Subgroups — #25966822

Order 11008.

1860 conjugacy classes of subgroups.

The subgroup lattice has 1084 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19148342	C₂	1	2	yes	maximal, complemented
2	#19145299	C₂	1	2	yes	maximal, complemented
3	#19145298	C₂	1	2	yes	maximal, complemented
4	#19145270	C₂	1	2	yes	maximal, complemented
5	#19145267	C₂	1	2	yes	maximal, complemented
6	#19145251	C₂	1	1	yes	maximal, characteristic, complemented
7	#19145250	C₂	1	1	yes	maximal, characteristic, complemented
8	#19145237	C₂	1	1	yes	maximal, characteristic, complemented
9	#19145236	C₂	1	1	yes	maximal, characteristic, complemented
10	#19145176	C₂	1	1	yes	maximal, characteristic, complemented
11	#19145166	C₂	1	1	yes	maximal, characteristic, complemented
12	#19145165	C₂	1	1	yes	maximal, characteristic, complemented
13	#19145128	C₂	1	1	yes	maximal, characteristic, complemented
14	#19145083	C₂	1	1	yes	maximal, characteristic, complemented
15	#19144955	C₂	1	2	yes	maximal, complemented
16	#19144222	C₂	1	2	yes	maximal, complemented
17	#19144178	C₂	1	1	yes	maximal, characteristic
18	#467×D₄₃	C₂	1	1	yes	maximal, characteristic, complemented
19	#19143470	C₂	1	1	yes	maximal, characteristic, complemented
20	#19143458	C₂	1	1	yes	maximal, characteristic, complemented
21	#19143433	C₂	1	2	yes	maximal, complemented
22	C₂×#14582853	C₂	1	1	yes	maximal, characteristic, complemented
23	C₄₃×#3170	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#13063357	C₂²	1	2	yes	—
25	C₂×#13063348	C₂²	1	1	yes	characteristic
26	C₂×Q₁₆×D₄₃	C₂²	1	1	yes	characteristic
27	C₂²×#10621872	C₂²	1	1	yes	characteristic
28	C₂²×C₈×D₄₃	C₂²	1	1	yes	characteristic
29	#14583621	—	2	2	no	—
30	#14583603	—	2	2	no	—
31	#14583590	—	2	2	no	—
32	#14583582	—	2	2	no	—
33	#14583581	—	2	2	no	—
34	#14583581	—	2	2	no	—
35	#14583576	—	2	2	no	—
36	#14583573	—	2	2	no	—
37	#14583526	C₂²	1	2	yes	—
38	#14583523	C₂²	1	2	yes	—
39	#14583521	C₂²	1	2	yes	—
40	#14583510	C₂²	1	2	yes	—
41	#14583507	C₂²	1	2	yes	—
42	#14583474	C₂²	1	2	yes	—
43	#14583451	C₂²	1	2	yes	—
44	#14583435	C₂²	1	2	yes	—
45	#14583433	C₂²	1	2	yes	—
46	#14583412	C₂²	1	2	yes	—
47	C₂²⋊Q₈×D₄₃	C₂²	1	2	yes	—
48	#14583381	C₂²	1	2	yes	—
49	#14583375	C₂²	1	2	yes	—
50	C₂×#13063282	C₂²	1	1	yes	characteristic
51	#14583307	C₂²	1	2	yes	complemented
52	#14583305	C₂²	1	2	yes	complemented
53	#14583303	C₂²	1	1	yes	characteristic, complemented
54	#14583301	C₂²	1	1	yes	characteristic, complemented
55	#14583300	C₂²	1	1	yes	characteristic, complemented
56	#14583292	C₂²	1	2	yes	complemented
57	#14583291	C₂²	1	2	yes	complemented
58	#14583284	C₂²	1	1	yes	characteristic, complemented
59	#14583283	C₂²	1	1	yes	characteristic, complemented
60	#14583277	C₂²	1	1	yes	characteristic, complemented
61	#14583267	C₂²	1	2	yes	complemented
62	#14583266	C₂²	1	2	yes	complemented
63	#14583261	C₂²	1	2	yes	complemented
64	#14583260	C₂²	1	2	yes	complemented
65	#14583255	C₂²	1	2	yes	complemented
66	#14583254	C₂²	1	2	yes	complemented
67	#14583248	C₂²	1	2	yes	complemented
68	#14583156	C₂²	1	2	yes	—
69	#14583154	C₂²	1	2	yes	—
70	#14583148	C₂²	1	2	yes	—
71	#14583146	C₂²	1	2	yes	—
72	#14583141	C₂²	1	1	yes	characteristic
73	#14583140	C₂²	1	1	yes	characteristic
74	#14583139	C₂²	1	2	yes	—
75	#14583138	C₂²	1	2	yes	—
76	#14583138	C₂²	1	2	yes	—
77	#14583137	C₂²	1	1	yes	characteristic
78	#14583137	C₂²	1	1	yes	characteristic
79	#14583136	C₂²	1	1	yes	characteristic
80	#14583135	C₂²	1	1	yes	characteristic
81	#14583131	C₂²	1	2	yes	—
82	#14583130	C₂²	1	2	yes	—
83	#14583130	C₂²	1	2	yes	—
84	#14583128	C₂²	1	2	yes	—
85	#14583006	C₂²	1	2	yes	complemented
86	#14583004	C₂²	1	2	yes	complemented
87	#14583004	C₂²	1	2	yes	complemented
88	#14583003	C₂²	1	2	yes	complemented
89	#14583002	C₂²	1	2	yes	complemented
90	#14582998	C₂²	1	2	yes	complemented
91	#14582997	C₂²	1	2	yes	complemented
92	#14582997	C₂²	1	2	yes	complemented
93	C₄×Dic₁₇₂	C₂²	1	1	yes	characteristic, complemented
94	Q₁₆×Dic₄₃	C₂²	1	1	yes	characteristic, complemented
95	Q₁₆×Dic₄₃	C₂²	1	1	yes	characteristic, complemented
96	#14582993	C₂²	1	1	yes	characteristic, complemented
97	#14582991	C₂²	1	2	yes	complemented
98	C₄×#10621873	C₂²	1	2	yes	complemented
99	#14582984	C₂²	1	2	yes	complemented
100	C₄×D₃₄₄	C₂²	1	1	yes	characteristic, complemented
101	#14582981	C₂²	1	1	yes	characteristic, complemented
102	#14582940	C₂²	1	2	yes	—
103	#14582936	C₂²	1	1	yes	characteristic
104	#107×D₄₃	C₂²	1	1	yes	characteristic
105	#14582906	C₂²	1	2	yes	—
106	#14582899	C₂²	1	2	yes	—
107	#14582894	C₂²	1	2	yes	—
108	#103×D₄₃	C₂²	1	2	yes	—
109	#14582853	C₂²	1	1	yes	characteristic
110	#14582853	C₂²	1	1	yes	characteristic
111	#14582853	C₂²	1	1	yes	characteristic
112	#14582853	C₂²	1	1	yes	characteristic
113	#14582853	C₂²	1	1	yes	characteristic
114	#14582853	C₂²	1	1	yes	characteristic
115	#14582853	C₂²	1	1	yes	characteristic
116	#14582853	C₂²	1	1	yes	characteristic
117	C₂×#13063236	C₂²	1	1	yes	characteristic
118	C₂×#13063235	C₂²	1	1	yes	characteristic
119	C₂×C₈×Dic₄₃	C₂²	1	1	yes	characteristic
120	C₄₃×#533	C₂²	1	2	yes	—
121	C₄₃×#500	C₂²	1	1	yes	characteristic, complemented
122	C₄₃×#494	C₂²	1	1	yes	characteristic, complemented
123	C₄₃×#487	C₂²	1	2	yes	complemented
124	C₄₃×#467	C₂²	1	2	yes	—
125	C₄₃×#467	C₂²	1	1	yes	characteristic
126	C₄₃×#467	C₂²	1	1	yes	characteristic
127	C₄×Q₁₆×C₄₃	C₂²	1	2	yes	complemented
128	C₄×Q₁₆×C₄₃	C₂²	1	1	yes	characteristic, complemented
129	C₄×Q₁₆×C₄₃	C₂²	1	1	yes	characteristic, complemented
130	C₂×C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
131	C₂×#10621902	C₂³	1	2	yes	—
132	C₂×Q₈×D₄₃	C₂³	1	2	yes	—
133	C₂²×C₄×D₄₃	C₂³	1	1	yes	characteristic
134	#13063357	—	2	8	no	—
135	#13063348	—	2	4	no	—
136	C₂×Dic₁₇₂	C₂³	1	1	yes	characteristic
137	C₂×#10621885	C₂³	1	2	yes	—
138	C₂×#10621885	C₂³	1	2	yes	—
139	Q₁₆×D₄₃	—	2	4	no	—
140	C₂×#10621873	C₂³	1	2	yes	—
141	C₂×#10621884	C₂³	1	2	yes	—
142	C₂×#10621884	C₂³	1	2	yes	—
143	C₂×D₃₄₄	C₂³	1	1	yes	characteristic
144	C₂×#10621872	—	2	4	no	—
145	C₂×#10621872	C₂³	1	1	yes	characteristic
146	C₂×#10621872	C₂³	1	1	yes	characteristic
147	C₂×#10621872	C₂³	1	1	yes	characteristic
148	C₂×#10621872	C₂³	1	1	yes	characteristic
149	C₂²×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
150	C₂²×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
151	C₂×C₈×D₄₃	—	2	4	no	—
152	C₂×C₈×D₄₃	C₂³	1	1	yes	characteristic
153	C₂×C₈×D₄₃	C₂³	1	1	yes	characteristic
154	C₂×C₈×D₄₃	C₂³	1	1	yes	characteristic
155	C₂×C₈×D₄₃	C₂³	1	1	yes	characteristic
156	#13063324	C₂³	1	2	yes	—
157	#13063323	—	2	2	no	—
158	#13063323	C₂³	1	2	yes	—
159	#13063320	—	2	2	no	—
160	#13063320	—	2	2	no	—
161	#13063320	—	2	2	no	—
162	#13063320	—	2	2	no	—
163	#13063320	—	2	2	no	—
164	#13063319	—	2	2	no	—
165	#13063319	—	2	2	no	—
166	#13063319	—	2	2	no	—
167	#13063317	—	2	2	no	—
168	#13063317	C₂³	1	2	yes	—
169	#13063316	C₂³	1	2	yes	—
170	#13063315	—	2	2	no	—
171	#13063315	—	2	2	no	—
172	#13063315	—	2	2	no	—
173	#13063315	—	2	2	no	—
174	#13063315	—	2	2	no	—
175	#13063314	—	2	2	no	—
176	#13063314	C₂³	1	2	yes	—
177	#13063313	—	2	2	no	—
178	#13063313	C₂³	1	2	yes	—
179	#13063310	—	2	2	no	—
180	#13063310	—	2	2	no	—
181	#13063310	—	2	2	no	—
182	#13063310	—	2	2	no	—
183	#13063310	—	2	2	no	—
184	#13063309	—	2	2	no	—
185	#13063308	—	2	2	no	—
186	#13063305	C₂³	1	2	yes	—
187	#13063304	C₂³	1	2	yes	—
188	#13063303	—	2	2	no	—
189	#13063303	—	2	2	no	—
190	#13063303	—	2	2	no	—
191	#13063303	—	2	2	no	—
192	#13063303	—	2	2	no	—
193	#13063302	—	2	2	no	—
194	#13063302	—	2	2	no	—
195	#13063301	—	2	2	no	—
196	#13063301	—	2	2	no	—
197	#13063301	C₂³	1	2	yes	—
198	#13063301	C₂³	1	2	yes	—
199	#13063300	C₂³	1	2	yes	—
200	#13063299	C₂³	1	2	yes	—
201	#13063295	—	2	2	no	—
202	Q₈×Dic₄₃	C₂³	1	2	yes	—
203	Q₈×Dic₄₃	C₂³	1	2	yes	—
204	C₄×Dic₈₆	—	2	2	no	—
205	C₄×Dic₈₆	C₂³	1	2	yes	—
206	#13063290	—	2	2	no	—
207	#13063290	—	2	2	no	—
208	#13063290	C₂³	1	2	yes	—
209	C₄×D₁₇₂	—	2	2	no	—
210	C₄×D₁₇₂	C₂³	1	2	yes	—
211	#13063287	—	2	2	no	—
212	#13063287	—	2	2	no	—
213	#13063287	C₂³	1	2	yes	—
214	C₄×C₂²⋊D₄₃	—	2	2	no	—
215	(C₂²⋊D₄₃)⋊C₄	—	2	2	no	—
216	(C₂²⋊D₄₃)⋊C₄	—	2	2	no	—
217	#13063283	—	2	2	no	—
218	#13063283	—	2	2	no	—
219	#13063283	C₂³	1	2	yes	—
220	#13063282	—	2	2	no	—
221	#13063282	—	2	2	no	—
222	#13063282	—	2	2	no	—
223	#13063282	D₄	1	1	yes	characteristic
224	#13063282	D₄	1	1	yes	characteristic
225	#13063282	D₄	1	1	yes	characteristic
226	#13063282	D₄	1	1	yes	characteristic
227	#13063282	C₂³	1	1	yes	characteristic
228	#13063282	C₂³	1	1	yes	characteristic
229	#13063282	C₂³	1	1	yes	characteristic
230	#13063282	C₂³	1	1	yes	characteristic
231	#13063281	—	2	2	no	—
232	C₂×Dic₄₃⋊C₄	D₄	1	1	yes	characteristic
233	C₂×Dic₄₃⋊C₄	D₄	1	1	yes	characteristic
234	C₄⋊C₄×D₄₃	—	2	2	no	—
235	C₄⋊C₄×D₄₃	—	2	2	no	—
236	C₄⋊C₄×D₄₃	C₂³	1	2	yes	—
237	C₂×(C₂×D₄₃)⋊C₄	D₄	1	1	yes	characteristic
238	C₂×(C₂×D₄₃)⋊C₄	D₄	1	1	yes	characteristic
239	C₂²⋊C₄×D₄₃	—	2	2	no	—
240	C₂×C₄×Dic₄₃	C₂³	1	1	yes	characteristic
241	#13063259	C₂³	1	1	yes	characteristic
242	#13063259	C₂³	1	1	yes	characteristic
243	#13063258	C₂³	1	2	yes	—
244	#13063258	C₂³	1	2	yes	—
245	#13063257	C₂³	1	2	yes	—
246	#13063256	C₂³	1	2	yes	—
247	#13063256	C₂³	1	2	yes	—
248	#13063250	C₂³	1	2	yes	—
249	#13063250	C₂³	1	2	yes	—
250	#13063249	C₂³	1	2	yes	—
251	#13063249	C₂³	1	2	yes	—
252	#13063249	C₂³	1	2	yes	—
253	#13063249	C₂³	1	2	yes	—
254	#13063248	C₂³	1	2	yes	—
255	#13063248	C₂³	1	2	yes	—
256	#13063247	C₂³	1	2	yes	—
257	#13063247	C₂³	1	2	yes	—
258	#13063245	C₂³	1	2	yes	—
259	#13063245	C₂³	1	2	yes	—
260	#13063236	C₂³	1	1	yes	characteristic
261	#13063236	C₂³	1	1	yes	characteristic
262	#13063236	C₂³	1	1	yes	characteristic
263	#13063236	C₂³	1	1	yes	characteristic
264	#13063235	C₂³	1	1	yes	characteristic
265	#13063235	C₂³	1	1	yes	characteristic
266	#13063235	C₂³	1	1	yes	characteristic
267	#13063235	C₂³	1	1	yes	characteristic
268	C₈×Dic₄₃	C₂³	1	1	yes	characteristic
269	C₈×Dic₄₃	C₂³	1	1	yes	characteristic
270	C₈×Dic₄₃	C₂³	1	1	yes	characteristic
271	C₈×Dic₄₃	C₂³	1	1	yes	characteristic
272	C₂×Q₁₆×C₄₃	C₂³	1	1	yes	characteristic
273	C₂×Q₁₆×C₄₃	C₂³	1	1	yes	characteristic
274	C₂×Q₁₆×C₄₃	C₂³	1	2	yes	—
275	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
276	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
277	C₄⋊Q₈×C₄₃	C₂³	1	2	yes	—
278	C₄⋊Q₈×C₄₃	C₂³	1	2	yes	—
279	#125×C₄₃	—	2	2	no	—
280	C₂²⋊Q₈×C₄₃	—	2	2	no	—
281	C₂²⋊Q₈×C₄₃	C₂³	1	2	yes	—
282	C₂²⋊Q₈×C₄₃	C₂³	1	2	yes	—
283	C₄×Q₈×C₄₃	—	2	2	no	—
284	C₄×Q₈×C₄₃	C₂³	1	2	yes	—
285	C₄×Q₈×C₄₃	C₂³	1	2	yes	—
286	#117×C₄₃	—	2	2	no	—
287	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
288	#107×C₄₃	C₂³	1	1	yes	characteristic
289	#107×C₄₃	C₂³	1	1	yes	characteristic
290	#107×C₄₃	C₂³	1	2	yes	—
291	#103×C₄₃	C₂³	1	2	yes	—
292	#103×C₄₃	C₂³	1	2	yes	—
293	#103×C₄₃	C₂³	1	2	yes	—
294	#103×C₄₃	C₂³	1	2	yes	—
295	C₄×C₈×C₄₃	C₂³	1	1	yes	characteristic
296	C₄×C₈×C₄₃	C₂³	1	1	yes	characteristic
297	C₄×C₈×C₄₃	C₂³	1	1	yes	characteristic
298	C₄×C₈×C₄₃	C₂³	1	1	yes	characteristic
299	C₂³×D₄₃	C₂×D₄	1	1	yes	characteristic
300	C₂×Q₈×C₄₃	—	2	2	no	—
301	C₂×Q₈×C₄₃	C₂⁴	1	2	yes	—
302	C₂×Q₈×C₄₃	C₂⁴	1	2	yes	—
303	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
304	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
305	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
306	C₂×C₂²⋊D₄₃	—	2	2	no	—
307	C₂²×Dic₄₃	C₂×D₄	1	1	yes	characteristic
308	C₂²×Dic₄₃	C₂×D₄	1	1	yes	characteristic
309	C₂²×Dic₄₃	C₂×D₄	1	1	yes	characteristic
310	#10621902	—	2	4	no	—
311	#10621902	—	2	4	no	—
312	Q₈×D₄₃	—	2	4	no	—
313	Q₈×D₄₃	—	2	4	no	—
314	C₂×D₁₇₂	—	2	2	no	—
315	C₂×D₁₇₂	—	2	2	no	—
316	C₂×D₁₇₂	C₂⁴	1	2	yes	—
317	C₂×C₄×D₄₃	—	2	2	no	—
318	C₂×C₄×D₄₃	—	2	2	no	—
319	C₂×C₄×D₄₃	—	2	2	no	—
320	C₂×C₄×D₄₃	—	2	2	no	—
321	C₂×C₄×D₄₃	—	2	2	no	—
322	C₂×C₄×D₄₃	—	2	2	no	—
323	C₂×C₄×D₄₃	—	2	2	no	—
324	C₂×C₄×D₄₃	C₂×D₄	1	1	yes	characteristic
325	C₂×C₄×D₄₃	C₂×D₄	1	1	yes	characteristic
326	C₂×C₄×D₄₃	C₂⁴	1	1	yes	characteristic
327	C₂×C₄×D₄₃	C₂⁴	1	1	yes	characteristic
328	C₂×Dic₈₆	—	2	2	no	—
329	C₂×Dic₈₆	—	2	2	no	—
330	C₂×Dic₈₆	C₂⁴	1	2	yes	—
331	Q₁₆×C₄₃	—	2	2	no	—
332	Q₁₆×C₄₃	—	2	2	no	—
333	Q₁₆×C₄₃	—	2	4	no	—
334	C₂×C₈×C₄₃	—	2	2	no	—
335	C₂×C₈×C₄₃	—	2	2	no	—
336	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
337	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
338	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
339	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
340	C₄⋊C₄×C₄₃	—	2	2	no	—
341	C₄⋊C₄×C₄₃	—	2	2	no	—
342	C₄⋊C₄×C₄₃	—	2	2	no	—
343	C₄⋊C₄×C₄₃	—	2	2	no	—
344	C₄⋊C₄×C₄₃	—	2	2	no	—
345	C₄⋊C₄×C₄₃	—	2	2	no	—
346	C₄⋊C₄×C₄₃	—	2	2	no	—
347	C₄⋊C₄×C₄₃	C₂⁴	1	2	yes	—
348	C₄⋊C₄×C₄₃	C₂⁴	1	2	yes	—
349	C₂²⋊C₄×C₄₃	—	2	2	no	—
350	C₂²⋊C₄×C₄₃	—	2	2	no	—
351	C₄²×C₄₃	—	2	2	no	—
352	C₄²×C₄₃	—	2	2	no	—
353	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
354	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
355	C₄²×C₄₃	C₂⁴	1	1	yes	characteristic
356	C₄²×C₄₃	C₂⁴	1	1	yes	characteristic
357	C₂²⋊Dic₄₃	—	2	2	no	—
358	#10621885	—	2	4	no	—
359	#10621885	—	2	4	no	—
360	#10621884	—	2	4	no	—
361	#10621884	—	2	4	no	—
362	(C₂×D₄₃)⋊C₄	—	2	2	no	—
363	(C₂×D₄₃)⋊C₄	—	2	2	no	—
364	(C₂×D₄₃)⋊C₄	—	2	2	no	—
365	(C₂×D₄₃)⋊C₄	—	2	2	no	—
366	(C₂×D₄₃)⋊C₄	—	2	2	no	—
367	(C₂×D₄₃)⋊C₄	—	2	2	no	—
368	(C₂×D₄₃)⋊C₄	—	2	2	no	—
369	(C₂×D₄₃)⋊C₄	—	2	2	no	—
370	(C₂×D₄₃)⋊C₄	—	2	2	no	—
371	(C₂×D₄₃)⋊C₄	—	2	2	no	—
372	(C₂×D₄₃)⋊C₄	—	2	2	no	—
373	(C₂×D₄₃)⋊C₄	—	2	2	no	—
374	(C₂×D₄₃)⋊C₄	C₂×D₄	1	1	yes	characteristic
375	(C₂×D₄₃)⋊C₄	C₂×D₄	1	1	yes	characteristic
376	(C₂×D₄₃)⋊C₄	C₂×D₄	1	1	yes	characteristic
377	(C₂×D₄₃)⋊C₄	C₂×D₄	1	1	yes	characteristic
378	(C₂×D₄₃)⋊C₄	C₂×D₄	1	1	yes	characteristic
379	(C₂×D₄₃)⋊C₄	C₂×D₄	1	1	yes	characteristic
380	(C₂×D₄₃)⋊C₄	C₂×D₄	1	1	yes	characteristic
381	(C₂×D₄₃)⋊C₄	C₂×D₄	1	1	yes	characteristic
382	C₄⋊Dic₄₃	—	2	2	no	—
383	C₄⋊Dic₄₃	—	2	2	no	—
384	C₄⋊Dic₄₃	—	2	2	no	—
385	C₄⋊Dic₄₃	—	2	2	no	—
386	C₄⋊Dic₄₃	C₂⁴	1	2	yes	—
387	C₄⋊Dic₄₃	C₂⁴	1	2	yes	—
388	Dic₄₃⋊C₄	—	2	2	no	—
389	Dic₄₃⋊C₄	—	2	2	no	—
390	Dic₄₃⋊C₄	—	2	2	no	—
391	Dic₄₃⋊C₄	—	2	2	no	—
392	Dic₄₃⋊C₄	—	2	2	no	—
393	Dic₄₃⋊C₄	—	2	2	no	—
394	Dic₄₃⋊C₄	—	2	2	no	—
395	Dic₄₃⋊C₄	—	2	2	no	—
396	Dic₄₃⋊C₄	—	2	2	no	—
397	Dic₄₃⋊C₄	—	2	2	no	—
398	Dic₄₃⋊C₄	—	2	2	no	—
399	Dic₄₃⋊C₄	—	2	2	no	—
400	Dic₄₃⋊C₄	C₂×D₄	1	1	yes	characteristic
401	Dic₄₃⋊C₄	C₂×D₄	1	1	yes	characteristic
402	Dic₄₃⋊C₄	C₂×D₄	1	1	yes	characteristic
403	Dic₄₃⋊C₄	C₂×D₄	1	1	yes	characteristic
404	Dic₄₃⋊C₄	C₂×D₄	1	1	yes	characteristic
405	Dic₄₃⋊C₄	C₂×D₄	1	1	yes	characteristic
406	Dic₄₃⋊C₄	C₂×D₄	1	1	yes	characteristic
407	Dic₄₃⋊C₄	C₂×D₄	1	1	yes	characteristic
408	C₄×Dic₄₃	—	2	2	no	—
409	C₄×Dic₄₃	—	2	2	no	—
410	C₄×Dic₄₃	—	2	2	no	—
411	C₄×Dic₄₃	—	2	2	no	—
412	C₄×Dic₄₃	—	2	2	no	—
413	C₄×Dic₄₃	C₂×D₄	1	1	yes	characteristic
414	C₄×Dic₄₃	C₂×D₄	1	1	yes	characteristic
415	C₄×Dic₄₃	C₂⁴	1	1	yes	characteristic
416	C₄×Dic₄₃	C₂⁴	1	1	yes	characteristic
417	C₂×C₄₃⋊C₈	—	2	2	no	—
418	C₂×C₄₃⋊C₈	—	2	2	no	—
419	C₂×C₄₃⋊C₈	C₂⁴	1	1	yes	characteristic
420	C₂×C₄₃⋊C₈	C₂⁴	1	1	yes	characteristic
421	C₂×C₄₃⋊C₈	C₂⁴	1	1	yes	characteristic
422	C₂×C₄₃⋊C₈	C₂⁴	1	1	yes	characteristic
423	Dic₁₇₂	—	2	2	no	—
424	D₃₄₄	—	2	2	no	—
425	#10621873	—	2	4	no	—
426	#10621872	—	2	2	no	—
427	#10621872	—	2	2	no	—
428	#10621872	—	2	2	no	—
429	#10621872	#41	1	4	yes	—
430	C₈×D₄₃	—	2	2	no	—
431	C₈×D₄₃	—	2	2	no	—
432	C₈×D₄₃	—	2	2	no	—
433	C₈×D₄₃	#41	1	4	yes	—
434	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
435	C₂²×D₄₃	—	2	2	no	—
436	C₂²×D₄₃	—	2	2	no	—
437	C₂²×D₄₃	—	2	2	no	—
438	C₂²×D₄₃	—	4	1	no	—
439	C₂²×D₄₃	C₂²×D₄	1	1	yes	characteristic
440	C₂²×D₄₃	C₂²×D₄	1	1	yes	characteristic
441	Q₈×C₄₃	—	2	2	no	—
442	Q₈×C₄₃	—	2	2	no	—
443	Q₈×C₄₃	—	2	2	no	—
444	Q₈×C₄₃	—	2	2	no	—
445	Q₈×C₄₃	—	8	2	no	—
446	C₂×C₄×C₄₃	—	2	2	no	—
447	C₂×C₄×C₄₃	—	2	1	no	—
448	C₂×C₄×C₄₃	—	2	1	no	—
449	C₂×C₄×C₄₃	—	2	2	no	—
450	C₂×C₄×C₄₃	—	2	2	no	—
451	C₂×C₄×C₄₃	—	2	2	no	—
452	C₂×C₄×C₄₃	—	2	2	no	—
453	C₂×C₄×C₄₃	—	4	1	no	—
454	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
455	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
456	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
457	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
458	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
459	C₂×C₄×C₄₃	C₂⁵	1	1	yes	characteristic
460	C₂²⋊D₄₃	—	4	4	no	—
461	C₂×Dic₄₃	—	2	2	no	—
462	C₂×Dic₄₃	—	2	2	no	—
463	C₂×Dic₄₃	—	2	2	no	—
464	C₂×Dic₄₃	—	2	2	no	—
465	C₂×Dic₄₃	—	2	2	no	—
466	C₂×Dic₄₃	—	4	1	no	—
467	C₂×Dic₄₃	C₂²×D₄	1	1	yes	characteristic
468	C₂×Dic₄₃	C₂²×D₄	1	1	yes	characteristic
469	C₂×Dic₄₃	C₂²×D₄	1	1	yes	characteristic
470	C₂×Dic₄₃	C₂²×D₄	1	1	yes	characteristic
471	C₂×Dic₄₃	C₂²×D₄	1	1	yes	characteristic
472	C₂×Dic₄₃	C₂²×D₄	1	1	yes	characteristic
473	D₁₇₂	—	2	2	no	—
474	D₁₇₂	—	2	2	no	—
475	D₁₇₂	—	4	4	no	—
476	D₁₇₂	—	8	2	no	—
477	C₄×D₄₃	—	2	2	no	—
478	C₄×D₄₃	—	2	1	no	—
479	C₄×D₄₃	—	2	1	no	—
480	C₄×D₄₃	—	2	2	no	—
481	C₄×D₄₃	—	4	4	no	—
482	C₄×D₄₃	—	4	4	no	—
483	C₄×D₄₃	—	8	2	no	—
484	C₄×D₄₃	—	8	2	no	—
485	C₄×D₄₃	—	8	2	no	—
486	C₄×D₄₃	C₂×#41	1	2	yes	—
487	C₄×D₄₃	C₂×#41	1	2	yes	—
488	Dic₈₆	—	2	2	no	—
489	Dic₈₆	—	2	2	no	—
490	Dic₈₆	—	4	4	no	—
491	Dic₈₆	—	8	2	no	—
492	C₈×C₄₃	—	2	1	no	—
493	C₈×C₄₃	—	2	1	no	—
494	C₈×C₄₃	C₂×#41	1	2	yes	—
495	C₈×C₄₃	C₂×#41	1	2	yes	—
496	C₄₃⋊C₈	—	2	1	no	—
497	C₄₃⋊C₈	—	2	1	no	—
498	C₄₃⋊C₈	C₂×#41	1	2	yes	—
499	C₄₃⋊C₈	C₂×#41	1	2	yes	—
500	#60708	—	43	1	no	maximal, Sylow
501	C₂²×C₄₃	—	2	1	no	—
502	C₂²×C₄₃	—	2	1	no	—
503	C₂²×C₄₃	#578	1	2	yes	—
504	C₂²×C₄₃	C₂³×D₄	1	1	yes	characteristic
505	C₂×D₄₃	—	2	1	no	—
506	C₂×D₄₃	—	2	1	no	—
507	C₂×D₄₃	—	2	1	no	—
508	C₂×D₄₃	—	2	1	no	—
509	C₂×D₄₃	—	2	1	no	—
510	C₂×D₄₃	—	4	4	no	—
511	C₂×D₄₃	—	4	2	no	—
512	C₂×D₄₃	—	4	2	no	—
513	C₂×D₄₃	—	4	2	no	—
514	C₂×D₄₃	#532	1	2	yes	—
515	C₄×C₄₃	—	2	1	no	—
516	C₄×C₄₃	—	2	1	no	—
517	C₄×C₄₃	—	2	1	no	—
518	C₄×C₄₃	—	2	1	no	—
519	C₄×C₄₃	—	2	1	no	—
520	C₄×C₄₃	—	4	2	no	—
521	C₄×C₄₃	—	4	2	no	—
522	C₄×C₄₃	—	4	2	no	—
523	C₄×C₄₃	—	4	2	no	—
524	C₄×C₄₃	C₂²×#41	1	1	yes	characteristic
525	C₄×C₄₃	C₂²×#41	1	1	yes	characteristic
526	Dic₄₃	—	2	1	no	—
527	Dic₄₃	—	2	1	no	—
528	Dic₄₃	—	2	1	no	—
529	Dic₄₃	—	2	1	no	—
530	Dic₄₃	—	2	1	no	—
531	Dic₄₃	—	4	2	no	—
532	Dic₄₃	—	4	2	no	—
533	Dic₄₃	—	4	2	no	—
534	Dic₄₃	#532	1	2	yes	—
535	#3495	—	43	2	no	—
536	#3181	—	43	2	no	—
537	#3181	—	43	2	no	—
538	#3178	—	43	2	no	—
539	#3178	—	43	2	no	—
540	#3177	—	43	1	no	—
541	#3177	—	43	1	no	—
542	#3175	—	43	1	no	—
543	#3175	—	43	1	no	—
544	#3170	—	43	1	no	—
545	#3170	D₄₃	1	1	yes	characteristic, complemented
546	#3168	—	43	1	no	—
547	#3168	—	43	1	no	—
548	#3164	—	43	1	no	—
549	#3156	—	43	1	no	—
550	#3137	—	43	2	no	—
551	#3056	—	43	2	no	—
552	#3050	—	43	1	no	—
553	C₂×#467	—	43	1	no	—
554	#2951	—	43	1	no	—
555	#2950	—	43	1	no	—
556	#2947	—	43	2	no	—
557	C₂×#405	—	43	1	no	—
558	C₂×C₄₃	—	2	2	no	—
559	C₂×C₄₃	C₂×#532	1	1	yes	characteristic
560	C₂×C₄₃	C₂×#578	1	1	yes	characteristic
561	C₂×C₄₃	#3584	1	1	yes	characteristic
562	D₄₃	—	2	2	no	—
563	D₄₃	—	4	1	no	—
564	D₄₃	—	8	2	no	—
565	C₂×#137	—	43	2	no	—
566	C₂×#135	—	43	1	no	—
567	C₂²×Q₁₆	—	43	1	no	—
568	C₂²×M₁₆	—	43	1	no	—
569	C₂³×C₈	—	43	1	no	—
570	#556	—	86	2	no	—
571	#554	—	86	2	no	—
572	#552	—	86	2	no	—
573	#552	—	86	2	no	—
574	#552	—	86	2	no	—
575	#552	—	86	2	no	—
576	#551	—	86	2	no	—
577	#551	—	86	2	no	—
578	#544	—	43	2	no	—
579	#542	—	43	2	no	—
580	#542	—	43	2	no	—
581	#541	—	43	2	no	—
582	#541	—	43	2	no	—
583	#536	—	43	2	no	—
584	#533	—	43	2	no	—
585	#533	C₂×D₄₃	1	2	yes	—
586	#529	—	43	2	no	—
587	#529	—	43	2	no	—
588	#525	—	43	2	no	—
589	C₂×C₂²⋊Q₈	—	43	2	no	—
590	#520	—	43	2	no	—
591	#519	—	43	2	no	—
592	C₂×#117	—	43	1	no	—
593	#501	—	43	2	no	—
594	#501	—	43	2	no	—
595	#500	—	43	1	no	—
596	#500	C₂×D₄₃	1	1	yes	characteristic, complemented
597	#499	—	43	1	no	—
598	#499	—	43	1	no	—
599	#497	—	43	2	no	—
600	#497	—	43	2	no	—
601	#495	—	43	1	no	—
602	#495	—	43	1	no	—
603	#494	—	43	1	no	—
604	#494	C₂×D₄₃	1	1	yes	characteristic, complemented
605	#491	—	43	2	no	—
606	#491	—	43	2	no	—
607	#489	—	43	2	no	—
608	#489	—	43	2	no	—
609	#488	—	43	2	no	—
610	#488	—	43	2	no	—
611	#487	—	43	2	no	—
612	#487	C₂×D₄₃	1	2	yes	complemented
613	#470	—	43	2	no	—
614	#470	—	43	2	no	—
615	#468	—	43	2	no	—
616	#468	—	43	2	no	—
617	#467	—	43	1	no	—
618	#467	—	43	1	no	—
619	#467	—	43	1	no	—
620	#467	—	43	2	no	—
621	#467	—	43	2	no	—
622	#467	—	43	1	no	—
623	#467	—	43	2	no	—
624	#467	C₂×D₄₃	1	1	yes	characteristic
625	#467	C₂×D₄₃	1	1	yes	characteristic
626	#467	C₂×D₄₃	1	2	yes	—
627	#466	—	43	1	no	—
628	#466	—	43	1	no	—
629	#465	—	43	2	no	—
630	#465	—	43	2	no	—
631	#465	—	43	2	no	—
632	#465	—	43	2	no	—
633	#441	—	43	2	no	—
634	#441	—	43	2	no	—
635	#441	—	43	2	no	—
636	#441	—	43	2	no	—
637	#440	—	43	2	no	—
638	#440	—	43	2	no	—
639	#440	—	43	2	no	—
640	#440	—	43	2	no	—
641	C₄×Q₁₆	—	43	1	no	—
642	C₄×Q₁₆	—	43	1	no	—
643	C₄×Q₁₆	—	43	1	no	—
644	C₄×Q₁₆	—	43	2	no	—
645	C₄×Q₁₆	—	43	1	no	—
646	C₄×Q₁₆	C₂×D₄₃	1	1	yes	characteristic, complemented
647	C₄×Q₁₆	C₂×D₄₃	1	1	yes	characteristic, complemented
648	C₄×Q₁₆	C₂×D₄₃	1	2	yes	complemented
649	C₄×SD₁₆	—	43	2	no	—
650	C₄×SD₁₆	—	43	2	no	—
651	C₄×D₈	—	43	1	no	—
652	C₄×D₈	—	43	1	no	—
653	#428	—	43	2	no	—
654	#427	—	43	1	no	—
655	C₂×#107	—	43	1	no	—
656	#419	—	43	2	no	—
657	#417	—	43	2	no	—
658	#416	—	43	2	no	—
659	C₂×#103	—	43	2	no	—
660	#405	—	43	1	no	—
661	#405	—	43	1	no	—
662	#405	—	43	1	no	—
663	#405	—	43	1	no	—
664	#405	—	43	1	no	—
665	#405	—	43	1	no	—
666	#405	—	43	1	no	—
667	#405	—	43	1	no	—
668	C₂×#97	—	43	1	no	—
669	C₂×#97	—	43	1	no	—
670	C₂×C₄×C₈	—	43	1	no	—
671	C₂×C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
672	C₄₃	#60708	1	1	yes	characteristic, complemented, Sylow
673	C₂×#41	—	43	2	no	—
674	C₂²×Q₈	—	43	2	no	—
675	C₂³×C₄	—	43	1	no	—
676	#137	—	86	8	no	—
677	#135	—	86	4	no	—
678	C₂×Q₁₆	—	43	2	no	—
679	C₂×Q₁₆	—	43	2	no	—
680	C₂×Q₁₆	—	43	1	no	—
681	C₂×Q₁₆	—	86	4	no	—
682	C₂×Q₁₆	C₂²×D₄₃	1	1	yes	characteristic
683	C₂×Q₁₆	C₂²×D₄₃	1	1	yes	characteristic
684	C₂×Q₁₆	C₂²×D₄₃	1	2	yes	—
685	C₂×SD₁₆	—	43	2	no	—
686	C₂×SD₁₆	—	43	2	no	—
687	C₂×SD₁₆	—	43	2	no	—
688	C₂×D₈	—	43	1	no	—
689	C₂×M₁₆	—	43	1	no	—
690	C₂×M₁₆	—	43	1	no	—
691	C₂×M₁₆	—	43	1	no	—
692	C₂×M₁₆	—	43	1	no	—
693	C₂×M₁₆	—	86	4	no	—
694	C₂²×C₈	—	43	1	no	—
695	C₂²×C₈	—	43	1	no	—
696	C₂²×C₈	—	43	1	no	—
697	C₂²×C₈	—	43	1	no	—
698	C₂²×C₈	—	43	1	no	—
699	C₂²×C₈	—	43	1	no	—
700	C₂²×C₈	—	86	4	no	—
701	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
702	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
703	C₄⋊Q₈	—	43	2	no	—
704	C₄⋊Q₈	—	43	2	no	—
705	C₄⋊Q₈	—	86	2	no	—
706	C₄⋊Q₈	C₂²×D₄₃	1	2	yes	—
707	C₄⋊Q₈	C₂²×D₄₃	1	2	yes	—
708	#126	—	86	2	no	—
709	#126	—	86	2	no	—
710	#126	—	86	2	no	—
711	#126	—	86	2	no	—
712	#126	—	86	2	no	—
713	#126	—	86	2	no	—
714	#126	—	86	2	no	—
715	#126	—	86	2	no	—
716	#125	—	2	2	no	—
717	#125	—	43	2	no	—
718	#125	—	43	2	no	—
719	#125	—	86	2	no	—
720	#125	—	86	2	no	—
721	#125	—	86	2	no	—
722	#125	—	86	2	no	—
723	#125	—	86	2	no	—
724	#125	—	86	2	no	—
725	#124	—	43	2	no	—
726	#124	—	43	2	no	—
727	#124	—	86	2	no	—
728	#124	—	86	2	no	—
729	#123	—	86	2	no	—
730	#123	—	86	2	no	—
731	#123	—	86	2	no	—
732	#123	—	86	2	no	—
733	#123	—	86	2	no	—
734	#123	—	86	2	no	—
735	#123	—	86	2	no	—
736	C₂²⋊Q₈	—	2	2	no	—
737	C₂²⋊Q₈	—	43	2	no	—
738	C₂²⋊Q₈	—	43	2	no	—
739	C₂²⋊Q₈	—	43	2	no	—
740	C₂²⋊Q₈	—	43	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	2	yes	—
751	C₂²⋊Q₈	C₂²×D₄₃	1	2	yes	—
752	#121	—	43	2	no	—
753	#121	—	43	2	no	—
754	#120	—	86	2	no	—
755	C₄×Q₈	—	2	2	no	—
756	C₄×Q₈	—	43	2	no	—
757	C₄×Q₈	—	43	2	no	—
758	C₄×Q₈	—	43	2	no	—
759	C₄×Q₈	—	43	2	no	—
760	C₄×Q₈	—	86	2	no	—
761	C₄×Q₈	—	86	2	no	—
762	C₄×Q₈	—	86	2	no	—
763	C₄×Q₈	C₂²×D₄₃	1	2	yes	—
764	C₄×Q₈	C₂²×D₄₃	1	2	yes	—
765	C₄×D₄	—	43	2	no	—
766	C₄×D₄	—	43	2	no	—
767	C₄×D₄	—	86	2	no	—
768	C₄×D₄	—	86	2	no	—
769	C₄×D₄	—	86	2	no	—
770	C₄×D₄	—	86	2	no	—
771	C₄×D₄	—	86	2	no	—
772	C₄×D₄	—	86	2	no	—
773	#117	—	2	2	no	—
774	#117	—	43	1	no	—
775	#117	—	43	1	no	—
776	#117	—	43	1	no	—
777	#117	—	43	1	no	—
778	#117	—	43	1	no	—
779	#117	—	43	1	no	—
780	#117	—	43	1	no	—
781	#117	—	43	1	no	—
782	#117	—	43	2	no	—
783	#117	—	86	2	no	—
784	#117	—	86	2	no	—
785	#117	—	86	2	no	—
786	#117	—	86	2	no	—
787	#117	—	86	2	no	—
788	#117	—	86	2	no	—
789	C₂×C₄⋊C₄	—	43	1	no	—
790	C₂×C₄⋊C₄	—	43	1	no	—
791	C₂×C₄⋊C₄	—	43	2	no	—
792	C₂×C₄⋊C₄	—	86	2	no	—
793	C₂×C₄⋊C₄	—	86	2	no	—
794	C₂×C₂²⋊C₄	—	43	1	no	—
795	C₂×C₂²⋊C₄	—	43	1	no	—
796	C₂×C₂²⋊C₄	—	86	2	no	—
797	C₂×C₄²	—	43	1	no	—
798	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
799	#107	—	43	1	no	—
800	#107	—	43	1	no	—
801	#107	—	43	2	no	—
802	#107	—	43	2	no	—
803	#107	C₂²×D₄₃	1	1	yes	characteristic
804	#107	C₂²×D₄₃	1	1	yes	characteristic
805	#107	C₂²×D₄₃	1	2	yes	—
806	#106	—	43	2	no	—
807	#106	—	43	2	no	—
808	#106	—	43	2	no	—
809	#103	—	43	2	no	—
810	#103	—	43	2	no	—
811	#103	—	43	2	no	—
812	#103	—	43	2	no	—
813	#103	—	43	2	no	—
814	#103	—	43	2	no	—
815	#103	—	43	2	no	—
816	#103	—	43	2	no	—
817	#103	C₂²×D₄₃	1	2	yes	—
818	#103	C₂²×D₄₃	1	2	yes	—
819	#103	C₂²×D₄₃	1	2	yes	—
820	#103	C₂²×D₄₃	1	2	yes	—
821	#102	—	43	2	no	—
822	#102	—	43	2	no	—
823	#102	—	43	2	no	—
824	#102	—	43	2	no	—
825	#97	—	43	1	no	—
826	#97	—	43	1	no	—
827	#97	—	43	1	no	—
828	#97	—	43	1	no	—
829	#97	—	43	1	no	—
830	#97	—	43	1	no	—
831	#97	—	43	1	no	—
832	#97	—	43	1	no	—
833	C₄×C₈	—	43	1	no	—
834	C₄×C₈	—	43	1	no	—
835	C₄×C₈	—	43	1	no	—
836	C₄×C₈	—	43	1	no	—
837	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
838	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
839	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
840	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
841	C₂⁴	—	43	1	no	—
842	#41	—	86	4	no	—
843	#41	—	86	4	no	—
844	C₂×Q₈	—	2	2	no	—
845	C₂×Q₈	—	43	2	no	—
846	C₂×Q₈	—	86	2	no	—
847	C₂×Q₈	—	86	2	no	—
848	C₂×Q₈	—	86	4	no	—
849	C₂×Q₈	—	86	4	no	—
850	C₂×Q₈	C₂³×D₄₃	1	2	yes	—
851	C₂×Q₈	C₂³×D₄₃	1	2	yes	—
852	C₂×D₄	—	43	2	no	—
853	C₂×D₄	—	86	2	no	—
854	C₂×D₄	—	86	2	no	—
855	C₂×D₄	—	86	2	no	—
856	C₂²×C₄	—	43	1	no	—
857	C₂²×C₄	—	43	1	no	—
858	C₂²×C₄	—	43	1	no	—
859	C₂²×C₄	—	43	1	no	—
860	C₂²×C₄	—	43	1	no	—
861	C₂²×C₄	—	43	1	no	—
862	C₂²×C₄	—	43	1	no	—
863	C₂²×C₄	—	86	2	no	—
864	C₂²×C₄	—	86	2	no	—
865	C₂²×C₄	—	86	2	no	—
866	C₂²×C₄	—	86	2	no	—
867	C₂²×C₄	—	86	2	no	—
868	C₂²×C₄	—	86	2	no	—
869	C₂²×C₄	—	86	2	no	—
870	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
871	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
872	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
873	Q₁₆	—	2	2	no	—
874	Q₁₆	—	2	2	no	—
875	Q₁₆	—	2	4	no	—
876	Q₁₆	—	86	4	no	—
877	Q₁₆	—	86	4	no	—
878	Q₁₆	—	86	2	no	—
879	SD₁₆	—	86	4	no	—
880	SD₁₆	—	86	4	no	—
881	SD₁₆	—	86	4	no	—
882	D₈	—	86	2	no	—
883	M₁₆	—	43	4	no	—
884	M₁₆	—	86	2	no	—
885	M₁₆	—	86	2	no	—
886	M₁₆	—	86	2	no	—
887	C₂×C₈	—	2	2	no	—
888	C₂×C₈	—	2	2	no	—
889	C₂×C₈	—	43	1	no	—
890	C₂×C₈	—	43	1	no	—
891	C₂×C₈	—	43	4	no	—
892	C₂×C₈	—	43	1	no	—
893	C₂×C₈	—	43	1	no	—
894	C₂×C₈	—	86	2	no	—
895	C₂×C₈	—	86	2	no	—
896	C₂×C₈	—	86	2	no	—
897	C₂×C₈	—	86	2	no	—
898	C₂×C₈	—	86	2	no	—
899	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
900	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
901	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
902	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
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	2	no	—
910	C₄⋊C₄	—	43	1	no	—
911	C₄⋊C₄	—	43	1	no	—
912	C₄⋊C₄	—	43	1	no	—
913	C₄⋊C₄	—	43	1	no	—
914	C₄⋊C₄	—	43	1	no	—
915	C₄⋊C₄	—	43	1	no	—
916	C₄⋊C₄	—	43	1	no	—
917	C₄⋊C₄	—	43	1	no	—
918	C₄⋊C₄	—	43	2	no	—
919	C₄⋊C₄	—	43	2	no	—
920	C₄⋊C₄	—	86	2	no	—
921	C₄⋊C₄	—	86	2	no	—
922	C₄⋊C₄	—	86	2	no	—
923	C₄⋊C₄	—	86	2	no	—
924	C₄⋊C₄	—	86	2	no	—
925	C₄⋊C₄	—	86	2	no	—
926	C₄⋊C₄	—	86	2	no	—
927	C₄⋊C₄	—	86	2	no	—
928	C₄⋊C₄	—	86	2	no	—
929	C₄⋊C₄	—	86	2	no	—
930	C₄⋊C₄	—	86	2	no	—
931	C₄⋊C₄	—	86	2	no	—
932	C₄⋊C₄	—	86	2	no	—
933	C₄⋊C₄	—	86	2	no	—
934	C₄⋊C₄	—	86	2	no	—
935	C₄⋊C₄	—	86	2	no	—
936	C₄⋊C₄	C₂³×D₄₃	1	2	yes	—
937	C₄⋊C₄	C₂³×D₄₃	1	2	yes	—
938	C₂²⋊C₄	—	2	2	no	—
939	C₂²⋊C₄	—	2	2	no	—
940	C₂²⋊C₄	—	43	1	no	—
941	C₂²⋊C₄	—	43	1	no	—
942	C₂²⋊C₄	—	43	1	no	—
943	C₂²⋊C₄	—	43	1	no	—
944	C₂²⋊C₄	—	43	1	no	—
945	C₂²⋊C₄	—	43	1	no	—
946	C₂²⋊C₄	—	43	1	no	—
947	C₂²⋊C₄	—	43	1	no	—
948	C₂²⋊C₄	—	86	2	no	—
949	C₂²⋊C₄	—	86	2	no	—
950	C₂²⋊C₄	—	86	2	no	—
951	C₂²⋊C₄	—	86	2	no	—
952	C₂²⋊C₄	—	86	2	no	—
953	C₂²⋊C₄	—	86	2	no	—
954	C₂²⋊C₄	—	86	2	no	—
955	C₂²⋊C₄	—	86	2	no	—
956	C₂²⋊C₄	—	86	2	no	—
957	C₂²⋊C₄	—	86	2	no	—
958	C₂²⋊C₄	—	86	2	no	—
959	C₂²⋊C₄	—	86	2	no	—
960	C₂²⋊C₄	—	86	2	no	—
961	C₄²	—	2	2	no	—
962	C₄²	—	2	2	no	—
963	C₄²	—	43	1	no	—
964	C₄²	—	43	1	no	—
965	C₄²	—	43	1	no	—
966	C₄²	—	43	1	no	—
967	C₄²	—	86	2	no	—
968	C₄²	—	86	2	no	—
969	C₄²	—	86	2	no	—
970	C₄²	—	86	2	no	—
971	C₄²	—	86	2	no	—
972	C₄²	D₄×D₄₃	1	1	yes	characteristic
973	C₄²	D₄×D₄₃	1	1	yes	characteristic
974	C₄²	C₂³×D₄₃	1	1	yes	characteristic
975	C₄²	C₂³×D₄₃	1	1	yes	characteristic
976	C₂³	—	43	1	no	—
977	C₂³	—	43	1	no	—
978	C₂³	—	86	2	no	—
979	C₂³	—	86	2	no	—
980	C₂³	—	86	2	no	—
981	C₂³	—	172	1	no	—
982	C₂³	C₂×D₄×D₄₃	1	1	yes	characteristic
983	Q₈	—	2	2	no	—
984	Q₈	—	2	2	no	—
985	Q₈	—	2	2	no	—
986	Q₈	—	2	2	no	—
987	Q₈	—	8	2	no	—
988	Q₈	—	86	2	no	—
989	Q₈	—	86	2	no	—
990	Q₈	—	344	2	no	—
991	Q₈	—	172	4	no	—
992	D₄	—	86	2	no	—
993	D₄	—	86	2	no	—
994	D₄	—	344	2	no	—
995	D₄	—	172	4	no	—
996	D₄	—	172	4	no	—
997	C₂×C₄	—	2	2	no	—
998	C₂×C₄	—	2	1	no	—
999	C₂×C₄	—	2	1	no	—
1000	C₂×C₄	—	2	2	no	—
1001	C₂×C₄	—	2	2	no	—
1002	C₂×C₄	—	2	2	no	—
1003	C₂×C₄	—	2	2	no	—
1004	C₂×C₄	—	4	1	no	—
1005	C₂×C₄	—	43	1	no	—
1006	C₂×C₄	—	43	2	no	—
1007	C₂×C₄	—	43	2	no	—
1008	C₂×C₄	—	43	1	no	—
1009	C₂×C₄	—	43	1	no	—
1010	C₂×C₄	—	43	1	no	—
1011	C₂×C₄	—	43	1	no	—
1012	C₂×C₄	—	43	1	no	—
1013	C₂×C₄	—	86	2	no	—
1014	C₂×C₄	—	86	2	no	—
1015	C₂×C₄	—	86	2	no	—
1016	C₂×C₄	—	86	2	no	—
1017	C₂×C₄	—	86	1	no	—
1018	C₂×C₄	—	86	1	no	—
1019	C₂×C₄	—	86	2	no	—
1020	C₂×C₄	—	86	2	no	—
1021	C₂×C₄	—	86	2	no	—
1022	C₂×C₄	—	344	2	no	—
1023	C₂×C₄	—	344	2	no	—
1024	C₂×C₄	—	344	2	no	—
1025	C₂×C₄	—	172	4	no	—
1026	C₂×C₄	—	172	4	no	—
1027	C₂×C₄	—	172	1	no	—
1028	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
1029	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
1030	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
1031	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
1032	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
1033	C₂×C₄	C₂⁴×D₄₃	1	1	yes	characteristic
1034	C₈	—	2	1	no	—
1035	C₈	—	2	1	no	—
1036	C₈	—	43	2	no	—
1037	C₈	—	43	2	no	—
1038	C₈	—	86	1	no	—
1039	C₈	—	86	1	no	—
1040	C₈	#41×D₄₃	1	2	yes	—
1041	C₈	#41×D₄₃	1	2	yes	—
1042	C₂²	—	2	1	no	—
1043	C₂²	—	2	1	no	—
1044	C₂²	—	43	2	no	—
1045	C₂²	—	86	1	no	—
1046	C₂²	—	86	1	no	—
1047	C₂²	—	86	1	no	—
1048	C₂²	—	86	1	no	—
1049	C₂²	—	86	1	no	—
1050	C₂²	—	172	4	no	—
1051	C₂²	—	172	2	no	—
1052	C₂²	—	172	2	no	—
1053	C₂²	—	172	2	no	—
1054	C₂²	#14583712	1	2	yes	—
1055	C₂²	C₂²×D₄×D₄₃	1	1	yes	characteristic
1056	C₄	—	2	1	no	—
1057	C₄	—	2	1	no	—
1058	C₄	—	2	1	no	—
1059	C₄	—	2	1	no	—
1060	C₄	—	2	1	no	—
1061	C₄	—	4	2	no	—
1062	C₄	—	4	2	no	—
1063	C₄	—	4	2	no	—
1064	C₄	—	4	2	no	—
1065	C₄	—	43	2	no	—
1066	C₄	—	86	1	no	—
1067	C₄	—	86	1	no	—
1068	C₄	—	86	1	no	—
1069	C₄	—	86	1	no	—
1070	C₄	—	86	1	no	—
1071	C₄	—	172	2	no	—
1072	C₄	—	172	2	no	—
1073	C₄	—	172	2	no	—
1074	C₄	C₂×#41×D₄₃	1	1	yes	characteristic
1075	C₄	C₂×#41×D₄₃	1	1	yes	characteristic
1076	C₂	—	2	2	no	—
1077	C₂	—	86	2	no	—
1078	C₂	—	344	2	no	—
1079	C₂	—	172	1	no	—
1080	C₂	#532×D₄₃	1	1	yes	characteristic
1081	C₂	C₂×#14583712	1	1	yes	characteristic
1082	C₂	#19149364	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂²×D₄×D₄₃
commutator, cosocle	C₂×C₄×C₄₃	C₂⁵
Frattini	C₂×C₄	C₂⁴×D₄₃
Fitting	C₄₃×#3170	C₂
socle	C₂²×C₄₃	C₂³×D₄
prime radical	#19144178	C₂
hypercenter	#3170	D₄₃
hypocenter	C₄₃	#60708
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #3170

Complements

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

N	H ≅ G/N	type
1. #19148342	C₂	semidirect
2. #19145299	C₂	semidirect
3. #19145298	C₂	semidirect
4. #19145270	C₂	semidirect
5. #19145267	C₂	semidirect
6. #19145251	C₂	semidirect
7. #19145250	C₂	semidirect
8. #19145237	C₂	semidirect
9. #19145236	C₂	semidirect
10. #19145176	C₂	semidirect
11. #19145166	C₂	semidirect
12. #19145165	C₂	semidirect
13. #19145128	C₂	semidirect
14. #19145083	C₂	semidirect
15. #19144955	C₂	semidirect
16. #19144222	C₂	semidirect
18. #467×D₄₃	C₂	semidirect
19. #19143470	C₂	semidirect
20. #19143458	C₂	semidirect
21. #19143433	C₂	semidirect
22. C₂×#14582853	C₂	semidirect
23. C₄₃×#3170	C₂	semidirect
51. #14583307	C₂²	semidirect
52. #14583305	C₂²	semidirect
53. #14583303	C₂²	semidirect
54. #14583301	C₂²	semidirect
55. #14583300	C₂²	semidirect
56. #14583292	C₂²	semidirect
57. #14583291	C₂²	semidirect
58. #14583284	C₂²	semidirect
59. #14583283	C₂²	semidirect
60. #14583277	C₂²	semidirect
61. #14583267	C₂²	semidirect
62. #14583266	C₂²	semidirect
63. #14583261	C₂²	semidirect
64. #14583260	C₂²	semidirect
65. #14583255	C₂²	semidirect
66. #14583254	C₂²	semidirect
67. #14583248	C₂²	semidirect
85. #14583006	C₂²	semidirect
86. #14583004	C₂²	semidirect
87. #14583004	C₂²	semidirect
88. #14583003	C₂²	semidirect
89. #14583002	C₂²	semidirect
90. #14582998	C₂²	semidirect
91. #14582997	C₂²	semidirect
92. #14582997	C₂²	semidirect
93. C₄×Dic₁₇₂	C₂²	semidirect
94. Q₁₆×Dic₄₃	C₂²	semidirect
95. Q₁₆×Dic₄₃	C₂²	semidirect
96. #14582993	C₂²	semidirect
97. #14582991	C₂²	semidirect
98. C₄×#10621873	C₂²	semidirect
99. #14582984	C₂²	semidirect
100. C₄×D₃₄₄	C₂²	semidirect
101. #14582981	C₂²	semidirect
121. C₄₃×#500	C₂²	semidirect
122. C₄₃×#494	C₂²	semidirect
123. C₄₃×#487	C₂²	semidirect
127. C₄×Q₁₆×C₄₃	C₂²	semidirect
128. C₄×Q₁₆×C₄₃	C₂²	semidirect
129. C₄×Q₁₆×C₄₃	C₂²	semidirect
545. #3170	D₄₃	semidirect
596. #500	C₂×D₄₃	semidirect
604. #494	C₂×D₄₃	semidirect
612. #487	C₂×D₄₃	semidirect
646. C₄×Q₁₆	C₂×D₄₃	semidirect
647. C₄×Q₁₆	C₂×D₄₃	semidirect
648. C₄×Q₁₆	C₂×D₄₃	semidirect
672. C₄₃	#60708	semidirect

Maximal subgroups

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

subgroup	index
#19148342	2
#19145299	2
#19145298	2
#19145270	2
#19145267	2
#19145251	2
#19145250	2
#19145237	2
#19145236	2
#19145176	2
#19145166	2
#19145165	2
#19145128	2
#19145083	2
#19144955	2
#19144222	2
#19144178	2
#467×D₄₃	2
#19143470	2
#19143458	2
#19143433	2
C₂×#14582853	2
C₄₃×#3170	2
#60708	43