Subgroups — C₈₉×#62592 #36440440

Order 22784.

1790 conjugacy classes of subgroups.

The subgroup lattice has 876 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈₉×#3514	C₂	1	1	yes	maximal, characteristic, complemented
2	C₈₉×#3511	C₂	1	1	yes	maximal, characteristic, complemented
3	C₈₉×#3361	C₂	1	2	yes	maximal, complemented
4	C₈₉×#3360	C₂	1	2	yes	maximal, complemented
5	C₈₉×#3329	C₂	1	2	yes	maximal, complemented
6	C₈₉×#3326	C₂	1	4	yes	maximal, complemented
7	C₈₉×#3325	C₂	1	2	yes	maximal, complemented
8	C₈₉×#3322	C₂	1	4	yes	maximal, complemented
9	C₈₉×#3240	C₂	1	2	yes	maximal, complemented
10	C₈₉×#3238	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈₉×#3214	C₂	1	1	yes	maximal, characteristic, complemented
12	C₈₉×#3213	C₂	1	2	yes	maximal, complemented
13	C₈₉×#3171	C₂	1	1	yes	maximal, characteristic, complemented
14	C₈₉×#3171	C₂	1	2	yes	maximal, complemented
15	C₈₉×#3141	C₂	1	1	yes	maximal, characteristic, complemented
16	C₈₉×#3140	C₂	1	2	yes	maximal, complemented
17	C₈₉×#2971	C₂	1	1	yes	maximal, characteristic, complemented
18	#559×C₈₉	C₂²	1	1	yes	characteristic
19	#556×C₈₉	—	2	1	no	—
20	#556×C₈₉	C₂²	1	1	yes	characteristic
21	#555×C₈₉	—	2	1	no	—
22	#555×C₈₉	C₂²	1	2	yes	—
23	#554×C₈₉	C₂²	1	2	yes	complemented
24	#553×C₈₉	C₂²	1	4	yes	complemented
25	#551×C₈₉	—	2	2	no	—
26	D₄×Q₈×C₈₉	C₂²	1	1	yes	characteristic
27	#548×C₈₉	—	2	2	no	—
28	#548×C₈₉	C₂²	1	2	yes	—
29	#547×C₈₉	—	2	1	no	—
30	#546×C₈₉	—	2	1	no	—
31	#546×C₈₉	C₂²	1	2	yes	—
32	D₄²×C₈₉	C₂²	1	1	yes	characteristic
33	#542×C₈₉	—	2	1	no	—
34	#542×C₈₉	—	2	2	no	—
35	#538×C₈₉	—	2	2	no	—
36	#537×C₈₉	—	2	1	no	—
37	#533×C₈₉	C₂²	1	2	yes	complemented
38	#532×C₈₉	C₂²	1	1	yes	characteristic
39	#532×C₈₉	C₂²	1	2	yes	complemented
40	#532×C₈₉	C₂²	1	1	yes	characteristic, complemented
41	C₂×C₄⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic, complemented
42	#529×C₈₉	C₂²	1	1	yes	characteristic
43	#529×C₈₉	C₂²	1	2	yes	—
44	C₂×#124×C₈₉	C₂²	1	2	yes	—
45	#520×C₈₉	—	2	1	no	—
46	#518×C₈₉	—	2	1	no	—
47	C₄×#41×C₈₉	C₂²	1	1	yes	characteristic
48	#501×C₈₉	C₂²	1	2	yes	complemented
49	#501×C₈₉	C₂²	1	1	yes	characteristic, complemented
50	#496×C₈₉	C₂²	1	1	yes	characteristic
51	#496×C₈₉	C₂²	1	2	yes	complemented
52	#490×C₈₉	C₂²	1	1	yes	characteristic, complemented
53	#489×C₈₉	C₂²	1	1	yes	characteristic
54	#489×C₈₉	C₂²	1	2	yes	—
55	#489×C₈₉	C₂²	1	2	yes	complemented
56	#489×C₈₉	C₂²	1	2	yes	complemented
57	#489×C₈₉	C₂²	1	2	yes	complemented
58	#488×C₈₉	C₂²	1	4	yes	—
59	#488×C₈₉	C₂²	1	4	yes	complemented
60	#487×C₈₉	C₂²	1	2	yes	complemented
61	#486×C₈₉	C₂²	1	2	yes	—
62	#485×C₈₉	C₂²	1	4	yes	complemented
63	#483×C₈₉	C₂²	1	2	yes	complemented
64	#482×C₈₉	C₂²	1	4	yes	—
65	#480×C₈₉	C₂²	1	2	yes	—
66	#479×C₈₉	C₂²	1	4	yes	complemented
67	#478×C₈₉	C₂²	1	4	yes	complemented
68	#477×C₈₉	C₂²	1	2	yes	complemented
69	#476×C₈₉	C₂²	1	2	yes	—
70	#469×C₈₉	C₂²	1	2	yes	—
71	#469×C₈₉	C₂²	1	4	yes	—
72	#468×C₈₉	C₂²	1	4	yes	complemented
73	#468×C₈₉	C₂²	1	2	yes	complemented
74	#463×C₈₉	C₂²	1	4	yes	—
75	#463×C₈₉	C₂²	1	4	yes	complemented
76	#461×C₈₉	C₂²	1	2	yes	complemented
77	#459×C₈₉	C₂²	1	2	yes	—
78	#449×C₈₉	C₂²	1	4	yes	complemented
79	#448×C₈₉	C₂²	1	4	yes	complemented
80	#447×C₈₉	C₂²	1	4	yes	—
81	C₈×Q₈×C₈₉	C₂²	1	2	yes	complemented
82	C₄×SD₁₆×C₈₉	C₂²	1	4	yes	complemented
83	C₄×SD₁₆×C₈₉	C₂²	1	2	yes	complemented
84	C₄×D₈×C₈₉	C₂²	1	2	yes	—
85	C₄×D₈×C₈₉	C₂²	1	4	yes	complemented
86	#436×C₈₉	C₂²	1	2	yes	—
87	#436×C₈₉	C₂²	1	4	yes	complemented
88	#432×C₈₉	C₂²	1	2	yes	complemented
89	#432×C₈₉	C₂²	1	1	yes	characteristic, complemented
90	#419×C₈₉	C₂²	1	4	yes	complemented
91	#418×C₈₉	C₂²	1	4	yes	—
92	#417×C₈₉	C₂²	1	4	yes	complemented
93	C₄×M₁₆×C₈₉	C₂²	1	2	yes	complemented
94	C₄×M₁₆×C₈₉	C₂²	1	1	yes	characteristic, complemented
95	C₂×#41×C₈₉	—	2	1	no	—
96	C₂×#41×C₈₉	—	2	2	no	—
97	C₂×#41×C₈₉	D₄	1	1	yes	characteristic
98	C₂×#41×C₈₉	C₂³	1	2	yes	—
99	C₂²×Q₈×C₈₉	—	2	1	no	—
100	C₂²×Q₈×C₈₉	C₂³	1	2	yes	—
101	C₂²×D₄×C₈₉	—	2	1	no	—
102	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
103	C₂×SD₁₆×C₈₉	C₂³	1	2	yes	—
104	C₂×SD₁₆×C₈₉	C₂³	1	4	yes	—
105	C₂×D₈×C₈₉	C₂³	1	2	yes	—
106	C₂×D₈×C₈₉	C₂³	1	4	yes	—
107	C₂×M₁₆×C₈₉	C₂³	1	2	yes	—
108	C₂×M₁₆×C₈₉	C₂³	1	4	yes	—
109	C₄⋊Q₈×C₈₉	—	2	1	no	—
110	C₄⋊Q₈×C₈₉	—	2	1	no	—
111	C₄⋊Q₈×C₈₉	—	2	1	no	—
112	C₄⋊Q₈×C₈₉	C₂³	1	1	yes	characteristic
113	C₄⋊Q₈×C₈₉	C₂³	1	2	yes	—
114	C₄⋊Q₈×C₈₉	C₂³	1	2	yes	—
115	C₄⋊Q₈×C₈₉	C₂³	1	1	yes	characteristic
116	#127×C₈₉	C₂³	1	1	yes	characteristic
117	#127×C₈₉	C₂³	1	1	yes	characteristic
118	#126×C₈₉	—	2	2	no	—
119	#126×C₈₉	—	2	4	no	—
120	#126×C₈₉	—	2	2	no	—
121	#126×C₈₉	—	2	1	no	—
122	#125×C₈₉	C₂³	1	4	yes	—
123	#125×C₈₉	C₂³	1	1	yes	characteristic
124	#124×C₈₉	—	2	1	no	—
125	#124×C₈₉	—	2	2	no	—
126	#124×C₈₉	—	2	4	no	—
127	#124×C₈₉	—	2	2	no	—
128	#124×C₈₉	—	2	2	no	—
129	#124×C₈₉	—	2	1	no	—
130	#124×C₈₉	—	2	2	no	—
131	#124×C₈₉	C₂³	1	2	yes	—
132	#124×C₈₉	C₂³	1	2	yes	—
133	#124×C₈₉	C₂³	1	1	yes	characteristic
134	#124×C₈₉	C₂³	1	2	yes	—
135	#123×C₈₉	—	2	1	no	—
136	#123×C₈₉	—	2	2	no	—
137	#123×C₈₉	—	2	2	no	—
138	#123×C₈₉	—	2	2	no	—
139	#123×C₈₉	—	2	4	no	—
140	C₂²⋊Q₈×C₈₉	—	2	2	no	—
141	C₂²⋊Q₈×C₈₉	—	2	1	no	—
142	C₂²⋊Q₈×C₈₉	—	2	2	no	—
143	C₂²⋊Q₈×C₈₉	—	2	2	no	—
144	C₂²⋊Q₈×C₈₉	—	2	4	no	—
145	C₂²⋊Q₈×C₈₉	—	2	2	no	—
146	C₂²⋊Q₈×C₈₉	—	2	2	no	—
147	C₂²⋊Q₈×C₈₉	C₂³	1	1	yes	characteristic
148	C₂²⋊Q₈×C₈₉	C₂³	1	2	yes	—
149	#121×C₈₉	—	2	2	no	—
150	#121×C₈₉	—	2	4	no	—
151	#121×C₈₉	—	2	2	no	—
152	#121×C₈₉	—	2	1	no	—
153	#121×C₈₉	—	2	1	no	—
154	#121×C₈₉	—	2	2	no	—
155	#121×C₈₉	—	2	1	no	—
156	#121×C₈₉	—	2	1	no	—
157	#121×C₈₉	—	2	2	no	—
158	#121×C₈₉	C₂³	1	4	yes	—
159	#121×C₈₉	C₂³	1	2	yes	—
160	#121×C₈₉	C₂³	1	1	yes	characteristic
161	#121×C₈₉	C₂³	1	2	yes	—
162	#120×C₈₉	—	2	2	no	—
163	#120×C₈₉	—	2	2	no	—
164	C₄×Q₈×C₈₉	—	2	2	no	—
165	C₄×Q₈×C₈₉	—	2	2	no	—
166	C₄×Q₈×C₈₉	D₄	1	1	yes	characteristic
167	C₄×Q₈×C₈₉	C₂³	1	1	yes	characteristic
168	C₄×Q₈×C₈₉	C₂³	1	2	yes	—
169	C₄×Q₈×C₈₉	C₂³	1	1	yes	characteristic
170	C₄×D₄×C₈₉	—	2	1	no	—
171	C₄×D₄×C₈₉	—	2	2	no	—
172	C₄×D₄×C₈₉	—	2	1	no	—
173	C₄×D₄×C₈₉	—	2	1	no	—
174	C₄×D₄×C₈₉	—	2	2	no	—
175	C₄×D₄×C₈₉	—	2	4	no	—
176	C₄×D₄×C₈₉	—	2	1	no	—
177	C₄×D₄×C₈₉	—	2	2	no	—
178	C₄×D₄×C₈₉	—	2	1	no	—
179	C₄×D₄×C₈₉	—	2	1	no	—
180	C₄×D₄×C₈₉	D₄	1	1	yes	characteristic
181	C₄×D₄×C₈₉	D₄	1	2	yes	—
182	C₄×D₄×C₈₉	C₂³	1	1	yes	characteristic
183	C₄×D₄×C₈₉	C₂³	1	2	yes	—
184	C₄×D₄×C₈₉	C₂³	1	2	yes	—
185	C₄×D₄×C₈₉	C₂³	1	4	yes	—
186	C₄×D₄×C₈₉	C₂³	1	1	yes	characteristic
187	C₄×D₄×C₈₉	C₂³	1	2	yes	—
188	#117×C₈₉	—	2	1	no	—
189	#117×C₈₉	—	2	2	no	—
190	#117×C₈₉	—	2	1	no	—
191	#117×C₈₉	—	2	2	no	—
192	#117×C₈₉	D₄	1	1	yes	characteristic
193	#117×C₈₉	D₄	1	2	yes	—
194	#117×C₈₉	C₂³	1	4	yes	—
195	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
196	C₂×C₄⋊C₄×C₈₉	—	2	2	no	—
197	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
198	C₂×C₂²⋊C₄×C₈₉	—	2	2	no	—
199	C₂×C₂²⋊C₄×C₈₉	—	2	2	no	—
200	C₂×C₂²⋊C₄×C₈₉	—	2	2	no	—
201	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
202	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
203	#107×C₈₉	C₂³	1	2	yes	—
204	#107×C₈₉	C₂³	1	4	yes	—
205	#106×C₈₉	C₂³	1	4	yes	—
206	#106×C₈₉	C₂³	1	2	yes	—
207	C₄⋊C₈×C₈₉	C₂³	1	2	yes	—
208	C₄⋊C₈×C₈₉	C₂³	1	4	yes	—
209	#103×C₈₉	C₂³	1	4	yes	—
210	#103×C₈₉	C₂³	1	4	yes	—
211	#103×C₈₉	C₂³	1	2	yes	—
212	#103×C₈₉	C₂³	1	4	yes	—
213	#103×C₈₉	C₂³	1	4	yes	—
214	#102×C₈₉	C₂³	1	4	yes	—
215	#102×C₈₉	C₂³	1	4	yes	—
216	#102×C₈₉	C₂³	1	2	yes	—
217	#102×C₈₉	C₂³	1	4	yes	—
218	#102×C₈₉	C₂³	1	4	yes	—
219	#102×C₈₉	C₂³	1	2	yes	—
220	#102×C₈₉	C₂³	1	2	yes	—
221	C₂²⋊C₈×C₈₉	C₂³	1	4	yes	—
222	C₂²⋊C₈×C₈₉	C₂³	1	2	yes	—
223	#97×C₈₉	C₂³	1	1	yes	characteristic
224	#97×C₈₉	C₂³	1	2	yes	—
225	#97×C₈₉	C₂³	1	1	yes	characteristic
226	C₄×C₈×C₈₉	C₂³	1	2	yes	—
227	C₄×C₈×C₈₉	C₂³	1	4	yes	—
228	C₂⁴×C₈₉	—	2	2	no	—
229	#41×C₈₉	—	4	2	no	—
230	#41×C₈₉	—	4	4	no	—
231	#41×C₈₉	—	4	4	no	—
232	#41×C₈₉	—	8	4	no	—
233	C₂×Q₈×C₈₉	—	2	1	no	—
234	C₂×Q₈×C₈₉	—	2	2	no	—
235	C₂×Q₈×C₈₉	—	2	2	no	—
236	C₂×Q₈×C₈₉	—	2	2	no	—
237	C₂×Q₈×C₈₉	—	4	4	no	—
238	C₂×Q₈×C₈₉	—	8	2	no	—
239	C₂×Q₈×C₈₉	C₂×D₄	1	1	yes	characteristic
240	C₂×Q₈×C₈₉	C₂⁴	1	1	yes	characteristic
241	C₂×Q₈×C₈₉	C₂⁴	1	2	yes	—
242	C₂×D₄×C₈₉	—	2	2	no	—
243	C₂×D₄×C₈₉	—	2	2	no	—
244	C₂×D₄×C₈₉	—	2	1	no	—
245	C₂×D₄×C₈₉	—	2	2	no	—
246	C₂×D₄×C₈₉	—	2	4	no	—
247	C₂×D₄×C₈₉	—	2	1	no	—
248	C₂×D₄×C₈₉	—	2	1	no	—
249	C₂×D₄×C₈₉	—	2	1	no	—
250	C₂×D₄×C₈₉	—	2	1	no	—
251	C₂×D₄×C₈₉	—	2	2	no	—
252	C₂×D₄×C₈₉	—	4	4	no	—
253	C₂×D₄×C₈₉	—	4	4	no	—
254	C₂×D₄×C₈₉	C₂×D₄	1	1	yes	characteristic
255	C₂×D₄×C₈₉	C₂×D₄	1	2	yes	—
256	C₂×D₄×C₈₉	C₂⁴	1	1	yes	characteristic
257	C₂×D₄×C₈₉	C₂⁴	1	2	yes	—
258	C₂×D₄×C₈₉	C₂⁴	1	2	yes	—
259	C₂²×C₄×C₈₉	—	2	2	no	—
260	C₂²×C₄×C₈₉	—	2	2	no	—
261	C₂²×C₄×C₈₉	—	2	2	no	—
262	C₂²×C₄×C₈₉	—	2	1	no	—
263	C₂²×C₄×C₈₉	—	2	2	no	—
264	C₂²×C₄×C₈₉	—	2	2	no	—
265	C₂²×C₄×C₈₉	—	2	4	no	—
266	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
267	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
268	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
269	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
270	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
271	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
272	SD₁₆×C₈₉	—	4	2	no	—
273	SD₁₆×C₈₉	—	4	4	no	—
274	D₈×C₈₉	—	4	4	no	—
275	D₈×C₈₉	—	4	2	no	—
276	M₁₆×C₈₉	—	4	4	no	—
277	M₁₆×C₈₉	—	4	2	no	—
278	C₂×C₈×C₈₉	C₂⁴	1	2	yes	—
279	C₂×C₈×C₈₉	C₂⁴	1	2	yes	—
280	C₂×C₈×C₈₉	C₂⁴	1	4	yes	—
281	C₄⋊C₄×C₈₉	—	2	2	no	—
282	C₄⋊C₄×C₈₉	—	2	2	no	—
283	C₄⋊C₄×C₈₉	—	2	4	no	—
284	C₄⋊C₄×C₈₉	—	2	2	no	—
285	C₄⋊C₄×C₈₉	—	2	1	no	—
286	C₄⋊C₄×C₈₉	—	2	1	no	—
287	C₄⋊C₄×C₈₉	—	2	1	no	—
288	C₄⋊C₄×C₈₉	—	2	1	no	—
289	C₄⋊C₄×C₈₉	—	2	2	no	—
290	C₄⋊C₄×C₈₉	—	2	1	no	—
291	C₄⋊C₄×C₈₉	—	2	1	no	—
292	C₄⋊C₄×C₈₉	—	2	4	no	—
293	C₄⋊C₄×C₈₉	—	2	2	no	—
294	C₄⋊C₄×C₈₉	—	2	1	no	—
295	C₄⋊C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
296	C₄⋊C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
297	C₄⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
298	C₄⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
299	C₄⋊C₄×C₈₉	C₂⁴	1	4	yes	—
300	C₄⋊C₄×C₈₉	C₂⁴	1	2	yes	—
301	C₄⋊C₄×C₈₉	C₂⁴	1	1	yes	characteristic
302	C₄⋊C₄×C₈₉	C₂⁴	1	1	yes	characteristic
303	C₂²⋊C₄×C₈₉	—	2	2	no	—
304	C₂²⋊C₄×C₈₉	—	2	4	no	—
305	C₂²⋊C₄×C₈₉	—	2	1	no	—
306	C₂²⋊C₄×C₈₉	—	2	2	no	—
307	C₂²⋊C₄×C₈₉	—	2	1	no	—
308	C₂²⋊C₄×C₈₉	—	2	1	no	—
309	C₂²⋊C₄×C₈₉	—	2	1	no	—
310	C₂²⋊C₄×C₈₉	—	2	2	no	—
311	C₂²⋊C₄×C₈₉	—	2	2	no	—
312	C₂²⋊C₄×C₈₉	—	2	2	no	—
313	C₂²⋊C₄×C₈₉	—	2	2	no	—
314	C₂²⋊C₄×C₈₉	—	2	2	no	—
315	C₂²⋊C₄×C₈₉	—	2	4	no	—
316	C₂²⋊C₄×C₈₉	—	2	2	no	—
317	C₂²⋊C₄×C₈₉	—	2	2	no	—
318	C₂²⋊C₄×C₈₉	—	2	1	no	—
319	C₂²⋊C₄×C₈₉	—	2	2	no	—
320	C₂²⋊C₄×C₈₉	—	2	4	no	—
321	C₂²⋊C₄×C₈₉	—	2	2	no	—
322	C₂²⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
323	C₂²⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
324	C₂²⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
325	C₄²×C₈₉	—	2	2	no	—
326	C₄²×C₈₉	—	2	4	no	—
327	C₄²×C₈₉	—	2	1	no	—
328	C₄²×C₈₉	C₂×D₄	1	2	yes	—
329	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
330	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
331	C₄²×C₈₉	C₂×D₄	1	2	yes	—
332	C₄²×C₈₉	C₂⁴	1	2	yes	—
333	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
334	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
335	C₂³×C₈₉	—	2	1	no	—
336	C₂³×C₈₉	—	2	2	no	—
337	C₂³×C₈₉	—	2	2	no	—
338	C₂³×C₈₉	—	4	4	no	—
339	C₂³×C₈₉	—	8	2	no	—
340	C₂³×C₈₉	—	8	2	no	—
341	C₂³×C₈₉	C₂²×D₄	1	2	yes	—
342	C₂³×C₈₉	C₂²×D₄	1	1	yes	characteristic
343	Q₈×C₈₉	—	2	2	no	—
344	Q₈×C₈₉	—	2	2	no	—
345	Q₈×C₈₉	—	2	4	no	—
346	Q₈×C₈₉	—	4	4	no	—
347	Q₈×C₈₉	—	4	2	no	—
348	Q₈×C₈₉	—	8	2	no	—
349	Q₈×C₈₉	—	8	2	no	—
350	D₄×C₈₉	—	2	2	no	—
351	D₄×C₈₉	—	2	2	no	—
352	D₄×C₈₉	—	2	2	no	—
353	D₄×C₈₉	—	2	2	no	—
354	D₄×C₈₉	—	2	4	no	—
355	D₄×C₈₉	—	4	2	no	—
356	D₄×C₈₉	—	4	2	no	—
357	D₄×C₈₉	—	4	2	no	—
358	D₄×C₈₉	—	4	4	no	—
359	D₄×C₈₉	—	4	4	no	—
360	D₄×C₈₉	—	4	2	no	—
361	D₄×C₈₉	—	8	1	no	—
362	D₄×C₈₉	—	8	2	no	—
363	D₄×C₈₉	—	8	1	no	—
364	D₄×C₈₉	—	8	2	no	—
365	D₄×C₈₉	—	8	4	no	—
366	C₂×C₄×C₈₉	—	2	2	no	—
367	C₂×C₄×C₈₉	—	2	4	no	—
368	C₂×C₄×C₈₉	—	2	2	no	—
369	C₂×C₄×C₈₉	—	2	1	no	—
370	C₂×C₄×C₈₉	—	2	2	no	—
371	C₂×C₄×C₈₉	—	2	1	no	—
372	C₂×C₄×C₈₉	—	2	1	no	—
373	C₂×C₄×C₈₉	—	2	2	no	—
374	C₂×C₄×C₈₉	—	2	4	no	—
375	C₂×C₄×C₈₉	—	4	1	no	—
376	C₂×C₄×C₈₉	—	4	2	no	—
377	C₂×C₄×C₈₉	—	4	2	no	—
378	C₂×C₄×C₈₉	—	4	2	no	—
379	C₂×C₄×C₈₉	—	4	4	no	—
380	C₂×C₄×C₈₉	—	8	2	no	—
381	C₂×C₄×C₈₉	—	8	2	no	—
382	C₂×C₄×C₈₉	—	8	4	no	—
383	C₂×C₄×C₈₉	—	8	2	no	—
384	C₂×C₄×C₈₉	—	8	2	no	—
385	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
386	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
387	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
388	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
389	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
390	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
391	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
392	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
393	C₂×C₄×C₈₉	C₂⁵	1	1	yes	characteristic
394	C₈×C₈₉	—	2	2	no	—
395	C₈×C₈₉	—	2	2	no	—
396	C₈×C₈₉	—	2	4	no	—
397	C₂²×C₈₉	—	2	1	no	—
398	C₂²×C₈₉	—	2	2	no	—
399	C₂²×C₈₉	—	2	2	no	—
400	C₂²×C₈₉	—	2	1	no	—
401	C₂²×C₈₉	—	2	1	no	—
402	C₂²×C₈₉	—	2	2	no	—
403	C₂²×C₈₉	—	4	2	no	—
404	C₂²×C₈₉	—	4	2	no	—
405	C₂²×C₈₉	—	4	1	no	—
406	C₂²×C₈₉	—	4	2	no	—
407	C₂²×C₈₉	—	4	1	no	—
408	C₂²×C₈₉	—	4	2	no	—
409	C₂²×C₈₉	—	4	2	no	—
410	C₂²×C₈₉	—	4	1	no	—
411	C₂²×C₈₉	—	4	2	no	—
412	C₂²×C₈₉	—	16	4	no	—
413	C₂²×C₈₉	C₂³×D₄	1	1	yes	characteristic
414	C₄×C₈₉	—	2	1	no	—
415	C₄×C₈₉	—	2	2	no	—
416	C₄×C₈₉	—	2	1	no	—
417	C₄×C₈₉	—	2	1	no	—
418	C₄×C₈₉	—	2	2	no	—
419	C₄×C₈₉	—	2	1	no	—
420	C₄×C₈₉	—	2	2	no	—
421	C₄×C₈₉	—	4	1	no	—
422	C₄×C₈₉	—	4	4	no	—
423	C₄×C₈₉	—	4	2	no	—
424	C₄×C₈₉	—	4	1	no	—
425	C₄×C₈₉	—	4	1	no	—
426	C₄×C₈₉	—	4	2	no	—
427	C₄×C₈₉	#575	1	2	yes	—
428	C₄×C₈₉	#585	1	2	yes	—
429	#62592	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
430	C₂×C₈₉	—	4	1	no	—
431	C₂×C₈₉	—	4	2	no	—
432	C₂×C₈₉	—	8	2	no	—
433	C₂×C₈₉	—	8	2	no	—
434	C₂×C₈₉	—	8	1	no	—
435	C₂×C₈₉	#3500	1	1	yes	characteristic
436	C₂×C₈₉	C₂×#575	1	1	yes	characteristic
437	C₂×C₈₉	#3585	1	1	yes	characteristic
438	#3514	C₂×C₈₉	1	1	yes	characteristic, complemented
439	#3511	C₂×C₈₉	1	1	yes	characteristic, complemented
440	#3361	C₂×C₈₉	1	2	yes	complemented
441	#3360	C₂×C₈₉	1	2	yes	complemented
442	#3329	C₂×C₈₉	1	2	yes	complemented
443	#3326	C₂×C₈₉	1	4	yes	complemented
444	#3325	C₂×C₈₉	1	2	yes	complemented
445	#3322	C₂×C₈₉	1	4	yes	complemented
446	#3240	C₂×C₈₉	1	2	yes	complemented
447	#3238	C₂×C₈₉	1	1	yes	characteristic, complemented
448	#3214	C₂×C₈₉	1	1	yes	characteristic, complemented
449	#3213	C₂×C₈₉	1	2	yes	complemented
450	#3171	C₂×C₈₉	1	1	yes	characteristic, complemented
451	#3171	C₂×C₈₉	1	2	yes	complemented
452	#3141	C₂×C₈₉	1	1	yes	characteristic, complemented
453	#3140	C₂×C₈₉	1	2	yes	complemented
454	#2971	C₂×C₈₉	1	1	yes	characteristic, complemented
455	C₈₉	#62592	1	1	yes	characteristic, direct product factor, Sylow
456	#559	C₂²×C₈₉	1	1	yes	characteristic
457	#556	—	2	1	no	—
458	#556	C₂²×C₈₉	1	1	yes	characteristic
459	#555	—	2	1	no	—
460	#555	C₂²×C₈₉	1	2	yes	—
461	#554	C₂²×C₈₉	1	2	yes	complemented
462	#553	C₂²×C₈₉	1	4	yes	complemented
463	#551	—	2	2	no	—
464	D₄×Q₈	C₂²×C₈₉	1	1	yes	characteristic
465	#548	—	2	2	no	—
466	#548	C₂²×C₈₉	1	2	yes	—
467	#547	—	2	1	no	—
468	#546	—	2	1	no	—
469	#546	C₂²×C₈₉	1	2	yes	—
470	D₄²	C₂²×C₈₉	1	1	yes	characteristic
471	#542	—	2	1	no	—
472	#542	—	2	2	no	—
473	#538	—	2	2	no	—
474	#537	—	2	1	no	—
475	#533	C₂²×C₈₉	1	2	yes	complemented
476	#532	C₂²×C₈₉	1	1	yes	characteristic
477	#532	C₂²×C₈₉	1	2	yes	complemented
478	#532	C₂²×C₈₉	1	1	yes	characteristic, complemented
479	C₂×C₄⋊Q₈	C₂²×C₈₉	1	1	yes	characteristic, complemented
480	#529	C₂²×C₈₉	1	1	yes	characteristic
481	#529	C₂²×C₈₉	1	2	yes	—
482	C₂×#124	C₂²×C₈₉	1	2	yes	—
483	#520	—	2	1	no	—
484	#518	—	2	1	no	—
485	C₄×#41	C₂²×C₈₉	1	1	yes	characteristic
486	#501	C₂²×C₈₉	1	2	yes	complemented
487	#501	C₂²×C₈₉	1	1	yes	characteristic, complemented
488	#496	C₂²×C₈₉	1	1	yes	characteristic
489	#496	C₂²×C₈₉	1	2	yes	complemented
490	#490	C₂²×C₈₉	1	1	yes	characteristic, complemented
491	#489	C₂²×C₈₉	1	1	yes	characteristic
492	#489	C₂²×C₈₉	1	2	yes	—
493	#489	C₂²×C₈₉	1	2	yes	complemented
494	#489	C₂²×C₈₉	1	2	yes	complemented
495	#489	C₂²×C₈₉	1	2	yes	complemented
496	#488	C₂²×C₈₉	1	4	yes	—
497	#488	C₂²×C₈₉	1	4	yes	complemented
498	#487	C₂²×C₈₉	1	2	yes	complemented
499	#486	C₂²×C₈₉	1	2	yes	—
500	#485	C₂²×C₈₉	1	4	yes	complemented
501	#483	C₂²×C₈₉	1	2	yes	complemented
502	#482	C₂²×C₈₉	1	4	yes	—
503	#480	C₂²×C₈₉	1	2	yes	—
504	#479	C₂²×C₈₉	1	4	yes	complemented
505	#478	C₂²×C₈₉	1	4	yes	complemented
506	#477	C₂²×C₈₉	1	2	yes	complemented
507	#476	C₂²×C₈₉	1	2	yes	—
508	#469	C₂²×C₈₉	1	2	yes	—
509	#469	C₂²×C₈₉	1	4	yes	—
510	#468	C₂²×C₈₉	1	4	yes	complemented
511	#468	C₂²×C₈₉	1	2	yes	complemented
512	#463	C₂²×C₈₉	1	4	yes	—
513	#463	C₂²×C₈₉	1	4	yes	complemented
514	#461	C₂²×C₈₉	1	2	yes	complemented
515	#459	C₂²×C₈₉	1	2	yes	—
516	#449	C₂²×C₈₉	1	4	yes	complemented
517	#448	C₂²×C₈₉	1	4	yes	complemented
518	#447	C₂²×C₈₉	1	4	yes	—
519	C₈×Q₈	C₂²×C₈₉	1	2	yes	complemented
520	C₄×SD₁₆	C₂²×C₈₉	1	2	yes	complemented
521	C₄×SD₁₆	C₂²×C₈₉	1	4	yes	complemented
522	C₄×D₈	C₂²×C₈₉	1	2	yes	—
523	C₄×D₈	C₂²×C₈₉	1	4	yes	complemented
524	#436	C₂²×C₈₉	1	2	yes	—
525	#436	C₂²×C₈₉	1	4	yes	complemented
526	#432	C₂²×C₈₉	1	2	yes	complemented
527	#432	C₂²×C₈₉	1	1	yes	characteristic, complemented
528	#419	C₂²×C₈₉	1	4	yes	complemented
529	#418	C₂²×C₈₉	1	4	yes	—
530	#417	C₂²×C₈₉	1	4	yes	complemented
531	C₄×M₁₆	C₂²×C₈₉	1	2	yes	complemented
532	C₄×M₁₆	C₂²×C₈₉	1	1	yes	characteristic, complemented
533	C₂×#41	—	2	1	no	—
534	C₂×#41	—	2	2	no	—
535	C₂×#41	D₄×C₈₉	1	1	yes	characteristic
536	C₂×#41	C₂³×C₈₉	1	2	yes	—
537	C₂²×Q₈	—	2	1	no	—
538	C₂²×Q₈	C₂³×C₈₉	1	2	yes	—
539	C₂²×D₄	—	2	1	no	—
540	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
541	C₂×SD₁₆	C₂³×C₈₉	1	2	yes	—
542	C₂×SD₁₆	C₂³×C₈₉	1	4	yes	—
543	C₂×D₈	C₂³×C₈₉	1	2	yes	—
544	C₂×D₈	C₂³×C₈₉	1	4	yes	—
545	C₂×M₁₆	C₂³×C₈₉	1	2	yes	—
546	C₂×M₁₆	C₂³×C₈₉	1	4	yes	—
547	C₄⋊Q₈	—	2	1	no	—
548	C₄⋊Q₈	—	2	1	no	—
549	C₄⋊Q₈	—	2	1	no	—
550	C₄⋊Q₈	C₂³×C₈₉	1	1	yes	characteristic
551	C₄⋊Q₈	C₂³×C₈₉	1	2	yes	—
552	C₄⋊Q₈	C₂³×C₈₉	1	2	yes	—
553	C₄⋊Q₈	C₂³×C₈₉	1	1	yes	characteristic
554	#127	C₂³×C₈₉	1	1	yes	characteristic
555	#127	C₂³×C₈₉	1	1	yes	characteristic
556	#126	—	2	2	no	—
557	#126	—	2	4	no	—
558	#126	—	2	2	no	—
559	#126	—	2	1	no	—
560	#125	C₂³×C₈₉	1	1	yes	characteristic
561	#125	C₂³×C₈₉	1	4	yes	—
562	#124	—	2	1	no	—
563	#124	—	2	2	no	—
564	#124	—	2	4	no	—
565	#124	—	2	2	no	—
566	#124	—	2	2	no	—
567	#124	—	2	1	no	—
568	#124	—	2	2	no	—
569	#124	C₂³×C₈₉	1	1	yes	characteristic
570	#124	C₂³×C₈₉	1	2	yes	—
571	#124	C₂³×C₈₉	1	2	yes	—
572	#124	C₂³×C₈₉	1	2	yes	—
573	#123	—	2	1	no	—
574	#123	—	2	2	no	—
575	#123	—	2	2	no	—
576	#123	—	2	2	no	—
577	#123	—	2	4	no	—
578	C₂²⋊Q₈	—	2	2	no	—
579	C₂²⋊Q₈	—	2	1	no	—
580	C₂²⋊Q₈	—	2	2	no	—
581	C₂²⋊Q₈	—	2	2	no	—
582	C₂²⋊Q₈	—	2	4	no	—
583	C₂²⋊Q₈	—	2	2	no	—
584	C₂²⋊Q₈	—	2	2	no	—
585	C₂²⋊Q₈	C₂³×C₈₉	1	2	yes	—
586	C₂²⋊Q₈	C₂³×C₈₉	1	1	yes	characteristic
587	#121	—	2	2	no	—
588	#121	—	2	4	no	—
589	#121	—	2	2	no	—
590	#121	—	2	1	no	—
591	#121	—	2	1	no	—
592	#121	—	2	2	no	—
593	#121	—	2	1	no	—
594	#121	—	2	1	no	—
595	#121	—	2	2	no	—
596	#121	C₂³×C₈₉	1	2	yes	—
597	#121	C₂³×C₈₉	1	1	yes	characteristic
598	#121	C₂³×C₈₉	1	2	yes	—
599	#121	C₂³×C₈₉	1	4	yes	—
600	#120	—	2	2	no	—
601	#120	—	2	2	no	—
602	C₄×Q₈	—	2	2	no	—
603	C₄×Q₈	—	2	2	no	—
604	C₄×Q₈	D₄×C₈₉	1	1	yes	characteristic
605	C₄×Q₈	C₂³×C₈₉	1	2	yes	—
606	C₄×Q₈	C₂³×C₈₉	1	1	yes	characteristic
607	C₄×Q₈	C₂³×C₈₉	1	1	yes	characteristic
608	C₄×D₄	—	2	1	no	—
609	C₄×D₄	—	2	2	no	—
610	C₄×D₄	—	2	1	no	—
611	C₄×D₄	—	2	1	no	—
612	C₄×D₄	—	2	2	no	—
613	C₄×D₄	—	2	4	no	—
614	C₄×D₄	—	2	1	no	—
615	C₄×D₄	—	2	2	no	—
616	C₄×D₄	—	2	1	no	—
617	C₄×D₄	—	2	1	no	—
618	C₄×D₄	D₄×C₈₉	1	1	yes	characteristic
619	C₄×D₄	D₄×C₈₉	1	2	yes	—
620	C₄×D₄	C₂³×C₈₉	1	1	yes	characteristic
621	C₄×D₄	C₂³×C₈₉	1	2	yes	—
622	C₄×D₄	C₂³×C₈₉	1	4	yes	—
623	C₄×D₄	C₂³×C₈₉	1	2	yes	—
624	C₄×D₄	C₂³×C₈₉	1	1	yes	characteristic
625	C₄×D₄	C₂³×C₈₉	1	2	yes	—
626	#117	—	2	1	no	—
627	#117	—	2	2	no	—
628	#117	—	2	1	no	—
629	#117	—	2	2	no	—
630	#117	D₄×C₈₉	1	1	yes	characteristic
631	#117	D₄×C₈₉	1	2	yes	—
632	#117	C₂³×C₈₉	1	4	yes	—
633	C₂×C₄⋊C₄	—	2	1	no	—
634	C₂×C₄⋊C₄	—	2	2	no	—
635	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
636	C₂×C₂²⋊C₄	—	2	2	no	—
637	C₂×C₂²⋊C₄	—	2	2	no	—
638	C₂×C₂²⋊C₄	—	2	2	no	—
639	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
640	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
641	#107	C₂³×C₈₉	1	2	yes	—
642	#107	C₂³×C₈₉	1	4	yes	—
643	#106	C₂³×C₈₉	1	4	yes	—
644	#106	C₂³×C₈₉	1	2	yes	—
645	C₄⋊C₈	C₂³×C₈₉	1	2	yes	—
646	C₄⋊C₈	C₂³×C₈₉	1	4	yes	—
647	#103	C₂³×C₈₉	1	4	yes	—
648	#103	C₂³×C₈₉	1	4	yes	—
649	#103	C₂³×C₈₉	1	2	yes	—
650	#103	C₂³×C₈₉	1	4	yes	—
651	#103	C₂³×C₈₉	1	4	yes	—
652	#102	C₂³×C₈₉	1	4	yes	—
653	#102	C₂³×C₈₉	1	4	yes	—
654	#102	C₂³×C₈₉	1	2	yes	—
655	#102	C₂³×C₈₉	1	4	yes	—
656	#102	C₂³×C₈₉	1	4	yes	—
657	#102	C₂³×C₈₉	1	2	yes	—
658	#102	C₂³×C₈₉	1	2	yes	—
659	C₂²⋊C₈	C₂³×C₈₉	1	4	yes	—
660	C₂²⋊C₈	C₂³×C₈₉	1	2	yes	—
661	#97	C₂³×C₈₉	1	1	yes	characteristic
662	#97	C₂³×C₈₉	1	2	yes	—
663	#97	C₂³×C₈₉	1	1	yes	characteristic
664	C₄×C₈	C₂³×C₈₉	1	2	yes	—
665	C₄×C₈	C₂³×C₈₉	1	4	yes	—
666	C₂⁴	—	2	2	no	—
667	#41	—	4	2	no	—
668	#41	—	4	4	no	—
669	#41	—	4	4	no	—
670	#41	—	8	4	no	—
671	C₂×Q₈	—	2	1	no	—
672	C₂×Q₈	—	2	2	no	—
673	C₂×Q₈	—	2	2	no	—
674	C₂×Q₈	—	2	2	no	—
675	C₂×Q₈	—	4	4	no	—
676	C₂×Q₈	—	8	2	no	—
677	C₂×Q₈	C₂×D₄×C₈₉	1	1	yes	characteristic
678	C₂×Q₈	C₂⁴×C₈₉	1	1	yes	characteristic
679	C₂×Q₈	C₂⁴×C₈₉	1	2	yes	—
680	C₂×D₄	—	2	2	no	—
681	C₂×D₄	—	2	2	no	—
682	C₂×D₄	—	2	1	no	—
683	C₂×D₄	—	2	2	no	—
684	C₂×D₄	—	2	4	no	—
685	C₂×D₄	—	2	1	no	—
686	C₂×D₄	—	2	1	no	—
687	C₂×D₄	—	2	1	no	—
688	C₂×D₄	—	2	1	no	—
689	C₂×D₄	—	2	2	no	—
690	C₂×D₄	—	4	4	no	—
691	C₂×D₄	—	4	4	no	—
692	C₂×D₄	C₂×D₄×C₈₉	1	1	yes	characteristic
693	C₂×D₄	C₂×D₄×C₈₉	1	2	yes	—
694	C₂×D₄	C₂⁴×C₈₉	1	1	yes	characteristic
695	C₂×D₄	C₂⁴×C₈₉	1	2	yes	—
696	C₂×D₄	C₂⁴×C₈₉	1	2	yes	—
697	C₂²×C₄	—	2	2	no	—
698	C₂²×C₄	—	2	2	no	—
699	C₂²×C₄	—	2	2	no	—
700	C₂²×C₄	—	2	1	no	—
701	C₂²×C₄	—	2	2	no	—
702	C₂²×C₄	—	2	2	no	—
703	C₂²×C₄	—	2	4	no	—
704	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
705	C₂²×C₄	C₂×D₄×C₈₉	1	2	yes	—
706	C₂²×C₄	C₂×D₄×C₈₉	1	2	yes	—
707	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
708	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
709	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
710	SD₁₆	—	4	2	no	—
711	SD₁₆	—	4	4	no	—
712	D₈	—	4	4	no	—
713	D₈	—	4	2	no	—
714	M₁₆	—	4	4	no	—
715	M₁₆	—	4	2	no	—
716	C₂×C₈	C₂⁴×C₈₉	1	2	yes	—
717	C₂×C₈	C₂⁴×C₈₉	1	2	yes	—
718	C₂×C₈	C₂⁴×C₈₉	1	4	yes	—
719	C₄⋊C₄	—	2	2	no	—
720	C₄⋊C₄	—	2	2	no	—
721	C₄⋊C₄	—	2	4	no	—
722	C₄⋊C₄	—	2	2	no	—
723	C₄⋊C₄	—	2	1	no	—
724	C₄⋊C₄	—	2	1	no	—
725	C₄⋊C₄	—	2	1	no	—
726	C₄⋊C₄	—	2	1	no	—
727	C₄⋊C₄	—	2	2	no	—
728	C₄⋊C₄	—	2	1	no	—
729	C₄⋊C₄	—	2	1	no	—
730	C₄⋊C₄	—	2	4	no	—
731	C₄⋊C₄	—	2	2	no	—
732	C₄⋊C₄	—	2	1	no	—
733	C₄⋊C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
734	C₄⋊C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
735	C₄⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
736	C₄⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
737	C₄⋊C₄	C₂⁴×C₈₉	1	4	yes	—
738	C₄⋊C₄	C₂⁴×C₈₉	1	2	yes	—
739	C₄⋊C₄	C₂⁴×C₈₉	1	1	yes	characteristic
740	C₄⋊C₄	C₂⁴×C₈₉	1	1	yes	characteristic
741	C₂²⋊C₄	—	2	2	no	—
742	C₂²⋊C₄	—	2	4	no	—
743	C₂²⋊C₄	—	2	1	no	—
744	C₂²⋊C₄	—	2	2	no	—
745	C₂²⋊C₄	—	2	1	no	—
746	C₂²⋊C₄	—	2	1	no	—
747	C₂²⋊C₄	—	2	1	no	—
748	C₂²⋊C₄	—	2	2	no	—
749	C₂²⋊C₄	—	2	2	no	—
750	C₂²⋊C₄	—	2	2	no	—
751	C₂²⋊C₄	—	2	2	no	—
752	C₂²⋊C₄	—	2	2	no	—
753	C₂²⋊C₄	—	2	4	no	—
754	C₂²⋊C₄	—	2	2	no	—
755	C₂²⋊C₄	—	2	2	no	—
756	C₂²⋊C₄	—	2	1	no	—
757	C₂²⋊C₄	—	2	2	no	—
758	C₂²⋊C₄	—	2	4	no	—
759	C₂²⋊C₄	—	2	2	no	—
760	C₂²⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
761	C₂²⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
762	C₂²⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
763	C₄²	—	2	2	no	—
764	C₄²	—	2	4	no	—
765	C₄²	—	2	1	no	—
766	C₄²	C₂×D₄×C₈₉	1	2	yes	—
767	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
768	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
769	C₄²	C₂×D₄×C₈₉	1	2	yes	—
770	C₄²	C₂⁴×C₈₉	1	2	yes	—
771	C₄²	C₂⁴×C₈₉	1	1	yes	characteristic
772	C₄²	C₂⁴×C₈₉	1	1	yes	characteristic
773	C₂³	—	2	1	no	—
774	C₂³	—	2	2	no	—
775	C₂³	—	2	2	no	—
776	C₂³	—	4	4	no	—
777	C₂³	—	8	2	no	—
778	C₂³	—	8	2	no	—
779	C₂³	C₂²×D₄×C₈₉	1	2	yes	—
780	C₂³	C₂²×D₄×C₈₉	1	1	yes	characteristic
781	Q₈	—	2	2	no	—
782	Q₈	—	2	2	no	—
783	Q₈	—	2	4	no	—
784	Q₈	—	4	4	no	—
785	Q₈	—	4	2	no	—
786	Q₈	—	8	2	no	—
787	Q₈	—	8	2	no	—
788	D₄	—	2	2	no	—
789	D₄	—	2	2	no	—
790	D₄	—	2	2	no	—
791	D₄	—	2	2	no	—
792	D₄	—	2	4	no	—
793	D₄	—	4	2	no	—
794	D₄	—	4	2	no	—
795	D₄	—	4	2	no	—
796	D₄	—	4	4	no	—
797	D₄	—	4	4	no	—
798	D₄	—	4	2	no	—
799	D₄	—	8	1	no	—
800	D₄	—	8	2	no	—
801	D₄	—	8	1	no	—
802	D₄	—	8	2	no	—
803	D₄	—	8	4	no	—
804	C₂×C₄	—	2	2	no	—
805	C₂×C₄	—	2	4	no	—
806	C₂×C₄	—	2	2	no	—
807	C₂×C₄	—	2	1	no	—
808	C₂×C₄	—	2	2	no	—
809	C₂×C₄	—	2	1	no	—
810	C₂×C₄	—	2	1	no	—
811	C₂×C₄	—	2	2	no	—
812	C₂×C₄	—	2	4	no	—
813	C₂×C₄	—	4	1	no	—
814	C₂×C₄	—	4	2	no	—
815	C₂×C₄	—	4	2	no	—
816	C₂×C₄	—	4	2	no	—
817	C₂×C₄	—	4	4	no	—
818	C₂×C₄	—	8	2	no	—
819	C₂×C₄	—	8	2	no	—
820	C₂×C₄	—	8	4	no	—
821	C₂×C₄	—	8	2	no	—
822	C₂×C₄	—	8	2	no	—
823	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
824	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
825	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
826	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
827	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
828	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
829	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
830	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
831	C₂×C₄	C₂⁵×C₈₉	1	1	yes	characteristic
832	C₈	—	2	2	no	—
833	C₈	—	2	2	no	—
834	C₈	—	2	4	no	—
835	C₂²	—	2	1	no	—
836	C₂²	—	2	2	no	—
837	C₂²	—	2	1	no	—
838	C₂²	—	2	2	no	—
839	C₂²	—	2	2	no	—
840	C₂²	—	2	1	no	—
841	C₂²	—	4	2	no	—
842	C₂²	—	4	1	no	—
843	C₂²	—	4	2	no	—
844	C₂²	—	4	2	no	—
845	C₂²	—	4	2	no	—
846	C₂²	—	4	1	no	—
847	C₂²	—	4	2	no	—
848	C₂²	—	4	1	no	—
849	C₂²	—	4	2	no	—
850	C₂²	—	16	4	no	—
851	C₂²	C₂³×D₄×C₈₉	1	1	yes	characteristic
852	C₄	—	2	1	no	—
853	C₄	—	2	2	no	—
854	C₄	—	2	1	no	—
855	C₄	—	2	2	no	—
856	C₄	—	2	1	no	—
857	C₄	—	2	1	no	—
858	C₄	—	2	2	no	—
859	C₄	—	4	1	no	—
860	C₄	—	4	2	no	—
861	C₄	—	4	4	no	—
862	C₄	—	4	1	no	—
863	C₄	—	4	2	no	—
864	C₄	—	4	1	no	—
865	C₄	#575×C₈₉	1	2	yes	—
866	C₄	#585×C₈₉	1	2	yes	—
867	C₂	—	4	1	no	—
868	C₂	—	4	2	no	—
869	C₂	—	8	2	no	—
870	C₂	—	8	2	no	—
871	C₂	—	8	1	no	—
872	C₂	C₈₉×#3500	1	1	yes	characteristic
873	C₂	C₂×#575×C₈₉	1	1	yes	characteristic
874	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 ◁ C₄×#41×C₈₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₈₉×#3514	C₂	semidirect
2. C₈₉×#3511	C₂	semidirect
3. C₈₉×#3361	C₂	semidirect
4. C₈₉×#3360	C₂	semidirect
5. C₈₉×#3329	C₂	semidirect
6. C₈₉×#3326	C₂	semidirect
7. C₈₉×#3325	C₂	semidirect
8. C₈₉×#3322	C₂	semidirect
9. C₈₉×#3240	C₂	semidirect
10. C₈₉×#3238	C₂	semidirect
11. C₈₉×#3214	C₂	semidirect
12. C₈₉×#3213	C₂	semidirect
13. C₈₉×#3171	C₂	semidirect
14. C₈₉×#3171	C₂	semidirect
15. C₈₉×#3141	C₂	semidirect
16. C₈₉×#3140	C₂	semidirect
17. C₈₉×#2971	C₂	semidirect
23. #554×C₈₉	C₂²	semidirect
24. #553×C₈₉	C₂²	semidirect
37. #533×C₈₉	C₂²	semidirect
39. #532×C₈₉	C₂²	semidirect
40. #532×C₈₉	C₂²	semidirect
41. C₂×C₄⋊Q₈×C₈₉	C₂²	semidirect
48. #501×C₈₉	C₂²	semidirect
49. #501×C₈₉	C₂²	semidirect
51. #496×C₈₉	C₂²	semidirect
52. #490×C₈₉	C₂²	semidirect
55. #489×C₈₉	C₂²	semidirect
56. #489×C₈₉	C₂²	semidirect
57. #489×C₈₉	C₂²	semidirect
59. #488×C₈₉	C₂²	semidirect
60. #487×C₈₉	C₂²	semidirect
62. #485×C₈₉	C₂²	semidirect
63. #483×C₈₉	C₂²	semidirect
66. #479×C₈₉	C₂²	semidirect
67. #478×C₈₉	C₂²	semidirect
68. #477×C₈₉	C₂²	semidirect
72. #468×C₈₉	C₂²	semidirect
73. #468×C₈₉	C₂²	semidirect
75. #463×C₈₉	C₂²	semidirect
76. #461×C₈₉	C₂²	semidirect
78. #449×C₈₉	C₂²	semidirect
79. #448×C₈₉	C₂²	semidirect
81. C₈×Q₈×C₈₉	C₂²	semidirect
82. C₄×SD₁₆×C₈₉	C₂²	semidirect
83. C₄×SD₁₆×C₈₉	C₂²	semidirect
85. C₄×D₈×C₈₉	C₂²	semidirect
87. #436×C₈₉	C₂²	semidirect
88. #432×C₈₉	C₂²	semidirect
89. #432×C₈₉	C₂²	semidirect
90. #419×C₈₉	C₂²	semidirect
92. #417×C₈₉	C₂²	semidirect
93. C₄×M₁₆×C₈₉	C₂²	semidirect
94. C₄×M₁₆×C₈₉	C₂²	semidirect
429. #62592	C₈₉	direct (N × H)
438. #3514	C₂×C₈₉	semidirect
439. #3511	C₂×C₈₉	semidirect
440. #3361	C₂×C₈₉	semidirect
441. #3360	C₂×C₈₉	semidirect
442. #3329	C₂×C₈₉	semidirect
443. #3326	C₂×C₈₉	semidirect
444. #3325	C₂×C₈₉	semidirect
445. #3322	C₂×C₈₉	semidirect
446. #3240	C₂×C₈₉	semidirect
447. #3238	C₂×C₈₉	semidirect
448. #3214	C₂×C₈₉	semidirect
449. #3213	C₂×C₈₉	semidirect
450. #3171	C₂×C₈₉	semidirect
451. #3171	C₂×C₈₉	semidirect
452. #3141	C₂×C₈₉	semidirect
453. #3140	C₂×C₈₉	semidirect
454. #2971	C₂×C₈₉	semidirect
455. C₈₉	#62592	direct (N × H)
461. #554	C₂²×C₈₉	semidirect
462. #553	C₂²×C₈₉	semidirect
475. #533	C₂²×C₈₉	semidirect
477. #532	C₂²×C₈₉	semidirect
478. #532	C₂²×C₈₉	semidirect
479. C₂×C₄⋊Q₈	C₂²×C₈₉	semidirect
486. #501	C₂²×C₈₉	semidirect
487. #501	C₂²×C₈₉	semidirect
489. #496	C₂²×C₈₉	semidirect
490. #490	C₂²×C₈₉	semidirect
493. #489	C₂²×C₈₉	semidirect
494. #489	C₂²×C₈₉	semidirect
495. #489	C₂²×C₈₉	semidirect
497. #488	C₂²×C₈₉	semidirect
498. #487	C₂²×C₈₉	semidirect
500. #485	C₂²×C₈₉	semidirect
501. #483	C₂²×C₈₉	semidirect
504. #479	C₂²×C₈₉	semidirect
505. #478	C₂²×C₈₉	semidirect
506. #477	C₂²×C₈₉	semidirect
510. #468	C₂²×C₈₉	semidirect
511. #468	C₂²×C₈₉	semidirect
513. #463	C₂²×C₈₉	semidirect
514. #461	C₂²×C₈₉	semidirect
516. #449	C₂²×C₈₉	semidirect
517. #448	C₂²×C₈₉	semidirect
519. C₈×Q₈	C₂²×C₈₉	semidirect
520. C₄×SD₁₆	C₂²×C₈₉	semidirect
521. C₄×SD₁₆	C₂²×C₈₉	semidirect
523. C₄×D₈	C₂²×C₈₉	semidirect
525. #436	C₂²×C₈₉	semidirect
526. #432	C₂²×C₈₉	semidirect
527. #432	C₂²×C₈₉	semidirect
528. #419	C₂²×C₈₉	semidirect
530. #417	C₂²×C₈₉	semidirect
531. C₄×M₁₆	C₂²×C₈₉	semidirect
532. C₄×M₁₆	C₂²×C₈₉	semidirect

Maximal subgroups

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

subgroup	index
C₈₉×#3514	2
C₈₉×#3511	2
C₈₉×#3361	2
C₈₉×#3360	2
C₈₉×#3329	2
C₈₉×#3326	2
C₈₉×#3325	2
C₈₉×#3322	2
C₈₉×#3240	2
C₈₉×#3238	2
C₈₉×#3214	2
C₈₉×#3213	2
C₈₉×#3171	2
C₈₉×#3141	2
C₈₉×#3140	2
C₈₉×#2971	2
#62592	89

Subgroups — C89×#62592 #36440440

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#62592 #36440440