Subgroups — #27108525

Order 12032.

1952 conjugacy classes of subgroups.

The subgroup lattice has 1188 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20257351	C₂	1	1	yes	maximal, characteristic, complemented
2	#20256998	C₂	1	1	yes	maximal, characteristic, complemented
3	#20256398	C₂	1	1	yes	maximal, characteristic, complemented
4	#20256382	C₂	1	1	yes	maximal, characteristic, complemented
5	#20256046	C₂	1	1	yes	maximal, characteristic, complemented
6	#20256035	C₂	1	1	yes	maximal, characteristic, complemented
7	#20255293	C₂	1	2	yes	maximal, complemented
8	#20255266	C₂	1	1	yes	maximal, characteristic, complemented
9	#20255241	C₂	1	2	yes	maximal, complemented
10	#20255214	C₂	1	1	yes	maximal, characteristic, complemented
11	#20255093	C₂	1	2	yes	maximal, complemented
12	SD₁₆×D₁₈₈	C₂	1	1	yes	maximal, characteristic, complemented
13	#20255071	C₂	1	2	yes	maximal, complemented
14	D₈×D₁₈₈	C₂	1	1	yes	maximal, characteristic, complemented
15	#20254742	C₂	1	2	yes	maximal, complemented
16	#20254714	C₂	1	1	yes	maximal, characteristic, complemented
17	#20254357	C₂	1	2	yes	maximal, complemented
18	#20254323	C₂	1	1	yes	maximal, characteristic, complemented
19	#20253440	C₂	1	2	yes	maximal, complemented
20	#20252843	C₂	1	1	yes	maximal, characteristic, complemented
21	#463×D₄₇	C₂	1	2	yes	maximal, complemented
22	#20252496	C₂	1	1	yes	maximal, characteristic, complemented
23	C₄₇×#3102	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#13094044	C₂²	1	2	yes	complemented
25	C₂×SD₁₆×D₄₇	C₂²	1	2	yes	complemented
26	C₂×D₈×D₄₇	C₂²	1	2	yes	—
27	#15689858	C₂²	1	1	yes	characteristic, complemented
28	#15689858	C₂²	1	1	yes	characteristic, complemented
29	#15689843	C₂²	1	1	yes	characteristic, complemented
30	#15689838	—	2	1	no	—
31	#15689833	C₂²	1	1	yes	characteristic
32	#15689830	C₂²	1	1	yes	characteristic, complemented
33	#15689819	—	2	1	no	—
34	#15689817	C₂²	1	2	yes	complemented
35	#15689798	—	2	2	no	—
36	#15689797	—	2	2	no	—
37	Q₈×D₁₈₈	C₂²	1	1	yes	characteristic
38	#15689783	C₂²	1	2	yes	complemented
39	#15689770	C₂²	1	2	yes	complemented
40	#15689769	—	2	1	no	—
41	#15689769	—	2	1	no	—
42	#15689761	C₂²	1	2	yes	complemented
43	D₄×D₁₈₈	C₂²	1	1	yes	characteristic
44	D₄×D₁₈₈	C₂²	1	1	yes	characteristic
45	#15689744	—	2	1	no	—
46	#15689709	—	2	2	no	—
47	#15689673	C₂²	1	1	yes	characteristic, complemented
48	#15689673	C₂²	1	1	yes	characteristic, complemented
49	#15689660	C₂²	1	2	yes	complemented
50	#15689658	C₂²	1	2	yes	complemented
51	#15689657	—	2	1	no	—
52	#124×D₄₇	C₂²	1	2	yes	complemented
53	#15689632	—	2	2	no	—
54	#15689597	—	2	1	no	—
55	C₄×#10625350	C₂²	1	1	yes	characteristic
56	C₂×C₄×D₁₈₈	—	2	1	no	—
57	C₄×D₄×D₄₇	C₂²	1	2	yes	complemented
58	#15689508	C₂²	1	2	yes	complemented
59	#15689504	C₂²	1	2	yes	complemented
60	#15689500	C₂²	1	1	yes	characteristic
61	#15689496	C₂²	1	1	yes	characteristic, complemented
62	#15689479	C₂²	1	2	yes	complemented
63	#15689476	C₂²	1	2	yes	complemented
64	#15689474	C₂²	1	1	yes	characteristic, complemented
65	#15689470	C₂²	1	1	yes	characteristic, complemented
66	#15689460	C₂²	1	2	yes	complemented
67	#15689443	C₂²	1	2	yes	complemented
68	#15689429	C₂²	1	2	yes	complemented
69	#15689422	C₂²	1	2	yes	complemented
70	#15689420	C₂²	1	2	yes	complemented
71	#15689418	C₂²	1	1	yes	characteristic, complemented
72	#15689413	C₂²	1	1	yes	characteristic, complemented
73	#15689363	C₂²	1	2	yes	complemented
74	#15689360	C₂²	1	2	yes	—
75	#15689357	C₂²	1	2	yes	complemented
76	#15689355	C₂²	1	2	yes	complemented
77	#15689354	C₂²	1	2	yes	complemented
78	#15689353	C₂²	1	2	yes	complemented
79	#15689348	C₂²	1	2	yes	complemented
80	#15689345	C₂²	1	2	yes	complemented
81	#15689341	C₂²	1	2	yes	complemented
82	#15689341	C₂²	1	2	yes	complemented
83	#15689340	C₂²	1	2	yes	complemented
84	#15689339	C₂²	1	2	yes	complemented
85	#15689339	C₂²	1	2	yes	complemented
86	#15689338	C₂²	1	2	yes	complemented
87	#15689337	C₂²	1	2	yes	complemented
88	#15689336	C₂²	1	2	yes	—
89	#15689335	C₂²	1	2	yes	complemented
90	#15689333	C₂²	1	1	yes	characteristic, complemented
91	#15689328	C₂²	1	1	yes	characteristic, complemented
92	#15689323	C₂²	1	1	yes	characteristic, complemented
93	#15689323	C₂²	1	1	yes	characteristic, complemented
94	#15689318	C₂²	1	1	yes	characteristic
95	#15689318	C₂²	1	1	yes	characteristic
96	#15689277	C₂²	1	2	yes	complemented
97	#15689275	C₂²	1	2	yes	complemented
98	#15689272	C₂²	1	2	yes	complemented
99	#15689270	C₂²	1	2	yes	complemented
100	#15689270	C₂²	1	2	yes	complemented
101	#15689263	C₂²	1	2	yes	complemented
102	#15689258	C₂²	1	2	yes	—
103	#15689258	C₂²	1	2	yes	—
104	C₈×Dic₉₄	C₂²	1	1	yes	characteristic, complemented
105	C₈×Dic₉₄	C₂²	1	1	yes	characteristic, complemented
106	#15689214	C₂²	1	2	yes	complemented
107	#15689210	C₂²	1	2	yes	complemented
108	#15689205	C₂²	1	2	yes	complemented
109	#15689203	C₂²	1	2	yes	complemented
110	C₈×D₁₈₈	C₂²	1	1	yes	characteristic
111	C₈×D₁₈₈	C₂²	1	1	yes	characteristic
112	(C₂²⋊D₄₇)⋊C₈	C₂²	1	2	yes	complemented
113	(C₂²⋊D₄₇)⋊C₈	C₂²	1	2	yes	complemented
114	#15689175	C₂²	1	2	yes	complemented
115	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic, complemented
116	C₄⋊C₈×D₄₇	C₂²	1	2	yes	complemented
117	#15689117	C₂²	1	2	yes	complemented
118	#103×D₄₇	C₂²	1	2	yes	complemented
119	#102×D₄₇	C₂²	1	2	yes	complemented
120	C₄₇×#529	C₂²	1	1	yes	characteristic, complemented
121	C₄×#41×C₄₇	C₂²	1	1	yes	characteristic, complemented
122	C₄₇×#485	C₂²	1	1	yes	characteristic, complemented
123	C₄₇×#482	C₂²	1	1	yes	characteristic, complemented
124	C₄₇×#479	C₂²	1	1	yes	characteristic, complemented
125	C₄₇×#478	C₂²	1	1	yes	characteristic, complemented
126	C₄₇×#464	C₂²	1	1	yes	characteristic, complemented
127	C₄₇×#463	C₂²	1	1	yes	characteristic
128	C₄₇×#452	C₂²	1	1	yes	characteristic, complemented
129	C₄₇×#449	C₂²	1	1	yes	characteristic
130	C₄×Q₁₆×C₄₇	C₂²	1	1	yes	characteristic, complemented
131	C₄×SD₁₆×C₄₇	C₂²	1	1	yes	characteristic, complemented
132	C₄×SD₁₆×C₄₇	C₂²	1	1	yes	characteristic, complemented
133	C₄×D₈×C₄₇	C₂²	1	1	yes	characteristic
134	C₄₇×#431	C₂²	1	1	yes	characteristic, complemented
135	C₂×#10625350	—	2	1	no	—
136	C₂×#10625350	D₄	1	1	yes	characteristic
137	C₂×#10625350	C₂³	1	2	yes	—
138	C₂×Q₈×D₄₇	C₂³	1	2	yes	—
139	C₂²×D₁₈₈	—	2	1	no	—
140	C₂²×D₁₈₈	—	2	1	no	—
141	C₂×D₄×D₄₇	C₂³	1	2	yes	—
142	C₂×D₄×D₄₇	C₂³	1	2	yes	—
143	C₂²×C₄×D₄₇	—	2	2	no	—
144	#13094044	—	4	4	no	—
145	C₂×#10625337	C₂³	1	2	yes	—
146	C₂×#10625325	C₂³	1	2	yes	—
147	C₂×#10625325	C₂³	1	2	yes	—
148	C₂×#10625335	C₂³	1	2	yes	—
149	C₂×#10625336	C₂³	1	2	yes	—
150	C₂×#10625336	C₂³	1	2	yes	—
151	SD₁₆×D₄₇	—	4	4	no	—
152	C₂×D₃₇₆	C₂³	1	2	yes	—
153	C₂×D₃₇₆	C₂³	1	2	yes	—
154	C₂×#10625334	C₂³	1	2	yes	—
155	C₂×#10625334	C₂³	1	2	yes	—
156	D₈×D₄₇	—	4	4	no	—
157	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
158	C₂×C₈×D₄₇	C₂³	1	2	yes	—
159	C₂×C₈×D₄₇	C₂³	1	2	yes	—
160	#13094024	—	2	1	no	—
161	#13094024	C₂³	1	1	yes	characteristic
162	#13094024	C₂³	1	1	yes	characteristic
163	#13094021	C₂³	1	1	yes	characteristic
164	#13094021	C₂³	1	1	yes	characteristic
165	#13094019	—	2	2	no	—
166	#13094019	—	2	2	no	—
167	#13094018	—	2	2	no	—
168	#13094017	—	2	2	no	—
169	#13094016	—	2	1	no	—
170	#13094015	C₂³	1	2	yes	—
171	#13094013	C₂³	1	2	yes	—
172	#13094013	C₂³	1	2	yes	—
173	#13094012	—	2	1	no	—
174	#13094012	—	2	1	no	—
175	#13094012	—	2	1	no	—
176	#13094012	C₂³	1	2	yes	—
177	#13094011	C₂³	1	2	yes	—
178	#13094010	—	2	2	no	—
179	#13094010	—	2	2	no	—
180	#13094010	—	2	2	no	—
181	#13094009	—	2	2	no	—
182	#13094009	—	2	2	no	—
183	#13094009	—	2	2	no	—
184	#13094009	—	2	2	no	—
185	#13094007	—	2	2	no	—
186	#13094006	—	2	2	no	—
187	#13094006	—	2	2	no	—
188	#13094004	—	2	2	no	—
189	#13094004	C₂³	1	2	yes	—
190	#13094003	—	2	1	no	—
191	#13094003	—	2	1	no	—
192	#13094002	—	2	2	no	—
193	#13094002	—	2	2	no	—
194	#13094001	—	2	2	no	—
195	#13094000	C₂³	1	2	yes	—
196	#13093999	C₂³	1	2	yes	—
197	#13093999	C₂³	1	2	yes	—
198	#13093998	—	2	1	no	—
199	#13093998	—	2	1	no	—
200	#13093998	—	2	1	no	—
201	#13093998	—	2	1	no	—
202	#13093998	—	2	1	no	—
203	#13093998	C₂³	1	2	yes	—
204	#13093997	—	2	2	no	—
205	#13093997	—	2	2	no	—
206	#13093996	—	2	2	no	—
207	#13093995	—	2	2	no	—
208	#13093994	—	2	2	no	—
209	#13093994	—	2	2	no	—
210	#13093992	—	2	2	no	—
211	#13093992	—	2	2	no	—
212	C₄×Dic₉₄	D₄	1	1	yes	characteristic
213	C₄×Dic₉₄	C₂³	1	1	yes	characteristic
214	#13093989	C₂³	1	2	yes	—
215	C₄×D₁₈₈	—	2	1	no	—
216	C₄×D₁₈₈	—	2	1	no	—
217	C₄×D₁₈₈	—	2	2	no	—
218	C₄×D₁₈₈	—	2	1	no	—
219	C₄×D₁₈₈	—	2	1	no	—
220	C₄×D₁₈₈	—	2	1	no	—
221	C₄×D₁₈₈	—	2	2	no	—
222	C₄×D₁₈₈	—	2	1	no	—
223	C₄×D₁₈₈	—	2	1	no	—
224	C₄×D₁₈₈	D₄	1	1	yes	characteristic
225	C₄×D₁₈₈	C₂³	1	1	yes	characteristic
226	C₄×D₁₈₈	C₂³	1	2	yes	—
227	D₄×Dic₄₇	C₂³	1	2	yes	—
228	#13093986	—	2	2	no	—
229	#13093986	—	2	2	no	—
230	#13093986	C₂³	1	2	yes	—
231	#13093986	C₂³	1	2	yes	—
232	C₄×C₂²⋊D₄₇	—	2	2	no	—
233	C₄×C₂²⋊D₄₇	D₄	1	2	yes	—
234	C₄×C₂²⋊D₄₇	C₂³	1	2	yes	—
235	(C₂²⋊D₄₇)⋊C₄	—	2	2	no	—
236	#13093983	—	2	1	no	—
237	#13093983	D₄	1	1	yes	characteristic
238	#13093982	—	2	2	no	—
239	#13093981	—	2	2	no	—
240	#13093981	D₄	1	2	yes	—
241	C₂×C₄⋊Dic₄₇	—	2	1	no	—
242	C₄⋊C₄×D₄₇	C₂³	1	2	yes	—
243	C₂×(C₂×D₄₇)⋊C₄	—	2	2	no	—
244	C₂²⋊C₄×D₄₇	—	2	2	no	—
245	C₂²⋊C₄×D₄₇	—	2	2	no	—
246	C₂²⋊C₄×D₄₇	—	2	2	no	—
247	C₂²⋊C₄×D₄₇	—	2	2	no	—
248	C₄²×D₄₇	C₂³	1	2	yes	—
249	#13093957	C₂³	1	2	yes	—
250	#13093955	C₂³	1	2	yes	—
251	C₄⋊(C₄₇⋊C₈)	C₂³	1	1	yes	characteristic
252	C₄⋊(C₄₇⋊C₈)	C₂³	1	1	yes	characteristic
253	C₄⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
254	Dic₄₇⋊C₈	C₂³	1	2	yes	—
255	Dic₄₇⋊C₈	C₂³	1	2	yes	—
256	#13093949	C₂³	1	2	yes	—
257	#13093949	C₂³	1	2	yes	—
258	#13093948	C₂³	1	2	yes	—
259	#13093947	C₂³	1	2	yes	—
260	#13093947	C₂³	1	2	yes	—
261	#13093946	C₂³	1	2	yes	—
262	#13093946	C₂³	1	2	yes	—
263	#13093945	C₂³	1	2	yes	—
264	#13093944	C₂³	1	2	yes	—
265	#13093944	C₂³	1	2	yes	—
266	#13093944	C₂³	1	2	yes	—
267	#13093944	C₂³	1	2	yes	—
268	(C₂×D₄₇)⋊C₈	C₂³	1	2	yes	—
269	(C₂×D₄₇)⋊C₈	C₂³	1	2	yes	—
270	C₈×Dic₄₇	C₂³	1	2	yes	—
271	C₈×Dic₄₇	C₂³	1	2	yes	—
272	C₂×#41×C₄₇	C₂³	1	1	yes	characteristic
273	C₂×Q₁₆×C₄₇	C₂³	1	1	yes	characteristic
274	C₂×SD₁₆×C₄₇	C₂³	1	1	yes	characteristic
275	C₂×SD₁₆×C₄₇	C₂³	1	1	yes	characteristic
276	C₂×D₈×C₄₇	C₂³	1	1	yes	characteristic
277	#126×C₄₇	—	2	1	no	—
278	#125×C₄₇	C₂³	1	1	yes	characteristic
279	#124×C₄₇	C₂³	1	1	yes	characteristic
280	#123×C₄₇	—	2	1	no	—
281	C₂²⋊Q₈×C₄₇	C₂³	1	1	yes	characteristic
282	#121×C₄₇	C₂³	1	1	yes	characteristic
283	C₄×Q₈×C₄₇	C₂³	1	1	yes	characteristic
284	C₄×Q₈×C₄₇	C₂³	1	1	yes	characteristic
285	C₄×Q₈×C₄₇	C₂³	1	1	yes	characteristic
286	C₄×D₄×C₄₇	—	2	1	no	—
287	C₄×D₄×C₄₇	—	2	1	no	—
288	C₄×D₄×C₄₇	—	2	1	no	—
289	C₄×D₄×C₄₇	C₂³	1	1	yes	characteristic
290	C₄×D₄×C₄₇	C₂³	1	1	yes	characteristic
291	C₄×D₄×C₄₇	C₂³	1	1	yes	characteristic
292	#117×C₄₇	—	2	1	no	—
293	#117×C₄₇	—	2	1	no	—
294	#117×C₄₇	C₂³	1	1	yes	characteristic
295	C₂×C₄²×C₄₇	—	2	1	no	—
296	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
297	#107×C₄₇	C₂³	1	1	yes	characteristic
298	#107×C₄₇	C₂³	1	1	yes	characteristic
299	#106×C₄₇	C₂³	1	1	yes	characteristic
300	#106×C₄₇	C₂³	1	1	yes	characteristic
301	C₄⋊C₈×C₄₇	C₂³	1	1	yes	characteristic
302	C₄⋊C₈×C₄₇	C₂³	1	1	yes	characteristic
303	#103×C₄₇	C₂³	1	1	yes	characteristic
304	#103×C₄₇	C₂³	1	1	yes	characteristic
305	#103×C₄₇	C₂³	1	1	yes	characteristic
306	#103×C₄₇	C₂³	1	1	yes	characteristic
307	#102×C₄₇	C₂³	1	1	yes	characteristic
308	#102×C₄₇	C₂³	1	1	yes	characteristic
309	#102×C₄₇	C₂³	1	1	yes	characteristic
310	#102×C₄₇	C₂³	1	1	yes	characteristic
311	C₂²⋊C₈×C₄₇	C₂³	1	1	yes	characteristic
312	C₂²⋊C₈×C₄₇	C₂³	1	1	yes	characteristic
313	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
314	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
315	C₂³×D₄₇	—	2	2	no	—
316	C₂³×D₄₇	—	2	2	no	—
317	#41×C₄₇	—	2	2	no	—
318	#41×C₄₇	—	4	1	no	—
319	C₂×Q₈×C₄₇	C₂⁴	1	1	yes	characteristic
320	C₂×Q₈×C₄₇	C₂⁴	1	1	yes	characteristic
321	C₂×D₄×C₄₇	—	2	1	no	—
322	C₂×D₄×C₄₇	—	2	1	no	—
323	C₂×D₄×C₄₇	C₂⁴	1	1	yes	characteristic
324	C₂×D₄×C₄₇	C₂⁴	1	1	yes	characteristic
325	C₂²×C₄×C₄₇	—	2	1	no	—
326	C₂²×C₄×C₄₇	—	2	1	no	—
327	C₂²×C₄×C₄₇	—	2	1	no	—
328	C₂²×C₄×C₄₇	—	2	1	no	—
329	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
330	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
331	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
332	C₂×C₂²⋊D₄₇	—	2	2	no	—
333	C₂×C₂²⋊D₄₇	—	2	2	no	—
334	C₂×C₂²⋊D₄₇	—	2	2	no	—
335	C₂×C₂²⋊D₄₇	—	2	2	no	—
336	C₂×C₂²⋊D₄₇	C₂×D₄	1	2	yes	—
337	C₂²×Dic₄₇	—	2	2	no	—
338	Q₈×D₄₇	—	4	2	no	—
339	Q₈×D₄₇	—	4	2	no	—
340	D₄×D₄₇	—	2	4	no	—
341	D₄×D₄₇	—	4	2	no	—
342	D₄×D₄₇	—	4	2	no	—
343	D₄×D₄₇	—	4	2	no	—
344	#10625350	—	2	4	no	—
345	#10625350	—	4	2	no	—
346	#10625350	—	4	2	no	—
347	#10625350	—	8	2	no	—
348	C₂×D₁₈₈	—	2	2	no	—
349	C₂×D₁₈₈	—	2	2	no	—
350	C₂×D₁₈₈	—	2	1	no	—
351	C₂×D₁₈₈	—	2	1	no	—
352	C₂×D₁₈₈	—	2	1	no	—
353	C₂×D₁₈₈	—	2	1	no	—
354	C₂×D₁₈₈	—	4	4	no	—
355	C₂×D₁₈₈	—	4	4	no	—
356	C₂×D₁₈₈	C₂×D₄	1	1	yes	characteristic
357	C₂×D₁₈₈	C₂⁴	1	2	yes	—
358	C₂×D₁₈₈	C₂⁴	1	2	yes	—
359	C₂×C₄×D₄₇	—	2	2	no	—
360	C₂×C₄×D₄₇	—	2	2	no	—
361	C₂×C₄×D₄₇	—	2	2	no	—
362	C₂×C₄×D₄₇	—	2	2	no	—
363	C₂×C₄×D₄₇	—	2	2	no	—
364	C₂×C₄×D₄₇	—	2	2	no	—
365	C₂×C₄×D₄₇	—	8	4	no	—
366	C₂×C₄×D₄₇	C₂×D₄	1	2	yes	—
367	C₂×C₄×D₄₇	C₂×D₄	1	2	yes	—
368	C₂×C₄×D₄₇	C₂⁴	1	2	yes	—
369	C₂×Dic₉₄	—	2	1	no	—
370	C₂×Dic₉₄	—	2	2	no	—
371	C₂×Dic₉₄	C₂×D₄	1	1	yes	characteristic
372	C₂×Dic₉₄	C₂⁴	1	2	yes	—
373	Q₁₆×C₄₇	—	4	1	no	—
374	SD₁₆×C₄₇	—	2	2	no	—
375	SD₁₆×C₄₇	—	4	1	no	—
376	D₈×C₄₇	—	2	2	no	—
377	C₂×C₈×C₄₇	C₂⁴	1	1	yes	characteristic
378	C₂×C₈×C₄₇	C₂⁴	1	1	yes	characteristic
379	C₂×C₈×C₄₇	C₂⁴	1	1	yes	characteristic
380	C₂×C₈×C₄₇	C₂⁴	1	1	yes	characteristic
381	C₄⋊C₄×C₄₇	—	2	1	no	—
382	C₄⋊C₄×C₄₇	—	2	1	no	—
383	C₄⋊C₄×C₄₇	—	2	1	no	—
384	C₄⋊C₄×C₄₇	—	2	1	no	—
385	C₄⋊C₄×C₄₇	—	2	1	no	—
386	C₄⋊C₄×C₄₇	—	2	1	no	—
387	C₄⋊C₄×C₄₇	C₂⁴	1	1	yes	characteristic
388	C₄⋊C₄×C₄₇	C₂⁴	1	1	yes	characteristic
389	C₄⋊C₄×C₄₇	C₂⁴	1	1	yes	characteristic
390	C₄⋊C₄×C₄₇	C₂⁴	1	1	yes	characteristic
391	C₂²⋊C₄×C₄₇	—	2	1	no	—
392	C₂²⋊C₄×C₄₇	—	2	1	no	—
393	C₂²⋊C₄×C₄₇	—	2	1	no	—
394	C₂²⋊C₄×C₄₇	—	2	1	no	—
395	C₂²⋊C₄×C₄₇	—	2	1	no	—
396	C₂²⋊C₄×C₄₇	—	2	1	no	—
397	C₂²⋊C₄×C₄₇	—	2	1	no	—
398	C₂²⋊C₄×C₄₇	—	2	1	no	—
399	C₄²×C₄₇	—	2	1	no	—
400	C₄²×C₄₇	—	2	1	no	—
401	C₄²×C₄₇	—	2	1	no	—
402	C₄²×C₄₇	—	2	1	no	—
403	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
404	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
405	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
406	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
407	C₂²⋊Dic₄₇	—	2	2	no	—
408	C₂²⋊Dic₄₇	—	2	2	no	—
409	C₂²⋊Dic₄₇	—	2	2	no	—
410	C₂²⋊Dic₄₇	C₂×D₄	1	2	yes	—
411	#10625337	—	4	2	no	—
412	#10625336	—	4	2	no	—
413	#10625336	—	4	2	no	—
414	#10625335	—	2	4	no	—
415	#10625334	—	2	4	no	—
416	#10625334	—	4	2	no	—
417	(C₂×D₄₇)⋊C₄	—	2	2	no	—
418	(C₂×D₄₇)⋊C₄	—	2	2	no	—
419	(C₂×D₄₇)⋊C₄	—	2	2	no	—
420	(C₂×D₄₇)⋊C₄	—	2	2	no	—
421	(C₂×D₄₇)⋊C₄	—	2	2	no	—
422	(C₂×D₄₇)⋊C₄	—	2	2	no	—
423	(C₂×D₄₇)⋊C₄	—	2	2	no	—
424	(C₂×D₄₇)⋊C₄	—	2	2	no	—
425	(C₂×D₄₇)⋊C₄	—	2	2	no	—
426	(C₂×D₄₇)⋊C₄	—	2	2	no	—
427	(C₂×D₄₇)⋊C₄	—	2	2	no	—
428	(C₂×D₄₇)⋊C₄	—	2	2	no	—
429	(C₂×D₄₇)⋊C₄	—	2	2	no	—
430	(C₂×D₄₇)⋊C₄	—	2	2	no	—
431	(C₂×D₄₇)⋊C₄	C₂×D₄	1	2	yes	—
432	(C₂×D₄₇)⋊C₄	C₂×D₄	1	2	yes	—
433	C₄⋊Dic₄₇	—	2	1	no	—
434	C₄⋊Dic₄₇	—	2	1	no	—
435	C₄⋊Dic₄₇	—	2	1	no	—
436	C₄⋊Dic₄₇	—	2	2	no	—
437	C₄⋊Dic₄₇	—	2	2	no	—
438	C₄⋊Dic₄₇	C₂×D₄	1	1	yes	characteristic
439	C₄⋊Dic₄₇	C₂×D₄	1	1	yes	characteristic
440	C₄⋊Dic₄₇	C₂⁴	1	2	yes	—
441	Dic₄₇⋊C₄	—	2	2	no	—
442	Dic₄₇⋊C₄	—	2	2	no	—
443	Dic₄₇⋊C₄	—	2	2	no	—
444	Dic₄₇⋊C₄	—	2	2	no	—
445	Dic₄₇⋊C₄	C₂×D₄	1	2	yes	—
446	Dic₄₇⋊C₄	C₂×D₄	1	2	yes	—
447	C₄×Dic₄₇	—	2	2	no	—
448	C₄×Dic₄₇	C₂×D₄	1	2	yes	—
449	C₄×Dic₄₇	C₂×D₄	1	2	yes	—
450	C₄×Dic₄₇	C₂⁴	1	2	yes	—
451	C₂×C₄₇⋊C₈	—	4	2	no	—
452	C₂×C₄₇⋊C₈	C₂⁴	1	2	yes	—
453	C₂×C₄₇⋊C₈	C₂⁴	1	2	yes	—
454	D₃₇₆	—	4	2	no	—
455	D₃₇₆	—	4	2	no	—
456	#10625325	—	4	2	no	—
457	#10625325	—	4	2	no	—
458	C₈×D₄₇	—	4	2	no	—
459	C₈×D₄₇	—	4	2	no	—
460	C₂³×C₄₇	—	2	1	no	—
461	C₂³×C₄₇	—	2	1	no	—
462	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
463	C₂²×D₄₇	—	2	2	no	—
464	C₂²×D₄₇	—	2	2	no	—
465	C₂²×D₄₇	—	4	4	no	—
466	C₂²×D₄₇	—	4	4	no	—
467	C₂²×D₄₇	—	4	4	no	—
468	C₂²×D₄₇	—	8	2	no	—
469	C₂²×D₄₇	—	8	2	no	—
470	C₂²×D₄₇	—	8	2	no	—
471	C₂²×D₄₇	C₂²×D₄	1	2	yes	—
472	Q₈×C₄₇	—	2	1	no	—
473	Q₈×C₄₇	—	2	1	no	—
474	Q₈×C₄₇	—	2	1	no	—
475	Q₈×C₄₇	—	2	1	no	—
476	D₄×C₄₇	—	2	1	no	—
477	D₄×C₄₇	—	2	1	no	—
478	D₄×C₄₇	—	2	1	no	—
479	D₄×C₄₇	—	4	2	no	—
480	D₄×C₄₇	—	8	1	no	—
481	D₄×C₄₇	H(5,𝔽₂)	1	2	yes	—
482	C₂×C₄×C₄₇	—	2	2	no	—
483	C₂×C₄×C₄₇	—	2	1	no	—
484	C₂×C₄×C₄₇	—	2	1	no	—
485	C₂×C₄×C₄₇	—	2	1	no	—
486	C₂×C₄×C₄₇	—	2	1	no	—
487	C₂×C₄×C₄₇	—	2	1	no	—
488	C₂×C₄×C₄₇	—	2	1	no	—
489	C₂×C₄×C₄₇	—	2	1	no	—
490	C₂×C₄×C₄₇	—	2	1	no	—
491	C₂×C₄×C₄₇	—	4	1	no	—
492	C₂×C₄×C₄₇	—	4	2	no	—
493	C₂×C₄×C₄₇	—	4	2	no	—
494	C₂×C₄×C₄₇	—	4	2	no	—
495	C₂×C₄×C₄₇	—	4	2	no	—
496	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
497	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
498	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
499	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
500	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
501	C₂×C₄×C₄₇	C₂⁵	1	1	yes	characteristic
502	C₂²⋊D₄₇	—	2	4	no	—
503	C₂²⋊D₄₇	—	4	4	no	—
504	C₂²⋊D₄₇	—	8	2	no	—
505	C₂²⋊D₄₇	—	8	2	no	—
506	C₂²⋊D₄₇	—	8	2	no	—
507	C₂×Dic₄₇	—	2	2	no	—
508	C₂×Dic₄₇	—	2	2	no	—
509	C₂×Dic₄₇	—	8	2	no	—
510	C₂×Dic₄₇	C₂²×D₄	1	2	yes	—
511	C₂×Dic₄₇	C₂²×D₄	1	2	yes	—
512	C₂×Dic₄₇	C₂²×D₄	1	2	yes	—
513	D₁₈₈	—	2	2	no	—
514	D₁₈₈	—	2	2	no	—
515	D₁₈₈	—	2	2	no	—
516	D₁₈₈	—	2	2	no	—
517	D₁₈₈	—	4	4	no	—
518	D₁₈₈	—	4	4	no	—
519	D₁₈₈	—	4	2	no	—
520	D₁₈₈	—	4	2	no	—
521	D₁₈₈	—	8	1	no	—
522	D₁₈₈	—	8	1	no	—
523	D₁₈₈	#135	1	4	yes	complemented
524	C₄×D₄₇	—	2	4	no	—
525	C₄×D₄₇	—	2	2	no	—
526	C₄×D₄₇	—	2	2	no	—
527	C₄×D₄₇	—	4	2	no	—
528	C₄×D₄₇	—	4	4	no	—
529	C₄×D₄₇	—	8	2	no	—
530	C₄×D₄₇	—	8	2	no	—
531	C₄×D₄₇	—	8	2	no	—
532	C₄×D₄₇	—	8	2	no	—
533	C₄×D₄₇	—	8	2	no	—
534	Dic₉₄	—	2	2	no	—
535	Dic₉₄	—	2	2	no	—
536	Dic₉₄	—	2	2	no	—
537	Dic₉₄	—	8	2	no	—
538	Dic₉₄	—	8	1	no	—
539	C₈×C₄₇	—	2	1	no	—
540	C₈×C₄₇	—	2	1	no	—
541	C₈×C₄₇	—	2	1	no	—
542	C₈×C₄₇	—	2	1	no	—
543	C₄₇⋊C₈	—	2	2	no	—
544	C₄₇⋊C₈	—	2	2	no	—
545	#61955	—	47	1	no	maximal, Sylow
546	C₂²×C₄₇	—	2	1	no	—
547	C₂²×C₄₇	—	2	2	no	—
548	C₂²×C₄₇	—	2	1	no	—
549	C₂²×C₄₇	—	2	1	no	—
550	C₂²×C₄₇	—	4	1	no	—
551	C₂²×C₄₇	—	4	1	no	—
552	C₂²×C₄₇	—	4	1	no	—
553	C₂²×C₄₇	—	4	1	no	—
554	C₂²×C₄₇	—	4	1	no	—
555	C₂²×C₄₇	C₂³×D₄	1	1	yes	characteristic
556	C₂×D₄₇	—	2	2	no	—
557	C₂×D₄₇	—	2	2	no	—
558	C₂×D₄₇	—	4	2	no	—
559	C₂×D₄₇	—	4	2	no	—
560	C₂×D₄₇	—	4	2	no	—
561	C₂×D₄₇	—	4	2	no	—
562	C₂×D₄₇	—	4	2	no	—
563	C₂×D₄₇	—	4	2	no	—
564	C₂×D₄₇	—	8	8	no	—
565	C₂×D₄₇	—	16	4	no	—
566	C₂×D₄₇	C₂×#135	1	4	yes	—
567	C₄×C₄₇	—	2	1	no	—
568	C₄×C₄₇	—	2	1	no	—
569	C₄×C₄₇	—	2	1	no	—
570	C₄×C₄₇	—	2	1	no	—
571	C₄×C₄₇	—	4	1	no	—
572	C₄×C₄₇	—	4	1	no	—
573	C₄×C₄₇	—	4	1	no	—
574	C₄×C₄₇	—	4	1	no	—
575	C₄×C₄₇	—	4	1	no	—
576	C₄×C₄₇	—	4	1	no	—
577	C₄×C₄₇	C₂×#135	1	2	yes	—
578	C₄×C₄₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
579	C₄×C₄₇	#585	1	1	yes	characteristic
580	Dic₄₇	—	2	2	no	—
581	Dic₄₇	—	2	2	no	—
582	Dic₄₇	—	2	2	no	—
583	Dic₄₇	—	4	2	no	—
584	Dic₄₇	—	4	2	no	—
585	#3514	—	47	1	no	—
586	#3481	—	47	1	no	—
587	#3396	—	47	1	no	—
588	#3394	—	47	1	no	—
589	#3361	—	47	1	no	—
590	#3360	—	47	1	no	—
591	#3301	—	47	2	no	—
592	#3299	—	47	1	no	—
593	#3297	—	47	2	no	—
594	#3295	—	47	1	no	—
595	#3282	—	47	2	no	—
596	D₄×SD₁₆	—	47	1	no	—
597	#3280	—	47	2	no	—
598	D₄×D₈	—	47	1	no	—
599	#3250	—	47	2	no	—
600	#3247	—	47	1	no	—
601	#3211	—	47	2	no	—
602	#3207	—	47	1	no	—
603	#3105	—	47	2	no	—
604	#3102	D₄₇	1	1	yes	characteristic, complemented
605	#3035	—	47	1	no	—
606	C₂×#463	—	47	2	no	—
607	#2988	—	47	1	no	—
608	C₂×C₄₇	—	4	2	no	—
609	C₂×C₄₇	—	4	1	no	—
610	C₂×C₄₇	—	8	1	no	—
611	C₂×C₄₇	#3488	1	1	yes	characteristic
612	C₂×C₄₇	C₂²×#135	1	1	yes	characteristic
613	C₂×C₄₇	#3585	1	1	yes	characteristic
614	D₄₇	—	2	4	no	—
615	D₄₇	—	8	2	no	—
616	D₄₇	—	8	2	no	—
617	C₂×#135	—	47	2	no	—
618	C₂²×SD₁₆	—	47	2	no	—
619	C₂²×D₈	—	47	2	no	—
620	#559	—	47	1	no	—
621	#559	—	47	1	no	—
622	#556	—	47	1	no	—
623	#555	—	94	1	no	—
624	#554	—	47	1	no	—
625	#554	—	47	1	no	—
626	#553	—	47	2	no	—
627	#553	—	94	1	no	—
628	#551	—	94	2	no	—
629	#551	—	94	2	no	—
630	D₄×Q₈	—	47	1	no	—
631	#548	—	47	2	no	—
632	#546	—	47	2	no	—
633	#546	—	47	2	no	—
634	#546	—	94	1	no	—
635	#546	—	94	1	no	—
636	D₄²	—	47	1	no	—
637	D₄²	—	47	1	no	—
638	#542	—	94	1	no	—
639	#538	—	94	2	no	—
640	#532	—	47	1	no	—
641	#532	—	47	1	no	—
642	#529	—	47	2	no	—
643	#529	—	47	2	no	—
644	#529	—	94	1	no	—
645	#529	C₂×D₄₇	1	1	yes	characteristic, complemented
646	C₂×#124	—	47	2	no	—
647	#525	—	94	2	no	—
648	#518	—	94	1	no	—
649	C₄×#41	—	47	1	no	—
650	C₄×#41	C₂×D₄₇	1	1	yes	characteristic, complemented
651	C₂×C₄×D₄	—	47	2	no	—
652	C₂×C₄×D₄	—	94	1	no	—
653	#495	—	47	2	no	—
654	#495	—	47	2	no	—
655	#493	—	47	1	no	—
656	#492	—	47	1	no	—
657	#488	—	47	2	no	—
658	#488	—	47	2	no	—
659	#487	—	47	1	no	—
660	#486	—	47	1	no	—
661	#485	C₂×D₄₇	1	1	yes	characteristic, complemented
662	#484	—	47	2	no	—
663	#482	C₂×D₄₇	1	1	yes	characteristic, complemented
664	#481	—	47	2	no	—
665	#479	—	47	2	no	—
666	#479	C₂×D₄₇	1	1	yes	characteristic, complemented
667	#478	—	47	2	no	—
668	#478	—	47	2	no	—
669	#478	C₂×D₄₇	1	1	yes	characteristic, complemented
670	#477	—	47	1	no	—
671	#476	—	47	1	no	—
672	#467	—	47	2	no	—
673	#466	—	47	2	no	—
674	#466	—	47	2	no	—
675	#465	—	47	2	no	—
676	#465	—	47	2	no	—
677	#465	—	47	2	no	—
678	#464	—	47	2	no	—
679	#464	—	47	2	no	—
680	#464	C₂×D₄₇	1	1	yes	characteristic, complemented
681	#463	—	47	2	no	—
682	#463	—	47	2	no	—
683	#463	—	47	2	no	—
684	#463	—	47	2	no	—
685	#463	—	47	2	no	—
686	#463	—	47	2	no	—
687	#463	—	47	2	no	—
688	#463	—	47	2	no	—
689	#463	—	47	2	no	—
690	#463	C₂×D₄₇	1	1	yes	characteristic
691	#462	—	47	1	no	—
692	#461	—	47	1	no	—
693	#460	—	47	1	no	—
694	#460	—	47	1	no	—
695	#459	—	47	1	no	—
696	#459	—	47	1	no	—
697	#452	C₂×D₄₇	1	1	yes	characteristic, complemented
698	#451	—	47	2	no	—
699	#450	—	47	2	no	—
700	#450	—	47	2	no	—
701	#449	—	47	2	no	—
702	#449	—	47	2	no	—
703	#449	C₂×D₄₇	1	1	yes	characteristic
704	#448	—	47	2	no	—
705	#447	—	47	2	no	—
706	#447	—	47	2	no	—
707	C₈×Q₈	—	47	1	no	—
708	C₈×Q₈	—	47	1	no	—
709	C₄×Q₁₆	C₂×D₄₇	1	1	yes	characteristic, complemented
710	C₄×SD₁₆	—	47	2	no	—
711	C₄×SD₁₆	—	47	2	no	—
712	C₄×SD₁₆	C₂×D₄₇	1	1	yes	characteristic, complemented
713	C₄×SD₁₆	C₂×D₄₇	1	1	yes	characteristic, complemented
714	C₄×D₈	—	47	2	no	—
715	C₄×D₈	—	47	2	no	—
716	C₄×D₈	C₂×D₄₇	1	1	yes	characteristic
717	C₈×D₄	—	47	2	no	—
718	C₈×D₄	—	47	2	no	—
719	C₈×D₄	—	47	1	no	—
720	C₈×D₄	—	47	1	no	—
721	#431	—	47	2	no	—
722	#431	C₂×D₄₇	1	1	yes	characteristic, complemented
723	C₂×C₄⋊C₈	—	47	1	no	—
724	C₂×C₄⋊C₈	—	47	2	no	—
725	#416	—	47	2	no	—
726	C₂×#103	—	47	2	no	—
727	C₂×#102	—	47	2	no	—
728	C₄₇	#61955	1	1	yes	characteristic, complemented, Sylow
729	C₂×#41	—	47	1	no	—
730	C₂×#41	—	47	2	no	—
731	C₂×#41	—	94	1	no	—
732	C₂×#41	C₂²×D₄₇	1	1	yes	characteristic
733	C₂²×Q₈	—	47	2	no	—
734	C₂²×D₄	—	47	2	no	—
735	C₂²×D₄	—	47	2	no	—
736	C₂²×D₄	—	94	1	no	—
737	C₂²×D₄	—	94	1	no	—
738	C₂³×C₄	—	94	2	no	—
739	#135	—	188	4	no	—
740	C₂×Q₁₆	—	47	2	no	—
741	C₂×Q₁₆	C₂²×D₄₇	1	1	yes	characteristic
742	C₂×SD₁₆	—	47	2	no	—
743	C₂×SD₁₆	—	47	2	no	—
744	C₂×SD₁₆	—	47	2	no	—
745	C₂×SD₁₆	—	47	2	no	—
746	C₂×SD₁₆	—	47	2	no	—
747	C₂×SD₁₆	—	188	4	no	—
748	C₂×SD₁₆	C₂²×D₄₇	1	1	yes	characteristic
749	C₂×SD₁₆	C₂²×D₄₇	1	1	yes	characteristic
750	C₂×D₈	—	47	2	no	—
751	C₂×D₈	—	47	2	no	—
752	C₂×D₈	—	47	2	no	—
753	C₂×D₈	—	47	2	no	—
754	C₂×D₈	—	188	4	no	—
755	C₂×D₈	C₂²×D₄₇	1	1	yes	characteristic
756	C₂²×C₈	—	47	2	no	—
757	C₂²×C₈	—	47	2	no	—
758	C₂²×C₈	—	47	2	no	—
759	C₄⋊Q₈	—	47	1	no	—
760	C₄⋊Q₈	—	47	1	no	—
761	C₄⋊Q₈	—	94	1	no	—
762	#127	—	47	1	no	—
763	#127	—	47	1	no	—
764	#126	—	2	1	no	—
765	#126	—	94	2	no	—
766	#126	—	94	2	no	—
767	#126	—	94	2	no	—
768	#126	—	94	2	no	—
769	#125	—	47	2	no	—
770	#125	—	94	1	no	—
771	#125	C₂²×D₄₇	1	1	yes	characteristic
772	#124	—	47	2	no	—
773	#124	—	47	2	no	—
774	#124	—	47	2	no	—
775	#124	—	47	2	no	—
776	#124	—	94	1	no	—
777	#124	—	94	1	no	—
778	#124	—	94	2	no	—
779	#124	—	94	2	no	—
780	#124	—	94	2	no	—
781	#124	—	94	1	no	—
782	#124	C₂²×D₄₇	1	1	yes	characteristic
783	#123	—	2	1	no	—
784	#123	—	94	2	no	—
785	#123	—	94	2	no	—
786	#123	—	94	2	no	—
787	#123	—	94	2	no	—
788	#123	—	94	2	no	—
789	#123	—	94	2	no	—
790	#123	—	94	2	no	—
791	C₂²⋊Q₈	—	47	2	no	—
792	C₂²⋊Q₈	—	47	2	no	—
793	C₂²⋊Q₈	—	94	2	no	—
794	C₂²⋊Q₈	—	94	2	no	—
795	C₂²⋊Q₈	—	94	2	no	—
796	C₂²⋊Q₈	—	94	2	no	—
797	C₂²⋊Q₈	—	94	1	no	—
798	C₂²⋊Q₈	—	94	1	no	—
799	C₂²⋊Q₈	C₂²×D₄₇	1	1	yes	characteristic
800	#121	—	47	2	no	—
801	#121	—	47	2	no	—
802	#121	—	47	2	no	—
803	#121	—	94	2	no	—
804	#121	—	94	2	no	—
805	#121	—	94	2	no	—
806	#121	—	94	2	no	—
807	#121	—	94	1	no	—
808	#121	—	94	1	no	—
809	#121	—	94	1	no	—
810	#121	—	94	1	no	—
811	#121	—	94	1	no	—
812	#121	C₂²×D₄₇	1	1	yes	characteristic
813	#120	—	94	2	no	—
814	#120	—	94	2	no	—
815	#120	—	94	2	no	—
816	#120	—	94	2	no	—
817	C₄×Q₈	—	47	1	no	—
818	C₄×Q₈	—	47	1	no	—
819	C₄×Q₈	—	47	2	no	—
820	C₄×Q₈	C₂²×D₄₇	1	1	yes	characteristic
821	C₄×Q₈	C₂²×D₄₇	1	1	yes	characteristic
822	C₄×Q₈	C₂²×D₄₇	1	1	yes	characteristic
823	C₄×D₄	—	2	1	no	—
824	C₄×D₄	—	2	1	no	—
825	C₄×D₄	—	2	1	no	—
826	C₄×D₄	—	47	2	no	—
827	C₄×D₄	—	47	2	no	—
828	C₄×D₄	—	47	2	no	—
829	C₄×D₄	—	47	2	no	—
830	C₄×D₄	—	47	2	no	—
831	C₄×D₄	—	47	1	no	—
832	C₄×D₄	—	47	1	no	—
833	C₄×D₄	—	47	2	no	—
834	C₄×D₄	—	94	2	no	—
835	C₄×D₄	—	94	1	no	—
836	C₄×D₄	—	94	1	no	—
837	C₄×D₄	—	94	2	no	—
838	C₄×D₄	—	94	1	no	—
839	C₄×D₄	—	94	1	no	—
840	C₄×D₄	—	94	2	no	—
841	C₄×D₄	—	94	2	no	—
842	C₄×D₄	—	94	2	no	—
843	C₄×D₄	—	94	2	no	—
844	C₄×D₄	—	94	1	no	—
845	C₄×D₄	—	94	1	no	—
846	C₄×D₄	—	94	1	no	—
847	C₄×D₄	C₂²×D₄₇	1	1	yes	characteristic
848	C₄×D₄	C₂²×D₄₇	1	1	yes	characteristic
849	C₄×D₄	C₂²×D₄₇	1	1	yes	characteristic
850	#117	—	2	1	no	—
851	#117	—	2	1	no	—
852	#117	—	47	1	no	—
853	#117	—	47	2	no	—
854	#117	—	94	2	no	—
855	#117	—	94	2	no	—
856	#117	—	94	1	no	—
857	#117	C₂²×D₄₇	1	1	yes	characteristic
858	C₂×C₄⋊C₄	—	47	2	no	—
859	C₂×C₄⋊C₄	—	94	1	no	—
860	C₂×C₂²⋊C₄	—	94	2	no	—
861	C₂×C₂²⋊C₄	—	94	2	no	—
862	C₂×C₂²⋊C₄	—	94	2	no	—
863	C₂×C₂²⋊C₄	—	94	2	no	—
864	C₂×C₂²⋊C₄	—	94	2	no	—
865	C₂×C₄²	—	2	1	no	—
866	C₂×C₄²	—	47	2	no	—
867	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
868	#107	—	47	2	no	—
869	#107	C₂²×D₄₇	1	1	yes	characteristic
870	#107	C₂²×D₄₇	1	1	yes	characteristic
871	#106	—	47	2	no	—
872	#106	C₂²×D₄₇	1	1	yes	characteristic
873	#106	C₂²×D₄₇	1	1	yes	characteristic
874	C₄⋊C₈	—	47	2	no	—
875	C₄⋊C₈	—	47	2	no	—
876	C₄⋊C₈	—	47	2	no	—
877	C₄⋊C₈	—	47	1	no	—
878	C₄⋊C₈	—	47	1	no	—
879	C₄⋊C₈	C₂²×D₄₇	1	1	yes	characteristic
880	C₄⋊C₈	C₂²×D₄₇	1	1	yes	characteristic
881	#103	—	47	2	no	—
882	#103	—	47	2	no	—
883	#103	—	47	2	no	—
884	#103	—	47	2	no	—
885	#103	—	47	2	no	—
886	#103	C₂²×D₄₇	1	1	yes	characteristic
887	#103	C₂²×D₄₇	1	1	yes	characteristic
888	#103	C₂²×D₄₇	1	1	yes	characteristic
889	#103	C₂²×D₄₇	1	1	yes	characteristic
890	#102	—	47	2	no	—
891	#102	—	47	2	no	—
892	#102	—	47	2	no	—
893	#102	—	47	2	no	—
894	#102	—	47	2	no	—
895	#102	—	47	2	no	—
896	#102	—	47	2	no	—
897	#102	C₂²×D₄₇	1	1	yes	characteristic
898	#102	C₂²×D₄₇	1	1	yes	characteristic
899	#102	C₂²×D₄₇	1	1	yes	characteristic
900	#102	C₂²×D₄₇	1	1	yes	characteristic
901	C₂²⋊C₈	—	47	2	no	—
902	C₂²⋊C₈	—	47	2	no	—
903	C₂²⋊C₈	C₂²×D₄₇	1	1	yes	characteristic
904	C₂²⋊C₈	C₂²×D₄₇	1	1	yes	characteristic
905	C₄×C₈	—	47	2	no	—
906	C₄×C₈	—	47	2	no	—
907	C₄×C₈	C₂²×D₄₇	1	1	yes	characteristic
908	C₄×C₈	C₂²×D₄₇	1	1	yes	characteristic
909	C₂⁴	—	94	2	no	—
910	C₂⁴	—	94	2	no	—
911	#41	—	2	2	no	—
912	#41	—	4	1	no	—
913	#41	—	94	4	no	—
914	#41	—	376	2	no	—
915	#41	—	188	2	no	—
916	#41	—	188	2	no	—
917	C₂×Q₈	—	47	1	no	—
918	C₂×Q₈	—	47	2	no	—
919	C₂×Q₈	—	94	2	no	—
920	C₂×Q₈	—	94	1	no	—
921	C₂×Q₈	—	188	2	no	—
922	C₂×Q₈	—	188	2	no	—
923	C₂×Q₈	C₂³×D₄₇	1	1	yes	characteristic
924	C₂×Q₈	C₂³×D₄₇	1	1	yes	characteristic
925	C₂×D₄	—	2	1	no	—
926	C₂×D₄	—	2	1	no	—
927	C₂×D₄	—	47	2	no	—
928	C₂×D₄	—	47	1	no	—
929	C₂×D₄	—	47	2	no	—
930	C₂×D₄	—	47	2	no	—
931	C₂×D₄	—	94	2	no	—
932	C₂×D₄	—	94	2	no	—
933	C₂×D₄	—	94	2	no	—
934	C₂×D₄	—	94	2	no	—
935	C₂×D₄	—	94	4	no	—
936	C₂×D₄	—	94	2	no	—
937	C₂×D₄	—	94	2	no	—
938	C₂×D₄	—	94	1	no	—
939	C₂×D₄	—	94	1	no	—
940	C₂×D₄	—	94	1	no	—
941	C₂×D₄	—	94	1	no	—
942	C₂×D₄	—	188	4	no	—
943	C₂×D₄	—	188	4	no	—
944	C₂×D₄	—	188	2	no	—
945	C₂×D₄	—	188	2	no	—
946	C₂×D₄	—	188	2	no	—
947	C₂×D₄	C₂³×D₄₇	1	1	yes	characteristic
948	C₂×D₄	C₂³×D₄₇	1	1	yes	characteristic
949	C₂²×C₄	—	2	1	no	—
950	C₂²×C₄	—	2	1	no	—
951	C₂²×C₄	—	2	1	no	—
952	C₂²×C₄	—	2	1	no	—
953	C₂²×C₄	—	47	2	no	—
954	C₂²×C₄	—	47	2	no	—
955	C₂²×C₄	—	47	2	no	—
956	C₂²×C₄	—	94	2	no	—
957	C₂²×C₄	—	94	2	no	—
958	C₂²×C₄	—	94	2	no	—
959	C₂²×C₄	—	94	2	no	—
960	C₂²×C₄	—	94	2	no	—
961	C₂²×C₄	—	94	2	no	—
962	C₂²×C₄	—	94	2	no	—
963	C₂²×C₄	—	376	4	no	—
964	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
965	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
966	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
967	Q₁₆	—	4	1	no	—
968	Q₁₆	—	188	2	no	—
969	SD₁₆	—	2	2	no	—
970	SD₁₆	—	4	1	no	—
971	SD₁₆	—	94	4	no	—
972	SD₁₆	—	188	2	no	—
973	SD₁₆	—	188	2	no	—
974	SD₁₆	—	188	2	no	—
975	SD₁₆	—	188	2	no	—
976	D₈	—	2	2	no	—
977	D₈	—	94	4	no	—
978	D₈	—	188	2	no	—
979	D₈	—	188	2	no	—
980	D₈	—	188	2	no	—
981	C₂×C₈	—	47	2	no	—
982	C₂×C₈	—	47	2	no	—
983	C₂×C₈	—	188	2	no	—
984	C₂×C₈	—	188	2	no	—
985	C₂×C₈	—	188	2	no	—
986	C₂×C₈	C₂³×D₄₇	1	1	yes	characteristic
987	C₂×C₈	C₂³×D₄₇	1	1	yes	characteristic
988	C₂×C₈	C₂³×D₄₇	1	1	yes	characteristic
989	C₂×C₈	C₂³×D₄₇	1	1	yes	characteristic
990	C₄⋊C₄	—	2	1	no	—
991	C₄⋊C₄	—	2	1	no	—
992	C₄⋊C₄	—	2	1	no	—
993	C₄⋊C₄	—	2	1	no	—
994	C₄⋊C₄	—	2	1	no	—
995	C₄⋊C₄	—	2	1	no	—
996	C₄⋊C₄	—	47	2	no	—
997	C₄⋊C₄	—	47	2	no	—
998	C₄⋊C₄	—	47	1	no	—
999	C₄⋊C₄	—	47	1	no	—
1000	C₄⋊C₄	—	47	2	no	—
1001	C₄⋊C₄	—	94	2	no	—
1002	C₄⋊C₄	—	94	2	no	—
1003	C₄⋊C₄	—	94	2	no	—
1004	C₄⋊C₄	—	94	2	no	—
1005	C₄⋊C₄	—	94	2	no	—
1006	C₄⋊C₄	—	94	2	no	—
1007	C₄⋊C₄	—	94	1	no	—
1008	C₄⋊C₄	—	94	1	no	—
1009	C₄⋊C₄	—	94	1	no	—
1010	C₄⋊C₄	C₂³×D₄₇	1	1	yes	characteristic
1011	C₄⋊C₄	C₂³×D₄₇	1	1	yes	characteristic
1012	C₄⋊C₄	C₂³×D₄₇	1	1	yes	characteristic
1013	C₄⋊C₄	C₂³×D₄₇	1	1	yes	characteristic
1014	C₂²⋊C₄	—	2	1	no	—
1015	C₂²⋊C₄	—	2	1	no	—
1016	C₂²⋊C₄	—	2	1	no	—
1017	C₂²⋊C₄	—	2	1	no	—
1018	C₂²⋊C₄	—	2	1	no	—
1019	C₂²⋊C₄	—	2	1	no	—
1020	C₂²⋊C₄	—	2	1	no	—
1021	C₂²⋊C₄	—	2	1	no	—
1022	C₂²⋊C₄	—	47	2	no	—
1023	C₂²⋊C₄	—	47	2	no	—
1024	C₂²⋊C₄	—	47	2	no	—
1025	C₂²⋊C₄	—	94	2	no	—
1026	C₂²⋊C₄	—	94	2	no	—
1027	C₂²⋊C₄	—	94	2	no	—
1028	C₂²⋊C₄	—	94	2	no	—
1029	C₂²⋊C₄	—	94	2	no	—
1030	C₂²⋊C₄	—	94	2	no	—
1031	C₂²⋊C₄	—	94	2	no	—
1032	C₂²⋊C₄	—	94	2	no	—
1033	C₂²⋊C₄	—	94	2	no	—
1034	C₂²⋊C₄	—	94	2	no	—
1035	C₂²⋊C₄	—	94	2	no	—
1036	C₂²⋊C₄	—	94	2	no	—
1037	C₂²⋊C₄	—	94	2	no	—
1038	C₂²⋊C₄	—	94	2	no	—
1039	C₂²⋊C₄	—	94	2	no	—
1040	C₂²⋊C₄	—	94	2	no	—
1041	C₂²⋊C₄	—	94	2	no	—
1042	C₄²	—	2	1	no	—
1043	C₄²	—	2	1	no	—
1044	C₄²	—	2	1	no	—
1045	C₄²	—	2	1	no	—
1046	C₄²	—	47	2	no	—
1047	C₄²	—	47	2	no	—
1048	C₄²	—	47	2	no	—
1049	C₄²	—	94	2	no	—
1050	C₄²	D₄×D₄₇	1	1	yes	characteristic
1051	C₄²	D₄×D₄₇	1	1	yes	characteristic
1052	C₄²	C₂³×D₄₇	1	1	yes	characteristic
1053	C₄²	C₂³×D₄₇	1	1	yes	characteristic
1054	C₂³	—	2	1	no	—
1055	C₂³	—	2	1	no	—
1056	C₂³	—	47	2	no	—
1057	C₂³	—	94	2	no	—
1058	C₂³	—	94	2	no	—
1059	C₂³	—	376	2	no	—
1060	C₂³	—	376	2	no	—
1061	C₂³	—	376	2	no	—
1062	C₂³	—	188	4	no	—
1063	C₂³	—	188	4	no	—
1064	C₂³	—	188	4	no	—
1065	C₂³	C₂×D₄×D₄₇	1	1	yes	characteristic
1066	Q₈	—	2	1	no	—
1067	Q₈	—	2	1	no	—
1068	Q₈	—	2	1	no	—
1069	Q₈	—	2	1	no	—
1070	Q₈	—	94	2	no	—
1071	Q₈	—	94	2	no	—
1072	Q₈	—	94	2	no	—
1073	Q₈	—	376	1	no	—
1074	Q₈	—	376	2	no	—
1075	D₄	—	2	1	no	—
1076	D₄	—	2	1	no	—
1077	D₄	—	2	1	no	—
1078	D₄	—	4	2	no	—
1079	D₄	—	8	1	no	—
1080	D₄	—	47	4	no	—
1081	D₄	—	94	4	no	—
1082	D₄	—	94	2	no	—
1083	D₄	—	94	2	no	—
1084	D₄	—	94	2	no	—
1085	D₄	—	94	2	no	—
1086	D₄	—	376	1	no	—
1087	D₄	—	376	1	no	—
1088	D₄	—	376	2	no	—
1089	D₄	—	376	2	no	—
1090	D₄	—	376	2	no	—
1091	D₄	—	188	4	no	—
1092	D₄	—	188	4	no	—
1093	D₄	—	188	4	no	—
1094	D₄	—	188	2	no	—
1095	D₄	—	188	2	no	—
1096	D₄	#13094070	1	2	yes	—
1097	C₂×C₄	—	2	2	no	—
1098	C₂×C₄	—	2	1	no	—
1099	C₂×C₄	—	2	1	no	—
1100	C₂×C₄	—	2	1	no	—
1101	C₂×C₄	—	2	1	no	—
1102	C₂×C₄	—	2	1	no	—
1103	C₂×C₄	—	2	1	no	—
1104	C₂×C₄	—	2	1	no	—
1105	C₂×C₄	—	2	1	no	—
1106	C₂×C₄	—	4	1	no	—
1107	C₂×C₄	—	4	2	no	—
1108	C₂×C₄	—	4	2	no	—
1109	C₂×C₄	—	4	2	no	—
1110	C₂×C₄	—	4	2	no	—
1111	C₂×C₄	—	47	2	no	—
1112	C₂×C₄	—	47	2	no	—
1113	C₂×C₄	—	47	2	no	—
1114	C₂×C₄	—	94	4	no	—
1115	C₂×C₄	—	94	2	no	—
1116	C₂×C₄	—	94	2	no	—
1117	C₂×C₄	—	94	2	no	—
1118	C₂×C₄	—	94	2	no	—
1119	C₂×C₄	—	376	2	no	—
1120	C₂×C₄	—	376	2	no	—
1121	C₂×C₄	—	376	2	no	—
1122	C₂×C₄	—	376	2	no	—
1123	C₂×C₄	—	376	2	no	—
1124	C₂×C₄	—	376	2	no	—
1125	C₂×C₄	—	188	2	no	—
1126	C₂×C₄	—	188	4	no	—
1127	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
1128	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
1129	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
1130	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
1131	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
1132	C₂×C₄	C₂⁴×D₄₇	1	1	yes	characteristic
1133	C₈	—	2	1	no	—
1134	C₈	—	2	1	no	—
1135	C₈	—	2	1	no	—
1136	C₈	—	2	1	no	—
1137	C₈	—	94	2	no	—
1138	C₈	—	94	2	no	—
1139	C₂²	—	2	1	no	—
1140	C₂²	—	2	2	no	—
1141	C₂²	—	2	1	no	—
1142	C₂²	—	2	1	no	—
1143	C₂²	—	4	1	no	—
1144	C₂²	—	4	1	no	—
1145	C₂²	—	4	1	no	—
1146	C₂²	—	4	1	no	—
1147	C₂²	—	4	1	no	—
1148	C₂²	—	47	4	no	—
1149	C₂²	—	94	2	no	—
1150	C₂²	—	94	2	no	—
1151	C₂²	—	376	8	no	—
1152	C₂²	—	188	2	no	—
1153	C₂²	—	188	2	no	—
1154	C₂²	—	188	2	no	—
1155	C₂²	—	188	2	no	—
1156	C₂²	—	188	2	no	—
1157	C₂²	—	188	2	no	—
1158	C₂²	—	752	4	no	—
1159	C₂²	C₂²×D₄×D₄₇	1	1	yes	characteristic
1160	C₄	—	2	1	no	—
1161	C₄	—	2	1	no	—
1162	C₄	—	2	1	no	—
1163	C₄	—	2	1	no	—
1164	C₄	—	4	1	no	—
1165	C₄	—	4	1	no	—
1166	C₄	—	4	1	no	—
1167	C₄	—	4	1	no	—
1168	C₄	—	4	1	no	—
1169	C₄	—	4	1	no	—
1170	C₄	—	94	2	no	—
1171	C₄	—	94	2	no	—
1172	C₄	—	94	2	no	—
1173	C₄	—	188	2	no	—
1174	C₄	—	188	2	no	—
1175	C₄	#135×D₄₇	1	2	yes	—
1176	C₄	C₂×#13094070	1	1	yes	characteristic
1177	C₄	#15689959	1	1	yes	characteristic
1178	C₂	—	4	1	no	—
1179	C₂	—	4	2	no	—
1180	C₂	—	8	1	no	—
1181	C₂	—	94	4	no	—
1182	C₂	—	376	2	no	—
1183	C₂	—	376	2	no	—
1184	C₂	#20257049	1	1	yes	characteristic
1185	C₂	C₂×#135×D₄₇	1	1	yes	characteristic
1186	C₂	#20258165	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂²×D₄×D₄₇
commutator, cosocle	C₂×C₄×C₄₇	C₂⁵
Frattini	C₂×C₄	C₂⁴×D₄₇
Fitting	C₄₇×#3102	C₂
socle	C₂²×C₄₇	C₂³×D₄
hypercenter	#3102	D₄₇
hypocenter	C₄₇	#61955
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #3102

Complements

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

N	H ≅ G/N	type
1. #20257351	C₂	semidirect
2. #20256998	C₂	semidirect
3. #20256398	C₂	semidirect
4. #20256382	C₂	semidirect
5. #20256046	C₂	semidirect
6. #20256035	C₂	semidirect
7. #20255293	C₂	semidirect
8. #20255266	C₂	semidirect
9. #20255241	C₂	semidirect
10. #20255214	C₂	semidirect
11. #20255093	C₂	semidirect
12. SD₁₆×D₁₈₈	C₂	semidirect
13. #20255071	C₂	semidirect
14. D₈×D₁₈₈	C₂	semidirect
15. #20254742	C₂	semidirect
16. #20254714	C₂	semidirect
17. #20254357	C₂	semidirect
18. #20254323	C₂	semidirect
19. #20253440	C₂	semidirect
20. #20252843	C₂	semidirect
21. #463×D₄₇	C₂	semidirect
22. #20252496	C₂	semidirect
23. C₄₇×#3102	C₂	semidirect
24. C₂×#13094044	C₂²	semidirect
25. C₂×SD₁₆×D₄₇	C₂²	semidirect
27. #15689858	C₂²	semidirect
28. #15689858	C₂²	semidirect
29. #15689843	C₂²	semidirect
32. #15689830	C₂²	semidirect
34. #15689817	C₂²	semidirect
38. #15689783	C₂²	semidirect
39. #15689770	C₂²	semidirect
42. #15689761	C₂²	semidirect
47. #15689673	C₂²	semidirect
48. #15689673	C₂²	semidirect
49. #15689660	C₂²	semidirect
50. #15689658	C₂²	semidirect
52. #124×D₄₇	C₂²	semidirect
57. C₄×D₄×D₄₇	C₂²	semidirect
58. #15689508	C₂²	semidirect
59. #15689504	C₂²	semidirect
61. #15689496	C₂²	semidirect
62. #15689479	C₂²	semidirect
63. #15689476	C₂²	semidirect
64. #15689474	C₂²	semidirect
65. #15689470	C₂²	semidirect
66. #15689460	C₂²	semidirect
67. #15689443	C₂²	semidirect
68. #15689429	C₂²	semidirect
69. #15689422	C₂²	semidirect
70. #15689420	C₂²	semidirect
71. #15689418	C₂²	semidirect
72. #15689413	C₂²	semidirect
73. #15689363	C₂²	semidirect
75. #15689357	C₂²	semidirect
76. #15689355	C₂²	semidirect
77. #15689354	C₂²	semidirect
78. #15689353	C₂²	semidirect
79. #15689348	C₂²	semidirect
80. #15689345	C₂²	semidirect
81. #15689341	C₂²	semidirect
82. #15689341	C₂²	semidirect
83. #15689340	C₂²	semidirect
84. #15689339	C₂²	semidirect
85. #15689339	C₂²	semidirect
86. #15689338	C₂²	semidirect
87. #15689337	C₂²	semidirect
89. #15689335	C₂²	semidirect
90. #15689333	C₂²	semidirect
91. #15689328	C₂²	semidirect
92. #15689323	C₂²	semidirect
93. #15689323	C₂²	semidirect
96. #15689277	C₂²	semidirect
97. #15689275	C₂²	semidirect
98. #15689272	C₂²	semidirect
99. #15689270	C₂²	semidirect
100. #15689270	C₂²	semidirect
101. #15689263	C₂²	semidirect
104. C₈×Dic₉₄	C₂²	semidirect
105. C₈×Dic₉₄	C₂²	semidirect
106. #15689214	C₂²	semidirect
107. #15689210	C₂²	semidirect
108. #15689205	C₂²	semidirect
109. #15689203	C₂²	semidirect
112. (C₂²⋊D₄₇)⋊C₈	C₂²	semidirect
113. (C₂²⋊D₄₇)⋊C₈	C₂²	semidirect
114. #15689175	C₂²	semidirect
115. C₂×C₄⋊(C₄₇⋊C₈)	C₂²	semidirect
116. C₄⋊C₈×D₄₇	C₂²	semidirect
117. #15689117	C₂²	semidirect
118. #103×D₄₇	C₂²	semidirect
119. #102×D₄₇	C₂²	semidirect
120. C₄₇×#529	C₂²	semidirect
121. C₄×#41×C₄₇	C₂²	semidirect
122. C₄₇×#485	C₂²	semidirect
123. C₄₇×#482	C₂²	semidirect
124. C₄₇×#479	C₂²	semidirect
125. C₄₇×#478	C₂²	semidirect
126. C₄₇×#464	C₂²	semidirect
128. C₄₇×#452	C₂²	semidirect
130. C₄×Q₁₆×C₄₇	C₂²	semidirect
131. C₄×SD₁₆×C₄₇	C₂²	semidirect
132. C₄×SD₁₆×C₄₇	C₂²	semidirect
134. C₄₇×#431	C₂²	semidirect
523. D₁₈₈	#135	semidirect
604. #3102	D₄₇	semidirect
645. #529	C₂×D₄₇	semidirect
650. C₄×#41	C₂×D₄₇	semidirect
661. #485	C₂×D₄₇	semidirect
663. #482	C₂×D₄₇	semidirect
666. #479	C₂×D₄₇	semidirect
669. #478	C₂×D₄₇	semidirect
680. #464	C₂×D₄₇	semidirect
697. #452	C₂×D₄₇	semidirect
709. C₄×Q₁₆	C₂×D₄₇	semidirect
712. C₄×SD₁₆	C₂×D₄₇	semidirect
713. C₄×SD₁₆	C₂×D₄₇	semidirect
722. #431	C₂×D₄₇	semidirect
728. C₄₇	#61955	semidirect

Maximal subgroups

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

subgroup	index
#20257351	2
#20256998	2
#20256398	2
#20256382	2
#20256046	2
#20256035	2
#20255293	2
#20255266	2
#20255241	2
#20255214	2
#20255093	2
SD₁₆×D₁₈₈	2
#20255071	2
D₈×D₁₈₈	2
#20254742	2
#20254714	2
#20254357	2
#20254323	2
#20253440	2
#20252843	2
#463×D₄₇	2
#20252496	2
C₄₇×#3102	2
#61955	47