Subgroups — #27109514

Order 12032.

1868 conjugacy classes of subgroups.

The subgroup lattice has 1166 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	#20256384	C₂	1	1	yes	maximal, characteristic, complemented
4	#20256080	C₂	1	1	yes	maximal, characteristic, complemented
5	#20256069	C₂	1	1	yes	maximal, characteristic, complemented
6	#20255671	C₂	1	1	yes	maximal, characteristic, complemented
7	#20255641	C₂	1	2	yes	maximal, complemented
8	#20255619	C₂	1	1	yes	maximal, characteristic, complemented
9	#20255589	C₂	1	2	yes	maximal, complemented
10	#20255050	C₂	1	1	yes	maximal, characteristic, complemented
11	#20255041	C₂	1	2	yes	maximal, complemented
12	#20255015	C₂	1	2	yes	maximal, complemented
13	#20255004	C₂	1	1	yes	maximal, characteristic, complemented
14	#20254784	C₂	1	2	yes	maximal, complemented
15	#20254750	C₂	1	1	yes	maximal, characteristic, complemented
16	#20254353	C₂	1	2	yes	maximal, complemented
17	#20254321	C₂	1	1	yes	maximal, characteristic, complemented
18	#20253464	C₂	1	1	yes	maximal, characteristic, complemented
19	#20253400	C₂	1	2	yes	maximal, complemented
20	#20252878	C₂	1	2	yes	maximal, complemented
21	#20252856	C₂	1	1	yes	maximal, characteristic, complemented
22	#20252520	C₂	1	1	yes	maximal, characteristic, complemented
23	C₄₇×#3514	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#13094055	C₂²	1	2	yes	complemented
25	C₂×#13094054	C₂²	1	2	yes	complemented
26	C₂×#13094050	C₂²	1	2	yes	—
27	#15689858	C₂²	1	1	yes	characteristic, complemented
28	#15689856	—	2	1	no	—
29	#15689851	C₂²	1	1	yes	characteristic, complemented
30	#15689845	—	2	1	no	—
31	#15689843	C₂²	1	1	yes	characteristic
32	#15689822	—	2	2	no	—
33	#15689819	C₂²	1	2	yes	complemented
34	#15689794	C₂²	1	1	yes	characteristic
35	#15689782	C₂²	1	2	yes	complemented
36	#15689673	C₂²	1	1	yes	characteristic, complemented
37	#15689669	—	2	1	no	—
38	#15689657	C₂²	1	2	yes	complemented
39	#15689651	—	2	2	no	—
40	C₄×#10625350	C₂²	1	2	yes	complemented
41	#15689591	—	2	1	no	—
42	C₂×C₄×Dic₉₄	C₂²	1	1	yes	characteristic, complemented
43	#15689505	C₂²	1	2	yes	—
44	#15689505	C₂²	1	2	yes	complemented
45	#15689499	C₂²	1	1	yes	characteristic
46	#15689497	C₂²	1	1	yes	characteristic, complemented
47	#15689477	C₂²	1	2	yes	—
48	#15689477	C₂²	1	2	yes	complemented
49	#15689473	C₂²	1	1	yes	characteristic, complemented
50	#15689469	C₂²	1	1	yes	characteristic
51	#15689461	C₂²	1	2	yes	complemented
52	#15689451	C₂²	1	1	yes	characteristic, complemented
53	#15689444	C₂²	1	2	yes	—
54	#15689434	C₂²	1	1	yes	characteristic
55	#15689430	C₂²	1	2	yes	complemented
56	#15689427	C₂²	1	1	yes	characteristic, complemented
57	#15689427	C₂²	1	1	yes	characteristic, complemented
58	#15689423	C₂²	1	2	yes	complemented
59	#15689420	C₂²	1	2	yes	complemented
60	#15689408	C₂²	1	1	yes	characteristic, complemented
61	#15689403	C₂²	1	1	yes	characteristic
62	#15689379	C₂²	1	2	yes	complemented
63	#15689374	C₂²	1	2	yes	—
64	#15689374	C₂²	1	2	yes	—
65	#15689371	C₂²	1	2	yes	complemented
66	#15689371	C₂²	1	2	yes	complemented
67	#15689367	C₂²	1	2	yes	—
68	#15689345	C₂²	1	2	yes	complemented
69	#15689342	C₂²	1	1	yes	characteristic
70	#15689342	C₂²	1	1	yes	characteristic
71	#15689342	C₂²	1	2	yes	—
72	#15689342	C₂²	1	2	yes	complemented
73	#15689342	C₂²	1	2	yes	complemented
74	#15689342	C₂²	1	2	yes	complemented
75	#15689338	C₂²	1	2	yes	complemented
76	#15689335	C₂²	1	2	yes	—
77	#15689335	C₂²	1	2	yes	—
78	#15689335	C₂²	1	2	yes	complemented
79	#15689335	C₂²	1	2	yes	complemented
80	#15689335	C₂²	1	2	yes	complemented
81	#15689330	C₂²	1	1	yes	characteristic, complemented
82	#15689330	C₂²	1	1	yes	characteristic, complemented
83	#15689323	C₂²	1	1	yes	characteristic, complemented
84	#15689320	C₂²	1	1	yes	characteristic
85	#15689320	C₂²	1	1	yes	characteristic
86	#15689318	C₂²	1	1	yes	characteristic
87	#15689283	C₂²	1	2	yes	complemented
88	#15689279	C₂²	1	2	yes	complemented
89	#15689278	C₂²	1	1	yes	characteristic, complemented
90	#15689274	C₂²	1	2	yes	—
91	#15689268	C₂²	1	2	yes	complemented
92	#15689268	C₂²	1	2	yes	complemented
93	#15689266	C₂²	1	2	yes	—
94	#15689262	C₂²	1	2	yes	complemented
95	#15689261	C₂²	1	1	yes	characteristic
96	#15689257	C₂²	1	2	yes	—
97	Q₈×C₄₇⋊C₈	C₂²	1	1	yes	characteristic, complemented
98	Q₈×C₄₇⋊C₈	C₂²	1	1	yes	characteristic, complemented
99	C₄×#10625337	C₂²	1	1	yes	characteristic, complemented
100	C₄×#10625337	C₂²	1	1	yes	characteristic, complemented
101	C₄×#10625337	C₂²	1	2	yes	complemented
102	C₄×#10625336	C₂²	1	2	yes	complemented
103	C₄×#10625335	C₂²	1	1	yes	characteristic
104	C₄×#10625335	C₂²	1	1	yes	characteristic
105	C₄×#10625335	C₂²	1	2	yes	complemented
106	C₄×#10625334	C₂²	1	2	yes	complemented
107	#15689201	C₂²	1	1	yes	characteristic
108	#15689201	C₂²	1	1	yes	characteristic
109	#15689201	C₂²	1	2	yes	complemented
110	#15689201	C₂²	1	2	yes	complemented
111	#15689176	C₂²	1	1	yes	characteristic, complemented
112	#15689176	C₂²	1	2	yes	complemented
113	#15689147	C₂²	1	1	yes	characteristic, complemented
114	#15689147	C₂²	1	2	yes	complemented
115	#15689132	C₂²	1	2	yes	complemented
116	#15689128	C₂²	1	2	yes	—
117	#15689124	C₂²	1	2	yes	complemented
118	C₄₇×#559	C₂²	1	1	yes	characteristic
119	C₄₇×#556	C₂²	1	1	yes	characteristic
120	C₄₇×#555	—	2	1	no	—
121	C₄₇×#551	—	2	2	no	—
122	D₄×Q₈×C₄₇	C₂²	1	1	yes	characteristic
123	C₄₇×#548	C₂²	1	2	yes	—
124	C₄₇×#546	—	2	1	no	—
125	C₄₇×#546	C₂²	1	2	yes	—
126	D₄²×C₄₇	C₂²	1	1	yes	characteristic
127	C₄₇×#542	—	2	1	no	—
128	C₄₇×#538	—	2	2	no	—
129	C₄₇×#532	C₂²	1	1	yes	characteristic
130	C₄₇×#529	C₂²	1	1	yes	characteristic
131	C₄₇×#529	C₂²	1	2	yes	—
132	C₂×#124×C₄₇	C₂²	1	2	yes	—
133	C₄₇×#518	—	2	1	no	—
134	C₄×#41×C₄₇	C₂²	1	1	yes	characteristic
135	C₂×#10625350	—	2	1	no	—
136	C₂×#10625350	C₂³	1	2	yes	—
137	C₂²×Dic₉₄	C₂³	1	1	yes	characteristic
138	#13094055	—	4	4	no	—
139	#13094054	—	4	4	no	—
140	#13094050	—	4	4	no	—
141	C₂×#10625337	C₂³	1	1	yes	characteristic
142	C₂×#10625337	C₂³	1	2	yes	—
143	C₂×#10625337	C₂³	1	1	yes	characteristic
144	C₂×#10625337	C₂³	1	2	yes	—
145	C₂×#10625335	C₂³	1	1	yes	characteristic
146	C₂×#10625335	C₂³	1	2	yes	—
147	C₂×#10625335	C₂³	1	1	yes	characteristic
148	C₂×#10625335	C₂³	1	2	yes	—
149	C₂×#10625336	C₂³	1	2	yes	—
150	C₂×#10625336	C₂³	1	2	yes	—
151	C₂×#10625336	C₂³	1	2	yes	—
152	C₂×#10625334	C₂³	1	2	yes	—
153	C₂×#10625334	C₂³	1	2	yes	—
154	C₂×#10625334	C₂³	1	2	yes	—
155	C₂×#10625329	C₂³	1	2	yes	—
156	C₂×#10625329	C₂³	1	2	yes	—
157	C₂×#10625329	C₂³	1	2	yes	—
158	#13094024	C₂³	1	1	yes	characteristic
159	#13094022	—	2	1	no	—
160	#13094021	C₂³	1	1	yes	characteristic
161	#13094020	—	2	1	no	—
162	#13094019	—	2	2	no	—
163	#13094018	—	2	2	no	—
164	#13094017	—	2	2	no	—
165	#13094016	C₂³	1	2	yes	—
166	#13094014	—	2	2	no	—
167	#13094013	—	2	1	no	—
168	#13094012	—	2	1	no	—
169	#13094012	C₂³	1	2	yes	—
170	#13094011	—	2	1	no	—
171	#13094010	—	2	2	no	—
172	#13094009	—	2	2	no	—
173	#13094007	—	2	2	no	—
174	#13094006	—	2	2	no	—
175	#13094003	C₂³	1	2	yes	—
176	#13094002	—	2	2	no	—
177	#13093998	—	2	1	no	—
178	#13093998	C₂³	1	2	yes	—
179	#13093998	C₂³	1	2	yes	—
180	#13093997	—	2	2	no	—
181	#13093996	—	2	2	no	—
182	#13093996	—	2	2	no	—
183	C₄×Dic₉₄	—	2	1	no	—
184	C₄×Dic₉₄	—	2	1	no	—
185	C₄×Dic₉₄	C₂³	1	2	yes	—
186	C₄×Dic₉₄	C₂³	1	1	yes	characteristic
187	C₄×Dic₉₄	C₂³	1	1	yes	characteristic
188	C₄×Dic₉₄	C₂³	1	1	yes	characteristic
189	C₄×Dic₉₄	C₂³	1	1	yes	characteristic
190	#13093989	—	2	1	no	—
191	#13093989	—	2	1	no	—
192	C₄×D₁₈₈	—	2	1	no	—
193	C₄×D₁₈₈	C₂³	1	2	yes	—
194	C₄×D₁₈₈	C₂³	1	2	yes	—
195	#13093986	—	2	1	no	—
196	#13093986	—	2	1	no	—
197	C₄×C₂²⋊D₄₇	—	2	2	no	—
198	C₄×C₂²⋊D₄₇	—	2	2	no	—
199	C₄×C₂²⋊D₄₇	—	2	2	no	—
200	(C₂²⋊D₄₇)⋊C₄	—	2	2	no	—
201	(C₂²⋊D₄₇)⋊C₄	—	2	2	no	—
202	#13093983	C₂³	1	2	yes	—
203	#13093981	—	2	2	no	—
204	#13093981	—	2	2	no	—
205	C₂×C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic
206	C₂×Dic₄₇⋊C₄	—	2	1	no	—
207	C₂×C₄×Dic₄₇	—	2	1	no	—
208	C₄²×D₄₇	—	2	2	no	—
209	#13093957	C₂³	1	2	yes	—
210	#13093957	C₂³	1	1	yes	characteristic
211	#13093957	C₂³	1	1	yes	characteristic
212	#13093955	C₂³	1	1	yes	characteristic
213	#13093955	C₂³	1	2	yes	—
214	#13093955	C₂³	1	1	yes	characteristic
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	C₄⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
220	C₄⋊(C₄₇⋊C₈)	C₂³	1	1	yes	characteristic
221	C₄⋊(C₄₇⋊C₈)	C₂³	1	1	yes	characteristic
222	#13093948	C₂³	1	2	yes	—
223	#13093948	C₂³	1	1	yes	characteristic
224	#13093948	C₂³	1	1	yes	characteristic
225	#13093948	C₂³	1	2	yes	—
226	#13093948	C₂³	1	2	yes	—
227	#13093948	C₂³	1	2	yes	—
228	#13093948	C₂³	1	2	yes	—
229	#13093947	C₂³	1	1	yes	characteristic
230	#13093947	C₂³	1	1	yes	characteristic
231	#13093947	C₂³	1	1	yes	characteristic
232	#13093947	C₂³	1	1	yes	characteristic
233	#13093945	C₂³	1	1	yes	characteristic
234	#13093945	C₂³	1	2	yes	—
235	#13093945	C₂³	1	2	yes	—
236	#13093945	C₂³	1	2	yes	—
237	#13093945	C₂³	1	2	yes	—
238	#13093945	C₂³	1	2	yes	—
239	#13093945	C₂³	1	1	yes	characteristic
240	#13093944	C₂³	1	2	yes	—
241	#13093944	C₂³	1	2	yes	—
242	C₂²⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
243	C₂²⋊(C₄₇⋊C₈)	C₂³	1	1	yes	characteristic
244	C₂²⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
245	C₂²⋊(C₄₇⋊C₈)	C₂³	1	1	yes	characteristic
246	C₄×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
247	C₄×C₄₇⋊C₈	C₂³	1	2	yes	—
248	C₄×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
249	C₄×C₄₇⋊C₈	C₂³	1	2	yes	—
250	C₂×#41×C₄₇	D₄	1	1	yes	characteristic
251	C₂×#41×C₄₇	C₂³	1	2	yes	—
252	C₂²×Q₈×C₄₇	C₂³	1	2	yes	—
253	C₂²×D₄×C₄₇	—	2	1	no	—
254	C₂²×D₄×C₄₇	C₂³	1	2	yes	—
255	C₄⋊Q₈×C₄₇	—	2	1	no	—
256	C₄⋊Q₈×C₄₇	C₂³	1	1	yes	characteristic
257	#127×C₄₇	C₂³	1	1	yes	characteristic
258	#126×C₄₇	—	2	2	no	—
259	#126×C₄₇	—	2	2	no	—
260	#126×C₄₇	—	2	1	no	—
261	#125×C₄₇	C₂³	1	1	yes	characteristic
262	#124×C₄₇	—	2	1	no	—
263	#124×C₄₇	—	2	2	no	—
264	#124×C₄₇	—	2	2	no	—
265	#124×C₄₇	—	2	2	no	—
266	#124×C₄₇	C₂³	1	2	yes	—
267	#124×C₄₇	C₂³	1	2	yes	—
268	#124×C₄₇	C₂³	1	1	yes	characteristic
269	#124×C₄₇	C₂³	1	2	yes	—
270	#123×C₄₇	—	2	1	no	—
271	#123×C₄₇	—	2	2	no	—
272	#123×C₄₇	—	2	2	no	—
273	#123×C₄₇	—	2	2	no	—
274	C₂²⋊Q₈×C₄₇	—	2	1	no	—
275	C₂²⋊Q₈×C₄₇	—	2	2	no	—
276	C₂²⋊Q₈×C₄₇	—	2	2	no	—
277	C₂²⋊Q₈×C₄₇	C₂³	1	1	yes	characteristic
278	C₂²⋊Q₈×C₄₇	C₂³	1	2	yes	—
279	#121×C₄₇	—	2	2	no	—
280	#121×C₄₇	—	2	1	no	—
281	#121×C₄₇	—	2	1	no	—
282	#121×C₄₇	—	2	1	no	—
283	#121×C₄₇	—	2	2	no	—
284	#121×C₄₇	C₂³	1	1	yes	characteristic
285	#121×C₄₇	C₂³	1	2	yes	—
286	#120×C₄₇	—	2	2	no	—
287	#120×C₄₇	—	2	2	no	—
288	C₄×Q₈×C₄₇	D₄	1	1	yes	characteristic
289	C₄×Q₈×C₄₇	C₂³	1	1	yes	characteristic
290	C₄×Q₈×C₄₇	C₂³	1	2	yes	—
291	C₄×Q₈×C₄₇	C₂³	1	1	yes	characteristic
292	C₄×D₄×C₄₇	—	2	1	no	—
293	C₄×D₄×C₄₇	—	2	2	no	—
294	C₄×D₄×C₄₇	—	2	1	no	—
295	C₄×D₄×C₄₇	—	2	1	no	—
296	C₄×D₄×C₄₇	—	2	2	no	—
297	C₄×D₄×C₄₇	—	2	1	no	—
298	C₄×D₄×C₄₇	—	2	1	no	—
299	C₄×D₄×C₄₇	D₄	1	1	yes	characteristic
300	C₄×D₄×C₄₇	D₄	1	2	yes	—
301	C₄×D₄×C₄₇	C₂³	1	1	yes	characteristic
302	C₄×D₄×C₄₇	C₂³	1	2	yes	—
303	C₄×D₄×C₄₇	C₂³	1	2	yes	—
304	C₄×D₄×C₄₇	C₂³	1	1	yes	characteristic
305	#117×C₄₇	—	2	1	no	—
306	#117×C₄₇	—	2	1	no	—
307	#117×C₄₇	—	2	2	no	—
308	#117×C₄₇	D₄	1	2	yes	—
309	#117×C₄₇	D₄	1	1	yes	characteristic
310	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
311	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
312	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
313	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
314	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
315	C₂⁴×C₄₇	—	2	2	no	—
316	#41×C₄₇	—	4	2	no	—
317	#41×C₄₇	—	4	2	no	—
318	#41×C₄₇	—	4	2	no	—
319	C₂×Q₈×C₄₇	—	2	2	no	—
320	C₂×Q₈×C₄₇	—	4	2	no	—
321	C₂×Q₈×C₄₇	—	4	2	no	—
322	C₂×Q₈×C₄₇	C₂×D₄	1	1	yes	characteristic
323	C₂×Q₈×C₄₇	C₂⁴	1	1	yes	characteristic
324	C₂×Q₈×C₄₇	C₂⁴	1	2	yes	—
325	C₂×D₄×C₄₇	—	2	2	no	—
326	C₂×D₄×C₄₇	—	2	1	no	—
327	C₂×D₄×C₄₇	—	2	2	no	—
328	C₂×D₄×C₄₇	—	2	1	no	—
329	C₂×D₄×C₄₇	—	2	1	no	—
330	C₂×D₄×C₄₇	—	2	2	no	—
331	C₂×D₄×C₄₇	—	4	2	no	—
332	C₂×D₄×C₄₇	—	4	2	no	—
333	C₂×D₄×C₄₇	—	4	4	no	—
334	C₂×D₄×C₄₇	C₂×D₄	1	1	yes	characteristic
335	C₂×D₄×C₄₇	C₂×D₄	1	2	yes	—
336	C₂×D₄×C₄₇	C₂⁴	1	1	yes	characteristic
337	C₂×D₄×C₄₇	C₂⁴	1	2	yes	—
338	C₂²×C₄×C₄₇	—	2	2	no	—
339	C₂²×C₄×C₄₇	—	2	1	no	—
340	C₂²×C₄×C₄₇	—	2	2	no	—
341	C₂²×C₄×C₄₇	—	2	2	no	—
342	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
343	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
344	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
345	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
346	C₂²×C₄×C₄₇	C₂⁴	1	2	yes	—
347	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
348	C₂×C₂²⋊D₄₇	—	2	2	no	—
349	C₂×C₂²⋊D₄₇	—	2	2	no	—
350	C₂×C₂²⋊D₄₇	—	2	2	no	—
351	C₂²×Dic₄₇	—	2	1	no	—
352	C₂²×Dic₄₇	—	2	1	no	—
353	#10625350	—	2	4	no	—
354	#10625350	—	4	2	no	—
355	#10625350	—	4	4	no	—
356	C₂×D₁₈₈	—	2	1	no	—
357	C₂×D₁₈₈	—	2	1	no	—
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×Dic₉₄	—	2	2	no	—
363	C₂×Dic₉₄	—	2	1	no	—
364	C₂×Dic₉₄	—	2	1	no	—
365	C₂×Dic₉₄	—	4	1	no	—
366	C₂×Dic₉₄	C₂⁴	1	1	yes	characteristic
367	C₂×Dic₉₄	C₂⁴	1	1	yes	characteristic
368	C₄⋊C₄×C₄₇	—	2	1	no	—
369	C₄⋊C₄×C₄₇	—	2	1	no	—
370	C₄⋊C₄×C₄₇	—	2	1	no	—
371	C₄⋊C₄×C₄₇	—	2	1	no	—
372	C₄⋊C₄×C₄₇	—	2	2	no	—
373	C₄⋊C₄×C₄₇	—	2	1	no	—
374	C₄⋊C₄×C₄₇	—	2	2	no	—
375	C₄⋊C₄×C₄₇	—	2	1	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	1	yes	characteristic
382	C₂²⋊C₄×C₄₇	—	2	2	no	—
383	C₂²⋊C₄×C₄₇	—	2	1	no	—
384	C₂²⋊C₄×C₄₇	—	2	2	no	—
385	C₂²⋊C₄×C₄₇	—	2	1	no	—
386	C₂²⋊C₄×C₄₇	—	2	1	no	—
387	C₂²⋊C₄×C₄₇	—	2	1	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	2	no	—
392	C₂²⋊C₄×C₄₇	—	2	2	no	—
393	C₂²⋊C₄×C₄₇	—	2	2	no	—
394	C₂²⋊C₄×C₄₇	—	2	1	no	—
395	C₂²⋊C₄×C₄₇	—	2	2	no	—
396	C₂²⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
397	C₂²⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
398	C₂²⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
399	C₄²×C₄₇	—	2	2	no	—
400	C₄²×C₄₇	—	2	1	no	—
401	C₄²×C₄₇	C₂×D₄	1	2	yes	—
402	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
403	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
404	C₄²×C₄₇	C₂×D₄	1	2	yes	—
405	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
406	C₄²×C₄₇	C₂⁴	1	2	yes	—
407	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
408	C₂²⋊Dic₄₇	—	2	2	no	—
409	C₂²⋊Dic₄₇	—	2	2	no	—
410	#10625337	—	2	4	no	—
411	#10625337	—	2	2	no	—
412	#10625337	—	4	1	no	—
413	#10625337	—	4	2	no	—
414	#10625336	—	4	2	no	—
415	#10625336	—	4	2	no	—
416	#10625336	—	4	2	no	—
417	#10625335	—	2	2	no	—
418	#10625335	—	2	4	no	—
419	#10625335	—	4	1	no	—
420	#10625335	—	4	2	no	—
421	#10625334	—	4	2	no	—
422	#10625334	—	4	2	no	—
423	#10625334	—	4	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	C₄⋊Dic₄₇	—	2	1	no	—
431	C₄⋊Dic₄₇	—	2	1	no	—
432	C₄⋊Dic₄₇	C₂⁴	1	1	yes	characteristic
433	C₄⋊Dic₄₇	C₂⁴	1	1	yes	characteristic
434	C₄⋊Dic₄₇	C₂⁴	1	2	yes	—
435	Dic₄₇⋊C₄	—	2	1	no	—
436	Dic₄₇⋊C₄	—	2	1	no	—
437	Dic₄₇⋊C₄	—	2	1	no	—
438	Dic₄₇⋊C₄	—	2	1	no	—
439	Dic₄₇⋊C₄	—	2	2	no	—
440	Dic₄₇⋊C₄	—	2	2	no	—
441	Dic₄₇⋊C₄	—	2	2	no	—
442	Dic₄₇⋊C₄	—	2	2	no	—
443	C₄×Dic₄₇	—	2	1	no	—
444	C₄×Dic₄₇	—	2	2	no	—
445	C₄×Dic₄₇	—	2	2	no	—
446	C₄×Dic₄₇	—	2	1	no	—
447	C₄×Dic₄₇	—	2	1	no	—
448	C₄×Dic₄₇	—	2	1	no	—
449	#10625329	—	4	2	no	—
450	#10625329	—	4	2	no	—
451	#10625329	—	4	2	no	—
452	C₂×C₄₇⋊C₈	C₂⁴	1	1	yes	characteristic
453	C₂×C₄₇⋊C₈	C₂⁴	1	1	yes	characteristic
454	C₂×C₄₇⋊C₈	C₂⁴	1	2	yes	—
455	C₂×C₄₇⋊C₈	C₂⁴	1	2	yes	—
456	C₂×C₄₇⋊C₈	C₂⁴	1	1	yes	characteristic
457	C₂×C₄₇⋊C₈	C₂⁴	1	1	yes	characteristic
458	C₂³×C₄₇	—	2	1	no	—
459	C₂³×C₄₇	—	2	2	no	—
460	C₂³×C₄₇	—	4	4	no	—
461	C₂³×C₄₇	—	8	2	no	—
462	C₂³×C₄₇	—	8	2	no	—
463	C₂³×C₄₇	C₂²×D₄	1	2	yes	—
464	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
465	C₂²×D₄₇	—	2	2	no	—
466	Q₈×C₄₇	—	2	2	no	—
467	Q₈×C₄₇	—	2	1	no	—
468	Q₈×C₄₇	—	2	2	no	—
469	Q₈×C₄₇	—	2	2	no	—
470	Q₈×C₄₇	—	2	1	no	—
471	Q₈×C₄₇	—	8	2	no	—
472	D₄×C₄₇	—	2	2	no	—
473	D₄×C₄₇	—	2	1	no	—
474	D₄×C₄₇	—	2	2	no	—
475	D₄×C₄₇	—	2	2	no	—
476	D₄×C₄₇	—	2	1	no	—
477	D₄×C₄₇	—	4	2	no	—
478	D₄×C₄₇	—	4	4	no	—
479	D₄×C₄₇	—	4	2	no	—
480	D₄×C₄₇	—	8	1	no	—
481	D₄×C₄₇	—	8	2	no	—
482	D₄×C₄₇	—	8	1	no	—
483	D₄×C₄₇	—	8	2	no	—
484	C₂×C₄×C₄₇	—	2	2	no	—
485	C₂×C₄×C₄₇	—	2	1	no	—
486	C₂×C₄×C₄₇	—	2	2	no	—
487	C₂×C₄×C₄₇	—	2	1	no	—
488	C₂×C₄×C₄₇	—	2	2	no	—
489	C₂×C₄×C₄₇	—	2	1	no	—
490	C₂×C₄×C₄₇	—	2	1	no	—
491	C₂×C₄×C₄₇	—	2	1	no	—
492	C₂×C₄×C₄₇	—	2	2	no	—
493	C₂×C₄×C₄₇	—	4	2	no	—
494	C₂×C₄×C₄₇	—	4	1	no	—
495	C₂×C₄×C₄₇	—	4	2	no	—
496	C₂×C₄×C₄₇	—	4	2	no	—
497	C₂×C₄×C₄₇	—	8	2	no	—
498	C₂×C₄×C₄₇	—	8	2	no	—
499	C₂×C₄×C₄₇	—	8	2	no	—
500	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
501	C₂×C₄×C₄₇	C₂²×D₄	1	2	yes	—
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	C₂²×D₄	1	2	yes	—
506	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
507	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
508	C₂×C₄×C₄₇	C₂⁵	1	1	yes	characteristic
509	C₂²⋊D₄₇	—	4	4	no	—
510	C₂²⋊D₄₇	—	4	4	no	—
511	C₂²⋊D₄₇	—	8	2	no	—
512	C₂×Dic₄₇	—	2	1	no	—
513	C₂×Dic₄₇	—	2	1	no	—
514	C₂×Dic₄₇	—	2	1	no	—
515	C₂×Dic₄₇	—	2	2	no	—
516	C₂×Dic₄₇	—	2	1	no	—
517	C₂×Dic₄₇	—	4	2	no	—
518	C₂×Dic₄₇	—	8	1	no	—
519	D₁₈₈	—	2	2	no	—
520	D₁₈₈	—	2	2	no	—
521	D₁₈₈	—	4	2	no	—
522	D₁₈₈	—	8	1	no	—
523	C₄×D₄₇	—	4	4	no	—
524	C₄×D₄₇	—	4	4	no	—
525	C₄×D₄₇	—	8	2	no	—
526	Dic₉₄	—	2	1	no	—
527	Dic₉₄	—	2	1	no	—
528	Dic₉₄	—	2	1	no	—
529	Dic₉₄	—	4	2	no	—
530	Dic₉₄	—	4	2	no	—
531	Dic₉₄	H(5,𝔽₂)	1	2	yes	—
532	C₄₇⋊C₈	—	2	1	no	—
533	C₄₇⋊C₈	—	2	2	no	—
534	C₄₇⋊C₈	—	2	2	no	—
535	C₄₇⋊C₈	—	2	1	no	—
536	C₄₇⋊C₈	—	2	1	no	—
537	C₄₇⋊C₈	—	2	1	no	—
538	#62006	—	47	1	no	maximal, Sylow
539	C₂²×C₄₇	—	2	1	no	—
540	C₂²×C₄₇	—	2	2	no	—
541	C₂²×C₄₇	—	2	1	no	—
542	C₂²×C₄₇	—	2	2	no	—
543	C₂²×C₄₇	—	2	1	no	—
544	C₂²×C₄₇	—	2	2	no	—
545	C₂²×C₄₇	—	4	2	no	—
546	C₂²×C₄₇	—	4	1	no	—
547	C₂²×C₄₇	—	4	2	no	—
548	C₂²×C₄₇	—	4	1	no	—
549	C₂²×C₄₇	—	4	1	no	—
550	C₂²×C₄₇	—	4	2	no	—
551	C₂²×C₄₇	—	16	4	no	—
552	C₂²×C₄₇	C₂³×D₄	1	1	yes	characteristic
553	C₂×D₄₇	—	4	2	no	—
554	C₂×D₄₇	—	4	2	no	—
555	C₂×D₄₇	—	4	2	no	—
556	C₄×C₄₇	—	2	2	no	—
557	C₄×C₄₇	—	2	1	no	—
558	C₄×C₄₇	—	2	1	no	—
559	C₄×C₄₇	—	2	1	no	—
560	C₄×C₄₇	—	2	2	no	—
561	C₄×C₄₇	—	2	1	no	—
562	C₄×C₄₇	—	2	2	no	—
563	C₄×C₄₇	—	4	1	no	—
564	C₄×C₄₇	—	4	2	no	—
565	C₄×C₄₇	—	4	1	no	—
566	C₄×C₄₇	—	4	1	no	—
567	C₄×C₄₇	#575	1	2	yes	—
568	C₄×C₄₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
569	C₄×C₄₇	#585	1	1	yes	characteristic
570	Dic₄₇	—	2	2	no	—
571	Dic₄₇	—	4	1	no	—
572	Dic₄₇	—	4	1	no	—
573	Dic₄₇	—	4	1	no	—
574	Dic₄₇	—	4	2	no	—
575	#3514	D₄₇	1	1	yes	characteristic, complemented
576	#3480	—	47	1	no	—
577	#3396	—	47	1	no	—
578	#3394	—	47	1	no	—
579	#3365	—	47	1	no	—
580	#3364	—	47	1	no	—
581	#3328	—	47	1	no	—
582	#3326	—	47	2	no	—
583	#3324	—	47	1	no	—
584	#3322	—	47	2	no	—
585	#3278	—	47	1	no	—
586	#3277	—	47	2	no	—
587	#3275	—	47	2	no	—
588	#3274	—	47	1	no	—
589	#3256	—	47	2	no	—
590	#3251	—	47	1	no	—
591	#3211	—	47	2	no	—
592	#3207	—	47	1	no	—
593	#3108	—	47	1	no	—
594	#3102	—	47	2	no	—
595	#3040	—	47	2	no	—
596	#3037	—	47	1	no	—
597	#2991	—	47	1	no	—
598	C₂×C₄₇	—	4	1	no	—
599	C₂×C₄₇	—	4	2	no	—
600	C₂×C₄₇	—	8	2	no	—
601	C₂×C₄₇	—	8	1	no	—
602	C₂×C₄₇	#3488	1	1	yes	characteristic
603	C₂×C₄₇	C₂×#575	1	1	yes	characteristic
604	C₂×C₄₇	#3584	1	1	yes	characteristic
605	D₄₇	—	8	2	no	—
606	C₂×#137	—	47	2	no	—
607	C₂×#137	—	47	2	no	—
608	C₂×AGL(1,ℤ/8)	—	47	2	no	—
609	#559	—	47	1	no	—
610	#559	—	94	1	no	—
611	#559	C₂×D₄₇	1	1	yes	characteristic
612	#557	—	47	1	no	—
613	#556	—	47	1	no	—
614	#556	—	94	1	no	—
615	#556	C₂×D₄₇	1	1	yes	characteristic
616	#555	—	2	1	no	—
617	#553	—	47	2	no	—
618	#553	—	94	2	no	—
619	#551	—	2	2	no	—
620	#550	—	47	1	no	—
621	D₄×Q₈	C₂×D₄₇	1	1	yes	characteristic
622	#548	—	47	2	no	—
623	#548	C₂×D₄₇	1	2	yes	—
624	#546	—	2	1	no	—
625	#546	C₂×D₄₇	1	2	yes	—
626	D₄²	C₂×D₄₇	1	1	yes	characteristic
627	#542	—	2	1	no	—
628	#538	—	2	2	no	—
629	#532	—	47	1	no	—
630	#532	—	94	1	no	—
631	#532	C₂×D₄₇	1	1	yes	characteristic
632	#529	—	47	2	no	—
633	#529	—	94	2	no	—
634	#529	C₂×D₄₇	1	2	yes	—
635	#529	C₂×D₄₇	1	1	yes	characteristic
636	C₂×#124	C₂×D₄₇	1	2	yes	—
637	#518	—	2	1	no	—
638	C₄×#41	—	47	2	no	—
639	C₄×#41	—	94	1	no	—
640	C₄×#41	C₂×D₄₇	1	1	yes	characteristic
641	C₂×C₄×Q₈	—	47	1	no	—
642	#495	—	47	2	no	—
643	#495	—	47	2	no	—
644	#493	—	47	1	no	—
645	#492	—	47	1	no	—
646	#488	—	47	2	no	—
647	#488	—	47	2	no	—
648	#487	—	47	1	no	—
649	#486	—	47	1	no	—
650	#485	—	47	2	no	—
651	#483	—	47	1	no	—
652	#482	—	47	2	no	—
653	#480	—	47	1	no	—
654	#479	—	47	1	no	—
655	#479	—	47	1	no	—
656	#479	—	47	2	no	—
657	#478	—	47	2	no	—
658	#478	—	47	2	no	—
659	#475	—	47	1	no	—
660	#474	—	47	1	no	—
661	#470	—	47	2	no	—
662	#469	—	47	2	no	—
663	#469	—	47	2	no	—
664	#468	—	47	2	no	—
665	#468	—	47	2	no	—
666	#468	—	47	2	no	—
667	#464	—	47	2	no	—
668	#464	—	47	1	no	—
669	#464	—	47	1	no	—
670	#464	—	47	2	no	—
671	#464	—	47	2	no	—
672	#464	—	47	2	no	—
673	#464	—	47	2	no	—
674	#463	—	47	2	no	—
675	#463	—	47	2	no	—
676	#463	—	47	2	no	—
677	#463	—	47	2	no	—
678	#463	—	47	2	no	—
679	#463	—	47	2	no	—
680	#462	—	47	1	no	—
681	#462	—	47	1	no	—
682	#460	—	47	1	no	—
683	#460	—	47	1	no	—
684	#460	—	47	1	no	—
685	#459	—	47	1	no	—
686	#452	—	47	2	no	—
687	#451	—	47	2	no	—
688	#451	—	47	1	no	—
689	#450	—	47	2	no	—
690	#449	—	47	2	no	—
691	#449	—	47	2	no	—
692	#449	—	47	2	no	—
693	#448	—	47	2	no	—
694	#448	—	47	1	no	—
695	#447	—	47	2	no	—
696	C₈×Q₈	—	47	1	no	—
697	C₈×Q₈	—	47	1	no	—
698	C₄×Q₁₆	—	47	1	no	—
699	C₄×Q₁₆	—	47	2	no	—
700	C₄×Q₁₆	—	47	1	no	—
701	C₄×SD₁₆	—	47	2	no	—
702	C₄×SD₁₆	—	47	2	no	—
703	C₄×SD₁₆	—	47	1	no	—
704	C₄×SD₁₆	—	47	1	no	—
705	C₄×D₈	—	47	2	no	—
706	#436	—	47	1	no	—
707	#436	—	47	2	no	—
708	#436	—	47	2	no	—
709	#436	—	47	1	no	—
710	#431	—	47	2	no	—
711	#431	—	47	1	no	—
712	#423	—	47	1	no	—
713	#423	—	47	2	no	—
714	#419	—	47	2	no	—
715	#418	—	47	2	no	—
716	#417	—	47	2	no	—
717	C₄₇	#62006	1	1	yes	characteristic, complemented, Sylow
718	C₂×#41	—	47	2	no	—
719	C₂×#41	—	94	1	no	—
720	C₂×#41	C₂²⋊D₄₇	1	1	yes	characteristic
721	C₂×#41	C₂²×D₄₇	1	2	yes	—
722	C₂²×Q₈	—	47	1	no	—
723	C₂²×Q₈	C₂²×D₄₇	1	2	yes	—
724	C₂²×D₄	—	2	1	no	—
725	C₂²×D₄	C₂²×D₄₇	1	2	yes	—
726	#137	—	188	4	no	—
727	#137	—	188	4	no	—
728	AGL(1,ℤ/8)	—	188	4	no	—
729	C₂×Q₁₆	—	47	1	no	—
730	C₂×Q₁₆	—	47	2	no	—
731	C₂×Q₁₆	—	47	2	no	—
732	C₂×Q₁₆	—	47	1	no	—
733	C₂×SD₁₆	—	47	1	no	—
734	C₂×SD₁₆	—	47	2	no	—
735	C₂×SD₁₆	—	47	2	no	—
736	C₂×SD₁₆	—	47	2	no	—
737	C₂×SD₁₆	—	47	2	no	—
738	C₂×SD₁₆	—	47	2	no	—
739	C₂×SD₁₆	—	47	1	no	—
740	C₂×D₈	—	47	2	no	—
741	C₂×D₈	—	47	2	no	—
742	C₂×D₈	—	47	2	no	—
743	C₂×M₁₆	—	47	2	no	—
744	C₂×M₁₆	—	47	2	no	—
745	C₂×M₁₆	—	47	2	no	—
746	C₄⋊Q₈	—	2	1	no	—
747	C₄⋊Q₈	—	47	1	no	—
748	C₄⋊Q₈	—	94	1	no	—
749	C₄⋊Q₈	C₂²×D₄₇	1	1	yes	characteristic
750	#127	—	47	1	no	—
751	#127	—	94	1	no	—
752	#127	C₂²×D₄₇	1	1	yes	characteristic
753	#126	—	2	2	no	—
754	#126	—	2	2	no	—
755	#126	—	2	1	no	—
756	#126	—	94	2	no	—
757	#126	—	94	2	no	—
758	#126	—	94	2	no	—
759	#125	—	47	2	no	—
760	#125	—	94	2	no	—
761	#125	C₂²×D₄₇	1	1	yes	characteristic
762	#124	—	2	1	no	—
763	#124	—	2	2	no	—
764	#124	—	2	2	no	—
765	#124	—	2	2	no	—
766	#124	—	47	2	no	—
767	#124	—	94	1	no	—
768	#124	—	94	1	no	—
769	#124	—	94	2	no	—
770	#124	—	94	1	no	—
771	#124	C₂²×D₄₇	1	1	yes	characteristic
772	#124	C₂²×D₄₇	1	2	yes	—
773	#124	C₂²×D₄₇	1	2	yes	—
774	#124	C₂²×D₄₇	1	2	yes	—
775	#123	—	2	1	no	—
776	#123	—	2	2	no	—
777	#123	—	2	2	no	—
778	#123	—	2	2	no	—
779	#123	—	94	2	no	—
780	#123	—	94	2	no	—
781	#123	—	94	2	no	—
782	C₂²⋊Q₈	—	2	1	no	—
783	C₂²⋊Q₈	—	2	2	no	—
784	C₂²⋊Q₈	—	2	2	no	—
785	C₂²⋊Q₈	—	47	2	no	—
786	C₂²⋊Q₈	—	94	2	no	—
787	C₂²⋊Q₈	C₂²×D₄₇	1	2	yes	—
788	C₂²⋊Q₈	C₂²×D₄₇	1	1	yes	characteristic
789	#121	—	2	2	no	—
790	#121	—	2	1	no	—
791	#121	—	2	1	no	—
792	#121	—	2	1	no	—
793	#121	—	2	2	no	—
794	#121	—	47	2	no	—
795	#121	—	47	2	no	—
796	#121	—	94	2	no	—
797	#121	—	94	2	no	—
798	#121	—	94	1	no	—
799	#121	—	94	2	no	—
800	#121	C₂²×D₄₇	1	2	yes	—
801	#121	C₂²×D₄₇	1	1	yes	characteristic
802	#120	—	2	2	no	—
803	#120	—	2	2	no	—
804	C₄×Q₈	—	47	1	no	—
805	C₄×Q₈	—	47	1	no	—
806	C₄×Q₈	—	47	1	no	—
807	C₄×Q₈	—	47	1	no	—
808	C₄×Q₈	—	47	2	no	—
809	C₄×Q₈	—	94	1	no	—
810	C₄×Q₈	—	94	1	no	—
811	C₄×Q₈	—	94	1	no	—
812	C₄×Q₈	—	94	1	no	—
813	C₄×Q₈	C₂²⋊D₄₇	1	1	yes	characteristic
814	C₄×Q₈	C₂²×D₄₇	1	2	yes	—
815	C₄×Q₈	C₂²×D₄₇	1	1	yes	characteristic
816	C₄×Q₈	C₂²×D₄₇	1	1	yes	characteristic
817	C₄×D₄	—	2	1	no	—
818	C₄×D₄	—	2	2	no	—
819	C₄×D₄	—	2	1	no	—
820	C₄×D₄	—	2	1	no	—
821	C₄×D₄	—	2	2	no	—
822	C₄×D₄	—	2	1	no	—
823	C₄×D₄	—	2	1	no	—
824	C₄×D₄	—	47	2	no	—
825	C₄×D₄	—	47	2	no	—
826	C₄×D₄	—	94	2	no	—
827	C₄×D₄	—	94	2	no	—
828	C₄×D₄	—	94	2	no	—
829	C₄×D₄	—	94	1	no	—
830	C₄×D₄	—	94	1	no	—
831	C₄×D₄	—	94	2	no	—
832	C₄×D₄	—	94	2	no	—
833	C₄×D₄	—	94	1	no	—
834	C₄×D₄	C₂²⋊D₄₇	1	1	yes	characteristic
835	C₄×D₄	C₂²⋊D₄₇	1	2	yes	—
836	C₄×D₄	C₂²×D₄₇	1	1	yes	characteristic
837	C₄×D₄	C₂²×D₄₇	1	2	yes	—
838	C₄×D₄	C₂²×D₄₇	1	1	yes	characteristic
839	C₄×D₄	C₂²×D₄₇	1	2	yes	—
840	#117	—	2	1	no	—
841	#117	—	2	1	no	—
842	#117	—	2	2	no	—
843	#117	—	47	2	no	—
844	#117	—	94	2	no	—
845	#117	—	94	2	no	—
846	#117	C₂²⋊D₄₇	1	1	yes	characteristic
847	#117	C₂²⋊D₄₇	1	2	yes	—
848	C₂×C₄⋊C₄	—	47	1	no	—
849	C₂×C₄⋊C₄	—	94	1	no	—
850	C₂×C₂²⋊C₄	—	2	2	no	—
851	C₂×C₂²⋊C₄	—	2	2	no	—
852	C₂×C₂²⋊C₄	—	2	2	no	—
853	C₂×C₄²	—	94	1	no	—
854	C₂×C₄²	—	94	2	no	—
855	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
856	C₂×C₄²	C₂²×D₄₇	1	2	yes	—
857	#107	—	47	1	no	—
858	#107	—	47	2	no	—
859	#107	—	47	1	no	—
860	#106	—	47	1	no	—
861	#106	—	47	1	no	—
862	#106	—	47	2	no	—
863	C₄⋊C₈	—	47	1	no	—
864	C₄⋊C₈	—	47	2	no	—
865	C₄⋊C₈	—	47	1	no	—
866	C₄⋊C₈	—	47	1	no	—
867	C₄⋊C₈	—	47	2	no	—
868	C₄⋊C₈	—	47	2	no	—
869	C₄⋊C₈	—	47	1	no	—
870	#103	—	47	2	no	—
871	#103	—	47	2	no	—
872	#103	—	47	1	no	—
873	#103	—	47	2	no	—
874	#103	—	47	2	no	—
875	#103	—	47	1	no	—
876	#103	—	47	2	no	—
877	#103	—	47	1	no	—
878	#103	—	47	1	no	—
879	#103	—	47	1	no	—
880	#103	—	47	1	no	—
881	#102	—	47	2	no	—
882	#102	—	47	2	no	—
883	#102	—	47	1	no	—
884	#102	—	47	2	no	—
885	#102	—	47	2	no	—
886	#102	—	47	1	no	—
887	#102	—	47	2	no	—
888	#102	—	47	2	no	—
889	#102	—	47	2	no	—
890	C₂²⋊C₈	—	47	2	no	—
891	C₂²⋊C₈	—	47	1	no	—
892	C₂²⋊C₈	—	47	2	no	—
893	C₂²⋊C₈	—	47	1	no	—
894	C₄×C₈	—	47	2	no	—
895	C₄×C₈	—	47	2	no	—
896	C₄×C₈	—	47	1	no	—
897	C₄×C₈	—	47	1	no	—
898	C₂⁴	—	2	2	no	—
899	#41	—	4	2	no	—
900	#41	—	4	2	no	—
901	#41	—	4	2	no	—
902	#41	—	94	4	no	—
903	#41	—	188	2	no	—
904	#41	—	188	4	no	—
905	C₂×Q₈	—	2	2	no	—
906	C₂×Q₈	—	4	2	no	—
907	C₂×Q₈	—	4	2	no	—
908	C₂×Q₈	—	47	1	no	—
909	C₂×Q₈	—	47	1	no	—
910	C₂×Q₈	—	94	2	no	—
911	C₂×Q₈	—	94	1	no	—
912	C₂×Q₈	—	94	1	no	—
913	C₂×Q₈	—	188	1	no	—
914	C₂×Q₈	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
915	C₂×Q₈	C₂³×D₄₇	1	1	yes	characteristic
916	C₂×Q₈	C₂³×D₄₇	1	2	yes	—
917	C₂×D₄	—	2	2	no	—
918	C₂×D₄	—	2	1	no	—
919	C₂×D₄	—	2	2	no	—
920	C₂×D₄	—	2	1	no	—
921	C₂×D₄	—	2	1	no	—
922	C₂×D₄	—	2	2	no	—
923	C₂×D₄	—	4	2	no	—
924	C₂×D₄	—	4	2	no	—
925	C₂×D₄	—	4	4	no	—
926	C₂×D₄	—	47	2	no	—
927	C₂×D₄	—	94	2	no	—
928	C₂×D₄	—	94	2	no	—
929	C₂×D₄	—	94	2	no	—
930	C₂×D₄	—	94	1	no	—
931	C₂×D₄	—	94	1	no	—
932	C₂×D₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
933	C₂×D₄	C₂×C₂²⋊D₄₇	1	2	yes	—
934	C₂×D₄	C₂³×D₄₇	1	1	yes	characteristic
935	C₂×D₄	C₂³×D₄₇	1	2	yes	—
936	C₂²×C₄	—	2	2	no	—
937	C₂²×C₄	—	2	1	no	—
938	C₂²×C₄	—	2	2	no	—
939	C₂²×C₄	—	2	2	no	—
940	C₂²×C₄	—	94	1	no	—
941	C₂²×C₄	—	94	1	no	—
942	C₂²×C₄	—	94	2	no	—
943	C₂²×C₄	—	94	2	no	—
944	C₂²×C₄	—	94	2	no	—
945	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
946	C₂²×C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
947	C₂²×C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
948	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
949	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
950	C₂²×C₄	C₂³×D₄₇	1	2	yes	—
951	Q₁₆	—	94	2	no	—
952	Q₁₆	—	94	4	no	—
953	Q₁₆	—	188	1	no	—
954	Q₁₆	—	188	2	no	—
955	SD₁₆	—	94	2	no	—
956	SD₁₆	—	94	4	no	—
957	SD₁₆	—	188	1	no	—
958	SD₁₆	—	188	2	no	—
959	SD₁₆	—	188	2	no	—
960	SD₁₆	—	188	2	no	—
961	SD₁₆	—	188	2	no	—
962	D₈	—	188	2	no	—
963	D₈	—	188	2	no	—
964	D₈	—	188	2	no	—
965	M₁₆	—	188	2	no	—
966	M₁₆	—	188	2	no	—
967	M₁₆	—	188	2	no	—
968	C₂×C₈	—	47	1	no	—
969	C₂×C₈	—	47	1	no	—
970	C₂×C₈	—	47	2	no	—
971	C₂×C₈	—	47	1	no	—
972	C₂×C₈	—	47	2	no	—
973	C₂×C₈	—	47	1	no	—
974	C₄⋊C₄	—	2	1	no	—
975	C₄⋊C₄	—	2	1	no	—
976	C₄⋊C₄	—	2	1	no	—
977	C₄⋊C₄	—	2	1	no	—
978	C₄⋊C₄	—	2	2	no	—
979	C₄⋊C₄	—	2	1	no	—
980	C₄⋊C₄	—	2	2	no	—
981	C₄⋊C₄	—	2	1	no	—
982	C₄⋊C₄	—	47	1	no	—
983	C₄⋊C₄	—	47	1	no	—
984	C₄⋊C₄	—	47	2	no	—
985	C₄⋊C₄	—	94	1	no	—
986	C₄⋊C₄	—	94	1	no	—
987	C₄⋊C₄	—	94	1	no	—
988	C₄⋊C₄	—	94	1	no	—
989	C₄⋊C₄	—	94	2	no	—
990	C₄⋊C₄	—	94	2	no	—
991	C₄⋊C₄	—	94	2	no	—
992	C₄⋊C₄	—	94	2	no	—
993	C₄⋊C₄	—	94	1	no	—
994	C₄⋊C₄	—	94	1	no	—
995	C₄⋊C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
996	C₄⋊C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
997	C₄⋊C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
998	C₄⋊C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
999	C₄⋊C₄	C₂³×D₄₇	1	1	yes	characteristic
1000	C₄⋊C₄	C₂³×D₄₇	1	1	yes	characteristic
1001	C₂²⋊C₄	—	2	2	no	—
1002	C₂²⋊C₄	—	2	1	no	—
1003	C₂²⋊C₄	—	2	2	no	—
1004	C₂²⋊C₄	—	2	1	no	—
1005	C₂²⋊C₄	—	2	1	no	—
1006	C₂²⋊C₄	—	2	1	no	—
1007	C₂²⋊C₄	—	2	2	no	—
1008	C₂²⋊C₄	—	2	2	no	—
1009	C₂²⋊C₄	—	2	2	no	—
1010	C₂²⋊C₄	—	2	2	no	—
1011	C₂²⋊C₄	—	2	2	no	—
1012	C₂²⋊C₄	—	2	2	no	—
1013	C₂²⋊C₄	—	2	1	no	—
1014	C₂²⋊C₄	—	2	2	no	—
1015	C₂²⋊C₄	—	94	2	no	—
1016	C₂²⋊C₄	—	94	2	no	—
1017	C₂²⋊C₄	—	94	2	no	—
1018	C₂²⋊C₄	—	94	2	no	—
1019	C₂²⋊C₄	—	94	2	no	—
1020	C₂²⋊C₄	—	94	2	no	—
1021	C₂²⋊C₄	—	94	2	no	—
1022	C₂²⋊C₄	—	94	2	no	—
1023	C₂²⋊C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
1024	C₂²⋊C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
1025	C₂²⋊C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
1026	C₄²	—	2	2	no	—
1027	C₄²	—	2	1	no	—
1028	C₄²	—	94	1	no	—
1029	C₄²	—	94	2	no	—
1030	C₄²	—	94	1	no	—
1031	C₄²	—	94	2	no	—
1032	C₄²	—	94	1	no	—
1033	C₄²	—	94	1	no	—
1034	C₄²	C₂×C₂²⋊D₄₇	1	2	yes	—
1035	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
1036	C₄²	C₂×C₂²⋊D₄₇	1	2	yes	—
1037	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
1038	C₄²	C₂³×D₄₇	1	2	yes	—
1039	C₄²	C₂³×D₄₇	1	1	yes	characteristic
1040	C₄²	C₂³×D₄₇	1	1	yes	characteristic
1041	C₂³	—	2	1	no	—
1042	C₂³	—	2	2	no	—
1043	C₂³	—	4	4	no	—
1044	C₂³	—	8	2	no	—
1045	C₂³	—	8	2	no	—
1046	C₂³	—	94	2	no	—
1047	C₂³	C₂²×C₂²⋊D₄₇	1	2	yes	—
1048	C₂³	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
1049	Q₈	—	2	2	no	—
1050	Q₈	—	2	1	no	—
1051	Q₈	—	2	2	no	—
1052	Q₈	—	2	2	no	—
1053	Q₈	—	2	1	no	—
1054	Q₈	—	8	2	no	—
1055	Q₈	—	47	2	no	—
1056	Q₈	—	94	1	no	—
1057	Q₈	—	94	1	no	—
1058	Q₈	—	94	1	no	—
1059	Q₈	—	188	2	no	—
1060	Q₈	—	188	2	no	—
1061	D₄	—	2	2	no	—
1062	D₄	—	2	1	no	—
1063	D₄	—	2	2	no	—
1064	D₄	—	2	2	no	—
1065	D₄	—	2	1	no	—
1066	D₄	—	4	2	no	—
1067	D₄	—	4	4	no	—
1068	D₄	—	4	2	no	—
1069	D₄	—	8	1	no	—
1070	D₄	—	8	2	no	—
1071	D₄	—	8	1	no	—
1072	D₄	—	8	2	no	—
1073	D₄	—	94	2	no	—
1074	D₄	—	94	2	no	—
1075	D₄	—	376	1	no	—
1076	D₄	—	376	2	no	—
1077	D₄	—	188	4	no	—
1078	D₄	—	188	4	no	—
1079	D₄	—	188	2	no	—
1080	C₂×C₄	—	2	2	no	—
1081	C₂×C₄	—	2	2	no	—
1082	C₂×C₄	—	2	1	no	—
1083	C₂×C₄	—	2	2	no	—
1084	C₂×C₄	—	2	1	no	—
1085	C₂×C₄	—	2	1	no	—
1086	C₂×C₄	—	2	1	no	—
1087	C₂×C₄	—	2	1	no	—
1088	C₂×C₄	—	2	2	no	—
1089	C₂×C₄	—	4	2	no	—
1090	C₂×C₄	—	4	1	no	—
1091	C₂×C₄	—	4	2	no	—
1092	C₂×C₄	—	4	2	no	—
1093	C₂×C₄	—	8	2	no	—
1094	C₂×C₄	—	8	2	no	—
1095	C₂×C₄	—	8	2	no	—
1096	C₂×C₄	—	94	1	no	—
1097	C₂×C₄	—	94	1	no	—
1098	C₂×C₄	—	94	1	no	—
1099	C₂×C₄	—	94	2	no	—
1100	C₂×C₄	—	94	1	no	—
1101	C₂×C₄	—	376	2	no	—
1102	C₂×C₄	—	376	1	no	—
1103	C₂×C₄	—	188	4	no	—
1104	C₂×C₄	—	188	4	no	—
1105	C₂×C₄	—	188	2	no	—
1106	C₂×C₄	C₂²×C₂²⋊D₄₇	1	2	yes	—
1107	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
1108	C₂×C₄	C₂²×C₂²⋊D₄₇	1	2	yes	—
1109	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
1110	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
1111	C₂×C₄	C₂²×C₂²⋊D₄₇	1	2	yes	—
1112	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
1113	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
1114	C₂×C₄	C₂⁴×D₄₇	1	1	yes	characteristic
1115	C₈	—	94	1	no	—
1116	C₈	—	94	2	no	—
1117	C₈	—	94	2	no	—
1118	C₈	—	94	1	no	—
1119	C₈	—	94	1	no	—
1120	C₈	—	94	1	no	—
1121	C₂²	—	2	2	no	—
1122	C₂²	—	2	1	no	—
1123	C₂²	—	2	1	no	—
1124	C₂²	—	2	2	no	—
1125	C₂²	—	2	1	no	—
1126	C₂²	—	2	2	no	—
1127	C₂²	—	4	2	no	—
1128	C₂²	—	4	1	no	—
1129	C₂²	—	4	1	no	—
1130	C₂²	—	4	2	no	—
1131	C₂²	—	4	2	no	—
1132	C₂²	—	4	1	no	—
1133	C₂²	—	16	4	no	—
1134	C₂²	—	188	2	no	—
1135	C₂²	—	188	2	no	—
1136	C₂²	—	188	2	no	—
1137	C₂²	C₂³×C₂²⋊D₄₇	1	1	yes	characteristic
1138	C₄	—	2	1	no	—
1139	C₄	—	2	2	no	—
1140	C₄	—	2	1	no	—
1141	C₄	—	2	2	no	—
1142	C₄	—	2	1	no	—
1143	C₄	—	2	2	no	—
1144	C₄	—	2	1	no	—
1145	C₄	—	4	2	no	—
1146	C₄	—	4	1	no	—
1147	C₄	—	4	1	no	—
1148	C₄	—	4	1	no	—
1149	C₄	—	94	2	no	—
1150	C₄	—	188	1	no	—
1151	C₄	—	188	2	no	—
1152	C₄	—	188	1	no	—
1153	C₄	—	188	1	no	—
1154	C₄	#15689921	1	2	yes	—
1155	C₄	H(5,𝔽₂)×D₄₇	1	1	yes	characteristic
1156	C₄	#15689958	1	1	yes	characteristic
1157	C₂	—	4	2	no	—
1158	C₂	—	4	1	no	—
1159	C₂	—	8	1	no	—
1160	C₂	—	8	2	no	—
1161	C₂	—	376	2	no	—
1162	C₂	#20257050	1	1	yes	characteristic
1163	C₂	C₂×#15689921	1	1	yes	characteristic
1164	C₂	#20258159	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×#3514	C₂
socle	C₂²×C₄₇	C₂³×D₄
hypercenter	#3514	D₄₇
hypocenter	C₄₇	#62006
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₄×#41 ◁ #3514

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. #20256384	C₂	semidirect
4. #20256080	C₂	semidirect
5. #20256069	C₂	semidirect
6. #20255671	C₂	semidirect
7. #20255641	C₂	semidirect
8. #20255619	C₂	semidirect
9. #20255589	C₂	semidirect
10. #20255050	C₂	semidirect
11. #20255041	C₂	semidirect
12. #20255015	C₂	semidirect
13. #20255004	C₂	semidirect
14. #20254784	C₂	semidirect
15. #20254750	C₂	semidirect
16. #20254353	C₂	semidirect
17. #20254321	C₂	semidirect
18. #20253464	C₂	semidirect
19. #20253400	C₂	semidirect
20. #20252878	C₂	semidirect
21. #20252856	C₂	semidirect
22. #20252520	C₂	semidirect
23. C₄₇×#3514	C₂	semidirect
24. C₂×#13094055	C₂²	semidirect
25. C₂×#13094054	C₂²	semidirect
27. #15689858	C₂²	semidirect
29. #15689851	C₂²	semidirect
33. #15689819	C₂²	semidirect
35. #15689782	C₂²	semidirect
36. #15689673	C₂²	semidirect
38. #15689657	C₂²	semidirect
40. C₄×#10625350	C₂²	semidirect
42. C₂×C₄×Dic₉₄	C₂²	semidirect
44. #15689505	C₂²	semidirect
46. #15689497	C₂²	semidirect
48. #15689477	C₂²	semidirect
49. #15689473	C₂²	semidirect
51. #15689461	C₂²	semidirect
52. #15689451	C₂²	semidirect
55. #15689430	C₂²	semidirect
56. #15689427	C₂²	semidirect
57. #15689427	C₂²	semidirect
58. #15689423	C₂²	semidirect
59. #15689420	C₂²	semidirect
60. #15689408	C₂²	semidirect
62. #15689379	C₂²	semidirect
65. #15689371	C₂²	semidirect
66. #15689371	C₂²	semidirect
68. #15689345	C₂²	semidirect
72. #15689342	C₂²	semidirect
73. #15689342	C₂²	semidirect
74. #15689342	C₂²	semidirect
75. #15689338	C₂²	semidirect
78. #15689335	C₂²	semidirect
79. #15689335	C₂²	semidirect
80. #15689335	C₂²	semidirect
81. #15689330	C₂²	semidirect
82. #15689330	C₂²	semidirect
83. #15689323	C₂²	semidirect
87. #15689283	C₂²	semidirect
88. #15689279	C₂²	semidirect
89. #15689278	C₂²	semidirect
91. #15689268	C₂²	semidirect
92. #15689268	C₂²	semidirect
94. #15689262	C₂²	semidirect
97. Q₈×C₄₇⋊C₈	C₂²	semidirect
98. Q₈×C₄₇⋊C₈	C₂²	semidirect
99. C₄×#10625337	C₂²	semidirect
100. C₄×#10625337	C₂²	semidirect
101. C₄×#10625337	C₂²	semidirect
102. C₄×#10625336	C₂²	semidirect
105. C₄×#10625335	C₂²	semidirect
106. C₄×#10625334	C₂²	semidirect
109. #15689201	C₂²	semidirect
110. #15689201	C₂²	semidirect
111. #15689176	C₂²	semidirect
112. #15689176	C₂²	semidirect
113. #15689147	C₂²	semidirect
114. #15689147	C₂²	semidirect
115. #15689132	C₂²	semidirect
117. #15689124	C₂²	semidirect
575. #3514	D₄₇	semidirect
717. C₄₇	#62006	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
#20256384	2
#20256080	2
#20256069	2
#20255671	2
#20255641	2
#20255619	2
#20255589	2
#20255050	2
#20255041	2
#20255015	2
#20255004	2
#20254784	2
#20254750	2
#20254353	2
#20254321	2
#20253464	2
#20253400	2
#20252878	2
#20252856	2
#20252520	2
C₄₇×#3514	2
#62006	47