Subgroups — #27096327

Order 12032.

1764 conjugacy classes of subgroups.

The subgroup lattice has 1122 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20257209	C₂	1	1	yes	maximal, characteristic, complemented
2	#20256224	C₂	1	2	yes	maximal, complemented
3	#20256209	C₂	1	2	yes	maximal, complemented
4	#20256150	C₂	1	2	yes	maximal, complemented
5	#20256135	C₂	1	2	yes	maximal, complemented
6	#20256080	C₂	1	2	yes	maximal, complemented
7	#20256069	C₂	1	2	yes	maximal, complemented
8	#20256044	C₂	1	2	yes	maximal, complemented
9	#20256033	C₂	1	2	yes	maximal, complemented
10	#20253753	C₂	1	1	yes	maximal, characteristic, complemented
11	#20253742	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#15689477	C₂	1	1	yes	maximal, characteristic, complemented
13	#20253230	C₂	1	1	yes	maximal, characteristic, complemented
14	#20253219	C₂	1	1	yes	maximal, characteristic, complemented
15	#20253210	C₂	1	1	yes	maximal, characteristic, complemented
16	#20252934	C₂	1	1	yes	maximal, characteristic, complemented
17	#20252923	C₂	1	1	yes	maximal, characteristic
18	#20252878	C₂	1	1	yes	maximal, characteristic, complemented
19	#20252323	C₂	1	1	yes	maximal, characteristic, complemented
20	#20252231	C₂	1	1	yes	maximal, characteristic, complemented
21	#20252220	C₂	1	1	yes	maximal, characteristic, complemented
22	C₄×#13094044	C₂	1	1	yes	maximal, characteristic, complemented
23	C₄₇×#3510	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#13094055	C₂²	1	1	yes	characteristic
25	C₂×#13094050	C₂²	1	1	yes	characteristic
26	C₂×#13094044	C₂²	1	1	yes	characteristic
27	#15689851	C₂²	1	2	yes	complemented
28	#15689851	C₂²	1	2	yes	complemented
29	#15689833	C₂²	1	2	yes	complemented
30	#15689833	C₂²	1	2	yes	complemented
31	#15689827	—	2	2	no	—
32	#15689827	—	2	2	no	—
33	#15689751	C₂²	1	1	yes	characteristic
34	#15689751	C₂²	1	1	yes	characteristic
35	#15689750	—	2	1	no	—
36	#15689750	—	2	1	no	—
37	#15689679	—	2	1	no	—
38	C₂×#13094016	C₂²	1	1	yes	characteristic
39	#125×D₄₇	—	2	1	no	—
40	#15689603	C₂²	1	1	yes	characteristic
41	#15689603	C₂²	1	1	yes	characteristic
42	C₄×#10625350	C₂²	1	1	yes	characteristic
43	#15689491	C₂²	1	2	yes	complemented
44	#15689487	C₂²	1	2	yes	—
45	#15689482	C₂²	1	2	yes	—
46	#15689482	C₂²	1	2	yes	complemented
47	#15689477	C₂²	1	2	yes	—
48	#15689477	C₂²	1	2	yes	—
49	#15689477	C₂²	1	2	yes	—
50	#15689477	C₂²	1	2	yes	—
51	#15689477	C₂²	1	2	yes	—
52	#15689477	C₂²	1	2	yes	complemented
53	#15689473	C₂²	1	2	yes	complemented
54	#15689469	C₂²	1	2	yes	—
55	#15689430	C₂²	1	2	yes	complemented
56	#15689430	C₂²	1	2	yes	complemented
57	#15689430	C₂²	1	2	yes	complemented
58	#15689430	C₂²	1	2	yes	complemented
59	#15689423	C₂²	1	2	yes	—
60	#15689423	C₂²	1	2	yes	—
61	#15689423	C₂²	1	2	yes	complemented
62	#15689423	C₂²	1	2	yes	complemented
63	#15689418	C₂²	1	2	yes	complemented
64	#15689413	C₂²	1	2	yes	—
65	#15689408	C₂²	1	2	yes	complemented
66	#15689403	C₂²	1	2	yes	—
67	#15689342	C₂²	1	2	yes	—
68	#15689342	C₂²	1	2	yes	—
69	#15689342	C₂²	1	2	yes	—
70	#15689342	C₂²	1	2	yes	complemented
71	#15689335	C₂²	1	2	yes	—
72	#15689335	C₂²	1	2	yes	—
73	#15689335	C₂²	1	2	yes	—
74	#15689335	C₂²	1	2	yes	complemented
75	#15689330	C₂²	1	2	yes	complemented
76	#15689325	C₂²	1	2	yes	complemented
77	#15689320	C₂²	1	2	yes	—
78	#15689315	C₂²	1	2	yes	—
79	#15689254	C₂²	1	2	yes	complemented
80	#15689254	C₂²	1	2	yes	complemented
81	Q₈×C₄₇⋊C₈	C₂²	1	2	yes	complemented
82	Q₈×C₄₇⋊C₈	C₂²	1	2	yes	complemented
83	#15689233	C₂²	1	2	yes	—
84	#15689228	C₂²	1	2	yes	complemented
85	#15689223	C₂²	1	2	yes	—
86	#15689221	C₂²	1	2	yes	complemented
87	C₄×#10625337	C₂²	1	1	yes	characteristic, complemented
88	C₄×#10625337	C₂²	1	2	yes	complemented
89	C₄×#10625337	C₂²	1	1	yes	characteristic, complemented
90	C₄×#10625336	C₂²	1	1	yes	characteristic, complemented
91	C₄×#10625336	C₂²	1	2	yes	complemented
92	C₄×#10625336	C₂²	1	1	yes	characteristic, complemented
93	C₄×#10625335	C₂²	1	2	yes	—
94	C₄×#10625335	C₂²	1	1	yes	characteristic, complemented
95	C₄×#10625335	C₂²	1	1	yes	characteristic, complemented
96	C₄×#10625334	C₂²	1	2	yes	—
97	C₄×#10625334	C₂²	1	1	yes	characteristic, complemented
98	C₄×#10625334	C₂²	1	1	yes	characteristic, complemented
99	#15689166	C₂²	1	1	yes	characteristic
100	#15689166	C₂²	1	1	yes	characteristic
101	#15689159	C₂²	1	1	yes	characteristic
102	#15689150	C₂²	1	1	yes	characteristic
103	#15689150	C₂²	1	1	yes	characteristic
104	#15689147	C₂²	1	1	yes	characteristic
105	#15689132	C₂²	1	1	yes	characteristic
106	#15689128	C₂²	1	1	yes	characteristic
107	#15689124	C₂²	1	1	yes	characteristic
108	#15689124	C₂²	1	1	yes	characteristic
109	#15689119	C₂²	1	1	yes	characteristic
110	#15689117	C₂²	1	1	yes	characteristic
111	C₂×#13093948	C₂²	1	1	yes	characteristic
112	C₂×#13093948	C₂²	1	1	yes	characteristic
113	C₂×#13093945	C₂²	1	1	yes	characteristic
114	C₂×#13093945	C₂²	1	1	yes	characteristic
115	#15689079	C₂²	1	1	yes	characteristic
116	#15689079	C₂²	1	1	yes	characteristic
117	C₂×C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
118	C₄₇×#559	C₂²	1	2	yes	—
119	C₄₇×#559	C₂²	1	2	yes	—
120	C₄₇×#556	C₂²	1	2	yes	—
121	C₄₇×#556	C₂²	1	2	yes	—
122	C₄₇×#551	—	2	2	no	—
123	C₄₇×#551	—	2	2	no	—
124	C₄₇×#542	—	2	1	no	—
125	C₄₇×#542	—	2	1	no	—
126	C₄₇×#536	C₂²	1	1	yes	characteristic
127	C₄₇×#535	C₂²	1	1	yes	characteristic
128	C₄₇×#533	C₂²	1	1	yes	characteristic
129	C₄₇×#529	—	2	1	no	—
130	C₄₇×#529	—	2	1	no	—
131	C₂×#124×C₄₇	C₂²	1	1	yes	characteristic
132	C₄₇×#519	C₂²	1	1	yes	characteristic
133	C₄₇×#518	C₂²	1	1	yes	characteristic
134	C₄×#41×C₄₇	C₂²	1	1	yes	characteristic
135	C₂×#10625350	C₂³	1	1	yes	characteristic
136	#13094055	—	2	4	no	—
137	#13094050	—	2	4	no	—
138	#13094044	—	2	4	no	—
139	C₂×#10625337	C₂³	1	1	yes	characteristic
140	C₂×#10625337	C₂³	1	2	yes	—
141	C₂×#10625335	C₂³	1	2	yes	—
142	C₂×#10625335	C₂³	1	1	yes	characteristic
143	C₂×#10625336	C₂³	1	2	yes	—
144	C₂×#10625336	C₂³	1	1	yes	characteristic
145	C₂×#10625334	C₂³	1	2	yes	—
146	C₂×#10625334	C₂³	1	1	yes	characteristic
147	C₂×#10625329	C₂³	1	1	yes	characteristic
148	C₂×#10625329	C₂³	1	1	yes	characteristic
149	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
150	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
151	#13094024	C₂³	1	2	yes	—
152	#13094024	C₂³	1	2	yes	—
153	#13094023	—	2	1	no	—
154	#13094023	—	2	1	no	—
155	#13094022	—	2	2	no	—
156	#13094022	—	2	2	no	—
157	#13094016	—	2	1	no	—
158	#13094016	—	2	1	no	—
159	#13094016	C₂³	1	2	yes	—
160	#13094016	C₂³	1	2	yes	—
161	#13094016	C₂³	1	2	yes	—
162	#13094016	C₂³	1	2	yes	—
163	#13094015	—	2	1	no	—
164	#13094015	—	2	1	no	—
165	#13094014	—	2	2	no	—
166	#13094014	—	2	2	no	—
167	#13094014	—	2	2	no	—
168	#13094014	—	2	2	no	—
169	#13094002	—	2	2	no	—
170	#13094002	—	2	2	no	—
171	#13094002	—	2	2	no	—
172	#13094002	—	2	2	no	—
173	#13094001	—	2	2	no	—
174	#13094001	—	2	2	no	—
175	#13094000	—	2	2	no	—
176	#13094000	—	2	2	no	—
177	C₄×Dic₉₄	C₂³	1	2	yes	—
178	C₄×Dic₉₄	C₂³	1	1	yes	characteristic
179	C₄×Dic₉₄	C₂³	1	1	yes	characteristic
180	C₄×Dic₉₄	C₂³	1	2	yes	—
181	#13093989	—	2	2	no	—
182	#13093989	—	2	2	no	—
183	C₄×D₁₈₈	C₂³	1	2	yes	—
184	C₄×D₁₈₈	C₂³	1	2	yes	—
185	C₄×D₁₈₈	C₂³	1	1	yes	characteristic
186	C₄×D₁₈₈	C₂³	1	1	yes	characteristic
187	C₄×C₂²⋊D₄₇	—	2	1	no	—
188	C₄×C₂²⋊D₄₇	—	2	1	no	—
189	(C₂²⋊D₄₇)⋊C₄	—	2	2	no	—
190	(C₂²⋊D₄₇)⋊C₄	—	2	2	no	—
191	#13093983	C₂³	1	1	yes	characteristic
192	#13093982	—	2	1	no	—
193	#13093982	—	2	1	no	—
194	#13093981	—	2	1	no	—
195	C₂×C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic
196	C₂×C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic
197	C₂×Dic₄₇⋊C₄	—	2	1	no	—
198	C₂×Dic₄₇⋊C₄	—	2	1	no	—
199	C₄⋊C₄×D₄₇	—	2	1	no	—
200	C₄⋊C₄×D₄₇	—	2	1	no	—
201	C₄⋊C₄×D₄₇	—	2	2	no	—
202	C₄⋊C₄×D₄₇	—	2	2	no	—
203	C₄²×D₄₇	—	2	1	no	—
204	#13093957	C₂³	1	2	yes	—
205	#13093957	C₂³	1	1	yes	characteristic
206	#13093957	C₂³	1	1	yes	characteristic
207	#13093957	C₂³	1	2	yes	—
208	#13093955	C₂³	1	2	yes	—
209	#13093955	C₂³	1	2	yes	—
210	#13093955	C₂³	1	1	yes	characteristic
211	#13093955	C₂³	1	1	yes	characteristic
212	C₄⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
213	C₄⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
214	C₄⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
215	C₄⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
216	C₄⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
217	C₄⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
218	#13093948	C₂³	1	1	yes	characteristic
219	#13093948	C₂³	1	2	yes	—
220	#13093948	C₂³	1	1	yes	characteristic
221	#13093948	C₂³	1	2	yes	—
222	#13093948	C₂³	1	2	yes	—
223	#13093948	C₂³	1	2	yes	—
224	#13093948	C₂³	1	2	yes	—
225	#13093948	C₂³	1	2	yes	—
226	#13093948	C₂³	1	2	yes	—
227	#13093948	C₂³	1	2	yes	—
228	#13093947	C₂³	1	1	yes	characteristic
229	#13093947	C₂³	1	1	yes	characteristic
230	#13093945	C₂³	1	2	yes	—
231	#13093945	C₂³	1	2	yes	—
232	#13093945	C₂³	1	2	yes	—
233	#13093945	C₂³	1	2	yes	—
234	#13093945	C₂³	1	2	yes	—
235	#13093945	C₂³	1	1	yes	characteristic
236	#13093945	C₂³	1	2	yes	—
237	#13093945	C₂³	1	2	yes	—
238	#13093945	C₂³	1	1	yes	characteristic
239	#13093945	C₂³	1	2	yes	—
240	#13093944	C₂³	1	1	yes	characteristic
241	#13093944	C₂³	1	1	yes	characteristic
242	#13093935	C₂³	1	2	yes	—
243	#13093935	C₂³	1	2	yes	—
244	C₄×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
245	C₄×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
246	C₄×C₄₇⋊C₈	C₂³	1	2	yes	—
247	C₄×C₄₇⋊C₈	C₂³	1	2	yes	—
248	C₄×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
249	C₄×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
250	C₂×#41×C₄₇	C₂³	1	1	yes	characteristic
251	C₂²×Q₈×C₄₇	C₂³	1	1	yes	characteristic
252	C₂²×D₄×C₄₇	C₂³	1	1	yes	characteristic
253	C₄⋊Q₈×C₄₇	D₄	1	1	yes	characteristic
254	C₄⋊Q₈×C₄₇	D₄	1	1	yes	characteristic
255	C₄⋊Q₈×C₄₇	C₂³	1	2	yes	—
256	#127×C₄₇	C₂³	1	2	yes	—
257	#126×C₄₇	—	2	2	no	—
258	#126×C₄₇	—	2	2	no	—
259	#126×C₄₇	—	2	2	no	—
260	#126×C₄₇	—	2	2	no	—
261	#125×C₄₇	D₄	1	1	yes	characteristic
262	#125×C₄₇	D₄	1	1	yes	characteristic
263	#124×C₄₇	—	2	2	no	—
264	#124×C₄₇	—	2	2	no	—
265	#124×C₄₇	—	2	1	no	—
266	#124×C₄₇	—	2	1	no	—
267	#124×C₄₇	C₂³	1	2	yes	—
268	#124×C₄₇	C₂³	1	2	yes	—
269	#124×C₄₇	C₂³	1	2	yes	—
270	#124×C₄₇	C₂³	1	2	yes	—
271	#123×C₄₇	—	2	2	no	—
272	#123×C₄₇	—	2	2	no	—
273	#123×C₄₇	—	2	2	no	—
274	#123×C₄₇	—	2	2	no	—
275	#123×C₄₇	—	2	2	no	—
276	C₂²⋊Q₈×C₄₇	—	2	2	no	—
277	C₂²⋊Q₈×C₄₇	—	2	2	no	—
278	C₂²⋊Q₈×C₄₇	—	2	1	no	—
279	C₂²⋊Q₈×C₄₇	—	2	1	no	—
280	C₂²⋊Q₈×C₄₇	D₄	1	2	yes	—
281	C₂²⋊Q₈×C₄₇	D₄	1	2	yes	—
282	#121×C₄₇	—	2	1	no	—
283	#121×C₄₇	—	2	1	no	—
284	#120×C₄₇	—	2	2	no	—
285	C₄×Q₈×C₄₇	—	2	1	no	—
286	C₄×Q₈×C₄₇	—	2	1	no	—
287	C₄×Q₈×C₄₇	C₂³	1	2	yes	—
288	C₄×Q₈×C₄₇	C₂³	1	1	yes	characteristic
289	C₄×Q₈×C₄₇	C₂³	1	1	yes	characteristic
290	C₄×Q₈×C₄₇	C₂³	1	2	yes	—
291	C₄×Q₈×C₄₇	C₂³	1	2	yes	—
292	C₄×Q₈×C₄₇	C₂³	1	2	yes	—
293	C₄×D₄×C₄₇	—	2	1	no	—
294	C₄×D₄×C₄₇	—	2	1	no	—
295	C₄×D₄×C₄₇	—	2	1	no	—
296	C₄×D₄×C₄₇	—	2	1	no	—
297	C₄×D₄×C₄₇	—	2	2	no	—
298	C₄×D₄×C₄₇	—	2	2	no	—
299	C₄×D₄×C₄₇	C₂³	1	2	yes	—
300	C₄×D₄×C₄₇	C₂³	1	2	yes	—
301	C₄×D₄×C₄₇	C₂³	1	1	yes	characteristic
302	C₄×D₄×C₄₇	C₂³	1	1	yes	characteristic
303	#117×C₄₇	—	2	2	no	—
304	#117×C₄₇	—	2	2	no	—
305	#117×C₄₇	—	2	2	no	—
306	#117×C₄₇	—	2	1	no	—
307	#117×C₄₇	C₂³	1	1	yes	characteristic
308	#117×C₄₇	C₂³	1	1	yes	characteristic
309	#117×C₄₇	C₂³	1	1	yes	characteristic
310	C₂×C₂²⋊C₄×C₄₇	—	2	1	no	—
311	C₂×C₂²⋊C₄×C₄₇	—	2	1	no	—
312	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
313	C₂×C₄²×C₄₇	—	2	1	no	—
314	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
315	C₂⁴×C₄₇	—	2	1	no	—
316	#41×C₄₇	—	2	2	no	—
317	#41×C₄₇	—	2	2	no	—
318	C₂×Q₈×C₄₇	—	2	1	no	—
319	C₂×Q₈×C₄₇	—	2	2	no	—
320	C₂×Q₈×C₄₇	—	2	2	no	—
321	C₂×Q₈×C₄₇	C₂×D₄	1	2	yes	—
322	C₂×Q₈×C₄₇	C₂×D₄	1	2	yes	—
323	C₂×Q₈×C₄₇	C₂⁴	1	2	yes	—
324	C₂×Q₈×C₄₇	C₂⁴	1	1	yes	characteristic
325	C₂×D₄×C₄₇	—	2	1	no	—
326	C₂×D₄×C₄₇	—	2	1	no	—
327	C₂×D₄×C₄₇	—	2	2	no	—
328	C₂×D₄×C₄₇	—	2	2	no	—
329	C₂×D₄×C₄₇	—	2	2	no	—
330	C₂×D₄×C₄₇	—	2	2	no	—
331	C₂×D₄×C₄₇	C₂⁴	1	2	yes	—
332	C₂×D₄×C₄₇	C₂⁴	1	1	yes	characteristic
333	C₂²×C₄×C₄₇	—	2	1	no	—
334	C₂²×C₄×C₄₇	—	2	1	no	—
335	C₂²×C₄×C₄₇	—	2	1	no	—
336	C₂²×C₄×C₄₇	—	2	1	no	—
337	C₂²×C₄×C₄₇	—	2	2	no	—
338	C₂²×C₄×C₄₇	—	2	2	no	—
339	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
340	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
341	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
342	C₂×C₂²⋊D₄₇	—	2	1	no	—
343	C₂²×Dic₄₇	—	2	1	no	—
344	C₂²×Dic₄₇	—	2	1	no	—
345	#10625350	—	2	2	no	—
346	#10625350	#41	1	4	yes	—
347	C₂×D₁₈₈	C₂⁴	1	1	yes	characteristic
348	C₂×C₄×D₄₇	—	2	1	no	—
349	C₂×C₄×D₄₇	—	2	1	no	—
350	C₂×C₄×D₄₇	—	2	1	no	—
351	C₂×C₄×D₄₇	—	2	2	no	—
352	C₂×C₄×D₄₇	—	2	2	no	—
353	C₂×Dic₉₄	—	2	2	no	—
354	C₂×Dic₉₄	—	2	2	no	—
355	C₂×Dic₉₄	C₂⁴	1	1	yes	characteristic
356	C₄⋊C₄×C₄₇	—	2	1	no	—
357	C₄⋊C₄×C₄₇	—	2	1	no	—
358	C₄⋊C₄×C₄₇	—	2	2	no	—
359	C₄⋊C₄×C₄₇	—	2	2	no	—
360	C₄⋊C₄×C₄₇	—	2	2	no	—
361	C₄⋊C₄×C₄₇	—	2	2	no	—
362	C₄⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
363	C₄⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
364	C₄⋊C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
365	C₄⋊C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
366	C₄⋊C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
367	C₄⋊C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
368	C₄⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
369	C₄⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
370	C₄⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
371	C₄⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
372	C₄⋊C₄×C₄₇	C₂⁴	1	1	yes	characteristic
373	C₄⋊C₄×C₄₇	C₂⁴	1	1	yes	characteristic
374	C₂²⋊C₄×C₄₇	—	2	1	no	—
375	C₂²⋊C₄×C₄₇	—	2	2	no	—
376	C₂²⋊C₄×C₄₇	—	2	2	no	—
377	C₂²⋊C₄×C₄₇	—	2	2	no	—
378	C₂²⋊C₄×C₄₇	—	2	2	no	—
379	C₂²⋊C₄×C₄₇	—	2	2	no	—
380	C₂²⋊C₄×C₄₇	—	2	2	no	—
381	C₂²⋊C₄×C₄₇	—	2	1	no	—
382	C₂²⋊C₄×C₄₇	—	2	1	no	—
383	C₂²⋊C₄×C₄₇	—	2	2	no	—
384	C₂²⋊C₄×C₄₇	—	2	2	no	—
385	C₂²⋊C₄×C₄₇	—	2	2	no	—
386	C₂²⋊C₄×C₄₇	—	2	2	no	—
387	C₂²⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
388	C₂²⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
389	C₄²×C₄₇	—	2	1	no	—
390	C₄²×C₄₇	—	2	1	no	—
391	C₄²×C₄₇	—	2	1	no	—
392	C₄²×C₄₇	—	2	2	no	—
393	C₄²×C₄₇	—	2	2	no	—
394	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
395	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
396	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
397	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
398	C₄²×C₄₇	C₂⁴	1	2	yes	—
399	C₄²×C₄₇	C₂⁴	1	2	yes	—
400	C₂²⋊Dic₄₇	—	2	1	no	—
401	#10625337	—	2	2	no	—
402	#10625337	—	2	4	no	—
403	#10625336	—	2	2	no	—
404	#10625336	—	2	4	no	—
405	#10625335	—	2	2	no	—
406	#10625335	—	2	4	no	—
407	#10625334	—	2	2	no	—
408	#10625334	—	2	4	no	—
409	(C₂×D₄₇)⋊C₄	—	2	1	no	—
410	(C₂×D₄₇)⋊C₄	—	2	1	no	—
411	(C₂×D₄₇)⋊C₄	—	2	2	no	—
412	(C₂×D₄₇)⋊C₄	—	2	2	no	—
413	C₄⋊Dic₄₇	—	2	1	no	—
414	C₄⋊Dic₄₇	—	2	1	no	—
415	C₄⋊Dic₄₇	—	2	2	no	—
416	C₄⋊Dic₄₇	—	2	2	no	—
417	C₄⋊Dic₄₇	C₂⁴	1	2	yes	—
418	C₄⋊Dic₄₇	C₂⁴	1	2	yes	—
419	C₄⋊Dic₄₇	C₂⁴	1	1	yes	characteristic
420	C₄⋊Dic₄₇	C₂⁴	1	1	yes	characteristic
421	Dic₄₇⋊C₄	—	2	2	no	—
422	Dic₄₇⋊C₄	—	2	2	no	—
423	Dic₄₇⋊C₄	—	2	2	no	—
424	Dic₄₇⋊C₄	—	2	2	no	—
425	Dic₄₇⋊C₄	—	2	2	no	—
426	Dic₄₇⋊C₄	—	2	2	no	—
427	Dic₄₇⋊C₄	—	2	2	no	—
428	Dic₄₇⋊C₄	—	2	2	no	—
429	Dic₄₇⋊C₄	—	2	1	no	—
430	Dic₄₇⋊C₄	—	2	1	no	—
431	Dic₄₇⋊C₄	—	2	2	no	—
432	Dic₄₇⋊C₄	—	2	2	no	—
433	C₄×Dic₄₇	—	2	1	no	—
434	C₄×Dic₄₇	—	2	1	no	—
435	C₄×Dic₄₇	—	2	1	no	—
436	C₄×Dic₄₇	—	2	2	no	—
437	C₄×Dic₄₇	—	2	2	no	—
438	#10625329	—	2	2	no	—
439	#10625329	—	2	2	no	—
440	C₂×C₄₇⋊C₈	—	2	2	no	—
441	C₂×C₄₇⋊C₈	—	2	2	no	—
442	C₂×C₄₇⋊C₈	C₂⁴	1	1	yes	characteristic
443	C₂×C₄₇⋊C₈	C₂⁴	1	1	yes	characteristic
444	C₂×C₄₇⋊C₈	C₂⁴	1	1	yes	characteristic
445	C₂×C₄₇⋊C₈	C₂⁴	1	1	yes	characteristic
446	C₂×C₄₇⋊C₈	C₂⁴	1	2	yes	—
447	C₂×C₄₇⋊C₈	C₂⁴	1	2	yes	—
448	C₂³×C₄₇	—	2	2	no	—
449	C₂³×C₄₇	—	2	1	no	—
450	C₂³×C₄₇	—	4	2	no	—
451	C₂³×C₄₇	—	8	1	no	—
452	C₂³×C₄₇	—	8	1	no	—
453	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
454	C₂²×D₄₇	—	2	1	no	—
455	Q₈×C₄₇	—	2	2	no	—
456	Q₈×C₄₇	—	2	1	no	—
457	Q₈×C₄₇	—	2	2	no	—
458	Q₈×C₄₇	—	2	1	no	—
459	Q₈×C₄₇	—	4	2	no	—
460	Q₈×C₄₇	—	4	2	no	—
461	Q₈×C₄₇	—	4	2	no	—
462	D₄×C₄₇	—	2	2	no	—
463	D₄×C₄₇	—	2	1	no	—
464	D₄×C₄₇	—	2	2	no	—
465	D₄×C₄₇	—	2	1	no	—
466	D₄×C₄₇	—	4	2	no	—
467	D₄×C₄₇	—	4	2	no	—
468	D₄×C₄₇	—	8	2	no	—
469	D₄×C₄₇	—	8	2	no	—
470	C₂×C₄×C₄₇	—	2	1	no	—
471	C₂×C₄×C₄₇	—	2	1	no	—
472	C₂×C₄×C₄₇	—	2	2	no	—
473	C₂×C₄×C₄₇	—	2	1	no	—
474	C₂×C₄×C₄₇	—	4	1	no	—
475	C₂×C₄×C₄₇	—	4	1	no	—
476	C₂×C₄×C₄₇	—	4	2	no	—
477	C₂×C₄×C₄₇	—	4	2	no	—
478	C₂×C₄×C₄₇	—	8	2	no	—
479	C₂×C₄×C₄₇	—	8	1	no	—
480	C₂×C₄×C₄₇	—	8	1	no	—
481	C₂×C₄×C₄₇	—	8	2	no	—
482	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
483	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
484	C₂×C₄×C₄₇	C₂²×D₄	1	2	yes	—
485	C₂×C₄×C₄₇	C₂²×D₄	1	2	yes	—
486	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
487	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
488	C₂×C₄×C₄₇	C₂²×D₄	1	2	yes	—
489	C₂×C₄×C₄₇	C₂²×D₄	1	2	yes	—
490	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
491	C₂×C₄×C₄₇	C₂×#41	1	2	yes	—
492	C₂×C₄×C₄₇	2₋¹⁺⁴	1	2	yes	—
493	C₂×C₄×C₄₇	C₂⁵	1	1	yes	characteristic
494	C₂²⋊D₄₇	—	2	4	no	—
495	C₂×Dic₄₇	—	2	1	no	—
496	C₂×Dic₄₇	—	2	1	no	—
497	C₂×Dic₄₇	—	2	1	no	—
498	C₂×Dic₄₇	—	2	2	no	—
499	C₂×Dic₄₇	—	2	2	no	—
500	C₂×Dic₄₇	—	8	1	no	—
501	C₂×Dic₄₇	—	8	1	no	—
502	D₁₈₈	—	2	1	no	—
503	D₁₈₈	C₂×#41	1	2	yes	—
504	C₄×D₄₇	—	2	4	no	—
505	C₄×D₄₇	—	8	1	no	—
506	C₄×D₄₇	—	8	1	no	—
507	C₄×D₄₇	—	8	2	no	—
508	C₄×D₄₇	—	8	2	no	—
509	Dic₉₄	—	2	1	no	—
510	Dic₉₄	—	8	2	no	—
511	Dic₉₄	—	8	2	no	—
512	Dic₉₄	C₂×#41	1	2	yes	—
513	C₄₇⋊C₈	—	2	1	no	—
514	C₄₇⋊C₈	—	2	1	no	—
515	C₄₇⋊C₈	—	2	2	no	—
516	C₄₇⋊C₈	—	2	2	no	—
517	C₄₇⋊C₈	—	2	1	no	—
518	C₄₇⋊C₈	—	2	1	no	—
519	#61331	—	47	1	no	maximal, Sylow
520	C₂²×C₄₇	—	2	1	no	—
521	C₂²×C₄₇	—	2	1	no	—
522	C₂²×C₄₇	—	4	1	no	—
523	C₂²×C₄₇	—	4	1	no	—
524	C₂²×C₄₇	—	4	2	no	—
525	C₂²×C₄₇	—	4	2	no	—
526	C₂²×C₄₇	—	4	1	no	—
527	C₂²×C₄₇	—	4	2	no	—
528	C₂²×C₄₇	—	16	2	no	—
529	C₂²×C₄₇	#548	1	2	yes	—
530	C₂²×C₄₇	C₂³×D₄	1	1	yes	characteristic
531	C₂×D₄₇	—	2	2	no	—
532	C₂×D₄₇	—	4	1	no	—
533	C₂×D₄₇	—	4	1	no	—
534	C₄×C₄₇	—	2	2	no	—
535	C₄×C₄₇	—	2	2	no	—
536	C₄×C₄₇	—	2	1	no	—
537	C₄×C₄₇	—	2	1	no	—
538	C₄×C₄₇	—	2	2	no	—
539	C₄×C₄₇	—	2	2	no	—
540	C₄×C₄₇	—	2	1	no	—
541	C₄×C₄₇	—	2	1	no	—
542	C₄×C₄₇	—	4	1	no	—
543	C₄×C₄₇	—	4	1	no	—
544	C₄×C₄₇	—	4	1	no	—
545	C₄×C₄₇	—	4	2	no	—
546	C₄×C₄₇	#548	1	2	yes	—
547	C₄×C₄₇	C₂²×#41	1	1	yes	characteristic
548	C₄×C₄₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
549	Dic₄₇	—	2	2	no	—
550	Dic₄₇	—	4	1	no	—
551	Dic₄₇	—	4	1	no	—
552	Dic₄₇	—	4	2	no	—
553	Dic₄₇	—	4	2	no	—
554	#3510	D₄₇	1	1	yes	characteristic, complemented
555	#3504	—	47	1	no	—
556	#3377	—	47	2	no	—
557	#3376	—	47	2	no	—
558	#3371	—	47	2	no	—
559	#3370	—	47	2	no	—
560	#3365	—	47	2	no	—
561	#3364	—	47	2	no	—
562	#3361	—	47	2	no	—
563	#3360	—	47	2	no	—
564	#3137	—	47	1	no	—
565	#3136	—	47	1	no	—
566	C₂×#488	—	47	1	no	—
567	#3082	—	47	1	no	—
568	#3081	—	47	1	no	—
569	#3080	—	47	1	no	—
570	#3046	—	47	1	no	—
571	#3045	—	47	1	no	—
572	#3040	—	47	1	no	—
573	#2960	—	47	1	no	—
574	#2947	—	47	1	no	—
575	#2946	—	47	1	no	—
576	C₄×#135	—	47	1	no	—
577	C₂×C₄₇	—	2	2	no	—
578	C₂×C₄₇	—	8	1	no	—
579	C₂×C₄₇	—	8	2	no	—
580	C₂×C₄₇	C₂×#548	1	1	yes	characteristic
581	C₂×C₄₇	#3584	1	1	yes	characteristic
582	C₂×C₄₇	#3584	1	1	yes	characteristic
583	D₄₇	—	4	2	no	—
584	C₂×#137	—	47	1	no	—
585	C₂×AGL(1,ℤ/8)	—	47	1	no	—
586	C₂×#135	—	47	1	no	—
587	#559	C₂×D₄₇	1	2	yes	—
588	#559	C₂×D₄₇	1	2	yes	—
589	#557	—	47	2	no	—
590	#557	—	47	2	no	—
591	#556	C₂×D₄₇	1	2	yes	—
592	#556	C₂×D₄₇	1	2	yes	—
593	#554	—	47	2	no	—
594	#554	—	47	2	no	—
595	#554	—	94	2	no	—
596	#554	—	94	2	no	—
597	#551	—	2	2	no	—
598	#551	—	2	2	no	—
599	#544	—	47	1	no	—
600	#544	—	47	1	no	—
601	#544	—	94	1	no	—
602	#544	—	94	1	no	—
603	#542	—	2	1	no	—
604	#542	—	2	1	no	—
605	#536	C₂×D₄₇	1	1	yes	characteristic
606	#535	C₂×D₄₇	1	1	yes	characteristic
607	#533	—	94	1	no	—
608	#533	C₂×D₄₇	1	1	yes	characteristic
609	#529	—	2	1	no	—
610	#529	—	2	1	no	—
611	C₂×#125	—	47	1	no	—
612	C₂×#125	—	94	1	no	—
613	C₂×#124	C₂×D₄₇	1	1	yes	characteristic
614	#520	—	47	1	no	—
615	#520	—	47	1	no	—
616	#519	C₂×D₄₇	1	1	yes	characteristic
617	#518	C₂×D₄₇	1	1	yes	characteristic
618	C₄×#41	—	47	1	no	—
619	C₄×#41	C₂×D₄₇	1	1	yes	characteristic
620	#491	—	47	2	no	—
621	#490	—	47	2	no	—
622	#489	—	47	2	no	—
623	#489	—	47	2	no	—
624	#488	—	47	2	no	—
625	#488	—	47	2	no	—
626	#488	—	47	2	no	—
627	#488	—	47	2	no	—
628	#488	—	47	2	no	—
629	#488	—	47	2	no	—
630	#487	—	47	2	no	—
631	#486	—	47	2	no	—
632	#479	—	47	2	no	—
633	#479	—	47	2	no	—
634	#479	—	47	2	no	—
635	#479	—	47	2	no	—
636	#478	—	47	2	no	—
637	#478	—	47	2	no	—
638	#478	—	47	2	no	—
639	#478	—	47	2	no	—
640	#477	—	47	2	no	—
641	#476	—	47	2	no	—
642	#475	—	47	2	no	—
643	#474	—	47	2	no	—
644	#464	—	47	2	no	—
645	#464	—	47	2	no	—
646	#464	—	47	2	no	—
647	#464	—	47	2	no	—
648	#463	—	47	2	no	—
649	#463	—	47	2	no	—
650	#463	—	47	2	no	—
651	#463	—	47	2	no	—
652	#462	—	47	2	no	—
653	#461	—	47	2	no	—
654	#460	—	47	2	no	—
655	#459	—	47	2	no	—
656	#446	—	47	2	no	—
657	#446	—	47	2	no	—
658	C₈×Q₈	—	47	2	no	—
659	C₈×Q₈	—	47	2	no	—
660	#442	—	47	2	no	—
661	#441	—	47	2	no	—
662	#440	—	47	2	no	—
663	#440	—	47	2	no	—
664	C₄×Q₁₆	—	47	1	no	—
665	C₄×Q₁₆	—	47	2	no	—
666	C₄×Q₁₆	—	47	1	no	—
667	C₄×SD₁₆	—	47	1	no	—
668	C₄×SD₁₆	—	47	2	no	—
669	C₄×SD₁₆	—	47	1	no	—
670	C₄×SD₁₆	—	47	2	no	—
671	C₄×SD₁₆	—	47	1	no	—
672	C₄×SD₁₆	—	47	1	no	—
673	C₄×D₈	—	47	2	no	—
674	C₄×D₈	—	47	1	no	—
675	C₄×D₈	—	47	1	no	—
676	#428	—	47	1	no	—
677	#428	—	47	1	no	—
678	#427	—	47	1	no	—
679	#424	—	47	1	no	—
680	#424	—	47	1	no	—
681	#423	—	47	1	no	—
682	#419	—	47	1	no	—
683	#418	—	47	1	no	—
684	#417	—	47	1	no	—
685	#417	—	47	1	no	—
686	#416	—	47	1	no	—
687	#416	—	47	1	no	—
688	C₂×#103	—	47	1	no	—
689	C₂×#103	—	47	1	no	—
690	C₂×#102	—	47	1	no	—
691	C₂×#102	—	47	1	no	—
692	#405	—	47	1	no	—
693	#405	—	47	1	no	—
694	C₂×C₄×C₈	—	47	1	no	—
695	C₄₇	#61331	1	1	yes	characteristic, complemented, Sylow
696	C₂×#41	—	47	1	no	—
697	C₂×#41	C₂²×D₄₇	1	1	yes	characteristic
698	C₂²×Q₈	C₂²×D₄₇	1	1	yes	characteristic
699	C₂²×D₄	C₂²×D₄₇	1	1	yes	characteristic
700	#137	—	94	4	no	—
701	AGL(1,ℤ/8)	—	94	4	no	—
702	#135	—	94	4	no	—
703	C₂×Q₁₆	—	47	1	no	—
704	C₂×Q₁₆	—	47	2	no	—
705	C₂×SD₁₆	—	47	1	no	—
706	C₂×SD₁₆	—	47	2	no	—
707	C₂×SD₁₆	—	47	1	no	—
708	C₂×SD₁₆	—	47	2	no	—
709	C₂×D₈	—	47	1	no	—
710	C₂×D₈	—	47	2	no	—
711	C₂×M₁₆	—	47	1	no	—
712	C₂×M₁₆	—	47	1	no	—
713	C₂²×C₈	—	47	1	no	—
714	C₂²×C₈	—	47	1	no	—
715	C₄⋊Q₈	—	47	2	no	—
716	C₄⋊Q₈	—	47	2	no	—
717	C₄⋊Q₈	—	94	2	no	—
718	C₄⋊Q₈	—	94	2	no	—
719	C₄⋊Q₈	—	94	1	no	—
720	C₄⋊Q₈	—	94	1	no	—
721	C₄⋊Q₈	C₂²⋊D₄₇	1	1	yes	characteristic
722	C₄⋊Q₈	C₂²⋊D₄₇	1	1	yes	characteristic
723	C₄⋊Q₈	C₂²×D₄₇	1	2	yes	—
724	#127	C₂²×D₄₇	1	2	yes	—
725	#126	—	2	2	no	—
726	#126	—	2	2	no	—
727	#126	—	2	2	no	—
728	#126	—	2	2	no	—
729	#125	—	47	2	no	—
730	#125	—	47	2	no	—
731	#125	—	47	2	no	—
732	#125	—	47	2	no	—
733	#125	—	94	1	no	—
734	#125	—	94	1	no	—
735	#125	—	94	2	no	—
736	#125	—	94	2	no	—
737	#125	—	94	2	no	—
738	#125	—	94	2	no	—
739	#125	—	94	1	no	—
740	#125	—	94	1	no	—
741	#125	C₂²⋊D₄₇	1	1	yes	characteristic
742	#125	C₂²⋊D₄₇	1	1	yes	characteristic
743	#124	—	2	2	no	—
744	#124	—	2	2	no	—
745	#124	—	2	1	no	—
746	#124	—	2	1	no	—
747	#124	C₂²×D₄₇	1	2	yes	—
748	#124	C₂²×D₄₇	1	2	yes	—
749	#124	C₂²×D₄₇	1	2	yes	—
750	#124	C₂²×D₄₇	1	2	yes	—
751	#123	—	2	2	no	—
752	#123	—	2	2	no	—
753	#123	—	2	2	no	—
754	#123	—	2	2	no	—
755	#123	—	2	2	no	—
756	C₂²⋊Q₈	—	2	2	no	—
757	C₂²⋊Q₈	—	2	2	no	—
758	C₂²⋊Q₈	—	2	1	no	—
759	C₂²⋊Q₈	—	2	1	no	—
760	C₂²⋊Q₈	—	94	2	no	—
761	C₂²⋊Q₈	—	94	2	no	—
762	C₂²⋊Q₈	—	94	2	no	—
763	C₂²⋊Q₈	—	94	2	no	—
764	C₂²⋊Q₈	—	94	2	no	—
765	C₂²⋊Q₈	—	94	2	no	—
766	C₂²⋊Q₈	—	94	2	no	—
767	C₂²⋊Q₈	—	94	2	no	—
768	C₂²⋊Q₈	C₂²⋊D₄₇	1	2	yes	—
769	C₂²⋊Q₈	C₂²⋊D₄₇	1	2	yes	—
770	#121	—	2	1	no	—
771	#121	—	2	1	no	—
772	#120	—	2	2	no	—
773	C₄×Q₈	—	2	1	no	—
774	C₄×Q₈	—	2	1	no	—
775	C₄×Q₈	—	47	1	no	—
776	C₄×Q₈	—	47	1	no	—
777	C₄×Q₈	—	47	2	no	—
778	C₄×Q₈	—	47	2	no	—
779	C₄×Q₈	—	94	2	no	—
780	C₄×Q₈	—	94	2	no	—
781	C₄×Q₈	C₂²×D₄₇	1	1	yes	characteristic
782	C₄×Q₈	C₂²×D₄₇	1	1	yes	characteristic
783	C₄×Q₈	C₂²×D₄₇	1	2	yes	—
784	C₄×Q₈	C₂²×D₄₇	1	2	yes	—
785	C₄×Q₈	C₂²×D₄₇	1	2	yes	—
786	C₄×Q₈	C₂²×D₄₇	1	2	yes	—
787	C₄×D₄	—	2	1	no	—
788	C₄×D₄	—	2	1	no	—
789	C₄×D₄	—	2	1	no	—
790	C₄×D₄	—	2	1	no	—
791	C₄×D₄	—	2	2	no	—
792	C₄×D₄	—	2	2	no	—
793	C₄×D₄	—	47	1	no	—
794	C₄×D₄	—	47	1	no	—
795	C₄×D₄	—	47	2	no	—
796	C₄×D₄	—	47	2	no	—
797	C₄×D₄	—	94	1	no	—
798	C₄×D₄	—	94	1	no	—
799	C₄×D₄	—	94	2	no	—
800	C₄×D₄	—	94	2	no	—
801	C₄×D₄	C₂²×D₄₇	1	1	yes	characteristic
802	C₄×D₄	C₂²×D₄₇	1	1	yes	characteristic
803	C₄×D₄	C₂²×D₄₇	1	2	yes	—
804	C₄×D₄	C₂²×D₄₇	1	2	yes	—
805	#117	—	2	2	no	—
806	#117	—	2	2	no	—
807	#117	—	2	2	no	—
808	#117	—	2	1	no	—
809	#117	—	47	1	no	—
810	#117	—	94	1	no	—
811	#117	—	94	1	no	—
812	#117	—	94	1	no	—
813	#117	C₂²×D₄₇	1	1	yes	characteristic
814	#117	C₂²×D₄₇	1	1	yes	characteristic
815	#117	C₂²×D₄₇	1	1	yes	characteristic
816	C₂×C₄⋊C₄	—	47	1	no	—
817	C₂×C₄⋊C₄	—	47	1	no	—
818	C₂×C₄⋊C₄	—	94	1	no	—
819	C₂×C₄⋊C₄	—	94	1	no	—
820	C₂×C₄⋊C₄	—	94	1	no	—
821	C₂×C₄⋊C₄	—	94	1	no	—
822	C₂×C₄⋊C₄	—	94	2	no	—
823	C₂×C₄⋊C₄	—	94	2	no	—
824	C₂×C₂²⋊C₄	—	2	1	no	—
825	C₂×C₂²⋊C₄	—	2	1	no	—
826	C₂×C₂²⋊C₄	—	2	2	no	—
827	C₂×C₄²	—	2	1	no	—
828	C₂×C₄²	—	94	1	no	—
829	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
830	#107	—	47	1	no	—
831	#107	—	47	1	no	—
832	#107	—	47	2	no	—
833	#107	—	47	2	no	—
834	#106	—	47	1	no	—
835	#106	—	47	1	no	—
836	#106	—	47	2	no	—
837	#106	—	47	2	no	—
838	C₄⋊C₈	—	47	2	no	—
839	C₄⋊C₈	—	47	2	no	—
840	C₄⋊C₈	—	47	2	no	—
841	C₄⋊C₈	—	47	2	no	—
842	C₄⋊C₈	—	47	2	no	—
843	C₄⋊C₈	—	47	2	no	—
844	#103	—	47	2	no	—
845	#103	—	47	2	no	—
846	#103	—	47	2	no	—
847	#103	—	47	2	no	—
848	#103	—	47	1	no	—
849	#103	—	47	1	no	—
850	#103	—	47	2	no	—
851	#103	—	47	2	no	—
852	#103	—	47	2	no	—
853	#103	—	47	2	no	—
854	#103	—	47	1	no	—
855	#103	—	47	1	no	—
856	#102	—	47	2	no	—
857	#102	—	47	2	no	—
858	#102	—	47	2	no	—
859	#102	—	47	2	no	—
860	#102	—	47	1	no	—
861	#102	—	47	1	no	—
862	#102	—	47	2	no	—
863	#102	—	47	2	no	—
864	#102	—	47	2	no	—
865	#102	—	47	2	no	—
866	#102	—	47	1	no	—
867	#102	—	47	1	no	—
868	#97	—	47	2	no	—
869	#97	—	47	2	no	—
870	C₄×C₈	—	47	1	no	—
871	C₄×C₈	—	47	1	no	—
872	C₄×C₈	—	47	1	no	—
873	C₄×C₈	—	47	1	no	—
874	C₄×C₈	—	47	2	no	—
875	C₄×C₈	—	47	2	no	—
876	C₂⁴	—	2	1	no	—
877	#41	—	2	2	no	—
878	#41	—	2	2	no	—
879	#41	—	47	4	no	—
880	#41	—	94	2	no	—
881	C₂×Q₈	—	2	1	no	—
882	C₂×Q₈	—	2	2	no	—
883	C₂×Q₈	—	2	2	no	—
884	C₂×Q₈	—	47	1	no	—
885	C₂×Q₈	—	94	2	no	—
886	C₂×Q₈	—	94	2	no	—
887	C₂×Q₈	C₂×C₂²⋊D₄₇	1	2	yes	—
888	C₂×Q₈	C₂×C₂²⋊D₄₇	1	2	yes	—
889	C₂×Q₈	C₂³×D₄₇	1	2	yes	—
890	C₂×Q₈	C₂³×D₄₇	1	1	yes	characteristic
891	C₂×D₄	—	2	1	no	—
892	C₂×D₄	—	2	1	no	—
893	C₂×D₄	—	2	2	no	—
894	C₂×D₄	—	2	2	no	—
895	C₂×D₄	—	2	2	no	—
896	C₂×D₄	—	2	2	no	—
897	C₂×D₄	—	47	1	no	—
898	C₂×D₄	—	94	1	no	—
899	C₂×D₄	C₂³×D₄₇	1	2	yes	—
900	C₂×D₄	C₂³×D₄₇	1	1	yes	characteristic
901	C₂²×C₄	—	2	1	no	—
902	C₂²×C₄	—	2	1	no	—
903	C₂²×C₄	—	2	1	no	—
904	C₂²×C₄	—	2	1	no	—
905	C₂²×C₄	—	2	2	no	—
906	C₂²×C₄	—	2	2	no	—
907	C₂²×C₄	—	94	1	no	—
908	C₂²×C₄	—	94	1	no	—
909	C₂²×C₄	—	94	1	no	—
910	C₂²×C₄	—	94	1	no	—
911	C₂²×C₄	—	94	1	no	—
912	C₂²×C₄	—	94	2	no	—
913	C₂²×C₄	—	94	2	no	—
914	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
915	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
916	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
917	Q₁₆	—	94	2	no	—
918	Q₁₆	—	94	4	no	—
919	SD₁₆	—	94	2	no	—
920	SD₁₆	—	94	4	no	—
921	SD₁₆	—	94	2	no	—
922	SD₁₆	—	94	4	no	—
923	D₈	—	94	2	no	—
924	D₈	—	94	4	no	—
925	M₁₆	—	94	2	no	—
926	M₁₆	—	94	2	no	—
927	C₂×C₈	—	47	1	no	—
928	C₂×C₈	—	47	1	no	—
929	C₂×C₈	—	47	1	no	—
930	C₂×C₈	—	47	1	no	—
931	C₂×C₈	—	47	2	no	—
932	C₂×C₈	—	47	2	no	—
933	C₂×C₈	—	94	2	no	—
934	C₂×C₈	—	94	2	no	—
935	C₄⋊C₄	—	2	1	no	—
936	C₄⋊C₄	—	2	1	no	—
937	C₄⋊C₄	—	2	2	no	—
938	C₄⋊C₄	—	2	2	no	—
939	C₄⋊C₄	—	2	2	no	—
940	C₄⋊C₄	—	2	2	no	—
941	C₄⋊C₄	—	47	2	no	—
942	C₄⋊C₄	—	47	2	no	—
943	C₄⋊C₄	—	47	1	no	—
944	C₄⋊C₄	—	47	1	no	—
945	C₄⋊C₄	—	94	2	no	—
946	C₄⋊C₄	—	94	2	no	—
947	C₄⋊C₄	—	94	2	no	—
948	C₄⋊C₄	—	94	2	no	—
949	C₄⋊C₄	—	94	2	no	—
950	C₄⋊C₄	—	94	2	no	—
951	C₄⋊C₄	—	94	2	no	—
952	C₄⋊C₄	—	94	2	no	—
953	C₄⋊C₄	—	94	1	no	—
954	C₄⋊C₄	—	94	1	no	—
955	C₄⋊C₄	—	94	2	no	—
956	C₄⋊C₄	—	94	2	no	—
957	C₄⋊C₄	—	94	1	no	—
958	C₄⋊C₄	—	94	1	no	—
959	C₄⋊C₄	—	94	2	no	—
960	C₄⋊C₄	—	94	2	no	—
961	C₄⋊C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
962	C₄⋊C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
963	C₄⋊C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
964	C₄⋊C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
965	C₄⋊C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
966	C₄⋊C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
967	C₄⋊C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
968	C₄⋊C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
969	C₄⋊C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
970	C₄⋊C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
971	C₄⋊C₄	C₂³×D₄₇	1	1	yes	characteristic
972	C₄⋊C₄	C₂³×D₄₇	1	1	yes	characteristic
973	C₂²⋊C₄	—	2	1	no	—
974	C₂²⋊C₄	—	2	2	no	—
975	C₂²⋊C₄	—	2	2	no	—
976	C₂²⋊C₄	—	2	2	no	—
977	C₂²⋊C₄	—	2	2	no	—
978	C₂²⋊C₄	—	2	2	no	—
979	C₂²⋊C₄	—	2	2	no	—
980	C₂²⋊C₄	—	2	1	no	—
981	C₂²⋊C₄	—	2	1	no	—
982	C₂²⋊C₄	—	2	2	no	—
983	C₂²⋊C₄	—	2	2	no	—
984	C₂²⋊C₄	—	2	2	no	—
985	C₂²⋊C₄	—	2	2	no	—
986	C₂²⋊C₄	—	94	1	no	—
987	C₂²⋊C₄	—	94	1	no	—
988	C₂²⋊C₄	—	94	1	no	—
989	C₂²⋊C₄	—	94	2	no	—
990	C₂²⋊C₄	—	94	2	no	—
991	C₂²⋊C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
992	C₂²⋊C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
993	C₄²	—	2	1	no	—
994	C₄²	—	2	1	no	—
995	C₄²	—	2	1	no	—
996	C₄²	—	2	2	no	—
997	C₄²	—	2	2	no	—
998	C₄²	—	94	1	no	—
999	C₄²	—	94	1	no	—
1000	C₄²	—	94	1	no	—
1001	C₄²	—	94	2	no	—
1002	C₄²	—	94	2	no	—
1003	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
1004	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
1005	C₄²	C₂³×D₄₇	1	1	yes	characteristic
1006	C₄²	C₂³×D₄₇	1	1	yes	characteristic
1007	C₄²	C₂³×D₄₇	1	2	yes	—
1008	C₄²	C₂³×D₄₇	1	2	yes	—
1009	C₂³	—	2	2	no	—
1010	C₂³	—	2	1	no	—
1011	C₂³	—	4	2	no	—
1012	C₂³	—	8	1	no	—
1013	C₂³	—	8	1	no	—
1014	C₂³	—	94	1	no	—
1015	C₂³	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
1016	Q₈	—	2	2	no	—
1017	Q₈	—	2	1	no	—
1018	Q₈	—	2	2	no	—
1019	Q₈	—	2	1	no	—
1020	Q₈	—	4	2	no	—
1021	Q₈	—	4	2	no	—
1022	Q₈	—	4	2	no	—
1023	Q₈	—	47	2	no	—
1024	Q₈	—	94	1	no	—
1025	Q₈	—	376	2	no	—
1026	Q₈	—	376	2	no	—
1027	D₄	—	2	2	no	—
1028	D₄	—	2	1	no	—
1029	D₄	—	2	2	no	—
1030	D₄	—	2	1	no	—
1031	D₄	—	4	2	no	—
1032	D₄	—	4	2	no	—
1033	D₄	—	8	2	no	—
1034	D₄	—	8	2	no	—
1035	D₄	—	47	2	no	—
1036	D₄	—	94	4	no	—
1037	D₄	—	94	1	no	—
1038	C₂×C₄	—	2	1	no	—
1039	C₂×C₄	—	2	1	no	—
1040	C₂×C₄	—	2	2	no	—
1041	C₂×C₄	—	2	1	no	—
1042	C₂×C₄	—	4	1	no	—
1043	C₂×C₄	—	4	1	no	—
1044	C₂×C₄	—	4	2	no	—
1045	C₂×C₄	—	4	2	no	—
1046	C₂×C₄	—	8	1	no	—
1047	C₂×C₄	—	8	1	no	—
1048	C₂×C₄	—	8	2	no	—
1049	C₂×C₄	—	8	2	no	—
1050	C₂×C₄	—	94	1	no	—
1051	C₂×C₄	—	94	4	no	—
1052	C₂×C₄	—	94	1	no	—
1053	C₂×C₄	—	94	1	no	—
1054	C₂×C₄	—	94	2	no	—
1055	C₂×C₄	—	94	2	no	—
1056	C₂×C₄	—	376	1	no	—
1057	C₂×C₄	—	376	1	no	—
1058	C₂×C₄	—	376	2	no	—
1059	C₂×C₄	—	376	2	no	—
1060	C₂×C₄	—	376	1	no	—
1061	C₂×C₄	—	376	1	no	—
1062	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
1063	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
1064	C₂×C₄	C₂²×C₂²⋊D₄₇	1	2	yes	—
1065	C₂×C₄	C₂²×C₂²⋊D₄₇	1	2	yes	—
1066	C₂×C₄	C₂²×C₂²⋊D₄₇	1	2	yes	—
1067	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
1068	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
1069	C₂×C₄	C₂²×C₂²⋊D₄₇	1	2	yes	—
1070	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
1071	C₂×C₄	#41×D₄₇	1	2	yes	—
1072	C₂×C₄	#13094071	1	2	yes	—
1073	C₂×C₄	C₂⁴×D₄₇	1	1	yes	characteristic
1074	C₈	—	94	1	no	—
1075	C₈	—	94	1	no	—
1076	C₈	—	94	2	no	—
1077	C₈	—	94	2	no	—
1078	C₈	—	94	1	no	—
1079	C₈	—	94	1	no	—
1080	C₂²	—	2	1	no	—
1081	C₂²	—	2	1	no	—
1082	C₂²	—	4	1	no	—
1083	C₂²	—	4	2	no	—
1084	C₂²	—	4	1	no	—
1085	C₂²	—	4	1	no	—
1086	C₂²	—	4	2	no	—
1087	C₂²	—	4	2	no	—
1088	C₂²	—	16	2	no	—
1089	C₂²	—	94	2	no	—
1090	C₂²	—	188	1	no	—
1091	C₂²	—	188	1	no	—
1092	C₂²	#15689780	1	2	yes	—
1093	C₂²	C₂³×C₂²⋊D₄₇	1	1	yes	characteristic
1094	C₄	—	2	1	no	—
1095	C₄	—	2	1	no	—
1096	C₄	—	2	1	no	—
1097	C₄	—	2	1	no	—
1098	C₄	—	2	2	no	—
1099	C₄	—	2	2	no	—
1100	C₄	—	2	2	no	—
1101	C₄	—	2	2	no	—
1102	C₄	—	4	1	no	—
1103	C₄	—	4	2	no	—
1104	C₄	—	4	1	no	—
1105	C₄	—	4	1	no	—
1106	C₄	—	94	2	no	—
1107	C₄	—	188	2	no	—
1108	C₄	—	188	2	no	—
1109	C₄	—	188	1	no	—
1110	C₄	—	188	1	no	—
1111	C₄	#15689780	1	2	yes	—
1112	C₄	C₂×#41×D₄₇	1	1	yes	characteristic
1113	C₄	C₂×#13094071	1	1	yes	characteristic
1114	C₂	—	2	2	no	—
1115	C₂	—	8	2	no	—
1116	C₂	—	8	1	no	—
1117	C₂	—	188	2	no	—
1118	C₂	C₂×#15689780	1	1	yes	characteristic
1119	C₂	#20258159	1	1	yes	characteristic
1120	C₂	#20258159	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂³×C₂²⋊D₄₇
commutator, cosocle	C₂×C₄×C₄₇	C₂⁵
Frattini	C₂×C₄	C₂⁴×D₄₇
Fitting	C₄₇×#3510	C₂
socle	C₂²×C₄₇	C₂³×D₄
prime radical	#20252923	C₂
hypercenter	#3510	D₄₇
hypocenter	C₄₇	#61331
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ #533 ◁ #3510

Complements

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

N	H ≅ G/N	type
1. #20257209	C₂	semidirect
2. #20256224	C₂	semidirect
3. #20256209	C₂	semidirect
4. #20256150	C₂	semidirect
5. #20256135	C₂	semidirect
6. #20256080	C₂	semidirect
7. #20256069	C₂	semidirect
8. #20256044	C₂	semidirect
9. #20256033	C₂	semidirect
10. #20253753	C₂	semidirect
11. #20253742	C₂	semidirect
12. C₂×#15689477	C₂	semidirect
13. #20253230	C₂	semidirect
14. #20253219	C₂	semidirect
15. #20253210	C₂	semidirect
16. #20252934	C₂	semidirect
18. #20252878	C₂	semidirect
19. #20252323	C₂	semidirect
20. #20252231	C₂	semidirect
21. #20252220	C₂	semidirect
22. C₄×#13094044	C₂	semidirect
23. C₄₇×#3510	C₂	semidirect
27. #15689851	C₂²	semidirect
28. #15689851	C₂²	semidirect
29. #15689833	C₂²	semidirect
30. #15689833	C₂²	semidirect
43. #15689491	C₂²	semidirect
46. #15689482	C₂²	semidirect
52. #15689477	C₂²	semidirect
53. #15689473	C₂²	semidirect
55. #15689430	C₂²	semidirect
56. #15689430	C₂²	semidirect
57. #15689430	C₂²	semidirect
58. #15689430	C₂²	semidirect
61. #15689423	C₂²	semidirect
62. #15689423	C₂²	semidirect
63. #15689418	C₂²	semidirect
65. #15689408	C₂²	semidirect
70. #15689342	C₂²	semidirect
74. #15689335	C₂²	semidirect
75. #15689330	C₂²	semidirect
76. #15689325	C₂²	semidirect
79. #15689254	C₂²	semidirect
80. #15689254	C₂²	semidirect
81. Q₈×C₄₇⋊C₈	C₂²	semidirect
82. Q₈×C₄₇⋊C₈	C₂²	semidirect
84. #15689228	C₂²	semidirect
86. #15689221	C₂²	semidirect
87. C₄×#10625337	C₂²	semidirect
88. C₄×#10625337	C₂²	semidirect
89. C₄×#10625337	C₂²	semidirect
90. C₄×#10625336	C₂²	semidirect
91. C₄×#10625336	C₂²	semidirect
92. C₄×#10625336	C₂²	semidirect
94. C₄×#10625335	C₂²	semidirect
95. C₄×#10625335	C₂²	semidirect
97. C₄×#10625334	C₂²	semidirect
98. C₄×#10625334	C₂²	semidirect
554. #3510	D₄₇	semidirect
695. C₄₇	#61331	semidirect

Maximal subgroups

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

subgroup	index
#20257209	2
#20256224	2
#20256209	2
#20256150	2
#20256135	2
#20256080	2
#20256069	2
#20256044	2
#20256033	2
#20253753	2
#20253742	2
C₂×#15689477	2
#20253230	2
#20253219	2
#20253210	2
#20252934	2
#20252923	2
#20252878	2
#20252323	2
#20252231	2
#20252220	2
C₄×#13094044	2
C₄₇×#3510	2
#61331	47