Subgroups — #27086128

Order 12032.

1878 conjugacy classes of subgroups.

The subgroup lattice has 1100 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20256775	C₂	1	2	yes	maximal, complemented
2	#20254043	C₂	1	1	yes	maximal, characteristic, complemented
3	#20254040	C₂	1	1	yes	maximal, characteristic, complemented
4	#20254034	C₂	1	1	yes	maximal, characteristic, complemented
5	#20254031	C₂	1	1	yes	maximal, characteristic, complemented
6	#20254030	C₂	1	1	yes	maximal, characteristic, complemented
7	#20254027	C₂	1	1	yes	maximal, characteristic, complemented
8	#20254024	C₂	1	1	yes	maximal, characteristic, complemented
9	#20254014	C₂	1	2	yes	maximal, complemented
10	#20254011	C₂	1	2	yes	maximal, complemented
11	#20254004	C₂	1	2	yes	maximal, complemented
12	#20253999	C₂	1	2	yes	maximal, complemented
13	#20253899	C₂	1	1	yes	maximal, characteristic, complemented
14	#20253813	C₂	1	1	yes	maximal, characteristic, complemented
15	#20253730	C₂	1	2	yes	maximal, complemented
16	#20252992	C₂	1	2	yes	maximal, complemented
17	#20252971	C₂	1	1	yes	maximal, characteristic, complemented
18	#20252967	C₂	1	1	yes	maximal, characteristic, complemented
19	#20252183	C₂	1	2	yes	maximal, complemented
20	C₄×#13094047	C₂	1	1	yes	maximal, characteristic, complemented
21	C₄×#13094043	C₂	1	1	yes	maximal, characteristic, complemented
22	#405×D₄₇	C₂	1	1	yes	maximal, characteristic, complemented
23	C₄₇×#3175	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#13094047	C₂²	1	1	yes	characteristic
25	C₂×#13094045	C₂²	1	2	yes	—
26	C₂×#13094043	C₂²	1	1	yes	characteristic
27	C₂×M₁₆×D₄₇	C₂²	1	1	yes	characteristic
28	C₂²×C₈×D₄₇	C₂²	1	1	yes	characteristic
29	#15689747	C₂²	1	2	yes	—
30	#15689744	C₂²	1	2	yes	—
31	#15689742	C₂²	1	2	yes	—
32	#15689733	C₂²	1	2	yes	—
33	#15689731	C₂²	1	2	yes	—
34	#15689726	C₂²	1	2	yes	—
35	#15689724	C₂²	1	2	yes	—
36	#15689719	—	2	2	no	—
37	#15689714	—	2	2	no	—
38	#15689709	—	2	2	no	—
39	#15689707	—	2	2	no	—
40	#15689678	C₂²	1	2	yes	—
41	#15689672	C₂²	1	2	yes	—
42	#15689659	—	2	2	no	—
43	#15689656	—	2	2	no	—
44	#15689652	—	2	2	no	—
45	#15689650	—	2	2	no	—
46	#15689636	C₂²	1	2	yes	—
47	#15689633	C₂²	1	2	yes	—
48	C₄×#10625354	C₂²	1	2	yes	—
49	C₄×#10625352	C₂²	1	2	yes	—
50	#117×D₄₇	C₂²	1	1	yes	characteristic
51	#15689528	C₂²	1	1	yes	characteristic, complemented
52	#15689524	C₂²	1	2	yes	complemented
53	#15689524	C₂²	1	1	yes	characteristic, complemented
54	#15689524	C₂²	1	1	yes	characteristic, complemented
55	#15689519	C₂²	1	2	yes	complemented
56	#15689507	C₂²	1	1	yes	characteristic, complemented
57	#15689505	C₂²	1	2	yes	complemented
58	#15689501	C₂²	1	1	yes	characteristic, complemented
59	#15689498	C₂²	1	1	yes	characteristic, complemented
60	#15689494	C₂²	1	2	yes	complemented
61	#15689490	C₂²	1	2	yes	complemented
62	#15689490	C₂²	1	2	yes	complemented
63	#15689486	C₂²	1	2	yes	complemented
64	#15689486	C₂²	1	2	yes	complemented
65	#15689485	C₂²	1	2	yes	complemented
66	#15689483	C₂²	1	2	yes	complemented
67	#15689482	C₂²	1	2	yes	complemented
68	#15689380	C₂²	1	2	yes	—
69	#15689379	C₂²	1	2	yes	—
70	#15689375	C₂²	1	2	yes	—
71	#15689374	C₂²	1	2	yes	—
72	#15689370	C₂²	1	2	yes	—
73	#15689369	C₂²	1	2	yes	—
74	#15689366	C₂²	1	2	yes	—
75	#15689365	C₂²	1	1	yes	characteristic
76	#15689364	C₂²	1	1	yes	characteristic
77	#15689361	C₂²	1	1	yes	characteristic
78	#15689360	C₂²	1	1	yes	characteristic
79	#15689359	C₂²	1	1	yes	characteristic
80	#15689356	C₂²	1	1	yes	characteristic
81	#15689355	C₂²	1	2	yes	—
82	#15689354	C₂²	1	2	yes	—
83	#15689351	C₂²	1	2	yes	—
84	#15689350	C₂²	1	2	yes	—
85	#15689233	C₂²	1	2	yes	complemented
86	#15689232	C₂²	1	2	yes	complemented
87	#15689228	C₂²	1	2	yes	complemented
88	#15689227	C₂²	1	2	yes	complemented
89	#15689225	C₂²	1	2	yes	complemented
90	#15689224	C₂²	1	2	yes	complemented
91	#15689222	C₂²	1	2	yes	complemented
92	C₄×Dic₁₈₈	C₂²	1	1	yes	characteristic, complemented
93	Q₁₆×Dic₄₇	C₂²	1	1	yes	characteristic, complemented
94	#15689217	C₂²	1	1	yes	characteristic, complemented
95	#15689214	C₂²	1	2	yes	complemented
96	C₄×#10625336	C₂²	1	2	yes	complemented
97	C₄×#10625335	C₂²	1	2	yes	complemented
98	#15689208	C₂²	1	2	yes	complemented
99	C₄×D₃₇₆	C₂²	1	1	yes	characteristic, complemented
100	D₈×Dic₄₇	C₂²	1	1	yes	characteristic, complemented
101	#15689205	C₂²	1	1	yes	characteristic, complemented
102	#15689160	C₂²	1	1	yes	characteristic
103	#15689160	C₂²	1	2	yes	—
104	#15689160	C₂²	1	1	yes	characteristic
105	#15689118	C₂²	1	2	yes	—
106	#15689118	C₂²	1	2	yes	—
107	#15689116	C₂²	1	2	yes	—
108	#15689116	C₂²	1	2	yes	—
109	#15689081	C₂²	1	1	yes	characteristic
110	#15689080	C₂²	1	1	yes	characteristic
111	#15689080	C₂²	1	1	yes	characteristic
112	#15689079	C₂²	1	1	yes	characteristic
113	#15689078	C₂²	1	1	yes	characteristic
114	#15689077	C₂²	1	1	yes	characteristic
115	#15689077	C₂²	1	1	yes	characteristic
116	#97×D₄₇	C₂²	1	1	yes	characteristic
117	#97×D₄₇	C₂²	1	1	yes	characteristic
118	C₄×C₈×D₄₇	C₂²	1	1	yes	characteristic
119	C₄×C₈×D₄₇	C₂²	1	1	yes	characteristic
120	C₄₇×#542	C₂²	1	2	yes	—
121	C₄₇×#500	C₂²	1	1	yes	characteristic, complemented
122	C₄₇×#495	C₂²	1	1	yes	characteristic, complemented
123	C₄₇×#489	C₂²	1	2	yes	complemented
124	C₄₇×#468	C₂²	1	2	yes	—
125	C₄₇×#467	C₂²	1	1	yes	characteristic
126	C₄₇×#466	C₂²	1	1	yes	characteristic
127	C₄₇×#440	C₂²	1	2	yes	complemented
128	C₄×Q₁₆×C₄₇	C₂²	1	1	yes	characteristic, complemented
129	C₄×D₈×C₄₇	C₂²	1	1	yes	characteristic, complemented
130	C₄₇×#405	C₂²	1	1	yes	characteristic
131	C₂×#10625354	C₂³	1	2	yes	—
132	C₂×#10625352	C₂³	1	2	yes	—
133	C₂²×C₄×D₄₇	C₂³	1	1	yes	characteristic
134	#13094047	—	2	4	no	—
135	#13094045	—	2	8	no	—
136	#13094043	—	2	4	no	—
137	C₂×Dic₁₈₈	C₂³	1	1	yes	characteristic
138	C₂×#10625337	C₂³	1	2	yes	—
139	C₂×#10625325	C₂³	1	2	yes	—
140	C₂×#10625335	C₂³	1	2	yes	—
141	C₂×#10625336	C₂³	1	2	yes	—
142	C₂×D₃₇₆	C₂³	1	1	yes	characteristic
143	C₂×#10625334	C₂³	1	2	yes	—
144	C₂×#10625329	C₂³	1	1	yes	characteristic
145	C₂×#10625324	C₂³	1	1	yes	characteristic
146	C₂×#10625324	C₂³	1	1	yes	characteristic
147	M₁₆×D₄₇	—	2	4	no	—
148	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
149	C₂×C₈×D₄₇	—	2	4	no	—
150	C₂×C₈×D₄₇	C₂³	1	1	yes	characteristic
151	C₂×C₈×D₄₇	C₂³	1	1	yes	characteristic
152	C₂×C₈×D₄₇	C₂³	1	1	yes	characteristic
153	C₂×C₈×D₄₇	C₂³	1	1	yes	characteristic
154	C₂×C₈×D₄₇	C₂³	1	1	yes	characteristic
155	C₂×C₈×D₄₇	C₂³	1	1	yes	characteristic
156	#13094024	C₂³	1	2	yes	—
157	#13094022	C₂³	1	2	yes	—
158	#13094020	C₂³	1	2	yes	—
159	#13094019	—	2	2	no	—
160	#13094019	—	2	2	no	—
161	#13094019	—	2	2	no	—
162	#13094018	—	2	2	no	—
163	#13094017	—	2	2	no	—
164	#13094017	—	2	2	no	—
165	#13094017	—	2	2	no	—
166	#13094016	—	2	2	no	—
167	#13094015	—	2	2	no	—
168	#13094015	C₂³	1	2	yes	—
169	#13094015	C₂³	1	2	yes	—
170	#13094014	—	2	2	no	—
171	#13094014	—	2	2	no	—
172	#13094013	—	2	2	no	—
173	#13094012	C₂³	1	2	yes	—
174	#13094010	—	2	2	no	—
175	#13094010	—	2	2	no	—
176	#13094009	—	2	2	no	—
177	#13094009	—	2	2	no	—
178	#13094008	—	2	2	no	—
179	#13094008	—	2	2	no	—
180	#13094007	—	2	2	no	—
181	#13094006	—	2	2	no	—
182	#13094006	—	2	2	no	—
183	#13094006	—	2	2	no	—
184	#13094006	—	2	2	no	—
185	#13094004	—	2	2	no	—
186	#13094004	C₂³	1	2	yes	—
187	#13094003	C₂³	1	2	yes	—
188	#13094002	—	2	2	no	—
189	#13094001	—	2	2	no	—
190	#13094000	—	2	2	no	—
191	#13094000	—	2	2	no	—
192	#13094000	C₂³	1	2	yes	—
193	#13093999	C₂³	1	2	yes	—
194	#13093998	—	2	2	no	—
195	#13093998	C₂³	1	2	yes	—
196	#13093997	—	2	2	no	—
197	#13093997	—	2	2	no	—
198	#13093997	—	2	2	no	—
199	#13093996	—	2	2	no	—
200	#13093995	—	2	2	no	—
201	#13093995	C₂³	1	2	yes	—
202	#13093994	—	2	2	no	—
203	#13093992	—	2	2	no	—
204	Q₈×Dic₄₇	—	2	2	no	—
205	Q₈×Dic₄₇	C₂³	1	2	yes	—
206	C₄×Dic₉₄	C₂³	1	2	yes	—
207	#13093989	—	2	2	no	—
208	#13093989	C₂³	1	2	yes	—
209	C₄×D₁₈₈	—	2	2	no	—
210	C₄×D₁₈₈	C₂³	1	2	yes	—
211	D₄×Dic₄₇	—	2	2	no	—
212	D₄×Dic₄₇	C₂³	1	2	yes	—
213	#13093986	—	2	2	no	—
214	#13093986	—	2	2	no	—
215	#13093986	C₂³	1	2	yes	—
216	C₄×C₂²⋊D₄₇	—	2	2	no	—
217	(C₂²⋊D₄₇)⋊C₄	—	2	2	no	—
218	(C₂²⋊D₄₇)⋊C₄	—	2	2	no	—
219	(C₂²⋊D₄₇)⋊C₄	—	2	2	no	—
220	(C₂²⋊D₄₇)⋊C₄	—	2	2	no	—
221	(C₂²⋊D₄₇)⋊C₄	—	2	2	no	—
222	#13093983	C₂³	1	1	yes	characteristic
223	#13093982	—	2	2	no	—
224	#13093982	D₄	1	1	yes	characteristic
225	#13093982	D₄	1	1	yes	characteristic
226	#13093982	C₂³	1	2	yes	—
227	#13093982	C₂³	1	2	yes	—
228	#13093981	C₂³	1	1	yes	characteristic
229	#13093981	C₂³	1	1	yes	characteristic
230	#13093980	—	2	2	no	—
231	#13093980	D₄	1	1	yes	characteristic
232	#13093980	D₄	1	1	yes	characteristic
233	C₄⋊C₄×D₄₇	D₄	1	1	yes	characteristic
234	C₄⋊C₄×D₄₇	D₄	1	1	yes	characteristic
235	C₂²⋊C₄×D₄₇	D₄	1	1	yes	characteristic
236	C₂²⋊C₄×D₄₇	D₄	1	1	yes	characteristic
237	C₂×C₄×Dic₄₇	—	2	2	no	—
238	C₄²×D₄₇	—	2	2	no	—
239	C₄²×D₄₇	C₂³	1	1	yes	characteristic
240	C₄²×D₄₇	C₂³	1	1	yes	characteristic
241	#13093958	C₂³	1	1	yes	characteristic
242	#13093958	C₂³	1	1	yes	characteristic
243	#13093958	C₂³	1	2	yes	—
244	#13093955	C₂³	1	2	yes	—
245	#13093955	C₂³	1	2	yes	—
246	#13093955	C₂³	1	2	yes	—
247	#13093955	C₂³	1	2	yes	—
248	#13093949	C₂³	1	2	yes	—
249	#13093949	C₂³	1	2	yes	—
250	#13093948	C₂³	1	2	yes	—
251	#13093948	C₂³	1	2	yes	—
252	#13093947	C₂³	1	2	yes	—
253	#13093947	C₂³	1	2	yes	—
254	#13093946	C₂³	1	2	yes	—
255	#13093946	C₂³	1	2	yes	—
256	#13093945	C₂³	1	2	yes	—
257	#13093945	C₂³	1	2	yes	—
258	#13093944	C₂³	1	2	yes	—
259	#13093944	C₂³	1	2	yes	—
260	#13093935	C₂³	1	1	yes	characteristic
261	#13093935	C₂³	1	1	yes	characteristic
262	#13093934	C₂³	1	1	yes	characteristic
263	#13093934	C₂³	1	1	yes	characteristic
264	#13093934	C₂³	1	1	yes	characteristic
265	#13093934	C₂³	1	1	yes	characteristic
266	C₄×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
267	C₄×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
268	C₈×Dic₄₇	C₂³	1	1	yes	characteristic
269	C₈×Dic₄₇	C₂³	1	1	yes	characteristic
270	C₈×Dic₄₇	C₂³	1	1	yes	characteristic
271	C₈×Dic₄₇	C₂³	1	1	yes	characteristic
272	C₂×Q₁₆×C₄₇	C₂³	1	1	yes	characteristic
273	C₂×SD₁₆×C₄₇	C₂³	1	2	yes	—
274	C₂×D₈×C₄₇	C₂³	1	1	yes	characteristic
275	C₂×M₁₆×C₄₇	C₂³	1	1	yes	characteristic
276	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
277	C₄⋊Q₈×C₄₇	C₂³	1	2	yes	—
278	#126×C₄₇	—	2	2	no	—
279	#124×C₄₇	—	2	2	no	—
280	#124×C₄₇	C₂³	1	2	yes	—
281	#123×C₄₇	—	2	2	no	—
282	C₂²⋊Q₈×C₄₇	—	2	2	no	—
283	C₂²⋊Q₈×C₄₇	C₂³	1	2	yes	—
284	#121×C₄₇	C₂³	1	2	yes	—
285	C₄×Q₈×C₄₇	C₂³	1	2	yes	—
286	C₄×D₄×C₄₇	C₂³	1	2	yes	—
287	#117×C₄₇	C₂³	1	1	yes	characteristic
288	#107×C₄₇	C₂³	1	1	yes	characteristic
289	#107×C₄₇	C₂³	1	2	yes	—
290	#107×C₄₇	C₂³	1	1	yes	characteristic
291	#103×C₄₇	C₂³	1	2	yes	—
292	#103×C₄₇	C₂³	1	2	yes	—
293	#102×C₄₇	C₂³	1	2	yes	—
294	#102×C₄₇	C₂³	1	2	yes	—
295	#97×C₄₇	C₂³	1	1	yes	characteristic
296	#97×C₄₇	C₂³	1	1	yes	characteristic
297	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
298	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
299	C₂³×D₄₇	C₂×D₄	1	1	yes	characteristic
300	C₂×Q₈×C₄₇	—	2	2	no	—
301	C₂×Q₈×C₄₇	C₂⁴	1	2	yes	—
302	C₂×D₄×C₄₇	—	2	2	no	—
303	C₂×D₄×C₄₇	C₂⁴	1	2	yes	—
304	C₂²×C₄×C₄₇	—	2	2	no	—
305	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
306	C₂×C₂²⋊D₄₇	—	2	2	no	—
307	C₂×C₂²⋊D₄₇	—	2	2	no	—
308	C₂×C₂²⋊D₄₇	—	2	2	no	—
309	C₂×C₂²⋊D₄₇	—	2	2	no	—
310	C₂×C₂²⋊D₄₇	—	2	2	no	—
311	C₂²×Dic₄₇	—	2	2	no	—
312	C₂²×Dic₄₇	—	2	2	no	—
313	C₂²×Dic₄₇	C₂×D₄	1	1	yes	characteristic
314	#10625354	—	2	4	no	—
315	#10625354	—	2	4	no	—
316	#10625352	—	2	4	no	—
317	#10625352	—	2	4	no	—
318	C₂×D₁₈₈	—	2	2	no	—
319	C₂×D₁₈₈	—	2	2	no	—
320	C₂×D₁₈₈	C₂⁴	1	2	yes	—
321	C₂×C₄×D₄₇	—	2	2	no	—
322	C₂×C₄×D₄₇	—	2	2	no	—
323	C₂×C₄×D₄₇	—	2	2	no	—
324	C₂×C₄×D₄₇	—	2	2	no	—
325	C₂×C₄×D₄₇	—	2	2	no	—
326	C₂×C₄×D₄₇	C₂×D₄	1	1	yes	characteristic
327	C₂×C₄×D₄₇	C₂×D₄	1	1	yes	characteristic
328	C₂×C₄×D₄₇	C₂×D₄	1	1	yes	characteristic
329	C₂×C₄×D₄₇	C₂×D₄	1	1	yes	characteristic
330	C₂×C₄×D₄₇	C₂×D₄	1	1	yes	characteristic
331	C₂×C₄×D₄₇	C₂×D₄	1	1	yes	characteristic
332	C₂×C₄×D₄₇	C₂⁴	1	1	yes	characteristic
333	C₂×C₄×D₄₇	C₂⁴	1	1	yes	characteristic
334	C₂×Dic₉₄	—	2	2	no	—
335	C₂×Dic₉₄	C₂⁴	1	2	yes	—
336	Q₁₆×C₄₇	—	2	2	no	—
337	SD₁₆×C₄₇	—	2	4	no	—
338	D₈×C₄₇	—	2	2	no	—
339	M₁₆×C₄₇	—	2	2	no	—
340	C₂×C₈×C₄₇	—	2	2	no	—
341	C₂×C₈×C₄₇	C₂⁴	1	1	yes	characteristic
342	C₂×C₈×C₄₇	C₂⁴	1	1	yes	characteristic
343	C₂×C₈×C₄₇	C₂⁴	1	1	yes	characteristic
344	C₂×C₈×C₄₇	C₂⁴	1	1	yes	characteristic
345	C₄⋊C₄×C₄₇	—	2	2	no	—
346	C₄⋊C₄×C₄₇	—	2	2	no	—
347	C₄⋊C₄×C₄₇	—	2	2	no	—
348	C₄⋊C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
349	C₄⋊C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
350	C₄⋊C₄×C₄₇	C₂⁴	1	2	yes	—
351	C₄⋊C₄×C₄₇	C₂⁴	1	2	yes	—
352	C₂²⋊C₄×C₄₇	—	2	2	no	—
353	C₂²⋊C₄×C₄₇	—	2	2	no	—
354	C₂²⋊C₄×C₄₇	—	2	2	no	—
355	C₂²⋊C₄×C₄₇	—	2	2	no	—
356	C₂²⋊C₄×C₄₇	—	2	2	no	—
357	C₂²⋊C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
358	C₂²⋊C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
359	C₄²×C₄₇	—	2	2	no	—
360	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
361	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
362	C₂²⋊Dic₄₇	—	2	2	no	—
363	C₂²⋊Dic₄₇	—	2	2	no	—
364	C₂²⋊Dic₄₇	—	2	2	no	—
365	C₂²⋊Dic₄₇	C₂×D₄	1	1	yes	characteristic
366	C₂²⋊Dic₄₇	C₂×D₄	1	1	yes	characteristic
367	#10625337	—	2	4	no	—
368	#10625336	—	2	4	no	—
369	#10625335	—	2	4	no	—
370	#10625334	—	2	4	no	—
371	(C₂×D₄₇)⋊C₄	—	2	2	no	—
372	(C₂×D₄₇)⋊C₄	—	2	2	no	—
373	(C₂×D₄₇)⋊C₄	—	2	2	no	—
374	(C₂×D₄₇)⋊C₄	—	2	2	no	—
375	(C₂×D₄₇)⋊C₄	—	2	2	no	—
376	(C₂×D₄₇)⋊C₄	—	2	2	no	—
377	(C₂×D₄₇)⋊C₄	—	2	2	no	—
378	(C₂×D₄₇)⋊C₄	—	2	2	no	—
379	(C₂×D₄₇)⋊C₄	—	2	2	no	—
380	(C₂×D₄₇)⋊C₄	—	2	2	no	—
381	(C₂×D₄₇)⋊C₄	C₂×D₄	1	1	yes	characteristic
382	(C₂×D₄₇)⋊C₄	C₂×D₄	1	1	yes	characteristic
383	(C₂×D₄₇)⋊C₄	C₂×D₄	1	1	yes	characteristic
384	(C₂×D₄₇)⋊C₄	C₂×D₄	1	1	yes	characteristic
385	C₄⋊Dic₄₇	—	2	2	no	—
386	C₄⋊Dic₄₇	—	2	2	no	—
387	C₄⋊Dic₄₇	—	2	2	no	—
388	C₄⋊Dic₄₇	—	2	2	no	—
389	C₄⋊Dic₄₇	—	2	2	no	—
390	C₄⋊Dic₄₇	C₂×D₄	1	1	yes	characteristic
391	C₄⋊Dic₄₇	C₂×D₄	1	1	yes	characteristic
392	C₄⋊Dic₄₇	C₂⁴	1	2	yes	—
393	C₄⋊Dic₄₇	C₂⁴	1	2	yes	—
394	Dic₄₇⋊C₄	—	2	2	no	—
395	Dic₄₇⋊C₄	—	2	2	no	—
396	Dic₄₇⋊C₄	—	2	2	no	—
397	Dic₄₇⋊C₄	—	2	2	no	—
398	Dic₄₇⋊C₄	—	2	2	no	—
399	Dic₄₇⋊C₄	—	2	2	no	—
400	Dic₄₇⋊C₄	—	2	2	no	—
401	Dic₄₇⋊C₄	—	2	2	no	—
402	Dic₄₇⋊C₄	C₂×D₄	1	1	yes	characteristic
403	Dic₄₇⋊C₄	C₂×D₄	1	1	yes	characteristic
404	Dic₄₇⋊C₄	C₂×D₄	1	1	yes	characteristic
405	Dic₄₇⋊C₄	C₂×D₄	1	1	yes	characteristic
406	C₄×Dic₄₇	—	2	2	no	—
407	C₄×Dic₄₇	—	2	2	no	—
408	C₄×Dic₄₇	—	2	2	no	—
409	C₄×Dic₄₇	—	2	2	no	—
410	C₄×Dic₄₇	—	2	2	no	—
411	C₄×Dic₄₇	C₂×D₄	1	1	yes	characteristic
412	C₄×Dic₄₇	C₂×D₄	1	1	yes	characteristic
413	C₄×Dic₄₇	C₂×D₄	1	1	yes	characteristic
414	C₄×Dic₄₇	C₂×D₄	1	1	yes	characteristic
415	C₄×Dic₄₇	C₂⁴	1	1	yes	characteristic
416	C₄×Dic₄₇	C₂⁴	1	1	yes	characteristic
417	#10625329	—	2	2	no	—
418	C₂×C₄₇⋊C₈	—	2	2	no	—
419	C₂×C₄₇⋊C₈	C₂⁴	1	1	yes	characteristic
420	C₂×C₄₇⋊C₈	C₂⁴	1	1	yes	characteristic
421	C₂×C₄₇⋊C₈	C₂⁴	1	1	yes	characteristic
422	C₂×C₄₇⋊C₈	C₂⁴	1	1	yes	characteristic
423	Dic₁₈₈	—	2	2	no	—
424	D₃₇₆	—	2	2	no	—
425	#10625325	—	2	4	no	—
426	#10625324	—	2	2	no	—
427	#10625324	—	2	2	no	—
428	C₈×D₄₇	—	2	2	no	—
429	C₈×D₄₇	—	2	2	no	—
430	C₈×D₄₇	—	2	2	no	—
431	C₈×D₄₇	—	2	2	no	—
432	C₈×D₄₇	#41	1	4	yes	—
433	C₈×D₄₇	#41	1	4	yes	—
434	C₂³×C₄₇	—	2	2	no	—
435	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
436	C₂²×D₄₇	—	2	2	no	—
437	C₂²×D₄₇	—	2	2	no	—
438	C₂²×D₄₇	—	4	1	no	—
439	C₂²×D₄₇	—	4	1	no	—
440	C₂²×D₄₇	C₂²×D₄	1	1	yes	characteristic
441	C₂²×D₄₇	C₂²×D₄	1	1	yes	characteristic
442	Q₈×C₄₇	—	2	2	no	—
443	Q₈×C₄₇	—	2	2	no	—
444	Q₈×C₄₇	—	8	2	no	—
445	D₄×C₄₇	—	2	2	no	—
446	D₄×C₄₇	—	2	2	no	—
447	D₄×C₄₇	—	8	2	no	—
448	C₂×C₄×C₄₇	—	2	1	no	—
449	C₂×C₄×C₄₇	—	2	1	no	—
450	C₂×C₄×C₄₇	—	2	2	no	—
451	C₂×C₄×C₄₇	—	2	2	no	—
452	C₂×C₄×C₄₇	—	2	2	no	—
453	C₂×C₄×C₄₇	—	8	2	no	—
454	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
455	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
456	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
457	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
458	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
459	C₂×C₄×C₄₇	C₂⁵	1	1	yes	characteristic
460	C₂²⋊D₄₇	—	4	4	no	—
461	C₂²⋊D₄₇	—	8	2	no	—
462	C₂²⋊D₄₇	—	8	2	no	—
463	C₂²⋊D₄₇	—	8	2	no	—
464	C₂²⋊D₄₇	—	8	2	no	—
465	C₂×Dic₄₇	—	2	2	no	—
466	C₂×Dic₄₇	—	2	2	no	—
467	C₂×Dic₄₇	—	2	2	no	—
468	C₂×Dic₄₇	—	2	2	no	—
469	C₂×Dic₄₇	—	4	4	no	—
470	C₂×Dic₄₇	—	8	2	no	—
471	C₂×Dic₄₇	C₂²×D₄	1	1	yes	characteristic
472	C₂×Dic₄₇	C₂²×D₄	1	1	yes	characteristic
473	C₂×Dic₄₇	C₂²×D₄	1	1	yes	characteristic
474	C₂×Dic₄₇	C₂²×D₄	1	1	yes	characteristic
475	C₂×Dic₄₇	C₂²×D₄	1	1	yes	characteristic
476	C₂×Dic₄₇	C₂²×D₄	1	1	yes	characteristic
477	D₁₈₈	—	2	2	no	—
478	D₁₈₈	—	2	2	no	—
479	D₁₈₈	—	4	4	no	—
480	D₁₈₈	—	8	2	no	—
481	C₄×D₄₇	—	2	2	no	—
482	C₄×D₄₇	—	2	1	no	—
483	C₄×D₄₇	—	2	1	no	—
484	C₄×D₄₇	—	2	2	no	—
485	C₄×D₄₇	—	4	1	no	—
486	C₄×D₄₇	—	4	1	no	—
487	C₄×D₄₇	—	4	1	no	—
488	C₄×D₄₇	—	4	1	no	—
489	C₄×D₄₇	—	4	4	no	—
490	C₄×D₄₇	—	8	2	no	—
491	C₄×D₄₇	—	8	2	no	—
492	C₄×D₄₇	C₂×#41	1	2	yes	—
493	C₄×D₄₇	C₂×#41	1	2	yes	—
494	Dic₉₄	—	2	2	no	—
495	Dic₉₄	—	2	2	no	—
496	Dic₉₄	—	8	2	no	—
497	C₈×C₄₇	—	2	1	no	—
498	C₈×C₄₇	—	2	1	no	—
499	C₈×C₄₇	C₂×#41	1	2	yes	—
500	C₈×C₄₇	C₂×#41	1	2	yes	—
501	C₄₇⋊C₈	—	2	1	no	—
502	C₄₇⋊C₈	—	2	1	no	—
503	C₄₇⋊C₈	C₂×#41	1	2	yes	—
504	C₄₇⋊C₈	C₂×#41	1	2	yes	—
505	#60682	—	47	1	no	maximal, Sylow
506	C₂²×C₄₇	—	2	1	no	—
507	C₂²×C₄₇	—	2	1	no	—
508	C₂²×C₄₇	—	2	1	no	—
509	C₂²×C₄₇	—	4	2	no	—
510	C₂²×C₄₇	—	4	2	no	—
511	C₂²×C₄₇	—	4	2	no	—
512	C₂²×C₄₇	C₂³×D₄	1	1	yes	characteristic
513	C₂×D₄₇	—	2	1	no	—
514	C₂×D₄₇	—	2	1	no	—
515	C₂×D₄₇	—	2	1	no	—
516	C₂×D₄₇	—	2	1	no	—
517	C₂×D₄₇	—	2	1	no	—
518	C₂×D₄₇	—	4	4	no	—
519	C₂×D₄₇	—	4	2	no	—
520	C₂×D₄₇	—	4	2	no	—
521	C₂×D₄₇	—	4	2	no	—
522	C₂×D₄₇	#532	1	2	yes	—
523	C₄×C₄₇	—	2	1	no	—
524	C₄×C₄₇	—	2	1	no	—
525	C₄×C₄₇	—	2	1	no	—
526	C₄×C₄₇	—	2	1	no	—
527	C₄×C₄₇	—	2	1	no	—
528	C₄×C₄₇	—	4	2	no	—
529	C₄×C₄₇	—	4	2	no	—
530	C₄×C₄₇	—	4	2	no	—
531	C₄×C₄₇	C₂²×#41	1	1	yes	characteristic
532	C₄×C₄₇	C₂²×#41	1	1	yes	characteristic
533	Dic₄₇	—	2	1	no	—
534	Dic₄₇	—	2	1	no	—
535	Dic₄₇	—	2	1	no	—
536	Dic₄₇	—	2	1	no	—
537	Dic₄₇	—	2	1	no	—
538	Dic₄₇	—	4	2	no	—
539	Dic₄₇	—	4	2	no	—
540	Dic₄₇	—	4	2	no	—
541	Dic₄₇	#532	1	2	yes	—
542	#3455	—	47	2	no	—
543	#3177	—	47	1	no	—
544	#3177	—	47	1	no	—
545	#3176	—	47	1	no	—
546	#3176	—	47	1	no	—
547	#3175	—	47	1	no	—
548	#3175	—	47	1	no	—
549	#3175	—	47	1	no	—
550	#3175	D₄₇	1	1	yes	characteristic, complemented
551	#3174	—	47	2	no	—
552	#3174	—	47	2	no	—
553	#3173	—	47	2	no	—
554	#3173	—	47	2	no	—
555	#3160	—	47	1	no	—
556	#3147	—	47	1	no	—
557	#3135	—	47	2	no	—
558	#3054	—	47	2	no	—
559	#3050	—	47	1	no	—
560	#3050	—	47	1	no	—
561	#2943	—	47	2	no	—
562	C₄×#135	—	47	1	no	—
563	C₄×#135	—	47	1	no	—
564	C₂×#405	—	47	1	no	—
565	C₂×C₄₇	—	4	1	no	—
566	C₂×C₄₇	—	8	2	no	—
567	C₂×C₄₇	C₂×#532	1	1	yes	characteristic
568	C₂×C₄₇	#3584	1	1	yes	characteristic
569	C₂×C₄₇	#3584	1	1	yes	characteristic
570	D₄₇	—	2	2	no	—
571	D₄₇	—	4	1	no	—
572	D₄₇	—	8	2	no	—
573	C₂×#135	—	47	1	no	—
574	C₂×#135	—	47	2	no	—
575	C₂×#135	—	47	1	no	—
576	C₂²×M₁₆	—	47	1	no	—
577	C₂³×C₈	—	47	1	no	—
578	#542	—	47	2	no	—
579	#542	—	47	2	no	—
580	#542	—	47	2	no	—
581	#542	C₂×D₄₇	1	2	yes	—
582	#541	—	47	2	no	—
583	#541	—	47	2	no	—
584	#540	—	47	2	no	—
585	#540	—	47	2	no	—
586	#539	—	94	2	no	—
587	#539	—	94	2	no	—
588	#538	—	94	2	no	—
589	#538	—	94	2	no	—
590	#533	—	47	2	no	—
591	#532	—	47	2	no	—
592	#529	—	94	2	no	—
593	#529	—	94	2	no	—
594	#529	—	94	2	no	—
595	#529	—	94	2	no	—
596	#525	—	47	2	no	—
597	#525	—	47	2	no	—
598	C₄×#41	—	47	2	no	—
599	C₄×#41	—	47	2	no	—
600	C₂×#117	—	47	1	no	—
601	#500	—	47	1	no	—
602	#500	C₂×D₄₇	1	1	yes	characteristic, complemented
603	#499	—	47	2	no	—
604	#499	—	47	1	no	—
605	#499	—	47	1	no	—
606	#498	—	47	2	no	—
607	#495	—	47	2	no	—
608	#495	—	47	1	no	—
609	#495	C₂×D₄₇	1	1	yes	characteristic, complemented
610	#494	—	47	1	no	—
611	#493	—	47	1	no	—
612	#492	—	47	2	no	—
613	#491	—	47	2	no	—
614	#491	—	47	2	no	—
615	#490	—	47	2	no	—
616	#490	—	47	2	no	—
617	#489	—	47	2	no	—
618	#489	—	47	2	no	—
619	#489	—	47	2	no	—
620	#489	C₂×D₄₇	1	2	yes	complemented
621	#470	—	47	2	no	—
622	#470	—	47	2	no	—
623	#469	—	47	2	no	—
624	#469	—	47	2	no	—
625	#468	—	47	2	no	—
626	#468	—	47	2	no	—
627	#468	—	47	2	no	—
628	#468	C₂×D₄₇	1	2	yes	—
629	#467	—	47	1	no	—
630	#467	—	47	1	no	—
631	#467	—	47	1	no	—
632	#467	C₂×D₄₇	1	1	yes	characteristic
633	#466	—	47	1	no	—
634	#466	—	47	1	no	—
635	#466	—	47	1	no	—
636	#466	C₂×D₄₇	1	1	yes	characteristic
637	#465	—	47	2	no	—
638	#465	—	47	2	no	—
639	#465	—	47	2	no	—
640	#465	—	47	2	no	—
641	#442	—	47	2	no	—
642	#442	—	47	2	no	—
643	#441	—	47	2	no	—
644	#441	—	47	2	no	—
645	#440	—	47	2	no	—
646	#440	—	47	2	no	—
647	#440	—	47	2	no	—
648	#440	C₂×D₄₇	1	2	yes	complemented
649	C₄×Q₁₆	—	47	1	no	—
650	C₄×Q₁₆	—	47	1	no	—
651	C₄×Q₁₆	—	47	1	no	—
652	C₄×Q₁₆	C₂×D₄₇	1	1	yes	characteristic, complemented
653	C₄×SD₁₆	—	47	2	no	—
654	C₄×SD₁₆	—	47	2	no	—
655	C₄×SD₁₆	—	47	2	no	—
656	C₄×SD₁₆	—	47	2	no	—
657	C₄×D₈	—	47	1	no	—
658	C₄×D₈	—	47	1	no	—
659	C₄×D₈	—	47	1	no	—
660	C₄×D₈	C₂×D₄₇	1	1	yes	characteristic, complemented
661	#427	—	47	1	no	—
662	#427	—	47	1	no	—
663	#427	—	47	2	no	—
664	#416	—	47	2	no	—
665	#416	—	47	2	no	—
666	#416	—	47	2	no	—
667	#416	—	47	2	no	—
668	#405	—	47	1	no	—
669	#405	—	47	1	no	—
670	#405	—	47	1	no	—
671	#405	—	47	1	no	—
672	#405	—	47	1	no	—
673	#405	—	47	1	no	—
674	#405	—	47	1	no	—
675	#405	C₂×D₄₇	1	1	yes	characteristic
676	C₂×#97	—	47	1	no	—
677	C₂×#97	—	47	1	no	—
678	C₂×C₄×C₈	—	47	1	no	—
679	C₂×C₄×C₈	—	47	1	no	—
680	C₄₇	#60682	1	1	yes	characteristic, complemented, Sylow
681	C₂×#41	—	47	2	no	—
682	C₂×#41	—	47	2	no	—
683	C₂³×C₄	—	47	1	no	—
684	#135	—	94	4	no	—
685	#135	—	94	8	no	—
686	#135	—	94	4	no	—
687	C₂×Q₁₆	—	47	2	no	—
688	C₂×Q₁₆	—	47	1	no	—
689	C₂×Q₁₆	C₂²×D₄₇	1	1	yes	characteristic
690	C₂×SD₁₆	—	47	2	no	—
691	C₂×SD₁₆	—	47	2	no	—
692	C₂×SD₁₆	—	47	2	no	—
693	C₂×SD₁₆	C₂²×D₄₇	1	2	yes	—
694	C₂×D₈	—	47	2	no	—
695	C₂×D₈	—	47	1	no	—
696	C₂×D₈	C₂²×D₄₇	1	1	yes	characteristic
697	C₂×M₁₆	—	47	1	no	—
698	C₂×M₁₆	—	47	1	no	—
699	C₂×M₁₆	—	47	1	no	—
700	C₂×M₁₆	—	94	4	no	—
701	C₂×M₁₆	C₂²×D₄₇	1	1	yes	characteristic
702	C₂²×C₈	—	47	1	no	—
703	C₂²×C₈	—	47	1	no	—
704	C₂²×C₈	—	47	1	no	—
705	C₂²×C₈	—	47	1	no	—
706	C₂²×C₈	—	47	1	no	—
707	C₂²×C₈	—	47	1	no	—
708	C₂²×C₈	—	47	1	no	—
709	C₂²×C₈	—	94	4	no	—
710	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
711	C₄⋊Q₈	—	47	2	no	—
712	C₄⋊Q₈	—	47	2	no	—
713	C₄⋊Q₈	C₂²×D₄₇	1	2	yes	—
714	#127	—	47	2	no	—
715	#126	—	2	2	no	—
716	#126	—	94	2	no	—
717	#126	—	94	2	no	—
718	#126	—	94	2	no	—
719	#126	—	94	2	no	—
720	#126	—	94	2	no	—
721	#126	—	94	2	no	—
722	#126	—	94	2	no	—
723	#125	—	47	2	no	—
724	#125	—	47	2	no	—
725	#125	—	94	2	no	—
726	#125	—	94	2	no	—
727	#125	—	94	2	no	—
728	#125	—	94	2	no	—
729	#124	—	2	2	no	—
730	#124	—	47	2	no	—
731	#124	—	94	2	no	—
732	#124	—	94	2	no	—
733	#124	—	94	2	no	—
734	#124	C₂²×D₄₇	1	2	yes	—
735	#123	—	2	2	no	—
736	#123	—	94	2	no	—
737	#123	—	94	2	no	—
738	#123	—	94	2	no	—
739	#123	—	94	2	no	—
740	#123	—	94	2	no	—
741	#123	—	94	2	no	—
742	#123	—	94	2	no	—
743	#123	—	94	2	no	—
744	#123	—	94	2	no	—
745	C₂²⋊Q₈	—	2	2	no	—
746	C₂²⋊Q₈	—	47	2	no	—
747	C₂²⋊Q₈	—	47	2	no	—
748	C₂²⋊Q₈	—	47	2	no	—
749	C₂²⋊Q₈	—	94	2	no	—
750	C₂²⋊Q₈	—	94	2	no	—
751	C₂²⋊Q₈	—	94	2	no	—
752	C₂²⋊Q₈	—	94	2	no	—
753	C₂²⋊Q₈	—	94	2	no	—
754	C₂²⋊Q₈	C₂²×D₄₇	1	2	yes	—
755	#121	—	47	2	no	—
756	#121	—	47	2	no	—
757	#121	—	47	2	no	—
758	#121	—	94	2	no	—
759	#121	—	94	2	no	—
760	#121	—	94	2	no	—
761	#121	—	94	2	no	—
762	#121	—	94	2	no	—
763	#121	—	94	2	no	—
764	#121	C₂²×D₄₇	1	2	yes	—
765	#120	—	94	2	no	—
766	#120	—	94	2	no	—
767	C₄×Q₈	—	47	2	no	—
768	C₄×Q₈	—	47	2	no	—
769	C₄×Q₈	—	47	2	no	—
770	C₄×Q₈	—	94	2	no	—
771	C₄×Q₈	—	94	2	no	—
772	C₄×Q₈	C₂²×D₄₇	1	2	yes	—
773	C₄×D₄	—	47	2	no	—
774	C₄×D₄	—	47	2	no	—
775	C₄×D₄	—	47	2	no	—
776	C₄×D₄	—	94	2	no	—
777	C₄×D₄	—	94	2	no	—
778	C₄×D₄	—	94	2	no	—
779	C₄×D₄	—	94	2	no	—
780	C₄×D₄	—	94	2	no	—
781	C₄×D₄	—	94	2	no	—
782	C₄×D₄	—	94	2	no	—
783	C₄×D₄	—	94	2	no	—
784	C₄×D₄	—	94	2	no	—
785	C₄×D₄	—	94	2	no	—
786	C₄×D₄	C₂²×D₄₇	1	2	yes	—
787	#117	—	47	1	no	—
788	#117	—	47	1	no	—
789	#117	—	47	1	no	—
790	#117	—	47	1	no	—
791	#117	—	47	1	no	—
792	#117	—	47	1	no	—
793	#117	—	47	1	no	—
794	#117	—	47	2	no	—
795	#117	—	47	2	no	—
796	#117	—	94	2	no	—
797	#117	—	94	2	no	—
798	#117	C₂²×D₄₇	1	1	yes	characteristic
799	C₂×C₄⋊C₄	—	47	1	no	—
800	C₂×C₄⋊C₄	—	47	1	no	—
801	C₂×C₂²⋊C₄	—	47	1	no	—
802	C₂×C₂²⋊C₄	—	47	1	no	—
803	C₂×C₄²	—	47	1	no	—
804	C₂×C₄²	—	47	1	no	—
805	C₂×C₄²	—	94	2	no	—
806	C₂×C₄²	—	94	2	no	—
807	#107	—	47	1	no	—
808	#107	—	47	1	no	—
809	#107	—	47	2	no	—
810	#107	C₂²×D₄₇	1	1	yes	characteristic
811	#107	C₂²×D₄₇	1	1	yes	characteristic
812	#107	C₂²×D₄₇	1	2	yes	—
813	#106	—	47	2	no	—
814	#106	—	47	2	no	—
815	#106	—	47	2	no	—
816	#106	—	47	2	no	—
817	#103	—	47	2	no	—
818	#103	—	47	2	no	—
819	#103	—	47	2	no	—
820	#103	—	47	2	no	—
821	#103	—	47	2	no	—
822	#103	—	47	2	no	—
823	#103	C₂²×D₄₇	1	2	yes	—
824	#103	C₂²×D₄₇	1	2	yes	—
825	#102	—	47	2	no	—
826	#102	—	47	2	no	—
827	#102	—	47	2	no	—
828	#102	—	47	2	no	—
829	#102	—	47	2	no	—
830	#102	—	47	2	no	—
831	#102	C₂²×D₄₇	1	2	yes	—
832	#102	C₂²×D₄₇	1	2	yes	—
833	#97	—	47	1	no	—
834	#97	—	47	1	no	—
835	#97	—	47	1	no	—
836	#97	—	47	1	no	—
837	#97	—	47	1	no	—
838	#97	—	47	1	no	—
839	#97	C₂²×D₄₇	1	1	yes	characteristic
840	#97	C₂²×D₄₇	1	1	yes	characteristic
841	C₄×C₈	—	47	1	no	—
842	C₄×C₈	—	47	1	no	—
843	C₄×C₈	—	47	1	no	—
844	C₄×C₈	—	47	1	no	—
845	C₄×C₈	—	47	1	no	—
846	C₄×C₈	—	47	1	no	—
847	C₄×C₈	C₂²×D₄₇	1	1	yes	characteristic
848	C₄×C₈	C₂²×D₄₇	1	1	yes	characteristic
849	C₂⁴	—	47	1	no	—
850	#41	—	94	4	no	—
851	#41	—	94	4	no	—
852	#41	—	94	4	no	—
853	#41	—	94	4	no	—
854	C₂×Q₈	—	2	2	no	—
855	C₂×Q₈	—	47	2	no	—
856	C₂×Q₈	—	94	2	no	—
857	C₂×Q₈	C₂³×D₄₇	1	2	yes	—
858	C₂×D₄	—	2	2	no	—
859	C₂×D₄	—	47	2	no	—
860	C₂×D₄	—	94	2	no	—
861	C₂×D₄	—	94	2	no	—
862	C₂×D₄	—	94	2	no	—
863	C₂×D₄	—	94	2	no	—
864	C₂×D₄	—	94	2	no	—
865	C₂×D₄	—	94	2	no	—
866	C₂×D₄	—	94	2	no	—
867	C₂×D₄	C₂³×D₄₇	1	2	yes	—
868	C₂²×C₄	—	2	2	no	—
869	C₂²×C₄	—	47	1	no	—
870	C₂²×C₄	—	47	1	no	—
871	C₂²×C₄	—	47	1	no	—
872	C₂²×C₄	—	47	1	no	—
873	C₂²×C₄	—	47	1	no	—
874	C₂²×C₄	—	47	1	no	—
875	C₂²×C₄	—	47	1	no	—
876	C₂²×C₄	—	47	1	no	—
877	C₂²×C₄	—	47	1	no	—
878	C₂²×C₄	—	94	2	no	—
879	C₂²×C₄	—	94	2	no	—
880	C₂²×C₄	—	94	2	no	—
881	C₂²×C₄	—	94	2	no	—
882	C₂²×C₄	—	94	2	no	—
883	C₂²×C₄	—	94	2	no	—
884	C₂²×C₄	—	94	2	no	—
885	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
886	Q₁₆	—	2	2	no	—
887	Q₁₆	—	94	4	no	—
888	Q₁₆	—	94	2	no	—
889	SD₁₆	—	2	4	no	—
890	SD₁₆	—	94	4	no	—
891	SD₁₆	—	94	4	no	—
892	SD₁₆	—	94	4	no	—
893	D₈	—	2	2	no	—
894	D₈	—	94	4	no	—
895	D₈	—	94	2	no	—
896	M₁₆	—	2	2	no	—
897	M₁₆	—	94	2	no	—
898	M₁₆	—	94	2	no	—
899	M₁₆	—	94	2	no	—
900	C₂×C₈	—	2	2	no	—
901	C₂×C₈	—	47	1	no	—
902	C₂×C₈	—	47	1	no	—
903	C₂×C₈	—	47	4	no	—
904	C₂×C₈	—	47	4	no	—
905	C₂×C₈	—	47	1	no	—
906	C₂×C₈	—	47	1	no	—
907	C₂×C₈	—	94	2	no	—
908	C₂×C₈	—	94	2	no	—
909	C₂×C₈	—	94	2	no	—
910	C₂×C₈	—	94	2	no	—
911	C₂×C₈	—	94	2	no	—
912	C₂×C₈	C₂³×D₄₇	1	1	yes	characteristic
913	C₂×C₈	C₂³×D₄₇	1	1	yes	characteristic
914	C₂×C₈	C₂³×D₄₇	1	1	yes	characteristic
915	C₂×C₈	C₂³×D₄₇	1	1	yes	characteristic
916	C₄⋊C₄	—	2	2	no	—
917	C₄⋊C₄	—	2	2	no	—
918	C₄⋊C₄	—	2	2	no	—
919	C₄⋊C₄	—	47	1	no	—
920	C₄⋊C₄	—	47	1	no	—
921	C₄⋊C₄	—	47	1	no	—
922	C₄⋊C₄	—	47	1	no	—
923	C₄⋊C₄	—	47	1	no	—
924	C₄⋊C₄	—	47	1	no	—
925	C₄⋊C₄	—	47	2	no	—
926	C₄⋊C₄	—	47	2	no	—
927	C₄⋊C₄	—	94	2	no	—
928	C₄⋊C₄	—	94	2	no	—
929	C₄⋊C₄	—	94	2	no	—
930	C₄⋊C₄	—	94	2	no	—
931	C₄⋊C₄	—	94	2	no	—
932	C₄⋊C₄	—	94	2	no	—
933	C₄⋊C₄	—	94	2	no	—
934	C₄⋊C₄	—	94	2	no	—
935	C₄⋊C₄	—	94	2	no	—
936	C₄⋊C₄	—	94	2	no	—
937	C₄⋊C₄	—	94	2	no	—
938	C₄⋊C₄	—	94	2	no	—
939	C₄⋊C₄	—	94	2	no	—
940	C₄⋊C₄	D₄×D₄₇	1	1	yes	characteristic
941	C₄⋊C₄	D₄×D₄₇	1	1	yes	characteristic
942	C₄⋊C₄	C₂³×D₄₇	1	2	yes	—
943	C₄⋊C₄	C₂³×D₄₇	1	2	yes	—
944	C₂²⋊C₄	—	2	2	no	—
945	C₂²⋊C₄	—	2	2	no	—
946	C₂²⋊C₄	—	2	2	no	—
947	C₂²⋊C₄	—	2	2	no	—
948	C₂²⋊C₄	—	2	2	no	—
949	C₂²⋊C₄	—	47	1	no	—
950	C₂²⋊C₄	—	47	1	no	—
951	C₂²⋊C₄	—	47	1	no	—
952	C₂²⋊C₄	—	47	1	no	—
953	C₂²⋊C₄	—	47	1	no	—
954	C₂²⋊C₄	—	47	1	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	2	no	—
961	C₂²⋊C₄	—	94	2	no	—
962	C₂²⋊C₄	—	94	2	no	—
963	C₂²⋊C₄	—	94	2	no	—
964	C₂²⋊C₄	—	94	2	no	—
965	C₂²⋊C₄	—	94	2	no	—
966	C₂²⋊C₄	—	94	2	no	—
967	C₂²⋊C₄	—	94	2	no	—
968	C₂²⋊C₄	D₄×D₄₇	1	1	yes	characteristic
969	C₂²⋊C₄	D₄×D₄₇	1	1	yes	characteristic
970	C₄²	—	2	2	no	—
971	C₄²	—	47	1	no	—
972	C₄²	—	47	1	no	—
973	C₄²	—	47	1	no	—
974	C₄²	—	47	1	no	—
975	C₄²	—	47	1	no	—
976	C₄²	—	47	1	no	—
977	C₄²	—	94	2	no	—
978	C₄²	—	94	2	no	—
979	C₄²	—	94	2	no	—
980	C₄²	—	94	2	no	—
981	C₄²	—	94	2	no	—
982	C₄²	C₂³×D₄₇	1	1	yes	characteristic
983	C₄²	C₂³×D₄₇	1	1	yes	characteristic
984	C₂³	—	2	2	no	—
985	C₂³	—	47	1	no	—
986	C₂³	—	47	1	no	—
987	C₂³	—	94	2	no	—
988	C₂³	—	94	2	no	—
989	C₂³	—	188	1	no	—
990	C₂³	—	188	1	no	—
991	C₂³	C₂×D₄×D₄₇	1	1	yes	characteristic
992	Q₈	—	2	2	no	—
993	Q₈	—	2	2	no	—
994	Q₈	—	8	2	no	—
995	Q₈	—	94	2	no	—
996	Q₈	—	94	2	no	—
997	Q₈	—	376	2	no	—
998	D₄	—	2	2	no	—
999	D₄	—	2	2	no	—
1000	D₄	—	8	2	no	—
1001	D₄	—	94	2	no	—
1002	D₄	—	94	2	no	—
1003	D₄	—	376	2	no	—
1004	D₄	—	376	2	no	—
1005	D₄	—	376	2	no	—
1006	D₄	—	376	2	no	—
1007	D₄	—	376	2	no	—
1008	D₄	—	188	4	no	—
1009	D₄	—	188	4	no	—
1010	C₂×C₄	—	2	1	no	—
1011	C₂×C₄	—	2	1	no	—
1012	C₂×C₄	—	2	2	no	—
1013	C₂×C₄	—	2	2	no	—
1014	C₂×C₄	—	2	2	no	—
1015	C₂×C₄	—	8	2	no	—
1016	C₂×C₄	—	47	1	no	—
1017	C₂×C₄	—	47	2	no	—
1018	C₂×C₄	—	47	2	no	—
1019	C₂×C₄	—	47	1	no	—
1020	C₂×C₄	—	47	1	no	—
1021	C₂×C₄	—	47	1	no	—
1022	C₂×C₄	—	47	1	no	—
1023	C₂×C₄	—	47	1	no	—
1024	C₂×C₄	—	94	2	no	—
1025	C₂×C₄	—	94	2	no	—
1026	C₂×C₄	—	94	2	no	—
1027	C₂×C₄	—	94	1	no	—
1028	C₂×C₄	—	94	1	no	—
1029	C₂×C₄	—	94	2	no	—
1030	C₂×C₄	—	94	2	no	—
1031	C₂×C₄	—	94	2	no	—
1032	C₂×C₄	—	376	2	no	—
1033	C₂×C₄	—	376	2	no	—
1034	C₂×C₄	—	376	2	no	—
1035	C₂×C₄	—	188	1	no	—
1036	C₂×C₄	—	188	1	no	—
1037	C₂×C₄	—	188	1	no	—
1038	C₂×C₄	—	188	1	no	—
1039	C₂×C₄	—	188	4	no	—
1040	C₂×C₄	—	188	4	no	—
1041	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
1042	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
1043	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
1044	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
1045	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
1046	C₂×C₄	C₂⁴×D₄₇	1	1	yes	characteristic
1047	C₈	—	2	1	no	—
1048	C₈	—	2	1	no	—
1049	C₈	—	47	2	no	—
1050	C₈	—	47	2	no	—
1051	C₈	—	94	1	no	—
1052	C₈	—	94	1	no	—
1053	C₈	#41×D₄₇	1	2	yes	—
1054	C₈	#41×D₄₇	1	2	yes	—
1055	C₂²	—	2	1	no	—
1056	C₂²	—	2	1	no	—
1057	C₂²	—	2	1	no	—
1058	C₂²	—	4	2	no	—
1059	C₂²	—	4	2	no	—
1060	C₂²	—	4	2	no	—
1061	C₂²	—	47	2	no	—
1062	C₂²	—	94	1	no	—
1063	C₂²	—	94	1	no	—
1064	C₂²	—	94	1	no	—
1065	C₂²	—	94	1	no	—
1066	C₂²	—	94	1	no	—
1067	C₂²	—	188	4	no	—
1068	C₂²	—	188	2	no	—
1069	C₂²	—	188	2	no	—
1070	C₂²	—	188	2	no	—
1071	C₂²	C₂²×D₄×D₄₇	1	1	yes	characteristic
1072	C₄	—	2	1	no	—
1073	C₄	—	2	1	no	—
1074	C₄	—	2	1	no	—
1075	C₄	—	2	1	no	—
1076	C₄	—	2	1	no	—
1077	C₄	—	4	2	no	—
1078	C₄	—	4	2	no	—
1079	C₄	—	4	2	no	—
1080	C₄	—	47	2	no	—
1081	C₄	—	94	1	no	—
1082	C₄	—	94	1	no	—
1083	C₄	—	94	1	no	—
1084	C₄	—	94	1	no	—
1085	C₄	—	94	1	no	—
1086	C₄	—	188	2	no	—
1087	C₄	—	188	2	no	—
1088	C₄	—	188	2	no	—
1089	C₄	C₂×#41×D₄₇	1	1	yes	characteristic
1090	C₄	C₂×#41×D₄₇	1	1	yes	characteristic
1091	C₂	—	4	1	no	—
1092	C₂	—	8	2	no	—
1093	C₂	—	94	2	no	—
1094	C₂	—	376	2	no	—
1095	C₂	—	188	1	no	—
1096	C₂	#532×D₄₇	1	1	yes	characteristic
1097	C₂	#20258156	1	1	yes	characteristic
1098	C₂	#20258158	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂²×D₄×D₄₇
commutator, cosocle	C₂×C₄×C₄₇	C₂⁵
Frattini	C₂×C₄	C₂⁴×D₄₇
Fitting	C₄₇×#3175	C₂
socle	C₂²×C₄₇	C₂³×D₄
hypercenter	#3175	D₄₇
hypocenter	C₄₇	#60682
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ #117 ◁ #3175

Complements

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

N	H ≅ G/N	type
1. #20256775	C₂	semidirect
2. #20254043	C₂	semidirect
3. #20254040	C₂	semidirect
4. #20254034	C₂	semidirect
5. #20254031	C₂	semidirect
6. #20254030	C₂	semidirect
7. #20254027	C₂	semidirect
8. #20254024	C₂	semidirect
9. #20254014	C₂	semidirect
10. #20254011	C₂	semidirect
11. #20254004	C₂	semidirect
12. #20253999	C₂	semidirect
13. #20253899	C₂	semidirect
14. #20253813	C₂	semidirect
15. #20253730	C₂	semidirect
16. #20252992	C₂	semidirect
17. #20252971	C₂	semidirect
18. #20252967	C₂	semidirect
19. #20252183	C₂	semidirect
20. C₄×#13094047	C₂	semidirect
21. C₄×#13094043	C₂	semidirect
22. #405×D₄₇	C₂	semidirect
23. C₄₇×#3175	C₂	semidirect
51. #15689528	C₂²	semidirect
52. #15689524	C₂²	semidirect
53. #15689524	C₂²	semidirect
54. #15689524	C₂²	semidirect
55. #15689519	C₂²	semidirect
56. #15689507	C₂²	semidirect
57. #15689505	C₂²	semidirect
58. #15689501	C₂²	semidirect
59. #15689498	C₂²	semidirect
60. #15689494	C₂²	semidirect
61. #15689490	C₂²	semidirect
62. #15689490	C₂²	semidirect
63. #15689486	C₂²	semidirect
64. #15689486	C₂²	semidirect
65. #15689485	C₂²	semidirect
66. #15689483	C₂²	semidirect
67. #15689482	C₂²	semidirect
85. #15689233	C₂²	semidirect
86. #15689232	C₂²	semidirect
87. #15689228	C₂²	semidirect
88. #15689227	C₂²	semidirect
89. #15689225	C₂²	semidirect
90. #15689224	C₂²	semidirect
91. #15689222	C₂²	semidirect
92. C₄×Dic₁₈₈	C₂²	semidirect
93. Q₁₆×Dic₄₇	C₂²	semidirect
94. #15689217	C₂²	semidirect
95. #15689214	C₂²	semidirect
96. C₄×#10625336	C₂²	semidirect
97. C₄×#10625335	C₂²	semidirect
98. #15689208	C₂²	semidirect
99. C₄×D₃₇₆	C₂²	semidirect
100. D₈×Dic₄₇	C₂²	semidirect
101. #15689205	C₂²	semidirect
121. C₄₇×#500	C₂²	semidirect
122. C₄₇×#495	C₂²	semidirect
123. C₄₇×#489	C₂²	semidirect
127. C₄₇×#440	C₂²	semidirect
128. C₄×Q₁₆×C₄₇	C₂²	semidirect
129. C₄×D₈×C₄₇	C₂²	semidirect
550. #3175	D₄₇	semidirect
602. #500	C₂×D₄₇	semidirect
609. #495	C₂×D₄₇	semidirect
620. #489	C₂×D₄₇	semidirect
648. #440	C₂×D₄₇	semidirect
652. C₄×Q₁₆	C₂×D₄₇	semidirect
660. C₄×D₈	C₂×D₄₇	semidirect
680. C₄₇	#60682	semidirect

Maximal subgroups

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

subgroup	index
#20256775	2
#20254043	2
#20254040	2
#20254034	2
#20254031	2
#20254030	2
#20254027	2
#20254024	2
#20254014	2
#20254011	2
#20254004	2
#20253999	2
#20253899	2
#20253813	2
#20253730	2
#20252992	2
#20252971	2
#20252967	2
#20252183	2
C₄×#13094047	2
C₄×#13094043	2
#405×D₄₇	2
C₄₇×#3175	2
#60682	47