Subgroups — #25966607

Order 11008.

1978 conjugacy classes of subgroups.

The subgroup lattice has 1130 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19148015	C₂	1	2	yes	maximal, complemented
2	#19145276	C₂	1	2	yes	maximal, complemented
3	#19145272	C₂	1	2	yes	maximal, complemented
4	#19145245	C₂	1	1	yes	maximal, characteristic, complemented
5	#19145241	C₂	1	1	yes	maximal, characteristic, complemented
6	#19145236	C₂	1	1	yes	maximal, characteristic, complemented
7	#19145193	C₂	1	2	yes	maximal, complemented
8	#19145183	C₂	1	2	yes	maximal, complemented
9	#19145175	C₂	1	1	yes	maximal, characteristic, complemented
10	#19145169	C₂	1	1	yes	maximal, characteristic, complemented
11	#19145166	C₂	1	1	yes	maximal, characteristic, complemented
12	#19145162	C₂	1	1	yes	maximal, characteristic, complemented
13	#19145128	C₂	1	1	yes	maximal, characteristic, complemented
14	#19145077	C₂	1	1	yes	maximal, characteristic, complemented
15	#19144946	C₂	1	2	yes	maximal, complemented
16	#19144270	C₂	1	2	yes	maximal, complemented
17	#19144266	C₂	1	1	yes	maximal, characteristic, complemented
18	#19144238	C₂	1	1	yes	maximal, characteristic, complemented
19	#19143400	C₂	1	2	yes	maximal, complemented
20	C₄×#13063348	C₂	1	1	yes	maximal, characteristic, complemented
21	C₄×D₈×D₄₃	C₂	1	1	yes	maximal, characteristic, complemented
22	#19143017	C₂	1	1	yes	maximal, characteristic, complemented
23	C₄₃×#3175	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#13063352	C₂²	1	2	yes	—
25	C₂×#13063348	C₂²	1	1	yes	characteristic
26	C₂×D₈×D₄₃	C₂²	1	1	yes	characteristic
27	C₂×#13063333	C₂²	1	1	yes	characteristic
28	C₂×#13063331	C₂²	1	1	yes	characteristic
29	#14583526	C₂²	1	2	yes	—
30	#14583521	C₂²	1	2	yes	complemented
31	#14583519	—	2	2	no	—
32	#14583504	C₂²	1	2	yes	complemented
33	#14583501	—	2	2	no	—
34	#14583500	C₂²	1	2	yes	complemented
35	#14583488	—	2	2	no	—
36	#14583483	—	2	2	no	—
37	#14583479	C₂²	1	2	yes	—
38	#14583467	C₂²	1	2	yes	—
39	#14583465	C₂²	1	2	yes	—
40	#14583450	C₂²	1	2	yes	complemented
41	#14583448	—	2	2	no	—
42	#14583444	C₂²	1	2	yes	complemented
43	#14583435	C₂²	1	2	yes	complemented
44	#14583432	—	2	2	no	—
45	#14583428	C₂²	1	2	yes	complemented
46	#14583412	—	2	2	no	—
47	#14583407	—	2	2	no	—
48	C₄×#10621902	C₂²	1	2	yes	—
49	#14583367	C₂²	1	1	yes	characteristic
50	C₄×D₄×D₄₃	C₂²	1	2	yes	—
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	#14583289	C₂²	1	2	yes	—
57	#14583285	C₂²	1	2	yes	—
58	#14583284	C₂²	1	1	yes	characteristic
59	#14583276	C₂²	1	1	yes	characteristic
60	#14583274	C₂²	1	1	yes	characteristic
61	#14583264	C₂²	1	2	yes	complemented
62	#14583262	C₂²	1	2	yes	complemented
63	#14583260	C₂²	1	2	yes	complemented
64	#14583255	C₂²	1	2	yes	complemented
65	#14583253	C₂²	1	2	yes	complemented
66	#14583247	C₂²	1	2	yes	complemented
67	#14583244	C₂²	1	2	yes	complemented
68	#14583152	C₂²	1	2	yes	complemented
69	#14583151	C₂²	1	2	yes	—
70	#14583151	C₂²	1	2	yes	complemented
71	#14583150	C₂²	1	2	yes	—
72	#14583148	C₂²	1	2	yes	complemented
73	#14583148	C₂²	1	2	yes	complemented
74	#14583147	C₂²	1	2	yes	complemented
75	#14583137	C₂²	1	1	yes	characteristic, complemented
76	#14583136	C₂²	1	1	yes	characteristic
77	#14583136	C₂²	1	1	yes	characteristic, complemented
78	#14583136	C₂²	1	2	yes	complemented
79	#14583135	C₂²	1	1	yes	characteristic
80	#14583135	C₂²	1	1	yes	characteristic, complemented
81	#14583133	C₂²	1	2	yes	complemented
82	#14583132	C₂²	1	1	yes	characteristic
83	#14583130	C₂²	1	2	yes	complemented
84	#14583125	C₂²	1	2	yes	complemented
85	#14583012	C₂²	1	2	yes	complemented
86	#14583009	C₂²	1	2	yes	complemented
87	#14582997	C₂²	1	2	yes	complemented
88	Q₁₆×Dic₄₃	C₂²	1	1	yes	characteristic, complemented
89	SD₁₆×Dic₄₃	C₂²	1	2	yes	complemented
90	C₄×#10621884	C₂²	1	2	yes	complemented
91	#14582984	C₂²	1	2	yes	complemented
92	#14582984	C₂²	1	2	yes	complemented
93	C₄×D₃₄₄	C₂²	1	1	yes	characteristic
94	C₄×D₃₄₄	C₂²	1	1	yes	characteristic, complemented
95	D₈×Dic₄₃	C₂²	1	1	yes	characteristic
96	#14582981	C₂²	1	1	yes	characteristic
97	#14582981	C₂²	1	1	yes	characteristic, complemented
98	#14582981	C₂²	1	2	yes	complemented
99	C₄×#10621882	C₂²	1	2	yes	—
100	#14582979	C₂²	1	2	yes	—
101	#14582979	C₂²	1	2	yes	complemented
102	#14582940	C₂²	1	2	yes	—
103	#14582936	C₂²	1	1	yes	characteristic
104	#107×D₄₃	C₂²	1	1	yes	characteristic
105	#14582902	C₂²	1	2	yes	—
106	#14582899	C₂²	1	2	yes	—
107	#14582894	C₂²	1	2	yes	—
108	#102×D₄₃	C₂²	1	2	yes	—
109	#14582856	C₂²	1	1	yes	characteristic
110	#14582856	C₂²	1	1	yes	characteristic, complemented
111	#14582855	C₂²	1	1	yes	characteristic, complemented
112	#14582853	C₂²	1	1	yes	characteristic
113	#14582853	C₂²	1	1	yes	characteristic, complemented
114	#14582851	C₂²	1	1	yes	characteristic
115	#14582851	C₂²	1	1	yes	characteristic, complemented
116	M₁₆×Dic₄₃	C₂²	1	1	yes	characteristic, complemented
117	C₂×C₈×Dic₄₃	C₂²	1	1	yes	characteristic, complemented
118	C₄×C₈×D₄₃	C₂²	1	1	yes	characteristic
119	C₄×C₈×D₄₃	C₂²	1	1	yes	characteristic, complemented
120	C₄₃×#542	C₂²	1	2	yes	complemented
121	C₄₃×#500	C₂²	1	1	yes	characteristic, complemented
122	C₄₃×#495	C₂²	1	1	yes	characteristic
123	C₄₃×#489	C₂²	1	2	yes	complemented
124	C₄₃×#468	C₂²	1	2	yes	complemented
125	C₄₃×#467	C₂²	1	1	yes	characteristic, complemented
126	C₄₃×#466	C₂²	1	1	yes	characteristic
127	C₄₃×#440	C₂²	1	2	yes	complemented
128	C₄×Q₁₆×C₄₃	C₂²	1	1	yes	characteristic, complemented
129	C₄×D₈×C₄₃	C₂²	1	1	yes	characteristic
130	C₄₃×#405	C₂²	1	1	yes	characteristic, complemented
131	C₂×#10621902	—	2	2	no	—
132	C₂×#10621902	C₂³	1	2	yes	—
133	C₂×#10621898	C₂³	1	1	yes	characteristic
134	C₂×#10621900	—	2	2	no	—
135	C₂×D₄×D₄₃	C₂³	1	2	yes	—
136	C₂²×C₄×D₄₃	—	2	2	no	—
137	#13063352	—	2	8	no	—
138	#13063348	—	2	4	no	—
139	C₂×#10621884	C₂³	1	2	yes	—
140	C₂×#10621884	C₂³	1	2	yes	—
141	C₂×D₃₄₄	C₂³	1	1	yes	characteristic
142	C₂×D₃₄₄	C₂³	1	1	yes	characteristic
143	C₂×D₃₄₄	C₂³	1	2	yes	—
144	C₂×#10621882	C₂³	1	2	yes	—
145	C₂×#10621882	C₂³	1	2	yes	—
146	D₈×D₄₃	—	2	4	no	—
147	#13063333	—	2	4	no	—
148	#13063331	—	2	4	no	—
149	C₂×#10621877	C₂³	1	1	yes	characteristic
150	C₂×#10621872	C₂³	1	1	yes	characteristic
151	C₂×#10621872	C₂³	1	1	yes	characteristic
152	C₂×#10621872	C₂³	1	1	yes	characteristic
153	C₂×#10621872	C₂³	1	1	yes	characteristic
154	C₂²×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
155	C₂×C₈×D₄₃	C₂³	1	1	yes	characteristic
156	C₂×C₈×D₄₃	C₂³	1	1	yes	characteristic
157	C₂×C₈×D₄₃	C₂³	1	1	yes	characteristic
158	C₂×C₈×D₄₃	C₂³	1	1	yes	characteristic
159	#13063324	C₂³	1	2	yes	—
160	#13063323	—	2	2	no	—
161	#13063322	C₂³	1	2	yes	—
162	#13063321	—	2	2	no	—
163	#13063321	C₂³	1	2	yes	—
164	#13063320	—	2	2	no	—
165	#13063319	—	2	2	no	—
166	#13063318	—	2	2	no	—
167	#13063317	C₂³	1	2	yes	—
168	#13063316	C₂³	1	2	yes	—
169	#13063315	—	2	2	no	—
170	#13063314	—	2	2	no	—
171	#13063314	C₂³	1	2	yes	—
172	#13063313	—	2	2	no	—
173	#13063311	—	2	2	no	—
174	#13063311	—	2	2	no	—
175	#13063310	—	2	2	no	—
176	#13063310	—	2	2	no	—
177	#13063310	—	2	2	no	—
178	#13063309	—	2	2	no	—
179	#13063308	—	2	2	no	—
180	#13063307	—	2	2	no	—
181	#13063307	—	2	2	no	—
182	#13063303	—	2	2	no	—
183	#13063303	—	2	2	no	—
184	#13063303	—	2	2	no	—
185	#13063301	—	2	2	no	—
186	#13063301	C₂³	1	2	yes	—
187	#13063300	—	2	2	no	—
188	#13063300	—	2	2	no	—
189	#13063300	C₂³	1	2	yes	—
190	#13063300	C₂³	1	2	yes	—
191	#13063299	—	2	2	no	—
192	#13063299	C₂³	1	2	yes	—
193	#13063299	C₂³	1	2	yes	—
194	#13063298	—	2	2	no	—
195	#13063298	—	2	2	no	—
196	#13063298	—	2	2	no	—
197	#13063298	—	2	2	no	—
198	#13063298	—	2	2	no	—
199	#13063298	—	2	2	no	—
200	#13063298	—	2	2	no	—
201	#13063297	—	2	2	no	—
202	#13063296	C₂³	1	2	yes	—
203	#13063295	—	2	2	no	—
204	#13063295	—	2	2	no	—
205	#13063295	—	2	2	no	—
206	#13063293	—	2	2	no	—
207	Q₈×Dic₄₃	C₂³	1	2	yes	—
208	#13063290	D₄	1	1	yes	characteristic
209	#13063290	D₄	1	1	yes	characteristic
210	C₄×D₁₇₂	—	2	2	no	—
211	C₄×D₁₇₂	C₂³	1	2	yes	—
212	C₄×D₁₇₂	C₂³	1	2	yes	—
213	D₄×Dic₄₃	C₂³	1	2	yes	—
214	#13063287	—	2	2	no	—
215	#13063287	—	2	2	no	—
216	#13063287	D₄	1	1	yes	characteristic
217	#13063287	D₄	1	1	yes	characteristic
218	#13063287	C₂³	1	2	yes	—
219	#13063287	C₂³	1	2	yes	—
220	C₄×C₂²⋊D₄₃	—	2	2	no	—
221	(C₂²⋊D₄₃)⋊C₄	—	2	2	no	—
222	(C₂²⋊D₄₃)⋊C₄	—	2	2	no	—
223	(C₂²⋊D₄₃)⋊C₄	—	2	2	no	—
224	(C₂²⋊D₄₃)⋊C₄	—	2	2	no	—
225	(C₂²⋊D₄₃)⋊C₄	D₄	1	1	yes	characteristic
226	(C₂²⋊D₄₃)⋊C₄	D₄	1	1	yes	characteristic
227	(C₂²⋊D₄₃)⋊C₄	D₄	1	1	yes	characteristic
228	(C₂²⋊D₄₃)⋊C₄	D₄	1	1	yes	characteristic
229	#13063283	—	2	2	no	—
230	#13063283	—	2	2	no	—
231	#13063283	C₂³	1	2	yes	—
232	#13063282	C₂³	1	1	yes	characteristic
233	#13063282	C₂³	1	1	yes	characteristic
234	#13063281	—	2	2	no	—
235	C₄⋊C₄×D₄₃	C₂³	1	2	yes	—
236	C₂²⋊C₄×D₄₃	—	2	2	no	—
237	C₂×C₄×Dic₄₃	C₂³	1	1	yes	characteristic
238	C₄²×D₄₃	—	2	2	no	—
239	C₄²×D₄₃	C₂³	1	1	yes	characteristic
240	C₄²×D₄₃	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	#13063249	C₂³	1	2	yes	—
249	#13063249	C₂³	1	2	yes	—
250	#13063247	C₂³	1	2	yes	—
251	#13063247	C₂³	1	2	yes	—
252	#13063247	C₂³	1	2	yes	—
253	#13063247	C₂³	1	2	yes	—
254	#13063246	C₂³	1	2	yes	—
255	#13063246	C₂³	1	2	yes	—
256	#13063245	C₂³	1	2	yes	—
257	#13063245	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	#13063235	C₂³	1	1	yes	characteristic
263	#13063235	C₂³	1	1	yes	characteristic
264	C₄×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
265	C₄×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
266	C₈×Dic₄₃	C₂³	1	1	yes	characteristic
267	C₈×Dic₄₃	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×SD₁₆×C₄₃	C₂³	1	2	yes	—
274	C₂×D₈×C₄₃	C₂³	1	1	yes	characteristic
275	C₂×M₁₆×C₄₃	C₂³	1	1	yes	characteristic
276	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
277	C₄⋊Q₈×C₄₃	C₂³	1	2	yes	—
278	#126×C₄₃	—	2	2	no	—
279	#124×C₄₃	—	2	2	no	—
280	#124×C₄₃	C₂³	1	2	yes	—
281	#123×C₄₃	—	2	2	no	—
282	C₂²⋊Q₈×C₄₃	—	2	2	no	—
283	C₂²⋊Q₈×C₄₃	C₂³	1	2	yes	—
284	#121×C₄₃	C₂³	1	2	yes	—
285	C₄×Q₈×C₄₃	C₂³	1	2	yes	—
286	C₄×D₄×C₄₃	C₂³	1	2	yes	—
287	#117×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	#102×C₄₃	C₂³	1	2	yes	—
294	#102×C₄₃	C₂³	1	2	yes	—
295	#97×C₄₃	C₂³	1	1	yes	characteristic
296	#97×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	—	2	2	no	—
300	C₂×Q₈×C₄₃	—	2	2	no	—
301	C₂×Q₈×C₄₃	C₂⁴	1	2	yes	—
302	C₂×D₄×C₄₃	—	2	2	no	—
303	C₂×D₄×C₄₃	C₂⁴	1	2	yes	—
304	C₂²×C₄×C₄₃	—	2	2	no	—
305	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
306	C₂×C₂²⋊D₄₃	—	2	2	no	—
307	C₂×C₂²⋊D₄₃	—	2	2	no	—
308	C₂×C₂²⋊D₄₃	—	2	2	no	—
309	C₂×C₂²⋊D₄₃	—	2	2	no	—
310	C₂×C₂²⋊D₄₃	—	2	2	no	—
311	C₂×C₂²⋊D₄₃	—	2	2	no	—
312	C₂×C₂²⋊D₄₃	C₂×D₄	1	1	yes	characteristic
313	C₂×C₂²⋊D₄₃	C₂×D₄	1	1	yes	characteristic
314	C₂²×Dic₄₃	—	2	2	no	—
315	C₂²×Dic₄₃	C₂×D₄	1	1	yes	characteristic
316	C₂²×Dic₄₃	C₂×D₄	1	1	yes	characteristic
317	#10621902	—	2	4	no	—
318	#10621902	—	2	4	no	—
319	#10621902	—	8	4	no	—
320	#10621900	—	8	4	no	—
321	D₄×D₄₃	—	2	4	no	—
322	D₄×D₄₃	—	2	4	no	—
323	#10621898	—	2	2	no	—
324	#10621898	—	2	2	no	—
325	C₂×D₁₇₂	—	2	2	no	—
326	C₂×D₁₇₂	—	2	2	no	—
327	C₂×D₁₇₂	—	2	2	no	—
328	C₂×D₁₇₂	—	2	2	no	—
329	C₂×D₁₇₂	—	2	2	no	—
330	C₂×D₁₇₂	C₂×D₄	1	1	yes	characteristic
331	C₂×D₁₇₂	C₂⁴	1	2	yes	—
332	C₂×D₁₇₂	C₂⁴	1	2	yes	—
333	C₂×C₄×D₄₃	—	2	2	no	—
334	C₂×C₄×D₄₃	—	2	2	no	—
335	C₂×C₄×D₄₃	—	2	2	no	—
336	C₂×C₄×D₄₃	—	2	2	no	—
337	C₂×C₄×D₄₃	—	2	2	no	—
338	C₂×C₄×D₄₃	—	2	2	no	—
339	C₂×C₄×D₄₃	—	8	4	no	—
340	C₂×C₄×D₄₃	C₂×D₄	1	1	yes	characteristic
341	C₂×C₄×D₄₃	C₂×D₄	1	1	yes	characteristic
342	C₂×C₄×D₄₃	C₂×D₄	1	1	yes	characteristic
343	C₂×C₄×D₄₃	C₂×D₄	1	1	yes	characteristic
344	C₂×C₄×D₄₃	C₂⁴	1	1	yes	characteristic
345	C₂×C₄×D₄₃	C₂⁴	1	1	yes	characteristic
346	C₂×Dic₈₆	—	2	2	no	—
347	C₂×Dic₈₆	C₂×D₄	1	1	yes	characteristic
348	Q₁₆×C₄₃	—	2	2	no	—
349	SD₁₆×C₄₃	—	2	4	no	—
350	D₈×C₄₃	—	2	2	no	—
351	M₁₆×C₄₃	—	2	2	no	—
352	C₂×C₈×C₄₃	—	2	2	no	—
353	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
354	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
355	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
356	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
357	C₄⋊C₄×C₄₃	—	2	2	no	—
358	C₄⋊C₄×C₄₃	—	2	2	no	—
359	C₄⋊C₄×C₄₃	—	2	2	no	—
360	C₄⋊C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
361	C₄⋊C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
362	C₄⋊C₄×C₄₃	C₂⁴	1	2	yes	—
363	C₄⋊C₄×C₄₃	C₂⁴	1	2	yes	—
364	C₂²⋊C₄×C₄₃	—	2	2	no	—
365	C₂²⋊C₄×C₄₃	—	2	2	no	—
366	C₂²⋊C₄×C₄₃	—	2	2	no	—
367	C₂²⋊C₄×C₄₃	—	2	2	no	—
368	C₂²⋊C₄×C₄₃	—	2	2	no	—
369	C₂²⋊C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
370	C₂²⋊C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
371	C₄²×C₄₃	—	2	2	no	—
372	C₄²×C₄₃	C₂⁴	1	1	yes	characteristic
373	C₄²×C₄₃	C₂⁴	1	1	yes	characteristic
374	C₂²⋊Dic₄₃	—	2	2	no	—
375	C₂²⋊Dic₄₃	—	2	2	no	—
376	#10621884	—	2	4	no	—
377	#10621884	—	2	4	no	—
378	#10621882	—	2	4	no	—
379	#10621882	—	2	4	no	—
380	(C₂×D₄₃)⋊C₄	—	2	2	no	—
381	(C₂×D₄₃)⋊C₄	—	2	2	no	—
382	(C₂×D₄₃)⋊C₄	—	2	2	no	—
383	(C₂×D₄₃)⋊C₄	—	2	2	no	—
384	(C₂×D₄₃)⋊C₄	—	2	2	no	—
385	(C₂×D₄₃)⋊C₄	—	2	2	no	—
386	(C₂×D₄₃)⋊C₄	—	2	2	no	—
387	(C₂×D₄₃)⋊C₄	—	2	2	no	—
388	(C₂×D₄₃)⋊C₄	—	2	2	no	—
389	(C₂×D₄₃)⋊C₄	—	2	2	no	—
390	(C₂×D₄₃)⋊C₄	—	2	2	no	—
391	(C₂×D₄₃)⋊C₄	—	2	2	no	—
392	(C₂×D₄₃)⋊C₄	C₂×D₄	1	1	yes	characteristic
393	(C₂×D₄₃)⋊C₄	C₂×D₄	1	1	yes	characteristic
394	(C₂×D₄₃)⋊C₄	C₂×D₄	1	1	yes	characteristic
395	(C₂×D₄₃)⋊C₄	C₂×D₄	1	1	yes	characteristic
396	C₄⋊Dic₄₃	—	2	2	no	—
397	C₄⋊Dic₄₃	—	2	2	no	—
398	C₄⋊Dic₄₃	C₂⁴	1	2	yes	—
399	C₄⋊Dic₄₃	C₂⁴	1	2	yes	—
400	Dic₄₃⋊C₄	—	2	2	no	—
401	Dic₄₃⋊C₄	—	2	2	no	—
402	Dic₄₃⋊C₄	—	2	2	no	—
403	Dic₄₃⋊C₄	—	2	2	no	—
404	Dic₄₃⋊C₄	—	2	2	no	—
405	Dic₄₃⋊C₄	—	2	2	no	—
406	Dic₄₃⋊C₄	C₂×D₄	1	1	yes	characteristic
407	Dic₄₃⋊C₄	C₂×D₄	1	1	yes	characteristic
408	Dic₄₃⋊C₄	C₂×D₄	1	1	yes	characteristic
409	Dic₄₃⋊C₄	C₂×D₄	1	1	yes	characteristic
410	C₄×Dic₄₃	—	2	2	no	—
411	C₄×Dic₄₃	—	2	2	no	—
412	C₄×Dic₄₃	C₂×D₄	1	1	yes	characteristic
413	C₄×Dic₄₃	C₂×D₄	1	1	yes	characteristic
414	C₄×Dic₄₃	C₂×D₄	1	1	yes	characteristic
415	C₄×Dic₄₃	C₂×D₄	1	1	yes	characteristic
416	C₄×Dic₄₃	C₂×D₄	1	1	yes	characteristic
417	C₄×Dic₄₃	C₂×D₄	1	1	yes	characteristic
418	C₄×Dic₄₃	C₂⁴	1	1	yes	characteristic
419	C₄×Dic₄₃	C₂⁴	1	1	yes	characteristic
420	#10621877	—	2	2	no	—
421	C₂×C₄₃⋊C₈	—	2	2	no	—
422	C₂×C₄₃⋊C₈	C₂⁴	1	1	yes	characteristic
423	C₂×C₄₃⋊C₈	C₂⁴	1	1	yes	characteristic
424	C₂×C₄₃⋊C₈	C₂⁴	1	1	yes	characteristic
425	C₂×C₄₃⋊C₈	C₂⁴	1	1	yes	characteristic
426	D₃₄₄	—	2	2	no	—
427	D₃₄₄	—	2	2	no	—
428	D₃₄₄	—	2	4	no	—
429	#10621872	—	2	2	no	—
430	#10621872	—	2	2	no	—
431	#10621872	—	2	2	no	—
432	#10621872	#41	1	4	yes	complemented
433	C₈×D₄₃	—	2	2	no	—
434	C₈×D₄₃	—	2	2	no	—
435	C₈×D₄₃	—	2	2	no	—
436	C₈×D₄₃	#41	1	4	yes	complemented
437	C₂³×C₄₃	—	2	2	no	—
438	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
439	C₂²×D₄₃	—	2	2	no	—
440	C₂²×D₄₃	—	2	2	no	—
441	C₂²×D₄₃	—	4	4	no	—
442	C₂²×D₄₃	—	8	2	no	—
443	C₂²×D₄₃	—	8	2	no	—
444	C₂²×D₄₃	C₂²×D₄	1	1	yes	characteristic
445	C₂²×D₄₃	C₂²×D₄	1	1	yes	characteristic
446	Q₈×C₄₃	—	2	2	no	—
447	Q₈×C₄₃	—	2	2	no	—
448	Q₈×C₄₃	—	8	2	no	—
449	D₄×C₄₃	—	2	2	no	—
450	D₄×C₄₃	—	2	2	no	—
451	D₄×C₄₃	—	8	2	no	—
452	C₂×C₄×C₄₃	—	2	1	no	—
453	C₂×C₄×C₄₃	—	2	1	no	—
454	C₂×C₄×C₄₃	—	2	2	no	—
455	C₂×C₄×C₄₃	—	2	2	no	—
456	C₂×C₄×C₄₃	—	2	2	no	—
457	C₂×C₄×C₄₃	—	8	2	no	—
458	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
459	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
460	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
461	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
462	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
463	C₂×C₄×C₄₃	C₂⁵	1	1	yes	characteristic
464	C₂²⋊D₄₃	—	2	2	no	—
465	C₂²⋊D₄₃	—	2	2	no	—
466	C₂²⋊D₄₃	—	4	4	no	—
467	C₂²⋊D₄₃	—	8	2	no	—
468	C₂²⋊D₄₃	—	8	2	no	—
469	C₂²⋊D₄₃	—	8	2	no	—
470	C₂²⋊D₄₃	—	8	2	no	—
471	C₂²⋊D₄₃	—	8	2	no	—
472	C₂×Dic₄₃	—	2	2	no	—
473	C₂×Dic₄₃	—	2	2	no	—
474	C₂×Dic₄₃	—	2	2	no	—
475	C₂×Dic₄₃	—	4	1	no	—
476	C₂×Dic₄₃	—	4	4	no	—
477	C₂×Dic₄₃	C₂²×D₄	1	1	yes	characteristic
478	C₂×Dic₄₃	C₂²×D₄	1	1	yes	characteristic
479	C₂×Dic₄₃	C₂²×D₄	1	1	yes	characteristic
480	C₂×Dic₄₃	C₂²×D₄	1	1	yes	characteristic
481	C₂×Dic₄₃	C₂²×D₄	1	1	yes	characteristic
482	C₂×Dic₄₃	C₂²×D₄	1	1	yes	characteristic
483	D₁₇₂	—	2	2	no	—
484	D₁₇₂	—	2	2	no	—
485	D₁₇₂	—	2	2	no	—
486	D₁₇₂	—	2	2	no	—
487	D₁₇₂	—	2	2	no	—
488	D₁₇₂	—	4	4	no	—
489	D₁₇₂	—	8	2	no	—
490	D₁₇₂	—	8	2	no	—
491	D₁₇₂	—	8	2	no	—
492	D₁₇₂	—	8	2	no	—
493	C₄×D₄₃	—	2	1	no	—
494	C₄×D₄₃	—	2	1	no	—
495	C₄×D₄₃	—	2	2	no	—
496	C₄×D₄₃	—	2	2	no	—
497	C₄×D₄₃	—	4	1	no	—
498	C₄×D₄₃	—	4	1	no	—
499	C₄×D₄₃	—	4	4	no	—
500	C₄×D₄₃	—	4	4	no	—
501	C₄×D₄₃	—	4	4	no	—
502	C₄×D₄₃	—	8	2	no	—
503	C₄×D₄₃	—	8	2	no	—
504	C₄×D₄₃	—	8	2	no	—
505	C₄×D₄₃	C₂×#41	1	2	yes	—
506	C₄×D₄₃	C₂×#41	1	2	yes	—
507	Dic₈₆	—	2	2	no	—
508	Dic₈₆	—	8	2	no	—
509	C₈×C₄₃	—	2	1	no	—
510	C₈×C₄₃	—	2	1	no	—
511	C₈×C₄₃	C₂×#41	1	2	yes	—
512	C₈×C₄₃	C₂×#41	1	2	yes	—
513	C₄₃⋊C₈	—	2	1	no	—
514	C₄₃⋊C₈	—	2	1	no	—
515	C₄₃⋊C₈	C₂×#41	1	2	yes	—
516	C₄₃⋊C₈	C₂×#41	1	2	yes	—
517	#60695	—	43	1	no	maximal, Sylow
518	C₂²×C₄₃	—	2	1	no	—
519	C₂²×C₄₃	—	2	1	no	—
520	C₂²×C₄₃	—	2	1	no	—
521	C₂²×C₄₃	—	4	2	no	—
522	C₂²×C₄₃	—	4	2	no	—
523	C₂²×C₄₃	—	4	2	no	—
524	C₂²×C₄₃	C₂³×D₄	1	1	yes	characteristic
525	C₂×D₄₃	—	2	1	no	—
526	C₂×D₄₃	—	2	1	no	—
527	C₂×D₄₃	—	2	1	no	—
528	C₂×D₄₃	—	2	1	no	—
529	C₂×D₄₃	—	2	1	no	—
530	C₂×D₄₃	—	4	2	no	—
531	C₂×D₄₃	—	4	2	no	—
532	C₂×D₄₃	—	4	2	no	—
533	C₂×D₄₃	—	4	2	no	—
534	C₂×D₄₃	—	4	2	no	—
535	C₂×D₄₃	—	4	2	no	—
536	C₂×D₄₃	—	8	8	no	—
537	C₂×D₄₃	#532	1	2	yes	—
538	C₄×C₄₃	—	2	1	no	—
539	C₄×C₄₃	—	2	1	no	—
540	C₄×C₄₃	—	2	1	no	—
541	C₄×C₄₃	—	2	1	no	—
542	C₄×C₄₃	—	2	1	no	—
543	C₄×C₄₃	—	4	2	no	—
544	C₄×C₄₃	—	4	2	no	—
545	C₄×C₄₃	—	4	2	no	—
546	C₄×C₄₃	C₂²×#41	1	1	yes	characteristic
547	C₄×C₄₃	C₂²×#41	1	1	yes	characteristic
548	Dic₄₃	—	2	1	no	—
549	Dic₄₃	—	2	1	no	—
550	Dic₄₃	—	2	1	no	—
551	Dic₄₃	—	2	1	no	—
552	Dic₄₃	—	4	2	no	—
553	Dic₄₃	—	4	2	no	—
554	Dic₄₃	#532	1	2	yes	—
555	Dic₄₃	#576	1	2	yes	—
556	#3460	—	43	2	no	—
557	#3179	—	43	2	no	—
558	#3179	—	43	2	no	—
559	#3176	—	43	1	no	—
560	#3176	—	43	1	no	—
561	#3175	—	43	1	no	—
562	#3175	D₄₃	1	1	yes	characteristic, complemented
563	#3171	—	43	2	no	—
564	#3171	—	43	2	no	—
565	#3169	—	43	1	no	—
566	#3169	—	43	1	no	—
567	#3168	—	43	1	no	—
568	#3168	—	43	1	no	—
569	#3164	—	43	1	no	—
570	#3155	—	43	1	no	—
571	#3136	—	43	2	no	—
572	#3062	—	43	2	no	—
573	#3061	—	43	1	no	—
574	#3058	—	43	1	no	—
575	C₄×AGL(1,ℤ/8)	—	43	2	no	—
576	C₄×#135	—	43	1	no	—
577	C₂×C₄×D₈	—	43	1	no	—
578	C₄×#131	—	43	1	no	—
579	C₂×C₄₃	—	4	1	no	—
580	C₂×C₄₃	—	8	2	no	—
581	C₂×C₄₃	C₂×#532	1	1	yes	characteristic
582	C₂×C₄₃	C₂×#576	1	1	yes	characteristic
583	C₂×C₄₃	#3584	1	1	yes	characteristic
584	D₄₃	—	2	2	no	—
585	D₄₃	—	4	1	no	—
586	D₄₃	—	8	2	no	—
587	D₄₃	—	8	2	no	—
588	C₂×AGL(1,ℤ/8)	—	43	2	no	—
589	C₂×#135	—	43	1	no	—
590	C₂²×D₈	—	43	1	no	—
591	C₂×#131	—	43	1	no	—
592	C₂×#131	—	43	1	no	—
593	#544	—	43	2	no	—
594	#542	—	43	2	no	—
595	#542	—	86	2	no	—
596	#542	C₂×D₄₃	1	2	yes	complemented
597	#540	—	43	2	no	—
598	#540	—	43	2	no	—
599	#540	—	86	2	no	—
600	#538	—	86	2	no	—
601	#538	—	86	2	no	—
602	#537	—	43	2	no	—
603	#535	—	43	2	no	—
604	#535	—	43	2	no	—
605	#532	—	43	2	no	—
606	#532	—	43	2	no	—
607	#532	—	86	2	no	—
608	#529	—	43	2	no	—
609	#529	—	43	2	no	—
610	#529	—	86	2	no	—
611	#525	—	86	2	no	—
612	#525	—	86	2	no	—
613	C₄×#41	—	43	1	no	—
614	C₄×#41	—	43	2	no	—
615	C₂×C₄×D₄	—	43	2	no	—
616	#501	—	43	2	no	—
617	#501	—	43	2	no	—
618	#500	—	43	1	no	—
619	#500	C₂×D₄₃	1	1	yes	characteristic, complemented
620	#499	—	43	1	no	—
621	#499	—	43	1	no	—
622	#496	—	43	2	no	—
623	#496	—	43	2	no	—
624	#495	—	43	1	no	—
625	#495	C₂×D₄₃	1	1	yes	characteristic
626	#493	—	43	1	no	—
627	#493	—	43	1	no	—
628	#490	—	43	2	no	—
629	#490	—	43	2	no	—
630	#489	—	43	2	no	—
631	#489	C₂×D₄₃	1	2	yes	complemented
632	#488	—	43	2	no	—
633	#488	—	43	2	no	—
634	#486	—	43	2	no	—
635	#486	—	43	2	no	—
636	#469	—	43	2	no	—
637	#469	—	43	2	no	—
638	#469	—	43	2	no	—
639	#469	—	43	2	no	—
640	#468	—	43	2	no	—
641	#468	—	43	2	no	—
642	#468	—	43	2	no	—
643	#468	C₂×D₄₃	1	2	yes	complemented
644	#467	—	43	1	no	—
645	#467	C₂×D₄₃	1	1	yes	characteristic, complemented
646	#466	—	43	1	no	—
647	#466	—	43	1	no	—
648	#466	—	43	1	no	—
649	#466	—	43	2	no	—
650	#466	—	43	1	no	—
651	#466	—	43	1	no	—
652	#466	—	43	2	no	—
653	#466	C₂×D₄₃	1	1	yes	characteristic
654	#465	—	43	2	no	—
655	#465	—	43	2	no	—
656	#442	—	43	2	no	—
657	#442	—	43	2	no	—
658	#440	—	43	2	no	—
659	#440	C₂×D₄₃	1	2	yes	complemented
660	C₄×Q₁₆	—	43	1	no	—
661	C₄×Q₁₆	C₂×D₄₃	1	1	yes	characteristic, complemented
662	C₄×SD₁₆	—	43	2	no	—
663	C₄×SD₁₆	—	43	2	no	—
664	C₄×SD₁₆	—	43	2	no	—
665	C₄×SD₁₆	—	43	2	no	—
666	C₄×D₈	—	43	1	no	—
667	C₄×D₈	—	43	2	no	—
668	C₄×D₈	—	43	1	no	—
669	C₄×D₈	—	43	1	no	—
670	C₄×D₈	—	43	2	no	—
671	C₄×D₈	—	43	2	no	—
672	C₄×D₈	—	43	2	no	—
673	C₄×D₈	—	43	1	no	—
674	C₄×D₈	—	43	1	no	—
675	C₄×D₈	C₂×D₄₃	1	1	yes	characteristic
676	#428	—	43	2	no	—
677	#427	—	43	1	no	—
678	C₂×#107	—	43	1	no	—
679	#418	—	43	2	no	—
680	#417	—	43	2	no	—
681	#416	—	43	2	no	—
682	C₂×#102	—	43	2	no	—
683	#405	—	43	1	no	—
684	#405	—	43	1	no	—
685	#405	—	43	1	no	—
686	#405	—	43	1	no	—
687	#405	—	43	1	no	—
688	#405	C₂×D₄₃	1	1	yes	characteristic, complemented
689	C₄×M₁₆	—	43	1	no	—
690	C₄×M₁₆	—	43	1	no	—
691	C₄×M₁₆	—	43	1	no	—
692	C₂×C₄×C₈	—	43	1	no	—
693	C₂×C₄×C₈	—	43	1	no	—
694	C₂×C₄×C₈	—	43	1	no	—
695	C₄₃	#60695	1	1	yes	characteristic, complemented, Sylow
696	C₂×#41	—	43	1	no	—
697	C₂×#41	—	43	2	no	—
698	C₂×#41	—	86	2	no	—
699	C₂×#41	—	86	2	no	—
700	C₂²×D₄	—	43	2	no	—
701	C₂³×C₄	—	86	2	no	—
702	AGL(1,ℤ/8)	—	86	8	no	—
703	#135	—	86	4	no	—
704	C₂×Q₁₆	C₂²×D₄₃	1	1	yes	characteristic
705	C₂×SD₁₆	—	43	2	no	—
706	C₂×SD₁₆	—	43	2	no	—
707	C₂×SD₁₆	C₂²×D₄₃	1	2	yes	—
708	C₂×D₈	—	43	2	no	—
709	C₂×D₈	—	43	2	no	—
710	C₂×D₈	—	43	1	no	—
711	C₂×D₈	—	43	1	no	—
712	C₂×D₈	—	43	2	no	—
713	C₂×D₈	—	86	4	no	—
714	C₂×D₈	C₂²×D₄₃	1	1	yes	characteristic
715	#131	—	86	4	no	—
716	#131	—	86	4	no	—
717	C₂×M₁₆	—	43	1	no	—
718	C₂×M₁₆	—	43	1	no	—
719	C₂×M₁₆	—	43	1	no	—
720	C₂×M₁₆	—	43	1	no	—
721	C₂×M₁₆	—	43	1	no	—
722	C₂×M₁₆	C₂²×D₄₃	1	1	yes	characteristic
723	C₂²×C₈	—	43	1	no	—
724	C₂²×C₈	—	43	1	no	—
725	C₂²×C₈	—	43	1	no	—
726	C₂²×C₈	—	43	1	no	—
727	C₂²×C₈	—	43	1	no	—
728	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
729	C₄⋊Q₈	—	43	2	no	—
730	C₄⋊Q₈	—	86	2	no	—
731	C₄⋊Q₈	C₂²×D₄₃	1	2	yes	—
732	#127	—	43	2	no	—
733	#127	—	43	2	no	—
734	#127	—	86	2	no	—
735	#126	—	2	2	no	—
736	#126	—	86	2	no	—
737	#126	—	86	2	no	—
738	#126	—	86	2	no	—
739	#125	—	43	2	no	—
740	#125	—	43	2	no	—
741	#125	—	86	2	no	—
742	#124	—	2	2	no	—
743	#124	—	43	2	no	—
744	#124	—	86	2	no	—
745	#124	—	86	2	no	—
746	#124	—	86	2	no	—
747	#124	—	86	2	no	—
748	#124	C₂²×D₄₃	1	2	yes	—
749	#123	—	2	2	no	—
750	#123	—	86	2	no	—
751	#123	—	86	2	no	—
752	#123	—	86	2	no	—
753	#123	—	86	2	no	—
754	#123	—	86	2	no	—
755	#123	—	86	2	no	—
756	#123	—	86	2	no	—
757	C₂²⋊Q₈	—	2	2	no	—
758	C₂²⋊Q₈	—	43	2	no	—
759	C₂²⋊Q₈	—	86	2	no	—
760	C₂²⋊Q₈	—	86	2	no	—
761	C₂²⋊Q₈	—	86	2	no	—
762	C₂²⋊Q₈	—	86	2	no	—
763	C₂²⋊Q₈	C₂²×D₄₃	1	2	yes	—
764	#121	—	43	2	no	—
765	#121	—	43	2	no	—
766	#121	—	43	2	no	—
767	#121	—	43	2	no	—
768	#121	—	43	2	no	—
769	#121	—	86	2	no	—
770	#121	—	86	2	no	—
771	#121	—	86	2	no	—
772	#121	—	86	2	no	—
773	#121	—	86	2	no	—
774	#121	—	86	2	no	—
775	#121	—	86	2	no	—
776	#121	—	86	2	no	—
777	#121	—	86	2	no	—
778	#121	—	86	2	no	—
779	#121	—	86	2	no	—
780	#121	C₂²×D₄₃	1	2	yes	—
781	#120	—	86	2	no	—
782	#120	—	86	2	no	—
783	#120	—	86	2	no	—
784	#120	—	86	2	no	—
785	C₄×Q₈	—	43	1	no	—
786	C₄×Q₈	—	43	1	no	—
787	C₄×Q₈	—	43	2	no	—
788	C₄×Q₈	C₂²×D₄₃	1	2	yes	—
789	C₄×D₄	—	43	1	no	—
790	C₄×D₄	—	43	1	no	—
791	C₄×D₄	—	43	1	no	—
792	C₄×D₄	—	43	1	no	—
793	C₄×D₄	—	43	1	no	—
794	C₄×D₄	—	43	1	no	—
795	C₄×D₄	—	43	2	no	—
796	C₄×D₄	—	43	2	no	—
797	C₄×D₄	—	43	2	no	—
798	C₄×D₄	—	43	2	no	—
799	C₄×D₄	—	43	2	no	—
800	C₄×D₄	—	86	2	no	—
801	C₄×D₄	—	86	2	no	—
802	C₄×D₄	—	86	2	no	—
803	C₄×D₄	—	86	2	no	—
804	C₄×D₄	—	86	2	no	—
805	C₄×D₄	—	86	2	no	—
806	C₄×D₄	—	86	2	no	—
807	C₄×D₄	—	86	2	no	—
808	C₄×D₄	C₂²×D₄₃	1	2	yes	—
809	#117	—	43	1	no	—
810	#117	—	43	1	no	—
811	#117	—	43	2	no	—
812	#117	—	86	2	no	—
813	#117	—	86	2	no	—
814	#117	—	86	2	no	—
815	#117	C₂²×D₄₃	1	1	yes	characteristic
816	C₂×C₄⋊C₄	—	43	2	no	—
817	C₂×C₂²⋊C₄	—	86	2	no	—
818	C₂×C₄²	—	43	1	no	—
819	C₂×C₄²	—	43	1	no	—
820	C₂×C₄²	—	43	1	no	—
821	C₂×C₄²	—	86	2	no	—
822	#107	—	43	1	no	—
823	#107	—	43	1	no	—
824	#107	—	43	2	no	—
825	#107	—	43	2	no	—
826	#107	C₂²×D₄₃	1	1	yes	characteristic
827	#107	C₂²×D₄₃	1	1	yes	characteristic
828	#107	C₂²×D₄₃	1	2	yes	—
829	#106	—	43	2	no	—
830	#106	—	43	2	no	—
831	#106	—	43	2	no	—
832	#103	—	43	2	no	—
833	#103	—	43	2	no	—
834	#103	C₂²×D₄₃	1	2	yes	—
835	#103	C₂²×D₄₃	1	2	yes	—
836	#102	—	43	2	no	—
837	#102	—	43	2	no	—
838	#102	—	43	2	no	—
839	#102	—	43	2	no	—
840	#102	—	43	2	no	—
841	#102	—	43	2	no	—
842	#102	—	43	2	no	—
843	#102	—	43	2	no	—
844	#102	—	43	2	no	—
845	#102	—	43	2	no	—
846	#102	C₂²×D₄₃	1	2	yes	—
847	#102	C₂²×D₄₃	1	2	yes	—
848	#97	—	43	1	no	—
849	#97	—	43	1	no	—
850	#97	—	43	1	no	—
851	#97	—	43	1	no	—
852	#97	C₂²×D₄₃	1	1	yes	characteristic
853	#97	C₂²×D₄₃	1	1	yes	characteristic
854	C₄×C₈	—	43	1	no	—
855	C₄×C₈	—	43	1	no	—
856	C₄×C₈	—	43	1	no	—
857	C₄×C₈	—	43	1	no	—
858	C₄×C₈	—	43	1	no	—
859	C₄×C₈	—	43	1	no	—
860	C₄×C₈	—	43	1	no	—
861	C₄×C₈	—	43	1	no	—
862	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
863	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
864	C₂⁴	—	86	2	no	—
865	#41	—	86	2	no	—
866	#41	—	86	2	no	—
867	#41	—	86	4	no	—
868	#41	—	86	4	no	—
869	#41	—	344	4	no	—
870	#41	—	344	4	no	—
871	C₂×Q₈	—	2	2	no	—
872	C₂×Q₈	—	43	1	no	—
873	C₂×Q₈	—	86	2	no	—
874	C₂×Q₈	C₂³×D₄₃	1	2	yes	—
875	C₂×D₄	—	2	2	no	—
876	C₂×D₄	—	43	1	no	—
877	C₂×D₄	—	43	1	no	—
878	C₂×D₄	—	43	1	no	—
879	C₂×D₄	—	43	2	no	—
880	C₂×D₄	—	43	2	no	—
881	C₂×D₄	—	86	2	no	—
882	C₂×D₄	—	86	2	no	—
883	C₂×D₄	—	86	2	no	—
884	C₂×D₄	—	86	4	no	—
885	C₂×D₄	—	86	4	no	—
886	C₂×D₄	—	86	2	no	—
887	C₂×D₄	—	86	2	no	—
888	C₂×D₄	—	86	2	no	—
889	C₂×D₄	—	86	2	no	—
890	C₂×D₄	—	86	2	no	—
891	C₂×D₄	—	86	2	no	—
892	C₂×D₄	—	86	2	no	—
893	C₂×D₄	—	86	2	no	—
894	C₂×D₄	C₂³×D₄₃	1	2	yes	—
895	C₂²×C₄	—	2	2	no	—
896	C₂²×C₄	—	43	1	no	—
897	C₂²×C₄	—	43	1	no	—
898	C₂²×C₄	—	43	1	no	—
899	C₂²×C₄	—	43	1	no	—
900	C₂²×C₄	—	43	1	no	—
901	C₂²×C₄	—	43	1	no	—
902	C₂²×C₄	—	43	1	no	—
903	C₂²×C₄	—	43	1	no	—
904	C₂²×C₄	—	86	2	no	—
905	C₂²×C₄	—	86	2	no	—
906	C₂²×C₄	—	86	2	no	—
907	C₂²×C₄	—	86	2	no	—
908	C₂²×C₄	—	86	2	no	—
909	C₂²×C₄	—	86	2	no	—
910	C₂²×C₄	—	86	2	no	—
911	C₂²×C₄	—	344	4	no	—
912	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
913	Q₁₆	—	2	2	no	—
914	SD₁₆	—	2	4	no	—
915	SD₁₆	—	86	4	no	—
916	SD₁₆	—	86	4	no	—
917	D₈	—	2	2	no	—
918	D₈	—	86	4	no	—
919	D₈	—	86	4	no	—
920	D₈	—	86	2	no	—
921	D₈	—	86	2	no	—
922	D₈	—	86	4	no	—
923	M₁₆	—	2	2	no	—
924	M₁₆	—	43	4	no	—
925	M₁₆	—	86	2	no	—
926	M₁₆	—	86	2	no	—
927	M₁₆	—	86	2	no	—
928	M₁₆	—	86	2	no	—
929	C₂×C₈	—	2	2	no	—
930	C₂×C₈	—	43	1	no	—
931	C₂×C₈	—	43	1	no	—
932	C₂×C₈	—	43	4	no	—
933	C₂×C₈	—	43	1	no	—
934	C₂×C₈	—	43	1	no	—
935	C₂×C₈	—	86	2	no	—
936	C₂×C₈	—	86	2	no	—
937	C₂×C₈	—	86	2	no	—
938	C₂×C₈	—	86	2	no	—
939	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
940	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
941	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
942	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
943	C₄⋊C₄	—	2	2	no	—
944	C₄⋊C₄	—	2	2	no	—
945	C₄⋊C₄	—	2	2	no	—
946	C₄⋊C₄	—	43	1	no	—
947	C₄⋊C₄	—	43	1	no	—
948	C₄⋊C₄	—	43	1	no	—
949	C₄⋊C₄	—	43	1	no	—
950	C₄⋊C₄	—	43	2	no	—
951	C₄⋊C₄	—	43	2	no	—
952	C₄⋊C₄	—	86	2	no	—
953	C₄⋊C₄	—	86	2	no	—
954	C₄⋊C₄	—	86	2	no	—
955	C₄⋊C₄	—	86	2	no	—
956	C₄⋊C₄	—	86	2	no	—
957	C₄⋊C₄	—	86	2	no	—
958	C₄⋊C₄	—	86	2	no	—
959	C₄⋊C₄	—	86	2	no	—
960	C₄⋊C₄	D₄×D₄₃	1	1	yes	characteristic
961	C₄⋊C₄	D₄×D₄₃	1	1	yes	characteristic
962	C₄⋊C₄	C₂³×D₄₃	1	2	yes	—
963	C₄⋊C₄	C₂³×D₄₃	1	2	yes	—
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	—	43	1	no	—
970	C₂²⋊C₄	—	43	1	no	—
971	C₂²⋊C₄	—	43	1	no	—
972	C₂²⋊C₄	—	43	1	no	—
973	C₂²⋊C₄	—	86	2	no	—
974	C₂²⋊C₄	—	86	2	no	—
975	C₂²⋊C₄	—	86	2	no	—
976	C₂²⋊C₄	—	86	2	no	—
977	C₂²⋊C₄	—	86	2	no	—
978	C₂²⋊C₄	—	86	2	no	—
979	C₂²⋊C₄	—	86	2	no	—
980	C₂²⋊C₄	—	86	2	no	—
981	C₂²⋊C₄	—	86	2	no	—
982	C₂²⋊C₄	—	86	2	no	—
983	C₂²⋊C₄	—	86	2	no	—
984	C₂²⋊C₄	—	86	2	no	—
985	C₂²⋊C₄	—	86	2	no	—
986	C₂²⋊C₄	—	86	2	no	—
987	C₂²⋊C₄	D₄×D₄₃	1	1	yes	characteristic
988	C₂²⋊C₄	D₄×D₄₃	1	1	yes	characteristic
989	C₄²	—	2	2	no	—
990	C₄²	—	43	1	no	—
991	C₄²	—	43	1	no	—
992	C₄²	—	43	1	no	—
993	C₄²	—	43	1	no	—
994	C₄²	—	43	1	no	—
995	C₄²	—	43	1	no	—
996	C₄²	—	43	1	no	—
997	C₄²	—	43	1	no	—
998	C₄²	—	86	2	no	—
999	C₄²	—	86	2	no	—
1000	C₄²	C₂³×D₄₃	1	1	yes	characteristic
1001	C₄²	C₂³×D₄₃	1	1	yes	characteristic
1002	C₂³	—	2	2	no	—
1003	C₂³	—	43	1	no	—
1004	C₂³	—	43	1	no	—
1005	C₂³	—	86	2	no	—
1006	C₂³	—	86	2	no	—
1007	C₂³	—	344	2	no	—
1008	C₂³	—	344	2	no	—
1009	C₂³	—	172	4	no	—
1010	C₂³	C₂×D₄×D₄₃	1	1	yes	characteristic
1011	Q₈	—	2	2	no	—
1012	Q₈	—	2	2	no	—
1013	Q₈	—	8	2	no	—
1014	Q₈	—	86	2	no	—
1015	Q₈	—	344	2	no	—
1016	D₄	—	2	2	no	—
1017	D₄	—	2	2	no	—
1018	D₄	—	8	2	no	—
1019	D₄	—	86	2	no	—
1020	D₄	—	86	2	no	—
1021	D₄	—	86	2	no	—
1022	D₄	—	86	2	no	—
1023	D₄	—	86	2	no	—
1024	D₄	—	86	2	no	—
1025	D₄	—	86	2	no	—
1026	D₄	—	344	2	no	—
1027	D₄	—	344	2	no	—
1028	D₄	—	344	2	no	—
1029	D₄	—	344	2	no	—
1030	D₄	—	344	2	no	—
1031	D₄	—	344	2	no	—
1032	D₄	—	344	2	no	—
1033	D₄	—	344	2	no	—
1034	D₄	—	344	2	no	—
1035	D₄	—	172	4	no	—
1036	D₄	—	172	4	no	—
1037	C₂×C₄	—	2	1	no	—
1038	C₂×C₄	—	2	1	no	—
1039	C₂×C₄	—	2	2	no	—
1040	C₂×C₄	—	2	2	no	—
1041	C₂×C₄	—	2	2	no	—
1042	C₂×C₄	—	8	2	no	—
1043	C₂×C₄	—	43	1	no	—
1044	C₂×C₄	—	43	1	no	—
1045	C₂×C₄	—	43	2	no	—
1046	C₂×C₄	—	43	2	no	—
1047	C₂×C₄	—	43	1	no	—
1048	C₂×C₄	—	43	1	no	—
1049	C₂×C₄	—	43	1	no	—
1050	C₂×C₄	—	43	1	no	—
1051	C₂×C₄	—	86	2	no	—
1052	C₂×C₄	—	86	2	no	—
1053	C₂×C₄	—	86	2	no	—
1054	C₂×C₄	—	86	1	no	—
1055	C₂×C₄	—	86	1	no	—
1056	C₂×C₄	—	86	2	no	—
1057	C₂×C₄	—	86	2	no	—
1058	C₂×C₄	—	344	2	no	—
1059	C₂×C₄	—	344	2	no	—
1060	C₂×C₄	—	344	2	no	—
1061	C₂×C₄	—	172	1	no	—
1062	C₂×C₄	—	172	1	no	—
1063	C₂×C₄	—	172	4	no	—
1064	C₂×C₄	—	172	4	no	—
1065	C₂×C₄	—	172	4	no	—
1066	C₂×C₄	—	172	4	no	—
1067	C₂×C₄	—	172	1	no	—
1068	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
1069	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
1070	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
1071	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
1072	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
1073	C₂×C₄	C₂⁴×D₄₃	1	1	yes	characteristic
1074	C₈	—	2	1	no	—
1075	C₈	—	2	1	no	—
1076	C₈	—	43	2	no	—
1077	C₈	—	43	2	no	—
1078	C₈	—	86	1	no	—
1079	C₈	—	86	1	no	—
1080	C₈	#41×D₄₃	1	2	yes	—
1081	C₈	#41×D₄₃	1	2	yes	—
1082	C₂²	—	2	1	no	—
1083	C₂²	—	2	1	no	—
1084	C₂²	—	2	1	no	—
1085	C₂²	—	4	2	no	—
1086	C₂²	—	4	2	no	—
1087	C₂²	—	4	2	no	—
1088	C₂²	—	43	2	no	—
1089	C₂²	—	86	1	no	—
1090	C₂²	—	86	1	no	—
1091	C₂²	—	86	1	no	—
1092	C₂²	—	86	1	no	—
1093	C₂²	—	86	1	no	—
1094	C₂²	—	344	8	no	—
1095	C₂²	—	172	2	no	—
1096	C₂²	—	172	2	no	—
1097	C₂²	—	172	2	no	—
1098	C₂²	—	172	2	no	—
1099	C₂²	—	172	2	no	—
1100	C₂²	—	172	2	no	—
1101	C₂²	C₂²×D₄×D₄₃	1	1	yes	characteristic
1102	C₄	—	2	1	no	—
1103	C₄	—	2	1	no	—
1104	C₄	—	2	1	no	—
1105	C₄	—	2	1	no	—
1106	C₄	—	2	1	no	—
1107	C₄	—	4	2	no	—
1108	C₄	—	4	2	no	—
1109	C₄	—	4	2	no	—
1110	C₄	—	43	2	no	—
1111	C₄	—	43	2	no	—
1112	C₄	—	86	1	no	—
1113	C₄	—	86	1	no	—
1114	C₄	—	86	1	no	—
1115	C₄	—	86	1	no	—
1116	C₄	—	172	2	no	—
1117	C₄	—	172	2	no	—
1118	C₄	C₂×#41×D₄₃	1	1	yes	characteristic
1119	C₄	C₂×#41×D₄₃	1	1	yes	characteristic
1120	C₂	—	4	1	no	—
1121	C₂	—	8	2	no	—
1122	C₂	—	86	2	no	—
1123	C₂	—	344	2	no	—
1124	C₂	—	344	2	no	—
1125	C₂	—	172	1	no	—
1126	C₂	#532×D₄₃	1	1	yes	characteristic
1127	C₂	#576×D₄₃	1	1	yes	characteristic
1128	C₂	#19149365	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×#3175	C₂
socle	C₂²×C₄₃	C₂³×D₄
hypercenter	#3175	D₄₃
hypocenter	C₄₃	#60695
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ #117 ◁ #3175

Complements

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

N	H ≅ G/N	type
1. #19148015	C₂	semidirect
2. #19145276	C₂	semidirect
3. #19145272	C₂	semidirect
4. #19145245	C₂	semidirect
5. #19145241	C₂	semidirect
6. #19145236	C₂	semidirect
7. #19145193	C₂	semidirect
8. #19145183	C₂	semidirect
9. #19145175	C₂	semidirect
10. #19145169	C₂	semidirect
11. #19145166	C₂	semidirect
12. #19145162	C₂	semidirect
13. #19145128	C₂	semidirect
14. #19145077	C₂	semidirect
15. #19144946	C₂	semidirect
16. #19144270	C₂	semidirect
17. #19144266	C₂	semidirect
18. #19144238	C₂	semidirect
19. #19143400	C₂	semidirect
20. C₄×#13063348	C₂	semidirect
21. C₄×D₈×D₄₃	C₂	semidirect
22. #19143017	C₂	semidirect
23. C₄₃×#3175	C₂	semidirect
30. #14583521	C₂²	semidirect
32. #14583504	C₂²	semidirect
34. #14583500	C₂²	semidirect
40. #14583450	C₂²	semidirect
42. #14583444	C₂²	semidirect
43. #14583435	C₂²	semidirect
45. #14583428	C₂²	semidirect
51. #14583307	C₂²	semidirect
52. #14583305	C₂²	semidirect
53. #14583303	C₂²	semidirect
54. #14583301	C₂²	semidirect
55. #14583300	C₂²	semidirect
61. #14583264	C₂²	semidirect
62. #14583262	C₂²	semidirect
63. #14583260	C₂²	semidirect
64. #14583255	C₂²	semidirect
65. #14583253	C₂²	semidirect
66. #14583247	C₂²	semidirect
67. #14583244	C₂²	semidirect
68. #14583152	C₂²	semidirect
70. #14583151	C₂²	semidirect
72. #14583148	C₂²	semidirect
73. #14583148	C₂²	semidirect
74. #14583147	C₂²	semidirect
75. #14583137	C₂²	semidirect
77. #14583136	C₂²	semidirect
78. #14583136	C₂²	semidirect
80. #14583135	C₂²	semidirect
81. #14583133	C₂²	semidirect
83. #14583130	C₂²	semidirect
84. #14583125	C₂²	semidirect
85. #14583012	C₂²	semidirect
86. #14583009	C₂²	semidirect
87. #14582997	C₂²	semidirect
88. Q₁₆×Dic₄₃	C₂²	semidirect
89. SD₁₆×Dic₄₃	C₂²	semidirect
90. C₄×#10621884	C₂²	semidirect
91. #14582984	C₂²	semidirect
92. #14582984	C₂²	semidirect
94. C₄×D₃₄₄	C₂²	semidirect
97. #14582981	C₂²	semidirect
98. #14582981	C₂²	semidirect
101. #14582979	C₂²	semidirect
110. #14582856	C₂²	semidirect
111. #14582855	C₂²	semidirect
113. #14582853	C₂²	semidirect
115. #14582851	C₂²	semidirect
116. M₁₆×Dic₄₃	C₂²	semidirect
117. C₂×C₈×Dic₄₃	C₂²	semidirect
119. C₄×C₈×D₄₃	C₂²	semidirect
120. C₄₃×#542	C₂²	semidirect
121. C₄₃×#500	C₂²	semidirect
123. C₄₃×#489	C₂²	semidirect
124. C₄₃×#468	C₂²	semidirect
125. C₄₃×#467	C₂²	semidirect
127. C₄₃×#440	C₂²	semidirect
128. C₄×Q₁₆×C₄₃	C₂²	semidirect
130. C₄₃×#405	C₂²	semidirect
432. #10621872	#41	semidirect
436. C₈×D₄₃	#41	semidirect
562. #3175	D₄₃	semidirect
596. #542	C₂×D₄₃	semidirect
619. #500	C₂×D₄₃	semidirect
631. #489	C₂×D₄₃	semidirect
643. #468	C₂×D₄₃	semidirect
645. #467	C₂×D₄₃	semidirect
659. #440	C₂×D₄₃	semidirect
661. C₄×Q₁₆	C₂×D₄₃	semidirect
688. #405	C₂×D₄₃	semidirect
695. C₄₃	#60695	semidirect

Maximal subgroups

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

subgroup	index
#19148015	2
#19145276	2
#19145272	2
#19145245	2
#19145241	2
#19145236	2
#19145193	2
#19145183	2
#19145175	2
#19145169	2
#19145166	2
#19145162	2
#19145128	2
#19145077	2
#19144946	2
#19144270	2
#19144266	2
#19144238	2
#19143400	2
C₄×#13063348	2
C₄×D₈×D₄₃	2
#19143017	2
C₄₃×#3175	2
#60695	43