Subgroups — C₈₉×#62755 #36440603

Order 22784.

6644 conjugacy classes of subgroups.

The subgroup lattice has 1156 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈₉×#3566	C₂	1	8	yes	maximal, complemented
2	C₈₉×#3564	C₂	1	4	yes	maximal, complemented
3	C₈₉×#3560	C₂	1	4	yes	maximal, complemented
4	C₈₉×#3553	C₂	1	4	yes	maximal, complemented
5	C₈₉×#3545	C₂	1	4	yes	maximal, complemented
6	C₈₉×#3535	C₂	1	4	yes	maximal, complemented
7	C₈₉×#3534	C₂	1	4	yes	maximal, complemented
8	C₈₉×#3531	C₂	1	2	yes	maximal, complemented
9	C₈₉×#3529	C₂	1	2	yes	maximal, complemented
10	C₈₉×#3481	C₂	1	4	yes	maximal, complemented
11	C₈₉×#3475	C₂	1	8	yes	maximal, complemented
12	C₈₉×#3461	C₂	1	4	yes	maximal, complemented
13	C₈₉×#3459	C₂	1	4	yes	maximal, complemented
14	C₈₉×#3455	C₂	1	4	yes	maximal, complemented
15	C₈₉×#3444	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#529×C₈₉	C₂	1	2	yes	maximal, complemented
17	#564×C₈₉	C₂²	1	2	yes	complemented
18	#563×C₈₉	C₂²	1	2	yes	complemented
19	#563×C₈₉	C₂²	1	4	yes	complemented
20	#563×C₈₉	C₂²	1	8	yes	complemented
21	#563×C₈₉	C₂²	1	4	yes	complemented
22	#563×C₈₉	C₂²	1	8	yes	complemented
23	#562×C₈₉	C₂²	1	8	yes	complemented
24	#562×C₈₉	C₂²	1	4	yes	complemented
25	#562×C₈₉	C₂²	1	8	yes	complemented
26	#562×C₈₉	C₂²	1	2	yes	complemented
27	H(3,𝔽₄)×C₈₉	C₂²	1	2	yes	complemented
28	#560×C₈₉	C₂²	1	8	yes	complemented
29	#560×C₈₉	C₂²	1	4	yes	complemented
30	#559×C₈₉	C₂²	1	4	yes	complemented
31	#556×C₈₉	C₂²	1	8	yes	complemented
32	#555×C₈₉	C₂²	1	8	yes	complemented
33	#554×C₈₉	C₂²	1	8	yes	complemented
34	#554×C₈₉	C₂²	1	8	yes	complemented
35	#553×C₈₉	C₂²	1	8	yes	complemented
36	#553×C₈₉	C₂²	1	8	yes	complemented
37	#553×C₈₉	C₂²	1	8	yes	complemented
38	#553×C₈₉	C₂²	1	8	yes	complemented
39	#552×C₈₉	C₂²	1	8	yes	complemented
40	#552×C₈₉	C₂²	1	8	yes	complemented
41	#552×C₈₉	C₂²	1	8	yes	complemented
42	#552×C₈₉	C₂²	1	8	yes	complemented
43	#551×C₈₉	C₂²	1	8	yes	complemented
44	#551×C₈₉	C₂²	1	8	yes	complemented
45	#551×C₈₉	C₂²	1	8	yes	complemented
46	#551×C₈₉	C₂²	1	8	yes	complemented
47	#551×C₈₉	C₂²	1	4	yes	complemented
48	#551×C₈₉	C₂²	1	8	yes	complemented
49	#551×C₈₉	C₂²	1	4	yes	complemented
50	#547×C₈₉	C₂²	1	8	yes	complemented
51	#546×C₈₉	C₂²	1	8	yes	complemented
52	#546×C₈₉	C₂²	1	8	yes	complemented
53	#546×C₈₉	C₂²	1	8	yes	complemented
54	#546×C₈₉	C₂²	1	8	yes	complemented
55	D₄²×C₈₉	C₂²	1	4	yes	complemented
56	#544×C₈₉	C₂²	1	4	yes	complemented
57	#543×C₈₉	C₂²	1	4	yes	complemented
58	#542×C₈₉	C₂²	1	8	yes	complemented
59	#542×C₈₉	C₂²	1	8	yes	complemented
60	#542×C₈₉	C₂²	1	8	yes	complemented
61	#542×C₈₉	C₂²	1	8	yes	complemented
62	#541×C₈₉	C₂²	1	8	yes	complemented
63	#541×C₈₉	C₂²	1	8	yes	complemented
64	#541×C₈₉	C₂²	1	8	yes	complemented
65	#540×C₈₉	C₂²	1	8	yes	complemented
66	#539×C₈₉	C₂²	1	8	yes	complemented
67	#539×C₈₉	C₂²	1	8	yes	complemented
68	#539×C₈₉	C₂²	1	8	yes	complemented
69	#539×C₈₉	C₂²	1	8	yes	complemented
70	#539×C₈₉	C₂²	1	8	yes	complemented
71	#539×C₈₉	C₂²	1	8	yes	complemented
72	#539×C₈₉	C₂²	1	4	yes	complemented
73	#539×C₈₉	C₂²	1	4	yes	complemented
74	#538×C₈₉	C₂²	1	4	yes	—
75	#538×C₈₉	C₂²	1	8	yes	complemented
76	#538×C₈₉	C₂²	1	8	yes	complemented
77	#538×C₈₉	C₂²	1	4	yes	complemented
78	#538×C₈₉	C₂²	1	8	yes	complemented
79	#538×C₈₉	C₂²	1	8	yes	complemented
80	#537×C₈₉	C₂²	1	4	yes	—
81	#536×C₈₉	C₂²	1	8	yes	complemented
82	#534×C₈₉	C₂²	1	8	yes	complemented
83	#534×C₈₉	C₂²	1	4	yes	complemented
84	#533×C₈₉	C₂²	1	1	yes	characteristic, complemented
85	#533×C₈₉	C₂²	1	2	yes	complemented
86	#533×C₈₉	C₂²	1	4	yes	complemented
87	#533×C₈₉	C₂²	1	8	yes	complemented
88	#532×C₈₉	C₂²	1	1	yes	characteristic, complemented
89	#532×C₈₉	C₂²	1	2	yes	complemented
90	#532×C₈₉	C₂²	1	4	yes	complemented
91	#529×C₈₉	C₂²	1	4	yes	complemented
92	#529×C₈₉	C₂²	1	4	yes	complemented
93	#529×C₈₉	C₂²	1	4	yes	complemented
94	#529×C₈₉	C₂²	1	4	yes	complemented
95	#529×C₈₉	C₂²	1	4	yes	complemented
96	#529×C₈₉	C₂²	1	4	yes	complemented
97	#529×C₈₉	C₂²	1	4	yes	complemented
98	#529×C₈₉	C₂²	1	4	yes	complemented
99	#529×C₈₉	C₂²	1	4	yes	complemented
100	#529×C₈₉	C₂²	1	4	yes	complemented
101	#529×C₈₉	C₂²	1	4	yes	complemented
102	#529×C₈₉	C₂²	1	8	yes	complemented
103	#529×C₈₉	C₂²	1	8	yes	complemented
104	#529×C₈₉	C₂²	1	8	yes	complemented
105	#529×C₈₉	C₂²	1	8	yes	complemented
106	#529×C₈₉	C₂²	1	8	yes	complemented
107	#529×C₈₉	C₂²	1	8	yes	complemented
108	C₂×#126×C₈₉	C₂²	1	4	yes	complemented
109	C₂×#125×C₈₉	C₂²	1	2	yes	complemented
110	C₂×#124×C₈₉	C₂²	1	2	yes	complemented
111	#525×C₈₉	C₂²	1	2	yes	complemented
112	#525×C₈₉	C₂²	1	4	yes	complemented
113	#525×C₈₉	C₂²	1	4	yes	complemented
114	#525×C₈₉	C₂²	1	4	yes	complemented
115	#525×C₈₉	C₂²	1	8	yes	complemented
116	#525×C₈₉	C₂²	1	8	yes	complemented
117	C₂×#123×C₈₉	C₂²	1	4	yes	complemented
118	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	2	yes	complemented
119	C₂×#121×C₈₉	C₂²	1	2	yes	—
120	C₄×#41×C₈₉	C₂²	1	2	yes	complemented
121	C₄×#41×C₈₉	C₂²	1	4	yes	complemented
122	C₄×#41×C₈₉	C₂²	1	4	yes	complemented
123	C₄×#41×C₈₉	C₂²	1	8	yes	complemented
124	C₂×C₄×Q₈×C₈₉	C₂²	1	2	yes	complemented
125	C₂×C₄×D₄×C₈₉	C₂²	1	2	yes	complemented
126	C₂×C₄×D₄×C₈₉	C₂²	1	4	yes	complemented
127	C₂×C₄×D₄×C₈₉	C₂²	1	8	yes	complemented
128	C₂×#117×C₈₉	C₂²	1	4	yes	complemented
129	C₂×#117×C₈₉	C₂²	1	4	yes	complemented
130	C₂²×C₄²×C₈₉	C₂²	1	1	yes	characteristic, complemented
131	C₂×#41×C₈₉	C₂³	1	4	yes	—
132	C₂×#41×C₈₉	C₂³	1	2	yes	—
133	C₂×#41×C₈₉	C₂³	1	4	yes	—
134	C₂×#41×C₈₉	C₂³	1	8	yes	—
135	C₂²×Q₈×C₈₉	C₂³	1	2	yes	—
136	C₂²×D₄×C₈₉	C₂³	1	4	yes	—
137	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
138	C₂²×D₄×C₈₉	C₂³	1	8	yes	—
139	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
140	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
141	C₂³×C₄×C₈₉	C₂³	1	4	yes	—
142	C₂³×C₄×C₈₉	C₂³	1	4	yes	—
143	C₄⋊Q₈×C₈₉	C₂³	1	1	yes	characteristic
144	C₄⋊Q₈×C₈₉	C₂³	1	2	yes	—
145	C₄⋊Q₈×C₈₉	C₂³	1	4	yes	—
146	C₄⋊Q₈×C₈₉	C₂³	1	8	yes	—
147	C₄⋊Q₈×C₈₉	C₂³	1	8	yes	—
148	C₄⋊Q₈×C₈₉	C₂³	1	8	yes	—
149	#127×C₈₉	C₂³	1	1	yes	characteristic
150	#127×C₈₉	C₂³	1	4	yes	—
151	#126×C₈₉	C₂³	1	8	yes	—
152	#126×C₈₉	C₂³	1	8	yes	—
153	#126×C₈₉	C₂³	1	8	yes	—
154	#126×C₈₉	C₂³	1	8	yes	—
155	#126×C₈₉	C₂³	1	8	yes	—
156	#126×C₈₉	C₂³	1	8	yes	—
157	#126×C₈₉	C₂³	1	8	yes	—
158	#126×C₈₉	C₂³	1	8	yes	—
159	#126×C₈₉	C₂³	1	8	yes	—
160	#126×C₈₉	C₂³	1	8	yes	—
161	#126×C₈₉	C₂³	1	8	yes	—
162	#126×C₈₉	C₂³	1	8	yes	—
163	#126×C₈₉	C₂³	1	8	yes	—
164	#126×C₈₉	C₂³	1	8	yes	—
165	#126×C₈₉	C₂³	1	8	yes	—
166	#126×C₈₉	C₂³	1	8	yes	—
167	#126×C₈₉	C₂³	1	8	yes	—
168	#125×C₈₉	C₂³	1	4	yes	—
169	#125×C₈₉	C₂³	1	4	yes	—
170	#125×C₈₉	C₂³	1	4	yes	—
171	#125×C₈₉	C₂³	1	4	yes	—
172	#125×C₈₉	C₂³	1	4	yes	—
173	#125×C₈₉	C₂³	1	2	yes	—
174	#125×C₈₉	C₂³	1	8	yes	—
175	#125×C₈₉	C₂³	1	8	yes	—
176	#125×C₈₉	C₂³	1	8	yes	—
177	#125×C₈₉	C₂³	1	8	yes	—
178	#125×C₈₉	C₂³	1	8	yes	—
179	#125×C₈₉	C₂³	1	8	yes	—
180	#125×C₈₉	C₂³	1	8	yes	—
181	#125×C₈₉	C₂³	1	8	yes	—
182	#125×C₈₉	C₂³	1	8	yes	—
183	#124×C₈₉	C₂³	1	4	yes	—
184	#124×C₈₉	C₂³	1	4	yes	—
185	#124×C₈₉	C₂³	1	4	yes	—
186	#124×C₈₉	C₂³	1	4	yes	—
187	#124×C₈₉	C₂³	1	4	yes	—
188	#124×C₈₉	C₂³	1	2	yes	—
189	#124×C₈₉	C₂³	1	8	yes	—
190	#124×C₈₉	C₂³	1	8	yes	—
191	#124×C₈₉	C₂³	1	8	yes	—
192	#124×C₈₉	C₂³	1	8	yes	—
193	#124×C₈₉	C₂³	1	8	yes	—
194	#124×C₈₉	C₂³	1	8	yes	—
195	#124×C₈₉	C₂³	1	4	yes	—
196	#124×C₈₉	C₂³	1	4	yes	—
197	#123×C₈₉	C₂³	1	8	yes	—
198	#123×C₈₉	C₂³	1	8	yes	—
199	#123×C₈₉	C₂³	1	8	yes	—
200	#123×C₈₉	C₂³	1	8	yes	—
201	#123×C₈₉	C₂³	1	8	yes	—
202	#123×C₈₉	C₂³	1	4	yes	—
203	#123×C₈₉	C₂³	1	8	yes	—
204	#123×C₈₉	C₂³	1	8	yes	—
205	#123×C₈₉	C₂³	1	8	yes	—
206	#123×C₈₉	C₂³	1	8	yes	—
207	#123×C₈₉	C₂³	1	8	yes	—
208	#123×C₈₉	C₂³	1	4	yes	—
209	#123×C₈₉	C₂³	1	4	yes	—
210	#123×C₈₉	C₂³	1	8	yes	—
211	#123×C₈₉	C₂³	1	8	yes	—
212	#123×C₈₉	C₂³	1	8	yes	—
213	#123×C₈₉	C₂³	1	8	yes	—
214	#123×C₈₉	C₂³	1	8	yes	—
215	#123×C₈₉	C₂³	1	8	yes	—
216	#123×C₈₉	C₂³	1	8	yes	—
217	#123×C₈₉	C₂³	1	8	yes	—
218	#123×C₈₉	C₂³	1	8	yes	—
219	#123×C₈₉	C₂³	1	8	yes	—
220	#123×C₈₉	C₂³	1	8	yes	—
221	#123×C₈₉	C₂³	1	8	yes	—
222	C₂²⋊Q₈×C₈₉	C₂³	1	4	yes	—
223	C₂²⋊Q₈×C₈₉	C₂³	1	4	yes	—
224	C₂²⋊Q₈×C₈₉	C₂³	1	4	yes	—
225	C₂²⋊Q₈×C₈₉	C₂³	1	4	yes	—
226	C₂²⋊Q₈×C₈₉	C₂³	1	4	yes	—
227	C₂²⋊Q₈×C₈₉	C₂³	1	4	yes	—
228	C₂²⋊Q₈×C₈₉	C₂³	1	4	yes	—
229	C₂²⋊Q₈×C₈₉	C₂³	1	8	yes	—
230	C₂²⋊Q₈×C₈₉	C₂³	1	8	yes	—
231	C₂²⋊Q₈×C₈₉	C₂³	1	8	yes	—
232	C₂²⋊Q₈×C₈₉	C₂³	1	8	yes	—
233	C₂²⋊Q₈×C₈₉	C₂³	1	8	yes	—
234	C₂²⋊Q₈×C₈₉	C₂³	1	8	yes	—
235	C₂²⋊Q₈×C₈₉	C₂³	1	8	yes	—
236	C₂²⋊Q₈×C₈₉	C₂³	1	8	yes	—
237	C₂²⋊Q₈×C₈₉	C₂³	1	8	yes	—
238	C₂²⋊Q₈×C₈₉	C₂³	1	8	yes	—
239	C₂²⋊Q₈×C₈₉	C₂³	1	8	yes	—
240	C₂²⋊Q₈×C₈₉	C₂³	1	8	yes	—
241	C₂²⋊Q₈×C₈₉	C₂³	1	8	yes	—
242	C₂²⋊Q₈×C₈₉	C₂³	1	8	yes	—
243	C₂²⋊Q₈×C₈₉	C₂³	1	8	yes	—
244	C₂²⋊Q₈×C₈₉	C₂³	1	8	yes	—
245	C₂²⋊Q₈×C₈₉	C₂³	1	8	yes	—
246	C₂²⋊Q₈×C₈₉	C₂³	1	8	yes	—
247	#121×C₈₉	C₂³	1	4	yes	—
248	#121×C₈₉	C₂³	1	4	yes	—
249	#121×C₈₉	C₂³	1	4	yes	—
250	#121×C₈₉	C₂³	1	4	yes	—
251	#121×C₈₉	C₂³	1	4	yes	—
252	#121×C₈₉	C₂³	1	4	yes	—
253	#121×C₈₉	C₂³	1	4	yes	—
254	#121×C₈₉	C₂³	1	8	yes	—
255	#121×C₈₉	C₂³	1	8	yes	—
256	#121×C₈₉	C₂³	1	8	yes	—
257	#121×C₈₉	C₂³	1	8	yes	—
258	#121×C₈₉	C₂³	1	8	yes	—
259	#121×C₈₉	C₂³	1	8	yes	—
260	#121×C₈₉	C₂³	1	8	yes	—
261	#121×C₈₉	C₂³	1	8	yes	—
262	#121×C₈₉	C₂³	1	8	yes	—
263	#121×C₈₉	C₂³	1	8	yes	—
264	#121×C₈₉	C₂³	1	8	yes	—
265	#121×C₈₉	C₂³	1	8	yes	—
266	#121×C₈₉	C₂³	1	8	yes	—
267	#121×C₈₉	C₂³	1	8	yes	—
268	#120×C₈₉	C₂³	1	4	yes	—
269	#120×C₈₉	C₂³	1	8	yes	—
270	#120×C₈₉	C₂³	1	8	yes	—
271	#120×C₈₉	C₂³	1	8	yes	—
272	#120×C₈₉	C₂³	1	8	yes	—
273	#120×C₈₉	C₂³	1	8	yes	—
274	#120×C₈₉	C₂³	1	4	yes	—
275	#120×C₈₉	C₂³	1	4	yes	—
276	C₄×Q₈×C₈₉	C₂³	1	4	yes	—
277	C₄×Q₈×C₈₉	C₂³	1	4	yes	—
278	C₄×Q₈×C₈₉	C₂³	1	4	yes	—
279	C₄×Q₈×C₈₉	C₂³	1	4	yes	—
280	C₄×Q₈×C₈₉	C₂³	1	8	yes	—
281	C₄×Q₈×C₈₉	C₂³	1	4	yes	—
282	C₄×Q₈×C₈₉	C₂³	1	4	yes	—
283	C₄×Q₈×C₈₉	C₂³	1	4	yes	—
284	C₄×Q₈×C₈₉	C₂³	1	8	yes	—
285	C₄×Q₈×C₈₉	C₂³	1	8	yes	—
286	C₄×D₄×C₈₉	C₂³	1	8	yes	—
287	C₄×D₄×C₈₉	C₂³	1	8	yes	—
288	C₄×D₄×C₈₉	C₂³	1	4	yes	—
289	C₄×D₄×C₈₉	C₂³	1	4	yes	—
290	C₄×D₄×C₈₉	C₂³	1	8	yes	—
291	C₄×D₄×C₈₉	C₂³	1	8	yes	—
292	C₄×D₄×C₈₉	C₂³	1	8	yes	—
293	C₄×D₄×C₈₉	C₂³	1	4	yes	—
294	C₄×D₄×C₈₉	C₂³	1	4	yes	—
295	C₄×D₄×C₈₉	C₂³	1	8	yes	—
296	C₄×D₄×C₈₉	C₂³	1	8	yes	—
297	C₄×D₄×C₈₉	C₂³	1	8	yes	—
298	C₄×D₄×C₈₉	C₂³	1	8	yes	—
299	C₄×D₄×C₈₉	C₂³	1	8	yes	—
300	C₄×D₄×C₈₉	C₂³	1	8	yes	—
301	C₄×D₄×C₈₉	C₂³	1	8	yes	—
302	C₄×D₄×C₈₉	C₂³	1	4	yes	—
303	C₄×D₄×C₈₉	C₂³	1	8	yes	—
304	C₄×D₄×C₈₉	C₂³	1	8	yes	—
305	C₄×D₄×C₈₉	C₂³	1	4	yes	—
306	C₄×D₄×C₈₉	C₂³	1	4	yes	—
307	C₄×D₄×C₈₉	C₂³	1	8	yes	—
308	C₄×D₄×C₈₉	C₂³	1	8	yes	—
309	C₄×D₄×C₈₉	C₂³	1	8	yes	—
310	C₄×D₄×C₈₉	C₂³	1	8	yes	—
311	C₄×D₄×C₈₉	C₂³	1	8	yes	—
312	C₄×D₄×C₈₉	C₂³	1	8	yes	—
313	#117×C₈₉	C₂³	1	8	yes	—
314	#117×C₈₉	C₂³	1	8	yes	—
315	#117×C₈₉	C₂³	1	8	yes	—
316	#117×C₈₉	C₂³	1	8	yes	—
317	#117×C₈₉	C₂³	1	8	yes	—
318	#117×C₈₉	C₂³	1	8	yes	—
319	#117×C₈₉	C₂³	1	8	yes	—
320	#117×C₈₉	C₂³	1	4	yes	—
321	#117×C₈₉	C₂³	1	2	yes	—
322	#117×C₈₉	C₂³	1	4	yes	—
323	#117×C₈₉	C₂³	1	4	yes	—
324	#117×C₈₉	C₂³	1	8	yes	—
325	#117×C₈₉	C₂³	1	8	yes	—
326	#117×C₈₉	C₂³	1	8	yes	—
327	#117×C₈₉	C₂³	1	8	yes	—
328	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
329	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
330	C₂×C₄⋊C₄×C₈₉	C₂³	1	8	yes	—
331	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
332	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
333	C₂×C₄⋊C₄×C₈₉	C₂³	1	8	yes	—
334	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
335	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
336	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
337	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
338	C₂×C₂²⋊C₄×C₈₉	C₂³	1	8	yes	—
339	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
340	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
341	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
342	C₂×C₂²⋊C₄×C₈₉	C₂³	1	8	yes	—
343	C₂×C₂²⋊C₄×C₈₉	C₂³	1	8	yes	—
344	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
345	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
346	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
347	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
348	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
349	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
350	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
351	C₂×C₄²×C₈₉	C₂³	1	4	yes	—
352	C₂×C₄²×C₈₉	C₂³	1	4	yes	—
353	C₂×C₄²×C₈₉	C₂³	1	4	yes	—
354	C₂×C₄²×C₈₉	C₂³	1	8	yes	—
355	C₂⁴×C₈₉	C₂⁴	1	1	yes	characteristic
356	C₂⁴×C₈₉	C₂⁴	1	4	yes	—
357	C₂⁴×C₈₉	C₂⁴	1	4	yes	—
358	#41×C₈₉	—	4	8	no	—
359	#41×C₈₉	—	4	4	no	—
360	#41×C₈₉	—	4	8	no	—
361	#41×C₈₉	—	4	16	no	—
362	C₂×Q₈×C₈₉	—	4	4	no	—
363	C₂×Q₈×C₈₉	C₂⁴	1	4	yes	—
364	C₂×Q₈×C₈₉	C₂⁴	1	4	yes	—
365	C₂×Q₈×C₈₉	C₂⁴	1	4	yes	—
366	C₂×Q₈×C₈₉	C₂⁴	1	8	yes	—
367	C₂×Q₈×C₈₉	C₂⁴	1	4	yes	—
368	C₂×Q₈×C₈₉	C₂⁴	1	2	yes	—
369	C₂×D₄×C₈₉	—	4	4	no	—
370	C₂×D₄×C₈₉	—	4	8	no	—
371	C₂×D₄×C₈₉	—	4	16	no	—
372	C₂×D₄×C₈₉	C₂⁴	1	8	yes	—
373	C₂×D₄×C₈₉	C₂⁴	1	8	yes	—
374	C₂×D₄×C₈₉	C₂⁴	1	4	yes	—
375	C₂×D₄×C₈₉	C₂⁴	1	8	yes	—
376	C₂×D₄×C₈₉	C₂⁴	1	8	yes	—
377	C₂×D₄×C₈₉	C₂⁴	1	4	yes	—
378	C₂×D₄×C₈₉	C₂⁴	1	4	yes	—
379	C₂×D₄×C₈₉	C₂⁴	1	8	yes	—
380	C₂×D₄×C₈₉	C₂⁴	1	4	yes	—
381	C₂×D₄×C₈₉	C₂⁴	1	4	yes	—
382	C₂×D₄×C₈₉	C₂⁴	1	2	yes	—
383	C₂×D₄×C₈₉	C₂⁴	1	8	yes	—
384	C₂×D₄×C₈₉	C₂⁴	1	8	yes	—
385	C₂²×C₄×C₈₉	—	4	2	no	—
386	C₂²×C₄×C₈₉	—	4	8	no	—
387	C₂²×C₄×C₈₉	—	4	8	no	—
388	C₂²×C₄×C₈₉	—	4	4	no	—
389	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
390	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
391	C₂²×C₄×C₈₉	C₂⁴	1	4	yes	—
392	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
393	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
394	C₂²×C₄×C₈₉	C₂⁴	1	4	yes	—
395	C₂²×C₄×C₈₉	C₂⁴	1	8	yes	—
396	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
397	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
398	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
399	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
400	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
401	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
402	C₂²×C₄×C₈₉	C₂⁴	1	8	yes	—
403	C₂²×C₄×C₈₉	C₂⁴	1	4	yes	—
404	C₂²×C₄×C₈₉	C₂⁴	1	8	yes	—
405	C₂²×C₄×C₈₉	C₂⁴	1	8	yes	—
406	C₂²×C₄×C₈₉	C₂⁴	1	8	yes	—
407	C₂²×C₄×C₈₉	C₂⁴	1	4	yes	—
408	C₂²×C₄×C₈₉	C₂⁴	1	8	yes	—
409	C₂²×C₄×C₈₉	C₂⁴	1	8	yes	—
410	C₂²×C₄×C₈₉	C₂⁴	1	4	yes	—
411	C₄⋊C₄×C₈₉	C₂⁴	1	8	yes	—
412	C₄⋊C₄×C₈₉	C₂⁴	1	8	yes	—
413	C₄⋊C₄×C₈₉	C₂⁴	1	8	yes	—
414	C₄⋊C₄×C₈₉	C₂⁴	1	8	yes	—
415	C₄⋊C₄×C₈₉	C₂⁴	1	8	yes	—
416	C₄⋊C₄×C₈₉	C₂⁴	1	8	yes	—
417	C₄⋊C₄×C₈₉	C₂⁴	1	8	yes	—
418	C₄⋊C₄×C₈₉	C₂⁴	1	8	yes	—
419	C₄⋊C₄×C₈₉	C₂⁴	1	8	yes	—
420	C₄⋊C₄×C₈₉	C₂⁴	1	8	yes	—
421	C₄⋊C₄×C₈₉	C₂⁴	1	4	yes	—
422	C₄⋊C₄×C₈₉	C₂⁴	1	4	yes	—
423	C₄⋊C₄×C₈₉	C₂⁴	1	8	yes	—
424	C₄⋊C₄×C₈₉	C₂⁴	1	4	yes	—
425	C₄⋊C₄×C₈₉	C₂⁴	1	4	yes	—
426	C₄⋊C₄×C₈₉	C₂⁴	1	8	yes	—
427	C₄⋊C₄×C₈₉	C₂⁴	1	8	yes	—
428	C₄⋊C₄×C₈₉	C₂⁴	1	8	yes	—
429	C₄⋊C₄×C₈₉	C₂⁴	1	8	yes	—
430	C₄⋊C₄×C₈₉	C₂⁴	1	8	yes	—
431	C₄⋊C₄×C₈₉	C₂⁴	1	8	yes	—
432	C₄⋊C₄×C₈₉	C₂⁴	1	4	yes	—
433	C₄⋊C₄×C₈₉	C₂⁴	1	4	yes	—
434	C₄⋊C₄×C₈₉	C₂⁴	1	4	yes	—
435	C₄⋊C₄×C₈₉	C₂⁴	1	8	yes	—
436	C₄⋊C₄×C₈₉	C₂⁴	1	8	yes	—
437	C₄⋊C₄×C₈₉	C₂⁴	1	8	yes	—
438	C₂²⋊C₄×C₈₉	C₂⁴	1	8	yes	—
439	C₂²⋊C₄×C₈₉	C₂⁴	1	8	yes	—
440	C₂²⋊C₄×C₈₉	C₂⁴	1	8	yes	—
441	C₂²⋊C₄×C₈₉	C₂⁴	1	8	yes	—
442	C₂²⋊C₄×C₈₉	C₂⁴	1	8	yes	—
443	C₂²⋊C₄×C₈₉	C₂⁴	1	8	yes	—
444	C₂²⋊C₄×C₈₉	C₂⁴	1	8	yes	—
445	C₂²⋊C₄×C₈₉	C₂⁴	1	8	yes	—
446	C₂²⋊C₄×C₈₉	C₂⁴	1	8	yes	—
447	C₂²⋊C₄×C₈₉	C₂⁴	1	8	yes	—
448	C₂²⋊C₄×C₈₉	C₂⁴	1	8	yes	—
449	C₂²⋊C₄×C₈₉	C₂⁴	1	8	yes	—
450	C₂²⋊C₄×C₈₉	C₂⁴	1	8	yes	—
451	C₂²⋊C₄×C₈₉	C₂⁴	1	8	yes	—
452	C₂²⋊C₄×C₈₉	C₂⁴	1	8	yes	—
453	C₂²⋊C₄×C₈₉	C₂⁴	1	8	yes	—
454	C₂²⋊C₄×C₈₉	C₂⁴	1	8	yes	—
455	C₂²⋊C₄×C₈₉	C₂⁴	1	8	yes	—
456	C₂²⋊C₄×C₈₉	C₂⁴	1	8	yes	—
457	C₂²⋊C₄×C₈₉	C₂⁴	1	4	yes	—
458	C₂²⋊C₄×C₈₉	C₂⁴	1	8	yes	—
459	C₂²⋊C₄×C₈₉	C₂⁴	1	4	yes	—
460	C₂²⋊C₄×C₈₉	C₂⁴	1	8	yes	—
461	C₂²⋊C₄×C₈₉	C₂⁴	1	8	yes	—
462	C₂²⋊C₄×C₈₉	C₂⁴	1	4	yes	—
463	C₄²×C₈₉	C₂⁴	1	2	yes	—
464	C₄²×C₈₉	C₂⁴	1	2	yes	—
465	C₄²×C₈₉	C₂⁴	1	2	yes	—
466	C₄²×C₈₉	C₂⁴	1	2	yes	—
467	C₄²×C₈₉	C₂⁴	1	2	yes	—
468	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
469	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
470	C₄²×C₈₉	C₂⁴	1	4	yes	—
471	C₄²×C₈₉	C₂⁴	1	8	yes	—
472	C₄²×C₈₉	C₂⁴	1	8	yes	—
473	C₄²×C₈₉	C₂⁴	1	8	yes	—
474	C₄²×C₈₉	C₂⁴	1	4	yes	—
475	C₄²×C₈₉	C₂⁴	1	8	yes	—
476	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
477	C₄²×C₈₉	C₂⁴	1	8	yes	—
478	C₄²×C₈₉	C₂⁴	1	2	yes	—
479	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
480	C₄²×C₈₉	C₂⁴	1	4	yes	—
481	C₂³×C₈₉	—	2	4	no	—
482	C₂³×C₈₉	—	2	8	no	—
483	C₂³×C₈₉	—	4	1	no	—
484	C₂³×C₈₉	—	4	4	no	—
485	C₂³×C₈₉	—	4	4	no	—
486	C₂³×C₈₉	—	4	4	no	—
487	C₂³×C₈₉	—	4	8	no	—
488	C₂³×C₈₉	C₂⁵	1	8	yes	—
489	C₂³×C₈₉	C₂⁵	1	4	yes	—
490	C₂³×C₈₉	C₂⁵	1	1	yes	characteristic
491	C₂³×C₈₉	C₂⁵	1	2	yes	—
492	Q₈×C₈₉	—	4	4	no	—
493	Q₈×C₈₉	—	4	4	no	—
494	Q₈×C₈₉	—	4	4	no	—
495	Q₈×C₈₉	—	4	2	no	—
496	Q₈×C₈₉	—	4	4	no	—
497	Q₈×C₈₉	—	4	8	no	—
498	D₄×C₈₉	—	2	16	no	—
499	D₄×C₈₉	—	2	16	no	—
500	D₄×C₈₉	—	4	4	no	—
501	D₄×C₈₉	—	4	4	no	—
502	D₄×C₈₉	—	4	8	no	—
503	D₄×C₈₉	—	4	8	no	—
504	D₄×C₈₉	—	4	8	no	—
505	D₄×C₈₉	—	4	8	no	—
506	D₄×C₈₉	—	4	4	no	—
507	D₄×C₈₉	—	4	4	no	—
508	D₄×C₈₉	—	4	2	no	—
509	D₄×C₈₉	—	4	4	no	—
510	D₄×C₈₉	—	4	8	no	—
511	C₂×C₄×C₈₉	—	2	4	no	—
512	C₂×C₄×C₈₉	—	2	4	no	—
513	C₂×C₄×C₈₉	—	2	8	no	—
514	C₂×C₄×C₈₉	—	2	4	no	—
515	C₂×C₄×C₈₉	—	2	16	no	—
516	C₂×C₄×C₈₉	—	2	2	no	—
517	C₂×C₄×C₈₉	—	2	8	no	—
518	C₂×C₄×C₈₉	—	4	1	no	—
519	C₂×C₄×C₈₉	—	4	8	no	—
520	C₂×C₄×C₈₉	—	4	2	no	—
521	C₂×C₄×C₈₉	—	4	2	no	—
522	C₂×C₄×C₈₉	—	4	2	no	—
523	C₂×C₄×C₈₉	—	4	4	no	—
524	C₂×C₄×C₈₉	—	4	4	no	—
525	C₂×C₄×C₈₉	—	4	8	no	—
526	C₂×C₄×C₈₉	—	4	2	no	—
527	C₂×C₄×C₈₉	—	4	2	no	—
528	C₂×C₄×C₈₉	—	4	4	no	—
529	C₂×C₄×C₈₉	—	4	8	no	—
530	C₂×C₄×C₈₉	—	4	8	no	—
531	C₂×C₄×C₈₉	—	4	8	no	—
532	C₂×C₄×C₈₉	—	4	8	no	—
533	C₂×C₄×C₈₉	C₂⁵	1	2	yes	—
534	C₂×C₄×C₈₉	C₂⁵	1	2	yes	—
535	C₂×C₄×C₈₉	C₂⁵	1	8	yes	—
536	C₂×C₄×C₈₉	C₂⁵	1	2	yes	—
537	C₂×C₄×C₈₉	C₂⁵	1	2	yes	—
538	C₂×C₄×C₈₉	C₂⁵	1	2	yes	—
539	C₂×C₄×C₈₉	C₂⁵	1	1	yes	characteristic
540	C₂×C₄×C₈₉	C₂⁵	1	4	yes	—
541	C₂×C₄×C₈₉	C₂⁵	1	8	yes	—
542	C₂×C₄×C₈₉	C₂⁵	1	8	yes	—
543	C₂×C₄×C₈₉	C₂⁵	1	8	yes	—
544	C₂×C₄×C₈₉	C₂⁵	1	1	yes	characteristic
545	C₂²×C₈₉	—	2	2	no	—
546	C₂²×C₈₉	—	2	2	no	—
547	C₂²×C₈₉	—	2	8	no	—
548	C₂²×C₈₉	—	2	1	no	—
549	C₂²×C₈₉	—	2	4	no	—
550	C₂²×C₈₉	—	2	8	no	—
551	C₂²×C₈₉	—	2	2	no	—
552	C₂²×C₈₉	—	2	8	no	—
553	C₂²×C₈₉	—	2	8	no	—
554	C₂²×C₈₉	—	4	4	no	—
555	C₂²×C₈₉	—	8	8	no	—
556	C₂²×C₈₉	—	8	8	no	—
557	C₂²×C₈₉	#585	1	4	yes	—
558	C₂²×C₈₉	C₂⁶	1	1	yes	characteristic
559	C₄×C₈₉	—	2	2	no	—
560	C₄×C₈₉	—	2	2	no	—
561	C₄×C₈₉	—	2	8	no	—
562	C₄×C₈₉	—	2	2	no	—
563	C₄×C₈₉	—	2	2	no	—
564	C₄×C₈₉	—	2	2	no	—
565	C₄×C₈₉	—	2	1	no	—
566	C₄×C₈₉	—	2	4	no	—
567	C₄×C₈₉	—	2	8	no	—
568	C₄×C₈₉	—	2	8	no	—
569	C₄×C₈₉	—	2	8	no	—
570	C₄×C₈₉	#585	1	2	yes	—
571	#62755	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
572	C₂×C₈₉	—	2	4	no	—
573	C₂×C₈₉	—	4	1	no	—
574	C₂×C₈₉	—	4	4	no	—
575	C₂×C₈₉	—	4	8	no	—
576	C₂×C₈₉	C₂×#585	1	2	yes	—
577	C₂×C₈₉	C₂×#585	1	1	yes	characteristic
578	#3566	C₂×C₈₉	1	8	yes	complemented
579	#3564	C₂×C₈₉	1	4	yes	complemented
580	#3560	C₂×C₈₉	1	4	yes	complemented
581	#3553	C₂×C₈₉	1	4	yes	complemented
582	#3545	C₂×C₈₉	1	4	yes	complemented
583	#3535	C₂×C₈₉	1	4	yes	complemented
584	#3534	C₂×C₈₉	1	4	yes	complemented
585	#3531	C₂×C₈₉	1	2	yes	complemented
586	#3529	C₂×C₈₉	1	2	yes	complemented
587	#3481	C₂×C₈₉	1	4	yes	complemented
588	#3475	C₂×C₈₉	1	8	yes	complemented
589	#3461	C₂×C₈₉	1	4	yes	complemented
590	#3459	C₂×C₈₉	1	4	yes	complemented
591	#3455	C₂×C₈₉	1	4	yes	complemented
592	#3444	C₂×C₈₉	1	1	yes	characteristic, complemented
593	C₂×#529	C₂×C₈₉	1	2	yes	complemented
594	C₈₉	#62755	1	1	yes	characteristic, direct product factor, Sylow
595	#564	C₂²×C₈₉	1	2	yes	complemented
596	#563	C₂²×C₈₉	1	2	yes	complemented
597	#563	C₂²×C₈₉	1	4	yes	complemented
598	#563	C₂²×C₈₉	1	8	yes	complemented
599	#563	C₂²×C₈₉	1	4	yes	complemented
600	#563	C₂²×C₈₉	1	8	yes	complemented
601	#562	C₂²×C₈₉	1	8	yes	complemented
602	#562	C₂²×C₈₉	1	4	yes	complemented
603	#562	C₂²×C₈₉	1	8	yes	complemented
604	#562	C₂²×C₈₉	1	2	yes	complemented
605	H(3,𝔽₄)	C₂²×C₈₉	1	2	yes	complemented
606	#560	C₂²×C₈₉	1	8	yes	complemented
607	#560	C₂²×C₈₉	1	4	yes	complemented
608	#559	C₂²×C₈₉	1	4	yes	complemented
609	#556	C₂²×C₈₉	1	8	yes	complemented
610	#555	C₂²×C₈₉	1	8	yes	complemented
611	#554	C₂²×C₈₉	1	8	yes	complemented
612	#554	C₂²×C₈₉	1	8	yes	complemented
613	#553	C₂²×C₈₉	1	8	yes	complemented
614	#553	C₂²×C₈₉	1	8	yes	complemented
615	#553	C₂²×C₈₉	1	8	yes	complemented
616	#553	C₂²×C₈₉	1	8	yes	complemented
617	#552	C₂²×C₈₉	1	8	yes	complemented
618	#552	C₂²×C₈₉	1	8	yes	complemented
619	#552	C₂²×C₈₉	1	8	yes	complemented
620	#552	C₂²×C₈₉	1	8	yes	complemented
621	#551	C₂²×C₈₉	1	8	yes	complemented
622	#551	C₂²×C₈₉	1	8	yes	complemented
623	#551	C₂²×C₈₉	1	8	yes	complemented
624	#551	C₂²×C₈₉	1	8	yes	complemented
625	#551	C₂²×C₈₉	1	4	yes	complemented
626	#551	C₂²×C₈₉	1	8	yes	complemented
627	#551	C₂²×C₈₉	1	4	yes	complemented
628	#547	C₂²×C₈₉	1	8	yes	complemented
629	#546	C₂²×C₈₉	1	8	yes	complemented
630	#546	C₂²×C₈₉	1	8	yes	complemented
631	#546	C₂²×C₈₉	1	8	yes	complemented
632	#546	C₂²×C₈₉	1	8	yes	complemented
633	D₄²	C₂²×C₈₉	1	4	yes	complemented
634	#544	C₂²×C₈₉	1	4	yes	complemented
635	#543	C₂²×C₈₉	1	4	yes	complemented
636	#542	C₂²×C₈₉	1	8	yes	complemented
637	#542	C₂²×C₈₉	1	8	yes	complemented
638	#542	C₂²×C₈₉	1	8	yes	complemented
639	#542	C₂²×C₈₉	1	8	yes	complemented
640	#541	C₂²×C₈₉	1	8	yes	complemented
641	#541	C₂²×C₈₉	1	8	yes	complemented
642	#541	C₂²×C₈₉	1	8	yes	complemented
643	#540	C₂²×C₈₉	1	8	yes	complemented
644	#539	C₂²×C₈₉	1	8	yes	complemented
645	#539	C₂²×C₈₉	1	8	yes	complemented
646	#539	C₂²×C₈₉	1	8	yes	complemented
647	#539	C₂²×C₈₉	1	8	yes	complemented
648	#539	C₂²×C₈₉	1	8	yes	complemented
649	#539	C₂²×C₈₉	1	8	yes	complemented
650	#539	C₂²×C₈₉	1	4	yes	complemented
651	#539	C₂²×C₈₉	1	4	yes	complemented
652	#538	C₂²×C₈₉	1	4	yes	—
653	#538	C₂²×C₈₉	1	8	yes	complemented
654	#538	C₂²×C₈₉	1	8	yes	complemented
655	#538	C₂²×C₈₉	1	4	yes	complemented
656	#538	C₂²×C₈₉	1	8	yes	complemented
657	#538	C₂²×C₈₉	1	8	yes	complemented
658	#537	C₂²×C₈₉	1	4	yes	—
659	#536	C₂²×C₈₉	1	8	yes	complemented
660	#534	C₂²×C₈₉	1	8	yes	complemented
661	#534	C₂²×C₈₉	1	4	yes	complemented
662	#533	C₂²×C₈₉	1	1	yes	characteristic, complemented
663	#533	C₂²×C₈₉	1	2	yes	complemented
664	#533	C₂²×C₈₉	1	4	yes	complemented
665	#533	C₂²×C₈₉	1	8	yes	complemented
666	#532	C₂²×C₈₉	1	1	yes	characteristic, complemented
667	#532	C₂²×C₈₉	1	2	yes	complemented
668	#532	C₂²×C₈₉	1	4	yes	complemented
669	#529	C₂²×C₈₉	1	4	yes	complemented
670	#529	C₂²×C₈₉	1	4	yes	complemented
671	#529	C₂²×C₈₉	1	4	yes	complemented
672	#529	C₂²×C₈₉	1	4	yes	complemented
673	#529	C₂²×C₈₉	1	4	yes	complemented
674	#529	C₂²×C₈₉	1	4	yes	complemented
675	#529	C₂²×C₈₉	1	4	yes	complemented
676	#529	C₂²×C₈₉	1	4	yes	complemented
677	#529	C₂²×C₈₉	1	4	yes	complemented
678	#529	C₂²×C₈₉	1	4	yes	complemented
679	#529	C₂²×C₈₉	1	4	yes	complemented
680	#529	C₂²×C₈₉	1	8	yes	complemented
681	#529	C₂²×C₈₉	1	8	yes	complemented
682	#529	C₂²×C₈₉	1	8	yes	complemented
683	#529	C₂²×C₈₉	1	8	yes	complemented
684	#529	C₂²×C₈₉	1	8	yes	complemented
685	#529	C₂²×C₈₉	1	8	yes	complemented
686	C₂×#126	C₂²×C₈₉	1	4	yes	complemented
687	C₂×#125	C₂²×C₈₉	1	2	yes	complemented
688	C₂×#124	C₂²×C₈₉	1	2	yes	complemented
689	#525	C₂²×C₈₉	1	2	yes	complemented
690	#525	C₂²×C₈₉	1	4	yes	complemented
691	#525	C₂²×C₈₉	1	4	yes	complemented
692	#525	C₂²×C₈₉	1	4	yes	complemented
693	#525	C₂²×C₈₉	1	8	yes	complemented
694	#525	C₂²×C₈₉	1	8	yes	complemented
695	C₂×#123	C₂²×C₈₉	1	4	yes	complemented
696	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	2	yes	complemented
697	C₂×#121	C₂²×C₈₉	1	2	yes	—
698	C₄×#41	C₂²×C₈₉	1	2	yes	complemented
699	C₄×#41	C₂²×C₈₉	1	4	yes	complemented
700	C₄×#41	C₂²×C₈₉	1	4	yes	complemented
701	C₄×#41	C₂²×C₈₉	1	8	yes	complemented
702	C₂×C₄×Q₈	C₂²×C₈₉	1	2	yes	complemented
703	C₂×C₄×D₄	C₂²×C₈₉	1	2	yes	complemented
704	C₂×C₄×D₄	C₂²×C₈₉	1	4	yes	complemented
705	C₂×C₄×D₄	C₂²×C₈₉	1	8	yes	complemented
706	C₂×#117	C₂²×C₈₉	1	4	yes	complemented
707	C₂×#117	C₂²×C₈₉	1	4	yes	complemented
708	C₂²×C₄²	C₂²×C₈₉	1	1	yes	characteristic, complemented
709	C₂×#41	C₂³×C₈₉	1	4	yes	—
710	C₂×#41	C₂³×C₈₉	1	2	yes	—
711	C₂×#41	C₂³×C₈₉	1	4	yes	—
712	C₂×#41	C₂³×C₈₉	1	8	yes	—
713	C₂²×Q₈	C₂³×C₈₉	1	2	yes	—
714	C₂²×D₄	C₂³×C₈₉	1	4	yes	—
715	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
716	C₂²×D₄	C₂³×C₈₉	1	8	yes	—
717	C₂³×C₄	C₂³×C₈₉	1	4	yes	—
718	C₂³×C₄	C₂³×C₈₉	1	4	yes	—
719	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
720	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
721	C₄⋊Q₈	C₂³×C₈₉	1	1	yes	characteristic
722	C₄⋊Q₈	C₂³×C₈₉	1	2	yes	—
723	C₄⋊Q₈	C₂³×C₈₉	1	4	yes	—
724	C₄⋊Q₈	C₂³×C₈₉	1	8	yes	—
725	C₄⋊Q₈	C₂³×C₈₉	1	8	yes	—
726	C₄⋊Q₈	C₂³×C₈₉	1	8	yes	—
727	#127	C₂³×C₈₉	1	1	yes	characteristic
728	#127	C₂³×C₈₉	1	4	yes	—
729	#126	C₂³×C₈₉	1	8	yes	—
730	#126	C₂³×C₈₉	1	8	yes	—
731	#126	C₂³×C₈₉	1	8	yes	—
732	#126	C₂³×C₈₉	1	8	yes	—
733	#126	C₂³×C₈₉	1	8	yes	—
734	#126	C₂³×C₈₉	1	8	yes	—
735	#126	C₂³×C₈₉	1	8	yes	—
736	#126	C₂³×C₈₉	1	8	yes	—
737	#126	C₂³×C₈₉	1	8	yes	—
738	#126	C₂³×C₈₉	1	8	yes	—
739	#126	C₂³×C₈₉	1	8	yes	—
740	#126	C₂³×C₈₉	1	8	yes	—
741	#126	C₂³×C₈₉	1	8	yes	—
742	#126	C₂³×C₈₉	1	8	yes	—
743	#126	C₂³×C₈₉	1	8	yes	—
744	#126	C₂³×C₈₉	1	8	yes	—
745	#126	C₂³×C₈₉	1	8	yes	—
746	#125	C₂³×C₈₉	1	4	yes	—
747	#125	C₂³×C₈₉	1	4	yes	—
748	#125	C₂³×C₈₉	1	4	yes	—
749	#125	C₂³×C₈₉	1	4	yes	—
750	#125	C₂³×C₈₉	1	4	yes	—
751	#125	C₂³×C₈₉	1	2	yes	—
752	#125	C₂³×C₈₉	1	8	yes	—
753	#125	C₂³×C₈₉	1	8	yes	—
754	#125	C₂³×C₈₉	1	8	yes	—
755	#125	C₂³×C₈₉	1	8	yes	—
756	#125	C₂³×C₈₉	1	8	yes	—
757	#125	C₂³×C₈₉	1	8	yes	—
758	#125	C₂³×C₈₉	1	8	yes	—
759	#125	C₂³×C₈₉	1	8	yes	—
760	#125	C₂³×C₈₉	1	8	yes	—
761	#124	C₂³×C₈₉	1	4	yes	—
762	#124	C₂³×C₈₉	1	4	yes	—
763	#124	C₂³×C₈₉	1	4	yes	—
764	#124	C₂³×C₈₉	1	4	yes	—
765	#124	C₂³×C₈₉	1	4	yes	—
766	#124	C₂³×C₈₉	1	2	yes	—
767	#124	C₂³×C₈₉	1	8	yes	—
768	#124	C₂³×C₈₉	1	8	yes	—
769	#124	C₂³×C₈₉	1	8	yes	—
770	#124	C₂³×C₈₉	1	8	yes	—
771	#124	C₂³×C₈₉	1	8	yes	—
772	#124	C₂³×C₈₉	1	8	yes	—
773	#124	C₂³×C₈₉	1	4	yes	—
774	#124	C₂³×C₈₉	1	4	yes	—
775	#123	C₂³×C₈₉	1	8	yes	—
776	#123	C₂³×C₈₉	1	8	yes	—
777	#123	C₂³×C₈₉	1	8	yes	—
778	#123	C₂³×C₈₉	1	8	yes	—
779	#123	C₂³×C₈₉	1	8	yes	—
780	#123	C₂³×C₈₉	1	4	yes	—
781	#123	C₂³×C₈₉	1	8	yes	—
782	#123	C₂³×C₈₉	1	8	yes	—
783	#123	C₂³×C₈₉	1	8	yes	—
784	#123	C₂³×C₈₉	1	8	yes	—
785	#123	C₂³×C₈₉	1	8	yes	—
786	#123	C₂³×C₈₉	1	4	yes	—
787	#123	C₂³×C₈₉	1	4	yes	—
788	#123	C₂³×C₈₉	1	8	yes	—
789	#123	C₂³×C₈₉	1	8	yes	—
790	#123	C₂³×C₈₉	1	8	yes	—
791	#123	C₂³×C₈₉	1	8	yes	—
792	#123	C₂³×C₈₉	1	8	yes	—
793	#123	C₂³×C₈₉	1	8	yes	—
794	#123	C₂³×C₈₉	1	8	yes	—
795	#123	C₂³×C₈₉	1	8	yes	—
796	#123	C₂³×C₈₉	1	8	yes	—
797	#123	C₂³×C₈₉	1	8	yes	—
798	#123	C₂³×C₈₉	1	8	yes	—
799	#123	C₂³×C₈₉	1	8	yes	—
800	C₂²⋊Q₈	C₂³×C₈₉	1	4	yes	—
801	C₂²⋊Q₈	C₂³×C₈₉	1	4	yes	—
802	C₂²⋊Q₈	C₂³×C₈₉	1	4	yes	—
803	C₂²⋊Q₈	C₂³×C₈₉	1	4	yes	—
804	C₂²⋊Q₈	C₂³×C₈₉	1	4	yes	—
805	C₂²⋊Q₈	C₂³×C₈₉	1	4	yes	—
806	C₂²⋊Q₈	C₂³×C₈₉	1	4	yes	—
807	C₂²⋊Q₈	C₂³×C₈₉	1	8	yes	—
808	C₂²⋊Q₈	C₂³×C₈₉	1	8	yes	—
809	C₂²⋊Q₈	C₂³×C₈₉	1	8	yes	—
810	C₂²⋊Q₈	C₂³×C₈₉	1	8	yes	—
811	C₂²⋊Q₈	C₂³×C₈₉	1	8	yes	—
812	C₂²⋊Q₈	C₂³×C₈₉	1	8	yes	—
813	C₂²⋊Q₈	C₂³×C₈₉	1	8	yes	—
814	C₂²⋊Q₈	C₂³×C₈₉	1	8	yes	—
815	C₂²⋊Q₈	C₂³×C₈₉	1	8	yes	—
816	C₂²⋊Q₈	C₂³×C₈₉	1	8	yes	—
817	C₂²⋊Q₈	C₂³×C₈₉	1	8	yes	—
818	C₂²⋊Q₈	C₂³×C₈₉	1	8	yes	—
819	C₂²⋊Q₈	C₂³×C₈₉	1	8	yes	—
820	C₂²⋊Q₈	C₂³×C₈₉	1	8	yes	—
821	C₂²⋊Q₈	C₂³×C₈₉	1	8	yes	—
822	C₂²⋊Q₈	C₂³×C₈₉	1	8	yes	—
823	C₂²⋊Q₈	C₂³×C₈₉	1	8	yes	—
824	C₂²⋊Q₈	C₂³×C₈₉	1	8	yes	—
825	#121	C₂³×C₈₉	1	4	yes	—
826	#121	C₂³×C₈₉	1	4	yes	—
827	#121	C₂³×C₈₉	1	4	yes	—
828	#121	C₂³×C₈₉	1	4	yes	—
829	#121	C₂³×C₈₉	1	4	yes	—
830	#121	C₂³×C₈₉	1	4	yes	—
831	#121	C₂³×C₈₉	1	4	yes	—
832	#121	C₂³×C₈₉	1	8	yes	—
833	#121	C₂³×C₈₉	1	8	yes	—
834	#121	C₂³×C₈₉	1	8	yes	—
835	#121	C₂³×C₈₉	1	8	yes	—
836	#121	C₂³×C₈₉	1	8	yes	—
837	#121	C₂³×C₈₉	1	8	yes	—
838	#121	C₂³×C₈₉	1	8	yes	—
839	#121	C₂³×C₈₉	1	8	yes	—
840	#121	C₂³×C₈₉	1	8	yes	—
841	#121	C₂³×C₈₉	1	8	yes	—
842	#121	C₂³×C₈₉	1	8	yes	—
843	#121	C₂³×C₈₉	1	8	yes	—
844	#121	C₂³×C₈₉	1	8	yes	—
845	#121	C₂³×C₈₉	1	8	yes	—
846	#120	C₂³×C₈₉	1	4	yes	—
847	#120	C₂³×C₈₉	1	8	yes	—
848	#120	C₂³×C₈₉	1	8	yes	—
849	#120	C₂³×C₈₉	1	8	yes	—
850	#120	C₂³×C₈₉	1	8	yes	—
851	#120	C₂³×C₈₉	1	8	yes	—
852	#120	C₂³×C₈₉	1	4	yes	—
853	#120	C₂³×C₈₉	1	4	yes	—
854	C₄×Q₈	C₂³×C₈₉	1	4	yes	—
855	C₄×Q₈	C₂³×C₈₉	1	4	yes	—
856	C₄×Q₈	C₂³×C₈₉	1	4	yes	—
857	C₄×Q₈	C₂³×C₈₉	1	4	yes	—
858	C₄×Q₈	C₂³×C₈₉	1	8	yes	—
859	C₄×Q₈	C₂³×C₈₉	1	4	yes	—
860	C₄×Q₈	C₂³×C₈₉	1	4	yes	—
861	C₄×Q₈	C₂³×C₈₉	1	4	yes	—
862	C₄×Q₈	C₂³×C₈₉	1	8	yes	—
863	C₄×Q₈	C₂³×C₈₉	1	8	yes	—
864	C₄×D₄	C₂³×C₈₉	1	8	yes	—
865	C₄×D₄	C₂³×C₈₉	1	8	yes	—
866	C₄×D₄	C₂³×C₈₉	1	4	yes	—
867	C₄×D₄	C₂³×C₈₉	1	4	yes	—
868	C₄×D₄	C₂³×C₈₉	1	8	yes	—
869	C₄×D₄	C₂³×C₈₉	1	8	yes	—
870	C₄×D₄	C₂³×C₈₉	1	8	yes	—
871	C₄×D₄	C₂³×C₈₉	1	4	yes	—
872	C₄×D₄	C₂³×C₈₉	1	4	yes	—
873	C₄×D₄	C₂³×C₈₉	1	8	yes	—
874	C₄×D₄	C₂³×C₈₉	1	8	yes	—
875	C₄×D₄	C₂³×C₈₉	1	8	yes	—
876	C₄×D₄	C₂³×C₈₉	1	8	yes	—
877	C₄×D₄	C₂³×C₈₉	1	8	yes	—
878	C₄×D₄	C₂³×C₈₉	1	8	yes	—
879	C₄×D₄	C₂³×C₈₉	1	8	yes	—
880	C₄×D₄	C₂³×C₈₉	1	4	yes	—
881	C₄×D₄	C₂³×C₈₉	1	8	yes	—
882	C₄×D₄	C₂³×C₈₉	1	8	yes	—
883	C₄×D₄	C₂³×C₈₉	1	4	yes	—
884	C₄×D₄	C₂³×C₈₉	1	4	yes	—
885	C₄×D₄	C₂³×C₈₉	1	8	yes	—
886	C₄×D₄	C₂³×C₈₉	1	8	yes	—
887	C₄×D₄	C₂³×C₈₉	1	8	yes	—
888	C₄×D₄	C₂³×C₈₉	1	8	yes	—
889	C₄×D₄	C₂³×C₈₉	1	8	yes	—
890	C₄×D₄	C₂³×C₈₉	1	8	yes	—
891	#117	C₂³×C₈₉	1	8	yes	—
892	#117	C₂³×C₈₉	1	8	yes	—
893	#117	C₂³×C₈₉	1	8	yes	—
894	#117	C₂³×C₈₉	1	8	yes	—
895	#117	C₂³×C₈₉	1	8	yes	—
896	#117	C₂³×C₈₉	1	8	yes	—
897	#117	C₂³×C₈₉	1	8	yes	—
898	#117	C₂³×C₈₉	1	4	yes	—
899	#117	C₂³×C₈₉	1	2	yes	—
900	#117	C₂³×C₈₉	1	4	yes	—
901	#117	C₂³×C₈₉	1	4	yes	—
902	#117	C₂³×C₈₉	1	8	yes	—
903	#117	C₂³×C₈₉	1	8	yes	—
904	#117	C₂³×C₈₉	1	8	yes	—
905	#117	C₂³×C₈₉	1	8	yes	—
906	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
907	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
908	C₂×C₄⋊C₄	C₂³×C₈₉	1	8	yes	—
909	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
910	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
911	C₂×C₄⋊C₄	C₂³×C₈₉	1	8	yes	—
912	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
913	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
914	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
915	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
916	C₂×C₂²⋊C₄	C₂³×C₈₉	1	8	yes	—
917	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
918	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
919	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
920	C₂×C₂²⋊C₄	C₂³×C₈₉	1	8	yes	—
921	C₂×C₂²⋊C₄	C₂³×C₈₉	1	8	yes	—
922	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
923	C₂×C₄²	C₂³×C₈₉	1	4	yes	—
924	C₂×C₄²	C₂³×C₈₉	1	4	yes	—
925	C₂×C₄²	C₂³×C₈₉	1	4	yes	—
926	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
927	C₂×C₄²	C₂³×C₈₉	1	8	yes	—
928	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
929	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
930	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
931	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
932	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
933	C₂⁴	C₂⁴×C₈₉	1	1	yes	characteristic
934	C₂⁴	C₂⁴×C₈₉	1	4	yes	—
935	C₂⁴	C₂⁴×C₈₉	1	4	yes	—
936	#41	—	4	8	no	—
937	#41	—	4	4	no	—
938	#41	—	4	8	no	—
939	#41	—	4	16	no	—
940	C₂×Q₈	—	4	4	no	—
941	C₂×Q₈	C₂⁴×C₈₉	1	4	yes	—
942	C₂×Q₈	C₂⁴×C₈₉	1	4	yes	—
943	C₂×Q₈	C₂⁴×C₈₉	1	4	yes	—
944	C₂×Q₈	C₂⁴×C₈₉	1	8	yes	—
945	C₂×Q₈	C₂⁴×C₈₉	1	4	yes	—
946	C₂×Q₈	C₂⁴×C₈₉	1	2	yes	—
947	C₂×D₄	—	4	4	no	—
948	C₂×D₄	—	4	8	no	—
949	C₂×D₄	—	4	16	no	—
950	C₂×D₄	C₂⁴×C₈₉	1	8	yes	—
951	C₂×D₄	C₂⁴×C₈₉	1	8	yes	—
952	C₂×D₄	C₂⁴×C₈₉	1	4	yes	—
953	C₂×D₄	C₂⁴×C₈₉	1	8	yes	—
954	C₂×D₄	C₂⁴×C₈₉	1	8	yes	—
955	C₂×D₄	C₂⁴×C₈₉	1	4	yes	—
956	C₂×D₄	C₂⁴×C₈₉	1	4	yes	—
957	C₂×D₄	C₂⁴×C₈₉	1	8	yes	—
958	C₂×D₄	C₂⁴×C₈₉	1	4	yes	—
959	C₂×D₄	C₂⁴×C₈₉	1	4	yes	—
960	C₂×D₄	C₂⁴×C₈₉	1	2	yes	—
961	C₂×D₄	C₂⁴×C₈₉	1	8	yes	—
962	C₂×D₄	C₂⁴×C₈₉	1	8	yes	—
963	C₂²×C₄	—	4	2	no	—
964	C₂²×C₄	—	4	8	no	—
965	C₂²×C₄	—	4	8	no	—
966	C₂²×C₄	—	4	4	no	—
967	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
968	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
969	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
970	C₂²×C₄	C₂⁴×C₈₉	1	4	yes	—
971	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
972	C₂²×C₄	C₂⁴×C₈₉	1	4	yes	—
973	C₂²×C₄	C₂⁴×C₈₉	1	8	yes	—
974	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
975	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
976	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
977	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
978	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
979	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
980	C₂²×C₄	C₂⁴×C₈₉	1	8	yes	—
981	C₂²×C₄	C₂⁴×C₈₉	1	4	yes	—
982	C₂²×C₄	C₂⁴×C₈₉	1	8	yes	—
983	C₂²×C₄	C₂⁴×C₈₉	1	8	yes	—
984	C₂²×C₄	C₂⁴×C₈₉	1	8	yes	—
985	C₂²×C₄	C₂⁴×C₈₉	1	4	yes	—
986	C₂²×C₄	C₂⁴×C₈₉	1	8	yes	—
987	C₂²×C₄	C₂⁴×C₈₉	1	8	yes	—
988	C₂²×C₄	C₂⁴×C₈₉	1	4	yes	—
989	C₄⋊C₄	C₂⁴×C₈₉	1	8	yes	—
990	C₄⋊C₄	C₂⁴×C₈₉	1	8	yes	—
991	C₄⋊C₄	C₂⁴×C₈₉	1	8	yes	—
992	C₄⋊C₄	C₂⁴×C₈₉	1	8	yes	—
993	C₄⋊C₄	C₂⁴×C₈₉	1	8	yes	—
994	C₄⋊C₄	C₂⁴×C₈₉	1	8	yes	—
995	C₄⋊C₄	C₂⁴×C₈₉	1	8	yes	—
996	C₄⋊C₄	C₂⁴×C₈₉	1	8	yes	—
997	C₄⋊C₄	C₂⁴×C₈₉	1	8	yes	—
998	C₄⋊C₄	C₂⁴×C₈₉	1	8	yes	—
999	C₄⋊C₄	C₂⁴×C₈₉	1	4	yes	—
1000	C₄⋊C₄	C₂⁴×C₈₉	1	4	yes	—
1001	C₄⋊C₄	C₂⁴×C₈₉	1	8	yes	—
1002	C₄⋊C₄	C₂⁴×C₈₉	1	4	yes	—
1003	C₄⋊C₄	C₂⁴×C₈₉	1	4	yes	—
1004	C₄⋊C₄	C₂⁴×C₈₉	1	8	yes	—
1005	C₄⋊C₄	C₂⁴×C₈₉	1	8	yes	—
1006	C₄⋊C₄	C₂⁴×C₈₉	1	8	yes	—
1007	C₄⋊C₄	C₂⁴×C₈₉	1	8	yes	—
1008	C₄⋊C₄	C₂⁴×C₈₉	1	8	yes	—
1009	C₄⋊C₄	C₂⁴×C₈₉	1	8	yes	—
1010	C₄⋊C₄	C₂⁴×C₈₉	1	4	yes	—
1011	C₄⋊C₄	C₂⁴×C₈₉	1	4	yes	—
1012	C₄⋊C₄	C₂⁴×C₈₉	1	4	yes	—
1013	C₄⋊C₄	C₂⁴×C₈₉	1	8	yes	—
1014	C₄⋊C₄	C₂⁴×C₈₉	1	8	yes	—
1015	C₄⋊C₄	C₂⁴×C₈₉	1	8	yes	—
1016	C₂²⋊C₄	C₂⁴×C₈₉	1	8	yes	—
1017	C₂²⋊C₄	C₂⁴×C₈₉	1	8	yes	—
1018	C₂²⋊C₄	C₂⁴×C₈₉	1	8	yes	—
1019	C₂²⋊C₄	C₂⁴×C₈₉	1	8	yes	—
1020	C₂²⋊C₄	C₂⁴×C₈₉	1	8	yes	—
1021	C₂²⋊C₄	C₂⁴×C₈₉	1	8	yes	—
1022	C₂²⋊C₄	C₂⁴×C₈₉	1	8	yes	—
1023	C₂²⋊C₄	C₂⁴×C₈₉	1	8	yes	—
1024	C₂²⋊C₄	C₂⁴×C₈₉	1	8	yes	—
1025	C₂²⋊C₄	C₂⁴×C₈₉	1	8	yes	—
1026	C₂²⋊C₄	C₂⁴×C₈₉	1	8	yes	—
1027	C₂²⋊C₄	C₂⁴×C₈₉	1	8	yes	—
1028	C₂²⋊C₄	C₂⁴×C₈₉	1	8	yes	—
1029	C₂²⋊C₄	C₂⁴×C₈₉	1	8	yes	—
1030	C₂²⋊C₄	C₂⁴×C₈₉	1	8	yes	—
1031	C₂²⋊C₄	C₂⁴×C₈₉	1	8	yes	—
1032	C₂²⋊C₄	C₂⁴×C₈₉	1	8	yes	—
1033	C₂²⋊C₄	C₂⁴×C₈₉	1	8	yes	—
1034	C₂²⋊C₄	C₂⁴×C₈₉	1	8	yes	—
1035	C₂²⋊C₄	C₂⁴×C₈₉	1	4	yes	—
1036	C₂²⋊C₄	C₂⁴×C₈₉	1	8	yes	—
1037	C₂²⋊C₄	C₂⁴×C₈₉	1	4	yes	—
1038	C₂²⋊C₄	C₂⁴×C₈₉	1	8	yes	—
1039	C₂²⋊C₄	C₂⁴×C₈₉	1	8	yes	—
1040	C₂²⋊C₄	C₂⁴×C₈₉	1	4	yes	—
1041	C₄²	C₂⁴×C₈₉	1	1	yes	characteristic
1042	C₄²	C₂⁴×C₈₉	1	2	yes	—
1043	C₄²	C₂⁴×C₈₉	1	8	yes	—
1044	C₄²	C₂⁴×C₈₉	1	2	yes	—
1045	C₄²	C₂⁴×C₈₉	1	4	yes	—
1046	C₄²	C₂⁴×C₈₉	1	1	yes	characteristic
1047	C₄²	C₂⁴×C₈₉	1	2	yes	—
1048	C₄²	C₂⁴×C₈₉	1	2	yes	—
1049	C₄²	C₂⁴×C₈₉	1	2	yes	—
1050	C₄²	C₂⁴×C₈₉	1	2	yes	—
1051	C₄²	C₂⁴×C₈₉	1	1	yes	characteristic
1052	C₄²	C₂⁴×C₈₉	1	1	yes	characteristic
1053	C₄²	C₂⁴×C₈₉	1	4	yes	—
1054	C₄²	C₂⁴×C₈₉	1	8	yes	—
1055	C₄²	C₂⁴×C₈₉	1	8	yes	—
1056	C₄²	C₂⁴×C₈₉	1	8	yes	—
1057	C₄²	C₂⁴×C₈₉	1	4	yes	—
1058	C₄²	C₂⁴×C₈₉	1	8	yes	—
1059	C₂³	—	2	4	no	—
1060	C₂³	—	2	8	no	—
1061	C₂³	—	4	1	no	—
1062	C₂³	—	4	4	no	—
1063	C₂³	—	4	4	no	—
1064	C₂³	—	4	4	no	—
1065	C₂³	—	4	8	no	—
1066	C₂³	C₂⁵×C₈₉	1	8	yes	—
1067	C₂³	C₂⁵×C₈₉	1	4	yes	—
1068	C₂³	C₂⁵×C₈₉	1	1	yes	characteristic
1069	C₂³	C₂⁵×C₈₉	1	2	yes	—
1070	Q₈	—	4	4	no	—
1071	Q₈	—	4	4	no	—
1072	Q₈	—	4	4	no	—
1073	Q₈	—	4	2	no	—
1074	Q₈	—	4	4	no	—
1075	Q₈	—	4	8	no	—
1076	D₄	—	2	16	no	—
1077	D₄	—	2	16	no	—
1078	D₄	—	4	4	no	—
1079	D₄	—	4	4	no	—
1080	D₄	—	4	8	no	—
1081	D₄	—	4	8	no	—
1082	D₄	—	4	8	no	—
1083	D₄	—	4	8	no	—
1084	D₄	—	4	4	no	—
1085	D₄	—	4	4	no	—
1086	D₄	—	4	2	no	—
1087	D₄	—	4	4	no	—
1088	D₄	—	4	8	no	—
1089	C₂×C₄	—	2	4	no	—
1090	C₂×C₄	—	2	4	no	—
1091	C₂×C₄	—	2	8	no	—
1092	C₂×C₄	—	2	4	no	—
1093	C₂×C₄	—	2	16	no	—
1094	C₂×C₄	—	2	2	no	—
1095	C₂×C₄	—	2	8	no	—
1096	C₂×C₄	—	4	1	no	—
1097	C₂×C₄	—	4	8	no	—
1098	C₂×C₄	—	4	2	no	—
1099	C₂×C₄	—	4	2	no	—
1100	C₂×C₄	—	4	2	no	—
1101	C₂×C₄	—	4	4	no	—
1102	C₂×C₄	—	4	4	no	—
1103	C₂×C₄	—	4	8	no	—
1104	C₂×C₄	—	4	2	no	—
1105	C₂×C₄	—	4	2	no	—
1106	C₂×C₄	—	4	4	no	—
1107	C₂×C₄	—	4	8	no	—
1108	C₂×C₄	—	4	8	no	—
1109	C₂×C₄	—	4	8	no	—
1110	C₂×C₄	—	4	8	no	—
1111	C₂×C₄	C₂⁵×C₈₉	1	2	yes	—
1112	C₂×C₄	C₂⁵×C₈₉	1	2	yes	—
1113	C₂×C₄	C₂⁵×C₈₉	1	8	yes	—
1114	C₂×C₄	C₂⁵×C₈₉	1	2	yes	—
1115	C₂×C₄	C₂⁵×C₈₉	1	2	yes	—
1116	C₂×C₄	C₂⁵×C₈₉	1	2	yes	—
1117	C₂×C₄	C₂⁵×C₈₉	1	1	yes	characteristic
1118	C₂×C₄	C₂⁵×C₈₉	1	4	yes	—
1119	C₂×C₄	C₂⁵×C₈₉	1	8	yes	—
1120	C₂×C₄	C₂⁵×C₈₉	1	8	yes	—
1121	C₂×C₄	C₂⁵×C₈₉	1	8	yes	—
1122	C₂×C₄	C₂⁵×C₈₉	1	1	yes	characteristic
1123	C₂²	—	2	2	no	—
1124	C₂²	—	2	2	no	—
1125	C₂²	—	2	8	no	—
1126	C₂²	—	2	1	no	—
1127	C₂²	—	2	4	no	—
1128	C₂²	—	2	8	no	—
1129	C₂²	—	2	2	no	—
1130	C₂²	—	2	8	no	—
1131	C₂²	—	2	8	no	—
1132	C₂²	—	4	4	no	—
1133	C₂²	—	8	8	no	—
1134	C₂²	—	8	8	no	—
1135	C₂²	#585×C₈₉	1	4	yes	—
1136	C₂²	C₂⁶×C₈₉	1	1	yes	characteristic
1137	C₄	—	2	2	no	—
1138	C₄	—	2	2	no	—
1139	C₄	—	2	8	no	—
1140	C₄	—	2	2	no	—
1141	C₄	—	2	2	no	—
1142	C₄	—	2	2	no	—
1143	C₄	—	2	1	no	—
1144	C₄	—	2	4	no	—
1145	C₄	—	2	8	no	—
1146	C₄	—	2	8	no	—
1147	C₄	—	2	8	no	—
1148	C₄	#585×C₈₉	1	2	yes	—
1149	C₂	—	2	4	no	—
1150	C₂	—	4	1	no	—
1151	C₂	—	4	4	no	—
1152	C₂	—	4	8	no	—
1153	C₂	C₂×#585×C₈₉	1	2	yes	—
1154	C₂	C₂×#585×C₈₉	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₈₉	C₂⁵
commutator, Frattini, cosocle	C₂²	C₂⁶×C₈₉
socle	C₂²×C₈₉	C₂⁶
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₈₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₈₉×#3566	C₂	semidirect
2. C₈₉×#3564	C₂	semidirect
3. C₈₉×#3560	C₂	semidirect
4. C₈₉×#3553	C₂	semidirect
5. C₈₉×#3545	C₂	semidirect
6. C₈₉×#3535	C₂	semidirect
7. C₈₉×#3534	C₂	semidirect
8. C₈₉×#3531	C₂	semidirect
9. C₈₉×#3529	C₂	semidirect
10. C₈₉×#3481	C₂	semidirect
11. C₈₉×#3475	C₂	semidirect
12. C₈₉×#3461	C₂	semidirect
13. C₈₉×#3459	C₂	semidirect
14. C₈₉×#3455	C₂	semidirect
15. C₈₉×#3444	C₂	semidirect
16. C₂×#529×C₈₉	C₂	semidirect
17. #564×C₈₉	C₂²	semidirect
18. #563×C₈₉	C₂²	semidirect
19. #563×C₈₉	C₂²	semidirect
20. #563×C₈₉	C₂²	semidirect
21. #563×C₈₉	C₂²	semidirect
22. #563×C₈₉	C₂²	semidirect
23. #562×C₈₉	C₂²	semidirect
24. #562×C₈₉	C₂²	semidirect
25. #562×C₈₉	C₂²	semidirect
26. #562×C₈₉	C₂²	semidirect
27. H(3,𝔽₄)×C₈₉	C₂²	semidirect
28. #560×C₈₉	C₂²	semidirect
29. #560×C₈₉	C₂²	semidirect
30. #559×C₈₉	C₂²	semidirect
31. #556×C₈₉	C₂²	semidirect
32. #555×C₈₉	C₂²	semidirect
33. #554×C₈₉	C₂²	semidirect
34. #554×C₈₉	C₂²	semidirect
35. #553×C₈₉	C₂²	semidirect
36. #553×C₈₉	C₂²	semidirect
37. #553×C₈₉	C₂²	semidirect
38. #553×C₈₉	C₂²	semidirect
39. #552×C₈₉	C₂²	semidirect
40. #552×C₈₉	C₂²	semidirect
41. #552×C₈₉	C₂²	semidirect
42. #552×C₈₉	C₂²	semidirect
43. #551×C₈₉	C₂²	semidirect
44. #551×C₈₉	C₂²	semidirect
45. #551×C₈₉	C₂²	semidirect
46. #551×C₈₉	C₂²	semidirect
47. #551×C₈₉	C₂²	semidirect
48. #551×C₈₉	C₂²	semidirect
49. #551×C₈₉	C₂²	semidirect
50. #547×C₈₉	C₂²	semidirect
51. #546×C₈₉	C₂²	semidirect
52. #546×C₈₉	C₂²	semidirect
53. #546×C₈₉	C₂²	semidirect
54. #546×C₈₉	C₂²	semidirect
55. D₄²×C₈₉	C₂²	semidirect
56. #544×C₈₉	C₂²	semidirect
57. #543×C₈₉	C₂²	semidirect
58. #542×C₈₉	C₂²	semidirect
59. #542×C₈₉	C₂²	semidirect
60. #542×C₈₉	C₂²	semidirect
61. #542×C₈₉	C₂²	semidirect
62. #541×C₈₉	C₂²	semidirect
63. #541×C₈₉	C₂²	semidirect
64. #541×C₈₉	C₂²	semidirect
65. #540×C₈₉	C₂²	semidirect
66. #539×C₈₉	C₂²	semidirect
67. #539×C₈₉	C₂²	semidirect
68. #539×C₈₉	C₂²	semidirect
69. #539×C₈₉	C₂²	semidirect
70. #539×C₈₉	C₂²	semidirect
71. #539×C₈₉	C₂²	semidirect
72. #539×C₈₉	C₂²	semidirect
73. #539×C₈₉	C₂²	semidirect
75. #538×C₈₉	C₂²	semidirect
76. #538×C₈₉	C₂²	semidirect
77. #538×C₈₉	C₂²	semidirect
78. #538×C₈₉	C₂²	semidirect
79. #538×C₈₉	C₂²	semidirect
81. #536×C₈₉	C₂²	semidirect
82. #534×C₈₉	C₂²	semidirect
83. #534×C₈₉	C₂²	semidirect
84. #533×C₈₉	C₂²	semidirect
85. #533×C₈₉	C₂²	semidirect
86. #533×C₈₉	C₂²	semidirect
87. #533×C₈₉	C₂²	semidirect
88. #532×C₈₉	C₂²	semidirect
89. #532×C₈₉	C₂²	semidirect
90. #532×C₈₉	C₂²	semidirect
91. #529×C₈₉	C₂²	semidirect
92. #529×C₈₉	C₂²	semidirect
93. #529×C₈₉	C₂²	semidirect
94. #529×C₈₉	C₂²	semidirect
95. #529×C₈₉	C₂²	semidirect
96. #529×C₈₉	C₂²	semidirect
97. #529×C₈₉	C₂²	semidirect
98. #529×C₈₉	C₂²	semidirect
99. #529×C₈₉	C₂²	semidirect
100. #529×C₈₉	C₂²	semidirect
101. #529×C₈₉	C₂²	semidirect
102. #529×C₈₉	C₂²	semidirect
103. #529×C₈₉	C₂²	semidirect
104. #529×C₈₉	C₂²	semidirect
105. #529×C₈₉	C₂²	semidirect
106. #529×C₈₉	C₂²	semidirect
107. #529×C₈₉	C₂²	semidirect
108. C₂×#126×C₈₉	C₂²	semidirect
109. C₂×#125×C₈₉	C₂²	semidirect
110. C₂×#124×C₈₉	C₂²	semidirect
111. #525×C₈₉	C₂²	semidirect
112. #525×C₈₉	C₂²	semidirect
113. #525×C₈₉	C₂²	semidirect
114. #525×C₈₉	C₂²	semidirect
115. #525×C₈₉	C₂²	semidirect
116. #525×C₈₉	C₂²	semidirect
117. C₂×#123×C₈₉	C₂²	semidirect
118. C₂×C₂²⋊Q₈×C₈₉	C₂²	semidirect
120. C₄×#41×C₈₉	C₂²	semidirect
121. C₄×#41×C₈₉	C₂²	semidirect
122. C₄×#41×C₈₉	C₂²	semidirect
123. C₄×#41×C₈₉	C₂²	semidirect
124. C₂×C₄×Q₈×C₈₉	C₂²	semidirect
125. C₂×C₄×D₄×C₈₉	C₂²	semidirect
126. C₂×C₄×D₄×C₈₉	C₂²	semidirect
127. C₂×C₄×D₄×C₈₉	C₂²	semidirect
128. C₂×#117×C₈₉	C₂²	semidirect
129. C₂×#117×C₈₉	C₂²	semidirect
130. C₂²×C₄²×C₈₉	C₂²	semidirect
571. #62755	C₈₉	direct (N × H)
578. #3566	C₂×C₈₉	semidirect
579. #3564	C₂×C₈₉	semidirect
580. #3560	C₂×C₈₉	semidirect
581. #3553	C₂×C₈₉	semidirect
582. #3545	C₂×C₈₉	semidirect
583. #3535	C₂×C₈₉	semidirect
584. #3534	C₂×C₈₉	semidirect
585. #3531	C₂×C₈₉	semidirect
586. #3529	C₂×C₈₉	semidirect
587. #3481	C₂×C₈₉	semidirect
588. #3475	C₂×C₈₉	semidirect
589. #3461	C₂×C₈₉	semidirect
590. #3459	C₂×C₈₉	semidirect
591. #3455	C₂×C₈₉	semidirect
592. #3444	C₂×C₈₉	semidirect
593. C₂×#529	C₂×C₈₉	semidirect
594. C₈₉	#62755	direct (N × H)
595. #564	C₂²×C₈₉	semidirect
596. #563	C₂²×C₈₉	semidirect
597. #563	C₂²×C₈₉	semidirect
598. #563	C₂²×C₈₉	semidirect
599. #563	C₂²×C₈₉	semidirect
600. #563	C₂²×C₈₉	semidirect
601. #562	C₂²×C₈₉	semidirect
602. #562	C₂²×C₈₉	semidirect
603. #562	C₂²×C₈₉	semidirect
604. #562	C₂²×C₈₉	semidirect
605. H(3,𝔽₄)	C₂²×C₈₉	semidirect
606. #560	C₂²×C₈₉	semidirect
607. #560	C₂²×C₈₉	semidirect
608. #559	C₂²×C₈₉	semidirect
609. #556	C₂²×C₈₉	semidirect
610. #555	C₂²×C₈₉	semidirect
611. #554	C₂²×C₈₉	semidirect
612. #554	C₂²×C₈₉	semidirect
613. #553	C₂²×C₈₉	semidirect
614. #553	C₂²×C₈₉	semidirect
615. #553	C₂²×C₈₉	semidirect
616. #553	C₂²×C₈₉	semidirect
617. #552	C₂²×C₈₉	semidirect
618. #552	C₂²×C₈₉	semidirect
619. #552	C₂²×C₈₉	semidirect
620. #552	C₂²×C₈₉	semidirect
621. #551	C₂²×C₈₉	semidirect
622. #551	C₂²×C₈₉	semidirect
623. #551	C₂²×C₈₉	semidirect
624. #551	C₂²×C₈₉	semidirect
625. #551	C₂²×C₈₉	semidirect
626. #551	C₂²×C₈₉	semidirect
627. #551	C₂²×C₈₉	semidirect
628. #547	C₂²×C₈₉	semidirect
629. #546	C₂²×C₈₉	semidirect
630. #546	C₂²×C₈₉	semidirect
631. #546	C₂²×C₈₉	semidirect
632. #546	C₂²×C₈₉	semidirect
633. D₄²	C₂²×C₈₉	semidirect
634. #544	C₂²×C₈₉	semidirect
635. #543	C₂²×C₈₉	semidirect
636. #542	C₂²×C₈₉	semidirect
637. #542	C₂²×C₈₉	semidirect
638. #542	C₂²×C₈₉	semidirect
639. #542	C₂²×C₈₉	semidirect
640. #541	C₂²×C₈₉	semidirect
641. #541	C₂²×C₈₉	semidirect
642. #541	C₂²×C₈₉	semidirect
643. #540	C₂²×C₈₉	semidirect
644. #539	C₂²×C₈₉	semidirect
645. #539	C₂²×C₈₉	semidirect
646. #539	C₂²×C₈₉	semidirect
647. #539	C₂²×C₈₉	semidirect
648. #539	C₂²×C₈₉	semidirect
649. #539	C₂²×C₈₉	semidirect
650. #539	C₂²×C₈₉	semidirect
651. #539	C₂²×C₈₉	semidirect
653. #538	C₂²×C₈₉	semidirect
654. #538	C₂²×C₈₉	semidirect
655. #538	C₂²×C₈₉	semidirect
656. #538	C₂²×C₈₉	semidirect
657. #538	C₂²×C₈₉	semidirect
659. #536	C₂²×C₈₉	semidirect
660. #534	C₂²×C₈₉	semidirect
661. #534	C₂²×C₈₉	semidirect
662. #533	C₂²×C₈₉	semidirect
663. #533	C₂²×C₈₉	semidirect
664. #533	C₂²×C₈₉	semidirect
665. #533	C₂²×C₈₉	semidirect
666. #532	C₂²×C₈₉	semidirect
667. #532	C₂²×C₈₉	semidirect
668. #532	C₂²×C₈₉	semidirect
669. #529	C₂²×C₈₉	semidirect
670. #529	C₂²×C₈₉	semidirect
671. #529	C₂²×C₈₉	semidirect
672. #529	C₂²×C₈₉	semidirect
673. #529	C₂²×C₈₉	semidirect
674. #529	C₂²×C₈₉	semidirect
675. #529	C₂²×C₈₉	semidirect
676. #529	C₂²×C₈₉	semidirect
677. #529	C₂²×C₈₉	semidirect
678. #529	C₂²×C₈₉	semidirect
679. #529	C₂²×C₈₉	semidirect
680. #529	C₂²×C₈₉	semidirect
681. #529	C₂²×C₈₉	semidirect
682. #529	C₂²×C₈₉	semidirect
683. #529	C₂²×C₈₉	semidirect
684. #529	C₂²×C₈₉	semidirect
685. #529	C₂²×C₈₉	semidirect
686. C₂×#126	C₂²×C₈₉	semidirect
687. C₂×#125	C₂²×C₈₉	semidirect
688. C₂×#124	C₂²×C₈₉	semidirect
689. #525	C₂²×C₈₉	semidirect
690. #525	C₂²×C₈₉	semidirect
691. #525	C₂²×C₈₉	semidirect
692. #525	C₂²×C₈₉	semidirect
693. #525	C₂²×C₈₉	semidirect
694. #525	C₂²×C₈₉	semidirect
695. C₂×#123	C₂²×C₈₉	semidirect
696. C₂×C₂²⋊Q₈	C₂²×C₈₉	semidirect
698. C₄×#41	C₂²×C₈₉	semidirect
699. C₄×#41	C₂²×C₈₉	semidirect
700. C₄×#41	C₂²×C₈₉	semidirect
701. C₄×#41	C₂²×C₈₉	semidirect
702. C₂×C₄×Q₈	C₂²×C₈₉	semidirect
703. C₂×C₄×D₄	C₂²×C₈₉	semidirect
704. C₂×C₄×D₄	C₂²×C₈₉	semidirect
705. C₂×C₄×D₄	C₂²×C₈₉	semidirect
706. C₂×#117	C₂²×C₈₉	semidirect
707. C₂×#117	C₂²×C₈₉	semidirect
708. C₂²×C₄²	C₂²×C₈₉	semidirect

Maximal subgroups

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

subgroup	index
C₈₉×#3566	2
C₈₉×#3564	2
C₈₉×#3560	2
C₈₉×#3553	2
C₈₉×#3545	2
C₈₉×#3535	2
C₈₉×#3534	2
C₈₉×#3531	2
C₈₉×#3529	2
C₈₉×#3481	2
C₈₉×#3475	2
C₈₉×#3461	2
C₈₉×#3459	2
C₈₉×#3455	2
C₈₉×#3444	2
C₂×#529×C₈₉	2
#62755	89

Subgroups — C89×#62755 #36440603

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#62755 #36440603