Subgroups — #27098917

Order 12032.

1750 conjugacy classes of subgroups.

The subgroup lattice has 1046 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20257475	C₂	1	2	yes	maximal
2	#20256392	C₂	1	1	yes	maximal, characteristic, complemented
3	#20256279	C₂	1	1	yes	maximal, characteristic, complemented
4	#20256186	C₂	1	2	yes	maximal, complemented
5	#20255815	C₂	1	1	yes	maximal, characteristic, complemented
6	#20255759	C₂	1	1	yes	maximal, characteristic, complemented
7	#20255757	C₂	1	1	yes	maximal, characteristic, complemented
8	#20255664	C₂	1	2	yes	maximal, complemented
9	#20255443	C₂	1	2	yes	maximal, complemented
10	#20255439	C₂	1	2	yes	maximal, complemented
11	Q₁₆×C₂²⋊D₄₇	C₂	1	1	yes	maximal, characteristic, complemented
12	Q₁₆×C₂²⋊D₄₇	C₂	1	1	yes	maximal, characteristic, complemented
13	#20254044	C₂	1	1	yes	maximal, characteristic, complemented
14	#20254040	C₂	1	1	yes	maximal, characteristic, complemented
15	#20253969	C₂	1	1	yes	maximal, characteristic, complemented
16	#20253686	C₂	1	2	yes	maximal, complemented
17	#20253682	C₂	1	2	yes	maximal, complemented
18	#20253513	C₂	1	2	yes	maximal, complemented
19	#20252356	C₂	1	1	yes	maximal, characteristic
20	#20252256	C₂	1	1	yes	maximal, characteristic, complemented
21	#20252251	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂×Q₁₆×Dic₄₇	C₂	1	1	yes	maximal, characteristic, complemented
23	D₄×Q₁₆×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×Q₁₆×D₄₇	C₂²	1	1	yes	characteristic
25	#15689849	C₂²	1	2	yes	—
26	#15689848	—	2	2	no	—
27	#15689848	C₂²	1	2	yes	—
28	#15689844	—	2	2	no	—
29	#15689844	C₂²	1	2	yes	—
30	#15689815	—	2	2	no	—
31	#15689815	C₂²	1	2	yes	—
32	#15689813	—	2	2	no	—
33	#15689813	C₂²	1	2	yes	—
34	Q₈×C₂²⋊D₄₇	C₂²	1	2	yes	—
35	Q₈×C₂²⋊D₄₇	C₂²	1	2	yes	—
36	#15689734	—	2	2	no	—
37	#15689734	C₂²	1	2	yes	—
38	#15689733	—	2	2	no	—
39	#15689733	C₂²	1	2	yes	—
40	#15689675	—	2	2	no	—
41	#15689675	C₂²	1	2	yes	—
42	#15689653	—	2	2	no	—
43	#15689653	C₂²	1	1	yes	characteristic
44	#15689601	C₂²	1	2	yes	—
45	#15689599	C₂²	1	2	yes	—
46	C₂×Q₈×Dic₄₇	C₂²	1	2	yes	—
47	#15689527	C₂²	1	1	yes	characteristic
48	#15689525	C₂²	1	1	yes	characteristic
49	#15689524	C₂²	1	1	yes	characteristic
50	#15689501	C₂²	1	1	yes	characteristic
51	#15689501	C₂²	1	1	yes	characteristic
52	#15689491	C₂²	1	2	yes	—
53	#15689490	C₂²	1	2	yes	—
54	#15689472	C₂²	1	2	yes	—
55	#15689465	C₂²	1	2	yes	—
56	#15689463	C₂²	1	2	yes	—
57	#15689462	C₂²	1	2	yes	—
58	#15689461	C₂²	1	2	yes	—
59	#15689454	C₂²	1	2	yes	—
60	#15689451	C₂²	1	2	yes	—
61	#15689432	C₂²	1	2	yes	—
62	#15689431	C₂²	1	2	yes	—
63	#15689430	C₂²	1	2	yes	—
64	#15689428	C₂²	1	2	yes	—
65	#15689406	C₂²	1	2	yes	—
66	#15689406	C₂²	1	2	yes	—
67	#15689379	C₂²	1	2	yes	—
68	#15689378	C₂²	1	2	yes	—
69	#15689364	C₂²	1	1	yes	characteristic
70	#15689364	C₂²	1	1	yes	characteristic
71	#15689362	C₂²	1	2	yes	—
72	#15689361	C₂²	1	1	yes	characteristic
73	#15689361	C₂²	1	1	yes	characteristic
74	#15689331	C₂²	1	2	yes	—
75	#15689331	C₂²	1	2	yes	—
76	#15689331	C₂²	1	2	yes	—
77	#15689331	C₂²	1	2	yes	—
78	#15689330	C₂²	1	2	yes	—
79	#15689279	C₂²	1	2	yes	—
80	#15689279	C₂²	1	2	yes	—
81	#15689277	C₂²	1	2	yes	—
82	#15689277	C₂²	1	2	yes	—
83	#15689252	C₂²	1	1	yes	characteristic
84	C₈×Dic₉₄	C₂²	1	1	yes	characteristic
85	#15689230	C₂²	1	2	yes	—
86	#15689230	C₂²	1	2	yes	—
87	#15689230	C₂²	1	2	yes	—
88	#15689228	C₂²	1	2	yes	—
89	#15689227	C₂²	1	2	yes	—
90	#15689227	C₂²	1	2	yes	—
91	C₄×Dic₁₈₈	C₂²	1	1	yes	characteristic
92	Q₁₆×Dic₄₇	C₂²	1	1	yes	characteristic
93	Q₁₆×Dic₄₇	C₂²	1	1	yes	characteristic
94	Q₁₆×Dic₄₇	C₂²	1	1	yes	characteristic
95	Q₁₆×Dic₄₇	C₂²	1	1	yes	characteristic
96	Q₁₆×Dic₄₇	C₂²	1	1	yes	characteristic
97	Q₁₆×Dic₄₇	C₂²	1	1	yes	characteristic
98	Q₁₆×Dic₄₇	C₂²	1	1	yes	characteristic
99	Q₁₆×Dic₄₇	C₂²	1	2	yes	—
100	Q₁₆×Dic₄₇	C₂²	1	2	yes	—
101	#15689217	C₂²	1	1	yes	characteristic
102	#15689215	C₂²	1	2	yes	—
103	#15689198	C₂²	1	1	yes	characteristic
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
108	#15689183	C₂²	1	1	yes	characteristic
109	#15689181	C₂²	1	1	yes	characteristic
110	#15689177	C₂²	1	1	yes	characteristic
111	#15689161	C₂²	1	1	yes	characteristic
112	#15689160	C₂²	1	1	yes	characteristic
113	C₂×#13093958	C₂²	1	1	yes	characteristic
114	#15689132	C₂²	1	2	yes	—
115	#15689130	C₂²	1	2	yes	—
116	C₂×#13093948	C₂²	1	2	yes	—
117	#15689078	C₂²	1	1	yes	characteristic
118	#15689077	C₂²	1	1	yes	characteristic
119	C₂×C₈×Dic₄₇	C₂²	1	1	yes	characteristic
120	C₂²×Q₁₆×C₄₇	C₂²	1	1	yes	characteristic
121	C₂²×Q₁₆×C₄₇	C₂²	1	1	yes	characteristic
122	D₄×Q₈×C₄₇	C₂²	1	2	yes	—
123	C₄₇×#494	C₂²	1	1	yes	characteristic
124	C₄₇×#467	C₂²	1	1	yes	characteristic
125	C₄₇×#467	C₂²	1	1	yes	characteristic
126	C₄₇×#462	C₂²	1	2	yes	—
127	C₄₇×#451	C₂²	1	2	yes	—
128	C₄₇×#451	C₂²	1	2	yes	—
129	C₄×Q₁₆×C₄₇	C₂²	1	1	yes	characteristic
130	C₈×D₄×C₄₇	C₂²	1	1	yes	characteristic
131	C₂×Q₈×D₄₇	C₂³	1	2	yes	—
132	C₂×Dic₁₈₈	C₂³	1	1	yes	characteristic
133	C₂×#10625337	C₂³	1	2	yes	—
134	C₂×#10625337	C₂³	1	2	yes	—
135	C₂×#10625337	C₂³	1	2	yes	—
136	Q₁₆×D₄₇	—	2	4	no	—
137	C₂×#10625329	C₂³	1	1	yes	characteristic
138	C₂×#10625324	C₂³	1	1	yes	characteristic
139	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
140	C₂×C₈×D₄₇	C₂³	1	1	yes	characteristic
141	#13094023	—	2	2	no	—
142	#13094023	C₂³	1	2	yes	—
143	#13094022	—	2	2	no	—
144	#13094022	—	2	2	no	—
145	#13094022	C₂³	1	2	yes	—
146	#13094022	C₂³	1	2	yes	—
147	#13094019	—	2	2	no	—
148	#13094019	—	2	2	no	—
149	#13094019	—	2	2	no	—
150	#13094019	—	2	2	no	—
151	#13094019	D₄	1	1	yes	characteristic
152	#13094017	—	2	2	no	—
153	#13094017	—	2	2	no	—
154	#13094017	—	2	2	no	—
155	#13094017	—	2	2	no	—
156	#13094017	D₄	1	1	yes	characteristic
157	#13094016	—	2	2	no	—
158	#13094016	C₂³	1	2	yes	—
159	#13094015	—	2	2	no	—
160	#13094015	—	2	2	no	—
161	#13094015	—	2	2	no	—
162	#13094015	—	2	2	no	—
163	#13094015	C₂³	1	2	yes	—
164	#13094014	—	2	2	no	—
165	#13094014	—	2	2	no	—
166	#13094014	—	2	2	no	—
167	#13094014	—	2	2	no	—
168	#13094014	—	2	2	no	—
169	#13094014	—	2	2	no	—
170	#13094014	—	2	2	no	—
171	#13094014	D₄	1	1	yes	characteristic
172	#13094010	—	2	2	no	—
173	#13094010	D₄	1	1	yes	characteristic
174	#13094008	—	2	2	no	—
175	#13094008	D₄	1	1	yes	characteristic
176	#13094005	—	2	2	no	—
177	#13094005	D₄	1	1	yes	characteristic
178	#13094003	—	2	2	no	—
179	#13094003	—	2	2	no	—
180	#13094003	C₂³	1	2	yes	—
181	#13094003	C₂³	1	2	yes	—
182	#13094001	—	2	2	no	—
183	#13094001	D₄	1	1	yes	characteristic
184	#13094000	—	2	2	no	—
185	#13094000	—	2	2	no	—
186	#13094000	C₂³	1	2	yes	—
187	#13094000	C₂³	1	2	yes	—
188	#13093996	D₄	1	1	yes	characteristic
189	Q₈×Dic₄₇	—	2	2	no	—
190	Q₈×Dic₄₇	—	2	2	no	—
191	Q₈×Dic₄₇	—	2	2	no	—
192	Q₈×Dic₄₇	—	2	2	no	—
193	Q₈×Dic₄₇	C₂³	1	2	yes	—
194	Q₈×Dic₄₇	C₂³	1	2	yes	—
195	Q₈×Dic₄₇	C₂³	1	2	yes	—
196	Q₈×Dic₄₇	C₂³	1	2	yes	—
197	Q₈×Dic₄₇	C₂³	1	2	yes	—
198	Q₈×Dic₄₇	C₂³	1	2	yes	—
199	Q₈×Dic₄₇	C₂³	1	2	yes	—
200	C₄×Dic₉₄	—	2	2	no	—
201	C₄×Dic₉₄	—	2	2	no	—
202	C₄×Dic₉₄	C₂³	1	2	yes	—
203	C₄×Dic₉₄	C₂³	1	1	yes	characteristic
204	#13093989	—	2	2	no	—
205	#13093989	—	2	2	no	—
206	#13093989	—	2	2	no	—
207	#13093989	—	2	2	no	—
208	#13093989	C₂³	1	2	yes	—
209	C₄×C₂²⋊D₄₇	—	2	2	no	—
210	C₄×C₂²⋊D₄₇	—	2	2	no	—
211	C₄×C₂²⋊D₄₇	C₂³	1	1	yes	characteristic
212	C₄×C₂²⋊D₄₇	C₂³	1	1	yes	characteristic
213	#13093983	—	2	2	no	—
214	#13093983	—	2	2	no	—
215	#13093983	C₂³	1	2	yes	—
216	#13093983	C₂³	1	1	yes	characteristic
217	#13093982	—	2	2	no	—
218	#13093982	C₂³	1	2	yes	—
219	#13093981	—	2	2	no	—
220	#13093981	C₂³	1	1	yes	characteristic
221	#13093980	—	2	2	no	—
222	#13093980	—	2	2	no	—
223	#13093980	—	2	2	no	—
224	C₂×C₄⋊Dic₄₇	—	2	2	no	—
225	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
226	C₂×C₄×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	1	yes	characteristic
231	#13093958	C₂³	1	2	yes	—
232	#13093957	C₂³	1	2	yes	—
233	#13093956	C₂³	1	2	yes	—
234	#13093956	C₂³	1	2	yes	—
235	#13093955	C₂³	1	2	yes	—
236	#13093955	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	#13093948	C₂³	1	2	yes	—
249	#13093948	C₂³	1	2	yes	—
250	#13093948	C₂³	1	2	yes	—
251	#13093948	C₂³	1	2	yes	—
252	#13093948	C₂³	1	2	yes	—
253	#13093948	C₂³	1	2	yes	—
254	#13093947	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	C₂²×Q₈×C₄₇	C₂³	1	2	yes	—
269	C₂²×Q₈×C₄₇	C₂³	1	2	yes	—
270	C₂×Q₁₆×C₄₇	—	2	4	no	—
271	C₂×Q₁₆×C₄₇	—	2	4	no	—
272	C₂×Q₁₆×C₄₇	C₂³	1	2	yes	—
273	C₂×Q₁₆×C₄₇	C₂³	1	2	yes	—
274	C₂×Q₁₆×C₄₇	C₂³	1	1	yes	characteristic
275	C₂×Q₁₆×C₄₇	C₂³	1	1	yes	characteristic
276	C₂×Q₁₆×C₄₇	C₂³	1	2	yes	—
277	C₂×Q₁₆×C₄₇	C₂³	1	1	yes	characteristic
278	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
279	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
280	C₄⋊Q₈×C₄₇	—	2	2	no	—
281	C₄⋊Q₈×C₄₇	C₂³	1	2	yes	—
282	C₂²⋊Q₈×C₄₇	—	2	2	no	—
283	C₂²⋊Q₈×C₄₇	—	2	2	no	—
284	C₂²⋊Q₈×C₄₇	C₂³	1	2	yes	—
285	C₂²⋊Q₈×C₄₇	C₂³	1	2	yes	—
286	C₄×Q₈×C₄₇	C₂³	1	2	yes	—
287	C₄×D₄×C₄₇	—	2	2	no	—
288	C₄×D₄×C₄₇	C₂³	1	1	yes	characteristic
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	#103×C₄₇	C₂³	1	2	yes	—
293	#103×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	C₂×Q₈×C₄₇	—	2	2	no	—
298	C₂×Q₈×C₄₇	—	2	2	no	—
299	C₂×Q₈×C₄₇	—	2	4	no	—
300	C₂×Q₈×C₄₇	—	2	4	no	—
301	C₂×Q₈×C₄₇	—	4	2	no	—
302	C₂×Q₈×C₄₇	—	4	2	no	—
303	C₂×Q₈×C₄₇	C₂⁴	1	2	yes	—
304	C₂×Q₈×C₄₇	C₂⁴	1	2	yes	—
305	C₂×Q₈×C₄₇	C₂⁴	1	2	yes	—
306	C₂×D₄×C₄₇	C₂×D₄	1	1	yes	characteristic
307	C₂²×C₄×C₄₇	—	2	2	no	—
308	C₂²×C₄×C₄₇	—	2	2	no	—
309	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
310	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
311	C₂×C₂²⋊D₄₇	C₂×D₄	1	1	yes	characteristic
312	C₂×C₂²⋊D₄₇	C₂×D₄	1	1	yes	characteristic
313	C₂²×Dic₄₇	—	2	2	no	—
314	C₂²×Dic₄₇	C₂×D₄	1	1	yes	characteristic
315	C₂²×Dic₄₇	C₂×D₄	1	1	yes	characteristic
316	Q₈×D₄₇	—	2	4	no	—
317	Q₈×D₄₇	—	4	2	no	—
318	C₂×C₄×D₄₇	—	2	2	no	—
319	C₂×C₄×D₄₇	C₂⁴	1	1	yes	characteristic
320	C₂×Dic₉₄	—	2	2	no	—
321	C₂×Dic₉₄	—	2	2	no	—
322	C₂×Dic₉₄	C₂×D₄	1	1	yes	characteristic
323	C₂×Dic₉₄	C₂⁴	1	2	yes	—
324	Q₁₆×C₄₇	—	2	4	no	—
325	Q₁₆×C₄₇	—	2	4	no	—
326	Q₁₆×C₄₇	—	2	2	no	—
327	Q₁₆×C₄₇	—	2	2	no	—
328	Q₁₆×C₄₇	—	4	2	no	—
329	Q₁₆×C₄₇	#41	1	4	yes	—
330	C₂×C₈×C₄₇	—	2	2	no	—
331	C₂×C₈×C₄₇	—	2	2	no	—
332	C₂×C₈×C₄₇	C₂⁴	1	1	yes	characteristic
333	C₂×C₈×C₄₇	C₂⁴	1	1	yes	characteristic
334	C₂×C₈×C₄₇	C₂⁴	1	1	yes	characteristic
335	C₂×C₈×C₄₇	C₂⁴	1	1	yes	characteristic
336	C₄⋊C₄×C₄₇	—	2	2	no	—
337	C₄⋊C₄×C₄₇	—	2	2	no	—
338	C₄⋊C₄×C₄₇	—	2	2	no	—
339	C₄⋊C₄×C₄₇	—	2	2	no	—
340	C₄⋊C₄×C₄₇	—	2	2	no	—
341	C₄⋊C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
342	C₄⋊C₄×C₄₇	C₂⁴	1	2	yes	—
343	C₂²⋊C₄×C₄₇	—	2	2	no	—
344	C₂²⋊C₄×C₄₇	—	2	2	no	—
345	C₂²⋊C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
346	C₂²⋊C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
347	C₄²×C₄₇	—	2	2	no	—
348	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
349	C₂²⋊Dic₄₇	—	2	2	no	—
350	C₂²⋊Dic₄₇	—	2	2	no	—
351	C₂²⋊Dic₄₇	—	2	2	no	—
352	C₂²⋊Dic₄₇	C₂×D₄	1	1	yes	characteristic
353	C₂²⋊Dic₄₇	C₂×D₄	1	1	yes	characteristic
354	C₂²⋊Dic₄₇	C₂×D₄	1	1	yes	characteristic
355	C₂²⋊Dic₄₇	C₂×D₄	1	1	yes	characteristic
356	#10625337	—	2	4	no	—
357	#10625337	—	4	2	no	—
358	#10625337	—	4	2	no	—
359	(C₂×D₄₇)⋊C₄	—	2	2	no	—
360	(C₂×D₄₇)⋊C₄	—	2	2	no	—
361	(C₂×D₄₇)⋊C₄	—	2	2	no	—
362	(C₂×D₄₇)⋊C₄	C₂×D₄	1	1	yes	characteristic
363	(C₂×D₄₇)⋊C₄	C₂×D₄	1	1	yes	characteristic
364	(C₂×D₄₇)⋊C₄	C₂×D₄	1	1	yes	characteristic
365	(C₂×D₄₇)⋊C₄	C₂×D₄	1	1	yes	characteristic
366	C₄⋊Dic₄₇	—	2	2	no	—
367	C₄⋊Dic₄₇	—	2	2	no	—
368	C₄⋊Dic₄₇	—	2	2	no	—
369	C₄⋊Dic₄₇	—	2	2	no	—
370	C₄⋊Dic₄₇	—	2	2	no	—
371	C₄⋊Dic₄₇	—	2	2	no	—
372	C₄⋊Dic₄₇	—	2	2	no	—
373	C₄⋊Dic₄₇	—	2	2	no	—
374	C₄⋊Dic₄₇	—	2	2	no	—
375	C₄⋊Dic₄₇	C₂×D₄	1	1	yes	characteristic
376	C₄⋊Dic₄₇	C₂×D₄	1	1	yes	characteristic
377	C₄⋊Dic₄₇	C₂×D₄	1	1	yes	characteristic
378	C₄⋊Dic₄₇	C₂⁴	1	2	yes	—
379	C₄⋊Dic₄₇	C₂⁴	1	2	yes	—
380	C₄⋊Dic₄₇	C₂⁴	1	2	yes	—
381	Dic₄₇⋊C₄	—	2	2	no	—
382	Dic₄₇⋊C₄	—	2	2	no	—
383	Dic₄₇⋊C₄	—	2	2	no	—
384	Dic₄₇⋊C₄	—	2	2	no	—
385	Dic₄₇⋊C₄	—	2	2	no	—
386	Dic₄₇⋊C₄	—	2	2	no	—
387	Dic₄₇⋊C₄	—	2	2	no	—
388	Dic₄₇⋊C₄	—	2	2	no	—
389	Dic₄₇⋊C₄	—	2	2	no	—
390	Dic₄₇⋊C₄	—	2	2	no	—
391	Dic₄₇⋊C₄	—	2	2	no	—
392	Dic₄₇⋊C₄	—	2	2	no	—
393	Dic₄₇⋊C₄	—	2	2	no	—
394	Dic₄₇⋊C₄	—	2	2	no	—
395	Dic₄₇⋊C₄	C₂×D₄	1	1	yes	characteristic
396	Dic₄₇⋊C₄	C₂×D₄	1	1	yes	characteristic
397	Dic₄₇⋊C₄	C₂×D₄	1	1	yes	characteristic
398	Dic₄₇⋊C₄	C₂×D₄	1	1	yes	characteristic
399	Dic₄₇⋊C₄	C₂×D₄	1	1	yes	characteristic
400	Dic₄₇⋊C₄	C₂×D₄	1	1	yes	characteristic
401	C₄×Dic₄₇	—	2	2	no	—
402	C₄×Dic₄₇	—	2	2	no	—
403	C₄×Dic₄₇	—	2	2	no	—
404	C₄×Dic₄₇	—	2	2	no	—
405	C₄×Dic₄₇	—	2	2	no	—
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	—	2	2	no	—
412	C₄×Dic₄₇	C₂×D₄	1	1	yes	characteristic
413	C₄×Dic₄₇	C₂×D₄	1	1	yes	characteristic
414	C₄×Dic₄₇	C₂⁴	1	1	yes	characteristic
415	C₄×Dic₄₇	C₂⁴	1	1	yes	characteristic
416	C₄×Dic₄₇	C₂⁴	1	1	yes	characteristic
417	#10625329	—	4	1	no	—
418	C₂×C₄₇⋊C₈	—	4	1	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	#10625324	—	4	1	no	—
425	C₈×D₄₇	—	2	2	no	—
426	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
427	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
428	C₂²×D₄₇	C₂²×D₄	1	1	yes	characteristic
429	Q₈×C₄₇	—	2	2	no	—
430	Q₈×C₄₇	—	2	2	no	—
431	Q₈×C₄₇	—	2	2	no	—
432	Q₈×C₄₇	—	2	2	no	—
433	Q₈×C₄₇	—	2	2	no	—
434	Q₈×C₄₇	—	4	4	no	—
435	Q₈×C₄₇	—	4	4	no	—
436	Q₈×C₄₇	C₂×#41	1	4	yes	—
437	D₄×C₄₇	—	2	2	no	—
438	C₂×C₄×C₄₇	—	2	2	no	—
439	C₂×C₄×C₄₇	—	2	1	no	—
440	C₂×C₄×C₄₇	—	2	1	no	—
441	C₂×C₄×C₄₇	—	2	1	no	—
442	C₂×C₄×C₄₇	—	2	1	no	—
443	C₂×C₄×C₄₇	—	2	2	no	—
444	C₂×C₄×C₄₇	—	2	2	no	—
445	C₂×C₄×C₄₇	—	2	2	no	—
446	C₂×C₄×C₄₇	—	4	4	no	—
447	C₂×C₄×C₄₇	—	4	4	no	—
448	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
449	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
450	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
451	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
452	C₂×C₄×C₄₇	C₂⁵	1	1	yes	characteristic
453	C₂²⋊D₄₇	—	2	2	no	—
454	C₂²⋊D₄₇	—	2	2	no	—
455	C₂×Dic₄₇	—	2	2	no	—
456	C₂×Dic₄₇	—	2	2	no	—
457	C₂×Dic₄₇	—	2	2	no	—
458	C₂×Dic₄₇	—	2	2	no	—
459	C₂×Dic₄₇	—	2	2	no	—
460	C₂×Dic₄₇	—	2	2	no	—
461	C₂×Dic₄₇	—	4	4	no	—
462	C₂×Dic₄₇	C₂²×D₄	1	1	yes	characteristic
463	C₂×Dic₄₇	C₂²×D₄	1	1	yes	characteristic
464	C₂×Dic₄₇	C₂²×D₄	1	1	yes	characteristic
465	C₂×Dic₄₇	C₂²×D₄	1	1	yes	characteristic
466	C₂×Dic₄₇	C₂²×D₄	1	1	yes	characteristic
467	C₂×Dic₄₇	C₂²×D₄	1	1	yes	characteristic
468	C₂×Dic₄₇	C₂²×D₄	1	1	yes	characteristic
469	C₄×D₄₇	—	2	1	no	—
470	C₄×D₄₇	—	2	1	no	—
471	C₄×D₄₇	—	4	4	no	—
472	Dic₉₄	—	2	2	no	—
473	Dic₉₄	—	2	2	no	—
474	Dic₉₄	—	2	2	no	—
475	Dic₉₄	—	4	4	no	—
476	Dic₉₄	—	4	4	no	—
477	C₈×C₄₇	—	2	1	no	—
478	C₈×C₄₇	—	2	1	no	—
479	C₈×C₄₇	—	2	1	no	—
480	C₈×C₄₇	C₂×#41	1	2	yes	—
481	C₄₇⋊C₈	—	2	1	no	—
482	C₄₇⋊C₈	—	2	1	no	—
483	C₄₇⋊C₈	—	2	1	no	—
484	C₄₇⋊C₈	—	2	1	no	—
485	#61484	—	47	1	no	maximal, Sylow
486	C₂²×C₄₇	—	2	1	no	—
487	C₂²×C₄₇	—	2	1	no	—
488	C₂²×C₄₇	—	2	1	no	—
489	C₂²×C₄₇	—	2	1	no	—
490	C₂²×C₄₇	—	2	1	no	—
491	C₂²×C₄₇	#578	1	2	yes	—
492	C₂²×C₄₇	C₂³×D₄	1	1	yes	characteristic
493	C₂×D₄₇	—	2	1	no	—
494	C₂×D₄₇	—	2	1	no	—
495	C₂×D₄₇	—	2	1	no	—
496	C₄×C₄₇	—	2	4	no	—
497	C₄×C₄₇	—	2	1	no	—
498	C₄×C₄₇	—	2	1	no	—
499	C₄×C₄₇	—	2	1	no	—
500	C₄×C₄₇	—	2	1	no	—
501	C₄×C₄₇	—	4	2	no	—
502	C₄×C₄₇	—	4	2	no	—
503	C₄×C₄₇	—	4	2	no	—
504	C₄×C₄₇	C₂²×#41	1	1	yes	characteristic
505	C₄×C₄₇	#585	1	1	yes	characteristic
506	Dic₄₇	—	2	1	no	—
507	Dic₄₇	—	2	1	no	—
508	Dic₄₇	—	2	1	no	—
509	Dic₄₇	—	2	1	no	—
510	Dic₄₇	—	2	1	no	—
511	Dic₄₇	—	2	1	no	—
512	Dic₄₇	—	4	2	no	—
513	Dic₄₇	—	4	2	no	—
514	Dic₄₇	—	4	2	no	—
515	Dic₄₇	—	4	2	no	—
516	Dic₄₇	#578	1	2	yes	—
517	#3523	—	47	2	no	—
518	#3395	—	47	1	no	—
519	#3383	—	47	1	no	—
520	#3374	—	47	2	no	—
521	#3342	—	47	1	no	—
522	#3336	—	47	1	no	—
523	#3336	—	47	1	no	—
524	#3328	—	47	2	no	—
525	#3312	—	47	2	no	—
526	#3312	—	47	2	no	—
527	D₄×Q₁₆	—	47	1	no	—
528	D₄×Q₁₆	—	47	1	no	—
529	D₄×Q₁₆	D₄₇	1	1	yes	characteristic, complemented
530	#3177	—	47	1	no	—
531	#3177	—	47	1	no	—
532	#3170	—	47	1	no	—
533	#3127	—	47	2	no	—
534	#3127	—	47	2	no	—
535	#3113	—	47	2	no	—
536	#2966	—	47	1	no	—
537	#2950	—	47	1	no	—
538	#2950	—	47	1	no	—
539	C₂×C₄×Q₁₆	—	47	1	no	—
540	C₂×C₄₇	—	2	2	no	—
541	C₂×C₄₇	—	4	1	no	—
542	C₂×C₄₇	D₄×#41	1	1	yes	characteristic
543	C₂×C₄₇	C₂×#578	1	1	yes	characteristic
544	C₂×C₄₇	C₂×#578	1	1	yes	characteristic
545	D₄₇	—	4	1	no	—
546	C₂²×Q₁₆	—	47	1	no	—
547	C₂²×Q₁₆	C₂×D₄₇	1	1	yes	characteristic
548	C₂²×Q₁₆	C₂×D₄₇	1	1	yes	characteristic
549	#557	—	47	2	no	—
550	#557	—	47	2	no	—
551	#557	—	94	2	no	—
552	#556	—	47	2	no	—
553	#556	—	94	2	no	—
554	#552	—	47	2	no	—
555	#552	—	47	2	no	—
556	#552	—	94	2	no	—
557	#552	—	94	2	no	—
558	D₄×Q₈	—	47	2	no	—
559	D₄×Q₈	—	47	2	no	—
560	D₄×Q₈	C₂×D₄₇	1	2	yes	—
561	#541	—	47	2	no	—
562	#541	—	47	2	no	—
563	#541	—	94	2	no	—
564	#541	—	94	2	no	—
565	#533	—	47	2	no	—
566	#533	—	94	2	no	—
567	#529	—	47	1	no	—
568	#529	—	94	2	no	—
569	#519	—	47	2	no	—
570	#519	—	47	2	no	—
571	C₂×C₄×Q₈	—	47	2	no	—
572	#500	—	47	1	no	—
573	#499	—	47	1	no	—
574	#499	—	47	1	no	—
575	#494	—	47	1	no	—
576	#494	—	47	1	no	—
577	#494	C₂×D₄₇	1	1	yes	characteristic
578	#491	—	47	2	no	—
579	#491	—	47	2	no	—
580	#487	—	47	2	no	—
581	#485	—	47	2	no	—
582	#485	—	47	2	no	—
583	#485	—	47	2	no	—
584	#485	—	47	2	no	—
585	#483	—	47	2	no	—
586	#483	—	47	2	no	—
587	#479	—	47	2	no	—
588	#479	—	47	2	no	—
589	#479	—	47	2	no	—
590	#479	—	47	2	no	—
591	#475	—	47	2	no	—
592	#475	—	47	2	no	—
593	#470	—	47	2	no	—
594	#470	—	47	2	no	—
595	#467	—	47	1	no	—
596	#467	—	47	1	no	—
597	#467	—	47	1	no	—
598	#467	—	47	1	no	—
599	#467	—	47	2	no	—
600	#467	C₂×D₄₇	1	1	yes	characteristic
601	#467	C₂×D₄₇	1	1	yes	characteristic
602	#462	—	47	2	no	—
603	#462	—	47	2	no	—
604	#462	—	47	2	no	—
605	#462	—	47	2	no	—
606	#462	—	47	2	no	—
607	#462	C₂×D₄₇	1	2	yes	—
608	#451	—	47	2	no	—
609	#451	—	47	2	no	—
610	#451	—	47	2	no	—
611	#451	—	47	2	no	—
612	#451	C₂×D₄₇	1	2	yes	—
613	#451	C₂×D₄₇	1	2	yes	—
614	#446	—	47	1	no	—
615	C₈×Q₈	—	47	1	no	—
616	#441	—	47	2	no	—
617	#441	—	47	2	no	—
618	#441	—	47	2	no	—
619	#441	—	47	2	no	—
620	#441	—	47	2	no	—
621	#441	—	47	2	no	—
622	C₄×Q₁₆	—	47	2	no	—
623	C₄×Q₁₆	—	47	1	no	—
624	C₄×Q₁₆	—	47	1	no	—
625	C₄×Q₁₆	—	47	2	no	—
626	C₄×Q₁₆	—	47	1	no	—
627	C₄×Q₁₆	—	47	1	no	—
628	C₄×Q₁₆	—	47	1	no	—
629	C₄×Q₁₆	—	47	1	no	—
630	C₄×Q₁₆	—	47	1	no	—
631	C₄×Q₁₆	—	47	1	no	—
632	C₄×Q₁₆	—	47	2	no	—
633	C₄×Q₁₆	—	47	1	no	—
634	C₄×Q₁₆	C₂×D₄₇	1	1	yes	characteristic
635	#436	—	47	1	no	—
636	#435	—	47	1	no	—
637	#435	—	47	1	no	—
638	C₈×D₄	—	47	1	no	—
639	C₈×D₄	—	47	1	no	—
640	C₈×D₄	C₂×D₄₇	1	1	yes	characteristic
641	#433	—	47	1	no	—
642	#433	—	47	1	no	—
643	#432	—	47	1	no	—
644	#427	—	47	1	no	—
645	#427	—	47	1	no	—
646	C₂×#107	—	47	1	no	—
647	#419	—	47	2	no	—
648	#419	—	47	2	no	—
649	C₂×#103	—	47	2	no	—
650	#405	—	47	1	no	—
651	#405	—	47	1	no	—
652	C₂×C₄×C₈	—	47	1	no	—
653	C₄₇	#61484	1	1	yes	characteristic, complemented, Sylow
654	C₂²×Q₈	—	47	2	no	—
655	C₂²×Q₈	C₂²×D₄₇	1	2	yes	—
656	C₂²×Q₈	C₂²×D₄₇	1	2	yes	—
657	C₂×Q₁₆	—	2	4	no	—
658	C₂×Q₁₆	—	2	4	no	—
659	C₂×Q₁₆	—	47	2	no	—
660	C₂×Q₁₆	—	47	2	no	—
661	C₂×Q₁₆	—	47	2	no	—
662	C₂×Q₁₆	—	47	1	no	—
663	C₂×Q₁₆	—	94	4	no	—
664	C₂×Q₁₆	C₂²×D₄₇	1	2	yes	—
665	C₂×Q₁₆	C₂²×D₄₇	1	1	yes	characteristic
666	C₂×Q₁₆	C₂²×D₄₇	1	1	yes	characteristic
667	C₂×Q₁₆	C₂²×D₄₇	1	2	yes	—
668	C₂×Q₁₆	C₂²×D₄₇	1	2	yes	—
669	C₂×Q₁₆	C₂²×D₄₇	1	1	yes	characteristic
670	C₂×M₁₆	—	47	1	no	—
671	C₂×M₁₆	—	47	1	no	—
672	C₂²×C₈	—	47	1	no	—
673	C₂²×C₈	—	47	1	no	—
674	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
675	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
676	C₄⋊Q₈	—	2	2	no	—
677	C₄⋊Q₈	—	47	2	no	—
678	C₄⋊Q₈	—	47	2	no	—
679	C₄⋊Q₈	—	47	2	no	—
680	C₄⋊Q₈	—	94	2	no	—
681	C₄⋊Q₈	—	94	2	no	—
682	C₄⋊Q₈	—	94	2	no	—
683	C₄⋊Q₈	C₂²×D₄₇	1	2	yes	—
684	#126	—	47	1	no	—
685	#126	—	47	1	no	—
686	#126	—	94	2	no	—
687	#126	—	94	2	no	—
688	#126	—	94	2	no	—
689	#126	—	94	2	no	—
690	#126	—	94	2	no	—
691	#126	—	94	2	no	—
692	#126	—	94	2	no	—
693	#126	—	94	2	no	—
694	#125	—	47	1	no	—
695	#125	—	47	2	no	—
696	#125	—	47	2	no	—
697	#125	—	94	2	no	—
698	#125	—	94	2	no	—
699	#125	—	94	2	no	—
700	#125	—	94	2	no	—
701	#125	—	94	2	no	—
702	#125	—	94	2	no	—
703	#125	—	94	2	no	—
704	#125	—	94	2	no	—
705	#125	—	94	2	no	—
706	#125	—	94	2	no	—
707	#125	—	94	2	no	—
708	#125	—	94	2	no	—
709	#124	—	47	1	no	—
710	#124	—	94	2	no	—
711	#123	—	47	1	no	—
712	#123	—	47	1	no	—
713	#123	—	94	2	no	—
714	#123	—	94	2	no	—
715	C₂²⋊Q₈	—	2	2	no	—
716	C₂²⋊Q₈	—	2	2	no	—
717	C₂²⋊Q₈	—	47	1	no	—
718	C₂²⋊Q₈	—	47	2	no	—
719	C₂²⋊Q₈	—	47	2	no	—
720	C₂²⋊Q₈	—	47	2	no	—
721	C₂²⋊Q₈	—	47	2	no	—
722	C₂²⋊Q₈	—	94	2	no	—
723	C₂²⋊Q₈	—	94	2	no	—
724	C₂²⋊Q₈	—	94	2	no	—
725	C₂²⋊Q₈	—	94	2	no	—
726	C₂²⋊Q₈	—	94	2	no	—
727	C₂²⋊Q₈	C₂²×D₄₇	1	2	yes	—
728	C₂²⋊Q₈	C₂²×D₄₇	1	2	yes	—
729	#121	—	47	1	no	—
730	C₄×Q₈	—	47	1	no	—
731	C₄×Q₈	—	47	2	no	—
732	C₄×Q₈	—	47	2	no	—
733	C₄×Q₈	—	47	2	no	—
734	C₄×Q₈	—	47	2	no	—
735	C₄×Q₈	—	47	2	no	—
736	C₄×Q₈	—	47	2	no	—
737	C₄×Q₈	—	47	2	no	—
738	C₄×Q₈	—	47	2	no	—
739	C₄×Q₈	—	47	2	no	—
740	C₄×Q₈	—	94	2	no	—
741	C₄×Q₈	—	94	2	no	—
742	C₄×Q₈	—	94	2	no	—
743	C₄×Q₈	—	94	2	no	—
744	C₄×Q₈	—	94	2	no	—
745	C₄×Q₈	—	94	2	no	—
746	C₄×Q₈	—	94	2	no	—
747	C₄×Q₈	—	94	2	no	—
748	C₄×Q₈	—	94	2	no	—
749	C₄×Q₈	—	94	2	no	—
750	C₄×Q₈	C₂²×D₄₇	1	2	yes	—
751	C₄×D₄	—	2	2	no	—
752	C₄×D₄	—	47	1	no	—
753	C₄×D₄	—	47	1	no	—
754	C₄×D₄	—	94	2	no	—
755	C₄×D₄	—	94	2	no	—
756	C₄×D₄	C₂²×D₄₇	1	1	yes	characteristic
757	#117	—	47	1	no	—
758	#117	—	47	1	no	—
759	#117	—	47	2	no	—
760	#117	—	47	2	no	—
761	#117	—	94	2	no	—
762	#117	—	94	2	no	—
763	#117	—	94	2	no	—
764	#117	—	94	2	no	—
765	#117	—	94	2	no	—
766	#117	—	94	2	no	—
767	#117	—	94	2	no	—
768	C₂×C₄⋊C₄	—	47	2	no	—
769	C₂×C₄⋊C₄	—	94	2	no	—
770	C₂×C₄²	—	47	1	no	—
771	C₂×C₄²	—	94	2	no	—
772	#107	—	47	1	no	—
773	#107	—	47	1	no	—
774	#107	—	47	2	no	—
775	#107	—	47	1	no	—
776	#107	—	47	2	no	—
777	#107	C₂²×D₄₇	1	1	yes	characteristic
778	#106	—	47	2	no	—
779	#106	—	47	2	no	—
780	#106	—	47	2	no	—
781	#106	—	47	2	no	—
782	C₄⋊C₈	—	47	1	no	—
783	C₄⋊C₈	—	47	1	no	—
784	C₄⋊C₈	—	47	1	no	—
785	C₄⋊C₈	—	47	1	no	—
786	C₄⋊C₈	—	47	1	no	—
787	C₄⋊C₈	C₂²×D₄₇	1	1	yes	characteristic
788	#103	—	47	2	no	—
789	#103	—	47	2	no	—
790	#103	—	47	2	no	—
791	#103	—	47	2	no	—
792	#103	—	47	2	no	—
793	#103	—	47	2	no	—
794	#103	—	47	2	no	—
795	#103	—	47	2	no	—
796	#103	—	47	2	no	—
797	#103	—	47	2	no	—
798	#103	—	47	2	no	—
799	#103	—	47	2	no	—
800	#103	—	47	2	no	—
801	#103	C₂²×D₄₇	1	2	yes	—
802	#103	C₂²×D₄₇	1	2	yes	—
803	#103	C₂²×D₄₇	1	2	yes	—
804	C₂²⋊C₈	—	47	1	no	—
805	C₂²⋊C₈	—	47	1	no	—
806	C₂²⋊C₈	—	47	1	no	—
807	C₂²⋊C₈	—	47	1	no	—
808	C₂²⋊C₈	C₂²×D₄₇	1	1	yes	characteristic
809	C₂²⋊C₈	C₂²×D₄₇	1	1	yes	characteristic
810	#97	—	47	1	no	—
811	#97	—	47	1	no	—
812	#97	—	47	1	no	—
813	#97	—	47	1	no	—
814	C₄×C₈	—	47	1	no	—
815	C₄×C₈	—	47	1	no	—
816	C₄×C₈	—	47	1	no	—
817	C₄×C₈	—	47	1	no	—
818	C₄×C₈	—	47	1	no	—
819	C₄×C₈	C₂²×D₄₇	1	1	yes	characteristic
820	C₂×Q₈	—	2	2	no	—
821	C₂×Q₈	—	2	2	no	—
822	C₂×Q₈	—	2	4	no	—
823	C₂×Q₈	—	2	4	no	—
824	C₂×Q₈	—	4	2	no	—
825	C₂×Q₈	—	4	2	no	—
826	C₂×Q₈	—	47	1	no	—
827	C₂×Q₈	—	47	2	no	—
828	C₂×Q₈	—	94	2	no	—
829	C₂×Q₈	—	94	2	no	—
830	C₂×Q₈	—	94	4	no	—
831	C₂×Q₈	—	188	2	no	—
832	C₂×Q₈	C₂³×D₄₇	1	2	yes	—
833	C₂×Q₈	C₂³×D₄₇	1	2	yes	—
834	C₂×Q₈	C₂³×D₄₇	1	2	yes	—
835	C₂×D₄	—	47	1	no	—
836	C₂×D₄	—	47	1	no	—
837	C₂×D₄	D₄×D₄₇	1	1	yes	characteristic
838	C₂²×C₄	—	2	2	no	—
839	C₂²×C₄	—	2	2	no	—
840	C₂²×C₄	—	47	1	no	—
841	C₂²×C₄	—	47	1	no	—
842	C₂²×C₄	—	47	1	no	—
843	C₂²×C₄	—	94	2	no	—
844	C₂²×C₄	—	94	2	no	—
845	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
846	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
847	Q₁₆	—	2	4	no	—
848	Q₁₆	—	2	4	no	—
849	Q₁₆	—	2	2	no	—
850	Q₁₆	—	2	2	no	—
851	Q₁₆	—	4	2	no	—
852	Q₁₆	—	94	4	no	—
853	Q₁₆	—	94	2	no	—
854	Q₁₆	—	188	2	no	—
855	Q₁₆	—	188	2	no	—
856	Q₁₆	#10625352	1	4	yes	—
857	M₁₆	—	188	1	no	—
858	M₁₆	—	188	1	no	—
859	C₂×C₈	—	2	2	no	—
860	C₂×C₈	—	2	2	no	—
861	C₂×C₈	—	47	1	no	—
862	C₂×C₈	—	47	1	no	—
863	C₂×C₈	—	47	1	no	—
864	C₂×C₈	—	47	1	no	—
865	C₂×C₈	—	94	2	no	—
866	C₂×C₈	—	188	1	no	—
867	C₂×C₈	C₂³×D₄₇	1	1	yes	characteristic
868	C₂×C₈	C₂³×D₄₇	1	1	yes	characteristic
869	C₂×C₈	C₂³×D₄₇	1	1	yes	characteristic
870	C₂×C₈	C₂³×D₄₇	1	1	yes	characteristic
871	C₄⋊C₄	—	2	2	no	—
872	C₄⋊C₄	—	2	2	no	—
873	C₄⋊C₄	—	2	2	no	—
874	C₄⋊C₄	—	2	2	no	—
875	C₄⋊C₄	—	2	2	no	—
876	C₄⋊C₄	—	47	1	no	—
877	C₄⋊C₄	—	47	1	no	—
878	C₄⋊C₄	—	47	1	no	—
879	C₄⋊C₄	—	47	1	no	—
880	C₄⋊C₄	—	47	1	no	—
881	C₄⋊C₄	—	47	1	no	—
882	C₄⋊C₄	—	47	1	no	—
883	C₄⋊C₄	—	47	1	no	—
884	C₄⋊C₄	—	47	1	no	—
885	C₄⋊C₄	—	47	2	no	—
886	C₄⋊C₄	—	47	2	no	—
887	C₄⋊C₄	—	47	2	no	—
888	C₄⋊C₄	—	94	2	no	—
889	C₄⋊C₄	—	94	2	no	—
890	C₄⋊C₄	—	94	2	no	—
891	C₄⋊C₄	—	94	2	no	—
892	C₄⋊C₄	—	94	2	no	—
893	C₄⋊C₄	—	94	2	no	—
894	C₄⋊C₄	—	94	2	no	—
895	C₄⋊C₄	—	94	2	no	—
896	C₄⋊C₄	—	94	2	no	—
897	C₄⋊C₄	—	94	2	no	—
898	C₄⋊C₄	—	94	2	no	—
899	C₄⋊C₄	—	94	2	no	—
900	C₄⋊C₄	—	94	2	no	—
901	C₄⋊C₄	—	94	2	no	—
902	C₄⋊C₄	—	94	2	no	—
903	C₄⋊C₄	—	94	2	no	—
904	C₄⋊C₄	—	94	2	no	—
905	C₄⋊C₄	—	94	2	no	—
906	C₄⋊C₄	—	94	2	no	—
907	C₄⋊C₄	—	94	2	no	—
908	C₄⋊C₄	—	94	2	no	—
909	C₄⋊C₄	—	94	2	no	—
910	C₄⋊C₄	—	94	2	no	—
911	C₄⋊C₄	D₄×D₄₇	1	1	yes	characteristic
912	C₄⋊C₄	C₂³×D₄₇	1	2	yes	—
913	C₂²⋊C₄	—	2	2	no	—
914	C₂²⋊C₄	—	2	2	no	—
915	C₂²⋊C₄	—	47	1	no	—
916	C₂²⋊C₄	—	47	1	no	—
917	C₂²⋊C₄	—	47	1	no	—
918	C₂²⋊C₄	—	47	1	no	—
919	C₂²⋊C₄	—	47	1	no	—
920	C₂²⋊C₄	—	47	1	no	—
921	C₂²⋊C₄	—	47	1	no	—
922	C₂²⋊C₄	—	47	1	no	—
923	C₂²⋊C₄	—	94	2	no	—
924	C₂²⋊C₄	—	94	2	no	—
925	C₂²⋊C₄	—	94	2	no	—
926	C₂²⋊C₄	—	94	2	no	—
927	C₂²⋊C₄	—	94	2	no	—
928	C₂²⋊C₄	—	94	2	no	—
929	C₂²⋊C₄	D₄×D₄₇	1	1	yes	characteristic
930	C₂²⋊C₄	D₄×D₄₇	1	1	yes	characteristic
931	C₄²	—	2	2	no	—
932	C₄²	—	47	1	no	—
933	C₄²	—	47	1	no	—
934	C₄²	—	47	1	no	—
935	C₄²	—	47	1	no	—
936	C₄²	—	47	1	no	—
937	C₄²	—	94	2	no	—
938	C₄²	—	94	2	no	—
939	C₄²	—	94	2	no	—
940	C₄²	—	94	2	no	—
941	C₄²	—	94	2	no	—
942	C₄²	—	94	2	no	—
943	C₄²	—	94	2	no	—
944	C₄²	—	94	2	no	—
945	C₄²	—	94	2	no	—
946	C₄²	—	94	2	no	—
947	C₄²	—	94	2	no	—
948	C₄²	C₂³×D₄₇	1	1	yes	characteristic
949	C₂³	—	47	1	no	—
950	C₂³	C₂×D₄×D₄₇	1	1	yes	characteristic
951	C₂³	C₂×D₄×D₄₇	1	1	yes	characteristic
952	Q₈	—	2	2	no	—
953	Q₈	—	2	2	no	—
954	Q₈	—	2	2	no	—
955	Q₈	—	2	2	no	—
956	Q₈	—	2	2	no	—
957	Q₈	—	4	4	no	—
958	Q₈	—	4	4	no	—
959	Q₈	—	94	2	no	—
960	Q₈	—	94	2	no	—
961	Q₈	—	94	2	no	—
962	Q₈	—	188	4	no	—
963	Q₈	—	188	4	no	—
964	Q₈	C₂×#10625352	1	4	yes	—
965	D₄	—	2	2	no	—
966	D₄	—	94	2	no	—
967	D₄	—	94	2	no	—
968	C₂×C₄	—	2	2	no	—
969	C₂×C₄	—	2	1	no	—
970	C₂×C₄	—	2	1	no	—
971	C₂×C₄	—	2	1	no	—
972	C₂×C₄	—	2	1	no	—
973	C₂×C₄	—	2	2	no	—
974	C₂×C₄	—	2	2	no	—
975	C₂×C₄	—	2	2	no	—
976	C₂×C₄	—	4	4	no	—
977	C₂×C₄	—	4	4	no	—
978	C₂×C₄	—	47	1	no	—
979	C₂×C₄	—	47	1	no	—
980	C₂×C₄	—	47	1	no	—
981	C₂×C₄	—	47	1	no	—
982	C₂×C₄	—	47	1	no	—
983	C₂×C₄	—	47	1	no	—
984	C₂×C₄	—	47	1	no	—
985	C₂×C₄	—	94	2	no	—
986	C₂×C₄	—	94	2	no	—
987	C₂×C₄	—	94	1	no	—
988	C₂×C₄	—	94	1	no	—
989	C₂×C₄	—	94	2	no	—
990	C₂×C₄	—	94	2	no	—
991	C₂×C₄	—	94	2	no	—
992	C₂×C₄	—	94	2	no	—
993	C₂×C₄	—	188	4	no	—
994	C₂×C₄	—	188	4	no	—
995	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
996	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
997	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
998	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
999	C₂×C₄	C₂⁴×D₄₇	1	1	yes	characteristic
1000	C₈	—	2	1	no	—
1001	C₈	—	2	1	no	—
1002	C₈	—	2	1	no	—
1003	C₈	—	94	1	no	—
1004	C₈	—	94	1	no	—
1005	C₈	—	94	1	no	—
1006	C₈	—	94	1	no	—
1007	C₈	C₂×#10625352	1	2	yes	—
1008	C₂²	—	2	1	no	—
1009	C₂²	—	2	1	no	—
1010	C₂²	—	2	1	no	—
1011	C₂²	—	2	1	no	—
1012	C₂²	—	2	1	no	—
1013	C₂²	—	94	1	no	—
1014	C₂²	—	94	1	no	—
1015	C₂²	—	94	1	no	—
1016	C₂²	#15689936	1	2	yes	—
1017	C₂²	C₂²×D₄×D₄₇	1	1	yes	characteristic
1018	C₄	—	2	1	no	—
1019	C₄	—	2	1	no	—
1020	C₄	—	2	4	no	—
1021	C₄	—	2	1	no	—
1022	C₄	—	2	1	no	—
1023	C₄	—	4	2	no	—
1024	C₄	—	4	2	no	—
1025	C₄	—	4	2	no	—
1026	C₄	—	47	2	no	—
1027	C₄	—	94	1	no	—
1028	C₄	—	94	1	no	—
1029	C₄	—	94	1	no	—
1030	C₄	—	94	1	no	—
1031	C₄	—	94	1	no	—
1032	C₄	—	94	1	no	—
1033	C₄	—	188	2	no	—
1034	C₄	—	188	2	no	—
1035	C₄	—	188	2	no	—
1036	C₄	—	188	2	no	—
1037	C₄	C₂²×#10625352	1	1	yes	characteristic
1038	C₄	#15689958	1	1	yes	characteristic
1039	C₂	—	2	2	no	—
1040	C₂	—	4	1	no	—
1041	C₂	—	188	1	no	—
1042	C₂	D₄×#10625352	1	1	yes	characteristic
1043	C₂	#578×D₄₇	1	1	yes	characteristic
1044	C₂	C₂×#15689936	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂²×D₄×D₄₇
commutator, cosocle	C₂×C₄×C₄₇	C₂⁵
Frattini	C₂×C₄	C₂⁴×D₄₇
Fitting	D₄×Q₁₆×C₄₇	C₂
socle	C₂²×C₄₇	C₂³×D₄
prime radical	#13093996	D₄
hypercenter	D₄×Q₁₆	D₄₇
hypocenter	C₄₇	#61484
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₄×D₄ ◁ D₄×Q₁₆

Complements

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

N	H ≅ G/N	type
2. #20256392	C₂	semidirect
3. #20256279	C₂	semidirect
4. #20256186	C₂	semidirect
5. #20255815	C₂	semidirect
6. #20255759	C₂	semidirect
7. #20255757	C₂	semidirect
8. #20255664	C₂	semidirect
9. #20255443	C₂	semidirect
10. #20255439	C₂	semidirect
11. Q₁₆×C₂²⋊D₄₇	C₂	semidirect
12. Q₁₆×C₂²⋊D₄₇	C₂	semidirect
13. #20254044	C₂	semidirect
14. #20254040	C₂	semidirect
15. #20253969	C₂	semidirect
16. #20253686	C₂	semidirect
17. #20253682	C₂	semidirect
18. #20253513	C₂	semidirect
20. #20252256	C₂	semidirect
21. #20252251	C₂	semidirect
22. C₂×Q₁₆×Dic₄₇	C₂	semidirect
23. D₄×Q₁₆×C₄₇	C₂	semidirect
529. D₄×Q₁₆	D₄₇	semidirect
653. C₄₇	#61484	semidirect

Maximal subgroups

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

subgroup	index
#20257475	2
#20256392	2
#20256279	2
#20256186	2
#20255815	2
#20255759	2
#20255757	2
#20255664	2
#20255443	2
#20255439	2
Q₁₆×C₂²⋊D₄₇	2
#20254044	2
#20254040	2
#20253969	2
#20253686	2
#20253682	2
#20253513	2
#20252356	2
#20252256	2
#20252251	2
C₂×Q₁₆×Dic₄₇	2
D₄×Q₁₆×C₄₇	2
#61484	47