Subgroups — #36542277

Order 22784.

784 conjugacy classes of subgroups.

The subgroup lattice has 528 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26031392	C₂	1	1	yes	maximal, characteristic, complemented
2	#26031173	C₂	1	1	yes	maximal, characteristic
3	#26030810	C₂	1	1	yes	maximal, characteristic
4	#26030795	C₂	1	1	yes	maximal, characteristic, complemented
5	#498×D₈₉	C₂	1	1	yes	maximal, characteristic, complemented
6	#26030706	C₂	1	1	yes	maximal, characteristic
7	#26019885	C₂	1	1	yes	maximal, characteristic, complemented
8	#26019884	C₂	1	1	yes	maximal, characteristic, complemented
9	#26019873	C₂	1	1	yes	maximal, characteristic, complemented
10	#26019850	C₂	1	1	yes	maximal, characteristic, complemented
11	#26019848	C₂	1	1	yes	maximal, characteristic, complemented
12	#26019838	C₂	1	1	yes	maximal, characteristic, complemented
13	#26019838	C₂	1	1	yes	maximal, characteristic, complemented
14	#26018531	C₂	1	1	yes	maximal, characteristic, complemented
15	C₈₉×#1714	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#15668041	—	2	2	no	—
17	#19152153	C₂²	1	1	yes	characteristic
18	#19152146	C₂²	1	1	yes	characteristic
19	C₄⋊Q₈×D₈₉	C₂²	1	1	yes	characteristic
20	C₄⋊Q₈×D₈₉	C₂²	1	1	yes	characteristic
21	#19152006	—	2	2	no	—
22	#19152001	C₂²	1	1	yes	characteristic
23	#19151996	C₂²	1	1	yes	characteristic
24	#19151996	C₂²	1	1	yes	characteristic
25	#19151996	C₂²	1	1	yes	characteristic
26	#19151995	—	2	2	no	—
27	#19151994	C₂²	1	1	yes	characteristic
28	#19151994	C₂²	1	1	yes	characteristic
29	#19151994	C₂²	1	1	yes	characteristic
30	#19151994	C₂²	1	1	yes	characteristic
31	#19151994	C₂²	1	1	yes	characteristic
32	#19151989	—	2	2	no	—
33	#19151978	C₂²	1	1	yes	characteristic
34	#19151977	C₂²	1	1	yes	characteristic
35	#19151970	C₂²	1	1	yes	characteristic
36	#19151970	C₂²	1	1	yes	characteristic
37	#19151970	C₂²	1	1	yes	characteristic
38	#19151949	C₂²	1	1	yes	characteristic
39	#19151949	C₂²	1	1	yes	characteristic
40	#19151948	C₂²	1	1	yes	characteristic
41	#19151948	C₂²	1	1	yes	characteristic
42	#19151927	—	2	2	no	—
43	#19151881	—	2	2	no	—
44	#19151826	—	2	2	no	—
45	#19151801	—	2	2	no	—
46	#19151735	—	2	2	no	—
47	#19151689	—	2	2	no	—
48	#19151649	C₂²	1	1	yes	characteristic
49	#19151639	—	2	2	no	—
50	#106×D₈₉	—	2	2	no	—
51	C₄×#13083557	C₂²	1	1	yes	characteristic
52	C₄×C₈×D₈₉	C₂²	1	1	yes	characteristic
53	#19151320	C₂²	1	1	yes	characteristic
54	C₈×#10623494	C₂²	1	1	yes	characteristic
55	C₈×#10623494	C₂²	1	1	yes	characteristic
56	#500×C₈₉	C₂²	1	1	yes	characteristic
57	#498×C₈₉	C₂²	1	1	yes	characteristic
58	#492×C₈₉	C₂²	1	1	yes	characteristic
59	#492×C₈₉	C₂²	1	1	yes	characteristic
60	#487×C₈₉	C₂²	1	1	yes	characteristic
61	#486×C₈₉	C₂²	1	1	yes	characteristic
62	#322×C₈₉	C₂²	1	1	yes	characteristic
63	C₂×#13083573	—	2	1	no	—
64	C₂×Q₈×D₈₉	—	2	1	no	—
65	C₂×Q₈×D₈₉	—	2	1	no	—
66	#15668041	—	4	8	no	—
67	C₂×Dic₃₅₆	—	2	2	no	—
68	C₂×#13083564	—	2	2	no	—
69	C₂×#13083562	—	2	2	no	—
70	C₂×#13083562	—	2	2	no	—
71	C₂×#13083562	—	2	2	no	—
72	C₂×#13083557	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	#15668010	—	2	1	no	—
83	#15668010	—	2	1	no	—
84	#15668003	—	2	1	no	—
85	#15667999	—	2	1	no	—
86	#15667992	—	2	1	no	—
87	#15667988	—	2	1	no	—
88	#15667983	—	2	1	no	—
89	#15667983	—	2	1	no	—
90	Q₈×Dic₈₉	—	2	1	no	—
91	#15667977	—	2	1	no	—
92	D₄×Dic₈₉	—	2	1	no	—
93	D₄×Dic₈₉	—	2	1	no	—
94	#15667970	—	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	C₄⋊C₄×D₈₉	—	2	1	no	—
99	C₄²×D₈₉	C₂³	1	1	yes	characteristic
100	#15667945	—	2	2	no	—
101	#15667944	—	2	2	no	—
102	#15667944	—	2	2	no	—
103	#15667944	—	2	2	no	—
104	#15667943	—	2	2	no	—
105	#15667943	—	2	2	no	—
106	#15667943	—	2	2	no	—
107	#15667943	—	2	2	no	—
108	#15667943	—	2	2	no	—
109	#15667941	D₄	1	2	yes	—
110	#15667937	—	2	2	no	—
111	#15667937	—	2	2	no	—
112	#15667936	—	2	2	no	—
113	#15667936	—	2	2	no	—
114	#15667924	D₄	1	2	yes	—
115	#15667922	D₄	1	2	yes	—
116	C₄×#10623494	C₂³	1	1	yes	characteristic
117	C₄×#10623494	C₂³	1	1	yes	characteristic
118	C₄×#10623494	C₂³	1	1	yes	characteristic
119	C₈×Dic₈₉	D₄	1	2	yes	—
120	C₂×SD₁₆×C₈₉	—	2	2	no	—
121	C₂×SD₁₆×C₈₉	—	2	2	no	—
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	#127×C₈₉	C₂³	1	1	yes	characteristic
126	#107×C₈₉	—	2	2	no	—
127	#106×C₈₉	—	2	2	no	—
128	#103×C₈₉	—	2	2	no	—
129	#102×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	#13083573	—	4	4	no	—
134	C₂×Dic₁₇₈	—	2	1	no	—
135	C₂×Dic₁₇₈	—	2	1	no	—
136	C₂×Dic₁₇₈	—	2	1	no	—
137	C₂×Dic₁₇₈	—	2	1	no	—
138	C₂×Dic₁₇₈	—	4	1	no	—
139	C₂×Dic₁₇₈	—	4	1	no	—
140	Q₈×D₈₉	—	4	4	no	—
141	Q₈×D₈₉	—	8	2	no	—
142	C₂×C₂²⋊D₈₉	—	4	1	no	—
143	C₂²×Dic₈₉	—	4	1	no	—
144	C₂×C₄×D₈₉	—	4	1	no	—
145	C₂×C₄×D₈₉	—	4	1	no	—
146	C₂×C₄×D₈₉	C₂×D₄	1	1	yes	characteristic
147	C₂×C₄×D₈₉	C₂×D₄	1	1	yes	characteristic
148	C₂×C₄×D₈₉	C₂×D₄	1	1	yes	characteristic
149	Dic₃₅₆	—	4	4	no	—
150	#13083564	—	4	4	no	—
151	#13083562	—	4	4	no	—
152	#13083562	—	4	4	no	—
153	#13083562	—	8	2	no	—
154	#13083557	SD₁₆	1	8	yes	complemented
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	C₄⋊Dic₈₉	—	2	1	no	—
160	C₄⋊Dic₈₉	—	2	1	no	—
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	—	4	1	no	—
168	#13083553	—	4	1	no	—
169	#13083553	—	4	1	no	—
170	#13083553	—	4	1	no	—
171	#13083553	—	4	1	no	—
172	#13083553	—	4	1	no	—
173	C₂²⋊Dic₈₉	—	4	1	no	—
174	C₂²⋊Dic₈₉	—	4	1	no	—
175	#13083551	—	4	1	no	—
176	C₄×Dic₈₉	—	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×D₄×C₈₉	—	2	1	no	—
184	C₂×D₄×C₈₉	—	2	1	no	—
185	C₂×D₄×C₈₉	—	2	1	no	—
186	SD₁₆×C₈₉	—	4	4	no	—
187	SD₁₆×C₈₉	—	8	2	no	—
188	C₂×C₈×C₈₉	C₂×D₄	1	2	yes	—
189	C₂×C₈×C₈₉	C₂×D₄	1	2	yes	—
190	C₂×C₈×C₈₉	C₂×D₄	1	2	yes	—
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	C₄⋊C₄×C₈₉	—	2	1	no	—
197	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
198	C₂³×C₈₉	—	4	1	no	—
199	C₂²×D₈₉	#127	1	1	yes	characteristic
200	Q₈×C₈₉	—	4	2	no	—
201	Q₈×C₈₉	—	4	2	no	—
202	Q₈×C₈₉	—	4	2	no	—
203	D₄×C₈₉	—	4	2	no	—
204	D₄×C₈₉	—	4	2	no	—
205	D₄×C₈₉	—	4	2	no	—
206	C₂×C₄×C₈₉	—	4	1	no	—
207	C₂×C₄×C₈₉	—	4	1	no	—
208	C₂×C₄×C₈₉	—	4	1	no	—
209	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
210	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
211	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
212	C₂²⋊D₈₉	—	8	2	no	—
213	C₂×Dic₈₉	—	4	1	no	—
214	C₂×Dic₈₉	—	4	1	no	—
215	C₂×Dic₈₉	—	4	1	no	—
216	C₂×Dic₈₉	—	4	1	no	—
217	C₂×Dic₈₉	—	8	2	no	—
218	C₂×Dic₈₉	#127	1	1	yes	characteristic
219	C₂×Dic₈₉	#127	1	1	yes	characteristic
220	C₂×Dic₈₉	#127	1	1	yes	characteristic
221	C₄×D₈₉	—	2	2	no	—
222	C₄×D₈₉	—	2	2	no	—
223	C₄×D₈₉	—	8	2	no	—
224	C₄×D₈₉	—	8	2	no	—
225	C₄×D₈₉	C₂×SD₁₆	1	4	yes	—
226	Dic₁₇₈	—	4	2	no	—
227	Dic₁₇₈	—	4	2	no	—
228	Dic₁₇₈	—	4	2	no	—
229	Dic₁₇₈	—	4	2	no	—
230	Dic₁₇₈	—	8	2	no	—
231	Dic₁₇₈	—	8	2	no	—
232	C₈×C₈₉	—	2	2	no	—
233	C₈×C₈₉	—	2	2	no	—
234	C₈×C₈₉	C₂×SD₁₆	1	4	yes	—
235	#10623494	—	2	2	no	—
236	#10623494	C₂×SD₁₆	1	4	yes	—
237	#10623494	#137	1	4	yes	complemented
238	C₂²×C₈₉	—	8	1	no	—
239	C₂²×C₈₉	—	8	1	no	—
240	C₂²×C₈₉	—	8	1	no	—
241	C₂²×C₈₉	C₂×#127	1	1	yes	characteristic
242	C₂×D₈₉	—	2	1	no	—
243	C₂×D₈₉	—	2	1	no	—
244	C₂×D₈₉	#492	1	2	yes	—
245	C₄×C₈₉	—	8	1	no	—
246	C₄×C₈₉	—	8	1	no	—
247	C₄×C₈₉	—	8	1	no	—
248	C₄×C₈₉	C₂²×SD₁₆	1	2	yes	—
249	C₄×C₈₉	C₂×#137	1	2	yes	—
250	C₄×C₈₉	#577	1	2	yes	—
251	Dic₈₉	—	2	1	no	—
252	Dic₈₉	—	2	1	no	—
253	Dic₈₉	—	8	1	no	—
254	Dic₈₉	—	8	1	no	—
255	Dic₈₉	—	8	1	no	—
256	Dic₈₉	—	8	1	no	—
257	Dic₈₉	#492	1	2	yes	—
258	#19622	—	89	1	no	maximal, Sylow
259	C₂×C₈₉	—	16	1	no	—
260	C₂×C₈₉	C₂×#492	1	1	yes	characteristic
261	C₂×C₈₉	#3152	1	1	yes	characteristic
262	C₂×C₈₉	#3154	1	1	yes	characteristic
263	D₈₉	—	2	2	no	—
264	#3229	—	89	1	no	—
265	#3206	—	89	1	no	—
266	#3167	—	89	1	no	—
267	#3165	—	89	1	no	—
268	C₂×#498	—	89	1	no	—
269	#3152	—	89	1	no	—
270	#1716	—	89	1	no	—
271	#1716	—	89	1	no	—
272	#1714	—	89	1	no	—
273	#1714	D₈₉	1	1	yes	characteristic, complemented
274	#1707	—	89	1	no	—
275	#1707	—	89	1	no	—
276	#1705	—	89	1	no	—
277	#1705	—	89	1	no	—
278	C₈×M₁₆	—	89	1	no	—
279	C₈₉	#19622	1	1	yes	characteristic, complemented, Sylow
280	C₂×#137	—	178	2	no	—
281	#533	—	89	1	no	—
282	#532	—	89	1	no	—
283	C₂×C₄⋊Q₈	—	89	1	no	—
284	C₂×C₄⋊Q₈	—	89	1	no	—
285	#501	—	178	2	no	—
286	#500	—	89	1	no	—
287	#500	C₂×D₈₉	1	1	yes	characteristic
288	#498	—	89	1	no	—
289	#498	—	89	1	no	—
290	#498	—	89	1	no	—
291	#498	—	89	1	no	—
292	#498	—	89	1	no	—
293	#498	—	89	1	no	—
294	#498	—	89	1	no	—
295	#498	—	89	1	no	—
296	#498	—	178	2	no	—
297	#498	C₂×D₈₉	1	1	yes	characteristic
298	#497	—	178	2	no	—
299	#494	—	89	1	no	—
300	#494	—	89	1	no	—
301	#492	—	89	1	no	—
302	#492	—	89	1	no	—
303	#492	—	89	1	no	—
304	#492	C₂×D₈₉	1	1	yes	characteristic
305	#492	C₂×D₈₉	1	1	yes	characteristic
306	#487	—	89	1	no	—
307	#487	—	89	1	no	—
308	#487	—	89	1	no	—
309	#487	—	89	1	no	—
310	#487	C₂×D₈₉	1	1	yes	characteristic
311	#486	C₂×D₈₉	1	1	yes	characteristic
312	#483	—	178	2	no	—
313	#475	—	178	2	no	—
314	#465	—	178	2	no	—
315	#461	—	178	2	no	—
316	#448	—	178	2	no	—
317	C₄×SD₁₆	—	178	2	no	—
318	#431	—	89	1	no	—
319	#428	—	178	2	no	—
320	C₂×#106	—	178	2	no	—
321	C₄×M₁₆	—	89	1	no	—
322	C₂×C₄×C₈	—	89	1	no	—
323	#322	—	89	1	no	—
324	#322	C₂×D₈₉	1	1	yes	characteristic
325	C₈²	—	89	1	no	—
326	C₈²	—	89	1	no	—
327	C₂×#41	—	178	1	no	—
328	C₂²×Q₈	—	178	1	no	—
329	C₂²×Q₈	—	178	1	no	—
330	#137	—	356	8	no	—
331	C₂×Q₁₆	—	178	2	no	—
332	C₂×Q₁₆	—	178	2	no	—
333	C₂×SD₁₆	—	2	2	no	—
334	C₂×SD₁₆	—	2	2	no	—
335	C₂×SD₁₆	—	178	2	no	—
336	C₂×SD₁₆	—	178	2	no	—
337	C₂×SD₁₆	—	178	2	no	—
338	C₂×M₁₆	—	89	2	no	—
339	C₂²×C₈	—	89	2	no	—
340	C₄⋊Q₈	—	89	1	no	—
341	C₄⋊Q₈	—	89	1	no	—
342	C₄⋊Q₈	—	89	1	no	—
343	C₄⋊Q₈	—	89	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	C₂²×D₈₉	1	1	yes	characteristic
351	C₄⋊Q₈	C₂²×D₈₉	1	1	yes	characteristic
352	C₄⋊Q₈	C₂²×D₈₉	1	1	yes	characteristic
353	#127	C₂²×D₈₉	1	1	yes	characteristic
354	#125	—	178	1	no	—
355	#124	—	178	1	no	—
356	C₂²⋊Q₈	—	178	1	no	—
357	C₂²⋊Q₈	—	178	1	no	—
358	#121	—	178	1	no	—
359	#121	—	178	1	no	—
360	C₄×Q₈	—	178	1	no	—
361	C₄×Q₈	—	178	1	no	—
362	C₄×D₄	—	178	1	no	—
363	C₄×D₄	—	178	1	no	—
364	#117	—	178	1	no	—
365	C₂×C₄⋊C₄	—	178	1	no	—
366	C₂×C₄⋊C₄	—	178	1	no	—
367	C₂×C₄⋊C₄	—	178	1	no	—
368	C₂×C₄⋊C₄	—	178	1	no	—
369	C₂×C₄²	—	89	1	no	—
370	#107	—	2	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	#106	—	178	2	no	—
377	#106	—	178	2	no	—
378	#106	—	178	2	no	—
379	#106	—	178	2	no	—
380	#106	—	178	2	no	—
381	C₄⋊C₈	—	89	2	no	—
382	#103	—	2	2	no	—
383	#103	—	178	2	no	—
384	#103	—	178	2	no	—
385	#103	—	178	2	no	—
386	#103	—	178	2	no	—
387	#102	—	2	2	no	—
388	C₂²⋊C₈	—	89	2	no	—
389	#97	—	89	2	no	—
390	C₄×C₈	—	89	2	no	—
391	C₄×C₈	—	89	1	no	—
392	C₄×C₈	—	89	1	no	—
393	C₄×C₈	—	89	1	no	—
394	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
395	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
396	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
397	#41	—	356	4	no	—
398	C₂×Q₈	—	2	1	no	—
399	C₂×Q₈	—	2	1	no	—
400	C₂×Q₈	—	2	1	no	—
401	C₂×Q₈	—	356	1	no	—
402	C₂×Q₈	—	356	1	no	—
403	C₂×Q₈	—	356	4	no	—
404	C₂×Q₈	—	178	1	no	—
405	C₂×Q₈	—	178	1	no	—
406	C₂×Q₈	—	178	1	no	—
407	C₂×Q₈	—	178	1	no	—
408	C₂×Q₈	—	712	2	no	—
409	C₂×D₄	—	2	1	no	—
410	C₂×D₄	—	2	1	no	—
411	C₂×D₄	—	2	1	no	—
412	C₂×D₄	—	356	1	no	—
413	C₂²×C₄	—	89	1	no	—
414	C₂²×C₄	—	89	1	no	—
415	C₂²×C₄	—	89	1	no	—
416	C₂²×C₄	—	356	1	no	—
417	C₂²×C₄	—	356	1	no	—
418	C₂²×C₄	—	356	1	no	—
419	Q₁₆	—	356	4	no	—
420	Q₁₆	—	356	4	no	—
421	SD₁₆	—	4	4	no	—
422	SD₁₆	—	8	2	no	—
423	SD₁₆	—	356	4	no	—
424	SD₁₆	—	356	4	no	—
425	SD₁₆	—	712	2	no	—
426	M₁₆	—	89	8	no	—
427	C₂×C₈	—	89	2	no	—
428	C₂×C₈	—	89	2	no	—
429	C₂×C₈	—	89	2	no	—
430	C₂×C₈	—	178	4	no	—
431	C₂×C₈	D₄×D₈₉	1	2	yes	—
432	C₂×C₈	D₄×D₈₉	1	2	yes	—
433	C₂×C₈	D₄×D₈₉	1	2	yes	—
434	C₄⋊C₄	—	2	1	no	—
435	C₄⋊C₄	—	2	1	no	—
436	C₄⋊C₄	—	2	1	no	—
437	C₄⋊C₄	—	2	1	no	—
438	C₄⋊C₄	—	2	1	no	—
439	C₄⋊C₄	—	2	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	—	356	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	C₄⋊C₄	—	178	1	no	—
454	C₂²⋊C₄	—	356	1	no	—
455	C₂²⋊C₄	—	356	1	no	—
456	C₂²⋊C₄	—	356	1	no	—
457	C₄²	—	89	1	no	—
458	C₄²	—	89	1	no	—
459	C₄²	—	89	1	no	—
460	C₄²	—	356	1	no	—
461	C₄²	C₂³×D₈₉	1	1	yes	characteristic
462	C₂³	—	4	1	no	—
463	C₂³	—	89	1	no	—
464	Q₈	—	4	2	no	—
465	Q₈	—	4	2	no	—
466	Q₈	—	4	2	no	—
467	Q₈	—	356	2	no	—
468	Q₈	—	356	2	no	—
469	Q₈	—	356	2	no	—
470	Q₈	—	356	2	no	—
471	Q₈	—	712	2	no	—
472	Q₈	—	712	2	no	—
473	D₄	—	4	2	no	—
474	D₄	—	4	2	no	—
475	D₄	—	4	2	no	—
476	D₄	—	712	2	no	—
477	C₂×C₄	—	4	1	no	—
478	C₂×C₄	—	4	1	no	—
479	C₂×C₄	—	4	1	no	—
480	C₂×C₄	—	89	1	no	—
481	C₂×C₄	—	89	4	no	—
482	C₂×C₄	—	89	1	no	—
483	C₂×C₄	—	89	1	no	—
484	C₂×C₄	—	356	1	no	—
485	C₂×C₄	—	356	1	no	—
486	C₂×C₄	—	356	1	no	—
487	C₂×C₄	—	356	1	no	—
488	C₂×C₄	—	178	2	no	—
489	C₂×C₄	—	178	2	no	—
490	C₂×C₄	—	712	2	no	—
491	C₂×C₄	—	712	2	no	—
492	C₂×C₄	—	712	2	no	—
493	C₂×C₄	C₂×D₄×D₈₉	1	1	yes	characteristic
494	C₂×C₄	C₂×D₄×D₈₉	1	1	yes	characteristic
495	C₂×C₄	C₂×D₄×D₈₉	1	1	yes	characteristic
496	C₈	—	2	2	no	—
497	C₈	—	2	2	no	—
498	C₈	—	89	4	no	—
499	C₈	—	89	4	no	—
500	C₈	—	178	2	no	—
501	C₈	SD₁₆×D₈₉	1	4	yes	—
502	C₂²	—	8	1	no	—
503	C₂²	—	8	1	no	—
504	C₂²	—	8	1	no	—
505	C₂²	—	89	2	no	—
506	C₂²	—	178	1	no	—
507	C₂²	—	178	1	no	—
508	C₂²	#127×D₈₉	1	1	yes	characteristic
509	C₄	—	8	1	no	—
510	C₄	—	8	1	no	—
511	C₄	—	8	1	no	—
512	C₄	—	89	2	no	—
513	C₄	—	178	1	no	—
514	C₄	—	178	1	no	—
515	C₄	—	712	1	no	—
516	C₄	—	712	1	no	—
517	C₄	—	712	1	no	—
518	C₄	—	712	1	no	—
519	C₄	C₂×SD₁₆×D₈₉	1	2	yes	—
520	C₄	#137×D₈₉	1	2	yes	—
521	C₄	#19152408	1	2	yes	—
522	C₂	—	16	1	no	—
523	C₂	—	178	2	no	—
524	C₂	#492×D₈₉	1	1	yes	characteristic
525	C₂	#26030708	1	1	yes	characteristic
526	C₂	#26030725	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#127×D₈₉
commutator, cosocle	C₄²×C₈₉	C₂⁴
Frattini	C₄²	C₂³×D₈₉
Fitting	C₈₉×#1714	C₂
socle	C₂²×C₈₉	C₂×#127
prime radical	#19152146	C₂²
hypercenter	#1714	D₈₉
hypocenter	C₈₉	#19622
LCS	G ▷ C₄²×C₈₉ ▷ C₂²×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #1714

Complements

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

N	H ≅ G/N	type
1. #26031392	C₂	semidirect
4. #26030795	C₂	semidirect
5. #498×D₈₉	C₂	semidirect
7. #26019885	C₂	semidirect
8. #26019884	C₂	semidirect
9. #26019873	C₂	semidirect
10. #26019850	C₂	semidirect
11. #26019848	C₂	semidirect
12. #26019838	C₂	semidirect
13. #26019838	C₂	semidirect
14. #26018531	C₂	semidirect
15. C₈₉×#1714	C₂	semidirect
154. #13083557	SD₁₆	semidirect
237. #10623494	#137	semidirect
273. #1714	D₈₉	semidirect
279. C₈₉	#19622	semidirect

Maximal subgroups

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

subgroup	index
#26031392	2
#26031173	2
#26030810	2
#26030795	2
#498×D₈₉	2
#26030706	2
#26019885	2
#26019884	2
#26019873	2
#26019850	2
#26019848	2
#26019838	2
#26018531	2
C₈₉×#1714	2
#19622	89