Subgroups — #25979201

Order 11008.

1882 conjugacy classes of subgroups.

The subgroup lattice has 1094 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19148642	C₂	1	2	yes	maximal, complemented
2	#19147580	C₂	1	1	yes	maximal, characteristic, complemented
3	#19147447	C₂	1	1	yes	maximal, characteristic, complemented
4	#19147310	C₂	1	2	yes	maximal, complemented
5	#19146987	C₂	1	1	yes	maximal, characteristic, complemented
6	#19146984	C₂	1	1	yes	maximal, characteristic, complemented
7	#19146939	C₂	1	1	yes	maximal, characteristic, complemented
8	#19146895	C₂	1	2	yes	maximal, complemented
9	#19146675	C₂	1	2	yes	maximal, complemented
10	#19146671	C₂	1	2	yes	maximal, complemented
11	#19146314	C₂	1	1	yes	maximal, characteristic, complemented
12	#19146283	C₂	1	1	yes	maximal, characteristic, complemented
13	#19146279	C₂	1	1	yes	maximal, characteristic, complemented
14	#19145230	C₂	1	1	yes	maximal, characteristic, complemented
15	#19145178	C₂	1	1	yes	maximal, characteristic, complemented
16	#19144855	C₂	1	2	yes	maximal, complemented
17	#19144851	C₂	1	2	yes	maximal, complemented
18	#19144692	C₂	1	2	yes	maximal, complemented
19	#19143566	C₂	1	1	yes	maximal, characteristic, complemented
20	#19143472	C₂	1	1	yes	maximal, characteristic, complemented
21	#19143470	C₂	1	1	yes	maximal, characteristic, complemented
22	C₄×D₈×D₄₃	C₂	1	1	yes	maximal, characteristic, complemented
23	C₄₃×#3175	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#13063348	C₂²	1	1	yes	characteristic
25	C₂×#13063347	C₂²	1	1	yes	characteristic
26	C₂×D₈×D₄₃	C₂²	1	1	yes	characteristic
27	#14583618	C₂²	1	2	yes	complemented
28	#14583610	C₂²	1	2	yes	—
29	#14583607	C₂²	1	2	yes	—
30	#14583585	—	2	2	no	—
31	#14583579	—	2	2	no	—
32	#14583574	—	2	2	no	—
33	#14583564	C₂²	1	2	yes	complemented
34	#14583557	—	2	2	no	—
35	#14583551	C₂²	1	2	yes	complemented
36	#14583549	C₂²	1	2	yes	complemented
37	#14583546	C₂²	1	2	yes	—
38	#14583542	C₂²	1	2	yes	—
39	#14583514	C₂²	1	2	yes	complemented
40	#14583495	—	2	2	no	—
41	#14583492	—	2	2	no	—
42	#14583453	C₂²	1	2	yes	—
43	#14583427	C₂²	1	1	yes	characteristic
44	#14583407	—	2	2	no	—
45	C₂²⋊Q₈×D₄₃	—	2	2	no	—
46	#14583381	C₂²	1	2	yes	complemented
47	#14583379	C₂²	1	2	yes	complemented
48	C₄×D₄×D₄₃	C₂²	1	2	yes	—
49	#14583303	C₂²	1	1	yes	characteristic, complemented
50	#14583303	C₂²	1	1	yes	characteristic, complemented
51	#14583282	C₂²	1	1	yes	characteristic
52	#14583277	C₂²	1	1	yes	characteristic, complemented
53	#14583257	C₂²	1	2	yes	complemented
54	#14583248	C₂²	1	2	yes	complemented
55	#14583236	C₂²	1	2	yes	—
56	#14583236	C₂²	1	2	yes	complemented
57	#14583233	C₂²	1	2	yes	—
58	#14583232	C₂²	1	2	yes	complemented
59	#14583211	C₂²	1	2	yes	complemented
60	#14583210	C₂²	1	2	yes	complemented
61	#14583192	C₂²	1	2	yes	complemented
62	#14583191	C₂²	1	2	yes	complemented
63	#14583178	C₂²	1	2	yes	complemented
64	#14583178	C₂²	1	2	yes	complemented
65	#14583177	C₂²	1	2	yes	complemented
66	#14583176	C₂²	1	2	yes	complemented
67	#14583144	C₂²	1	2	yes	complemented
68	#14583141	C₂²	1	1	yes	characteristic
69	#14583141	C₂²	1	1	yes	characteristic, complemented
70	#14583139	C₂²	1	2	yes	—
71	#14583137	C₂²	1	1	yes	characteristic
72	#14583132	C₂²	1	1	yes	characteristic
73	#14583119	C₂²	1	2	yes	complemented
74	#14583118	C₂²	1	2	yes	complemented
75	#14583113	C₂²	1	2	yes	—
76	#14583111	C₂²	1	2	yes	—
77	#14583103	C₂²	1	2	yes	complemented
78	#14583102	C₂²	1	2	yes	complemented
79	#14583064	C₂²	1	2	yes	complemented
80	#14583059	C₂²	1	2	yes	complemented
81	#14583051	C₂²	1	2	yes	—
82	#14583048	C₂²	1	2	yes	—
83	#14583043	C₂²	1	2	yes	—
84	#14583042	C₂²	1	2	yes	—
85	#14583027	C₂²	1	1	yes	characteristic, complemented
86	C₈×Dic₈₆	C₂²	1	1	yes	characteristic, complemented
87	#14583002	C₂²	1	2	yes	complemented
88	#14583001	C₂²	1	2	yes	complemented
89	#14583001	C₂²	1	2	yes	complemented
90	#14582999	C₂²	1	2	yes	complemented
91	#14582997	C₂²	1	2	yes	complemented
92	C₄×Dic₁₇₂	C₂²	1	1	yes	characteristic, complemented
93	C₄×Dic₁₇₂	C₂²	1	1	yes	characteristic, complemented
94	Q₁₆×Dic₄₃	C₂²	1	1	yes	characteristic, complemented
95	C₄×#10621885	C₂²	1	2	yes	complemented
96	C₄×D₃₄₄	C₂²	1	1	yes	characteristic
97	C₄×D₃₄₄	C₂²	1	1	yes	characteristic
98	D₈×Dic₄₃	C₂²	1	1	yes	characteristic
99	#14582981	C₂²	1	1	yes	characteristic
100	#14582981	C₂²	1	1	yes	characteristic
101	C₄×#10621882	C₂²	1	2	yes	—
102	#14582979	C₂²	1	2	yes	—
103	#14582975	C₂²	1	1	yes	characteristic, complemented
104	#14582972	C₂²	1	1	yes	characteristic
105	#14582968	C₂²	1	1	yes	characteristic
106	C₈×D₁₇₂	C₂²	1	1	yes	characteristic
107	C₈×C₂²⋊D₄₃	C₂²	1	1	yes	characteristic
108	C₈×C₂²⋊D₄₃	C₂²	1	1	yes	characteristic, complemented
109	#14582961	C₂²	1	1	yes	characteristic, complemented
110	#14582960	C₂²	1	1	yes	characteristic, complemented
111	#14582954	C₂²	1	1	yes	characteristic
112	C₂×#13063259	C₂²	1	1	yes	characteristic, complemented
113	#107×D₄₃	C₂²	1	1	yes	characteristic
114	#107×D₄₃	C₂²	1	1	yes	characteristic, complemented
115	#14582901	C₂²	1	2	yes	complemented
116	#14582899	C₂²	1	2	yes	complemented
117	#102×D₄₃	C₂²	1	2	yes	—
118	#14582853	C₂²	1	1	yes	characteristic, complemented
119	C₄×C₈×D₄₃	C₂²	1	1	yes	characteristic
120	C₄₃×#542	C₂²	1	2	yes	complemented
121	C₄₃×#500	C₂²	1	1	yes	characteristic, complemented
122	C₄₃×#495	C₂²	1	1	yes	characteristic
123	C₄₃×#489	C₂²	1	2	yes	complemented
124	C₄₃×#468	C₂²	1	2	yes	complemented
125	C₄₃×#467	C₂²	1	1	yes	characteristic, complemented
126	C₄₃×#466	C₂²	1	1	yes	characteristic
127	C₄₃×#440	C₂²	1	2	yes	complemented
128	C₄×Q₁₆×C₄₃	C₂²	1	1	yes	characteristic, complemented
129	C₄×D₈×C₄₃	C₂²	1	1	yes	characteristic
130	C₄₃×#405	C₂²	1	1	yes	characteristic, complemented
131	C₂×#10621902	C₂³	1	2	yes	—
132	C₂×#10621898	C₂³	1	2	yes	—
133	C₂×#10621900	—	2	2	no	—
134	C₂×Q₈×D₄₃	—	2	2	no	—
135	C₂×D₄×D₄₃	C₂³	1	2	yes	—
136	C₂²×C₄×D₄₃	—	2	2	no	—
137	#13063348	—	2	4	no	—
138	#13063347	—	2	4	no	—
139	C₂×Dic₁₇₂	C₂³	1	1	yes	characteristic
140	C₂×#10621885	C₂³	1	2	yes	—
141	C₂×#10621873	C₂³	1	2	yes	—
142	C₂×#10621883	C₂³	1	2	yes	—
143	C₂×#10621884	C₂³	1	2	yes	—
144	C₂×D₃₄₄	C₂³	1	1	yes	characteristic
145	C₂×#10621882	C₂³	1	2	yes	—
146	D₈×D₄₃	—	2	4	no	—
147	C₂×#10621872	C₂³	1	1	yes	characteristic
148	C₂×C₈×D₄₃	C₂³	1	1	yes	characteristic
149	C₂×C₈×D₄₃	C₂³	1	1	yes	characteristic
150	C₂×C₈×D₄₃	C₂³	1	1	yes	characteristic
151	#13063324	C₂³	1	2	yes	—
152	#13063324	C₂³	1	2	yes	—
153	#13063323	C₂³	1	2	yes	—
154	#13063320	D₄	1	1	yes	characteristic
155	#13063318	—	2	2	no	—
156	#13063318	—	2	2	no	—
157	#13063318	—	2	2	no	—
158	#13063318	D₄	1	1	yes	characteristic
159	#13063316	—	2	2	no	—
160	#13063315	—	2	2	no	—
161	#13063315	—	2	2	no	—
162	#13063315	D₄	1	1	yes	characteristic
163	#13063312	C₂³	1	2	yes	—
164	#13063311	—	2	2	no	—
165	#13063311	D₄	1	1	yes	characteristic
166	#13063310	—	2	2	no	—
167	#13063310	D₄	1	1	yes	characteristic
168	#13063308	—	2	2	no	—
169	#13063307	—	2	2	no	—
170	#13063307	—	2	2	no	—
171	#13063307	—	2	2	no	—
172	#13063307	—	2	2	no	—
173	#13063307	D₄	1	1	yes	characteristic
174	#13063306	—	2	2	no	—
175	#13063305	—	2	2	no	—
176	#13063305	C₂³	1	2	yes	—
177	#13063305	C₂³	1	2	yes	—
178	#13063304	—	2	2	no	—
179	#13063303	—	2	2	no	—
180	#13063303	—	2	2	no	—
181	#13063303	—	2	2	no	—
182	#13063303	D₄	1	1	yes	characteristic
183	#13063302	—	2	2	no	—
184	#13063302	—	2	2	no	—
185	#13063302	—	2	2	no	—
186	#13063301	—	2	2	no	—
187	#13063301	—	2	2	no	—
188	#13063301	—	2	2	no	—
189	#13063301	C₂³	1	2	yes	—
190	#13063298	—	2	2	no	—
191	#13063298	—	2	2	no	—
192	#13063298	D₄	1	1	yes	characteristic
193	#13063296	—	2	2	no	—
194	#13063296	C₂³	1	2	yes	—
195	#13063295	—	2	2	no	—
196	#13063293	—	2	2	no	—
197	Q₈×Dic₄₃	C₂³	1	2	yes	—
198	C₄×Dic₈₆	—	2	2	no	—
199	C₄×Dic₈₆	C₂³	1	2	yes	—
200	C₄×Dic₈₆	C₂³	1	2	yes	—
201	C₄×Dic₈₆	C₂³	1	1	yes	characteristic
202	C₄×D₁₇₂	—	2	2	no	—
203	C₄×D₁₇₂	C₂³	1	1	yes	characteristic
204	C₄×D₁₇₂	C₂³	1	2	yes	—
205	C₄×D₁₇₂	C₂³	1	2	yes	—
206	D₄×Dic₄₃	C₂³	1	2	yes	—
207	#13063287	—	2	2	no	—
208	#13063287	—	2	2	no	—
209	#13063287	C₂³	1	2	yes	—
210	#13063287	C₂³	1	2	yes	—
211	C₄×C₂²⋊D₄₃	—	2	2	no	—
212	C₄×C₂²⋊D₄₃	C₂³	1	1	yes	characteristic
213	C₄×C₂²⋊D₄₃	C₂³	1	1	yes	characteristic
214	(C₂²⋊D₄₃)⋊C₄	—	2	2	no	—
215	(C₂²⋊D₄₃)⋊C₄	—	2	2	no	—
216	(C₂²⋊D₄₃)⋊C₄	—	2	2	no	—
217	(C₂²⋊D₄₃)⋊C₄	—	2	2	no	—
218	#13063283	—	2	2	no	—
219	#13063282	—	2	2	no	—
220	#13063282	—	2	2	no	—
221	#13063282	C₂³	1	1	yes	characteristic
222	#13063281	—	2	2	no	—
223	C₂×C₄⋊Dic₄₃	C₂³	1	2	yes	—
224	C₄⋊C₄×D₄₃	—	2	2	no	—
225	C₄⋊C₄×D₄₃	—	2	2	no	—
226	C₄⋊C₄×D₄₃	—	2	2	no	—
227	C₄⋊C₄×D₄₃	C₂³	1	2	yes	—
228	C₄⋊C₄×D₄₃	C₂³	1	2	yes	—
229	C₂²⋊C₄×D₄₃	—	2	2	no	—
230	C₂²⋊C₄×D₄₃	—	2	2	no	—
231	C₂²⋊C₄×D₄₃	—	2	2	no	—
232	C₄²×D₄₃	C₂³	1	1	yes	characteristic
233	#13063259	C₂³	1	1	yes	characteristic
234	#13063259	C₂³	1	2	yes	—
235	#13063259	C₂³	1	1	yes	characteristic
236	#13063258	C₂³	1	2	yes	—
237	#13063258	C₂³	1	2	yes	—
238	#13063258	C₂³	1	2	yes	—
239	#13063258	C₂³	1	2	yes	—
240	C₄⋊(C₄₃⋊C₈)	C₂³	1	1	yes	characteristic
241	C₄⋊(C₄₃⋊C₈)	C₂³	1	1	yes	characteristic
242	Dic₄₃⋊C₈	C₂³	1	1	yes	characteristic
243	Dic₄₃⋊C₈	C₂³	1	1	yes	characteristic
244	Dic₄₃⋊C₈	C₂³	1	1	yes	characteristic
245	Dic₄₃⋊C₈	C₂³	1	1	yes	characteristic
246	#13063250	C₂³	1	2	yes	—
247	#13063250	C₂³	1	2	yes	—
248	#13063249	C₂³	1	2	yes	—
249	#13063249	C₂³	1	2	yes	—
250	#13063248	C₂³	1	2	yes	—
251	#13063248	C₂³	1	2	yes	—
252	#13063247	C₂³	1	2	yes	—
253	#13063247	C₂³	1	2	yes	—
254	#13063246	C₂³	1	2	yes	—
255	#13063246	C₂³	1	2	yes	—
256	#13063245	C₂³	1	2	yes	—
257	#13063245	C₂³	1	2	yes	—
258	C₂²⋊(C₄₃⋊C₈)	C₂³	1	1	yes	characteristic
259	C₂²⋊(C₄₃⋊C₈)	C₂³	1	1	yes	characteristic
260	(C₂×D₄₃)⋊C₈	C₂³	1	1	yes	characteristic
261	(C₂×D₄₃)⋊C₈	C₂³	1	1	yes	characteristic
262	(C₂×D₄₃)⋊C₈	C₂³	1	1	yes	characteristic
263	(C₂×D₄₃)⋊C₈	C₂³	1	1	yes	characteristic
264	#13063236	C₂³	1	1	yes	characteristic
265	#13063235	C₂³	1	1	yes	characteristic
266	C₄×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
267	C₈×Dic₄₃	C₂³	1	1	yes	characteristic
268	C₈×Dic₄₃	C₂³	1	1	yes	characteristic
269	C₈×Dic₄₃	C₂³	1	1	yes	characteristic
270	C₂×Q₁₆×C₄₃	C₂³	1	1	yes	characteristic
271	C₂×SD₁₆×C₄₃	C₂³	1	2	yes	—
272	C₂×D₈×C₄₃	C₂³	1	1	yes	characteristic
273	C₂×M₁₆×C₄₃	C₂³	1	1	yes	characteristic
274	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
275	C₄⋊Q₈×C₄₃	C₂³	1	2	yes	—
276	#126×C₄₃	—	2	2	no	—
277	#124×C₄₃	—	2	2	no	—
278	#124×C₄₃	C₂³	1	2	yes	—
279	#123×C₄₃	—	2	2	no	—
280	C₂²⋊Q₈×C₄₃	—	2	2	no	—
281	C₂²⋊Q₈×C₄₃	C₂³	1	2	yes	—
282	#121×C₄₃	C₂³	1	2	yes	—
283	C₄×Q₈×C₄₃	C₂³	1	2	yes	—
284	C₄×D₄×C₄₃	C₂³	1	2	yes	—
285	#117×C₄₃	C₂³	1	1	yes	characteristic
286	#107×C₄₃	C₂³	1	1	yes	characteristic
287	#107×C₄₃	C₂³	1	1	yes	characteristic
288	#107×C₄₃	C₂³	1	2	yes	—
289	#103×C₄₃	C₂³	1	2	yes	—
290	#103×C₄₃	C₂³	1	2	yes	—
291	#102×C₄₃	C₂³	1	2	yes	—
292	#102×C₄₃	C₂³	1	2	yes	—
293	#97×C₄₃	C₂³	1	1	yes	characteristic
294	#97×C₄₃	C₂³	1	1	yes	characteristic
295	C₄×C₈×C₄₃	C₂³	1	1	yes	characteristic
296	C₄×C₈×C₄₃	C₂³	1	1	yes	characteristic
297	C₂³×D₄₃	—	2	2	no	—
298	C₂×Q₈×C₄₃	—	2	2	no	—
299	C₂×Q₈×C₄₃	C₂⁴	1	2	yes	—
300	C₂×D₄×C₄₃	—	2	2	no	—
301	C₂×D₄×C₄₃	C₂⁴	1	2	yes	—
302	C₂²×C₄×C₄₃	—	2	2	no	—
303	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
304	C₂×C₂²⋊D₄₃	—	2	2	no	—
305	C₂×C₂²⋊D₄₃	—	2	2	no	—
306	C₂×C₂²⋊D₄₃	—	2	2	no	—
307	C₂×C₂²⋊D₄₃	C₂×D₄	1	1	yes	characteristic
308	C₂×C₂²⋊D₄₃	C₂×D₄	1	1	yes	characteristic
309	C₂²×Dic₄₃	—	2	2	no	—
310	C₂²×Dic₄₃	—	2	2	no	—
311	#10621902	—	2	4	no	—
312	#10621902	—	4	2	no	—
313	Q₈×D₄₃	—	8	4	no	—
314	#10621900	—	8	4	no	—
315	D₄×D₄₃	—	2	4	no	—
316	D₄×D₄₃	—	4	2	no	—
317	#10621898	—	2	4	no	—
318	#10621898	—	4	2	no	—
319	C₂×D₁₇₂	—	2	2	no	—
320	C₂×D₁₇₂	C₂×D₄	1	1	yes	characteristic
321	C₂×D₁₇₂	C₂⁴	1	2	yes	—
322	C₂×C₄×D₄₃	—	2	2	no	—
323	C₂×C₄×D₄₃	—	2	2	no	—
324	C₂×C₄×D₄₃	—	2	2	no	—
325	C₂×C₄×D₄₃	—	2	2	no	—
326	C₂×C₄×D₄₃	—	2	2	no	—
327	C₂×C₄×D₄₃	—	2	2	no	—
328	C₂×C₄×D₄₃	—	2	2	no	—
329	C₂×C₄×D₄₃	—	2	2	no	—
330	C₂×C₄×D₄₃	—	8	4	no	—
331	C₂×C₄×D₄₃	C₂×D₄	1	1	yes	characteristic
332	C₂×C₄×D₄₃	C₂×D₄	1	1	yes	characteristic
333	C₂×C₄×D₄₃	C₂⁴	1	1	yes	characteristic
334	C₂×C₄×D₄₃	C₂⁴	1	1	yes	characteristic
335	C₂×Dic₈₆	—	2	2	no	—
336	C₂×Dic₈₆	—	2	2	no	—
337	C₂×Dic₈₆	C₂×D₄	1	1	yes	characteristic
338	C₂×Dic₈₆	C₂⁴	1	2	yes	—
339	Q₁₆×C₄₃	—	2	2	no	—
340	SD₁₆×C₄₃	—	4	2	no	—
341	D₈×C₄₃	—	2	2	no	—
342	M₁₆×C₄₃	—	4	1	no	—
343	C₂×C₈×C₄₃	—	2	2	no	—
344	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
345	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
346	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
347	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
348	C₄⋊C₄×C₄₃	—	2	2	no	—
349	C₄⋊C₄×C₄₃	—	2	2	no	—
350	C₄⋊C₄×C₄₃	—	2	2	no	—
351	C₄⋊C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
352	C₄⋊C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
353	C₄⋊C₄×C₄₃	C₂⁴	1	2	yes	—
354	C₄⋊C₄×C₄₃	C₂⁴	1	2	yes	—
355	C₂²⋊C₄×C₄₃	—	2	2	no	—
356	C₂²⋊C₄×C₄₃	—	2	2	no	—
357	C₂²⋊C₄×C₄₃	—	2	2	no	—
358	C₂²⋊C₄×C₄₃	—	2	2	no	—
359	C₂²⋊C₄×C₄₃	—	2	2	no	—
360	C₂²⋊C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
361	C₂²⋊C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
362	C₄²×C₄₃	—	2	2	no	—
363	C₄²×C₄₃	C₂⁴	1	1	yes	characteristic
364	C₄²×C₄₃	C₂⁴	1	1	yes	characteristic
365	C₂²⋊Dic₄₃	—	2	2	no	—
366	C₂²⋊Dic₄₃	—	2	2	no	—
367	C₂²⋊Dic₄₃	—	2	2	no	—
368	C₂²⋊Dic₄₃	—	2	2	no	—
369	C₂²⋊Dic₄₃	C₂×D₄	1	1	yes	characteristic
370	C₂²⋊Dic₄₃	C₂×D₄	1	1	yes	characteristic
371	#10621885	—	4	2	no	—
372	#10621884	—	2	4	no	—
373	#10621883	—	4	2	no	—
374	#10621882	—	2	4	no	—
375	(C₂×D₄₃)⋊C₄	—	2	2	no	—
376	(C₂×D₄₃)⋊C₄	—	2	2	no	—
377	(C₂×D₄₃)⋊C₄	—	2	2	no	—
378	(C₂×D₄₃)⋊C₄	—	2	2	no	—
379	(C₂×D₄₃)⋊C₄	—	2	2	no	—
380	(C₂×D₄₃)⋊C₄	—	2	2	no	—
381	(C₂×D₄₃)⋊C₄	—	2	2	no	—
382	(C₂×D₄₃)⋊C₄	C₂×D₄	1	1	yes	characteristic
383	(C₂×D₄₃)⋊C₄	C₂×D₄	1	1	yes	characteristic
384	(C₂×D₄₃)⋊C₄	C₂×D₄	1	1	yes	characteristic
385	(C₂×D₄₃)⋊C₄	C₂×D₄	1	1	yes	characteristic
386	(C₂×D₄₃)⋊C₄	C₂×D₄	1	1	yes	characteristic
387	(C₂×D₄₃)⋊C₄	C₂×D₄	1	1	yes	characteristic
388	C₄⋊Dic₄₃	—	2	2	no	—
389	C₄⋊Dic₄₃	—	2	2	no	—
390	C₄⋊Dic₄₃	—	2	2	no	—
391	C₄⋊Dic₄₃	—	2	2	no	—
392	C₄⋊Dic₄₃	C₂×D₄	1	1	yes	characteristic
393	C₄⋊Dic₄₃	C₂×D₄	1	1	yes	characteristic
394	C₄⋊Dic₄₃	C₂⁴	1	2	yes	—
395	C₄⋊Dic₄₃	C₂⁴	1	2	yes	—
396	Dic₄₃⋊C₄	—	2	2	no	—
397	Dic₄₃⋊C₄	—	2	2	no	—
398	Dic₄₃⋊C₄	—	2	2	no	—
399	Dic₄₃⋊C₄	—	2	2	no	—
400	Dic₄₃⋊C₄	—	2	2	no	—
401	Dic₄₃⋊C₄	—	2	2	no	—
402	Dic₄₃⋊C₄	—	2	2	no	—
403	Dic₄₃⋊C₄	—	2	2	no	—
404	Dic₄₃⋊C₄	—	2	2	no	—
405	Dic₄₃⋊C₄	C₂×D₄	1	1	yes	characteristic
406	Dic₄₃⋊C₄	C₂×D₄	1	1	yes	characteristic
407	Dic₄₃⋊C₄	C₂×D₄	1	1	yes	characteristic
408	Dic₄₃⋊C₄	C₂×D₄	1	1	yes	characteristic
409	Dic₄₃⋊C₄	C₂×D₄	1	1	yes	characteristic
410	Dic₄₃⋊C₄	C₂×D₄	1	1	yes	characteristic
411	C₄×Dic₄₃	—	2	2	no	—
412	C₄×Dic₄₃	—	2	2	no	—
413	C₄×Dic₄₃	—	2	2	no	—
414	C₄×Dic₄₃	C₂×D₄	1	1	yes	characteristic
415	C₄×Dic₄₃	C₂×D₄	1	1	yes	characteristic
416	C₄×Dic₄₃	C₂⁴	1	1	yes	characteristic
417	C₄×Dic₄₃	C₂⁴	1	1	yes	characteristic
418	C₂×C₄₃⋊C₈	C₂⁴	1	1	yes	characteristic
419	C₂×C₄₃⋊C₈	C₂⁴	1	1	yes	characteristic
420	C₂×C₄₃⋊C₈	C₂⁴	1	1	yes	characteristic
421	C₂×C₄₃⋊C₈	C₂⁴	1	1	yes	characteristic
422	Dic₁₇₂	—	2	2	no	—
423	D₃₄₄	#41	1	4	yes	complemented
424	#10621873	—	2	4	no	—
425	#10621872	—	4	1	no	—
426	C₈×D₄₃	—	2	2	no	—
427	C₈×D₄₃	—	2	2	no	—
428	C₈×D₄₃	—	4	1	no	—
429	C₂³×C₄₃	—	2	2	no	—
430	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
431	C₂²×D₄₃	—	2	2	no	—
432	C₂²×D₄₃	—	4	4	no	—
433	C₂²×D₄₃	—	4	4	no	—
434	C₂²×D₄₃	—	8	2	no	—
435	C₂²×D₄₃	C₂²×D₄	1	1	yes	characteristic
436	C₂²×D₄₃	C₂²×D₄	1	1	yes	characteristic
437	Q₈×C₄₃	—	2	2	no	—
438	Q₈×C₄₃	—	2	2	no	—
439	Q₈×C₄₃	—	8	2	no	—
440	D₄×C₄₃	—	2	2	no	—
441	D₄×C₄₃	—	2	2	no	—
442	D₄×C₄₃	—	8	2	no	—
443	C₂×C₄×C₄₃	—	2	1	no	—
444	C₂×C₄×C₄₃	—	2	1	no	—
445	C₂×C₄×C₄₃	—	2	2	no	—
446	C₂×C₄×C₄₃	—	2	2	no	—
447	C₂×C₄×C₄₃	—	2	2	no	—
448	C₂×C₄×C₄₃	—	8	2	no	—
449	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
450	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
451	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
452	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
453	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
454	C₂×C₄×C₄₃	C₂⁵	1	1	yes	characteristic
455	C₂²⋊D₄₃	—	2	2	no	—
456	C₂²⋊D₄₃	—	2	2	no	—
457	C₂²⋊D₄₃	—	4	4	no	—
458	C₂²⋊D₄₃	—	4	4	no	—
459	C₂²⋊D₄₃	—	8	2	no	—
460	C₂×Dic₄₃	—	2	2	no	—
461	C₂×Dic₄₃	—	2	2	no	—
462	C₂×Dic₄₃	—	2	2	no	—
463	C₂×Dic₄₃	—	4	4	no	—
464	C₂×Dic₄₃	—	8	2	no	—
465	C₂×Dic₄₃	C₂²×D₄	1	1	yes	characteristic
466	C₂×Dic₄₃	C₂²×D₄	1	1	yes	characteristic
467	C₂×Dic₄₃	C₂²×D₄	1	1	yes	characteristic
468	C₂×Dic₄₃	C₂²×D₄	1	1	yes	characteristic
469	C₂×Dic₄₃	C₂²×D₄	1	1	yes	characteristic
470	C₂×Dic₄₃	C₂²×D₄	1	1	yes	characteristic
471	D₁₇₂	—	2	2	no	—
472	D₁₇₂	—	2	2	no	—
473	D₁₇₂	—	4	4	no	—
474	D₁₇₂	C₂×#41	1	4	yes	—
475	C₄×D₄₃	—	2	2	no	—
476	C₄×D₄₃	—	2	1	no	—
477	C₄×D₄₃	—	2	1	no	—
478	C₄×D₄₃	—	2	1	no	—
479	C₄×D₄₃	—	2	1	no	—
480	C₄×D₄₃	—	2	2	no	—
481	C₄×D₄₃	—	4	4	no	—
482	C₄×D₄₃	—	4	4	no	—
483	C₄×D₄₃	—	4	4	no	—
484	C₄×D₄₃	—	8	2	no	—
485	C₄×D₄₃	—	8	2	no	—
486	C₄×D₄₃	—	8	2	no	—
487	C₄×D₄₃	—	8	2	no	—
488	C₄×D₄₃	—	8	2	no	—
489	Dic₈₆	—	2	2	no	—
490	Dic₈₆	—	2	2	no	—
491	Dic₈₆	—	2	2	no	—
492	Dic₈₆	—	4	4	no	—
493	Dic₈₆	—	8	2	no	—
494	C₈×C₄₃	—	2	1	no	—
495	C₈×C₄₃	—	2	1	no	—
496	C₈×C₄₃	—	2	1	no	—
497	C₈×C₄₃	C₂×#41	1	2	yes	—
498	C₄₃⋊C₈	—	2	1	no	—
499	C₄₃⋊C₈	—	2	1	no	—
500	C₄₃⋊C₈	—	2	1	no	—
501	C₄₃⋊C₈	—	2	1	no	—
502	#61482	—	43	1	no	maximal, Sylow
503	C₂²×C₄₃	—	2	1	no	—
504	C₂²×C₄₃	—	2	1	no	—
505	C₂²×C₄₃	—	2	1	no	—
506	C₂²×C₄₃	—	4	2	no	—
507	C₂²×C₄₃	—	4	2	no	—
508	C₂²×C₄₃	—	4	2	no	—
509	C₂²×C₄₃	C₂³×D₄	1	1	yes	characteristic
510	C₂×D₄₃	—	2	1	no	—
511	C₂×D₄₃	—	2	1	no	—
512	C₂×D₄₃	—	2	4	no	—
513	C₂×D₄₃	—	2	1	no	—
514	C₂×D₄₃	—	2	1	no	—
515	C₂×D₄₃	—	2	1	no	—
516	C₂×D₄₃	—	4	2	no	—
517	C₂×D₄₃	—	4	2	no	—
518	C₂×D₄₃	—	8	8	no	—
519	C₂×D₄₃	#578	1	2	yes	—
520	C₄×C₄₃	—	2	1	no	—
521	C₄×C₄₃	—	2	1	no	—
522	C₄×C₄₃	—	2	1	no	—
523	C₄×C₄₃	—	2	1	no	—
524	C₄×C₄₃	—	2	1	no	—
525	C₄×C₄₃	—	4	2	no	—
526	C₄×C₄₃	—	4	2	no	—
527	C₄×C₄₃	—	4	2	no	—
528	C₄×C₄₃	C₂²×#41	1	1	yes	characteristic
529	C₄×C₄₃	#585	1	1	yes	characteristic
530	Dic₄₃	—	2	1	no	—
531	Dic₄₃	—	2	1	no	—
532	Dic₄₃	—	2	1	no	—
533	Dic₄₃	—	2	1	no	—
534	Dic₄₃	—	2	1	no	—
535	Dic₄₃	—	4	2	no	—
536	Dic₄₃	—	4	2	no	—
537	Dic₄₃	—	4	2	no	—
538	Dic₄₃	#576	1	2	yes	—
539	#3520	—	43	2	no	—
540	#3393	—	43	1	no	—
541	Q₈×D₈	—	43	1	no	—
542	#3367	—	43	2	no	—
543	#3338	—	43	1	no	—
544	#3338	—	43	1	no	—
545	#3334	—	43	1	no	—
546	#3330	—	43	2	no	—
547	#3314	—	43	2	no	—
548	#3314	—	43	2	no	—
549	#3283	—	43	1	no	—
550	#3280	—	43	1	no	—
551	#3280	—	43	1	no	—
552	#3175	—	43	1	no	—
553	#3175	D₄₃	1	1	yes	characteristic, complemented
554	#3170	—	43	1	no	—
555	#3124	—	43	2	no	—
556	#3124	—	43	2	no	—
557	#3110	—	43	2	no	—
558	#2966	—	43	1	no	—
559	#2951	—	43	1	no	—
560	#2951	—	43	1	no	—
561	C₂×C₄×D₈	—	43	1	no	—
562	C₂×C₄₃	—	4	1	no	—
563	C₂×C₄₃	—	8	2	no	—
564	C₂×C₄₃	D₄×#41	1	1	yes	characteristic
565	C₂×C₄₃	C₂×#576	1	1	yes	characteristic
566	C₂×C₄₃	C₂×#578	1	1	yes	characteristic
567	D₄₃	—	2	2	no	—
568	D₄₃	—	4	1	no	—
569	D₄₃	—	4	4	no	—
570	C₂×#135	—	43	1	no	—
571	C₂×#135	—	43	1	no	—
572	C₂²×D₈	—	43	1	no	—
573	#556	—	43	2	no	—
574	#554	—	43	2	no	—
575	#554	—	43	2	no	—
576	#552	—	86	2	no	—
577	#551	—	86	2	no	—
578	#551	—	86	2	no	—
579	D₄×Q₈	—	43	2	no	—
580	#548	—	86	2	no	—
581	#547	—	43	2	no	—
582	#547	—	43	2	no	—
583	#546	—	43	2	no	—
584	#546	—	43	2	no	—
585	#542	—	43	2	no	—
586	#542	C₂×D₄₃	1	2	yes	complemented
587	#539	—	86	2	no	—
588	#539	—	86	2	no	—
589	#533	—	43	2	no	—
590	#529	—	43	1	no	—
591	#525	—	86	2	no	—
592	C₂×C₂²⋊Q₈	—	86	2	no	—
593	#520	—	43	2	no	—
594	#520	—	43	2	no	—
595	C₂×C₄×D₄	—	43	2	no	—
596	#500	—	43	1	no	—
597	#500	—	43	1	no	—
598	#500	C₂×D₄₃	1	1	yes	characteristic, complemented
599	#495	—	43	1	no	—
600	#495	C₂×D₄₃	1	1	yes	characteristic
601	#494	—	43	1	no	—
602	#489	—	43	2	no	—
603	#489	C₂×D₄₃	1	2	yes	complemented
604	#487	—	43	2	no	—
605	#484	—	43	2	no	—
606	#484	—	43	2	no	—
607	#484	—	43	2	no	—
608	#484	—	43	2	no	—
609	#480	—	43	2	no	—
610	#480	—	43	2	no	—
611	#477	—	43	2	no	—
612	#477	—	43	2	no	—
613	#474	—	43	2	no	—
614	#474	—	43	2	no	—
615	#474	—	43	2	no	—
616	#474	—	43	2	no	—
617	#468	—	43	2	no	—
618	#468	C₂×D₄₃	1	2	yes	complemented
619	#467	—	43	1	no	—
620	#467	—	43	1	no	—
621	#467	—	43	1	no	—
622	#467	—	43	2	no	—
623	#467	C₂×D₄₃	1	1	yes	characteristic, complemented
624	#466	—	43	1	no	—
625	#466	C₂×D₄₃	1	1	yes	characteristic
626	#464	—	43	2	no	—
627	#464	—	43	2	no	—
628	#463	—	43	2	no	—
629	#463	—	43	2	no	—
630	#461	—	43	2	no	—
631	#461	—	43	2	no	—
632	#452	—	43	2	no	—
633	#452	—	43	2	no	—
634	#450	—	43	2	no	—
635	#450	—	43	2	no	—
636	#449	—	43	2	no	—
637	#449	—	43	2	no	—
638	#446	—	43	1	no	—
639	C₈×Q₈	—	43	1	no	—
640	#440	—	43	2	no	—
641	#440	—	43	2	no	—
642	#440	—	43	2	no	—
643	#440	—	43	2	no	—
644	#440	—	43	2	no	—
645	#440	C₂×D₄₃	1	2	yes	complemented
646	C₄×Q₁₆	—	43	1	no	—
647	C₄×Q₁₆	—	43	2	no	—
648	C₄×Q₁₆	—	43	1	no	—
649	C₄×Q₁₆	—	43	1	no	—
650	C₄×Q₁₆	C₂×D₄₃	1	1	yes	characteristic, complemented
651	C₄×D₈	—	43	1	no	—
652	C₄×D₈	—	43	2	no	—
653	C₄×D₈	—	43	1	no	—
654	C₄×D₈	—	43	1	no	—
655	C₄×D₈	—	43	2	no	—
656	C₄×D₈	—	43	1	no	—
657	C₄×D₈	—	43	1	no	—
658	C₄×D₈	C₂×D₄₃	1	1	yes	characteristic
659	#436	—	43	1	no	—
660	#435	—	43	1	no	—
661	#435	—	43	1	no	—
662	C₈×D₄	—	43	1	no	—
663	C₈×D₄	—	43	1	no	—
664	C₈×D₄	—	43	1	no	—
665	#433	—	43	1	no	—
666	#433	—	43	1	no	—
667	#432	—	43	1	no	—
668	C₂×#107	—	43	1	no	—
669	C₂×#107	—	43	1	no	—
670	C₂×#107	—	43	1	no	—
671	#417	—	43	2	no	—
672	#417	—	43	2	no	—
673	C₂×#102	—	43	2	no	—
674	#405	—	43	1	no	—
675	#405	C₂×D₄₃	1	1	yes	characteristic, complemented
676	C₂×C₄×C₈	—	43	1	no	—
677	C₄₃	#61482	1	1	yes	characteristic, complemented, Sylow
678	C₂×#41	—	43	2	no	—
679	C₂×#41	—	43	2	no	—
680	C₂×#41	—	86	2	no	—
681	C₂²×Q₈	—	86	2	no	—
682	C₂²×D₄	—	43	2	no	—
683	C₂³×C₄	—	86	2	no	—
684	#135	—	86	4	no	—
685	#135	—	86	4	no	—
686	C₂×Q₁₆	—	43	2	no	—
687	C₂×Q₁₆	—	43	1	no	—
688	C₂×Q₁₆	C₂²×D₄₃	1	1	yes	characteristic
689	C₂×SD₁₆	—	43	2	no	—
690	C₂×SD₁₆	—	43	2	no	—
691	C₂×SD₁₆	—	43	2	no	—
692	C₂×SD₁₆	C₂²×D₄₃	1	2	yes	—
693	C₂×D₈	—	43	2	no	—
694	C₂×D₈	—	43	1	no	—
695	C₂×D₈	—	86	4	no	—
696	C₂×D₈	C₂²×D₄₃	1	1	yes	characteristic
697	C₂×M₁₆	—	43	1	no	—
698	C₂×M₁₆	C₂²×D₄₃	1	1	yes	characteristic
699	C₂²×C₈	—	43	1	no	—
700	C₂²×C₈	—	43	1	no	—
701	C₂²×C₈	—	43	1	no	—
702	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
703	C₄⋊Q₈	—	43	2	no	—
704	C₄⋊Q₈	—	43	2	no	—
705	C₄⋊Q₈	—	43	2	no	—
706	C₄⋊Q₈	C₂²×D₄₃	1	2	yes	—
707	#126	—	2	2	no	—
708	#126	—	43	1	no	—
709	#126	—	43	1	no	—
710	#126	—	86	2	no	—
711	#126	—	86	2	no	—
712	#126	—	86	2	no	—
713	#125	—	43	1	no	—
714	#125	—	86	2	no	—
715	#125	—	86	2	no	—
716	#125	—	86	2	no	—
717	#124	—	2	2	no	—
718	#124	—	43	1	no	—
719	#124	—	43	2	no	—
720	#124	—	86	2	no	—
721	#124	C₂²×D₄₃	1	2	yes	—
722	#123	—	2	2	no	—
723	#123	—	43	1	no	—
724	#123	—	43	1	no	—
725	#123	—	86	2	no	—
726	#123	—	86	2	no	—
727	#123	—	86	2	no	—
728	#123	—	86	2	no	—
729	#123	—	86	2	no	—
730	#123	—	86	2	no	—
731	#123	—	86	2	no	—
732	C₂²⋊Q₈	—	2	2	no	—
733	C₂²⋊Q₈	—	43	1	no	—
734	C₂²⋊Q₈	—	43	2	no	—
735	C₂²⋊Q₈	—	43	2	no	—
736	C₂²⋊Q₈	—	43	2	no	—
737	C₂²⋊Q₈	—	86	2	no	—
738	C₂²⋊Q₈	—	86	2	no	—
739	C₂²⋊Q₈	—	86	2	no	—
740	C₂²⋊Q₈	—	86	2	no	—
741	C₂²⋊Q₈	—	86	2	no	—
742	C₂²⋊Q₈	—	86	2	no	—
743	C₂²⋊Q₈	—	86	2	no	—
744	C₂²⋊Q₈	—	86	2	no	—
745	C₂²⋊Q₈	—	86	2	no	—
746	C₂²⋊Q₈	—	86	2	no	—
747	C₂²⋊Q₈	—	86	2	no	—
748	C₂²⋊Q₈	C₂²×D₄₃	1	2	yes	—
749	#121	—	43	1	no	—
750	#121	—	43	2	no	—
751	#121	—	86	2	no	—
752	#121	—	86	2	no	—
753	#121	—	86	2	no	—
754	#121	C₂²×D₄₃	1	2	yes	—
755	#120	—	86	2	no	—
756	#120	—	86	2	no	—
757	C₄×Q₈	—	43	1	no	—
758	C₄×Q₈	—	43	2	no	—
759	C₄×Q₈	—	43	2	no	—
760	C₄×Q₈	—	43	2	no	—
761	C₄×Q₈	—	86	2	no	—
762	C₄×Q₈	C₂²×D₄₃	1	2	yes	—
763	C₄×D₄	—	43	1	no	—
764	C₄×D₄	—	43	1	no	—
765	C₄×D₄	—	43	2	no	—
766	C₄×D₄	—	43	2	no	—
767	C₄×D₄	—	43	2	no	—
768	C₄×D₄	—	43	1	no	—
769	C₄×D₄	—	43	2	no	—
770	C₄×D₄	—	43	2	no	—
771	C₄×D₄	—	86	2	no	—
772	C₄×D₄	—	86	2	no	—
773	C₄×D₄	—	86	2	no	—
774	C₄×D₄	—	86	2	no	—
775	C₄×D₄	—	86	2	no	—
776	C₄×D₄	—	86	2	no	—
777	C₄×D₄	—	86	2	no	—
778	C₄×D₄	—	86	2	no	—
779	C₄×D₄	C₂²×D₄₃	1	2	yes	—
780	#117	—	43	1	no	—
781	#117	—	86	2	no	—
782	#117	—	86	2	no	—
783	#117	—	86	2	no	—
784	#117	—	86	2	no	—
785	#117	C₂²×D₄₃	1	1	yes	characteristic
786	C₂×C₄⋊C₄	—	43	2	no	—
787	C₂×C₄⋊C₄	—	43	2	no	—
788	C₂×C₄⋊C₄	—	43	2	no	—
789	C₂×C₄⋊C₄	—	86	2	no	—
790	C₂×C₄⋊C₄	—	86	2	no	—
791	C₂×C₄⋊C₄	—	86	2	no	—
792	C₂×C₂²⋊C₄	—	86	2	no	—
793	C₂×C₂²⋊C₄	—	86	2	no	—
794	C₂×C₂²⋊C₄	—	86	2	no	—
795	C₂×C₄²	—	43	1	no	—
796	#107	—	43	1	no	—
797	#107	—	43	1	no	—
798	#107	—	43	2	no	—
799	#107	—	43	2	no	—
800	#107	—	43	2	no	—
801	#107	—	43	2	no	—
802	#107	—	43	2	no	—
803	#107	C₂²×D₄₃	1	1	yes	characteristic
804	#107	C₂²×D₄₃	1	1	yes	characteristic
805	#107	C₂²×D₄₃	1	2	yes	—
806	C₄⋊C₈	—	43	1	no	—
807	C₄⋊C₈	—	43	1	no	—
808	C₄⋊C₈	—	43	1	no	—
809	C₄⋊C₈	—	43	1	no	—
810	C₄⋊C₈	—	43	1	no	—
811	C₄⋊C₈	—	43	1	no	—
812	#103	—	43	2	no	—
813	#103	—	43	2	no	—
814	#103	—	43	2	no	—
815	#103	—	43	2	no	—
816	#103	—	43	2	no	—
817	#103	—	43	2	no	—
818	#103	C₂²×D₄₃	1	2	yes	—
819	#103	C₂²×D₄₃	1	2	yes	—
820	#102	—	43	2	no	—
821	#102	—	43	2	no	—
822	#102	—	43	2	no	—
823	#102	—	43	2	no	—
824	#102	—	43	2	no	—
825	#102	—	43	2	no	—
826	#102	C₂²×D₄₃	1	2	yes	—
827	#102	C₂²×D₄₃	1	2	yes	—
828	C₂²⋊C₈	—	43	1	no	—
829	C₂²⋊C₈	—	43	1	no	—
830	C₂²⋊C₈	—	43	1	no	—
831	C₂²⋊C₈	—	43	1	no	—
832	C₂²⋊C₈	—	43	1	no	—
833	C₂²⋊C₈	—	43	1	no	—
834	#97	—	43	1	no	—
835	#97	—	43	1	no	—
836	#97	C₂²×D₄₃	1	1	yes	characteristic
837	#97	C₂²×D₄₃	1	1	yes	characteristic
838	C₄×C₈	—	43	1	no	—
839	C₄×C₈	—	43	1	no	—
840	C₄×C₈	—	43	1	no	—
841	C₄×C₈	—	43	1	no	—
842	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
843	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
844	C₂⁴	—	86	2	no	—
845	#41	—	86	4	no	—
846	#41	—	86	4	no	—
847	#41	—	344	4	no	—
848	#41	—	172	2	no	—
849	#41	—	172	2	no	—
850	C₂×Q₈	—	2	2	no	—
851	C₂×Q₈	—	43	1	no	—
852	C₂×Q₈	—	43	2	no	—
853	C₂×Q₈	—	86	2	no	—
854	C₂×Q₈	—	86	2	no	—
855	C₂×Q₈	—	344	4	no	—
856	C₂×Q₈	C₂³×D₄₃	1	2	yes	—
857	C₂×D₄	—	2	2	no	—
858	C₂×D₄	—	43	1	no	—
859	C₂×D₄	—	43	1	no	—
860	C₂×D₄	—	43	1	no	—
861	C₂×D₄	—	43	2	no	—
862	C₂×D₄	—	86	2	no	—
863	C₂×D₄	—	86	2	no	—
864	C₂×D₄	—	86	4	no	—
865	C₂×D₄	—	86	2	no	—
866	C₂×D₄	—	86	2	no	—
867	C₂×D₄	—	172	2	no	—
868	C₂×D₄	C₂³×D₄₃	1	2	yes	—
869	C₂²×C₄	—	2	2	no	—
870	C₂²×C₄	—	43	1	no	—
871	C₂²×C₄	—	43	1	no	—
872	C₂²×C₄	—	43	1	no	—
873	C₂²×C₄	—	43	1	no	—
874	C₂²×C₄	—	86	2	no	—
875	C₂²×C₄	—	86	2	no	—
876	C₂²×C₄	—	86	2	no	—
877	C₂²×C₄	—	86	2	no	—
878	C₂²×C₄	—	86	2	no	—
879	C₂²×C₄	—	86	2	no	—
880	C₂²×C₄	—	86	2	no	—
881	C₂²×C₄	—	86	2	no	—
882	C₂²×C₄	—	86	2	no	—
883	C₂²×C₄	—	86	2	no	—
884	C₂²×C₄	—	344	4	no	—
885	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
886	Q₁₆	—	2	2	no	—
887	Q₁₆	—	86	2	no	—
888	Q₁₆	—	172	2	no	—
889	SD₁₆	—	4	2	no	—
890	SD₁₆	—	86	4	no	—
891	SD₁₆	—	86	4	no	—
892	SD₁₆	—	172	2	no	—
893	D₈	—	2	2	no	—
894	D₈	—	43	4	no	—
895	D₈	—	86	4	no	—
896	M₁₆	—	4	1	no	—
897	M₁₆	—	172	1	no	—
898	C₂×C₈	—	2	2	no	—
899	C₂×C₈	—	43	1	no	—
900	C₂×C₈	—	43	1	no	—
901	C₂×C₈	—	43	1	no	—
902	C₂×C₈	—	43	1	no	—
903	C₂×C₈	—	86	2	no	—
904	C₂×C₈	—	86	2	no	—
905	C₂×C₈	—	172	1	no	—
906	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
907	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
908	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
909	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
910	C₄⋊C₄	—	2	2	no	—
911	C₄⋊C₄	—	2	2	no	—
912	C₄⋊C₄	—	2	2	no	—
913	C₄⋊C₄	—	43	1	no	—
914	C₄⋊C₄	—	43	1	no	—
915	C₄⋊C₄	—	43	1	no	—
916	C₄⋊C₄	—	43	1	no	—
917	C₄⋊C₄	—	43	1	no	—
918	C₄⋊C₄	—	43	1	no	—
919	C₄⋊C₄	—	43	1	no	—
920	C₄⋊C₄	—	43	1	no	—
921	C₄⋊C₄	—	43	2	no	—
922	C₄⋊C₄	—	43	2	no	—
923	C₄⋊C₄	—	86	2	no	—
924	C₄⋊C₄	—	86	2	no	—
925	C₄⋊C₄	—	86	2	no	—
926	C₄⋊C₄	—	86	2	no	—
927	C₄⋊C₄	—	86	2	no	—
928	C₄⋊C₄	—	86	2	no	—
929	C₄⋊C₄	—	86	2	no	—
930	C₄⋊C₄	—	86	2	no	—
931	C₄⋊C₄	—	86	2	no	—
932	C₄⋊C₄	—	86	2	no	—
933	C₄⋊C₄	—	86	2	no	—
934	C₄⋊C₄	—	86	2	no	—
935	C₄⋊C₄	—	86	2	no	—
936	C₄⋊C₄	D₄×D₄₃	1	1	yes	characteristic
937	C₄⋊C₄	D₄×D₄₃	1	1	yes	characteristic
938	C₄⋊C₄	C₂³×D₄₃	1	2	yes	—
939	C₄⋊C₄	C₂³×D₄₃	1	2	yes	—
940	C₂²⋊C₄	—	2	2	no	—
941	C₂²⋊C₄	—	2	2	no	—
942	C₂²⋊C₄	—	2	2	no	—
943	C₂²⋊C₄	—	2	2	no	—
944	C₂²⋊C₄	—	2	2	no	—
945	C₂²⋊C₄	—	43	1	no	—
946	C₂²⋊C₄	—	43	1	no	—
947	C₂²⋊C₄	—	43	1	no	—
948	C₂²⋊C₄	—	43	1	no	—
949	C₂²⋊C₄	—	43	1	no	—
950	C₂²⋊C₄	—	43	1	no	—
951	C₂²⋊C₄	—	43	1	no	—
952	C₂²⋊C₄	—	43	1	no	—
953	C₂²⋊C₄	—	86	2	no	—
954	C₂²⋊C₄	—	86	2	no	—
955	C₂²⋊C₄	—	86	2	no	—
956	C₂²⋊C₄	—	86	2	no	—
957	C₂²⋊C₄	—	86	2	no	—
958	C₂²⋊C₄	—	86	2	no	—
959	C₂²⋊C₄	—	86	2	no	—
960	C₂²⋊C₄	—	86	2	no	—
961	C₂²⋊C₄	—	86	2	no	—
962	C₂²⋊C₄	—	86	2	no	—
963	C₂²⋊C₄	—	86	2	no	—
964	C₂²⋊C₄	D₄×D₄₃	1	1	yes	characteristic
965	C₂²⋊C₄	D₄×D₄₃	1	1	yes	characteristic
966	C₄²	—	2	2	no	—
967	C₄²	—	43	1	no	—
968	C₄²	—	43	1	no	—
969	C₄²	—	43	1	no	—
970	C₄²	—	43	1	no	—
971	C₄²	—	86	2	no	—
972	C₄²	—	86	2	no	—
973	C₄²	—	86	2	no	—
974	C₄²	C₂³×D₄₃	1	1	yes	characteristic
975	C₄²	C₂³×D₄₃	1	1	yes	characteristic
976	C₂³	—	2	2	no	—
977	C₂³	—	43	1	no	—
978	C₂³	—	43	1	no	—
979	C₂³	—	86	2	no	—
980	C₂³	—	344	2	no	—
981	C₂³	—	172	4	no	—
982	C₂³	—	172	4	no	—
983	C₂³	C₂×D₄×D₄₃	1	1	yes	characteristic
984	Q₈	—	2	2	no	—
985	Q₈	—	2	2	no	—
986	Q₈	—	8	2	no	—
987	Q₈	—	86	2	no	—
988	Q₈	—	86	2	no	—
989	Q₈	—	86	2	no	—
990	Q₈	—	344	2	no	—
991	Q₈	—	172	4	no	—
992	D₄	—	2	2	no	—
993	D₄	—	2	2	no	—
994	D₄	—	8	2	no	—
995	D₄	—	43	4	no	—
996	D₄	—	86	2	no	—
997	D₄	—	86	2	no	—
998	D₄	—	86	2	no	—
999	D₄	—	86	2	no	—
1000	D₄	—	344	2	no	—
1001	D₄	—	172	4	no	—
1002	D₄	—	172	4	no	—
1003	D₄	—	172	4	no	—
1004	C₂×C₄	—	2	1	no	—
1005	C₂×C₄	—	2	1	no	—
1006	C₂×C₄	—	2	2	no	—
1007	C₂×C₄	—	2	2	no	—
1008	C₂×C₄	—	2	2	no	—
1009	C₂×C₄	—	8	2	no	—
1010	C₂×C₄	—	43	1	no	—
1011	C₂×C₄	—	43	1	no	—
1012	C₂×C₄	—	43	1	no	—
1013	C₂×C₄	—	43	1	no	—
1014	C₂×C₄	—	43	1	no	—
1015	C₂×C₄	—	43	1	no	—
1016	C₂×C₄	—	86	2	no	—
1017	C₂×C₄	—	86	2	no	—
1018	C₂×C₄	—	86	1	no	—
1019	C₂×C₄	—	86	1	no	—
1020	C₂×C₄	—	86	1	no	—
1021	C₂×C₄	—	86	1	no	—
1022	C₂×C₄	—	86	2	no	—
1023	C₂×C₄	—	86	2	no	—
1024	C₂×C₄	—	86	2	no	—
1025	C₂×C₄	—	344	2	no	—
1026	C₂×C₄	—	344	2	no	—
1027	C₂×C₄	—	344	2	no	—
1028	C₂×C₄	—	344	2	no	—
1029	C₂×C₄	—	344	2	no	—
1030	C₂×C₄	—	344	2	no	—
1031	C₂×C₄	—	172	4	no	—
1032	C₂×C₄	—	172	4	no	—
1033	C₂×C₄	—	172	4	no	—
1034	C₂×C₄	—	172	4	no	—
1035	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
1036	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
1037	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
1038	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
1039	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
1040	C₂×C₄	C₂⁴×D₄₃	1	1	yes	characteristic
1041	C₈	—	2	1	no	—
1042	C₈	—	2	1	no	—
1043	C₈	—	2	1	no	—
1044	C₈	—	86	1	no	—
1045	C₈	—	86	1	no	—
1046	C₈	—	86	1	no	—
1047	C₈	—	86	1	no	—
1048	C₈	#41×D₄₃	1	2	yes	—
1049	C₂²	—	2	1	no	—
1050	C₂²	—	2	1	no	—
1051	C₂²	—	2	1	no	—
1052	C₂²	—	4	2	no	—
1053	C₂²	—	4	2	no	—
1054	C₂²	—	4	2	no	—
1055	C₂²	—	43	2	no	—
1056	C₂²	—	86	1	no	—
1057	C₂²	—	86	1	no	—
1058	C₂²	—	86	1	no	—
1059	C₂²	—	86	1	no	—
1060	C₂²	—	86	1	no	—
1061	C₂²	—	86	4	no	—
1062	C₂²	—	344	8	no	—
1063	C₂²	—	172	2	no	—
1064	C₂²	—	172	2	no	—
1065	C₂²	C₂²×D₄×D₄₃	1	1	yes	characteristic
1066	C₄	—	2	1	no	—
1067	C₄	—	2	1	no	—
1068	C₄	—	2	1	no	—
1069	C₄	—	2	1	no	—
1070	C₄	—	2	1	no	—
1071	C₄	—	4	2	no	—
1072	C₄	—	4	2	no	—
1073	C₄	—	4	2	no	—
1074	C₄	—	43	2	no	—
1075	C₄	—	86	1	no	—
1076	C₄	—	86	1	no	—
1077	C₄	—	86	1	no	—
1078	C₄	—	86	1	no	—
1079	C₄	—	86	1	no	—
1080	C₄	—	172	2	no	—
1081	C₄	—	172	2	no	—
1082	C₄	—	172	2	no	—
1083	C₄	C₂×#41×D₄₃	1	1	yes	characteristic
1084	C₄	#14583735	1	1	yes	characteristic
1085	C₂	—	4	1	no	—
1086	C₂	—	8	2	no	—
1087	C₂	—	86	2	no	—
1088	C₂	—	172	1	no	—
1089	C₂	—	172	4	no	—
1090	C₂	#19148081	1	1	yes	characteristic
1091	C₂	#576×D₄₃	1	1	yes	characteristic
1092	C₂	#578×D₄₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂²×D₄×D₄₃
commutator, cosocle	C₂×C₄×C₄₃	C₂⁵
Frattini	C₂×C₄	C₂⁴×D₄₃
Fitting	C₄₃×#3175	C₂
socle	C₂²×C₄₃	C₂³×D₄
hypercenter	#3175	D₄₃
hypocenter	C₄₃	#61482
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ #117 ◁ #3175

Complements

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

N	H ≅ G/N	type
1. #19148642	C₂	semidirect
2. #19147580	C₂	semidirect
3. #19147447	C₂	semidirect
4. #19147310	C₂	semidirect
5. #19146987	C₂	semidirect
6. #19146984	C₂	semidirect
7. #19146939	C₂	semidirect
8. #19146895	C₂	semidirect
9. #19146675	C₂	semidirect
10. #19146671	C₂	semidirect
11. #19146314	C₂	semidirect
12. #19146283	C₂	semidirect
13. #19146279	C₂	semidirect
14. #19145230	C₂	semidirect
15. #19145178	C₂	semidirect
16. #19144855	C₂	semidirect
17. #19144851	C₂	semidirect
18. #19144692	C₂	semidirect
19. #19143566	C₂	semidirect
20. #19143472	C₂	semidirect
21. #19143470	C₂	semidirect
22. C₄×D₈×D₄₃	C₂	semidirect
23. C₄₃×#3175	C₂	semidirect
27. #14583618	C₂²	semidirect
33. #14583564	C₂²	semidirect
35. #14583551	C₂²	semidirect
36. #14583549	C₂²	semidirect
39. #14583514	C₂²	semidirect
46. #14583381	C₂²	semidirect
47. #14583379	C₂²	semidirect
49. #14583303	C₂²	semidirect
50. #14583303	C₂²	semidirect
52. #14583277	C₂²	semidirect
53. #14583257	C₂²	semidirect
54. #14583248	C₂²	semidirect
56. #14583236	C₂²	semidirect
58. #14583232	C₂²	semidirect
59. #14583211	C₂²	semidirect
60. #14583210	C₂²	semidirect
61. #14583192	C₂²	semidirect
62. #14583191	C₂²	semidirect
63. #14583178	C₂²	semidirect
64. #14583178	C₂²	semidirect
65. #14583177	C₂²	semidirect
66. #14583176	C₂²	semidirect
67. #14583144	C₂²	semidirect
69. #14583141	C₂²	semidirect
73. #14583119	C₂²	semidirect
74. #14583118	C₂²	semidirect
77. #14583103	C₂²	semidirect
78. #14583102	C₂²	semidirect
79. #14583064	C₂²	semidirect
80. #14583059	C₂²	semidirect
85. #14583027	C₂²	semidirect
86. C₈×Dic₈₆	C₂²	semidirect
87. #14583002	C₂²	semidirect
88. #14583001	C₂²	semidirect
89. #14583001	C₂²	semidirect
90. #14582999	C₂²	semidirect
91. #14582997	C₂²	semidirect
92. C₄×Dic₁₇₂	C₂²	semidirect
93. C₄×Dic₁₇₂	C₂²	semidirect
94. Q₁₆×Dic₄₃	C₂²	semidirect
95. C₄×#10621885	C₂²	semidirect
103. #14582975	C₂²	semidirect
108. C₈×C₂²⋊D₄₃	C₂²	semidirect
109. #14582961	C₂²	semidirect
110. #14582960	C₂²	semidirect
112. C₂×#13063259	C₂²	semidirect
114. #107×D₄₃	C₂²	semidirect
115. #14582901	C₂²	semidirect
116. #14582899	C₂²	semidirect
118. #14582853	C₂²	semidirect
120. C₄₃×#542	C₂²	semidirect
121. C₄₃×#500	C₂²	semidirect
123. C₄₃×#489	C₂²	semidirect
124. C₄₃×#468	C₂²	semidirect
125. C₄₃×#467	C₂²	semidirect
127. C₄₃×#440	C₂²	semidirect
128. C₄×Q₁₆×C₄₃	C₂²	semidirect
130. C₄₃×#405	C₂²	semidirect
423. D₃₄₄	#41	semidirect
553. #3175	D₄₃	semidirect
586. #542	C₂×D₄₃	semidirect
598. #500	C₂×D₄₃	semidirect
603. #489	C₂×D₄₃	semidirect
618. #468	C₂×D₄₃	semidirect
623. #467	C₂×D₄₃	semidirect
645. #440	C₂×D₄₃	semidirect
650. C₄×Q₁₆	C₂×D₄₃	semidirect
675. #405	C₂×D₄₃	semidirect
677. C₄₃	#61482	semidirect

Maximal subgroups

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

subgroup	index
#19148642	2
#19147580	2
#19147447	2
#19147310	2
#19146987	2
#19146984	2
#19146939	2
#19146895	2
#19146675	2
#19146671	2
#19146314	2
#19146283	2
#19146279	2
#19145230	2
#19145178	2
#19144855	2
#19144851	2
#19144692	2
#19143566	2
#19143472	2
#19143470	2
C₄×D₈×D₄₃	2
C₄₃×#3175	2
#61482	43