Subgroups — #27107026

Order 12032.

1606 conjugacy classes of subgroups.

The subgroup lattice has 1052 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20257876	C₂	1	1	yes	maximal, characteristic
2	#20256351	C₂	1	2	yes	maximal, complemented
3	#20256320	C₂	1	1	yes	maximal, characteristic, complemented
4	#20256294	C₂	1	1	yes	maximal, characteristic, complemented
5	#20256275	C₂	1	2	yes	maximal, complemented
6	Q₈×#10625337	C₂	1	1	yes	maximal, characteristic, complemented
7	#20256259	C₂	1	1	yes	maximal, characteristic, complemented
8	#20256230	C₂	1	2	yes	maximal, complemented
9	#20256191	C₂	1	1	yes	maximal, characteristic, complemented
10	#20256128	C₂	1	1	yes	maximal, characteristic, complemented
11	#20256073	C₂	1	2	yes	maximal, complemented
12	#20256073	C₂	1	1	yes	maximal, characteristic, complemented
13	#20256066	C₂	1	1	yes	maximal, characteristic, complemented
14	#20254671	C₂	1	2	yes	maximal
15	#20254656	C₂	1	2	yes	maximal, complemented
16	#20254567	C₂	1	1	yes	maximal, characteristic
17	#20254547	C₂	1	1	yes	maximal, characteristic, complemented
18	#20253688	C₂	1	2	yes	maximal, complemented
19	#20253617	C₂	1	2	yes	maximal
20	#20253468	C₂	1	1	yes	maximal, characteristic
21	#20253427	C₂	1	1	yes	maximal, characteristic, complemented
22	#20252490	C₂	1	1	yes	maximal, characteristic, complemented
23	C₄₇×#3502	C₂	1	1	yes	maximal, characteristic, complemented
24	#15689874	—	2	2	no	—
25	Q₈×Dic₉₄	C₂²	1	1	yes	characteristic
26	#15689852	C₂²	1	1	yes	characteristic
27	#15689851	C₂²	1	2	yes	—
28	#15689846	C₂²	1	1	yes	characteristic
29	#15689846	C₂²	1	2	yes	—
30	#15689844	—	2	1	no	—
31	#15689833	C₂²	1	1	yes	characteristic
32	#15689807	—	2	1	no	—
33	#15689750	—	2	1	no	—
34	#15689744	C₂²	1	2	yes	—
35	#15689735	C₂²	1	2	yes	—
36	#15689734	—	2	1	no	—
37	#15689732	—	2	2	no	—
38	#15689680	C₂²	1	1	yes	characteristic
39	#15689657	C₂²	1	1	yes	characteristic
40	#15689533	C₂²	1	2	yes	—
41	#15689529	C₂²	1	2	yes	—
42	#15689526	C₂²	1	2	yes	—
43	#15689526	C₂²	1	1	yes	characteristic
44	#15689522	C₂²	1	2	yes	—
45	#15689522	C₂²	1	2	yes	—
46	#15689519	C₂²	1	1	yes	characteristic
47	#15689493	C₂²	1	2	yes	—
48	#15689485	C₂²	1	2	yes	—
49	#15689480	C₂²	1	2	yes	—
50	#15689480	C₂²	1	2	yes	—
51	#15689475	C₂²	1	2	yes	—
52	#15689475	C₂²	1	1	yes	characteristic
53	#15689475	C₂²	1	1	yes	characteristic
54	#15689464	C₂²	1	2	yes	—
55	#15689464	C₂²	1	2	yes	—
56	#15689464	C₂²	1	2	yes	—
57	#15689458	C₂²	1	2	yes	—
58	#15689453	C₂²	1	1	yes	characteristic
59	#15689447	C₂²	1	2	yes	—
60	#15689436	C₂²	1	1	yes	characteristic
61	#15689430	C₂²	1	2	yes	—
62	#15689430	C₂²	1	1	yes	characteristic
63	#15689430	C₂²	1	2	yes	—
64	#15689430	C₂²	1	1	yes	characteristic
65	#15689427	C₂²	1	2	yes	—
66	#15689427	C₂²	1	2	yes	—
67	#15689427	C₂²	1	2	yes	—
68	#15689427	C₂²	1	2	yes	—
69	#15689427	C₂²	1	2	yes	—
70	#15689420	C₂²	1	2	yes	—
71	#15689418	C₂²	1	1	yes	characteristic
72	#15689418	C₂²	1	2	yes	—
73	#15689418	C₂²	1	1	yes	characteristic
74	#15689415	C₂²	1	1	yes	characteristic
75	#15689415	C₂²	1	2	yes	—
76	#15689415	C₂²	1	2	yes	—
77	#15689410	C₂²	1	1	yes	characteristic
78	#15689408	C₂²	1	2	yes	—
79	#15689405	C₂²	1	2	yes	—
80	#15689405	C₂²	1	1	yes	characteristic
81	#15689400	C₂²	1	1	yes	characteristic
82	#15689400	C₂²	1	2	yes	—
83	#15689345	C₂²	1	1	yes	characteristic
84	#15689345	C₂²	1	1	yes	characteristic
85	#15689345	C₂²	1	2	yes	—
86	#15689345	C₂²	1	2	yes	—
87	#15689333	C₂²	1	1	yes	characteristic
88	#15689333	C₂²	1	2	yes	—
89	#15689333	C₂²	1	2	yes	—
90	#15689333	C₂²	1	1	yes	characteristic
91	#15689279	C₂²	1	1	yes	characteristic
92	#15689279	C₂²	1	2	yes	—
93	#15689262	C₂²	1	1	yes	characteristic
94	#15689254	C₂²	1	1	yes	characteristic
95	#15689254	C₂²	1	1	yes	characteristic
96	#15689254	C₂²	1	2	yes	—
97	Q₈×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
98	Q₈×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
99	Q₈×C₄₇⋊C₈	C₂²	1	2	yes	—
100	#15689228	C₂²	1	2	yes	—
101	#15689228	C₂²	1	2	yes	—
102	#15689228	C₂²	1	2	yes	—
103	#15689221	C₂²	1	2	yes	—
104	C₄×#10625337	C₂²	1	1	yes	characteristic
105	C₄×#10625337	C₂²	1	2	yes	—
106	C₄×#10625337	C₂²	1	2	yes	—
107	C₄×#10625337	C₂²	1	2	yes	—
108	C₄×#10625337	C₂²	1	2	yes	—
109	C₄×#10625337	C₂²	1	1	yes	characteristic
110	C₄×#10625337	C₂²	1	2	yes	—
111	C₄×#10625336	C₂²	1	1	yes	characteristic
112	C₄×#10625336	C₂²	1	2	yes	—
113	C₄×#10625336	C₂²	1	1	yes	characteristic
114	#15689184	C₂²	1	2	yes	—
115	#15689184	C₂²	1	2	yes	—
116	#15689176	C₂²	1	1	yes	characteristic
117	#15689176	C₂²	1	1	yes	characteristic
118	Q₈²×C₄₇	—	2	1	no	—
119	Q₈²×C₄₇	C₂²	1	1	yes	characteristic
120	Q₈²×C₄₇	C₂²	1	1	yes	characteristic
121	C₄₇×#557	—	2	1	no	—
122	C₄₇×#557	—	2	2	no	—
123	C₄₇×#557	C₂²	1	1	yes	characteristic
124	C₄₇×#557	C₂²	1	2	yes	—
125	C₄₇×#557	C₂²	1	1	yes	characteristic
126	C₄₇×#557	C₂²	1	2	yes	—
127	C₄₇×#544	—	2	2	no	—
128	C₄₇×#544	C₂²	1	2	yes	—
129	C₄₇×#533	—	2	1	no	—
130	C₄₇×#533	—	2	1	no	—
131	C₄₇×#533	C₂²	1	1	yes	characteristic
132	C₄₇×#533	C₂²	1	1	yes	characteristic
133	C₄₇×#519	C₂²	1	2	yes	—
134	C₂×C₄×Q₈×C₄₇	C₂²	1	1	yes	characteristic
135	C₂×#10625337	C₂³	1	1	yes	characteristic
136	C₂×#10625337	C₂³	1	2	yes	—
137	C₂×#10625337	C₂³	1	1	yes	characteristic
138	C₂×#10625337	C₂³	1	2	yes	—
139	C₂×#10625336	C₂³	1	1	yes	characteristic
140	C₂×#10625336	C₂³	1	1	yes	characteristic
141	#13094024	C₂³	1	1	yes	characteristic
142	#13094024	C₂³	1	2	yes	—
143	#13094024	C₂³	1	2	yes	—
144	#13094024	C₂³	1	1	yes	characteristic
145	#13094023	—	2	2	no	—
146	#13094023	—	2	1	no	—
147	#13094022	—	2	2	no	—
148	#13094019	—	2	2	no	—
149	#13094019	—	2	2	no	—
150	#13094019	—	2	2	no	—
151	#13094019	—	2	2	no	—
152	#13094018	—	2	1	no	—
153	#13094017	—	2	2	no	—
154	#13094017	—	2	2	no	—
155	#13094016	—	2	1	no	—
156	#13094016	C₂³	1	2	yes	—
157	#13094016	C₂³	1	1	yes	characteristic
158	#13094015	—	2	2	no	—
159	#13094015	—	2	1	no	—
160	#13094014	—	2	2	no	—
161	#13094014	—	2	2	no	—
162	#13094014	—	2	2	no	—
163	#13094014	—	2	2	no	—
164	#13094012	C₂³	1	1	yes	characteristic
165	#13094012	C₂³	1	2	yes	—
166	#13094010	—	2	2	no	—
167	#13094007	—	2	1	no	—
168	#13094006	—	2	2	no	—
169	#13094003	—	2	1	no	—
170	#13094003	C₂³	1	1	yes	characteristic
171	#13094003	C₂³	1	2	yes	—
172	#13094002	—	2	2	no	—
173	#13094002	—	2	2	no	—
174	#13094000	—	2	1	no	—
175	#13094000	—	2	1	no	—
176	#13094000	—	2	2	no	—
177	#13093998	C₂³	1	1	yes	characteristic
178	Q₈×Dic₄₇	—	2	1	no	—
179	Q₈×Dic₄₇	—	2	1	no	—
180	C₄×Dic₉₄	—	2	1	no	—
181	C₄×Dic₉₄	C₂³	1	2	yes	—
182	C₄×Dic₉₄	C₂³	1	1	yes	characteristic
183	C₄×Dic₉₄	C₂³	1	2	yes	—
184	C₄×Dic₉₄	C₂³	1	2	yes	—
185	C₄×Dic₉₄	C₂³	1	2	yes	—
186	#13093989	—	2	2	no	—
187	C₄×D₁₈₈	C₂³	1	2	yes	—
188	C₄×D₁₈₈	C₂³	1	1	yes	characteristic
189	C₄×C₂²⋊D₄₇	—	2	1	no	—
190	#13093983	—	2	1	no	—
191	#13093982	—	2	2	no	—
192	#13093982	—	2	1	no	—
193	#13093981	—	2	1	no	—
194	C₄⋊C₄×D₄₇	—	2	1	no	—
195	#13093957	C₂³	1	2	yes	—
196	#13093957	C₂³	1	2	yes	—
197	#13093957	C₂³	1	2	yes	—
198	#13093957	C₂³	1	2	yes	—
199	#13093957	C₂³	1	1	yes	characteristic
200	#13093957	C₂³	1	2	yes	—
201	#13093957	C₂³	1	1	yes	characteristic
202	#13093957	C₂³	1	2	yes	—
203	#13093955	C₂³	1	2	yes	—
204	#13093955	C₂³	1	2	yes	—
205	#13093955	C₂³	1	2	yes	—
206	#13093955	C₂³	1	2	yes	—
207	#13093955	C₂³	1	1	yes	characteristic
208	#13093955	C₂³	1	1	yes	characteristic
209	C₄⋊(C₄₇⋊C₈)	C₂³	1	1	yes	characteristic
210	C₄⋊(C₄₇⋊C₈)	C₂³	1	1	yes	characteristic
211	C₄⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
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	1	yes	characteristic
216	C₄⋊(C₄₇⋊C₈)	C₂³	1	1	yes	characteristic
217	#13093948	C₂³	1	1	yes	characteristic
218	#13093948	C₂³	1	2	yes	—
219	#13093948	C₂³	1	1	yes	characteristic
220	#13093948	C₂³	1	2	yes	—
221	#13093948	C₂³	1	1	yes	characteristic
222	#13093948	C₂³	1	1	yes	characteristic
223	#13093947	C₂³	1	2	yes	—
224	#13093947	C₂³	1	1	yes	characteristic
225	#13093947	C₂³	1	2	yes	—
226	#13093947	C₂³	1	2	yes	—
227	#13093947	C₂³	1	2	yes	—
228	#13093947	C₂³	1	2	yes	—
229	#13093947	C₂³	1	1	yes	characteristic
230	#13093947	C₂³	1	2	yes	—
231	#13093947	C₂³	1	2	yes	—
232	#13093947	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	1	yes	characteristic
237	C₂²⋊(C₄₇⋊C₈)	C₂³	1	1	yes	characteristic
238	C₂²⋊(C₄₇⋊C₈)	C₂³	1	1	yes	characteristic
239	C₂²⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
240	#13093935	C₂³	1	2	yes	—
241	#13093935	C₂³	1	2	yes	—
242	C₄×C₄₇⋊C₈	C₂³	1	2	yes	—
243	C₄×C₄₇⋊C₈	C₂³	1	2	yes	—
244	C₄×C₄₇⋊C₈	C₂³	1	2	yes	—
245	C₄×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
246	C₄×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
247	C₂²×Q₈×C₄₇	C₂³	1	1	yes	characteristic
248	C₄⋊Q₈×C₄₇	—	2	1	no	—
249	C₄⋊Q₈×C₄₇	—	2	1	no	—
250	C₄⋊Q₈×C₄₇	—	2	2	no	—
251	C₄⋊Q₈×C₄₇	—	2	2	no	—
252	C₄⋊Q₈×C₄₇	—	2	1	no	—
253	C₄⋊Q₈×C₄₇	—	2	1	no	—
254	C₄⋊Q₈×C₄₇	—	2	2	no	—
255	C₄⋊Q₈×C₄₇	—	2	2	no	—
256	C₄⋊Q₈×C₄₇	—	2	2	no	—
257	C₄⋊Q₈×C₄₇	D₄	1	1	yes	characteristic
258	C₄⋊Q₈×C₄₇	D₄	1	1	yes	characteristic
259	C₄⋊Q₈×C₄₇	C₂³	1	1	yes	characteristic
260	C₄⋊Q₈×C₄₇	C₂³	1	1	yes	characteristic
261	C₄⋊Q₈×C₄₇	C₂³	1	2	yes	—
262	C₄⋊Q₈×C₄₇	C₂³	1	2	yes	—
263	#125×C₄₇	—	2	2	no	—
264	#125×C₄₇	—	2	2	no	—
265	#125×C₄₇	—	2	2	no	—
266	#125×C₄₇	—	2	2	no	—
267	#125×C₄₇	—	2	2	no	—
268	#125×C₄₇	—	2	2	no	—
269	#125×C₄₇	—	2	2	no	—
270	#125×C₄₇	D₄	1	2	yes	—
271	#125×C₄₇	C₂³	1	2	yes	—
272	#125×C₄₇	C₂³	1	2	yes	—
273	#125×C₄₇	C₂³	1	2	yes	—
274	C₂²⋊Q₈×C₄₇	—	2	1	no	—
275	C₂²⋊Q₈×C₄₇	—	2	1	no	—
276	C₂²⋊Q₈×C₄₇	—	2	2	no	—
277	C₂²⋊Q₈×C₄₇	—	2	2	no	—
278	C₂²⋊Q₈×C₄₇	D₄	1	1	yes	characteristic
279	C₂²⋊Q₈×C₄₇	D₄	1	1	yes	characteristic
280	C₂²⋊Q₈×C₄₇	D₄	1	2	yes	—
281	C₄×Q₈×C₄₇	—	2	1	no	—
282	C₄×Q₈×C₄₇	—	2	1	no	—
283	C₄×Q₈×C₄₇	—	2	2	no	—
284	C₄×Q₈×C₄₇	—	2	2	no	—
285	C₄×Q₈×C₄₇	—	2	2	no	—
286	C₄×Q₈×C₄₇	—	2	2	no	—
287	C₄×Q₈×C₄₇	—	2	1	no	—
288	C₄×Q₈×C₄₇	—	2	1	no	—
289	C₄×Q₈×C₄₇	—	2	1	no	—
290	C₄×Q₈×C₄₇	—	2	1	no	—
291	C₄×Q₈×C₄₇	—	2	1	no	—
292	C₄×Q₈×C₄₇	—	2	1	no	—
293	C₄×Q₈×C₄₇	C₂³	1	1	yes	characteristic
294	C₄×Q₈×C₄₇	C₂³	1	1	yes	characteristic
295	C₄×Q₈×C₄₇	C₂³	1	2	yes	—
296	C₄×Q₈×C₄₇	C₂³	1	2	yes	—
297	C₄×Q₈×C₄₇	C₂³	1	2	yes	—
298	C₄×Q₈×C₄₇	C₂³	1	1	yes	characteristic
299	C₄×Q₈×C₄₇	C₂³	1	1	yes	characteristic
300	C₄×Q₈×C₄₇	C₂³	1	2	yes	—
301	C₄×Q₈×C₄₇	C₂³	1	1	yes	characteristic
302	C₄×Q₈×C₄₇	C₂³	1	2	yes	—
303	C₄×Q₈×C₄₇	C₂³	1	1	yes	characteristic
304	#117×C₄₇	—	2	2	no	—
305	#117×C₄₇	—	2	2	no	—
306	#117×C₄₇	C₂³	1	2	yes	—
307	#117×C₄₇	C₂³	1	2	yes	—
308	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
309	C₂×C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
310	C₂×C₄²×C₄₇	—	2	1	no	—
311	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
312	C₂×Q₈×C₄₇	—	2	2	no	—
313	C₂×Q₈×C₄₇	—	2	2	no	—
314	C₂×Q₈×C₄₇	—	2	1	no	—
315	C₂×Q₈×C₄₇	—	2	1	no	—
316	C₂×Q₈×C₄₇	—	2	1	no	—
317	C₂×Q₈×C₄₇	—	2	2	no	—
318	C₂×Q₈×C₄₇	—	2	2	no	—
319	C₂×Q₈×C₄₇	C₂×D₄	1	1	yes	characteristic
320	C₂×Q₈×C₄₇	C₂×D₄	1	1	yes	characteristic
321	C₂×Q₈×C₄₇	C₂×D₄	1	2	yes	—
322	C₂×Q₈×C₄₇	C₂⁴	1	1	yes	characteristic
323	C₂×Q₈×C₄₇	C₂⁴	1	1	yes	characteristic
324	C₂²×C₄×C₄₇	—	2	1	no	—
325	C₂²×C₄×C₄₇	—	2	1	no	—
326	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
327	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
328	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
329	C₂×C₂²⋊D₄₇	—	2	1	no	—
330	C₂×D₁₈₈	C₂⁴	1	1	yes	characteristic
331	C₂×C₄×D₄₇	—	2	1	no	—
332	C₂×C₄×D₄₇	—	2	2	no	—
333	C₂×Dic₉₄	—	2	2	no	—
334	C₂×Dic₉₄	—	2	1	no	—
335	C₂×Dic₉₄	C₂⁴	1	2	yes	—
336	C₂×Dic₉₄	C₂⁴	1	1	yes	characteristic
337	C₄⋊C₄×C₄₇	—	2	1	no	—
338	C₄⋊C₄×C₄₇	—	2	1	no	—
339	C₄⋊C₄×C₄₇	—	2	1	no	—
340	C₄⋊C₄×C₄₇	—	2	1	no	—
341	C₄⋊C₄×C₄₇	—	2	1	no	—
342	C₄⋊C₄×C₄₇	—	2	2	no	—
343	C₄⋊C₄×C₄₇	—	2	2	no	—
344	C₄⋊C₄×C₄₇	—	2	2	no	—
345	C₄⋊C₄×C₄₇	—	2	2	no	—
346	C₄⋊C₄×C₄₇	—	2	2	no	—
347	C₄⋊C₄×C₄₇	—	2	1	no	—
348	C₄⋊C₄×C₄₇	—	2	1	no	—
349	C₄⋊C₄×C₄₇	—	2	2	no	—
350	C₄⋊C₄×C₄₇	—	2	2	no	—
351	C₄⋊C₄×C₄₇	—	2	2	no	—
352	C₄⋊C₄×C₄₇	—	2	2	no	—
353	C₄⋊C₄×C₄₇	—	2	2	no	—
354	C₄⋊C₄×C₄₇	—	2	2	no	—
355	C₄⋊C₄×C₄₇	—	2	2	no	—
356	C₄⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
357	C₄⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
358	C₄⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
359	C₄⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
360	C₄⋊C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
361	C₄⋊C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
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	2	yes	—
365	C₄⋊C₄×C₄₇	C₂⁴	1	1	yes	characteristic
366	C₄⋊C₄×C₄₇	C₂⁴	1	1	yes	characteristic
367	C₄⋊C₄×C₄₇	C₂⁴	1	2	yes	—
368	C₄⋊C₄×C₄₇	C₂⁴	1	2	yes	—
369	C₂²⋊C₄×C₄₇	—	2	2	no	—
370	C₂²⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
371	C₂²⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
372	C₄²×C₄₇	—	2	1	no	—
373	C₄²×C₄₇	—	2	1	no	—
374	C₄²×C₄₇	—	2	1	no	—
375	C₄²×C₄₇	—	2	1	no	—
376	C₄²×C₄₇	—	2	2	no	—
377	C₄²×C₄₇	—	2	2	no	—
378	C₄²×C₄₇	—	2	2	no	—
379	C₄²×C₄₇	—	2	2	no	—
380	C₄²×C₄₇	—	2	2	no	—
381	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
382	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
383	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
384	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
385	C₄²×C₄₇	C₂⁴	1	2	yes	—
386	C₄²×C₄₇	C₂⁴	1	2	yes	—
387	C₂²⋊Dic₄₇	—	2	2	no	—
388	C₂²⋊Dic₄₇	—	2	1	no	—
389	#10625337	—	2	2	no	—
390	#10625337	—	2	4	no	—
391	#10625337	—	2	2	no	—
392	#10625337	—	2	4	no	—
393	#10625336	—	2	2	no	—
394	#10625336	—	2	2	no	—
395	(C₂×D₄₇)⋊C₄	—	2	1	no	—
396	(C₂×D₄₇)⋊C₄	—	2	1	no	—
397	(C₂×D₄₇)⋊C₄	—	2	1	no	—
398	(C₂×D₄₇)⋊C₄	—	2	2	no	—
399	(C₂×D₄₇)⋊C₄	—	2	2	no	—
400	(C₂×D₄₇)⋊C₄	—	2	2	no	—
401	(C₂×D₄₇)⋊C₄	—	2	1	no	—
402	C₄⋊Dic₄₇	—	2	1	no	—
403	C₄⋊Dic₄₇	—	2	1	no	—
404	C₄⋊Dic₄₇	—	2	2	no	—
405	C₄⋊Dic₄₇	—	2	1	no	—
406	C₄⋊Dic₄₇	—	2	2	no	—
407	C₄⋊Dic₄₇	—	2	2	no	—
408	C₄⋊Dic₄₇	C₂⁴	1	1	yes	characteristic
409	C₄⋊Dic₄₇	C₂⁴	1	2	yes	—
410	C₄⋊Dic₄₇	C₂⁴	1	1	yes	characteristic
411	Dic₄₇⋊C₄	—	2	2	no	—
412	Dic₄₇⋊C₄	—	2	1	no	—
413	Dic₄₇⋊C₄	—	2	1	no	—
414	Dic₄₇⋊C₄	—	2	1	no	—
415	Dic₄₇⋊C₄	—	2	2	no	—
416	Dic₄₇⋊C₄	—	2	2	no	—
417	Dic₄₇⋊C₄	—	2	2	no	—
418	Dic₄₇⋊C₄	—	2	2	no	—
419	Dic₄₇⋊C₄	—	2	2	no	—
420	Dic₄₇⋊C₄	—	2	2	no	—
421	Dic₄₇⋊C₄	—	2	1	no	—
422	C₄×Dic₄₇	—	2	1	no	—
423	C₄×Dic₄₇	—	2	2	no	—
424	C₄×Dic₄₇	—	2	2	no	—
425	C₄×Dic₄₇	—	2	2	no	—
426	C₄×Dic₄₇	—	2	2	no	—
427	C₂×C₄₇⋊C₈	C₂⁴	1	1	yes	characteristic
428	C₂×C₄₇⋊C₈	C₂⁴	1	2	yes	—
429	C₂×C₄₇⋊C₈	C₂⁴	1	1	yes	characteristic
430	C₂×C₄₇⋊C₈	C₂⁴	1	2	yes	—
431	C₂×C₄₇⋊C₈	C₂⁴	1	1	yes	characteristic
432	C₂×C₄₇⋊C₈	C₂⁴	1	1	yes	characteristic
433	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
434	C₂²×D₄₇	—	2	1	no	—
435	Q₈×C₄₇	—	2	4	no	—
436	Q₈×C₄₇	—	2	2	no	—
437	Q₈×C₄₇	—	2	2	no	—
438	Q₈×C₄₇	—	2	1	no	—
439	Q₈×C₄₇	—	2	1	no	—
440	Q₈×C₄₇	—	4	2	no	—
441	Q₈×C₄₇	—	4	2	no	—
442	Q₈×C₄₇	—	8	1	no	—
443	Q₈×C₄₇	—	8	2	no	—
444	Q₈×C₄₇	—	8	2	no	—
445	Q₈×C₄₇	2₋¹⁺⁴	1	2	yes	—
446	Q₈×C₄₇	2₋¹⁺⁴	1	2	yes	—
447	C₂×C₄×C₄₇	—	2	4	no	—
448	C₂×C₄×C₄₇	—	2	1	no	—
449	C₂×C₄×C₄₇	—	2	1	no	—
450	C₂×C₄×C₄₇	—	2	2	no	—
451	C₂×C₄×C₄₇	—	2	1	no	—
452	C₂×C₄×C₄₇	—	2	1	no	—
453	C₂×C₄×C₄₇	—	2	2	no	—
454	C₂×C₄×C₄₇	—	2	2	no	—
455	C₂×C₄×C₄₇	—	2	1	no	—
456	C₂×C₄×C₄₇	—	2	1	no	—
457	C₂×C₄×C₄₇	—	4	1	no	—
458	C₂×C₄×C₄₇	—	8	1	no	—
459	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
460	C₂×C₄×C₄₇	C₂²×D₄	1	2	yes	—
461	C₂×C₄×C₄₇	C₂²×D₄	1	2	yes	—
462	C₂×C₄×C₄₇	C₂²×D₄	1	2	yes	—
463	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
464	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
465	C₂×C₄×C₄₇	C₂²×D₄	1	2	yes	—
466	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
467	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
468	C₂×C₄×C₄₇	C₂⁵	1	1	yes	characteristic
469	C₂²⋊D₄₇	—	8	1	no	—
470	C₂×Dic₄₇	—	2	1	no	—
471	C₂×Dic₄₇	—	2	1	no	—
472	C₂×Dic₄₇	—	2	2	no	—
473	C₂×Dic₄₇	—	2	1	no	—
474	C₂×Dic₄₇	—	2	2	no	—
475	D₁₈₈	—	2	1	no	—
476	D₁₈₈	—	2	1	no	—
477	C₄×D₄₇	—	4	2	no	—
478	C₄×D₄₇	—	8	2	no	—
479	Dic₉₄	—	2	2	no	—
480	Dic₉₄	—	2	1	no	—
481	Dic₉₄	—	2	2	no	—
482	Dic₉₄	—	2	1	no	—
483	Dic₉₄	—	8	1	no	—
484	Dic₉₄	—	8	2	no	—
485	C₄₇⋊C₈	—	2	1	no	—
486	C₄₇⋊C₈	—	2	1	no	—
487	C₄₇⋊C₈	—	2	1	no	—
488	C₄₇⋊C₈	—	2	2	no	—
489	C₄₇⋊C₈	—	2	2	no	—
490	C₄₇⋊C₈	—	2	1	no	—
491	#61866	—	47	1	no	maximal, Sylow
492	C₂²×C₄₇	—	2	1	no	—
493	C₂²×C₄₇	—	2	1	no	—
494	C₂²×C₄₇	—	2	1	no	—
495	C₂²×C₄₇	C₂³×D₄	1	1	yes	characteristic
496	C₂×D₄₇	—	4	1	no	—
497	C₂×D₄₇	—	4	1	no	—
498	C₂×D₄₇	—	4	1	no	—
499	C₄×C₄₇	—	2	1	no	—
500	C₄×C₄₇	—	2	2	no	—
501	C₄×C₄₇	—	2	2	no	—
502	C₄×C₄₇	—	2	1	no	—
503	C₄×C₄₇	—	2	2	no	—
504	C₄×C₄₇	—	2	2	no	—
505	C₄×C₄₇	—	2	1	no	—
506	C₄×C₄₇	—	2	1	no	—
507	C₄×C₄₇	—	2	2	no	—
508	C₄×C₄₇	—	2	2	no	—
509	C₄×C₄₇	—	4	1	no	—
510	C₄×C₄₇	—	4	1	no	—
511	C₄×C₄₇	—	4	2	no	—
512	C₄×C₄₇	—	4	2	no	—
513	C₄×C₄₇	#578	1	2	yes	—
514	C₄×C₄₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
515	C₄×C₄₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
516	Dic₄₇	—	4	2	no	—
517	Dic₄₇	—	4	1	no	—
518	Dic₄₇	—	4	1	no	—
519	Dic₄₇	—	4	2	no	—
520	Dic₄₇	—	4	1	no	—
521	#3555	—	47	1	no	—
522	#3502	D₄₇	1	1	yes	characteristic, complemented
523	#3390	—	47	2	no	—
524	#3387	—	47	1	no	—
525	#3385	—	47	1	no	—
526	#3383	—	47	2	no	—
527	Q₈×Q₁₆	—	47	1	no	—
528	#3381	—	47	1	no	—
529	#3377	—	47	2	no	—
530	#3374	—	47	1	no	—
531	#3369	—	47	1	no	—
532	#3364	—	47	1	no	—
533	#3364	—	47	2	no	—
534	#3363	—	47	1	no	—
535	#3243	—	47	2	no	—
536	#3242	—	47	2	no	—
537	#3233	—	47	1	no	—
538	#3231	—	47	1	no	—
539	#3127	—	47	2	no	—
540	#3121	—	47	2	no	—
541	#3108	—	47	1	no	—
542	#3104	—	47	1	no	—
543	#2986	—	47	1	no	—
544	C₂×C₄₇	—	4	1	no	—
545	C₂×C₄₇	#3486	1	1	yes	characteristic
546	C₂×C₄₇	C₂×#578	1	1	yes	characteristic
547	C₂×C₄₇	#3584	1	1	yes	characteristic
548	D₄₇	—	8	1	no	—
549	#563	—	94	2	no	—
550	Q₈²	—	2	1	no	—
551	Q₈²	—	47	1	no	—
552	Q₈²	C₂×D₄₇	1	1	yes	characteristic
553	Q₈²	C₂×D₄₇	1	1	yes	characteristic
554	#557	—	2	1	no	—
555	#557	—	2	2	no	—
556	#557	—	47	2	no	—
557	#557	—	47	1	no	—
558	#557	C₂×D₄₇	1	1	yes	characteristic
559	#557	C₂×D₄₇	1	2	yes	—
560	#557	C₂×D₄₇	1	1	yes	characteristic
561	#557	C₂×D₄₇	1	2	yes	—
562	#556	—	47	1	no	—
563	#556	—	47	2	no	—
564	#556	—	94	1	no	—
565	#554	—	47	1	no	—
566	#552	—	94	1	no	—
567	#544	—	2	2	no	—
568	#544	—	94	1	no	—
569	#544	C₂×D₄₇	1	2	yes	—
570	#542	—	47	2	no	—
571	#541	—	47	2	no	—
572	#541	—	94	1	no	—
573	#541	—	94	2	no	—
574	#533	—	2	1	no	—
575	#533	—	2	1	no	—
576	#533	—	47	1	no	—
577	#533	C₂×D₄₇	1	1	yes	characteristic
578	#533	C₂×D₄₇	1	1	yes	characteristic
579	#529	—	47	1	no	—
580	#519	C₂×D₄₇	1	2	yes	—
581	C₂×C₄×Q₈	C₂×D₄₇	1	1	yes	characteristic
582	#501	—	47	2	no	—
583	#501	—	47	2	no	—
584	#500	—	47	2	no	—
585	#500	—	47	1	no	—
586	#499	—	47	2	no	—
587	#499	—	47	2	no	—
588	#498	—	47	1	no	—
589	#491	—	47	2	no	—
590	#489	—	47	2	no	—
591	#488	—	47	2	no	—
592	#488	—	47	2	no	—
593	#487	—	47	2	no	—
594	#487	—	47	1	no	—
595	#487	—	47	1	no	—
596	#485	—	47	2	no	—
597	#485	—	47	2	no	—
598	#485	—	47	2	no	—
599	#484	—	47	2	no	—
600	#483	—	47	1	no	—
601	#482	—	47	2	no	—
602	#480	—	47	1	no	—
603	#479	—	47	2	no	—
604	#479	—	47	2	no	—
605	#479	—	47	2	no	—
606	#479	—	47	2	no	—
607	#479	—	47	2	no	—
608	#479	—	47	1	no	—
609	#479	—	47	1	no	—
610	#479	—	47	2	no	—
611	#479	—	47	2	no	—
612	#478	—	47	2	no	—
613	#477	—	47	1	no	—
614	#477	—	47	2	no	—
615	#477	—	47	2	no	—
616	#477	—	47	1	no	—
617	#477	—	47	1	no	—
618	#477	—	47	2	no	—
619	#476	—	47	1	no	—
620	#475	—	47	2	no	—
621	#475	—	47	1	no	—
622	#475	—	47	2	no	—
623	#474	—	47	1	no	—
624	#474	—	47	2	no	—
625	#464	—	47	1	no	—
626	#464	—	47	1	no	—
627	#464	—	47	2	no	—
628	#464	—	47	2	no	—
629	#462	—	47	1	no	—
630	#462	—	47	1	no	—
631	#462	—	47	2	no	—
632	#462	—	47	2	no	—
633	#451	—	47	2	no	—
634	#451	—	47	1	no	—
635	#448	—	47	1	no	—
636	#446	—	47	1	no	—
637	#446	—	47	1	no	—
638	#446	—	47	2	no	—
639	C₈×Q₈	—	47	1	no	—
640	C₈×Q₈	—	47	1	no	—
641	C₈×Q₈	—	47	2	no	—
642	#441	—	47	2	no	—
643	#441	—	47	2	no	—
644	#441	—	47	2	no	—
645	#440	—	47	2	no	—
646	C₄×Q₁₆	—	47	2	no	—
647	C₄×Q₁₆	—	47	2	no	—
648	C₄×Q₁₆	—	47	1	no	—
649	C₄×Q₁₆	—	47	2	no	—
650	C₄×Q₁₆	—	47	1	no	—
651	C₄×Q₁₆	—	47	2	no	—
652	C₄×Q₁₆	—	47	2	no	—
653	C₄×SD₁₆	—	47	1	no	—
654	C₄×SD₁₆	—	47	1	no	—
655	C₄×SD₁₆	—	47	2	no	—
656	#433	—	47	2	no	—
657	#433	—	47	2	no	—
658	#431	—	47	1	no	—
659	#431	—	47	1	no	—
660	C₄₇	#61866	1	1	yes	characteristic, complemented, Sylow
661	C₂²×Q₈	C₂²×D₄₇	1	1	yes	characteristic
662	C₂×Q₁₆	—	47	2	no	—
663	C₂×Q₁₆	—	47	1	no	—
664	C₂×Q₁₆	—	47	2	no	—
665	C₂×Q₁₆	—	47	1	no	—
666	C₂×SD₁₆	—	47	1	no	—
667	C₂×SD₁₆	—	47	1	no	—
668	C₄⋊Q₈	—	2	1	no	—
669	C₄⋊Q₈	—	2	1	no	—
670	C₄⋊Q₈	—	2	2	no	—
671	C₄⋊Q₈	—	2	2	no	—
672	C₄⋊Q₈	—	2	1	no	—
673	C₄⋊Q₈	—	2	1	no	—
674	C₄⋊Q₈	—	2	2	no	—
675	C₄⋊Q₈	—	2	2	no	—
676	C₄⋊Q₈	—	2	2	no	—
677	C₄⋊Q₈	—	47	1	no	—
678	C₄⋊Q₈	—	47	2	no	—
679	C₄⋊Q₈	—	47	1	no	—
680	C₄⋊Q₈	—	47	2	no	—
681	C₄⋊Q₈	—	94	2	no	—
682	C₄⋊Q₈	—	94	2	no	—
683	C₄⋊Q₈	—	94	1	no	—
684	C₄⋊Q₈	C₂²⋊D₄₇	1	1	yes	characteristic
685	C₄⋊Q₈	C₂²⋊D₄₇	1	1	yes	characteristic
686	C₄⋊Q₈	C₂²×D₄₇	1	1	yes	characteristic
687	C₄⋊Q₈	C₂²×D₄₇	1	1	yes	characteristic
688	C₄⋊Q₈	C₂²×D₄₇	1	2	yes	—
689	C₄⋊Q₈	C₂²×D₄₇	1	2	yes	—
690	#126	—	94	2	no	—
691	#126	—	94	2	no	—
692	#126	—	94	2	no	—
693	#126	—	94	2	no	—
694	#126	—	94	2	no	—
695	#126	—	94	2	no	—
696	#126	—	94	1	no	—
697	#125	—	2	2	no	—
698	#125	—	2	2	no	—
699	#125	—	2	2	no	—
700	#125	—	2	2	no	—
701	#125	—	2	2	no	—
702	#125	—	2	2	no	—
703	#125	—	2	2	no	—
704	#125	—	47	1	no	—
705	#125	—	47	2	no	—
706	#125	—	94	2	no	—
707	#125	—	94	2	no	—
708	#125	—	94	2	no	—
709	#125	—	94	2	no	—
710	#125	—	94	2	no	—
711	#125	—	94	1	no	—
712	#125	—	94	1	no	—
713	#125	C₂²⋊D₄₇	1	2	yes	—
714	#125	C₂²×D₄₇	1	2	yes	—
715	#125	C₂²×D₄₇	1	2	yes	—
716	#125	C₂²×D₄₇	1	2	yes	—
717	#124	—	47	1	no	—
718	#124	—	47	2	no	—
719	#124	—	94	2	no	—
720	#123	—	94	1	no	—
721	#123	—	94	2	no	—
722	C₂²⋊Q₈	—	2	1	no	—
723	C₂²⋊Q₈	—	2	1	no	—
724	C₂²⋊Q₈	—	2	2	no	—
725	C₂²⋊Q₈	—	2	2	no	—
726	C₂²⋊Q₈	—	47	1	no	—
727	C₂²⋊Q₈	—	47	2	no	—
728	C₂²⋊Q₈	—	94	1	no	—
729	C₂²⋊Q₈	—	94	1	no	—
730	C₂²⋊Q₈	—	94	2	no	—
731	C₂²⋊Q₈	—	94	1	no	—
732	C₂²⋊Q₈	—	94	2	no	—
733	C₂²⋊Q₈	—	94	2	no	—
734	C₂²⋊Q₈	C₂²⋊D₄₇	1	1	yes	characteristic
735	C₂²⋊Q₈	C₂²⋊D₄₇	1	1	yes	characteristic
736	C₂²⋊Q₈	C₂²⋊D₄₇	1	2	yes	—
737	#121	—	47	1	no	—
738	C₄×Q₈	—	2	1	no	—
739	C₄×Q₈	—	2	1	no	—
740	C₄×Q₈	—	2	2	no	—
741	C₄×Q₈	—	2	2	no	—
742	C₄×Q₈	—	2	2	no	—
743	C₄×Q₈	—	2	2	no	—
744	C₄×Q₈	—	2	1	no	—
745	C₄×Q₈	—	2	1	no	—
746	C₄×Q₈	—	2	1	no	—
747	C₄×Q₈	—	2	1	no	—
748	C₄×Q₈	—	2	1	no	—
749	C₄×Q₈	—	2	1	no	—
750	C₄×Q₈	—	47	1	no	—
751	C₄×Q₈	—	47	2	no	—
752	C₄×Q₈	—	47	2	no	—
753	C₄×Q₈	—	47	2	no	—
754	C₄×Q₈	—	47	2	no	—
755	C₄×Q₈	—	94	1	no	—
756	C₄×Q₈	—	94	1	no	—
757	C₄×Q₈	—	94	2	no	—
758	C₄×Q₈	—	94	1	no	—
759	C₄×Q₈	C₂²×D₄₇	1	1	yes	characteristic
760	C₄×Q₈	C₂²×D₄₇	1	1	yes	characteristic
761	C₄×Q₈	C₂²×D₄₇	1	1	yes	characteristic
762	C₄×Q₈	C₂²×D₄₇	1	1	yes	characteristic
763	C₄×Q₈	C₂²×D₄₇	1	2	yes	—
764	C₄×Q₈	C₂²×D₄₇	1	2	yes	—
765	C₄×Q₈	C₂²×D₄₇	1	2	yes	—
766	C₄×Q₈	C₂²×D₄₇	1	2	yes	—
767	C₄×Q₈	C₂²×D₄₇	1	1	yes	characteristic
768	C₄×Q₈	C₂²×D₄₇	1	2	yes	—
769	C₄×Q₈	C₂²×D₄₇	1	1	yes	characteristic
770	C₄×D₄	—	47	1	no	—
771	C₄×D₄	—	47	2	no	—
772	C₄×D₄	—	94	1	no	—
773	#117	—	2	2	no	—
774	#117	—	2	2	no	—
775	#117	—	94	1	no	—
776	#117	—	94	2	no	—
777	#117	—	94	1	no	—
778	#117	—	94	1	no	—
779	#117	C₂²×D₄₇	1	2	yes	—
780	#117	C₂²×D₄₇	1	2	yes	—
781	C₂×C₄⋊C₄	—	2	1	no	—
782	C₂×C₄⋊C₄	—	94	1	no	—
783	C₂×C₄⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
784	C₂×C₄²	—	2	1	no	—
785	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
786	#107	—	47	2	no	—
787	#107	—	47	2	no	—
788	#107	—	47	2	no	—
789	#107	—	47	2	no	—
790	#107	—	47	2	no	—
791	#107	—	47	1	no	—
792	#107	—	47	1	no	—
793	#107	—	47	2	no	—
794	#106	—	47	1	no	—
795	#106	—	47	2	no	—
796	#106	—	47	1	no	—
797	#106	—	47	2	no	—
798	#106	—	47	2	no	—
799	#106	—	47	2	no	—
800	C₄⋊C₈	—	47	1	no	—
801	C₄⋊C₈	—	47	1	no	—
802	C₄⋊C₈	—	47	1	no	—
803	C₄⋊C₈	—	47	1	no	—
804	C₄⋊C₈	—	47	2	no	—
805	C₄⋊C₈	—	47	2	no	—
806	C₄⋊C₈	—	47	2	no	—
807	C₄⋊C₈	—	47	2	no	—
808	#103	—	47	2	no	—
809	#103	—	47	1	no	—
810	#103	—	47	1	no	—
811	#103	—	47	1	no	—
812	#103	—	47	2	no	—
813	#103	—	47	1	no	—
814	#103	—	47	2	no	—
815	#103	—	47	2	no	—
816	#103	—	47	2	no	—
817	#103	—	47	2	no	—
818	#103	—	47	2	no	—
819	#103	—	47	1	no	—
820	#103	—	47	1	no	—
821	#103	—	47	2	no	—
822	#103	—	47	2	no	—
823	#103	—	47	2	no	—
824	#102	—	47	1	no	—
825	#102	—	47	2	no	—
826	#102	—	47	1	no	—
827	#102	—	47	2	no	—
828	C₂²⋊C₈	—	47	1	no	—
829	C₂²⋊C₈	—	47	1	no	—
830	C₂²⋊C₈	—	47	2	no	—
831	#97	—	47	2	no	—
832	#97	—	47	2	no	—
833	C₄×C₈	—	47	1	no	—
834	C₄×C₈	—	47	1	no	—
835	C₄×C₈	—	47	2	no	—
836	C₄×C₈	—	47	2	no	—
837	C₄×C₈	—	47	2	no	—
838	C₂×Q₈	—	2	2	no	—
839	C₂×Q₈	—	2	2	no	—
840	C₂×Q₈	—	2	1	no	—
841	C₂×Q₈	—	2	1	no	—
842	C₂×Q₈	—	2	1	no	—
843	C₂×Q₈	—	2	2	no	—
844	C₂×Q₈	—	2	2	no	—
845	C₂×Q₈	—	47	2	no	—
846	C₂×Q₈	—	47	1	no	—
847	C₂×Q₈	—	94	1	no	—
848	C₂×Q₈	—	94	2	no	—
849	C₂×Q₈	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
850	C₂×Q₈	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
851	C₂×Q₈	C₂×C₂²⋊D₄₇	1	2	yes	—
852	C₂×Q₈	C₂³×D₄₇	1	1	yes	characteristic
853	C₂×Q₈	C₂³×D₄₇	1	1	yes	characteristic
854	C₂×D₄	—	47	1	no	—
855	C₂×D₄	—	94	1	no	—
856	C₂²×C₄	—	2	1	no	—
857	C₂²×C₄	—	2	1	no	—
858	C₂²×C₄	—	94	2	no	—
859	C₂²×C₄	—	94	1	no	—
860	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
861	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
862	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
863	Q₁₆	—	94	4	no	—
864	Q₁₆	—	94	2	no	—
865	Q₁₆	—	94	4	no	—
866	Q₁₆	—	94	2	no	—
867	SD₁₆	—	94	2	no	—
868	SD₁₆	—	94	2	no	—
869	C₂×C₈	—	47	1	no	—
870	C₂×C₈	—	47	2	no	—
871	C₂×C₈	—	47	1	no	—
872	C₂×C₈	—	47	1	no	—
873	C₂×C₈	—	47	2	no	—
874	C₂×C₈	—	47	1	no	—
875	C₄⋊C₄	—	2	1	no	—
876	C₄⋊C₄	—	2	1	no	—
877	C₄⋊C₄	—	2	1	no	—
878	C₄⋊C₄	—	2	1	no	—
879	C₄⋊C₄	—	2	1	no	—
880	C₄⋊C₄	—	2	2	no	—
881	C₄⋊C₄	—	2	2	no	—
882	C₄⋊C₄	—	2	2	no	—
883	C₄⋊C₄	—	2	2	no	—
884	C₄⋊C₄	—	2	2	no	—
885	C₄⋊C₄	—	2	1	no	—
886	C₄⋊C₄	—	2	1	no	—
887	C₄⋊C₄	—	2	2	no	—
888	C₄⋊C₄	—	2	2	no	—
889	C₄⋊C₄	—	2	2	no	—
890	C₄⋊C₄	—	2	2	no	—
891	C₄⋊C₄	—	2	2	no	—
892	C₄⋊C₄	—	2	2	no	—
893	C₄⋊C₄	—	2	2	no	—
894	C₄⋊C₄	—	47	1	no	—
895	C₄⋊C₄	—	47	2	no	—
896	C₄⋊C₄	—	47	1	no	—
897	C₄⋊C₄	—	94	2	no	—
898	C₄⋊C₄	—	94	1	no	—
899	C₄⋊C₄	—	94	1	no	—
900	C₄⋊C₄	—	94	1	no	—
901	C₄⋊C₄	—	94	2	no	—
902	C₄⋊C₄	—	94	2	no	—
903	C₄⋊C₄	—	94	2	no	—
904	C₄⋊C₄	—	94	2	no	—
905	C₄⋊C₄	—	94	1	no	—
906	C₄⋊C₄	—	94	2	no	—
907	C₄⋊C₄	—	94	2	no	—
908	C₄⋊C₄	—	94	1	no	—
909	C₄⋊C₄	—	94	1	no	—
910	C₄⋊C₄	—	94	2	no	—
911	C₄⋊C₄	—	94	1	no	—
912	C₄⋊C₄	—	94	2	no	—
913	C₄⋊C₄	—	94	2	no	—
914	C₄⋊C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
915	C₄⋊C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
916	C₄⋊C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
917	C₄⋊C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
918	C₄⋊C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
919	C₄⋊C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
920	C₄⋊C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
921	C₄⋊C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
922	C₄⋊C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
923	C₄⋊C₄	C₂³×D₄₇	1	2	yes	—
924	C₄⋊C₄	C₂³×D₄₇	1	1	yes	characteristic
925	C₄⋊C₄	C₂³×D₄₇	1	1	yes	characteristic
926	C₄⋊C₄	C₂³×D₄₇	1	2	yes	—
927	C₂²⋊C₄	—	2	2	no	—
928	C₂²⋊C₄	—	94	2	no	—
929	C₂²⋊C₄	—	94	1	no	—
930	C₂²⋊C₄	—	94	1	no	—
931	C₂²⋊C₄	—	94	1	no	—
932	C₂²⋊C₄	—	94	1	no	—
933	C₂²⋊C₄	—	94	2	no	—
934	C₂²⋊C₄	—	94	2	no	—
935	C₂²⋊C₄	—	94	1	no	—
936	C₂²⋊C₄	—	94	2	no	—
937	C₂²⋊C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
938	C₂²⋊C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
939	C₄²	—	2	1	no	—
940	C₄²	—	2	1	no	—
941	C₄²	—	2	1	no	—
942	C₄²	—	2	1	no	—
943	C₄²	—	2	2	no	—
944	C₄²	—	2	2	no	—
945	C₄²	—	2	2	no	—
946	C₄²	—	2	2	no	—
947	C₄²	—	2	2	no	—
948	C₄²	—	94	2	no	—
949	C₄²	—	94	1	no	—
950	C₄²	—	94	2	no	—
951	C₄²	—	94	2	no	—
952	C₄²	—	94	2	no	—
953	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
954	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
955	C₄²	C₂³×D₄₇	1	1	yes	characteristic
956	C₄²	C₂³×D₄₇	1	1	yes	characteristic
957	C₄²	C₂³×D₄₇	1	2	yes	—
958	C₄²	C₂³×D₄₇	1	2	yes	—
959	C₂³	—	94	1	no	—
960	C₂³	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
961	Q₈	—	2	4	no	—
962	Q₈	—	2	2	no	—
963	Q₈	—	2	2	no	—
964	Q₈	—	2	1	no	—
965	Q₈	—	2	1	no	—
966	Q₈	—	4	2	no	—
967	Q₈	—	4	2	no	—
968	Q₈	—	8	1	no	—
969	Q₈	—	8	2	no	—
970	Q₈	—	8	2	no	—
971	Q₈	—	94	2	no	—
972	Q₈	—	94	1	no	—
973	Q₈	—	94	2	no	—
974	Q₈	—	94	1	no	—
975	Q₈	—	376	1	no	—
976	Q₈	—	376	2	no	—
977	Q₈	#13094072	1	2	yes	—
978	Q₈	#13094072	1	2	yes	—
979	D₄	—	94	1	no	—
980	D₄	—	94	1	no	—
981	D₄	—	376	1	no	—
982	C₂×C₄	—	2	4	no	—
983	C₂×C₄	—	2	1	no	—
984	C₂×C₄	—	2	1	no	—
985	C₂×C₄	—	2	2	no	—
986	C₂×C₄	—	2	1	no	—
987	C₂×C₄	—	2	1	no	—
988	C₂×C₄	—	2	2	no	—
989	C₂×C₄	—	2	2	no	—
990	C₂×C₄	—	2	1	no	—
991	C₂×C₄	—	2	1	no	—
992	C₂×C₄	—	4	1	no	—
993	C₂×C₄	—	8	1	no	—
994	C₂×C₄	—	94	2	no	—
995	C₂×C₄	—	94	1	no	—
996	C₂×C₄	—	94	1	no	—
997	C₂×C₄	—	94	1	no	—
998	C₂×C₄	—	94	2	no	—
999	C₂×C₄	—	376	2	no	—
1000	C₂×C₄	—	188	2	no	—
1001	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
1002	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
1003	C₂×C₄	C₂²×C₂²⋊D₄₇	1	2	yes	—
1004	C₂×C₄	C₂²×C₂²⋊D₄₇	1	2	yes	—
1005	C₂×C₄	C₂²×C₂²⋊D₄₇	1	2	yes	—
1006	C₂×C₄	C₂²×C₂²⋊D₄₇	1	2	yes	—
1007	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
1008	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
1009	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
1010	C₂×C₄	C₂⁴×D₄₇	1	1	yes	characteristic
1011	C₈	—	94	1	no	—
1012	C₈	—	94	1	no	—
1013	C₈	—	94	1	no	—
1014	C₈	—	94	2	no	—
1015	C₈	—	94	1	no	—
1016	C₈	—	94	2	no	—
1017	C₂²	—	2	1	no	—
1018	C₂²	—	2	1	no	—
1019	C₂²	—	2	1	no	—
1020	C₂²	—	188	1	no	—
1021	C₂²	—	188	1	no	—
1022	C₂²	—	188	1	no	—
1023	C₂²	C₂³×C₂²⋊D₄₇	1	1	yes	characteristic
1024	C₄	—	2	2	no	—
1025	C₄	—	2	2	no	—
1026	C₄	—	2	1	no	—
1027	C₄	—	2	1	no	—
1028	C₄	—	2	2	no	—
1029	C₄	—	2	2	no	—
1030	C₄	—	2	1	no	—
1031	C₄	—	2	1	no	—
1032	C₄	—	2	2	no	—
1033	C₄	—	2	2	no	—
1034	C₄	—	4	2	no	—
1035	C₄	—	4	1	no	—
1036	C₄	—	4	1	no	—
1037	C₄	—	4	2	no	—
1038	C₄	—	188	2	no	—
1039	C₄	—	188	1	no	—
1040	C₄	—	188	1	no	—
1041	C₄	—	188	2	no	—
1042	C₄	—	188	1	no	—
1043	C₄	#15689938	1	2	yes	—
1044	C₄	C₂×#13094072	1	1	yes	characteristic
1045	C₄	C₂×#13094072	1	1	yes	characteristic
1046	C₂	—	4	1	no	—
1047	C₂	—	376	1	no	—
1048	C₂	#20257039	1	1	yes	characteristic
1049	C₂	C₂×#15689938	1	1	yes	characteristic
1050	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×#3502	C₂
socle	C₂²×C₄₇	C₂³×D₄
prime radical	#13093998	C₂³
hypercenter	#3502	D₄₇
hypocenter	C₄₇	#61866
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ #533 ◁ #3502

Complements

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

N	H ≅ G/N	type
2. #20256351	C₂	semidirect
3. #20256320	C₂	semidirect
4. #20256294	C₂	semidirect
5. #20256275	C₂	semidirect
6. Q₈×#10625337	C₂	semidirect
7. #20256259	C₂	semidirect
8. #20256230	C₂	semidirect
9. #20256191	C₂	semidirect
10. #20256128	C₂	semidirect
11. #20256073	C₂	semidirect
12. #20256073	C₂	semidirect
13. #20256066	C₂	semidirect
15. #20254656	C₂	semidirect
17. #20254547	C₂	semidirect
18. #20253688	C₂	semidirect
21. #20253427	C₂	semidirect
22. #20252490	C₂	semidirect
23. C₄₇×#3502	C₂	semidirect
522. #3502	D₄₇	semidirect
660. C₄₇	#61866	semidirect

Maximal subgroups

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

subgroup	index
#20257876	2
#20256351	2
#20256320	2
#20256294	2
#20256275	2
Q₈×#10625337	2
#20256259	2
#20256230	2
#20256191	2
#20256128	2
#20256073	2
#20256066	2
#20254671	2
#20254656	2
#20254567	2
#20254547	2
#20253688	2
#20253617	2
#20253468	2
#20253427	2
#20252490	2
C₄₇×#3502	2
#61866	47