Subgroups — #35374201

Order 21248.

648 conjugacy classes of subgroups.

The subgroup lattice has 582 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#24916428	C₂	1	1	yes	maximal, characteristic
2	#446×D₈₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×#14581824	C₂	1	1	yes	maximal, characteristic
4	#24906372	C₂	1	1	yes	maximal, characteristic, complemented
5	#24906369	C₂	1	1	yes	maximal, characteristic, complemented
6	#24906368	C₂	1	1	yes	maximal, characteristic, complemented
7	#24906364	C₂	1	1	yes	maximal, characteristic, complemented
8	#24906358	C₂	1	1	yes	maximal, characteristic, complemented
9	#24906355	C₂	1	1	yes	maximal, characteristic, complemented
10	#24906353	C₂	1	1	yes	maximal, characteristic, complemented
11	#24906214	C₂	1	1	yes	maximal, characteristic, complemented
12	#24905856	C₂	1	1	yes	maximal, characteristic, complemented
13	#24905849	C₂	1	1	yes	maximal, characteristic
14	C₈×#13050573	C₂	1	1	yes	maximal, characteristic, complemented
15	C₈₃×#1591	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#14581824	C₄	1	1	yes	characteristic
17	C₄×#13050591	C₂²	1	1	yes	characteristic
18	C₄×Q₈×D₈₃	C₂²	1	1	yes	characteristic
19	#19127832	C₂²	1	1	yes	characteristic
20	#19127832	C₂²	1	1	yes	characteristic
21	#19127831	C₂²	1	1	yes	characteristic
22	#19127830	—	2	1	no	—
23	#19127829	—	2	1	no	—
24	#19127828	C₂²	1	1	yes	characteristic
25	#19127808	C₄	1	1	yes	characteristic
26	#19127805	C₄	1	1	yes	characteristic
27	#19127804	C₄	1	1	yes	characteristic
28	#19127800	C₄	1	1	yes	characteristic
29	C₄×#13050580	C₂²	1	1	yes	characteristic
30	C₄×#13050579	C₂²	1	1	yes	characteristic
31	C₄×#13050577	C₂²	1	1	yes	characteristic
32	#19127780	C₂²	1	1	yes	characteristic
33	#19127778	C₂²	1	1	yes	characteristic
34	#19127774	—	2	1	no	—
35	#19127771	—	2	1	no	—
36	#19127753	—	2	1	no	—
37	#19127753	C₂²	1	1	yes	characteristic
38	#19127752	C₂²	1	1	yes	characteristic
39	#19127742	C₄	1	1	yes	characteristic
40	C₄⋊C₈×D₈₃	—	2	1	no	—
41	C₄⋊C₈×D₈₃	C₂²	1	1	yes	characteristic
42	#19127708	C₄	1	1	yes	characteristic
43	#19127701	C₄	1	1	yes	characteristic
44	#19127653	—	2	1	no	—
45	C₄×#13050573	C₂²	1	1	yes	characteristic
46	#97×D₈₃	—	2	1	no	—
47	C₄×C₈×D₈₃	C₂²	1	1	yes	characteristic
48	#19127453	C₂²	1	1	yes	characteristic
49	#19127452	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	#19127422	C₂²	1	1	yes	characteristic
59	C₈×C₈₃⋊C₈	C₂²	1	1	yes	characteristic
60	#446×C₈₃	C₂²	1	1	yes	characteristic
61	#446×C₈₃	C₂²	1	1	yes	characteristic
62	C₄×Q₁₆×C₈₃	C₂²	1	1	yes	characteristic
63	#335×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	C₈²×C₈₃	C₂²	1	1	yes	characteristic
67	C₂×#13050591	C₂×C₄	1	1	yes	characteristic
68	C₂×Q₈×D₈₃	C₂×C₄	1	1	yes	characteristic
69	#14581824	—	2	4	no	—
70	C₂×#13050580	C₂×C₄	1	1	yes	characteristic
71	C₂×#13050579	C₂×C₄	1	1	yes	characteristic
72	C₂×#13050577	C₂×C₄	1	1	yes	characteristic
73	C₂×#13050573	—	2	1	no	—
74	C₂×#13050573	—	2	1	no	—
75	C₂×#13050573	C₂×C₄	1	1	yes	characteristic
76	C₂×#13050573	C₂×C₄	1	1	yes	characteristic
77	C₂×C₈×D₈₃	—	2	1	no	—
78	C₂×C₈×D₈₃	D₄	1	1	yes	characteristic
79	C₂×C₈×D₈₃	D₄	1	1	yes	characteristic
80	Q₈×Dic₈₃	C₂×C₄	1	1	yes	characteristic
81	Q₈×Dic₈₃	C₂×C₄	1	1	yes	characteristic
82	C₄×Dic₁₆₆	—	2	1	no	—
83	C₄×Dic₁₆₆	C₂³	1	1	yes	characteristic
84	#14581757	—	2	1	no	—
85	#14581757	C₂×C₄	1	1	yes	characteristic
86	C₄×D₃₃₂	—	2	1	no	—
87	C₄×D₃₃₂	C₂³	1	1	yes	characteristic
88	#14581754	—	2	1	no	—
89	#14581754	C₂×C₄	1	1	yes	characteristic
90	#14581750	—	2	1	no	—
91	#14581750	C₂×C₄	1	1	yes	characteristic
92	C₄⋊C₄×D₈₃	—	2	1	no	—
93	C₄⋊C₄×D₈₃	C₂×C₄	1	1	yes	characteristic
94	C₄²×D₈₃	—	2	1	no	—
95	C₄²×D₈₃	—	2	1	no	—
96	C₄²×D₈₃	C₂³	1	1	yes	characteristic
97	#14581725	C₂×C₄	1	1	yes	characteristic
98	#14581724	C₂×C₄	1	1	yes	characteristic
99	#14581723	C₂×C₄	1	1	yes	characteristic
100	C₄⋊(C₈₃⋊C₈)	—	2	1	no	—
101	C₄⋊(C₈₃⋊C₈)	—	2	1	no	—
102	C₄⋊(C₈₃⋊C₈)	C₂³	1	1	yes	characteristic
103	C₄⋊(C₈₃⋊C₈)	C₂³	1	1	yes	characteristic
104	Dic₈₃⋊C₈	—	2	1	no	—
105	Dic₈₃⋊C₈	—	2	1	no	—
106	Dic₈₃⋊C₈	—	2	1	no	—
107	Dic₈₃⋊C₈	—	2	1	no	—
108	#14581717	C₂×C₄	1	1	yes	characteristic
109	#14581716	C₂×C₄	1	1	yes	characteristic
110	#14581716	C₂×C₄	1	1	yes	characteristic
111	#14581715	C₂×C₄	1	1	yes	characteristic
112	#14581714	C₂×C₄	1	1	yes	characteristic
113	#14581712	C₂×C₄	1	1	yes	characteristic
114	(C₂×D₈₃)⋊C₈	—	2	1	no	—
115	(C₂×D₈₃)⋊C₈	—	2	1	no	—
116	(C₂×D₈₃)⋊C₈	—	2	1	no	—
117	(C₂×D₈₃)⋊C₈	—	2	1	no	—
118	#14581703	—	2	1	no	—
119	#14581703	—	2	1	no	—
120	#14581702	—	2	1	no	—
121	#14581702	—	2	1	no	—
122	#14581702	C₂×C₄	1	1	yes	characteristic
123	#14581702	C₂×C₄	1	1	yes	characteristic
124	C₄×C₈₃⋊C₈	C₂³	1	1	yes	characteristic
125	C₄×C₈₃⋊C₈	C₂³	1	1	yes	characteristic
126	C₄×C₈₃⋊C₈	C₂³	1	1	yes	characteristic
127	C₈×Dic₈₃	—	2	1	no	—
128	C₈×Dic₈₃	D₄	1	1	yes	characteristic
129	C₈×Dic₈₃	D₄	1	1	yes	characteristic
130	C₂×Q₁₆×C₈₃	C₂×C₄	1	1	yes	characteristic
131	C₄×Q₈×C₈₃	C₂³	1	1	yes	characteristic
132	C₄×Q₈×C₈₃	C₂³	1	1	yes	characteristic
133	#107×C₈₃	C₂×C₄	1	1	yes	characteristic
134	C₄⋊C₈×C₈₃	—	2	1	no	—
135	C₄⋊C₈×C₈₃	—	2	1	no	—
136	C₄⋊C₈×C₈₃	C₂³	1	1	yes	characteristic
137	C₄⋊C₈×C₈₃	C₂³	1	1	yes	characteristic
138	#103×C₈₃	C₂×C₄	1	1	yes	characteristic
139	#103×C₈₃	C₂×C₄	1	1	yes	characteristic
140	#97×C₈₃	—	2	1	no	—
141	#97×C₈₃	—	2	1	no	—
142	C₄×C₈×C₈₃	C₂³	1	1	yes	characteristic
143	C₄×C₈×C₈₃	C₂³	1	1	yes	characteristic
144	C₄×C₈×C₈₃	C₂³	1	1	yes	characteristic
145	#13050591	—	2	2	no	—
146	#13050591	—	2	2	no	—
147	C₂×Dic₁₆₆	—	2	1	no	—
148	C₂×Dic₁₆₆	C₂²×C₄	1	1	yes	characteristic
149	Q₈×D₈₃	—	2	2	no	—
150	Q₈×D₈₃	—	2	2	no	—
151	C₂×D₃₃₂	—	2	1	no	—
152	C₂×D₃₃₂	C₂²×C₄	1	1	yes	characteristic
153	C₂×C₄×D₈₃	—	2	1	no	—
154	C₂×C₄×D₈₃	—	2	1	no	—
155	C₂×C₄×D₈₃	—	2	1	no	—
156	C₂×C₄×D₈₃	—	2	1	no	—
157	C₂×C₄×D₈₃	—	2	1	no	—
158	C₂×C₄×D₈₃	C₂²×C₄	1	1	yes	characteristic
159	C₂×C₄×D₈₃	C₂×D₄	1	1	yes	characteristic
160	C₂×C₄×D₈₃	#41	1	1	yes	characteristic
161	#13050580	—	2	2	no	—
162	#13050579	—	2	2	no	—
163	#13050577	—	2	2	no	—
164	#13050573	—	2	2	no	—
165	#13050573	—	4	2	no	—
166	#13050573	—	4	2	no	—
167	#13050573	M₁₆	1	4	yes	complemented
168	C₂×C₈₃⋊C₈	—	2	1	no	—
169	C₂×C₈₃⋊C₈	—	2	1	no	—
170	C₂×C₈₃⋊C₈	—	2	1	no	—
171	C₂×C₈₃⋊C₈	C₂²×C₄	1	1	yes	characteristic
172	C₂×C₈₃⋊C₈	C₂²×C₄	1	1	yes	characteristic
173	C₂×C₈₃⋊C₈	C₂×D₄	1	1	yes	characteristic
174	C₂×C₈₃⋊C₈	C₂×D₄	1	1	yes	characteristic
175	C₈×D₈₃	—	2	2	no	—
176	C₈×D₈₃	—	4	1	no	—
177	C₈×D₈₃	—	4	2	no	—
178	C₄⋊Dic₈₃	—	2	1	no	—
179	C₄⋊Dic₈₃	—	2	1	no	—
180	C₄⋊Dic₈₃	C₂²×C₄	1	1	yes	characteristic
181	C₄⋊Dic₈₃	C₂²×C₄	1	1	yes	characteristic
182	Dic₈₃⋊C₄	—	2	1	no	—
183	Dic₈₃⋊C₄	—	2	1	no	—
184	Dic₈₃⋊C₄	—	2	1	no	—
185	(C₂×D₈₃)⋊C₄	—	2	1	no	—
186	(C₂×D₈₃)⋊C₄	—	2	1	no	—
187	(C₂×D₈₃)⋊C₄	—	2	1	no	—
188	C₄×Dic₈₃	—	2	1	no	—
189	C₄×Dic₈₃	—	2	1	no	—
190	C₄×Dic₈₃	—	2	1	no	—
191	C₄×Dic₈₃	—	2	1	no	—
192	C₄×Dic₈₃	—	2	1	no	—
193	C₄×Dic₈₃	C₂²×C₄	1	1	yes	characteristic
194	C₄×Dic₈₃	C₂×D₄	1	1	yes	characteristic
195	C₄×Dic₈₃	#41	1	1	yes	characteristic
196	C₂×Q₈×C₈₃	C₂²×C₄	1	1	yes	characteristic
197	C₂×Q₈×C₈₃	C₂²×C₄	1	1	yes	characteristic
198	Q₁₆×C₈₃	—	2	2	no	—
199	C₂×C₈×C₈₃	—	2	1	no	—
200	C₂×C₈×C₈₃	—	2	1	no	—
201	C₂×C₈×C₈₃	—	2	1	no	—
202	C₂×C₈×C₈₃	C₂²×C₄	1	1	yes	characteristic
203	C₂×C₈×C₈₃	C₂²×C₄	1	1	yes	characteristic
204	C₂×C₈×C₈₃	C₂×D₄	1	1	yes	characteristic
205	C₂×C₈×C₈₃	C₂×D₄	1	1	yes	characteristic
206	C₄⋊C₄×C₈₃	—	2	1	no	—
207	C₄⋊C₄×C₈₃	—	2	1	no	—
208	C₄⋊C₄×C₈₃	C₂²×C₄	1	1	yes	characteristic
209	C₄⋊C₄×C₈₃	C₂²×C₄	1	1	yes	characteristic
210	C₄²×C₈₃	—	2	1	no	—
211	C₄²×C₈₃	—	2	1	no	—
212	C₄²×C₈₃	C₂⁴	1	1	yes	characteristic
213	C₂²×D₈₃	—	2	1	no	—
214	C₂²×D₈₃	C₄×D₄	1	1	yes	characteristic
215	Q₈×C₈₃	—	2	1	no	—
216	Q₈×C₈₃	—	2	1	no	—
217	Q₈×C₈₃	—	2	1	no	—
218	Q₈×C₈₃	—	2	1	no	—
219	C₂×C₄×C₈₃	—	2	1	no	—
220	C₂×C₄×C₈₃	—	2	1	no	—
221	C₂×C₄×C₈₃	—	2	1	no	—
222	C₂×C₄×C₈₃	—	2	1	no	—
223	C₂×C₄×C₈₃	C₂³×C₄	1	1	yes	characteristic
224	C₂×C₄×C₈₃	C₂²×D₄	1	1	yes	characteristic
225	C₂×C₄×C₈₃	C₂×#41	1	1	yes	characteristic
226	C₂×Dic₈₃	—	2	1	no	—
227	C₂×Dic₈₃	—	2	1	no	—
228	C₂×Dic₈₃	—	2	1	no	—
229	C₂×Dic₈₃	C₄×D₄	1	1	yes	characteristic
230	C₂×Dic₈₃	C₄×D₄	1	1	yes	characteristic
231	C₂×Dic₈₃	C₄×D₄	1	1	yes	characteristic
232	D₃₃₂	—	2	1	no	—
233	D₃₃₂	—	2	1	no	—
234	D₃₃₂	—	4	2	no	—
235	C₄×D₈₃	—	2	1	no	—
236	C₄×D₈₃	—	2	1	no	—
237	C₄×D₈₃	—	4	1	no	—
238	C₄×D₈₃	—	4	2	no	—
239	C₄×D₈₃	—	4	2	no	—
240	C₄×D₈₃	—	4	2	no	—
241	C₄×D₈₃	—	4	1	no	—
242	C₄×D₈₃	—	4	1	no	—
243	C₄×D₈₃	—	4	2	no	—
244	C₄×D₈₃	C₂×M₁₆	1	2	yes	—
245	C₄×D₈₃	#131	1	2	yes	—
246	Dic₁₆₆	—	2	1	no	—
247	Dic₁₆₆	—	2	1	no	—
248	Dic₁₆₆	—	4	2	no	—
249	C₈×C₈₃	—	2	1	no	—
250	C₈×C₈₃	—	2	1	no	—
251	C₈×C₈₃	—	4	1	no	—
252	C₈×C₈₃	—	4	1	no	—
253	C₈×C₈₃	—	4	1	no	—
254	C₈×C₈₃	C₂×M₁₆	1	2	yes	—
255	C₈×C₈₃	#137	1	2	yes	complemented
256	C₈₃⋊C₈	—	2	1	no	—
257	C₈₃⋊C₈	—	2	1	no	—
258	C₈₃⋊C₈	—	2	1	no	—
259	C₈₃⋊C₈	—	4	1	no	—
260	C₈₃⋊C₈	—	4	1	no	—
261	C₈₃⋊C₈	—	4	1	no	—
262	C₈₃⋊C₈	C₂×M₁₆	1	2	yes	—
263	C₂²×C₈₃	C₂×C₄×D₄	1	1	yes	characteristic
264	C₂×D₈₃	—	2	1	no	—
265	C₂×D₈₃	—	2	1	no	—
266	C₂×D₈₃	—	4	1	no	—
267	C₂×D₈₃	—	4	1	no	—
268	C₂×D₈₃	—	4	1	no	—
269	C₂×D₈₃	#436	1	2	yes	—
270	C₄×C₈₃	—	2	1	no	—
271	C₄×C₈₃	—	4	1	no	—
272	C₄×C₈₃	—	4	1	no	—
273	C₄×C₈₃	—	4	1	no	—
274	C₄×C₈₃	—	4	1	no	—
275	C₄×C₈₃	C₂²×M₁₆	1	1	yes	characteristic
276	C₄×C₈₃	C₂×#131	1	1	yes	characteristic
277	C₄×C₈₃	C₂×#137	1	1	yes	characteristic
278	C₄×C₈₃	#575	1	1	yes	characteristic
279	Dic₈₃	—	2	1	no	—
280	Dic₈₃	—	2	1	no	—
281	Dic₈₃	—	4	1	no	—
282	Dic₈₃	—	4	1	no	—
283	Dic₈₃	—	4	1	no	—
284	Dic₈₃	#436	1	2	yes	—
285	#17892	—	83	1	no	maximal, Sylow
286	C₂×C₈₃	C₂×#436	1	1	yes	characteristic
287	C₂×C₈₃	C₄×#137	1	1	yes	characteristic
288	C₂×C₈₃	#2955	1	1	yes	characteristic
289	D₈₃	—	2	2	no	—
290	D₈₃	—	8	1	no	—
291	#2965	—	83	1	no	—
292	C₂×#446	—	83	1	no	—
293	C₄×#137	—	83	1	no	—
294	#1593	—	83	1	no	—
295	#1593	—	83	1	no	—
296	#1592	—	83	1	no	—
297	#1592	—	83	1	no	—
298	#1591	—	83	1	no	—
299	#1591	D₈₃	1	1	yes	characteristic, complemented
300	#1590	—	83	1	no	—
301	#1590	—	83	1	no	—
302	#1565	—	83	1	no	—
303	#1479	—	83	1	no	—
304	#1477	—	83	1	no	—
305	C₈×M₁₆	—	83	1	no	—
306	C₈₃	#17892	1	1	yes	characteristic, complemented, Sylow
307	C₂×#137	—	83	1	no	—
308	C₄×#41	—	83	1	no	—
309	C₂×C₄×Q₈	—	83	1	no	—
310	#446	—	83	1	no	—
311	#446	—	83	1	no	—
312	#446	—	83	1	no	—
313	#446	—	83	1	no	—
314	#446	—	166	1	no	—
315	#446	—	166	1	no	—
316	#446	C₂×D₈₃	1	1	yes	characteristic
317	#446	C₂×D₈₃	1	1	yes	characteristic
318	#441	—	83	1	no	—
319	#441	—	83	1	no	—
320	#440	—	83	1	no	—
321	#440	—	83	1	no	—
322	C₄×Q₁₆	—	83	1	no	—
323	C₄×Q₁₆	C₂×D₈₃	1	1	yes	characteristic
324	C₄×SD₁₆	—	83	1	no	—
325	C₄×SD₁₆	—	83	1	no	—
326	#436	—	83	1	no	—
327	#436	—	83	1	no	—
328	#435	—	166	1	no	—
329	#435	—	166	1	no	—
330	#431	—	83	1	no	—
331	#431	—	83	1	no	—
332	#431	—	166	1	no	—
333	#428	—	83	1	no	—
334	C₂×C₄⋊C₈	—	83	1	no	—
335	C₂×C₄⋊C₈	—	166	1	no	—
336	#419	—	83	1	no	—
337	#417	—	83	1	no	—
338	C₄×M₁₆	—	83	1	no	—
339	C₄×M₁₆	—	166	1	no	—
340	C₂×#97	—	166	1	no	—
341	C₂×C₄×C₈	—	83	1	no	—
342	#335	—	83	1	no	—
343	#335	C₂×D₈₃	1	1	yes	characteristic
344	#334	—	83	1	no	—
345	#334	—	83	1	no	—
346	Q₈⋊C₈	—	83	1	no	—
347	Q₈⋊C₈	—	83	1	no	—
348	Q₈⋊C₈	—	83	1	no	—
349	Q₈⋊C₈	—	83	1	no	—
350	Q₈⋊C₈	C₂×D₈₃	1	1	yes	characteristic
351	Q₈⋊C₈	C₂×D₈₃	1	1	yes	characteristic
352	D₄⋊C₈	—	83	1	no	—
353	D₄⋊C₈	—	83	1	no	—
354	#322	—	83	1	no	—
355	#322	—	83	1	no	—
356	C₈²	—	83	1	no	—
357	C₈²	C₂×D₈₃	1	1	yes	characteristic
358	C₂×#41	—	83	1	no	—
359	C₂²×Q₈	—	83	1	no	—
360	#137	—	166	4	no	—
361	C₂×Q₁₆	—	83	1	no	—
362	C₂×Q₁₆	C₄×D₈₃	1	1	yes	characteristic
363	C₂×SD₁₆	—	83	1	no	—
364	C₂×SD₁₆	—	83	1	no	—
365	C₂×M₁₆	—	83	1	no	—
366	C₂×M₁₆	—	83	1	no	—
367	C₂×M₁₆	—	166	1	no	—
368	C₂×M₁₆	—	166	1	no	—
369	C₂²×C₈	—	83	1	no	—
370	C₂²×C₈	—	83	1	no	—
371	C₂²×C₈	—	166	1	no	—
372	C₄×Q₈	—	83	1	no	—
373	C₄×Q₈	—	83	1	no	—
374	C₄×Q₈	—	83	1	no	—
375	C₄×Q₈	—	83	1	no	—
376	C₄×Q₈	—	166	1	no	—
377	C₄×Q₈	—	166	1	no	—
378	C₄×Q₈	C₂²×D₈₃	1	1	yes	characteristic
379	C₄×Q₈	C₂²×D₈₃	1	1	yes	characteristic
380	C₄×D₄	—	83	1	no	—
381	C₄×D₄	—	83	1	no	—
382	C₄×D₄	—	166	1	no	—
383	C₄×D₄	—	166	1	no	—
384	#117	—	83	1	no	—
385	#117	—	166	1	no	—
386	C₂×C₄⋊C₄	—	83	1	no	—
387	C₂×C₄⋊C₄	—	166	1	no	—
388	C₂×C₄²	—	83	1	no	—
389	C₂×C₄²	—	166	1	no	—
390	C₂×C₄²	—	166	1	no	—
391	#107	—	83	1	no	—
392	#107	C₄×D₈₃	1	1	yes	characteristic
393	#106	—	83	1	no	—
394	#106	—	83	1	no	—
395	C₄⋊C₈	—	2	1	no	—
396	C₄⋊C₈	—	2	1	no	—
397	C₄⋊C₈	—	83	1	no	—
398	C₄⋊C₈	—	83	1	no	—
399	C₄⋊C₈	—	166	1	no	—
400	C₄⋊C₈	—	166	1	no	—
401	C₄⋊C₈	—	166	1	no	—
402	C₄⋊C₈	—	166	1	no	—
403	C₄⋊C₈	—	166	1	no	—
404	C₄⋊C₈	—	166	1	no	—
405	C₄⋊C₈	C₂²×D₈₃	1	1	yes	characteristic
406	C₄⋊C₈	C₂²×D₈₃	1	1	yes	characteristic
407	#103	—	83	1	no	—
408	#103	—	83	1	no	—
409	#103	—	83	1	no	—
410	#103	—	83	1	no	—
411	#103	C₄×D₈₃	1	1	yes	characteristic
412	#103	C₄×D₈₃	1	1	yes	characteristic
413	#102	—	83	1	no	—
414	#102	—	83	1	no	—
415	C₂²⋊C₈	—	166	1	no	—
416	C₂²⋊C₈	—	166	1	no	—
417	C₂²⋊C₈	—	166	1	no	—
418	C₂²⋊C₈	—	166	1	no	—
419	#97	—	2	1	no	—
420	#97	—	2	1	no	—
421	#97	—	83	1	no	—
422	#97	—	83	1	no	—
423	#97	—	166	1	no	—
424	#97	—	166	1	no	—
425	#97	—	166	1	no	—
426	#97	—	166	1	no	—
427	C₄×C₈	—	83	1	no	—
428	C₄×C₈	—	83	1	no	—
429	C₄×C₈	—	83	1	no	—
430	C₄×C₈	—	83	1	no	—
431	C₄×C₈	—	83	1	no	—
432	C₄×C₈	—	166	1	no	—
433	C₄×C₈	C₂²×D₈₃	1	1	yes	characteristic
434	C₄×C₈	C₂²×D₈₃	1	1	yes	characteristic
435	C₄×C₈	C₂²×D₈₃	1	1	yes	characteristic
436	#41	—	166	2	no	—
437	#41	—	166	2	no	—
438	C₂×Q₈	—	83	1	no	—
439	C₂×Q₈	—	166	1	no	—
440	C₂×Q₈	—	166	2	no	—
441	C₂×Q₈	—	166	2	no	—
442	C₂×Q₈	C₂×C₄×D₈₃	1	1	yes	characteristic
443	C₂×Q₈	C₂×C₄×D₈₃	1	1	yes	characteristic
444	C₂×D₄	—	83	1	no	—
445	C₂×D₄	—	166	1	no	—
446	C₂²×C₄	—	83	1	no	—
447	C₂²×C₄	—	83	1	no	—
448	C₂²×C₄	—	83	1	no	—
449	C₂²×C₄	—	166	1	no	—
450	C₂²×C₄	—	166	1	no	—
451	C₂²×C₄	—	166	1	no	—
452	C₂²×C₄	—	166	1	no	—
453	C₂²×C₄	—	166	1	no	—
454	Q₁₆	—	2	2	no	—
455	Q₁₆	—	166	2	no	—
456	SD₁₆	—	166	2	no	—
457	SD₁₆	—	166	2	no	—
458	M₁₆	—	332	2	no	—
459	M₁₆	—	332	2	no	—
460	M₁₆	—	83	4	no	—
461	M₁₆	—	166	2	no	—
462	C₂×C₈	—	2	1	no	—
463	C₂×C₈	—	2	1	no	—
464	C₂×C₈	—	2	1	no	—
465	C₂×C₈	—	332	1	no	—
466	C₂×C₈	—	332	2	no	—
467	C₂×C₈	—	83	1	no	—
468	C₂×C₈	—	83	1	no	—
469	C₂×C₈	—	83	1	no	—
470	C₂×C₈	—	83	1	no	—
471	C₂×C₈	—	166	1	no	—
472	C₂×C₈	—	166	1	no	—
473	C₂×C₈	—	166	1	no	—
474	C₂×C₈	—	166	2	no	—
475	C₂×C₈	C₂×C₄×D₈₃	1	1	yes	characteristic
476	C₂×C₈	C₂×C₄×D₈₃	1	1	yes	characteristic
477	C₂×C₈	D₄×D₈₃	1	1	yes	characteristic
478	C₂×C₈	D₄×D₈₃	1	1	yes	characteristic
479	C₄⋊C₄	—	2	1	no	—
480	C₄⋊C₄	—	2	1	no	—
481	C₄⋊C₄	—	83	1	no	—
482	C₄⋊C₄	—	83	1	no	—
483	C₄⋊C₄	—	166	1	no	—
484	C₄⋊C₄	—	166	1	no	—
485	C₄⋊C₄	—	166	1	no	—
486	C₄⋊C₄	—	166	1	no	—
487	C₄⋊C₄	—	166	1	no	—
488	C₄⋊C₄	C₂×C₄×D₈₃	1	1	yes	characteristic
489	C₄⋊C₄	C₂×C₄×D₈₃	1	1	yes	characteristic
490	C₂²⋊C₄	—	166	1	no	—
491	C₂²⋊C₄	—	166	1	no	—
492	C₂²⋊C₄	—	166	1	no	—
493	C₄²	—	2	1	no	—
494	C₄²	—	2	1	no	—
495	C₄²	—	83	1	no	—
496	C₄²	—	83	1	no	—
497	C₄²	—	83	1	no	—
498	C₄²	—	166	1	no	—
499	C₄²	—	166	1	no	—
500	C₄²	—	166	1	no	—
501	C₄²	—	166	1	no	—
502	C₄²	—	166	1	no	—
503	C₄²	C₂³×D₈₃	1	1	yes	characteristic
504	C₂³	—	83	1	no	—
505	C₂³	—	166	1	no	—
506	Q₈	—	2	1	no	—
507	Q₈	—	2	1	no	—
508	Q₈	—	2	1	no	—
509	Q₈	—	2	1	no	—
510	Q₈	—	332	2	no	—
511	Q₈	—	166	1	no	—
512	Q₈	—	166	1	no	—
513	D₄	—	332	2	no	—
514	D₄	—	166	1	no	—
515	D₄	—	166	1	no	—
516	C₂×C₄	—	2	1	no	—
517	C₂×C₄	—	2	1	no	—
518	C₂×C₄	—	2	1	no	—
519	C₂×C₄	—	2	1	no	—
520	C₂×C₄	—	332	1	no	—
521	C₂×C₄	—	332	2	no	—
522	C₂×C₄	—	332	2	no	—
523	C₂×C₄	—	332	2	no	—
524	C₂×C₄	—	332	2	no	—
525	C₂×C₄	—	332	1	no	—
526	C₂×C₄	—	332	1	no	—
527	C₂×C₄	—	83	1	no	—
528	C₂×C₄	—	83	2	no	—
529	C₂×C₄	—	83	2	no	—
530	C₂×C₄	—	83	1	no	—
531	C₂×C₄	—	83	1	no	—
532	C₂×C₄	—	166	1	no	—
533	C₂×C₄	—	166	1	no	—
534	C₂×C₄	—	166	1	no	—
535	C₂×C₄	—	166	1	no	—
536	C₂×C₄	—	166	1	no	—
537	C₂×C₄	C₂²×C₄×D₈₃	1	1	yes	characteristic
538	C₂×C₄	C₂×D₄×D₈₃	1	1	yes	characteristic
539	C₂×C₄	#41×D₈₃	1	1	yes	characteristic
540	C₈	—	2	1	no	—
541	C₈	—	2	1	no	—
542	C₈	—	4	1	no	—
543	C₈	—	4	1	no	—
544	C₈	—	4	1	no	—
545	C₈	—	332	1	no	—
546	C₈	—	332	1	no	—
547	C₈	—	332	1	no	—
548	C₈	—	83	2	no	—
549	C₈	—	166	1	no	—
550	C₈	—	166	1	no	—
551	C₈	—	166	1	no	—
552	C₈	M₁₆×D₈₃	1	2	yes	—
553	C₈	#14581824	1	2	yes	complemented
554	C₂²	—	332	1	no	—
555	C₂²	—	332	1	no	—
556	C₂²	—	332	1	no	—
557	C₂²	—	83	2	no	—
558	C₂²	—	166	1	no	—
559	C₂²	—	166	1	no	—
560	C₂²	C₄×D₄×D₈₃	1	1	yes	characteristic
561	C₄	—	2	1	no	—
562	C₄	—	4	1	no	—
563	C₄	—	4	1	no	—
564	C₄	—	4	1	no	—
565	C₄	—	4	1	no	—
566	C₄	—	332	1	no	—
567	C₄	—	332	1	no	—
568	C₄	—	332	1	no	—
569	C₄	—	83	2	no	—
570	C₄	—	166	1	no	—
571	C₄	—	166	1	no	—
572	C₄	C₂×M₁₆×D₈₃	1	1	yes	characteristic
573	C₄	#131×D₈₃	1	1	yes	characteristic
574	C₄	C₂×#14581824	1	1	yes	characteristic
575	C₄	#19128498	1	1	yes	characteristic
576	C₂	—	664	1	no	—
577	C₂	—	166	2	no	—
578	C₂	#436×D₈₃	1	1	yes	characteristic
579	C₂	C₄×#14581824	1	1	yes	characteristic
580	C₂	#24916361	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×#1591	C₂
socle	C₂²×C₈₃	C₂×C₄×D₄
prime radical	C₂×#13050591	C₂×C₄
cosocle	C₄²×C₈₃	C₂⁴
hypercenter	#1591	D₈₃
hypocenter	C₈₃	#17892
LCS	G ▷ C₂×C₄×C₈₃ ▷ C₂×C₈₃ ▷ C₈₃
UCS	C₁ ◁ C₂×C₄ ◁ C₄×C₈ ◁ #1591

Complements

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

N	H ≅ G/N	type
2. #446×D₈₃	C₂	semidirect
4. #24906372	C₂	semidirect
5. #24906369	C₂	semidirect
6. #24906368	C₂	semidirect
7. #24906364	C₂	semidirect
8. #24906358	C₂	semidirect
9. #24906355	C₂	semidirect
10. #24906353	C₂	semidirect
11. #24906214	C₂	semidirect
12. #24905856	C₂	semidirect
14. C₈×#13050573	C₂	semidirect
15. C₈₃×#1591	C₂	semidirect
167. #13050573	M₁₆	semidirect
255. C₈×C₈₃	#137	semidirect
299. #1591	D₈₃	semidirect
306. C₈₃	#17892	semidirect
553. C₈	#14581824	semidirect

Maximal subgroups

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

subgroup	index
#24916428	2
#446×D₈₃	2
C₄×#14581824	2
#24906372	2
#24906369	2
#24906368	2
#24906364	2
#24906358	2
#24906355	2
#24906353	2
#24906214	2
#24905856	2
#24905849	2
C₈×#13050573	2
C₈₃×#1591	2
#17892	83