Subgroups — #27106837

Order 12032.

1650 conjugacy classes of subgroups.

The subgroup lattice has 1072 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20257200	C₂	1	1	yes	maximal, characteristic, complemented
2	#20256351	C₂	1	2	yes	maximal, complemented
3	#20256305	C₂	1	2	yes	maximal, complemented
4	#20256298	C₂	1	1	yes	maximal, characteristic, complemented
5	#20256294	C₂	1	1	yes	maximal, characteristic, complemented
6	Q₈×#10625337	C₂	1	1	yes	maximal, characteristic, complemented
7	#20256251	C₂	1	1	yes	maximal, characteristic, complemented
8	#20256224	C₂	1	2	yes	maximal, complemented
9	#20256165	C₂	1	1	yes	maximal, characteristic, complemented
10	#20256124	C₂	1	1	yes	maximal, characteristic, complemented
11	#20256102	C₂	1	2	yes	maximal, complemented
12	#20256062	C₂	1	1	yes	maximal, characteristic, complemented
13	#20256033	C₂	1	1	yes	maximal, characteristic, complemented
14	#20254665	C₂	1	2	yes	maximal, complemented
15	#20254650	C₂	1	2	yes	maximal, complemented
16	#20254606	C₂	1	1	yes	maximal, characteristic, complemented
17	#20254536	C₂	1	1	yes	maximal, characteristic, complemented
18	#20253644	C₂	1	2	yes	maximal
19	#20253596	C₂	1	2	yes	maximal, complemented
20	#20253544	C₂	1	1	yes	maximal, characteristic, complemented
21	#20253400	C₂	1	1	yes	maximal, characteristic
22	#20252483	C₂	1	1	yes	maximal, characteristic, complemented
23	C₄₇×#3555	C₂	1	1	yes	maximal, characteristic, complemented
24	Q₈×Dic₉₄	C₂²	1	1	yes	characteristic
25	Q₈×Dic₉₄	C₂²	1	1	yes	characteristic
26	#15689851	C₂²	1	2	yes	—
27	#15689833	C₂²	1	1	yes	characteristic
28	#15689833	C₂²	1	1	yes	characteristic
29	#15689831	—	2	1	no	—
30	#15689831	—	2	1	no	—
31	Q₈×D₁₈₈	C₂²	1	2	yes	—
32	#15689786	—	2	2	no	—
33	#15689753	—	2	2	no	—
34	#15689751	C₂²	1	2	yes	—
35	#15689678	—	2	1	no	—
36	C₂×#13094024	C₂²	1	1	yes	characteristic
37	C₄⋊Q₈×D₄₇	—	2	1	no	—
38	#15689603	C₂²	1	2	yes	—
39	C₄×#10625350	C₂²	1	1	yes	characteristic
40	#15689533	C₂²	1	2	yes	—
41	#15689533	C₂²	1	2	yes	—
42	#15689529	C₂²	1	2	yes	—
43	#15689526	C₂²	1	2	yes	—
44	#15689526	C₂²	1	1	yes	characteristic
45	#15689526	C₂²	1	1	yes	characteristic
46	#15689522	C₂²	1	2	yes	—
47	#15689491	C₂²	1	2	yes	—
48	#15689482	C₂²	1	2	yes	—
49	#15689482	C₂²	1	2	yes	—
50	#15689477	C₂²	1	2	yes	—
51	#15689473	C₂²	1	1	yes	characteristic
52	#15689473	C₂²	1	2	yes	—
53	#15689473	C₂²	1	1	yes	characteristic
54	#15689461	C₂²	1	2	yes	—
55	#15689461	C₂²	1	1	yes	characteristic
56	#15689456	C₂²	1	2	yes	—
57	#15689456	C₂²	1	2	yes	—
58	#15689451	C₂²	1	2	yes	—
59	#15689444	C₂²	1	1	yes	characteristic
60	#15689434	C₂²	1	2	yes	—
61	#15689430	C₂²	1	2	yes	—
62	#15689430	C₂²	1	2	yes	—
63	#15689430	C₂²	1	2	yes	—
64	#15689427	C₂²	1	2	yes	—
65	#15689427	C₂²	1	1	yes	characteristic
66	#15689423	C₂²	1	2	yes	—
67	#15689420	C₂²	1	1	yes	characteristic
68	#15689420	C₂²	1	2	yes	—
69	#15689418	C₂²	1	2	yes	—
70	#15689418	C₂²	1	1	yes	characteristic
71	#15689418	C₂²	1	1	yes	characteristic
72	#15689418	C₂²	1	2	yes	—
73	#15689418	C₂²	1	2	yes	—
74	#15689418	C₂²	1	2	yes	—
75	#15689415	C₂²	1	1	yes	characteristic
76	#15689415	C₂²	1	2	yes	—
77	#15689413	C₂²	1	1	yes	characteristic
78	#15689413	C₂²	1	1	yes	characteristic
79	#15689410	C₂²	1	1	yes	characteristic
80	#15689408	C₂²	1	2	yes	—
81	#15689403	C₂²	1	2	yes	—
82	#15689400	C₂²	1	2	yes	—
83	#15689342	C₂²	1	2	yes	—
84	#15689342	C₂²	1	1	yes	characteristic
85	#15689335	C₂²	1	2	yes	—
86	#15689335	C₂²	1	1	yes	characteristic
87	#15689330	C₂²	1	1	yes	characteristic
88	#15689330	C₂²	1	2	yes	—
89	#15689325	C₂²	1	1	yes	characteristic
90	#15689325	C₂²	1	2	yes	—
91	#15689283	C₂²	1	2	yes	—
92	#15689283	C₂²	1	1	yes	characteristic
93	#15689266	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	#15689254	C₂²	1	2	yes	—
98	Q₈×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
99	Q₈×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
100	#15689228	C₂²	1	2	yes	—
101	#15689228	C₂²	1	2	yes	—
102	#15689223	C₂²	1	2	yes	—
103	#15689221	C₂²	1	2	yes	—
104	#15689221	C₂²	1	2	yes	—
105	#15689221	C₂²	1	2	yes	—
106	C₄×#10625337	C₂²	1	1	yes	characteristic
107	C₄×#10625337	C₂²	1	2	yes	—
108	C₄×#10625337	C₂²	1	2	yes	—
109	C₄×#10625336	C₂²	1	2	yes	—
110	C₄×#10625336	C₂²	1	1	yes	characteristic
111	C₄×#10625335	C₂²	1	1	yes	characteristic
112	C₄×#10625334	C₂²	1	1	yes	characteristic
113	C₄×#10625334	C₂²	1	2	yes	—
114	#15689184	C₂²	1	2	yes	—
115	#15689184	C₂²	1	2	yes	—
116	#15689180	C₂²	1	1	yes	characteristic
117	#15689176	C₂²	1	1	yes	characteristic
118	C₄₇×#563	—	2	2	no	—
119	Q₈²×C₄₇	C₂²	1	1	yes	characteristic
120	C₄₇×#557	C₂²	1	1	yes	characteristic
121	C₄₇×#557	C₂²	1	2	yes	—
122	C₄₇×#556	—	2	1	no	—
123	C₄₇×#556	C₂²	1	1	yes	characteristic
124	C₄₇×#556	C₂²	1	2	yes	—
125	C₄₇×#554	C₂²	1	1	yes	characteristic
126	C₄₇×#552	—	2	1	no	—
127	C₄₇×#544	—	2	1	no	—
128	C₄₇×#542	C₂²	1	2	yes	—
129	C₄₇×#541	—	2	1	no	—
130	C₄₇×#541	—	2	2	no	—
131	C₄₇×#541	C₂²	1	2	yes	—
132	C₄₇×#533	C₂²	1	1	yes	characteristic
133	C₄₇×#533	C₂²	1	1	yes	characteristic
134	C₄₇×#529	C₂²	1	1	yes	characteristic
135	C₂×#10625350	C₂³	1	1	yes	characteristic
136	C₂²×Dic₉₄	—	2	1	no	—
137	C₂×Q₈×D₄₇	—	2	2	no	—
138	C₂×#10625337	C₂³	1	1	yes	characteristic
139	C₂×#10625337	C₂³	1	2	yes	—
140	C₂×#10625335	C₂³	1	1	yes	characteristic
141	C₂×#10625336	C₂³	1	1	yes	characteristic
142	C₂×#10625336	C₂³	1	2	yes	—
143	C₂×#10625334	C₂³	1	1	yes	characteristic
144	#13094024	—	2	1	no	—
145	#13094024	—	2	1	no	—
146	#13094024	C₂³	1	2	yes	—
147	#13094024	C₂³	1	1	yes	characteristic
148	#13094024	C₂³	1	1	yes	characteristic
149	#13094024	C₂³	1	2	yes	—
150	#13094024	C₂³	1	2	yes	—
151	#13094023	—	2	2	no	—
152	#13094023	—	2	2	no	—
153	#13094023	—	2	2	no	—
154	#13094023	—	2	1	no	—
155	#13094023	—	2	1	no	—
156	#13094022	—	2	2	no	—
157	#13094016	C₂³	1	2	yes	—
158	#13094016	C₂³	1	2	yes	—
159	#13094015	—	2	2	no	—
160	#13094014	—	2	2	no	—
161	#13094014	—	2	2	no	—
162	#13094004	—	2	2	no	—
163	#13094004	—	2	2	no	—
164	#13094004	—	2	2	no	—
165	#13094002	—	2	2	no	—
166	#13094002	—	2	2	no	—
167	#13094001	—	2	2	no	—
168	#13094001	—	2	2	no	—
169	#13094000	—	2	1	no	—
170	#13094000	—	2	1	no	—
171	Q₈×Dic₄₇	—	2	1	no	—
172	Q₈×Dic₄₇	—	2	1	no	—
173	C₄×Dic₉₄	C₂³	1	2	yes	—
174	C₄×Dic₉₄	C₂³	1	2	yes	—
175	C₄×Dic₉₄	C₂³	1	1	yes	characteristic
176	C₄×Dic₉₄	C₂³	1	1	yes	characteristic
177	#13093989	—	2	2	no	—
178	C₄×D₁₈₈	C₂³	1	1	yes	characteristic
179	C₄×D₁₈₈	C₂³	1	2	yes	—
180	C₄×D₁₈₈	C₂³	1	2	yes	—
181	C₄×D₁₈₈	C₂³	1	1	yes	characteristic
182	C₄×C₂²⋊D₄₇	—	2	1	no	—
183	C₄×C₂²⋊D₄₇	—	2	1	no	—
184	(C₂²⋊D₄₇)⋊C₄	—	2	2	no	—
185	(C₂²⋊D₄₇)⋊C₄	—	2	2	no	—
186	#13093983	C₂³	1	1	yes	characteristic
187	#13093982	—	2	2	no	—
188	#13093981	—	2	1	no	—
189	C₂×C₄⋊Dic₄₇	—	2	1	no	—
190	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
191	C₄⋊C₄×D₄₇	—	2	2	no	—
192	C₄⋊C₄×D₄₇	—	2	1	no	—
193	C₄⋊C₄×D₄₇	—	2	1	no	—
194	C₄²×D₄₇	—	2	1	no	—
195	#13093957	C₂³	1	1	yes	characteristic
196	#13093957	C₂³	1	2	yes	—
197	#13093957	C₂³	1	2	yes	—
198	#13093957	C₂³	1	2	yes	—
199	#13093957	C₂³	1	2	yes	—
200	#13093957	C₂³	1	2	yes	—
201	#13093957	C₂³	1	2	yes	—
202	#13093957	C₂³	1	1	yes	characteristic
203	#13093957	C₂³	1	2	yes	—
204	#13093955	C₂³	1	2	yes	—
205	#13093955	C₂³	1	2	yes	—
206	#13093955	C₂³	1	1	yes	characteristic
207	#13093955	C₂³	1	1	yes	characteristic
208	#13093955	C₂³	1	2	yes	—
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	1	yes	characteristic
215	C₄⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
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	2	yes	—
220	#13093948	C₂³	1	2	yes	—
221	#13093948	C₂³	1	2	yes	—
222	#13093948	C₂³	1	2	yes	—
223	#13093948	C₂³	1	2	yes	—
224	#13093948	C₂³	1	2	yes	—
225	#13093948	C₂³	1	2	yes	—
226	#13093948	C₂³	1	1	yes	characteristic
227	#13093947	C₂³	1	1	yes	characteristic
228	#13093947	C₂³	1	2	yes	—
229	#13093947	C₂³	1	1	yes	characteristic
230	#13093945	C₂³	1	1	yes	characteristic
231	#13093945	C₂³	1	2	yes	—
232	#13093945	C₂³	1	1	yes	characteristic
233	#13093945	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	#13093935	C₂³	1	2	yes	—
243	C₄×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
244	C₄×C₄₇⋊C₈	C₂³	1	2	yes	—
245	C₄×C₄₇⋊C₈	C₂³	1	2	yes	—
246	C₄×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
247	C₄⋊Q₈×C₄₇	—	2	2	no	—
248	C₄⋊Q₈×C₄₇	—	2	2	no	—
249	C₄⋊Q₈×C₄₇	—	2	1	no	—
250	C₄⋊Q₈×C₄₇	D₄	1	1	yes	characteristic
251	C₄⋊Q₈×C₄₇	D₄	1	1	yes	characteristic
252	C₄⋊Q₈×C₄₇	C₂³	1	1	yes	characteristic
253	C₄⋊Q₈×C₄₇	C₂³	1	2	yes	—
254	C₄⋊Q₈×C₄₇	C₂³	1	1	yes	characteristic
255	C₄⋊Q₈×C₄₇	C₂³	1	2	yes	—
256	#126×C₄₇	—	2	2	no	—
257	#126×C₄₇	—	2	2	no	—
258	#126×C₄₇	—	2	2	no	—
259	#126×C₄₇	—	2	2	no	—
260	#126×C₄₇	—	2	2	no	—
261	#126×C₄₇	—	2	2	no	—
262	#126×C₄₇	—	2	1	no	—
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	1	no	—
269	#125×C₄₇	—	2	1	no	—
270	#125×C₄₇	D₄	1	2	yes	—
271	#125×C₄₇	C₂³	1	2	yes	—
272	#125×C₄₇	C₂³	1	1	yes	characteristic
273	#124×C₄₇	—	2	2	no	—
274	#124×C₄₇	C₂³	1	2	yes	—
275	#124×C₄₇	C₂³	1	1	yes	characteristic
276	#123×C₄₇	—	2	1	no	—
277	#123×C₄₇	—	2	2	no	—
278	C₂²⋊Q₈×C₄₇	—	2	1	no	—
279	C₂²⋊Q₈×C₄₇	—	2	1	no	—
280	C₂²⋊Q₈×C₄₇	—	2	2	no	—
281	C₂²⋊Q₈×C₄₇	—	2	1	no	—
282	C₂²⋊Q₈×C₄₇	—	2	2	no	—
283	C₂²⋊Q₈×C₄₇	—	2	2	no	—
284	C₂²⋊Q₈×C₄₇	D₄	1	2	yes	—
285	C₂²⋊Q₈×C₄₇	D₄	1	1	yes	characteristic
286	C₂²⋊Q₈×C₄₇	D₄	1	1	yes	characteristic
287	C₂²⋊Q₈×C₄₇	C₂³	1	1	yes	characteristic
288	C₂²⋊Q₈×C₄₇	C₂³	1	2	yes	—
289	#121×C₄₇	C₂³	1	1	yes	characteristic
290	C₄×Q₈×C₄₇	—	2	1	no	—
291	C₄×Q₈×C₄₇	—	2	1	no	—
292	C₄×Q₈×C₄₇	—	2	2	no	—
293	C₄×Q₈×C₄₇	—	2	1	no	—
294	C₄×Q₈×C₄₇	C₂³	1	2	yes	—
295	C₄×Q₈×C₄₇	C₂³	1	2	yes	—
296	C₄×Q₈×C₄₇	C₂³	1	1	yes	characteristic
297	C₄×Q₈×C₄₇	C₂³	1	2	yes	—
298	C₄×Q₈×C₄₇	C₂³	1	2	yes	—
299	C₄×Q₈×C₄₇	C₂³	1	1	yes	characteristic
300	C₄×Q₈×C₄₇	C₂³	1	1	yes	characteristic
301	C₄×Q₈×C₄₇	C₂³	1	2	yes	—
302	C₄×D₄×C₄₇	—	2	1	no	—
303	C₄×D₄×C₄₇	C₂³	1	2	yes	—
304	C₄×D₄×C₄₇	C₂³	1	1	yes	characteristic
305	#117×C₄₇	—	2	1	no	—
306	#117×C₄₇	—	2	2	no	—
307	#117×C₄₇	—	2	1	no	—
308	#117×C₄₇	—	2	1	no	—
309	#117×C₄₇	C₂³	1	2	yes	—
310	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
311	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
312	C₂×Q₈×C₄₇	—	2	1	no	—
313	C₂×Q₈×C₄₇	—	2	2	no	—
314	C₂×Q₈×C₄₇	C₂×D₄	1	1	yes	characteristic
315	C₂×Q₈×C₄₇	C₂×D₄	1	1	yes	characteristic
316	C₂×Q₈×C₄₇	C₂×D₄	1	2	yes	—
317	C₂×Q₈×C₄₇	C₂⁴	1	1	yes	characteristic
318	C₂×Q₈×C₄₇	C₂⁴	1	2	yes	—
319	C₂×D₄×C₄₇	—	2	1	no	—
320	C₂×D₄×C₄₇	C₂⁴	1	1	yes	characteristic
321	C₂²×C₄×C₄₇	—	2	1	no	—
322	C₂²×C₄×C₄₇	—	2	2	no	—
323	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
324	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
325	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
326	C₂×C₂²⋊D₄₇	—	2	1	no	—
327	C₂²×Dic₄₇	—	2	2	no	—
328	Q₈×D₄₇	—	8	4	no	—
329	#10625350	—	2	2	no	—
330	#10625350	—	2	2	no	—
331	C₂×D₁₈₈	C₂⁴	1	1	yes	characteristic
332	C₂×C₄×D₄₇	—	2	1	no	—
333	C₂×C₄×D₄₇	—	2	1	no	—
334	C₂×C₄×D₄₇	—	2	1	no	—
335	C₂×C₄×D₄₇	—	2	2	no	—
336	C₂×C₄×D₄₇	—	2	2	no	—
337	C₂×Dic₉₄	—	2	2	no	—
338	C₂×Dic₉₄	—	2	2	no	—
339	C₂×Dic₉₄	—	2	2	no	—
340	C₂×Dic₉₄	—	2	1	no	—
341	C₂×Dic₉₄	—	2	1	no	—
342	C₂×Dic₉₄	—	8	2	no	—
343	C₂×Dic₉₄	C₂⁴	1	1	yes	characteristic
344	C₄⋊C₄×C₄₇	—	2	1	no	—
345	C₄⋊C₄×C₄₇	—	2	2	no	—
346	C₄⋊C₄×C₄₇	—	2	1	no	—
347	C₄⋊C₄×C₄₇	—	2	2	no	—
348	C₄⋊C₄×C₄₇	—	2	1	no	—
349	C₄⋊C₄×C₄₇	—	2	1	no	—
350	C₄⋊C₄×C₄₇	—	2	1	no	—
351	C₄⋊C₄×C₄₇	—	2	2	no	—
352	C₄⋊C₄×C₄₇	—	2	2	no	—
353	C₄⋊C₄×C₄₇	—	2	1	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	2	no	—
358	C₄⋊C₄×C₄₇	—	2	2	no	—
359	C₄⋊C₄×C₄₇	—	2	2	no	—
360	C₄⋊C₄×C₄₇	—	2	1	no	—
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	1	yes	characteristic
364	C₄⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
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	C₂⁴	1	1	yes	characteristic
371	C₄⋊C₄×C₄₇	C₂⁴	1	2	yes	—
372	C₄⋊C₄×C₄₇	C₂⁴	1	1	yes	characteristic
373	C₂²⋊C₄×C₄₇	—	2	2	no	—
374	C₂²⋊C₄×C₄₇	—	2	1	no	—
375	C₂²⋊C₄×C₄₇	—	2	1	no	—
376	C₂²⋊C₄×C₄₇	—	2	1	no	—
377	C₂²⋊C₄×C₄₇	—	2	1	no	—
378	C₂²⋊C₄×C₄₇	—	2	2	no	—
379	C₂²⋊C₄×C₄₇	—	2	2	no	—
380	C₂²⋊C₄×C₄₇	—	2	1	no	—
381	C₂²⋊C₄×C₄₇	—	2	2	no	—
382	C₂²⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
383	C₂²⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
384	C₄²×C₄₇	—	2	2	no	—
385	C₄²×C₄₇	—	2	1	no	—
386	C₄²×C₄₇	—	2	2	no	—
387	C₄²×C₄₇	—	2	2	no	—
388	C₄²×C₄₇	—	2	2	no	—
389	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
390	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
391	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
392	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
393	C₄²×C₄₇	C₂⁴	1	2	yes	—
394	C₄²×C₄₇	C₂⁴	1	2	yes	—
395	C₂²⋊Dic₄₇	—	2	1	no	—
396	#10625337	—	2	2	no	—
397	#10625337	—	2	4	no	—
398	#10625336	—	2	2	no	—
399	#10625336	—	2	4	no	—
400	#10625335	—	2	2	no	—
401	#10625334	—	2	2	no	—
402	(C₂×D₄₇)⋊C₄	—	2	1	no	—
403	(C₂×D₄₇)⋊C₄	—	2	1	no	—
404	(C₂×D₄₇)⋊C₄	—	2	2	no	—
405	(C₂×D₄₇)⋊C₄	—	2	2	no	—
406	C₄⋊Dic₄₇	—	2	1	no	—
407	C₄⋊Dic₄₇	—	2	1	no	—
408	C₄⋊Dic₄₇	—	2	2	no	—
409	C₄⋊Dic₄₇	—	2	2	no	—
410	C₄⋊Dic₄₇	—	2	2	no	—
411	C₄⋊Dic₄₇	—	2	2	no	—
412	C₄⋊Dic₄₇	C₂⁴	1	1	yes	characteristic
413	C₄⋊Dic₄₇	C₂⁴	1	2	yes	—
414	C₄⋊Dic₄₇	C₂⁴	1	2	yes	—
415	C₄⋊Dic₄₇	C₂⁴	1	1	yes	characteristic
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	1	no	—
421	Dic₄₇⋊C₄	—	2	1	no	—
422	Dic₄₇⋊C₄	—	2	2	no	—
423	Dic₄₇⋊C₄	—	2	2	no	—
424	C₄×Dic₄₇	—	2	1	no	—
425	C₄×Dic₄₇	—	2	1	no	—
426	C₄×Dic₄₇	—	2	1	no	—
427	C₄×Dic₄₇	—	2	2	no	—
428	C₄×Dic₄₇	—	2	2	no	—
429	C₂×C₄₇⋊C₈	C₂⁴	1	1	yes	characteristic
430	C₂×C₄₇⋊C₈	C₂⁴	1	1	yes	characteristic
431	C₂×C₄₇⋊C₈	C₂⁴	1	2	yes	—
432	C₂×C₄₇⋊C₈	C₂⁴	1	1	yes	characteristic
433	C₂×C₄₇⋊C₈	C₂⁴	1	2	yes	—
434	C₂×C₄₇⋊C₈	C₂⁴	1	1	yes	characteristic
435	C₂³×C₄₇	—	2	1	no	—
436	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
437	C₂²×D₄₇	—	2	1	no	—
438	Q₈×C₄₇	—	2	2	no	—
439	Q₈×C₄₇	—	2	2	no	—
440	Q₈×C₄₇	—	2	1	no	—
441	Q₈×C₄₇	—	2	2	no	—
442	Q₈×C₄₇	—	2	1	no	—
443	Q₈×C₄₇	—	2	2	no	—
444	Q₈×C₄₇	—	4	2	no	—
445	Q₈×C₄₇	—	8	1	no	—
446	Q₈×C₄₇	—	8	2	no	—
447	D₄×C₄₇	—	2	1	no	—
448	D₄×C₄₇	—	2	1	no	—
449	D₄×C₄₇	—	8	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	1	no	—
455	C₂×C₄×C₄₇	—	2	1	no	—
456	C₂×C₄×C₄₇	—	2	1	no	—
457	C₂×C₄×C₄₇	—	2	2	no	—
458	C₂×C₄×C₄₇	—	4	1	no	—
459	C₂×C₄×C₄₇	—	4	2	no	—
460	C₂×C₄×C₄₇	—	8	2	no	—
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	2	yes	—
467	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
468	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
469	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
470	C₂×C₄×C₄₇	C₂⁵	1	1	yes	characteristic
471	C₂²⋊D₄₇	—	2	4	no	—
472	C₂×Dic₄₇	—	2	1	no	—
473	C₂×Dic₄₇	—	2	1	no	—
474	C₂×Dic₄₇	—	2	1	no	—
475	C₂×Dic₄₇	—	2	2	no	—
476	C₂×Dic₄₇	—	2	2	no	—
477	C₂×Dic₄₇	—	8	2	no	—
478	D₁₈₈	—	2	1	no	—
479	D₁₈₈	2₋¹⁺⁴	1	2	yes	—
480	C₄×D₄₇	—	2	4	no	—
481	C₄×D₄₇	—	4	2	no	—
482	C₄×D₄₇	—	4	2	no	—
483	C₄×D₄₇	—	8	2	no	—
484	C₄×D₄₇	—	8	2	no	—
485	Dic₉₄	—	2	1	no	—
486	Dic₉₄	—	4	4	no	—
487	Dic₉₄	—	8	1	no	—
488	Dic₉₄	—	8	1	no	—
489	Dic₉₄	—	8	2	no	—
490	Dic₉₄	—	8	2	no	—
491	Dic₉₄	2₋¹⁺⁴	1	2	yes	—
492	C₄₇⋊C₈	—	2	1	no	—
493	C₄₇⋊C₈	—	2	1	no	—
494	C₄₇⋊C₈	—	2	2	no	—
495	C₄₇⋊C₈	—	2	1	no	—
496	C₄₇⋊C₈	—	2	1	no	—
497	C₄₇⋊C₈	—	2	2	no	—
498	#61859	—	47	1	no	maximal, Sylow
499	C₂²×C₄₇	—	2	1	no	—
500	C₂²×C₄₇	—	2	1	no	—
501	C₂²×C₄₇	—	2	1	no	—
502	C₂²×C₄₇	—	4	1	no	—
503	C₂²×C₄₇	—	4	1	no	—
504	C₂²×C₄₇	—	4	1	no	—
505	C₂²×C₄₇	C₂³×D₄	1	1	yes	characteristic
506	C₂×D₄₇	—	2	2	no	—
507	C₂×D₄₇	—	4	1	no	—
508	C₂×D₄₇	—	4	1	no	—
509	C₄×C₄₇	—	2	1	no	—
510	C₄×C₄₇	—	2	1	no	—
511	C₄×C₄₇	—	2	2	no	—
512	C₄×C₄₇	—	2	2	no	—
513	C₄×C₄₇	—	2	1	no	—
514	C₄×C₄₇	—	2	1	no	—
515	C₄×C₄₇	—	2	2	no	—
516	C₄×C₄₇	—	2	2	no	—
517	C₄×C₄₇	—	4	2	no	—
518	C₄×C₄₇	—	4	1	no	—
519	C₄×C₄₇	—	4	2	no	—
520	C₄×C₄₇	—	4	1	no	—
521	C₄×C₄₇	—	4	1	no	—
522	C₄×C₄₇	#578	1	2	yes	—
523	C₄×C₄₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
524	C₄×C₄₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
525	Dic₄₇	—	2	2	no	—
526	Dic₄₇	—	4	2	no	—
527	Dic₄₇	—	4	2	no	—
528	Dic₄₇	—	4	1	no	—
529	Dic₄₇	—	4	1	no	—
530	#3555	D₄₇	1	1	yes	characteristic, complemented
531	#3503	—	47	1	no	—
532	#3390	—	47	2	no	—
533	#3386	—	47	2	no	—
534	#3385	—	47	1	no	—
535	#3385	—	47	1	no	—
536	Q₈×Q₁₆	—	47	1	no	—
537	#3380	—	47	1	no	—
538	#3377	—	47	2	no	—
539	#3372	—	47	1	no	—
540	#3369	—	47	1	no	—
541	#3367	—	47	2	no	—
542	#3363	—	47	1	no	—
543	#3360	—	47	1	no	—
544	#3243	—	47	2	no	—
545	#3242	—	47	2	no	—
546	#3238	—	47	1	no	—
547	#3230	—	47	1	no	—
548	#3124	—	47	2	no	—
549	#3120	—	47	2	no	—
550	#3116	—	47	1	no	—
551	#3102	—	47	1	no	—
552	#2985	—	47	1	no	—
553	C₂×C₄₇	—	4	1	no	—
554	C₂×C₄₇	—	8	1	no	—
555	C₂×C₄₇	#3486	1	1	yes	characteristic
556	C₂×C₄₇	C₂×#578	1	1	yes	characteristic
557	C₂×C₄₇	#3585	1	1	yes	characteristic
558	D₄₇	—	4	2	no	—
559	#563	—	2	2	no	—
560	Q₈²	—	47	1	no	—
561	Q₈²	—	47	1	no	—
562	Q₈²	C₂×D₄₇	1	1	yes	characteristic
563	#557	—	47	2	no	—
564	#557	C₂×D₄₇	1	1	yes	characteristic
565	#557	C₂×D₄₇	1	2	yes	—
566	#556	—	2	1	no	—
567	#556	C₂×D₄₇	1	1	yes	characteristic
568	#556	C₂×D₄₇	1	2	yes	—
569	#554	—	47	1	no	—
570	#554	—	47	1	no	—
571	#554	—	94	1	no	—
572	#554	—	94	1	no	—
573	#554	C₂×D₄₇	1	1	yes	characteristic
574	#552	—	2	1	no	—
575	D₄×Q₈	—	47	2	no	—
576	D₄×Q₈	—	94	2	no	—
577	#544	—	2	1	no	—
578	#544	—	47	2	no	—
579	#544	—	94	2	no	—
580	#542	C₂×D₄₇	1	2	yes	—
581	#541	—	2	1	no	—
582	#541	—	2	2	no	—
583	#541	C₂×D₄₇	1	2	yes	—
584	#533	—	94	1	no	—
585	#533	C₂×D₄₇	1	1	yes	characteristic
586	#533	C₂×D₄₇	1	1	yes	characteristic
587	C₂×C₄⋊Q₈	—	47	1	no	—
588	C₂×C₄⋊Q₈	—	94	1	no	—
589	#529	C₂×D₄₇	1	1	yes	characteristic
590	#520	—	47	2	no	—
591	C₄×#41	—	47	1	no	—
592	#501	—	47	2	no	—
593	#501	—	47	2	no	—
594	#501	—	47	2	no	—
595	#500	—	47	1	no	—
596	#500	—	47	2	no	—
597	#500	—	47	1	no	—
598	#499	—	47	2	no	—
599	#491	—	47	2	no	—
600	#489	—	47	2	no	—
601	#489	—	47	2	no	—
602	#488	—	47	2	no	—
603	#487	—	47	1	no	—
604	#487	—	47	2	no	—
605	#487	—	47	1	no	—
606	#485	—	47	1	no	—
607	#485	—	47	2	no	—
608	#484	—	47	2	no	—
609	#484	—	47	2	no	—
610	#483	—	47	2	no	—
611	#482	—	47	1	no	—
612	#480	—	47	2	no	—
613	#479	—	47	1	no	—
614	#479	—	47	2	no	—
615	#479	—	47	2	no	—
616	#479	—	47	2	no	—
617	#479	—	47	2	no	—
618	#478	—	47	1	no	—
619	#478	—	47	2	no	—
620	#478	—	47	2	no	—
621	#477	—	47	1	no	—
622	#477	—	47	2	no	—
623	#477	—	47	1	no	—
624	#477	—	47	2	no	—
625	#477	—	47	2	no	—
626	#477	—	47	2	no	—
627	#477	—	47	1	no	—
628	#477	—	47	2	no	—
629	#476	—	47	1	no	—
630	#476	—	47	1	no	—
631	#476	—	47	1	no	—
632	#475	—	47	2	no	—
633	#474	—	47	2	no	—
634	#474	—	47	2	no	—
635	#464	—	47	1	no	—
636	#464	—	47	2	no	—
637	#463	—	47	1	no	—
638	#463	—	47	2	no	—
639	#462	—	47	1	no	—
640	#462	—	47	2	no	—
641	#461	—	47	1	no	—
642	#461	—	47	2	no	—
643	#452	—	47	1	no	—
644	#452	—	47	2	no	—
645	#449	—	47	1	no	—
646	#446	—	47	2	no	—
647	#446	—	47	1	no	—
648	#446	—	47	1	no	—
649	#446	—	47	2	no	—
650	C₈×Q₈	—	47	1	no	—
651	C₈×Q₈	—	47	1	no	—
652	#441	—	47	2	no	—
653	#441	—	47	2	no	—
654	#440	—	47	2	no	—
655	#440	—	47	2	no	—
656	#440	—	47	2	no	—
657	#440	—	47	2	no	—
658	C₄×Q₁₆	—	47	1	no	—
659	C₄×Q₁₆	—	47	2	no	—
660	C₄×Q₁₆	—	47	2	no	—
661	C₄×SD₁₆	—	47	1	no	—
662	C₄×SD₁₆	—	47	2	no	—
663	C₄×SD₁₆	—	47	1	no	—
664	C₄×D₈	—	47	1	no	—
665	C₄×D₈	—	47	2	no	—
666	#433	—	47	2	no	—
667	#433	—	47	2	no	—
668	#432	—	47	1	no	—
669	#431	—	47	1	no	—
670	C₄₇	#61859	1	1	yes	characteristic, complemented, Sylow
671	C₂×#41	—	47	1	no	—
672	C₂²×Q₈	—	94	2	no	—
673	C₂²×Q₈	—	94	1	no	—
674	C₂×Q₁₆	—	47	1	no	—
675	C₂×Q₁₆	—	47	2	no	—
676	C₂×SD₁₆	—	47	1	no	—
677	C₂×SD₁₆	—	47	2	no	—
678	C₂×SD₁₆	—	47	1	no	—
679	C₂×D₈	—	47	1	no	—
680	C₄⋊Q₈	—	2	2	no	—
681	C₄⋊Q₈	—	2	2	no	—
682	C₄⋊Q₈	—	2	1	no	—
683	C₄⋊Q₈	—	47	2	no	—
684	C₄⋊Q₈	—	47	1	no	—
685	C₄⋊Q₈	—	47	1	no	—
686	C₄⋊Q₈	—	47	2	no	—
687	C₄⋊Q₈	—	47	2	no	—
688	C₄⋊Q₈	—	94	2	no	—
689	C₄⋊Q₈	—	94	2	no	—
690	C₄⋊Q₈	—	94	1	no	—
691	C₄⋊Q₈	—	94	1	no	—
692	C₄⋊Q₈	—	94	2	no	—
693	C₄⋊Q₈	—	94	2	no	—
694	C₄⋊Q₈	—	94	1	no	—
695	C₄⋊Q₈	—	94	1	no	—
696	C₄⋊Q₈	C₂²⋊D₄₇	1	1	yes	characteristic
697	C₄⋊Q₈	C₂²⋊D₄₇	1	1	yes	characteristic
698	C₄⋊Q₈	C₂²×D₄₇	1	1	yes	characteristic
699	C₄⋊Q₈	C₂²×D₄₇	1	2	yes	—
700	C₄⋊Q₈	C₂²×D₄₇	1	1	yes	characteristic
701	C₄⋊Q₈	C₂²×D₄₇	1	2	yes	—
702	#126	—	2	2	no	—
703	#126	—	2	2	no	—
704	#126	—	2	2	no	—
705	#126	—	2	2	no	—
706	#126	—	2	2	no	—
707	#126	—	2	2	no	—
708	#126	—	2	1	no	—
709	#125	—	2	2	no	—
710	#125	—	2	2	no	—
711	#125	—	2	2	no	—
712	#125	—	2	2	no	—
713	#125	—	2	2	no	—
714	#125	—	2	1	no	—
715	#125	—	2	1	no	—
716	#125	—	47	2	no	—
717	#125	—	47	2	no	—
718	#125	—	94	2	no	—
719	#125	—	94	2	no	—
720	#125	—	94	2	no	—
721	#125	C₂²⋊D₄₇	1	2	yes	—
722	#125	C₂²×D₄₇	1	1	yes	characteristic
723	#125	C₂²×D₄₇	1	2	yes	—
724	#124	—	2	2	no	—
725	#124	C₂²×D₄₇	1	1	yes	characteristic
726	#124	C₂²×D₄₇	1	2	yes	—
727	#123	—	2	1	no	—
728	#123	—	2	2	no	—
729	C₂²⋊Q₈	—	2	1	no	—
730	C₂²⋊Q₈	—	2	1	no	—
731	C₂²⋊Q₈	—	2	2	no	—
732	C₂²⋊Q₈	—	2	1	no	—
733	C₂²⋊Q₈	—	2	2	no	—
734	C₂²⋊Q₈	—	2	2	no	—
735	C₂²⋊Q₈	—	94	1	no	—
736	C₂²⋊Q₈	—	94	1	no	—
737	C₂²⋊Q₈	—	94	2	no	—
738	C₂²⋊Q₈	—	94	2	no	—
739	C₂²⋊Q₈	—	94	2	no	—
740	C₂²⋊Q₈	—	94	2	no	—
741	C₂²⋊Q₈	—	94	2	no	—
742	C₂²⋊Q₈	—	94	2	no	—
743	C₂²⋊Q₈	—	94	2	no	—
744	C₂²⋊Q₈	C₂²⋊D₄₇	1	2	yes	—
745	C₂²⋊Q₈	C₂²⋊D₄₇	1	1	yes	characteristic
746	C₂²⋊Q₈	C₂²⋊D₄₇	1	1	yes	characteristic
747	C₂²⋊Q₈	C₂²×D₄₇	1	1	yes	characteristic
748	C₂²⋊Q₈	C₂²×D₄₇	1	2	yes	—
749	#121	C₂²×D₄₇	1	1	yes	characteristic
750	C₄×Q₈	—	2	1	no	—
751	C₄×Q₈	—	2	1	no	—
752	C₄×Q₈	—	2	2	no	—
753	C₄×Q₈	—	2	1	no	—
754	C₄×Q₈	—	47	1	no	—
755	C₄×Q₈	—	47	1	no	—
756	C₄×Q₈	—	47	2	no	—
757	C₄×Q₈	—	47	2	no	—
758	C₄×Q₈	—	94	1	no	—
759	C₄×Q₈	—	94	1	no	—
760	C₄×Q₈	—	94	2	no	—
761	C₄×Q₈	C₂²×D₄₇	1	1	yes	characteristic
762	C₄×Q₈	C₂²×D₄₇	1	2	yes	—
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	1	yes	characteristic
769	C₄×D₄	—	2	1	no	—
770	C₄×D₄	—	47	1	no	—
771	C₄×D₄	—	47	1	no	—
772	C₄×D₄	—	47	2	no	—
773	C₄×D₄	—	47	2	no	—
774	C₄×D₄	—	94	1	no	—
775	C₄×D₄	—	94	1	no	—
776	C₄×D₄	—	94	2	no	—
777	C₄×D₄	—	94	2	no	—
778	C₄×D₄	C₂²×D₄₇	1	1	yes	characteristic
779	C₄×D₄	C₂²×D₄₇	1	2	yes	—
780	#117	—	2	1	no	—
781	#117	—	2	2	no	—
782	#117	—	2	1	no	—
783	#117	—	2	1	no	—
784	#117	—	47	1	no	—
785	#117	—	94	2	no	—
786	#117	—	94	1	no	—
787	#117	C₂²×D₄₇	1	2	yes	—
788	C₂×C₄⋊C₄	—	2	1	no	—
789	C₂×C₄⋊C₄	—	47	2	no	—
790	C₂×C₄⋊C₄	—	94	1	no	—
791	C₂×C₄⋊C₄	—	94	2	no	—
792	C₂×C₄⋊C₄	—	94	1	no	—
793	C₂×C₄⋊C₄	—	94	1	no	—
794	C₂×C₄²	—	94	1	no	—
795	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
796	#107	—	47	2	no	—
797	#107	—	47	1	no	—
798	#107	—	47	2	no	—
799	#107	—	47	1	no	—
800	#107	—	47	2	no	—
801	#107	—	47	2	no	—
802	#107	—	47	2	no	—
803	#107	—	47	2	no	—
804	#107	—	47	2	no	—
805	#106	—	47	1	no	—
806	#106	—	47	2	no	—
807	#106	—	47	1	no	—
808	#106	—	47	2	no	—
809	#106	—	47	2	no	—
810	C₄⋊C₈	—	47	1	no	—
811	C₄⋊C₈	—	47	1	no	—
812	C₄⋊C₈	—	47	1	no	—
813	C₄⋊C₈	—	47	1	no	—
814	C₄⋊C₈	—	47	2	no	—
815	C₄⋊C₈	—	47	2	no	—
816	C₄⋊C₈	—	47	2	no	—
817	C₄⋊C₈	—	47	2	no	—
818	#103	—	47	2	no	—
819	#103	—	47	1	no	—
820	#103	—	47	2	no	—
821	#103	—	47	1	no	—
822	#103	—	47	2	no	—
823	#103	—	47	2	no	—
824	#103	—	47	2	no	—
825	#103	—	47	2	no	—
826	#103	—	47	2	no	—
827	#103	—	47	2	no	—
828	#103	—	47	1	no	—
829	#103	—	47	1	no	—
830	#103	—	47	2	no	—
831	#102	—	47	2	no	—
832	#102	—	47	1	no	—
833	#102	—	47	1	no	—
834	#102	—	47	2	no	—
835	#102	—	47	1	no	—
836	#102	—	47	2	no	—
837	#102	—	47	1	no	—
838	C₂²⋊C₈	—	47	1	no	—
839	C₂²⋊C₈	—	47	1	no	—
840	C₂²⋊C₈	—	47	2	no	—
841	#97	—	47	2	no	—
842	#97	—	47	2	no	—
843	#97	—	47	2	no	—
844	C₄×C₈	—	47	1	no	—
845	C₄×C₈	—	47	1	no	—
846	C₄×C₈	—	47	2	no	—
847	C₄×C₈	—	47	2	no	—
848	#41	—	94	2	no	—
849	#41	—	94	2	no	—
850	C₂×Q₈	—	2	1	no	—
851	C₂×Q₈	—	2	2	no	—
852	C₂×Q₈	—	47	1	no	—
853	C₂×Q₈	—	94	2	no	—
854	C₂×Q₈	—	94	2	no	—
855	C₂×Q₈	—	94	1	no	—
856	C₂×Q₈	—	94	1	no	—
857	C₂×Q₈	—	94	2	no	—
858	C₂×Q₈	—	376	2	no	—
859	C₂×Q₈	—	376	4	no	—
860	C₂×Q₈	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
861	C₂×Q₈	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
862	C₂×Q₈	C₂×C₂²⋊D₄₇	1	2	yes	—
863	C₂×Q₈	C₂³×D₄₇	1	2	yes	—
864	C₂×Q₈	C₂³×D₄₇	1	1	yes	characteristic
865	C₂×D₄	—	2	1	no	—
866	C₂×D₄	—	47	1	no	—
867	C₂×D₄	—	94	1	no	—
868	C₂×D₄	C₂³×D₄₇	1	1	yes	characteristic
869	C₂²×C₄	—	2	1	no	—
870	C₂²×C₄	—	2	2	no	—
871	C₂²×C₄	—	94	1	no	—
872	C₂²×C₄	—	94	2	no	—
873	C₂²×C₄	—	94	2	no	—
874	C₂²×C₄	—	94	2	no	—
875	C₂²×C₄	—	94	1	no	—
876	C₂²×C₄	—	94	1	no	—
877	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
878	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
879	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
880	Q₁₆	—	94	2	no	—
881	Q₁₆	—	94	4	no	—
882	SD₁₆	—	94	2	no	—
883	SD₁₆	—	94	2	no	—
884	SD₁₆	—	94	4	no	—
885	D₈	—	94	2	no	—
886	C₂×C₈	—	47	1	no	—
887	C₂×C₈	—	47	1	no	—
888	C₂×C₈	—	47	2	no	—
889	C₂×C₈	—	47	1	no	—
890	C₂×C₈	—	47	1	no	—
891	C₂×C₈	—	47	2	no	—
892	C₄⋊C₄	—	2	1	no	—
893	C₄⋊C₄	—	2	2	no	—
894	C₄⋊C₄	—	2	1	no	—
895	C₄⋊C₄	—	2	2	no	—
896	C₄⋊C₄	—	2	1	no	—
897	C₄⋊C₄	—	2	1	no	—
898	C₄⋊C₄	—	2	1	no	—
899	C₄⋊C₄	—	2	2	no	—
900	C₄⋊C₄	—	2	2	no	—
901	C₄⋊C₄	—	2	1	no	—
902	C₄⋊C₄	—	2	2	no	—
903	C₄⋊C₄	—	2	2	no	—
904	C₄⋊C₄	—	2	2	no	—
905	C₄⋊C₄	—	2	2	no	—
906	C₄⋊C₄	—	2	2	no	—
907	C₄⋊C₄	—	2	2	no	—
908	C₄⋊C₄	—	2	1	no	—
909	C₄⋊C₄	—	47	1	no	—
910	C₄⋊C₄	—	47	2	no	—
911	C₄⋊C₄	—	47	2	no	—
912	C₄⋊C₄	—	47	1	no	—
913	C₄⋊C₄	—	94	2	no	—
914	C₄⋊C₄	—	94	2	no	—
915	C₄⋊C₄	—	94	2	no	—
916	C₄⋊C₄	—	94	2	no	—
917	C₄⋊C₄	—	94	1	no	—
918	C₄⋊C₄	—	94	1	no	—
919	C₄⋊C₄	—	94	2	no	—
920	C₄⋊C₄	—	94	2	no	—
921	C₄⋊C₄	—	94	2	no	—
922	C₄⋊C₄	—	94	1	no	—
923	C₄⋊C₄	—	94	1	no	—
924	C₄⋊C₄	—	94	2	no	—
925	C₄⋊C₄	—	94	2	no	—
926	C₄⋊C₄	—	94	2	no	—
927	C₄⋊C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
928	C₄⋊C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
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	C₂×C₂²⋊D₄₇	1	2	yes	—
933	C₄⋊C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
934	C₄⋊C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
935	C₄⋊C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
936	C₄⋊C₄	C₂³×D₄₇	1	1	yes	characteristic
937	C₄⋊C₄	C₂³×D₄₇	1	2	yes	—
938	C₄⋊C₄	C₂³×D₄₇	1	1	yes	characteristic
939	C₂²⋊C₄	—	2	2	no	—
940	C₂²⋊C₄	—	2	1	no	—
941	C₂²⋊C₄	—	2	1	no	—
942	C₂²⋊C₄	—	2	1	no	—
943	C₂²⋊C₄	—	2	1	no	—
944	C₂²⋊C₄	—	2	2	no	—
945	C₂²⋊C₄	—	2	2	no	—
946	C₂²⋊C₄	—	2	1	no	—
947	C₂²⋊C₄	—	2	2	no	—
948	C₂²⋊C₄	—	94	1	no	—
949	C₂²⋊C₄	—	94	1	no	—
950	C₂²⋊C₄	—	94	1	no	—
951	C₂²⋊C₄	—	94	2	no	—
952	C₂²⋊C₄	—	94	2	no	—
953	C₂²⋊C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
954	C₂²⋊C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
955	C₄²	—	2	2	no	—
956	C₄²	—	2	1	no	—
957	C₄²	—	2	2	no	—
958	C₄²	—	2	2	no	—
959	C₄²	—	2	2	no	—
960	C₄²	—	94	1	no	—
961	C₄²	—	94	1	no	—
962	C₄²	—	94	1	no	—
963	C₄²	—	94	2	no	—
964	C₄²	—	94	2	no	—
965	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
966	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
967	C₄²	C₂³×D₄₇	1	1	yes	characteristic
968	C₄²	C₂³×D₄₇	1	2	yes	—
969	C₄²	C₂³×D₄₇	1	2	yes	—
970	C₄²	C₂³×D₄₇	1	1	yes	characteristic
971	C₂³	—	2	1	no	—
972	C₂³	—	94	1	no	—
973	C₂³	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
974	Q₈	—	2	2	no	—
975	Q₈	—	2	2	no	—
976	Q₈	—	2	2	no	—
977	Q₈	—	2	1	no	—
978	Q₈	—	2	1	no	—
979	Q₈	—	2	2	no	—
980	Q₈	—	4	2	no	—
981	Q₈	—	8	1	no	—
982	Q₈	—	8	2	no	—
983	Q₈	—	47	2	no	—
984	Q₈	—	94	1	no	—
985	Q₈	—	376	1	no	—
986	Q₈	—	376	1	no	—
987	Q₈	—	376	2	no	—
988	Q₈	—	376	2	no	—
989	Q₈	—	188	4	no	—
990	D₄	—	2	1	no	—
991	D₄	—	2	1	no	—
992	D₄	—	8	1	no	—
993	D₄	—	47	2	no	—
994	D₄	—	94	4	no	—
995	D₄	—	94	1	no	—
996	C₂×C₄	—	2	2	no	—
997	C₂×C₄	—	2	1	no	—
998	C₂×C₄	—	2	1	no	—
999	C₂×C₄	—	2	2	no	—
1000	C₂×C₄	—	2	1	no	—
1001	C₂×C₄	—	2	1	no	—
1002	C₂×C₄	—	2	1	no	—
1003	C₂×C₄	—	2	2	no	—
1004	C₂×C₄	—	4	1	no	—
1005	C₂×C₄	—	4	2	no	—
1006	C₂×C₄	—	8	2	no	—
1007	C₂×C₄	—	94	4	no	—
1008	C₂×C₄	—	94	1	no	—
1009	C₂×C₄	—	94	1	no	—
1010	C₂×C₄	—	94	1	no	—
1011	C₂×C₄	—	94	2	no	—
1012	C₂×C₄	—	94	2	no	—
1013	C₂×C₄	—	376	2	no	—
1014	C₂×C₄	—	376	2	no	—
1015	C₂×C₄	—	376	2	no	—
1016	C₂×C₄	—	188	2	no	—
1017	C₂×C₄	—	188	2	no	—
1018	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
1019	C₂×C₄	C₂²×C₂²⋊D₄₇	1	2	yes	—
1020	C₂×C₄	C₂²×C₂²⋊D₄₇	1	2	yes	—
1021	C₂×C₄	C₂²×C₂²⋊D₄₇	1	2	yes	—
1022	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
1023	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
1024	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
1025	C₂×C₄	C₂²×C₂²⋊D₄₇	1	2	yes	—
1026	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
1027	C₂×C₄	C₂⁴×D₄₇	1	1	yes	characteristic
1028	C₈	—	94	1	no	—
1029	C₈	—	94	1	no	—
1030	C₈	—	94	2	no	—
1031	C₈	—	94	1	no	—
1032	C₈	—	94	1	no	—
1033	C₈	—	94	2	no	—
1034	C₂²	—	2	1	no	—
1035	C₂²	—	2	1	no	—
1036	C₂²	—	2	1	no	—
1037	C₂²	—	4	1	no	—
1038	C₂²	—	4	1	no	—
1039	C₂²	—	4	1	no	—
1040	C₂²	—	94	2	no	—
1041	C₂²	—	188	1	no	—
1042	C₂²	—	188	1	no	—
1043	C₂²	C₂³×C₂²⋊D₄₇	1	1	yes	characteristic
1044	C₄	—	2	1	no	—
1045	C₄	—	2	1	no	—
1046	C₄	—	2	2	no	—
1047	C₄	—	2	2	no	—
1048	C₄	—	2	1	no	—
1049	C₄	—	2	1	no	—
1050	C₄	—	2	2	no	—
1051	C₄	—	2	2	no	—
1052	C₄	—	4	2	no	—
1053	C₄	—	4	1	no	—
1054	C₄	—	4	1	no	—
1055	C₄	—	4	2	no	—
1056	C₄	—	4	1	no	—
1057	C₄	—	94	2	no	—
1058	C₄	—	188	1	no	—
1059	C₄	—	188	2	no	—
1060	C₄	—	188	2	no	—
1061	C₄	—	188	1	no	—
1062	C₄	#15689938	1	2	yes	—
1063	C₄	2₋¹⁺⁴×D₄₇	1	1	yes	characteristic
1064	C₄	2₋¹⁺⁴×D₄₇	1	1	yes	characteristic
1065	C₂	—	4	1	no	—
1066	C₂	—	8	1	no	—
1067	C₂	—	188	2	no	—
1068	C₂	#20257036	1	1	yes	characteristic
1069	C₂	C₂×#15689938	1	1	yes	characteristic
1070	C₂	#20258167	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×#3555	C₂
socle	C₂²×C₄₇	C₂³×D₄
prime radical	#15689266	C₂²
hypercenter	#3555	D₄₇
hypocenter	C₄₇	#61859
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ #533 ◁ #3555

Complements

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

N	H ≅ G/N	type
1. #20257200	C₂	semidirect
2. #20256351	C₂	semidirect
3. #20256305	C₂	semidirect
4. #20256298	C₂	semidirect
5. #20256294	C₂	semidirect
6. Q₈×#10625337	C₂	semidirect
7. #20256251	C₂	semidirect
8. #20256224	C₂	semidirect
9. #20256165	C₂	semidirect
10. #20256124	C₂	semidirect
11. #20256102	C₂	semidirect
12. #20256062	C₂	semidirect
13. #20256033	C₂	semidirect
14. #20254665	C₂	semidirect
15. #20254650	C₂	semidirect
16. #20254606	C₂	semidirect
17. #20254536	C₂	semidirect
19. #20253596	C₂	semidirect
20. #20253544	C₂	semidirect
22. #20252483	C₂	semidirect
23. C₄₇×#3555	C₂	semidirect
530. #3555	D₄₇	semidirect
670. C₄₇	#61859	semidirect

Maximal subgroups

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

subgroup	index
#20257200	2
#20256351	2
#20256305	2
#20256298	2
#20256294	2
Q₈×#10625337	2
#20256251	2
#20256224	2
#20256165	2
#20256124	2
#20256102	2
#20256062	2
#20256033	2
#20254665	2
#20254650	2
#20254606	2
#20254536	2
#20253644	2
#20253596	2
#20253544	2
#20253400	2
#20252483	2
C₄₇×#3555	2
#61859	47