Subgroups — #27098749

Order 12032.

1900 conjugacy classes of subgroups.

The subgroup lattice has 1176 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20257351	C₂	1	1	yes	maximal, characteristic, complemented
2	#20256396	C₂	1	1	yes	maximal, characteristic, complemented
3	Q₈×#10625334	C₂	1	1	yes	maximal, characteristic, complemented
4	#20256180	C₂	1	1	yes	maximal, characteristic, complemented
5	#20256176	C₂	1	1	yes	maximal, characteristic, complemented
6	#20255814	C₂	1	1	yes	maximal, characteristic, complemented
7	#20255806	C₂	1	2	yes	maximal, complemented
8	#20255619	C₂	1	1	yes	maximal, characteristic, complemented
9	#20255613	C₂	1	1	yes	maximal, characteristic, complemented
10	#20255544	C₂	1	2	yes	maximal, complemented
11	#20255538	C₂	1	2	yes	maximal, complemented
12	#20255069	C₂	1	2	yes	maximal, complemented
13	D₄×#10625334	C₂	1	1	yes	maximal, characteristic, complemented
14	#20254021	C₂	1	2	yes	maximal, complemented
15	#20253963	C₂	1	1	yes	maximal, characteristic, complemented
16	#20253572	C₂	1	2	yes	maximal, complemented
17	#20253566	C₂	1	2	yes	maximal, complemented
18	#20253539	C₂	1	1	yes	maximal, characteristic, complemented
19	#20253533	C₂	1	1	yes	maximal, characteristic, complemented
20	#20252364	C₂	1	1	yes	maximal, characteristic, complemented
21	#20252238	C₂	1	2	yes	maximal, complemented
22	C₄×#13094044	C₂	1	1	yes	maximal, characteristic, complemented
23	C₄₇×#3514	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#13094044	C₂²	1	1	yes	characteristic
25	C₂²×#10625334	C₂²	1	2	yes	—
26	#15689858	C₂²	1	1	yes	characteristic, complemented
27	#15689843	C₂²	1	1	yes	characteristic
28	#15689838	C₂²	1	2	yes	complemented
29	#15689798	—	2	2	no	—
30	Q₈×D₁₈₈	C₂²	1	1	yes	characteristic, complemented
31	#15689783	—	2	1	no	—
32	#15689770	—	2	1	no	—
33	#15689769	C₂²	1	2	yes	complemented
34	D₄×D₁₈₈	C₂²	1	1	yes	characteristic
35	#15689744	C₂²	1	2	yes	complemented
36	#15689709	—	2	2	no	—
37	#15689673	C₂²	1	1	yes	characteristic, complemented
38	#15689658	—	2	1	no	—
39	#124×D₄₇	—	2	1	no	—
40	#15689597	C₂²	1	2	yes	complemented
41	C₄×#10625350	C₂²	1	1	yes	characteristic, complemented
42	#15689526	C₂²	1	1	yes	characteristic, complemented
43	#15689526	C₂²	1	2	yes	complemented
44	#15689505	C₂²	1	2	yes	complemented
45	#15689499	C₂²	1	1	yes	characteristic
46	#15689485	C₂²	1	2	yes	complemented
47	#15689482	C₂²	1	2	yes	complemented
48	#15689471	C₂²	1	1	yes	characteristic, complemented
49	#15689469	C₂²	1	1	yes	characteristic, complemented
50	#15689464	C₂²	1	2	yes	complemented
51	#15689461	C₂²	1	2	yes	complemented
52	#15689447	C₂²	1	2	yes	complemented
53	#15689447	C₂²	1	2	yes	complemented
54	#15689444	C₂²	1	2	yes	complemented
55	#15689444	C₂²	1	2	yes	complemented
56	#15689413	C₂²	1	2	yes	complemented
57	#15689410	C₂²	1	2	yes	complemented
58	#15689408	C₂²	1	1	yes	characteristic, complemented
59	#15689405	C₂²	1	1	yes	characteristic, complemented
60	#15689403	C₂²	1	2	yes	complemented
61	#15689403	C₂²	1	1	yes	characteristic, complemented
62	#15689400	C₂²	1	2	yes	complemented
63	#15689400	C₂²	1	1	yes	characteristic, complemented
64	#15689371	C₂²	1	2	yes	complemented
65	#15689367	C₂²	1	2	yes	complemented
66	#15689362	C₂²	1	2	yes	complemented
67	#15689357	C₂²	1	2	yes	—
68	#15689357	C₂²	1	2	yes	complemented
69	#15689357	C₂²	1	2	yes	complemented
70	#15689338	C₂²	1	2	yes	complemented
71	#15689338	C₂²	1	2	yes	complemented
72	#15689335	C₂²	1	2	yes	complemented
73	#15689335	C₂²	1	2	yes	complemented
74	#15689323	C₂²	1	1	yes	characteristic, complemented
75	#15689320	C₂²	1	1	yes	characteristic, complemented
76	#15689318	C₂²	1	1	yes	characteristic
77	#15689315	C₂²	1	1	yes	characteristic
78	#15689274	C₂²	1	2	yes	complemented
79	#15689273	C₂²	1	2	yes	complemented
80	#15689268	C₂²	1	2	yes	complemented
81	#15689266	C₂²	1	2	yes	complemented
82	#15689257	C₂²	1	2	yes	—
83	#15689256	C₂²	1	2	yes	—
84	#15689254	C₂²	1	1	yes	characteristic, complemented
85	Q₈×C₄₇⋊C₈	C₂²	1	1	yes	characteristic, complemented
86	#15689233	C₂²	1	2	yes	complemented
87	#15689233	C₂²	1	2	yes	complemented
88	#15689233	C₂²	1	2	yes	complemented
89	#15689233	C₂²	1	2	yes	complemented
90	#15689223	C₂²	1	2	yes	complemented
91	#15689221	C₂²	1	2	yes	complemented
92	C₄×#10625337	C₂²	1	1	yes	characteristic, complemented
93	C₄×#10625337	C₂²	1	1	yes	characteristic, complemented
94	C₄×#10625336	C₂²	1	1	yes	characteristic, complemented
95	C₄×#10625336	C₂²	1	1	yes	characteristic, complemented
96	C₄×#10625335	C₂²	1	1	yes	characteristic, complemented
97	C₄×#10625335	C₂²	1	1	yes	characteristic, complemented
98	C₄×#10625334	C₂²	1	1	yes	characteristic
99	C₄×#10625334	C₂²	1	2	yes	—
100	C₄×#10625334	C₂²	1	1	yes	characteristic
101	C₄×#10625334	C₂²	1	2	yes	complemented
102	C₄×#10625334	C₂²	1	2	yes	complemented
103	C₄×#10625334	C₂²	1	2	yes	complemented
104	#15689201	C₂²	1	1	yes	characteristic
105	#15689195	C₂²	1	2	yes	complemented
106	D₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
107	D₄×C₄₇⋊C₈	C₂²	1	2	yes	complemented
108	#15689184	C₂²	1	2	yes	complemented
109	#15689180	C₂²	1	1	yes	characteristic, complemented
110	#15689159	C₂²	1	1	yes	characteristic, complemented
111	#15689159	C₂²	1	2	yes	complemented
112	#15689128	C₂²	1	2	yes	complemented
113	#15689127	C₂²	1	2	yes	complemented
114	#15689119	C₂²	1	1	yes	characteristic, complemented
115	#15689117	C₂²	1	1	yes	characteristic, complemented
116	#15689079	C₂²	1	2	yes	complemented
117	C₂×C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic, complemented
118	C₄₇×#559	C₂²	1	1	yes	characteristic, complemented
119	C₄₇×#556	C₂²	1	1	yes	characteristic
120	C₄₇×#555	C₂²	1	2	yes	complemented
121	C₄₇×#551	—	2	2	no	—
122	D₄×Q₈×C₄₇	C₂²	1	1	yes	characteristic, complemented
123	C₄₇×#548	—	2	1	no	—
124	C₄₇×#546	—	2	1	no	—
125	C₄₇×#546	C₂²	1	2	yes	complemented
126	D₄²×C₄₇	C₂²	1	1	yes	characteristic
127	C₄₇×#542	C₂²	1	2	yes	complemented
128	C₄₇×#538	—	2	2	no	—
129	C₄₇×#532	C₂²	1	1	yes	characteristic, complemented
130	C₄₇×#529	—	2	1	no	—
131	C₄₇×#529	C₂²	1	1	yes	characteristic
132	C₂×#124×C₄₇	—	2	1	no	—
133	C₄₇×#518	C₂²	1	2	yes	complemented
134	C₄×#41×C₄₇	C₂²	1	1	yes	characteristic, complemented
135	C₂×#10625350	—	2	1	no	—
136	C₂×#10625350	C₂³	1	1	yes	characteristic
137	C₂×Q₈×D₄₇	—	2	1	no	—
138	C₂²×D₁₈₈	C₂³	1	2	yes	—
139	C₂×D₄×D₄₇	—	2	1	no	—
140	#13094044	—	2	4	no	—
141	C₂×#10625337	C₂³	1	1	yes	characteristic
142	C₂×#10625335	C₂³	1	1	yes	characteristic
143	C₂×#10625335	C₂³	1	2	yes	—
144	C₂×#10625336	C₂³	1	1	yes	characteristic
145	C₂×#10625336	C₂³	1	2	yes	—
146	C₂×#10625334	—	2	8	no	—
147	C₂×#10625334	C₂³	1	2	yes	—
148	C₂×#10625334	C₂³	1	2	yes	—
149	C₂×#10625334	C₂³	1	2	yes	—
150	C₂×#10625334	C₂³	1	2	yes	—
151	C₂×#10625334	C₂³	1	1	yes	characteristic
152	C₂×#10625329	C₂³	1	2	yes	—
153	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
154	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
155	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
156	#13094024	C₂³	1	2	yes	—
157	#13094024	C₂³	1	1	yes	characteristic
158	#13094021	C₂³	1	1	yes	characteristic
159	#13094019	—	2	2	no	—
160	#13094017	—	2	2	no	—
161	#13094013	—	2	1	no	—
162	#13094012	—	2	1	no	—
163	#13094012	C₂³	1	2	yes	—
164	#13094011	—	2	1	no	—
165	#13094010	—	2	2	no	—
166	#13094010	—	2	2	no	—
167	#13094010	—	2	2	no	—
168	#13094009	—	2	2	no	—
169	#13094009	—	2	2	no	—
170	#13094006	—	2	2	no	—
171	#13094004	—	2	1	no	—
172	#13094004	—	2	2	no	—
173	#13094003	C₂³	1	2	yes	—
174	#13094002	—	2	2	no	—
175	#13093999	—	2	1	no	—
176	#13093998	—	2	1	no	—
177	#13093998	C₂³	1	2	yes	—
178	#13093998	C₂³	1	2	yes	—
179	#13093997	—	2	2	no	—
180	#13093995	—	2	2	no	—
181	#13093994	—	2	2	no	—
182	#13093992	—	2	2	no	—
183	C₄×Dic₉₄	C₂³	1	1	yes	characteristic
184	C₄×Dic₉₄	C₂³	1	1	yes	characteristic
185	#13093989	—	2	1	no	—
186	C₄×D₁₈₈	—	2	1	no	—
187	C₄×D₁₈₈	C₂³	1	2	yes	—
188	C₄×D₁₈₈	C₂³	1	1	yes	characteristic
189	C₄×D₁₈₈	C₂³	1	2	yes	—
190	C₄×D₁₈₈	C₂³	1	2	yes	—
191	C₄×D₁₈₈	C₂³	1	1	yes	characteristic
192	#13093986	—	2	1	no	—
193	#13093986	—	2	2	no	—
194	#13093986	—	2	2	no	—
195	C₄×C₂²⋊D₄₇	—	2	1	no	—
196	C₄×C₂²⋊D₄₇	—	2	1	no	—
197	#13093983	C₂³	1	1	yes	characteristic
198	#13093983	C₂³	1	2	yes	—
199	#13093982	—	2	2	no	—
200	#13093981	—	2	1	no	—
201	C₂²⋊C₄×D₄₇	—	2	2	no	—
202	C₂²⋊C₄×D₄₇	—	2	2	no	—
203	C₂²⋊C₄×D₄₇	—	2	2	no	—
204	C₄²×D₄₇	—	2	1	no	—
205	#13093957	C₂³	1	1	yes	characteristic
206	#13093957	C₂³	1	1	yes	characteristic
207	#13093957	C₂³	1	2	yes	—
208	#13093957	C₂³	1	2	yes	—
209	#13093957	C₂³	1	2	yes	—
210	#13093957	C₂³	1	2	yes	—
211	#13093955	C₂³	1	2	yes	—
212	#13093955	C₂³	1	2	yes	—
213	#13093955	C₂³	1	1	yes	characteristic
214	#13093955	C₂³	1	1	yes	characteristic
215	C₄⋊(C₄₇⋊C₈)	C₂³	1	1	yes	characteristic
216	C₄⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
217	C₄⋊(C₄₇⋊C₈)	C₂³	1	1	yes	characteristic
218	C₄⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
219	#13093948	C₂³	1	1	yes	characteristic
220	#13093948	C₂³	1	1	yes	characteristic
221	#13093948	C₂³	1	2	yes	—
222	#13093947	C₂³	1	1	yes	characteristic
223	#13093947	C₂³	1	1	yes	characteristic
224	#13093947	C₂³	1	2	yes	—
225	#13093945	C₂³	1	2	yes	—
226	#13093945	C₂³	1	2	yes	—
227	#13093945	C₂³	1	1	yes	characteristic
228	#13093945	C₂³	1	2	yes	—
229	#13093945	C₂³	1	2	yes	—
230	#13093945	C₂³	1	1	yes	characteristic
231	#13093945	C₂³	1	2	yes	—
232	#13093944	C₂³	1	2	yes	—
233	#13093944	C₂³	1	2	yes	—
234	#13093944	C₂³	1	1	yes	characteristic
235	#13093944	C₂³	1	2	yes	—
236	#13093944	C₂³	1	2	yes	—
237	#13093944	C₂³	1	1	yes	characteristic
238	#13093944	C₂³	1	2	yes	—
239	C₂²⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
240	C₂²⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
241	C₂²⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
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	1	yes	characteristic
248	C₄×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
249	C₂×#41×C₄₇	—	2	1	no	—
250	C₂×#41×C₄₇	C₂³	1	1	yes	characteristic
251	C₂²×Q₈×C₄₇	—	2	1	no	—
252	C₂²×D₄×C₄₇	—	2	1	no	—
253	C₂²×D₄×C₄₇	C₂³	1	2	yes	—
254	C₄⋊Q₈×C₄₇	C₂³	1	2	yes	—
255	C₄⋊Q₈×C₄₇	C₂³	1	1	yes	characteristic
256	#127×C₄₇	C₂³	1	1	yes	characteristic
257	#126×C₄₇	—	2	2	no	—
258	#126×C₄₇	—	2	2	no	—
259	#126×C₄₇	D₄	1	2	yes	—
260	#125×C₄₇	D₄	1	1	yes	characteristic
261	#124×C₄₇	—	2	1	no	—
262	#124×C₄₇	—	2	1	no	—
263	#124×C₄₇	—	2	2	no	—
264	#124×C₄₇	—	2	2	no	—
265	#124×C₄₇	—	2	2	no	—
266	#124×C₄₇	—	2	1	no	—
267	#124×C₄₇	D₄	1	1	yes	characteristic
268	#124×C₄₇	C₂³	1	2	yes	—
269	#123×C₄₇	—	2	2	no	—
270	#123×C₄₇	—	2	2	no	—
271	#123×C₄₇	—	2	2	no	—
272	#123×C₄₇	D₄	1	2	yes	—
273	C₂²⋊Q₈×C₄₇	—	2	1	no	—
274	C₂²⋊Q₈×C₄₇	—	2	2	no	—
275	C₂²⋊Q₈×C₄₇	—	2	2	no	—
276	C₂²⋊Q₈×C₄₇	D₄	1	1	yes	characteristic
277	C₂²⋊Q₈×C₄₇	C₂³	1	2	yes	—
278	#121×C₄₇	—	2	2	no	—
279	#121×C₄₇	—	2	1	no	—
280	#121×C₄₇	—	2	1	no	—
281	#121×C₄₇	—	2	2	no	—
282	#121×C₄₇	D₄	1	1	yes	characteristic
283	#121×C₄₇	C₂³	1	2	yes	—
284	#121×C₄₇	C₂³	1	2	yes	—
285	#120×C₄₇	—	2	2	no	—
286	#120×C₄₇	—	2	2	no	—
287	C₄×Q₈×C₄₇	—	2	1	no	—
288	C₄×Q₈×C₄₇	C₂³	1	1	yes	characteristic
289	C₄×Q₈×C₄₇	C₂³	1	1	yes	characteristic
290	C₄×Q₈×C₄₇	C₂³	1	1	yes	characteristic
291	C₄×D₄×C₄₇	—	2	1	no	—
292	C₄×D₄×C₄₇	—	2	1	no	—
293	C₄×D₄×C₄₇	—	2	2	no	—
294	C₄×D₄×C₄₇	—	2	2	no	—
295	C₄×D₄×C₄₇	—	2	1	no	—
296	C₄×D₄×C₄₇	—	2	1	no	—
297	C₄×D₄×C₄₇	C₂³	1	2	yes	—
298	C₄×D₄×C₄₇	C₂³	1	1	yes	characteristic
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	C₄×D₄×C₄₇	C₂³	1	2	yes	—
304	#117×C₄₇	—	2	2	no	—
305	#117×C₄₇	—	2	1	no	—
306	#117×C₄₇	C₂³	1	1	yes	characteristic
307	#117×C₄₇	C₂³	1	2	yes	—
308	#117×C₄₇	C₂³	1	2	yes	—
309	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
310	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
311	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
312	C₂×C₄²×C₄₇	—	2	1	no	—
313	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
314	C₂⁴×C₄₇	—	2	2	no	—
315	C₂³×D₄₇	—	2	2	no	—
316	#41×C₄₇	—	2	2	no	—
317	#41×C₄₇	—	4	1	no	—
318	#41×C₄₇	—	8	2	no	—
319	C₂×Q₈×C₄₇	—	2	1	no	—
320	C₂×Q₈×C₄₇	—	2	2	no	—
321	C₂×Q₈×C₄₇	—	8	2	no	—
322	C₂×Q₈×C₄₇	C₂×D₄	1	1	yes	characteristic
323	C₂×Q₈×C₄₇	C₂⁴	1	1	yes	characteristic
324	C₂×D₄×C₄₇	—	2	4	no	—
325	C₂×D₄×C₄₇	—	2	1	no	—
326	C₂×D₄×C₄₇	—	2	2	no	—
327	C₂×D₄×C₄₇	—	2	2	no	—
328	C₂×D₄×C₄₇	—	2	2	no	—
329	C₂×D₄×C₄₇	—	2	1	no	—
330	C₂×D₄×C₄₇	—	2	1	no	—
331	C₂×D₄×C₄₇	—	4	2	no	—
332	C₂×D₄×C₄₇	—	8	2	no	—
333	C₂×D₄×C₄₇	C₂×D₄	1	1	yes	characteristic
334	C₂×D₄×C₄₇	C₂×D₄	1	2	yes	—
335	C₂×D₄×C₄₇	C₂⁴	1	2	yes	—
336	C₂×D₄×C₄₇	C₂⁴	1	1	yes	characteristic
337	C₂²×C₄×C₄₇	—	2	1	no	—
338	C₂²×C₄×C₄₇	—	2	1	no	—
339	C₂²×C₄×C₄₇	—	2	1	no	—
340	C₂²×C₄×C₄₇	—	2	2	no	—
341	C₂²×C₄×C₄₇	—	2	2	no	—
342	C₂²×C₄×C₄₇	—	2	2	no	—
343	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
344	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
345	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
346	C₂²×C₄×C₄₇	C₂⁴	1	2	yes	—
347	C₂×C₂²⋊D₄₇	—	2	1	no	—
348	C₂×C₂²⋊D₄₇	—	2	2	no	—
349	C₂×C₂²⋊D₄₇	—	2	2	no	—
350	Q₈×D₄₇	—	8	2	no	—
351	D₄×D₄₇	—	8	2	no	—
352	#10625350	—	2	2	no	—
353	#10625350	—	4	1	no	—
354	#10625350	—	8	2	no	—
355	C₂×D₁₈₈	—	2	4	no	—
356	C₂×D₁₈₈	—	2	2	no	—
357	C₂×D₁₈₈	—	2	1	no	—
358	C₂×D₁₈₈	—	2	1	no	—
359	C₂×D₁₈₈	—	4	2	no	—
360	C₂×D₁₈₈	C₂⁴	1	2	yes	—
361	C₂×D₁₈₈	C₂⁴	1	1	yes	characteristic
362	C₂×C₄×D₄₇	—	2	1	no	—
363	C₂×C₄×D₄₇	—	2	1	no	—
364	C₂×C₄×D₄₇	—	2	1	no	—
365	C₂×C₄×D₄₇	—	2	2	no	—
366	C₂×C₄×D₄₇	—	2	2	no	—
367	C₂×C₄×D₄₇	—	2	2	no	—
368	C₂×Dic₉₄	—	2	1	no	—
369	C₂×Dic₉₄	—	2	2	no	—
370	C₂×Dic₉₄	C₂⁴	1	1	yes	characteristic
371	C₄⋊C₄×C₄₇	—	2	1	no	—
372	C₄⋊C₄×C₄₇	—	2	1	no	—
373	C₄⋊C₄×C₄₇	—	2	2	no	—
374	C₄⋊C₄×C₄₇	—	2	1	no	—
375	C₄⋊C₄×C₄₇	—	2	2	no	—
376	C₄⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
377	C₄⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
378	C₄⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
379	C₄⋊C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
380	C₄⋊C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
381	C₄⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
382	C₄⋊C₄×C₄₇	C₂⁴	1	1	yes	characteristic
383	C₄⋊C₄×C₄₇	C₂⁴	1	2	yes	—
384	C₄⋊C₄×C₄₇	C₂⁴	1	1	yes	characteristic
385	C₂²⋊C₄×C₄₇	—	2	2	no	—
386	C₂²⋊C₄×C₄₇	—	2	2	no	—
387	C₂²⋊C₄×C₄₇	—	2	1	no	—
388	C₂²⋊C₄×C₄₇	—	2	1	no	—
389	C₂²⋊C₄×C₄₇	—	2	2	no	—
390	C₂²⋊C₄×C₄₇	—	2	2	no	—
391	C₂²⋊C₄×C₄₇	—	2	2	no	—
392	C₂²⋊C₄×C₄₇	—	2	2	no	—
393	C₂²⋊C₄×C₄₇	—	2	2	no	—
394	C₂²⋊C₄×C₄₇	—	2	1	no	—
395	C₂²⋊C₄×C₄₇	—	2	2	no	—
396	C₂²⋊C₄×C₄₇	—	2	2	no	—
397	C₂²⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
398	C₂²⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
399	C₂²⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
400	C₂²⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
401	C₂²⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
402	C₄²×C₄₇	—	2	1	no	—
403	C₄²×C₄₇	—	2	1	no	—
404	C₄²×C₄₇	—	2	1	no	—
405	C₄²×C₄₇	—	2	2	no	—
406	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
407	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
408	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
409	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
410	C₄²×C₄₇	C₂⁴	1	2	yes	—
411	C₂²⋊Dic₄₇	—	2	2	no	—
412	C₂²⋊Dic₄₇	—	2	2	no	—
413	C₂²⋊Dic₄₇	—	2	1	no	—
414	#10625337	—	2	2	no	—
415	#10625336	—	2	2	no	—
416	#10625336	—	4	2	no	—
417	#10625335	—	2	2	no	—
418	#10625335	—	4	2	no	—
419	#10625334	—	2	4	no	—
420	#10625334	—	2	4	no	—
421	#10625334	—	2	4	no	—
422	#10625334	—	4	2	no	—
423	#10625334	#41	1	4	yes	complemented
424	(C₂×D₄₇)⋊C₄	—	2	1	no	—
425	(C₂×D₄₇)⋊C₄	—	2	2	no	—
426	(C₂×D₄₇)⋊C₄	—	2	2	no	—
427	(C₂×D₄₇)⋊C₄	—	2	2	no	—
428	(C₂×D₄₇)⋊C₄	—	2	2	no	—
429	(C₂×D₄₇)⋊C₄	—	2	2	no	—
430	(C₂×D₄₇)⋊C₄	—	2	1	no	—
431	(C₂×D₄₇)⋊C₄	—	2	2	no	—
432	(C₂×D₄₇)⋊C₄	—	2	2	no	—
433	C₄⋊Dic₄₇	—	2	2	no	—
434	C₄⋊Dic₄₇	—	2	1	no	—
435	C₄⋊Dic₄₇	C₂⁴	1	1	yes	characteristic
436	C₄⋊Dic₄₇	C₂⁴	1	2	yes	—
437	C₄⋊Dic₄₇	C₂⁴	1	1	yes	characteristic
438	Dic₄₇⋊C₄	—	2	1	no	—
439	Dic₄₇⋊C₄	—	2	1	no	—
440	Dic₄₇⋊C₄	—	2	2	no	—
441	C₄×Dic₄₇	—	2	1	no	—
442	C₄×Dic₄₇	—	2	1	no	—
443	C₄×Dic₄₇	—	2	1	no	—
444	C₄×Dic₄₇	—	2	2	no	—
445	#10625329	—	4	2	no	—
446	C₂×C₄₇⋊C₈	—	2	4	no	—
447	C₂×C₄₇⋊C₈	—	2	2	no	—
448	C₂×C₄₇⋊C₈	—	4	1	no	—
449	C₂×C₄₇⋊C₈	C₂⁴	1	1	yes	characteristic
450	C₂×C₄₇⋊C₈	C₂⁴	1	1	yes	characteristic
451	C₂×C₄₇⋊C₈	C₂⁴	1	1	yes	characteristic
452	C₂×C₄₇⋊C₈	C₂⁴	1	2	yes	—
453	C₂×C₄₇⋊C₈	C₂⁴	1	2	yes	—
454	C₂×C₄₇⋊C₈	C₂⁴	1	1	yes	characteristic
455	C₂³×C₄₇	—	2	1	no	—
456	C₂³×C₄₇	—	2	2	no	—
457	C₂³×C₄₇	—	4	4	no	—
458	C₂³×C₄₇	—	8	2	no	—
459	C₂³×C₄₇	—	8	2	no	—
460	C₂³×C₄₇	C₂²×D₄	1	2	yes	—
461	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
462	C₂²×D₄₇	—	2	1	no	—
463	C₂²×D₄₇	—	2	2	no	—
464	C₂²×D₄₇	—	4	4	no	—
465	C₂²×D₄₇	—	8	2	no	—
466	C₂²×D₄₇	—	8	2	no	—
467	Q₈×C₄₇	—	2	2	no	—
468	Q₈×C₄₇	—	2	1	no	—
469	Q₈×C₄₇	—	2	1	no	—
470	Q₈×C₄₇	—	4	2	no	—
471	Q₈×C₄₇	—	8	2	no	—
472	D₄×C₄₇	—	2	2	no	—
473	D₄×C₄₇	—	2	2	no	—
474	D₄×C₄₇	—	2	1	no	—
475	D₄×C₄₇	—	2	2	no	—
476	D₄×C₄₇	—	4	2	no	—
477	D₄×C₄₇	—	4	4	no	—
478	D₄×C₄₇	—	4	2	no	—
479	D₄×C₄₇	—	4	2	no	—
480	D₄×C₄₇	—	8	1	no	—
481	D₄×C₄₇	—	8	2	no	—
482	D₄×C₄₇	—	8	2	no	—
483	D₄×C₄₇	C₂×#41	1	2	yes	—
484	C₂×C₄×C₄₇	—	2	2	no	—
485	C₂×C₄×C₄₇	—	2	2	no	—
486	C₂×C₄×C₄₇	—	2	1	no	—
487	C₂×C₄×C₄₇	—	2	1	no	—
488	C₂×C₄×C₄₇	—	2	2	no	—
489	C₂×C₄×C₄₇	—	2	1	no	—
490	C₂×C₄×C₄₇	—	2	1	no	—
491	C₂×C₄×C₄₇	—	2	1	no	—
492	C₂×C₄×C₄₇	—	2	2	no	—
493	C₂×C₄×C₄₇	—	4	1	no	—
494	C₂×C₄×C₄₇	—	4	2	no	—
495	C₂×C₄×C₄₇	—	4	2	no	—
496	C₂×C₄×C₄₇	—	8	1	no	—
497	C₂×C₄×C₄₇	—	8	2	no	—
498	C₂×C₄×C₄₇	—	8	2	no	—
499	C₂×C₄×C₄₇	—	8	2	no	—
500	C₂×C₄×C₄₇	C₂²×D₄	1	2	yes	—
501	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
502	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
503	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
504	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
505	C₂×C₄×C₄₇	C₂²×D₄	1	2	yes	—
506	C₂×C₄×C₄₇	C₂²×D₄	1	2	yes	—
507	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
508	C₂×C₄×C₄₇	C₂⁵	1	1	yes	characteristic
509	C₂²⋊D₄₇	—	4	2	no	—
510	C₂²⋊D₄₇	—	8	2	no	—
511	C₂²⋊D₄₇	—	8	2	no	—
512	C₂×Dic₄₇	—	2	1	no	—
513	C₂×Dic₄₇	—	2	1	no	—
514	C₂×Dic₄₇	—	2	1	no	—
515	C₂×Dic₄₇	—	2	2	no	—
516	D₁₈₈	—	2	2	no	—
517	D₁₈₈	—	2	1	no	—
518	D₁₈₈	—	2	2	no	—
519	D₁₈₈	—	4	4	no	—
520	D₁₈₈	—	4	2	no	—
521	D₁₈₈	—	8	1	no	—
522	D₁₈₈	C₂×#41	1	2	yes	—
523	C₄×D₄₇	—	4	2	no	—
524	C₄×D₄₇	—	4	2	no	—
525	C₄×D₄₇	—	8	1	no	—
526	C₄×D₄₇	—	8	2	no	—
527	C₄×D₄₇	—	8	2	no	—
528	C₄×D₄₇	—	8	2	no	—
529	Dic₉₄	—	2	1	no	—
530	Dic₉₄	—	2	1	no	—
531	Dic₉₄	—	4	2	no	—
532	Dic₉₄	—	8	2	no	—
533	C₄₇⋊C₈	—	2	2	no	—
534	C₄₇⋊C₈	—	2	1	no	—
535	C₄₇⋊C₈	—	2	1	no	—
536	C₄₇⋊C₈	—	2	1	no	—
537	C₄₇⋊C₈	—	2	2	no	—
538	C₄₇⋊C₈	C₂×#41	1	2	yes	—
539	#61475	—	47	1	no	maximal, Sylow
540	C₂²×C₄₇	—	2	1	no	—
541	C₂²×C₄₇	—	2	2	no	—
542	C₂²×C₄₇	—	2	1	no	—
543	C₂²×C₄₇	—	2	2	no	—
544	C₂²×C₄₇	—	2	2	no	—
545	C₂²×C₄₇	—	2	1	no	—
546	C₂²×C₄₇	—	2	2	no	—
547	C₂²×C₄₇	—	4	1	no	—
548	C₂²×C₄₇	—	4	1	no	—
549	C₂²×C₄₇	—	4	2	no	—
550	C₂²×C₄₇	—	4	2	no	—
551	C₂²×C₄₇	—	4	2	no	—
552	C₂²×C₄₇	—	16	4	no	—
553	C₂²×C₄₇	C₂³×D₄	1	1	yes	characteristic
554	C₂×D₄₇	—	2	2	no	—
555	C₂×D₄₇	—	4	1	no	—
556	C₂×D₄₇	—	4	1	no	—
557	C₂×D₄₇	—	4	2	no	—
558	C₂×D₄₇	—	4	2	no	—
559	C₂×D₄₇	—	4	2	no	—
560	C₂×D₄₇	—	16	4	no	—
561	C₄×C₄₇	—	2	1	no	—
562	C₄×C₄₇	—	2	2	no	—
563	C₄×C₄₇	—	2	1	no	—
564	C₄×C₄₇	—	2	1	no	—
565	C₄×C₄₇	—	2	2	no	—
566	C₄×C₄₇	—	2	2	no	—
567	C₄×C₄₇	—	2	1	no	—
568	C₄×C₄₇	—	4	1	no	—
569	C₄×C₄₇	—	4	1	no	—
570	C₄×C₄₇	—	4	1	no	—
571	C₄×C₄₇	—	4	2	no	—
572	C₄×C₄₇	#576	1	2	yes	—
573	C₄×C₄₇	C₂²×#41	1	1	yes	characteristic
574	C₄×C₄₇	#585	1	1	yes	characteristic
575	Dic₄₇	—	4	1	no	—
576	Dic₄₇	—	4	1	no	—
577	Dic₄₇	—	4	2	no	—
578	Dic₄₇	—	4	1	no	—
579	#3514	—	47	1	no	—
580	#3514	D₄₇	1	1	yes	characteristic, complemented
581	#3396	—	47	1	no	—
582	Q₈×D₈	—	47	1	no	—
583	#3373	—	47	1	no	—
584	#3373	—	47	1	no	—
585	#3342	—	47	1	no	—
586	#3341	—	47	2	no	—
587	#3324	—	47	1	no	—
588	#3324	—	47	1	no	—
589	#3319	—	47	2	no	—
590	#3319	—	47	2	no	—
591	#3280	—	47	2	no	—
592	D₄×D₈	—	47	1	no	—
593	#3175	—	47	2	no	—
594	#3169	—	47	1	no	—
595	#3118	—	47	2	no	—
596	#3118	—	47	2	no	—
597	#3115	—	47	1	no	—
598	#3115	—	47	1	no	—
599	#2966	—	47	1	no	—
600	#2948	—	47	2	no	—
601	C₄×#135	—	47	1	no	—
602	C₂×C₄₇	—	4	2	no	—
603	C₂×C₄₇	—	4	1	no	—
604	C₂×C₄₇	—	4	2	no	—
605	C₂×C₄₇	—	8	2	no	—
606	C₂×C₄₇	D₄×#41	1	1	yes	characteristic
607	C₂×C₄₇	C₂×#576	1	1	yes	characteristic
608	C₂×C₄₇	#3584	1	1	yes	characteristic
609	D₄₇	—	4	2	no	—
610	D₄₇	—	8	2	no	—
611	C₂×#135	—	47	1	no	—
612	C₂²×D₈	—	47	2	no	—
613	#559	—	47	1	no	—
614	#559	C₂×D₄₇	1	1	yes	characteristic, complemented
615	#556	—	47	1	no	—
616	#556	C₂×D₄₇	1	1	yes	characteristic
617	#555	—	47	2	no	—
618	#555	C₂×D₄₇	1	2	yes	complemented
619	#551	—	2	2	no	—
620	#551	—	94	2	no	—
621	D₄×Q₈	—	47	1	no	—
622	D₄×Q₈	C₂×D₄₇	1	1	yes	characteristic, complemented
623	#548	—	2	1	no	—
624	#548	—	94	1	no	—
625	#546	—	2	1	no	—
626	#546	—	47	2	no	—
627	#546	—	94	1	no	—
628	#546	C₂×D₄₇	1	2	yes	complemented
629	D₄²	—	47	1	no	—
630	D₄²	C₂×D₄₇	1	1	yes	characteristic
631	#542	—	47	2	no	—
632	#542	C₂×D₄₇	1	2	yes	complemented
633	#538	—	2	2	no	—
634	#538	—	94	2	no	—
635	#532	—	47	1	no	—
636	#532	C₂×D₄₇	1	1	yes	characteristic, complemented
637	#529	—	2	1	no	—
638	#529	—	94	1	no	—
639	#529	C₂×D₄₇	1	1	yes	characteristic
640	C₂×#124	—	2	1	no	—
641	C₂×#124	—	94	1	no	—
642	#518	—	47	2	no	—
643	#518	C₂×D₄₇	1	2	yes	complemented
644	C₄×#41	—	47	1	no	—
645	C₄×#41	C₂×D₄₇	1	1	yes	characteristic, complemented
646	#500	—	47	2	no	—
647	#500	—	47	1	no	—
648	#495	—	47	2	no	—
649	#493	—	47	1	no	—
650	#489	—	47	2	no	—
651	#489	—	47	2	no	—
652	#486	—	47	1	no	—
653	#486	—	47	1	no	—
654	#485	—	47	2	no	—
655	#485	—	47	2	no	—
656	#482	—	47	2	no	—
657	#482	—	47	2	no	—
658	#482	—	47	2	no	—
659	#482	—	47	2	no	—
660	#476	—	47	2	no	—
661	#476	—	47	2	no	—
662	#475	—	47	1	no	—
663	#475	—	47	1	no	—
664	#474	—	47	1	no	—
665	#474	—	47	2	no	—
666	#474	—	47	1	no	—
667	#474	—	47	2	no	—
668	#468	—	47	2	no	—
669	#468	—	47	2	no	—
670	#467	—	47	2	no	—
671	#466	—	47	2	no	—
672	#466	—	47	2	no	—
673	#466	—	47	2	no	—
674	#463	—	47	2	no	—
675	#463	—	47	2	no	—
676	#463	—	47	2	no	—
677	#463	—	47	2	no	—
678	#460	—	47	1	no	—
679	#460	—	47	1	no	—
680	#459	—	47	1	no	—
681	#459	—	47	1	no	—
682	#450	—	47	2	no	—
683	#450	—	47	2	no	—
684	#449	—	47	2	no	—
685	#449	—	47	2	no	—
686	#447	—	47	2	no	—
687	#447	—	47	2	no	—
688	#446	—	47	1	no	—
689	C₈×Q₈	—	47	1	no	—
690	#442	—	47	2	no	—
691	#442	—	47	2	no	—
692	#442	—	47	2	no	—
693	#442	—	47	2	no	—
694	#440	—	47	2	no	—
695	#440	—	47	2	no	—
696	C₄×Q₁₆	—	47	1	no	—
697	C₄×Q₁₆	—	47	1	no	—
698	C₄×SD₁₆	—	47	1	no	—
699	C₄×SD₁₆	—	47	1	no	—
700	C₄×SD₁₆	—	47	1	no	—
701	C₄×SD₁₆	—	47	1	no	—
702	C₄×D₈	—	47	2	no	—
703	C₄×D₈	—	47	2	no	—
704	C₄×D₈	—	47	1	no	—
705	C₄×D₈	—	47	2	no	—
706	C₄×D₈	—	47	2	no	—
707	C₄×D₈	—	47	1	no	—
708	#436	—	47	1	no	—
709	#435	—	47	2	no	—
710	C₈×D₄	—	47	2	no	—
711	C₈×D₄	—	47	1	no	—
712	#433	—	47	2	no	—
713	#432	—	47	1	no	—
714	#427	—	47	1	no	—
715	#427	—	47	2	no	—
716	#418	—	47	2	no	—
717	#418	—	47	2	no	—
718	#416	—	47	1	no	—
719	#416	—	47	1	no	—
720	#405	—	47	2	no	—
721	C₂×C₄×C₈	—	47	1	no	—
722	C₄₇	#61475	1	1	yes	characteristic, complemented, Sylow
723	C₂×#41	—	2	1	no	—
724	C₂×#41	—	47	1	no	—
725	C₂×#41	—	94	1	no	—
726	C₂×#41	C₂²×D₄₇	1	1	yes	characteristic
727	C₂²×Q₈	—	2	1	no	—
728	C₂²×Q₈	—	94	1	no	—
729	C₂²×D₄	—	2	1	no	—
730	C₂²×D₄	—	47	2	no	—
731	C₂²×D₄	—	94	1	no	—
732	C₂²×D₄	C₂²×D₄₇	1	2	yes	—
733	#135	—	94	4	no	—
734	C₂×Q₁₆	—	47	1	no	—
735	C₂×SD₁₆	—	47	1	no	—
736	C₂×SD₁₆	—	47	1	no	—
737	C₂×SD₁₆	—	47	2	no	—
738	C₂×SD₁₆	—	47	2	no	—
739	C₂×D₈	—	47	1	no	—
740	C₂×D₈	—	47	2	no	—
741	C₂×D₈	—	47	2	no	—
742	C₂×D₈	—	47	2	no	—
743	C₂×D₈	—	47	2	no	—
744	C₂×D₈	—	94	8	no	—
745	C₂×M₁₆	—	47	2	no	—
746	C₂²×C₈	—	47	2	no	—
747	C₂²×C₈	—	47	1	no	—
748	C₂²×C₈	—	47	1	no	—
749	C₄⋊Q₈	—	47	1	no	—
750	C₄⋊Q₈	—	47	2	no	—
751	C₄⋊Q₈	C₂²×D₄₇	1	1	yes	characteristic
752	C₄⋊Q₈	C₂²×D₄₇	1	2	yes	—
753	#127	—	47	1	no	—
754	#127	C₂²×D₄₇	1	1	yes	characteristic
755	#126	—	2	2	no	—
756	#126	—	2	2	no	—
757	#126	—	94	2	no	—
758	#126	—	94	2	no	—
759	#126	C₂²⋊D₄₇	1	2	yes	—
760	#125	C₂²⋊D₄₇	1	1	yes	characteristic
761	#124	—	2	1	no	—
762	#124	—	2	1	no	—
763	#124	—	2	2	no	—
764	#124	—	2	2	no	—
765	#124	—	2	2	no	—
766	#124	—	2	1	no	—
767	#124	—	47	2	no	—
768	#124	—	94	1	no	—
769	#124	—	94	1	no	—
770	#124	—	94	2	no	—
771	#124	—	94	2	no	—
772	#124	—	94	2	no	—
773	#124	—	94	1	no	—
774	#124	C₂²⋊D₄₇	1	1	yes	characteristic
775	#124	C₂²×D₄₇	1	2	yes	—
776	#123	—	2	2	no	—
777	#123	—	2	2	no	—
778	#123	—	2	2	no	—
779	#123	—	94	2	no	—
780	#123	—	94	2	no	—
781	#123	—	94	2	no	—
782	#123	C₂²⋊D₄₇	1	2	yes	—
783	C₂²⋊Q₈	—	2	1	no	—
784	C₂²⋊Q₈	—	2	2	no	—
785	C₂²⋊Q₈	—	2	2	no	—
786	C₂²⋊Q₈	—	47	2	no	—
787	C₂²⋊Q₈	—	94	1	no	—
788	C₂²⋊Q₈	—	94	2	no	—
789	C₂²⋊Q₈	—	94	2	no	—
790	C₂²⋊Q₈	C₂²⋊D₄₇	1	1	yes	characteristic
791	C₂²⋊Q₈	C₂²×D₄₇	1	2	yes	—
792	#121	—	2	2	no	—
793	#121	—	2	1	no	—
794	#121	—	2	1	no	—
795	#121	—	2	2	no	—
796	#121	—	47	2	no	—
797	#121	—	47	2	no	—
798	#121	—	94	2	no	—
799	#121	—	94	1	no	—
800	#121	—	94	1	no	—
801	#121	—	94	2	no	—
802	#121	C₂²⋊D₄₇	1	1	yes	characteristic
803	#121	C₂²×D₄₇	1	2	yes	—
804	#121	C₂²×D₄₇	1	2	yes	—
805	#120	—	2	2	no	—
806	#120	—	2	2	no	—
807	#120	—	94	2	no	—
808	#120	—	94	2	no	—
809	C₄×Q₈	—	2	1	no	—
810	C₄×Q₈	—	47	1	no	—
811	C₄×Q₈	—	47	1	no	—
812	C₄×Q₈	—	94	1	no	—
813	C₄×Q₈	C₂²×D₄₇	1	1	yes	characteristic
814	C₄×Q₈	C₂²×D₄₇	1	1	yes	characteristic
815	C₄×Q₈	C₂²×D₄₇	1	1	yes	characteristic
816	C₄×D₄	—	2	1	no	—
817	C₄×D₄	—	2	1	no	—
818	C₄×D₄	—	2	2	no	—
819	C₄×D₄	—	2	2	no	—
820	C₄×D₄	—	2	1	no	—
821	C₄×D₄	—	2	1	no	—
822	C₄×D₄	—	47	1	no	—
823	C₄×D₄	—	47	1	no	—
824	C₄×D₄	—	47	2	no	—
825	C₄×D₄	—	47	2	no	—
826	C₄×D₄	—	47	2	no	—
827	C₄×D₄	—	94	1	no	—
828	C₄×D₄	—	94	1	no	—
829	C₄×D₄	—	94	2	no	—
830	C₄×D₄	—	94	2	no	—
831	C₄×D₄	—	94	1	no	—
832	C₄×D₄	—	94	1	no	—
833	C₄×D₄	C₂²×D₄₇	1	1	yes	characteristic
834	C₄×D₄	C₂²×D₄₇	1	1	yes	characteristic
835	C₄×D₄	C₂²×D₄₇	1	2	yes	—
836	C₄×D₄	C₂²×D₄₇	1	2	yes	—
837	C₄×D₄	C₂²×D₄₇	1	2	yes	—
838	C₄×D₄	C₂²×D₄₇	1	1	yes	characteristic
839	C₄×D₄	C₂²×D₄₇	1	2	yes	—
840	#117	—	2	2	no	—
841	#117	—	2	1	no	—
842	#117	—	47	1	no	—
843	#117	—	47	2	no	—
844	#117	—	94	2	no	—
845	#117	—	94	1	no	—
846	#117	C₂²×D₄₇	1	1	yes	characteristic
847	#117	C₂²×D₄₇	1	2	yes	—
848	#117	C₂²×D₄₇	1	2	yes	—
849	C₂×C₂²⋊C₄	—	2	2	no	—
850	C₂×C₂²⋊C₄	—	2	2	no	—
851	C₂×C₂²⋊C₄	—	2	2	no	—
852	C₂×C₂²⋊C₄	—	94	2	no	—
853	C₂×C₂²⋊C₄	—	94	2	no	—
854	C₂×C₂²⋊C₄	—	94	2	no	—
855	C₂×C₄²	—	2	1	no	—
856	C₂×C₄²	—	94	1	no	—
857	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
858	#107	—	47	1	no	—
859	#107	—	47	2	no	—
860	#107	—	47	1	no	—
861	#107	—	47	2	no	—
862	#107	—	47	2	no	—
863	#107	—	47	2	no	—
864	#106	—	47	1	no	—
865	#106	—	47	1	no	—
866	#106	—	47	2	no	—
867	#106	—	47	2	no	—
868	C₄⋊C₈	—	47	1	no	—
869	C₄⋊C₈	—	47	1	no	—
870	C₄⋊C₈	—	47	2	no	—
871	C₄⋊C₈	—	47	2	no	—
872	#103	—	47	1	no	—
873	#103	—	47	1	no	—
874	#103	—	47	2	no	—
875	#103	—	47	1	no	—
876	#103	—	47	1	no	—
877	#103	—	47	2	no	—
878	#102	—	47	1	no	—
879	#102	—	47	1	no	—
880	#102	—	47	2	no	—
881	#102	—	47	2	no	—
882	#102	—	47	2	no	—
883	#102	—	47	2	no	—
884	#102	—	47	2	no	—
885	#102	—	47	1	no	—
886	#102	—	47	1	no	—
887	#102	—	47	2	no	—
888	#102	—	47	2	no	—
889	#102	—	47	2	no	—
890	#102	—	47	2	no	—
891	#102	—	47	2	no	—
892	C₂²⋊C₈	—	47	2	no	—
893	C₂²⋊C₈	—	47	2	no	—
894	C₂²⋊C₈	—	47	2	no	—
895	#97	—	47	2	no	—
896	#97	—	47	2	no	—
897	C₄×C₈	—	47	1	no	—
898	C₄×C₈	—	47	1	no	—
899	C₄×C₈	—	47	1	no	—
900	C₄×C₈	—	47	1	no	—
901	C₄×C₈	—	47	2	no	—
902	C₂⁴	—	2	2	no	—
903	C₂⁴	—	94	2	no	—
904	#41	—	2	2	no	—
905	#41	—	4	1	no	—
906	#41	—	8	2	no	—
907	#41	—	94	2	no	—
908	#41	—	376	2	no	—
909	#41	—	188	1	no	—
910	C₂×Q₈	—	2	1	no	—
911	C₂×Q₈	—	2	2	no	—
912	C₂×Q₈	—	8	2	no	—
913	C₂×Q₈	—	47	1	no	—
914	C₂×Q₈	—	94	2	no	—
915	C₂×Q₈	—	94	1	no	—
916	C₂×Q₈	—	376	2	no	—
917	C₂×Q₈	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
918	C₂×Q₈	C₂³×D₄₇	1	1	yes	characteristic
919	C₂×D₄	—	2	4	no	—
920	C₂×D₄	—	2	1	no	—
921	C₂×D₄	—	2	2	no	—
922	C₂×D₄	—	2	2	no	—
923	C₂×D₄	—	2	2	no	—
924	C₂×D₄	—	2	1	no	—
925	C₂×D₄	—	2	1	no	—
926	C₂×D₄	—	4	2	no	—
927	C₂×D₄	—	8	2	no	—
928	C₂×D₄	—	47	1	no	—
929	C₂×D₄	—	47	2	no	—
930	C₂×D₄	—	94	4	no	—
931	C₂×D₄	—	94	2	no	—
932	C₂×D₄	—	94	2	no	—
933	C₂×D₄	—	94	1	no	—
934	C₂×D₄	—	94	1	no	—
935	C₂×D₄	—	94	2	no	—
936	C₂×D₄	—	94	1	no	—
937	C₂×D₄	—	376	2	no	—
938	C₂×D₄	—	188	2	no	—
939	C₂×D₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
940	C₂×D₄	C₂×C₂²⋊D₄₇	1	2	yes	—
941	C₂×D₄	C₂³×D₄₇	1	2	yes	—
942	C₂×D₄	C₂³×D₄₇	1	1	yes	characteristic
943	C₂²×C₄	—	2	1	no	—
944	C₂²×C₄	—	2	1	no	—
945	C₂²×C₄	—	2	1	no	—
946	C₂²×C₄	—	2	2	no	—
947	C₂²×C₄	—	2	2	no	—
948	C₂²×C₄	—	2	2	no	—
949	C₂²×C₄	—	94	1	no	—
950	C₂²×C₄	—	94	2	no	—
951	C₂²×C₄	—	94	2	no	—
952	C₂²×C₄	—	94	2	no	—
953	C₂²×C₄	—	94	1	no	—
954	C₂²×C₄	—	94	1	no	—
955	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
956	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
957	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
958	C₂²×C₄	C₂³×D₄₇	1	2	yes	—
959	Q₁₆	—	94	2	no	—
960	SD₁₆	—	94	2	no	—
961	SD₁₆	—	94	2	no	—
962	SD₁₆	—	188	2	no	—
963	SD₁₆	—	188	2	no	—
964	D₈	—	47	4	no	—
965	D₈	—	94	4	no	—
966	D₈	—	94	4	no	—
967	D₈	—	94	4	no	—
968	D₈	—	188	2	no	—
969	M₁₆	—	188	2	no	—
970	C₂×C₈	—	47	1	no	—
971	C₂×C₈	—	47	1	no	—
972	C₂×C₈	—	47	1	no	—
973	C₂×C₈	—	47	1	no	—
974	C₂×C₈	—	47	2	no	—
975	C₂×C₈	—	47	2	no	—
976	C₂×C₈	—	94	4	no	—
977	C₂×C₈	—	94	2	no	—
978	C₂×C₈	—	188	1	no	—
979	C₄⋊C₄	—	2	1	no	—
980	C₄⋊C₄	—	2	1	no	—
981	C₄⋊C₄	—	2	2	no	—
982	C₄⋊C₄	—	2	1	no	—
983	C₄⋊C₄	—	2	2	no	—
984	C₄⋊C₄	—	47	1	no	—
985	C₄⋊C₄	—	47	2	no	—
986	C₄⋊C₄	—	47	1	no	—
987	C₄⋊C₄	—	94	1	no	—
988	C₄⋊C₄	—	94	1	no	—
989	C₄⋊C₄	—	94	2	no	—
990	C₄⋊C₄	—	94	2	no	—
991	C₄⋊C₄	—	94	1	no	—
992	C₄⋊C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
993	C₄⋊C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
994	C₄⋊C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
995	C₄⋊C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
996	C₄⋊C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
997	C₄⋊C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
998	C₄⋊C₄	C₂³×D₄₇	1	1	yes	characteristic
999	C₄⋊C₄	C₂³×D₄₇	1	2	yes	—
1000	C₄⋊C₄	C₂³×D₄₇	1	1	yes	characteristic
1001	C₂²⋊C₄	—	2	2	no	—
1002	C₂²⋊C₄	—	2	2	no	—
1003	C₂²⋊C₄	—	2	1	no	—
1004	C₂²⋊C₄	—	2	1	no	—
1005	C₂²⋊C₄	—	2	2	no	—
1006	C₂²⋊C₄	—	2	2	no	—
1007	C₂²⋊C₄	—	2	2	no	—
1008	C₂²⋊C₄	—	2	2	no	—
1009	C₂²⋊C₄	—	2	2	no	—
1010	C₂²⋊C₄	—	2	1	no	—
1011	C₂²⋊C₄	—	2	2	no	—
1012	C₂²⋊C₄	—	2	2	no	—
1013	C₂²⋊C₄	—	94	2	no	—
1014	C₂²⋊C₄	—	94	2	no	—
1015	C₂²⋊C₄	—	94	1	no	—
1016	C₂²⋊C₄	—	94	1	no	—
1017	C₂²⋊C₄	—	94	2	no	—
1018	C₂²⋊C₄	—	94	2	no	—
1019	C₂²⋊C₄	—	94	2	no	—
1020	C₂²⋊C₄	—	94	2	no	—
1021	C₂²⋊C₄	—	94	2	no	—
1022	C₂²⋊C₄	—	94	1	no	—
1023	C₂²⋊C₄	—	94	2	no	—
1024	C₂²⋊C₄	—	94	2	no	—
1025	C₂²⋊C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
1026	C₂²⋊C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
1027	C₂²⋊C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
1028	C₂²⋊C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
1029	C₂²⋊C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
1030	C₄²	—	2	1	no	—
1031	C₄²	—	2	1	no	—
1032	C₄²	—	2	1	no	—
1033	C₄²	—	2	2	no	—
1034	C₄²	—	94	1	no	—
1035	C₄²	—	94	1	no	—
1036	C₄²	—	94	1	no	—
1037	C₄²	—	94	2	no	—
1038	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
1039	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
1040	C₄²	C₂³×D₄₇	1	1	yes	characteristic
1041	C₄²	C₂³×D₄₇	1	1	yes	characteristic
1042	C₄²	C₂³×D₄₇	1	2	yes	—
1043	C₂³	—	2	1	no	—
1044	C₂³	—	2	2	no	—
1045	C₂³	—	4	4	no	—
1046	C₂³	—	8	2	no	—
1047	C₂³	—	8	2	no	—
1048	C₂³	—	94	1	no	—
1049	C₂³	—	94	2	no	—
1050	C₂³	—	376	2	no	—
1051	C₂³	—	376	2	no	—
1052	C₂³	—	188	4	no	—
1053	C₂³	C₂²×C₂²⋊D₄₇	1	2	yes	—
1054	C₂³	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
1055	Q₈	—	2	2	no	—
1056	Q₈	—	2	1	no	—
1057	Q₈	—	2	1	no	—
1058	Q₈	—	4	2	no	—
1059	Q₈	—	8	2	no	—
1060	Q₈	—	94	1	no	—
1061	Q₈	—	94	1	no	—
1062	Q₈	—	376	2	no	—
1063	Q₈	—	188	2	no	—
1064	D₄	—	2	2	no	—
1065	D₄	—	2	2	no	—
1066	D₄	—	2	1	no	—
1067	D₄	—	2	2	no	—
1068	D₄	—	4	2	no	—
1069	D₄	—	4	4	no	—
1070	D₄	—	4	2	no	—
1071	D₄	—	4	2	no	—
1072	D₄	—	8	1	no	—
1073	D₄	—	8	2	no	—
1074	D₄	—	8	2	no	—
1075	D₄	—	47	2	no	—
1076	D₄	—	94	2	no	—
1077	D₄	—	94	1	no	—
1078	D₄	—	94	2	no	—
1079	D₄	—	376	1	no	—
1080	D₄	—	376	2	no	—
1081	D₄	—	376	2	no	—
1082	D₄	—	188	4	no	—
1083	D₄	—	188	2	no	—
1084	D₄	—	188	2	no	—
1085	D₄	#41×D₄₇	1	2	yes	—
1086	C₂×C₄	—	2	2	no	—
1087	C₂×C₄	—	2	2	no	—
1088	C₂×C₄	—	2	1	no	—
1089	C₂×C₄	—	2	1	no	—
1090	C₂×C₄	—	2	2	no	—
1091	C₂×C₄	—	2	1	no	—
1092	C₂×C₄	—	2	1	no	—
1093	C₂×C₄	—	2	1	no	—
1094	C₂×C₄	—	2	2	no	—
1095	C₂×C₄	—	4	1	no	—
1096	C₂×C₄	—	4	2	no	—
1097	C₂×C₄	—	4	2	no	—
1098	C₂×C₄	—	8	1	no	—
1099	C₂×C₄	—	8	2	no	—
1100	C₂×C₄	—	8	2	no	—
1101	C₂×C₄	—	8	2	no	—
1102	C₂×C₄	—	94	1	no	—
1103	C₂×C₄	—	94	1	no	—
1104	C₂×C₄	—	94	1	no	—
1105	C₂×C₄	—	94	2	no	—
1106	C₂×C₄	—	376	1	no	—
1107	C₂×C₄	—	376	2	no	—
1108	C₂×C₄	—	376	2	no	—
1109	C₂×C₄	—	376	2	no	—
1110	C₂×C₄	—	188	2	no	—
1111	C₂×C₄	—	188	2	no	—
1112	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
1113	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
1114	C₂×C₄	C₂²×C₂²⋊D₄₇	1	2	yes	—
1115	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
1116	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
1117	C₂×C₄	C₂²×C₂²⋊D₄₇	1	2	yes	—
1118	C₂×C₄	C₂²×C₂²⋊D₄₇	1	2	yes	—
1119	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
1120	C₂×C₄	C₂⁴×D₄₇	1	1	yes	characteristic
1121	C₈	—	47	2	no	—
1122	C₈	—	94	2	no	—
1123	C₈	—	94	1	no	—
1124	C₈	—	94	1	no	—
1125	C₈	—	94	1	no	—
1126	C₈	—	94	2	no	—
1127	C₂²	—	2	1	no	—
1128	C₂²	—	2	2	no	—
1129	C₂²	—	2	1	no	—
1130	C₂²	—	2	2	no	—
1131	C₂²	—	2	2	no	—
1132	C₂²	—	2	1	no	—
1133	C₂²	—	2	2	no	—
1134	C₂²	—	4	1	no	—
1135	C₂²	—	4	1	no	—
1136	C₂²	—	4	2	no	—
1137	C₂²	—	4	2	no	—
1138	C₂²	—	4	2	no	—
1139	C₂²	—	16	4	no	—
1140	C₂²	—	94	2	no	—
1141	C₂²	—	188	2	no	—
1142	C₂²	—	188	2	no	—
1143	C₂²	—	188	2	no	—
1144	C₂²	—	188	1	no	—
1145	C₂²	—	188	1	no	—
1146	C₂²	—	752	4	no	—
1147	C₂²	C₂³×C₂²⋊D₄₇	1	1	yes	characteristic
1148	C₄	—	2	1	no	—
1149	C₄	—	2	2	no	—
1150	C₄	—	2	1	no	—
1151	C₄	—	2	2	no	—
1152	C₄	—	2	1	no	—
1153	C₄	—	2	1	no	—
1154	C₄	—	2	2	no	—
1155	C₄	—	4	1	no	—
1156	C₄	—	4	2	no	—
1157	C₄	—	4	1	no	—
1158	C₄	—	4	1	no	—
1159	C₄	—	188	2	no	—
1160	C₄	—	188	1	no	—
1161	C₄	—	188	1	no	—
1162	C₄	—	188	1	no	—
1163	C₄	#15689926	1	2	yes	—
1164	C₄	C₂×#41×D₄₇	1	1	yes	characteristic
1165	C₄	#15689959	1	1	yes	characteristic
1166	C₂	—	4	2	no	—
1167	C₂	—	4	1	no	—
1168	C₂	—	4	2	no	—
1169	C₂	—	8	2	no	—
1170	C₂	—	376	2	no	—
1171	C₂	—	188	2	no	—
1172	C₂	#41×C₂²⋊D₄₇	1	1	yes	characteristic
1173	C₂	C₂×#15689926	1	1	yes	characteristic
1174	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×#3514	C₂
socle	C₂²×C₄₇	C₂³×D₄
hypercenter	#3514	D₄₇
hypocenter	C₄₇	#61475
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ #529 ◁ #3514

Complements

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

N	H ≅ G/N	type
1. #20257351	C₂	semidirect
2. #20256396	C₂	semidirect
3. Q₈×#10625334	C₂	semidirect
4. #20256180	C₂	semidirect
5. #20256176	C₂	semidirect
6. #20255814	C₂	semidirect
7. #20255806	C₂	semidirect
8. #20255619	C₂	semidirect
9. #20255613	C₂	semidirect
10. #20255544	C₂	semidirect
11. #20255538	C₂	semidirect
12. #20255069	C₂	semidirect
13. D₄×#10625334	C₂	semidirect
14. #20254021	C₂	semidirect
15. #20253963	C₂	semidirect
16. #20253572	C₂	semidirect
17. #20253566	C₂	semidirect
18. #20253539	C₂	semidirect
19. #20253533	C₂	semidirect
20. #20252364	C₂	semidirect
21. #20252238	C₂	semidirect
22. C₄×#13094044	C₂	semidirect
23. C₄₇×#3514	C₂	semidirect
26. #15689858	C₂²	semidirect
28. #15689838	C₂²	semidirect
30. Q₈×D₁₈₈	C₂²	semidirect
33. #15689769	C₂²	semidirect
35. #15689744	C₂²	semidirect
37. #15689673	C₂²	semidirect
40. #15689597	C₂²	semidirect
41. C₄×#10625350	C₂²	semidirect
42. #15689526	C₂²	semidirect
43. #15689526	C₂²	semidirect
44. #15689505	C₂²	semidirect
46. #15689485	C₂²	semidirect
47. #15689482	C₂²	semidirect
48. #15689471	C₂²	semidirect
49. #15689469	C₂²	semidirect
50. #15689464	C₂²	semidirect
51. #15689461	C₂²	semidirect
52. #15689447	C₂²	semidirect
53. #15689447	C₂²	semidirect
54. #15689444	C₂²	semidirect
55. #15689444	C₂²	semidirect
56. #15689413	C₂²	semidirect
57. #15689410	C₂²	semidirect
58. #15689408	C₂²	semidirect
59. #15689405	C₂²	semidirect
60. #15689403	C₂²	semidirect
61. #15689403	C₂²	semidirect
62. #15689400	C₂²	semidirect
63. #15689400	C₂²	semidirect
64. #15689371	C₂²	semidirect
65. #15689367	C₂²	semidirect
66. #15689362	C₂²	semidirect
68. #15689357	C₂²	semidirect
69. #15689357	C₂²	semidirect
70. #15689338	C₂²	semidirect
71. #15689338	C₂²	semidirect
72. #15689335	C₂²	semidirect
73. #15689335	C₂²	semidirect
74. #15689323	C₂²	semidirect
75. #15689320	C₂²	semidirect
78. #15689274	C₂²	semidirect
79. #15689273	C₂²	semidirect
80. #15689268	C₂²	semidirect
81. #15689266	C₂²	semidirect
84. #15689254	C₂²	semidirect
85. Q₈×C₄₇⋊C₈	C₂²	semidirect
86. #15689233	C₂²	semidirect
87. #15689233	C₂²	semidirect
88. #15689233	C₂²	semidirect
89. #15689233	C₂²	semidirect
90. #15689223	C₂²	semidirect
91. #15689221	C₂²	semidirect
92. C₄×#10625337	C₂²	semidirect
93. C₄×#10625337	C₂²	semidirect
94. C₄×#10625336	C₂²	semidirect
95. C₄×#10625336	C₂²	semidirect
96. C₄×#10625335	C₂²	semidirect
97. C₄×#10625335	C₂²	semidirect
101. C₄×#10625334	C₂²	semidirect
102. C₄×#10625334	C₂²	semidirect
103. C₄×#10625334	C₂²	semidirect
105. #15689195	C₂²	semidirect
107. D₄×C₄₇⋊C₈	C₂²	semidirect
108. #15689184	C₂²	semidirect
109. #15689180	C₂²	semidirect
110. #15689159	C₂²	semidirect
111. #15689159	C₂²	semidirect
112. #15689128	C₂²	semidirect
113. #15689127	C₂²	semidirect
114. #15689119	C₂²	semidirect
115. #15689117	C₂²	semidirect
116. #15689079	C₂²	semidirect
117. C₂×C₄×C₄₇⋊C₈	C₂²	semidirect
118. C₄₇×#559	C₂²	semidirect
120. C₄₇×#555	C₂²	semidirect
122. D₄×Q₈×C₄₇	C₂²	semidirect
125. C₄₇×#546	C₂²	semidirect
127. C₄₇×#542	C₂²	semidirect
129. C₄₇×#532	C₂²	semidirect
133. C₄₇×#518	C₂²	semidirect
134. C₄×#41×C₄₇	C₂²	semidirect
423. #10625334	#41	semidirect
580. #3514	D₄₇	semidirect
614. #559	C₂×D₄₇	semidirect
618. #555	C₂×D₄₇	semidirect
622. D₄×Q₈	C₂×D₄₇	semidirect
628. #546	C₂×D₄₇	semidirect
632. #542	C₂×D₄₇	semidirect
636. #532	C₂×D₄₇	semidirect
643. #518	C₂×D₄₇	semidirect
645. C₄×#41	C₂×D₄₇	semidirect
722. C₄₇	#61475	semidirect

Maximal subgroups

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

subgroup	index
#20257351	2
#20256396	2
Q₈×#10625334	2
#20256180	2
#20256176	2
#20255814	2
#20255806	2
#20255619	2
#20255613	2
#20255544	2
#20255538	2
#20255069	2
D₄×#10625334	2
#20254021	2
#20253963	2
#20253572	2
#20253566	2
#20253539	2
#20253533	2
#20252364	2
#20252238	2
C₄×#13094044	2
C₄₇×#3514	2
#61475	47