Subgroups — #35375016

Order 21248.

594 conjugacy classes of subgroups.

The subgroup lattice has 564 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#24918067	C₂	1	1	yes	maximal, characteristic
2	#24916440	C₂	1	1	yes	maximal, characteristic
3	#24916392	C₂	1	1	yes	maximal, characteristic, complemented
4	#24906360	C₂	1	1	yes	maximal, characteristic, complemented
5	#24906357	C₂	1	1	yes	maximal, characteristic, complemented
6	#24906352	C₂	1	1	yes	maximal, characteristic, complemented
7	#24906350	C₂	1	1	yes	maximal, characteristic, complemented
8	#24906280	C₂	1	1	yes	maximal, characteristic, complemented
9	#24906277	C₂	1	1	yes	maximal, characteristic, complemented
10	#24906273	C₂	1	1	yes	maximal, characteristic, complemented
11	#24906227	C₂	1	1	yes	maximal, characteristic, complemented
12	#24905934	C₂	1	1	yes	maximal, characteristic, complemented
13	#24905927	C₂	1	1	yes	maximal, characteristic
14	#24905742	C₂	1	1	yes	maximal, characteristic, complemented
15	C₈₃×#1579	C₂	1	1	yes	maximal, characteristic, complemented
16	#19128255	C₂²	1	1	yes	characteristic
17	#19128238	C₂²	1	1	yes	characteristic
18	#19128109	C₄	1	1	yes	characteristic
19	#19128094	C₄	1	1	yes	characteristic
20	#19128068	C₄	1	1	yes	characteristic
21	#19128062	C₄	1	1	yes	characteristic
22	#19127958	C₄	1	1	yes	characteristic
23	#19127956	C₄	1	1	yes	characteristic
24	#19127950	C₄	1	1	yes	characteristic
25	#19127948	C₄	1	1	yes	characteristic
26	#19127832	C₂²	1	1	yes	characteristic
27	#19127832	C₂²	1	1	yes	characteristic
28	#19127830	—	2	1	no	—
29	#19127828	C₂²	1	1	yes	characteristic
30	C₈×Dic₁₆₆	—	2	1	no	—
31	C₈×Dic₁₆₆	C₂²	1	1	yes	characteristic
32	C₄×#13050580	C₂²	1	1	yes	characteristic
33	C₄×#13050579	C₂²	1	1	yes	characteristic
34	C₄×#13050577	C₂²	1	1	yes	characteristic
35	#19127778	C₂²	1	1	yes	characteristic
36	#19127771	—	2	1	no	—
37	C₈×D₃₃₂	—	2	1	no	—
38	C₈×D₃₃₂	C₂²	1	1	yes	characteristic
39	#19127761	—	2	1	no	—
40	#19127757	C₂²	1	1	yes	characteristic
41	#19127752	C₂²	1	1	yes	characteristic
42	#19127726	—	2	1	no	—
43	#19127723	C₂²	1	1	yes	characteristic
44	#19127655	—	2	1	no	—
45	#19127655	—	2	1	no	—
46	C₄×#13050573	C₂²	1	1	yes	characteristic
47	C₄×C₈×D₈₃	C₂²	1	1	yes	characteristic
48	#19127454	C₂²	1	1	yes	characteristic
49	#19127453	C₂²	1	1	yes	characteristic
50	#19127451	C₂²	1	1	yes	characteristic
51	#19127433	C₂²	1	1	yes	characteristic
52	Q₈⋊(C₈₃⋊C₈)	C₂²	1	1	yes	characteristic
53	Q₈⋊(C₈₃⋊C₈)	C₂²	1	1	yes	characteristic
54	#19127431	C₂²	1	1	yes	characteristic
55	#19127430	C₂²	1	1	yes	characteristic
56	#19127428	C₂²	1	1	yes	characteristic
57	#19127423	C₂²	1	1	yes	characteristic
58	C₈×C₈₃⋊C₈	C₂²	1	1	yes	characteristic
59	C₈×C₈₃⋊C₈	C₂²	1	1	yes	characteristic
60	C₈×Q₈×C₈₃	C₂²	1	1	yes	characteristic
61	C₈×Q₈×C₈₃	C₂²	1	1	yes	characteristic
62	C₄×Q₁₆×C₈₃	C₂²	1	1	yes	characteristic
63	#334×C₈₃	C₂²	1	1	yes	characteristic
64	Q₈⋊C₈×C₈₃	C₂²	1	1	yes	characteristic
65	Q₈⋊C₈×C₈₃	C₂²	1	1	yes	characteristic
66	#322×C₈₃	C₂²	1	1	yes	characteristic
67	C₂×#13050580	C₂×C₄	1	1	yes	characteristic
68	C₂×#13050579	C₂×C₄	1	1	yes	characteristic
69	C₂×#13050577	C₂×C₄	1	1	yes	characteristic
70	C₂×#13050573	—	2	1	no	—
71	C₂×#13050573	—	2	1	no	—
72	C₂×#13050573	C₂×C₄	1	1	yes	characteristic
73	C₂×#13050573	C₂×C₄	1	1	yes	characteristic
74	C₂×C₈×D₈₃	—	2	1	no	—
75	C₂×C₈×D₈₃	D₄	1	1	yes	characteristic
76	C₂×C₈×D₈₃	D₄	1	1	yes	characteristic
77	#14581791	C₂×C₄	1	1	yes	characteristic
78	#14581790	C₂×C₄	1	1	yes	characteristic
79	#14581787	—	2	1	no	—
80	#14581783	C₂×C₄	1	1	yes	characteristic
81	#14581782	—	2	1	no	—
82	#14581781	C₂×C₄	1	1	yes	characteristic
83	#14581777	—	2	1	no	—
84	#14581772	C₂×C₄	1	1	yes	characteristic
85	#14581770	—	2	1	no	—
86	#14581768	C₂×C₄	1	1	yes	characteristic
87	#14581768	C₂×C₄	1	1	yes	characteristic
88	#14581767	C₂×C₄	1	1	yes	characteristic
89	C₄×Dic₁₆₆	—	2	1	no	—
90	C₄×Dic₁₆₆	C₂³	1	1	yes	characteristic
91	C₄×D₃₃₂	—	2	1	no	—
92	C₄×D₃₃₂	C₂³	1	1	yes	characteristic
93	#14581749	—	2	1	no	—
94	#14581749	—	2	1	no	—
95	C₄²×D₈₃	C₂³	1	1	yes	characteristic
96	#14581725	C₂×C₄	1	1	yes	characteristic
97	#14581724	C₂×C₄	1	1	yes	characteristic
98	#14581723	C₂×C₄	1	1	yes	characteristic
99	C₄⋊(C₈₃⋊C₈)	—	2	1	no	—
100	C₄⋊(C₈₃⋊C₈)	—	2	1	no	—
101	C₄⋊(C₈₃⋊C₈)	C₂³	1	1	yes	characteristic
102	C₄⋊(C₈₃⋊C₈)	C₂³	1	1	yes	characteristic
103	Dic₈₃⋊C₈	—	2	1	no	—
104	Dic₈₃⋊C₈	—	2	1	no	—
105	Dic₈₃⋊C₈	—	2	1	no	—
106	Dic₈₃⋊C₈	—	2	1	no	—
107	#14581717	C₂×C₄	1	1	yes	characteristic
108	#14581716	C₂×C₄	1	1	yes	characteristic
109	#14581716	C₂×C₄	1	1	yes	characteristic
110	#14581715	C₂×C₄	1	1	yes	characteristic
111	#14581714	C₂×C₄	1	1	yes	characteristic
112	#14581712	C₂×C₄	1	1	yes	characteristic
113	(C₂×D₈₃)⋊C₈	—	2	1	no	—
114	(C₂×D₈₃)⋊C₈	—	2	1	no	—
115	(C₂×D₈₃)⋊C₈	—	2	1	no	—
116	(C₂×D₈₃)⋊C₈	—	2	1	no	—
117	#14581703	—	2	1	no	—
118	#14581703	—	2	1	no	—
119	#14581702	—	2	1	no	—
120	#14581702	—	2	1	no	—
121	#14581702	C₂×C₄	1	1	yes	characteristic
122	#14581702	C₂×C₄	1	1	yes	characteristic
123	C₄×C₈₃⋊C₈	C₂³	1	1	yes	characteristic
124	C₄×C₈₃⋊C₈	C₂³	1	1	yes	characteristic
125	C₄×C₈₃⋊C₈	C₂³	1	1	yes	characteristic
126	C₈×Dic₈₃	—	2	1	no	—
127	C₈×Dic₈₃	D₄	1	1	yes	characteristic
128	C₈×Dic₈₃	D₄	1	1	yes	characteristic
129	C₂×Q₁₆×C₈₃	C₂×C₄	1	1	yes	characteristic
130	C₄×Q₈×C₈₃	C₂³	1	1	yes	characteristic
131	C₄×Q₈×C₈₃	C₂³	1	1	yes	characteristic
132	#107×C₈₃	C₂×C₄	1	1	yes	characteristic
133	C₄⋊C₈×C₈₃	—	2	1	no	—
134	C₄⋊C₈×C₈₃	—	2	1	no	—
135	C₄⋊C₈×C₈₃	C₂³	1	1	yes	characteristic
136	C₄⋊C₈×C₈₃	C₂³	1	1	yes	characteristic
137	#103×C₈₃	C₂×C₄	1	1	yes	characteristic
138	#103×C₈₃	C₂×C₄	1	1	yes	characteristic
139	C₄×C₈×C₈₃	—	2	1	no	—
140	C₄×C₈×C₈₃	—	2	1	no	—
141	C₄×C₈×C₈₃	C₂³	1	1	yes	characteristic
142	C₄×C₈×C₈₃	C₂³	1	1	yes	characteristic
143	C₄×C₈×C₈₃	C₂³	1	1	yes	characteristic
144	C₂×Dic₁₆₆	—	2	1	no	—
145	C₂×Dic₁₆₆	C₂²×C₄	1	1	yes	characteristic
146	C₂×D₃₃₂	—	2	1	no	—
147	C₂×D₃₃₂	C₂²×C₄	1	1	yes	characteristic
148	C₂×C₄×D₈₃	—	2	1	no	—
149	C₂×C₄×D₈₃	C₂²×C₄	1	1	yes	characteristic
150	C₂×C₄×D₈₃	C₂×D₄	1	1	yes	characteristic
151	C₂×C₄×D₈₃	#41	1	1	yes	characteristic
152	#13050580	—	2	2	no	—
153	#13050579	—	2	2	no	—
154	#13050577	—	2	2	no	—
155	#13050573	—	2	2	no	—
156	#13050573	—	2	2	no	—
157	#13050573	—	4	2	no	—
158	#13050573	—	4	2	no	—
159	C₂×C₈₃⋊C₈	—	2	1	no	—
160	C₂×C₈₃⋊C₈	—	2	1	no	—
161	C₂×C₈₃⋊C₈	—	2	1	no	—
162	C₂×C₈₃⋊C₈	C₂²×C₄	1	1	yes	characteristic
163	C₂×C₈₃⋊C₈	C₂²×C₄	1	1	yes	characteristic
164	C₂×C₈₃⋊C₈	C₂×D₄	1	1	yes	characteristic
165	C₂×C₈₃⋊C₈	C₂×D₄	1	1	yes	characteristic
166	C₈×D₈₃	—	2	2	no	—
167	C₈×D₈₃	—	4	1	no	—
168	C₈×D₈₃	—	4	2	no	—
169	C₄⋊Dic₈₃	—	2	1	no	—
170	C₄⋊Dic₈₃	—	2	1	no	—
171	C₄⋊Dic₈₃	C₂²×C₄	1	1	yes	characteristic
172	C₄⋊Dic₈₃	C₂²×C₄	1	1	yes	characteristic
173	Dic₈₃⋊C₄	—	2	1	no	—
174	Dic₈₃⋊C₄	—	2	1	no	—
175	Dic₈₃⋊C₄	—	2	1	no	—
176	Dic₈₃⋊C₄	—	2	1	no	—
177	Dic₈₃⋊C₄	—	2	1	no	—
178	Dic₈₃⋊C₄	—	2	1	no	—
179	Dic₈₃⋊C₄	—	2	1	no	—
180	(C₂×D₈₃)⋊C₄	—	2	1	no	—
181	(C₂×D₈₃)⋊C₄	—	2	1	no	—
182	(C₂×D₈₃)⋊C₄	—	2	1	no	—
183	(C₂×D₈₃)⋊C₄	—	2	1	no	—
184	(C₂×D₈₃)⋊C₄	—	2	1	no	—
185	(C₂×D₈₃)⋊C₄	—	2	1	no	—
186	(C₂×D₈₃)⋊C₄	—	2	1	no	—
187	C₄×Dic₈₃	—	2	1	no	—
188	C₄×Dic₈₃	C₂²×C₄	1	1	yes	characteristic
189	C₄×Dic₈₃	C₂×D₄	1	1	yes	characteristic
190	C₄×Dic₈₃	#41	1	1	yes	characteristic
191	C₂×Q₈×C₈₃	C₂²×C₄	1	1	yes	characteristic
192	C₂×Q₈×C₈₃	C₂²×C₄	1	1	yes	characteristic
193	Q₁₆×C₈₃	—	2	2	no	—
194	C₂×C₈×C₈₃	—	2	1	no	—
195	C₂×C₈×C₈₃	—	2	1	no	—
196	C₂×C₈×C₈₃	—	2	1	no	—
197	C₂×C₈×C₈₃	C₂²×C₄	1	1	yes	characteristic
198	C₂×C₈×C₈₃	C₂²×C₄	1	1	yes	characteristic
199	C₂×C₈×C₈₃	C₂×D₄	1	1	yes	characteristic
200	C₂×C₈×C₈₃	C₂×D₄	1	1	yes	characteristic
201	C₄⋊C₄×C₈₃	—	2	1	no	—
202	C₄⋊C₄×C₈₃	—	2	1	no	—
203	C₄⋊C₄×C₈₃	C₂²×C₄	1	1	yes	characteristic
204	C₄⋊C₄×C₈₃	C₂²×C₄	1	1	yes	characteristic
205	C₄²×C₈₃	—	2	1	no	—
206	C₄²×C₈₃	—	2	1	no	—
207	C₄²×C₈₃	C₂⁴	1	1	yes	characteristic
208	C₂²×D₈₃	—	2	1	no	—
209	C₂²×D₈₃	C₄×D₄	1	1	yes	characteristic
210	Q₈×C₈₃	—	2	1	no	—
211	Q₈×C₈₃	—	2	1	no	—
212	Q₈×C₈₃	—	2	1	no	—
213	Q₈×C₈₃	—	2	1	no	—
214	C₂×C₄×C₈₃	—	2	1	no	—
215	C₂×C₄×C₈₃	—	2	1	no	—
216	C₂×C₄×C₈₃	—	2	1	no	—
217	C₂×C₄×C₈₃	—	2	1	no	—
218	C₂×C₄×C₈₃	C₂³×C₄	1	1	yes	characteristic
219	C₂×C₄×C₈₃	C₂²×D₄	1	1	yes	characteristic
220	C₂×C₄×C₈₃	C₂×#41	1	1	yes	characteristic
221	C₂×Dic₈₃	—	2	1	no	—
222	C₂×Dic₈₃	—	2	1	no	—
223	C₂×Dic₈₃	—	2	1	no	—
224	C₂×Dic₈₃	C₄×D₄	1	1	yes	characteristic
225	C₂×Dic₈₃	C₄×D₄	1	1	yes	characteristic
226	C₂×Dic₈₃	C₄×D₄	1	1	yes	characteristic
227	D₃₃₂	—	2	1	no	—
228	D₃₃₂	—	2	1	no	—
229	D₃₃₂	—	4	2	no	—
230	C₄×D₈₃	—	2	1	no	—
231	C₄×D₈₃	—	2	1	no	—
232	C₄×D₈₃	—	2	1	no	—
233	C₄×D₈₃	—	2	1	no	—
234	C₄×D₈₃	—	4	1	no	—
235	C₄×D₈₃	—	4	1	no	—
236	C₄×D₈₃	—	4	1	no	—
237	Dic₁₆₆	—	2	1	no	—
238	Dic₁₆₆	—	2	1	no	—
239	Dic₁₆₆	—	4	2	no	—
240	C₈×C₈₃	—	2	1	no	—
241	C₈×C₈₃	—	2	1	no	—
242	C₈×C₈₃	—	2	1	no	—
243	C₈×C₈₃	—	4	1	no	—
244	C₈×C₈₃	—	4	1	no	—
245	C₈×C₈₃	—	4	1	no	—
246	C₈×C₈₃	#131	1	2	yes	—
247	C₈₃⋊C₈	—	2	1	no	—
248	C₈₃⋊C₈	—	2	1	no	—
249	C₈₃⋊C₈	—	4	1	no	—
250	C₈₃⋊C₈	—	4	1	no	—
251	C₈₃⋊C₈	—	4	1	no	—
252	C₈₃⋊C₈	#131	1	2	yes	—
253	C₈₃⋊C₈	#137	1	2	yes	—
254	C₂²×C₈₃	C₂×C₄×D₄	1	1	yes	characteristic
255	C₂×D₈₃	—	2	1	no	—
256	C₂×D₈₃	—	2	1	no	—
257	C₂×D₈₃	—	2	1	no	—
258	C₂×D₈₃	—	4	1	no	—
259	C₂×D₈₃	—	4	1	no	—
260	C₂×D₈₃	—	4	1	no	—
261	C₄×C₈₃	—	2	1	no	—
262	C₄×C₈₃	—	4	1	no	—
263	C₄×C₈₃	—	4	1	no	—
264	C₄×C₈₃	—	4	1	no	—
265	C₄×C₈₃	—	4	1	no	—
266	C₄×C₈₃	C₂×#131	1	1	yes	characteristic
267	C₄×C₈₃	C₂×#131	1	1	yes	characteristic
268	C₄×C₈₃	C₂×#137	1	1	yes	characteristic
269	C₄×C₈₃	#575	1	1	yes	characteristic
270	Dic₈₃	—	2	1	no	—
271	Dic₈₃	—	2	1	no	—
272	Dic₈₃	—	2	1	no	—
273	Dic₈₃	—	4	1	no	—
274	Dic₈₃	—	4	1	no	—
275	Dic₈₃	—	4	1	no	—
276	#17967	—	83	1	no	maximal, Sylow
277	C₂×C₈₃	#2931	1	1	yes	characteristic
278	C₂×C₈₃	C₄×#137	1	1	yes	characteristic
279	C₂×C₈₃	#2955	1	1	yes	characteristic
280	D₈₃	—	4	1	no	—
281	D₈₃	—	8	1	no	—
282	#3172	—	83	1	no	—
283	#2966	—	83	1	no	—
284	#2960	—	83	1	no	—
285	#1591	—	83	1	no	—
286	#1591	—	83	1	no	—
287	#1590	—	83	1	no	—
288	#1590	—	83	1	no	—
289	#1579	—	83	1	no	—
290	#1579	D₈₃	1	1	yes	characteristic, complemented
291	SD₁₆⋊C₈	—	83	1	no	—
292	SD₁₆⋊C₈	—	83	1	no	—
293	#1569	—	83	1	no	—
294	#1497	—	83	1	no	—
295	#1495	—	83	1	no	—
296	C₈×M₁₆	—	83	1	no	—
297	C₈₃	#17967	1	1	yes	characteristic, complemented, Sylow
298	#533	—	83	1	no	—
299	#529	—	83	1	no	—
300	#501	—	83	1	no	—
301	#497	—	83	1	no	—
302	#491	—	83	1	no	—
303	#489	—	83	1	no	—
304	#470	—	83	1	no	—
305	#470	—	83	1	no	—
306	#468	—	83	1	no	—
307	#468	—	83	1	no	—
308	#446	—	83	1	no	—
309	#446	—	83	1	no	—
310	#446	—	83	1	no	—
311	#446	—	166	1	no	—
312	C₈×Q₈	—	83	1	no	—
313	C₈×Q₈	—	166	1	no	—
314	C₈×Q₈	C₂×D₈₃	1	1	yes	characteristic
315	C₈×Q₈	C₂×D₈₃	1	1	yes	characteristic
316	C₄×Q₁₆	—	83	1	no	—
317	C₄×Q₁₆	C₂×D₈₃	1	1	yes	characteristic
318	C₄×SD₁₆	—	83	1	no	—
319	C₄×SD₁₆	—	83	1	no	—
320	#436	—	83	1	no	—
321	#435	—	166	1	no	—
322	C₈×D₄	—	83	1	no	—
323	C₈×D₄	—	166	1	no	—
324	#433	—	166	1	no	—
325	#432	—	83	1	no	—
326	#431	—	83	1	no	—
327	#424	—	166	1	no	—
328	#423	—	83	1	no	—
329	#405	—	166	1	no	—
330	#405	—	166	1	no	—
331	C₄×M₁₆	—	83	1	no	—
332	C₂×C₄×C₈	—	83	1	no	—
333	#335	—	83	1	no	—
334	#335	—	83	1	no	—
335	#334	—	83	1	no	—
336	#334	C₂×D₈₃	1	1	yes	characteristic
337	Q₈⋊C₈	—	83	1	no	—
338	Q₈⋊C₈	—	83	1	no	—
339	Q₈⋊C₈	—	83	1	no	—
340	Q₈⋊C₈	—	83	1	no	—
341	Q₈⋊C₈	C₂×D₈₃	1	1	yes	characteristic
342	Q₈⋊C₈	C₂×D₈₃	1	1	yes	characteristic
343	D₄⋊C₈	—	83	1	no	—
344	D₄⋊C₈	—	83	1	no	—
345	#322	—	83	1	no	—
346	#322	C₂×D₈₃	1	1	yes	characteristic
347	C₈²	—	83	1	no	—
348	C₈²	—	83	1	no	—
349	C₂×Q₁₆	—	83	1	no	—
350	C₂×Q₁₆	C₄×D₈₃	1	1	yes	characteristic
351	C₂×SD₁₆	—	83	1	no	—
352	C₂×SD₁₆	—	83	1	no	—
353	C₂×M₁₆	—	83	1	no	—
354	C₂×M₁₆	—	83	1	no	—
355	C₂×M₁₆	—	166	1	no	—
356	C₂×M₁₆	—	166	1	no	—
357	C₂²×C₈	—	83	1	no	—
358	C₂²×C₈	—	83	1	no	—
359	C₂²×C₈	—	166	1	no	—
360	C₄⋊Q₈	—	83	1	no	—
361	C₄⋊Q₈	—	83	1	no	—
362	#126	—	166	1	no	—
363	#125	—	83	1	no	—
364	#125	—	166	1	no	—
365	#124	—	83	1	no	—
366	#123	—	166	1	no	—
367	C₂²⋊Q₈	—	83	1	no	—
368	C₂²⋊Q₈	—	83	1	no	—
369	C₂²⋊Q₈	—	83	1	no	—
370	C₂²⋊Q₈	—	166	1	no	—
371	#121	—	83	1	no	—
372	C₄×Q₈	—	83	1	no	—
373	C₄×Q₈	—	166	1	no	—
374	C₄×Q₈	C₂²×D₈₃	1	1	yes	characteristic
375	C₄×Q₈	C₂²×D₈₃	1	1	yes	characteristic
376	C₄×D₄	—	83	1	no	—
377	C₄×D₄	—	166	1	no	—
378	#117	—	166	1	no	—
379	#117	—	166	1	no	—
380	C₂×C₄²	—	83	1	no	—
381	#107	—	83	1	no	—
382	#107	C₄×D₈₃	1	1	yes	characteristic
383	#106	—	83	1	no	—
384	#106	—	83	1	no	—
385	C₄⋊C₈	—	2	1	no	—
386	C₄⋊C₈	—	2	1	no	—
387	C₄⋊C₈	—	83	1	no	—
388	C₄⋊C₈	—	83	1	no	—
389	C₄⋊C₈	—	166	1	no	—
390	C₄⋊C₈	—	166	1	no	—
391	C₄⋊C₈	—	166	1	no	—
392	C₄⋊C₈	—	166	1	no	—
393	C₄⋊C₈	—	166	1	no	—
394	C₄⋊C₈	—	166	1	no	—
395	C₄⋊C₈	C₂²×D₈₃	1	1	yes	characteristic
396	C₄⋊C₈	C₂²×D₈₃	1	1	yes	characteristic
397	#103	—	83	1	no	—
398	#103	—	83	1	no	—
399	#103	—	83	1	no	—
400	#103	—	83	1	no	—
401	#103	C₄×D₈₃	1	1	yes	characteristic
402	#103	C₄×D₈₃	1	1	yes	characteristic
403	#102	—	83	1	no	—
404	#102	—	83	1	no	—
405	C₂²⋊C₈	—	166	1	no	—
406	C₂²⋊C₈	—	166	1	no	—
407	C₂²⋊C₈	—	166	1	no	—
408	C₂²⋊C₈	—	166	1	no	—
409	#97	—	83	1	no	—
410	#97	—	83	1	no	—
411	#97	—	166	1	no	—
412	#97	—	166	1	no	—
413	#97	—	166	1	no	—
414	#97	—	166	1	no	—
415	C₄×C₈	—	2	1	no	—
416	C₄×C₈	—	2	1	no	—
417	C₄×C₈	—	83	1	no	—
418	C₄×C₈	—	83	1	no	—
419	C₄×C₈	—	83	1	no	—
420	C₄×C₈	—	83	1	no	—
421	C₄×C₈	—	83	1	no	—
422	C₄×C₈	—	166	1	no	—
423	C₄×C₈	C₂²×D₈₃	1	1	yes	characteristic
424	C₄×C₈	C₂²×D₈₃	1	1	yes	characteristic
425	C₄×C₈	C₂²×D₈₃	1	1	yes	characteristic
426	C₂×Q₈	—	83	1	no	—
427	C₂×Q₈	—	166	1	no	—
428	C₂×Q₈	C₂×C₄×D₈₃	1	1	yes	characteristic
429	C₂×Q₈	C₂×C₄×D₈₃	1	1	yes	characteristic
430	C₂×D₄	—	83	1	no	—
431	C₂×D₄	—	166	1	no	—
432	C₂²×C₄	—	83	1	no	—
433	C₂²×C₄	—	83	1	no	—
434	C₂²×C₄	—	83	1	no	—
435	C₂²×C₄	—	166	1	no	—
436	Q₁₆	—	2	2	no	—
437	Q₁₆	—	166	2	no	—
438	SD₁₆	—	166	2	no	—
439	SD₁₆	—	166	2	no	—
440	M₁₆	—	332	2	no	—
441	M₁₆	—	332	2	no	—
442	M₁₆	—	166	2	no	—
443	M₁₆	—	166	2	no	—
444	C₂×C₈	—	2	1	no	—
445	C₂×C₈	—	2	1	no	—
446	C₂×C₈	—	2	1	no	—
447	C₂×C₈	—	332	2	no	—
448	C₂×C₈	—	332	1	no	—
449	C₂×C₈	—	83	1	no	—
450	C₂×C₈	—	83	1	no	—
451	C₂×C₈	—	83	1	no	—
452	C₂×C₈	—	83	1	no	—
453	C₂×C₈	—	166	2	no	—
454	C₂×C₈	—	166	1	no	—
455	C₂×C₈	—	166	1	no	—
456	C₂×C₈	—	166	1	no	—
457	C₂×C₈	C₂×C₄×D₈₃	1	1	yes	characteristic
458	C₂×C₈	C₂×C₄×D₈₃	1	1	yes	characteristic
459	C₂×C₈	D₄×D₈₃	1	1	yes	characteristic
460	C₂×C₈	D₄×D₈₃	1	1	yes	characteristic
461	C₄⋊C₄	—	2	1	no	—
462	C₄⋊C₄	—	2	1	no	—
463	C₄⋊C₄	—	83	1	no	—
464	C₄⋊C₄	—	83	1	no	—
465	C₄⋊C₄	—	166	1	no	—
466	C₄⋊C₄	—	166	1	no	—
467	C₄⋊C₄	—	166	1	no	—
468	C₄⋊C₄	—	166	1	no	—
469	C₄⋊C₄	—	166	1	no	—
470	C₄⋊C₄	—	166	1	no	—
471	C₄⋊C₄	—	166	1	no	—
472	C₄⋊C₄	—	166	1	no	—
473	C₄⋊C₄	—	166	1	no	—
474	C₄⋊C₄	C₂×C₄×D₈₃	1	1	yes	characteristic
475	C₄⋊C₄	C₂×C₄×D₈₃	1	1	yes	characteristic
476	C₂²⋊C₄	—	166	1	no	—
477	C₂²⋊C₄	—	166	1	no	—
478	C₂²⋊C₄	—	166	1	no	—
479	C₂²⋊C₄	—	166	1	no	—
480	C₂²⋊C₄	—	166	1	no	—
481	C₂²⋊C₄	—	166	1	no	—
482	C₂²⋊C₄	—	166	1	no	—
483	C₄²	—	2	1	no	—
484	C₄²	—	2	1	no	—
485	C₄²	—	83	1	no	—
486	C₄²	—	83	1	no	—
487	C₄²	—	83	1	no	—
488	C₄²	—	166	1	no	—
489	C₄²	C₂³×D₈₃	1	1	yes	characteristic
490	C₂³	—	83	1	no	—
491	C₂³	—	166	1	no	—
492	Q₈	—	2	1	no	—
493	Q₈	—	2	1	no	—
494	Q₈	—	2	1	no	—
495	Q₈	—	2	1	no	—
496	Q₈	—	332	2	no	—
497	Q₈	—	166	1	no	—
498	Q₈	—	166	1	no	—
499	D₄	—	332	2	no	—
500	D₄	—	166	1	no	—
501	D₄	—	166	1	no	—
502	C₂×C₄	—	2	1	no	—
503	C₂×C₄	—	2	1	no	—
504	C₂×C₄	—	2	1	no	—
505	C₂×C₄	—	2	1	no	—
506	C₂×C₄	—	332	1	no	—
507	C₂×C₄	—	332	1	no	—
508	C₂×C₄	—	332	1	no	—
509	C₂×C₄	—	83	1	no	—
510	C₂×C₄	—	83	1	no	—
511	C₂×C₄	—	83	1	no	—
512	C₂×C₄	—	166	1	no	—
513	C₂×C₄	—	166	1	no	—
514	C₂×C₄	—	166	1	no	—
515	C₂×C₄	—	166	1	no	—
516	C₂×C₄	—	166	1	no	—
517	C₂×C₄	—	166	1	no	—
518	C₂×C₄	—	166	1	no	—
519	C₂×C₄	C₂²×C₄×D₈₃	1	1	yes	characteristic
520	C₂×C₄	C₂×D₄×D₈₃	1	1	yes	characteristic
521	C₂×C₄	#41×D₈₃	1	1	yes	characteristic
522	C₈	—	2	1	no	—
523	C₈	—	2	1	no	—
524	C₈	—	2	1	no	—
525	C₈	—	4	1	no	—
526	C₈	—	4	1	no	—
527	C₈	—	4	1	no	—
528	C₈	—	332	1	no	—
529	C₈	—	332	1	no	—
530	C₈	—	332	1	no	—
531	C₈	—	83	2	no	—
532	C₈	—	83	2	no	—
533	C₈	—	166	1	no	—
534	C₈	—	166	1	no	—
535	C₈	#14581798	1	2	yes	—
536	C₂²	—	332	1	no	—
537	C₂²	—	332	1	no	—
538	C₂²	—	332	1	no	—
539	C₂²	—	166	1	no	—
540	C₂²	—	166	1	no	—
541	C₂²	—	166	1	no	—
542	C₂²	C₄×D₄×D₈₃	1	1	yes	characteristic
543	C₄	—	2	1	no	—
544	C₄	—	4	1	no	—
545	C₄	—	4	1	no	—
546	C₄	—	4	1	no	—
547	C₄	—	4	1	no	—
548	C₄	—	332	1	no	—
549	C₄	—	332	1	no	—
550	C₄	—	332	1	no	—
551	C₄	—	166	1	no	—
552	C₄	—	166	1	no	—
553	C₄	—	166	1	no	—
554	C₄	#131×D₈₃	1	1	yes	characteristic
555	C₄	C₂×#14581798	1	1	yes	characteristic
556	C₄	#137×D₈₃	1	1	yes	characteristic
557	C₄	#19128500	1	1	yes	characteristic
558	C₂	—	332	1	no	—
559	C₂	—	664	1	no	—
560	C₂	#24916170	1	1	yes	characteristic
561	C₂	#24916279	1	1	yes	characteristic
562	C₂	#24916363	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₈₃
commutator	C₂×C₄×C₈₃	C₂³×C₄
Frattini	C₄²	C₂³×D₈₃
Fitting	C₈₃×#1579	C₂
socle	C₂²×C₈₃	C₂×C₄×D₄
prime radical	#14581767	C₂×C₄
cosocle	C₄²×C₈₃	C₂⁴
hypercenter	#1579	D₈₃
hypocenter	C₈₃	#17967
LCS	G ▷ C₂×C₄×C₈₃ ▷ C₂×C₈₃ ▷ C₈₃
UCS	C₁ ◁ C₂×C₄ ◁ C₄×C₈ ◁ #1579

Complements

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

N	H ≅ G/N	type
3. #24916392	C₂	semidirect
4. #24906360	C₂	semidirect
5. #24906357	C₂	semidirect
6. #24906352	C₂	semidirect
7. #24906350	C₂	semidirect
8. #24906280	C₂	semidirect
9. #24906277	C₂	semidirect
10. #24906273	C₂	semidirect
11. #24906227	C₂	semidirect
12. #24905934	C₂	semidirect
14. #24905742	C₂	semidirect
15. C₈₃×#1579	C₂	semidirect
290. #1579	D₈₃	semidirect
297. C₈₃	#17967	semidirect

Maximal subgroups

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

subgroup	index
#24918067	2
#24916440	2
#24916392	2
#24906360	2
#24906357	2
#24906352	2
#24906350	2
#24906280	2
#24906277	2
#24906273	2
#24906227	2
#24905934	2
#24905927	2
#24905742	2
C₈₃×#1579	2
#17967	83