Subgroups — #35374382

Order 21248.

632 conjugacy classes of subgroups.

The subgroup lattice has 570 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#24917547	C₂	1	1	yes	maximal, characteristic
2	#24916437	C₂	1	1	yes	maximal, characteristic
3	C₈×Q₈×D₈₃	C₂	1	1	yes	maximal, characteristic, complemented
4	#24906343	C₂	1	1	yes	maximal, characteristic, complemented
5	#24906341	C₂	1	1	yes	maximal, characteristic, complemented
6	#24906332	C₂	1	1	yes	maximal, characteristic, complemented
7	Q₁₆×C₈₃⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
8	#24906267	C₂	1	1	yes	maximal, characteristic, complemented
9	#24906262	C₂	1	1	yes	maximal, characteristic, complemented
10	#24906260	C₂	1	1	yes	maximal, characteristic, complemented
11	#24906245	C₂	1	1	yes	maximal, characteristic, complemented
12	#24905908	C₂	1	1	yes	maximal, characteristic, complemented
13	#24905875	C₂	1	1	yes	maximal, characteristic
14	#24905742	C₂	1	1	yes	maximal, characteristic, complemented
15	C₈₃×#1587	C₂	1	1	yes	maximal, characteristic, complemented
16	#19128238	C₂²	1	1	yes	characteristic
17	C₄×Q₈×D₈₃	C₂²	1	1	yes	characteristic
18	#19128030	C₄	1	1	yes	characteristic
19	#19128016	C₄	1	1	yes	characteristic
20	#19128007	C₄	1	1	yes	characteristic
21	#19128006	C₄	1	1	yes	characteristic
22	#19127926	C₄	1	1	yes	characteristic
23	#19127925	C₄	1	1	yes	characteristic
24	#19127855	C₄	1	1	yes	characteristic
25	#19127841	C₄	1	1	yes	characteristic
26	Q₈×C₈₃⋊C₈	C₂²	1	1	yes	characteristic
27	Q₈×C₈₃⋊C₈	C₂²	1	1	yes	characteristic
28	C₈×Dic₁₆₆	—	2	1	no	—
29	C₈×Dic₁₆₆	C₂²	1	1	yes	characteristic
30	#19127825	—	2	1	no	—
31	#19127825	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	#19127780	C₂²	1	1	yes	characteristic
36	#19127774	—	2	1	no	—
37	#19127766	—	2	1	no	—
38	#19127766	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	C₄⋊C₈×D₈₃	—	2	1	no	—
43	C₄⋊C₈×D₈₃	C₂²	1	1	yes	characteristic
44	#19127658	—	2	1	no	—
45	C₄×#13050573	C₂²	1	1	yes	characteristic
46	C₄×C₈×D₈₃	—	2	1	no	—
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	#446×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×Q₈×D₈₃	C₂×C₄	1	1	yes	characteristic
68	C₂×#13050580	C₂×C₄	1	1	yes	characteristic
69	C₂×#13050579	C₂×C₄	1	1	yes	characteristic
70	C₂×#13050577	C₂×C₄	1	1	yes	characteristic
71	C₂×#13050573	—	2	1	no	—
72	C₂×#13050573	—	2	1	no	—
73	C₂×C₈×D₈₃	—	2	1	no	—
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	#14581787	—	2	1	no	—
78	#14581783	C₂×C₄	1	1	yes	characteristic
79	#14581781	C₂×C₄	1	1	yes	characteristic
80	#14581777	—	2	1	no	—
81	#14581768	C₂×C₄	1	1	yes	characteristic
82	#14581767	C₂×C₄	1	1	yes	characteristic
83	Q₈×Dic₈₃	C₂×C₄	1	1	yes	characteristic
84	C₄×Dic₁₆₆	—	2	1	no	—
85	C₄×Dic₁₆₆	C₂³	1	1	yes	characteristic
86	#14581757	—	2	1	no	—
87	#14581757	C₂×C₄	1	1	yes	characteristic
88	C₄×D₃₃₂	—	2	1	no	—
89	C₄×D₃₃₂	C₂³	1	1	yes	characteristic
90	#14581749	—	2	1	no	—
91	C₄⋊C₄×D₈₃	—	2	1	no	—
92	C₄⋊C₄×D₈₃	C₂×C₄	1	1	yes	characteristic
93	C₄²×D₈₃	—	2	1	no	—
94	C₄²×D₈₃	C₂³	1	1	yes	characteristic
95	#14581725	C₂×C₄	1	1	yes	characteristic
96	#14581724	C₂×C₄	1	1	yes	characteristic
97	#14581723	C₂×C₄	1	1	yes	characteristic
98	C₄⋊(C₈₃⋊C₈)	—	2	1	no	—
99	C₄⋊(C₈₃⋊C₈)	—	2	1	no	—
100	C₄⋊(C₈₃⋊C₈)	C₂³	1	1	yes	characteristic
101	C₄⋊(C₈₃⋊C₈)	C₂³	1	1	yes	characteristic
102	Dic₈₃⋊C₈	—	2	1	no	—
103	Dic₈₃⋊C₈	—	2	1	no	—
104	Dic₈₃⋊C₈	—	2	1	no	—
105	Dic₈₃⋊C₈	C₂×C₄	1	1	yes	characteristic
106	Dic₈₃⋊C₈	C₂×C₄	1	1	yes	characteristic
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	C₂×C₄	1	1	yes	characteristic
117	(C₂×D₈₃)⋊C₈	C₂×C₄	1	1	yes	characteristic
118	#14581702	—	2	1	no	—
119	#14581702	—	2	1	no	—
120	C₄×C₈₃⋊C₈	—	2	1	no	—
121	C₄×C₈₃⋊C₈	—	2	1	no	—
122	C₄×C₈₃⋊C₈	C₂³	1	1	yes	characteristic
123	C₄×C₈₃⋊C₈	C₂³	1	1	yes	characteristic
124	C₄×C₈₃⋊C₈	C₂³	1	1	yes	characteristic
125	C₈×Dic₈₃	—	2	1	no	—
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	#97×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	Q₈×D₈₃	—	2	2	no	—
147	Q₈×D₈₃	—	2	2	no	—
148	C₂×D₃₃₂	—	2	1	no	—
149	C₂×D₃₃₂	C₂²×C₄	1	1	yes	characteristic
150	C₂×C₄×D₈₃	—	2	1	no	—
151	C₂×C₄×D₈₃	—	2	1	no	—
152	C₂×C₄×D₈₃	—	2	1	no	—
153	C₂×C₄×D₈₃	C₂²×C₄	1	1	yes	characteristic
154	C₂×C₄×D₈₃	C₂×D₄	1	1	yes	characteristic
155	C₂×C₄×D₈₃	#41	1	1	yes	characteristic
156	#13050580	—	2	2	no	—
157	#13050579	—	2	2	no	—
158	#13050577	—	2	2	no	—
159	#13050573	—	2	4	no	—
160	#13050573	—	4	2	no	—
161	C₂×C₈₃⋊C₈	—	2	1	no	—
162	C₂×C₈₃⋊C₈	—	2	1	no	—
163	C₂×C₈₃⋊C₈	—	2	1	no	—
164	C₂×C₈₃⋊C₈	C₂²×C₄	1	1	yes	characteristic
165	C₂×C₈₃⋊C₈	C₂²×C₄	1	1	yes	characteristic
166	C₂×C₈₃⋊C₈	C₂×D₄	1	1	yes	characteristic
167	C₂×C₈₃⋊C₈	C₂×D₄	1	1	yes	characteristic
168	C₈×D₈₃	—	2	2	no	—
169	C₈×D₈₃	—	4	1	no	—
170	C₈×D₈₃	—	4	2	no	—
171	C₈×D₈₃	—	4	2	no	—
172	C₄⋊Dic₈₃	—	2	1	no	—
173	C₄⋊Dic₈₃	—	2	1	no	—
174	C₄⋊Dic₈₃	C₂²×C₄	1	1	yes	characteristic
175	C₄⋊Dic₈₃	C₂²×C₄	1	1	yes	characteristic
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	Dic₈₃⋊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	C₄×Dic₈₃	—	2	1	no	—
187	C₄×Dic₈₃	—	2	1	no	—
188	C₄×Dic₈₃	—	2	1	no	—
189	C₄×Dic₈₃	C₂²×C₄	1	1	yes	characteristic
190	C₄×Dic₈₃	C₂×D₄	1	1	yes	characteristic
191	C₄×Dic₈₃	#41	1	1	yes	characteristic
192	C₂×Q₈×C₈₃	C₂²×C₄	1	1	yes	characteristic
193	C₂×Q₈×C₈₃	C₂²×C₄	1	1	yes	characteristic
194	Q₁₆×C₈₃	—	2	2	no	—
195	C₂×C₈×C₈₃	—	2	1	no	—
196	C₂×C₈×C₈₃	—	2	1	no	—
197	C₂×C₈×C₈₃	—	2	1	no	—
198	C₂×C₈×C₈₃	C₂²×C₄	1	1	yes	characteristic
199	C₂×C₈×C₈₃	C₂²×C₄	1	1	yes	characteristic
200	C₂×C₈×C₈₃	C₂×D₄	1	1	yes	characteristic
201	C₂×C₈×C₈₃	C₂×D₄	1	1	yes	characteristic
202	C₄⋊C₄×C₈₃	—	2	1	no	—
203	C₄⋊C₄×C₈₃	—	2	1	no	—
204	C₄⋊C₄×C₈₃	C₂²×C₄	1	1	yes	characteristic
205	C₄⋊C₄×C₈₃	C₂²×C₄	1	1	yes	characteristic
206	C₄²×C₈₃	—	2	1	no	—
207	C₄²×C₈₃	—	2	1	no	—
208	C₄²×C₈₃	C₂⁴	1	1	yes	characteristic
209	C₂²×D₈₃	—	2	1	no	—
210	C₂²×D₈₃	C₄×D₄	1	1	yes	characteristic
211	Q₈×C₈₃	—	2	1	no	—
212	Q₈×C₈₃	—	2	1	no	—
213	Q₈×C₈₃	—	2	1	no	—
214	Q₈×C₈₃	#131	1	2	yes	—
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	—	2	1	no	—
219	C₂×C₄×C₈₃	C₂³×C₄	1	1	yes	characteristic
220	C₂×C₄×C₈₃	C₂²×D₄	1	1	yes	characteristic
221	C₂×C₄×C₈₃	C₂×#41	1	1	yes	characteristic
222	C₂×Dic₈₃	—	2	1	no	—
223	C₂×Dic₈₃	—	2	1	no	—
224	C₂×Dic₈₃	—	2	1	no	—
225	C₂×Dic₈₃	C₄×D₄	1	1	yes	characteristic
226	C₂×Dic₈₃	C₄×D₄	1	1	yes	characteristic
227	C₂×Dic₈₃	C₄×D₄	1	1	yes	characteristic
228	D₃₃₂	—	2	1	no	—
229	D₃₃₂	—	2	1	no	—
230	D₃₃₂	—	4	2	no	—
231	C₄×D₈₃	—	2	4	no	—
232	C₄×D₈₃	—	2	2	no	—
233	C₄×D₈₃	—	2	1	no	—
234	C₄×D₈₃	—	2	1	no	—
235	C₄×D₈₃	—	2	1	no	—
236	C₄×D₈₃	—	2	1	no	—
237	C₄×D₈₃	—	4	2	no	—
238	C₄×D₈₃	—	4	1	no	—
239	C₄×D₈₃	—	4	1	no	—
240	Dic₁₆₆	—	2	4	no	—
241	Dic₁₆₆	—	2	1	no	—
242	Dic₁₆₆	#131	1	2	yes	—
243	C₈×C₈₃	—	2	2	no	—
244	C₈×C₈₃	—	2	1	no	—
245	C₈×C₈₃	—	2	1	no	—
246	C₈×C₈₃	—	2	1	no	—
247	C₈×C₈₃	—	2	1	no	—
248	C₈×C₈₃	—	4	1	no	—
249	C₈×C₈₃	—	4	1	no	—
250	C₈₃⋊C₈	—	2	2	no	—
251	C₈₃⋊C₈	—	2	1	no	—
252	C₈₃⋊C₈	—	2	1	no	—
253	C₈₃⋊C₈	—	2	1	no	—
254	C₈₃⋊C₈	—	4	1	no	—
255	C₈₃⋊C₈	—	4	1	no	—
256	C₈₃⋊C₈	#137	1	2	yes	—
257	C₂²×C₈₃	C₂×C₄×D₄	1	1	yes	characteristic
258	C₂×D₈₃	—	2	1	no	—
259	C₂×D₈₃	—	2	1	no	—
260	C₂×D₈₃	—	4	1	no	—
261	C₂×D₈₃	—	4	1	no	—
262	C₂×D₈₃	—	4	1	no	—
263	C₂×D₈₃	#443	1	2	yes	—
264	C₄×C₈₃	—	2	2	no	—
265	C₄×C₈₃	—	2	1	no	—
266	C₄×C₈₃	—	4	1	no	—
267	C₄×C₈₃	—	4	1	no	—
268	C₄×C₈₃	—	4	1	no	—
269	C₄×C₈₃	C₂×#131	1	1	yes	characteristic
270	C₄×C₈₃	C₂×#131	1	1	yes	characteristic
271	C₄×C₈₃	C₂×#137	1	1	yes	characteristic
272	C₄×C₈₃	#575	1	1	yes	characteristic
273	Dic₈₃	—	2	1	no	—
274	Dic₈₃	—	2	2	no	—
275	Dic₈₃	—	2	1	no	—
276	Dic₈₃	—	2	1	no	—
277	Dic₈₃	—	4	1	no	—
278	Dic₈₃	—	4	1	no	—
279	#17911	—	83	1	no	maximal, Sylow
280	C₂×C₈₃	#2929	1	1	yes	characteristic
281	C₂×C₈₃	C₄×#137	1	1	yes	characteristic
282	C₂×C₈₃	C₂×#443	1	1	yes	characteristic
283	D₈₃	—	2	2	no	—
284	D₈₃	—	8	1	no	—
285	#3108	—	83	1	no	—
286	#2966	—	83	1	no	—
287	C₂×C₈×Q₈	—	83	1	no	—
288	#1588	—	83	1	no	—
289	#1588	—	83	1	no	—
290	#1587	—	83	1	no	—
291	#1587	D₈₃	1	1	yes	characteristic, complemented
292	C₈×Q₁₆	—	83	1	no	—
293	C₈×Q₁₆	—	83	1	no	—
294	C₈×SD₁₆	—	83	1	no	—
295	C₈×SD₁₆	—	83	1	no	—
296	#1573	—	83	1	no	—
297	#1491	—	83	1	no	—
298	#1483	—	83	1	no	—
299	C₈×M₁₆	—	83	1	no	—
300	C₈₃	#17911	1	1	yes	characteristic, complemented, Sylow
301	#529	—	83	1	no	—
302	C₂×C₄×Q₈	—	83	1	no	—
303	#483	—	83	1	no	—
304	#480	—	83	1	no	—
305	#479	—	83	1	no	—
306	#479	—	83	1	no	—
307	#464	—	83	1	no	—
308	#464	—	83	1	no	—
309	#451	—	83	1	no	—
310	#448	—	83	1	no	—
311	#446	C₂×D₈₃	1	1	yes	characteristic
312	C₈×Q₈	—	83	1	no	—
313	C₈×Q₈	—	83	1	no	—
314	C₈×Q₈	—	83	1	no	—
315	C₈×Q₈	—	83	1	no	—
316	C₈×Q₈	—	166	1	no	—
317	C₈×Q₈	—	166	1	no	—
318	C₈×Q₈	C₂×D₈₃	1	1	yes	characteristic
319	C₄×Q₁₆	—	83	1	no	—
320	C₄×Q₁₆	C₂×D₈₃	1	1	yes	characteristic
321	C₄×SD₁₆	—	83	1	no	—
322	C₄×SD₁₆	—	83	1	no	—
323	#436	—	83	1	no	—
324	#435	—	166	1	no	—
325	C₈×D₄	—	83	1	no	—
326	C₈×D₄	—	166	1	no	—
327	#433	—	166	1	no	—
328	#432	—	83	1	no	—
329	#431	—	83	1	no	—
330	C₂×C₄⋊C₈	—	83	1	no	—
331	C₂×C₄⋊C₈	—	166	1	no	—
332	#405	—	166	1	no	—
333	C₄×M₁₆	—	83	1	no	—
334	C₂×C₄×C₈	—	83	1	no	—
335	C₂×C₄×C₈	—	166	1	no	—
336	#335	—	83	1	no	—
337	#335	—	83	1	no	—
338	#334	—	83	1	no	—
339	#334	C₂×D₈₃	1	1	yes	characteristic
340	Q₈⋊C₈	—	83	1	no	—
341	Q₈⋊C₈	—	83	1	no	—
342	Q₈⋊C₈	—	83	1	no	—
343	Q₈⋊C₈	—	83	1	no	—
344	Q₈⋊C₈	C₂×D₈₃	1	1	yes	characteristic
345	Q₈⋊C₈	C₂×D₈₃	1	1	yes	characteristic
346	D₄⋊C₈	—	83	1	no	—
347	D₄⋊C₈	—	83	1	no	—
348	#322	—	83	1	no	—
349	#322	C₂×D₈₃	1	1	yes	characteristic
350	C₈²	—	83	1	no	—
351	C₈²	—	83	1	no	—
352	C₂²×Q₈	—	83	1	no	—
353	C₂×Q₁₆	—	83	1	no	—
354	C₂×Q₁₆	C₄×D₈₃	1	1	yes	characteristic
355	C₂×SD₁₆	—	83	1	no	—
356	C₂×SD₁₆	—	83	1	no	—
357	C₂×M₁₆	—	166	1	no	—
358	C₂×M₁₆	—	166	1	no	—
359	C₂²×C₈	—	83	1	no	—
360	C₂²×C₈	—	83	1	no	—
361	C₂²×C₈	—	166	1	no	—
362	C₂²×C₈	—	166	1	no	—
363	#126	—	166	1	no	—
364	#125	—	83	1	no	—
365	#124	—	83	1	no	—
366	#123	—	166	1	no	—
367	C₂²⋊Q₈	—	83	1	no	—
368	#121	—	83	1	no	—
369	C₄×Q₈	—	83	1	no	—
370	C₄×Q₈	—	83	1	no	—
371	C₄×Q₈	—	83	1	no	—
372	C₄×Q₈	—	166	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	C₂×C₄⋊C₄	—	83	1	no	—
380	C₂×C₄⋊C₄	—	166	1	no	—
381	C₂×C₄²	—	83	1	no	—
382	C₂×C₄²	—	166	1	no	—
383	#107	—	83	1	no	—
384	#107	C₄×D₈₃	1	1	yes	characteristic
385	#106	—	83	1	no	—
386	#106	—	83	1	no	—
387	C₄⋊C₈	—	2	1	no	—
388	C₄⋊C₈	—	2	1	no	—
389	C₄⋊C₈	—	83	1	no	—
390	C₄⋊C₈	—	83	1	no	—
391	C₄⋊C₈	—	83	1	no	—
392	C₄⋊C₈	—	83	1	no	—
393	C₄⋊C₈	—	166	1	no	—
394	C₄⋊C₈	—	166	1	no	—
395	C₄⋊C₈	—	166	1	no	—
396	C₄⋊C₈	—	166	1	no	—
397	C₄⋊C₈	—	166	1	no	—
398	C₄⋊C₈	C₂²×D₈₃	1	1	yes	characteristic
399	C₄⋊C₈	C₂²×D₈₃	1	1	yes	characteristic
400	#103	—	83	1	no	—
401	#103	—	83	1	no	—
402	#103	—	83	1	no	—
403	#103	—	83	1	no	—
404	#103	C₄×D₈₃	1	1	yes	characteristic
405	#103	C₄×D₈₃	1	1	yes	characteristic
406	#102	—	83	1	no	—
407	#102	—	83	1	no	—
408	C₂²⋊C₈	—	83	1	no	—
409	C₂²⋊C₈	—	83	1	no	—
410	C₂²⋊C₈	—	166	1	no	—
411	C₂²⋊C₈	—	166	1	no	—
412	C₂²⋊C₈	—	166	1	no	—
413	#97	—	2	1	no	—
414	#97	—	166	1	no	—
415	#97	—	166	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	—	166	1	no	—
424	C₄×C₈	—	166	1	no	—
425	C₄×C₈	—	166	1	no	—
426	C₄×C₈	C₂²×D₈₃	1	1	yes	characteristic
427	C₄×C₈	C₂²×D₈₃	1	1	yes	characteristic
428	C₄×C₈	C₂²×D₈₃	1	1	yes	characteristic
429	C₂×Q₈	—	83	1	no	—
430	C₂×Q₈	—	166	1	no	—
431	C₂×Q₈	—	166	2	no	—
432	C₂×Q₈	—	166	2	no	—
433	C₂×Q₈	C₂×C₄×D₈₃	1	1	yes	characteristic
434	C₂×Q₈	C₂×C₄×D₈₃	1	1	yes	characteristic
435	C₂×D₄	—	83	1	no	—
436	C₂×D₄	—	166	1	no	—
437	C₂²×C₄	—	83	1	no	—
438	C₂²×C₄	—	83	1	no	—
439	C₂²×C₄	—	83	1	no	—
440	C₂²×C₄	—	166	1	no	—
441	C₂²×C₄	—	166	1	no	—
442	C₂²×C₄	—	166	1	no	—
443	Q₁₆	—	2	2	no	—
444	Q₁₆	—	166	2	no	—
445	SD₁₆	—	166	2	no	—
446	SD₁₆	—	166	2	no	—
447	M₁₆	—	332	2	no	—
448	M₁₆	—	166	4	no	—
449	C₂×C₈	—	2	1	no	—
450	C₂×C₈	—	2	1	no	—
451	C₂×C₈	—	2	1	no	—
452	C₂×C₈	—	332	1	no	—
453	C₂×C₈	—	332	2	no	—
454	C₂×C₈	—	332	2	no	—
455	C₂×C₈	—	83	1	no	—
456	C₂×C₈	—	83	1	no	—
457	C₂×C₈	—	83	1	no	—
458	C₂×C₈	—	83	1	no	—
459	C₂×C₈	—	166	2	no	—
460	C₂×C₈	—	166	1	no	—
461	C₂×C₈	—	166	1	no	—
462	C₂×C₈	—	166	1	no	—
463	C₂×C₈	C₂×C₄×D₈₃	1	1	yes	characteristic
464	C₂×C₈	C₂×C₄×D₈₃	1	1	yes	characteristic
465	C₂×C₈	D₄×D₈₃	1	1	yes	characteristic
466	C₂×C₈	D₄×D₈₃	1	1	yes	characteristic
467	C₄⋊C₄	—	2	1	no	—
468	C₄⋊C₄	—	2	1	no	—
469	C₄⋊C₄	—	83	1	no	—
470	C₄⋊C₄	—	83	1	no	—
471	C₄⋊C₄	—	166	1	no	—
472	C₄⋊C₄	—	166	1	no	—
473	C₄⋊C₄	—	166	1	no	—
474	C₄⋊C₄	—	166	1	no	—
475	C₄⋊C₄	—	166	1	no	—
476	C₄⋊C₄	—	166	1	no	—
477	C₄⋊C₄	—	166	1	no	—
478	C₄⋊C₄	C₂×C₄×D₈₃	1	1	yes	characteristic
479	C₄⋊C₄	C₂×C₄×D₈₃	1	1	yes	characteristic
480	C₂²⋊C₄	—	166	1	no	—
481	C₂²⋊C₄	—	166	1	no	—
482	C₂²⋊C₄	—	166	1	no	—
483	C₂²⋊C₄	—	166	1	no	—
484	C₂²⋊C₄	—	166	1	no	—
485	C₄²	—	2	1	no	—
486	C₄²	—	2	1	no	—
487	C₄²	—	83	1	no	—
488	C₄²	—	83	1	no	—
489	C₄²	—	83	1	no	—
490	C₄²	—	166	1	no	—
491	C₄²	—	166	1	no	—
492	C₄²	—	166	1	no	—
493	C₄²	C₂³×D₈₃	1	1	yes	characteristic
494	C₂³	—	83	1	no	—
495	C₂³	—	166	1	no	—
496	Q₈	—	2	1	no	—
497	Q₈	—	2	1	no	—
498	Q₈	—	2	1	no	—
499	Q₈	—	83	2	no	—
500	Q₈	—	166	4	no	—
501	Q₈	—	166	1	no	—
502	Q₈	#14581800	1	2	yes	—
503	D₄	—	332	2	no	—
504	D₄	—	166	1	no	—
505	D₄	—	166	1	no	—
506	C₂×C₄	—	2	1	no	—
507	C₂×C₄	—	2	1	no	—
508	C₂×C₄	—	2	1	no	—
509	C₂×C₄	—	2	1	no	—
510	C₂×C₄	—	332	2	no	—
511	C₂×C₄	—	332	1	no	—
512	C₂×C₄	—	332	1	no	—
513	C₂×C₄	—	83	1	no	—
514	C₂×C₄	—	83	1	no	—
515	C₂×C₄	—	83	1	no	—
516	C₂×C₄	—	166	2	no	—
517	C₂×C₄	—	166	4	no	—
518	C₂×C₄	—	166	1	no	—
519	C₂×C₄	—	166	1	no	—
520	C₂×C₄	—	166	1	no	—
521	C₂×C₄	—	166	1	no	—
522	C₂×C₄	—	166	1	no	—
523	C₂×C₄	—	166	1	no	—
524	C₂×C₄	—	166	1	no	—
525	C₂×C₄	C₂²×C₄×D₈₃	1	1	yes	characteristic
526	C₂×C₄	C₂×D₄×D₈₃	1	1	yes	characteristic
527	C₂×C₄	#41×D₈₃	1	1	yes	characteristic
528	C₈	—	2	2	no	—
529	C₈	—	2	1	no	—
530	C₈	—	2	1	no	—
531	C₈	—	2	1	no	—
532	C₈	—	2	1	no	—
533	C₈	—	4	1	no	—
534	C₈	—	4	1	no	—
535	C₈	—	332	1	no	—
536	C₈	—	332	1	no	—
537	C₈	—	83	2	no	—
538	C₈	—	166	2	no	—
539	C₈	—	166	1	no	—
540	C₈	—	166	1	no	—
541	C₈	—	166	1	no	—
542	C₂²	—	332	1	no	—
543	C₂²	—	332	1	no	—
544	C₂²	—	332	1	no	—
545	C₂²	—	83	2	no	—
546	C₂²	—	166	1	no	—
547	C₂²	—	166	1	no	—
548	C₂²	C₄×D₄×D₈₃	1	1	yes	characteristic
549	C₄	—	2	1	no	—
550	C₄	—	2	2	no	—
551	C₄	—	4	1	no	—
552	C₄	—	4	1	no	—
553	C₄	—	4	1	no	—
554	C₄	—	332	1	no	—
555	C₄	—	332	1	no	—
556	C₄	—	166	1	no	—
557	C₄	—	166	1	no	—
558	C₄	—	166	1	no	—
559	C₄	—	166	2	no	—
560	C₄	#131×D₈₃	1	1	yes	characteristic
561	C₄	C₂×#14581800	1	1	yes	characteristic
562	C₄	#137×D₈₃	1	1	yes	characteristic
563	C₄	#19128500	1	1	yes	characteristic
564	C₂	—	664	1	no	—
565	C₂	—	166	2	no	—
566	C₂	#24916154	1	1	yes	characteristic
567	C₂	#24916279	1	1	yes	characteristic
568	C₂	#443×D₈₃	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×#1587	C₂
socle	C₂²×C₈₃	C₂×C₄×D₄
prime radical	#14581767	C₂×C₄
cosocle	C₄²×C₈₃	C₂⁴
hypercenter	#1587	D₈₃
hypocenter	C₈₃	#17911
LCS	G ▷ C₂×C₄×C₈₃ ▷ C₂×C₈₃ ▷ C₈₃
UCS	C₁ ◁ C₂×C₄ ◁ C₄×C₈ ◁ #1587

Complements

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

N	H ≅ G/N	type
3. C₈×Q₈×D₈₃	C₂	semidirect
4. #24906343	C₂	semidirect
5. #24906341	C₂	semidirect
6. #24906332	C₂	semidirect
7. Q₁₆×C₈₃⋊C₈	C₂	semidirect
8. #24906267	C₂	semidirect
9. #24906262	C₂	semidirect
10. #24906260	C₂	semidirect
11. #24906245	C₂	semidirect
12. #24905908	C₂	semidirect
14. #24905742	C₂	semidirect
15. C₈₃×#1587	C₂	semidirect
291. #1587	D₈₃	semidirect
300. C₈₃	#17911	semidirect

Maximal subgroups

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

subgroup	index
#24917547	2
#24916437	2
C₈×Q₈×D₈₃	2
#24906343	2
#24906341	2
#24906332	2
Q₁₆×C₈₃⋊C₈	2
#24906267	2
#24906262	2
#24906260	2
#24906245	2
#24905908	2
#24905875	2
#24905742	2
C₈₃×#1587	2
#17911	83