Subgroups — #27098877

Order 12032.

1882 conjugacy classes of subgroups.

The subgroup lattice has 1094 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20257424	C₂	1	2	yes	maximal, complemented
2	#20256373	C₂	1	1	yes	maximal, characteristic, complemented
3	D₈×Dic₉₄	C₂	1	1	yes	maximal, characteristic, complemented
4	#20256101	C₂	1	2	yes	maximal, complemented
5	#20255781	C₂	1	1	yes	maximal, characteristic, complemented
6	#20255777	C₂	1	1	yes	maximal, characteristic, complemented
7	#20255732	C₂	1	1	yes	maximal, characteristic, complemented
8	#20255686	C₂	1	2	yes	maximal, complemented
9	#20255473	C₂	1	2	yes	maximal, complemented
10	#20255469	C₂	1	2	yes	maximal, complemented
11	#20255104	C₂	1	1	yes	maximal, characteristic, complemented
12	#20255073	C₂	1	1	yes	maximal, characteristic, complemented
13	#20254024	C₂	1	1	yes	maximal, characteristic, complemented
14	#20254020	C₂	1	1	yes	maximal, characteristic, complemented
15	#20253969	C₂	1	1	yes	maximal, characteristic, complemented
16	#20253647	C₂	1	2	yes	maximal, complemented
17	#20253643	C₂	1	2	yes	maximal, complemented
18	#20253482	C₂	1	2	yes	maximal, complemented
19	#20252356	C₂	1	1	yes	maximal, characteristic, complemented
20	#20252264	C₂	1	1	yes	maximal, characteristic, complemented
21	#20252258	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂×D₈×Dic₄₇	C₂	1	1	yes	maximal, characteristic, complemented
23	C₄₇×#3280	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#13094043	C₂²	1	1	yes	characteristic
25	#15689842	C₂²	1	2	yes	complemented
26	#15689831	C₂²	1	2	yes	—
27	#15689830	C₂²	1	2	yes	—
28	#15689810	—	2	2	no	—
29	#15689804	—	2	2	no	—
30	#15689799	—	2	2	no	—
31	D₄×Dic₉₄	C₂²	1	2	yes	complemented
32	#15689779	—	2	2	no	—
33	#15689773	C₂²	1	2	yes	complemented
34	#15689772	C₂²	1	2	yes	complemented
35	#15689767	C₂²	1	2	yes	—
36	#15689742	C₂²	1	2	yes	complemented
37	#15689740	C₂²	1	2	yes	complemented
38	#15689718	—	2	2	no	—
39	#15689717	—	2	2	no	—
40	#15689675	C₂²	1	2	yes	—
41	#15689653	C₂²	1	1	yes	characteristic
42	#15689629	—	2	2	no	—
43	C₂×#13094001	—	2	2	no	—
44	#15689606	C₂²	1	2	yes	complemented
45	#15689602	C₂²	1	2	yes	complemented
46	C₂×D₄×Dic₄₇	C₂²	1	2	yes	—
47	#15689528	C₂²	1	1	yes	characteristic, complemented
48	#15689527	C₂²	1	1	yes	characteristic, complemented
49	#15689527	C₂²	1	1	yes	characteristic, complemented
50	#15689506	C₂²	1	1	yes	characteristic
51	#15689501	C₂²	1	1	yes	characteristic, complemented
52	#15689482	C₂²	1	2	yes	complemented
53	#15689481	C₂²	1	2	yes	complemented
54	#15689472	C₂²	1	2	yes	complemented
55	#15689459	C₂²	1	2	yes	—
56	#15689459	C₂²	1	2	yes	complemented
57	#15689457	C₂²	1	2	yes	complemented
58	#15689456	C₂²	1	2	yes	—
59	#15689435	C₂²	1	2	yes	complemented
60	#15689434	C₂²	1	2	yes	complemented
61	#15689419	C₂²	1	2	yes	complemented
62	#15689416	C₂²	1	2	yes	complemented
63	#15689403	C₂²	1	2	yes	complemented
64	#15689401	C₂²	1	2	yes	complemented
65	#15689401	C₂²	1	2	yes	complemented
66	#15689401	C₂²	1	2	yes	complemented
67	#15689367	C₂²	1	2	yes	complemented
68	#15689366	C₂²	1	2	yes	complemented
69	#15689364	C₂²	1	1	yes	characteristic
70	#15689364	C₂²	1	1	yes	characteristic, complemented
71	#15689362	C₂²	1	2	yes	—
72	#15689361	C₂²	1	1	yes	characteristic, complemented
73	#15689356	C₂²	1	1	yes	characteristic
74	#15689343	C₂²	1	2	yes	complemented
75	#15689342	C₂²	1	2	yes	complemented
76	#15689336	C₂²	1	2	yes	—
77	#15689326	C₂²	1	2	yes	complemented
78	#15689326	C₂²	1	2	yes	complemented
79	#15689285	C₂²	1	2	yes	complemented
80	#15689282	C₂²	1	2	yes	complemented
81	#15689274	C₂²	1	2	yes	—
82	#15689265	C₂²	1	2	yes	—
83	#15689252	C₂²	1	1	yes	characteristic, complemented
84	C₈×Dic₉₄	C₂²	1	1	yes	characteristic, complemented
85	#15689224	C₂²	1	2	yes	complemented
86	#15689224	C₂²	1	2	yes	complemented
87	#15689224	C₂²	1	2	yes	complemented
88	#15689223	C₂²	1	2	yes	complemented
89	#15689220	C₂²	1	2	yes	complemented
90	#15689220	C₂²	1	2	yes	complemented
91	C₄×Dic₁₈₈	C₂²	1	1	yes	characteristic, complemented
92	Q₁₆×Dic₄₇	C₂²	1	1	yes	characteristic, complemented
93	Q₁₆×Dic₄₇	C₂²	1	1	yes	characteristic, complemented
94	#15689217	C₂²	1	1	yes	characteristic, complemented
95	#15689215	C₂²	1	2	yes	complemented
96	D₈×Dic₄₇	C₂²	1	1	yes	characteristic
97	D₈×Dic₄₇	C₂²	1	1	yes	characteristic
98	D₈×Dic₄₇	C₂²	1	1	yes	characteristic
99	D₈×Dic₄₇	C₂²	1	2	yes	—
100	D₈×Dic₄₇	C₂²	1	1	yes	characteristic
101	D₈×Dic₄₇	C₂²	1	1	yes	characteristic
102	D₈×Dic₄₇	C₂²	1	2	yes	—
103	#15689198	C₂²	1	1	yes	characteristic, complemented
104	#15689195	C₂²	1	1	yes	characteristic
105	#15689191	C₂²	1	1	yes	characteristic
106	C₈×C₂²⋊D₄₇	C₂²	1	1	yes	characteristic
107	C₈×C₂²⋊D₄₇	C₂²	1	1	yes	characteristic, complemented
108	#15689183	C₂²	1	1	yes	characteristic, complemented
109	#15689181	C₂²	1	1	yes	characteristic, complemented
110	#15689177	C₂²	1	1	yes	characteristic
111	C₂×#13093958	C₂²	1	1	yes	characteristic
112	C₂×#13093958	C₂²	1	1	yes	characteristic, complemented
113	#107×D₄₇	C₂²	1	1	yes	characteristic, complemented
114	#15689124	C₂²	1	2	yes	complemented
115	#15689121	C₂²	1	2	yes	complemented
116	C₂×#13093945	C₂²	1	2	yes	—
117	#15689078	C₂²	1	1	yes	characteristic, complemented
118	#15689077	C₂²	1	1	yes	characteristic, complemented
119	C₂×C₈×Dic₄₇	C₂²	1	1	yes	characteristic
120	C₂×#135×C₄₇	C₂²	1	1	yes	characteristic
121	C₂²×D₈×C₄₇	C₂²	1	1	yes	characteristic
122	C₄₇×#546	C₂²	1	2	yes	—
123	C₄₇×#495	C₂²	1	1	yes	characteristic
124	C₄₇×#467	C₂²	1	1	yes	characteristic
125	C₄₇×#466	C₂²	1	1	yes	characteristic
126	C₄₇×#463	C₂²	1	2	yes	—
127	C₄₇×#450	C₂²	1	2	yes	—
128	C₄₇×#449	C₂²	1	2	yes	—
129	C₄×D₈×C₄₇	C₂²	1	1	yes	characteristic
130	C₈×D₄×C₄₇	C₂²	1	1	yes	characteristic
131	C₂×#10625352	—	2	2	no	—
132	C₂×#10625352	C₂³	1	2	yes	—
133	C₂²×Dic₉₄	—	2	2	no	—
134	C₂³×Dic₄₇	—	2	2	no	—
135	#13094043	—	2	4	no	—
136	C₂×Dic₁₈₈	C₂³	1	1	yes	characteristic
137	C₂×#10625337	C₂³	1	2	yes	—
138	C₂×#10625335	C₂³	1	2	yes	—
139	C₂×#10625335	C₂³	1	2	yes	—
140	C₂×#10625329	C₂³	1	1	yes	characteristic
141	C₂×#10625324	C₂³	1	1	yes	characteristic
142	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
143	C₂×C₈×D₄₇	C₂³	1	1	yes	characteristic
144	#13094024	C₂³	1	2	yes	—
145	#13094023	C₂³	1	2	yes	—
146	#13094023	C₂³	1	2	yes	—
147	#13094022	C₂³	1	2	yes	—
148	#13094019	D₄	1	1	yes	characteristic
149	#13094017	—	2	2	no	—
150	#13094017	—	2	2	no	—
151	#13094017	—	2	2	no	—
152	#13094017	—	2	2	no	—
153	#13094017	D₄	1	1	yes	characteristic
154	#13094015	—	2	2	no	—
155	#13094014	—	2	2	no	—
156	#13094014	—	2	2	no	—
157	#13094014	D₄	1	1	yes	characteristic
158	#13094011	—	2	2	no	—
159	#13094011	C₂³	1	2	yes	—
160	#13094010	—	2	2	no	—
161	#13094010	D₄	1	1	yes	characteristic
162	#13094008	—	2	2	no	—
163	#13094008	D₄	1	1	yes	characteristic
164	#13094007	—	2	2	no	—
165	#13094006	—	2	2	no	—
166	#13094005	—	2	2	no	—
167	#13094005	—	2	2	no	—
168	#13094005	—	2	2	no	—
169	#13094005	—	2	2	no	—
170	#13094005	D₄	1	1	yes	characteristic
171	#13094004	—	2	2	no	—
172	#13094003	—	2	2	no	—
173	#13094003	C₂³	1	2	yes	—
174	#13094003	C₂³	1	2	yes	—
175	#13094001	—	2	2	no	—
176	#13094001	—	2	2	no	—
177	#13094001	—	2	2	no	—
178	#13094001	—	2	2	no	—
179	#13094001	—	2	2	no	—
180	#13094001	—	2	2	no	—
181	#13094001	—	2	2	no	—
182	#13094001	—	2	2	no	—
183	#13094001	—	2	2	no	—
184	#13094001	—	2	2	no	—
185	#13094001	D₄	1	1	yes	characteristic
186	#13094000	C₂³	1	2	yes	—
187	#13093996	—	2	2	no	—
188	#13093996	—	2	2	no	—
189	#13093996	D₄	1	1	yes	characteristic
190	#13093995	C₂³	1	2	yes	—
191	#13093993	—	2	2	no	—
192	Q₈×Dic₄₇	C₂³	1	2	yes	—
193	Q₈×Dic₄₇	C₂³	1	2	yes	—
194	C₄×Dic₉₄	C₂³	1	2	yes	—
195	C₄×Dic₉₄	C₂³	1	1	yes	characteristic
196	#13093989	—	2	2	no	—
197	#13093989	C₂³	1	2	yes	—
198	D₄×Dic₄₇	—	2	2	no	—
199	D₄×Dic₄₇	—	2	2	no	—
200	D₄×Dic₄₇	—	2	2	no	—
201	D₄×Dic₄₇	—	2	2	no	—
202	D₄×Dic₄₇	—	2	2	no	—
203	D₄×Dic₄₇	C₂³	1	2	yes	—
204	D₄×Dic₄₇	C₂³	1	2	yes	—
205	D₄×Dic₄₇	C₂³	1	2	yes	—
206	D₄×Dic₄₇	C₂³	1	2	yes	—
207	D₄×Dic₄₇	C₂³	1	2	yes	—
208	C₄×C₂²⋊D₄₇	—	2	2	no	—
209	C₄×C₂²⋊D₄₇	C₂³	1	1	yes	characteristic
210	C₄×C₂²⋊D₄₇	C₂³	1	1	yes	characteristic
211	(C₂²⋊D₄₇)⋊C₄	—	2	2	no	—
212	(C₂²⋊D₄₇)⋊C₄	—	2	2	no	—
213	#13093983	—	2	2	no	—
214	#13093983	C₂³	1	1	yes	characteristic
215	#13093981	C₂³	1	1	yes	characteristic
216	#13093980	—	2	2	no	—
217	#13093980	—	2	2	no	—
218	#13093980	—	2	2	no	—
219	C₂×C₄⋊Dic₄₇	—	2	2	no	—
220	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
221	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
222	C₂×Dic₄₇⋊C₄	—	2	2	no	—
223	C₂×Dic₄₇⋊C₄	—	2	2	no	—
224	C₄⋊C₄×D₄₇	C₂³	1	2	yes	—
225	C₂×C₂²⋊Dic₄₇	—	2	2	no	—
226	C₂×C₂²⋊Dic₄₇	—	2	2	no	—
227	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
228	#13093958	C₂³	1	1	yes	characteristic
229	#13093958	C₂³	1	1	yes	characteristic
230	#13093958	C₂³	1	2	yes	—
231	#13093958	C₂³	1	2	yes	—
232	#13093958	C₂³	1	1	yes	characteristic
233	#13093958	C₂³	1	2	yes	—
234	#13093957	C₂³	1	2	yes	—
235	#13093957	C₂³	1	2	yes	—
236	#13093957	C₂³	1	2	yes	—
237	C₄⋊(C₄₇⋊C₈)	C₂³	1	1	yes	characteristic
238	Dic₄₇⋊C₈	C₂³	1	1	yes	characteristic
239	Dic₄₇⋊C₈	C₂³	1	1	yes	characteristic
240	Dic₄₇⋊C₈	C₂³	1	1	yes	characteristic
241	Dic₄₇⋊C₈	C₂³	1	1	yes	characteristic
242	#13093949	C₂³	1	2	yes	—
243	#13093949	C₂³	1	2	yes	—
244	#13093949	C₂³	1	2	yes	—
245	#13093948	C₂³	1	2	yes	—
246	#13093948	C₂³	1	2	yes	—
247	#13093948	C₂³	1	2	yes	—
248	#13093947	C₂³	1	2	yes	—
249	#13093945	C₂³	1	2	yes	—
250	#13093945	C₂³	1	2	yes	—
251	#13093945	C₂³	1	2	yes	—
252	#13093945	C₂³	1	2	yes	—
253	#13093945	C₂³	1	2	yes	—
254	#13093945	C₂³	1	2	yes	—
255	C₂²⋊(C₄₇⋊C₈)	C₂³	1	1	yes	characteristic
256	C₂²⋊(C₄₇⋊C₈)	C₂³	1	1	yes	characteristic
257	(C₂×D₄₇)⋊C₈	C₂³	1	1	yes	characteristic
258	(C₂×D₄₇)⋊C₈	C₂³	1	1	yes	characteristic
259	#13093935	C₂³	1	1	yes	characteristic
260	#13093934	C₂³	1	1	yes	characteristic
261	#13093934	C₂³	1	1	yes	characteristic
262	#13093934	C₂³	1	1	yes	characteristic
263	C₈×Dic₄₇	C₂³	1	1	yes	characteristic
264	C₈×Dic₄₇	C₂³	1	1	yes	characteristic
265	C₈×Dic₄₇	C₂³	1	1	yes	characteristic
266	C₈×Dic₄₇	C₂³	1	1	yes	characteristic
267	C₈×Dic₄₇	C₂³	1	1	yes	characteristic
268	C₂×#41×C₄₇	C₂³	1	2	yes	—
269	C₂²×D₄×C₄₇	C₂³	1	2	yes	—
270	#135×C₄₇	—	2	4	no	—
271	C₂×Q₁₆×C₄₇	C₂³	1	1	yes	characteristic
272	C₂×SD₁₆×C₄₇	C₂³	1	2	yes	—
273	C₂×SD₁₆×C₄₇	C₂³	1	2	yes	—
274	C₂×D₈×C₄₇	—	2	4	no	—
275	C₂×D₈×C₄₇	C₂³	1	2	yes	—
276	C₂×D₈×C₄₇	C₂³	1	1	yes	characteristic
277	C₂×D₈×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	#124×C₄₇	C₂³	1	2	yes	—
281	#123×C₄₇	—	2	2	no	—
282	C₂²⋊Q₈×C₄₇	C₂³	1	2	yes	—
283	#121×C₄₇	—	2	2	no	—
284	#121×C₄₇	C₂³	1	2	yes	—
285	#120×C₄₇	—	2	2	no	—
286	C₄×D₄×C₄₇	C₂³	1	2	yes	—
287	C₄×D₄×C₄₇	C₂³	1	1	yes	characteristic
288	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
289	#107×C₄₇	C₂³	1	1	yes	characteristic
290	C₄⋊C₈×C₄₇	C₂³	1	1	yes	characteristic
291	#103×C₄₇	C₂³	1	2	yes	—
292	#102×C₄₇	C₂³	1	2	yes	—
293	#102×C₄₇	C₂³	1	2	yes	—
294	C₂²⋊C₈×C₄₇	C₂³	1	1	yes	characteristic
295	C₂²⋊C₈×C₄₇	C₂³	1	1	yes	characteristic
296	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
297	C₂⁴×C₄₇	—	2	2	no	—
298	#41×C₄₇	—	2	4	no	—
299	#41×C₄₇	—	4	2	no	—
300	C₂×Q₈×C₄₇	C₂⁴	1	2	yes	—
301	C₂×D₄×C₄₇	—	2	4	no	—
302	C₂×D₄×C₄₇	—	2	2	no	—
303	C₂×D₄×C₄₇	—	2	2	no	—
304	C₂×D₄×C₄₇	—	2	2	no	—
305	C₂×D₄×C₄₇	—	4	2	no	—
306	C₂×D₄×C₄₇	C₂×D₄	1	1	yes	characteristic
307	C₂×D₄×C₄₇	C₂⁴	1	2	yes	—
308	C₂×D₄×C₄₇	C₂⁴	1	2	yes	—
309	C₂²×C₄×C₄₇	—	2	2	no	—
310	C₂²×C₄×C₄₇	—	2	2	no	—
311	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
312	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
313	C₂×C₂²⋊D₄₇	—	2	2	no	—
314	C₂×C₂²⋊D₄₇	—	2	2	no	—
315	C₂×C₂²⋊D₄₇	C₂×D₄	1	1	yes	characteristic
316	C₂×C₂²⋊D₄₇	C₂×D₄	1	1	yes	characteristic
317	C₂²×Dic₄₇	—	2	2	no	—
318	C₂²×Dic₄₇	—	2	2	no	—
319	C₂²×Dic₄₇	—	2	2	no	—
320	C₂²×Dic₄₇	—	2	2	no	—
321	C₂²×Dic₄₇	—	2	2	no	—
322	C₂²×Dic₄₇	—	2	2	no	—
323	C₂²×Dic₄₇	—	2	2	no	—
324	C₂²×Dic₄₇	—	2	2	no	—
325	C₂²×Dic₄₇	—	8	4	no	—
326	C₂²×Dic₄₇	C₂×D₄	1	1	yes	characteristic
327	C₂²×Dic₄₇	C₂×D₄	1	1	yes	characteristic
328	#10625352	—	2	4	no	—
329	#10625352	—	4	2	no	—
330	#10625352	—	8	4	no	—
331	C₂×C₄×D₄₇	—	2	2	no	—
332	C₂×C₄×D₄₇	C₂⁴	1	1	yes	characteristic
333	C₂×Dic₉₄	—	2	2	no	—
334	C₂×Dic₉₄	—	2	2	no	—
335	C₂×Dic₉₄	—	2	2	no	—
336	C₂×Dic₉₄	—	8	4	no	—
337	C₂×Dic₉₄	C₂×D₄	1	1	yes	characteristic
338	C₂×Dic₉₄	C₂⁴	1	2	yes	—
339	Q₁₆×C₄₇	—	2	2	no	—
340	SD₁₆×C₄₇	—	2	4	no	—
341	SD₁₆×C₄₇	—	4	2	no	—
342	D₈×C₄₇	—	2	4	no	—
343	D₈×C₄₇	—	2	2	no	—
344	D₈×C₄₇	#41	1	4	yes	complemented
345	C₂×C₈×C₄₇	—	2	2	no	—
346	C₂×C₈×C₄₇	—	2	2	no	—
347	C₂×C₈×C₄₇	C₂⁴	1	1	yes	characteristic
348	C₂×C₈×C₄₇	C₂⁴	1	1	yes	characteristic
349	C₂×C₈×C₄₇	C₂⁴	1	1	yes	characteristic
350	C₂×C₈×C₄₇	C₂⁴	1	1	yes	characteristic
351	C₄⋊C₄×C₄₇	—	2	2	no	—
352	C₄⋊C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
353	C₄⋊C₄×C₄₇	C₂⁴	1	2	yes	—
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	—	2	2	no	—
358	C₂²⋊C₄×C₄₇	—	2	2	no	—
359	C₂²⋊C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
360	C₂²⋊C₄×C₄₇	C₂×D₄	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	—	2	2	no	—
366	C₂²⋊Dic₄₇	—	2	2	no	—
367	C₂²⋊Dic₄₇	—	2	2	no	—
368	C₂²⋊Dic₄₇	—	2	2	no	—
369	C₂²⋊Dic₄₇	—	2	2	no	—
370	C₂²⋊Dic₄₇	—	2	2	no	—
371	C₂²⋊Dic₄₇	—	2	2	no	—
372	C₂²⋊Dic₄₇	C₂×D₄	1	1	yes	characteristic
373	C₂²⋊Dic₄₇	C₂×D₄	1	1	yes	characteristic
374	C₂²⋊Dic₄₇	C₂×D₄	1	1	yes	characteristic
375	C₂²⋊Dic₄₇	C₂×D₄	1	1	yes	characteristic
376	#10625337	—	4	2	no	—
377	#10625335	—	2	4	no	—
378	#10625335	—	4	2	no	—
379	(C₂×D₄₇)⋊C₄	—	2	2	no	—
380	(C₂×D₄₇)⋊C₄	C₂×D₄	1	1	yes	characteristic
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	C₄⋊Dic₄₇	—	2	2	no	—
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	C₂×D₄	1	1	yes	characteristic
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	C₄⋊Dic₄₇	C₂⁴	1	2	yes	—
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	—	2	2	no	—
403	Dic₄₇⋊C₄	—	2	2	no	—
404	Dic₄₇⋊C₄	—	2	2	no	—
405	Dic₄₇⋊C₄	C₂×D₄	1	1	yes	characteristic
406	Dic₄₇⋊C₄	C₂×D₄	1	1	yes	characteristic
407	Dic₄₇⋊C₄	C₂×D₄	1	1	yes	characteristic
408	Dic₄₇⋊C₄	C₂×D₄	1	1	yes	characteristic
409	Dic₄₇⋊C₄	C₂×D₄	1	1	yes	characteristic
410	Dic₄₇⋊C₄	C₂×D₄	1	1	yes	characteristic
411	C₄×Dic₄₇	—	2	2	no	—
412	C₄×Dic₄₇	—	2	2	no	—
413	C₄×Dic₄₇	—	2	2	no	—
414	C₄×Dic₄₇	—	2	2	no	—
415	C₄×Dic₄₇	C₂×D₄	1	1	yes	characteristic
416	C₄×Dic₄₇	C₂×D₄	1	1	yes	characteristic
417	C₄×Dic₄₇	C₂⁴	1	1	yes	characteristic
418	C₄×Dic₄₇	C₂⁴	1	1	yes	characteristic
419	C₄×Dic₄₇	C₂⁴	1	1	yes	characteristic
420	#10625329	—	4	1	no	—
421	C₂×C₄₇⋊C₈	—	4	1	no	—
422	C₂×C₄₇⋊C₈	C₂⁴	1	1	yes	characteristic
423	C₂×C₄₇⋊C₈	C₂⁴	1	1	yes	characteristic
424	C₂×C₄₇⋊C₈	C₂⁴	1	1	yes	characteristic
425	C₂×C₄₇⋊C₈	C₂⁴	1	1	yes	characteristic
426	Dic₁₈₈	—	2	2	no	—
427	#10625324	—	4	1	no	—
428	C₈×D₄₇	—	2	2	no	—
429	C₂³×C₄₇	—	2	2	no	—
430	C₂³×C₄₇	—	2	2	no	—
431	C₂³×C₄₇	—	4	4	no	—
432	C₂³×C₄₇	—	4	4	no	—
433	C₂³×C₄₇	—	8	2	no	—
434	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
435	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
436	C₂²×D₄₇	C₂²×D₄	1	1	yes	characteristic
437	Q₈×C₄₇	—	2	2	no	—
438	Q₈×C₄₇	—	2	2	no	—
439	D₄×C₄₇	—	2	2	no	—
440	D₄×C₄₇	—	2	2	no	—
441	D₄×C₄₇	—	2	2	no	—
442	D₄×C₄₇	—	2	2	no	—
443	D₄×C₄₇	—	4	4	no	—
444	D₄×C₄₇	—	4	4	no	—
445	D₄×C₄₇	—	8	2	no	—
446	D₄×C₄₇	C₂×#41	1	4	yes	—
447	C₂×C₄×C₄₇	—	2	1	no	—
448	C₂×C₄×C₄₇	—	2	1	no	—
449	C₂×C₄×C₄₇	—	2	1	no	—
450	C₂×C₄×C₄₇	—	2	1	no	—
451	C₂×C₄×C₄₇	—	2	2	no	—
452	C₂×C₄×C₄₇	—	2	2	no	—
453	C₂×C₄×C₄₇	—	4	4	no	—
454	C₂×C₄×C₄₇	—	8	2	no	—
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	—	2	2	no	—
461	C₂²⋊D₄₇	—	2	2	no	—
462	C₂²⋊D₄₇	—	4	4	no	—
463	C₂²⋊D₄₇	—	8	2	no	—
464	C₂×Dic₄₇	—	2	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	—	2	2	no	—
470	C₂×Dic₄₇	—	4	4	no	—
471	C₂×Dic₄₇	—	4	4	no	—
472	C₂×Dic₄₇	—	4	4	no	—
473	C₂×Dic₄₇	—	8	2	no	—
474	C₂×Dic₄₇	—	8	2	no	—
475	C₂×Dic₄₇	—	8	2	no	—
476	C₂×Dic₄₇	—	8	2	no	—
477	C₂×Dic₄₇	—	8	2	no	—
478	C₂×Dic₄₇	C₂²×D₄	1	1	yes	characteristic
479	C₂×Dic₄₇	C₂²×D₄	1	1	yes	characteristic
480	C₂×Dic₄₇	C₂²×D₄	1	1	yes	characteristic
481	C₂×Dic₄₇	C₂²×D₄	1	1	yes	characteristic
482	C₂×Dic₄₇	C₂²×D₄	1	1	yes	characteristic
483	C₂×Dic₄₇	C₂²×D₄	1	1	yes	characteristic
484	C₂×Dic₄₇	C₂²×D₄	1	1	yes	characteristic
485	C₄×D₄₇	—	2	1	no	—
486	C₄×D₄₇	—	2	1	no	—
487	C₄×D₄₇	—	8	2	no	—
488	Dic₉₄	—	2	2	no	—
489	Dic₉₄	—	2	2	no	—
490	Dic₉₄	—	2	2	no	—
491	Dic₉₄	—	4	4	no	—
492	Dic₉₄	—	8	2	no	—
493	Dic₉₄	—	8	2	no	—
494	C₈×C₄₇	—	2	1	no	—
495	C₈×C₄₇	—	2	1	no	—
496	C₈×C₄₇	—	2	1	no	—
497	C₈×C₄₇	C₂×#41	1	2	yes	—
498	C₄₇⋊C₈	—	2	1	no	—
499	C₄₇⋊C₈	—	2	1	no	—
500	C₄₇⋊C₈	—	2	1	no	—
501	C₄₇⋊C₈	—	2	1	no	—
502	#61482	—	47	1	no	maximal, Sylow
503	C₂²×C₄₇	—	2	1	no	—
504	C₂²×C₄₇	—	2	1	no	—
505	C₂²×C₄₇	—	2	4	no	—
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	—	4	2	no	—
513	C₂²×C₄₇	—	4	2	no	—
514	C₂²×C₄₇	—	8	8	no	—
515	C₂²×C₄₇	#578	1	2	yes	—
516	C₂²×C₄₇	C₂³×D₄	1	1	yes	characteristic
517	C₂×D₄₇	—	2	1	no	—
518	C₂×D₄₇	—	2	1	no	—
519	C₂×D₄₇	—	2	1	no	—
520	C₄×C₄₇	—	2	1	no	—
521	C₄×C₄₇	—	2	1	no	—
522	C₄×C₄₇	—	2	1	no	—
523	C₄×C₄₇	—	2	1	no	—
524	C₄×C₄₇	—	4	2	no	—
525	C₄×C₄₇	—	4	2	no	—
526	C₄×C₄₇	C₂²×#41	1	1	yes	characteristic
527	C₄×C₄₇	#585	1	1	yes	characteristic
528	Dic₄₇	—	2	1	no	—
529	Dic₄₇	—	2	1	no	—
530	Dic₄₇	—	2	1	no	—
531	Dic₄₇	—	2	1	no	—
532	Dic₄₇	—	2	1	no	—
533	Dic₄₇	—	2	1	no	—
534	Dic₄₇	—	4	2	no	—
535	Dic₄₇	—	4	2	no	—
536	Dic₄₇	—	4	2	no	—
537	Dic₄₇	—	4	2	no	—
538	Dic₄₇	#576	1	2	yes	—
539	#3520	—	47	2	no	—
540	#3393	—	47	1	no	—
541	Q₈×D₈	—	47	1	no	—
542	#3367	—	47	2	no	—
543	#3338	—	47	1	no	—
544	#3338	—	47	1	no	—
545	#3334	—	47	1	no	—
546	#3330	—	47	2	no	—
547	#3314	—	47	2	no	—
548	#3314	—	47	2	no	—
549	#3283	—	47	1	no	—
550	#3280	—	47	1	no	—
551	#3280	D₄₇	1	1	yes	characteristic, complemented
552	#3175	—	47	1	no	—
553	#3175	—	47	1	no	—
554	#3170	—	47	1	no	—
555	#3124	—	47	2	no	—
556	#3124	—	47	2	no	—
557	#3110	—	47	2	no	—
558	#2966	—	47	1	no	—
559	#2951	—	47	1	no	—
560	#2951	—	47	1	no	—
561	C₂×C₄×D₈	—	47	1	no	—
562	C₂×C₄₇	—	2	2	no	—
563	C₂×C₄₇	—	4	1	no	—
564	C₂×C₄₇	—	4	4	no	—
565	C₂×C₄₇	—	8	2	no	—
566	C₂×C₄₇	D₄×#41	1	1	yes	characteristic
567	C₂×C₄₇	C₂×#576	1	1	yes	characteristic
568	C₂×C₄₇	C₂×#578	1	1	yes	characteristic
569	D₄₇	—	4	1	no	—
570	C₂×#135	—	47	1	no	—
571	C₂×#135	C₂×D₄₇	1	1	yes	characteristic
572	C₂²×D₈	C₂×D₄₇	1	1	yes	characteristic
573	#556	—	47	2	no	—
574	#554	—	47	2	no	—
575	#554	—	47	2	no	—
576	#552	—	94	2	no	—
577	#551	—	94	2	no	—
578	#551	—	94	2	no	—
579	D₄×Q₈	—	47	2	no	—
580	#548	—	94	2	no	—
581	#547	—	47	2	no	—
582	#547	—	47	2	no	—
583	#546	—	47	2	no	—
584	#546	C₂×D₄₇	1	2	yes	—
585	#542	—	47	2	no	—
586	#542	—	47	2	no	—
587	#539	—	94	2	no	—
588	#539	—	94	2	no	—
589	#533	—	47	2	no	—
590	#529	—	47	1	no	—
591	#525	—	94	2	no	—
592	C₂×C₂²⋊Q₈	—	94	2	no	—
593	#520	—	47	2	no	—
594	#520	—	47	2	no	—
595	C₂×C₄×D₄	—	47	2	no	—
596	#500	—	47	1	no	—
597	#500	—	47	1	no	—
598	#500	—	47	1	no	—
599	#495	—	47	1	no	—
600	#495	C₂×D₄₇	1	1	yes	characteristic
601	#494	—	47	1	no	—
602	#489	—	47	2	no	—
603	#489	—	47	2	no	—
604	#487	—	47	2	no	—
605	#484	—	47	2	no	—
606	#484	—	47	2	no	—
607	#484	—	47	2	no	—
608	#484	—	47	2	no	—
609	#480	—	47	2	no	—
610	#480	—	47	2	no	—
611	#477	—	47	2	no	—
612	#477	—	47	2	no	—
613	#474	—	47	2	no	—
614	#474	—	47	2	no	—
615	#474	—	47	2	no	—
616	#474	—	47	2	no	—
617	#468	—	47	2	no	—
618	#468	—	47	2	no	—
619	#467	—	47	1	no	—
620	#467	—	47	1	no	—
621	#467	—	47	1	no	—
622	#467	—	47	2	no	—
623	#467	C₂×D₄₇	1	1	yes	characteristic
624	#466	—	47	1	no	—
625	#466	C₂×D₄₇	1	1	yes	characteristic
626	#464	—	47	2	no	—
627	#464	—	47	2	no	—
628	#463	—	47	2	no	—
629	#463	C₂×D₄₇	1	2	yes	—
630	#461	—	47	2	no	—
631	#461	—	47	2	no	—
632	#452	—	47	2	no	—
633	#452	—	47	2	no	—
634	#450	—	47	2	no	—
635	#450	C₂×D₄₇	1	2	yes	—
636	#449	—	47	2	no	—
637	#449	C₂×D₄₇	1	2	yes	—
638	#446	—	47	1	no	—
639	C₈×Q₈	—	47	1	no	—
640	#440	—	47	2	no	—
641	#440	—	47	2	no	—
642	#440	—	47	2	no	—
643	#440	—	47	2	no	—
644	#440	—	47	2	no	—
645	#440	—	47	2	no	—
646	C₄×Q₁₆	—	47	1	no	—
647	C₄×Q₁₆	—	47	1	no	—
648	C₄×Q₁₆	—	47	1	no	—
649	C₄×Q₁₆	—	47	2	no	—
650	C₄×Q₁₆	—	47	1	no	—
651	C₄×D₈	—	47	2	no	—
652	C₄×D₈	—	47	1	no	—
653	C₄×D₈	—	47	1	no	—
654	C₄×D₈	—	47	1	no	—
655	C₄×D₈	—	47	2	no	—
656	C₄×D₈	—	47	1	no	—
657	C₄×D₈	—	47	1	no	—
658	C₄×D₈	C₂×D₄₇	1	1	yes	characteristic
659	#436	—	47	1	no	—
660	#435	—	47	1	no	—
661	#435	—	47	1	no	—
662	C₈×D₄	—	47	1	no	—
663	C₈×D₄	—	47	1	no	—
664	C₈×D₄	C₂×D₄₇	1	1	yes	characteristic
665	#433	—	47	1	no	—
666	#433	—	47	1	no	—
667	#432	—	47	1	no	—
668	C₂×#107	—	47	1	no	—
669	C₂×#107	—	47	1	no	—
670	C₂×#107	—	47	1	no	—
671	#417	—	47	2	no	—
672	#417	—	47	2	no	—
673	C₂×#102	—	47	2	no	—
674	#405	—	47	1	no	—
675	#405	—	47	1	no	—
676	C₂×C₄×C₈	—	47	1	no	—
677	C₄₇	#61482	1	1	yes	characteristic, complemented, Sylow
678	C₂×#41	—	47	2	no	—
679	C₂×#41	—	94	2	no	—
680	C₂×#41	C₂²×D₄₇	1	2	yes	—
681	C₂²×Q₈	—	94	2	no	—
682	C₂²×D₄	C₂²×D₄₇	1	2	yes	—
683	C₂³×C₄	—	94	2	no	—
684	#135	—	2	4	no	—
685	#135	—	94	4	no	—
686	C₂×Q₁₆	—	47	2	no	—
687	C₂×Q₁₆	—	47	1	no	—
688	C₂×Q₁₆	C₂²×D₄₇	1	1	yes	characteristic
689	C₂×SD₁₆	—	47	2	no	—
690	C₂×SD₁₆	—	47	2	no	—
691	C₂×SD₁₆	C₂²×D₄₇	1	2	yes	—
692	C₂×SD₁₆	C₂²×D₄₇	1	2	yes	—
693	C₂×D₈	—	2	4	no	—
694	C₂×D₈	C₂²×D₄₇	1	2	yes	—
695	C₂×D₈	C₂²×D₄₇	1	1	yes	characteristic
696	C₂×D₈	C₂²×D₄₇	1	1	yes	characteristic
697	C₂×M₁₆	—	47	1	no	—
698	C₂×M₁₆	—	47	1	no	—
699	C₂²×C₈	—	47	1	no	—
700	C₂²×C₈	—	47	1	no	—
701	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
702	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
703	C₄⋊Q₈	—	47	2	no	—
704	C₄⋊Q₈	—	47	2	no	—
705	C₄⋊Q₈	—	47	2	no	—
706	C₄⋊Q₈	—	47	2	no	—
707	#126	—	47	1	no	—
708	#126	—	47	1	no	—
709	#126	—	94	2	no	—
710	#126	—	94	2	no	—
711	#126	—	94	2	no	—
712	#126	—	94	2	no	—
713	#125	—	47	1	no	—
714	#125	—	94	2	no	—
715	#125	—	94	2	no	—
716	#125	—	94	2	no	—
717	#124	—	47	1	no	—
718	#124	—	47	2	no	—
719	#124	—	94	2	no	—
720	#124	—	94	2	no	—
721	#124	C₂²×D₄₇	1	2	yes	—
722	#123	—	2	2	no	—
723	#123	—	47	1	no	—
724	#123	—	47	1	no	—
725	#123	—	94	2	no	—
726	#123	—	94	2	no	—
727	#123	—	94	2	no	—
728	#123	—	94	2	no	—
729	#123	—	94	2	no	—
730	#123	—	94	2	no	—
731	#123	—	94	2	no	—
732	C₂²⋊Q₈	—	47	1	no	—
733	C₂²⋊Q₈	—	47	2	no	—
734	C₂²⋊Q₈	—	47	2	no	—
735	C₂²⋊Q₈	—	47	2	no	—
736	C₂²⋊Q₈	—	94	2	no	—
737	C₂²⋊Q₈	—	94	2	no	—
738	C₂²⋊Q₈	—	94	2	no	—
739	C₂²⋊Q₈	—	94	2	no	—
740	C₂²⋊Q₈	—	94	2	no	—
741	C₂²⋊Q₈	—	94	2	no	—
742	C₂²⋊Q₈	—	94	2	no	—
743	C₂²⋊Q₈	—	94	2	no	—
744	C₂²⋊Q₈	—	94	2	no	—
745	C₂²⋊Q₈	—	94	2	no	—
746	C₂²⋊Q₈	—	94	2	no	—
747	C₂²⋊Q₈	—	94	2	no	—
748	C₂²⋊Q₈	C₂²×D₄₇	1	2	yes	—
749	#121	—	2	2	no	—
750	#121	—	47	1	no	—
751	#121	—	47	2	no	—
752	#121	—	94	2	no	—
753	#121	—	94	2	no	—
754	#121	C₂²×D₄₇	1	2	yes	—
755	#120	—	2	2	no	—
756	#120	—	94	2	no	—
757	C₄×Q₈	—	47	1	no	—
758	C₄×Q₈	—	47	2	no	—
759	C₄×Q₈	—	47	2	no	—
760	C₄×Q₈	—	47	2	no	—
761	C₄×Q₈	—	47	2	no	—
762	C₄×Q₈	—	94	2	no	—
763	C₄×D₄	—	47	1	no	—
764	C₄×D₄	—	47	1	no	—
765	C₄×D₄	—	47	2	no	—
766	C₄×D₄	—	47	2	no	—
767	C₄×D₄	—	47	2	no	—
768	C₄×D₄	—	47	2	no	—
769	C₄×D₄	—	47	2	no	—
770	C₄×D₄	—	94	2	no	—
771	C₄×D₄	—	94	2	no	—
772	C₄×D₄	—	94	2	no	—
773	C₄×D₄	—	94	2	no	—
774	C₄×D₄	—	94	2	no	—
775	C₄×D₄	—	94	2	no	—
776	C₄×D₄	—	94	2	no	—
777	C₄×D₄	—	94	2	no	—
778	C₄×D₄	C₂²×D₄₇	1	2	yes	—
779	C₄×D₄	C₂²×D₄₇	1	1	yes	characteristic
780	#117	—	47	1	no	—
781	#117	—	47	1	no	—
782	#117	—	94	2	no	—
783	#117	—	94	2	no	—
784	#117	—	94	2	no	—
785	#117	—	94	2	no	—
786	C₂×C₄⋊C₄	—	47	2	no	—
787	C₂×C₄⋊C₄	—	47	2	no	—
788	C₂×C₄⋊C₄	—	47	2	no	—
789	C₂×C₄⋊C₄	—	94	2	no	—
790	C₂×C₄⋊C₄	—	94	2	no	—
791	C₂×C₄⋊C₄	—	94	2	no	—
792	C₂×C₂²⋊C₄	—	2	2	no	—
793	C₂×C₂²⋊C₄	—	94	2	no	—
794	C₂×C₂²⋊C₄	—	94	2	no	—
795	C₂×C₄²	—	47	1	no	—
796	#107	—	47	1	no	—
797	#107	—	47	1	no	—
798	#107	—	47	2	no	—
799	#107	—	47	1	no	—
800	#107	—	47	2	no	—
801	#107	—	47	2	no	—
802	#107	—	47	2	no	—
803	#107	—	47	2	no	—
804	#107	—	47	2	no	—
805	#107	C₂²×D₄₇	1	1	yes	characteristic
806	C₄⋊C₈	—	47	1	no	—
807	C₄⋊C₈	—	47	1	no	—
808	C₄⋊C₈	—	47	1	no	—
809	C₄⋊C₈	—	47	1	no	—
810	C₄⋊C₈	—	47	1	no	—
811	C₄⋊C₈	C₂²×D₄₇	1	1	yes	characteristic
812	#103	—	47	2	no	—
813	#103	—	47	2	no	—
814	#103	—	47	2	no	—
815	#103	—	47	2	no	—
816	#103	—	47	2	no	—
817	#103	—	47	2	no	—
818	#103	—	47	2	no	—
819	#103	C₂²×D₄₇	1	2	yes	—
820	#102	—	47	2	no	—
821	#102	—	47	2	no	—
822	#102	—	47	2	no	—
823	#102	—	47	2	no	—
824	#102	—	47	2	no	—
825	#102	—	47	2	no	—
826	#102	C₂²×D₄₇	1	2	yes	—
827	#102	C₂²×D₄₇	1	2	yes	—
828	C₂²⋊C₈	—	47	1	no	—
829	C₂²⋊C₈	—	47	1	no	—
830	C₂²⋊C₈	—	47	1	no	—
831	C₂²⋊C₈	—	47	1	no	—
832	C₂²⋊C₈	C₂²×D₄₇	1	1	yes	characteristic
833	C₂²⋊C₈	C₂²×D₄₇	1	1	yes	characteristic
834	#97	—	47	1	no	—
835	#97	—	47	1	no	—
836	#97	—	47	1	no	—
837	#97	—	47	1	no	—
838	C₄×C₈	—	47	1	no	—
839	C₄×C₈	—	47	1	no	—
840	C₄×C₈	—	47	1	no	—
841	C₄×C₈	—	47	1	no	—
842	C₄×C₈	—	47	1	no	—
843	C₄×C₈	C₂²×D₄₇	1	1	yes	characteristic
844	C₂⁴	—	2	2	no	—
845	#41	—	2	4	no	—
846	#41	—	4	2	no	—
847	#41	—	94	4	no	—
848	#41	—	376	4	no	—
849	#41	—	188	2	no	—
850	C₂×Q₈	—	47	1	no	—
851	C₂×Q₈	—	47	2	no	—
852	C₂×Q₈	—	94	2	no	—
853	C₂×Q₈	—	94	2	no	—
854	C₂×Q₈	—	94	2	no	—
855	C₂×Q₈	—	376	4	no	—
856	C₂×Q₈	C₂³×D₄₇	1	2	yes	—
857	C₂×D₄	—	2	4	no	—
858	C₂×D₄	—	2	2	no	—
859	C₂×D₄	—	2	2	no	—
860	C₂×D₄	—	2	2	no	—
861	C₂×D₄	—	4	2	no	—
862	C₂×D₄	—	47	1	no	—
863	C₂×D₄	—	47	1	no	—
864	C₂×D₄	—	94	2	no	—
865	C₂×D₄	—	94	2	no	—
866	C₂×D₄	D₄×D₄₇	1	1	yes	characteristic
867	C₂×D₄	C₂³×D₄₇	1	2	yes	—
868	C₂×D₄	C₂³×D₄₇	1	2	yes	—
869	C₂²×C₄	—	2	2	no	—
870	C₂²×C₄	—	2	2	no	—
871	C₂²×C₄	—	47	1	no	—
872	C₂²×C₄	—	47	1	no	—
873	C₂²×C₄	—	47	1	no	—
874	C₂²×C₄	—	94	2	no	—
875	C₂²×C₄	—	94	2	no	—
876	C₂²×C₄	—	94	2	no	—
877	C₂²×C₄	—	94	2	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	—	376	4	no	—
884	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
885	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
886	Q₁₆	—	2	2	no	—
887	Q₁₆	—	94	2	no	—
888	Q₁₆	—	188	2	no	—
889	SD₁₆	—	2	4	no	—
890	SD₁₆	—	4	2	no	—
891	SD₁₆	—	94	4	no	—
892	SD₁₆	—	188	2	no	—
893	D₈	—	2	4	no	—
894	D₈	—	2	2	no	—
895	D₈	#10625352	1	4	yes	complemented
896	M₁₆	—	188	1	no	—
897	M₁₆	—	188	1	no	—
898	C₂×C₈	—	2	2	no	—
899	C₂×C₈	—	2	2	no	—
900	C₂×C₈	—	47	1	no	—
901	C₂×C₈	—	47	1	no	—
902	C₂×C₈	—	47	1	no	—
903	C₂×C₈	—	47	1	no	—
904	C₂×C₈	—	94	2	no	—
905	C₂×C₈	—	188	1	no	—
906	C₂×C₈	C₂³×D₄₇	1	1	yes	characteristic
907	C₂×C₈	C₂³×D₄₇	1	1	yes	characteristic
908	C₂×C₈	C₂³×D₄₇	1	1	yes	characteristic
909	C₂×C₈	C₂³×D₄₇	1	1	yes	characteristic
910	C₄⋊C₄	—	2	2	no	—
911	C₄⋊C₄	—	47	1	no	—
912	C₄⋊C₄	—	47	1	no	—
913	C₄⋊C₄	—	47	1	no	—
914	C₄⋊C₄	—	47	1	no	—
915	C₄⋊C₄	—	47	1	no	—
916	C₄⋊C₄	—	47	1	no	—
917	C₄⋊C₄	—	47	1	no	—
918	C₄⋊C₄	—	47	1	no	—
919	C₄⋊C₄	—	47	1	no	—
920	C₄⋊C₄	—	47	2	no	—
921	C₄⋊C₄	—	47	2	no	—
922	C₄⋊C₄	—	47	2	no	—
923	C₄⋊C₄	—	94	2	no	—
924	C₄⋊C₄	—	94	2	no	—
925	C₄⋊C₄	—	94	2	no	—
926	C₄⋊C₄	—	94	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	D₄×D₄₇	1	1	yes	characteristic
939	C₄⋊C₄	C₂³×D₄₇	1	2	yes	—
940	C₂²⋊C₄	—	2	2	no	—
941	C₂²⋊C₄	—	2	2	no	—
942	C₂²⋊C₄	—	2	2	no	—
943	C₂²⋊C₄	—	2	2	no	—
944	C₂²⋊C₄	—	2	2	no	—
945	C₂²⋊C₄	—	47	1	no	—
946	C₂²⋊C₄	—	47	1	no	—
947	C₂²⋊C₄	—	47	1	no	—
948	C₂²⋊C₄	—	47	1	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	—	94	2	no	—
954	C₂²⋊C₄	—	94	2	no	—
955	C₂²⋊C₄	—	94	2	no	—
956	C₂²⋊C₄	—	94	2	no	—
957	C₂²⋊C₄	—	94	2	no	—
958	C₂²⋊C₄	—	94	2	no	—
959	C₂²⋊C₄	—	94	2	no	—
960	C₂²⋊C₄	—	94	2	no	—
961	C₂²⋊C₄	—	94	2	no	—
962	C₂²⋊C₄	—	94	2	no	—
963	C₂²⋊C₄	—	94	2	no	—
964	C₂²⋊C₄	D₄×D₄₇	1	1	yes	characteristic
965	C₂²⋊C₄	D₄×D₄₇	1	1	yes	characteristic
966	C₄²	—	47	1	no	—
967	C₄²	—	47	1	no	—
968	C₄²	—	47	1	no	—
969	C₄²	—	47	1	no	—
970	C₄²	—	47	1	no	—
971	C₄²	—	94	2	no	—
972	C₄²	—	94	2	no	—
973	C₄²	—	94	2	no	—
974	C₄²	—	94	2	no	—
975	C₄²	C₂³×D₄₇	1	1	yes	characteristic
976	C₂³	—	2	2	no	—
977	C₂³	—	2	2	no	—
978	C₂³	—	4	4	no	—
979	C₂³	—	4	4	no	—
980	C₂³	—	8	2	no	—
981	C₂³	—	47	1	no	—
982	C₂³	C₂×D₄×D₄₇	1	1	yes	characteristic
983	C₂³	C₂×D₄×D₄₇	1	1	yes	characteristic
984	Q₈	—	2	2	no	—
985	Q₈	—	2	2	no	—
986	Q₈	—	94	2	no	—
987	Q₈	—	94	2	no	—
988	Q₈	—	94	2	no	—
989	Q₈	—	376	2	no	—
990	Q₈	—	376	2	no	—
991	Q₈	—	188	4	no	—
992	D₄	—	2	2	no	—
993	D₄	—	2	2	no	—
994	D₄	—	2	2	no	—
995	D₄	—	2	2	no	—
996	D₄	—	4	4	no	—
997	D₄	—	4	4	no	—
998	D₄	—	8	2	no	—
999	D₄	—	94	2	no	—
1000	D₄	—	94	2	no	—
1001	D₄	—	376	2	no	—
1002	D₄	—	188	4	no	—
1003	D₄	C₂×#10625352	1	4	yes	—
1004	C₂×C₄	—	2	1	no	—
1005	C₂×C₄	—	2	1	no	—
1006	C₂×C₄	—	2	1	no	—
1007	C₂×C₄	—	2	1	no	—
1008	C₂×C₄	—	2	2	no	—
1009	C₂×C₄	—	2	2	no	—
1010	C₂×C₄	—	4	4	no	—
1011	C₂×C₄	—	8	2	no	—
1012	C₂×C₄	—	47	1	no	—
1013	C₂×C₄	—	47	1	no	—
1014	C₂×C₄	—	47	1	no	—
1015	C₂×C₄	—	47	1	no	—
1016	C₂×C₄	—	47	1	no	—
1017	C₂×C₄	—	47	1	no	—
1018	C₂×C₄	—	47	1	no	—
1019	C₂×C₄	—	94	2	no	—
1020	C₂×C₄	—	94	2	no	—
1021	C₂×C₄	—	94	1	no	—
1022	C₂×C₄	—	94	1	no	—
1023	C₂×C₄	—	94	2	no	—
1024	C₂×C₄	—	94	2	no	—
1025	C₂×C₄	—	94	2	no	—
1026	C₂×C₄	—	94	2	no	—
1027	C₂×C₄	—	376	2	no	—
1028	C₂×C₄	—	376	2	no	—
1029	C₂×C₄	—	376	2	no	—
1030	C₂×C₄	—	376	2	no	—
1031	C₂×C₄	—	376	2	no	—
1032	C₂×C₄	—	376	2	no	—
1033	C₂×C₄	—	188	4	no	—
1034	C₂×C₄	—	188	4	no	—
1035	C₂×C₄	—	188	4	no	—
1036	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
1037	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
1038	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
1039	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
1040	C₂×C₄	C₂⁴×D₄₇	1	1	yes	characteristic
1041	C₈	—	2	1	no	—
1042	C₈	—	2	1	no	—
1043	C₈	—	2	1	no	—
1044	C₈	—	94	1	no	—
1045	C₈	—	94	1	no	—
1046	C₈	—	94	1	no	—
1047	C₈	—	94	1	no	—
1048	C₈	C₂×#10625352	1	2	yes	—
1049	C₂²	—	2	1	no	—
1050	C₂²	—	2	1	no	—
1051	C₂²	—	2	1	no	—
1052	C₂²	—	2	1	no	—
1053	C₂²	—	2	4	no	—
1054	C₂²	—	2	1	no	—
1055	C₂²	—	4	2	no	—
1056	C₂²	—	4	2	no	—
1057	C₂²	—	4	2	no	—
1058	C₂²	—	4	2	no	—
1059	C₂²	—	4	2	no	—
1060	C₂²	—	8	8	no	—
1061	C₂²	—	94	1	no	—
1062	C₂²	—	94	1	no	—
1063	C₂²	—	94	1	no	—
1064	C₂²	#15689937	1	2	yes	—
1065	C₂²	C₂²×D₄×D₄₇	1	1	yes	characteristic
1066	C₄	—	2	1	no	—
1067	C₄	—	2	1	no	—
1068	C₄	—	2	1	no	—
1069	C₄	—	2	1	no	—
1070	C₄	—	4	2	no	—
1071	C₄	—	4	2	no	—
1072	C₄	—	47	2	no	—
1073	C₄	—	94	1	no	—
1074	C₄	—	94	1	no	—
1075	C₄	—	94	1	no	—
1076	C₄	—	94	1	no	—
1077	C₄	—	94	1	no	—
1078	C₄	—	94	1	no	—
1079	C₄	—	188	2	no	—
1080	C₄	—	188	2	no	—
1081	C₄	—	188	2	no	—
1082	C₄	—	188	2	no	—
1083	C₄	C₂²×#10625352	1	1	yes	characteristic
1084	C₄	#15689958	1	1	yes	characteristic
1085	C₂	—	2	2	no	—
1086	C₂	—	4	1	no	—
1087	C₂	—	4	4	no	—
1088	C₂	—	8	2	no	—
1089	C₂	—	188	1	no	—
1090	C₂	D₄×#10625352	1	1	yes	characteristic
1091	C₂	#576×D₄₇	1	1	yes	characteristic
1092	C₂	C₂×#15689937	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×#3280	C₂
socle	C₂²×C₄₇	C₂³×D₄
hypercenter	#3280	D₄₇
hypocenter	C₄₇	#61482
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₄×D₄ ◁ #3280

Complements

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

N	H ≅ G/N	type
1. #20257424	C₂	semidirect
2. #20256373	C₂	semidirect
3. D₈×Dic₉₄	C₂	semidirect
4. #20256101	C₂	semidirect
5. #20255781	C₂	semidirect
6. #20255777	C₂	semidirect
7. #20255732	C₂	semidirect
8. #20255686	C₂	semidirect
9. #20255473	C₂	semidirect
10. #20255469	C₂	semidirect
11. #20255104	C₂	semidirect
12. #20255073	C₂	semidirect
13. #20254024	C₂	semidirect
14. #20254020	C₂	semidirect
15. #20253969	C₂	semidirect
16. #20253647	C₂	semidirect
17. #20253643	C₂	semidirect
18. #20253482	C₂	semidirect
19. #20252356	C₂	semidirect
20. #20252264	C₂	semidirect
21. #20252258	C₂	semidirect
22. C₂×D₈×Dic₄₇	C₂	semidirect
23. C₄₇×#3280	C₂	semidirect
25. #15689842	C₂²	semidirect
31. D₄×Dic₉₄	C₂²	semidirect
33. #15689773	C₂²	semidirect
34. #15689772	C₂²	semidirect
36. #15689742	C₂²	semidirect
37. #15689740	C₂²	semidirect
44. #15689606	C₂²	semidirect
45. #15689602	C₂²	semidirect
47. #15689528	C₂²	semidirect
48. #15689527	C₂²	semidirect
49. #15689527	C₂²	semidirect
51. #15689501	C₂²	semidirect
52. #15689482	C₂²	semidirect
53. #15689481	C₂²	semidirect
54. #15689472	C₂²	semidirect
56. #15689459	C₂²	semidirect
57. #15689457	C₂²	semidirect
59. #15689435	C₂²	semidirect
60. #15689434	C₂²	semidirect
61. #15689419	C₂²	semidirect
62. #15689416	C₂²	semidirect
63. #15689403	C₂²	semidirect
64. #15689401	C₂²	semidirect
65. #15689401	C₂²	semidirect
66. #15689401	C₂²	semidirect
67. #15689367	C₂²	semidirect
68. #15689366	C₂²	semidirect
70. #15689364	C₂²	semidirect
72. #15689361	C₂²	semidirect
74. #15689343	C₂²	semidirect
75. #15689342	C₂²	semidirect
77. #15689326	C₂²	semidirect
78. #15689326	C₂²	semidirect
79. #15689285	C₂²	semidirect
80. #15689282	C₂²	semidirect
83. #15689252	C₂²	semidirect
84. C₈×Dic₉₄	C₂²	semidirect
85. #15689224	C₂²	semidirect
86. #15689224	C₂²	semidirect
87. #15689224	C₂²	semidirect
88. #15689223	C₂²	semidirect
89. #15689220	C₂²	semidirect
90. #15689220	C₂²	semidirect
91. C₄×Dic₁₈₈	C₂²	semidirect
92. Q₁₆×Dic₄₇	C₂²	semidirect
93. Q₁₆×Dic₄₇	C₂²	semidirect
94. #15689217	C₂²	semidirect
95. #15689215	C₂²	semidirect
103. #15689198	C₂²	semidirect
107. C₈×C₂²⋊D₄₇	C₂²	semidirect
108. #15689183	C₂²	semidirect
109. #15689181	C₂²	semidirect
112. C₂×#13093958	C₂²	semidirect
113. #107×D₄₇	C₂²	semidirect
114. #15689124	C₂²	semidirect
115. #15689121	C₂²	semidirect
117. #15689078	C₂²	semidirect
118. #15689077	C₂²	semidirect
344. D₈×C₄₇	#41	semidirect
551. #3280	D₄₇	semidirect
677. C₄₇	#61482	semidirect
895. D₈	#10625352	semidirect

Maximal subgroups

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

subgroup	index
#20257424	2
#20256373	2
D₈×Dic₉₄	2
#20256101	2
#20255781	2
#20255777	2
#20255732	2
#20255686	2
#20255473	2
#20255469	2
#20255104	2
#20255073	2
#20254024	2
#20254020	2
#20253969	2
#20253647	2
#20253643	2
#20253482	2
#20252356	2
#20252264	2
#20252258	2
C₂×D₈×Dic₄₇	2
C₄₇×#3280	2
#61482	47