₈₉	semidirect
726. #542	C₂²×C₈₉	semidirect
727. #542	C₂²×C₈₉	semidirect
728. #542	C₂²×C₈₉	semidirect
729. #541	C₂²×C₈₉	semidirect
730. #541	C₂²×C₈₉	semidirect
731. #541	C₂²×C₈₉	semidirect
732. #540	C₂²×C₈₉	semidirect
733. #539	C₂²×C₈₉	semidirect
734. #539	C₂²×C₈₉	semidirect
735. #539	C₂²×C₈₉	semidirect
736. #539	C₂²×C₈₉	semidirect
737. #539	C₂²×C₈₉	semidirect
738. #539	C₂²×C₈₉	semidirect
740. #538	C₂²×C₈₉	semidirect
741. #538	C₂²×C₈₉	semidirect
742. #538	C₂²×C₈₉	semidirect
743. #538	C₂²×C₈₉	semidirect
744. #538	C₂²×C₈₉	semidirect
745. #536	C₂²×C₈₉	semidirect
746. #536	C₂²×C₈₉	semidirect
749. #534	C₂²×C₈₉	semidirect
750. #533	C₂²×C₈₉	semidirect
751. #533	C₂²×C₈₉	semidirect
752. #529	C₂²×C₈₉	semidirect
753. #529	C₂²×C₈₉	semidirect
754. #529	C₂²×C₈₉	semidirect
755. #529	C₂²×C₈₉	semidirect
756. #529	C₂²×C₈₉	semidirect
757. #529	C₂²×C₈₉	semidirect
758. #529	C₂²×C₈₉	semidirect
759. #529	C₂²×C₈₉	semidirect
760. C₂×#126	C₂²×C₈₉	semidirect
761. C₂×#126	C₂²×C₈₉	semidirect
762. C₂×#124	C₂²×C₈₉	semidirect
764. #525	C₂²×C₈₉	semidirect
765. #525	C₂²×C₈₉	semidirect
766. C₂×#123	C₂²×C₈₉	semidirect
767. C₂×#123	C₂²×C₈₉	semidirect
768. C₂×#123	C₂²×C₈₉	semidirect
769. C₂×C₂²⋊Q₈	C₂²×C₈₉	semidirect
771. C₂×#120	C₂²×C₈₉	semidirect
772. #520	C₂²×C₈₉	semidirect
773. #519	C₂²×C₈₉	semidirect
774. #518	C₂²×C₈₉	semidirect
775. #518	C₂²×C₈₉	semidirect
776. #518	C₂²×C₈₉	semidirect
777. C₄×#41	C₂²×C₈₉	semidirect
778. C₄×#41	C₂²×C₈₉	semidirect
779. C₂×C₄×D₄	C₂²×C₈₉	semidirect
780. C₂×#117	C₂²×C₈₉	semidirect
781. C₂×#117	C₂²×C₈₉	semidirect
782. C₂²×C₂²⋊C₄	C₂²×C₈₉	semidirect
794. C₄⋊Q₈	C₂³×C₈₉	semidirect
795. C₄⋊Q₈	C₂³×C₈₉	semidirect
796. C₄⋊Q₈	C₂³×C₈₉	semidirect
797. C₄⋊Q₈	C₂³×C₈₉	semidirect
798. C₄⋊Q₈	C₂³×C₈₉	semidirect
815. #126	C₂³×C₈₉	semidirect
816. #126	C₂³×C₈₉	semidirect
817. #126	C₂³×C₈₉	semidirect
818. #126	C₂³×C₈₉	semidirect
819. #126	C₂³×C₈₉	semidirect
820. #126	C₂³×C₈₉	semidirect
821. #126	C₂³×C₈₉	semidirect
822. #126	C₂³×C₈₉	semidirect
823. #126	C₂³×C₈₉	semidirect
824. #126	C₂³×C₈₉	semidirect
825. #126	C₂³×C₈₉	semidirect
826. #126	C₂³×C₈₉	semidirect
827. #125	C₂³×C₈₉	semidirect
828. #125	C₂³×C₈₉	semidirect
829. #125	C₂³×C₈₉	semidirect
830. #125	C₂³×C₈₉	semidirect
831. #125	C₂³×C₈₉	semidirect
832. #125	C₂³×C₈₉	semidirect
833. #125	C₂³×C₈₉	semidirect
834. #125	C₂³×C₈₉	semidirect
835. #125	C₂³×C₈₉	semidirect
836. #125	C₂³×C₈₉	semidirect
837. #125	C₂³×C₈₉	semidirect
838. #125	C₂³×C₈₉	semidirect
839. #125	C₂³×C₈₉	semidirect
853. #124	C₂³×C₈₉	semidirect
854. #124	C₂³×C₈₉	semidirect
855. #124	C₂³×C₈₉	semidirect
856. #124	C₂³×C₈₉	semidirect
886. #123	C₂³×C₈₉	semidirect
887. #123	C₂³×C₈₉	semidirect
888. #123	C₂³×C₈₉	semidirect
889. #123	C₂³×C₈₉	semidirect
890. #123	C₂³×C₈₉	semidirect
891. #123	C₂³×C₈₉	semidirect
892. #123	C₂³×C₈₉	semidirect
910. C₂²⋊Q₈	C₂³×C₈₉	semidirect
911. C₂²⋊Q₈	C₂³×C₈₉	semidirect
912. C₂²⋊Q₈	C₂³×C₈₉	semidirect
913. C₂²⋊Q₈	C₂³×C₈₉	semidirect
914. C₂²⋊Q₈	C₂³×C₈₉	semidirect
915. C₂²⋊Q₈	C₂³×C₈₉	semidirect
916. C₂²⋊Q₈	C₂³×C₈₉	semidirect
917. C₂²⋊Q₈	C₂³×C₈₉	semidirect
918. C₂²⋊Q₈	C₂³×C₈₉	semidirect
919. C₂²⋊Q₈	C₂³×C₈₉	semidirect
920. C₂²⋊Q₈	C₂³×C₈₉	semidirect
921. C₂²⋊Q₈	C₂³×C₈₉	semidirect
922. C₂²⋊Q₈	C₂³×C₈₉	semidirect
936. #121	C₂³×C₈₉	semidirect
937. #121	C₂³×C₈₉	semidirect
938. #121	C₂³×C₈₉	semidirect
953. #120	C₂³×C₈₉	semidirect
954. C₄×Q₈	C₂³×C₈₉	semidirect
955. C₄×Q₈	C₂³×C₈₉	semidirect
956. C₄×Q₈	C₂³×C₈₉	semidirect
957. C₄×Q₈	C₂³×C₈₉	semidirect
958. C₄×Q₈	C₂³×C₈₉	semidirect
959. C₄×Q₈	C₂³×C₈₉	semidirect
960. C₄×Q₈	C₂³×C₈₉	semidirect
961. C₄×Q₈	C₂³×C₈₉	semidirect
962. C₄×Q₈	C₂³×C₈₉	semidirect
985. C₄×D₄	C₂³×C₈₉	semidirect
986. C₄×D₄	C₂³×C₈₉	semidirect
987. C₄×D₄	C₂³×C₈₉	semidirect
988. C₄×D₄	C₂³×C₈₉	semidirect
989. C₄×D₄	C₂³×C₈₉	semidirect
990. C₄×D₄	C₂³×C₈₉	semidirect
991. C₄×D₄	C₂³×C₈₉	semidirect
1006. #117	C₂³×C₈₉	semidirect
1007. #117	C₂³×C₈₉	semidirect
1008. #117	C₂³×C₈₉	semidirect
1009. #117	C₂³×C₈₉	semidirect
1010. #117	C₂³×C₈₉	semidirect
1011. #117	C₂³×C₈₉	semidirect
1012. #117	C₂³×C₈₉	semidirect
1013. #117	C₂³×C₈₉	semidirect
1018. C₂×C₄⋊C₄	C₂³×C₈₉	semidirect
1019. C₂×C₄⋊C₄	C₂³×C₈₉	semidirect
1020. C₂×C₄⋊C₄	C₂³×C₈₉	semidirect
1037. C₂×C₂²⋊C₄	C₂³×C₈₉	semidirect
1040. C₂×C₄²	C₂³×C₈₉	semidirect
1041. C₂×C₄²	C₂³×C₈₉	semidirect

Maximal subgroups

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

subgroup	index
C₈₉×#3568	2
C₈₉×#3566	2
C₈₉×#3564	2
C₈₉×#3545	2
C₈₉×#3535	2
C₈₉×#3533	2
C₈₉×#3532	2
C₈₉×#3521	2
C₈₉×#3513	2
C₈₉×#3510	2
C₈₉×#3495	2
C₈₉×#3491	2
C₈₉×#3490	2
C₈₉×#3475	2
C₂×#551×C₈₉	2
#63026	89

Subgroups — C89×#63026 #36440874

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#63026 #36440874