Subgroups — #25969049

Order 11008.

1700 conjugacy classes of subgroups.

The subgroup lattice has 1114 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	#19145842	C₂	1	2	yes	maximal, complemented
5	#19145842	C₂	1	2	yes	maximal, complemented
6	#19145831	C₂	1	2	yes	maximal, complemented
7	#19145789	C₂	1	2	yes	maximal, complemented
8	#19145770	C₂	1	2	yes	maximal, complemented
9	#19145727	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	#19144949	C₂	1	1	yes	maximal, characteristic, complemented
13	#19144949	C₂	1	1	yes	maximal, characteristic, complemented
14	#19144531	C₂	1	1	yes	maximal, characteristic, complemented
15	#19144524	C₂	1	1	yes	maximal, characteristic, complemented
16	#19144504	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂×#14583220	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	#19144426	C₂	1	1	yes	maximal, characteristic, complemented
21	#19144426	C₂	1	1	yes	maximal, characteristic, complemented
22	#19143253	C₂	1	1	yes	maximal, characteristic, complemented
23	C₄₃×#3494	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	1	yes	characteristic
30	#14583527	C₂²	1	2	yes	complemented
31	#14583527	C₂²	1	2	yes	complemented
32	#14583525	—	2	2	no	—
33	#14583456	C₂²	1	2	yes	complemented
34	#14583456	C₂²	1	2	yes	complemented
35	#14583452	—	2	2	no	—
36	#14583452	—	2	1	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	#14583263	C₂²	1	2	yes	complemented
49	#14583263	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	#14583245	C₂²	1	2	yes	complemented
55	#14583245	C₂²	1	2	yes	complemented
56	#14583237	C₂²	1	1	yes	characteristic, complemented
57	#14583237	C₂²	1	2	yes	complemented
58	#14583237	C₂²	1	1	yes	characteristic, complemented
59	#14583237	C₂²	1	2	yes	complemented
60	#14583232	C₂²	1	1	yes	characteristic, complemented
61	#14583227	C₂²	1	1	yes	characteristic, complemented
62	#14583220	C₂²	1	2	yes	—
63	#14583220	C₂²	1	2	yes	—
64	#14583220	C₂²	1	2	yes	—
65	#14583220	C₂²	1	2	yes	—
66	#14583220	C₂²	1	2	yes	—
67	#14583220	C₂²	1	2	yes	—
68	#14583220	C₂²	1	1	yes	characteristic, complemented
69	#14583220	C₂²	1	1	yes	characteristic, complemented
70	#14583220	C₂²	1	2	yes	complemented
71	#14583220	C₂²	1	2	yes	complemented
72	#14583215	C₂²	1	2	yes	—
73	#14583215	C₂²	1	1	yes	characteristic, complemented
74	#14583210	C₂²	1	2	yes	—
75	#14583210	C₂²	1	1	yes	characteristic, complemented
76	#14583206	C₂²	1	2	yes	complemented
77	#14583206	C₂²	1	2	yes	complemented
78	#14583199	C₂²	1	2	yes	complemented
79	#14583199	C₂²	1	2	yes	complemented
80	#14583199	C₂²	1	2	yes	complemented
81	#14583199	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	#14583189	C₂²	1	2	yes	complemented
86	#14583189	C₂²	1	2	yes	complemented
87	#14583189	C₂²	1	2	yes	complemented
88	#14583184	C₂²	1	2	yes	complemented
89	#14583179	C₂²	1	2	yes	complemented
90	#14583179	C₂²	1	2	yes	complemented
91	#14583179	C₂²	1	2	yes	complemented
92	#14582960	C₂²	1	2	yes	complemented
93	#14582960	C₂²	1	2	yes	complemented
94	#14582956	C₂²	1	2	yes	complemented
95	#14582952	C₂²	1	2	yes	complemented
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	#14582904	C₂²	1	1	yes	characteristic
107	#14582904	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×#13063246	C₂²	1	1	yes	characteristic
113	C₂×#13063246	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×#555	—	2	1	no	—
119	C₄₃×#553	—	2	1	no	—
120	C₄₃×#553	—	2	1	no	—
121	C₄₃×#551	—	2	2	no	—
122	C₄₃×#547	—	2	1	no	—
123	C₄₃×#546	—	2	2	no	—
124	C₄₃×#544	C₂²	1	1	yes	characteristic
125	C₄₃×#542	C₂²	1	2	yes	—
126	C₄₃×#540	C₂²	1	2	yes	—
127	C₄₃×#535	C₂²	1	1	yes	characteristic
128	C₄₃×#532	C₂²	1	2	yes	—
129	C₄₃×#529	C₂²	1	2	yes	—
130	C₄₃×#525	C₂²	1	1	yes	characteristic
131	C₂×#121×C₄₃	C₂²	1	1	yes	characteristic
132	C₄₃×#520	C₂²	1	1	yes	characteristic
133	C₄₃×#518	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	1	no	—
147	#13063324	—	2	2	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	1	no	—
157	#13063316	—	2	2	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	1	yes	characteristic
218	#13063249	C₂³	1	1	yes	characteristic
219	#13063249	C₂³	1	1	yes	characteristic
220	#13063249	C₂³	1	1	yes	characteristic
221	#13063249	C₂³	1	2	yes	—
222	#13063249	C₂³	1	2	yes	—
223	#13063246	C₂³	1	2	yes	—
224	#13063246	C₂³	1	2	yes	—
225	#13063246	C₂³	1	2	yes	—
226	#13063246	C₂³	1	2	yes	—
227	#13063246	C₂³	1	1	yes	characteristic
228	#13063246	C₂³	1	1	yes	characteristic
229	#13063246	C₂³	1	1	yes	characteristic
230	#13063246	C₂³	1	1	yes	characteristic
231	#13063246	C₂³	1	2	yes	—
232	#13063246	C₂³	1	2	yes	—
233	#13063246	C₂³	1	2	yes	—
234	#13063246	C₂³	1	2	yes	—
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	—	2	2	no	—
248	C₂×#41×C₄₃	C₂³	1	1	yes	characteristic
249	C₂²×D₄×C₄₃	—	2	1	no	—
250	C₂²×D₄×C₄₃	C₂³	1	1	yes	characteristic
251	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
252	C₄⋊Q₈×C₄₃	—	2	1	no	—
253	C₄⋊Q₈×C₄₃	C₂³	1	2	yes	—
254	#127×C₄₃	C₂³	1	2	yes	—
255	#126×C₄₃	—	2	2	no	—
256	#126×C₄₃	—	2	2	no	—
257	#125×C₄₃	—	2	1	no	—
258	#125×C₄₃	C₂³	1	2	yes	—
259	#124×C₄₃	—	2	2	no	—
260	#124×C₄₃	—	2	2	no	—
261	#124×C₄₃	C₂³	1	2	yes	—
262	#123×C₄₃	—	2	1	no	—
263	#123×C₄₃	—	2	2	no	—
264	#123×C₄₃	—	2	2	no	—
265	#123×C₄₃	—	2	2	no	—
266	#123×C₄₃	—	2	2	no	—
267	C₂²⋊Q₈×C₄₃	—	2	2	no	—
268	C₂²⋊Q₈×C₄₃	—	2	2	no	—
269	C₂²⋊Q₈×C₄₃	C₂³	1	1	yes	characteristic
270	C₂²⋊Q₈×C₄₃	C₂³	1	1	yes	characteristic
271	#121×C₄₃	—	2	1	no	—
272	#121×C₄₃	—	2	1	no	—
273	#121×C₄₃	—	2	2	no	—
274	#121×C₄₃	—	2	1	no	—
275	#121×C₄₃	—	2	1	no	—
276	#121×C₄₃	—	2	2	no	—
277	#121×C₄₃	—	2	2	no	—
278	#121×C₄₃	C₂³	1	2	yes	—
279	#121×C₄₃	C₂³	1	2	yes	—
280	#121×C₄₃	C₂³	1	1	yes	characteristic
281	#121×C₄₃	C₂³	1	1	yes	characteristic
282	#120×C₄₃	—	2	1	no	—
283	#120×C₄₃	—	2	2	no	—
284	C₄×Q₈×C₄₃	C₂³	1	2	yes	—
285	C₄×D₄×C₄₃	—	2	1	no	—
286	C₄×D₄×C₄₃	—	2	1	no	—
287	C₄×D₄×C₄₃	—	2	2	no	—
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	C₄×D₄×C₄₃	C₂³	1	2	yes	—
294	C₄×D₄×C₄₃	C₂³	1	2	yes	—
295	#117×C₄₃	—	2	1	no	—
296	#117×C₄₃	—	2	2	no	—
297	#117×C₄₃	D₄	1	2	yes	—
298	#117×C₄₃	D₄	1	1	yes	characteristic
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	D₄	1	1	yes	characteristic
306	C₂×C₄⋊C₄×C₄₃	D₄	1	1	yes	characteristic
307	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
308	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
309	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
310	C₂×C₂²⋊C₄×C₄₃	D₄	1	2	yes	—
311	C₂×C₄²×C₄₃	C₂³	1	2	yes	—
312	C₂⁴×C₄₃	—	2	1	no	—
313	C₂⁴×C₄₃	C₂×D₄	1	1	yes	characteristic
314	#41×C₄₃	—	2	2	no	—
315	#41×C₄₃	—	2	2	no	—
316	#41×C₄₃	—	8	4	no	—
317	C₂×Q₈×C₄₃	—	2	2	no	—
318	C₂×Q₈×C₄₃	C₂⁴	1	1	yes	characteristic
319	C₂×D₄×C₄₃	—	2	1	no	—
320	C₂×D₄×C₄₃	—	2	2	no	—
321	C₂×D₄×C₄₃	—	2	2	no	—
322	C₂×D₄×C₄₃	—	2	1	no	—
323	C₂×D₄×C₄₃	—	2	1	no	—
324	C₂×D₄×C₄₃	—	2	2	no	—
325	C₂×D₄×C₄₃	—	2	1	no	—
326	C₂×D₄×C₄₃	—	2	2	no	—
327	C₂×D₄×C₄₃	—	2	2	no	—
328	C₂×D₄×C₄₃	—	2	2	no	—
329	C₂×D₄×C₄₃	—	8	2	no	—
330	C₂×D₄×C₄₃	C₂⁴	1	2	yes	—
331	C₂×D₄×C₄₃	C₂⁴	1	1	yes	characteristic
332	C₂²×C₄×C₄₃	—	2	2	no	—
333	C₂²×C₄×C₄₃	—	2	2	no	—
334	C₂²×C₄×C₄₃	—	2	1	no	—
335	C₂²×C₄×C₄₃	—	2	2	no	—
336	C₂²×C₄×C₄₃	—	2	2	no	—
337	C₂²×C₄×C₄₃	—	2	2	no	—
338	C₂²×C₄×C₄₃	—	2	1	no	—
339	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
340	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
341	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
342	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
343	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
344	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
345	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
346	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
347	C₂²×Dic₄₃	—	2	1	no	—
348	C₂²×Dic₄₃	—	2	1	no	—
349	C₂²×Dic₄₃	—	2	1	no	—
350	C₂²×Dic₄₃	—	2	1	no	—
351	C₂×Dic₈₆	—	2	2	no	—
352	C₂×Dic₈₆	—	2	2	no	—
353	C₂×Dic₈₆	—	2	2	no	—
354	C₂×Dic₈₆	—	2	2	no	—
355	C₄⋊C₄×C₄₃	—	2	1	no	—
356	C₄⋊C₄×C₄₃	—	2	2	no	—
357	C₄⋊C₄×C₄₃	—	2	1	no	—
358	C₄⋊C₄×C₄₃	—	2	2	no	—
359	C₄⋊C₄×C₄₃	—	2	2	no	—
360	C₄⋊C₄×C₄₃	—	2	2	no	—
361	C₄⋊C₄×C₄₃	—	2	1	no	—
362	C₄⋊C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
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	1	yes	characteristic
366	C₄⋊C₄×C₄₃	C₂×D₄	1	2	yes	—
367	C₄⋊C₄×C₄₃	C₂×D₄	1	2	yes	—
368	C₄⋊C₄×C₄₃	C₂⁴	1	2	yes	—
369	C₄⋊C₄×C₄₃	C₂⁴	1	1	yes	characteristic
370	C₄⋊C₄×C₄₃	C₂⁴	1	1	yes	characteristic
371	C₂²⋊C₄×C₄₃	—	2	2	no	—
372	C₂²⋊C₄×C₄₃	—	2	2	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	2	no	—
377	C₂²⋊C₄×C₄₃	—	2	1	no	—
378	C₂²⋊C₄×C₄₃	—	2	2	no	—
379	C₂²⋊C₄×C₄₃	—	2	1	no	—
380	C₂²⋊C₄×C₄₃	—	2	1	no	—
381	C₂²⋊C₄×C₄₃	—	2	1	no	—
382	C₂²⋊C₄×C₄₃	—	2	1	no	—
383	C₂²⋊C₄×C₄₃	C₂×D₄	1	2	yes	—
384	C₂²⋊C₄×C₄₃	C₂×D₄	1	2	yes	—
385	C₂²⋊C₄×C₄₃	C₂×D₄	1	2	yes	—
386	C₂²⋊C₄×C₄₃	C₂×D₄	1	2	yes	—
387	C₄²×C₄₃	—	2	2	no	—
388	C₄²×C₄₃	—	2	1	no	—
389	C₄²×C₄₃	C₂×D₄	1	2	yes	—
390	C₄²×C₄₃	C₂×D₄	1	2	yes	—
391	C₄²×C₄₃	C₂⁴	1	2	yes	—
392	C₄²×C₄₃	C₂⁴	1	2	yes	—
393	C₂²⋊Dic₄₃	—	2	2	no	—
394	C₂²⋊Dic₄₃	—	2	1	no	—
395	C₂²⋊Dic₄₃	—	2	1	no	—
396	C₂²⋊Dic₄₃	—	2	2	no	—
397	C₂²⋊Dic₄₃	—	2	1	no	—
398	C₂²⋊Dic₄₃	—	2	1	no	—
399	C₄⋊Dic₄₃	—	2	1	no	—
400	C₄⋊Dic₄₃	—	2	1	no	—
401	C₄⋊Dic₄₃	—	2	1	no	—
402	C₄⋊Dic₄₃	—	2	1	no	—
403	C₄⋊Dic₄₃	—	2	2	no	—
404	C₄⋊Dic₄₃	—	2	2	no	—
405	C₄⋊Dic₄₃	—	2	2	no	—
406	C₄⋊Dic₄₃	—	2	2	no	—
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	C₄⋊Dic₄₃	C₂⁴	1	1	yes	characteristic
412	C₄⋊Dic₄₃	C₂⁴	1	1	yes	characteristic
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	Dic₄₃⋊C₄	—	2	2	no	—
420	Dic₄₃⋊C₄	—	2	2	no	—
421	C₄×Dic₄₃	—	2	2	no	—
422	C₄×Dic₄₃	—	2	1	no	—
423	C₄×Dic₄₃	—	2	1	no	—
424	C₄×Dic₄₃	—	2	2	no	—
425	C₄×Dic₄₃	—	2	1	no	—
426	C₄×Dic₄₃	—	2	1	no	—
427	#10621877	—	2	2	no	—
428	#10621877	—	2	2	no	—
429	C₂×C₄₃⋊C₈	—	2	2	no	—
430	C₂×C₄₃⋊C₈	—	2	2	no	—
431	C₂×C₄₃⋊C₈	C₂⁴	1	1	yes	characteristic
432	C₂×C₄₃⋊C₈	C₂⁴	1	1	yes	characteristic
433	C₂×C₄₃⋊C₈	C₂⁴	1	2	yes	—
434	C₂×C₄₃⋊C₈	C₂⁴	1	2	yes	—
435	C₂×C₄₃⋊C₈	C₂⁴	1	1	yes	characteristic
436	C₂×C₄₃⋊C₈	C₂⁴	1	1	yes	characteristic
437	C₂³×C₄₃	—	2	2	no	—
438	C₂³×C₄₃	—	2	2	no	—
439	C₂³×C₄₃	—	2	1	no	—
440	C₂³×C₄₃	—	4	1	no	—
441	C₂³×C₄₃	—	4	1	no	—
442	C₂³×C₄₃	—	4	2	no	—
443	C₂³×C₄₃	—	8	1	no	—
444	C₂³×C₄₃	—	8	1	no	—
445	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
446	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
447	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
448	Q₈×C₄₃	—	2	1	no	—
449	Q₈×C₄₃	—	2	1	no	—
450	Q₈×C₄₃	—	8	2	no	—
451	D₄×C₄₃	—	2	2	no	—
452	D₄×C₄₃	—	2	2	no	—
453	D₄×C₄₃	—	2	1	no	—
454	D₄×C₄₃	—	2	1	no	—
455	D₄×C₄₃	—	4	4	no	—
456	D₄×C₄₃	—	4	2	no	—
457	D₄×C₄₃	—	4	2	no	—
458	D₄×C₄₃	—	4	2	no	—
459	D₄×C₄₃	—	8	2	no	—
460	D₄×C₄₃	—	8	2	no	—
461	D₄×C₄₃	—	8	1	no	—
462	D₄×C₄₃	—	8	2	no	—
463	C₂×C₄×C₄₃	—	2	2	no	—
464	C₂×C₄×C₄₃	—	2	2	no	—
465	C₂×C₄×C₄₃	—	2	2	no	—
466	C₂×C₄×C₄₃	—	2	1	no	—
467	C₂×C₄×C₄₃	—	2	1	no	—
468	C₂×C₄×C₄₃	—	2	1	no	—
469	C₂×C₄×C₄₃	—	2	1	no	—
470	C₂×C₄×C₄₃	—	2	1	no	—
471	C₂×C₄×C₄₃	—	2	1	no	—
472	C₂×C₄×C₄₃	—	2	1	no	—
473	C₂×C₄×C₄₃	—	2	2	no	—
474	C₂×C₄×C₄₃	—	4	2	no	—
475	C₂×C₄×C₄₃	—	4	2	no	—
476	C₂×C₄×C₄₃	—	4	2	no	—
477	C₂×C₄×C₄₃	—	8	2	no	—
478	C₂×C₄×C₄₃	—	8	2	no	—
479	C₂×C₄×C₄₃	—	8	2	no	—
480	C₂×C₄×C₄₃	—	8	1	no	—
481	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
482	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
483	C₂×C₄×C₄₃	C₂²×D₄	1	2	yes	—
484	C₂×C₄×C₄₃	C₂²×D₄	1	2	yes	—
485	C₂×C₄×C₄₃	C₂²×D₄	1	2	yes	—
486	C₂×C₄×C₄₃	C₂²×D₄	1	2	yes	—
487	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
488	C₂×C₄×C₄₃	2₋¹⁺⁴	1	2	yes	—
489	C₂×C₄×C₄₃	2₋¹⁺⁴	1	2	yes	—
490	C₂×C₄×C₄₃	C₂⁵	1	1	yes	characteristic
491	C₂×Dic₄₃	—	2	2	no	—
492	C₂×Dic₄₃	—	2	1	no	—
493	C₂×Dic₄₃	—	2	1	no	—
494	C₂×Dic₄₃	—	2	2	no	—
495	C₂×Dic₄₃	—	2	1	no	—
496	C₂×Dic₄₃	—	2	1	no	—
497	C₂×Dic₄₃	—	8	1	no	—
498	C₂×Dic₄₃	—	8	1	no	—
499	C₂×Dic₄₃	—	8	1	no	—
500	C₂×Dic₄₃	—	8	1	no	—
501	Dic₈₆	—	8	2	no	—
502	Dic₈₆	—	8	2	no	—
503	Dic₈₆	—	8	2	no	—
504	Dic₈₆	—	8	2	no	—
505	C₄₃⋊C₈	—	2	1	no	—
506	C₄₃⋊C₈	—	2	1	no	—
507	C₄₃⋊C₈	—	2	1	no	—
508	C₄₃⋊C₈	—	2	1	no	—
509	C₄₃⋊C₈	—	2	2	no	—
510	C₄₃⋊C₈	—	2	2	no	—
511	#60875	—	43	1	no	maximal, Sylow
512	C₂²×C₄₃	—	2	1	no	—
513	C₂²×C₄₃	—	2	1	no	—
514	C₂²×C₄₃	—	2	1	no	—
515	C₂²×C₄₃	—	2	1	no	—
516	C₂²×C₄₃	—	2	1	no	—
517	C₂²×C₄₃	—	2	1	no	—
518	C₂²×C₄₃	—	2	1	no	—
519	C₂²×C₄₃	—	2	1	no	—
520	C₂²×C₄₃	—	4	2	no	—
521	C₂²×C₄₃	—	4	1	no	—
522	C₂²×C₄₃	—	4	2	no	—
523	C₂²×C₄₃	—	4	1	no	—
524	C₂²×C₄₃	—	4	2	no	—
525	C₂²×C₄₃	—	4	1	no	—
526	C₂²×C₄₃	—	8	2	no	—
527	C₂²×C₄₃	—	16	2	no	—
528	C₂²×C₄₃	#536	1	2	yes	—
529	C₂²×C₄₃	C₂³×D₄	1	1	yes	characteristic
530	C₄×C₄₃	—	2	2	no	—
531	C₄×C₄₃	—	2	2	no	—
532	C₄×C₄₃	—	2	2	no	—
533	C₄×C₄₃	—	2	2	no	—
534	C₄×C₄₃	—	2	1	no	—
535	C₄×C₄₃	—	2	1	no	—
536	C₄×C₄₃	—	4	1	no	—
537	C₄×C₄₃	—	4	2	no	—
538	C₄×C₄₃	—	4	1	no	—
539	C₄×C₄₃	—	4	1	no	—
540	C₄×C₄₃	#536	1	2	yes	—
541	C₄×C₄₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
542	C₄×C₄₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
543	Dic₄₃	—	4	1	no	—
544	Dic₄₃	—	4	2	no	—
545	Dic₄₃	—	4	1	no	—
546	Dic₄₃	—	4	1	no	—
547	Dic₄₃	—	4	2	no	—
548	Dic₄₃	—	4	1	no	—
549	#3494	D₄₃	1	1	yes	characteristic
550	#3458	—	43	1	no	—
551	#3244	—	43	2	no	—
552	#3243	—	43	2	no	—
553	#3241	—	43	2	no	—
554	#3241	—	43	2	no	—
555	#3240	—	43	2	no	—
556	#3235	—	43	2	no	—
557	#3233	—	43	2	no	—
558	#3228	—	43	2	no	—
559	#3164	—	43	1	no	—
560	#3163	—	43	1	no	—
561	#3136	—	43	1	no	—
562	#3136	—	43	1	no	—
563	#3094	—	43	1	no	—
564	#3093	—	43	1	no	—
565	#3091	—	43	1	no	—
566	C₂×#482	—	43	1	no	—
567	#3084	—	43	1	no	—
568	#3083	—	43	1	no	—
569	#3081	—	43	1	no	—
570	#3081	—	43	1	no	—
571	#2924	—	43	1	no	—
572	C₂×C₄₃	—	2	2	no	—
573	C₂×C₄₃	—	4	1	no	—
574	C₂×C₄₃	—	4	1	no	—
575	C₂×C₄₃	—	8	1	no	—
576	C₂×C₄₃	—	8	2	no	—
577	C₂×C₄₃	C₂×#536	1	1	yes	characteristic
578	C₂×C₄₃	#3584	1	1	yes	characteristic
579	C₂×C₄₃	#3585	1	1	yes	characteristic
580	#555	—	2	1	no	—
581	#553	—	2	1	no	—
582	#553	—	2	1	no	—
583	#551	—	2	2	no	—
584	#547	—	2	1	no	—
585	#546	—	2	2	no	—
586	#544	—	43	1	no	—
587	#544	—	43	1	no	—
588	#544	—	43	1	no	—
589	#544	—	43	1	no	—
590	#544	—	43	2	no	—
591	#544	—	43	2	no	—
592	#544	—	86	1	no	—
593	#544	—	86	1	no	—
594	#544	C₂×D₄₃	1	1	yes	characteristic
595	#543	—	86	2	no	—
596	#542	C₂×D₄₃	1	2	yes	—
597	#540	C₂×D₄₃	1	2	yes	—
598	#535	C₂×D₄₃	1	1	yes	characteristic
599	#533	—	43	2	no	—
600	#533	—	43	2	no	—
601	#533	—	86	2	no	—
602	#533	—	86	1	no	—
603	#533	—	86	1	no	—
604	#532	C₂×D₄₃	1	2	yes	—
605	#529	C₂×D₄₃	1	2	yes	—
606	#525	C₂×D₄₃	1	1	yes	characteristic
607	C₂×#121	C₂×D₄₃	1	1	yes	characteristic
608	#520	C₂×D₄₃	1	1	yes	characteristic
609	#518	C₂×D₄₃	1	1	yes	characteristic
610	C₂×#117	—	43	1	no	—
611	C₂×#117	—	43	1	no	—
612	C₂×#117	C₂×D₄₃	1	1	yes	characteristic
613	#501	—	43	2	no	—
614	#501	—	43	2	no	—
615	#501	—	43	2	no	—
616	#501	—	43	2	no	—
617	#500	—	43	2	no	—
618	#499	—	43	2	no	—
619	#499	—	43	2	no	—
620	#498	—	43	2	no	—
621	#490	—	43	2	no	—
622	#490	—	43	2	no	—
623	#489	—	43	2	no	—
624	#489	—	43	2	no	—
625	#488	—	43	2	no	—
626	#488	—	43	2	no	—
627	#486	—	43	2	no	—
628	#486	—	43	2	no	—
629	#485	—	43	1	no	—
630	#485	—	43	1	no	—
631	#485	—	43	2	no	—
632	#485	—	43	2	no	—
633	#484	—	43	1	no	—
634	#483	—	43	1	no	—
635	#482	—	43	2	no	—
636	#482	—	43	2	no	—
637	#482	—	43	2	no	—
638	#482	—	43	2	no	—
639	#482	—	43	1	no	—
640	#482	—	43	1	no	—
641	#482	—	43	2	no	—
642	#482	—	43	2	no	—
643	#482	—	43	2	no	—
644	#482	—	43	2	no	—
645	#481	—	43	1	no	—
646	#481	—	43	2	no	—
647	#480	—	43	1	no	—
648	#480	—	43	2	no	—
649	#479	—	43	2	no	—
650	#479	—	43	2	no	—
651	#478	—	43	2	no	—
652	#478	—	43	2	no	—
653	#478	—	43	2	no	—
654	#478	—	43	2	no	—
655	#478	—	43	2	no	—
656	#478	—	43	2	no	—
657	#477	—	43	2	no	—
658	#476	—	43	2	no	—
659	#476	—	43	2	no	—
660	#476	—	43	2	no	—
661	#475	—	43	2	no	—
662	#474	—	43	2	no	—
663	#474	—	43	2	no	—
664	#474	—	43	2	no	—
665	#433	—	43	2	no	—
666	#433	—	43	2	no	—
667	#432	—	43	2	no	—
668	#431	—	43	2	no	—
669	#428	—	43	1	no	—
670	#428	—	43	1	no	—
671	#428	—	43	1	no	—
672	#428	—	43	1	no	—
673	#427	—	43	1	no	—
674	#427	—	43	1	no	—
675	C₂×#107	—	43	1	no	—
676	C₂×#106	—	43	1	no	—
677	#424	—	43	1	no	—
678	#424	—	43	1	no	—
679	#418	—	43	1	no	—
680	#418	—	43	1	no	—
681	#417	—	43	1	no	—
682	#417	—	43	1	no	—
683	#416	—	43	1	no	—
684	#416	—	43	1	no	—
685	C₂×#102	—	43	1	no	—
686	C₂×#102	—	43	1	no	—
687	#407	—	43	1	no	—
688	C₂×C₂²⋊C₈	—	43	1	no	—
689	#405	—	43	1	no	—
690	#405	—	43	1	no	—
691	C₄₃	#60875	1	1	yes	characteristic, complemented, Sylow
692	C₂×#41	—	2	2	no	—
693	C₂×#41	C₂²×D₄₃	1	1	yes	characteristic
694	C₂²×D₄	—	2	1	no	—
695	C₂²×D₄	C₂²×D₄₃	1	1	yes	characteristic
696	C₂³×C₄	C₂²×D₄₃	1	1	yes	characteristic
697	C₂×M₁₆	—	43	1	no	—
698	C₂×M₁₆	—	43	1	no	—
699	C₂²×C₈	—	43	1	no	—
700	C₂²×C₈	—	43	1	no	—
701	C₄⋊Q₈	—	2	1	no	—
702	C₄⋊Q₈	—	43	2	no	—
703	C₄⋊Q₈	—	43	2	no	—
704	C₄⋊Q₈	—	43	2	no	—
705	C₄⋊Q₈	—	43	2	no	—
706	C₄⋊Q₈	—	86	1	no	—
707	C₄⋊Q₈	—	86	1	no	—
708	C₄⋊Q₈	—	86	1	no	—
709	C₄⋊Q₈	—	86	1	no	—
710	C₄⋊Q₈	—	86	2	no	—
711	C₄⋊Q₈	—	86	2	no	—
712	C₄⋊Q₈	C₂²×D₄₃	1	2	yes	—
713	#127	C₂²×D₄₃	1	2	yes	—
714	#126	—	2	2	no	—
715	#126	—	2	2	no	—
716	#125	—	2	1	no	—
717	#125	—	43	2	no	—
718	#125	—	43	2	no	—
719	#125	—	43	2	no	—
720	#125	—	43	2	no	—
721	#125	—	86	1	no	—
722	#125	—	86	1	no	—
723	#125	—	86	1	no	—
724	#125	—	86	1	no	—
725	#125	—	86	2	no	—
726	#125	—	86	2	no	—
727	#125	C₂²×D₄₃	1	2	yes	—
728	#124	—	2	2	no	—
729	#124	—	2	2	no	—
730	#124	C₂²×D₄₃	1	2	yes	—
731	#123	—	2	1	no	—
732	#123	—	2	2	no	—
733	#123	—	2	2	no	—
734	#123	—	2	2	no	—
735	#123	—	2	2	no	—
736	C₂²⋊Q₈	—	2	2	no	—
737	C₂²⋊Q₈	—	2	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	—	86	2	no	—
749	C₂²⋊Q₈	—	86	2	no	—
750	C₂²⋊Q₈	C₂²×D₄₃	1	1	yes	characteristic
751	C₂²⋊Q₈	C₂²×D₄₃	1	1	yes	characteristic
752	#121	—	2	1	no	—
753	#121	—	2	1	no	—
754	#121	—	2	2	no	—
755	#121	—	2	1	no	—
756	#121	—	2	1	no	—
757	#121	—	2	2	no	—
758	#121	—	2	2	no	—
759	#121	C₂²×D₄₃	1	2	yes	—
760	#121	C₂²×D₄₃	1	2	yes	—
761	#121	C₂²×D₄₃	1	1	yes	characteristic
762	#121	C₂²×D₄₃	1	1	yes	characteristic
763	#120	—	2	1	no	—
764	#120	—	2	2	no	—
765	C₄×Q₈	—	86	2	no	—
766	C₄×Q₈	—	86	2	no	—
767	C₄×Q₈	—	86	2	no	—
768	C₄×Q₈	—	86	2	no	—
769	C₄×Q₈	C₂²×D₄₃	1	2	yes	—
770	C₄×D₄	—	2	1	no	—
771	C₄×D₄	—	2	1	no	—
772	C₄×D₄	—	2	2	no	—
773	C₄×D₄	—	2	1	no	—
774	C₄×D₄	—	2	1	no	—
775	C₄×D₄	—	2	2	no	—
776	C₄×D₄	—	2	2	no	—
777	C₄×D₄	C₂²×D₄₃	1	2	yes	—
778	C₄×D₄	C₂²×D₄₃	1	2	yes	—
779	C₄×D₄	C₂²×D₄₃	1	2	yes	—
780	#117	—	2	1	no	—
781	#117	—	2	2	no	—
782	#117	—	43	2	no	—
783	#117	—	43	1	no	—
784	#117	—	43	1	no	—
785	#117	—	43	1	no	—
786	#117	—	43	1	no	—
787	#117	—	43	2	no	—
788	#117	—	86	1	no	—
789	#117	—	86	1	no	—
790	#117	—	86	1	no	—
791	#117	—	86	1	no	—
792	#117	C₂²⋊D₄₃	1	2	yes	—
793	#117	C₂²⋊D₄₃	1	1	yes	characteristic
794	#117	C₂²⋊D₄₃	1	1	yes	characteristic
795	#117	C₂²×D₄₃	1	1	yes	characteristic
796	#117	C₂²×D₄₃	1	1	yes	characteristic
797	#117	C₂²×D₄₃	1	1	yes	characteristic
798	#117	C₂²×D₄₃	1	2	yes	—
799	C₂×C₄⋊C₄	—	2	1	no	—
800	C₂×C₄⋊C₄	—	43	1	no	—
801	C₂×C₄⋊C₄	—	43	1	no	—
802	C₂×C₄⋊C₄	—	43	1	no	—
803	C₂×C₄⋊C₄	—	43	1	no	—
804	C₂×C₄⋊C₄	C₂²⋊D₄₃	1	1	yes	characteristic
805	C₂×C₄⋊C₄	C₂²⋊D₄₃	1	1	yes	characteristic
806	C₂×C₄⋊C₄	C₂²×D₄₃	1	1	yes	characteristic
807	C₂×C₂²⋊C₄	—	2	1	no	—
808	C₂×C₂²⋊C₄	—	2	2	no	—
809	C₂×C₂²⋊C₄	—	86	1	no	—
810	C₂×C₂²⋊C₄	—	86	1	no	—
811	C₂×C₂²⋊C₄	C₂²⋊D₄₃	1	2	yes	—
812	C₂×C₄²	—	86	1	no	—
813	C₂×C₄²	—	86	1	no	—
814	C₂×C₄²	C₂²×D₄₃	1	2	yes	—
815	#107	—	43	2	no	—
816	#107	—	43	2	no	—
817	#107	—	43	1	no	—
818	#107	—	43	1	no	—
819	#107	—	43	1	no	—
820	#107	—	43	1	no	—
821	#107	—	43	2	no	—
822	#107	—	43	2	no	—
823	#107	—	43	2	no	—
824	#107	—	43	2	no	—
825	#106	—	43	2	no	—
826	#106	—	43	2	no	—
827	#106	—	43	1	no	—
828	#106	—	43	1	no	—
829	#106	—	43	1	no	—
830	#106	—	43	1	no	—
831	#106	—	43	2	no	—
832	#106	—	43	2	no	—
833	#106	—	43	2	no	—
834	#106	—	43	2	no	—
835	C₄⋊C₈	—	43	2	no	—
836	C₄⋊C₈	—	43	2	no	—
837	C₄⋊C₈	—	43	2	no	—
838	C₄⋊C₈	—	43	2	no	—
839	#103	—	43	1	no	—
840	#103	—	43	1	no	—
841	#103	—	43	1	no	—
842	#103	—	43	1	no	—
843	#103	—	43	2	no	—
844	#103	—	43	2	no	—
845	#102	—	43	2	no	—
846	#102	—	43	2	no	—
847	#102	—	43	2	no	—
848	#102	—	43	2	no	—
849	#102	—	43	1	no	—
850	#102	—	43	1	no	—
851	#102	—	43	1	no	—
852	#102	—	43	1	no	—
853	#102	—	43	2	no	—
854	#102	—	43	2	no	—
855	#102	—	43	2	no	—
856	#102	—	43	2	no	—
857	#102	—	43	2	no	—
858	#102	—	43	2	no	—
859	C₂²⋊C₈	—	43	1	no	—
860	C₂²⋊C₈	—	43	1	no	—
861	C₂²⋊C₈	—	43	1	no	—
862	C₂²⋊C₈	—	43	1	no	—
863	C₂²⋊C₈	—	43	2	no	—
864	C₂²⋊C₈	—	43	2	no	—
865	#97	—	43	2	no	—
866	#97	—	43	2	no	—
867	C₄×C₈	—	43	2	no	—
868	C₄×C₈	—	43	2	no	—
869	C₂⁴	—	2	1	no	—
870	C₂⁴	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
871	#41	—	2	2	no	—
872	#41	—	2	2	no	—
873	#41	—	8	4	no	—
874	C₂×Q₈	—	2	2	no	—
875	C₂×Q₈	—	86	2	no	—
876	C₂×Q₈	—	86	2	no	—
877	C₂×Q₈	—	86	2	no	—
878	C₂×Q₈	—	86	2	no	—
879	C₂×Q₈	C₂³×D₄₃	1	1	yes	characteristic
880	C₂×D₄	—	2	1	no	—
881	C₂×D₄	—	2	1	no	—
882	C₂×D₄	—	2	2	no	—
883	C₂×D₄	—	2	1	no	—
884	C₂×D₄	—	2	2	no	—
885	C₂×D₄	—	2	1	no	—
886	C₂×D₄	—	2	2	no	—
887	C₂×D₄	—	2	2	no	—
888	C₂×D₄	—	2	2	no	—
889	C₂×D₄	—	2	2	no	—
890	C₂×D₄	—	8	2	no	—
891	C₂×D₄	C₂³×D₄₃	1	2	yes	—
892	C₂×D₄	C₂³×D₄₃	1	1	yes	characteristic
893	C₂²×C₄	—	2	2	no	—
894	C₂²×C₄	—	2	2	no	—
895	C₂²×C₄	—	2	1	no	—
896	C₂²×C₄	—	2	1	no	—
897	C₂²×C₄	—	2	2	no	—
898	C₂²×C₄	—	2	2	no	—
899	C₂²×C₄	—	2	2	no	—
900	C₂²×C₄	—	86	1	no	—
901	C₂²×C₄	—	86	1	no	—
902	C₂²×C₄	—	86	1	no	—
903	C₂²×C₄	—	86	1	no	—
904	C₂²×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
905	C₂²×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
906	C₂²×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
907	C₂²×C₄	C₂×C₂²⋊D₄₃	1	2	yes	—
908	C₂²×C₄	C₂×C₂²⋊D₄₃	1	2	yes	—
909	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
910	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
911	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
912	M₁₆	—	86	2	no	—
913	M₁₆	—	86	2	no	—
914	C₂×C₈	—	43	1	no	—
915	C₂×C₈	—	43	1	no	—
916	C₂×C₈	—	43	2	no	—
917	C₂×C₈	—	43	2	no	—
918	C₂×C₈	—	43	1	no	—
919	C₂×C₈	—	43	1	no	—
920	C₂×C₈	—	86	2	no	—
921	C₂×C₈	—	86	2	no	—
922	C₄⋊C₄	—	2	1	no	—
923	C₄⋊C₄	—	2	2	no	—
924	C₄⋊C₄	—	2	1	no	—
925	C₄⋊C₄	—	2	2	no	—
926	C₄⋊C₄	—	2	2	no	—
927	C₄⋊C₄	—	2	2	no	—
928	C₄⋊C₄	—	2	1	no	—
929	C₄⋊C₄	—	43	2	no	—
930	C₄⋊C₄	—	43	1	no	—
931	C₄⋊C₄	—	43	1	no	—
932	C₄⋊C₄	—	43	2	no	—
933	C₄⋊C₄	—	43	1	no	—
934	C₄⋊C₄	—	43	1	no	—
935	C₄⋊C₄	—	86	1	no	—
936	C₄⋊C₄	—	86	1	no	—
937	C₄⋊C₄	—	86	1	no	—
938	C₄⋊C₄	—	86	1	no	—
939	C₄⋊C₄	—	86	2	no	—
940	C₄⋊C₄	—	86	2	no	—
941	C₄⋊C₄	—	86	2	no	—
942	C₄⋊C₄	—	86	2	no	—
943	C₄⋊C₄	—	86	2	no	—
944	C₄⋊C₄	—	86	2	no	—
945	C₄⋊C₄	—	86	2	no	—
946	C₄⋊C₄	—	86	2	no	—
947	C₄⋊C₄	—	86	2	no	—
948	C₄⋊C₄	—	86	2	no	—
949	C₄⋊C₄	—	86	2	no	—
950	C₄⋊C₄	—	86	2	no	—
951	C₄⋊C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
952	C₄⋊C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
953	C₄⋊C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
954	C₄⋊C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
955	C₄⋊C₄	C₂×C₂²⋊D₄₃	1	2	yes	—
956	C₄⋊C₄	C₂×C₂²⋊D₄₃	1	2	yes	—
957	C₄⋊C₄	C₂³×D₄₃	1	2	yes	—
958	C₄⋊C₄	C₂³×D₄₃	1	1	yes	characteristic
959	C₄⋊C₄	C₂³×D₄₃	1	1	yes	characteristic
960	C₂²⋊C₄	—	2	1	no	—
961	C₂²⋊C₄	—	2	1	no	—
962	C₂²⋊C₄	—	2	1	no	—
963	C₂²⋊C₄	—	2	2	no	—
964	C₂²⋊C₄	—	2	2	no	—
965	C₂²⋊C₄	—	2	2	no	—
966	C₂²⋊C₄	—	2	2	no	—
967	C₂²⋊C₄	—	2	2	no	—
968	C₂²⋊C₄	—	2	2	no	—
969	C₂²⋊C₄	—	2	1	no	—
970	C₂²⋊C₄	—	2	2	no	—
971	C₂²⋊C₄	—	2	1	no	—
972	C₂²⋊C₄	—	86	2	no	—
973	C₂²⋊C₄	—	86	1	no	—
974	C₂²⋊C₄	—	86	1	no	—
975	C₂²⋊C₄	—	86	2	no	—
976	C₂²⋊C₄	—	86	1	no	—
977	C₂²⋊C₄	—	86	1	no	—
978	C₂²⋊C₄	C₂×C₂²⋊D₄₃	1	2	yes	—
979	C₂²⋊C₄	C₂×C₂²⋊D₄₃	1	2	yes	—
980	C₂²⋊C₄	C₂×C₂²⋊D₄₃	1	2	yes	—
981	C₂²⋊C₄	C₂×C₂²⋊D₄₃	1	2	yes	—
982	C₄²	—	2	2	no	—
983	C₄²	—	2	1	no	—
984	C₄²	—	86	2	no	—
985	C₄²	—	86	1	no	—
986	C₄²	—	86	1	no	—
987	C₄²	—	86	2	no	—
988	C₄²	—	86	1	no	—
989	C₄²	—	86	1	no	—
990	C₄²	C₂×C₂²⋊D₄₃	1	2	yes	—
991	C₄²	C₂×C₂²⋊D₄₃	1	2	yes	—
992	C₄²	C₂³×D₄₃	1	2	yes	—
993	C₄²	C₂³×D₄₃	1	2	yes	—
994	C₂³	—	2	2	no	—
995	C₂³	—	2	2	no	—
996	C₂³	—	2	1	no	—
997	C₂³	—	4	1	no	—
998	C₂³	—	4	1	no	—
999	C₂³	—	4	2	no	—
1000	C₂³	—	8	1	no	—
1001	C₂³	—	8	1	no	—
1002	C₂³	C₂²×C₂²⋊D₄₃	1	1	yes	characteristic
1003	C₂³	C₂²×C₂²⋊D₄₃	1	1	yes	characteristic
1004	C₂³	C₂²×C₂²⋊D₄₃	1	1	yes	characteristic
1005	Q₈	—	2	1	no	—
1006	Q₈	—	2	1	no	—
1007	Q₈	—	8	2	no	—
1008	Q₈	—	344	2	no	—
1009	Q₈	—	344	2	no	—
1010	Q₈	—	344	2	no	—
1011	Q₈	—	344	2	no	—
1012	D₄	—	2	2	no	—
1013	D₄	—	2	2	no	—
1014	D₄	—	2	1	no	—
1015	D₄	—	2	1	no	—
1016	D₄	—	4	4	no	—
1017	D₄	—	4	2	no	—
1018	D₄	—	4	2	no	—
1019	D₄	—	4	2	no	—
1020	D₄	—	8	2	no	—
1021	D₄	—	8	2	no	—
1022	D₄	—	8	2	no	—
1023	D₄	—	8	1	no	—
1024	C₂×C₄	—	2	2	no	—
1025	C₂×C₄	—	2	2	no	—
1026	C₂×C₄	—	2	2	no	—
1027	C₂×C₄	—	2	1	no	—
1028	C₂×C₄	—	2	1	no	—
1029	C₂×C₄	—	2	1	no	—
1030	C₂×C₄	—	2	1	no	—
1031	C₂×C₄	—	2	1	no	—
1032	C₂×C₄	—	2	1	no	—
1033	C₂×C₄	—	2	1	no	—
1034	C₂×C₄	—	2	2	no	—
1035	C₂×C₄	—	4	2	no	—
1036	C₂×C₄	—	4	2	no	—
1037	C₂×C₄	—	4	2	no	—
1038	C₂×C₄	—	8	2	no	—
1039	C₂×C₄	—	8	2	no	—
1040	C₂×C₄	—	8	2	no	—
1041	C₂×C₄	—	8	1	no	—
1042	C₂×C₄	—	86	2	no	—
1043	C₂×C₄	—	86	1	no	—
1044	C₂×C₄	—	86	1	no	—
1045	C₂×C₄	—	86	2	no	—
1046	C₂×C₄	—	86	1	no	—
1047	C₂×C₄	—	86	1	no	—
1048	C₂×C₄	—	344	1	no	—
1049	C₂×C₄	—	344	1	no	—
1050	C₂×C₄	—	344	1	no	—
1051	C₂×C₄	—	344	1	no	—
1052	C₂×C₄	C₂²×C₂²⋊D₄₃	1	2	yes	—
1053	C₂×C₄	C₂²×C₂²⋊D₄₃	1	1	yes	characteristic
1054	C₂×C₄	C₂²×C₂²⋊D₄₃	1	1	yes	characteristic
1055	C₂×C₄	C₂²×C₂²⋊D₄₃	1	2	yes	—
1056	C₂×C₄	C₂²×C₂²⋊D₄₃	1	2	yes	—
1057	C₂×C₄	C₂²×C₂²⋊D₄₃	1	2	yes	—
1058	C₂×C₄	C₂²×C₂²⋊D₄₃	1	1	yes	characteristic
1059	C₂×C₄	#13063372	1	2	yes	—
1060	C₂×C₄	#13063372	1	2	yes	—
1061	C₂×C₄	C₂⁴×D₄₃	1	1	yes	characteristic
1062	C₈	—	86	1	no	—
1063	C₈	—	86	1	no	—
1064	C₈	—	86	1	no	—
1065	C₈	—	86	1	no	—
1066	C₈	—	86	2	no	—
1067	C₈	—	86	2	no	—
1068	C₂²	—	2	1	no	—
1069	C₂²	—	2	1	no	—
1070	C₂²	—	2	1	no	—
1071	C₂²	—	2	1	no	—
1072	C₂²	—	2	1	no	—
1073	C₂²	—	2	1	no	—
1074	C₂²	—	2	1	no	—
1075	C₂²	—	2	1	no	—
1076	C₂²	—	4	2	no	—
1077	C₂²	—	4	1	no	—
1078	C₂²	—	4	1	no	—
1079	C₂²	—	4	2	no	—
1080	C₂²	—	4	1	no	—
1081	C₂²	—	4	2	no	—
1082	C₂²	—	8	2	no	—
1083	C₂²	—	16	2	no	—
1084	C₂²	#14583470	1	2	yes	—
1085	C₂²	C₂³×C₂²⋊D₄₃	1	1	yes	characteristic
1086	C₄	—	2	2	no	—
1087	C₄	—	2	2	no	—
1088	C₄	—	2	2	no	—
1089	C₄	—	2	2	no	—
1090	C₄	—	2	1	no	—
1091	C₄	—	2	1	no	—
1092	C₄	—	4	1	no	—
1093	C₄	—	4	2	no	—
1094	C₄	—	4	1	no	—
1095	C₄	—	4	1	no	—
1096	C₄	—	172	2	no	—
1097	C₄	—	172	1	no	—
1098	C₄	—	172	1	no	—
1099	C₄	—	172	2	no	—
1100	C₄	—	172	1	no	—
1101	C₄	—	172	1	no	—
1102	C₄	#14583470	1	2	yes	—
1103	C₄	C₂×#13063372	1	1	yes	characteristic
1104	C₄	C₂×#13063372	1	1	yes	characteristic
1105	C₂	—	2	2	no	—
1106	C₂	—	4	1	no	—
1107	C₂	—	4	1	no	—
1108	C₂	—	8	2	no	—
1109	C₂	—	8	1	no	—
1110	C₂	C₂×#14583470	1	1	yes	characteristic
1111	C₂	#19149366	1	1	yes	characteristic
1112	C₂	#19149375	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂³×C₂²⋊D₄₃
commutator, cosocle	C₂×C₄×C₄₃	C₂⁵
Frattini	C₂×C₄	C₂⁴×D₄₃
Fitting, prime radical	C₄₃×#3494	C₂
socle	C₂²×C₄₃	C₂³×D₄
hypercenter	#3494	D₄₃
hypocenter	C₄₃	#60875
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₂×#117 ◁ #3494

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. #19145842	C₂	semidirect
5. #19145842	C₂	semidirect
6. #19145831	C₂	semidirect
7. #19145789	C₂	semidirect
8. #19145770	C₂	semidirect
9. #19145727	C₂	semidirect
10. #19145129	C₂	semidirect
11. #19145121	C₂	semidirect
12. #19144949	C₂	semidirect
13. #19144949	C₂	semidirect
14. #19144531	C₂	semidirect
15. #19144524	C₂	semidirect
16. #19144504	C₂	semidirect
17. C₂×#14583220	C₂	semidirect
18. #19144457	C₂	semidirect
19. #19144446	C₂	semidirect
20. #19144426	C₂	semidirect
21. #19144426	C₂	semidirect
22. #19143253	C₂	semidirect
30. #14583527	C₂²	semidirect
31. #14583527	C₂²	semidirect
33. #14583456	C₂²	semidirect
34. #14583456	C₂²	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. #14583263	C₂²	semidirect
49. #14583263	C₂²	semidirect
50. #14583258	C₂²	semidirect
51. #14583258	C₂²	semidirect
52. #14583253	C₂²	semidirect
53. #14583253	C₂²	semidirect
54. #14583245	C₂²	semidirect
55. #14583245	C₂²	semidirect
56. #14583237	C₂²	semidirect
57. #14583237	C₂²	semidirect
58. #14583237	C₂²	semidirect
59. #14583237	C₂²	semidirect
60. #14583232	C₂²	semidirect
61. #14583227	C₂²	semidirect
68. #14583220	C₂²	semidirect
69. #14583220	C₂²	semidirect
70. #14583220	C₂²	semidirect
71. #14583220	C₂²	semidirect
73. #14583215	C₂²	semidirect
75. #14583210	C₂²	semidirect
76. #14583206	C₂²	semidirect
77. #14583206	C₂²	semidirect
78. #14583199	C₂²	semidirect
79. #14583199	C₂²	semidirect
80. #14583199	C₂²	semidirect
81. #14583199	C₂²	semidirect
82. #14583199	C₂²	semidirect
83. #14583199	C₂²	semidirect
84. #14583194	C₂²	semidirect
85. #14583189	C₂²	semidirect
86. #14583189	C₂²	semidirect
87. #14583189	C₂²	semidirect
88. #14583184	C₂²	semidirect
89. #14583179	C₂²	semidirect
90. #14583179	C₂²	semidirect
91. #14583179	C₂²	semidirect
92. #14582960	C₂²	semidirect
93. #14582960	C₂²	semidirect
94. #14582956	C₂²	semidirect
95. #14582952	C₂²	semidirect
691. C₄₃	#60875	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
#19145842	2
#19145831	2
#19145789	2
#19145770	2
#19145727	2
#19145129	2
#19145121	2
#19144949	2
#19144531	2
#19144524	2
#19144504	2
C₂×#14583220	2
#19144457	2
#19144446	2
#19144426	2
#19143253	2
C₄₃×#3494	2
#60875	43