Subgroups — #25966601

Order 11008.

1914 conjugacy classes of subgroups.

The subgroup lattice has 1168 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19148022	C₂	1	1	yes	maximal, characteristic, complemented
2	#19148011	C₂	1	1	yes	maximal, characteristic, complemented
3	#19145282	C₂	1	2	yes	maximal, complemented
4	#19145267	C₂	1	2	yes	maximal, complemented
5	#19145219	C₂	1	2	yes	maximal, complemented
6	#19145208	C₂	1	2	yes	maximal, complemented
7	#19145199	C₂	1	2	yes	maximal, complemented
8	#19145188	C₂	1	2	yes	maximal, complemented
9	#19145161	C₂	1	2	yes	maximal, complemented
10	#19145151	C₂	1	2	yes	maximal, complemented
11	#19145127	C₂	1	1	yes	maximal, characteristic, complemented
12	#19145072	C₂	1	1	yes	maximal, characteristic, complemented
13	#19144964	C₂	1	1	yes	maximal, characteristic, complemented
14	#19144953	C₂	1	1	yes	maximal, characteristic, complemented
15	#19144289	C₂	1	1	yes	maximal, characteristic, complemented
16	#19144278	C₂	1	1	yes	maximal, characteristic, complemented
17	#19144253	C₂	1	1	yes	maximal, characteristic, complemented
18	#19144235	C₂	1	1	yes	maximal, characteristic, complemented
19	C₄×#13063355	C₂	1	1	yes	maximal, characteristic, complemented
20	C₄×#13063350	C₂	1	1	yes	maximal, characteristic, complemented
21	C₂×C₄×#10621873	C₂	1	1	yes	maximal, characteristic, complemented
22	C₄×#13063331	C₂	1	1	yes	maximal, characteristic, complemented
23	C₄×#135×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#13063355	C₂²	1	1	yes	characteristic
25	C₂×#13063350	C₂²	1	1	yes	characteristic
26	C₂²×#10621873	C₂²	1	1	yes	characteristic
27	C₂×#13063331	C₂²	1	1	yes	characteristic
28	C₂×#13063331	C₂²	1	1	yes	characteristic
29	#14583527	C₂²	1	1	yes	characteristic
30	#14583527	C₂²	1	1	yes	characteristic
31	#14583521	C₂²	1	2	yes	—
32	#14583520	—	2	1	no	—
33	#14583520	—	2	1	no	—
34	#14583514	C₂²	1	2	yes	complemented
35	#14583511	—	2	1	no	—
36	#14583507	C₂²	1	2	yes	complemented
37	#14583504	—	2	1	no	—
38	#14583500	C₂²	1	2	yes	—
39	#14583491	—	2	2	no	—
40	#14583482	—	2	2	no	—
41	#14583477	C₂²	1	1	yes	characteristic
42	#14583477	C₂²	1	1	yes	characteristic
43	#14583475	C₂²	1	1	yes	characteristic
44	#14583470	C₂²	1	1	yes	characteristic
45	#14583468	C₂²	1	1	yes	characteristic
46	#14583463	C₂²	1	1	yes	characteristic
47	#14583456	—	2	1	no	—
48	#14583453	C₂²	1	2	yes	complemented
49	#14583449	—	2	1	no	—
50	#14583446	C₂²	1	2	yes	—
51	#14583436	C₂²	1	2	yes	—
52	#14583433	—	2	1	no	—
53	#14583433	—	2	1	no	—
54	#14583431	C₂²	1	2	yes	complemented
55	#14583429	—	2	2	no	—
56	#14583408	—	2	2	no	—
57	C₄×#10621898	C₂²	1	1	yes	characteristic
58	C₂×C₄×Dic₈₆	C₂²	1	1	yes	characteristic
59	C₂×C₄×D₁₇₂	C₂²	1	1	yes	characteristic
60	#14583307	C₂²	1	2	yes	complemented
61	#14583307	C₂²	1	2	yes	complemented
62	#14583299	C₂²	1	2	yes	complemented
63	#14583296	C₂²	1	2	yes	complemented
64	#14583292	C₂²	1	2	yes	—
65	#14583287	C₂²	1	2	yes	—
66	#14583280	C₂²	1	2	yes	—
67	#14583270	C₂²	1	2	yes	—
68	#14583266	C₂²	1	2	yes	complemented
69	#14583262	C₂²	1	2	yes	—
70	#14583260	C₂²	1	2	yes	—
71	#14583257	C₂²	1	2	yes	complemented
72	#14583255	C₂²	1	2	yes	—
73	#14583252	C₂²	1	2	yes	complemented
74	#14583248	C₂²	1	2	yes	complemented
75	#14583244	C₂²	1	2	yes	—
76	#14583156	C₂²	1	2	yes	complemented
77	#14583154	C₂²	1	2	yes	complemented
78	#14583151	C₂²	1	2	yes	—
79	#14583149	C₂²	1	2	yes	complemented
80	#14583148	C₂²	1	2	yes	—
81	#14583146	C₂²	1	2	yes	—
82	#14583146	C₂²	1	2	yes	—
83	#14583144	C₂²	1	2	yes	complemented
84	#14583139	C₂²	1	2	yes	complemented
85	#14583134	C₂²	1	2	yes	—
86	#14583131	C₂²	1	2	yes	—
87	#14583129	C₂²	1	2	yes	—
88	#14583129	C₂²	1	2	yes	—
89	#14583127	C₂²	1	2	yes	complemented
90	#14583125	C₂²	1	2	yes	complemented
91	#14583125	C₂²	1	2	yes	complemented
92	#14583009	C₂²	1	2	yes	—
93	#14583004	C₂²	1	2	yes	complemented
94	#14582999	C₂²	1	2	yes	complemented
95	#14582997	C₂²	1	2	yes	—
96	C₄×#10621885	C₂²	1	2	yes	complemented
97	C₄×#10621873	C₂²	1	2	yes	—
98	C₄×#10621873	C₂²	1	2	yes	—
99	C₄×#10621873	C₂²	1	2	yes	—
100	C₄×#10621873	C₂²	1	2	yes	—
101	C₄×#10621884	C₂²	1	2	yes	—
102	C₄×#10621883	C₂²	1	2	yes	complemented
103	C₄×#10621882	C₂²	1	2	yes	—
104	#14582942	C₂²	1	1	yes	characteristic
105	#14582942	C₂²	1	1	yes	characteristic
106	C₂×#13063257	C₂²	1	1	yes	characteristic
107	#14582907	C₂²	1	1	yes	characteristic
108	#14582903	C₂²	1	1	yes	characteristic
109	#14582900	C₂²	1	1	yes	characteristic
110	#14582900	C₂²	1	1	yes	characteristic
111	C₂×#13063250	C₂²	1	1	yes	characteristic
112	C₂×#13063247	C₂²	1	1	yes	characteristic
113	#14582854	C₂²	1	1	yes	characteristic
114	#14582854	C₂²	1	1	yes	characteristic
115	#14582853	C₂²	1	2	yes	complemented
116	#14582853	C₂²	1	2	yes	complemented
117	C₄×#10621877	C₂²	1	1	yes	characteristic
118	C₄×#10621872	C₂²	1	2	yes	complemented
119	C₄×C₈×D₄₃	C₂²	1	2	yes	complemented
120	C₂×#135×C₄₃	C₂²	1	1	yes	characteristic
121	C₄×#41×C₄₃	C₂²	1	1	yes	characteristic
122	C₄×#41×C₄₃	C₂²	1	1	yes	characteristic
123	C₄×Q₁₆×C₄₃	C₂²	1	1	yes	characteristic, complemented
124	C₄×Q₁₆×C₄₃	C₂²	1	1	yes	characteristic, complemented
125	C₄×SD₁₆×C₄₃	C₂²	1	1	yes	characteristic, complemented
126	C₄×SD₁₆×C₄₃	C₂²	1	1	yes	characteristic, complemented
127	C₄×SD₁₆×C₄₃	C₂²	1	1	yes	characteristic, complemented
128	C₄×SD₁₆×C₄₃	C₂²	1	1	yes	characteristic, complemented
129	C₄×D₈×C₄₃	C₂²	1	1	yes	characteristic, complemented
130	C₄×D₈×C₄₃	C₂²	1	1	yes	characteristic, complemented
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×C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
135	C₂×#10621898	—	2	2	no	—
136	C₂×#10621898	C₂³	1	1	yes	characteristic
137	C₂²×Dic₈₆	C₂³	1	1	yes	characteristic
138	C₂²×D₁₇₂	C₂³	1	1	yes	characteristic
139	C₂²×C₄×D₄₃	—	2	1	no	—
140	#13063355	—	2	4	no	—
141	#13063350	—	2	4	no	—
142	C₂×#10621885	C₂³	1	2	yes	—
143	C₂×#10621873	—	2	4	no	—
144	C₂×#10621873	C₂³	1	2	yes	—
145	C₂×#10621873	C₂³	1	2	yes	—
146	C₂×#10621883	C₂³	1	2	yes	—
147	C₂×#10621884	C₂³	1	2	yes	—
148	C₂×#10621882	C₂³	1	2	yes	—
149	#13063331	—	2	4	no	—
150	#13063331	—	2	4	no	—
151	C₂×#10621877	C₂³	1	1	yes	characteristic
152	C₂×#10621877	C₂³	1	1	yes	characteristic
153	C₂×#10621872	C₂³	1	2	yes	—
154	C₂×#10621872	C₂³	1	2	yes	—
155	C₂×C₈×D₄₃	C₂³	1	2	yes	—
156	C₂×C₈×D₄₃	C₂³	1	2	yes	—
157	#13063325	—	2	1	no	—
158	#13063325	—	2	1	no	—
159	#13063325	—	2	1	no	—
160	#13063324	C₂³	1	2	yes	—
161	#13063324	C₂³	1	2	yes	—
162	#13063323	C₂³	1	2	yes	—
163	#13063322	—	2	1	no	—
164	#13063321	C₂³	1	2	yes	—
165	#13063320	—	2	2	no	—
166	#13063320	—	2	2	no	—
167	#13063319	—	2	2	no	—
168	#13063319	—	2	2	no	—
169	#13063318	—	2	2	no	—
170	#13063318	—	2	2	no	—
171	#13063317	—	2	1	no	—
172	#13063317	—	2	1	no	—
173	#13063317	—	2	2	no	—
174	#13063316	C₂³	1	2	yes	—
175	#13063316	C₂³	1	2	yes	—
176	#13063315	—	2	2	no	—
177	#13063315	—	2	2	no	—
178	#13063314	C₂³	1	2	yes	—
179	#13063313	—	2	1	no	—
180	#13063313	—	2	1	no	—
181	#13063313	—	2	2	no	—
182	#13063312	C₂³	1	2	yes	—
183	#13063311	—	2	2	no	—
184	#13063311	—	2	2	no	—
185	#13063310	—	2	2	no	—
186	#13063310	—	2	2	no	—
187	#13063309	—	2	2	no	—
188	#13063308	—	2	2	no	—
189	#13063308	—	2	2	no	—
190	#13063307	—	2	2	no	—
191	#13063307	—	2	2	no	—
192	#13063306	—	2	2	no	—
193	#13063305	C₂³	1	2	yes	—
194	#13063305	C₂³	1	2	yes	—
195	#13063304	—	2	1	no	—
196	#13063304	—	2	1	no	—
197	#13063304	—	2	1	no	—
198	#13063304	—	2	1	no	—
199	#13063304	—	2	2	no	—
200	#13063303	—	2	2	no	—
201	#13063303	—	2	2	no	—
202	#13063302	—	2	2	no	—
203	#13063302	—	2	2	no	—
204	#13063301	C₂³	1	2	yes	—
205	#13063301	C₂³	1	2	yes	—
206	#13063300	C₂³	1	2	yes	—
207	#13063300	C₂³	1	2	yes	—
208	#13063299	—	2	1	no	—
209	#13063299	—	2	1	no	—
210	#13063299	—	2	2	no	—
211	#13063299	—	2	1	no	—
212	#13063299	—	2	1	no	—
213	#13063298	—	2	2	no	—
214	#13063298	—	2	2	no	—
215	#13063297	—	2	2	no	—
216	#13063297	—	2	2	no	—
217	#13063296	C₂³	1	2	yes	—
218	#13063296	C₂³	1	2	yes	—
219	#13063295	—	2	2	no	—
220	#13063293	—	2	2	no	—
221	C₄×Dic₈₆	—	2	1	no	—
222	C₄×Dic₈₆	—	2	1	no	—
223	C₄×Dic₈₆	—	2	2	no	—
224	C₄×Dic₈₆	D₄	1	1	yes	characteristic
225	C₄×Dic₈₆	D₄	1	1	yes	characteristic
226	C₄×Dic₈₆	C₂³	1	2	yes	—
227	C₄×Dic₈₆	C₂³	1	2	yes	—
228	C₄×D₁₇₂	—	2	2	no	—
229	C₄×D₁₇₂	—	2	1	no	—
230	C₄×D₁₇₂	—	2	1	no	—
231	C₄×D₁₇₂	D₄	1	1	yes	characteristic
232	C₄×D₁₇₂	D₄	1	1	yes	characteristic
233	C₄×D₁₇₂	C₂³	1	2	yes	—
234	C₄×D₁₇₂	C₂³	1	2	yes	—
235	C₄×C₂²⋊D₄₃	—	2	2	no	—
236	C₄×C₂²⋊D₄₃	—	2	2	no	—
237	C₄×C₂²⋊D₄₃	D₄	1	2	yes	—
238	C₄×C₂²⋊D₄₃	D₄	1	2	yes	—
239	#13063284	—	2	2	no	—
240	#13063284	C₂³	1	1	yes	characteristic
241	#13063282	—	2	2	no	—
242	#13063282	—	2	2	no	—
243	#13063282	C₂³	1	2	yes	—
244	C₂×C₄⋊Dic₄₃	C₂³	1	1	yes	characteristic
245	C₂×C₄⋊Dic₄₃	C₂³	1	1	yes	characteristic
246	C₂×Dic₄₃⋊C₄	—	2	1	no	—
247	C₂×(C₂×D₄₃)⋊C₄	—	2	1	no	—
248	C₂×C₄×Dic₄₃	—	2	1	no	—
249	C₄²×D₄₃	C₂³	1	2	yes	—
250	#13063258	C₂³	1	2	yes	—
251	#13063258	C₂³	1	2	yes	—
252	#13063257	C₂³	1	2	yes	—
253	#13063257	C₂³	1	2	yes	—
254	#13063256	C₂³	1	2	yes	—
255	#13063256	C₂³	1	2	yes	—
256	#13063250	C₂³	1	2	yes	—
257	#13063250	C₂³	1	2	yes	—
258	#13063249	C₂³	1	2	yes	—
259	#13063249	C₂³	1	2	yes	—
260	#13063248	C₂³	1	2	yes	—
261	#13063248	C₂³	1	2	yes	—
262	#13063247	C₂³	1	2	yes	—
263	#13063247	C₂³	1	2	yes	—
264	#13063246	C₂³	1	2	yes	—
265	#13063246	C₂³	1	2	yes	—
266	#13063245	C₂³	1	2	yes	—
267	#13063245	C₂³	1	2	yes	—
268	#13063236	C₂³	1	2	yes	—
269	#13063235	C₂³	1	2	yes	—
270	#13063235	C₂³	1	2	yes	—
271	C₄×C₄₃⋊C₈	C₂³	1	2	yes	—
272	C₈×Dic₄₃	C₂³	1	2	yes	—
273	C₈×Dic₄₃	C₂³	1	2	yes	—
274	C₂×#41×C₄₃	C₂³	1	1	yes	characteristic
275	C₂×#41×C₄₃	C₂³	1	1	yes	characteristic
276	#135×C₄₃	—	2	4	no	—
277	C₂×Q₁₆×C₄₃	C₂³	1	1	yes	characteristic
278	C₂×SD₁₆×C₄₃	C₂³	1	1	yes	characteristic
279	C₂×SD₁₆×C₄₃	C₂³	1	1	yes	characteristic
280	C₂×D₈×C₄₃	C₂³	1	1	yes	characteristic
281	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
282	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
283	C₄×Q₈×C₄₃	C₂³	1	1	yes	characteristic
284	C₄×Q₈×C₄₃	C₂³	1	1	yes	characteristic
285	C₄×Q₈×C₄₃	C₂³	1	1	yes	characteristic
286	C₄×Q₈×C₄₃	C₂³	1	1	yes	characteristic
287	C₄×D₄×C₄₃	—	2	1	no	—
288	C₄×D₄×C₄₃	—	2	1	no	—
289	C₄×D₄×C₄₃	—	2	1	no	—
290	C₄×D₄×C₄₃	—	2	1	no	—
291	C₄×D₄×C₄₃	C₂³	1	1	yes	characteristic
292	C₄×D₄×C₄₃	C₂³	1	1	yes	characteristic
293	C₄×D₄×C₄₃	C₂³	1	1	yes	characteristic
294	C₄×D₄×C₄₃	C₂³	1	1	yes	characteristic
295	#117×C₄₃	—	2	1	no	—
296	#117×C₄₃	—	2	1	no	—
297	#117×C₄₃	C₂³	1	1	yes	characteristic
298	#117×C₄₃	C₂³	1	1	yes	characteristic
299	C₂×C₄²×C₄₃	—	2	1	no	—
300	C₂×C₄²×C₄₃	—	2	1	no	—
301	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
302	#107×C₄₃	C₂³	1	1	yes	characteristic
303	#107×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	C₄×C₈×C₄₃	C₂³	1	1	yes	characteristic
315	C₄×C₈×C₄₃	C₂³	1	1	yes	characteristic
316	C₄×C₈×C₄₃	C₂³	1	1	yes	characteristic
317	C₄×C₈×C₄₃	C₂³	1	1	yes	characteristic
318	C₂³×D₄₃	—	2	1	no	—
319	#41×C₄₃	—	2	2	no	—
320	#41×C₄₃	—	2	2	no	—
321	#41×C₄₃	—	2	2	no	—
322	#41×C₄₃	—	2	2	no	—
323	C₂×Q₈×C₄₃	C₂⁴	1	1	yes	characteristic
324	C₂×Q₈×C₄₃	C₂⁴	1	1	yes	characteristic
325	C₂×D₄×C₄₃	—	2	1	no	—
326	C₂×D₄×C₄₃	—	2	1	no	—
327	C₂×D₄×C₄₃	C₂⁴	1	1	yes	characteristic
328	C₂×D₄×C₄₃	C₂⁴	1	1	yes	characteristic
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	—	2	1	no	—
333	C₂²×C₄×C₄₃	—	2	1	no	—
334	C₂²×C₄×C₄₃	—	2	1	no	—
335	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
336	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
337	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
338	C₂×C₂²⋊D₄₃	—	2	2	no	—
339	C₂×C₂²⋊D₄₃	—	2	2	no	—
340	C₂×C₂²⋊D₄₃	—	2	2	no	—
341	C₂×C₂²⋊D₄₃	—	2	2	no	—
342	C₂×C₂²⋊D₄₃	C₂×D₄	1	2	yes	—
343	C₂²×Dic₄₃	—	2	1	no	—
344	C₂²×Dic₄₃	—	2	1	no	—
345	C₂²×Dic₄₃	—	2	1	no	—
346	#10621898	—	2	2	no	—
347	#10621898	—	2	2	no	—
348	#10621898	—	8	4	no	—
349	C₂×D₁₇₂	—	2	1	no	—
350	C₂×D₁₇₂	—	2	2	no	—
351	C₂×D₁₇₂	—	2	2	no	—
352	C₂×D₁₇₂	—	2	2	no	—
353	C₂×D₁₇₂	—	2	2	no	—
354	C₂×D₁₇₂	C₂×D₄	1	1	yes	characteristic
355	C₂×D₁₇₂	C₂⁴	1	2	yes	—
356	C₂×C₄×D₄₃	—	2	2	no	—
357	C₂×C₄×D₄₃	—	2	2	no	—
358	C₂×C₄×D₄₃	—	8	2	no	—
359	C₂×C₄×D₄₃	C₂×D₄	1	2	yes	—
360	C₂×C₄×D₄₃	C₂×D₄	1	2	yes	—
361	C₂×C₄×D₄₃	C₂⁴	1	2	yes	—
362	C₂×Dic₈₆	—	2	2	no	—
363	C₂×Dic₈₆	—	2	2	no	—
364	C₂×Dic₈₆	—	2	1	no	—
365	C₂×Dic₈₆	—	2	2	no	—
366	C₂×Dic₈₆	—	2	2	no	—
367	C₂×Dic₈₆	C₂×D₄	1	1	yes	characteristic
368	C₂×Dic₈₆	C₂⁴	1	2	yes	—
369	Q₁₆×C₄₃	—	2	2	no	—
370	SD₁₆×C₄₃	—	2	2	no	—
371	SD₁₆×C₄₃	—	2	2	no	—
372	D₈×C₄₃	—	2	2	no	—
373	C₂×C₈×C₄₃	—	2	2	no	—
374	C₂×C₈×C₄₃	#41	1	4	yes	complemented
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	C₂²⋊C₄×C₄₃	—	2	1	no	—
388	C₂²⋊C₄×C₄₃	—	2	1	no	—
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	C₄²×C₄₃	—	2	1	no	—
394	C₄²×C₄₃	—	2	1	no	—
395	C₄²×C₄₃	—	2	1	no	—
396	C₄²×C₄₃	—	2	1	no	—
397	C₄²×C₄₃	—	2	1	no	—
398	C₄²×C₄₃	—	2	1	no	—
399	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
400	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
401	C₄²×C₄₃	C₂⁴	1	1	yes	characteristic
402	C₄²×C₄₃	C₂⁴	1	1	yes	characteristic
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	C₂×D₄	1	2	yes	—
408	#10621885	—	2	4	no	—
409	#10621884	—	2	4	no	—
410	#10621883	—	2	4	no	—
411	#10621882	—	2	4	no	—
412	(C₂×D₄₃)⋊C₄	—	2	2	no	—
413	(C₂×D₄₃)⋊C₄	—	2	2	no	—
414	(C₂×D₄₃)⋊C₄	—	2	2	no	—
415	(C₂×D₄₃)⋊C₄	—	2	2	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	(C₂×D₄₃)⋊C₄	—	2	2	no	—
421	(C₂×D₄₃)⋊C₄	—	2	2	no	—
422	(C₂×D₄₃)⋊C₄	C₂×D₄	1	2	yes	—
423	(C₂×D₄₃)⋊C₄	C₂×D₄	1	2	yes	—
424	C₄⋊Dic₄₃	—	2	1	no	—
425	C₄⋊Dic₄₃	—	2	1	no	—
426	C₄⋊Dic₄₃	—	2	2	no	—
427	C₄⋊Dic₄₃	—	2	2	no	—
428	C₄⋊Dic₄₃	—	2	2	no	—
429	C₄⋊Dic₄₃	—	2	2	no	—
430	C₄⋊Dic₄₃	C₂×D₄	1	1	yes	characteristic
431	C₄⋊Dic₄₃	C₂×D₄	1	1	yes	characteristic
432	C₄⋊Dic₄₃	C₂⁴	1	2	yes	—
433	C₄⋊Dic₄₃	C₂⁴	1	2	yes	—
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	Dic₄₃⋊C₄	—	2	2	no	—
443	Dic₄₃⋊C₄	—	2	2	no	—
444	Dic₄₃⋊C₄	C₂×D₄	1	2	yes	—
445	Dic₄₃⋊C₄	C₂×D₄	1	2	yes	—
446	C₄×Dic₄₃	—	2	2	no	—
447	C₄×Dic₄₃	—	2	2	no	—
448	C₄×Dic₄₃	C₂×D₄	1	2	yes	—
449	C₄×Dic₄₃	C₂×D₄	1	2	yes	—
450	C₄×Dic₄₃	C₂⁴	1	2	yes	—
451	#10621877	—	2	2	no	—
452	#10621877	#41	1	4	yes	complemented
453	C₂×C₄₃⋊C₈	C₂⁴	1	2	yes	—
454	C₂×C₄₃⋊C₈	C₂⁴	1	2	yes	—
455	#10621873	—	2	4	no	—
456	#10621873	—	2	4	no	—
457	#10621872	—	2	4	no	—
458	#10621872	—	2	4	no	—
459	C₈×D₄₃	—	2	4	no	—
460	C₈×D₄₃	—	2	4	no	—
461	C₂³×C₄₃	—	2	1	no	—
462	C₂³×C₄₃	—	2	1	no	—
463	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
464	C₂²×D₄₃	—	2	2	no	—
465	C₂²×D₄₃	—	4	2	no	—
466	C₂²×D₄₃	—	8	1	no	—
467	C₂²×D₄₃	—	8	1	no	—
468	C₂²×D₄₃	C₂²×D₄	1	2	yes	—
469	Q₈×C₄₃	—	2	1	no	—
470	Q₈×C₄₃	—	2	1	no	—
471	Q₈×C₄₃	—	2	1	no	—
472	Q₈×C₄₃	—	2	1	no	—
473	D₄×C₄₃	—	2	1	no	—
474	D₄×C₄₃	—	2	1	no	—
475	D₄×C₄₃	—	2	1	no	—
476	D₄×C₄₃	—	2	1	no	—
477	D₄×C₄₃	—	4	2	no	—
478	D₄×C₄₃	—	4	2	no	—
479	C₂×C₄×C₄₃	—	2	2	no	—
480	C₂×C₄×C₄₃	—	2	1	no	—
481	C₂×C₄×C₄₃	—	2	1	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	—	4	1	no	—
487	C₂×C₄×C₄₃	—	4	2	no	—
488	C₂×C₄×C₄₃	—	4	2	no	—
489	C₂×C₄×C₄₃	—	4	2	no	—
490	C₂×C₄×C₄₃	—	4	2	no	—
491	C₂×C₄×C₄₃	—	8	1	no	—
492	C₂×C₄×C₄₃	—	8	1	no	—
493	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
494	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
495	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
496	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
497	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
498	C₂×C₄×C₄₃	C₂×#41	1	2	yes	—
499	C₂×C₄×C₄₃	C₂×#41	1	2	yes	—
500	C₂×C₄×C₄₃	C₂⁵	1	1	yes	characteristic
501	C₂²⋊D₄₃	—	2	4	no	—
502	C₂²⋊D₄₃	—	8	2	no	—
503	C₂²⋊D₄₃	—	8	2	no	—
504	C₂²⋊D₄₃	—	8	2	no	—
505	C₂²⋊D₄₃	—	8	2	no	—
506	C₂×Dic₄₃	—	2	2	no	—
507	C₂×Dic₄₃	—	2	2	no	—
508	C₂×Dic₄₃	—	2	2	no	—
509	C₂×Dic₄₃	—	4	2	no	—
510	C₂×Dic₄₃	—	8	1	no	—
511	C₂×Dic₄₃	—	8	1	no	—
512	C₂×Dic₄₃	C₂²×D₄	1	2	yes	—
513	C₂×Dic₄₃	C₂²×D₄	1	2	yes	—
514	C₂×Dic₄₃	C₂²×D₄	1	2	yes	—
515	D₁₇₂	—	2	2	no	—
516	D₁₇₂	—	2	2	no	—
517	D₁₇₂	—	2	2	no	—
518	D₁₇₂	—	4	2	no	—
519	D₁₇₂	—	8	2	no	—
520	D₁₇₂	—	8	2	no	—
521	C₄×D₄₃	—	2	4	no	—
522	C₄×D₄₃	—	2	2	no	—
523	C₄×D₄₃	—	2	2	no	—
524	C₄×D₄₃	—	4	2	no	—
525	C₄×D₄₃	—	4	4	no	—
526	C₄×D₄₃	—	8	2	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	—	8	2	no	—
533	C₈×C₄₃	—	2	1	no	—
534	C₈×C₄₃	—	2	1	no	—
535	C₈×C₄₃	C₂×#41	1	2	yes	—
536	C₈×C₄₃	C₂×#41	1	2	yes	—
537	C₄₃⋊C₈	—	2	2	no	—
538	C₄₃⋊C₈	C₂×#41	1	4	yes	—
539	#60694	—	43	1	no	maximal, Sylow
540	C₂²×C₄₃	—	2	1	no	—
541	C₂²×C₄₃	—	2	1	no	—
542	C₂²×C₄₃	—	4	1	no	—
543	C₂²×C₄₃	—	4	1	no	—
544	C₂²×C₄₃	—	4	1	no	—
545	C₂²×C₄₃	—	4	1	no	—
546	C₂²×C₄₃	—	4	1	no	—
547	C₂²×C₄₃	—	4	1	no	—
548	C₂²×C₄₃	#532	1	2	yes	—
549	C₂²×C₄₃	C₂³×D₄	1	1	yes	characteristic
550	C₂×D₄₃	—	2	2	no	—
551	C₂×D₄₃	—	2	2	no	—
552	C₂×D₄₃	—	2	2	no	—
553	C₂×D₄₃	—	4	2	no	—
554	C₂×D₄₃	—	4	2	no	—
555	C₂×D₄₃	—	4	2	no	—
556	C₂×D₄₃	—	8	4	no	—
557	C₄×C₄₃	—	2	1	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	#532	1	2	yes	—
567	C₄×C₄₃	#577	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	—	4	2	no	—
574	Dic₄₃	—	4	2	no	—
575	Dic₄₃	—	4	2	no	—
576	#3461	—	43	1	no	—
577	#3460	—	43	1	no	—
578	#3179	—	43	2	no	—
579	#3178	—	43	2	no	—
580	#3174	—	43	2	no	—
581	#3173	—	43	2	no	—
582	#3172	—	43	2	no	—
583	#3171	—	43	2	no	—
584	#3168	—	43	2	no	—
585	#3167	—	43	2	no	—
586	#3163	—	43	1	no	—
587	#3154	—	43	1	no	—
588	#3137	—	43	1	no	—
589	#3136	—	43	1	no	—
590	#3063	—	43	1	no	—
591	#3062	—	43	1	no	—
592	#3060	—	43	1	no	—
593	#3057	—	43	1	no	—
594	C₄×#137	—	43	1	no	—
595	C₄×AGL(1,ℤ/8)	—	43	1	no	—
596	C₄×#135	D₄₃	1	1	yes	characteristic, complemented
597	C₂×C₄×SD₁₆	—	43	1	no	—
598	C₄×#131	—	43	1	no	—
599	C₂×C₄₃	—	2	2	no	—
600	C₂×C₄₃	—	8	1	no	—
601	C₂×C₄₃	—	8	1	no	—
602	C₂×C₄₃	C₂×#532	1	1	yes	characteristic
603	C₂×C₄₃	C₂×#577	1	1	yes	characteristic
604	C₂×C₄₃	#3584	1	1	yes	characteristic
605	D₄₃	—	4	2	no	—
606	D₄₃	—	8	2	no	—
607	C₂×#137	—	43	1	no	—
608	C₂×AGL(1,ℤ/8)	—	43	1	no	—
609	C₂×#135	C₂×D₄₃	1	1	yes	characteristic
610	C₂²×SD₁₆	—	43	1	no	—
611	C₂×#131	—	43	1	no	—
612	C₂×#131	—	43	1	no	—
613	#544	—	43	1	no	—
614	#544	—	43	1	no	—
615	#542	—	43	2	no	—
616	#542	—	43	2	no	—
617	#542	—	86	1	no	—
618	#542	—	86	1	no	—
619	#541	—	43	2	no	—
620	#541	—	86	1	no	—
621	#540	—	43	2	no	—
622	#540	—	86	1	no	—
623	#539	—	86	2	no	—
624	#538	—	86	2	no	—
625	#537	—	43	1	no	—
626	#537	—	43	1	no	—
627	#536	—	43	1	no	—
628	#536	—	43	1	no	—
629	#535	—	43	1	no	—
630	#535	—	43	1	no	—
631	#533	—	43	2	no	—
632	#533	—	86	1	no	—
633	#532	—	43	2	no	—
634	#532	—	86	1	no	—
635	#529	—	43	2	no	—
636	#529	—	43	2	no	—
637	#529	—	86	1	no	—
638	#529	—	86	1	no	—
639	#529	—	86	2	no	—
640	#525	—	86	2	no	—
641	C₄×#41	—	43	1	no	—
642	C₄×#41	C₂×D₄₃	1	1	yes	characteristic
643	C₄×#41	C₂×D₄₃	1	1	yes	characteristic
644	C₂×C₄×Q₈	—	43	1	no	—
645	C₂×C₄×D₄	—	43	1	no	—
646	#501	—	43	2	no	—
647	#501	—	43	2	no	—
648	#499	—	43	2	no	—
649	#498	—	43	2	no	—
650	#497	—	43	2	no	—
651	#496	—	43	2	no	—
652	#495	—	43	2	no	—
653	#492	—	43	2	no	—
654	#491	—	43	2	no	—
655	#490	—	43	2	no	—
656	#489	—	43	2	no	—
657	#489	—	43	2	no	—
658	#488	—	43	2	no	—
659	#488	—	43	2	no	—
660	#487	—	43	2	no	—
661	#486	—	43	2	no	—
662	#470	—	43	2	no	—
663	#470	—	43	2	no	—
664	#469	—	43	2	no	—
665	#469	—	43	2	no	—
666	#468	—	43	2	no	—
667	#468	—	43	2	no	—
668	#468	—	43	2	no	—
669	#468	—	43	2	no	—
670	#467	—	43	2	no	—
671	#466	—	43	2	no	—
672	#465	—	43	2	no	—
673	#465	—	43	2	no	—
674	#465	—	43	2	no	—
675	#465	—	43	2	no	—
676	#465	—	43	2	no	—
677	#465	—	43	2	no	—
678	#442	—	43	2	no	—
679	#441	—	43	2	no	—
680	#440	—	43	2	no	—
681	#440	—	43	2	no	—
682	C₄×Q₁₆	—	43	2	no	—
683	C₄×Q₁₆	C₂×D₄₃	1	1	yes	characteristic, complemented
684	C₄×Q₁₆	C₂×D₄₃	1	1	yes	characteristic, complemented
685	C₄×SD₁₆	—	43	2	no	—
686	C₄×SD₁₆	—	43	2	no	—
687	C₄×SD₁₆	—	43	2	no	—
688	C₄×SD₁₆	—	43	2	no	—
689	C₄×SD₁₆	—	43	2	no	—
690	C₄×SD₁₆	—	43	2	no	—
691	C₄×SD₁₆	C₂×D₄₃	1	1	yes	characteristic, complemented
692	C₄×SD₁₆	C₂×D₄₃	1	1	yes	characteristic, complemented
693	C₄×SD₁₆	C₂×D₄₃	1	1	yes	characteristic, complemented
694	C₄×SD₁₆	C₂×D₄₃	1	1	yes	characteristic, complemented
695	C₄×D₈	—	43	2	no	—
696	C₄×D₈	C₂×D₄₃	1	1	yes	characteristic, complemented
697	C₄×D₈	C₂×D₄₃	1	1	yes	characteristic, complemented
698	#428	—	43	1	no	—
699	#428	—	43	1	no	—
700	#427	C₂×D₄₃	1	1	yes	characteristic
701	C₂×#106	—	43	1	no	—
702	#419	—	43	1	no	—
703	#418	—	43	1	no	—
704	#417	—	43	1	no	—
705	#417	—	43	1	no	—
706	#416	C₂×D₄₃	1	1	yes	characteristic
707	#416	C₂×D₄₃	1	1	yes	characteristic
708	C₂×#103	—	43	1	no	—
709	C₂×#102	—	43	1	no	—
710	#405	—	43	1	no	—
711	#405	—	43	1	no	—
712	#405	—	43	2	no	—
713	#405	—	43	2	no	—
714	C₄×M₁₆	—	43	1	no	—
715	C₄×M₁₆	—	43	2	no	—
716	C₂×C₄×C₈	—	43	2	no	—
717	C₂×C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
718	C₄₃	#60694	1	1	yes	characteristic, complemented, Sylow
719	C₂×#41	—	43	1	no	—
720	C₂×#41	—	86	2	no	—
721	C₂×#41	C₂²×D₄₃	1	1	yes	characteristic
722	C₂×#41	C₂²×D₄₃	1	1	yes	characteristic
723	C₂²×Q₈	—	43	1	no	—
724	C₂²×D₄	—	43	1	no	—
725	C₂³×C₄	—	86	1	no	—
726	#137	—	86	4	no	—
727	AGL(1,ℤ/8)	—	86	4	no	—
728	#135	—	2	4	no	—
729	C₂×Q₁₆	—	43	2	no	—
730	C₂×Q₁₆	C₂²×D₄₃	1	1	yes	characteristic
731	C₂×SD₁₆	—	43	2	no	—
732	C₂×SD₁₆	—	43	2	no	—
733	C₂×SD₁₆	—	43	2	no	—
734	C₂×SD₁₆	—	43	2	no	—
735	C₂×SD₁₆	—	86	4	no	—
736	C₂×SD₁₆	C₂²×D₄₃	1	1	yes	characteristic
737	C₂×SD₁₆	C₂²×D₄₃	1	1	yes	characteristic
738	C₂×D₈	—	43	2	no	—
739	C₂×D₈	C₂²×D₄₃	1	1	yes	characteristic
740	#131	—	86	4	no	—
741	#131	—	86	4	no	—
742	C₂×M₁₆	—	43	1	no	—
743	C₂×M₁₆	—	43	1	no	—
744	C₂×M₁₆	—	43	2	no	—
745	C₂×M₁₆	—	43	2	no	—
746	C₂²×C₈	—	43	2	no	—
747	C₂²×C₈	—	43	2	no	—
748	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
749	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
750	C₄⋊Q₈	—	43	2	no	—
751	C₄⋊Q₈	—	43	2	no	—
752	C₄⋊Q₈	—	43	2	no	—
753	C₄⋊Q₈	—	86	1	no	—
754	C₄⋊Q₈	—	86	1	no	—
755	C₄⋊Q₈	—	86	1	no	—
756	#127	—	43	2	no	—
757	#127	—	86	1	no	—
758	#126	—	86	2	no	—
759	#126	—	86	2	no	—
760	#126	—	86	2	no	—
761	#126	—	86	2	no	—
762	#126	—	86	2	no	—
763	#126	—	86	2	no	—
764	#125	—	43	2	no	—
765	#125	—	43	2	no	—
766	#125	—	86	1	no	—
767	#125	—	86	1	no	—
768	#125	—	86	2	no	—
769	#125	—	86	2	no	—
770	#125	—	86	2	no	—
771	#124	—	43	2	no	—
772	#124	—	43	2	no	—
773	#124	—	86	2	no	—
774	#124	—	86	1	no	—
775	#124	—	86	1	no	—
776	#124	—	86	2	no	—
777	#124	—	86	2	no	—
778	#123	—	86	2	no	—
779	#123	—	86	2	no	—
780	#123	—	86	2	no	—
781	#123	—	86	2	no	—
782	#123	—	86	2	no	—
783	#123	—	86	2	no	—
784	#123	—	86	2	no	—
785	#123	—	86	2	no	—
786	C₂²⋊Q₈	—	43	2	no	—
787	C₂²⋊Q₈	—	43	2	no	—
788	C₂²⋊Q₈	—	43	2	no	—
789	C₂²⋊Q₈	—	43	2	no	—
790	C₂²⋊Q₈	—	86	2	no	—
791	C₂²⋊Q₈	—	86	2	no	—
792	C₂²⋊Q₈	—	86	2	no	—
793	C₂²⋊Q₈	—	86	2	no	—
794	C₂²⋊Q₈	—	86	1	no	—
795	C₂²⋊Q₈	—	86	1	no	—
796	C₂²⋊Q₈	—	86	2	no	—
797	C₂²⋊Q₈	—	86	1	no	—
798	C₂²⋊Q₈	—	86	1	no	—
799	#121	—	43	2	no	—
800	#121	—	43	2	no	—
801	#121	—	43	2	no	—
802	#121	—	43	2	no	—
803	#121	—	86	2	no	—
804	#121	—	86	2	no	—
805	#121	—	86	2	no	—
806	#121	—	86	1	no	—
807	#121	—	86	1	no	—
808	#121	—	86	1	no	—
809	#121	—	86	1	no	—
810	#121	—	86	2	no	—
811	#121	—	86	2	no	—
812	#120	—	86	2	no	—
813	#120	—	86	2	no	—
814	C₄×Q₈	—	43	1	no	—
815	C₄×Q₈	—	43	1	no	—
816	C₄×Q₈	—	43	2	no	—
817	C₄×Q₈	—	43	2	no	—
818	C₄×Q₈	—	86	2	no	—
819	C₄×Q₈	—	86	1	no	—
820	C₄×Q₈	—	86	1	no	—
821	C₄×Q₈	C₂²×D₄₃	1	1	yes	characteristic
822	C₄×Q₈	C₂²×D₄₃	1	1	yes	characteristic
823	C₄×Q₈	C₂²×D₄₃	1	1	yes	characteristic
824	C₄×Q₈	C₂²×D₄₃	1	1	yes	characteristic
825	C₄×D₄	—	2	1	no	—
826	C₄×D₄	—	2	1	no	—
827	C₄×D₄	—	2	1	no	—
828	C₄×D₄	—	2	1	no	—
829	C₄×D₄	—	43	2	no	—
830	C₄×D₄	—	43	2	no	—
831	C₄×D₄	—	43	1	no	—
832	C₄×D₄	—	43	1	no	—
833	C₄×D₄	—	43	2	no	—
834	C₄×D₄	—	43	2	no	—
835	C₄×D₄	—	86	2	no	—
836	C₄×D₄	—	86	2	no	—
837	C₄×D₄	—	86	2	no	—
838	C₄×D₄	—	86	1	no	—
839	C₄×D₄	—	86	1	no	—
840	C₄×D₄	C₂²×D₄₃	1	1	yes	characteristic
841	C₄×D₄	C₂²×D₄₃	1	1	yes	characteristic
842	C₄×D₄	C₂²×D₄₃	1	1	yes	characteristic
843	C₄×D₄	C₂²×D₄₃	1	1	yes	characteristic
844	#117	—	2	1	no	—
845	#117	—	2	1	no	—
846	#117	—	43	1	no	—
847	#117	—	43	2	no	—
848	#117	—	86	2	no	—
849	#117	—	86	2	no	—
850	#117	—	86	2	no	—
851	#117	C₂²×D₄₃	1	1	yes	characteristic
852	#117	C₂²×D₄₃	1	1	yes	characteristic
853	C₂×C₄⋊C₄	—	43	1	no	—
854	C₂×C₄⋊C₄	—	43	1	no	—
855	C₂×C₄⋊C₄	—	86	1	no	—
856	C₂×C₂²⋊C₄	—	86	1	no	—
857	C₂×C₄²	—	2	1	no	—
858	C₂×C₄²	—	2	1	no	—
859	C₂×C₄²	—	43	2	no	—
860	C₂×C₄²	—	86	1	no	—
861	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
862	#107	—	43	2	no	—
863	#107	—	43	2	no	—
864	#107	C₂²×D₄₃	1	1	yes	characteristic
865	#107	C₂²×D₄₃	1	1	yes	characteristic
866	#106	—	43	2	no	—
867	#106	—	43	2	no	—
868	#106	—	43	2	no	—
869	#106	—	43	2	no	—
870	#106	C₂²×D₄₃	1	1	yes	characteristic
871	#106	C₂²×D₄₃	1	1	yes	characteristic
872	#103	—	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	C₂²×D₄₃	1	1	yes	characteristic
879	#103	C₂²×D₄₃	1	1	yes	characteristic
880	#103	C₂²×D₄₃	1	1	yes	characteristic
881	#103	C₂²×D₄₃	1	1	yes	characteristic
882	#102	—	43	2	no	—
883	#102	—	43	2	no	—
884	#102	—	43	2	no	—
885	#102	—	43	2	no	—
886	#102	—	43	2	no	—
887	#102	—	43	2	no	—
888	#102	C₂²×D₄₃	1	1	yes	characteristic
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	#97	—	43	2	no	—
893	#97	—	43	2	no	—
894	#97	—	43	2	no	—
895	C₄×C₈	—	43	2	no	—
896	C₄×C₈	—	43	2	no	—
897	C₄×C₈	—	43	2	no	—
898	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
899	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
900	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
901	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
902	C₂⁴	—	86	1	no	—
903	#41	—	2	2	no	—
904	#41	—	2	2	no	—
905	#41	—	2	2	no	—
906	#41	—	2	2	no	—
907	#41	—	86	2	no	—
908	#41	—	86	2	no	—
909	#41	—	344	4	no	—
910	C₂×Q₈	—	43	1	no	—
911	C₂×Q₈	—	43	2	no	—
912	C₂×Q₈	—	86	2	no	—
913	C₂×Q₈	—	86	2	no	—
914	C₂×Q₈	—	86	1	no	—
915	C₂×Q₈	—	86	2	no	—
916	C₂×Q₈	—	86	2	no	—
917	C₂×Q₈	C₂³×D₄₃	1	1	yes	characteristic
918	C₂×Q₈	C₂³×D₄₃	1	1	yes	characteristic
919	C₂×D₄	—	2	1	no	—
920	C₂×D₄	—	2	1	no	—
921	C₂×D₄	—	43	2	no	—
922	C₂×D₄	—	43	1	no	—
923	C₂×D₄	—	43	2	no	—
924	C₂×D₄	—	86	2	no	—
925	C₂×D₄	—	86	2	no	—
926	C₂×D₄	—	86	2	no	—
927	C₂×D₄	—	86	2	no	—
928	C₂×D₄	—	86	2	no	—
929	C₂×D₄	—	86	2	no	—
930	C₂×D₄	—	86	1	no	—
931	C₂×D₄	—	86	2	no	—
932	C₂×D₄	—	86	2	no	—
933	C₂×D₄	C₂³×D₄₃	1	1	yes	characteristic
934	C₂×D₄	C₂³×D₄₃	1	1	yes	characteristic
935	C₂²×C₄	—	2	1	no	—
936	C₂²×C₄	—	2	1	no	—
937	C₂²×C₄	—	2	1	no	—
938	C₂²×C₄	—	2	1	no	—
939	C₂²×C₄	—	2	1	no	—
940	C₂²×C₄	—	2	1	no	—
941	C₂²×C₄	—	43	2	no	—
942	C₂²×C₄	—	43	2	no	—
943	C₂²×C₄	—	43	2	no	—
944	C₂²×C₄	—	86	1	no	—
945	C₂²×C₄	—	86	1	no	—
946	C₂²×C₄	—	86	1	no	—
947	C₂²×C₄	—	86	2	no	—
948	C₂²×C₄	—	86	2	no	—
949	C₂²×C₄	—	344	2	no	—
950	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
951	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
952	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
953	Q₁₆	—	2	2	no	—
954	Q₁₆	—	86	4	no	—
955	SD₁₆	—	2	2	no	—
956	SD₁₆	—	2	2	no	—
957	SD₁₆	—	86	4	no	—
958	SD₁₆	—	86	4	no	—
959	SD₁₆	—	86	4	no	—
960	SD₁₆	—	86	4	no	—
961	D₈	—	2	2	no	—
962	D₈	—	86	4	no	—
963	M₁₆	—	43	4	no	—
964	M₁₆	—	86	4	no	—
965	M₁₆	—	86	2	no	—
966	M₁₆	—	86	4	no	—
967	C₂×C₈	—	2	2	no	—
968	C₂×C₈	—	43	2	no	—
969	C₂×C₈	—	43	2	no	—
970	C₂×C₈	—	86	4	no	—
971	C₂×C₈	—	86	4	no	—
972	C₂×C₈	#10621898	1	4	yes	complemented
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	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
977	C₄⋊C₄	—	2	1	no	—
978	C₄⋊C₄	—	2	1	no	—
979	C₄⋊C₄	—	2	1	no	—
980	C₄⋊C₄	—	2	1	no	—
981	C₄⋊C₄	—	43	1	no	—
982	C₄⋊C₄	—	43	1	no	—
983	C₄⋊C₄	—	43	2	no	—
984	C₄⋊C₄	—	43	2	no	—
985	C₄⋊C₄	—	43	2	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	1	no	—
1001	C₄⋊C₄	—	86	2	no	—
1002	C₄⋊C₄	—	86	2	no	—
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	C₂²⋊C₄	—	2	1	no	—
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	—	43	2	no	—
1014	C₂²⋊C₄	—	43	2	no	—
1015	C₂²⋊C₄	—	43	2	no	—
1016	C₂²⋊C₄	—	86	2	no	—
1017	C₂²⋊C₄	—	86	2	no	—
1018	C₂²⋊C₄	—	86	2	no	—
1019	C₂²⋊C₄	—	86	2	no	—
1020	C₂²⋊C₄	—	86	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	—	2	1	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	D₄×D₄₃	1	1	yes	characteristic
1042	C₄²	D₄×D₄₃	1	1	yes	characteristic
1043	C₄²	C₂³×D₄₃	1	1	yes	characteristic
1044	C₄²	C₂³×D₄₃	1	1	yes	characteristic
1045	C₂³	—	2	1	no	—
1046	C₂³	—	2	1	no	—
1047	C₂³	—	43	2	no	—
1048	C₂³	—	86	2	no	—
1049	C₂³	—	344	1	no	—
1050	C₂³	—	344	1	no	—
1051	C₂³	—	172	2	no	—
1052	C₂³	C₂×D₄×D₄₃	1	1	yes	characteristic
1053	Q₈	—	2	1	no	—
1054	Q₈	—	2	1	no	—
1055	Q₈	—	2	1	no	—
1056	Q₈	—	2	1	no	—
1057	Q₈	—	86	2	no	—
1058	Q₈	—	86	2	no	—
1059	Q₈	—	86	2	no	—
1060	Q₈	—	344	2	no	—
1061	Q₈	—	344	2	no	—
1062	Q₈	—	172	2	no	—
1063	D₄	—	2	1	no	—
1064	D₄	—	2	1	no	—
1065	D₄	—	2	1	no	—
1066	D₄	—	2	1	no	—
1067	D₄	—	4	2	no	—
1068	D₄	—	4	2	no	—
1069	D₄	—	86	4	no	—
1070	D₄	—	86	2	no	—
1071	D₄	—	86	2	no	—
1072	D₄	—	86	2	no	—
1073	D₄	—	344	2	no	—
1074	D₄	—	344	2	no	—
1075	D₄	—	344	2	no	—
1076	D₄	—	344	2	no	—
1077	D₄	—	344	2	no	—
1078	D₄	—	344	2	no	—
1079	D₄	—	172	2	no	—
1080	C₂×C₄	—	2	2	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	—	4	1	no	—
1088	C₂×C₄	—	4	2	no	—
1089	C₂×C₄	—	4	2	no	—
1090	C₂×C₄	—	4	2	no	—
1091	C₂×C₄	—	4	2	no	—
1092	C₂×C₄	—	8	1	no	—
1093	C₂×C₄	—	8	1	no	—
1094	C₂×C₄	—	43	2	no	—
1095	C₂×C₄	—	43	2	no	—
1096	C₂×C₄	—	43	2	no	—
1097	C₂×C₄	—	86	4	no	—
1098	C₂×C₄	—	86	2	no	—
1099	C₂×C₄	—	86	2	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	1	no	—
1105	C₂×C₄	—	344	1	no	—
1106	C₂×C₄	—	172	2	no	—
1107	C₂×C₄	—	172	2	no	—
1108	C₂×C₄	—	172	4	no	—
1109	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
1110	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
1111	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
1112	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
1113	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
1114	C₂×C₄	#41×D₄₃	1	2	yes	—
1115	C₂×C₄	C₂×#10621898	1	2	yes	—
1116	C₂×C₄	C₂⁴×D₄₃	1	1	yes	characteristic
1117	C₈	—	2	1	no	—
1118	C₈	—	2	1	no	—
1119	C₈	—	43	4	no	—
1120	C₈	—	86	2	no	—
1121	C₈	C₂×#10621898	1	2	yes	—
1122	C₈	C₂×#10621898	1	2	yes	—
1123	C₂²	—	2	1	no	—
1124	C₂²	—	2	1	no	—
1125	C₂²	—	4	1	no	—
1126	C₂²	—	4	1	no	—
1127	C₂²	—	4	1	no	—
1128	C₂²	—	4	1	no	—
1129	C₂²	—	4	1	no	—
1130	C₂²	—	4	1	no	—
1131	C₂²	—	86	2	no	—
1132	C₂²	—	86	2	no	—
1133	C₂²	—	86	2	no	—
1134	C₂²	—	344	4	no	—
1135	C₂²	—	172	2	no	—
1136	C₂²	—	172	2	no	—
1137	C₂²	—	172	2	no	—
1138	C₂²	#14583446	1	2	yes	—
1139	C₂²	C₂²×D₄×D₄₃	1	1	yes	characteristic
1140	C₄	—	2	1	no	—
1141	C₄	—	2	1	no	—
1142	C₄	—	2	1	no	—
1143	C₄	—	4	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	—	86	2	no	—
1150	C₄	—	86	2	no	—
1151	C₄	—	86	2	no	—
1152	C₄	—	172	2	no	—
1153	C₄	—	172	2	no	—
1154	C₄	—	172	2	no	—
1155	C₄	#14583446	1	2	yes	—
1156	C₄	#14583706	1	2	yes	—
1157	C₄	C₂×#41×D₄₃	1	1	yes	characteristic
1158	C₄	C₂²×#10621898	1	1	yes	characteristic
1159	C₂	—	2	2	no	—
1160	C₂	—	8	1	no	—
1161	C₂	—	8	1	no	—
1162	C₂	—	344	2	no	—
1163	C₂	—	172	2	no	—
1164	C₂	C₂×#14583446	1	1	yes	characteristic
1165	C₂	C₂×#14583706	1	1	yes	characteristic
1166	C₂	#19149364	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₄₃
commutator, cosocle	C₂×C₄×C₄₃	C₂⁵
Frattini	C₂×C₄	C₂⁴×D₄₃
Fitting	C₄×#135×C₄₃	C₂
socle	C₂²×C₄₃	C₂³×D₄
hypercenter	C₄×#135	D₄₃
hypocenter	C₄₃	#60694
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₄×#135

Complements

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

N	H ≅ G/N	type
1. #19148022	C₂	semidirect
2. #19148011	C₂	semidirect
3. #19145282	C₂	semidirect
4. #19145267	C₂	semidirect
5. #19145219	C₂	semidirect
6. #19145208	C₂	semidirect
7. #19145199	C₂	semidirect
8. #19145188	C₂	semidirect
9. #19145161	C₂	semidirect
10. #19145151	C₂	semidirect
11. #19145127	C₂	semidirect
12. #19145072	C₂	semidirect
13. #19144964	C₂	semidirect
14. #19144953	C₂	semidirect
15. #19144289	C₂	semidirect
16. #19144278	C₂	semidirect
17. #19144253	C₂	semidirect
18. #19144235	C₂	semidirect
19. C₄×#13063355	C₂	semidirect
20. C₄×#13063350	C₂	semidirect
21. C₂×C₄×#10621873	C₂	semidirect
22. C₄×#13063331	C₂	semidirect
23. C₄×#135×C₄₃	C₂	semidirect
34. #14583514	C₂²	semidirect
36. #14583507	C₂²	semidirect
48. #14583453	C₂²	semidirect
54. #14583431	C₂²	semidirect
60. #14583307	C₂²	semidirect
61. #14583307	C₂²	semidirect
62. #14583299	C₂²	semidirect
63. #14583296	C₂²	semidirect
68. #14583266	C₂²	semidirect
71. #14583257	C₂²	semidirect
73. #14583252	C₂²	semidirect
74. #14583248	C₂²	semidirect
76. #14583156	C₂²	semidirect
77. #14583154	C₂²	semidirect
79. #14583149	C₂²	semidirect
83. #14583144	C₂²	semidirect
84. #14583139	C₂²	semidirect
89. #14583127	C₂²	semidirect
90. #14583125	C₂²	semidirect
91. #14583125	C₂²	semidirect
93. #14583004	C₂²	semidirect
94. #14582999	C₂²	semidirect
96. C₄×#10621885	C₂²	semidirect
102. C₄×#10621883	C₂²	semidirect
115. #14582853	C₂²	semidirect
116. #14582853	C₂²	semidirect
118. C₄×#10621872	C₂²	semidirect
119. C₄×C₈×D₄₃	C₂²	semidirect
123. C₄×Q₁₆×C₄₃	C₂²	semidirect
124. C₄×Q₁₆×C₄₃	C₂²	semidirect
125. C₄×SD₁₆×C₄₃	C₂²	semidirect
126. C₄×SD₁₆×C₄₃	C₂²	semidirect
127. C₄×SD₁₆×C₄₃	C₂²	semidirect
128. C₄×SD₁₆×C₄₃	C₂²	semidirect
129. C₄×D₈×C₄₃	C₂²	semidirect
130. C₄×D₈×C₄₃	C₂²	semidirect
374. C₂×C₈×C₄₃	#41	semidirect
452. #10621877	#41	semidirect
596. C₄×#135	D₄₃	semidirect
683. C₄×Q₁₆	C₂×D₄₃	semidirect
684. C₄×Q₁₆	C₂×D₄₃	semidirect
691. C₄×SD₁₆	C₂×D₄₃	semidirect
692. C₄×SD₁₆	C₂×D₄₃	semidirect
693. C₄×SD₁₆	C₂×D₄₃	semidirect
694. C₄×SD₁₆	C₂×D₄₃	semidirect
696. C₄×D₈	C₂×D₄₃	semidirect
697. C₄×D₈	C₂×D₄₃	semidirect
718. C₄₃	#60694	semidirect
972. C₂×C₈	#10621898	semidirect

Maximal subgroups

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

subgroup	index
#19148022	2
#19148011	2
#19145282	2
#19145267	2
#19145219	2
#19145208	2
#19145199	2
#19145188	2
#19145161	2
#19145151	2
#19145127	2
#19145072	2
#19144964	2
#19144953	2
#19144289	2
#19144278	2
#19144253	2
#19144235	2
C₄×#13063355	2
C₄×#13063350	2
C₂×C₄×#10621873	2
C₄×#13063331	2
C₄×#135×C₄₃	2
#60694	43