Subgroups — #27091199

Order 12032.

1724 conjugacy classes of subgroups.

The subgroup lattice has 1258 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20257299	C₂	1	1	yes	maximal, characteristic, complemented
2	#20254808	C₂	1	2	yes	maximal, complemented
3	#20254793	C₂	1	2	yes	maximal, complemented
4	#20254615	C₂	1	1	yes	maximal, characteristic, complemented
5	#20254606	C₂	1	1	yes	maximal, characteristic, complemented
6	#20254594	C₂	1	1	yes	maximal, characteristic, complemented
7	#20254578	C₂	1	1	yes	maximal, characteristic, complemented
8	#20254421	C₂	1	1	yes	maximal, characteristic, complemented
9	#20254421	C₂	1	1	yes	maximal, characteristic, complemented
10	#20254399	C₂	1	1	yes	maximal, characteristic, complemented
11	#20254383	C₂	1	1	yes	maximal, characteristic, complemented
12	#20254294	C₂	1	2	yes	maximal, complemented
13	#20254285	C₂	1	2	yes	maximal, complemented
14	#20254098	C₂	1	1	yes	maximal, characteristic, complemented
15	#20254087	C₂	1	1	yes	maximal, characteristic, complemented
16	#20253995	C₂	1	1	yes	maximal, characteristic, complemented
17	#20253984	C₂	1	1	yes	maximal, characteristic, complemented
18	#20253665	C₂	1	2	yes	maximal, complemented
19	#20253650	C₂	1	2	yes	maximal, complemented
20	#20253596	C₂	1	2	yes	maximal, complemented
21	#20253581	C₂	1	2	yes	maximal, complemented
22	#20252039	C₂	1	1	yes	maximal, characteristic, complemented
23	C₄₇×#3512	C₂	1	1	yes	maximal, characteristic, complemented
24	#15689846	—	2	1	no	—
25	#15689838	—	2	1	no	—
26	#15689833	—	2	1	no	—
27	#15689819	—	2	1	no	—
28	#15689819	—	2	1	no	—
29	#15689782	—	2	1	no	—
30	#15689782	—	2	1	no	—
31	#15689778	—	2	1	no	—
32	#15689744	C₂²	1	2	yes	—
33	#15689744	C₂²	1	2	yes	—
34	#15689701	C₂²	1	2	yes	—
35	#15689680	C₂²	1	1	yes	characteristic
36	#15689680	C₂²	1	1	yes	characteristic
37	#15689673	C₂²	1	1	yes	characteristic
38	#15689673	C₂²	1	1	yes	characteristic
39	#15689673	C₂²	1	1	yes	characteristic
40	C₂×#13094024	C₂²	1	1	yes	characteristic
41	#15689603	C₂²	1	2	yes	—
42	#15689533	C₂²	1	1	yes	characteristic
43	#15689533	C₂²	1	1	yes	characteristic
44	#15689533	C₂²	1	1	yes	characteristic
45	#15689533	C₂²	1	1	yes	characteristic
46	#15689518	C₂²	1	1	yes	characteristic
47	#15689518	C₂²	1	1	yes	characteristic
48	#15689513	C₂²	1	1	yes	characteristic
49	#15689513	C₂²	1	1	yes	characteristic
50	#15689493	C₂²	1	1	yes	characteristic
51	#15689493	C₂²	1	1	yes	characteristic
52	#15689489	C₂²	1	1	yes	characteristic
53	#15689489	C₂²	1	1	yes	characteristic
54	#15689482	C₂²	1	1	yes	characteristic
55	#15689482	C₂²	1	1	yes	characteristic
56	#15689482	C₂²	1	1	yes	characteristic
57	#15689482	C₂²	1	1	yes	characteristic
58	#15689458	C₂²	1	2	yes	—
59	#15689456	C₂²	1	2	yes	—
60	#15689453	C₂²	1	2	yes	—
61	#15689451	C₂²	1	2	yes	—
62	#15689441	C₂²	1	2	yes	—
63	#15689439	C₂²	1	2	yes	—
64	#15689436	C₂²	1	2	yes	—
65	#15689434	C₂²	1	2	yes	—
66	#15689427	C₂²	1	2	yes	—
67	#15689427	C₂²	1	2	yes	—
68	#15689420	C₂²	1	2	yes	—
69	#15689420	C₂²	1	2	yes	—
70	#15689418	C₂²	1	2	yes	—
71	#15689413	C₂²	1	2	yes	—
72	#15689408	C₂²	1	2	yes	—
73	#15689403	C₂²	1	2	yes	—
74	#15689379	C₂²	1	2	yes	—
75	#15689374	C₂²	1	2	yes	—
76	#15689371	C₂²	1	2	yes	—
77	#15689367	C₂²	1	2	yes	—
78	#15689362	C₂²	1	2	yes	—
79	#15689357	C₂²	1	2	yes	—
80	#15689354	C₂²	1	2	yes	—
81	#15689350	C₂²	1	2	yes	—
82	#15689345	C₂²	1	2	yes	—
83	#15689345	C₂²	1	2	yes	—
84	#15689338	C₂²	1	2	yes	—
85	#15689338	C₂²	1	2	yes	—
86	#15689330	C₂²	1	2	yes	—
87	#15689325	C₂²	1	2	yes	—
88	#15689320	C₂²	1	2	yes	—
89	#15689315	C₂²	1	2	yes	—
90	#15689285	C₂²	1	2	yes	—
91	#15689285	C₂²	1	2	yes	—
92	#15689283	C₂²	1	2	yes	—
93	#15689283	C₂²	1	2	yes	—
94	#15689268	C₂²	1	2	yes	—
95	#15689268	C₂²	1	2	yes	—
96	#15689266	C₂²	1	2	yes	—
97	#15689266	C₂²	1	2	yes	—
98	#15689233	C₂²	1	2	yes	—
99	#15689228	C₂²	1	2	yes	—
100	#15689223	C₂²	1	2	yes	—
101	#15689221	C₂²	1	2	yes	—
102	C₄×#10625337	C₂²	1	2	yes	—
103	C₄×#10625336	C₂²	1	2	yes	—
104	C₄×#10625335	C₂²	1	2	yes	—
105	C₄×#10625334	C₂²	1	2	yes	—
106	#15689184	C₂²	1	2	yes	—
107	#15689184	C₂²	1	2	yes	—
108	#15689180	C₂²	1	1	yes	characteristic
109	#15689180	C₂²	1	1	yes	characteristic
110	#15689180	C₂²	1	1	yes	characteristic
111	#15689180	C₂²	1	1	yes	characteristic
112	#15689150	C₂²	1	2	yes	—
113	#15689090	C₂²	1	2	yes	—
114	C₄×#10625329	C₂²	1	1	yes	characteristic
115	C₂×#13093935	C₂²	1	1	yes	characteristic
116	C₄₇×#553	—	2	1	no	—
117	C₄₇×#553	—	2	1	no	—
118	C₄₇×#553	—	2	1	no	—
119	C₄₇×#553	—	2	1	no	—
120	C₄₇×#553	—	2	1	no	—
121	C₄₇×#553	—	2	1	no	—
122	C₄₇×#552	—	2	1	no	—
123	C₄₇×#552	—	2	1	no	—
124	C₄₇×#541	C₂²	1	1	yes	characteristic
125	C₄₇×#541	C₂²	1	1	yes	characteristic
126	C₄₇×#540	C₂²	1	1	yes	characteristic
127	C₄₇×#540	C₂²	1	1	yes	characteristic
128	C₄₇×#537	C₂²	1	1	yes	characteristic
129	C₄₇×#537	C₂²	1	1	yes	characteristic
130	C₄₇×#532	C₂²	1	1	yes	characteristic
131	C₄₇×#529	C₂²	1	1	yes	characteristic
132	C₄₇×#529	C₂²	1	1	yes	characteristic
133	C₄₇×#529	C₂²	1	1	yes	characteristic
134	C₄₇×#529	C₂²	1	1	yes	characteristic
135	C₂×#125×C₄₇	C₂²	1	1	yes	characteristic
136	C₄₇×#520	C₂²	1	1	yes	characteristic
137	C₄₇×#520	C₂²	1	1	yes	characteristic
138	C₄×#41×C₄₇	C₂²	1	1	yes	characteristic
139	C₂×#10625350	—	2	1	no	—
140	C₂×#10625350	—	2	1	no	—
141	C₂×#10625350	C₂³	1	2	yes	—
142	C₂²×Dic₉₄	—	2	1	no	—
143	C₂×#10625337	C₂³	1	2	yes	—
144	C₂×#10625337	C₂³	1	2	yes	—
145	C₂×#10625335	C₂³	1	2	yes	—
146	C₂×#10625335	C₂³	1	2	yes	—
147	C₂×#10625336	C₂³	1	2	yes	—
148	C₂×#10625336	C₂³	1	2	yes	—
149	C₂×#10625334	C₂³	1	2	yes	—
150	C₂×#10625334	C₂³	1	2	yes	—
151	C₂×#10625329	C₂³	1	2	yes	—
152	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
153	#13094024	—	2	1	no	—
154	#13094024	—	2	1	no	—
155	#13094024	C₂³	1	1	yes	characteristic
156	#13094024	C₂³	1	1	yes	characteristic
157	#13094024	C₂³	1	1	yes	characteristic
158	#13094024	C₂³	1	2	yes	—
159	#13094021	C₂³	1	1	yes	characteristic
160	#13094019	—	2	2	no	—
161	#13094019	—	2	2	no	—
162	#13094016	—	2	1	no	—
163	#13094016	—	2	1	no	—
164	#13094012	—	2	1	no	—
165	#13094012	—	2	1	no	—
166	#13094012	C₂³	1	2	yes	—
167	#13094010	—	2	2	no	—
168	#13094010	—	2	2	no	—
169	#13094006	—	2	2	no	—
170	#13094006	—	2	2	no	—
171	#13094003	—	2	1	no	—
172	#13094003	—	2	1	no	—
173	#13094003	C₂³	1	2	yes	—
174	#13094003	C₂³	1	2	yes	—
175	#13094002	—	2	2	no	—
176	#13094002	—	2	2	no	—
177	#13094000	—	2	2	no	—
178	#13093998	—	2	1	no	—
179	#13093998	—	2	1	no	—
180	#13093998	—	2	1	no	—
181	#13093998	—	2	1	no	—
182	#13093998	C₂³	1	2	yes	—
183	#13093998	C₂³	1	2	yes	—
184	#13093996	—	2	2	no	—
185	#13093996	—	2	2	no	—
186	#13093995	—	2	2	no	—
187	C₄×Dic₉₄	—	2	1	no	—
188	C₄×Dic₉₄	—	2	1	no	—
189	C₄×Dic₉₄	C₂³	1	2	yes	—
190	C₄×Dic₉₄	C₂³	1	2	yes	—
191	C₄×D₁₈₈	—	2	1	no	—
192	C₄×D₁₈₈	—	2	1	no	—
193	C₄×D₁₈₈	—	2	1	no	—
194	C₄×D₁₈₈	—	2	1	no	—
195	C₄×D₁₈₈	C₂³	1	2	yes	—
196	C₄×D₁₈₈	C₂³	1	2	yes	—
197	(C₂²⋊D₄₇)⋊C₄	—	2	2	no	—
198	(C₂²⋊D₄₇)⋊C₄	—	2	2	no	—
199	#13093983	—	2	1	no	—
200	#13093983	—	2	1	no	—
201	#13093982	—	2	2	no	—
202	C₂×C₄⋊Dic₄₇	—	2	1	no	—
203	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
204	C₄⋊C₄×D₄₇	—	2	2	no	—
205	#13093957	C₂³	1	2	yes	—
206	#13093957	C₂³	1	2	yes	—
207	#13093957	C₂³	1	2	yes	—
208	#13093957	C₂³	1	2	yes	—
209	#13093955	C₂³	1	2	yes	—
210	#13093955	C₂³	1	2	yes	—
211	#13093955	C₂³	1	2	yes	—
212	#13093955	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	#13093948	C₂³	1	2	yes	—
218	#13093948	C₂³	1	2	yes	—
219	#13093948	C₂³	1	2	yes	—
220	#13093948	C₂³	1	2	yes	—
221	#13093947	C₂³	1	2	yes	—
222	#13093947	C₂³	1	2	yes	—
223	#13093947	C₂³	1	2	yes	—
224	#13093947	C₂³	1	2	yes	—
225	#13093945	C₂³	1	2	yes	—
226	#13093945	C₂³	1	2	yes	—
227	#13093945	C₂³	1	2	yes	—
228	#13093945	C₂³	1	2	yes	—
229	#13093944	C₂³	1	2	yes	—
230	#13093944	C₂³	1	2	yes	—
231	#13093944	C₂³	1	2	yes	—
232	#13093944	C₂³	1	2	yes	—
233	C₂²⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
234	C₂²⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
235	C₂²⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
236	C₂²⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
237	#13093935	C₂³	1	2	yes	—
238	#13093935	C₂³	1	1	yes	characteristic
239	#13093935	C₂³	1	1	yes	characteristic
240	#13093935	C₂³	1	1	yes	characteristic
241	#13093935	C₂³	1	1	yes	characteristic
242	C₄×C₄₇⋊C₈	C₂³	1	2	yes	—
243	C₂×#41×C₄₇	C₂³	1	1	yes	characteristic
244	C₂×#41×C₄₇	C₂³	1	1	yes	characteristic
245	C₂×#41×C₄₇	C₂³	1	1	yes	characteristic
246	C₄⋊Q₈×C₄₇	C₂³	1	1	yes	characteristic
247	#127×C₄₇	C₂³	1	1	yes	characteristic
248	#126×C₄₇	—	2	1	no	—
249	#126×C₄₇	—	2	1	no	—
250	#126×C₄₇	—	2	1	no	—
251	#126×C₄₇	—	2	1	no	—
252	#126×C₄₇	—	2	1	no	—
253	#126×C₄₇	—	2	1	no	—
254	#126×C₄₇	—	2	1	no	—
255	#126×C₄₇	—	2	1	no	—
256	#125×C₄₇	—	2	1	no	—
257	#125×C₄₇	—	2	1	no	—
258	#125×C₄₇	—	2	1	no	—
259	#125×C₄₇	—	2	1	no	—
260	#125×C₄₇	—	2	1	no	—
261	#125×C₄₇	—	2	1	no	—
262	#125×C₄₇	C₂³	1	1	yes	characteristic
263	#125×C₄₇	C₂³	1	1	yes	characteristic
264	#125×C₄₇	C₂³	1	1	yes	characteristic
265	#125×C₄₇	C₂³	1	1	yes	characteristic
266	#124×C₄₇	C₂³	1	1	yes	characteristic
267	#124×C₄₇	C₂³	1	1	yes	characteristic
268	#123×C₄₇	—	2	1	no	—
269	#123×C₄₇	—	2	1	no	—
270	#123×C₄₇	—	2	1	no	—
271	#123×C₄₇	—	2	1	no	—
272	#123×C₄₇	—	2	1	no	—
273	#123×C₄₇	—	2	1	no	—
274	#123×C₄₇	—	2	1	no	—
275	#123×C₄₇	—	2	1	no	—
276	C₂²⋊Q₈×C₄₇	—	2	1	no	—
277	C₂²⋊Q₈×C₄₇	—	2	1	no	—
278	C₂²⋊Q₈×C₄₇	C₂³	1	1	yes	characteristic
279	C₂²⋊Q₈×C₄₇	C₂³	1	1	yes	characteristic
280	C₂²⋊Q₈×C₄₇	C₂³	1	1	yes	characteristic
281	C₂²⋊Q₈×C₄₇	C₂³	1	1	yes	characteristic
282	#121×C₄₇	—	2	1	no	—
283	#121×C₄₇	—	2	1	no	—
284	#121×C₄₇	—	2	1	no	—
285	#121×C₄₇	—	2	1	no	—
286	#121×C₄₇	—	2	1	no	—
287	#121×C₄₇	—	2	1	no	—
288	#121×C₄₇	—	2	1	no	—
289	#121×C₄₇	—	2	1	no	—
290	#121×C₄₇	—	2	1	no	—
291	#121×C₄₇	—	2	1	no	—
292	#121×C₄₇	—	2	1	no	—
293	#121×C₄₇	—	2	1	no	—
294	#121×C₄₇	C₂³	1	1	yes	characteristic
295	#121×C₄₇	C₂³	1	1	yes	characteristic
296	#121×C₄₇	C₂³	1	1	yes	characteristic
297	#121×C₄₇	C₂³	1	1	yes	characteristic
298	C₄×Q₈×C₄₇	D₄	1	1	yes	characteristic
299	C₄×Q₈×C₄₇	D₄	1	1	yes	characteristic
300	C₄×Q₈×C₄₇	C₂³	1	1	yes	characteristic
301	C₄×Q₈×C₄₇	C₂³	1	1	yes	characteristic
302	C₄×Q₈×C₄₇	C₂³	1	1	yes	characteristic
303	C₄×Q₈×C₄₇	C₂³	1	1	yes	characteristic
304	C₄×D₄×C₄₇	—	2	1	no	—
305	C₄×D₄×C₄₇	—	2	1	no	—
306	C₄×D₄×C₄₇	—	2	1	no	—
307	C₄×D₄×C₄₇	—	2	1	no	—
308	C₄×D₄×C₄₇	—	2	1	no	—
309	C₄×D₄×C₄₇	—	2	1	no	—
310	C₄×D₄×C₄₇	—	2	1	no	—
311	C₄×D₄×C₄₇	—	2	1	no	—
312	C₄×D₄×C₄₇	—	2	1	no	—
313	C₄×D₄×C₄₇	—	2	1	no	—
314	C₄×D₄×C₄₇	D₄	1	1	yes	characteristic
315	C₄×D₄×C₄₇	D₄	1	1	yes	characteristic
316	C₄×D₄×C₄₇	D₄	1	1	yes	characteristic
317	C₄×D₄×C₄₇	D₄	1	1	yes	characteristic
318	C₄×D₄×C₄₇	D₄	1	1	yes	characteristic
319	C₄×D₄×C₄₇	D₄	1	1	yes	characteristic
320	C₄×D₄×C₄₇	C₂³	1	1	yes	characteristic
321	C₄×D₄×C₄₇	C₂³	1	1	yes	characteristic
322	C₄×D₄×C₄₇	C₂³	1	1	yes	characteristic
323	C₄×D₄×C₄₇	C₂³	1	1	yes	characteristic
324	#117×C₄₇	—	2	1	no	—
325	#117×C₄₇	—	2	1	no	—
326	#117×C₄₇	—	2	1	no	—
327	#117×C₄₇	—	2	1	no	—
328	#117×C₄₇	—	2	1	no	—
329	#117×C₄₇	—	2	1	no	—
330	#117×C₄₇	C₂³	1	1	yes	characteristic
331	#117×C₄₇	C₂³	1	1	yes	characteristic
332	#117×C₄₇	C₂³	1	1	yes	characteristic
333	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
334	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
335	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
336	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
337	C₂×C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
338	C₂×C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
339	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
340	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
341	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
342	#41×C₄₇	—	4	2	no	—
343	#41×C₄₇	—	4	2	no	—
344	#41×C₄₇	—	4	2	no	—
345	C₂×Q₈×C₄₇	C₂×D₄	1	1	yes	characteristic
346	C₂×Q₈×C₄₇	C₂⁴	1	1	yes	characteristic
347	C₂×Q₈×C₄₇	C₂⁴	1	1	yes	characteristic
348	C₂×D₄×C₄₇	—	2	1	no	—
349	C₂×D₄×C₄₇	—	2	1	no	—
350	C₂×D₄×C₄₇	—	2	1	no	—
351	C₂×D₄×C₄₇	—	2	1	no	—
352	C₂×D₄×C₄₇	—	2	1	no	—
353	C₂×D₄×C₄₇	—	2	1	no	—
354	C₂×D₄×C₄₇	—	2	1	no	—
355	C₂×D₄×C₄₇	—	2	1	no	—
356	C₂×D₄×C₄₇	C₂×D₄	1	1	yes	characteristic
357	C₂×D₄×C₄₇	C₂×D₄	1	1	yes	characteristic
358	C₂×D₄×C₄₇	C₂×D₄	1	1	yes	characteristic
359	C₂×D₄×C₄₇	C₂⁴	1	1	yes	characteristic
360	C₂×D₄×C₄₇	C₂⁴	1	1	yes	characteristic
361	C₂²×C₄×C₄₇	—	2	1	no	—
362	C₂²×C₄×C₄₇	—	2	1	no	—
363	C₂²×C₄×C₄₇	—	2	1	no	—
364	C₂²×C₄×C₄₇	—	2	1	no	—
365	C₂²×C₄×C₄₇	—	2	1	no	—
366	C₂²×C₄×C₄₇	—	2	1	no	—
367	C₂²×C₄×C₄₇	—	2	1	no	—
368	C₂²×C₄×C₄₇	—	2	1	no	—
369	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
370	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
371	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
372	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
373	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
374	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
375	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
376	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
377	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
378	C₂×C₂²⋊D₄₇	—	2	2	no	—
379	C₂×C₂²⋊D₄₇	—	2	2	no	—
380	C₂×C₂²⋊D₄₇	—	2	2	no	—
381	C₂²×Dic₄₇	—	2	2	no	—
382	#10625350	—	4	2	no	—
383	#10625350	—	4	2	no	—
384	#10625350	—	8	2	no	—
385	#10625350	—	8	2	no	—
386	C₂×D₁₈₈	—	2	1	no	—
387	C₂×D₁₈₈	—	2	1	no	—
388	C₂×D₁₈₈	C₂⁴	1	2	yes	—
389	C₂×C₄×D₄₇	—	2	2	no	—
390	C₂×C₄×D₄₇	—	2	2	no	—
391	C₂×C₄×D₄₇	—	2	2	no	—
392	C₂×Dic₉₄	—	2	1	no	—
393	C₂×Dic₉₄	—	2	1	no	—
394	C₂×Dic₉₄	—	2	2	no	—
395	C₂×Dic₉₄	—	8	2	no	—
396	C₂×Dic₉₄	C₂⁴	1	2	yes	—
397	C₄⋊C₄×C₄₇	—	2	1	no	—
398	C₄⋊C₄×C₄₇	—	2	1	no	—
399	C₄⋊C₄×C₄₇	—	2	1	no	—
400	C₄⋊C₄×C₄₇	—	2	1	no	—
401	C₄⋊C₄×C₄₇	—	2	1	no	—
402	C₄⋊C₄×C₄₇	—	2	1	no	—
403	C₄⋊C₄×C₄₇	—	2	1	no	—
404	C₄⋊C₄×C₄₇	—	2	1	no	—
405	C₄⋊C₄×C₄₇	—	2	1	no	—
406	C₄⋊C₄×C₄₇	—	2	1	no	—
407	C₄⋊C₄×C₄₇	—	2	1	no	—
408	C₄⋊C₄×C₄₇	—	2	1	no	—
409	C₄⋊C₄×C₄₇	—	2	1	no	—
410	C₄⋊C₄×C₄₇	—	2	1	no	—
411	C₄⋊C₄×C₄₇	—	2	1	no	—
412	C₄⋊C₄×C₄₇	—	2	1	no	—
413	C₄⋊C₄×C₄₇	—	2	1	no	—
414	C₄⋊C₄×C₄₇	—	2	1	no	—
415	C₄⋊C₄×C₄₇	—	2	1	no	—
416	C₄⋊C₄×C₄₇	—	2	1	no	—
417	C₄⋊C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
418	C₄⋊C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
419	C₄⋊C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
420	C₄⋊C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
421	C₄⋊C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
422	C₄⋊C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
423	C₄⋊C₄×C₄₇	C₂⁴	1	1	yes	characteristic
424	C₄⋊C₄×C₄₇	C₂⁴	1	1	yes	characteristic
425	C₄⋊C₄×C₄₇	C₂⁴	1	1	yes	characteristic
426	C₄⋊C₄×C₄₇	C₂⁴	1	1	yes	characteristic
427	C₂²⋊C₄×C₄₇	—	2	1	no	—
428	C₂²⋊C₄×C₄₇	—	2	1	no	—
429	C₂²⋊C₄×C₄₇	—	2	1	no	—
430	C₂²⋊C₄×C₄₇	—	2	1	no	—
431	C₂²⋊C₄×C₄₇	—	2	1	no	—
432	C₂²⋊C₄×C₄₇	—	2	1	no	—
433	C₂²⋊C₄×C₄₇	—	2	1	no	—
434	C₂²⋊C₄×C₄₇	—	2	1	no	—
435	C₂²⋊C₄×C₄₇	—	2	1	no	—
436	C₂²⋊C₄×C₄₇	—	2	1	no	—
437	C₂²⋊C₄×C₄₇	—	2	1	no	—
438	C₂²⋊C₄×C₄₇	—	2	1	no	—
439	C₂²⋊C₄×C₄₇	—	2	1	no	—
440	C₂²⋊C₄×C₄₇	—	2	1	no	—
441	C₂²⋊C₄×C₄₇	—	2	1	no	—
442	C₂²⋊C₄×C₄₇	—	2	1	no	—
443	C₂²⋊C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
444	C₂²⋊C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
445	C₂²⋊C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
446	C₂²⋊C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
447	C₂²⋊C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
448	C₂²⋊C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
449	C₄²×C₄₇	—	2	1	no	—
450	C₄²×C₄₇	—	2	1	no	—
451	C₄²×C₄₇	—	2	1	no	—
452	C₄²×C₄₇	—	2	1	no	—
453	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
454	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
455	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
456	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
457	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
458	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
459	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
460	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
461	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
462	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
463	C₂²⋊Dic₄₇	—	2	2	no	—
464	C₂²⋊Dic₄₇	—	2	2	no	—
465	#10625337	—	4	2	no	—
466	#10625337	—	4	2	no	—
467	#10625336	—	4	2	no	—
468	#10625336	—	4	2	no	—
469	#10625335	—	4	2	no	—
470	#10625335	—	4	2	no	—
471	#10625334	—	4	2	no	—
472	#10625334	—	4	2	no	—
473	(C₂×D₄₇)⋊C₄	—	2	2	no	—
474	(C₂×D₄₇)⋊C₄	—	2	2	no	—
475	(C₂×D₄₇)⋊C₄	—	2	2	no	—
476	(C₂×D₄₇)⋊C₄	—	2	2	no	—
477	(C₂×D₄₇)⋊C₄	—	2	2	no	—
478	(C₂×D₄₇)⋊C₄	—	2	2	no	—
479	C₄⋊Dic₄₇	—	2	2	no	—
480	C₄⋊Dic₄₇	—	2	1	no	—
481	C₄⋊Dic₄₇	—	2	1	no	—
482	C₄⋊Dic₄₇	—	2	2	no	—
483	C₄⋊Dic₄₇	—	2	1	no	—
484	C₄⋊Dic₄₇	—	2	1	no	—
485	C₄⋊Dic₄₇	C₂⁴	1	2	yes	—
486	C₄⋊Dic₄₇	C₂⁴	1	2	yes	—
487	Dic₄₇⋊C₄	—	2	2	no	—
488	Dic₄₇⋊C₄	—	2	2	no	—
489	Dic₄₇⋊C₄	—	2	2	no	—
490	Dic₄₇⋊C₄	—	2	2	no	—
491	C₄×Dic₄₇	—	2	2	no	—
492	C₄×Dic₄₇	—	2	2	no	—
493	#10625329	—	4	2	no	—
494	C₂×C₄₇⋊C₈	—	4	2	no	—
495	C₂×C₄₇⋊C₈	C₂⁴	1	2	yes	—
496	C₂×C₄₇⋊C₈	C₂⁴	1	2	yes	—
497	C₂×C₄₇⋊C₈	C₂⁴	1	2	yes	—
498	C₂×C₄₇⋊C₈	C₂⁴	1	2	yes	—
499	C₂³×C₄₇	—	2	1	no	—
500	C₂³×C₄₇	—	2	1	no	—
501	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
502	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
503	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
504	C₂²×D₄₇	—	2	2	no	—
505	Q₈×C₄₇	—	2	2	no	—
506	Q₈×C₄₇	—	2	2	no	—
507	Q₈×C₄₇	—	4	1	no	—
508	D₄×C₄₇	—	2	2	no	—
509	D₄×C₄₇	—	2	2	no	—
510	D₄×C₄₇	—	4	1	no	—
511	D₄×C₄₇	—	4	1	no	—
512	D₄×C₄₇	—	4	1	no	—
513	D₄×C₄₇	—	4	2	no	—
514	D₄×C₄₇	—	4	2	no	—
515	D₄×C₄₇	—	8	1	no	—
516	D₄×C₄₇	—	8	1	no	—
517	D₄×C₄₇	—	8	1	no	—
518	D₄×C₄₇	—	8	1	no	—
519	D₄×C₄₇	—	8	1	no	—
520	D₄×C₄₇	—	8	1	no	—
521	C₂×C₄×C₄₇	—	2	2	no	—
522	C₂×C₄×C₄₇	—	2	2	no	—
523	C₂×C₄×C₄₇	—	2	2	no	—
524	C₂×C₄×C₄₇	—	2	1	no	—
525	C₂×C₄×C₄₇	—	2	1	no	—
526	C₂×C₄×C₄₇	—	2	1	no	—
527	C₂×C₄×C₄₇	—	2	1	no	—
528	C₂×C₄×C₄₇	—	2	1	no	—
529	C₂×C₄×C₄₇	—	2	1	no	—
530	C₂×C₄×C₄₇	—	4	1	no	—
531	C₂×C₄×C₄₇	—	4	1	no	—
532	C₂×C₄×C₄₇	—	4	1	no	—
533	C₂×C₄×C₄₇	—	4	1	no	—
534	C₂×C₄×C₄₇	—	4	1	no	—
535	C₂×C₄×C₄₇	—	4	1	no	—
536	C₂×C₄×C₄₇	—	4	2	no	—
537	C₂×C₄×C₄₇	—	4	2	no	—
538	C₂×C₄×C₄₇	—	8	1	no	—
539	C₂×C₄×C₄₇	—	8	1	no	—
540	C₂×C₄×C₄₇	—	8	1	no	—
541	C₂×C₄×C₄₇	—	8	1	no	—
542	C₂×C₄×C₄₇	—	8	1	no	—
543	C₂×C₄×C₄₇	—	8	1	no	—
544	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
545	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
546	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
547	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
548	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
549	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
550	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
551	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
552	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
553	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
554	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
555	C₂×C₄×C₄₇	C₂⁵	1	1	yes	characteristic
556	C₂²⋊D₄₇	—	4	4	no	—
557	C₂²⋊D₄₇	—	8	2	no	—
558	C₂²⋊D₄₇	—	8	2	no	—
559	C₂×Dic₄₇	—	2	2	no	—
560	C₂×Dic₄₇	—	2	2	no	—
561	C₂×Dic₄₇	—	2	2	no	—
562	C₂×Dic₄₇	—	8	2	no	—
563	D₁₈₈	—	2	2	no	—
564	D₁₈₈	—	2	2	no	—
565	D₁₈₈	—	4	2	no	—
566	D₁₈₈	—	4	2	no	—
567	C₄×D₄₇	—	4	4	no	—
568	C₄×D₄₇	—	8	2	no	—
569	C₄×D₄₇	—	8	2	no	—
570	Dic₉₄	—	2	2	no	—
571	Dic₉₄	—	2	2	no	—
572	Dic₉₄	—	4	2	no	—
573	Dic₉₄	—	4	2	no	—
574	Dic₉₄	—	8	2	no	—
575	C₄₇⋊C₈	—	2	2	no	—
576	C₄₇⋊C₈	—	2	2	no	—
577	C₄₇⋊C₈	—	2	2	no	—
578	C₄₇⋊C₈	—	2	2	no	—
579	#61021	—	47	1	no	maximal, Sylow
580	C₂²×C₄₇	—	2	1	no	—
581	C₂²×C₄₇	—	2	1	no	—
582	C₂²×C₄₇	—	2	1	no	—
583	C₂²×C₄₇	—	2	1	no	—
584	C₂²×C₄₇	—	2	1	no	—
585	C₂²×C₄₇	—	2	1	no	—
586	C₂²×C₄₇	—	2	1	no	—
587	C₂²×C₄₇	—	2	1	no	—
588	C₂²×C₄₇	—	2	1	no	—
589	C₂²×C₄₇	—	4	1	no	—
590	C₂²×C₄₇	—	4	1	no	—
591	C₂²×C₄₇	—	4	1	no	—
592	C₂²×C₄₇	—	4	1	no	—
593	C₂²×C₄₇	—	4	1	no	—
594	C₂²×C₄₇	—	4	1	no	—
595	C₂²×C₄₇	C₂³×D₄	1	1	yes	characteristic
596	C₂×D₄₇	—	4	2	no	—
597	C₂×D₄₇	—	4	2	no	—
598	C₂×D₄₇	—	4	2	no	—
599	C₄×C₄₇	—	2	1	no	—
600	C₄×C₄₇	—	2	1	no	—
601	C₄×C₄₇	—	2	1	no	—
602	C₄×C₄₇	—	2	1	no	—
603	C₄×C₄₇	—	2	1	no	—
604	C₄×C₄₇	—	2	1	no	—
605	C₄×C₄₇	—	2	1	no	—
606	C₄×C₄₇	—	2	1	no	—
607	C₄×C₄₇	—	2	1	no	—
608	C₄×C₄₇	—	2	1	no	—
609	C₄×C₄₇	—	2	1	no	—
610	C₄×C₄₇	—	4	1	no	—
611	C₄×C₄₇	—	4	1	no	—
612	C₄×C₄₇	—	4	1	no	—
613	C₄×C₄₇	—	4	1	no	—
614	C₄×C₄₇	—	4	1	no	—
615	C₄×C₄₇	—	4	1	no	—
616	C₄×C₄₇	#585	1	2	yes	—
617	Dic₄₇	—	4	2	no	—
618	Dic₄₇	—	4	2	no	—
619	Dic₄₇	—	4	2	no	—
620	#3512	D₄₇	1	1	yes	characteristic, complemented
621	#3511	—	47	1	no	—
622	#3258	—	47	2	no	—
623	#3257	—	47	2	no	—
624	#3239	—	47	1	no	—
625	#3238	—	47	1	no	—
626	#3236	—	47	1	no	—
627	#3234	—	47	1	no	—
628	#3219	—	47	1	no	—
629	#3219	—	47	1	no	—
630	#3216	—	47	1	no	—
631	#3214	—	47	1	no	—
632	#3204	—	47	2	no	—
633	#3203	—	47	2	no	—
634	#3181	—	47	1	no	—
635	#3180	—	47	1	no	—
636	#3172	—	47	1	no	—
637	#3171	—	47	1	no	—
638	#3125	—	47	2	no	—
639	#3124	—	47	2	no	—
640	#3120	—	47	2	no	—
641	#3119	—	47	2	no	—
642	#2923	—	47	1	no	—
643	C₂×C₄₇	—	4	1	no	—
644	C₂×C₄₇	—	4	1	no	—
645	C₂×C₄₇	—	4	1	no	—
646	C₂×C₄₇	—	8	1	no	—
647	C₂×C₄₇	—	8	1	no	—
648	C₂×C₄₇	#3449	1	1	yes	characteristic
649	C₂×C₄₇	#3585	1	1	yes	characteristic
650	C₂×C₄₇	#3586	1	1	yes	characteristic
651	D₄₇	—	8	2	no	—
652	#556	—	94	1	no	—
653	#555	—	94	1	no	—
654	#554	—	94	1	no	—
655	#553	—	2	1	no	—
656	#553	—	2	1	no	—
657	#553	—	2	1	no	—
658	#553	—	2	1	no	—
659	#553	—	2	1	no	—
660	#553	—	2	1	no	—
661	#553	—	94	1	no	—
662	#553	—	94	1	no	—
663	#552	—	2	1	no	—
664	#552	—	2	1	no	—
665	#548	—	94	1	no	—
666	#548	—	94	1	no	—
667	#547	—	94	1	no	—
668	#542	—	47	2	no	—
669	#542	—	47	2	no	—
670	#541	C₂×D₄₇	1	1	yes	characteristic
671	#541	C₂×D₄₇	1	1	yes	characteristic
672	#540	C₂×D₄₇	1	1	yes	characteristic
673	#540	C₂×D₄₇	1	1	yes	characteristic
674	#537	—	47	2	no	—
675	#537	C₂×D₄₇	1	1	yes	characteristic
676	#537	C₂×D₄₇	1	1	yes	characteristic
677	#533	—	47	1	no	—
678	#533	—	47	1	no	—
679	#532	—	47	1	no	—
680	#532	—	47	1	no	—
681	#532	—	47	1	no	—
682	#532	C₂×D₄₇	1	1	yes	characteristic
683	C₂×C₄⋊Q₈	—	47	1	no	—
684	#529	C₂×D₄₇	1	1	yes	characteristic
685	#529	C₂×D₄₇	1	1	yes	characteristic
686	#529	C₂×D₄₇	1	1	yes	characteristic
687	#529	C₂×D₄₇	1	1	yes	characteristic
688	C₂×#125	C₂×D₄₇	1	1	yes	characteristic
689	#520	—	47	2	no	—
690	#520	C₂×D₄₇	1	1	yes	characteristic
691	#520	C₂×D₄₇	1	1	yes	characteristic
692	C₄×#41	C₂×D₄₇	1	1	yes	characteristic
693	#501	—	47	1	no	—
694	#501	—	47	1	no	—
695	#501	—	47	1	no	—
696	#501	—	47	1	no	—
697	#497	—	47	1	no	—
698	#497	—	47	1	no	—
699	#496	—	47	1	no	—
700	#496	—	47	1	no	—
701	#491	—	47	1	no	—
702	#491	—	47	1	no	—
703	#490	—	47	1	no	—
704	#490	—	47	1	no	—
705	#489	—	47	1	no	—
706	#489	—	47	1	no	—
707	#489	—	47	1	no	—
708	#489	—	47	1	no	—
709	#484	—	47	2	no	—
710	#484	—	47	2	no	—
711	#483	—	47	2	no	—
712	#483	—	47	2	no	—
713	#481	—	47	2	no	—
714	#481	—	47	2	no	—
715	#480	—	47	2	no	—
716	#480	—	47	2	no	—
717	#479	—	47	2	no	—
718	#479	—	47	2	no	—
719	#478	—	47	2	no	—
720	#478	—	47	2	no	—
721	#477	—	47	2	no	—
722	#476	—	47	2	no	—
723	#475	—	47	2	no	—
724	#474	—	47	2	no	—
725	#470	—	47	2	no	—
726	#469	—	47	2	no	—
727	#468	—	47	2	no	—
728	#468	—	47	2	no	—
729	#467	—	47	2	no	—
730	#466	—	47	2	no	—
731	#465	—	47	2	no	—
732	#465	—	47	2	no	—
733	#464	—	47	2	no	—
734	#464	—	47	2	no	—
735	#463	—	47	2	no	—
736	#463	—	47	2	no	—
737	#462	—	47	2	no	—
738	#461	—	47	2	no	—
739	#460	—	47	2	no	—
740	#459	—	47	2	no	—
741	#452	—	47	2	no	—
742	#452	—	47	2	no	—
743	#452	—	47	2	no	—
744	#452	—	47	2	no	—
745	#449	—	47	2	no	—
746	#449	—	47	2	no	—
747	#449	—	47	2	no	—
748	#449	—	47	2	no	—
749	#442	—	47	2	no	—
750	#441	—	47	2	no	—
751	#440	—	47	2	no	—
752	#440	—	47	2	no	—
753	C₄×Q₁₆	—	47	2	no	—
754	C₄×SD₁₆	—	47	2	no	—
755	C₄×SD₁₆	—	47	2	no	—
756	C₄×D₈	—	47	2	no	—
757	#433	—	47	2	no	—
758	#433	—	47	2	no	—
759	#432	—	47	1	no	—
760	#432	—	47	1	no	—
761	#432	—	47	1	no	—
762	#432	—	47	1	no	—
763	#424	—	47	2	no	—
764	#408	—	47	2	no	—
765	C₄×M₁₆	—	47	1	no	—
766	C₂×#97	—	47	1	no	—
767	C₄₇	#61021	1	1	yes	characteristic, complemented, Sylow
768	C₂×#41	—	47	2	no	—
769	C₂×#41	—	94	1	no	—
770	C₂×#41	—	94	1	no	—
771	C₂×#41	C₂²×D₄₇	1	1	yes	characteristic
772	C₂×#41	C₂²×D₄₇	1	1	yes	characteristic
773	C₂×#41	C₂²×D₄₇	1	1	yes	characteristic
774	C₂²×Q₈	—	94	1	no	—
775	C₂×Q₁₆	—	47	2	no	—
776	C₂×Q₁₆	—	47	2	no	—
777	C₂×SD₁₆	—	47	2	no	—
778	C₂×SD₁₆	—	47	2	no	—
779	C₂×SD₁₆	—	47	2	no	—
780	C₂×SD₁₆	—	47	2	no	—
781	C₂×D₈	—	47	2	no	—
782	C₂×D₈	—	47	2	no	—
783	C₂×M₁₆	—	47	2	no	—
784	C₂²×C₈	—	47	2	no	—
785	C₄⋊Q₈	—	47	1	no	—
786	C₄⋊Q₈	—	47	1	no	—
787	C₄⋊Q₈	—	47	2	no	—
788	C₄⋊Q₈	—	47	1	no	—
789	C₄⋊Q₈	—	94	1	no	—
790	C₄⋊Q₈	—	94	1	no	—
791	C₄⋊Q₈	C₂²×D₄₇	1	1	yes	characteristic
792	#127	—	47	1	no	—
793	#127	C₂²×D₄₇	1	1	yes	characteristic
794	#126	—	2	1	no	—
795	#126	—	2	1	no	—
796	#126	—	2	1	no	—
797	#126	—	2	1	no	—
798	#126	—	2	1	no	—
799	#126	—	2	1	no	—
800	#126	—	2	1	no	—
801	#126	—	2	1	no	—
802	#126	—	94	2	no	—
803	#126	—	94	2	no	—
804	#125	—	2	1	no	—
805	#125	—	2	1	no	—
806	#125	—	2	1	no	—
807	#125	—	2	1	no	—
808	#125	—	2	1	no	—
809	#125	—	2	1	no	—
810	#125	—	94	1	no	—
811	#125	—	94	1	no	—
812	#125	C₂²×D₄₇	1	1	yes	characteristic
813	#125	C₂²×D₄₇	1	1	yes	characteristic
814	#125	C₂²×D₄₇	1	1	yes	characteristic
815	#125	C₂²×D₄₇	1	1	yes	characteristic
816	#124	—	47	2	no	—
817	#124	—	94	2	no	—
818	#124	—	94	2	no	—
819	#124	—	94	1	no	—
820	#124	—	94	1	no	—
821	#124	C₂²×D₄₇	1	1	yes	characteristic
822	#124	C₂²×D₄₇	1	1	yes	characteristic
823	#123	—	2	1	no	—
824	#123	—	2	1	no	—
825	#123	—	2	1	no	—
826	#123	—	2	1	no	—
827	#123	—	2	1	no	—
828	#123	—	2	1	no	—
829	#123	—	2	1	no	—
830	#123	—	2	1	no	—
831	#123	—	94	2	no	—
832	#123	—	94	2	no	—
833	C₂²⋊Q₈	—	2	1	no	—
834	C₂²⋊Q₈	—	2	1	no	—
835	C₂²⋊Q₈	—	47	2	no	—
836	C₂²⋊Q₈	—	47	2	no	—
837	C₂²⋊Q₈	—	94	2	no	—
838	C₂²⋊Q₈	—	94	1	no	—
839	C₂²⋊Q₈	—	94	1	no	—
840	C₂²⋊Q₈	—	94	2	no	—
841	C₂²⋊Q₈	—	94	2	no	—
842	C₂²⋊Q₈	C₂²×D₄₇	1	1	yes	characteristic
843	C₂²⋊Q₈	C₂²×D₄₇	1	1	yes	characteristic
844	C₂²⋊Q₈	C₂²×D₄₇	1	1	yes	characteristic
845	C₂²⋊Q₈	C₂²×D₄₇	1	1	yes	characteristic
846	#121	—	2	1	no	—
847	#121	—	2	1	no	—
848	#121	—	2	1	no	—
849	#121	—	2	1	no	—
850	#121	—	2	1	no	—
851	#121	—	2	1	no	—
852	#121	—	2	1	no	—
853	#121	—	2	1	no	—
854	#121	—	2	1	no	—
855	#121	—	2	1	no	—
856	#121	—	2	1	no	—
857	#121	—	2	1	no	—
858	#121	—	47	2	no	—
859	#121	—	47	2	no	—
860	#121	—	94	2	no	—
861	#121	—	94	2	no	—
862	#121	—	94	2	no	—
863	#121	—	94	1	no	—
864	#121	—	94	1	no	—
865	#121	—	94	1	no	—
866	#121	—	94	1	no	—
867	#121	C₂²×D₄₇	1	1	yes	characteristic
868	#121	C₂²×D₄₇	1	1	yes	characteristic
869	#121	C₂²×D₄₇	1	1	yes	characteristic
870	#121	C₂²×D₄₇	1	1	yes	characteristic
871	C₄×Q₈	—	47	2	no	—
872	C₄×Q₈	—	47	2	no	—
873	C₄×Q₈	—	94	1	no	—
874	C₄×Q₈	—	94	1	no	—
875	C₄×Q₈	C₂²⋊D₄₇	1	1	yes	characteristic
876	C₄×Q₈	C₂²⋊D₄₇	1	1	yes	characteristic
877	C₄×Q₈	C₂²×D₄₇	1	1	yes	characteristic
878	C₄×Q₈	C₂²×D₄₇	1	1	yes	characteristic
879	C₄×Q₈	C₂²×D₄₇	1	1	yes	characteristic
880	C₄×Q₈	C₂²×D₄₇	1	1	yes	characteristic
881	C₄×D₄	—	2	1	no	—
882	C₄×D₄	—	2	1	no	—
883	C₄×D₄	—	2	1	no	—
884	C₄×D₄	—	2	1	no	—
885	C₄×D₄	—	2	1	no	—
886	C₄×D₄	—	2	1	no	—
887	C₄×D₄	—	2	1	no	—
888	C₄×D₄	—	2	1	no	—
889	C₄×D₄	—	2	1	no	—
890	C₄×D₄	—	2	1	no	—
891	C₄×D₄	—	47	2	no	—
892	C₄×D₄	—	47	2	no	—
893	C₄×D₄	—	94	2	no	—
894	C₄×D₄	—	94	2	no	—
895	C₄×D₄	—	94	1	no	—
896	C₄×D₄	—	94	1	no	—
897	C₄×D₄	—	94	1	no	—
898	C₄×D₄	—	94	1	no	—
899	C₄×D₄	C₂²⋊D₄₇	1	1	yes	characteristic
900	C₄×D₄	C₂²⋊D₄₇	1	1	yes	characteristic
901	C₄×D₄	C₂²⋊D₄₇	1	1	yes	characteristic
902	C₄×D₄	C₂²⋊D₄₇	1	1	yes	characteristic
903	C₄×D₄	C₂²⋊D₄₇	1	1	yes	characteristic
904	C₄×D₄	C₂²⋊D₄₇	1	1	yes	characteristic
905	C₄×D₄	C₂²×D₄₇	1	1	yes	characteristic
906	C₄×D₄	C₂²×D₄₇	1	1	yes	characteristic
907	C₄×D₄	C₂²×D₄₇	1	1	yes	characteristic
908	C₄×D₄	C₂²×D₄₇	1	1	yes	characteristic
909	#117	—	2	1	no	—
910	#117	—	2	1	no	—
911	#117	—	2	1	no	—
912	#117	—	2	1	no	—
913	#117	—	2	1	no	—
914	#117	—	2	1	no	—
915	#117	—	94	1	no	—
916	#117	—	94	1	no	—
917	#117	—	94	2	no	—
918	#117	C₂²×D₄₇	1	1	yes	characteristic
919	#117	C₂²×D₄₇	1	1	yes	characteristic
920	#117	C₂²×D₄₇	1	1	yes	characteristic
921	C₂×C₄⋊C₄	—	2	1	no	—
922	C₂×C₄⋊C₄	—	2	1	no	—
923	C₂×C₄⋊C₄	—	2	1	no	—
924	C₂×C₄⋊C₄	—	2	1	no	—
925	C₂×C₄⋊C₄	—	47	2	no	—
926	C₂×C₄⋊C₄	—	94	1	no	—
927	C₂×C₄⋊C₄	—	94	2	no	—
928	C₂×C₄⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
929	C₂×C₄⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
930	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
931	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
932	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
933	#107	—	47	2	no	—
934	#107	—	47	2	no	—
935	#107	—	47	2	no	—
936	#107	—	47	2	no	—
937	#106	—	47	2	no	—
938	#106	—	47	2	no	—
939	#106	—	47	2	no	—
940	#106	—	47	2	no	—
941	C₄⋊C₈	—	47	2	no	—
942	C₄⋊C₈	—	47	2	no	—
943	C₄⋊C₈	—	47	2	no	—
944	C₄⋊C₈	—	47	2	no	—
945	#103	—	47	2	no	—
946	#103	—	47	2	no	—
947	#103	—	47	2	no	—
948	#103	—	47	2	no	—
949	#103	—	47	2	no	—
950	#103	—	47	2	no	—
951	#103	—	47	2	no	—
952	#103	—	47	2	no	—
953	#102	—	47	2	no	—
954	#102	—	47	2	no	—
955	#102	—	47	2	no	—
956	#102	—	47	2	no	—
957	#102	—	47	2	no	—
958	#102	—	47	2	no	—
959	#102	—	47	2	no	—
960	#102	—	47	2	no	—
961	C₂²⋊C₈	—	47	2	no	—
962	C₂²⋊C₈	—	47	2	no	—
963	C₂²⋊C₈	—	47	2	no	—
964	C₂²⋊C₈	—	47	2	no	—
965	#97	—	47	1	no	—
966	#97	—	47	1	no	—
967	#97	—	47	2	no	—
968	#97	—	47	1	no	—
969	#97	—	47	1	no	—
970	C₄×C₈	—	47	2	no	—
971	#41	—	4	2	no	—
972	#41	—	4	2	no	—
973	#41	—	4	2	no	—
974	#41	—	376	2	no	—
975	#41	—	376	2	no	—
976	#41	—	188	2	no	—
977	#41	—	188	2	no	—
978	C₂×Q₈	—	47	2	no	—
979	C₂×Q₈	—	94	2	no	—
980	C₂×Q₈	—	94	1	no	—
981	C₂×Q₈	—	94	1	no	—
982	C₂×Q₈	—	376	2	no	—
983	C₂×Q₈	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
984	C₂×Q₈	C₂³×D₄₇	1	1	yes	characteristic
985	C₂×Q₈	C₂³×D₄₇	1	1	yes	characteristic
986	C₂×D₄	—	2	1	no	—
987	C₂×D₄	—	2	1	no	—
988	C₂×D₄	—	2	1	no	—
989	C₂×D₄	—	2	1	no	—
990	C₂×D₄	—	2	1	no	—
991	C₂×D₄	—	2	1	no	—
992	C₂×D₄	—	2	1	no	—
993	C₂×D₄	—	2	1	no	—
994	C₂×D₄	—	47	2	no	—
995	C₂×D₄	—	94	2	no	—
996	C₂×D₄	—	94	2	no	—
997	C₂×D₄	—	94	2	no	—
998	C₂×D₄	—	94	1	no	—
999	C₂×D₄	—	94	1	no	—
1000	C₂×D₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
1001	C₂×D₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
1002	C₂×D₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
1003	C₂×D₄	C₂³×D₄₇	1	1	yes	characteristic
1004	C₂×D₄	C₂³×D₄₇	1	1	yes	characteristic
1005	C₂²×C₄	—	2	1	no	—
1006	C₂²×C₄	—	2	1	no	—
1007	C₂²×C₄	—	2	1	no	—
1008	C₂²×C₄	—	2	1	no	—
1009	C₂²×C₄	—	2	1	no	—
1010	C₂²×C₄	—	2	1	no	—
1011	C₂²×C₄	—	2	1	no	—
1012	C₂²×C₄	—	2	1	no	—
1013	C₂²×C₄	—	94	2	no	—
1014	C₂²×C₄	—	94	2	no	—
1015	C₂²×C₄	—	94	2	no	—
1016	C₂²×C₄	—	94	2	no	—
1017	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
1018	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
1019	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
1020	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
1021	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
1022	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
1023	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
1024	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
1025	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
1026	Q₁₆	—	188	2	no	—
1027	Q₁₆	—	188	2	no	—
1028	SD₁₆	—	188	2	no	—
1029	SD₁₆	—	188	2	no	—
1030	SD₁₆	—	188	2	no	—
1031	SD₁₆	—	188	2	no	—
1032	D₈	—	188	2	no	—
1033	D₈	—	188	2	no	—
1034	M₁₆	—	188	2	no	—
1035	C₂×C₈	—	47	2	no	—
1036	C₂×C₈	—	47	2	no	—
1037	C₂×C₈	—	47	2	no	—
1038	C₂×C₈	—	47	2	no	—
1039	C₂×C₈	—	188	2	no	—
1040	C₄⋊C₄	—	2	1	no	—
1041	C₄⋊C₄	—	2	1	no	—
1042	C₄⋊C₄	—	2	1	no	—
1043	C₄⋊C₄	—	2	1	no	—
1044	C₄⋊C₄	—	2	1	no	—
1045	C₄⋊C₄	—	2	1	no	—
1046	C₄⋊C₄	—	2	1	no	—
1047	C₄⋊C₄	—	2	1	no	—
1048	C₄⋊C₄	—	2	1	no	—
1049	C₄⋊C₄	—	2	1	no	—
1050	C₄⋊C₄	—	2	1	no	—
1051	C₄⋊C₄	—	2	1	no	—
1052	C₄⋊C₄	—	2	1	no	—
1053	C₄⋊C₄	—	2	1	no	—
1054	C₄⋊C₄	—	2	1	no	—
1055	C₄⋊C₄	—	2	1	no	—
1056	C₄⋊C₄	—	2	1	no	—
1057	C₄⋊C₄	—	2	1	no	—
1058	C₄⋊C₄	—	2	1	no	—
1059	C₄⋊C₄	—	2	1	no	—
1060	C₄⋊C₄	—	47	2	no	—
1061	C₄⋊C₄	—	47	2	no	—
1062	C₄⋊C₄	—	94	2	no	—
1063	C₄⋊C₄	—	94	2	no	—
1064	C₄⋊C₄	—	94	2	no	—
1065	C₄⋊C₄	—	94	2	no	—
1066	C₄⋊C₄	—	94	2	no	—
1067	C₄⋊C₄	—	94	1	no	—
1068	C₄⋊C₄	—	94	1	no	—
1069	C₄⋊C₄	—	94	2	no	—
1070	C₄⋊C₄	—	94	1	no	—
1071	C₄⋊C₄	—	94	1	no	—
1072	C₄⋊C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
1073	C₄⋊C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
1074	C₄⋊C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
1075	C₄⋊C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
1076	C₄⋊C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
1077	C₄⋊C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
1078	C₄⋊C₄	C₂³×D₄₇	1	1	yes	characteristic
1079	C₄⋊C₄	C₂³×D₄₇	1	1	yes	characteristic
1080	C₄⋊C₄	C₂³×D₄₇	1	1	yes	characteristic
1081	C₄⋊C₄	C₂³×D₄₇	1	1	yes	characteristic
1082	C₂²⋊C₄	—	2	1	no	—
1083	C₂²⋊C₄	—	2	1	no	—
1084	C₂²⋊C₄	—	2	1	no	—
1085	C₂²⋊C₄	—	2	1	no	—
1086	C₂²⋊C₄	—	2	1	no	—
1087	C₂²⋊C₄	—	2	1	no	—
1088	C₂²⋊C₄	—	2	1	no	—
1089	C₂²⋊C₄	—	2	1	no	—
1090	C₂²⋊C₄	—	2	1	no	—
1091	C₂²⋊C₄	—	2	1	no	—
1092	C₂²⋊C₄	—	2	1	no	—
1093	C₂²⋊C₄	—	2	1	no	—
1094	C₂²⋊C₄	—	2	1	no	—
1095	C₂²⋊C₄	—	2	1	no	—
1096	C₂²⋊C₄	—	2	1	no	—
1097	C₂²⋊C₄	—	2	1	no	—
1098	C₂²⋊C₄	—	94	2	no	—
1099	C₂²⋊C₄	—	94	2	no	—
1100	C₂²⋊C₄	—	94	2	no	—
1101	C₂²⋊C₄	—	94	2	no	—
1102	C₂²⋊C₄	—	94	2	no	—
1103	C₂²⋊C₄	—	94	2	no	—
1104	C₂²⋊C₄	—	94	2	no	—
1105	C₂²⋊C₄	—	94	2	no	—
1106	C₂²⋊C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
1107	C₂²⋊C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
1108	C₂²⋊C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
1109	C₂²⋊C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
1110	C₂²⋊C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
1111	C₂²⋊C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
1112	C₄²	—	2	1	no	—
1113	C₄²	—	2	1	no	—
1114	C₄²	—	2	1	no	—
1115	C₄²	—	2	1	no	—
1116	C₄²	—	94	2	no	—
1117	C₄²	—	94	2	no	—
1118	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
1119	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
1120	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
1121	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
1122	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
1123	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
1124	C₄²	C₂³×D₄₇	1	1	yes	characteristic
1125	C₄²	C₂³×D₄₇	1	1	yes	characteristic
1126	C₄²	C₂³×D₄₇	1	1	yes	characteristic
1127	C₄²	C₂³×D₄₇	1	1	yes	characteristic
1128	C₂³	—	2	1	no	—
1129	C₂³	—	2	1	no	—
1130	C₂³	—	94	2	no	—
1131	C₂³	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
1132	C₂³	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
1133	C₂³	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
1134	Q₈	—	2	2	no	—
1135	Q₈	—	2	2	no	—
1136	Q₈	—	4	1	no	—
1137	Q₈	—	94	2	no	—
1138	Q₈	—	94	2	no	—
1139	Q₈	—	376	2	no	—
1140	Q₈	—	188	2	no	—
1141	Q₈	—	188	2	no	—
1142	D₄	—	2	2	no	—
1143	D₄	—	2	2	no	—
1144	D₄	—	4	1	no	—
1145	D₄	—	4	1	no	—
1146	D₄	—	4	1	no	—
1147	D₄	—	4	2	no	—
1148	D₄	—	4	2	no	—
1149	D₄	—	8	1	no	—
1150	D₄	—	8	1	no	—
1151	D₄	—	8	1	no	—
1152	D₄	—	8	1	no	—
1153	D₄	—	8	1	no	—
1154	D₄	—	8	1	no	—
1155	D₄	—	94	2	no	—
1156	D₄	—	94	2	no	—
1157	D₄	—	376	2	no	—
1158	D₄	—	376	2	no	—
1159	D₄	—	188	2	no	—
1160	D₄	—	188	2	no	—
1161	D₄	—	188	4	no	—
1162	C₂×C₄	—	2	2	no	—
1163	C₂×C₄	—	2	2	no	—
1164	C₂×C₄	—	2	2	no	—
1165	C₂×C₄	—	2	1	no	—
1166	C₂×C₄	—	2	1	no	—
1167	C₂×C₄	—	2	1	no	—
1168	C₂×C₄	—	2	1	no	—
1169	C₂×C₄	—	2	1	no	—
1170	C₂×C₄	—	2	1	no	—
1171	C₂×C₄	—	4	1	no	—
1172	C₂×C₄	—	4	1	no	—
1173	C₂×C₄	—	4	1	no	—
1174	C₂×C₄	—	4	1	no	—
1175	C₂×C₄	—	4	1	no	—
1176	C₂×C₄	—	4	1	no	—
1177	C₂×C₄	—	4	2	no	—
1178	C₂×C₄	—	4	2	no	—
1179	C₂×C₄	—	8	1	no	—
1180	C₂×C₄	—	8	1	no	—
1181	C₂×C₄	—	8	1	no	—
1182	C₂×C₄	—	8	1	no	—
1183	C₂×C₄	—	8	1	no	—
1184	C₂×C₄	—	8	1	no	—
1185	C₂×C₄	—	94	2	no	—
1186	C₂×C₄	—	94	2	no	—
1187	C₂×C₄	—	94	2	no	—
1188	C₂×C₄	—	376	2	no	—
1189	C₂×C₄	—	376	2	no	—
1190	C₂×C₄	—	376	2	no	—
1191	C₂×C₄	—	188	4	no	—
1192	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
1193	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
1194	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
1195	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
1196	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
1197	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
1198	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
1199	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
1200	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
1201	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
1202	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
1203	C₂×C₄	C₂⁴×D₄₇	1	1	yes	characteristic
1204	C₈	—	94	2	no	—
1205	C₈	—	94	2	no	—
1206	C₈	—	94	2	no	—
1207	C₈	—	94	2	no	—
1208	C₂²	—	2	1	no	—
1209	C₂²	—	2	1	no	—
1210	C₂²	—	2	1	no	—
1211	C₂²	—	2	1	no	—
1212	C₂²	—	2	1	no	—
1213	C₂²	—	2	1	no	—
1214	C₂²	—	2	1	no	—
1215	C₂²	—	2	1	no	—
1216	C₂²	—	2	1	no	—
1217	C₂²	—	4	1	no	—
1218	C₂²	—	4	1	no	—
1219	C₂²	—	4	1	no	—
1220	C₂²	—	4	1	no	—
1221	C₂²	—	4	1	no	—
1222	C₂²	—	4	1	no	—
1223	C₂²	—	188	2	no	—
1224	C₂²	—	188	2	no	—
1225	C₂²	—	188	2	no	—
1226	C₂²	C₂³×C₂²⋊D₄₇	1	1	yes	characteristic
1227	C₄	—	2	1	no	—
1228	C₄	—	2	1	no	—
1229	C₄	—	2	1	no	—
1230	C₄	—	2	1	no	—
1231	C₄	—	2	1	no	—
1232	C₄	—	2	1	no	—
1233	C₄	—	2	1	no	—
1234	C₄	—	2	1	no	—
1235	C₄	—	2	1	no	—
1236	C₄	—	2	1	no	—
1237	C₄	—	2	1	no	—
1238	C₄	—	4	1	no	—
1239	C₄	—	4	1	no	—
1240	C₄	—	4	1	no	—
1241	C₄	—	4	1	no	—
1242	C₄	—	4	1	no	—
1243	C₄	—	4	1	no	—
1244	C₄	—	188	2	no	—
1245	C₄	—	188	2	no	—
1246	C₄	—	188	2	no	—
1247	C₄	#15689959	1	2	yes	—
1248	C₂	—	4	1	no	—
1249	C₂	—	4	1	no	—
1250	C₂	—	4	1	no	—
1251	C₂	—	8	1	no	—
1252	C₂	—	8	1	no	—
1253	C₂	—	376	2	no	—
1254	C₂	#20256717	1	1	yes	characteristic
1255	C₂	#20258167	1	1	yes	characteristic
1256	C₂	#20258174	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×#3512	C₂
socle	C₂²×C₄₇	C₂³×D₄
hypercenter	#3512	D₄₇
hypocenter	C₄₇	#61021
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₄×#41 ◁ #3512

Complements

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

N	H ≅ G/N	type
1. #20257299	C₂	semidirect
2. #20254808	C₂	semidirect
3. #20254793	C₂	semidirect
4. #20254615	C₂	semidirect
5. #20254606	C₂	semidirect
6. #20254594	C₂	semidirect
7. #20254578	C₂	semidirect
8. #20254421	C₂	semidirect
9. #20254421	C₂	semidirect
10. #20254399	C₂	semidirect
11. #20254383	C₂	semidirect
12. #20254294	C₂	semidirect
13. #20254285	C₂	semidirect
14. #20254098	C₂	semidirect
15. #20254087	C₂	semidirect
16. #20253995	C₂	semidirect
17. #20253984	C₂	semidirect
18. #20253665	C₂	semidirect
19. #20253650	C₂	semidirect
20. #20253596	C₂	semidirect
21. #20253581	C₂	semidirect
22. #20252039	C₂	semidirect
23. C₄₇×#3512	C₂	semidirect
620. #3512	D₄₇	semidirect
767. C₄₇	#61021	semidirect

Maximal subgroups

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

subgroup	index
#20257299	2
#20254808	2
#20254793	2
#20254615	2
#20254606	2
#20254594	2
#20254578	2
#20254421	2
#20254399	2
#20254383	2
#20254294	2
#20254285	2
#20254098	2
#20254087	2
#20253995	2
#20253984	2
#20253665	2
#20253650	2
#20253596	2
#20253581	2
#20252039	2
C₄₇×#3512	2
#61021	47