Subgroups — #36285066

Order 21248.

1682 conjugacy classes of subgroups.

The subgroup lattice has 990 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#24921270	C₂	1	2	yes	maximal
2	#24920430	C₂	1	2	yes	maximal, complemented
3	#24920426	C₂	1	2	yes	maximal, complemented
4	#24920398	C₂	1	2	yes	maximal, complemented
5	#24920390	C₂	1	2	yes	maximal, complemented
6	#24920355	C₂	1	1	yes	maximal, characteristic, complemented
7	#24920354	C₂	1	1	yes	maximal, characteristic, complemented
8	#24920354	C₂	1	1	yes	maximal, characteristic, complemented
9	#24920351	C₂	1	1	yes	maximal, characteristic, complemented
10	#24920351	C₂	1	1	yes	maximal, characteristic, complemented
11	Q₁₆×Dic₁₆₆	C₂	1	1	yes	maximal, characteristic, complemented
12	#24920346	C₂	1	1	yes	maximal, characteristic, complemented
13	#24918000	C₂	1	1	yes	maximal, characteristic
14	#24917996	C₂	1	1	yes	maximal, characteristic
15	#24917976	C₂	1	1	yes	maximal, characteristic
16	#24917302	C₂	1	2	yes	maximal
17	#24917298	C₂	1	2	yes	maximal
18	#24917266	C₂	1	2	yes	maximal
19	#24916392	C₂	1	1	yes	maximal, characteristic
20	#24916326	C₂	1	1	yes	maximal, characteristic
21	#24916326	C₂	1	1	yes	maximal, characteristic
22	C₄×Q₁₆×D₈₃	C₂	1	1	yes	maximal, characteristic
23	C₈₃×#3383	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×Q₁₆×D₈₃	C₂²	1	1	yes	characteristic
25	Q₈×Dic₁₆₆	C₂²	1	2	yes	—
26	#19128431	—	2	2	no	—
27	#19128431	C₂²	1	2	yes	—
28	#19128429	—	2	2	no	—
29	#19128429	C₂²	1	2	yes	—
30	#19128428	—	2	2	no	—
31	#19128428	—	2	2	no	—
32	#19128428	C₂²	1	2	yes	—
33	#19128428	C₂²	1	2	yes	—
34	#19128427	C₂²	1	2	yes	—
35	#19128427	C₂²	1	2	yes	—
36	#19128331	—	2	2	no	—
37	#19128331	C₂²	1	2	yes	—
38	#19128328	—	2	2	no	—
39	#19128328	C₂²	1	2	yes	—
40	#19128257	—	2	2	no	—
41	#19128257	C₂²	1	2	yes	—
42	#19128255	—	2	2	no	—
43	#19128255	C₂²	1	1	yes	characteristic
44	#19128177	C₂²	1	2	yes	—
45	#19128177	C₂²	1	2	yes	—
46	C₄×Q₈×D₈₃	C₂²	1	2	yes	—
47	#19128111	C₂²	1	2	yes	—
48	#19128109	C₂²	1	2	yes	—
49	#19128108	C₂²	1	2	yes	—
50	#19128107	C₂²	1	2	yes	—
51	#19128106	C₂²	1	1	yes	characteristic
52	#19128105	C₂²	1	1	yes	characteristic
53	#19128105	C₂²	1	1	yes	characteristic
54	#19128105	C₂²	1	1	yes	characteristic
55	#19128105	C₂²	1	1	yes	characteristic
56	#19128103	C₂²	1	1	yes	characteristic
57	#19128103	C₂²	1	1	yes	characteristic
58	#19128102	C₂²	1	1	yes	characteristic
59	#19128102	C₂²	1	1	yes	characteristic
60	#19128100	C₂²	1	2	yes	—
61	#19128098	C₂²	1	2	yes	—
62	#19128011	C₂²	1	2	yes	—
63	#19128011	C₂²	1	2	yes	—
64	#19128009	C₂²	1	2	yes	—
65	#19128009	C₂²	1	2	yes	—
66	#19128008	C₂²	1	2	yes	—
67	#19128008	C₂²	1	2	yes	—
68	#19128006	C₂²	1	2	yes	—
69	#19128006	C₂²	1	2	yes	—
70	#19128005	C₂²	1	2	yes	—
71	#19128005	C₂²	1	2	yes	—
72	#19127996	C₂²	1	2	yes	—
73	#19127995	C₂²	1	2	yes	—
74	#19127995	C₂²	1	2	yes	—
75	#19127994	C₂²	1	2	yes	—
76	#19127994	C₂²	1	2	yes	—
77	#19127993	C₂²	1	2	yes	—
78	#19127987	C₂²	1	2	yes	—
79	#19127985	C₂²	1	2	yes	—
80	#19127985	C₂²	1	2	yes	—
81	#19127984	C₂²	1	2	yes	—
82	#19127984	C₂²	1	2	yes	—
83	#19127832	C₂²	1	1	yes	characteristic
84	#19127830	C₂²	1	1	yes	characteristic
85	#19127830	C₂²	1	1	yes	characteristic
86	#19127828	C₂²	1	1	yes	characteristic
87	C₈×Dic₁₆₆	C₂²	1	1	yes	characteristic
88	C₈×Dic₁₆₆	C₂²	1	1	yes	characteristic
89	C₈×Dic₁₆₆	C₂²	1	1	yes	characteristic
90	#19127806	C₂²	1	2	yes	—
91	#19127806	C₂²	1	2	yes	—
92	#19127805	C₂²	1	2	yes	—
93	#19127805	C₂²	1	2	yes	—
94	C₄×Dic₃₃₂	C₂²	1	1	yes	characteristic
95	C₄×Dic₃₃₂	C₂²	1	1	yes	characteristic
96	C₄×Dic₃₃₂	C₂²	1	1	yes	characteristic
97	Q₁₆×Dic₈₃	C₂²	1	1	yes	characteristic
98	Q₁₆×Dic₈₃	C₂²	1	1	yes	characteristic
99	Q₁₆×Dic₈₃	C₂²	1	1	yes	characteristic
100	#19127795	C₂²	1	1	yes	characteristic
101	#19127795	C₂²	1	1	yes	characteristic
102	#19127795	C₂²	1	1	yes	characteristic
103	C₄×#13050580	C₂²	1	2	yes	—
104	#19127793	C₂²	1	2	yes	—
105	#19127742	C₂²	1	2	yes	—
106	#19127740	C₂²	1	2	yes	—
107	#19127738	C₂²	1	1	yes	characteristic
108	#19127738	C₂²	1	1	yes	characteristic
109	#19127736	C₂²	1	2	yes	—
110	#107×D₈₃	C₂²	1	1	yes	characteristic
111	#19127726	C₂²	1	1	yes	characteristic
112	#19127726	C₂²	1	1	yes	characteristic
113	#19127723	C₂²	1	1	yes	characteristic
114	#19127708	C₂²	1	2	yes	—
115	#19127708	C₂²	1	2	yes	—
116	#103×D₈₃	C₂²	1	2	yes	—
117	#19127655	C₂²	1	1	yes	characteristic
118	#19127655	C₂²	1	1	yes	characteristic
119	C₄×C₈×D₈₃	C₂²	1	1	yes	characteristic
120	#557×C₈₃	C₂²	1	2	yes	—
121	#500×C₈₃	C₂²	1	1	yes	characteristic
122	#499×C₈₃	C₂²	1	1	yes	characteristic
123	#499×C₈₃	C₂²	1	1	yes	characteristic
124	#479×C₈₃	C₂²	1	2	yes	—
125	#479×C₈₃	C₂²	1	2	yes	—
126	#475×C₈₃	C₂²	1	2	yes	—
127	C₈×Q₈×C₈₃	C₂²	1	1	yes	characteristic
128	C₄×Q₁₆×C₈₃	C₂²	1	1	yes	characteristic
129	C₄×Q₁₆×C₈₃	C₂²	1	1	yes	characteristic
130	C₄×Q₁₆×C₈₃	C₂²	1	1	yes	characteristic
131	C₂×Q₈×D₈₃	C₂³	1	2	yes	—
132	C₂×Dic₃₃₂	C₂³	1	1	yes	characteristic
133	C₂×#13050580	C₂³	1	2	yes	—
134	Q₁₆×D₈₃	Q₈	1	8	yes	complemented
135	C₂×#13050573	C₂³	1	1	yes	characteristic
136	C₂×#13050573	C₂³	1	1	yes	characteristic
137	C₂×C₈×D₈₃	C₂³	1	1	yes	characteristic
138	C₂×C₈×D₈₃	C₂³	1	1	yes	characteristic
139	#14581792	—	2	2	no	—
140	#14581792	C₂³	1	2	yes	—
141	#14581791	—	2	2	no	—
142	#14581791	—	2	2	no	—
143	#14581791	—	2	2	no	—
144	#14581791	—	2	2	no	—
145	#14581791	—	2	2	no	—
146	#14581791	—	2	2	no	—
147	#14581791	—	2	2	no	—
148	#14581791	—	2	2	no	—
149	#14581791	D₄	1	1	yes	characteristic
150	#14581791	C₂³	1	2	yes	—
151	#14581791	C₂³	1	2	yes	—
152	#14581791	C₂³	1	2	yes	—
153	#14581791	C₂³	1	2	yes	—
154	#14581790	—	2	2	no	—
155	#14581790	—	2	2	no	—
156	#14581790	—	2	2	no	—
157	#14581790	—	2	2	no	—
158	#14581790	D₄	1	1	yes	characteristic
159	#14581784	—	2	2	no	—
160	#14581784	—	2	2	no	—
161	#14581784	C₂³	1	2	yes	—
162	#14581784	C₂³	1	2	yes	—
163	#14581783	—	2	2	no	—
164	#14581783	—	2	2	no	—
165	#14581783	C₂³	1	2	yes	—
166	#14581783	C₂³	1	2	yes	—
167	#14581782	—	2	2	no	—
168	#14581782	—	2	2	no	—
169	#14581782	—	2	2	no	—
170	#14581782	—	2	2	no	—
171	#14581782	—	2	2	no	—
172	#14581782	—	2	2	no	—
173	#14581782	—	2	2	no	—
174	#14581782	—	2	2	no	—
175	#14581782	D₄	1	1	yes	characteristic
176	#14581782	D₄	1	1	yes	characteristic
177	#14581772	—	2	2	no	—
178	#14581772	D₄	1	1	yes	characteristic
179	#14581770	—	2	2	no	—
180	#14581770	—	2	2	no	—
181	#14581770	—	2	2	no	—
182	#14581770	—	2	2	no	—
183	#14581770	D₄	1	1	yes	characteristic
184	#14581770	D₄	1	1	yes	characteristic
185	#14581768	—	2	2	no	—
186	#14581768	D₄	1	1	yes	characteristic
187	Q₈×Dic₈₃	C₂³	1	2	yes	—
188	Q₈×Dic₈₃	C₂³	1	2	yes	—
189	Q₈×Dic₈₃	C₂³	1	2	yes	—
190	C₄×Dic₁₆₆	—	2	2	no	—
191	C₄×Dic₁₆₆	—	2	2	no	—
192	C₄×Dic₁₆₆	—	2	2	no	—
193	C₄×Dic₁₆₆	—	2	2	no	—
194	C₄×Dic₁₆₆	—	2	2	no	—
195	C₄×Dic₁₆₆	—	2	2	no	—
196	C₄×Dic₁₆₆	C₂³	1	2	yes	—
197	C₄×Dic₁₆₆	C₂³	1	2	yes	—
198	C₄×Dic₁₆₆	C₂³	1	2	yes	—
199	C₄×Dic₁₆₆	C₂³	1	1	yes	characteristic
200	C₄×Dic₁₆₆	C₂³	1	1	yes	characteristic
201	C₄×Dic₁₆₆	C₂³	1	1	yes	characteristic
202	#14581757	—	2	2	no	—
203	#14581757	—	2	2	no	—
204	#14581757	—	2	2	no	—
205	#14581757	—	2	2	no	—
206	#14581757	—	2	2	no	—
207	#14581757	—	2	2	no	—
208	#14581757	—	2	2	no	—
209	#14581757	—	2	2	no	—
210	#14581757	—	2	2	no	—
211	#14581757	C₂³	1	2	yes	—
212	#14581757	C₂³	1	2	yes	—
213	#14581757	C₂³	1	2	yes	—
214	#14581750	—	2	2	no	—
215	#14581750	—	2	2	no	—
216	#14581750	C₂³	1	2	yes	—
217	#14581750	C₂³	1	2	yes	—
218	#14581749	—	2	2	no	—
219	#14581749	—	2	2	no	—
220	#14581749	C₂³	1	1	yes	characteristic
221	#14581749	C₂³	1	1	yes	characteristic
222	C₄⋊C₄×D₈₃	—	2	2	no	—
223	C₄⋊C₄×D₈₃	C₂³	1	2	yes	—
224	C₄²×D₈₃	—	2	2	no	—
225	C₄²×D₈₃	C₂³	1	1	yes	characteristic
226	#14581726	C₂³	1	1	yes	characteristic
227	#14581726	C₂³	1	1	yes	characteristic
228	#14581726	C₂³	1	1	yes	characteristic
229	#14581726	C₂³	1	2	yes	—
230	#14581725	C₂³	1	2	yes	—
231	#14581725	C₂³	1	2	yes	—
232	#14581725	C₂³	1	2	yes	—
233	#14581725	C₂³	1	2	yes	—
234	#14581725	C₂³	1	2	yes	—
235	#14581724	C₂³	1	2	yes	—
236	#14581724	C₂³	1	2	yes	—
237	#14581723	C₂³	1	2	yes	—
238	#14581723	C₂³	1	2	yes	—
239	#14581723	C₂³	1	2	yes	—
240	#14581723	C₂³	1	2	yes	—
241	C₄⋊(C₈₃⋊C₈)	C₂³	1	1	yes	characteristic
242	C₄⋊(C₈₃⋊C₈)	C₂³	1	1	yes	characteristic
243	C₄⋊(C₈₃⋊C₈)	C₂³	1	1	yes	characteristic
244	Dic₈₃⋊C₈	C₂³	1	1	yes	characteristic
245	Dic₈₃⋊C₈	C₂³	1	1	yes	characteristic
246	Dic₈₃⋊C₈	C₂³	1	1	yes	characteristic
247	Dic₈₃⋊C₈	C₂³	1	1	yes	characteristic
248	Dic₈₃⋊C₈	C₂³	1	1	yes	characteristic
249	Dic₈₃⋊C₈	C₂³	1	1	yes	characteristic
250	#14581717	C₂³	1	2	yes	—
251	#14581717	C₂³	1	2	yes	—
252	#14581717	C₂³	1	2	yes	—
253	#14581716	C₂³	1	2	yes	—
254	#14581716	C₂³	1	2	yes	—
255	#14581716	C₂³	1	2	yes	—
256	#14581715	C₂³	1	2	yes	—
257	#14581715	C₂³	1	2	yes	—
258	#14581715	C₂³	1	2	yes	—
259	#14581703	C₂³	1	1	yes	characteristic
260	#14581703	C₂³	1	1	yes	characteristic
261	#14581702	C₂³	1	1	yes	characteristic
262	#14581702	C₂³	1	1	yes	characteristic
263	C₄×C₈₃⋊C₈	C₂³	1	1	yes	characteristic
264	C₈×Dic₈₃	C₂³	1	1	yes	characteristic
265	C₈×Dic₈₃	C₂³	1	1	yes	characteristic
266	C₈×Dic₈₃	C₂³	1	1	yes	characteristic
267	C₈×Dic₈₃	C₂³	1	1	yes	characteristic
268	C₂×Q₁₆×C₈₃	C₂³	1	1	yes	characteristic
269	C₄⋊Q₈×C₈₃	—	2	2	no	—
270	C₄⋊Q₈×C₈₃	C₂³	1	2	yes	—
271	#125×C₈₃	—	2	2	no	—
272	#125×C₈₃	—	2	2	no	—
273	#125×C₈₃	C₂³	1	2	yes	—
274	#125×C₈₃	C₂³	1	2	yes	—
275	C₄×Q₈×C₈₃	—	2	2	no	—
276	C₄×Q₈×C₈₃	C₂³	1	2	yes	—
277	C₄×Q₈×C₈₃	C₂³	1	2	yes	—
278	C₄×Q₈×C₈₃	C₂³	1	2	yes	—
279	C₄×Q₈×C₈₃	C₂³	1	1	yes	characteristic
280	#107×C₈₃	C₂³	1	2	yes	—
281	#107×C₈₃	C₂³	1	1	yes	characteristic
282	#107×C₈₃	C₂³	1	1	yes	characteristic
283	#107×C₈₃	C₂³	1	1	yes	characteristic
284	#106×C₈₃	C₂³	1	2	yes	—
285	#106×C₈₃	C₂³	1	2	yes	—
286	C₄⋊C₈×C₈₃	C₂³	1	1	yes	characteristic
287	C₄⋊C₈×C₈₃	C₂³	1	1	yes	characteristic
288	C₄⋊C₈×C₈₃	C₂³	1	1	yes	characteristic
289	#103×C₈₃	C₂³	1	2	yes	—
290	#103×C₈₃	C₂³	1	2	yes	—
291	#103×C₈₃	C₂³	1	2	yes	—
292	C₄×C₈×C₈₃	C₂³	1	1	yes	characteristic
293	C₄×C₈×C₈₃	C₂³	1	1	yes	characteristic
294	C₄×C₈×C₈₃	C₂³	1	1	yes	characteristic
295	C₂×Dic₁₆₆	—	2	2	no	—
296	C₂×Dic₁₆₆	—	2	2	no	—
297	C₂×Dic₁₆₆	—	2	2	no	—
298	C₂×Dic₁₆₆	—	2	2	no	—
299	C₂×Dic₁₆₆	—	2	2	no	—
300	C₂×Dic₁₆₆	—	2	2	no	—
301	C₂×Dic₁₆₆	C₂×D₄	1	1	yes	characteristic
302	C₂×Dic₁₆₆	C₂×D₄	1	1	yes	characteristic
303	C₂×Dic₁₆₆	C₂×D₄	1	1	yes	characteristic
304	C₂×Dic₁₆₆	C₂⁴	1	2	yes	—
305	Q₈×D₈₃	—	2	4	no	—
306	Q₈×D₈₃	C₂×Q₈	1	8	yes	—
307	C₂×C₄×D₈₃	—	2	2	no	—
308	C₂×C₄×D₈₃	—	2	2	no	—
309	C₂×C₄×D₈₃	C₂×D₄	1	1	yes	characteristic
310	C₂×C₄×D₈₃	C₂×D₄	1	1	yes	characteristic
311	C₂×C₄×D₈₃	C₂⁴	1	1	yes	characteristic
312	Dic₃₃₂	C₂×Q₈	1	4	yes	—
313	#13050580	C₂×Q₈	1	8	yes	—
314	#13050573	—	2	2	no	—
315	#13050573	—	2	2	no	—
316	C₂×C₈₃⋊C₈	C₂⁴	1	1	yes	characteristic
317	C₂×C₈₃⋊C₈	C₂⁴	1	1	yes	characteristic
318	C₂×C₈₃⋊C₈	C₂⁴	1	1	yes	characteristic
319	C₂×C₈₃⋊C₈	C₂⁴	1	1	yes	characteristic
320	C₈×D₈₃	—	2	2	no	—
321	C₈×D₈₃	C₂×Q₈	1	4	yes	—
322	C₄⋊Dic₈₃	—	2	2	no	—
323	C₄⋊Dic₈₃	—	2	2	no	—
324	C₄⋊Dic₈₃	—	2	2	no	—
325	C₄⋊Dic₈₃	—	2	2	no	—
326	C₄⋊Dic₈₃	—	2	2	no	—
327	C₄⋊Dic₈₃	—	2	2	no	—
328	C₄⋊Dic₈₃	C₂×D₄	1	1	yes	characteristic
329	C₄⋊Dic₈₃	C₂×D₄	1	1	yes	characteristic
330	C₄⋊Dic₈₃	C₂×D₄	1	1	yes	characteristic
331	C₄⋊Dic₈₃	C₂⁴	1	2	yes	—
332	C₄⋊Dic₈₃	C₂⁴	1	2	yes	—
333	C₄⋊Dic₈₃	C₂⁴	1	2	yes	—
334	Dic₈₃⋊C₄	—	2	2	no	—
335	Dic₈₃⋊C₄	—	2	2	no	—
336	Dic₈₃⋊C₄	—	2	2	no	—
337	Dic₈₃⋊C₄	—	2	2	no	—
338	Dic₈₃⋊C₄	—	2	2	no	—
339	Dic₈₃⋊C₄	—	2	2	no	—
340	Dic₈₃⋊C₄	—	2	2	no	—
341	Dic₈₃⋊C₄	—	2	2	no	—
342	Dic₈₃⋊C₄	—	2	2	no	—
343	Dic₈₃⋊C₄	—	2	2	no	—
344	Dic₈₃⋊C₄	—	2	2	no	—
345	Dic₈₃⋊C₄	—	2	2	no	—
346	Dic₈₃⋊C₄	—	2	2	no	—
347	Dic₈₃⋊C₄	—	2	2	no	—
348	Dic₈₃⋊C₄	—	2	2	no	—
349	Dic₈₃⋊C₄	—	2	2	no	—
350	Dic₈₃⋊C₄	—	2	2	no	—
351	Dic₈₃⋊C₄	C₂×D₄	1	1	yes	characteristic
352	Dic₈₃⋊C₄	C₂×D₄	1	1	yes	characteristic
353	Dic₈₃⋊C₄	C₂×D₄	1	1	yes	characteristic
354	Dic₈₃⋊C₄	C₂×D₄	1	1	yes	characteristic
355	Dic₈₃⋊C₄	C₂×D₄	1	1	yes	characteristic
356	Dic₈₃⋊C₄	C₂×D₄	1	1	yes	characteristic
357	Dic₈₃⋊C₄	C₂×D₄	1	1	yes	characteristic
358	Dic₈₃⋊C₄	C₂×D₄	1	1	yes	characteristic
359	Dic₈₃⋊C₄	C₂×D₄	1	1	yes	characteristic
360	Dic₈₃⋊C₄	C₂×D₄	1	1	yes	characteristic
361	(C₂×D₈₃)⋊C₄	—	2	2	no	—
362	(C₂×D₈₃)⋊C₄	—	2	2	no	—
363	(C₂×D₈₃)⋊C₄	C₂×D₄	1	1	yes	characteristic
364	(C₂×D₈₃)⋊C₄	C₂×D₄	1	1	yes	characteristic
365	(C₂×D₈₃)⋊C₄	C₂×D₄	1	1	yes	characteristic
366	(C₂×D₈₃)⋊C₄	C₂×D₄	1	1	yes	characteristic
367	C₄×Dic₈₃	—	2	2	no	—
368	C₄×Dic₈₃	—	2	2	no	—
369	C₄×Dic₈₃	—	2	2	no	—
370	C₄×Dic₈₃	—	2	2	no	—
371	C₄×Dic₈₃	—	2	2	no	—
372	C₄×Dic₈₃	—	2	2	no	—
373	C₄×Dic₈₃	—	2	2	no	—
374	C₄×Dic₈₃	—	2	2	no	—
375	C₄×Dic₈₃	—	2	2	no	—
376	C₄×Dic₈₃	—	2	2	no	—
377	C₄×Dic₈₃	—	2	2	no	—
378	C₄×Dic₈₃	C₂×D₄	1	1	yes	characteristic
379	C₄×Dic₈₃	C₂×D₄	1	1	yes	characteristic
380	C₄×Dic₈₃	C₂⁴	1	1	yes	characteristic
381	C₄×Dic₈₃	C₂⁴	1	1	yes	characteristic
382	C₄×Dic₈₃	C₂⁴	1	1	yes	characteristic
383	C₂×Q₈×C₈₃	—	2	2	no	—
384	C₂×Q₈×C₈₃	C₂×D₄	1	1	yes	characteristic
385	C₂×Q₈×C₈₃	C₂⁴	1	2	yes	—
386	Q₁₆×C₈₃	C₂×Q₈	1	4	yes	—
387	C₂×C₈×C₈₃	C₂⁴	1	1	yes	characteristic
388	C₂×C₈×C₈₃	C₂⁴	1	1	yes	characteristic
389	C₂×C₈×C₈₃	C₂⁴	1	1	yes	characteristic
390	C₂×C₈×C₈₃	C₂⁴	1	1	yes	characteristic
391	C₄⋊C₄×C₈₃	—	2	2	no	—
392	C₄⋊C₄×C₈₃	—	2	2	no	—
393	C₄⋊C₄×C₈₃	—	2	2	no	—
394	C₄⋊C₄×C₈₃	—	2	2	no	—
395	C₄⋊C₄×C₈₃	—	2	2	no	—
396	C₄⋊C₄×C₈₃	—	2	2	no	—
397	C₄⋊C₄×C₈₃	—	2	2	no	—
398	C₄⋊C₄×C₈₃	—	2	2	no	—
399	C₄⋊C₄×C₈₃	C₂×D₄	1	1	yes	characteristic
400	C₄⋊C₄×C₈₃	C₂×D₄	1	1	yes	characteristic
401	C₄⋊C₄×C₈₃	C₂×D₄	1	1	yes	characteristic
402	C₄⋊C₄×C₈₃	C₂⁴	1	2	yes	—
403	C₄⋊C₄×C₈₃	C₂⁴	1	2	yes	—
404	C₄⋊C₄×C₈₃	C₂⁴	1	2	yes	—
405	C₄²×C₈₃	—	2	2	no	—
406	C₄²×C₈₃	—	2	2	no	—
407	C₄²×C₈₃	—	2	2	no	—
408	C₄²×C₈₃	C₂⁴	1	1	yes	characteristic
409	C₄²×C₈₃	C₂⁴	1	1	yes	characteristic
410	C₄²×C₈₃	C₂⁴	1	1	yes	characteristic
411	C₂²×D₈₃	C₂²×D₄	1	1	yes	characteristic
412	Q₈×C₈₃	—	2	2	no	—
413	Q₈×C₈₃	—	4	1	no	—
414	Q₈×C₈₃	—	8	2	no	—
415	Q₈×C₈₃	C₂²×Q₈	1	4	yes	—
416	C₂×C₄×C₈₃	—	2	2	no	—
417	C₂×C₄×C₈₃	—	2	2	no	—
418	C₂×C₄×C₈₃	—	2	2	no	—
419	C₂×C₄×C₈₃	—	2	2	no	—
420	C₂×C₄×C₈₃	C₂²×D₄	1	1	yes	characteristic
421	C₂×C₄×C₈₃	C₂²×D₄	1	1	yes	characteristic
422	C₂×C₄×C₈₃	C₂²×D₄	1	1	yes	characteristic
423	C₂×C₄×C₈₃	C₂²×D₄	1	1	yes	characteristic
424	C₂×C₄×C₈₃	C₂²×D₄	1	1	yes	characteristic
425	C₂×C₄×C₈₃	C₂²×D₄	1	1	yes	characteristic
426	C₂×C₄×C₈₃	C₂⁵	1	1	yes	characteristic
427	C₂×Dic₈₃	—	2	2	no	—
428	C₂×Dic₈₃	—	2	2	no	—
429	C₂×Dic₈₃	—	2	2	no	—
430	C₂×Dic₈₃	—	2	2	no	—
431	C₂×Dic₈₃	C₂²×D₄	1	1	yes	characteristic
432	C₂×Dic₈₃	C₂²×D₄	1	1	yes	characteristic
433	C₂×Dic₈₃	C₂²×D₄	1	1	yes	characteristic
434	C₂×Dic₈₃	C₂²×D₄	1	1	yes	characteristic
435	C₂×Dic₈₃	C₂²×D₄	1	1	yes	characteristic
436	C₂×Dic₈₃	C₂²×D₄	1	1	yes	characteristic
437	C₂×Dic₈₃	C₂²×D₄	1	1	yes	characteristic
438	C₄×D₈₃	—	2	8	no	—
439	C₄×D₈₃	—	2	2	no	—
440	C₄×D₈₃	—	4	1	no	—
441	C₄×D₈₃	—	8	2	no	—
442	C₄×D₈₃	C₂²×Q₈	1	2	yes	—
443	C₄×D₈₃	2₋¹⁺⁴	1	2	yes	—
444	Dic₁₆₆	—	2	2	no	—
445	Dic₁₆₆	—	2	8	no	—
446	Dic₁₆₆	—	2	2	no	—
447	Dic₁₆₆	—	2	2	no	—
448	Dic₁₆₆	—	4	1	no	—
449	Dic₁₆₆	—	4	4	no	—
450	Dic₁₆₆	—	8	2	no	—
451	Dic₁₆₆	—	8	2	no	—
452	Dic₁₆₆	—	8	2	no	—
453	Dic₁₆₆	—	8	2	no	—
454	Dic₁₆₆	C₂²×Q₈	1	4	yes	—
455	C₈×C₈₃	—	2	1	no	—
456	C₈×C₈₃	—	2	1	no	—
457	C₈×C₈₃	—	2	1	no	—
458	C₈×C₈₃	C₂²×Q₈	1	2	yes	—
459	C₈₃⋊C₈	—	2	1	no	—
460	C₈₃⋊C₈	—	2	1	no	—
461	C₈₃⋊C₈	—	2	1	no	—
462	C₈₃⋊C₈	C₂²×Q₈	1	2	yes	—
463	C₂²×C₈₃	C₂³×D₄	1	1	yes	characteristic
464	C₂×D₈₃	—	2	1	no	—
465	C₂×D₈₃	—	2	1	no	—
466	C₂×D₈₃	D₄×Q₈	1	2	yes	—
467	C₄×C₈₃	—	2	1	no	—
468	C₄×C₈₃	—	2	1	no	—
469	C₄×C₈₃	—	2	1	no	—
470	C₄×C₈₃	—	2	4	no	—
471	C₄×C₈₃	—	2	1	no	—
472	C₄×C₈₃	—	2	1	no	—
473	C₄×C₈₃	—	2	1	no	—
474	C₄×C₈₃	—	4	2	no	—
475	C₄×C₈₃	—	4	2	no	—
476	C₄×C₈₃	—	4	2	no	—
477	C₄×C₈₃	C₂³×Q₈	1	1	yes	characteristic
478	C₄×C₈₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
479	Dic₈₃	—	2	1	no	—
480	Dic₈₃	—	2	1	no	—
481	Dic₈₃	—	2	1	no	—
482	Dic₈₃	—	2	4	no	—
483	Dic₈₃	—	2	1	no	—
484	Dic₈₃	—	2	1	no	—
485	Dic₈₃	—	4	2	no	—
486	Dic₈₃	—	4	2	no	—
487	Dic₈₃	—	4	2	no	—
488	Dic₈₃	D₄×Q₈	1	2	yes	—
489	Dic₈₃	#578	1	2	yes	—
490	#61372	—	83	1	no	maximal, Sylow
491	C₂×C₈₃	C₂×D₄×Q₈	1	1	yes	characteristic
492	C₂×C₈₃	C₂×#578	1	1	yes	characteristic
493	C₂×C₈₃	#3584	1	1	yes	characteristic
494	D₈₃	—	2	2	no	—
495	#3502	—	83	2	no	—
496	#3390	—	83	2	no	—
497	#3390	—	83	2	no	—
498	#3387	—	83	2	no	—
499	#3387	—	83	2	no	—
500	#3383	—	83	1	no	—
501	#3383	—	83	1	no	—
502	#3383	—	83	1	no	—
503	#3383	—	83	1	no	—
504	#3383	—	83	1	no	—
505	#3383	D₈₃	1	1	yes	characteristic, complemented
506	Q₈×Q₁₆	—	83	1	no	—
507	Q₈×Q₁₆	—	83	1	no	—
508	#3164	—	83	1	no	—
509	#3164	—	83	1	no	—
510	#3160	—	83	1	no	—
511	#3082	—	83	2	no	—
512	#3082	—	83	2	no	—
513	#3078	—	83	2	no	—
514	#2960	—	83	1	no	—
515	#2950	—	83	1	no	—
516	#2950	—	83	1	no	—
517	C₂×C₄×Q₁₆	—	83	1	no	—
518	C₈₃	#61372	1	1	yes	characteristic, complemented, Sylow
519	C₂²×Q₁₆	—	83	1	no	—
520	Q₈²	—	83	2	no	—
521	Q₈²	—	83	2	no	—
522	Q₈²	—	166	2	no	—
523	#557	—	83	2	no	—
524	#557	—	83	2	no	—
525	#557	—	83	2	no	—
526	#557	—	83	2	no	—
527	#557	—	83	2	no	—
528	#557	—	166	2	no	—
529	#557	—	166	2	no	—
530	#557	—	166	2	no	—
531	#557	C₂×D₈₃	1	2	yes	—
532	#544	—	83	2	no	—
533	#544	—	83	2	no	—
534	#544	—	166	2	no	—
535	#544	—	166	2	no	—
536	#533	—	83	1	no	—
537	#533	—	83	2	no	—
538	#533	—	166	2	no	—
539	#533	—	166	2	no	—
540	#519	—	83	2	no	—
541	#519	—	83	2	no	—
542	C₂×C₄×Q₈	—	83	2	no	—
543	#501	—	83	2	no	—
544	#501	—	83	2	no	—
545	#501	—	83	2	no	—
546	#501	—	83	2	no	—
547	#500	—	83	1	no	—
548	#500	—	83	1	no	—
549	#500	—	83	1	no	—
550	#500	—	83	1	no	—
551	#500	—	83	1	no	—
552	#500	C₂×D₈₃	1	1	yes	characteristic
553	#499	—	83	2	no	—
554	#499	—	83	1	no	—
555	#499	—	83	1	no	—
556	#499	—	83	1	no	—
557	#499	—	83	1	no	—
558	#499	C₂×D₈₃	1	1	yes	characteristic
559	#499	C₂×D₈₃	1	1	yes	characteristic
560	#498	—	83	2	no	—
561	#479	—	83	2	no	—
562	#479	—	83	2	no	—
563	#479	—	83	2	no	—
564	#479	—	83	2	no	—
565	#479	—	83	2	no	—
566	#479	—	83	2	no	—
567	#479	—	83	2	no	—
568	#479	—	83	2	no	—
569	#479	—	83	2	no	—
570	#479	—	83	2	no	—
571	#479	C₂×D₈₃	1	2	yes	—
572	#479	C₂×D₈₃	1	2	yes	—
573	#477	—	83	2	no	—
574	#477	—	83	2	no	—
575	#477	—	83	2	no	—
576	#477	—	83	2	no	—
577	#477	—	83	2	no	—
578	#477	—	83	2	no	—
579	#475	—	83	2	no	—
580	#475	—	83	2	no	—
581	#475	—	83	2	no	—
582	#475	—	83	2	no	—
583	#475	—	83	2	no	—
584	#475	C₂×D₈₃	1	2	yes	—
585	#446	—	83	1	no	—
586	#446	—	83	1	no	—
587	#446	—	83	1	no	—
588	#446	—	83	1	no	—
589	C₈×Q₈	—	83	1	no	—
590	C₈×Q₈	—	83	1	no	—
591	C₈×Q₈	—	83	1	no	—
592	C₈×Q₈	C₂×D₈₃	1	1	yes	characteristic
593	#441	—	83	2	no	—
594	#441	—	83	2	no	—
595	#441	—	83	2	no	—
596	#441	—	83	2	no	—
597	C₄×Q₁₆	—	83	1	no	—
598	C₄×Q₁₆	—	83	1	no	—
599	C₄×Q₁₆	—	83	1	no	—
600	C₄×Q₁₆	—	83	2	no	—
601	C₄×Q₁₆	—	83	1	no	—
602	C₄×Q₁₆	—	83	1	no	—
603	C₄×Q₁₆	—	83	1	no	—
604	C₄×Q₁₆	—	83	2	no	—
605	C₄×Q₁₆	—	83	1	no	—
606	C₄×Q₁₆	—	83	1	no	—
607	C₄×Q₁₆	—	83	1	no	—
608	C₄×Q₁₆	C₂×D₈₃	1	1	yes	characteristic
609	C₄×Q₁₆	C₂×D₈₃	1	1	yes	characteristic
610	C₄×Q₁₆	C₂×D₈₃	1	1	yes	characteristic
611	#428	—	83	2	no	—
612	#428	—	83	2	no	—
613	#427	—	83	1	no	—
614	#427	—	83	1	no	—
615	#427	—	83	2	no	—
616	C₂×#107	—	83	1	no	—
617	#424	—	83	1	no	—
618	#424	—	83	1	no	—
619	#423	—	83	1	no	—
620	#419	—	83	2	no	—
621	#419	—	83	2	no	—
622	C₂×#103	—	83	2	no	—
623	#405	—	83	1	no	—
624	#405	—	83	1	no	—
625	C₂×C₄×C₈	—	83	1	no	—
626	C₂²×Q₈	—	83	2	no	—
627	C₂×Q₁₆	—	83	2	no	—
628	C₂×Q₁₆	—	83	8	no	—
629	C₂×Q₁₆	—	83	1	no	—
630	C₂×Q₁₆	C₂²×D₈₃	1	1	yes	characteristic
631	C₂×M₁₆	—	83	1	no	—
632	C₂×M₁₆	—	83	1	no	—
633	C₂²×C₈	—	83	1	no	—
634	C₂²×C₈	—	83	1	no	—
635	C₄⋊Q₈	—	2	2	no	—
636	C₄⋊Q₈	—	83	1	no	—
637	C₄⋊Q₈	—	83	1	no	—
638	C₄⋊Q₈	—	83	2	no	—
639	C₄⋊Q₈	—	83	2	no	—
640	C₄⋊Q₈	—	83	2	no	—
641	C₄⋊Q₈	—	83	2	no	—
642	C₄⋊Q₈	—	83	2	no	—
643	C₄⋊Q₈	—	166	2	no	—
644	C₄⋊Q₈	—	166	2	no	—
645	C₄⋊Q₈	—	166	2	no	—
646	C₄⋊Q₈	—	166	2	no	—
647	C₄⋊Q₈	—	166	2	no	—
648	C₄⋊Q₈	—	166	2	no	—
649	C₄⋊Q₈	—	166	2	no	—
650	C₄⋊Q₈	—	166	2	no	—
651	C₄⋊Q₈	—	166	2	no	—
652	C₄⋊Q₈	—	166	2	no	—
653	C₄⋊Q₈	—	166	2	no	—
654	C₄⋊Q₈	—	166	2	no	—
655	C₄⋊Q₈	—	166	2	no	—
656	C₄⋊Q₈	C₂²×D₈₃	1	2	yes	—
657	#125	—	2	2	no	—
658	#125	—	2	2	no	—
659	#125	—	83	1	no	—
660	#125	—	83	1	no	—
661	#125	—	83	2	no	—
662	#125	—	83	2	no	—
663	#125	—	83	2	no	—
664	#125	—	83	2	no	—
665	#125	—	166	2	no	—
666	#125	—	166	2	no	—
667	#125	—	166	2	no	—
668	#125	—	166	2	no	—
669	#125	—	166	2	no	—
670	#125	—	166	2	no	—
671	#125	—	166	2	no	—
672	#125	—	166	2	no	—
673	#125	—	166	2	no	—
674	#125	—	166	2	no	—
675	#125	—	166	2	no	—
676	#125	—	166	2	no	—
677	#125	C₂²×D₈₃	1	2	yes	—
678	#125	C₂²×D₈₃	1	2	yes	—
679	C₂²⋊Q₈	—	83	1	no	—
680	C₂²⋊Q₈	—	83	1	no	—
681	C₂²⋊Q₈	—	83	1	no	—
682	C₂²⋊Q₈	—	83	1	no	—
683	C₂²⋊Q₈	—	166	2	no	—
684	C₂²⋊Q₈	—	166	2	no	—
685	C₂²⋊Q₈	—	166	2	no	—
686	C₂²⋊Q₈	—	166	2	no	—
687	C₂²⋊Q₈	—	166	2	no	—
688	C₂²⋊Q₈	—	166	2	no	—
689	C₄×Q₈	—	2	2	no	—
690	C₄×Q₈	—	83	1	no	—
691	C₄×Q₈	—	83	1	no	—
692	C₄×Q₈	—	83	1	no	—
693	C₄×Q₈	—	83	2	no	—
694	C₄×Q₈	—	83	2	no	—
695	C₄×Q₈	—	83	2	no	—
696	C₄×Q₈	—	83	2	no	—
697	C₄×Q₈	—	83	2	no	—
698	C₄×Q₈	—	83	2	no	—
699	C₄×Q₈	—	83	2	no	—
700	C₄×Q₈	—	83	2	no	—
701	C₄×Q₈	—	83	2	no	—
702	C₄×Q₈	—	166	2	no	—
703	C₄×Q₈	—	166	2	no	—
704	C₄×Q₈	—	166	2	no	—
705	C₄×Q₈	—	166	2	no	—
706	C₄×Q₈	—	166	2	no	—
707	C₄×Q₈	—	166	2	no	—
708	C₄×Q₈	—	166	2	no	—
709	C₄×Q₈	—	166	2	no	—
710	C₄×Q₈	—	166	2	no	—
711	C₄×Q₈	—	166	2	no	—
712	C₄×Q₈	—	166	2	no	—
713	C₄×Q₈	—	166	2	no	—
714	C₄×Q₈	—	166	2	no	—
715	C₄×Q₈	—	166	2	no	—
716	C₄×Q₈	—	166	2	no	—
717	C₄×Q₈	C₂²×D₈₃	1	2	yes	—
718	C₄×Q₈	C₂²×D₈₃	1	2	yes	—
719	C₄×Q₈	C₂²×D₈₃	1	2	yes	—
720	C₄×Q₈	C₂²×D₈₃	1	1	yes	characteristic
721	#117	—	83	1	no	—
722	#117	—	83	1	no	—
723	#117	—	83	2	no	—
724	#117	—	83	2	no	—
725	#117	—	166	2	no	—
726	#117	—	166	2	no	—
727	#117	—	166	2	no	—
728	#117	—	166	2	no	—
729	C₂×C₄⋊C₄	—	83	2	no	—
730	C₂×C₄⋊C₄	—	166	2	no	—
731	C₂×C₄²	—	83	1	no	—
732	C₂×C₄²	—	166	2	no	—
733	#107	—	83	1	no	—
734	#107	—	83	1	no	—
735	#107	—	83	1	no	—
736	#107	—	83	2	no	—
737	#107	—	83	2	no	—
738	#107	—	83	2	no	—
739	#107	—	83	2	no	—
740	#107	—	83	2	no	—
741	#107	—	83	2	no	—
742	#107	C₂²×D₈₃	1	1	yes	characteristic
743	#107	C₂²×D₈₃	1	1	yes	characteristic
744	#107	C₂²×D₈₃	1	1	yes	characteristic
745	#107	C₂²×D₈₃	1	2	yes	—
746	#106	—	83	2	no	—
747	#106	—	83	2	no	—
748	#106	—	83	2	no	—
749	#106	—	83	2	no	—
750	#106	—	83	2	no	—
751	#106	—	83	2	no	—
752	#106	C₂²×D₈₃	1	2	yes	—
753	#106	C₂²×D₈₃	1	2	yes	—
754	C₄⋊C₈	—	83	1	no	—
755	C₄⋊C₈	—	83	1	no	—
756	C₄⋊C₈	—	83	1	no	—
757	C₄⋊C₈	—	83	1	no	—
758	C₄⋊C₈	—	83	1	no	—
759	C₄⋊C₈	—	83	1	no	—
760	C₄⋊C₈	—	83	1	no	—
761	C₄⋊C₈	—	83	1	no	—
762	C₄⋊C₈	—	83	1	no	—
763	C₄⋊C₈	C₂²×D₈₃	1	1	yes	characteristic
764	C₄⋊C₈	C₂²×D₈₃	1	1	yes	characteristic
765	C₄⋊C₈	C₂²×D₈₃	1	1	yes	characteristic
766	#103	—	83	2	no	—
767	#103	—	83	2	no	—
768	#103	—	83	2	no	—
769	#103	—	83	2	no	—
770	#103	—	83	2	no	—
771	#103	—	83	2	no	—
772	#103	—	83	2	no	—
773	#103	—	83	2	no	—
774	#103	—	83	2	no	—
775	#103	C₂²×D₈₃	1	2	yes	—
776	#103	C₂²×D₈₃	1	2	yes	—
777	#103	C₂²×D₈₃	1	2	yes	—
778	#97	—	83	1	no	—
779	#97	—	83	1	no	—
780	#97	—	83	1	no	—
781	#97	—	83	1	no	—
782	C₄×C₈	—	83	1	no	—
783	C₄×C₈	—	83	1	no	—
784	C₄×C₈	—	83	1	no	—
785	C₄×C₈	—	83	1	no	—
786	C₄×C₈	—	83	1	no	—
787	C₄×C₈	C₂²×D₈₃	1	1	yes	characteristic
788	C₄×C₈	C₂²×D₈₃	1	1	yes	characteristic
789	C₄×C₈	C₂²×D₈₃	1	1	yes	characteristic
790	C₂×Q₈	—	2	2	no	—
791	C₂×Q₈	—	83	1	no	—
792	C₂×Q₈	—	83	1	no	—
793	C₂×Q₈	—	83	1	no	—
794	C₂×Q₈	—	83	8	no	—
795	C₂×Q₈	—	83	2	no	—
796	C₂×Q₈	—	166	2	no	—
797	C₂×Q₈	—	166	2	no	—
798	C₂×Q₈	—	166	2	no	—
799	C₂×Q₈	—	166	2	no	—
800	C₂×Q₈	—	166	2	no	—
801	C₂×Q₈	—	166	4	no	—
802	C₂×Q₈	—	166	2	no	—
803	C₂×Q₈	D₄×D₈₃	1	1	yes	characteristic
804	C₂×Q₈	C₂³×D₈₃	1	2	yes	—
805	C₂²×C₄	—	83	1	no	—
806	C₂²×C₄	—	83	1	no	—
807	C₂²×C₄	—	83	1	no	—
808	C₂²×C₄	—	166	2	no	—
809	C₂²×C₄	—	166	2	no	—
810	Q₁₆	—	83	8	no	—
811	Q₁₆	—	83	4	no	—
812	Q₁₆	Q₈×D₈₃	1	4	yes	—
813	M₁₆	—	166	2	no	—
814	M₁₆	—	166	2	no	—
815	C₂×C₈	—	83	1	no	—
816	C₂×C₈	—	83	4	no	—
817	C₂×C₈	—	83	1	no	—
818	C₂×C₈	—	83	1	no	—
819	C₂×C₈	—	83	1	no	—
820	C₂×C₈	—	166	2	no	—
821	C₂×C₈	C₂³×D₈₃	1	1	yes	characteristic
822	C₂×C₈	C₂³×D₈₃	1	1	yes	characteristic
823	C₂×C₈	C₂³×D₈₃	1	1	yes	characteristic
824	C₂×C₈	C₂³×D₈₃	1	1	yes	characteristic
825	C₄⋊C₄	—	2	2	no	—
826	C₄⋊C₄	—	2	2	no	—
827	C₄⋊C₄	—	2	2	no	—
828	C₄⋊C₄	—	2	2	no	—
829	C₄⋊C₄	—	2	2	no	—
830	C₄⋊C₄	—	2	2	no	—
831	C₄⋊C₄	—	2	2	no	—
832	C₄⋊C₄	—	2	2	no	—
833	C₄⋊C₄	—	83	1	no	—
834	C₄⋊C₄	—	83	1	no	—
835	C₄⋊C₄	—	83	1	no	—
836	C₄⋊C₄	—	83	1	no	—
837	C₄⋊C₄	—	83	1	no	—
838	C₄⋊C₄	—	83	1	no	—
839	C₄⋊C₄	—	83	1	no	—
840	C₄⋊C₄	—	83	1	no	—
841	C₄⋊C₄	—	83	1	no	—
842	C₄⋊C₄	—	83	1	no	—
843	C₄⋊C₄	—	83	1	no	—
844	C₄⋊C₄	—	83	1	no	—
845	C₄⋊C₄	—	83	1	no	—
846	C₄⋊C₄	—	83	2	no	—
847	C₄⋊C₄	—	83	2	no	—
848	C₄⋊C₄	—	83	2	no	—
849	C₄⋊C₄	—	166	2	no	—
850	C₄⋊C₄	—	166	2	no	—
851	C₄⋊C₄	—	166	2	no	—
852	C₄⋊C₄	—	166	2	no	—
853	C₄⋊C₄	—	166	2	no	—
854	C₄⋊C₄	—	166	2	no	—
855	C₄⋊C₄	—	166	2	no	—
856	C₄⋊C₄	—	166	2	no	—
857	C₄⋊C₄	—	166	2	no	—
858	C₄⋊C₄	—	166	2	no	—
859	C₄⋊C₄	—	166	2	no	—
860	C₄⋊C₄	—	166	2	no	—
861	C₄⋊C₄	—	166	2	no	—
862	C₄⋊C₄	—	166	2	no	—
863	C₄⋊C₄	—	166	2	no	—
864	C₄⋊C₄	—	166	2	no	—
865	C₄⋊C₄	—	166	2	no	—
866	C₄⋊C₄	—	166	2	no	—
867	C₄⋊C₄	—	166	2	no	—
868	C₄⋊C₄	—	166	2	no	—
869	C₄⋊C₄	—	166	2	no	—
870	C₄⋊C₄	—	166	2	no	—
871	C₄⋊C₄	—	166	2	no	—
872	C₄⋊C₄	D₄×D₈₃	1	1	yes	characteristic
873	C₄⋊C₄	D₄×D₈₃	1	1	yes	characteristic
874	C₄⋊C₄	D₄×D₈₃	1	1	yes	characteristic
875	C₄⋊C₄	C₂³×D₈₃	1	2	yes	—
876	C₄⋊C₄	C₂³×D₈₃	1	2	yes	—
877	C₄⋊C₄	C₂³×D₈₃	1	2	yes	—
878	C₂²⋊C₄	—	83	1	no	—
879	C₂²⋊C₄	—	83	1	no	—
880	C₂²⋊C₄	—	83	1	no	—
881	C₂²⋊C₄	—	83	1	no	—
882	C₂²⋊C₄	—	166	2	no	—
883	C₂²⋊C₄	—	166	2	no	—
884	C₄²	—	2	2	no	—
885	C₄²	—	2	2	no	—
886	C₄²	—	2	2	no	—
887	C₄²	—	83	1	no	—
888	C₄²	—	83	1	no	—
889	C₄²	—	83	1	no	—
890	C₄²	—	83	1	no	—
891	C₄²	—	83	1	no	—
892	C₄²	—	166	2	no	—
893	C₄²	—	166	2	no	—
894	C₄²	—	166	2	no	—
895	C₄²	—	166	2	no	—
896	C₄²	—	166	2	no	—
897	C₄²	—	166	2	no	—
898	C₄²	—	166	2	no	—
899	C₄²	—	166	2	no	—
900	C₄²	—	166	2	no	—
901	C₄²	—	166	2	no	—
902	C₄²	—	166	2	no	—
903	C₄²	C₂³×D₈₃	1	1	yes	characteristic
904	C₄²	C₂³×D₈₃	1	1	yes	characteristic
905	C₄²	C₂³×D₈₃	1	1	yes	characteristic
906	C₂³	—	83	1	no	—
907	Q₈	—	2	2	no	—
908	Q₈	—	4	1	no	—
909	Q₈	—	8	2	no	—
910	Q₈	—	332	1	no	—
911	Q₈	—	332	4	no	—
912	Q₈	—	83	4	no	—
913	Q₈	—	664	2	no	—
914	Q₈	—	664	2	no	—
915	Q₈	—	664	2	no	—
916	Q₈	—	664	2	no	—
917	Q₈	—	166	8	no	—
918	Q₈	—	166	2	no	—
919	Q₈	—	166	2	no	—
920	Q₈	—	166	2	no	—
921	Q₈	C₂×Q₈×D₈₃	1	4	yes	—
922	C₂×C₄	—	2	2	no	—
923	C₂×C₄	—	2	2	no	—
924	C₂×C₄	—	2	2	no	—
925	C₂×C₄	—	2	2	no	—
926	C₂×C₄	—	332	1	no	—
927	C₂×C₄	—	83	1	no	—
928	C₂×C₄	—	83	1	no	—
929	C₂×C₄	—	83	2	no	—
930	C₂×C₄	—	83	2	no	—
931	C₂×C₄	—	83	1	no	—
932	C₂×C₄	—	83	1	no	—
933	C₂×C₄	—	83	1	no	—
934	C₂×C₄	—	83	1	no	—
935	C₂×C₄	—	83	1	no	—
936	C₂×C₄	—	664	2	no	—
937	C₂×C₄	—	166	2	no	—
938	C₂×C₄	—	166	8	no	—
939	C₂×C₄	—	166	2	no	—
940	C₂×C₄	—	166	2	no	—
941	C₂×C₄	—	166	2	no	—
942	C₂×C₄	—	166	2	no	—
943	C₂×C₄	C₂×D₄×D₈₃	1	1	yes	characteristic
944	C₂×C₄	C₂×D₄×D₈₃	1	1	yes	characteristic
945	C₂×C₄	C₂×D₄×D₈₃	1	1	yes	characteristic
946	C₂×C₄	C₂×D₄×D₈₃	1	1	yes	characteristic
947	C₂×C₄	C₂×D₄×D₈₃	1	1	yes	characteristic
948	C₂×C₄	C₂×D₄×D₈₃	1	1	yes	characteristic
949	C₂×C₄	C₂⁴×D₈₃	1	1	yes	characteristic
950	C₈	—	2	1	no	—
951	C₈	—	2	1	no	—
952	C₈	—	2	1	no	—
953	C₈	—	83	2	no	—
954	C₈	—	166	1	no	—
955	C₈	—	166	1	no	—
956	C₈	—	166	1	no	—
957	C₈	C₂×Q₈×D₈₃	1	2	yes	—
958	C₂²	—	83	2	no	—
959	C₂²	—	166	1	no	—
960	C₂²	—	166	1	no	—
961	C₂²	C₂²×D₄×D₈₃	1	1	yes	characteristic
962	C₄	—	2	4	no	—
963	C₄	—	2	1	no	—
964	C₄	—	2	1	no	—
965	C₄	—	2	1	no	—
966	C₄	—	2	1	no	—
967	C₄	—	2	1	no	—
968	C₄	—	2	1	no	—
969	C₄	—	4	2	no	—
970	C₄	—	4	2	no	—
971	C₄	—	4	2	no	—
972	C₄	—	332	2	no	—
973	C₄	—	332	2	no	—
974	C₄	—	332	2	no	—
975	C₄	—	83	2	no	—
976	C₄	—	83	2	no	—
977	C₄	—	166	4	no	—
978	C₄	—	166	1	no	—
979	C₄	—	166	1	no	—
980	C₄	—	166	1	no	—
981	C₄	—	166	1	no	—
982	C₄	—	166	1	no	—
983	C₄	C₂²×Q₈×D₈₃	1	1	yes	characteristic
984	C₄	2₋¹⁺⁴×D₈₃	1	1	yes	characteristic
985	C₂	—	166	2	no	—
986	C₂	D₄×Q₈×D₈₃	1	1	yes	characteristic
987	C₂	#578×D₈₃	1	1	yes	characteristic
988	C₂	#24922232	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂²×D₄×D₈₃
commutator, cosocle	C₂×C₄×C₈₃	C₂⁵
Frattini	C₂×C₄	C₂⁴×D₈₃
Fitting	C₈₃×#3383	C₂
socle	C₂²×C₈₃	C₂³×D₄
prime radical	C₂²×D₈₃	C₂²×D₄
hypercenter	#3383	D₈₃
hypocenter	C₈₃	#61372
LCS	G ▷ C₂×C₄×C₈₃ ▷ C₂×C₈₃ ▷ C₈₃
UCS	C₁ ◁ C₂² ◁ C₄×Q₈ ◁ #3383

Complements

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

N	H ≅ G/N	type
2. #24920430	C₂	semidirect
3. #24920426	C₂	semidirect
4. #24920398	C₂	semidirect
5. #24920390	C₂	semidirect
6. #24920355	C₂	semidirect
7. #24920354	C₂	semidirect
8. #24920354	C₂	semidirect
9. #24920351	C₂	semidirect
10. #24920351	C₂	semidirect
11. Q₁₆×Dic₁₆₆	C₂	semidirect
12. #24920346	C₂	semidirect
23. C₈₃×#3383	C₂	semidirect
134. Q₁₆×D₈₃	Q₈	semidirect
505. #3383	D₈₃	semidirect
518. C₈₃	#61372	semidirect

Maximal subgroups

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

subgroup	index
#24921270	2
#24920430	2
#24920426	2
#24920398	2
#24920390	2
#24920355	2
#24920354	2
#24920351	2
Q₁₆×Dic₁₆₆	2
#24920346	2
#24918000	2
#24917996	2
#24917976	2
#24917302	2
#24917298	2
#24917266	2
#24916392	2
#24916326	2
C₄×Q₁₆×D₈₃	2
C₈₃×#3383	2
#61372	83