Subgroups — #25979068

Order 11008.

1900 conjugacy classes of subgroups.

The subgroup lattice has 1176 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19148558	C₂	1	1	yes	maximal, characteristic, complemented
2	#19147603	C₂	1	1	yes	maximal, characteristic, complemented
3	Q₈×#10621882	C₂	1	1	yes	maximal, characteristic, complemented
4	#19147387	C₂	1	1	yes	maximal, characteristic, complemented
5	#19147383	C₂	1	1	yes	maximal, characteristic, complemented
6	#19147021	C₂	1	1	yes	maximal, characteristic, complemented
7	#19147013	C₂	1	2	yes	maximal, complemented
8	#19146826	C₂	1	1	yes	maximal, characteristic, complemented
9	#19146820	C₂	1	1	yes	maximal, characteristic, complemented
10	#19146751	C₂	1	2	yes	maximal, complemented
11	#19146745	C₂	1	2	yes	maximal, complemented
12	#19146276	C₂	1	2	yes	maximal, complemented
13	D₄×#10621882	C₂	1	1	yes	maximal, characteristic, complemented
14	#19145228	C₂	1	2	yes	maximal, complemented
15	#19145170	C₂	1	1	yes	maximal, characteristic, complemented
16	#19144779	C₂	1	2	yes	maximal, complemented
17	#19144773	C₂	1	2	yes	maximal, complemented
18	#19144746	C₂	1	1	yes	maximal, characteristic, complemented
19	#19144740	C₂	1	1	yes	maximal, characteristic, complemented
20	#19143571	C₂	1	1	yes	maximal, characteristic, complemented
21	#19143445	C₂	1	2	yes	maximal, complemented
22	C₄×#13063345	C₂	1	1	yes	maximal, characteristic, complemented
23	C₄₃×#3514	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#13063345	C₂²	1	1	yes	characteristic
25	C₂²×#10621882	C₂²	1	2	yes	—
26	#14583634	C₂²	1	1	yes	characteristic, complemented
27	#14583619	C₂²	1	1	yes	characteristic
28	#14583614	C₂²	1	2	yes	complemented
29	#14583574	—	2	2	no	—
30	Q₈×D₁₇₂	C₂²	1	1	yes	characteristic, complemented
31	#14583559	—	2	1	no	—
32	#14583546	—	2	1	no	—
33	#14583545	C₂²	1	2	yes	complemented
34	D₄×D₁₇₂	C₂²	1	1	yes	characteristic
35	#14583520	C₂²	1	2	yes	complemented
36	#14583485	—	2	2	no	—
37	#14583449	C₂²	1	1	yes	characteristic, complemented
38	#14583434	—	2	1	no	—
39	#124×D₄₃	—	2	1	no	—
40	#14583373	C₂²	1	2	yes	complemented
41	C₄×#10621898	C₂²	1	1	yes	characteristic, complemented
42	#14583302	C₂²	1	2	yes	complemented
43	#14583302	C₂²	1	1	yes	characteristic, complemented
44	#14583281	C₂²	1	2	yes	complemented
45	#14583275	C₂²	1	1	yes	characteristic
46	#14583261	C₂²	1	2	yes	complemented
47	#14583258	C₂²	1	2	yes	complemented
48	#14583247	C₂²	1	1	yes	characteristic, complemented
49	#14583245	C₂²	1	1	yes	characteristic, complemented
50	#14583240	C₂²	1	2	yes	complemented
51	#14583237	C₂²	1	2	yes	complemented
52	#14583223	C₂²	1	2	yes	complemented
53	#14583223	C₂²	1	2	yes	complemented
54	#14583220	C₂²	1	2	yes	complemented
55	#14583220	C₂²	1	2	yes	complemented
56	#14583189	C₂²	1	2	yes	complemented
57	#14583186	C₂²	1	2	yes	complemented
58	#14583184	C₂²	1	1	yes	characteristic, complemented
59	#14583181	C₂²	1	1	yes	characteristic, complemented
60	#14583179	C₂²	1	1	yes	characteristic, complemented
61	#14583179	C₂²	1	2	yes	complemented
62	#14583176	C₂²	1	1	yes	characteristic, complemented
63	#14583176	C₂²	1	2	yes	complemented
64	#14583147	C₂²	1	2	yes	complemented
65	#14583143	C₂²	1	2	yes	complemented
66	#14583138	C₂²	1	2	yes	complemented
67	#14583133	C₂²	1	2	yes	—
68	#14583133	C₂²	1	2	yes	complemented
69	#14583133	C₂²	1	2	yes	complemented
70	#14583114	C₂²	1	2	yes	complemented
71	#14583114	C₂²	1	2	yes	complemented
72	#14583111	C₂²	1	2	yes	complemented
73	#14583111	C₂²	1	2	yes	complemented
74	#14583099	C₂²	1	1	yes	characteristic, complemented
75	#14583096	C₂²	1	1	yes	characteristic, complemented
76	#14583094	C₂²	1	1	yes	characteristic
77	#14583091	C₂²	1	1	yes	characteristic
78	#14583050	C₂²	1	2	yes	complemented
79	#14583049	C₂²	1	2	yes	complemented
80	#14583044	C₂²	1	2	yes	complemented
81	#14583042	C₂²	1	2	yes	complemented
82	#14583033	C₂²	1	2	yes	—
83	#14583032	C₂²	1	2	yes	—
84	#14583030	C₂²	1	1	yes	characteristic, complemented
85	Q₈×C₄₃⋊C₈	C₂²	1	1	yes	characteristic, complemented
86	#14583009	C₂²	1	2	yes	complemented
87	#14583009	C₂²	1	2	yes	complemented
88	#14583009	C₂²	1	2	yes	complemented
89	#14583009	C₂²	1	2	yes	complemented
90	#14582999	C₂²	1	2	yes	complemented
91	#14582997	C₂²	1	2	yes	complemented
92	C₄×#10621885	C₂²	1	1	yes	characteristic, complemented
93	C₄×#10621885	C₂²	1	1	yes	characteristic, complemented
94	C₄×#10621884	C₂²	1	1	yes	characteristic, complemented
95	C₄×#10621884	C₂²	1	1	yes	characteristic, complemented
96	C₄×#10621883	C₂²	1	1	yes	characteristic, complemented
97	C₄×#10621883	C₂²	1	1	yes	characteristic, complemented
98	C₄×#10621882	C₂²	1	1	yes	characteristic
99	C₄×#10621882	C₂²	1	2	yes	—
100	C₄×#10621882	C₂²	1	1	yes	characteristic
101	C₄×#10621882	C₂²	1	2	yes	complemented
102	C₄×#10621882	C₂²	1	2	yes	complemented
103	C₄×#10621882	C₂²	1	2	yes	complemented
104	#14582977	C₂²	1	1	yes	characteristic
105	#14582971	C₂²	1	2	yes	complemented
106	D₄×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
107	D₄×C₄₃⋊C₈	C₂²	1	2	yes	complemented
108	#14582960	C₂²	1	2	yes	complemented
109	#14582956	C₂²	1	1	yes	characteristic, complemented
110	#14582935	C₂²	1	1	yes	characteristic, complemented
111	#14582935	C₂²	1	2	yes	complemented
112	#14582904	C₂²	1	2	yes	complemented
113	#14582903	C₂²	1	2	yes	complemented
114	#14582895	C₂²	1	1	yes	characteristic, complemented
115	#14582893	C₂²	1	1	yes	characteristic, complemented
116	#14582855	C₂²	1	2	yes	complemented
117	C₂×C₄×C₄₃⋊C₈	C₂²	1	1	yes	characteristic, complemented
118	C₄₃×#559	C₂²	1	1	yes	characteristic, complemented
119	C₄₃×#556	C₂²	1	1	yes	characteristic
120	C₄₃×#555	C₂²	1	2	yes	complemented
121	C₄₃×#551	—	2	2	no	—
122	D₄×Q₈×C₄₃	C₂²	1	1	yes	characteristic, complemented
123	C₄₃×#548	—	2	1	no	—
124	C₄₃×#546	—	2	1	no	—
125	C₄₃×#546	C₂²	1	2	yes	complemented
126	D₄²×C₄₃	C₂²	1	1	yes	characteristic
127	C₄₃×#542	C₂²	1	2	yes	complemented
128	C₄₃×#538	—	2	2	no	—
129	C₄₃×#532	C₂²	1	1	yes	characteristic, complemented
130	C₄₃×#529	—	2	1	no	—
131	C₄₃×#529	C₂²	1	1	yes	characteristic
132	C₂×#124×C₄₃	—	2	1	no	—
133	C₄₃×#518	C₂²	1	2	yes	complemented
134	C₄×#41×C₄₃	C₂²	1	1	yes	characteristic, complemented
135	C₂×#10621898	—	2	1	no	—
136	C₂×#10621898	C₂³	1	1	yes	characteristic
137	C₂×Q₈×D₄₃	—	2	1	no	—
138	C₂²×D₁₇₂	C₂³	1	2	yes	—
139	C₂×D₄×D₄₃	—	2	1	no	—
140	#13063345	—	2	4	no	—
141	C₂×#10621885	C₂³	1	1	yes	characteristic
142	C₂×#10621883	C₂³	1	1	yes	characteristic
143	C₂×#10621883	C₂³	1	2	yes	—
144	C₂×#10621884	C₂³	1	1	yes	characteristic
145	C₂×#10621884	C₂³	1	2	yes	—
146	C₂×#10621882	—	2	8	no	—
147	C₂×#10621882	C₂³	1	2	yes	—
148	C₂×#10621882	C₂³	1	2	yes	—
149	C₂×#10621882	C₂³	1	2	yes	—
150	C₂×#10621882	C₂³	1	2	yes	—
151	C₂×#10621882	C₂³	1	1	yes	characteristic
152	C₂×#10621877	C₂³	1	2	yes	—
153	C₂²×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
154	C₂²×C₄₃⋊C₈	C₂³	1	2	yes	—
155	C₂²×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
156	#13063325	C₂³	1	2	yes	—
157	#13063325	C₂³	1	1	yes	characteristic
158	#13063322	C₂³	1	1	yes	characteristic
159	#13063320	—	2	2	no	—
160	#13063318	—	2	2	no	—
161	#13063314	—	2	1	no	—
162	#13063313	—	2	1	no	—
163	#13063313	C₂³	1	2	yes	—
164	#13063312	—	2	1	no	—
165	#13063311	—	2	2	no	—
166	#13063311	—	2	2	no	—
167	#13063311	—	2	2	no	—
168	#13063310	—	2	2	no	—
169	#13063310	—	2	2	no	—
170	#13063307	—	2	2	no	—
171	#13063305	—	2	2	no	—
172	#13063305	—	2	1	no	—
173	#13063304	C₂³	1	2	yes	—
174	#13063303	—	2	2	no	—
175	#13063300	—	2	1	no	—
176	#13063299	—	2	1	no	—
177	#13063299	C₂³	1	2	yes	—
178	#13063299	C₂³	1	2	yes	—
179	#13063298	—	2	2	no	—
180	#13063296	—	2	2	no	—
181	#13063295	—	2	2	no	—
182	#13063293	—	2	2	no	—
183	C₄×Dic₈₆	C₂³	1	1	yes	characteristic
184	C₄×Dic₈₆	C₂³	1	1	yes	characteristic
185	#13063290	—	2	1	no	—
186	C₄×D₁₇₂	—	2	1	no	—
187	C₄×D₁₇₂	C₂³	1	1	yes	characteristic
188	C₄×D₁₇₂	C₂³	1	2	yes	—
189	C₄×D₁₇₂	C₂³	1	2	yes	—
190	C₄×D₁₇₂	C₂³	1	1	yes	characteristic
191	C₄×D₁₇₂	C₂³	1	2	yes	—
192	#13063287	—	2	2	no	—
193	#13063287	—	2	2	no	—
194	#13063287	—	2	1	no	—
195	C₄×C₂²⋊D₄₃	—	2	1	no	—
196	C₄×C₂²⋊D₄₃	—	2	1	no	—
197	#13063284	C₂³	1	1	yes	characteristic
198	#13063284	C₂³	1	2	yes	—
199	#13063283	—	2	2	no	—
200	#13063282	—	2	1	no	—
201	C₂²⋊C₄×D₄₃	—	2	2	no	—
202	C₂²⋊C₄×D₄₃	—	2	2	no	—
203	C₂²⋊C₄×D₄₃	—	2	2	no	—
204	C₄²×D₄₃	—	2	1	no	—
205	#13063258	C₂³	1	1	yes	characteristic
206	#13063258	C₂³	1	2	yes	—
207	#13063258	C₂³	1	2	yes	—
208	#13063258	C₂³	1	2	yes	—
209	#13063258	C₂³	1	2	yes	—
210	#13063258	C₂³	1	1	yes	characteristic
211	#13063256	C₂³	1	2	yes	—
212	#13063256	C₂³	1	2	yes	—
213	#13063256	C₂³	1	1	yes	characteristic
214	#13063256	C₂³	1	1	yes	characteristic
215	C₄⋊(C₄₃⋊C₈)	C₂³	1	1	yes	characteristic
216	C₄⋊(C₄₃⋊C₈)	C₂³	1	1	yes	characteristic
217	C₄⋊(C₄₃⋊C₈)	C₂³	1	2	yes	—
218	C₄⋊(C₄₃⋊C₈)	C₂³	1	2	yes	—
219	#13063249	C₂³	1	2	yes	—
220	#13063249	C₂³	1	1	yes	characteristic
221	#13063249	C₂³	1	1	yes	characteristic
222	#13063248	C₂³	1	2	yes	—
223	#13063248	C₂³	1	1	yes	characteristic
224	#13063248	C₂³	1	1	yes	characteristic
225	#13063246	C₂³	1	2	yes	—
226	#13063246	C₂³	1	2	yes	—
227	#13063246	C₂³	1	2	yes	—
228	#13063246	C₂³	1	2	yes	—
229	#13063246	C₂³	1	2	yes	—
230	#13063246	C₂³	1	1	yes	characteristic
231	#13063246	C₂³	1	1	yes	characteristic
232	#13063245	C₂³	1	2	yes	—
233	#13063245	C₂³	1	2	yes	—
234	#13063245	C₂³	1	2	yes	—
235	#13063245	C₂³	1	2	yes	—
236	#13063245	C₂³	1	2	yes	—
237	#13063245	C₂³	1	1	yes	characteristic
238	#13063245	C₂³	1	1	yes	characteristic
239	C₂²⋊(C₄₃⋊C₈)	C₂³	1	2	yes	—
240	C₂²⋊(C₄₃⋊C₈)	C₂³	1	2	yes	—
241	C₂²⋊(C₄₃⋊C₈)	C₂³	1	2	yes	—
242	#13063236	C₂³	1	2	yes	—
243	#13063236	C₂³	1	2	yes	—
244	C₄×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
245	C₄×C₄₃⋊C₈	C₂³	1	2	yes	—
246	C₄×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
247	C₄×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
248	C₄×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
249	C₂×#41×C₄₃	—	2	1	no	—
250	C₂×#41×C₄₃	C₂³	1	1	yes	characteristic
251	C₂²×Q₈×C₄₃	—	2	1	no	—
252	C₂²×D₄×C₄₃	—	2	1	no	—
253	C₂²×D₄×C₄₃	C₂³	1	2	yes	—
254	C₄⋊Q₈×C₄₃	C₂³	1	1	yes	characteristic
255	C₄⋊Q₈×C₄₃	C₂³	1	2	yes	—
256	#127×C₄₃	C₂³	1	1	yes	characteristic
257	#126×C₄₃	—	2	2	no	—
258	#126×C₄₃	—	2	2	no	—
259	#126×C₄₃	D₄	1	2	yes	—
260	#125×C₄₃	D₄	1	1	yes	characteristic
261	#124×C₄₃	—	2	1	no	—
262	#124×C₄₃	—	2	1	no	—
263	#124×C₄₃	—	2	2	no	—
264	#124×C₄₃	—	2	2	no	—
265	#124×C₄₃	—	2	2	no	—
266	#124×C₄₃	—	2	1	no	—
267	#124×C₄₃	D₄	1	1	yes	characteristic
268	#124×C₄₃	C₂³	1	2	yes	—
269	#123×C₄₃	—	2	2	no	—
270	#123×C₄₃	—	2	2	no	—
271	#123×C₄₃	—	2	2	no	—
272	#123×C₄₃	D₄	1	2	yes	—
273	C₂²⋊Q₈×C₄₃	—	2	1	no	—
274	C₂²⋊Q₈×C₄₃	—	2	2	no	—
275	C₂²⋊Q₈×C₄₃	—	2	2	no	—
276	C₂²⋊Q₈×C₄₃	D₄	1	1	yes	characteristic
277	C₂²⋊Q₈×C₄₃	C₂³	1	2	yes	—
278	#121×C₄₃	—	2	2	no	—
279	#121×C₄₃	—	2	1	no	—
280	#121×C₄₃	—	2	1	no	—
281	#121×C₄₃	—	2	2	no	—
282	#121×C₄₃	D₄	1	1	yes	characteristic
283	#121×C₄₃	C₂³	1	2	yes	—
284	#121×C₄₃	C₂³	1	2	yes	—
285	#120×C₄₃	—	2	2	no	—
286	#120×C₄₃	—	2	2	no	—
287	C₄×Q₈×C₄₃	—	2	1	no	—
288	C₄×Q₈×C₄₃	C₂³	1	1	yes	characteristic
289	C₄×Q₈×C₄₃	C₂³	1	1	yes	characteristic
290	C₄×Q₈×C₄₃	C₂³	1	1	yes	characteristic
291	C₄×D₄×C₄₃	—	2	1	no	—
292	C₄×D₄×C₄₃	—	2	1	no	—
293	C₄×D₄×C₄₃	—	2	2	no	—
294	C₄×D₄×C₄₃	—	2	2	no	—
295	C₄×D₄×C₄₃	—	2	1	no	—
296	C₄×D₄×C₄₃	—	2	1	no	—
297	C₄×D₄×C₄₃	C₂³	1	1	yes	characteristic
298	C₄×D₄×C₄₃	C₂³	1	1	yes	characteristic
299	C₄×D₄×C₄₃	C₂³	1	2	yes	—
300	C₄×D₄×C₄₃	C₂³	1	2	yes	—
301	C₄×D₄×C₄₃	C₂³	1	2	yes	—
302	C₄×D₄×C₄₃	C₂³	1	1	yes	characteristic
303	C₄×D₄×C₄₃	C₂³	1	2	yes	—
304	#117×C₄₃	—	2	2	no	—
305	#117×C₄₃	—	2	1	no	—
306	#117×C₄₃	C₂³	1	1	yes	characteristic
307	#117×C₄₃	C₂³	1	2	yes	—
308	#117×C₄₃	C₂³	1	2	yes	—
309	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
310	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
311	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
312	C₂×C₄²×C₄₃	—	2	1	no	—
313	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
314	C₂⁴×C₄₃	—	2	2	no	—
315	C₂³×D₄₃	—	2	2	no	—
316	#41×C₄₃	—	2	2	no	—
317	#41×C₄₃	—	4	1	no	—
318	#41×C₄₃	—	8	2	no	—
319	C₂×Q₈×C₄₃	—	2	1	no	—
320	C₂×Q₈×C₄₃	—	2	2	no	—
321	C₂×Q₈×C₄₃	—	8	2	no	—
322	C₂×Q₈×C₄₃	C₂×D₄	1	1	yes	characteristic
323	C₂×Q₈×C₄₃	C₂⁴	1	1	yes	characteristic
324	C₂×D₄×C₄₃	—	2	2	no	—
325	C₂×D₄×C₄₃	—	2	1	no	—
326	C₂×D₄×C₄₃	—	2	1	no	—
327	C₂×D₄×C₄₃	—	2	1	no	—
328	C₂×D₄×C₄₃	—	2	2	no	—
329	C₂×D₄×C₄₃	—	2	2	no	—
330	C₂×D₄×C₄₃	—	2	4	no	—
331	C₂×D₄×C₄₃	—	4	2	no	—
332	C₂×D₄×C₄₃	—	8	2	no	—
333	C₂×D₄×C₄₃	C₂×D₄	1	1	yes	characteristic
334	C₂×D₄×C₄₃	C₂×D₄	1	2	yes	—
335	C₂×D₄×C₄₃	C₂⁴	1	2	yes	—
336	C₂×D₄×C₄₃	C₂⁴	1	1	yes	characteristic
337	C₂²×C₄×C₄₃	—	2	1	no	—
338	C₂²×C₄×C₄₃	—	2	1	no	—
339	C₂²×C₄×C₄₃	—	2	1	no	—
340	C₂²×C₄×C₄₃	—	2	2	no	—
341	C₂²×C₄×C₄₃	—	2	2	no	—
342	C₂²×C₄×C₄₃	—	2	2	no	—
343	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
344	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
345	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
346	C₂²×C₄×C₄₃	C₂⁴	1	2	yes	—
347	C₂×C₂²⋊D₄₃	—	2	1	no	—
348	C₂×C₂²⋊D₄₃	—	2	2	no	—
349	C₂×C₂²⋊D₄₃	—	2	2	no	—
350	Q₈×D₄₃	—	8	2	no	—
351	D₄×D₄₃	—	8	2	no	—
352	#10621898	—	2	2	no	—
353	#10621898	—	4	1	no	—
354	#10621898	—	8	2	no	—
355	C₂×D₁₇₂	—	2	2	no	—
356	C₂×D₁₇₂	—	2	1	no	—
357	C₂×D₁₇₂	—	2	1	no	—
358	C₂×D₁₇₂	—	2	4	no	—
359	C₂×D₁₇₂	—	4	2	no	—
360	C₂×D₁₇₂	C₂⁴	1	2	yes	—
361	C₂×D₁₇₂	C₂⁴	1	1	yes	characteristic
362	C₂×C₄×D₄₃	—	2	1	no	—
363	C₂×C₄×D₄₃	—	2	1	no	—
364	C₂×C₄×D₄₃	—	2	1	no	—
365	C₂×C₄×D₄₃	—	2	2	no	—
366	C₂×C₄×D₄₃	—	2	2	no	—
367	C₂×C₄×D₄₃	—	2	2	no	—
368	C₂×Dic₈₆	—	2	1	no	—
369	C₂×Dic₈₆	—	2	2	no	—
370	C₂×Dic₈₆	C₂⁴	1	1	yes	characteristic
371	C₄⋊C₄×C₄₃	—	2	1	no	—
372	C₄⋊C₄×C₄₃	—	2	1	no	—
373	C₄⋊C₄×C₄₃	—	2	2	no	—
374	C₄⋊C₄×C₄₃	—	2	1	no	—
375	C₄⋊C₄×C₄₃	—	2	2	no	—
376	C₄⋊C₄×C₄₃	C₂×D₄	1	2	yes	—
377	C₄⋊C₄×C₄₃	C₂×D₄	1	2	yes	—
378	C₄⋊C₄×C₄₃	C₂×D₄	1	2	yes	—
379	C₄⋊C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
380	C₄⋊C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
381	C₄⋊C₄×C₄₃	C₂×D₄	1	2	yes	—
382	C₄⋊C₄×C₄₃	C₂⁴	1	1	yes	characteristic
383	C₄⋊C₄×C₄₃	C₂⁴	1	2	yes	—
384	C₄⋊C₄×C₄₃	C₂⁴	1	1	yes	characteristic
385	C₂²⋊C₄×C₄₃	—	2	1	no	—
386	C₂²⋊C₄×C₄₃	—	2	2	no	—
387	C₂²⋊C₄×C₄₃	—	2	2	no	—
388	C₂²⋊C₄×C₄₃	—	2	2	no	—
389	C₂²⋊C₄×C₄₃	—	2	2	no	—
390	C₂²⋊C₄×C₄₃	—	2	2	no	—
391	C₂²⋊C₄×C₄₃	—	2	1	no	—
392	C₂²⋊C₄×C₄₃	—	2	2	no	—
393	C₂²⋊C₄×C₄₃	—	2	2	no	—
394	C₂²⋊C₄×C₄₃	—	2	2	no	—
395	C₂²⋊C₄×C₄₃	—	2	2	no	—
396	C₂²⋊C₄×C₄₃	—	2	1	no	—
397	C₂²⋊C₄×C₄₃	C₂×D₄	1	2	yes	—
398	C₂²⋊C₄×C₄₃	C₂×D₄	1	2	yes	—
399	C₂²⋊C₄×C₄₃	C₂×D₄	1	2	yes	—
400	C₂²⋊C₄×C₄₃	C₂×D₄	1	2	yes	—
401	C₂²⋊C₄×C₄₃	C₂×D₄	1	2	yes	—
402	C₄²×C₄₃	—	2	1	no	—
403	C₄²×C₄₃	—	2	1	no	—
404	C₄²×C₄₃	—	2	1	no	—
405	C₄²×C₄₃	—	2	2	no	—
406	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
407	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
408	C₄²×C₄₃	C₂⁴	1	1	yes	characteristic
409	C₄²×C₄₃	C₂⁴	1	1	yes	characteristic
410	C₄²×C₄₃	C₂⁴	1	2	yes	—
411	C₂²⋊Dic₄₃	—	2	2	no	—
412	C₂²⋊Dic₄₃	—	2	2	no	—
413	C₂²⋊Dic₄₃	—	2	1	no	—
414	#10621885	—	2	2	no	—
415	#10621884	—	2	2	no	—
416	#10621884	—	4	2	no	—
417	#10621883	—	2	2	no	—
418	#10621883	—	4	2	no	—
419	#10621882	—	2	4	no	—
420	#10621882	—	2	4	no	—
421	#10621882	—	2	4	no	—
422	#10621882	—	4	2	no	—
423	#10621882	#41	1	4	yes	complemented
424	(C₂×D₄₃)⋊C₄	—	2	1	no	—
425	(C₂×D₄₃)⋊C₄	—	2	2	no	—
426	(C₂×D₄₃)⋊C₄	—	2	2	no	—
427	(C₂×D₄₃)⋊C₄	—	2	2	no	—
428	(C₂×D₄₃)⋊C₄	—	2	2	no	—
429	(C₂×D₄₃)⋊C₄	—	2	2	no	—
430	(C₂×D₄₃)⋊C₄	—	2	1	no	—
431	(C₂×D₄₃)⋊C₄	—	2	2	no	—
432	(C₂×D₄₃)⋊C₄	—	2	2	no	—
433	C₄⋊Dic₄₃	—	2	2	no	—
434	C₄⋊Dic₄₃	—	2	1	no	—
435	C₄⋊Dic₄₃	C₂⁴	1	1	yes	characteristic
436	C₄⋊Dic₄₃	C₂⁴	1	2	yes	—
437	C₄⋊Dic₄₃	C₂⁴	1	1	yes	characteristic
438	Dic₄₃⋊C₄	—	2	1	no	—
439	Dic₄₃⋊C₄	—	2	1	no	—
440	Dic₄₃⋊C₄	—	2	2	no	—
441	C₄×Dic₄₃	—	2	1	no	—
442	C₄×Dic₄₃	—	2	1	no	—
443	C₄×Dic₄₃	—	2	1	no	—
444	C₄×Dic₄₃	—	2	2	no	—
445	#10621877	—	4	2	no	—
446	C₂×C₄₃⋊C₈	—	2	4	no	—
447	C₂×C₄₃⋊C₈	—	2	2	no	—
448	C₂×C₄₃⋊C₈	—	4	1	no	—
449	C₂×C₄₃⋊C₈	C₂⁴	1	1	yes	characteristic
450	C₂×C₄₃⋊C₈	C₂⁴	1	1	yes	characteristic
451	C₂×C₄₃⋊C₈	C₂⁴	1	1	yes	characteristic
452	C₂×C₄₃⋊C₈	C₂⁴	1	2	yes	—
453	C₂×C₄₃⋊C₈	C₂⁴	1	2	yes	—
454	C₂×C₄₃⋊C₈	C₂⁴	1	1	yes	characteristic
455	C₂³×C₄₃	—	2	1	no	—
456	C₂³×C₄₃	—	2	2	no	—
457	C₂³×C₄₃	—	4	4	no	—
458	C₂³×C₄₃	—	8	2	no	—
459	C₂³×C₄₃	—	8	2	no	—
460	C₂³×C₄₃	C₂²×D₄	1	2	yes	—
461	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
462	C₂²×D₄₃	—	2	1	no	—
463	C₂²×D₄₃	—	2	2	no	—
464	C₂²×D₄₃	—	4	4	no	—
465	C₂²×D₄₃	—	8	2	no	—
466	C₂²×D₄₃	—	8	2	no	—
467	Q₈×C₄₃	—	2	2	no	—
468	Q₈×C₄₃	—	2	1	no	—
469	Q₈×C₄₃	—	2	1	no	—
470	Q₈×C₄₃	—	4	2	no	—
471	Q₈×C₄₃	—	8	2	no	—
472	D₄×C₄₃	—	2	2	no	—
473	D₄×C₄₃	—	2	2	no	—
474	D₄×C₄₃	—	2	1	no	—
475	D₄×C₄₃	—	2	2	no	—
476	D₄×C₄₃	—	4	2	no	—
477	D₄×C₄₃	—	4	4	no	—
478	D₄×C₄₃	—	4	2	no	—
479	D₄×C₄₃	—	4	2	no	—
480	D₄×C₄₃	—	8	1	no	—
481	D₄×C₄₃	—	8	2	no	—
482	D₄×C₄₃	—	8	2	no	—
483	D₄×C₄₃	C₂×#41	1	2	yes	—
484	C₂×C₄×C₄₃	—	2	2	no	—
485	C₂×C₄×C₄₃	—	2	2	no	—
486	C₂×C₄×C₄₃	—	2	1	no	—
487	C₂×C₄×C₄₃	—	2	1	no	—
488	C₂×C₄×C₄₃	—	2	2	no	—
489	C₂×C₄×C₄₃	—	2	1	no	—
490	C₂×C₄×C₄₃	—	2	1	no	—
491	C₂×C₄×C₄₃	—	2	1	no	—
492	C₂×C₄×C₄₃	—	2	2	no	—
493	C₂×C₄×C₄₃	—	4	1	no	—
494	C₂×C₄×C₄₃	—	4	2	no	—
495	C₂×C₄×C₄₃	—	4	2	no	—
496	C₂×C₄×C₄₃	—	8	1	no	—
497	C₂×C₄×C₄₃	—	8	2	no	—
498	C₂×C₄×C₄₃	—	8	2	no	—
499	C₂×C₄×C₄₃	—	8	2	no	—
500	C₂×C₄×C₄₃	C₂²×D₄	1	2	yes	—
501	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
502	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
503	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
504	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
505	C₂×C₄×C₄₃	C₂²×D₄	1	2	yes	—
506	C₂×C₄×C₄₃	C₂²×D₄	1	2	yes	—
507	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
508	C₂×C₄×C₄₃	C₂⁵	1	1	yes	characteristic
509	C₂²⋊D₄₃	—	4	2	no	—
510	C₂²⋊D₄₃	—	8	2	no	—
511	C₂²⋊D₄₃	—	8	2	no	—
512	C₂×Dic₄₃	—	2	1	no	—
513	C₂×Dic₄₃	—	2	1	no	—
514	C₂×Dic₄₃	—	2	1	no	—
515	C₂×Dic₄₃	—	2	2	no	—
516	D₁₇₂	—	2	2	no	—
517	D₁₇₂	—	2	1	no	—
518	D₁₇₂	—	2	2	no	—
519	D₁₇₂	—	4	4	no	—
520	D₁₇₂	—	4	2	no	—
521	D₁₇₂	—	8	1	no	—
522	D₁₇₂	C₂×#41	1	2	yes	—
523	C₄×D₄₃	—	4	2	no	—
524	C₄×D₄₃	—	4	2	no	—
525	C₄×D₄₃	—	8	1	no	—
526	C₄×D₄₃	—	8	2	no	—
527	C₄×D₄₃	—	8	2	no	—
528	C₄×D₄₃	—	8	2	no	—
529	Dic₈₆	—	2	1	no	—
530	Dic₈₆	—	2	1	no	—
531	Dic₈₆	—	4	2	no	—
532	Dic₈₆	—	8	2	no	—
533	C₄₃⋊C₈	—	2	2	no	—
534	C₄₃⋊C₈	—	2	1	no	—
535	C₄₃⋊C₈	—	2	1	no	—
536	C₄₃⋊C₈	—	2	1	no	—
537	C₄₃⋊C₈	—	2	2	no	—
538	C₄₃⋊C₈	C₂×#41	1	2	yes	—
539	#61475	—	43	1	no	maximal, Sylow
540	C₂²×C₄₃	—	2	2	no	—
541	C₂²×C₄₃	—	2	1	no	—
542	C₂²×C₄₃	—	2	2	no	—
543	C₂²×C₄₃	—	2	2	no	—
544	C₂²×C₄₃	—	2	1	no	—
545	C₂²×C₄₃	—	2	2	no	—
546	C₂²×C₄₃	—	2	1	no	—
547	C₂²×C₄₃	—	4	1	no	—
548	C₂²×C₄₃	—	4	1	no	—
549	C₂²×C₄₃	—	4	2	no	—
550	C₂²×C₄₃	—	4	2	no	—
551	C₂²×C₄₃	—	4	2	no	—
552	C₂²×C₄₃	—	16	4	no	—
553	C₂²×C₄₃	C₂³×D₄	1	1	yes	characteristic
554	C₂×D₄₃	—	2	2	no	—
555	C₂×D₄₃	—	4	1	no	—
556	C₂×D₄₃	—	4	1	no	—
557	C₂×D₄₃	—	4	2	no	—
558	C₂×D₄₃	—	4	2	no	—
559	C₂×D₄₃	—	4	2	no	—
560	C₂×D₄₃	—	16	4	no	—
561	C₄×C₄₃	—	2	1	no	—
562	C₄×C₄₃	—	2	2	no	—
563	C₄×C₄₃	—	2	1	no	—
564	C₄×C₄₃	—	2	1	no	—
565	C₄×C₄₃	—	2	2	no	—
566	C₄×C₄₃	—	2	2	no	—
567	C₄×C₄₃	—	2	1	no	—
568	C₄×C₄₃	—	4	1	no	—
569	C₄×C₄₃	—	4	1	no	—
570	C₄×C₄₃	—	4	1	no	—
571	C₄×C₄₃	—	4	2	no	—
572	C₄×C₄₃	#576	1	2	yes	—
573	C₄×C₄₃	C₂²×#41	1	1	yes	characteristic
574	C₄×C₄₃	#585	1	1	yes	characteristic
575	Dic₄₃	—	4	1	no	—
576	Dic₄₃	—	4	1	no	—
577	Dic₄₃	—	4	2	no	—
578	Dic₄₃	—	4	1	no	—
579	#3514	—	43	1	no	—
580	#3514	D₄₃	1	1	yes	characteristic, complemented
581	#3396	—	43	1	no	—
582	Q₈×D₈	—	43	1	no	—
583	#3373	—	43	1	no	—
584	#3373	—	43	1	no	—
585	#3342	—	43	1	no	—
586	#3341	—	43	2	no	—
587	#3324	—	43	1	no	—
588	#3324	—	43	1	no	—
589	#3319	—	43	2	no	—
590	#3319	—	43	2	no	—
591	#3280	—	43	2	no	—
592	D₄×D₈	—	43	1	no	—
593	#3175	—	43	2	no	—
594	#3169	—	43	1	no	—
595	#3118	—	43	2	no	—
596	#3118	—	43	2	no	—
597	#3115	—	43	1	no	—
598	#3115	—	43	1	no	—
599	#2966	—	43	1	no	—
600	#2948	—	43	2	no	—
601	C₄×#135	—	43	1	no	—
602	C₂×C₄₃	—	4	2	no	—
603	C₂×C₄₃	—	4	1	no	—
604	C₂×C₄₃	—	4	2	no	—
605	C₂×C₄₃	—	8	2	no	—
606	C₂×C₄₃	D₄×#41	1	1	yes	characteristic
607	C₂×C₄₃	C₂×#576	1	1	yes	characteristic
608	C₂×C₄₃	#3584	1	1	yes	characteristic
609	D₄₃	—	4	2	no	—
610	D₄₃	—	8	2	no	—
611	C₂×#135	—	43	1	no	—
612	C₂²×D₈	—	43	2	no	—
613	#559	—	43	1	no	—
614	#559	C₂×D₄₃	1	1	yes	characteristic, complemented
615	#556	—	43	1	no	—
616	#556	C₂×D₄₃	1	1	yes	characteristic
617	#555	—	43	2	no	—
618	#555	C₂×D₄₃	1	2	yes	complemented
619	#551	—	2	2	no	—
620	#551	—	86	2	no	—
621	D₄×Q₈	—	43	1	no	—
622	D₄×Q₈	C₂×D₄₃	1	1	yes	characteristic, complemented
623	#548	—	2	1	no	—
624	#548	—	86	1	no	—
625	#546	—	2	1	no	—
626	#546	—	43	2	no	—
627	#546	—	86	1	no	—
628	#546	C₂×D₄₃	1	2	yes	complemented
629	D₄²	—	43	1	no	—
630	D₄²	C₂×D₄₃	1	1	yes	characteristic
631	#542	—	43	2	no	—
632	#542	C₂×D₄₃	1	2	yes	complemented
633	#538	—	2	2	no	—
634	#538	—	86	2	no	—
635	#532	—	43	1	no	—
636	#532	C₂×D₄₃	1	1	yes	characteristic, complemented
637	#529	—	2	1	no	—
638	#529	—	86	1	no	—
639	#529	C₂×D₄₃	1	1	yes	characteristic
640	C₂×#124	—	2	1	no	—
641	C₂×#124	—	86	1	no	—
642	#518	—	43	2	no	—
643	#518	C₂×D₄₃	1	2	yes	complemented
644	C₄×#41	—	43	1	no	—
645	C₄×#41	C₂×D₄₃	1	1	yes	characteristic, complemented
646	#500	—	43	2	no	—
647	#500	—	43	1	no	—
648	#495	—	43	2	no	—
649	#493	—	43	1	no	—
650	#489	—	43	2	no	—
651	#489	—	43	2	no	—
652	#486	—	43	1	no	—
653	#486	—	43	1	no	—
654	#485	—	43	2	no	—
655	#485	—	43	2	no	—
656	#482	—	43	2	no	—
657	#482	—	43	2	no	—
658	#482	—	43	2	no	—
659	#482	—	43	2	no	—
660	#476	—	43	2	no	—
661	#476	—	43	2	no	—
662	#475	—	43	1	no	—
663	#475	—	43	1	no	—
664	#474	—	43	1	no	—
665	#474	—	43	2	no	—
666	#474	—	43	1	no	—
667	#474	—	43	2	no	—
668	#468	—	43	2	no	—
669	#468	—	43	2	no	—
670	#467	—	43	2	no	—
671	#466	—	43	2	no	—
672	#466	—	43	2	no	—
673	#466	—	43	2	no	—
674	#463	—	43	2	no	—
675	#463	—	43	2	no	—
676	#463	—	43	2	no	—
677	#463	—	43	2	no	—
678	#460	—	43	1	no	—
679	#460	—	43	1	no	—
680	#459	—	43	1	no	—
681	#459	—	43	1	no	—
682	#450	—	43	2	no	—
683	#450	—	43	2	no	—
684	#449	—	43	2	no	—
685	#449	—	43	2	no	—
686	#447	—	43	2	no	—
687	#447	—	43	2	no	—
688	#446	—	43	1	no	—
689	C₈×Q₈	—	43	1	no	—
690	#442	—	43	2	no	—
691	#442	—	43	2	no	—
692	#442	—	43	2	no	—
693	#442	—	43	2	no	—
694	#440	—	43	2	no	—
695	#440	—	43	2	no	—
696	C₄×Q₁₆	—	43	1	no	—
697	C₄×Q₁₆	—	43	1	no	—
698	C₄×SD₁₆	—	43	1	no	—
699	C₄×SD₁₆	—	43	1	no	—
700	C₄×SD₁₆	—	43	1	no	—
701	C₄×SD₁₆	—	43	1	no	—
702	C₄×D₈	—	43	2	no	—
703	C₄×D₈	—	43	2	no	—
704	C₄×D₈	—	43	1	no	—
705	C₄×D₈	—	43	2	no	—
706	C₄×D₈	—	43	2	no	—
707	C₄×D₈	—	43	1	no	—
708	#436	—	43	1	no	—
709	#435	—	43	2	no	—
710	C₈×D₄	—	43	2	no	—
711	C₈×D₄	—	43	1	no	—
712	#433	—	43	2	no	—
713	#432	—	43	1	no	—
714	#427	—	43	1	no	—
715	#427	—	43	2	no	—
716	#418	—	43	2	no	—
717	#418	—	43	2	no	—
718	#416	—	43	1	no	—
719	#416	—	43	1	no	—
720	#405	—	43	2	no	—
721	C₂×C₄×C₈	—	43	1	no	—
722	C₄₃	#61475	1	1	yes	characteristic, complemented, Sylow
723	C₂×#41	—	2	1	no	—
724	C₂×#41	—	43	1	no	—
725	C₂×#41	—	86	1	no	—
726	C₂×#41	C₂²×D₄₃	1	1	yes	characteristic
727	C₂²×Q₈	—	2	1	no	—
728	C₂²×Q₈	—	86	1	no	—
729	C₂²×D₄	—	2	1	no	—
730	C₂²×D₄	—	43	2	no	—
731	C₂²×D₄	—	86	1	no	—
732	C₂²×D₄	C₂²×D₄₃	1	2	yes	—
733	#135	—	86	4	no	—
734	C₂×Q₁₆	—	43	1	no	—
735	C₂×SD₁₆	—	43	1	no	—
736	C₂×SD₁₆	—	43	1	no	—
737	C₂×SD₁₆	—	43	2	no	—
738	C₂×SD₁₆	—	43	2	no	—
739	C₂×D₈	—	43	1	no	—
740	C₂×D₈	—	43	2	no	—
741	C₂×D₈	—	43	2	no	—
742	C₂×D₈	—	43	2	no	—
743	C₂×D₈	—	43	2	no	—
744	C₂×D₈	—	86	8	no	—
745	C₂×M₁₆	—	43	2	no	—
746	C₂²×C₈	—	43	2	no	—
747	C₂²×C₈	—	43	1	no	—
748	C₂²×C₈	—	43	1	no	—
749	C₄⋊Q₈	—	43	1	no	—
750	C₄⋊Q₈	—	43	2	no	—
751	C₄⋊Q₈	C₂²×D₄₃	1	1	yes	characteristic
752	C₄⋊Q₈	C₂²×D₄₃	1	2	yes	—
753	#127	—	43	1	no	—
754	#127	C₂²×D₄₃	1	1	yes	characteristic
755	#126	—	2	2	no	—
756	#126	—	2	2	no	—
757	#126	—	86	2	no	—
758	#126	—	86	2	no	—
759	#126	C₂²⋊D₄₃	1	2	yes	—
760	#125	C₂²⋊D₄₃	1	1	yes	characteristic
761	#124	—	2	1	no	—
762	#124	—	2	1	no	—
763	#124	—	2	2	no	—
764	#124	—	2	2	no	—
765	#124	—	2	2	no	—
766	#124	—	2	1	no	—
767	#124	—	43	2	no	—
768	#124	—	86	1	no	—
769	#124	—	86	1	no	—
770	#124	—	86	2	no	—
771	#124	—	86	2	no	—
772	#124	—	86	2	no	—
773	#124	—	86	1	no	—
774	#124	C₂²⋊D₄₃	1	1	yes	characteristic
775	#124	C₂²×D₄₃	1	2	yes	—
776	#123	—	2	2	no	—
777	#123	—	2	2	no	—
778	#123	—	2	2	no	—
779	#123	—	86	2	no	—
780	#123	—	86	2	no	—
781	#123	—	86	2	no	—
782	#123	C₂²⋊D₄₃	1	2	yes	—
783	C₂²⋊Q₈	—	2	1	no	—
784	C₂²⋊Q₈	—	2	2	no	—
785	C₂²⋊Q₈	—	2	2	no	—
786	C₂²⋊Q₈	—	43	2	no	—
787	C₂²⋊Q₈	—	86	1	no	—
788	C₂²⋊Q₈	—	86	2	no	—
789	C₂²⋊Q₈	—	86	2	no	—
790	C₂²⋊Q₈	C₂²⋊D₄₃	1	1	yes	characteristic
791	C₂²⋊Q₈	C₂²×D₄₃	1	2	yes	—
792	#121	—	2	2	no	—
793	#121	—	2	1	no	—
794	#121	—	2	1	no	—
795	#121	—	2	2	no	—
796	#121	—	43	2	no	—
797	#121	—	43	2	no	—
798	#121	—	86	2	no	—
799	#121	—	86	1	no	—
800	#121	—	86	1	no	—
801	#121	—	86	2	no	—
802	#121	C₂²⋊D₄₃	1	1	yes	characteristic
803	#121	C₂²×D₄₃	1	2	yes	—
804	#121	C₂²×D₄₃	1	2	yes	—
805	#120	—	2	2	no	—
806	#120	—	2	2	no	—
807	#120	—	86	2	no	—
808	#120	—	86	2	no	—
809	C₄×Q₈	—	2	1	no	—
810	C₄×Q₈	—	43	1	no	—
811	C₄×Q₈	—	43	1	no	—
812	C₄×Q₈	—	86	1	no	—
813	C₄×Q₈	C₂²×D₄₃	1	1	yes	characteristic
814	C₄×Q₈	C₂²×D₄₃	1	1	yes	characteristic
815	C₄×Q₈	C₂²×D₄₃	1	1	yes	characteristic
816	C₄×D₄	—	2	1	no	—
817	C₄×D₄	—	2	1	no	—
818	C₄×D₄	—	2	2	no	—
819	C₄×D₄	—	2	2	no	—
820	C₄×D₄	—	2	1	no	—
821	C₄×D₄	—	2	1	no	—
822	C₄×D₄	—	43	1	no	—
823	C₄×D₄	—	43	1	no	—
824	C₄×D₄	—	43	2	no	—
825	C₄×D₄	—	43	2	no	—
826	C₄×D₄	—	43	2	no	—
827	C₄×D₄	—	86	1	no	—
828	C₄×D₄	—	86	1	no	—
829	C₄×D₄	—	86	2	no	—
830	C₄×D₄	—	86	2	no	—
831	C₄×D₄	—	86	1	no	—
832	C₄×D₄	—	86	1	no	—
833	C₄×D₄	C₂²×D₄₃	1	1	yes	characteristic
834	C₄×D₄	C₂²×D₄₃	1	1	yes	characteristic
835	C₄×D₄	C₂²×D₄₃	1	2	yes	—
836	C₄×D₄	C₂²×D₄₃	1	2	yes	—
837	C₄×D₄	C₂²×D₄₃	1	2	yes	—
838	C₄×D₄	C₂²×D₄₃	1	1	yes	characteristic
839	C₄×D₄	C₂²×D₄₃	1	2	yes	—
840	#117	—	2	2	no	—
841	#117	—	2	1	no	—
842	#117	—	43	1	no	—
843	#117	—	43	2	no	—
844	#117	—	86	2	no	—
845	#117	—	86	1	no	—
846	#117	C₂²×D₄₃	1	1	yes	characteristic
847	#117	C₂²×D₄₃	1	2	yes	—
848	#117	C₂²×D₄₃	1	2	yes	—
849	C₂×C₂²⋊C₄	—	2	2	no	—
850	C₂×C₂²⋊C₄	—	2	2	no	—
851	C₂×C₂²⋊C₄	—	2	2	no	—
852	C₂×C₂²⋊C₄	—	86	2	no	—
853	C₂×C₂²⋊C₄	—	86	2	no	—
854	C₂×C₂²⋊C₄	—	86	2	no	—
855	C₂×C₄²	—	2	1	no	—
856	C₂×C₄²	—	86	1	no	—
857	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
858	#107	—	43	1	no	—
859	#107	—	43	2	no	—
860	#107	—	43	1	no	—
861	#107	—	43	2	no	—
862	#107	—	43	2	no	—
863	#107	—	43	2	no	—
864	#106	—	43	1	no	—
865	#106	—	43	1	no	—
866	#106	—	43	2	no	—
867	#106	—	43	2	no	—
868	C₄⋊C₈	—	43	1	no	—
869	C₄⋊C₈	—	43	1	no	—
870	C₄⋊C₈	—	43	2	no	—
871	C₄⋊C₈	—	43	2	no	—
872	#103	—	43	1	no	—
873	#103	—	43	1	no	—
874	#103	—	43	2	no	—
875	#103	—	43	1	no	—
876	#103	—	43	1	no	—
877	#103	—	43	2	no	—
878	#102	—	43	1	no	—
879	#102	—	43	1	no	—
880	#102	—	43	2	no	—
881	#102	—	43	2	no	—
882	#102	—	43	2	no	—
883	#102	—	43	2	no	—
884	#102	—	43	2	no	—
885	#102	—	43	1	no	—
886	#102	—	43	1	no	—
887	#102	—	43	2	no	—
888	#102	—	43	2	no	—
889	#102	—	43	2	no	—
890	#102	—	43	2	no	—
891	#102	—	43	2	no	—
892	C₂²⋊C₈	—	43	2	no	—
893	C₂²⋊C₈	—	43	2	no	—
894	C₂²⋊C₈	—	43	2	no	—
895	#97	—	43	2	no	—
896	#97	—	43	2	no	—
897	C₄×C₈	—	43	1	no	—
898	C₄×C₈	—	43	1	no	—
899	C₄×C₈	—	43	1	no	—
900	C₄×C₈	—	43	1	no	—
901	C₄×C₈	—	43	2	no	—
902	C₂⁴	—	2	2	no	—
903	C₂⁴	—	86	2	no	—
904	#41	—	2	2	no	—
905	#41	—	4	1	no	—
906	#41	—	8	2	no	—
907	#41	—	86	2	no	—
908	#41	—	344	2	no	—
909	#41	—	172	1	no	—
910	C₂×Q₈	—	2	1	no	—
911	C₂×Q₈	—	2	2	no	—
912	C₂×Q₈	—	8	2	no	—
913	C₂×Q₈	—	43	1	no	—
914	C₂×Q₈	—	86	2	no	—
915	C₂×Q₈	—	86	1	no	—
916	C₂×Q₈	—	344	2	no	—
917	C₂×Q₈	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
918	C₂×Q₈	C₂³×D₄₃	1	1	yes	characteristic
919	C₂×D₄	—	2	4	no	—
920	C₂×D₄	—	2	1	no	—
921	C₂×D₄	—	2	2	no	—
922	C₂×D₄	—	2	2	no	—
923	C₂×D₄	—	2	2	no	—
924	C₂×D₄	—	2	1	no	—
925	C₂×D₄	—	2	1	no	—
926	C₂×D₄	—	4	2	no	—
927	C₂×D₄	—	8	2	no	—
928	C₂×D₄	—	43	1	no	—
929	C₂×D₄	—	43	2	no	—
930	C₂×D₄	—	86	4	no	—
931	C₂×D₄	—	86	2	no	—
932	C₂×D₄	—	86	2	no	—
933	C₂×D₄	—	86	1	no	—
934	C₂×D₄	—	86	1	no	—
935	C₂×D₄	—	86	2	no	—
936	C₂×D₄	—	86	1	no	—
937	C₂×D₄	—	344	2	no	—
938	C₂×D₄	—	172	2	no	—
939	C₂×D₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
940	C₂×D₄	C₂×C₂²⋊D₄₃	1	2	yes	—
941	C₂×D₄	C₂³×D₄₃	1	2	yes	—
942	C₂×D₄	C₂³×D₄₃	1	1	yes	characteristic
943	C₂²×C₄	—	2	1	no	—
944	C₂²×C₄	—	2	1	no	—
945	C₂²×C₄	—	2	1	no	—
946	C₂²×C₄	—	2	2	no	—
947	C₂²×C₄	—	2	2	no	—
948	C₂²×C₄	—	2	2	no	—
949	C₂²×C₄	—	86	1	no	—
950	C₂²×C₄	—	86	2	no	—
951	C₂²×C₄	—	86	2	no	—
952	C₂²×C₄	—	86	2	no	—
953	C₂²×C₄	—	86	1	no	—
954	C₂²×C₄	—	86	1	no	—
955	C₂²×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
956	C₂²×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
957	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
958	C₂²×C₄	C₂³×D₄₃	1	2	yes	—
959	Q₁₆	—	86	2	no	—
960	SD₁₆	—	86	2	no	—
961	SD₁₆	—	86	2	no	—
962	SD₁₆	—	172	2	no	—
963	SD₁₆	—	172	2	no	—
964	D₈	—	43	4	no	—
965	D₈	—	86	4	no	—
966	D₈	—	86	4	no	—
967	D₈	—	86	4	no	—
968	D₈	—	172	2	no	—
969	M₁₆	—	172	2	no	—
970	C₂×C₈	—	43	1	no	—
971	C₂×C₈	—	43	1	no	—
972	C₂×C₈	—	43	1	no	—
973	C₂×C₈	—	43	1	no	—
974	C₂×C₈	—	43	2	no	—
975	C₂×C₈	—	43	2	no	—
976	C₂×C₈	—	86	4	no	—
977	C₂×C₈	—	86	2	no	—
978	C₂×C₈	—	172	1	no	—
979	C₄⋊C₄	—	2	1	no	—
980	C₄⋊C₄	—	2	1	no	—
981	C₄⋊C₄	—	2	2	no	—
982	C₄⋊C₄	—	2	1	no	—
983	C₄⋊C₄	—	2	2	no	—
984	C₄⋊C₄	—	43	1	no	—
985	C₄⋊C₄	—	43	2	no	—
986	C₄⋊C₄	—	43	1	no	—
987	C₄⋊C₄	—	86	1	no	—
988	C₄⋊C₄	—	86	1	no	—
989	C₄⋊C₄	—	86	2	no	—
990	C₄⋊C₄	—	86	1	no	—
991	C₄⋊C₄	—	86	2	no	—
992	C₄⋊C₄	C₂×C₂²⋊D₄₃	1	2	yes	—
993	C₄⋊C₄	C₂×C₂²⋊D₄₃	1	2	yes	—
994	C₄⋊C₄	C₂×C₂²⋊D₄₃	1	2	yes	—
995	C₄⋊C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
996	C₄⋊C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
997	C₄⋊C₄	C₂×C₂²⋊D₄₃	1	2	yes	—
998	C₄⋊C₄	C₂³×D₄₃	1	1	yes	characteristic
999	C₄⋊C₄	C₂³×D₄₃	1	2	yes	—
1000	C₄⋊C₄	C₂³×D₄₃	1	1	yes	characteristic
1001	C₂²⋊C₄	—	2	2	no	—
1002	C₂²⋊C₄	—	2	2	no	—
1003	C₂²⋊C₄	—	2	1	no	—
1004	C₂²⋊C₄	—	2	1	no	—
1005	C₂²⋊C₄	—	2	2	no	—
1006	C₂²⋊C₄	—	2	2	no	—
1007	C₂²⋊C₄	—	2	2	no	—
1008	C₂²⋊C₄	—	2	2	no	—
1009	C₂²⋊C₄	—	2	2	no	—
1010	C₂²⋊C₄	—	2	1	no	—
1011	C₂²⋊C₄	—	2	2	no	—
1012	C₂²⋊C₄	—	2	2	no	—
1013	C₂²⋊C₄	—	86	2	no	—
1014	C₂²⋊C₄	—	86	2	no	—
1015	C₂²⋊C₄	—	86	1	no	—
1016	C₂²⋊C₄	—	86	1	no	—
1017	C₂²⋊C₄	—	86	2	no	—
1018	C₂²⋊C₄	—	86	2	no	—
1019	C₂²⋊C₄	—	86	2	no	—
1020	C₂²⋊C₄	—	86	2	no	—
1021	C₂²⋊C₄	—	86	2	no	—
1022	C₂²⋊C₄	—	86	1	no	—
1023	C₂²⋊C₄	—	86	2	no	—
1024	C₂²⋊C₄	—	86	2	no	—
1025	C₂²⋊C₄	C₂×C₂²⋊D₄₃	1	2	yes	—
1026	C₂²⋊C₄	C₂×C₂²⋊D₄₃	1	2	yes	—
1027	C₂²⋊C₄	C₂×C₂²⋊D₄₃	1	2	yes	—
1028	C₂²⋊C₄	C₂×C₂²⋊D₄₃	1	2	yes	—
1029	C₂²⋊C₄	C₂×C₂²⋊D₄₃	1	2	yes	—
1030	C₄²	—	2	1	no	—
1031	C₄²	—	2	1	no	—
1032	C₄²	—	2	1	no	—
1033	C₄²	—	2	2	no	—
1034	C₄²	—	86	1	no	—
1035	C₄²	—	86	1	no	—
1036	C₄²	—	86	1	no	—
1037	C₄²	—	86	2	no	—
1038	C₄²	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
1039	C₄²	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
1040	C₄²	C₂³×D₄₃	1	1	yes	characteristic
1041	C₄²	C₂³×D₄₃	1	1	yes	characteristic
1042	C₄²	C₂³×D₄₃	1	2	yes	—
1043	C₂³	—	2	1	no	—
1044	C₂³	—	2	2	no	—
1045	C₂³	—	4	4	no	—
1046	C₂³	—	8	2	no	—
1047	C₂³	—	8	2	no	—
1048	C₂³	—	86	1	no	—
1049	C₂³	—	86	2	no	—
1050	C₂³	—	344	2	no	—
1051	C₂³	—	344	2	no	—
1052	C₂³	—	172	4	no	—
1053	C₂³	C₂²×C₂²⋊D₄₃	1	2	yes	—
1054	C₂³	C₂²×C₂²⋊D₄₃	1	1	yes	characteristic
1055	Q₈	—	2	2	no	—
1056	Q₈	—	2	1	no	—
1057	Q₈	—	2	1	no	—
1058	Q₈	—	4	2	no	—
1059	Q₈	—	8	2	no	—
1060	Q₈	—	86	1	no	—
1061	Q₈	—	86	1	no	—
1062	Q₈	—	344	2	no	—
1063	Q₈	—	172	2	no	—
1064	D₄	—	2	2	no	—
1065	D₄	—	2	2	no	—
1066	D₄	—	2	1	no	—
1067	D₄	—	2	2	no	—
1068	D₄	—	4	2	no	—
1069	D₄	—	4	4	no	—
1070	D₄	—	4	2	no	—
1071	D₄	—	4	2	no	—
1072	D₄	—	8	1	no	—
1073	D₄	—	8	2	no	—
1074	D₄	—	8	2	no	—
1075	D₄	—	43	2	no	—
1076	D₄	—	86	2	no	—
1077	D₄	—	86	1	no	—
1078	D₄	—	86	2	no	—
1079	D₄	—	344	1	no	—
1080	D₄	—	344	2	no	—
1081	D₄	—	344	2	no	—
1082	D₄	—	172	4	no	—
1083	D₄	—	172	2	no	—
1084	D₄	—	172	2	no	—
1085	D₄	#41×D₄₃	1	2	yes	—
1086	C₂×C₄	—	2	2	no	—
1087	C₂×C₄	—	2	2	no	—
1088	C₂×C₄	—	2	1	no	—
1089	C₂×C₄	—	2	1	no	—
1090	C₂×C₄	—	2	2	no	—
1091	C₂×C₄	—	2	1	no	—
1092	C₂×C₄	—	2	1	no	—
1093	C₂×C₄	—	2	1	no	—
1094	C₂×C₄	—	2	2	no	—
1095	C₂×C₄	—	4	1	no	—
1096	C₂×C₄	—	4	2	no	—
1097	C₂×C₄	—	4	2	no	—
1098	C₂×C₄	—	8	2	no	—
1099	C₂×C₄	—	8	2	no	—
1100	C₂×C₄	—	8	1	no	—
1101	C₂×C₄	—	8	2	no	—
1102	C₂×C₄	—	86	1	no	—
1103	C₂×C₄	—	86	1	no	—
1104	C₂×C₄	—	86	1	no	—
1105	C₂×C₄	—	86	2	no	—
1106	C₂×C₄	—	344	2	no	—
1107	C₂×C₄	—	344	2	no	—
1108	C₂×C₄	—	344	1	no	—
1109	C₂×C₄	—	344	2	no	—
1110	C₂×C₄	—	172	2	no	—
1111	C₂×C₄	—	172	2	no	—
1112	C₂×C₄	C₂²×C₂²⋊D₄₃	1	1	yes	characteristic
1113	C₂×C₄	C₂²×C₂²⋊D₄₃	1	1	yes	characteristic
1114	C₂×C₄	C₂²×C₂²⋊D₄₃	1	2	yes	—
1115	C₂×C₄	C₂²×C₂²⋊D₄₃	1	1	yes	characteristic
1116	C₂×C₄	C₂²×C₂²⋊D₄₃	1	1	yes	characteristic
1117	C₂×C₄	C₂²×C₂²⋊D₄₃	1	2	yes	—
1118	C₂×C₄	C₂²×C₂²⋊D₄₃	1	2	yes	—
1119	C₂×C₄	C₂²×C₂²⋊D₄₃	1	1	yes	characteristic
1120	C₂×C₄	C₂⁴×D₄₃	1	1	yes	characteristic
1121	C₈	—	43	2	no	—
1122	C₈	—	86	2	no	—
1123	C₈	—	86	1	no	—
1124	C₈	—	86	1	no	—
1125	C₈	—	86	1	no	—
1126	C₈	—	86	2	no	—
1127	C₂²	—	2	1	no	—
1128	C₂²	—	2	2	no	—
1129	C₂²	—	2	1	no	—
1130	C₂²	—	2	2	no	—
1131	C₂²	—	2	2	no	—
1132	C₂²	—	2	1	no	—
1133	C₂²	—	2	2	no	—
1134	C₂²	—	4	1	no	—
1135	C₂²	—	4	1	no	—
1136	C₂²	—	4	2	no	—
1137	C₂²	—	4	2	no	—
1138	C₂²	—	4	2	no	—
1139	C₂²	—	16	4	no	—
1140	C₂²	—	86	2	no	—
1141	C₂²	—	172	2	no	—
1142	C₂²	—	172	2	no	—
1143	C₂²	—	172	2	no	—
1144	C₂²	—	172	1	no	—
1145	C₂²	—	172	1	no	—
1146	C₂²	—	688	4	no	—
1147	C₂²	C₂³×C₂²⋊D₄₃	1	1	yes	characteristic
1148	C₄	—	2	1	no	—
1149	C₄	—	2	2	no	—
1150	C₄	—	2	1	no	—
1151	C₄	—	2	2	no	—
1152	C₄	—	2	1	no	—
1153	C₄	—	2	1	no	—
1154	C₄	—	2	2	no	—
1155	C₄	—	4	1	no	—
1156	C₄	—	4	2	no	—
1157	C₄	—	4	1	no	—
1158	C₄	—	4	1	no	—
1159	C₄	—	172	2	no	—
1160	C₄	—	172	1	no	—
1161	C₄	—	172	1	no	—
1162	C₄	—	172	1	no	—
1163	C₄	#14583702	1	2	yes	—
1164	C₄	C₂×#41×D₄₃	1	1	yes	characteristic
1165	C₄	#14583735	1	1	yes	characteristic
1166	C₂	—	4	2	no	—
1167	C₂	—	4	1	no	—
1168	C₂	—	4	2	no	—
1169	C₂	—	8	2	no	—
1170	C₂	—	344	2	no	—
1171	C₂	—	172	2	no	—
1172	C₂	#41×C₂²⋊D₄₃	1	1	yes	characteristic
1173	C₂	C₂×#14583702	1	1	yes	characteristic
1174	C₂	#19149366	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂³×C₂²⋊D₄₃
commutator, cosocle	C₂×C₄×C₄₃	C₂⁵
Frattini	C₂×C₄	C₂⁴×D₄₃
Fitting	C₄₃×#3514	C₂
socle	C₂²×C₄₃	C₂³×D₄
hypercenter	#3514	D₄₃
hypocenter	C₄₃	#61475
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ #529 ◁ #3514

Complements

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

N	H ≅ G/N	type
1. #19148558	C₂	semidirect
2. #19147603	C₂	semidirect
3. Q₈×#10621882	C₂	semidirect
4. #19147387	C₂	semidirect
5. #19147383	C₂	semidirect
6. #19147021	C₂	semidirect
7. #19147013	C₂	semidirect
8. #19146826	C₂	semidirect
9. #19146820	C₂	semidirect
10. #19146751	C₂	semidirect
11. #19146745	C₂	semidirect
12. #19146276	C₂	semidirect
13. D₄×#10621882	C₂	semidirect
14. #19145228	C₂	semidirect
15. #19145170	C₂	semidirect
16. #19144779	C₂	semidirect
17. #19144773	C₂	semidirect
18. #19144746	C₂	semidirect
19. #19144740	C₂	semidirect
20. #19143571	C₂	semidirect
21. #19143445	C₂	semidirect
22. C₄×#13063345	C₂	semidirect
23. C₄₃×#3514	C₂	semidirect
26. #14583634	C₂²	semidirect
28. #14583614	C₂²	semidirect
30. Q₈×D₁₇₂	C₂²	semidirect
33. #14583545	C₂²	semidirect
35. #14583520	C₂²	semidirect
37. #14583449	C₂²	semidirect
40. #14583373	C₂²	semidirect
41. C₄×#10621898	C₂²	semidirect
42. #14583302	C₂²	semidirect
43. #14583302	C₂²	semidirect
44. #14583281	C₂²	semidirect
46. #14583261	C₂²	semidirect
47. #14583258	C₂²	semidirect
48. #14583247	C₂²	semidirect
49. #14583245	C₂²	semidirect
50. #14583240	C₂²	semidirect
51. #14583237	C₂²	semidirect
52. #14583223	C₂²	semidirect
53. #14583223	C₂²	semidirect
54. #14583220	C₂²	semidirect
55. #14583220	C₂²	semidirect
56. #14583189	C₂²	semidirect
57. #14583186	C₂²	semidirect
58. #14583184	C₂²	semidirect
59. #14583181	C₂²	semidirect
60. #14583179	C₂²	semidirect
61. #14583179	C₂²	semidirect
62. #14583176	C₂²	semidirect
63. #14583176	C₂²	semidirect
64. #14583147	C₂²	semidirect
65. #14583143	C₂²	semidirect
66. #14583138	C₂²	semidirect
68. #14583133	C₂²	semidirect
69. #14583133	C₂²	semidirect
70. #14583114	C₂²	semidirect
71. #14583114	C₂²	semidirect
72. #14583111	C₂²	semidirect
73. #14583111	C₂²	semidirect
74. #14583099	C₂²	semidirect
75. #14583096	C₂²	semidirect
78. #14583050	C₂²	semidirect
79. #14583049	C₂²	semidirect
80. #14583044	C₂²	semidirect
81. #14583042	C₂²	semidirect
84. #14583030	C₂²	semidirect
85. Q₈×C₄₃⋊C₈	C₂²	semidirect
86. #14583009	C₂²	semidirect
87. #14583009	C₂²	semidirect
88. #14583009	C₂²	semidirect
89. #14583009	C₂²	semidirect
90. #14582999	C₂²	semidirect
91. #14582997	C₂²	semidirect
92. C₄×#10621885	C₂²	semidirect
93. C₄×#10621885	C₂²	semidirect
94. C₄×#10621884	C₂²	semidirect
95. C₄×#10621884	C₂²	semidirect
96. C₄×#10621883	C₂²	semidirect
97. C₄×#10621883	C₂²	semidirect
101. C₄×#10621882	C₂²	semidirect
102. C₄×#10621882	C₂²	semidirect
103. C₄×#10621882	C₂²	semidirect
105. #14582971	C₂²	semidirect
107. D₄×C₄₃⋊C₈	C₂²	semidirect
108. #14582960	C₂²	semidirect
109. #14582956	C₂²	semidirect
110. #14582935	C₂²	semidirect
111. #14582935	C₂²	semidirect
112. #14582904	C₂²	semidirect
113. #14582903	C₂²	semidirect
114. #14582895	C₂²	semidirect
115. #14582893	C₂²	semidirect
116. #14582855	C₂²	semidirect
117. C₂×C₄×C₄₃⋊C₈	C₂²	semidirect
118. C₄₃×#559	C₂²	semidirect
120. C₄₃×#555	C₂²	semidirect
122. D₄×Q₈×C₄₃	C₂²	semidirect
125. C₄₃×#546	C₂²	semidirect
127. C₄₃×#542	C₂²	semidirect
129. C₄₃×#532	C₂²	semidirect
133. C₄₃×#518	C₂²	semidirect
134. C₄×#41×C₄₃	C₂²	semidirect
423. #10621882	#41	semidirect
580. #3514	D₄₃	semidirect
614. #559	C₂×D₄₃	semidirect
618. #555	C₂×D₄₃	semidirect
622. D₄×Q₈	C₂×D₄₃	semidirect
628. #546	C₂×D₄₃	semidirect
632. #542	C₂×D₄₃	semidirect
636. #532	C₂×D₄₃	semidirect
643. #518	C₂×D₄₃	semidirect
645. C₄×#41	C₂×D₄₃	semidirect
722. C₄₃	#61475	semidirect

Maximal subgroups

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

subgroup	index
#19148558	2
#19147603	2
Q₈×#10621882	2
#19147387	2
#19147383	2
#19147021	2
#19147013	2
#19146826	2
#19146820	2
#19146751	2
#19146745	2
#19146276	2
D₄×#10621882	2
#19145228	2
#19145170	2
#19144779	2
#19144773	2
#19144746	2
#19144740	2
#19143571	2
#19143445	2
C₄×#13063345	2
C₄₃×#3514	2
#61475	43