Subgroups — #27098920

Order 12032.

1750 conjugacy classes of subgroups.

The subgroup lattice has 1092 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20257482	C₂	1	1	yes	maximal, characteristic
2	#20256391	C₂	1	1	yes	maximal, characteristic, complemented
3	#20256275	C₂	1	1	yes	maximal, characteristic, complemented
4	#20256191	C₂	1	1	yes	maximal, characteristic, complemented
5	#20256187	C₂	1	1	yes	maximal, characteristic, complemented
6	#20255814	C₂	1	1	yes	maximal, characteristic, complemented
7	#20255750	C₂	1	2	yes	maximal, complemented
8	#20255671	C₂	1	1	yes	maximal, characteristic, complemented
9	#20255665	C₂	1	1	yes	maximal, characteristic, complemented
10	#20255439	C₂	1	2	yes	maximal, complemented
11	#20255433	C₂	1	2	yes	maximal, complemented
12	D₄×#10625337	C₂	1	2	yes	maximal, complemented
13	D₄×#10625337	C₂	1	1	yes	maximal, characteristic, complemented
14	#20254041	C₂	1	2	yes	maximal, complemented
15	#20253970	C₂	1	1	yes	maximal, characteristic, complemented
16	#20253688	C₂	1	2	yes	maximal, complemented
17	#20253683	C₂	1	2	yes	maximal, complemented
18	#20253518	C₂	1	1	yes	maximal, characteristic, complemented
19	#20253514	C₂	1	1	yes	maximal, characteristic, complemented
20	#20252364	C₂	1	1	yes	maximal, characteristic
21	#20252254	C₂	1	2	yes	maximal, complemented
22	C₂×C₄×#10625337	C₂	1	1	yes	maximal, characteristic, complemented
23	C₄₇×#3523	C₂	1	1	yes	maximal, characteristic
24	C₂²×#10625337	C₂²	1	2	yes	—
25	C₂²×#10625337	C₂²	1	1	yes	characteristic
26	#15689852	C₂²	1	1	yes	characteristic
27	#15689851	C₂²	1	1	yes	characteristic
28	#15689850	—	2	1	no	—
29	#15689843	C₂²	1	1	yes	characteristic
30	#15689842	—	2	1	no	—
31	#15689813	C₂²	1	2	yes	—
32	#15689810	—	2	2	no	—
33	D₄×Dic₉₄	C₂²	1	1	yes	characteristic
34	D₄×Dic₉₄	C₂²	1	2	yes	—
35	#15689735	C₂²	1	2	yes	—
36	#15689730	—	2	2	no	—
37	#15689680	C₂²	1	1	yes	characteristic
38	#15689675	—	2	1	no	—
39	#15689654	—	2	1	no	—
40	#15689600	C₂²	1	2	yes	—
41	C₂×C₄×Dic₉₄	C₂²	1	1	yes	characteristic
42	#15689526	C₂²	1	1	yes	characteristic
43	#15689522	C₂²	1	2	yes	—
44	#15689502	C₂²	1	1	yes	characteristic
45	#15689502	C₂²	1	2	yes	—
46	#15689493	C₂²	1	2	yes	—
47	#15689491	C₂²	1	2	yes	—
48	#15689475	C₂²	1	1	yes	characteristic
49	#15689473	C₂²	1	1	yes	characteristic
50	#15689464	C₂²	1	2	yes	—
51	#15689464	C₂²	1	2	yes	—
52	#15689461	C₂²	1	2	yes	—
53	#15689461	C₂²	1	2	yes	—
54	#15689453	C₂²	1	2	yes	—
55	#15689451	C₂²	1	2	yes	—
56	#15689430	C₂²	1	2	yes	—
57	#15689430	C₂²	1	2	yes	—
58	#15689427	C₂²	1	2	yes	—
59	#15689427	C₂²	1	2	yes	—
60	#15689408	C₂²	1	1	yes	characteristic
61	#15689408	C₂²	1	1	yes	characteristic
62	#15689405	C₂²	1	1	yes	characteristic
63	#15689405	C₂²	1	1	yes	characteristic
64	#15689379	C₂²	1	2	yes	—
65	#15689379	C₂²	1	2	yes	—
66	#15689362	C₂²	1	2	yes	—
67	#15689362	C₂²	1	2	yes	—
68	#15689362	C₂²	1	2	yes	—
69	#15689362	C₂²	1	2	yes	—
70	#15689333	C₂²	1	1	yes	characteristic
71	#15689333	C₂²	1	1	yes	characteristic
72	#15689333	C₂²	1	2	yes	—
73	#15689333	C₂²	1	2	yes	—
74	#15689330	C₂²	1	1	yes	characteristic
75	#15689330	C₂²	1	1	yes	characteristic
76	#15689330	C₂²	1	2	yes	—
77	#15689330	C₂²	1	2	yes	—
78	#15689279	C₂²	1	2	yes	—
79	#15689279	C₂²	1	2	yes	—
80	#15689279	C₂²	1	2	yes	—
81	#15689278	C₂²	1	2	yes	—
82	#15689278	C₂²	1	2	yes	—
83	#15689278	C₂²	1	2	yes	—
84	#15689254	C₂²	1	1	yes	characteristic
85	Q₈×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
86	#15689228	C₂²	1	2	yes	—
87	#15689228	C₂²	1	2	yes	—
88	#15689228	C₂²	1	2	yes	—
89	#15689228	C₂²	1	2	yes	—
90	#15689228	C₂²	1	2	yes	—
91	#15689228	C₂²	1	2	yes	—
92	C₄×#10625337	C₂²	1	2	yes	—
93	C₄×#10625337	C₂²	1	2	yes	—
94	C₄×#10625337	C₂²	1	2	yes	—
95	C₄×#10625337	C₂²	1	2	yes	—
96	C₄×#10625337	C₂²	1	1	yes	characteristic
97	C₄×#10625337	C₂²	1	1	yes	characteristic
98	C₄×#10625337	C₂²	1	1	yes	characteristic
99	C₄×#10625337	C₂²	1	1	yes	characteristic
100	C₄×#10625337	C₂²	1	1	yes	characteristic
101	C₄×#10625337	C₂²	1	1	yes	characteristic
102	C₄×#10625337	C₂²	1	1	yes	characteristic
103	C₄×#10625337	C₂²	1	1	yes	characteristic
104	#15689201	C₂²	1	1	yes	characteristic
105	#15689195	C₂²	1	2	yes	—
106	D₄×C₄₇⋊C₈	C₂²	1	2	yes	—
107	D₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
108	#15689184	C₂²	1	2	yes	—
109	#15689180	C₂²	1	1	yes	characteristic
110	#15689159	C₂²	1	2	yes	—
111	C₂×#13093957	C₂²	1	1	yes	characteristic
112	#15689132	C₂²	1	2	yes	—
113	#15689131	C₂²	1	2	yes	—
114	C₂×#13093948	C₂²	1	1	yes	characteristic
115	C₂×#13093947	C₂²	1	1	yes	characteristic
116	#15689079	C₂²	1	2	yes	—
117	C₂×C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
118	C₄₇×#557	—	2	1	no	—
119	C₄₇×#557	C₂²	1	1	yes	characteristic
120	C₄₇×#557	C₂²	1	1	yes	characteristic
121	C₄₇×#556	—	2	1	no	—
122	C₄₇×#556	C₂²	1	1	yes	characteristic
123	C₄₇×#552	—	2	2	no	—
124	C₄₇×#552	C₂²	1	2	yes	—
125	D₄×Q₈×C₄₇	C₂²	1	1	yes	characteristic
126	D₄×Q₈×C₄₇	C₂²	1	2	yes	—
127	C₄₇×#541	—	2	2	no	—
128	C₄₇×#541	C₂²	1	2	yes	—
129	C₄₇×#533	—	2	1	no	—
130	C₄₇×#533	C₂²	1	1	yes	characteristic
131	C₄₇×#529	—	2	1	no	—
132	C₄₇×#529	C₂²	1	1	yes	characteristic
133	C₄₇×#519	C₂²	1	2	yes	—
134	C₂×C₄×Q₈×C₄₇	C₂²	1	1	yes	characteristic
135	C₂²×Dic₉₄	C₂³	1	1	yes	characteristic
136	C₂²×Dic₉₄	C₂³	1	2	yes	—
137	C₂×#10625337	—	2	8	no	—
138	C₂×#10625337	—	2	4	no	—
139	C₂×#10625337	C₂³	1	2	yes	—
140	C₂×#10625337	C₂³	1	1	yes	characteristic
141	C₂×#10625337	C₂³	1	1	yes	characteristic
142	C₂×#10625337	C₂³	1	1	yes	characteristic
143	C₂×#10625337	C₂³	1	2	yes	—
144	C₂×#10625337	C₂³	1	2	yes	—
145	C₂×#10625337	C₂³	1	2	yes	—
146	C₂×#10625337	C₂³	1	2	yes	—
147	C₂×#10625337	C₂³	1	2	yes	—
148	C₂×#10625337	C₂³	1	1	yes	characteristic
149	C₂×#10625329	C₂³	1	2	yes	—
150	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
151	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
152	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
153	#13094024	C₂³	1	1	yes	characteristic
154	#13094024	C₂³	1	2	yes	—
155	#13094024	C₂³	1	1	yes	characteristic
156	#13094023	—	2	2	no	—
157	#13094023	—	2	1	no	—
158	#13094022	—	2	1	no	—
159	#13094017	—	2	2	no	—
160	#13094017	—	2	2	no	—
161	#13094017	—	2	2	no	—
162	#13094017	—	2	2	no	—
163	#13094016	—	2	1	no	—
164	#13094016	C₂³	1	2	yes	—
165	#13094015	—	2	2	no	—
166	#13094015	—	2	1	no	—
167	#13094014	—	2	2	no	—
168	#13094014	—	2	2	no	—
169	#13094014	—	2	2	no	—
170	#13094014	—	2	2	no	—
171	#13094011	—	2	1	no	—
172	#13094005	—	2	2	no	—
173	#13094003	—	2	1	no	—
174	#13094003	C₂³	1	2	yes	—
175	#13094003	C₂³	1	2	yes	—
176	#13094003	C₂³	1	2	yes	—
177	#13094001	—	2	2	no	—
178	#13094001	—	2	2	no	—
179	#13094001	—	2	2	no	—
180	Q₈×Dic₄₇	—	2	1	no	—
181	C₄×Dic₉₄	—	2	1	no	—
182	C₄×Dic₉₄	—	2	1	no	—
183	C₄×Dic₉₄	—	2	1	no	—
184	C₄×Dic₉₄	C₂³	1	1	yes	characteristic
185	C₄×Dic₉₄	C₂³	1	2	yes	—
186	C₄×Dic₉₄	C₂³	1	1	yes	characteristic
187	C₄×Dic₉₄	C₂³	1	1	yes	characteristic
188	C₄×Dic₉₄	C₂³	1	1	yes	characteristic
189	C₄×Dic₉₄	C₂³	1	2	yes	—
190	C₄×Dic₉₄	C₂³	1	2	yes	—
191	#13093989	—	2	2	no	—
192	#13093989	—	2	2	no	—
193	#13093989	—	2	1	no	—
194	#13093989	—	2	1	no	—
195	D₄×Dic₄₇	—	2	2	no	—
196	D₄×Dic₄₇	—	2	1	no	—
197	#13093983	—	2	1	no	—
198	#13093983	C₂³	1	2	yes	—
199	#13093980	—	2	2	no	—
200	#13093980	—	2	2	no	—
201	#13093980	—	2	2	no	—
202	C₂×C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic
203	C₂×Dic₄₇⋊C₄	—	2	1	no	—
204	C₂×C₄×Dic₄₇	—	2	1	no	—
205	#13093957	C₂³	1	1	yes	characteristic
206	#13093957	C₂³	1	1	yes	characteristic
207	#13093957	C₂³	1	2	yes	—
208	#13093957	C₂³	1	1	yes	characteristic
209	#13093957	C₂³	1	1	yes	characteristic
210	#13093957	C₂³	1	2	yes	—
211	#13093955	C₂³	1	2	yes	—
212	#13093955	C₂³	1	2	yes	—
213	#13093955	C₂³	1	2	yes	—
214	#13093955	C₂³	1	2	yes	—
215	C₄⋊(C₄₇⋊C₈)	C₂³	1	1	yes	characteristic
216	C₄⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
217	C₄⋊(C₄₇⋊C₈)	C₂³	1	1	yes	characteristic
218	C₄⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
219	#13093948	C₂³	1	1	yes	characteristic
220	#13093948	C₂³	1	1	yes	characteristic
221	#13093948	C₂³	1	1	yes	characteristic
222	#13093948	C₂³	1	1	yes	characteristic
223	#13093948	C₂³	1	2	yes	—
224	#13093948	C₂³	1	2	yes	—
225	#13093948	C₂³	1	2	yes	—
226	#13093948	C₂³	1	2	yes	—
227	#13093948	C₂³	1	2	yes	—
228	#13093948	C₂³	1	2	yes	—
229	#13093947	C₂³	1	1	yes	characteristic
230	#13093947	C₂³	1	1	yes	characteristic
231	#13093947	C₂³	1	1	yes	characteristic
232	#13093947	C₂³	1	1	yes	characteristic
233	#13093947	C₂³	1	2	yes	—
234	#13093947	C₂³	1	2	yes	—
235	#13093947	C₂³	1	2	yes	—
236	#13093947	C₂³	1	2	yes	—
237	#13093947	C₂³	1	2	yes	—
238	#13093947	C₂³	1	2	yes	—
239	C₂²⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
240	C₂²⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
241	C₂²⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
242	#13093935	C₂³	1	2	yes	—
243	#13093935	C₂³	1	2	yes	—
244	C₄×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
245	C₄×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
246	C₄×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
247	C₄×C₄₇⋊C₈	C₂³	1	2	yes	—
248	C₄×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
249	C₂²×Q₈×C₄₇	C₂³	1	1	yes	characteristic
250	C₂²×Q₈×C₄₇	C₂³	1	2	yes	—
251	C₄⋊Q₈×C₄₇	—	2	1	no	—
252	C₄⋊Q₈×C₄₇	—	2	1	no	—
253	C₄⋊Q₈×C₄₇	—	2	2	no	—
254	C₄⋊Q₈×C₄₇	C₂³	1	1	yes	characteristic
255	C₄⋊Q₈×C₄₇	C₂³	1	2	yes	—
256	C₄⋊Q₈×C₄₇	C₂³	1	1	yes	characteristic
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	D₄	1	2	yes	—
262	#125×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	D₄	1	1	yes	characteristic
270	#125×C₄₇	C₂³	1	2	yes	—
271	#124×C₄₇	—	2	1	no	—
272	#124×C₄₇	D₄	1	1	yes	characteristic
273	#123×C₄₇	—	2	2	no	—
274	#123×C₄₇	D₄	1	2	yes	—
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	—	2	2	no	—
279	C₂²⋊Q₈×C₄₇	D₄	1	1	yes	characteristic
280	C₂²⋊Q₈×C₄₇	C₂³	1	2	yes	—
281	C₂²⋊Q₈×C₄₇	C₂³	1	2	yes	—
282	C₂²⋊Q₈×C₄₇	C₂³	1	2	yes	—
283	#121×C₄₇	D₄	1	1	yes	characteristic
284	C₄×Q₈×C₄₇	—	2	1	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	C₂³	1	1	yes	characteristic
293	C₄×Q₈×C₄₇	C₂³	1	1	yes	characteristic
294	C₄×Q₈×C₄₇	C₂³	1	2	yes	—
295	C₄×Q₈×C₄₇	C₂³	1	1	yes	characteristic
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×D₄×C₄₇	—	2	2	no	—
301	C₄×D₄×C₄₇	—	2	1	no	—
302	C₄×D₄×C₄₇	C₂³	1	2	yes	—
303	C₄×D₄×C₄₇	C₂³	1	1	yes	characteristic
304	#117×C₄₇	—	2	1	no	—
305	#117×C₄₇	—	2	2	no	—
306	#117×C₄₇	—	2	2	no	—
307	#117×C₄₇	—	2	2	no	—
308	#117×C₄₇	C₂³	1	2	yes	—
309	#117×C₄₇	C₂³	1	2	yes	—
310	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
311	C₂×C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
312	C₂×C₄²×C₄₇	—	2	1	no	—
313	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
314	C₂×Q₈×C₄₇	—	2	1	no	—
315	C₂×Q₈×C₄₇	—	2	2	no	—
316	C₂×Q₈×C₄₇	—	2	1	no	—
317	C₂×Q₈×C₄₇	—	2	2	no	—
318	C₂×Q₈×C₄₇	—	2	4	no	—
319	C₂×Q₈×C₄₇	—	4	1	no	—
320	C₂×Q₈×C₄₇	—	4	2	no	—
321	C₂×Q₈×C₄₇	C₂×D₄	1	1	yes	characteristic
322	C₂×Q₈×C₄₇	C₂⁴	1	1	yes	characteristic
323	C₂×Q₈×C₄₇	C₂⁴	1	2	yes	—
324	C₂×Q₈×C₄₇	C₂⁴	1	1	yes	characteristic
325	C₂×D₄×C₄₇	C₂×D₄	1	2	yes	—
326	C₂×D₄×C₄₇	C₂×D₄	1	1	yes	characteristic
327	C₂²×C₄×C₄₇	—	2	1	no	—
328	C₂²×C₄×C₄₇	—	2	1	no	—
329	C₂²×C₄×C₄₇	—	2	2	no	—
330	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
331	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
332	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
333	C₂²×C₄×C₄₇	C₂⁴	1	2	yes	—
334	C₂²×Dic₄₇	—	2	1	no	—
335	C₂²×Dic₄₇	—	2	1	no	—
336	C₂²×Dic₄₇	—	2	2	no	—
337	C₂×Dic₉₄	—	2	2	no	—
338	C₂×Dic₉₄	—	2	4	no	—
339	C₂×Dic₉₄	—	2	1	no	—
340	C₂×Dic₉₄	—	2	2	no	—
341	C₂×Dic₉₄	—	2	1	no	—
342	C₂×Dic₉₄	—	4	1	no	—
343	C₂×Dic₉₄	—	4	2	no	—
344	C₂×Dic₉₄	C₂⁴	1	1	yes	characteristic
345	C₂×Dic₉₄	C₂⁴	1	2	yes	—
346	C₂×Dic₉₄	C₂⁴	1	1	yes	characteristic
347	C₄⋊C₄×C₄₇	—	2	1	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	1	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	1	no	—
356	C₄⋊C₄×C₄₇	—	2	2	no	—
357	C₄⋊C₄×C₄₇	—	2	1	no	—
358	C₄⋊C₄×C₄₇	—	2	2	no	—
359	C₄⋊C₄×C₄₇	—	2	1	no	—
360	C₄⋊C₄×C₄₇	—	2	2	no	—
361	C₄⋊C₄×C₄₇	—	2	2	no	—
362	C₄⋊C₄×C₄₇	—	2	2	no	—
363	C₄⋊C₄×C₄₇	—	2	2	no	—
364	C₄⋊C₄×C₄₇	—	2	2	no	—
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	1	yes	characteristic
368	C₄⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
369	C₄⋊C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
370	C₄⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
371	C₄⋊C₄×C₄₇	C₂⁴	1	1	yes	characteristic
372	C₄⋊C₄×C₄₇	C₂⁴	1	1	yes	characteristic
373	C₄⋊C₄×C₄₇	C₂⁴	1	2	yes	—
374	C₂²⋊C₄×C₄₇	—	2	2	no	—
375	C₂²⋊C₄×C₄₇	—	2	2	no	—
376	C₂²⋊C₄×C₄₇	—	2	2	no	—
377	C₂²⋊C₄×C₄₇	—	2	2	no	—
378	C₂²⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
379	C₂²⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
380	C₂²⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
381	C₂²⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
382	C₂²⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
383	C₄²×C₄₇	—	2	1	no	—
384	C₄²×C₄₇	—	2	1	no	—
385	C₄²×C₄₇	—	2	1	no	—
386	C₄²×C₄₇	—	2	1	no	—
387	C₄²×C₄₇	—	2	2	no	—
388	C₄²×C₄₇	—	2	2	no	—
389	C₄²×C₄₇	—	2	2	no	—
390	C₄²×C₄₇	—	2	2	no	—
391	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
392	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
393	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
394	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
395	C₄²×C₄₇	C₂⁴	1	2	yes	—
396	C₂²⋊Dic₄₇	—	2	2	no	—
397	C₂²⋊Dic₄₇	—	2	2	no	—
398	C₂²⋊Dic₄₇	—	2	2	no	—
399	C₂²⋊Dic₄₇	—	2	2	no	—
400	#10625337	—	2	2	no	—
401	#10625337	—	2	4	no	—
402	#10625337	—	2	2	no	—
403	#10625337	—	2	4	no	—
404	#10625337	—	2	4	no	—
405	#10625337	—	2	2	no	—
406	#10625337	—	4	2	no	—
407	#10625337	—	4	2	no	—
408	#10625337	—	4	2	no	—
409	#10625337	#41	1	4	yes	—
410	C₄⋊Dic₄₇	—	2	1	no	—
411	C₄⋊Dic₄₇	—	2	1	no	—
412	C₄⋊Dic₄₇	—	2	1	no	—
413	C₄⋊Dic₄₇	—	2	1	no	—
414	C₄⋊Dic₄₇	—	2	2	no	—
415	C₄⋊Dic₄₇	—	2	2	no	—
416	C₄⋊Dic₄₇	C₂⁴	1	1	yes	characteristic
417	C₄⋊Dic₄₇	C₂⁴	1	1	yes	characteristic
418	C₄⋊Dic₄₇	C₂⁴	1	2	yes	—
419	Dic₄₇⋊C₄	—	2	1	no	—
420	Dic₄₇⋊C₄	—	2	1	no	—
421	Dic₄₇⋊C₄	—	2	1	no	—
422	Dic₄₇⋊C₄	—	2	1	no	—
423	Dic₄₇⋊C₄	—	2	2	no	—
424	Dic₄₇⋊C₄	—	2	2	no	—
425	Dic₄₇⋊C₄	—	2	2	no	—
426	Dic₄₇⋊C₄	—	2	2	no	—
427	Dic₄₇⋊C₄	—	2	2	no	—
428	Dic₄₇⋊C₄	—	2	2	no	—
429	Dic₄₇⋊C₄	—	2	2	no	—
430	Dic₄₇⋊C₄	—	2	2	no	—
431	C₄×Dic₄₇	—	2	1	no	—
432	C₄×Dic₄₇	—	2	1	no	—
433	C₄×Dic₄₇	—	2	1	no	—
434	C₄×Dic₄₇	—	2	1	no	—
435	C₄×Dic₄₇	—	2	2	no	—
436	C₄×Dic₄₇	—	2	2	no	—
437	C₄×Dic₄₇	—	2	2	no	—
438	C₄×Dic₄₇	—	2	2	no	—
439	#10625329	—	4	2	no	—
440	C₂×C₄₇⋊C₈	—	2	2	no	—
441	C₂×C₄₇⋊C₈	—	2	4	no	—
442	C₂×C₄₇⋊C₈	—	4	1	no	—
443	C₂×C₄₇⋊C₈	C₂⁴	1	1	yes	characteristic
444	C₂×C₄₇⋊C₈	C₂⁴	1	1	yes	characteristic
445	C₂×C₄₇⋊C₈	C₂⁴	1	1	yes	characteristic
446	C₂×C₄₇⋊C₈	C₂⁴	1	2	yes	—
447	C₂×C₄₇⋊C₈	C₂⁴	1	2	yes	—
448	C₂×C₄₇⋊C₈	C₂⁴	1	1	yes	characteristic
449	C₂³×C₄₇	C₂²×D₄	1	2	yes	—
450	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
451	Q₈×C₄₇	—	2	2	no	—
452	Q₈×C₄₇	—	2	1	no	—
453	Q₈×C₄₇	—	2	1	no	—
454	Q₈×C₄₇	—	2	2	no	—
455	Q₈×C₄₇	—	2	2	no	—
456	Q₈×C₄₇	—	2	1	no	—
457	Q₈×C₄₇	—	4	2	no	—
458	Q₈×C₄₇	—	4	4	no	—
459	Q₈×C₄₇	—	4	2	no	—
460	Q₈×C₄₇	C₂×#41	1	2	yes	—
461	D₄×C₄₇	—	2	4	no	—
462	D₄×C₄₇	—	2	2	no	—
463	C₂×C₄×C₄₇	—	2	2	no	—
464	C₂×C₄×C₄₇	—	2	1	no	—
465	C₂×C₄×C₄₇	—	2	2	no	—
466	C₂×C₄×C₄₇	—	2	1	no	—
467	C₂×C₄×C₄₇	—	2	2	no	—
468	C₂×C₄×C₄₇	—	2	1	no	—
469	C₂×C₄×C₄₇	—	2	2	no	—
470	C₂×C₄×C₄₇	—	2	1	no	—
471	C₂×C₄×C₄₇	—	2	2	no	—
472	C₂×C₄×C₄₇	—	2	1	no	—
473	C₂×C₄×C₄₇	—	2	1	no	—
474	C₂×C₄×C₄₇	—	2	2	no	—
475	C₂×C₄×C₄₇	—	4	2	no	—
476	C₂×C₄×C₄₇	—	4	4	no	—
477	C₂×C₄×C₄₇	—	4	2	no	—
478	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
479	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
480	C₂×C₄×C₄₇	C₂²×D₄	1	2	yes	—
481	C₂×C₄×C₄₇	C₂²×D₄	1	2	yes	—
482	C₂×C₄×C₄₇	C₂²×D₄	1	2	yes	—
483	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
484	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
485	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
486	C₂×C₄×C₄₇	C₂⁵	1	1	yes	characteristic
487	C₂×Dic₄₇	—	2	1	no	—
488	C₂×Dic₄₇	—	2	1	no	—
489	C₂×Dic₄₇	—	2	2	no	—
490	C₂×Dic₄₇	—	2	1	no	—
491	C₂×Dic₄₇	—	2	1	no	—
492	C₂×Dic₄₇	—	2	2	no	—
493	C₂×Dic₄₇	—	4	2	no	—
494	C₂×Dic₄₇	—	4	4	no	—
495	C₂×Dic₄₇	—	4	2	no	—
496	Dic₉₄	—	2	1	no	—
497	Dic₉₄	—	2	1	no	—
498	Dic₉₄	—	2	2	no	—
499	Dic₉₄	—	2	2	no	—
500	Dic₉₄	—	2	1	no	—
501	Dic₉₄	—	4	4	no	—
502	Dic₉₄	—	4	2	no	—
503	Dic₉₄	—	4	2	no	—
504	Dic₉₄	C₂×#41	1	2	yes	—
505	C₄₇⋊C₈	—	2	1	no	—
506	C₄₇⋊C₈	—	2	2	no	—
507	C₄₇⋊C₈	—	2	1	no	—
508	C₄₇⋊C₈	—	2	1	no	—
509	C₄₇⋊C₈	—	2	2	no	—
510	C₄₇⋊C₈	C₂×#41	1	2	yes	—
511	#61484	—	47	1	no	maximal, Sylow
512	C₂²×C₄₇	—	2	1	no	—
513	C₂²×C₄₇	—	2	1	no	—
514	C₂²×C₄₇	—	2	2	no	—
515	C₂²×C₄₇	—	2	2	no	—
516	C₂²×C₄₇	—	2	2	no	—
517	C₂²×C₄₇	#578	1	2	yes	—
518	C₂²×C₄₇	C₂³×D₄	1	1	yes	characteristic
519	C₄×C₄₇	—	2	1	no	—
520	C₄×C₄₇	—	2	2	no	—
521	C₄×C₄₇	—	2	2	no	—
522	C₄×C₄₇	—	2	1	no	—
523	C₄×C₄₇	—	2	1	no	—
524	C₄×C₄₇	—	2	1	no	—
525	C₄×C₄₇	—	2	2	no	—
526	C₄×C₄₇	—	2	2	no	—
527	C₄×C₄₇	—	4	1	no	—
528	C₄×C₄₇	—	4	2	no	—
529	C₄×C₄₇	—	4	1	no	—
530	C₄×C₄₇	—	4	1	no	—
531	C₄×C₄₇	—	4	2	no	—
532	C₄×C₄₇	#578	1	2	yes	—
533	C₄×C₄₇	C₂²×#41	1	1	yes	characteristic
534	C₄×C₄₇	#585	1	1	yes	characteristic
535	Dic₄₇	—	2	2	no	—
536	Dic₄₇	—	4	2	no	—
537	Dic₄₇	—	4	1	no	—
538	Dic₄₇	—	4	2	no	—
539	Dic₄₇	—	4	1	no	—
540	Dic₄₇	—	4	1	no	—
541	#3523	—	47	1	no	—
542	#3523	D₄₇	1	1	yes	characteristic
543	#3395	—	47	1	no	—
544	#3383	—	47	1	no	—
545	#3374	—	47	1	no	—
546	#3374	—	47	1	no	—
547	#3342	—	47	1	no	—
548	#3336	—	47	2	no	—
549	#3328	—	47	1	no	—
550	#3328	—	47	1	no	—
551	#3312	—	47	2	no	—
552	#3312	—	47	2	no	—
553	D₄×Q₁₆	—	47	1	no	—
554	D₄×Q₁₆	—	47	2	no	—
555	#3177	—	47	2	no	—
556	#3170	—	47	1	no	—
557	#3127	—	47	2	no	—
558	#3127	—	47	2	no	—
559	#3113	—	47	1	no	—
560	#3113	—	47	1	no	—
561	#2966	—	47	1	no	—
562	#2950	—	47	2	no	—
563	C₂×C₄×Q₁₆	—	47	1	no	—
564	C₂×C₄₇	—	2	2	no	—
565	C₂×C₄₇	—	4	2	no	—
566	C₂×C₄₇	D₄×#41	1	1	yes	characteristic
567	C₂×C₄₇	C₂×#578	1	1	yes	characteristic
568	C₂×C₄₇	C₂×#578	1	1	yes	characteristic
569	C₂²×Q₁₆	—	47	1	no	—
570	C₂²×Q₁₆	—	47	2	no	—
571	#557	—	2	1	no	—
572	#557	—	47	1	no	—
573	#557	—	47	1	no	—
574	#557	—	94	1	no	—
575	#557	C₂×D₄₇	1	1	yes	characteristic
576	#557	C₂×D₄₇	1	1	yes	characteristic
577	#556	—	2	1	no	—
578	#556	—	47	1	no	—
579	#556	—	94	1	no	—
580	#556	C₂×D₄₇	1	1	yes	characteristic
581	#552	—	2	2	no	—
582	#552	—	47	2	no	—
583	#552	—	94	2	no	—
584	#552	C₂×D₄₇	1	2	yes	—
585	D₄×Q₈	—	47	1	no	—
586	D₄×Q₈	—	47	2	no	—
587	D₄×Q₈	C₂×D₄₇	1	1	yes	characteristic
588	D₄×Q₈	C₂×D₄₇	1	2	yes	—
589	#541	—	2	2	no	—
590	#541	—	47	2	no	—
591	#541	—	94	2	no	—
592	#541	C₂×D₄₇	1	2	yes	—
593	#533	—	2	1	no	—
594	#533	—	47	1	no	—
595	#533	—	94	1	no	—
596	#533	C₂×D₄₇	1	1	yes	characteristic
597	#529	—	2	1	no	—
598	#529	—	94	1	no	—
599	#529	C₂×D₄₇	1	1	yes	characteristic
600	#519	—	47	2	no	—
601	#519	C₂×D₄₇	1	2	yes	—
602	C₂×C₄×Q₈	—	47	1	no	—
603	C₂×C₄×Q₈	C₂×D₄₇	1	1	yes	characteristic
604	#500	—	47	1	no	—
605	#499	—	47	2	no	—
606	#494	—	47	1	no	—
607	#494	—	47	2	no	—
608	#491	—	47	2	no	—
609	#491	—	47	2	no	—
610	#487	—	47	1	no	—
611	#487	—	47	1	no	—
612	#485	—	47	2	no	—
613	#485	—	47	2	no	—
614	#485	—	47	2	no	—
615	#485	—	47	2	no	—
616	#483	—	47	2	no	—
617	#483	—	47	2	no	—
618	#479	—	47	2	no	—
619	#479	—	47	2	no	—
620	#479	—	47	2	no	—
621	#479	—	47	2	no	—
622	#475	—	47	1	no	—
623	#475	—	47	1	no	—
624	#475	—	47	1	no	—
625	#475	—	47	1	no	—
626	#470	—	47	2	no	—
627	#470	—	47	2	no	—
628	#467	—	47	2	no	—
629	#467	—	47	2	no	—
630	#467	—	47	2	no	—
631	#467	—	47	2	no	—
632	#462	—	47	1	no	—
633	#462	—	47	1	no	—
634	#462	—	47	2	no	—
635	#462	—	47	2	no	—
636	#462	—	47	1	no	—
637	#462	—	47	1	no	—
638	#462	—	47	2	no	—
639	#462	—	47	2	no	—
640	#451	—	47	2	no	—
641	#451	—	47	2	no	—
642	#451	—	47	2	no	—
643	#451	—	47	2	no	—
644	#451	—	47	2	no	—
645	#451	—	47	2	no	—
646	#446	—	47	1	no	—
647	C₈×Q₈	—	47	1	no	—
648	#441	—	47	2	no	—
649	#441	—	47	2	no	—
650	#441	—	47	2	no	—
651	#441	—	47	2	no	—
652	#441	—	47	2	no	—
653	#441	—	47	2	no	—
654	C₄×Q₁₆	—	47	1	no	—
655	C₄×Q₁₆	—	47	1	no	—
656	C₄×Q₁₆	—	47	2	no	—
657	C₄×Q₁₆	—	47	1	no	—
658	C₄×Q₁₆	—	47	2	no	—
659	C₄×Q₁₆	—	47	1	no	—
660	C₄×Q₁₆	—	47	1	no	—
661	C₄×Q₁₆	—	47	1	no	—
662	C₄×Q₁₆	—	47	2	no	—
663	C₄×Q₁₆	—	47	2	no	—
664	C₄×Q₁₆	—	47	1	no	—
665	C₄×Q₁₆	—	47	1	no	—
666	#436	—	47	1	no	—
667	#435	—	47	2	no	—
668	C₈×D₄	—	47	2	no	—
669	C₈×D₄	—	47	1	no	—
670	#433	—	47	2	no	—
671	#432	—	47	1	no	—
672	#427	—	47	2	no	—
673	C₂×#107	—	47	1	no	—
674	#419	—	47	2	no	—
675	#419	—	47	2	no	—
676	C₂×#103	—	47	1	no	—
677	C₂×#103	—	47	1	no	—
678	#405	—	47	2	no	—
679	C₂×C₄×C₈	—	47	1	no	—
680	C₄₇	#61484	1	1	yes	characteristic, complemented, Sylow
681	C₂²×Q₈	—	47	1	no	—
682	C₂²×Q₈	—	47	2	no	—
683	C₂²×Q₈	C₂²×D₄₇	1	1	yes	characteristic
684	C₂²×Q₈	C₂²×D₄₇	1	2	yes	—
685	C₂×Q₁₆	—	47	1	no	—
686	C₂×Q₁₆	—	47	1	no	—
687	C₂×Q₁₆	—	47	1	no	—
688	C₂×Q₁₆	—	47	1	no	—
689	C₂×Q₁₆	—	47	2	no	—
690	C₂×Q₁₆	—	47	2	no	—
691	C₂×Q₁₆	—	47	2	no	—
692	C₂×Q₁₆	—	47	2	no	—
693	C₂×Q₁₆	—	47	2	no	—
694	C₂×Q₁₆	—	47	2	no	—
695	C₂×Q₁₆	—	94	4	no	—
696	C₂×Q₁₆	—	94	8	no	—
697	C₂×M₁₆	—	47	2	no	—
698	C₂²×C₈	—	47	1	no	—
699	C₂²×C₈	—	47	2	no	—
700	C₂²×C₈	—	47	1	no	—
701	C₄⋊Q₈	—	2	1	no	—
702	C₄⋊Q₈	—	2	1	no	—
703	C₄⋊Q₈	—	2	2	no	—
704	C₄⋊Q₈	—	47	1	no	—
705	C₄⋊Q₈	—	47	1	no	—
706	C₄⋊Q₈	—	47	2	no	—
707	C₄⋊Q₈	—	94	1	no	—
708	C₄⋊Q₈	—	94	1	no	—
709	C₄⋊Q₈	—	94	2	no	—
710	C₄⋊Q₈	C₂²×D₄₇	1	1	yes	characteristic
711	C₄⋊Q₈	C₂²×D₄₇	1	2	yes	—
712	C₄⋊Q₈	C₂²×D₄₇	1	1	yes	characteristic
713	#126	—	2	2	no	—
714	#126	—	2	2	no	—
715	#126	—	2	2	no	—
716	#126	—	2	2	no	—
717	#126	—	94	2	no	—
718	#126	—	94	2	no	—
719	#126	—	94	2	no	—
720	#126	—	94	2	no	—
721	#126	C₂²⋊D₄₇	1	2	yes	—
722	#125	—	2	1	no	—
723	#125	—	2	2	no	—
724	#125	—	2	2	no	—
725	#125	—	2	2	no	—
726	#125	—	2	2	no	—
727	#125	—	2	2	no	—
728	#125	—	2	1	no	—
729	#125	—	47	2	no	—
730	#125	—	94	1	no	—
731	#125	—	94	2	no	—
732	#125	—	94	2	no	—
733	#125	—	94	2	no	—
734	#125	—	94	2	no	—
735	#125	—	94	2	no	—
736	#125	—	94	1	no	—
737	#125	C₂²⋊D₄₇	1	1	yes	characteristic
738	#125	C₂²×D₄₇	1	2	yes	—
739	#124	—	2	1	no	—
740	#124	—	94	1	no	—
741	#124	C₂²⋊D₄₇	1	1	yes	characteristic
742	#123	—	2	2	no	—
743	#123	—	94	2	no	—
744	#123	C₂²⋊D₄₇	1	2	yes	—
745	C₂²⋊Q₈	—	2	1	no	—
746	C₂²⋊Q₈	—	2	2	no	—
747	C₂²⋊Q₈	—	2	2	no	—
748	C₂²⋊Q₈	—	2	2	no	—
749	C₂²⋊Q₈	—	47	2	no	—
750	C₂²⋊Q₈	—	47	2	no	—
751	C₂²⋊Q₈	—	47	2	no	—
752	C₂²⋊Q₈	—	94	1	no	—
753	C₂²⋊Q₈	—	94	2	no	—
754	C₂²⋊Q₈	—	94	2	no	—
755	C₂²⋊Q₈	—	94	2	no	—
756	C₂²⋊Q₈	C₂²⋊D₄₇	1	1	yes	characteristic
757	C₂²⋊Q₈	C₂²×D₄₇	1	2	yes	—
758	C₂²⋊Q₈	C₂²×D₄₇	1	2	yes	—
759	C₂²⋊Q₈	C₂²×D₄₇	1	2	yes	—
760	#121	C₂²⋊D₄₇	1	1	yes	characteristic
761	C₄×Q₈	—	2	1	no	—
762	C₄×Q₈	—	2	2	no	—
763	C₄×Q₈	—	2	2	no	—
764	C₄×Q₈	—	2	1	no	—
765	C₄×Q₈	—	2	1	no	—
766	C₄×Q₈	—	2	1	no	—
767	C₄×Q₈	—	2	1	no	—
768	C₄×Q₈	—	2	1	no	—
769	C₄×Q₈	—	47	1	no	—
770	C₄×Q₈	—	47	1	no	—
771	C₄×Q₈	—	47	1	no	—
772	C₄×Q₈	—	47	1	no	—
773	C₄×Q₈	—	47	2	no	—
774	C₄×Q₈	—	47	2	no	—
775	C₄×Q₈	—	47	2	no	—
776	C₄×Q₈	—	94	1	no	—
777	C₄×Q₈	—	94	2	no	—
778	C₄×Q₈	—	94	2	no	—
779	C₄×Q₈	—	94	1	no	—
780	C₄×Q₈	—	94	1	no	—
781	C₄×Q₈	—	94	1	no	—
782	C₄×Q₈	—	94	1	no	—
783	C₄×Q₈	—	94	1	no	—
784	C₄×Q₈	C₂²×D₄₇	1	1	yes	characteristic
785	C₄×Q₈	C₂²×D₄₇	1	1	yes	characteristic
786	C₄×Q₈	C₂²×D₄₇	1	1	yes	characteristic
787	C₄×Q₈	C₂²×D₄₇	1	1	yes	characteristic
788	C₄×Q₈	C₂²×D₄₇	1	2	yes	—
789	C₄×Q₈	C₂²×D₄₇	1	2	yes	—
790	C₄×Q₈	C₂²×D₄₇	1	2	yes	—
791	C₄×Q₈	C₂²×D₄₇	1	1	yes	characteristic
792	C₄×D₄	—	2	2	no	—
793	C₄×D₄	—	2	1	no	—
794	C₄×D₄	—	94	2	no	—
795	C₄×D₄	—	94	1	no	—
796	C₄×D₄	C₂²×D₄₇	1	2	yes	—
797	C₄×D₄	C₂²×D₄₇	1	1	yes	characteristic
798	#117	—	2	1	no	—
799	#117	—	2	2	no	—
800	#117	—	2	2	no	—
801	#117	—	2	2	no	—
802	#117	—	47	2	no	—
803	#117	—	94	1	no	—
804	#117	—	94	2	no	—
805	#117	—	94	2	no	—
806	#117	—	94	2	no	—
807	#117	C₂²×D₄₇	1	2	yes	—
808	#117	C₂²×D₄₇	1	2	yes	—
809	C₂×C₄⋊C₄	—	2	1	no	—
810	C₂×C₄⋊C₄	—	47	1	no	—
811	C₂×C₄⋊C₄	—	94	1	no	—
812	C₂×C₄⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
813	C₂×C₄²	—	2	1	no	—
814	C₂×C₄²	—	94	1	no	—
815	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
816	#107	—	47	1	no	—
817	#107	—	47	1	no	—
818	#107	—	47	1	no	—
819	#107	—	47	1	no	—
820	#107	—	47	2	no	—
821	#107	—	47	2	no	—
822	#106	—	47	2	no	—
823	#106	—	47	2	no	—
824	#106	—	47	2	no	—
825	#106	—	47	2	no	—
826	C₄⋊C₈	—	47	1	no	—
827	C₄⋊C₈	—	47	1	no	—
828	C₄⋊C₈	—	47	2	no	—
829	C₄⋊C₈	—	47	2	no	—
830	#103	—	47	1	no	—
831	#103	—	47	1	no	—
832	#103	—	47	1	no	—
833	#103	—	47	1	no	—
834	#103	—	47	2	no	—
835	#103	—	47	2	no	—
836	#103	—	47	2	no	—
837	#103	—	47	2	no	—
838	#103	—	47	2	no	—
839	#103	—	47	2	no	—
840	#103	—	47	1	no	—
841	#103	—	47	1	no	—
842	#103	—	47	1	no	—
843	#103	—	47	1	no	—
844	#103	—	47	2	no	—
845	#103	—	47	2	no	—
846	#103	—	47	2	no	—
847	#103	—	47	2	no	—
848	#103	—	47	2	no	—
849	#103	—	47	2	no	—
850	C₂²⋊C₈	—	47	2	no	—
851	C₂²⋊C₈	—	47	2	no	—
852	C₂²⋊C₈	—	47	2	no	—
853	#97	—	47	2	no	—
854	#97	—	47	2	no	—
855	C₄×C₈	—	47	1	no	—
856	C₄×C₈	—	47	1	no	—
857	C₄×C₈	—	47	1	no	—
858	C₄×C₈	—	47	1	no	—
859	C₄×C₈	—	47	2	no	—
860	C₂×Q₈	—	2	1	no	—
861	C₂×Q₈	—	2	2	no	—
862	C₂×Q₈	—	2	1	no	—
863	C₂×Q₈	—	2	2	no	—
864	C₂×Q₈	—	2	4	no	—
865	C₂×Q₈	—	4	1	no	—
866	C₂×Q₈	—	4	2	no	—
867	C₂×Q₈	—	47	1	no	—
868	C₂×Q₈	—	47	1	no	—
869	C₂×Q₈	—	47	2	no	—
870	C₂×Q₈	—	94	2	no	—
871	C₂×Q₈	—	94	4	no	—
872	C₂×Q₈	—	94	1	no	—
873	C₂×Q₈	—	94	2	no	—
874	C₂×Q₈	—	94	1	no	—
875	C₂×Q₈	—	188	1	no	—
876	C₂×Q₈	—	188	2	no	—
877	C₂×Q₈	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
878	C₂×Q₈	C₂³×D₄₇	1	1	yes	characteristic
879	C₂×Q₈	C₂³×D₄₇	1	2	yes	—
880	C₂×Q₈	C₂³×D₄₇	1	1	yes	characteristic
881	C₂×D₄	C₂×C₂²⋊D₄₇	1	2	yes	—
882	C₂×D₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
883	C₂²×C₄	—	2	1	no	—
884	C₂²×C₄	—	2	1	no	—
885	C₂²×C₄	—	2	2	no	—
886	C₂²×C₄	—	94	1	no	—
887	C₂²×C₄	—	94	1	no	—
888	C₂²×C₄	—	94	2	no	—
889	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
890	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
891	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
892	C₂²×C₄	C₂³×D₄₇	1	2	yes	—
893	Q₁₆	—	47	4	no	—
894	Q₁₆	—	94	2	no	—
895	Q₁₆	—	94	4	no	—
896	Q₁₆	—	94	2	no	—
897	Q₁₆	—	94	4	no	—
898	Q₁₆	—	94	2	no	—
899	Q₁₆	—	94	4	no	—
900	Q₁₆	—	188	2	no	—
901	Q₁₆	—	188	2	no	—
902	Q₁₆	—	188	2	no	—
903	M₁₆	—	188	2	no	—
904	C₂×C₈	—	47	1	no	—
905	C₂×C₈	—	47	1	no	—
906	C₂×C₈	—	47	1	no	—
907	C₂×C₈	—	47	1	no	—
908	C₂×C₈	—	47	2	no	—
909	C₂×C₈	—	47	2	no	—
910	C₂×C₈	—	94	2	no	—
911	C₂×C₈	—	94	4	no	—
912	C₂×C₈	—	188	1	no	—
913	C₄⋊C₄	—	2	1	no	—
914	C₄⋊C₄	—	2	1	no	—
915	C₄⋊C₄	—	2	1	no	—
916	C₄⋊C₄	—	2	1	no	—
917	C₄⋊C₄	—	2	1	no	—
918	C₄⋊C₄	—	2	2	no	—
919	C₄⋊C₄	—	2	2	no	—
920	C₄⋊C₄	—	2	2	no	—
921	C₄⋊C₄	—	2	1	no	—
922	C₄⋊C₄	—	2	2	no	—
923	C₄⋊C₄	—	2	1	no	—
924	C₄⋊C₄	—	2	2	no	—
925	C₄⋊C₄	—	2	1	no	—
926	C₄⋊C₄	—	2	2	no	—
927	C₄⋊C₄	—	2	2	no	—
928	C₄⋊C₄	—	2	2	no	—
929	C₄⋊C₄	—	2	2	no	—
930	C₄⋊C₄	—	2	2	no	—
931	C₄⋊C₄	—	47	1	no	—
932	C₄⋊C₄	—	47	1	no	—
933	C₄⋊C₄	—	47	2	no	—
934	C₄⋊C₄	—	94	1	no	—
935	C₄⋊C₄	—	94	1	no	—
936	C₄⋊C₄	—	94	1	no	—
937	C₄⋊C₄	—	94	1	no	—
938	C₄⋊C₄	—	94	2	no	—
939	C₄⋊C₄	—	94	2	no	—
940	C₄⋊C₄	—	94	2	no	—
941	C₄⋊C₄	—	94	2	no	—
942	C₄⋊C₄	—	94	2	no	—
943	C₄⋊C₄	—	94	2	no	—
944	C₄⋊C₄	—	94	2	no	—
945	C₄⋊C₄	—	94	2	no	—
946	C₄⋊C₄	—	94	1	no	—
947	C₄⋊C₄	—	94	1	no	—
948	C₄⋊C₄	—	94	1	no	—
949	C₄⋊C₄	—	94	1	no	—
950	C₄⋊C₄	—	94	2	no	—
951	C₄⋊C₄	—	94	2	no	—
952	C₄⋊C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
953	C₄⋊C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
954	C₄⋊C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
955	C₄⋊C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
956	C₄⋊C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
957	C₄⋊C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
958	C₄⋊C₄	C₂³×D₄₇	1	1	yes	characteristic
959	C₄⋊C₄	C₂³×D₄₇	1	1	yes	characteristic
960	C₄⋊C₄	C₂³×D₄₇	1	2	yes	—
961	C₂²⋊C₄	—	2	2	no	—
962	C₂²⋊C₄	—	2	2	no	—
963	C₂²⋊C₄	—	2	2	no	—
964	C₂²⋊C₄	—	2	2	no	—
965	C₂²⋊C₄	—	94	2	no	—
966	C₂²⋊C₄	—	94	2	no	—
967	C₂²⋊C₄	—	94	2	no	—
968	C₂²⋊C₄	—	94	2	no	—
969	C₂²⋊C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
970	C₂²⋊C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
971	C₂²⋊C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
972	C₂²⋊C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
973	C₂²⋊C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
974	C₄²	—	2	1	no	—
975	C₄²	—	2	1	no	—
976	C₄²	—	2	1	no	—
977	C₄²	—	2	1	no	—
978	C₄²	—	2	2	no	—
979	C₄²	—	2	2	no	—
980	C₄²	—	2	2	no	—
981	C₄²	—	2	2	no	—
982	C₄²	—	94	1	no	—
983	C₄²	—	94	1	no	—
984	C₄²	—	94	1	no	—
985	C₄²	—	94	1	no	—
986	C₄²	—	94	2	no	—
987	C₄²	—	94	2	no	—
988	C₄²	—	94	2	no	—
989	C₄²	—	94	2	no	—
990	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
991	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
992	C₄²	C₂³×D₄₇	1	1	yes	characteristic
993	C₄²	C₂³×D₄₇	1	1	yes	characteristic
994	C₄²	C₂³×D₄₇	1	2	yes	—
995	C₂³	C₂²×C₂²⋊D₄₇	1	2	yes	—
996	C₂³	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
997	Q₈	—	2	2	no	—
998	Q₈	—	2	1	no	—
999	Q₈	—	2	1	no	—
1000	Q₈	—	2	2	no	—
1001	Q₈	—	2	2	no	—
1002	Q₈	—	2	1	no	—
1003	Q₈	—	4	2	no	—
1004	Q₈	—	4	4	no	—
1005	Q₈	—	4	2	no	—
1006	Q₈	—	47	2	no	—
1007	Q₈	—	94	1	no	—
1008	Q₈	—	94	1	no	—
1009	Q₈	—	94	2	no	—
1010	Q₈	—	94	2	no	—
1011	Q₈	—	94	1	no	—
1012	Q₈	—	188	2	no	—
1013	Q₈	—	188	4	no	—
1014	Q₈	—	188	2	no	—
1015	Q₈	#41×D₄₇	1	2	yes	—
1016	D₄	—	2	4	no	—
1017	D₄	—	2	2	no	—
1018	C₂×C₄	—	2	2	no	—
1019	C₂×C₄	—	2	1	no	—
1020	C₂×C₄	—	2	2	no	—
1021	C₂×C₄	—	2	1	no	—
1022	C₂×C₄	—	2	2	no	—
1023	C₂×C₄	—	2	1	no	—
1024	C₂×C₄	—	2	2	no	—
1025	C₂×C₄	—	2	1	no	—
1026	C₂×C₄	—	2	2	no	—
1027	C₂×C₄	—	2	1	no	—
1028	C₂×C₄	—	2	1	no	—
1029	C₂×C₄	—	2	2	no	—
1030	C₂×C₄	—	4	2	no	—
1031	C₂×C₄	—	4	4	no	—
1032	C₂×C₄	—	4	2	no	—
1033	C₂×C₄	—	94	1	no	—
1034	C₂×C₄	—	94	1	no	—
1035	C₂×C₄	—	94	2	no	—
1036	C₂×C₄	—	94	1	no	—
1037	C₂×C₄	—	94	1	no	—
1038	C₂×C₄	—	94	2	no	—
1039	C₂×C₄	—	188	2	no	—
1040	C₂×C₄	—	188	4	no	—
1041	C₂×C₄	—	188	2	no	—
1042	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
1043	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
1044	C₂×C₄	C₂²×C₂²⋊D₄₇	1	2	yes	—
1045	C₂×C₄	C₂²×C₂²⋊D₄₇	1	2	yes	—
1046	C₂×C₄	C₂²×C₂²⋊D₄₇	1	2	yes	—
1047	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
1048	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
1049	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
1050	C₂×C₄	C₂⁴×D₄₇	1	1	yes	characteristic
1051	C₈	—	47	2	no	—
1052	C₈	—	94	1	no	—
1053	C₈	—	94	2	no	—
1054	C₈	—	94	1	no	—
1055	C₈	—	94	1	no	—
1056	C₈	—	94	2	no	—
1057	C₂²	—	2	1	no	—
1058	C₂²	—	2	1	no	—
1059	C₂²	—	2	2	no	—
1060	C₂²	—	2	2	no	—
1061	C₂²	—	2	2	no	—
1062	C₂²	#15689938	1	2	yes	—
1063	C₂²	C₂³×C₂²⋊D₄₇	1	1	yes	characteristic
1064	C₄	—	2	1	no	—
1065	C₄	—	2	2	no	—
1066	C₄	—	2	2	no	—
1067	C₄	—	2	1	no	—
1068	C₄	—	2	1	no	—
1069	C₄	—	2	1	no	—
1070	C₄	—	2	2	no	—
1071	C₄	—	2	2	no	—
1072	C₄	—	4	1	no	—
1073	C₄	—	4	2	no	—
1074	C₄	—	4	1	no	—
1075	C₄	—	4	1	no	—
1076	C₄	—	4	2	no	—
1077	C₄	—	94	2	no	—
1078	C₄	—	188	1	no	—
1079	C₄	—	188	2	no	—
1080	C₄	—	188	1	no	—
1081	C₄	—	188	1	no	—
1082	C₄	—	188	2	no	—
1083	C₄	#15689938	1	2	yes	—
1084	C₄	C₂×#41×D₄₇	1	1	yes	characteristic
1085	C₄	#15689959	1	1	yes	characteristic
1086	C₂	—	2	2	no	—
1087	C₂	—	4	2	no	—
1088	C₂	#41×C₂²⋊D₄₇	1	1	yes	characteristic
1089	C₂	C₂×#15689938	1	1	yes	characteristic
1090	C₂	C₂×#15689938	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×#3523	C₂
socle	C₂²×C₄₇	C₂³×D₄
prime radical	#121×C₄₇	D₄
hypercenter	#3523	D₄₇
hypocenter	C₄₇	#61484
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ #529 ◁ #3523

Complements

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

N	H ≅ G/N	type
2. #20256391	C₂	semidirect
3. #20256275	C₂	semidirect
4. #20256191	C₂	semidirect
5. #20256187	C₂	semidirect
6. #20255814	C₂	semidirect
7. #20255750	C₂	semidirect
8. #20255671	C₂	semidirect
9. #20255665	C₂	semidirect
10. #20255439	C₂	semidirect
11. #20255433	C₂	semidirect
12. D₄×#10625337	C₂	semidirect
13. D₄×#10625337	C₂	semidirect
14. #20254041	C₂	semidirect
15. #20253970	C₂	semidirect
16. #20253688	C₂	semidirect
17. #20253683	C₂	semidirect
18. #20253518	C₂	semidirect
19. #20253514	C₂	semidirect
21. #20252254	C₂	semidirect
22. C₂×C₄×#10625337	C₂	semidirect
680. C₄₇	#61484	semidirect

Maximal subgroups

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

subgroup	index
#20257482	2
#20256391	2
#20256275	2
#20256191	2
#20256187	2
#20255814	2
#20255750	2
#20255671	2
#20255665	2
#20255439	2
#20255433	2
D₄×#10625337	2
#20254041	2
#20253970	2
#20253688	2
#20253683	2
#20253518	2
#20253514	2
#20252364	2
#20252254	2
C₂×C₄×#10625337	2
C₄₇×#3523	2
#61484	47