Subgroups — #27098562

Order 12032.

2102 conjugacy classes of subgroups.

The subgroup lattice has 1196 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20257003	C₂	1	1	yes	maximal, characteristic, complemented
2	D₄×#10625350	C₂	1	1	yes	maximal, characteristic, complemented
3	#20256367	C₂	1	1	yes	maximal, characteristic, complemented
4	D₈×Dic₉₄	C₂	1	1	yes	maximal, characteristic, complemented
5	#20256028	C₂	1	1	yes	maximal, characteristic, complemented
6	#20256021	C₂	1	1	yes	maximal, characteristic, complemented
7	#20255974	C₂	1	1	yes	maximal, characteristic, complemented
8	#20255968	C₂	1	2	yes	maximal, complemented
9	#20255695	C₂	1	1	yes	maximal, characteristic, complemented
10	#20255689	C₂	1	2	yes	maximal, complemented
11	#20255621	C₂	1	1	yes	maximal, characteristic, complemented
12	#20255615	C₂	1	2	yes	maximal, complemented
13	#20254989	C₂	1	1	yes	maximal, characteristic, complemented
14	#20254982	C₂	1	2	yes	maximal, complemented
15	#20254106	C₂	1	1	yes	maximal, characteristic, complemented
16	#20254103	C₂	1	2	yes	maximal, complemented
17	#20253539	C₂	1	1	yes	maximal, characteristic, complemented
18	#20253535	C₂	1	2	yes	maximal, complemented
19	#20253487	C₂	1	1	yes	maximal, characteristic, complemented
20	#20253485	C₂	1	2	yes	maximal, complemented
21	#20252406	C₂	1	1	yes	maximal, characteristic, complemented
22	#20252199	C₂	1	2	yes	maximal, complemented
23	C₄×AGL(1,ℤ/8)×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂²×#10625350	—	2	1	no	—
25	C₂×#13094048	C₂²	1	2	yes	—
26	#15689851	C₂²	1	1	yes	characteristic, complemented
27	#15689846	C₂²	1	1	yes	characteristic, complemented
28	#15689841	C₂²	1	2	yes	complemented
29	#15689813	—	2	1	no	—
30	#15689806	—	2	2	no	—
31	#15689794	C₂²	1	1	yes	characteristic
32	D₄×Dic₉₄	C₂²	1	1	yes	characteristic
33	D₄×Dic₉₄	C₂²	1	1	yes	characteristic, complemented
34	#15689782	—	2	1	no	—
35	#15689782	—	2	1	no	—
36	#15689778	C₂²	1	1	yes	characteristic
37	#15689777	C₂²	1	1	yes	characteristic, complemented
38	#15689774	C₂²	1	2	yes	—
39	#15689772	C₂²	1	2	yes	complemented
40	#15689769	—	2	1	no	—
41	#15689763	—	2	2	no	—
42	D₄×D₁₈₈	C₂²	1	1	yes	characteristic
43	D₄×C₂²⋊D₄₇	C₂²	1	2	yes	—
44	#15689680	C₂²	1	1	yes	characteristic, complemented
45	#15689677	C₂²	1	2	yes	complemented
46	#15689673	C₂²	1	1	yes	characteristic
47	#15689670	C₂²	1	2	yes	—
48	#15689657	—	2	1	no	—
49	#15689653	—	2	2	no	—
50	#15689634	—	2	1	no	—
51	#15689632	—	2	2	no	—
52	C₄×#10625350	C₂²	1	1	yes	characteristic
53	C₄×#10625352	C₂²	1	2	yes	complemented
54	C₂×C₄×Dic₉₄	—	2	1	no	—
55	C₄×D₄×D₄₇	C₂²	1	2	yes	—
56	#15689528	C₂²	1	1	yes	characteristic, complemented
57	#15689527	C₂²	1	2	yes	complemented
58	#15689496	C₂²	1	1	yes	characteristic, complemented
59	#15689494	C₂²	1	2	yes	complemented
60	#15689474	C₂²	1	1	yes	characteristic, complemented
61	#15689472	C₂²	1	2	yes	complemented
62	#15689470	C₂²	1	1	yes	characteristic, complemented
63	#15689468	C₂²	1	2	yes	complemented
64	#15689460	C₂²	1	2	yes	complemented
65	#15689458	C₂²	1	2	yes	complemented
66	#15689457	C₂²	1	2	yes	complemented
67	#15689449	C₂²	1	2	yes	complemented
68	#15689447	C₂²	1	2	yes	complemented
69	#15689445	C₂²	1	2	yes	complemented
70	#15689408	C₂²	1	1	yes	characteristic, complemented
71	#15689407	C₂²	1	2	yes	complemented
72	#15689403	C₂²	1	1	yes	characteristic
73	#15689403	C₂²	1	1	yes	characteristic, complemented
74	#15689403	C₂²	1	1	yes	characteristic, complemented
75	#15689402	C₂²	1	2	yes	complemented
76	#15689401	C₂²	1	2	yes	—
77	#15689401	C₂²	1	2	yes	complemented
78	#15689372	C₂²	1	2	yes	complemented
79	#15689370	C₂²	1	2	yes	complemented
80	#15689369	C₂²	1	2	yes	complemented
81	#15689369	C₂²	1	2	yes	complemented
82	#15689368	C₂²	1	2	yes	complemented
83	#15689366	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	#15689322	C₂²	1	2	yes	complemented
90	#15689318	C₂²	1	1	yes	characteristic, complemented
91	#15689316	C₂²	1	2	yes	complemented
92	#15689275	C₂²	1	2	yes	—
93	#15689274	C₂²	1	2	yes	—
94	#15689272	C₂²	1	2	yes	—
95	#15689269	C₂²	1	2	yes	complemented
96	#15689268	C₂²	1	2	yes	complemented
97	#15689265	C₂²	1	2	yes	complemented
98	C₈×Dic₉₄	C₂²	1	1	yes	characteristic, complemented
99	C₈×Dic₉₄	C₂²	1	1	yes	characteristic, complemented
100	#15689233	C₂²	1	2	yes	complemented
101	#15689225	C₂²	1	2	yes	complemented
102	#15689225	C₂²	1	2	yes	complemented
103	#15689223	C₂²	1	2	yes	—
104	#15689223	C₂²	1	2	yes	complemented
105	#15689221	C₂²	1	2	yes	complemented
106	#15689214	C₂²	1	2	yes	—
107	#15689210	C₂²	1	2	yes	complemented
108	D₈×Dic₄₇	C₂²	1	2	yes	—
109	#15689203	C₂²	1	2	yes	complemented
110	#15689202	C₂²	1	1	yes	characteristic, complemented
111	#15689202	C₂²	1	1	yes	characteristic, complemented
112	#15689199	C₂²	1	2	yes	complemented
113	#15689199	C₂²	1	2	yes	complemented
114	#15689180	C₂²	1	1	yes	characteristic, complemented
115	#15689178	C₂²	1	2	yes	complemented
116	#15689162	C₂²	1	2	yes	complemented
117	#15689126	C₂²	1	2	yes	—
118	#15689121	C₂²	1	2	yes	complemented
119	#15689075	C₂²	1	2	yes	complemented
120	C₂×AGL(1,ℤ/8)×C₄₇	C₂²	1	1	yes	characteristic
121	C₄×#41×C₄₇	C₂²	1	1	yes	characteristic, complemented
122	C₂×C₄×D₄×C₄₇	C₂²	1	1	yes	characteristic
123	C₄₇×#442	C₂²	1	1	yes	characteristic
124	C₄₇×#442	C₂²	1	1	yes	characteristic, complemented
125	C₄₇×#440	C₂²	1	1	yes	characteristic
126	C₄₇×#440	C₂²	1	1	yes	characteristic, complemented
127	C₄×SD₁₆×C₄₇	C₂²	1	1	yes	characteristic
128	C₄×SD₁₆×C₄₇	C₂²	1	1	yes	characteristic, complemented
129	C₄×D₈×C₄₇	C₂²	1	1	yes	characteristic
130	C₄×D₈×C₄₇	C₂²	1	1	yes	characteristic, complemented
131	C₄₇×#428	C₂²	1	1	yes	characteristic, complemented
132	C₄₇×#418	C₂²	1	1	yes	characteristic
133	C₄₇×#417	C₂²	1	1	yes	characteristic, complemented
134	C₄×M₁₆×C₄₇	C₂²	1	1	yes	characteristic, complemented
135	C₂×#10625350	—	2	1	no	—
136	C₂×#10625350	—	2	2	no	—
137	C₂×#10625350	—	2	1	no	—
138	C₂×#10625350	—	2	2	no	—
139	C₂×#10625350	—	2	1	no	—
140	C₂×#10625350	—	4	8	no	—
141	C₂×#10625350	D₄	1	1	yes	characteristic
142	C₂×#10625352	C₂³	1	2	yes	—
143	C₂²×Dic₉₄	—	2	1	no	—
144	C₂²×Dic₉₄	—	2	1	no	—
145	C₂²×D₁₈₈	—	2	1	no	—
146	C₂²×C₂²⋊D₄₇	—	2	2	no	—
147	C₂×D₄×D₄₇	C₂³	1	2	yes	—
148	C₂²×C₄×D₄₇	—	2	2	no	—
149	#13094048	—	2	8	no	—
150	C₂×#10625325	C₂³	1	2	yes	—
151	C₂×#10625325	C₂³	1	2	yes	—
152	C₂×#10625335	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×#10625324	C₂³	1	2	yes	—
157	C₂×#10625324	C₂³	1	2	yes	—
158	#13094024	C₂³	1	1	yes	characteristic
159	#13094024	C₂³	1	1	yes	characteristic
160	#13094024	C₂³	1	1	yes	characteristic
161	#13094023	C₂³	1	2	yes	—
162	#13094023	C₂³	1	2	yes	—
163	#13094022	C₂³	1	2	yes	—
164	#13094021	C₂³	1	1	yes	characteristic
165	#13094020	C₂³	1	2	yes	—
166	#13094019	—	2	2	no	—
167	#13094018	—	2	2	no	—
168	#13094017	—	2	2	no	—
169	#13094016	—	2	1	no	—
170	#13094016	—	2	1	no	—
171	#13094014	—	2	2	no	—
172	#13094014	—	2	2	no	—
173	#13094012	—	2	1	no	—
174	#13094012	—	2	1	no	—
175	#13094010	—	2	2	no	—
176	#13094010	—	2	2	no	—
177	#13094009	—	2	2	no	—
178	#13094008	—	2	2	no	—
179	#13094007	—	2	2	no	—
180	#13094007	—	2	2	no	—
181	#13094006	—	2	2	no	—
182	#13094005	—	2	2	no	—
183	#13094004	C₂³	1	2	yes	—
184	#13094003	—	2	1	no	—
185	#13094003	—	2	1	no	—
186	#13094003	—	2	1	no	—
187	#13094003	—	2	1	no	—
188	#13094003	C₂³	1	2	yes	—
189	#13094002	—	2	2	no	—
190	#13094002	—	2	2	no	—
191	#13094001	—	2	2	no	—
192	#13094001	—	2	2	no	—
193	#13094000	C₂³	1	2	yes	—
194	#13093999	C₂³	1	2	yes	—
195	#13093998	—	2	1	no	—
196	#13093998	—	2	1	no	—
197	#13093998	—	2	1	no	—
198	#13093998	—	2	1	no	—
199	#13093998	C₂³	1	2	yes	—
200	#13093997	—	2	2	no	—
201	#13093997	—	2	2	no	—
202	#13093996	—	2	2	no	—
203	#13093996	—	2	2	no	—
204	#13093995	C₂³	1	2	yes	—
205	#13093994	—	2	2	no	—
206	#13093993	—	2	2	no	—
207	#13093992	—	2	2	no	—
208	C₄×Dic₉₄	—	2	1	no	—
209	C₄×Dic₉₄	—	2	1	no	—
210	C₄×Dic₉₄	—	2	1	no	—
211	C₄×Dic₉₄	—	2	2	no	—
212	C₄×Dic₉₄	—	2	2	no	—
213	C₄×Dic₉₄	D₄	1	1	yes	characteristic
214	C₄×Dic₉₄	C₂³	1	2	yes	—
215	C₄×Dic₉₄	C₂³	1	1	yes	characteristic
216	#13093989	C₂³	1	2	yes	—
217	C₄×D₁₈₈	—	2	1	no	—
218	C₄×D₁₈₈	D₄	1	1	yes	characteristic
219	C₄×D₁₈₈	C₂³	1	1	yes	characteristic
220	C₄×D₁₈₈	C₂³	1	2	yes	—
221	D₄×Dic₄₇	C₂³	1	2	yes	—
222	D₄×Dic₄₇	C₂³	1	2	yes	—
223	#13093986	C₂³	1	2	yes	—
224	C₄×C₂²⋊D₄₇	—	2	2	no	—
225	C₄×C₂²⋊D₄₇	—	2	2	no	—
226	C₄×C₂²⋊D₄₇	—	2	2	no	—
227	C₄×C₂²⋊D₄₇	D₄	1	2	yes	—
228	C₄×C₂²⋊D₄₇	C₂³	1	2	yes	—
229	(C₂²⋊D₄₇)⋊C₄	—	2	2	no	—
230	(C₂²⋊D₄₇)⋊C₄	—	2	2	no	—
231	#13093983	—	2	1	no	—
232	#13093983	D₄	1	1	yes	characteristic
233	#13093982	C₂³	1	2	yes	—
234	#13093981	—	2	2	no	—
235	#13093981	D₄	1	2	yes	—
236	#13093980	—	2	2	no	—
237	C₂×C₄⋊Dic₄₇	—	2	1	no	—
238	C₂×Dic₄₇⋊C₄	—	2	2	no	—
239	C₄⋊C₄×D₄₇	C₂³	1	2	yes	—
240	C₂²⋊C₄×D₄₇	—	2	2	no	—
241	C₂×C₄×Dic₄₇	—	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	#13093955	C₂³	1	2	yes	—
249	C₄⋊(C₄₇⋊C₈)	C₂³	1	1	yes	characteristic
250	C₄⋊(C₄₇⋊C₈)	C₂³	1	1	yes	characteristic
251	Dic₄₇⋊C₈	C₂³	1	2	yes	—
252	Dic₄₇⋊C₈	C₂³	1	2	yes	—
253	#13093949	C₂³	1	2	yes	—
254	#13093949	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	#13093945	C₂³	1	2	yes	—
263	#13093944	C₂³	1	2	yes	—
264	#13093944	C₂³	1	2	yes	—
265	C₂²⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
266	(C₂×D₄₇)⋊C₈	C₂³	1	2	yes	—
267	(C₂×D₄₇)⋊C₈	C₂³	1	2	yes	—
268	#13093935	C₂³	1	2	yes	—
269	C₈×Dic₄₇	C₂³	1	2	yes	—
270	C₈×Dic₄₇	C₂³	1	2	yes	—
271	C₂×#41×C₄₇	C₂³	1	1	yes	characteristic
272	C₂²×D₄×C₄₇	C₂³	1	1	yes	characteristic
273	C₂³×C₄×C₄₇	—	2	1	no	—
274	AGL(1,ℤ/8)×C₄₇	—	2	4	no	—
275	C₂×SD₁₆×C₄₇	C₂³	1	1	yes	characteristic
276	C₂×SD₁₆×C₄₇	C₂³	1	1	yes	characteristic
277	C₂×D₈×C₄₇	C₂³	1	1	yes	characteristic
278	C₂×D₈×C₄₇	C₂³	1	1	yes	characteristic
279	C₂×M₁₆×C₄₇	C₂³	1	1	yes	characteristic
280	C₂×M₁₆×C₄₇	C₂³	1	1	yes	characteristic
281	C₄×Q₈×C₄₇	C₂³	1	1	yes	characteristic
282	C₄×Q₈×C₄₇	C₂³	1	1	yes	characteristic
283	C₄×D₄×C₄₇	—	2	1	no	—
284	C₄×D₄×C₄₇	—	2	1	no	—
285	C₄×D₄×C₄₇	—	2	1	no	—
286	C₄×D₄×C₄₇	—	2	1	no	—
287	C₄×D₄×C₄₇	C₂³	1	1	yes	characteristic
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	C₄×D₄×C₄₇	C₂³	1	1	yes	characteristic
293	#117×C₄₇	—	2	1	no	—
294	#117×C₄₇	C₂³	1	1	yes	characteristic
295	C₂×C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
296	C₂×C₂²⋊C₄×C₄₇	—	2	1	no	—
297	C₂×C₄²×C₄₇	—	2	1	no	—
298	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
299	#107×C₄₇	C₂³	1	1	yes	characteristic
300	#107×C₄₇	C₂³	1	1	yes	characteristic
301	#106×C₄₇	C₂³	1	1	yes	characteristic
302	#106×C₄₇	C₂³	1	1	yes	characteristic
303	#103×C₄₇	C₂³	1	1	yes	characteristic
304	#103×C₄₇	C₂³	1	1	yes	characteristic
305	#102×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	#102×C₄₇	C₂³	1	1	yes	characteristic
311	#97×C₄₇	C₂³	1	1	yes	characteristic
312	#97×C₄₇	C₂³	1	1	yes	characteristic
313	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
314	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
315	C₂⁴×C₄₇	—	2	1	no	—
316	C₂³×D₄₇	—	2	2	no	—
317	#41×C₄₇	—	2	2	no	—
318	#41×C₄₇	—	4	1	no	—
319	C₂×Q₈×C₄₇	C₂⁴	1	1	yes	characteristic
320	C₂×D₄×C₄₇	—	2	2	no	—
321	C₂×D₄×C₄₇	—	2	1	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	C₂×D₄×C₄₇	C₂⁴	1	1	yes	characteristic
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	—	2	1	no	—
334	C₂²×C₄×C₄₇	—	2	1	no	—
335	C₂²×C₄×C₄₇	—	4	4	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	—	2	2	no	—
342	C₂×C₂²⋊D₄₇	—	2	2	no	—
343	C₂×C₂²⋊D₄₇	—	2	2	no	—
344	C₂×C₂²⋊D₄₇	—	2	2	no	—
345	C₂×C₂²⋊D₄₇	—	4	8	no	—
346	C₂×C₂²⋊D₄₇	C₂×D₄	1	2	yes	—
347	C₂²×Dic₄₇	—	2	2	no	—
348	C₂²×Dic₄₇	—	2	2	no	—
349	C₂²×Dic₄₇	—	2	2	no	—
350	#10625352	—	2	4	no	—
351	#10625352	—	4	2	no	—
352	D₄×D₄₇	—	2	4	no	—
353	D₄×D₄₇	—	4	2	no	—
354	#10625350	—	2	4	no	—
355	#10625350	—	4	8	no	—
356	#10625350	—	4	4	no	—
357	#10625350	—	4	8	no	—
358	#10625350	—	4	4	no	—
359	#10625350	—	4	4	no	—
360	C₂×D₁₈₈	—	2	2	no	—
361	C₂×D₁₈₈	—	2	1	no	—
362	C₂×D₁₈₈	—	2	1	no	—
363	C₂×D₁₈₈	—	4	4	no	—
364	C₂×D₁₈₈	C₂×D₄	1	1	yes	characteristic
365	C₂×D₁₈₈	C₂⁴	1	2	yes	—
366	C₂×C₄×D₄₇	—	2	2	no	—
367	C₂×C₄×D₄₇	—	2	2	no	—
368	C₂×C₄×D₄₇	—	2	2	no	—
369	C₂×C₄×D₄₇	—	4	8	no	—
370	C₂×C₄×D₄₇	C₂×D₄	1	2	yes	—
371	C₂×C₄×D₄₇	C₂×D₄	1	2	yes	—
372	C₂×C₄×D₄₇	C₂⁴	1	2	yes	—
373	C₂×Dic₉₄	—	2	1	no	—
374	C₂×Dic₉₄	—	2	1	no	—
375	C₂×Dic₉₄	—	2	2	no	—
376	C₂×Dic₉₄	—	2	2	no	—
377	C₂×Dic₉₄	—	4	4	no	—
378	C₂×Dic₉₄	—	4	4	no	—
379	C₂×Dic₉₄	C₂×D₄	1	1	yes	characteristic
380	C₂×Dic₉₄	C₂⁴	1	2	yes	—
381	SD₁₆×C₄₇	—	2	2	no	—
382	SD₁₆×C₄₇	—	2	2	no	—
383	D₈×C₄₇	—	2	2	no	—
384	D₈×C₄₇	#41	1	4	yes	complemented
385	M₁₆×C₄₇	—	2	2	no	—
386	M₁₆×C₄₇	—	4	1	no	—
387	C₂×C₈×C₄₇	C₂⁴	1	1	yes	characteristic
388	C₂×C₈×C₄₇	C₂⁴	1	1	yes	characteristic
389	C₂×C₈×C₄₇	C₂⁴	1	1	yes	characteristic
390	C₂×C₈×C₄₇	C₂⁴	1	1	yes	characteristic
391	C₄⋊C₄×C₄₇	—	2	1	no	—
392	C₄⋊C₄×C₄₇	—	2	1	no	—
393	C₄⋊C₄×C₄₇	—	2	1	no	—
394	C₄⋊C₄×C₄₇	C₂⁴	1	1	yes	characteristic
395	C₄⋊C₄×C₄₇	C₂⁴	1	1	yes	characteristic
396	C₄⋊C₄×C₄₇	C₂⁴	1	1	yes	characteristic
397	C₄⋊C₄×C₄₇	C₂⁴	1	1	yes	characteristic
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	C₂²⋊C₄×C₄₇	—	2	1	no	—
403	C₂²⋊C₄×C₄₇	—	2	1	no	—
404	C₂²⋊C₄×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	#10625336	—	4	2	no	—
418	#10625335	—	2	4	no	—
419	#10625335	—	4	2	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	C₂×D₄	1	2	yes	—
429	(C₂×D₄₇)⋊C₄	C₂×D₄	1	2	yes	—
430	C₄⋊Dic₄₇	—	2	1	no	—
431	C₄⋊Dic₄₇	—	2	1	no	—
432	C₄⋊Dic₄₇	—	2	1	no	—
433	C₄⋊Dic₄₇	—	2	1	no	—
434	C₄⋊Dic₄₇	—	2	2	no	—
435	C₄⋊Dic₄₇	C₂×D₄	1	1	yes	characteristic
436	C₄⋊Dic₄₇	C₂×D₄	1	1	yes	characteristic
437	C₄⋊Dic₄₇	C₂⁴	1	2	yes	—
438	C₄⋊Dic₄₇	C₂⁴	1	2	yes	—
439	Dic₄₇⋊C₄	—	2	2	no	—
440	Dic₄₇⋊C₄	—	2	2	no	—
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	C₂×D₄	1	2	yes	—
449	Dic₄₇⋊C₄	C₂×D₄	1	2	yes	—
450	C₄×Dic₄₇	—	2	2	no	—
451	C₄×Dic₄₇	—	2	2	no	—
452	C₄×Dic₄₇	—	2	2	no	—
453	C₄×Dic₄₇	C₂×D₄	1	2	yes	—
454	C₄×Dic₄₇	C₂×D₄	1	2	yes	—
455	C₄×Dic₄₇	C₂⁴	1	2	yes	—
456	C₂×C₄₇⋊C₈	C₂⁴	1	2	yes	—
457	C₂×C₄₇⋊C₈	C₂⁴	1	2	yes	—
458	#10625325	—	2	4	no	—
459	#10625325	—	4	2	no	—
460	#10625324	—	2	4	no	—
461	#10625324	—	4	2	no	—
462	C₂³×C₄₇	—	2	1	no	—
463	C₂³×C₄₇	—	2	1	no	—
464	C₂³×C₄₇	—	2	1	no	—
465	C₂³×C₄₇	—	4	2	no	—
466	C₂³×C₄₇	—	4	2	no	—
467	C₂³×C₄₇	—	8	1	no	—
468	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
469	C₂²×D₄₇	—	2	2	no	—
470	C₂²×D₄₇	—	4	4	no	—
471	C₂²×D₄₇	—	4	4	no	—
472	C₂²×D₄₇	—	8	2	no	—
473	C₂²×D₄₇	C₂²×D₄	1	2	yes	—
474	Q₈×C₄₇	—	2	1	no	—
475	Q₈×C₄₇	—	2	1	no	—
476	D₄×C₄₇	—	2	1	no	—
477	D₄×C₄₇	—	2	1	no	—
478	D₄×C₄₇	—	2	1	no	—
479	D₄×C₄₇	—	2	1	no	—
480	D₄×C₄₇	—	4	2	no	—
481	D₄×C₄₇	—	4	2	no	—
482	D₄×C₄₇	C₂×#41	1	2	yes	—
483	D₄×C₄₇	C₂×#41	1	2	yes	complemented
484	C₂×C₄×C₄₇	—	2	2	no	—
485	C₂×C₄×C₄₇	—	2	1	no	—
486	C₂×C₄×C₄₇	—	2	1	no	—
487	C₂×C₄×C₄₇	—	2	1	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	—	4	1	no	—
493	C₂×C₄×C₄₇	—	4	2	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	—	4	2	no	—
498	C₂×C₄×C₄₇	—	4	2	no	—
499	C₂×C₄×C₄₇	—	4	2	no	—
500	C₂×C₄×C₄₇	—	4	2	no	—
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	C₂²×D₄	1	1	yes	characteristic
505	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
506	C₂×C₄×C₄₇	C₂⁵	1	1	yes	characteristic
507	C₂²⋊D₄₇	—	2	4	no	—
508	C₂²⋊D₄₇	—	4	4	no	—
509	C₂²⋊D₄₇	—	4	4	no	—
510	C₂²⋊D₄₇	—	4	4	no	—
511	C₂²⋊D₄₇	—	4	4	no	—
512	C₂²⋊D₄₇	—	4	4	no	—
513	C₂²⋊D₄₇	—	8	2	no	—
514	C₂×Dic₄₇	—	2	2	no	—
515	C₂×Dic₄₇	—	2	2	no	—
516	C₂×Dic₄₇	—	2	2	no	—
517	C₂×Dic₄₇	—	4	4	no	—
518	C₂×Dic₄₇	—	4	4	no	—
519	C₂×Dic₄₇	—	4	4	no	—
520	C₂×Dic₄₇	C₂²×D₄	1	2	yes	—
521	C₂×Dic₄₇	C₂²×D₄	1	2	yes	—
522	C₂×Dic₄₇	C₂²×D₄	1	2	yes	—
523	D₁₈₈	—	2	2	no	—
524	D₁₈₈	—	2	2	no	—
525	D₁₈₈	—	2	2	no	—
526	D₁₈₈	—	4	4	no	—
527	D₁₈₈	—	4	2	no	—
528	D₁₈₈	—	8	1	no	—
529	C₄×D₄₇	—	2	2	no	—
530	C₄×D₄₇	—	2	2	no	—
531	C₄×D₄₇	—	2	4	no	—
532	C₄×D₄₇	—	4	2	no	—
533	C₄×D₄₇	—	4	4	no	—
534	C₄×D₄₇	—	4	4	no	—
535	C₄×D₄₇	—	4	4	no	—
536	Dic₉₄	—	2	2	no	—
537	Dic₉₄	—	2	2	no	—
538	Dic₉₄	—	4	2	no	—
539	Dic₉₄	—	4	2	no	—
540	Dic₉₄	—	4	4	no	—
541	Dic₉₄	—	4	4	no	—
542	Dic₉₄	AGL(1,ℤ/8)	1	4	yes	complemented
543	C₈×C₄₇	—	2	1	no	—
544	C₈×C₄₇	—	2	1	no	—
545	C₈×C₄₇	—	2	1	no	—
546	C₈×C₄₇	C₂×#41	1	2	yes	complemented
547	C₄₇⋊C₈	—	2	2	no	—
548	C₄₇⋊C₈	—	2	2	no	—
549	#61466	—	47	1	no	maximal, Sylow
550	C₂²×C₄₇	—	2	1	no	—
551	C₂²×C₄₇	—	2	2	no	—
552	C₂²×C₄₇	—	2	2	no	—
553	C₂²×C₄₇	—	2	1	no	—
554	C₂²×C₄₇	—	2	1	no	—
555	C₂²×C₄₇	—	4	1	no	—
556	C₂²×C₄₇	—	4	1	no	—
557	C₂²×C₄₇	—	4	1	no	—
558	C₂²×C₄₇	—	4	1	no	—
559	C₂²×C₄₇	—	4	1	no	—
560	C₂²×C₄₇	—	4	1	no	—
561	C₂²×C₄₇	—	4	1	no	—
562	C₂²×C₄₇	—	8	4	no	—
563	C₂²×C₄₇	C₂³×D₄	1	1	yes	characteristic
564	C₂×D₄₇	—	2	2	no	—
565	C₂×D₄₇	—	2	2	no	—
566	C₂×D₄₇	—	2	2	no	—
567	C₂×D₄₇	—	4	2	no	—
568	C₂×D₄₇	—	4	2	no	—
569	C₂×D₄₇	—	4	2	no	—
570	C₂×D₄₇	—	8	8	no	—
571	C₄×C₄₇	—	2	1	no	—
572	C₄×C₄₇	—	2	1	no	—
573	C₄×C₄₇	—	2	1	no	—
574	C₄×C₄₇	—	2	1	no	—
575	C₄×C₄₇	—	4	1	no	—
576	C₄×C₄₇	—	4	1	no	—
577	C₄×C₄₇	—	4	1	no	—
578	C₄×C₄₇	—	4	1	no	—
579	C₄×C₄₇	—	4	1	no	—
580	C₄×C₄₇	C₂×AGL(1,ℤ/8)	1	2	yes	—
581	C₄×C₄₇	C₂²×#41	1	1	yes	characteristic
582	C₄×C₄₇	#585	1	1	yes	characteristic
583	Dic₄₇	—	2	2	no	—
584	Dic₄₇	—	2	2	no	—
585	Dic₄₇	—	4	2	no	—
586	Dic₄₇	—	4	2	no	—
587	Dic₄₇	—	4	2	no	—
588	Dic₄₇	C₂×AGL(1,ℤ/8)	1	4	yes	—
589	#3482	—	47	1	no	—
590	D₄×#41	—	47	1	no	—
591	#3392	—	47	1	no	—
592	Q₈×D₈	—	47	1	no	—
593	#3359	—	47	1	no	—
594	#3358	—	47	1	no	—
595	#3353	—	47	1	no	—
596	#3353	—	47	2	no	—
597	#3330	—	47	1	no	—
598	#3330	—	47	2	no	—
599	#3324	—	47	1	no	—
600	#3324	—	47	2	no	—
601	#3272	—	47	1	no	—
602	#3272	—	47	2	no	—
603	#3182	—	47	2	no	—
604	#3182	—	47	1	no	—
605	#3115	—	47	2	no	—
606	#3115	—	47	1	no	—
607	#3110	—	47	2	no	—
608	#3110	—	47	1	no	—
609	#2971	—	47	1	no	—
610	C₄×AGL(1,ℤ/8)	—	47	2	no	—
611	C₄×AGL(1,ℤ/8)	D₄₇	1	1	yes	characteristic, complemented
612	C₂×C₄₇	—	4	2	no	—
613	C₂×C₄₇	—	4	1	no	—
614	C₂×C₄₇	—	4	2	no	—
615	C₂×C₄₇	—	8	1	no	—
616	C₂×C₄₇	D₄×#41	1	1	yes	characteristic
617	C₂×C₄₇	C₂²×AGL(1,ℤ/8)	1	1	yes	characteristic
618	C₂×C₄₇	#3586	1	1	yes	characteristic
619	D₄₇	—	4	2	no	—
620	D₄₇	—	8	2	no	—
621	C₂²×#41	—	94	1	no	—
622	C₂×AGL(1,ℤ/8)	—	47	2	no	—
623	C₂×AGL(1,ℤ/8)	C₂×D₄₇	1	1	yes	characteristic
624	#557	—	47	1	no	—
625	#556	—	47	1	no	—
626	#556	—	47	2	no	—
627	#552	—	94	2	no	—
628	#552	—	94	1	no	—
629	#550	—	47	1	no	—
630	D₄×Q₈	—	47	1	no	—
631	D₄×Q₈	—	47	1	no	—
632	#548	—	94	1	no	—
633	#548	—	94	1	no	—
634	#547	—	47	1	no	—
635	#547	—	47	2	no	—
636	#547	—	47	2	no	—
637	#547	—	47	1	no	—
638	#546	—	94	2	no	—
639	#546	—	94	1	no	—
640	D₄²	—	47	2	no	—
641	D₄²	—	47	1	no	—
642	#533	—	47	2	no	—
643	#533	—	47	1	no	—
644	#532	—	47	2	no	—
645	#532	—	47	1	no	—
646	#529	—	94	1	no	—
647	#529	—	94	2	no	—
648	#525	—	94	2	no	—
649	#525	—	94	1	no	—
650	C₄×#41	—	47	1	no	—
651	C₄×#41	—	47	2	no	—
652	C₄×#41	C₂×D₄₇	1	1	yes	characteristic, complemented
653	C₂×C₄×Q₈	—	94	1	no	—
654	C₂×C₄×D₄	—	47	2	no	—
655	C₂×C₄×D₄	C₂×D₄₇	1	1	yes	characteristic
656	#500	—	47	2	no	—
657	#500	—	47	1	no	—
658	#492	—	47	2	no	—
659	#492	—	47	1	no	—
660	#487	—	47	2	no	—
661	#487	—	47	1	no	—
662	#486	—	47	2	no	—
663	#486	—	47	1	no	—
664	#484	—	47	2	no	—
665	#484	—	47	2	no	—
666	#484	—	47	2	no	—
667	#482	—	47	2	no	—
668	#482	—	47	2	no	—
669	#482	—	47	2	no	—
670	#475	—	47	1	no	—
671	#475	—	47	2	no	—
672	#474	—	47	1	no	—
673	#474	—	47	1	no	—
674	#474	—	47	1	no	—
675	#474	—	47	2	no	—
676	#474	—	47	2	no	—
677	#474	—	47	2	no	—
678	#468	—	47	2	no	—
679	#468	—	47	2	no	—
680	#468	—	47	2	no	—
681	#468	—	47	2	no	—
682	#468	—	47	2	no	—
683	#468	—	47	2	no	—
684	#461	—	47	2	no	—
685	#461	—	47	1	no	—
686	#461	—	47	1	no	—
687	#461	—	47	2	no	—
688	#460	—	47	1	no	—
689	#460	—	47	2	no	—
690	#459	—	47	2	no	—
691	#459	—	47	1	no	—
692	#450	—	47	2	no	—
693	#450	—	47	2	no	—
694	#450	—	47	2	no	—
695	#449	—	47	2	no	—
696	#449	—	47	2	no	—
697	#449	—	47	2	no	—
698	C₈×Q₈	—	47	1	no	—
699	C₈×Q₈	—	47	1	no	—
700	#442	—	47	2	no	—
701	#442	C₂×D₄₇	1	1	yes	characteristic
702	#442	C₂×D₄₇	1	1	yes	characteristic, complemented
703	#440	—	47	2	no	—
704	#440	—	47	2	no	—
705	#440	—	47	2	no	—
706	#440	—	47	2	no	—
707	#440	—	47	2	no	—
708	#440	C₂×D₄₇	1	1	yes	characteristic
709	#440	C₂×D₄₇	1	1	yes	characteristic, complemented
710	C₄×SD₁₆	—	47	2	no	—
711	C₄×SD₁₆	—	47	2	no	—
712	C₄×SD₁₆	C₂×D₄₇	1	1	yes	characteristic
713	C₄×SD₁₆	C₂×D₄₇	1	1	yes	characteristic, complemented
714	C₄×D₈	—	47	2	no	—
715	C₄×D₈	—	47	2	no	—
716	C₄×D₈	C₂×D₄₇	1	1	yes	characteristic
717	C₄×D₈	C₂×D₄₇	1	1	yes	characteristic, complemented
718	#436	—	47	2	no	—
719	#436	—	47	2	no	—
720	#436	—	47	1	no	—
721	#436	—	47	1	no	—
722	#432	—	47	1	no	—
723	#432	—	47	2	no	—
724	#428	—	47	2	no	—
725	#428	C₂×D₄₇	1	1	yes	characteristic, complemented
726	#418	—	47	2	no	—
727	#418	C₂×D₄₇	1	1	yes	characteristic
728	#417	—	47	2	no	—
729	#417	C₂×D₄₇	1	1	yes	characteristic, complemented
730	C₄×M₁₆	—	47	2	no	—
731	C₄×M₁₆	C₂×D₄₇	1	1	yes	characteristic, complemented
732	C₄₇	#61466	1	1	yes	characteristic, complemented, Sylow
733	C₂×#41	—	47	1	no	—
734	C₂×#41	—	47	2	no	—
735	C₂×#41	—	94	2	no	—
736	C₂×#41	—	94	2	no	—
737	C₂×#41	—	94	1	no	—
738	C₂×#41	—	94	1	no	—
739	C₂×#41	—	94	1	no	—
740	C₂×#41	—	188	8	no	—
741	C₂×#41	C₂²×D₄₇	1	1	yes	characteristic
742	C₂²×Q₈	—	94	1	no	—
743	C₂²×Q₈	—	94	1	no	—
744	C₂²×D₄	—	47	2	no	—
745	C₂²×D₄	—	94	1	no	—
746	C₂²×D₄	—	94	2	no	—
747	C₂²×D₄	C₂²×D₄₇	1	1	yes	characteristic
748	C₂³×C₄	—	2	1	no	—
749	C₂³×C₄	—	94	2	no	—
750	AGL(1,ℤ/8)	—	2	4	no	—
751	AGL(1,ℤ/8)	—	94	8	no	—
752	C₂×SD₁₆	—	47	2	no	—
753	C₂×SD₁₆	—	47	2	no	—
754	C₂×SD₁₆	—	47	2	no	—
755	C₂×SD₁₆	—	47	2	no	—
756	C₂×SD₁₆	—	47	2	no	—
757	C₂×SD₁₆	C₂²×D₄₇	1	1	yes	characteristic
758	C₂×SD₁₆	C₂²×D₄₇	1	1	yes	characteristic
759	C₂×D₈	—	47	2	no	—
760	C₂×D₈	C₂²×D₄₇	1	1	yes	characteristic
761	C₂×D₈	C₂²×D₄₇	1	1	yes	characteristic
762	C₂×M₁₆	—	47	2	no	—
763	C₂×M₁₆	—	47	2	no	—
764	C₂×M₁₆	C₂²×D₄₇	1	1	yes	characteristic
765	C₂×M₁₆	C₂²×D₄₇	1	1	yes	characteristic
766	C₄⋊Q₈	—	47	2	no	—
767	C₄⋊Q₈	—	47	2	no	—
768	C₄⋊Q₈	—	47	2	no	—
769	C₄⋊Q₈	—	47	1	no	—
770	C₄⋊Q₈	—	47	1	no	—
771	C₄⋊Q₈	—	47	1	no	—
772	#127	—	47	2	no	—
773	#127	—	47	1	no	—
774	#126	—	94	2	no	—
775	#126	—	94	2	no	—
776	#126	—	94	2	no	—
777	#125	—	94	1	no	—
778	#125	—	94	2	no	—
779	#125	—	94	2	no	—
780	#125	—	94	1	no	—
781	#124	—	94	1	no	—
782	#124	—	94	2	no	—
783	#124	—	94	2	no	—
784	#124	—	94	1	no	—
785	#123	—	94	2	no	—
786	#123	—	94	2	no	—
787	#123	—	94	2	no	—
788	#123	—	94	2	no	—
789	#123	—	94	2	no	—
790	#123	—	94	2	no	—
791	C₂²⋊Q₈	—	47	2	no	—
792	C₂²⋊Q₈	—	47	2	no	—
793	C₂²⋊Q₈	—	47	2	no	—
794	C₂²⋊Q₈	—	94	2	no	—
795	C₂²⋊Q₈	—	94	2	no	—
796	C₂²⋊Q₈	—	94	2	no	—
797	C₂²⋊Q₈	—	94	2	no	—
798	C₂²⋊Q₈	—	94	1	no	—
799	C₂²⋊Q₈	—	94	1	no	—
800	C₂²⋊Q₈	—	94	1	no	—
801	C₂²⋊Q₈	—	94	1	no	—
802	#121	—	47	2	no	—
803	#121	—	47	2	no	—
804	#121	—	47	2	no	—
805	#121	—	94	2	no	—
806	#121	—	94	2	no	—
807	#121	—	94	1	no	—
808	#121	—	94	1	no	—
809	#121	—	94	2	no	—
810	#121	—	94	1	no	—
811	#121	—	94	2	no	—
812	#121	—	94	1	no	—
813	#120	—	94	2	no	—
814	#120	—	94	2	no	—
815	#120	—	94	2	no	—
816	C₄×Q₈	—	47	1	no	—
817	C₄×Q₈	—	47	1	no	—
818	C₄×Q₈	—	47	2	no	—
819	C₄×Q₈	—	47	2	no	—
820	C₄×Q₈	—	94	2	no	—
821	C₄×Q₈	—	94	2	no	—
822	C₄×Q₈	—	94	1	no	—
823	C₄×Q₈	—	94	1	no	—
824	C₄×Q₈	—	94	1	no	—
825	C₄×Q₈	C₂²×D₄₇	1	1	yes	characteristic
826	C₄×Q₈	C₂²×D₄₇	1	1	yes	characteristic
827	C₄×D₄	—	2	1	no	—
828	C₄×D₄	—	2	1	no	—
829	C₄×D₄	—	2	1	no	—
830	C₄×D₄	—	2	1	no	—
831	C₄×D₄	—	47	2	no	—
832	C₄×D₄	—	47	2	no	—
833	C₄×D₄	—	47	2	no	—
834	C₄×D₄	—	47	2	no	—
835	C₄×D₄	—	47	2	no	—
836	C₄×D₄	—	47	1	no	—
837	C₄×D₄	—	47	1	no	—
838	C₄×D₄	—	47	2	no	—
839	C₄×D₄	—	94	2	no	—
840	C₄×D₄	—	94	2	no	—
841	C₄×D₄	—	94	2	no	—
842	C₄×D₄	—	94	2	no	—
843	C₄×D₄	—	94	2	no	—
844	C₄×D₄	—	94	1	no	—
845	C₄×D₄	C₂²×D₄₇	1	1	yes	characteristic
846	C₄×D₄	C₂²×D₄₇	1	1	yes	characteristic
847	C₄×D₄	C₂²×D₄₇	1	1	yes	characteristic
848	C₄×D₄	C₂²×D₄₇	1	1	yes	characteristic
849	C₄×D₄	C₂²×D₄₇	1	1	yes	characteristic
850	C₄×D₄	C₂²×D₄₇	1	1	yes	characteristic
851	#117	—	2	1	no	—
852	#117	—	47	1	no	—
853	#117	—	47	2	no	—
854	#117	—	47	2	no	—
855	#117	—	94	2	no	—
856	#117	—	94	2	no	—
857	#117	—	94	1	no	—
858	#117	C₂²×D₄₇	1	1	yes	characteristic
859	C₂×C₄⋊C₄	—	47	2	no	—
860	C₂×C₄⋊C₄	—	94	2	no	—
861	C₂×C₄⋊C₄	—	94	1	no	—
862	C₂×C₄⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
863	C₂×C₂²⋊C₄	—	2	1	no	—
864	C₂×C₂²⋊C₄	—	94	2	no	—
865	C₂×C₄²	—	2	1	no	—
866	C₂×C₄²	—	47	2	no	—
867	C₂×C₄²	—	94	2	no	—
868	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
869	#107	—	47	2	no	—
870	#107	—	47	2	no	—
871	#107	—	47	2	no	—
872	#107	—	47	2	no	—
873	#107	—	47	2	no	—
874	#107	C₂²×D₄₇	1	1	yes	characteristic
875	#107	C₂²×D₄₇	1	1	yes	characteristic
876	#106	—	47	2	no	—
877	#106	C₂²×D₄₇	1	1	yes	characteristic
878	#106	C₂²×D₄₇	1	1	yes	characteristic
879	C₄⋊C₈	—	47	2	no	—
880	C₄⋊C₈	—	47	2	no	—
881	C₄⋊C₈	—	47	1	no	—
882	C₄⋊C₈	—	47	1	no	—
883	#103	—	47	2	no	—
884	#103	—	47	2	no	—
885	#103	—	47	2	no	—
886	#103	—	47	2	no	—
887	#103	—	47	2	no	—
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	—	47	2	no	—
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	#102	C₂²×D₄₇	1	1	yes	characteristic
901	#102	C₂²×D₄₇	1	1	yes	characteristic
902	#102	C₂²×D₄₇	1	1	yes	characteristic
903	C₂²⋊C₈	—	47	2	no	—
904	C₂²⋊C₈	—	47	2	no	—
905	C₂²⋊C₈	—	47	2	no	—
906	#97	—	47	2	no	—
907	#97	C₂²×D₄₇	1	1	yes	characteristic
908	#97	C₂²×D₄₇	1	1	yes	characteristic
909	C₄×C₈	—	47	2	no	—
910	C₄×C₈	—	47	2	no	—
911	C₄×C₈	C₂²×D₄₇	1	1	yes	characteristic
912	C₄×C₈	C₂²×D₄₇	1	1	yes	characteristic
913	C₂⁴	—	2	1	no	—
914	C₂⁴	—	94	2	no	—
915	#41	—	2	2	no	—
916	#41	—	4	1	no	—
917	#41	—	94	4	no	—
918	#41	—	94	4	no	—
919	#41	—	188	4	no	—
920	#41	—	188	8	no	—
921	#41	—	188	8	no	—
922	#41	—	188	4	no	—
923	#41	—	188	4	no	—
924	#41	—	188	2	no	—
925	C₂×Q₈	—	47	1	no	—
926	C₂×Q₈	—	47	2	no	—
927	C₂×Q₈	—	94	2	no	—
928	C₂×Q₈	—	94	2	no	—
929	C₂×Q₈	—	94	1	no	—
930	C₂×Q₈	—	94	1	no	—
931	C₂×Q₈	—	188	4	no	—
932	C₂×Q₈	—	188	4	no	—
933	C₂×Q₈	C₂³×D₄₇	1	1	yes	characteristic
934	C₂×D₄	—	2	2	no	—
935	C₂×D₄	—	2	1	no	—
936	C₂×D₄	—	2	1	no	—
937	C₂×D₄	—	4	1	no	—
938	C₂×D₄	—	47	2	no	—
939	C₂×D₄	—	47	1	no	—
940	C₂×D₄	—	47	2	no	—
941	C₂×D₄	—	94	2	no	—
942	C₂×D₄	—	94	2	no	—
943	C₂×D₄	—	94	2	no	—
944	C₂×D₄	—	94	2	no	—
945	C₂×D₄	—	94	4	no	—
946	C₂×D₄	—	94	2	no	—
947	C₂×D₄	—	94	2	no	—
948	C₂×D₄	—	94	2	no	—
949	C₂×D₄	—	94	1	no	—
950	C₂×D₄	—	94	1	no	—
951	C₂×D₄	—	188	4	no	—
952	C₂×D₄	—	188	2	no	—
953	C₂×D₄	—	188	8	no	—
954	C₂×D₄	C₂³×D₄₇	1	1	yes	characteristic
955	C₂×D₄	C₂³×D₄₇	1	1	yes	characteristic
956	C₂×D₄	C₂³×D₄₇	1	1	yes	characteristic
957	C₂²×C₄	—	2	1	no	—
958	C₂²×C₄	—	2	1	no	—
959	C₂²×C₄	—	2	1	no	—
960	C₂²×C₄	—	2	1	no	—
961	C₂²×C₄	—	2	1	no	—
962	C₂²×C₄	—	2	1	no	—
963	C₂²×C₄	—	2	1	no	—
964	C₂²×C₄	—	2	1	no	—
965	C₂²×C₄	—	4	4	no	—
966	C₂²×C₄	—	47	2	no	—
967	C₂²×C₄	—	47	2	no	—
968	C₂²×C₄	—	47	2	no	—
969	C₂²×C₄	—	94	2	no	—
970	C₂²×C₄	—	94	2	no	—
971	C₂²×C₄	—	94	2	no	—
972	C₂²×C₄	—	94	2	no	—
973	C₂²×C₄	—	94	2	no	—
974	C₂²×C₄	—	94	2	no	—
975	C₂²×C₄	—	188	8	no	—
976	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
977	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
978	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
979	SD₁₆	—	2	2	no	—
980	SD₁₆	—	2	2	no	—
981	SD₁₆	—	94	4	no	—
982	SD₁₆	—	94	4	no	—
983	SD₁₆	—	188	2	no	—
984	SD₁₆	—	188	2	no	—
985	SD₁₆	—	188	2	no	—
986	D₈	—	2	2	no	—
987	D₈	—	94	4	no	—
988	D₈	#10625350	1	4	yes	complemented
989	M₁₆	—	2	2	no	—
990	M₁₆	—	4	1	no	—
991	M₁₆	—	94	4	no	—
992	M₁₆	—	188	2	no	—
993	C₂×C₈	—	47	2	no	—
994	C₂×C₈	—	47	2	no	—
995	C₂×C₈	C₂³×D₄₇	1	1	yes	characteristic
996	C₂×C₈	C₂³×D₄₇	1	1	yes	characteristic
997	C₂×C₈	C₂³×D₄₇	1	1	yes	characteristic
998	C₂×C₈	C₂³×D₄₇	1	1	yes	characteristic
999	C₄⋊C₄	—	2	1	no	—
1000	C₄⋊C₄	—	2	1	no	—
1001	C₄⋊C₄	—	2	1	no	—
1002	C₄⋊C₄	—	47	2	no	—
1003	C₄⋊C₄	—	47	2	no	—
1004	C₄⋊C₄	—	47	1	no	—
1005	C₄⋊C₄	—	47	1	no	—
1006	C₄⋊C₄	—	47	2	no	—
1007	C₄⋊C₄	—	47	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	2	no	—
1013	C₄⋊C₄	—	94	2	no	—
1014	C₄⋊C₄	—	94	2	no	—
1015	C₄⋊C₄	—	94	2	no	—
1016	C₄⋊C₄	—	94	2	no	—
1017	C₄⋊C₄	—	94	2	no	—
1018	C₄⋊C₄	—	94	1	no	—
1019	C₄⋊C₄	—	94	1	no	—
1020	C₄⋊C₄	—	94	1	no	—
1021	C₄⋊C₄	—	94	1	no	—
1022	C₄⋊C₄	C₂³×D₄₇	1	1	yes	characteristic
1023	C₄⋊C₄	C₂³×D₄₇	1	1	yes	characteristic
1024	C₄⋊C₄	C₂³×D₄₇	1	1	yes	characteristic
1025	C₄⋊C₄	C₂³×D₄₇	1	1	yes	characteristic
1026	C₂²⋊C₄	—	2	1	no	—
1027	C₂²⋊C₄	—	2	1	no	—
1028	C₂²⋊C₄	—	2	1	no	—
1029	C₂²⋊C₄	—	2	1	no	—
1030	C₂²⋊C₄	—	2	1	no	—
1031	C₂²⋊C₄	—	2	1	no	—
1032	C₂²⋊C₄	—	2	1	no	—
1033	C₂²⋊C₄	—	47	2	no	—
1034	C₂²⋊C₄	—	47	2	no	—
1035	C₂²⋊C₄	—	47	2	no	—
1036	C₂²⋊C₄	—	94	2	no	—
1037	C₂²⋊C₄	—	94	2	no	—
1038	C₂²⋊C₄	—	94	2	no	—
1039	C₂²⋊C₄	—	94	2	no	—
1040	C₂²⋊C₄	—	94	2	no	—
1041	C₂²⋊C₄	—	94	2	no	—
1042	C₂²⋊C₄	—	94	2	no	—
1043	C₂²⋊C₄	—	94	2	no	—
1044	C₂²⋊C₄	—	94	2	no	—
1045	C₂²⋊C₄	—	94	2	no	—
1046	C₂²⋊C₄	—	94	2	no	—
1047	C₄²	—	2	1	no	—
1048	C₄²	—	2	1	no	—
1049	C₄²	—	2	1	no	—
1050	C₄²	—	47	2	no	—
1051	C₄²	—	47	2	no	—
1052	C₄²	—	47	2	no	—
1053	C₄²	—	94	2	no	—
1054	C₄²	—	94	2	no	—
1055	C₄²	—	94	2	no	—
1056	C₄²	D₄×D₄₇	1	1	yes	characteristic
1057	C₄²	D₄×D₄₇	1	1	yes	characteristic
1058	C₄²	C₂³×D₄₇	1	1	yes	characteristic
1059	C₄²	C₂³×D₄₇	1	1	yes	characteristic
1060	C₂³	—	2	1	no	—
1061	C₂³	—	2	1	no	—
1062	C₂³	—	2	1	no	—
1063	C₂³	—	4	2	no	—
1064	C₂³	—	4	2	no	—
1065	C₂³	—	8	1	no	—
1066	C₂³	—	47	2	no	—
1067	C₂³	—	94	2	no	—
1068	C₂³	—	376	2	no	—
1069	C₂³	—	188	4	no	—
1070	C₂³	—	188	4	no	—
1071	C₂³	C₂×D₄×D₄₇	1	1	yes	characteristic
1072	Q₈	—	2	1	no	—
1073	Q₈	—	2	1	no	—
1074	Q₈	—	47	4	no	—
1075	Q₈	—	94	2	no	—
1076	Q₈	—	94	2	no	—
1077	Q₈	—	188	4	no	—
1078	Q₈	—	188	4	no	—
1079	Q₈	—	188	2	no	—
1080	Q₈	—	188	2	no	—
1081	D₄	—	2	1	no	—
1082	D₄	—	2	1	no	—
1083	D₄	—	2	1	no	—
1084	D₄	—	2	1	no	—
1085	D₄	—	4	2	no	—
1086	D₄	—	4	2	no	—
1087	D₄	—	94	4	no	—
1088	D₄	—	94	2	no	—
1089	D₄	—	94	2	no	—
1090	D₄	—	94	2	no	—
1091	D₄	—	376	1	no	—
1092	D₄	—	376	2	no	—
1093	D₄	—	188	4	no	—
1094	D₄	—	188	4	no	—
1095	D₄	—	188	4	no	—
1096	D₄	—	188	4	no	—
1097	D₄	—	188	4	no	—
1098	D₄	—	188	4	no	—
1099	D₄	—	188	2	no	—
1100	D₄	C₂×#10625350	1	2	yes	—
1101	D₄	C₂×#10625350	1	2	yes	complemented
1102	C₂×C₄	—	2	2	no	—
1103	C₂×C₄	—	2	1	no	—
1104	C₂×C₄	—	2	1	no	—
1105	C₂×C₄	—	2	1	no	—
1106	C₂×C₄	—	2	1	no	—
1107	C₂×C₄	—	2	1	no	—
1108	C₂×C₄	—	2	1	no	—
1109	C₂×C₄	—	2	1	no	—
1110	C₂×C₄	—	4	1	no	—
1111	C₂×C₄	—	4	2	no	—
1112	C₂×C₄	—	4	2	no	—
1113	C₂×C₄	—	4	2	no	—
1114	C₂×C₄	—	4	2	no	—
1115	C₂×C₄	—	4	2	no	—
1116	C₂×C₄	—	4	2	no	—
1117	C₂×C₄	—	4	2	no	—
1118	C₂×C₄	—	4	2	no	—
1119	C₂×C₄	—	47	2	no	—
1120	C₂×C₄	—	47	2	no	—
1121	C₂×C₄	—	47	2	no	—
1122	C₂×C₄	—	94	4	no	—
1123	C₂×C₄	—	94	2	no	—
1124	C₂×C₄	—	94	2	no	—
1125	C₂×C₄	—	94	2	no	—
1126	C₂×C₄	—	94	2	no	—
1127	C₂×C₄	—	94	2	no	—
1128	C₂×C₄	—	188	2	no	—
1129	C₂×C₄	—	188	4	no	—
1130	C₂×C₄	—	188	4	no	—
1131	C₂×C₄	—	188	4	no	—
1132	C₂×C₄	—	188	4	no	—
1133	C₂×C₄	—	188	4	no	—
1134	C₂×C₄	—	188	4	no	—
1135	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
1136	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
1137	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
1138	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
1139	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
1140	C₂×C₄	C₂⁴×D₄₇	1	1	yes	characteristic
1141	C₈	—	2	1	no	—
1142	C₈	—	2	1	no	—
1143	C₈	—	2	1	no	—
1144	C₈	—	94	2	no	—
1145	C₈	—	94	2	no	—
1146	C₈	C₂×#10625350	1	2	yes	complemented
1147	C₂²	—	2	1	no	—
1148	C₂²	—	2	1	no	—
1149	C₂²	—	2	2	no	—
1150	C₂²	—	2	2	no	—
1151	C₂²	—	2	1	no	—
1152	C₂²	—	4	1	no	—
1153	C₂²	—	4	1	no	—
1154	C₂²	—	4	1	no	—
1155	C₂²	—	4	1	no	—
1156	C₂²	—	4	1	no	—
1157	C₂²	—	4	1	no	—
1158	C₂²	—	4	1	no	—
1159	C₂²	—	8	4	no	—
1160	C₂²	—	94	2	no	—
1161	C₂²	—	94	2	no	—
1162	C₂²	—	94	2	no	—
1163	C₂²	—	376	8	no	—
1164	C₂²	—	188	2	no	—
1165	C₂²	—	188	2	no	—
1166	C₂²	—	188	2	no	—
1167	C₂²	C₂²×D₄×D₄₇	1	1	yes	characteristic
1168	C₄	—	2	1	no	—
1169	C₄	—	2	1	no	—
1170	C₄	—	2	1	no	—
1171	C₄	—	2	1	no	—
1172	C₄	—	4	1	no	—
1173	C₄	—	4	1	no	—
1174	C₄	—	4	1	no	—
1175	C₄	—	4	1	no	—
1176	C₄	—	4	1	no	—
1177	C₄	—	47	4	no	—
1178	C₄	—	94	2	no	—
1179	C₄	—	94	2	no	—
1180	C₄	—	188	2	no	—
1181	C₄	—	188	2	no	—
1182	C₄	—	188	2	no	—
1183	C₄	AGL(1,ℤ/8)×D₄₇	1	2	yes	—
1184	C₄	C₂²×#10625350	1	1	yes	characteristic
1185	C₄	#15689959	1	1	yes	characteristic
1186	C₂	—	4	1	no	—
1187	C₂	—	4	2	no	—
1188	C₂	—	4	2	no	—
1189	C₂	—	8	1	no	—
1190	C₂	—	376	2	no	—
1191	C₂	—	188	2	no	—
1192	C₂	D₄×#10625350	1	1	yes	characteristic
1193	C₂	C₂×AGL(1,ℤ/8)×D₄₇	1	1	yes	characteristic
1194	C₂	#20258172	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂²×D₄×D₄₇
commutator, cosocle	C₂×C₄×C₄₇	C₂⁵
Frattini	C₂×C₄	C₂⁴×D₄₇
Fitting	C₄×AGL(1,ℤ/8)×C₄₇	C₂
socle	C₂²×C₄₇	C₂³×D₄
hypercenter	C₄×AGL(1,ℤ/8)	D₄₇
hypocenter	C₄₇	#61466
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ C₄×AGL(1,ℤ/8)

Complements

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

N	H ≅ G/N	type
1. #20257003	C₂	semidirect
2. D₄×#10625350	C₂	semidirect
3. #20256367	C₂	semidirect
4. D₈×Dic₉₄	C₂	semidirect
5. #20256028	C₂	semidirect
6. #20256021	C₂	semidirect
7. #20255974	C₂	semidirect
8. #20255968	C₂	semidirect
9. #20255695	C₂	semidirect
10. #20255689	C₂	semidirect
11. #20255621	C₂	semidirect
12. #20255615	C₂	semidirect
13. #20254989	C₂	semidirect
14. #20254982	C₂	semidirect
15. #20254106	C₂	semidirect
16. #20254103	C₂	semidirect
17. #20253539	C₂	semidirect
18. #20253535	C₂	semidirect
19. #20253487	C₂	semidirect
20. #20253485	C₂	semidirect
21. #20252406	C₂	semidirect
22. #20252199	C₂	semidirect
23. C₄×AGL(1,ℤ/8)×C₄₇	C₂	semidirect
26. #15689851	C₂²	semidirect
27. #15689846	C₂²	semidirect
28. #15689841	C₂²	semidirect
33. D₄×Dic₉₄	C₂²	semidirect
37. #15689777	C₂²	semidirect
39. #15689772	C₂²	semidirect
44. #15689680	C₂²	semidirect
45. #15689677	C₂²	semidirect
53. C₄×#10625352	C₂²	semidirect
56. #15689528	C₂²	semidirect
57. #15689527	C₂²	semidirect
58. #15689496	C₂²	semidirect
59. #15689494	C₂²	semidirect
60. #15689474	C₂²	semidirect
61. #15689472	C₂²	semidirect
62. #15689470	C₂²	semidirect
63. #15689468	C₂²	semidirect
64. #15689460	C₂²	semidirect
65. #15689458	C₂²	semidirect
66. #15689457	C₂²	semidirect
67. #15689449	C₂²	semidirect
68. #15689447	C₂²	semidirect
69. #15689445	C₂²	semidirect
70. #15689408	C₂²	semidirect
71. #15689407	C₂²	semidirect
73. #15689403	C₂²	semidirect
74. #15689403	C₂²	semidirect
75. #15689402	C₂²	semidirect
77. #15689401	C₂²	semidirect
78. #15689372	C₂²	semidirect
79. #15689370	C₂²	semidirect
80. #15689369	C₂²	semidirect
81. #15689369	C₂²	semidirect
82. #15689368	C₂²	semidirect
83. #15689366	C₂²	semidirect
85. #15689328	C₂²	semidirect
86. #15689327	C₂²	semidirect
88. #15689323	C₂²	semidirect
89. #15689322	C₂²	semidirect
90. #15689318	C₂²	semidirect
91. #15689316	C₂²	semidirect
95. #15689269	C₂²	semidirect
96. #15689268	C₂²	semidirect
97. #15689265	C₂²	semidirect
98. C₈×Dic₉₄	C₂²	semidirect
99. C₈×Dic₉₄	C₂²	semidirect
100. #15689233	C₂²	semidirect
101. #15689225	C₂²	semidirect
102. #15689225	C₂²	semidirect
104. #15689223	C₂²	semidirect
105. #15689221	C₂²	semidirect
107. #15689210	C₂²	semidirect
109. #15689203	C₂²	semidirect
110. #15689202	C₂²	semidirect
111. #15689202	C₂²	semidirect
112. #15689199	C₂²	semidirect
113. #15689199	C₂²	semidirect
114. #15689180	C₂²	semidirect
115. #15689178	C₂²	semidirect
116. #15689162	C₂²	semidirect
118. #15689121	C₂²	semidirect
119. #15689075	C₂²	semidirect
121. C₄×#41×C₄₇	C₂²	semidirect
124. C₄₇×#442	C₂²	semidirect
126. C₄₇×#440	C₂²	semidirect
128. C₄×SD₁₆×C₄₇	C₂²	semidirect
130. C₄×D₈×C₄₇	C₂²	semidirect
131. C₄₇×#428	C₂²	semidirect
133. C₄₇×#417	C₂²	semidirect
134. C₄×M₁₆×C₄₇	C₂²	semidirect
384. D₈×C₄₇	#41	semidirect
483. D₄×C₄₇	C₂×#41	semidirect
542. Dic₉₄	AGL(1,ℤ/8)	semidirect
546. C₈×C₄₇	C₂×#41	semidirect
611. C₄×AGL(1,ℤ/8)	D₄₇	semidirect
652. C₄×#41	C₂×D₄₇	semidirect
702. #442	C₂×D₄₇	semidirect
709. #440	C₂×D₄₇	semidirect
713. C₄×SD₁₆	C₂×D₄₇	semidirect
717. C₄×D₈	C₂×D₄₇	semidirect
725. #428	C₂×D₄₇	semidirect
729. #417	C₂×D₄₇	semidirect
731. C₄×M₁₆	C₂×D₄₇	semidirect
732. C₄₇	#61466	semidirect
988. D₈	#10625350	semidirect
1101. D₄	C₂×#10625350	semidirect
1146. C₈	C₂×#10625350	semidirect

Maximal subgroups

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

subgroup	index
#20257003	2
D₄×#10625350	2
#20256367	2
D₈×Dic₉₄	2
#20256028	2
#20256021	2
#20255974	2
#20255968	2
#20255695	2
#20255689	2
#20255621	2
#20255615	2
#20254989	2
#20254982	2
#20254106	2
#20254103	2
#20253539	2
#20253535	2
#20253487	2
#20253485	2
#20252406	2
#20252199	2
C₄×AGL(1,ℤ/8)×C₄₇	2
#61466	47