Subgroups — C₈₉×#62184 #36440032

Order 22784.

1682 conjugacy classes of subgroups.

The subgroup lattice has 1098 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, complemented
2	C₈₉×#3518	C₂	1	1	yes	maximal, characteristic, complemented
3	C₈₉×#3387	C₂	1	1	yes	maximal, characteristic, complemented
4	Q₈×SD₁₆×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
5	C₈₉×#3367	C₂	1	1	yes	maximal, characteristic, complemented
6	C₈₉×#3364	C₂	1	1	yes	maximal, characteristic, complemented
7	C₈₉×#3356	C₂	1	2	yes	maximal, complemented
8	C₈₉×#3354	C₂	1	1	yes	maximal, characteristic, complemented
9	C₈₉×#3350	C₂	1	2	yes	maximal, complemented
10	C₈₉×#3340	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈₉×#3328	C₂	1	1	yes	maximal, characteristic, complemented
12	C₈₉×#3326	C₂	1	2	yes	maximal, complemented
13	C₈₉×#3316	C₂	1	2	yes	maximal, complemented
14	C₈₉×#3298	C₂	1	1	yes	maximal, characteristic, complemented
15	C₈₉×#3263	C₂	1	2	yes	maximal, complemented
16	C₈₉×#3252	C₂	1	1	yes	maximal, characteristic, complemented
17	C₈₉×#3244	C₂	1	2	yes	maximal, complemented
18	C₈₉×#3229	C₂	1	1	yes	maximal, characteristic, complemented
19	C₈₉×#3121	C₂	1	2	yes	maximal, complemented
20	C₈₉×#3102	C₂	1	1	yes	maximal, characteristic, complemented
21	C₈₉×#3082	C₂	1	2	yes	maximal, complemented
22	C₈₉×#3079	C₂	1	1	yes	maximal, characteristic, complemented
23	C₈₉×#2993	C₂	1	1	yes	maximal, characteristic, complemented
24	#563×C₈₉	—	2	2	no	—
25	Q₈²×C₈₉	C₂²	1	1	yes	characteristic
26	#557×C₈₉	C₂²	1	1	yes	characteristic
27	#556×C₈₉	—	2	2	no	—
28	#556×C₈₉	—	2	1	no	—
29	#556×C₈₉	C₂²	1	1	yes	characteristic
30	#556×C₈₉	C₂²	1	1	yes	characteristic
31	#556×C₈₉	C₂²	1	2	yes	—
32	#555×C₈₉	—	2	1	no	—
33	#555×C₈₉	C₂²	1	1	yes	characteristic
34	#554×C₈₉	C₂²	1	2	yes	—
35	#553×C₈₉	C₂²	1	2	yes	—
36	D₄×Q₈×C₈₉	—	2	1	no	—
37	D₄×Q₈×C₈₉	C₂²	1	1	yes	characteristic
38	D₄×Q₈×C₈₉	C₂²	1	1	yes	characteristic
39	#548×C₈₉	—	2	1	no	—
40	#548×C₈₉	C₂²	1	2	yes	—
41	#547×C₈₉	C₂²	1	1	yes	characteristic
42	#544×C₈₉	C₂²	1	2	yes	—
43	#542×C₈₉	—	2	2	no	—
44	#542×C₈₉	C₂²	1	2	yes	—
45	#542×C₈₉	C₂²	1	2	yes	—
46	#541×C₈₉	—	2	1	no	—
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	C₄×#41×C₈₉	C₂²	1	1	yes	characteristic
57	#501×C₈₉	C₂²	1	2	yes	—
58	#498×C₈₉	C₂²	1	1	yes	characteristic
59	#498×C₈₉	C₂²	1	1	yes	characteristic
60	#498×C₈₉	C₂²	1	2	yes	—
61	#489×C₈₉	C₂²	1	2	yes	—
62	#488×C₈₉	C₂²	1	2	yes	—
63	#487×C₈₉	C₂²	1	1	yes	characteristic
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	1	yes	characteristic
68	#483×C₈₉	C₂²	1	2	yes	—
69	#483×C₈₉	C₂²	1	2	yes	—
70	#483×C₈₉	C₂²	1	2	yes	—
71	#482×C₈₉	C₂²	1	2	yes	—
72	#482×C₈₉	C₂²	1	1	yes	characteristic
73	#482×C₈₉	C₂²	1	2	yes	—
74	#481×C₈₉	C₂²	1	2	yes	—
75	#479×C₈₉	C₂²	1	2	yes	—
76	#479×C₈₉	C₂²	1	1	yes	characteristic
77	#479×C₈₉	C₂²	1	2	yes	—
78	#479×C₈₉	C₂²	1	2	yes	—
79	#478×C₈₉	C₂²	1	1	yes	characteristic
80	#477×C₈₉	C₂²	1	2	yes	—
81	#477×C₈₉	C₂²	1	2	yes	—
82	#477×C₈₉	C₂²	1	1	yes	characteristic
83	#476×C₈₉	C₂²	1	2	yes	—
84	#476×C₈₉	C₂²	1	2	yes	—
85	#476×C₈₉	C₂²	1	1	yes	characteristic
86	#475×C₈₉	C₂²	1	1	yes	characteristic
87	#475×C₈₉	C₂²	1	1	yes	characteristic
88	#475×C₈₉	C₂²	1	2	yes	—
89	#475×C₈₉	C₂²	1	2	yes	—
90	#475×C₈₉	C₂²	1	2	yes	—
91	#475×C₈₉	C₂²	1	2	yes	—
92	#474×C₈₉	C₂²	1	1	yes	characteristic
93	#474×C₈₉	C₂²	1	1	yes	characteristic
94	#470×C₈₉	C₂²	1	2	yes	—
95	#470×C₈₉	C₂²	1	2	yes	—
96	#469×C₈₉	C₂²	1	2	yes	—
97	#468×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	2	yes	—
102	#464×C₈₉	C₂²	1	2	yes	—
103	#463×C₈₉	C₂²	1	2	yes	—
104	#463×C₈₉	C₂²	1	1	yes	characteristic
105	#462×C₈₉	C₂²	1	1	yes	characteristic
106	#461×C₈₉	C₂²	1	1	yes	characteristic
107	#452×C₈₉	C₂²	1	1	yes	characteristic
108	#451×C₈₉	C₂²	1	2	yes	—
109	#449×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	2	yes	—
117	C₄×SD₁₆×C₈₉	C₂²	1	2	yes	—
118	C₄×SD₁₆×C₈₉	C₂²	1	1	yes	characteristic
119	C₄×SD₁₆×C₈₉	C₂²	1	1	yes	characteristic
120	C₄×D₈×C₈₉	C₂²	1	1	yes	characteristic
121	#436×C₈₉	C₂²	1	2	yes	—
122	#436×C₈₉	C₂²	1	1	yes	characteristic
123	#435×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	#428×C₈₉	C₂²	1	2	yes	—
129	#427×C₈₉	C₂²	1	2	yes	—
130	#424×C₈₉	C₂²	1	2	yes	—
131	#423×C₈₉	C₂²	1	1	yes	characteristic
132	#419×C₈₉	C₂²	1	2	yes	—
133	#417×C₈₉	C₂²	1	2	yes	—
134	C₂×#103×C₈₉	C₂²	1	2	yes	—
135	C₂×#41×C₈₉	—	2	1	no	—
136	C₂×#41×C₈₉	C₂³	1	1	yes	characteristic
137	C₂²×Q₈×C₈₉	—	2	1	no	—
138	C₂²×Q₈×C₈₉	—	2	1	no	—
139	C₂²×Q₈×C₈₉	C₂³	1	2	yes	—
140	C₂×Q₁₆×C₈₉	C₂³	1	1	yes	characteristic
141	C₂×Q₁₆×C₈₉	C₂³	1	2	yes	—
142	C₂×SD₁₆×C₈₉	C₂³	1	1	yes	characteristic
143	C₂×SD₁₆×C₈₉	C₂³	1	1	yes	characteristic
144	C₂×SD₁₆×C₈₉	C₂³	1	2	yes	—
145	C₂×D₈×C₈₉	C₂³	1	1	yes	characteristic
146	C₂×M₁₆×C₈₉	C₂³	1	2	yes	—
147	C₂×M₁₆×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	1	yes	characteristic
158	C₄⋊Q₈×C₈₉	C₂³	1	1	yes	characteristic
159	C₄⋊Q₈×C₈₉	C₂³	1	2	yes	—
160	C₄⋊Q₈×C₈₉	C₂³	1	2	yes	—
161	C₄⋊Q₈×C₈₉	C₂³	1	2	yes	—
162	C₄⋊Q₈×C₈₉	C₂³	1	1	yes	characteristic
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	2	no	—
173	#125×C₈₉	—	2	2	no	—
174	#125×C₈₉	—	2	2	no	—
175	#125×C₈₉	—	2	1	no	—
176	#125×C₈₉	D₄	1	1	yes	characteristic
177	#125×C₈₉	C₂³	1	1	yes	characteristic
178	#125×C₈₉	C₂³	1	2	yes	—
179	#124×C₈₉	—	2	1	no	—
180	#124×C₈₉	—	2	2	no	—
181	#124×C₈₉	—	2	2	no	—
182	#124×C₈₉	—	2	2	no	—
183	#124×C₈₉	—	2	2	no	—
184	#124×C₈₉	—	2	2	no	—
185	#124×C₈₉	D₄	1	1	yes	characteristic
186	#124×C₈₉	C₂³	1	1	yes	characteristic
187	#124×C₈₉	C₂³	1	2	yes	—
188	#123×C₈₉	—	2	1	no	—
189	#123×C₈₉	—	2	2	no	—
190	#123×C₈₉	—	2	2	no	—
191	#123×C₈₉	—	2	2	no	—
192	#123×C₈₉	—	2	2	no	—
193	#123×C₈₉	D₄	1	2	yes	—
194	C₂²⋊Q₈×C₈₉	—	2	1	no	—
195	C₂²⋊Q₈×C₈₉	—	2	1	no	—
196	C₂²⋊Q₈×C₈₉	—	2	2	no	—
197	C₂²⋊Q₈×C₈₉	—	2	2	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	D₄	1	1	yes	characteristic
208	C₂²⋊Q₈×C₈₉	C₂³	1	2	yes	—
209	C₂²⋊Q₈×C₈₉	C₂³	1	1	yes	characteristic
210	C₂²⋊Q₈×C₈₉	C₂³	1	2	yes	—
211	C₂²⋊Q₈×C₈₉	C₂³	1	2	yes	—
212	#121×C₈₉	—	2	1	no	—
213	#121×C₈₉	—	2	2	no	—
214	#121×C₈₉	—	2	2	no	—
215	#121×C₈₉	D₄	1	1	yes	characteristic
216	#121×C₈₉	C₂³	1	2	yes	—
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	2	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	C₂³	1	1	yes	characteristic
227	C₄×Q₈×C₈₉	C₂³	1	1	yes	characteristic
228	C₄×Q₈×C₈₉	C₂³	1	2	yes	—
229	C₄×Q₈×C₈₉	C₂³	1	2	yes	—
230	C₄×Q₈×C₈₉	C₂³	1	2	yes	—
231	C₄×Q₈×C₈₉	C₂³	1	2	yes	—
232	C₄×Q₈×C₈₉	C₂³	1	1	yes	characteristic
233	C₄×Q₈×C₈₉	C₂³	1	1	yes	characteristic
234	C₄×D₄×C₈₉	—	2	1	no	—
235	C₄×D₄×C₈₉	—	2	2	no	—
236	C₄×D₄×C₈₉	—	2	1	no	—
237	C₄×D₄×C₈₉	—	2	1	no	—
238	C₄×D₄×C₈₉	—	2	1	no	—
239	C₄×D₄×C₈₉	—	2	2	no	—
240	C₄×D₄×C₈₉	—	2	2	no	—
241	C₄×D₄×C₈₉	C₂³	1	1	yes	characteristic
242	C₄×D₄×C₈₉	C₂³	1	1	yes	characteristic
243	C₄×D₄×C₈₉	C₂³	1	2	yes	—
244	C₄×D₄×C₈₉	C₂³	1	1	yes	characteristic
245	C₄×D₄×C₈₉	C₂³	1	1	yes	characteristic
246	C₄×D₄×C₈₉	C₂³	1	2	yes	—
247	#117×C₈₉	—	2	1	no	—
248	#117×C₈₉	—	2	1	no	—
249	#117×C₈₉	—	2	1	no	—
250	#117×C₈₉	—	2	2	no	—
251	#117×C₈₉	—	2	2	no	—
252	#117×C₈₉	—	2	1	no	—
253	#117×C₈₉	—	2	1	no	—
254	#117×C₈₉	C₂³	1	2	yes	—
255	#117×C₈₉	C₂³	1	2	yes	—
256	#117×C₈₉	C₂³	1	1	yes	characteristic
257	#117×C₈₉	C₂³	1	2	yes	—
258	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
259	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
260	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
261	C₂×C₄²×C₈₉	—	2	1	no	—
262	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
263	#107×C₈₉	C₂³	1	2	yes	—
264	#107×C₈₉	C₂³	1	2	yes	—
265	#107×C₈₉	C₂³	1	1	yes	characteristic
266	#107×C₈₉	C₂³	1	2	yes	—
267	#107×C₈₉	C₂³	1	1	yes	characteristic
268	#106×C₈₉	C₂³	1	1	yes	characteristic
269	#106×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	2	yes	—
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	1	yes	characteristic
290	#103×C₈₉	C₂³	1	2	yes	—
291	#103×C₈₉	C₂³	1	2	yes	—
292	#103×C₈₉	C₂³	1	1	yes	characteristic
293	#103×C₈₉	C₂³	1	2	yes	—
294	#103×C₈₉	C₂³	1	1	yes	characteristic
295	#103×C₈₉	C₂³	1	2	yes	—
296	#103×C₈₉	C₂³	1	2	yes	—
297	#102×C₈₉	C₂³	1	2	yes	—
298	#102×C₈₉	C₂³	1	2	yes	—
299	#102×C₈₉	C₂³	1	1	yes	characteristic
300	#102×C₈₉	C₂³	1	1	yes	characteristic
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	—	2	2	no	—
313	#41×C₈₉	—	4	1	no	—
314	#41×C₈₉	—	8	2	no	—
315	C₂×Q₈×C₈₉	—	2	2	no	—
316	C₂×Q₈×C₈₉	—	2	1	no	—
317	C₂×Q₈×C₈₉	—	2	1	no	—
318	C₂×Q₈×C₈₉	—	2	1	no	—
319	C₂×Q₈×C₈₉	—	2	2	no	—
320	C₂×Q₈×C₈₉	—	2	2	no	—
321	C₂×Q₈×C₈₉	—	2	2	no	—
322	C₂×Q₈×C₈₉	—	2	4	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	2	yes	—
328	C₂×Q₈×C₈₉	C₂⁴	1	1	yes	characteristic
329	C₂×Q₈×C₈₉	C₂⁴	1	1	yes	characteristic
330	C₂×D₄×C₈₉	—	2	1	no	—
331	C₂×D₄×C₈₉	—	2	1	no	—
332	C₂×D₄×C₈₉	—	2	2	no	—
333	C₂×D₄×C₈₉	—	2	2	no	—
334	C₂×D₄×C₈₉	C₂×D₄	1	1	yes	characteristic
335	C₂×D₄×C₈₉	C₂×D₄	1	2	yes	—
336	C₂×D₄×C₈₉	C₂⁴	1	1	yes	characteristic
337	C₂×D₄×C₈₉	C₂⁴	1	1	yes	characteristic
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	1	no	—
343	C₂²×C₄×C₈₉	—	2	1	no	—
344	C₂²×C₄×C₈₉	—	2	1	no	—
345	C₂²×C₄×C₈₉	—	2	2	no	—
346	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
347	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
348	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
349	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
350	Q₁₆×C₈₉	—	2	2	no	—
351	Q₁₆×C₈₉	—	4	2	no	—
352	SD₁₆×C₈₉	—	2	2	no	—
353	SD₁₆×C₈₉	—	4	1	no	—
354	SD₁₆×C₈₉	—	4	2	no	—
355	D₈×C₈₉	—	4	1	no	—
356	M₁₆×C₈₉	—	4	2	no	—
357	M₁₆×C₈₉	—	4	2	no	—
358	C₂×C₈×C₈₉	—	4	2	no	—
359	C₂×C₈×C₈₉	C₂⁴	1	1	yes	characteristic
360	C₂×C₈×C₈₉	C₂⁴	1	1	yes	characteristic
361	C₂×C₈×C₈₉	C₂⁴	1	2	yes	—
362	C₂×C₈×C₈₉	C₂⁴	1	1	yes	characteristic
363	C₂×C₈×C₈₉	C₂⁴	1	1	yes	characteristic
364	C₂×C₈×C₈₉	C₂⁴	1	2	yes	—
365	C₄⋊C₄×C₈₉	—	2	1	no	—
366	C₄⋊C₄×C₈₉	—	2	2	no	—
367	C₄⋊C₄×C₈₉	—	2	1	no	—
368	C₄⋊C₄×C₈₉	—	2	2	no	—
369	C₄⋊C₄×C₈₉	—	2	2	no	—
370	C₄⋊C₄×C₈₉	—	2	1	no	—
371	C₄⋊C₄×C₈₉	—	2	1	no	—
372	C₄⋊C₄×C₈₉	—	2	1	no	—
373	C₄⋊C₄×C₈₉	—	2	1	no	—
374	C₄⋊C₄×C₈₉	—	2	2	no	—
375	C₄⋊C₄×C₈₉	—	2	2	no	—
376	C₄⋊C₄×C₈₉	—	2	2	no	—
377	C₄⋊C₄×C₈₉	—	2	1	no	—
378	C₄⋊C₄×C₈₉	—	2	1	no	—
379	C₄⋊C₄×C₈₉	—	2	2	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	2	no	—
384	C₄⋊C₄×C₈₉	—	2	1	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	1	no	—
390	C₄⋊C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
391	C₄⋊C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
392	C₄⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
393	C₄⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
394	C₄⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
395	C₄⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
396	C₄⋊C₄×C₈₉	C₂⁴	1	1	yes	characteristic
397	C₄⋊C₄×C₈₉	C₂⁴	1	2	yes	—
398	C₄⋊C₄×C₈₉	C₂⁴	1	2	yes	—
399	C₄⋊C₄×C₈₉	C₂⁴	1	1	yes	characteristic
400	C₄⋊C₄×C₈₉	C₂⁴	1	1	yes	characteristic
401	C₄⋊C₄×C₈₉	C₂⁴	1	2	yes	—
402	C₄⋊C₄×C₈₉	C₂⁴	1	1	yes	characteristic
403	C₂²⋊C₄×C₈₉	—	2	2	no	—
404	C₂²⋊C₄×C₈₉	—	2	2	no	—
405	C₂²⋊C₄×C₈₉	—	2	1	no	—
406	C₂²⋊C₄×C₈₉	—	2	2	no	—
407	C₂²⋊C₄×C₈₉	—	2	1	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	1	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	2	no	—
420	C₂²⋊C₄×C₈₉	—	2	1	no	—
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	C₂²⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
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	2	no	—
433	C₄²×C₈₉	—	2	1	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	—	2	1	no	—
443	C₂³×C₈₉	C₂²×D₄	1	2	yes	—
444	C₂³×C₈₉	C₂²×D₄	1	1	yes	characteristic
445	Q₈×C₈₉	—	2	2	no	—
446	Q₈×C₈₉	—	2	1	no	—
447	Q₈×C₈₉	—	2	1	no	—
448	Q₈×C₈₉	—	2	2	no	—
449	Q₈×C₈₉	—	2	1	no	—
450	Q₈×C₈₉	—	2	2	no	—
451	Q₈×C₈₉	—	4	4	no	—
452	Q₈×C₈₉	—	4	2	no	—
453	Q₈×C₈₉	—	4	2	no	—
454	Q₈×C₈₉	—	8	1	no	—
455	Q₈×C₈₉	—	8	2	no	—
456	Q₈×C₈₉	—	8	2	no	—
457	Q₈×C₈₉	—	8	2	no	—
458	Q₈×C₈₉	2₋¹⁺⁴	1	2	yes	—
459	D₄×C₈₉	—	2	2	no	—
460	D₄×C₈₉	—	2	1	no	—
461	D₄×C₈₉	—	2	1	no	—
462	D₄×C₈₉	—	2	1	no	—
463	D₄×C₈₉	—	2	1	no	—
464	D₄×C₈₉	—	4	2	no	—
465	D₄×C₈₉	—	4	2	no	—
466	D₄×C₈₉	—	4	2	no	—
467	D₄×C₈₉	—	8	2	no	—
468	D₄×C₈₉	—	8	2	no	—
469	C₂×C₄×C₈₉	—	2	1	no	—
470	C₂×C₄×C₈₉	—	2	2	no	—
471	C₂×C₄×C₈₉	—	2	2	no	—
472	C₂×C₄×C₈₉	—	2	1	no	—
473	C₂×C₄×C₈₉	—	2	2	no	—
474	C₂×C₄×C₈₉	—	2	1	no	—
475	C₂×C₄×C₈₉	—	2	1	no	—
476	C₂×C₄×C₈₉	—	2	1	no	—
477	C₂×C₄×C₈₉	—	2	1	no	—
478	C₂×C₄×C₈₉	—	2	2	no	—
479	C₂×C₄×C₈₉	—	2	2	no	—
480	C₂×C₄×C₈₉	—	2	1	no	—
481	C₂×C₄×C₈₉	—	2	2	no	—
482	C₂×C₄×C₈₉	—	2	2	no	—
483	C₂×C₄×C₈₉	—	2	1	no	—
484	C₂×C₄×C₈₉	—	4	1	no	—
485	C₂×C₄×C₈₉	—	4	2	no	—
486	C₂×C₄×C₈₉	—	4	4	no	—
487	C₂×C₄×C₈₉	—	4	2	no	—
488	C₂×C₄×C₈₉	—	4	2	no	—
489	C₂×C₄×C₈₉	—	8	1	no	—
490	C₂×C₄×C₈₉	—	8	2	no	—
491	C₂×C₄×C₈₉	—	8	2	no	—
492	C₂×C₄×C₈₉	—	8	2	no	—
493	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
494	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
495	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
496	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
497	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
498	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
499	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
500	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
501	C₂×C₄×C₈₉	C₂⁵	1	1	yes	characteristic
502	C₈×C₈₉	—	2	1	no	—
503	C₈×C₈₉	—	2	1	no	—
504	C₈×C₈₉	—	2	1	no	—
505	C₈×C₈₉	—	2	2	no	—
506	C₈×C₈₉	—	2	1	no	—
507	C₈×C₈₉	—	2	2	no	—
508	C₂²×C₈₉	—	2	1	no	—
509	C₂²×C₈₉	—	2	2	no	—
510	C₂²×C₈₉	—	2	2	no	—
511	C₂²×C₈₉	—	2	1	no	—
512	C₂²×C₈₉	—	2	1	no	—
513	C₂²×C₈₉	—	2	2	no	—
514	C₂²×C₈₉	—	4	1	no	—
515	C₂²×C₈₉	—	4	1	no	—
516	C₂²×C₈₉	—	4	1	no	—
517	C₂²×C₈₉	—	4	1	no	—
518	C₂²×C₈₉	—	4	1	no	—
519	C₂²×C₈₉	—	4	1	no	—
520	C₂²×C₈₉	C₂³×D₄	1	1	yes	characteristic
521	C₄×C₈₉	—	2	1	no	—
522	C₄×C₈₉	—	2	1	no	—
523	C₄×C₈₉	—	2	2	no	—
524	C₄×C₈₉	—	2	1	no	—
525	C₄×C₈₉	—	2	2	no	—
526	C₄×C₈₉	—	2	2	no	—
527	C₄×C₈₉	—	2	1	no	—
528	C₄×C₈₉	—	2	2	no	—
529	C₄×C₈₉	—	4	1	no	—
530	C₄×C₈₉	—	4	1	no	—
531	C₄×C₈₉	—	4	2	no	—
532	C₄×C₈₉	—	4	2	no	—
533	C₄×C₈₉	—	4	1	no	—
534	C₄×C₈₉	—	4	1	no	—
535	C₄×C₈₉	—	4	1	no	—
536	C₄×C₈₉	—	4	2	no	—
537	C₄×C₈₉	—	4	2	no	—
538	C₄×C₈₉	#577	1	2	yes	—
539	C₄×C₈₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
540	C₄×C₈₉	#585	1	1	yes	characteristic
541	#62184	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
542	C₂×C₈₉	—	4	1	no	—
543	C₂×C₈₉	—	4	2	no	—
544	C₂×C₈₉	—	8	1	no	—
545	C₂×C₈₉	—	8	1	no	—
546	C₂×C₈₉	#3489	1	1	yes	characteristic
547	C₂×C₈₉	C₂×#577	1	1	yes	characteristic
548	C₂×C₈₉	#3586	1	1	yes	characteristic
549	#3552	C₂×C₈₉	1	1	yes	characteristic, complemented
550	#3518	C₂×C₈₉	1	1	yes	characteristic, complemented
551	#3387	C₂×C₈₉	1	1	yes	characteristic, complemented
552	Q₈×SD₁₆	C₂×C₈₉	1	1	yes	characteristic, complemented
553	#3367	C₂×C₈₉	1	1	yes	characteristic, complemented
554	#3364	C₂×C₈₉	1	1	yes	characteristic, complemented
555	#3356	C₂×C₈₉	1	2	yes	complemented
556	#3354	C₂×C₈₉	1	1	yes	characteristic, complemented
557	#3350	C₂×C₈₉	1	2	yes	complemented
558	#3340	C₂×C₈₉	1	1	yes	characteristic, complemented
559	#3328	C₂×C₈₉	1	1	yes	characteristic, complemented
560	#3326	C₂×C₈₉	1	2	yes	complemented
561	#3316	C₂×C₈₉	1	2	yes	complemented
562	#3298	C₂×C₈₉	1	1	yes	characteristic, complemented
563	#3263	C₂×C₈₉	1	2	yes	complemented
564	#3252	C₂×C₈₉	1	1	yes	characteristic, complemented
565	#3244	C₂×C₈₉	1	2	yes	complemented
566	#3229	C₂×C₈₉	1	1	yes	characteristic, complemented
567	#3121	C₂×C₈₉	1	2	yes	complemented
568	#3102	C₂×C₈₉	1	1	yes	characteristic, complemented
569	#3082	C₂×C₈₉	1	2	yes	complemented
570	#3079	C₂×C₈₉	1	1	yes	characteristic, complemented
571	#2993	C₂×C₈₉	1	1	yes	characteristic, complemented
572	C₈₉	#62184	1	1	yes	characteristic, direct product factor, Sylow
573	#563	—	2	2	no	—
574	Q₈²	C₂²×C₈₉	1	1	yes	characteristic
575	#557	C₂²×C₈₉	1	1	yes	characteristic
576	#556	—	2	2	no	—
577	#556	—	2	1	no	—
578	#556	C₂²×C₈₉	1	1	yes	characteristic
579	#556	C₂²×C₈₉	1	1	yes	characteristic
580	#556	C₂²×C₈₉	1	2	yes	—
581	#555	—	2	1	no	—
582	#555	C₂²×C₈₉	1	1	yes	characteristic
583	#554	C₂²×C₈₉	1	2	yes	—
584	#553	C₂²×C₈₉	1	2	yes	—
585	D₄×Q₈	—	2	1	no	—
586	D₄×Q₈	C₂²×C₈₉	1	1	yes	characteristic
587	D₄×Q₈	C₂²×C₈₉	1	1	yes	characteristic
588	#548	—	2	1	no	—
589	#548	C₂²×C₈₉	1	2	yes	—
590	#547	C₂²×C₈₉	1	1	yes	characteristic
591	#544	C₂²×C₈₉	1	2	yes	—
592	#542	—	2	2	no	—
593	#542	C₂²×C₈₉	1	2	yes	—
594	#542	C₂²×C₈₉	1	2	yes	—
595	#541	—	2	1	no	—
596	#539	—	2	2	no	—
597	#536	—	2	1	no	—
598	#533	—	2	1	no	—
599	#533	C₂²×C₈₉	1	1	yes	characteristic
600	C₂×C₄⋊Q₈	C₂²×C₈₉	1	1	yes	characteristic
601	#529	—	2	1	no	—
602	#529	C₂²×C₈₉	1	1	yes	characteristic
603	#529	C₂²×C₈₉	1	1	yes	characteristic
604	#519	C₂²×C₈₉	1	2	yes	—
605	C₄×#41	C₂²×C₈₉	1	1	yes	characteristic
606	#501	C₂²×C₈₉	1	2	yes	—
607	#498	C₂²×C₈₉	1	1	yes	characteristic
608	#498	C₂²×C₈₉	1	1	yes	characteristic
609	#498	C₂²×C₈₉	1	2	yes	—
610	#489	C₂²×C₈₉	1	2	yes	—
611	#488	C₂²×C₈₉	1	2	yes	—
612	#487	C₂²×C₈₉	1	1	yes	characteristic
613	#487	C₂²×C₈₉	1	1	yes	characteristic
614	#485	C₂²×C₈₉	1	2	yes	—
615	#485	C₂²×C₈₉	1	2	yes	—
616	#485	C₂²×C₈₉	1	1	yes	characteristic
617	#483	C₂²×C₈₉	1	2	yes	—
618	#483	C₂²×C₈₉	1	2	yes	—
619	#483	C₂²×C₈₉	1	2	yes	—
620	#482	C₂²×C₈₉	1	2	yes	—
621	#482	C₂²×C₈₉	1	1	yes	characteristic
622	#482	C₂²×C₈₉	1	2	yes	—
623	#481	C₂²×C₈₉	1	2	yes	—
624	#479	C₂²×C₈₉	1	1	yes	characteristic
625	#479	C₂²×C₈₉	1	2	yes	—
626	#479	C₂²×C₈₉	1	2	yes	—
627	#479	C₂²×C₈₉	1	2	yes	—
628	#478	C₂²×C₈₉	1	1	yes	characteristic
629	#477	C₂²×C₈₉	1	2	yes	—
630	#477	C₂²×C₈₉	1	2	yes	—
631	#477	C₂²×C₈₉	1	1	yes	characteristic
632	#476	C₂²×C₈₉	1	2	yes	—
633	#476	C₂²×C₈₉	1	2	yes	—
634	#476	C₂²×C₈₉	1	1	yes	characteristic
635	#475	C₂²×C₈₉	1	1	yes	characteristic
636	#475	C₂²×C₈₉	1	1	yes	characteristic
637	#475	C₂²×C₈₉	1	2	yes	—
638	#475	C₂²×C₈₉	1	2	yes	—
639	#475	C₂²×C₈₉	1	2	yes	—
640	#475	C₂²×C₈₉	1	2	yes	—
641	#474	C₂²×C₈₉	1	1	yes	characteristic
642	#474	C₂²×C₈₉	1	1	yes	characteristic
643	#470	C₂²×C₈₉	1	2	yes	—
644	#470	C₂²×C₈₉	1	2	yes	—
645	#469	C₂²×C₈₉	1	2	yes	—
646	#468	C₂²×C₈₉	1	2	yes	—
647	#465	C₂²×C₈₉	1	2	yes	—
648	#465	C₂²×C₈₉	1	2	yes	—
649	#464	C₂²×C₈₉	1	1	yes	characteristic
650	#464	C₂²×C₈₉	1	2	yes	—
651	#464	C₂²×C₈₉	1	2	yes	—
652	#463	C₂²×C₈₉	1	1	yes	characteristic
653	#463	C₂²×C₈₉	1	2	yes	—
654	#462	C₂²×C₈₉	1	1	yes	characteristic
655	#461	C₂²×C₈₉	1	1	yes	characteristic
656	#452	C₂²×C₈₉	1	1	yes	characteristic
657	#451	C₂²×C₈₉	1	2	yes	—
658	#449	C₂²×C₈₉	1	1	yes	characteristic
659	#448	C₂²×C₈₉	1	2	yes	—
660	#446	C₂²×C₈₉	1	1	yes	characteristic
661	C₈×Q₈	C₂²×C₈₉	1	1	yes	characteristic
662	#441	C₂²×C₈₉	1	2	yes	—
663	#440	C₂²×C₈₉	1	2	yes	—
664	C₄×Q₁₆	C₂²×C₈₉	1	1	yes	characteristic
665	C₄×Q₁₆	C₂²×C₈₉	1	2	yes	—
666	C₄×SD₁₆	C₂²×C₈₉	1	1	yes	characteristic
667	C₄×SD₁₆	C₂²×C₈₉	1	1	yes	characteristic
668	C₄×SD₁₆	C₂²×C₈₉	1	2	yes	—
669	C₄×D₈	C₂²×C₈₉	1	1	yes	characteristic
670	#436	C₂²×C₈₉	1	1	yes	characteristic
671	#436	C₂²×C₈₉	1	2	yes	—
672	#435	C₂²×C₈₉	1	2	yes	—
673	C₈×D₄	C₂²×C₈₉	1	1	yes	characteristic
674	#433	C₂²×C₈₉	1	2	yes	—
675	#431	C₂²×C₈₉	1	1	yes	characteristic
676	#428	C₂²×C₈₉	1	2	yes	—
677	#428	C₂²×C₈₉	1	2	yes	—
678	#427	C₂²×C₈₉	1	2	yes	—
679	#424	C₂²×C₈₉	1	2	yes	—
680	#423	C₂²×C₈₉	1	1	yes	characteristic
681	#419	C₂²×C₈₉	1	2	yes	—
682	#417	C₂²×C₈₉	1	2	yes	—
683	C₂×#103	C₂²×C₈₉	1	2	yes	—
684	C₂×#41	—	2	1	no	—
685	C₂×#41	C₂³×C₈₉	1	1	yes	characteristic
686	C₂²×Q₈	—	2	1	no	—
687	C₂²×Q₈	—	2	1	no	—
688	C₂²×Q₈	C₂³×C₈₉	1	2	yes	—
689	C₂×Q₁₆	C₂³×C₈₉	1	1	yes	characteristic
690	C₂×Q₁₆	C₂³×C₈₉	1	2	yes	—
691	C₂×SD₁₆	C₂³×C₈₉	1	1	yes	characteristic
692	C₂×SD₁₆	C₂³×C₈₉	1	1	yes	characteristic
693	C₂×SD₁₆	C₂³×C₈₉	1	2	yes	—
694	C₂×D₈	C₂³×C₈₉	1	1	yes	characteristic
695	C₂×M₁₆	C₂³×C₈₉	1	2	yes	—
696	C₂×M₁₆	C₂³×C₈₉	1	2	yes	—
697	C₂²×C₈	C₂³×C₈₉	1	2	yes	—
698	C₄⋊Q₈	—	2	1	no	—
699	C₄⋊Q₈	—	2	1	no	—
700	C₄⋊Q₈	—	2	1	no	—
701	C₄⋊Q₈	—	2	2	no	—
702	C₄⋊Q₈	—	2	2	no	—
703	C₄⋊Q₈	—	2	1	no	—
704	C₄⋊Q₈	—	2	1	no	—
705	C₄⋊Q₈	C₂³×C₈₉	1	1	yes	characteristic
706	C₄⋊Q₈	C₂³×C₈₉	1	2	yes	—
707	C₄⋊Q₈	C₂³×C₈₉	1	1	yes	characteristic
708	C₄⋊Q₈	C₂³×C₈₉	1	1	yes	characteristic
709	C₄⋊Q₈	C₂³×C₈₉	1	1	yes	characteristic
710	C₄⋊Q₈	C₂³×C₈₉	1	2	yes	—
711	C₄⋊Q₈	C₂³×C₈₉	1	2	yes	—
712	#126	—	2	2	no	—
713	#126	—	2	2	no	—
714	#126	—	2	2	no	—
715	#126	—	2	2	no	—
716	#126	—	2	2	no	—
717	#126	—	2	2	no	—
718	#126	—	2	2	no	—
719	#126	—	2	1	no	—
720	#126	D₄×C₈₉	1	2	yes	—
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	#124	—	2	1	no	—
729	#124	—	2	2	no	—
730	#124	—	2	2	no	—
731	#124	—	2	2	no	—
732	#124	—	2	2	no	—
733	#124	—	2	2	no	—
734	#124	D₄×C₈₉	1	1	yes	characteristic
735	#124	C₂³×C₈₉	1	1	yes	characteristic
736	#124	C₂³×C₈₉	1	2	yes	—
737	#123	—	2	1	no	—
738	#123	—	2	2	no	—
739	#123	—	2	2	no	—
740	#123	—	2	2	no	—
741	#123	—	2	2	no	—
742	#123	D₄×C₈₉	1	2	yes	—
743	C₂²⋊Q₈	—	2	1	no	—
744	C₂²⋊Q₈	—	2	1	no	—
745	C₂²⋊Q₈	—	2	2	no	—
746	C₂²⋊Q₈	—	2	2	no	—
747	C₂²⋊Q₈	—	2	2	no	—
748	C₂²⋊Q₈	—	2	1	no	—
749	C₂²⋊Q₈	—	2	1	no	—
750	C₂²⋊Q₈	—	2	2	no	—
751	C₂²⋊Q₈	—	2	2	no	—
752	C₂²⋊Q₈	—	2	2	no	—
753	C₂²⋊Q₈	—	2	2	no	—
754	C₂²⋊Q₈	—	2	2	no	—
755	C₂²⋊Q₈	—	2	2	no	—
756	C₂²⋊Q₈	D₄×C₈₉	1	1	yes	characteristic
757	C₂²⋊Q₈	C₂³×C₈₉	1	1	yes	characteristic
758	C₂²⋊Q₈	C₂³×C₈₉	1	2	yes	—
759	C₂²⋊Q₈	C₂³×C₈₉	1	2	yes	—
760	C₂²⋊Q₈	C₂³×C₈₉	1	2	yes	—
761	#121	—	2	1	no	—
762	#121	—	2	2	no	—
763	#121	—	2	2	no	—
764	#121	D₄×C₈₉	1	1	yes	characteristic
765	#121	C₂³×C₈₉	1	1	yes	characteristic
766	#121	C₂³×C₈₉	1	2	yes	—
767	#121	C₂³×C₈₉	1	2	yes	—
768	C₄×Q₈	—	2	1	no	—
769	C₄×Q₈	—	2	2	no	—
770	C₄×Q₈	—	2	2	no	—
771	C₄×Q₈	—	2	2	no	—
772	C₄×Q₈	—	2	1	no	—
773	C₄×Q₈	—	2	1	no	—
774	C₄×Q₈	—	2	1	no	—
775	C₄×Q₈	C₂³×C₈₉	1	1	yes	characteristic
776	C₄×Q₈	C₂³×C₈₉	1	1	yes	characteristic
777	C₄×Q₈	C₂³×C₈₉	1	2	yes	—
778	C₄×Q₈	C₂³×C₈₉	1	2	yes	—
779	C₄×Q₈	C₂³×C₈₉	1	2	yes	—
780	C₄×Q₈	C₂³×C₈₉	1	1	yes	characteristic
781	C₄×Q₈	C₂³×C₈₉	1	2	yes	—
782	C₄×Q₈	C₂³×C₈₉	1	1	yes	characteristic
783	C₄×D₄	—	2	1	no	—
784	C₄×D₄	—	2	2	no	—
785	C₄×D₄	—	2	1	no	—
786	C₄×D₄	—	2	1	no	—
787	C₄×D₄	—	2	1	no	—
788	C₄×D₄	—	2	2	no	—
789	C₄×D₄	—	2	2	no	—
790	C₄×D₄	C₂³×C₈₉	1	1	yes	characteristic
791	C₄×D₄	C₂³×C₈₉	1	1	yes	characteristic
792	C₄×D₄	C₂³×C₈₉	1	1	yes	characteristic
793	C₄×D₄	C₂³×C₈₉	1	2	yes	—
794	C₄×D₄	C₂³×C₈₉	1	1	yes	characteristic
795	C₄×D₄	C₂³×C₈₉	1	2	yes	—
796	#117	—	2	1	no	—
797	#117	—	2	1	no	—
798	#117	—	2	1	no	—
799	#117	—	2	2	no	—
800	#117	—	2	2	no	—
801	#117	—	2	1	no	—
802	#117	—	2	1	no	—
803	#117	C₂³×C₈₉	1	1	yes	characteristic
804	#117	C₂³×C₈₉	1	2	yes	—
805	#117	C₂³×C₈₉	1	2	yes	—
806	#117	C₂³×C₈₉	1	2	yes	—
807	C₂×C₄⋊C₄	—	2	1	no	—
808	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
809	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
810	C₂×C₄²	—	2	1	no	—
811	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
812	#107	C₂³×C₈₉	1	2	yes	—
813	#107	C₂³×C₈₉	1	2	yes	—
814	#107	C₂³×C₈₉	1	1	yes	characteristic
815	#107	C₂³×C₈₉	1	2	yes	—
816	#107	C₂³×C₈₉	1	1	yes	characteristic
817	#106	C₂³×C₈₉	1	1	yes	characteristic
818	#106	C₂³×C₈₉	1	2	yes	—
819	#106	C₂³×C₈₉	1	2	yes	—
820	#106	C₂³×C₈₉	1	2	yes	—
821	#106	C₂³×C₈₉	1	2	yes	—
822	#106	C₂³×C₈₉	1	2	yes	—
823	#106	C₂³×C₈₉	1	2	yes	—
824	#106	C₂³×C₈₉	1	1	yes	characteristic
825	#106	C₂³×C₈₉	1	2	yes	—
826	C₄⋊C₈	C₂³×C₈₉	1	2	yes	—
827	C₄⋊C₈	C₂³×C₈₉	1	1	yes	characteristic
828	C₄⋊C₈	C₂³×C₈₉	1	1	yes	characteristic
829	C₄⋊C₈	C₂³×C₈₉	1	1	yes	characteristic
830	C₄⋊C₈	C₂³×C₈₉	1	2	yes	—
831	C₄⋊C₈	C₂³×C₈₉	1	2	yes	—
832	C₄⋊C₈	C₂³×C₈₉	1	1	yes	characteristic
833	#103	C₂³×C₈₉	1	1	yes	characteristic
834	#103	C₂³×C₈₉	1	2	yes	—
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	2	yes	—
840	#103	C₂³×C₈₉	1	2	yes	—
841	#103	C₂³×C₈₉	1	1	yes	characteristic
842	#103	C₂³×C₈₉	1	2	yes	—
843	#103	C₂³×C₈₉	1	1	yes	characteristic
844	#103	C₂³×C₈₉	1	2	yes	—
845	#103	C₂³×C₈₉	1	2	yes	—
846	#102	C₂³×C₈₉	1	2	yes	—
847	#102	C₂³×C₈₉	1	2	yes	—
848	#102	C₂³×C₈₉	1	1	yes	characteristic
849	#102	C₂³×C₈₉	1	1	yes	characteristic
850	#102	C₂³×C₈₉	1	1	yes	characteristic
851	#102	C₂³×C₈₉	1	1	yes	characteristic
852	#102	C₂³×C₈₉	1	2	yes	—
853	C₂²⋊C₈	C₂³×C₈₉	1	1	yes	characteristic
854	C₂²⋊C₈	C₂³×C₈₉	1	1	yes	characteristic
855	C₂²⋊C₈	C₂³×C₈₉	1	2	yes	—
856	C₂²⋊C₈	C₂³×C₈₉	1	2	yes	—
857	#97	C₂³×C₈₉	1	2	yes	—
858	C₄×C₈	C₂³×C₈₉	1	1	yes	characteristic
859	C₄×C₈	C₂³×C₈₉	1	1	yes	characteristic
860	C₄×C₈	C₂³×C₈₉	1	2	yes	—
861	#41	—	2	2	no	—
862	#41	—	4	1	no	—
863	#41	—	8	2	no	—
864	C₂×Q₈	—	2	2	no	—
865	C₂×Q₈	—	2	1	no	—
866	C₂×Q₈	—	2	1	no	—
867	C₂×Q₈	—	2	1	no	—
868	C₂×Q₈	—	2	2	no	—
869	C₂×Q₈	—	2	2	no	—
870	C₂×Q₈	—	2	2	no	—
871	C₂×Q₈	—	2	4	no	—
872	C₂×Q₈	—	4	2	no	—
873	C₂×Q₈	—	8	2	no	—
874	C₂×Q₈	—	8	2	no	—
875	C₂×Q₈	C₂×D₄×C₈₉	1	1	yes	characteristic
876	C₂×Q₈	C₂⁴×C₈₉	1	2	yes	—
877	C₂×Q₈	C₂⁴×C₈₉	1	1	yes	characteristic
878	C₂×Q₈	C₂⁴×C₈₉	1	1	yes	characteristic
879	C₂×D₄	—	2	1	no	—
880	C₂×D₄	—	2	1	no	—
881	C₂×D₄	—	2	2	no	—
882	C₂×D₄	—	2	2	no	—
883	C₂×D₄	C₂×D₄×C₈₉	1	1	yes	characteristic
884	C₂×D₄	C₂×D₄×C₈₉	1	2	yes	—
885	C₂×D₄	C₂⁴×C₈₉	1	1	yes	characteristic
886	C₂×D₄	C₂⁴×C₈₉	1	1	yes	characteristic
887	C₂²×C₄	—	2	2	no	—
888	C₂²×C₄	—	2	2	no	—
889	C₂²×C₄	—	2	2	no	—
890	C₂²×C₄	—	2	1	no	—
891	C₂²×C₄	—	2	1	no	—
892	C₂²×C₄	—	2	1	no	—
893	C₂²×C₄	—	2	1	no	—
894	C₂²×C₄	—	2	2	no	—
895	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
896	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
897	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
898	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
899	Q₁₆	—	2	2	no	—
900	Q₁₆	—	4	2	no	—
901	SD₁₆	—	2	2	no	—
902	SD₁₆	—	4	1	no	—
903	SD₁₆	—	4	2	no	—
904	D₈	—	4	1	no	—
905	M₁₆	—	4	2	no	—
906	M₁₆	—	4	2	no	—
907	C₂×C₈	—	4	2	no	—
908	C₂×C₈	C₂⁴×C₈₉	1	1	yes	characteristic
909	C₂×C₈	C₂⁴×C₈₉	1	1	yes	characteristic
910	C₂×C₈	C₂⁴×C₈₉	1	2	yes	—
911	C₂×C₈	C₂⁴×C₈₉	1	1	yes	characteristic
912	C₂×C₈	C₂⁴×C₈₉	1	1	yes	characteristic
913	C₂×C₈	C₂⁴×C₈₉	1	2	yes	—
914	C₄⋊C₄	—	2	1	no	—
915	C₄⋊C₄	—	2	2	no	—
916	C₄⋊C₄	—	2	1	no	—
917	C₄⋊C₄	—	2	2	no	—
918	C₄⋊C₄	—	2	2	no	—
919	C₄⋊C₄	—	2	1	no	—
920	C₄⋊C₄	—	2	1	no	—
921	C₄⋊C₄	—	2	1	no	—
922	C₄⋊C₄	—	2	1	no	—
923	C₄⋊C₄	—	2	2	no	—
924	C₄⋊C₄	—	2	2	no	—
925	C₄⋊C₄	—	2	2	no	—
926	C₄⋊C₄	—	2	1	no	—
927	C₄⋊C₄	—	2	1	no	—
928	C₄⋊C₄	—	2	2	no	—
929	C₄⋊C₄	—	2	2	no	—
930	C₄⋊C₄	—	2	1	no	—
931	C₄⋊C₄	—	2	2	no	—
932	C₄⋊C₄	—	2	2	no	—
933	C₄⋊C₄	—	2	1	no	—
934	C₄⋊C₄	—	2	2	no	—
935	C₄⋊C₄	—	2	2	no	—
936	C₄⋊C₄	—	2	2	no	—
937	C₄⋊C₄	—	2	2	no	—
938	C₄⋊C₄	—	2	1	no	—
939	C₄⋊C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
940	C₄⋊C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
941	C₄⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
942	C₄⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
943	C₄⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
944	C₄⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
945	C₄⋊C₄	C₂⁴×C₈₉	1	1	yes	characteristic
946	C₄⋊C₄	C₂⁴×C₈₉	1	2	yes	—
947	C₄⋊C₄	C₂⁴×C₈₉	1	2	yes	—
948	C₄⋊C₄	C₂⁴×C₈₉	1	1	yes	characteristic
949	C₄⋊C₄	C₂⁴×C₈₉	1	1	yes	characteristic
950	C₄⋊C₄	C₂⁴×C₈₉	1	2	yes	—
951	C₄⋊C₄	C₂⁴×C₈₉	1	1	yes	characteristic
952	C₂²⋊C₄	—	2	2	no	—
953	C₂²⋊C₄	—	2	2	no	—
954	C₂²⋊C₄	—	2	1	no	—
955	C₂²⋊C₄	—	2	2	no	—
956	C₂²⋊C₄	—	2	1	no	—
957	C₂²⋊C₄	—	2	2	no	—
958	C₂²⋊C₄	—	2	2	no	—
959	C₂²⋊C₄	—	2	1	no	—
960	C₂²⋊C₄	—	2	1	no	—
961	C₂²⋊C₄	—	2	2	no	—
962	C₂²⋊C₄	—	2	2	no	—
963	C₂²⋊C₄	—	2	1	no	—
964	C₂²⋊C₄	—	2	1	no	—
965	C₂²⋊C₄	—	2	2	no	—
966	C₂²⋊C₄	—	2	1	no	—
967	C₂²⋊C₄	—	2	2	no	—
968	C₂²⋊C₄	—	2	2	no	—
969	C₂²⋊C₄	—	2	1	no	—
970	C₂²⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
971	C₂²⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
972	C₂²⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
973	C₂²⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
974	C₂²⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
975	C₄²	—	2	1	no	—
976	C₄²	—	2	1	no	—
977	C₄²	—	2	1	no	—
978	C₄²	—	2	2	no	—
979	C₄²	—	2	2	no	—
980	C₄²	—	2	2	no	—
981	C₄²	—	2	2	no	—
982	C₄²	—	2	1	no	—
983	C₄²	—	2	2	no	—
984	C₄²	—	2	2	no	—
985	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
986	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
987	C₄²	C₂⁴×C₈₉	1	1	yes	characteristic
988	C₄²	C₂⁴×C₈₉	1	2	yes	—
989	C₄²	C₂⁴×C₈₉	1	1	yes	characteristic
990	C₂³	—	2	1	no	—
991	C₂³	—	2	1	no	—
992	C₂³	C₂²×D₄×C₈₉	1	2	yes	—
993	C₂³	C₂²×D₄×C₈₉	1	1	yes	characteristic
994	Q₈	—	2	2	no	—
995	Q₈	—	2	1	no	—
996	Q₈	—	2	1	no	—
997	Q₈	—	2	2	no	—
998	Q₈	—	2	1	no	—
999	Q₈	—	2	2	no	—
1000	Q₈	—	4	4	no	—
1001	Q₈	—	4	2	no	—
1002	Q₈	—	4	2	no	—
1003	Q₈	—	8	1	no	—
1004	Q₈	—	8	2	no	—
1005	Q₈	—	8	2	no	—
1006	Q₈	—	8	2	no	—
1007	Q₈	2₋¹⁺⁴×C₈₉	1	2	yes	—
1008	D₄	—	2	2	no	—
1009	D₄	—	2	1	no	—
1010	D₄	—	2	1	no	—
1011	D₄	—	2	1	no	—
1012	D₄	—	2	1	no	—
1013	D₄	—	4	2	no	—
1014	D₄	—	4	2	no	—
1015	D₄	—	4	2	no	—
1016	D₄	—	8	2	no	—
1017	D₄	—	8	2	no	—
1018	C₂×C₄	—	2	1	no	—
1019	C₂×C₄	—	2	2	no	—
1020	C₂×C₄	—	2	2	no	—
1021	C₂×C₄	—	2	1	no	—
1022	C₂×C₄	—	2	2	no	—
1023	C₂×C₄	—	2	1	no	—
1024	C₂×C₄	—	2	1	no	—
1025	C₂×C₄	—	2	1	no	—
1026	C₂×C₄	—	2	1	no	—
1027	C₂×C₄	—	2	2	no	—
1028	C₂×C₄	—	2	2	no	—
1029	C₂×C₄	—	2	1	no	—
1030	C₂×C₄	—	2	2	no	—
1031	C₂×C₄	—	2	2	no	—
1032	C₂×C₄	—	2	1	no	—
1033	C₂×C₄	—	4	1	no	—
1034	C₂×C₄	—	4	2	no	—
1035	C₂×C₄	—	4	4	no	—
1036	C₂×C₄	—	4	2	no	—
1037	C₂×C₄	—	4	2	no	—
1038	C₂×C₄	—	8	1	no	—
1039	C₂×C₄	—	8	2	no	—
1040	C₂×C₄	—	8	2	no	—
1041	C₂×C₄	—	8	2	no	—
1042	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
1043	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
1044	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
1045	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
1046	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
1047	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
1048	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
1049	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
1050	C₂×C₄	C₂⁵×C₈₉	1	1	yes	characteristic
1051	C₈	—	2	1	no	—
1052	C₈	—	2	1	no	—
1053	C₈	—	2	1	no	—
1054	C₈	—	2	2	no	—
1055	C₈	—	2	1	no	—
1056	C₈	—	2	2	no	—
1057	C₂²	—	2	1	no	—
1058	C₂²	—	2	2	no	—
1059	C₂²	—	2	1	no	—
1060	C₂²	—	2	2	no	—
1061	C₂²	—	2	2	no	—
1062	C₂²	—	2	1	no	—
1063	C₂²	—	4	1	no	—
1064	C₂²	—	4	1	no	—
1065	C₂²	—	4	1	no	—
1066	C₂²	—	4	1	no	—
1067	C₂²	—	4	1	no	—
1068	C₂²	—	4	1	no	—
1069	C₂²	C₂³×D₄×C₈₉	1	1	yes	characteristic
1070	C₄	—	2	1	no	—
1071	C₄	—	2	2	no	—
1072	C₄	—	2	1	no	—
1073	C₄	—	2	1	no	—
1074	C₄	—	2	2	no	—
1075	C₄	—	2	1	no	—
1076	C₄	—	2	2	no	—
1077	C₄	—	2	2	no	—
1078	C₄	—	4	1	no	—
1079	C₄	—	4	1	no	—
1080	C₄	—	4	2	no	—
1081	C₄	—	4	2	no	—
1082	C₄	—	4	1	no	—
1083	C₄	—	4	1	no	—
1084	C₄	—	4	2	no	—
1085	C₄	—	4	2	no	—
1086	C₄	—	4	1	no	—
1087	C₄	#577×C₈₉	1	2	yes	—
1088	C₄	C₂×2₋¹⁺⁴×C₈₉	1	1	yes	characteristic
1089	C₄	#585×C₈₉	1	1	yes	characteristic
1090	C₂	—	4	1	no	—
1091	C₂	—	4	2	no	—
1092	C₂	—	8	1	no	—
1093	C₂	—	8	1	no	—
1094	C₂	C₈₉×#3489	1	1	yes	characteristic
1095	C₂	C₂×#577×C₈₉	1	1	yes	characteristic
1096	C₂	C₈₉×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₈₉	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₈₉
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
1. C₈₉×#3552	C₂	semidirect
2. C₈₉×#3518	C₂	semidirect
3. C₈₉×#3387	C₂	semidirect
4. Q₈×SD₁₆×C₈₉	C₂	semidirect
5. C₈₉×#3367	C₂	semidirect
6. C₈₉×#3364	C₂	semidirect
7. C₈₉×#3356	C₂	semidirect
8. C₈₉×#3354	C₂	semidirect
9. C₈₉×#3350	C₂	semidirect
10. C₈₉×#3340	C₂	semidirect
11. C₈₉×#3328	C₂	semidirect
12. C₈₉×#3326	C₂	semidirect
13. C₈₉×#3316	C₂	semidirect
14. C₈₉×#3298	C₂	semidirect
15. C₈₉×#3263	C₂	semidirect
16. C₈₉×#3252	C₂	semidirect
17. C₈₉×#3244	C₂	semidirect
18. C₈₉×#3229	C₂	semidirect
19. C₈₉×#3121	C₂	semidirect
20. C₈₉×#3102	C₂	semidirect
21. C₈₉×#3082	C₂	semidirect
22. C₈₉×#3079	C₂	semidirect
23. C₈₉×#2993	C₂	semidirect
541. #62184	C₈₉	direct (N × H)
549. #3552	C₂×C₈₉	semidirect
550. #3518	C₂×C₈₉	semidirect
551. #3387	C₂×C₈₉	semidirect
552. Q₈×SD₁₆	C₂×C₈₉	semidirect
553. #3367	C₂×C₈₉	semidirect
554. #3364	C₂×C₈₉	semidirect
555. #3356	C₂×C₈₉	semidirect
556. #3354	C₂×C₈₉	semidirect
557. #3350	C₂×C₈₉	semidirect
558. #3340	C₂×C₈₉	semidirect
559. #3328	C₂×C₈₉	semidirect
560. #3326	C₂×C₈₉	semidirect
561. #3316	C₂×C₈₉	semidirect
562. #3298	C₂×C₈₉	semidirect
563. #3263	C₂×C₈₉	semidirect
564. #3252	C₂×C₈₉	semidirect
565. #3244	C₂×C₈₉	semidirect
566. #3229	C₂×C₈₉	semidirect
567. #3121	C₂×C₈₉	semidirect
568. #3102	C₂×C₈₉	semidirect
569. #3082	C₂×C₈₉	semidirect
570. #3079	C₂×C₈₉	semidirect
571. #2993	C₂×C₈₉	semidirect
572. C₈₉	#62184	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×#3518	2
C₈₉×#3387	2
Q₈×SD₁₆×C₈₉	2
C₈₉×#3367	2
C₈₉×#3364	2
C₈₉×#3356	2
C₈₉×#3354	2
C₈₉×#3350	2
C₈₉×#3340	2
C₈₉×#3328	2
C₈₉×#3326	2
C₈₉×#3316	2
C₈₉×#3298	2
C₈₉×#3263	2
C₈₉×#3252	2
C₈₉×#3244	2
C₈₉×#3229	2
C₈₉×#3121	2
C₈₉×#3102	2
C₈₉×#3082	2
C₈₉×#3079	2
C₈₉×#2993	2
#62184	89

Subgroups — C89×#62184 #36440032

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#62184 #36440032