Subgroups — #25977958

Order 11008.

1868 conjugacy classes of subgroups.

The subgroup lattice has 1190 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19148491	C₂	1	1	yes	maximal, characteristic, complemented
2	#19148457	C₂	1	1	yes	maximal, characteristic, complemented
3	#19147678	C₂	1	2	yes	maximal, complemented
4	#19147674	C₂	1	2	yes	maximal, complemented
5	#19147659	C₂	1	2	yes	maximal, complemented
6	#19147654	C₂	1	2	yes	maximal, complemented
7	#19147643	C₂	1	2	yes	maximal, complemented
8	#19147621	C₂	1	2	yes	maximal, complemented
9	#19147594	C₂	1	2	yes	maximal, complemented
10	#19147578	C₂	1	2	yes	maximal, complemented
11	#19145090	C₂	1	1	yes	maximal, characteristic, complemented
12	#19145072	C₂	1	1	yes	maximal, characteristic, complemented
13	#19145063	C₂	1	1	yes	maximal, characteristic, complemented
14	#19144143	C₂	1	1	yes	maximal, characteristic, complemented
15	#19144132	C₂	1	1	yes	maximal, characteristic, complemented
16	#19144128	C₂	1	1	yes	maximal, characteristic, complemented
17	#19144110	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×#14583122	C₂	1	1	yes	maximal, characteristic, complemented
19	#19143538	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	C₄×#13063355	C₂	1	1	yes	maximal, characteristic, complemented
23	C₄₃×#3035	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#13063355	C₂²	1	1	yes	characteristic
25	C₂×#13063355	C₂²	1	1	yes	characteristic
26	C₂×#13063355	C₂²	1	1	yes	characteristic
27	C₂×#13063350	C₂²	1	1	yes	characteristic
28	C₂×#13063350	C₂²	1	1	yes	characteristic
29	C₂²×Dic₁₇₂	C₂²	1	1	yes	characteristic
30	C₂²×#10621873	C₂²	1	1	yes	characteristic
31	#14583635	C₂²	1	2	yes	complemented
32	#14583632	C₂²	1	2	yes	—
33	#14583632	C₂²	1	2	yes	—
34	#14583624	C₂²	1	2	yes	complemented
35	#14583621	C₂²	1	2	yes	—
36	#14583621	C₂²	1	2	yes	—
37	#14583619	—	2	1	no	—
38	#14583618	C₂²	1	2	yes	complemented
39	#14583618	C₂²	1	2	yes	complemented
40	#14583606	—	2	1	no	—
41	#14583589	—	2	1	no	—
42	#14583589	—	2	1	no	—
43	#14583578	—	2	2	no	—
44	#14583578	—	2	2	no	—
45	#14583520	—	2	1	no	—
46	#14583520	—	2	1	no	—
47	#14583494	—	2	2	no	—
48	#14583470	C₂²	1	1	yes	characteristic
49	#14583470	C₂²	1	1	yes	characteristic
50	#14583470	C₂²	1	1	yes	characteristic
51	#14583463	C₂²	1	1	yes	characteristic
52	#14583456	C₂²	1	1	yes	characteristic
53	#14583433	—	2	1	no	—
54	#14583433	—	2	1	no	—
55	#14583430	—	2	2	no	—
56	C₂×#13063313	C₂²	1	1	yes	characteristic
57	#14583382	C₂²	1	1	yes	characteristic
58	#14583382	C₂²	1	1	yes	characteristic
59	#14583376	C₂²	1	1	yes	characteristic
60	#14583373	C₂²	1	1	yes	characteristic
61	C₂×C₄×Dic₈₆	C₂²	1	1	yes	characteristic
62	#14583292	C₂²	1	2	yes	—
63	#14583291	C₂²	1	2	yes	—
64	#14583290	C₂²	1	2	yes	complemented
65	#14583290	C₂²	1	2	yes	complemented
66	#14583287	C₂²	1	2	yes	—
67	#14583286	C₂²	1	2	yes	—
68	#14583282	C₂²	1	2	yes	complemented
69	#14583281	C₂²	1	2	yes	—
70	#14583281	C₂²	1	2	yes	—
71	#14583280	C₂²	1	2	yes	—
72	#14583277	C₂²	1	2	yes	complemented
73	#14583270	C₂²	1	2	yes	—
74	#14583123	C₂²	1	2	yes	—
75	#14583122	C₂²	1	2	yes	—
76	#14583122	C₂²	1	2	yes	—
77	#14583122	C₂²	1	2	yes	—
78	#14583122	C₂²	1	2	yes	—
79	#14583120	C₂²	1	2	yes	complemented
80	#14583120	C₂²	1	2	yes	complemented
81	#14583119	C₂²	1	2	yes	complemented
82	#14583116	C₂²	1	2	yes	—
83	#14583113	C₂²	1	2	yes	—
84	#14583113	C₂²	1	2	yes	—
85	#14583112	C₂²	1	2	yes	complemented
86	#14583108	C₂²	1	2	yes	complemented
87	#14583108	C₂²	1	2	yes	complemented
88	#14583107	C₂²	1	2	yes	complemented
89	#14583103	C₂²	1	2	yes	—
90	#14583103	C₂²	1	2	yes	—
91	#14583102	C₂²	1	2	yes	complemented
92	#14583097	C₂²	1	2	yes	—
93	#14583092	C₂²	1	2	yes	—
94	#14583028	C₂²	1	2	yes	complemented
95	#14583028	C₂²	1	2	yes	complemented
96	#14583026	C₂²	1	2	yes	complemented
97	#14583023	C₂²	1	2	yes	complemented
98	#14583008	C₂²	1	2	yes	—
99	#14583004	C₂²	1	2	yes	complemented
100	#14583003	C₂²	1	2	yes	complemented
101	#14583002	C₂²	1	2	yes	—
102	#14582999	C₂²	1	2	yes	complemented
103	#14582996	C₂²	1	2	yes	complemented
104	C₄×#10621885	C₂²	1	2	yes	complemented
105	#14582991	C₂²	1	2	yes	complemented
106	#14582990	C₂²	1	2	yes	complemented
107	C₄×#10621883	C₂²	1	2	yes	complemented
108	#14582984	C₂²	1	2	yes	—
109	#14582979	C₂²	1	2	yes	—
110	#14582942	C₂²	1	1	yes	characteristic
111	#14582925	C₂²	1	1	yes	characteristic
112	#14582925	C₂²	1	1	yes	characteristic
113	#14582907	C₂²	1	1	yes	characteristic
114	#14582900	C₂²	1	1	yes	characteristic
115	C₂×#13063250	C₂²	1	1	yes	characteristic
116	C₂×#13063247	C₂²	1	1	yes	characteristic
117	#14582854	C₂²	1	1	yes	characteristic
118	#14582854	C₂²	1	1	yes	characteristic
119	C₄×#10621877	C₂²	1	1	yes	characteristic
120	C₂×#135×C₄₃	C₂²	1	1	yes	characteristic
121	C₂×#135×C₄₃	C₂²	1	1	yes	characteristic
122	C₄₃×#532	C₂²	1	1	yes	characteristic
123	C₄×#41×C₄₃	C₂²	1	1	yes	characteristic
124	C₄₃×#464	C₂²	1	1	yes	characteristic, complemented
125	C₄₃×#464	C₂²	1	1	yes	characteristic, complemented
126	C₄₃×#463	C₂²	1	1	yes	characteristic, complemented
127	C₄₃×#463	C₂²	1	1	yes	characteristic, complemented
128	C₄₃×#462	C₂²	1	1	yes	characteristic, complemented
129	C₄₃×#461	C₂²	1	1	yes	characteristic, complemented
130	C₄₃×#460	C₂²	1	1	yes	characteristic, complemented
131	C₄₃×#459	C₂²	1	1	yes	characteristic, complemented
132	C₂×C₄⋊C₈×C₄₃	C₂²	1	1	yes	characteristic
133	C₄₃×#416	C₂²	1	1	yes	characteristic
134	C₄₃×#416	C₂²	1	1	yes	characteristic
135	C₂²×Dic₈₆	C₂³	1	1	yes	characteristic
136	C₂²×Dic₈₆	C₂³	1	1	yes	characteristic
137	C₂²×D₁₇₂	C₂³	1	1	yes	characteristic
138	#13063355	—	2	4	no	—
139	#13063355	—	2	4	no	—
140	#13063355	—	4	2	no	—
141	#13063350	—	2	4	no	—
142	#13063350	—	4	2	no	—
143	C₂×Dic₁₇₂	—	4	2	no	—
144	C₂×Dic₁₇₂	C₂³	1	2	yes	—
145	C₂×Dic₁₇₂	C₂³	1	2	yes	—
146	C₂×#10621885	C₂³	1	2	yes	—
147	C₂×#10621885	C₂³	1	2	yes	—
148	C₂×#10621885	C₂³	1	2	yes	—
149	C₂×#10621873	—	4	2	no	—
150	C₂×#10621873	C₂³	1	2	yes	—
151	C₂×#10621873	C₂³	1	2	yes	—
152	C₂×#10621883	C₂³	1	2	yes	—
153	C₂×#10621883	C₂³	1	2	yes	—
154	C₂×#10621883	C₂³	1	2	yes	—
155	C₂×#10621884	C₂³	1	2	yes	—
156	C₂×#10621884	C₂³	1	2	yes	—
157	C₂×#10621882	C₂³	1	2	yes	—
158	C₂×#10621882	C₂³	1	2	yes	—
159	C₂×#10621877	C₂³	1	1	yes	characteristic
160	C₂×#10621877	C₂³	1	1	yes	characteristic
161	#13063325	D₄	1	1	yes	characteristic
162	#13063325	D₄	1	1	yes	characteristic
163	#13063323	C₂³	1	2	yes	—
164	#13063323	C₂³	1	2	yes	—
165	#13063323	C₂³	1	2	yes	—
166	#13063321	C₂³	1	2	yes	—
167	#13063320	—	2	2	no	—
168	#13063320	—	2	2	no	—
169	#13063319	—	2	2	no	—
170	#13063319	—	2	2	no	—
171	#13063318	—	2	2	no	—
172	#13063318	—	2	2	no	—
173	#13063318	—	2	2	no	—
174	#13063318	—	2	2	no	—
175	#13063317	D₄	1	1	yes	characteristic
176	#13063317	D₄	1	1	yes	characteristic
177	#13063316	—	2	2	no	—
178	#13063315	—	2	2	no	—
179	#13063315	—	2	2	no	—
180	#13063314	C₂³	1	2	yes	—
181	#13063313	—	2	1	no	—
182	#13063313	—	2	1	no	—
183	#13063313	C₂³	1	2	yes	—
184	#13063313	C₂³	1	2	yes	—
185	#13063312	—	2	2	no	—
186	#13063312	C₂³	1	2	yes	—
187	#13063312	C₂³	1	2	yes	—
188	#13063312	C₂³	1	2	yes	—
189	#13063311	—	2	2	no	—
190	#13063311	—	2	2	no	—
191	#13063308	—	2	2	no	—
192	#13063308	—	2	2	no	—
193	#13063307	—	2	2	no	—
194	#13063307	—	2	2	no	—
195	#13063306	—	2	2	no	—
196	#13063306	—	2	2	no	—
197	#13063306	—	2	2	no	—
198	#13063306	—	2	2	no	—
199	#13063306	—	2	2	no	—
200	#13063304	—	2	1	no	—
201	#13063304	—	2	1	no	—
202	#13063304	—	2	1	no	—
203	#13063304	—	2	1	no	—
204	#13063304	—	2	1	no	—
205	#13063304	—	2	1	no	—
206	#13063304	D₄	1	2	yes	—
207	#13063304	D₄	1	2	yes	—
208	#13063303	—	2	2	no	—
209	#13063303	—	2	2	no	—
210	#13063302	—	2	2	no	—
211	#13063302	—	2	2	no	—
212	#13063299	—	2	1	no	—
213	#13063299	—	2	1	no	—
214	#13063293	—	2	2	no	—
215	Q₈×Dic₄₃	C₂³	1	2	yes	—
216	Q₈×Dic₄₃	C₂³	1	2	yes	—
217	C₄×Dic₈₆	—	2	1	no	—
218	C₄×Dic₈₆	—	2	1	no	—
219	C₄×Dic₈₆	—	2	1	no	—
220	C₄×Dic₈₆	—	2	1	no	—
221	C₄×Dic₈₆	C₂³	1	2	yes	—
222	C₄×Dic₈₆	C₂³	1	2	yes	—
223	C₄×Dic₈₆	C₂³	1	2	yes	—
224	C₄×Dic₈₆	C₂³	1	2	yes	—
225	#13063290	—	2	2	no	—
226	#13063290	C₂³	1	2	yes	—
227	#13063290	C₂³	1	2	yes	—
228	C₄×D₁₇₂	—	2	1	no	—
229	C₄×D₁₇₂	—	2	1	no	—
230	D₄×Dic₄₃	—	2	2	no	—
231	D₄×Dic₄₃	—	2	2	no	—
232	D₄×Dic₄₃	—	2	2	no	—
233	D₄×Dic₄₃	C₂³	1	2	yes	—
234	D₄×Dic₄₃	C₂³	1	2	yes	—
235	#13063287	C₂³	1	2	yes	—
236	#13063287	C₂³	1	2	yes	—
237	C₄×C₂²⋊D₄₃	—	2	2	no	—
238	C₄×C₂²⋊D₄₃	—	2	2	no	—
239	#13063284	—	2	1	no	—
240	#13063284	—	2	1	no	—
241	#13063284	C₂³	1	1	yes	characteristic
242	#13063284	C₂³	1	1	yes	characteristic
243	#13063282	—	2	2	no	—
244	#13063282	—	2	2	no	—
245	#13063281	—	2	2	no	—
246	#13063281	—	2	2	no	—
247	#13063281	—	2	2	no	—
248	C₂×C₄⋊Dic₄₃	—	2	1	no	—
249	C₂×C₄⋊Dic₄₃	—	2	1	no	—
250	C₂×C₄⋊Dic₄₃	C₂³	1	1	yes	characteristic
251	C₂×Dic₄₃⋊C₄	—	2	1	no	—
252	C₂×(C₂×D₄₃)⋊C₄	—	2	1	no	—
253	C₂×(C₂×D₄₃)⋊C₄	—	2	1	no	—
254	C₂²⋊C₄×D₄₃	—	2	2	no	—
255	C₂×C₄×Dic₄₃	—	2	1	no	—
256	#13063258	C₂³	1	2	yes	—
257	#13063256	C₂³	1	2	yes	—
258	Dic₄₃⋊C₈	C₂³	1	2	yes	—
259	Dic₄₃⋊C₈	C₂³	1	2	yes	—
260	Dic₄₃⋊C₈	C₂³	1	2	yes	—
261	Dic₄₃⋊C₈	C₂³	1	2	yes	—
262	#13063250	C₂³	1	2	yes	—
263	#13063250	C₂³	1	2	yes	—
264	#13063249	C₂³	1	2	yes	—
265	#13063248	C₂³	1	2	yes	—
266	#13063248	C₂³	1	2	yes	—
267	#13063247	C₂³	1	2	yes	—
268	#13063247	C₂³	1	2	yes	—
269	#13063246	C₂³	1	2	yes	—
270	#13063236	C₂³	1	2	yes	—
271	#13063235	C₂³	1	2	yes	—
272	#13063235	C₂³	1	2	yes	—
273	C₄×C₄₃⋊C₈	C₂³	1	2	yes	—
274	C₈×Dic₄₃	C₂³	1	2	yes	—
275	C₈×Dic₄₃	C₂³	1	2	yes	—
276	C₂×#41×C₄₃	C₂³	1	1	yes	characteristic
277	C₂×#41×C₄₃	C₂³	1	1	yes	characteristic
278	C₂×#41×C₄₃	C₂³	1	1	yes	characteristic
279	#135×C₄₃	—	4	2	no	—
280	#135×C₄₃	—	4	2	no	—
281	C₂×Q₁₆×C₄₃	C₂³	1	1	yes	characteristic
282	C₂×Q₁₆×C₄₃	C₂³	1	1	yes	characteristic
283	C₂×SD₁₆×C₄₃	C₂³	1	1	yes	characteristic
284	C₂×SD₁₆×C₄₃	C₂³	1	1	yes	characteristic
285	C₂×SD₁₆×C₄₃	C₂³	1	1	yes	characteristic
286	C₂×SD₁₆×C₄₃	C₂³	1	1	yes	characteristic
287	C₂×D₈×C₄₃	C₂³	1	1	yes	characteristic
288	C₂×D₈×C₄₃	C₂³	1	1	yes	characteristic
289	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
290	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
291	C₄⋊Q₈×C₄₃	C₂³	1	1	yes	characteristic
292	#127×C₄₃	C₂³	1	1	yes	characteristic
293	#124×C₄₃	C₂³	1	1	yes	characteristic
294	#124×C₄₃	C₂³	1	1	yes	characteristic
295	#121×C₄₃	—	2	1	no	—
296	#121×C₄₃	—	2	1	no	—
297	C₄×Q₈×C₄₃	C₂³	1	1	yes	characteristic
298	C₄×Q₈×C₄₃	C₂³	1	1	yes	characteristic
299	C₄×D₄×C₄₃	—	2	1	no	—
300	C₄×D₄×C₄₃	—	2	1	no	—
301	C₄×D₄×C₄₃	—	2	1	no	—
302	C₄×D₄×C₄₃	—	2	1	no	—
303	C₄×D₄×C₄₃	C₂³	1	1	yes	characteristic
304	C₄×D₄×C₄₃	C₂³	1	1	yes	characteristic
305	#117×C₄₃	—	2	1	no	—
306	#117×C₄₃	C₂³	1	1	yes	characteristic
307	C₂×C₄²×C₄₃	—	2	1	no	—
308	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
309	C₄⋊C₈×C₄₃	C₂³	1	1	yes	characteristic
310	C₄⋊C₈×C₄₃	C₂³	1	1	yes	characteristic
311	C₄⋊C₈×C₄₃	C₂³	1	1	yes	characteristic
312	C₄⋊C₈×C₄₃	C₂³	1	1	yes	characteristic
313	#103×C₄₃	C₂³	1	1	yes	characteristic
314	#103×C₄₃	C₂³	1	1	yes	characteristic
315	#103×C₄₃	C₂³	1	1	yes	characteristic
316	#103×C₄₃	C₂³	1	1	yes	characteristic
317	#102×C₄₃	C₂³	1	1	yes	characteristic
318	#102×C₄₃	C₂³	1	1	yes	characteristic
319	#102×C₄₃	C₂³	1	1	yes	characteristic
320	#102×C₄₃	C₂³	1	1	yes	characteristic
321	C₂³×D₄₃	—	2	1	no	—
322	#41×C₄₃	—	2	2	no	—
323	#41×C₄₃	—	2	2	no	—
324	#41×C₄₃	—	2	2	no	—
325	#41×C₄₃	—	2	2	no	—
326	#41×C₄₃	—	2	2	no	—
327	#41×C₄₃	—	2	2	no	—
328	C₂×Q₈×C₄₃	C₂⁴	1	1	yes	characteristic
329	C₂×Q₈×C₄₃	C₂⁴	1	1	yes	characteristic
330	C₂×Q₈×C₄₃	C₂⁴	1	1	yes	characteristic
331	C₂×D₄×C₄₃	—	2	1	no	—
332	C₂×D₄×C₄₃	—	2	1	no	—
333	C₂×D₄×C₄₃	—	2	1	no	—
334	C₂×D₄×C₄₃	—	2	1	no	—
335	C₂×D₄×C₄₃	—	2	1	no	—
336	C₂×D₄×C₄₃	C₂⁴	1	1	yes	characteristic
337	C₂×D₄×C₄₃	C₂⁴	1	1	yes	characteristic
338	C₂×D₄×C₄₃	C₂⁴	1	1	yes	characteristic
339	C₂²×C₄×C₄₃	—	2	1	no	—
340	C₂²×C₄×C₄₃	—	2	1	no	—
341	C₂²×C₄×C₄₃	—	2	1	no	—
342	C₂²×C₄×C₄₃	—	2	1	no	—
343	C₂²×C₄×C₄₃	—	2	1	no	—
344	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
345	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
346	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
347	C₂×C₂²⋊D₄₃	—	2	2	no	—
348	C₂×C₂²⋊D₄₃	—	2	2	no	—
349	C₂²×Dic₄₃	—	2	2	no	—
350	C₂²×Dic₄₃	—	2	2	no	—
351	C₂²×Dic₄₃	—	2	1	no	—
352	C₂²×Dic₄₃	—	2	1	no	—
353	C₂²×Dic₄₃	—	2	1	no	—
354	C₂×D₁₇₂	—	2	1	no	—
355	C₂×D₁₇₂	—	2	2	no	—
356	C₂×D₁₇₂	—	2	2	no	—
357	C₂×D₁₇₂	C₂⁴	1	2	yes	—
358	C₂×C₄×D₄₃	—	2	2	no	—
359	C₂×C₄×D₄₃	—	2	2	no	—
360	C₂×Dic₈₆	—	2	2	no	—
361	C₂×Dic₈₆	—	2	2	no	—
362	C₂×Dic₈₆	—	2	2	no	—
363	C₂×Dic₈₆	—	2	2	no	—
364	C₂×Dic₈₆	—	2	1	no	—
365	C₂×Dic₈₆	—	2	1	no	—
366	C₂×Dic₈₆	C₂×D₄	1	2	yes	—
367	C₂×Dic₈₆	C₂×D₄	1	2	yes	—
368	C₂×Dic₈₆	C₂⁴	1	2	yes	—
369	C₂×Dic₈₆	C₂⁴	1	2	yes	—
370	Q₁₆×C₄₃	—	4	1	no	—
371	Q₁₆×C₄₃	—	4	1	no	—
372	SD₁₆×C₄₃	—	4	1	no	—
373	SD₁₆×C₄₃	—	4	1	no	—
374	SD₁₆×C₄₃	—	4	1	no	—
375	SD₁₆×C₄₃	—	4	1	no	—
376	D₈×C₄₃	—	4	1	no	—
377	D₈×C₄₃	—	4	1	no	—
378	C₂×C₈×C₄₃	—	2	2	no	—
379	C₂×C₈×C₄₃	—	2	2	no	—
380	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
381	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
382	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
383	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
384	C₄⋊C₄×C₄₃	—	2	1	no	—
385	C₄⋊C₄×C₄₃	—	2	1	no	—
386	C₄⋊C₄×C₄₃	—	2	1	no	—
387	C₄⋊C₄×C₄₃	—	2	1	no	—
388	C₄⋊C₄×C₄₃	C₂⁴	1	1	yes	characteristic
389	C₄⋊C₄×C₄₃	C₂⁴	1	1	yes	characteristic
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	C₄²×C₄₃	—	2	1	no	—
398	C₄²×C₄₃	—	2	1	no	—
399	C₄²×C₄₃	—	2	1	no	—
400	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
401	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
402	C₄²×C₄₃	C₂⁴	1	1	yes	characteristic
403	C₄²×C₄₃	C₂⁴	1	1	yes	characteristic
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	—	2	2	no	—
409	C₂²⋊Dic₄₃	—	2	2	no	—
410	C₂²⋊Dic₄₃	—	2	2	no	—
411	C₂²⋊Dic₄₃	—	2	2	no	—
412	C₂²⋊Dic₄₃	C₂×D₄	1	2	yes	—
413	C₂²⋊Dic₄₃	C₂×D₄	1	2	yes	—
414	#10621885	—	2	4	no	—
415	#10621885	—	2	4	no	—
416	#10621885	—	4	2	no	—
417	#10621884	—	2	4	no	—
418	#10621884	—	4	2	no	—
419	#10621883	—	2	4	no	—
420	#10621883	—	2	4	no	—
421	#10621883	—	4	2	no	—
422	#10621882	—	2	4	no	—
423	#10621882	—	4	2	no	—
424	(C₂×D₄₃)⋊C₄	—	2	2	no	—
425	(C₂×D₄₃)⋊C₄	—	2	2	no	—
426	(C₂×D₄₃)⋊C₄	—	2	2	no	—
427	(C₂×D₄₃)⋊C₄	—	2	2	no	—
428	(C₂×D₄₃)⋊C₄	—	2	2	no	—
429	(C₂×D₄₃)⋊C₄	—	2	2	no	—
430	(C₂×D₄₃)⋊C₄	—	2	2	no	—
431	(C₂×D₄₃)⋊C₄	—	2	2	no	—
432	C₄⋊Dic₄₃	—	2	1	no	—
433	C₄⋊Dic₄₃	—	2	2	no	—
434	C₄⋊Dic₄₃	—	2	2	no	—
435	C₄⋊Dic₄₃	C₂×D₄	1	1	yes	characteristic
436	C₄⋊Dic₄₃	C₂×D₄	1	1	yes	characteristic
437	C₄⋊Dic₄₃	C₂×D₄	1	1	yes	characteristic
438	C₄⋊Dic₄₃	C₂×D₄	1	1	yes	characteristic
439	C₄⋊Dic₄₃	C₂×D₄	1	2	yes	—
440	C₄⋊Dic₄₃	C₂×D₄	1	2	yes	—
441	C₄⋊Dic₄₃	C₂⁴	1	2	yes	—
442	Dic₄₃⋊C₄	—	2	2	no	—
443	Dic₄₃⋊C₄	—	2	2	no	—
444	Dic₄₃⋊C₄	—	2	2	no	—
445	Dic₄₃⋊C₄	—	2	2	no	—
446	Dic₄₃⋊C₄	—	2	2	no	—
447	Dic₄₃⋊C₄	—	2	2	no	—
448	Dic₄₃⋊C₄	—	2	2	no	—
449	Dic₄₃⋊C₄	—	2	2	no	—
450	Dic₄₃⋊C₄	—	2	2	no	—
451	Dic₄₃⋊C₄	—	2	2	no	—
452	Dic₄₃⋊C₄	C₂×D₄	1	2	yes	—
453	Dic₄₃⋊C₄	C₂×D₄	1	2	yes	—
454	Dic₄₃⋊C₄	C₂×D₄	1	2	yes	—
455	Dic₄₃⋊C₄	C₂×D₄	1	2	yes	—
456	C₄×Dic₄₃	—	2	2	no	—
457	C₄×Dic₄₃	—	2	2	no	—
458	C₄×Dic₄₃	—	2	2	no	—
459	C₄×Dic₄₃	—	2	2	no	—
460	C₄×Dic₄₃	—	2	2	no	—
461	C₄×Dic₄₃	—	2	2	no	—
462	C₄×Dic₄₃	C₂⁴	1	2	yes	—
463	C₄×Dic₄₃	C₂⁴	1	2	yes	—
464	#10621877	—	2	2	no	—
465	#10621877	#41	1	4	yes	—
466	C₂×C₄₃⋊C₈	C₂⁴	1	2	yes	—
467	C₂×C₄₃⋊C₈	C₂⁴	1	2	yes	—
468	Dic₁₇₂	—	4	2	no	—
469	Dic₁₇₂	—	4	2	no	—
470	#10621873	—	4	2	no	—
471	#10621873	—	4	2	no	—
472	C₂³×C₄₃	—	2	1	no	—
473	C₂³×C₄₃	—	2	1	no	—
474	C₂³×C₄₃	—	2	1	no	—
475	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
476	C₂²×D₄₃	—	2	2	no	—
477	C₂²×D₄₃	—	4	2	no	—
478	C₂²×D₄₃	—	8	1	no	—
479	C₂²×D₄₃	—	8	1	no	—
480	Q₈×C₄₃	—	2	1	no	—
481	Q₈×C₄₃	—	2	1	no	—
482	Q₈×C₄₃	—	2	1	no	—
483	Q₈×C₄₃	—	2	1	no	—
484	Q₈×C₄₃	—	2	1	no	—
485	Q₈×C₄₃	—	2	1	no	—
486	D₄×C₄₃	—	2	1	no	—
487	D₄×C₄₃	—	2	1	no	—
488	D₄×C₄₃	—	2	1	no	—
489	D₄×C₄₃	—	2	1	no	—
490	D₄×C₄₃	—	2	1	no	—
491	D₄×C₄₃	—	2	1	no	—
492	D₄×C₄₃	—	4	2	no	—
493	D₄×C₄₃	—	4	2	no	—
494	D₄×C₄₃	—	4	2	no	—
495	D₄×C₄₃	—	4	2	no	—
496	D₄×C₄₃	—	8	1	no	—
497	C₂×C₄×C₄₃	—	2	1	no	—
498	C₂×C₄×C₄₃	—	2	1	no	—
499	C₂×C₄×C₄₃	—	2	1	no	—
500	C₂×C₄×C₄₃	—	2	1	no	—
501	C₂×C₄×C₄₃	—	2	1	no	—
502	C₂×C₄×C₄₃	—	4	1	no	—
503	C₂×C₄×C₄₃	—	4	1	no	—
504	C₂×C₄×C₄₃	—	4	2	no	—
505	C₂×C₄×C₄₃	—	4	2	no	—
506	C₂×C₄×C₄₃	—	4	2	no	—
507	C₂×C₄×C₄₃	—	8	1	no	—
508	C₂×C₄×C₄₃	—	8	1	no	—
509	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
510	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
511	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
512	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
513	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
514	C₂×C₄×C₄₃	C₂×#41	1	2	yes	—
515	C₂×C₄×C₄₃	H(5,𝔽₂)	1	2	yes	—
516	C₂×C₄×C₄₃	C₂⁵	1	1	yes	characteristic
517	C₂²⋊D₄₃	—	8	2	no	—
518	C₂²⋊D₄₃	—	8	2	no	—
519	C₂×Dic₄₃	—	2	2	no	—
520	C₂×Dic₄₃	—	2	2	no	—
521	C₂×Dic₄₃	—	2	2	no	—
522	C₂×Dic₄₃	—	4	2	no	—
523	C₂×Dic₄₃	—	4	2	no	—
524	C₂×Dic₄₃	—	8	2	no	—
525	C₂×Dic₄₃	—	8	2	no	—
526	C₂×Dic₄₃	—	8	1	no	—
527	C₂×Dic₄₃	C₂²×D₄	1	2	yes	—
528	C₂×Dic₄₃	C₂²×D₄	1	2	yes	—
529	C₂×Dic₄₃	C₂²×D₄	1	2	yes	—
530	C₂×Dic₄₃	C₂²×D₄	1	2	yes	—
531	D₁₇₂	—	2	2	no	—
532	D₁₇₂	—	2	2	no	—
533	D₁₇₂	—	4	2	no	—
534	C₄×D₄₃	—	8	2	no	—
535	C₄×D₄₃	—	8	2	no	—
536	Dic₈₆	—	2	2	no	—
537	Dic₈₆	—	2	2	no	—
538	Dic₈₆	—	2	2	no	—
539	Dic₈₆	—	2	2	no	—
540	Dic₈₆	—	4	2	no	—
541	Dic₈₆	—	4	2	no	—
542	Dic₈₆	—	4	2	no	—
543	Dic₈₆	—	4	2	no	—
544	C₈×C₄₃	—	2	1	no	—
545	C₈×C₄₃	—	2	1	no	—
546	C₈×C₄₃	—	2	1	no	—
547	C₈×C₄₃	—	2	1	no	—
548	C₄₃⋊C₈	—	2	2	no	—
549	C₄₃⋊C₈	C₂×#41	1	4	yes	—
550	#61423	—	43	1	no	maximal, Sylow
551	C₂²×C₄₃	—	2	1	no	—
552	C₂²×C₄₃	—	2	1	no	—
553	C₂²×C₄₃	—	4	1	no	—
554	C₂²×C₄₃	—	4	1	no	—
555	C₂²×C₄₃	—	4	1	no	—
556	C₂²×C₄₃	—	4	1	no	—
557	C₂²×C₄₃	—	4	1	no	—
558	C₂²×C₄₃	—	4	1	no	—
559	C₂²×C₄₃	—	4	1	no	—
560	C₂²×C₄₃	—	4	1	no	—
561	C₂²×C₄₃	—	4	1	no	—
562	C₂²×C₄₃	#550	1	2	yes	—
563	C₂²×C₄₃	C₂³×D₄	1	1	yes	characteristic
564	C₂×D₄₃	—	4	2	no	—
565	C₂×D₄₃	—	4	2	no	—
566	C₂×D₄₃	—	4	2	no	—
567	C₂×D₄₃	—	16	2	no	—
568	C₄×C₄₃	—	2	1	no	—
569	C₄×C₄₃	—	2	1	no	—
570	C₄×C₄₃	—	2	1	no	—
571	C₄×C₄₃	—	2	1	no	—
572	C₄×C₄₃	—	4	1	no	—
573	C₄×C₄₃	—	4	1	no	—
574	C₄×C₄₃	—	4	1	no	—
575	C₄×C₄₃	—	4	1	no	—
576	C₄×C₄₃	—	4	1	no	—
577	C₄×C₄₃	#550	1	2	yes	—
578	C₄×C₄₃	C₂²×#41	1	1	yes	characteristic
579	C₄×C₄₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
580	Dic₄₃	—	2	2	no	—
581	Dic₄₃	—	2	2	no	—
582	Dic₄₃	—	2	2	no	—
583	Dic₄₃	—	2	2	no	—
584	Dic₄₃	—	4	2	no	—
585	Dic₄₃	—	4	2	no	—
586	Dic₄₃	—	4	2	no	—
587	#3510	—	43	1	no	—
588	#3507	—	43	1	no	—
589	#3403	—	43	2	no	—
590	#3402	—	43	2	no	—
591	#3401	—	43	2	no	—
592	#3401	—	43	2	no	—
593	#3400	—	43	2	no	—
594	#3398	—	43	2	no	—
595	#3394	—	43	2	no	—
596	#3393	—	43	2	no	—
597	#3156	—	43	1	no	—
598	#3154	—	43	1	no	—
599	#3153	—	43	1	no	—
600	#3046	—	43	1	no	—
601	#3045	—	43	1	no	—
602	#3044	—	43	1	no	—
603	#3042	—	43	1	no	—
604	#3035	D₄₃	1	1	yes	characteristic, complemented
605	C₂×#464	—	43	1	no	—
606	#2962	—	43	1	no	—
607	#2947	—	43	1	no	—
608	#2946	—	43	1	no	—
609	C₄×#137	—	43	1	no	—
610	C₂×C₄₃	—	2	2	no	—
611	C₂×C₄₃	—	8	1	no	—
612	C₂×C₄₃	—	8	1	no	—
613	C₂×C₄₃	—	8	1	no	—
614	C₂×C₄₃	C₂×#550	1	1	yes	characteristic
615	C₂×C₄₃	#3584	1	1	yes	characteristic
616	C₂×C₄₃	#3586	1	1	yes	characteristic
617	D₄₃	—	8	2	no	—
618	C₂×#137	—	43	1	no	—
619	C₂×#137	—	43	1	no	—
620	C₂×#137	—	43	1	no	—
621	C₂×AGL(1,ℤ/8)	—	43	1	no	—
622	C₂×AGL(1,ℤ/8)	—	43	1	no	—
623	C₂×#135	C₂×D₄₃	1	1	yes	characteristic
624	C₂×#135	C₂×D₄₃	1	1	yes	characteristic
625	C₂²×Q₁₆	—	43	1	no	—
626	C₂²×SD₁₆	—	43	1	no	—
627	#559	—	43	2	no	—
628	#559	—	43	2	no	—
629	#559	—	43	2	no	—
630	#557	—	43	2	no	—
631	#556	—	43	2	no	—
632	#556	—	43	2	no	—
633	#556	—	43	2	no	—
634	#556	—	43	2	no	—
635	#556	—	86	1	no	—
636	#554	—	86	1	no	—
637	#552	—	86	1	no	—
638	#552	—	86	1	no	—
639	#551	—	86	2	no	—
640	#551	—	86	2	no	—
641	#542	—	86	1	no	—
642	#542	—	86	1	no	—
643	#539	—	86	2	no	—
644	#536	—	43	1	no	—
645	#536	—	43	1	no	—
646	#536	—	43	1	no	—
647	#535	—	43	1	no	—
648	#533	—	43	1	no	—
649	#532	C₂×D₄₃	1	1	yes	characteristic
650	#529	—	86	1	no	—
651	#529	—	86	1	no	—
652	#529	—	86	2	no	—
653	C₂×#124	—	43	1	no	—
654	#520	—	43	1	no	—
655	#520	—	43	1	no	—
656	#519	—	43	1	no	—
657	#518	—	43	1	no	—
658	C₄×#41	C₂×D₄₃	1	1	yes	characteristic
659	C₂×C₄×Q₈	—	43	1	no	—
660	#497	—	43	2	no	—
661	#497	—	43	2	no	—
662	#497	—	43	2	no	—
663	#497	—	43	2	no	—
664	#496	—	43	2	no	—
665	#496	—	43	2	no	—
666	#495	—	43	2	no	—
667	#495	—	43	2	no	—
668	#495	—	43	2	no	—
669	#495	—	43	2	no	—
670	#494	—	43	2	no	—
671	#492	—	43	2	no	—
672	#464	—	43	2	no	—
673	#464	—	43	2	no	—
674	#464	—	43	2	no	—
675	#464	—	43	2	no	—
676	#464	—	43	2	no	—
677	#464	—	43	2	no	—
678	#464	—	43	2	no	—
679	#464	—	43	2	no	—
680	#464	C₂×D₄₃	1	1	yes	characteristic, complemented
681	#464	C₂×D₄₃	1	1	yes	characteristic, complemented
682	#463	—	43	2	no	—
683	#463	—	43	2	no	—
684	#463	—	43	2	no	—
685	#463	—	43	2	no	—
686	#463	C₂×D₄₃	1	1	yes	characteristic, complemented
687	#463	C₂×D₄₃	1	1	yes	characteristic, complemented
688	#462	—	43	2	no	—
689	#462	—	43	2	no	—
690	#462	—	43	2	no	—
691	#462	C₂×D₄₃	1	1	yes	characteristic, complemented
692	#461	—	43	2	no	—
693	#461	—	43	2	no	—
694	#461	—	43	2	no	—
695	#461	C₂×D₄₃	1	1	yes	characteristic, complemented
696	#460	—	43	2	no	—
697	#460	C₂×D₄₃	1	1	yes	characteristic, complemented
698	#459	—	43	2	no	—
699	#459	C₂×D₄₃	1	1	yes	characteristic, complemented
700	#446	—	43	2	no	—
701	#446	—	43	2	no	—
702	#446	—	43	2	no	—
703	C₈×Q₈	—	43	2	no	—
704	#442	—	43	2	no	—
705	#441	—	43	2	no	—
706	#441	—	43	2	no	—
707	#440	—	43	2	no	—
708	#440	—	43	2	no	—
709	#440	—	43	2	no	—
710	C₄×Q₁₆	—	43	2	no	—
711	C₄×Q₁₆	—	43	2	no	—
712	C₄×SD₁₆	—	43	2	no	—
713	C₄×SD₁₆	—	43	2	no	—
714	C₄×SD₁₆	—	43	2	no	—
715	C₄×D₈	—	43	2	no	—
716	#428	—	43	1	no	—
717	#424	—	43	1	no	—
718	#424	—	43	1	no	—
719	C₂×C₄⋊C₈	C₂×D₄₃	1	1	yes	characteristic
720	#419	—	43	1	no	—
721	#417	—	43	1	no	—
722	#416	C₂×D₄₃	1	1	yes	characteristic
723	#416	C₂×D₄₃	1	1	yes	characteristic
724	C₂×#103	—	43	1	no	—
725	C₂×#102	—	43	1	no	—
726	#405	—	43	1	no	—
727	#405	—	43	1	no	—
728	C₄×M₁₆	—	43	1	no	—
729	C₄₃	#61423	1	1	yes	characteristic, complemented, Sylow
730	C₂×#41	C₂²×D₄₃	1	1	yes	characteristic
731	C₂×#41	C₂²×D₄₃	1	1	yes	characteristic
732	C₂×#41	C₂²×D₄₃	1	1	yes	characteristic
733	C₂²×Q₈	—	43	1	no	—
734	C₂²×Q₈	—	43	1	no	—
735	C₂²×D₄	—	43	1	no	—
736	#137	—	86	4	no	—
737	#137	—	86	4	no	—
738	#137	—	172	2	no	—
739	AGL(1,ℤ/8)	—	86	4	no	—
740	AGL(1,ℤ/8)	—	172	2	no	—
741	#135	—	4	2	no	—
742	#135	—	4	2	no	—
743	C₂×Q₁₆	—	43	2	no	—
744	C₂×Q₁₆	—	43	2	no	—
745	C₂×Q₁₆	—	43	2	no	—
746	C₂×Q₁₆	—	43	2	no	—
747	C₂×Q₁₆	—	43	2	no	—
748	C₂×Q₁₆	—	172	2	no	—
749	C₂×Q₁₆	C₂²×D₄₃	1	1	yes	characteristic
750	C₂×Q₁₆	C₂²×D₄₃	1	1	yes	characteristic
751	C₂×SD₁₆	—	43	2	no	—
752	C₂×SD₁₆	—	43	2	no	—
753	C₂×SD₁₆	—	43	2	no	—
754	C₂×SD₁₆	—	43	2	no	—
755	C₂×SD₁₆	—	43	2	no	—
756	C₂×SD₁₆	—	43	2	no	—
757	C₂×SD₁₆	—	43	2	no	—
758	C₂×SD₁₆	—	172	2	no	—
759	C₂×SD₁₆	C₂²×D₄₃	1	1	yes	characteristic
760	C₂×SD₁₆	C₂²×D₄₃	1	1	yes	characteristic
761	C₂×SD₁₆	C₂²×D₄₃	1	1	yes	characteristic
762	C₂×SD₁₆	C₂²×D₄₃	1	1	yes	characteristic
763	C₂×D₈	—	43	2	no	—
764	C₂×D₈	—	43	2	no	—
765	C₂×D₈	C₂²×D₄₃	1	1	yes	characteristic
766	C₂×D₈	C₂²×D₄₃	1	1	yes	characteristic
767	C₂×M₁₆	—	43	1	no	—
768	C₂×M₁₆	—	43	1	no	—
769	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
770	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
771	C₄⋊Q₈	—	43	2	no	—
772	C₄⋊Q₈	—	43	2	no	—
773	C₄⋊Q₈	—	43	2	no	—
774	C₄⋊Q₈	—	43	1	no	—
775	C₄⋊Q₈	—	43	1	no	—
776	C₄⋊Q₈	C₂²×D₄₃	1	1	yes	characteristic
777	#127	—	43	2	no	—
778	#127	C₂²×D₄₃	1	1	yes	characteristic
779	#126	—	86	2	no	—
780	#126	—	86	2	no	—
781	#126	—	86	2	no	—
782	#126	—	86	2	no	—
783	#126	—	86	2	no	—
784	#126	—	86	2	no	—
785	#126	—	86	2	no	—
786	#126	—	86	2	no	—
787	#125	—	43	1	no	—
788	#125	—	43	1	no	—
789	#125	—	86	2	no	—
790	#125	—	86	2	no	—
791	#125	—	86	2	no	—
792	#124	—	43	2	no	—
793	#124	—	43	2	no	—
794	#124	—	43	2	no	—
795	#124	—	43	2	no	—
796	#124	—	43	2	no	—
797	#124	—	43	2	no	—
798	#124	—	86	2	no	—
799	#124	—	86	2	no	—
800	#124	—	86	2	no	—
801	#124	—	86	1	no	—
802	#124	—	86	1	no	—
803	#124	C₂²×D₄₃	1	1	yes	characteristic
804	#124	C₂²×D₄₃	1	1	yes	characteristic
805	#123	—	86	2	no	—
806	#123	—	86	2	no	—
807	#123	—	86	2	no	—
808	#123	—	86	2	no	—
809	#123	—	86	2	no	—
810	#123	—	86	2	no	—
811	#123	—	86	2	no	—
812	#123	—	86	2	no	—
813	#123	—	86	2	no	—
814	C₂²⋊Q₈	—	43	2	no	—
815	C₂²⋊Q₈	—	43	2	no	—
816	C₂²⋊Q₈	—	86	2	no	—
817	C₂²⋊Q₈	—	86	2	no	—
818	C₂²⋊Q₈	—	86	2	no	—
819	C₂²⋊Q₈	—	86	2	no	—
820	C₂²⋊Q₈	—	86	1	no	—
821	C₂²⋊Q₈	—	86	1	no	—
822	C₂²⋊Q₈	—	86	1	no	—
823	C₂²⋊Q₈	—	86	1	no	—
824	C₂²⋊Q₈	—	86	1	no	—
825	C₂²⋊Q₈	—	86	1	no	—
826	#121	—	2	1	no	—
827	#121	—	2	1	no	—
828	#121	—	86	1	no	—
829	#121	—	86	1	no	—
830	#120	—	86	2	no	—
831	C₄×Q₈	—	43	2	no	—
832	C₄×Q₈	—	43	2	no	—
833	C₄×Q₈	—	43	2	no	—
834	C₄×Q₈	—	43	2	no	—
835	C₄×Q₈	—	43	2	no	—
836	C₄×Q₈	—	43	2	no	—
837	C₄×Q₈	—	43	2	no	—
838	C₄×Q₈	—	43	2	no	—
839	C₄×Q₈	—	86	1	no	—
840	C₄×Q₈	—	86	1	no	—
841	C₄×Q₈	—	86	2	no	—
842	C₄×Q₈	—	86	1	no	—
843	C₄×Q₈	—	86	1	no	—
844	C₄×Q₈	C₂²×D₄₃	1	1	yes	characteristic
845	C₄×Q₈	C₂²×D₄₃	1	1	yes	characteristic
846	C₄×D₄	—	2	1	no	—
847	C₄×D₄	—	2	1	no	—
848	C₄×D₄	—	2	1	no	—
849	C₄×D₄	—	2	1	no	—
850	C₄×D₄	—	43	2	no	—
851	C₄×D₄	—	43	2	no	—
852	C₄×D₄	—	43	2	no	—
853	C₄×D₄	—	43	2	no	—
854	C₄×D₄	—	86	1	no	—
855	C₄×D₄	—	86	1	no	—
856	C₄×D₄	—	86	2	no	—
857	C₄×D₄	—	86	2	no	—
858	C₄×D₄	—	86	2	no	—
859	C₄×D₄	—	86	2	no	—
860	C₄×D₄	—	86	2	no	—
861	C₄×D₄	C₂²×D₄₃	1	1	yes	characteristic
862	C₄×D₄	C₂²×D₄₃	1	1	yes	characteristic
863	#117	—	2	1	no	—
864	#117	—	43	1	no	—
865	#117	—	43	1	no	—
866	#117	—	86	2	no	—
867	#117	—	86	2	no	—
868	#117	—	86	2	no	—
869	#117	—	86	2	no	—
870	#117	—	86	2	no	—
871	#117	—	86	1	no	—
872	#117	—	86	1	no	—
873	#117	C₂²×D₄₃	1	1	yes	characteristic
874	C₂×C₄⋊C₄	—	43	1	no	—
875	C₂×C₄⋊C₄	—	86	1	no	—
876	C₂×C₄⋊C₄	—	86	1	no	—
877	C₂×C₄⋊C₄	—	86	1	no	—
878	C₂×C₂²⋊C₄	—	86	2	no	—
879	C₂×C₂²⋊C₄	—	86	1	no	—
880	C₂×C₂²⋊C₄	—	86	1	no	—
881	C₂×C₄²	—	2	1	no	—
882	C₂×C₄²	—	86	1	no	—
883	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
884	#107	—	43	2	no	—
885	#106	—	43	2	no	—
886	C₄⋊C₈	—	43	2	no	—
887	C₄⋊C₈	—	43	2	no	—
888	C₄⋊C₈	—	43	2	no	—
889	C₄⋊C₈	—	43	2	no	—
890	C₄⋊C₈	C₂²×D₄₃	1	1	yes	characteristic
891	C₄⋊C₈	C₂²×D₄₃	1	1	yes	characteristic
892	C₄⋊C₈	C₂²×D₄₃	1	1	yes	characteristic
893	C₄⋊C₈	C₂²×D₄₃	1	1	yes	characteristic
894	#103	—	43	2	no	—
895	#103	—	43	2	no	—
896	#103	—	43	2	no	—
897	#103	—	43	2	no	—
898	#103	—	43	2	no	—
899	#103	C₂²×D₄₃	1	1	yes	characteristic
900	#103	C₂²×D₄₃	1	1	yes	characteristic
901	#103	C₂²×D₄₃	1	1	yes	characteristic
902	#103	C₂²×D₄₃	1	1	yes	characteristic
903	#102	—	43	2	no	—
904	#102	—	43	2	no	—
905	#102	—	43	2	no	—
906	#102	C₂²×D₄₃	1	1	yes	characteristic
907	#102	C₂²×D₄₃	1	1	yes	characteristic
908	#102	C₂²×D₄₃	1	1	yes	characteristic
909	#102	C₂²×D₄₃	1	1	yes	characteristic
910	#97	—	43	2	no	—
911	#97	—	43	2	no	—
912	#97	—	43	2	no	—
913	C₄×C₈	—	43	2	no	—
914	C₄×C₈	—	43	2	no	—
915	C₄×C₈	—	43	2	no	—
916	C₂⁴	—	86	1	no	—
917	#41	—	2	2	no	—
918	#41	—	2	2	no	—
919	#41	—	2	2	no	—
920	#41	—	2	2	no	—
921	#41	—	2	2	no	—
922	#41	—	2	2	no	—
923	C₂×Q₈	—	43	2	no	—
924	C₂×Q₈	—	43	2	no	—
925	C₂×Q₈	—	43	2	no	—
926	C₂×Q₈	—	43	2	no	—
927	C₂×Q₈	—	86	1	no	—
928	C₂×Q₈	—	86	1	no	—
929	C₂×Q₈	—	86	2	no	—
930	C₂×Q₈	—	86	2	no	—
931	C₂×Q₈	—	86	2	no	—
932	C₂×Q₈	—	86	2	no	—
933	C₂×Q₈	C₂³×D₄₃	1	1	yes	characteristic
934	C₂×Q₈	C₂³×D₄₃	1	1	yes	characteristic
935	C₂×Q₈	C₂³×D₄₃	1	1	yes	characteristic
936	C₂×D₄	—	2	1	no	—
937	C₂×D₄	—	2	1	no	—
938	C₂×D₄	—	2	1	no	—
939	C₂×D₄	—	2	1	no	—
940	C₂×D₄	—	2	1	no	—
941	C₂×D₄	—	43	2	no	—
942	C₂×D₄	—	86	2	no	—
943	C₂×D₄	—	86	2	no	—
944	C₂×D₄	—	86	1	no	—
945	C₂×D₄	—	86	2	no	—
946	C₂×D₄	—	86	2	no	—
947	C₂×D₄	C₂³×D₄₃	1	1	yes	characteristic
948	C₂×D₄	C₂³×D₄₃	1	1	yes	characteristic
949	C₂×D₄	C₂³×D₄₃	1	1	yes	characteristic
950	C₂²×C₄	—	2	1	no	—
951	C₂²×C₄	—	2	1	no	—
952	C₂²×C₄	—	2	1	no	—
953	C₂²×C₄	—	2	1	no	—
954	C₂²×C₄	—	2	1	no	—
955	C₂²×C₄	—	86	2	no	—
956	C₂²×C₄	—	86	2	no	—
957	C₂²×C₄	—	86	2	no	—
958	C₂²×C₄	—	86	2	no	—
959	C₂²×C₄	—	86	1	no	—
960	C₂²×C₄	—	86	1	no	—
961	C₂²×C₄	—	86	1	no	—
962	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
963	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
964	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
965	Q₁₆	—	4	1	no	—
966	Q₁₆	—	4	1	no	—
967	Q₁₆	—	86	4	no	—
968	Q₁₆	—	86	4	no	—
969	Q₁₆	—	172	2	no	—
970	Q₁₆	—	172	2	no	—
971	Q₁₆	—	172	2	no	—
972	SD₁₆	—	4	1	no	—
973	SD₁₆	—	4	1	no	—
974	SD₁₆	—	4	1	no	—
975	SD₁₆	—	4	1	no	—
976	SD₁₆	—	86	4	no	—
977	SD₁₆	—	86	4	no	—
978	SD₁₆	—	86	4	no	—
979	SD₁₆	—	172	2	no	—
980	SD₁₆	—	172	2	no	—
981	SD₁₆	—	172	2	no	—
982	SD₁₆	—	172	2	no	—
983	D₈	—	4	1	no	—
984	D₈	—	4	1	no	—
985	D₈	—	86	4	no	—
986	D₈	—	172	2	no	—
987	M₁₆	—	43	4	no	—
988	M₁₆	—	86	2	no	—
989	C₂×C₈	—	2	2	no	—
990	C₂×C₈	—	2	2	no	—
991	C₂×C₈	—	43	2	no	—
992	C₂×C₈	—	43	2	no	—
993	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
994	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
995	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
996	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
997	C₄⋊C₄	—	2	1	no	—
998	C₄⋊C₄	—	2	1	no	—
999	C₄⋊C₄	—	2	1	no	—
1000	C₄⋊C₄	—	2	1	no	—
1001	C₄⋊C₄	—	43	1	no	—
1002	C₄⋊C₄	—	43	1	no	—
1003	C₄⋊C₄	—	43	1	no	—
1004	C₄⋊C₄	—	43	1	no	—
1005	C₄⋊C₄	—	43	2	no	—
1006	C₄⋊C₄	—	43	2	no	—
1007	C₄⋊C₄	—	43	2	no	—
1008	C₄⋊C₄	—	43	2	no	—
1009	C₄⋊C₄	—	43	2	no	—
1010	C₄⋊C₄	—	43	2	no	—
1011	C₄⋊C₄	—	43	2	no	—
1012	C₄⋊C₄	—	86	2	no	—
1013	C₄⋊C₄	—	86	2	no	—
1014	C₄⋊C₄	—	86	2	no	—
1015	C₄⋊C₄	—	86	2	no	—
1016	C₄⋊C₄	—	86	2	no	—
1017	C₄⋊C₄	—	86	2	no	—
1018	C₄⋊C₄	—	86	2	no	—
1019	C₄⋊C₄	—	86	2	no	—
1020	C₄⋊C₄	—	86	2	no	—
1021	C₄⋊C₄	—	86	2	no	—
1022	C₄⋊C₄	—	86	1	no	—
1023	C₄⋊C₄	—	86	2	no	—
1024	C₄⋊C₄	—	86	2	no	—
1025	C₄⋊C₄	C₂³×D₄₃	1	1	yes	characteristic
1026	C₄⋊C₄	C₂³×D₄₃	1	1	yes	characteristic
1027	C₂²⋊C₄	—	2	1	no	—
1028	C₂²⋊C₄	—	2	1	no	—
1029	C₂²⋊C₄	—	2	1	no	—
1030	C₂²⋊C₄	—	2	1	no	—
1031	C₂²⋊C₄	—	2	1	no	—
1032	C₂²⋊C₄	—	2	1	no	—
1033	C₂²⋊C₄	—	2	1	no	—
1034	C₂²⋊C₄	—	43	2	no	—
1035	C₂²⋊C₄	—	43	2	no	—
1036	C₂²⋊C₄	—	86	2	no	—
1037	C₂²⋊C₄	—	86	2	no	—
1038	C₂²⋊C₄	—	86	2	no	—
1039	C₂²⋊C₄	—	86	2	no	—
1040	C₂²⋊C₄	—	86	2	no	—
1041	C₂²⋊C₄	—	86	2	no	—
1042	C₂²⋊C₄	—	86	2	no	—
1043	C₂²⋊C₄	—	86	2	no	—
1044	C₂²⋊C₄	—	86	2	no	—
1045	C₂²⋊C₄	—	86	2	no	—
1046	C₂²⋊C₄	—	86	2	no	—
1047	C₂²⋊C₄	—	86	2	no	—
1048	C₂²⋊C₄	—	86	2	no	—
1049	C₂²⋊C₄	—	86	2	no	—
1050	C₂²⋊C₄	—	86	2	no	—
1051	C₂²⋊C₄	—	86	2	no	—
1052	C₄²	—	2	1	no	—
1053	C₄²	—	2	1	no	—
1054	C₄²	—	2	1	no	—
1055	C₄²	—	43	2	no	—
1056	C₄²	—	43	2	no	—
1057	C₄²	—	86	2	no	—
1058	C₄²	—	86	2	no	—
1059	C₄²	—	86	2	no	—
1060	C₄²	—	86	2	no	—
1061	C₄²	—	86	2	no	—
1062	C₄²	—	86	2	no	—
1063	C₄²	D₄×D₄₃	1	1	yes	characteristic
1064	C₄²	D₄×D₄₃	1	1	yes	characteristic
1065	C₄²	C₂³×D₄₃	1	1	yes	characteristic
1066	C₄²	C₂³×D₄₃	1	1	yes	characteristic
1067	C₂³	—	2	1	no	—
1068	C₂³	—	2	1	no	—
1069	C₂³	—	2	1	no	—
1070	C₂³	—	86	2	no	—
1071	C₂³	—	344	1	no	—
1072	C₂³	—	344	1	no	—
1073	C₂³	—	172	2	no	—
1074	C₂³	C₂×D₄×D₄₃	1	1	yes	characteristic
1075	Q₈	—	2	1	no	—
1076	Q₈	—	2	1	no	—
1077	Q₈	—	2	1	no	—
1078	Q₈	—	2	1	no	—
1079	Q₈	—	2	1	no	—
1080	Q₈	—	2	1	no	—
1081	Q₈	—	86	2	no	—
1082	Q₈	—	86	2	no	—
1083	Q₈	—	86	2	no	—
1084	Q₈	—	86	2	no	—
1085	Q₈	—	172	2	no	—
1086	Q₈	—	172	2	no	—
1087	Q₈	—	172	2	no	—
1088	Q₈	—	172	2	no	—
1089	D₄	—	2	1	no	—
1090	D₄	—	2	1	no	—
1091	D₄	—	2	1	no	—
1092	D₄	—	2	1	no	—
1093	D₄	—	2	1	no	—
1094	D₄	—	2	1	no	—
1095	D₄	—	4	2	no	—
1096	D₄	—	4	2	no	—
1097	D₄	—	4	2	no	—
1098	D₄	—	4	2	no	—
1099	D₄	—	8	1	no	—
1100	D₄	—	86	2	no	—
1101	D₄	—	86	2	no	—
1102	D₄	—	344	2	no	—
1103	D₄	—	344	2	no	—
1104	D₄	—	172	2	no	—
1105	C₂×C₄	—	2	1	no	—
1106	C₂×C₄	—	2	1	no	—
1107	C₂×C₄	—	2	1	no	—
1108	C₂×C₄	—	2	1	no	—
1109	C₂×C₄	—	2	1	no	—
1110	C₂×C₄	—	4	1	no	—
1111	C₂×C₄	—	4	1	no	—
1112	C₂×C₄	—	4	2	no	—
1113	C₂×C₄	—	4	2	no	—
1114	C₂×C₄	—	4	2	no	—
1115	C₂×C₄	—	8	1	no	—
1116	C₂×C₄	—	8	1	no	—
1117	C₂×C₄	—	43	2	no	—
1118	C₂×C₄	—	43	2	no	—
1119	C₂×C₄	—	43	2	no	—
1120	C₂×C₄	—	43	2	no	—
1121	C₂×C₄	—	86	2	no	—
1122	C₂×C₄	—	86	2	no	—
1123	C₂×C₄	—	86	2	no	—
1124	C₂×C₄	—	344	2	no	—
1125	C₂×C₄	—	344	2	no	—
1126	C₂×C₄	—	344	2	no	—
1127	C₂×C₄	—	344	2	no	—
1128	C₂×C₄	—	344	1	no	—
1129	C₂×C₄	—	172	2	no	—
1130	C₂×C₄	—	172	2	no	—
1131	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
1132	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
1133	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
1134	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
1135	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
1136	C₂×C₄	#41×D₄₃	1	2	yes	—
1137	C₂×C₄	#13063370	1	2	yes	—
1138	C₂×C₄	C₂⁴×D₄₃	1	1	yes	characteristic
1139	C₈	—	2	1	no	—
1140	C₈	—	2	1	no	—
1141	C₈	—	2	1	no	—
1142	C₈	—	2	1	no	—
1143	C₈	—	43	4	no	—
1144	C₈	—	86	2	no	—
1145	C₂²	—	2	1	no	—
1146	C₂²	—	2	1	no	—
1147	C₂²	—	4	1	no	—
1148	C₂²	—	4	1	no	—
1149	C₂²	—	4	1	no	—
1150	C₂²	—	4	1	no	—
1151	C₂²	—	4	1	no	—
1152	C₂²	—	4	1	no	—
1153	C₂²	—	4	1	no	—
1154	C₂²	—	4	1	no	—
1155	C₂²	—	4	1	no	—
1156	C₂²	—	172	2	no	—
1157	C₂²	—	172	2	no	—
1158	C₂²	—	172	2	no	—
1159	C₂²	—	688	2	no	—
1160	C₂²	#14583567	1	2	yes	—
1161	C₂²	C₂²×D₄×D₄₃	1	1	yes	characteristic
1162	C₄	—	2	1	no	—
1163	C₄	—	2	1	no	—
1164	C₄	—	2	1	no	—
1165	C₄	—	2	1	no	—
1166	C₄	—	4	1	no	—
1167	C₄	—	4	1	no	—
1168	C₄	—	4	1	no	—
1169	C₄	—	4	1	no	—
1170	C₄	—	4	1	no	—
1171	C₄	—	86	2	no	—
1172	C₄	—	86	2	no	—
1173	C₄	—	86	2	no	—
1174	C₄	—	86	2	no	—
1175	C₄	—	172	2	no	—
1176	C₄	—	172	2	no	—
1177	C₄	—	172	2	no	—
1178	C₄	#14583567	1	2	yes	—
1179	C₄	C₂×#41×D₄₃	1	1	yes	characteristic
1180	C₄	C₂×#13063370	1	1	yes	characteristic
1181	C₂	—	2	2	no	—
1182	C₂	—	8	1	no	—
1183	C₂	—	8	1	no	—
1184	C₂	—	8	1	no	—
1185	C₂	—	344	2	no	—
1186	C₂	C₂×#14583567	1	1	yes	characteristic
1187	C₂	#19149364	1	1	yes	characteristic
1188	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×#3035	C₂
socle	C₂²×C₄₃	C₂³×D₄
hypercenter	#3035	D₄₃
hypocenter	C₄₃	#61423
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #3035

Complements

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

N	H ≅ G/N	type
1. #19148491	C₂	semidirect
2. #19148457	C₂	semidirect
3. #19147678	C₂	semidirect
4. #19147674	C₂	semidirect
5. #19147659	C₂	semidirect
6. #19147654	C₂	semidirect
7. #19147643	C₂	semidirect
8. #19147621	C₂	semidirect
9. #19147594	C₂	semidirect
10. #19147578	C₂	semidirect
11. #19145090	C₂	semidirect
12. #19145072	C₂	semidirect
13. #19145063	C₂	semidirect
14. #19144143	C₂	semidirect
15. #19144132	C₂	semidirect
16. #19144128	C₂	semidirect
17. #19144110	C₂	semidirect
18. C₂×#14583122	C₂	semidirect
19. #19143538	C₂	semidirect
20. #19143441	C₂	semidirect
21. #19143430	C₂	semidirect
22. C₄×#13063355	C₂	semidirect
23. C₄₃×#3035	C₂	semidirect
31. #14583635	C₂²	semidirect
34. #14583624	C₂²	semidirect
38. #14583618	C₂²	semidirect
39. #14583618	C₂²	semidirect
64. #14583290	C₂²	semidirect
65. #14583290	C₂²	semidirect
68. #14583282	C₂²	semidirect
72. #14583277	C₂²	semidirect
79. #14583120	C₂²	semidirect
80. #14583120	C₂²	semidirect
81. #14583119	C₂²	semidirect
85. #14583112	C₂²	semidirect
86. #14583108	C₂²	semidirect
87. #14583108	C₂²	semidirect
88. #14583107	C₂²	semidirect
91. #14583102	C₂²	semidirect
94. #14583028	C₂²	semidirect
95. #14583028	C₂²	semidirect
96. #14583026	C₂²	semidirect
97. #14583023	C₂²	semidirect
99. #14583004	C₂²	semidirect
100. #14583003	C₂²	semidirect
102. #14582999	C₂²	semidirect
103. #14582996	C₂²	semidirect
104. C₄×#10621885	C₂²	semidirect
105. #14582991	C₂²	semidirect
106. #14582990	C₂²	semidirect
107. C₄×#10621883	C₂²	semidirect
124. C₄₃×#464	C₂²	semidirect
125. C₄₃×#464	C₂²	semidirect
126. C₄₃×#463	C₂²	semidirect
127. C₄₃×#463	C₂²	semidirect
128. C₄₃×#462	C₂²	semidirect
129. C₄₃×#461	C₂²	semidirect
130. C₄₃×#460	C₂²	semidirect
131. C₄₃×#459	C₂²	semidirect
604. #3035	D₄₃	semidirect
680. #464	C₂×D₄₃	semidirect
681. #464	C₂×D₄₃	semidirect
686. #463	C₂×D₄₃	semidirect
687. #463	C₂×D₄₃	semidirect
691. #462	C₂×D₄₃	semidirect
695. #461	C₂×D₄₃	semidirect
697. #460	C₂×D₄₃	semidirect
699. #459	C₂×D₄₃	semidirect
729. C₄₃	#61423	semidirect

Maximal subgroups

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

subgroup	index
#19148491	2
#19148457	2
#19147678	2
#19147674	2
#19147659	2
#19147654	2
#19147643	2
#19147621	2
#19147594	2
#19147578	2
#19145090	2
#19145072	2
#19145063	2
#19144143	2
#19144132	2
#19144128	2
#19144110	2
C₂×#14583122	2
#19143538	2
#19143441	2
#19143430	2
C₄×#13063355	2
C₄₃×#3035	2
#61423	43