Subgroups — #27086296

Order 12032.

1978 conjugacy classes of subgroups.

The subgroup lattice has 1130 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20256803	C₂	1	2	yes	maximal, complemented
2	#20254077	C₂	1	2	yes	maximal, complemented
3	#20254073	C₂	1	2	yes	maximal, complemented
4	#20254034	C₂	1	1	yes	maximal, characteristic, complemented
5	#20254027	C₂	1	1	yes	maximal, characteristic, complemented
6	#20254023	C₂	1	1	yes	maximal, characteristic, complemented
7	#20253982	C₂	1	2	yes	maximal, complemented
8	#20253978	C₂	1	2	yes	maximal, complemented
9	#20253965	C₂	1	1	yes	maximal, characteristic, complemented
10	#20253962	C₂	1	1	yes	maximal, characteristic, complemented
11	#20253960	C₂	1	1	yes	maximal, characteristic, complemented
12	#20253953	C₂	1	1	yes	maximal, characteristic, complemented
13	#20253925	C₂	1	1	yes	maximal, characteristic, complemented
14	#20253868	C₂	1	1	yes	maximal, characteristic, complemented
15	#20253743	C₂	1	2	yes	maximal, complemented
16	#20253065	C₂	1	2	yes	maximal, complemented
17	#20253053	C₂	1	1	yes	maximal, characteristic, complemented
18	#20253031	C₂	1	1	yes	maximal, characteristic, complemented
19	#20252199	C₂	1	2	yes	maximal, complemented
20	C₄×#13094043	C₂	1	1	yes	maximal, characteristic, complemented
21	C₄×D₈×D₄₇	C₂	1	1	yes	maximal, characteristic, complemented
22	#20251810	C₂	1	1	yes	maximal, characteristic, complemented
23	C₄₇×#3176	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#13094048	C₂²	1	2	yes	—
25	C₂×#13094043	C₂²	1	1	yes	characteristic
26	C₂×D₈×D₄₇	C₂²	1	1	yes	characteristic
27	C₂×#13094032	C₂²	1	1	yes	characteristic
28	C₂×#13094030	C₂²	1	1	yes	characteristic
29	#15689753	C₂²	1	2	yes	—
30	#15689744	C₂²	1	2	yes	complemented
31	#15689741	—	2	2	no	—
32	#15689738	C₂²	1	2	yes	complemented
33	#15689724	C₂²	1	2	yes	complemented
34	#15689723	—	2	2	no	—
35	#15689709	—	2	2	no	—
36	#15689705	—	2	2	no	—
37	#15689702	C₂²	1	2	yes	—
38	#15689689	C₂²	1	2	yes	—
39	#15689686	C₂²	1	2	yes	—
40	#15689671	C₂²	1	2	yes	complemented
41	#15689668	—	2	2	no	—
42	#15689668	C₂²	1	2	yes	complemented
43	#15689658	C₂²	1	2	yes	complemented
44	#15689654	C₂²	1	2	yes	complemented
45	#15689650	—	2	2	no	—
46	#15689633	—	2	2	no	—
47	#15689631	—	2	2	no	—
48	#15689591	C₂²	1	1	yes	characteristic
49	C₄×#10625352	C₂²	1	2	yes	—
50	C₄×D₄×D₄₇	C₂²	1	2	yes	—
51	#15689533	C₂²	1	2	yes	complemented
52	#15689530	C₂²	1	2	yes	complemented
53	#15689528	C₂²	1	1	yes	characteristic, complemented
54	#15689527	C₂²	1	1	yes	characteristic, complemented
55	#15689524	C₂²	1	1	yes	characteristic, complemented
56	#15689511	C₂²	1	2	yes	—
57	#15689510	C₂²	1	2	yes	—
58	#15689507	C₂²	1	1	yes	characteristic
59	#15689506	C₂²	1	1	yes	characteristic
60	#15689498	C₂²	1	1	yes	characteristic
61	#15689486	C₂²	1	2	yes	complemented
62	#15689483	C₂²	1	2	yes	complemented
63	#15689481	C₂²	1	2	yes	complemented
64	#15689480	C₂²	1	2	yes	complemented
65	#15689476	C₂²	1	2	yes	complemented
66	#15689469	C₂²	1	2	yes	complemented
67	#15689468	C₂²	1	2	yes	complemented
68	#15689375	C₂²	1	2	yes	—
69	#15689375	C₂²	1	2	yes	complemented
70	#15689374	C₂²	1	2	yes	—
71	#15689369	C₂²	1	2	yes	complemented
72	#15689368	C₂²	1	2	yes	complemented
73	#15689368	C₂²	1	2	yes	complemented
74	#15689367	C₂²	1	2	yes	complemented
75	#15689365	C₂²	1	1	yes	characteristic, complemented
76	#15689364	C₂²	1	1	yes	characteristic, complemented
77	#15689360	C₂²	1	1	yes	characteristic
78	#15689359	C₂²	1	1	yes	characteristic
79	#15689357	C₂²	1	2	yes	complemented
80	#15689356	C₂²	1	1	yes	characteristic
81	#15689356	C₂²	1	1	yes	characteristic, complemented
82	#15689356	C₂²	1	2	yes	complemented
83	#15689353	C₂²	1	2	yes	complemented
84	#15689350	C₂²	1	2	yes	complemented
85	#15689233	C₂²	1	2	yes	complemented
86	#15689225	C₂²	1	2	yes	complemented
87	#15689223	C₂²	1	2	yes	complemented
88	C₄×Dic₁₈₈	C₂²	1	1	yes	characteristic, complemented
89	#15689217	C₂²	1	1	yes	characteristic, complemented
90	#15689214	C₂²	1	2	yes	complemented
91	#15689214	C₂²	1	2	yes	complemented
92	#15689210	C₂²	1	2	yes	complemented
93	C₄×#10625335	C₂²	1	2	yes	complemented
94	C₄×D₃₇₆	C₂²	1	1	yes	characteristic
95	D₈×Dic₄₇	C₂²	1	1	yes	characteristic
96	D₈×Dic₄₇	C₂²	1	1	yes	characteristic, complemented
97	D₈×Dic₄₇	C₂²	1	2	yes	complemented
98	#15689205	C₂²	1	1	yes	characteristic
99	C₄×#10625334	C₂²	1	2	yes	—
100	#15689203	C₂²	1	2	yes	—
101	#15689203	C₂²	1	2	yes	complemented
102	#15689162	C₂²	1	2	yes	—
103	#15689160	C₂²	1	1	yes	characteristic
104	#107×D₄₇	C₂²	1	1	yes	characteristic
105	#15689126	C₂²	1	2	yes	—
106	#15689121	C₂²	1	2	yes	—
107	#15689116	C₂²	1	2	yes	—
108	#102×D₄₇	C₂²	1	2	yes	—
109	#15689080	C₂²	1	1	yes	characteristic
110	#15689080	C₂²	1	1	yes	characteristic, complemented
111	#15689079	C₂²	1	1	yes	characteristic, complemented
112	#15689077	C₂²	1	1	yes	characteristic
113	#15689077	C₂²	1	1	yes	characteristic, complemented
114	#15689075	C₂²	1	1	yes	characteristic
115	#15689075	C₂²	1	1	yes	characteristic, complemented
116	M₁₆×Dic₄₇	C₂²	1	1	yes	characteristic, complemented
117	C₂×C₈×Dic₄₇	C₂²	1	1	yes	characteristic, complemented
118	C₄×C₈×D₄₇	C₂²	1	1	yes	characteristic
119	C₄×C₈×D₄₇	C₂²	1	1	yes	characteristic, complemented
120	C₄₇×#540	C₂²	1	2	yes	complemented
121	C₄₇×#499	C₂²	1	1	yes	characteristic, complemented
122	C₄₇×#493	C₂²	1	1	yes	characteristic
123	C₄₇×#490	C₂²	1	2	yes	complemented
124	C₄₇×#469	C₂²	1	2	yes	complemented
125	C₄₇×#466	C₂²	1	1	yes	characteristic
126	C₄₇×#466	C₂²	1	1	yes	characteristic, complemented
127	C₄₇×#442	C₂²	1	2	yes	complemented
128	C₄×D₈×C₄₇	C₂²	1	1	yes	characteristic
129	C₄×D₈×C₄₇	C₂²	1	1	yes	characteristic, complemented
130	C₄₇×#405	C₂²	1	1	yes	characteristic, complemented
131	C₂×#10625350	C₂³	1	1	yes	characteristic
132	C₂×#10625352	—	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	#13094048	—	2	8	no	—
138	#13094043	—	2	4	no	—
139	C₂×Dic₁₈₈	C₂³	1	1	yes	characteristic
140	C₂×#10625325	C₂³	1	2	yes	—
141	C₂×#10625335	C₂³	1	2	yes	—
142	C₂×#10625335	C₂³	1	2	yes	—
143	C₂×D₃₇₆	C₂³	1	1	yes	characteristic
144	C₂×#10625334	C₂³	1	2	yes	—
145	C₂×#10625334	C₂³	1	2	yes	—
146	D₈×D₄₇	—	2	4	no	—
147	#13094032	—	2	4	no	—
148	#13094030	—	2	4	no	—
149	C₂×#10625329	C₂³	1	1	yes	characteristic
150	C₂×#10625324	C₂³	1	1	yes	characteristic
151	C₂×#10625324	C₂³	1	1	yes	characteristic
152	C₂×#10625324	C₂³	1	1	yes	characteristic
153	C₂×#10625324	C₂³	1	1	yes	characteristic
154	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
155	C₂×C₈×D₄₇	C₂³	1	1	yes	characteristic
156	C₂×C₈×D₄₇	C₂³	1	1	yes	characteristic
157	C₂×C₈×D₄₇	C₂³	1	1	yes	characteristic
158	C₂×C₈×D₄₇	C₂³	1	1	yes	characteristic
159	#13094024	C₂³	1	2	yes	—
160	#13094023	—	2	2	no	—
161	#13094023	C₂³	1	2	yes	—
162	#13094020	—	2	2	no	—
163	#13094020	C₂³	1	2	yes	—
164	#13094019	—	2	2	no	—
165	#13094019	—	2	2	no	—
166	#13094017	—	2	2	no	—
167	#13094017	—	2	2	no	—
168	#13094015	C₂³	1	2	yes	—
169	#13094014	—	2	2	no	—
170	#13094012	C₂³	1	2	yes	—
171	#13094011	—	2	2	no	—
172	#13094011	C₂³	1	2	yes	—
173	#13094010	—	2	2	no	—
174	#13094010	—	2	2	no	—
175	#13094010	—	2	2	no	—
176	#13094010	—	2	2	no	—
177	#13094009	—	2	2	no	—
178	#13094007	—	2	2	no	—
179	#13094007	—	2	2	no	—
180	#13094006	—	2	2	no	—
181	#13094006	—	2	2	no	—
182	#13094005	—	2	2	no	—
183	#13094004	—	2	2	no	—
184	#13094004	C₂³	1	2	yes	—
185	#13094003	—	2	2	no	—
186	#13094003	C₂³	1	2	yes	—
187	#13094002	—	2	2	no	—
188	#13094002	—	2	2	no	—
189	#13094001	—	2	2	no	—
190	#13093999	C₂³	1	2	yes	—
191	#13093998	—	2	2	no	—
192	#13093998	C₂³	1	2	yes	—
193	#13093997	—	2	2	no	—
194	#13093997	—	2	2	no	—
195	#13093996	—	2	2	no	—
196	#13093996	—	2	2	no	—
197	#13093996	—	2	2	no	—
198	#13093996	—	2	2	no	—
199	#13093995	—	2	2	no	—
200	#13093995	—	2	2	no	—
201	#13093995	C₂³	1	2	yes	—
202	#13093995	C₂³	1	2	yes	—
203	#13093994	—	2	2	no	—
204	#13093992	—	2	2	no	—
205	#13093992	—	2	2	no	—
206	#13093992	—	2	2	no	—
207	C₄×Dic₉₄	C₂³	1	2	yes	—
208	#13093989	D₄	1	1	yes	characteristic
209	#13093989	D₄	1	1	yes	characteristic
210	#13093989	C₂³	1	2	yes	—
211	C₄×D₁₈₈	C₂³	1	2	yes	—
212	D₄×Dic₄₇	—	2	2	no	—
213	D₄×Dic₄₇	—	2	2	no	—
214	D₄×Dic₄₇	C₂³	1	2	yes	—
215	D₄×Dic₄₇	C₂³	1	2	yes	—
216	#13093986	—	2	2	no	—
217	#13093986	D₄	1	1	yes	characteristic
218	#13093986	D₄	1	1	yes	characteristic
219	#13093986	C₂³	1	2	yes	—
220	C₄×C₂²⋊D₄₇	—	2	2	no	—
221	C₄×C₂²⋊D₄₇	—	2	2	no	—
222	(C₂²⋊D₄₇)⋊C₄	—	2	2	no	—
223	(C₂²⋊D₄₇)⋊C₄	—	2	2	no	—
224	(C₂²⋊D₄₇)⋊C₄	—	2	2	no	—
225	(C₂²⋊D₄₇)⋊C₄	D₄	1	1	yes	characteristic
226	(C₂²⋊D₄₇)⋊C₄	D₄	1	1	yes	characteristic
227	(C₂²⋊D₄₇)⋊C₄	D₄	1	1	yes	characteristic
228	(C₂²⋊D₄₇)⋊C₄	D₄	1	1	yes	characteristic
229	#13093982	—	2	2	no	—
230	#13093982	C₂³	1	2	yes	—
231	#13093981	C₂³	1	1	yes	characteristic
232	#13093981	C₂³	1	1	yes	characteristic
233	#13093980	—	2	2	no	—
234	#13093980	—	2	2	no	—
235	C₄⋊C₄×D₄₇	C₂³	1	2	yes	—
236	C₂²⋊C₄×D₄₇	—	2	2	no	—
237	C₂×C₄×Dic₄₇	—	2	2	no	—
238	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
239	C₄²×D₄₇	C₂³	1	1	yes	characteristic
240	C₄²×D₄₇	C₂³	1	1	yes	characteristic
241	#13093958	C₂³	1	1	yes	characteristic
242	#13093958	C₂³	1	2	yes	—
243	#13093958	C₂³	1	1	yes	characteristic
244	#13093957	C₂³	1	2	yes	—
245	#13093957	C₂³	1	2	yes	—
246	#13093955	C₂³	1	2	yes	—
247	#13093955	C₂³	1	2	yes	—
248	#13093949	C₂³	1	2	yes	—
249	#13093949	C₂³	1	2	yes	—
250	#13093947	C₂³	1	2	yes	—
251	#13093947	C₂³	1	2	yes	—
252	#13093946	C₂³	1	2	yes	—
253	#13093946	C₂³	1	2	yes	—
254	#13093945	C₂³	1	2	yes	—
255	#13093945	C₂³	1	2	yes	—
256	#13093945	C₂³	1	2	yes	—
257	#13093945	C₂³	1	2	yes	—
258	#13093944	C₂³	1	2	yes	—
259	#13093944	C₂³	1	2	yes	—
260	#13093935	C₂³	1	1	yes	characteristic
261	#13093935	C₂³	1	1	yes	characteristic
262	#13093934	C₂³	1	1	yes	characteristic
263	#13093934	C₂³	1	1	yes	characteristic
264	C₄×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
265	C₄×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
266	C₈×Dic₄₇	C₂³	1	1	yes	characteristic
267	C₈×Dic₄₇	C₂³	1	1	yes	characteristic
268	C₈×Dic₄₇	C₂³	1	1	yes	characteristic
269	C₈×Dic₄₇	C₂³	1	1	yes	characteristic
270	C₈×Dic₄₇	C₂³	1	1	yes	characteristic
271	C₈×Dic₄₇	C₂³	1	1	yes	characteristic
272	C₂×D₈×C₄₇	C₂³	1	1	yes	characteristic
273	C₂×D₈×C₄₇	C₂³	1	1	yes	characteristic
274	C₂×D₈×C₄₇	C₂³	1	2	yes	—
275	C₂×M₁₆×C₄₇	C₂³	1	1	yes	characteristic
276	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
277	#127×C₄₇	C₂³	1	2	yes	—
278	#125×C₄₇	C₂³	1	2	yes	—
279	#123×C₄₇	—	2	2	no	—
280	#123×C₄₇	—	2	2	no	—
281	#121×C₄₇	—	2	2	no	—
282	#121×C₄₇	—	2	2	no	—
283	#121×C₄₇	C₂³	1	2	yes	—
284	#121×C₄₇	C₂³	1	2	yes	—
285	C₄×D₄×C₄₇	C₂³	1	2	yes	—
286	C₄×D₄×C₄₇	C₂³	1	2	yes	—
287	#117×C₄₇	C₂³	1	1	yes	characteristic
288	#107×C₄₇	C₂³	1	1	yes	characteristic
289	#107×C₄₇	C₂³	1	1	yes	characteristic
290	#106×C₄₇	C₂³	1	2	yes	—
291	#102×C₄₇	C₂³	1	2	yes	—
292	#102×C₄₇	C₂³	1	2	yes	—
293	#102×C₄₇	C₂³	1	2	yes	—
294	#102×C₄₇	C₂³	1	2	yes	—
295	#97×C₄₇	C₂³	1	1	yes	characteristic
296	#97×C₄₇	C₂³	1	1	yes	characteristic
297	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
298	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
299	C₂³×D₄₇	—	2	2	no	—
300	C₂×D₄×C₄₇	—	2	2	no	—
301	C₂×D₄×C₄₇	—	2	2	no	—
302	C₂×D₄×C₄₇	—	2	2	no	—
303	C₂×D₄×C₄₇	—	2	2	no	—
304	C₂×D₄×C₄₇	C₂⁴	1	2	yes	—
305	C₂×D₄×C₄₇	C₂⁴	1	2	yes	—
306	C₂²×C₄×C₄₇	—	2	2	no	—
307	C₂²×C₄×C₄₇	—	2	2	no	—
308	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
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	C₂×D₄	1	1	yes	characteristic
317	C₂×C₂²⋊D₄₇	C₂×D₄	1	1	yes	characteristic
318	C₂²×Dic₄₇	—	2	2	no	—
319	C₂²×Dic₄₇	—	2	2	no	—
320	C₂²×Dic₄₇	—	2	2	no	—
321	C₂²×Dic₄₇	C₂×D₄	1	1	yes	characteristic
322	C₂²×Dic₄₇	C₂×D₄	1	1	yes	characteristic
323	#10625352	—	2	4	no	—
324	#10625352	—	2	4	no	—
325	#10625352	—	8	4	no	—
326	#10625352	—	8	4	no	—
327	D₄×D₄₇	—	2	4	no	—
328	D₄×D₄₇	—	2	4	no	—
329	#10625350	—	2	2	no	—
330	#10625350	—	2	2	no	—
331	C₂×D₁₈₈	—	2	2	no	—
332	C₂×D₁₈₈	C₂×D₄	1	1	yes	characteristic
333	C₂×D₁₈₈	C₂⁴	1	2	yes	—
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	—	8	4	no	—
338	C₂×C₄×D₄₇	C₂×D₄	1	1	yes	characteristic
339	C₂×C₄×D₄₇	C₂×D₄	1	1	yes	characteristic
340	C₂×C₄×D₄₇	C₂×D₄	1	1	yes	characteristic
341	C₂×C₄×D₄₇	C₂×D₄	1	1	yes	characteristic
342	C₂×C₄×D₄₇	C₂⁴	1	1	yes	characteristic
343	C₂×C₄×D₄₇	C₂⁴	1	1	yes	characteristic
344	C₂×Dic₉₄	—	2	2	no	—
345	C₂×Dic₉₄	—	2	2	no	—
346	C₂×Dic₉₄	C₂×D₄	1	1	yes	characteristic
347	C₂×Dic₉₄	C₂⁴	1	2	yes	—
348	D₈×C₄₇	—	2	2	no	—
349	D₈×C₄₇	—	2	2	no	—
350	D₈×C₄₇	—	2	4	no	—
351	M₁₆×C₄₇	—	2	2	no	—
352	C₂×C₈×C₄₇	—	2	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	—	2	2	no	—
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	C₄⋊C₄×C₄₇	C₂⁴	1	2	yes	—
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	C₂×D₄	1	1	yes	characteristic
368	C₂²⋊C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
369	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
370	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
371	C₂²⋊Dic₄₇	—	2	2	no	—
372	C₂²⋊Dic₄₇	—	2	2	no	—
373	C₂²⋊Dic₄₇	—	2	2	no	—
374	C₂²⋊Dic₄₇	—	2	2	no	—
375	C₂²⋊Dic₄₇	—	2	2	no	—
376	C₂²⋊Dic₄₇	—	2	2	no	—
377	C₂²⋊Dic₄₇	—	2	2	no	—
378	#10625335	—	2	4	no	—
379	#10625335	—	2	4	no	—
380	#10625334	—	2	4	no	—
381	#10625334	—	2	4	no	—
382	(C₂×D₄₇)⋊C₄	—	2	2	no	—
383	(C₂×D₄₇)⋊C₄	—	2	2	no	—
384	(C₂×D₄₇)⋊C₄	—	2	2	no	—
385	(C₂×D₄₇)⋊C₄	—	2	2	no	—
386	(C₂×D₄₇)⋊C₄	—	2	2	no	—
387	(C₂×D₄₇)⋊C₄	—	2	2	no	—
388	(C₂×D₄₇)⋊C₄	—	2	2	no	—
389	(C₂×D₄₇)⋊C₄	—	2	2	no	—
390	(C₂×D₄₇)⋊C₄	C₂×D₄	1	1	yes	characteristic
391	(C₂×D₄₇)⋊C₄	C₂×D₄	1	1	yes	characteristic
392	(C₂×D₄₇)⋊C₄	C₂×D₄	1	1	yes	characteristic
393	(C₂×D₄₇)⋊C₄	C₂×D₄	1	1	yes	characteristic
394	C₄⋊Dic₄₇	—	2	2	no	—
395	C₄⋊Dic₄₇	—	2	2	no	—
396	C₄⋊Dic₄₇	—	2	2	no	—
397	C₄⋊Dic₄₇	C₂⁴	1	2	yes	—
398	C₄⋊Dic₄₇	C₂⁴	1	2	yes	—
399	Dic₄₇⋊C₄	—	2	2	no	—
400	Dic₄₇⋊C₄	—	2	2	no	—
401	Dic₄₇⋊C₄	—	2	2	no	—
402	Dic₄₇⋊C₄	—	2	2	no	—
403	Dic₄₇⋊C₄	—	2	2	no	—
404	Dic₄₇⋊C₄	—	2	2	no	—
405	Dic₄₇⋊C₄	C₂×D₄	1	1	yes	characteristic
406	Dic₄₇⋊C₄	C₂×D₄	1	1	yes	characteristic
407	Dic₄₇⋊C₄	C₂×D₄	1	1	yes	characteristic
408	Dic₄₇⋊C₄	C₂×D₄	1	1	yes	characteristic
409	C₄×Dic₄₇	—	2	2	no	—
410	C₄×Dic₄₇	—	2	2	no	—
411	C₄×Dic₄₇	—	2	2	no	—
412	C₄×Dic₄₇	C₂×D₄	1	1	yes	characteristic
413	C₄×Dic₄₇	C₂×D₄	1	1	yes	characteristic
414	C₄×Dic₄₇	C₂×D₄	1	1	yes	characteristic
415	C₄×Dic₄₇	C₂×D₄	1	1	yes	characteristic
416	C₄×Dic₄₇	C₂×D₄	1	1	yes	characteristic
417	C₄×Dic₄₇	C₂×D₄	1	1	yes	characteristic
418	C₄×Dic₄₇	C₂⁴	1	1	yes	characteristic
419	C₄×Dic₄₇	C₂⁴	1	1	yes	characteristic
420	#10625329	—	2	2	no	—
421	C₂×C₄₇⋊C₈	—	2	2	no	—
422	C₂×C₄₇⋊C₈	C₂⁴	1	1	yes	characteristic
423	C₂×C₄₇⋊C₈	C₂⁴	1	1	yes	characteristic
424	C₂×C₄₇⋊C₈	C₂⁴	1	1	yes	characteristic
425	C₂×C₄₇⋊C₈	C₂⁴	1	1	yes	characteristic
426	Dic₁₈₈	—	2	2	no	—
427	D₃₇₆	—	2	2	no	—
428	#10625325	—	2	4	no	—
429	#10625324	—	2	2	no	—
430	#10625324	—	2	2	no	—
431	#10625324	—	2	2	no	—
432	#10625324	#41	1	4	yes	complemented
433	C₈×D₄₇	—	2	2	no	—
434	C₈×D₄₇	—	2	2	no	—
435	C₈×D₄₇	—	2	2	no	—
436	C₈×D₄₇	#41	1	4	yes	complemented
437	C₂³×C₄₇	—	2	2	no	—
438	C₂³×C₄₇	—	2	2	no	—
439	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
440	C₂²×D₄₇	—	2	2	no	—
441	C₂²×D₄₇	—	4	4	no	—
442	C₂²×D₄₇	—	8	2	no	—
443	C₂²×D₄₇	—	8	2	no	—
444	C₂²×D₄₇	C₂²×D₄	1	1	yes	characteristic
445	C₂²×D₄₇	C₂²×D₄	1	1	yes	characteristic
446	D₄×C₄₇	—	2	2	no	—
447	D₄×C₄₇	—	2	2	no	—
448	D₄×C₄₇	—	2	2	no	—
449	D₄×C₄₇	—	2	2	no	—
450	D₄×C₄₇	—	8	2	no	—
451	D₄×C₄₇	—	8	2	no	—
452	D₄×C₄₇	—	8	2	no	—
453	D₄×C₄₇	—	8	2	no	—
454	C₂×C₄×C₄₇	—	2	1	no	—
455	C₂×C₄×C₄₇	—	2	1	no	—
456	C₂×C₄×C₄₇	—	2	2	no	—
457	C₂×C₄×C₄₇	—	2	2	no	—
458	C₂×C₄×C₄₇	—	8	2	no	—
459	C₂×C₄×C₄₇	—	8	2	no	—
460	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
461	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
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	C₂⁵	1	1	yes	characteristic
466	C₂²⋊D₄₇	—	2	2	no	—
467	C₂²⋊D₄₇	—	2	2	no	—
468	C₂²⋊D₄₇	—	4	4	no	—
469	C₂²⋊D₄₇	—	4	4	no	—
470	C₂²⋊D₄₇	—	8	2	no	—
471	C₂²⋊D₄₇	—	8	2	no	—
472	C₂²⋊D₄₇	—	8	2	no	—
473	C₂²⋊D₄₇	—	8	2	no	—
474	C₂²⋊D₄₇	—	8	2	no	—
475	C₂×Dic₄₇	—	2	2	no	—
476	C₂×Dic₄₇	—	2	2	no	—
477	C₂×Dic₄₇	—	2	2	no	—
478	C₂×Dic₄₇	—	2	2	no	—
479	C₂×Dic₄₇	—	4	1	no	—
480	C₂×Dic₄₇	—	4	4	no	—
481	C₂×Dic₄₇	—	4	4	no	—
482	C₂×Dic₄₇	—	4	4	no	—
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	—	8	2	no	—
493	C₄×D₄₇	—	2	1	no	—
494	C₄×D₄₇	—	2	1	no	—
495	C₄×D₄₇	—	2	2	no	—
496	C₄×D₄₇	—	2	2	no	—
497	C₄×D₄₇	—	4	1	no	—
498	C₄×D₄₇	—	4	1	no	—
499	C₄×D₄₇	—	4	4	no	—
500	C₄×D₄₇	—	8	2	no	—
501	C₄×D₄₇	—	8	2	no	—
502	C₄×D₄₇	C₂×#41	1	2	yes	—
503	C₄×D₄₇	C₂×#41	1	2	yes	—
504	Dic₉₄	—	2	2	no	—
505	Dic₉₄	—	2	2	no	—
506	Dic₉₄	—	2	2	no	—
507	Dic₉₄	—	8	2	no	—
508	Dic₉₄	—	8	2	no	—
509	C₈×C₄₇	—	2	1	no	—
510	C₈×C₄₇	—	2	1	no	—
511	C₈×C₄₇	C₂×#41	1	2	yes	—
512	C₈×C₄₇	C₂×#41	1	2	yes	—
513	C₄₇⋊C₈	—	2	1	no	—
514	C₄₇⋊C₈	—	2	1	no	—
515	C₄₇⋊C₈	C₂×#41	1	2	yes	—
516	C₄₇⋊C₈	C₂×#41	1	2	yes	—
517	#60695	—	47	1	no	maximal, Sylow
518	C₂²×C₄₇	—	2	1	no	—
519	C₂²×C₄₇	—	2	1	no	—
520	C₂²×C₄₇	—	2	1	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	—	4	2	no	—
527	C₂²×C₄₇	C₂³×D₄	1	1	yes	characteristic
528	C₂×D₄₇	—	2	1	no	—
529	C₂×D₄₇	—	2	1	no	—
530	C₂×D₄₇	—	2	1	no	—
531	C₂×D₄₇	—	2	1	no	—
532	C₂×D₄₇	—	2	1	no	—
533	C₂×D₄₇	—	4	2	no	—
534	C₂×D₄₇	—	4	2	no	—
535	C₂×D₄₇	—	4	2	no	—
536	C₂×D₄₇	—	8	8	no	—
537	C₂×D₄₇	#532	1	2	yes	—
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	C₂²×#41	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	—	4	2	no	—
552	Dic₄₇	—	4	2	no	—
553	Dic₄₇	—	4	2	no	—
554	Dic₄₇	#532	1	2	yes	—
555	Dic₄₇	#576	1	2	yes	—
556	#3460	—	47	2	no	—
557	#3179	—	47	2	no	—
558	#3179	—	47	2	no	—
559	#3176	—	47	1	no	—
560	#3176	D₄₇	1	1	yes	characteristic, complemented
561	#3175	—	47	1	no	—
562	#3175	—	47	1	no	—
563	#3171	—	47	2	no	—
564	#3171	—	47	2	no	—
565	#3169	—	47	1	no	—
566	#3169	—	47	1	no	—
567	#3168	—	47	1	no	—
568	#3168	—	47	1	no	—
569	#3164	—	47	1	no	—
570	#3155	—	47	1	no	—
571	#3136	—	47	2	no	—
572	#3062	—	47	2	no	—
573	#3061	—	47	1	no	—
574	#3058	—	47	1	no	—
575	C₄×AGL(1,ℤ/8)	—	47	2	no	—
576	C₄×#135	—	47	1	no	—
577	C₂×C₄×D₈	—	47	1	no	—
578	C₄×#131	—	47	1	no	—
579	C₂×C₄₇	—	4	1	no	—
580	C₂×C₄₇	—	8	2	no	—
581	C₂×C₄₇	—	8	2	no	—
582	C₂×C₄₇	C₂×#532	1	1	yes	characteristic
583	C₂×C₄₇	C₂×#576	1	1	yes	characteristic
584	C₂×C₄₇	#3584	1	1	yes	characteristic
585	D₄₇	—	2	2	no	—
586	D₄₇	—	4	1	no	—
587	D₄₇	—	8	2	no	—
588	C₂×AGL(1,ℤ/8)	—	47	2	no	—
589	C₂×#135	—	47	1	no	—
590	C₂²×D₈	—	47	1	no	—
591	C₂×#131	—	47	1	no	—
592	C₂×#131	—	47	1	no	—
593	#544	—	47	2	no	—
594	#542	—	47	2	no	—
595	#542	—	47	2	no	—
596	#542	—	94	2	no	—
597	#540	—	47	2	no	—
598	#540	—	94	2	no	—
599	#540	C₂×D₄₇	1	2	yes	complemented
600	#538	—	94	2	no	—
601	#538	—	94	2	no	—
602	#537	—	47	2	no	—
603	#535	—	47	2	no	—
604	#535	—	47	2	no	—
605	#532	—	47	2	no	—
606	#532	—	47	2	no	—
607	#532	—	94	2	no	—
608	#529	—	47	2	no	—
609	#529	—	47	2	no	—
610	#529	—	94	2	no	—
611	#525	—	94	2	no	—
612	#525	—	94	2	no	—
613	C₄×#41	—	47	1	no	—
614	C₄×#41	—	47	2	no	—
615	C₂×C₄×D₄	—	47	2	no	—
616	#501	—	47	2	no	—
617	#501	—	47	2	no	—
618	#500	—	47	1	no	—
619	#500	—	47	1	no	—
620	#499	—	47	1	no	—
621	#499	C₂×D₄₇	1	1	yes	characteristic, complemented
622	#496	—	47	2	no	—
623	#496	—	47	2	no	—
624	#495	—	47	1	no	—
625	#495	—	47	1	no	—
626	#493	—	47	1	no	—
627	#493	C₂×D₄₇	1	1	yes	characteristic
628	#490	—	47	2	no	—
629	#490	C₂×D₄₇	1	2	yes	complemented
630	#489	—	47	2	no	—
631	#489	—	47	2	no	—
632	#488	—	47	2	no	—
633	#488	—	47	2	no	—
634	#486	—	47	2	no	—
635	#486	—	47	2	no	—
636	#469	—	47	2	no	—
637	#469	—	47	2	no	—
638	#469	—	47	2	no	—
639	#469	C₂×D₄₇	1	2	yes	complemented
640	#468	—	47	2	no	—
641	#468	—	47	2	no	—
642	#468	—	47	2	no	—
643	#468	—	47	2	no	—
644	#467	—	47	1	no	—
645	#467	—	47	1	no	—
646	#466	—	47	1	no	—
647	#466	—	47	1	no	—
648	#466	—	47	2	no	—
649	#466	—	47	1	no	—
650	#466	—	47	2	no	—
651	#466	—	47	1	no	—
652	#466	C₂×D₄₇	1	1	yes	characteristic
653	#466	C₂×D₄₇	1	1	yes	characteristic, complemented
654	#465	—	47	2	no	—
655	#465	—	47	2	no	—
656	#442	—	47	2	no	—
657	#442	C₂×D₄₇	1	2	yes	complemented
658	#440	—	47	2	no	—
659	#440	—	47	2	no	—
660	C₄×Q₁₆	—	47	1	no	—
661	C₄×Q₁₆	—	47	1	no	—
662	C₄×SD₁₆	—	47	2	no	—
663	C₄×SD₁₆	—	47	2	no	—
664	C₄×SD₁₆	—	47	2	no	—
665	C₄×SD₁₆	—	47	2	no	—
666	C₄×D₈	—	47	1	no	—
667	C₄×D₈	—	47	1	no	—
668	C₄×D₈	—	47	2	no	—
669	C₄×D₈	—	47	2	no	—
670	C₄×D₈	—	47	1	no	—
671	C₄×D₈	—	47	2	no	—
672	C₄×D₈	—	47	2	no	—
673	C₄×D₈	—	47	1	no	—
674	C₄×D₈	C₂×D₄₇	1	1	yes	characteristic
675	C₄×D₈	C₂×D₄₇	1	1	yes	characteristic, complemented
676	#428	—	47	2	no	—
677	#427	—	47	1	no	—
678	C₂×#107	—	47	1	no	—
679	#418	—	47	2	no	—
680	#417	—	47	2	no	—
681	#416	—	47	2	no	—
682	C₂×#102	—	47	2	no	—
683	#405	—	47	1	no	—
684	#405	—	47	1	no	—
685	#405	—	47	1	no	—
686	#405	—	47	1	no	—
687	#405	—	47	1	no	—
688	#405	C₂×D₄₇	1	1	yes	characteristic, complemented
689	C₄×M₁₆	—	47	1	no	—
690	C₄×M₁₆	—	47	1	no	—
691	C₄×M₁₆	—	47	1	no	—
692	C₂×C₄×C₈	—	47	1	no	—
693	C₂×C₄×C₈	—	47	1	no	—
694	C₂×C₄×C₈	—	47	1	no	—
695	C₄₇	#60695	1	1	yes	characteristic, complemented, Sylow
696	C₂×#41	—	47	1	no	—
697	C₂×#41	—	47	2	no	—
698	C₂×#41	—	94	2	no	—
699	C₂×#41	—	94	2	no	—
700	C₂²×D₄	—	47	2	no	—
701	C₂³×C₄	—	94	2	no	—
702	AGL(1,ℤ/8)	—	94	8	no	—
703	#135	—	94	4	no	—
704	C₂×Q₁₆	—	47	1	no	—
705	C₂×SD₁₆	—	47	2	no	—
706	C₂×SD₁₆	—	47	2	no	—
707	C₂×SD₁₆	—	47	2	no	—
708	C₂×D₈	—	47	2	no	—
709	C₂×D₈	—	47	2	no	—
710	C₂×D₈	—	47	1	no	—
711	C₂×D₈	—	94	4	no	—
712	C₂×D₈	C₂²×D₄₇	1	1	yes	characteristic
713	C₂×D₈	C₂²×D₄₇	1	1	yes	characteristic
714	C₂×D₈	C₂²×D₄₇	1	2	yes	—
715	#131	—	94	4	no	—
716	#131	—	94	4	no	—
717	C₂×M₁₆	—	47	1	no	—
718	C₂×M₁₆	—	47	1	no	—
719	C₂×M₁₆	—	47	1	no	—
720	C₂×M₁₆	—	47	1	no	—
721	C₂×M₁₆	—	47	1	no	—
722	C₂×M₁₆	C₂²×D₄₇	1	1	yes	characteristic
723	C₂²×C₈	—	47	1	no	—
724	C₂²×C₈	—	47	1	no	—
725	C₂²×C₈	—	47	1	no	—
726	C₂²×C₈	—	47	1	no	—
727	C₂²×C₈	—	47	1	no	—
728	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
729	C₄⋊Q₈	—	47	2	no	—
730	C₄⋊Q₈	—	47	2	no	—
731	C₄⋊Q₈	—	94	2	no	—
732	#127	—	47	2	no	—
733	#127	—	94	2	no	—
734	#127	C₂²×D₄₇	1	2	yes	—
735	#126	—	94	2	no	—
736	#126	—	94	2	no	—
737	#126	—	94	2	no	—
738	#126	—	94	2	no	—
739	#125	—	47	2	no	—
740	#125	—	94	2	no	—
741	#125	C₂²×D₄₇	1	2	yes	—
742	#124	—	47	2	no	—
743	#124	—	47	2	no	—
744	#124	—	94	2	no	—
745	#124	—	94	2	no	—
746	#124	—	94	2	no	—
747	#124	—	94	2	no	—
748	#124	—	94	2	no	—
749	#123	—	2	2	no	—
750	#123	—	2	2	no	—
751	#123	—	94	2	no	—
752	#123	—	94	2	no	—
753	#123	—	94	2	no	—
754	#123	—	94	2	no	—
755	#123	—	94	2	no	—
756	#123	—	94	2	no	—
757	C₂²⋊Q₈	—	47	2	no	—
758	C₂²⋊Q₈	—	47	2	no	—
759	C₂²⋊Q₈	—	94	2	no	—
760	C₂²⋊Q₈	—	94	2	no	—
761	C₂²⋊Q₈	—	94	2	no	—
762	C₂²⋊Q₈	—	94	2	no	—
763	C₂²⋊Q₈	—	94	2	no	—
764	#121	—	2	2	no	—
765	#121	—	2	2	no	—
766	#121	—	47	2	no	—
767	#121	—	47	2	no	—
768	#121	—	47	2	no	—
769	#121	—	47	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	C₂²×D₄₇	1	2	yes	—
780	#121	C₂²×D₄₇	1	2	yes	—
781	#120	—	94	2	no	—
782	#120	—	94	2	no	—
783	#120	—	94	2	no	—
784	#120	—	94	2	no	—
785	C₄×Q₈	—	47	1	no	—
786	C₄×Q₈	—	47	1	no	—
787	C₄×Q₈	—	47	2	no	—
788	C₄×Q₈	—	47	2	no	—
789	C₄×D₄	—	47	1	no	—
790	C₄×D₄	—	47	1	no	—
791	C₄×D₄	—	47	1	no	—
792	C₄×D₄	—	47	1	no	—
793	C₄×D₄	—	47	1	no	—
794	C₄×D₄	—	47	1	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	—	94	2	no	—
800	C₄×D₄	—	94	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	C₂²×D₄₇	1	2	yes	—
808	C₄×D₄	C₂²×D₄₇	1	2	yes	—
809	#117	—	47	1	no	—
810	#117	—	47	1	no	—
811	#117	—	47	2	no	—
812	#117	—	94	2	no	—
813	#117	—	94	2	no	—
814	#117	—	94	2	no	—
815	#117	C₂²×D₄₇	1	1	yes	characteristic
816	C₂×C₄⋊C₄	—	47	2	no	—
817	C₂×C₂²⋊C₄	—	94	2	no	—
818	C₂×C₄²	—	47	1	no	—
819	C₂×C₄²	—	47	1	no	—
820	C₂×C₄²	—	47	1	no	—
821	C₂×C₄²	—	94	2	no	—
822	#107	—	47	1	no	—
823	#107	—	47	1	no	—
824	#107	—	47	2	no	—
825	#107	—	47	2	no	—
826	#107	—	47	2	no	—
827	#107	C₂²×D₄₇	1	1	yes	characteristic
828	#107	C₂²×D₄₇	1	1	yes	characteristic
829	#106	—	47	2	no	—
830	#106	—	47	2	no	—
831	#106	C₂²×D₄₇	1	2	yes	—
832	#103	—	47	2	no	—
833	#103	—	47	2	no	—
834	#103	—	47	2	no	—
835	#103	—	47	2	no	—
836	#102	—	47	2	no	—
837	#102	—	47	2	no	—
838	#102	—	47	2	no	—
839	#102	—	47	2	no	—
840	#102	—	47	2	no	—
841	#102	—	47	2	no	—
842	#102	—	47	2	no	—
843	#102	—	47	2	no	—
844	#102	C₂²×D₄₇	1	2	yes	—
845	#102	C₂²×D₄₇	1	2	yes	—
846	#102	C₂²×D₄₇	1	2	yes	—
847	#102	C₂²×D₄₇	1	2	yes	—
848	#97	—	47	1	no	—
849	#97	—	47	1	no	—
850	#97	—	47	1	no	—
851	#97	—	47	1	no	—
852	#97	C₂²×D₄₇	1	1	yes	characteristic
853	#97	C₂²×D₄₇	1	1	yes	characteristic
854	C₄×C₈	—	47	1	no	—
855	C₄×C₈	—	47	1	no	—
856	C₄×C₈	—	47	1	no	—
857	C₄×C₈	—	47	1	no	—
858	C₄×C₈	—	47	1	no	—
859	C₄×C₈	—	47	1	no	—
860	C₄×C₈	—	47	1	no	—
861	C₄×C₈	—	47	1	no	—
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	2	no	—
866	#41	—	94	2	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	2	no	—
873	C₂×Q₈	—	94	2	no	—
874	C₂×Q₈	—	94	2	no	—
875	C₂×D₄	—	2	2	no	—
876	C₂×D₄	—	2	2	no	—
877	C₂×D₄	—	2	2	no	—
878	C₂×D₄	—	2	2	no	—
879	C₂×D₄	—	47	1	no	—
880	C₂×D₄	—	47	1	no	—
881	C₂×D₄	—	47	1	no	—
882	C₂×D₄	—	47	2	no	—
883	C₂×D₄	—	94	2	no	—
884	C₂×D₄	—	94	4	no	—
885	C₂×D₄	—	94	4	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	C₂³×D₄₇	1	2	yes	—
894	C₂×D₄	C₂³×D₄₇	1	2	yes	—
895	C₂²×C₄	—	2	2	no	—
896	C₂²×C₄	—	2	2	no	—
897	C₂²×C₄	—	47	1	no	—
898	C₂²×C₄	—	47	1	no	—
899	C₂²×C₄	—	47	1	no	—
900	C₂²×C₄	—	47	1	no	—
901	C₂²×C₄	—	47	1	no	—
902	C₂²×C₄	—	47	1	no	—
903	C₂²×C₄	—	47	1	no	—
904	C₂²×C₄	—	47	1	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	—	94	2	no	—
911	C₂²×C₄	—	376	4	no	—
912	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
913	Q₁₆	—	94	2	no	—
914	SD₁₆	—	94	4	no	—
915	SD₁₆	—	94	4	no	—
916	SD₁₆	—	94	4	no	—
917	D₈	—	2	2	no	—
918	D₈	—	2	2	no	—
919	D₈	—	2	4	no	—
920	D₈	—	94	4	no	—
921	D₈	—	94	4	no	—
922	D₈	—	94	2	no	—
923	M₁₆	—	2	2	no	—
924	M₁₆	—	47	4	no	—
925	M₁₆	—	94	2	no	—
926	M₁₆	—	94	2	no	—
927	M₁₆	—	94	2	no	—
928	M₁₆	—	94	2	no	—
929	C₂×C₈	—	2	2	no	—
930	C₂×C₈	—	47	1	no	—
931	C₂×C₈	—	47	1	no	—
932	C₂×C₈	—	47	4	no	—
933	C₂×C₈	—	47	1	no	—
934	C₂×C₈	—	47	1	no	—
935	C₂×C₈	—	94	2	no	—
936	C₂×C₈	—	94	2	no	—
937	C₂×C₈	—	94	2	no	—
938	C₂×C₈	—	94	2	no	—
939	C₂×C₈	C₂³×D₄₇	1	1	yes	characteristic
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	C₄⋊C₄	—	2	2	no	—
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	2	no	—
950	C₄⋊C₄	—	47	2	no	—
951	C₄⋊C₄	—	94	2	no	—
952	C₄⋊C₄	—	94	2	no	—
953	C₄⋊C₄	—	94	2	no	—
954	C₄⋊C₄	—	94	2	no	—
955	C₄⋊C₄	—	94	2	no	—
956	C₄⋊C₄	—	94	2	no	—
957	C₄⋊C₄	—	94	2	no	—
958	C₄⋊C₄	—	94	2	no	—
959	C₄⋊C₄	—	94	2	no	—
960	C₄⋊C₄	D₄×D₄₇	1	1	yes	characteristic
961	C₄⋊C₄	D₄×D₄₇	1	1	yes	characteristic
962	C₄⋊C₄	C₂³×D₄₇	1	2	yes	—
963	C₄⋊C₄	C₂³×D₄₇	1	2	yes	—
964	C₂²⋊C₄	—	2	2	no	—
965	C₂²⋊C₄	—	2	2	no	—
966	C₂²⋊C₄	—	2	2	no	—
967	C₂²⋊C₄	—	2	2	no	—
968	C₂²⋊C₄	—	47	1	no	—
969	C₂²⋊C₄	—	47	1	no	—
970	C₂²⋊C₄	—	47	1	no	—
971	C₂²⋊C₄	—	47	1	no	—
972	C₂²⋊C₄	—	94	2	no	—
973	C₂²⋊C₄	—	94	2	no	—
974	C₂²⋊C₄	—	94	2	no	—
975	C₂²⋊C₄	—	94	2	no	—
976	C₂²⋊C₄	—	94	2	no	—
977	C₂²⋊C₄	—	94	2	no	—
978	C₂²⋊C₄	—	94	2	no	—
979	C₂²⋊C₄	—	94	2	no	—
980	C₂²⋊C₄	—	94	2	no	—
981	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	D₄×D₄₇	1	1	yes	characteristic
988	C₂²⋊C₄	D₄×D₄₇	1	1	yes	characteristic
989	C₄²	—	47	1	no	—
990	C₄²	—	47	1	no	—
991	C₄²	—	47	1	no	—
992	C₄²	—	47	1	no	—
993	C₄²	—	47	1	no	—
994	C₄²	—	47	1	no	—
995	C₄²	—	47	1	no	—
996	C₄²	—	47	1	no	—
997	C₄²	—	94	2	no	—
998	C₄²	—	94	2	no	—
999	C₄²	—	94	2	no	—
1000	C₄²	C₂³×D₄₇	1	1	yes	characteristic
1001	C₄²	C₂³×D₄₇	1	1	yes	characteristic
1002	C₂³	—	2	2	no	—
1003	C₂³	—	2	2	no	—
1004	C₂³	—	47	1	no	—
1005	C₂³	—	47	1	no	—
1006	C₂³	—	94	2	no	—
1007	C₂³	—	376	2	no	—
1008	C₂³	—	376	2	no	—
1009	C₂³	—	188	4	no	—
1010	C₂³	C₂×D₄×D₄₇	1	1	yes	characteristic
1011	Q₈	—	94	2	no	—
1012	Q₈	—	94	2	no	—
1013	Q₈	—	94	2	no	—
1014	Q₈	—	376	2	no	—
1015	Q₈	—	376	2	no	—
1016	D₄	—	2	2	no	—
1017	D₄	—	2	2	no	—
1018	D₄	—	2	2	no	—
1019	D₄	—	2	2	no	—
1020	D₄	—	8	2	no	—
1021	D₄	—	8	2	no	—
1022	D₄	—	8	2	no	—
1023	D₄	—	8	2	no	—
1024	D₄	—	94	2	no	—
1025	D₄	—	94	2	no	—
1026	D₄	—	94	2	no	—
1027	D₄	—	94	2	no	—
1028	D₄	—	94	2	no	—
1029	D₄	—	376	2	no	—
1030	D₄	—	376	2	no	—
1031	D₄	—	376	2	no	—
1032	D₄	—	376	2	no	—
1033	D₄	—	376	2	no	—
1034	D₄	—	376	2	no	—
1035	D₄	—	188	4	no	—
1036	D₄	—	188	4	no	—
1037	C₂×C₄	—	2	1	no	—
1038	C₂×C₄	—	2	1	no	—
1039	C₂×C₄	—	2	2	no	—
1040	C₂×C₄	—	2	2	no	—
1041	C₂×C₄	—	8	2	no	—
1042	C₂×C₄	—	8	2	no	—
1043	C₂×C₄	—	47	1	no	—
1044	C₂×C₄	—	47	1	no	—
1045	C₂×C₄	—	47	2	no	—
1046	C₂×C₄	—	47	2	no	—
1047	C₂×C₄	—	47	1	no	—
1048	C₂×C₄	—	47	1	no	—
1049	C₂×C₄	—	47	1	no	—
1050	C₂×C₄	—	47	1	no	—
1051	C₂×C₄	—	94	2	no	—
1052	C₂×C₄	—	94	2	no	—
1053	C₂×C₄	—	94	2	no	—
1054	C₂×C₄	—	94	1	no	—
1055	C₂×C₄	—	94	1	no	—
1056	C₂×C₄	—	94	2	no	—
1057	C₂×C₄	—	94	2	no	—
1058	C₂×C₄	—	94	2	no	—
1059	C₂×C₄	—	376	2	no	—
1060	C₂×C₄	—	376	2	no	—
1061	C₂×C₄	—	188	1	no	—
1062	C₂×C₄	—	188	1	no	—
1063	C₂×C₄	—	188	4	no	—
1064	C₂×C₄	—	188	4	no	—
1065	C₂×C₄	—	188	4	no	—
1066	C₂×C₄	—	188	4	no	—
1067	C₂×C₄	—	188	1	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	C₂⁴×D₄₇	1	1	yes	characteristic
1074	C₈	—	2	1	no	—
1075	C₈	—	2	1	no	—
1076	C₈	—	47	2	no	—
1077	C₈	—	47	2	no	—
1078	C₈	—	94	1	no	—
1079	C₈	—	94	1	no	—
1080	C₈	#41×D₄₇	1	2	yes	—
1081	C₈	#41×D₄₇	1	2	yes	—
1082	C₂²	—	2	1	no	—
1083	C₂²	—	2	1	no	—
1084	C₂²	—	2	1	no	—
1085	C₂²	—	4	2	no	—
1086	C₂²	—	4	2	no	—
1087	C₂²	—	4	2	no	—
1088	C₂²	—	4	2	no	—
1089	C₂²	—	4	2	no	—
1090	C₂²	—	4	2	no	—
1091	C₂²	—	47	2	no	—
1092	C₂²	—	94	1	no	—
1093	C₂²	—	94	1	no	—
1094	C₂²	—	94	1	no	—
1095	C₂²	—	94	1	no	—
1096	C₂²	—	94	1	no	—
1097	C₂²	—	376	8	no	—
1098	C₂²	—	188	2	no	—
1099	C₂²	—	188	2	no	—
1100	C₂²	—	188	2	no	—
1101	C₂²	C₂²×D₄×D₄₇	1	1	yes	characteristic
1102	C₄	—	2	1	no	—
1103	C₄	—	2	1	no	—
1104	C₄	—	2	1	no	—
1105	C₄	—	2	1	no	—
1106	C₄	—	2	1	no	—
1107	C₄	—	4	2	no	—
1108	C₄	—	4	2	no	—
1109	C₄	—	47	2	no	—
1110	C₄	—	47	2	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	—	188	2	no	—
1118	C₄	C₂×#41×D₄₇	1	1	yes	characteristic
1119	C₄	C₂×#41×D₄₇	1	1	yes	characteristic
1120	C₂	—	4	1	no	—
1121	C₂	—	8	2	no	—
1122	C₂	—	8	2	no	—
1123	C₂	—	94	2	no	—
1124	C₂	—	376	2	no	—
1125	C₂	—	188	1	no	—
1126	C₂	#532×D₄₇	1	1	yes	characteristic
1127	C₂	#576×D₄₇	1	1	yes	characteristic
1128	C₂	#20258156	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×#3176	C₂
socle	C₂²×C₄₇	C₂³×D₄
hypercenter	#3176	D₄₇
hypocenter	C₄₇	#60695
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ #117 ◁ #3176

Complements

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

N	H ≅ G/N	type
1. #20256803	C₂	semidirect
2. #20254077	C₂	semidirect
3. #20254073	C₂	semidirect
4. #20254034	C₂	semidirect
5. #20254027	C₂	semidirect
6. #20254023	C₂	semidirect
7. #20253982	C₂	semidirect
8. #20253978	C₂	semidirect
9. #20253965	C₂	semidirect
10. #20253962	C₂	semidirect
11. #20253960	C₂	semidirect
12. #20253953	C₂	semidirect
13. #20253925	C₂	semidirect
14. #20253868	C₂	semidirect
15. #20253743	C₂	semidirect
16. #20253065	C₂	semidirect
17. #20253053	C₂	semidirect
18. #20253031	C₂	semidirect
19. #20252199	C₂	semidirect
20. C₄×#13094043	C₂	semidirect
21. C₄×D₈×D₄₇	C₂	semidirect
22. #20251810	C₂	semidirect
23. C₄₇×#3176	C₂	semidirect
30. #15689744	C₂²	semidirect
32. #15689738	C₂²	semidirect
33. #15689724	C₂²	semidirect
40. #15689671	C₂²	semidirect
42. #15689668	C₂²	semidirect
43. #15689658	C₂²	semidirect
44. #15689654	C₂²	semidirect
51. #15689533	C₂²	semidirect
52. #15689530	C₂²	semidirect
53. #15689528	C₂²	semidirect
54. #15689527	C₂²	semidirect
55. #15689524	C₂²	semidirect
61. #15689486	C₂²	semidirect
62. #15689483	C₂²	semidirect
63. #15689481	C₂²	semidirect
64. #15689480	C₂²	semidirect
65. #15689476	C₂²	semidirect
66. #15689469	C₂²	semidirect
67. #15689468	C₂²	semidirect
69. #15689375	C₂²	semidirect
71. #15689369	C₂²	semidirect
72. #15689368	C₂²	semidirect
73. #15689368	C₂²	semidirect
74. #15689367	C₂²	semidirect
75. #15689365	C₂²	semidirect
76. #15689364	C₂²	semidirect
79. #15689357	C₂²	semidirect
81. #15689356	C₂²	semidirect
82. #15689356	C₂²	semidirect
83. #15689353	C₂²	semidirect
84. #15689350	C₂²	semidirect
85. #15689233	C₂²	semidirect
86. #15689225	C₂²	semidirect
87. #15689223	C₂²	semidirect
88. C₄×Dic₁₈₈	C₂²	semidirect
89. #15689217	C₂²	semidirect
90. #15689214	C₂²	semidirect
91. #15689214	C₂²	semidirect
92. #15689210	C₂²	semidirect
93. C₄×#10625335	C₂²	semidirect
96. D₈×Dic₄₇	C₂²	semidirect
97. D₈×Dic₄₇	C₂²	semidirect
101. #15689203	C₂²	semidirect
110. #15689080	C₂²	semidirect
111. #15689079	C₂²	semidirect
113. #15689077	C₂²	semidirect
115. #15689075	C₂²	semidirect
116. M₁₆×Dic₄₇	C₂²	semidirect
117. C₂×C₈×Dic₄₇	C₂²	semidirect
119. C₄×C₈×D₄₇	C₂²	semidirect
120. C₄₇×#540	C₂²	semidirect
121. C₄₇×#499	C₂²	semidirect
123. C₄₇×#490	C₂²	semidirect
124. C₄₇×#469	C₂²	semidirect
126. C₄₇×#466	C₂²	semidirect
127. C₄₇×#442	C₂²	semidirect
129. C₄×D₈×C₄₇	C₂²	semidirect
130. C₄₇×#405	C₂²	semidirect
432. #10625324	#41	semidirect
436. C₈×D₄₇	#41	semidirect
560. #3176	D₄₇	semidirect
599. #540	C₂×D₄₇	semidirect
621. #499	C₂×D₄₇	semidirect
629. #490	C₂×D₄₇	semidirect
639. #469	C₂×D₄₇	semidirect
653. #466	C₂×D₄₇	semidirect
657. #442	C₂×D₄₇	semidirect
675. C₄×D₈	C₂×D₄₇	semidirect
688. #405	C₂×D₄₇	semidirect
695. C₄₇	#60695	semidirect

Maximal subgroups

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

subgroup	index
#20256803	2
#20254077	2
#20254073	2
#20254034	2
#20254027	2
#20254023	2
#20253982	2
#20253978	2
#20253965	2
#20253962	2
#20253960	2
#20253953	2
#20253925	2
#20253868	2
#20253743	2
#20253065	2
#20253053	2
#20253031	2
#20252199	2
C₄×#13094043	2
C₄×D₈×D₄₇	2
#20251810	2
C₄₇×#3176	2
#60695	47