Subgroups — #25965398

Order 11008.

2024 conjugacy classes of subgroups.

The subgroup lattice has 1170 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19148349	C₂	1	1	yes	maximal, characteristic, complemented
2	#19147796	C₂	1	1	yes	maximal, characteristic, complemented
3	#19144875	C₂	1	2	yes	maximal, complemented
4	#19144852	C₂	1	2	yes	maximal, complemented
5	#19144812	C₂	1	2	yes	maximal, complemented
6	#19144804	C₂	1	2	yes	maximal, complemented
7	#19144752	C₂	1	2	yes	maximal, complemented
8	#19144699	C₂	1	2	yes	maximal, complemented
9	#19144661	C₂	1	2	yes	maximal, complemented
10	#19144608	C₂	1	2	yes	maximal, complemented
11	#19144543	C₂	1	1	yes	maximal, characteristic, complemented
12	#19144440	C₂	1	1	yes	maximal, characteristic, complemented
13	#19144429	C₂	1	1	yes	maximal, characteristic, complemented
14	#19144128	C₂	1	1	yes	maximal, characteristic, complemented
15	#19144110	C₂	1	1	yes	maximal, characteristic, complemented
16	#19143835	C₂	1	1	yes	maximal, characteristic
17	C₂×#14583063	C₂	1	1	yes	maximal, characteristic, complemented
18	#19143462	C₂	1	1	yes	maximal, characteristic, complemented
19	#19143453	C₂	1	1	yes	maximal, characteristic, complemented
20	#19143441	C₂	1	1	yes	maximal, characteristic, complemented
21	#19143430	C₂	1	1	yes	maximal, characteristic, complemented
22	#19143249	C₂	1	1	yes	maximal, characteristic, complemented
23	C₄₃×#3091	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂²×#10621898	C₂²	1	1	yes	characteristic
25	C₂×#13063355	C₂²	1	1	yes	characteristic
26	C₂×#13063350	C₂²	1	1	yes	characteristic
27	C₂²×Dic₁₇₂	C₂²	1	1	yes	characteristic
28	C₂²×#10621873	C₂²	1	1	yes	characteristic
29	#14583619	—	2	1	no	—
30	#14583606	—	2	1	no	—
31	#14583589	—	2	1	no	—
32	#14583589	—	2	1	no	—
33	#14583586	—	2	2	no	—
34	#14583580	—	2	2	no	—
35	#14583527	C₂²	1	1	yes	characteristic
36	#14583516	C₂²	1	2	yes	complemented
37	#14583509	C₂²	1	2	yes	complemented
38	#14583470	C₂²	1	1	yes	characteristic
39	#14583451	C₂²	1	2	yes	complemented
40	#14583430	C₂²	1	2	yes	complemented
41	C₂×#13063304	C₂²	1	1	yes	characteristic
42	#14583382	C₂²	1	1	yes	characteristic
43	#14583380	C₂²	1	2	yes	—
44	#14583380	C₂²	1	2	yes	—
45	#14583379	—	2	1	no	—
46	#14583379	—	2	1	no	—
47	#14583376	C₂²	1	1	yes	characteristic
48	#14583376	C₂²	1	1	yes	characteristic
49	#14583376	C₂²	1	1	yes	characteristic
50	#14583373	C₂²	1	1	yes	characteristic
51	#14583373	C₂²	1	1	yes	characteristic
52	#14583372	—	2	2	no	—
53	C₄×#10621898	—	2	1	no	—
54	C₄×#10621898	—	2	1	no	—
55	#14583367	C₂²	1	2	yes	—
56	#14583367	C₂²	1	2	yes	—
57	C₂×#13063284	C₂²	1	1	yes	characteristic
58	#117×D₄₃	—	2	2	no	—
59	#14583240	C₂²	1	2	yes	complemented
60	#14583240	C₂²	1	2	yes	complemented
61	#14583234	C₂²	1	2	yes	complemented
62	#14583229	C₂²	1	2	yes	complemented
63	#14583209	C₂²	1	2	yes	complemented
64	#14583205	C₂²	1	2	yes	complemented
65	#14583202	C₂²	1	2	yes	complemented
66	#14583198	C₂²	1	2	yes	complemented
67	#14583193	C₂²	1	2	yes	complemented
68	#14583188	C₂²	1	2	yes	complemented
69	#14583183	C₂²	1	2	yes	complemented
70	#14583178	C₂²	1	2	yes	complemented
71	#14583120	C₂²	1	2	yes	complemented
72	#14583120	C₂²	1	2	yes	complemented
73	#14583113	C₂²	1	2	yes	complemented
74	#14583113	C₂²	1	2	yes	complemented
75	#14583108	C₂²	1	2	yes	complemented
76	#14583108	C₂²	1	2	yes	complemented
77	#14583103	C₂²	1	2	yes	complemented
78	#14583103	C₂²	1	2	yes	complemented
79	#14583063	C₂²	1	2	yes	—
80	#14583063	C₂²	1	2	yes	—
81	#14583063	C₂²	1	2	yes	—
82	#14583063	C₂²	1	2	yes	—
83	#14583059	C₂²	1	2	yes	—
84	#14583059	C₂²	1	2	yes	—
85	#14583042	C₂²	1	2	yes	—
86	#14583042	C₂²	1	2	yes	—
87	#14583008	C₂²	1	2	yes	complemented
88	#14583005	C₂²	1	2	yes	complemented
89	#14583005	C₂²	1	2	yes	complemented
90	#14583003	C₂²	1	2	yes	complemented
91	#14583002	C₂²	1	2	yes	complemented
92	#14582998	C₂²	1	2	yes	complemented
93	#14582998	C₂²	1	2	yes	complemented
94	#14582996	C₂²	1	2	yes	complemented
95	#14582993	C₂²	1	2	yes	complemented
96	#14582993	C₂²	1	2	yes	complemented
97	#14582991	C₂²	1	2	yes	complemented
98	#14582990	C₂²	1	2	yes	complemented
99	#14582986	C₂²	1	2	yes	complemented
100	#14582986	C₂²	1	2	yes	complemented
101	#14582984	C₂²	1	2	yes	complemented
102	#14582979	C₂²	1	2	yes	complemented
103	#14582957	C₂²	1	2	yes	complemented
104	#14582957	C₂²	1	2	yes	complemented
105	#14582953	C₂²	1	2	yes	complemented
106	#14582949	C₂²	1	2	yes	complemented
107	#14582942	C₂²	1	1	yes	characteristic
108	#14582942	C₂²	1	1	yes	characteristic
109	#14582925	C₂²	1	1	yes	characteristic
110	#14582925	C₂²	1	1	yes	characteristic
111	#14582907	C₂²	1	1	yes	characteristic
112	#14582907	C₂²	1	1	yes	characteristic
113	#14582907	C₂²	1	1	yes	characteristic
114	#14582903	C₂²	1	1	yes	characteristic
115	C₂×#13063250	C₂²	1	1	yes	characteristic
116	C₂×#13063247	C₂²	1	1	yes	characteristic
117	#14582863	C₂²	1	1	yes	characteristic
118	#14582854	C₂²	1	1	yes	characteristic
119	#14582854	C₂²	1	1	yes	characteristic
120	C₄₃×#525	C₂²	1	1	yes	characteristic
121	C₂×#117×C₄₃	C₂²	1	1	yes	characteristic
122	C₄₃×#485	C₂²	1	1	yes	characteristic, complemented
123	C₄₃×#485	C₂²	1	1	yes	characteristic, complemented
124	C₄₃×#484	C₂²	1	1	yes	characteristic, complemented
125	C₄₃×#483	C₂²	1	1	yes	characteristic, complemented
126	C₄₃×#482	C₂²	1	1	yes	characteristic, complemented
127	C₄₃×#482	C₂²	1	1	yes	characteristic, complemented
128	C₄₃×#481	C₂²	1	1	yes	characteristic, complemented
129	C₄₃×#480	C₂²	1	1	yes	characteristic, complemented
130	C₄₃×#427	C₂²	1	1	yes	characteristic
131	C₄₃×#427	C₂²	1	1	yes	characteristic
132	C₄₃×#416	C₂²	1	1	yes	characteristic
133	C₄₃×#416	C₂²	1	1	yes	characteristic
134	C₂×C₂²⋊C₈×C₄₃	C₂²	1	1	yes	characteristic
135	C₂×#10621898	—	2	1	no	—
136	C₂×#10621898	—	2	1	no	—
137	C₂×#10621898	—	2	4	no	—
138	C₂×#10621898	—	2	4	no	—
139	C₂×#10621898	C₂³	1	2	yes	—
140	C₂×#10621898	C₂³	1	2	yes	—
141	C₂²×Dic₈₆	C₂³	1	1	yes	characteristic
142	C₂²×Dic₈₆	C₂³	1	1	yes	characteristic
143	C₂²×D₁₇₂	C₂³	1	1	yes	characteristic
144	C₂²×C₂²⋊D₄₃	—	2	1	no	—
145	C₂²×C₄×D₄₃	—	2	1	no	—
146	#13063355	—	2	4	no	—
147	#13063350	—	2	4	no	—
148	C₂×Dic₁₇₂	—	2	4	no	—
149	C₂×Dic₁₇₂	C₂³	1	2	yes	—
150	C₂×Dic₁₇₂	C₂³	1	2	yes	—
151	C₂×#10621885	C₂³	1	2	yes	—
152	C₂×#10621873	—	2	4	no	—
153	C₂×#10621873	C₂³	1	2	yes	—
154	C₂×#10621873	C₂³	1	2	yes	—
155	C₂×#10621883	C₂³	1	2	yes	—
156	C₂×#10621884	C₂³	1	2	yes	—
157	C₂×#10621882	C₂³	1	2	yes	—
158	C₂×#10621877	C₂³	1	1	yes	characteristic
159	C₂×#10621877	C₂³	1	1	yes	characteristic
160	#13063325	—	2	1	no	—
161	#13063324	C₂³	1	2	yes	—
162	#13063323	C₂³	1	2	yes	—
163	#13063318	—	2	2	no	—
164	#13063318	—	2	2	no	—
165	#13063318	—	2	2	no	—
166	#13063318	—	2	2	no	—
167	#13063317	—	2	1	no	—
168	#13063316	—	2	2	no	—
169	#13063316	C₂³	1	2	yes	—
170	#13063315	—	2	2	no	—
171	#13063315	—	2	2	no	—
172	#13063312	—	2	2	no	—
173	#13063312	C₂³	1	2	yes	—
174	#13063306	—	2	2	no	—
175	#13063306	—	2	2	no	—
176	#13063306	—	2	2	no	—
177	#13063304	—	2	1	no	—
178	#13063304	—	2	1	no	—
179	#13063304	—	2	1	no	—
180	#13063304	—	2	1	no	—
181	#13063304	C₂³	1	2	yes	—
182	#13063304	C₂³	1	2	yes	—
183	#13063302	—	2	2	no	—
184	#13063302	—	2	2	no	—
185	#13063302	—	2	2	no	—
186	Q₈×Dic₄₃	C₂³	1	2	yes	—
187	C₄×Dic₈₆	—	2	1	no	—
188	C₄×Dic₈₆	—	2	1	no	—
189	C₄×Dic₈₆	—	2	1	no	—
190	C₄×Dic₈₆	—	2	1	no	—
191	C₄×Dic₈₆	—	2	1	no	—
192	C₄×Dic₈₆	—	2	1	no	—
193	#13063290	—	2	2	no	—
194	#13063290	C₂³	1	2	yes	—
195	#13063290	C₂³	1	2	yes	—
196	#13063290	C₂³	1	2	yes	—
197	#13063290	C₂³	1	2	yes	—
198	#13063290	C₂³	1	2	yes	—
199	#13063290	C₂³	1	2	yes	—
200	C₄×D₁₇₂	—	2	1	no	—
201	C₄×D₁₇₂	—	2	1	no	—
202	C₄×D₁₇₂	—	2	1	no	—
203	C₄×D₁₇₂	—	2	1	no	—
204	D₄×Dic₄₃	—	2	2	no	—
205	D₄×Dic₄₃	—	2	2	no	—
206	D₄×Dic₄₃	C₂³	1	2	yes	—
207	#13063287	C₂³	1	2	yes	—
208	#13063287	C₂³	1	2	yes	—
209	#13063287	C₂³	1	2	yes	—
210	#13063287	C₂³	1	2	yes	—
211	C₄×C₂²⋊D₄₃	—	2	2	no	—
212	C₄×C₂²⋊D₄₃	—	2	2	no	—
213	C₄×C₂²⋊D₄₃	—	2	2	no	—
214	C₄×C₂²⋊D₄₃	—	2	2	no	—
215	(C₂²⋊D₄₃)⋊C₄	—	2	2	no	—
216	(C₂²⋊D₄₃)⋊C₄	—	2	2	no	—
217	(C₂²⋊D₄₃)⋊C₄	—	2	2	no	—
218	(C₂²⋊D₄₃)⋊C₄	—	2	2	no	—
219	#13063284	—	2	1	no	—
220	#13063284	D₄	1	2	yes	—
221	#13063284	D₄	1	1	yes	characteristic
222	#13063284	D₄	1	1	yes	characteristic
223	#13063284	C₂³	1	1	yes	characteristic
224	#13063284	C₂³	1	1	yes	characteristic
225	#13063284	C₂³	1	2	yes	—
226	#13063283	—	2	2	no	—
227	#13063283	—	2	2	no	—
228	#13063282	—	2	2	no	—
229	#13063282	—	2	2	no	—
230	#13063281	—	2	2	no	—
231	#13063281	—	2	2	no	—
232	#13063281	—	2	2	no	—
233	#13063281	—	2	2	no	—
234	#13063281	—	2	2	no	—
235	C₂×C₄⋊Dic₄₃	—	2	1	no	—
236	C₂×C₄⋊Dic₄₃	D₄	1	1	yes	characteristic
237	C₂×C₄⋊Dic₄₃	D₄	1	1	yes	characteristic
238	C₂×C₄⋊Dic₄₃	C₂³	1	1	yes	characteristic
239	C₂×Dic₄₃⋊C₄	—	2	1	no	—
240	C₄⋊C₄×D₄₃	—	2	2	no	—
241	C₄⋊C₄×D₄₃	—	2	2	no	—
242	C₂×C₂²⋊Dic₄₃	—	2	1	no	—
243	C₂×C₂²⋊Dic₄₃	D₄	1	2	yes	—
244	C₂²⋊C₄×D₄₃	—	2	2	no	—
245	C₂²⋊C₄×D₄₃	—	2	2	no	—
246	C₂×C₄×Dic₄₃	C₂³	1	2	yes	—
247	C₄²×D₄₃	—	2	2	no	—
248	C₄²×D₄₃	—	2	2	no	—
249	#13063258	C₂³	1	2	yes	—
250	#13063258	C₂³	1	2	yes	—
251	#13063256	C₂³	1	2	yes	—
252	#13063256	C₂³	1	2	yes	—
253	Dic₄₃⋊C₈	C₂³	1	2	yes	—
254	Dic₄₃⋊C₈	C₂³	1	2	yes	—
255	Dic₄₃⋊C₈	C₂³	1	2	yes	—
256	Dic₄₃⋊C₈	C₂³	1	2	yes	—
257	#13063250	C₂³	1	2	yes	—
258	#13063250	C₂³	1	2	yes	—
259	#13063248	C₂³	1	2	yes	—
260	#13063248	C₂³	1	2	yes	—
261	#13063248	C₂³	1	2	yes	—
262	#13063248	C₂³	1	2	yes	—
263	#13063248	C₂³	1	2	yes	—
264	#13063248	C₂³	1	2	yes	—
265	#13063247	C₂³	1	2	yes	—
266	#13063247	C₂³	1	2	yes	—
267	#13063245	C₂³	1	2	yes	—
268	#13063245	C₂³	1	2	yes	—
269	C₂²⋊(C₄₃⋊C₈)	C₂³	1	2	yes	—
270	C₂²⋊(C₄₃⋊C₈)	C₂³	1	2	yes	—
271	#13063235	C₂³	1	2	yes	—
272	#13063235	C₂³	1	2	yes	—
273	C₈×Dic₄₃	C₂³	1	2	yes	—
274	C₈×Dic₄₃	C₂³	1	2	yes	—
275	C₂×#41×C₄₃	C₂³	1	1	yes	characteristic
276	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
277	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
278	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
279	#123×C₄₃	—	2	1	no	—
280	C₂²⋊Q₈×C₄₃	C₂³	1	1	yes	characteristic
281	C₂²⋊Q₈×C₄₃	C₂³	1	1	yes	characteristic
282	#121×C₄₃	C₂³	1	1	yes	characteristic
283	#121×C₄₃	C₂³	1	1	yes	characteristic
284	#120×C₄₃	—	2	1	no	—
285	C₄×D₄×C₄₃	—	2	1	no	—
286	C₄×D₄×C₄₃	—	2	1	no	—
287	#117×C₄₃	—	2	1	no	—
288	#117×C₄₃	—	2	1	no	—
289	#117×C₄₃	C₂³	1	1	yes	characteristic
290	#117×C₄₃	C₂³	1	1	yes	characteristic
291	#117×C₄₃	C₂³	1	1	yes	characteristic
292	#117×C₄₃	C₂³	1	1	yes	characteristic
293	#117×C₄₃	C₂³	1	1	yes	characteristic
294	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
295	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
296	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
297	C₂×C₄²×C₄₃	—	2	1	no	—
298	#107×C₄₃	C₂³	1	1	yes	characteristic
299	#107×C₄₃	C₂³	1	1	yes	characteristic
300	#107×C₄₃	C₂³	1	1	yes	characteristic
301	#107×C₄₃	C₂³	1	1	yes	characteristic
302	#106×C₄₃	C₂³	1	1	yes	characteristic
303	#106×C₄₃	C₂³	1	1	yes	characteristic
304	#106×C₄₃	C₂³	1	1	yes	characteristic
305	#106×C₄₃	C₂³	1	1	yes	characteristic
306	#103×C₄₃	C₂³	1	1	yes	characteristic
307	#103×C₄₃	C₂³	1	1	yes	characteristic
308	#103×C₄₃	C₂³	1	1	yes	characteristic
309	#103×C₄₃	C₂³	1	1	yes	characteristic
310	#102×C₄₃	C₂³	1	1	yes	characteristic
311	#102×C₄₃	C₂³	1	1	yes	characteristic
312	#102×C₄₃	C₂³	1	1	yes	characteristic
313	#102×C₄₃	C₂³	1	1	yes	characteristic
314	C₂²⋊C₈×C₄₃	C₂³	1	1	yes	characteristic
315	C₂²⋊C₈×C₄₃	C₂³	1	1	yes	characteristic
316	C₂²⋊C₈×C₄₃	C₂³	1	1	yes	characteristic
317	C₂²⋊C₈×C₄₃	C₂³	1	1	yes	characteristic
318	C₂⁴×C₄₃	C₂×D₄	1	1	yes	characteristic
319	C₂³×D₄₃	—	2	1	no	—
320	#41×C₄₃	—	2	2	no	—
321	#41×C₄₃	—	2	2	no	—
322	C₂×Q₈×C₄₃	C₂⁴	1	1	yes	characteristic
323	C₂×D₄×C₄₃	—	2	1	no	—
324	C₂×D₄×C₄₃	—	2	1	no	—
325	C₂×D₄×C₄₃	—	2	1	no	—
326	C₂×D₄×C₄₃	C₂⁴	1	1	yes	characteristic
327	C₂²×C₄×C₄₃	—	2	2	no	—
328	C₂²×C₄×C₄₃	—	2	2	no	—
329	C₂²×C₄×C₄₃	—	2	1	no	—
330	C₂²×C₄×C₄₃	—	2	1	no	—
331	C₂²×C₄×C₄₃	—	2	1	no	—
332	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
333	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
334	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
335	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
336	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
337	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
338	C₂×C₂²⋊D₄₃	—	2	8	no	—
339	C₂×C₂²⋊D₄₃	—	2	2	no	—
340	C₂×C₂²⋊D₄₃	—	2	2	no	—
341	C₂²×Dic₄₃	—	2	2	no	—
342	C₂²×Dic₄₃	—	2	1	no	—
343	C₂²×Dic₄₃	—	2	1	no	—
344	C₂²×Dic₄₃	—	2	1	no	—
345	C₂²×Dic₄₃	C₂×D₄	1	2	yes	—
346	C₂²×Dic₄₃	C₂×D₄	1	2	yes	—
347	#10621898	—	2	8	no	—
348	#10621898	—	2	8	no	—
349	#10621898	—	2	4	no	—
350	#10621898	—	2	4	no	—
351	#10621898	—	2	4	no	—
352	#10621898	—	2	4	no	—
353	C₂×D₁₇₂	—	2	1	no	—
354	C₂×D₁₇₂	—	2	2	no	—
355	C₂×D₁₇₂	#41	1	4	yes	—
356	C₂×D₁₇₂	C₂⁴	1	2	yes	—
357	C₂×C₄×D₄₃	—	2	8	no	—
358	C₂×C₄×D₄₃	—	2	2	no	—
359	C₂×C₄×D₄₃	—	2	2	no	—
360	C₂×C₄×D₄₃	—	2	2	no	—
361	C₂×C₄×D₄₃	—	2	2	no	—
362	C₂×C₄×D₄₃	—	2	2	no	—
363	C₂×C₄×D₄₃	—	2	2	no	—
364	C₂×Dic₈₆	—	2	1	no	—
365	C₂×Dic₈₆	—	2	2	no	—
366	C₂×Dic₈₆	—	2	2	no	—
367	C₂×Dic₈₆	—	2	2	no	—
368	C₂×Dic₈₆	—	2	1	no	—
369	C₂×Dic₈₆	—	2	2	no	—
370	C₂×Dic₈₆	#41	1	4	yes	—
371	C₂×Dic₈₆	C₂⁴	1	2	yes	—
372	C₂×Dic₈₆	C₂⁴	1	2	yes	—
373	C₂×C₈×C₄₃	—	2	2	no	—
374	C₂×C₈×C₄₃	—	2	2	no	—
375	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
376	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
377	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
378	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
379	C₄⋊C₄×C₄₃	—	2	1	no	—
380	C₄⋊C₄×C₄₃	—	2	1	no	—
381	C₄⋊C₄×C₄₃	—	2	1	no	—
382	C₄⋊C₄×C₄₃	—	2	1	no	—
383	C₄⋊C₄×C₄₃	C₂⁴	1	1	yes	characteristic
384	C₄⋊C₄×C₄₃	C₂⁴	1	1	yes	characteristic
385	C₄⋊C₄×C₄₃	C₂⁴	1	1	yes	characteristic
386	C₄⋊C₄×C₄₃	C₂⁴	1	1	yes	characteristic
387	C₄⋊C₄×C₄₃	C₂⁴	1	1	yes	characteristic
388	C₄⋊C₄×C₄₃	C₂⁴	1	1	yes	characteristic
389	C₂²⋊C₄×C₄₃	—	2	1	no	—
390	C₂²⋊C₄×C₄₃	—	2	1	no	—
391	C₂²⋊C₄×C₄₃	—	2	1	no	—
392	C₂²⋊C₄×C₄₃	—	2	1	no	—
393	C₂²⋊C₄×C₄₃	—	2	1	no	—
394	C₂²⋊C₄×C₄₃	—	2	1	no	—
395	C₂²⋊C₄×C₄₃	—	2	1	no	—
396	C₂²⋊C₄×C₄₃	—	2	1	no	—
397	C₂²⋊C₄×C₄₃	—	2	1	no	—
398	C₄²×C₄₃	—	2	1	no	—
399	C₄²×C₄₃	—	2	1	no	—
400	C₄²×C₄₃	—	2	1	no	—
401	C₄²×C₄₃	—	2	1	no	—
402	C₄²×C₄₃	—	2	1	no	—
403	C₂²⋊Dic₄₃	—	2	2	no	—
404	C₂²⋊Dic₄₃	—	2	2	no	—
405	C₂²⋊Dic₄₃	—	2	2	no	—
406	C₂²⋊Dic₄₃	—	2	2	no	—
407	C₂²⋊Dic₄₃	—	2	2	no	—
408	C₂²⋊Dic₄₃	C₂×D₄	1	2	yes	—
409	C₂²⋊Dic₄₃	C₂×D₄	1	2	yes	—
410	C₂²⋊Dic₄₃	C₂×D₄	1	2	yes	—
411	C₂²⋊Dic₄₃	C₂×D₄	1	2	yes	—
412	#10621885	—	2	4	no	—
413	#10621884	—	2	4	no	—
414	#10621883	—	2	4	no	—
415	#10621882	—	2	4	no	—
416	(C₂×D₄₃)⋊C₄	—	2	2	no	—
417	(C₂×D₄₃)⋊C₄	—	2	2	no	—
418	(C₂×D₄₃)⋊C₄	—	2	2	no	—
419	(C₂×D₄₃)⋊C₄	—	2	2	no	—
420	C₄⋊Dic₄₃	—	2	1	no	—
421	C₄⋊Dic₄₃	—	2	2	no	—
422	C₄⋊Dic₄₃	—	2	2	no	—
423	C₄⋊Dic₄₃	C₂×D₄	1	2	yes	—
424	C₄⋊Dic₄₃	C₂×D₄	1	2	yes	—
425	C₄⋊Dic₄₃	C₂×D₄	1	1	yes	characteristic
426	C₄⋊Dic₄₃	C₂×D₄	1	1	yes	characteristic
427	C₄⋊Dic₄₃	C₂×D₄	1	1	yes	characteristic
428	C₄⋊Dic₄₃	C₂×D₄	1	1	yes	characteristic
429	C₄⋊Dic₄₃	C₂⁴	1	2	yes	—
430	Dic₄₃⋊C₄	—	2	2	no	—
431	Dic₄₃⋊C₄	—	2	2	no	—
432	Dic₄₃⋊C₄	—	2	2	no	—
433	Dic₄₃⋊C₄	—	2	2	no	—
434	Dic₄₃⋊C₄	—	2	2	no	—
435	Dic₄₃⋊C₄	—	2	2	no	—
436	Dic₄₃⋊C₄	—	2	2	no	—
437	Dic₄₃⋊C₄	—	2	2	no	—
438	Dic₄₃⋊C₄	—	2	2	no	—
439	Dic₄₃⋊C₄	—	2	2	no	—
440	Dic₄₃⋊C₄	—	2	2	no	—
441	Dic₄₃⋊C₄	—	2	2	no	—
442	C₄×Dic₄₃	—	2	2	no	—
443	C₄×Dic₄₃	—	2	2	no	—
444	C₄×Dic₄₃	—	2	2	no	—
445	C₄×Dic₄₃	—	2	2	no	—
446	C₄×Dic₄₃	—	2	2	no	—
447	C₄×Dic₄₃	—	2	2	no	—
448	C₄×Dic₄₃	—	2	2	no	—
449	C₄×Dic₄₃	C₂×D₄	1	2	yes	—
450	C₄×Dic₄₃	C₂×D₄	1	2	yes	—
451	C₄×Dic₄₃	C₂⁴	1	2	yes	—
452	C₄×Dic₄₃	C₂⁴	1	2	yes	—
453	#10621877	—	2	2	no	—
454	#10621877	—	2	2	no	—
455	C₂×C₄₃⋊C₈	C₂⁴	1	2	yes	—
456	C₂×C₄₃⋊C₈	C₂⁴	1	2	yes	—
457	Dic₁₇₂	—	2	4	no	—
458	Dic₁₇₂	—	2	4	no	—
459	#10621873	—	2	4	no	—
460	#10621873	—	2	4	no	—
461	C₂³×C₄₃	—	2	2	no	—
462	C₂³×C₄₃	—	2	1	no	—
463	C₂³×C₄₃	—	4	1	no	—
464	C₂³×C₄₃	—	4	1	no	—
465	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
466	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
467	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
468	C₂²×D₄₃	—	2	2	no	—
469	C₂²×D₄₃	—	2	4	no	—
470	C₂²×D₄₃	—	8	1	no	—
471	C₂²×D₄₃	—	8	1	no	—
472	Q₈×C₄₃	—	2	1	no	—
473	Q₈×C₄₃	—	2	1	no	—
474	D₄×C₄₃	—	2	1	no	—
475	D₄×C₄₃	—	2	1	no	—
476	D₄×C₄₃	—	4	2	no	—
477	D₄×C₄₃	—	4	2	no	—
478	D₄×C₄₃	—	8	1	no	—
479	C₂×C₄×C₄₃	—	2	2	no	—
480	C₂×C₄×C₄₃	—	2	2	no	—
481	C₂×C₄×C₄₃	—	2	2	no	—
482	C₂×C₄×C₄₃	—	2	1	no	—
483	C₂×C₄×C₄₃	—	2	1	no	—
484	C₂×C₄×C₄₃	—	2	1	no	—
485	C₂×C₄×C₄₃	—	2	1	no	—
486	C₂×C₄×C₄₃	—	2	1	no	—
487	C₂×C₄×C₄₃	—	2	1	no	—
488	C₂×C₄×C₄₃	—	2	1	no	—
489	C₂×C₄×C₄₃	—	2	1	no	—
490	C₂×C₄×C₄₃	—	2	1	no	—
491	C₂×C₄×C₄₃	—	2	1	no	—
492	C₂×C₄×C₄₃	—	2	1	no	—
493	C₂×C₄×C₄₃	—	4	2	no	—
494	C₂×C₄×C₄₃	—	8	1	no	—
495	C₂×C₄×C₄₃	—	8	1	no	—
496	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
497	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
498	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
499	C₂×C₄×C₄₃	C₂×#41	1	2	yes	—
500	C₂×C₄×C₄₃	C₂×#41	1	2	yes	—
501	C₂×C₄×C₄₃	C₂⁵	1	1	yes	characteristic
502	C₂²⋊D₄₃	—	2	8	no	—
503	C₂²⋊D₄₃	—	2	8	no	—
504	C₂×Dic₄₃	—	2	4	no	—
505	C₂×Dic₄₃	—	2	2	no	—
506	C₂×Dic₄₃	—	2	2	no	—
507	C₂×Dic₄₃	—	2	2	no	—
508	C₂×Dic₄₃	—	4	2	no	—
509	C₂×Dic₄₃	—	4	2	no	—
510	C₂×Dic₄₃	—	4	2	no	—
511	C₂×Dic₄₃	—	8	2	no	—
512	C₂×Dic₄₃	—	8	1	no	—
513	C₂×Dic₄₃	C₂²×D₄	1	2	yes	—
514	C₂×Dic₄₃	C₂²×D₄	1	2	yes	—
515	C₂×Dic₄₃	C₂²×D₄	1	2	yes	—
516	C₂×Dic₄₃	C₂²×D₄	1	2	yes	—
517	D₁₇₂	—	2	4	no	—
518	D₁₇₂	—	2	2	no	—
519	D₁₇₂	C₂×#41	1	4	yes	—
520	C₄×D₄₃	—	2	8	no	—
521	C₄×D₄₃	—	2	8	no	—
522	C₄×D₄₃	—	8	2	no	—
523	C₄×D₄₃	—	8	2	no	—
524	C₄×D₄₃	—	8	2	no	—
525	C₄×D₄₃	—	8	2	no	—
526	Dic₈₆	—	2	4	no	—
527	Dic₈₆	—	2	2	no	—
528	Dic₈₆	—	2	2	no	—
529	Dic₈₆	—	2	2	no	—
530	Dic₈₆	—	4	2	no	—
531	Dic₈₆	—	8	2	no	—
532	Dic₈₆	C₂×#41	1	4	yes	—
533	C₈×C₄₃	—	2	1	no	—
534	C₈×C₄₃	—	2	1	no	—
535	C₈×C₄₃	—	2	1	no	—
536	C₈×C₄₃	—	2	1	no	—
537	C₄₃⋊C₈	—	2	2	no	—
538	C₄₃⋊C₈	—	2	2	no	—
539	#60581	—	43	1	no	maximal, Sylow
540	C₂²×C₄₃	—	2	1	no	—
541	C₂²×C₄₃	—	2	1	no	—
542	C₂²×C₄₃	—	2	1	no	—
543	C₂²×C₄₃	—	2	1	no	—
544	C₂²×C₄₃	—	2	1	no	—
545	C₂²×C₄₃	—	2	1	no	—
546	C₂²×C₄₃	—	2	1	no	—
547	C₂²×C₄₃	—	2	1	no	—
548	C₂²×C₄₃	—	4	1	no	—
549	C₂²×C₄₃	—	4	1	no	—
550	C₂²×C₄₃	—	4	1	no	—
551	C₂²×C₄₃	—	8	2	no	—
552	C₂²×C₄₃	#525	1	2	yes	—
553	C₂²×C₄₃	C₂³×D₄	1	1	yes	characteristic
554	C₂×D₄₃	—	2	4	no	—
555	C₂×D₄₃	—	4	2	no	—
556	C₂×D₄₃	—	4	2	no	—
557	C₂×D₄₃	—	8	4	no	—
558	C₄×C₄₃	—	2	1	no	—
559	C₄×C₄₃	—	2	1	no	—
560	C₄×C₄₃	—	4	1	no	—
561	C₄×C₄₃	—	4	1	no	—
562	C₄×C₄₃	—	4	1	no	—
563	C₄×C₄₃	—	4	1	no	—
564	C₄×C₄₃	—	4	1	no	—
565	C₄×C₄₃	—	4	1	no	—
566	C₄×C₄₃	—	4	1	no	—
567	C₄×C₄₃	#525	1	2	yes	—
568	C₄×C₄₃	C₂²×#41	1	1	yes	characteristic
569	C₄×C₄₃	C₂²×#41	1	1	yes	characteristic
570	Dic₄₃	—	2	2	no	—
571	Dic₄₃	—	2	2	no	—
572	Dic₄₃	—	2	2	no	—
573	Dic₄₃	—	2	2	no	—
574	Dic₄₃	—	2	4	no	—
575	Dic₄₃	—	4	2	no	—
576	Dic₄₃	—	4	2	no	—
577	#3495	—	43	1	no	—
578	#3428	—	43	1	no	—
579	#3125	—	43	2	no	—
580	#3124	—	43	2	no	—
581	#3120	—	43	2	no	—
582	#3120	—	43	2	no	—
583	#3116	—	43	2	no	—
584	#3111	—	43	2	no	—
585	#3107	—	43	2	no	—
586	#3102	—	43	2	no	—
587	#3095	—	43	1	no	—
588	#3091	D₄₃	1	1	yes	characteristic, complemented
589	#3082	—	43	1	no	—
590	#3081	—	43	1	no	—
591	#3044	—	43	1	no	—
592	#3042	—	43	1	no	—
593	#3005	—	43	1	no	—
594	C₂×#452	—	43	1	no	—
595	#2950	—	43	1	no	—
596	#2949	—	43	1	no	—
597	#2947	—	43	1	no	—
598	#2946	—	43	1	no	—
599	#2924	—	43	1	no	—
600	C₂×C₄₃	—	2	2	no	—
601	C₂×C₄₃	—	4	1	no	—
602	C₂×C₄₃	—	4	1	no	—
603	C₂×C₄₃	—	8	1	no	—
604	C₂×C₄₃	C₂×#525	1	1	yes	characteristic
605	C₂×C₄₃	#3584	1	1	yes	characteristic
606	C₂×C₄₃	#3586	1	1	yes	characteristic
607	D₄₃	—	4	4	no	—
608	C₂²×#41	—	43	1	no	—
609	C₂×#137	—	43	1	no	—
610	C₂×AGL(1,ℤ/8)	—	43	1	no	—
611	C₂²×Q₁₆	—	43	1	no	—
612	C₂²×SD₁₆	—	43	1	no	—
613	#556	—	86	1	no	—
614	#554	—	86	1	no	—
615	#552	—	86	1	no	—
616	#552	—	86	1	no	—
617	#552	—	86	2	no	—
618	#551	—	86	2	no	—
619	#544	—	43	1	no	—
620	#542	—	43	2	no	—
621	#541	—	43	2	no	—
622	#536	—	43	1	no	—
623	#533	—	43	2	no	—
624	#529	—	43	2	no	—
625	#525	C₂×D₄₃	1	1	yes	characteristic
626	C₂×C₂²⋊Q₈	—	43	1	no	—
627	#520	—	43	1	no	—
628	#520	—	43	2	no	—
629	#520	—	43	2	no	—
630	#520	—	86	1	no	—
631	#520	—	86	1	no	—
632	#519	—	43	1	no	—
633	#519	—	43	1	no	—
634	#519	—	43	1	no	—
635	#518	—	43	1	no	—
636	#518	—	43	1	no	—
637	#518	—	86	2	no	—
638	C₄×#41	—	43	2	no	—
639	C₄×#41	—	43	2	no	—
640	C₄×#41	—	86	1	no	—
641	C₄×#41	—	86	1	no	—
642	C₂×#117	—	43	1	no	—
643	C₂×#117	—	86	2	no	—
644	C₂×#117	C₂×D₄₃	1	1	yes	characteristic
645	#485	—	43	2	no	—
646	#485	—	43	2	no	—
647	#485	C₂×D₄₃	1	1	yes	characteristic, complemented
648	#485	C₂×D₄₃	1	1	yes	characteristic, complemented
649	#484	—	43	2	no	—
650	#484	C₂×D₄₃	1	1	yes	characteristic, complemented
651	#483	—	43	2	no	—
652	#483	C₂×D₄₃	1	1	yes	characteristic, complemented
653	#482	C₂×D₄₃	1	1	yes	characteristic, complemented
654	#482	C₂×D₄₃	1	1	yes	characteristic, complemented
655	#481	C₂×D₄₃	1	1	yes	characteristic, complemented
656	#480	C₂×D₄₃	1	1	yes	characteristic, complemented
657	#479	—	43	2	no	—
658	#479	—	43	2	no	—
659	#478	—	43	2	no	—
660	#478	—	43	2	no	—
661	#477	—	43	2	no	—
662	#476	—	43	2	no	—
663	#475	—	43	2	no	—
664	#474	—	43	2	no	—
665	#464	—	43	2	no	—
666	#464	—	43	2	no	—
667	#463	—	43	2	no	—
668	#463	—	43	2	no	—
669	#462	—	43	2	no	—
670	#462	—	43	2	no	—
671	#461	—	43	2	no	—
672	#461	—	43	2	no	—
673	#452	—	43	2	no	—
674	#452	—	43	2	no	—
675	#452	—	43	2	no	—
676	#452	—	43	2	no	—
677	#452	—	43	2	no	—
678	#452	—	43	2	no	—
679	#449	—	43	2	no	—
680	#449	—	43	2	no	—
681	#442	—	43	2	no	—
682	#441	—	43	2	no	—
683	#441	—	43	2	no	—
684	#441	—	43	2	no	—
685	#440	—	43	2	no	—
686	#440	—	43	2	no	—
687	#440	—	43	2	no	—
688	#440	—	43	2	no	—
689	C₄×Q₁₆	—	43	2	no	—
690	C₄×Q₁₆	—	43	2	no	—
691	C₄×Q₁₆	—	43	2	no	—
692	C₄×SD₁₆	—	43	2	no	—
693	C₄×SD₁₆	—	43	2	no	—
694	C₄×SD₁₆	—	43	2	no	—
695	C₄×SD₁₆	—	43	2	no	—
696	C₄×D₈	—	43	2	no	—
697	#433	—	43	2	no	—
698	#433	—	43	2	no	—
699	#432	—	43	2	no	—
700	#431	—	43	2	no	—
701	#428	—	43	1	no	—
702	#428	—	43	1	no	—
703	#427	C₂×D₄₃	1	1	yes	characteristic
704	#427	C₂×D₄₃	1	1	yes	characteristic
705	#424	—	43	1	no	—
706	#424	—	43	1	no	—
707	#419	—	43	1	no	—
708	#419	—	43	1	no	—
709	#419	—	43	1	no	—
710	#418	—	43	1	no	—
711	#416	C₂×D₄₃	1	1	yes	characteristic
712	#416	C₂×D₄₃	1	1	yes	characteristic
713	C₂×#103	—	43	1	no	—
714	C₂×#102	—	43	1	no	—
715	#407	—	43	1	no	—
716	C₂×C₂²⋊C₈	C₂×D₄₃	1	1	yes	characteristic
717	#405	—	43	1	no	—
718	#405	—	43	1	no	—
719	C₄₃	#60581	1	1	yes	characteristic, complemented, Sylow
720	C₂×#41	—	43	2	no	—
721	C₂×#41	—	43	2	no	—
722	C₂×#41	—	86	4	no	—
723	C₂×#41	—	86	4	no	—
724	C₂×#41	—	86	1	no	—
725	C₂×#41	—	86	1	no	—
726	C₂×#41	C₂²×D₄₃	1	1	yes	characteristic
727	C₂²×Q₈	—	43	1	no	—
728	C₂²×Q₈	—	43	1	no	—
729	C₂²×D₄	—	43	1	no	—
730	C₂²×D₄	—	86	1	no	—
731	C₂³×C₄	—	86	1	no	—
732	C₂³×C₄	C₂²×D₄₃	1	1	yes	characteristic
733	#137	—	86	4	no	—
734	AGL(1,ℤ/8)	—	86	4	no	—
735	C₂×Q₁₆	—	43	2	no	—
736	C₂×Q₁₆	—	43	2	no	—
737	C₂×Q₁₆	—	43	2	no	—
738	C₂×Q₁₆	—	86	4	no	—
739	C₂×SD₁₆	—	43	2	no	—
740	C₂×SD₁₆	—	43	2	no	—
741	C₂×SD₁₆	—	43	2	no	—
742	C₂×SD₁₆	—	43	2	no	—
743	C₂×SD₁₆	—	86	4	no	—
744	C₂×D₈	—	43	2	no	—
745	C₂×M₁₆	—	43	1	no	—
746	C₂×M₁₆	—	43	1	no	—
747	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
748	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
749	C₄⋊Q₈	—	43	2	no	—
750	C₄⋊Q₈	—	43	2	no	—
751	C₄⋊Q₈	—	86	1	no	—
752	#126	—	86	2	no	—
753	#126	—	86	2	no	—
754	#126	—	86	2	no	—
755	#126	—	86	2	no	—
756	#125	—	43	2	no	—
757	#125	—	86	1	no	—
758	#125	—	86	2	no	—
759	#125	—	86	2	no	—
760	#125	—	86	2	no	—
761	#124	—	43	2	no	—
762	#124	—	86	2	no	—
763	#123	—	2	1	no	—
764	#123	—	86	2	no	—
765	#123	—	86	2	no	—
766	#123	—	86	2	no	—
767	C₂²⋊Q₈	—	43	2	no	—
768	C₂²⋊Q₈	—	43	2	no	—
769	C₂²⋊Q₈	—	86	2	no	—
770	C₂²⋊Q₈	—	86	2	no	—
771	C₂²⋊Q₈	—	86	2	no	—
772	C₂²⋊Q₈	—	86	1	no	—
773	C₂²⋊Q₈	—	86	1	no	—
774	C₂²⋊Q₈	—	86	1	no	—
775	C₂²⋊Q₈	—	86	1	no	—
776	C₂²⋊Q₈	C₂²×D₄₃	1	1	yes	characteristic
777	C₂²⋊Q₈	C₂²×D₄₃	1	1	yes	characteristic
778	#121	C₂²×D₄₃	1	1	yes	characteristic
779	#121	C₂²×D₄₃	1	1	yes	characteristic
780	#120	—	2	1	no	—
781	C₄×Q₈	—	43	2	no	—
782	C₄×Q₈	—	43	2	no	—
783	C₄×Q₈	—	43	2	no	—
784	C₄×Q₈	—	43	2	no	—
785	C₄×Q₈	—	43	2	no	—
786	C₄×Q₈	—	43	2	no	—
787	C₄×Q₈	—	43	2	no	—
788	C₄×Q₈	—	86	1	no	—
789	C₄×Q₈	—	86	1	no	—
790	C₄×Q₈	—	86	1	no	—
791	C₄×Q₈	—	86	1	no	—
792	C₄×Q₈	—	86	1	no	—
793	C₄×Q₈	—	86	1	no	—
794	C₄×Q₈	—	86	2	no	—
795	C₄×D₄	—	2	1	no	—
796	C₄×D₄	—	2	1	no	—
797	C₄×D₄	—	43	2	no	—
798	C₄×D₄	—	43	2	no	—
799	C₄×D₄	—	43	2	no	—
800	C₄×D₄	—	43	2	no	—
801	C₄×D₄	—	43	2	no	—
802	C₄×D₄	—	86	1	no	—
803	C₄×D₄	—	86	1	no	—
804	C₄×D₄	—	86	1	no	—
805	C₄×D₄	—	86	1	no	—
806	C₄×D₄	—	86	2	no	—
807	C₄×D₄	—	86	2	no	—
808	C₄×D₄	—	86	2	no	—
809	C₄×D₄	—	86	2	no	—
810	C₄×D₄	—	86	2	no	—
811	C₄×D₄	—	86	2	no	—
812	C₄×D₄	—	86	2	no	—
813	C₄×D₄	—	86	2	no	—
814	C₄×D₄	—	86	2	no	—
815	C₄×D₄	—	86	2	no	—
816	#117	—	2	1	no	—
817	#117	—	2	1	no	—
818	#117	—	43	2	no	—
819	#117	—	43	1	no	—
820	#117	—	43	1	no	—
821	#117	—	43	1	no	—
822	#117	—	43	1	no	—
823	#117	—	43	2	no	—
824	#117	—	86	2	no	—
825	#117	—	86	2	no	—
826	#117	—	86	2	no	—
827	#117	—	86	2	no	—
828	#117	—	86	2	no	—
829	#117	—	86	2	no	—
830	#117	—	86	2	no	—
831	#117	—	86	2	no	—
832	#117	—	86	2	no	—
833	#117	—	86	1	no	—
834	#117	C₂²×D₄₃	1	1	yes	characteristic
835	#117	C₂²×D₄₃	1	1	yes	characteristic
836	#117	C₂²×D₄₃	1	1	yes	characteristic
837	#117	C₂²×D₄₃	1	1	yes	characteristic
838	#117	C₂²×D₄₃	1	1	yes	characteristic
839	C₂×C₄⋊C₄	—	43	1	no	—
840	C₂×C₄⋊C₄	—	43	1	no	—
841	C₂×C₄⋊C₄	—	43	1	no	—
842	C₂×C₄⋊C₄	—	86	2	no	—
843	C₂×C₄⋊C₄	—	86	2	no	—
844	C₂×C₄⋊C₄	—	86	1	no	—
845	C₂×C₄⋊C₄	—	86	1	no	—
846	C₂×C₄⋊C₄	C₂²×D₄₃	1	1	yes	characteristic
847	C₂×C₄⋊C₄	C₂²×D₄₃	1	1	yes	characteristic
848	C₂×C₂²⋊C₄	—	2	1	no	—
849	C₂×C₂²⋊C₄	—	43	2	no	—
850	C₂×C₂²⋊C₄	—	86	2	no	—
851	C₂×C₂²⋊C₄	—	86	2	no	—
852	C₂×C₂²⋊C₄	—	86	1	no	—
853	C₂×C₄²	—	2	1	no	—
854	C₂×C₄²	—	43	2	no	—
855	C₂×C₄²	—	86	2	no	—
856	C₂×C₄²	—	86	2	no	—
857	#107	—	43	2	no	—
858	#107	—	43	2	no	—
859	#107	C₂²×D₄₃	1	1	yes	characteristic
860	#107	C₂²×D₄₃	1	1	yes	characteristic
861	#107	C₂²×D₄₃	1	1	yes	characteristic
862	#107	C₂²×D₄₃	1	1	yes	characteristic
863	#106	—	43	2	no	—
864	#106	—	43	2	no	—
865	#106	C₂²×D₄₃	1	1	yes	characteristic
866	#106	C₂²×D₄₃	1	1	yes	characteristic
867	#106	C₂²×D₄₃	1	1	yes	characteristic
868	#106	C₂²×D₄₃	1	1	yes	characteristic
869	C₄⋊C₈	—	43	2	no	—
870	C₄⋊C₈	—	43	2	no	—
871	C₄⋊C₈	—	43	2	no	—
872	C₄⋊C₈	—	43	2	no	—
873	#103	—	43	2	no	—
874	#103	—	43	2	no	—
875	#103	—	43	2	no	—
876	#103	—	43	2	no	—
877	#103	—	43	2	no	—
878	#103	—	43	2	no	—
879	#103	—	43	2	no	—
880	#103	—	43	2	no	—
881	#103	C₂²×D₄₃	1	1	yes	characteristic
882	#103	C₂²×D₄₃	1	1	yes	characteristic
883	#103	C₂²×D₄₃	1	1	yes	characteristic
884	#103	C₂²×D₄₃	1	1	yes	characteristic
885	#102	—	43	2	no	—
886	#102	—	43	2	no	—
887	#102	—	43	2	no	—
888	#102	—	43	2	no	—
889	#102	C₂²×D₄₃	1	1	yes	characteristic
890	#102	C₂²×D₄₃	1	1	yes	characteristic
891	#102	C₂²×D₄₃	1	1	yes	characteristic
892	#102	C₂²×D₄₃	1	1	yes	characteristic
893	C₂²⋊C₈	—	43	2	no	—
894	C₂²⋊C₈	—	43	2	no	—
895	C₂²⋊C₈	C₂²×D₄₃	1	1	yes	characteristic
896	C₂²⋊C₈	C₂²×D₄₃	1	1	yes	characteristic
897	C₂²⋊C₈	C₂²×D₄₃	1	1	yes	characteristic
898	C₂²⋊C₈	C₂²×D₄₃	1	1	yes	characteristic
899	#97	—	43	2	no	—
900	#97	—	43	2	no	—
901	C₄×C₈	—	43	2	no	—
902	C₄×C₈	—	43	2	no	—
903	C₂⁴	—	86	1	no	—
904	C₂⁴	D₄×D₄₃	1	1	yes	characteristic
905	#41	—	2	2	no	—
906	#41	—	2	2	no	—
907	#41	—	86	4	no	—
908	#41	—	86	4	no	—
909	#41	—	86	4	no	—
910	#41	—	86	4	no	—
911	#41	—	86	8	no	—
912	#41	—	86	8	no	—
913	C₂×Q₈	—	43	4	no	—
914	C₂×Q₈	—	43	2	no	—
915	C₂×Q₈	—	43	2	no	—
916	C₂×Q₈	—	86	2	no	—
917	C₂×Q₈	—	86	1	no	—
918	C₂×Q₈	—	86	1	no	—
919	C₂×Q₈	—	86	2	no	—
920	C₂×Q₈	—	86	2	no	—
921	C₂×Q₈	—	86	2	no	—
922	C₂×Q₈	C₂³×D₄₃	1	1	yes	characteristic
923	C₂×D₄	—	2	1	no	—
924	C₂×D₄	—	2	1	no	—
925	C₂×D₄	—	2	1	no	—
926	C₂×D₄	—	43	4	no	—
927	C₂×D₄	—	43	2	no	—
928	C₂×D₄	—	86	8	no	—
929	C₂×D₄	—	86	2	no	—
930	C₂×D₄	—	86	2	no	—
931	C₂×D₄	—	86	1	no	—
932	C₂×D₄	—	86	2	no	—
933	C₂×D₄	C₂³×D₄₃	1	1	yes	characteristic
934	C₂²×C₄	—	2	2	no	—
935	C₂²×C₄	—	2	2	no	—
936	C₂²×C₄	—	2	1	no	—
937	C₂²×C₄	—	2	1	no	—
938	C₂²×C₄	—	2	1	no	—
939	C₂²×C₄	—	43	2	no	—
940	C₂²×C₄	—	43	2	no	—
941	C₂²×C₄	—	86	2	no	—
942	C₂²×C₄	—	86	2	no	—
943	C₂²×C₄	—	86	2	no	—
944	C₂²×C₄	—	86	2	no	—
945	C₂²×C₄	—	86	8	no	—
946	C₂²×C₄	—	86	2	no	—
947	C₂²×C₄	—	86	1	no	—
948	C₂²×C₄	—	86	2	no	—
949	C₂²×C₄	—	86	2	no	—
950	C₂²×C₄	—	86	1	no	—
951	C₂²×C₄	—	86	1	no	—
952	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
953	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
954	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
955	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
956	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
957	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
958	Q₁₆	—	86	4	no	—
959	Q₁₆	—	86	4	no	—
960	Q₁₆	—	86	4	no	—
961	SD₁₆	—	86	4	no	—
962	SD₁₆	—	86	4	no	—
963	SD₁₆	—	86	4	no	—
964	SD₁₆	—	86	4	no	—
965	D₈	—	86	4	no	—
966	M₁₆	—	86	2	no	—
967	M₁₆	—	86	2	no	—
968	C₂×C₈	—	2	2	no	—
969	C₂×C₈	—	2	2	no	—
970	C₂×C₈	—	43	2	no	—
971	C₂×C₈	—	43	2	no	—
972	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
973	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
974	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
975	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
976	C₄⋊C₄	—	2	1	no	—
977	C₄⋊C₄	—	2	1	no	—
978	C₄⋊C₄	—	2	1	no	—
979	C₄⋊C₄	—	2	1	no	—
980	C₄⋊C₄	—	43	2	no	—
981	C₄⋊C₄	—	43	2	no	—
982	C₄⋊C₄	—	43	1	no	—
983	C₄⋊C₄	—	43	1	no	—
984	C₄⋊C₄	—	43	1	no	—
985	C₄⋊C₄	—	43	1	no	—
986	C₄⋊C₄	—	43	2	no	—
987	C₄⋊C₄	—	86	2	no	—
988	C₄⋊C₄	—	86	2	no	—
989	C₄⋊C₄	—	86	2	no	—
990	C₄⋊C₄	—	86	2	no	—
991	C₄⋊C₄	—	86	2	no	—
992	C₄⋊C₄	—	86	2	no	—
993	C₄⋊C₄	—	86	2	no	—
994	C₄⋊C₄	—	86	2	no	—
995	C₄⋊C₄	—	86	2	no	—
996	C₄⋊C₄	—	86	2	no	—
997	C₄⋊C₄	—	86	2	no	—
998	C₄⋊C₄	—	86	2	no	—
999	C₄⋊C₄	—	86	1	no	—
1000	C₄⋊C₄	—	86	2	no	—
1001	C₄⋊C₄	—	86	2	no	—
1002	C₄⋊C₄	C₂³×D₄₃	1	1	yes	characteristic
1003	C₄⋊C₄	C₂³×D₄₃	1	1	yes	characteristic
1004	C₄⋊C₄	C₂³×D₄₃	1	1	yes	characteristic
1005	C₄⋊C₄	C₂³×D₄₃	1	1	yes	characteristic
1006	C₄⋊C₄	C₂³×D₄₃	1	1	yes	characteristic
1007	C₄⋊C₄	C₂³×D₄₃	1	1	yes	characteristic
1008	C₂²⋊C₄	—	2	1	no	—
1009	C₂²⋊C₄	—	2	1	no	—
1010	C₂²⋊C₄	—	2	1	no	—
1011	C₂²⋊C₄	—	2	1	no	—
1012	C₂²⋊C₄	—	2	1	no	—
1013	C₂²⋊C₄	—	2	1	no	—
1014	C₂²⋊C₄	—	2	1	no	—
1015	C₂²⋊C₄	—	2	1	no	—
1016	C₂²⋊C₄	—	2	1	no	—
1017	C₂²⋊C₄	—	43	2	no	—
1018	C₂²⋊C₄	—	43	2	no	—
1019	C₂²⋊C₄	—	43	2	no	—
1020	C₂²⋊C₄	—	43	2	no	—
1021	C₂²⋊C₄	—	86	2	no	—
1022	C₂²⋊C₄	—	86	2	no	—
1023	C₂²⋊C₄	—	86	2	no	—
1024	C₂²⋊C₄	—	86	2	no	—
1025	C₂²⋊C₄	—	86	2	no	—
1026	C₂²⋊C₄	—	86	2	no	—
1027	C₂²⋊C₄	—	86	2	no	—
1028	C₂²⋊C₄	—	86	2	no	—
1029	C₂²⋊C₄	—	86	2	no	—
1030	C₄²	—	2	1	no	—
1031	C₄²	—	2	1	no	—
1032	C₄²	—	2	1	no	—
1033	C₄²	—	2	1	no	—
1034	C₄²	—	2	1	no	—
1035	C₄²	—	43	2	no	—
1036	C₄²	—	43	2	no	—
1037	C₄²	—	43	2	no	—
1038	C₄²	—	43	2	no	—
1039	C₄²	—	86	2	no	—
1040	C₄²	—	86	2	no	—
1041	C₄²	—	86	2	no	—
1042	C₄²	—	86	2	no	—
1043	C₄²	—	86	2	no	—
1044	C₄²	—	86	2	no	—
1045	C₄²	—	86	2	no	—
1046	C₂³	—	2	2	no	—
1047	C₂³	—	2	1	no	—
1048	C₂³	—	4	1	no	—
1049	C₂³	—	4	1	no	—
1050	C₂³	—	86	4	no	—
1051	C₂³	—	86	2	no	—
1052	C₂³	—	344	1	no	—
1053	C₂³	—	344	1	no	—
1054	C₂³	C₂×D₄×D₄₃	1	1	yes	characteristic
1055	C₂³	C₂×D₄×D₄₃	1	1	yes	characteristic
1056	C₂³	C₂×D₄×D₄₃	1	1	yes	characteristic
1057	Q₈	—	2	1	no	—
1058	Q₈	—	2	1	no	—
1059	Q₈	—	43	4	no	—
1060	Q₈	—	86	4	no	—
1061	Q₈	—	86	2	no	—
1062	Q₈	—	86	2	no	—
1063	Q₈	—	86	2	no	—
1064	Q₈	—	344	2	no	—
1065	Q₈	—	172	2	no	—
1066	D₄	—	2	1	no	—
1067	D₄	—	2	1	no	—
1068	D₄	—	4	2	no	—
1069	D₄	—	4	2	no	—
1070	D₄	—	8	1	no	—
1071	D₄	—	43	4	no	—
1072	D₄	—	86	8	no	—
1073	D₄	—	86	8	no	—
1074	D₄	—	86	4	no	—
1075	D₄	—	86	2	no	—
1076	C₂×C₄	—	2	2	no	—
1077	C₂×C₄	—	2	2	no	—
1078	C₂×C₄	—	2	2	no	—
1079	C₂×C₄	—	2	1	no	—
1080	C₂×C₄	—	2	1	no	—
1081	C₂×C₄	—	2	1	no	—
1082	C₂×C₄	—	2	1	no	—
1083	C₂×C₄	—	2	1	no	—
1084	C₂×C₄	—	2	1	no	—
1085	C₂×C₄	—	2	1	no	—
1086	C₂×C₄	—	2	1	no	—
1087	C₂×C₄	—	2	1	no	—
1088	C₂×C₄	—	2	1	no	—
1089	C₂×C₄	—	2	1	no	—
1090	C₂×C₄	—	4	2	no	—
1091	C₂×C₄	—	8	1	no	—
1092	C₂×C₄	—	8	1	no	—
1093	C₂×C₄	—	43	2	no	—
1094	C₂×C₄	—	43	2	no	—
1095	C₂×C₄	—	43	2	no	—
1096	C₂×C₄	—	43	2	no	—
1097	C₂×C₄	—	86	8	no	—
1098	C₂×C₄	—	86	8	no	—
1099	C₂×C₄	—	86	4	no	—
1100	C₂×C₄	—	86	2	no	—
1101	C₂×C₄	—	86	2	no	—
1102	C₂×C₄	—	86	2	no	—
1103	C₂×C₄	—	344	2	no	—
1104	C₂×C₄	—	344	2	no	—
1105	C₂×C₄	—	344	2	no	—
1106	C₂×C₄	—	344	2	no	—
1107	C₂×C₄	—	344	2	no	—
1108	C₂×C₄	—	344	1	no	—
1109	C₂×C₄	—	172	2	no	—
1110	C₂×C₄	—	172	2	no	—
1111	C₂×C₄	—	172	2	no	—
1112	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
1113	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
1114	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
1115	C₂×C₄	#41×D₄₃	1	2	yes	—
1116	C₂×C₄	#41×D₄₃	1	2	yes	—
1117	C₂×C₄	C₂⁴×D₄₃	1	1	yes	characteristic
1118	C₈	—	2	1	no	—
1119	C₈	—	2	1	no	—
1120	C₈	—	2	1	no	—
1121	C₈	—	2	1	no	—
1122	C₈	—	86	2	no	—
1123	C₈	—	86	2	no	—
1124	C₂²	—	2	1	no	—
1125	C₂²	—	2	1	no	—
1126	C₂²	—	2	1	no	—
1127	C₂²	—	2	1	no	—
1128	C₂²	—	2	1	no	—
1129	C₂²	—	2	1	no	—
1130	C₂²	—	2	1	no	—
1131	C₂²	—	2	1	no	—
1132	C₂²	—	4	1	no	—
1133	C₂²	—	4	1	no	—
1134	C₂²	—	4	1	no	—
1135	C₂²	—	8	2	no	—
1136	C₂²	—	86	4	no	—
1137	C₂²	—	344	4	no	—
1138	C₂²	—	172	2	no	—
1139	C₂²	—	172	2	no	—
1140	C₂²	#14583407	1	2	yes	—
1141	C₂²	C₂²×D₄×D₄₃	1	1	yes	characteristic
1142	C₄	—	2	1	no	—
1143	C₄	—	2	1	no	—
1144	C₄	—	4	1	no	—
1145	C₄	—	4	1	no	—
1146	C₄	—	4	1	no	—
1147	C₄	—	4	1	no	—
1148	C₄	—	4	1	no	—
1149	C₄	—	4	1	no	—
1150	C₄	—	4	1	no	—
1151	C₄	—	86	2	no	—
1152	C₄	—	86	2	no	—
1153	C₄	—	86	4	no	—
1154	C₄	—	86	2	no	—
1155	C₄	—	86	2	no	—
1156	C₄	—	172	2	no	—
1157	C₄	—	172	2	no	—
1158	C₄	#14583407	1	2	yes	—
1159	C₄	C₂×#41×D₄₃	1	1	yes	characteristic
1160	C₄	C₂×#41×D₄₃	1	1	yes	characteristic
1161	C₂	—	2	2	no	—
1162	C₂	—	4	1	no	—
1163	C₂	—	4	1	no	—
1164	C₂	—	8	1	no	—
1165	C₂	—	172	4	no	—
1166	C₂	C₂×#14583407	1	1	yes	characteristic
1167	C₂	#19149364	1	1	yes	characteristic
1168	C₂	#19149379	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×#3091	C₂
socle	C₂²×C₄₃	C₂³×D₄
prime radical	#19143835	C₂
hypercenter	#3091	D₄₃
hypocenter	C₄₃	#60581
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₂³×C₄ ◁ #3091

Complements

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

N	H ≅ G/N	type
1. #19148349	C₂	semidirect
2. #19147796	C₂	semidirect
3. #19144875	C₂	semidirect
4. #19144852	C₂	semidirect
5. #19144812	C₂	semidirect
6. #19144804	C₂	semidirect
7. #19144752	C₂	semidirect
8. #19144699	C₂	semidirect
9. #19144661	C₂	semidirect
10. #19144608	C₂	semidirect
11. #19144543	C₂	semidirect
12. #19144440	C₂	semidirect
13. #19144429	C₂	semidirect
14. #19144128	C₂	semidirect
15. #19144110	C₂	semidirect
17. C₂×#14583063	C₂	semidirect
18. #19143462	C₂	semidirect
19. #19143453	C₂	semidirect
20. #19143441	C₂	semidirect
21. #19143430	C₂	semidirect
22. #19143249	C₂	semidirect
23. C₄₃×#3091	C₂	semidirect
36. #14583516	C₂²	semidirect
37. #14583509	C₂²	semidirect
39. #14583451	C₂²	semidirect
40. #14583430	C₂²	semidirect
59. #14583240	C₂²	semidirect
60. #14583240	C₂²	semidirect
61. #14583234	C₂²	semidirect
62. #14583229	C₂²	semidirect
63. #14583209	C₂²	semidirect
64. #14583205	C₂²	semidirect
65. #14583202	C₂²	semidirect
66. #14583198	C₂²	semidirect
67. #14583193	C₂²	semidirect
68. #14583188	C₂²	semidirect
69. #14583183	C₂²	semidirect
70. #14583178	C₂²	semidirect
71. #14583120	C₂²	semidirect
72. #14583120	C₂²	semidirect
73. #14583113	C₂²	semidirect
74. #14583113	C₂²	semidirect
75. #14583108	C₂²	semidirect
76. #14583108	C₂²	semidirect
77. #14583103	C₂²	semidirect
78. #14583103	C₂²	semidirect
87. #14583008	C₂²	semidirect
88. #14583005	C₂²	semidirect
89. #14583005	C₂²	semidirect
90. #14583003	C₂²	semidirect
91. #14583002	C₂²	semidirect
92. #14582998	C₂²	semidirect
93. #14582998	C₂²	semidirect
94. #14582996	C₂²	semidirect
95. #14582993	C₂²	semidirect
96. #14582993	C₂²	semidirect
97. #14582991	C₂²	semidirect
98. #14582990	C₂²	semidirect
99. #14582986	C₂²	semidirect
100. #14582986	C₂²	semidirect
101. #14582984	C₂²	semidirect
102. #14582979	C₂²	semidirect
103. #14582957	C₂²	semidirect
104. #14582957	C₂²	semidirect
105. #14582953	C₂²	semidirect
106. #14582949	C₂²	semidirect
122. C₄₃×#485	C₂²	semidirect
123. C₄₃×#485	C₂²	semidirect
124. C₄₃×#484	C₂²	semidirect
125. C₄₃×#483	C₂²	semidirect
126. C₄₃×#482	C₂²	semidirect
127. C₄₃×#482	C₂²	semidirect
128. C₄₃×#481	C₂²	semidirect
129. C₄₃×#480	C₂²	semidirect
588. #3091	D₄₃	semidirect
647. #485	C₂×D₄₃	semidirect
648. #485	C₂×D₄₃	semidirect
650. #484	C₂×D₄₃	semidirect
652. #483	C₂×D₄₃	semidirect
653. #482	C₂×D₄₃	semidirect
654. #482	C₂×D₄₃	semidirect
655. #481	C₂×D₄₃	semidirect
656. #480	C₂×D₄₃	semidirect
719. C₄₃	#60581	semidirect

Maximal subgroups

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

subgroup	index
#19148349	2
#19147796	2
#19144875	2
#19144852	2
#19144812	2
#19144804	2
#19144752	2
#19144699	2
#19144661	2
#19144608	2
#19144543	2
#19144440	2
#19144429	2
#19144128	2
#19144110	2
#19143835	2
C₂×#14583063	2
#19143462	2
#19143453	2
#19143441	2
#19143430	2
#19143249	2
C₄₃×#3091	2
#60581	43