Subgroups — #35374363

Order 21248.

626 conjugacy classes of subgroups.

The subgroup lattice has 580 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#24916439	C₂	1	1	yes	maximal, characteristic, complemented
2	#41×C₈₃⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
3	#24906342	C₂	1	1	yes	maximal, characteristic, complemented
4	#24906335	C₂	1	1	yes	maximal, characteristic, complemented
5	#24906328	C₂	1	1	yes	maximal, characteristic, complemented
6	#24906321	C₂	1	1	yes	maximal, characteristic, complemented
7	#24906287	C₂	1	1	yes	maximal, characteristic, complemented
8	#24906282	C₂	1	1	yes	maximal, characteristic, complemented
9	SD₁₆⋊(C₈₃⋊C₈)	C₂	1	1	yes	maximal, characteristic, complemented
10	SD₁₆⋊(C₈₃⋊C₈)	C₂	1	1	yes	maximal, characteristic, complemented
11	#24906243	C₂	1	1	yes	maximal, characteristic, complemented
12	#24905897	C₂	1	1	yes	maximal, characteristic, complemented
13	#24905871	C₂	1	1	yes	maximal, characteristic, complemented
14	#24905756	C₂	1	1	yes	maximal, characteristic, complemented
15	C₈₃×#3102	C₂	1	1	yes	maximal, characteristic
16	#19127832	C₂²	1	1	yes	characteristic
17	Q₈×C₈₃⋊C₈	C₂²	1	1	yes	characteristic
18	Q₈×C₈₃⋊C₈	C₂²	1	1	yes	characteristic
19	Q₈×C₈₃⋊C₈	C₂²	1	1	yes	characteristic
20	#19127779	C₂²	1	1	yes	characteristic
21	#19127773	—	2	1	no	—
22	D₄×C₈₃⋊C₈	—	2	1	no	—
23	D₄×C₈₃⋊C₈	—	2	1	no	—
24	D₄×C₈₃⋊C₈	—	2	1	no	—
25	D₄×C₈₃⋊C₈	C₂²	1	1	yes	characteristic
26	D₄×C₈₃⋊C₈	C₂²	1	1	yes	characteristic
27	D₄×C₈₃⋊C₈	C₂²	1	1	yes	characteristic
28	#19127762	—	2	1	no	—
29	#19127758	C₂²	1	1	yes	characteristic
30	#19127754	—	2	1	no	—
31	#19127754	C₂²	1	1	yes	characteristic
32	#19127754	C₂²	1	1	yes	characteristic
33	#19127657	—	2	1	no	—
34	C₂×C₄×C₈₃⋊C₈	—	2	1	no	—
35	C₂×C₄×C₈₃⋊C₈	C₂²	1	1	yes	characteristic
36	#19127454	C₂²	1	1	yes	characteristic
37	#19127454	C₂²	1	1	yes	characteristic
38	#19127452	C₂²	1	1	yes	characteristic
39	#19127452	C₂²	1	1	yes	characteristic
40	Q₈⋊(C₈₃⋊C₈)	C₂²	1	1	yes	characteristic
41	Q₈⋊(C₈₃⋊C₈)	C₂²	1	1	yes	characteristic
42	Q₈⋊(C₈₃⋊C₈)	C₂²	1	1	yes	characteristic
43	Q₈⋊(C₈₃⋊C₈)	C₂²	1	1	yes	characteristic
44	D₄⋊(C₈₃⋊C₈)	C₂²	1	1	yes	characteristic
45	D₄⋊(C₈₃⋊C₈)	C₂²	1	1	yes	characteristic
46	D₄⋊(C₈₃⋊C₈)	C₂²	1	1	yes	characteristic
47	D₄⋊(C₈₃⋊C₈)	C₂²	1	1	yes	characteristic
48	#19127423	C₂²	1	1	yes	characteristic
49	#19127423	C₂²	1	1	yes	characteristic
50	#19127422	C₂²	1	1	yes	characteristic
51	#19127422	C₂²	1	1	yes	characteristic
52	#529×C₈₃	C₂²	1	1	yes	characteristic
53	C₄×#41×C₈₃	C₂²	1	1	yes	characteristic
54	#485×C₈₃	C₄	1	1	yes	characteristic
55	#482×C₈₃	C₄	1	1	yes	characteristic
56	#479×C₈₃	C₄	1	1	yes	characteristic
57	#478×C₈₃	C₄	1	1	yes	characteristic
58	#464×C₈₃	C₄	1	1	yes	characteristic
59	#463×C₈₃	C₄	1	1	yes	characteristic
60	#452×C₈₃	C₄	1	1	yes	characteristic
61	#449×C₈₃	C₄	1	1	yes	characteristic
62	C₄×Q₁₆×C₈₃	C₂²	1	1	yes	characteristic
63	C₄×SD₁₆×C₈₃	C₂²	1	1	yes	characteristic
64	C₄×SD₁₆×C₈₃	C₂²	1	1	yes	characteristic
65	C₄×D₈×C₈₃	C₂²	1	1	yes	characteristic
66	#431×C₈₃	C₂²	1	1	yes	characteristic
67	C₂×#13050574	—	2	1	no	—
68	C₂²×C₈₃⋊C₈	—	2	1	no	—
69	C₂²×C₈₃⋊C₈	—	2	1	no	—
70	C₂²×C₈₃⋊C₈	—	2	1	no	—
71	C₂²×C₈₃⋊C₈	D₄	1	1	yes	characteristic
72	C₂²×C₈₃⋊C₈	D₄	1	1	yes	characteristic
73	C₄⋊(C₈₃⋊C₈)	—	2	1	no	—
74	C₄⋊(C₈₃⋊C₈)	—	2	1	no	—
75	C₄⋊(C₈₃⋊C₈)	—	2	1	no	—
76	C₄⋊(C₈₃⋊C₈)	—	2	1	no	—
77	C₄⋊(C₈₃⋊C₈)	—	2	1	no	—
78	C₄⋊(C₈₃⋊C₈)	C₂³	1	1	yes	characteristic
79	C₄⋊(C₈₃⋊C₈)	C₂³	1	1	yes	characteristic
80	C₄⋊(C₈₃⋊C₈)	C₂³	1	1	yes	characteristic
81	C₄⋊(C₈₃⋊C₈)	C₂³	1	1	yes	characteristic
82	C₂²⋊(C₈₃⋊C₈)	—	2	1	no	—
83	C₂²⋊(C₈₃⋊C₈)	—	2	1	no	—
84	C₂²⋊(C₈₃⋊C₈)	—	2	1	no	—
85	C₂²⋊(C₈₃⋊C₈)	—	2	1	no	—
86	C₂²⋊(C₈₃⋊C₈)	—	2	1	no	—
87	C₂²⋊(C₈₃⋊C₈)	—	2	1	no	—
88	C₂²⋊(C₈₃⋊C₈)	—	2	1	no	—
89	#14581703	—	2	1	no	—
90	#14581703	—	2	1	no	—
91	C₄×C₈₃⋊C₈	—	2	1	no	—
92	C₄×C₈₃⋊C₈	—	2	1	no	—
93	C₄×C₈₃⋊C₈	—	2	1	no	—
94	C₄×C₈₃⋊C₈	—	2	1	no	—
95	C₄×C₈₃⋊C₈	D₄	1	1	yes	characteristic
96	C₄×C₈₃⋊C₈	D₄	1	1	yes	characteristic
97	C₄×C₈₃⋊C₈	C₂³	1	1	yes	characteristic
98	C₄×C₈₃⋊C₈	C₂³	1	1	yes	characteristic
99	C₄×C₈₃⋊C₈	C₂³	1	1	yes	characteristic
100	C₄×C₈₃⋊C₈	C₂³	1	1	yes	characteristic
101	C₂×#41×C₈₃	C₂×C₄	1	1	yes	characteristic
102	C₂×Q₁₆×C₈₃	C₂×C₄	1	1	yes	characteristic
103	C₂×SD₁₆×C₈₃	C₂×C₄	1	1	yes	characteristic
104	C₂×SD₁₆×C₈₃	C₂×C₄	1	1	yes	characteristic
105	C₂×D₈×C₈₃	C₂×C₄	1	1	yes	characteristic
106	#126×C₈₃	—	2	1	no	—
107	#125×C₈₃	C₂×C₄	1	1	yes	characteristic
108	#124×C₈₃	C₂×C₄	1	1	yes	characteristic
109	#123×C₈₃	—	2	1	no	—
110	C₂²⋊Q₈×C₈₃	C₂×C₄	1	1	yes	characteristic
111	#121×C₈₃	C₂×C₄	1	1	yes	characteristic
112	C₄×Q₈×C₈₃	C₂×C₄	1	1	yes	characteristic
113	C₄×Q₈×C₈₃	C₂³	1	1	yes	characteristic
114	C₄×Q₈×C₈₃	C₂³	1	1	yes	characteristic
115	C₄×D₄×C₈₃	—	2	1	no	—
116	C₄×D₄×C₈₃	—	2	1	no	—
117	C₄×D₄×C₈₃	—	2	1	no	—
118	C₄×D₄×C₈₃	C₂×C₄	1	1	yes	characteristic
119	C₄×D₄×C₈₃	C₂³	1	1	yes	characteristic
120	C₄×D₄×C₈₃	C₂³	1	1	yes	characteristic
121	#117×C₈₃	—	2	1	no	—
122	#117×C₈₃	—	2	1	no	—
123	#117×C₈₃	C₂×C₄	1	1	yes	characteristic
124	C₂×C₄²×C₈₃	—	2	1	no	—
125	C₂×C₄²×C₈₃	C₂³	1	1	yes	characteristic
126	#107×C₈₃	C₂×C₄	1	1	yes	characteristic
127	#107×C₈₃	C₂×C₄	1	1	yes	characteristic
128	#106×C₈₃	C₂×C₄	1	1	yes	characteristic
129	#106×C₈₃	C₂×C₄	1	1	yes	characteristic
130	C₄⋊C₈×C₈₃	C₂×C₄	1	1	yes	characteristic
131	C₄⋊C₈×C₈₃	C₂×C₄	1	1	yes	characteristic
132	#103×C₈₃	C₂×C₄	1	1	yes	characteristic
133	#103×C₈₃	C₂×C₄	1	1	yes	characteristic
134	#103×C₈₃	C₂×C₄	1	1	yes	characteristic
135	#103×C₈₃	C₂×C₄	1	1	yes	characteristic
136	#102×C₈₃	C₂×C₄	1	1	yes	characteristic
137	#102×C₈₃	C₂×C₄	1	1	yes	characteristic
138	#102×C₈₃	C₂×C₄	1	1	yes	characteristic
139	#102×C₈₃	C₂×C₄	1	1	yes	characteristic
140	C₂²⋊C₈×C₈₃	C₂×C₄	1	1	yes	characteristic
141	C₂²⋊C₈×C₈₃	C₂×C₄	1	1	yes	characteristic
142	C₄×C₈×C₈₃	C₂³	1	1	yes	characteristic
143	C₄×C₈×C₈₃	C₂³	1	1	yes	characteristic
144	#13050574	—	4	2	no	—
145	C₂×C₈₃⋊C₈	—	2	1	no	—
146	C₂×C₈₃⋊C₈	—	2	1	no	—
147	C₂×C₈₃⋊C₈	—	2	1	no	—
148	C₂×C₈₃⋊C₈	—	2	1	no	—
149	C₂×C₈₃⋊C₈	—	2	1	no	—
150	C₂×C₈₃⋊C₈	—	2	1	no	—
151	C₂×C₈₃⋊C₈	—	4	1	no	—
152	C₂×C₈₃⋊C₈	—	4	1	no	—
153	C₂×C₈₃⋊C₈	—	4	2	no	—
154	C₂×C₈₃⋊C₈	—	4	2	no	—
155	C₂×C₈₃⋊C₈	—	4	2	no	—
156	C₂×C₈₃⋊C₈	C₂×D₄	1	1	yes	characteristic
157	C₂×C₈₃⋊C₈	C₂×D₄	1	1	yes	characteristic
158	C₂×C₈₃⋊C₈	C₂×D₄	1	1	yes	characteristic
159	C₂×C₈₃⋊C₈	C₂×D₄	1	1	yes	characteristic
160	#41×C₈₃	—	2	2	no	—
161	#41×C₈₃	—	2	2	no	—
162	C₂×Q₈×C₈₃	C₂²×C₄	1	1	yes	characteristic
163	C₂×Q₈×C₈₃	C₂²×C₄	1	1	yes	characteristic
164	C₂×D₄×C₈₃	—	2	1	no	—
165	C₂×D₄×C₈₃	—	2	1	no	—
166	C₂×D₄×C₈₃	C₂²×C₄	1	1	yes	characteristic
167	C₂×D₄×C₈₃	C₂²×C₄	1	1	yes	characteristic
168	C₂²×C₄×C₈₃	—	2	1	no	—
169	C₂²×C₄×C₈₃	—	2	1	no	—
170	C₂²×C₄×C₈₃	—	2	1	no	—
171	C₂²×C₄×C₈₃	—	2	1	no	—
172	C₂²×C₄×C₈₃	C₂²×C₄	1	1	yes	characteristic
173	C₂²×C₄×C₈₃	C₂×D₄	1	1	yes	characteristic
174	C₂²×C₄×C₈₃	#41	1	1	yes	characteristic
175	Q₁₆×C₈₃	—	2	2	no	—
176	SD₁₆×C₈₃	—	2	2	no	—
177	SD₁₆×C₈₃	—	2	2	no	—
178	D₈×C₈₃	—	2	2	no	—
179	C₂×C₈×C₈₃	C₂²×C₄	1	1	yes	characteristic
180	C₂×C₈×C₈₃	C₂²×C₄	1	1	yes	characteristic
181	C₂×C₈×C₈₃	C₂²×C₄	1	1	yes	characteristic
182	C₂×C₈×C₈₃	C₂²×C₄	1	1	yes	characteristic
183	C₄⋊C₄×C₈₃	—	2	1	no	—
184	C₄⋊C₄×C₈₃	—	2	1	no	—
185	C₄⋊C₄×C₈₃	—	2	1	no	—
186	C₄⋊C₄×C₈₃	—	2	1	no	—
187	C₄⋊C₄×C₈₃	—	2	1	no	—
188	C₄⋊C₄×C₈₃	—	2	1	no	—
189	C₄⋊C₄×C₈₃	C₂²×C₄	1	1	yes	characteristic
190	C₄⋊C₄×C₈₃	C₂²×C₄	1	1	yes	characteristic
191	C₄⋊C₄×C₈₃	C₂²×C₄	1	1	yes	characteristic
192	C₄⋊C₄×C₈₃	C₂²×C₄	1	1	yes	characteristic
193	C₂²⋊C₄×C₈₃	—	2	1	no	—
194	C₂²⋊C₄×C₈₃	—	2	1	no	—
195	C₂²⋊C₄×C₈₃	—	2	1	no	—
196	C₂²⋊C₄×C₈₃	—	2	1	no	—
197	C₂²⋊C₄×C₈₃	—	2	1	no	—
198	C₂²⋊C₄×C₈₃	—	2	1	no	—
199	C₂²⋊C₄×C₈₃	—	2	1	no	—
200	C₂²⋊C₄×C₈₃	—	2	1	no	—
201	C₄²×C₈₃	—	2	1	no	—
202	C₄²×C₈₃	—	2	1	no	—
203	C₄²×C₈₃	—	2	1	no	—
204	C₄²×C₈₃	—	2	1	no	—
205	C₄²×C₈₃	C₂²×C₄	1	1	yes	characteristic
206	C₄²×C₈₃	C₂×D₄	1	1	yes	characteristic
207	C₄²×C₈₃	#41	1	1	yes	characteristic
208	C₄²×C₈₃	C₂⁴	1	1	yes	characteristic
209	C₂³×C₈₃	—	2	1	no	—
210	C₂³×C₈₃	—	2	1	no	—
211	C₂³×C₈₃	C₄×D₄	1	1	yes	characteristic
212	Q₈×C₈₃	—	2	1	no	—
213	Q₈×C₈₃	—	2	1	no	—
214	Q₈×C₈₃	—	2	1	no	—
215	Q₈×C₈₃	#131	1	2	yes	—
216	D₄×C₈₃	—	2	4	no	—
217	D₄×C₈₃	—	2	1	no	—
218	D₄×C₈₃	—	2	1	no	—
219	D₄×C₈₃	—	2	1	no	—
220	D₄×C₈₃	—	4	2	no	—
221	D₄×C₈₃	#131	1	2	yes	—
222	C₂×C₄×C₈₃	—	2	4	no	—
223	C₂×C₄×C₈₃	—	2	1	no	—
224	C₂×C₄×C₈₃	—	2	1	no	—
225	C₂×C₄×C₈₃	—	2	1	no	—
226	C₂×C₄×C₈₃	—	2	1	no	—
227	C₂×C₄×C₈₃	—	2	1	no	—
228	C₂×C₄×C₈₃	—	2	1	no	—
229	C₂×C₄×C₈₃	—	2	1	no	—
230	C₂×C₄×C₈₃	—	2	1	no	—
231	C₂×C₄×C₈₃	—	2	1	no	—
232	C₂×C₄×C₈₃	—	2	1	no	—
233	C₂×C₄×C₈₃	—	4	1	no	—
234	C₂×C₄×C₈₃	—	4	2	no	—
235	C₂×C₄×C₈₃	—	4	1	no	—
236	C₂×C₄×C₈₃	—	4	1	no	—
237	C₂×C₄×C₈₃	—	4	1	no	—
238	C₂×C₄×C₈₃	—	4	1	no	—
239	C₂×C₄×C₈₃	C₄×D₄	1	1	yes	characteristic
240	C₂×C₄×C₈₃	C₄×D₄	1	1	yes	characteristic
241	C₂×C₄×C₈₃	C₄×D₄	1	1	yes	characteristic
242	C₂×C₄×C₈₃	C₂³×C₄	1	1	yes	characteristic
243	C₂×C₄×C₈₃	C₂²×D₄	1	1	yes	characteristic
244	C₂×C₄×C₈₃	C₂×#41	1	1	yes	characteristic
245	C₈×C₈₃	—	2	1	no	—
246	C₈×C₈₃	—	2	1	no	—
247	C₈×C₈₃	—	2	1	no	—
248	C₈×C₈₃	—	2	1	no	—
249	C₈₃⋊C₈	—	2	1	no	—
250	C₈₃⋊C₈	—	2	1	no	—
251	C₈₃⋊C₈	—	2	1	no	—
252	C₈₃⋊C₈	—	2	1	no	—
253	C₈₃⋊C₈	—	4	1	no	—
254	C₈₃⋊C₈	—	4	1	no	—
255	C₈₃⋊C₈	—	4	1	no	—
256	C₈₃⋊C₈	—	4	1	no	—
257	C₈₃⋊C₈	—	4	1	no	—
258	C₈₃⋊C₈	—	4	1	no	—
259	C₂²×C₈₃	—	2	1	no	—
260	C₂²×C₈₃	—	2	2	no	—
261	C₂²×C₈₃	—	2	1	no	—
262	C₂²×C₈₃	—	2	1	no	—
263	C₂²×C₈₃	—	4	1	no	—
264	C₂²×C₈₃	—	4	1	no	—
265	C₂²×C₈₃	—	4	1	no	—
266	C₂²×C₈₃	—	4	1	no	—
267	C₂²×C₈₃	—	4	1	no	—
268	C₂²×C₈₃	C₂×C₄×D₄	1	1	yes	characteristic
269	C₄×C₈₃	—	2	1	no	—
270	C₄×C₈₃	—	2	2	no	—
271	C₄×C₈₃	—	2	1	no	—
272	C₄×C₈₃	—	2	1	no	—
273	C₄×C₈₃	—	2	1	no	—
274	C₄×C₈₃	—	4	1	no	—
275	C₄×C₈₃	—	4	1	no	—
276	C₄×C₈₃	—	4	1	no	—
277	C₄×C₈₃	—	4	1	no	—
278	C₄×C₈₃	—	4	1	no	—
279	C₄×C₈₃	C₂×#131	1	1	yes	characteristic
280	C₄×C₈₃	C₂×#131	1	1	yes	characteristic
281	C₄×C₈₃	#575	1	1	yes	characteristic
282	C₄×C₈₃	#575	1	1	yes	characteristic
283	#17909	—	83	1	no	maximal, Sylow
284	C₂×C₈₃	—	4	1	no	—
285	C₂×C₈₃	—	4	2	no	—
286	C₂×C₈₃	—	8	1	no	—
287	C₂×C₈₃	#2929	1	1	yes	characteristic
288	C₂×C₈₃	#2943	1	1	yes	characteristic
289	C₂×C₈₃	#2955	1	1	yes	characteristic
290	#3102	D₈₃	1	1	yes	characteristic
291	#2966	—	83	1	no	—
292	C₈×#41	—	83	1	no	—
293	#1588	—	83	1	no	—
294	#1587	—	83	1	no	—
295	#1586	—	83	1	no	—
296	#1585	—	83	1	no	—
297	#1580	—	83	1	no	—
298	#1579	—	83	1	no	—
299	SD₁₆⋊C₈	—	83	1	no	—
300	SD₁₆⋊C₈	—	83	1	no	—
301	#1572	—	83	1	no	—
302	#1488	—	83	1	no	—
303	#1482	—	83	1	no	—
304	#1452	—	83	1	no	—
305	C₈₃	#17909	1	1	yes	characteristic, complemented, Sylow
306	#529	C₂×D₈₃	1	1	yes	characteristic
307	C₄×#41	C₂×D₈₃	1	1	yes	characteristic
308	#485	Dic₈₃	1	1	yes	characteristic
309	#482	Dic₈₃	1	1	yes	characteristic
310	#479	Dic₈₃	1	1	yes	characteristic
311	#478	Dic₈₃	1	1	yes	characteristic
312	#464	Dic₈₃	1	1	yes	characteristic
313	#463	Dic₈₃	1	1	yes	characteristic
314	#452	Dic₈₃	1	1	yes	characteristic
315	#449	Dic₈₃	1	1	yes	characteristic
316	#446	—	83	1	no	—
317	C₈×Q₈	—	83	1	no	—
318	C₈×Q₈	—	83	1	no	—
319	C₈×Q₈	—	83	1	no	—
320	C₄×Q₁₆	C₂×D₈₃	1	1	yes	characteristic
321	C₄×SD₁₆	C₂×D₈₃	1	1	yes	characteristic
322	C₄×SD₁₆	C₂×D₈₃	1	1	yes	characteristic
323	C₄×D₈	C₂×D₈₃	1	1	yes	characteristic
324	#436	—	83	1	no	—
325	#435	—	166	1	no	—
326	C₈×D₄	—	83	1	no	—
327	C₈×D₄	—	83	1	no	—
328	C₈×D₄	—	83	1	no	—
329	C₈×D₄	—	166	1	no	—
330	C₈×D₄	—	166	1	no	—
331	C₈×D₄	—	166	1	no	—
332	#433	—	166	1	no	—
333	#432	—	83	1	no	—
334	#431	—	83	1	no	—
335	#431	—	83	1	no	—
336	#431	—	166	1	no	—
337	#431	C₂×D₈₃	1	1	yes	characteristic
338	#405	—	166	1	no	—
339	C₂×C₄×C₈	—	83	1	no	—
340	C₂×C₄×C₈	—	166	1	no	—
341	#335	—	83	1	no	—
342	#335	—	83	1	no	—
343	#334	—	83	1	no	—
344	#334	—	83	1	no	—
345	Q₈⋊C₈	—	83	1	no	—
346	Q₈⋊C₈	—	83	1	no	—
347	Q₈⋊C₈	—	83	1	no	—
348	Q₈⋊C₈	—	83	1	no	—
349	D₄⋊C₈	—	83	1	no	—
350	D₄⋊C₈	—	83	1	no	—
351	D₄⋊C₈	—	83	1	no	—
352	D₄⋊C₈	—	83	1	no	—
353	#322	—	83	1	no	—
354	#322	—	83	1	no	—
355	#322	—	83	1	no	—
356	#322	—	83	1	no	—
357	C₂×#41	C₂×Dic₈₃	1	1	yes	characteristic
358	C₂×Q₁₆	C₂×Dic₈₃	1	1	yes	characteristic
359	C₂×SD₁₆	C₂×Dic₈₃	1	1	yes	characteristic
360	C₂×SD₁₆	C₂×Dic₈₃	1	1	yes	characteristic
361	C₂×D₈	C₂×Dic₈₃	1	1	yes	characteristic
362	C₂×M₁₆	—	166	1	no	—
363	C₂²×C₈	—	83	1	no	—
364	C₂²×C₈	—	83	1	no	—
365	C₂²×C₈	—	166	1	no	—
366	C₂²×C₈	—	166	1	no	—
367	C₂²×C₈	—	166	1	no	—
368	#126	—	2	1	no	—
369	#125	C₂×Dic₈₃	1	1	yes	characteristic
370	#124	C₂×Dic₈₃	1	1	yes	characteristic
371	#123	—	2	1	no	—
372	C₂²⋊Q₈	C₂×Dic₈₃	1	1	yes	characteristic
373	#121	C₂×Dic₈₃	1	1	yes	characteristic
374	C₄×Q₈	C₂×Dic₈₃	1	1	yes	characteristic
375	C₄×Q₈	C₂²×D₈₃	1	1	yes	characteristic
376	C₄×Q₈	C₂²×D₈₃	1	1	yes	characteristic
377	C₄×D₄	—	2	1	no	—
378	C₄×D₄	—	2	1	no	—
379	C₄×D₄	—	2	1	no	—
380	C₄×D₄	C₂×Dic₈₃	1	1	yes	characteristic
381	C₄×D₄	C₂²×D₈₃	1	1	yes	characteristic
382	C₄×D₄	C₂²×D₈₃	1	1	yes	characteristic
383	#117	—	2	1	no	—
384	#117	—	2	1	no	—
385	#117	C₂×Dic₈₃	1	1	yes	characteristic
386	C₂×C₄²	—	2	1	no	—
387	C₂×C₄²	C₂²×D₈₃	1	1	yes	characteristic
388	#107	C₂×Dic₈₃	1	1	yes	characteristic
389	#107	C₂×Dic₈₃	1	1	yes	characteristic
390	#106	C₂×Dic₈₃	1	1	yes	characteristic
391	#106	C₂×Dic₈₃	1	1	yes	characteristic
392	C₄⋊C₈	—	83	1	no	—
393	C₄⋊C₈	—	83	1	no	—
394	C₄⋊C₈	—	83	1	no	—
395	C₄⋊C₈	—	83	1	no	—
396	C₄⋊C₈	—	166	1	no	—
397	C₄⋊C₈	—	166	1	no	—
398	C₄⋊C₈	—	166	1	no	—
399	C₄⋊C₈	—	166	1	no	—
400	C₄⋊C₈	—	166	1	no	—
401	C₄⋊C₈	C₂×Dic₈₃	1	1	yes	characteristic
402	C₄⋊C₈	C₂×Dic₈₃	1	1	yes	characteristic
403	#103	C₂×Dic₈₃	1	1	yes	characteristic
404	#103	C₂×Dic₈₃	1	1	yes	characteristic
405	#103	C₂×Dic₈₃	1	1	yes	characteristic
406	#103	C₂×Dic₈₃	1	1	yes	characteristic
407	#102	C₂×Dic₈₃	1	1	yes	characteristic
408	#102	C₂×Dic₈₃	1	1	yes	characteristic
409	#102	C₂×Dic₈₃	1	1	yes	characteristic
410	#102	C₂×Dic₈₃	1	1	yes	characteristic
411	C₂²⋊C₈	—	166	1	no	—
412	C₂²⋊C₈	—	166	1	no	—
413	C₂²⋊C₈	—	166	1	no	—
414	C₂²⋊C₈	—	166	1	no	—
415	C₂²⋊C₈	—	166	1	no	—
416	C₂²⋊C₈	—	166	1	no	—
417	C₂²⋊C₈	—	166	1	no	—
418	C₂²⋊C₈	C₂×Dic₈₃	1	1	yes	characteristic
419	C₂²⋊C₈	C₂×Dic₈₃	1	1	yes	characteristic
420	#97	—	166	1	no	—
421	#97	—	166	1	no	—
422	C₄×C₈	—	83	1	no	—
423	C₄×C₈	—	83	1	no	—
424	C₄×C₈	—	83	1	no	—
425	C₄×C₈	—	83	1	no	—
426	C₄×C₈	—	83	1	no	—
427	C₄×C₈	—	83	1	no	—
428	C₄×C₈	—	166	1	no	—
429	C₄×C₈	—	166	1	no	—
430	C₄×C₈	—	166	1	no	—
431	C₄×C₈	—	166	1	no	—
432	C₄×C₈	C₂²×D₈₃	1	1	yes	characteristic
433	C₄×C₈	C₂²×D₈₃	1	1	yes	characteristic
434	#41	—	2	2	no	—
435	#41	—	2	2	no	—
436	C₂×Q₈	C₂²×Dic₈₃	1	1	yes	characteristic
437	C₂×Q₈	C₂²×Dic₈₃	1	1	yes	characteristic
438	C₂×D₄	—	2	1	no	—
439	C₂×D₄	—	2	1	no	—
440	C₂×D₄	C₂²×Dic₈₃	1	1	yes	characteristic
441	C₂×D₄	C₂²×Dic₈₃	1	1	yes	characteristic
442	C₂²×C₄	—	2	1	no	—
443	C₂²×C₄	—	2	1	no	—
444	C₂²×C₄	—	2	1	no	—
445	C₂²×C₄	—	2	1	no	—
446	C₂²×C₄	C₂²×Dic₈₃	1	1	yes	characteristic
447	C₂²×C₄	D₄×D₈₃	1	1	yes	characteristic
448	C₂²×C₄	#13050589	1	1	yes	characteristic
449	Q₁₆	—	2	2	no	—
450	SD₁₆	—	2	2	no	—
451	SD₁₆	—	2	2	no	—
452	D₈	—	2	2	no	—
453	M₁₆	—	332	2	no	—
454	C₂×C₈	—	332	2	no	—
455	C₂×C₈	—	332	2	no	—
456	C₂×C₈	—	332	2	no	—
457	C₂×C₈	—	332	1	no	—
458	C₂×C₈	—	332	1	no	—
459	C₂×C₈	—	83	1	no	—
460	C₂×C₈	—	83	1	no	—
461	C₂×C₈	—	83	1	no	—
462	C₂×C₈	—	83	1	no	—
463	C₂×C₈	—	166	1	no	—
464	C₂×C₈	—	166	1	no	—
465	C₂×C₈	—	166	1	no	—
466	C₂×C₈	—	166	1	no	—
467	C₂×C₈	—	166	1	no	—
468	C₂×C₈	—	166	1	no	—
469	C₂×C₈	C₂²×Dic₈₃	1	1	yes	characteristic
470	C₂×C₈	C₂²×Dic₈₃	1	1	yes	characteristic
471	C₂×C₈	C₂²×Dic₈₃	1	1	yes	characteristic
472	C₂×C₈	C₂²×Dic₈₃	1	1	yes	characteristic
473	C₄⋊C₄	—	2	1	no	—
474	C₄⋊C₄	—	2	1	no	—
475	C₄⋊C₄	—	2	1	no	—
476	C₄⋊C₄	—	2	1	no	—
477	C₄⋊C₄	—	2	1	no	—
478	C₄⋊C₄	—	2	1	no	—
479	C₄⋊C₄	C₂²×Dic₈₃	1	1	yes	characteristic
480	C₄⋊C₄	C₂²×Dic₈₃	1	1	yes	characteristic
481	C₄⋊C₄	C₂²×Dic₈₃	1	1	yes	characteristic
482	C₄⋊C₄	C₂²×Dic₈₃	1	1	yes	characteristic
483	C₂²⋊C₄	—	2	1	no	—
484	C₂²⋊C₄	—	2	1	no	—
485	C₂²⋊C₄	—	2	1	no	—
486	C₂²⋊C₄	—	2	1	no	—
487	C₂²⋊C₄	—	2	1	no	—
488	C₂²⋊C₄	—	2	1	no	—
489	C₂²⋊C₄	—	2	1	no	—
490	C₂²⋊C₄	—	2	1	no	—
491	C₄²	—	2	1	no	—
492	C₄²	—	2	1	no	—
493	C₄²	—	2	1	no	—
494	C₄²	—	2	1	no	—
495	C₄²	C₂²×Dic₈₃	1	1	yes	characteristic
496	C₄²	D₄×D₈₃	1	1	yes	characteristic
497	C₄²	#13050589	1	1	yes	characteristic
498	C₄²	C₂³×D₈₃	1	1	yes	characteristic
499	C₂³	—	2	1	no	—
500	C₂³	—	2	1	no	—
501	C₂³	D₄×Dic₈₃	1	1	yes	characteristic
502	Q₈	—	2	1	no	—
503	Q₈	—	2	1	no	—
504	Q₈	—	2	1	no	—
505	Q₈	#14581799	1	2	yes	—
506	D₄	—	2	4	no	—
507	D₄	—	2	1	no	—
508	D₄	—	2	1	no	—
509	D₄	—	2	1	no	—
510	D₄	—	4	2	no	—
511	D₄	#14581799	1	2	yes	—
512	C₂×C₄	—	2	4	no	—
513	C₂×C₄	—	2	1	no	—
514	C₂×C₄	—	2	1	no	—
515	C₂×C₄	—	2	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	—	2	1	no	—
521	C₂×C₄	—	2	1	no	—
522	C₂×C₄	—	2	1	no	—
523	C₂×C₄	—	4	1	no	—
524	C₂×C₄	—	4	2	no	—
525	C₂×C₄	—	4	1	no	—
526	C₂×C₄	—	4	1	no	—
527	C₂×C₄	—	4	1	no	—
528	C₂×C₄	—	4	1	no	—
529	C₂×C₄	D₄×Dic₈₃	1	1	yes	characteristic
530	C₂×C₄	D₄×Dic₈₃	1	1	yes	characteristic
531	C₂×C₄	D₄×Dic₈₃	1	1	yes	characteristic
532	C₂×C₄	C₂³×Dic₈₃	1	1	yes	characteristic
533	C₂×C₄	C₂×D₄×D₈₃	1	1	yes	characteristic
534	C₂×C₄	C₂×#13050589	1	1	yes	characteristic
535	C₈	—	2	1	no	—
536	C₈	—	2	1	no	—
537	C₈	—	2	1	no	—
538	C₈	—	2	1	no	—
539	C₈	—	332	1	no	—
540	C₈	—	332	1	no	—
541	C₈	—	332	1	no	—
542	C₈	—	332	1	no	—
543	C₈	—	332	1	no	—
544	C₈	—	332	1	no	—
545	C₈	—	166	1	no	—
546	C₈	—	166	1	no	—
547	C₈	—	166	1	no	—
548	C₈	—	166	1	no	—
549	C₂²	—	2	1	no	—
550	C₂²	—	2	1	no	—
551	C₂²	—	2	1	no	—
552	C₂²	—	2	2	no	—
553	C₂²	—	4	1	no	—
554	C₂²	—	4	1	no	—
555	C₂²	—	4	1	no	—
556	C₂²	—	4	1	no	—
557	C₂²	—	4	1	no	—
558	C₂²	C₂×D₄×Dic₈₃	1	1	yes	characteristic
559	C₄	—	2	1	no	—
560	C₄	—	2	1	no	—
561	C₄	—	2	1	no	—
562	C₄	—	2	1	no	—
563	C₄	—	2	2	no	—
564	C₄	—	4	1	no	—
565	C₄	—	4	1	no	—
566	C₄	—	4	1	no	—
567	C₄	—	4	1	no	—
568	C₄	—	4	1	no	—
569	C₄	C₂×#14581799	1	1	yes	characteristic
570	C₄	C₂×#14581799	1	1	yes	characteristic
571	C₄	#19128498	1	1	yes	characteristic
572	C₄	#19128498	1	1	yes	characteristic
573	C₂	—	4	1	no	—
574	C₂	—	4	2	no	—
575	C₂	—	8	1	no	—
576	C₂	#24916158	1	1	yes	characteristic
577	C₂	#24916264	1	1	yes	characteristic
578	C₂	#24916366	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×#3102	C₂
socle	C₂²×C₈₃	C₂×C₄×D₄
prime radical	#449×C₈₃	C₄
cosocle	C₄²×C₈₃	C₂⁴
hypercenter	#3102	D₈₃
hypocenter	C₈₃	#17909
LCS	G ▷ C₂×C₄×C₈₃ ▷ C₂×C₈₃ ▷ C₈₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #3102

Complements

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

N	H ≅ G/N	type
1. #24916439	C₂	semidirect
2. #41×C₈₃⋊C₈	C₂	semidirect
3. #24906342	C₂	semidirect
4. #24906335	C₂	semidirect
5. #24906328	C₂	semidirect
6. #24906321	C₂	semidirect
7. #24906287	C₂	semidirect
8. #24906282	C₂	semidirect
9. SD₁₆⋊(C₈₃⋊C₈)	C₂	semidirect
10. SD₁₆⋊(C₈₃⋊C₈)	C₂	semidirect
11. #24906243	C₂	semidirect
12. #24905897	C₂	semidirect
13. #24905871	C₂	semidirect
14. #24905756	C₂	semidirect
305. C₈₃	#17909	semidirect

Maximal subgroups

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

subgroup	index
#24916439	2
#41×C₈₃⋊C₈	2
#24906342	2
#24906335	2
#24906328	2
#24906321	2
#24906287	2
#24906282	2
SD₁₆⋊(C₈₃⋊C₈)	2
#24906243	2
#24905897	2
#24905871	2
#24905756	2
C₈₃×#3102	2
#17909	83