Subgroups — #25969302

Order 11008.

1700 conjugacy classes of subgroups.

The subgroup lattice has 1100 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19148011	C₂	1	1	yes	maximal, characteristic
2	#19145893	C₂	1	2	yes	maximal, complemented
3	#19145878	C₂	1	2	yes	maximal, complemented
4	#19145848	C₂	1	2	yes	maximal, complemented
5	#19145848	C₂	1	2	yes	maximal, complemented
6	#19145835	C₂	1	2	yes	maximal, complemented
7	#19145785	C₂	1	2	yes	maximal, complemented
8	#19145763	C₂	1	2	yes	maximal, complemented
9	#19145731	C₂	1	2	yes	maximal, complemented
10	#19145129	C₂	1	1	yes	maximal, characteristic, complemented
11	#19145121	C₂	1	1	yes	maximal, characteristic, complemented
12	#19144954	C₂	1	1	yes	maximal, characteristic, complemented
13	#19144954	C₂	1	1	yes	maximal, characteristic, complemented
14	#19144584	C₂	1	1	yes	maximal, characteristic, complemented
15	#19144573	C₂	1	1	yes	maximal, characteristic, complemented
16	#19144553	C₂	1	1	yes	maximal, characteristic, complemented
17	#19144553	C₂	1	1	yes	maximal, characteristic, complemented
18	#19144413	C₂	1	1	yes	maximal, characteristic, complemented
19	#19144388	C₂	1	1	yes	maximal, characteristic, complemented
20	#19144377	C₂	1	1	yes	maximal, characteristic, complemented
21	C₂×#14583196	C₂	1	1	yes	maximal, characteristic, complemented
22	#19143261	C₂	1	1	yes	maximal, characteristic, complemented
23	C₄₃×#3504	C₂	1	1	yes	maximal, characteristic, complemented
24	#14583527	C₂²	1	1	yes	characteristic
25	#14583521	—	2	1	no	—
26	#14583520	C₂²	1	2	yes	—
27	#14583504	C₂²	1	2	yes	—
28	#14583500	—	2	1	no	—
29	#14583482	—	2	2	no	—
30	#14583477	C₂²	1	1	yes	characteristic
31	#14583468	C₂²	1	1	yes	characteristic
32	#14583463	C₂²	1	1	yes	characteristic
33	#14583449	C₂²	1	2	yes	—
34	#14583446	—	2	1	no	—
35	#14583436	—	2	1	no	—
36	#14583433	C₂²	1	2	yes	—
37	#14583408	—	2	2	no	—
38	C₄×#10621898	C₂²	1	1	yes	characteristic
39	C₂×C₄×D₁₇₂	C₂²	1	1	yes	characteristic
40	#14583309	C₂²	1	2	yes	complemented
41	#14583309	C₂²	1	2	yes	complemented
42	#14583305	C₂²	1	2	yes	complemented
43	#14583305	C₂²	1	2	yes	complemented
44	#14583302	C₂²	1	2	yes	complemented
45	#14583298	C₂²	1	2	yes	complemented
46	#14583298	C₂²	1	2	yes	complemented
47	#14583295	C₂²	1	2	yes	complemented
48	#14583265	C₂²	1	2	yes	—
49	#14583265	C₂²	1	2	yes	—
50	#14583261	C₂²	1	2	yes	—
51	#14583261	C₂²	1	2	yes	—
52	#14583256	C₂²	1	2	yes	—
53	#14583256	C₂²	1	2	yes	—
54	#14583247	C₂²	1	2	yes	—
55	#14583247	C₂²	1	2	yes	—
56	#14583240	C₂²	1	2	yes	complemented
57	#14583240	C₂²	1	2	yes	complemented
58	#14583234	C₂²	1	2	yes	complemented
59	#14583229	C₂²	1	2	yes	complemented
60	#14583223	C₂²	1	2	yes	—
61	#14583223	C₂²	1	2	yes	—
62	#14583223	C₂²	1	2	yes	—
63	#14583223	C₂²	1	2	yes	—
64	#14583223	C₂²	1	2	yes	complemented
65	#14583223	C₂²	1	2	yes	complemented
66	#14583217	C₂²	1	2	yes	—
67	#14583217	C₂²	1	2	yes	—
68	#14583217	C₂²	1	2	yes	complemented
69	#14583212	C₂²	1	2	yes	—
70	#14583212	C₂²	1	2	yes	—
71	#14583212	C₂²	1	2	yes	complemented
72	#14583203	C₂²	1	1	yes	characteristic, complemented
73	#14583203	C₂²	1	2	yes	complemented
74	#14583203	C₂²	1	1	yes	characteristic, complemented
75	#14583203	C₂²	1	2	yes	complemented
76	#14583196	C₂²	1	2	yes	—
77	#14583196	C₂²	1	2	yes	—
78	#14583196	C₂²	1	2	yes	—
79	#14583196	C₂²	1	2	yes	—
80	#14583196	C₂²	1	2	yes	—
81	#14583196	C₂²	1	2	yes	—
82	#14583196	C₂²	1	1	yes	characteristic, complemented
83	#14583196	C₂²	1	2	yes	complemented
84	#14583196	C₂²	1	1	yes	characteristic, complemented
85	#14583196	C₂²	1	2	yes	complemented
86	#14583191	C₂²	1	1	yes	characteristic, complemented
87	#14583186	C₂²	1	2	yes	—
88	#14583186	C₂²	1	1	yes	characteristic, complemented
89	#14583181	C₂²	1	1	yes	characteristic, complemented
90	#14583176	C₂²	1	2	yes	—
91	#14583176	C₂²	1	1	yes	characteristic, complemented
92	#14582960	C₂²	1	2	yes	complemented
93	#14582960	C₂²	1	2	yes	complemented
94	#14582956	C₂²	1	2	yes	complemented
95	#14582952	C₂²	1	2	yes	complemented
96	#14582942	C₂²	1	1	yes	characteristic
97	#14582942	C₂²	1	1	yes	characteristic
98	#14582939	C₂²	1	1	yes	characteristic
99	#14582939	C₂²	1	1	yes	characteristic
100	#14582935	C₂²	1	1	yes	characteristic
101	#14582935	C₂²	1	1	yes	characteristic
102	C₂×#13063258	C₂²	1	1	yes	characteristic
103	C₂×#13063256	C₂²	1	1	yes	characteristic
104	#14582923	C₂²	1	1	yes	characteristic
105	C₂×C₄⋊(C₄₃⋊C₈)	C₂²	1	1	yes	characteristic
106	#14582903	C₂²	1	1	yes	characteristic
107	#14582903	C₂²	1	1	yes	characteristic
108	#14582898	C₂²	1	1	yes	characteristic
109	#14582898	C₂²	1	1	yes	characteristic
110	#14582893	C₂²	1	1	yes	characteristic
111	#14582893	C₂²	1	1	yes	characteristic
112	C₂×#13063245	C₂²	1	1	yes	characteristic
113	C₂×#13063245	C₂²	1	1	yes	characteristic
114	#14582866	C₂²	1	1	yes	characteristic
115	#14582866	C₂²	1	1	yes	characteristic
116	#14582855	C₂²	1	1	yes	characteristic
117	#14582855	C₂²	1	1	yes	characteristic
118	C₄₃×#557	—	2	1	no	—
119	C₄₃×#557	—	2	1	no	—
120	C₄₃×#554	—	2	2	no	—
121	C₄₃×#554	—	2	2	no	—
122	C₄₃×#554	—	2	1	no	—
123	C₄₃×#554	—	2	1	no	—
124	C₄₃×#544	C₂²	1	1	yes	characteristic
125	C₄₃×#544	C₂²	1	1	yes	characteristic
126	C₄₃×#544	C₂²	1	2	yes	complemented
127	C₄₃×#544	C₂²	1	2	yes	complemented
128	C₄₃×#533	C₂²	1	1	yes	characteristic
129	C₄₃×#533	C₂²	1	2	yes	complemented
130	C₂×#125×C₄₃	C₂²	1	1	yes	characteristic
131	C₂×#125×C₄₃	C₂²	1	2	yes	complemented
132	C₄₃×#520	C₂²	1	1	yes	characteristic
133	C₄₃×#520	C₂²	1	1	yes	characteristic
134	C₄×#41×C₄₃	C₂²	1	1	yes	characteristic
135	C₂×#10621898	—	2	2	no	—
136	C₂×#10621898	C₂³	1	1	yes	characteristic
137	C₂²×D₁₇₂	C₂³	1	1	yes	characteristic
138	C₂²×C₄×D₄₃	—	2	1	no	—
139	C₂×#10621877	C₂³	1	1	yes	characteristic
140	C₂×#10621877	C₂³	1	1	yes	characteristic
141	C₂²×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
142	C₂²×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
143	#13063325	C₂³	1	2	yes	—
144	#13063324	—	2	1	no	—
145	#13063322	C₂³	1	2	yes	—
146	#13063321	—	2	1	no	—
147	#13063320	—	2	2	no	—
148	#13063319	—	2	2	no	—
149	#13063317	C₂³	1	2	yes	—
150	#13063316	—	2	1	no	—
151	#13063314	—	2	1	no	—
152	#13063313	—	2	2	no	—
153	#13063313	C₂³	1	2	yes	—
154	#13063311	—	2	2	no	—
155	#13063310	—	2	2	no	—
156	#13063310	—	2	2	no	—
157	#13063308	—	2	2	no	—
158	#13063307	—	2	2	no	—
159	#13063304	C₂³	1	2	yes	—
160	#13063303	—	2	2	no	—
161	#13063302	—	2	2	no	—
162	#13063301	—	2	1	no	—
163	#13063300	—	2	1	no	—
164	#13063300	—	2	1	no	—
165	#13063299	—	2	2	no	—
166	#13063299	C₂³	1	2	yes	—
167	#13063299	C₂³	1	2	yes	—
168	#13063299	C₂³	1	2	yes	—
169	#13063298	—	2	2	no	—
170	#13063298	—	2	2	no	—
171	#13063297	—	2	2	no	—
172	#13063296	—	2	1	no	—
173	#13063295	—	2	2	no	—
174	#13063293	—	2	2	no	—
175	C₄×Dic₈₆	C₂³	1	1	yes	characteristic
176	C₄×Dic₈₆	C₂³	1	1	yes	characteristic
177	C₄×D₁₇₂	—	2	1	no	—
178	C₄×D₁₇₂	—	2	1	no	—
179	C₄×D₁₇₂	—	2	2	no	—
180	C₄×D₁₇₂	C₂³	1	2	yes	—
181	C₄×D₁₇₂	C₂³	1	2	yes	—
182	C₄×D₁₇₂	C₂³	1	1	yes	characteristic
183	C₄×D₁₇₂	C₂³	1	1	yes	characteristic
184	C₄×C₂²⋊D₄₃	—	2	1	no	—
185	C₄×C₂²⋊D₄₃	—	2	1	no	—
186	C₄×C₂²⋊D₄₃	—	2	2	no	—
187	#13063284	C₂³	1	1	yes	characteristic
188	#13063282	—	2	1	no	—
189	#13063282	—	2	2	no	—
190	C₂×C₄⋊Dic₄₃	C₂³	1	1	yes	characteristic
191	C₂×(C₂×D₄₃)⋊C₄	—	2	1	no	—
192	C₄²×D₄₃	—	2	1	no	—
193	#13063258	C₂³	1	1	yes	characteristic
194	#13063258	C₂³	1	2	yes	—
195	#13063258	C₂³	1	2	yes	—
196	#13063258	C₂³	1	2	yes	—
197	#13063258	C₂³	1	1	yes	characteristic
198	#13063258	C₂³	1	2	yes	—
199	#13063258	C₂³	1	2	yes	—
200	#13063258	C₂³	1	1	yes	characteristic
201	#13063258	C₂³	1	2	yes	—
202	#13063258	C₂³	1	1	yes	characteristic
203	#13063256	C₂³	1	1	yes	characteristic
204	#13063256	C₂³	1	2	yes	—
205	#13063256	C₂³	1	2	yes	—
206	#13063256	C₂³	1	2	yes	—
207	#13063256	C₂³	1	1	yes	characteristic
208	#13063256	C₂³	1	2	yes	—
209	#13063256	C₂³	1	2	yes	—
210	#13063256	C₂³	1	1	yes	characteristic
211	#13063256	C₂³	1	2	yes	—
212	#13063256	C₂³	1	1	yes	characteristic
213	C₄⋊(C₄₃⋊C₈)	C₂³	1	1	yes	characteristic
214	C₄⋊(C₄₃⋊C₈)	C₂³	1	1	yes	characteristic
215	C₄⋊(C₄₃⋊C₈)	C₂³	1	1	yes	characteristic
216	C₄⋊(C₄₃⋊C₈)	C₂³	1	1	yes	characteristic
217	C₄⋊(C₄₃⋊C₈)	C₂³	1	2	yes	—
218	C₄⋊(C₄₃⋊C₈)	C₂³	1	2	yes	—
219	#13063248	C₂³	1	1	yes	characteristic
220	#13063248	C₂³	1	1	yes	characteristic
221	#13063248	C₂³	1	1	yes	characteristic
222	#13063248	C₂³	1	1	yes	characteristic
223	#13063248	C₂³	1	2	yes	—
224	#13063248	C₂³	1	2	yes	—
225	#13063245	C₂³	1	2	yes	—
226	#13063245	C₂³	1	2	yes	—
227	#13063245	C₂³	1	2	yes	—
228	#13063245	C₂³	1	2	yes	—
229	#13063245	C₂³	1	1	yes	characteristic
230	#13063245	C₂³	1	1	yes	characteristic
231	#13063245	C₂³	1	1	yes	characteristic
232	#13063245	C₂³	1	1	yes	characteristic
233	#13063245	C₂³	1	2	yes	—
234	#13063245	C₂³	1	2	yes	—
235	#13063245	C₂³	1	2	yes	—
236	#13063245	C₂³	1	2	yes	—
237	#13063245	C₂³	1	2	yes	—
238	#13063245	C₂³	1	2	yes	—
239	C₂²⋊(C₄₃⋊C₈)	C₂³	1	2	yes	—
240	C₂²⋊(C₄₃⋊C₈)	C₂³	1	2	yes	—
241	C₂²⋊(C₄₃⋊C₈)	C₂³	1	2	yes	—
242	C₂²⋊(C₄₃⋊C₈)	C₂³	1	2	yes	—
243	#13063236	C₂³	1	2	yes	—
244	#13063236	C₂³	1	2	yes	—
245	C₄×C₄₃⋊C₈	C₂³	1	2	yes	—
246	C₄×C₄₃⋊C₈	C₂³	1	2	yes	—
247	C₂×#41×C₄₃	C₂³	1	1	yes	characteristic
248	C₄⋊Q₈×C₄₃	—	2	1	no	—
249	C₄⋊Q₈×C₄₃	—	2	1	no	—
250	C₄⋊Q₈×C₄₃	—	2	2	no	—
251	C₄⋊Q₈×C₄₃	—	2	2	no	—
252	C₄⋊Q₈×C₄₃	C₂³	1	2	yes	—
253	C₄⋊Q₈×C₄₃	C₂³	1	2	yes	—
254	C₄⋊Q₈×C₄₃	C₂³	1	1	yes	characteristic
255	C₄⋊Q₈×C₄₃	C₂³	1	1	yes	characteristic
256	#125×C₄₃	—	2	1	no	—
257	#125×C₄₃	—	2	1	no	—
258	#125×C₄₃	—	2	2	no	—
259	#125×C₄₃	—	2	2	no	—
260	#125×C₄₃	—	2	1	no	—
261	#125×C₄₃	—	2	1	no	—
262	#125×C₄₃	—	2	2	no	—
263	#125×C₄₃	—	2	2	no	—
264	#125×C₄₃	C₂³	1	2	yes	—
265	#125×C₄₃	C₂³	1	2	yes	—
266	#125×C₄₃	C₂³	1	2	yes	—
267	#125×C₄₃	C₂³	1	2	yes	—
268	#125×C₄₃	C₂³	1	1	yes	characteristic
269	#125×C₄₃	C₂³	1	1	yes	characteristic
270	C₂²⋊Q₈×C₄₃	—	2	1	no	—
271	C₂²⋊Q₈×C₄₃	—	2	1	no	—
272	C₂²⋊Q₈×C₄₃	—	2	2	no	—
273	C₂²⋊Q₈×C₄₃	—	2	2	no	—
274	C₂²⋊Q₈×C₄₃	—	2	2	no	—
275	C₂²⋊Q₈×C₄₃	—	2	2	no	—
276	C₂²⋊Q₈×C₄₃	—	2	2	no	—
277	C₂²⋊Q₈×C₄₃	—	2	2	no	—
278	C₂²⋊Q₈×C₄₃	—	2	2	no	—
279	C₂²⋊Q₈×C₄₃	—	2	2	no	—
280	C₄×Q₈×C₄₃	—	2	1	no	—
281	C₄×Q₈×C₄₃	—	2	1	no	—
282	C₄×Q₈×C₄₃	—	2	1	no	—
283	C₄×Q₈×C₄₃	—	2	1	no	—
284	C₄×Q₈×C₄₃	—	2	2	no	—
285	C₄×Q₈×C₄₃	—	2	2	no	—
286	C₄×Q₈×C₄₃	D₄	1	1	yes	characteristic
287	C₄×Q₈×C₄₃	D₄	1	1	yes	characteristic
288	C₄×D₄×C₄₃	—	2	2	no	—
289	C₄×D₄×C₄₃	—	2	2	no	—
290	C₄×D₄×C₄₃	—	2	1	no	—
291	C₄×D₄×C₄₃	—	2	1	no	—
292	C₄×D₄×C₄₃	D₄	1	2	yes	—
293	C₄×D₄×C₄₃	D₄	1	1	yes	characteristic
294	C₄×D₄×C₄₃	D₄	1	2	yes	—
295	C₄×D₄×C₄₃	D₄	1	1	yes	characteristic
296	#117×C₄₃	C₂³	1	1	yes	characteristic
297	#117×C₄₃	C₂³	1	1	yes	characteristic
298	#117×C₄₃	C₂³	1	2	yes	—
299	#117×C₄₃	C₂³	1	2	yes	—
300	#117×C₄₃	C₂³	1	1	yes	characteristic
301	#117×C₄₃	C₂³	1	2	yes	—
302	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
303	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
304	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
305	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
306	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
307	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
308	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
309	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
310	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
311	C₂×C₄²×C₄₃	C₂³	1	2	yes	—
312	C₂³×D₄₃	—	2	1	no	—
313	#41×C₄₃	—	2	2	no	—
314	#41×C₄₃	—	2	2	no	—
315	C₂×Q₈×C₄₃	—	2	1	no	—
316	C₂×Q₈×C₄₃	—	2	2	no	—
317	C₂×Q₈×C₄₃	—	2	2	no	—
318	C₂×Q₈×C₄₃	—	2	1	no	—
319	C₂×Q₈×C₄₃	C₂×D₄	1	1	yes	characteristic
320	C₂×D₄×C₄₃	C₂×D₄	1	2	yes	—
321	C₂×D₄×C₄₃	C₂×D₄	1	1	yes	characteristic
322	C₂²×C₄×C₄₃	—	2	2	no	—
323	C₂²×C₄×C₄₃	—	2	2	no	—
324	C₂²×C₄×C₄₃	—	2	1	no	—
325	C₂²×C₄×C₄₃	—	2	1	no	—
326	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
327	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
328	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
329	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
330	C₂²×C₄×C₄₃	C₂⁴	1	2	yes	—
331	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
332	C₂×C₂²⋊D₄₃	—	2	1	no	—
333	C₂×C₂²⋊D₄₃	—	2	2	no	—
334	C₂×C₂²⋊D₄₃	—	2	2	no	—
335	C₂×C₂²⋊D₄₃	—	2	2	no	—
336	C₂²×Dic₄₃	—	2	1	no	—
337	#10621898	—	2	2	no	—
338	#10621898	—	2	2	no	—
339	#10621898	—	8	4	no	—
340	C₂×D₁₇₂	—	2	1	no	—
341	C₂×D₁₇₂	—	2	2	no	—
342	C₂×D₁₇₂	—	2	2	no	—
343	C₂×D₁₇₂	—	2	2	no	—
344	C₂×D₁₇₂	—	2	2	no	—
345	C₂×D₁₇₂	C₂⁴	1	2	yes	—
346	C₂×D₁₇₂	C₂⁴	1	1	yes	characteristic
347	C₂×C₄×D₄₃	—	2	1	no	—
348	C₂×C₄×D₄₃	—	2	1	no	—
349	C₂×C₄×D₄₃	—	2	2	no	—
350	C₂×C₄×D₄₃	—	2	1	no	—
351	C₂×C₄×D₄₃	—	2	2	no	—
352	C₂×C₄×D₄₃	—	8	2	no	—
353	C₂×Dic₈₆	—	2	2	no	—
354	C₂×Dic₈₆	C₂⁴	1	1	yes	characteristic
355	C₄⋊C₄×C₄₃	—	2	2	no	—
356	C₄⋊C₄×C₄₃	—	2	1	no	—
357	C₄⋊C₄×C₄₃	—	2	2	no	—
358	C₄⋊C₄×C₄₃	—	2	1	no	—
359	C₄⋊C₄×C₄₃	—	2	2	no	—
360	C₄⋊C₄×C₄₃	—	2	2	no	—
361	C₄⋊C₄×C₄₃	—	2	2	no	—
362	C₄⋊C₄×C₄₃	—	2	2	no	—
363	C₄⋊C₄×C₄₃	—	2	2	no	—
364	C₄⋊C₄×C₄₃	—	2	2	no	—
365	C₄⋊C₄×C₄₃	—	2	2	no	—
366	C₄⋊C₄×C₄₃	—	2	2	no	—
367	C₄⋊C₄×C₄₃	—	2	1	no	—
368	C₄⋊C₄×C₄₃	—	2	1	no	—
369	C₄⋊C₄×C₄₃	—	2	1	no	—
370	C₄⋊C₄×C₄₃	—	2	1	no	—
371	C₄⋊C₄×C₄₃	—	2	1	no	—
372	C₄⋊C₄×C₄₃	—	2	2	no	—
373	C₄⋊C₄×C₄₃	—	2	2	no	—
374	C₄⋊C₄×C₄₃	—	2	1	no	—
375	C₄⋊C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
376	C₄⋊C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
377	C₄⋊C₄×C₄₃	C₂×D₄	1	2	yes	—
378	C₄⋊C₄×C₄₃	C₂×D₄	1	2	yes	—
379	C₄⋊C₄×C₄₃	C₂⁴	1	2	yes	—
380	C₄⋊C₄×C₄₃	C₂⁴	1	1	yes	characteristic
381	C₄⋊C₄×C₄₃	C₂⁴	1	2	yes	—
382	C₄⋊C₄×C₄₃	C₂⁴	1	1	yes	characteristic
383	C₄⋊C₄×C₄₃	C₂⁴	1	1	yes	characteristic
384	C₄⋊C₄×C₄₃	C₂⁴	1	1	yes	characteristic
385	C₂²⋊C₄×C₄₃	—	2	2	no	—
386	C₂²⋊C₄×C₄₃	—	2	2	no	—
387	C₂²⋊C₄×C₄₃	—	2	1	no	—
388	C₂²⋊C₄×C₄₃	—	2	1	no	—
389	C₂²⋊C₄×C₄₃	C₂×D₄	1	2	yes	—
390	C₂²⋊C₄×C₄₃	C₂×D₄	1	2	yes	—
391	C₂²⋊C₄×C₄₃	C₂×D₄	1	2	yes	—
392	C₄²×C₄₃	—	2	2	no	—
393	C₄²×C₄₃	—	2	2	no	—
394	C₄²×C₄₃	—	2	1	no	—
395	C₄²×C₄₃	—	2	1	no	—
396	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
397	C₄²×C₄₃	C₂×D₄	1	2	yes	—
398	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
399	C₄²×C₄₃	C₂×D₄	1	2	yes	—
400	C₄²×C₄₃	C₂⁴	1	1	yes	characteristic
401	C₄²×C₄₃	C₂⁴	1	2	yes	—
402	C₄²×C₄₃	C₂⁴	1	1	yes	characteristic
403	C₂²⋊Dic₄₃	—	2	1	no	—
404	C₂²⋊Dic₄₃	—	2	2	no	—
405	(C₂×D₄₃)⋊C₄	—	2	2	no	—
406	(C₂×D₄₃)⋊C₄	—	2	2	no	—
407	(C₂×D₄₃)⋊C₄	—	2	1	no	—
408	(C₂×D₄₃)⋊C₄	—	2	1	no	—
409	(C₂×D₄₃)⋊C₄	—	2	2	no	—
410	(C₂×D₄₃)⋊C₄	—	2	2	no	—
411	(C₂×D₄₃)⋊C₄	—	2	2	no	—
412	(C₂×D₄₃)⋊C₄	—	2	2	no	—
413	(C₂×D₄₃)⋊C₄	—	2	2	no	—
414	C₄⋊Dic₄₃	—	2	1	no	—
415	C₄⋊Dic₄₃	—	2	2	no	—
416	C₄⋊Dic₄₃	C₂⁴	1	2	yes	—
417	C₄⋊Dic₄₃	C₂⁴	1	1	yes	characteristic
418	C₄⋊Dic₄₃	C₂⁴	1	1	yes	characteristic
419	Dic₄₃⋊C₄	—	2	1	no	—
420	Dic₄₃⋊C₄	—	2	1	no	—
421	Dic₄₃⋊C₄	—	2	2	no	—
422	Dic₄₃⋊C₄	—	2	2	no	—
423	Dic₄₃⋊C₄	—	2	2	no	—
424	C₄×Dic₄₃	—	2	1	no	—
425	C₄×Dic₄₃	—	2	1	no	—
426	C₄×Dic₄₃	—	2	1	no	—
427	#10621877	—	2	2	no	—
428	#10621877	—	2	2	no	—
429	C₂×C₄₃⋊C₈	—	2	2	no	—
430	C₂×C₄₃⋊C₈	—	2	2	no	—
431	C₂×C₄₃⋊C₈	C₂⁴	1	1	yes	characteristic
432	C₂×C₄₃⋊C₈	C₂⁴	1	1	yes	characteristic
433	C₂×C₄₃⋊C₈	C₂⁴	1	2	yes	—
434	C₂×C₄₃⋊C₈	C₂⁴	1	2	yes	—
435	C₂×C₄₃⋊C₈	C₂⁴	1	1	yes	characteristic
436	C₂×C₄₃⋊C₈	C₂⁴	1	1	yes	characteristic
437	C₂³×C₄₃	C₂²×D₄	1	2	yes	—
438	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
439	C₂²×D₄₃	—	2	2	no	—
440	C₂²×D₄₃	—	2	1	no	—
441	C₂²×D₄₃	—	4	2	no	—
442	C₂²×D₄₃	—	8	1	no	—
443	C₂²×D₄₃	—	8	1	no	—
444	Q₈×C₄₃	—	2	2	no	—
445	Q₈×C₄₃	—	8	1	no	—
446	Q₈×C₄₃	—	8	2	no	—
447	Q₈×C₄₃	—	8	2	no	—
448	Q₈×C₄₃	—	8	1	no	—
449	D₄×C₄₃	—	2	4	no	—
450	D₄×C₄₃	—	2	2	no	—
451	C₂×C₄×C₄₃	—	2	2	no	—
452	C₂×C₄×C₄₃	—	2	2	no	—
453	C₂×C₄×C₄₃	—	2	1	no	—
454	C₂×C₄×C₄₃	—	2	1	no	—
455	C₂×C₄×C₄₃	—	2	2	no	—
456	C₂×C₄×C₄₃	—	2	1	no	—
457	C₂×C₄×C₄₃	—	2	2	no	—
458	C₂×C₄×C₄₃	—	2	1	no	—
459	C₂×C₄×C₄₃	—	4	1	no	—
460	C₂×C₄×C₄₃	—	4	2	no	—
461	C₂×C₄×C₄₃	—	4	1	no	—
462	C₂×C₄×C₄₃	—	4	2	no	—
463	C₂×C₄×C₄₃	—	8	1	no	—
464	C₂×C₄×C₄₃	—	8	2	no	—
465	C₂×C₄×C₄₃	—	8	1	no	—
466	C₂×C₄×C₄₃	—	8	2	no	—
467	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
468	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
469	C₂×C₄×C₄₃	C₂²×D₄	1	2	yes	—
470	C₂×C₄×C₄₃	C₂²×D₄	1	2	yes	—
471	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
472	C₂×C₄×C₄₃	C₂²×D₄	1	2	yes	—
473	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
474	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
475	C₂×C₄×C₄₃	2₋¹⁺⁴	1	2	yes	—
476	C₂×C₄×C₄₃	2₋¹⁺⁴	1	2	yes	—
477	C₂×C₄×C₄₃	C₂⁵	1	1	yes	characteristic
478	C₂²⋊D₄₃	—	4	2	no	—
479	C₂²⋊D₄₃	—	8	2	no	—
480	C₂²⋊D₄₃	—	8	2	no	—
481	C₂²⋊D₄₃	—	8	2	no	—
482	C₂×Dic₄₃	—	2	1	no	—
483	C₂×Dic₄₃	—	2	1	no	—
484	C₂×Dic₄₃	—	2	1	no	—
485	C₂×Dic₄₃	—	2	2	no	—
486	C₂×Dic₄₃	—	8	1	no	—
487	D₁₇₂	—	2	2	no	—
488	D₁₇₂	—	2	2	no	—
489	D₁₇₂	—	2	1	no	—
490	D₁₇₂	—	2	1	no	—
491	D₁₇₂	—	4	2	no	—
492	D₁₇₂	—	8	2	no	—
493	D₁₇₂	—	8	2	no	—
494	C₄×D₄₃	—	4	4	no	—
495	C₄×D₄₃	—	4	2	no	—
496	C₄×D₄₃	—	4	2	no	—
497	C₄×D₄₃	—	8	1	no	—
498	C₄×D₄₃	—	8	2	no	—
499	Dic₈₆	—	2	1	no	—
500	Dic₈₆	—	2	1	no	—
501	Dic₈₆	—	8	2	no	—
502	C₄₃⋊C₈	—	2	1	no	—
503	C₄₃⋊C₈	—	2	1	no	—
504	C₄₃⋊C₈	—	2	1	no	—
505	C₄₃⋊C₈	—	2	1	no	—
506	C₄₃⋊C₈	—	2	2	no	—
507	C₄₃⋊C₈	—	2	2	no	—
508	#60890	—	43	1	no	maximal, Sylow
509	C₂²×C₄₃	—	2	1	no	—
510	C₂²×C₄₃	—	2	1	no	—
511	C₂²×C₄₃	—	2	2	no	—
512	C₂²×C₄₃	—	2	2	no	—
513	C₂²×C₄₃	—	2	2	no	—
514	C₂²×C₄₃	#536	1	2	yes	—
515	C₂²×C₄₃	C₂³×D₄	1	1	yes	characteristic
516	C₂×D₄₃	—	4	2	no	—
517	C₂×D₄₃	—	4	1	no	—
518	C₂×D₄₃	—	4	2	no	—
519	C₂×D₄₃	—	4	1	no	—
520	C₂×D₄₃	—	4	2	no	—
521	C₂×D₄₃	—	4	1	no	—
522	C₂×D₄₃	—	8	4	no	—
523	C₄×C₄₃	—	2	1	no	—
524	C₄×C₄₃	—	2	2	no	—
525	C₄×C₄₃	—	2	1	no	—
526	C₄×C₄₃	—	2	2	no	—
527	C₄×C₄₃	—	2	1	no	—
528	C₄×C₄₃	—	2	1	no	—
529	C₄×C₄₃	—	2	2	no	—
530	C₄×C₄₃	—	4	2	no	—
531	C₄×C₄₃	—	4	1	no	—
532	C₄×C₄₃	—	4	1	no	—
533	C₄×C₄₃	—	4	2	no	—
534	C₄×C₄₃	—	4	1	no	—
535	C₄×C₄₃	—	4	1	no	—
536	C₄×C₄₃	#536	1	2	yes	—
537	C₄×C₄₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
538	C₄×C₄₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
539	Dic₄₃	—	4	1	no	—
540	Dic₄₃	—	4	1	no	—
541	Dic₄₃	—	4	2	no	—
542	Dic₄₃	—	4	1	no	—
543	#3504	D₄₃	1	1	yes	characteristic, complemented
544	#3460	—	43	1	no	—
545	#3244	—	43	2	no	—
546	#3243	—	43	2	no	—
547	#3241	—	43	2	no	—
548	#3241	—	43	2	no	—
549	#3240	—	43	2	no	—
550	#3234	—	43	2	no	—
551	#3232	—	43	2	no	—
552	#3228	—	43	2	no	—
553	#3164	—	43	1	no	—
554	#3163	—	43	1	no	—
555	#3136	—	43	1	no	—
556	#3136	—	43	1	no	—
557	#3099	—	43	1	no	—
558	#3098	—	43	1	no	—
559	#3096	—	43	1	no	—
560	#3096	—	43	1	no	—
561	#3080	—	43	1	no	—
562	#3077	—	43	1	no	—
563	#3076	—	43	1	no	—
564	C₂×#478	—	43	1	no	—
565	#2925	—	43	1	no	—
566	C₂×C₄₃	—	2	2	no	—
567	C₂×C₄₃	—	4	2	no	—
568	C₂×C₄₃	C₂×#536	1	1	yes	characteristic
569	C₂×C₄₃	#3584	1	1	yes	characteristic
570	C₂×C₄₃	#3585	1	1	yes	characteristic
571	D₄₃	—	8	1	no	—
572	D₄₃	—	8	2	no	—
573	#557	—	2	1	no	—
574	#557	—	2	1	no	—
575	#554	—	2	2	no	—
576	#554	—	2	2	no	—
577	#554	—	2	1	no	—
578	#554	—	2	1	no	—
579	#544	—	43	1	no	—
580	#544	C₂×D₄₃	1	1	yes	characteristic
581	#544	C₂×D₄₃	1	1	yes	characteristic
582	#544	C₂×D₄₃	1	2	yes	complemented
583	#544	C₂×D₄₃	1	2	yes	complemented
584	#542	—	43	2	no	—
585	#542	—	86	1	no	—
586	#540	—	43	2	no	—
587	#540	—	86	1	no	—
588	#538	—	86	2	no	—
589	#537	—	43	1	no	—
590	#535	—	43	1	no	—
591	#535	—	43	1	no	—
592	#533	C₂×D₄₃	1	1	yes	characteristic
593	#533	C₂×D₄₃	1	2	yes	complemented
594	#532	—	43	2	no	—
595	#532	—	86	1	no	—
596	#529	—	43	2	no	—
597	#529	—	86	1	no	—
598	C₂×#125	C₂×D₄₃	1	1	yes	characteristic
599	C₂×#125	C₂×D₄₃	1	2	yes	complemented
600	#525	—	86	2	no	—
601	#520	C₂×D₄₃	1	1	yes	characteristic
602	#520	C₂×D₄₃	1	1	yes	characteristic
603	C₄×#41	—	43	1	no	—
604	C₄×#41	C₂×D₄₃	1	1	yes	characteristic
605	C₂×C₄×D₄	—	43	1	no	—
606	#501	—	43	2	no	—
607	#501	—	43	2	no	—
608	#501	—	43	2	no	—
609	#501	—	43	2	no	—
610	#500	—	43	2	no	—
611	#499	—	43	2	no	—
612	#499	—	43	2	no	—
613	#498	—	43	2	no	—
614	#490	—	43	2	no	—
615	#490	—	43	2	no	—
616	#489	—	43	2	no	—
617	#489	—	43	2	no	—
618	#488	—	43	2	no	—
619	#488	—	43	2	no	—
620	#486	—	43	2	no	—
621	#486	—	43	2	no	—
622	#485	—	43	2	no	—
623	#485	—	43	2	no	—
624	#484	—	43	2	no	—
625	#483	—	43	2	no	—
626	#482	—	43	2	no	—
627	#482	—	43	2	no	—
628	#482	—	43	2	no	—
629	#482	—	43	2	no	—
630	#482	—	43	2	no	—
631	#482	—	43	2	no	—
632	#481	—	43	2	no	—
633	#481	—	43	2	no	—
634	#481	—	43	2	no	—
635	#480	—	43	2	no	—
636	#480	—	43	2	no	—
637	#480	—	43	2	no	—
638	#479	—	43	1	no	—
639	#479	—	43	1	no	—
640	#479	—	43	2	no	—
641	#479	—	43	2	no	—
642	#478	—	43	2	no	—
643	#478	—	43	2	no	—
644	#478	—	43	2	no	—
645	#478	—	43	2	no	—
646	#478	—	43	1	no	—
647	#478	—	43	1	no	—
648	#478	—	43	2	no	—
649	#478	—	43	2	no	—
650	#478	—	43	2	no	—
651	#478	—	43	2	no	—
652	#477	—	43	1	no	—
653	#476	—	43	1	no	—
654	#476	—	43	2	no	—
655	#475	—	43	1	no	—
656	#474	—	43	1	no	—
657	#474	—	43	2	no	—
658	#433	—	43	2	no	—
659	#433	—	43	2	no	—
660	#432	—	43	2	no	—
661	#431	—	43	2	no	—
662	#428	—	43	1	no	—
663	#428	—	43	1	no	—
664	#428	—	43	1	no	—
665	#428	—	43	1	no	—
666	#427	—	43	1	no	—
667	#427	—	43	1	no	—
668	C₂×#107	—	43	1	no	—
669	C₂×#106	—	43	1	no	—
670	#423	—	43	1	no	—
671	C₂×C₄⋊C₈	—	43	1	no	—
672	#418	—	43	1	no	—
673	#418	—	43	1	no	—
674	#417	—	43	1	no	—
675	#417	—	43	1	no	—
676	#416	—	43	1	no	—
677	#416	—	43	1	no	—
678	C₂×#102	—	43	1	no	—
679	C₂×#102	—	43	1	no	—
680	#408	—	43	1	no	—
681	#408	—	43	1	no	—
682	#405	—	43	1	no	—
683	#405	—	43	1	no	—
684	C₄₃	#60890	1	1	yes	characteristic, complemented, Sylow
685	C₂×#41	—	43	1	no	—
686	C₂×#41	—	86	2	no	—
687	C₂×#41	C₂²×D₄₃	1	1	yes	characteristic
688	C₂²×D₄	—	43	1	no	—
689	C₂³×C₄	—	86	1	no	—
690	C₂×M₁₆	—	43	1	no	—
691	C₂×M₁₆	—	43	1	no	—
692	C₂²×C₈	—	43	1	no	—
693	C₂²×C₈	—	43	1	no	—
694	C₄⋊Q₈	—	2	1	no	—
695	C₄⋊Q₈	—	2	1	no	—
696	C₄⋊Q₈	—	2	2	no	—
697	C₄⋊Q₈	—	2	2	no	—
698	C₄⋊Q₈	—	43	2	no	—
699	C₄⋊Q₈	—	86	1	no	—
700	C₄⋊Q₈	C₂²×D₄₃	1	1	yes	characteristic
701	C₄⋊Q₈	C₂²×D₄₃	1	1	yes	characteristic
702	C₄⋊Q₈	C₂²×D₄₃	1	2	yes	—
703	C₄⋊Q₈	C₂²×D₄₃	1	2	yes	—
704	#127	—	43	2	no	—
705	#127	—	86	1	no	—
706	#126	—	86	2	no	—
707	#126	—	86	2	no	—
708	#125	—	2	1	no	—
709	#125	—	2	1	no	—
710	#125	—	2	2	no	—
711	#125	—	2	2	no	—
712	#125	—	2	1	no	—
713	#125	—	2	1	no	—
714	#125	—	2	2	no	—
715	#125	—	2	2	no	—
716	#125	—	43	2	no	—
717	#125	—	86	1	no	—
718	#125	C₂²×D₄₃	1	2	yes	—
719	#125	C₂²×D₄₃	1	2	yes	—
720	#125	C₂²×D₄₃	1	1	yes	characteristic
721	#125	C₂²×D₄₃	1	2	yes	—
722	#125	C₂²×D₄₃	1	2	yes	—
723	#125	C₂²×D₄₃	1	1	yes	characteristic
724	#124	—	43	2	no	—
725	#124	—	86	1	no	—
726	#124	—	86	2	no	—
727	#124	—	86	2	no	—
728	#123	—	86	2	no	—
729	#123	—	86	2	no	—
730	#123	—	86	2	no	—
731	#123	—	86	2	no	—
732	C₂²⋊Q₈	—	2	1	no	—
733	C₂²⋊Q₈	—	2	1	no	—
734	C₂²⋊Q₈	—	2	2	no	—
735	C₂²⋊Q₈	—	2	2	no	—
736	C₂²⋊Q₈	—	2	2	no	—
737	C₂²⋊Q₈	—	2	2	no	—
738	C₂²⋊Q₈	—	2	2	no	—
739	C₂²⋊Q₈	—	2	2	no	—
740	C₂²⋊Q₈	—	2	2	no	—
741	C₂²⋊Q₈	—	2	2	no	—
742	C₂²⋊Q₈	—	43	2	no	—
743	C₂²⋊Q₈	—	86	1	no	—
744	C₂²⋊Q₈	—	86	2	no	—
745	C₂²⋊Q₈	—	86	2	no	—
746	#121	—	43	2	no	—
747	#121	—	43	2	no	—
748	#121	—	43	2	no	—
749	#121	—	86	2	no	—
750	#121	—	86	1	no	—
751	#121	—	86	2	no	—
752	#121	—	86	1	no	—
753	#121	—	86	1	no	—
754	#121	—	86	2	no	—
755	#121	—	86	2	no	—
756	#120	—	86	2	no	—
757	#120	—	86	2	no	—
758	C₄×Q₈	—	2	1	no	—
759	C₄×Q₈	—	2	1	no	—
760	C₄×Q₈	—	2	1	no	—
761	C₄×Q₈	—	2	1	no	—
762	C₄×Q₈	—	2	2	no	—
763	C₄×Q₈	—	2	2	no	—
764	C₄×Q₈	—	43	1	no	—
765	C₄×Q₈	—	43	1	no	—
766	C₄×Q₈	C₂²⋊D₄₃	1	1	yes	characteristic
767	C₄×Q₈	C₂²⋊D₄₃	1	1	yes	characteristic
768	C₄×D₄	—	2	2	no	—
769	C₄×D₄	—	2	2	no	—
770	C₄×D₄	—	2	1	no	—
771	C₄×D₄	—	2	1	no	—
772	C₄×D₄	—	43	2	no	—
773	C₄×D₄	—	43	2	no	—
774	C₄×D₄	—	43	1	no	—
775	C₄×D₄	—	43	1	no	—
776	C₄×D₄	—	86	1	no	—
777	C₄×D₄	—	86	1	no	—
778	C₄×D₄	—	86	2	no	—
779	C₄×D₄	—	86	1	no	—
780	C₄×D₄	—	86	1	no	—
781	C₄×D₄	—	86	2	no	—
782	C₄×D₄	C₂²⋊D₄₃	1	2	yes	—
783	C₄×D₄	C₂²⋊D₄₃	1	1	yes	characteristic
784	C₄×D₄	C₂²⋊D₄₃	1	2	yes	—
785	C₄×D₄	C₂²⋊D₄₃	1	1	yes	characteristic
786	#117	—	43	1	no	—
787	#117	—	86	1	no	—
788	#117	—	86	2	no	—
789	#117	C₂²×D₄₃	1	1	yes	characteristic
790	#117	C₂²×D₄₃	1	1	yes	characteristic
791	#117	C₂²×D₄₃	1	2	yes	—
792	#117	C₂²×D₄₃	1	2	yes	—
793	#117	C₂²×D₄₃	1	1	yes	characteristic
794	#117	C₂²×D₄₃	1	2	yes	—
795	C₂×C₄⋊C₄	—	2	1	no	—
796	C₂×C₄⋊C₄	—	2	1	no	—
797	C₂×C₄⋊C₄	—	2	2	no	—
798	C₂×C₄⋊C₄	—	2	2	no	—
799	C₂×C₄⋊C₄	—	43	1	no	—
800	C₂×C₄⋊C₄	C₂²×D₄₃	1	1	yes	characteristic
801	C₂×C₄⋊C₄	C₂²×D₄₃	1	1	yes	characteristic
802	C₂×C₄⋊C₄	C₂²×D₄₃	1	2	yes	—
803	C₂×C₄⋊C₄	C₂²×D₄₃	1	2	yes	—
804	C₂×C₂²⋊C₄	—	86	1	no	—
805	C₂×C₄²	—	86	1	no	—
806	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
807	C₂×C₄²	C₂²×D₄₃	1	2	yes	—
808	#107	—	43	2	no	—
809	#107	—	43	2	no	—
810	#107	—	43	1	no	—
811	#107	—	43	1	no	—
812	#107	—	43	1	no	—
813	#107	—	43	1	no	—
814	#107	—	43	2	no	—
815	#107	—	43	2	no	—
816	#107	—	43	2	no	—
817	#107	—	43	2	no	—
818	#106	—	43	2	no	—
819	#106	—	43	2	no	—
820	#106	—	43	1	no	—
821	#106	—	43	1	no	—
822	#106	—	43	1	no	—
823	#106	—	43	1	no	—
824	#106	—	43	2	no	—
825	#106	—	43	2	no	—
826	#106	—	43	2	no	—
827	#106	—	43	2	no	—
828	C₄⋊C₈	—	43	1	no	—
829	C₄⋊C₈	—	43	1	no	—
830	C₄⋊C₈	—	43	1	no	—
831	C₄⋊C₈	—	43	1	no	—
832	C₄⋊C₈	—	43	2	no	—
833	C₄⋊C₈	—	43	2	no	—
834	#103	—	43	1	no	—
835	#103	—	43	1	no	—
836	#103	—	43	1	no	—
837	#103	—	43	1	no	—
838	#103	—	43	2	no	—
839	#103	—	43	2	no	—
840	#102	—	43	2	no	—
841	#102	—	43	2	no	—
842	#102	—	43	2	no	—
843	#102	—	43	2	no	—
844	#102	—	43	1	no	—
845	#102	—	43	1	no	—
846	#102	—	43	1	no	—
847	#102	—	43	1	no	—
848	#102	—	43	2	no	—
849	#102	—	43	2	no	—
850	#102	—	43	2	no	—
851	#102	—	43	2	no	—
852	#102	—	43	2	no	—
853	#102	—	43	2	no	—
854	C₂²⋊C₈	—	43	2	no	—
855	C₂²⋊C₈	—	43	2	no	—
856	C₂²⋊C₈	—	43	2	no	—
857	C₂²⋊C₈	—	43	2	no	—
858	#97	—	43	2	no	—
859	#97	—	43	2	no	—
860	C₄×C₈	—	43	2	no	—
861	C₄×C₈	—	43	2	no	—
862	C₂⁴	—	86	1	no	—
863	#41	—	2	2	no	—
864	#41	—	2	2	no	—
865	#41	—	86	2	no	—
866	#41	—	86	2	no	—
867	#41	—	344	4	no	—
868	C₂×Q₈	—	2	1	no	—
869	C₂×Q₈	—	2	2	no	—
870	C₂×Q₈	—	2	1	no	—
871	C₂×Q₈	—	2	2	no	—
872	C₂×Q₈	—	43	1	no	—
873	C₂×Q₈	—	86	2	no	—
874	C₂×Q₈	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
875	C₂×D₄	—	43	2	no	—
876	C₂×D₄	—	43	1	no	—
877	C₂×D₄	—	86	2	no	—
878	C₂×D₄	—	86	2	no	—
879	C₂×D₄	—	86	2	no	—
880	C₂×D₄	—	86	1	no	—
881	C₂×D₄	—	86	2	no	—
882	C₂×D₄	—	86	2	no	—
883	C₂×D₄	—	86	1	no	—
884	C₂×D₄	—	86	2	no	—
885	C₂×D₄	—	86	2	no	—
886	C₂×D₄	C₂×C₂²⋊D₄₃	1	2	yes	—
887	C₂×D₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
888	C₂²×C₄	—	2	2	no	—
889	C₂²×C₄	—	2	2	no	—
890	C₂²×C₄	—	2	1	no	—
891	C₂²×C₄	—	2	1	no	—
892	C₂²×C₄	—	86	1	no	—
893	C₂²×C₄	—	86	1	no	—
894	C₂²×C₄	—	86	2	no	—
895	C₂²×C₄	—	86	1	no	—
896	C₂²×C₄	—	86	1	no	—
897	C₂²×C₄	—	86	2	no	—
898	C₂²×C₄	—	344	2	no	—
899	C₂²×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
900	C₂²×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
901	C₂²×C₄	C₂×C₂²⋊D₄₃	1	2	yes	—
902	C₂²×C₄	C₂×C₂²⋊D₄₃	1	2	yes	—
903	C₂²×C₄	C₂³×D₄₃	1	2	yes	—
904	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
905	M₁₆	—	86	2	no	—
906	M₁₆	—	86	2	no	—
907	C₂×C₈	—	43	1	no	—
908	C₂×C₈	—	43	1	no	—
909	C₂×C₈	—	43	2	no	—
910	C₂×C₈	—	43	2	no	—
911	C₂×C₈	—	43	1	no	—
912	C₂×C₈	—	43	1	no	—
913	C₂×C₈	—	86	2	no	—
914	C₂×C₈	—	86	2	no	—
915	C₄⋊C₄	—	2	2	no	—
916	C₄⋊C₄	—	2	1	no	—
917	C₄⋊C₄	—	2	2	no	—
918	C₄⋊C₄	—	2	1	no	—
919	C₄⋊C₄	—	2	2	no	—
920	C₄⋊C₄	—	2	2	no	—
921	C₄⋊C₄	—	2	2	no	—
922	C₄⋊C₄	—	2	2	no	—
923	C₄⋊C₄	—	2	2	no	—
924	C₄⋊C₄	—	2	2	no	—
925	C₄⋊C₄	—	2	2	no	—
926	C₄⋊C₄	—	2	2	no	—
927	C₄⋊C₄	—	2	1	no	—
928	C₄⋊C₄	—	2	1	no	—
929	C₄⋊C₄	—	2	1	no	—
930	C₄⋊C₄	—	2	1	no	—
931	C₄⋊C₄	—	2	1	no	—
932	C₄⋊C₄	—	2	2	no	—
933	C₄⋊C₄	—	2	1	no	—
934	C₄⋊C₄	—	2	2	no	—
935	C₄⋊C₄	—	43	2	no	—
936	C₄⋊C₄	—	43	1	no	—
937	C₄⋊C₄	—	43	1	no	—
938	C₄⋊C₄	—	86	1	no	—
939	C₄⋊C₄	—	86	1	no	—
940	C₄⋊C₄	—	86	1	no	—
941	C₄⋊C₄	—	86	2	no	—
942	C₄⋊C₄	—	86	2	no	—
943	C₄⋊C₄	—	86	2	no	—
944	C₄⋊C₄	—	86	2	no	—
945	C₄⋊C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
946	C₄⋊C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
947	C₄⋊C₄	C₂×C₂²⋊D₄₃	1	2	yes	—
948	C₄⋊C₄	C₂×C₂²⋊D₄₃	1	2	yes	—
949	C₄⋊C₄	C₂³×D₄₃	1	2	yes	—
950	C₄⋊C₄	C₂³×D₄₃	1	1	yes	characteristic
951	C₄⋊C₄	C₂³×D₄₃	1	1	yes	characteristic
952	C₄⋊C₄	C₂³×D₄₃	1	2	yes	—
953	C₄⋊C₄	C₂³×D₄₃	1	1	yes	characteristic
954	C₄⋊C₄	C₂³×D₄₃	1	1	yes	characteristic
955	C₂²⋊C₄	—	2	2	no	—
956	C₂²⋊C₄	—	2	2	no	—
957	C₂²⋊C₄	—	2	1	no	—
958	C₂²⋊C₄	—	2	1	no	—
959	C₂²⋊C₄	—	86	1	no	—
960	C₂²⋊C₄	—	86	2	no	—
961	C₂²⋊C₄	—	86	2	no	—
962	C₂²⋊C₄	—	86	2	no	—
963	C₂²⋊C₄	—	86	1	no	—
964	C₂²⋊C₄	—	86	1	no	—
965	C₂²⋊C₄	—	86	2	no	—
966	C₂²⋊C₄	—	86	2	no	—
967	C₂²⋊C₄	—	86	2	no	—
968	C₂²⋊C₄	—	86	2	no	—
969	C₂²⋊C₄	—	86	2	no	—
970	C₂²⋊C₄	C₂×C₂²⋊D₄₃	1	2	yes	—
971	C₂²⋊C₄	C₂×C₂²⋊D₄₃	1	2	yes	—
972	C₂²⋊C₄	C₂×C₂²⋊D₄₃	1	2	yes	—
973	C₄²	—	2	2	no	—
974	C₄²	—	2	2	no	—
975	C₄²	—	2	1	no	—
976	C₄²	—	2	1	no	—
977	C₄²	—	86	1	no	—
978	C₄²	—	86	1	no	—
979	C₄²	—	86	1	no	—
980	C₄²	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
981	C₄²	C₂×C₂²⋊D₄₃	1	2	yes	—
982	C₄²	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
983	C₄²	C₂×C₂²⋊D₄₃	1	2	yes	—
984	C₄²	C₂³×D₄₃	1	2	yes	—
985	C₄²	C₂³×D₄₃	1	1	yes	characteristic
986	C₄²	C₂³×D₄₃	1	1	yes	characteristic
987	C₂³	—	86	2	no	—
988	C₂³	—	86	1	no	—
989	C₂³	—	344	1	no	—
990	C₂³	—	344	1	no	—
991	C₂³	—	172	2	no	—
992	C₂³	C₂²×C₂²⋊D₄₃	1	2	yes	—
993	C₂³	C₂²×C₂²⋊D₄₃	1	1	yes	characteristic
994	Q₈	—	2	2	no	—
995	Q₈	—	8	1	no	—
996	Q₈	—	8	2	no	—
997	Q₈	—	8	1	no	—
998	Q₈	—	8	2	no	—
999	Q₈	—	86	1	no	—
1000	Q₈	—	86	1	no	—
1001	Q₈	—	344	2	no	—
1002	D₄	—	2	4	no	—
1003	D₄	—	2	2	no	—
1004	D₄	—	86	2	no	—
1005	D₄	—	86	2	no	—
1006	D₄	—	86	1	no	—
1007	D₄	—	86	1	no	—
1008	D₄	—	344	2	no	—
1009	D₄	—	344	2	no	—
1010	D₄	—	344	2	no	—
1011	D₄	—	344	2	no	—
1012	D₄	—	344	2	no	—
1013	D₄	—	172	2	no	—
1014	D₄	—	172	2	no	—
1015	C₂×C₄	—	2	2	no	—
1016	C₂×C₄	—	2	2	no	—
1017	C₂×C₄	—	2	1	no	—
1018	C₂×C₄	—	2	1	no	—
1019	C₂×C₄	—	2	2	no	—
1020	C₂×C₄	—	2	1	no	—
1021	C₂×C₄	—	2	2	no	—
1022	C₂×C₄	—	2	1	no	—
1023	C₂×C₄	—	4	1	no	—
1024	C₂×C₄	—	4	2	no	—
1025	C₂×C₄	—	4	1	no	—
1026	C₂×C₄	—	4	2	no	—
1027	C₂×C₄	—	8	1	no	—
1028	C₂×C₄	—	8	2	no	—
1029	C₂×C₄	—	8	1	no	—
1030	C₂×C₄	—	8	2	no	—
1031	C₂×C₄	—	86	1	no	—
1032	C₂×C₄	—	86	1	no	—
1033	C₂×C₄	—	86	1	no	—
1034	C₂×C₄	—	86	2	no	—
1035	C₂×C₄	—	344	2	no	—
1036	C₂×C₄	—	344	1	no	—
1037	C₂×C₄	—	344	1	no	—
1038	C₂×C₄	—	172	4	no	—
1039	C₂×C₄	—	172	2	no	—
1040	C₂×C₄	—	172	2	no	—
1041	C₂×C₄	C₂²×C₂²⋊D₄₃	1	2	yes	—
1042	C₂×C₄	C₂²×C₂²⋊D₄₃	1	1	yes	characteristic
1043	C₂×C₄	C₂²×C₂²⋊D₄₃	1	1	yes	characteristic
1044	C₂×C₄	C₂²×C₂²⋊D₄₃	1	1	yes	characteristic
1045	C₂×C₄	C₂²×C₂²⋊D₄₃	1	2	yes	—
1046	C₂×C₄	C₂²×C₂²⋊D₄₃	1	1	yes	characteristic
1047	C₂×C₄	C₂²×C₂²⋊D₄₃	1	2	yes	—
1048	C₂×C₄	C₂²×C₂²⋊D₄₃	1	1	yes	characteristic
1049	C₂×C₄	#13063373	1	2	yes	—
1050	C₂×C₄	#13063373	1	2	yes	—
1051	C₂×C₄	C₂⁴×D₄₃	1	1	yes	characteristic
1052	C₈	—	86	1	no	—
1053	C₈	—	86	1	no	—
1054	C₈	—	86	1	no	—
1055	C₈	—	86	1	no	—
1056	C₈	—	86	2	no	—
1057	C₈	—	86	2	no	—
1058	C₂²	—	2	1	no	—
1059	C₂²	—	2	1	no	—
1060	C₂²	—	2	2	no	—
1061	C₂²	—	2	2	no	—
1062	C₂²	—	2	2	no	—
1063	C₂²	—	344	4	no	—
1064	C₂²	—	172	1	no	—
1065	C₂²	—	172	2	no	—
1066	C₂²	—	172	2	no	—
1067	C₂²	—	172	1	no	—
1068	C₂²	—	172	1	no	—
1069	C₂²	—	172	2	no	—
1070	C₂²	#14583473	1	2	yes	—
1071	C₂²	C₂³×C₂²⋊D₄₃	1	1	yes	characteristic
1072	C₄	—	2	1	no	—
1073	C₄	—	2	1	no	—
1074	C₄	—	2	2	no	—
1075	C₄	—	2	1	no	—
1076	C₄	—	2	1	no	—
1077	C₄	—	2	2	no	—
1078	C₄	—	2	2	no	—
1079	C₄	—	4	2	no	—
1080	C₄	—	4	1	no	—
1081	C₄	—	4	1	no	—
1082	C₄	—	4	2	no	—
1083	C₄	—	4	1	no	—
1084	C₄	—	4	1	no	—
1085	C₄	—	172	1	no	—
1086	C₄	—	172	2	no	—
1087	C₄	—	172	1	no	—
1088	C₄	—	172	1	no	—
1089	C₄	#14583473	1	2	yes	—
1090	C₄	C₂×#13063373	1	1	yes	characteristic
1091	C₄	C₂×#13063373	1	1	yes	characteristic
1092	C₂	—	2	2	no	—
1093	C₂	—	4	2	no	—
1094	C₂	—	344	2	no	—
1095	C₂	—	344	1	no	—
1096	C₂	C₂×#14583473	1	1	yes	characteristic
1097	C₂	#19149366	1	1	yes	characteristic
1098	C₂	#19149374	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂³×C₂²⋊D₄₃
commutator, cosocle	C₂×C₄×C₄₃	C₂⁵
Frattini	C₂×C₄	C₂⁴×D₄₃
Fitting	C₄₃×#3504	C₂
socle	C₂²×C₄₃	C₂³×D₄
prime radical	#19148011	C₂
hypercenter	#3504	D₄₃
hypocenter	C₄₃	#60890
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₄×#41 ◁ #3504

Complements

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

N	H ≅ G/N	type
2. #19145893	C₂	semidirect
3. #19145878	C₂	semidirect
4. #19145848	C₂	semidirect
5. #19145848	C₂	semidirect
6. #19145835	C₂	semidirect
7. #19145785	C₂	semidirect
8. #19145763	C₂	semidirect
9. #19145731	C₂	semidirect
10. #19145129	C₂	semidirect
11. #19145121	C₂	semidirect
12. #19144954	C₂	semidirect
13. #19144954	C₂	semidirect
14. #19144584	C₂	semidirect
15. #19144573	C₂	semidirect
16. #19144553	C₂	semidirect
17. #19144553	C₂	semidirect
18. #19144413	C₂	semidirect
19. #19144388	C₂	semidirect
20. #19144377	C₂	semidirect
21. C₂×#14583196	C₂	semidirect
22. #19143261	C₂	semidirect
23. C₄₃×#3504	C₂	semidirect
40. #14583309	C₂²	semidirect
41. #14583309	C₂²	semidirect
42. #14583305	C₂²	semidirect
43. #14583305	C₂²	semidirect
44. #14583302	C₂²	semidirect
45. #14583298	C₂²	semidirect
46. #14583298	C₂²	semidirect
47. #14583295	C₂²	semidirect
56. #14583240	C₂²	semidirect
57. #14583240	C₂²	semidirect
58. #14583234	C₂²	semidirect
59. #14583229	C₂²	semidirect
64. #14583223	C₂²	semidirect
65. #14583223	C₂²	semidirect
68. #14583217	C₂²	semidirect
71. #14583212	C₂²	semidirect
72. #14583203	C₂²	semidirect
73. #14583203	C₂²	semidirect
74. #14583203	C₂²	semidirect
75. #14583203	C₂²	semidirect
82. #14583196	C₂²	semidirect
83. #14583196	C₂²	semidirect
84. #14583196	C₂²	semidirect
85. #14583196	C₂²	semidirect
86. #14583191	C₂²	semidirect
88. #14583186	C₂²	semidirect
89. #14583181	C₂²	semidirect
91. #14583176	C₂²	semidirect
92. #14582960	C₂²	semidirect
93. #14582960	C₂²	semidirect
94. #14582956	C₂²	semidirect
95. #14582952	C₂²	semidirect
126. C₄₃×#544	C₂²	semidirect
127. C₄₃×#544	C₂²	semidirect
129. C₄₃×#533	C₂²	semidirect
131. C₂×#125×C₄₃	C₂²	semidirect
543. #3504	D₄₃	semidirect
582. #544	C₂×D₄₃	semidirect
583. #544	C₂×D₄₃	semidirect
593. #533	C₂×D₄₃	semidirect
599. C₂×#125	C₂×D₄₃	semidirect
684. C₄₃	#60890	semidirect

Maximal subgroups

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

subgroup	index
#19148011	2
#19145893	2
#19145878	2
#19145848	2
#19145835	2
#19145785	2
#19145763	2
#19145731	2
#19145129	2
#19145121	2
#19144954	2
#19144584	2
#19144573	2
#19144553	2
#19144413	2
#19144388	2
#19144377	2
C₂×#14583196	2
#19143261	2
C₄₃×#3504	2
#60890	43