Subgroups — C₈₉×#63047 #36440895

Order 22784.

6492 conjugacy classes of subgroups.

The subgroup lattice has 946 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈₉×#3567	C₂	1	6	yes	maximal, complemented
2	C₈₉×#3563	C₂	1	3	yes	maximal, complemented
3	C₈₉×#3559	C₂	1	3	yes	maximal, complemented
4	C₈₉×#3559	C₂	1	6	yes	maximal, complemented
5	C₈₉×#3553	C₂	1	6	yes	maximal, complemented
6	C₈₉×#3548	C₂	1	3	yes	maximal, complemented
7	C₈₉×#3539	C₂	1	6	yes	maximal, complemented
8	C₈₉×#3539	C₂	1	12	yes	maximal, complemented
9	C₈₉×#3529	C₂	1	2	yes	maximal, complemented
10	C₈₉×#3529	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈₉×#3517	C₂	1	3	yes	maximal, complemented
12	C₈₉×#3515	C₂	1	3	yes	maximal, complemented
13	C₈₉×#3512	C₂	1	3	yes	maximal, complemented
14	C₈₉×#3492	C₂	1	6	yes	maximal, complemented
15	#564×C₈₉	C₂²	1	6	yes	complemented
16	#563×C₈₉	C₂²	1	3	yes	—
17	#563×C₈₉	C₂²	1	6	yes	—
18	#563×C₈₉	C₂²	1	6	yes	complemented
19	#562×C₈₉	C₂²	1	6	yes	—
20	#562×C₈₉	C₂²	1	3	yes	—
21	#562×C₈₉	C₂²	1	6	yes	—
22	#562×C₈₉	C₂²	1	3	yes	—
23	#562×C₈₉	C₂²	1	6	yes	complemented
24	H(3,𝔽₄)×C₈₉	C₂²	1	1	yes	characteristic
25	#560×C₈₉	C₂²	1	12	yes	—
26	#560×C₈₉	C₂²	1	6	yes	—
27	#560×C₈₉	C₂²	1	12	yes	complemented
28	#557×C₈₉	C₂²	1	1	yes	characteristic, complemented
29	#557×C₈₉	C₂²	1	3	yes	complemented
30	#554×C₈₉	C₂²	1	3	yes	—
31	#554×C₈₉	C₂²	1	6	yes	complemented
32	#554×C₈₉	C₂²	1	12	yes	complemented
33	#554×C₈₉	C₂²	1	3	yes	complemented
34	#554×C₈₉	C₂²	1	6	yes	complemented
35	#553×C₈₉	C₂²	1	6	yes	—
36	#553×C₈₉	C₂²	1	12	yes	—
37	#553×C₈₉	C₂²	1	6	yes	—
38	#553×C₈₉	C₂²	1	12	yes	—
39	#553×C₈₉	C₂²	1	6	yes	complemented
40	#553×C₈₉	C₂²	1	6	yes	complemented
41	#553×C₈₉	C₂²	1	12	yes	complemented
42	#553×C₈₉	C₂²	1	12	yes	complemented
43	#553×C₈₉	C₂²	1	12	yes	complemented
44	#553×C₈₉	C₂²	1	12	yes	complemented
45	#552×C₈₉	C₂²	1	6	yes	—
46	#552×C₈₉	C₂²	1	6	yes	complemented
47	#552×C₈₉	C₂²	1	12	yes	complemented
48	#552×C₈₉	C₂²	1	6	yes	complemented
49	#552×C₈₉	C₂²	1	12	yes	complemented
50	#552×C₈₉	C₂²	1	6	yes	complemented
51	#552×C₈₉	C₂²	1	12	yes	complemented
52	#550×C₈₉	C₂²	1	6	yes	—
53	#550×C₈₉	C₂²	1	3	yes	—
54	#550×C₈₉	C₂²	1	6	yes	—
55	#550×C₈₉	C₂²	1	1	yes	characteristic, complemented
56	#550×C₈₉	C₂²	1	6	yes	complemented
57	#547×C₈₉	C₂²	1	3	yes	—
58	#547×C₈₉	C₂²	1	12	yes	—
59	#547×C₈₉	C₂²	1	3	yes	—
60	#547×C₈₉	C₂²	1	6	yes	complemented
61	#547×C₈₉	C₂²	1	6	yes	complemented
62	#547×C₈₉	C₂²	1	6	yes	complemented
63	#547×C₈₉	C₂²	1	12	yes	complemented
64	#544×C₈₉	C₂²	1	6	yes	complemented
65	#544×C₈₉	C₂²	1	6	yes	complemented
66	#541×C₈₉	C₂²	1	6	yes	complemented
67	#541×C₈₉	C₂²	1	6	yes	complemented
68	#541×C₈₉	C₂²	1	12	yes	complemented
69	#540×C₈₉	C₂²	1	6	yes	—
70	#540×C₈₉	C₂²	1	12	yes	—
71	#540×C₈₉	C₂²	1	12	yes	—
72	#540×C₈₉	C₂²	1	6	yes	complemented
73	#540×C₈₉	C₂²	1	12	yes	complemented
74	#540×C₈₉	C₂²	1	12	yes	complemented
75	#539×C₈₉	C₂²	1	12	yes	—
76	#539×C₈₉	C₂²	1	6	yes	—
77	#539×C₈₉	C₂²	1	12	yes	complemented
78	#539×C₈₉	C₂²	1	12	yes	complemented
79	#539×C₈₉	C₂²	1	12	yes	complemented
80	#539×C₈₉	C₂²	1	12	yes	complemented
81	#539×C₈₉	C₂²	1	12	yes	complemented
82	#539×C₈₉	C₂²	1	6	yes	complemented
83	#537×C₈₉	C₂²	1	6	yes	—
84	#537×C₈₉	C₂²	1	3	yes	—
85	#537×C₈₉	C₂²	1	6	yes	—
86	#537×C₈₉	C₂²	1	3	yes	complemented
87	#537×C₈₉	C₂²	1	12	yes	complemented
88	#533×C₈₉	C₂²	1	3	yes	complemented
89	#532×C₈₉	C₂²	1	3	yes	—
90	#532×C₈₉	C₂²	1	6	yes	—
91	#532×C₈₉	C₂²	1	3	yes	complemented
92	#529×C₈₉	C₂²	1	6	yes	—
93	#529×C₈₉	C₂²	1	3	yes	—
94	#529×C₈₉	C₂²	1	6	yes	—
95	#529×C₈₉	C₂²	1	3	yes	—
96	#529×C₈₉	C₂²	1	6	yes	complemented
97	#529×C₈₉	C₂²	1	6	yes	complemented
98	C₂×#125×C₈₉	C₂²	1	3	yes	complemented
99	C₂×#125×C₈₉	C₂²	1	6	yes	complemented
100	#525×C₈₉	C₂²	1	6	yes	—
101	#525×C₈₉	C₂²	1	12	yes	—
102	#525×C₈₉	C₂²	1	6	yes	complemented
103	#525×C₈₉	C₂²	1	12	yes	complemented
104	#520×C₈₉	C₂²	1	3	yes	—
105	#520×C₈₉	C₂²	1	6	yes	complemented
106	#520×C₈₉	C₂²	1	1	yes	characteristic, complemented
107	C₄×#41×C₈₉	C₂²	1	3	yes	complemented
108	C₂²×C₄⋊C₄×C₈₉	C₂²	1	2	yes	complemented
109	C₂×#41×C₈₉	C₂³	1	3	yes	—
110	C₂×#41×C₈₉	C₂³	1	3	yes	—
111	C₂×#41×C₈₉	C₂³	1	6	yes	—
112	C₂×#41×C₈₉	C₂³	1	1	yes	characteristic
113	C₂×#41×C₈₉	C₂³	1	6	yes	—
114	C₂×#41×C₈₉	C₂³	1	12	yes	—
115	C₂×#41×C₈₉	C₂³	1	2	yes	—
116	C₂×#41×C₈₉	C₂³	1	6	yes	—
117	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
118	C₂³×C₄×C₈₉	C₂³	1	4	yes	—
119	C₄⋊Q₈×C₈₉	C₂³	1	3	yes	—
120	C₄⋊Q₈×C₈₉	C₂³	1	6	yes	—
121	C₄⋊Q₈×C₈₉	C₂³	1	3	yes	—
122	C₄⋊Q₈×C₈₉	C₂³	1	3	yes	—
123	C₄⋊Q₈×C₈₉	C₂³	1	3	yes	—
124	C₄⋊Q₈×C₈₉	C₂³	1	12	yes	—
125	#127×C₈₉	C₂³	1	6	yes	—
126	#127×C₈₉	C₂³	1	3	yes	—
127	#127×C₈₉	C₂³	1	3	yes	—
128	#127×C₈₉	C₂³	1	12	yes	—
129	#126×C₈₉	C₂³	1	6	yes	—
130	#126×C₈₉	C₂³	1	12	yes	—
131	#126×C₈₉	C₂³	1	12	yes	—
132	#126×C₈₉	C₂³	1	6	yes	—
133	#126×C₈₉	C₂³	1	12	yes	—
134	#126×C₈₉	C₂³	1	12	yes	—
135	#126×C₈₉	C₂³	1	12	yes	—
136	#126×C₈₉	C₂³	1	12	yes	—
137	#126×C₈₉	C₂³	1	12	yes	—
138	#126×C₈₉	C₂³	1	12	yes	—
139	#125×C₈₉	C₂³	1	3	yes	—
140	#125×C₈₉	C₂³	1	6	yes	—
141	#125×C₈₉	C₂³	1	6	yes	—
142	#125×C₈₉	C₂³	1	12	yes	—
143	#125×C₈₉	C₂³	1	6	yes	—
144	#125×C₈₉	C₂³	1	12	yes	—
145	#125×C₈₉	C₂³	1	6	yes	—
146	#125×C₈₉	C₂³	1	6	yes	—
147	#125×C₈₉	C₂³	1	6	yes	—
148	#125×C₈₉	C₂³	1	6	yes	—
149	#125×C₈₉	C₂³	1	3	yes	—
150	#125×C₈₉	C₂³	1	12	yes	—
151	#125×C₈₉	C₂³	1	12	yes	—
152	#125×C₈₉	C₂³	1	12	yes	—
153	#125×C₈₉	C₂³	1	12	yes	—
154	#125×C₈₉	C₂³	1	12	yes	—
155	#125×C₈₉	C₂³	1	12	yes	—
156	#124×C₈₉	C₂³	1	3	yes	—
157	#124×C₈₉	C₂³	1	3	yes	—
158	#124×C₈₉	C₂³	1	3	yes	—
159	#124×C₈₉	C₂³	1	3	yes	—
160	#124×C₈₉	C₂³	1	6	yes	—
161	#123×C₈₉	C₂³	1	6	yes	—
162	#123×C₈₉	C₂³	1	12	yes	—
163	#123×C₈₉	C₂³	1	6	yes	—
164	#123×C₈₉	C₂³	1	12	yes	—
165	#123×C₈₉	C₂³	1	12	yes	—
166	#123×C₈₉	C₂³	1	12	yes	—
167	#123×C₈₉	C₂³	1	12	yes	—
168	#123×C₈₉	C₂³	1	6	yes	—
169	#123×C₈₉	C₂³	1	12	yes	—
170	#123×C₈₉	C₂³	1	12	yes	—
171	#123×C₈₉	C₂³	1	6	yes	—
172	#123×C₈₉	C₂³	1	12	yes	—
173	#123×C₈₉	C₂³	1	12	yes	—
174	#123×C₈₉	C₂³	1	12	yes	—
175	#123×C₈₉	C₂³	1	12	yes	—
176	#123×C₈₉	C₂³	1	12	yes	—
177	#123×C₈₉	C₂³	1	12	yes	—
178	#123×C₈₉	C₂³	1	12	yes	—
179	#123×C₈₉	C₂³	1	12	yes	—
180	C₂²⋊Q₈×C₈₉	C₂³	1	12	yes	—
181	C₂²⋊Q₈×C₈₉	C₂³	1	6	yes	—
182	C₂²⋊Q₈×C₈₉	C₂³	1	6	yes	—
183	C₂²⋊Q₈×C₈₉	C₂³	1	12	yes	—
184	C₂²⋊Q₈×C₈₉	C₂³	1	12	yes	—
185	C₂²⋊Q₈×C₈₉	C₂³	1	6	yes	—
186	C₂²⋊Q₈×C₈₉	C₂³	1	6	yes	—
187	C₂²⋊Q₈×C₈₉	C₂³	1	12	yes	—
188	C₂²⋊Q₈×C₈₉	C₂³	1	6	yes	—
189	C₂²⋊Q₈×C₈₉	C₂³	1	3	yes	—
190	C₂²⋊Q₈×C₈₉	C₂³	1	6	yes	—
191	C₂²⋊Q₈×C₈₉	C₂³	1	3	yes	—
192	C₂²⋊Q₈×C₈₉	C₂³	1	6	yes	—
193	C₂²⋊Q₈×C₈₉	C₂³	1	6	yes	—
194	C₂²⋊Q₈×C₈₉	C₂³	1	6	yes	—
195	C₂²⋊Q₈×C₈₉	C₂³	1	6	yes	—
196	C₂²⋊Q₈×C₈₉	C₂³	1	12	yes	—
197	C₂²⋊Q₈×C₈₉	C₂³	1	12	yes	—
198	C₂²⋊Q₈×C₈₉	C₂³	1	12	yes	—
199	C₂²⋊Q₈×C₈₉	C₂³	1	12	yes	—
200	#121×C₈₉	C₂³	1	12	yes	—
201	#121×C₈₉	C₂³	1	12	yes	—
202	#121×C₈₉	C₂³	1	6	yes	—
203	#121×C₈₉	C₂³	1	6	yes	—
204	#121×C₈₉	C₂³	1	12	yes	—
205	#121×C₈₉	C₂³	1	6	yes	—
206	#121×C₈₉	C₂³	1	6	yes	—
207	#121×C₈₉	C₂³	1	12	yes	—
208	#121×C₈₉	C₂³	1	3	yes	—
209	#121×C₈₉	C₂³	1	6	yes	—
210	#121×C₈₉	C₂³	1	3	yes	—
211	#121×C₈₉	C₂³	1	6	yes	—
212	#121×C₈₉	C₂³	1	6	yes	—
213	#121×C₈₉	C₂³	1	6	yes	—
214	#121×C₈₉	C₂³	1	6	yes	—
215	#121×C₈₉	C₂³	1	12	yes	—
216	#121×C₈₉	C₂³	1	12	yes	—
217	#121×C₈₉	C₂³	1	6	yes	—
218	#121×C₈₉	C₂³	1	6	yes	—
219	#121×C₈₉	C₂³	1	6	yes	—
220	#121×C₈₉	C₂³	1	12	yes	—
221	#121×C₈₉	C₂³	1	12	yes	—
222	#121×C₈₉	C₂³	1	12	yes	—
223	#121×C₈₉	C₂³	1	12	yes	—
224	#121×C₈₉	C₂³	1	12	yes	—
225	#121×C₈₉	C₂³	1	12	yes	—
226	#121×C₈₉	C₂³	1	12	yes	—
227	#121×C₈₉	C₂³	1	12	yes	—
228	#120×C₈₉	C₂³	1	6	yes	—
229	#120×C₈₉	C₂³	1	6	yes	—
230	#120×C₈₉	C₂³	1	12	yes	—
231	C₄×Q₈×C₈₉	C₂³	1	3	yes	—
232	C₄×Q₈×C₈₉	C₂³	1	3	yes	—
233	C₄×Q₈×C₈₉	C₂³	1	6	yes	—
234	C₄×Q₈×C₈₉	C₂³	1	2	yes	—
235	C₄×Q₈×C₈₉	C₂³	1	6	yes	—
236	C₄×Q₈×C₈₉	C₂³	1	1	yes	characteristic
237	C₄×Q₈×C₈₉	C₂³	1	2	yes	—
238	C₄×Q₈×C₈₉	C₂³	1	1	yes	characteristic
239	C₄×Q₈×C₈₉	C₂³	1	6	yes	—
240	C₄×Q₈×C₈₉	C₂³	1	6	yes	—
241	C₄×D₄×C₈₉	C₂³	1	3	yes	—
242	C₄×D₄×C₈₉	C₂³	1	6	yes	—
243	C₄×D₄×C₈₉	C₂³	1	3	yes	—
244	C₄×D₄×C₈₉	C₂³	1	6	yes	—
245	C₄×D₄×C₈₉	C₂³	1	6	yes	—
246	C₄×D₄×C₈₉	C₂³	1	12	yes	—
247	C₄×D₄×C₈₉	C₂³	1	12	yes	—
248	C₄×D₄×C₈₉	C₂³	1	12	yes	—
249	C₄×D₄×C₈₉	C₂³	1	6	yes	—
250	C₄×D₄×C₈₉	C₂³	1	6	yes	—
251	C₄×D₄×C₈₉	C₂³	1	3	yes	—
252	C₄×D₄×C₈₉	C₂³	1	3	yes	—
253	C₄×D₄×C₈₉	C₂³	1	6	yes	—
254	C₄×D₄×C₈₉	C₂³	1	6	yes	—
255	C₄×D₄×C₈₉	C₂³	1	6	yes	—
256	C₄×D₄×C₈₉	C₂³	1	12	yes	—
257	C₄×D₄×C₈₉	C₂³	1	12	yes	—
258	C₄×D₄×C₈₉	C₂³	1	12	yes	—
259	C₄×D₄×C₈₉	C₂³	1	12	yes	—
260	C₄×D₄×C₈₉	C₂³	1	12	yes	—
261	C₄×D₄×C₈₉	C₂³	1	6	yes	—
262	C₄×D₄×C₈₉	C₂³	1	12	yes	—
263	C₄×D₄×C₈₉	C₂³	1	12	yes	—
264	C₄×D₄×C₈₉	C₂³	1	6	yes	—
265	#117×C₈₉	C₂³	1	3	yes	—
266	#117×C₈₉	C₂³	1	6	yes	—
267	#117×C₈₉	C₂³	1	6	yes	—
268	#117×C₈₉	C₂³	1	6	yes	—
269	#117×C₈₉	C₂³	1	12	yes	—
270	#117×C₈₉	C₂³	1	12	yes	—
271	#117×C₈₉	C₂³	1	12	yes	—
272	#117×C₈₉	C₂³	1	12	yes	—
273	#117×C₈₉	C₂³	1	6	yes	—
274	C₂×C₄⋊C₄×C₈₉	C₂³	1	6	yes	—
275	C₂×C₄⋊C₄×C₈₉	C₂³	1	6	yes	—
276	C₂×C₄⋊C₄×C₈₉	C₂³	1	12	yes	—
277	C₂×C₄⋊C₄×C₈₉	C₂³	1	3	yes	—
278	C₂×C₄⋊C₄×C₈₉	C₂³	1	3	yes	—
279	C₂×C₄⋊C₄×C₈₉	C₂³	1	12	yes	—
280	C₂×C₄⋊C₄×C₈₉	C₂³	1	6	yes	—
281	C₂×C₄⋊C₄×C₈₉	C₂³	1	12	yes	—
282	C₂×C₄⋊C₄×C₈₉	C₂³	1	6	yes	—
283	C₂×C₄⋊C₄×C₈₉	C₂³	1	6	yes	—
284	C₂×C₄⋊C₄×C₈₉	C₂³	1	6	yes	—
285	C₂×C₄²×C₈₉	C₂³	1	6	yes	—
286	C₂×C₄²×C₈₉	C₂³	1	3	yes	—
287	C₂⁴×C₈₉	C₂⁴	1	2	yes	—
288	#41×C₈₉	—	4	6	no	—
289	#41×C₈₉	—	4	2	no	—
290	#41×C₈₉	—	4	12	no	—
291	#41×C₈₉	—	4	6	no	—
292	#41×C₈₉	—	8	6	no	—
293	#41×C₈₉	—	8	12	no	—
294	#41×C₈₉	—	8	2	no	—
295	#41×C₈₉	—	8	6	no	—
296	C₂×Q₈×C₈₉	C₂⁴	1	3	yes	—
297	C₂×Q₈×C₈₉	C₂⁴	1	1	yes	characteristic
298	C₂×Q₈×C₈₉	C₂⁴	1	3	yes	—
299	C₂×Q₈×C₈₉	C₂⁴	1	1	yes	characteristic
300	C₂×Q₈×C₈₉	C₂⁴	1	6	yes	—
301	C₂×Q₈×C₈₉	C₂⁴	1	6	yes	—
302	C₂×Q₈×C₈₉	C₂⁴	1	1	yes	characteristic
303	C₂×D₄×C₈₉	C₂⁴	1	3	yes	—
304	C₂×D₄×C₈₉	C₂⁴	1	3	yes	—
305	C₂×D₄×C₈₉	C₂⁴	1	12	yes	—
306	C₂×D₄×C₈₉	C₂⁴	1	6	yes	—
307	C₂×D₄×C₈₉	C₂⁴	1	6	yes	—
308	C₂×D₄×C₈₉	C₂⁴	1	3	yes	—
309	C₂×D₄×C₈₉	C₂⁴	1	6	yes	—
310	C₂×D₄×C₈₉	C₂⁴	1	12	yes	—
311	C₂×D₄×C₈₉	C₂⁴	1	3	yes	—
312	C₂×D₄×C₈₉	C₂⁴	1	6	yes	—
313	C₂×D₄×C₈₉	C₂⁴	1	3	yes	—
314	C₂×D₄×C₈₉	C₂⁴	1	6	yes	—
315	C₂×D₄×C₈₉	C₂⁴	1	12	yes	—
316	C₂×D₄×C₈₉	C₂⁴	1	12	yes	—
317	C₂×D₄×C₈₉	C₂⁴	1	6	yes	—
318	C₂²×C₄×C₈₉	—	4	4	no	—
319	C₂²×C₄×C₈₉	—	8	4	no	—
320	C₂²×C₄×C₈₉	C₂⁴	1	3	yes	—
321	C₂²×C₄×C₈₉	C₂⁴	1	6	yes	—
322	C₂²×C₄×C₈₉	C₂⁴	1	3	yes	—
323	C₂²×C₄×C₈₉	C₂⁴	1	6	yes	—
324	C₂²×C₄×C₈₉	C₂⁴	1	6	yes	—
325	C₂²×C₄×C₈₉	C₂⁴	1	6	yes	—
326	C₂²×C₄×C₈₉	C₂⁴	1	3	yes	—
327	C₂²×C₄×C₈₉	C₂⁴	1	6	yes	—
328	C₂²×C₄×C₈₉	C₂⁴	1	12	yes	—
329	C₂²×C₄×C₈₉	C₂⁴	1	6	yes	—
330	C₂²×C₄×C₈₉	C₂⁴	1	12	yes	—
331	C₂²×C₄×C₈₉	C₂⁴	1	12	yes	—
332	C₂²×C₄×C₈₉	C₂⁴	1	12	yes	—
333	C₂²×C₄×C₈₉	C₂⁴	1	6	yes	—
334	C₄⋊C₄×C₈₉	C₂⁴	1	1	yes	characteristic
335	C₄⋊C₄×C₈₉	C₂⁴	1	6	yes	—
336	C₄⋊C₄×C₈₉	C₂⁴	1	12	yes	—
337	C₄⋊C₄×C₈₉	C₂⁴	1	12	yes	—
338	C₄⋊C₄×C₈₉	C₂⁴	1	3	yes	—
339	C₄⋊C₄×C₈₉	C₂⁴	1	6	yes	—
340	C₄⋊C₄×C₈₉	C₂⁴	1	6	yes	—
341	C₄⋊C₄×C₈₉	C₂⁴	1	6	yes	—
342	C₄⋊C₄×C₈₉	C₂⁴	1	12	yes	—
343	C₄⋊C₄×C₈₉	C₂⁴	1	3	yes	—
344	C₄⋊C₄×C₈₉	C₂⁴	1	6	yes	—
345	C₄⋊C₄×C₈₉	C₂⁴	1	3	yes	—
346	C₄⋊C₄×C₈₉	C₂⁴	1	12	yes	—
347	C₄⋊C₄×C₈₉	C₂⁴	1	12	yes	—
348	C₄⋊C₄×C₈₉	C₂⁴	1	12	yes	—
349	C₄⋊C₄×C₈₉	C₂⁴	1	12	yes	—
350	C₄⋊C₄×C₈₉	C₂⁴	1	6	yes	—
351	C₄⋊C₄×C₈₉	C₂⁴	1	12	yes	—
352	C₄⋊C₄×C₈₉	C₂⁴	1	12	yes	—
353	C₄⋊C₄×C₈₉	C₂⁴	1	6	yes	—
354	C₄⋊C₄×C₈₉	C₂⁴	1	12	yes	—
355	C₄⋊C₄×C₈₉	C₂⁴	1	6	yes	—
356	C₄⋊C₄×C₈₉	C₂⁴	1	6	yes	—
357	C₄⋊C₄×C₈₉	C₂⁴	1	6	yes	—
358	C₄⋊C₄×C₈₉	C₂⁴	1	6	yes	—
359	C₄⋊C₄×C₈₉	C₂⁴	1	6	yes	—
360	C₄⋊C₄×C₈₉	C₂⁴	1	6	yes	—
361	C₄⋊C₄×C₈₉	C₂⁴	1	3	yes	—
362	C₄⋊C₄×C₈₉	C₂⁴	1	3	yes	—
363	C₂²⋊C₄×C₈₉	C₂⁴	1	6	yes	—
364	C₂²⋊C₄×C₈₉	C₂⁴	1	6	yes	—
365	C₂²⋊C₄×C₈₉	C₂⁴	1	12	yes	—
366	C₂²⋊C₄×C₈₉	C₂⁴	1	6	yes	—
367	C₂²⋊C₄×C₈₉	C₂⁴	1	12	yes	—
368	C₂²⋊C₄×C₈₉	C₂⁴	1	6	yes	—
369	C₂²⋊C₄×C₈₉	C₂⁴	1	6	yes	—
370	C₂²⋊C₄×C₈₉	C₂⁴	1	6	yes	—
371	C₂²⋊C₄×C₈₉	C₂⁴	1	12	yes	—
372	C₂²⋊C₄×C₈₉	C₂⁴	1	6	yes	—
373	C₂²⋊C₄×C₈₉	C₂⁴	1	6	yes	—
374	C₂²⋊C₄×C₈₉	C₂⁴	1	12	yes	—
375	C₂²⋊C₄×C₈₉	C₂⁴	1	12	yes	—
376	C₂²⋊C₄×C₈₉	C₂⁴	1	6	yes	—
377	C₂²⋊C₄×C₈₉	C₂⁴	1	6	yes	—
378	C₂²⋊C₄×C₈₉	C₂⁴	1	12	yes	—
379	C₂²⋊C₄×C₈₉	C₂⁴	1	12	yes	—
380	C₂²⋊C₄×C₈₉	C₂⁴	1	12	yes	—
381	C₂²⋊C₄×C₈₉	C₂⁴	1	6	yes	—
382	C₄²×C₈₉	C₂⁴	1	3	yes	—
383	C₄²×C₈₉	C₂⁴	1	6	yes	—
384	C₄²×C₈₉	C₂⁴	1	6	yes	—
385	C₄²×C₈₉	C₂⁴	1	3	yes	—
386	C₄²×C₈₉	C₂⁴	1	3	yes	—
387	C₄²×C₈₉	C₂⁴	1	3	yes	—
388	C₄²×C₈₉	C₂⁴	1	6	yes	—
389	C₄²×C₈₉	C₂⁴	1	12	yes	—
390	C₄²×C₈₉	C₂⁴	1	12	yes	—
391	C₂³×C₈₉	—	4	2	no	—
392	C₂³×C₈₉	—	4	2	no	—
393	C₂³×C₈₉	—	4	2	no	—
394	C₂³×C₈₉	C₂⁵	1	6	yes	—
395	C₂³×C₈₉	C₂⁵	1	3	yes	—
396	C₂³×C₈₉	C₂⁵	1	6	yes	—
397	Q₈×C₈₉	—	2	6	no	—
398	Q₈×C₈₉	—	4	1	no	—
399	Q₈×C₈₉	—	4	3	no	—
400	Q₈×C₈₉	—	4	1	no	—
401	Q₈×C₈₉	—	4	6	no	—
402	Q₈×C₈₉	—	4	6	no	—
403	Q₈×C₈₉	—	4	1	no	—
404	D₄×C₈₉	—	2	6	no	—
405	D₄×C₈₉	—	4	12	no	—
406	D₄×C₈₉	—	4	3	no	—
407	D₄×C₈₉	—	4	6	no	—
408	D₄×C₈₉	—	4	6	no	—
409	D₄×C₈₉	—	4	6	no	—
410	D₄×C₈₉	—	4	3	no	—
411	D₄×C₈₉	—	4	3	no	—
412	D₄×C₈₉	—	4	12	no	—
413	D₄×C₈₉	—	4	6	no	—
414	D₄×C₈₉	—	4	12	no	—
415	D₄×C₈₉	—	4	6	no	—
416	D₄×C₈₉	—	4	12	no	—
417	D₄×C₈₉	—	4	3	no	—
418	D₄×C₈₉	—	4	6	no	—
419	C₂×C₄×C₈₉	—	2	12	no	—
420	C₂×C₄×C₈₉	—	2	6	no	—
421	C₂×C₄×C₈₉	—	4	6	no	—
422	C₂×C₄×C₈₉	—	4	12	no	—
423	C₂×C₄×C₈₉	—	4	12	no	—
424	C₂×C₄×C₈₉	—	4	6	no	—
425	C₂×C₄×C₈₉	—	4	6	no	—
426	C₂×C₄×C₈₉	—	4	3	no	—
427	C₂×C₄×C₈₉	—	4	12	no	—
428	C₂×C₄×C₈₉	—	4	6	no	—
429	C₂×C₄×C₈₉	—	4	6	no	—
430	C₂×C₄×C₈₉	—	4	6	no	—
431	C₂×C₄×C₈₉	—	4	12	no	—
432	C₂×C₄×C₈₉	—	4	3	no	—
433	C₂×C₄×C₈₉	C₂⁵	1	3	yes	—
434	C₂×C₄×C₈₉	C₂⁵	1	2	yes	—
435	C₂×C₄×C₈₉	C₂⁵	1	3	yes	—
436	C₂×C₄×C₈₉	C₂⁵	1	6	yes	—
437	C₂×C₄×C₈₉	C₂⁵	1	3	yes	—
438	C₂×C₄×C₈₉	C₂⁵	1	6	yes	—
439	C₂×C₄×C₈₉	C₂⁵	1	3	yes	—
440	C₂×C₄×C₈₉	C₂⁵	1	6	yes	—
441	C₂×C₄×C₈₉	C₂⁵	1	3	yes	—
442	C₂×C₄×C₈₉	C₂⁵	1	12	yes	—
443	C₂×C₄×C₈₉	C₂⁵	1	1	yes	characteristic
444	C₂²×C₈₉	—	2	6	no	—
445	C₂²×C₈₉	—	2	3	no	—
446	C₂²×C₈₉	—	2	6	no	—
447	C₂²×C₈₉	—	2	6	no	—
448	C₂²×C₈₉	—	2	3	no	—
449	C₂²×C₈₉	—	2	6	no	—
450	C₂²×C₈₉	—	2	3	no	—
451	C₂²×C₈₉	—	2	6	no	—
452	C₂²×C₈₉	—	2	6	no	—
453	C₂²×C₈₉	—	4	8	no	—
454	C₂²×C₈₉	C₂⁶	1	1	yes	characteristic
455	C₄×C₈₉	—	2	6	no	—
456	C₄×C₈₉	—	2	3	no	—
457	C₄×C₈₉	—	2	6	no	—
458	C₄×C₈₉	—	2	2	no	—
459	C₄×C₈₉	—	2	12	no	—
460	C₄×C₈₉	—	2	3	no	—
461	C₄×C₈₉	—	2	3	no	—
462	C₄×C₈₉	—	2	6	no	—
463	C₄×C₈₉	—	2	3	no	—
464	C₄×C₈₉	—	2	3	no	—
465	C₄×C₈₉	#585	1	2	yes	—
466	#63047	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
467	C₂×C₈₉	—	4	3	no	—
468	C₂×C₈₉	—	4	6	no	—
469	C₂×C₈₉	—	4	6	no	—
470	C₂×C₈₉	C₂×#585	1	1	yes	characteristic
471	C₂×C₈₉	H(7,𝔽₂)	1	1	yes	characteristic
472	C₂×C₈₉	2₋¹⁺⁶	1	1	yes	characteristic
473	#3567	C₂×C₈₉	1	6	yes	complemented
474	#3563	C₂×C₈₉	1	3	yes	complemented
475	#3559	C₂×C₈₉	1	3	yes	complemented
476	#3559	C₂×C₈₉	1	6	yes	complemented
477	#3553	C₂×C₈₉	1	6	yes	complemented
478	#3548	C₂×C₈₉	1	3	yes	complemented
479	#3539	C₂×C₈₉	1	6	yes	complemented
480	#3539	C₂×C₈₉	1	12	yes	complemented
481	#3529	C₂×C₈₉	1	2	yes	complemented
482	#3529	C₂×C₈₉	1	1	yes	characteristic, complemented
483	#3517	C₂×C₈₉	1	3	yes	complemented
484	#3515	C₂×C₈₉	1	3	yes	complemented
485	#3512	C₂×C₈₉	1	3	yes	complemented
486	#3492	C₂×C₈₉	1	6	yes	complemented
487	C₈₉	#63047	1	1	yes	characteristic, direct product factor, Sylow
488	#564	C₂²×C₈₉	1	6	yes	complemented
489	#563	C₂²×C₈₉	1	3	yes	—
490	#563	C₂²×C₈₉	1	6	yes	—
491	#563	C₂²×C₈₉	1	6	yes	complemented
492	#562	C₂²×C₈₉	1	6	yes	—
493	#562	C₂²×C₈₉	1	3	yes	—
494	#562	C₂²×C₈₉	1	6	yes	—
495	#562	C₂²×C₈₉	1	3	yes	—
496	#562	C₂²×C₈₉	1	6	yes	complemented
497	H(3,𝔽₄)	C₂²×C₈₉	1	1	yes	characteristic
498	#560	C₂²×C₈₉	1	12	yes	—
499	#560	C₂²×C₈₉	1	6	yes	—
500	#560	C₂²×C₈₉	1	12	yes	complemented
501	#557	C₂²×C₈₉	1	1	yes	characteristic, complemented
502	#557	C₂²×C₈₉	1	3	yes	complemented
503	#554	C₂²×C₈₉	1	3	yes	—
504	#554	C₂²×C₈₉	1	6	yes	complemented
505	#554	C₂²×C₈₉	1	12	yes	complemented
506	#554	C₂²×C₈₉	1	3	yes	complemented
507	#554	C₂²×C₈₉	1	6	yes	complemented
508	#553	C₂²×C₈₉	1	6	yes	—
509	#553	C₂²×C₈₉	1	12	yes	—
510	#553	C₂²×C₈₉	1	6	yes	—
511	#553	C₂²×C₈₉	1	12	yes	—
512	#553	C₂²×C₈₉	1	6	yes	complemented
513	#553	C₂²×C₈₉	1	6	yes	complemented
514	#553	C₂²×C₈₉	1	12	yes	complemented
515	#553	C₂²×C₈₉	1	12	yes	complemented
516	#553	C₂²×C₈₉	1	12	yes	complemented
517	#553	C₂²×C₈₉	1	12	yes	complemented
518	#552	C₂²×C₈₉	1	6	yes	—
519	#552	C₂²×C₈₉	1	6	yes	complemented
520	#552	C₂²×C₈₉	1	12	yes	complemented
521	#552	C₂²×C₈₉	1	6	yes	complemented
522	#552	C₂²×C₈₉	1	12	yes	complemented
523	#552	C₂²×C₈₉	1	6	yes	complemented
524	#552	C₂²×C₈₉	1	12	yes	complemented
525	#550	C₂²×C₈₉	1	6	yes	—
526	#550	C₂²×C₈₉	1	3	yes	—
527	#550	C₂²×C₈₉	1	6	yes	—
528	#550	C₂²×C₈₉	1	1	yes	characteristic, complemented
529	#550	C₂²×C₈₉	1	6	yes	complemented
530	#547	C₂²×C₈₉	1	3	yes	—
531	#547	C₂²×C₈₉	1	12	yes	—
532	#547	C₂²×C₈₉	1	3	yes	—
533	#547	C₂²×C₈₉	1	6	yes	complemented
534	#547	C₂²×C₈₉	1	6	yes	complemented
535	#547	C₂²×C₈₉	1	6	yes	complemented
536	#547	C₂²×C₈₉	1	12	yes	complemented
537	#544	C₂²×C₈₉	1	6	yes	complemented
538	#544	C₂²×C₈₉	1	6	yes	complemented
539	#541	C₂²×C₈₉	1	6	yes	complemented
540	#541	C₂²×C₈₉	1	6	yes	complemented
541	#541	C₂²×C₈₉	1	12	yes	complemented
542	#540	C₂²×C₈₉	1	6	yes	—
543	#540	C₂²×C₈₉	1	12	yes	—
544	#540	C₂²×C₈₉	1	12	yes	—
545	#540	C₂²×C₈₉	1	6	yes	complemented
546	#540	C₂²×C₈₉	1	12	yes	complemented
547	#540	C₂²×C₈₉	1	12	yes	complemented
548	#539	C₂²×C₈₉	1	12	yes	—
549	#539	C₂²×C₈₉	1	6	yes	—
550	#539	C₂²×C₈₉	1	12	yes	complemented
551	#539	C₂²×C₈₉	1	12	yes	complemented
552	#539	C₂²×C₈₉	1	12	yes	complemented
553	#539	C₂²×C₈₉	1	12	yes	complemented
554	#539	C₂²×C₈₉	1	12	yes	complemented
555	#539	C₂²×C₈₉	1	6	yes	complemented
556	#537	C₂²×C₈₉	1	6	yes	—
557	#537	C₂²×C₈₉	1	3	yes	—
558	#537	C₂²×C₈₉	1	6	yes	—
559	#537	C₂²×C₈₉	1	3	yes	complemented
560	#537	C₂²×C₈₉	1	12	yes	complemented
561	#533	C₂²×C₈₉	1	3	yes	complemented
562	#532	C₂²×C₈₉	1	3	yes	—
563	#532	C₂²×C₈₉	1	6	yes	—
564	#532	C₂²×C₈₉	1	3	yes	complemented
565	#529	C₂²×C₈₉	1	6	yes	—
566	#529	C₂²×C₈₉	1	3	yes	—
567	#529	C₂²×C₈₉	1	6	yes	—
568	#529	C₂²×C₈₉	1	3	yes	—
569	#529	C₂²×C₈₉	1	6	yes	complemented
570	#529	C₂²×C₈₉	1	6	yes	complemented
571	C₂×#125	C₂²×C₈₉	1	3	yes	complemented
572	C₂×#125	C₂²×C₈₉	1	6	yes	complemented
573	#525	C₂²×C₈₉	1	6	yes	—
574	#525	C₂²×C₈₉	1	12	yes	—
575	#525	C₂²×C₈₉	1	6	yes	complemented
576	#525	C₂²×C₈₉	1	12	yes	complemented
577	#520	C₂²×C₈₉	1	3	yes	—
578	#520	C₂²×C₈₉	1	6	yes	complemented
579	#520	C₂²×C₈₉	1	1	yes	characteristic, complemented
580	C₄×#41	C₂²×C₈₉	1	3	yes	complemented
581	C₂²×C₄⋊C₄	C₂²×C₈₉	1	2	yes	complemented
582	C₂×#41	C₂³×C₈₉	1	3	yes	—
583	C₂×#41	C₂³×C₈₉	1	3	yes	—
584	C₂×#41	C₂³×C₈₉	1	6	yes	—
585	C₂×#41	C₂³×C₈₉	1	1	yes	characteristic
586	C₂×#41	C₂³×C₈₉	1	6	yes	—
587	C₂×#41	C₂³×C₈₉	1	12	yes	—
588	C₂×#41	C₂³×C₈₉	1	2	yes	—
589	C₂×#41	C₂³×C₈₉	1	6	yes	—
590	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
591	C₂³×C₄	C₂³×C₈₉	1	4	yes	—
592	C₄⋊Q₈	C₂³×C₈₉	1	3	yes	—
593	C₄⋊Q₈	C₂³×C₈₉	1	6	yes	—
594	C₄⋊Q₈	C₂³×C₈₉	1	3	yes	—
595	C₄⋊Q₈	C₂³×C₈₉	1	3	yes	—
596	C₄⋊Q₈	C₂³×C₈₉	1	3	yes	—
597	C₄⋊Q₈	C₂³×C₈₉	1	12	yes	—
598	#127	C₂³×C₈₉	1	6	yes	—
599	#127	C₂³×C₈₉	1	3	yes	—
600	#127	C₂³×C₈₉	1	3	yes	—
601	#127	C₂³×C₈₉	1	12	yes	—
602	#126	C₂³×C₈₉	1	6	yes	—
603	#126	C₂³×C₈₉	1	12	yes	—
604	#126	C₂³×C₈₉	1	12	yes	—
605	#126	C₂³×C₈₉	1	6	yes	—
606	#126	C₂³×C₈₉	1	12	yes	—
607	#126	C₂³×C₈₉	1	12	yes	—
608	#126	C₂³×C₈₉	1	12	yes	—
609	#126	C₂³×C₈₉	1	12	yes	—
610	#126	C₂³×C₈₉	1	12	yes	—
611	#126	C₂³×C₈₉	1	12	yes	—
612	#125	C₂³×C₈₉	1	3	yes	—
613	#125	C₂³×C₈₉	1	6	yes	—
614	#125	C₂³×C₈₉	1	6	yes	—
615	#125	C₂³×C₈₉	1	12	yes	—
616	#125	C₂³×C₈₉	1	6	yes	—
617	#125	C₂³×C₈₉	1	12	yes	—
618	#125	C₂³×C₈₉	1	6	yes	—
619	#125	C₂³×C₈₉	1	6	yes	—
620	#125	C₂³×C₈₉	1	6	yes	—
621	#125	C₂³×C₈₉	1	6	yes	—
622	#125	C₂³×C₈₉	1	3	yes	—
623	#125	C₂³×C₈₉	1	12	yes	—
624	#125	C₂³×C₈₉	1	12	yes	—
625	#125	C₂³×C₈₉	1	12	yes	—
626	#125	C₂³×C₈₉	1	12	yes	—
627	#125	C₂³×C₈₉	1	12	yes	—
628	#125	C₂³×C₈₉	1	12	yes	—
629	#124	C₂³×C₈₉	1	3	yes	—
630	#124	C₂³×C₈₉	1	3	yes	—
631	#124	C₂³×C₈₉	1	3	yes	—
632	#124	C₂³×C₈₉	1	3	yes	—
633	#124	C₂³×C₈₉	1	6	yes	—
634	#123	C₂³×C₈₉	1	6	yes	—
635	#123	C₂³×C₈₉	1	12	yes	—
636	#123	C₂³×C₈₉	1	6	yes	—
637	#123	C₂³×C₈₉	1	12	yes	—
638	#123	C₂³×C₈₉	1	12	yes	—
639	#123	C₂³×C₈₉	1	12	yes	—
640	#123	C₂³×C₈₉	1	12	yes	—
641	#123	C₂³×C₈₉	1	6	yes	—
642	#123	C₂³×C₈₉	1	12	yes	—
643	#123	C₂³×C₈₉	1	12	yes	—
644	#123	C₂³×C₈₉	1	6	yes	—
645	#123	C₂³×C₈₉	1	12	yes	—
646	#123	C₂³×C₈₉	1	12	yes	—
647	#123	C₂³×C₈₉	1	12	yes	—
648	#123	C₂³×C₈₉	1	12	yes	—
649	#123	C₂³×C₈₉	1	12	yes	—
650	#123	C₂³×C₈₉	1	12	yes	—
651	#123	C₂³×C₈₉	1	12	yes	—
652	#123	C₂³×C₈₉	1	12	yes	—
653	C₂²⋊Q₈	C₂³×C₈₉	1	12	yes	—
654	C₂²⋊Q₈	C₂³×C₈₉	1	6	yes	—
655	C₂²⋊Q₈	C₂³×C₈₉	1	6	yes	—
656	C₂²⋊Q₈	C₂³×C₈₉	1	12	yes	—
657	C₂²⋊Q₈	C₂³×C₈₉	1	12	yes	—
658	C₂²⋊Q₈	C₂³×C₈₉	1	6	yes	—
659	C₂²⋊Q₈	C₂³×C₈₉	1	6	yes	—
660	C₂²⋊Q₈	C₂³×C₈₉	1	12	yes	—
661	C₂²⋊Q₈	C₂³×C₈₉	1	6	yes	—
662	C₂²⋊Q₈	C₂³×C₈₉	1	3	yes	—
663	C₂²⋊Q₈	C₂³×C₈₉	1	6	yes	—
664	C₂²⋊Q₈	C₂³×C₈₉	1	3	yes	—
665	C₂²⋊Q₈	C₂³×C₈₉	1	6	yes	—
666	C₂²⋊Q₈	C₂³×C₈₉	1	6	yes	—
667	C₂²⋊Q₈	C₂³×C₈₉	1	6	yes	—
668	C₂²⋊Q₈	C₂³×C₈₉	1	6	yes	—
669	C₂²⋊Q₈	C₂³×C₈₉	1	12	yes	—
670	C₂²⋊Q₈	C₂³×C₈₉	1	12	yes	—
671	C₂²⋊Q₈	C₂³×C₈₉	1	12	yes	—
672	C₂²⋊Q₈	C₂³×C₈₉	1	12	yes	—
673	#121	C₂³×C₈₉	1	12	yes	—
674	#121	C₂³×C₈₉	1	12	yes	—
675	#121	C₂³×C₈₉	1	6	yes	—
676	#121	C₂³×C₈₉	1	6	yes	—
677	#121	C₂³×C₈₉	1	12	yes	—
678	#121	C₂³×C₈₉	1	6	yes	—
679	#121	C₂³×C₈₉	1	6	yes	—
680	#121	C₂³×C₈₉	1	12	yes	—
681	#121	C₂³×C₈₉	1	3	yes	—
682	#121	C₂³×C₈₉	1	6	yes	—
683	#121	C₂³×C₈₉	1	3	yes	—
684	#121	C₂³×C₈₉	1	6	yes	—
685	#121	C₂³×C₈₉	1	6	yes	—
686	#121	C₂³×C₈₉	1	6	yes	—
687	#121	C₂³×C₈₉	1	6	yes	—
688	#121	C₂³×C₈₉	1	12	yes	—
689	#121	C₂³×C₈₉	1	12	yes	—
690	#121	C₂³×C₈₉	1	6	yes	—
691	#121	C₂³×C₈₉	1	6	yes	—
692	#121	C₂³×C₈₉	1	6	yes	—
693	#121	C₂³×C₈₉	1	12	yes	—
694	#121	C₂³×C₈₉	1	12	yes	—
695	#121	C₂³×C₈₉	1	12	yes	—
696	#121	C₂³×C₈₉	1	12	yes	—
697	#121	C₂³×C₈₉	1	12	yes	—
698	#121	C₂³×C₈₉	1	12	yes	—
699	#121	C₂³×C₈₉	1	12	yes	—
700	#121	C₂³×C₈₉	1	12	yes	—
701	#120	C₂³×C₈₉	1	6	yes	—
702	#120	C₂³×C₈₉	1	6	yes	—
703	#120	C₂³×C₈₉	1	12	yes	—
704	C₄×Q₈	C₂³×C₈₉	1	3	yes	—
705	C₄×Q₈	C₂³×C₈₉	1	3	yes	—
706	C₄×Q₈	C₂³×C₈₉	1	6	yes	—
707	C₄×Q₈	C₂³×C₈₉	1	2	yes	—
708	C₄×Q₈	C₂³×C₈₉	1	6	yes	—
709	C₄×Q₈	C₂³×C₈₉	1	1	yes	characteristic
710	C₄×Q₈	C₂³×C₈₉	1	2	yes	—
711	C₄×Q₈	C₂³×C₈₉	1	1	yes	characteristic
712	C₄×Q₈	C₂³×C₈₉	1	6	yes	—
713	C₄×Q₈	C₂³×C₈₉	1	6	yes	—
714	C₄×D₄	C₂³×C₈₉	1	3	yes	—
715	C₄×D₄	C₂³×C₈₉	1	6	yes	—
716	C₄×D₄	C₂³×C₈₉	1	3	yes	—
717	C₄×D₄	C₂³×C₈₉	1	6	yes	—
718	C₄×D₄	C₂³×C₈₉	1	6	yes	—
719	C₄×D₄	C₂³×C₈₉	1	12	yes	—
720	C₄×D₄	C₂³×C₈₉	1	12	yes	—
721	C₄×D₄	C₂³×C₈₉	1	12	yes	—
722	C₄×D₄	C₂³×C₈₉	1	6	yes	—
723	C₄×D₄	C₂³×C₈₉	1	6	yes	—
724	C₄×D₄	C₂³×C₈₉	1	3	yes	—
725	C₄×D₄	C₂³×C₈₉	1	3	yes	—
726	C₄×D₄	C₂³×C₈₉	1	6	yes	—
727	C₄×D₄	C₂³×C₈₉	1	6	yes	—
728	C₄×D₄	C₂³×C₈₉	1	6	yes	—
729	C₄×D₄	C₂³×C₈₉	1	12	yes	—
730	C₄×D₄	C₂³×C₈₉	1	12	yes	—
731	C₄×D₄	C₂³×C₈₉	1	12	yes	—
732	C₄×D₄	C₂³×C₈₉	1	12	yes	—
733	C₄×D₄	C₂³×C₈₉	1	12	yes	—
734	C₄×D₄	C₂³×C₈₉	1	6	yes	—
735	C₄×D₄	C₂³×C₈₉	1	12	yes	—
736	C₄×D₄	C₂³×C₈₉	1	12	yes	—
737	C₄×D₄	C₂³×C₈₉	1	6	yes	—
738	#117	C₂³×C₈₉	1	3	yes	—
739	#117	C₂³×C₈₉	1	6	yes	—
740	#117	C₂³×C₈₉	1	6	yes	—
741	#117	C₂³×C₈₉	1	6	yes	—
742	#117	C₂³×C₈₉	1	12	yes	—
743	#117	C₂³×C₈₉	1	12	yes	—
744	#117	C₂³×C₈₉	1	12	yes	—
745	#117	C₂³×C₈₉	1	12	yes	—
746	#117	C₂³×C₈₉	1	6	yes	—
747	C₂×C₄⋊C₄	C₂³×C₈₉	1	6	yes	—
748	C₂×C₄⋊C₄	C₂³×C₈₉	1	6	yes	—
749	C₂×C₄⋊C₄	C₂³×C₈₉	1	12	yes	—
750	C₂×C₄⋊C₄	C₂³×C₈₉	1	3	yes	—
751	C₂×C₄⋊C₄	C₂³×C₈₉	1	3	yes	—
752	C₂×C₄⋊C₄	C₂³×C₈₉	1	12	yes	—
753	C₂×C₄⋊C₄	C₂³×C₈₉	1	6	yes	—
754	C₂×C₄⋊C₄	C₂³×C₈₉	1	12	yes	—
755	C₂×C₄⋊C₄	C₂³×C₈₉	1	6	yes	—
756	C₂×C₄⋊C₄	C₂³×C₈₉	1	6	yes	—
757	C₂×C₄⋊C₄	C₂³×C₈₉	1	6	yes	—
758	C₂×C₄²	C₂³×C₈₉	1	6	yes	—
759	C₂×C₄²	C₂³×C₈₉	1	3	yes	—
760	C₂⁴	C₂⁴×C₈₉	1	2	yes	—
761	#41	—	4	6	no	—
762	#41	—	4	2	no	—
763	#41	—	4	12	no	—
764	#41	—	4	6	no	—
765	#41	—	8	6	no	—
766	#41	—	8	12	no	—
767	#41	—	8	2	no	—
768	#41	—	8	6	no	—
769	C₂×Q₈	C₂⁴×C₈₉	1	3	yes	—
770	C₂×Q₈	C₂⁴×C₈₉	1	1	yes	characteristic
771	C₂×Q₈	C₂⁴×C₈₉	1	3	yes	—
772	C₂×Q₈	C₂⁴×C₈₉	1	1	yes	characteristic
773	C₂×Q₈	C₂⁴×C₈₉	1	6	yes	—
774	C₂×Q₈	C₂⁴×C₈₉	1	6	yes	—
775	C₂×Q₈	C₂⁴×C₈₉	1	1	yes	characteristic
776	C₂×D₄	C₂⁴×C₈₉	1	3	yes	—
777	C₂×D₄	C₂⁴×C₈₉	1	3	yes	—
778	C₂×D₄	C₂⁴×C₈₉	1	12	yes	—
779	C₂×D₄	C₂⁴×C₈₉	1	6	yes	—
780	C₂×D₄	C₂⁴×C₈₉	1	6	yes	—
781	C₂×D₄	C₂⁴×C₈₉	1	3	yes	—
782	C₂×D₄	C₂⁴×C₈₉	1	6	yes	—
783	C₂×D₄	C₂⁴×C₈₉	1	12	yes	—
784	C₂×D₄	C₂⁴×C₈₉	1	3	yes	—
785	C₂×D₄	C₂⁴×C₈₉	1	6	yes	—
786	C₂×D₄	C₂⁴×C₈₉	1	3	yes	—
787	C₂×D₄	C₂⁴×C₈₉	1	6	yes	—
788	C₂×D₄	C₂⁴×C₈₉	1	12	yes	—
789	C₂×D₄	C₂⁴×C₈₉	1	12	yes	—
790	C₂×D₄	C₂⁴×C₈₉	1	6	yes	—
791	C₂²×C₄	—	4	4	no	—
792	C₂²×C₄	—	8	4	no	—
793	C₂²×C₄	C₂⁴×C₈₉	1	3	yes	—
794	C₂²×C₄	C₂⁴×C₈₉	1	6	yes	—
795	C₂²×C₄	C₂⁴×C₈₉	1	3	yes	—
796	C₂²×C₄	C₂⁴×C₈₉	1	6	yes	—
797	C₂²×C₄	C₂⁴×C₈₉	1	6	yes	—
798	C₂²×C₄	C₂⁴×C₈₉	1	6	yes	—
799	C₂²×C₄	C₂⁴×C₈₉	1	3	yes	—
800	C₂²×C₄	C₂⁴×C₈₉	1	6	yes	—
801	C₂²×C₄	C₂⁴×C₈₉	1	12	yes	—
802	C₂²×C₄	C₂⁴×C₈₉	1	6	yes	—
803	C₂²×C₄	C₂⁴×C₈₉	1	12	yes	—
804	C₂²×C₄	C₂⁴×C₈₉	1	12	yes	—
805	C₂²×C₄	C₂⁴×C₈₉	1	12	yes	—
806	C₂²×C₄	C₂⁴×C₈₉	1	6	yes	—
807	C₄⋊C₄	C₂⁴×C₈₉	1	1	yes	characteristic
808	C₄⋊C₄	C₂⁴×C₈₉	1	6	yes	—
809	C₄⋊C₄	C₂⁴×C₈₉	1	12	yes	—
810	C₄⋊C₄	C₂⁴×C₈₉	1	12	yes	—
811	C₄⋊C₄	C₂⁴×C₈₉	1	3	yes	—
812	C₄⋊C₄	C₂⁴×C₈₉	1	6	yes	—
813	C₄⋊C₄	C₂⁴×C₈₉	1	6	yes	—
814	C₄⋊C₄	C₂⁴×C₈₉	1	6	yes	—
815	C₄⋊C₄	C₂⁴×C₈₉	1	12	yes	—
816	C₄⋊C₄	C₂⁴×C₈₉	1	3	yes	—
817	C₄⋊C₄	C₂⁴×C₈₉	1	6	yes	—
818	C₄⋊C₄	C₂⁴×C₈₉	1	3	yes	—
819	C₄⋊C₄	C₂⁴×C₈₉	1	12	yes	—
820	C₄⋊C₄	C₂⁴×C₈₉	1	12	yes	—
821	C₄⋊C₄	C₂⁴×C₈₉	1	12	yes	—
822	C₄⋊C₄	C₂⁴×C₈₉	1	12	yes	—
823	C₄⋊C₄	C₂⁴×C₈₉	1	6	yes	—
824	C₄⋊C₄	C₂⁴×C₈₉	1	12	yes	—
825	C₄⋊C₄	C₂⁴×C₈₉	1	12	yes	—
826	C₄⋊C₄	C₂⁴×C₈₉	1	6	yes	—
827	C₄⋊C₄	C₂⁴×C₈₉	1	12	yes	—
828	C₄⋊C₄	C₂⁴×C₈₉	1	6	yes	—
829	C₄⋊C₄	C₂⁴×C₈₉	1	6	yes	—
830	C₄⋊C₄	C₂⁴×C₈₉	1	6	yes	—
831	C₄⋊C₄	C₂⁴×C₈₉	1	6	yes	—
832	C₄⋊C₄	C₂⁴×C₈₉	1	6	yes	—
833	C₄⋊C₄	C₂⁴×C₈₉	1	6	yes	—
834	C₄⋊C₄	C₂⁴×C₈₉	1	3	yes	—
835	C₄⋊C₄	C₂⁴×C₈₉	1	3	yes	—
836	C₂²⋊C₄	C₂⁴×C₈₉	1	6	yes	—
837	C₂²⋊C₄	C₂⁴×C₈₉	1	6	yes	—
838	C₂²⋊C₄	C₂⁴×C₈₉	1	12	yes	—
839	C₂²⋊C₄	C₂⁴×C₈₉	1	6	yes	—
840	C₂²⋊C₄	C₂⁴×C₈₉	1	12	yes	—
841	C₂²⋊C₄	C₂⁴×C₈₉	1	6	yes	—
842	C₂²⋊C₄	C₂⁴×C₈₉	1	6	yes	—
843	C₂²⋊C₄	C₂⁴×C₈₉	1	6	yes	—
844	C₂²⋊C₄	C₂⁴×C₈₉	1	12	yes	—
845	C₂²⋊C₄	C₂⁴×C₈₉	1	6	yes	—
846	C₂²⋊C₄	C₂⁴×C₈₉	1	6	yes	—
847	C₂²⋊C₄	C₂⁴×C₈₉	1	12	yes	—
848	C₂²⋊C₄	C₂⁴×C₈₉	1	12	yes	—
849	C₂²⋊C₄	C₂⁴×C₈₉	1	6	yes	—
850	C₂²⋊C₄	C₂⁴×C₈₉	1	6	yes	—
851	C₂²⋊C₄	C₂⁴×C₈₉	1	12	yes	—
852	C₂²⋊C₄	C₂⁴×C₈₉	1	12	yes	—
853	C₂²⋊C₄	C₂⁴×C₈₉	1	12	yes	—
854	C₂²⋊C₄	C₂⁴×C₈₉	1	6	yes	—
855	C₄²	C₂⁴×C₈₉	1	3	yes	—
856	C₄²	C₂⁴×C₈₉	1	6	yes	—
857	C₄²	C₂⁴×C₈₉	1	6	yes	—
858	C₄²	C₂⁴×C₈₉	1	3	yes	—
859	C₄²	C₂⁴×C₈₉	1	3	yes	—
860	C₄²	C₂⁴×C₈₉	1	3	yes	—
861	C₄²	C₂⁴×C₈₉	1	6	yes	—
862	C₄²	C₂⁴×C₈₉	1	12	yes	—
863	C₄²	C₂⁴×C₈₉	1	12	yes	—
864	C₂³	—	4	2	no	—
865	C₂³	—	4	2	no	—
866	C₂³	—	4	2	no	—
867	C₂³	C₂⁵×C₈₉	1	6	yes	—
868	C₂³	C₂⁵×C₈₉	1	3	yes	—
869	C₂³	C₂⁵×C₈₉	1	6	yes	—
870	Q₈	—	2	6	no	—
871	Q₈	—	4	1	no	—
872	Q₈	—	4	3	no	—
873	Q₈	—	4	1	no	—
874	Q₈	—	4	6	no	—
875	Q₈	—	4	6	no	—
876	Q₈	—	4	1	no	—
877	D₄	—	2	6	no	—
878	D₄	—	4	12	no	—
879	D₄	—	4	3	no	—
880	D₄	—	4	6	no	—
881	D₄	—	4	6	no	—
882	D₄	—	4	6	no	—
883	D₄	—	4	3	no	—
884	D₄	—	4	3	no	—
885	D₄	—	4	12	no	—
886	D₄	—	4	6	no	—
887	D₄	—	4	12	no	—
888	D₄	—	4	6	no	—
889	D₄	—	4	12	no	—
890	D₄	—	4	3	no	—
891	D₄	—	4	6	no	—
892	C₂×C₄	—	2	12	no	—
893	C₂×C₄	—	2	6	no	—
894	C₂×C₄	—	4	6	no	—
895	C₂×C₄	—	4	12	no	—
896	C₂×C₄	—	4	12	no	—
897	C₂×C₄	—	4	6	no	—
898	C₂×C₄	—	4	6	no	—
899	C₂×C₄	—	4	3	no	—
900	C₂×C₄	—	4	12	no	—
901	C₂×C₄	—	4	6	no	—
902	C₂×C₄	—	4	6	no	—
903	C₂×C₄	—	4	6	no	—
904	C₂×C₄	—	4	12	no	—
905	C₂×C₄	—	4	3	no	—
906	C₂×C₄	C₂⁵×C₈₉	1	3	yes	—
907	C₂×C₄	C₂⁵×C₈₉	1	2	yes	—
908	C₂×C₄	C₂⁵×C₈₉	1	3	yes	—
909	C₂×C₄	C₂⁵×C₈₉	1	6	yes	—
910	C₂×C₄	C₂⁵×C₈₉	1	3	yes	—
911	C₂×C₄	C₂⁵×C₈₉	1	6	yes	—
912	C₂×C₄	C₂⁵×C₈₉	1	3	yes	—
913	C₂×C₄	C₂⁵×C₈₉	1	6	yes	—
914	C₂×C₄	C₂⁵×C₈₉	1	3	yes	—
915	C₂×C₄	C₂⁵×C₈₉	1	12	yes	—
916	C₂×C₄	C₂⁵×C₈₉	1	1	yes	characteristic
917	C₂²	—	2	6	no	—
918	C₂²	—	2	3	no	—
919	C₂²	—	2	6	no	—
920	C₂²	—	2	6	no	—
921	C₂²	—	2	3	no	—
922	C₂²	—	2	6	no	—
923	C₂²	—	2	3	no	—
924	C₂²	—	2	6	no	—
925	C₂²	—	2	6	no	—
926	C₂²	—	4	8	no	—
927	C₂²	C₂⁶×C₈₉	1	1	yes	characteristic
928	C₄	—	2	6	no	—
929	C₄	—	2	3	no	—
930	C₄	—	2	6	no	—
931	C₄	—	2	2	no	—
932	C₄	—	2	12	no	—
933	C₄	—	2	3	no	—
934	C₄	—	2	3	no	—
935	C₄	—	2	6	no	—
936	C₄	—	2	3	no	—
937	C₄	—	2	3	no	—
938	C₄	#585×C₈₉	1	2	yes	—
939	C₂	—	4	3	no	—
940	C₂	—	4	6	no	—
941	C₂	—	4	6	no	—
942	C₂	C₂×#585×C₈₉	1	1	yes	characteristic
943	C₂	C₈₉×H(7,𝔽₂)	1	1	yes	characteristic
944	C₂	C₈₉×2₋¹⁺⁶	1	1	yes	characteristic

	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×#3567	C₂	semidirect
2. C₈₉×#3563	C₂	semidirect
3. C₈₉×#3559	C₂	semidirect
4. C₈₉×#3559	C₂	semidirect
5. C₈₉×#3553	C₂	semidirect
6. C₈₉×#3548	C₂	semidirect
7. C₈₉×#3539	C₂	semidirect
8. C₈₉×#3539	C₂	semidirect
9. C₈₉×#3529	C₂	semidirect
10. C₈₉×#3529	C₂	semidirect
11. C₈₉×#3517	C₂	semidirect
12. C₈₉×#3515	C₂	semidirect
13. C₈₉×#3512	C₂	semidirect
14. C₈₉×#3492	C₂	semidirect
15. #564×C₈₉	C₂²	semidirect
18. #563×C₈₉	C₂²	semidirect
23. #562×C₈₉	C₂²	semidirect
27. #560×C₈₉	C₂²	semidirect
28. #557×C₈₉	C₂²	semidirect
29. #557×C₈₉	C₂²	semidirect
31. #554×C₈₉	C₂²	semidirect
32. #554×C₈₉	C₂²	semidirect
33. #554×C₈₉	C₂²	semidirect
34. #554×C₈₉	C₂²	semidirect
39. #553×C₈₉	C₂²	semidirect
40. #553×C₈₉	C₂²	semidirect
41. #553×C₈₉	C₂²	semidirect
42. #553×C₈₉	C₂²	semidirect
43. #553×C₈₉	C₂²	semidirect
44. #553×C₈₉	C₂²	semidirect
46. #552×C₈₉	C₂²	semidirect
47. #552×C₈₉	C₂²	semidirect
48. #552×C₈₉	C₂²	semidirect
49. #552×C₈₉	C₂²	semidirect
50. #552×C₈₉	C₂²	semidirect
51. #552×C₈₉	C₂²	semidirect
55. #550×C₈₉	C₂²	semidirect
56. #550×C₈₉	C₂²	semidirect
60. #547×C₈₉	C₂²	semidirect
61. #547×C₈₉	C₂²	semidirect
62. #547×C₈₉	C₂²	semidirect
63. #547×C₈₉	C₂²	semidirect
64. #544×C₈₉	C₂²	semidirect
65. #544×C₈₉	C₂²	semidirect
66. #541×C₈₉	C₂²	semidirect
67. #541×C₈₉	C₂²	semidirect
68. #541×C₈₉	C₂²	semidirect
72. #540×C₈₉	C₂²	semidirect
73. #540×C₈₉	C₂²	semidirect
74. #540×C₈₉	C₂²	semidirect
77. #539×C₈₉	C₂²	semidirect
78. #539×C₈₉	C₂²	semidirect
79. #539×C₈₉	C₂²	semidirect
80. #539×C₈₉	C₂²	semidirect
81. #539×C₈₉	C₂²	semidirect
82. #539×C₈₉	C₂²	semidirect
86. #537×C₈₉	C₂²	semidirect
87. #537×C₈₉	C₂²	semidirect
88. #533×C₈₉	C₂²	semidirect
91. #532×C₈₉	C₂²	semidirect
96. #529×C₈₉	C₂²	semidirect
97. #529×C₈₉	C₂²	semidirect
98. C₂×#125×C₈₉	C₂²	semidirect
99. C₂×#125×C₈₉	C₂²	semidirect
102. #525×C₈₉	C₂²	semidirect
103. #525×C₈₉	C₂²	semidirect
105. #520×C₈₉	C₂²	semidirect
106. #520×C₈₉	C₂²	semidirect
107. C₄×#41×C₈₉	C₂²	semidirect
108. C₂²×C₄⋊C₄×C₈₉	C₂²	semidirect
466. #63047	C₈₉	direct (N × H)
473. #3567	C₂×C₈₉	semidirect
474. #3563	C₂×C₈₉	semidirect
475. #3559	C₂×C₈₉	semidirect
476. #3559	C₂×C₈₉	semidirect
477. #3553	C₂×C₈₉	semidirect
478. #3548	C₂×C₈₉	semidirect
479. #3539	C₂×C₈₉	semidirect
480. #3539	C₂×C₈₉	semidirect
481. #3529	C₂×C₈₉	semidirect
482. #3529	C₂×C₈₉	semidirect
483. #3517	C₂×C₈₉	semidirect
484. #3515	C₂×C₈₉	semidirect
485. #3512	C₂×C₈₉	semidirect
486. #3492	C₂×C₈₉	semidirect
487. C₈₉	#63047	direct (N × H)
488. #564	C₂²×C₈₉	semidirect
491. #563	C₂²×C₈₉	semidirect
496. #562	C₂²×C₈₉	semidirect
500. #560	C₂²×C₈₉	semidirect
501. #557	C₂²×C₈₉	semidirect
502. #557	C₂²×C₈₉	semidirect
504. #554	C₂²×C₈₉	semidirect
505. #554	C₂²×C₈₉	semidirect
506. #554	C₂²×C₈₉	semidirect
507. #554	C₂²×C₈₉	semidirect
512. #553	C₂²×C₈₉	semidirect
513. #553	C₂²×C₈₉	semidirect
514. #553	C₂²×C₈₉	semidirect
515. #553	C₂²×C₈₉	semidirect
516. #553	C₂²×C₈₉	semidirect
517. #553	C₂²×C₈₉	semidirect
519. #552	C₂²×C₈₉	semidirect
520. #552	C₂²×C₈₉	semidirect
521. #552	C₂²×C₈₉	semidirect
522. #552	C₂²×C₈₉	semidirect
523. #552	C₂²×C₈₉	semidirect
524. #552	C₂²×C₈₉	semidirect
528. #550	C₂²×C₈₉	semidirect
529. #550	C₂²×C₈₉	semidirect
533. #547	C₂²×C₈₉	semidirect
534. #547	C₂²×C₈₉	semidirect
535. #547	C₂²×C₈₉	semidirect
536. #547	C₂²×C₈₉	semidirect
537. #544	C₂²×C₈₉	semidirect
538. #544	C₂²×C₈₉	semidirect
539. #541	C₂²×C₈₉	semidirect
540. #541	C₂²×C₈₉	semidirect
541. #541	C₂²×C₈₉	semidirect
545. #540	C₂²×C₈₉	semidirect
546. #540	C₂²×C₈₉	semidirect
547. #540	C₂²×C₈₉	semidirect
550. #539	C₂²×C₈₉	semidirect
551. #539	C₂²×C₈₉	semidirect
552. #539	C₂²×C₈₉	semidirect
553. #539	C₂²×C₈₉	semidirect
554. #539	C₂²×C₈₉	semidirect
555. #539	C₂²×C₈₉	semidirect
559. #537	C₂²×C₈₉	semidirect
560. #537	C₂²×C₈₉	semidirect
561. #533	C₂²×C₈₉	semidirect
564. #532	C₂²×C₈₉	semidirect
569. #529	C₂²×C₈₉	semidirect
570. #529	C₂²×C₈₉	semidirect
571. C₂×#125	C₂²×C₈₉	semidirect
572. C₂×#125	C₂²×C₈₉	semidirect
575. #525	C₂²×C₈₉	semidirect
576. #525	C₂²×C₈₉	semidirect
578. #520	C₂²×C₈₉	semidirect
579. #520	C₂²×C₈₉	semidirect
580. C₄×#41	C₂²×C₈₉	semidirect
581. C₂²×C₄⋊C₄	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×#3567	2
C₈₉×#3563	2
C₈₉×#3559	2
C₈₉×#3553	2
C₈₉×#3548	2
C₈₉×#3539	2
C₈₉×#3529	2
C₈₉×#3517	2
C₈₉×#3515	2
C₈₉×#3512	2
C₈₉×#3492	2
#63047	89

Subgroups — C89×#63047 #36440895

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#63047 #36440895