Subgroups — C₈₉×#62203 #36440051

Order 22784.

1678 conjugacy classes of subgroups.

The subgroup lattice has 1086 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈₉×#3552	C₂	1	1	yes	maximal, characteristic
2	C₈₉×#3523	C₂	1	1	yes	maximal, characteristic, complemented
3	C₈₉×#3386	C₂	1	1	yes	maximal, characteristic, complemented
4	C₈₉×#3383	C₂	1	1	yes	maximal, characteristic, complemented
5	C₈₉×#3374	C₂	1	1	yes	maximal, characteristic, complemented
6	C₈₉×#3359	C₂	1	1	yes	maximal, characteristic, complemented
7	C₈₉×#3353	C₂	1	1	yes	maximal, characteristic, complemented
8	C₈₉×#3344	C₂	1	2	yes	maximal, complemented
9	C₈₉×#3342	C₂	1	1	yes	maximal, characteristic, complemented
10	C₈₉×#3337	C₂	1	2	yes	maximal, complemented
11	C₈₉×#3328	C₂	1	1	yes	maximal, characteristic, complemented
12	C₈₉×#3320	C₂	1	2	yes	maximal, complemented
13	C₈₉×#3299	C₂	1	2	yes	maximal, complemented
14	C₈₉×#3298	C₂	1	1	yes	maximal, characteristic, complemented
15	C₈₉×#3258	C₂	1	2	yes	maximal, complemented
16	C₈₉×#3248	C₂	1	1	yes	maximal, characteristic, complemented
17	C₈₉×#3242	C₂	1	2	yes	maximal, complemented
18	C₈₉×#3230	C₂	1	1	yes	maximal, characteristic, complemented
19	C₈₉×#3121	C₂	1	2	yes	maximal, complemented
20	C₈₉×#3108	C₂	1	1	yes	maximal, characteristic, complemented
21	C₈₉×#3082	C₂	1	2	yes	maximal, complemented
22	C₂×#475×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
23	C₈₉×#2994	C₂	1	1	yes	maximal, characteristic, complemented
24	#563×C₈₉	—	2	2	no	—
25	#557×C₈₉	—	2	1	no	—
26	#557×C₈₉	C₂²	1	1	yes	characteristic
27	#557×C₈₉	C₂²	1	1	yes	characteristic
28	#557×C₈₉	C₂²	1	1	yes	characteristic
29	#556×C₈₉	—	2	1	no	—
30	#556×C₈₉	C₂²	1	1	yes	characteristic
31	#556×C₈₉	C₂²	1	1	yes	characteristic
32	#554×C₈₉	C₂²	1	2	yes	—
33	#553×C₈₉	C₂²	1	2	yes	—
34	#552×C₈₉	—	2	2	no	—
35	#552×C₈₉	C₂²	1	2	yes	—
36	D₄×Q₈×C₈₉	—	2	1	no	—
37	D₄×Q₈×C₈₉	C₂²	1	2	yes	—
38	D₄×Q₈×C₈₉	C₂²	1	1	yes	characteristic
39	D₄×Q₈×C₈₉	C₂²	1	1	yes	characteristic
40	#548×C₈₉	—	2	1	no	—
41	#547×C₈₉	C₂²	1	1	yes	characteristic
42	#544×C₈₉	C₂²	1	2	yes	—
43	#542×C₈₉	C₂²	1	2	yes	—
44	#541×C₈₉	—	2	2	no	—
45	#541×C₈₉	—	2	1	no	—
46	#541×C₈₉	C₂²	1	2	yes	—
47	#539×C₈₉	—	2	2	no	—
48	#536×C₈₉	—	2	1	no	—
49	#533×C₈₉	—	2	1	no	—
50	#533×C₈₉	C₂²	1	1	yes	characteristic
51	C₂×C₄⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic
52	#529×C₈₉	—	2	1	no	—
53	#529×C₈₉	C₂²	1	1	yes	characteristic
54	#529×C₈₉	C₂²	1	1	yes	characteristic
55	#519×C₈₉	C₂²	1	2	yes	—
56	C₂×C₄×Q₈×C₈₉	C₂²	1	1	yes	characteristic
57	#501×C₈₉	C₂²	1	2	yes	—
58	#500×C₈₉	C₂²	1	1	yes	characteristic
59	#500×C₈₉	C₂²	1	1	yes	characteristic
60	#499×C₈₉	C₂²	1	2	yes	—
61	#491×C₈₉	C₂²	1	2	yes	—
62	#487×C₈₉	C₂²	1	1	yes	characteristic
63	#487×C₈₉	C₂²	1	2	yes	—
64	#487×C₈₉	C₂²	1	1	yes	characteristic
65	#485×C₈₉	C₂²	1	2	yes	—
66	#485×C₈₉	C₂²	1	2	yes	—
67	#485×C₈₉	C₂²	1	2	yes	—
68	#484×C₈₉	C₂²	1	2	yes	—
69	#484×C₈₉	C₂²	1	2	yes	—
70	#484×C₈₉	C₂²	1	2	yes	—
71	#483×C₈₉	C₂²	1	1	yes	characteristic
72	#483×C₈₉	C₂²	1	2	yes	—
73	#482×C₈₉	C₂²	1	2	yes	—
74	#480×C₈₉	C₂²	1	1	yes	characteristic
75	#479×C₈₉	C₂²	1	2	yes	—
76	#479×C₈₉	C₂²	1	2	yes	—
77	#479×C₈₉	C₂²	1	1	yes	characteristic
78	#479×C₈₉	C₂²	1	2	yes	—
79	#479×C₈₉	C₂²	1	2	yes	—
80	#479×C₈₉	C₂²	1	1	yes	characteristic
81	#478×C₈₉	C₂²	1	2	yes	—
82	#477×C₈₉	C₂²	1	2	yes	—
83	#477×C₈₉	C₂²	1	2	yes	—
84	#477×C₈₉	C₂²	1	2	yes	—
85	#475×C₈₉	C₂²	1	1	yes	characteristic
86	#475×C₈₉	C₂²	1	2	yes	—
87	#475×C₈₉	C₂²	1	1	yes	characteristic
88	#475×C₈₉	C₂²	1	1	yes	characteristic
89	#475×C₈₉	C₂²	1	1	yes	characteristic
90	#475×C₈₉	C₂²	1	2	yes	—
91	#475×C₈₉	C₂²	1	2	yes	—
92	#475×C₈₉	C₂²	1	1	yes	characteristic
93	#474×C₈₉	C₂²	1	1	yes	characteristic
94	#470×C₈₉	C₂²	1	2	yes	—
95	#468×C₈₉	C₂²	1	2	yes	—
96	#467×C₈₉	C₂²	1	2	yes	—
97	#467×C₈₉	C₂²	1	2	yes	—
98	#465×C₈₉	C₂²	1	2	yes	—
99	#465×C₈₉	C₂²	1	2	yes	—
100	#464×C₈₉	C₂²	1	1	yes	characteristic
101	#464×C₈₉	C₂²	1	1	yes	characteristic
102	#464×C₈₉	C₂²	1	2	yes	—
103	#462×C₈₉	C₂²	1	1	yes	characteristic
104	#462×C₈₉	C₂²	1	2	yes	—
105	#461×C₈₉	C₂²	1	2	yes	—
106	#461×C₈₉	C₂²	1	1	yes	characteristic
107	#451×C₈₉	C₂²	1	2	yes	—
108	#451×C₈₉	C₂²	1	1	yes	characteristic
109	#448×C₈₉	C₂²	1	1	yes	characteristic
110	#448×C₈₉	C₂²	1	2	yes	—
111	#446×C₈₉	C₂²	1	1	yes	characteristic
112	C₈×Q₈×C₈₉	C₂²	1	1	yes	characteristic
113	#441×C₈₉	C₂²	1	2	yes	—
114	#440×C₈₉	C₂²	1	2	yes	—
115	C₄×Q₁₆×C₈₉	C₂²	1	1	yes	characteristic
116	C₄×Q₁₆×C₈₉	C₂²	1	1	yes	characteristic
117	C₄×Q₁₆×C₈₉	C₂²	1	2	yes	—
118	C₄×SD₁₆×C₈₉	C₂²	1	2	yes	—
119	C₄×SD₁₆×C₈₉	C₂²	1	1	yes	characteristic
120	C₄×SD₁₆×C₈₉	C₂²	1	1	yes	characteristic
121	#436×C₈₉	C₂²	1	1	yes	characteristic
122	#435×C₈₉	C₂²	1	2	yes	—
123	C₈×D₄×C₈₉	C₂²	1	2	yes	—
124	C₈×D₄×C₈₉	C₂²	1	1	yes	characteristic
125	#433×C₈₉	C₂²	1	2	yes	—
126	#431×C₈₉	C₂²	1	1	yes	characteristic
127	#428×C₈₉	C₂²	1	2	yes	—
128	#427×C₈₉	C₂²	1	2	yes	—
129	C₂×#106×C₈₉	C₂²	1	2	yes	—
130	#424×C₈₉	C₂²	1	2	yes	—
131	C₂×C₄⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
132	#419×C₈₉	C₂²	1	2	yes	—
133	C₂×#103×C₈₉	C₂²	1	2	yes	—
134	C₂×#103×C₈₉	C₂²	1	2	yes	—
135	C₂×#41×C₈₉	—	2	1	no	—
136	C₂²×Q₈×C₈₉	—	2	1	no	—
137	C₂²×Q₈×C₈₉	—	2	1	no	—
138	C₂²×Q₈×C₈₉	C₂³	1	1	yes	characteristic
139	C₂²×Q₈×C₈₉	C₂³	1	2	yes	—
140	C₂×Q₁₆×C₈₉	C₂³	1	1	yes	characteristic
141	C₂×Q₁₆×C₈₉	C₂³	1	1	yes	characteristic
142	C₂×Q₁₆×C₈₉	C₂³	1	2	yes	—
143	C₂×SD₁₆×C₈₉	C₂³	1	1	yes	characteristic
144	C₂×SD₁₆×C₈₉	C₂³	1	2	yes	—
145	C₂×SD₁₆×C₈₉	C₂³	1	1	yes	characteristic
146	C₂×M₁₆×C₈₉	C₂³	1	2	yes	—
147	C₂²×C₈×C₈₉	C₂³	1	2	yes	—
148	C₂²×C₈×C₈₉	C₂³	1	2	yes	—
149	C₄⋊Q₈×C₈₉	—	2	1	no	—
150	C₄⋊Q₈×C₈₉	—	2	1	no	—
151	C₄⋊Q₈×C₈₉	—	2	1	no	—
152	C₄⋊Q₈×C₈₉	—	2	2	no	—
153	C₄⋊Q₈×C₈₉	—	2	2	no	—
154	C₄⋊Q₈×C₈₉	—	2	1	no	—
155	C₄⋊Q₈×C₈₉	—	2	1	no	—
156	C₄⋊Q₈×C₈₉	C₂³	1	1	yes	characteristic
157	C₄⋊Q₈×C₈₉	C₂³	1	2	yes	—
158	C₄⋊Q₈×C₈₉	C₂³	1	1	yes	characteristic
159	C₄⋊Q₈×C₈₉	C₂³	1	2	yes	—
160	C₄⋊Q₈×C₈₉	C₂³	1	1	yes	characteristic
161	C₄⋊Q₈×C₈₉	C₂³	1	1	yes	characteristic
162	C₄⋊Q₈×C₈₉	C₂³	1	2	yes	—
163	#126×C₈₉	—	2	2	no	—
164	#126×C₈₉	—	2	2	no	—
165	#126×C₈₉	—	2	2	no	—
166	#126×C₈₉	—	2	2	no	—
167	#126×C₈₉	—	2	2	no	—
168	#126×C₈₉	—	2	2	no	—
169	#126×C₈₉	—	2	2	no	—
170	#126×C₈₉	—	2	1	no	—
171	#126×C₈₉	D₄	1	2	yes	—
172	#125×C₈₉	—	2	1	no	—
173	#125×C₈₉	—	2	2	no	—
174	#125×C₈₉	—	2	2	no	—
175	#125×C₈₉	—	2	2	no	—
176	#125×C₈₉	—	2	2	no	—
177	#125×C₈₉	—	2	2	no	—
178	#125×C₈₉	—	2	2	no	—
179	#125×C₈₉	—	2	2	no	—
180	#125×C₈₉	—	2	2	no	—
181	#125×C₈₉	—	2	1	no	—
182	#125×C₈₉	D₄	1	1	yes	characteristic
183	#125×C₈₉	C₂³	1	2	yes	—
184	#125×C₈₉	C₂³	1	1	yes	characteristic
185	#125×C₈₉	C₂³	1	2	yes	—
186	#124×C₈₉	—	2	1	no	—
187	#124×C₈₉	—	2	1	no	—
188	#124×C₈₉	—	2	2	no	—
189	#124×C₈₉	D₄	1	1	yes	characteristic
190	#124×C₈₉	C₂³	1	1	yes	characteristic
191	#123×C₈₉	—	2	2	no	—
192	#123×C₈₉	—	2	1	no	—
193	#123×C₈₉	—	2	2	no	—
194	#123×C₈₉	—	2	2	no	—
195	#123×C₈₉	—	2	2	no	—
196	#123×C₈₉	D₄	1	2	yes	—
197	C₂²⋊Q₈×C₈₉	—	2	1	no	—
198	C₂²⋊Q₈×C₈₉	—	2	2	no	—
199	C₂²⋊Q₈×C₈₉	—	2	1	no	—
200	C₂²⋊Q₈×C₈₉	—	2	1	no	—
201	C₂²⋊Q₈×C₈₉	—	2	2	no	—
202	C₂²⋊Q₈×C₈₉	—	2	2	no	—
203	C₂²⋊Q₈×C₈₉	—	2	2	no	—
204	C₂²⋊Q₈×C₈₉	—	2	2	no	—
205	C₂²⋊Q₈×C₈₉	—	2	2	no	—
206	C₂²⋊Q₈×C₈₉	—	2	2	no	—
207	C₂²⋊Q₈×C₈₉	—	2	2	no	—
208	C₂²⋊Q₈×C₈₉	—	2	2	no	—
209	C₂²⋊Q₈×C₈₉	D₄	1	1	yes	characteristic
210	C₂²⋊Q₈×C₈₉	C₂³	1	1	yes	characteristic
211	C₂²⋊Q₈×C₈₉	C₂³	1	2	yes	—
212	C₂²⋊Q₈×C₈₉	C₂³	1	2	yes	—
213	C₂²⋊Q₈×C₈₉	C₂³	1	2	yes	—
214	C₂²⋊Q₈×C₈₉	C₂³	1	2	yes	—
215	#121×C₈₉	—	2	2	no	—
216	#121×C₈₉	D₄	1	1	yes	characteristic
217	#121×C₈₉	C₂³	1	1	yes	characteristic
218	#121×C₈₉	C₂³	1	2	yes	—
219	C₄×Q₈×C₈₉	—	2	1	no	—
220	C₄×Q₈×C₈₉	—	2	2	no	—
221	C₄×Q₈×C₈₉	—	2	2	no	—
222	C₄×Q₈×C₈₉	—	2	1	no	—
223	C₄×Q₈×C₈₉	—	2	1	no	—
224	C₄×Q₈×C₈₉	—	2	1	no	—
225	C₄×Q₈×C₈₉	—	2	1	no	—
226	C₄×Q₈×C₈₉	—	2	1	no	—
227	C₄×Q₈×C₈₉	—	2	1	no	—
228	C₄×Q₈×C₈₉	—	2	1	no	—
229	C₄×Q₈×C₈₉	C₂³	1	1	yes	characteristic
230	C₄×Q₈×C₈₉	C₂³	1	1	yes	characteristic
231	C₄×Q₈×C₈₉	C₂³	1	2	yes	—
232	C₄×Q₈×C₈₉	C₂³	1	1	yes	characteristic
233	C₄×Q₈×C₈₉	C₂³	1	2	yes	—
234	C₄×Q₈×C₈₉	C₂³	1	2	yes	—
235	C₄×Q₈×C₈₉	C₂³	1	1	yes	characteristic
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×D₄×C₈₉	—	2	2	no	—
240	C₄×D₄×C₈₉	—	2	1	no	—
241	C₄×D₄×C₈₉	—	2	2	no	—
242	C₄×D₄×C₈₉	—	2	1	no	—
243	C₄×D₄×C₈₉	—	2	2	no	—
244	C₄×D₄×C₈₉	C₂³	1	1	yes	characteristic
245	C₄×D₄×C₈₉	C₂³	1	2	yes	—
246	C₄×D₄×C₈₉	C₂³	1	2	yes	—
247	C₄×D₄×C₈₉	C₂³	1	1	yes	characteristic
248	#117×C₈₉	—	2	1	no	—
249	#117×C₈₉	—	2	2	no	—
250	#117×C₈₉	—	2	2	no	—
251	#117×C₈₉	—	2	2	no	—
252	#117×C₈₉	—	2	1	no	—
253	#117×C₈₉	C₂³	1	2	yes	—
254	#117×C₈₉	C₂³	1	2	yes	—
255	#117×C₈₉	C₂³	1	2	yes	—
256	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
257	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
258	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
259	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
260	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
261	C₂×C₄²×C₈₉	—	2	1	no	—
262	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
263	#107×C₈₉	C₂³	1	1	yes	characteristic
264	#107×C₈₉	C₂³	1	2	yes	—
265	#107×C₈₉	C₂³	1	2	yes	—
266	#107×C₈₉	C₂³	1	2	yes	—
267	#107×C₈₉	C₂³	1	2	yes	—
268	#107×C₈₉	C₂³	1	1	yes	characteristic
269	#107×C₈₉	C₂³	1	2	yes	—
270	#106×C₈₉	C₂³	1	2	yes	—
271	#106×C₈₉	C₂³	1	2	yes	—
272	#106×C₈₉	C₂³	1	2	yes	—
273	#106×C₈₉	C₂³	1	2	yes	—
274	#106×C₈₉	C₂³	1	2	yes	—
275	#106×C₈₉	C₂³	1	1	yes	characteristic
276	#106×C₈₉	C₂³	1	1	yes	characteristic
277	C₄⋊C₈×C₈₉	C₂³	1	2	yes	—
278	C₄⋊C₈×C₈₉	C₂³	1	1	yes	characteristic
279	C₄⋊C₈×C₈₉	C₂³	1	1	yes	characteristic
280	C₄⋊C₈×C₈₉	C₂³	1	1	yes	characteristic
281	C₄⋊C₈×C₈₉	C₂³	1	2	yes	—
282	C₄⋊C₈×C₈₉	C₂³	1	2	yes	—
283	C₄⋊C₈×C₈₉	C₂³	1	1	yes	characteristic
284	#103×C₈₉	C₂³	1	1	yes	characteristic
285	#103×C₈₉	C₂³	1	2	yes	—
286	#103×C₈₉	C₂³	1	2	yes	—
287	#103×C₈₉	C₂³	1	2	yes	—
288	#103×C₈₉	C₂³	1	2	yes	—
289	#103×C₈₉	C₂³	1	2	yes	—
290	#103×C₈₉	C₂³	1	2	yes	—
291	#103×C₈₉	C₂³	1	1	yes	characteristic
292	#103×C₈₉	C₂³	1	2	yes	—
293	#103×C₈₉	C₂³	1	2	yes	—
294	#103×C₈₉	C₂³	1	2	yes	—
295	#103×C₈₉	C₂³	1	1	yes	characteristic
296	#103×C₈₉	C₂³	1	1	yes	characteristic
297	#103×C₈₉	C₂³	1	1	yes	characteristic
298	#103×C₈₉	C₂³	1	2	yes	—
299	#103×C₈₉	C₂³	1	1	yes	characteristic
300	#103×C₈₉	C₂³	1	2	yes	—
301	#102×C₈₉	C₂³	1	1	yes	characteristic
302	#102×C₈₉	C₂³	1	1	yes	characteristic
303	#102×C₈₉	C₂³	1	2	yes	—
304	C₂²⋊C₈×C₈₉	C₂³	1	1	yes	characteristic
305	C₂²⋊C₈×C₈₉	C₂³	1	1	yes	characteristic
306	C₂²⋊C₈×C₈₉	C₂³	1	2	yes	—
307	C₂²⋊C₈×C₈₉	C₂³	1	2	yes	—
308	#97×C₈₉	C₂³	1	2	yes	—
309	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
310	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
311	C₄×C₈×C₈₉	C₂³	1	2	yes	—
312	#41×C₈₉	—	8	2	no	—
313	C₂×Q₈×C₈₉	—	2	1	no	—
314	C₂×Q₈×C₈₉	—	2	2	no	—
315	C₂×Q₈×C₈₉	—	2	1	no	—
316	C₂×Q₈×C₈₉	—	2	1	no	—
317	C₂×Q₈×C₈₉	—	2	1	no	—
318	C₂×Q₈×C₈₉	—	2	2	no	—
319	C₂×Q₈×C₈₉	—	2	2	no	—
320	C₂×Q₈×C₈₉	—	2	2	no	—
321	C₂×Q₈×C₈₉	—	2	4	no	—
322	C₂×Q₈×C₈₉	—	4	1	no	—
323	C₂×Q₈×C₈₉	—	4	2	no	—
324	C₂×Q₈×C₈₉	—	8	2	no	—
325	C₂×Q₈×C₈₉	—	8	2	no	—
326	C₂×Q₈×C₈₉	C₂×D₄	1	1	yes	characteristic
327	C₂×Q₈×C₈₉	C₂⁴	1	1	yes	characteristic
328	C₂×Q₈×C₈₉	C₂⁴	1	2	yes	—
329	C₂×Q₈×C₈₉	C₂⁴	1	1	yes	characteristic
330	C₂×Q₈×C₈₉	C₂⁴	1	1	yes	characteristic
331	C₂×D₄×C₈₉	—	2	1	no	—
332	C₂×D₄×C₈₉	—	2	2	no	—
333	C₂×D₄×C₈₉	C₂×D₄	1	2	yes	—
334	C₂×D₄×C₈₉	C₂×D₄	1	1	yes	characteristic
335	C₂×D₄×C₈₉	C₂⁴	1	1	yes	characteristic
336	C₂²×C₄×C₈₉	—	2	1	no	—
337	C₂²×C₄×C₈₉	—	2	1	no	—
338	C₂²×C₄×C₈₉	—	2	2	no	—
339	C₂²×C₄×C₈₉	—	2	2	no	—
340	C₂²×C₄×C₈₉	—	2	2	no	—
341	C₂²×C₄×C₈₉	—	2	1	no	—
342	C₂²×C₄×C₈₉	—	2	2	no	—
343	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
344	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
345	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
346	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
347	Q₁₆×C₈₉	—	2	2	no	—
348	Q₁₆×C₈₉	—	4	1	no	—
349	Q₁₆×C₈₉	—	4	2	no	—
350	SD₁₆×C₈₉	—	2	2	no	—
351	SD₁₆×C₈₉	—	4	2	no	—
352	SD₁₆×C₈₉	—	4	1	no	—
353	M₁₆×C₈₉	—	4	2	no	—
354	C₂×C₈×C₈₉	—	4	2	no	—
355	C₂×C₈×C₈₉	—	4	2	no	—
356	C₂×C₈×C₈₉	C₂⁴	1	1	yes	characteristic
357	C₂×C₈×C₈₉	C₂⁴	1	1	yes	characteristic
358	C₂×C₈×C₈₉	C₂⁴	1	1	yes	characteristic
359	C₂×C₈×C₈₉	C₂⁴	1	2	yes	—
360	C₂×C₈×C₈₉	C₂⁴	1	1	yes	characteristic
361	C₂×C₈×C₈₉	C₂⁴	1	2	yes	—
362	C₄⋊C₄×C₈₉	—	2	1	no	—
363	C₄⋊C₄×C₈₉	—	2	1	no	—
364	C₄⋊C₄×C₈₉	—	2	1	no	—
365	C₄⋊C₄×C₈₉	—	2	1	no	—
366	C₄⋊C₄×C₈₉	—	2	1	no	—
367	C₄⋊C₄×C₈₉	—	2	2	no	—
368	C₄⋊C₄×C₈₉	—	2	1	no	—
369	C₄⋊C₄×C₈₉	—	2	1	no	—
370	C₄⋊C₄×C₈₉	—	2	2	no	—
371	C₄⋊C₄×C₈₉	—	2	2	no	—
372	C₄⋊C₄×C₈₉	—	2	2	no	—
373	C₄⋊C₄×C₈₉	—	2	2	no	—
374	C₄⋊C₄×C₈₉	—	2	2	no	—
375	C₄⋊C₄×C₈₉	—	2	1	no	—
376	C₄⋊C₄×C₈₉	—	2	1	no	—
377	C₄⋊C₄×C₈₉	—	2	1	no	—
378	C₄⋊C₄×C₈₉	—	2	2	no	—
379	C₄⋊C₄×C₈₉	—	2	1	no	—
380	C₄⋊C₄×C₈₉	—	2	2	no	—
381	C₄⋊C₄×C₈₉	—	2	1	no	—
382	C₄⋊C₄×C₈₉	—	2	2	no	—
383	C₄⋊C₄×C₈₉	—	2	1	no	—
384	C₄⋊C₄×C₈₉	—	2	2	no	—
385	C₄⋊C₄×C₈₉	—	2	2	no	—
386	C₄⋊C₄×C₈₉	—	2	2	no	—
387	C₄⋊C₄×C₈₉	—	2	2	no	—
388	C₄⋊C₄×C₈₉	—	2	2	no	—
389	C₄⋊C₄×C₈₉	—	2	2	no	—
390	C₄⋊C₄×C₈₉	—	2	2	no	—
391	C₄⋊C₄×C₈₉	—	2	2	no	—
392	C₄⋊C₄×C₈₉	—	2	2	no	—
393	C₄⋊C₄×C₈₉	—	2	1	no	—
394	C₄⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
395	C₄⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
396	C₄⋊C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
397	C₄⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
398	C₄⋊C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
399	C₄⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
400	C₄⋊C₄×C₈₉	C₂⁴	1	1	yes	characteristic
401	C₄⋊C₄×C₈₉	C₂⁴	1	1	yes	characteristic
402	C₄⋊C₄×C₈₉	C₂⁴	1	2	yes	—
403	C₄⋊C₄×C₈₉	C₂⁴	1	1	yes	characteristic
404	C₄⋊C₄×C₈₉	C₂⁴	1	2	yes	—
405	C₄⋊C₄×C₈₉	C₂⁴	1	2	yes	—
406	C₄⋊C₄×C₈₉	C₂⁴	1	1	yes	characteristic
407	C₂²⋊C₄×C₈₉	—	2	2	no	—
408	C₂²⋊C₄×C₈₉	—	2	2	no	—
409	C₂²⋊C₄×C₈₉	—	2	2	no	—
410	C₂²⋊C₄×C₈₉	—	2	1	no	—
411	C₂²⋊C₄×C₈₉	—	2	2	no	—
412	C₂²⋊C₄×C₈₉	—	2	2	no	—
413	C₂²⋊C₄×C₈₉	—	2	2	no	—
414	C₂²⋊C₄×C₈₉	—	2	1	no	—
415	C₂²⋊C₄×C₈₉	—	2	1	no	—
416	C₂²⋊C₄×C₈₉	—	2	2	no	—
417	C₂²⋊C₄×C₈₉	—	2	1	no	—
418	C₂²⋊C₄×C₈₉	—	2	2	no	—
419	C₂²⋊C₄×C₈₉	—	2	1	no	—
420	C₂²⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
421	C₂²⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
422	C₂²⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
423	C₂²⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
424	C₂²⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
425	C₄²×C₈₉	—	2	1	no	—
426	C₄²×C₈₉	—	2	1	no	—
427	C₄²×C₈₉	—	2	1	no	—
428	C₄²×C₈₉	—	2	1	no	—
429	C₄²×C₈₉	—	2	2	no	—
430	C₄²×C₈₉	—	2	2	no	—
431	C₄²×C₈₉	—	2	2	no	—
432	C₄²×C₈₉	—	2	1	no	—
433	C₄²×C₈₉	—	2	2	no	—
434	C₄²×C₈₉	—	2	2	no	—
435	C₄²×C₈₉	—	2	2	no	—
436	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
437	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
438	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
439	C₄²×C₈₉	C₂⁴	1	2	yes	—
440	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
441	C₂³×C₈₉	—	2	1	no	—
442	C₂³×C₈₉	C₂²×D₄	1	2	yes	—
443	C₂³×C₈₉	C₂²×D₄	1	1	yes	characteristic
444	Q₈×C₈₉	—	2	2	no	—
445	Q₈×C₈₉	—	2	1	no	—
446	Q₈×C₈₉	—	2	1	no	—
447	Q₈×C₈₉	—	2	1	no	—
448	Q₈×C₈₉	—	2	2	no	—
449	Q₈×C₈₉	—	2	2	no	—
450	Q₈×C₈₉	—	2	1	no	—
451	Q₈×C₈₉	—	2	1	no	—
452	Q₈×C₈₉	—	4	2	no	—
453	Q₈×C₈₉	—	4	4	no	—
454	Q₈×C₈₉	—	4	2	no	—
455	Q₈×C₈₉	—	4	2	no	—
456	Q₈×C₈₉	—	4	2	no	—
457	Q₈×C₈₉	—	8	2	no	—
458	Q₈×C₈₉	—	8	2	no	—
459	Q₈×C₈₉	2₋¹⁺⁴	1	2	yes	—
460	D₄×C₈₉	—	2	4	no	—
461	D₄×C₈₉	—	2	2	no	—
462	D₄×C₈₉	—	2	1	no	—
463	D₄×C₈₉	—	2	1	no	—
464	D₄×C₈₉	—	4	2	no	—
465	D₄×C₈₉	—	8	2	no	—
466	C₂×C₄×C₈₉	—	2	2	no	—
467	C₂×C₄×C₈₉	—	2	1	no	—
468	C₂×C₄×C₈₉	—	2	2	no	—
469	C₂×C₄×C₈₉	—	2	1	no	—
470	C₂×C₄×C₈₉	—	2	2	no	—
471	C₂×C₄×C₈₉	—	2	1	no	—
472	C₂×C₄×C₈₉	—	2	2	no	—
473	C₂×C₄×C₈₉	—	2	1	no	—
474	C₂×C₄×C₈₉	—	2	1	no	—
475	C₂×C₄×C₈₉	—	2	1	no	—
476	C₂×C₄×C₈₉	—	2	2	no	—
477	C₂×C₄×C₈₉	—	2	1	no	—
478	C₂×C₄×C₈₉	—	2	1	no	—
479	C₂×C₄×C₈₉	—	2	2	no	—
480	C₂×C₄×C₈₉	—	2	2	no	—
481	C₂×C₄×C₈₉	—	2	2	no	—
482	C₂×C₄×C₈₉	—	2	1	no	—
483	C₂×C₄×C₈₉	—	4	2	no	—
484	C₂×C₄×C₈₉	—	4	4	no	—
485	C₂×C₄×C₈₉	—	4	2	no	—
486	C₂×C₄×C₈₉	—	4	2	no	—
487	C₂×C₄×C₈₉	—	8	2	no	—
488	C₂×C₄×C₈₉	—	8	2	no	—
489	C₂×C₄×C₈₉	—	8	2	no	—
490	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
491	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
492	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
493	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
494	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
495	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
496	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
497	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
498	C₂×C₄×C₈₉	C₂⁵	1	1	yes	characteristic
499	C₈×C₈₉	—	2	1	no	—
500	C₈×C₈₉	—	2	1	no	—
501	C₈×C₈₉	—	2	2	no	—
502	C₈×C₈₉	—	2	1	no	—
503	C₈×C₈₉	—	2	2	no	—
504	C₈×C₈₉	—	2	1	no	—
505	C₂²×C₈₉	—	2	1	no	—
506	C₂²×C₈₉	—	2	1	no	—
507	C₂²×C₈₉	—	2	2	no	—
508	C₂²×C₈₉	—	2	2	no	—
509	C₂²×C₈₉	—	2	2	no	—
510	C₂²×C₈₉	—	4	1	no	—
511	C₂²×C₈₉	—	4	1	no	—
512	C₂²×C₈₉	—	4	1	no	—
513	C₂²×C₈₉	#578	1	2	yes	—
514	C₂²×C₈₉	C₂³×D₄	1	1	yes	characteristic
515	C₄×C₈₉	—	2	1	no	—
516	C₄×C₈₉	—	2	2	no	—
517	C₄×C₈₉	—	2	2	no	—
518	C₄×C₈₉	—	2	1	no	—
519	C₄×C₈₉	—	2	2	no	—
520	C₄×C₈₉	—	2	1	no	—
521	C₄×C₈₉	—	2	1	no	—
522	C₄×C₈₉	—	2	2	no	—
523	C₄×C₈₉	—	4	1	no	—
524	C₄×C₈₉	—	4	2	no	—
525	C₄×C₈₉	—	4	1	no	—
526	C₄×C₈₉	—	4	1	no	—
527	C₄×C₈₉	—	4	2	no	—
528	C₄×C₈₉	—	4	2	no	—
529	C₄×C₈₉	—	4	2	no	—
530	C₄×C₈₉	—	4	1	no	—
531	C₄×C₈₉	—	4	1	no	—
532	C₄×C₈₉	—	4	1	no	—
533	C₄×C₈₉	#577	1	2	yes	—
534	C₄×C₈₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
535	C₄×C₈₉	#585	1	1	yes	characteristic
536	#62203	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
537	C₂×C₈₉	—	2	2	no	—
538	C₂×C₈₉	—	4	2	no	—
539	C₂×C₈₉	—	8	1	no	—
540	C₂×C₈₉	#3489	1	1	yes	characteristic
541	C₂×C₈₉	C₂×#577	1	1	yes	characteristic
542	C₂×C₈₉	C₂×#578	1	1	yes	characteristic
543	#3552	C₂×C₈₉	1	1	yes	characteristic
544	#3523	C₂×C₈₉	1	1	yes	characteristic, complemented
545	#3386	C₂×C₈₉	1	1	yes	characteristic, complemented
546	#3383	C₂×C₈₉	1	1	yes	characteristic, complemented
547	#3374	C₂×C₈₉	1	1	yes	characteristic, complemented
548	#3359	C₂×C₈₉	1	1	yes	characteristic, complemented
549	#3353	C₂×C₈₉	1	1	yes	characteristic, complemented
550	#3344	C₂×C₈₉	1	2	yes	complemented
551	#3342	C₂×C₈₉	1	1	yes	characteristic, complemented
552	#3337	C₂×C₈₉	1	2	yes	complemented
553	#3328	C₂×C₈₉	1	1	yes	characteristic, complemented
554	#3320	C₂×C₈₉	1	2	yes	complemented
555	#3299	C₂×C₈₉	1	2	yes	complemented
556	#3298	C₂×C₈₉	1	1	yes	characteristic, complemented
557	#3258	C₂×C₈₉	1	2	yes	complemented
558	#3248	C₂×C₈₉	1	1	yes	characteristic, complemented
559	#3242	C₂×C₈₉	1	2	yes	complemented
560	#3230	C₂×C₈₉	1	1	yes	characteristic, complemented
561	#3121	C₂×C₈₉	1	2	yes	complemented
562	#3108	C₂×C₈₉	1	1	yes	characteristic, complemented
563	#3082	C₂×C₈₉	1	2	yes	complemented
564	C₂×#475	C₂×C₈₉	1	1	yes	characteristic, complemented
565	#2994	C₂×C₈₉	1	1	yes	characteristic, complemented
566	C₈₉	#62203	1	1	yes	characteristic, direct product factor, Sylow
567	#563	—	2	2	no	—
568	#557	—	2	1	no	—
569	#557	C₂²×C₈₉	1	1	yes	characteristic
570	#557	C₂²×C₈₉	1	1	yes	characteristic
571	#557	C₂²×C₈₉	1	1	yes	characteristic
572	#556	—	2	1	no	—
573	#556	C₂²×C₈₉	1	1	yes	characteristic
574	#556	C₂²×C₈₉	1	1	yes	characteristic
575	#554	C₂²×C₈₉	1	2	yes	—
576	#553	C₂²×C₈₉	1	2	yes	—
577	#552	—	2	2	no	—
578	#552	C₂²×C₈₉	1	2	yes	—
579	D₄×Q₈	—	2	1	no	—
580	D₄×Q₈	C₂²×C₈₉	1	1	yes	characteristic
581	D₄×Q₈	C₂²×C₈₉	1	2	yes	—
582	D₄×Q₈	C₂²×C₈₉	1	1	yes	characteristic
583	#548	—	2	1	no	—
584	#547	C₂²×C₈₉	1	1	yes	characteristic
585	#544	C₂²×C₈₉	1	2	yes	—
586	#542	C₂²×C₈₉	1	2	yes	—
587	#541	—	2	2	no	—
588	#541	—	2	1	no	—
589	#541	C₂²×C₈₉	1	2	yes	—
590	#539	—	2	2	no	—
591	#536	—	2	1	no	—
592	#533	—	2	1	no	—
593	#533	C₂²×C₈₉	1	1	yes	characteristic
594	C₂×C₄⋊Q₈	C₂²×C₈₉	1	1	yes	characteristic
595	#529	—	2	1	no	—
596	#529	C₂²×C₈₉	1	1	yes	characteristic
597	#529	C₂²×C₈₉	1	1	yes	characteristic
598	#519	C₂²×C₈₉	1	2	yes	—
599	C₂×C₄×Q₈	C₂²×C₈₉	1	1	yes	characteristic
600	#501	C₂²×C₈₉	1	2	yes	—
601	#500	C₂²×C₈₉	1	1	yes	characteristic
602	#500	C₂²×C₈₉	1	1	yes	characteristic
603	#499	C₂²×C₈₉	1	2	yes	—
604	#491	C₂²×C₈₉	1	2	yes	—
605	#487	C₂²×C₈₉	1	1	yes	characteristic
606	#487	C₂²×C₈₉	1	2	yes	—
607	#487	C₂²×C₈₉	1	1	yes	characteristic
608	#485	C₂²×C₈₉	1	2	yes	—
609	#485	C₂²×C₈₉	1	2	yes	—
610	#485	C₂²×C₈₉	1	2	yes	—
611	#484	C₂²×C₈₉	1	2	yes	—
612	#484	C₂²×C₈₉	1	2	yes	—
613	#484	C₂²×C₈₉	1	2	yes	—
614	#483	C₂²×C₈₉	1	1	yes	characteristic
615	#483	C₂²×C₈₉	1	2	yes	—
616	#482	C₂²×C₈₉	1	2	yes	—
617	#480	C₂²×C₈₉	1	1	yes	characteristic
618	#479	C₂²×C₈₉	1	2	yes	—
619	#479	C₂²×C₈₉	1	1	yes	characteristic
620	#479	C₂²×C₈₉	1	2	yes	—
621	#479	C₂²×C₈₉	1	2	yes	—
622	#479	C₂²×C₈₉	1	2	yes	—
623	#479	C₂²×C₈₉	1	1	yes	characteristic
624	#478	C₂²×C₈₉	1	2	yes	—
625	#477	C₂²×C₈₉	1	2	yes	—
626	#477	C₂²×C₈₉	1	2	yes	—
627	#477	C₂²×C₈₉	1	2	yes	—
628	#475	C₂²×C₈₉	1	1	yes	characteristic
629	#475	C₂²×C₈₉	1	2	yes	—
630	#475	C₂²×C₈₉	1	1	yes	characteristic
631	#475	C₂²×C₈₉	1	1	yes	characteristic
632	#475	C₂²×C₈₉	1	1	yes	characteristic
633	#475	C₂²×C₈₉	1	2	yes	—
634	#475	C₂²×C₈₉	1	2	yes	—
635	#475	C₂²×C₈₉	1	1	yes	characteristic
636	#474	C₂²×C₈₉	1	1	yes	characteristic
637	#470	C₂²×C₈₉	1	2	yes	—
638	#468	C₂²×C₈₉	1	2	yes	—
639	#467	C₂²×C₈₉	1	2	yes	—
640	#467	C₂²×C₈₉	1	2	yes	—
641	#465	C₂²×C₈₉	1	2	yes	—
642	#465	C₂²×C₈₉	1	2	yes	—
643	#464	C₂²×C₈₉	1	1	yes	characteristic
644	#464	C₂²×C₈₉	1	1	yes	characteristic
645	#464	C₂²×C₈₉	1	2	yes	—
646	#462	C₂²×C₈₉	1	1	yes	characteristic
647	#462	C₂²×C₈₉	1	2	yes	—
648	#461	C₂²×C₈₉	1	1	yes	characteristic
649	#461	C₂²×C₈₉	1	2	yes	—
650	#451	C₂²×C₈₉	1	2	yes	—
651	#451	C₂²×C₈₉	1	1	yes	characteristic
652	#448	C₂²×C₈₉	1	1	yes	characteristic
653	#448	C₂²×C₈₉	1	2	yes	—
654	#446	C₂²×C₈₉	1	1	yes	characteristic
655	C₈×Q₈	C₂²×C₈₉	1	1	yes	characteristic
656	#441	C₂²×C₈₉	1	2	yes	—
657	#440	C₂²×C₈₉	1	2	yes	—
658	C₄×Q₁₆	C₂²×C₈₉	1	1	yes	characteristic
659	C₄×Q₁₆	C₂²×C₈₉	1	1	yes	characteristic
660	C₄×Q₁₆	C₂²×C₈₉	1	2	yes	—
661	C₄×SD₁₆	C₂²×C₈₉	1	2	yes	—
662	C₄×SD₁₆	C₂²×C₈₉	1	1	yes	characteristic
663	C₄×SD₁₆	C₂²×C₈₉	1	1	yes	characteristic
664	#436	C₂²×C₈₉	1	1	yes	characteristic
665	#435	C₂²×C₈₉	1	2	yes	—
666	C₈×D₄	C₂²×C₈₉	1	2	yes	—
667	C₈×D₄	C₂²×C₈₉	1	1	yes	characteristic
668	#433	C₂²×C₈₉	1	2	yes	—
669	#431	C₂²×C₈₉	1	1	yes	characteristic
670	#428	C₂²×C₈₉	1	2	yes	—
671	#427	C₂²×C₈₉	1	2	yes	—
672	C₂×#106	C₂²×C₈₉	1	2	yes	—
673	#424	C₂²×C₈₉	1	2	yes	—
674	C₂×C₄⋊C₈	C₂²×C₈₉	1	1	yes	characteristic
675	#419	C₂²×C₈₉	1	2	yes	—
676	C₂×#103	C₂²×C₈₉	1	2	yes	—
677	C₂×#103	C₂²×C₈₉	1	2	yes	—
678	C₂×#41	—	2	1	no	—
679	C₂²×Q₈	—	2	1	no	—
680	C₂²×Q₈	—	2	1	no	—
681	C₂²×Q₈	C₂³×C₈₉	1	1	yes	characteristic
682	C₂²×Q₈	C₂³×C₈₉	1	2	yes	—
683	C₂×Q₁₆	C₂³×C₈₉	1	1	yes	characteristic
684	C₂×Q₁₆	C₂³×C₈₉	1	1	yes	characteristic
685	C₂×Q₁₆	C₂³×C₈₉	1	2	yes	—
686	C₂×SD₁₆	C₂³×C₈₉	1	1	yes	characteristic
687	C₂×SD₁₆	C₂³×C₈₉	1	2	yes	—
688	C₂×SD₁₆	C₂³×C₈₉	1	1	yes	characteristic
689	C₂×M₁₆	C₂³×C₈₉	1	2	yes	—
690	C₂²×C₈	C₂³×C₈₉	1	2	yes	—
691	C₂²×C₈	C₂³×C₈₉	1	2	yes	—
692	C₄⋊Q₈	—	2	1	no	—
693	C₄⋊Q₈	—	2	1	no	—
694	C₄⋊Q₈	—	2	1	no	—
695	C₄⋊Q₈	—	2	2	no	—
696	C₄⋊Q₈	—	2	2	no	—
697	C₄⋊Q₈	—	2	1	no	—
698	C₄⋊Q₈	—	2	1	no	—
699	C₄⋊Q₈	C₂³×C₈₉	1	1	yes	characteristic
700	C₄⋊Q₈	C₂³×C₈₉	1	2	yes	—
701	C₄⋊Q₈	C₂³×C₈₉	1	2	yes	—
702	C₄⋊Q₈	C₂³×C₈₉	1	1	yes	characteristic
703	C₄⋊Q₈	C₂³×C₈₉	1	1	yes	characteristic
704	C₄⋊Q₈	C₂³×C₈₉	1	1	yes	characteristic
705	C₄⋊Q₈	C₂³×C₈₉	1	2	yes	—
706	#126	—	2	2	no	—
707	#126	—	2	2	no	—
708	#126	—	2	2	no	—
709	#126	—	2	2	no	—
710	#126	—	2	2	no	—
711	#126	—	2	2	no	—
712	#126	—	2	2	no	—
713	#126	—	2	1	no	—
714	#126	D₄×C₈₉	1	2	yes	—
715	#125	—	2	1	no	—
716	#125	—	2	2	no	—
717	#125	—	2	2	no	—
718	#125	—	2	2	no	—
719	#125	—	2	2	no	—
720	#125	—	2	2	no	—
721	#125	—	2	2	no	—
722	#125	—	2	2	no	—
723	#125	—	2	2	no	—
724	#125	—	2	1	no	—
725	#125	D₄×C₈₉	1	1	yes	characteristic
726	#125	C₂³×C₈₉	1	1	yes	characteristic
727	#125	C₂³×C₈₉	1	2	yes	—
728	#125	C₂³×C₈₉	1	2	yes	—
729	#124	—	2	1	no	—
730	#124	—	2	1	no	—
731	#124	—	2	2	no	—
732	#124	D₄×C₈₉	1	1	yes	characteristic
733	#124	C₂³×C₈₉	1	1	yes	characteristic
734	#123	—	2	2	no	—
735	#123	—	2	1	no	—
736	#123	—	2	2	no	—
737	#123	—	2	2	no	—
738	#123	—	2	2	no	—
739	#123	D₄×C₈₉	1	2	yes	—
740	C₂²⋊Q₈	—	2	1	no	—
741	C₂²⋊Q₈	—	2	2	no	—
742	C₂²⋊Q₈	—	2	1	no	—
743	C₂²⋊Q₈	—	2	1	no	—
744	C₂²⋊Q₈	—	2	2	no	—
745	C₂²⋊Q₈	—	2	2	no	—
746	C₂²⋊Q₈	—	2	2	no	—
747	C₂²⋊Q₈	—	2	2	no	—
748	C₂²⋊Q₈	—	2	2	no	—
749	C₂²⋊Q₈	—	2	2	no	—
750	C₂²⋊Q₈	—	2	2	no	—
751	C₂²⋊Q₈	—	2	2	no	—
752	C₂²⋊Q₈	D₄×C₈₉	1	1	yes	characteristic
753	C₂²⋊Q₈	C₂³×C₈₉	1	1	yes	characteristic
754	C₂²⋊Q₈	C₂³×C₈₉	1	2	yes	—
755	C₂²⋊Q₈	C₂³×C₈₉	1	2	yes	—
756	C₂²⋊Q₈	C₂³×C₈₉	1	2	yes	—
757	C₂²⋊Q₈	C₂³×C₈₉	1	2	yes	—
758	#121	—	2	2	no	—
759	#121	D₄×C₈₉	1	1	yes	characteristic
760	#121	C₂³×C₈₉	1	1	yes	characteristic
761	#121	C₂³×C₈₉	1	2	yes	—
762	C₄×Q₈	—	2	1	no	—
763	C₄×Q₈	—	2	2	no	—
764	C₄×Q₈	—	2	2	no	—
765	C₄×Q₈	—	2	1	no	—
766	C₄×Q₈	—	2	1	no	—
767	C₄×Q₈	—	2	1	no	—
768	C₄×Q₈	—	2	1	no	—
769	C₄×Q₈	—	2	1	no	—
770	C₄×Q₈	—	2	1	no	—
771	C₄×Q₈	—	2	1	no	—
772	C₄×Q₈	C₂³×C₈₉	1	1	yes	characteristic
773	C₄×Q₈	C₂³×C₈₉	1	1	yes	characteristic
774	C₄×Q₈	C₂³×C₈₉	1	1	yes	characteristic
775	C₄×Q₈	C₂³×C₈₉	1	1	yes	characteristic
776	C₄×Q₈	C₂³×C₈₉	1	2	yes	—
777	C₄×Q₈	C₂³×C₈₉	1	2	yes	—
778	C₄×Q₈	C₂³×C₈₉	1	2	yes	—
779	C₄×Q₈	C₂³×C₈₉	1	1	yes	characteristic
780	C₄×Q₈	C₂³×C₈₉	1	2	yes	—
781	C₄×Q₈	C₂³×C₈₉	1	1	yes	characteristic
782	C₄×D₄	—	2	2	no	—
783	C₄×D₄	—	2	1	no	—
784	C₄×D₄	—	2	2	no	—
785	C₄×D₄	—	2	1	no	—
786	C₄×D₄	—	2	2	no	—
787	C₄×D₄	C₂³×C₈₉	1	1	yes	characteristic
788	C₄×D₄	C₂³×C₈₉	1	2	yes	—
789	C₄×D₄	C₂³×C₈₉	1	1	yes	characteristic
790	C₄×D₄	C₂³×C₈₉	1	2	yes	—
791	#117	—	2	1	no	—
792	#117	—	2	2	no	—
793	#117	—	2	2	no	—
794	#117	—	2	2	no	—
795	#117	—	2	1	no	—
796	#117	C₂³×C₈₉	1	2	yes	—
797	#117	C₂³×C₈₉	1	2	yes	—
798	#117	C₂³×C₈₉	1	2	yes	—
799	C₂×C₄⋊C₄	—	2	1	no	—
800	C₂×C₄⋊C₄	—	2	1	no	—
801	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
802	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
803	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
804	C₂×C₄²	—	2	1	no	—
805	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
806	#107	C₂³×C₈₉	1	1	yes	characteristic
807	#107	C₂³×C₈₉	1	2	yes	—
808	#107	C₂³×C₈₉	1	2	yes	—
809	#107	C₂³×C₈₉	1	2	yes	—
810	#107	C₂³×C₈₉	1	2	yes	—
811	#107	C₂³×C₈₉	1	1	yes	characteristic
812	#107	C₂³×C₈₉	1	2	yes	—
813	#106	C₂³×C₈₉	1	2	yes	—
814	#106	C₂³×C₈₉	1	2	yes	—
815	#106	C₂³×C₈₉	1	2	yes	—
816	#106	C₂³×C₈₉	1	2	yes	—
817	#106	C₂³×C₈₉	1	2	yes	—
818	#106	C₂³×C₈₉	1	1	yes	characteristic
819	#106	C₂³×C₈₉	1	1	yes	characteristic
820	C₄⋊C₈	C₂³×C₈₉	1	2	yes	—
821	C₄⋊C₈	C₂³×C₈₉	1	1	yes	characteristic
822	C₄⋊C₈	C₂³×C₈₉	1	1	yes	characteristic
823	C₄⋊C₈	C₂³×C₈₉	1	1	yes	characteristic
824	C₄⋊C₈	C₂³×C₈₉	1	2	yes	—
825	C₄⋊C₈	C₂³×C₈₉	1	2	yes	—
826	C₄⋊C₈	C₂³×C₈₉	1	1	yes	characteristic
827	#103	C₂³×C₈₉	1	1	yes	characteristic
828	#103	C₂³×C₈₉	1	2	yes	—
829	#103	C₂³×C₈₉	1	2	yes	—
830	#103	C₂³×C₈₉	1	2	yes	—
831	#103	C₂³×C₈₉	1	2	yes	—
832	#103	C₂³×C₈₉	1	2	yes	—
833	#103	C₂³×C₈₉	1	2	yes	—
834	#103	C₂³×C₈₉	1	1	yes	characteristic
835	#103	C₂³×C₈₉	1	2	yes	—
836	#103	C₂³×C₈₉	1	2	yes	—
837	#103	C₂³×C₈₉	1	2	yes	—
838	#103	C₂³×C₈₉	1	1	yes	characteristic
839	#103	C₂³×C₈₉	1	1	yes	characteristic
840	#103	C₂³×C₈₉	1	1	yes	characteristic
841	#103	C₂³×C₈₉	1	2	yes	—
842	#103	C₂³×C₈₉	1	1	yes	characteristic
843	#103	C₂³×C₈₉	1	2	yes	—
844	#102	C₂³×C₈₉	1	1	yes	characteristic
845	#102	C₂³×C₈₉	1	1	yes	characteristic
846	#102	C₂³×C₈₉	1	2	yes	—
847	C₂²⋊C₈	C₂³×C₈₉	1	1	yes	characteristic
848	C₂²⋊C₈	C₂³×C₈₉	1	1	yes	characteristic
849	C₂²⋊C₈	C₂³×C₈₉	1	2	yes	—
850	C₂²⋊C₈	C₂³×C₈₉	1	2	yes	—
851	#97	C₂³×C₈₉	1	2	yes	—
852	C₄×C₈	C₂³×C₈₉	1	1	yes	characteristic
853	C₄×C₈	C₂³×C₈₉	1	1	yes	characteristic
854	C₄×C₈	C₂³×C₈₉	1	2	yes	—
855	#41	—	8	2	no	—
856	C₂×Q₈	—	2	1	no	—
857	C₂×Q₈	—	2	2	no	—
858	C₂×Q₈	—	2	1	no	—
859	C₂×Q₈	—	2	1	no	—
860	C₂×Q₈	—	2	1	no	—
861	C₂×Q₈	—	2	2	no	—
862	C₂×Q₈	—	2	2	no	—
863	C₂×Q₈	—	2	2	no	—
864	C₂×Q₈	—	2	4	no	—
865	C₂×Q₈	—	4	1	no	—
866	C₂×Q₈	—	4	2	no	—
867	C₂×Q₈	—	8	2	no	—
868	C₂×Q₈	—	8	2	no	—
869	C₂×Q₈	C₂×D₄×C₈₉	1	1	yes	characteristic
870	C₂×Q₈	C₂⁴×C₈₉	1	1	yes	characteristic
871	C₂×Q₈	C₂⁴×C₈₉	1	2	yes	—
872	C₂×Q₈	C₂⁴×C₈₉	1	1	yes	characteristic
873	C₂×Q₈	C₂⁴×C₈₉	1	1	yes	characteristic
874	C₂×D₄	—	2	1	no	—
875	C₂×D₄	—	2	2	no	—
876	C₂×D₄	C₂×D₄×C₈₉	1	2	yes	—
877	C₂×D₄	C₂×D₄×C₈₉	1	1	yes	characteristic
878	C₂×D₄	C₂⁴×C₈₉	1	1	yes	characteristic
879	C₂²×C₄	—	2	1	no	—
880	C₂²×C₄	—	2	1	no	—
881	C₂²×C₄	—	2	2	no	—
882	C₂²×C₄	—	2	2	no	—
883	C₂²×C₄	—	2	2	no	—
884	C₂²×C₄	—	2	1	no	—
885	C₂²×C₄	—	2	2	no	—
886	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
887	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
888	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
889	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
890	Q₁₆	—	2	2	no	—
891	Q₁₆	—	4	1	no	—
892	Q₁₆	—	4	2	no	—
893	SD₁₆	—	2	2	no	—
894	SD₁₆	—	4	2	no	—
895	SD₁₆	—	4	1	no	—
896	M₁₆	—	4	2	no	—
897	C₂×C₈	—	4	2	no	—
898	C₂×C₈	—	4	2	no	—
899	C₂×C₈	C₂⁴×C₈₉	1	1	yes	characteristic
900	C₂×C₈	C₂⁴×C₈₉	1	1	yes	characteristic
901	C₂×C₈	C₂⁴×C₈₉	1	1	yes	characteristic
902	C₂×C₈	C₂⁴×C₈₉	1	2	yes	—
903	C₂×C₈	C₂⁴×C₈₉	1	1	yes	characteristic
904	C₂×C₈	C₂⁴×C₈₉	1	2	yes	—
905	C₄⋊C₄	—	2	1	no	—
906	C₄⋊C₄	—	2	1	no	—
907	C₄⋊C₄	—	2	1	no	—
908	C₄⋊C₄	—	2	1	no	—
909	C₄⋊C₄	—	2	1	no	—
910	C₄⋊C₄	—	2	2	no	—
911	C₄⋊C₄	—	2	1	no	—
912	C₄⋊C₄	—	2	1	no	—
913	C₄⋊C₄	—	2	2	no	—
914	C₄⋊C₄	—	2	2	no	—
915	C₄⋊C₄	—	2	2	no	—
916	C₄⋊C₄	—	2	2	no	—
917	C₄⋊C₄	—	2	2	no	—
918	C₄⋊C₄	—	2	1	no	—
919	C₄⋊C₄	—	2	1	no	—
920	C₄⋊C₄	—	2	1	no	—
921	C₄⋊C₄	—	2	2	no	—
922	C₄⋊C₄	—	2	1	no	—
923	C₄⋊C₄	—	2	2	no	—
924	C₄⋊C₄	—	2	1	no	—
925	C₄⋊C₄	—	2	2	no	—
926	C₄⋊C₄	—	2	1	no	—
927	C₄⋊C₄	—	2	2	no	—
928	C₄⋊C₄	—	2	2	no	—
929	C₄⋊C₄	—	2	2	no	—
930	C₄⋊C₄	—	2	2	no	—
931	C₄⋊C₄	—	2	2	no	—
932	C₄⋊C₄	—	2	2	no	—
933	C₄⋊C₄	—	2	2	no	—
934	C₄⋊C₄	—	2	2	no	—
935	C₄⋊C₄	—	2	2	no	—
936	C₄⋊C₄	—	2	1	no	—
937	C₄⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
938	C₄⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
939	C₄⋊C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
940	C₄⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
941	C₄⋊C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
942	C₄⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
943	C₄⋊C₄	C₂⁴×C₈₉	1	1	yes	characteristic
944	C₄⋊C₄	C₂⁴×C₈₉	1	1	yes	characteristic
945	C₄⋊C₄	C₂⁴×C₈₉	1	2	yes	—
946	C₄⋊C₄	C₂⁴×C₈₉	1	1	yes	characteristic
947	C₄⋊C₄	C₂⁴×C₈₉	1	2	yes	—
948	C₄⋊C₄	C₂⁴×C₈₉	1	2	yes	—
949	C₄⋊C₄	C₂⁴×C₈₉	1	1	yes	characteristic
950	C₂²⋊C₄	—	2	2	no	—
951	C₂²⋊C₄	—	2	2	no	—
952	C₂²⋊C₄	—	2	2	no	—
953	C₂²⋊C₄	—	2	1	no	—
954	C₂²⋊C₄	—	2	2	no	—
955	C₂²⋊C₄	—	2	2	no	—
956	C₂²⋊C₄	—	2	2	no	—
957	C₂²⋊C₄	—	2	1	no	—
958	C₂²⋊C₄	—	2	1	no	—
959	C₂²⋊C₄	—	2	2	no	—
960	C₂²⋊C₄	—	2	1	no	—
961	C₂²⋊C₄	—	2	2	no	—
962	C₂²⋊C₄	—	2	1	no	—
963	C₂²⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
964	C₂²⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
965	C₂²⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
966	C₂²⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
967	C₂²⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
968	C₄²	—	2	1	no	—
969	C₄²	—	2	1	no	—
970	C₄²	—	2	1	no	—
971	C₄²	—	2	1	no	—
972	C₄²	—	2	2	no	—
973	C₄²	—	2	2	no	—
974	C₄²	—	2	2	no	—
975	C₄²	—	2	1	no	—
976	C₄²	—	2	2	no	—
977	C₄²	—	2	2	no	—
978	C₄²	—	2	2	no	—
979	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
980	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
981	C₄²	C₂⁴×C₈₉	1	1	yes	characteristic
982	C₄²	C₂⁴×C₈₉	1	2	yes	—
983	C₄²	C₂⁴×C₈₉	1	1	yes	characteristic
984	C₂³	—	2	1	no	—
985	C₂³	C₂²×D₄×C₈₉	1	2	yes	—
986	C₂³	C₂²×D₄×C₈₉	1	1	yes	characteristic
987	Q₈	—	2	2	no	—
988	Q₈	—	2	1	no	—
989	Q₈	—	2	1	no	—
990	Q₈	—	2	1	no	—
991	Q₈	—	2	2	no	—
992	Q₈	—	2	2	no	—
993	Q₈	—	2	1	no	—
994	Q₈	—	2	1	no	—
995	Q₈	—	4	2	no	—
996	Q₈	—	4	4	no	—
997	Q₈	—	4	2	no	—
998	Q₈	—	4	2	no	—
999	Q₈	—	4	2	no	—
1000	Q₈	—	8	2	no	—
1001	Q₈	—	8	2	no	—
1002	Q₈	2₋¹⁺⁴×C₈₉	1	2	yes	—
1003	D₄	—	2	4	no	—
1004	D₄	—	2	2	no	—
1005	D₄	—	2	1	no	—
1006	D₄	—	2	1	no	—
1007	D₄	—	4	2	no	—
1008	D₄	—	8	2	no	—
1009	C₂×C₄	—	2	2	no	—
1010	C₂×C₄	—	2	1	no	—
1011	C₂×C₄	—	2	2	no	—
1012	C₂×C₄	—	2	1	no	—
1013	C₂×C₄	—	2	2	no	—
1014	C₂×C₄	—	2	1	no	—
1015	C₂×C₄	—	2	2	no	—
1016	C₂×C₄	—	2	1	no	—
1017	C₂×C₄	—	2	1	no	—
1018	C₂×C₄	—	2	1	no	—
1019	C₂×C₄	—	2	2	no	—
1020	C₂×C₄	—	2	1	no	—
1021	C₂×C₄	—	2	1	no	—
1022	C₂×C₄	—	2	2	no	—
1023	C₂×C₄	—	2	2	no	—
1024	C₂×C₄	—	2	2	no	—
1025	C₂×C₄	—	2	1	no	—
1026	C₂×C₄	—	4	2	no	—
1027	C₂×C₄	—	4	4	no	—
1028	C₂×C₄	—	4	2	no	—
1029	C₂×C₄	—	4	2	no	—
1030	C₂×C₄	—	8	2	no	—
1031	C₂×C₄	—	8	2	no	—
1032	C₂×C₄	—	8	2	no	—
1033	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
1034	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
1035	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
1036	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
1037	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
1038	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
1039	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
1040	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
1041	C₂×C₄	C₂⁵×C₈₉	1	1	yes	characteristic
1042	C₈	—	2	1	no	—
1043	C₈	—	2	1	no	—
1044	C₈	—	2	2	no	—
1045	C₈	—	2	1	no	—
1046	C₈	—	2	2	no	—
1047	C₈	—	2	1	no	—
1048	C₂²	—	2	1	no	—
1049	C₂²	—	2	1	no	—
1050	C₂²	—	2	2	no	—
1051	C₂²	—	2	2	no	—
1052	C₂²	—	2	2	no	—
1053	C₂²	—	4	1	no	—
1054	C₂²	—	4	1	no	—
1055	C₂²	—	4	1	no	—
1056	C₂²	#578×C₈₉	1	2	yes	—
1057	C₂²	C₂³×D₄×C₈₉	1	1	yes	characteristic
1058	C₄	—	2	1	no	—
1059	C₄	—	2	2	no	—
1060	C₄	—	2	1	no	—
1061	C₄	—	2	1	no	—
1062	C₄	—	2	2	no	—
1063	C₄	—	2	1	no	—
1064	C₄	—	2	2	no	—
1065	C₄	—	2	2	no	—
1066	C₄	—	4	1	no	—
1067	C₄	—	4	2	no	—
1068	C₄	—	4	2	no	—
1069	C₄	—	4	2	no	—
1070	C₄	—	4	1	no	—
1071	C₄	—	4	1	no	—
1072	C₄	—	4	1	no	—
1073	C₄	—	4	1	no	—
1074	C₄	—	4	2	no	—
1075	C₄	—	4	1	no	—
1076	C₄	#577×C₈₉	1	2	yes	—
1077	C₄	C₂×2₋¹⁺⁴×C₈₉	1	1	yes	characteristic
1078	C₄	#585×C₈₉	1	1	yes	characteristic
1079	C₂	—	2	2	no	—
1080	C₂	—	4	2	no	—
1081	C₂	—	8	1	no	—
1082	C₂	C₈₉×#3489	1	1	yes	characteristic
1083	C₂	C₂×#577×C₈₉	1	1	yes	characteristic
1084	C₂	C₂×#578×C₈₉	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₈₉	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₈₉
prime radical	C₈₉×#3552	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₈₉ ◁ #529×C₈₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₈₉×#3523	C₂	semidirect
3. C₈₉×#3386	C₂	semidirect
4. C₈₉×#3383	C₂	semidirect
5. C₈₉×#3374	C₂	semidirect
6. C₈₉×#3359	C₂	semidirect
7. C₈₉×#3353	C₂	semidirect
8. C₈₉×#3344	C₂	semidirect
9. C₈₉×#3342	C₂	semidirect
10. C₈₉×#3337	C₂	semidirect
11. C₈₉×#3328	C₂	semidirect
12. C₈₉×#3320	C₂	semidirect
13. C₈₉×#3299	C₂	semidirect
14. C₈₉×#3298	C₂	semidirect
15. C₈₉×#3258	C₂	semidirect
16. C₈₉×#3248	C₂	semidirect
17. C₈₉×#3242	C₂	semidirect
18. C₈₉×#3230	C₂	semidirect
19. C₈₉×#3121	C₂	semidirect
20. C₈₉×#3108	C₂	semidirect
21. C₈₉×#3082	C₂	semidirect
22. C₂×#475×C₈₉	C₂	semidirect
23. C₈₉×#2994	C₂	semidirect
536. #62203	C₈₉	direct (N × H)
544. #3523	C₂×C₈₉	semidirect
545. #3386	C₂×C₈₉	semidirect
546. #3383	C₂×C₈₉	semidirect
547. #3374	C₂×C₈₉	semidirect
548. #3359	C₂×C₈₉	semidirect
549. #3353	C₂×C₈₉	semidirect
550. #3344	C₂×C₈₉	semidirect
551. #3342	C₂×C₈₉	semidirect
552. #3337	C₂×C₈₉	semidirect
553. #3328	C₂×C₈₉	semidirect
554. #3320	C₂×C₈₉	semidirect
555. #3299	C₂×C₈₉	semidirect
556. #3298	C₂×C₈₉	semidirect
557. #3258	C₂×C₈₉	semidirect
558. #3248	C₂×C₈₉	semidirect
559. #3242	C₂×C₈₉	semidirect
560. #3230	C₂×C₈₉	semidirect
561. #3121	C₂×C₈₉	semidirect
562. #3108	C₂×C₈₉	semidirect
563. #3082	C₂×C₈₉	semidirect
564. C₂×#475	C₂×C₈₉	semidirect
565. #2994	C₂×C₈₉	semidirect
566. C₈₉	#62203	direct (N × H)

Maximal subgroups

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

subgroup	index
C₈₉×#3552	2
C₈₉×#3523	2
C₈₉×#3386	2
C₈₉×#3383	2
C₈₉×#3374	2
C₈₉×#3359	2
C₈₉×#3353	2
C₈₉×#3344	2
C₈₉×#3342	2
C₈₉×#3337	2
C₈₉×#3328	2
C₈₉×#3320	2
C₈₉×#3299	2
C₈₉×#3298	2
C₈₉×#3258	2
C₈₉×#3248	2
C₈₉×#3242	2
C₈₉×#3230	2
C₈₉×#3121	2
C₈₉×#3108	2
C₈₉×#3082	2
C₂×#475×C₈₉	2
C₈₉×#2994	2
#62203	89

Subgroups — C89×#62203 #36440051

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#62203 #36440051