Subgroups — #1723×D₈₉ #36542222

Order 22784.

798 conjugacy classes of subgroups.

The subgroup lattice has 520 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#500×D₈₉	C₂	1	1	yes	maximal, characteristic
2	#500×D₈₉	C₂	1	1	yes	maximal, characteristic
3	#498×D₈₉	C₂	1	1	yes	maximal, characteristic
4	#494×D₈₉	C₂	1	1	yes	maximal, characteristic
5	#487×D₈₉	C₂	1	1	yes	maximal, characteristic
6	#487×D₈₉	C₂	1	1	yes	maximal, characteristic
7	#26019932	C₂	1	1	yes	maximal, characteristic, complemented
8	#26019931	C₂	1	1	yes	maximal, characteristic, complemented
9	#26019930	C₂	1	1	yes	maximal, characteristic, complemented
10	#26019929	C₂	1	1	yes	maximal, characteristic, complemented
11	#26019928	C₂	1	1	yes	maximal, characteristic, complemented
12	#26019927	C₂	1	1	yes	maximal, characteristic, complemented
13	#26019926	C₂	1	1	yes	maximal, characteristic, complemented
14	#322×D₈₉	C₂	1	1	yes	maximal, characteristic
15	C₈₉×#1723	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×Q₁₆×D₈₉	—	2	2	no	—
17	C₄⋊Q₈×D₈₉	C₂²	1	1	yes	characteristic
18	C₄⋊Q₈×D₈₉	C₂²	1	1	yes	characteristic
19	C₄⋊Q₈×D₈₉	C₂²	1	1	yes	characteristic
20	C₄⋊Q₈×D₈₉	C₂²	1	1	yes	characteristic
21	#19152003	C₂²	1	1	yes	characteristic
22	#19152003	C₂²	1	1	yes	characteristic
23	#19152002	—	2	2	no	—
24	#19152002	—	2	2	no	—
25	#19152001	C₂²	1	1	yes	characteristic
26	#19152001	C₂²	1	1	yes	characteristic
27	#19152001	C₂²	1	1	yes	characteristic
28	#19152001	C₂²	1	1	yes	characteristic
29	#19151996	C₂²	1	1	yes	characteristic
30	#19151995	—	2	2	no	—
31	#19151994	C₂²	1	1	yes	characteristic
32	#19151994	C₂²	1	1	yes	characteristic
33	#19151978	C₂²	1	1	yes	characteristic
34	#19151977	C₂²	1	1	yes	characteristic
35	#19151977	C₂²	1	1	yes	characteristic
36	#19151976	—	2	2	no	—
37	#19151950	C₂²	1	1	yes	characteristic
38	#19151950	C₂²	1	1	yes	characteristic
39	#19151949	C₂²	1	1	yes	characteristic
40	#19151949	C₂²	1	1	yes	characteristic
41	#19151948	C₂²	1	1	yes	characteristic
42	#19151948	C₂²	1	1	yes	characteristic
43	#19151947	—	2	2	no	—
44	#19151947	—	2	2	no	—
45	#107×D₈₉	—	2	2	no	—
46	#107×D₈₉	—	2	2	no	—
47	#106×D₈₉	—	2	2	no	—
48	#103×D₈₉	—	2	2	no	—
49	#103×D₈₉	—	2	2	no	—
50	C₄×C₈×D₈₉	C₂²	1	1	yes	characteristic
51	C₄×C₈×D₈₉	C₂²	1	1	yes	characteristic
52	C₄×C₈×D₈₉	C₂²	1	1	yes	characteristic
53	#19151320	C₂²	1	1	yes	characteristic
54	#19151320	C₂²	1	1	yes	characteristic
55	#19151319	C₂²	1	1	yes	characteristic
56	#500×C₈₉	C₂²	1	1	yes	characteristic
57	#500×C₈₉	C₂²	1	1	yes	characteristic
58	#498×C₈₉	C₂²	1	1	yes	characteristic
59	#494×C₈₉	C₂²	1	1	yes	characteristic
60	#487×C₈₉	C₂²	1	1	yes	characteristic
61	#487×C₈₉	C₂²	1	1	yes	characteristic
62	#322×C₈₉	C₂²	1	1	yes	characteristic
63	C₂×Q₈×D₈₉	—	2	1	no	—
64	C₂×Q₈×D₈₉	—	2	1	no	—
65	C₂×Q₈×D₈₉	—	2	1	no	—
66	C₂×Q₈×D₈₉	—	2	1	no	—
67	C₂×Dic₃₅₆	—	2	2	no	—
68	C₂×#13083564	—	2	2	no	—
69	C₂×#13083564	—	2	2	no	—
70	Q₁₆×D₈₉	—	4	8	no	—
71	C₂×C₈×D₈₉	D₄	1	2	yes	—
72	C₂×C₈×D₈₉	D₄	1	2	yes	—
73	C₂×C₈×D₈₉	D₄	1	2	yes	—
74	#15668012	C₂³	1	1	yes	characteristic
75	#15668012	C₂³	1	1	yes	characteristic
76	#15668012	C₂³	1	1	yes	characteristic
77	#15668012	C₂³	1	1	yes	characteristic
78	#15668011	—	2	1	no	—
79	#15668011	—	2	1	no	—
80	#15668011	—	2	1	no	—
81	#15668011	—	2	1	no	—
82	#15668011	—	2	1	no	—
83	#15668011	—	2	1	no	—
84	#15668011	—	2	1	no	—
85	#15668011	—	2	1	no	—
86	#15668010	—	2	1	no	—
87	#15668010	—	2	1	no	—
88	#15668010	—	2	1	no	—
89	#15668010	—	2	1	no	—
90	C₄⋊C₄×D₈₉	—	2	1	no	—
91	C₄⋊C₄×D₈₉	—	2	1	no	—
92	C₄⋊C₄×D₈₉	—	2	1	no	—
93	C₄⋊C₄×D₈₉	—	2	1	no	—
94	C₄⋊C₄×D₈₉	—	2	1	no	—
95	C₄⋊C₄×D₈₉	—	2	1	no	—
96	C₄⋊C₄×D₈₉	—	2	1	no	—
97	C₄⋊C₄×D₈₉	—	2	1	no	—
98	C₄²×D₈₉	C₂³	1	1	yes	characteristic
99	#15667946	—	2	2	no	—
100	#15667946	—	2	2	no	—
101	#15667945	—	2	2	no	—
102	#15667945	—	2	2	no	—
103	#15667945	—	2	2	no	—
104	#15667945	—	2	2	no	—
105	#15667944	—	2	2	no	—
106	#15667943	—	2	2	no	—
107	#15667943	—	2	2	no	—
108	#15667937	—	2	2	no	—
109	#15667937	—	2	2	no	—
110	#15667936	—	2	2	no	—
111	#15667936	—	2	2	no	—
112	#15667935	—	2	2	no	—
113	#15667935	—	2	2	no	—
114	C₄×#10623494	C₂³	1	1	yes	characteristic
115	C₄×#10623494	C₂³	1	1	yes	characteristic
116	C₄×#10623494	C₂³	1	1	yes	characteristic
117	C₈×Dic₈₉	D₄	1	2	yes	—
118	C₈×Dic₈₉	D₄	1	2	yes	—
119	C₈×Dic₈₉	D₄	1	2	yes	—
120	C₂×Q₁₆×C₈₉	—	2	2	no	—
121	C₄⋊Q₈×C₈₉	C₂³	1	1	yes	characteristic
122	C₄⋊Q₈×C₈₉	C₂³	1	1	yes	characteristic
123	C₄⋊Q₈×C₈₉	C₂³	1	1	yes	characteristic
124	C₄⋊Q₈×C₈₉	C₂³	1	1	yes	characteristic
125	#107×C₈₉	—	2	2	no	—
126	#107×C₈₉	—	2	2	no	—
127	#106×C₈₉	—	2	2	no	—
128	#103×C₈₉	—	2	2	no	—
129	#103×C₈₉	—	2	2	no	—
130	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
131	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
132	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
133	C₂×Dic₁₇₈	—	2	1	no	—
134	C₂×Dic₁₇₈	—	2	1	no	—
135	C₂×Dic₁₇₈	—	2	1	no	—
136	C₂×Dic₁₇₈	—	2	1	no	—
137	C₂×Dic₁₇₈	—	4	1	no	—
138	C₂×Dic₁₇₈	—	4	1	no	—
139	C₂×Dic₁₇₈	—	4	1	no	—
140	C₂×Dic₁₇₈	—	4	1	no	—
141	Q₈×D₈₉	—	4	4	no	—
142	Q₈×D₈₉	—	4	4	no	—
143	Q₈×D₈₉	—	4	4	no	—
144	Q₈×D₈₉	—	4	4	no	—
145	C₂×C₄×D₈₉	—	4	1	no	—
146	C₂×C₄×D₈₉	—	4	1	no	—
147	C₂×C₄×D₈₉	—	4	1	no	—
148	C₂×C₄×D₈₉	—	4	1	no	—
149	C₂×C₄×D₈₉	C₂×D₄	1	1	yes	characteristic
150	C₂×C₄×D₈₉	C₂×D₄	1	1	yes	characteristic
151	C₂×C₄×D₈₉	C₂×D₄	1	1	yes	characteristic
152	Dic₃₅₆	—	4	4	no	—
153	#13083564	—	4	4	no	—
154	#13083564	—	4	4	no	—
155	C₂×#10623494	C₂×D₄	1	2	yes	—
156	C₂×#10623494	C₂×D₄	1	2	yes	—
157	C₂×#10623494	C₂×D₄	1	2	yes	—
158	C₈×D₈₉	—	2	4	no	—
159	C₈×D₈₉	—	2	4	no	—
160	C₈×D₈₉	Q₁₆	1	8	yes	complemented
161	C₄⋊Dic₈₉	—	2	1	no	—
162	C₄⋊Dic₈₉	—	2	1	no	—
163	C₄⋊Dic₈₉	—	2	1	no	—
164	C₄⋊Dic₈₉	—	2	1	no	—
165	C₄⋊Dic₈₉	—	2	1	no	—
166	C₄⋊Dic₈₉	—	2	1	no	—
167	C₄⋊Dic₈₉	—	2	1	no	—
168	C₄⋊Dic₈₉	—	2	1	no	—
169	#13083553	—	4	1	no	—
170	#13083553	—	4	1	no	—
171	#13083553	—	4	1	no	—
172	#13083553	—	4	1	no	—
173	#13083553	—	4	1	no	—
174	#13083553	—	4	1	no	—
175	#13083553	—	4	1	no	—
176	#13083553	—	4	1	no	—
177	C₄×Dic₈₉	C₂×D₄	1	1	yes	characteristic
178	C₄×Dic₈₉	C₂×D₄	1	1	yes	characteristic
179	C₄×Dic₈₉	C₂×D₄	1	1	yes	characteristic
180	C₂×Q₈×C₈₉	—	2	1	no	—
181	C₂×Q₈×C₈₉	—	2	1	no	—
182	C₂×Q₈×C₈₉	—	2	1	no	—
183	C₂×Q₈×C₈₉	—	2	1	no	—
184	Q₁₆×C₈₉	—	4	4	no	—
185	C₂×C₈×C₈₉	C₂×D₄	1	2	yes	—
186	C₂×C₈×C₈₉	C₂×D₄	1	2	yes	—
187	C₂×C₈×C₈₉	C₂×D₄	1	2	yes	—
188	C₄⋊C₄×C₈₉	—	2	1	no	—
189	C₄⋊C₄×C₈₉	—	2	1	no	—
190	C₄⋊C₄×C₈₉	—	2	1	no	—
191	C₄⋊C₄×C₈₉	—	2	1	no	—
192	C₄⋊C₄×C₈₉	—	2	1	no	—
193	C₄⋊C₄×C₈₉	—	2	1	no	—
194	C₄⋊C₄×C₈₉	—	2	1	no	—
195	C₄⋊C₄×C₈₉	—	2	1	no	—
196	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
197	C₂²×D₈₉	#127	1	1	yes	characteristic
198	Q₈×C₈₉	—	4	2	no	—
199	Q₈×C₈₉	—	4	2	no	—
200	Q₈×C₈₉	—	4	2	no	—
201	Q₈×C₈₉	—	4	2	no	—
202	C₂×C₄×C₈₉	—	4	1	no	—
203	C₂×C₄×C₈₉	—	4	1	no	—
204	C₂×C₄×C₈₉	—	4	1	no	—
205	C₂×C₄×C₈₉	—	4	1	no	—
206	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
207	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
208	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
209	C₂×Dic₈₉	—	4	1	no	—
210	C₂×Dic₈₉	—	4	1	no	—
211	C₂×Dic₈₉	—	4	1	no	—
212	C₂×Dic₈₉	—	4	1	no	—
213	C₂×Dic₈₉	#127	1	1	yes	characteristic
214	C₂×Dic₈₉	#127	1	1	yes	characteristic
215	C₂×Dic₈₉	#127	1	1	yes	characteristic
216	C₄×D₈₉	—	8	2	no	—
217	C₄×D₈₉	—	8	2	no	—
218	C₄×D₈₉	—	8	2	no	—
219	C₄×D₈₉	—	8	2	no	—
220	C₄×D₈₉	C₂×Q₁₆	1	4	yes	—
221	C₄×D₈₉	AGL(1,ℤ/8)	1	4	yes	—
222	C₄×D₈₉	#137	1	4	yes	—
223	Dic₁₇₈	—	4	2	no	—
224	Dic₁₇₈	—	4	2	no	—
225	Dic₁₇₈	—	4	2	no	—
226	Dic₁₇₈	—	4	2	no	—
227	Dic₁₇₈	—	8	2	no	—
228	Dic₁₇₈	—	8	2	no	—
229	Dic₁₇₈	—	8	2	no	—
230	Dic₁₇₈	—	8	2	no	—
231	C₈×C₈₉	—	2	2	no	—
232	C₈×C₈₉	—	2	2	no	—
233	C₈×C₈₉	C₂×Q₁₆	1	4	yes	complemented
234	#10623494	—	2	2	no	—
235	#10623494	—	2	2	no	—
236	#10623494	C₂×Q₁₆	1	4	yes	complemented
237	C₂²×C₈₉	C₂×#127	1	1	yes	characteristic
238	C₂×D₈₉	#494	1	2	yes	—
239	C₂×D₈₉	#496	1	2	yes	—
240	C₂×D₈₉	#497	1	2	yes	—
241	C₄×C₈₉	—	8	1	no	—
242	C₄×C₈₉	—	8	1	no	—
243	C₄×C₈₉	—	8	1	no	—
244	C₄×C₈₉	—	8	1	no	—
245	C₄×C₈₉	C₂²×Q₁₆	1	2	yes	—
246	C₄×C₈₉	C₂×AGL(1,ℤ/8)	1	2	yes	—
247	C₄×C₈₉	C₂×#137	1	2	yes	—
248	Dic₈₉	—	8	1	no	—
249	Dic₈₉	—	8	1	no	—
250	Dic₈₉	—	8	1	no	—
251	Dic₈₉	—	8	1	no	—
252	Dic₈₉	#494	1	2	yes	—
253	Dic₈₉	#496	1	2	yes	—
254	Dic₈₉	#497	1	2	yes	—
255	C₂×#1723	—	89	1	no	maximal, Sylow
256	C₂×C₈₉	C₂×#494	1	1	yes	characteristic
257	C₂×C₈₉	C₂×#496	1	1	yes	characteristic
258	C₂×C₈₉	C₂×#497	1	1	yes	characteristic
259	D₈₉	#1723	1	4	yes	direct product factor
260	C₂×#500	—	89	1	no	—
261	C₂×#500	—	89	1	no	—
262	C₂×#498	—	89	1	no	—
263	C₂×#494	—	89	1	no	—
264	C₂×#487	—	89	1	no	—
265	C₂×#487	—	89	1	no	—
266	#1723	—	89	1	no	—
267	#1723	—	89	1	no	—
268	#1723	—	89	1	no	—
269	#1723	—	89	1	no	—
270	#1723	—	89	1	no	—
271	#1723	—	89	1	no	—
272	#1723	—	89	1	no	—
273	#1723	D₈₉	1	1	yes	characteristic, direct product factor
274	C₂×#322	—	89	1	no	—
275	C₈₉	C₂×#1723	1	1	yes	characteristic, complemented, Sylow
276	C₂²×Q₁₆	—	178	2	no	—
277	C₂×C₄⋊Q₈	—	89	1	no	—
278	C₂×C₄⋊Q₈	—	89	1	no	—
279	C₂×C₄⋊Q₈	—	89	1	no	—
280	C₂×C₄⋊Q₈	—	89	1	no	—
281	#500	—	89	1	no	—
282	#500	—	89	1	no	—
283	#500	—	89	1	no	—
284	#500	—	89	1	no	—
285	#500	—	89	1	no	—
286	#500	—	89	1	no	—
287	#500	—	178	2	no	—
288	#500	—	178	2	no	—
289	#500	C₂×D₈₉	1	1	yes	characteristic
290	#500	C₂×D₈₉	1	1	yes	characteristic
291	#498	—	89	1	no	—
292	#498	—	89	1	no	—
293	#498	—	89	1	no	—
294	#498	—	178	2	no	—
295	#498	C₂×D₈₉	1	1	yes	characteristic
296	#494	—	89	1	no	—
297	#494	—	89	1	no	—
298	#494	—	89	1	no	—
299	#494	—	178	2	no	—
300	#494	C₂×D₈₉	1	1	yes	characteristic
301	#487	—	89	1	no	—
302	#487	—	89	1	no	—
303	#487	—	89	1	no	—
304	#487	—	89	1	no	—
305	#487	—	89	1	no	—
306	#487	—	89	1	no	—
307	#487	—	178	2	no	—
308	#487	—	178	2	no	—
309	#487	C₂×D₈₉	1	1	yes	characteristic
310	#487	C₂×D₈₉	1	1	yes	characteristic
311	C₂×#107	—	178	2	no	—
312	C₂×#107	—	178	2	no	—
313	C₂×#106	—	178	2	no	—
314	C₂×#103	—	178	2	no	—
315	C₂×#103	—	178	2	no	—
316	C₂×C₄×C₈	—	89	1	no	—
317	C₂×C₄×C₈	—	89	1	no	—
318	C₂×C₄×C₈	—	89	1	no	—
319	#322	—	89	1	no	—
320	#322	—	89	1	no	—
321	#322	—	89	1	no	—
322	#322	C₂×D₈₉	1	1	yes	characteristic
323	C₂²×Q₈	—	178	1	no	—
324	C₂²×Q₈	—	178	1	no	—
325	C₂²×Q₈	—	178	1	no	—
326	C₂²×Q₈	—	178	1	no	—
327	C₂×Q₁₆	—	2	2	no	—
328	C₂×Q₁₆	—	356	8	no	—
329	C₂×Q₁₆	—	178	2	no	—
330	C₂×Q₁₆	—	178	2	no	—
331	C₂×Q₁₆	—	178	2	no	—
332	C₂²×C₈	—	89	2	no	—
333	C₂²×C₈	—	89	2	no	—
334	C₂²×C₈	—	89	2	no	—
335	C₄⋊Q₈	—	89	1	no	—
336	C₄⋊Q₈	—	89	1	no	—
337	C₄⋊Q₈	—	89	1	no	—
338	C₄⋊Q₈	—	89	1	no	—
339	C₄⋊Q₈	—	178	1	no	—
340	C₄⋊Q₈	—	178	1	no	—
341	C₄⋊Q₈	—	178	1	no	—
342	C₄⋊Q₈	—	178	1	no	—
343	C₄⋊Q₈	—	178	1	no	—
344	C₄⋊Q₈	—	178	1	no	—
345	C₄⋊Q₈	—	178	1	no	—
346	C₄⋊Q₈	—	178	1	no	—
347	C₄⋊Q₈	—	178	1	no	—
348	C₄⋊Q₈	—	178	1	no	—
349	C₄⋊Q₈	—	178	1	no	—
350	C₄⋊Q₈	—	178	1	no	—
351	C₄⋊Q₈	C₂²×D₈₉	1	1	yes	characteristic
352	C₄⋊Q₈	C₂²×D₈₉	1	1	yes	characteristic
353	C₄⋊Q₈	C₂²×D₈₉	1	1	yes	characteristic
354	C₄⋊Q₈	C₂²×D₈₉	1	1	yes	characteristic
355	C₂×C₄⋊C₄	—	178	1	no	—
356	C₂×C₄⋊C₄	—	178	1	no	—
357	C₂×C₄⋊C₄	—	178	1	no	—
358	C₂×C₄⋊C₄	—	178	1	no	—
359	C₂×C₄⋊C₄	—	178	1	no	—
360	C₂×C₄⋊C₄	—	178	1	no	—
361	C₂×C₄⋊C₄	—	178	1	no	—
362	C₂×C₄⋊C₄	—	178	1	no	—
363	C₂×C₄²	—	89	1	no	—
364	#107	—	2	2	no	—
365	#107	—	2	2	no	—
366	#107	—	178	2	no	—
367	#107	—	178	2	no	—
368	#107	—	178	2	no	—
369	#107	—	178	2	no	—
370	#107	—	178	2	no	—
371	#107	—	178	2	no	—
372	#106	—	2	2	no	—
373	#106	—	178	2	no	—
374	#106	—	178	2	no	—
375	#106	—	178	2	no	—
376	#103	—	2	2	no	—
377	#103	—	2	2	no	—
378	#103	—	178	2	no	—
379	#103	—	178	2	no	—
380	#103	—	178	2	no	—
381	#103	—	178	2	no	—
382	#103	—	178	2	no	—
383	#103	—	178	2	no	—
384	C₄×C₈	—	89	2	no	—
385	C₄×C₈	—	89	2	no	—
386	C₄×C₈	—	89	2	no	—
387	C₄×C₈	—	89	1	no	—
388	C₄×C₈	—	89	1	no	—
389	C₄×C₈	—	89	1	no	—
390	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
391	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
392	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
393	C₂×Q₈	—	2	1	no	—
394	C₂×Q₈	—	2	1	no	—
395	C₂×Q₈	—	2	1	no	—
396	C₂×Q₈	—	2	1	no	—
397	C₂×Q₈	—	356	1	no	—
398	C₂×Q₈	—	356	1	no	—
399	C₂×Q₈	—	356	1	no	—
400	C₂×Q₈	—	356	1	no	—
401	C₂×Q₈	—	356	4	no	—
402	C₂×Q₈	—	356	4	no	—
403	C₂×Q₈	—	356	4	no	—
404	C₂×Q₈	—	356	4	no	—
405	C₂×Q₈	—	178	1	no	—
406	C₂×Q₈	—	178	1	no	—
407	C₂×Q₈	—	178	1	no	—
408	C₂×Q₈	—	178	1	no	—
409	C₂²×C₄	—	89	1	no	—
410	C₂²×C₄	—	89	1	no	—
411	C₂²×C₄	—	89	1	no	—
412	C₂²×C₄	—	356	1	no	—
413	C₂²×C₄	—	356	1	no	—
414	C₂²×C₄	—	356	1	no	—
415	C₂²×C₄	—	356	1	no	—
416	Q₁₆	—	4	4	no	—
417	Q₁₆	—	356	4	no	—
418	Q₁₆	—	356	4	no	—
419	Q₁₆	—	356	4	no	—
420	C₂×C₈	—	89	2	no	—
421	C₂×C₈	—	89	8	no	—
422	C₂×C₈	—	89	2	no	—
423	C₂×C₈	—	89	2	no	—
424	C₂×C₈	—	178	4	no	—
425	C₂×C₈	—	178	4	no	—
426	C₂×C₈	D₄×D₈₉	1	2	yes	—
427	C₂×C₈	D₄×D₈₉	1	2	yes	—
428	C₂×C₈	D₄×D₈₉	1	2	yes	—
429	C₄⋊C₄	—	2	1	no	—
430	C₄⋊C₄	—	2	1	no	—
431	C₄⋊C₄	—	2	1	no	—
432	C₄⋊C₄	—	2	1	no	—
433	C₄⋊C₄	—	2	1	no	—
434	C₄⋊C₄	—	2	1	no	—
435	C₄⋊C₄	—	2	1	no	—
436	C₄⋊C₄	—	2	1	no	—
437	C₄⋊C₄	—	356	1	no	—
438	C₄⋊C₄	—	356	1	no	—
439	C₄⋊C₄	—	356	1	no	—
440	C₄⋊C₄	—	356	1	no	—
441	C₄⋊C₄	—	356	1	no	—
442	C₄⋊C₄	—	356	1	no	—
443	C₄⋊C₄	—	356	1	no	—
444	C₄⋊C₄	—	356	1	no	—
445	C₄⋊C₄	—	178	1	no	—
446	C₄⋊C₄	—	178	1	no	—
447	C₄⋊C₄	—	178	1	no	—
448	C₄⋊C₄	—	178	1	no	—
449	C₄⋊C₄	—	178	1	no	—
450	C₄⋊C₄	—	178	1	no	—
451	C₄⋊C₄	—	178	1	no	—
452	C₄⋊C₄	—	178	1	no	—
453	C₄²	—	89	1	no	—
454	C₄²	—	89	1	no	—
455	C₄²	—	89	1	no	—
456	C₄²	C₂³×D₈₉	1	1	yes	characteristic
457	C₂³	—	89	1	no	—
458	Q₈	—	4	2	no	—
459	Q₈	—	4	2	no	—
460	Q₈	—	4	2	no	—
461	Q₈	—	4	2	no	—
462	Q₈	—	356	2	no	—
463	Q₈	—	356	2	no	—
464	Q₈	—	356	2	no	—
465	Q₈	—	356	2	no	—
466	Q₈	—	712	2	no	—
467	Q₈	—	712	2	no	—
468	Q₈	—	712	2	no	—
469	Q₈	—	712	2	no	—
470	C₂×C₄	—	4	1	no	—
471	C₂×C₄	—	4	1	no	—
472	C₂×C₄	—	4	1	no	—
473	C₂×C₄	—	4	1	no	—
474	C₂×C₄	—	89	1	no	—
475	C₂×C₄	—	89	1	no	—
476	C₂×C₄	—	89	1	no	—
477	C₂×C₄	—	89	4	no	—
478	C₂×C₄	—	89	4	no	—
479	C₂×C₄	—	89	4	no	—
480	C₂×C₄	—	356	1	no	—
481	C₂×C₄	—	356	1	no	—
482	C₂×C₄	—	356	1	no	—
483	C₂×C₄	—	356	1	no	—
484	C₂×C₄	—	712	2	no	—
485	C₂×C₄	—	712	2	no	—
486	C₂×C₄	—	712	2	no	—
487	C₂×C₄	—	712	2	no	—
488	C₂×C₄	C₂×D₄×D₈₉	1	1	yes	characteristic
489	C₂×C₄	C₂×D₄×D₈₉	1	1	yes	characteristic
490	C₂×C₄	C₂×D₄×D₈₉	1	1	yes	characteristic
491	C₈	—	2	2	no	—
492	C₈	—	2	2	no	—
493	C₈	—	89	4	no	—
494	C₈	—	178	2	no	—
495	C₈	—	178	2	no	—
496	C₈	Q₁₆×D₈₉	1	4	yes	complemented
497	C₂²	—	89	2	no	—
498	C₂²	—	89	2	no	—
499	C₂²	—	89	2	no	—
500	C₂²	#127×D₈₉	1	1	yes	characteristic
501	C₄	—	8	1	no	—
502	C₄	—	8	1	no	—
503	C₄	—	8	1	no	—
504	C₄	—	8	1	no	—
505	C₄	—	89	2	no	—
506	C₄	—	89	2	no	—
507	C₄	—	89	2	no	—
508	C₄	—	712	1	no	—
509	C₄	—	712	1	no	—
510	C₄	—	712	1	no	—
511	C₄	—	712	1	no	—
512	C₄	C₂×Q₁₆×D₈₉	1	2	yes	—
513	C₄	AGL(1,ℤ/8)×D₈₉	1	2	yes	—
514	C₄	#137×D₈₉	1	2	yes	—
515	C₂	—	89	4	no	—
516	C₂	#494×D₈₉	1	1	yes	characteristic
517	C₂	#496×D₈₉	1	1	yes	characteristic
518	C₂	#497×D₈₉	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#127×D₈₉
commutator, cosocle	C₄²×C₈₉	C₂⁴
Frattini	C₄²	C₂³×D₈₉
Fitting	C₈₉×#1723	C₂
socle	C₂²×C₈₉	C₂×#127
prime radical	C₂²×D₈₉	#127
hypercenter	#1723	D₈₉
hypocenter	C₈₉	C₂×#1723
LCS	G ▷ C₄²×C₈₉ ▷ C₂²×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #1723

Complements

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

N	H ≅ G/N	type
7. #26019932	C₂	semidirect
8. #26019931	C₂	semidirect
9. #26019930	C₂	semidirect
10. #26019929	C₂	semidirect
11. #26019928	C₂	semidirect
12. #26019927	C₂	semidirect
13. #26019926	C₂	semidirect
15. C₈₉×#1723	C₂	semidirect
160. C₈×D₈₉	Q₁₆	semidirect
233. C₈×C₈₉	C₂×Q₁₆	semidirect
236. #10623494	C₂×Q₁₆	semidirect
259. D₈₉	#1723	direct (N × H)
273. #1723	D₈₉	direct (N × H)
275. C₈₉	C₂×#1723	semidirect
496. C₈	Q₁₆×D₈₉	semidirect

Maximal subgroups

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

subgroup	index
#500×D₈₉	2
#498×D₈₉	2
#494×D₈₉	2
#487×D₈₉	2
#26019932	2
#26019931	2
#26019930	2
#26019929	2
#26019928	2
#26019927	2
#26019926	2
#322×D₈₉	2
C₈₉×#1723	2
C₂×#1723	89

Subgroups — #1723×D89 #36542222

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #1723×D₈₉ #36542222