Subgroups — #27097389

Order 12032.

1986 conjugacy classes of subgroups.

The subgroup lattice has 1128 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20257236	C₂	1	2	yes	maximal, complemented
2	#20256476	C₂	1	2	yes	maximal, complemented
3	#20256472	C₂	1	2	yes	maximal, complemented
4	#20256411	C₂	1	2	yes	maximal, complemented
5	#20256403	C₂	1	2	yes	maximal, complemented
6	#20256401	C₂	1	1	yes	maximal, characteristic, complemented
7	#20256400	C₂	1	1	yes	maximal, characteristic, complemented
8	#20256397	C₂	1	1	yes	maximal, characteristic, complemented
9	#20256376	C₂	1	1	yes	maximal, characteristic, complemented
10	#20256373	C₂	1	1	yes	maximal, characteristic, complemented
11	#20256362	C₂	1	1	yes	maximal, characteristic, complemented
12	#20256361	C₂	1	1	yes	maximal, characteristic, complemented
13	#20253870	C₂	1	1	yes	maximal, characteristic, complemented
14	#20253868	C₂	1	1	yes	maximal, characteristic, complemented
15	#20253813	C₂	1	1	yes	maximal, characteristic, complemented
16	#20252928	C₂	1	2	yes	maximal, complemented
17	#20252924	C₂	1	2	yes	maximal, complemented
18	#20252850	C₂	1	2	yes	maximal, complemented
19	#20252317	C₂	1	1	yes	maximal, characteristic, complemented
20	#20252263	C₂	1	1	yes	maximal, characteristic, complemented
21	#20252258	C₂	1	1	yes	maximal, characteristic, complemented
22	C₄×D₈×D₄₇	C₂	1	1	yes	maximal, characteristic, complemented
23	C₄₇×#3396	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#13094051	C₂²	1	2	yes	—
25	C₂×#13094048	C₂²	1	2	yes	—
26	C₂×#13094047	C₂²	1	1	yes	characteristic
27	C₂×#13094045	C₂²	1	2	yes	—
28	C₂×#13094043	C₂²	1	1	yes	characteristic
29	C₂×D₈×D₄₇	C₂²	1	1	yes	characteristic
30	#15689858	C₂²	1	2	yes	complemented
31	#15689856	C₂²	1	2	yes	complemented
32	#15689855	C₂²	1	2	yes	complemented
33	#15689845	C₂²	1	2	yes	complemented
34	#15689842	C₂²	1	2	yes	complemented
35	#15689835	—	2	2	no	—
36	#15689822	—	2	2	no	—
37	#15689818	—	2	2	no	—
38	#15689794	C₂²	1	2	yes	complemented
39	#15689793	C₂²	1	2	yes	complemented
40	#15689771	—	2	2	no	—
41	#15689709	—	2	2	no	—
42	#15689707	—	2	2	no	—
43	#15689691	C₂²	1	2	yes	—
44	#15689686	C₂²	1	2	yes	—
45	#15689677	C₂²	1	1	yes	characteristic
46	#15689672	C₂²	1	2	yes	—
47	#15689632	—	2	2	no	—
48	#15689631	—	2	2	no	—
49	#15689605	C₂²	1	2	yes	—
50	#15689602	C₂²	1	2	yes	—
51	C₄×D₄×D₄₇	C₂²	1	2	yes	—
52	#15689513	C₂²	1	2	yes	—
53	#15689511	C₂²	1	2	yes	—
54	#15689510	C₂²	1	2	yes	—
55	#15689509	C₂²	1	2	yes	—
56	#15689508	C₂²	1	1	yes	characteristic
57	#15689507	C₂²	1	1	yes	characteristic
58	#15689507	C₂²	1	1	yes	characteristic, complemented
59	#15689506	C₂²	1	1	yes	characteristic
60	#15689505	C₂²	1	2	yes	complemented
61	#15689501	C₂²	1	1	yes	characteristic, complemented
62	#15689500	C₂²	1	1	yes	characteristic
63	#15689498	C₂²	1	1	yes	characteristic
64	#15689498	C₂²	1	1	yes	characteristic
65	#15689498	C₂²	1	1	yes	characteristic, complemented
66	#15689494	C₂²	1	2	yes	complemented
67	#15689348	C₂²	1	2	yes	complemented
68	#15689345	C₂²	1	2	yes	complemented
69	#15689343	C₂²	1	2	yes	complemented
70	#15689342	C₂²	1	2	yes	complemented
71	#15689340	C₂²	1	2	yes	complemented
72	#15689339	C₂²	1	2	yes	complemented
73	#15689339	C₂²	1	2	yes	complemented
74	#15689338	C₂²	1	2	yes	complemented
75	#15689337	C₂²	1	2	yes	complemented
76	#15689335	C₂²	1	2	yes	complemented
77	#15689327	C₂²	1	2	yes	complemented
78	#15689326	C₂²	1	2	yes	complemented
79	#15689324	C₂²	1	2	yes	complemented
80	#15689322	C₂²	1	2	yes	complemented
81	#15689321	C₂²	1	2	yes	complemented
82	#15689318	C₂²	1	2	yes	complemented
83	#15689317	C₂²	1	2	yes	complemented
84	#15689317	C₂²	1	2	yes	complemented
85	#15689316	C₂²	1	2	yes	complemented
86	#15689316	C₂²	1	2	yes	complemented
87	#15689315	C₂²	1	2	yes	complemented
88	#15689254	C₂²	1	1	yes	characteristic, complemented
89	#15689252	C₂²	1	1	yes	characteristic, complemented
90	#15689252	C₂²	1	1	yes	characteristic, complemented
91	#15689250	C₂²	1	1	yes	characteristic, complemented
92	C₈×Dic₉₄	C₂²	1	1	yes	characteristic, complemented
93	C₈×Dic₉₄	C₂²	1	1	yes	characteristic, complemented
94	C₈×Dic₉₄	C₂²	1	1	yes	characteristic, complemented
95	#15689226	C₂²	1	2	yes	complemented
96	#15689223	C₂²	1	2	yes	complemented
97	#15689221	C₂²	1	2	yes	complemented
98	#15689220	C₂²	1	2	yes	complemented
99	C₄×Dic₁₈₈	C₂²	1	1	yes	characteristic, complemented
100	Q₁₆×Dic₄₇	C₂²	1	1	yes	characteristic, complemented
101	#15689217	C₂²	1	1	yes	characteristic, complemented
102	C₄×D₃₇₆	C₂²	1	1	yes	characteristic
103	C₄×D₃₇₆	C₂²	1	1	yes	characteristic, complemented
104	D₈×Dic₄₇	C₂²	1	1	yes	characteristic
105	D₈×Dic₄₇	C₂²	1	1	yes	characteristic, complemented
106	#15689205	C₂²	1	1	yes	characteristic
107	#15689205	C₂²	1	1	yes	characteristic, complemented
108	C₄×#10625334	C₂²	1	2	yes	—
109	#15689203	C₂²	1	2	yes	—
110	#107×D₄₇	C₂²	1	1	yes	characteristic
111	#15689148	C₂²	1	1	yes	characteristic
112	#15689148	C₂²	1	1	yes	characteristic
113	#15689145	C₂²	1	1	yes	characteristic
114	#15689123	C₂²	1	2	yes	—
115	#15689121	C₂²	1	2	yes	—
116	#102×D₄₇	C₂²	1	2	yes	—
117	#15689077	C₂²	1	1	yes	characteristic
118	#15689077	C₂²	1	1	yes	characteristic
119	C₄×C₈×D₄₇	C₂²	1	1	yes	characteristic
120	C₄₇×#559	C₂²	1	2	yes	complemented
121	C₄₇×#495	C₂²	1	1	yes	characteristic
122	C₄₇×#495	C₂²	1	1	yes	characteristic, complemented
123	C₄₇×#493	C₂²	1	1	yes	characteristic
124	C₄₇×#463	C₂²	1	2	yes	complemented
125	C₄₇×#463	C₂²	1	2	yes	complemented
126	C₄₇×#460	C₂²	1	2	yes	complemented
127	C₈×Q₈×C₄₇	C₂²	1	1	yes	characteristic, complemented
128	C₄×Q₁₆×C₄₇	C₂²	1	1	yes	characteristic, complemented
129	C₄×D₈×C₄₇	C₂²	1	1	yes	characteristic
130	C₄×D₈×C₄₇	C₂²	1	1	yes	characteristic, complemented
131	C₂×#10625354	C₂³	1	2	yes	—
132	C₂×#10625350	—	2	2	no	—
133	C₂×#10625352	—	2	2	no	—
134	C₂×#10625352	C₂³	1	2	yes	—
135	C₂×D₄×D₄₇	C₂³	1	2	yes	—
136	C₂²×C₄×D₄₇	—	2	2	no	—
137	#13094051	—	4	4	no	—
138	#13094048	—	4	4	no	—
139	#13094047	—	2	4	no	—
140	#13094045	—	4	4	no	—
141	#13094043	—	2	4	no	—
142	C₂×Dic₁₈₈	C₂³	1	1	yes	characteristic
143	C₂×#10625337	C₂³	1	2	yes	—
144	C₂×#10625325	C₂³	1	2	yes	—
145	C₂×#10625325	C₂³	1	2	yes	—
146	C₂×#10625335	C₂³	1	2	yes	—
147	C₂×#10625335	C₂³	1	2	yes	—
148	C₂×#10625336	C₂³	1	2	yes	—
149	C₂×#10625336	C₂³	1	2	yes	—
150	C₂×D₃₇₆	C₂³	1	1	yes	characteristic
151	C₂×D₃₇₆	C₂³	1	1	yes	characteristic
152	C₂×D₃₇₆	C₂³	1	2	yes	—
153	C₂×#10625334	C₂³	1	2	yes	—
154	C₂×#10625334	C₂³	1	2	yes	—
155	C₂×#10625334	C₂³	1	2	yes	—
156	C₂×#10625334	C₂³	1	2	yes	—
157	D₈×D₄₇	—	2	4	no	—
158	C₂×#10625324	C₂³	1	1	yes	characteristic
159	C₂×#10625324	C₂³	1	1	yes	characteristic
160	C₂×C₈×D₄₇	C₂³	1	1	yes	characteristic
161	C₂×C₈×D₄₇	C₂³	1	1	yes	characteristic
162	#13094023	D₄	1	1	yes	characteristic
163	#13094022	D₄	1	1	yes	characteristic
164	#13094022	C₂³	1	2	yes	—
165	#13094021	C₂³	1	2	yes	—
166	#13094020	C₂³	1	2	yes	—
167	#13094020	C₂³	1	2	yes	—
168	#13094020	C₂³	1	2	yes	—
169	#13094019	—	2	2	no	—
170	#13094018	—	2	2	no	—
171	#13094017	—	2	2	no	—
172	#13094017	—	2	2	no	—
173	#13094014	D₄	1	1	yes	characteristic
174	#13094014	D₄	1	1	yes	characteristic
175	#13094013	—	2	2	no	—
176	#13094013	C₂³	1	2	yes	—
177	#13094012	C₂³	1	2	yes	—
178	#13094012	C₂³	1	2	yes	—
179	#13094011	C₂³	1	2	yes	—
180	#13094010	—	2	2	no	—
181	#13094010	—	2	2	no	—
182	#13094009	—	2	2	no	—
183	#13094009	—	2	2	no	—
184	#13094008	—	2	2	no	—
185	#13094007	—	2	2	no	—
186	#13094006	—	2	2	no	—
187	#13094006	—	2	2	no	—
188	#13094004	D₄	1	1	yes	characteristic
189	#13094002	—	2	2	no	—
190	#13094002	D₄	1	1	yes	characteristic
191	#13094002	D₄	1	1	yes	characteristic
192	#13094001	—	2	2	no	—
193	#13094000	D₄	1	1	yes	characteristic
194	#13093998	—	2	2	no	—
195	#13093997	—	2	2	no	—
196	#13093997	—	2	2	no	—
197	#13093997	—	2	2	no	—
198	#13093997	—	2	2	no	—
199	#13093997	—	2	2	no	—
200	#13093997	—	2	2	no	—
201	#13093996	—	2	2	no	—
202	#13093996	—	2	2	no	—
203	#13093996	—	2	2	no	—
204	#13093996	—	2	2	no	—
205	#13093995	—	2	2	no	—
206	#13093994	—	2	2	no	—
207	#13093994	—	2	2	no	—
208	#13093992	—	2	2	no	—
209	#13093992	—	2	2	no	—
210	Q₈×Dic₄₇	C₂³	1	2	yes	—
211	C₄×Dic₉₄	C₂³	1	2	yes	—
212	C₄×Dic₉₄	C₂³	1	1	yes	characteristic
213	C₄×Dic₉₄	C₂³	1	1	yes	characteristic
214	C₄×Dic₉₄	C₂³	1	1	yes	characteristic
215	#13093989	C₂³	1	2	yes	—
216	C₄×D₁₈₈	—	2	2	no	—
217	C₄×D₁₈₈	C₂³	1	2	yes	—
218	C₄×D₁₈₈	C₂³	1	2	yes	—
219	D₄×Dic₄₇	C₂³	1	2	yes	—
220	D₄×Dic₄₇	C₂³	1	2	yes	—
221	#13093986	—	2	2	no	—
222	#13093986	—	2	2	no	—
223	#13093986	C₂³	1	2	yes	—
224	#13093986	C₂³	1	2	yes	—
225	C₄×C₂²⋊D₄₇	—	2	2	no	—
226	C₄×C₂²⋊D₄₇	—	2	2	no	—
227	C₄×C₂²⋊D₄₇	—	2	2	no	—
228	(C₂²⋊D₄₇)⋊C₄	—	2	2	no	—
229	(C₂²⋊D₄₇)⋊C₄	—	2	2	no	—
230	(C₂²⋊D₄₇)⋊C₄	—	2	2	no	—
231	(C₂²⋊D₄₇)⋊C₄	—	2	2	no	—
232	(C₂²⋊D₄₇)⋊C₄	—	2	2	no	—
233	#13093981	—	2	2	no	—
234	#13093981	—	2	2	no	—
235	#13093981	C₂³	1	1	yes	characteristic
236	#13093981	C₂³	1	1	yes	characteristic
237	#13093980	—	2	2	no	—
238	#13093980	—	2	2	no	—
239	C₂×Dic₄₇⋊C₄	—	2	2	no	—
240	C₄⋊C₄×D₄₇	—	2	2	no	—
241	C₄⋊C₄×D₄₇	C₂³	1	2	yes	—
242	C₂²⋊C₄×D₄₇	—	2	2	no	—
243	C₄²×D₄₇	C₂³	1	1	yes	characteristic
244	#13093958	C₂³	1	1	yes	characteristic
245	#13093957	C₂³	1	2	yes	—
246	C₄⋊(C₄₇⋊C₈)	C₂³	1	1	yes	characteristic
247	C₄⋊(C₄₇⋊C₈)	C₂³	1	1	yes	characteristic
248	C₄⋊(C₄₇⋊C₈)	C₂³	1	1	yes	characteristic
249	Dic₄₇⋊C₈	C₂³	1	1	yes	characteristic
250	Dic₄₇⋊C₈	C₂³	1	1	yes	characteristic
251	Dic₄₇⋊C₈	C₂³	1	1	yes	characteristic
252	Dic₄₇⋊C₈	C₂³	1	1	yes	characteristic
253	Dic₄₇⋊C₈	C₂³	1	1	yes	characteristic
254	Dic₄₇⋊C₈	C₂³	1	1	yes	characteristic
255	#13093949	C₂³	1	2	yes	—
256	#13093948	C₂³	1	2	yes	—
257	#13093947	C₂³	1	2	yes	—
258	#13093946	C₂³	1	2	yes	—
259	#13093946	C₂³	1	2	yes	—
260	#13093945	C₂³	1	2	yes	—
261	#13093945	C₂³	1	2	yes	—
262	#13093944	C₂³	1	2	yes	—
263	#13093944	C₂³	1	2	yes	—
264	#13093935	C₂³	1	1	yes	characteristic
265	#13093935	C₂³	1	1	yes	characteristic
266	#13093934	C₂³	1	1	yes	characteristic
267	#13093934	C₂³	1	1	yes	characteristic
268	C₄×C₄₇⋊C₈	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	C₈×Dic₄₇	C₂³	1	1	yes	characteristic
273	C₂×Q₁₆×C₄₇	C₂³	1	1	yes	characteristic
274	C₂×SD₁₆×C₄₇	C₂³	1	2	yes	—
275	C₂×SD₁₆×C₄₇	C₂³	1	2	yes	—
276	C₂×D₈×C₄₇	C₂³	1	1	yes	characteristic
277	C₂×D₈×C₄₇	C₂³	1	1	yes	characteristic
278	C₂×D₈×C₄₇	C₂³	1	2	yes	—
279	#127×C₄₇	C₂³	1	2	yes	—
280	#124×C₄₇	—	2	2	no	—
281	#124×C₄₇	C₂³	1	2	yes	—
282	#124×C₄₇	C₂³	1	2	yes	—
283	#123×C₄₇	—	2	2	no	—
284	#123×C₄₇	—	2	2	no	—
285	C₄×Q₈×C₄₇	C₂³	1	2	yes	—
286	C₄×Q₈×C₄₇	C₂³	1	1	yes	characteristic
287	C₄×D₄×C₄₇	—	2	2	no	—
288	C₄×D₄×C₄₇	C₂³	1	2	yes	—
289	C₄×D₄×C₄₇	C₂³	1	2	yes	—
290	#107×C₄₇	C₂³	1	1	yes	characteristic
291	C₄⋊C₈×C₄₇	C₂³	1	1	yes	characteristic
292	C₄⋊C₈×C₄₇	C₂³	1	1	yes	characteristic
293	C₄⋊C₈×C₄₇	C₂³	1	1	yes	characteristic
294	#103×C₄₇	C₂³	1	2	yes	—
295	#102×C₄₇	C₂³	1	2	yes	—
296	#102×C₄₇	C₂³	1	2	yes	—
297	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
298	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
299	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
300	C₂³×D₄₇	—	2	2	no	—
301	C₂×Q₈×C₄₇	C₂×D₄	1	1	yes	characteristic
302	C₂×Q₈×C₄₇	C₂⁴	1	2	yes	—
303	C₂×D₄×C₄₇	—	2	2	no	—
304	C₂×D₄×C₄₇	—	2	2	no	—
305	C₂×D₄×C₄₇	C₂⁴	1	2	yes	—
306	C₂×D₄×C₄₇	C₂⁴	1	2	yes	—
307	C₂²×C₄×C₄₇	—	2	2	no	—
308	C₂²×C₄×C₄₇	—	2	2	no	—
309	C₂×C₂²⋊D₄₇	—	2	2	no	—
310	C₂×C₂²⋊D₄₇	—	2	2	no	—
311	C₂×C₂²⋊D₄₇	—	2	2	no	—
312	C₂×C₂²⋊D₄₇	—	2	2	no	—
313	C₂×C₂²⋊D₄₇	—	2	2	no	—
314	C₂×C₂²⋊D₄₇	—	2	2	no	—
315	C₂×C₂²⋊D₄₇	—	2	2	no	—
316	C₂×C₂²⋊D₄₇	—	2	2	no	—
317	C₂²×Dic₄₇	—	2	2	no	—
318	C₂²×Dic₄₇	—	2	2	no	—
319	C₂²×Dic₄₇	—	2	2	no	—
320	#10625354	—	2	4	no	—
321	#10625354	—	2	4	no	—
322	#10625352	—	2	4	no	—
323	#10625352	—	2	4	no	—
324	#10625352	—	8	4	no	—
325	D₄×D₄₇	—	2	4	no	—
326	D₄×D₄₇	—	2	4	no	—
327	#10625350	—	8	4	no	—
328	C₂×D₁₈₈	—	2	2	no	—
329	C₂×D₁₈₈	—	2	2	no	—
330	C₂×D₁₈₈	—	2	2	no	—
331	C₂×D₁₈₈	C₂⁴	1	2	yes	—
332	C₂×D₁₈₈	C₂⁴	1	2	yes	—
333	C₂×C₄×D₄₇	—	2	2	no	—
334	C₂×C₄×D₄₇	—	2	2	no	—
335	C₂×C₄×D₄₇	—	2	2	no	—
336	C₂×C₄×D₄₇	—	2	2	no	—
337	C₂×C₄×D₄₇	—	2	2	no	—
338	C₂×C₄×D₄₇	—	2	2	no	—
339	C₂×C₄×D₄₇	—	8	4	no	—
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×Dic₉₄	C₂×D₄	1	1	yes	characteristic
344	C₂×Dic₉₄	C₂×D₄	1	1	yes	characteristic
345	C₂×Dic₉₄	C₂×D₄	1	1	yes	characteristic
346	C₂×Dic₉₄	C₂⁴	1	2	yes	—
347	Q₁₆×C₄₇	—	2	2	no	—
348	SD₁₆×C₄₇	—	4	2	no	—
349	SD₁₆×C₄₇	—	4	2	no	—
350	D₈×C₄₇	—	2	2	no	—
351	D₈×C₄₇	—	2	2	no	—
352	D₈×C₄₇	—	4	2	no	—
353	C₂×C₈×C₄₇	C₂⁴	1	1	yes	characteristic
354	C₂×C₈×C₄₇	C₂⁴	1	1	yes	characteristic
355	C₂×C₈×C₄₇	C₂⁴	1	1	yes	characteristic
356	C₂×C₈×C₄₇	C₂⁴	1	1	yes	characteristic
357	C₄⋊C₄×C₄₇	—	2	2	no	—
358	C₄⋊C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
359	C₄⋊C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
360	C₄⋊C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
361	C₄⋊C₄×C₄₇	C₂⁴	1	2	yes	—
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	C₂²⋊C₄×C₄₇	—	2	2	no	—
367	C₂²⋊C₄×C₄₇	—	2	2	no	—
368	C₄²×C₄₇	—	2	2	no	—
369	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
370	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
371	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
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	—	4	2	no	—
377	#10625336	—	2	4	no	—
378	#10625336	—	4	2	no	—
379	#10625335	—	2	4	no	—
380	#10625335	—	4	2	no	—
381	#10625334	—	2	4	no	—
382	#10625334	—	4	2	no	—
383	#10625334	—	4	2	no	—
384	#10625334	—	4	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	(C₂×D₄₇)⋊C₄	—	2	2	no	—
391	(C₂×D₄₇)⋊C₄	—	2	2	no	—
392	(C₂×D₄₇)⋊C₄	—	2	2	no	—
393	(C₂×D₄₇)⋊C₄	—	2	2	no	—
394	(C₂×D₄₇)⋊C₄	—	2	2	no	—
395	(C₂×D₄₇)⋊C₄	C₂×D₄	1	1	yes	characteristic
396	(C₂×D₄₇)⋊C₄	C₂×D₄	1	1	yes	characteristic
397	(C₂×D₄₇)⋊C₄	C₂×D₄	1	1	yes	characteristic
398	(C₂×D₄₇)⋊C₄	C₂×D₄	1	1	yes	characteristic
399	C₄⋊Dic₄₇	—	2	2	no	—
400	C₄⋊Dic₄₇	C₂×D₄	1	1	yes	characteristic
401	C₄⋊Dic₄₇	C₂×D₄	1	1	yes	characteristic
402	C₄⋊Dic₄₇	C₂×D₄	1	1	yes	characteristic
403	C₄⋊Dic₄₇	C₂⁴	1	2	yes	—
404	Dic₄₇⋊C₄	—	2	2	no	—
405	Dic₄₇⋊C₄	—	2	2	no	—
406	Dic₄₇⋊C₄	—	2	2	no	—
407	Dic₄₇⋊C₄	—	2	2	no	—
408	Dic₄₇⋊C₄	—	2	2	no	—
409	Dic₄₇⋊C₄	C₂×D₄	1	1	yes	characteristic
410	Dic₄₇⋊C₄	C₂×D₄	1	1	yes	characteristic
411	Dic₄₇⋊C₄	C₂×D₄	1	1	yes	characteristic
412	Dic₄₇⋊C₄	C₂×D₄	1	1	yes	characteristic
413	Dic₄₇⋊C₄	C₂×D₄	1	1	yes	characteristic
414	Dic₄₇⋊C₄	C₂×D₄	1	1	yes	characteristic
415	Dic₄₇⋊C₄	C₂×D₄	1	1	yes	characteristic
416	Dic₄₇⋊C₄	C₂×D₄	1	1	yes	characteristic
417	Dic₄₇⋊C₄	C₂×D₄	1	1	yes	characteristic
418	Dic₄₇⋊C₄	C₂×D₄	1	1	yes	characteristic
419	C₄×Dic₄₇	—	2	2	no	—
420	C₄×Dic₄₇	—	2	2	no	—
421	C₄×Dic₄₇	—	2	2	no	—
422	C₄×Dic₄₇	C₂×D₄	1	1	yes	characteristic
423	C₄×Dic₄₇	C₂×D₄	1	1	yes	characteristic
424	C₄×Dic₄₇	C₂⁴	1	1	yes	characteristic
425	C₄×Dic₄₇	C₂⁴	1	1	yes	characteristic
426	C₄×Dic₄₇	C₂⁴	1	1	yes	characteristic
427	C₂×C₄₇⋊C₈	C₂⁴	1	1	yes	characteristic
428	C₂×C₄₇⋊C₈	C₂⁴	1	1	yes	characteristic
429	C₂×C₄₇⋊C₈	C₂⁴	1	1	yes	characteristic
430	C₂×C₄₇⋊C₈	C₂⁴	1	1	yes	characteristic
431	Dic₁₈₈	—	2	2	no	—
432	D₃₇₆	—	2	2	no	—
433	D₃₇₆	—	2	2	no	—
434	D₃₇₆	—	4	2	no	—
435	#10625325	—	4	2	no	—
436	#10625325	—	4	2	no	—
437	#10625324	—	2	2	no	—
438	#10625324	—	2	2	no	—
439	C₈×D₄₇	—	2	2	no	—
440	C₈×D₄₇	#41	1	4	yes	complemented
441	C₂³×C₄₇	—	2	2	no	—
442	C₂³×C₄₇	—	2	2	no	—
443	C₂²×D₄₇	—	2	2	no	—
444	C₂²×D₄₇	—	2	2	no	—
445	C₂²×D₄₇	—	4	4	no	—
446	C₂²×D₄₇	—	8	2	no	—
447	C₂²×D₄₇	—	8	2	no	—
448	C₂²×D₄₇	C₂²×D₄	1	1	yes	characteristic
449	Q₈×C₄₇	—	2	2	no	—
450	Q₈×C₄₇	—	2	2	no	—
451	Q₈×C₄₇	—	4	1	no	—
452	D₄×C₄₇	—	2	2	no	—
453	D₄×C₄₇	—	2	2	no	—
454	D₄×C₄₇	—	2	2	no	—
455	D₄×C₄₇	—	2	2	no	—
456	D₄×C₄₇	—	8	2	no	—
457	D₄×C₄₇	—	8	2	no	—
458	C₂×C₄×C₄₇	—	2	2	no	—
459	C₂×C₄×C₄₇	—	2	2	no	—
460	C₂×C₄×C₄₇	—	8	2	no	—
461	C₂×C₄×C₄₇	—	8	2	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	C₂²×D₄	1	1	yes	characteristic
468	C₂×C₄×C₄₇	C₂⁵	1	1	yes	characteristic
469	C₂²⋊D₄₇	—	4	4	no	—
470	C₂²⋊D₄₇	—	4	4	no	—
471	C₂²⋊D₄₇	—	4	4	no	—
472	C₂²⋊D₄₇	—	8	2	no	—
473	C₂²⋊D₄₇	—	8	2	no	—
474	C₂²⋊D₄₇	—	8	2	no	—
475	C₂²⋊D₄₇	—	8	2	no	—
476	C₂²⋊D₄₇	—	8	2	no	—
477	C₂×Dic₄₇	—	2	2	no	—
478	C₂×Dic₄₇	—	2	2	no	—
479	C₂×Dic₄₇	—	4	4	no	—
480	C₂×Dic₄₇	—	4	4	no	—
481	C₂×Dic₄₇	—	8	2	no	—
482	C₂×Dic₄₇	C₂²×D₄	1	1	yes	characteristic
483	C₂×Dic₄₇	C₂²×D₄	1	1	yes	characteristic
484	C₂×Dic₄₇	C₂²×D₄	1	1	yes	characteristic
485	C₂×Dic₄₇	C₂²×D₄	1	1	yes	characteristic
486	C₂×Dic₄₇	C₂²×D₄	1	1	yes	characteristic
487	C₂×Dic₄₇	C₂²×D₄	1	1	yes	characteristic
488	C₂×Dic₄₇	C₂²×D₄	1	1	yes	characteristic
489	D₁₈₈	—	2	2	no	—
490	D₁₈₈	—	2	2	no	—
491	D₁₈₈	—	2	2	no	—
492	D₁₈₈	—	2	2	no	—
493	D₁₈₈	—	4	4	no	—
494	D₁₈₈	—	8	2	no	—
495	D₁₈₈	—	8	2	no	—
496	C₄×D₄₇	—	2	2	no	—
497	C₄×D₄₇	—	4	1	no	—
498	C₄×D₄₇	—	4	4	no	—
499	C₄×D₄₇	—	4	4	no	—
500	C₄×D₄₇	—	8	2	no	—
501	C₄×D₄₇	—	8	2	no	—
502	C₄×D₄₇	—	8	2	no	—
503	C₄×D₄₇	—	8	2	no	—
504	C₄×D₄₇	C₂×#41	1	2	yes	—
505	C₄×D₄₇	H(5,𝔽₂)	1	2	yes	—
506	Dic₉₄	—	2	2	no	—
507	Dic₉₄	—	2	2	no	—
508	Dic₉₄	—	2	2	no	—
509	Dic₉₄	—	2	2	no	—
510	Dic₉₄	—	4	1	no	—
511	C₈×C₄₇	—	2	1	no	—
512	C₈×C₄₇	—	2	1	no	—
513	C₈×C₄₇	—	2	1	no	—
514	C₈×C₄₇	C₂×#41	1	2	yes	—
515	C₄₇⋊C₈	—	2	1	no	—
516	C₄₇⋊C₈	—	2	1	no	—
517	C₄₇⋊C₈	—	2	1	no	—
518	C₄₇⋊C₈	C₂×#41	1	2	yes	—
519	#61406	—	47	1	no	maximal, Sylow
520	C₂²×C₄₇	—	4	2	no	—
521	C₂²×C₄₇	—	4	2	no	—
522	C₂²×C₄₇	—	4	2	no	—
523	C₂²×C₄₇	—	4	2	no	—
524	C₂²×C₄₇	—	4	2	no	—
525	C₂²×C₄₇	—	4	2	no	—
526	C₂²×C₄₇	C₂³×D₄	1	1	yes	characteristic
527	C₂×D₄₇	—	2	1	no	—
528	C₂×D₄₇	—	2	1	no	—
529	C₂×D₄₇	—	4	2	no	—
530	C₂×D₄₇	—	4	2	no	—
531	C₂×D₄₇	—	4	2	no	—
532	C₂×D₄₇	—	4	2	no	—
533	C₂×D₄₇	—	4	2	no	—
534	C₂×D₄₇	—	4	2	no	—
535	C₂×D₄₇	—	8	8	no	—
536	C₂×D₄₇	#550	1	2	yes	—
537	C₄×C₄₇	—	2	1	no	—
538	C₄×C₄₇	—	2	1	no	—
539	C₄×C₄₇	—	2	1	no	—
540	C₄×C₄₇	—	2	1	no	—
541	C₄×C₄₇	—	2	1	no	—
542	C₄×C₄₇	—	2	1	no	—
543	C₄×C₄₇	—	4	2	no	—
544	C₄×C₄₇	—	4	2	no	—
545	C₄×C₄₇	C₂²×#41	1	1	yes	characteristic
546	C₄×C₄₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
547	Dic₄₇	—	2	1	no	—
548	Dic₄₇	—	2	1	no	—
549	Dic₄₇	—	2	1	no	—
550	Dic₄₇	—	2	1	no	—
551	Dic₄₇	—	2	1	no	—
552	Dic₄₇	—	4	2	no	—
553	Dic₄₇	—	4	2	no	—
554	Dic₄₇	#550	1	2	yes	—
555	Dic₄₇	#576	1	2	yes	—
556	#3506	—	47	2	no	—
557	#3403	—	47	2	no	—
558	#3403	—	47	2	no	—
559	#3397	—	47	2	no	—
560	#3397	—	47	2	no	—
561	#3396	—	47	1	no	—
562	#3396	—	47	1	no	—
563	#3396	—	47	1	no	—
564	#3396	D₄₇	1	1	yes	characteristic, complemented
565	#3393	—	47	1	no	—
566	#3393	—	47	1	no	—
567	#3391	—	47	1	no	—
568	#3391	—	47	1	no	—
569	#3155	—	47	1	no	—
570	#3155	—	47	1	no	—
571	#3147	—	47	1	no	—
572	#3045	—	47	2	no	—
573	#3045	—	47	2	no	—
574	#3036	—	47	2	no	—
575	#2960	—	47	1	no	—
576	#2951	—	47	1	no	—
577	#2951	—	47	1	no	—
578	C₂×C₄×D₈	—	47	1	no	—
579	C₂×C₄₇	—	8	2	no	—
580	C₂×C₄₇	—	8	2	no	—
581	C₂×C₄₇	C₂×#550	1	1	yes	characteristic
582	C₂×C₄₇	C₂×#576	1	1	yes	characteristic
583	C₂×C₄₇	#3584	1	1	yes	characteristic
584	D₄₇	—	2	2	no	—
585	D₄₇	—	8	2	no	—
586	D₄₇	—	8	2	no	—
587	C₂×AGL(1,ℤ/8)	—	47	2	no	—
588	C₂×AGL(1,ℤ/8)	—	47	2	no	—
589	C₂×#135	—	47	1	no	—
590	C₂×#135	—	47	2	no	—
591	C₂×#135	—	47	1	no	—
592	C₂²×D₈	—	47	1	no	—
593	#559	—	47	2	no	—
594	#559	—	47	2	no	—
595	#559	—	47	2	no	—
596	#559	C₂×D₄₇	1	2	yes	complemented
597	#556	—	47	2	no	—
598	#556	—	47	2	no	—
599	#555	—	94	2	no	—
600	#553	—	94	2	no	—
601	#553	—	94	2	no	—
602	#550	—	47	2	no	—
603	#550	—	47	2	no	—
604	#547	—	94	2	no	—
605	#538	—	94	2	no	—
606	#538	—	94	2	no	—
607	#535	—	47	2	no	—
608	#535	—	47	2	no	—
609	#533	—	47	1	no	—
610	#532	—	47	2	no	—
611	#525	—	94	2	no	—
612	#525	—	94	2	no	—
613	#520	—	47	2	no	—
614	#520	—	47	2	no	—
615	C₂×C₄×D₄	—	47	2	no	—
616	#496	—	47	2	no	—
617	#496	—	47	2	no	—
618	#496	—	47	2	no	—
619	#496	—	47	2	no	—
620	#495	—	47	1	no	—
621	#495	—	47	1	no	—
622	#495	—	47	2	no	—
623	#495	—	47	1	no	—
624	#495	—	47	1	no	—
625	#495	C₂×D₄₇	1	1	yes	characteristic
626	#495	C₂×D₄₇	1	1	yes	characteristic, complemented
627	#494	—	47	1	no	—
628	#493	—	47	1	no	—
629	#493	—	47	1	no	—
630	#493	—	47	1	no	—
631	#493	—	47	1	no	—
632	#493	C₂×D₄₇	1	1	yes	characteristic
633	#492	—	47	2	no	—
634	#464	—	47	2	no	—
635	#464	—	47	2	no	—
636	#464	—	47	2	no	—
637	#464	—	47	2	no	—
638	#463	—	47	2	no	—
639	#463	—	47	2	no	—
640	#463	—	47	2	no	—
641	#463	—	47	2	no	—
642	#463	—	47	2	no	—
643	#463	—	47	2	no	—
644	#463	C₂×D₄₇	1	2	yes	complemented
645	#463	C₂×D₄₇	1	2	yes	complemented
646	#461	—	47	2	no	—
647	#461	—	47	2	no	—
648	#460	—	47	2	no	—
649	#460	—	47	2	no	—
650	#460	—	47	2	no	—
651	#460	C₂×D₄₇	1	2	yes	complemented
652	#459	—	47	2	no	—
653	#459	—	47	2	no	—
654	#459	—	47	2	no	—
655	#459	—	47	2	no	—
656	#459	—	47	2	no	—
657	#459	—	47	2	no	—
658	#446	—	47	1	no	—
659	#446	—	47	1	no	—
660	#446	—	47	1	no	—
661	#446	—	47	1	no	—
662	C₈×Q₈	—	47	1	no	—
663	C₈×Q₈	—	47	1	no	—
664	C₈×Q₈	—	47	1	no	—
665	C₈×Q₈	C₂×D₄₇	1	1	yes	characteristic, complemented
666	#440	—	47	2	no	—
667	#440	—	47	2	no	—
668	#440	—	47	2	no	—
669	#440	—	47	2	no	—
670	C₄×Q₁₆	—	47	1	no	—
671	C₄×Q₁₆	—	47	1	no	—
672	C₄×Q₁₆	—	47	1	no	—
673	C₄×Q₁₆	C₂×D₄₇	1	1	yes	characteristic, complemented
674	C₄×D₈	—	47	1	no	—
675	C₄×D₈	—	47	1	no	—
676	C₄×D₈	—	47	2	no	—
677	C₄×D₈	—	47	1	no	—
678	C₄×D₈	—	47	1	no	—
679	C₄×D₈	—	47	2	no	—
680	C₄×D₈	—	47	1	no	—
681	C₄×D₈	—	47	1	no	—
682	C₄×D₈	C₂×D₄₇	1	1	yes	characteristic
683	C₄×D₈	C₂×D₄₇	1	1	yes	characteristic, complemented
684	C₂×#107	—	47	1	no	—
685	#424	—	47	1	no	—
686	#424	—	47	1	no	—
687	#423	—	47	1	no	—
688	#417	—	47	2	no	—
689	#417	—	47	2	no	—
690	C₂×#102	—	47	2	no	—
691	#405	—	47	1	no	—
692	#405	—	47	1	no	—
693	C₂×C₄×C₈	—	47	1	no	—
694	C₄₇	#61406	1	1	yes	characteristic, complemented, Sylow
695	C₂×#41	—	47	2	no	—
696	C₂×#41	—	47	2	no	—
697	C₂×#41	—	94	2	no	—
698	C₂×#41	—	94	2	no	—
699	C₂²×D₄	—	47	2	no	—
700	C₂³×C₄	—	94	2	no	—
701	AGL(1,ℤ/8)	—	188	4	no	—
702	AGL(1,ℤ/8)	—	188	4	no	—
703	#135	—	94	4	no	—
704	#135	—	94	4	no	—
705	#135	—	188	4	no	—
706	C₂×Q₁₆	—	47	2	no	—
707	C₂×Q₁₆	—	47	1	no	—
708	C₂×Q₁₆	C₂²×D₄₇	1	1	yes	characteristic
709	C₂×SD₁₆	—	47	2	no	—
710	C₂×SD₁₆	—	47	2	no	—
711	C₂×SD₁₆	—	47	2	no	—
712	C₂×SD₁₆	—	47	2	no	—
713	C₂×SD₁₆	—	47	2	no	—
714	C₂×SD₁₆	—	47	2	no	—
715	C₂×SD₁₆	C₂²×D₄₇	1	2	yes	—
716	C₂×SD₁₆	C₂²×D₄₇	1	2	yes	—
717	C₂×D₈	—	47	2	no	—
718	C₂×D₈	—	47	2	no	—
719	C₂×D₈	—	47	2	no	—
720	C₂×D₈	—	47	2	no	—
721	C₂×D₈	—	47	1	no	—
722	C₂×D₈	—	47	1	no	—
723	C₂×D₈	—	47	2	no	—
724	C₂×D₈	—	94	4	no	—
725	C₂×D₈	C₂²×D₄₇	1	1	yes	characteristic
726	C₂×D₈	C₂²×D₄₇	1	1	yes	characteristic
727	C₂×D₈	C₂²×D₄₇	1	2	yes	—
728	C₂×M₁₆	—	47	1	no	—
729	C₂×M₁₆	—	47	1	no	—
730	C₂²×C₈	—	47	1	no	—
731	C₂²×C₈	—	47	1	no	—
732	C₄⋊Q₈	—	47	1	no	—
733	C₄⋊Q₈	—	47	1	no	—
734	C₄⋊Q₈	—	47	2	no	—
735	#127	—	47	2	no	—
736	#127	—	47	2	no	—
737	#127	—	47	2	no	—
738	#127	—	47	2	no	—
739	#127	C₂²×D₄₇	1	2	yes	—
740	#126	—	94	2	no	—
741	#126	—	94	2	no	—
742	#126	—	94	2	no	—
743	#126	—	94	2	no	—
744	#125	—	47	1	no	—
745	#125	—	47	1	no	—
746	#124	—	2	2	no	—
747	#124	—	47	2	no	—
748	#124	—	47	2	no	—
749	#124	—	47	2	no	—
750	#124	—	47	2	no	—
751	#124	—	94	2	no	—
752	#124	—	94	2	no	—
753	#124	—	94	2	no	—
754	#124	C₂²×D₄₇	1	2	yes	—
755	#124	C₂²×D₄₇	1	2	yes	—
756	#123	—	2	2	no	—
757	#123	—	2	2	no	—
758	#123	—	94	2	no	—
759	#123	—	94	2	no	—
760	#123	—	94	2	no	—
761	#123	—	94	2	no	—
762	#123	—	94	2	no	—
763	#123	—	94	2	no	—
764	C₂²⋊Q₈	—	47	1	no	—
765	C₂²⋊Q₈	—	47	1	no	—
766	C₂²⋊Q₈	—	47	1	no	—
767	C₂²⋊Q₈	—	47	1	no	—
768	C₂²⋊Q₈	—	94	2	no	—
769	C₂²⋊Q₈	—	94	2	no	—
770	#121	—	94	2	no	—
771	#121	—	94	2	no	—
772	#121	—	94	2	no	—
773	#121	—	94	2	no	—
774	#121	—	94	2	no	—
775	#121	—	94	2	no	—
776	#121	—	94	2	no	—
777	#121	—	94	2	no	—
778	#121	—	94	2	no	—
779	#121	—	94	2	no	—
780	#121	—	94	2	no	—
781	#121	—	94	2	no	—
782	#120	—	94	2	no	—
783	#120	—	94	2	no	—
784	#120	—	94	2	no	—
785	#120	—	94	2	no	—
786	C₄×Q₈	—	47	1	no	—
787	C₄×Q₈	—	47	1	no	—
788	C₄×Q₈	—	47	1	no	—
789	C₄×Q₈	—	47	2	no	—
790	C₄×Q₈	—	47	2	no	—
791	C₄×Q₈	—	47	2	no	—
792	C₄×Q₈	C₂²×D₄₇	1	2	yes	—
793	C₄×Q₈	C₂²×D₄₇	1	1	yes	characteristic
794	C₄×D₄	—	2	2	no	—
795	C₄×D₄	—	47	2	no	—
796	C₄×D₄	—	47	2	no	—
797	C₄×D₄	—	47	2	no	—
798	C₄×D₄	—	47	2	no	—
799	C₄×D₄	—	47	2	no	—
800	C₄×D₄	—	47	2	no	—
801	C₄×D₄	—	94	2	no	—
802	C₄×D₄	—	94	2	no	—
803	C₄×D₄	—	94	2	no	—
804	C₄×D₄	—	94	2	no	—
805	C₄×D₄	—	94	2	no	—
806	C₄×D₄	—	94	2	no	—
807	C₄×D₄	—	94	2	no	—
808	C₄×D₄	—	94	2	no	—
809	C₄×D₄	—	94	2	no	—
810	C₄×D₄	—	94	2	no	—
811	C₄×D₄	—	94	2	no	—
812	C₄×D₄	C₂²×D₄₇	1	2	yes	—
813	C₄×D₄	C₂²×D₄₇	1	2	yes	—
814	#117	—	47	1	no	—
815	#117	—	47	1	no	—
816	#117	—	94	2	no	—
817	#117	—	94	2	no	—
818	#117	—	94	2	no	—
819	#117	—	94	2	no	—
820	C₂×C₄⋊C₄	—	47	2	no	—
821	C₂×C₄⋊C₄	—	94	2	no	—
822	C₂×C₄⋊C₄	—	94	2	no	—
823	C₂×C₂²⋊C₄	—	94	2	no	—
824	C₂×C₄²	—	47	1	no	—
825	#107	—	47	1	no	—
826	#107	—	47	2	no	—
827	#107	C₂²×D₄₇	1	1	yes	characteristic
828	C₄⋊C₈	—	47	1	no	—
829	C₄⋊C₈	—	47	1	no	—
830	C₄⋊C₈	—	47	1	no	—
831	C₄⋊C₈	—	47	1	no	—
832	C₄⋊C₈	—	47	1	no	—
833	C₄⋊C₈	—	47	1	no	—
834	C₄⋊C₈	—	47	1	no	—
835	C₄⋊C₈	—	47	1	no	—
836	C₄⋊C₈	—	47	1	no	—
837	C₄⋊C₈	C₂²×D₄₇	1	1	yes	characteristic
838	C₄⋊C₈	C₂²×D₄₇	1	1	yes	characteristic
839	C₄⋊C₈	C₂²×D₄₇	1	1	yes	characteristic
840	#103	—	47	2	no	—
841	#103	—	47	2	no	—
842	#103	—	47	2	no	—
843	#103	C₂²×D₄₇	1	2	yes	—
844	#102	—	47	2	no	—
845	#102	—	47	2	no	—
846	#102	—	47	2	no	—
847	#102	—	47	2	no	—
848	#102	—	47	2	no	—
849	#102	—	47	2	no	—
850	#102	C₂²×D₄₇	1	2	yes	—
851	#102	C₂²×D₄₇	1	2	yes	—
852	#97	—	47	1	no	—
853	#97	—	47	1	no	—
854	#97	—	47	1	no	—
855	#97	—	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	1	no	—
860	C₄×C₈	—	47	1	no	—
861	C₄×C₈	C₂²×D₄₇	1	1	yes	characteristic
862	C₄×C₈	C₂²×D₄₇	1	1	yes	characteristic
863	C₄×C₈	C₂²×D₄₇	1	1	yes	characteristic
864	C₂⁴	—	94	2	no	—
865	#41	—	94	4	no	—
866	#41	—	94	4	no	—
867	#41	—	94	4	no	—
868	#41	—	94	4	no	—
869	#41	—	376	4	no	—
870	#41	—	376	4	no	—
871	C₂×Q₈	—	47	1	no	—
872	C₂×Q₈	—	47	1	no	—
873	C₂×Q₈	—	47	1	no	—
874	C₂×Q₈	—	47	2	no	—
875	C₂×Q₈	D₄×D₄₇	1	1	yes	characteristic
876	C₂×Q₈	C₂³×D₄₇	1	2	yes	—
877	C₂×D₄	—	2	2	no	—
878	C₂×D₄	—	2	2	no	—
879	C₂×D₄	—	47	2	no	—
880	C₂×D₄	—	47	2	no	—
881	C₂×D₄	—	94	2	no	—
882	C₂×D₄	—	94	4	no	—
883	C₂×D₄	—	94	4	no	—
884	C₂×D₄	—	94	2	no	—
885	C₂×D₄	—	94	2	no	—
886	C₂×D₄	—	94	2	no	—
887	C₂×D₄	—	94	2	no	—
888	C₂×D₄	—	94	2	no	—
889	C₂×D₄	—	94	2	no	—
890	C₂×D₄	—	94	2	no	—
891	C₂×D₄	—	94	2	no	—
892	C₂×D₄	—	94	2	no	—
893	C₂×D₄	—	94	2	no	—
894	C₂×D₄	C₂³×D₄₇	1	2	yes	—
895	C₂×D₄	C₂³×D₄₇	1	2	yes	—
896	C₂²×C₄	—	2	2	no	—
897	C₂²×C₄	—	2	2	no	—
898	C₂²×C₄	—	47	1	no	—
899	C₂²×C₄	—	47	1	no	—
900	C₂²×C₄	—	47	1	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	—	94	2	no	—
906	C₂²×C₄	—	94	2	no	—
907	C₂²×C₄	—	94	2	no	—
908	C₂²×C₄	—	94	2	no	—
909	C₂²×C₄	—	94	2	no	—
910	C₂²×C₄	—	376	4	no	—
911	Q₁₆	—	2	2	no	—
912	Q₁₆	—	94	2	no	—
913	Q₁₆	—	188	2	no	—
914	SD₁₆	—	4	2	no	—
915	SD₁₆	—	4	2	no	—
916	SD₁₆	—	94	4	no	—
917	SD₁₆	—	94	4	no	—
918	SD₁₆	—	188	2	no	—
919	SD₁₆	—	188	2	no	—
920	SD₁₆	—	188	2	no	—
921	SD₁₆	—	188	2	no	—
922	D₈	—	2	2	no	—
923	D₈	—	2	2	no	—
924	D₈	—	4	2	no	—
925	D₈	—	94	4	no	—
926	D₈	—	94	2	no	—
927	D₈	—	94	2	no	—
928	D₈	—	188	2	no	—
929	D₈	—	188	2	no	—
930	D₈	—	188	2	no	—
931	D₈	—	188	2	no	—
932	M₁₆	—	94	2	no	—
933	M₁₆	—	94	2	no	—
934	C₂×C₈	—	47	1	no	—
935	C₂×C₈	—	47	4	no	—
936	C₂×C₈	—	47	1	no	—
937	C₂×C₈	—	47	1	no	—
938	C₂×C₈	—	47	1	no	—
939	C₂×C₈	—	94	2	no	—
940	C₂×C₈	C₂³×D₄₇	1	1	yes	characteristic
941	C₂×C₈	C₂³×D₄₇	1	1	yes	characteristic
942	C₂×C₈	C₂³×D₄₇	1	1	yes	characteristic
943	C₂×C₈	C₂³×D₄₇	1	1	yes	characteristic
944	C₄⋊C₄	—	2	2	no	—
945	C₄⋊C₄	—	47	1	no	—
946	C₄⋊C₄	—	47	1	no	—
947	C₄⋊C₄	—	47	1	no	—
948	C₄⋊C₄	—	47	1	no	—
949	C₄⋊C₄	—	47	1	no	—
950	C₄⋊C₄	—	47	1	no	—
951	C₄⋊C₄	—	47	1	no	—
952	C₄⋊C₄	—	47	1	no	—
953	C₄⋊C₄	—	47	1	no	—
954	C₄⋊C₄	—	47	1	no	—
955	C₄⋊C₄	—	47	1	no	—
956	C₄⋊C₄	—	47	1	no	—
957	C₄⋊C₄	—	47	1	no	—
958	C₄⋊C₄	—	47	2	no	—
959	C₄⋊C₄	—	94	2	no	—
960	C₄⋊C₄	—	94	2	no	—
961	C₄⋊C₄	—	94	2	no	—
962	C₄⋊C₄	—	94	2	no	—
963	C₄⋊C₄	—	94	2	no	—
964	C₄⋊C₄	—	94	2	no	—
965	C₄⋊C₄	D₄×D₄₇	1	1	yes	characteristic
966	C₄⋊C₄	D₄×D₄₇	1	1	yes	characteristic
967	C₄⋊C₄	D₄×D₄₇	1	1	yes	characteristic
968	C₄⋊C₄	C₂³×D₄₇	1	2	yes	—
969	C₂²⋊C₄	—	2	2	no	—
970	C₂²⋊C₄	—	2	2	no	—
971	C₂²⋊C₄	—	2	2	no	—
972	C₂²⋊C₄	—	2	2	no	—
973	C₂²⋊C₄	—	2	2	no	—
974	C₂²⋊C₄	—	2	2	no	—
975	C₂²⋊C₄	—	47	1	no	—
976	C₂²⋊C₄	—	47	1	no	—
977	C₂²⋊C₄	—	47	1	no	—
978	C₂²⋊C₄	—	47	1	no	—
979	C₂²⋊C₄	—	94	2	no	—
980	C₂²⋊C₄	—	94	2	no	—
981	C₂²⋊C₄	—	94	2	no	—
982	C₂²⋊C₄	—	94	2	no	—
983	C₂²⋊C₄	—	94	2	no	—
984	C₂²⋊C₄	—	94	2	no	—
985	C₂²⋊C₄	—	94	2	no	—
986	C₂²⋊C₄	—	94	2	no	—
987	C₂²⋊C₄	—	94	2	no	—
988	C₂²⋊C₄	—	94	2	no	—
989	C₂²⋊C₄	—	94	2	no	—
990	C₂²⋊C₄	—	94	2	no	—
991	C₂²⋊C₄	—	94	2	no	—
992	C₂²⋊C₄	—	94	2	no	—
993	C₄²	—	2	2	no	—
994	C₄²	—	47	1	no	—
995	C₄²	—	47	1	no	—
996	C₄²	—	47	1	no	—
997	C₄²	—	47	1	no	—
998	C₄²	—	47	1	no	—
999	C₄²	—	94	2	no	—
1000	C₄²	—	94	2	no	—
1001	C₄²	—	94	2	no	—
1002	C₄²	C₂³×D₄₇	1	1	yes	characteristic
1003	C₄²	C₂³×D₄₇	1	1	yes	characteristic
1004	C₄²	C₂³×D₄₇	1	1	yes	characteristic
1005	C₂³	—	2	2	no	—
1006	C₂³	—	2	2	no	—
1007	C₂³	—	47	1	no	—
1008	C₂³	—	94	2	no	—
1009	C₂³	—	94	2	no	—
1010	C₂³	—	376	2	no	—
1011	C₂³	—	376	2	no	—
1012	C₂³	—	188	4	no	—
1013	Q₈	—	2	2	no	—
1014	Q₈	—	2	2	no	—
1015	Q₈	—	4	1	no	—
1016	Q₈	—	94	2	no	—
1017	Q₈	—	94	2	no	—
1018	Q₈	—	94	2	no	—
1019	Q₈	—	94	2	no	—
1020	Q₈	—	188	1	no	—
1021	D₄	—	2	2	no	—
1022	D₄	—	2	2	no	—
1023	D₄	—	2	2	no	—
1024	D₄	—	2	2	no	—
1025	D₄	—	8	2	no	—
1026	D₄	—	8	2	no	—
1027	D₄	—	94	2	no	—
1028	D₄	—	94	2	no	—
1029	D₄	—	94	2	no	—
1030	D₄	—	94	2	no	—
1031	D₄	—	376	2	no	—
1032	D₄	—	376	2	no	—
1033	D₄	—	376	2	no	—
1034	D₄	—	376	2	no	—
1035	D₄	—	376	2	no	—
1036	D₄	—	376	2	no	—
1037	D₄	—	376	2	no	—
1038	D₄	—	188	4	no	—
1039	D₄	—	188	4	no	—
1040	D₄	—	188	4	no	—
1041	D₄	—	188	4	no	—
1042	C₂×C₄	—	2	2	no	—
1043	C₂×C₄	—	2	2	no	—
1044	C₂×C₄	—	8	2	no	—
1045	C₂×C₄	—	8	2	no	—
1046	C₂×C₄	—	47	1	no	—
1047	C₂×C₄	—	47	1	no	—
1048	C₂×C₄	—	47	2	no	—
1049	C₂×C₄	—	47	2	no	—
1050	C₂×C₄	—	47	1	no	—
1051	C₂×C₄	—	47	1	no	—
1052	C₂×C₄	—	47	1	no	—
1053	C₂×C₄	—	47	1	no	—
1054	C₂×C₄	—	47	1	no	—
1055	C₂×C₄	—	94	2	no	—
1056	C₂×C₄	—	94	2	no	—
1057	C₂×C₄	—	94	2	no	—
1058	C₂×C₄	—	376	2	no	—
1059	C₂×C₄	—	376	2	no	—
1060	C₂×C₄	—	376	2	no	—
1061	C₂×C₄	—	376	2	no	—
1062	C₂×C₄	—	376	2	no	—
1063	C₂×C₄	—	188	1	no	—
1064	C₂×C₄	—	188	4	no	—
1065	C₂×C₄	—	188	4	no	—
1066	C₂×C₄	—	188	4	no	—
1067	C₂×C₄	—	188	4	no	—
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	C₂×D₄×D₄₇	1	1	yes	characteristic
1072	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
1073	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
1074	C₂×C₄	C₂⁴×D₄₇	1	1	yes	characteristic
1075	C₈	—	2	1	no	—
1076	C₈	—	2	1	no	—
1077	C₈	—	2	1	no	—
1078	C₈	—	47	2	no	—
1079	C₈	—	94	1	no	—
1080	C₈	—	94	1	no	—
1081	C₈	—	94	1	no	—
1082	C₈	#41×D₄₇	1	2	yes	—
1083	C₂²	—	4	2	no	—
1084	C₂²	—	4	2	no	—
1085	C₂²	—	4	2	no	—
1086	C₂²	—	4	2	no	—
1087	C₂²	—	4	2	no	—
1088	C₂²	—	4	2	no	—
1089	C₂²	—	47	2	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	—	188	2	no	—
1097	C₂²	—	188	2	no	—
1098	C₂²	—	188	2	no	—
1099	C₂²	C₂²×D₄×D₄₇	1	1	yes	characteristic
1100	C₄	—	2	1	no	—
1101	C₄	—	2	1	no	—
1102	C₄	—	2	1	no	—
1103	C₄	—	2	1	no	—
1104	C₄	—	2	1	no	—
1105	C₄	—	2	1	no	—
1106	C₄	—	4	2	no	—
1107	C₄	—	4	2	no	—
1108	C₄	—	47	2	no	—
1109	C₄	—	47	2	no	—
1110	C₄	—	94	1	no	—
1111	C₄	—	94	1	no	—
1112	C₄	—	94	1	no	—
1113	C₄	—	94	1	no	—
1114	C₄	—	94	1	no	—
1115	C₄	—	188	2	no	—
1116	C₄	—	188	2	no	—
1117	C₄	C₂×#41×D₄₇	1	1	yes	characteristic
1118	C₄	H(5,𝔽₂)×D₄₇	1	1	yes	characteristic
1119	C₂	—	8	2	no	—
1120	C₂	—	8	2	no	—
1121	C₂	—	94	2	no	—
1122	C₂	—	376	2	no	—
1123	C₂	—	376	2	no	—
1124	C₂	#550×D₄₇	1	1	yes	characteristic
1125	C₂	#576×D₄₇	1	1	yes	characteristic
1126	C₂	#20258157	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×#3396	C₂
socle	C₂²×C₄₇	C₂³×D₄
hypercenter	#3396	D₄₇
hypocenter	C₄₇	#61406
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₄×Q₈ ◁ #3396

Complements

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

N	H ≅ G/N	type
1. #20257236	C₂	semidirect
2. #20256476	C₂	semidirect
3. #20256472	C₂	semidirect
4. #20256411	C₂	semidirect
5. #20256403	C₂	semidirect
6. #20256401	C₂	semidirect
7. #20256400	C₂	semidirect
8. #20256397	C₂	semidirect
9. #20256376	C₂	semidirect
10. #20256373	C₂	semidirect
11. #20256362	C₂	semidirect
12. #20256361	C₂	semidirect
13. #20253870	C₂	semidirect
14. #20253868	C₂	semidirect
15. #20253813	C₂	semidirect
16. #20252928	C₂	semidirect
17. #20252924	C₂	semidirect
18. #20252850	C₂	semidirect
19. #20252317	C₂	semidirect
20. #20252263	C₂	semidirect
21. #20252258	C₂	semidirect
22. C₄×D₈×D₄₇	C₂	semidirect
23. C₄₇×#3396	C₂	semidirect
30. #15689858	C₂²	semidirect
31. #15689856	C₂²	semidirect
32. #15689855	C₂²	semidirect
33. #15689845	C₂²	semidirect
34. #15689842	C₂²	semidirect
38. #15689794	C₂²	semidirect
39. #15689793	C₂²	semidirect
58. #15689507	C₂²	semidirect
60. #15689505	C₂²	semidirect
61. #15689501	C₂²	semidirect
65. #15689498	C₂²	semidirect
66. #15689494	C₂²	semidirect
67. #15689348	C₂²	semidirect
68. #15689345	C₂²	semidirect
69. #15689343	C₂²	semidirect
70. #15689342	C₂²	semidirect
71. #15689340	C₂²	semidirect
72. #15689339	C₂²	semidirect
73. #15689339	C₂²	semidirect
74. #15689338	C₂²	semidirect
75. #15689337	C₂²	semidirect
76. #15689335	C₂²	semidirect
77. #15689327	C₂²	semidirect
78. #15689326	C₂²	semidirect
79. #15689324	C₂²	semidirect
80. #15689322	C₂²	semidirect
81. #15689321	C₂²	semidirect
82. #15689318	C₂²	semidirect
83. #15689317	C₂²	semidirect
84. #15689317	C₂²	semidirect
85. #15689316	C₂²	semidirect
86. #15689316	C₂²	semidirect
87. #15689315	C₂²	semidirect
88. #15689254	C₂²	semidirect
89. #15689252	C₂²	semidirect
90. #15689252	C₂²	semidirect
91. #15689250	C₂²	semidirect
92. C₈×Dic₉₄	C₂²	semidirect
93. C₈×Dic₉₄	C₂²	semidirect
94. C₈×Dic₉₄	C₂²	semidirect
95. #15689226	C₂²	semidirect
96. #15689223	C₂²	semidirect
97. #15689221	C₂²	semidirect
98. #15689220	C₂²	semidirect
99. C₄×Dic₁₈₈	C₂²	semidirect
100. Q₁₆×Dic₄₇	C₂²	semidirect
101. #15689217	C₂²	semidirect
103. C₄×D₃₇₆	C₂²	semidirect
105. D₈×Dic₄₇	C₂²	semidirect
107. #15689205	C₂²	semidirect
120. C₄₇×#559	C₂²	semidirect
122. C₄₇×#495	C₂²	semidirect
124. C₄₇×#463	C₂²	semidirect
125. C₄₇×#463	C₂²	semidirect
126. C₄₇×#460	C₂²	semidirect
127. C₈×Q₈×C₄₇	C₂²	semidirect
128. C₄×Q₁₆×C₄₇	C₂²	semidirect
130. C₄×D₈×C₄₇	C₂²	semidirect
440. C₈×D₄₇	#41	semidirect
564. #3396	D₄₇	semidirect
596. #559	C₂×D₄₇	semidirect
626. #495	C₂×D₄₇	semidirect
644. #463	C₂×D₄₇	semidirect
645. #463	C₂×D₄₇	semidirect
651. #460	C₂×D₄₇	semidirect
665. C₈×Q₈	C₂×D₄₇	semidirect
673. C₄×Q₁₆	C₂×D₄₇	semidirect
683. C₄×D₈	C₂×D₄₇	semidirect
694. C₄₇	#61406	semidirect

Maximal subgroups

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

subgroup	index
#20257236	2
#20256476	2
#20256472	2
#20256411	2
#20256403	2
#20256401	2
#20256400	2
#20256397	2
#20256376	2
#20256373	2
#20256362	2
#20256361	2
#20253870	2
#20253868	2
#20253813	2
#20252928	2
#20252924	2
#20252850	2
#20252317	2
#20252263	2
#20252258	2
C₄×D₈×D₄₇	2
C₄₇×#3396	2
#61406	47