Subgroups — #27097155

Order 12032.

1690 conjugacy classes of subgroups.

The subgroup lattice has 1058 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20257209	C₂	1	1	yes	maximal, characteristic
2	#20256351	C₂	1	2	yes	maximal, complemented
3	#20256351	C₂	1	2	yes	maximal, complemented
4	#20256327	C₂	1	2	yes	maximal, complemented
5	#20256327	C₂	1	2	yes	maximal, complemented
6	#20256316	C₂	1	2	yes	maximal, complemented
7	#20256294	C₂	1	2	yes	maximal, complemented
8	#20256275	C₂	1	2	yes	maximal, complemented
9	#20256259	C₂	1	2	yes	maximal, complemented
10	#20253941	C₂	1	1	yes	maximal, characteristic, complemented
11	#20253922	C₂	1	1	yes	maximal, characteristic, complemented
12	#20253914	C₂	1	1	yes	maximal, characteristic, complemented
13	#20253246	C₂	1	1	yes	maximal, characteristic
14	#20253235	C₂	1	1	yes	maximal, characteristic
15	#20253230	C₂	1	1	yes	maximal, characteristic, complemented
16	#20253230	C₂	1	1	yes	maximal, characteristic, complemented
17	#20253170	C₂	1	1	yes	maximal, characteristic
18	C₂×#15689430	C₂	1	1	yes	maximal, characteristic, complemented
19	#20252337	C₂	1	1	yes	maximal, characteristic, complemented
20	#20252231	C₂	1	1	yes	maximal, characteristic
21	#20252231	C₂	1	1	yes	maximal, characteristic
22	C₄×#13094055	C₂	1	1	yes	maximal, characteristic
23	C₄₇×#3502	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#13094055	C₂²	1	1	yes	characteristic
25	#15689851	C₂²	1	2	yes	—
26	#15689851	C₂²	1	2	yes	—
27	#15689833	C₂²	1	2	yes	—
28	#15689833	C₂²	1	2	yes	—
29	#15689827	—	2	2	no	—
30	#15689827	—	2	2	no	—
31	#15689751	C₂²	1	1	yes	characteristic
32	#15689751	C₂²	1	1	yes	characteristic
33	#15689750	—	2	1	no	—
34	#15689750	—	2	1	no	—
35	#15689679	—	2	1	no	—
36	C₂×#13094016	C₂²	1	1	yes	characteristic
37	#125×D₄₇	—	2	1	no	—
38	#15689603	C₂²	1	1	yes	characteristic
39	#15689603	C₂²	1	1	yes	characteristic
40	C₄×#10625350	C₂²	1	1	yes	characteristic
41	#15689533	C₂²	1	2	yes	—
42	#15689533	C₂²	1	2	yes	—
43	#15689529	C₂²	1	2	yes	—
44	#15689529	C₂²	1	2	yes	—
45	#15689529	C₂²	1	2	yes	—
46	#15689529	C₂²	1	2	yes	—
47	#15689526	C₂²	1	2	yes	—
48	#15689522	C₂²	1	2	yes	—
49	#15689522	C₂²	1	2	yes	—
50	#15689522	C₂²	1	2	yes	—
51	#15689522	C₂²	1	2	yes	—
52	#15689519	C₂²	1	2	yes	—
53	#15689430	C₂²	1	2	yes	—
54	#15689430	C₂²	1	2	yes	—
55	#15689430	C₂²	1	2	yes	—
56	#15689430	C₂²	1	2	yes	—
57	#15689430	C₂²	1	2	yes	—
58	#15689430	C₂²	1	2	yes	—
59	#15689430	C₂²	1	2	yes	—
60	#15689430	C₂²	1	2	yes	—
61	#15689427	C₂²	1	1	yes	characteristic
62	#15689427	C₂²	1	2	yes	—
63	#15689427	C₂²	1	2	yes	—
64	#15689427	C₂²	1	1	yes	characteristic
65	#15689420	C₂²	1	1	yes	characteristic
66	#15689420	C₂²	1	2	yes	—
67	#15689420	C₂²	1	2	yes	—
68	#15689420	C₂²	1	1	yes	characteristic
69	#15689418	C₂²	1	2	yes	—
70	#15689418	C₂²	1	2	yes	—
71	#15689415	C₂²	1	2	yes	—
72	#15689415	C₂²	1	1	yes	characteristic
73	#15689410	C₂²	1	2	yes	—
74	#15689410	C₂²	1	1	yes	characteristic
75	#15689408	C₂²	1	2	yes	—
76	#15689408	C₂²	1	2	yes	—
77	#15689405	C₂²	1	2	yes	—
78	#15689405	C₂²	1	1	yes	characteristic
79	#15689400	C₂²	1	2	yes	—
80	#15689400	C₂²	1	1	yes	characteristic
81	#15689254	C₂²	1	2	yes	—
82	#15689254	C₂²	1	2	yes	—
83	#15689254	C₂²	1	2	yes	—
84	Q₈×C₄₇⋊C₈	C₂²	1	2	yes	—
85	#15689228	C₂²	1	2	yes	—
86	#15689228	C₂²	1	2	yes	—
87	#15689228	C₂²	1	2	yes	—
88	#15689221	C₂²	1	2	yes	—
89	#15689221	C₂²	1	2	yes	—
90	#15689221	C₂²	1	2	yes	—
91	C₄×#10625337	C₂²	1	2	yes	—
92	C₄×#10625337	C₂²	1	2	yes	—
93	C₄×#10625337	C₂²	1	2	yes	—
94	C₄×#10625336	C₂²	1	2	yes	—
95	C₄×#10625336	C₂²	1	2	yes	—
96	C₄×#10625336	C₂²	1	2	yes	—
97	#15689166	C₂²	1	1	yes	characteristic
98	#15689166	C₂²	1	1	yes	characteristic
99	#15689166	C₂²	1	1	yes	characteristic
100	#15689166	C₂²	1	1	yes	characteristic
101	#15689163	C₂²	1	1	yes	characteristic
102	#15689159	C₂²	1	1	yes	characteristic
103	#15689159	C₂²	1	1	yes	characteristic
104	C₂×#13093957	C₂²	1	1	yes	characteristic
105	C₂×#13093955	C₂²	1	1	yes	characteristic
106	#15689150	C₂²	1	1	yes	characteristic
107	#15689150	C₂²	1	1	yes	characteristic
108	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
109	#15689132	C₂²	1	1	yes	characteristic
110	#15689122	C₂²	1	1	yes	characteristic
111	#15689117	C₂²	1	1	yes	characteristic
112	#15689117	C₂²	1	1	yes	characteristic
113	C₂×#13093948	C₂²	1	1	yes	characteristic
114	C₂×#13093948	C₂²	1	1	yes	characteristic
115	#15689079	C₂²	1	1	yes	characteristic
116	#15689079	C₂²	1	1	yes	characteristic
117	C₄×#10625329	C₂²	1	1	yes	characteristic
118	Q₈²×C₄₇	—	2	1	no	—
119	Q₈²×C₄₇	C₂²	1	2	yes	—
120	C₄₇×#557	—	2	1	no	—
121	C₄₇×#557	—	2	1	no	—
122	C₄₇×#557	—	2	1	no	—
123	C₄₇×#557	C₂²	1	2	yes	—
124	C₄₇×#557	C₂²	1	2	yes	—
125	C₄₇×#557	C₂²	1	2	yes	—
126	C₄₇×#544	—	2	2	no	—
127	C₄₇×#544	C₂²	1	1	yes	characteristic
128	C₄₇×#544	C₂²	1	1	yes	characteristic
129	C₄₇×#533	—	2	2	no	—
130	C₄₇×#533	C₂²	1	1	yes	characteristic
131	C₄₇×#533	C₂²	1	1	yes	characteristic
132	C₄₇×#519	C₂²	1	1	yes	characteristic
133	C₄₇×#519	C₂²	1	1	yes	characteristic
134	C₂×C₄×Q₈×C₄₇	C₂²	1	1	yes	characteristic
135	C₂×#10625350	C₂³	1	1	yes	characteristic
136	#13094055	Q₈	1	8	yes	complemented
137	C₂×#10625337	C₂³	1	2	yes	—
138	C₂×#10625336	C₂³	1	2	yes	—
139	C₂×#10625329	C₂³	1	1	yes	characteristic
140	C₂×#10625329	C₂³	1	1	yes	characteristic
141	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
142	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
143	#13094024	C₂³	1	2	yes	—
144	#13094024	C₂³	1	2	yes	—
145	#13094023	—	2	1	no	—
146	#13094023	—	2	1	no	—
147	#13094022	—	2	2	no	—
148	#13094022	—	2	2	no	—
149	#13094016	—	2	1	no	—
150	#13094016	—	2	1	no	—
151	#13094016	C₂³	1	2	yes	—
152	#13094016	C₂³	1	2	yes	—
153	#13094016	C₂³	1	2	yes	—
154	#13094016	C₂³	1	2	yes	—
155	#13094015	—	2	1	no	—
156	#13094015	—	2	1	no	—
157	#13094014	—	2	2	no	—
158	#13094014	—	2	2	no	—
159	#13094014	—	2	2	no	—
160	#13094014	—	2	2	no	—
161	#13094002	—	2	2	no	—
162	#13094002	—	2	2	no	—
163	#13094002	—	2	2	no	—
164	#13094002	—	2	2	no	—
165	#13094001	—	2	2	no	—
166	#13094001	—	2	2	no	—
167	#13094000	—	2	2	no	—
168	#13094000	—	2	2	no	—
169	C₄×Dic₉₄	C₂³	1	1	yes	characteristic
170	C₄×Dic₉₄	C₂³	1	2	yes	—
171	C₄×Dic₉₄	C₂³	1	2	yes	—
172	C₄×Dic₉₄	C₂³	1	1	yes	characteristic
173	#13093989	—	2	2	no	—
174	#13093989	—	2	2	no	—
175	C₄×D₁₈₈	C₂³	1	1	yes	characteristic
176	C₄×D₁₈₈	C₂³	1	2	yes	—
177	C₄×D₁₈₈	C₂³	1	2	yes	—
178	C₄×D₁₈₈	C₂³	1	1	yes	characteristic
179	C₄×C₂²⋊D₄₇	—	2	1	no	—
180	C₄×C₂²⋊D₄₇	—	2	1	no	—
181	(C₂²⋊D₄₇)⋊C₄	—	2	2	no	—
182	(C₂²⋊D₄₇)⋊C₄	—	2	2	no	—
183	#13093983	C₂³	1	1	yes	characteristic
184	#13093982	—	2	1	no	—
185	#13093982	—	2	1	no	—
186	#13093981	—	2	1	no	—
187	C₂×C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic
188	C₂×C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic
189	C₂×Dic₄₇⋊C₄	—	2	1	no	—
190	C₂×Dic₄₇⋊C₄	—	2	1	no	—
191	C₄⋊C₄×D₄₇	—	2	1	no	—
192	C₄⋊C₄×D₄₇	—	2	1	no	—
193	C₄⋊C₄×D₄₇	—	2	2	no	—
194	C₄⋊C₄×D₄₇	—	2	2	no	—
195	C₄²×D₄₇	—	2	1	no	—
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	2	yes	—
202	#13093957	C₂³	1	2	yes	—
203	#13093957	C₂³	1	1	yes	characteristic
204	#13093957	C₂³	1	1	yes	characteristic
205	#13093957	C₂³	1	2	yes	—
206	#13093957	C₂³	1	1	yes	characteristic
207	#13093955	C₂³	1	2	yes	—
208	#13093955	C₂³	1	2	yes	—
209	#13093955	C₂³	1	2	yes	—
210	#13093955	C₂³	1	1	yes	characteristic
211	#13093955	C₂³	1	2	yes	—
212	#13093955	C₂³	1	1	yes	characteristic
213	#13093955	C₂³	1	2	yes	—
214	#13093955	C₂³	1	2	yes	—
215	#13093955	C₂³	1	1	yes	characteristic
216	#13093955	C₂³	1	2	yes	—
217	#13093955	C₂³	1	1	yes	characteristic
218	C₄⋊(C₄₇⋊C₈)	C₂³	1	1	yes	characteristic
219	C₄⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
220	C₄⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
221	C₄⋊(C₄₇⋊C₈)	C₂³	1	1	yes	characteristic
222	C₄⋊(C₄₇⋊C₈)	C₂³	1	1	yes	characteristic
223	C₄⋊(C₄₇⋊C₈)	C₂³	1	1	yes	characteristic
224	C₄⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
225	C₄⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
226	#13093948	C₂³	1	2	yes	—
227	#13093948	C₂³	1	2	yes	—
228	#13093948	C₂³	1	2	yes	—
229	#13093948	C₂³	1	2	yes	—
230	#13093948	C₂³	1	2	yes	—
231	#13093948	C₂³	1	2	yes	—
232	#13093947	C₂³	1	1	yes	characteristic
233	#13093947	C₂³	1	1	yes	characteristic
234	#13093947	C₂³	1	2	yes	—
235	#13093947	C₂³	1	1	yes	characteristic
236	#13093947	C₂³	1	1	yes	characteristic
237	#13093944	C₂³	1	1	yes	characteristic
238	#13093944	C₂³	1	1	yes	characteristic
239	#13093944	C₂³	1	2	yes	—
240	#13093944	C₂³	1	1	yes	characteristic
241	#13093944	C₂³	1	1	yes	characteristic
242	#13093935	C₂³	1	2	yes	—
243	#13093935	C₂³	1	2	yes	—
244	#13093935	C₂³	1	2	yes	—
245	C₄×C₄₇⋊C₈	C₂³	1	2	yes	—
246	C₄×C₄₇⋊C₈	C₂³	1	2	yes	—
247	C₄×C₄₇⋊C₈	C₂³	1	2	yes	—
248	C₂²×Q₈×C₄₇	C₂³	1	1	yes	characteristic
249	C₄⋊Q₈×C₄₇	—	2	2	no	—
250	C₄⋊Q₈×C₄₇	—	2	2	no	—
251	C₄⋊Q₈×C₄₇	—	2	2	no	—
252	C₄⋊Q₈×C₄₇	—	2	2	no	—
253	C₄⋊Q₈×C₄₇	—	2	2	no	—
254	C₄⋊Q₈×C₄₇	—	2	2	no	—
255	C₄⋊Q₈×C₄₇	—	2	1	no	—
256	C₄⋊Q₈×C₄₇	—	2	1	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	2	yes	—
260	C₄⋊Q₈×C₄₇	C₂³	1	2	yes	—
261	C₄⋊Q₈×C₄₇	C₂³	1	1	yes	characteristic
262	C₄⋊Q₈×C₄₇	C₂³	1	1	yes	characteristic
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	1	no	—
270	#125×C₄₇	—	2	1	no	—
271	#125×C₄₇	D₄	1	1	yes	characteristic
272	#125×C₄₇	D₄	1	1	yes	characteristic
273	#125×C₄₇	C₂³	1	1	yes	characteristic
274	#125×C₄₇	C₂³	1	1	yes	characteristic
275	#125×C₄₇	C₂³	1	2	yes	—
276	#125×C₄₇	C₂³	1	2	yes	—
277	C₂²⋊Q₈×C₄₇	—	2	1	no	—
278	C₂²⋊Q₈×C₄₇	—	2	1	no	—
279	C₂²⋊Q₈×C₄₇	—	2	2	no	—
280	C₂²⋊Q₈×C₄₇	—	2	2	no	—
281	C₂²⋊Q₈×C₄₇	D₄	1	2	yes	—
282	C₂²⋊Q₈×C₄₇	D₄	1	2	yes	—
283	C₄×Q₈×C₄₇	—	2	2	no	—
284	C₄×Q₈×C₄₇	—	2	1	no	—
285	C₄×Q₈×C₄₇	—	2	1	no	—
286	C₄×Q₈×C₄₇	—	2	1	no	—
287	C₄×Q₈×C₄₇	—	2	1	no	—
288	C₄×Q₈×C₄₇	—	2	2	no	—
289	C₄×Q₈×C₄₇	—	2	2	no	—
290	C₄×Q₈×C₄₇	—	2	2	no	—
291	C₄×Q₈×C₄₇	—	2	1	no	—
292	C₄×Q₈×C₄₇	—	2	1	no	—
293	C₄×Q₈×C₄₇	—	2	1	no	—
294	C₄×Q₈×C₄₇	—	2	1	no	—
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	2	yes	—
299	C₄×Q₈×C₄₇	C₂³	1	2	yes	—
300	C₄×Q₈×C₄₇	C₂³	1	2	yes	—
301	C₄×Q₈×C₄₇	C₂³	1	2	yes	—
302	C₄×Q₈×C₄₇	C₂³	1	2	yes	—
303	#117×C₄₇	—	2	2	no	—
304	#117×C₄₇	—	2	2	no	—
305	#117×C₄₇	C₂³	1	1	yes	characteristic
306	#117×C₄₇	C₂³	1	1	yes	characteristic
307	#117×C₄₇	C₂³	1	1	yes	characteristic
308	#117×C₄₇	C₂³	1	1	yes	characteristic
309	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
310	C₂×C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
311	C₂×C₄²×C₄₇	—	2	1	no	—
312	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
313	C₂×Q₈×C₄₇	—	2	1	no	—
314	C₂×Q₈×C₄₇	—	2	1	no	—
315	C₂×Q₈×C₄₇	—	2	1	no	—
316	C₂×Q₈×C₄₇	—	2	2	no	—
317	C₂×Q₈×C₄₇	—	2	2	no	—
318	C₂×Q₈×C₄₇	—	2	2	no	—
319	C₂×Q₈×C₄₇	C₂×D₄	1	2	yes	—
320	C₂×Q₈×C₄₇	C₂×D₄	1	2	yes	—
321	C₂×Q₈×C₄₇	C₂×Q₈	1	4	yes	—
322	C₂×Q₈×C₄₇	C₂⁴	1	2	yes	—
323	C₂²×C₄×C₄₇	—	2	1	no	—
324	C₂²×C₄×C₄₇	—	2	1	no	—
325	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
326	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
327	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
328	C₂×C₂²⋊D₄₇	—	2	1	no	—
329	C₂²×Dic₄₇	—	2	1	no	—
330	C₂²×Dic₄₇	—	2	1	no	—
331	#10625350	—	2	2	no	—
332	#10625350	C₂×Q₈	1	4	yes	—
333	C₂×D₁₈₈	C₂⁴	1	1	yes	characteristic
334	C₂×C₄×D₄₇	—	2	1	no	—
335	C₂×C₄×D₄₇	—	2	1	no	—
336	C₂×C₄×D₄₇	—	2	1	no	—
337	C₂×C₄×D₄₇	—	2	2	no	—
338	C₂×C₄×D₄₇	—	2	2	no	—
339	C₂×Dic₉₄	—	2	2	no	—
340	C₂×Dic₉₄	—	2	2	no	—
341	C₂×Dic₉₄	C₂⁴	1	1	yes	characteristic
342	C₄⋊C₄×C₄₇	—	2	2	no	—
343	C₄⋊C₄×C₄₇	—	2	2	no	—
344	C₄⋊C₄×C₄₇	—	2	1	no	—
345	C₄⋊C₄×C₄₇	—	2	2	no	—
346	C₄⋊C₄×C₄₇	—	2	2	no	—
347	C₄⋊C₄×C₄₇	—	2	2	no	—
348	C₄⋊C₄×C₄₇	—	2	2	no	—
349	C₄⋊C₄×C₄₇	—	2	1	no	—
350	C₄⋊C₄×C₄₇	—	2	1	no	—
351	C₄⋊C₄×C₄₇	—	2	1	no	—
352	C₄⋊C₄×C₄₇	—	2	1	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	—	2	2	no	—
357	C₄⋊C₄×C₄₇	—	2	1	no	—
358	C₄⋊C₄×C₄₇	—	2	1	no	—
359	C₄⋊C₄×C₄₇	—	2	2	no	—
360	C₄⋊C₄×C₄₇	—	2	2	no	—
361	C₄⋊C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
362	C₄⋊C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
363	C₄⋊C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
364	C₄⋊C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
365	C₄⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
366	C₄⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
367	C₄⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
368	C₄⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
369	C₄⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
370	C₄⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
371	C₄⋊C₄×C₄₇	C₂⁴	1	2	yes	—
372	C₄⋊C₄×C₄₇	C₂⁴	1	1	yes	characteristic
373	C₄⋊C₄×C₄₇	C₂⁴	1	1	yes	characteristic
374	C₄⋊C₄×C₄₇	C₂⁴	1	1	yes	characteristic
375	C₄⋊C₄×C₄₇	C₂⁴	1	1	yes	characteristic
376	C₂²⋊C₄×C₄₇	—	2	1	no	—
377	C₂²⋊C₄×C₄₇	—	2	1	no	—
378	C₂²⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
379	C₂²⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
380	C₄²×C₄₇	—	2	2	no	—
381	C₄²×C₄₇	—	2	2	no	—
382	C₄²×C₄₇	—	2	2	no	—
383	C₄²×C₄₇	—	2	2	no	—
384	C₄²×C₄₇	—	2	2	no	—
385	C₄²×C₄₇	—	2	2	no	—
386	C₄²×C₄₇	—	2	1	no	—
387	C₄²×C₄₇	—	2	1	no	—
388	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
389	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
390	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
391	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
392	C₄²×C₄₇	C₂⁴	1	2	yes	—
393	C₄²×C₄₇	C₂⁴	1	2	yes	—
394	C₂²⋊Dic₄₇	—	2	1	no	—
395	#10625337	C₂×Q₈	1	8	yes	—
396	#10625336	C₂×Q₈	1	8	yes	—
397	(C₂×D₄₇)⋊C₄	—	2	1	no	—
398	(C₂×D₄₇)⋊C₄	—	2	1	no	—
399	(C₂×D₄₇)⋊C₄	—	2	2	no	—
400	(C₂×D₄₇)⋊C₄	—	2	2	no	—
401	C₄⋊Dic₄₇	—	2	1	no	—
402	C₄⋊Dic₄₇	—	2	1	no	—
403	C₄⋊Dic₄₇	—	2	2	no	—
404	C₄⋊Dic₄₇	—	2	2	no	—
405	C₄⋊Dic₄₇	C₂⁴	1	2	yes	—
406	C₄⋊Dic₄₇	C₂⁴	1	1	yes	characteristic
407	C₄⋊Dic₄₇	C₂⁴	1	2	yes	—
408	C₄⋊Dic₄₇	C₂⁴	1	1	yes	characteristic
409	Dic₄₇⋊C₄	—	2	2	no	—
410	Dic₄₇⋊C₄	—	2	2	no	—
411	Dic₄₇⋊C₄	—	2	2	no	—
412	Dic₄₇⋊C₄	—	2	2	no	—
413	Dic₄₇⋊C₄	—	2	2	no	—
414	Dic₄₇⋊C₄	—	2	2	no	—
415	Dic₄₇⋊C₄	—	2	2	no	—
416	Dic₄₇⋊C₄	—	2	2	no	—
417	Dic₄₇⋊C₄	—	2	1	no	—
418	Dic₄₇⋊C₄	—	2	1	no	—
419	Dic₄₇⋊C₄	—	2	2	no	—
420	Dic₄₇⋊C₄	—	2	2	no	—
421	C₄×Dic₄₇	—	2	1	no	—
422	C₄×Dic₄₇	—	2	1	no	—
423	C₄×Dic₄₇	—	2	1	no	—
424	C₄×Dic₄₇	—	2	2	no	—
425	C₄×Dic₄₇	—	2	2	no	—
426	#10625329	—	2	2	no	—
427	#10625329	C₂×Q₈	1	4	yes	—
428	C₂×C₄₇⋊C₈	—	2	2	no	—
429	C₂×C₄₇⋊C₈	—	2	2	no	—
430	C₂×C₄₇⋊C₈	C₂⁴	1	1	yes	characteristic
431	C₂×C₄₇⋊C₈	C₂⁴	1	1	yes	characteristic
432	C₂×C₄₇⋊C₈	C₂⁴	1	2	yes	—
433	C₂×C₄₇⋊C₈	C₂⁴	1	1	yes	characteristic
434	C₂×C₄₇⋊C₈	C₂⁴	1	1	yes	characteristic
435	C₂×C₄₇⋊C₈	C₂⁴	1	2	yes	—
436	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
437	C₂²×D₄₇	—	2	1	no	—
438	Q₈×C₄₇	—	2	4	no	—
439	Q₈×C₄₇	—	2	2	no	—
440	Q₈×C₄₇	—	4	2	no	—
441	Q₈×C₄₇	—	4	2	no	—
442	Q₈×C₄₇	—	4	2	no	—
443	Q₈×C₄₇	—	8	2	no	—
444	Q₈×C₄₇	—	8	1	no	—
445	Q₈×C₄₇	—	8	2	no	—
446	Q₈×C₄₇	C₂²×Q₈	1	4	yes	—
447	C₂×C₄×C₄₇	—	2	4	no	—
448	C₂×C₄×C₄₇	—	2	2	no	—
449	C₂×C₄×C₄₇	—	2	1	no	—
450	C₂×C₄×C₄₇	—	2	1	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	—	4	1	no	—
455	C₂×C₄×C₄₇	—	4	1	no	—
456	C₂×C₄×C₄₇	—	8	1	no	—
457	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
458	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
459	C₂×C₄×C₄₇	C₂²×D₄	1	2	yes	—
460	C₂×C₄×C₄₇	C₂²×D₄	1	2	yes	—
461	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
462	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
463	C₂×C₄×C₄₇	C₂²×D₄	1	2	yes	—
464	C₂×C₄×C₄₇	C₂²×D₄	1	2	yes	—
465	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
466	C₂×C₄×C₄₇	C₂²×Q₈	1	2	yes	—
467	C₂×C₄×C₄₇	2₋¹⁺⁴	1	2	yes	—
468	C₂×C₄×C₄₇	C₂⁵	1	1	yes	characteristic
469	C₂²⋊D₄₇	—	2	4	no	—
470	C₂×Dic₄₇	—	2	1	no	—
471	C₂×Dic₄₇	—	2	1	no	—
472	C₂×Dic₄₇	—	2	1	no	—
473	C₂×Dic₄₇	—	2	2	no	—
474	C₂×Dic₄₇	—	2	2	no	—
475	C₂×Dic₄₇	—	8	1	no	—
476	C₂×Dic₄₇	—	8	1	no	—
477	D₁₈₈	—	2	1	no	—
478	D₁₈₈	C₂²×Q₈	1	2	yes	—
479	C₄×D₄₇	—	2	4	no	—
480	C₄×D₄₇	—	8	1	no	—
481	C₄×D₄₇	—	8	2	no	—
482	C₄×D₄₇	—	8	1	no	—
483	C₄×D₄₇	—	8	2	no	—
484	Dic₉₄	—	2	1	no	—
485	Dic₉₄	—	8	2	no	—
486	Dic₉₄	—	8	2	no	—
487	Dic₉₄	C₂²×Q₈	1	2	yes	—
488	C₄₇⋊C₈	—	2	1	no	—
489	C₄₇⋊C₈	—	2	1	no	—
490	C₄₇⋊C₈	—	2	1	no	—
491	C₄₇⋊C₈	—	2	1	no	—
492	C₄₇⋊C₈	—	2	2	no	—
493	C₄₇⋊C₈	C₂²×Q₈	1	4	yes	—
494	#61386	—	47	1	no	maximal, Sylow
495	C₂²×C₄₇	—	2	1	no	—
496	C₂²×C₄₇	—	2	1	no	—
497	C₂²×C₄₇	D₄×Q₈	1	2	yes	—
498	C₂²×C₄₇	C₂³×D₄	1	1	yes	characteristic
499	C₂×D₄₇	—	2	2	no	—
500	C₂×D₄₇	—	4	1	no	—
501	C₂×D₄₇	—	4	1	no	—
502	C₄×C₄₇	—	2	2	no	—
503	C₄×C₄₇	—	2	1	no	—
504	C₄×C₄₇	—	2	2	no	—
505	C₄×C₄₇	—	2	1	no	—
506	C₄×C₄₇	—	2	2	no	—
507	C₄×C₄₇	—	2	1	no	—
508	C₄×C₄₇	—	2	2	no	—
509	C₄×C₄₇	—	2	1	no	—
510	C₄×C₄₇	—	2	4	no	—
511	C₄×C₄₇	—	4	2	no	—
512	C₄×C₄₇	—	4	1	no	—
513	C₄×C₄₇	—	4	1	no	—
514	C₄×C₄₇	—	4	1	no	—
515	C₄×C₄₇	—	4	1	no	—
516	C₄×C₄₇	D₄×Q₈	1	2	yes	—
517	C₄×C₄₇	C₂³×Q₈	1	1	yes	characteristic
518	C₄×C₄₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
519	Dic₄₇	—	2	2	no	—
520	Dic₄₇	—	4	1	no	—
521	Dic₄₇	—	4	2	no	—
522	Dic₄₇	—	4	1	no	—
523	Dic₄₇	—	4	2	no	—
524	#3504	—	47	1	no	—
525	#3502	D₄₇	1	1	yes	characteristic, complemented
526	#3390	—	47	2	no	—
527	#3390	—	47	2	no	—
528	#3388	—	47	2	no	—
529	#3388	—	47	2	no	—
530	#3387	—	47	2	no	—
531	#3385	—	47	2	no	—
532	#3383	—	47	2	no	—
533	#3381	—	47	2	no	—
534	#3166	—	47	1	no	—
535	#3164	—	47	1	no	—
536	#3163	—	47	1	no	—
537	#3084	—	47	1	no	—
538	#3083	—	47	1	no	—
539	#3082	—	47	1	no	—
540	#3082	—	47	1	no	—
541	#3076	—	47	1	no	—
542	C₂×#479	—	47	1	no	—
543	#2962	—	47	1	no	—
544	#2947	—	47	1	no	—
545	#2947	—	47	1	no	—
546	C₄×#137	—	47	1	no	—
547	C₂×C₄₇	—	2	2	no	—
548	C₂×C₄₇	C₂×D₄×Q₈	1	1	yes	characteristic
549	C₂×C₄₇	#3584	1	1	yes	characteristic
550	C₂×C₄₇	#3586	1	1	yes	characteristic
551	D₄₇	—	4	2	no	—
552	C₂×#137	—	47	1	no	—
553	Q₈²	—	2	1	no	—
554	Q₈²	C₂×D₄₇	1	2	yes	—
555	#557	—	2	1	no	—
556	#557	—	2	1	no	—
557	#557	—	2	1	no	—
558	#557	—	47	2	no	—
559	#557	—	47	2	no	—
560	#557	C₂×D₄₇	1	2	yes	—
561	#557	C₂×D₄₇	1	2	yes	—
562	#557	C₂×D₄₇	1	2	yes	—
563	#554	—	47	2	no	—
564	#554	—	47	2	no	—
565	#554	—	94	2	no	—
566	#554	—	94	2	no	—
567	#544	—	2	2	no	—
568	#544	—	47	1	no	—
569	#544	—	47	1	no	—
570	#544	—	94	1	no	—
571	#544	—	94	1	no	—
572	#544	C₂×D₄₇	1	1	yes	characteristic
573	#544	C₂×D₄₇	1	1	yes	characteristic
574	#533	—	2	2	no	—
575	#533	—	94	1	no	—
576	#533	C₂×D₄₇	1	1	yes	characteristic
577	#533	C₂×D₄₇	1	1	yes	characteristic
578	C₂×#125	—	47	1	no	—
579	C₂×#125	—	94	1	no	—
580	#520	—	47	1	no	—
581	#520	—	47	1	no	—
582	#519	C₂×D₄₇	1	1	yes	characteristic
583	#519	C₂×D₄₇	1	1	yes	characteristic
584	C₄×#41	—	47	1	no	—
585	C₂×C₄×Q₈	C₂×D₄₇	1	1	yes	characteristic
586	#501	—	47	2	no	—
587	#501	—	47	2	no	—
588	#501	—	47	2	no	—
589	#501	—	47	2	no	—
590	#501	—	47	2	no	—
591	#501	—	47	2	no	—
592	#500	—	47	2	no	—
593	#499	—	47	2	no	—
594	#499	—	47	2	no	—
595	#499	—	47	2	no	—
596	#499	—	47	2	no	—
597	#498	—	47	2	no	—
598	#479	—	47	1	no	—
599	#479	—	47	1	no	—
600	#479	—	47	2	no	—
601	#479	—	47	2	no	—
602	#479	—	47	2	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	2	no	—
609	#479	—	47	2	no	—
610	#478	—	47	1	no	—
611	#478	—	47	1	no	—
612	#478	—	47	2	no	—
613	#478	—	47	2	no	—
614	#477	—	47	1	no	—
615	#477	—	47	2	no	—
616	#477	—	47	2	no	—
617	#477	—	47	2	no	—
618	#476	—	47	1	no	—
619	#476	—	47	2	no	—
620	#475	—	47	1	no	—
621	#475	—	47	2	no	—
622	#475	—	47	2	no	—
623	#475	—	47	2	no	—
624	#474	—	47	1	no	—
625	#474	—	47	2	no	—
626	#446	—	47	2	no	—
627	#446	—	47	2	no	—
628	#446	—	47	2	no	—
629	C₈×Q₈	—	47	2	no	—
630	#441	—	47	2	no	—
631	#441	—	47	2	no	—
632	#441	—	47	2	no	—
633	#440	—	47	2	no	—
634	#440	—	47	2	no	—
635	#440	—	47	2	no	—
636	C₄×Q₁₆	—	47	2	no	—
637	C₄×Q₁₆	—	47	2	no	—
638	C₄×Q₁₆	—	47	2	no	—
639	C₄×SD₁₆	—	47	2	no	—
640	C₄×SD₁₆	—	47	2	no	—
641	C₄×SD₁₆	—	47	2	no	—
642	#428	—	47	1	no	—
643	#428	—	47	1	no	—
644	#428	—	47	1	no	—
645	#428	—	47	1	no	—
646	#428	—	47	1	no	—
647	#427	—	47	1	no	—
648	#427	—	47	1	no	—
649	C₂×#107	—	47	1	no	—
650	C₂×#106	—	47	1	no	—
651	#424	—	47	1	no	—
652	#424	—	47	1	no	—
653	C₂×C₄⋊C₈	—	47	1	no	—
654	#419	—	47	1	no	—
655	#417	—	47	1	no	—
656	#416	—	47	1	no	—
657	#416	—	47	1	no	—
658	C₂×#103	—	47	1	no	—
659	C₂×#103	—	47	1	no	—
660	#405	—	47	1	no	—
661	#405	—	47	1	no	—
662	C₄×M₁₆	—	47	1	no	—
663	C₄₇	#61386	1	1	yes	characteristic, complemented, Sylow
664	C₂×#41	—	47	1	no	—
665	C₂²×Q₈	C₂²×D₄₇	1	1	yes	characteristic
666	#137	—	47	8	no	—
667	C₂×Q₁₆	—	47	2	no	—
668	C₂×SD₁₆	—	47	2	no	—
669	C₂×M₁₆	—	47	1	no	—
670	C₂×M₁₆	—	47	1	no	—
671	C₂²×C₈	—	47	1	no	—
672	C₂²×C₈	—	47	1	no	—
673	C₄⋊Q₈	—	2	2	no	—
674	C₄⋊Q₈	—	2	2	no	—
675	C₄⋊Q₈	—	2	2	no	—
676	C₄⋊Q₈	—	2	2	no	—
677	C₄⋊Q₈	—	2	2	no	—
678	C₄⋊Q₈	—	2	2	no	—
679	C₄⋊Q₈	—	2	1	no	—
680	C₄⋊Q₈	—	2	1	no	—
681	C₄⋊Q₈	—	47	2	no	—
682	C₄⋊Q₈	—	47	2	no	—
683	C₄⋊Q₈	—	94	2	no	—
684	C₄⋊Q₈	—	94	2	no	—
685	C₄⋊Q₈	—	94	1	no	—
686	C₄⋊Q₈	—	94	1	no	—
687	C₄⋊Q₈	C₂²⋊D₄₇	1	1	yes	characteristic
688	C₄⋊Q₈	C₂²⋊D₄₇	1	1	yes	characteristic
689	C₄⋊Q₈	C₂²×D₄₇	1	1	yes	characteristic
690	C₄⋊Q₈	C₂²×D₄₇	1	1	yes	characteristic
691	C₄⋊Q₈	C₂²×D₄₇	1	2	yes	—
692	C₄⋊Q₈	C₂²×D₄₇	1	2	yes	—
693	#125	—	2	2	no	—
694	#125	—	2	2	no	—
695	#125	—	2	2	no	—
696	#125	—	2	2	no	—
697	#125	—	2	2	no	—
698	#125	—	2	2	no	—
699	#125	—	2	1	no	—
700	#125	—	2	1	no	—
701	#125	—	47	2	no	—
702	#125	—	47	2	no	—
703	#125	—	47	2	no	—
704	#125	—	47	2	no	—
705	#125	—	94	1	no	—
706	#125	—	94	1	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	1	yes	characteristic
714	#125	C₂²⋊D₄₇	1	1	yes	characteristic
715	#125	C₂²×D₄₇	1	1	yes	characteristic
716	#125	C₂²×D₄₇	1	1	yes	characteristic
717	#125	C₂²×D₄₇	1	2	yes	—
718	#125	C₂²×D₄₇	1	2	yes	—
719	C₂²⋊Q₈	—	2	1	no	—
720	C₂²⋊Q₈	—	2	1	no	—
721	C₂²⋊Q₈	—	2	2	no	—
722	C₂²⋊Q₈	—	2	2	no	—
723	C₂²⋊Q₈	—	94	2	no	—
724	C₂²⋊Q₈	—	94	2	no	—
725	C₂²⋊Q₈	—	94	2	no	—
726	C₂²⋊Q₈	—	94	2	no	—
727	C₂²⋊Q₈	—	94	2	no	—
728	C₂²⋊Q₈	—	94	2	no	—
729	C₂²⋊Q₈	—	94	2	no	—
730	C₂²⋊Q₈	—	94	2	no	—
731	C₂²⋊Q₈	C₂²⋊D₄₇	1	2	yes	—
732	C₂²⋊Q₈	C₂²⋊D₄₇	1	2	yes	—
733	C₄×Q₈	—	2	2	no	—
734	C₄×Q₈	—	2	1	no	—
735	C₄×Q₈	—	2	1	no	—
736	C₄×Q₈	—	2	1	no	—
737	C₄×Q₈	—	2	1	no	—
738	C₄×Q₈	—	2	2	no	—
739	C₄×Q₈	—	2	2	no	—
740	C₄×Q₈	—	2	2	no	—
741	C₄×Q₈	—	2	1	no	—
742	C₄×Q₈	—	2	1	no	—
743	C₄×Q₈	—	2	1	no	—
744	C₄×Q₈	—	2	1	no	—
745	C₄×Q₈	—	47	1	no	—
746	C₄×Q₈	—	47	1	no	—
747	C₄×Q₈	—	47	2	no	—
748	C₄×Q₈	—	47	2	no	—
749	C₄×Q₈	—	94	2	no	—
750	C₄×Q₈	—	94	2	no	—
751	C₄×Q₈	C₂²×D₄₇	1	2	yes	—
752	C₄×Q₈	C₂²×D₄₇	1	2	yes	—
753	C₄×Q₈	C₂²×D₄₇	1	2	yes	—
754	C₄×Q₈	C₂²×D₄₇	1	2	yes	—
755	C₄×Q₈	C₂²×D₄₇	1	2	yes	—
756	C₄×Q₈	C₂²×D₄₇	1	2	yes	—
757	C₄×Q₈	C₂²×D₄₇	1	2	yes	—
758	C₄×Q₈	C₂²×D₄₇	1	2	yes	—
759	C₄×D₄	—	47	1	no	—
760	C₄×D₄	—	47	1	no	—
761	C₄×D₄	—	47	2	no	—
762	C₄×D₄	—	47	2	no	—
763	C₄×D₄	—	94	1	no	—
764	C₄×D₄	—	94	1	no	—
765	C₄×D₄	—	94	2	no	—
766	C₄×D₄	—	94	2	no	—
767	#117	—	2	2	no	—
768	#117	—	2	2	no	—
769	#117	—	47	1	no	—
770	#117	—	94	1	no	—
771	#117	—	94	1	no	—
772	#117	—	94	1	no	—
773	#117	C₂²×D₄₇	1	1	yes	characteristic
774	#117	C₂²×D₄₇	1	1	yes	characteristic
775	#117	C₂²×D₄₇	1	1	yes	characteristic
776	#117	C₂²×D₄₇	1	1	yes	characteristic
777	C₂×C₄⋊C₄	—	2	1	no	—
778	C₂×C₄⋊C₄	—	47	1	no	—
779	C₂×C₄⋊C₄	—	47	1	no	—
780	C₂×C₄⋊C₄	—	94	1	no	—
781	C₂×C₄⋊C₄	—	94	1	no	—
782	C₂×C₄⋊C₄	—	94	1	no	—
783	C₂×C₄⋊C₄	—	94	1	no	—
784	C₂×C₄⋊C₄	—	94	2	no	—
785	C₂×C₄⋊C₄	—	94	2	no	—
786	C₂×C₄⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
787	C₂×C₄²	—	2	1	no	—
788	C₂×C₄²	—	94	1	no	—
789	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
790	#107	—	47	2	no	—
791	#107	—	47	2	no	—
792	#107	—	47	1	no	—
793	#107	—	47	1	no	—
794	#107	—	47	1	no	—
795	#107	—	47	1	no	—
796	#107	—	47	2	no	—
797	#107	—	47	2	no	—
798	#107	—	47	2	no	—
799	#107	—	47	2	no	—
800	#107	—	47	2	no	—
801	#106	—	47	2	no	—
802	#106	—	47	2	no	—
803	#106	—	47	1	no	—
804	#106	—	47	1	no	—
805	#106	—	47	1	no	—
806	#106	—	47	1	no	—
807	#106	—	47	2	no	—
808	#106	—	47	2	no	—
809	#106	—	47	2	no	—
810	#106	—	47	2	no	—
811	#106	—	47	2	no	—
812	C₄⋊C₈	—	47	1	no	—
813	C₄⋊C₈	—	47	1	no	—
814	C₄⋊C₈	—	47	1	no	—
815	C₄⋊C₈	—	47	1	no	—
816	C₄⋊C₈	—	47	2	no	—
817	C₄⋊C₈	—	47	2	no	—
818	C₄⋊C₈	—	47	2	no	—
819	C₄⋊C₈	—	47	2	no	—
820	#103	—	47	2	no	—
821	#103	—	47	2	no	—
822	#103	—	47	2	no	—
823	#103	—	47	2	no	—
824	#103	—	47	2	no	—
825	#103	—	47	2	no	—
826	#103	—	47	1	no	—
827	#103	—	47	1	no	—
828	#103	—	47	1	no	—
829	#103	—	47	1	no	—
830	#103	—	47	2	no	—
831	#102	—	47	1	no	—
832	#102	—	47	1	no	—
833	#102	—	47	1	no	—
834	#102	—	47	1	no	—
835	#102	—	47	2	no	—
836	#97	—	47	2	no	—
837	#97	—	47	2	no	—
838	#97	—	47	2	no	—
839	C₄×C₈	—	47	2	no	—
840	C₄×C₈	—	47	2	no	—
841	C₄×C₈	—	47	2	no	—
842	#41	—	47	4	no	—
843	#41	—	94	2	no	—
844	C₂×Q₈	—	2	1	no	—
845	C₂×Q₈	—	2	1	no	—
846	C₂×Q₈	—	2	1	no	—
847	C₂×Q₈	—	2	2	no	—
848	C₂×Q₈	—	2	2	no	—
849	C₂×Q₈	—	2	2	no	—
850	C₂×Q₈	—	47	1	no	—
851	C₂×Q₈	—	94	2	no	—
852	C₂×Q₈	—	94	2	no	—
853	C₂×Q₈	Q₈×D₄₇	1	4	yes	—
854	C₂×Q₈	C₂×C₂²⋊D₄₇	1	2	yes	—
855	C₂×Q₈	C₂×C₂²⋊D₄₇	1	2	yes	—
856	C₂×Q₈	C₂³×D₄₇	1	2	yes	—
857	C₂×D₄	—	47	1	no	—
858	C₂×D₄	—	94	1	no	—
859	C₂²×C₄	—	2	1	no	—
860	C₂²×C₄	—	2	1	no	—
861	C₂²×C₄	—	94	1	no	—
862	C₂²×C₄	—	94	1	no	—
863	C₂²×C₄	—	94	1	no	—
864	C₂²×C₄	—	94	1	no	—
865	C₂²×C₄	—	94	1	no	—
866	C₂²×C₄	—	94	2	no	—
867	C₂²×C₄	—	94	2	no	—
868	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
869	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
870	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
871	Q₁₆	—	47	8	no	—
872	SD₁₆	—	47	8	no	—
873	M₁₆	—	47	4	no	—
874	M₁₆	—	94	2	no	—
875	C₂×C₈	—	47	2	no	—
876	C₂×C₈	—	47	1	no	—
877	C₂×C₈	—	47	1	no	—
878	C₂×C₈	—	47	2	no	—
879	C₂×C₈	—	47	1	no	—
880	C₂×C₈	—	47	1	no	—
881	C₂×C₈	—	94	2	no	—
882	C₂×C₈	—	94	2	no	—
883	C₄⋊C₄	—	2	2	no	—
884	C₄⋊C₄	—	2	2	no	—
885	C₄⋊C₄	—	2	1	no	—
886	C₄⋊C₄	—	2	2	no	—
887	C₄⋊C₄	—	2	2	no	—
888	C₄⋊C₄	—	2	2	no	—
889	C₄⋊C₄	—	2	2	no	—
890	C₄⋊C₄	—	2	1	no	—
891	C₄⋊C₄	—	2	1	no	—
892	C₄⋊C₄	—	2	1	no	—
893	C₄⋊C₄	—	2	1	no	—
894	C₄⋊C₄	—	2	2	no	—
895	C₄⋊C₄	—	2	2	no	—
896	C₄⋊C₄	—	2	2	no	—
897	C₄⋊C₄	—	2	2	no	—
898	C₄⋊C₄	—	2	1	no	—
899	C₄⋊C₄	—	2	1	no	—
900	C₄⋊C₄	—	2	2	no	—
901	C₄⋊C₄	—	2	2	no	—
902	C₄⋊C₄	—	47	2	no	—
903	C₄⋊C₄	—	47	1	no	—
904	C₄⋊C₄	—	47	2	no	—
905	C₄⋊C₄	—	47	1	no	—
906	C₄⋊C₄	—	94	2	no	—
907	C₄⋊C₄	—	94	2	no	—
908	C₄⋊C₄	—	94	2	no	—
909	C₄⋊C₄	—	94	2	no	—
910	C₄⋊C₄	—	94	2	no	—
911	C₄⋊C₄	—	94	2	no	—
912	C₄⋊C₄	—	94	2	no	—
913	C₄⋊C₄	—	94	2	no	—
914	C₄⋊C₄	—	94	1	no	—
915	C₄⋊C₄	—	94	1	no	—
916	C₄⋊C₄	—	94	2	no	—
917	C₄⋊C₄	—	94	2	no	—
918	C₄⋊C₄	—	94	1	no	—
919	C₄⋊C₄	—	94	1	no	—
920	C₄⋊C₄	—	94	2	no	—
921	C₄⋊C₄	—	94	2	no	—
922	C₄⋊C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
923	C₄⋊C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
924	C₄⋊C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
925	C₄⋊C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
926	C₄⋊C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
927	C₄⋊C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
928	C₄⋊C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
929	C₄⋊C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
930	C₄⋊C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
931	C₄⋊C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
932	C₄⋊C₄	C₂³×D₄₇	1	2	yes	—
933	C₄⋊C₄	C₂³×D₄₇	1	1	yes	characteristic
934	C₄⋊C₄	C₂³×D₄₇	1	1	yes	characteristic
935	C₄⋊C₄	C₂³×D₄₇	1	1	yes	characteristic
936	C₄⋊C₄	C₂³×D₄₇	1	1	yes	characteristic
937	C₂²⋊C₄	—	2	1	no	—
938	C₂²⋊C₄	—	2	1	no	—
939	C₂²⋊C₄	—	94	1	no	—
940	C₂²⋊C₄	—	94	1	no	—
941	C₂²⋊C₄	—	94	1	no	—
942	C₂²⋊C₄	—	94	2	no	—
943	C₂²⋊C₄	—	94	2	no	—
944	C₂²⋊C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
945	C₂²⋊C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
946	C₄²	—	2	2	no	—
947	C₄²	—	2	2	no	—
948	C₄²	—	2	2	no	—
949	C₄²	—	2	2	no	—
950	C₄²	—	2	2	no	—
951	C₄²	—	2	2	no	—
952	C₄²	—	2	1	no	—
953	C₄²	—	2	1	no	—
954	C₄²	—	94	1	no	—
955	C₄²	—	94	1	no	—
956	C₄²	—	94	1	no	—
957	C₄²	—	94	2	no	—
958	C₄²	—	94	2	no	—
959	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
960	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
961	C₄²	C₂³×D₄₇	1	1	yes	characteristic
962	C₄²	C₂³×D₄₇	1	2	yes	—
963	C₄²	C₂³×D₄₇	1	2	yes	—
964	C₄²	C₂³×D₄₇	1	1	yes	characteristic
965	C₂³	—	94	1	no	—
966	C₂³	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
967	Q₈	—	2	4	no	—
968	Q₈	—	2	2	no	—
969	Q₈	—	4	2	no	—
970	Q₈	—	4	2	no	—
971	Q₈	—	4	2	no	—
972	Q₈	—	8	1	no	—
973	Q₈	—	8	2	no	—
974	Q₈	—	8	2	no	—
975	Q₈	—	47	2	no	—
976	Q₈	—	94	1	no	—
977	Q₈	—	376	2	no	—
978	Q₈	—	376	2	no	—
979	Q₈	C₂×Q₈×D₄₇	1	4	yes	—
980	D₄	—	47	2	no	—
981	D₄	—	94	4	no	—
982	D₄	—	94	1	no	—
983	C₂×C₄	—	2	4	no	—
984	C₂×C₄	—	2	2	no	—
985	C₂×C₄	—	2	1	no	—
986	C₂×C₄	—	2	1	no	—
987	C₂×C₄	—	2	1	no	—
988	C₂×C₄	—	2	1	no	—
989	C₂×C₄	—	2	2	no	—
990	C₂×C₄	—	4	1	no	—
991	C₂×C₄	—	4	1	no	—
992	C₂×C₄	—	8	1	no	—
993	C₂×C₄	—	94	1	no	—
994	C₂×C₄	—	94	4	no	—
995	C₂×C₄	—	94	1	no	—
996	C₂×C₄	—	94	1	no	—
997	C₂×C₄	—	94	2	no	—
998	C₂×C₄	—	94	2	no	—
999	C₂×C₄	—	376	1	no	—
1000	C₂×C₄	—	376	2	no	—
1001	C₂×C₄	—	376	1	no	—
1002	C₂×C₄	—	376	2	no	—
1003	C₂×C₄	—	376	1	no	—
1004	C₂×C₄	—	376	1	no	—
1005	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
1006	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
1007	C₂×C₄	C₂²×C₂²⋊D₄₇	1	2	yes	—
1008	C₂×C₄	C₂²×C₂²⋊D₄₇	1	2	yes	—
1009	C₂×C₄	C₂²×C₂²⋊D₄₇	1	2	yes	—
1010	C₂×C₄	C₂²×C₂²⋊D₄₇	1	2	yes	—
1011	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
1012	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
1013	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
1014	C₂×C₄	C₂×Q₈×D₄₇	1	2	yes	—
1015	C₂×C₄	#13094072	1	2	yes	—
1016	C₂×C₄	C₂⁴×D₄₇	1	1	yes	characteristic
1017	C₈	—	47	4	no	—
1018	C₈	—	94	1	no	—
1019	C₈	—	94	1	no	—
1020	C₈	—	94	1	no	—
1021	C₈	—	94	1	no	—
1022	C₈	—	94	2	no	—
1023	C₂²	—	2	1	no	—
1024	C₂²	—	2	1	no	—
1025	C₂²	—	94	2	no	—
1026	C₂²	—	188	1	no	—
1027	C₂²	—	188	1	no	—
1028	C₂²	Q₈×C₂²⋊D₄₇	1	2	yes	—
1029	C₂²	C₂³×C₂²⋊D₄₇	1	1	yes	characteristic
1030	C₄	—	2	4	no	—
1031	C₄	—	2	1	no	—
1032	C₄	—	2	1	no	—
1033	C₄	—	2	2	no	—
1034	C₄	—	2	2	no	—
1035	C₄	—	2	1	no	—
1036	C₄	—	2	1	no	—
1037	C₄	—	2	2	no	—
1038	C₄	—	2	2	no	—
1039	C₄	—	4	2	no	—
1040	C₄	—	4	1	no	—
1041	C₄	—	4	1	no	—
1042	C₄	—	4	1	no	—
1043	C₄	—	4	1	no	—
1044	C₄	—	94	2	no	—
1045	C₄	—	188	2	no	—
1046	C₄	—	188	1	no	—
1047	C₄	—	188	2	no	—
1048	C₄	—	188	1	no	—
1049	C₄	Q₈×C₂²⋊D₄₇	1	2	yes	—
1050	C₄	C₂²×Q₈×D₄₇	1	1	yes	characteristic
1051	C₄	C₂×#13094072	1	1	yes	characteristic
1052	C₂	—	2	2	no	—
1053	C₂	—	188	2	no	—
1054	C₂	C₂×Q₈×C₂²⋊D₄₇	1	1	yes	characteristic
1055	C₂	#20258159	1	1	yes	characteristic
1056	C₂	#20258175	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	C₂×#10625350	C₂³
hypercenter	#3502	D₄₇
hypocenter	C₄₇	#61386
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. #20256351	C₂	semidirect
4. #20256327	C₂	semidirect
5. #20256327	C₂	semidirect
6. #20256316	C₂	semidirect
7. #20256294	C₂	semidirect
8. #20256275	C₂	semidirect
9. #20256259	C₂	semidirect
10. #20253941	C₂	semidirect
11. #20253922	C₂	semidirect
12. #20253914	C₂	semidirect
15. #20253230	C₂	semidirect
16. #20253230	C₂	semidirect
18. C₂×#15689430	C₂	semidirect
19. #20252337	C₂	semidirect
23. C₄₇×#3502	C₂	semidirect
136. #13094055	Q₈	semidirect
525. #3502	D₄₇	semidirect
663. C₄₇	#61386	semidirect

Maximal subgroups

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

subgroup	index
#20257209	2
#20256351	2
#20256327	2
#20256316	2
#20256294	2
#20256275	2
#20256259	2
#20253941	2
#20253922	2
#20253914	2
#20253246	2
#20253235	2
#20253230	2
#20253170	2
C₂×#15689430	2
#20252337	2
#20252231	2
C₄×#13094055	2
C₄₇×#3502	2
#61386	47