Subgroups — C₈₉×#61833 #36439681

Order 22784.

1730 conjugacy classes of subgroups.

The subgroup lattice has 1100 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈₉×#3522	C₂	1	1	yes	maximal, characteristic, complemented
2	Q₈×#41×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₈₉×#3389	C₂	1	2	yes	maximal, complemented
4	C₈₉×#3388	C₂	1	2	yes	maximal, complemented
5	C₈₉×#3387	C₂	1	1	yes	maximal, characteristic, complemented
6	C₈₉×#3385	C₂	1	1	yes	maximal, characteristic, complemented
7	C₈₉×#3385	C₂	1	1	yes	maximal, characteristic, complemented
8	C₈₉×#3384	C₂	1	1	yes	maximal, characteristic, complemented
9	C₈₉×#3375	C₂	1	1	yes	maximal, characteristic, complemented
10	C₈₉×#3373	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈₉×#3371	C₂	1	2	yes	maximal, complemented
12	C₈₉×#3370	C₂	1	2	yes	maximal, complemented
13	C₈₉×#3368	C₂	1	1	yes	maximal, characteristic, complemented
14	C₈₉×#3366	C₂	1	1	yes	maximal, characteristic, complemented
15	C₈₉×#3240	C₂	1	2	yes	maximal, complemented
16	C₈₉×#3235	C₂	1	2	yes	maximal, complemented
17	C₈₉×#3233	C₂	1	1	yes	maximal, characteristic, complemented
18	C₈₉×#3228	C₂	1	1	yes	maximal, characteristic, complemented
19	C₈₉×#3115	C₂	1	2	yes	maximal, complemented
20	C₈₉×#3111	C₂	1	2	yes	maximal, complemented
21	C₈₉×#3106	C₂	1	1	yes	maximal, characteristic, complemented
22	C₈₉×#3102	C₂	1	1	yes	maximal, characteristic, complemented
23	C₈₉×#2983	C₂	1	1	yes	maximal, characteristic, complemented
24	#559×C₈₉	C₂²	1	2	yes	—
25	#559×C₈₉	C₂²	1	1	yes	characteristic
26	Q₈²×C₈₉	C₂²	1	1	yes	characteristic
27	Q₈²×C₈₉	C₂²	1	1	yes	characteristic
28	#557×C₈₉	C₂²	1	1	yes	characteristic
29	#557×C₈₉	C₂²	1	2	yes	—
30	#554×C₈₉	—	2	1	no	—
31	#554×C₈₉	—	2	2	no	—
32	#554×C₈₉	C₂²	1	1	yes	characteristic
33	#554×C₈₉	C₂²	1	2	yes	—
34	#554×C₈₉	C₂²	1	1	yes	characteristic
35	#554×C₈₉	C₂²	1	2	yes	—
36	#550×C₈₉	C₂²	1	1	yes	characteristic
37	D₄×Q₈×C₈₉	—	2	1	no	—
38	D₄×Q₈×C₈₉	C₂²	1	1	yes	characteristic
39	#548×C₈₉	—	2	1	no	—
40	#547×C₈₉	—	2	2	no	—
41	#547×C₈₉	—	2	1	no	—
42	#542×C₈₉	—	2	1	no	—
43	#542×C₈₉	—	2	2	no	—
44	#533×C₈₉	—	2	1	no	—
45	#533×C₈₉	—	2	2	no	—
46	#533×C₈₉	C₂²	1	1	yes	characteristic
47	#533×C₈₉	C₂²	1	2	yes	—
48	#532×C₈₉	C₂²	1	1	yes	characteristic
49	#532×C₈₉	C₂²	1	2	yes	—
50	#529×C₈₉	C₂²	1	1	yes	characteristic
51	#529×C₈₉	C₂²	1	2	yes	—
52	#520×C₈₉	—	2	1	no	—
53	C₄×#41×C₈₉	C₂²	1	1	yes	characteristic
54	C₄×#41×C₈₉	C₂²	1	2	yes	—
55	C₂×C₄×Q₈×C₈₉	—	2	1	no	—
56	C₂×C₄×Q₈×C₈₉	C₂²	1	1	yes	characteristic
57	#501×C₈₉	C₂²	1	2	yes	—
58	#501×C₈₉	C₂²	1	2	yes	—
59	#501×C₈₉	C₂²	1	2	yes	—
60	#501×C₈₉	C₂²	1	2	yes	—
61	#500×C₈₉	C₂²	1	1	yes	characteristic
62	#499×C₈₉	C₂²	1	2	yes	—
63	#498×C₈₉	C₂²	1	1	yes	characteristic
64	#490×C₈₉	C₂²	1	2	yes	—
65	#490×C₈₉	C₂²	1	2	yes	—
66	#489×C₈₉	C₂²	1	2	yes	—
67	#489×C₈₉	C₂²	1	2	yes	—
68	#488×C₈₉	C₂²	1	2	yes	—
69	#486×C₈₉	C₂²	1	1	yes	characteristic
70	#486×C₈₉	C₂²	1	1	yes	characteristic
71	#485×C₈₉	C₂²	1	1	yes	characteristic
72	#485×C₈₉	C₂²	1	2	yes	—
73	#482×C₈₉	C₂²	1	1	yes	characteristic
74	#482×C₈₉	C₂²	1	2	yes	—
75	#482×C₈₉	C₂²	1	2	yes	—
76	#482×C₈₉	C₂²	1	2	yes	—
77	#482×C₈₉	C₂²	1	2	yes	—
78	#479×C₈₉	C₂²	1	1	yes	characteristic
79	#479×C₈₉	C₂²	1	2	yes	—
80	#479×C₈₉	C₂²	1	2	yes	—
81	#479×C₈₉	C₂²	1	2	yes	—
82	#478×C₈₉	C₂²	1	1	yes	characteristic
83	#478×C₈₉	C₂²	1	2	yes	—
84	#478×C₈₉	C₂²	1	2	yes	—
85	#478×C₈₉	C₂²	1	2	yes	—
86	#478×C₈₉	C₂²	1	2	yes	—
87	#478×C₈₉	C₂²	1	2	yes	—
88	#477×C₈₉	C₂²	1	1	yes	characteristic
89	#477×C₈₉	C₂²	1	1	yes	characteristic
90	#476×C₈₉	C₂²	1	1	yes	characteristic
91	#476×C₈₉	C₂²	1	1	yes	characteristic
92	#476×C₈₉	C₂²	1	2	yes	—
93	#476×C₈₉	C₂²	1	2	yes	—
94	#475×C₈₉	C₂²	1	2	yes	—
95	#475×C₈₉	C₂²	1	1	yes	characteristic
96	#474×C₈₉	C₂²	1	1	yes	characteristic
97	#474×C₈₉	C₂²	1	2	yes	—
98	#474×C₈₉	C₂²	1	2	yes	—
99	#474×C₈₉	C₂²	1	2	yes	—
100	#464×C₈₉	C₂²	1	1	yes	characteristic
101	#464×C₈₉	C₂²	1	2	yes	—
102	#463×C₈₉	C₂²	1	1	yes	characteristic
103	#463×C₈₉	C₂²	1	2	yes	—
104	#460×C₈₉	C₂²	1	1	yes	characteristic
105	#460×C₈₉	C₂²	1	2	yes	—
106	#459×C₈₉	C₂²	1	1	yes	characteristic
107	#459×C₈₉	C₂²	1	2	yes	—
108	#452×C₈₉	C₂²	1	1	yes	characteristic
109	#449×C₈₉	C₂²	1	1	yes	characteristic
110	#449×C₈₉	C₂²	1	2	yes	—
111	#446×C₈₉	C₂²	1	1	yes	characteristic
112	#446×C₈₉	C₂²	1	1	yes	characteristic
113	#446×C₈₉	C₂²	1	2	yes	—
114	#446×C₈₉	C₂²	1	2	yes	—
115	#446×C₈₉	C₂²	1	1	yes	characteristic
116	#446×C₈₉	C₂²	1	1	yes	characteristic
117	#442×C₈₉	C₂²	1	2	yes	—
118	#442×C₈₉	C₂²	1	2	yes	—
119	#442×C₈₉	C₂²	1	2	yes	—
120	#441×C₈₉	C₂²	1	2	yes	—
121	#440×C₈₉	C₂²	1	2	yes	—
122	#440×C₈₉	C₂²	1	2	yes	—
123	#440×C₈₉	C₂²	1	2	yes	—
124	#440×C₈₉	C₂²	1	2	yes	—
125	C₄×Q₁₆×C₈₉	C₂²	1	1	yes	characteristic
126	C₄×SD₁₆×C₈₉	C₂²	1	1	yes	characteristic
127	C₄×SD₁₆×C₈₉	C₂²	1	1	yes	characteristic
128	C₄×SD₁₆×C₈₉	C₂²	1	2	yes	—
129	C₄×D₈×C₈₉	C₂²	1	1	yes	characteristic
130	C₄×D₈×C₈₉	C₂²	1	2	yes	—
131	#432×C₈₉	C₂²	1	2	yes	—
132	#432×C₈₉	C₂²	1	2	yes	—
133	#431×C₈₉	C₂²	1	1	yes	characteristic
134	#431×C₈₉	C₂²	1	1	yes	characteristic
135	C₂×#41×C₈₉	—	2	1	no	—
136	C₂×#41×C₈₉	—	2	1	no	—
137	C₂×#41×C₈₉	—	2	2	no	—
138	C₂×#41×C₈₉	C₂³	1	1	yes	characteristic
139	C₂²×Q₈×C₈₉	—	2	1	no	—
140	C₂²×Q₈×C₈₉	D₄	1	1	yes	characteristic
141	C₂×Q₁₆×C₈₉	C₂³	1	1	yes	characteristic
142	C₂×SD₁₆×C₈₉	C₂³	1	1	yes	characteristic
143	C₂×SD₁₆×C₈₉	C₂³	1	2	yes	—
144	C₂×SD₁₆×C₈₉	C₂³	1	1	yes	characteristic
145	C₂×D₈×C₈₉	C₂³	1	1	yes	characteristic
146	C₂×D₈×C₈₉	C₂³	1	2	yes	—
147	C₄⋊Q₈×C₈₉	—	2	1	no	—
148	C₄⋊Q₈×C₈₉	—	2	2	no	—
149	C₄⋊Q₈×C₈₉	—	2	1	no	—
150	C₄⋊Q₈×C₈₉	—	2	2	no	—
151	C₄⋊Q₈×C₈₉	—	2	1	no	—
152	C₄⋊Q₈×C₈₉	—	2	2	no	—
153	C₄⋊Q₈×C₈₉	C₂³	1	2	yes	—
154	C₄⋊Q₈×C₈₉	C₂³	1	1	yes	characteristic
155	C₄⋊Q₈×C₈₉	C₂³	1	2	yes	—
156	C₄⋊Q₈×C₈₉	C₂³	1	2	yes	—
157	C₄⋊Q₈×C₈₉	C₂³	1	1	yes	characteristic
158	C₄⋊Q₈×C₈₉	C₂³	1	1	yes	characteristic
159	#127×C₈₉	C₂³	1	1	yes	characteristic
160	#127×C₈₉	C₂³	1	2	yes	—
161	#126×C₈₉	—	2	2	no	—
162	#126×C₈₉	—	2	1	no	—
163	#125×C₈₉	—	2	2	no	—
164	#125×C₈₉	—	2	2	no	—
165	#125×C₈₉	—	2	2	no	—
166	#125×C₈₉	C₂³	1	2	yes	—
167	#125×C₈₉	C₂³	1	2	yes	—
168	#125×C₈₉	C₂³	1	2	yes	—
169	#125×C₈₉	C₂³	1	1	yes	characteristic
170	#125×C₈₉	C₂³	1	2	yes	—
171	#124×C₈₉	—	2	1	no	—
172	#124×C₈₉	—	2	2	no	—
173	#124×C₈₉	—	2	2	no	—
174	#124×C₈₉	—	2	1	no	—
175	#124×C₈₉	C₂³	1	1	yes	characteristic
176	#124×C₈₉	C₂³	1	2	yes	—
177	#123×C₈₉	—	2	1	no	—
178	#123×C₈₉	—	2	2	no	—
179	#123×C₈₉	—	2	2	no	—
180	#123×C₈₉	—	2	2	no	—
181	#123×C₈₉	—	2	2	no	—
182	C₂²⋊Q₈×C₈₉	—	2	1	no	—
183	C₂²⋊Q₈×C₈₉	—	2	2	no	—
184	C₂²⋊Q₈×C₈₉	—	2	1	no	—
185	C₂²⋊Q₈×C₈₉	—	2	2	no	—
186	C₂²⋊Q₈×C₈₉	—	2	1	no	—
187	C₂²⋊Q₈×C₈₉	—	2	2	no	—
188	C₂²⋊Q₈×C₈₉	—	2	1	no	—
189	C₂²⋊Q₈×C₈₉	—	2	2	no	—
190	C₂²⋊Q₈×C₈₉	—	2	1	no	—
191	C₂²⋊Q₈×C₈₉	—	2	2	no	—
192	C₂²⋊Q₈×C₈₉	—	2	2	no	—
193	C₂²⋊Q₈×C₈₉	—	2	2	no	—
194	C₂²⋊Q₈×C₈₉	—	2	2	no	—
195	C₂²⋊Q₈×C₈₉	—	2	2	no	—
196	C₂²⋊Q₈×C₈₉	—	2	2	no	—
197	C₂²⋊Q₈×C₈₉	—	2	2	no	—
198	C₂²⋊Q₈×C₈₉	C₂³	1	1	yes	characteristic
199	#121×C₈₉	—	2	1	no	—
200	#121×C₈₉	—	2	2	no	—
201	#121×C₈₉	—	2	1	no	—
202	#121×C₈₉	—	2	2	no	—
203	#121×C₈₉	C₂³	1	1	yes	characteristic
204	#121×C₈₉	C₂³	1	2	yes	—
205	C₄×Q₈×C₈₉	—	2	1	no	—
206	C₄×Q₈×C₈₉	—	2	1	no	—
207	C₄×Q₈×C₈₉	—	2	1	no	—
208	C₄×Q₈×C₈₉	—	2	2	no	—
209	C₄×Q₈×C₈₉	—	2	1	no	—
210	C₄×Q₈×C₈₉	—	2	2	no	—
211	C₄×Q₈×C₈₉	—	2	2	no	—
212	C₄×Q₈×C₈₉	—	2	1	no	—
213	C₄×Q₈×C₈₉	D₄	1	1	yes	characteristic
214	C₄×Q₈×C₈₉	D₄	1	1	yes	characteristic
215	C₄×Q₈×C₈₉	D₄	1	2	yes	—
216	C₄×Q₈×C₈₉	C₂³	1	1	yes	characteristic
217	C₄×Q₈×C₈₉	C₂³	1	1	yes	characteristic
218	C₄×Q₈×C₈₉	C₂³	1	1	yes	characteristic
219	C₄×Q₈×C₈₉	C₂³	1	2	yes	—
220	C₄×Q₈×C₈₉	C₂³	1	2	yes	—
221	C₄×Q₈×C₈₉	C₂³	1	2	yes	—
222	C₄×Q₈×C₈₉	C₂³	1	1	yes	characteristic
223	C₄×Q₈×C₈₉	C₂³	1	1	yes	characteristic
224	C₄×Q₈×C₈₉	C₂³	1	2	yes	—
225	C₄×D₄×C₈₉	—	2	1	no	—
226	C₄×D₄×C₈₉	—	2	2	no	—
227	C₄×D₄×C₈₉	—	2	1	no	—
228	C₄×D₄×C₈₉	—	2	2	no	—
229	C₄×D₄×C₈₉	—	2	1	no	—
230	C₄×D₄×C₈₉	—	2	2	no	—
231	C₄×D₄×C₈₉	—	2	2	no	—
232	C₄×D₄×C₈₉	—	2	1	no	—
233	C₄×D₄×C₈₉	—	2	1	no	—
234	C₄×D₄×C₈₉	—	2	2	no	—
235	C₄×D₄×C₈₉	C₂³	1	1	yes	characteristic
236	C₄×D₄×C₈₉	C₂³	1	1	yes	characteristic
237	C₄×D₄×C₈₉	C₂³	1	1	yes	characteristic
238	C₄×D₄×C₈₉	C₂³	1	2	yes	—
239	C₄×D₄×C₈₉	C₂³	1	2	yes	—
240	C₄×D₄×C₈₉	C₂³	1	2	yes	—
241	C₄×D₄×C₈₉	C₂³	1	2	yes	—
242	C₄×D₄×C₈₉	C₂³	1	2	yes	—
243	C₄×D₄×C₈₉	C₂³	1	2	yes	—
244	#117×C₈₉	—	2	2	no	—
245	#117×C₈₉	—	2	1	no	—
246	#117×C₈₉	—	2	1	no	—
247	#117×C₈₉	—	2	2	no	—
248	#117×C₈₉	C₂³	1	1	yes	characteristic
249	#117×C₈₉	C₂³	1	2	yes	—
250	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
251	C₂×C₄⋊C₄×C₈₉	—	2	2	no	—
252	C₂×C₄⋊C₄×C₈₉	—	2	2	no	—
253	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
254	C₂×C₄⋊C₄×C₈₉	D₄	1	2	yes	—
255	C₂×C₄⋊C₄×C₈₉	D₄	1	1	yes	characteristic
256	C₂×C₄²×C₈₉	—	2	1	no	—
257	C₂×C₄²×C₈₉	—	2	2	no	—
258	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
259	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
260	#107×C₈₉	C₂³	1	2	yes	—
261	#107×C₈₉	C₂³	1	1	yes	characteristic
262	#107×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	2	yes	—
266	#107×C₈₉	C₂³	1	2	yes	—
267	#106×C₈₉	C₂³	1	1	yes	characteristic
268	#106×C₈₉	C₂³	1	2	yes	—
269	#106×C₈₉	C₂³	1	1	yes	characteristic
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	C₄⋊C₈×C₈₉	C₂³	1	1	yes	characteristic
275	C₄⋊C₈×C₈₉	C₂³	1	1	yes	characteristic
276	C₄⋊C₈×C₈₉	C₂³	1	1	yes	characteristic
277	C₄⋊C₈×C₈₉	C₂³	1	1	yes	characteristic
278	C₄⋊C₈×C₈₉	C₂³	1	2	yes	—
279	C₄⋊C₈×C₈₉	C₂³	1	2	yes	—
280	C₄⋊C₈×C₈₉	C₂³	1	2	yes	—
281	C₄⋊C₈×C₈₉	C₂³	1	2	yes	—
282	#103×C₈₉	C₂³	1	1	yes	characteristic
283	#103×C₈₉	C₂³	1	2	yes	—
284	#103×C₈₉	C₂³	1	1	yes	characteristic
285	#103×C₈₉	C₂³	1	1	yes	characteristic
286	#103×C₈₉	C₂³	1	1	yes	characteristic
287	#103×C₈₉	C₂³	1	2	yes	—
288	#103×C₈₉	C₂³	1	2	yes	—
289	#102×C₈₉	C₂³	1	2	yes	—
290	#102×C₈₉	C₂³	1	1	yes	characteristic
291	#102×C₈₉	C₂³	1	2	yes	—
292	#102×C₈₉	C₂³	1	1	yes	characteristic
293	#102×C₈₉	C₂³	1	1	yes	characteristic
294	#102×C₈₉	C₂³	1	2	yes	—
295	#102×C₈₉	C₂³	1	1	yes	characteristic
296	#102×C₈₉	C₂³	1	2	yes	—
297	#102×C₈₉	C₂³	1	2	yes	—
298	#102×C₈₉	C₂³	1	2	yes	—
299	#102×C₈₉	C₂³	1	2	yes	—
300	#102×C₈₉	C₂³	1	2	yes	—
301	#102×C₈₉	C₂³	1	2	yes	—
302	C₂²⋊C₈×C₈₉	C₂³	1	1	yes	characteristic
303	C₂²⋊C₈×C₈₉	C₂³	1	2	yes	—
304	C₂²⋊C₈×C₈₉	C₂³	1	1	yes	characteristic
305	#97×C₈₉	C₂³	1	2	yes	—
306	#97×C₈₉	C₂³	1	2	yes	—
307	#97×C₈₉	C₂³	1	2	yes	—
308	#97×C₈₉	C₂³	1	2	yes	—
309	C₄×C₈×C₈₉	C₂³	1	2	yes	—
310	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
311	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
312	#41×C₈₉	—	2	2	no	—
313	#41×C₈₉	—	2	2	no	—
314	#41×C₈₉	—	4	4	no	—
315	#41×C₈₉	—	8	2	no	—
316	#41×C₈₉	—	8	4	no	—
317	C₂×Q₈×C₈₉	—	2	2	no	—
318	C₂×Q₈×C₈₉	—	2	1	no	—
319	C₂×Q₈×C₈₉	—	2	2	no	—
320	C₂×Q₈×C₈₉	—	2	1	no	—
321	C₂×Q₈×C₈₉	—	2	2	no	—
322	C₂×Q₈×C₈₉	—	2	1	no	—
323	C₂×Q₈×C₈₉	—	4	2	no	—
324	C₂×Q₈×C₈₉	—	4	4	no	—
325	C₂×Q₈×C₈₉	C₂×D₄	1	1	yes	characteristic
326	C₂×Q₈×C₈₉	C₂×D₄	1	1	yes	characteristic
327	C₂×Q₈×C₈₉	C₂×D₄	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	—	2	1	no	—
335	C₂×D₄×C₈₉	—	2	2	no	—
336	C₂×D₄×C₈₉	—	2	1	no	—
337	C₂×D₄×C₈₉	C₂⁴	1	2	yes	—
338	C₂×D₄×C₈₉	C₂⁴	1	1	yes	characteristic
339	C₂×D₄×C₈₉	C₂⁴	1	1	yes	characteristic
340	C₂²×C₄×C₈₉	—	2	1	no	—
341	C₂²×C₄×C₈₉	—	2	2	no	—
342	C₂²×C₄×C₈₉	—	2	1	no	—
343	C₂²×C₄×C₈₉	—	2	2	no	—
344	C₂²×C₄×C₈₉	—	2	1	no	—
345	C₂²×C₄×C₈₉	—	2	1	no	—
346	C₂²×C₄×C₈₉	—	2	2	no	—
347	C₂²×C₄×C₈₉	—	2	2	no	—
348	C₂²×C₄×C₈₉	—	2	2	no	—
349	C₂²×C₄×C₈₉	—	2	2	no	—
350	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
351	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
352	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
353	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
354	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
355	Q₁₆×C₈₉	—	2	2	no	—
356	SD₁₆×C₈₉	—	2	2	no	—
357	SD₁₆×C₈₉	—	2	4	no	—
358	SD₁₆×C₈₉	—	2	2	no	—
359	D₈×C₈₉	—	2	2	no	—
360	D₈×C₈₉	—	2	4	no	—
361	C₂×C₈×C₈₉	C₂⁴	1	1	yes	characteristic
362	C₂×C₈×C₈₉	C₂⁴	1	2	yes	—
363	C₂×C₈×C₈₉	C₂⁴	1	1	yes	characteristic
364	C₂×C₈×C₈₉	C₂⁴	1	1	yes	characteristic
365	C₂×C₈×C₈₉	C₂⁴	1	2	yes	—
366	C₂×C₈×C₈₉	C₂⁴	1	1	yes	characteristic
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	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	2	no	—
378	C₄⋊C₄×C₈₉	—	2	1	no	—
379	C₄⋊C₄×C₈₉	—	2	2	no	—
380	C₄⋊C₄×C₈₉	—	2	1	no	—
381	C₄⋊C₄×C₈₉	—	2	2	no	—
382	C₄⋊C₄×C₈₉	—	2	1	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	2	yes	—
391	C₄⋊C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
392	C₄⋊C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
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	C₂×D₄	1	2	yes	—
397	C₄⋊C₄×C₈₉	C₂⁴	1	1	yes	characteristic
398	C₄⋊C₄×C₈₉	C₂⁴	1	2	yes	—
399	C₄⋊C₄×C₈₉	C₂⁴	1	1	yes	characteristic
400	C₄⋊C₄×C₈₉	C₂⁴	1	2	yes	—
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	C₂²⋊C₄×C₈₉	—	2	1	no	—
405	C₂²⋊C₄×C₈₉	—	2	2	no	—
406	C₂²⋊C₄×C₈₉	—	2	1	no	—
407	C₂²⋊C₄×C₈₉	—	2	1	no	—
408	C₂²⋊C₄×C₈₉	—	2	2	no	—
409	C₂²⋊C₄×C₈₉	—	2	1	no	—
410	C₂²⋊C₄×C₈₉	—	2	2	no	—
411	C₂²⋊C₄×C₈₉	—	2	2	no	—
412	C₂²⋊C₄×C₈₉	—	2	1	no	—
413	C₂²⋊C₄×C₈₉	—	2	2	no	—
414	C₂²⋊C₄×C₈₉	—	2	1	no	—
415	C₂²⋊C₄×C₈₉	—	2	2	no	—
416	C₂²⋊C₄×C₈₉	—	2	1	no	—
417	C₂²⋊C₄×C₈₉	—	2	2	no	—
418	C₂²⋊C₄×C₈₉	—	2	1	no	—
419	C₂²⋊C₄×C₈₉	—	2	2	no	—
420	C₂²⋊C₄×C₈₉	—	2	2	no	—
421	C₂²⋊C₄×C₈₉	—	2	2	no	—
422	C₄²×C₈₉	—	2	1	no	—
423	C₄²×C₈₉	—	2	2	no	—
424	C₄²×C₈₉	—	2	1	no	—
425	C₄²×C₈₉	—	2	2	no	—
426	C₄²×C₈₉	—	2	2	no	—
427	C₄²×C₈₉	—	2	1	no	—
428	C₄²×C₈₉	—	2	2	no	—
429	C₄²×C₈₉	—	2	1	no	—
430	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
431	C₄²×C₈₉	C₂×D₄	1	2	yes	—
432	C₄²×C₈₉	C₂×D₄	1	2	yes	—
433	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
434	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
435	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
436	C₄²×C₈₉	C₂⁴	1	2	yes	—
437	C₄²×C₈₉	C₂⁴	1	2	yes	—
438	C₂³×C₈₉	—	2	1	no	—
439	C₂³×C₈₉	—	2	2	no	—
440	C₂³×C₈₉	—	2	1	no	—
441	C₂³×C₈₉	C₂²×D₄	1	1	yes	characteristic
442	Q₈×C₈₉	—	2	2	no	—
443	Q₈×C₈₉	—	2	2	no	—
444	Q₈×C₈₉	—	2	1	no	—
445	Q₈×C₈₉	—	2	1	no	—
446	Q₈×C₈₉	—	2	1	no	—
447	Q₈×C₈₉	—	4	2	no	—
448	Q₈×C₈₉	—	4	4	no	—
449	Q₈×C₈₉	—	4	2	no	—
450	Q₈×C₈₉	—	8	2	no	—
451	Q₈×C₈₉	—	8	1	no	—
452	Q₈×C₈₉	—	8	2	no	—
453	Q₈×C₈₉	—	8	1	no	—
454	Q₈×C₈₉	2₋¹⁺⁴	1	2	yes	—
455	D₄×C₈₉	—	2	4	no	—
456	D₄×C₈₉	—	2	1	no	—
457	D₄×C₈₉	—	2	2	no	—
458	D₄×C₈₉	—	2	1	no	—
459	D₄×C₈₉	—	2	2	no	—
460	D₄×C₈₉	—	2	1	no	—
461	D₄×C₈₉	—	4	4	no	—
462	D₄×C₈₉	—	4	4	no	—
463	D₄×C₈₉	—	4	2	no	—
464	D₄×C₈₉	—	4	2	no	—
465	D₄×C₈₉	—	8	2	no	—
466	D₄×C₈₉	—	8	1	no	—
467	D₄×C₈₉	2₋¹⁺⁴	1	2	yes	—
468	C₂×C₄×C₈₉	—	2	4	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	1	no	—
473	C₂×C₄×C₈₉	—	2	1	no	—
474	C₂×C₄×C₈₉	—	2	2	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	2	no	—
479	C₂×C₄×C₈₉	—	2	1	no	—
480	C₂×C₄×C₈₉	—	2	1	no	—
481	C₂×C₄×C₈₉	—	4	2	no	—
482	C₂×C₄×C₈₉	—	4	1	no	—
483	C₂×C₄×C₈₉	—	4	2	no	—
484	C₂×C₄×C₈₉	—	4	4	no	—
485	C₂×C₄×C₈₉	—	4	4	no	—
486	C₂×C₄×C₈₉	—	4	2	no	—
487	C₂×C₄×C₈₉	—	4	2	no	—
488	C₂×C₄×C₈₉	—	8	1	no	—
489	C₂×C₄×C₈₉	—	8	2	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	2	yes	—
498	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
499	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
500	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
501	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
502	C₂×C₄×C₈₉	C₂⁵	1	1	yes	characteristic
503	C₈×C₈₉	—	2	2	no	—
504	C₈×C₈₉	—	2	1	no	—
505	C₈×C₈₉	—	2	2	no	—
506	C₈×C₈₉	—	2	1	no	—
507	C₈×C₈₉	—	2	1	no	—
508	C₈×C₈₉	—	2	1	no	—
509	C₂²×C₈₉	—	2	1	no	—
510	C₂²×C₈₉	—	2	1	no	—
511	C₂²×C₈₉	—	2	2	no	—
512	C₂²×C₈₉	—	2	1	no	—
513	C₂²×C₈₉	—	4	1	no	—
514	C₂²×C₈₉	—	4	1	no	—
515	C₂²×C₈₉	—	4	2	no	—
516	C₂²×C₈₉	—	4	1	no	—
517	C₂²×C₈₉	—	4	2	no	—
518	C₂²×C₈₉	—	4	1	no	—
519	C₂²×C₈₉	—	4	2	no	—
520	C₂²×C₈₉	—	4	1	no	—
521	C₂²×C₈₉	C₂³×D₄	1	1	yes	characteristic
522	C₄×C₈₉	—	2	1	no	—
523	C₄×C₈₉	—	2	2	no	—
524	C₄×C₈₉	—	2	2	no	—
525	C₄×C₈₉	—	2	1	no	—
526	C₄×C₈₉	—	2	1	no	—
527	C₄×C₈₉	—	2	2	no	—
528	C₄×C₈₉	—	2	1	no	—
529	C₄×C₈₉	—	2	2	no	—
530	C₄×C₈₉	—	2	2	no	—
531	C₄×C₈₉	—	4	2	no	—
532	C₄×C₈₉	—	4	1	no	—
533	C₄×C₈₉	—	4	1	no	—
534	C₄×C₈₉	—	4	2	no	—
535	C₄×C₈₉	—	4	1	no	—
536	C₄×C₈₉	—	4	1	no	—
537	C₄×C₈₉	—	4	2	no	—
538	C₄×C₈₉	—	4	1	no	—
539	C₄×C₈₉	#575	1	2	yes	—
540	C₄×C₈₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
541	C₄×C₈₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
542	#61833	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
543	C₂×C₈₉	—	4	1	no	—
544	C₂×C₈₉	—	4	2	no	—
545	C₂×C₈₉	—	8	2	no	—
546	C₂×C₈₉	—	8	1	no	—
547	C₂×C₈₉	#3486	1	1	yes	characteristic
548	C₂×C₈₉	C₂×#575	1	1	yes	characteristic
549	C₂×C₈₉	#3585	1	1	yes	characteristic
550	#3522	C₂×C₈₉	1	1	yes	characteristic, complemented
551	Q₈×#41	C₂×C₈₉	1	1	yes	characteristic, complemented
552	#3389	C₂×C₈₉	1	2	yes	complemented
553	#3388	C₂×C₈₉	1	2	yes	complemented
554	#3387	C₂×C₈₉	1	1	yes	characteristic, complemented
555	#3385	C₂×C₈₉	1	1	yes	characteristic, complemented
556	#3385	C₂×C₈₉	1	1	yes	characteristic, complemented
557	#3384	C₂×C₈₉	1	1	yes	characteristic, complemented
558	#3375	C₂×C₈₉	1	1	yes	characteristic, complemented
559	#3373	C₂×C₈₉	1	1	yes	characteristic, complemented
560	#3371	C₂×C₈₉	1	2	yes	complemented
561	#3370	C₂×C₈₉	1	2	yes	complemented
562	#3368	C₂×C₈₉	1	1	yes	characteristic, complemented
563	#3366	C₂×C₈₉	1	1	yes	characteristic, complemented
564	#3240	C₂×C₈₉	1	2	yes	complemented
565	#3235	C₂×C₈₉	1	2	yes	complemented
566	#3233	C₂×C₈₉	1	1	yes	characteristic, complemented
567	#3228	C₂×C₈₉	1	1	yes	characteristic, complemented
568	#3115	C₂×C₈₉	1	2	yes	complemented
569	#3111	C₂×C₈₉	1	2	yes	complemented
570	#3106	C₂×C₈₉	1	1	yes	characteristic, complemented
571	#3102	C₂×C₈₉	1	1	yes	characteristic, complemented
572	#2983	C₂×C₈₉	1	1	yes	characteristic, complemented
573	C₈₉	#61833	1	1	yes	characteristic, direct product factor, Sylow
574	#559	C₂²×C₈₉	1	2	yes	—
575	#559	C₂²×C₈₉	1	1	yes	characteristic
576	Q₈²	C₂²×C₈₉	1	1	yes	characteristic
577	Q₈²	C₂²×C₈₉	1	1	yes	characteristic
578	#557	C₂²×C₈₉	1	1	yes	characteristic
579	#557	C₂²×C₈₉	1	2	yes	—
580	#554	—	2	1	no	—
581	#554	—	2	2	no	—
582	#554	C₂²×C₈₉	1	1	yes	characteristic
583	#554	C₂²×C₈₉	1	2	yes	—
584	#554	C₂²×C₈₉	1	1	yes	characteristic
585	#554	C₂²×C₈₉	1	2	yes	—
586	#550	C₂²×C₈₉	1	1	yes	characteristic
587	D₄×Q₈	—	2	1	no	—
588	D₄×Q₈	C₂²×C₈₉	1	1	yes	characteristic
589	#548	—	2	1	no	—
590	#547	—	2	2	no	—
591	#547	—	2	1	no	—
592	#542	—	2	1	no	—
593	#542	—	2	2	no	—
594	#533	—	2	1	no	—
595	#533	—	2	2	no	—
596	#533	C₂²×C₈₉	1	1	yes	characteristic
597	#533	C₂²×C₈₉	1	2	yes	—
598	#532	C₂²×C₈₉	1	1	yes	characteristic
599	#532	C₂²×C₈₉	1	2	yes	—
600	#529	C₂²×C₈₉	1	1	yes	characteristic
601	#529	C₂²×C₈₉	1	2	yes	—
602	#520	—	2	1	no	—
603	C₄×#41	C₂²×C₈₉	1	1	yes	characteristic
604	C₄×#41	C₂²×C₈₉	1	2	yes	—
605	C₂×C₄×Q₈	—	2	1	no	—
606	C₂×C₄×Q₈	C₂²×C₈₉	1	1	yes	characteristic
607	#501	C₂²×C₈₉	1	2	yes	—
608	#501	C₂²×C₈₉	1	2	yes	—
609	#501	C₂²×C₈₉	1	2	yes	—
610	#501	C₂²×C₈₉	1	2	yes	—
611	#500	C₂²×C₈₉	1	1	yes	characteristic
612	#499	C₂²×C₈₉	1	2	yes	—
613	#498	C₂²×C₈₉	1	1	yes	characteristic
614	#490	C₂²×C₈₉	1	2	yes	—
615	#490	C₂²×C₈₉	1	2	yes	—
616	#489	C₂²×C₈₉	1	2	yes	—
617	#489	C₂²×C₈₉	1	2	yes	—
618	#488	C₂²×C₈₉	1	2	yes	—
619	#486	C₂²×C₈₉	1	1	yes	characteristic
620	#486	C₂²×C₈₉	1	1	yes	characteristic
621	#485	C₂²×C₈₉	1	1	yes	characteristic
622	#485	C₂²×C₈₉	1	2	yes	—
623	#482	C₂²×C₈₉	1	1	yes	characteristic
624	#482	C₂²×C₈₉	1	2	yes	—
625	#482	C₂²×C₈₉	1	2	yes	—
626	#482	C₂²×C₈₉	1	2	yes	—
627	#482	C₂²×C₈₉	1	2	yes	—
628	#479	C₂²×C₈₉	1	1	yes	characteristic
629	#479	C₂²×C₈₉	1	2	yes	—
630	#479	C₂²×C₈₉	1	2	yes	—
631	#479	C₂²×C₈₉	1	2	yes	—
632	#478	C₂²×C₈₉	1	1	yes	characteristic
633	#478	C₂²×C₈₉	1	2	yes	—
634	#478	C₂²×C₈₉	1	2	yes	—
635	#478	C₂²×C₈₉	1	2	yes	—
636	#478	C₂²×C₈₉	1	2	yes	—
637	#478	C₂²×C₈₉	1	2	yes	—
638	#477	C₂²×C₈₉	1	1	yes	characteristic
639	#477	C₂²×C₈₉	1	1	yes	characteristic
640	#476	C₂²×C₈₉	1	1	yes	characteristic
641	#476	C₂²×C₈₉	1	1	yes	characteristic
642	#476	C₂²×C₈₉	1	2	yes	—
643	#476	C₂²×C₈₉	1	2	yes	—
644	#475	C₂²×C₈₉	1	2	yes	—
645	#475	C₂²×C₈₉	1	1	yes	characteristic
646	#474	C₂²×C₈₉	1	1	yes	characteristic
647	#474	C₂²×C₈₉	1	2	yes	—
648	#474	C₂²×C₈₉	1	2	yes	—
649	#474	C₂²×C₈₉	1	2	yes	—
650	#464	C₂²×C₈₉	1	1	yes	characteristic
651	#464	C₂²×C₈₉	1	2	yes	—
652	#463	C₂²×C₈₉	1	1	yes	characteristic
653	#463	C₂²×C₈₉	1	2	yes	—
654	#460	C₂²×C₈₉	1	1	yes	characteristic
655	#460	C₂²×C₈₉	1	2	yes	—
656	#459	C₂²×C₈₉	1	1	yes	characteristic
657	#459	C₂²×C₈₉	1	2	yes	—
658	#452	C₂²×C₈₉	1	1	yes	characteristic
659	#449	C₂²×C₈₉	1	1	yes	characteristic
660	#449	C₂²×C₈₉	1	2	yes	—
661	#446	C₂²×C₈₉	1	1	yes	characteristic
662	#446	C₂²×C₈₉	1	1	yes	characteristic
663	#446	C₂²×C₈₉	1	2	yes	—
664	#446	C₂²×C₈₉	1	2	yes	—
665	#446	C₂²×C₈₉	1	1	yes	characteristic
666	#446	C₂²×C₈₉	1	1	yes	characteristic
667	#442	C₂²×C₈₉	1	2	yes	—
668	#442	C₂²×C₈₉	1	2	yes	—
669	#442	C₂²×C₈₉	1	2	yes	—
670	#441	C₂²×C₈₉	1	2	yes	—
671	#440	C₂²×C₈₉	1	2	yes	—
672	#440	C₂²×C₈₉	1	2	yes	—
673	#440	C₂²×C₈₉	1	2	yes	—
674	#440	C₂²×C₈₉	1	2	yes	—
675	C₄×Q₁₆	C₂²×C₈₉	1	1	yes	characteristic
676	C₄×SD₁₆	C₂²×C₈₉	1	1	yes	characteristic
677	C₄×SD₁₆	C₂²×C₈₉	1	1	yes	characteristic
678	C₄×SD₁₆	C₂²×C₈₉	1	2	yes	—
679	C₄×D₈	C₂²×C₈₉	1	1	yes	characteristic
680	C₄×D₈	C₂²×C₈₉	1	2	yes	—
681	#432	C₂²×C₈₉	1	2	yes	—
682	#432	C₂²×C₈₉	1	2	yes	—
683	#431	C₂²×C₈₉	1	1	yes	characteristic
684	#431	C₂²×C₈₉	1	1	yes	characteristic
685	C₂×#41	—	2	1	no	—
686	C₂×#41	—	2	1	no	—
687	C₂×#41	—	2	2	no	—
688	C₂×#41	C₂³×C₈₉	1	1	yes	characteristic
689	C₂²×Q₈	—	2	1	no	—
690	C₂²×Q₈	D₄×C₈₉	1	1	yes	characteristic
691	C₂×Q₁₆	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×SD₁₆	C₂³×C₈₉	1	1	yes	characteristic
695	C₂×D₈	C₂³×C₈₉	1	1	yes	characteristic
696	C₂×D₈	C₂³×C₈₉	1	2	yes	—
697	C₄⋊Q₈	—	2	1	no	—
698	C₄⋊Q₈	—	2	2	no	—
699	C₄⋊Q₈	—	2	1	no	—
700	C₄⋊Q₈	—	2	2	no	—
701	C₄⋊Q₈	—	2	1	no	—
702	C₄⋊Q₈	—	2	2	no	—
703	C₄⋊Q₈	C₂³×C₈₉	1	2	yes	—
704	C₄⋊Q₈	C₂³×C₈₉	1	1	yes	characteristic
705	C₄⋊Q₈	C₂³×C₈₉	1	1	yes	characteristic
706	C₄⋊Q₈	C₂³×C₈₉	1	2	yes	—
707	C₄⋊Q₈	C₂³×C₈₉	1	2	yes	—
708	C₄⋊Q₈	C₂³×C₈₉	1	1	yes	characteristic
709	#127	C₂³×C₈₉	1	1	yes	characteristic
710	#127	C₂³×C₈₉	1	2	yes	—
711	#126	—	2	2	no	—
712	#126	—	2	1	no	—
713	#125	—	2	2	no	—
714	#125	—	2	2	no	—
715	#125	—	2	2	no	—
716	#125	C₂³×C₈₉	1	1	yes	characteristic
717	#125	C₂³×C₈₉	1	2	yes	—
718	#125	C₂³×C₈₉	1	2	yes	—
719	#125	C₂³×C₈₉	1	2	yes	—
720	#125	C₂³×C₈₉	1	2	yes	—
721	#124	—	2	1	no	—
722	#124	—	2	2	no	—
723	#124	—	2	2	no	—
724	#124	—	2	1	no	—
725	#124	C₂³×C₈₉	1	1	yes	characteristic
726	#124	C₂³×C₈₉	1	2	yes	—
727	#123	—	2	1	no	—
728	#123	—	2	2	no	—
729	#123	—	2	2	no	—
730	#123	—	2	2	no	—
731	#123	—	2	2	no	—
732	C₂²⋊Q₈	—	2	1	no	—
733	C₂²⋊Q₈	—	2	2	no	—
734	C₂²⋊Q₈	—	2	1	no	—
735	C₂²⋊Q₈	—	2	2	no	—
736	C₂²⋊Q₈	—	2	1	no	—
737	C₂²⋊Q₈	—	2	2	no	—
738	C₂²⋊Q₈	—	2	1	no	—
739	C₂²⋊Q₈	—	2	2	no	—
740	C₂²⋊Q₈	—	2	1	no	—
741	C₂²⋊Q₈	—	2	2	no	—
742	C₂²⋊Q₈	—	2	2	no	—
743	C₂²⋊Q₈	—	2	2	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	C₂³×C₈₉	1	1	yes	characteristic
749	#121	—	2	1	no	—
750	#121	—	2	2	no	—
751	#121	—	2	1	no	—
752	#121	—	2	2	no	—
753	#121	C₂³×C₈₉	1	1	yes	characteristic
754	#121	C₂³×C₈₉	1	2	yes	—
755	C₄×Q₈	—	2	1	no	—
756	C₄×Q₈	—	2	1	no	—
757	C₄×Q₈	—	2	1	no	—
758	C₄×Q₈	—	2	2	no	—
759	C₄×Q₈	—	2	1	no	—
760	C₄×Q₈	—	2	2	no	—
761	C₄×Q₈	—	2	2	no	—
762	C₄×Q₈	—	2	1	no	—
763	C₄×Q₈	D₄×C₈₉	1	1	yes	characteristic
764	C₄×Q₈	D₄×C₈₉	1	1	yes	characteristic
765	C₄×Q₈	D₄×C₈₉	1	2	yes	—
766	C₄×Q₈	C₂³×C₈₉	1	1	yes	characteristic
767	C₄×Q₈	C₂³×C₈₉	1	2	yes	—
768	C₄×Q₈	C₂³×C₈₉	1	1	yes	characteristic
769	C₄×Q₈	C₂³×C₈₉	1	2	yes	—
770	C₄×Q₈	C₂³×C₈₉	1	1	yes	characteristic
771	C₄×Q₈	C₂³×C₈₉	1	2	yes	—
772	C₄×Q₈	C₂³×C₈₉	1	1	yes	characteristic
773	C₄×Q₈	C₂³×C₈₉	1	1	yes	characteristic
774	C₄×Q₈	C₂³×C₈₉	1	2	yes	—
775	C₄×D₄	—	2	1	no	—
776	C₄×D₄	—	2	2	no	—
777	C₄×D₄	—	2	1	no	—
778	C₄×D₄	—	2	2	no	—
779	C₄×D₄	—	2	1	no	—
780	C₄×D₄	—	2	2	no	—
781	C₄×D₄	—	2	2	no	—
782	C₄×D₄	—	2	1	no	—
783	C₄×D₄	—	2	1	no	—
784	C₄×D₄	—	2	2	no	—
785	C₄×D₄	C₂³×C₈₉	1	1	yes	characteristic
786	C₄×D₄	C₂³×C₈₉	1	2	yes	—
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	C₄×D₄	C₂³×C₈₉	1	2	yes	—
792	C₄×D₄	C₂³×C₈₉	1	2	yes	—
793	C₄×D₄	C₂³×C₈₉	1	2	yes	—
794	#117	—	2	2	no	—
795	#117	—	2	1	no	—
796	#117	—	2	1	no	—
797	#117	—	2	2	no	—
798	#117	C₂³×C₈₉	1	1	yes	characteristic
799	#117	C₂³×C₈₉	1	2	yes	—
800	C₂×C₄⋊C₄	—	2	1	no	—
801	C₂×C₄⋊C₄	—	2	2	no	—
802	C₂×C₄⋊C₄	—	2	2	no	—
803	C₂×C₄⋊C₄	—	2	1	no	—
804	C₂×C₄⋊C₄	D₄×C₈₉	1	2	yes	—
805	C₂×C₄⋊C₄	D₄×C₈₉	1	1	yes	characteristic
806	C₂×C₄²	—	2	1	no	—
807	C₂×C₄²	—	2	2	no	—
808	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
809	C₂×C₄²	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	1	yes	characteristic
813	#107	C₂³×C₈₉	1	2	yes	—
814	#107	C₂³×C₈₉	1	2	yes	—
815	#107	C₂³×C₈₉	1	2	yes	—
816	#107	C₂³×C₈₉	1	2	yes	—
817	#106	C₂³×C₈₉	1	1	yes	characteristic
818	#106	C₂³×C₈₉	1	2	yes	—
819	#106	C₂³×C₈₉	1	1	yes	characteristic
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	C₄⋊C₈	C₂³×C₈₉	1	1	yes	characteristic
825	C₄⋊C₈	C₂³×C₈₉	1	1	yes	characteristic
826	C₄⋊C₈	C₂³×C₈₉	1	1	yes	characteristic
827	C₄⋊C₈	C₂³×C₈₉	1	1	yes	characteristic
828	C₄⋊C₈	C₂³×C₈₉	1	2	yes	—
829	C₄⋊C₈	C₂³×C₈₉	1	2	yes	—
830	C₄⋊C₈	C₂³×C₈₉	1	2	yes	—
831	C₄⋊C₈	C₂³×C₈₉	1	2	yes	—
832	#103	C₂³×C₈₉	1	1	yes	characteristic
833	#103	C₂³×C₈₉	1	2	yes	—
834	#103	C₂³×C₈₉	1	1	yes	characteristic
835	#103	C₂³×C₈₉	1	1	yes	characteristic
836	#103	C₂³×C₈₉	1	1	yes	characteristic
837	#103	C₂³×C₈₉	1	2	yes	—
838	#103	C₂³×C₈₉	1	2	yes	—
839	#102	C₂³×C₈₉	1	2	yes	—
840	#102	C₂³×C₈₉	1	1	yes	characteristic
841	#102	C₂³×C₈₉	1	2	yes	—
842	#102	C₂³×C₈₉	1	1	yes	characteristic
843	#102	C₂³×C₈₉	1	1	yes	characteristic
844	#102	C₂³×C₈₉	1	2	yes	—
845	#102	C₂³×C₈₉	1	1	yes	characteristic
846	#102	C₂³×C₈₉	1	2	yes	—
847	#102	C₂³×C₈₉	1	2	yes	—
848	#102	C₂³×C₈₉	1	2	yes	—
849	#102	C₂³×C₈₉	1	2	yes	—
850	#102	C₂³×C₈₉	1	2	yes	—
851	#102	C₂³×C₈₉	1	2	yes	—
852	C₂²⋊C₈	C₂³×C₈₉	1	1	yes	characteristic
853	C₂²⋊C₈	C₂³×C₈₉	1	2	yes	—
854	C₂²⋊C₈	C₂³×C₈₉	1	1	yes	characteristic
855	#97	C₂³×C₈₉	1	2	yes	—
856	#97	C₂³×C₈₉	1	2	yes	—
857	#97	C₂³×C₈₉	1	2	yes	—
858	#97	C₂³×C₈₉	1	2	yes	—
859	C₄×C₈	C₂³×C₈₉	1	2	yes	—
860	C₄×C₈	C₂³×C₈₉	1	1	yes	characteristic
861	C₄×C₈	C₂³×C₈₉	1	1	yes	characteristic
862	#41	—	2	2	no	—
863	#41	—	2	2	no	—
864	#41	—	4	4	no	—
865	#41	—	8	2	no	—
866	#41	—	8	4	no	—
867	C₂×Q₈	—	2	2	no	—
868	C₂×Q₈	—	2	1	no	—
869	C₂×Q₈	—	2	2	no	—
870	C₂×Q₈	—	2	1	no	—
871	C₂×Q₈	—	2	2	no	—
872	C₂×Q₈	—	2	1	no	—
873	C₂×Q₈	—	4	2	no	—
874	C₂×Q₈	—	4	4	no	—
875	C₂×Q₈	C₂×D₄×C₈₉	1	1	yes	characteristic
876	C₂×Q₈	C₂×D₄×C₈₉	1	1	yes	characteristic
877	C₂×Q₈	C₂×D₄×C₈₉	1	2	yes	—
878	C₂×Q₈	C₂⁴×C₈₉	1	1	yes	characteristic
879	C₂×Q₈	C₂⁴×C₈₉	1	1	yes	characteristic
880	C₂×D₄	—	2	1	no	—
881	C₂×D₄	—	2	1	no	—
882	C₂×D₄	—	2	2	no	—
883	C₂×D₄	—	2	2	no	—
884	C₂×D₄	—	2	1	no	—
885	C₂×D₄	—	2	2	no	—
886	C₂×D₄	—	2	1	no	—
887	C₂×D₄	C₂⁴×C₈₉	1	2	yes	—
888	C₂×D₄	C₂⁴×C₈₉	1	1	yes	characteristic
889	C₂×D₄	C₂⁴×C₈₉	1	1	yes	characteristic
890	C₂²×C₄	—	2	1	no	—
891	C₂²×C₄	—	2	2	no	—
892	C₂²×C₄	—	2	1	no	—
893	C₂²×C₄	—	2	2	no	—
894	C₂²×C₄	—	2	1	no	—
895	C₂²×C₄	—	2	1	no	—
896	C₂²×C₄	—	2	2	no	—
897	C₂²×C₄	—	2	2	no	—
898	C₂²×C₄	—	2	2	no	—
899	C₂²×C₄	—	2	2	no	—
900	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
901	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
902	C₂²×C₄	C₂×D₄×C₈₉	1	2	yes	—
903	C₂²×C₄	C₂×D₄×C₈₉	1	2	yes	—
904	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
905	Q₁₆	—	2	2	no	—
906	SD₁₆	—	2	2	no	—
907	SD₁₆	—	2	4	no	—
908	SD₁₆	—	2	2	no	—
909	D₈	—	2	2	no	—
910	D₈	—	2	4	no	—
911	C₂×C₈	C₂⁴×C₈₉	1	1	yes	characteristic
912	C₂×C₈	C₂⁴×C₈₉	1	2	yes	—
913	C₂×C₈	C₂⁴×C₈₉	1	1	yes	characteristic
914	C₂×C₈	C₂⁴×C₈₉	1	1	yes	characteristic
915	C₂×C₈	C₂⁴×C₈₉	1	2	yes	—
916	C₂×C₈	C₂⁴×C₈₉	1	1	yes	characteristic
917	C₄⋊C₄	—	2	1	no	—
918	C₄⋊C₄	—	2	2	no	—
919	C₄⋊C₄	—	2	2	no	—
920	C₄⋊C₄	—	2	1	no	—
921	C₄⋊C₄	—	2	2	no	—
922	C₄⋊C₄	—	2	2	no	—
923	C₄⋊C₄	—	2	2	no	—
924	C₄⋊C₄	—	2	2	no	—
925	C₄⋊C₄	—	2	1	no	—
926	C₄⋊C₄	—	2	1	no	—
927	C₄⋊C₄	—	2	2	no	—
928	C₄⋊C₄	—	2	1	no	—
929	C₄⋊C₄	—	2	2	no	—
930	C₄⋊C₄	—	2	1	no	—
931	C₄⋊C₄	—	2	2	no	—
932	C₄⋊C₄	—	2	1	no	—
933	C₄⋊C₄	—	2	2	no	—
934	C₄⋊C₄	—	2	1	no	—
935	C₄⋊C₄	—	2	2	no	—
936	C₄⋊C₄	—	2	2	no	—
937	C₄⋊C₄	—	2	2	no	—
938	C₄⋊C₄	—	2	2	no	—
939	C₄⋊C₄	—	2	1	no	—
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	1	yes	characteristic
943	C₄⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
944	C₄⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
945	C₄⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
946	C₄⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
947	C₄⋊C₄	C₂⁴×C₈₉	1	1	yes	characteristic
948	C₄⋊C₄	C₂⁴×C₈₉	1	2	yes	—
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	C₄⋊C₄	C₂⁴×C₈₉	1	2	yes	—
953	C₄⋊C₄	C₂⁴×C₈₉	1	1	yes	characteristic
954	C₂²⋊C₄	—	2	1	no	—
955	C₂²⋊C₄	—	2	2	no	—
956	C₂²⋊C₄	—	2	1	no	—
957	C₂²⋊C₄	—	2	1	no	—
958	C₂²⋊C₄	—	2	2	no	—
959	C₂²⋊C₄	—	2	1	no	—
960	C₂²⋊C₄	—	2	2	no	—
961	C₂²⋊C₄	—	2	2	no	—
962	C₂²⋊C₄	—	2	1	no	—
963	C₂²⋊C₄	—	2	2	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	1	no	—
969	C₂²⋊C₄	—	2	2	no	—
970	C₂²⋊C₄	—	2	2	no	—
971	C₂²⋊C₄	—	2	2	no	—
972	C₄²	—	2	1	no	—
973	C₄²	—	2	2	no	—
974	C₄²	—	2	1	no	—
975	C₄²	—	2	2	no	—
976	C₄²	—	2	2	no	—
977	C₄²	—	2	1	no	—
978	C₄²	—	2	2	no	—
979	C₄²	—	2	1	no	—
980	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
981	C₄²	C₂×D₄×C₈₉	1	2	yes	—
982	C₄²	C₂×D₄×C₈₉	1	2	yes	—
983	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
984	C₄²	C₂⁴×C₈₉	1	1	yes	characteristic
985	C₄²	C₂⁴×C₈₉	1	1	yes	characteristic
986	C₄²	C₂⁴×C₈₉	1	2	yes	—
987	C₄²	C₂⁴×C₈₉	1	2	yes	—
988	C₂³	—	2	1	no	—
989	C₂³	—	2	2	no	—
990	C₂³	—	2	1	no	—
991	C₂³	C₂²×D₄×C₈₉	1	1	yes	characteristic
992	Q₈	—	2	2	no	—
993	Q₈	—	2	2	no	—
994	Q₈	—	2	1	no	—
995	Q₈	—	2	1	no	—
996	Q₈	—	2	1	no	—
997	Q₈	—	4	2	no	—
998	Q₈	—	4	4	no	—
999	Q₈	—	4	2	no	—
1000	Q₈	—	8	2	no	—
1001	Q₈	—	8	1	no	—
1002	Q₈	—	8	2	no	—
1003	Q₈	—	8	1	no	—
1004	Q₈	2₋¹⁺⁴×C₈₉	1	2	yes	—
1005	D₄	—	2	4	no	—
1006	D₄	—	2	1	no	—
1007	D₄	—	2	2	no	—
1008	D₄	—	2	1	no	—
1009	D₄	—	2	2	no	—
1010	D₄	—	2	1	no	—
1011	D₄	—	4	4	no	—
1012	D₄	—	4	4	no	—
1013	D₄	—	4	2	no	—
1014	D₄	—	4	2	no	—
1015	D₄	—	8	2	no	—
1016	D₄	—	8	1	no	—
1017	D₄	2₋¹⁺⁴×C₈₉	1	2	yes	—
1018	C₂×C₄	—	2	4	no	—
1019	C₂×C₄	—	2	1	no	—
1020	C₂×C₄	—	2	2	no	—
1021	C₂×C₄	—	2	1	no	—
1022	C₂×C₄	—	2	1	no	—
1023	C₂×C₄	—	2	1	no	—
1024	C₂×C₄	—	2	2	no	—
1025	C₂×C₄	—	2	1	no	—
1026	C₂×C₄	—	2	2	no	—
1027	C₂×C₄	—	2	1	no	—
1028	C₂×C₄	—	2	2	no	—
1029	C₂×C₄	—	2	1	no	—
1030	C₂×C₄	—	2	1	no	—
1031	C₂×C₄	—	4	2	no	—
1032	C₂×C₄	—	4	1	no	—
1033	C₂×C₄	—	4	2	no	—
1034	C₂×C₄	—	4	4	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	—	8	2	no	—
1043	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
1044	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
1045	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
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	2	yes	—
1050	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
1051	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
1052	C₂×C₄	C₂⁵×C₈₉	1	1	yes	characteristic
1053	C₈	—	2	2	no	—
1054	C₈	—	2	1	no	—
1055	C₈	—	2	2	no	—
1056	C₈	—	2	1	no	—
1057	C₈	—	2	1	no	—
1058	C₈	—	2	1	no	—
1059	C₂²	—	2	1	no	—
1060	C₂²	—	2	1	no	—
1061	C₂²	—	2	1	no	—
1062	C₂²	—	2	2	no	—
1063	C₂²	—	4	1	no	—
1064	C₂²	—	4	1	no	—
1065	C₂²	—	4	2	no	—
1066	C₂²	—	4	1	no	—
1067	C₂²	—	4	2	no	—
1068	C₂²	—	4	1	no	—
1069	C₂²	—	4	2	no	—
1070	C₂²	—	4	1	no	—
1071	C₂²	C₂³×D₄×C₈₉	1	1	yes	characteristic
1072	C₄	—	2	1	no	—
1073	C₄	—	2	2	no	—
1074	C₄	—	2	2	no	—
1075	C₄	—	2	1	no	—
1076	C₄	—	2	2	no	—
1077	C₄	—	2	2	no	—
1078	C₄	—	2	1	no	—
1079	C₄	—	2	1	no	—
1080	C₄	—	2	2	no	—
1081	C₄	—	4	1	no	—
1082	C₄	—	4	2	no	—
1083	C₄	—	4	1	no	—
1084	C₄	—	4	2	no	—
1085	C₄	—	4	1	no	—
1086	C₄	—	4	1	no	—
1087	C₄	—	4	2	no	—
1088	C₄	—	4	1	no	—
1089	C₄	#575×C₈₉	1	2	yes	—
1090	C₄	C₂×2₋¹⁺⁴×C₈₉	1	1	yes	characteristic
1091	C₄	C₂×2₋¹⁺⁴×C₈₉	1	1	yes	characteristic
1092	C₂	—	4	1	no	—
1093	C₂	—	4	2	no	—
1094	C₂	—	8	2	no	—
1095	C₂	—	8	1	no	—
1096	C₂	C₈₉×#3486	1	1	yes	characteristic
1097	C₂	C₂×#575×C₈₉	1	1	yes	characteristic
1098	C₂	C₈₉×#3585	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 ◁ C₂×C₄×Q₈×C₈₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₈₉×#3522	C₂	semidirect
2. Q₈×#41×C₈₉	C₂	semidirect
3. C₈₉×#3389	C₂	semidirect
4. C₈₉×#3388	C₂	semidirect
5. C₈₉×#3387	C₂	semidirect
6. C₈₉×#3385	C₂	semidirect
7. C₈₉×#3385	C₂	semidirect
8. C₈₉×#3384	C₂	semidirect
9. C₈₉×#3375	C₂	semidirect
10. C₈₉×#3373	C₂	semidirect
11. C₈₉×#3371	C₂	semidirect
12. C₈₉×#3370	C₂	semidirect
13. C₈₉×#3368	C₂	semidirect
14. C₈₉×#3366	C₂	semidirect
15. C₈₉×#3240	C₂	semidirect
16. C₈₉×#3235	C₂	semidirect
17. C₈₉×#3233	C₂	semidirect
18. C₈₉×#3228	C₂	semidirect
19. C₈₉×#3115	C₂	semidirect
20. C₈₉×#3111	C₂	semidirect
21. C₈₉×#3106	C₂	semidirect
22. C₈₉×#3102	C₂	semidirect
23. C₈₉×#2983	C₂	semidirect
542. #61833	C₈₉	direct (N × H)
550. #3522	C₂×C₈₉	semidirect
551. Q₈×#41	C₂×C₈₉	semidirect
552. #3389	C₂×C₈₉	semidirect
553. #3388	C₂×C₈₉	semidirect
554. #3387	C₂×C₈₉	semidirect
555. #3385	C₂×C₈₉	semidirect
556. #3385	C₂×C₈₉	semidirect
557. #3384	C₂×C₈₉	semidirect
558. #3375	C₂×C₈₉	semidirect
559. #3373	C₂×C₈₉	semidirect
560. #3371	C₂×C₈₉	semidirect
561. #3370	C₂×C₈₉	semidirect
562. #3368	C₂×C₈₉	semidirect
563. #3366	C₂×C₈₉	semidirect
564. #3240	C₂×C₈₉	semidirect
565. #3235	C₂×C₈₉	semidirect
566. #3233	C₂×C₈₉	semidirect
567. #3228	C₂×C₈₉	semidirect
568. #3115	C₂×C₈₉	semidirect
569. #3111	C₂×C₈₉	semidirect
570. #3106	C₂×C₈₉	semidirect
571. #3102	C₂×C₈₉	semidirect
572. #2983	C₂×C₈₉	semidirect
573. C₈₉	#61833	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×#3522	2
Q₈×#41×C₈₉	2
C₈₉×#3389	2
C₈₉×#3388	2
C₈₉×#3387	2
C₈₉×#3385	2
C₈₉×#3384	2
C₈₉×#3375	2
C₈₉×#3373	2
C₈₉×#3371	2
C₈₉×#3370	2
C₈₉×#3368	2
C₈₉×#3366	2
C₈₉×#3240	2
C₈₉×#3235	2
C₈₉×#3233	2
C₈₉×#3228	2
C₈₉×#3115	2
C₈₉×#3111	2
C₈₉×#3106	2
C₈₉×#3102	2
C₈₉×#2983	2
#61833	89

Subgroups — C89×#61833 #36439681

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#61833 #36439681