Subgroups — D₄₇×#3168 #27085996

Order 12032.

2070 conjugacy classes of subgroups.

The subgroup lattice has 1126 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#529×D₄₇	C₂	1	2	yes	maximal, complemented
2	#20253961	C₂	1	1	yes	maximal, characteristic, complemented
3	#20253960	C₂	1	1	yes	maximal, characteristic, complemented
4	#20253959	C₂	1	1	yes	maximal, characteristic, complemented
5	#20253958	C₂	1	1	yes	maximal, characteristic, complemented
6	#20253957	C₂	1	2	yes	maximal, complemented
7	#20253956	C₂	1	1	yes	maximal, characteristic, complemented
8	#20253955	C₂	1	1	yes	maximal, characteristic, complemented
9	#20253954	C₂	1	2	yes	maximal, complemented
10	#20253953	C₂	1	1	yes	maximal, characteristic, complemented
11	#20253952	C₂	1	2	yes	maximal, complemented
12	#20253951	C₂	1	2	yes	maximal, complemented
13	#499×D₄₇	C₂	1	1	yes	maximal, characteristic, complemented
14	#495×D₄₇	C₂	1	1	yes	maximal, characteristic, complemented
15	#488×D₄₇	C₂	1	2	yes	maximal, complemented
16	#467×D₄₇	C₂	1	1	yes	maximal, characteristic, complemented
17	#466×D₄₇	C₂	1	1	yes	maximal, characteristic
18	#465×D₄₇	C₂	1	2	yes	maximal, complemented
19	C₄×Q₁₆×D₄₇	C₂	1	1	yes	maximal, characteristic, complemented
20	C₄×SD₁₆×D₄₇	C₂	1	2	yes	maximal, complemented
21	C₄×D₈×D₄₇	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂×C₄×C₈×D₄₇	C₂	1	1	yes	maximal, characteristic, complemented
23	C₄₇×#3168	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×Q₁₆×D₄₇	C₂²	1	1	yes	characteristic
25	C₂×SD₁₆×D₄₇	C₂²	1	2	yes	—
26	C₂×D₈×D₄₇	C₂²	1	1	yes	characteristic
27	C₂²×C₈×D₄₇	C₂²	1	1	yes	characteristic
28	C₂²×C₈×D₄₇	C₂²	1	1	yes	characteristic
29	#15689660	C₂²	1	2	yes	complemented
30	#15689659	C₂²	1	2	yes	complemented
31	#15689658	C₂²	1	2	yes	complemented
32	#15689657	C₂²	1	2	yes	complemented
33	#15689656	—	2	2	no	—
34	#15689655	C₂²	1	2	yes	complemented
35	#15689654	C₂²	1	2	yes	complemented
36	#15689653	—	2	2	no	—
37	#15689652	C₂²	1	2	yes	complemented
38	#15689651	—	2	2	no	—
39	#15689650	—	2	2	no	—
40	#126×D₄₇	—	2	2	no	—
41	#125×D₄₇	C₂²	1	2	yes	—
42	#124×D₄₇	C₂²	1	2	yes	—
43	#123×D₄₇	—	2	2	no	—
44	C₂²⋊Q₈×D₄₇	C₂²	1	2	yes	—
45	#121×D₄₇	C₂²	1	2	yes	—
46	C₄×Q₈×D₄₇	C₂²	1	2	yes	—
47	C₄×D₄×D₄₇	—	2	2	no	—
48	C₄×D₄×D₄₇	C₂²	1	2	yes	—
49	#117×D₄₇	—	2	2	no	—
50	C₂×C₄²×D₄₇	C₂²	1	1	yes	characteristic
51	#15689525	C₂²	1	1	yes	characteristic, complemented
52	#15689524	C₂²	1	1	yes	characteristic, complemented
53	#15689524	C₂²	1	1	yes	characteristic, complemented
54	#15689523	C₂²	1	2	yes	complemented
55	#15689522	C₂²	1	2	yes	complemented
56	#15689508	C₂²	1	1	yes	characteristic, complemented
57	#15689507	C₂²	1	1	yes	characteristic, complemented
58	#15689506	C₂²	1	1	yes	characteristic, complemented
59	#15689505	C₂²	1	2	yes	complemented
60	#15689504	C₂²	1	2	yes	complemented
61	#15689480	C₂²	1	2	yes	complemented
62	#15689479	C₂²	1	2	yes	complemented
63	#15689479	C₂²	1	2	yes	complemented
64	#15689478	C₂²	1	2	yes	complemented
65	#15689477	C₂²	1	2	yes	complemented
66	#15689476	C₂²	1	2	yes	complemented
67	#15689476	C₂²	1	2	yes	complemented
68	#15689365	C₂²	1	1	yes	characteristic, complemented
69	#15689364	C₂²	1	1	yes	characteristic, complemented
70	#15689363	C₂²	1	2	yes	complemented
71	#15689362	C₂²	1	2	yes	complemented
72	#15689361	C₂²	1	1	yes	characteristic, complemented
73	#15689360	C₂²	1	1	yes	characteristic
74	#15689359	C₂²	1	1	yes	characteristic
75	#15689358	C₂²	1	2	yes	—
76	#15689357	C₂²	1	2	yes	—
77	#15689356	C₂²	1	1	yes	characteristic
78	#15689355	C₂²	1	2	yes	complemented
79	#15689354	C₂²	1	2	yes	complemented
80	#15689353	C₂²	1	2	yes	complemented
81	#15689352	C₂²	1	2	yes	complemented
82	#15689351	C₂²	1	2	yes	complemented
83	#15689350	C₂²	1	2	yes	complemented
84	#15689349	C₂²	1	2	yes	complemented
85	C₄×Dic₁₈₈	C₂²	1	1	yes	characteristic, complemented
86	Q₁₆×Dic₄₇	C₂²	1	1	yes	characteristic, complemented
87	#15689217	C₂²	1	1	yes	characteristic, complemented
88	C₄×#10625337	C₂²	1	2	yes	complemented
89	#15689215	C₂²	1	2	yes	complemented
90	#15689214	C₂²	1	2	yes	complemented
91	C₄×#10625325	C₂²	1	2	yes	complemented
92	SD₁₆×Dic₄₇	C₂²	1	2	yes	complemented
93	C₄×#10625336	C₂²	1	2	yes	complemented
94	#15689210	C₂²	1	2	yes	complemented
95	C₄×#10625335	C₂²	1	2	yes	complemented
96	#15689208	C₂²	1	2	yes	complemented
97	C₄×D₃₇₆	C₂²	1	1	yes	characteristic, complemented
98	D₈×Dic₄₇	C₂²	1	1	yes	characteristic, complemented
99	#15689205	C₂²	1	1	yes	characteristic, complemented
100	C₄×#10625334	C₂²	1	2	yes	complemented
101	#15689203	C₂²	1	2	yes	complemented
102	#107×D₄₇	C₂²	1	1	yes	characteristic
103	#107×D₄₇	C₂²	1	1	yes	characteristic
104	#106×D₄₇	C₂²	1	2	yes	—
105	#103×D₄₇	C₂²	1	2	yes	—
106	#103×D₄₇	C₂²	1	2	yes	—
107	#102×D₄₇	C₂²	1	2	yes	—
108	#102×D₄₇	C₂²	1	2	yes	—
109	C₂×C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic, complemented
110	C₂×C₈×Dic₄₇	C₂²	1	1	yes	characteristic, complemented
111	C₂×C₈×Dic₄₇	C₂²	1	1	yes	characteristic, complemented
112	C₄×C₈×D₄₇	C₂²	1	1	yes	characteristic
113	C₄×C₈×D₄₇	C₂²	1	1	yes	characteristic
114	C₄×C₈×D₄₇	C₂²	1	1	yes	characteristic
115	C₄×C₈×D₄₇	C₂²	1	1	yes	characteristic
116	C₄×C₈×D₄₇	C₂²	1	1	yes	characteristic, complemented
117	C₄×C₈×D₄₇	C₂²	1	1	yes	characteristic, complemented
118	C₄×C₈×D₄₇	C₂²	1	1	yes	characteristic, complemented
119	C₄×C₈×D₄₇	C₂²	1	1	yes	characteristic, complemented
120	C₄₇×#529	C₂²	1	2	yes	complemented
121	C₄₇×#499	C₂²	1	1	yes	characteristic, complemented
122	C₄₇×#495	C₂²	1	1	yes	characteristic, complemented
123	C₄₇×#488	C₂²	1	2	yes	complemented
124	C₄₇×#467	C₂²	1	1	yes	characteristic, complemented
125	C₄₇×#466	C₂²	1	1	yes	characteristic
126	C₄₇×#465	C₂²	1	2	yes	complemented
127	C₄×Q₁₆×C₄₇	C₂²	1	1	yes	characteristic, complemented
128	C₄×SD₁₆×C₄₇	C₂²	1	2	yes	complemented
129	C₄×D₈×C₄₇	C₂²	1	1	yes	characteristic, complemented
130	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic, complemented
131	C₂×Q₈×D₄₇	C₂³	1	2	yes	—
132	C₂×D₄×D₄₇	—	2	2	no	—
133	C₂×D₄×D₄₇	C₂³	1	2	yes	—
134	C₂²×C₄×D₄₇	—	2	2	no	—
135	C₂²×C₄×D₄₇	D₄	1	1	yes	characteristic
136	C₂²×C₄×D₄₇	D₄	1	1	yes	characteristic
137	C₂²×C₄×D₄₇	C₂³	1	1	yes	characteristic
138	C₂×Dic₁₈₈	C₂³	1	1	yes	characteristic
139	C₂×#10625337	C₂³	1	2	yes	—
140	Q₁₆×D₄₇	—	2	4	no	—
141	C₂×#10625325	C₂³	1	2	yes	—
142	C₂×#10625335	C₂³	1	2	yes	—
143	C₂×#10625336	C₂³	1	2	yes	—
144	SD₁₆×D₄₇	—	2	8	no	—
145	C₂×D₃₇₆	C₂³	1	1	yes	characteristic
146	C₂×#10625334	C₂³	1	2	yes	—
147	D₈×D₄₇	—	2	4	no	—
148	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
149	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
150	C₂×C₈×D₄₇	—	2	4	no	—
151	C₂×C₈×D₄₇	—	2	4	no	—
152	C₂×C₈×D₄₇	C₂³	1	1	yes	characteristic
153	C₂×C₈×D₄₇	C₂³	1	1	yes	characteristic
154	C₂×C₈×D₄₇	C₂³	1	1	yes	characteristic
155	C₂×C₈×D₄₇	C₂³	1	1	yes	characteristic
156	C₂×C₈×D₄₇	C₂³	1	1	yes	characteristic
157	C₂×C₈×D₄₇	C₂³	1	1	yes	characteristic
158	C₂×C₈×D₄₇	C₂³	1	1	yes	characteristic
159	C₂×C₈×D₄₇	C₂³	1	1	yes	characteristic
160	#13094019	—	2	2	no	—
161	#13094019	—	2	2	no	—
162	#13094019	—	2	2	no	—
163	#13094018	—	2	2	no	—
164	#13094017	—	2	2	no	—
165	#13094017	—	2	2	no	—
166	#13094017	—	2	2	no	—
167	#13094016	C₂³	1	2	yes	—
168	#13094015	C₂³	1	2	yes	—
169	#13094015	C₂³	1	2	yes	—
170	#13094014	—	2	2	no	—
171	#13094014	—	2	2	no	—
172	#13094013	C₂³	1	2	yes	—
173	#13094012	C₂³	1	2	yes	—
174	#13094011	C₂³	1	2	yes	—
175	#13094010	—	2	2	no	—
176	#13094010	—	2	2	no	—
177	#13094009	—	2	2	no	—
178	#13094009	—	2	2	no	—
179	#13094008	—	2	2	no	—
180	#13094007	—	2	2	no	—
181	#13094006	—	2	2	no	—
182	#13094006	—	2	2	no	—
183	#13094005	—	2	2	no	—
184	#13094004	C₂³	1	2	yes	—
185	#13094003	C₂³	1	2	yes	—
186	#13094002	—	2	2	no	—
187	#13094001	—	2	2	no	—
188	#13094000	C₂³	1	2	yes	—
189	#13093999	C₂³	1	2	yes	—
190	#13093998	C₂³	1	2	yes	—
191	#13093997	—	2	2	no	—
192	#13093996	—	2	2	no	—
193	#13093995	C₂³	1	2	yes	—
194	Q₈×Dic₄₇	C₂³	1	2	yes	—
195	C₄×Dic₉₄	—	2	2	no	—
196	C₄×Dic₉₄	C₂³	1	2	yes	—
197	#13093989	—	2	2	no	—
198	#13093989	C₂³	1	2	yes	—
199	C₄×D₁₈₈	—	2	2	no	—
200	C₄×D₁₈₈	C₂³	1	2	yes	—
201	D₄×Dic₄₇	—	2	2	no	—
202	D₄×Dic₄₇	C₂³	1	2	yes	—
203	#13093986	—	2	2	no	—
204	#13093986	C₂³	1	2	yes	—
205	C₄×C₂²⋊D₄₇	—	2	2	no	—
206	C₄×C₂²⋊D₄₇	—	2	2	no	—
207	C₄×C₂²⋊D₄₇	—	2	2	no	—
208	(C₂²⋊D₄₇)⋊C₄	—	2	2	no	—
209	(C₂²⋊D₄₇)⋊C₄	—	2	2	no	—
210	(C₂²⋊D₄₇)⋊C₄	—	2	2	no	—
211	#13093983	—	2	2	no	—
212	#13093982	—	2	2	no	—
213	#13093982	—	2	2	no	—
214	#13093981	—	2	2	no	—
215	#13093981	—	2	2	no	—
216	#13093980	—	2	2	no	—
217	#13093980	—	2	2	no	—
218	C₄⋊C₄×D₄₇	—	2	2	no	—
219	C₄⋊C₄×D₄₇	—	2	2	no	—
220	C₄⋊C₄×D₄₇	—	2	2	no	—
221	C₄⋊C₄×D₄₇	—	2	2	no	—
222	C₄⋊C₄×D₄₇	C₂³	1	2	yes	—
223	C₄⋊C₄×D₄₇	C₂³	1	2	yes	—
224	C₂²⋊C₄×D₄₇	—	2	2	no	—
225	C₂²⋊C₄×D₄₇	—	2	2	no	—
226	C₂²⋊C₄×D₄₇	—	2	2	no	—
227	C₂²⋊C₄×D₄₇	—	2	2	no	—
228	C₂²⋊C₄×D₄₇	—	2	2	no	—
229	C₂×C₄×Dic₄₇	D₄	1	1	yes	characteristic
230	C₂×C₄×Dic₄₇	D₄	1	1	yes	characteristic
231	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
232	C₄²×D₄₇	—	2	2	no	—
233	C₄²×D₄₇	D₄	1	1	yes	characteristic
234	C₄²×D₄₇	D₄	1	1	yes	characteristic
235	C₄²×D₄₇	D₄	1	1	yes	characteristic
236	C₄²×D₄₇	D₄	1	1	yes	characteristic
237	C₄²×D₄₇	C₂³	1	1	yes	characteristic
238	C₄²×D₄₇	C₂³	1	1	yes	characteristic
239	C₄²×D₄₇	C₂³	1	1	yes	characteristic
240	C₄²×D₄₇	C₂³	1	1	yes	characteristic
241	#13093958	C₂³	1	1	yes	characteristic
242	#13093958	C₂³	1	1	yes	characteristic
243	#13093957	C₂³	1	2	yes	—
244	#13093957	C₂³	1	2	yes	—
245	#13093956	C₂³	1	2	yes	—
246	#13093955	C₂³	1	2	yes	—
247	#13093955	C₂³	1	2	yes	—
248	#13093949	C₂³	1	2	yes	—
249	#13093949	C₂³	1	2	yes	—
250	#13093948	C₂³	1	2	yes	—
251	#13093948	C₂³	1	2	yes	—
252	#13093947	C₂³	1	2	yes	—
253	#13093947	C₂³	1	2	yes	—
254	#13093946	C₂³	1	2	yes	—
255	#13093946	C₂³	1	2	yes	—
256	#13093945	C₂³	1	2	yes	—
257	#13093945	C₂³	1	2	yes	—
258	#13093944	C₂³	1	2	yes	—
259	#13093944	C₂³	1	2	yes	—
260	C₄×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
261	C₄×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
262	C₄×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
263	C₄×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
264	C₈×Dic₄₇	C₂³	1	1	yes	characteristic
265	C₈×Dic₄₇	C₂³	1	1	yes	characteristic
266	C₈×Dic₄₇	C₂³	1	1	yes	characteristic
267	C₈×Dic₄₇	C₂³	1	1	yes	characteristic
268	C₈×Dic₄₇	C₂³	1	1	yes	characteristic
269	C₈×Dic₄₇	C₂³	1	1	yes	characteristic
270	C₈×Dic₄₇	C₂³	1	1	yes	characteristic
271	C₈×Dic₄₇	C₂³	1	1	yes	characteristic
272	C₂×Q₁₆×C₄₇	C₂³	1	1	yes	characteristic
273	C₂×SD₁₆×C₄₇	C₂³	1	2	yes	—
274	C₂×D₈×C₄₇	C₂³	1	1	yes	characteristic
275	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
276	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
277	#126×C₄₇	—	2	2	no	—
278	#125×C₄₇	C₂³	1	2	yes	—
279	#124×C₄₇	C₂³	1	2	yes	—
280	#123×C₄₇	—	2	2	no	—
281	C₂²⋊Q₈×C₄₇	C₂³	1	2	yes	—
282	#121×C₄₇	C₂³	1	2	yes	—
283	C₄×Q₈×C₄₇	C₂³	1	2	yes	—
284	C₄×D₄×C₄₇	—	2	2	no	—
285	C₄×D₄×C₄₇	C₂³	1	2	yes	—
286	#117×C₄₇	—	2	2	no	—
287	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
288	#107×C₄₇	C₂³	1	1	yes	characteristic
289	#107×C₄₇	C₂³	1	1	yes	characteristic
290	#106×C₄₇	C₂³	1	2	yes	—
291	#103×C₄₇	C₂³	1	2	yes	—
292	#103×C₄₇	C₂³	1	2	yes	—
293	#102×C₄₇	C₂³	1	2	yes	—
294	#102×C₄₇	C₂³	1	2	yes	—
295	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
296	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
297	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
298	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
299	C₂³×D₄₇	—	2	2	no	—
300	C₂³×D₄₇	C₂×D₄	1	1	yes	characteristic
301	C₂×Q₈×C₄₇	C₂⁴	1	2	yes	—
302	C₂×D₄×C₄₇	—	2	2	no	—
303	C₂×D₄×C₄₇	C₂⁴	1	2	yes	—
304	C₂²×C₄×C₄₇	—	2	2	no	—
305	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
306	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
307	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
308	C₂×C₂²⋊D₄₇	—	2	2	no	—
309	C₂×C₂²⋊D₄₇	—	2	2	no	—
310	C₂×C₂²⋊D₄₇	—	2	2	no	—
311	C₂²×Dic₄₇	—	2	2	no	—
312	C₂²×Dic₄₇	C₂×D₄	1	1	yes	characteristic
313	C₂²×Dic₄₇	C₂×D₄	1	1	yes	characteristic
314	C₂²×Dic₄₇	C₂×D₄	1	1	yes	characteristic
315	Q₈×D₄₇	—	2	4	no	—
316	Q₈×D₄₇	—	2	4	no	—
317	D₄×D₄₇	—	2	4	no	—
318	D₄×D₄₇	—	2	4	no	—
319	D₄×D₄₇	—	4	8	no	—
320	C₂×D₁₈₈	—	2	2	no	—
321	C₂×D₁₈₈	C₂⁴	1	2	yes	—
322	C₂×C₄×D₄₇	—	2	4	no	—
323	C₂×C₄×D₄₇	—	2	4	no	—
324	C₂×C₄×D₄₇	—	2	2	no	—
325	C₂×C₄×D₄₇	—	2	2	no	—
326	C₂×C₄×D₄₇	—	2	2	no	—
327	C₂×C₄×D₄₇	—	2	2	no	—
328	C₂×C₄×D₄₇	—	2	2	no	—
329	C₂×C₄×D₄₇	—	2	2	no	—
330	C₂×C₄×D₄₇	—	2	2	no	—
331	C₂×C₄×D₄₇	—	4	8	no	—
332	C₂×C₄×D₄₇	C₂×D₄	1	1	yes	characteristic
333	C₂×C₄×D₄₇	C₂×D₄	1	1	yes	characteristic
334	C₂×C₄×D₄₇	C₂×D₄	1	1	yes	characteristic
335	C₂×C₄×D₄₇	C₂×D₄	1	1	yes	characteristic
336	C₂×C₄×D₄₇	C₂×D₄	1	1	yes	characteristic
337	C₂×C₄×D₄₇	C₂×D₄	1	1	yes	characteristic
338	C₂×C₄×D₄₇	C₂×D₄	1	1	yes	characteristic
339	C₂×C₄×D₄₇	C₂×D₄	1	1	yes	characteristic
340	C₂×C₄×D₄₇	C₂×D₄	1	1	yes	characteristic
341	C₂×C₄×D₄₇	C₂×D₄	1	1	yes	characteristic
342	C₂×C₄×D₄₇	C₂⁴	1	1	yes	characteristic
343	C₂×C₄×D₄₇	C₂⁴	1	1	yes	characteristic
344	C₂×Dic₉₄	—	2	2	no	—
345	C₂×Dic₉₄	C₂⁴	1	2	yes	—
346	Q₁₆×C₄₇	—	2	2	no	—
347	SD₁₆×C₄₇	—	2	4	no	—
348	D₈×C₄₇	—	2	2	no	—
349	C₂×C₈×C₄₇	—	2	2	no	—
350	C₂×C₈×C₄₇	—	2	2	no	—
351	C₂×C₈×C₄₇	C₂⁴	1	1	yes	characteristic
352	C₂×C₈×C₄₇	C₂⁴	1	1	yes	characteristic
353	C₂×C₈×C₄₇	C₂⁴	1	1	yes	characteristic
354	C₂×C₈×C₄₇	C₂⁴	1	1	yes	characteristic
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	C₂⁴	1	2	yes	—
360	C₄⋊C₄×C₄₇	C₂⁴	1	2	yes	—
361	C₂²⋊C₄×C₄₇	—	2	2	no	—
362	C₂²⋊C₄×C₄₇	—	2	2	no	—
363	C₂²⋊C₄×C₄₇	—	2	2	no	—
364	C₂²⋊C₄×C₄₇	—	2	2	no	—
365	C₂²⋊C₄×C₄₇	—	2	2	no	—
366	C₄²×C₄₇	—	2	2	no	—
367	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
368	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
369	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
370	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
371	C₂²⋊Dic₄₇	—	2	2	no	—
372	C₂²⋊Dic₄₇	—	2	2	no	—
373	C₂²⋊Dic₄₇	—	2	2	no	—
374	C₂²⋊Dic₄₇	—	2	2	no	—
375	C₂²⋊Dic₄₇	—	2	2	no	—
376	#10625337	—	2	4	no	—
377	#10625336	—	2	4	no	—
378	#10625335	—	2	4	no	—
379	#10625334	—	2	4	no	—
380	(C₂×D₄₇)⋊C₄	—	2	2	no	—
381	(C₂×D₄₇)⋊C₄	—	2	2	no	—
382	(C₂×D₄₇)⋊C₄	—	2	2	no	—
383	(C₂×D₄₇)⋊C₄	—	2	2	no	—
384	(C₂×D₄₇)⋊C₄	—	2	2	no	—
385	(C₂×D₄₇)⋊C₄	—	2	2	no	—
386	(C₂×D₄₇)⋊C₄	—	2	2	no	—
387	(C₂×D₄₇)⋊C₄	—	2	2	no	—
388	(C₂×D₄₇)⋊C₄	—	2	2	no	—
389	(C₂×D₄₇)⋊C₄	—	2	2	no	—
390	C₄⋊Dic₄₇	—	2	2	no	—
391	C₄⋊Dic₄₇	—	2	2	no	—
392	C₄⋊Dic₄₇	—	2	2	no	—
393	C₄⋊Dic₄₇	—	2	2	no	—
394	C₄⋊Dic₄₇	C₂⁴	1	2	yes	—
395	C₄⋊Dic₄₇	C₂⁴	1	2	yes	—
396	Dic₄₇⋊C₄	—	2	2	no	—
397	Dic₄₇⋊C₄	—	2	2	no	—
398	Dic₄₇⋊C₄	—	2	2	no	—
399	Dic₄₇⋊C₄	—	2	2	no	—
400	Dic₄₇⋊C₄	—	2	2	no	—
401	Dic₄₇⋊C₄	—	2	2	no	—
402	Dic₄₇⋊C₄	—	2	2	no	—
403	Dic₄₇⋊C₄	—	2	2	no	—
404	Dic₄₇⋊C₄	—	2	2	no	—
405	Dic₄₇⋊C₄	—	2	2	no	—
406	C₄×Dic₄₇	—	2	2	no	—
407	C₄×Dic₄₇	—	2	2	no	—
408	C₄×Dic₄₇	—	2	2	no	—
409	C₄×Dic₄₇	C₂×D₄	1	1	yes	characteristic
410	C₄×Dic₄₇	C₂×D₄	1	1	yes	characteristic
411	C₄×Dic₄₇	C₂×D₄	1	1	yes	characteristic
412	C₄×Dic₄₇	C₂×D₄	1	1	yes	characteristic
413	C₄×Dic₄₇	C₂×D₄	1	1	yes	characteristic
414	C₄×Dic₄₇	C₂×D₄	1	1	yes	characteristic
415	C₄×Dic₄₇	C₂×D₄	1	1	yes	characteristic
416	C₄×Dic₄₇	C₂×D₄	1	1	yes	characteristic
417	C₄×Dic₄₇	C₂×D₄	1	1	yes	characteristic
418	C₄×Dic₄₇	C₂×D₄	1	1	yes	characteristic
419	C₄×Dic₄₇	C₂⁴	1	1	yes	characteristic
420	C₄×Dic₄₇	C₂⁴	1	1	yes	characteristic
421	C₂×C₄₇⋊C₈	—	2	2	no	—
422	C₂×C₄₇⋊C₈	—	2	2	no	—
423	C₂×C₄₇⋊C₈	C₂⁴	1	1	yes	characteristic
424	C₂×C₄₇⋊C₈	C₂⁴	1	1	yes	characteristic
425	C₂×C₄₇⋊C₈	C₂⁴	1	1	yes	characteristic
426	C₂×C₄₇⋊C₈	C₂⁴	1	1	yes	characteristic
427	Dic₁₈₈	—	2	2	no	—
428	D₃₇₆	—	2	2	no	—
429	#10625325	—	2	4	no	—
430	C₈×D₄₇	—	2	2	no	—
431	C₈×D₄₇	—	2	2	no	—
432	C₈×D₄₇	—	2	2	no	—
433	C₈×D₄₇	—	2	2	no	—
434	C₈×D₄₇	—	2	2	no	—
435	C₈×D₄₇	—	2	2	no	—
436	C₈×D₄₇	#41	1	4	yes	—
437	C₈×D₄₇	#41	1	4	yes	—
438	C₂³×C₄₇	—	2	2	no	—
439	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
440	C₂²×D₄₇	—	2	2	no	—
441	C₂²×D₄₇	—	2	2	no	—
442	C₂²×D₄₇	—	2	2	no	—
443	C₂²×D₄₇	—	4	4	no	—
444	C₂²×D₄₇	—	4	4	no	—
445	C₂²×D₄₇	—	4	4	no	—
446	C₂²×D₄₇	#135	1	4	yes	—
447	C₂²×D₄₇	C₂²×D₄	1	1	yes	characteristic
448	C₂²×D₄₇	C₂²×D₄	1	1	yes	characteristic
449	Q₈×C₄₇	—	2	2	no	—
450	Q₈×C₄₇	—	2	2	no	—
451	D₄×C₄₇	—	2	2	no	—
452	D₄×C₄₇	—	2	2	no	—
453	D₄×C₄₇	—	4	4	no	—
454	C₂×C₄×C₄₇	—	2	2	no	—
455	C₂×C₄×C₄₇	—	2	2	no	—
456	C₂×C₄×C₄₇	—	2	1	no	—
457	C₂×C₄×C₄₇	—	2	1	no	—
458	C₂×C₄×C₄₇	—	2	2	no	—
459	C₂×C₄×C₄₇	—	2	2	no	—
460	C₂×C₄×C₄₇	—	2	2	no	—
461	C₂×C₄×C₄₇	—	4	4	no	—
462	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
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	1	yes	characteristic
466	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
467	C₂×C₄×C₄₇	C₂⁵	1	1	yes	characteristic
468	C₂²⋊D₄₇	—	4	4	no	—
469	C₂²⋊D₄₇	—	4	4	no	—
470	C₂²⋊D₄₇	—	4	4	no	—
471	C₂×Dic₄₇	—	2	2	no	—
472	C₂×Dic₄₇	—	2	2	no	—
473	C₂×Dic₄₇	—	2	2	no	—
474	C₂×Dic₄₇	—	2	2	no	—
475	C₂×Dic₄₇	—	2	2	no	—
476	C₂×Dic₄₇	—	2	2	no	—
477	C₂×Dic₄₇	—	4	4	no	—
478	C₂×Dic₄₇	C₂²×D₄	1	1	yes	characteristic
479	C₂×Dic₄₇	C₂²×D₄	1	1	yes	characteristic
480	C₂×Dic₄₇	C₂²×D₄	1	1	yes	characteristic
481	C₂×Dic₄₇	C₂²×D₄	1	1	yes	characteristic
482	C₂×Dic₄₇	C₂²×D₄	1	1	yes	characteristic
483	C₂×Dic₄₇	C₂²×D₄	1	1	yes	characteristic
484	D₁₈₈	—	2	2	no	—
485	D₁₈₈	—	2	2	no	—
486	D₁₈₈	—	4	4	no	—
487	C₄×D₄₇	—	2	2	no	—
488	C₄×D₄₇	—	2	2	no	—
489	C₄×D₄₇	—	2	2	no	—
490	C₄×D₄₇	—	2	2	no	—
491	C₄×D₄₇	—	2	2	no	—
492	C₄×D₄₇	—	2	2	no	—
493	C₄×D₄₇	—	2	2	no	—
494	C₄×D₄₇	—	2	1	no	—
495	C₄×D₄₇	—	2	1	no	—
496	C₄×D₄₇	—	2	2	no	—
497	C₄×D₄₇	—	2	2	no	—
498	C₄×D₄₇	—	4	4	no	—
499	C₄×D₄₇	—	4	4	no	—
500	C₄×D₄₇	—	4	4	no	—
501	C₄×D₄₇	—	4	4	no	—
502	C₄×D₄₇	—	4	4	no	—
503	C₄×D₄₇	#135	1	4	yes	—
504	C₄×D₄₇	C₂×#41	1	2	yes	—
505	C₄×D₄₇	C₂×#41	1	2	yes	—
506	Dic₉₄	—	2	2	no	—
507	Dic₉₄	—	2	2	no	—
508	Dic₉₄	—	4	4	no	—
509	C₈×C₄₇	—	2	1	no	—
510	C₈×C₄₇	—	2	1	no	—
511	C₈×C₄₇	C₂×#41	1	2	yes	—
512	C₈×C₄₇	C₂×#41	1	2	yes	—
513	C₄₇⋊C₈	—	2	1	no	—
514	C₄₇⋊C₈	—	2	1	no	—
515	C₄₇⋊C₈	C₂×#41	1	2	yes	—
516	C₄₇⋊C₈	C₂×#41	1	2	yes	—
517	C₂×#3168	—	47	1	no	maximal, Sylow
518	C₂²×C₄₇	—	2	1	no	—
519	C₂²×C₄₇	—	2	1	no	—
520	C₂²×C₄₇	—	4	2	no	—
521	C₂²×C₄₇	—	4	2	no	—
522	C₂²×C₄₇	—	4	2	no	—
523	C₂²×C₄₇	C₂×#135	1	2	yes	—
524	C₂²×C₄₇	C₂³×D₄	1	1	yes	characteristic
525	C₂×D₄₇	—	2	1	no	—
526	C₂×D₄₇	—	2	1	no	—
527	C₂×D₄₇	—	2	8	no	—
528	C₂×D₄₇	—	4	2	no	—
529	C₂×D₄₇	—	4	2	no	—
530	C₂×D₄₇	—	4	2	no	—
531	C₂×D₄₇	—	8	8	no	—
532	C₂×D₄₇	#532	1	2	yes	—
533	C₂×D₄₇	C₂×#135	1	2	yes	—
534	C₂×D₄₇	C₂×#135	1	2	yes	—
535	C₂×D₄₇	C₂×#135	1	2	yes	—
536	C₄×C₄₇	—	2	1	no	—
537	C₄×C₄₇	—	2	1	no	—
538	C₄×C₄₇	—	2	1	no	—
539	C₄×C₄₇	—	2	1	no	—
540	C₄×C₄₇	—	4	2	no	—
541	C₄×C₄₇	—	4	2	no	—
542	C₄×C₄₇	—	4	2	no	—
543	C₄×C₄₇	C₂×#135	1	2	yes	—
544	C₄×C₄₇	C₂²×#41	1	1	yes	characteristic
545	C₄×C₄₇	C₂²×#41	1	1	yes	characteristic
546	Dic₄₇	—	2	1	no	—
547	Dic₄₇	—	2	1	no	—
548	Dic₄₇	—	2	1	no	—
549	Dic₄₇	—	2	1	no	—
550	Dic₄₇	—	4	2	no	—
551	Dic₄₇	—	4	2	no	—
552	Dic₄₇	—	4	2	no	—
553	Dic₄₇	#532	1	2	yes	—
554	Dic₄₇	C₂×#135	1	2	yes	—
555	C₂×#529	—	47	2	no	—
556	#3168	—	47	1	no	—
557	#3168	—	47	1	no	—
558	#3168	—	47	2	no	—
559	#3168	—	47	1	no	—
560	#3168	—	47	1	no	—
561	#3168	—	47	2	no	—
562	#3168	—	47	1	no	—
563	#3168	—	47	2	no	—
564	#3168	—	47	1	no	—
565	#3168	—	47	1	no	—
566	#3168	—	47	2	no	—
567	#3168	D₄₇	1	1	yes	characteristic, direct product factor
568	C₂×#499	—	47	1	no	—
569	C₂×#495	—	47	1	no	—
570	C₂×#488	—	47	2	no	—
571	C₂×#467	—	47	1	no	—
572	C₂×#466	—	47	1	no	—
573	C₂×#465	—	47	2	no	—
574	C₂×C₄×Q₁₆	—	47	1	no	—
575	C₂×C₄×SD₁₆	—	47	2	no	—
576	C₂×C₄×D₈	—	47	1	no	—
577	C₂²×C₄×C₈	—	47	1	no	—
578	C₂×C₄₇	—	2	2	no	—
579	C₂×C₄₇	—	8	2	no	—
580	C₂×C₄₇	C₂×#532	1	1	yes	characteristic
581	C₂×C₄₇	C₂²×#135	1	1	yes	characteristic
582	C₂×C₄₇	C₂²×#135	1	1	yes	characteristic
583	D₄₇	—	2	2	no	—
584	D₄₇	—	8	2	no	—
585	D₄₇	#3168	1	4	yes	direct product factor
586	C₂²×Q₁₆	—	47	1	no	—
587	C₂²×SD₁₆	—	47	2	no	—
588	C₂²×D₈	—	47	1	no	—
589	C₂³×C₈	—	47	1	no	—
590	C₂³×C₈	—	47	1	no	—
591	#529	—	47	2	no	—
592	#529	—	47	2	no	—
593	#529	—	47	2	no	—
594	#529	—	47	2	no	—
595	#529	—	47	2	no	—
596	#529	—	47	2	no	—
597	#529	—	47	2	no	—
598	#529	—	94	2	no	—
599	#529	—	94	2	no	—
600	#529	—	94	2	no	—
601	#529	—	94	2	no	—
602	#529	C₂×D₄₇	1	2	yes	complemented
603	C₂×#126	—	94	2	no	—
604	C₂×#125	—	47	2	no	—
605	C₂×#124	—	47	2	no	—
606	C₂×#123	—	94	2	no	—
607	C₂×C₂²⋊Q₈	—	47	2	no	—
608	C₂×#121	—	47	2	no	—
609	C₂×C₄×Q₈	—	47	2	no	—
610	C₂×C₄×D₄	—	47	2	no	—
611	C₂×C₄×D₄	—	94	2	no	—
612	C₂×#117	—	94	2	no	—
613	C₂²×C₄²	—	47	1	no	—
614	#499	—	47	2	no	—
615	#499	—	47	1	no	—
616	#499	—	47	1	no	—
617	#499	—	47	2	no	—
618	#499	—	47	1	no	—
619	#499	C₂×D₄₇	1	1	yes	characteristic, complemented
620	#495	—	47	1	no	—
621	#495	—	47	2	no	—
622	#495	—	47	1	no	—
623	#495	—	47	2	no	—
624	#495	—	47	1	no	—
625	#495	C₂×D₄₇	1	1	yes	characteristic, complemented
626	#488	—	47	2	no	—
627	#488	—	47	2	no	—
628	#488	—	47	2	no	—
629	#488	—	47	2	no	—
630	#488	—	47	2	no	—
631	#488	—	47	2	no	—
632	#488	—	47	2	no	—
633	#488	C₂×D₄₇	1	2	yes	complemented
634	#467	—	47	1	no	—
635	#467	—	47	1	no	—
636	#467	—	47	2	no	—
637	#467	—	47	1	no	—
638	#467	—	47	2	no	—
639	#467	C₂×D₄₇	1	1	yes	characteristic, complemented
640	#466	—	47	1	no	—
641	#466	—	47	1	no	—
642	#466	—	47	2	no	—
643	#466	—	47	1	no	—
644	#466	—	47	2	no	—
645	#466	C₂×D₄₇	1	1	yes	characteristic
646	#465	—	47	2	no	—
647	#465	—	47	2	no	—
648	#465	—	47	2	no	—
649	#465	—	47	2	no	—
650	#465	—	47	2	no	—
651	#465	—	47	2	no	—
652	#465	—	47	2	no	—
653	#465	C₂×D₄₇	1	2	yes	complemented
654	C₄×Q₁₆	—	47	1	no	—
655	C₄×Q₁₆	—	47	2	no	—
656	C₄×Q₁₆	—	47	1	no	—
657	C₄×Q₁₆	—	47	2	no	—
658	C₄×Q₁₆	—	47	1	no	—
659	C₄×Q₁₆	C₂×D₄₇	1	1	yes	characteristic, complemented
660	C₄×SD₁₆	—	47	2	no	—
661	C₄×SD₁₆	—	47	2	no	—
662	C₄×SD₁₆	—	47	2	no	—
663	C₄×SD₁₆	—	47	2	no	—
664	C₄×SD₁₆	—	47	2	no	—
665	C₄×SD₁₆	—	47	2	no	—
666	C₄×SD₁₆	—	47	2	no	—
667	C₄×SD₁₆	C₂×D₄₇	1	2	yes	complemented
668	C₄×D₈	—	47	1	no	—
669	C₄×D₈	—	47	2	no	—
670	C₄×D₈	—	47	1	no	—
671	C₄×D₈	—	47	2	no	—
672	C₄×D₈	—	47	1	no	—
673	C₄×D₈	C₂×D₄₇	1	1	yes	characteristic, complemented
674	C₂×#107	—	47	1	no	—
675	C₂×#107	—	47	1	no	—
676	C₂×#106	—	47	2	no	—
677	C₂×#103	—	47	2	no	—
678	C₂×#103	—	47	2	no	—
679	C₂×#102	—	47	2	no	—
680	C₂×#102	—	47	2	no	—
681	C₂×C₄×C₈	—	47	1	no	—
682	C₂×C₄×C₈	—	47	1	no	—
683	C₂×C₄×C₈	—	47	1	no	—
684	C₂×C₄×C₈	—	47	1	no	—
685	C₂×C₄×C₈	—	47	1	no	—
686	C₂×C₄×C₈	—	47	1	no	—
687	C₂×C₄×C₈	—	47	1	no	—
688	C₂×C₄×C₈	—	47	1	no	—
689	C₂×C₄×C₈	—	47	1	no	—
690	C₂×C₄×C₈	—	47	1	no	—
691	C₂×C₄×C₈	—	47	1	no	—
692	C₂×C₄×C₈	C₂×D₄₇	1	1	yes	characteristic, complemented
693	C₄₇	C₂×#3168	1	1	yes	characteristic, complemented, Sylow
694	C₂²×Q₈	—	47	2	no	—
695	C₂²×D₄	—	47	2	no	—
696	C₂²×D₄	—	94	2	no	—
697	C₂³×C₄	—	47	1	no	—
698	C₂³×C₄	—	47	1	no	—
699	C₂³×C₄	—	47	1	no	—
700	C₂³×C₄	—	94	2	no	—
701	C₂×Q₁₆	—	47	2	no	—
702	C₂×Q₁₆	—	47	1	no	—
703	C₂×Q₁₆	—	94	4	no	—
704	C₂×Q₁₆	C₂²×D₄₇	1	1	yes	characteristic
705	C₂×SD₁₆	—	47	2	no	—
706	C₂×SD₁₆	—	47	2	no	—
707	C₂×SD₁₆	—	47	2	no	—
708	C₂×SD₁₆	—	94	8	no	—
709	C₂×SD₁₆	C₂²×D₄₇	1	2	yes	—
710	C₂×D₈	—	47	2	no	—
711	C₂×D₈	—	47	1	no	—
712	C₂×D₈	—	94	4	no	—
713	C₂×D₈	C₂²×D₄₇	1	1	yes	characteristic
714	C₂²×C₈	—	47	1	no	—
715	C₂²×C₈	—	47	1	no	—
716	C₂²×C₈	—	47	1	no	—
717	C₂²×C₈	—	47	1	no	—
718	C₂²×C₈	—	47	1	no	—
719	C₂²×C₈	—	47	1	no	—
720	C₂²×C₈	—	47	1	no	—
721	C₂²×C₈	—	47	1	no	—
722	C₂²×C₈	—	47	1	no	—
723	C₂²×C₈	—	47	1	no	—
724	C₂²×C₈	—	94	4	no	—
725	C₂²×C₈	—	94	4	no	—
726	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
727	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
728	#126	—	2	2	no	—
729	#126	—	94	2	no	—
730	#126	—	94	2	no	—
731	#126	—	94	2	no	—
732	#126	—	94	2	no	—
733	#126	—	94	2	no	—
734	#126	—	94	2	no	—
735	#126	—	94	2	no	—
736	#125	—	47	2	no	—
737	#125	—	47	2	no	—
738	#125	—	47	2	no	—
739	#125	—	94	2	no	—
740	#125	—	94	2	no	—
741	#125	C₂²×D₄₇	1	2	yes	—
742	#124	—	47	2	no	—
743	#124	—	47	2	no	—
744	#124	—	47	2	no	—
745	#124	—	94	2	no	—
746	#124	—	94	2	no	—
747	#124	C₂²×D₄₇	1	2	yes	—
748	#123	—	2	2	no	—
749	#123	—	94	2	no	—
750	#123	—	94	2	no	—
751	#123	—	94	2	no	—
752	#123	—	94	2	no	—
753	#123	—	94	2	no	—
754	#123	—	94	2	no	—
755	#123	—	94	2	no	—
756	C₂²⋊Q₈	—	47	2	no	—
757	C₂²⋊Q₈	—	47	2	no	—
758	C₂²⋊Q₈	—	47	2	no	—
759	C₂²⋊Q₈	—	94	2	no	—
760	C₂²⋊Q₈	—	94	2	no	—
761	C₂²⋊Q₈	C₂²×D₄₇	1	2	yes	—
762	#121	—	47	2	no	—
763	#121	—	47	2	no	—
764	#121	—	47	2	no	—
765	#121	—	94	2	no	—
766	#121	—	94	2	no	—
767	#121	C₂²×D₄₇	1	2	yes	—
768	C₄×Q₈	—	47	2	no	—
769	C₄×Q₈	—	47	2	no	—
770	C₄×Q₈	—	47	2	no	—
771	C₄×Q₈	—	94	2	no	—
772	C₄×Q₈	—	94	2	no	—
773	C₄×Q₈	C₂²×D₄₇	1	2	yes	—
774	C₄×D₄	—	2	2	no	—
775	C₄×D₄	—	47	2	no	—
776	C₄×D₄	—	47	2	no	—
777	C₄×D₄	—	47	2	no	—
778	C₄×D₄	—	94	2	no	—
779	C₄×D₄	—	94	2	no	—
780	C₄×D₄	—	94	2	no	—
781	C₄×D₄	—	94	2	no	—
782	C₄×D₄	—	94	2	no	—
783	C₄×D₄	—	94	2	no	—
784	C₄×D₄	—	94	2	no	—
785	C₄×D₄	—	94	2	no	—
786	C₄×D₄	—	94	2	no	—
787	C₄×D₄	C₂²×D₄₇	1	2	yes	—
788	#117	—	2	2	no	—
789	#117	—	94	2	no	—
790	#117	—	94	2	no	—
791	#117	—	94	2	no	—
792	#117	—	94	2	no	—
793	#117	—	94	2	no	—
794	#117	—	94	2	no	—
795	#117	—	94	2	no	—
796	C₂×C₄⋊C₄	—	47	2	no	—
797	C₂×C₄⋊C₄	—	47	2	no	—
798	C₂×C₄⋊C₄	—	94	2	no	—
799	C₂×C₄⋊C₄	—	94	2	no	—
800	C₂×C₄⋊C₄	—	94	2	no	—
801	C₂×C₄⋊C₄	—	94	2	no	—
802	C₂×C₂²⋊C₄	—	94	2	no	—
803	C₂×C₂²⋊C₄	—	94	2	no	—
804	C₂×C₂²⋊C₄	—	94	2	no	—
805	C₂×C₂²⋊C₄	—	94	2	no	—
806	C₂×C₂²⋊C₄	—	94	2	no	—
807	C₂×C₄²	—	47	1	no	—
808	C₂×C₄²	—	47	1	no	—
809	C₂×C₄²	—	47	1	no	—
810	C₂×C₄²	—	47	1	no	—
811	C₂×C₄²	—	47	1	no	—
812	C₂×C₄²	—	47	1	no	—
813	C₂×C₄²	—	47	1	no	—
814	C₂×C₄²	—	47	1	no	—
815	C₂×C₄²	—	47	1	no	—
816	C₂×C₄²	—	47	1	no	—
817	C₂×C₄²	—	47	1	no	—
818	C₂×C₄²	—	94	2	no	—
819	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
820	#107	—	47	1	no	—
821	#107	—	47	1	no	—
822	#107	—	47	2	no	—
823	#107	—	47	2	no	—
824	#107	C₂²×D₄₇	1	1	yes	characteristic
825	#107	C₂²×D₄₇	1	1	yes	characteristic
826	#106	—	47	2	no	—
827	#106	—	47	2	no	—
828	#106	—	47	2	no	—
829	#106	C₂²×D₄₇	1	2	yes	—
830	#103	—	47	2	no	—
831	#103	—	47	2	no	—
832	#103	—	47	2	no	—
833	#103	—	47	2	no	—
834	#103	—	47	2	no	—
835	#103	—	47	2	no	—
836	#103	C₂²×D₄₇	1	2	yes	—
837	#103	C₂²×D₄₇	1	2	yes	—
838	#102	—	47	2	no	—
839	#102	—	47	2	no	—
840	#102	—	47	2	no	—
841	#102	—	47	2	no	—
842	#102	—	47	2	no	—
843	#102	—	47	2	no	—
844	#102	C₂²×D₄₇	1	2	yes	—
845	#102	C₂²×D₄₇	1	2	yes	—
846	C₄×C₈	—	47	1	no	—
847	C₄×C₈	—	47	1	no	—
848	C₄×C₈	—	47	1	no	—
849	C₄×C₈	—	47	1	no	—
850	C₄×C₈	—	47	1	no	—
851	C₄×C₈	—	47	1	no	—
852	C₄×C₈	—	47	1	no	—
853	C₄×C₈	—	47	1	no	—
854	C₄×C₈	—	47	1	no	—
855	C₄×C₈	—	47	1	no	—
856	C₄×C₈	—	47	1	no	—
857	C₄×C₈	—	47	1	no	—
858	C₄×C₈	C₂²×D₄₇	1	1	yes	characteristic
859	C₄×C₈	C₂²×D₄₇	1	1	yes	characteristic
860	C₄×C₈	C₂²×D₄₇	1	1	yes	characteristic
861	C₄×C₈	C₂²×D₄₇	1	1	yes	characteristic
862	C₂⁴	—	47	1	no	—
863	C₂⁴	—	94	2	no	—
864	C₂×Q₈	—	47	2	no	—
865	C₂×Q₈	—	94	2	no	—
866	C₂×Q₈	—	94	4	no	—
867	C₂×Q₈	—	94	4	no	—
868	C₂×Q₈	C₂³×D₄₇	1	2	yes	—
869	C₂×D₄	—	2	2	no	—
870	C₂×D₄	—	47	2	no	—
871	C₂×D₄	—	94	2	no	—
872	C₂×D₄	—	94	4	no	—
873	C₂×D₄	—	94	4	no	—
874	C₂×D₄	—	94	2	no	—
875	C₂×D₄	—	94	2	no	—
876	C₂×D₄	—	94	2	no	—
877	C₂×D₄	—	188	8	no	—
878	C₂×D₄	C₂³×D₄₇	1	2	yes	—
879	C₂²×C₄	—	2	2	no	—
880	C₂²×C₄	—	47	1	no	—
881	C₂²×C₄	—	47	1	no	—
882	C₂²×C₄	—	47	1	no	—
883	C₂²×C₄	—	47	1	no	—
884	C₂²×C₄	—	47	1	no	—
885	C₂²×C₄	—	47	1	no	—
886	C₂²×C₄	—	47	1	no	—
887	C₂²×C₄	—	47	1	no	—
888	C₂²×C₄	—	47	1	no	—
889	C₂²×C₄	—	47	1	no	—
890	C₂²×C₄	—	47	1	no	—
891	C₂²×C₄	—	47	1	no	—
892	C₂²×C₄	—	47	1	no	—
893	C₂²×C₄	—	47	1	no	—
894	C₂²×C₄	—	47	1	no	—
895	C₂²×C₄	—	94	2	no	—
896	C₂²×C₄	—	94	2	no	—
897	C₂²×C₄	—	94	4	no	—
898	C₂²×C₄	—	94	2	no	—
899	C₂²×C₄	—	94	4	no	—
900	C₂²×C₄	—	94	2	no	—
901	C₂²×C₄	—	94	2	no	—
902	C₂²×C₄	—	94	2	no	—
903	C₂²×C₄	—	94	2	no	—
904	C₂²×C₄	—	94	2	no	—
905	C₂²×C₄	—	188	8	no	—
906	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
907	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
908	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
909	Q₁₆	—	2	2	no	—
910	Q₁₆	—	94	4	no	—
911	Q₁₆	—	94	2	no	—
912	SD₁₆	—	2	4	no	—
913	SD₁₆	—	94	4	no	—
914	SD₁₆	—	94	4	no	—
915	SD₁₆	—	94	4	no	—
916	D₈	—	2	2	no	—
917	D₈	—	94	4	no	—
918	D₈	—	94	2	no	—
919	C₂×C₈	—	2	2	no	—
920	C₂×C₈	—	2	2	no	—
921	C₂×C₈	—	47	1	no	—
922	C₂×C₈	—	47	1	no	—
923	C₂×C₈	—	47	4	no	—
924	C₂×C₈	—	47	4	no	—
925	C₂×C₈	—	47	1	no	—
926	C₂×C₈	—	47	1	no	—
927	C₂×C₈	—	94	2	no	—
928	C₂×C₈	—	94	2	no	—
929	C₂×C₈	—	94	2	no	—
930	C₂×C₈	—	94	2	no	—
931	C₂×C₈	—	94	2	no	—
932	C₂×C₈	—	94	2	no	—
933	C₂×C₈	—	94	2	no	—
934	C₂×C₈	—	94	2	no	—
935	C₂×C₈	C₂³×D₄₇	1	1	yes	characteristic
936	C₂×C₈	C₂³×D₄₇	1	1	yes	characteristic
937	C₂×C₈	C₂³×D₄₇	1	1	yes	characteristic
938	C₂×C₈	C₂³×D₄₇	1	1	yes	characteristic
939	C₄⋊C₄	—	2	2	no	—
940	C₄⋊C₄	—	2	2	no	—
941	C₄⋊C₄	—	2	2	no	—
942	C₄⋊C₄	—	2	2	no	—
943	C₄⋊C₄	—	47	2	no	—
944	C₄⋊C₄	—	47	2	no	—
945	C₄⋊C₄	—	94	2	no	—
946	C₄⋊C₄	—	94	2	no	—
947	C₄⋊C₄	—	94	2	no	—
948	C₄⋊C₄	—	94	2	no	—
949	C₄⋊C₄	—	94	2	no	—
950	C₄⋊C₄	—	94	2	no	—
951	C₄⋊C₄	—	94	2	no	—
952	C₄⋊C₄	—	94	2	no	—
953	C₄⋊C₄	—	94	2	no	—
954	C₄⋊C₄	—	94	2	no	—
955	C₄⋊C₄	—	94	2	no	—
956	C₄⋊C₄	—	94	2	no	—
957	C₄⋊C₄	—	94	2	no	—
958	C₄⋊C₄	—	94	2	no	—
959	C₄⋊C₄	C₂³×D₄₇	1	2	yes	—
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	—	2	2	no	—
966	C₂²⋊C₄	—	94	2	no	—
967	C₂²⋊C₄	—	94	2	no	—
968	C₂²⋊C₄	—	94	2	no	—
969	C₂²⋊C₄	—	94	2	no	—
970	C₂²⋊C₄	—	94	2	no	—
971	C₂²⋊C₄	—	94	2	no	—
972	C₂²⋊C₄	—	94	2	no	—
973	C₂²⋊C₄	—	94	2	no	—
974	C₂²⋊C₄	—	94	2	no	—
975	C₂²⋊C₄	—	94	2	no	—
976	C₂²⋊C₄	—	94	2	no	—
977	C₂²⋊C₄	—	94	2	no	—
978	C₂²⋊C₄	—	94	2	no	—
979	C₂²⋊C₄	—	94	2	no	—
980	C₂²⋊C₄	—	94	2	no	—
981	C₄²	—	2	2	no	—
982	C₄²	—	47	1	no	—
983	C₄²	—	47	1	no	—
984	C₄²	—	47	1	no	—
985	C₄²	—	47	1	no	—
986	C₄²	—	47	1	no	—
987	C₄²	—	47	1	no	—
988	C₄²	—	47	1	no	—
989	C₄²	—	47	1	no	—
990	C₄²	—	47	1	no	—
991	C₄²	—	47	1	no	—
992	C₄²	—	47	1	no	—
993	C₄²	—	47	1	no	—
994	C₄²	—	94	2	no	—
995	C₄²	—	94	2	no	—
996	C₄²	—	94	2	no	—
997	C₄²	D₄×D₄₇	1	1	yes	characteristic
998	C₄²	D₄×D₄₇	1	1	yes	characteristic
999	C₄²	C₂³×D₄₇	1	1	yes	characteristic
1000	C₄²	C₂³×D₄₇	1	1	yes	characteristic
1001	C₂³	—	2	2	no	—
1002	C₂³	—	47	1	no	—
1003	C₂³	—	47	4	no	—
1004	C₂³	—	47	1	no	—
1005	C₂³	—	94	2	no	—
1006	C₂³	—	94	2	no	—
1007	C₂³	—	94	2	no	—
1008	C₂³	—	188	4	no	—
1009	C₂³	—	188	4	no	—
1010	C₂³	—	188	4	no	—
1011	C₂³	C₂×D₄×D₄₇	1	1	yes	characteristic
1012	Q₈	—	2	2	no	—
1013	Q₈	—	2	2	no	—
1014	Q₈	—	94	2	no	—
1015	Q₈	—	94	2	no	—
1016	Q₈	—	188	4	no	—
1017	D₄	—	2	2	no	—
1018	D₄	—	2	2	no	—
1019	D₄	—	4	4	no	—
1020	D₄	—	94	2	no	—
1021	D₄	—	94	2	no	—
1022	D₄	—	188	4	no	—
1023	D₄	—	188	4	no	—
1024	D₄	—	188	4	no	—
1025	D₄	—	188	4	no	—
1026	C₂×C₄	—	2	2	no	—
1027	C₂×C₄	—	2	2	no	—
1028	C₂×C₄	—	2	1	no	—
1029	C₂×C₄	—	2	1	no	—
1030	C₂×C₄	—	2	2	no	—
1031	C₂×C₄	—	2	2	no	—
1032	C₂×C₄	—	2	2	no	—
1033	C₂×C₄	—	4	4	no	—
1034	C₂×C₄	—	47	1	no	—
1035	C₂×C₄	—	47	1	no	—
1036	C₂×C₄	—	47	4	no	—
1037	C₂×C₄	—	47	2	no	—
1038	C₂×C₄	—	47	2	no	—
1039	C₂×C₄	—	47	1	no	—
1040	C₂×C₄	—	47	1	no	—
1041	C₂×C₄	—	47	1	no	—
1042	C₂×C₄	—	47	1	no	—
1043	C₂×C₄	—	94	2	no	—
1044	C₂×C₄	—	94	2	no	—
1045	C₂×C₄	—	94	2	no	—
1046	C₂×C₄	—	94	2	no	—
1047	C₂×C₄	—	94	2	no	—
1048	C₂×C₄	—	94	2	no	—
1049	C₂×C₄	—	94	2	no	—
1050	C₂×C₄	—	94	2	no	—
1051	C₂×C₄	—	94	2	no	—
1052	C₂×C₄	—	94	2	no	—
1053	C₂×C₄	—	94	2	no	—
1054	C₂×C₄	—	94	2	no	—
1055	C₂×C₄	—	94	1	no	—
1056	C₂×C₄	—	94	1	no	—
1057	C₂×C₄	—	94	2	no	—
1058	C₂×C₄	—	94	2	no	—
1059	C₂×C₄	—	94	2	no	—
1060	C₂×C₄	—	188	4	no	—
1061	C₂×C₄	—	188	4	no	—
1062	C₂×C₄	—	188	4	no	—
1063	C₂×C₄	—	188	4	no	—
1064	C₂×C₄	—	188	4	no	—
1065	C₂×C₄	—	188	4	no	—
1066	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
1067	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
1068	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
1069	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
1070	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
1071	C₂×C₄	C₂⁴×D₄₇	1	1	yes	characteristic
1072	C₈	—	2	1	no	—
1073	C₈	—	2	1	no	—
1074	C₈	—	47	2	no	—
1075	C₈	—	47	2	no	—
1076	C₈	—	94	1	no	—
1077	C₈	—	94	1	no	—
1078	C₈	#41×D₄₇	1	2	yes	—
1079	C₈	#41×D₄₇	1	2	yes	—
1080	C₂²	—	2	1	no	—
1081	C₂²	—	2	1	no	—
1082	C₂²	—	4	2	no	—
1083	C₂²	—	4	2	no	—
1084	C₂²	—	4	2	no	—
1085	C₂²	—	47	2	no	—
1086	C₂²	—	47	2	no	—
1087	C₂²	—	47	2	no	—
1088	C₂²	—	47	2	no	—
1089	C₂²	—	94	8	no	—
1090	C₂²	—	94	1	no	—
1091	C₂²	—	94	1	no	—
1092	C₂²	—	376	8	no	—
1093	C₂²	—	188	2	no	—
1094	C₂²	—	188	2	no	—
1095	C₂²	—	188	2	no	—
1096	C₂²	#135×D₄₇	1	2	yes	—
1097	C₂²	C₂²×D₄×D₄₇	1	1	yes	characteristic
1098	C₄	—	2	1	no	—
1099	C₄	—	2	1	no	—
1100	C₄	—	2	1	no	—
1101	C₄	—	2	1	no	—
1102	C₄	—	4	2	no	—
1103	C₄	—	4	2	no	—
1104	C₄	—	4	2	no	—
1105	C₄	—	47	2	no	—
1106	C₄	—	47	2	no	—
1107	C₄	—	94	1	no	—
1108	C₄	—	94	1	no	—
1109	C₄	—	94	1	no	—
1110	C₄	—	94	1	no	—
1111	C₄	—	188	2	no	—
1112	C₄	—	188	2	no	—
1113	C₄	—	188	2	no	—
1114	C₄	#135×D₄₇	1	2	yes	—
1115	C₄	C₂×#41×D₄₇	1	1	yes	characteristic
1116	C₄	C₂×#41×D₄₇	1	1	yes	characteristic
1117	C₂	—	2	2	no	—
1118	C₂	—	8	2	no	—
1119	C₂	—	47	4	no	—
1120	C₂	—	94	2	no	—
1121	C₂	—	376	2	no	—
1122	C₂	#532×D₄₇	1	1	yes	characteristic
1123	C₂	C₂×#135×D₄₇	1	1	yes	characteristic
1124	C₂	C₂×#135×D₄₇	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₄₇
commutator, cosocle	C₂×C₄×C₄₇	C₂⁵
Frattini	C₂×C₄	C₂⁴×D₄₇
Fitting	C₄₇×#3168	C₂
socle	C₂²×C₄₇	C₂³×D₄
prime radical	#466×D₄₇	C₂
hypercenter	#3168	D₄₇
hypocenter	C₄₇	C₂×#3168
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #3168

Complements

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

N	H ≅ G/N	type
1. #529×D₄₇	C₂	semidirect
2. #20253961	C₂	semidirect
3. #20253960	C₂	semidirect
4. #20253959	C₂	semidirect
5. #20253958	C₂	semidirect
6. #20253957	C₂	semidirect
7. #20253956	C₂	semidirect
8. #20253955	C₂	semidirect
9. #20253954	C₂	semidirect
10. #20253953	C₂	semidirect
11. #20253952	C₂	semidirect
12. #20253951	C₂	semidirect
13. #499×D₄₇	C₂	semidirect
14. #495×D₄₇	C₂	semidirect
15. #488×D₄₇	C₂	semidirect
16. #467×D₄₇	C₂	semidirect
18. #465×D₄₇	C₂	semidirect
19. C₄×Q₁₆×D₄₇	C₂	semidirect
20. C₄×SD₁₆×D₄₇	C₂	semidirect
21. C₄×D₈×D₄₇	C₂	semidirect
22. C₂×C₄×C₈×D₄₇	C₂	semidirect
23. C₄₇×#3168	C₂	semidirect
29. #15689660	C₂²	semidirect
30. #15689659	C₂²	semidirect
31. #15689658	C₂²	semidirect
32. #15689657	C₂²	semidirect
34. #15689655	C₂²	semidirect
35. #15689654	C₂²	semidirect
37. #15689652	C₂²	semidirect
51. #15689525	C₂²	semidirect
52. #15689524	C₂²	semidirect
53. #15689524	C₂²	semidirect
54. #15689523	C₂²	semidirect
55. #15689522	C₂²	semidirect
56. #15689508	C₂²	semidirect
57. #15689507	C₂²	semidirect
58. #15689506	C₂²	semidirect
59. #15689505	C₂²	semidirect
60. #15689504	C₂²	semidirect
61. #15689480	C₂²	semidirect
62. #15689479	C₂²	semidirect
63. #15689479	C₂²	semidirect
64. #15689478	C₂²	semidirect
65. #15689477	C₂²	semidirect
66. #15689476	C₂²	semidirect
67. #15689476	C₂²	semidirect
68. #15689365	C₂²	semidirect
69. #15689364	C₂²	semidirect
70. #15689363	C₂²	semidirect
71. #15689362	C₂²	semidirect
72. #15689361	C₂²	semidirect
78. #15689355	C₂²	semidirect
79. #15689354	C₂²	semidirect
80. #15689353	C₂²	semidirect
81. #15689352	C₂²	semidirect
82. #15689351	C₂²	semidirect
83. #15689350	C₂²	semidirect
84. #15689349	C₂²	semidirect
85. C₄×Dic₁₈₈	C₂²	semidirect
86. Q₁₆×Dic₄₇	C₂²	semidirect
87. #15689217	C₂²	semidirect
88. C₄×#10625337	C₂²	semidirect
89. #15689215	C₂²	semidirect
90. #15689214	C₂²	semidirect
91. C₄×#10625325	C₂²	semidirect
92. SD₁₆×Dic₄₇	C₂²	semidirect
93. C₄×#10625336	C₂²	semidirect
94. #15689210	C₂²	semidirect
95. C₄×#10625335	C₂²	semidirect
96. #15689208	C₂²	semidirect
97. C₄×D₃₇₆	C₂²	semidirect
98. D₈×Dic₄₇	C₂²	semidirect
99. #15689205	C₂²	semidirect
100. C₄×#10625334	C₂²	semidirect
101. #15689203	C₂²	semidirect
109. C₂×C₄×C₄₇⋊C₈	C₂²	semidirect
110. C₂×C₈×Dic₄₇	C₂²	semidirect
111. C₂×C₈×Dic₄₇	C₂²	semidirect
116. C₄×C₈×D₄₇	C₂²	semidirect
117. C₄×C₈×D₄₇	C₂²	semidirect
118. C₄×C₈×D₄₇	C₂²	semidirect
119. C₄×C₈×D₄₇	C₂²	semidirect
120. C₄₇×#529	C₂²	semidirect
121. C₄₇×#499	C₂²	semidirect
122. C₄₇×#495	C₂²	semidirect
123. C₄₇×#488	C₂²	semidirect
124. C₄₇×#467	C₂²	semidirect
126. C₄₇×#465	C₂²	semidirect
127. C₄×Q₁₆×C₄₇	C₂²	semidirect
128. C₄×SD₁₆×C₄₇	C₂²	semidirect
129. C₄×D₈×C₄₇	C₂²	semidirect
130. C₂×C₄×C₈×C₄₇	C₂²	semidirect
567. #3168	D₄₇	direct (N × H)
585. D₄₇	#3168	direct (N × H)
602. #529	C₂×D₄₇	semidirect
619. #499	C₂×D₄₇	semidirect
625. #495	C₂×D₄₇	semidirect
633. #488	C₂×D₄₇	semidirect
639. #467	C₂×D₄₇	semidirect
653. #465	C₂×D₄₇	semidirect
659. C₄×Q₁₆	C₂×D₄₇	semidirect
667. C₄×SD₁₆	C₂×D₄₇	semidirect
673. C₄×D₈	C₂×D₄₇	semidirect
692. C₂×C₄×C₈	C₂×D₄₇	semidirect
693. C₄₇	C₂×#3168	semidirect

Maximal subgroups

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

subgroup	index
#529×D₄₇	2
#20253961	2
#20253960	2
#20253959	2
#20253958	2
#20253957	2
#20253956	2
#20253955	2
#20253954	2
#20253953	2
#20253952	2
#20253951	2
#499×D₄₇	2
#495×D₄₇	2
#488×D₄₇	2
#467×D₄₇	2
#466×D₄₇	2
#465×D₄₇	2
C₄×Q₁₆×D₄₇	2
C₄×SD₁₆×D₄₇	2
C₄×D₈×D₄₇	2
C₂×C₄×C₈×D₄₇	2
C₄₇×#3168	2
C₂×#3168	47

Subgroups — D47×#3168 #27085996

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₄₇×#3168 #27085996