Subgroups — #35375147

Order 21248.

590 conjugacy classes of subgroups.

The subgroup lattice has 554 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#24918046	C₂	1	1	yes	maximal, characteristic
2	#24916394	C₂	1	1	yes	maximal, characteristic
3	#24916392	C₂	1	1	yes	maximal, characteristic
4	#24906337	C₂	1	1	yes	maximal, characteristic, complemented
5	#24906336	C₂	1	1	yes	maximal, characteristic, complemented
6	#24906335	C₂	1	1	yes	maximal, characteristic, complemented
7	#24906334	C₂	1	1	yes	maximal, characteristic, complemented
8	#24906333	C₂	1	1	yes	maximal, characteristic, complemented
9	#24906332	C₂	1	1	yes	maximal, characteristic, complemented
10	#24906331	C₂	1	1	yes	maximal, characteristic, complemented
11	#24906217	C₂	1	1	yes	maximal, characteristic
12	#24905916	C₂	1	1	yes	maximal, characteristic
13	#24905916	C₂	1	1	yes	maximal, characteristic
14	#322×D₈₃	C₂	1	1	yes	maximal, characteristic
15	C₈₃×#1587	C₂	1	1	yes	maximal, characteristic, complemented
16	#19128255	C₂²	1	1	yes	characteristic
17	#19128255	C₂²	1	1	yes	characteristic
18	#19128105	C₄	1	1	yes	characteristic
19	#19128079	C₄	1	1	yes	characteristic
20	#19128050	C₄	1	1	yes	characteristic
21	#19128050	C₄	1	1	yes	characteristic
22	#19127943	C₄	1	1	yes	characteristic
23	#19127941	C₄	1	1	yes	characteristic
24	#19127941	C₄	1	1	yes	characteristic
25	#19127939	C₄	1	1	yes	characteristic
26	#19127832	C₂²	1	1	yes	characteristic
27	#19127831	C₂²	1	1	yes	characteristic
28	#19127830	—	2	1	no	—
29	#19127829	—	2	1	no	—
30	#19127828	C₂²	1	1	yes	characteristic
31	Q₈×C₈₃⋊C₈	C₂²	1	1	yes	characteristic
32	C₈×Dic₁₆₆	—	2	1	no	—
33	C₈×Dic₁₆₆	C₂²	1	1	yes	characteristic
34	#19127825	—	2	1	no	—
35	#19127825	C₂²	1	1	yes	characteristic
36	C₄×Dic₃₃₂	C₂²	1	1	yes	characteristic
37	C₄×#13050580	C₂²	1	1	yes	characteristic
38	C₄×#13050580	C₂²	1	1	yes	characteristic
39	#19127726	—	2	1	no	—
40	#19127726	—	2	1	no	—
41	#19127723	C₂²	1	1	yes	characteristic
42	#19127723	C₂²	1	1	yes	characteristic
43	#19127658	—	2	1	no	—
44	#19127655	—	2	1	no	—
45	C₄×C₈×D₈₃	C₂²	1	1	yes	characteristic
46	C₄×C₈×D₈₃	C₂²	1	1	yes	characteristic
47	C₄×C₈×D₈₃	C₂²	1	1	yes	characteristic
48	#19127452	C₂²	1	1	yes	characteristic
49	#19127451	C₂²	1	1	yes	characteristic
50	#19127451	C₂²	1	1	yes	characteristic
51	#19127433	C₂²	1	1	yes	characteristic
52	#19127433	C₂²	1	1	yes	characteristic
53	Q₈⋊(C₈₃⋊C₈)	C₂²	1	1	yes	characteristic
54	Q₈⋊(C₈₃⋊C₈)	C₂²	1	1	yes	characteristic
55	#19127431	C₂²	1	1	yes	characteristic
56	#19127431	C₂²	1	1	yes	characteristic
57	#19127423	C₂²	1	1	yes	characteristic
58	#19127423	C₂²	1	1	yes	characteristic
59	#19127422	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×Dic₃₃₂	C₂×C₄	1	1	yes	characteristic
68	C₂×#13050580	C₂×C₄	1	1	yes	characteristic
69	C₂×#13050580	C₂×C₄	1	1	yes	characteristic
70	C₂×#13050573	—	2	1	no	—
71	C₂×#13050573	—	2	1	no	—
72	C₂×C₈×D₈₃	—	2	1	no	—
73	C₂×C₈×D₈₃	C₂×C₄	1	1	yes	characteristic
74	C₂×C₈×D₈₃	C₂×C₄	1	1	yes	characteristic
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	#14581791	C₂×C₄	1	1	yes	characteristic
79	#14581790	C₂×C₄	1	1	yes	characteristic
80	#14581790	C₂×C₄	1	1	yes	characteristic
81	#14581782	—	2	1	no	—
82	#14581782	—	2	1	no	—
83	#14581772	C₂×C₄	1	1	yes	characteristic
84	#14581772	C₂×C₄	1	1	yes	characteristic
85	#14581770	—	2	1	no	—
86	#14581770	—	2	1	no	—
87	#14581768	C₂×C₄	1	1	yes	characteristic
88	#14581768	C₂×C₄	1	1	yes	characteristic
89	C₄×Dic₁₆₆	—	2	1	no	—
90	C₄×Dic₁₆₆	—	2	1	no	—
91	C₄×Dic₁₆₆	C₂³	1	1	yes	characteristic
92	C₄×Dic₁₆₆	C₂³	1	1	yes	characteristic
93	#14581749	—	2	1	no	—
94	#14581749	—	2	1	no	—
95	C₄²×D₈₃	C₂³	1	1	yes	characteristic
96	#14581726	C₂×C₄	1	1	yes	characteristic
97	#14581725	C₂×C₄	1	1	yes	characteristic
98	#14581725	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	Dic₈₃⋊C₈	—	2	1	no	—
108	Dic₈₃⋊C₈	—	2	1	no	—
109	#14581717	C₂×C₄	1	1	yes	characteristic
110	#14581717	C₂×C₄	1	1	yes	characteristic
111	#14581716	C₂×C₄	1	1	yes	characteristic
112	#14581716	C₂×C₄	1	1	yes	characteristic
113	#14581715	C₂×C₄	1	1	yes	characteristic
114	#14581715	C₂×C₄	1	1	yes	characteristic
115	#14581703	—	2	1	no	—
116	#14581702	—	2	1	no	—
117	#14581702	—	2	1	no	—
118	C₄×C₈₃⋊C₈	—	2	1	no	—
119	C₄×C₈₃⋊C₈	C₂³	1	1	yes	characteristic
120	C₄×C₈₃⋊C₈	C₂³	1	1	yes	characteristic
121	C₄×C₈₃⋊C₈	C₂³	1	1	yes	characteristic
122	C₈×Dic₈₃	—	2	1	no	—
123	C₈×Dic₈₃	—	2	1	no	—
124	C₈×Dic₈₃	—	2	1	no	—
125	C₈×Dic₈₃	C₂×C₄	1	1	yes	characteristic
126	C₈×Dic₈₃	C₂×C₄	1	1	yes	characteristic
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	—	2	1	no	—
146	C₂×Dic₁₆₆	C₂²×C₄	1	1	yes	characteristic
147	C₂×Dic₁₆₆	C₂²×C₄	1	1	yes	characteristic
148	C₂×C₄×D₈₃	C₂²×C₄	1	1	yes	characteristic
149	C₂×C₄×D₈₃	C₂×D₄	1	1	yes	characteristic
150	C₂×C₄×D₈₃	#41	1	1	yes	characteristic
151	Dic₃₃₂	—	4	1	no	—
152	#13050580	—	4	1	no	—
153	#13050580	—	4	1	no	—
154	#13050573	—	4	2	no	—
155	#13050573	—	4	2	no	—
156	C₂×C₈₃⋊C₈	—	2	1	no	—
157	C₂×C₈₃⋊C₈	—	2	1	no	—
158	C₂×C₈₃⋊C₈	—	2	1	no	—
159	C₂×C₈₃⋊C₈	C₂²×C₄	1	1	yes	characteristic
160	C₂×C₈₃⋊C₈	C₂²×C₄	1	1	yes	characteristic
161	C₂×C₈₃⋊C₈	C₂×D₄	1	1	yes	characteristic
162	C₂×C₈₃⋊C₈	C₂×D₄	1	1	yes	characteristic
163	C₈×D₈₃	—	2	4	no	—
164	C₈×D₈₃	—	2	2	no	—
165	C₈×D₈₃	—	2	2	no	—
166	C₈×D₈₃	—	4	1	no	—
167	C₈×D₈₃	—	4	1	no	—
168	C₄⋊Dic₈₃	—	2	1	no	—
169	C₄⋊Dic₈₃	—	2	1	no	—
170	C₄⋊Dic₈₃	C₂²×C₄	1	1	yes	characteristic
171	C₄⋊Dic₈₃	C₂²×C₄	1	1	yes	characteristic
172	Dic₈₃⋊C₄	—	2	1	no	—
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	Dic₈₃⋊C₄	—	2	1	no	—
181	Dic₈₃⋊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	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	—	4	1	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	C₄×D₄	1	1	yes	characteristic
209	Q₈×C₈₃	—	2	1	no	—
210	Q₈×C₈₃	—	2	1	no	—
211	Q₈×C₈₃	—	2	1	no	—
212	Q₈×C₈₃	—	2	1	no	—
213	C₂×C₄×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	C₂³×C₄	1	1	yes	characteristic
218	C₂×C₄×C₈₃	C₂²×D₄	1	1	yes	characteristic
219	C₂×C₄×C₈₃	C₂×#41	1	1	yes	characteristic
220	C₂×Dic₈₃	—	2	1	no	—
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	C₄×D₈₃	—	2	1	no	—
228	C₄×D₈₃	—	2	1	no	—
229	C₄×D₈₃	—	2	2	no	—
230	C₄×D₈₃	#137	1	2	yes	—
231	C₄×D₈₃	#137	1	2	yes	—
232	Dic₁₆₆	—	2	1	no	—
233	Dic₁₆₆	—	2	1	no	—
234	Dic₁₆₆	—	2	1	no	—
235	Dic₁₆₆	—	2	1	no	—
236	Dic₁₆₆	—	4	2	no	—
237	Dic₁₆₆	—	4	2	no	—
238	C₈×C₈₃	—	2	2	no	—
239	C₈×C₈₃	—	2	1	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	C₈₃⋊C₈	—	2	2	no	—
246	C₈₃⋊C₈	—	2	1	no	—
247	C₈₃⋊C₈	—	2	1	no	—
248	C₈₃⋊C₈	—	2	1	no	—
249	C₈₃⋊C₈	—	2	1	no	—
250	C₈₃⋊C₈	—	4	1	no	—
251	C₈₃⋊C₈	—	4	1	no	—
252	C₂²×C₈₃	C₂×C₄×D₄	1	1	yes	characteristic
253	C₂×D₈₃	—	2	1	no	—
254	C₂×D₈₃	—	2	1	no	—
255	C₂×D₈₃	#441	1	2	yes	—
256	C₄×C₈₃	—	2	1	no	—
257	C₄×C₈₃	—	4	1	no	—
258	C₄×C₈₃	—	4	1	no	—
259	C₄×C₈₃	—	4	1	no	—
260	C₄×C₈₃	—	4	1	no	—
261	C₄×C₈₃	#568	1	1	yes	characteristic
262	C₄×C₈₃	#568	1	1	yes	characteristic
263	C₄×C₈₃	C₂×#137	1	1	yes	characteristic
264	C₄×C₈₃	C₂×#137	1	1	yes	characteristic
265	Dic₈₃	—	2	1	no	—
266	Dic₈₃	—	4	1	no	—
267	Dic₈₃	—	4	1	no	—
268	Dic₈₃	—	4	1	no	—
269	Dic₈₃	—	4	1	no	—
270	Dic₈₃	#441	1	2	yes	—
271	Dic₈₃	#443	1	2	yes	—
272	#17980	—	83	1	no	maximal, Sylow
273	C₂×C₈₃	#2932	1	1	yes	characteristic
274	C₂×C₈₃	C₂×#441	1	1	yes	characteristic
275	C₂×C₈₃	C₂×#443	1	1	yes	characteristic
276	D₈₃	—	2	2	no	—
277	#3170	—	83	1	no	—
278	#2960	—	83	1	no	—
279	#2960	—	83	1	no	—
280	#1587	—	83	1	no	—
281	#1587	—	83	1	no	—
282	#1587	—	83	1	no	—
283	#1587	—	83	1	no	—
284	#1587	—	83	1	no	—
285	#1587	—	83	1	no	—
286	#1587	—	83	1	no	—
287	#1587	D₈₃	1	1	yes	characteristic, complemented
288	#1566	—	83	1	no	—
289	#1493	—	83	1	no	—
290	#1493	—	83	1	no	—
291	C₂×#322	—	83	1	no	—
292	C₈₃	#17980	1	1	yes	characteristic, complemented, Sylow
293	#533	—	83	1	no	—
294	#533	—	83	1	no	—
295	#500	—	83	1	no	—
296	#494	—	83	1	no	—
297	#487	—	83	1	no	—
298	#487	—	83	1	no	—
299	#467	—	83	1	no	—
300	#467	—	83	1	no	—
301	#467	—	83	1	no	—
302	#467	—	83	1	no	—
303	#446	—	83	1	no	—
304	#446	—	83	1	no	—
305	#446	—	83	1	no	—
306	#446	—	166	1	no	—
307	#446	—	166	1	no	—
308	#446	C₂×D₈₃	1	1	yes	characteristic
309	C₈×Q₈	—	83	1	no	—
310	C₈×Q₈	—	83	1	no	—
311	C₈×Q₈	—	83	1	no	—
312	C₈×Q₈	—	166	1	no	—
313	C₈×Q₈	—	166	1	no	—
314	C₈×Q₈	C₂×D₈₃	1	1	yes	characteristic
315	C₄×Q₁₆	—	83	1	no	—
316	C₄×Q₁₆	—	83	1	no	—
317	C₄×Q₁₆	—	83	1	no	—
318	C₄×Q₁₆	C₂×D₈₃	1	1	yes	characteristic
319	#424	—	166	1	no	—
320	#424	—	166	1	no	—
321	#423	—	83	1	no	—
322	#423	—	83	1	no	—
323	#405	—	166	1	no	—
324	#405	—	166	1	no	—
325	C₂×C₄×C₈	—	83	1	no	—
326	C₂×C₄×C₈	—	83	1	no	—
327	C₂×C₄×C₈	—	83	1	no	—
328	#334	—	83	1	no	—
329	#334	—	83	1	no	—
330	#334	—	83	1	no	—
331	#334	C₂×D₈₃	1	1	yes	characteristic
332	Q₈⋊C₈	—	83	1	no	—
333	Q₈⋊C₈	—	83	1	no	—
334	Q₈⋊C₈	—	83	1	no	—
335	Q₈⋊C₈	—	83	1	no	—
336	Q₈⋊C₈	—	83	1	no	—
337	Q₈⋊C₈	—	83	1	no	—
338	Q₈⋊C₈	C₂×D₈₃	1	1	yes	characteristic
339	Q₈⋊C₈	C₂×D₈₃	1	1	yes	characteristic
340	#322	—	83	1	no	—
341	#322	—	83	1	no	—
342	#322	—	83	1	no	—
343	#322	C₂×D₈₃	1	1	yes	characteristic
344	C₂×Q₁₆	—	83	1	no	—
345	C₂×Q₁₆	—	83	1	no	—
346	C₂×Q₁₆	—	83	1	no	—
347	C₂×Q₁₆	C₄×D₈₃	1	1	yes	characteristic
348	C₂×M₁₆	—	166	1	no	—
349	C₂×M₁₆	—	166	1	no	—
350	C₂²×C₈	—	83	1	no	—
351	C₂²×C₈	—	83	1	no	—
352	C₂²×C₈	—	83	1	no	—
353	C₂²×C₈	—	83	1	no	—
354	C₂²×C₈	—	166	1	no	—
355	C₄⋊Q₈	—	83	1	no	—
356	C₄⋊Q₈	—	83	1	no	—
357	C₄⋊Q₈	—	83	1	no	—
358	C₄⋊Q₈	—	83	1	no	—
359	#125	—	166	1	no	—
360	#125	—	166	1	no	—
361	C₂²⋊Q₈	—	83	1	no	—
362	C₂²⋊Q₈	—	83	1	no	—
363	C₂²⋊Q₈	—	83	1	no	—
364	C₂²⋊Q₈	—	83	1	no	—
365	C₂²⋊Q₈	—	166	1	no	—
366	C₂²⋊Q₈	—	166	1	no	—
367	C₄×Q₈	—	83	1	no	—
368	C₄×Q₈	—	83	1	no	—
369	C₄×Q₈	—	166	1	no	—
370	C₄×Q₈	—	166	1	no	—
371	C₄×Q₈	C₂²×D₈₃	1	1	yes	characteristic
372	C₄×Q₈	C₂²×D₈₃	1	1	yes	characteristic
373	#117	—	166	1	no	—
374	#117	—	166	1	no	—
375	C₂×C₄²	—	83	1	no	—
376	#107	—	83	1	no	—
377	#107	—	83	1	no	—
378	#107	—	83	1	no	—
379	#107	C₄×D₈₃	1	1	yes	characteristic
380	C₄⋊C₈	—	2	1	no	—
381	C₄⋊C₈	—	2	1	no	—
382	C₄⋊C₈	—	83	1	no	—
383	C₄⋊C₈	—	83	1	no	—
384	C₄⋊C₈	—	166	1	no	—
385	C₄⋊C₈	—	166	1	no	—
386	C₄⋊C₈	—	166	1	no	—
387	C₄⋊C₈	—	166	1	no	—
388	C₄⋊C₈	—	166	1	no	—
389	C₄⋊C₈	—	166	1	no	—
390	C₄⋊C₈	—	166	1	no	—
391	C₄⋊C₈	—	166	1	no	—
392	C₄⋊C₈	C₂²×D₈₃	1	1	yes	characteristic
393	C₄⋊C₈	C₂²×D₈₃	1	1	yes	characteristic
394	#103	—	83	1	no	—
395	#103	—	83	1	no	—
396	#103	—	83	1	no	—
397	#103	—	83	1	no	—
398	#103	—	83	1	no	—
399	#103	—	83	1	no	—
400	#103	C₄×D₈₃	1	1	yes	characteristic
401	#103	C₄×D₈₃	1	1	yes	characteristic
402	#97	—	2	1	no	—
403	#97	—	166	1	no	—
404	#97	—	166	1	no	—
405	#97	—	166	1	no	—
406	C₄×C₈	—	2	1	no	—
407	C₄×C₈	—	83	1	no	—
408	C₄×C₈	—	83	1	no	—
409	C₄×C₈	—	83	1	no	—
410	C₄×C₈	—	83	1	no	—
411	C₄×C₈	—	83	1	no	—
412	C₄×C₈	—	83	1	no	—
413	C₄×C₈	—	83	1	no	—
414	C₄×C₈	—	166	1	no	—
415	C₄×C₈	—	166	1	no	—
416	C₄×C₈	—	166	1	no	—
417	C₄×C₈	—	166	1	no	—
418	C₄×C₈	C₂²×D₈₃	1	1	yes	characteristic
419	C₄×C₈	C₂²×D₈₃	1	1	yes	characteristic
420	C₄×C₈	C₂²×D₈₃	1	1	yes	characteristic
421	C₂×Q₈	—	83	1	no	—
422	C₂×Q₈	—	83	1	no	—
423	C₂×Q₈	—	166	1	no	—
424	C₂×Q₈	—	166	1	no	—
425	C₂×Q₈	C₂×C₄×D₈₃	1	1	yes	characteristic
426	C₂×Q₈	C₂×C₄×D₈₃	1	1	yes	characteristic
427	C₂²×C₄	—	83	1	no	—
428	C₂²×C₄	—	83	1	no	—
429	C₂²×C₄	—	83	1	no	—
430	Q₁₆	—	4	1	no	—
431	Q₁₆	—	332	1	no	—
432	Q₁₆	—	332	1	no	—
433	Q₁₆	—	332	1	no	—
434	M₁₆	—	332	2	no	—
435	M₁₆	—	332	2	no	—
436	C₂×C₈	—	2	1	no	—
437	C₂×C₈	—	2	1	no	—
438	C₂×C₈	—	2	1	no	—
439	C₂×C₈	—	332	1	no	—
440	C₂×C₈	—	332	1	no	—
441	C₂×C₈	—	83	1	no	—
442	C₂×C₈	—	83	1	no	—
443	C₂×C₈	—	83	1	no	—
444	C₂×C₈	—	83	1	no	—
445	C₂×C₈	—	166	2	no	—
446	C₂×C₈	—	166	2	no	—
447	C₂×C₈	—	166	4	no	—
448	C₂×C₈	—	166	1	no	—
449	C₂×C₈	—	166	1	no	—
450	C₂×C₈	—	166	1	no	—
451	C₂×C₈	C₂×C₄×D₈₃	1	1	yes	characteristic
452	C₂×C₈	C₂×C₄×D₈₃	1	1	yes	characteristic
453	C₂×C₈	D₄×D₈₃	1	1	yes	characteristic
454	C₂×C₈	D₄×D₈₃	1	1	yes	characteristic
455	C₄⋊C₄	—	2	1	no	—
456	C₄⋊C₄	—	2	1	no	—
457	C₄⋊C₄	—	83	1	no	—
458	C₄⋊C₄	—	83	1	no	—
459	C₄⋊C₄	—	166	1	no	—
460	C₄⋊C₄	—	166	1	no	—
461	C₄⋊C₄	—	166	1	no	—
462	C₄⋊C₄	—	166	1	no	—
463	C₄⋊C₄	—	166	1	no	—
464	C₄⋊C₄	—	166	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	C₂×C₄×D₈₃	1	1	yes	characteristic
472	C₄⋊C₄	C₂×C₄×D₈₃	1	1	yes	characteristic
473	C₂²⋊C₄	—	166	1	no	—
474	C₂²⋊C₄	—	166	1	no	—
475	C₂²⋊C₄	—	166	1	no	—
476	C₂²⋊C₄	—	166	1	no	—
477	C₄²	—	2	1	no	—
478	C₄²	—	2	1	no	—
479	C₄²	—	83	1	no	—
480	C₄²	—	83	1	no	—
481	C₄²	—	83	1	no	—
482	C₄²	—	166	1	no	—
483	C₄²	—	166	1	no	—
484	C₄²	C₂³×D₈₃	1	1	yes	characteristic
485	C₂³	—	83	1	no	—
486	Q₈	—	2	1	no	—
487	Q₈	—	2	1	no	—
488	Q₈	—	2	1	no	—
489	Q₈	—	2	1	no	—
490	Q₈	—	332	2	no	—
491	Q₈	—	332	2	no	—
492	Q₈	—	166	1	no	—
493	Q₈	—	166	1	no	—
494	Q₈	—	166	1	no	—
495	Q₈	—	166	1	no	—
496	C₂×C₄	—	2	1	no	—
497	C₂×C₄	—	2	1	no	—
498	C₂×C₄	—	2	1	no	—
499	C₂×C₄	—	2	1	no	—
500	C₂×C₄	—	83	1	no	—
501	C₂×C₄	—	83	1	no	—
502	C₂×C₄	—	83	2	no	—
503	C₂×C₄	—	83	2	no	—
504	C₂×C₄	—	83	1	no	—
505	C₂×C₄	—	166	2	no	—
506	C₂×C₄	—	166	1	no	—
507	C₂×C₄	—	166	1	no	—
508	C₂×C₄	—	166	1	no	—
509	C₂×C₄	—	166	1	no	—
510	C₂×C₄	—	166	1	no	—
511	C₂×C₄	—	166	1	no	—
512	C₂×C₄	C₂²×C₄×D₈₃	1	1	yes	characteristic
513	C₂×C₄	C₂×D₄×D₈₃	1	1	yes	characteristic
514	C₂×C₄	#41×D₈₃	1	1	yes	characteristic
515	C₈	—	2	2	no	—
516	C₈	—	2	1	no	—
517	C₈	—	2	1	no	—
518	C₈	—	2	1	no	—
519	C₈	—	2	1	no	—
520	C₈	—	4	1	no	—
521	C₈	—	4	1	no	—
522	C₈	—	332	1	no	—
523	C₈	—	332	1	no	—
524	C₈	—	166	2	no	—
525	C₈	—	166	1	no	—
526	C₈	—	166	1	no	—
527	C₈	—	166	1	no	—
528	C₈	—	166	1	no	—
529	C₂²	—	83	2	no	—
530	C₂²	—	166	1	no	—
531	C₂²	—	166	1	no	—
532	C₂²	C₄×D₄×D₈₃	1	1	yes	characteristic
533	C₄	—	2	1	no	—
534	C₄	—	4	1	no	—
535	C₄	—	4	1	no	—
536	C₄	—	4	1	no	—
537	C₄	—	4	1	no	—
538	C₄	—	332	1	no	—
539	C₄	—	332	1	no	—
540	C₄	—	332	1	no	—
541	C₄	—	332	1	no	—
542	C₄	—	83	2	no	—
543	C₄	—	83	2	no	—
544	C₄	—	166	1	no	—
545	C₄	#19128466	1	1	yes	characteristic
546	C₄	#19128467	1	1	yes	characteristic
547	C₄	#137×D₈₃	1	1	yes	characteristic
548	C₄	#137×D₈₃	1	1	yes	characteristic
549	C₂	—	166	2	no	—
550	C₂	#24916177	1	1	yes	characteristic
551	C₂	#441×D₈₃	1	1	yes	characteristic
552	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	C₂²×D₈₃	C₄×D₄
cosocle	C₄²×C₈₃	C₂⁴
hypercenter	#1587	D₈₃
hypocenter	C₈₃	#17980
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
4. #24906337	C₂	semidirect
5. #24906336	C₂	semidirect
6. #24906335	C₂	semidirect
7. #24906334	C₂	semidirect
8. #24906333	C₂	semidirect
9. #24906332	C₂	semidirect
10. #24906331	C₂	semidirect
15. C₈₃×#1587	C₂	semidirect
287. #1587	D₈₃	semidirect
292. C₈₃	#17980	semidirect

Maximal subgroups

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

subgroup	index
#24918046	2
#24916394	2
#24916392	2
#24906337	2
#24906336	2
#24906335	2
#24906334	2
#24906333	2
#24906332	2
#24906331	2
#24906217	2
#24905916	2
#322×D₈₃	2
C₈₃×#1587	2
#17980	83