Subgroups — D₄₃×#3174 #25966399

Order 11008.

1970 conjugacy classes of subgroups.

The subgroup lattice has 1048 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#541×D₄₃	C₂	1	1	yes	maximal, characteristic, complemented
2	#540×D₄₃	C₂	1	1	yes	maximal, characteristic
3	#19145226	C₂	1	1	yes	maximal, characteristic, complemented
4	#19145225	C₂	1	1	yes	maximal, characteristic, complemented
5	#19145224	C₂	1	1	yes	maximal, characteristic, complemented
6	#19145223	C₂	1	1	yes	maximal, characteristic, complemented
7	#19145222	C₂	1	1	yes	maximal, characteristic, complemented
8	#19145221	C₂	1	2	yes	maximal, complemented
9	#19145220	C₂	1	1	yes	maximal, characteristic, complemented
10	#19145219	C₂	1	2	yes	maximal, complemented
11	#19145218	C₂	1	2	yes	maximal, complemented
12	#19145217	C₂	1	1	yes	maximal, characteristic, complemented
13	#19145216	C₂	1	2	yes	maximal, complemented
14	#499×D₄₃	C₂	1	1	yes	maximal, characteristic, complemented
15	#492×D₄₃	C₂	1	1	yes	maximal, characteristic, complemented
16	#491×D₄₃	C₂	1	1	yes	maximal, characteristic, complemented
17	#490×D₄₃	C₂	1	1	yes	maximal, characteristic, complemented
18	#468×D₄₃	C₂	1	2	yes	maximal, complemented
19	#465×D₄₃	C₂	1	2	yes	maximal, complemented
20	#440×D₄₃	C₂	1	2	yes	maximal, complemented
21	C₄×SD₁₆×D₄₃	C₂	1	2	yes	maximal, complemented
22	#405×D₄₃	C₂	1	1	yes	maximal, characteristic, complemented
23	C₄₃×#3174	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×SD₁₆×D₄₃	C₂²	1	2	yes	—
25	C₂×SD₁₆×D₄₃	C₂²	1	2	yes	—
26	C₂×M₁₆×D₄₃	C₂²	1	1	yes	characteristic
27	C₂²×C₈×D₄₃	C₂²	1	1	yes	characteristic
28	#14583512	C₂²	1	1	yes	characteristic, complemented
29	#14583511	C₂²	1	1	yes	characteristic, complemented
30	#14583510	C₂²	1	1	yes	characteristic, complemented
31	#14583509	C₂²	1	2	yes	complemented
32	#14583508	—	2	2	no	—
33	#14583507	C₂²	1	2	yes	complemented
34	#14583506	—	2	2	no	—
35	#14583505	C₂²	1	1	yes	characteristic
36	#14583504	C₂²	1	1	yes	characteristic
37	#14583503	C₂²	1	1	yes	characteristic
38	#14583502	C₂²	1	2	yes	—
39	#14583501	—	2	2	no	—
40	#14583500	C₂²	1	2	yes	—
41	#14583499	—	2	2	no	—
42	C₄⋊Q₈×D₄₃	C₂²	1	1	yes	characteristic
43	#127×D₄₃	C₂²	1	1	yes	characteristic
44	#126×D₄₃	—	2	2	no	—
45	#125×D₄₃	—	2	2	no	—
46	#125×D₄₃	C₂²	1	1	yes	characteristic
47	#125×D₄₃	C₂²	1	1	yes	characteristic
48	#123×D₄₃	—	2	2	no	—
49	C₂²⋊Q₈×D₄₃	C₂²	1	2	yes	—
50	#121×D₄₃	—	2	2	no	—
51	#121×D₄₃	C₂²	1	2	yes	—
52	C₄×Q₈×D₄₃	C₂²	1	2	yes	—
53	C₄×D₄×D₄₃	C₂²	1	2	yes	—
54	#117×D₄₃	C₂²	1	1	yes	characteristic
55	#14583301	C₂²	1	1	yes	characteristic, complemented
56	#14583300	C₂²	1	2	yes	complemented
57	#14583299	C₂²	1	2	yes	complemented
58	#14583298	C₂²	1	1	yes	characteristic, complemented
59	#14583298	C₂²	1	1	yes	characteristic, complemented
60	#14583273	C₂²	1	1	yes	characteristic, complemented
61	#14583272	C₂²	1	1	yes	characteristic, complemented
62	#14583271	C₂²	1	1	yes	characteristic, complemented
63	#14583270	C₂²	1	2	yes	complemented
64	#14583270	C₂²	1	2	yes	complemented
65	#14583269	C₂²	1	1	yes	characteristic, complemented
66	#14583268	C₂²	1	1	yes	characteristic, complemented
67	#14583267	C₂²	1	1	yes	characteristic, complemented
68	#14583266	C₂²	1	2	yes	complemented
69	#14583266	C₂²	1	2	yes	complemented
70	#14583265	C₂²	1	1	yes	characteristic, complemented
71	#14583264	C₂²	1	1	yes	characteristic, complemented
72	#14583263	C₂²	1	1	yes	characteristic, complemented
73	#14583262	C₂²	1	2	yes	complemented
74	#14583262	C₂²	1	2	yes	complemented
75	#14583148	C₂²	1	2	yes	complemented
76	#14583147	C₂²	1	2	yes	complemented
77	#14583146	C₂²	1	2	yes	complemented
78	#14583145	C₂²	1	2	yes	complemented
79	#14583144	C₂²	1	2	yes	complemented
80	#14583143	C₂²	1	2	yes	complemented
81	#14583142	C₂²	1	2	yes	complemented
82	#14583131	C₂²	1	2	yes	complemented
83	#14583130	C₂²	1	2	yes	complemented
84	#14583129	C₂²	1	2	yes	complemented
85	#14583128	C₂²	1	2	yes	complemented
86	#14583127	C₂²	1	2	yes	complemented
87	#14583126	C₂²	1	2	yes	complemented
88	#14583125	C₂²	1	2	yes	complemented
89	#14583002	C₂²	1	2	yes	complemented
90	#14583001	C₂²	1	2	yes	complemented
91	#14583000	C₂²	1	2	yes	complemented
92	#14582999	C₂²	1	2	yes	complemented
93	#14582998	C₂²	1	2	yes	complemented
94	#14582997	C₂²	1	2	yes	complemented
95	#14582996	C₂²	1	2	yes	complemented
96	#14582990	C₂²	1	2	yes	complemented
97	C₄×#10621873	C₂²	1	2	yes	complemented
98	SD₁₆×Dic₄₃	C₂²	1	2	yes	complemented
99	C₄×#10621884	C₂²	1	2	yes	complemented
100	#14582986	C₂²	1	2	yes	complemented
101	C₄×#10621883	C₂²	1	2	yes	complemented
102	#14582984	C₂²	1	2	yes	complemented
103	#107×D₄₃	C₂²	1	2	yes	—
104	#106×D₄₃	C₂²	1	2	yes	—
105	#103×D₄₃	C₂²	1	2	yes	—
106	#103×D₄₃	C₂²	1	2	yes	—
107	#102×D₄₃	C₂²	1	2	yes	—
108	#102×D₄₃	C₂²	1	2	yes	—
109	#14582857	C₂²	1	1	yes	characteristic, complemented
110	#14582856	C₂²	1	1	yes	characteristic, complemented
111	#14582856	C₂²	1	1	yes	characteristic, complemented
112	#14582855	C₂²	1	1	yes	characteristic, complemented
113	#14582854	C₂²	1	1	yes	characteristic, complemented
114	#14582853	C₂²	1	1	yes	characteristic, complemented
115	#14582853	C₂²	1	1	yes	characteristic, complemented
116	#97×D₄₃	C₂²	1	1	yes	characteristic
117	#97×D₄₃	C₂²	1	1	yes	characteristic
118	C₄×C₈×D₄₃	C₂²	1	1	yes	characteristic
119	C₄×C₈×D₄₃	C₂²	1	1	yes	characteristic
120	C₄₃×#541	C₂²	1	1	yes	characteristic, complemented
121	C₄₃×#540	C₂²	1	1	yes	characteristic
122	C₄₃×#499	C₂²	1	1	yes	characteristic, complemented
123	C₄₃×#492	C₂²	1	1	yes	characteristic, complemented
124	C₄₃×#491	C₂²	1	1	yes	characteristic, complemented
125	C₄₃×#490	C₂²	1	1	yes	characteristic, complemented
126	C₄₃×#468	C₂²	1	2	yes	complemented
127	C₄₃×#465	C₂²	1	2	yes	complemented
128	C₄₃×#440	C₂²	1	2	yes	complemented
129	C₄×SD₁₆×C₄₃	C₂²	1	2	yes	complemented
130	C₄₃×#405	C₂²	1	1	yes	characteristic, complemented
131	C₂×Q₈×D₄₃	C₂³	1	2	yes	—
132	C₂×D₄×D₄₃	—	2	2	no	—
133	C₂×D₄×D₄₃	—	2	2	no	—
134	C₂×D₄×D₄₃	C₂³	1	2	yes	—
135	C₂²×C₄×D₄₃	—	2	2	no	—
136	C₂²×C₄×D₄₃	C₂³	1	1	yes	characteristic
137	C₂×#10621873	C₂³	1	2	yes	—
138	C₂×#10621873	C₂³	1	2	yes	—
139	C₂×#10621883	C₂³	1	2	yes	—
140	C₂×#10621883	C₂³	1	2	yes	—
141	C₂×#10621884	C₂³	1	2	yes	—
142	C₂×#10621884	C₂³	1	2	yes	—
143	SD₁₆×D₄₃	—	2	8	no	—
144	SD₁₆×D₄₃	—	2	8	no	—
145	C₂×#10621877	C₂³	1	1	yes	characteristic
146	C₂×#10621872	C₂³	1	1	yes	characteristic
147	C₂×#10621872	C₂³	1	1	yes	characteristic
148	M₁₆×D₄₃	—	2	4	no	—
149	C₂²×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
150	C₂×C₈×D₄₃	—	2	4	no	—
151	C₂×C₈×D₄₃	C₂³	1	1	yes	characteristic
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	C₂×C₈×D₄₃	C₂³	1	1	yes	characteristic
157	#13063325	C₂³	1	1	yes	characteristic
158	#13063324	—	2	2	no	—
159	#13063323	C₂³	1	2	yes	—
160	#13063322	C₂³	1	1	yes	characteristic
161	#13063321	—	2	2	no	—
162	#13063321	C₂³	1	2	yes	—
163	#13063320	—	2	2	no	—
164	#13063320	—	2	2	no	—
165	#13063320	—	2	2	no	—
166	#13063319	—	2	2	no	—
167	#13063318	—	2	2	no	—
168	#13063318	—	2	2	no	—
169	#13063318	—	2	2	no	—
170	#13063317	—	2	2	no	—
171	#13063317	C₂³	1	1	yes	characteristic
172	#13063317	C₂³	1	1	yes	characteristic
173	#13063316	—	2	2	no	—
174	#13063316	—	2	2	no	—
175	#13063316	C₂³	1	2	yes	—
176	#13063316	C₂³	1	2	yes	—
177	#13063315	—	2	2	no	—
178	#13063315	—	2	2	no	—
179	#13063315	—	2	2	no	—
180	#13063315	—	2	2	no	—
181	#13063315	—	2	2	no	—
182	#13063315	—	2	2	no	—
183	#13063310	—	2	2	no	—
184	#13063310	—	2	2	no	—
185	#13063309	—	2	2	no	—
186	#13063308	—	2	2	no	—
187	#13063307	—	2	2	no	—
188	#13063307	—	2	2	no	—
189	#13063306	—	2	2	no	—
190	#13063305	C₂³	1	2	yes	—
191	#13063304	C₂³	1	2	yes	—
192	#13063303	—	2	2	no	—
193	#13063302	—	2	2	no	—
194	#13063301	C₂³	1	2	yes	—
195	#13063300	—	2	2	no	—
196	#13063300	C₂³	1	2	yes	—
197	#13063299	—	2	2	no	—
198	#13063299	C₂³	1	2	yes	—
199	#13063298	—	2	2	no	—
200	#13063298	—	2	2	no	—
201	#13063298	—	2	2	no	—
202	#13063297	—	2	2	no	—
203	#13063297	—	2	2	no	—
204	#13063297	—	2	2	no	—
205	#13063296	—	2	2	no	—
206	#13063296	C₂³	1	2	yes	—
207	Q₈×Dic₄₃	C₂³	1	2	yes	—
208	C₄×Dic₈₆	—	2	2	no	—
209	C₄×Dic₈₆	C₂³	1	2	yes	—
210	#13063290	—	2	2	no	—
211	#13063290	C₂³	1	2	yes	—
212	C₄×D₁₇₂	C₂³	1	2	yes	—
213	D₄×Dic₄₃	C₂³	1	2	yes	—
214	#13063287	C₂³	1	2	yes	—
215	C₄×C₂²⋊D₄₃	—	2	2	no	—
216	(C₂²⋊D₄₃)⋊C₄	—	2	2	no	—
217	#13063284	C₂³	1	1	yes	characteristic
218	#13063283	D₄	1	2	yes	—
219	#13063282	C₂³	1	1	yes	characteristic
220	#13063282	C₂³	1	1	yes	characteristic
221	#13063281	D₄	1	2	yes	—
222	C₄⋊C₄×D₄₃	—	2	2	no	—
223	C₄⋊C₄×D₄₃	—	2	2	no	—
224	C₄⋊C₄×D₄₃	—	2	2	no	—
225	C₄⋊C₄×D₄₃	—	2	2	no	—
226	C₄⋊C₄×D₄₃	—	2	2	no	—
227	C₄⋊C₄×D₄₃	D₄	1	2	yes	—
228	C₄⋊C₄×D₄₃	C₂³	1	2	yes	—
229	C₄⋊C₄×D₄₃	C₂³	1	2	yes	—
230	C₂²⋊C₄×D₄₃	—	2	2	no	—
231	C₂²⋊C₄×D₄₃	—	2	2	no	—
232	C₂²⋊C₄×D₄₃	—	2	2	no	—
233	C₂²⋊C₄×D₄₃	D₄	1	2	yes	—
234	C₄²×D₄₃	—	2	2	no	—
235	C₄²×D₄₃	C₂³	1	1	yes	characteristic
236	C₄²×D₄₃	C₂³	1	1	yes	characteristic
237	#13063259	C₂³	1	2	yes	—
238	#13063258	C₂³	1	2	yes	—
239	#13063258	C₂³	1	2	yes	—
240	#13063257	C₂³	1	2	yes	—
241	#13063256	C₂³	1	2	yes	—
242	#13063256	C₂³	1	2	yes	—
243	#13063250	C₂³	1	2	yes	—
244	#13063250	C₂³	1	2	yes	—
245	#13063249	C₂³	1	2	yes	—
246	#13063249	C₂³	1	2	yes	—
247	#13063248	C₂³	1	2	yes	—
248	#13063248	C₂³	1	2	yes	—
249	#13063247	C₂³	1	2	yes	—
250	#13063247	C₂³	1	2	yes	—
251	#13063246	C₂³	1	2	yes	—
252	#13063246	C₂³	1	2	yes	—
253	#13063245	C₂³	1	2	yes	—
254	#13063245	C₂³	1	2	yes	—
255	#13063236	C₂³	1	1	yes	characteristic
256	#13063236	C₂³	1	1	yes	characteristic
257	#13063235	C₂³	1	1	yes	characteristic
258	#13063235	C₂³	1	1	yes	characteristic
259	#13063235	C₂³	1	1	yes	characteristic
260	#13063235	C₂³	1	1	yes	characteristic
261	C₄×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
262	C₄×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
263	C₈×Dic₄₃	C₂³	1	1	yes	characteristic
264	C₈×Dic₄₃	C₂³	1	1	yes	characteristic
265	C₈×Dic₄₃	C₂³	1	1	yes	characteristic
266	C₈×Dic₄₃	C₂³	1	1	yes	characteristic
267	C₂×SD₁₆×C₄₃	C₂³	1	2	yes	—
268	C₂×SD₁₆×C₄₃	C₂³	1	2	yes	—
269	C₂×M₁₆×C₄₃	C₂³	1	1	yes	characteristic
270	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
271	C₄⋊Q₈×C₄₃	C₂³	1	1	yes	characteristic
272	#127×C₄₃	C₂³	1	1	yes	characteristic
273	#126×C₄₃	—	2	2	no	—
274	#125×C₄₃	—	2	2	no	—
275	#125×C₄₃	C₂³	1	1	yes	characteristic
276	#125×C₄₃	C₂³	1	1	yes	characteristic
277	#123×C₄₃	—	2	2	no	—
278	C₂²⋊Q₈×C₄₃	C₂³	1	2	yes	—
279	#121×C₄₃	—	2	2	no	—
280	#121×C₄₃	C₂³	1	2	yes	—
281	C₄×Q₈×C₄₃	C₂³	1	2	yes	—
282	C₄×D₄×C₄₃	C₂³	1	2	yes	—
283	#117×C₄₃	C₂³	1	1	yes	characteristic
284	#107×C₄₃	C₂³	1	2	yes	—
285	#106×C₄₃	C₂³	1	2	yes	—
286	#103×C₄₃	C₂³	1	2	yes	—
287	#103×C₄₃	C₂³	1	2	yes	—
288	#102×C₄₃	C₂³	1	2	yes	—
289	#102×C₄₃	C₂³	1	2	yes	—
290	#97×C₄₃	C₂³	1	1	yes	characteristic
291	#97×C₄₃	C₂³	1	1	yes	characteristic
292	C₄×C₈×C₄₃	C₂³	1	1	yes	characteristic
293	C₄×C₈×C₄₃	C₂³	1	1	yes	characteristic
294	C₂³×D₄₃	—	2	2	no	—
295	C₂³×D₄₃	C₂×D₄	1	1	yes	characteristic
296	C₂×Q₈×C₄₃	C₂⁴	1	2	yes	—
297	C₂×D₄×C₄₃	—	2	2	no	—
298	C₂×D₄×C₄₃	—	2	2	no	—
299	C₂×D₄×C₄₃	C₂⁴	1	2	yes	—
300	C₂²×C₄×C₄₃	—	2	2	no	—
301	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
302	C₂×C₂²⋊D₄₃	—	2	2	no	—
303	C₂×C₂²⋊D₄₃	—	2	2	no	—
304	C₂×C₂²⋊D₄₃	—	2	2	no	—
305	C₂×C₂²⋊D₄₃	—	2	2	no	—
306	C₂×C₂²⋊D₄₃	—	2	2	no	—
307	C₂²×Dic₄₃	—	2	2	no	—
308	C₂²×Dic₄₃	C₂×D₄	1	1	yes	characteristic
309	Q₈×D₄₃	—	2	4	no	—
310	Q₈×D₄₃	—	2	4	no	—
311	D₄×D₄₃	—	2	4	no	—
312	D₄×D₄₃	—	2	4	no	—
313	D₄×D₄₃	—	8	4	no	—
314	D₄×D₄₃	—	8	4	no	—
315	C₂×D₁₇₂	—	2	2	no	—
316	C₂×D₁₇₂	—	2	2	no	—
317	C₂×D₁₇₂	C₂⁴	1	2	yes	—
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	—	2	2	no	—
325	C₂×C₄×D₄₃	—	8	4	no	—
326	C₂×C₄×D₄₃	C₂×D₄	1	2	yes	—
327	C₂×C₄×D₄₃	C₂×D₄	1	2	yes	—
328	C₂×C₄×D₄₃	C₂×D₄	1	1	yes	characteristic
329	C₂×C₄×D₄₃	C₂×D₄	1	1	yes	characteristic
330	C₂×C₄×D₄₃	C₂⁴	1	1	yes	characteristic
331	C₂×C₄×D₄₃	C₂⁴	1	1	yes	characteristic
332	C₂×Dic₈₆	—	2	2	no	—
333	C₂×Dic₈₆	C₂⁴	1	2	yes	—
334	SD₁₆×C₄₃	—	2	4	no	—
335	SD₁₆×C₄₃	—	2	4	no	—
336	M₁₆×C₄₃	—	2	2	no	—
337	C₂×C₈×C₄₃	—	2	2	no	—
338	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
339	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
340	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
341	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
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	C₂×D₄	1	2	yes	—
348	C₄⋊C₄×C₄₃	C₂⁴	1	2	yes	—
349	C₄⋊C₄×C₄₃	C₂⁴	1	2	yes	—
350	C₂²⋊C₄×C₄₃	—	2	2	no	—
351	C₂²⋊C₄×C₄₃	—	2	2	no	—
352	C₂²⋊C₄×C₄₃	—	2	2	no	—
353	C₂²⋊C₄×C₄₃	C₂×D₄	1	2	yes	—
354	C₄²×C₄₃	—	2	2	no	—
355	C₄²×C₄₃	C₂⁴	1	1	yes	characteristic
356	C₄²×C₄₃	C₂⁴	1	1	yes	characteristic
357	C₂²⋊Dic₄₃	—	2	2	no	—
358	C₂²⋊Dic₄₃	—	2	2	no	—
359	C₂²⋊Dic₄₃	—	2	2	no	—
360	C₂²⋊Dic₄₃	C₂×D₄	1	2	yes	—
361	#10621884	—	2	4	no	—
362	#10621884	—	2	4	no	—
363	#10621883	—	2	4	no	—
364	#10621883	—	2	4	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	C₂×D₄	1	2	yes	—
372	(C₂×D₄₃)⋊C₄	C₂×D₄	1	2	yes	—
373	C₄⋊Dic₄₃	—	2	2	no	—
374	C₄⋊Dic₄₃	—	2	2	no	—
375	C₄⋊Dic₄₃	—	2	2	no	—
376	C₄⋊Dic₄₃	—	2	2	no	—
377	C₄⋊Dic₄₃	—	2	2	no	—
378	C₄⋊Dic₄₃	C₂×D₄	1	2	yes	—
379	C₄⋊Dic₄₃	C₂⁴	1	2	yes	—
380	C₄⋊Dic₄₃	C₂⁴	1	2	yes	—
381	Dic₄₃⋊C₄	—	2	2	no	—
382	Dic₄₃⋊C₄	—	2	2	no	—
383	Dic₄₃⋊C₄	—	2	2	no	—
384	Dic₄₃⋊C₄	—	2	2	no	—
385	Dic₄₃⋊C₄	—	2	2	no	—
386	Dic₄₃⋊C₄	—	2	2	no	—
387	Dic₄₃⋊C₄	—	2	2	no	—
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	C₂×D₄	1	2	yes	—
394	Dic₄₃⋊C₄	C₂×D₄	1	2	yes	—
395	C₄×Dic₄₃	—	2	2	no	—
396	C₄×Dic₄₃	—	2	2	no	—
397	C₄×Dic₄₃	—	2	2	no	—
398	C₄×Dic₄₃	C₂×D₄	1	2	yes	—
399	C₄×Dic₄₃	C₂×D₄	1	2	yes	—
400	C₄×Dic₄₃	C₂⁴	1	1	yes	characteristic
401	C₄×Dic₄₃	C₂⁴	1	1	yes	characteristic
402	#10621877	—	2	2	no	—
403	C₂×C₄₃⋊C₈	—	2	2	no	—
404	C₂×C₄₃⋊C₈	C₂⁴	1	1	yes	characteristic
405	C₂×C₄₃⋊C₈	C₂⁴	1	1	yes	characteristic
406	C₂×C₄₃⋊C₈	C₂⁴	1	1	yes	characteristic
407	C₂×C₄₃⋊C₈	C₂⁴	1	1	yes	characteristic
408	#10621873	—	2	4	no	—
409	#10621873	—	2	4	no	—
410	#10621872	—	2	2	no	—
411	#10621872	—	2	2	no	—
412	C₈×D₄₃	—	2	2	no	—
413	C₈×D₄₃	—	2	2	no	—
414	C₈×D₄₃	—	2	2	no	—
415	C₈×D₄₃	—	2	2	no	—
416	C₈×D₄₃	#41	1	4	yes	—
417	C₈×D₄₃	#41	1	4	yes	—
418	C₂³×C₄₃	—	2	2	no	—
419	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
420	C₂²×D₄₃	—	2	2	no	—
421	C₂²×D₄₃	—	2	4	no	—
422	C₂²×D₄₃	—	2	2	no	—
423	C₂²×D₄₃	—	4	4	no	—
424	C₂²×D₄₃	—	4	4	no	—
425	C₂²×D₄₃	—	4	4	no	—
426	C₂²×D₄₃	C₂²×D₄	1	1	yes	characteristic
427	C₂²×D₄₃	C₂²×D₄	1	1	yes	characteristic
428	Q₈×C₄₃	—	2	2	no	—
429	Q₈×C₄₃	—	2	2	no	—
430	D₄×C₄₃	—	2	2	no	—
431	D₄×C₄₃	—	2	2	no	—
432	D₄×C₄₃	—	8	2	no	—
433	D₄×C₄₃	—	8	2	no	—
434	C₂×C₄×C₄₃	—	2	1	no	—
435	C₂×C₄×C₄₃	—	2	1	no	—
436	C₂×C₄×C₄₃	—	2	2	no	—
437	C₂×C₄×C₄₃	—	2	2	no	—
438	C₂×C₄×C₄₃	—	2	2	no	—
439	C₂×C₄×C₄₃	—	8	2	no	—
440	C₂×C₄×C₄₃	C₂²×D₄	1	2	yes	—
441	C₂×C₄×C₄₃	C₂²×D₄	1	2	yes	—
442	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
443	C₂×C₄×C₄₃	C₂⁵	1	1	yes	characteristic
444	C₂²⋊D₄₃	—	4	4	no	—
445	C₂²⋊D₄₃	—	8	2	no	—
446	C₂²⋊D₄₃	—	8	2	no	—
447	C₂²⋊D₄₃	—	8	2	no	—
448	C₂²⋊D₄₃	—	8	2	no	—
449	C₂×Dic₄₃	—	2	2	no	—
450	C₂×Dic₄₃	—	2	2	no	—
451	C₂×Dic₄₃	—	2	2	no	—
452	C₂×Dic₄₃	—	2	2	no	—
453	C₂×Dic₄₃	—	8	2	no	—
454	C₂×Dic₄₃	C₂²×D₄	1	2	yes	—
455	C₂×Dic₄₃	C₂²×D₄	1	2	yes	—
456	C₂×Dic₄₃	C₂²×D₄	1	1	yes	characteristic
457	C₂×Dic₄₃	C₂²×D₄	1	1	yes	characteristic
458	D₁₇₂	—	2	2	no	—
459	D₁₇₂	—	2	2	no	—
460	D₁₇₂	—	8	2	no	—
461	D₁₇₂	—	8	2	no	—
462	C₄×D₄₃	—	2	2	no	—
463	C₄×D₄₃	—	2	4	no	—
464	C₄×D₄₃	—	2	4	no	—
465	C₄×D₄₃	—	2	1	no	—
466	C₄×D₄₃	—	2	1	no	—
467	C₄×D₄₃	—	2	2	no	—
468	C₄×D₄₃	—	4	4	no	—
469	C₄×D₄₃	—	4	4	no	—
470	C₄×D₄₃	—	4	4	no	—
471	C₄×D₄₃	—	8	2	no	—
472	C₄×D₄₃	—	8	2	no	—
473	C₄×D₄₃	C₂×#41	1	2	yes	—
474	C₄×D₄₃	C₂×#41	1	2	yes	—
475	Dic₈₆	—	2	2	no	—
476	Dic₈₆	—	2	2	no	—
477	Dic₈₆	—	4	4	no	—
478	C₈×C₄₃	—	2	1	no	—
479	C₈×C₄₃	—	2	1	no	—
480	C₈×C₄₃	C₂×#41	1	2	yes	—
481	C₈×C₄₃	C₂×#41	1	2	yes	—
482	C₄₃⋊C₈	—	2	1	no	—
483	C₄₃⋊C₈	—	2	1	no	—
484	C₄₃⋊C₈	C₂×#41	1	2	yes	—
485	C₄₃⋊C₈	C₂×#41	1	2	yes	—
486	C₂×#3174	—	43	1	no	maximal, Sylow
487	C₂²×C₄₃	—	2	1	no	—
488	C₂²×C₄₃	—	2	2	no	—
489	C₂²×C₄₃	—	4	2	no	—
490	C₂²×C₄₃	—	4	2	no	—
491	C₂²×C₄₃	—	4	2	no	—
492	C₂²×C₄₃	C₂³×D₄	1	1	yes	characteristic
493	C₂×D₄₃	—	2	1	no	—
494	C₂×D₄₃	—	2	2	no	—
495	C₂×D₄₃	—	4	4	no	—
496	C₂×D₄₃	—	4	2	no	—
497	C₂×D₄₃	—	4	2	no	—
498	C₂×D₄₃	—	4	2	no	—
499	C₂×D₄₃	—	8	8	no	—
500	C₂×D₄₃	#532	1	2	yes	—
501	C₂×D₄₃	#577	1	4	yes	—
502	C₄×C₄₃	—	2	1	no	—
503	C₄×C₄₃	—	2	2	no	—
504	C₄×C₄₃	—	2	2	no	—
505	C₄×C₄₃	—	4	2	no	—
506	C₄×C₄₃	—	4	2	no	—
507	C₄×C₄₃	—	4	2	no	—
508	C₄×C₄₃	C₂²×#41	1	1	yes	characteristic
509	C₄×C₄₃	C₂²×#41	1	1	yes	characteristic
510	Dic₄₃	—	2	1	no	—
511	Dic₄₃	—	2	2	no	—
512	Dic₄₃	—	2	2	no	—
513	Dic₄₃	—	4	2	no	—
514	Dic₄₃	—	4	2	no	—
515	Dic₄₃	—	4	2	no	—
516	Dic₄₃	#532	1	2	yes	—
517	C₂×#541	—	43	1	no	—
518	C₂×#540	—	43	1	no	—
519	#3174	—	43	1	no	—
520	#3174	—	43	1	no	—
521	#3174	—	43	1	no	—
522	#3174	—	43	1	no	—
523	#3174	—	43	2	no	—
524	#3174	—	43	2	no	—
525	#3174	—	43	2	no	—
526	#3174	—	43	2	no	—
527	#3174	—	43	1	no	—
528	#3174	—	43	1	no	—
529	#3174	—	43	1	no	—
530	#3174	D₄₃	1	1	yes	characteristic, direct product factor
531	C₂×#499	—	43	1	no	—
532	C₂×#492	—	43	1	no	—
533	C₂×#491	—	43	1	no	—
534	C₂×#490	—	43	1	no	—
535	C₂×#468	—	43	2	no	—
536	C₂×#465	—	43	2	no	—
537	C₂×#440	—	43	2	no	—
538	C₂×C₄×SD₁₆	—	43	2	no	—
539	C₂×#405	—	43	1	no	—
540	C₂×C₄₃	—	4	1	no	—
541	C₂×C₄₃	—	8	2	no	—
542	C₂×C₄₃	C₂×#532	1	1	yes	characteristic
543	C₂×C₄₃	C₂×#577	1	2	yes	—
544	D₄₃	—	4	1	no	—
545	D₄₃	—	8	2	no	—
546	D₄₃	#3174	1	4	yes	direct product factor
547	C₂²×SD₁₆	—	43	2	no	—
548	C₂²×SD₁₆	—	43	2	no	—
549	C₂²×M₁₆	—	43	1	no	—
550	C₂³×C₈	—	43	1	no	—
551	#541	—	43	1	no	—
552	#541	—	43	1	no	—
553	#541	—	43	2	no	—
554	#541	—	43	2	no	—
555	#541	—	43	1	no	—
556	#541	—	86	2	no	—
557	#541	—	86	2	no	—
558	#541	C₂×D₄₃	1	1	yes	characteristic, complemented
559	#540	—	43	1	no	—
560	#540	—	43	1	no	—
561	#540	—	43	2	no	—
562	#540	—	43	2	no	—
563	#540	—	43	1	no	—
564	#540	—	86	2	no	—
565	#540	—	86	2	no	—
566	#540	C₂×D₄₃	1	1	yes	characteristic
567	C₂×C₄⋊Q₈	—	43	1	no	—
568	C₂×#127	—	43	1	no	—
569	C₂×#126	—	86	2	no	—
570	C₂×#125	—	43	1	no	—
571	C₂×#125	—	43	1	no	—
572	C₂×#125	—	86	2	no	—
573	C₂×#123	—	86	2	no	—
574	C₂×C₂²⋊Q₈	—	43	2	no	—
575	C₂×#121	—	43	2	no	—
576	C₂×#121	—	86	2	no	—
577	C₂×C₄×Q₈	—	43	2	no	—
578	C₂×C₄×D₄	—	43	2	no	—
579	C₂×#117	—	43	1	no	—
580	#499	—	43	1	no	—
581	#499	—	43	1	no	—
582	#499	—	43	2	no	—
583	#499	—	43	2	no	—
584	#499	—	43	1	no	—
585	#499	C₂×D₄₃	1	1	yes	characteristic, complemented
586	#492	—	43	2	no	—
587	#492	—	43	2	no	—
588	#492	—	43	1	no	—
589	#492	—	43	1	no	—
590	#492	—	43	1	no	—
591	#492	C₂×D₄₃	1	1	yes	characteristic, complemented
592	#491	—	43	1	no	—
593	#491	—	43	1	no	—
594	#491	—	43	2	no	—
595	#491	—	43	2	no	—
596	#491	—	43	1	no	—
597	#491	C₂×D₄₃	1	1	yes	characteristic, complemented
598	#490	—	43	1	no	—
599	#490	—	43	1	no	—
600	#490	—	43	2	no	—
601	#490	—	43	2	no	—
602	#490	—	43	1	no	—
603	#490	C₂×D₄₃	1	1	yes	characteristic, complemented
604	#468	—	43	2	no	—
605	#468	—	43	2	no	—
606	#468	—	43	2	no	—
607	#468	—	43	2	no	—
608	#468	—	43	2	no	—
609	#468	—	43	2	no	—
610	#468	—	43	2	no	—
611	#468	C₂×D₄₃	1	2	yes	complemented
612	#465	—	43	2	no	—
613	#465	—	43	2	no	—
614	#465	—	43	2	no	—
615	#465	—	43	2	no	—
616	#465	—	43	2	no	—
617	#465	—	43	2	no	—
618	#465	—	43	2	no	—
619	#465	C₂×D₄₃	1	2	yes	complemented
620	#440	—	43	2	no	—
621	#440	—	43	2	no	—
622	#440	—	43	2	no	—
623	#440	—	43	2	no	—
624	#440	—	43	2	no	—
625	#440	—	43	2	no	—
626	#440	—	43	2	no	—
627	#440	C₂×D₄₃	1	2	yes	complemented
628	C₄×SD₁₆	—	43	2	no	—
629	C₄×SD₁₆	—	43	2	no	—
630	C₄×SD₁₆	—	43	2	no	—
631	C₄×SD₁₆	—	43	2	no	—
632	C₄×SD₁₆	—	43	2	no	—
633	C₄×SD₁₆	—	43	2	no	—
634	C₄×SD₁₆	—	43	2	no	—
635	C₄×SD₁₆	C₂×D₄₃	1	2	yes	complemented
636	C₂×#107	—	43	2	no	—
637	C₂×#106	—	43	2	no	—
638	C₂×#103	—	43	2	no	—
639	C₂×#103	—	43	2	no	—
640	C₂×#102	—	43	2	no	—
641	C₂×#102	—	43	2	no	—
642	#405	—	43	1	no	—
643	#405	—	43	1	no	—
644	#405	—	43	1	no	—
645	#405	—	43	1	no	—
646	#405	—	43	1	no	—
647	#405	—	43	1	no	—
648	#405	—	43	1	no	—
649	#405	C₂×D₄₃	1	1	yes	characteristic, complemented
650	C₂×#97	—	43	1	no	—
651	C₂×#97	—	43	1	no	—
652	C₂×C₄×C₈	—	43	1	no	—
653	C₂×C₄×C₈	—	43	1	no	—
654	C₄₃	C₂×#3174	1	1	yes	characteristic, complemented, Sylow
655	C₂²×Q₈	—	43	2	no	—
656	C₂²×D₄	—	43	2	no	—
657	C₂²×D₄	—	86	2	no	—
658	C₂²×D₄	—	86	2	no	—
659	C₂³×C₄	—	43	1	no	—
660	C₂³×C₄	—	86	2	no	—
661	C₂×SD₁₆	—	43	2	no	—
662	C₂×SD₁₆	—	43	2	no	—
663	C₂×SD₁₆	—	43	2	no	—
664	C₂×SD₁₆	—	43	2	no	—
665	C₂×SD₁₆	—	43	2	no	—
666	C₂×SD₁₆	—	43	2	no	—
667	C₂×SD₁₆	—	86	8	no	—
668	C₂×SD₁₆	—	86	8	no	—
669	C₂×SD₁₆	C₂²×D₄₃	1	2	yes	—
670	C₂×SD₁₆	C₂²×D₄₃	1	2	yes	—
671	C₂×M₁₆	—	43	1	no	—
672	C₂×M₁₆	—	43	1	no	—
673	C₂×M₁₆	—	43	1	no	—
674	C₂×M₁₆	—	86	4	no	—
675	C₂×M₁₆	C₂²×D₄₃	1	1	yes	characteristic
676	C₂²×C₈	—	43	1	no	—
677	C₂²×C₈	—	43	1	no	—
678	C₂²×C₈	—	43	1	no	—
679	C₂²×C₈	—	43	1	no	—
680	C₂²×C₈	—	43	1	no	—
681	C₂²×C₈	—	43	1	no	—
682	C₂²×C₈	—	43	1	no	—
683	C₂²×C₈	—	86	4	no	—
684	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
685	C₄⋊Q₈	—	43	2	no	—
686	C₄⋊Q₈	—	43	1	no	—
687	C₄⋊Q₈	—	86	2	no	—
688	C₄⋊Q₈	C₂²×D₄₃	1	1	yes	characteristic
689	#127	—	43	2	no	—
690	#127	—	43	1	no	—
691	#127	—	86	2	no	—
692	#127	C₂²×D₄₃	1	1	yes	characteristic
693	#126	—	2	2	no	—
694	#126	—	86	2	no	—
695	#126	—	86	2	no	—
696	#126	—	86	2	no	—
697	#126	—	86	2	no	—
698	#126	—	86	2	no	—
699	#126	—	86	2	no	—
700	#126	—	86	2	no	—
701	#125	—	2	2	no	—
702	#125	—	43	2	no	—
703	#125	—	43	2	no	—
704	#125	—	43	1	no	—
705	#125	—	43	1	no	—
706	#125	—	86	2	no	—
707	#125	—	86	2	no	—
708	#125	—	86	2	no	—
709	#125	—	86	2	no	—
710	#125	—	86	2	no	—
711	#125	—	86	2	no	—
712	#125	—	86	2	no	—
713	#125	—	86	2	no	—
714	#125	—	86	2	no	—
715	#125	C₂²×D₄₃	1	1	yes	characteristic
716	#125	C₂²×D₄₃	1	1	yes	characteristic
717	#123	—	2	2	no	—
718	#123	—	86	2	no	—
719	#123	—	86	2	no	—
720	#123	—	86	2	no	—
721	#123	—	86	2	no	—
722	#123	—	86	2	no	—
723	#123	—	86	2	no	—
724	#123	—	86	2	no	—
725	C₂²⋊Q₈	—	43	2	no	—
726	C₂²⋊Q₈	—	43	2	no	—
727	C₂²⋊Q₈	—	43	2	no	—
728	C₂²⋊Q₈	—	86	2	no	—
729	C₂²⋊Q₈	—	86	2	no	—
730	C₂²⋊Q₈	C₂²×D₄₃	1	2	yes	—
731	#121	—	2	2	no	—
732	#121	—	43	2	no	—
733	#121	—	43	2	no	—
734	#121	—	43	2	no	—
735	#121	—	86	2	no	—
736	#121	—	86	2	no	—
737	#121	—	86	2	no	—
738	#121	—	86	2	no	—
739	#121	—	86	2	no	—
740	#121	—	86	2	no	—
741	#121	—	86	2	no	—
742	#121	—	86	2	no	—
743	#121	—	86	2	no	—
744	#121	C₂²×D₄₃	1	2	yes	—
745	C₄×Q₈	—	43	2	no	—
746	C₄×Q₈	—	43	2	no	—
747	C₄×Q₈	—	43	2	no	—
748	C₄×Q₈	—	86	2	no	—
749	C₄×Q₈	—	86	2	no	—
750	C₄×Q₈	C₂²×D₄₃	1	2	yes	—
751	C₄×D₄	—	43	2	no	—
752	C₄×D₄	—	43	2	no	—
753	C₄×D₄	—	43	2	no	—
754	C₄×D₄	—	86	2	no	—
755	C₄×D₄	—	86	2	no	—
756	C₄×D₄	C₂²×D₄₃	1	2	yes	—
757	#117	—	43	1	no	—
758	#117	—	43	2	no	—
759	#117	—	43	2	no	—
760	#117	—	43	1	no	—
761	#117	—	43	1	no	—
762	#117	C₂²×D₄₃	1	1	yes	characteristic
763	C₂×C₄⋊C₄	—	43	2	no	—
764	C₂×C₄⋊C₄	—	43	2	no	—
765	C₂×C₄⋊C₄	—	43	2	no	—
766	C₂×C₄⋊C₄	—	86	2	no	—
767	C₂×C₄⋊C₄	—	86	2	no	—
768	C₂×C₄⋊C₄	—	86	2	no	—
769	C₂×C₄⋊C₄	—	86	2	no	—
770	C₂×C₄⋊C₄	—	86	2	no	—
771	C₂×C₂²⋊C₄	—	43	2	no	—
772	C₂×C₂²⋊C₄	—	86	2	no	—
773	C₂×C₂²⋊C₄	—	86	2	no	—
774	C₂×C₂²⋊C₄	—	86	2	no	—
775	C₂×C₄²	—	43	1	no	—
776	C₂×C₄²	—	43	1	no	—
777	C₂×C₄²	—	86	2	no	—
778	#107	—	43	2	no	—
779	#107	—	43	2	no	—
780	#107	—	43	2	no	—
781	#107	C₂²×D₄₃	1	2	yes	—
782	#106	—	43	2	no	—
783	#106	—	43	2	no	—
784	#106	—	43	2	no	—
785	#106	C₂²×D₄₃	1	2	yes	—
786	#103	—	43	2	no	—
787	#103	—	43	2	no	—
788	#103	—	43	2	no	—
789	#103	—	43	2	no	—
790	#103	—	43	2	no	—
791	#103	—	43	2	no	—
792	#103	C₂²×D₄₃	1	2	yes	—
793	#103	C₂²×D₄₃	1	2	yes	—
794	#102	—	43	2	no	—
795	#102	—	43	2	no	—
796	#102	—	43	2	no	—
797	#102	—	43	2	no	—
798	#102	—	43	2	no	—
799	#102	—	43	2	no	—
800	#102	C₂²×D₄₃	1	2	yes	—
801	#102	C₂²×D₄₃	1	2	yes	—
802	#97	—	43	1	no	—
803	#97	—	43	1	no	—
804	#97	—	43	1	no	—
805	#97	—	43	1	no	—
806	#97	—	43	1	no	—
807	#97	—	43	1	no	—
808	#97	C₂²×D₄₃	1	1	yes	characteristic
809	#97	C₂²×D₄₃	1	1	yes	characteristic
810	C₄×C₈	—	43	1	no	—
811	C₄×C₈	—	43	1	no	—
812	C₄×C₈	—	43	1	no	—
813	C₄×C₈	—	43	1	no	—
814	C₄×C₈	—	43	1	no	—
815	C₄×C₈	—	43	1	no	—
816	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
817	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
818	C₂⁴	—	43	1	no	—
819	C₂⁴	—	86	2	no	—
820	C₂×Q₈	—	43	2	no	—
821	C₂×Q₈	—	86	2	no	—
822	C₂×Q₈	—	86	4	no	—
823	C₂×Q₈	—	86	4	no	—
824	C₂×Q₈	C₂³×D₄₃	1	2	yes	—
825	C₂×D₄	—	2	2	no	—
826	C₂×D₄	—	2	2	no	—
827	C₂×D₄	—	43	2	no	—
828	C₂×D₄	—	86	2	no	—
829	C₂×D₄	—	86	4	no	—
830	C₂×D₄	—	86	4	no	—
831	C₂×D₄	—	86	2	no	—
832	C₂×D₄	—	86	2	no	—
833	C₂×D₄	—	86	2	no	—
834	C₂×D₄	—	86	2	no	—
835	C₂×D₄	—	86	2	no	—
836	C₂×D₄	—	86	2	no	—
837	C₂×D₄	—	344	4	no	—
838	C₂×D₄	—	344	4	no	—
839	C₂×D₄	C₂³×D₄₃	1	2	yes	—
840	C₂²×C₄	—	2	2	no	—
841	C₂²×C₄	—	43	1	no	—
842	C₂²×C₄	—	43	1	no	—
843	C₂²×C₄	—	43	2	no	—
844	C₂²×C₄	—	43	2	no	—
845	C₂²×C₄	—	43	1	no	—
846	C₂²×C₄	—	43	1	no	—
847	C₂²×C₄	—	43	1	no	—
848	C₂²×C₄	—	86	2	no	—
849	C₂²×C₄	—	86	2	no	—
850	C₂²×C₄	—	86	2	no	—
851	C₂²×C₄	—	86	2	no	—
852	C₂²×C₄	—	86	2	no	—
853	C₂²×C₄	—	86	2	no	—
854	C₂²×C₄	—	86	2	no	—
855	C₂²×C₄	—	86	2	no	—
856	C₂²×C₄	—	344	4	no	—
857	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
858	SD₁₆	—	2	4	no	—
859	SD₁₆	—	2	4	no	—
860	SD₁₆	—	86	4	no	—
861	SD₁₆	—	86	4	no	—
862	SD₁₆	—	86	4	no	—
863	SD₁₆	—	86	4	no	—
864	SD₁₆	—	86	4	no	—
865	SD₁₆	—	86	4	no	—
866	M₁₆	—	2	2	no	—
867	M₁₆	—	86	2	no	—
868	M₁₆	—	86	2	no	—
869	M₁₆	—	86	2	no	—
870	C₂×C₈	—	2	2	no	—
871	C₂×C₈	—	43	1	no	—
872	C₂×C₈	—	43	1	no	—
873	C₂×C₈	—	43	4	no	—
874	C₂×C₈	—	43	4	no	—
875	C₂×C₈	—	43	1	no	—
876	C₂×C₈	—	43	1	no	—
877	C₂×C₈	—	86	2	no	—
878	C₂×C₈	—	86	2	no	—
879	C₂×C₈	—	86	2	no	—
880	C₂×C₈	—	86	2	no	—
881	C₂×C₈	—	86	2	no	—
882	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
883	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
884	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
885	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
886	C₄⋊C₄	—	2	2	no	—
887	C₄⋊C₄	—	2	2	no	—
888	C₄⋊C₄	—	2	2	no	—
889	C₄⋊C₄	—	2	2	no	—
890	C₄⋊C₄	—	2	2	no	—
891	C₄⋊C₄	—	43	2	no	—
892	C₄⋊C₄	—	43	2	no	—
893	C₄⋊C₄	—	43	2	no	—
894	C₄⋊C₄	—	43	2	no	—
895	C₄⋊C₄	—	43	2	no	—
896	C₄⋊C₄	—	86	2	no	—
897	C₄⋊C₄	—	86	2	no	—
898	C₄⋊C₄	—	86	2	no	—
899	C₄⋊C₄	—	86	2	no	—
900	C₄⋊C₄	—	86	2	no	—
901	C₄⋊C₄	—	86	2	no	—
902	C₄⋊C₄	—	86	2	no	—
903	C₄⋊C₄	—	86	2	no	—
904	C₄⋊C₄	—	86	2	no	—
905	C₄⋊C₄	—	86	2	no	—
906	C₄⋊C₄	—	86	2	no	—
907	C₄⋊C₄	—	86	2	no	—
908	C₄⋊C₄	—	86	2	no	—
909	C₄⋊C₄	—	86	2	no	—
910	C₄⋊C₄	—	86	2	no	—
911	C₄⋊C₄	—	86	2	no	—
912	C₄⋊C₄	—	86	2	no	—
913	C₄⋊C₄	D₄×D₄₃	1	2	yes	—
914	C₄⋊C₄	C₂³×D₄₃	1	2	yes	—
915	C₄⋊C₄	C₂³×D₄₃	1	2	yes	—
916	C₂²⋊C₄	—	2	2	no	—
917	C₂²⋊C₄	—	2	2	no	—
918	C₂²⋊C₄	—	2	2	no	—
919	C₂²⋊C₄	—	43	2	no	—
920	C₂²⋊C₄	—	43	2	no	—
921	C₂²⋊C₄	—	43	2	no	—
922	C₂²⋊C₄	—	86	2	no	—
923	C₂²⋊C₄	—	86	2	no	—
924	C₂²⋊C₄	—	86	2	no	—
925	C₂²⋊C₄	—	86	2	no	—
926	C₂²⋊C₄	—	86	2	no	—
927	C₂²⋊C₄	—	86	2	no	—
928	C₂²⋊C₄	—	86	2	no	—
929	C₂²⋊C₄	—	86	2	no	—
930	C₂²⋊C₄	—	86	2	no	—
931	C₂²⋊C₄	D₄×D₄₃	1	2	yes	—
932	C₄²	—	2	2	no	—
933	C₄²	—	43	2	no	—
934	C₄²	—	43	2	no	—
935	C₄²	—	43	1	no	—
936	C₄²	—	43	1	no	—
937	C₄²	—	86	2	no	—
938	C₄²	—	86	2	no	—
939	C₄²	—	86	2	no	—
940	C₄²	C₂³×D₄₃	1	1	yes	characteristic
941	C₄²	C₂³×D₄₃	1	1	yes	characteristic
942	C₂³	—	2	2	no	—
943	C₂³	—	43	1	no	—
944	C₂³	—	43	1	no	—
945	C₂³	—	86	2	no	—
946	C₂³	—	86	4	no	—
947	C₂³	—	86	2	no	—
948	C₂³	—	172	4	no	—
949	C₂³	—	172	4	no	—
950	C₂³	—	172	4	no	—
951	C₂³	C₂×D₄×D₄₃	1	1	yes	characteristic
952	Q₈	—	2	2	no	—
953	Q₈	—	2	2	no	—
954	Q₈	—	86	2	no	—
955	Q₈	—	86	2	no	—
956	Q₈	—	172	4	no	—
957	D₄	—	2	2	no	—
958	D₄	—	2	2	no	—
959	D₄	—	8	2	no	—
960	D₄	—	8	2	no	—
961	D₄	—	86	2	no	—
962	D₄	—	86	2	no	—
963	D₄	—	344	2	no	—
964	D₄	—	344	2	no	—
965	D₄	—	344	2	no	—
966	D₄	—	344	2	no	—
967	D₄	—	344	2	no	—
968	D₄	—	344	2	no	—
969	D₄	—	172	4	no	—
970	C₂×C₄	—	2	1	no	—
971	C₂×C₄	—	2	1	no	—
972	C₂×C₄	—	2	2	no	—
973	C₂×C₄	—	2	2	no	—
974	C₂×C₄	—	2	2	no	—
975	C₂×C₄	—	8	2	no	—
976	C₂×C₄	—	43	1	no	—
977	C₂×C₄	—	43	2	no	—
978	C₂×C₄	—	43	2	no	—
979	C₂×C₄	—	43	2	no	—
980	C₂×C₄	—	43	2	no	—
981	C₂×C₄	—	43	1	no	—
982	C₂×C₄	—	86	2	no	—
983	C₂×C₄	—	86	2	no	—
984	C₂×C₄	—	86	4	no	—
985	C₂×C₄	—	86	4	no	—
986	C₂×C₄	—	86	2	no	—
987	C₂×C₄	—	86	1	no	—
988	C₂×C₄	—	86	1	no	—
989	C₂×C₄	—	86	2	no	—
990	C₂×C₄	—	86	2	no	—
991	C₂×C₄	—	86	2	no	—
992	C₂×C₄	—	344	2	no	—
993	C₂×C₄	—	344	2	no	—
994	C₂×C₄	—	344	2	no	—
995	C₂×C₄	—	172	4	no	—
996	C₂×C₄	—	172	4	no	—
997	C₂×C₄	—	172	4	no	—
998	C₂×C₄	C₂×D₄×D₄₃	1	2	yes	—
999	C₂×C₄	C₂×D₄×D₄₃	1	2	yes	—
1000	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
1001	C₂×C₄	C₂⁴×D₄₃	1	1	yes	characteristic
1002	C₈	—	2	1	no	—
1003	C₈	—	2	1	no	—
1004	C₈	—	43	2	no	—
1005	C₈	—	43	2	no	—
1006	C₈	—	86	1	no	—
1007	C₈	—	86	1	no	—
1008	C₈	#41×D₄₃	1	2	yes	—
1009	C₈	#41×D₄₃	1	2	yes	—
1010	C₂²	—	2	2	no	—
1011	C₂²	—	2	1	no	—
1012	C₂²	—	4	2	no	—
1013	C₂²	—	4	2	no	—
1014	C₂²	—	4	2	no	—
1015	C₂²	—	43	4	no	—
1016	C₂²	—	43	2	no	—
1017	C₂²	—	86	2	no	—
1018	C₂²	—	86	1	no	—
1019	C₂²	—	344	8	no	—
1020	C₂²	—	172	4	no	—
1021	C₂²	—	172	2	no	—
1022	C₂²	—	172	2	no	—
1023	C₂²	—	172	2	no	—
1024	C₂²	C₂²×D₄×D₄₃	1	1	yes	characteristic
1025	C₄	—	2	2	no	—
1026	C₄	—	2	2	no	—
1027	C₄	—	2	1	no	—
1028	C₄	—	4	2	no	—
1029	C₄	—	4	2	no	—
1030	C₄	—	4	2	no	—
1031	C₄	—	43	2	no	—
1032	C₄	—	86	2	no	—
1033	C₄	—	86	2	no	—
1034	C₄	—	86	1	no	—
1035	C₄	—	172	2	no	—
1036	C₄	—	172	2	no	—
1037	C₄	—	172	2	no	—
1038	C₄	C₂×#41×D₄₃	1	1	yes	characteristic
1039	C₄	C₂×#41×D₄₃	1	1	yes	characteristic
1040	C₂	—	4	1	no	—
1041	C₂	—	8	2	no	—
1042	C₂	—	43	4	no	—
1043	C₂	—	344	2	no	—
1044	C₂	—	172	1	no	—
1045	C₂	#532×D₄₃	1	1	yes	characteristic
1046	C₂	#577×D₄₃	1	2	yes	—

	subgroup	G/H
center	C₂²	C₂²×D₄×D₄₃
commutator, cosocle	C₂×C₄×C₄₃	C₂⁵
Frattini	C₂×C₄	C₂⁴×D₄₃
Fitting	C₄₃×#3174	C₂
socle	C₂²×C₄₃	C₂³×D₄
prime radical	#540×D₄₃	C₂
hypercenter	#3174	D₄₃
hypocenter	C₄₃	C₂×#3174
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ #117 ◁ #3174

Complements

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

N	H ≅ G/N	type
1. #541×D₄₃	C₂	semidirect
3. #19145226	C₂	semidirect
4. #19145225	C₂	semidirect
5. #19145224	C₂	semidirect
6. #19145223	C₂	semidirect
7. #19145222	C₂	semidirect
8. #19145221	C₂	semidirect
9. #19145220	C₂	semidirect
10. #19145219	C₂	semidirect
11. #19145218	C₂	semidirect
12. #19145217	C₂	semidirect
13. #19145216	C₂	semidirect
14. #499×D₄₃	C₂	semidirect
15. #492×D₄₃	C₂	semidirect
16. #491×D₄₃	C₂	semidirect
17. #490×D₄₃	C₂	semidirect
18. #468×D₄₃	C₂	semidirect
19. #465×D₄₃	C₂	semidirect
20. #440×D₄₃	C₂	semidirect
21. C₄×SD₁₆×D₄₃	C₂	semidirect
22. #405×D₄₃	C₂	semidirect
23. C₄₃×#3174	C₂	semidirect
28. #14583512	C₂²	semidirect
29. #14583511	C₂²	semidirect
30. #14583510	C₂²	semidirect
31. #14583509	C₂²	semidirect
33. #14583507	C₂²	semidirect
55. #14583301	C₂²	semidirect
56. #14583300	C₂²	semidirect
57. #14583299	C₂²	semidirect
58. #14583298	C₂²	semidirect
59. #14583298	C₂²	semidirect
60. #14583273	C₂²	semidirect
61. #14583272	C₂²	semidirect
62. #14583271	C₂²	semidirect
63. #14583270	C₂²	semidirect
64. #14583270	C₂²	semidirect
65. #14583269	C₂²	semidirect
66. #14583268	C₂²	semidirect
67. #14583267	C₂²	semidirect
68. #14583266	C₂²	semidirect
69. #14583266	C₂²	semidirect
70. #14583265	C₂²	semidirect
71. #14583264	C₂²	semidirect
72. #14583263	C₂²	semidirect
73. #14583262	C₂²	semidirect
74. #14583262	C₂²	semidirect
75. #14583148	C₂²	semidirect
76. #14583147	C₂²	semidirect
77. #14583146	C₂²	semidirect
78. #14583145	C₂²	semidirect
79. #14583144	C₂²	semidirect
80. #14583143	C₂²	semidirect
81. #14583142	C₂²	semidirect
82. #14583131	C₂²	semidirect
83. #14583130	C₂²	semidirect
84. #14583129	C₂²	semidirect
85. #14583128	C₂²	semidirect
86. #14583127	C₂²	semidirect
87. #14583126	C₂²	semidirect
88. #14583125	C₂²	semidirect
89. #14583002	C₂²	semidirect
90. #14583001	C₂²	semidirect
91. #14583000	C₂²	semidirect
92. #14582999	C₂²	semidirect
93. #14582998	C₂²	semidirect
94. #14582997	C₂²	semidirect
95. #14582996	C₂²	semidirect
96. #14582990	C₂²	semidirect
97. C₄×#10621873	C₂²	semidirect
98. SD₁₆×Dic₄₃	C₂²	semidirect
99. C₄×#10621884	C₂²	semidirect
100. #14582986	C₂²	semidirect
101. C₄×#10621883	C₂²	semidirect
102. #14582984	C₂²	semidirect
109. #14582857	C₂²	semidirect
110. #14582856	C₂²	semidirect
111. #14582856	C₂²	semidirect
112. #14582855	C₂²	semidirect
113. #14582854	C₂²	semidirect
114. #14582853	C₂²	semidirect
115. #14582853	C₂²	semidirect
120. C₄₃×#541	C₂²	semidirect
122. C₄₃×#499	C₂²	semidirect
123. C₄₃×#492	C₂²	semidirect
124. C₄₃×#491	C₂²	semidirect
125. C₄₃×#490	C₂²	semidirect
126. C₄₃×#468	C₂²	semidirect
127. C₄₃×#465	C₂²	semidirect
128. C₄₃×#440	C₂²	semidirect
129. C₄×SD₁₆×C₄₃	C₂²	semidirect
130. C₄₃×#405	C₂²	semidirect
530. #3174	D₄₃	direct (N × H)
546. D₄₃	#3174	direct (N × H)
558. #541	C₂×D₄₃	semidirect
585. #499	C₂×D₄₃	semidirect
591. #492	C₂×D₄₃	semidirect
597. #491	C₂×D₄₃	semidirect
603. #490	C₂×D₄₃	semidirect
611. #468	C₂×D₄₃	semidirect
619. #465	C₂×D₄₃	semidirect
627. #440	C₂×D₄₃	semidirect
635. C₄×SD₁₆	C₂×D₄₃	semidirect
649. #405	C₂×D₄₃	semidirect
654. C₄₃	C₂×#3174	semidirect

Maximal subgroups

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

subgroup	index
#541×D₄₃	2
#540×D₄₃	2
#19145226	2
#19145225	2
#19145224	2
#19145223	2
#19145222	2
#19145221	2
#19145220	2
#19145219	2
#19145218	2
#19145217	2
#19145216	2
#499×D₄₃	2
#492×D₄₃	2
#491×D₄₃	2
#490×D₄₃	2
#468×D₄₃	2
#465×D₄₃	2
#440×D₄₃	2
C₄×SD₁₆×D₄₃	2
#405×D₄₃	2
C₄₃×#3174	2
C₂×#3174	43

Subgroups — D43×#3174 #25966399

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₄₃×#3174 #25966399