Subgroups — #27096836

Order 12032.

1766 conjugacy classes of subgroups.

The subgroup lattice has 1088 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Q₈×#10625350	C₂	1	1	yes	maximal, characteristic, complemented
2	#20256351	C₂	1	2	yes	maximal, complemented
3	#20256342	C₂	1	2	yes	maximal, complemented
4	#20256333	C₂	1	2	yes	maximal, complemented
5	#20256327	C₂	1	2	yes	maximal, complemented
6	#20256320	C₂	1	1	yes	maximal, characteristic, complemented
7	#20256316	C₂	1	1	yes	maximal, characteristic, complemented
8	#20256309	C₂	1	1	yes	maximal, characteristic, complemented
9	#20256305	C₂	1	1	yes	maximal, characteristic, complemented
10	#20256298	C₂	1	1	yes	maximal, characteristic, complemented
11	#20256294	C₂	1	1	yes	maximal, characteristic, complemented
12	#20256287	C₂	1	1	yes	maximal, characteristic, complemented
13	#20256283	C₂	1	1	yes	maximal, characteristic, complemented
14	#20253910	C₂	1	2	yes	maximal, complemented
15	#20253898	C₂	1	1	yes	maximal, characteristic, complemented
16	#20253176	C₂	1	2	yes	maximal, complemented
17	#20253176	C₂	1	1	yes	maximal, characteristic, complemented
18	#20253170	C₂	1	1	yes	maximal, characteristic, complemented
19	#20253170	C₂	1	2	yes	maximal, complemented
20	C₂×#15689254	C₂	1	1	yes	maximal, characteristic, complemented
21	#20252186	C₂	1	2	yes	maximal
22	C₄×#13094044	C₂	1	1	yes	maximal, characteristic
23	Q₈×#41×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#13094044	C₂²	1	1	yes	characteristic
25	Q₈×Dic₉₄	C₂²	1	1	yes	characteristic
26	#15689851	C₂²	1	1	yes	characteristic
27	#15689851	C₂²	1	2	yes	—
28	#15689833	C₂²	1	1	yes	characteristic
29	#15689833	C₂²	1	2	yes	—
30	#15689828	—	2	2	no	—
31	#15689828	—	2	1	no	—
32	Q₈×D₁₈₈	C₂²	1	1	yes	characteristic
33	Q₈×C₂²⋊D₄₇	—	2	1	no	—
34	#15689680	C₂²	1	1	yes	characteristic
35	#15689680	C₂²	1	2	yes	—
36	#15689677	—	2	1	no	—
37	#15689677	—	2	2	no	—
38	C₄×#10625350	C₂²	1	2	yes	—
39	C₄×#10625350	C₂²	1	1	yes	characteristic
40	C₄×Q₈×D₄₇	—	2	1	no	—
41	#15689533	C₂²	1	2	yes	—
42	#15689533	C₂²	1	2	yes	—
43	#15689533	C₂²	1	2	yes	—
44	#15689533	C₂²	1	2	yes	—
45	#15689529	C₂²	1	2	yes	—
46	#15689529	C₂²	1	2	yes	—
47	#15689529	C₂²	1	2	yes	—
48	#15689529	C₂²	1	2	yes	—
49	#15689526	C₂²	1	1	yes	characteristic
50	#15689526	C₂²	1	1	yes	characteristic
51	#15689522	C₂²	1	2	yes	—
52	#15689522	C₂²	1	2	yes	—
53	#15689519	C₂²	1	1	yes	characteristic
54	#15689519	C₂²	1	1	yes	characteristic
55	#15689430	C₂²	1	2	yes	—
56	#15689430	C₂²	1	2	yes	—
57	#15689430	C₂²	1	2	yes	—
58	#15689427	C₂²	1	2	yes	—
59	#15689427	C₂²	1	2	yes	—
60	#15689427	C₂²	1	2	yes	—
61	#15689423	C₂²	1	2	yes	—
62	#15689423	C₂²	1	2	yes	—
63	#15689423	C₂²	1	2	yes	—
64	#15689420	C₂²	1	2	yes	—
65	#15689420	C₂²	1	2	yes	—
66	#15689420	C₂²	1	2	yes	—
67	#15689418	C₂²	1	1	yes	characteristic
68	#15689418	C₂²	1	2	yes	—
69	#15689415	C₂²	1	1	yes	characteristic
70	#15689415	C₂²	1	2	yes	—
71	#15689413	C₂²	1	1	yes	characteristic
72	#15689413	C₂²	1	2	yes	—
73	#15689410	C₂²	1	2	yes	—
74	#15689410	C₂²	1	1	yes	characteristic
75	#15689408	C₂²	1	1	yes	characteristic
76	#15689408	C₂²	1	2	yes	—
77	#15689405	C₂²	1	1	yes	characteristic
78	#15689405	C₂²	1	2	yes	—
79	#15689403	C₂²	1	1	yes	characteristic
80	#15689403	C₂²	1	2	yes	—
81	#15689400	C₂²	1	1	yes	characteristic
82	#15689400	C₂²	1	2	yes	—
83	#15689254	C₂²	1	1	yes	characteristic
84	#15689254	C₂²	1	1	yes	characteristic
85	#15689254	C₂²	1	1	yes	characteristic
86	#15689254	C₂²	1	1	yes	characteristic
87	#15689254	C₂²	1	2	yes	—
88	#15689254	C₂²	1	2	yes	—
89	#15689233	C₂²	1	2	yes	—
90	#15689233	C₂²	1	2	yes	—
91	#15689228	C₂²	1	2	yes	—
92	#15689228	C₂²	1	2	yes	—
93	#15689223	C₂²	1	2	yes	—
94	#15689223	C₂²	1	2	yes	—
95	#15689221	C₂²	1	2	yes	—
96	#15689221	C₂²	1	2	yes	—
97	C₄×#10625337	C₂²	1	1	yes	characteristic
98	C₄×#10625337	C₂²	1	1	yes	characteristic
99	C₄×#10625336	C₂²	1	1	yes	characteristic
100	C₄×#10625336	C₂²	1	1	yes	characteristic
101	C₄×#10625335	C₂²	1	1	yes	characteristic
102	C₄×#10625335	C₂²	1	1	yes	characteristic
103	C₄×#10625334	C₂²	1	1	yes	characteristic
104	C₄×#10625334	C₂²	1	1	yes	characteristic
105	#15689159	C₂²	1	2	yes	—
106	#15689159	C₂²	1	2	yes	—
107	#15689159	C₂²	1	1	yes	characteristic
108	#15689159	C₂²	1	2	yes	—
109	#15689159	C₂²	1	2	yes	—
110	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
111	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	2	yes	—
112	#15689119	C₂²	1	2	yes	—
113	#15689119	C₂²	1	1	yes	characteristic
114	#15689117	C₂²	1	2	yes	—
115	#15689117	C₂²	1	1	yes	characteristic
116	C₂×#13093935	C₂²	1	2	yes	—
117	C₂×C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
118	Q₈²×C₄₇	C₂²	1	1	yes	characteristic
119	C₄₇×#557	C₂²	1	1	yes	characteristic
120	C₄₇×#557	C₂²	1	2	yes	—
121	C₄₇×#554	—	2	2	no	—
122	C₄₇×#554	—	2	1	no	—
123	C₄₇×#554	C₂²	1	1	yes	characteristic
124	C₄₇×#554	C₂²	1	2	yes	—
125	D₄×Q₈×C₄₇	—	2	1	no	—
126	D₄×Q₈×C₄₇	C₂²	1	1	yes	characteristic
127	C₄₇×#533	—	2	1	no	—
128	C₄₇×#533	—	2	2	no	—
129	C₄₇×#533	C₂²	1	1	yes	characteristic
130	C₄₇×#533	C₂²	1	2	yes	—
131	C₄×#41×C₄₇	C₂²	1	2	yes	—
132	C₄×#41×C₄₇	C₂²	1	1	yes	characteristic
133	C₂×C₄×Q₈×C₄₇	—	2	1	no	—
134	C₂×C₄×Q₈×C₄₇	C₂²	1	1	yes	characteristic
135	C₂×#10625350	C₂³	1	1	yes	characteristic
136	C₂×Q₈×D₄₇	—	2	1	no	—
137	#13094044	Q₈	1	8	yes	complemented
138	C₂×#10625337	C₂³	1	1	yes	characteristic
139	C₂×#10625335	C₂³	1	1	yes	characteristic
140	C₂×#10625336	C₂³	1	1	yes	characteristic
141	C₂×#10625334	C₂³	1	1	yes	characteristic
142	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
143	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
144	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
145	#13094024	C₂³	1	1	yes	characteristic
146	#13094024	C₂³	1	1	yes	characteristic
147	#13094024	C₂³	1	2	yes	—
148	#13094024	C₂³	1	2	yes	—
149	#13094023	—	2	1	no	—
150	#13094023	—	2	2	no	—
151	#13094022	—	2	1	no	—
152	#13094022	—	2	2	no	—
153	#13094016	C₂³	1	2	yes	—
154	#13094016	C₂³	1	2	yes	—
155	#13094016	C₂³	1	2	yes	—
156	#13094014	—	2	2	no	—
157	#13094014	—	2	2	no	—
158	#13094014	—	2	2	no	—
159	#13094004	—	2	1	no	—
160	#13094004	—	2	2	no	—
161	#13094003	—	2	1	no	—
162	#13094003	—	2	2	no	—
163	#13094003	—	2	1	no	—
164	#13094003	—	2	2	no	—
165	#13094002	—	2	2	no	—
166	#13094002	—	2	2	no	—
167	#13094002	—	2	2	no	—
168	#13094000	—	2	1	no	—
169	#13094000	—	2	2	no	—
170	Q₈×Dic₄₇	—	2	1	no	—
171	C₄×Dic₉₄	—	2	1	no	—
172	C₄×Dic₉₄	—	2	2	no	—
173	C₄×Dic₉₄	—	2	2	no	—
174	C₄×Dic₉₄	—	2	1	no	—
175	C₄×Dic₉₄	C₂³	1	1	yes	characteristic
176	C₄×Dic₉₄	C₂³	1	1	yes	characteristic
177	C₄×Dic₉₄	C₂³	1	2	yes	—
178	C₄×Dic₉₄	C₂³	1	2	yes	—
179	#13093989	—	2	2	no	—
180	#13093989	—	2	1	no	—
181	C₄×D₁₈₈	C₂³	1	2	yes	—
182	C₄×D₁₈₈	C₂³	1	2	yes	—
183	C₄×D₁₈₈	C₂³	1	1	yes	characteristic
184	C₄×D₁₈₈	C₂³	1	1	yes	characteristic
185	C₄×C₂²⋊D₄₇	—	2	1	no	—
186	C₄×C₂²⋊D₄₇	—	2	2	no	—
187	C₄×C₂²⋊D₄₇	—	2	2	no	—
188	C₄×C₂²⋊D₄₇	—	2	1	no	—
189	#13093983	C₂³	1	2	yes	—
190	#13093983	C₂³	1	1	yes	characteristic
191	#13093981	—	2	2	no	—
192	#13093981	—	2	1	no	—
193	C₄⋊C₄×D₄₇	—	2	2	no	—
194	C₄⋊C₄×D₄₇	—	2	1	no	—
195	C₄²×D₄₇	—	2	1	no	—
196	C₄²×D₄₇	—	2	2	no	—
197	#13093957	C₂³	1	1	yes	characteristic
198	#13093957	C₂³	1	1	yes	characteristic
199	#13093957	C₂³	1	2	yes	—
200	#13093957	C₂³	1	2	yes	—
201	#13093957	C₂³	1	2	yes	—
202	#13093957	C₂³	1	2	yes	—
203	#13093957	C₂³	1	2	yes	—
204	#13093957	C₂³	1	2	yes	—
205	#13093957	C₂³	1	2	yes	—
206	#13093957	C₂³	1	2	yes	—
207	#13093955	C₂³	1	2	yes	—
208	#13093955	C₂³	1	2	yes	—
209	#13093955	C₂³	1	2	yes	—
210	#13093955	C₂³	1	2	yes	—
211	#13093955	C₂³	1	1	yes	characteristic
212	#13093955	C₂³	1	1	yes	characteristic
213	#13093955	C₂³	1	2	yes	—
214	#13093955	C₂³	1	2	yes	—
215	#13093955	C₂³	1	2	yes	—
216	#13093955	C₂³	1	2	yes	—
217	C₄⋊(C₄₇⋊C₈)	C₂³	1	1	yes	characteristic
218	C₄⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
219	C₄⋊(C₄₇⋊C₈)	C₂³	1	1	yes	characteristic
220	C₄⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
221	C₄⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
222	C₄⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
223	C₄⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
224	#13093948	C₂³	1	1	yes	characteristic
225	#13093948	C₂³	1	1	yes	characteristic
226	#13093948	C₂³	1	2	yes	—
227	#13093948	C₂³	1	2	yes	—
228	#13093947	C₂³	1	1	yes	characteristic
229	#13093947	C₂³	1	1	yes	characteristic
230	#13093947	C₂³	1	2	yes	—
231	#13093947	C₂³	1	2	yes	—
232	#13093945	C₂³	1	2	yes	—
233	#13093945	C₂³	1	2	yes	—
234	#13093945	C₂³	1	1	yes	characteristic
235	#13093945	C₂³	1	1	yes	characteristic
236	#13093944	C₂³	1	2	yes	—
237	#13093944	C₂³	1	2	yes	—
238	#13093944	C₂³	1	1	yes	characteristic
239	#13093944	C₂³	1	1	yes	characteristic
240	#13093935	C₂³	1	2	yes	—
241	#13093935	C₂³	1	2	yes	—
242	#13093935	C₂³	1	2	yes	—
243	#13093935	C₂³	1	2	yes	—
244	C₄×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
245	C₄×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
246	C₄×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
247	C₄×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
248	C₂×#41×C₄₇	C₂³	1	1	yes	characteristic
249	C₂²×Q₈×C₄₇	—	2	1	no	—
250	C₂²×Q₈×C₄₇	D₄	1	1	yes	characteristic
251	C₄⋊Q₈×C₄₇	—	2	1	no	—
252	C₄⋊Q₈×C₄₇	—	2	2	no	—
253	C₄⋊Q₈×C₄₇	—	2	1	no	—
254	C₄⋊Q₈×C₄₇	—	2	2	no	—
255	C₄⋊Q₈×C₄₇	C₂³	1	1	yes	characteristic
256	C₄⋊Q₈×C₄₇	C₂³	1	1	yes	characteristic
257	C₄⋊Q₈×C₄₇	C₂³	1	2	yes	—
258	C₄⋊Q₈×C₄₇	C₂³	1	2	yes	—
259	#125×C₄₇	—	2	2	no	—
260	#125×C₄₇	—	2	2	no	—
261	#125×C₄₇	—	2	2	no	—
262	#125×C₄₇	C₂³	1	2	yes	—
263	#125×C₄₇	C₂³	1	2	yes	—
264	#125×C₄₇	C₂³	1	2	yes	—
265	C₂²⋊Q₈×C₄₇	—	2	1	no	—
266	C₂²⋊Q₈×C₄₇	—	2	2	no	—
267	C₂²⋊Q₈×C₄₇	—	2	1	no	—
268	C₂²⋊Q₈×C₄₇	—	2	2	no	—
269	C₂²⋊Q₈×C₄₇	—	2	1	no	—
270	C₂²⋊Q₈×C₄₇	—	2	2	no	—
271	C₂²⋊Q₈×C₄₇	—	2	1	no	—
272	C₂²⋊Q₈×C₄₇	—	2	2	no	—
273	C₂²⋊Q₈×C₄₇	—	2	2	no	—
274	C₂²⋊Q₈×C₄₇	—	2	2	no	—
275	C₂²⋊Q₈×C₄₇	—	2	2	no	—
276	C₄×Q₈×C₄₇	—	2	1	no	—
277	C₄×Q₈×C₄₇	—	2	2	no	—
278	C₄×Q₈×C₄₇	—	2	1	no	—
279	C₄×Q₈×C₄₇	—	2	1	no	—
280	C₄×Q₈×C₄₇	—	2	2	no	—
281	C₄×Q₈×C₄₇	—	2	2	no	—
282	C₄×Q₈×C₄₇	—	2	1	no	—
283	C₄×Q₈×C₄₇	D₄	1	1	yes	characteristic
284	C₄×Q₈×C₄₇	D₄	1	1	yes	characteristic
285	C₄×Q₈×C₄₇	D₄	1	2	yes	—
286	C₄×Q₈×C₄₇	C₂³	1	1	yes	characteristic
287	C₄×Q₈×C₄₇	C₂³	1	1	yes	characteristic
288	C₄×Q₈×C₄₇	C₂³	1	2	yes	—
289	C₄×Q₈×C₄₇	C₂³	1	2	yes	—
290	C₄×Q₈×C₄₇	C₂³	1	1	yes	characteristic
291	C₄×Q₈×C₄₇	C₂³	1	1	yes	characteristic
292	C₄×Q₈×C₄₇	C₂³	1	2	yes	—
293	C₄×D₄×C₄₇	—	2	1	no	—
294	C₄×D₄×C₄₇	—	2	2	no	—
295	C₄×D₄×C₄₇	—	2	2	no	—
296	C₄×D₄×C₄₇	—	2	1	no	—
297	C₄×D₄×C₄₇	C₂³	1	2	yes	—
298	C₄×D₄×C₄₇	C₂³	1	2	yes	—
299	C₄×D₄×C₄₇	C₂³	1	1	yes	characteristic
300	C₄×D₄×C₄₇	C₂³	1	1	yes	characteristic
301	#117×C₄₇	—	2	2	no	—
302	#117×C₄₇	—	2	1	no	—
303	#117×C₄₇	C₂³	1	2	yes	—
304	#117×C₄₇	C₂³	1	1	yes	characteristic
305	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
306	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
307	C₂×C₄⋊C₄×C₄₇	D₄	1	2	yes	—
308	C₂×C₄⋊C₄×C₄₇	D₄	1	1	yes	characteristic
309	C₂×C₄²×C₄₇	—	2	1	no	—
310	C₂×C₄²×C₄₇	—	2	2	no	—
311	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
312	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
313	#41×C₄₇	—	2	2	no	—
314	#41×C₄₇	C₂×Q₈	1	4	yes	complemented
315	C₂×Q₈×C₄₇	—	2	2	no	—
316	C₂×Q₈×C₄₇	—	2	1	no	—
317	C₂×Q₈×C₄₇	—	2	2	no	—
318	C₂×Q₈×C₄₇	—	2	1	no	—
319	C₂×Q₈×C₄₇	—	4	2	no	—
320	C₂×Q₈×C₄₇	—	4	4	no	—
321	C₂×Q₈×C₄₇	C₂×D₄	1	1	yes	characteristic
322	C₂×Q₈×C₄₇	C₂×D₄	1	1	yes	characteristic
323	C₂×Q₈×C₄₇	C₂×D₄	1	2	yes	—
324	C₂×Q₈×C₄₇	C₂⁴	1	1	yes	characteristic
325	C₂×D₄×C₄₇	—	2	1	no	—
326	C₂×D₄×C₄₇	C₂⁴	1	1	yes	characteristic
327	C₂²×C₄×C₄₇	—	2	1	no	—
328	C₂²×C₄×C₄₇	—	2	2	no	—
329	C₂²×C₄×C₄₇	—	2	1	no	—
330	C₂²×C₄×C₄₇	—	2	1	no	—
331	C₂²×C₄×C₄₇	—	2	2	no	—
332	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
333	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
334	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
335	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
336	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
337	C₂×C₂²⋊D₄₇	—	2	1	no	—
338	Q₈×D₄₇	—	4	4	no	—
339	#10625350	—	2	2	no	—
340	#10625350	C₂×Q₈	1	4	yes	complemented
341	C₂×D₁₈₈	C₂⁴	1	1	yes	characteristic
342	C₂×C₄×D₄₇	—	2	1	no	—
343	C₂×C₄×D₄₇	—	2	2	no	—
344	C₂×C₄×D₄₇	—	2	1	no	—
345	C₂×C₄×D₄₇	—	2	1	no	—
346	C₂×C₄×D₄₇	—	2	2	no	—
347	C₂×Dic₉₄	—	2	2	no	—
348	C₂×Dic₉₄	—	2	1	no	—
349	C₂×Dic₉₄	—	2	2	no	—
350	C₂×Dic₉₄	—	2	1	no	—
351	C₂×Dic₉₄	C₂⁴	1	1	yes	characteristic
352	C₄⋊C₄×C₄₇	—	2	2	no	—
353	C₄⋊C₄×C₄₇	—	2	2	no	—
354	C₄⋊C₄×C₄₇	—	2	2	no	—
355	C₄⋊C₄×C₄₇	—	2	2	no	—
356	C₄⋊C₄×C₄₇	—	2	1	no	—
357	C₄⋊C₄×C₄₇	—	2	2	no	—
358	C₄⋊C₄×C₄₇	—	2	2	no	—
359	C₄⋊C₄×C₄₇	—	2	1	no	—
360	C₄⋊C₄×C₄₇	—	2	1	no	—
361	C₄⋊C₄×C₄₇	—	2	2	no	—
362	C₄⋊C₄×C₄₇	—	2	1	no	—
363	C₄⋊C₄×C₄₇	—	2	2	no	—
364	C₄⋊C₄×C₄₇	—	2	2	no	—
365	C₄⋊C₄×C₄₇	—	2	2	no	—
366	C₄⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
367	C₄⋊C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
368	C₄⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
369	C₄⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
370	C₄⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
371	C₄⋊C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
372	C₄⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
373	C₄⋊C₄×C₄₇	C₂⁴	1	2	yes	—
374	C₄⋊C₄×C₄₇	C₂⁴	1	2	yes	—
375	C₄⋊C₄×C₄₇	C₂⁴	1	1	yes	characteristic
376	C₄⋊C₄×C₄₇	C₂⁴	1	1	yes	characteristic
377	C₂²⋊C₄×C₄₇	—	2	2	no	—
378	C₂²⋊C₄×C₄₇	—	2	1	no	—
379	C₂²⋊C₄×C₄₇	—	2	2	no	—
380	C₂²⋊C₄×C₄₇	—	2	2	no	—
381	C₂²⋊C₄×C₄₇	—	2	1	no	—
382	C₂²⋊C₄×C₄₇	—	2	1	no	—
383	C₄²×C₄₇	—	2	1	no	—
384	C₄²×C₄₇	—	2	2	no	—
385	C₄²×C₄₇	—	2	1	no	—
386	C₄²×C₄₇	—	2	2	no	—
387	C₄²×C₄₇	—	2	2	no	—
388	C₄²×C₄₇	—	2	1	no	—
389	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
390	C₄²×C₄₇	C₂×D₄	1	2	yes	—
391	C₄²×C₄₇	C₂×D₄	1	2	yes	—
392	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
393	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
394	C₄²×C₄₇	C₂⁴	1	2	yes	—
395	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
396	C₄²×C₄₇	C₂⁴	1	2	yes	—
397	C₂²⋊Dic₄₇	—	2	2	no	—
398	C₂²⋊Dic₄₇	—	2	1	no	—
399	#10625337	C₂×Q₈	1	4	yes	complemented
400	#10625336	C₂×Q₈	1	4	yes	complemented
401	#10625335	C₂×Q₈	1	4	yes	complemented
402	#10625334	C₂×Q₈	1	4	yes	complemented
403	(C₂×D₄₇)⋊C₄	—	2	2	no	—
404	(C₂×D₄₇)⋊C₄	—	2	1	no	—
405	(C₂×D₄₇)⋊C₄	—	2	2	no	—
406	(C₂×D₄₇)⋊C₄	—	2	1	no	—
407	C₄⋊Dic₄₇	—	2	2	no	—
408	C₄⋊Dic₄₇	—	2	1	no	—
409	C₄⋊Dic₄₇	—	2	2	no	—
410	C₄⋊Dic₄₇	—	2	1	no	—
411	C₄⋊Dic₄₇	C₂⁴	1	2	yes	—
412	C₄⋊Dic₄₇	C₂⁴	1	2	yes	—
413	C₄⋊Dic₄₇	C₂⁴	1	1	yes	characteristic
414	C₄⋊Dic₄₇	C₂⁴	1	1	yes	characteristic
415	Dic₄₇⋊C₄	—	2	2	no	—
416	Dic₄₇⋊C₄	—	2	2	no	—
417	Dic₄₇⋊C₄	—	2	2	no	—
418	Dic₄₇⋊C₄	—	2	2	no	—
419	Dic₄₇⋊C₄	—	2	1	no	—
420	Dic₄₇⋊C₄	—	2	2	no	—
421	Dic₄₇⋊C₄	—	2	1	no	—
422	Dic₄₇⋊C₄	—	2	2	no	—
423	Dic₄₇⋊C₄	—	2	2	no	—
424	Dic₄₇⋊C₄	—	2	2	no	—
425	C₄×Dic₄₇	—	2	1	no	—
426	C₄×Dic₄₇	—	2	2	no	—
427	C₄×Dic₄₇	—	2	1	no	—
428	C₄×Dic₄₇	—	2	2	no	—
429	C₄×Dic₄₇	—	2	2	no	—
430	C₄×Dic₄₇	—	2	1	no	—
431	C₂×C₄₇⋊C₈	—	2	2	no	—
432	C₂×C₄₇⋊C₈	—	2	4	no	—
433	C₂×C₄₇⋊C₈	C₂×Q₈	1	4	yes	complemented
434	C₂×C₄₇⋊C₈	C₂⁴	1	1	yes	characteristic
435	C₂×C₄₇⋊C₈	C₂⁴	1	1	yes	characteristic
436	C₂×C₄₇⋊C₈	C₂⁴	1	2	yes	—
437	C₂×C₄₇⋊C₈	C₂⁴	1	2	yes	—
438	C₂×C₄₇⋊C₈	C₂⁴	1	1	yes	characteristic
439	C₂×C₄₇⋊C₈	C₂⁴	1	1	yes	characteristic
440	C₂³×C₄₇	—	2	1	no	—
441	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
442	C₂²×D₄₇	—	2	1	no	—
443	Q₈×C₄₇	—	2	2	no	—
444	Q₈×C₄₇	—	2	2	no	—
445	Q₈×C₄₇	—	2	1	no	—
446	Q₈×C₄₇	—	4	2	no	—
447	Q₈×C₄₇	—	4	4	no	—
448	Q₈×C₄₇	—	4	2	no	—
449	Q₈×C₄₇	—	8	1	no	—
450	Q₈×C₄₇	—	8	2	no	—
451	Q₈×C₄₇	C₂²×Q₈	1	2	yes	—
452	D₄×C₄₇	—	2	4	no	—
453	D₄×C₄₇	—	2	1	no	—
454	D₄×C₄₇	C₂²×Q₈	1	2	yes	—
455	C₂×C₄×C₄₇	—	2	1	no	—
456	C₂×C₄×C₄₇	—	2	4	no	—
457	C₂×C₄×C₄₇	—	2	2	no	—
458	C₂×C₄×C₄₇	—	2	2	no	—
459	C₂×C₄×C₄₇	—	2	1	no	—
460	C₂×C₄×C₄₇	—	2	2	no	—
461	C₂×C₄×C₄₇	—	2	1	no	—
462	C₂×C₄×C₄₇	—	4	2	no	—
463	C₂×C₄×C₄₇	—	4	1	no	—
464	C₂×C₄×C₄₇	—	4	2	no	—
465	C₂×C₄×C₄₇	—	4	4	no	—
466	C₂×C₄×C₄₇	—	4	2	no	—
467	C₂×C₄×C₄₇	—	8	2	no	—
468	C₂×C₄×C₄₇	—	8	1	no	—
469	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
470	C₂×C₄×C₄₇	C₂²×D₄	1	2	yes	—
471	C₂×C₄×C₄₇	C₂²×D₄	1	2	yes	—
472	C₂×C₄×C₄₇	C₂²×D₄	1	2	yes	—
473	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
474	C₂×C₄×C₄₇	C₂²×D₄	1	2	yes	—
475	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
476	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
477	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
478	C₂×C₄×C₄₇	C₂²×Q₈	1	2	yes	—
479	C₂×C₄×C₄₇	2₋¹⁺⁴	1	2	yes	—
480	C₂×C₄×C₄₇	C₂⁵	1	1	yes	characteristic
481	C₂²⋊D₄₇	—	2	4	no	—
482	C₂×Dic₄₇	—	2	1	no	—
483	C₂×Dic₄₇	—	2	2	no	—
484	C₂×Dic₄₇	—	2	1	no	—
485	C₂×Dic₄₇	—	2	1	no	—
486	C₂×Dic₄₇	—	2	2	no	—
487	D₁₈₈	—	2	1	no	—
488	D₁₈₈	C₂²×Q₈	1	2	yes	—
489	C₄×D₄₇	—	2	4	no	—
490	C₄×D₄₇	—	4	4	no	—
491	C₄×D₄₇	—	4	2	no	—
492	C₄×D₄₇	—	8	1	no	—
493	C₄×D₄₇	—	8	2	no	—
494	Dic₉₄	—	2	1	no	—
495	Dic₉₄	—	4	4	no	—
496	Dic₉₄	—	4	2	no	—
497	Dic₉₄	—	8	2	no	—
498	Dic₉₄	—	8	1	no	—
499	Dic₉₄	C₂²×Q₈	1	2	yes	—
500	C₄₇⋊C₈	—	2	1	no	—
501	C₄₇⋊C₈	—	2	1	no	—
502	C₄₇⋊C₈	—	2	2	no	—
503	C₄₇⋊C₈	—	2	2	no	—
504	C₄₇⋊C₈	C₂²×Q₈	1	2	yes	—
505	C₄₇⋊C₈	C₂²×Q₈	1	2	yes	—
506	#61365	—	47	1	no	maximal, Sylow
507	C₂²×C₄₇	—	2	1	no	—
508	C₂²×C₄₇	—	2	1	no	—
509	C₂²×C₄₇	—	2	2	no	—
510	C₂²×C₄₇	—	4	1	no	—
511	C₂²×C₄₇	—	4	1	no	—
512	C₂²×C₄₇	D₄×Q₈	1	2	yes	—
513	C₂²×C₄₇	C₂³×D₄	1	1	yes	characteristic
514	C₂×D₄₇	—	2	2	no	—
515	C₂×D₄₇	—	4	1	no	—
516	C₂×D₄₇	—	4	1	no	—
517	C₄×C₄₇	—	2	2	no	—
518	C₄×C₄₇	—	2	1	no	—
519	C₄×C₄₇	—	2	1	no	—
520	C₄×C₄₇	—	2	2	no	—
521	C₄×C₄₇	—	2	2	no	—
522	C₄×C₄₇	—	2	2	no	—
523	C₄×C₄₇	—	2	1	no	—
524	C₄×C₄₇	—	2	2	no	—
525	C₄×C₄₇	—	4	2	no	—
526	C₄×C₄₇	—	4	1	no	—
527	C₄×C₄₇	—	4	2	no	—
528	C₄×C₄₇	—	4	1	no	—
529	C₄×C₄₇	D₄×Q₈	1	2	yes	—
530	C₄×C₄₇	#575	1	2	yes	—
531	C₄×C₄₇	C₂³×Q₈	1	1	yes	characteristic
532	C₄×C₄₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
533	Dic₄₇	—	2	2	no	—
534	Dic₄₇	—	4	1	no	—
535	Dic₄₇	—	4	2	no	—
536	Dic₄₇	—	4	1	no	—
537	Dic₄₇	—	4	2	no	—
538	Q₈×#41	—	47	1	no	—
539	Q₈×#41	D₄₇	1	1	yes	characteristic, complemented
540	#3390	—	47	2	no	—
541	#3389	—	47	2	no	—
542	#3388	—	47	2	no	—
543	#3388	—	47	2	no	—
544	#3387	—	47	1	no	—
545	#3387	—	47	1	no	—
546	#3386	—	47	1	no	—
547	#3386	—	47	1	no	—
548	#3385	—	47	1	no	—
549	#3385	—	47	1	no	—
550	#3384	—	47	1	no	—
551	#3384	—	47	1	no	—
552	#3162	—	47	2	no	—
553	#3160	—	47	1	no	—
554	#3076	—	47	1	no	—
555	#3076	—	47	2	no	—
556	#3076	—	47	1	no	—
557	#3076	—	47	2	no	—
558	C₂×#446	—	47	1	no	—
559	#2943	—	47	2	no	—
560	C₄×#135	—	47	1	no	—
561	C₂×C₄₇	—	2	2	no	—
562	C₂×C₄₇	—	4	2	no	—
563	C₂×C₄₇	C₂×D₄×Q₈	1	1	yes	characteristic
564	C₂×C₄₇	C₂×#575	1	1	yes	characteristic
565	C₂×C₄₇	#3584	1	1	yes	characteristic
566	D₄₇	—	4	2	no	—
567	C₂×#135	—	47	1	no	—
568	Q₈²	—	47	1	no	—
569	Q₈²	C₂×D₄₇	1	1	yes	characteristic
570	#557	—	47	1	no	—
571	#557	—	47	2	no	—
572	#557	C₂×D₄₇	1	1	yes	characteristic
573	#557	C₂×D₄₇	1	2	yes	—
574	#554	—	2	2	no	—
575	#554	—	2	1	no	—
576	#554	—	47	1	no	—
577	#554	—	47	2	no	—
578	#554	—	94	2	no	—
579	#554	—	94	1	no	—
580	#554	C₂×D₄₇	1	1	yes	characteristic
581	#554	C₂×D₄₇	1	2	yes	—
582	D₄×Q₈	—	2	1	no	—
583	D₄×Q₈	—	47	1	no	—
584	D₄×Q₈	—	94	1	no	—
585	D₄×Q₈	C₂×D₄₇	1	1	yes	characteristic
586	#533	—	2	1	no	—
587	#533	—	2	2	no	—
588	#533	—	47	1	no	—
589	#533	—	47	2	no	—
590	#533	—	94	1	no	—
591	#533	—	94	2	no	—
592	#533	C₂×D₄₇	1	1	yes	characteristic
593	#533	C₂×D₄₇	1	2	yes	—
594	C₄×#41	—	47	1	no	—
595	C₄×#41	—	47	2	no	—
596	C₄×#41	C₂×D₄₇	1	1	yes	characteristic
597	C₄×#41	C₂×D₄₇	1	2	yes	—
598	C₂×C₄×Q₈	—	2	1	no	—
599	C₂×C₄×Q₈	—	94	1	no	—
600	C₂×C₄×Q₈	C₂×D₄₇	1	1	yes	characteristic
601	#501	—	47	2	no	—
602	#501	—	47	2	no	—
603	#501	—	47	2	no	—
604	#501	—	47	2	no	—
605	#501	—	47	2	no	—
606	#501	—	47	2	no	—
607	#501	—	47	2	no	—
608	#501	—	47	2	no	—
609	#500	—	47	1	no	—
610	#500	—	47	1	no	—
611	#499	—	47	2	no	—
612	#499	—	47	2	no	—
613	#498	—	47	1	no	—
614	#498	—	47	1	no	—
615	#479	—	47	2	no	—
616	#479	—	47	2	no	—
617	#479	—	47	2	no	—
618	#479	—	47	2	no	—
619	#479	—	47	2	no	—
620	#479	—	47	2	no	—
621	#478	—	47	2	no	—
622	#478	—	47	2	no	—
623	#478	—	47	2	no	—
624	#478	—	47	2	no	—
625	#478	—	47	2	no	—
626	#478	—	47	2	no	—
627	#477	—	47	1	no	—
628	#477	—	47	2	no	—
629	#477	—	47	1	no	—
630	#477	—	47	2	no	—
631	#476	—	47	1	no	—
632	#476	—	47	2	no	—
633	#476	—	47	1	no	—
634	#476	—	47	2	no	—
635	#475	—	47	1	no	—
636	#475	—	47	2	no	—
637	#475	—	47	1	no	—
638	#475	—	47	2	no	—
639	#474	—	47	1	no	—
640	#474	—	47	2	no	—
641	#474	—	47	1	no	—
642	#474	—	47	2	no	—
643	#446	—	47	1	no	—
644	#446	—	47	1	no	—
645	#446	—	47	1	no	—
646	#446	—	47	1	no	—
647	#446	—	47	2	no	—
648	#446	—	47	2	no	—
649	#442	—	47	2	no	—
650	#442	—	47	2	no	—
651	#441	—	47	2	no	—
652	#441	—	47	2	no	—
653	#440	—	47	2	no	—
654	#440	—	47	2	no	—
655	#440	—	47	2	no	—
656	#440	—	47	2	no	—
657	C₄×Q₁₆	—	47	1	no	—
658	C₄×Q₁₆	—	47	1	no	—
659	C₄×SD₁₆	—	47	1	no	—
660	C₄×SD₁₆	—	47	1	no	—
661	C₄×SD₁₆	—	47	1	no	—
662	C₄×SD₁₆	—	47	1	no	—
663	C₄×D₈	—	47	1	no	—
664	C₄×D₈	—	47	1	no	—
665	#427	—	47	2	no	—
666	#427	—	47	2	no	—
667	#427	—	47	2	no	—
668	#427	—	47	2	no	—
669	#427	—	47	1	no	—
670	C₂×C₄⋊C₈	—	47	1	no	—
671	C₂×C₄⋊C₈	—	47	2	no	—
672	#416	—	47	1	no	—
673	#416	—	47	2	no	—
674	#416	—	47	1	no	—
675	#416	—	47	2	no	—
676	C₂×#97	—	47	2	no	—
677	C₂×C₄×C₈	—	47	1	no	—
678	C₄₇	#61365	1	1	yes	characteristic, complemented, Sylow
679	C₂×#41	—	47	1	no	—
680	C₂×#41	C₂²×D₄₇	1	1	yes	characteristic
681	C₂²×Q₈	—	2	1	no	—
682	C₂²×Q₈	—	94	1	no	—
683	C₂²×Q₈	C₂²⋊D₄₇	1	1	yes	characteristic
684	#135	—	47	8	no	—
685	C₂×Q₁₆	—	47	1	no	—
686	C₂×SD₁₆	—	47	1	no	—
687	C₂×SD₁₆	—	47	1	no	—
688	C₂×D₈	—	47	1	no	—
689	C₂²×C₈	—	47	1	no	—
690	C₂²×C₈	—	47	1	no	—
691	C₂²×C₈	—	47	2	no	—
692	C₄⋊Q₈	—	2	1	no	—
693	C₄⋊Q₈	—	2	2	no	—
694	C₄⋊Q₈	—	2	1	no	—
695	C₄⋊Q₈	—	2	2	no	—
696	C₄⋊Q₈	—	47	1	no	—
697	C₄⋊Q₈	—	47	2	no	—
698	C₄⋊Q₈	—	47	2	no	—
699	C₄⋊Q₈	—	47	1	no	—
700	C₄⋊Q₈	—	94	1	no	—
701	C₄⋊Q₈	—	94	2	no	—
702	C₄⋊Q₈	—	94	1	no	—
703	C₄⋊Q₈	—	94	2	no	—
704	C₄⋊Q₈	C₂²×D₄₇	1	1	yes	characteristic
705	C₄⋊Q₈	C₂²×D₄₇	1	2	yes	—
706	C₄⋊Q₈	C₂²×D₄₇	1	2	yes	—
707	C₄⋊Q₈	C₂²×D₄₇	1	1	yes	characteristic
708	#125	—	2	2	no	—
709	#125	—	2	2	no	—
710	#125	—	2	2	no	—
711	#125	—	47	2	no	—
712	#125	—	47	2	no	—
713	#125	—	47	2	no	—
714	#125	—	94	2	no	—
715	#125	—	94	2	no	—
716	#125	—	94	2	no	—
717	#125	C₂²×D₄₇	1	2	yes	—
718	#125	C₂²×D₄₇	1	2	yes	—
719	#125	C₂²×D₄₇	1	2	yes	—
720	C₂²⋊Q₈	—	2	1	no	—
721	C₂²⋊Q₈	—	2	2	no	—
722	C₂²⋊Q₈	—	2	1	no	—
723	C₂²⋊Q₈	—	2	2	no	—
724	C₂²⋊Q₈	—	2	1	no	—
725	C₂²⋊Q₈	—	2	2	no	—
726	C₂²⋊Q₈	—	2	1	no	—
727	C₂²⋊Q₈	—	2	2	no	—
728	C₂²⋊Q₈	—	2	2	no	—
729	C₂²⋊Q₈	—	2	2	no	—
730	C₂²⋊Q₈	—	2	2	no	—
731	C₂²⋊Q₈	—	94	1	no	—
732	C₂²⋊Q₈	—	94	2	no	—
733	C₂²⋊Q₈	—	94	1	no	—
734	C₂²⋊Q₈	—	94	2	no	—
735	C₂²⋊Q₈	—	94	1	no	—
736	C₂²⋊Q₈	—	94	2	no	—
737	C₂²⋊Q₈	—	94	1	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	C₄×Q₈	—	2	1	no	—
743	C₄×Q₈	—	2	2	no	—
744	C₄×Q₈	—	2	1	no	—
745	C₄×Q₈	—	2	1	no	—
746	C₄×Q₈	—	2	2	no	—
747	C₄×Q₈	—	2	2	no	—
748	C₄×Q₈	—	2	1	no	—
749	C₄×Q₈	—	47	1	no	—
750	C₄×Q₈	—	47	2	no	—
751	C₄×Q₈	—	47	1	no	—
752	C₄×Q₈	—	47	2	no	—
753	C₄×Q₈	—	94	1	no	—
754	C₄×Q₈	—	94	2	no	—
755	C₄×Q₈	—	94	1	no	—
756	C₄×Q₈	—	94	1	no	—
757	C₄×Q₈	—	94	2	no	—
758	C₄×Q₈	—	94	2	no	—
759	C₄×Q₈	—	94	1	no	—
760	C₄×Q₈	C₂²⋊D₄₇	1	1	yes	characteristic
761	C₄×Q₈	C₂²⋊D₄₇	1	1	yes	characteristic
762	C₄×Q₈	C₂²⋊D₄₇	1	2	yes	—
763	C₄×Q₈	C₂²×D₄₇	1	1	yes	characteristic
764	C₄×Q₈	C₂²×D₄₇	1	2	yes	—
765	C₄×Q₈	C₂²×D₄₇	1	1	yes	characteristic
766	C₄×Q₈	C₂²×D₄₇	1	2	yes	—
767	C₄×Q₈	C₂²×D₄₇	1	1	yes	characteristic
768	C₄×Q₈	C₂²×D₄₇	1	1	yes	characteristic
769	C₄×Q₈	C₂²×D₄₇	1	2	yes	—
770	C₄×D₄	—	2	1	no	—
771	C₄×D₄	—	2	2	no	—
772	C₄×D₄	—	2	1	no	—
773	C₄×D₄	—	2	2	no	—
774	C₄×D₄	—	47	1	no	—
775	C₄×D₄	—	47	2	no	—
776	C₄×D₄	—	47	1	no	—
777	C₄×D₄	—	47	2	no	—
778	C₄×D₄	—	94	1	no	—
779	C₄×D₄	—	94	2	no	—
780	C₄×D₄	—	94	1	no	—
781	C₄×D₄	—	94	2	no	—
782	C₄×D₄	C₂²×D₄₇	1	1	yes	characteristic
783	C₄×D₄	C₂²×D₄₇	1	2	yes	—
784	C₄×D₄	C₂²×D₄₇	1	1	yes	characteristic
785	C₄×D₄	C₂²×D₄₇	1	2	yes	—
786	#117	—	2	2	no	—
787	#117	—	2	1	no	—
788	#117	—	47	1	no	—
789	#117	—	47	2	no	—
790	#117	—	94	2	no	—
791	#117	—	94	1	no	—
792	#117	C₂²×D₄₇	1	1	yes	characteristic
793	#117	C₂²×D₄₇	1	2	yes	—
794	C₂×C₄⋊C₄	—	2	2	no	—
795	C₂×C₄⋊C₄	—	2	1	no	—
796	C₂×C₄⋊C₄	—	94	2	no	—
797	C₂×C₄⋊C₄	—	94	1	no	—
798	C₂×C₄⋊C₄	C₂²⋊D₄₇	1	2	yes	—
799	C₂×C₄⋊C₄	C₂²⋊D₄₇	1	1	yes	characteristic
800	C₂×C₄²	—	2	1	no	—
801	C₂×C₄²	—	2	2	no	—
802	C₂×C₄²	—	94	1	no	—
803	C₂×C₄²	—	94	2	no	—
804	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
805	C₂×C₄²	C₂²×D₄₇	1	2	yes	—
806	#107	—	47	1	no	—
807	#107	—	47	1	no	—
808	#107	—	47	2	no	—
809	#107	—	47	2	no	—
810	#107	—	47	2	no	—
811	#107	—	47	2	no	—
812	#107	—	47	2	no	—
813	#107	—	47	2	no	—
814	#107	—	47	2	no	—
815	#107	—	47	2	no	—
816	#106	—	47	1	no	—
817	#106	—	47	1	no	—
818	#106	—	47	2	no	—
819	#106	—	47	2	no	—
820	#106	—	47	2	no	—
821	#106	—	47	2	no	—
822	#106	—	47	2	no	—
823	#106	—	47	2	no	—
824	#106	—	47	2	no	—
825	#106	—	47	2	no	—
826	C₄⋊C₈	—	47	1	no	—
827	C₄⋊C₈	—	47	1	no	—
828	C₄⋊C₈	—	47	2	no	—
829	C₄⋊C₈	—	47	2	no	—
830	C₄⋊C₈	—	47	2	no	—
831	C₄⋊C₈	—	47	2	no	—
832	C₄⋊C₈	—	47	2	no	—
833	#103	—	47	1	no	—
834	#103	—	47	1	no	—
835	#103	—	47	2	no	—
836	#103	—	47	2	no	—
837	#103	—	47	1	no	—
838	#103	—	47	1	no	—
839	#103	—	47	2	no	—
840	#103	—	47	2	no	—
841	#102	—	47	1	no	—
842	#102	—	47	1	no	—
843	#102	—	47	2	no	—
844	#102	—	47	2	no	—
845	#102	—	47	1	no	—
846	#102	—	47	1	no	—
847	#102	—	47	2	no	—
848	#102	—	47	2	no	—
849	#97	—	47	2	no	—
850	#97	—	47	2	no	—
851	#97	—	47	2	no	—
852	#97	—	47	2	no	—
853	C₄×C₈	—	47	1	no	—
854	C₄×C₈	—	47	1	no	—
855	C₄×C₈	—	47	1	no	—
856	C₄×C₈	—	47	1	no	—
857	#41	—	2	2	no	—
858	#41	—	47	4	no	—
859	#41	—	94	2	no	—
860	#41	Q₈×D₄₇	1	4	yes	complemented
861	C₂×Q₈	—	2	2	no	—
862	C₂×Q₈	—	2	1	no	—
863	C₂×Q₈	—	2	2	no	—
864	C₂×Q₈	—	2	1	no	—
865	C₂×Q₈	—	4	2	no	—
866	C₂×Q₈	—	4	4	no	—
867	C₂×Q₈	—	47	1	no	—
868	C₂×Q₈	—	94	2	no	—
869	C₂×Q₈	—	94	1	no	—
870	C₂×Q₈	—	94	2	no	—
871	C₂×Q₈	—	94	1	no	—
872	C₂×Q₈	—	188	4	no	—
873	C₂×Q₈	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
874	C₂×Q₈	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
875	C₂×Q₈	C₂×C₂²⋊D₄₇	1	2	yes	—
876	C₂×Q₈	C₂³×D₄₇	1	1	yes	characteristic
877	C₂×D₄	—	2	1	no	—
878	C₂×D₄	—	47	1	no	—
879	C₂×D₄	—	94	1	no	—
880	C₂×D₄	C₂³×D₄₇	1	1	yes	characteristic
881	C₂²×C₄	—	2	1	no	—
882	C₂²×C₄	—	2	2	no	—
883	C₂²×C₄	—	2	1	no	—
884	C₂²×C₄	—	2	1	no	—
885	C₂²×C₄	—	2	2	no	—
886	C₂²×C₄	—	94	1	no	—
887	C₂²×C₄	—	94	1	no	—
888	C₂²×C₄	—	94	2	no	—
889	C₂²×C₄	—	94	2	no	—
890	C₂²×C₄	—	94	1	no	—
891	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
892	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
893	C₂²×C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
894	C₂²×C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
895	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
896	Q₁₆	—	47	4	no	—
897	SD₁₆	—	47	4	no	—
898	SD₁₆	—	47	4	no	—
899	D₈	—	47	4	no	—
900	C₂×C₈	—	47	4	no	—
901	C₂×C₈	—	47	1	no	—
902	C₂×C₈	—	47	1	no	—
903	C₂×C₈	—	47	1	no	—
904	C₂×C₈	—	47	1	no	—
905	C₂×C₈	—	47	2	no	—
906	C₂×C₈	—	47	2	no	—
907	C₂×C₈	—	94	2	no	—
908	C₂×C₈	—	94	4	no	—
909	C₄⋊C₄	—	2	2	no	—
910	C₄⋊C₄	—	2	2	no	—
911	C₄⋊C₄	—	2	2	no	—
912	C₄⋊C₄	—	2	2	no	—
913	C₄⋊C₄	—	2	1	no	—
914	C₄⋊C₄	—	2	2	no	—
915	C₄⋊C₄	—	2	2	no	—
916	C₄⋊C₄	—	2	1	no	—
917	C₄⋊C₄	—	2	1	no	—
918	C₄⋊C₄	—	2	2	no	—
919	C₄⋊C₄	—	2	1	no	—
920	C₄⋊C₄	—	2	2	no	—
921	C₄⋊C₄	—	2	2	no	—
922	C₄⋊C₄	—	2	2	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	1	no	—
933	C₄⋊C₄	—	94	1	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	1	no	—
939	C₄⋊C₄	—	94	2	no	—
940	C₄⋊C₄	—	94	1	no	—
941	C₄⋊C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
942	C₄⋊C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
943	C₄⋊C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
944	C₄⋊C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
945	C₄⋊C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
946	C₄⋊C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
947	C₄⋊C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
948	C₄⋊C₄	C₂³×D₄₇	1	1	yes	characteristic
949	C₄⋊C₄	C₂³×D₄₇	1	1	yes	characteristic
950	C₄⋊C₄	C₂³×D₄₇	1	2	yes	—
951	C₄⋊C₄	C₂³×D₄₇	1	2	yes	—
952	C₂²⋊C₄	—	2	1	no	—
953	C₂²⋊C₄	—	2	2	no	—
954	C₂²⋊C₄	—	2	2	no	—
955	C₂²⋊C₄	—	2	2	no	—
956	C₂²⋊C₄	—	2	1	no	—
957	C₂²⋊C₄	—	2	1	no	—
958	C₂²⋊C₄	—	94	1	no	—
959	C₂²⋊C₄	—	94	2	no	—
960	C₂²⋊C₄	—	94	2	no	—
961	C₂²⋊C₄	—	94	2	no	—
962	C₂²⋊C₄	—	94	1	no	—
963	C₂²⋊C₄	—	94	1	no	—
964	C₄²	—	2	1	no	—
965	C₄²	—	2	2	no	—
966	C₄²	—	2	2	no	—
967	C₄²	—	2	1	no	—
968	C₄²	—	2	1	no	—
969	C₄²	—	2	2	no	—
970	C₄²	—	94	1	no	—
971	C₄²	—	94	2	no	—
972	C₄²	—	94	2	no	—
973	C₄²	—	94	1	no	—
974	C₄²	—	94	1	no	—
975	C₄²	—	94	2	no	—
976	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
977	C₄²	C₂×C₂²⋊D₄₇	1	2	yes	—
978	C₄²	C₂×C₂²⋊D₄₇	1	2	yes	—
979	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
980	C₄²	C₂³×D₄₇	1	1	yes	characteristic
981	C₄²	C₂³×D₄₇	1	1	yes	characteristic
982	C₄²	C₂³×D₄₇	1	2	yes	—
983	C₄²	C₂³×D₄₇	1	2	yes	—
984	C₂³	—	2	1	no	—
985	C₂³	—	94	1	no	—
986	C₂³	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
987	Q₈	—	2	2	no	—
988	Q₈	—	2	2	no	—
989	Q₈	—	2	1	no	—
990	Q₈	—	4	2	no	—
991	Q₈	—	4	4	no	—
992	Q₈	—	4	2	no	—
993	Q₈	—	8	2	no	—
994	Q₈	—	8	1	no	—
995	Q₈	—	47	2	no	—
996	Q₈	—	94	1	no	—
997	Q₈	—	376	2	no	—
998	Q₈	—	376	1	no	—
999	Q₈	—	188	4	no	—
1000	Q₈	—	188	2	no	—
1001	Q₈	C₂×Q₈×D₄₇	1	2	yes	—
1002	D₄	—	2	4	no	—
1003	D₄	—	2	1	no	—
1004	D₄	—	47	2	no	—
1005	D₄	—	94	4	no	—
1006	D₄	—	94	1	no	—
1007	D₄	C₂×Q₈×D₄₇	1	2	yes	—
1008	C₂×C₄	—	2	1	no	—
1009	C₂×C₄	—	2	4	no	—
1010	C₂×C₄	—	2	2	no	—
1011	C₂×C₄	—	2	2	no	—
1012	C₂×C₄	—	2	1	no	—
1013	C₂×C₄	—	2	2	no	—
1014	C₂×C₄	—	2	1	no	—
1015	C₂×C₄	—	4	1	no	—
1016	C₂×C₄	—	4	2	no	—
1017	C₂×C₄	—	4	2	no	—
1018	C₂×C₄	—	4	4	no	—
1019	C₂×C₄	—	4	2	no	—
1020	C₂×C₄	—	8	1	no	—
1021	C₂×C₄	—	8	2	no	—
1022	C₂×C₄	—	94	1	no	—
1023	C₂×C₄	—	94	4	no	—
1024	C₂×C₄	—	94	2	no	—
1025	C₂×C₄	—	94	1	no	—
1026	C₂×C₄	—	94	2	no	—
1027	C₂×C₄	—	94	1	no	—
1028	C₂×C₄	—	376	1	no	—
1029	C₂×C₄	—	376	2	no	—
1030	C₂×C₄	—	188	4	no	—
1031	C₂×C₄	—	188	2	no	—
1032	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
1033	C₂×C₄	C₂²×C₂²⋊D₄₇	1	2	yes	—
1034	C₂×C₄	C₂²×C₂²⋊D₄₇	1	2	yes	—
1035	C₂×C₄	C₂²×C₂²⋊D₄₇	1	2	yes	—
1036	C₂×C₄	C₂²×C₂²⋊D₄₇	1	2	yes	—
1037	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
1038	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
1039	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
1040	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
1041	C₂×C₄	C₂×Q₈×D₄₇	1	2	yes	—
1042	C₂×C₄	#13094072	1	2	yes	—
1043	C₂×C₄	C₂⁴×D₄₇	1	1	yes	characteristic
1044	C₈	—	47	2	no	—
1045	C₈	—	47	2	no	—
1046	C₈	—	94	1	no	—
1047	C₈	—	94	1	no	—
1048	C₈	—	94	2	no	—
1049	C₈	—	94	2	no	—
1050	C₂²	—	2	1	no	—
1051	C₂²	—	2	1	no	—
1052	C₂²	—	2	2	no	—
1053	C₂²	—	4	1	no	—
1054	C₂²	—	4	1	no	—
1055	C₂²	—	94	2	no	—
1056	C₂²	—	188	1	no	—
1057	C₂²	—	188	1	no	—
1058	C₂²	Q₈×C₂²⋊D₄₇	1	2	yes	—
1059	C₂²	C₂³×C₂²⋊D₄₇	1	1	yes	characteristic
1060	C₄	—	2	1	no	—
1061	C₄	—	2	2	no	—
1062	C₄	—	2	2	no	—
1063	C₄	—	2	2	no	—
1064	C₄	—	2	1	no	—
1065	C₄	—	2	2	no	—
1066	C₄	—	2	2	no	—
1067	C₄	—	2	1	no	—
1068	C₄	—	4	2	no	—
1069	C₄	—	4	1	no	—
1070	C₄	—	4	1	no	—
1071	C₄	—	4	2	no	—
1072	C₄	—	94	2	no	—
1073	C₄	—	188	2	no	—
1074	C₄	—	188	1	no	—
1075	C₄	—	188	1	no	—
1076	C₄	—	188	2	no	—
1077	C₄	Q₈×C₂²⋊D₄₇	1	2	yes	—
1078	C₄	#15689921	1	2	yes	—
1079	C₄	C₂²×Q₈×D₄₇	1	1	yes	characteristic
1080	C₄	C₂×#13094072	1	1	yes	characteristic
1081	C₂	—	2	2	no	—
1082	C₂	—	4	2	no	—
1083	C₂	—	188	2	no	—
1084	C₂	C₂×Q₈×C₂²⋊D₄₇	1	1	yes	characteristic
1085	C₂	C₂×#15689921	1	1	yes	characteristic
1086	C₂	#20258159	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×C₂²⋊D₄₇
commutator, cosocle	C₂×C₄×C₄₇	C₂⁵
Frattini	C₂×C₄	C₂⁴×D₄₇
Fitting	Q₈×#41×C₄₇	C₂
socle	C₂²×C₄₇	C₂³×D₄
prime radical	C₂×#13094044	C₂²
hypercenter	Q₈×#41	D₄₇
hypocenter	C₄₇	#61365
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄×Q₈ ◁ Q₈×#41

Complements

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

N	H ≅ G/N	type
1. Q₈×#10625350	C₂	semidirect
2. #20256351	C₂	semidirect
3. #20256342	C₂	semidirect
4. #20256333	C₂	semidirect
5. #20256327	C₂	semidirect
6. #20256320	C₂	semidirect
7. #20256316	C₂	semidirect
8. #20256309	C₂	semidirect
9. #20256305	C₂	semidirect
10. #20256298	C₂	semidirect
11. #20256294	C₂	semidirect
12. #20256287	C₂	semidirect
13. #20256283	C₂	semidirect
14. #20253910	C₂	semidirect
15. #20253898	C₂	semidirect
16. #20253176	C₂	semidirect
17. #20253176	C₂	semidirect
18. #20253170	C₂	semidirect
19. #20253170	C₂	semidirect
20. C₂×#15689254	C₂	semidirect
23. Q₈×#41×C₄₇	C₂	semidirect
137. #13094044	Q₈	semidirect
314. #41×C₄₇	C₂×Q₈	semidirect
340. #10625350	C₂×Q₈	semidirect
399. #10625337	C₂×Q₈	semidirect
400. #10625336	C₂×Q₈	semidirect
401. #10625335	C₂×Q₈	semidirect
402. #10625334	C₂×Q₈	semidirect
433. C₂×C₄₇⋊C₈	C₂×Q₈	semidirect
539. Q₈×#41	D₄₇	semidirect
678. C₄₇	#61365	semidirect
860. #41	Q₈×D₄₇	semidirect

Maximal subgroups

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

subgroup	index
Q₈×#10625350	2
#20256351	2
#20256342	2
#20256333	2
#20256327	2
#20256320	2
#20256316	2
#20256309	2
#20256305	2
#20256298	2
#20256294	2
#20256287	2
#20256283	2
#20253910	2
#20253898	2
#20253176	2
#20253170	2
C₂×#15689254	2
#20252186	2
C₄×#13094044	2
Q₈×#41×C₄₇	2
#61365	47