Subgroups — C₈₉×#62881 #36440729

Order 22784.

6610 conjugacy classes of subgroups.

The subgroup lattice has 880 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈₉×#3559	C₂	1	8	yes	maximal, complemented
2	C₈₉×#3557	C₂	1	4	yes	maximal, complemented
3	C₈₉×#3554	C₂	1	8	yes	maximal, complemented
4	C₈₉×#3548	C₂	1	4	yes	maximal, complemented
5	C₈₉×#3547	C₂	1	8	yes	maximal, complemented
6	C₈₉×#3536	C₂	1	8	yes	maximal, complemented
7	C₈₉×#3535	C₂	1	8	yes	maximal, complemented
8	C₈₉×#3508	C₂	1	2	yes	maximal, complemented
9	C₈₉×#3506	C₂	1	2	yes	maximal, complemented
10	C₈₉×#3504	C₂	1	2	yes	maximal, complemented
11	C₈₉×#3501	C₂	1	2	yes	maximal, complemented
12	C₈₉×#3494	C₂	1	4	yes	maximal, complemented
13	C₈₉×#3458	C₂	1	1	yes	maximal, characteristic, complemented
14	C₈₉×#3455	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×#540×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
16	#563×C₈₉	C₂²	1	16	yes	complemented
17	#562×C₈₉	C₂²	1	16	yes	complemented
18	#562×C₈₉	C₂²	1	16	yes	complemented
19	#562×C₈₉	C₂²	1	16	yes	complemented
20	#559×C₈₉	C₂²	1	8	yes	complemented
21	#559×C₈₉	C₂²	1	8	yes	complemented
22	#557×C₈₉	C₂²	1	8	yes	complemented
23	#556×C₈₉	C₂²	1	4	yes	complemented
24	#555×C₈₉	C₂²	1	8	yes	complemented
25	#555×C₈₉	C₂²	1	4	yes	complemented
26	#554×C₈₉	C₂²	1	16	yes	—
27	#554×C₈₉	C₂²	1	8	yes	complemented
28	#554×C₈₉	C₂²	1	8	yes	complemented
29	#554×C₈₉	C₂²	1	4	yes	complemented
30	#554×C₈₉	C₂²	1	4	yes	complemented
31	#554×C₈₉	C₂²	1	8	yes	complemented
32	#553×C₈₉	C₂²	1	8	yes	complemented
33	#553×C₈₉	C₂²	1	8	yes	complemented
34	#553×C₈₉	C₂²	1	8	yes	complemented
35	#552×C₈₉	C₂²	1	16	yes	complemented
36	#551×C₈₉	C₂²	1	16	yes	—
37	#550×C₈₉	C₂²	1	4	yes	complemented
38	#550×C₈₉	C₂²	1	8	yes	complemented
39	D₄×Q₈×C₈₉	C₂²	1	4	yes	complemented
40	D₄×Q₈×C₈₉	C₂²	1	4	yes	complemented
41	#548×C₈₉	C₂²	1	16	yes	complemented
42	#547×C₈₉	C₂²	1	8	yes	complemented
43	#547×C₈₉	C₂²	1	4	yes	complemented
44	#547×C₈₉	C₂²	1	16	yes	complemented
45	#547×C₈₉	C₂²	1	16	yes	complemented
46	#546×C₈₉	C₂²	1	16	yes	—
47	#546×C₈₉	C₂²	1	16	yes	—
48	#544×C₈₉	C₂²	1	4	yes	—
49	#544×C₈₉	C₂²	1	4	yes	—
50	#544×C₈₉	C₂²	1	4	yes	complemented
51	#544×C₈₉	C₂²	1	4	yes	complemented
52	#544×C₈₉	C₂²	1	8	yes	complemented
53	#543×C₈₉	C₂²	1	4	yes	—
54	#543×C₈₉	C₂²	1	8	yes	—
55	#542×C₈₉	C₂²	1	4	yes	complemented
56	#542×C₈₉	C₂²	1	8	yes	complemented
57	#542×C₈₉	C₂²	1	16	yes	complemented
58	#542×C₈₉	C₂²	1	16	yes	complemented
59	#541×C₈₉	C₂²	1	2	yes	complemented
60	#540×C₈₉	C₂²	1	8	yes	—
61	#540×C₈₉	C₂²	1	4	yes	—
62	#540×C₈₉	C₂²	1	4	yes	—
63	#540×C₈₉	C₂²	1	2	yes	complemented
64	#540×C₈₉	C₂²	1	8	yes	complemented
65	#540×C₈₉	C₂²	1	4	yes	complemented
66	#540×C₈₉	C₂²	1	4	yes	complemented
67	#539×C₈₉	C₂²	1	4	yes	—
68	#539×C₈₉	C₂²	1	16	yes	complemented
69	#539×C₈₉	C₂²	1	16	yes	complemented
70	#539×C₈₉	C₂²	1	16	yes	complemented
71	#538×C₈₉	C₂²	1	4	yes	—
72	#538×C₈₉	C₂²	1	8	yes	—
73	#537×C₈₉	C₂²	1	16	yes	complemented
74	#537×C₈₉	C₂²	1	16	yes	complemented
75	#536×C₈₉	C₂²	1	16	yes	complemented
76	#535×C₈₉	C₂²	1	4	yes	—
77	#533×C₈₉	C₂²	1	1	yes	characteristic
78	#533×C₈₉	C₂²	1	2	yes	—
79	#533×C₈₉	C₂²	1	2	yes	—
80	#533×C₈₉	C₂²	1	4	yes	complemented
81	#533×C₈₉	C₂²	1	4	yes	complemented
82	#533×C₈₉	C₂²	1	4	yes	complemented
83	#532×C₈₉	C₂²	1	1	yes	characteristic
84	#532×C₈₉	C₂²	1	8	yes	complemented
85	#532×C₈₉	C₂²	1	8	yes	complemented
86	C₂×#127×C₈₉	C₂²	1	1	yes	characteristic
87	#529×C₈₉	C₂²	1	8	yes	complemented
88	#529×C₈₉	C₂²	1	8	yes	complemented
89	C₂×#125×C₈₉	C₂²	1	1	yes	characteristic
90	C₂×#125×C₈₉	C₂²	1	4	yes	complemented
91	#525×C₈₉	C₂²	1	2	yes	—
92	#525×C₈₉	C₂²	1	8	yes	—
93	C₂×#123×C₈₉	C₂²	1	4	yes	—
94	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	8	yes	—
95	C₂×#121×C₈₉	C₂²	1	2	yes	—
96	C₂×#121×C₈₉	C₂²	1	4	yes	—
97	#520×C₈₉	C₂²	1	4	yes	—
98	#518×C₈₉	C₂²	1	4	yes	—
99	C₄×#41×C₈₉	C₂²	1	2	yes	—
100	C₂×C₄×D₄×C₈₉	C₂²	1	2	yes	—
101	C₂×#117×C₈₉	C₂²	1	1	yes	characteristic
102	C₂×#117×C₈₉	C₂²	1	2	yes	—
103	C₂×#41×C₈₉	C₂³	1	2	yes	—
104	C₂×#41×C₈₉	C₂³	1	8	yes	—
105	C₂×#41×C₈₉	C₂³	1	16	yes	—
106	C₂×#41×C₈₉	C₂³	1	16	yes	—
107	C₂²×Q₈×C₈₉	C₂³	1	8	yes	—
108	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
109	C₂²×D₄×C₈₉	C₂³	1	4	yes	—
110	C₂²×D₄×C₈₉	C₂³	1	4	yes	—
111	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
112	C₂³×C₄×C₈₉	C₂³	1	4	yes	—
113	C₄⋊Q₈×C₈₉	C₂³	1	1	yes	characteristic
114	C₄⋊Q₈×C₈₉	C₂³	1	4	yes	—
115	C₄⋊Q₈×C₈₉	C₂³	1	8	yes	—
116	C₄⋊Q₈×C₈₉	C₂³	1	2	yes	—
117	C₄⋊Q₈×C₈₉	C₂³	1	2	yes	—
118	C₄⋊Q₈×C₈₉	C₂³	1	2	yes	—
119	C₄⋊Q₈×C₈₉	C₂³	1	8	yes	—
120	C₄⋊Q₈×C₈₉	C₂³	1	8	yes	—
121	C₄⋊Q₈×C₈₉	C₂³	1	8	yes	—
122	C₄⋊Q₈×C₈₉	C₂³	1	16	yes	—
123	#127×C₈₉	C₂³	1	4	yes	—
124	#127×C₈₉	C₂³	1	4	yes	—
125	#127×C₈₉	C₂³	1	1	yes	characteristic
126	#127×C₈₉	C₂³	1	8	yes	—
127	#126×C₈₉	C₂³	1	8	yes	—
128	#126×C₈₉	C₂³	1	8	yes	—
129	#126×C₈₉	C₂³	1	16	yes	—
130	#126×C₈₉	C₂³	1	16	yes	—
131	#126×C₈₉	C₂³	1	16	yes	—
132	#125×C₈₉	C₂³	1	4	yes	—
133	#125×C₈₉	C₂³	1	4	yes	—
134	#125×C₈₉	C₂³	1	2	yes	—
135	#125×C₈₉	C₂³	1	16	yes	—
136	#125×C₈₉	C₂³	1	8	yes	—
137	#125×C₈₉	C₂³	1	8	yes	—
138	#125×C₈₉	C₂³	1	8	yes	—
139	#125×C₈₉	C₂³	1	2	yes	—
140	#125×C₈₉	C₂³	1	2	yes	—
141	#125×C₈₉	C₂³	1	4	yes	—
142	#125×C₈₉	C₂³	1	8	yes	—
143	#125×C₈₉	C₂³	1	8	yes	—
144	#125×C₈₉	C₂³	1	16	yes	—
145	#124×C₈₉	C₂³	1	8	yes	—
146	#124×C₈₉	C₂³	1	8	yes	—
147	#124×C₈₉	C₂³	1	2	yes	—
148	#124×C₈₉	C₂³	1	16	yes	—
149	#124×C₈₉	C₂³	1	16	yes	—
150	#124×C₈₉	C₂³	1	16	yes	—
151	#124×C₈₉	C₂³	1	16	yes	—
152	#123×C₈₉	C₂³	1	16	yes	—
153	#123×C₈₉	C₂³	1	16	yes	—
154	#123×C₈₉	C₂³	1	16	yes	—
155	#123×C₈₉	C₂³	1	4	yes	—
156	#123×C₈₉	C₂³	1	8	yes	—
157	#123×C₈₉	C₂³	1	8	yes	—
158	#123×C₈₉	C₂³	1	16	yes	—
159	#123×C₈₉	C₂³	1	16	yes	—
160	#123×C₈₉	C₂³	1	16	yes	—
161	#123×C₈₉	C₂³	1	16	yes	—
162	#123×C₈₉	C₂³	1	16	yes	—
163	#123×C₈₉	C₂³	1	16	yes	—
164	#123×C₈₉	C₂³	1	16	yes	—
165	C₂²⋊Q₈×C₈₉	C₂³	1	4	yes	—
166	C₂²⋊Q₈×C₈₉	C₂³	1	4	yes	—
167	C₂²⋊Q₈×C₈₉	C₂³	1	16	yes	—
168	C₂²⋊Q₈×C₈₉	C₂³	1	8	yes	—
169	C₂²⋊Q₈×C₈₉	C₂³	1	8	yes	—
170	C₂²⋊Q₈×C₈₉	C₂³	1	16	yes	—
171	C₂²⋊Q₈×C₈₉	C₂³	1	4	yes	—
172	C₂²⋊Q₈×C₈₉	C₂³	1	4	yes	—
173	C₂²⋊Q₈×C₈₉	C₂³	1	8	yes	—
174	C₂²⋊Q₈×C₈₉	C₂³	1	8	yes	—
175	C₂²⋊Q₈×C₈₉	C₂³	1	8	yes	—
176	C₂²⋊Q₈×C₈₉	C₂³	1	16	yes	—
177	C₂²⋊Q₈×C₈₉	C₂³	1	8	yes	—
178	C₂²⋊Q₈×C₈₉	C₂³	1	8	yes	—
179	C₂²⋊Q₈×C₈₉	C₂³	1	8	yes	—
180	C₂²⋊Q₈×C₈₉	C₂³	1	8	yes	—
181	C₂²⋊Q₈×C₈₉	C₂³	1	16	yes	—
182	C₂²⋊Q₈×C₈₉	C₂³	1	16	yes	—
183	C₂²⋊Q₈×C₈₉	C₂³	1	16	yes	—
184	C₂²⋊Q₈×C₈₉	C₂³	1	16	yes	—
185	C₂²⋊Q₈×C₈₉	C₂³	1	16	yes	—
186	C₂²⋊Q₈×C₈₉	C₂³	1	16	yes	—
187	C₂²⋊Q₈×C₈₉	C₂³	1	16	yes	—
188	#121×C₈₉	C₂³	1	8	yes	—
189	#121×C₈₉	C₂³	1	16	yes	—
190	#121×C₈₉	C₂³	1	16	yes	—
191	#121×C₈₉	C₂³	1	8	yes	—
192	#121×C₈₉	C₂³	1	4	yes	—
193	#121×C₈₉	C₂³	1	4	yes	—
194	#121×C₈₉	C₂³	1	8	yes	—
195	#121×C₈₉	C₂³	1	8	yes	—
196	#121×C₈₉	C₂³	1	8	yes	—
197	#121×C₈₉	C₂³	1	8	yes	—
198	#121×C₈₉	C₂³	1	16	yes	—
199	#121×C₈₉	C₂³	1	16	yes	—
200	#121×C₈₉	C₂³	1	16	yes	—
201	#121×C₈₉	C₂³	1	16	yes	—
202	#121×C₈₉	C₂³	1	16	yes	—
203	#121×C₈₉	C₂³	1	16	yes	—
204	#121×C₈₉	C₂³	1	16	yes	—
205	#120×C₈₉	C₂³	1	16	yes	—
206	#120×C₈₉	C₂³	1	4	yes	—
207	C₄×Q₈×C₈₉	C₂³	1	4	yes	—
208	C₄×Q₈×C₈₉	C₂³	1	8	yes	—
209	C₄×Q₈×C₈₉	C₂³	1	4	yes	—
210	C₄×Q₈×C₈₉	C₂³	1	4	yes	—
211	C₄×Q₈×C₈₉	C₂³	1	4	yes	—
212	C₄×Q₈×C₈₉	C₂³	1	8	yes	—
213	C₄×Q₈×C₈₉	C₂³	1	16	yes	—
214	C₄×D₄×C₈₉	C₂³	1	4	yes	—
215	C₄×D₄×C₈₉	C₂³	1	4	yes	—
216	C₄×D₄×C₈₉	C₂³	1	4	yes	—
217	C₄×D₄×C₈₉	C₂³	1	4	yes	—
218	C₄×D₄×C₈₉	C₂³	1	8	yes	—
219	C₄×D₄×C₈₉	C₂³	1	4	yes	—
220	C₄×D₄×C₈₉	C₂³	1	8	yes	—
221	C₄×D₄×C₈₉	C₂³	1	8	yes	—
222	C₄×D₄×C₈₉	C₂³	1	8	yes	—
223	C₄×D₄×C₈₉	C₂³	1	8	yes	—
224	C₄×D₄×C₈₉	C₂³	1	16	yes	—
225	C₄×D₄×C₈₉	C₂³	1	8	yes	—
226	C₄×D₄×C₈₉	C₂³	1	8	yes	—
227	C₄×D₄×C₈₉	C₂³	1	16	yes	—
228	C₄×D₄×C₈₉	C₂³	1	4	yes	—
229	C₄×D₄×C₈₉	C₂³	1	16	yes	—
230	C₄×D₄×C₈₉	C₂³	1	16	yes	—
231	C₄×D₄×C₈₉	C₂³	1	16	yes	—
232	#117×C₈₉	C₂³	1	4	yes	—
233	#117×C₈₉	C₂³	1	4	yes	—
234	#117×C₈₉	C₂³	1	2	yes	—
235	#117×C₈₉	C₂³	1	2	yes	—
236	#117×C₈₉	C₂³	1	4	yes	—
237	#117×C₈₉	C₂³	1	4	yes	—
238	#117×C₈₉	C₂³	1	2	yes	—
239	#117×C₈₉	C₂³	1	2	yes	—
240	#117×C₈₉	C₂³	1	2	yes	—
241	#117×C₈₉	C₂³	1	4	yes	—
242	#117×C₈₉	C₂³	1	8	yes	—
243	#117×C₈₉	C₂³	1	8	yes	—
244	#117×C₈₉	C₂³	1	16	yes	—
245	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
246	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
247	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
248	C₂×C₄⋊C₄×C₈₉	C₂³	1	8	yes	—
249	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
250	C₂×C₄⋊C₄×C₈₉	C₂³	1	16	yes	—
251	C₂×C₄⋊C₄×C₈₉	C₂³	1	8	yes	—
252	C₂×C₄⋊C₄×C₈₉	C₂³	1	16	yes	—
253	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
254	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
255	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
256	C₂×C₂²⋊C₄×C₈₉	C₂³	1	16	yes	—
257	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
258	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
259	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
260	C₂×C₄²×C₈₉	C₂³	1	4	yes	—
261	C₂×C₄²×C₈₉	C₂³	1	4	yes	—
262	C₂⁴×C₈₉	C₂⁴	1	1	yes	characteristic
263	C₂⁴×C₈₉	C₂⁴	1	4	yes	—
264	#41×C₈₉	—	2	8	no	—
265	#41×C₈₉	—	8	8	no	—
266	#41×C₈₉	—	8	16	no	—
267	#41×C₈₉	—	8	16	no	—
268	C₂×Q₈×C₈₉	—	8	8	no	—
269	C₂×Q₈×C₈₉	C₂⁴	1	2	yes	—
270	C₂×Q₈×C₈₉	C₂⁴	1	4	yes	—
271	C₂×Q₈×C₈₉	C₂⁴	1	4	yes	—
272	C₂×Q₈×C₈₉	C₂⁴	1	16	yes	—
273	C₂×Q₈×C₈₉	C₂⁴	1	4	yes	—
274	C₂×Q₈×C₈₉	C₂⁴	1	8	yes	—
275	C₂×D₄×C₈₉	—	2	8	no	—
276	C₂×D₄×C₈₉	—	8	4	no	—
277	C₂×D₄×C₈₉	—	8	4	no	—
278	C₂×D₄×C₈₉	C₂⁴	1	4	yes	—
279	C₂×D₄×C₈₉	C₂⁴	1	4	yes	—
280	C₂×D₄×C₈₉	C₂⁴	1	4	yes	—
281	C₂×D₄×C₈₉	C₂⁴	1	2	yes	—
282	C₂×D₄×C₈₉	C₂⁴	1	8	yes	—
283	C₂×D₄×C₈₉	C₂⁴	1	16	yes	—
284	C₂×D₄×C₈₉	C₂⁴	1	16	yes	—
285	C₂×D₄×C₈₉	C₂⁴	1	16	yes	—
286	C₂×D₄×C₈₉	C₂⁴	1	4	yes	—
287	C₂×D₄×C₈₉	C₂⁴	1	16	yes	—
288	C₂²×C₄×C₈₉	—	2	4	no	—
289	C₂²×C₄×C₈₉	—	8	4	no	—
290	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
291	C₂²×C₄×C₈₉	C₂⁴	1	4	yes	—
292	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
293	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
294	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
295	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
296	C₂²×C₄×C₈₉	C₂⁴	1	8	yes	—
297	C₂²×C₄×C₈₉	C₂⁴	1	8	yes	—
298	C₂²×C₄×C₈₉	C₂⁴	1	4	yes	—
299	C₂²×C₄×C₈₉	C₂⁴	1	16	yes	—
300	C₂²×C₄×C₈₉	C₂⁴	1	16	yes	—
301	C₂²×C₄×C₈₉	C₂⁴	1	16	yes	—
302	C₂²×C₄×C₈₉	C₂⁴	1	8	yes	—
303	C₂²×C₄×C₈₉	C₂⁴	1	8	yes	—
304	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
305	C₄⋊C₄×C₈₉	C₂⁴	1	4	yes	—
306	C₄⋊C₄×C₈₉	C₂⁴	1	4	yes	—
307	C₄⋊C₄×C₈₉	C₂⁴	1	16	yes	—
308	C₄⋊C₄×C₈₉	C₂⁴	1	16	yes	—
309	C₄⋊C₄×C₈₉	C₂⁴	1	8	yes	—
310	C₄⋊C₄×C₈₉	C₂⁴	1	16	yes	—
311	C₄⋊C₄×C₈₉	C₂⁴	1	8	yes	—
312	C₄⋊C₄×C₈₉	C₂⁴	1	8	yes	—
313	C₄⋊C₄×C₈₉	C₂⁴	1	4	yes	—
314	C₄⋊C₄×C₈₉	C₂⁴	1	4	yes	—
315	C₄⋊C₄×C₈₉	C₂⁴	1	4	yes	—
316	C₄⋊C₄×C₈₉	C₂⁴	1	8	yes	—
317	C₄⋊C₄×C₈₉	C₂⁴	1	4	yes	—
318	C₄⋊C₄×C₈₉	C₂⁴	1	4	yes	—
319	C₄⋊C₄×C₈₉	C₂⁴	1	16	yes	—
320	C₄⋊C₄×C₈₉	C₂⁴	1	4	yes	—
321	C₄⋊C₄×C₈₉	C₂⁴	1	16	yes	—
322	C₄⋊C₄×C₈₉	C₂⁴	1	4	yes	—
323	C₄⋊C₄×C₈₉	C₂⁴	1	8	yes	—
324	C₄⋊C₄×C₈₉	C₂⁴	1	4	yes	—
325	C₄⋊C₄×C₈₉	C₂⁴	1	4	yes	—
326	C₄⋊C₄×C₈₉	C₂⁴	1	8	yes	—
327	C₄⋊C₄×C₈₉	C₂⁴	1	8	yes	—
328	C₄⋊C₄×C₈₉	C₂⁴	1	8	yes	—
329	C₄⋊C₄×C₈₉	C₂⁴	1	8	yes	—
330	C₂²⋊C₄×C₈₉	C₂⁴	1	4	yes	—
331	C₂²⋊C₄×C₈₉	C₂⁴	1	8	yes	—
332	C₂²⋊C₄×C₈₉	C₂⁴	1	4	yes	—
333	C₂²⋊C₄×C₈₉	C₂⁴	1	4	yes	—
334	C₂²⋊C₄×C₈₉	C₂⁴	1	4	yes	—
335	C₂²⋊C₄×C₈₉	C₂⁴	1	4	yes	—
336	C₂²⋊C₄×C₈₉	C₂⁴	1	16	yes	—
337	C₂²⋊C₄×C₈₉	C₂⁴	1	8	yes	—
338	C₂²⋊C₄×C₈₉	C₂⁴	1	16	yes	—
339	C₂²⋊C₄×C₈₉	C₂⁴	1	16	yes	—
340	C₂²⋊C₄×C₈₉	C₂⁴	1	8	yes	—
341	C₂²⋊C₄×C₈₉	C₂⁴	1	16	yes	—
342	C₂²⋊C₄×C₈₉	C₂⁴	1	8	yes	—
343	C₂²⋊C₄×C₈₉	C₂⁴	1	16	yes	—
344	C₂²⋊C₄×C₈₉	C₂⁴	1	16	yes	—
345	C₂²⋊C₄×C₈₉	C₂⁴	1	8	yes	—
346	C₂²⋊C₄×C₈₉	C₂⁴	1	8	yes	—
347	C₂²⋊C₄×C₈₉	C₂⁴	1	8	yes	—
348	C₄²×C₈₉	C₂⁴	1	2	yes	—
349	C₄²×C₈₉	C₂⁴	1	4	yes	—
350	C₄²×C₈₉	C₂⁴	1	2	yes	—
351	C₄²×C₈₉	C₂⁴	1	4	yes	—
352	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
353	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
354	C₄²×C₈₉	C₂⁴	1	4	yes	—
355	C₄²×C₈₉	C₂⁴	1	8	yes	—
356	C₄²×C₈₉	C₂⁴	1	2	yes	—
357	C₄²×C₈₉	C₂⁴	1	8	yes	—
358	C₄²×C₈₉	C₂⁴	1	16	yes	—
359	C₂³×C₈₉	—	2	2	no	—
360	C₂³×C₈₉	—	2	8	no	—
361	C₂³×C₈₉	—	4	4	no	—
362	C₂³×C₈₉	—	4	2	no	—
363	C₂³×C₈₉	—	4	4	no	—
364	C₂³×C₈₉	C₂⁵	1	2	yes	—
365	C₂³×C₈₉	C₂⁵	1	8	yes	—
366	C₂³×C₈₉	C₂⁵	1	4	yes	—
367	C₂³×C₈₉	C₂⁵	1	1	yes	characteristic
368	Q₈×C₈₉	—	2	4	no	—
369	Q₈×C₈₉	—	4	4	no	—
370	Q₈×C₈₉	—	4	4	no	—
371	Q₈×C₈₉	—	4	16	no	—
372	Q₈×C₈₉	—	4	4	no	—
373	Q₈×C₈₉	—	4	8	no	—
374	D₄×C₈₉	—	2	8	no	—
375	D₄×C₈₉	—	2	8	no	—
376	D₄×C₈₉	—	2	8	no	—
377	D₄×C₈₉	—	2	4	no	—
378	D₄×C₈₉	—	4	16	no	—
379	D₄×C₈₉	—	4	16	no	—
380	D₄×C₈₉	—	4	16	no	—
381	D₄×C₈₉	—	4	4	no	—
382	D₄×C₈₉	—	4	8	no	—
383	D₄×C₈₉	—	4	16	no	—
384	C₂×C₄×C₈₉	—	2	2	no	—
385	C₂×C₄×C₈₉	—	2	4	no	—
386	C₂×C₄×C₈₉	—	2	4	no	—
387	C₂×C₄×C₈₉	—	2	8	no	—
388	C₂×C₄×C₈₉	—	4	2	no	—
389	C₂×C₄×C₈₉	—	4	4	no	—
390	C₂×C₄×C₈₉	—	4	8	no	—
391	C₂×C₄×C₈₉	—	4	8	no	—
392	C₂×C₄×C₈₉	—	4	2	no	—
393	C₂×C₄×C₈₉	—	4	16	no	—
394	C₂×C₄×C₈₉	—	4	16	no	—
395	C₂×C₄×C₈₉	—	4	16	no	—
396	C₂×C₄×C₈₉	—	4	8	no	—
397	C₂×C₄×C₈₉	—	4	8	no	—
398	C₂×C₄×C₈₉	2₋¹⁺⁴	1	4	yes	—
399	C₂×C₄×C₈₉	C₂⁵	1	4	yes	—
400	C₂×C₄×C₈₉	C₂⁵	1	2	yes	—
401	C₂×C₄×C₈₉	C₂⁵	1	8	yes	—
402	C₂×C₄×C₈₉	C₂⁵	1	4	yes	—
403	C₂×C₄×C₈₉	C₂⁵	1	2	yes	—
404	C₂×C₄×C₈₉	C₂⁵	1	8	yes	—
405	C₂×C₄×C₈₉	C₂⁵	1	2	yes	—
406	C₂×C₄×C₈₉	C₂⁵	1	8	yes	—
407	C₂×C₄×C₈₉	C₂⁵	1	8	yes	—
408	C₂×C₄×C₈₉	C₂⁵	1	1	yes	characteristic
409	C₂×C₄×C₈₉	C₂⁵	1	1	yes	characteristic
410	C₂²×C₈₉	—	2	2	no	—
411	C₂²×C₈₉	—	2	2	no	—
412	C₂²×C₈₉	—	2	4	no	—
413	C₂²×C₈₉	—	2	8	no	—
414	C₂²×C₈₉	—	2	8	no	—
415	C₂²×C₈₉	—	2	8	no	—
416	C₂²×C₈₉	—	2	4	no	—
417	C₂²×C₈₉	—	2	8	no	—
418	C₂²×C₈₉	—	8	2	no	—
419	C₂²×C₈₉	—	8	8	no	—
420	C₂²×C₈₉	C₂×2₋¹⁺⁴	1	2	yes	—
421	C₂²×C₈₉	C₂⁶	1	1	yes	characteristic
422	C₄×C₈₉	—	2	2	no	—
423	C₄×C₈₉	—	2	4	no	—
424	C₄×C₈₉	—	2	2	no	—
425	C₄×C₈₉	—	2	8	no	—
426	C₄×C₈₉	—	2	8	no	—
427	C₄×C₈₉	—	2	8	no	—
428	C₄×C₈₉	—	2	2	no	—
429	C₄×C₈₉	—	2	4	no	—
430	C₄×C₈₉	—	2	8	no	—
431	C₄×C₈₉	C₂×2₋¹⁺⁴	1	2	yes	—
432	C₄×C₈₉	C₂×2₋¹⁺⁴	1	2	yes	—
433	#62881	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
434	C₂×C₈₉	—	2	2	no	—
435	C₂×C₈₉	—	4	4	no	—
436	C₂×C₈₉	—	4	2	no	—
437	C₂×C₈₉	—	4	8	no	—
438	C₂×C₈₉	C₂²×2₋¹⁺⁴	1	1	yes	characteristic
439	C₂×C₈₉	H(7,𝔽₂)	1	2	yes	—
440	#3559	C₂×C₈₉	1	8	yes	complemented
441	#3557	C₂×C₈₉	1	4	yes	complemented
442	#3554	C₂×C₈₉	1	8	yes	complemented
443	#3548	C₂×C₈₉	1	4	yes	complemented
444	#3547	C₂×C₈₉	1	8	yes	complemented
445	#3536	C₂×C₈₉	1	8	yes	complemented
446	#3535	C₂×C₈₉	1	8	yes	complemented
447	#3508	C₂×C₈₉	1	2	yes	complemented
448	#3506	C₂×C₈₉	1	2	yes	complemented
449	#3504	C₂×C₈₉	1	2	yes	complemented
450	#3501	C₂×C₈₉	1	2	yes	complemented
451	#3494	C₂×C₈₉	1	4	yes	complemented
452	#3458	C₂×C₈₉	1	1	yes	characteristic, complemented
453	#3455	C₂×C₈₉	1	1	yes	characteristic, complemented
454	C₂×#540	C₂×C₈₉	1	1	yes	characteristic, complemented
455	C₈₉	#62881	1	1	yes	characteristic, direct product factor, Sylow
456	#563	C₂²×C₈₉	1	16	yes	complemented
457	#562	C₂²×C₈₉	1	16	yes	complemented
458	#562	C₂²×C₈₉	1	16	yes	complemented
459	#562	C₂²×C₈₉	1	16	yes	complemented
460	#559	C₂²×C₈₉	1	8	yes	complemented
461	#559	C₂²×C₈₉	1	8	yes	complemented
462	#557	C₂²×C₈₉	1	8	yes	complemented
463	#556	C₂²×C₈₉	1	4	yes	complemented
464	#555	C₂²×C₈₉	1	8	yes	complemented
465	#555	C₂²×C₈₉	1	4	yes	complemented
466	#554	C₂²×C₈₉	1	16	yes	—
467	#554	C₂²×C₈₉	1	8	yes	complemented
468	#554	C₂²×C₈₉	1	8	yes	complemented
469	#554	C₂²×C₈₉	1	4	yes	complemented
470	#554	C₂²×C₈₉	1	4	yes	complemented
471	#554	C₂²×C₈₉	1	8	yes	complemented
472	#553	C₂²×C₈₉	1	8	yes	complemented
473	#553	C₂²×C₈₉	1	8	yes	complemented
474	#553	C₂²×C₈₉	1	8	yes	complemented
475	#552	C₂²×C₈₉	1	16	yes	complemented
476	#551	C₂²×C₈₉	1	16	yes	—
477	#550	C₂²×C₈₉	1	4	yes	complemented
478	#550	C₂²×C₈₉	1	8	yes	complemented
479	D₄×Q₈	C₂²×C₈₉	1	4	yes	complemented
480	D₄×Q₈	C₂²×C₈₉	1	4	yes	complemented
481	#548	C₂²×C₈₉	1	16	yes	complemented
482	#547	C₂²×C₈₉	1	8	yes	complemented
483	#547	C₂²×C₈₉	1	4	yes	complemented
484	#547	C₂²×C₈₉	1	16	yes	complemented
485	#547	C₂²×C₈₉	1	16	yes	complemented
486	#546	C₂²×C₈₉	1	16	yes	—
487	#546	C₂²×C₈₉	1	16	yes	—
488	#544	C₂²×C₈₉	1	4	yes	—
489	#544	C₂²×C₈₉	1	4	yes	—
490	#544	C₂²×C₈₉	1	4	yes	complemented
491	#544	C₂²×C₈₉	1	4	yes	complemented
492	#544	C₂²×C₈₉	1	8	yes	complemented
493	#543	C₂²×C₈₉	1	4	yes	—
494	#543	C₂²×C₈₉	1	8	yes	—
495	#542	C₂²×C₈₉	1	4	yes	complemented
496	#542	C₂²×C₈₉	1	8	yes	complemented
497	#542	C₂²×C₈₉	1	16	yes	complemented
498	#542	C₂²×C₈₉	1	16	yes	complemented
499	#541	C₂²×C₈₉	1	2	yes	complemented
500	#540	C₂²×C₈₉	1	8	yes	—
501	#540	C₂²×C₈₉	1	4	yes	—
502	#540	C₂²×C₈₉	1	4	yes	—
503	#540	C₂²×C₈₉	1	2	yes	complemented
504	#540	C₂²×C₈₉	1	8	yes	complemented
505	#540	C₂²×C₈₉	1	4	yes	complemented
506	#540	C₂²×C₈₉	1	4	yes	complemented
507	#539	C₂²×C₈₉	1	4	yes	—
508	#539	C₂²×C₈₉	1	16	yes	complemented
509	#539	C₂²×C₈₉	1	16	yes	complemented
510	#539	C₂²×C₈₉	1	16	yes	complemented
511	#538	C₂²×C₈₉	1	4	yes	—
512	#538	C₂²×C₈₉	1	8	yes	—
513	#537	C₂²×C₈₉	1	16	yes	complemented
514	#537	C₂²×C₈₉	1	16	yes	complemented
515	#536	C₂²×C₈₉	1	16	yes	complemented
516	#535	C₂²×C₈₉	1	4	yes	—
517	#533	C₂²×C₈₉	1	1	yes	characteristic
518	#533	C₂²×C₈₉	1	2	yes	—
519	#533	C₂²×C₈₉	1	2	yes	—
520	#533	C₂²×C₈₉	1	4	yes	complemented
521	#533	C₂²×C₈₉	1	4	yes	complemented
522	#533	C₂²×C₈₉	1	4	yes	complemented
523	#532	C₂²×C₈₉	1	1	yes	characteristic
524	#532	C₂²×C₈₉	1	8	yes	complemented
525	#532	C₂²×C₈₉	1	8	yes	complemented
526	C₂×#127	C₂²×C₈₉	1	1	yes	characteristic
527	#529	C₂²×C₈₉	1	8	yes	complemented
528	#529	C₂²×C₈₉	1	8	yes	complemented
529	C₂×#125	C₂²×C₈₉	1	1	yes	characteristic
530	C₂×#125	C₂²×C₈₉	1	4	yes	complemented
531	#525	C₂²×C₈₉	1	2	yes	—
532	#525	C₂²×C₈₉	1	8	yes	—
533	C₂×#123	C₂²×C₈₉	1	4	yes	—
534	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	8	yes	—
535	C₂×#121	C₂²×C₈₉	1	2	yes	—
536	C₂×#121	C₂²×C₈₉	1	4	yes	—
537	#520	C₂²×C₈₉	1	4	yes	—
538	#518	C₂²×C₈₉	1	4	yes	—
539	C₄×#41	C₂²×C₈₉	1	2	yes	—
540	C₂×C₄×D₄	C₂²×C₈₉	1	2	yes	—
541	C₂×#117	C₂²×C₈₉	1	1	yes	characteristic
542	C₂×#117	C₂²×C₈₉	1	2	yes	—
543	C₂×#41	C₂³×C₈₉	1	2	yes	—
544	C₂×#41	C₂³×C₈₉	1	8	yes	—
545	C₂×#41	C₂³×C₈₉	1	16	yes	—
546	C₂×#41	C₂³×C₈₉	1	16	yes	—
547	C₂²×Q₈	C₂³×C₈₉	1	8	yes	—
548	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
549	C₂²×D₄	C₂³×C₈₉	1	4	yes	—
550	C₂²×D₄	C₂³×C₈₉	1	4	yes	—
551	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
552	C₂³×C₄	C₂³×C₈₉	1	4	yes	—
553	C₄⋊Q₈	C₂³×C₈₉	1	1	yes	characteristic
554	C₄⋊Q₈	C₂³×C₈₉	1	4	yes	—
555	C₄⋊Q₈	C₂³×C₈₉	1	8	yes	—
556	C₄⋊Q₈	C₂³×C₈₉	1	2	yes	—
557	C₄⋊Q₈	C₂³×C₈₉	1	2	yes	—
558	C₄⋊Q₈	C₂³×C₈₉	1	2	yes	—
559	C₄⋊Q₈	C₂³×C₈₉	1	8	yes	—
560	C₄⋊Q₈	C₂³×C₈₉	1	8	yes	—
561	C₄⋊Q₈	C₂³×C₈₉	1	8	yes	—
562	C₄⋊Q₈	C₂³×C₈₉	1	16	yes	—
563	#127	C₂³×C₈₉	1	4	yes	—
564	#127	C₂³×C₈₉	1	4	yes	—
565	#127	C₂³×C₈₉	1	1	yes	characteristic
566	#127	C₂³×C₈₉	1	8	yes	—
567	#126	C₂³×C₈₉	1	8	yes	—
568	#126	C₂³×C₈₉	1	8	yes	—
569	#126	C₂³×C₈₉	1	16	yes	—
570	#126	C₂³×C₈₉	1	16	yes	—
571	#126	C₂³×C₈₉	1	16	yes	—
572	#125	C₂³×C₈₉	1	4	yes	—
573	#125	C₂³×C₈₉	1	4	yes	—
574	#125	C₂³×C₈₉	1	2	yes	—
575	#125	C₂³×C₈₉	1	16	yes	—
576	#125	C₂³×C₈₉	1	8	yes	—
577	#125	C₂³×C₈₉	1	8	yes	—
578	#125	C₂³×C₈₉	1	8	yes	—
579	#125	C₂³×C₈₉	1	2	yes	—
580	#125	C₂³×C₈₉	1	2	yes	—
581	#125	C₂³×C₈₉	1	4	yes	—
582	#125	C₂³×C₈₉	1	8	yes	—
583	#125	C₂³×C₈₉	1	8	yes	—
584	#125	C₂³×C₈₉	1	16	yes	—
585	#124	C₂³×C₈₉	1	8	yes	—
586	#124	C₂³×C₈₉	1	8	yes	—
587	#124	C₂³×C₈₉	1	2	yes	—
588	#124	C₂³×C₈₉	1	16	yes	—
589	#124	C₂³×C₈₉	1	16	yes	—
590	#124	C₂³×C₈₉	1	16	yes	—
591	#124	C₂³×C₈₉	1	16	yes	—
592	#123	C₂³×C₈₉	1	16	yes	—
593	#123	C₂³×C₈₉	1	16	yes	—
594	#123	C₂³×C₈₉	1	16	yes	—
595	#123	C₂³×C₈₉	1	4	yes	—
596	#123	C₂³×C₈₉	1	8	yes	—
597	#123	C₂³×C₈₉	1	8	yes	—
598	#123	C₂³×C₈₉	1	16	yes	—
599	#123	C₂³×C₈₉	1	16	yes	—
600	#123	C₂³×C₈₉	1	16	yes	—
601	#123	C₂³×C₈₉	1	16	yes	—
602	#123	C₂³×C₈₉	1	16	yes	—
603	#123	C₂³×C₈₉	1	16	yes	—
604	#123	C₂³×C₈₉	1	16	yes	—
605	C₂²⋊Q₈	C₂³×C₈₉	1	4	yes	—
606	C₂²⋊Q₈	C₂³×C₈₉	1	4	yes	—
607	C₂²⋊Q₈	C₂³×C₈₉	1	16	yes	—
608	C₂²⋊Q₈	C₂³×C₈₉	1	8	yes	—
609	C₂²⋊Q₈	C₂³×C₈₉	1	8	yes	—
610	C₂²⋊Q₈	C₂³×C₈₉	1	16	yes	—
611	C₂²⋊Q₈	C₂³×C₈₉	1	4	yes	—
612	C₂²⋊Q₈	C₂³×C₈₉	1	4	yes	—
613	C₂²⋊Q₈	C₂³×C₈₉	1	8	yes	—
614	C₂²⋊Q₈	C₂³×C₈₉	1	8	yes	—
615	C₂²⋊Q₈	C₂³×C₈₉	1	8	yes	—
616	C₂²⋊Q₈	C₂³×C₈₉	1	16	yes	—
617	C₂²⋊Q₈	C₂³×C₈₉	1	8	yes	—
618	C₂²⋊Q₈	C₂³×C₈₉	1	8	yes	—
619	C₂²⋊Q₈	C₂³×C₈₉	1	8	yes	—
620	C₂²⋊Q₈	C₂³×C₈₉	1	8	yes	—
621	C₂²⋊Q₈	C₂³×C₈₉	1	16	yes	—
622	C₂²⋊Q₈	C₂³×C₈₉	1	16	yes	—
623	C₂²⋊Q₈	C₂³×C₈₉	1	16	yes	—
624	C₂²⋊Q₈	C₂³×C₈₉	1	16	yes	—
625	C₂²⋊Q₈	C₂³×C₈₉	1	16	yes	—
626	C₂²⋊Q₈	C₂³×C₈₉	1	16	yes	—
627	C₂²⋊Q₈	C₂³×C₈₉	1	16	yes	—
628	#121	C₂³×C₈₉	1	8	yes	—
629	#121	C₂³×C₈₉	1	16	yes	—
630	#121	C₂³×C₈₉	1	16	yes	—
631	#121	C₂³×C₈₉	1	8	yes	—
632	#121	C₂³×C₈₉	1	4	yes	—
633	#121	C₂³×C₈₉	1	4	yes	—
634	#121	C₂³×C₈₉	1	8	yes	—
635	#121	C₂³×C₈₉	1	8	yes	—
636	#121	C₂³×C₈₉	1	8	yes	—
637	#121	C₂³×C₈₉	1	8	yes	—
638	#121	C₂³×C₈₉	1	16	yes	—
639	#121	C₂³×C₈₉	1	16	yes	—
640	#121	C₂³×C₈₉	1	16	yes	—
641	#121	C₂³×C₈₉	1	16	yes	—
642	#121	C₂³×C₈₉	1	16	yes	—
643	#121	C₂³×C₈₉	1	16	yes	—
644	#121	C₂³×C₈₉	1	16	yes	—
645	#120	C₂³×C₈₉	1	16	yes	—
646	#120	C₂³×C₈₉	1	4	yes	—
647	C₄×Q₈	C₂³×C₈₉	1	4	yes	—
648	C₄×Q₈	C₂³×C₈₉	1	8	yes	—
649	C₄×Q₈	C₂³×C₈₉	1	4	yes	—
650	C₄×Q₈	C₂³×C₈₉	1	4	yes	—
651	C₄×Q₈	C₂³×C₈₉	1	4	yes	—
652	C₄×Q₈	C₂³×C₈₉	1	8	yes	—
653	C₄×Q₈	C₂³×C₈₉	1	16	yes	—
654	C₄×D₄	C₂³×C₈₉	1	4	yes	—
655	C₄×D₄	C₂³×C₈₉	1	4	yes	—
656	C₄×D₄	C₂³×C₈₉	1	4	yes	—
657	C₄×D₄	C₂³×C₈₉	1	4	yes	—
658	C₄×D₄	C₂³×C₈₉	1	8	yes	—
659	C₄×D₄	C₂³×C₈₉	1	4	yes	—
660	C₄×D₄	C₂³×C₈₉	1	8	yes	—
661	C₄×D₄	C₂³×C₈₉	1	8	yes	—
662	C₄×D₄	C₂³×C₈₉	1	8	yes	—
663	C₄×D₄	C₂³×C₈₉	1	8	yes	—
664	C₄×D₄	C₂³×C₈₉	1	16	yes	—
665	C₄×D₄	C₂³×C₈₉	1	8	yes	—
666	C₄×D₄	C₂³×C₈₉	1	8	yes	—
667	C₄×D₄	C₂³×C₈₉	1	16	yes	—
668	C₄×D₄	C₂³×C₈₉	1	4	yes	—
669	C₄×D₄	C₂³×C₈₉	1	16	yes	—
670	C₄×D₄	C₂³×C₈₉	1	16	yes	—
671	C₄×D₄	C₂³×C₈₉	1	16	yes	—
672	#117	C₂³×C₈₉	1	4	yes	—
673	#117	C₂³×C₈₉	1	4	yes	—
674	#117	C₂³×C₈₉	1	2	yes	—
675	#117	C₂³×C₈₉	1	2	yes	—
676	#117	C₂³×C₈₉	1	4	yes	—
677	#117	C₂³×C₈₉	1	4	yes	—
678	#117	C₂³×C₈₉	1	2	yes	—
679	#117	C₂³×C₈₉	1	2	yes	—
680	#117	C₂³×C₈₉	1	2	yes	—
681	#117	C₂³×C₈₉	1	4	yes	—
682	#117	C₂³×C₈₉	1	8	yes	—
683	#117	C₂³×C₈₉	1	8	yes	—
684	#117	C₂³×C₈₉	1	16	yes	—
685	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
686	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
687	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
688	C₂×C₄⋊C₄	C₂³×C₈₉	1	8	yes	—
689	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
690	C₂×C₄⋊C₄	C₂³×C₈₉	1	16	yes	—
691	C₂×C₄⋊C₄	C₂³×C₈₉	1	8	yes	—
692	C₂×C₄⋊C₄	C₂³×C₈₉	1	16	yes	—
693	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
694	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
695	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
696	C₂×C₂²⋊C₄	C₂³×C₈₉	1	16	yes	—
697	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
698	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
699	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
700	C₂×C₄²	C₂³×C₈₉	1	4	yes	—
701	C₂×C₄²	C₂³×C₈₉	1	4	yes	—
702	C₂⁴	C₂⁴×C₈₉	1	1	yes	characteristic
703	C₂⁴	C₂⁴×C₈₉	1	4	yes	—
704	#41	—	2	8	no	—
705	#41	—	8	8	no	—
706	#41	—	8	16	no	—
707	#41	—	8	16	no	—
708	C₂×Q₈	—	8	8	no	—
709	C₂×Q₈	C₂⁴×C₈₉	1	2	yes	—
710	C₂×Q₈	C₂⁴×C₈₉	1	4	yes	—
711	C₂×Q₈	C₂⁴×C₈₉	1	4	yes	—
712	C₂×Q₈	C₂⁴×C₈₉	1	16	yes	—
713	C₂×Q₈	C₂⁴×C₈₉	1	4	yes	—
714	C₂×Q₈	C₂⁴×C₈₉	1	8	yes	—
715	C₂×D₄	—	2	8	no	—
716	C₂×D₄	—	8	4	no	—
717	C₂×D₄	—	8	4	no	—
718	C₂×D₄	C₂⁴×C₈₉	1	4	yes	—
719	C₂×D₄	C₂⁴×C₈₉	1	4	yes	—
720	C₂×D₄	C₂⁴×C₈₉	1	4	yes	—
721	C₂×D₄	C₂⁴×C₈₉	1	2	yes	—
722	C₂×D₄	C₂⁴×C₈₉	1	8	yes	—
723	C₂×D₄	C₂⁴×C₈₉	1	16	yes	—
724	C₂×D₄	C₂⁴×C₈₉	1	16	yes	—
725	C₂×D₄	C₂⁴×C₈₉	1	16	yes	—
726	C₂×D₄	C₂⁴×C₈₉	1	4	yes	—
727	C₂×D₄	C₂⁴×C₈₉	1	16	yes	—
728	C₂²×C₄	—	2	4	no	—
729	C₂²×C₄	—	8	4	no	—
730	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
731	C₂²×C₄	C₂⁴×C₈₉	1	4	yes	—
732	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
733	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
734	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
735	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
736	C₂²×C₄	C₂⁴×C₈₉	1	8	yes	—
737	C₂²×C₄	C₂⁴×C₈₉	1	8	yes	—
738	C₂²×C₄	C₂⁴×C₈₉	1	4	yes	—
739	C₂²×C₄	C₂⁴×C₈₉	1	16	yes	—
740	C₂²×C₄	C₂⁴×C₈₉	1	16	yes	—
741	C₂²×C₄	C₂⁴×C₈₉	1	16	yes	—
742	C₂²×C₄	C₂⁴×C₈₉	1	8	yes	—
743	C₂²×C₄	C₂⁴×C₈₉	1	8	yes	—
744	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
745	C₄⋊C₄	C₂⁴×C₈₉	1	4	yes	—
746	C₄⋊C₄	C₂⁴×C₈₉	1	4	yes	—
747	C₄⋊C₄	C₂⁴×C₈₉	1	16	yes	—
748	C₄⋊C₄	C₂⁴×C₈₉	1	16	yes	—
749	C₄⋊C₄	C₂⁴×C₈₉	1	8	yes	—
750	C₄⋊C₄	C₂⁴×C₈₉	1	16	yes	—
751	C₄⋊C₄	C₂⁴×C₈₉	1	8	yes	—
752	C₄⋊C₄	C₂⁴×C₈₉	1	8	yes	—
753	C₄⋊C₄	C₂⁴×C₈₉	1	4	yes	—
754	C₄⋊C₄	C₂⁴×C₈₉	1	4	yes	—
755	C₄⋊C₄	C₂⁴×C₈₉	1	4	yes	—
756	C₄⋊C₄	C₂⁴×C₈₉	1	8	yes	—
757	C₄⋊C₄	C₂⁴×C₈₉	1	4	yes	—
758	C₄⋊C₄	C₂⁴×C₈₉	1	4	yes	—
759	C₄⋊C₄	C₂⁴×C₈₉	1	16	yes	—
760	C₄⋊C₄	C₂⁴×C₈₉	1	4	yes	—
761	C₄⋊C₄	C₂⁴×C₈₉	1	16	yes	—
762	C₄⋊C₄	C₂⁴×C₈₉	1	4	yes	—
763	C₄⋊C₄	C₂⁴×C₈₉	1	8	yes	—
764	C₄⋊C₄	C₂⁴×C₈₉	1	4	yes	—
765	C₄⋊C₄	C₂⁴×C₈₉	1	4	yes	—
766	C₄⋊C₄	C₂⁴×C₈₉	1	8	yes	—
767	C₄⋊C₄	C₂⁴×C₈₉	1	8	yes	—
768	C₄⋊C₄	C₂⁴×C₈₉	1	8	yes	—
769	C₄⋊C₄	C₂⁴×C₈₉	1	8	yes	—
770	C₂²⋊C₄	C₂⁴×C₈₉	1	4	yes	—
771	C₂²⋊C₄	C₂⁴×C₈₉	1	8	yes	—
772	C₂²⋊C₄	C₂⁴×C₈₉	1	4	yes	—
773	C₂²⋊C₄	C₂⁴×C₈₉	1	4	yes	—
774	C₂²⋊C₄	C₂⁴×C₈₉	1	4	yes	—
775	C₂²⋊C₄	C₂⁴×C₈₉	1	4	yes	—
776	C₂²⋊C₄	C₂⁴×C₈₉	1	16	yes	—
777	C₂²⋊C₄	C₂⁴×C₈₉	1	8	yes	—
778	C₂²⋊C₄	C₂⁴×C₈₉	1	16	yes	—
779	C₂²⋊C₄	C₂⁴×C₈₉	1	16	yes	—
780	C₂²⋊C₄	C₂⁴×C₈₉	1	8	yes	—
781	C₂²⋊C₄	C₂⁴×C₈₉	1	16	yes	—
782	C₂²⋊C₄	C₂⁴×C₈₉	1	8	yes	—
783	C₂²⋊C₄	C₂⁴×C₈₉	1	16	yes	—
784	C₂²⋊C₄	C₂⁴×C₈₉	1	16	yes	—
785	C₂²⋊C₄	C₂⁴×C₈₉	1	8	yes	—
786	C₂²⋊C₄	C₂⁴×C₈₉	1	8	yes	—
787	C₂²⋊C₄	C₂⁴×C₈₉	1	8	yes	—
788	C₄²	C₂⁴×C₈₉	1	2	yes	—
789	C₄²	C₂⁴×C₈₉	1	4	yes	—
790	C₄²	C₂⁴×C₈₉	1	2	yes	—
791	C₄²	C₂⁴×C₈₉	1	4	yes	—
792	C₄²	C₂⁴×C₈₉	1	1	yes	characteristic
793	C₄²	C₂⁴×C₈₉	1	1	yes	characteristic
794	C₄²	C₂⁴×C₈₉	1	4	yes	—
795	C₄²	C₂⁴×C₈₉	1	8	yes	—
796	C₄²	C₂⁴×C₈₉	1	2	yes	—
797	C₄²	C₂⁴×C₈₉	1	8	yes	—
798	C₄²	C₂⁴×C₈₉	1	16	yes	—
799	C₂³	—	2	2	no	—
800	C₂³	—	2	8	no	—
801	C₂³	—	4	4	no	—
802	C₂³	—	4	2	no	—
803	C₂³	—	4	4	no	—
804	C₂³	C₂⁵×C₈₉	1	2	yes	—
805	C₂³	C₂⁵×C₈₉	1	8	yes	—
806	C₂³	C₂⁵×C₈₉	1	4	yes	—
807	C₂³	C₂⁵×C₈₉	1	1	yes	characteristic
808	Q₈	—	2	4	no	—
809	Q₈	—	4	4	no	—
810	Q₈	—	4	4	no	—
811	Q₈	—	4	16	no	—
812	Q₈	—	4	4	no	—
813	Q₈	—	4	8	no	—
814	D₄	—	2	8	no	—
815	D₄	—	2	8	no	—
816	D₄	—	2	8	no	—
817	D₄	—	2	4	no	—
818	D₄	—	4	16	no	—
819	D₄	—	4	16	no	—
820	D₄	—	4	16	no	—
821	D₄	—	4	4	no	—
822	D₄	—	4	8	no	—
823	D₄	—	4	16	no	—
824	C₂×C₄	—	2	2	no	—
825	C₂×C₄	—	2	4	no	—
826	C₂×C₄	—	2	4	no	—
827	C₂×C₄	—	2	8	no	—
828	C₂×C₄	—	4	2	no	—
829	C₂×C₄	—	4	4	no	—
830	C₂×C₄	—	4	8	no	—
831	C₂×C₄	—	4	8	no	—
832	C₂×C₄	—	4	2	no	—
833	C₂×C₄	—	4	16	no	—
834	C₂×C₄	—	4	16	no	—
835	C₂×C₄	—	4	16	no	—
836	C₂×C₄	—	4	8	no	—
837	C₂×C₄	—	4	8	no	—
838	C₂×C₄	2₋¹⁺⁴×C₈₉	1	4	yes	—
839	C₂×C₄	C₂⁵×C₈₉	1	4	yes	—
840	C₂×C₄	C₂⁵×C₈₉	1	2	yes	—
841	C₂×C₄	C₂⁵×C₈₉	1	8	yes	—
842	C₂×C₄	C₂⁵×C₈₉	1	4	yes	—
843	C₂×C₄	C₂⁵×C₈₉	1	2	yes	—
844	C₂×C₄	C₂⁵×C₈₉	1	8	yes	—
845	C₂×C₄	C₂⁵×C₈₉	1	2	yes	—
846	C₂×C₄	C₂⁵×C₈₉	1	8	yes	—
847	C₂×C₄	C₂⁵×C₈₉	1	8	yes	—
848	C₂×C₄	C₂⁵×C₈₉	1	1	yes	characteristic
849	C₂×C₄	C₂⁵×C₈₉	1	1	yes	characteristic
850	C₂²	—	2	2	no	—
851	C₂²	—	2	2	no	—
852	C₂²	—	2	4	no	—
853	C₂²	—	2	8	no	—
854	C₂²	—	2	8	no	—
855	C₂²	—	2	8	no	—
856	C₂²	—	2	4	no	—
857	C₂²	—	2	8	no	—
858	C₂²	—	8	2	no	—
859	C₂²	—	8	8	no	—
860	C₂²	C₂×2₋¹⁺⁴×C₈₉	1	2	yes	—
861	C₂²	C₂⁶×C₈₉	1	1	yes	characteristic
862	C₄	—	2	2	no	—
863	C₄	—	2	4	no	—
864	C₄	—	2	2	no	—
865	C₄	—	2	8	no	—
866	C₄	—	2	8	no	—
867	C₄	—	2	8	no	—
868	C₄	—	2	2	no	—
869	C₄	—	2	4	no	—
870	C₄	—	2	8	no	—
871	C₄	C₂×2₋¹⁺⁴×C₈₉	1	2	yes	—
872	C₄	C₂×2₋¹⁺⁴×C₈₉	1	2	yes	—
873	C₂	—	2	2	no	—
874	C₂	—	4	4	no	—
875	C₂	—	4	2	no	—
876	C₂	—	4	8	no	—
877	C₂	C₂²×2₋¹⁺⁴×C₈₉	1	1	yes	characteristic
878	C₂	C₈₉×H(7,𝔽₂)	1	2	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×#3559	C₂	semidirect
2. C₈₉×#3557	C₂	semidirect
3. C₈₉×#3554	C₂	semidirect
4. C₈₉×#3548	C₂	semidirect
5. C₈₉×#3547	C₂	semidirect
6. C₈₉×#3536	C₂	semidirect
7. C₈₉×#3535	C₂	semidirect
8. C₈₉×#3508	C₂	semidirect
9. C₈₉×#3506	C₂	semidirect
10. C₈₉×#3504	C₂	semidirect
11. C₈₉×#3501	C₂	semidirect
12. C₈₉×#3494	C₂	semidirect
13. C₈₉×#3458	C₂	semidirect
14. C₈₉×#3455	C₂	semidirect
15. C₂×#540×C₈₉	C₂	semidirect
16. #563×C₈₉	C₂²	semidirect
17. #562×C₈₉	C₂²	semidirect
18. #562×C₈₉	C₂²	semidirect
19. #562×C₈₉	C₂²	semidirect
20. #559×C₈₉	C₂²	semidirect
21. #559×C₈₉	C₂²	semidirect
22. #557×C₈₉	C₂²	semidirect
23. #556×C₈₉	C₂²	semidirect
24. #555×C₈₉	C₂²	semidirect
25. #555×C₈₉	C₂²	semidirect
27. #554×C₈₉	C₂²	semidirect
28. #554×C₈₉	C₂²	semidirect
29. #554×C₈₉	C₂²	semidirect
30. #554×C₈₉	C₂²	semidirect
31. #554×C₈₉	C₂²	semidirect
32. #553×C₈₉	C₂²	semidirect
33. #553×C₈₉	C₂²	semidirect
34. #553×C₈₉	C₂²	semidirect
35. #552×C₈₉	C₂²	semidirect
37. #550×C₈₉	C₂²	semidirect
38. #550×C₈₉	C₂²	semidirect
39. D₄×Q₈×C₈₉	C₂²	semidirect
40. D₄×Q₈×C₈₉	C₂²	semidirect
41. #548×C₈₉	C₂²	semidirect
42. #547×C₈₉	C₂²	semidirect
43. #547×C₈₉	C₂²	semidirect
44. #547×C₈₉	C₂²	semidirect
45. #547×C₈₉	C₂²	semidirect
50. #544×C₈₉	C₂²	semidirect
51. #544×C₈₉	C₂²	semidirect
52. #544×C₈₉	C₂²	semidirect
55. #542×C₈₉	C₂²	semidirect
56. #542×C₈₉	C₂²	semidirect
57. #542×C₈₉	C₂²	semidirect
58. #542×C₈₉	C₂²	semidirect
59. #541×C₈₉	C₂²	semidirect
63. #540×C₈₉	C₂²	semidirect
64. #540×C₈₉	C₂²	semidirect
65. #540×C₈₉	C₂²	semidirect
66. #540×C₈₉	C₂²	semidirect
68. #539×C₈₉	C₂²	semidirect
69. #539×C₈₉	C₂²	semidirect
70. #539×C₈₉	C₂²	semidirect
73. #537×C₈₉	C₂²	semidirect
74. #537×C₈₉	C₂²	semidirect
75. #536×C₈₉	C₂²	semidirect
80. #533×C₈₉	C₂²	semidirect
81. #533×C₈₉	C₂²	semidirect
82. #533×C₈₉	C₂²	semidirect
84. #532×C₈₉	C₂²	semidirect
85. #532×C₈₉	C₂²	semidirect
87. #529×C₈₉	C₂²	semidirect
88. #529×C₈₉	C₂²	semidirect
90. C₂×#125×C₈₉	C₂²	semidirect
433. #62881	C₈₉	direct (N × H)
440. #3559	C₂×C₈₉	semidirect
441. #3557	C₂×C₈₉	semidirect
442. #3554	C₂×C₈₉	semidirect
443. #3548	C₂×C₈₉	semidirect
444. #3547	C₂×C₈₉	semidirect
445. #3536	C₂×C₈₉	semidirect
446. #3535	C₂×C₈₉	semidirect
447. #3508	C₂×C₈₉	semidirect
448. #3506	C₂×C₈₉	semidirect
449. #3504	C₂×C₈₉	semidirect
450. #3501	C₂×C₈₉	semidirect
451. #3494	C₂×C₈₉	semidirect
452. #3458	C₂×C₈₉	semidirect
453. #3455	C₂×C₈₉	semidirect
454. C₂×#540	C₂×C₈₉	semidirect
455. C₈₉	#62881	direct (N × H)
456. #563	C₂²×C₈₉	semidirect
457. #562	C₂²×C₈₉	semidirect
458. #562	C₂²×C₈₉	semidirect
459. #562	C₂²×C₈₉	semidirect
460. #559	C₂²×C₈₉	semidirect
461. #559	C₂²×C₈₉	semidirect
462. #557	C₂²×C₈₉	semidirect
463. #556	C₂²×C₈₉	semidirect
464. #555	C₂²×C₈₉	semidirect
465. #555	C₂²×C₈₉	semidirect
467. #554	C₂²×C₈₉	semidirect
468. #554	C₂²×C₈₉	semidirect
469. #554	C₂²×C₈₉	semidirect
470. #554	C₂²×C₈₉	semidirect
471. #554	C₂²×C₈₉	semidirect
472. #553	C₂²×C₈₉	semidirect
473. #553	C₂²×C₈₉	semidirect
474. #553	C₂²×C₈₉	semidirect
475. #552	C₂²×C₈₉	semidirect
477. #550	C₂²×C₈₉	semidirect
478. #550	C₂²×C₈₉	semidirect
479. D₄×Q₈	C₂²×C₈₉	semidirect
480. D₄×Q₈	C₂²×C₈₉	semidirect
481. #548	C₂²×C₈₉	semidirect
482. #547	C₂²×C₈₉	semidirect
483. #547	C₂²×C₈₉	semidirect
484. #547	C₂²×C₈₉	semidirect
485. #547	C₂²×C₈₉	semidirect
490. #544	C₂²×C₈₉	semidirect
491. #544	C₂²×C₈₉	semidirect
492. #544	C₂²×C₈₉	semidirect
495. #542	C₂²×C₈₉	semidirect
496. #542	C₂²×C₈₉	semidirect
497. #542	C₂²×C₈₉	semidirect
498. #542	C₂²×C₈₉	semidirect
499. #541	C₂²×C₈₉	semidirect
503. #540	C₂²×C₈₉	semidirect
504. #540	C₂²×C₈₉	semidirect
505. #540	C₂²×C₈₉	semidirect
506. #540	C₂²×C₈₉	semidirect
508. #539	C₂²×C₈₉	semidirect
509. #539	C₂²×C₈₉	semidirect
510. #539	C₂²×C₈₉	semidirect
513. #537	C₂²×C₈₉	semidirect
514. #537	C₂²×C₈₉	semidirect
515. #536	C₂²×C₈₉	semidirect
520. #533	C₂²×C₈₉	semidirect
521. #533	C₂²×C₈₉	semidirect
522. #533	C₂²×C₈₉	semidirect
524. #532	C₂²×C₈₉	semidirect
525. #532	C₂²×C₈₉	semidirect
527. #529	C₂²×C₈₉	semidirect
528. #529	C₂²×C₈₉	semidirect
530. C₂×#125	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×#3559	2
C₈₉×#3557	2
C₈₉×#3554	2
C₈₉×#3548	2
C₈₉×#3547	2
C₈₉×#3536	2
C₈₉×#3535	2
C₈₉×#3508	2
C₈₉×#3506	2
C₈₉×#3504	2
C₈₉×#3501	2
C₈₉×#3494	2
C₈₉×#3458	2
C₈₉×#3455	2
C₂×#540×C₈₉	2
#62881	89

Subgroups — C89×#62881 #36440729

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#62881 #36440729