Subgroups — #27098837

Order 12032.

2010 conjugacy classes of subgroups.

The subgroup lattice has 1144 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20257407	C₂	1	2	yes	maximal, complemented
2	#20256361	C₂	1	1	yes	maximal, characteristic, complemented
3	#20256255	C₂	1	1	yes	maximal, characteristic, complemented
4	#20256090	C₂	1	2	yes	maximal, complemented
5	#20255807	C₂	1	1	yes	maximal, characteristic, complemented
6	#20255793	C₂	1	1	yes	maximal, characteristic, complemented
7	#20255791	C₂	1	1	yes	maximal, characteristic, complemented
8	#20255623	C₂	1	2	yes	maximal, complemented
9	#20255533	C₂	1	2	yes	maximal, complemented
10	#20255529	C₂	1	2	yes	maximal, complemented
11	D₈×C₂²⋊D₄₇	C₂	1	1	yes	maximal, characteristic, complemented
12	D₈×C₂²⋊D₄₇	C₂	1	1	yes	maximal, characteristic, complemented
13	#20254035	C₂	1	1	yes	maximal, characteristic, complemented
14	#20254031	C₂	1	1	yes	maximal, characteristic, complemented
15	#20253962	C₂	1	1	yes	maximal, characteristic, complemented
16	#20253629	C₂	1	2	yes	maximal, complemented
17	#20253625	C₂	1	2	yes	maximal, complemented
18	#20253474	C₂	1	2	yes	maximal, complemented
19	#20252356	C₂	1	1	yes	maximal, characteristic, complemented
20	#20252240	C₂	1	1	yes	maximal, characteristic, complemented
21	#20252235	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂×D₈×Dic₄₇	C₂	1	1	yes	maximal, characteristic, complemented
23	D₄×D₈×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×D₈×D₄₇	C₂²	1	1	yes	characteristic
25	#15689837	C₂²	1	2	yes	complemented
26	#15689832	C₂²	1	2	yes	complemented
27	#15689825	C₂²	1	2	yes	complemented
28	#15689819	C₂²	1	2	yes	complemented
29	#15689816	—	2	2	no	—
30	#15689793	C₂²	1	2	yes	complemented
31	#15689767	—	2	2	no	—
32	#15689760	—	2	2	no	—
33	#15689760	—	2	2	no	—
34	D₄×C₂²⋊D₄₇	C₂²	1	2	yes	complemented
35	D₄×C₂²⋊D₄₇	C₂²	1	2	yes	complemented
36	#15689727	C₂²	1	2	yes	complemented
37	#15689726	C₂²	1	2	yes	complemented
38	#15689710	—	2	2	no	—
39	#15689708	—	2	2	no	—
40	#15689668	C₂²	1	2	yes	complemented
41	#15689653	C₂²	1	1	yes	characteristic
42	#15689629	—	2	2	no	—
43	C₂×#13093996	—	2	2	no	—
44	#15689598	C₂²	1	2	yes	complemented
45	#15689595	C₂²	1	2	yes	complemented
46	C₂×D₄×Dic₄₇	C₂²	1	2	yes	complemented
47	#15689527	C₂²	1	1	yes	characteristic, complemented
48	#15689525	C₂²	1	1	yes	characteristic, complemented
49	#15689524	C₂²	1	1	yes	characteristic, complemented
50	#15689498	C₂²	1	1	yes	characteristic, complemented
51	#15689498	C₂²	1	1	yes	characteristic, complemented
52	#15689487	C₂²	1	2	yes	complemented
53	#15689486	C₂²	1	2	yes	complemented
54	#15689468	C₂²	1	2	yes	complemented
55	#15689448	C₂²	1	2	yes	complemented
56	#15689446	C₂²	1	2	yes	complemented
57	#15689445	C₂²	1	2	yes	complemented
58	#15689444	C₂²	1	2	yes	complemented
59	#15689442	C₂²	1	2	yes	complemented
60	#15689439	C₂²	1	2	yes	complemented
61	#15689425	C₂²	1	2	yes	complemented
62	#15689424	C₂²	1	2	yes	complemented
63	#15689423	C₂²	1	2	yes	complemented
64	#15689421	C₂²	1	2	yes	complemented
65	#15689411	C₂²	1	2	yes	complemented
66	#15689411	C₂²	1	2	yes	complemented
67	#15689374	C₂²	1	2	yes	complemented
68	#15689373	C₂²	1	2	yes	complemented
69	#15689359	C₂²	1	1	yes	characteristic, complemented
70	#15689359	C₂²	1	1	yes	characteristic, complemented
71	#15689357	C₂²	1	2	yes	complemented
72	#15689356	C₂²	1	1	yes	characteristic, complemented
73	#15689356	C₂²	1	1	yes	characteristic, complemented
74	#15689316	C₂²	1	2	yes	complemented
75	#15689316	C₂²	1	2	yes	complemented
76	#15689316	C₂²	1	2	yes	complemented
77	#15689316	C₂²	1	2	yes	complemented
78	#15689315	C₂²	1	2	yes	complemented
79	#15689257	C₂²	1	2	yes	complemented
80	#15689257	C₂²	1	2	yes	complemented
81	#15689255	C₂²	1	2	yes	complemented
82	#15689255	C₂²	1	2	yes	complemented
83	#15689252	C₂²	1	1	yes	characteristic, complemented
84	C₈×Dic₉₄	C₂²	1	1	yes	characteristic, complemented
85	#15689235	C₂²	1	2	yes	complemented
86	#15689235	C₂²	1	2	yes	complemented
87	#15689235	C₂²	1	2	yes	complemented
88	#15689233	C₂²	1	2	yes	complemented
89	#15689232	C₂²	1	2	yes	complemented
90	#15689232	C₂²	1	2	yes	complemented
91	C₄×D₃₇₆	C₂²	1	1	yes	characteristic, complemented
92	D₈×Dic₄₇	C₂²	1	1	yes	characteristic
93	D₈×Dic₄₇	C₂²	1	1	yes	characteristic
94	D₈×Dic₄₇	C₂²	1	1	yes	characteristic
95	D₈×Dic₄₇	C₂²	1	1	yes	characteristic, complemented
96	D₈×Dic₄₇	C₂²	1	1	yes	characteristic, complemented
97	D₈×Dic₄₇	C₂²	1	1	yes	characteristic, complemented
98	D₈×Dic₄₇	C₂²	1	1	yes	characteristic, complemented
99	D₈×Dic₄₇	C₂²	1	2	yes	complemented
100	D₈×Dic₄₇	C₂²	1	2	yes	complemented
101	#15689205	C₂²	1	1	yes	characteristic, complemented
102	#15689203	C₂²	1	2	yes	complemented
103	#15689198	C₂²	1	1	yes	characteristic, complemented
104	#15689195	C₂²	1	1	yes	characteristic, complemented
105	#15689191	C₂²	1	1	yes	characteristic, complemented
106	C₈×C₂²⋊D₄₇	C₂²	1	1	yes	characteristic, complemented
107	C₈×C₂²⋊D₄₇	C₂²	1	1	yes	characteristic, complemented
108	#15689183	C₂²	1	1	yes	characteristic, complemented
109	#15689181	C₂²	1	1	yes	characteristic, complemented
110	#15689177	C₂²	1	1	yes	characteristic, complemented
111	#15689161	C₂²	1	1	yes	characteristic, complemented
112	#15689160	C₂²	1	1	yes	characteristic, complemented
113	C₂×#13093958	C₂²	1	1	yes	characteristic, complemented
114	#15689128	C₂²	1	2	yes	complemented
115	#15689126	C₂²	1	2	yes	complemented
116	C₂×#13093945	C₂²	1	2	yes	complemented
117	#15689078	C₂²	1	1	yes	characteristic, complemented
118	#15689077	C₂²	1	1	yes	characteristic, complemented
119	C₂×C₈×Dic₄₇	C₂²	1	1	yes	characteristic, complemented
120	C₂²×D₈×C₄₇	C₂²	1	1	yes	characteristic
121	C₂²×D₈×C₄₇	C₂²	1	1	yes	characteristic
122	D₄²×C₄₇	C₂²	1	2	yes	complemented
123	C₄₇×#493	C₂²	1	1	yes	characteristic, complemented
124	C₄₇×#466	C₂²	1	1	yes	characteristic, complemented
125	C₄₇×#466	C₂²	1	1	yes	characteristic, complemented
126	C₄₇×#459	C₂²	1	2	yes	complemented
127	C₄₇×#447	C₂²	1	2	yes	complemented
128	C₄₇×#447	C₂²	1	2	yes	complemented
129	C₄×D₈×C₄₇	C₂²	1	1	yes	characteristic
130	C₈×D₄×C₄₇	C₂²	1	1	yes	characteristic, complemented
131	C₂×#10625352	—	2	2	no	—
132	C₂×#10625352	—	2	2	no	—
133	C₂²×C₂²⋊D₄₇	—	2	2	no	—
134	C₂²×C₂²⋊D₄₇	—	2	2	no	—
135	C₂×D₄×D₄₇	C₂³	1	2	yes	—
136	C₂³×Dic₄₇	—	2	2	no	—
137	C₂×D₃₇₆	C₂³	1	1	yes	characteristic
138	C₂×#10625334	C₂³	1	2	yes	—
139	C₂×#10625334	C₂³	1	2	yes	—
140	C₂×#10625334	C₂³	1	2	yes	—
141	D₈×D₄₇	—	2	4	no	—
142	C₂×#10625329	C₂³	1	1	yes	characteristic
143	C₂×#10625324	C₂³	1	1	yes	characteristic
144	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
145	C₂×C₈×D₄₇	C₂³	1	1	yes	characteristic
146	#13094023	C₂³	1	2	yes	—
147	#13094020	C₂³	1	2	yes	—
148	#13094020	C₂³	1	2	yes	—
149	#13094019	—	2	2	no	—
150	#13094019	D₄	1	1	yes	characteristic
151	#13094017	—	2	2	no	—
152	#13094017	D₄	1	1	yes	characteristic
153	#13094016	C₂³	1	2	yes	—
154	#13094015	C₂³	1	2	yes	—
155	#13094014	D₄	1	1	yes	characteristic
156	#13094011	—	2	2	no	—
157	#13094010	—	2	2	no	—
158	#13094010	—	2	2	no	—
159	#13094010	D₄	1	1	yes	characteristic
160	#13094008	—	2	2	no	—
161	#13094008	—	2	2	no	—
162	#13094008	D₄	1	1	yes	characteristic
163	#13094006	—	2	2	no	—
164	#13094006	—	2	2	no	—
165	#13094005	—	2	2	no	—
166	#13094005	—	2	2	no	—
167	#13094005	D₄	1	1	yes	characteristic
168	#13094003	—	2	2	no	—
169	#13094001	—	2	2	no	—
170	#13094001	—	2	2	no	—
171	#13094001	D₄	1	1	yes	characteristic
172	#13093998	C₂³	1	2	yes	—
173	#13093998	C₂³	1	2	yes	—
174	#13093996	—	2	2	no	—
175	#13093996	—	2	2	no	—
176	#13093996	—	2	2	no	—
177	#13093996	—	2	2	no	—
178	#13093996	—	2	2	no	—
179	#13093996	—	2	2	no	—
180	#13093996	—	2	2	no	—
181	#13093996	—	2	2	no	—
182	#13093996	—	2	2	no	—
183	#13093996	—	2	2	no	—
184	#13093996	—	2	2	no	—
185	#13093996	D₄	1	1	yes	characteristic
186	#13093995	—	2	2	no	—
187	#13093995	—	2	2	no	—
188	#13093995	C₂³	1	2	yes	—
189	#13093995	C₂³	1	2	yes	—
190	#13093993	—	2	2	no	—
191	#13093993	—	2	2	no	—
192	#13093992	—	2	2	no	—
193	#13093992	—	2	2	no	—
194	C₄×Dic₉₄	C₂³	1	1	yes	characteristic
195	C₄×D₁₈₈	C₂³	1	2	yes	—
196	D₄×Dic₄₇	—	2	2	no	—
197	D₄×Dic₄₇	—	2	2	no	—
198	D₄×Dic₄₇	—	2	2	no	—
199	D₄×Dic₄₇	—	2	2	no	—
200	D₄×Dic₄₇	—	2	2	no	—
201	D₄×Dic₄₇	C₂³	1	2	yes	—
202	D₄×Dic₄₇	C₂³	1	2	yes	—
203	D₄×Dic₄₇	C₂³	1	2	yes	—
204	D₄×Dic₄₇	C₂³	1	2	yes	—
205	D₄×Dic₄₇	C₂³	1	2	yes	—
206	D₄×Dic₄₇	C₂³	1	2	yes	—
207	D₄×Dic₄₇	C₂³	1	2	yes	—
208	#13093986	C₂³	1	2	yes	—
209	C₄×C₂²⋊D₄₇	—	2	2	no	—
210	C₄×C₂²⋊D₄₇	C₂³	1	1	yes	characteristic
211	C₄×C₂²⋊D₄₇	C₂³	1	1	yes	characteristic
212	(C₂²⋊D₄₇)⋊C₄	—	2	2	no	—
213	(C₂²⋊D₄₇)⋊C₄	—	2	2	no	—
214	(C₂²⋊D₄₇)⋊C₄	—	2	2	no	—
215	#13093983	C₂³	1	2	yes	—
216	#13093983	C₂³	1	1	yes	characteristic
217	#13093982	C₂³	1	2	yes	—
218	#13093981	C₂³	1	1	yes	characteristic
219	#13093980	—	2	2	no	—
220	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
221	C₂×Dic₄₇⋊C₄	—	2	2	no	—
222	C₂×C₂²⋊Dic₄₇	—	2	2	no	—
223	C₂×C₂²⋊Dic₄₇	—	2	2	no	—
224	C₂×C₂²⋊Dic₄₇	—	2	2	no	—
225	C₂×(C₂×D₄₇)⋊C₄	—	2	2	no	—
226	C₂²⋊C₄×D₄₇	—	2	2	no	—
227	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
228	#13093958	C₂³	1	1	yes	characteristic
229	#13093958	C₂³	1	1	yes	characteristic
230	#13093958	C₂³	1	1	yes	characteristic
231	#13093958	C₂³	1	2	yes	—
232	#13093957	C₂³	1	2	yes	—
233	#13093956	C₂³	1	2	yes	—
234	#13093956	C₂³	1	2	yes	—
235	#13093955	C₂³	1	2	yes	—
236	#13093955	C₂³	1	2	yes	—
237	C₄⋊(C₄₇⋊C₈)	C₂³	1	1	yes	characteristic
238	Dic₄₇⋊C₈	C₂³	1	1	yes	characteristic
239	Dic₄₇⋊C₈	C₂³	1	1	yes	characteristic
240	Dic₄₇⋊C₈	C₂³	1	1	yes	characteristic
241	Dic₄₇⋊C₈	C₂³	1	1	yes	characteristic
242	#13093946	C₂³	1	2	yes	—
243	#13093946	C₂³	1	2	yes	—
244	#13093946	C₂³	1	2	yes	—
245	#13093945	C₂³	1	2	yes	—
246	#13093945	C₂³	1	2	yes	—
247	#13093945	C₂³	1	2	yes	—
248	#13093945	C₂³	1	2	yes	—
249	#13093945	C₂³	1	2	yes	—
250	#13093945	C₂³	1	2	yes	—
251	#13093945	C₂³	1	2	yes	—
252	#13093945	C₂³	1	2	yes	—
253	#13093945	C₂³	1	2	yes	—
254	#13093944	C₂³	1	2	yes	—
255	C₂²⋊(C₄₇⋊C₈)	C₂³	1	1	yes	characteristic
256	C₂²⋊(C₄₇⋊C₈)	C₂³	1	1	yes	characteristic
257	(C₂×D₄₇)⋊C₈	C₂³	1	1	yes	characteristic
258	(C₂×D₄₇)⋊C₈	C₂³	1	1	yes	characteristic
259	#13093935	C₂³	1	1	yes	characteristic
260	#13093934	C₂³	1	1	yes	characteristic
261	#13093934	C₂³	1	1	yes	characteristic
262	#13093934	C₂³	1	1	yes	characteristic
263	C₈×Dic₄₇	C₂³	1	1	yes	characteristic
264	C₈×Dic₄₇	C₂³	1	1	yes	characteristic
265	C₈×Dic₄₇	C₂³	1	1	yes	characteristic
266	C₈×Dic₄₇	C₂³	1	1	yes	characteristic
267	C₈×Dic₄₇	C₂³	1	1	yes	characteristic
268	C₂²×D₄×C₄₇	—	2	2	no	—
269	C₂²×D₄×C₄₇	C₂³	1	2	yes	—
270	C₂²×D₄×C₄₇	C₂³	1	2	yes	—
271	C₂×D₈×C₄₇	—	2	4	no	—
272	C₂×D₈×C₄₇	—	2	4	no	—
273	C₂×D₈×C₄₇	C₂³	1	2	yes	—
274	C₂×D₈×C₄₇	C₂³	1	2	yes	—
275	C₂×D₈×C₄₇	C₂³	1	1	yes	characteristic
276	C₂×D₈×C₄₇	C₂³	1	1	yes	characteristic
277	C₂×D₈×C₄₇	C₂³	1	2	yes	—
278	C₂×D₈×C₄₇	C₂³	1	1	yes	characteristic
279	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
280	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
281	#127×C₄₇	C₂³	1	2	yes	—
282	#121×C₄₇	—	2	2	no	—
283	#121×C₄₇	C₂³	1	2	yes	—
284	#121×C₄₇	C₂³	1	2	yes	—
285	#120×C₄₇	—	2	2	no	—
286	#120×C₄₇	—	2	2	no	—
287	C₄×D₄×C₄₇	C₂³	1	2	yes	—
288	C₄×D₄×C₄₇	C₂³	1	1	yes	characteristic
289	#107×C₄₇	C₂³	1	1	yes	characteristic
290	C₄⋊C₈×C₄₇	C₂³	1	1	yes	characteristic
291	#102×C₄₇	C₂³	1	2	yes	—
292	#102×C₄₇	C₂³	1	2	yes	—
293	#102×C₄₇	C₂³	1	2	yes	—
294	C₂²⋊C₈×C₄₇	C₂³	1	1	yes	characteristic
295	C₂²⋊C₈×C₄₇	C₂³	1	1	yes	characteristic
296	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
297	C₂⁴×C₄₇	—	2	2	no	—
298	C₂⁴×C₄₇	—	2	2	no	—
299	C₂³×D₄₇	—	2	2	no	—
300	C₂×D₄×C₄₇	—	2	4	no	—
301	C₂×D₄×C₄₇	—	2	4	no	—
302	C₂×D₄×C₄₇	—	2	2	no	—
303	C₂×D₄×C₄₇	—	2	2	no	—
304	C₂×D₄×C₄₇	—	2	2	no	—
305	C₂×D₄×C₄₇	—	2	2	no	—
306	C₂×D₄×C₄₇	—	2	2	no	—
307	C₂×D₄×C₄₇	—	2	2	no	—
308	C₂×D₄×C₄₇	—	4	2	no	—
309	C₂×D₄×C₄₇	—	4	2	no	—
310	C₂×D₄×C₄₇	—	8	4	no	—
311	C₂×D₄×C₄₇	C₂×D₄	1	1	yes	characteristic
312	C₂×D₄×C₄₇	C₂⁴	1	2	yes	—
313	C₂×D₄×C₄₇	C₂⁴	1	2	yes	—
314	C₂×D₄×C₄₇	C₂⁴	1	2	yes	—
315	C₂²×C₄×C₄₇	—	2	2	no	—
316	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
317	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
318	C₂×C₂²⋊D₄₇	—	2	2	no	—
319	C₂×C₂²⋊D₄₇	—	2	2	no	—
320	C₂×C₂²⋊D₄₇	—	2	2	no	—
321	C₂×C₂²⋊D₄₇	—	2	2	no	—
322	C₂×C₂²⋊D₄₇	—	2	2	no	—
323	C₂×C₂²⋊D₄₇	—	2	2	no	—
324	C₂×C₂²⋊D₄₇	—	2	2	no	—
325	C₂×C₂²⋊D₄₇	—	2	2	no	—
326	C₂×C₂²⋊D₄₇	—	2	2	no	—
327	C₂×C₂²⋊D₄₇	—	8	4	no	—
328	C₂×C₂²⋊D₄₇	—	8	4	no	—
329	C₂×C₂²⋊D₄₇	C₂×D₄	1	1	yes	characteristic
330	C₂×C₂²⋊D₄₇	C₂×D₄	1	1	yes	characteristic
331	C₂²×Dic₄₇	—	2	2	no	—
332	C₂²×Dic₄₇	—	2	2	no	—
333	C₂²×Dic₄₇	—	2	2	no	—
334	C₂²×Dic₄₇	—	2	2	no	—
335	C₂²×Dic₄₇	—	2	2	no	—
336	C₂²×Dic₄₇	—	2	2	no	—
337	C₂²×Dic₄₇	—	2	2	no	—
338	C₂²×Dic₄₇	—	2	2	no	—
339	C₂²×Dic₄₇	—	8	4	no	—
340	C₂²×Dic₄₇	C₂×D₄	1	1	yes	characteristic
341	C₂²×Dic₄₇	C₂×D₄	1	1	yes	characteristic
342	#10625352	—	8	4	no	—
343	#10625352	—	8	4	no	—
344	D₄×D₄₇	—	2	4	no	—
345	D₄×D₄₇	—	4	2	no	—
346	C₂×D₁₈₈	C₂⁴	1	2	yes	—
347	C₂×C₄×D₄₇	—	2	2	no	—
348	C₂×C₄×D₄₇	—	2	2	no	—
349	C₂×C₄×D₄₇	C₂⁴	1	1	yes	characteristic
350	C₂×Dic₉₄	—	2	2	no	—
351	C₂×Dic₉₄	C₂×D₄	1	1	yes	characteristic
352	D₈×C₄₇	—	2	4	no	—
353	D₈×C₄₇	—	2	4	no	—
354	D₈×C₄₇	—	2	2	no	—
355	D₈×C₄₇	—	2	2	no	—
356	D₈×C₄₇	—	4	2	no	—
357	D₈×C₄₇	#41	1	4	yes	complemented
358	C₂×C₈×C₄₇	—	2	2	no	—
359	C₂×C₈×C₄₇	—	2	2	no	—
360	C₂×C₈×C₄₇	C₂⁴	1	1	yes	characteristic
361	C₂×C₈×C₄₇	C₂⁴	1	1	yes	characteristic
362	C₂×C₈×C₄₇	C₂⁴	1	1	yes	characteristic
363	C₂×C₈×C₄₇	C₂⁴	1	1	yes	characteristic
364	C₄⋊C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
365	C₄⋊C₄×C₄₇	C₂⁴	1	2	yes	—
366	C₂²⋊C₄×C₄₇	—	2	2	no	—
367	C₂²⋊C₄×C₄₇	—	2	2	no	—
368	C₂²⋊C₄×C₄₇	—	2	2	no	—
369	C₂²⋊C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
370	C₂²⋊C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
371	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
372	C₂²⋊Dic₄₇	—	2	2	no	—
373	C₂²⋊Dic₄₇	—	2	2	no	—
374	C₂²⋊Dic₄₇	—	2	2	no	—
375	C₂²⋊Dic₄₇	—	2	2	no	—
376	C₂²⋊Dic₄₇	—	2	2	no	—
377	C₂²⋊Dic₄₇	—	2	2	no	—
378	C₂²⋊Dic₄₇	—	2	2	no	—
379	C₂²⋊Dic₄₇	—	2	2	no	—
380	C₂²⋊Dic₄₇	—	2	2	no	—
381	C₂²⋊Dic₄₇	—	2	2	no	—
382	C₂²⋊Dic₄₇	C₂×D₄	1	1	yes	characteristic
383	C₂²⋊Dic₄₇	C₂×D₄	1	1	yes	characteristic
384	C₂²⋊Dic₄₇	C₂×D₄	1	1	yes	characteristic
385	C₂²⋊Dic₄₇	C₂×D₄	1	1	yes	characteristic
386	#10625334	—	2	4	no	—
387	#10625334	—	4	2	no	—
388	#10625334	—	4	2	no	—
389	(C₂×D₄₇)⋊C₄	—	2	2	no	—
390	(C₂×D₄₇)⋊C₄	—	2	2	no	—
391	(C₂×D₄₇)⋊C₄	—	2	2	no	—
392	(C₂×D₄₇)⋊C₄	—	2	2	no	—
393	(C₂×D₄₇)⋊C₄	—	2	2	no	—
394	(C₂×D₄₇)⋊C₄	C₂×D₄	1	1	yes	characteristic
395	(C₂×D₄₇)⋊C₄	C₂×D₄	1	1	yes	characteristic
396	(C₂×D₄₇)⋊C₄	C₂×D₄	1	1	yes	characteristic
397	(C₂×D₄₇)⋊C₄	C₂×D₄	1	1	yes	characteristic
398	C₄⋊Dic₄₇	—	2	2	no	—
399	C₄⋊Dic₄₇	—	2	2	no	—
400	C₄⋊Dic₄₇	C₂×D₄	1	1	yes	characteristic
401	C₄⋊Dic₄₇	C₂×D₄	1	1	yes	characteristic
402	C₄⋊Dic₄₇	C₂×D₄	1	1	yes	characteristic
403	C₄⋊Dic₄₇	C₂⁴	1	2	yes	—
404	C₄⋊Dic₄₇	C₂⁴	1	2	yes	—
405	C₄⋊Dic₄₇	C₂⁴	1	2	yes	—
406	Dic₄₇⋊C₄	—	2	2	no	—
407	Dic₄₇⋊C₄	—	2	2	no	—
408	Dic₄₇⋊C₄	—	2	2	no	—
409	Dic₄₇⋊C₄	—	2	2	no	—
410	Dic₄₇⋊C₄	C₂×D₄	1	1	yes	characteristic
411	Dic₄₇⋊C₄	C₂×D₄	1	1	yes	characteristic
412	Dic₄₇⋊C₄	C₂×D₄	1	1	yes	characteristic
413	Dic₄₇⋊C₄	C₂×D₄	1	1	yes	characteristic
414	Dic₄₇⋊C₄	C₂×D₄	1	1	yes	characteristic
415	Dic₄₇⋊C₄	C₂×D₄	1	1	yes	characteristic
416	C₄×Dic₄₇	—	2	2	no	—
417	C₄×Dic₄₇	—	2	2	no	—
418	C₄×Dic₄₇	C₂×D₄	1	1	yes	characteristic
419	C₄×Dic₄₇	C₂×D₄	1	1	yes	characteristic
420	C₄×Dic₄₇	C₂⁴	1	1	yes	characteristic
421	C₄×Dic₄₇	C₂⁴	1	1	yes	characteristic
422	C₄×Dic₄₇	C₂⁴	1	1	yes	characteristic
423	#10625329	—	4	1	no	—
424	C₂×C₄₇⋊C₈	—	4	1	no	—
425	C₂×C₄₇⋊C₈	C₂⁴	1	1	yes	characteristic
426	C₂×C₄₇⋊C₈	C₂⁴	1	1	yes	characteristic
427	C₂×C₄₇⋊C₈	C₂⁴	1	1	yes	characteristic
428	C₂×C₄₇⋊C₈	C₂⁴	1	1	yes	characteristic
429	D₃₇₆	—	2	2	no	—
430	#10625324	—	4	1	no	—
431	C₈×D₄₇	—	2	2	no	—
432	C₂³×C₄₇	—	2	2	no	—
433	C₂³×C₄₇	—	2	2	no	—
434	C₂³×C₄₇	—	2	2	no	—
435	C₂³×C₄₇	—	4	4	no	—
436	C₂³×C₄₇	—	4	4	no	—
437	C₂³×C₄₇	—	4	4	no	—
438	C₂³×C₄₇	—	8	2	no	—
439	C₂³×C₄₇	—	8	2	no	—
440	C₂³×C₄₇	—	8	2	no	—
441	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
442	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
443	C₂²×D₄₇	—	2	2	no	—
444	C₂²×D₄₇	—	4	4	no	—
445	C₂²×D₄₇	—	8	2	no	—
446	C₂²×D₄₇	—	8	2	no	—
447	C₂²×D₄₇	C₂²×D₄	1	1	yes	characteristic
448	D₄×C₄₇	—	2	2	no	—
449	D₄×C₄₇	—	2	2	no	—
450	D₄×C₄₇	—	2	2	no	—
451	D₄×C₄₇	—	2	2	no	—
452	D₄×C₄₇	—	2	2	no	—
453	D₄×C₄₇	—	2	2	no	—
454	D₄×C₄₇	—	4	4	no	—
455	D₄×C₄₇	—	4	4	no	—
456	D₄×C₄₇	—	4	4	no	—
457	D₄×C₄₇	—	8	2	no	—
458	D₄×C₄₇	—	8	2	no	—
459	D₄×C₄₇	—	8	2	no	—
460	D₄×C₄₇	C₂×#41	1	4	yes	—
461	C₂×C₄×C₄₇	—	2	1	no	—
462	C₂×C₄×C₄₇	—	2	1	no	—
463	C₂×C₄×C₄₇	—	2	1	no	—
464	C₂×C₄×C₄₇	—	2	1	no	—
465	C₂×C₄×C₄₇	—	2	2	no	—
466	C₂×C₄×C₄₇	—	8	2	no	—
467	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
468	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
469	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
470	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
471	C₂×C₄×C₄₇	C₂⁵	1	1	yes	characteristic
472	C₂²⋊D₄₇	—	2	2	no	—
473	C₂²⋊D₄₇	—	2	2	no	—
474	C₂²⋊D₄₇	—	4	4	no	—
475	C₂²⋊D₄₇	—	4	4	no	—
476	C₂²⋊D₄₇	—	4	4	no	—
477	C₂²⋊D₄₇	—	8	2	no	—
478	C₂²⋊D₄₇	—	8	2	no	—
479	C₂²⋊D₄₇	—	8	2	no	—
480	C₂²⋊D₄₇	—	8	2	no	—
481	C₂²⋊D₄₇	—	8	2	no	—
482	C₂²⋊D₄₇	—	8	2	no	—
483	C₂×Dic₄₇	—	2	2	no	—
484	C₂×Dic₄₇	—	2	2	no	—
485	C₂×Dic₄₇	—	2	2	no	—
486	C₂×Dic₄₇	—	2	2	no	—
487	C₂×Dic₄₇	—	2	2	no	—
488	C₂×Dic₄₇	—	4	4	no	—
489	C₂×Dic₄₇	—	4	4	no	—
490	C₂×Dic₄₇	—	8	2	no	—
491	C₂×Dic₄₇	—	8	2	no	—
492	C₂×Dic₄₇	—	8	2	no	—
493	C₂×Dic₄₇	—	8	2	no	—
494	C₂×Dic₄₇	—	8	2	no	—
495	C₂×Dic₄₇	—	8	2	no	—
496	C₂×Dic₄₇	C₂²×D₄	1	1	yes	characteristic
497	C₂×Dic₄₇	C₂²×D₄	1	1	yes	characteristic
498	C₂×Dic₄₇	C₂²×D₄	1	1	yes	characteristic
499	C₂×Dic₄₇	C₂²×D₄	1	1	yes	characteristic
500	C₂×Dic₄₇	C₂²×D₄	1	1	yes	characteristic
501	C₂×Dic₄₇	C₂²×D₄	1	1	yes	characteristic
502	C₂×Dic₄₇	C₂²×D₄	1	1	yes	characteristic
503	D₁₈₈	—	2	2	no	—
504	D₁₈₈	—	2	2	no	—
505	C₄×D₄₇	—	2	1	no	—
506	C₄×D₄₇	—	2	1	no	—
507	C₄×D₄₇	—	8	2	no	—
508	C₄×D₄₇	—	8	2	no	—
509	Dic₉₄	—	2	2	no	—
510	Dic₉₄	—	8	2	no	—
511	C₈×C₄₇	—	2	1	no	—
512	C₈×C₄₇	—	2	1	no	—
513	C₈×C₄₇	—	2	1	no	—
514	C₈×C₄₇	C₂×#41	1	2	yes	—
515	C₄₇⋊C₈	—	2	1	no	—
516	C₄₇⋊C₈	—	2	1	no	—
517	C₄₇⋊C₈	—	2	1	no	—
518	C₄₇⋊C₈	—	2	1	no	—
519	#61480	—	47	1	no	maximal, Sylow
520	C₂²×C₄₇	—	2	1	no	—
521	C₂²×C₄₇	—	2	1	no	—
522	C₂²×C₄₇	—	2	4	no	—
523	C₂²×C₄₇	—	2	1	no	—
524	C₂²×C₄₇	—	2	1	no	—
525	C₂²×C₄₇	—	2	1	no	—
526	C₂²×C₄₇	—	4	2	no	—
527	C₂²×C₄₇	—	4	2	no	—
528	C₂²×C₄₇	—	4	2	no	—
529	C₂²×C₄₇	—	4	2	no	—
530	C₂²×C₄₇	—	4	2	no	—
531	C₂²×C₄₇	—	4	2	no	—
532	C₂²×C₄₇	—	4	2	no	—
533	C₂²×C₄₇	—	4	2	no	—
534	C₂²×C₄₇	—	8	8	no	—
535	C₂²×C₄₇	—	16	4	no	—
536	C₂²×C₄₇	#576	1	2	yes	—
537	C₂²×C₄₇	C₂³×D₄	1	1	yes	characteristic
538	C₂×D₄₇	—	2	1	no	—
539	C₂×D₄₇	—	2	1	no	—
540	C₂×D₄₇	—	2	1	no	—
541	C₂×D₄₇	—	4	2	no	—
542	C₂×D₄₇	—	4	2	no	—
543	C₂×D₄₇	—	4	2	no	—
544	C₂×D₄₇	—	16	4	no	—
545	C₄×C₄₇	—	2	1	no	—
546	C₄×C₄₇	—	2	1	no	—
547	C₄×C₄₇	—	2	1	no	—
548	C₄×C₄₇	—	2	1	no	—
549	C₄×C₄₇	—	4	2	no	—
550	C₄×C₄₇	C₂²×#41	1	1	yes	characteristic
551	C₄×C₄₇	#585	1	1	yes	characteristic
552	Dic₄₇	—	2	1	no	—
553	Dic₄₇	—	2	1	no	—
554	Dic₄₇	—	2	1	no	—
555	Dic₄₇	—	2	1	no	—
556	Dic₄₇	—	2	1	no	—
557	Dic₄₇	—	2	1	no	—
558	Dic₄₇	—	4	2	no	—
559	Dic₄₇	—	4	2	no	—
560	Dic₄₇	—	4	2	no	—
561	Dic₄₇	#576	1	2	yes	—
562	#3519	—	47	2	no	—
563	#3391	—	47	1	no	—
564	#3380	—	47	1	no	—
565	#3366	—	47	2	no	—
566	#3341	—	47	1	no	—
567	#3339	—	47	1	no	—
568	#3339	—	47	1	no	—
569	#3325	—	47	2	no	—
570	#3318	—	47	2	no	—
571	#3318	—	47	2	no	—
572	D₄×D₈	—	47	1	no	—
573	D₄×D₈	—	47	1	no	—
574	D₄×D₈	D₄₇	1	1	yes	characteristic, complemented
575	#3176	—	47	1	no	—
576	#3176	—	47	1	no	—
577	#3169	—	47	1	no	—
578	#3122	—	47	2	no	—
579	#3122	—	47	2	no	—
580	#3109	—	47	2	no	—
581	#2966	—	47	1	no	—
582	#2948	—	47	1	no	—
583	#2948	—	47	1	no	—
584	C₂×C₄×D₈	—	47	1	no	—
585	C₂×C₄₇	—	2	2	no	—
586	C₂×C₄₇	—	4	4	no	—
587	C₂×C₄₇	—	4	1	no	—
588	C₂×C₄₇	—	8	2	no	—
589	C₂×C₄₇	—	8	2	no	—
590	C₂×C₄₇	D₄×#41	1	1	yes	characteristic
591	C₂×C₄₇	C₂×#576	1	1	yes	characteristic
592	C₂×C₄₇	C₂×#576	1	1	yes	characteristic
593	D₄₇	—	4	1	no	—
594	D₄₇	—	8	2	no	—
595	C₂²×D₈	—	47	1	no	—
596	C₂²×D₈	C₂×D₄₇	1	1	yes	characteristic
597	C₂²×D₈	C₂×D₄₇	1	1	yes	characteristic
598	#555	—	47	2	no	—
599	#554	—	47	2	no	—
600	#553	—	47	2	no	—
601	#553	—	47	2	no	—
602	#553	—	94	2	no	—
603	#550	—	47	2	no	—
604	#546	—	94	2	no	—
605	#546	—	94	2	no	—
606	#546	—	94	2	no	—
607	D₄²	—	47	2	no	—
608	D₄²	—	47	2	no	—
609	D₄²	C₂×D₄₇	1	2	yes	complemented
610	#540	—	47	2	no	—
611	#540	—	47	2	no	—
612	#538	—	94	2	no	—
613	#538	—	94	2	no	—
614	#532	—	47	2	no	—
615	#529	—	47	1	no	—
616	#525	—	94	2	no	—
617	C₂×#121	—	94	2	no	—
618	#518	—	47	2	no	—
619	#518	—	47	2	no	—
620	C₂×C₄×D₄	—	47	2	no	—
621	#500	—	47	1	no	—
622	#499	—	47	1	no	—
623	#499	—	47	1	no	—
624	#493	—	47	1	no	—
625	#493	—	47	1	no	—
626	#493	C₂×D₄₇	1	1	yes	characteristic, complemented
627	#490	—	47	2	no	—
628	#490	—	47	2	no	—
629	#486	—	47	2	no	—
630	#482	—	47	2	no	—
631	#482	—	47	2	no	—
632	#482	—	47	2	no	—
633	#482	—	47	2	no	—
634	#481	—	47	2	no	—
635	#481	—	47	2	no	—
636	#478	—	47	2	no	—
637	#478	—	47	2	no	—
638	#478	—	47	2	no	—
639	#478	—	47	2	no	—
640	#476	—	47	2	no	—
641	#476	—	47	2	no	—
642	#469	—	47	2	no	—
643	#469	—	47	2	no	—
644	#466	—	47	1	no	—
645	#466	—	47	1	no	—
646	#466	—	47	1	no	—
647	#466	—	47	1	no	—
648	#466	—	47	2	no	—
649	#466	C₂×D₄₇	1	1	yes	characteristic, complemented
650	#466	C₂×D₄₇	1	1	yes	characteristic, complemented
651	#459	—	47	2	no	—
652	#459	—	47	2	no	—
653	#459	—	47	2	no	—
654	#459	—	47	2	no	—
655	#459	—	47	2	no	—
656	#459	C₂×D₄₇	1	2	yes	complemented
657	#447	—	47	2	no	—
658	#447	—	47	2	no	—
659	#447	—	47	2	no	—
660	#447	—	47	2	no	—
661	#447	C₂×D₄₇	1	2	yes	complemented
662	#447	C₂×D₄₇	1	2	yes	complemented
663	#446	—	47	1	no	—
664	C₈×Q₈	—	47	1	no	—
665	#442	—	47	2	no	—
666	#442	—	47	2	no	—
667	#442	—	47	2	no	—
668	#442	—	47	2	no	—
669	#442	—	47	2	no	—
670	#442	—	47	2	no	—
671	C₄×D₈	—	47	1	no	—
672	C₄×D₈	—	47	1	no	—
673	C₄×D₈	—	47	2	no	—
674	C₄×D₈	—	47	2	no	—
675	C₄×D₈	—	47	1	no	—
676	C₄×D₈	—	47	1	no	—
677	C₄×D₈	—	47	1	no	—
678	C₄×D₈	—	47	1	no	—
679	C₄×D₈	—	47	1	no	—
680	C₄×D₈	—	47	1	no	—
681	C₄×D₈	—	47	2	no	—
682	C₄×D₈	—	47	1	no	—
683	C₄×D₈	C₂×D₄₇	1	1	yes	characteristic
684	#436	—	47	1	no	—
685	#435	—	47	1	no	—
686	#435	—	47	1	no	—
687	C₈×D₄	—	47	1	no	—
688	C₈×D₄	—	47	1	no	—
689	C₈×D₄	C₂×D₄₇	1	1	yes	characteristic, complemented
690	#433	—	47	1	no	—
691	#433	—	47	1	no	—
692	#432	—	47	1	no	—
693	#427	—	47	1	no	—
694	#427	—	47	1	no	—
695	C₂×#107	—	47	1	no	—
696	#418	—	47	2	no	—
697	#418	—	47	2	no	—
698	C₂×#102	—	47	2	no	—
699	#405	—	47	1	no	—
700	#405	—	47	1	no	—
701	C₂×C₄×C₈	—	47	1	no	—
702	C₄₇	#61480	1	1	yes	characteristic, complemented, Sylow
703	C₂×#41	—	94	2	no	—
704	C₂×#41	—	94	2	no	—
705	C₂²×D₄	—	2	2	no	—
706	C₂²×D₄	—	47	2	no	—
707	C₂²×D₄	—	94	2	no	—
708	C₂²×D₄	—	94	2	no	—
709	C₂²×D₄	C₂²×D₄₇	1	2	yes	—
710	C₂²×D₄	C₂²×D₄₇	1	2	yes	—
711	C₂³×C₄	—	94	2	no	—
712	C₂×D₈	—	2	4	no	—
713	C₂×D₈	—	2	4	no	—
714	C₂×D₈	—	47	2	no	—
715	C₂×D₈	—	47	2	no	—
716	C₂×D₈	—	47	2	no	—
717	C₂×D₈	—	47	1	no	—
718	C₂×D₈	—	94	4	no	—
719	C₂×D₈	C₂²×D₄₇	1	2	yes	—
720	C₂×D₈	C₂²×D₄₇	1	1	yes	characteristic
721	C₂×D₈	C₂²×D₄₇	1	1	yes	characteristic
722	C₂×D₈	C₂²×D₄₇	1	2	yes	—
723	C₂×D₈	C₂²×D₄₇	1	2	yes	—
724	C₂×D₈	C₂²×D₄₇	1	1	yes	characteristic
725	C₂×M₁₆	—	47	1	no	—
726	C₂×M₁₆	—	47	1	no	—
727	C₂²×C₈	—	47	1	no	—
728	C₂²×C₈	—	47	1	no	—
729	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
730	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
731	C₄⋊Q₈	—	47	2	no	—
732	#127	—	47	2	no	—
733	#127	—	47	2	no	—
734	#127	C₂²×D₄₇	1	2	yes	—
735	#126	—	47	1	no	—
736	#126	—	47	1	no	—
737	#126	—	94	2	no	—
738	#126	—	94	2	no	—
739	#125	—	47	1	no	—
740	#125	—	47	2	no	—
741	#125	—	47	2	no	—
742	#124	—	47	1	no	—
743	#124	—	94	2	no	—
744	#124	—	94	2	no	—
745	#124	—	94	2	no	—
746	#123	—	47	1	no	—
747	#123	—	47	1	no	—
748	#123	—	94	2	no	—
749	#123	—	94	2	no	—
750	#123	—	94	2	no	—
751	#123	—	94	2	no	—
752	#123	—	94	2	no	—
753	#123	—	94	2	no	—
754	C₂²⋊Q₈	—	47	1	no	—
755	C₂²⋊Q₈	—	94	2	no	—
756	C₂²⋊Q₈	—	94	2	no	—
757	C₂²⋊Q₈	—	94	2	no	—
758	#121	—	2	2	no	—
759	#121	—	47	1	no	—
760	#121	—	47	2	no	—
761	#121	—	47	2	no	—
762	#121	—	47	2	no	—
763	#121	—	47	2	no	—
764	#121	—	94	2	no	—
765	#121	—	94	2	no	—
766	#121	—	94	2	no	—
767	#121	—	94	2	no	—
768	#121	—	94	2	no	—
769	#121	—	94	2	no	—
770	#121	—	94	2	no	—
771	#121	—	94	2	no	—
772	#121	—	94	2	no	—
773	#121	—	94	2	no	—
774	#121	—	94	2	no	—
775	#121	—	94	2	no	—
776	#121	—	94	2	no	—
777	#121	C₂²×D₄₇	1	2	yes	—
778	#121	C₂²×D₄₇	1	2	yes	—
779	#120	—	2	2	no	—
780	#120	—	2	2	no	—
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×D₄	—	47	1	no	—
787	C₄×D₄	—	47	1	no	—
788	C₄×D₄	—	47	2	no	—
789	C₄×D₄	—	47	2	no	—
790	C₄×D₄	—	47	2	no	—
791	C₄×D₄	—	47	2	no	—
792	C₄×D₄	—	47	2	no	—
793	C₄×D₄	—	47	2	no	—
794	C₄×D₄	—	47	2	no	—
795	C₄×D₄	—	47	2	no	—
796	C₄×D₄	—	47	2	no	—
797	C₄×D₄	—	94	2	no	—
798	C₄×D₄	—	94	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	C₂²×D₄₇	1	2	yes	—
807	C₄×D₄	C₂²×D₄₇	1	1	yes	characteristic
808	#117	—	47	1	no	—
809	#117	—	47	1	no	—
810	#117	—	47	2	no	—
811	#117	—	47	2	no	—
812	#117	—	94	2	no	—
813	C₂×C₄⋊C₄	—	47	2	no	—
814	C₂×C₄⋊C₄	—	94	2	no	—
815	C₂×C₂²⋊C₄	—	94	2	no	—
816	C₂×C₂²⋊C₄	—	94	2	no	—
817	C₂×C₂²⋊C₄	—	94	2	no	—
818	C₂×C₂²⋊C₄	—	94	2	no	—
819	C₂×C₂²⋊C₄	—	94	2	no	—
820	C₂×C₄²	—	47	1	no	—
821	#107	—	47	1	no	—
822	#107	—	47	1	no	—
823	#107	—	47	2	no	—
824	#107	—	47	1	no	—
825	#107	—	47	2	no	—
826	#107	C₂²×D₄₇	1	1	yes	characteristic
827	#106	—	47	2	no	—
828	#106	—	47	2	no	—
829	#106	—	47	2	no	—
830	#106	—	47	2	no	—
831	C₄⋊C₈	—	47	1	no	—
832	C₄⋊C₈	—	47	1	no	—
833	C₄⋊C₈	—	47	1	no	—
834	C₄⋊C₈	—	47	1	no	—
835	C₄⋊C₈	—	47	1	no	—
836	C₄⋊C₈	C₂²×D₄₇	1	1	yes	characteristic
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	—	47	2	no	—
845	#102	—	47	2	no	—
846	#102	—	47	2	no	—
847	#102	—	47	2	no	—
848	#102	—	47	2	no	—
849	#102	—	47	2	no	—
850	#102	C₂²×D₄₇	1	2	yes	—
851	#102	C₂²×D₄₇	1	2	yes	—
852	#102	C₂²×D₄₇	1	2	yes	—
853	C₂²⋊C₈	—	47	1	no	—
854	C₂²⋊C₈	—	47	1	no	—
855	C₂²⋊C₈	—	47	1	no	—
856	C₂²⋊C₈	—	47	1	no	—
857	C₂²⋊C₈	C₂²×D₄₇	1	1	yes	characteristic
858	C₂²⋊C₈	C₂²×D₄₇	1	1	yes	characteristic
859	#97	—	47	1	no	—
860	#97	—	47	1	no	—
861	#97	—	47	1	no	—
862	#97	—	47	1	no	—
863	C₄×C₈	—	47	1	no	—
864	C₄×C₈	—	47	1	no	—
865	C₄×C₈	—	47	1	no	—
866	C₄×C₈	—	47	1	no	—
867	C₄×C₈	—	47	1	no	—
868	C₄×C₈	C₂²×D₄₇	1	1	yes	characteristic
869	C₂⁴	—	2	2	no	—
870	C₂⁴	—	2	2	no	—
871	C₂⁴	—	94	2	no	—
872	#41	—	376	4	no	—
873	#41	—	376	4	no	—
874	C₂×Q₈	—	47	1	no	—
875	C₂×Q₈	—	94	2	no	—
876	C₂×D₄	—	2	4	no	—
877	C₂×D₄	—	2	4	no	—
878	C₂×D₄	—	2	2	no	—
879	C₂×D₄	—	2	2	no	—
880	C₂×D₄	—	2	2	no	—
881	C₂×D₄	—	2	2	no	—
882	C₂×D₄	—	2	2	no	—
883	C₂×D₄	—	2	2	no	—
884	C₂×D₄	—	4	2	no	—
885	C₂×D₄	—	4	2	no	—
886	C₂×D₄	—	8	4	no	—
887	C₂×D₄	—	47	1	no	—
888	C₂×D₄	—	47	1	no	—
889	C₂×D₄	—	47	2	no	—
890	C₂×D₄	—	94	2	no	—
891	C₂×D₄	—	94	2	no	—
892	C₂×D₄	—	94	2	no	—
893	C₂×D₄	—	94	2	no	—
894	C₂×D₄	—	94	2	no	—
895	C₂×D₄	—	94	4	no	—
896	C₂×D₄	—	94	2	no	—
897	C₂×D₄	—	94	2	no	—
898	C₂×D₄	—	94	2	no	—
899	C₂×D₄	—	94	2	no	—
900	C₂×D₄	—	376	4	no	—
901	C₂×D₄	—	376	4	no	—
902	C₂×D₄	—	188	2	no	—
903	C₂×D₄	D₄×D₄₇	1	1	yes	characteristic
904	C₂×D₄	C₂³×D₄₇	1	2	yes	—
905	C₂×D₄	C₂³×D₄₇	1	2	yes	—
906	C₂×D₄	C₂³×D₄₇	1	2	yes	—
907	C₂²×C₄	—	2	2	no	—
908	C₂²×C₄	—	47	1	no	—
909	C₂²×C₄	—	47	1	no	—
910	C₂²×C₄	—	47	1	no	—
911	C₂²×C₄	—	94	2	no	—
912	C₂²×C₄	—	94	2	no	—
913	C₂²×C₄	—	94	2	no	—
914	C₂²×C₄	—	94	2	no	—
915	C₂²×C₄	—	94	2	no	—
916	C₂²×C₄	—	94	2	no	—
917	C₂²×C₄	—	94	2	no	—
918	C₂²×C₄	—	94	2	no	—
919	C₂²×C₄	—	94	2	no	—
920	C₂²×C₄	—	94	2	no	—
921	C₂²×C₄	—	376	4	no	—
922	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
923	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
924	D₈	—	2	4	no	—
925	D₈	—	2	4	no	—
926	D₈	—	2	2	no	—
927	D₈	—	2	2	no	—
928	D₈	—	4	2	no	—
929	D₈	—	94	4	no	—
930	D₈	—	94	2	no	—
931	D₈	—	188	2	no	—
932	D₈	—	188	2	no	—
933	D₈	#10625352	1	4	yes	complemented
934	M₁₆	—	188	1	no	—
935	M₁₆	—	188	1	no	—
936	C₂×C₈	—	2	2	no	—
937	C₂×C₈	—	2	2	no	—
938	C₂×C₈	—	47	1	no	—
939	C₂×C₈	—	47	1	no	—
940	C₂×C₈	—	47	1	no	—
941	C₂×C₈	—	47	1	no	—
942	C₂×C₈	—	94	2	no	—
943	C₂×C₈	—	188	1	no	—
944	C₂×C₈	C₂³×D₄₇	1	1	yes	characteristic
945	C₂×C₈	C₂³×D₄₇	1	1	yes	characteristic
946	C₂×C₈	C₂³×D₄₇	1	1	yes	characteristic
947	C₂×C₈	C₂³×D₄₇	1	1	yes	characteristic
948	C₄⋊C₄	—	47	1	no	—
949	C₄⋊C₄	—	47	1	no	—
950	C₄⋊C₄	—	47	1	no	—
951	C₄⋊C₄	—	47	1	no	—
952	C₄⋊C₄	—	47	1	no	—
953	C₄⋊C₄	—	47	1	no	—
954	C₄⋊C₄	—	47	1	no	—
955	C₄⋊C₄	—	47	1	no	—
956	C₄⋊C₄	—	47	1	no	—
957	C₄⋊C₄	—	47	2	no	—
958	C₄⋊C₄	—	47	2	no	—
959	C₄⋊C₄	—	47	2	no	—
960	C₄⋊C₄	—	94	2	no	—
961	C₄⋊C₄	—	94	2	no	—
962	C₄⋊C₄	—	94	2	no	—
963	C₄⋊C₄	—	94	2	no	—
964	C₄⋊C₄	—	94	2	no	—
965	C₄⋊C₄	—	94	2	no	—
966	C₄⋊C₄	D₄×D₄₇	1	1	yes	characteristic
967	C₄⋊C₄	C₂³×D₄₇	1	2	yes	—
968	C₂²⋊C₄	—	2	2	no	—
969	C₂²⋊C₄	—	2	2	no	—
970	C₂²⋊C₄	—	2	2	no	—
971	C₂²⋊C₄	—	47	1	no	—
972	C₂²⋊C₄	—	47	1	no	—
973	C₂²⋊C₄	—	47	1	no	—
974	C₂²⋊C₄	—	47	1	no	—
975	C₂²⋊C₄	—	47	1	no	—
976	C₂²⋊C₄	—	47	1	no	—
977	C₂²⋊C₄	—	47	1	no	—
978	C₂²⋊C₄	—	47	1	no	—
979	C₂²⋊C₄	—	94	2	no	—
980	C₂²⋊C₄	—	94	2	no	—
981	C₂²⋊C₄	—	94	2	no	—
982	C₂²⋊C₄	—	94	2	no	—
983	C₂²⋊C₄	—	94	2	no	—
984	C₂²⋊C₄	—	94	2	no	—
985	C₂²⋊C₄	—	94	2	no	—
986	C₂²⋊C₄	—	94	2	no	—
987	C₂²⋊C₄	—	94	2	no	—
988	C₂²⋊C₄	—	94	2	no	—
989	C₂²⋊C₄	—	94	2	no	—
990	C₂²⋊C₄	—	94	2	no	—
991	C₂²⋊C₄	—	94	2	no	—
992	C₂²⋊C₄	—	94	2	no	—
993	C₂²⋊C₄	—	94	2	no	—
994	C₂²⋊C₄	D₄×D₄₇	1	1	yes	characteristic
995	C₂²⋊C₄	D₄×D₄₇	1	1	yes	characteristic
996	C₄²	—	47	1	no	—
997	C₄²	—	47	1	no	—
998	C₄²	—	47	1	no	—
999	C₄²	—	47	1	no	—
1000	C₄²	—	47	1	no	—
1001	C₄²	—	94	2	no	—
1002	C₄²	—	94	2	no	—
1003	C₄²	C₂³×D₄₇	1	1	yes	characteristic
1004	C₂³	—	2	2	no	—
1005	C₂³	—	2	2	no	—
1006	C₂³	—	2	2	no	—
1007	C₂³	—	4	4	no	—
1008	C₂³	—	4	4	no	—
1009	C₂³	—	4	4	no	—
1010	C₂³	—	8	2	no	—
1011	C₂³	—	8	2	no	—
1012	C₂³	—	8	2	no	—
1013	C₂³	—	47	1	no	—
1014	C₂³	—	94	2	no	—
1015	C₂³	—	376	2	no	—
1016	C₂³	—	376	2	no	—
1017	C₂³	—	188	4	no	—
1018	C₂³	C₂×D₄×D₄₇	1	1	yes	characteristic
1019	C₂³	C₂×D₄×D₄₇	1	1	yes	characteristic
1020	Q₈	—	94	2	no	—
1021	Q₈	—	376	2	no	—
1022	D₄	—	2	2	no	—
1023	D₄	—	2	2	no	—
1024	D₄	—	2	2	no	—
1025	D₄	—	2	2	no	—
1026	D₄	—	2	2	no	—
1027	D₄	—	2	2	no	—
1028	D₄	—	4	4	no	—
1029	D₄	—	4	4	no	—
1030	D₄	—	4	4	no	—
1031	D₄	—	8	2	no	—
1032	D₄	—	8	2	no	—
1033	D₄	—	8	2	no	—
1034	D₄	—	94	2	no	—
1035	D₄	—	94	2	no	—
1036	D₄	—	94	2	no	—
1037	D₄	—	94	2	no	—
1038	D₄	—	376	2	no	—
1039	D₄	—	376	2	no	—
1040	D₄	—	376	2	no	—
1041	D₄	—	376	2	no	—
1042	D₄	—	376	2	no	—
1043	D₄	—	376	2	no	—
1044	D₄	—	188	4	no	—
1045	D₄	—	188	4	no	—
1046	D₄	—	188	4	no	—
1047	D₄	C₂×#10625352	1	4	yes	—
1048	C₂×C₄	—	2	1	no	—
1049	C₂×C₄	—	2	1	no	—
1050	C₂×C₄	—	2	1	no	—
1051	C₂×C₄	—	2	1	no	—
1052	C₂×C₄	—	2	2	no	—
1053	C₂×C₄	—	8	2	no	—
1054	C₂×C₄	—	47	1	no	—
1055	C₂×C₄	—	47	1	no	—
1056	C₂×C₄	—	47	1	no	—
1057	C₂×C₄	—	47	1	no	—
1058	C₂×C₄	—	47	1	no	—
1059	C₂×C₄	—	47	1	no	—
1060	C₂×C₄	—	47	1	no	—
1061	C₂×C₄	—	94	2	no	—
1062	C₂×C₄	—	94	2	no	—
1063	C₂×C₄	—	94	1	no	—
1064	C₂×C₄	—	94	1	no	—
1065	C₂×C₄	—	94	2	no	—
1066	C₂×C₄	—	94	2	no	—
1067	C₂×C₄	—	94	2	no	—
1068	C₂×C₄	—	376	2	no	—
1069	C₂×C₄	—	376	2	no	—
1070	C₂×C₄	—	376	2	no	—
1071	C₂×C₄	—	376	2	no	—
1072	C₂×C₄	—	376	2	no	—
1073	C₂×C₄	—	376	2	no	—
1074	C₂×C₄	—	376	2	no	—
1075	C₂×C₄	—	376	2	no	—
1076	C₂×C₄	—	188	4	no	—
1077	C₂×C₄	—	188	4	no	—
1078	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
1079	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
1080	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
1081	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
1082	C₂×C₄	C₂⁴×D₄₇	1	1	yes	characteristic
1083	C₈	—	2	1	no	—
1084	C₈	—	2	1	no	—
1085	C₈	—	2	1	no	—
1086	C₈	—	94	1	no	—
1087	C₈	—	94	1	no	—
1088	C₈	—	94	1	no	—
1089	C₈	—	94	1	no	—
1090	C₈	C₂×#10625352	1	2	yes	—
1091	C₂²	—	2	1	no	—
1092	C₂²	—	2	1	no	—
1093	C₂²	—	2	1	no	—
1094	C₂²	—	2	1	no	—
1095	C₂²	—	2	1	no	—
1096	C₂²	—	2	4	no	—
1097	C₂²	—	4	2	no	—
1098	C₂²	—	4	2	no	—
1099	C₂²	—	4	2	no	—
1100	C₂²	—	4	2	no	—
1101	C₂²	—	4	2	no	—
1102	C₂²	—	4	2	no	—
1103	C₂²	—	4	2	no	—
1104	C₂²	—	4	2	no	—
1105	C₂²	—	8	8	no	—
1106	C₂²	—	16	4	no	—
1107	C₂²	—	94	1	no	—
1108	C₂²	—	94	1	no	—
1109	C₂²	—	94	1	no	—
1110	C₂²	—	188	2	no	—
1111	C₂²	—	188	2	no	—
1112	C₂²	—	188	2	no	—
1113	C₂²	—	752	4	no	—
1114	C₂²	#15689924	1	2	yes	—
1115	C₂²	C₂²×D₄×D₄₇	1	1	yes	characteristic
1116	C₄	—	2	1	no	—
1117	C₄	—	2	1	no	—
1118	C₄	—	2	1	no	—
1119	C₄	—	2	1	no	—
1120	C₄	—	4	2	no	—
1121	C₄	—	47	2	no	—
1122	C₄	—	94	1	no	—
1123	C₄	—	94	1	no	—
1124	C₄	—	94	1	no	—
1125	C₄	—	94	1	no	—
1126	C₄	—	94	1	no	—
1127	C₄	—	94	1	no	—
1128	C₄	—	188	2	no	—
1129	C₄	—	188	2	no	—
1130	C₄	—	188	2	no	—
1131	C₄	C₂²×#10625352	1	1	yes	characteristic
1132	C₄	#15689958	1	1	yes	characteristic
1133	C₂	—	2	2	no	—
1134	C₂	—	4	1	no	—
1135	C₂	—	4	4	no	—
1136	C₂	—	8	2	no	—
1137	C₂	—	8	2	no	—
1138	C₂	—	376	2	no	—
1139	C₂	—	188	1	no	—
1140	C₂	D₄×#10625352	1	1	yes	characteristic
1141	C₂	#576×D₄₇	1	1	yes	characteristic
1142	C₂	C₂×#15689924	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂²×D₄×D₄₇
commutator, cosocle	C₂×C₄×C₄₇	C₂⁵
Frattini	C₂×C₄	C₂⁴×D₄₇
Fitting	D₄×D₈×C₄₇	C₂
socle	C₂²×C₄₇	C₂³×D₄
hypercenter	D₄×D₈	D₄₇
hypocenter	C₄₇	#61480
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₄×D₄ ◁ D₄×D₈

Complements

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

N	H ≅ G/N	type
1. #20257407	C₂	semidirect
2. #20256361	C₂	semidirect
3. #20256255	C₂	semidirect
4. #20256090	C₂	semidirect
5. #20255807	C₂	semidirect
6. #20255793	C₂	semidirect
7. #20255791	C₂	semidirect
8. #20255623	C₂	semidirect
9. #20255533	C₂	semidirect
10. #20255529	C₂	semidirect
11. D₈×C₂²⋊D₄₇	C₂	semidirect
12. D₈×C₂²⋊D₄₇	C₂	semidirect
13. #20254035	C₂	semidirect
14. #20254031	C₂	semidirect
15. #20253962	C₂	semidirect
16. #20253629	C₂	semidirect
17. #20253625	C₂	semidirect
18. #20253474	C₂	semidirect
19. #20252356	C₂	semidirect
20. #20252240	C₂	semidirect
21. #20252235	C₂	semidirect
22. C₂×D₈×Dic₄₇	C₂	semidirect
23. D₄×D₈×C₄₇	C₂	semidirect
25. #15689837	C₂²	semidirect
26. #15689832	C₂²	semidirect
27. #15689825	C₂²	semidirect
28. #15689819	C₂²	semidirect
30. #15689793	C₂²	semidirect
34. D₄×C₂²⋊D₄₇	C₂²	semidirect
35. D₄×C₂²⋊D₄₇	C₂²	semidirect
36. #15689727	C₂²	semidirect
37. #15689726	C₂²	semidirect
40. #15689668	C₂²	semidirect
44. #15689598	C₂²	semidirect
45. #15689595	C₂²	semidirect
46. C₂×D₄×Dic₄₇	C₂²	semidirect
47. #15689527	C₂²	semidirect
48. #15689525	C₂²	semidirect
49. #15689524	C₂²	semidirect
50. #15689498	C₂²	semidirect
51. #15689498	C₂²	semidirect
52. #15689487	C₂²	semidirect
53. #15689486	C₂²	semidirect
54. #15689468	C₂²	semidirect
55. #15689448	C₂²	semidirect
56. #15689446	C₂²	semidirect
57. #15689445	C₂²	semidirect
58. #15689444	C₂²	semidirect
59. #15689442	C₂²	semidirect
60. #15689439	C₂²	semidirect
61. #15689425	C₂²	semidirect
62. #15689424	C₂²	semidirect
63. #15689423	C₂²	semidirect
64. #15689421	C₂²	semidirect
65. #15689411	C₂²	semidirect
66. #15689411	C₂²	semidirect
67. #15689374	C₂²	semidirect
68. #15689373	C₂²	semidirect
69. #15689359	C₂²	semidirect
70. #15689359	C₂²	semidirect
71. #15689357	C₂²	semidirect
72. #15689356	C₂²	semidirect
73. #15689356	C₂²	semidirect
74. #15689316	C₂²	semidirect
75. #15689316	C₂²	semidirect
76. #15689316	C₂²	semidirect
77. #15689316	C₂²	semidirect
78. #15689315	C₂²	semidirect
79. #15689257	C₂²	semidirect
80. #15689257	C₂²	semidirect
81. #15689255	C₂²	semidirect
82. #15689255	C₂²	semidirect
83. #15689252	C₂²	semidirect
84. C₈×Dic₉₄	C₂²	semidirect
85. #15689235	C₂²	semidirect
86. #15689235	C₂²	semidirect
87. #15689235	C₂²	semidirect
88. #15689233	C₂²	semidirect
89. #15689232	C₂²	semidirect
90. #15689232	C₂²	semidirect
91. C₄×D₃₇₆	C₂²	semidirect
95. D₈×Dic₄₇	C₂²	semidirect
96. D₈×Dic₄₇	C₂²	semidirect
97. D₈×Dic₄₇	C₂²	semidirect
98. D₈×Dic₄₇	C₂²	semidirect
99. D₈×Dic₄₇	C₂²	semidirect
100. D₈×Dic₄₇	C₂²	semidirect
101. #15689205	C₂²	semidirect
102. #15689203	C₂²	semidirect
103. #15689198	C₂²	semidirect
104. #15689195	C₂²	semidirect
105. #15689191	C₂²	semidirect
106. C₈×C₂²⋊D₄₇	C₂²	semidirect
107. C₈×C₂²⋊D₄₇	C₂²	semidirect
108. #15689183	C₂²	semidirect
109. #15689181	C₂²	semidirect
110. #15689177	C₂²	semidirect
111. #15689161	C₂²	semidirect
112. #15689160	C₂²	semidirect
113. C₂×#13093958	C₂²	semidirect
114. #15689128	C₂²	semidirect
115. #15689126	C₂²	semidirect
116. C₂×#13093945	C₂²	semidirect
117. #15689078	C₂²	semidirect
118. #15689077	C₂²	semidirect
119. C₂×C₈×Dic₄₇	C₂²	semidirect
122. D₄²×C₄₇	C₂²	semidirect
123. C₄₇×#493	C₂²	semidirect
124. C₄₇×#466	C₂²	semidirect
125. C₄₇×#466	C₂²	semidirect
126. C₄₇×#459	C₂²	semidirect
127. C₄₇×#447	C₂²	semidirect
128. C₄₇×#447	C₂²	semidirect
130. C₈×D₄×C₄₇	C₂²	semidirect
357. D₈×C₄₇	#41	semidirect
574. D₄×D₈	D₄₇	semidirect
609. D₄²	C₂×D₄₇	semidirect
626. #493	C₂×D₄₇	semidirect
649. #466	C₂×D₄₇	semidirect
650. #466	C₂×D₄₇	semidirect
656. #459	C₂×D₄₇	semidirect
661. #447	C₂×D₄₇	semidirect
662. #447	C₂×D₄₇	semidirect
689. C₈×D₄	C₂×D₄₇	semidirect
702. C₄₇	#61480	semidirect
933. D₈	#10625352	semidirect

Maximal subgroups

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

subgroup	index
#20257407	2
#20256361	2
#20256255	2
#20256090	2
#20255807	2
#20255793	2
#20255791	2
#20255623	2
#20255533	2
#20255529	2
D₈×C₂²⋊D₄₇	2
#20254035	2
#20254031	2
#20253962	2
#20253629	2
#20253625	2
#20253474	2
#20252356	2
#20252240	2
#20252235	2
C₂×D₈×Dic₄₇	2
D₄×D₈×C₄₇	2
#61480	47