Subgroups — #25969072

Order 11008.

1640 conjugacy classes of subgroups.

The subgroup lattice has 1086 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19148000	C₂	1	1	yes	maximal, characteristic, complemented
2	#19145887	C₂	1	2	yes	maximal, complemented
3	#19145872	C₂	1	2	yes	maximal, complemented
4	#19145857	C₂	1	2	yes	maximal, complemented
5	#19145857	C₂	1	2	yes	maximal, complemented
6	#19145831	C₂	1	2	yes	maximal, complemented
7	#19145805	C₂	1	2	yes	maximal, complemented
8	#19145770	C₂	1	2	yes	maximal, complemented
9	#19145750	C₂	1	2	yes	maximal, complemented
10	#19145129	C₂	1	1	yes	maximal, characteristic, complemented
11	#19145121	C₂	1	1	yes	maximal, characteristic, complemented
12	#19144960	C₂	1	1	yes	maximal, characteristic, complemented
13	#19144960	C₂	1	1	yes	maximal, characteristic, complemented
14	#19144539	C₂	1	1	yes	maximal, characteristic, complemented
15	#19144524	C₂	1	1	yes	maximal, characteristic
16	#19144504	C₂	1	1	yes	maximal, characteristic
17	C₂×#14583237	C₂	1	1	yes	maximal, characteristic, complemented
18	#19144457	C₂	1	1	yes	maximal, characteristic, complemented
19	#19144446	C₂	1	1	yes	maximal, characteristic, complemented
20	#19144437	C₂	1	1	yes	maximal, characteristic, complemented
21	#19144437	C₂	1	1	yes	maximal, characteristic, complemented
22	#19143253	C₂	1	1	yes	maximal, characteristic, complemented
23	C₄₃×#3495	C₂	1	1	yes	maximal, characteristic
24	#14583530	—	2	1	no	—
25	#14583530	—	2	1	no	—
26	#14583527	C₂²	1	1	yes	characteristic
27	#14583527	C₂²	1	1	yes	characteristic
28	#14583527	C₂²	1	1	yes	characteristic
29	#14583527	C₂²	1	2	yes	—
30	#14583527	C₂²	1	2	yes	—
31	#14583527	C₂²	1	1	yes	characteristic
32	#14583525	—	2	2	no	—
33	#14583456	C₂²	1	2	yes	—
34	#14583456	C₂²	1	2	yes	—
35	#14583452	—	2	1	no	—
36	#14583452	—	2	2	no	—
37	#14583452	—	2	1	no	—
38	C₂×#13063284	C₂²	1	1	yes	characteristic
39	C₂×#13063284	C₂²	1	1	yes	characteristic
40	#14583309	C₂²	1	2	yes	complemented
41	#14583309	C₂²	1	2	yes	complemented
42	#14583305	C₂²	1	2	yes	complemented
43	#14583305	C₂²	1	2	yes	complemented
44	#14583302	C₂²	1	2	yes	complemented
45	#14583298	C₂²	1	2	yes	complemented
46	#14583298	C₂²	1	2	yes	complemented
47	#14583295	C₂²	1	2	yes	complemented
48	#14583267	C₂²	1	2	yes	complemented
49	#14583267	C₂²	1	2	yes	complemented
50	#14583258	C₂²	1	2	yes	complemented
51	#14583258	C₂²	1	2	yes	complemented
52	#14583253	C₂²	1	2	yes	complemented
53	#14583253	C₂²	1	2	yes	complemented
54	#14583249	C₂²	1	2	yes	complemented
55	#14583249	C₂²	1	2	yes	complemented
56	#14583237	C₂²	1	1	yes	characteristic
57	#14583237	C₂²	1	2	yes	—
58	#14583237	C₂²	1	2	yes	—
59	#14583237	C₂²	1	2	yes	—
60	#14583237	C₂²	1	2	yes	—
61	#14583237	C₂²	1	2	yes	—
62	#14583237	C₂²	1	2	yes	—
63	#14583237	C₂²	1	2	yes	—
64	#14583237	C₂²	1	1	yes	characteristic
65	#14583237	C₂²	1	2	yes	—
66	#14583232	C₂²	1	1	yes	characteristic
67	#14583232	C₂²	1	2	yes	—
68	#14583227	C₂²	1	1	yes	characteristic
69	#14583227	C₂²	1	2	yes	—
70	#14583220	C₂²	1	1	yes	characteristic
71	#14583220	C₂²	1	2	yes	—
72	#14583220	C₂²	1	1	yes	characteristic
73	#14583220	C₂²	1	2	yes	—
74	#14583215	C₂²	1	1	yes	characteristic
75	#14583210	C₂²	1	1	yes	characteristic
76	#14583206	C₂²	1	2	yes	complemented
77	#14583206	C₂²	1	2	yes	complemented
78	#14583206	C₂²	1	2	yes	complemented
79	#14583206	C₂²	1	2	yes	complemented
80	#14583206	C₂²	1	2	yes	complemented
81	#14583206	C₂²	1	2	yes	complemented
82	#14583199	C₂²	1	2	yes	complemented
83	#14583199	C₂²	1	2	yes	complemented
84	#14583194	C₂²	1	2	yes	complemented
85	#14583194	C₂²	1	2	yes	complemented
86	#14583194	C₂²	1	2	yes	complemented
87	#14583189	C₂²	1	2	yes	complemented
88	#14583184	C₂²	1	2	yes	complemented
89	#14583184	C₂²	1	2	yes	complemented
90	#14583184	C₂²	1	2	yes	complemented
91	#14583179	C₂²	1	2	yes	complemented
92	#14582960	C₂²	1	2	yes	—
93	#14582960	C₂²	1	2	yes	—
94	#14582956	C₂²	1	2	yes	—
95	#14582952	C₂²	1	2	yes	—
96	#14582942	C₂²	1	1	yes	characteristic
97	#14582942	C₂²	1	1	yes	characteristic
98	#14582939	C₂²	1	1	yes	characteristic
99	#14582939	C₂²	1	1	yes	characteristic
100	#14582935	C₂²	1	1	yes	characteristic
101	#14582935	C₂²	1	1	yes	characteristic
102	C₂×#13063258	C₂²	1	1	yes	characteristic
103	C₂×#13063256	C₂²	1	1	yes	characteristic
104	#14582926	C₂²	1	1	yes	characteristic
105	#14582926	C₂²	1	1	yes	characteristic
106	#14582908	C₂²	1	1	yes	characteristic
107	#14582908	C₂²	1	1	yes	characteristic
108	#14582900	C₂²	1	1	yes	characteristic
109	#14582900	C₂²	1	1	yes	characteristic
110	#14582895	C₂²	1	1	yes	characteristic
111	#14582895	C₂²	1	1	yes	characteristic
112	C₂×#13063249	C₂²	1	1	yes	characteristic
113	C₂×#13063249	C₂²	1	1	yes	characteristic
114	#14582863	C₂²	1	1	yes	characteristic
115	C₂×C₂²⋊(C₄₃⋊C₈)	C₂²	1	1	yes	characteristic
116	#14582855	C₂²	1	1	yes	characteristic
117	#14582855	C₂²	1	1	yes	characteristic
118	C₄₃×#556	—	2	1	no	—
119	C₄₃×#554	—	2	1	no	—
120	C₄₃×#552	—	2	2	no	—
121	C₄₃×#552	—	2	1	no	—
122	C₄₃×#552	—	2	1	no	—
123	C₄₃×#551	—	2	2	no	—
124	C₄₃×#544	C₂²	1	1	yes	characteristic
125	C₄₃×#542	C₂²	1	2	yes	—
126	C₄₃×#541	C₂²	1	2	yes	—
127	C₄₃×#536	C₂²	1	1	yes	characteristic
128	C₄₃×#533	C₂²	1	2	yes	—
129	C₄₃×#529	C₂²	1	2	yes	—
130	C₄₃×#525	C₂²	1	1	yes	characteristic
131	C₂×C₂²⋊Q₈×C₄₃	C₂²	1	1	yes	characteristic
132	C₄₃×#520	C₂²	1	1	yes	characteristic
133	C₄₃×#519	C₂²	1	1	yes	characteristic
134	C₂×#117×C₄₃	C₂²	1	1	yes	characteristic
135	C₂×#10621877	C₂³	1	1	yes	characteristic
136	C₂×#10621877	C₂³	1	1	yes	characteristic
137	C₂²×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
138	C₂²×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
139	#13063325	C₂³	1	2	yes	—
140	#13063325	C₂³	1	2	yes	—
141	#13063325	C₂³	1	2	yes	—
142	#13063325	C₂³	1	2	yes	—
143	#13063324	—	2	1	no	—
144	#13063324	—	2	1	no	—
145	#13063324	—	2	1	no	—
146	#13063324	—	2	2	no	—
147	#13063324	—	2	1	no	—
148	#13063324	—	2	2	no	—
149	#13063317	C₂³	1	2	yes	—
150	#13063317	C₂³	1	2	yes	—
151	#13063317	C₂³	1	2	yes	—
152	#13063317	C₂³	1	2	yes	—
153	#13063316	—	2	1	no	—
154	#13063316	—	2	1	no	—
155	#13063316	—	2	1	no	—
156	#13063316	—	2	2	no	—
157	#13063316	—	2	1	no	—
158	#13063316	—	2	2	no	—
159	#13063304	—	2	2	no	—
160	#13063304	—	2	2	no	—
161	#13063304	—	2	2	no	—
162	#13063304	—	2	2	no	—
163	#13063302	—	2	2	no	—
164	#13063302	—	2	2	no	—
165	#13063302	—	2	2	no	—
166	#13063302	—	2	2	no	—
167	#13063302	—	2	2	no	—
168	#13063302	—	2	2	no	—
169	#13063302	—	2	2	no	—
170	#13063302	—	2	2	no	—
171	C₄×Dic₈₆	—	2	2	no	—
172	C₄×Dic₈₆	—	2	2	no	—
173	C₄×Dic₈₆	—	2	2	no	—
174	C₄×Dic₈₆	—	2	2	no	—
175	#13063284	—	2	1	no	—
176	#13063284	—	2	1	no	—
177	#13063284	—	2	1	no	—
178	#13063284	—	2	1	no	—
179	#13063284	C₂³	1	1	yes	characteristic
180	#13063284	C₂³	1	1	yes	characteristic
181	#13063284	C₂³	1	2	yes	—
182	#13063284	C₂³	1	1	yes	characteristic
183	#13063284	C₂³	1	1	yes	characteristic
184	#13063284	C₂³	1	2	yes	—
185	C₂×C₄⋊Dic₄₃	C₂³	1	1	yes	characteristic
186	C₂×C₄⋊Dic₄₃	C₂³	1	1	yes	characteristic
187	C₂×C₄⋊Dic₄₃	C₂³	1	1	yes	characteristic
188	C₂×C₄⋊Dic₄₃	C₂³	1	1	yes	characteristic
189	C₂×C₂²⋊Dic₄₃	—	2	1	no	—
190	C₂×C₂²⋊Dic₄₃	—	2	1	no	—
191	C₂×C₄×Dic₄₃	—	2	1	no	—
192	C₂×C₄×Dic₄₃	—	2	1	no	—
193	#13063258	C₂³	1	1	yes	characteristic
194	#13063258	C₂³	1	2	yes	—
195	#13063258	C₂³	1	2	yes	—
196	#13063258	C₂³	1	2	yes	—
197	#13063258	C₂³	1	1	yes	characteristic
198	#13063258	C₂³	1	2	yes	—
199	#13063258	C₂³	1	2	yes	—
200	#13063258	C₂³	1	1	yes	characteristic
201	#13063258	C₂³	1	2	yes	—
202	#13063258	C₂³	1	1	yes	characteristic
203	#13063256	C₂³	1	1	yes	characteristic
204	#13063256	C₂³	1	2	yes	—
205	#13063256	C₂³	1	2	yes	—
206	#13063256	C₂³	1	2	yes	—
207	#13063256	C₂³	1	1	yes	characteristic
208	#13063256	C₂³	1	2	yes	—
209	#13063256	C₂³	1	2	yes	—
210	#13063256	C₂³	1	1	yes	characteristic
211	#13063256	C₂³	1	2	yes	—
212	#13063256	C₂³	1	1	yes	characteristic
213	C₄⋊(C₄₃⋊C₈)	C₂³	1	2	yes	—
214	C₄⋊(C₄₃⋊C₈)	C₂³	1	2	yes	—
215	C₄⋊(C₄₃⋊C₈)	C₂³	1	2	yes	—
216	C₄⋊(C₄₃⋊C₈)	C₂³	1	2	yes	—
217	#13063249	C₂³	1	2	yes	—
218	#13063249	C₂³	1	2	yes	—
219	#13063249	C₂³	1	2	yes	—
220	#13063249	C₂³	1	2	yes	—
221	#13063249	C₂³	1	1	yes	characteristic
222	#13063249	C₂³	1	1	yes	characteristic
223	#13063249	C₂³	1	1	yes	characteristic
224	#13063249	C₂³	1	1	yes	characteristic
225	#13063249	C₂³	1	2	yes	—
226	#13063249	C₂³	1	2	yes	—
227	#13063249	C₂³	1	2	yes	—
228	#13063249	C₂³	1	2	yes	—
229	#13063249	C₂³	1	2	yes	—
230	#13063249	C₂³	1	2	yes	—
231	#13063246	C₂³	1	1	yes	characteristic
232	#13063246	C₂³	1	1	yes	characteristic
233	#13063246	C₂³	1	1	yes	characteristic
234	#13063246	C₂³	1	1	yes	characteristic
235	#13063246	C₂³	1	2	yes	—
236	#13063246	C₂³	1	2	yes	—
237	C₂²⋊(C₄₃⋊C₈)	C₂³	1	1	yes	characteristic
238	C₂²⋊(C₄₃⋊C₈)	C₂³	1	1	yes	characteristic
239	C₂²⋊(C₄₃⋊C₈)	C₂³	1	1	yes	characteristic
240	C₂²⋊(C₄₃⋊C₈)	C₂³	1	1	yes	characteristic
241	C₂²⋊(C₄₃⋊C₈)	C₂³	1	2	yes	—
242	C₂²⋊(C₄₃⋊C₈)	C₂³	1	2	yes	—
243	#13063236	C₂³	1	2	yes	—
244	#13063236	C₂³	1	2	yes	—
245	C₄×C₄₃⋊C₈	C₂³	1	2	yes	—
246	C₄×C₄₃⋊C₈	C₂³	1	2	yes	—
247	C₂×#41×C₄₃	C₂³	1	1	yes	characteristic
248	C₂²×Q₈×C₄₃	C₂³	1	1	yes	characteristic
249	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
250	C₄⋊Q₈×C₄₃	—	2	1	no	—
251	C₄⋊Q₈×C₄₃	C₂³	1	2	yes	—
252	C₄⋊Q₈×C₄₃	C₂³	1	2	yes	—
253	#126×C₄₃	—	2	2	no	—
254	#126×C₄₃	—	2	2	no	—
255	#126×C₄₃	—	2	2	no	—
256	#126×C₄₃	—	2	2	no	—
257	#125×C₄₃	—	2	2	no	—
258	#125×C₄₃	—	2	2	no	—
259	#125×C₄₃	—	2	1	no	—
260	#125×C₄₃	—	2	2	no	—
261	#125×C₄₃	C₂³	1	2	yes	—
262	#124×C₄₃	—	2	2	no	—
263	#124×C₄₃	C₂³	1	2	yes	—
264	#123×C₄₃	—	2	1	no	—
265	#123×C₄₃	—	2	2	no	—
266	#123×C₄₃	—	2	2	no	—
267	#123×C₄₃	—	2	2	no	—
268	C₂²⋊Q₈×C₄₃	—	2	1	no	—
269	C₂²⋊Q₈×C₄₃	—	2	1	no	—
270	C₂²⋊Q₈×C₄₃	—	2	2	no	—
271	C₂²⋊Q₈×C₄₃	—	2	1	no	—
272	C₂²⋊Q₈×C₄₃	—	2	1	no	—
273	C₂²⋊Q₈×C₄₃	—	2	2	no	—
274	C₂²⋊Q₈×C₄₃	—	2	2	no	—
275	C₂²⋊Q₈×C₄₃	C₂³	1	2	yes	—
276	C₂²⋊Q₈×C₄₃	C₂³	1	2	yes	—
277	C₂²⋊Q₈×C₄₃	C₂³	1	1	yes	characteristic
278	C₂²⋊Q₈×C₄₃	C₂³	1	1	yes	characteristic
279	#121×C₄₃	C₂³	1	1	yes	characteristic
280	#121×C₄₃	C₂³	1	1	yes	characteristic
281	#120×C₄₃	—	2	1	no	—
282	C₄×Q₈×C₄₃	—	2	1	no	—
283	C₄×Q₈×C₄₃	—	2	1	no	—
284	C₄×Q₈×C₄₃	—	2	2	no	—
285	C₄×Q₈×C₄₃	C₂³	1	2	yes	—
286	C₄×Q₈×C₄₃	C₂³	1	2	yes	—
287	C₄×Q₈×C₄₃	C₂³	1	2	yes	—
288	C₄×D₄×C₄₃	—	2	1	no	—
289	C₄×D₄×C₄₃	—	2	1	no	—
290	C₄×D₄×C₄₃	—	2	2	no	—
291	C₄×D₄×C₄₃	—	2	2	no	—
292	C₄×D₄×C₄₃	C₂³	1	2	yes	—
293	#117×C₄₃	—	2	2	no	—
294	#117×C₄₃	—	2	1	no	—
295	#117×C₄₃	—	2	2	no	—
296	#117×C₄₃	—	2	2	no	—
297	#117×C₄₃	D₄	1	1	yes	characteristic
298	#117×C₄₃	D₄	1	2	yes	—
299	#117×C₄₃	D₄	1	1	yes	characteristic
300	#117×C₄₃	C₂³	1	1	yes	characteristic
301	#117×C₄₃	C₂³	1	1	yes	characteristic
302	#117×C₄₃	C₂³	1	1	yes	characteristic
303	#117×C₄₃	C₂³	1	2	yes	—
304	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
305	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
306	C₂×C₄⋊C₄×C₄₃	D₄	1	1	yes	characteristic
307	C₂×C₄⋊C₄×C₄₃	D₄	1	1	yes	characteristic
308	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
309	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
310	C₂×C₂²⋊C₄×C₄₃	D₄	1	2	yes	—
311	C₂×C₄²×C₄₃	C₂³	1	2	yes	—
312	C₂⁴×C₄₃	C₂×D₄	1	1	yes	characteristic
313	#41×C₄₃	—	2	2	no	—
314	#41×C₄₃	—	2	2	no	—
315	C₂×Q₈×C₄₃	—	2	1	no	—
316	C₂×Q₈×C₄₃	—	2	2	no	—
317	C₂×Q₈×C₄₃	—	2	2	no	—
318	C₂×Q₈×C₄₃	—	2	2	no	—
319	C₂×Q₈×C₄₃	C₂⁴	1	2	yes	—
320	C₂×Q₈×C₄₃	C₂⁴	1	1	yes	characteristic
321	C₂×D₄×C₄₃	—	2	1	no	—
322	C₂×D₄×C₄₃	—	2	1	no	—
323	C₂×D₄×C₄₃	—	2	1	no	—
324	C₂×D₄×C₄₃	C₂⁴	1	1	yes	characteristic
325	C₂²×C₄×C₄₃	—	2	2	no	—
326	C₂²×C₄×C₄₃	—	2	2	no	—
327	C₂²×C₄×C₄₃	—	2	1	no	—
328	C₂²×C₄×C₄₃	—	2	2	no	—
329	C₂²×C₄×C₄₃	—	2	1	no	—
330	C₂²×C₄×C₄₃	—	2	1	no	—
331	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
332	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
333	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
334	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
335	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
336	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
337	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
338	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
339	C₂²×Dic₄₃	—	2	1	no	—
340	C₂²×Dic₄₃	—	2	1	no	—
341	C₂²×Dic₄₃	—	2	1	no	—
342	C₂²×Dic₄₃	—	2	1	no	—
343	C₂×Dic₈₆	—	2	2	no	—
344	C₂×Dic₈₆	—	2	2	no	—
345	C₂×Dic₈₆	—	2	2	no	—
346	C₂×Dic₈₆	—	2	2	no	—
347	C₄⋊C₄×C₄₃	—	2	1	no	—
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	—	2	2	no	—
352	C₄⋊C₄×C₄₃	—	2	2	no	—
353	C₄⋊C₄×C₄₃	—	2	2	no	—
354	C₄⋊C₄×C₄₃	—	2	2	no	—
355	C₄⋊C₄×C₄₃	—	2	2	no	—
356	C₄⋊C₄×C₄₃	—	2	1	no	—
357	C₄⋊C₄×C₄₃	—	2	2	no	—
358	C₄⋊C₄×C₄₃	—	2	1	no	—
359	C₄⋊C₄×C₄₃	—	2	2	no	—
360	C₄⋊C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
361	C₄⋊C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
362	C₄⋊C₄×C₄₃	C₂×D₄	1	2	yes	—
363	C₄⋊C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
364	C₄⋊C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
365	C₄⋊C₄×C₄₃	C₂×D₄	1	2	yes	—
366	C₄⋊C₄×C₄₃	C₂⁴	1	2	yes	—
367	C₄⋊C₄×C₄₃	C₂⁴	1	1	yes	characteristic
368	C₄⋊C₄×C₄₃	C₂⁴	1	1	yes	characteristic
369	C₂²⋊C₄×C₄₃	—	2	1	no	—
370	C₂²⋊C₄×C₄₃	—	2	2	no	—
371	C₂²⋊C₄×C₄₃	—	2	2	no	—
372	C₂²⋊C₄×C₄₃	—	2	1	no	—
373	C₂²⋊C₄×C₄₃	—	2	2	no	—
374	C₂²⋊C₄×C₄₃	—	2	2	no	—
375	C₂²⋊C₄×C₄₃	—	2	2	no	—
376	C₂²⋊C₄×C₄₃	—	2	1	no	—
377	C₂²⋊C₄×C₄₃	—	2	1	no	—
378	C₂²⋊C₄×C₄₃	—	2	1	no	—
379	C₂²⋊C₄×C₄₃	C₂×D₄	1	2	yes	—
380	C₂²⋊C₄×C₄₃	C₂×D₄	1	2	yes	—
381	C₂²⋊C₄×C₄₃	C₂×D₄	1	2	yes	—
382	C₂²⋊C₄×C₄₃	C₂×D₄	1	2	yes	—
383	C₄²×C₄₃	—	2	2	no	—
384	C₄²×C₄₃	—	2	2	no	—
385	C₄²×C₄₃	—	2	2	no	—
386	C₄²×C₄₃	—	2	1	no	—
387	C₄²×C₄₃	C₂×D₄	1	2	yes	—
388	C₄²×C₄₃	C₂×D₄	1	2	yes	—
389	C₄²×C₄₃	C₂⁴	1	2	yes	—
390	C₄²×C₄₃	C₂⁴	1	2	yes	—
391	C₂²⋊Dic₄₃	—	2	2	no	—
392	C₂²⋊Dic₄₃	—	2	1	no	—
393	C₂²⋊Dic₄₃	—	2	1	no	—
394	C₂²⋊Dic₄₃	—	2	2	no	—
395	C₂²⋊Dic₄₃	—	2	1	no	—
396	C₂²⋊Dic₄₃	—	2	1	no	—
397	C₄⋊Dic₄₃	—	2	1	no	—
398	C₄⋊Dic₄₃	—	2	1	no	—
399	C₄⋊Dic₄₃	—	2	1	no	—
400	C₄⋊Dic₄₃	—	2	1	no	—
401	C₄⋊Dic₄₃	—	2	2	no	—
402	C₄⋊Dic₄₃	—	2	2	no	—
403	C₄⋊Dic₄₃	—	2	2	no	—
404	C₄⋊Dic₄₃	—	2	2	no	—
405	C₄⋊Dic₄₃	C₂⁴	1	1	yes	characteristic
406	C₄⋊Dic₄₃	C₂⁴	1	1	yes	characteristic
407	C₄⋊Dic₄₃	C₂⁴	1	2	yes	—
408	C₄⋊Dic₄₃	C₂⁴	1	1	yes	characteristic
409	C₄⋊Dic₄₃	C₂⁴	1	1	yes	characteristic
410	C₄⋊Dic₄₃	C₂⁴	1	2	yes	—
411	Dic₄₃⋊C₄	—	2	2	no	—
412	Dic₄₃⋊C₄	—	2	2	no	—
413	Dic₄₃⋊C₄	—	2	2	no	—
414	Dic₄₃⋊C₄	—	2	2	no	—
415	Dic₄₃⋊C₄	—	2	2	no	—
416	Dic₄₃⋊C₄	—	2	2	no	—
417	Dic₄₃⋊C₄	—	2	2	no	—
418	Dic₄₃⋊C₄	—	2	2	no	—
419	C₄×Dic₄₃	—	2	2	no	—
420	C₄×Dic₄₃	—	2	1	no	—
421	C₄×Dic₄₃	—	2	1	no	—
422	C₄×Dic₄₃	—	2	2	no	—
423	C₄×Dic₄₃	—	2	1	no	—
424	C₄×Dic₄₃	—	2	1	no	—
425	#10621877	—	2	2	no	—
426	#10621877	—	2	2	no	—
427	C₂×C₄₃⋊C₈	—	2	2	no	—
428	C₂×C₄₃⋊C₈	—	2	2	no	—
429	C₂×C₄₃⋊C₈	C₂⁴	1	1	yes	characteristic
430	C₂×C₄₃⋊C₈	C₂⁴	1	1	yes	characteristic
431	C₂×C₄₃⋊C₈	C₂⁴	1	2	yes	—
432	C₂×C₄₃⋊C₈	C₂⁴	1	2	yes	—
433	C₂×C₄₃⋊C₈	C₂⁴	1	1	yes	characteristic
434	C₂×C₄₃⋊C₈	C₂⁴	1	1	yes	characteristic
435	C₂³×C₄₃	—	2	2	no	—
436	C₂³×C₄₃	—	2	1	no	—
437	C₂³×C₄₃	—	4	1	no	—
438	C₂³×C₄₃	—	4	1	no	—
439	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
440	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
441	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
442	Q₈×C₄₃	—	2	2	no	—
443	Q₈×C₄₃	—	2	2	no	—
444	Q₈×C₄₃	—	2	1	no	—
445	Q₈×C₄₃	—	2	1	no	—
446	Q₈×C₄₃	—	4	2	no	—
447	Q₈×C₄₃	—	8	2	no	—
448	D₄×C₄₃	—	2	1	no	—
449	D₄×C₄₃	—	2	1	no	—
450	D₄×C₄₃	—	4	2	no	—
451	D₄×C₄₃	—	4	2	no	—
452	D₄×C₄₃	—	8	1	no	—
453	C₂×C₄×C₄₃	—	2	2	no	—
454	C₂×C₄×C₄₃	—	2	2	no	—
455	C₂×C₄×C₄₃	—	2	2	no	—
456	C₂×C₄×C₄₃	—	2	1	no	—
457	C₂×C₄×C₄₃	—	2	1	no	—
458	C₂×C₄×C₄₃	—	2	1	no	—
459	C₂×C₄×C₄₃	—	2	1	no	—
460	C₂×C₄×C₄₃	—	2	1	no	—
461	C₂×C₄×C₄₃	—	2	1	no	—
462	C₂×C₄×C₄₃	—	2	2	no	—
463	C₂×C₄×C₄₃	—	2	1	no	—
464	C₂×C₄×C₄₃	—	2	2	no	—
465	C₂×C₄×C₄₃	—	4	2	no	—
466	C₂×C₄×C₄₃	—	4	2	no	—
467	C₂×C₄×C₄₃	—	4	2	no	—
468	C₂×C₄×C₄₃	—	4	2	no	—
469	C₂×C₄×C₄₃	—	8	2	no	—
470	C₂×C₄×C₄₃	—	8	1	no	—
471	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
472	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
473	C₂×C₄×C₄₃	C₂²×D₄	1	2	yes	—
474	C₂×C₄×C₄₃	C₂²×D₄	1	2	yes	—
475	C₂×C₄×C₄₃	C₂²×D₄	1	2	yes	—
476	C₂×C₄×C₄₃	C₂²×D₄	1	2	yes	—
477	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
478	C₂×C₄×C₄₃	2₋¹⁺⁴	1	2	yes	—
479	C₂×C₄×C₄₃	2₋¹⁺⁴	1	2	yes	—
480	C₂×C₄×C₄₃	C₂⁵	1	1	yes	characteristic
481	C₂×Dic₄₃	—	2	2	no	—
482	C₂×Dic₄₃	—	2	1	no	—
483	C₂×Dic₄₃	—	2	1	no	—
484	C₂×Dic₄₃	—	2	2	no	—
485	C₂×Dic₄₃	—	2	1	no	—
486	C₂×Dic₄₃	—	2	1	no	—
487	C₂×Dic₄₃	—	8	1	no	—
488	C₂×Dic₄₃	—	8	1	no	—
489	C₂×Dic₄₃	—	8	1	no	—
490	C₂×Dic₄₃	—	8	1	no	—
491	Dic₈₆	—	8	2	no	—
492	Dic₈₆	—	8	2	no	—
493	Dic₈₆	—	8	2	no	—
494	Dic₈₆	—	8	2	no	—
495	C₄₃⋊C₈	—	2	1	no	—
496	C₄₃⋊C₈	—	2	1	no	—
497	C₄₃⋊C₈	—	2	1	no	—
498	C₄₃⋊C₈	—	2	1	no	—
499	C₄₃⋊C₈	—	2	2	no	—
500	C₄₃⋊C₈	—	2	2	no	—
501	#60876	—	43	1	no	maximal, Sylow
502	C₂²×C₄₃	—	2	1	no	—
503	C₂²×C₄₃	—	2	1	no	—
504	C₂²×C₄₃	—	2	1	no	—
505	C₂²×C₄₃	—	2	1	no	—
506	C₂²×C₄₃	—	2	1	no	—
507	C₂²×C₄₃	—	2	1	no	—
508	C₂²×C₄₃	—	2	1	no	—
509	C₂²×C₄₃	—	2	1	no	—
510	C₂²×C₄₃	—	4	1	no	—
511	C₂²×C₄₃	—	4	1	no	—
512	C₂²×C₄₃	—	4	1	no	—
513	C₂²×C₄₃	—	8	2	no	—
514	C₂²×C₄₃	#536	1	2	yes	—
515	C₂²×C₄₃	C₂³×D₄	1	1	yes	characteristic
516	C₄×C₄₃	—	2	2	no	—
517	C₄×C₄₃	—	2	2	no	—
518	C₄×C₄₃	—	2	2	no	—
519	C₄×C₄₃	—	2	2	no	—
520	C₄×C₄₃	—	2	1	no	—
521	C₄×C₄₃	—	2	1	no	—
522	C₄×C₄₃	—	4	2	no	—
523	C₄×C₄₃	—	4	1	no	—
524	C₄×C₄₃	—	4	1	no	—
525	C₄×C₄₃	—	4	1	no	—
526	C₄×C₄₃	—	4	2	no	—
527	C₄×C₄₃	#536	1	2	yes	—
528	C₄×C₄₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
529	C₄×C₄₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
530	Dic₄₃	—	4	1	no	—
531	Dic₄₃	—	4	2	no	—
532	Dic₄₃	—	4	1	no	—
533	Dic₄₃	—	4	2	no	—
534	Dic₄₃	—	4	1	no	—
535	Dic₄₃	—	4	1	no	—
536	#3495	D₄₃	1	1	yes	characteristic
537	#3458	—	43	1	no	—
538	#3244	—	43	2	no	—
539	#3243	—	43	2	no	—
540	#3242	—	43	2	no	—
541	#3242	—	43	2	no	—
542	#3240	—	43	2	no	—
543	#3237	—	43	2	no	—
544	#3233	—	43	2	no	—
545	#3231	—	43	2	no	—
546	#3164	—	43	1	no	—
547	#3163	—	43	1	no	—
548	#3137	—	43	1	no	—
549	#3137	—	43	1	no	—
550	#3095	—	43	1	no	—
551	#3093	—	43	1	no	—
552	#3091	—	43	1	no	—
553	C₂×#485	—	43	1	no	—
554	#3084	—	43	1	no	—
555	#3083	—	43	1	no	—
556	#3082	—	43	1	no	—
557	#3082	—	43	1	no	—
558	#2924	—	43	1	no	—
559	C₂×C₄₃	—	2	2	no	—
560	C₂×C₄₃	—	4	1	no	—
561	C₂×C₄₃	—	4	1	no	—
562	C₂×C₄₃	—	8	1	no	—
563	C₂×C₄₃	C₂×#536	1	1	yes	characteristic
564	C₂×C₄₃	#3584	1	1	yes	characteristic
565	C₂×C₄₃	#3586	1	1	yes	characteristic
566	#556	—	2	1	no	—
567	#554	—	2	1	no	—
568	#552	—	2	2	no	—
569	#552	—	2	1	no	—
570	#552	—	2	1	no	—
571	#551	—	2	2	no	—
572	#544	—	43	1	no	—
573	#544	—	43	1	no	—
574	#544	—	43	1	no	—
575	#544	—	43	1	no	—
576	#544	—	43	2	no	—
577	#544	—	43	2	no	—
578	#544	—	86	1	no	—
579	#544	—	86	1	no	—
580	#544	C₂×D₄₃	1	1	yes	characteristic
581	#543	—	86	2	no	—
582	#542	C₂×D₄₃	1	2	yes	—
583	#541	C₂×D₄₃	1	2	yes	—
584	#536	C₂×D₄₃	1	1	yes	characteristic
585	#533	—	43	2	no	—
586	#533	—	43	2	no	—
587	#533	—	86	2	no	—
588	#533	—	86	1	no	—
589	#533	—	86	1	no	—
590	#533	C₂×D₄₃	1	2	yes	—
591	#529	C₂×D₄₃	1	2	yes	—
592	#525	C₂×D₄₃	1	1	yes	characteristic
593	C₂×C₂²⋊Q₈	C₂×D₄₃	1	1	yes	characteristic
594	#520	C₂×D₄₃	1	1	yes	characteristic
595	#519	C₂×D₄₃	1	1	yes	characteristic
596	C₂×#117	—	43	1	no	—
597	C₂×#117	—	43	1	no	—
598	C₂×#117	C₂×D₄₃	1	1	yes	characteristic
599	#501	—	43	2	no	—
600	#501	—	43	2	no	—
601	#501	—	43	2	no	—
602	#501	—	43	2	no	—
603	#500	—	43	2	no	—
604	#499	—	43	2	no	—
605	#499	—	43	2	no	—
606	#498	—	43	2	no	—
607	#491	—	43	2	no	—
608	#491	—	43	2	no	—
609	#489	—	43	2	no	—
610	#489	—	43	2	no	—
611	#488	—	43	2	no	—
612	#488	—	43	2	no	—
613	#487	—	43	2	no	—
614	#487	—	43	2	no	—
615	#485	—	43	2	no	—
616	#485	—	43	2	no	—
617	#485	—	43	2	no	—
618	#485	—	43	2	no	—
619	#485	—	43	1	no	—
620	#485	—	43	1	no	—
621	#485	—	43	2	no	—
622	#485	—	43	2	no	—
623	#485	—	43	2	no	—
624	#485	—	43	2	no	—
625	#484	—	43	1	no	—
626	#484	—	43	2	no	—
627	#483	—	43	1	no	—
628	#483	—	43	2	no	—
629	#482	—	43	1	no	—
630	#482	—	43	1	no	—
631	#482	—	43	2	no	—
632	#482	—	43	2	no	—
633	#481	—	43	1	no	—
634	#480	—	43	1	no	—
635	#479	—	43	2	no	—
636	#479	—	43	2	no	—
637	#479	—	43	2	no	—
638	#479	—	43	2	no	—
639	#479	—	43	2	no	—
640	#479	—	43	2	no	—
641	#478	—	43	2	no	—
642	#478	—	43	2	no	—
643	#477	—	43	2	no	—
644	#477	—	43	2	no	—
645	#477	—	43	2	no	—
646	#476	—	43	2	no	—
647	#475	—	43	2	no	—
648	#475	—	43	2	no	—
649	#475	—	43	2	no	—
650	#474	—	43	2	no	—
651	#433	—	43	2	no	—
652	#433	—	43	2	no	—
653	#432	—	43	2	no	—
654	#431	—	43	2	no	—
655	#428	—	43	1	no	—
656	#428	—	43	1	no	—
657	#428	—	43	1	no	—
658	#428	—	43	1	no	—
659	#427	—	43	1	no	—
660	#427	—	43	1	no	—
661	C₂×#107	—	43	1	no	—
662	C₂×#106	—	43	1	no	—
663	#424	—	43	1	no	—
664	#424	—	43	1	no	—
665	#419	—	43	1	no	—
666	#419	—	43	1	no	—
667	#417	—	43	1	no	—
668	#417	—	43	1	no	—
669	#416	—	43	1	no	—
670	#416	—	43	1	no	—
671	C₂×#103	—	43	1	no	—
672	C₂×#103	—	43	1	no	—
673	#407	—	43	1	no	—
674	C₂×C₂²⋊C₈	—	43	1	no	—
675	#405	—	43	1	no	—
676	#405	—	43	1	no	—
677	C₄₃	#60876	1	1	yes	characteristic, complemented, Sylow
678	C₂×#41	C₂²×D₄₃	1	1	yes	characteristic
679	C₂²×Q₈	C₂²×D₄₃	1	1	yes	characteristic
680	C₂³×C₄	C₂²×D₄₃	1	1	yes	characteristic
681	C₂×M₁₆	—	43	1	no	—
682	C₂×M₁₆	—	43	1	no	—
683	C₂²×C₈	—	43	1	no	—
684	C₂²×C₈	—	43	1	no	—
685	C₄⋊Q₈	—	2	1	no	—
686	C₄⋊Q₈	—	43	2	no	—
687	C₄⋊Q₈	—	43	2	no	—
688	C₄⋊Q₈	—	43	2	no	—
689	C₄⋊Q₈	—	43	2	no	—
690	C₄⋊Q₈	—	86	1	no	—
691	C₄⋊Q₈	—	86	1	no	—
692	C₄⋊Q₈	—	86	1	no	—
693	C₄⋊Q₈	—	86	2	no	—
694	C₄⋊Q₈	—	86	1	no	—
695	C₄⋊Q₈	—	86	2	no	—
696	C₄⋊Q₈	C₂²×D₄₃	1	2	yes	—
697	C₄⋊Q₈	C₂²×D₄₃	1	2	yes	—
698	#126	—	2	2	no	—
699	#126	—	2	2	no	—
700	#126	—	2	2	no	—
701	#126	—	2	2	no	—
702	#125	—	2	2	no	—
703	#125	—	2	2	no	—
704	#125	—	2	1	no	—
705	#125	—	2	2	no	—
706	#125	—	43	2	no	—
707	#125	—	43	2	no	—
708	#125	—	43	2	no	—
709	#125	—	43	2	no	—
710	#125	—	86	1	no	—
711	#125	—	86	1	no	—
712	#125	—	86	1	no	—
713	#125	—	86	2	no	—
714	#125	—	86	1	no	—
715	#125	—	86	2	no	—
716	#125	C₂²×D₄₃	1	2	yes	—
717	#124	—	2	2	no	—
718	#124	C₂²×D₄₃	1	2	yes	—
719	#123	—	2	1	no	—
720	#123	—	2	2	no	—
721	#123	—	2	2	no	—
722	#123	—	2	2	no	—
723	C₂²⋊Q₈	—	2	1	no	—
724	C₂²⋊Q₈	—	2	1	no	—
725	C₂²⋊Q₈	—	2	2	no	—
726	C₂²⋊Q₈	—	2	1	no	—
727	C₂²⋊Q₈	—	2	1	no	—
728	C₂²⋊Q₈	—	2	2	no	—
729	C₂²⋊Q₈	—	2	2	no	—
730	C₂²⋊Q₈	—	86	2	no	—
731	C₂²⋊Q₈	—	86	2	no	—
732	C₂²⋊Q₈	—	86	2	no	—
733	C₂²⋊Q₈	—	86	2	no	—
734	C₂²⋊Q₈	—	86	2	no	—
735	C₂²⋊Q₈	—	86	2	no	—
736	C₂²⋊Q₈	—	86	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	C₂²×D₄₃	1	2	yes	—
743	C₂²⋊Q₈	C₂²×D₄₃	1	2	yes	—
744	C₂²⋊Q₈	C₂²×D₄₃	1	1	yes	characteristic
745	C₂²⋊Q₈	C₂²×D₄₃	1	1	yes	characteristic
746	#121	C₂²×D₄₃	1	1	yes	characteristic
747	#121	C₂²×D₄₃	1	1	yes	characteristic
748	#120	—	2	1	no	—
749	C₄×Q₈	—	2	1	no	—
750	C₄×Q₈	—	2	1	no	—
751	C₄×Q₈	—	2	2	no	—
752	C₄×Q₈	—	86	2	no	—
753	C₄×Q₈	—	86	2	no	—
754	C₄×Q₈	—	86	2	no	—
755	C₄×Q₈	—	86	2	no	—
756	C₄×Q₈	C₂²×D₄₃	1	2	yes	—
757	C₄×Q₈	C₂²×D₄₃	1	2	yes	—
758	C₄×Q₈	C₂²×D₄₃	1	2	yes	—
759	C₄×D₄	—	2	1	no	—
760	C₄×D₄	—	2	1	no	—
761	C₄×D₄	—	2	2	no	—
762	C₄×D₄	—	2	2	no	—
763	C₄×D₄	C₂²×D₄₃	1	2	yes	—
764	#117	—	2	2	no	—
765	#117	—	2	1	no	—
766	#117	—	2	2	no	—
767	#117	—	2	2	no	—
768	#117	—	43	2	no	—
769	#117	—	43	1	no	—
770	#117	—	43	1	no	—
771	#117	—	43	1	no	—
772	#117	—	43	1	no	—
773	#117	—	43	2	no	—
774	#117	—	86	1	no	—
775	#117	—	86	1	no	—
776	#117	—	86	1	no	—
777	#117	—	86	1	no	—
778	#117	C₂²⋊D₄₃	1	1	yes	characteristic
779	#117	C₂²⋊D₄₃	1	2	yes	—
780	#117	C₂²⋊D₄₃	1	1	yes	characteristic
781	#117	C₂²×D₄₃	1	1	yes	characteristic
782	#117	C₂²×D₄₃	1	1	yes	characteristic
783	#117	C₂²×D₄₃	1	1	yes	characteristic
784	#117	C₂²×D₄₃	1	2	yes	—
785	C₂×C₄⋊C₄	—	2	1	no	—
786	C₂×C₄⋊C₄	—	2	1	no	—
787	C₂×C₄⋊C₄	—	43	1	no	—
788	C₂×C₄⋊C₄	—	43	1	no	—
789	C₂×C₄⋊C₄	—	43	1	no	—
790	C₂×C₄⋊C₄	—	43	1	no	—
791	C₂×C₄⋊C₄	C₂²⋊D₄₃	1	1	yes	characteristic
792	C₂×C₄⋊C₄	C₂²⋊D₄₃	1	1	yes	characteristic
793	C₂×C₄⋊C₄	C₂²×D₄₃	1	1	yes	characteristic
794	C₂×C₂²⋊C₄	—	2	1	no	—
795	C₂×C₂²⋊C₄	—	86	1	no	—
796	C₂×C₂²⋊C₄	—	86	1	no	—
797	C₂×C₂²⋊C₄	C₂²⋊D₄₃	1	2	yes	—
798	C₂×C₄²	—	86	1	no	—
799	C₂×C₄²	—	86	1	no	—
800	C₂×C₄²	C₂²×D₄₃	1	2	yes	—
801	#107	—	43	2	no	—
802	#107	—	43	2	no	—
803	#107	—	43	1	no	—
804	#107	—	43	1	no	—
805	#107	—	43	1	no	—
806	#107	—	43	1	no	—
807	#107	—	43	2	no	—
808	#107	—	43	2	no	—
809	#107	—	43	2	no	—
810	#107	—	43	2	no	—
811	#106	—	43	2	no	—
812	#106	—	43	2	no	—
813	#106	—	43	1	no	—
814	#106	—	43	1	no	—
815	#106	—	43	1	no	—
816	#106	—	43	1	no	—
817	#106	—	43	2	no	—
818	#106	—	43	2	no	—
819	#106	—	43	2	no	—
820	#106	—	43	2	no	—
821	C₄⋊C₈	—	43	2	no	—
822	C₄⋊C₈	—	43	2	no	—
823	C₄⋊C₈	—	43	2	no	—
824	C₄⋊C₈	—	43	2	no	—
825	#103	—	43	2	no	—
826	#103	—	43	2	no	—
827	#103	—	43	2	no	—
828	#103	—	43	2	no	—
829	#103	—	43	1	no	—
830	#103	—	43	1	no	—
831	#103	—	43	1	no	—
832	#103	—	43	1	no	—
833	#103	—	43	2	no	—
834	#103	—	43	2	no	—
835	#103	—	43	2	no	—
836	#103	—	43	2	no	—
837	#103	—	43	2	no	—
838	#103	—	43	2	no	—
839	#102	—	43	1	no	—
840	#102	—	43	1	no	—
841	#102	—	43	1	no	—
842	#102	—	43	1	no	—
843	#102	—	43	2	no	—
844	#102	—	43	2	no	—
845	C₂²⋊C₈	—	43	1	no	—
846	C₂²⋊C₈	—	43	1	no	—
847	C₂²⋊C₈	—	43	1	no	—
848	C₂²⋊C₈	—	43	1	no	—
849	C₂²⋊C₈	—	43	2	no	—
850	C₂²⋊C₈	—	43	2	no	—
851	#97	—	43	2	no	—
852	#97	—	43	2	no	—
853	C₄×C₈	—	43	2	no	—
854	C₄×C₈	—	43	2	no	—
855	C₂⁴	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
856	#41	—	2	2	no	—
857	#41	—	2	2	no	—
858	C₂×Q₈	—	2	1	no	—
859	C₂×Q₈	—	2	2	no	—
860	C₂×Q₈	—	2	2	no	—
861	C₂×Q₈	—	2	2	no	—
862	C₂×Q₈	—	86	2	no	—
863	C₂×Q₈	—	86	2	no	—
864	C₂×Q₈	—	86	2	no	—
865	C₂×Q₈	—	86	2	no	—
866	C₂×Q₈	C₂³×D₄₃	1	2	yes	—
867	C₂×Q₈	C₂³×D₄₃	1	1	yes	characteristic
868	C₂×D₄	—	2	1	no	—
869	C₂×D₄	—	2	1	no	—
870	C₂×D₄	—	2	1	no	—
871	C₂×D₄	C₂³×D₄₃	1	1	yes	characteristic
872	C₂²×C₄	—	2	2	no	—
873	C₂²×C₄	—	2	2	no	—
874	C₂²×C₄	—	2	1	no	—
875	C₂²×C₄	—	2	1	no	—
876	C₂²×C₄	—	2	1	no	—
877	C₂²×C₄	—	2	2	no	—
878	C₂²×C₄	—	86	1	no	—
879	C₂²×C₄	—	86	1	no	—
880	C₂²×C₄	—	86	1	no	—
881	C₂²×C₄	—	86	1	no	—
882	C₂²×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
883	C₂²×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
884	C₂²×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
885	C₂²×C₄	C₂×C₂²⋊D₄₃	1	2	yes	—
886	C₂²×C₄	C₂×C₂²⋊D₄₃	1	2	yes	—
887	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
888	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
889	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
890	M₁₆	—	86	2	no	—
891	M₁₆	—	86	2	no	—
892	C₂×C₈	—	43	1	no	—
893	C₂×C₈	—	43	1	no	—
894	C₂×C₈	—	43	2	no	—
895	C₂×C₈	—	43	2	no	—
896	C₂×C₈	—	43	1	no	—
897	C₂×C₈	—	43	1	no	—
898	C₂×C₈	—	86	2	no	—
899	C₂×C₈	—	86	2	no	—
900	C₄⋊C₄	—	2	1	no	—
901	C₄⋊C₄	—	2	2	no	—
902	C₄⋊C₄	—	2	2	no	—
903	C₄⋊C₄	—	2	2	no	—
904	C₄⋊C₄	—	2	2	no	—
905	C₄⋊C₄	—	2	2	no	—
906	C₄⋊C₄	—	2	2	no	—
907	C₄⋊C₄	—	2	2	no	—
908	C₄⋊C₄	—	2	2	no	—
909	C₄⋊C₄	—	2	1	no	—
910	C₄⋊C₄	—	2	2	no	—
911	C₄⋊C₄	—	2	1	no	—
912	C₄⋊C₄	—	2	2	no	—
913	C₄⋊C₄	—	43	1	no	—
914	C₄⋊C₄	—	43	1	no	—
915	C₄⋊C₄	—	43	2	no	—
916	C₄⋊C₄	—	43	1	no	—
917	C₄⋊C₄	—	43	1	no	—
918	C₄⋊C₄	—	43	2	no	—
919	C₄⋊C₄	—	86	1	no	—
920	C₄⋊C₄	—	86	1	no	—
921	C₄⋊C₄	—	86	1	no	—
922	C₄⋊C₄	—	86	1	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	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
936	C₄⋊C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
937	C₄⋊C₄	C₂×C₂²⋊D₄₃	1	2	yes	—
938	C₄⋊C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
939	C₄⋊C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
940	C₄⋊C₄	C₂×C₂²⋊D₄₃	1	2	yes	—
941	C₄⋊C₄	C₂³×D₄₃	1	2	yes	—
942	C₄⋊C₄	C₂³×D₄₃	1	1	yes	characteristic
943	C₄⋊C₄	C₂³×D₄₃	1	1	yes	characteristic
944	C₂²⋊C₄	—	2	2	no	—
945	C₂²⋊C₄	—	2	2	no	—
946	C₂²⋊C₄	—	2	1	no	—
947	C₂²⋊C₄	—	2	1	no	—
948	C₂²⋊C₄	—	2	1	no	—
949	C₂²⋊C₄	—	2	1	no	—
950	C₂²⋊C₄	—	2	2	no	—
951	C₂²⋊C₄	—	2	2	no	—
952	C₂²⋊C₄	—	2	1	no	—
953	C₂²⋊C₄	—	2	2	no	—
954	C₂²⋊C₄	—	86	2	no	—
955	C₂²⋊C₄	—	86	1	no	—
956	C₂²⋊C₄	—	86	1	no	—
957	C₂²⋊C₄	—	86	2	no	—
958	C₂²⋊C₄	—	86	1	no	—
959	C₂²⋊C₄	—	86	1	no	—
960	C₂²⋊C₄	C₂×C₂²⋊D₄₃	1	2	yes	—
961	C₂²⋊C₄	C₂×C₂²⋊D₄₃	1	2	yes	—
962	C₂²⋊C₄	C₂×C₂²⋊D₄₃	1	2	yes	—
963	C₂²⋊C₄	C₂×C₂²⋊D₄₃	1	2	yes	—
964	C₄²	—	2	2	no	—
965	C₄²	—	2	2	no	—
966	C₄²	—	2	2	no	—
967	C₄²	—	2	1	no	—
968	C₄²	—	86	2	no	—
969	C₄²	—	86	1	no	—
970	C₄²	—	86	1	no	—
971	C₄²	—	86	2	no	—
972	C₄²	—	86	1	no	—
973	C₄²	—	86	1	no	—
974	C₄²	C₂×C₂²⋊D₄₃	1	2	yes	—
975	C₄²	C₂×C₂²⋊D₄₃	1	2	yes	—
976	C₄²	C₂³×D₄₃	1	2	yes	—
977	C₄²	C₂³×D₄₃	1	2	yes	—
978	C₂³	—	2	2	no	—
979	C₂³	—	2	1	no	—
980	C₂³	—	4	1	no	—
981	C₂³	—	4	1	no	—
982	C₂³	C₂²×C₂²⋊D₄₃	1	1	yes	characteristic
983	C₂³	C₂²×C₂²⋊D₄₃	1	1	yes	characteristic
984	C₂³	C₂²×C₂²⋊D₄₃	1	1	yes	characteristic
985	Q₈	—	2	2	no	—
986	Q₈	—	2	2	no	—
987	Q₈	—	2	1	no	—
988	Q₈	—	2	1	no	—
989	Q₈	—	4	2	no	—
990	Q₈	—	8	2	no	—
991	Q₈	—	344	2	no	—
992	Q₈	—	344	2	no	—
993	Q₈	—	344	2	no	—
994	Q₈	—	344	2	no	—
995	D₄	—	2	1	no	—
996	D₄	—	2	1	no	—
997	D₄	—	4	2	no	—
998	D₄	—	4	2	no	—
999	D₄	—	8	1	no	—
1000	C₂×C₄	—	2	2	no	—
1001	C₂×C₄	—	2	2	no	—
1002	C₂×C₄	—	2	2	no	—
1003	C₂×C₄	—	2	1	no	—
1004	C₂×C₄	—	2	1	no	—
1005	C₂×C₄	—	2	1	no	—
1006	C₂×C₄	—	2	1	no	—
1007	C₂×C₄	—	2	1	no	—
1008	C₂×C₄	—	2	1	no	—
1009	C₂×C₄	—	2	2	no	—
1010	C₂×C₄	—	2	1	no	—
1011	C₂×C₄	—	2	2	no	—
1012	C₂×C₄	—	4	2	no	—
1013	C₂×C₄	—	4	2	no	—
1014	C₂×C₄	—	4	2	no	—
1015	C₂×C₄	—	4	2	no	—
1016	C₂×C₄	—	8	2	no	—
1017	C₂×C₄	—	8	1	no	—
1018	C₂×C₄	—	86	2	no	—
1019	C₂×C₄	—	86	1	no	—
1020	C₂×C₄	—	86	1	no	—
1021	C₂×C₄	—	86	2	no	—
1022	C₂×C₄	—	86	1	no	—
1023	C₂×C₄	—	86	1	no	—
1024	C₂×C₄	—	344	1	no	—
1025	C₂×C₄	—	344	1	no	—
1026	C₂×C₄	—	344	1	no	—
1027	C₂×C₄	—	344	1	no	—
1028	C₂×C₄	C₂²×C₂²⋊D₄₃	1	2	yes	—
1029	C₂×C₄	C₂²×C₂²⋊D₄₃	1	2	yes	—
1030	C₂×C₄	C₂²×C₂²⋊D₄₃	1	1	yes	characteristic
1031	C₂×C₄	C₂²×C₂²⋊D₄₃	1	1	yes	characteristic
1032	C₂×C₄	C₂²×C₂²⋊D₄₃	1	2	yes	—
1033	C₂×C₄	C₂²×C₂²⋊D₄₃	1	2	yes	—
1034	C₂×C₄	C₂²×C₂²⋊D₄₃	1	1	yes	characteristic
1035	C₂×C₄	#13063372	1	2	yes	—
1036	C₂×C₄	#13063372	1	2	yes	—
1037	C₂×C₄	C₂⁴×D₄₃	1	1	yes	characteristic
1038	C₈	—	86	1	no	—
1039	C₈	—	86	1	no	—
1040	C₈	—	86	1	no	—
1041	C₈	—	86	1	no	—
1042	C₈	—	86	2	no	—
1043	C₈	—	86	2	no	—
1044	C₂²	—	2	1	no	—
1045	C₂²	—	2	1	no	—
1046	C₂²	—	2	1	no	—
1047	C₂²	—	2	1	no	—
1048	C₂²	—	2	1	no	—
1049	C₂²	—	2	1	no	—
1050	C₂²	—	2	1	no	—
1051	C₂²	—	2	1	no	—
1052	C₂²	—	4	1	no	—
1053	C₂²	—	4	1	no	—
1054	C₂²	—	4	1	no	—
1055	C₂²	—	8	2	no	—
1056	C₂²	#14583470	1	2	yes	—
1057	C₂²	C₂³×C₂²⋊D₄₃	1	1	yes	characteristic
1058	C₄	—	2	2	no	—
1059	C₄	—	2	2	no	—
1060	C₄	—	2	2	no	—
1061	C₄	—	2	2	no	—
1062	C₄	—	2	1	no	—
1063	C₄	—	2	1	no	—
1064	C₄	—	4	2	no	—
1065	C₄	—	4	1	no	—
1066	C₄	—	4	1	no	—
1067	C₄	—	4	1	no	—
1068	C₄	—	4	2	no	—
1069	C₄	—	172	2	no	—
1070	C₄	—	172	1	no	—
1071	C₄	—	172	1	no	—
1072	C₄	—	172	2	no	—
1073	C₄	—	172	1	no	—
1074	C₄	—	172	1	no	—
1075	C₄	#14583470	1	2	yes	—
1076	C₄	C₂×#13063372	1	1	yes	characteristic
1077	C₄	C₂×#13063372	1	1	yes	characteristic
1078	C₂	—	2	2	no	—
1079	C₂	—	4	1	no	—
1080	C₂	—	4	1	no	—
1081	C₂	—	8	1	no	—
1082	C₂	C₂×#14583470	1	1	yes	characteristic
1083	C₂	#19149366	1	1	yes	characteristic
1084	C₂	#19149382	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×#3495	C₂
socle	C₂²×C₄₃	C₂³×D₄
prime radical	C₄₃×#525	C₂²
hypercenter	#3495	D₄₃
hypocenter	C₄₃	#60876
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₂×#117 ◁ #3495

Complements

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

N	H ≅ G/N	type
1. #19148000	C₂	semidirect
2. #19145887	C₂	semidirect
3. #19145872	C₂	semidirect
4. #19145857	C₂	semidirect
5. #19145857	C₂	semidirect
6. #19145831	C₂	semidirect
7. #19145805	C₂	semidirect
8. #19145770	C₂	semidirect
9. #19145750	C₂	semidirect
10. #19145129	C₂	semidirect
11. #19145121	C₂	semidirect
12. #19144960	C₂	semidirect
13. #19144960	C₂	semidirect
14. #19144539	C₂	semidirect
17. C₂×#14583237	C₂	semidirect
18. #19144457	C₂	semidirect
19. #19144446	C₂	semidirect
20. #19144437	C₂	semidirect
21. #19144437	C₂	semidirect
22. #19143253	C₂	semidirect
40. #14583309	C₂²	semidirect
41. #14583309	C₂²	semidirect
42. #14583305	C₂²	semidirect
43. #14583305	C₂²	semidirect
44. #14583302	C₂²	semidirect
45. #14583298	C₂²	semidirect
46. #14583298	C₂²	semidirect
47. #14583295	C₂²	semidirect
48. #14583267	C₂²	semidirect
49. #14583267	C₂²	semidirect
50. #14583258	C₂²	semidirect
51. #14583258	C₂²	semidirect
52. #14583253	C₂²	semidirect
53. #14583253	C₂²	semidirect
54. #14583249	C₂²	semidirect
55. #14583249	C₂²	semidirect
76. #14583206	C₂²	semidirect
77. #14583206	C₂²	semidirect
78. #14583206	C₂²	semidirect
79. #14583206	C₂²	semidirect
80. #14583206	C₂²	semidirect
81. #14583206	C₂²	semidirect
82. #14583199	C₂²	semidirect
83. #14583199	C₂²	semidirect
84. #14583194	C₂²	semidirect
85. #14583194	C₂²	semidirect
86. #14583194	C₂²	semidirect
87. #14583189	C₂²	semidirect
88. #14583184	C₂²	semidirect
89. #14583184	C₂²	semidirect
90. #14583184	C₂²	semidirect
91. #14583179	C₂²	semidirect
677. C₄₃	#60876	semidirect

Maximal subgroups

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

subgroup	index
#19148000	2
#19145887	2
#19145872	2
#19145857	2
#19145831	2
#19145805	2
#19145770	2
#19145750	2
#19145129	2
#19145121	2
#19144960	2
#19144539	2
#19144524	2
#19144504	2
C₂×#14583237	2
#19144457	2
#19144446	2
#19144437	2
#19143253	2
C₄₃×#3495	2
#60876	43