Subgroups — #27084864

Order 12032.

2088 conjugacy classes of subgroups.

The subgroup lattice has 1184 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20256815	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄×#13094070	C₂	1	1	yes	maximal, characteristic, complemented
3	#20253671	C₂	1	2	yes	maximal, complemented
4	#20253637	C₂	1	2	yes	maximal, complemented
5	#20253608	C₂	1	2	yes	maximal, complemented
6	#20253568	C₂	1	2	yes	maximal, complemented
7	#20253457	C₂	1	2	yes	maximal, complemented
8	#20253433	C₂	1	2	yes	maximal, complemented
9	#20253404	C₂	1	2	yes	maximal, complemented
10	#20253394	C₂	1	2	yes	maximal, complemented
11	#20253375	C₂	1	1	yes	maximal, characteristic, complemented
12	#20253360	C₂	1	1	yes	maximal, characteristic, complemented
13	#20253248	C₂	1	1	yes	maximal, characteristic, complemented
14	#20253222	C₂	1	1	yes	maximal, characteristic, complemented
15	#20252936	C₂	1	1	yes	maximal, characteristic, complemented
16	#20252903	C₂	1	1	yes	maximal, characteristic, complemented
17	#20252688	C₂	1	1	yes	maximal, characteristic
18	#20252668	C₂	1	1	yes	maximal, characteristic, complemented
19	C₄×#13094054	C₂	1	1	yes	maximal, characteristic, complemented
20	C₄×#13094049	C₂	1	1	yes	maximal, characteristic, complemented
21	C₂×C₄×#10625325	C₂	1	1	yes	maximal, characteristic, complemented
22	#20252030	C₂	1	1	yes	maximal, characteristic, complemented
23	C₄×#135×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#13094070	C₂²	1	1	yes	characteristic
25	C₂×#13094054	C₂²	1	1	yes	characteristic
26	C₂×#13094049	C₂²	1	1	yes	characteristic
27	C₂²×#10625325	C₂²	1	1	yes	characteristic
28	#15689751	C₂²	1	1	yes	characteristic, complemented
29	#15689744	—	2	1	no	—
30	#15689738	C₂²	1	2	yes	complemented
31	#15689735	—	2	1	no	—
32	#15689731	C₂²	1	2	yes	complemented
33	#15689715	—	2	2	no	—
34	#15689701	C₂²	1	1	yes	characteristic
35	#15689699	C₂²	1	1	yes	characteristic
36	#15689694	C₂²	1	1	yes	characteristic, complemented
37	#15689680	—	2	1	no	—
38	#15689677	C₂²	1	2	yes	complemented
39	#15689657	—	2	1	no	—
40	#15689655	C₂²	1	2	yes	complemented
41	#15689653	—	2	2	no	—
42	#15689606	C₂²	1	1	yes	characteristic
43	#15689605	C₂²	1	2	yes	—
44	#15689603	—	2	1	no	—
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×Dic₉₄	C₂²	1	1	yes	characteristic, complemented
54	C₂×C₄×D₁₈₈	—	2	1	no	—
55	C₂×C₄×D₁₈₈	C₂²	1	1	yes	characteristic
56	C₄×D₄×D₄₇	—	2	2	no	—
57	C₄×D₄×D₄₇	C₂²	1	2	yes	—
58	#15689467	C₂²	1	2	yes	complemented
59	#15689466	C₂²	1	2	yes	complemented
60	#15689462	C₂²	1	2	yes	complemented
61	#15689460	C₂²	1	2	yes	complemented
62	#15689455	C₂²	1	2	yes	complemented
63	#15689452	C₂²	1	2	yes	complemented
64	#15689446	C₂²	1	2	yes	complemented
65	#15689440	C₂²	1	2	yes	complemented
66	#15689428	C₂²	1	2	yes	complemented
67	#15689426	C₂²	1	2	yes	complemented
68	#15689425	C₂²	1	2	yes	complemented
69	#15689422	C₂²	1	2	yes	complemented
70	#15689412	C₂²	1	2	yes	complemented
71	#15689411	C₂²	1	2	yes	complemented
72	#15689406	C₂²	1	2	yes	complemented
73	#15689402	C₂²	1	2	yes	complemented
74	#15689343	C₂²	1	2	yes	complemented
75	#15689337	C₂²	1	2	yes	complemented
76	#15689337	C₂²	1	2	yes	complemented
77	#15689336	C₂²	1	2	yes	complemented
78	#15689331	C₂²	1	2	yes	complemented
79	#15689327	C₂²	1	2	yes	complemented
80	#15689327	C₂²	1	2	yes	complemented
81	#15689326	C₂²	1	2	yes	complemented
82	#15689288	C₂²	1	2	yes	—
83	#15689288	C₂²	1	2	yes	—
84	#15689284	C₂²	1	2	yes	—
85	#15689275	C₂²	1	2	yes	—
86	#15689275	C₂²	1	2	yes	—
87	#15689272	C₂²	1	2	yes	—
88	#15689267	C₂²	1	2	yes	—
89	#15689255	C₂²	1	2	yes	—
90	#15689233	C₂²	1	2	yes	complemented
91	#15689228	C₂²	1	2	yes	complemented
92	#15689223	C₂²	1	2	yes	complemented
93	#15689221	C₂²	1	2	yes	complemented
94	C₄×#10625337	C₂²	1	2	yes	complemented
95	C₄×#10625325	C₂²	1	2	yes	complemented
96	C₄×#10625325	C₂²	1	2	yes	complemented
97	C₄×#10625325	C₂²	1	2	yes	complemented
98	C₄×#10625325	C₂²	1	2	yes	complemented
99	C₄×#10625336	C₂²	1	2	yes	complemented
100	C₄×#10625335	C₂²	1	2	yes	complemented
101	C₄×#10625334	C₂²	1	2	yes	complemented
102	#15689182	C₂²	1	2	yes	complemented
103	#15689182	C₂²	1	2	yes	complemented
104	#15689174	C₂²	1	2	yes	complemented
105	#15689174	C₂²	1	2	yes	complemented
106	#15689166	C₂²	1	1	yes	characteristic, complemented
107	#15689166	C₂²	1	1	yes	characteristic, complemented
108	C₂×#13093956	C₂²	1	1	yes	characteristic, complemented
109	#15689149	C₂²	1	1	yes	characteristic, complemented
110	#15689149	C₂²	1	1	yes	characteristic, complemented
111	#15689131	C₂²	1	1	yes	characteristic, complemented
112	#15689127	C₂²	1	1	yes	characteristic
113	#15689124	C₂²	1	1	yes	characteristic
114	#15689124	C₂²	1	1	yes	characteristic, complemented
115	C₂×#13093949	C₂²	1	1	yes	characteristic, complemented
116	C₂×#13093946	C₂²	1	1	yes	characteristic
117	#15689089	C₂²	1	1	yes	characteristic
118	#15689089	C₂²	1	1	yes	characteristic
119	C₄×#10625329	C₂²	1	1	yes	characteristic, complemented
120	C₂×#135×C₄₇	C₂²	1	1	yes	characteristic
121	C₄×#41×C₄₇	C₂²	1	1	yes	characteristic
122	C₄×#41×C₄₇	C₂²	1	1	yes	characteristic, complemented
123	C₄×Q₁₆×C₄₇	C₂²	1	1	yes	characteristic, complemented
124	C₄×Q₁₆×C₄₇	C₂²	1	1	yes	characteristic, complemented
125	C₄×SD₁₆×C₄₇	C₂²	1	1	yes	characteristic, complemented
126	C₄×SD₁₆×C₄₇	C₂²	1	1	yes	characteristic, complemented
127	C₄×SD₁₆×C₄₇	C₂²	1	1	yes	characteristic, complemented
128	C₄×SD₁₆×C₄₇	C₂²	1	1	yes	characteristic, complemented
129	C₄×D₈×C₄₇	C₂²	1	1	yes	characteristic, complemented
130	C₄×D₈×C₄₇	C₂²	1	1	yes	characteristic, complemented
131	C₄₇×#427	C₂²	1	1	yes	characteristic, complemented
132	C₄₇×#416	C₂²	1	1	yes	characteristic
133	C₄₇×#416	C₂²	1	1	yes	characteristic, complemented
134	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic, complemented
135	#13094070	—	2	4	no	—
136	#13094070	—	2	4	no	—
137	C₂×#10625354	C₂³	1	2	yes	—
138	C₂×#10625350	—	2	1	no	—
139	C₂×#10625350	C₂³	1	1	yes	characteristic
140	C₂²×Dic₉₄	C₂³	1	1	yes	characteristic
141	C₂²×D₁₈₈	—	2	1	no	—
142	C₂²×D₁₈₈	C₂³	1	1	yes	characteristic
143	C₂×D₄×D₄₇	—	2	2	no	—
144	C₂×D₄×D₄₇	C₂³	1	2	yes	—
145	C₂²×C₄×D₄₇	—	2	1	no	—
146	C₂²×C₄×D₄₇	—	2	2	no	—
147	#13094054	—	2	4	no	—
148	#13094049	—	2	4	no	—
149	C₂×#10625337	C₂³	1	2	yes	—
150	C₂×#10625325	—	2	4	no	—
151	C₂×#10625325	C₂³	1	2	yes	—
152	C₂×#10625325	C₂³	1	2	yes	—
153	C₂×#10625335	C₂³	1	2	yes	—
154	C₂×#10625336	C₂³	1	2	yes	—
155	C₂×#10625334	C₂³	1	2	yes	—
156	C₂×#10625329	C₂³	1	1	yes	characteristic
157	C₂×#10625329	C₂³	1	1	yes	characteristic
158	#13094024	—	2	1	no	—
159	#13094024	—	2	1	no	—
160	#13094023	C₂³	1	2	yes	—
161	#13094022	C₂³	1	2	yes	—
162	#13094019	—	2	2	no	—
163	#13094018	—	2	2	no	—
164	#13094017	—	2	2	no	—
165	#13094017	—	2	2	no	—
166	#13094016	—	2	1	no	—
167	#13094016	—	2	2	no	—
168	#13094015	C₂³	1	2	yes	—
169	#13094014	—	2	2	no	—
170	#13094014	—	2	2	no	—
171	#13094012	—	2	1	no	—
172	#13094011	C₂³	1	2	yes	—
173	#13094010	—	2	2	no	—
174	#13094008	—	2	2	no	—
175	#13094007	—	2	2	no	—
176	#13094006	—	2	2	no	—
177	#13094005	—	2	2	no	—
178	#13094004	C₂³	1	2	yes	—
179	#13094004	C₂³	1	2	yes	—
180	#13094003	—	2	1	no	—
181	#13094003	—	2	1	no	—
182	#13094003	—	2	1	no	—
183	#13094003	—	2	2	no	—
184	#13094002	—	2	2	no	—
185	#13094001	—	2	2	no	—
186	#13094000	C₂³	1	2	yes	—
187	#13093998	—	2	1	no	—
188	#13093996	—	2	2	no	—
189	#13093995	C₂³	1	2	yes	—
190	Q₈×Dic₄₇	C₂³	1	2	yes	—
191	C₄×Dic₉₄	—	2	1	no	—
192	C₄×Dic₉₄	—	2	1	no	—
193	C₄×Dic₉₄	—	2	1	no	—
194	C₄×Dic₉₄	—	2	2	no	—
195	C₄×Dic₉₄	D₄	1	1	yes	characteristic
196	C₄×Dic₉₄	D₄	1	1	yes	characteristic
197	C₄×Dic₉₄	C₂³	1	2	yes	—
198	C₄×Dic₉₄	C₂³	1	2	yes	—
199	C₄×D₁₈₈	—	2	1	no	—
200	C₄×D₁₈₈	—	2	2	no	—
201	C₄×D₁₈₈	—	2	1	no	—
202	C₄×D₁₈₈	—	2	1	no	—
203	C₄×D₁₈₈	—	2	2	no	—
204	C₄×D₁₈₈	—	2	1	no	—
205	C₄×D₁₈₈	—	2	1	no	—
206	C₄×D₁₈₈	D₄	1	1	yes	characteristic
207	C₄×D₁₈₈	D₄	1	1	yes	characteristic
208	C₄×D₁₈₈	C₂³	1	2	yes	—
209	C₄×D₁₈₈	C₂³	1	2	yes	—
210	D₄×Dic₄₇	—	2	2	no	—
211	D₄×Dic₄₇	C₂³	1	2	yes	—
212	#13093986	—	2	2	no	—
213	#13093986	—	2	2	no	—
214	#13093986	C₂³	1	2	yes	—
215	#13093986	C₂³	1	2	yes	—
216	C₄×C₂²⋊D₄₇	—	2	2	no	—
217	C₄×C₂²⋊D₄₇	—	2	2	no	—
218	C₄×C₂²⋊D₄₇	—	2	2	no	—
219	C₄×C₂²⋊D₄₇	D₄	1	2	yes	—
220	C₄×C₂²⋊D₄₇	D₄	1	2	yes	—
221	(C₂²⋊D₄₇)⋊C₄	—	2	2	no	—
222	(C₂²⋊D₄₇)⋊C₄	—	2	2	no	—
223	(C₂²⋊D₄₇)⋊C₄	—	2	2	no	—
224	#13093983	—	2	1	no	—
225	#13093983	—	2	2	no	—
226	#13093983	C₂³	1	1	yes	characteristic
227	#13093982	—	2	2	no	—
228	#13093982	C₂³	1	2	yes	—
229	#13093981	—	2	2	no	—
230	#13093981	—	2	2	no	—
231	#13093981	C₂³	1	2	yes	—
232	C₂×C₄⋊Dic₄₇	—	2	1	no	—
233	C₂×C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic
234	C₂×C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic
235	C₂×Dic₄₇⋊C₄	—	2	1	no	—
236	C₄⋊C₄×D₄₇	—	2	2	no	—
237	C₄⋊C₄×D₄₇	C₂³	1	2	yes	—
238	C₂×(C₂×D₄₇)⋊C₄	—	2	1	no	—
239	C₂×(C₂×D₄₇)⋊C₄	—	2	2	no	—
240	C₂²⋊C₄×D₄₇	—	2	2	no	—
241	C₂²⋊C₄×D₄₇	—	2	2	no	—
242	C₂²⋊C₄×D₄₇	—	2	2	no	—
243	C₂×C₄×Dic₄₇	—	2	1	no	—
244	C₄²×D₄₇	—	2	2	no	—
245	C₄²×D₄₇	C₂³	1	2	yes	—
246	#13093957	C₂³	1	2	yes	—
247	#13093957	C₂³	1	2	yes	—
248	#13093956	C₂³	1	2	yes	—
249	#13093956	C₂³	1	2	yes	—
250	#13093955	C₂³	1	2	yes	—
251	#13093955	C₂³	1	2	yes	—
252	Dic₄₇⋊C₈	C₂³	1	2	yes	—
253	Dic₄₇⋊C₈	C₂³	1	2	yes	—
254	Dic₄₇⋊C₈	C₂³	1	2	yes	—
255	Dic₄₇⋊C₈	C₂³	1	2	yes	—
256	#13093949	C₂³	1	2	yes	—
257	#13093949	C₂³	1	2	yes	—
258	#13093948	C₂³	1	2	yes	—
259	#13093948	C₂³	1	2	yes	—
260	#13093947	C₂³	1	2	yes	—
261	#13093947	C₂³	1	2	yes	—
262	#13093946	C₂³	1	2	yes	—
263	#13093946	C₂³	1	2	yes	—
264	#13093945	C₂³	1	2	yes	—
265	#13093945	C₂³	1	2	yes	—
266	#13093944	C₂³	1	2	yes	—
267	#13093944	C₂³	1	2	yes	—
268	(C₂×D₄₇)⋊C₈	C₂³	1	2	yes	—
269	(C₂×D₄₇)⋊C₈	C₂³	1	2	yes	—
270	(C₂×D₄₇)⋊C₈	C₂³	1	2	yes	—
271	(C₂×D₄₇)⋊C₈	C₂³	1	2	yes	—
272	#13093935	C₂³	1	2	yes	—
273	C₄×C₄₇⋊C₈	C₂³	1	2	yes	—
274	C₂×#41×C₄₇	C₂³	1	1	yes	characteristic
275	C₂×#41×C₄₇	C₂³	1	1	yes	characteristic
276	#135×C₄₇	—	2	4	no	—
277	C₂×Q₁₆×C₄₇	C₂³	1	1	yes	characteristic
278	C₂×SD₁₆×C₄₇	C₂³	1	1	yes	characteristic
279	C₂×SD₁₆×C₄₇	C₂³	1	1	yes	characteristic
280	C₂×D₈×C₄₇	C₂³	1	1	yes	characteristic
281	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
282	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
283	C₄×Q₈×C₄₇	C₂³	1	1	yes	characteristic
284	C₄×Q₈×C₄₇	C₂³	1	1	yes	characteristic
285	C₄×Q₈×C₄₇	C₂³	1	1	yes	characteristic
286	C₄×Q₈×C₄₇	C₂³	1	1	yes	characteristic
287	C₄×D₄×C₄₇	—	2	1	no	—
288	C₄×D₄×C₄₇	—	2	1	no	—
289	C₄×D₄×C₄₇	—	2	1	no	—
290	C₄×D₄×C₄₇	—	2	1	no	—
291	C₄×D₄×C₄₇	C₂³	1	1	yes	characteristic
292	C₄×D₄×C₄₇	C₂³	1	1	yes	characteristic
293	C₄×D₄×C₄₇	C₂³	1	1	yes	characteristic
294	C₄×D₄×C₄₇	C₂³	1	1	yes	characteristic
295	#117×C₄₇	—	2	1	no	—
296	#117×C₄₇	—	2	1	no	—
297	#117×C₄₇	C₂³	1	1	yes	characteristic
298	#117×C₄₇	C₂³	1	1	yes	characteristic
299	C₂×C₄²×C₄₇	—	2	1	no	—
300	C₂×C₄²×C₄₇	—	2	1	no	—
301	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
302	#107×C₄₇	C₂³	1	1	yes	characteristic
303	#107×C₄₇	C₂³	1	1	yes	characteristic
304	#106×C₄₇	C₂³	1	1	yes	characteristic
305	#106×C₄₇	C₂³	1	1	yes	characteristic
306	#103×C₄₇	C₂³	1	1	yes	characteristic
307	#103×C₄₇	C₂³	1	1	yes	characteristic
308	#103×C₄₇	C₂³	1	1	yes	characteristic
309	#103×C₄₇	C₂³	1	1	yes	characteristic
310	#102×C₄₇	C₂³	1	1	yes	characteristic
311	#102×C₄₇	C₂³	1	1	yes	characteristic
312	#102×C₄₇	C₂³	1	1	yes	characteristic
313	#102×C₄₇	C₂³	1	1	yes	characteristic
314	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
315	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
316	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
317	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
318	C₂³×D₄₇	—	2	1	no	—
319	C₂³×D₄₇	—	2	2	no	—
320	#41×C₄₇	—	2	2	no	—
321	#41×C₄₇	—	2	2	no	—
322	#41×C₄₇	—	2	2	no	—
323	#41×C₄₇	#41	1	4	yes	—
324	C₂×Q₈×C₄₇	C₂⁴	1	1	yes	characteristic
325	C₂×Q₈×C₄₇	C₂⁴	1	1	yes	characteristic
326	C₂×D₄×C₄₇	—	2	1	no	—
327	C₂×D₄×C₄₇	—	2	1	no	—
328	C₂×D₄×C₄₇	C₂⁴	1	1	yes	characteristic
329	C₂×D₄×C₄₇	C₂⁴	1	1	yes	characteristic
330	C₂²×C₄×C₄₇	—	2	1	no	—
331	C₂²×C₄×C₄₇	—	2	1	no	—
332	C₂²×C₄×C₄₇	—	2	1	no	—
333	C₂²×C₄×C₄₇	—	2	1	no	—
334	C₂²×C₄×C₄₇	—	2	1	no	—
335	C₂²×C₄×C₄₇	—	2	1	no	—
336	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
337	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
338	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
339	C₂×C₂²⋊D₄₇	—	2	2	no	—
340	C₂×C₂²⋊D₄₇	—	2	2	no	—
341	C₂×C₂²⋊D₄₇	C₂×D₄	1	2	yes	—
342	C₂²×Dic₄₇	—	2	1	no	—
343	C₂²×Dic₄₇	—	2	1	no	—
344	C₂²×Dic₄₇	—	2	1	no	—
345	C₂²×Dic₄₇	—	2	2	no	—
346	#10625354	—	2	4	no	—
347	#10625354	—	2	4	no	—
348	D₄×D₄₇	—	2	16	no	—
349	D₄×D₄₇	—	2	4	no	—
350	D₄×D₄₇	—	2	4	no	—
351	#10625350	—	2	8	no	—
352	#10625350	—	2	2	no	—
353	#10625350	—	2	2	no	—
354	C₂×D₁₈₈	—	2	8	no	—
355	C₂×D₁₈₈	—	2	2	no	—
356	C₂×D₁₈₈	—	2	1	no	—
357	C₂×D₁₈₈	—	2	2	no	—
358	C₂×D₁₈₈	C₂×D₄	1	1	yes	characteristic
359	C₂×D₁₈₈	#41	1	4	yes	—
360	C₂×D₁₈₈	C₂⁴	1	2	yes	—
361	C₂×C₄×D₄₇	—	2	2	no	—
362	C₂×C₄×D₄₇	—	2	2	no	—
363	C₂×C₄×D₄₇	—	2	2	no	—
364	C₂×C₄×D₄₇	—	2	2	no	—
365	C₂×C₄×D₄₇	—	2	2	no	—
366	C₂×C₄×D₄₇	—	2	2	no	—
367	C₂×C₄×D₄₇	—	8	4	no	—
368	C₂×C₄×D₄₇	—	8	2	no	—
369	C₂×C₄×D₄₇	C₂×D₄	1	2	yes	—
370	C₂×C₄×D₄₇	C₂×D₄	1	2	yes	—
371	C₂×C₄×D₄₇	C₂⁴	1	2	yes	—
372	C₂×Dic₉₄	—	2	2	no	—
373	C₂×Dic₉₄	—	2	2	no	—
374	C₂×Dic₉₄	—	2	1	no	—
375	C₂×Dic₉₄	—	2	2	no	—
376	C₂×Dic₉₄	C₂×D₄	1	1	yes	characteristic
377	C₂×Dic₉₄	C₂⁴	1	2	yes	—
378	Q₁₆×C₄₇	—	2	2	no	—
379	SD₁₆×C₄₇	—	2	2	no	—
380	SD₁₆×C₄₇	—	2	2	no	—
381	D₈×C₄₇	—	2	2	no	—
382	C₂×C₈×C₄₇	—	2	2	no	—
383	C₂×C₈×C₄₇	—	2	2	no	—
384	C₂×C₈×C₄₇	C₂⁴	1	1	yes	characteristic
385	C₂×C₈×C₄₇	C₂⁴	1	1	yes	characteristic
386	C₂×C₈×C₄₇	C₂⁴	1	1	yes	characteristic
387	C₂×C₈×C₄₇	C₂⁴	1	1	yes	characteristic
388	C₄⋊C₄×C₄₇	—	2	1	no	—
389	C₄⋊C₄×C₄₇	—	2	1	no	—
390	C₄⋊C₄×C₄₇	—	2	1	no	—
391	C₄⋊C₄×C₄₇	—	2	1	no	—
392	C₄⋊C₄×C₄₇	C₂⁴	1	1	yes	characteristic
393	C₄⋊C₄×C₄₇	C₂⁴	1	1	yes	characteristic
394	C₄⋊C₄×C₄₇	C₂⁴	1	1	yes	characteristic
395	C₄⋊C₄×C₄₇	C₂⁴	1	1	yes	characteristic
396	C₂²⋊C₄×C₄₇	—	2	1	no	—
397	C₂²⋊C₄×C₄₇	—	2	1	no	—
398	C₂²⋊C₄×C₄₇	—	2	1	no	—
399	C₂²⋊C₄×C₄₇	—	2	1	no	—
400	C₂²⋊C₄×C₄₇	—	2	1	no	—
401	C₂²⋊C₄×C₄₇	—	2	1	no	—
402	C₄²×C₄₇	—	2	1	no	—
403	C₄²×C₄₇	—	2	1	no	—
404	C₄²×C₄₇	—	2	1	no	—
405	C₄²×C₄₇	—	2	1	no	—
406	C₄²×C₄₇	—	2	1	no	—
407	C₄²×C₄₇	—	2	1	no	—
408	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
409	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
410	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
411	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
412	C₂²⋊Dic₄₇	—	2	2	no	—
413	C₂²⋊Dic₄₇	—	2	2	no	—
414	C₂²⋊Dic₄₇	—	2	2	no	—
415	C₂²⋊Dic₄₇	—	2	2	no	—
416	C₂²⋊Dic₄₇	C₂×D₄	1	2	yes	—
417	#10625337	—	2	4	no	—
418	#10625336	—	2	4	no	—
419	#10625335	—	2	4	no	—
420	#10625334	—	2	4	no	—
421	(C₂×D₄₇)⋊C₄	—	2	2	no	—
422	(C₂×D₄₇)⋊C₄	—	2	2	no	—
423	(C₂×D₄₇)⋊C₄	—	2	2	no	—
424	(C₂×D₄₇)⋊C₄	—	2	2	no	—
425	(C₂×D₄₇)⋊C₄	—	2	2	no	—
426	(C₂×D₄₇)⋊C₄	—	2	2	no	—
427	(C₂×D₄₇)⋊C₄	—	2	2	no	—
428	(C₂×D₄₇)⋊C₄	—	2	2	no	—
429	(C₂×D₄₇)⋊C₄	C₂×D₄	1	2	yes	—
430	(C₂×D₄₇)⋊C₄	C₂×D₄	1	2	yes	—
431	C₄⋊Dic₄₇	—	2	1	no	—
432	C₄⋊Dic₄₇	—	2	1	no	—
433	C₄⋊Dic₄₇	—	2	2	no	—
434	C₄⋊Dic₄₇	—	2	2	no	—
435	C₄⋊Dic₄₇	—	2	2	no	—
436	C₄⋊Dic₄₇	—	2	2	no	—
437	C₄⋊Dic₄₇	C₂×D₄	1	1	yes	characteristic
438	C₄⋊Dic₄₇	C₂×D₄	1	1	yes	characteristic
439	C₄⋊Dic₄₇	C₂⁴	1	2	yes	—
440	C₄⋊Dic₄₇	C₂⁴	1	2	yes	—
441	Dic₄₇⋊C₄	—	2	2	no	—
442	Dic₄₇⋊C₄	—	2	2	no	—
443	Dic₄₇⋊C₄	—	2	2	no	—
444	Dic₄₇⋊C₄	—	2	2	no	—
445	Dic₄₇⋊C₄	—	2	2	no	—
446	Dic₄₇⋊C₄	—	2	2	no	—
447	Dic₄₇⋊C₄	—	2	2	no	—
448	Dic₄₇⋊C₄	—	2	2	no	—
449	Dic₄₇⋊C₄	C₂×D₄	1	2	yes	—
450	Dic₄₇⋊C₄	C₂×D₄	1	2	yes	—
451	C₄×Dic₄₇	—	2	2	no	—
452	C₄×Dic₄₇	—	2	2	no	—
453	C₄×Dic₄₇	—	2	2	no	—
454	C₄×Dic₄₇	—	2	2	no	—
455	C₄×Dic₄₇	C₂×D₄	1	2	yes	—
456	C₄×Dic₄₇	C₂×D₄	1	2	yes	—
457	C₄×Dic₄₇	C₂⁴	1	2	yes	—
458	#10625329	—	2	2	no	—
459	#10625329	—	2	2	no	—
460	C₂×C₄₇⋊C₈	C₂⁴	1	2	yes	—
461	C₂×C₄₇⋊C₈	C₂⁴	1	2	yes	—
462	#10625325	—	2	4	no	—
463	#10625325	—	2	4	no	—
464	C₂³×C₄₇	—	2	1	no	—
465	C₂³×C₄₇	—	2	1	no	—
466	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
467	C₂²×D₄₇	—	2	2	no	—
468	C₂²×D₄₇	—	2	8	no	—
469	C₂²×D₄₇	—	2	4	no	—
470	C₂²×D₄₇	—	8	2	no	—
471	C₂²×D₄₇	—	8	2	no	—
472	C₂²×D₄₇	—	8	1	no	—
473	C₂²×D₄₇	—	8	1	no	—
474	C₂²×D₄₇	C₂²×D₄	1	2	yes	—
475	Q₈×C₄₇	—	2	1	no	—
476	Q₈×C₄₇	—	2	1	no	—
477	Q₈×C₄₇	—	2	1	no	—
478	Q₈×C₄₇	C₂×#41	1	2	yes	—
479	D₄×C₄₇	—	2	4	no	—
480	D₄×C₄₇	—	2	1	no	—
481	D₄×C₄₇	—	2	1	no	—
482	D₄×C₄₇	—	2	1	no	—
483	D₄×C₄₇	—	4	2	no	—
484	D₄×C₄₇	C₂×#41	1	2	yes	—
485	C₂×C₄×C₄₇	—	2	1	no	—
486	C₂×C₄×C₄₇	—	2	4	no	—
487	C₂×C₄×C₄₇	—	2	2	no	—
488	C₂×C₄×C₄₇	—	2	1	no	—
489	C₂×C₄×C₄₇	—	2	1	no	—
490	C₂×C₄×C₄₇	—	2	1	no	—
491	C₂×C₄×C₄₇	—	2	1	no	—
492	C₂×C₄×C₄₇	—	2	1	no	—
493	C₂×C₄×C₄₇	—	4	1	no	—
494	C₂×C₄×C₄₇	—	4	2	no	—
495	C₂×C₄×C₄₇	—	4	2	no	—
496	C₂×C₄×C₄₇	—	4	2	no	—
497	C₂×C₄×C₄₇	—	8	1	no	—
498	C₂×C₄×C₄₇	—	8	1	no	—
499	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
500	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
501	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
502	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
503	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
504	C₂×C₄×C₄₇	C₂×#41	1	2	yes	—
505	C₂×C₄×C₄₇	C₂×#41	1	2	yes	—
506	C₂×C₄×C₄₇	C₂⁵	1	1	yes	characteristic
507	C₂²⋊D₄₇	—	2	8	no	—
508	C₂²⋊D₄₇	—	2	4	no	—
509	C₂²⋊D₄₇	—	8	2	no	—
510	C₂×Dic₄₇	—	2	2	no	—
511	C₂×Dic₄₇	—	2	2	no	—
512	C₂×Dic₄₇	—	2	2	no	—
513	C₂×Dic₄₇	—	4	2	no	—
514	C₂×Dic₄₇	—	8	2	no	—
515	C₂×Dic₄₇	—	8	1	no	—
516	C₂×Dic₄₇	—	8	1	no	—
517	C₂×Dic₄₇	C₂²×D₄	1	2	yes	—
518	C₂×Dic₄₇	C₂²×D₄	1	2	yes	—
519	C₂×Dic₄₇	C₂²×D₄	1	2	yes	—
520	D₁₈₈	—	2	8	no	—
521	D₁₈₈	—	2	2	no	—
522	D₁₈₈	—	2	4	no	—
523	D₁₈₈	—	2	2	no	—
524	D₁₈₈	C₂×#41	1	4	yes	—
525	C₄×D₄₇	—	2	8	no	—
526	C₄×D₄₇	—	2	4	no	—
527	C₄×D₄₇	—	2	2	no	—
528	C₄×D₄₇	—	2	2	no	—
529	C₄×D₄₇	—	4	2	no	—
530	C₄×D₄₇	—	4	4	no	—
531	C₄×D₄₇	—	8	2	no	—
532	C₄×D₄₇	—	8	2	no	—
533	C₄×D₄₇	—	8	2	no	—
534	C₄×D₄₇	—	8	2	no	—
535	Dic₉₄	—	2	2	no	—
536	Dic₉₄	—	2	2	no	—
537	Dic₉₄	—	2	2	no	—
538	Dic₉₄	—	4	2	no	—
539	Dic₉₄	—	8	2	no	—
540	C₈×C₄₇	—	2	1	no	—
541	C₈×C₄₇	—	2	1	no	—
542	C₈×C₄₇	—	2	1	no	—
543	C₈×C₄₇	—	2	1	no	—
544	C₄₇⋊C₈	—	2	2	no	—
545	C₄₇⋊C₈	—	2	2	no	—
546	#60571	—	47	1	no	maximal, Sylow
547	C₂²×C₄₇	—	2	1	no	—
548	C₂²×C₄₇	—	2	1	no	—
549	C₂²×C₄₇	—	2	2	no	—
550	C₂²×C₄₇	—	4	1	no	—
551	C₂²×C₄₇	—	4	1	no	—
552	C₂²×C₄₇	—	4	1	no	—
553	C₂²×C₄₇	—	4	1	no	—
554	C₂²×C₄₇	—	4	1	no	—
555	C₂²×C₄₇	#525	1	2	yes	—
556	C₂²×C₄₇	C₂³×D₄	1	1	yes	characteristic
557	C₂×D₄₇	—	2	2	no	—
558	C₂×D₄₇	—	2	2	no	—
559	C₂×D₄₇	—	2	4	no	—
560	C₂×D₄₇	—	2	2	no	—
561	C₂×D₄₇	—	4	2	no	—
562	C₂×D₄₇	—	4	2	no	—
563	C₂×D₄₇	—	8	4	no	—
564	C₂×D₄₇	—	8	8	no	—
565	C₄×C₄₇	—	2	1	no	—
566	C₄×C₄₇	—	2	1	no	—
567	C₄×C₄₇	—	2	2	no	—
568	C₄×C₄₇	—	2	1	no	—
569	C₄×C₄₇	—	4	1	no	—
570	C₄×C₄₇	—	4	1	no	—
571	C₄×C₄₇	—	4	1	no	—
572	C₄×C₄₇	—	4	1	no	—
573	C₄×C₄₇	—	4	1	no	—
574	C₄×C₄₇	#525	1	2	yes	—
575	C₄×C₄₇	#577	1	2	yes	—
576	C₄×C₄₇	C₂²×#41	1	1	yes	characteristic
577	C₄×C₄₇	C₂²×#41	1	1	yes	characteristic
578	Dic₄₇	—	2	2	no	—
579	Dic₄₇	—	2	2	no	—
580	Dic₄₇	—	2	2	no	—
581	Dic₄₇	—	4	2	no	—
582	Dic₄₇	—	4	2	no	—
583	Dic₄₇	—	4	2	no	—
584	#3461	—	47	1	no	—
585	C₄×H(5,𝔽₂)	—	47	1	no	—
586	#3125	—	47	2	no	—
587	#3123	—	47	2	no	—
588	#3120	—	47	2	no	—
589	#3118	—	47	2	no	—
590	#3107	—	47	2	no	—
591	#3105	—	47	2	no	—
592	#3102	—	47	2	no	—
593	#3101	—	47	2	no	—
594	#3099	—	47	1	no	—
595	#3097	—	47	1	no	—
596	#3084	—	47	1	no	—
597	#3081	—	47	1	no	—
598	#3046	—	47	1	no	—
599	#3042	—	47	1	no	—
600	#3012	—	47	1	no	—
601	#3009	—	47	1	no	—
602	C₄×#137	—	47	1	no	—
603	C₄×AGL(1,ℤ/8)	—	47	1	no	—
604	C₄×#135	D₄₇	1	1	yes	characteristic, complemented
605	C₂×C₄×SD₁₆	—	47	1	no	—
606	#2922	—	47	1	no	—
607	C₂×C₄₇	—	2	2	no	—
608	C₂×C₄₇	—	4	2	no	—
609	C₂×C₄₇	—	8	1	no	—
610	C₂×C₄₇	C₂×#525	1	1	yes	characteristic
611	C₂×C₄₇	C₂×#577	1	1	yes	characteristic
612	C₂×C₄₇	#3584	1	1	yes	characteristic
613	D₄₇	—	4	2	no	—
614	D₄₇	—	4	4	no	—
615	C₂×H(5,𝔽₂)	—	47	1	no	—
616	C₂×#137	—	47	1	no	—
617	C₂×AGL(1,ℤ/8)	—	47	1	no	—
618	C₂×#135	C₂×D₄₇	1	1	yes	characteristic
619	C₂²×SD₁₆	—	47	1	no	—
620	#544	—	47	1	no	—
621	#542	—	47	2	no	—
622	#542	—	94	1	no	—
623	#541	—	47	2	no	—
624	#541	—	94	1	no	—
625	#539	—	94	2	no	—
626	#537	—	47	1	no	—
627	#536	—	47	1	no	—
628	#536	—	47	1	no	—
629	#533	—	47	2	no	—
630	#533	—	94	1	no	—
631	#529	—	47	2	no	—
632	#529	—	94	1	no	—
633	#529	—	94	2	no	—
634	#520	—	47	1	no	—
635	#520	—	47	1	no	—
636	#520	—	47	2	no	—
637	#520	—	94	1	no	—
638	#518	—	47	2	no	—
639	#518	—	47	1	no	—
640	#518	—	94	1	no	—
641	#518	—	94	2	no	—
642	C₄×#41	—	47	1	no	—
643	C₄×#41	—	47	2	no	—
644	C₄×#41	—	94	1	no	—
645	C₄×#41	C₂×D₄₇	1	1	yes	characteristic
646	C₄×#41	C₂×D₄₇	1	1	yes	characteristic, complemented
647	C₂×C₄×Q₈	—	47	1	no	—
648	C₂×C₄×D₄	—	47	2	no	—
649	C₂×C₄×D₄	—	47	1	no	—
650	C₂×C₄×D₄	—	94	1	no	—
651	C₂×C₄×D₄	—	94	2	no	—
652	#485	—	47	2	no	—
653	#485	—	47	2	no	—
654	#485	—	47	2	no	—
655	#484	—	47	2	no	—
656	#483	—	47	2	no	—
657	#483	—	47	2	no	—
658	#482	—	47	2	no	—
659	#481	—	47	2	no	—
660	#479	—	47	2	no	—
661	#478	—	47	2	no	—
662	#478	—	47	2	no	—
663	#478	—	47	2	no	—
664	#476	—	47	2	no	—
665	#476	—	47	2	no	—
666	#475	—	47	2	no	—
667	#474	—	47	2	no	—
668	#464	—	47	2	no	—
669	#463	—	47	2	no	—
670	#463	—	47	2	no	—
671	#463	—	47	2	no	—
672	#462	—	47	2	no	—
673	#461	—	47	2	no	—
674	#461	—	47	2	no	—
675	#461	—	47	2	no	—
676	#452	—	47	2	no	—
677	#452	—	47	2	no	—
678	#452	—	47	2	no	—
679	#450	—	47	2	no	—
680	#450	—	47	2	no	—
681	#450	—	47	2	no	—
682	#449	—	47	2	no	—
683	#447	—	47	2	no	—
684	#442	—	47	2	no	—
685	#441	—	47	2	no	—
686	#440	—	47	2	no	—
687	#440	—	47	2	no	—
688	C₄×Q₁₆	—	47	2	no	—
689	C₄×Q₁₆	C₂×D₄₇	1	1	yes	characteristic, complemented
690	C₄×Q₁₆	C₂×D₄₇	1	1	yes	characteristic, complemented
691	C₄×SD₁₆	—	47	2	no	—
692	C₄×SD₁₆	—	47	2	no	—
693	C₄×SD₁₆	—	47	2	no	—
694	C₄×SD₁₆	—	47	2	no	—
695	C₄×SD₁₆	—	47	2	no	—
696	C₄×SD₁₆	—	47	2	no	—
697	C₄×SD₁₆	C₂×D₄₇	1	1	yes	characteristic, complemented
698	C₄×SD₁₆	C₂×D₄₇	1	1	yes	characteristic, complemented
699	C₄×SD₁₆	C₂×D₄₇	1	1	yes	characteristic, complemented
700	C₄×SD₁₆	C₂×D₄₇	1	1	yes	characteristic, complemented
701	C₄×D₈	—	47	2	no	—
702	C₄×D₈	C₂×D₄₇	1	1	yes	characteristic, complemented
703	C₄×D₈	C₂×D₄₇	1	1	yes	characteristic, complemented
704	#433	—	47	2	no	—
705	#433	—	47	2	no	—
706	#431	—	47	2	no	—
707	#431	—	47	2	no	—
708	#428	—	47	1	no	—
709	#428	—	47	1	no	—
710	#427	C₂×D₄₇	1	1	yes	characteristic, complemented
711	C₂×#106	—	47	1	no	—
712	#424	—	47	1	no	—
713	#424	—	47	1	no	—
714	#419	—	47	1	no	—
715	#418	—	47	1	no	—
716	#417	—	47	1	no	—
717	#417	—	47	1	no	—
718	#416	C₂×D₄₇	1	1	yes	characteristic
719	#416	C₂×D₄₇	1	1	yes	characteristic, complemented
720	C₂×#103	—	47	1	no	—
721	C₂×#102	—	47	1	no	—
722	#408	—	47	1	no	—
723	#408	—	47	1	no	—
724	C₄×M₁₆	—	47	1	no	—
725	C₂×C₄×C₈	C₂×D₄₇	1	1	yes	characteristic, complemented
726	C₄₇	#60571	1	1	yes	characteristic, complemented, Sylow
727	H(5,𝔽₂)	—	94	4	no	—
728	H(5,𝔽₂)	—	94	4	no	—
729	C₂×#41	—	47	1	no	—
730	C₂×#41	—	47	2	no	—
731	C₂×#41	—	94	1	no	—
732	C₂×#41	C₂²×D₄₇	1	1	yes	characteristic
733	C₂×#41	C₂²×D₄₇	1	1	yes	characteristic
734	C₂²×Q₈	—	47	1	no	—
735	C₂²×D₄	—	47	2	no	—
736	C₂²×D₄	—	47	1	no	—
737	C₂²×D₄	—	94	1	no	—
738	C₂²×D₄	—	94	2	no	—
739	C₂³×C₄	—	94	2	no	—
740	C₂³×C₄	—	94	1	no	—
741	#137	—	94	4	no	—
742	AGL(1,ℤ/8)	—	94	4	no	—
743	#135	—	2	4	no	—
744	C₂×Q₁₆	—	47	2	no	—
745	C₂×Q₁₆	C₂²×D₄₇	1	1	yes	characteristic
746	C₂×SD₁₆	—	47	2	no	—
747	C₂×SD₁₆	—	47	2	no	—
748	C₂×SD₁₆	—	47	2	no	—
749	C₂×SD₁₆	—	47	2	no	—
750	C₂×SD₁₆	—	94	4	no	—
751	C₂×SD₁₆	C₂²×D₄₇	1	1	yes	characteristic
752	C₂×SD₁₆	C₂²×D₄₇	1	1	yes	characteristic
753	C₂×D₈	—	47	2	no	—
754	C₂×D₈	C₂²×D₄₇	1	1	yes	characteristic
755	C₂×M₁₆	—	47	1	no	—
756	C₂×M₁₆	—	47	1	no	—
757	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
758	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
759	C₄⋊Q₈	—	47	2	no	—
760	C₄⋊Q₈	—	47	2	no	—
761	C₄⋊Q₈	—	94	1	no	—
762	C₄⋊Q₈	—	94	1	no	—
763	#126	—	94	2	no	—
764	#126	—	94	2	no	—
765	#126	—	94	2	no	—
766	#126	—	94	2	no	—
767	#125	—	47	2	no	—
768	#125	—	94	1	no	—
769	#125	—	94	2	no	—
770	#125	—	94	2	no	—
771	#125	—	94	2	no	—
772	#124	—	47	2	no	—
773	#124	—	94	1	no	—
774	#124	—	94	2	no	—
775	#123	—	94	2	no	—
776	#123	—	94	2	no	—
777	#123	—	94	2	no	—
778	#123	—	94	2	no	—
779	C₂²⋊Q₈	—	47	2	no	—
780	C₂²⋊Q₈	—	47	2	no	—
781	C₂²⋊Q₈	—	47	2	no	—
782	C₂²⋊Q₈	—	94	2	no	—
783	C₂²⋊Q₈	—	94	2	no	—
784	C₂²⋊Q₈	—	94	1	no	—
785	C₂²⋊Q₈	—	94	1	no	—
786	C₂²⋊Q₈	—	94	2	no	—
787	C₂²⋊Q₈	—	94	1	no	—
788	#121	—	47	2	no	—
789	#121	—	94	1	no	—
790	#121	—	94	2	no	—
791	C₄×Q₈	—	47	1	no	—
792	C₄×Q₈	—	47	1	no	—
793	C₄×Q₈	—	47	2	no	—
794	C₄×Q₈	—	47	2	no	—
795	C₄×Q₈	—	47	2	no	—
796	C₄×Q₈	—	94	2	no	—
797	C₄×Q₈	—	94	1	no	—
798	C₄×Q₈	—	94	1	no	—
799	C₄×Q₈	—	94	1	no	—
800	C₄×Q₈	C₂²×D₄₇	1	1	yes	characteristic
801	C₄×Q₈	C₂²×D₄₇	1	1	yes	characteristic
802	C₄×Q₈	C₂²×D₄₇	1	1	yes	characteristic
803	C₄×Q₈	C₂²×D₄₇	1	1	yes	characteristic
804	C₄×D₄	—	2	1	no	—
805	C₄×D₄	—	2	1	no	—
806	C₄×D₄	—	2	1	no	—
807	C₄×D₄	—	2	1	no	—
808	C₄×D₄	—	47	2	no	—
809	C₄×D₄	—	47	2	no	—
810	C₄×D₄	—	47	2	no	—
811	C₄×D₄	—	47	2	no	—
812	C₄×D₄	—	47	2	no	—
813	C₄×D₄	—	47	1	no	—
814	C₄×D₄	—	47	1	no	—
815	C₄×D₄	—	47	2	no	—
816	C₄×D₄	—	47	2	no	—
817	C₄×D₄	—	94	2	no	—
818	C₄×D₄	—	94	1	no	—
819	C₄×D₄	—	94	1	no	—
820	C₄×D₄	—	94	2	no	—
821	C₄×D₄	—	94	1	no	—
822	C₄×D₄	—	94	2	no	—
823	C₄×D₄	—	94	2	no	—
824	C₄×D₄	—	94	2	no	—
825	C₄×D₄	—	94	2	no	—
826	C₄×D₄	—	94	2	no	—
827	C₄×D₄	—	94	2	no	—
828	C₄×D₄	—	94	2	no	—
829	C₄×D₄	—	94	2	no	—
830	C₄×D₄	—	94	2	no	—
831	C₄×D₄	—	94	1	no	—
832	C₄×D₄	—	94	1	no	—
833	C₄×D₄	C₂²×D₄₇	1	1	yes	characteristic
834	C₄×D₄	C₂²×D₄₇	1	1	yes	characteristic
835	C₄×D₄	C₂²×D₄₇	1	1	yes	characteristic
836	C₄×D₄	C₂²×D₄₇	1	1	yes	characteristic
837	#117	—	2	1	no	—
838	#117	—	2	1	no	—
839	#117	—	47	1	no	—
840	#117	—	47	2	no	—
841	#117	—	47	2	no	—
842	#117	—	94	2	no	—
843	#117	—	94	2	no	—
844	#117	—	94	2	no	—
845	#117	—	94	2	no	—
846	#117	—	94	1	no	—
847	#117	C₂²×D₄₇	1	1	yes	characteristic
848	#117	C₂²×D₄₇	1	1	yes	characteristic
849	C₂×C₄⋊C₄	—	47	1	no	—
850	C₂×C₄⋊C₄	—	47	1	no	—
851	C₂×C₄⋊C₄	—	47	2	no	—
852	C₂×C₄⋊C₄	—	94	2	no	—
853	C₂×C₄⋊C₄	—	94	1	no	—
854	C₂×C₄⋊C₄	—	94	1	no	—
855	C₂×C₂²⋊C₄	—	94	2	no	—
856	C₂×C₂²⋊C₄	—	94	2	no	—
857	C₂×C₂²⋊C₄	—	94	2	no	—
858	C₂×C₂²⋊C₄	—	94	2	no	—
859	C₂×C₂²⋊C₄	—	94	1	no	—
860	C₂×C₄²	—	2	1	no	—
861	C₂×C₄²	—	2	1	no	—
862	C₂×C₄²	—	47	2	no	—
863	C₂×C₄²	—	94	2	no	—
864	C₂×C₄²	—	94	1	no	—
865	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
866	#107	—	47	2	no	—
867	#107	—	47	2	no	—
868	#107	C₂²×D₄₇	1	1	yes	characteristic
869	#107	C₂²×D₄₇	1	1	yes	characteristic
870	#106	—	47	2	no	—
871	#106	—	47	2	no	—
872	#106	—	47	2	no	—
873	#106	—	47	2	no	—
874	#106	C₂²×D₄₇	1	1	yes	characteristic
875	#106	C₂²×D₄₇	1	1	yes	characteristic
876	C₄⋊C₈	—	47	2	no	—
877	C₄⋊C₈	—	47	2	no	—
878	C₄⋊C₈	—	47	2	no	—
879	C₄⋊C₈	—	47	2	no	—
880	#103	—	47	2	no	—
881	#103	—	47	2	no	—
882	#103	—	47	2	no	—
883	#103	—	47	2	no	—
884	#103	—	47	2	no	—
885	#103	—	47	2	no	—
886	#103	C₂²×D₄₇	1	1	yes	characteristic
887	#103	C₂²×D₄₇	1	1	yes	characteristic
888	#103	C₂²×D₄₇	1	1	yes	characteristic
889	#103	C₂²×D₄₇	1	1	yes	characteristic
890	#102	—	47	2	no	—
891	#102	—	47	2	no	—
892	#102	—	47	2	no	—
893	#102	—	47	2	no	—
894	#102	—	47	2	no	—
895	#102	—	47	2	no	—
896	#102	C₂²×D₄₇	1	1	yes	characteristic
897	#102	C₂²×D₄₇	1	1	yes	characteristic
898	#102	C₂²×D₄₇	1	1	yes	characteristic
899	#102	C₂²×D₄₇	1	1	yes	characteristic
900	C₂²⋊C₈	—	47	2	no	—
901	C₂²⋊C₈	—	47	2	no	—
902	C₂²⋊C₈	—	47	2	no	—
903	C₂²⋊C₈	—	47	2	no	—
904	#97	—	47	2	no	—
905	C₄×C₈	—	47	2	no	—
906	C₄×C₈	C₂²×D₄₇	1	1	yes	characteristic
907	C₄×C₈	C₂²×D₄₇	1	1	yes	characteristic
908	C₄×C₈	C₂²×D₄₇	1	1	yes	characteristic
909	C₄×C₈	C₂²×D₄₇	1	1	yes	characteristic
910	C₂⁴	—	94	2	no	—
911	C₂⁴	—	94	1	no	—
912	#41	—	2	2	no	—
913	#41	—	2	2	no	—
914	#41	—	2	2	no	—
915	#41	—	94	8	no	—
916	#41	—	94	4	no	—
917	#41	—	94	4	no	—
918	#41	—	94	2	no	—
919	#41	—	94	2	no	—
920	#41	#10625350	1	4	yes	—
921	C₂×Q₈	—	47	1	no	—
922	C₂×Q₈	—	47	2	no	—
923	C₂×Q₈	—	94	2	no	—
924	C₂×Q₈	—	94	1	no	—
925	C₂×Q₈	—	94	2	no	—
926	C₂×Q₈	—	94	2	no	—
927	C₂×Q₈	C₂³×D₄₇	1	1	yes	characteristic
928	C₂×Q₈	C₂³×D₄₇	1	1	yes	characteristic
929	C₂×D₄	—	2	1	no	—
930	C₂×D₄	—	2	1	no	—
931	C₂×D₄	—	47	2	no	—
932	C₂×D₄	—	47	1	no	—
933	C₂×D₄	—	47	4	no	—
934	C₂×D₄	—	47	2	no	—
935	C₂×D₄	—	94	2	no	—
936	C₂×D₄	—	94	8	no	—
937	C₂×D₄	—	94	2	no	—
938	C₂×D₄	—	94	4	no	—
939	C₂×D₄	—	94	16	no	—
940	C₂×D₄	—	94	4	no	—
941	C₂×D₄	—	94	2	no	—
942	C₂×D₄	—	94	1	no	—
943	C₂×D₄	—	94	2	no	—
944	C₂×D₄	C₂³×D₄₇	1	1	yes	characteristic
945	C₂×D₄	C₂³×D₄₇	1	1	yes	characteristic
946	C₂²×C₄	—	2	1	no	—
947	C₂²×C₄	—	2	1	no	—
948	C₂²×C₄	—	2	1	no	—
949	C₂²×C₄	—	2	1	no	—
950	C₂²×C₄	—	2	1	no	—
951	C₂²×C₄	—	2	1	no	—
952	C₂²×C₄	—	47	2	no	—
953	C₂²×C₄	—	47	2	no	—
954	C₂²×C₄	—	47	2	no	—
955	C₂²×C₄	—	94	2	no	—
956	C₂²×C₄	—	94	2	no	—
957	C₂²×C₄	—	94	2	no	—
958	C₂²×C₄	—	94	2	no	—
959	C₂²×C₄	—	94	2	no	—
960	C₂²×C₄	—	94	1	no	—
961	C₂²×C₄	—	94	1	no	—
962	C₂²×C₄	—	94	1	no	—
963	C₂²×C₄	—	94	2	no	—
964	C₂²×C₄	—	94	2	no	—
965	C₂²×C₄	—	376	2	no	—
966	C₂²×C₄	—	376	4	no	—
967	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
968	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
969	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
970	Q₁₆	—	2	2	no	—
971	Q₁₆	—	94	4	no	—
972	SD₁₆	—	2	2	no	—
973	SD₁₆	—	2	2	no	—
974	SD₁₆	—	94	4	no	—
975	SD₁₆	—	94	4	no	—
976	SD₁₆	—	94	4	no	—
977	SD₁₆	—	94	4	no	—
978	D₈	—	2	2	no	—
979	D₈	—	94	4	no	—
980	M₁₆	—	94	2	no	—
981	M₁₆	—	94	2	no	—
982	C₂×C₈	—	2	2	no	—
983	C₂×C₈	—	2	2	no	—
984	C₂×C₈	—	47	2	no	—
985	C₂×C₈	—	47	2	no	—
986	C₂×C₈	C₂³×D₄₇	1	1	yes	characteristic
987	C₂×C₈	C₂³×D₄₇	1	1	yes	characteristic
988	C₂×C₈	C₂³×D₄₇	1	1	yes	characteristic
989	C₂×C₈	C₂³×D₄₇	1	1	yes	characteristic
990	C₄⋊C₄	—	2	1	no	—
991	C₄⋊C₄	—	2	1	no	—
992	C₄⋊C₄	—	2	1	no	—
993	C₄⋊C₄	—	2	1	no	—
994	C₄⋊C₄	—	47	2	no	—
995	C₄⋊C₄	—	47	2	no	—
996	C₄⋊C₄	—	47	1	no	—
997	C₄⋊C₄	—	47	1	no	—
998	C₄⋊C₄	—	47	2	no	—
999	C₄⋊C₄	—	47	2	no	—
1000	C₄⋊C₄	—	94	2	no	—
1001	C₄⋊C₄	—	94	2	no	—
1002	C₄⋊C₄	—	94	2	no	—
1003	C₄⋊C₄	—	94	2	no	—
1004	C₄⋊C₄	—	94	2	no	—
1005	C₄⋊C₄	—	94	2	no	—
1006	C₄⋊C₄	—	94	2	no	—
1007	C₄⋊C₄	—	94	2	no	—
1008	C₄⋊C₄	—	94	2	no	—
1009	C₄⋊C₄	—	94	2	no	—
1010	C₄⋊C₄	—	94	2	no	—
1011	C₄⋊C₄	—	94	2	no	—
1012	C₄⋊C₄	—	94	1	no	—
1013	C₄⋊C₄	—	94	1	no	—
1014	C₄⋊C₄	C₂³×D₄₇	1	1	yes	characteristic
1015	C₄⋊C₄	C₂³×D₄₇	1	1	yes	characteristic
1016	C₄⋊C₄	C₂³×D₄₇	1	1	yes	characteristic
1017	C₄⋊C₄	C₂³×D₄₇	1	1	yes	characteristic
1018	C₂²⋊C₄	—	2	1	no	—
1019	C₂²⋊C₄	—	2	1	no	—
1020	C₂²⋊C₄	—	2	1	no	—
1021	C₂²⋊C₄	—	2	1	no	—
1022	C₂²⋊C₄	—	2	1	no	—
1023	C₂²⋊C₄	—	2	1	no	—
1024	C₂²⋊C₄	—	47	2	no	—
1025	C₂²⋊C₄	—	47	2	no	—
1026	C₂²⋊C₄	—	47	2	no	—
1027	C₂²⋊C₄	—	94	2	no	—
1028	C₂²⋊C₄	—	94	2	no	—
1029	C₂²⋊C₄	—	94	2	no	—
1030	C₂²⋊C₄	—	94	2	no	—
1031	C₂²⋊C₄	—	94	2	no	—
1032	C₂²⋊C₄	—	94	2	no	—
1033	C₂²⋊C₄	—	94	2	no	—
1034	C₂²⋊C₄	—	94	2	no	—
1035	C₂²⋊C₄	—	94	2	no	—
1036	C₂²⋊C₄	—	94	2	no	—
1037	C₂²⋊C₄	—	94	2	no	—
1038	C₂²⋊C₄	—	94	2	no	—
1039	C₄²	—	2	1	no	—
1040	C₄²	—	2	1	no	—
1041	C₄²	—	2	1	no	—
1042	C₄²	—	2	1	no	—
1043	C₄²	—	2	1	no	—
1044	C₄²	—	2	1	no	—
1045	C₄²	—	47	2	no	—
1046	C₄²	—	47	2	no	—
1047	C₄²	—	47	2	no	—
1048	C₄²	—	94	2	no	—
1049	C₄²	—	94	2	no	—
1050	C₄²	—	94	2	no	—
1051	C₄²	—	94	2	no	—
1052	C₄²	D₄×D₄₇	1	1	yes	characteristic
1053	C₄²	D₄×D₄₇	1	1	yes	characteristic
1054	C₄²	C₂³×D₄₇	1	1	yes	characteristic
1055	C₄²	C₂³×D₄₇	1	1	yes	characteristic
1056	C₂³	—	2	1	no	—
1057	C₂³	—	2	1	no	—
1058	C₂³	—	47	2	no	—
1059	C₂³	—	94	8	no	—
1060	C₂³	—	94	4	no	—
1061	C₂³	—	94	2	no	—
1062	C₂³	—	376	1	no	—
1063	C₂³	—	376	1	no	—
1064	C₂³	—	376	2	no	—
1065	C₂³	—	376	2	no	—
1066	C₂³	C₂×D₄×D₄₇	1	1	yes	characteristic
1067	Q₈	—	2	1	no	—
1068	Q₈	—	2	1	no	—
1069	Q₈	—	2	1	no	—
1070	Q₈	—	94	2	no	—
1071	Q₈	—	94	2	no	—
1072	Q₈	—	94	2	no	—
1073	Q₈	—	376	2	no	—
1074	Q₈	—	188	2	no	—
1075	Q₈	C₂×#10625350	1	2	yes	—
1076	D₄	—	2	4	no	—
1077	D₄	—	2	1	no	—
1078	D₄	—	2	1	no	—
1079	D₄	—	2	1	no	—
1080	D₄	—	4	2	no	—
1081	D₄	—	47	4	no	—
1082	D₄	—	94	8	no	—
1083	D₄	—	94	8	no	—
1084	D₄	—	94	4	no	—
1085	D₄	—	94	4	no	—
1086	D₄	—	94	2	no	—
1087	D₄	—	94	2	no	—
1088	D₄	—	376	2	no	—
1089	D₄	C₂×#10625350	1	2	yes	—
1090	C₂×C₄	—	2	1	no	—
1091	C₂×C₄	—	2	4	no	—
1092	C₂×C₄	—	2	2	no	—
1093	C₂×C₄	—	2	1	no	—
1094	C₂×C₄	—	2	1	no	—
1095	C₂×C₄	—	2	1	no	—
1096	C₂×C₄	—	2	1	no	—
1097	C₂×C₄	—	2	1	no	—
1098	C₂×C₄	—	4	1	no	—
1099	C₂×C₄	—	4	2	no	—
1100	C₂×C₄	—	4	2	no	—
1101	C₂×C₄	—	4	2	no	—
1102	C₂×C₄	—	8	1	no	—
1103	C₂×C₄	—	8	1	no	—
1104	C₂×C₄	—	47	2	no	—
1105	C₂×C₄	—	47	2	no	—
1106	C₂×C₄	—	47	2	no	—
1107	C₂×C₄	—	94	8	no	—
1108	C₂×C₄	—	94	4	no	—
1109	C₂×C₄	—	94	2	no	—
1110	C₂×C₄	—	94	2	no	—
1111	C₂×C₄	—	94	2	no	—
1112	C₂×C₄	—	94	2	no	—
1113	C₂×C₄	—	94	2	no	—
1114	C₂×C₄	—	376	2	no	—
1115	C₂×C₄	—	376	2	no	—
1116	C₂×C₄	—	376	2	no	—
1117	C₂×C₄	—	376	2	no	—
1118	C₂×C₄	—	376	2	no	—
1119	C₂×C₄	—	376	1	no	—
1120	C₂×C₄	—	376	1	no	—
1121	C₂×C₄	—	188	2	no	—
1122	C₂×C₄	—	188	2	no	—
1123	C₂×C₄	—	188	4	no	—
1124	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
1125	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
1126	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
1127	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
1128	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
1129	C₂×C₄	#41×D₄₇	1	2	yes	—
1130	C₂×C₄	C₂×#10625350	1	2	yes	—
1131	C₂×C₄	C₂⁴×D₄₇	1	1	yes	characteristic
1132	C₈	—	2	1	no	—
1133	C₈	—	2	1	no	—
1134	C₈	—	2	1	no	—
1135	C₈	—	2	1	no	—
1136	C₈	—	94	2	no	—
1137	C₈	—	94	2	no	—
1138	C₂²	—	2	1	no	—
1139	C₂²	—	2	1	no	—
1140	C₂²	—	2	2	no	—
1141	C₂²	—	4	1	no	—
1142	C₂²	—	4	1	no	—
1143	C₂²	—	4	1	no	—
1144	C₂²	—	4	1	no	—
1145	C₂²	—	4	1	no	—
1146	C₂²	—	94	2	no	—
1147	C₂²	—	94	2	no	—
1148	C₂²	—	94	4	no	—
1149	C₂²	—	94	2	no	—
1150	C₂²	—	376	4	no	—
1151	C₂²	—	376	8	no	—
1152	C₂²	—	188	2	no	—
1153	C₂²	—	188	2	no	—
1154	C₂²	#15689632	1	2	yes	—
1155	C₂²	C₂²×D₄×D₄₇	1	1	yes	characteristic
1156	C₄	—	2	1	no	—
1157	C₄	—	2	1	no	—
1158	C₄	—	2	1	no	—
1159	C₄	—	2	2	no	—
1160	C₄	—	4	1	no	—
1161	C₄	—	4	1	no	—
1162	C₄	—	4	1	no	—
1163	C₄	—	4	1	no	—
1164	C₄	—	4	1	no	—
1165	C₄	—	94	2	no	—
1166	C₄	—	94	2	no	—
1167	C₄	—	94	2	no	—
1168	C₄	—	188	2	no	—
1169	C₄	—	188	2	no	—
1170	C₄	—	188	2	no	—
1171	C₄	#15689632	1	2	yes	—
1172	C₄	#15689930	1	2	yes	—
1173	C₄	C₂×#41×D₄₇	1	1	yes	characteristic
1174	C₄	C₂²×#10625350	1	1	yes	characteristic
1175	C₂	—	2	2	no	—
1176	C₂	—	4	2	no	—
1177	C₂	—	8	1	no	—
1178	C₂	—	188	2	no	—
1179	C₂	—	188	4	no	—
1180	C₂	C₂×#15689632	1	1	yes	characteristic
1181	C₂	C₂×#15689930	1	1	yes	characteristic
1182	C₂	#20258157	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₄₇
commutator, cosocle	C₂×C₄×C₄₇	C₂⁵
Frattini	C₂×C₄	C₂⁴×D₄₇
Fitting	C₄×#135×C₄₇	C₂
socle	C₂²×C₄₇	C₂³×D₄
prime radical	#20252688	C₂
hypercenter	C₄×#135	D₄₇
hypocenter	C₄₇	#60571
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₄×#135

Complements

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

N	H ≅ G/N	type
1. #20256815	C₂	semidirect
2. C₄×#13094070	C₂	semidirect
3. #20253671	C₂	semidirect
4. #20253637	C₂	semidirect
5. #20253608	C₂	semidirect
6. #20253568	C₂	semidirect
7. #20253457	C₂	semidirect
8. #20253433	C₂	semidirect
9. #20253404	C₂	semidirect
10. #20253394	C₂	semidirect
11. #20253375	C₂	semidirect
12. #20253360	C₂	semidirect
13. #20253248	C₂	semidirect
14. #20253222	C₂	semidirect
15. #20252936	C₂	semidirect
16. #20252903	C₂	semidirect
18. #20252668	C₂	semidirect
19. C₄×#13094054	C₂	semidirect
20. C₄×#13094049	C₂	semidirect
21. C₂×C₄×#10625325	C₂	semidirect
22. #20252030	C₂	semidirect
23. C₄×#135×C₄₇	C₂	semidirect
28. #15689751	C₂²	semidirect
30. #15689738	C₂²	semidirect
32. #15689731	C₂²	semidirect
36. #15689694	C₂²	semidirect
38. #15689677	C₂²	semidirect
40. #15689655	C₂²	semidirect
53. C₂×C₄×Dic₉₄	C₂²	semidirect
58. #15689467	C₂²	semidirect
59. #15689466	C₂²	semidirect
60. #15689462	C₂²	semidirect
61. #15689460	C₂²	semidirect
62. #15689455	C₂²	semidirect
63. #15689452	C₂²	semidirect
64. #15689446	C₂²	semidirect
65. #15689440	C₂²	semidirect
66. #15689428	C₂²	semidirect
67. #15689426	C₂²	semidirect
68. #15689425	C₂²	semidirect
69. #15689422	C₂²	semidirect
70. #15689412	C₂²	semidirect
71. #15689411	C₂²	semidirect
72. #15689406	C₂²	semidirect
73. #15689402	C₂²	semidirect
74. #15689343	C₂²	semidirect
75. #15689337	C₂²	semidirect
76. #15689337	C₂²	semidirect
77. #15689336	C₂²	semidirect
78. #15689331	C₂²	semidirect
79. #15689327	C₂²	semidirect
80. #15689327	C₂²	semidirect
81. #15689326	C₂²	semidirect
90. #15689233	C₂²	semidirect
91. #15689228	C₂²	semidirect
92. #15689223	C₂²	semidirect
93. #15689221	C₂²	semidirect
94. C₄×#10625337	C₂²	semidirect
95. C₄×#10625325	C₂²	semidirect
96. C₄×#10625325	C₂²	semidirect
97. C₄×#10625325	C₂²	semidirect
98. C₄×#10625325	C₂²	semidirect
99. C₄×#10625336	C₂²	semidirect
100. C₄×#10625335	C₂²	semidirect
101. C₄×#10625334	C₂²	semidirect
102. #15689182	C₂²	semidirect
103. #15689182	C₂²	semidirect
104. #15689174	C₂²	semidirect
105. #15689174	C₂²	semidirect
106. #15689166	C₂²	semidirect
107. #15689166	C₂²	semidirect
108. C₂×#13093956	C₂²	semidirect
109. #15689149	C₂²	semidirect
110. #15689149	C₂²	semidirect
111. #15689131	C₂²	semidirect
114. #15689124	C₂²	semidirect
115. C₂×#13093949	C₂²	semidirect
119. C₄×#10625329	C₂²	semidirect
122. C₄×#41×C₄₇	C₂²	semidirect
123. C₄×Q₁₆×C₄₇	C₂²	semidirect
124. C₄×Q₁₆×C₄₇	C₂²	semidirect
125. C₄×SD₁₆×C₄₇	C₂²	semidirect
126. C₄×SD₁₆×C₄₇	C₂²	semidirect
127. C₄×SD₁₆×C₄₇	C₂²	semidirect
128. C₄×SD₁₆×C₄₇	C₂²	semidirect
129. C₄×D₈×C₄₇	C₂²	semidirect
130. C₄×D₈×C₄₇	C₂²	semidirect
131. C₄₇×#427	C₂²	semidirect
133. C₄₇×#416	C₂²	semidirect
134. C₂×C₄×C₈×C₄₇	C₂²	semidirect
604. C₄×#135	D₄₇	semidirect
646. C₄×#41	C₂×D₄₇	semidirect
689. C₄×Q₁₆	C₂×D₄₇	semidirect
690. C₄×Q₁₆	C₂×D₄₇	semidirect
697. C₄×SD₁₆	C₂×D₄₇	semidirect
698. C₄×SD₁₆	C₂×D₄₇	semidirect
699. C₄×SD₁₆	C₂×D₄₇	semidirect
700. C₄×SD₁₆	C₂×D₄₇	semidirect
702. C₄×D₈	C₂×D₄₇	semidirect
703. C₄×D₈	C₂×D₄₇	semidirect
710. #427	C₂×D₄₇	semidirect
719. #416	C₂×D₄₇	semidirect
725. C₂×C₄×C₈	C₂×D₄₇	semidirect
726. C₄₇	#60571	semidirect

Maximal subgroups

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

subgroup	index
#20256815	2
C₄×#13094070	2
#20253671	2
#20253637	2
#20253608	2
#20253568	2
#20253457	2
#20253433	2
#20253404	2
#20253394	2
#20253375	2
#20253360	2
#20253248	2
#20253222	2
#20252936	2
#20252903	2
#20252688	2
#20252668	2
C₄×#13094054	2
C₄×#13094049	2
C₂×C₄×#10625325	2
#20252030	2
C₄×#135×C₄₇	2
#60571	47