Subgroups — #27098861

Order 12032.

1880 conjugacy classes of subgroups.

The subgroup lattice has 1160 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20257484	C₂	1	1	yes	maximal, characteristic, complemented
2	#20257420	C₂	1	1	yes	maximal, characteristic
3	#20256367	C₂	1	1	yes	maximal, characteristic, complemented
4	#20256261	C₂	1	1	yes	maximal, characteristic, complemented
5	#20256167	C₂	1	1	yes	maximal, characteristic, complemented
6	#20256115	C₂	1	1	yes	maximal, characteristic, complemented
7	#20255803	C₂	1	1	yes	maximal, characteristic, complemented
8	#20255763	C₂	1	2	yes	maximal, complemented
9	#20255684	C₂	1	1	yes	maximal, characteristic, complemented
10	#20255621	C₂	1	1	yes	maximal, characteristic, complemented
11	#20255555	C₂	1	2	yes	maximal, complemented
12	#20255405	C₂	1	2	yes	maximal, complemented
13	SD₁₆×D₁₈₈	C₂	1	1	yes	maximal, characteristic, complemented
14	SD₁₆×C₂²⋊D₄₇	C₂	1	2	yes	maximal, complemented
15	#20254012	C₂	1	2	yes	maximal, complemented
16	#20253947	C₂	1	1	yes	maximal, characteristic, complemented
17	#20253676	C₂	1	2	yes	maximal, complemented
18	#20253637	C₂	1	2	yes	maximal, complemented
19	#20253510	C₂	1	1	yes	maximal, characteristic, complemented
20	#20253487	C₂	1	1	yes	maximal, characteristic, complemented
21	#20252363	C₂	1	1	yes	maximal, characteristic, complemented
22	#20252242	C₂	1	2	yes	maximal, complemented
23	C₂×C₄×SD₁₆×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×SD₁₆×D₄₇	C₂²	1	2	yes	—
25	#15689852	C₂²	1	1	yes	characteristic, complemented
26	#15689851	—	2	1	no	—
27	#15689851	C₂²	1	1	yes	characteristic, complemented
28	#15689846	—	2	1	no	—
29	#15689846	C₂²	1	1	yes	characteristic, complemented
30	#15689838	C₂²	1	1	yes	characteristic
31	#15689830	C₂²	1	1	yes	characteristic
32	#15689821	C₂²	1	2	yes	—
33	#15689819	—	2	1	no	—
34	#15689808	—	2	2	no	—
35	#15689808	C₂²	1	2	yes	complemented
36	#15689794	C₂²	1	1	yes	characteristic
37	Q₈×D₁₈₈	C₂²	1	1	yes	characteristic, complemented
38	Q₈×C₂²⋊D₄₇	C₂²	1	2	yes	complemented
39	#15689769	—	2	1	no	—
40	#15689763	—	2	2	no	—
41	D₄×D₁₈₈	C₂²	1	1	yes	characteristic
42	D₄×C₂²⋊D₄₇	C₂²	1	2	yes	—
43	#15689731	—	2	2	no	—
44	#15689731	C₂²	1	2	yes	complemented
45	#15689724	C₂²	1	2	yes	—
46	#15689706	—	2	2	no	—
47	#15689680	—	2	1	no	—
48	#15689680	C₂²	1	1	yes	characteristic, complemented
49	#15689673	C₂²	1	1	yes	characteristic
50	#15689657	—	2	1	no	—
51	#15689657	C₂²	1	1	yes	characteristic
52	#15689634	—	2	1	no	—
53	C₂×#13093998	—	2	1	no	—
54	#15689599	C₂²	1	2	yes	complemented
55	#15689595	C₂²	1	2	yes	—
56	#15689523	C₂²	1	2	yes	complemented
57	#15689521	C₂²	1	1	yes	characteristic, complemented
58	#15689496	C₂²	1	1	yes	characteristic, complemented
59	#15689494	C₂²	1	2	yes	complemented
60	#15689490	C₂²	1	2	yes	complemented
61	#15689486	C₂²	1	2	yes	complemented
62	#15689474	C₂²	1	1	yes	characteristic, complemented
63	#15689470	C₂²	1	1	yes	characteristic, complemented
64	#15689467	C₂²	1	2	yes	complemented
65	#15689462	C₂²	1	2	yes	complemented
66	#15689458	C₂²	1	2	yes	complemented
67	#15689449	C₂²	1	2	yes	complemented
68	#15689446	C₂²	1	2	yes	complemented
69	#15689436	C₂²	1	2	yes	complemented
70	#15689433	C₂²	1	2	yes	complemented
71	#15689428	C₂²	1	2	yes	complemented
72	#15689425	C₂²	1	2	yes	—
73	#15689422	C₂²	1	2	yes	complemented
74	#15689418	C₂²	1	1	yes	characteristic, complemented
75	#15689418	C₂²	1	1	yes	characteristic, complemented
76	#15689403	C₂²	1	1	yes	characteristic
77	#15689403	C₂²	1	1	yes	characteristic, complemented
78	#15689372	C₂²	1	2	yes	complemented
79	#15689368	C₂²	1	2	yes	complemented
80	#15689353	C₂²	1	2	yes	complemented
81	#15689352	C₂²	1	2	yes	complemented
82	#15689352	C₂²	1	2	yes	complemented
83	#15689349	C₂²	1	2	yes	complemented
84	#15689328	C₂²	1	1	yes	characteristic
85	#15689328	C₂²	1	1	yes	characteristic, complemented
86	#15689327	C₂²	1	2	yes	complemented
87	#15689326	C₂²	1	2	yes	—
88	#15689323	C₂²	1	1	yes	characteristic, complemented
89	#15689323	C₂²	1	1	yes	characteristic, complemented
90	#15689322	C₂²	1	2	yes	complemented
91	#15689321	C₂²	1	2	yes	complemented
92	#15689275	C₂²	1	2	yes	—
93	#15689274	C₂²	1	2	yes	—
94	#15689272	C₂²	1	2	yes	—
95	#15689263	C₂²	1	2	yes	complemented
96	#15689262	C₂²	1	2	yes	complemented
97	#15689260	C₂²	1	2	yes	complemented
98	#15689253	C₂²	1	1	yes	characteristic, complemented
99	C₈×Dic₉₄	C₂²	1	1	yes	characteristic, complemented
100	#15689226	C₂²	1	2	yes	complemented
101	#15689223	C₂²	1	2	yes	—
102	#15689223	C₂²	1	2	yes	complemented
103	#15689221	C₂²	1	2	yes	complemented
104	#15689221	C₂²	1	2	yes	complemented
105	#15689220	C₂²	1	2	yes	—
106	C₄×#10625325	C₂²	1	2	yes	complemented
107	C₄×#10625325	C₂²	1	2	yes	complemented
108	SD₁₆×Dic₄₇	C₂²	1	2	yes	—
109	#15689210	C₂²	1	2	yes	complemented
110	#15689202	C₂²	1	1	yes	characteristic, complemented
111	#15689194	C₂²	1	2	yes	complemented
112	C₈×D₁₈₈	C₂²	1	1	yes	characteristic, complemented
113	C₈×C₂²⋊D₄₇	C₂²	1	2	yes	complemented
114	#15689182	C₂²	1	2	yes	complemented
115	#15689180	C₂²	1	1	yes	characteristic, complemented
116	#15689158	C₂²	1	2	yes	complemented
117	#15689130	C₂²	1	2	yes	complemented
118	#15689126	C₂²	1	2	yes	—
119	#15689077	C₂²	1	2	yes	complemented
120	C₂²×SD₁₆×C₄₇	C₂²	1	1	yes	characteristic
121	C₂×C₄×Q₈×C₄₇	C₂²	1	1	yes	characteristic, complemented
122	C₂×C₄×D₄×C₄₇	C₂²	1	1	yes	characteristic
123	C₄×SD₁₆×C₄₇	C₂²	1	1	yes	characteristic
124	C₄×SD₁₆×C₄₇	C₂²	1	1	yes	characteristic
125	C₄×SD₁₆×C₄₇	C₂²	1	1	yes	characteristic
126	C₄×SD₁₆×C₄₇	C₂²	1	1	yes	characteristic
127	C₄×SD₁₆×C₄₇	C₂²	1	1	yes	characteristic, complemented
128	C₄×SD₁₆×C₄₇	C₂²	1	1	yes	characteristic, complemented
129	C₄×SD₁₆×C₄₇	C₂²	1	1	yes	characteristic, complemented
130	C₄×SD₁₆×C₄₇	C₂²	1	1	yes	characteristic, complemented
131	C₂×#106×C₄₇	C₂²	1	1	yes	characteristic, complemented
132	C₂×#103×C₄₇	C₂²	1	1	yes	characteristic, complemented
133	C₂×#102×C₄₇	C₂²	1	1	yes	characteristic
134	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic, complemented
135	C₂×#10625350	—	2	1	no	—
136	C₂×#10625350	—	2	1	no	—
137	C₂×Q₈×D₄₇	C₂³	1	2	yes	—
138	C₂²×D₁₈₈	—	2	1	no	—
139	C₂²×C₂²⋊D₄₇	—	2	2	no	—
140	C₂×D₄×D₄₇	C₂³	1	2	yes	—
141	C₂×#10625325	C₂³	1	2	yes	—
142	C₂×#10625325	C₂³	1	2	yes	—
143	C₂×#10625335	C₂³	1	2	yes	—
144	C₂×#10625335	C₂³	1	2	yes	—
145	C₂×#10625336	C₂³	1	2	yes	—
146	C₂×#10625336	C₂³	1	2	yes	—
147	SD₁₆×D₄₇	—	2	8	no	—
148	C₂×#10625324	C₂³	1	2	yes	—
149	C₂×C₈×D₄₇	C₂³	1	2	yes	—
150	#13094024	—	2	1	no	—
151	#13094024	—	2	1	no	—
152	#13094024	C₂³	1	1	yes	characteristic
153	#13094024	C₂³	1	1	yes	characteristic
154	#13094024	C₂³	1	1	yes	characteristic
155	#13094022	—	2	2	no	—
156	#13094022	C₂³	1	2	yes	—
157	#13094021	C₂³	1	1	yes	characteristic
158	#13094020	C₂³	1	2	yes	—
159	#13094019	—	2	2	no	—
160	#13094019	—	2	2	no	—
161	#13094019	—	2	2	no	—
162	#13094019	—	2	2	no	—
163	#13094018	—	2	2	no	—
164	#13094018	D₄	1	2	yes	—
165	#13094016	—	2	1	no	—
166	#13094016	—	2	1	no	—
167	#13094016	—	2	2	no	—
168	#13094016	D₄	1	1	yes	characteristic
169	#13094015	—	2	2	no	—
170	#13094015	C₂³	1	2	yes	—
171	#13094015	C₂³	1	2	yes	—
172	#13094014	—	2	2	no	—
173	#13094014	—	2	2	no	—
174	#13094014	—	2	2	no	—
175	#13094012	—	2	1	no	—
176	#13094012	—	2	1	no	—
177	#13094012	D₄	1	1	yes	characteristic
178	#13094010	—	2	2	no	—
179	#13094009	—	2	2	no	—
180	#13094007	—	2	2	no	—
181	#13094007	—	2	2	no	—
182	#13094007	D₄	1	2	yes	—
183	#13094006	—	2	2	no	—
184	#13094004	—	2	2	no	—
185	#13094004	C₂³	1	2	yes	—
186	#13094003	—	2	1	no	—
187	#13094003	—	2	1	no	—
188	#13094003	—	2	2	no	—
189	#13094003	D₄	1	1	yes	characteristic
190	#13094003	C₂³	1	2	yes	—
191	#13094001	—	2	2	no	—
192	#13094000	—	2	2	no	—
193	#13094000	C₂³	1	2	yes	—
194	#13093999	C₂³	1	2	yes	—
195	#13093998	—	2	1	no	—
196	#13093998	—	2	2	no	—
197	#13093998	—	2	1	no	—
198	#13093998	—	2	2	no	—
199	#13093998	—	2	1	no	—
200	#13093998	—	2	1	no	—
201	#13093998	D₄	1	1	yes	characteristic
202	#13093998	C₂³	1	2	yes	—
203	#13093997	—	2	2	no	—
204	#13093997	—	2	2	no	—
205	#13093996	—	2	2	no	—
206	#13093995	C₂³	1	2	yes	—
207	#13093994	—	2	2	no	—
208	#13093993	—	2	2	no	—
209	#13093992	—	2	2	no	—
210	Q₈×Dic₄₇	C₂³	1	2	yes	—
211	C₄×Dic₉₄	—	2	1	no	—
212	C₄×Dic₉₄	—	2	1	no	—
213	C₄×Dic₉₄	—	2	1	no	—
214	C₄×Dic₉₄	—	2	1	no	—
215	C₄×Dic₉₄	—	2	2	no	—
216	C₄×Dic₉₄	C₂³	1	2	yes	—
217	C₄×Dic₉₄	C₂³	1	1	yes	characteristic
218	#13093989	—	2	2	no	—
219	#13093989	C₂³	1	2	yes	—
220	C₄×D₁₈₈	—	2	1	no	—
221	C₄×D₁₈₈	—	2	1	no	—
222	C₄×D₁₈₈	C₂³	1	1	yes	characteristic
223	C₄×D₁₈₈	C₂³	1	2	yes	—
224	D₄×Dic₄₇	C₂³	1	2	yes	—
225	#13093986	C₂³	1	2	yes	—
226	C₄×C₂²⋊D₄₇	—	2	2	no	—
227	C₄×C₂²⋊D₄₇	—	2	2	no	—
228	C₄×C₂²⋊D₄₇	—	2	2	no	—
229	C₄×C₂²⋊D₄₇	C₂³	1	2	yes	—
230	(C₂²⋊D₄₇)⋊C₄	—	2	2	no	—
231	#13093983	—	2	1	no	—
232	#13093983	—	2	2	no	—
233	#13093983	—	2	1	no	—
234	#13093982	—	2	2	no	—
235	#13093982	C₂³	1	2	yes	—
236	#13093982	C₂³	1	2	yes	—
237	#13093981	—	2	2	no	—
238	#13093981	C₂³	1	2	yes	—
239	C₂×C₄⋊Dic₄₇	—	2	1	no	—
240	C₂×(C₂×D₄₇)⋊C₄	—	2	2	no	—
241	C₂²⋊C₄×D₄₇	—	2	2	no	—
242	#13093957	C₂³	1	2	yes	—
243	#13093957	C₂³	1	2	yes	—
244	#13093957	C₂³	1	2	yes	—
245	#13093957	C₂³	1	2	yes	—
246	#13093956	C₂³	1	2	yes	—
247	#13093956	C₂³	1	2	yes	—
248	C₄⋊(C₄₇⋊C₈)	C₂³	1	1	yes	characteristic
249	C₄⋊(C₄₇⋊C₈)	C₂³	1	1	yes	characteristic
250	Dic₄₇⋊C₈	C₂³	1	2	yes	—
251	Dic₄₇⋊C₈	C₂³	1	2	yes	—
252	#13093949	C₂³	1	2	yes	—
253	#13093949	C₂³	1	2	yes	—
254	#13093948	C₂³	1	2	yes	—
255	#13093948	C₂³	1	2	yes	—
256	#13093947	C₂³	1	2	yes	—
257	#13093947	C₂³	1	2	yes	—
258	#13093946	C₂³	1	2	yes	—
259	#13093946	C₂³	1	2	yes	—
260	#13093945	C₂³	1	2	yes	—
261	#13093945	C₂³	1	2	yes	—
262	#13093944	C₂³	1	2	yes	—
263	#13093944	C₂³	1	2	yes	—
264	C₂²⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
265	(C₂×D₄₇)⋊C₈	C₂³	1	2	yes	—
266	(C₂×D₄₇)⋊C₈	C₂³	1	2	yes	—
267	#13093935	C₂³	1	2	yes	—
268	#13093934	C₂³	1	2	yes	—
269	C₈×Dic₄₇	C₂³	1	2	yes	—
270	C₂²×Q₈×C₄₇	C₂³	1	1	yes	characteristic
271	C₂²×D₄×C₄₇	C₂³	1	1	yes	characteristic
272	C₂³×C₄×C₄₇	—	2	1	no	—
273	C₂×SD₁₆×C₄₇	—	2	4	no	—
274	C₂×SD₁₆×C₄₇	C₂³	1	1	yes	characteristic
275	C₂×SD₁₆×C₄₇	C₂³	1	1	yes	characteristic
276	C₂×SD₁₆×C₄₇	C₂³	1	1	yes	characteristic
277	C₂×SD₁₆×C₄₇	C₂³	1	1	yes	characteristic
278	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
279	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
280	C₄×Q₈×C₄₇	—	2	1	no	—
281	C₄×Q₈×C₄₇	—	2	1	no	—
282	C₄×Q₈×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×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	C₄×D₄×C₄₇	C₂³	1	1	yes	characteristic
291	C₄×D₄×C₄₇	C₂³	1	1	yes	characteristic
292	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
293	C₂×C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
294	C₂×C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
295	C₂×C₂²⋊C₄×C₄₇	—	2	1	no	—
296	C₂×C₄²×C₄₇	—	2	1	no	—
297	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
298	#106×C₄₇	C₂³	1	1	yes	characteristic
299	#106×C₄₇	C₂³	1	1	yes	characteristic
300	#106×C₄₇	C₂³	1	1	yes	characteristic
301	#106×C₄₇	C₂³	1	1	yes	characteristic
302	#103×C₄₇	C₂³	1	1	yes	characteristic
303	#103×C₄₇	C₂³	1	1	yes	characteristic
304	#103×C₄₇	C₂³	1	1	yes	characteristic
305	#103×C₄₇	C₂³	1	1	yes	characteristic
306	#102×C₄₇	C₂³	1	1	yes	characteristic
307	#102×C₄₇	C₂³	1	1	yes	characteristic
308	#102×C₄₇	C₂³	1	1	yes	characteristic
309	#102×C₄₇	C₂³	1	1	yes	characteristic
310	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
311	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
312	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
313	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
314	C₂⁴×C₄₇	—	2	1	no	—
315	C₂³×D₄₇	—	2	2	no	—
316	C₂×Q₈×C₄₇	—	2	1	no	—
317	C₂×Q₈×C₄₇	—	2	2	no	—
318	C₂×Q₈×C₄₇	—	4	1	no	—
319	C₂×Q₈×C₄₇	C₂⁴	1	1	yes	characteristic
320	C₂×Q₈×C₄₇	C₂⁴	1	1	yes	characteristic
321	C₂×D₄×C₄₇	—	2	2	no	—
322	C₂×D₄×C₄₇	—	2	1	no	—
323	C₂×D₄×C₄₇	—	4	1	no	—
324	C₂×D₄×C₄₇	C₂⁴	1	1	yes	characteristic
325	C₂×D₄×C₄₇	C₂⁴	1	1	yes	characteristic
326	C₂²×C₄×C₄₇	—	2	1	no	—
327	C₂²×C₄×C₄₇	—	2	1	no	—
328	C₂²×C₄×C₄₇	—	2	1	no	—
329	C₂²×C₄×C₄₇	—	2	1	no	—
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	—	8	2	no	—
334	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
335	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
336	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
337	C₂×C₂²⋊D₄₇	—	2	2	no	—
338	C₂×C₂²⋊D₄₇	—	2	2	no	—
339	C₂×C₂²⋊D₄₇	—	2	2	no	—
340	C₂×C₂²⋊D₄₇	—	2	2	no	—
341	C₂×C₂²⋊D₄₇	—	2	2	no	—
342	C₂×C₂²⋊D₄₇	—	8	4	no	—
343	C₂×C₂²⋊D₄₇	C₂×D₄	1	2	yes	—
344	C₂²×Dic₄₇	—	2	2	no	—
345	Q₈×D₄₇	—	2	4	no	—
346	Q₈×D₄₇	—	4	2	no	—
347	D₄×D₄₇	—	2	4	no	—
348	D₄×D₄₇	—	4	2	no	—
349	#10625350	—	8	2	no	—
350	#10625350	—	8	2	no	—
351	C₂×D₁₈₈	—	2	1	no	—
352	C₂×D₁₈₈	—	2	2	no	—
353	C₂×D₁₈₈	—	2	1	no	—
354	C₂×D₁₈₈	—	8	2	no	—
355	C₂×D₁₈₈	C₂×D₄	1	1	yes	characteristic
356	C₂×D₁₈₈	C₂⁴	1	2	yes	—
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	C₂⁴	1	2	yes	—
361	C₂×Dic₉₄	—	2	1	no	—
362	C₂×Dic₉₄	—	2	2	no	—
363	C₂×Dic₉₄	—	2	1	no	—
364	C₂×Dic₉₄	C₂×D₄	1	1	yes	characteristic
365	C₂×Dic₉₄	C₂⁴	1	2	yes	—
366	SD₁₆×C₄₇	—	2	2	no	—
367	SD₁₆×C₄₇	—	2	2	no	—
368	SD₁₆×C₄₇	—	2	2	no	—
369	SD₁₆×C₄₇	#41	1	4	yes	complemented
370	C₂×C₈×C₄₇	—	2	2	no	—
371	C₂×C₈×C₄₇	—	4	1	no	—
372	C₂×C₈×C₄₇	C₂⁴	1	1	yes	characteristic
373	C₂×C₈×C₄₇	C₂⁴	1	1	yes	characteristic
374	C₂×C₈×C₄₇	C₂⁴	1	1	yes	characteristic
375	C₂×C₈×C₄₇	C₂⁴	1	1	yes	characteristic
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	C₂²⋊C₄×C₄₇	—	2	1	no	—
387	C₂²⋊C₄×C₄₇	—	2	1	no	—
388	C₂²⋊C₄×C₄₇	—	2	1	no	—
389	C₂²⋊C₄×C₄₇	—	2	1	no	—
390	C₄²×C₄₇	—	2	1	no	—
391	C₄²×C₄₇	—	2	1	no	—
392	C₄²×C₄₇	—	2	1	no	—
393	C₄²×C₄₇	—	2	1	no	—
394	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
395	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
396	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
397	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
398	C₂²⋊Dic₄₇	—	2	2	no	—
399	C₂²⋊Dic₄₇	—	2	2	no	—
400	C₂²⋊Dic₄₇	—	2	2	no	—
401	C₂²⋊Dic₄₇	C₂×D₄	1	2	yes	—
402	#10625336	—	2	4	no	—
403	#10625336	—	4	2	no	—
404	#10625335	—	2	4	no	—
405	#10625335	—	4	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	—	2	2	no	—
412	(C₂×D₄₇)⋊C₄	—	2	2	no	—
413	(C₂×D₄₇)⋊C₄	—	2	2	no	—
414	(C₂×D₄₇)⋊C₄	C₂×D₄	1	2	yes	—
415	(C₂×D₄₇)⋊C₄	C₂×D₄	1	2	yes	—
416	(C₂×D₄₇)⋊C₄	C₂×D₄	1	2	yes	—
417	(C₂×D₄₇)⋊C₄	C₂×D₄	1	2	yes	—
418	C₄⋊Dic₄₇	—	2	1	no	—
419	C₄⋊Dic₄₇	—	2	1	no	—
420	C₄⋊Dic₄₇	—	2	1	no	—
421	C₄⋊Dic₄₇	—	2	1	no	—
422	C₄⋊Dic₄₇	—	2	2	no	—
423	C₄⋊Dic₄₇	—	2	2	no	—
424	C₄⋊Dic₄₇	—	2	2	no	—
425	C₄⋊Dic₄₇	—	2	2	no	—
426	C₄⋊Dic₄₇	C₂×D₄	1	1	yes	characteristic
427	C₄⋊Dic₄₇	C₂×D₄	1	1	yes	characteristic
428	C₄⋊Dic₄₇	C₂⁴	1	2	yes	—
429	C₄⋊Dic₄₇	C₂⁴	1	2	yes	—
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	—	2	2	no	—
436	Dic₄₇⋊C₄	—	2	2	no	—
437	Dic₄₇⋊C₄	—	2	2	no	—
438	Dic₄₇⋊C₄	C₂×D₄	1	2	yes	—
439	Dic₄₇⋊C₄	C₂×D₄	1	2	yes	—
440	Dic₄₇⋊C₄	C₂×D₄	1	2	yes	—
441	Dic₄₇⋊C₄	C₂×D₄	1	2	yes	—
442	C₄×Dic₄₇	—	2	2	no	—
443	C₄×Dic₄₇	—	2	2	no	—
444	C₄×Dic₄₇	—	2	2	no	—
445	C₄×Dic₄₇	—	2	2	no	—
446	C₄×Dic₄₇	—	2	2	no	—
447	C₄×Dic₄₇	C₂⁴	1	2	yes	—
448	C₂×C₄₇⋊C₈	C₂⁴	1	2	yes	—
449	C₂×C₄₇⋊C₈	C₂⁴	1	2	yes	—
450	#10625325	—	2	4	no	—
451	#10625325	—	4	2	no	—
452	#10625324	—	4	2	no	—
453	C₈×D₄₇	—	2	4	no	—
454	C₂³×C₄₇	—	2	1	no	—
455	C₂³×C₄₇	—	2	1	no	—
456	C₂³×C₄₇	—	4	2	no	—
457	C₂³×C₄₇	—	4	2	no	—
458	C₂³×C₄₇	—	8	1	no	—
459	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
460	C₂²×D₄₇	—	2	2	no	—
461	C₂²×D₄₇	—	4	4	no	—
462	C₂²×D₄₇	—	8	2	no	—
463	C₂²×D₄₇	—	8	2	no	—
464	C₂²×D₄₇	C₂²×D₄	1	2	yes	—
465	Q₈×C₄₇	—	2	1	no	—
466	Q₈×C₄₇	—	2	1	no	—
467	Q₈×C₄₇	—	2	1	no	—
468	Q₈×C₄₇	—	4	2	no	—
469	Q₈×C₄₇	C₂×#41	1	2	yes	—
470	D₄×C₄₇	—	2	1	no	—
471	D₄×C₄₇	—	2	1	no	—
472	D₄×C₄₇	—	2	1	no	—
473	D₄×C₄₇	—	4	2	no	—
474	D₄×C₄₇	C₂×#41	1	2	yes	—
475	C₂×C₄×C₄₇	—	2	2	no	—
476	C₂×C₄×C₄₇	—	2	1	no	—
477	C₂×C₄×C₄₇	—	2	2	no	—
478	C₂×C₄×C₄₇	—	2	1	no	—
479	C₂×C₄×C₄₇	—	2	1	no	—
480	C₂×C₄×C₄₇	—	2	1	no	—
481	C₂×C₄×C₄₇	—	2	1	no	—
482	C₂×C₄×C₄₇	—	2	1	no	—
483	C₂×C₄×C₄₇	—	2	1	no	—
484	C₂×C₄×C₄₇	—	2	1	no	—
485	C₂×C₄×C₄₇	—	4	2	no	—
486	C₂×C₄×C₄₇	—	4	2	no	—
487	C₂×C₄×C₄₇	—	4	2	no	—
488	C₂×C₄×C₄₇	—	4	2	no	—
489	C₂×C₄×C₄₇	—	8	1	no	—
490	C₂×C₄×C₄₇	—	8	1	no	—
491	C₂×C₄×C₄₇	—	8	1	no	—
492	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
493	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
494	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
495	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
496	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
497	C₂×C₄×C₄₇	C₂⁵	1	1	yes	characteristic
498	C₂²⋊D₄₇	—	2	4	no	—
499	C₂²⋊D₄₇	—	4	4	no	—
500	C₂²⋊D₄₇	—	4	4	no	—
501	C₂²⋊D₄₇	—	8	2	no	—
502	C₂²⋊D₄₇	—	8	2	no	—
503	C₂²⋊D₄₇	—	8	2	no	—
504	C₂×Dic₄₇	—	2	2	no	—
505	C₂×Dic₄₇	—	2	2	no	—
506	C₂×Dic₄₇	—	2	2	no	—
507	C₂×Dic₄₇	—	8	2	no	—
508	C₂×Dic₄₇	C₂²×D₄	1	2	yes	—
509	C₂×Dic₄₇	C₂²×D₄	1	2	yes	—
510	C₂×Dic₄₇	C₂²×D₄	1	2	yes	—
511	D₁₈₈	—	2	2	no	—
512	D₁₈₈	—	2	2	no	—
513	D₁₈₈	—	2	2	no	—
514	D₁₈₈	—	4	2	no	—
515	D₁₈₈	—	8	1	no	—
516	D₁₈₈	—	8	2	no	—
517	C₄×D₄₇	—	2	2	no	—
518	C₄×D₄₇	—	2	2	no	—
519	C₄×D₄₇	—	4	4	no	—
520	C₄×D₄₇	—	8	2	no	—
521	C₄×D₄₇	—	8	2	no	—
522	Dic₉₄	—	2	2	no	—
523	Dic₉₄	—	2	2	no	—
524	Dic₉₄	—	2	2	no	—
525	Dic₉₄	—	4	4	no	—
526	Dic₉₄	—	4	2	no	—
527	Dic₉₄	—	8	1	no	—
528	C₈×C₄₇	—	2	1	no	—
529	C₈×C₄₇	—	2	1	no	—
530	C₈×C₄₇	—	2	1	no	—
531	C₈×C₄₇	C₂×#41	1	2	yes	—
532	C₄₇⋊C₈	—	2	2	no	—
533	C₄₇⋊C₈	—	2	2	no	—
534	#61481	—	47	1	no	maximal, Sylow
535	C₂²×C₄₇	—	2	1	no	—
536	C₂²×C₄₇	—	2	1	no	—
537	C₂²×C₄₇	—	2	2	no	—
538	C₂²×C₄₇	—	4	1	no	—
539	C₂²×C₄₇	—	4	1	no	—
540	C₂²×C₄₇	—	4	1	no	—
541	C₂²×C₄₇	—	4	1	no	—
542	C₂²×C₄₇	—	4	1	no	—
543	C₂²×C₄₇	—	8	4	no	—
544	C₂²×C₄₇	#577	1	2	yes	—
545	C₂²×C₄₇	C₂³×D₄	1	1	yes	characteristic
546	C₂×D₄₇	—	2	2	no	—
547	C₂×D₄₇	—	2	2	no	—
548	C₂×D₄₇	—	2	2	no	—
549	C₂×D₄₇	—	4	2	no	—
550	C₂×D₄₇	—	4	2	no	—
551	C₂×D₄₇	—	4	2	no	—
552	C₂×D₄₇	—	16	4	no	—
553	C₄×C₄₇	—	2	2	no	—
554	C₄×C₄₇	—	2	1	no	—
555	C₄×C₄₇	—	2	1	no	—
556	C₄×C₄₇	—	2	1	no	—
557	C₄×C₄₇	—	2	1	no	—
558	C₄×C₄₇	—	4	1	no	—
559	C₄×C₄₇	—	4	1	no	—
560	C₄×C₄₇	—	4	1	no	—
561	C₄×C₄₇	—	4	1	no	—
562	C₄×C₄₇	—	4	1	no	—
563	C₄×C₄₇	#577	1	2	yes	—
564	C₄×C₄₇	C₂²×#41	1	1	yes	characteristic
565	C₄×C₄₇	#585	1	1	yes	characteristic
566	Dic₄₇	—	2	2	no	—
567	Dic₄₇	—	2	2	no	—
568	Dic₄₇	—	2	2	no	—
569	Dic₄₇	—	4	2	no	—
570	Dic₄₇	—	4	2	no	—
571	Dic₄₇	—	4	2	no	—
572	#3523	—	47	1	no	—
573	#3519	—	47	1	no	—
574	#3392	—	47	1	no	—
575	#3381	—	47	1	no	—
576	#3372	—	47	1	no	—
577	#3368	—	47	1	no	—
578	#3340	—	47	1	no	—
579	#3337	—	47	2	no	—
580	#3329	—	47	1	no	—
581	#3324	—	47	1	no	—
582	#3320	—	47	2	no	—
583	#3310	—	47	2	no	—
584	D₄×SD₁₆	—	47	1	no	—
585	D₄×SD₁₆	—	47	2	no	—
586	#3174	—	47	2	no	—
587	#3167	—	47	1	no	—
588	#3126	—	47	2	no	—
589	#3123	—	47	2	no	—
590	#3112	—	47	1	no	—
591	#3110	—	47	1	no	—
592	#2966	—	47	1	no	—
593	#2949	—	47	2	no	—
594	C₂×C₄×SD₁₆	D₄₇	1	1	yes	characteristic, complemented
595	C₂×C₄₇	—	2	2	no	—
596	C₂×C₄₇	—	4	2	no	—
597	C₂×C₄₇	—	8	1	no	—
598	C₂×C₄₇	D₄×#41	1	1	yes	characteristic
599	C₂×C₄₇	C₂×#577	1	1	yes	characteristic
600	C₂×C₄₇	C₂×#577	1	1	yes	characteristic
601	D₄₇	—	4	2	no	—
602	D₄₇	—	8	2	no	—
603	C₂²×SD₁₆	—	47	2	no	—
604	C₂²×SD₁₆	C₂×D₄₇	1	1	yes	characteristic
605	#557	—	47	1	no	—
606	#557	—	47	1	no	—
607	#557	—	94	1	no	—
608	#556	—	47	1	no	—
609	#556	—	94	1	no	—
610	#555	—	47	1	no	—
611	#554	—	47	1	no	—
612	#553	—	47	2	no	—
613	#553	—	94	1	no	—
614	#552	—	47	2	no	—
615	#552	—	94	2	no	—
616	#550	—	47	1	no	—
617	D₄×Q₈	—	47	2	no	—
618	D₄×Q₈	—	47	1	no	—
619	#546	—	94	2	no	—
620	#546	—	94	1	no	—
621	D₄²	—	47	2	no	—
622	D₄²	—	47	1	no	—
623	#541	—	47	2	no	—
624	#541	—	94	2	no	—
625	#540	—	47	2	no	—
626	#538	—	94	2	no	—
627	#533	—	47	1	no	—
628	#533	—	94	1	no	—
629	#532	—	47	1	no	—
630	#529	—	47	1	no	—
631	#529	—	94	1	no	—
632	#525	—	94	1	no	—
633	C₂×#121	—	94	1	no	—
634	#519	—	47	2	no	—
635	#518	—	47	2	no	—
636	C₂×C₄×Q₈	C₂×D₄₇	1	1	yes	characteristic, complemented
637	C₂×C₄×D₄	C₂×D₄₇	1	1	yes	characteristic
638	#499	—	47	2	no	—
639	#498	—	47	1	no	—
640	#492	—	47	2	no	—
641	#492	—	47	1	no	—
642	#491	—	47	2	no	—
643	#490	—	47	2	no	—
644	#487	—	47	1	no	—
645	#486	—	47	1	no	—
646	#485	—	47	2	no	—
647	#485	—	47	2	no	—
648	#484	—	47	2	no	—
649	#482	—	47	2	no	—
650	#482	—	47	2	no	—
651	#480	—	47	2	no	—
652	#479	—	47	2	no	—
653	#479	—	47	2	no	—
654	#478	—	47	2	no	—
655	#478	—	47	2	no	—
656	#477	—	47	1	no	—
657	#477	—	47	1	no	—
658	#474	—	47	1	no	—
659	#474	—	47	1	no	—
660	#468	—	47	2	no	—
661	#468	—	47	2	no	—
662	#465	—	47	2	no	—
663	#465	—	47	2	no	—
664	#465	—	47	2	no	—
665	#465	—	47	2	no	—
666	#461	—	47	2	no	—
667	#461	—	47	1	no	—
668	#461	—	47	1	no	—
669	#461	—	47	2	no	—
670	#460	—	47	2	no	—
671	#460	—	47	1	no	—
672	#460	—	47	1	no	—
673	#460	—	47	2	no	—
674	#450	—	47	2	no	—
675	#450	—	47	2	no	—
676	#450	—	47	2	no	—
677	#448	—	47	2	no	—
678	#448	—	47	2	no	—
679	#448	—	47	2	no	—
680	#446	—	47	1	no	—
681	C₈×Q₈	—	47	1	no	—
682	#440	—	47	2	no	—
683	#440	—	47	2	no	—
684	#440	—	47	2	no	—
685	#440	—	47	2	no	—
686	#440	—	47	2	no	—
687	#440	—	47	2	no	—
688	C₄×SD₁₆	—	47	2	no	—
689	C₄×SD₁₆	—	47	2	no	—
690	C₄×SD₁₆	—	47	2	no	—
691	C₄×SD₁₆	—	47	2	no	—
692	C₄×SD₁₆	C₂×D₄₇	1	1	yes	characteristic
693	C₄×SD₁₆	C₂×D₄₇	1	1	yes	characteristic
694	C₄×SD₁₆	C₂×D₄₇	1	1	yes	characteristic
695	C₄×SD₁₆	C₂×D₄₇	1	1	yes	characteristic
696	C₄×SD₁₆	C₂×D₄₇	1	1	yes	characteristic, complemented
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	#436	—	47	1	no	—
701	#435	—	47	2	no	—
702	C₈×D₄	—	47	2	no	—
703	C₈×D₄	—	47	1	no	—
704	#433	—	47	2	no	—
705	#432	—	47	1	no	—
706	#427	—	47	2	no	—
707	C₂×#106	C₂×D₄₇	1	1	yes	characteristic, complemented
708	#419	—	47	2	no	—
709	#418	—	47	2	no	—
710	C₂×#103	C₂×D₄₇	1	1	yes	characteristic, complemented
711	C₂×#102	C₂×D₄₇	1	1	yes	characteristic
712	#405	—	47	2	no	—
713	C₂×C₄×C₈	C₂×D₄₇	1	1	yes	characteristic, complemented
714	C₄₇	#61481	1	1	yes	characteristic, complemented, Sylow
715	C₂×#41	—	94	1	no	—
716	C₂×#41	—	94	1	no	—
717	C₂²×Q₈	—	47	2	no	—
718	C₂²×Q₈	C₂²×D₄₇	1	1	yes	characteristic
719	C₂²×D₄	—	47	2	no	—
720	C₂²×D₄	—	94	1	no	—
721	C₂²×D₄	—	94	2	no	—
722	C₂²×D₄	C₂²×D₄₇	1	1	yes	characteristic
723	C₂³×C₄	—	2	1	no	—
724	C₂×SD₁₆	—	2	4	no	—
725	C₂×SD₁₆	—	47	2	no	—
726	C₂×SD₁₆	—	47	2	no	—
727	C₂×SD₁₆	—	47	2	no	—
728	C₂×SD₁₆	—	47	2	no	—
729	C₂×SD₁₆	—	47	2	no	—
730	C₂×SD₁₆	—	47	2	no	—
731	C₂×SD₁₆	—	94	8	no	—
732	C₂×SD₁₆	C₂²×D₄₇	1	1	yes	characteristic
733	C₂×SD₁₆	C₂²×D₄₇	1	1	yes	characteristic
734	C₂×SD₁₆	C₂²×D₄₇	1	1	yes	characteristic
735	C₂×SD₁₆	C₂²×D₄₇	1	1	yes	characteristic
736	C₂×M₁₆	—	47	2	no	—
737	C₂²×C₈	—	47	2	no	—
738	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
739	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
740	C₄⋊Q₈	—	47	2	no	—
741	C₄⋊Q₈	—	47	1	no	—
742	C₄⋊Q₈	—	47	1	no	—
743	C₄⋊Q₈	—	47	1	no	—
744	C₄⋊Q₈	—	94	1	no	—
745	C₄⋊Q₈	—	94	1	no	—
746	C₄⋊Q₈	—	94	2	no	—
747	#127	—	47	2	no	—
748	#127	—	47	1	no	—
749	#126	—	47	2	no	—
750	#126	—	94	2	no	—
751	#126	—	94	2	no	—
752	#126	—	94	2	no	—
753	#126	—	94	2	no	—
754	#126	—	94	2	no	—
755	#125	—	47	2	no	—
756	#125	—	47	2	no	—
757	#125	—	47	1	no	—
758	#125	—	94	1	no	—
759	#125	—	94	2	no	—
760	#125	—	94	2	no	—
761	#125	—	94	2	no	—
762	#125	—	94	2	no	—
763	#125	—	94	2	no	—
764	#125	—	94	1	no	—
765	#124	—	47	1	no	—
766	#124	—	94	1	no	—
767	#124	—	94	2	no	—
768	#124	—	94	1	no	—
769	#123	—	47	2	no	—
770	#123	—	94	2	no	—
771	#123	—	94	2	no	—
772	#123	—	94	2	no	—
773	#123	—	94	2	no	—
774	C₂²⋊Q₈	—	47	1	no	—
775	C₂²⋊Q₈	—	47	2	no	—
776	C₂²⋊Q₈	—	47	2	no	—
777	C₂²⋊Q₈	—	47	2	no	—
778	C₂²⋊Q₈	—	94	2	no	—
779	C₂²⋊Q₈	—	94	2	no	—
780	C₂²⋊Q₈	—	94	2	no	—
781	C₂²⋊Q₈	—	94	2	no	—
782	C₂²⋊Q₈	—	94	1	no	—
783	C₂²⋊Q₈	—	94	1	no	—
784	#121	—	47	1	no	—
785	#121	—	47	2	no	—
786	#121	—	47	2	no	—
787	#121	—	47	2	no	—
788	#121	—	94	2	no	—
789	#121	—	94	2	no	—
790	#121	—	94	2	no	—
791	#121	—	94	1	no	—
792	#121	—	94	1	no	—
793	#121	—	94	2	no	—
794	#121	—	94	2	no	—
795	#121	—	94	1	no	—
796	#121	—	94	1	no	—
797	#120	—	94	2	no	—
798	#120	—	94	2	no	—
799	#120	—	94	2	no	—
800	C₄×Q₈	—	2	1	no	—
801	C₄×Q₈	—	2	1	no	—
802	C₄×Q₈	—	47	1	no	—
803	C₄×Q₈	—	47	2	no	—
804	C₄×Q₈	—	47	2	no	—
805	C₄×Q₈	—	47	2	no	—
806	C₄×Q₈	—	94	2	no	—
807	C₄×Q₈	—	94	1	no	—
808	C₄×Q₈	—	94	1	no	—
809	C₄×Q₈	—	94	1	no	—
810	C₄×Q₈	—	94	2	no	—
811	C₄×Q₈	—	94	1	no	—
812	C₄×Q₈	C₂²×D₄₇	1	1	yes	characteristic
813	C₄×Q₈	C₂²×D₄₇	1	1	yes	characteristic
814	C₄×Q₈	C₂²×D₄₇	1	1	yes	characteristic
815	C₄×Q₈	C₂²×D₄₇	1	1	yes	characteristic
816	C₄×D₄	—	2	1	no	—
817	C₄×D₄	—	2	1	no	—
818	C₄×D₄	—	47	2	no	—
819	C₄×D₄	—	47	2	no	—
820	C₄×D₄	—	47	2	no	—
821	C₄×D₄	—	47	1	no	—
822	C₄×D₄	—	47	2	no	—
823	C₄×D₄	—	94	1	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	1	no	—
829	C₄×D₄	C₂²×D₄₇	1	1	yes	characteristic
830	C₄×D₄	C₂²×D₄₇	1	1	yes	characteristic
831	C₄×D₄	C₂²×D₄₇	1	1	yes	characteristic
832	C₄×D₄	C₂²×D₄₇	1	1	yes	characteristic
833	#117	—	47	2	no	—
834	#117	—	47	2	no	—
835	#117	—	47	2	no	—
836	#117	—	94	2	no	—
837	#117	—	94	2	no	—
838	#117	—	94	2	no	—
839	#117	—	94	1	no	—
840	#117	—	94	1	no	—
841	C₂×C₄⋊C₄	—	2	1	no	—
842	C₂×C₄⋊C₄	—	94	1	no	—
843	C₂×C₄⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
844	C₂×C₄⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
845	C₂×C₂²⋊C₄	—	2	1	no	—
846	C₂×C₂²⋊C₄	—	94	2	no	—
847	C₂×C₂²⋊C₄	—	94	2	no	—
848	C₂×C₄²	—	2	1	no	—
849	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
850	#107	—	47	2	no	—
851	#107	—	47	2	no	—
852	#107	—	47	2	no	—
853	#107	—	47	2	no	—
854	#106	—	47	2	no	—
855	#106	—	47	2	no	—
856	#106	C₂²×D₄₇	1	1	yes	characteristic
857	#106	C₂²×D₄₇	1	1	yes	characteristic
858	#106	C₂²×D₄₇	1	1	yes	characteristic
859	#106	C₂²×D₄₇	1	1	yes	characteristic
860	C₄⋊C₈	—	47	2	no	—
861	C₄⋊C₈	—	47	2	no	—
862	C₄⋊C₈	—	47	1	no	—
863	C₄⋊C₈	—	47	1	no	—
864	#103	—	47	2	no	—
865	#103	—	47	2	no	—
866	#103	—	47	2	no	—
867	#103	—	47	2	no	—
868	#103	—	47	2	no	—
869	#103	—	47	2	no	—
870	#103	C₂²×D₄₇	1	1	yes	characteristic
871	#103	C₂²×D₄₇	1	1	yes	characteristic
872	#103	C₂²×D₄₇	1	1	yes	characteristic
873	#103	C₂²×D₄₇	1	1	yes	characteristic
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	C₂²×D₄₇	1	1	yes	characteristic
881	#102	C₂²×D₄₇	1	1	yes	characteristic
882	#102	C₂²×D₄₇	1	1	yes	characteristic
883	#102	C₂²×D₄₇	1	1	yes	characteristic
884	C₂²⋊C₈	—	47	2	no	—
885	C₂²⋊C₈	—	47	2	no	—
886	C₂²⋊C₈	—	47	2	no	—
887	#97	—	47	2	no	—
888	#97	—	47	2	no	—
889	C₄×C₈	—	47	2	no	—
890	C₄×C₈	C₂²×D₄₇	1	1	yes	characteristic
891	C₄×C₈	C₂²×D₄₇	1	1	yes	characteristic
892	C₄×C₈	C₂²×D₄₇	1	1	yes	characteristic
893	C₄×C₈	C₂²×D₄₇	1	1	yes	characteristic
894	C₂⁴	—	2	1	no	—
895	C₂⁴	—	94	2	no	—
896	#41	—	376	2	no	—
897	#41	—	376	2	no	—
898	C₂×Q₈	—	2	1	no	—
899	C₂×Q₈	—	2	2	no	—
900	C₂×Q₈	—	4	1	no	—
901	C₂×Q₈	—	47	1	no	—
902	C₂×Q₈	—	47	2	no	—
903	C₂×Q₈	—	94	2	no	—
904	C₂×Q₈	—	94	1	no	—
905	C₂×Q₈	—	94	1	no	—
906	C₂×Q₈	—	94	4	no	—
907	C₂×Q₈	—	188	2	no	—
908	C₂×Q₈	C₂³×D₄₇	1	1	yes	characteristic
909	C₂×Q₈	C₂³×D₄₇	1	1	yes	characteristic
910	C₂×D₄	—	2	2	no	—
911	C₂×D₄	—	2	1	no	—
912	C₂×D₄	—	4	1	no	—
913	C₂×D₄	—	47	2	no	—
914	C₂×D₄	—	47	1	no	—
915	C₂×D₄	—	47	2	no	—
916	C₂×D₄	—	94	2	no	—
917	C₂×D₄	—	94	2	no	—
918	C₂×D₄	—	94	2	no	—
919	C₂×D₄	—	94	2	no	—
920	C₂×D₄	—	94	4	no	—
921	C₂×D₄	—	94	2	no	—
922	C₂×D₄	—	94	2	no	—
923	C₂×D₄	—	94	1	no	—
924	C₂×D₄	—	94	1	no	—
925	C₂×D₄	—	376	2	no	—
926	C₂×D₄	—	376	4	no	—
927	C₂×D₄	—	188	2	no	—
928	C₂×D₄	C₂³×D₄₇	1	1	yes	characteristic
929	C₂×D₄	C₂³×D₄₇	1	1	yes	characteristic
930	C₂²×C₄	—	2	1	no	—
931	C₂²×C₄	—	2	1	no	—
932	C₂²×C₄	—	2	1	no	—
933	C₂²×C₄	—	2	1	no	—
934	C₂²×C₄	—	2	1	no	—
935	C₂²×C₄	—	2	1	no	—
936	C₂²×C₄	—	2	1	no	—
937	C₂²×C₄	—	8	2	no	—
938	C₂²×C₄	—	47	2	no	—
939	C₂²×C₄	—	94	2	no	—
940	C₂²×C₄	—	94	2	no	—
941	C₂²×C₄	—	94	2	no	—
942	C₂²×C₄	—	94	2	no	—
943	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
944	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
945	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
946	SD₁₆	—	2	2	no	—
947	SD₁₆	—	2	2	no	—
948	SD₁₆	—	2	2	no	—
949	SD₁₆	—	94	4	no	—
950	SD₁₆	—	94	4	no	—
951	SD₁₆	—	94	4	no	—
952	SD₁₆	—	188	2	no	—
953	SD₁₆	—	188	2	no	—
954	SD₁₆	—	188	2	no	—
955	SD₁₆	#10625350	1	4	yes	complemented
956	M₁₆	—	188	2	no	—
957	C₂×C₈	—	2	2	no	—
958	C₂×C₈	—	4	1	no	—
959	C₂×C₈	—	47	2	no	—
960	C₂×C₈	—	47	2	no	—
961	C₂×C₈	—	94	4	no	—
962	C₂×C₈	C₂³×D₄₇	1	1	yes	characteristic
963	C₂×C₈	C₂³×D₄₇	1	1	yes	characteristic
964	C₂×C₈	C₂³×D₄₇	1	1	yes	characteristic
965	C₂×C₈	C₂³×D₄₇	1	1	yes	characteristic
966	C₄⋊C₄	—	2	1	no	—
967	C₄⋊C₄	—	2	1	no	—
968	C₄⋊C₄	—	2	1	no	—
969	C₄⋊C₄	—	2	1	no	—
970	C₄⋊C₄	—	2	1	no	—
971	C₄⋊C₄	—	2	1	no	—
972	C₄⋊C₄	—	47	2	no	—
973	C₄⋊C₄	—	47	2	no	—
974	C₄⋊C₄	—	47	2	no	—
975	C₄⋊C₄	—	47	2	no	—
976	C₄⋊C₄	—	47	1	no	—
977	C₄⋊C₄	—	47	1	no	—
978	C₄⋊C₄	—	47	2	no	—
979	C₄⋊C₄	—	47	2	no	—
980	C₄⋊C₄	—	94	2	no	—
981	C₄⋊C₄	—	94	2	no	—
982	C₄⋊C₄	—	94	2	no	—
983	C₄⋊C₄	—	94	2	no	—
984	C₄⋊C₄	—	94	2	no	—
985	C₄⋊C₄	—	94	2	no	—
986	C₄⋊C₄	—	94	2	no	—
987	C₄⋊C₄	—	94	2	no	—
988	C₄⋊C₄	—	94	2	no	—
989	C₄⋊C₄	—	94	2	no	—
990	C₄⋊C₄	—	94	2	no	—
991	C₄⋊C₄	—	94	2	no	—
992	C₄⋊C₄	—	94	1	no	—
993	C₄⋊C₄	—	94	1	no	—
994	C₄⋊C₄	—	94	1	no	—
995	C₄⋊C₄	—	94	1	no	—
996	C₄⋊C₄	C₂³×D₄₇	1	1	yes	characteristic
997	C₄⋊C₄	C₂³×D₄₇	1	1	yes	characteristic
998	C₄⋊C₄	C₂³×D₄₇	1	1	yes	characteristic
999	C₄⋊C₄	C₂³×D₄₇	1	1	yes	characteristic
1000	C₂²⋊C₄	—	2	1	no	—
1001	C₂²⋊C₄	—	2	1	no	—
1002	C₂²⋊C₄	—	2	1	no	—
1003	C₂²⋊C₄	—	2	1	no	—
1004	C₂²⋊C₄	—	47	2	no	—
1005	C₂²⋊C₄	—	47	2	no	—
1006	C₂²⋊C₄	—	47	2	no	—
1007	C₂²⋊C₄	—	47	2	no	—
1008	C₂²⋊C₄	—	47	2	no	—
1009	C₂²⋊C₄	—	94	2	no	—
1010	C₂²⋊C₄	—	94	2	no	—
1011	C₂²⋊C₄	—	94	2	no	—
1012	C₂²⋊C₄	—	94	2	no	—
1013	C₂²⋊C₄	—	94	2	no	—
1014	C₂²⋊C₄	—	94	2	no	—
1015	C₂²⋊C₄	—	94	2	no	—
1016	C₂²⋊C₄	—	94	2	no	—
1017	C₂²⋊C₄	—	94	2	no	—
1018	C₂²⋊C₄	—	94	2	no	—
1019	C₂²⋊C₄	—	94	2	no	—
1020	C₄²	—	2	1	no	—
1021	C₄²	—	2	1	no	—
1022	C₄²	—	2	1	no	—
1023	C₄²	—	2	1	no	—
1024	C₄²	—	47	2	no	—
1025	C₄²	—	94	2	no	—
1026	C₄²	—	94	2	no	—
1027	C₄²	—	94	2	no	—
1028	C₄²	—	94	2	no	—
1029	C₄²	—	94	2	no	—
1030	C₄²	D₄×D₄₇	1	1	yes	characteristic
1031	C₄²	D₄×D₄₇	1	1	yes	characteristic
1032	C₄²	C₂³×D₄₇	1	1	yes	characteristic
1033	C₄²	C₂³×D₄₇	1	1	yes	characteristic
1034	C₂³	—	2	1	no	—
1035	C₂³	—	2	1	no	—
1036	C₂³	—	4	2	no	—
1037	C₂³	—	4	2	no	—
1038	C₂³	—	8	1	no	—
1039	C₂³	—	47	2	no	—
1040	C₂³	—	94	2	no	—
1041	C₂³	—	376	2	no	—
1042	C₂³	—	376	2	no	—
1043	C₂³	—	188	4	no	—
1044	C₂³	C₂×D₄×D₄₇	1	1	yes	characteristic
1045	Q₈	—	2	1	no	—
1046	Q₈	—	2	1	no	—
1047	Q₈	—	2	1	no	—
1048	Q₈	—	4	2	no	—
1049	Q₈	—	94	2	no	—
1050	Q₈	—	94	2	no	—
1051	Q₈	—	94	2	no	—
1052	Q₈	—	376	1	no	—
1053	Q₈	—	188	4	no	—
1054	Q₈	—	188	2	no	—
1055	Q₈	C₂×#10625350	1	2	yes	—
1056	D₄	—	2	1	no	—
1057	D₄	—	2	1	no	—
1058	D₄	—	2	1	no	—
1059	D₄	—	4	2	no	—
1060	D₄	—	94	4	no	—
1061	D₄	—	94	2	no	—
1062	D₄	—	94	2	no	—
1063	D₄	—	94	2	no	—
1064	D₄	—	376	1	no	—
1065	D₄	—	376	2	no	—
1066	D₄	—	376	2	no	—
1067	D₄	—	376	2	no	—
1068	D₄	—	376	2	no	—
1069	D₄	—	188	4	no	—
1070	D₄	—	188	4	no	—
1071	D₄	—	188	2	no	—
1072	D₄	C₂×#10625350	1	2	yes	—
1073	C₂×C₄	—	2	2	no	—
1074	C₂×C₄	—	2	1	no	—
1075	C₂×C₄	—	2	2	no	—
1076	C₂×C₄	—	2	1	no	—
1077	C₂×C₄	—	2	1	no	—
1078	C₂×C₄	—	2	1	no	—
1079	C₂×C₄	—	2	1	no	—
1080	C₂×C₄	—	2	1	no	—
1081	C₂×C₄	—	2	1	no	—
1082	C₂×C₄	—	2	1	no	—
1083	C₂×C₄	—	4	2	no	—
1084	C₂×C₄	—	4	2	no	—
1085	C₂×C₄	—	4	2	no	—
1086	C₂×C₄	—	4	2	no	—
1087	C₂×C₄	—	8	1	no	—
1088	C₂×C₄	—	8	1	no	—
1089	C₂×C₄	—	8	1	no	—
1090	C₂×C₄	—	47	2	no	—
1091	C₂×C₄	—	47	2	no	—
1092	C₂×C₄	—	47	2	no	—
1093	C₂×C₄	—	94	2	no	—
1094	C₂×C₄	—	94	2	no	—
1095	C₂×C₄	—	94	2	no	—
1096	C₂×C₄	—	94	2	no	—
1097	C₂×C₄	—	94	2	no	—
1098	C₂×C₄	—	376	2	no	—
1099	C₂×C₄	—	376	2	no	—
1100	C₂×C₄	—	376	2	no	—
1101	C₂×C₄	—	188	4	no	—
1102	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
1103	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
1104	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
1105	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
1106	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
1107	C₂×C₄	C₂⁴×D₄₇	1	1	yes	characteristic
1108	C₈	—	2	1	no	—
1109	C₈	—	2	1	no	—
1110	C₈	—	2	1	no	—
1111	C₈	—	94	2	no	—
1112	C₈	—	94	2	no	—
1113	C₈	C₂×#10625350	1	2	yes	—
1114	C₂²	—	2	1	no	—
1115	C₂²	—	2	1	no	—
1116	C₂²	—	2	2	no	—
1117	C₂²	—	4	1	no	—
1118	C₂²	—	4	1	no	—
1119	C₂²	—	4	1	no	—
1120	C₂²	—	4	1	no	—
1121	C₂²	—	4	1	no	—
1122	C₂²	—	8	4	no	—
1123	C₂²	—	94	2	no	—
1124	C₂²	—	94	2	no	—
1125	C₂²	—	94	2	no	—
1126	C₂²	—	188	2	no	—
1127	C₂²	—	188	2	no	—
1128	C₂²	—	188	2	no	—
1129	C₂²	—	752	4	no	—
1130	C₂²	#15689930	1	2	yes	—
1131	C₂²	C₂²×D₄×D₄₇	1	1	yes	characteristic
1132	C₄	—	2	1	no	—
1133	C₄	—	2	1	no	—
1134	C₄	—	2	1	no	—
1135	C₄	—	2	1	no	—
1136	C₄	—	2	2	no	—
1137	C₄	—	4	1	no	—
1138	C₄	—	4	1	no	—
1139	C₄	—	4	1	no	—
1140	C₄	—	4	1	no	—
1141	C₄	—	4	1	no	—
1142	C₄	—	94	2	no	—
1143	C₄	—	94	2	no	—
1144	C₄	—	94	2	no	—
1145	C₄	—	188	2	no	—
1146	C₄	—	188	2	no	—
1147	C₄	—	188	2	no	—
1148	C₄	#15689929	1	2	yes	—
1149	C₄	C₂²×#10625350	1	1	yes	characteristic
1150	C₄	#15689959	1	1	yes	characteristic
1151	C₂	—	2	2	no	—
1152	C₂	—	4	2	no	—
1153	C₂	—	8	1	no	—
1154	C₂	—	376	2	no	—
1155	C₂	—	188	2	no	—
1156	C₂	D₄×#10625350	1	1	yes	characteristic
1157	C₂	C₂×#15689929	1	1	yes	characteristic
1158	C₂	C₂×#15689930	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂²×D₄×D₄₇
commutator, cosocle	C₂×C₄×C₄₇	C₂⁵
Frattini	C₂×C₄	C₂⁴×D₄₇
Fitting	C₂×C₄×SD₁₆×C₄₇	C₂
socle	C₂²×C₄₇	C₂³×D₄
prime radical	#20257420	C₂
hypercenter	C₂×C₄×SD₁₆	D₄₇
hypocenter	C₄₇	#61481
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ C₂×C₄×SD₁₆

Complements

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

N	H ≅ G/N	type
1. #20257484	C₂	semidirect
3. #20256367	C₂	semidirect
4. #20256261	C₂	semidirect
5. #20256167	C₂	semidirect
6. #20256115	C₂	semidirect
7. #20255803	C₂	semidirect
8. #20255763	C₂	semidirect
9. #20255684	C₂	semidirect
10. #20255621	C₂	semidirect
11. #20255555	C₂	semidirect
12. #20255405	C₂	semidirect
13. SD₁₆×D₁₈₈	C₂	semidirect
14. SD₁₆×C₂²⋊D₄₇	C₂	semidirect
15. #20254012	C₂	semidirect
16. #20253947	C₂	semidirect
17. #20253676	C₂	semidirect
18. #20253637	C₂	semidirect
19. #20253510	C₂	semidirect
20. #20253487	C₂	semidirect
21. #20252363	C₂	semidirect
22. #20252242	C₂	semidirect
23. C₂×C₄×SD₁₆×C₄₇	C₂	semidirect
25. #15689852	C₂²	semidirect
27. #15689851	C₂²	semidirect
29. #15689846	C₂²	semidirect
35. #15689808	C₂²	semidirect
37. Q₈×D₁₈₈	C₂²	semidirect
38. Q₈×C₂²⋊D₄₇	C₂²	semidirect
44. #15689731	C₂²	semidirect
48. #15689680	C₂²	semidirect
54. #15689599	C₂²	semidirect
56. #15689523	C₂²	semidirect
57. #15689521	C₂²	semidirect
58. #15689496	C₂²	semidirect
59. #15689494	C₂²	semidirect
60. #15689490	C₂²	semidirect
61. #15689486	C₂²	semidirect
62. #15689474	C₂²	semidirect
63. #15689470	C₂²	semidirect
64. #15689467	C₂²	semidirect
65. #15689462	C₂²	semidirect
66. #15689458	C₂²	semidirect
67. #15689449	C₂²	semidirect
68. #15689446	C₂²	semidirect
69. #15689436	C₂²	semidirect
70. #15689433	C₂²	semidirect
71. #15689428	C₂²	semidirect
73. #15689422	C₂²	semidirect
74. #15689418	C₂²	semidirect
75. #15689418	C₂²	semidirect
77. #15689403	C₂²	semidirect
78. #15689372	C₂²	semidirect
79. #15689368	C₂²	semidirect
80. #15689353	C₂²	semidirect
81. #15689352	C₂²	semidirect
82. #15689352	C₂²	semidirect
83. #15689349	C₂²	semidirect
85. #15689328	C₂²	semidirect
86. #15689327	C₂²	semidirect
88. #15689323	C₂²	semidirect
89. #15689323	C₂²	semidirect
90. #15689322	C₂²	semidirect
91. #15689321	C₂²	semidirect
95. #15689263	C₂²	semidirect
96. #15689262	C₂²	semidirect
97. #15689260	C₂²	semidirect
98. #15689253	C₂²	semidirect
99. C₈×Dic₉₄	C₂²	semidirect
100. #15689226	C₂²	semidirect
102. #15689223	C₂²	semidirect
103. #15689221	C₂²	semidirect
104. #15689221	C₂²	semidirect
106. C₄×#10625325	C₂²	semidirect
107. C₄×#10625325	C₂²	semidirect
109. #15689210	C₂²	semidirect
110. #15689202	C₂²	semidirect
111. #15689194	C₂²	semidirect
112. C₈×D₁₈₈	C₂²	semidirect
113. C₈×C₂²⋊D₄₇	C₂²	semidirect
114. #15689182	C₂²	semidirect
115. #15689180	C₂²	semidirect
116. #15689158	C₂²	semidirect
117. #15689130	C₂²	semidirect
119. #15689077	C₂²	semidirect
121. C₂×C₄×Q₈×C₄₇	C₂²	semidirect
127. C₄×SD₁₆×C₄₇	C₂²	semidirect
128. C₄×SD₁₆×C₄₇	C₂²	semidirect
129. C₄×SD₁₆×C₄₇	C₂²	semidirect
130. C₄×SD₁₆×C₄₇	C₂²	semidirect
131. C₂×#106×C₄₇	C₂²	semidirect
132. C₂×#103×C₄₇	C₂²	semidirect
134. C₂×C₄×C₈×C₄₇	C₂²	semidirect
369. SD₁₆×C₄₇	#41	semidirect
594. C₂×C₄×SD₁₆	D₄₇	semidirect
636. C₂×C₄×Q₈	C₂×D₄₇	semidirect
696. C₄×SD₁₆	C₂×D₄₇	semidirect
697. C₄×SD₁₆	C₂×D₄₇	semidirect
698. C₄×SD₁₆	C₂×D₄₇	semidirect
699. C₄×SD₁₆	C₂×D₄₇	semidirect
707. C₂×#106	C₂×D₄₇	semidirect
710. C₂×#103	C₂×D₄₇	semidirect
713. C₂×C₄×C₈	C₂×D₄₇	semidirect
714. C₄₇	#61481	semidirect
955. SD₁₆	#10625350	semidirect

Maximal subgroups

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

subgroup	index
#20257484	2
#20257420	2
#20256367	2
#20256261	2
#20256167	2
#20256115	2
#20255803	2
#20255763	2
#20255684	2
#20255621	2
#20255555	2
#20255405	2
SD₁₆×D₁₈₈	2
SD₁₆×C₂²⋊D₄₇	2
#20254012	2
#20253947	2
#20253676	2
#20253637	2
#20253510	2
#20253487	2
#20252363	2
#20252242	2
C₂×C₄×SD₁₆×C₄₇	2
#61481	47