Subgroups — #27098596

Order 12032.

1908 conjugacy classes of subgroups.

The subgroup lattice has 1160 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20256981	C₂	1	1	yes	maximal, characteristic, complemented
2	#20256396	C₂	1	1	yes	maximal, characteristic, complemented
3	#20256263	C₂	1	1	yes	maximal, characteristic, complemented
4	#20256080	C₂	1	1	yes	maximal, characteristic, complemented
5	#20256048	C₂	1	1	yes	maximal, characteristic, complemented
6	#20256003	C₂	1	1	yes	maximal, characteristic, complemented
7	#20255988	C₂	1	2	yes	maximal, complemented
8	#20255720	C₂	1	1	yes	maximal, characteristic, complemented
9	#20255635	C₂	1	2	yes	maximal, complemented
10	#20255619	C₂	1	1	yes	maximal, characteristic, complemented
11	#20255589	C₂	1	2	yes	maximal, complemented
12	#20255015	C₂	1	2	yes	maximal, complemented
13	#20255004	C₂	1	1	yes	maximal, characteristic, complemented
14	#20254122	C₂	1	1	yes	maximal, characteristic, complemented
15	#20254111	C₂	1	2	yes	maximal, complemented
16	#20253539	C₂	1	1	yes	maximal, characteristic, complemented
17	#20253526	C₂	1	2	yes	maximal, complemented
18	#20253506	C₂	1	1	yes	maximal, characteristic, complemented
19	#20253491	C₂	1	2	yes	maximal, complemented
20	#20252408	C₂	1	1	yes	maximal, characteristic, complemented
21	C₄×#13094054	C₂	1	1	yes	maximal, characteristic, complemented
22	C₄×#13094050	C₂	1	2	yes	maximal, complemented
23	C₄₇×#3481	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#13094054	C₂²	1	1	yes	characteristic
25	C₂×#13094050	C₂²	1	2	yes	—
26	#15689858	C₂²	1	1	yes	characteristic, complemented
27	#15689856	—	2	1	no	—
28	#15689851	C₂²	1	1	yes	characteristic, complemented
29	#15689845	—	2	1	no	—
30	#15689843	C₂²	1	1	yes	characteristic
31	#15689822	—	2	2	no	—
32	#15689819	C₂²	1	2	yes	complemented
33	#15689794	C₂²	1	1	yes	characteristic
34	#15689782	C₂²	1	2	yes	complemented
35	#15689673	C₂²	1	1	yes	characteristic, complemented
36	#15689669	—	2	1	no	—
37	#15689657	C₂²	1	2	yes	complemented
38	#15689651	—	2	2	no	—
39	C₄×#10625350	C₂²	1	2	yes	complemented
40	#15689591	—	2	1	no	—
41	C₂×C₄×Dic₉₄	C₂²	1	1	yes	characteristic, complemented
42	#15689522	C₂²	1	2	yes	complemented
43	#15689519	C₂²	1	1	yes	characteristic, complemented
44	#15689505	C₂²	1	2	yes	complemented
45	#15689499	C₂²	1	1	yes	characteristic
46	#15689480	C₂²	1	2	yes	complemented
47	#15689477	C₂²	1	2	yes	complemented
48	#15689471	C₂²	1	1	yes	characteristic, complemented
49	#15689469	C₂²	1	1	yes	characteristic
50	#15689461	C₂²	1	2	yes	complemented
51	#15689453	C₂²	1	2	yes	complemented
52	#15689447	C₂²	1	2	yes	complemented
53	#15689444	C₂²	1	2	yes	—
54	#15689436	C₂²	1	2	yes	complemented
55	#15689434	C₂²	1	2	yes	complemented
56	#15689427	C₂²	1	2	yes	complemented
57	#15689423	C₂²	1	2	yes	—
58	#15689423	C₂²	1	2	yes	complemented
59	#15689420	C₂²	1	2	yes	complemented
60	#15689415	C₂²	1	1	yes	characteristic, complemented
61	#15689415	C₂²	1	1	yes	characteristic, complemented
62	#15689408	C₂²	1	1	yes	characteristic, complemented
63	#15689403	C₂²	1	1	yes	characteristic
64	#15689379	C₂²	1	2	yes	complemented
65	#15689374	C₂²	1	2	yes	—
66	#15689374	C₂²	1	2	yes	complemented
67	#15689374	C₂²	1	2	yes	complemented
68	#15689371	C₂²	1	2	yes	complemented
69	#15689367	C₂²	1	2	yes	—
70	#15689342	C₂²	1	2	yes	complemented
71	#15689338	C₂²	1	2	yes	—
72	#15689338	C₂²	1	2	yes	complemented
73	#15689335	C₂²	1	2	yes	complemented
74	#15689323	C₂²	1	1	yes	characteristic, complemented
75	#15689320	C₂²	1	1	yes	characteristic
76	#15689320	C₂²	1	1	yes	characteristic
77	#15689318	C₂²	1	1	yes	characteristic
78	#15689283	C₂²	1	2	yes	complemented
79	#15689274	C₂²	1	2	yes	—
80	#15689268	C₂²	1	2	yes	—
81	#15689266	C₂²	1	2	yes	—
82	#15689261	C₂²	1	2	yes	complemented
83	#15689257	C₂²	1	2	yes	—
84	Q₈×C₄₇⋊C₈	C₂²	1	1	yes	characteristic, complemented
85	Q₈×C₄₇⋊C₈	C₂²	1	1	yes	characteristic, complemented
86	#15689233	C₂²	1	2	yes	—
87	#15689233	C₂²	1	2	yes	complemented
88	#15689233	C₂²	1	2	yes	complemented
89	#15689228	C₂²	1	1	yes	characteristic, complemented
90	#15689228	C₂²	1	1	yes	characteristic, complemented
91	#15689223	C₂²	1	1	yes	characteristic
92	#15689223	C₂²	1	1	yes	characteristic
93	#15689223	C₂²	1	2	yes	complemented
94	#15689223	C₂²	1	2	yes	complemented
95	#15689221	C₂²	1	2	yes	complemented
96	C₄×#10625337	C₂²	1	1	yes	characteristic, complemented
97	C₄×#10625337	C₂²	1	1	yes	characteristic, complemented
98	C₄×#10625335	C₂²	1	1	yes	characteristic
99	C₄×#10625335	C₂²	1	2	yes	—
100	C₄×#10625335	C₂²	1	1	yes	characteristic
101	C₄×#10625335	C₂²	1	2	yes	complemented
102	C₄×#10625334	C₂²	1	2	yes	—
103	C₄×#10625334	C₂²	1	2	yes	complemented
104	#15689201	C₂²	1	1	yes	characteristic
105	#15689201	C₂²	1	1	yes	characteristic
106	#15689201	C₂²	1	2	yes	complemented
107	#15689201	C₂²	1	2	yes	complemented
108	#15689180	C₂²	1	2	yes	complemented
109	#15689180	C₂²	1	1	yes	characteristic, complemented
110	#15689166	C₂²	1	1	yes	characteristic, complemented
111	#15689163	C₂²	1	2	yes	complemented
112	#15689131	C₂²	1	1	yes	characteristic, complemented
113	#15689128	C₂²	1	2	yes	—
114	#15689124	C₂²	1	1	yes	characteristic
115	#15689122	C₂²	1	2	yes	complemented
116	C₄×#10625329	C₂²	1	2	yes	complemented
117	C₄×#10625329	C₂²	1	1	yes	characteristic, complemented
118	C₄₇×#559	C₂²	1	1	yes	characteristic
119	C₄₇×#554	C₂²	1	1	yes	characteristic
120	C₄₇×#554	C₂²	1	1	yes	characteristic
121	C₄₇×#553	—	2	1	no	—
122	C₄₇×#553	C₂²	1	2	yes	—
123	C₄₇×#551	—	2	2	no	—
124	C₄₇×#546	—	2	1	no	—
125	C₄₇×#546	C₂²	1	2	yes	—
126	D₄²×C₄₇	C₂²	1	1	yes	characteristic
127	C₄₇×#532	C₂²	1	1	yes	characteristic
128	C₄₇×#529	—	2	1	no	—
129	C₄₇×#529	C₂²	1	2	yes	—
130	C₄₇×#525	—	2	2	no	—
131	C₄×#41×C₄₇	C₂²	1	1	yes	characteristic
132	C₄×#41×C₄₇	C₂²	1	1	yes	characteristic
133	C₂×C₄×D₄×C₄₇	—	2	1	no	—
134	C₂×C₄×D₄×C₄₇	C₂²	1	2	yes	—
135	C₂×#10625350	—	2	1	no	—
136	C₂×#10625350	C₂³	1	2	yes	—
137	C₂²×Dic₉₄	C₂³	1	1	yes	characteristic
138	#13094054	—	2	4	no	—
139	#13094050	—	2	8	no	—
140	C₂×#10625337	C₂³	1	1	yes	characteristic
141	C₂×#10625337	C₂³	1	1	yes	characteristic
142	C₂×#10625335	C₂³	1	1	yes	characteristic
143	C₂×#10625335	C₂³	1	2	yes	—
144	C₂×#10625335	C₂³	1	2	yes	—
145	C₂×#10625335	C₂³	1	1	yes	characteristic
146	C₂×#10625336	C₂³	1	2	yes	—
147	C₂×#10625334	C₂³	1	2	yes	—
148	C₂×#10625334	C₂³	1	2	yes	—
149	C₂×#10625334	C₂³	1	2	yes	—
150	C₂×#10625329	C₂³	1	2	yes	—
151	C₂×#10625329	C₂³	1	1	yes	characteristic
152	C₂×#10625329	C₂³	1	2	yes	—
153	C₂×#10625329	C₂³	1	1	yes	characteristic
154	#13094024	C₂³	1	1	yes	characteristic
155	#13094022	—	2	1	no	—
156	#13094021	C₂³	1	1	yes	characteristic
157	#13094020	—	2	1	no	—
158	#13094019	—	2	2	no	—
159	#13094018	—	2	2	no	—
160	#13094017	—	2	2	no	—
161	#13094016	C₂³	1	2	yes	—
162	#13094014	—	2	2	no	—
163	#13094013	—	2	1	no	—
164	#13094012	—	2	1	no	—
165	#13094012	C₂³	1	2	yes	—
166	#13094011	—	2	1	no	—
167	#13094010	—	2	2	no	—
168	#13094009	—	2	2	no	—
169	#13094007	—	2	2	no	—
170	#13094006	—	2	2	no	—
171	#13094003	C₂³	1	2	yes	—
172	#13094002	—	2	2	no	—
173	#13093998	—	2	1	no	—
174	#13093998	C₂³	1	2	yes	—
175	#13093998	C₂³	1	2	yes	—
176	#13093997	—	2	2	no	—
177	#13093996	—	2	2	no	—
178	#13093996	—	2	2	no	—
179	C₄×Dic₉₄	—	2	1	no	—
180	C₄×Dic₉₄	—	2	1	no	—
181	C₄×Dic₉₄	C₂³	1	1	yes	characteristic
182	C₄×Dic₉₄	C₂³	1	1	yes	characteristic
183	C₄×Dic₉₄	C₂³	1	1	yes	characteristic
184	C₄×Dic₉₄	C₂³	1	1	yes	characteristic
185	C₄×Dic₉₄	C₂³	1	2	yes	—
186	#13093989	—	2	1	no	—
187	#13093989	—	2	1	no	—
188	C₄×D₁₈₈	—	2	1	no	—
189	C₄×D₁₈₈	C₂³	1	2	yes	—
190	C₄×D₁₈₈	C₂³	1	2	yes	—
191	#13093986	—	2	1	no	—
192	#13093986	—	2	1	no	—
193	C₄×C₂²⋊D₄₇	—	2	2	no	—
194	C₄×C₂²⋊D₄₇	—	2	2	no	—
195	C₄×C₂²⋊D₄₇	—	2	2	no	—
196	(C₂²⋊D₄₇)⋊C₄	—	2	2	no	—
197	(C₂²⋊D₄₇)⋊C₄	—	2	2	no	—
198	#13093983	C₂³	1	2	yes	—
199	#13093981	—	2	2	no	—
200	#13093981	—	2	2	no	—
201	C₂×C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic
202	C₂×Dic₄₇⋊C₄	—	2	1	no	—
203	C₂×C₄×Dic₄₇	—	2	1	no	—
204	C₄²×D₄₇	—	2	2	no	—
205	#13093957	C₂³	1	1	yes	characteristic
206	#13093957	C₂³	1	1	yes	characteristic
207	#13093957	C₂³	1	2	yes	—
208	#13093957	C₂³	1	2	yes	—
209	#13093957	C₂³	1	2	yes	—
210	#13093955	C₂³	1	1	yes	characteristic
211	#13093955	C₂³	1	1	yes	characteristic
212	#13093955	C₂³	1	2	yes	—
213	#13093955	C₂³	1	2	yes	—
214	#13093955	C₂³	1	2	yes	—
215	C₄⋊(C₄₇⋊C₈)	C₂³	1	1	yes	characteristic
216	C₄⋊(C₄₇⋊C₈)	C₂³	1	1	yes	characteristic
217	C₄⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
218	C₄⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
219	#13093948	C₂³	1	1	yes	characteristic
220	#13093948	C₂³	1	1	yes	characteristic
221	#13093948	C₂³	1	2	yes	—
222	#13093947	C₂³	1	1	yes	characteristic
223	#13093947	C₂³	1	1	yes	characteristic
224	#13093947	C₂³	1	2	yes	—
225	#13093947	C₂³	1	2	yes	—
226	#13093947	C₂³	1	1	yes	characteristic
227	#13093947	C₂³	1	1	yes	characteristic
228	#13093945	C₂³	1	2	yes	—
229	#13093945	C₂³	1	2	yes	—
230	#13093945	C₂³	1	1	yes	characteristic
231	#13093945	C₂³	1	1	yes	characteristic
232	#13093945	C₂³	1	2	yes	—
233	#13093945	C₂³	1	2	yes	—
234	#13093945	C₂³	1	2	yes	—
235	#13093944	C₂³	1	2	yes	—
236	#13093944	C₂³	1	2	yes	—
237	#13093944	C₂³	1	2	yes	—
238	#13093944	C₂³	1	2	yes	—
239	C₂²⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
240	C₂²⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
241	C₂²⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
242	#13093935	C₂³	1	2	yes	—
243	#13093935	C₂³	1	1	yes	characteristic
244	#13093935	C₂³	1	1	yes	characteristic
245	C₄×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
246	C₄×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
247	C₄×C₄₇⋊C₈	C₂³	1	2	yes	—
248	C₄×C₄₇⋊C₈	C₂³	1	2	yes	—
249	C₂×#41×C₄₇	—	2	1	no	—
250	C₂×#41×C₄₇	D₄	1	1	yes	characteristic
251	C₂×#41×C₄₇	C₂³	1	1	yes	characteristic
252	C₂²×D₄×C₄₇	—	2	1	no	—
253	C₂²×D₄×C₄₇	C₂³	1	2	yes	—
254	C₂³×C₄×C₄₇	—	2	2	no	—
255	C₄⋊Q₈×C₄₇	C₂³	1	1	yes	characteristic
256	#127×C₄₇	C₂³	1	1	yes	characteristic
257	#126×C₄₇	—	2	2	no	—
258	#126×C₄₇	—	2	2	no	—
259	#125×C₄₇	—	2	1	no	—
260	#125×C₄₇	C₂³	1	2	yes	—
261	#124×C₄₇	—	2	1	no	—
262	#124×C₄₇	—	2	1	no	—
263	#124×C₄₇	C₂³	1	2	yes	—
264	#123×C₄₇	—	2	2	no	—
265	#123×C₄₇	—	2	2	no	—
266	#123×C₄₇	—	2	2	no	—
267	#123×C₄₇	—	2	2	no	—
268	C₂²⋊Q₈×C₄₇	—	2	1	no	—
269	C₂²⋊Q₈×C₄₇	—	2	2	no	—
270	C₂²⋊Q₈×C₄₇	—	2	2	no	—
271	C₂²⋊Q₈×C₄₇	C₂³	1	2	yes	—
272	#121×C₄₇	—	2	2	no	—
273	#121×C₄₇	—	2	1	no	—
274	#121×C₄₇	—	2	1	no	—
275	#121×C₄₇	—	2	2	no	—
276	#121×C₄₇	C₂³	1	2	yes	—
277	#121×C₄₇	C₂³	1	2	yes	—
278	#120×C₄₇	—	2	2	no	—
279	#120×C₄₇	—	2	2	no	—
280	C₄×Q₈×C₄₇	D₄	1	1	yes	characteristic
281	C₄×Q₈×C₄₇	C₂³	1	1	yes	characteristic
282	C₄×Q₈×C₄₇	C₂³	1	1	yes	characteristic
283	C₄×Q₈×C₄₇	C₂³	1	1	yes	characteristic
284	C₄×D₄×C₄₇	—	2	1	no	—
285	C₄×D₄×C₄₇	—	2	2	no	—
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	—	2	2	no	—
290	C₄×D₄×C₄₇	—	2	1	no	—
291	C₄×D₄×C₄₇	—	2	2	no	—
292	C₄×D₄×C₄₇	—	2	2	no	—
293	C₄×D₄×C₄₇	D₄	1	1	yes	characteristic
294	C₄×D₄×C₄₇	D₄	1	2	yes	—
295	C₄×D₄×C₄₇	C₂³	1	1	yes	characteristic
296	C₄×D₄×C₄₇	C₂³	1	2	yes	—
297	C₄×D₄×C₄₇	C₂³	1	2	yes	—
298	C₄×D₄×C₄₇	C₂³	1	2	yes	—
299	C₄×D₄×C₄₇	C₂³	1	1	yes	characteristic
300	C₄×D₄×C₄₇	C₂³	1	2	yes	—
301	C₄×D₄×C₄₇	C₂³	1	1	yes	characteristic
302	#117×C₄₇	—	2	1	no	—
303	#117×C₄₇	—	2	2	no	—
304	#117×C₄₇	D₄	1	2	yes	—
305	#117×C₄₇	D₄	1	1	yes	characteristic
306	#117×C₄₇	C₂³	1	1	yes	characteristic
307	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
308	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
309	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
310	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
311	C₂×C₄²×C₄₇	—	2	1	no	—
312	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
313	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
314	C₂⁴×C₄₇	—	2	2	no	—
315	#41×C₄₇	—	2	2	no	—
316	#41×C₄₇	—	4	2	no	—
317	#41×C₄₇	—	4	1	no	—
318	#41×C₄₇	—	8	2	no	—
319	C₂×Q₈×C₄₇	—	2	1	no	—
320	C₂×Q₈×C₄₇	C₂×D₄	1	1	yes	characteristic
321	C₂×Q₈×C₄₇	C₂⁴	1	1	yes	characteristic
322	C₂×D₄×C₄₇	—	2	4	no	—
323	C₂×D₄×C₄₇	—	2	1	no	—
324	C₂×D₄×C₄₇	—	2	2	no	—
325	C₂×D₄×C₄₇	—	2	2	no	—
326	C₂×D₄×C₄₇	—	2	2	no	—
327	C₂×D₄×C₄₇	—	2	1	no	—
328	C₂×D₄×C₄₇	—	2	1	no	—
329	C₂×D₄×C₄₇	—	4	2	no	—
330	C₂×D₄×C₄₇	—	4	4	no	—
331	C₂×D₄×C₄₇	C₂×D₄	1	1	yes	characteristic
332	C₂×D₄×C₄₇	C₂×D₄	1	2	yes	—
333	C₂×D₄×C₄₇	C₂⁴	1	2	yes	—
334	C₂×D₄×C₄₇	C₂⁴	1	1	yes	characteristic
335	C₂²×C₄×C₄₇	—	2	2	no	—
336	C₂²×C₄×C₄₇	—	2	1	no	—
337	C₂²×C₄×C₄₇	—	2	1	no	—
338	C₂²×C₄×C₄₇	—	2	1	no	—
339	C₂²×C₄×C₄₇	—	2	2	no	—
340	C₂²×C₄×C₄₇	—	2	2	no	—
341	C₂²×C₄×C₄₇	—	2	2	no	—
342	C₂²×C₄×C₄₇	—	8	4	no	—
343	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
344	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
345	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
346	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
347	C₂²×C₄×C₄₇	C₂⁴	1	2	yes	—
348	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
349	C₂×C₂²⋊D₄₇	—	2	2	no	—
350	C₂×C₂²⋊D₄₇	—	2	2	no	—
351	C₂×C₂²⋊D₄₇	—	2	2	no	—
352	C₂²×Dic₄₇	—	2	1	no	—
353	C₂²×Dic₄₇	—	2	1	no	—
354	#10625350	—	2	4	no	—
355	#10625350	—	4	2	no	—
356	#10625350	—	4	4	no	—
357	C₂×D₁₈₈	—	2	1	no	—
358	C₂×D₁₈₈	—	2	1	no	—
359	C₂×D₁₈₈	C₂⁴	1	2	yes	—
360	C₂×C₄×D₄₇	—	2	2	no	—
361	C₂×C₄×D₄₇	—	2	2	no	—
362	C₂×C₄×D₄₇	—	2	2	no	—
363	C₂×Dic₉₄	—	2	2	no	—
364	C₂×Dic₉₄	—	2	1	no	—
365	C₂×Dic₉₄	—	2	1	no	—
366	C₂×Dic₉₄	—	4	1	no	—
367	C₂×Dic₉₄	C₂⁴	1	1	yes	characteristic
368	C₂×Dic₉₄	C₂⁴	1	1	yes	characteristic
369	C₄⋊C₄×C₄₇	—	2	1	no	—
370	C₄⋊C₄×C₄₇	—	2	2	no	—
371	C₄⋊C₄×C₄₇	—	2	2	no	—
372	C₄⋊C₄×C₄₇	—	2	1	no	—
373	C₄⋊C₄×C₄₇	—	2	1	no	—
374	C₄⋊C₄×C₄₇	—	2	2	no	—
375	C₄⋊C₄×C₄₇	—	2	2	no	—
376	C₄⋊C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
377	C₄⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
378	C₄⋊C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
379	C₄⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
380	C₄⋊C₄×C₄₇	C₂⁴	1	1	yes	characteristic
381	C₄⋊C₄×C₄₇	C₂⁴	1	2	yes	—
382	C₄⋊C₄×C₄₇	C₂⁴	1	1	yes	characteristic
383	C₂²⋊C₄×C₄₇	—	2	2	no	—
384	C₂²⋊C₄×C₄₇	—	2	1	no	—
385	C₂²⋊C₄×C₄₇	—	2	1	no	—
386	C₂²⋊C₄×C₄₇	—	2	2	no	—
387	C₂²⋊C₄×C₄₇	—	2	2	no	—
388	C₂²⋊C₄×C₄₇	—	2	2	no	—
389	C₂²⋊C₄×C₄₇	—	2	2	no	—
390	C₂²⋊C₄×C₄₇	—	2	2	no	—
391	C₂²⋊C₄×C₄₇	—	2	1	no	—
392	C₂²⋊C₄×C₄₇	—	2	2	no	—
393	C₂²⋊C₄×C₄₇	—	2	2	no	—
394	C₂²⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
395	C₂²⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
396	C₂²⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
397	C₄²×C₄₇	—	2	1	no	—
398	C₄²×C₄₇	—	2	1	no	—
399	C₄²×C₄₇	—	2	1	no	—
400	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
401	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
402	C₄²×C₄₇	C₂×D₄	1	2	yes	—
403	C₄²×C₄₇	C₂×D₄	1	2	yes	—
404	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
405	C₄²×C₄₇	C₂⁴	1	2	yes	—
406	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
407	C₂²⋊Dic₄₇	—	2	2	no	—
408	C₂²⋊Dic₄₇	—	2	2	no	—
409	#10625337	—	2	2	no	—
410	#10625337	—	2	2	no	—
411	#10625336	—	4	2	no	—
412	#10625335	—	2	2	no	—
413	#10625335	—	2	4	no	—
414	#10625335	—	4	2	no	—
415	#10625335	#41	1	4	yes	complemented
416	#10625334	—	2	4	no	—
417	#10625334	—	2	4	no	—
418	#10625334	—	4	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	C₄⋊Dic₄₇	—	2	1	no	—
426	C₄⋊Dic₄₇	—	2	1	no	—
427	C₄⋊Dic₄₇	C₂⁴	1	2	yes	—
428	C₄⋊Dic₄₇	C₂⁴	1	1	yes	characteristic
429	C₄⋊Dic₄₇	C₂⁴	1	1	yes	characteristic
430	Dic₄₇⋊C₄	—	2	1	no	—
431	Dic₄₇⋊C₄	—	2	1	no	—
432	Dic₄₇⋊C₄	—	2	1	no	—
433	Dic₄₇⋊C₄	—	2	1	no	—
434	Dic₄₇⋊C₄	—	2	2	no	—
435	Dic₄₇⋊C₄	—	2	2	no	—
436	Dic₄₇⋊C₄	—	2	2	no	—
437	Dic₄₇⋊C₄	—	2	2	no	—
438	C₄×Dic₄₇	—	2	1	no	—
439	C₄×Dic₄₇	—	2	2	no	—
440	C₄×Dic₄₇	—	2	2	no	—
441	C₄×Dic₄₇	—	2	1	no	—
442	C₄×Dic₄₇	—	2	1	no	—
443	C₄×Dic₄₇	—	2	1	no	—
444	#10625329	—	2	4	no	—
445	#10625329	—	2	2	no	—
446	#10625329	—	4	1	no	—
447	#10625329	—	4	2	no	—
448	C₂×C₄₇⋊C₈	C₂⁴	1	1	yes	characteristic
449	C₂×C₄₇⋊C₈	C₂⁴	1	1	yes	characteristic
450	C₂×C₄₇⋊C₈	C₂⁴	1	2	yes	—
451	C₂×C₄₇⋊C₈	C₂⁴	1	2	yes	—
452	C₂×C₄₇⋊C₈	C₂⁴	1	1	yes	characteristic
453	C₂×C₄₇⋊C₈	C₂⁴	1	1	yes	characteristic
454	C₂³×C₄₇	—	2	1	no	—
455	C₂³×C₄₇	—	2	2	no	—
456	C₂³×C₄₇	—	4	4	no	—
457	C₂³×C₄₇	—	4	4	no	—
458	C₂³×C₄₇	—	8	2	no	—
459	C₂³×C₄₇	C₂²×D₄	1	2	yes	—
460	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
461	C₂²×D₄₇	—	2	2	no	—
462	Q₈×C₄₇	—	2	2	no	—
463	Q₈×C₄₇	—	2	1	no	—
464	Q₈×C₄₇	—	2	1	no	—
465	Q₈×C₄₇	—	8	1	no	—
466	D₄×C₄₇	—	2	2	no	—
467	D₄×C₄₇	—	2	2	no	—
468	D₄×C₄₇	—	2	1	no	—
469	D₄×C₄₇	—	2	2	no	—
470	D₄×C₄₇	—	4	2	no	—
471	D₄×C₄₇	—	4	4	no	—
472	D₄×C₄₇	—	4	2	no	—
473	D₄×C₄₇	—	4	4	no	—
474	D₄×C₄₇	—	4	2	no	—
475	D₄×C₄₇	—	8	1	no	—
476	D₄×C₄₇	—	8	2	no	—
477	D₄×C₄₇	C₂×#41	1	2	yes	—
478	C₂×C₄×C₄₇	—	2	2	no	—
479	C₂×C₄×C₄₇	—	2	1	no	—
480	C₂×C₄×C₄₇	—	2	2	no	—
481	C₂×C₄×C₄₇	—	2	1	no	—
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	2	no	—
487	C₂×C₄×C₄₇	—	4	2	no	—
488	C₂×C₄×C₄₇	—	4	2	no	—
489	C₂×C₄×C₄₇	—	4	1	no	—
490	C₂×C₄×C₄₇	—	4	2	no	—
491	C₂×C₄×C₄₇	—	4	2	no	—
492	C₂×C₄×C₄₇	—	4	4	no	—
493	C₂×C₄×C₄₇	—	4	2	no	—
494	C₂×C₄×C₄₇	—	8	2	no	—
495	C₂×C₄×C₄₇	—	8	2	no	—
496	C₂×C₄×C₄₇	—	8	2	no	—
497	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
498	C₂×C₄×C₄₇	C₂²×D₄	1	2	yes	—
499	C₂×C₄×C₄₇	C₂²×D₄	1	2	yes	—
500	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
501	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
502	C₂×C₄×C₄₇	C₂²×D₄	1	2	yes	—
503	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
504	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
505	C₂×C₄×C₄₇	C₂⁵	1	1	yes	characteristic
506	C₂²⋊D₄₇	—	4	4	no	—
507	C₂²⋊D₄₇	—	4	4	no	—
508	C₂²⋊D₄₇	—	8	2	no	—
509	C₂×Dic₄₇	—	2	1	no	—
510	C₂×Dic₄₇	—	2	1	no	—
511	C₂×Dic₄₇	—	2	1	no	—
512	C₂×Dic₄₇	—	2	2	no	—
513	C₂×Dic₄₇	—	2	1	no	—
514	C₂×Dic₄₇	—	4	2	no	—
515	C₂×Dic₄₇	—	8	1	no	—
516	D₁₈₈	—	2	2	no	—
517	D₁₈₈	—	2	2	no	—
518	D₁₈₈	—	4	2	no	—
519	D₁₈₈	—	8	1	no	—
520	C₄×D₄₇	—	4	4	no	—
521	C₄×D₄₇	—	4	4	no	—
522	C₄×D₄₇	—	8	2	no	—
523	Dic₉₄	—	2	1	no	—
524	Dic₉₄	—	2	1	no	—
525	Dic₉₄	—	2	1	no	—
526	Dic₉₄	—	4	2	no	—
527	Dic₉₄	—	4	2	no	—
528	Dic₉₄	C₂×#41	1	2	yes	—
529	C₄₇⋊C₈	—	2	2	no	—
530	C₄₇⋊C₈	—	2	1	no	—
531	C₄₇⋊C₈	—	2	1	no	—
532	C₄₇⋊C₈	—	2	1	no	—
533	C₄₇⋊C₈	—	2	2	no	—
534	C₄₇⋊C₈	C₂×#41	1	2	yes	—
535	#61468	—	47	1	no	maximal, Sylow
536	C₂²×C₄₇	—	2	1	no	—
537	C₂²×C₄₇	—	2	2	no	—
538	C₂²×C₄₇	—	2	1	no	—
539	C₂²×C₄₇	—	2	2	no	—
540	C₂²×C₄₇	—	2	2	no	—
541	C₂²×C₄₇	—	2	1	no	—
542	C₂²×C₄₇	—	2	2	no	—
543	C₂²×C₄₇	—	4	1	no	—
544	C₂²×C₄₇	—	4	1	no	—
545	C₂²×C₄₇	—	4	2	no	—
546	C₂²×C₄₇	—	4	2	no	—
547	C₂²×C₄₇	—	4	2	no	—
548	C₂²×C₄₇	—	8	8	no	—
549	C₂²×C₄₇	C₂³×D₄	1	1	yes	characteristic
550	C₂×D₄₇	—	4	2	no	—
551	C₂×D₄₇	—	4	2	no	—
552	C₂×D₄₇	—	4	2	no	—
553	C₄×C₄₇	—	2	2	no	—
554	C₄×C₄₇	—	2	1	no	—
555	C₄×C₄₇	—	2	1	no	—
556	C₄×C₄₇	—	2	1	no	—
557	C₄×C₄₇	—	2	2	no	—
558	C₄×C₄₇	—	2	1	no	—
559	C₄×C₄₇	—	2	2	no	—
560	C₄×C₄₇	—	4	1	no	—
561	C₄×C₄₇	—	4	2	no	—
562	C₄×C₄₇	—	4	1	no	—
563	C₄×C₄₇	—	4	1	no	—
564	C₄×C₄₇	#575	1	2	yes	—
565	C₄×C₄₇	C₂²×#41	1	1	yes	characteristic
566	C₄×C₄₇	#585	1	1	yes	characteristic
567	Dic₄₇	—	2	2	no	—
568	Dic₄₇	—	4	1	no	—
569	Dic₄₇	—	4	1	no	—
570	Dic₄₇	—	4	1	no	—
571	Dic₄₇	—	4	2	no	—
572	#3481	D₄₇	1	1	yes	characteristic, complemented
573	#3480	—	47	1	no	—
574	#3396	—	47	1	no	—
575	#3381	—	47	1	no	—
576	#3365	—	47	1	no	—
577	#3361	—	47	1	no	—
578	#3356	—	47	1	no	—
579	#3355	—	47	2	no	—
580	#3333	—	47	1	no	—
581	#3326	—	47	2	no	—
582	#3324	—	47	1	no	—
583	#3322	—	47	2	no	—
584	#3275	—	47	2	no	—
585	#3274	—	47	1	no	—
586	#3184	—	47	1	no	—
587	#3183	—	47	2	no	—
588	#3115	—	47	1	no	—
589	#3114	—	47	2	no	—
590	#3112	—	47	1	no	—
591	#3111	—	47	2	no	—
592	#2971	—	47	1	no	—
593	C₄×#137	—	47	1	no	—
594	C₄×AGL(1,ℤ/8)	—	47	2	no	—
595	C₂×C₄₇	—	4	1	no	—
596	C₂×C₄₇	—	4	2	no	—
597	C₂×C₄₇	—	4	2	no	—
598	C₂×C₄₇	—	8	2	no	—
599	C₂×C₄₇	D₄×#41	1	1	yes	characteristic
600	C₂×C₄₇	C₂×#575	1	1	yes	characteristic
601	C₂×C₄₇	#3585	1	1	yes	characteristic
602	D₄₇	—	8	2	no	—
603	C₂×#137	—	47	1	no	—
604	C₂×AGL(1,ℤ/8)	—	47	2	no	—
605	#559	—	47	1	no	—
606	#559	—	94	1	no	—
607	#559	C₂×D₄₇	1	1	yes	characteristic
608	#557	—	47	1	no	—
609	#556	—	47	1	no	—
610	#556	—	94	1	no	—
611	#554	C₂×D₄₇	1	1	yes	characteristic
612	#554	C₂×D₄₇	1	1	yes	characteristic
613	#553	—	2	1	no	—
614	#553	—	47	2	no	—
615	#553	—	94	2	no	—
616	#553	C₂×D₄₇	1	2	yes	—
617	#551	—	2	2	no	—
618	#550	—	47	1	no	—
619	#548	—	47	2	no	—
620	#546	—	2	1	no	—
621	#546	C₂×D₄₇	1	2	yes	—
622	D₄²	C₂×D₄₇	1	1	yes	characteristic
623	#532	—	47	1	no	—
624	#532	—	94	1	no	—
625	#532	C₂×D₄₇	1	1	yes	characteristic
626	#529	—	2	1	no	—
627	#529	—	47	2	no	—
628	#529	—	94	2	no	—
629	#529	C₂×D₄₇	1	2	yes	—
630	#525	—	2	2	no	—
631	C₄×#41	—	47	2	no	—
632	C₄×#41	—	94	1	no	—
633	C₄×#41	C₂×D₄₇	1	1	yes	characteristic
634	C₄×#41	C₂×D₄₇	1	1	yes	characteristic
635	C₂×C₄×Q₈	—	47	1	no	—
636	C₂×C₄×D₄	—	2	1	no	—
637	C₂×C₄×D₄	C₂×D₄₇	1	2	yes	—
638	#499	—	47	2	no	—
639	#498	—	47	1	no	—
640	#495	—	47	2	no	—
641	#493	—	47	1	no	—
642	#488	—	47	2	no	—
643	#488	—	47	2	no	—
644	#486	—	47	1	no	—
645	#486	—	47	1	no	—
646	#485	—	47	2	no	—
647	#483	—	47	2	no	—
648	#482	—	47	2	no	—
649	#482	—	47	2	no	—
650	#480	—	47	2	no	—
651	#480	—	47	2	no	—
652	#479	—	47	2	no	—
653	#478	—	47	2	no	—
654	#478	—	47	2	no	—
655	#478	—	47	2	no	—
656	#477	—	47	1	no	—
657	#477	—	47	1	no	—
658	#475	—	47	1	no	—
659	#474	—	47	1	no	—
660	#470	—	47	2	no	—
661	#469	—	47	2	no	—
662	#469	—	47	2	no	—
663	#469	—	47	2	no	—
664	#468	—	47	2	no	—
665	#468	—	47	2	no	—
666	#464	—	47	2	no	—
667	#463	—	47	2	no	—
668	#463	—	47	2	no	—
669	#463	—	47	2	no	—
670	#460	—	47	1	no	—
671	#460	—	47	1	no	—
672	#460	—	47	1	no	—
673	#459	—	47	1	no	—
674	#452	—	47	2	no	—
675	#450	—	47	2	no	—
676	#449	—	47	2	no	—
677	#449	—	47	2	no	—
678	#448	—	47	2	no	—
679	#447	—	47	2	no	—
680	C₈×Q₈	—	47	1	no	—
681	C₈×Q₈	—	47	1	no	—
682	#442	—	47	2	no	—
683	#442	—	47	2	no	—
684	#442	—	47	2	no	—
685	#441	—	47	1	no	—
686	#441	—	47	1	no	—
687	#440	—	47	2	no	—
688	#440	—	47	1	no	—
689	#440	—	47	1	no	—
690	#440	—	47	2	no	—
691	#440	—	47	2	no	—
692	C₄×Q₁₆	—	47	1	no	—
693	C₄×Q₁₆	—	47	1	no	—
694	C₄×SD₁₆	—	47	1	no	—
695	C₄×SD₁₆	—	47	2	no	—
696	C₄×SD₁₆	—	47	2	no	—
697	C₄×SD₁₆	—	47	1	no	—
698	C₄×D₈	—	47	2	no	—
699	C₄×D₈	—	47	2	no	—
700	#436	—	47	1	no	—
701	#436	—	47	2	no	—
702	#436	—	47	1	no	—
703	#436	—	47	2	no	—
704	#432	—	47	2	no	—
705	#432	—	47	1	no	—
706	#428	—	47	1	no	—
707	#428	—	47	2	no	—
708	#419	—	47	1	no	—
709	#418	—	47	2	no	—
710	#417	—	47	1	no	—
711	#417	—	47	2	no	—
712	C₄×M₁₆	—	47	2	no	—
713	C₄×M₁₆	—	47	1	no	—
714	C₄₇	#61468	1	1	yes	characteristic, complemented, Sylow
715	C₂×#41	—	2	1	no	—
716	C₂×#41	—	47	2	no	—
717	C₂×#41	—	94	1	no	—
718	C₂×#41	C₂²⋊D₄₇	1	1	yes	characteristic
719	C₂×#41	C₂²×D₄₇	1	1	yes	characteristic
720	C₂²×Q₈	—	47	1	no	—
721	C₂²×D₄	—	2	1	no	—
722	C₂²×D₄	C₂²×D₄₇	1	2	yes	—
723	C₂³×C₄	—	2	2	no	—
724	#137	—	94	4	no	—
725	AGL(1,ℤ/8)	—	94	8	no	—
726	C₂×Q₁₆	—	47	1	no	—
727	C₂×Q₁₆	—	47	1	no	—
728	C₂×SD₁₆	—	47	1	no	—
729	C₂×SD₁₆	—	47	2	no	—
730	C₂×SD₁₆	—	47	1	no	—
731	C₂×SD₁₆	—	47	2	no	—
732	C₂×SD₁₆	—	47	2	no	—
733	C₂×D₈	—	47	2	no	—
734	C₂×D₈	—	47	2	no	—
735	C₂×D₈	—	47	2	no	—
736	C₂×M₁₆	—	47	2	no	—
737	C₂×M₁₆	—	47	1	no	—
738	C₂×M₁₆	—	47	2	no	—
739	C₂×M₁₆	—	47	1	no	—
740	C₄⋊Q₈	—	47	1	no	—
741	C₄⋊Q₈	—	94	1	no	—
742	C₄⋊Q₈	C₂²×D₄₇	1	1	yes	characteristic
743	#127	—	47	1	no	—
744	#127	—	94	1	no	—
745	#127	C₂²×D₄₇	1	1	yes	characteristic
746	#126	—	2	2	no	—
747	#126	—	2	2	no	—
748	#126	—	94	2	no	—
749	#126	—	94	2	no	—
750	#126	—	94	2	no	—
751	#125	—	2	1	no	—
752	#125	—	47	2	no	—
753	#125	—	94	2	no	—
754	#125	C₂²×D₄₇	1	2	yes	—
755	#124	—	2	1	no	—
756	#124	—	2	1	no	—
757	#124	—	47	2	no	—
758	#124	—	94	1	no	—
759	#124	—	94	1	no	—
760	#124	—	94	2	no	—
761	#124	—	94	1	no	—
762	#124	C₂²×D₄₇	1	2	yes	—
763	#123	—	2	2	no	—
764	#123	—	2	2	no	—
765	#123	—	2	2	no	—
766	#123	—	2	2	no	—
767	#123	—	94	2	no	—
768	#123	—	94	2	no	—
769	#123	—	94	2	no	—
770	C₂²⋊Q₈	—	2	1	no	—
771	C₂²⋊Q₈	—	2	2	no	—
772	C₂²⋊Q₈	—	2	2	no	—
773	C₂²⋊Q₈	—	47	2	no	—
774	C₂²⋊Q₈	—	94	2	no	—
775	C₂²⋊Q₈	C₂²×D₄₇	1	2	yes	—
776	#121	—	2	2	no	—
777	#121	—	2	1	no	—
778	#121	—	2	1	no	—
779	#121	—	2	2	no	—
780	#121	—	47	2	no	—
781	#121	—	47	2	no	—
782	#121	—	94	2	no	—
783	#121	—	94	2	no	—
784	#121	—	94	1	no	—
785	#121	—	94	2	no	—
786	#121	C₂²×D₄₇	1	2	yes	—
787	#121	C₂²×D₄₇	1	2	yes	—
788	#120	—	2	2	no	—
789	#120	—	2	2	no	—
790	C₄×Q₈	—	47	1	no	—
791	C₄×Q₈	—	47	1	no	—
792	C₄×Q₈	—	47	1	no	—
793	C₄×Q₈	—	47	1	no	—
794	C₄×Q₈	—	47	2	no	—
795	C₄×Q₈	—	94	1	no	—
796	C₄×Q₈	—	94	1	no	—
797	C₄×Q₈	—	94	1	no	—
798	C₄×Q₈	—	94	1	no	—
799	C₄×Q₈	C₂²⋊D₄₇	1	1	yes	characteristic
800	C₄×Q₈	C₂²×D₄₇	1	1	yes	characteristic
801	C₄×Q₈	C₂²×D₄₇	1	1	yes	characteristic
802	C₄×Q₈	C₂²×D₄₇	1	1	yes	characteristic
803	C₄×D₄	—	2	1	no	—
804	C₄×D₄	—	2	2	no	—
805	C₄×D₄	—	2	1	no	—
806	C₄×D₄	—	2	1	no	—
807	C₄×D₄	—	2	1	no	—
808	C₄×D₄	—	2	2	no	—
809	C₄×D₄	—	2	1	no	—
810	C₄×D₄	—	2	2	no	—
811	C₄×D₄	—	2	2	no	—
812	C₄×D₄	—	47	2	no	—
813	C₄×D₄	—	47	2	no	—
814	C₄×D₄	—	94	2	no	—
815	C₄×D₄	—	94	2	no	—
816	C₄×D₄	—	94	2	no	—
817	C₄×D₄	—	94	1	no	—
818	C₄×D₄	—	94	1	no	—
819	C₄×D₄	—	94	2	no	—
820	C₄×D₄	—	94	2	no	—
821	C₄×D₄	—	94	1	no	—
822	C₄×D₄	C₂²⋊D₄₇	1	1	yes	characteristic
823	C₄×D₄	C₂²⋊D₄₇	1	2	yes	—
824	C₄×D₄	C₂²×D₄₇	1	1	yes	characteristic
825	C₄×D₄	C₂²×D₄₇	1	2	yes	—
826	C₄×D₄	C₂²×D₄₇	1	2	yes	—
827	C₄×D₄	C₂²×D₄₇	1	2	yes	—
828	C₄×D₄	C₂²×D₄₇	1	1	yes	characteristic
829	C₄×D₄	C₂²×D₄₇	1	1	yes	characteristic
830	C₄×D₄	C₂²×D₄₇	1	2	yes	—
831	#117	—	2	1	no	—
832	#117	—	2	2	no	—
833	#117	—	47	2	no	—
834	#117	—	94	2	no	—
835	#117	—	94	2	no	—
836	#117	C₂²⋊D₄₇	1	1	yes	characteristic
837	#117	C₂²⋊D₄₇	1	2	yes	—
838	#117	C₂²×D₄₇	1	1	yes	characteristic
839	C₂×C₄⋊C₄	—	2	1	no	—
840	C₂×C₄⋊C₄	—	47	1	no	—
841	C₂×C₄⋊C₄	—	94	1	no	—
842	C₂×C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
843	C₂×C₂²⋊C₄	—	2	2	no	—
844	C₂×C₂²⋊C₄	—	2	2	no	—
845	C₂×C₄²	—	2	1	no	—
846	C₂×C₄²	—	94	1	no	—
847	C₂×C₄²	—	94	2	no	—
848	C₂×C₄²	C₂²×D₄₇	1	2	yes	—
849	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
850	#107	—	47	1	no	—
851	#107	—	47	2	no	—
852	#107	—	47	1	no	—
853	#107	—	47	2	no	—
854	#107	—	47	2	no	—
855	#106	—	47	1	no	—
856	#106	—	47	1	no	—
857	#106	—	47	2	no	—
858	#106	—	47	2	no	—
859	#106	—	47	2	no	—
860	C₄⋊C₈	—	47	1	no	—
861	C₄⋊C₈	—	47	1	no	—
862	C₄⋊C₈	—	47	2	no	—
863	C₄⋊C₈	—	47	2	no	—
864	#103	—	47	1	no	—
865	#103	—	47	1	no	—
866	#103	—	47	2	no	—
867	#103	—	47	1	no	—
868	#103	—	47	2	no	—
869	#103	—	47	1	no	—
870	#103	—	47	1	no	—
871	#103	—	47	1	no	—
872	#103	—	47	2	no	—
873	#102	—	47	1	no	—
874	#102	—	47	1	no	—
875	#102	—	47	2	no	—
876	#102	—	47	2	no	—
877	#102	—	47	2	no	—
878	#102	—	47	2	no	—
879	#102	—	47	2	no	—
880	#102	—	47	2	no	—
881	#102	—	47	2	no	—
882	#102	—	47	2	no	—
883	#102	—	47	2	no	—
884	C₂²⋊C₈	—	47	2	no	—
885	C₂²⋊C₈	—	47	2	no	—
886	C₂²⋊C₈	—	47	2	no	—
887	#97	—	47	1	no	—
888	#97	—	47	2	no	—
889	#97	—	47	1	no	—
890	C₄×C₈	—	47	2	no	—
891	C₄×C₈	—	47	2	no	—
892	C₄×C₈	—	47	1	no	—
893	C₄×C₈	—	47	1	no	—
894	C₂⁴	—	2	2	no	—
895	#41	—	2	2	no	—
896	#41	—	4	2	no	—
897	#41	—	4	1	no	—
898	#41	—	8	2	no	—
899	#41	—	94	4	no	—
900	#41	—	188	2	no	—
901	#41	—	188	4	no	—
902	C₂×Q₈	—	2	1	no	—
903	C₂×Q₈	—	47	1	no	—
904	C₂×Q₈	—	47	1	no	—
905	C₂×Q₈	—	94	2	no	—
906	C₂×Q₈	—	94	1	no	—
907	C₂×Q₈	—	94	1	no	—
908	C₂×Q₈	—	188	1	no	—
909	C₂×Q₈	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
910	C₂×Q₈	C₂³×D₄₇	1	1	yes	characteristic
911	C₂×D₄	—	2	4	no	—
912	C₂×D₄	—	2	1	no	—
913	C₂×D₄	—	2	2	no	—
914	C₂×D₄	—	2	2	no	—
915	C₂×D₄	—	2	2	no	—
916	C₂×D₄	—	2	1	no	—
917	C₂×D₄	—	2	1	no	—
918	C₂×D₄	—	4	2	no	—
919	C₂×D₄	—	4	4	no	—
920	C₂×D₄	—	47	2	no	—
921	C₂×D₄	—	94	2	no	—
922	C₂×D₄	—	94	2	no	—
923	C₂×D₄	—	94	2	no	—
924	C₂×D₄	—	94	1	no	—
925	C₂×D₄	—	94	1	no	—
926	C₂×D₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
927	C₂×D₄	C₂×C₂²⋊D₄₇	1	2	yes	—
928	C₂×D₄	C₂³×D₄₇	1	2	yes	—
929	C₂×D₄	C₂³×D₄₇	1	1	yes	characteristic
930	C₂²×C₄	—	2	2	no	—
931	C₂²×C₄	—	2	1	no	—
932	C₂²×C₄	—	2	1	no	—
933	C₂²×C₄	—	2	1	no	—
934	C₂²×C₄	—	2	2	no	—
935	C₂²×C₄	—	2	2	no	—
936	C₂²×C₄	—	2	2	no	—
937	C₂²×C₄	—	8	4	no	—
938	C₂²×C₄	—	94	1	no	—
939	C₂²×C₄	—	94	1	no	—
940	C₂²×C₄	—	94	2	no	—
941	C₂²×C₄	—	94	2	no	—
942	C₂²×C₄	—	94	2	no	—
943	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
944	C₂²×C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
945	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
946	C₂²×C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
947	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
948	C₂²×C₄	C₂³×D₄₇	1	2	yes	—
949	Q₁₆	—	94	2	no	—
950	Q₁₆	—	94	2	no	—
951	SD₁₆	—	47	4	no	—
952	SD₁₆	—	94	4	no	—
953	SD₁₆	—	94	2	no	—
954	SD₁₆	—	188	2	no	—
955	SD₁₆	—	188	2	no	—
956	D₈	—	94	4	no	—
957	D₈	—	94	4	no	—
958	D₈	—	188	2	no	—
959	M₁₆	—	94	4	no	—
960	M₁₆	—	94	2	no	—
961	M₁₆	—	188	1	no	—
962	M₁₆	—	188	2	no	—
963	C₂×C₈	—	47	1	no	—
964	C₂×C₈	—	47	1	no	—
965	C₂×C₈	—	47	1	no	—
966	C₂×C₈	—	47	2	no	—
967	C₂×C₈	—	47	2	no	—
968	C₂×C₈	—	47	1	no	—
969	C₄⋊C₄	—	2	1	no	—
970	C₄⋊C₄	—	2	2	no	—
971	C₄⋊C₄	—	2	2	no	—
972	C₄⋊C₄	—	2	1	no	—
973	C₄⋊C₄	—	2	1	no	—
974	C₄⋊C₄	—	2	2	no	—
975	C₄⋊C₄	—	2	2	no	—
976	C₄⋊C₄	—	47	2	no	—
977	C₄⋊C₄	—	47	1	no	—
978	C₄⋊C₄	—	47	1	no	—
979	C₄⋊C₄	—	94	1	no	—
980	C₄⋊C₄	—	94	1	no	—
981	C₄⋊C₄	—	94	1	no	—
982	C₄⋊C₄	—	94	1	no	—
983	C₄⋊C₄	—	94	2	no	—
984	C₄⋊C₄	—	94	2	no	—
985	C₄⋊C₄	—	94	2	no	—
986	C₄⋊C₄	—	94	2	no	—
987	C₄⋊C₄	—	94	1	no	—
988	C₄⋊C₄	—	94	1	no	—
989	C₄⋊C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
990	C₄⋊C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
991	C₄⋊C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
992	C₄⋊C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
993	C₄⋊C₄	C₂³×D₄₇	1	1	yes	characteristic
994	C₄⋊C₄	C₂³×D₄₇	1	2	yes	—
995	C₄⋊C₄	C₂³×D₄₇	1	1	yes	characteristic
996	C₂²⋊C₄	—	2	2	no	—
997	C₂²⋊C₄	—	2	1	no	—
998	C₂²⋊C₄	—	2	1	no	—
999	C₂²⋊C₄	—	2	2	no	—
1000	C₂²⋊C₄	—	2	2	no	—
1001	C₂²⋊C₄	—	2	2	no	—
1002	C₂²⋊C₄	—	2	2	no	—
1003	C₂²⋊C₄	—	2	2	no	—
1004	C₂²⋊C₄	—	2	1	no	—
1005	C₂²⋊C₄	—	2	2	no	—
1006	C₂²⋊C₄	—	2	2	no	—
1007	C₂²⋊C₄	—	94	2	no	—
1008	C₂²⋊C₄	—	94	2	no	—
1009	C₂²⋊C₄	—	94	2	no	—
1010	C₂²⋊C₄	—	94	2	no	—
1011	C₂²⋊C₄	—	94	2	no	—
1012	C₂²⋊C₄	—	94	2	no	—
1013	C₂²⋊C₄	—	94	2	no	—
1014	C₂²⋊C₄	—	94	2	no	—
1015	C₂²⋊C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
1016	C₂²⋊C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
1017	C₂²⋊C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
1018	C₄²	—	2	1	no	—
1019	C₄²	—	2	1	no	—
1020	C₄²	—	2	1	no	—
1021	C₄²	—	94	1	no	—
1022	C₄²	—	94	2	no	—
1023	C₄²	—	94	1	no	—
1024	C₄²	—	94	2	no	—
1025	C₄²	—	94	1	no	—
1026	C₄²	—	94	1	no	—
1027	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
1028	C₄²	C₂×C₂²⋊D₄₇	1	2	yes	—
1029	C₄²	C₂×C₂²⋊D₄₇	1	2	yes	—
1030	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
1031	C₄²	C₂³×D₄₇	1	2	yes	—
1032	C₄²	C₂³×D₄₇	1	1	yes	characteristic
1033	C₄²	C₂³×D₄₇	1	1	yes	characteristic
1034	C₂³	—	2	1	no	—
1035	C₂³	—	2	2	no	—
1036	C₂³	—	4	4	no	—
1037	C₂³	—	4	4	no	—
1038	C₂³	—	8	2	no	—
1039	C₂³	—	94	2	no	—
1040	C₂³	C₂²×C₂²⋊D₄₇	1	2	yes	—
1041	C₂³	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
1042	Q₈	—	2	2	no	—
1043	Q₈	—	2	1	no	—
1044	Q₈	—	2	1	no	—
1045	Q₈	—	8	1	no	—
1046	Q₈	—	47	2	no	—
1047	Q₈	—	94	1	no	—
1048	Q₈	—	94	1	no	—
1049	Q₈	—	94	1	no	—
1050	Q₈	—	188	2	no	—
1051	Q₈	—	188	2	no	—
1052	D₄	—	2	2	no	—
1053	D₄	—	2	2	no	—
1054	D₄	—	2	1	no	—
1055	D₄	—	2	2	no	—
1056	D₄	—	4	2	no	—
1057	D₄	—	4	4	no	—
1058	D₄	—	4	2	no	—
1059	D₄	—	4	4	no	—
1060	D₄	—	4	2	no	—
1061	D₄	—	8	1	no	—
1062	D₄	—	8	2	no	—
1063	D₄	—	94	2	no	—
1064	D₄	—	94	2	no	—
1065	D₄	—	376	1	no	—
1066	D₄	—	376	2	no	—
1067	D₄	—	188	4	no	—
1068	D₄	—	188	4	no	—
1069	D₄	—	188	2	no	—
1070	D₄	#41×D₄₇	1	2	yes	—
1071	C₂×C₄	—	2	2	no	—
1072	C₂×C₄	—	2	2	no	—
1073	C₂×C₄	—	2	1	no	—
1074	C₂×C₄	—	2	2	no	—
1075	C₂×C₄	—	2	1	no	—
1076	C₂×C₄	—	2	1	no	—
1077	C₂×C₄	—	2	1	no	—
1078	C₂×C₄	—	2	1	no	—
1079	C₂×C₄	—	2	2	no	—
1080	C₂×C₄	—	4	2	no	—
1081	C₂×C₄	—	4	2	no	—
1082	C₂×C₄	—	4	1	no	—
1083	C₂×C₄	—	4	2	no	—
1084	C₂×C₄	—	4	2	no	—
1085	C₂×C₄	—	4	4	no	—
1086	C₂×C₄	—	4	2	no	—
1087	C₂×C₄	—	8	2	no	—
1088	C₂×C₄	—	8	2	no	—
1089	C₂×C₄	—	8	2	no	—
1090	C₂×C₄	—	94	1	no	—
1091	C₂×C₄	—	94	1	no	—
1092	C₂×C₄	—	94	1	no	—
1093	C₂×C₄	—	94	2	no	—
1094	C₂×C₄	—	94	1	no	—
1095	C₂×C₄	—	376	2	no	—
1096	C₂×C₄	—	376	1	no	—
1097	C₂×C₄	—	188	4	no	—
1098	C₂×C₄	—	188	4	no	—
1099	C₂×C₄	—	188	2	no	—
1100	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
1101	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
1102	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
1103	C₂×C₄	C₂²×C₂²⋊D₄₇	1	2	yes	—
1104	C₂×C₄	C₂²×C₂²⋊D₄₇	1	2	yes	—
1105	C₂×C₄	C₂²×C₂²⋊D₄₇	1	2	yes	—
1106	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
1107	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
1108	C₂×C₄	C₂⁴×D₄₇	1	1	yes	characteristic
1109	C₈	—	47	2	no	—
1110	C₈	—	94	2	no	—
1111	C₈	—	94	1	no	—
1112	C₈	—	94	1	no	—
1113	C₈	—	94	1	no	—
1114	C₈	—	94	2	no	—
1115	C₂²	—	2	1	no	—
1116	C₂²	—	2	2	no	—
1117	C₂²	—	2	1	no	—
1118	C₂²	—	2	2	no	—
1119	C₂²	—	2	2	no	—
1120	C₂²	—	2	2	no	—
1121	C₂²	—	2	1	no	—
1122	C₂²	—	4	1	no	—
1123	C₂²	—	4	1	no	—
1124	C₂²	—	4	2	no	—
1125	C₂²	—	4	2	no	—
1126	C₂²	—	4	2	no	—
1127	C₂²	—	8	8	no	—
1128	C₂²	—	188	2	no	—
1129	C₂²	—	188	2	no	—
1130	C₂²	—	188	2	no	—
1131	C₂²	C₂³×C₂²⋊D₄₇	1	1	yes	characteristic
1132	C₄	—	2	1	no	—
1133	C₄	—	2	2	no	—
1134	C₄	—	2	1	no	—
1135	C₄	—	2	2	no	—
1136	C₄	—	2	1	no	—
1137	C₄	—	2	2	no	—
1138	C₄	—	2	1	no	—
1139	C₄	—	4	1	no	—
1140	C₄	—	4	1	no	—
1141	C₄	—	4	1	no	—
1142	C₄	—	4	2	no	—
1143	C₄	—	94	2	no	—
1144	C₄	—	188	2	no	—
1145	C₄	—	188	1	no	—
1146	C₄	—	188	1	no	—
1147	C₄	—	188	1	no	—
1148	C₄	#15689921	1	2	yes	—
1149	C₄	C₂×#41×D₄₇	1	1	yes	characteristic
1150	C₄	#15689959	1	1	yes	characteristic
1151	C₂	—	4	2	no	—
1152	C₂	—	4	1	no	—
1153	C₂	—	4	2	no	—
1154	C₂	—	8	2	no	—
1155	C₂	—	376	2	no	—
1156	C₂	#41×C₂²⋊D₄₇	1	1	yes	characteristic
1157	C₂	C₂×#15689921	1	1	yes	characteristic
1158	C₂	#20258168	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂³×C₂²⋊D₄₇
commutator, cosocle	C₂×C₄×C₄₇	C₂⁵
Frattini	C₂×C₄	C₂⁴×D₄₇
Fitting	C₄₇×#3481	C₂
socle	C₂²×C₄₇	C₂³×D₄
hypercenter	#3481	D₄₇
hypocenter	C₄₇	#61468
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₄×#41 ◁ #3481

Complements

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

N	H ≅ G/N	type
1. #20256981	C₂	semidirect
2. #20256396	C₂	semidirect
3. #20256263	C₂	semidirect
4. #20256080	C₂	semidirect
5. #20256048	C₂	semidirect
6. #20256003	C₂	semidirect
7. #20255988	C₂	semidirect
8. #20255720	C₂	semidirect
9. #20255635	C₂	semidirect
10. #20255619	C₂	semidirect
11. #20255589	C₂	semidirect
12. #20255015	C₂	semidirect
13. #20255004	C₂	semidirect
14. #20254122	C₂	semidirect
15. #20254111	C₂	semidirect
16. #20253539	C₂	semidirect
17. #20253526	C₂	semidirect
18. #20253506	C₂	semidirect
19. #20253491	C₂	semidirect
20. #20252408	C₂	semidirect
21. C₄×#13094054	C₂	semidirect
22. C₄×#13094050	C₂	semidirect
23. C₄₇×#3481	C₂	semidirect
26. #15689858	C₂²	semidirect
28. #15689851	C₂²	semidirect
32. #15689819	C₂²	semidirect
34. #15689782	C₂²	semidirect
35. #15689673	C₂²	semidirect
37. #15689657	C₂²	semidirect
39. C₄×#10625350	C₂²	semidirect
41. C₂×C₄×Dic₉₄	C₂²	semidirect
42. #15689522	C₂²	semidirect
43. #15689519	C₂²	semidirect
44. #15689505	C₂²	semidirect
46. #15689480	C₂²	semidirect
47. #15689477	C₂²	semidirect
48. #15689471	C₂²	semidirect
50. #15689461	C₂²	semidirect
51. #15689453	C₂²	semidirect
52. #15689447	C₂²	semidirect
54. #15689436	C₂²	semidirect
55. #15689434	C₂²	semidirect
56. #15689427	C₂²	semidirect
58. #15689423	C₂²	semidirect
59. #15689420	C₂²	semidirect
60. #15689415	C₂²	semidirect
61. #15689415	C₂²	semidirect
62. #15689408	C₂²	semidirect
64. #15689379	C₂²	semidirect
66. #15689374	C₂²	semidirect
67. #15689374	C₂²	semidirect
68. #15689371	C₂²	semidirect
70. #15689342	C₂²	semidirect
72. #15689338	C₂²	semidirect
73. #15689335	C₂²	semidirect
74. #15689323	C₂²	semidirect
78. #15689283	C₂²	semidirect
82. #15689261	C₂²	semidirect
84. Q₈×C₄₇⋊C₈	C₂²	semidirect
85. Q₈×C₄₇⋊C₈	C₂²	semidirect
87. #15689233	C₂²	semidirect
88. #15689233	C₂²	semidirect
89. #15689228	C₂²	semidirect
90. #15689228	C₂²	semidirect
93. #15689223	C₂²	semidirect
94. #15689223	C₂²	semidirect
95. #15689221	C₂²	semidirect
96. C₄×#10625337	C₂²	semidirect
97. C₄×#10625337	C₂²	semidirect
101. C₄×#10625335	C₂²	semidirect
103. C₄×#10625334	C₂²	semidirect
106. #15689201	C₂²	semidirect
107. #15689201	C₂²	semidirect
108. #15689180	C₂²	semidirect
109. #15689180	C₂²	semidirect
110. #15689166	C₂²	semidirect
111. #15689163	C₂²	semidirect
112. #15689131	C₂²	semidirect
115. #15689122	C₂²	semidirect
116. C₄×#10625329	C₂²	semidirect
117. C₄×#10625329	C₂²	semidirect
415. #10625335	#41	semidirect
572. #3481	D₄₇	semidirect
714. C₄₇	#61468	semidirect

Maximal subgroups

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

subgroup	index
#20256981	2
#20256396	2
#20256263	2
#20256080	2
#20256048	2
#20256003	2
#20255988	2
#20255720	2
#20255635	2
#20255619	2
#20255589	2
#20255015	2
#20255004	2
#20254122	2
#20254111	2
#20253539	2
#20253526	2
#20253506	2
#20253491	2
#20252408	2
C₄×#13094054	2
C₄×#13094050	2
C₄₇×#3481	2
#61468	47