Subgroups — #27083948

Order 12032.

2054 conjugacy classes of subgroups.

The subgroup lattice has 1140 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20257209	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄×#13094070	C₂	1	1	yes	maximal, characteristic
3	#20253248	C₂	1	1	yes	maximal, characteristic, complemented
4	#20253247	C₂	1	2	yes	maximal, complemented
5	#20253237	C₂	1	1	yes	maximal, characteristic, complemented
6	#20253236	C₂	1	2	yes	maximal, complemented
7	#20253222	C₂	1	1	yes	maximal, characteristic, complemented
8	#20253222	C₂	1	1	yes	maximal, characteristic, complemented
9	#20253214	C₂	1	2	yes	maximal, complemented
10	#20253212	C₂	1	2	yes	maximal, complemented
11	#20253210	C₂	1	1	yes	maximal, characteristic, complemented
12	#20253207	C₂	1	2	yes	maximal, complemented
13	#20253183	C₂	1	2	yes	maximal, complemented
14	#20253181	C₂	1	1	yes	maximal, characteristic, complemented
15	#20253175	C₂	1	2	yes	maximal, complemented
16	C₂×#15689424	C₂	1	1	yes	maximal, characteristic, complemented
17	#478×D₄₇	C₂	1	2	yes	maximal, complemented
18	#20251985	C₂	1	1	yes	maximal, characteristic, complemented
19	#20251980	C₂	1	1	yes	maximal, characteristic, complemented
20	#20251953	C₂	1	1	yes	maximal, characteristic, complemented
21	#20251910	C₂	1	1	yes	maximal, characteristic
22	#20251910	C₂	1	1	yes	maximal, characteristic
23	C₄₇×#3076	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#13094070	C₂²	1	1	yes	characteristic
25	C₂×#13094030	C₂²	1	1	yes	characteristic
26	C₂×#13094030	C₂²	1	1	yes	characteristic
27	#15689851	—	2	1	no	—
28	#15689851	—	2	1	no	—
29	#15689833	—	2	1	no	—
30	#15689833	—	2	1	no	—
31	#15689827	—	2	2	no	—
32	#15689827	—	2	2	no	—
33	#15689751	C₂²	1	1	yes	characteristic, complemented
34	#15689751	C₂²	1	1	yes	characteristic, complemented
35	#15689750	C₂²	1	2	yes	complemented
36	#15689750	C₂²	1	2	yes	complemented
37	#15689679	C₂²	1	2	yes	complemented
38	C₂×#13094016	C₂²	1	1	yes	characteristic, complemented
39	#125×D₄₇	C₂²	1	2	yes	complemented
40	#15689606	C₂²	1	1	yes	characteristic
41	#15689605	C₂²	1	2	yes	—
42	#15689603	—	2	1	no	—
43	#15689603	C₂²	1	1	yes	characteristic
44	#15689603	C₂²	1	1	yes	characteristic
45	#15689603	C₂²	1	1	yes	characteristic
46	#15689597	—	2	1	no	—
47	#15689597	C₂²	1	1	yes	characteristic
48	#15689595	—	2	2	no	—
49	#15689595	C₂²	1	2	yes	—
50	C₄×#10625354	C₂²	1	2	yes	—
51	C₄×#10625350	—	2	1	no	—
52	C₄×#10625350	C₂²	1	1	yes	characteristic
53	C₂×C₄×D₁₈₈	—	2	1	no	—
54	C₂×C₄×D₁₈₈	C₂²	1	1	yes	characteristic
55	C₄×D₄×D₄₇	—	2	2	no	—
56	C₄×D₄×D₄₇	C₂²	1	2	yes	—
57	#15689432	C₂²	1	2	yes	complemented
58	#15689430	C₂²	1	2	yes	complemented
59	#15689430	C₂²	1	2	yes	complemented
60	#15689428	C₂²	1	2	yes	complemented
61	#15689426	C₂²	1	2	yes	complemented
62	#15689426	C₂²	1	2	yes	complemented
63	#15689425	C₂²	1	2	yes	complemented
64	#15689424	C₂²	1	2	yes	complemented
65	#15689424	C₂²	1	2	yes	complemented
66	#15689424	C₂²	1	2	yes	complemented
67	#15689424	C₂²	1	2	yes	complemented
68	#15689423	C₂²	1	2	yes	complemented
69	#15689423	C₂²	1	2	yes	complemented
70	#15689422	C₂²	1	2	yes	complemented
71	#15689422	C₂²	1	2	yes	complemented
72	#15689421	C₂²	1	2	yes	complemented
73	#15689420	C₂²	1	2	yes	complemented
74	#15689420	C₂²	1	2	yes	complemented
75	#15689416	C₂²	1	2	yes	complemented
76	#15689412	C₂²	1	2	yes	complemented
77	#15689412	C₂²	1	2	yes	complemented
78	#15689411	C₂²	1	2	yes	complemented
79	#15689410	C₂²	1	2	yes	complemented
80	#15689406	C₂²	1	2	yes	complemented
81	#15689402	C₂²	1	2	yes	complemented
82	#15689402	C₂²	1	2	yes	complemented
83	#15689401	C₂²	1	2	yes	complemented
84	#15689400	C₂²	1	2	yes	complemented
85	#15689166	C₂²	1	1	yes	characteristic, complemented
86	#15689166	C₂²	1	1	yes	characteristic, complemented
87	#15689166	C₂²	1	1	yes	characteristic, complemented
88	#15689166	C₂²	1	1	yes	characteristic, complemented
89	#15689164	C₂²	1	2	yes	complemented
90	#15689164	C₂²	1	2	yes	complemented
91	#15689162	C₂²	1	2	yes	complemented
92	#15689162	C₂²	1	2	yes	complemented
93	#15689160	C₂²	1	2	yes	complemented
94	#15689158	C₂²	1	2	yes	complemented
95	C₂×#13093958	C₂²	1	1	yes	characteristic, complemented
96	#107×D₄₇	C₂²	1	2	yes	complemented
97	C₂×#13093956	C₂²	1	1	yes	characteristic, complemented
98	#106×D₄₇	C₂²	1	2	yes	complemented
99	#15689149	C₂²	1	1	yes	characteristic, complemented
100	#15689149	C₂²	1	1	yes	characteristic, complemented
101	#15689148	C₂²	1	2	yes	complemented
102	#15689148	C₂²	1	2	yes	complemented
103	#15689147	C₂²	1	1	yes	characteristic, complemented
104	#15689145	C₂²	1	2	yes	complemented
105	C₄⋊C₈×D₄₇	C₂²	1	2	yes	complemented
106	#15689127	C₂²	1	1	yes	characteristic
107	#15689127	C₂²	1	1	yes	characteristic
108	#15689126	C₂²	1	2	yes	—
109	#15689126	C₂²	1	2	yes	—
110	#15689124	C₂²	1	1	yes	characteristic
111	#15689124	C₂²	1	1	yes	characteristic
112	#15689123	C₂²	1	2	yes	—
113	#15689123	C₂²	1	2	yes	—
114	#15689118	C₂²	1	2	yes	—
115	#15689118	C₂²	1	2	yes	—
116	C₂×#13093946	C₂²	1	1	yes	characteristic
117	C₂×#13093946	C₂²	1	1	yes	characteristic
118	#102×D₄₇	C₂²	1	2	yes	—
119	#102×D₄₇	C₂²	1	2	yes	—
120	C₄₇×#533	C₂²	1	1	yes	characteristic, complemented
121	C₄×#41×C₄₇	C₂²	1	1	yes	characteristic
122	C₄₇×#479	C₂²	1	1	yes	characteristic, complemented
123	C₄₇×#479	C₂²	1	1	yes	characteristic, complemented
124	C₄₇×#478	C₂²	1	1	yes	characteristic, complemented
125	C₄₇×#478	C₂²	1	1	yes	characteristic, complemented
126	C₄₇×#477	C₂²	1	1	yes	characteristic, complemented
127	C₄₇×#476	C₂²	1	1	yes	characteristic, complemented
128	C₄₇×#475	C₂²	1	1	yes	characteristic, complemented
129	C₄₇×#474	C₂²	1	1	yes	characteristic, complemented
130	C₄₇×#427	C₂²	1	1	yes	characteristic, complemented
131	C₄₇×#427	C₂²	1	1	yes	characteristic, complemented
132	C₂×C₄⋊C₈×C₄₇	C₂²	1	1	yes	characteristic, complemented
133	C₄₇×#416	C₂²	1	1	yes	characteristic
134	C₄₇×#416	C₂²	1	1	yes	characteristic
135	#13094070	—	2	4	no	—
136	#13094070	Q₈	1	8	yes	complemented
137	C₂×#10625354	C₂³	1	2	yes	—
138	C₂×#10625350	—	2	1	no	—
139	C₂×#10625350	C₂³	1	1	yes	characteristic
140	C₂²×D₁₈₈	—	2	1	no	—
141	C₂²×D₁₈₈	C₂³	1	1	yes	characteristic
142	C₂×D₄×D₄₇	—	2	2	no	—
143	C₂×D₄×D₄₇	C₂³	1	2	yes	—
144	C₂²×C₄×D₄₇	—	2	1	no	—
145	C₂²×C₄×D₄₇	—	2	2	no	—
146	#13094030	—	2	4	no	—
147	#13094030	—	2	4	no	—
148	C₂×#10625329	C₂³	1	1	yes	characteristic
149	C₂×#10625329	C₂³	1	1	yes	characteristic
150	C₂×#10625324	C₂³	1	2	yes	—
151	C₂×#10625324	C₂³	1	2	yes	—
152	C₂×C₈×D₄₇	C₂³	1	2	yes	—
153	C₂×C₈×D₄₇	C₂³	1	2	yes	—
154	#13094024	—	2	1	no	—
155	#13094024	—	2	1	no	—
156	#13094023	C₂³	1	2	yes	—
157	#13094023	C₂³	1	2	yes	—
158	#13094022	—	2	2	no	—
159	#13094022	—	2	2	no	—
160	#13094016	—	2	1	no	—
161	#13094016	—	2	1	no	—
162	#13094016	—	2	1	no	—
163	#13094016	—	2	1	no	—
164	#13094016	C₂³	1	2	yes	—
165	#13094016	C₂³	1	2	yes	—
166	#13094015	C₂³	1	2	yes	—
167	#13094015	C₂³	1	2	yes	—
168	#13094014	—	2	2	no	—
169	#13094014	—	2	2	no	—
170	#13094014	—	2	2	no	—
171	#13094014	—	2	2	no	—
172	#13094002	—	2	2	no	—
173	#13094002	—	2	2	no	—
174	#13094002	—	2	2	no	—
175	#13094002	—	2	2	no	—
176	#13094001	—	2	2	no	—
177	#13094001	—	2	2	no	—
178	#13094000	—	2	2	no	—
179	#13094000	—	2	2	no	—
180	Q₈×Dic₄₇	C₂³	1	2	yes	—
181	C₄×Dic₉₄	—	2	1	no	—
182	C₄×Dic₉₄	—	2	1	no	—
183	C₄×Dic₉₄	—	2	1	no	—
184	C₄×Dic₉₄	D₄	1	1	yes	characteristic
185	C₄×Dic₉₄	D₄	1	1	yes	characteristic
186	#13093989	—	2	2	no	—
187	#13093989	—	2	2	no	—
188	C₄×D₁₈₈	—	2	1	no	—
189	C₄×D₁₈₈	—	2	1	no	—
190	C₄×D₁₈₈	—	2	1	no	—
191	C₄×D₁₈₈	—	2	2	no	—
192	C₄×D₁₈₈	—	2	1	no	—
193	C₄×D₁₈₈	—	2	1	no	—
194	C₄×D₁₈₈	—	2	2	no	—
195	C₄×D₁₈₈	—	2	1	no	—
196	C₄×D₁₈₈	—	2	1	no	—
197	C₄×D₁₈₈	D₄	1	1	yes	characteristic
198	C₄×D₁₈₈	D₄	1	1	yes	characteristic
199	C₄×D₁₈₈	C₂³	1	2	yes	—
200	C₄×D₁₈₈	C₂³	1	2	yes	—
201	D₄×Dic₄₇	—	2	2	no	—
202	D₄×Dic₄₇	C₂³	1	2	yes	—
203	#13093986	—	2	2	no	—
204	#13093986	—	2	2	no	—
205	#13093986	C₂³	1	2	yes	—
206	#13093986	C₂³	1	2	yes	—
207	C₄×C₂²⋊D₄₇	—	2	2	no	—
208	C₄×C₂²⋊D₄₇	—	2	2	no	—
209	C₄×C₂²⋊D₄₇	D₄	1	2	yes	—
210	C₄×C₂²⋊D₄₇	D₄	1	2	yes	—
211	(C₂²⋊D₄₇)⋊C₄	—	2	2	no	—
212	(C₂²⋊D₄₇)⋊C₄	—	2	2	no	—
213	(C₂²⋊D₄₇)⋊C₄	—	2	2	no	—
214	(C₂²⋊D₄₇)⋊C₄	—	2	2	no	—
215	(C₂²⋊D₄₇)⋊C₄	—	2	2	no	—
216	#13093983	—	2	1	no	—
217	#13093983	C₂³	1	1	yes	characteristic
218	#13093982	—	2	2	no	—
219	#13093982	C₂³	1	2	yes	—
220	#13093982	C₂³	1	2	yes	—
221	#13093982	C₂³	1	2	yes	—
222	#13093981	—	2	2	no	—
223	#13093981	C₂³	1	2	yes	—
224	C₂×C₄⋊Dic₄₇	—	2	1	no	—
225	C₂×C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic
226	C₂×C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic
227	C₂×C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic
228	C₂×Dic₄₇⋊C₄	—	2	1	no	—
229	C₂×Dic₄₇⋊C₄	—	2	1	no	—
230	C₄⋊C₄×D₄₇	—	2	2	no	—
231	C₄⋊C₄×D₄₇	—	2	2	no	—
232	C₄⋊C₄×D₄₇	—	2	2	no	—
233	C₄⋊C₄×D₄₇	C₂³	1	2	yes	—
234	C₄⋊C₄×D₄₇	C₂³	1	2	yes	—
235	C₄⋊C₄×D₄₇	C₂³	1	2	yes	—
236	C₂×(C₂×D₄₇)⋊C₄	—	2	1	no	—
237	C₂×(C₂×D₄₇)⋊C₄	—	2	2	no	—
238	C₂²⋊C₄×D₄₇	—	2	2	no	—
239	C₂²⋊C₄×D₄₇	—	2	2	no	—
240	C₂²⋊C₄×D₄₇	—	2	2	no	—
241	C₄²×D₄₇	—	2	2	no	—
242	C₄²×D₄₇	C₂³	1	2	yes	—
243	#13093958	C₂³	1	2	yes	—
244	#13093958	C₂³	1	2	yes	—
245	#13093957	C₂³	1	2	yes	—
246	#13093957	C₂³	1	2	yes	—
247	#13093957	C₂³	1	2	yes	—
248	#13093957	C₂³	1	2	yes	—
249	#13093956	C₂³	1	2	yes	—
250	#13093956	C₂³	1	2	yes	—
251	#13093955	C₂³	1	2	yes	—
252	#13093955	C₂³	1	2	yes	—
253	#13093955	C₂³	1	2	yes	—
254	#13093955	C₂³	1	2	yes	—
255	C₄⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
256	C₄⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
257	Dic₄₇⋊C₈	C₂³	1	2	yes	—
258	Dic₄₇⋊C₈	C₂³	1	2	yes	—
259	Dic₄₇⋊C₈	C₂³	1	2	yes	—
260	Dic₄₇⋊C₈	C₂³	1	2	yes	—
261	#13093948	C₂³	1	2	yes	—
262	#13093948	C₂³	1	2	yes	—
263	#13093946	C₂³	1	2	yes	—
264	#13093946	C₂³	1	2	yes	—
265	#13093946	C₂³	1	2	yes	—
266	#13093946	C₂³	1	2	yes	—
267	#13093945	C₂³	1	2	yes	—
268	#13093945	C₂³	1	2	yes	—
269	#13093944	C₂³	1	2	yes	—
270	#13093944	C₂³	1	2	yes	—
271	#13093944	C₂³	1	2	yes	—
272	#13093944	C₂³	1	2	yes	—
273	C₂×#41×C₄₇	C₂³	1	1	yes	characteristic
274	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
275	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
276	C₄⋊Q₈×C₄₇	C₂³	1	1	yes	characteristic
277	C₄⋊Q₈×C₄₇	C₂³	1	1	yes	characteristic
278	#125×C₄₇	C₂³	1	1	yes	characteristic
279	#125×C₄₇	C₂³	1	1	yes	characteristic
280	C₂²⋊Q₈×C₄₇	—	2	1	no	—
281	C₂²⋊Q₈×C₄₇	—	2	1	no	—
282	C₄×Q₈×C₄₇	—	2	1	no	—
283	C₄×Q₈×C₄₇	—	2	1	no	—
284	C₄×Q₈×C₄₇	C₂³	1	1	yes	characteristic
285	C₄×Q₈×C₄₇	C₂³	1	1	yes	characteristic
286	C₄×D₄×C₄₇	—	2	1	no	—
287	C₄×D₄×C₄₇	—	2	1	no	—
288	C₄×D₄×C₄₇	C₂³	1	1	yes	characteristic
289	C₄×D₄×C₄₇	C₂³	1	1	yes	characteristic
290	#117×C₄₇	—	2	1	no	—
291	#117×C₄₇	C₂³	1	1	yes	characteristic
292	#117×C₄₇	C₂³	1	1	yes	characteristic
293	#117×C₄₇	C₂³	1	1	yes	characteristic
294	C₂×C₄²×C₄₇	—	2	1	no	—
295	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
296	#107×C₄₇	C₂³	1	1	yes	characteristic
297	#107×C₄₇	C₂³	1	1	yes	characteristic
298	#107×C₄₇	C₂³	1	1	yes	characteristic
299	#107×C₄₇	C₂³	1	1	yes	characteristic
300	#106×C₄₇	C₂³	1	1	yes	characteristic
301	#106×C₄₇	C₂³	1	1	yes	characteristic
302	#106×C₄₇	C₂³	1	1	yes	characteristic
303	#106×C₄₇	C₂³	1	1	yes	characteristic
304	C₄⋊C₈×C₄₇	C₂³	1	1	yes	characteristic
305	C₄⋊C₈×C₄₇	C₂³	1	1	yes	characteristic
306	C₄⋊C₈×C₄₇	C₂³	1	1	yes	characteristic
307	C₄⋊C₈×C₄₇	C₂³	1	1	yes	characteristic
308	#103×C₄₇	C₂³	1	1	yes	characteristic
309	#103×C₄₇	C₂³	1	1	yes	characteristic
310	#103×C₄₇	C₂³	1	1	yes	characteristic
311	#103×C₄₇	C₂³	1	1	yes	characteristic
312	#102×C₄₇	C₂³	1	1	yes	characteristic
313	#102×C₄₇	C₂³	1	1	yes	characteristic
314	#102×C₄₇	C₂³	1	1	yes	characteristic
315	#102×C₄₇	C₂³	1	1	yes	characteristic
316	C₂³×D₄₇	—	2	1	no	—
317	C₂³×D₄₇	—	2	2	no	—
318	#41×C₄₇	—	2	2	no	—
319	#41×C₄₇	C₂×Q₈	1	4	yes	—
320	C₂×Q₈×C₄₇	—	2	1	no	—
321	C₂×Q₈×C₄₇	—	2	1	no	—
322	C₂×Q₈×C₄₇	C₂⁴	1	1	yes	characteristic
323	C₂×D₄×C₄₇	—	2	1	no	—
324	C₂×D₄×C₄₇	C₂⁴	1	1	yes	characteristic
325	C₂²×C₄×C₄₇	—	2	1	no	—
326	C₂²×C₄×C₄₇	—	2	1	no	—
327	C₂²×C₄×C₄₇	—	2	1	no	—
328	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
329	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
330	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
331	C₂×C₂²⋊D₄₇	—	2	2	no	—
332	C₂×C₂²⋊D₄₇	C₂×D₄	1	2	yes	—
333	C₂²×Dic₄₇	—	2	1	no	—
334	C₂²×Dic₄₇	—	2	1	no	—
335	C₂²×Dic₄₇	—	2	1	no	—
336	C₂²×Dic₄₇	—	2	2	no	—
337	#10625354	—	2	4	no	—
338	#10625354	C₂×Q₈	1	8	yes	—
339	D₄×D₄₇	—	2	16	no	—
340	D₄×D₄₇	—	2	4	no	—
341	D₄×D₄₇	C₂×Q₈	1	8	yes	—
342	#10625350	—	2	8	no	—
343	#10625350	C₂×Q₈	1	4	yes	—
344	#10625350	#41	1	4	yes	—
345	C₂×D₁₈₈	—	2	2	no	—
346	C₂×D₁₈₈	—	2	1	no	—
347	C₂×D₁₈₈	—	2	2	no	—
348	C₂×D₁₈₈	—	2	8	no	—
349	C₂×D₁₈₈	C₂×D₄	1	1	yes	characteristic
350	C₂×D₁₈₈	C₂×Q₈	1	4	yes	—
351	C₂×D₁₈₈	C₂⁴	1	2	yes	—
352	C₂×C₄×D₄₇	—	2	2	no	—
353	C₂×C₄×D₄₇	—	2	2	no	—
354	C₂×C₄×D₄₇	—	2	2	no	—
355	C₂×C₄×D₄₇	—	2	2	no	—
356	C₂×C₄×D₄₇	—	2	2	no	—
357	C₂×C₄×D₄₇	—	2	2	no	—
358	C₂×C₄×D₄₇	—	2	2	no	—
359	C₂×C₄×D₄₇	—	2	2	no	—
360	C₂×C₄×D₄₇	—	8	4	no	—
361	C₂×C₄×D₄₇	—	8	2	no	—
362	C₂×C₄×D₄₇	C₂×D₄	1	2	yes	—
363	C₂×C₄×D₄₇	C₂×D₄	1	2	yes	—
364	C₂×C₄×D₄₇	C₂⁴	1	2	yes	—
365	C₂×Dic₉₄	—	2	2	no	—
366	C₂×Dic₉₄	—	2	2	no	—
367	C₂×Dic₉₄	C₂×D₄	1	1	yes	characteristic
368	C₂×C₈×C₄₇	—	2	2	no	—
369	C₂×C₈×C₄₇	—	2	2	no	—
370	C₂×C₈×C₄₇	C₂⁴	1	1	yes	characteristic
371	C₂×C₈×C₄₇	C₂⁴	1	1	yes	characteristic
372	C₂×C₈×C₄₇	C₂⁴	1	1	yes	characteristic
373	C₂×C₈×C₄₇	C₂⁴	1	1	yes	characteristic
374	C₄⋊C₄×C₄₇	—	2	1	no	—
375	C₄⋊C₄×C₄₇	—	2	1	no	—
376	C₄⋊C₄×C₄₇	—	2	1	no	—
377	C₄⋊C₄×C₄₇	—	2	1	no	—
378	C₄⋊C₄×C₄₇	—	2	1	no	—
379	C₄⋊C₄×C₄₇	—	2	1	no	—
380	C₄⋊C₄×C₄₇	—	2	1	no	—
381	C₄⋊C₄×C₄₇	—	2	1	no	—
382	C₄⋊C₄×C₄₇	C₂⁴	1	1	yes	characteristic
383	C₄⋊C₄×C₄₇	C₂⁴	1	1	yes	characteristic
384	C₄⋊C₄×C₄₇	C₂⁴	1	1	yes	characteristic
385	C₄⋊C₄×C₄₇	C₂⁴	1	1	yes	characteristic
386	C₄⋊C₄×C₄₇	C₂⁴	1	1	yes	characteristic
387	C₄⋊C₄×C₄₇	C₂⁴	1	1	yes	characteristic
388	C₂²⋊C₄×C₄₇	—	2	1	no	—
389	C₂²⋊C₄×C₄₇	—	2	1	no	—
390	C₂²⋊C₄×C₄₇	—	2	1	no	—
391	C₂²⋊C₄×C₄₇	—	2	1	no	—
392	C₂²⋊C₄×C₄₇	—	2	1	no	—
393	C₄²×C₄₇	—	2	1	no	—
394	C₄²×C₄₇	—	2	1	no	—
395	C₄²×C₄₇	—	2	1	no	—
396	C₄²×C₄₇	—	2	1	no	—
397	C₄²×C₄₇	—	2	1	no	—
398	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
399	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
400	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
401	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
402	C₂²⋊Dic₄₇	—	2	2	no	—
403	C₂²⋊Dic₄₇	C₂×D₄	1	2	yes	—
404	(C₂×D₄₇)⋊C₄	—	2	2	no	—
405	(C₂×D₄₇)⋊C₄	—	2	2	no	—
406	(C₂×D₄₇)⋊C₄	—	2	2	no	—
407	(C₂×D₄₇)⋊C₄	—	2	2	no	—
408	(C₂×D₄₇)⋊C₄	—	2	2	no	—
409	(C₂×D₄₇)⋊C₄	—	2	2	no	—
410	(C₂×D₄₇)⋊C₄	—	2	2	no	—
411	(C₂×D₄₇)⋊C₄	C₂×D₄	1	2	yes	—
412	(C₂×D₄₇)⋊C₄	C₂×D₄	1	2	yes	—
413	C₄⋊Dic₄₇	—	2	1	no	—
414	C₄⋊Dic₄₇	—	2	1	no	—
415	C₄⋊Dic₄₇	—	2	1	no	—
416	C₄⋊Dic₄₇	—	2	2	no	—
417	C₄⋊Dic₄₇	—	2	2	no	—
418	C₄⋊Dic₄₇	—	2	2	no	—
419	C₄⋊Dic₄₇	C₂×D₄	1	1	yes	characteristic
420	C₄⋊Dic₄₇	C₂×D₄	1	1	yes	characteristic
421	C₄⋊Dic₄₇	C₂⁴	1	2	yes	—
422	C₄⋊Dic₄₇	C₂⁴	1	2	yes	—
423	C₄⋊Dic₄₇	C₂⁴	1	2	yes	—
424	Dic₄₇⋊C₄	—	2	2	no	—
425	Dic₄₇⋊C₄	—	2	2	no	—
426	Dic₄₇⋊C₄	—	2	2	no	—
427	Dic₄₇⋊C₄	—	2	2	no	—
428	Dic₄₇⋊C₄	—	2	2	no	—
429	Dic₄₇⋊C₄	—	2	2	no	—
430	Dic₄₇⋊C₄	—	2	2	no	—
431	Dic₄₇⋊C₄	—	2	2	no	—
432	Dic₄₇⋊C₄	—	2	2	no	—
433	Dic₄₇⋊C₄	—	2	2	no	—
434	Dic₄₇⋊C₄	—	2	2	no	—
435	Dic₄₇⋊C₄	C₂×D₄	1	2	yes	—
436	Dic₄₇⋊C₄	C₂×D₄	1	2	yes	—
437	C₄×Dic₄₇	—	2	2	no	—
438	C₄×Dic₄₇	—	2	2	no	—
439	C₄×Dic₄₇	—	2	2	no	—
440	C₄×Dic₄₇	—	2	2	no	—
441	C₄×Dic₄₇	C₂×D₄	1	2	yes	—
442	C₄×Dic₄₇	C₂×D₄	1	2	yes	—
443	C₄×Dic₄₇	C₂⁴	1	2	yes	—
444	#10625329	—	2	2	no	—
445	#10625329	—	2	2	no	—
446	C₂×C₄₇⋊C₈	C₂⁴	1	2	yes	—
447	C₂×C₄₇⋊C₈	C₂⁴	1	2	yes	—
448	#10625324	—	2	4	no	—
449	#10625324	—	2	4	no	—
450	C₈×D₄₇	—	2	4	no	—
451	C₈×D₄₇	—	2	4	no	—
452	C₂³×C₄₇	—	2	1	no	—
453	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
454	C₂²×D₄₇	—	2	2	no	—
455	C₂²×D₄₇	—	2	4	no	—
456	C₂²×D₄₇	—	2	8	no	—
457	C₂²×D₄₇	—	8	2	no	—
458	C₂²×D₄₇	—	8	2	no	—
459	C₂²×D₄₇	—	8	1	no	—
460	C₂²×D₄₇	—	8	1	no	—
461	C₂²×D₄₇	C₂²×D₄	1	2	yes	—
462	Q₈×C₄₇	—	2	1	no	—
463	Q₈×C₄₇	—	8	1	no	—
464	Q₈×C₄₇	—	8	1	no	—
465	Q₈×C₄₇	C₂²×Q₈	1	2	yes	—
466	D₄×C₄₇	—	2	4	no	—
467	D₄×C₄₇	—	2	1	no	—
468	D₄×C₄₇	C₂²×Q₈	1	2	yes	—
469	C₂×C₄×C₄₇	—	2	1	no	—
470	C₂×C₄×C₄₇	—	2	4	no	—
471	C₂×C₄×C₄₇	—	2	1	no	—
472	C₂×C₄×C₄₇	—	2	1	no	—
473	C₂×C₄×C₄₇	—	2	1	no	—
474	C₂×C₄×C₄₇	—	2	1	no	—
475	C₂×C₄×C₄₇	—	2	1	no	—
476	C₂×C₄×C₄₇	—	2	1	no	—
477	C₂×C₄×C₄₇	—	4	1	no	—
478	C₂×C₄×C₄₇	—	4	1	no	—
479	C₂×C₄×C₄₇	—	4	2	no	—
480	C₂×C₄×C₄₇	—	8	1	no	—
481	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
482	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
483	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
484	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
485	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
486	C₂×C₄×C₄₇	C₂²×Q₈	1	2	yes	—
487	C₂×C₄×C₄₇	C₂×#41	1	2	yes	—
488	C₂×C₄×C₄₇	C₂⁵	1	1	yes	characteristic
489	C₂²⋊D₄₇	—	2	8	no	—
490	C₂²⋊D₄₇	C₂²⋊Q₈	1	8	yes	—
491	C₂×Dic₄₇	—	2	2	no	—
492	C₂×Dic₄₇	—	2	2	no	—
493	C₂×Dic₄₇	—	2	2	no	—
494	C₂×Dic₄₇	—	8	2	no	—
495	C₂×Dic₄₇	—	8	1	no	—
496	C₂×Dic₄₇	—	8	1	no	—
497	C₂×Dic₄₇	—	8	1	no	—
498	C₂×Dic₄₇	C₂²×D₄	1	2	yes	—
499	C₂×Dic₄₇	C₂²×D₄	1	2	yes	—
500	C₂×Dic₄₇	C₂²×D₄	1	2	yes	—
501	D₁₈₈	—	2	8	no	—
502	D₁₈₈	—	2	4	no	—
503	D₁₈₈	—	2	2	no	—
504	D₁₈₈	C₂²⋊Q₈	1	4	yes	—
505	D₁₈₈	C₂²×Q₈	1	4	yes	—
506	C₄×D₄₇	—	2	8	no	—
507	C₄×D₄₇	—	4	2	no	—
508	C₄×D₄₇	—	4	2	no	—
509	C₄×D₄₇	—	4	4	no	—
510	C₄×D₄₇	—	8	2	no	—
511	C₄×D₄₇	—	8	2	no	—
512	C₄×D₄₇	—	8	2	no	—
513	C₄×D₄₇	—	8	2	no	—
514	C₄×D₄₇	—	8	2	no	—
515	C₄×D₄₇	—	8	2	no	—
516	C₄×D₄₇	C₂²×Q₈	1	4	yes	—
517	C₄×D₄₇	C₂×#41	1	4	yes	—
518	Dic₉₄	—	8	2	no	—
519	Dic₉₄	—	8	2	no	—
520	Dic₉₄	C₂²⋊Q₈	1	4	yes	—
521	C₈×C₄₇	—	2	1	no	—
522	C₈×C₄₇	—	2	1	no	—
523	C₈×C₄₇	—	2	1	no	—
524	C₈×C₄₇	—	2	1	no	—
525	C₄₇⋊C₈	—	2	2	no	—
526	C₄₇⋊C₈	—	2	2	no	—
527	#60496	—	47	1	no	maximal, Sylow
528	C₂²×C₄₇	—	2	1	no	—
529	C₂²×C₄₇	—	2	1	no	—
530	C₂²×C₄₇	—	2	2	no	—
531	C₂²×C₄₇	—	4	1	no	—
532	C₂²×C₄₇	—	4	1	no	—
533	C₂²×C₄₇	C₂×C₂²⋊Q₈	1	2	yes	—
534	C₂²×C₄₇	C₂³×D₄	1	1	yes	characteristic
535	C₂×D₄₇	—	2	2	no	—
536	C₂×D₄₇	—	2	2	no	—
537	C₂×D₄₇	—	2	4	no	—
538	C₂×D₄₇	—	4	2	no	—
539	C₂×D₄₇	—	4	2	no	—
540	C₂×D₄₇	—	8	8	no	—
541	C₂×D₄₇	—	8	4	no	—
542	C₂×D₄₇	C₂×C₂²⋊Q₈	1	4	yes	—
543	C₄×C₄₇	—	2	1	no	—
544	C₄×C₄₇	—	2	1	no	—
545	C₄×C₄₇	—	2	1	no	—
546	C₄×C₄₇	—	2	1	no	—
547	C₄×C₄₇	—	2	2	no	—
548	C₄×C₄₇	—	4	1	no	—
549	C₄×C₄₇	—	4	1	no	—
550	C₄×C₄₇	—	4	1	no	—
551	C₄×C₄₇	—	4	1	no	—
552	C₄×C₄₇	—	4	1	no	—
553	C₄×C₄₇	—	4	1	no	—
554	C₄×C₄₇	C₂×C₂²⋊Q₈	1	2	yes	—
555	C₄×C₄₇	C₂³×Q₈	1	1	yes	characteristic
556	C₄×C₄₇	C₂²×#41	1	1	yes	characteristic
557	Dic₄₇	—	2	2	no	—
558	Dic₄₇	—	2	2	no	—
559	Dic₄₇	—	4	2	no	—
560	Dic₄₇	—	4	2	no	—
561	Dic₄₇	—	4	2	no	—
562	Dic₄₇	C₂×C₂²⋊Q₈	1	4	yes	—
563	#3504	—	47	1	no	—
564	C₄×H(5,𝔽₂)	—	47	1	no	—
565	#3084	—	47	2	no	—
566	#3084	—	47	1	no	—
567	#3083	—	47	2	no	—
568	#3083	—	47	1	no	—
569	#3081	—	47	2	no	—
570	#3081	—	47	2	no	—
571	#3081	—	47	1	no	—
572	#3081	—	47	1	no	—
573	#3080	—	47	2	no	—
574	#3080	—	47	1	no	—
575	#3077	—	47	2	no	—
576	#3077	—	47	1	no	—
577	#3076	—	47	2	no	—
578	#3076	D₄₇	1	1	yes	characteristic, complemented
579	C₂×#478	—	47	2	no	—
580	C₂×#478	—	47	1	no	—
581	#2913	—	47	1	no	—
582	#2912	—	47	1	no	—
583	#2906	—	47	1	no	—
584	#2897	—	47	1	no	—
585	#2897	—	47	1	no	—
586	C₂×C₄₇	—	2	2	no	—
587	C₂×C₄₇	—	4	2	no	—
588	C₂×C₄₇	C₂²×C₂²⋊Q₈	1	1	yes	characteristic
589	C₂×C₄₇	#3584	1	1	yes	characteristic
590	C₂×C₄₇	#3585	1	1	yes	characteristic
591	D₄₇	—	2	4	no	—
592	D₄₇	—	4	4	no	—
593	C₂×H(5,𝔽₂)	—	47	1	no	—
594	C₂×#131	—	47	1	no	—
595	C₂×#131	—	47	1	no	—
596	#557	—	94	1	no	—
597	#557	—	94	1	no	—
598	#554	—	94	1	no	—
599	#554	—	94	1	no	—
600	#554	—	94	2	no	—
601	#554	—	94	2	no	—
602	#544	—	47	2	no	—
603	#544	—	47	2	no	—
604	#544	—	47	1	no	—
605	#544	—	47	1	no	—
606	#533	—	47	2	no	—
607	#533	C₂×D₄₇	1	1	yes	characteristic, complemented
608	C₂×#125	—	47	2	no	—
609	C₂×#125	—	47	1	no	—
610	#520	—	47	1	no	—
611	#520	—	47	1	no	—
612	#520	—	47	1	no	—
613	#520	—	47	1	no	—
614	#520	—	47	2	no	—
615	#520	—	94	1	no	—
616	#518	—	47	2	no	—
617	#518	—	47	1	no	—
618	#518	—	94	1	no	—
619	#518	—	94	2	no	—
620	C₄×#41	—	47	1	no	—
621	C₄×#41	—	47	2	no	—
622	C₄×#41	—	94	1	no	—
623	C₄×#41	C₂×D₄₇	1	1	yes	characteristic
624	C₂×C₄×D₄	—	47	2	no	—
625	C₂×C₄×D₄	—	47	1	no	—
626	C₂×C₄×D₄	—	94	1	no	—
627	C₂×C₄×D₄	—	94	2	no	—
628	#479	—	47	2	no	—
629	#479	—	47	2	no	—
630	#479	—	47	2	no	—
631	#479	—	47	2	no	—
632	#479	C₂×D₄₇	1	1	yes	characteristic, complemented
633	#479	C₂×D₄₇	1	1	yes	characteristic, complemented
634	#478	—	47	2	no	—
635	#478	—	47	2	no	—
636	#478	—	47	2	no	—
637	#478	—	47	2	no	—
638	#478	—	47	2	no	—
639	#478	—	47	2	no	—
640	#478	—	47	2	no	—
641	#478	—	47	2	no	—
642	#478	—	47	2	no	—
643	#478	—	47	2	no	—
644	#478	—	47	2	no	—
645	#478	—	47	2	no	—
646	#478	—	47	2	no	—
647	#478	—	47	2	no	—
648	#478	C₂×D₄₇	1	1	yes	characteristic, complemented
649	#478	C₂×D₄₇	1	1	yes	characteristic, complemented
650	#477	—	47	2	no	—
651	#477	C₂×D₄₇	1	1	yes	characteristic, complemented
652	#476	—	47	2	no	—
653	#476	—	47	2	no	—
654	#476	—	47	2	no	—
655	#476	—	47	2	no	—
656	#476	C₂×D₄₇	1	1	yes	characteristic, complemented
657	#475	—	47	2	no	—
658	#475	C₂×D₄₇	1	1	yes	characteristic, complemented
659	#474	—	47	2	no	—
660	#474	—	47	2	no	—
661	#474	—	47	2	no	—
662	#474	—	47	2	no	—
663	#474	C₂×D₄₇	1	1	yes	characteristic, complemented
664	#428	—	47	1	no	—
665	#428	—	47	1	no	—
666	#428	—	47	1	no	—
667	#428	—	47	1	no	—
668	#428	—	47	2	no	—
669	#428	—	47	2	no	—
670	#428	—	47	2	no	—
671	#428	—	47	2	no	—
672	#427	—	47	2	no	—
673	#427	—	47	2	no	—
674	#427	C₂×D₄₇	1	1	yes	characteristic, complemented
675	#427	C₂×D₄₇	1	1	yes	characteristic, complemented
676	C₂×#107	—	47	1	no	—
677	C₂×#107	—	47	2	no	—
678	C₂×#106	—	47	1	no	—
679	C₂×#106	—	47	2	no	—
680	#424	—	47	1	no	—
681	#424	—	47	1	no	—
682	#424	—	47	2	no	—
683	#424	—	47	2	no	—
684	#423	—	47	1	no	—
685	#423	—	47	2	no	—
686	C₂×C₄⋊C₈	—	47	2	no	—
687	C₂×C₄⋊C₈	C₂×D₄₇	1	1	yes	characteristic, complemented
688	#418	—	47	1	no	—
689	#418	—	47	1	no	—
690	#418	—	47	2	no	—
691	#418	—	47	2	no	—
692	#417	—	47	1	no	—
693	#417	—	47	1	no	—
694	#417	—	47	2	no	—
695	#417	—	47	2	no	—
696	#416	—	47	2	no	—
697	#416	—	47	2	no	—
698	#416	C₂×D₄₇	1	1	yes	characteristic
699	#416	C₂×D₄₇	1	1	yes	characteristic
700	C₂×#102	—	47	1	no	—
701	C₂×#102	—	47	1	no	—
702	C₂×#102	—	47	2	no	—
703	C₂×#102	—	47	2	no	—
704	C₄₇	#60496	1	1	yes	characteristic, complemented, Sylow
705	H(5,𝔽₂)	—	47	8	no	—
706	H(5,𝔽₂)	—	94	4	no	—
707	C₂×#41	—	47	1	no	—
708	C₂×#41	—	47	2	no	—
709	C₂×#41	—	94	1	no	—
710	C₂×#41	C₂²×D₄₇	1	1	yes	characteristic
711	C₂²×D₄	—	47	2	no	—
712	C₂²×D₄	—	47	1	no	—
713	C₂²×D₄	—	94	1	no	—
714	C₂²×D₄	—	94	2	no	—
715	C₂³×C₄	—	94	2	no	—
716	C₂³×C₄	—	94	1	no	—
717	#131	—	94	4	no	—
718	#131	—	94	4	no	—
719	C₂×M₁₆	—	47	1	no	—
720	C₂×M₁₆	—	47	1	no	—
721	C₂×M₁₆	—	47	2	no	—
722	C₂×M₁₆	—	47	2	no	—
723	C₂²×C₈	—	47	2	no	—
724	C₂²×C₈	—	47	2	no	—
725	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
726	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
727	C₄⋊Q₈	—	47	2	no	—
728	C₄⋊Q₈	—	47	2	no	—
729	C₄⋊Q₈	—	94	1	no	—
730	C₄⋊Q₈	—	94	1	no	—
731	C₄⋊Q₈	—	94	2	no	—
732	C₄⋊Q₈	—	94	2	no	—
733	C₄⋊Q₈	C₂²×D₄₇	1	1	yes	characteristic
734	C₄⋊Q₈	C₂²×D₄₇	1	1	yes	characteristic
735	#125	—	47	2	no	—
736	#125	—	47	2	no	—
737	#125	—	47	2	no	—
738	#125	—	47	2	no	—
739	#125	—	94	1	no	—
740	#125	—	94	1	no	—
741	#125	—	94	2	no	—
742	#125	—	94	2	no	—
743	#125	—	94	2	no	—
744	#125	—	94	2	no	—
745	#125	—	94	1	no	—
746	#125	—	94	1	no	—
747	#125	C₂²×D₄₇	1	1	yes	characteristic
748	#125	C₂²×D₄₇	1	1	yes	characteristic
749	C₂²⋊Q₈	—	2	1	no	—
750	C₂²⋊Q₈	—	2	1	no	—
751	C₂²⋊Q₈	—	94	2	no	—
752	C₂²⋊Q₈	—	94	2	no	—
753	C₂²⋊Q₈	—	94	2	no	—
754	C₂²⋊Q₈	—	94	2	no	—
755	C₂²⋊Q₈	—	94	2	no	—
756	C₂²⋊Q₈	—	94	2	no	—
757	C₂²⋊Q₈	—	94	2	no	—
758	C₂²⋊Q₈	—	94	2	no	—
759	C₄×Q₈	—	2	1	no	—
760	C₄×Q₈	—	2	1	no	—
761	C₄×Q₈	—	47	1	no	—
762	C₄×Q₈	—	47	1	no	—
763	C₄×Q₈	—	47	2	no	—
764	C₄×Q₈	—	94	1	no	—
765	C₄×Q₈	—	94	1	no	—
766	C₄×Q₈	—	94	1	no	—
767	C₄×Q₈	—	94	2	no	—
768	C₄×Q₈	—	94	2	no	—
769	C₄×Q₈	C₂²×D₄₇	1	1	yes	characteristic
770	C₄×Q₈	C₂²×D₄₇	1	1	yes	characteristic
771	C₄×D₄	—	2	1	no	—
772	C₄×D₄	—	2	1	no	—
773	C₄×D₄	—	47	2	no	—
774	C₄×D₄	—	47	2	no	—
775	C₄×D₄	—	47	2	no	—
776	C₄×D₄	—	47	2	no	—
777	C₄×D₄	—	47	2	no	—
778	C₄×D₄	—	47	1	no	—
779	C₄×D₄	—	47	1	no	—
780	C₄×D₄	—	47	2	no	—
781	C₄×D₄	—	47	2	no	—
782	C₄×D₄	—	94	2	no	—
783	C₄×D₄	—	94	1	no	—
784	C₄×D₄	—	94	1	no	—
785	C₄×D₄	—	94	2	no	—
786	C₄×D₄	—	94	1	no	—
787	C₄×D₄	—	94	1	no	—
788	C₄×D₄	—	94	1	no	—
789	C₄×D₄	—	94	2	no	—
790	C₄×D₄	—	94	2	no	—
791	C₄×D₄	—	94	2	no	—
792	C₄×D₄	—	94	2	no	—
793	C₄×D₄	—	94	2	no	—
794	C₄×D₄	—	94	2	no	—
795	C₄×D₄	—	94	2	no	—
796	C₄×D₄	—	94	2	no	—
797	C₄×D₄	—	94	2	no	—
798	C₄×D₄	—	94	2	no	—
799	C₄×D₄	—	94	1	no	—
800	C₄×D₄	—	94	1	no	—
801	C₄×D₄	C₂²×D₄₇	1	1	yes	characteristic
802	C₄×D₄	C₂²×D₄₇	1	1	yes	characteristic
803	#117	—	2	1	no	—
804	#117	—	47	1	no	—
805	#117	—	47	2	no	—
806	#117	—	47	2	no	—
807	#117	—	47	2	no	—
808	#117	—	47	2	no	—
809	#117	—	94	2	no	—
810	#117	—	94	2	no	—
811	#117	—	94	1	no	—
812	#117	C₂²×D₄₇	1	1	yes	characteristic
813	#117	C₂²×D₄₇	1	1	yes	characteristic
814	#117	C₂²×D₄₇	1	1	yes	characteristic
815	C₂×C₄⋊C₄	—	47	1	no	—
816	C₂×C₄⋊C₄	—	47	1	no	—
817	C₂×C₄⋊C₄	—	47	1	no	—
818	C₂×C₄⋊C₄	—	47	2	no	—
819	C₂×C₄⋊C₄	—	47	2	no	—
820	C₂×C₄⋊C₄	—	47	2	no	—
821	C₂×C₄⋊C₄	—	94	2	no	—
822	C₂×C₄⋊C₄	—	94	2	no	—
823	C₂×C₄⋊C₄	—	94	2	no	—
824	C₂×C₄⋊C₄	—	94	1	no	—
825	C₂×C₄⋊C₄	—	94	1	no	—
826	C₂×C₄⋊C₄	—	94	1	no	—
827	C₂×C₂²⋊C₄	—	94	2	no	—
828	C₂×C₂²⋊C₄	—	94	2	no	—
829	C₂×C₂²⋊C₄	—	94	2	no	—
830	C₂×C₂²⋊C₄	—	94	2	no	—
831	C₂×C₂²⋊C₄	—	94	1	no	—
832	C₂×C₄²	—	2	1	no	—
833	C₂×C₄²	—	47	2	no	—
834	C₂×C₄²	—	94	2	no	—
835	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
836	#107	—	47	2	no	—
837	#107	—	47	2	no	—
838	#107	—	47	2	no	—
839	#107	—	47	2	no	—
840	#107	—	47	2	no	—
841	#107	—	47	2	no	—
842	#107	C₂²×D₄₇	1	1	yes	characteristic
843	#107	C₂²×D₄₇	1	1	yes	characteristic
844	#107	C₂²×D₄₇	1	1	yes	characteristic
845	#107	C₂²×D₄₇	1	1	yes	characteristic
846	#106	—	47	2	no	—
847	#106	—	47	2	no	—
848	#106	—	47	2	no	—
849	#106	—	47	2	no	—
850	#106	—	47	2	no	—
851	#106	—	47	2	no	—
852	#106	C₂²×D₄₇	1	1	yes	characteristic
853	#106	C₂²×D₄₇	1	1	yes	characteristic
854	#106	C₂²×D₄₇	1	1	yes	characteristic
855	#106	C₂²×D₄₇	1	1	yes	characteristic
856	C₄⋊C₈	—	47	2	no	—
857	C₄⋊C₈	—	47	2	no	—
858	C₄⋊C₈	—	47	2	no	—
859	C₄⋊C₈	—	47	2	no	—
860	C₄⋊C₈	—	47	2	no	—
861	C₄⋊C₈	—	47	2	no	—
862	C₄⋊C₈	C₂²×D₄₇	1	1	yes	characteristic
863	C₄⋊C₈	C₂²×D₄₇	1	1	yes	characteristic
864	C₄⋊C₈	C₂²×D₄₇	1	1	yes	characteristic
865	C₄⋊C₈	C₂²×D₄₇	1	1	yes	characteristic
866	#103	—	47	2	no	—
867	#103	—	47	2	no	—
868	#103	C₂²×D₄₇	1	1	yes	characteristic
869	#103	C₂²×D₄₇	1	1	yes	characteristic
870	#103	C₂²×D₄₇	1	1	yes	characteristic
871	#103	C₂²×D₄₇	1	1	yes	characteristic
872	#102	—	47	2	no	—
873	#102	—	47	2	no	—
874	#102	—	47	2	no	—
875	#102	—	47	2	no	—
876	#102	—	47	2	no	—
877	#102	—	47	2	no	—
878	#102	—	47	2	no	—
879	#102	—	47	2	no	—
880	#102	—	47	2	no	—
881	#102	—	47	2	no	—
882	#102	C₂²×D₄₇	1	1	yes	characteristic
883	#102	C₂²×D₄₇	1	1	yes	characteristic
884	#102	C₂²×D₄₇	1	1	yes	characteristic
885	#102	C₂²×D₄₇	1	1	yes	characteristic
886	C₂⁴	—	94	2	no	—
887	C₂⁴	—	94	1	no	—
888	#41	—	2	2	no	—
889	#41	—	47	4	no	—
890	#41	—	47	4	no	—
891	#41	—	47	8	no	—
892	#41	—	94	8	no	—
893	#41	—	94	4	no	—
894	#41	Q₈×D₄₇	1	4	yes	—
895	C₂×Q₈	—	2	1	no	—
896	C₂×Q₈	—	2	1	no	—
897	C₂×Q₈	—	47	1	no	—
898	C₂×Q₈	—	94	2	no	—
899	C₂×Q₈	—	94	2	no	—
900	C₂×Q₈	C₂³×D₄₇	1	1	yes	characteristic
901	C₂×D₄	—	2	1	no	—
902	C₂×D₄	—	47	2	no	—
903	C₂×D₄	—	47	8	no	—
904	C₂×D₄	—	47	1	no	—
905	C₂×D₄	—	47	4	no	—
906	C₂×D₄	—	47	2	no	—
907	C₂×D₄	—	94	8	no	—
908	C₂×D₄	—	94	2	no	—
909	C₂×D₄	—	94	4	no	—
910	C₂×D₄	—	94	2	no	—
911	C₂×D₄	—	94	16	no	—
912	C₂×D₄	—	94	1	no	—
913	C₂×D₄	—	94	2	no	—
914	C₂×D₄	C₂³×D₄₇	1	1	yes	characteristic
915	C₂²×C₄	—	2	1	no	—
916	C₂²×C₄	—	2	1	no	—
917	C₂²×C₄	—	2	1	no	—
918	C₂²×C₄	—	47	2	no	—
919	C₂²×C₄	—	47	2	no	—
920	C₂²×C₄	—	47	2	no	—
921	C₂²×C₄	—	94	2	no	—
922	C₂²×C₄	—	94	2	no	—
923	C₂²×C₄	—	94	2	no	—
924	C₂²×C₄	—	94	2	no	—
925	C₂²×C₄	—	94	2	no	—
926	C₂²×C₄	—	94	2	no	—
927	C₂²×C₄	—	94	2	no	—
928	C₂²×C₄	—	94	1	no	—
929	C₂²×C₄	—	94	1	no	—
930	C₂²×C₄	—	94	1	no	—
931	C₂²×C₄	—	94	2	no	—
932	C₂²×C₄	—	94	2	no	—
933	C₂²×C₄	—	376	2	no	—
934	C₂²×C₄	—	376	4	no	—
935	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
936	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
937	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
938	M₁₆	—	94	4	no	—
939	M₁₆	—	94	4	no	—
940	M₁₆	—	94	2	no	—
941	M₁₆	—	94	2	no	—
942	C₂×C₈	—	2	2	no	—
943	C₂×C₈	—	2	2	no	—
944	C₂×C₈	—	47	2	no	—
945	C₂×C₈	—	47	2	no	—
946	C₂×C₈	—	94	4	no	—
947	C₂×C₈	—	94	4	no	—
948	C₂×C₈	C₂³×D₄₇	1	1	yes	characteristic
949	C₂×C₈	C₂³×D₄₇	1	1	yes	characteristic
950	C₂×C₈	C₂³×D₄₇	1	1	yes	characteristic
951	C₂×C₈	C₂³×D₄₇	1	1	yes	characteristic
952	C₄⋊C₄	—	2	1	no	—
953	C₄⋊C₄	—	2	1	no	—
954	C₄⋊C₄	—	2	1	no	—
955	C₄⋊C₄	—	2	1	no	—
956	C₄⋊C₄	—	2	1	no	—
957	C₄⋊C₄	—	2	1	no	—
958	C₄⋊C₄	—	2	1	no	—
959	C₄⋊C₄	—	2	1	no	—
960	C₄⋊C₄	—	47	2	no	—
961	C₄⋊C₄	—	47	2	no	—
962	C₄⋊C₄	—	47	1	no	—
963	C₄⋊C₄	—	47	1	no	—
964	C₄⋊C₄	—	47	2	no	—
965	C₄⋊C₄	—	47	2	no	—
966	C₄⋊C₄	—	47	2	no	—
967	C₄⋊C₄	—	94	2	no	—
968	C₄⋊C₄	—	94	2	no	—
969	C₄⋊C₄	—	94	2	no	—
970	C₄⋊C₄	—	94	2	no	—
971	C₄⋊C₄	—	94	2	no	—
972	C₄⋊C₄	—	94	2	no	—
973	C₄⋊C₄	—	94	2	no	—
974	C₄⋊C₄	—	94	2	no	—
975	C₄⋊C₄	—	94	2	no	—
976	C₄⋊C₄	—	94	2	no	—
977	C₄⋊C₄	—	94	2	no	—
978	C₄⋊C₄	—	94	2	no	—
979	C₄⋊C₄	—	94	2	no	—
980	C₄⋊C₄	—	94	2	no	—
981	C₄⋊C₄	—	94	1	no	—
982	C₄⋊C₄	—	94	1	no	—
983	C₄⋊C₄	—	94	1	no	—
984	C₄⋊C₄	C₂³×D₄₇	1	1	yes	characteristic
985	C₄⋊C₄	C₂³×D₄₇	1	1	yes	characteristic
986	C₄⋊C₄	C₂³×D₄₇	1	1	yes	characteristic
987	C₄⋊C₄	C₂³×D₄₇	1	1	yes	characteristic
988	C₄⋊C₄	C₂³×D₄₇	1	1	yes	characteristic
989	C₄⋊C₄	C₂³×D₄₇	1	1	yes	characteristic
990	C₂²⋊C₄	—	2	1	no	—
991	C₂²⋊C₄	—	2	1	no	—
992	C₂²⋊C₄	—	2	1	no	—
993	C₂²⋊C₄	—	2	1	no	—
994	C₂²⋊C₄	—	2	1	no	—
995	C₂²⋊C₄	—	47	2	no	—
996	C₂²⋊C₄	—	47	2	no	—
997	C₂²⋊C₄	—	47	2	no	—
998	C₂²⋊C₄	—	94	2	no	—
999	C₂²⋊C₄	—	94	2	no	—
1000	C₂²⋊C₄	—	94	2	no	—
1001	C₂²⋊C₄	—	94	2	no	—
1002	C₂²⋊C₄	—	94	2	no	—
1003	C₂²⋊C₄	—	94	2	no	—
1004	C₂²⋊C₄	—	94	2	no	—
1005	C₂²⋊C₄	—	94	2	no	—
1006	C₄²	—	2	1	no	—
1007	C₄²	—	2	1	no	—
1008	C₄²	—	2	1	no	—
1009	C₄²	—	2	1	no	—
1010	C₄²	—	2	1	no	—
1011	C₄²	—	47	2	no	—
1012	C₄²	—	47	2	no	—
1013	C₄²	—	47	2	no	—
1014	C₄²	—	94	2	no	—
1015	C₄²	—	94	2	no	—
1016	C₄²	—	94	2	no	—
1017	C₄²	—	94	2	no	—
1018	C₄²	D₄×D₄₇	1	1	yes	characteristic
1019	C₄²	D₄×D₄₇	1	1	yes	characteristic
1020	C₄²	C₂³×D₄₇	1	1	yes	characteristic
1021	C₄²	C₂³×D₄₇	1	1	yes	characteristic
1022	C₂³	—	2	1	no	—
1023	C₂³	—	47	2	no	—
1024	C₂³	—	94	8	no	—
1025	C₂³	—	94	4	no	—
1026	C₂³	—	94	2	no	—
1027	C₂³	—	376	1	no	—
1028	C₂³	—	376	1	no	—
1029	C₂³	—	376	2	no	—
1030	C₂³	—	376	2	no	—
1031	C₂³	C₂×D₄×D₄₇	1	1	yes	characteristic
1032	Q₈	—	2	1	no	—
1033	Q₈	—	8	1	no	—
1034	Q₈	—	8	1	no	—
1035	Q₈	—	47	4	no	—
1036	Q₈	—	376	2	no	—
1037	Q₈	—	376	2	no	—
1038	Q₈	C₂×Q₈×D₄₇	1	2	yes	—
1039	D₄	—	2	4	no	—
1040	D₄	—	2	1	no	—
1041	D₄	—	47	8	no	—
1042	D₄	—	47	4	no	—
1043	D₄	—	47	4	no	—
1044	D₄	—	94	8	no	—
1045	D₄	—	94	8	no	—
1046	D₄	—	94	4	no	—
1047	D₄	—	94	2	no	—
1048	D₄	C₂×Q₈×D₄₇	1	2	yes	—
1049	C₂×C₄	—	2	1	no	—
1050	C₂×C₄	—	2	4	no	—
1051	C₂×C₄	—	2	1	no	—
1052	C₂×C₄	—	2	1	no	—
1053	C₂×C₄	—	2	1	no	—
1054	C₂×C₄	—	2	1	no	—
1055	C₂×C₄	—	2	1	no	—
1056	C₂×C₄	—	2	1	no	—
1057	C₂×C₄	—	4	1	no	—
1058	C₂×C₄	—	4	1	no	—
1059	C₂×C₄	—	4	2	no	—
1060	C₂×C₄	—	8	1	no	—
1061	C₂×C₄	—	47	2	no	—
1062	C₂×C₄	—	47	4	no	—
1063	C₂×C₄	—	47	4	no	—
1064	C₂×C₄	—	47	2	no	—
1065	C₂×C₄	—	47	2	no	—
1066	C₂×C₄	—	94	8	no	—
1067	C₂×C₄	—	94	2	no	—
1068	C₂×C₄	—	94	2	no	—
1069	C₂×C₄	—	94	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	—	376	2	no	—
1077	C₂×C₄	—	376	1	no	—
1078	C₂×C₄	—	376	1	no	—
1079	C₂×C₄	—	376	1	no	—
1080	C₂×C₄	—	188	2	no	—
1081	C₂×C₄	—	188	2	no	—
1082	C₂×C₄	—	188	4	no	—
1083	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
1084	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
1085	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
1086	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
1087	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
1088	C₂×C₄	C₂×Q₈×D₄₇	1	2	yes	—
1089	C₂×C₄	#41×D₄₇	1	2	yes	—
1090	C₂×C₄	C₂⁴×D₄₇	1	1	yes	characteristic
1091	C₈	—	2	1	no	—
1092	C₈	—	2	1	no	—
1093	C₈	—	2	1	no	—
1094	C₈	—	2	1	no	—
1095	C₈	—	94	2	no	—
1096	C₈	—	94	2	no	—
1097	C₂²	—	2	1	no	—
1098	C₂²	—	2	1	no	—
1099	C₂²	—	2	2	no	—
1100	C₂²	—	4	1	no	—
1101	C₂²	—	4	1	no	—
1102	C₂²	—	47	4	no	—
1103	C₂²	—	94	2	no	—
1104	C₂²	—	94	2	no	—
1105	C₂²	—	94	4	no	—
1106	C₂²	—	376	4	no	—
1107	C₂²	—	376	8	no	—
1108	C₂²	—	188	2	no	—
1109	C₂²	—	188	2	no	—
1110	C₂²	C₂²⋊Q₈×D₄₇	1	2	yes	—
1111	C₂²	C₂²×D₄×D₄₇	1	1	yes	characteristic
1112	C₄	—	2	2	no	—
1113	C₄	—	2	1	no	—
1114	C₄	—	2	1	no	—
1115	C₄	—	2	1	no	—
1116	C₄	—	2	1	no	—
1117	C₄	—	4	1	no	—
1118	C₄	—	4	1	no	—
1119	C₄	—	4	1	no	—
1120	C₄	—	4	1	no	—
1121	C₄	—	4	1	no	—
1122	C₄	—	4	1	no	—
1123	C₄	—	47	4	no	—
1124	C₄	—	94	2	no	—
1125	C₄	—	94	2	no	—
1126	C₄	—	188	2	no	—
1127	C₄	—	188	2	no	—
1128	C₄	—	188	2	no	—
1129	C₄	C₂²⋊Q₈×D₄₇	1	2	yes	—
1130	C₄	C₂²×Q₈×D₄₇	1	1	yes	characteristic
1131	C₄	C₂×#41×D₄₇	1	1	yes	characteristic
1132	C₂	—	2	2	no	—
1133	C₂	—	4	2	no	—
1134	C₂	—	94	4	no	—
1135	C₂	—	188	4	no	—
1136	C₂	C₂×C₂²⋊Q₈×D₄₇	1	1	yes	characteristic
1137	C₂	#20258157	1	1	yes	characteristic
1138	C₂	#20258165	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×#3076	C₂
socle	C₂²×C₄₇	C₂³×D₄
prime radical	C₂×#13094070	C₂²
hypercenter	#3076	D₄₇
hypocenter	C₄₇	#60496
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #3076

Complements

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

N	H ≅ G/N	type
1. #20257209	C₂	semidirect
3. #20253248	C₂	semidirect
4. #20253247	C₂	semidirect
5. #20253237	C₂	semidirect
6. #20253236	C₂	semidirect
7. #20253222	C₂	semidirect
8. #20253222	C₂	semidirect
9. #20253214	C₂	semidirect
10. #20253212	C₂	semidirect
11. #20253210	C₂	semidirect
12. #20253207	C₂	semidirect
13. #20253183	C₂	semidirect
14. #20253181	C₂	semidirect
15. #20253175	C₂	semidirect
16. C₂×#15689424	C₂	semidirect
17. #478×D₄₇	C₂	semidirect
18. #20251985	C₂	semidirect
19. #20251980	C₂	semidirect
20. #20251953	C₂	semidirect
23. C₄₇×#3076	C₂	semidirect
33. #15689751	C₂²	semidirect
34. #15689751	C₂²	semidirect
35. #15689750	C₂²	semidirect
36. #15689750	C₂²	semidirect
37. #15689679	C₂²	semidirect
38. C₂×#13094016	C₂²	semidirect
39. #125×D₄₇	C₂²	semidirect
57. #15689432	C₂²	semidirect
58. #15689430	C₂²	semidirect
59. #15689430	C₂²	semidirect
60. #15689428	C₂²	semidirect
61. #15689426	C₂²	semidirect
62. #15689426	C₂²	semidirect
63. #15689425	C₂²	semidirect
64. #15689424	C₂²	semidirect
65. #15689424	C₂²	semidirect
66. #15689424	C₂²	semidirect
67. #15689424	C₂²	semidirect
68. #15689423	C₂²	semidirect
69. #15689423	C₂²	semidirect
70. #15689422	C₂²	semidirect
71. #15689422	C₂²	semidirect
72. #15689421	C₂²	semidirect
73. #15689420	C₂²	semidirect
74. #15689420	C₂²	semidirect
75. #15689416	C₂²	semidirect
76. #15689412	C₂²	semidirect
77. #15689412	C₂²	semidirect
78. #15689411	C₂²	semidirect
79. #15689410	C₂²	semidirect
80. #15689406	C₂²	semidirect
81. #15689402	C₂²	semidirect
82. #15689402	C₂²	semidirect
83. #15689401	C₂²	semidirect
84. #15689400	C₂²	semidirect
85. #15689166	C₂²	semidirect
86. #15689166	C₂²	semidirect
87. #15689166	C₂²	semidirect
88. #15689166	C₂²	semidirect
89. #15689164	C₂²	semidirect
90. #15689164	C₂²	semidirect
91. #15689162	C₂²	semidirect
92. #15689162	C₂²	semidirect
93. #15689160	C₂²	semidirect
94. #15689158	C₂²	semidirect
95. C₂×#13093958	C₂²	semidirect
96. #107×D₄₇	C₂²	semidirect
97. C₂×#13093956	C₂²	semidirect
98. #106×D₄₇	C₂²	semidirect
99. #15689149	C₂²	semidirect
100. #15689149	C₂²	semidirect
101. #15689148	C₂²	semidirect
102. #15689148	C₂²	semidirect
103. #15689147	C₂²	semidirect
104. #15689145	C₂²	semidirect
105. C₄⋊C₈×D₄₇	C₂²	semidirect
120. C₄₇×#533	C₂²	semidirect
122. C₄₇×#479	C₂²	semidirect
123. C₄₇×#479	C₂²	semidirect
124. C₄₇×#478	C₂²	semidirect
125. C₄₇×#478	C₂²	semidirect
126. C₄₇×#477	C₂²	semidirect
127. C₄₇×#476	C₂²	semidirect
128. C₄₇×#475	C₂²	semidirect
129. C₄₇×#474	C₂²	semidirect
130. C₄₇×#427	C₂²	semidirect
131. C₄₇×#427	C₂²	semidirect
132. C₂×C₄⋊C₈×C₄₇	C₂²	semidirect
136. #13094070	Q₈	semidirect
578. #3076	D₄₇	semidirect
607. #533	C₂×D₄₇	semidirect
632. #479	C₂×D₄₇	semidirect
633. #479	C₂×D₄₇	semidirect
648. #478	C₂×D₄₇	semidirect
649. #478	C₂×D₄₇	semidirect
651. #477	C₂×D₄₇	semidirect
656. #476	C₂×D₄₇	semidirect
658. #475	C₂×D₄₇	semidirect
663. #474	C₂×D₄₇	semidirect
674. #427	C₂×D₄₇	semidirect
675. #427	C₂×D₄₇	semidirect
687. C₂×C₄⋊C₈	C₂×D₄₇	semidirect
704. C₄₇	#60496	semidirect

Maximal subgroups

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

subgroup	index
#20257209	2
C₄×#13094070	2
#20253248	2
#20253247	2
#20253237	2
#20253236	2
#20253222	2
#20253214	2
#20253212	2
#20253210	2
#20253207	2
#20253183	2
#20253181	2
#20253175	2
C₂×#15689424	2
#478×D₄₇	2
#20251985	2
#20251980	2
#20251953	2
#20251910	2
C₄₇×#3076	2
#60496	47