Subgroups — #27081315

Order 12032.

1658 conjugacy classes of subgroups.

The subgroup lattice has 1074 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
2	#20252493	C₂	1	2	yes	maximal, complemented
3	#20252491	C₂	1	2	yes	maximal, complemented
4	#20252489	C₂	1	1	yes	maximal, characteristic, complemented
5	#20252488	C₂	1	1	yes	maximal, characteristic, complemented
6	#20252485	C₂	1	1	yes	maximal, characteristic, complemented
7	#20252482	C₂	1	2	yes	maximal, complemented
8	#20252481	C₂	1	2	yes	maximal, complemented
9	#20252479	C₂	1	1	yes	maximal, characteristic, complemented
10	#20252474	C₂	1	1	yes	maximal, characteristic, complemented
11	#20252473	C₂	1	1	yes	maximal, characteristic, complemented
12	#20252470	C₂	1	1	yes	maximal, characteristic, complemented
13	#20252340	C₂	1	1	yes	maximal, characteristic, complemented
14	#20252333	C₂	1	2	yes	maximal, complemented
15	#20252330	C₂	1	1	yes	maximal, characteristic, complemented
16	#20252324	C₂	1	2	yes	maximal, complemented
17	#20252317	C₂	1	1	yes	maximal, characteristic, complemented
18	#446×D₄₇	C₂	1	1	yes	maximal, characteristic, complemented
19	#20252055	C₂	1	1	yes	maximal, characteristic
20	#20252049	C₂	1	2	yes	maximal
21	#20252034	C₂	1	2	yes	maximal
22	#20252027	C₂	1	1	yes	maximal, characteristic
23	C₄₇×#2984	C₂	1	1	yes	maximal, characteristic, complemented
24	Q₈×Dic₉₄	C₄	1	1	yes	characteristic
25	#15689851	C₄	1	1	yes	characteristic
26	#15689851	C₄	1	2	yes	—
27	#15689833	C₄	1	1	yes	characteristic
28	#15689833	C₄	1	2	yes	—
29	#15689828	C₄	1	1	yes	characteristic
30	#15689828	C₄	1	1	yes	characteristic
31	#15689828	C₄	1	2	yes	—
32	#15689828	C₄	1	2	yes	—
33	Q₈×D₁₈₈	C₄	1	1	yes	characteristic
34	Q₈×C₂²⋊D₄₇	C₄	1	1	yes	characteristic
35	Q₈×C₂²⋊D₄₇	C₄	1	1	yes	characteristic
36	#15689680	C₂²	1	2	yes	—
37	#15689680	C₂²	1	1	yes	characteristic
38	#15689677	C₂²	1	1	yes	characteristic
39	#15689677	C₂²	1	2	yes	—
40	#15689677	C₂²	1	1	yes	characteristic
41	#15689677	C₂²	1	2	yes	—
42	C₄×#10625350	C₂²	1	1	yes	characteristic
43	C₄×#10625350	C₂²	1	2	yes	—
44	C₄×Q₈×D₄₇	C₂²	1	1	yes	characteristic
45	C₄×Q₈×D₄₇	C₂²	1	1	yes	characteristic
46	#15689254	C₂²	1	1	yes	characteristic
47	#15689254	C₂²	1	1	yes	characteristic
48	#15689254	C₂²	1	1	yes	characteristic
49	#15689254	C₂²	1	2	yes	—
50	#15689254	C₂²	1	1	yes	characteristic
51	#15689254	C₂²	1	2	yes	—
52	#15689253	C₂²	1	1	yes	characteristic
53	#15689253	C₂²	1	2	yes	—
54	#15689253	C₂²	1	2	yes	—
55	#15689253	C₂²	1	1	yes	characteristic
56	#15689252	C₂²	1	2	yes	—
57	#15689252	C₂²	1	2	yes	—
58	#15689252	C₂²	1	2	yes	—
59	#15689252	C₂²	1	2	yes	—
60	#15689252	C₂²	1	2	yes	—
61	#15689252	C₂²	1	2	yes	—
62	#15689252	C₂²	1	2	yes	—
63	#15689252	C₂²	1	2	yes	—
64	#15689251	C₂²	1	2	yes	—
65	#15689251	C₂²	1	2	yes	—
66	#15689251	C₂²	1	2	yes	—
67	#15689251	C₂²	1	2	yes	—
68	#15689251	C₂²	1	2	yes	—
69	#15689251	C₂²	1	2	yes	—
70	#15689250	C₂²	1	1	yes	characteristic
71	#15689250	C₂²	1	1	yes	characteristic
72	#15689250	C₂²	1	2	yes	—
73	C₈×Dic₉₄	C₂²	1	1	yes	characteristic
74	C₈×Dic₉₄	C₂²	1	1	yes	characteristic
75	C₈×Dic₉₄	C₂²	1	2	yes	—
76	C₈×Dic₉₄	C₂²	1	2	yes	—
77	#15689247	C₂²	1	1	yes	characteristic
78	#15689247	C₂²	1	2	yes	—
79	#15689247	C₂²	1	1	yes	characteristic
80	#15689185	C₂²	1	2	yes	—
81	#15689183	C₂²	1	2	yes	—
82	#15689183	C₂²	1	1	yes	characteristic
83	#15689183	C₂²	1	2	yes	—
84	#15689183	C₂²	1	1	yes	characteristic
85	#15689182	C₂²	1	2	yes	—
86	#15689182	C₂²	1	2	yes	—
87	#15689181	C₂²	1	1	yes	characteristic
88	#15689181	C₂²	1	2	yes	—
89	#15689181	C₂²	1	2	yes	—
90	#15689181	C₂²	1	2	yes	—
91	#15689181	C₂²	1	2	yes	—
92	#15689181	C₂²	1	2	yes	—
93	#15689181	C₂²	1	1	yes	characteristic
94	#15689180	C₂²	1	2	yes	—
95	#15689180	C₂²	1	2	yes	—
96	#15689179	C₂²	1	2	yes	—
97	#15689179	C₂²	1	1	yes	characteristic
98	#15689178	C₂²	1	2	yes	—
99	#15689178	C₂²	1	2	yes	—
100	#15689176	C₂²	1	1	yes	characteristic
101	#15689176	C₂²	1	1	yes	characteristic
102	#15689175	C₂²	1	1	yes	characteristic
103	#15689175	C₂²	1	2	yes	—
104	#15689174	C₂²	1	1	yes	characteristic
105	#15689174	C₂²	1	1	yes	characteristic
106	#15689148	C₂²	1	1	yes	characteristic
107	#15689148	C₂²	1	1	yes	characteristic
108	#15689148	C₂²	1	2	yes	—
109	#15689148	C₂²	1	2	yes	—
110	#15689145	C₂²	1	2	yes	—
111	#15689145	C₂²	1	1	yes	characteristic
112	C₄⋊C₈×D₄₇	C₂²	1	2	yes	—
113	C₄⋊C₈×D₄₇	C₂²	1	1	yes	characteristic
114	#15689088	C₂²	1	1	yes	characteristic
115	#15689088	C₂²	1	1	yes	characteristic
116	#15689088	C₂²	1	2	yes	—
117	#15689080	C₂²	1	2	yes	—
118	#15689077	C₂²	1	2	yes	—
119	#15689077	C₂²	1	2	yes	—
120	#15689075	C₂²	1	2	yes	—
121	C₄×#10625324	C₂²	1	1	yes	characteristic
122	#97×D₄₇	C₂²	1	2	yes	—
123	C₄×C₈×D₄₇	C₂²	1	1	yes	characteristic
124	C₂×C₄×Q₈×C₄₇	C₂²	1	1	yes	characteristic
125	C₄₇×#446	C₂²	1	1	yes	characteristic
126	C₄₇×#446	C₂²	1	1	yes	characteristic
127	C₄₇×#446	C₂²	1	2	yes	—
128	C₄₇×#446	C₂²	1	2	yes	—
129	C₈×Q₈×C₄₇	C₂²	1	1	yes	characteristic
130	C₈×Q₈×C₄₇	C₂²	1	1	yes	characteristic
131	C₄₇×#432	C₂²	1	1	yes	characteristic
132	C₄₇×#432	C₂²	1	2	yes	—
133	C₄₇×#431	C₂²	1	2	yes	—
134	C₄₇×#431	C₂²	1	1	yes	characteristic
135	C₂×#10625350	C₂³	1	1	yes	characteristic
136	C₂×Q₈×D₄₇	C₂×C₄	1	1	yes	characteristic
137	C₂×Q₈×D₄₇	C₂×C₄	1	1	yes	characteristic
138	C₂×#10625324	C₂³	1	1	yes	characteristic
139	C₂×#10625324	C₂³	1	1	yes	characteristic
140	C₂×#10625324	C₂³	1	2	yes	—
141	C₂×C₈×D₄₇	C₂³	1	1	yes	characteristic
142	C₂×C₈×D₄₇	C₂³	1	1	yes	characteristic
143	C₂×C₈×D₄₇	C₂³	1	2	yes	—
144	#13094024	C₂×C₄	1	1	yes	characteristic
145	#13094024	C₂×C₄	1	2	yes	—
146	#13094024	C₂×C₄	1	2	yes	—
147	#13094024	C₂×C₄	1	1	yes	characteristic
148	#13094023	C₂×C₄	1	1	yes	characteristic
149	#13094023	C₂×C₄	1	2	yes	—
150	#13094023	C₂×C₄	1	1	yes	characteristic
151	#13094023	C₂×C₄	1	2	yes	—
152	#13094022	C₂×C₄	1	1	yes	characteristic
153	#13094022	C₂×C₄	1	1	yes	characteristic
154	#13094022	C₂×C₄	1	2	yes	—
155	#13094022	C₂×C₄	1	2	yes	—
156	#13094016	C₂×C₄	1	2	yes	—
157	#13094016	C₂×C₄	1	2	yes	—
158	#13094016	C₂×C₄	1	2	yes	—
159	#13094014	C₂×C₄	1	2	yes	—
160	#13094014	C₂×C₄	1	2	yes	—
161	#13094014	C₂×C₄	1	2	yes	—
162	#13094014	C₂×C₄	1	2	yes	—
163	#13094014	C₂×C₄	1	2	yes	—
164	#13094014	C₂×C₄	1	2	yes	—
165	#13094004	C₂×C₄	1	1	yes	characteristic
166	#13094004	C₂×C₄	1	1	yes	characteristic
167	#13094004	C₂×C₄	1	2	yes	—
168	#13094004	C₂×C₄	1	2	yes	—
169	#13094003	C₂×C₄	1	1	yes	characteristic
170	#13094003	C₂×C₄	1	1	yes	characteristic
171	#13094003	C₂×C₄	1	2	yes	—
172	#13094003	C₂×C₄	1	2	yes	—
173	#13094003	C₂×C₄	1	2	yes	—
174	#13094003	C₂×C₄	1	2	yes	—
175	#13094003	C₂×C₄	1	2	yes	—
176	#13094002	C₂×C₄	1	2	yes	—
177	#13094002	C₂×C₄	1	2	yes	—
178	#13094002	C₂×C₄	1	2	yes	—
179	#13094002	C₂×C₄	1	2	yes	—
180	#13094002	C₂×C₄	1	2	yes	—
181	#13094002	C₂×C₄	1	2	yes	—
182	#13094000	C₂×C₄	1	1	yes	characteristic
183	#13094000	C₂×C₄	1	1	yes	characteristic
184	#13094000	C₂×C₄	1	2	yes	—
185	#13094000	C₂×C₄	1	2	yes	—
186	Q₈×Dic₄₇	C₂×C₄	1	1	yes	characteristic
187	Q₈×Dic₄₇	C₂×C₄	1	1	yes	characteristic
188	C₄×Dic₉₄	C₂×C₄	1	1	yes	characteristic
189	C₄×Dic₉₄	C₂×C₄	1	2	yes	—
190	C₄×Dic₉₄	C₂×C₄	1	1	yes	characteristic
191	C₄×Dic₉₄	C₂×C₄	1	2	yes	—
192	C₄×Dic₉₄	C₂³	1	1	yes	characteristic
193	C₄×Dic₉₄	C₂³	1	1	yes	characteristic
194	C₄×Dic₉₄	C₂³	1	2	yes	—
195	C₄×Dic₉₄	C₂³	1	2	yes	—
196	C₄×Dic₉₄	C₂³	1	2	yes	—
197	C₄×Dic₉₄	C₂³	1	2	yes	—
198	C₄×Dic₉₄	C₂³	1	2	yes	—
199	#13093989	C₂×C₄	1	1	yes	characteristic
200	#13093989	C₂×C₄	1	1	yes	characteristic
201	#13093989	C₂×C₄	1	2	yes	—
202	#13093989	C₂×C₄	1	2	yes	—
203	C₄×D₁₈₈	C₂×C₄	1	1	yes	characteristic
204	C₄×D₁₈₈	C₂×C₄	1	2	yes	—
205	C₄×D₁₈₈	C₂×C₄	1	1	yes	characteristic
206	C₄×D₁₈₈	C₂×C₄	1	2	yes	—
207	C₄×C₂²⋊D₄₇	C₂×C₄	1	1	yes	characteristic
208	C₄×C₂²⋊D₄₇	C₂×C₄	1	1	yes	characteristic
209	C₄×C₂²⋊D₄₇	C₂×C₄	1	2	yes	—
210	C₄×C₂²⋊D₄₇	C₂×C₄	1	2	yes	—
211	C₄×C₂²⋊D₄₇	C₂×C₄	1	1	yes	characteristic
212	C₄×C₂²⋊D₄₇	C₂×C₄	1	1	yes	characteristic
213	C₄×C₂²⋊D₄₇	C₂×C₄	1	2	yes	—
214	C₄×C₂²⋊D₄₇	C₂×C₄	1	2	yes	—
215	#13093983	C₂³	1	1	yes	characteristic
216	#13093983	C₂³	1	2	yes	—
217	#13093981	C₂³	1	2	yes	—
218	#13093981	C₂³	1	1	yes	characteristic
219	#13093981	C₂³	1	2	yes	—
220	#13093981	C₂³	1	1	yes	characteristic
221	C₄⋊C₄×D₄₇	C₂×C₄	1	1	yes	characteristic
222	C₄⋊C₄×D₄₇	C₂×C₄	1	1	yes	characteristic
223	C₄⋊C₄×D₄₇	C₂×C₄	1	2	yes	—
224	C₄⋊C₄×D₄₇	C₂×C₄	1	2	yes	—
225	C₄²×D₄₇	C₂³	1	1	yes	characteristic
226	C₄²×D₄₇	C₂³	1	2	yes	—
227	C₄²×D₄₇	C₂³	1	1	yes	characteristic
228	C₄²×D₄₇	C₂³	1	2	yes	—
229	C₄⋊(C₄₇⋊C₈)	C₂³	1	1	yes	characteristic
230	C₄⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
231	C₄⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
232	C₄⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
233	C₄⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
234	C₄⋊(C₄₇⋊C₈)	C₂³	1	1	yes	characteristic
235	C₄⋊(C₄₇⋊C₈)	C₂³	1	1	yes	characteristic
236	C₄⋊(C₄₇⋊C₈)	C₂³	1	1	yes	characteristic
237	Dic₄₇⋊C₈	C₂³	1	2	yes	—
238	Dic₄₇⋊C₈	C₂³	1	2	yes	—
239	Dic₄₇⋊C₈	C₂³	1	2	yes	—
240	Dic₄₇⋊C₈	C₂³	1	2	yes	—
241	Dic₄₇⋊C₈	C₂³	1	1	yes	characteristic
242	Dic₄₇⋊C₈	C₂³	1	2	yes	—
243	Dic₄₇⋊C₈	C₂³	1	2	yes	—
244	Dic₄₇⋊C₈	C₂³	1	2	yes	—
245	Dic₄₇⋊C₈	C₂³	1	2	yes	—
246	Dic₄₇⋊C₈	C₂³	1	2	yes	—
247	Dic₄₇⋊C₈	C₂³	1	1	yes	characteristic
248	Dic₄₇⋊C₈	C₂³	1	1	yes	characteristic
249	Dic₄₇⋊C₈	C₂³	1	2	yes	—
250	Dic₄₇⋊C₈	C₂³	1	1	yes	characteristic
251	C₂²⋊(C₄₇⋊C₈)	C₂³	1	1	yes	characteristic
252	C₂²⋊(C₄₇⋊C₈)	C₂³	1	1	yes	characteristic
253	C₂²⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
254	(C₂×D₄₇)⋊C₈	C₂³	1	1	yes	characteristic
255	(C₂×D₄₇)⋊C₈	C₂³	1	1	yes	characteristic
256	(C₂×D₄₇)⋊C₈	C₂³	1	1	yes	characteristic
257	(C₂×D₄₇)⋊C₈	C₂³	1	1	yes	characteristic
258	(C₂×D₄₇)⋊C₈	C₂³	1	2	yes	—
259	(C₂×D₄₇)⋊C₈	C₂³	1	2	yes	—
260	#13093935	C₂³	1	2	yes	—
261	#13093935	C₂³	1	2	yes	—
262	#13093935	C₂³	1	2	yes	—
263	#13093935	C₂³	1	2	yes	—
264	#13093934	C₂³	1	2	yes	—
265	#13093934	C₂³	1	2	yes	—
266	#13093934	C₂³	1	2	yes	—
267	#13093934	C₂³	1	2	yes	—
268	#13093934	C₂³	1	1	yes	characteristic
269	#13093934	C₂³	1	2	yes	—
270	#13093934	C₂³	1	1	yes	characteristic
271	C₄×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
272	C₄×C₄₇⋊C₈	C₂³	1	2	yes	—
273	C₄×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
274	C₈×Dic₄₇	C₂³	1	2	yes	—
275	C₈×Dic₄₇	C₂³	1	2	yes	—
276	C₈×Dic₄₇	C₂³	1	2	yes	—
277	C₈×Dic₄₇	C₂³	1	2	yes	—
278	C₈×Dic₄₇	C₂³	1	1	yes	characteristic
279	C₈×Dic₄₇	C₂³	1	2	yes	—
280	C₈×Dic₄₇	C₂³	1	1	yes	characteristic
281	C₂²×Q₈×C₄₇	C₂×C₄	1	1	yes	characteristic
282	C₄×Q₈×C₄₇	C₂×C₄	1	1	yes	characteristic
283	C₄×Q₈×C₄₇	C₂×C₄	1	1	yes	characteristic
284	C₄×Q₈×C₄₇	C₂×C₄	1	2	yes	—
285	C₄×Q₈×C₄₇	C₂³	1	1	yes	characteristic
286	C₄×Q₈×C₄₇	C₂³	1	1	yes	characteristic
287	C₄×Q₈×C₄₇	C₂³	1	2	yes	—
288	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
289	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
290	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
291	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
292	C₄⋊C₈×C₄₇	C₂³	1	1	yes	characteristic
293	C₄⋊C₈×C₄₇	C₂³	1	1	yes	characteristic
294	C₄⋊C₈×C₄₇	C₂³	1	1	yes	characteristic
295	C₄⋊C₈×C₄₇	C₂³	1	1	yes	characteristic
296	C₄⋊C₈×C₄₇	C₂³	1	2	yes	—
297	C₄⋊C₈×C₄₇	C₂³	1	2	yes	—
298	C₄⋊C₈×C₄₇	C₂³	1	2	yes	—
299	C₄⋊C₈×C₄₇	C₂³	1	2	yes	—
300	C₂²⋊C₈×C₄₇	C₂³	1	1	yes	characteristic
301	C₂²⋊C₈×C₄₇	C₂³	1	1	yes	characteristic
302	C₂²⋊C₈×C₄₇	C₂³	1	2	yes	—
303	#97×C₄₇	C₂³	1	2	yes	—
304	#97×C₄₇	C₂³	1	2	yes	—
305	#97×C₄₇	C₂³	1	2	yes	—
306	C₄×C₈×C₄₇	C₂³	1	2	yes	—
307	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
308	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
309	C₄×C₈×C₄₇	C₂³	1	2	yes	—
310	C₂×Q₈×C₄₇	—	4	2	no	—
311	C₂×Q₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
312	C₂×Q₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
313	C₂×Q₈×C₄₇	C₂²×C₄	1	2	yes	—
314	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
315	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
316	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
317	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
318	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
319	C₂×C₂²⋊D₄₇	C₂²×C₄	1	1	yes	characteristic
320	C₂×C₂²⋊D₄₇	C₂²×C₄	1	1	yes	characteristic
321	Q₈×D₄₇	—	4	2	no	—
322	Q₈×D₄₇	—	4	2	no	—
323	#10625350	—	2	2	no	—
324	#10625350	—	2	2	no	—
325	C₂×D₁₈₈	C₂²×C₄	1	1	yes	characteristic
326	C₂×C₄×D₄₇	C₂²×C₄	1	1	yes	characteristic
327	C₂×C₄×D₄₇	C₂²×C₄	1	1	yes	characteristic
328	C₂×C₄×D₄₇	C₂²×C₄	1	1	yes	characteristic
329	C₂×C₄×D₄₇	C₂²×C₄	1	2	yes	—
330	C₂×C₄×D₄₇	C₂²×C₄	1	1	yes	characteristic
331	C₂×C₄×D₄₇	C₂²×C₄	1	2	yes	—
332	C₂×C₄×D₄₇	C₂²×C₄	1	2	yes	—
333	C₂×C₄×D₄₇	C₂²×C₄	1	2	yes	—
334	C₂×C₄×D₄₇	C₂⁴	1	1	yes	characteristic
335	C₂×C₄×D₄₇	C₂⁴	1	1	yes	characteristic
336	C₂×Dic₉₄	C₂²×C₄	1	1	yes	characteristic
337	C₂×Dic₉₄	C₂²×C₄	1	1	yes	characteristic
338	C₂×Dic₉₄	C₂²×C₄	1	1	yes	characteristic
339	C₂×Dic₉₄	C₂²×C₄	1	2	yes	—
340	C₂×Dic₉₄	C₂²×C₄	1	2	yes	—
341	C₂×Dic₉₄	C₂²×C₄	1	2	yes	—
342	C₂×Dic₉₄	C₂²×C₄	1	2	yes	—
343	C₂×Dic₉₄	C₂²×C₄	1	2	yes	—
344	C₂×C₈×C₄₇	C₂⁴	1	1	yes	characteristic
345	C₂×C₈×C₄₇	C₂⁴	1	1	yes	characteristic
346	C₂×C₈×C₄₇	C₂⁴	1	2	yes	—
347	C₂×C₈×C₄₇	C₂⁴	1	2	yes	—
348	C₂×C₈×C₄₇	C₂⁴	1	1	yes	characteristic
349	C₂×C₈×C₄₇	C₂⁴	1	1	yes	characteristic
350	C₄⋊C₄×C₄₇	C₂²×C₄	1	2	yes	—
351	C₄⋊C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
352	C₄⋊C₄×C₄₇	C₂²×C₄	1	2	yes	—
353	C₄⋊C₄×C₄₇	C₂²×C₄	1	2	yes	—
354	C₄⋊C₄×C₄₇	C₂²×C₄	1	2	yes	—
355	C₄⋊C₄×C₄₇	C₂²×C₄	1	2	yes	—
356	C₄⋊C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
357	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
358	C₄²×C₄₇	C₂²×C₄	1	2	yes	—
359	C₄²×C₄₇	C₂²×C₄	1	2	yes	—
360	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
361	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
362	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
363	C₄²×C₄₇	C₂⁴	1	2	yes	—
364	C₄²×C₄₇	C₂⁴	1	2	yes	—
365	C₂²⋊Dic₄₇	C₂²×C₄	1	2	yes	—
366	C₂²⋊Dic₄₇	C₂²×C₄	1	2	yes	—
367	C₂²⋊Dic₄₇	C₂²×C₄	1	1	yes	characteristic
368	C₂²⋊Dic₄₇	C₂²×C₄	1	1	yes	characteristic
369	(C₂×D₄₇)⋊C₄	C₂²×C₄	1	2	yes	—
370	(C₂×D₄₇)⋊C₄	C₂²×C₄	1	1	yes	characteristic
371	(C₂×D₄₇)⋊C₄	C₂²×C₄	1	2	yes	—
372	(C₂×D₄₇)⋊C₄	C₂²×C₄	1	1	yes	characteristic
373	(C₂×D₄₇)⋊C₄	C₂²×C₄	1	2	yes	—
374	(C₂×D₄₇)⋊C₄	C₂²×C₄	1	1	yes	characteristic
375	(C₂×D₄₇)⋊C₄	C₂²×C₄	1	2	yes	—
376	(C₂×D₄₇)⋊C₄	C₂²×C₄	1	1	yes	characteristic
377	C₄⋊Dic₄₇	C₂²×C₄	1	2	yes	—
378	C₄⋊Dic₄₇	C₂²×C₄	1	2	yes	—
379	C₄⋊Dic₄₇	C₂²×C₄	1	1	yes	characteristic
380	C₄⋊Dic₄₇	C₂²×C₄	1	1	yes	characteristic
381	C₄⋊Dic₄₇	C₂²×C₄	1	2	yes	—
382	C₄⋊Dic₄₇	C₂²×C₄	1	1	yes	characteristic
383	C₄⋊Dic₄₇	C₂²×C₄	1	1	yes	characteristic
384	C₄⋊Dic₄₇	C₂²×C₄	1	2	yes	—
385	C₄⋊Dic₄₇	C₂²×C₄	1	2	yes	—
386	C₄⋊Dic₄₇	C₂²×C₄	1	2	yes	—
387	C₄⋊Dic₄₇	C₂²×C₄	1	2	yes	—
388	Dic₄₇⋊C₄	C₂²×C₄	1	2	yes	—
389	Dic₄₇⋊C₄	C₂²×C₄	1	2	yes	—
390	Dic₄₇⋊C₄	C₂²×C₄	1	2	yes	—
391	Dic₄₇⋊C₄	C₂²×C₄	1	2	yes	—
392	Dic₄₇⋊C₄	C₂²×C₄	1	2	yes	—
393	Dic₄₇⋊C₄	C₂²×C₄	1	2	yes	—
394	Dic₄₇⋊C₄	C₂²×C₄	1	2	yes	—
395	Dic₄₇⋊C₄	C₂²×C₄	1	1	yes	characteristic
396	Dic₄₇⋊C₄	C₂²×C₄	1	2	yes	—
397	Dic₄₇⋊C₄	C₂²×C₄	1	1	yes	characteristic
398	Dic₄₇⋊C₄	C₂²×C₄	1	2	yes	—
399	Dic₄₇⋊C₄	C₂²×C₄	1	1	yes	characteristic
400	Dic₄₇⋊C₄	C₂²×C₄	1	2	yes	—
401	Dic₄₇⋊C₄	C₂²×C₄	1	1	yes	characteristic
402	Dic₄₇⋊C₄	C₂²×C₄	1	2	yes	—
403	Dic₄₇⋊C₄	C₂²×C₄	1	2	yes	—
404	Dic₄₇⋊C₄	C₂²×C₄	1	2	yes	—
405	Dic₄₇⋊C₄	C₂²×C₄	1	2	yes	—
406	Dic₄₇⋊C₄	C₂²×C₄	1	2	yes	—
407	Dic₄₇⋊C₄	C₂²×C₄	1	2	yes	—
408	C₄×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
409	C₄×Dic₄₇	C₂²×C₄	1	2	yes	—
410	C₄×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
411	C₄×Dic₄₇	C₂²×C₄	1	2	yes	—
412	C₄×Dic₄₇	C₂²×C₄	1	2	yes	—
413	C₄×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
414	C₄×Dic₄₇	C₂²×C₄	1	2	yes	—
415	C₄×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
416	C₄×Dic₄₇	C₂⁴	1	2	yes	—
417	C₄×Dic₄₇	C₂⁴	1	2	yes	—
418	C₄×Dic₄₇	C₂⁴	1	1	yes	characteristic
419	C₄×Dic₄₇	C₂⁴	1	1	yes	characteristic
420	C₂×C₄₇⋊C₈	C₂⁴	1	2	yes	—
421	C₂×C₄₇⋊C₈	C₂⁴	1	1	yes	characteristic
422	C₂×C₄₇⋊C₈	C₂⁴	1	1	yes	characteristic
423	C₂×C₄₇⋊C₈	C₂⁴	1	1	yes	characteristic
424	C₂×C₄₇⋊C₈	C₂⁴	1	2	yes	—
425	C₂×C₄₇⋊C₈	C₂⁴	1	1	yes	characteristic
426	#10625324	—	2	2	no	—
427	#10625324	—	2	2	no	—
428	#10625324	—	2	4	no	—
429	C₈×D₄₇	—	2	2	no	—
430	C₈×D₄₇	—	2	4	no	—
431	C₈×D₄₇	—	2	2	no	—
432	C₂³×C₄₇	C₂³×C₄	1	1	yes	characteristic
433	C₂²×D₄₇	C₂³×C₄	1	1	yes	characteristic
434	C₂²×D₄₇	C₂³×C₄	1	1	yes	characteristic
435	Q₈×C₄₇	—	2	2	no	—
436	Q₈×C₄₇	—	2	2	no	—
437	Q₈×C₄₇	—	4	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	—	4	1	no	—
442	C₂×C₄×C₄₇	—	4	2	no	—
443	C₂×C₄×C₄₇	—	4	2	no	—
444	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
445	C₂×C₄×C₄₇	C₂³×C₄	1	2	yes	—
446	C₂×C₄×C₄₇	C₂³×C₄	1	2	yes	—
447	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
448	C₂×C₄×C₄₇	C₂³×C₄	1	2	yes	—
449	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
450	C₂×C₄×C₄₇	C₂³×C₄	1	2	yes	—
451	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
452	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
453	C₂×C₄×C₄₇	C₂⁵	1	1	yes	characteristic
454	C₂²⋊D₄₇	—	2	2	no	—
455	C₂²⋊D₄₇	—	2	2	no	—
456	C₂×Dic₄₇	C₂³×C₄	1	1	yes	characteristic
457	C₂×Dic₄₇	C₂³×C₄	1	2	yes	—
458	C₂×Dic₄₇	C₂³×C₄	1	2	yes	—
459	C₂×Dic₄₇	C₂³×C₄	1	1	yes	characteristic
460	C₂×Dic₄₇	C₂³×C₄	1	1	yes	characteristic
461	C₂×Dic₄₇	C₂³×C₄	1	2	yes	—
462	C₂×Dic₄₇	C₂³×C₄	1	1	yes	characteristic
463	C₂×Dic₄₇	C₂³×C₄	1	2	yes	—
464	C₂×Dic₄₇	C₂³×C₄	1	1	yes	characteristic
465	C₂×Dic₄₇	C₂³×C₄	1	1	yes	characteristic
466	D₁₈₈	—	2	2	no	—
467	C₄×D₄₇	—	2	2	no	—
468	C₄×D₄₇	—	2	2	no	—
469	C₄×D₄₇	—	2	1	no	—
470	C₄×D₄₇	—	2	1	no	—
471	C₄×D₄₇	—	4	1	no	—
472	C₄×D₄₇	—	4	2	no	—
473	C₄×D₄₇	—	4	1	no	—
474	C₄×D₄₇	—	4	2	no	—
475	C₄×D₄₇	—	4	2	no	—
476	C₄×D₄₇	—	4	2	no	—
477	C₄×D₄₇	2₋¹⁺⁴	1	2	yes	—
478	C₄×D₄₇	2₋¹⁺⁴	1	2	yes	—
479	Dic₉₄	—	2	2	no	—
480	Dic₉₄	—	2	2	no	—
481	Dic₉₄	—	2	2	no	—
482	Dic₉₄	—	4	2	no	—
483	Dic₉₄	—	4	2	no	—
484	Dic₉₄	—	4	2	no	—
485	Dic₉₄	—	4	2	no	—
486	Dic₉₄	—	4	2	no	—
487	C₈×C₄₇	—	2	1	no	—
488	C₈×C₄₇	—	2	2	no	—
489	C₈×C₄₇	—	2	1	no	—
490	C₈×C₄₇	—	2	1	no	—
491	C₈×C₄₇	—	2	2	no	—
492	C₈×C₄₇	—	2	1	no	—
493	C₄₇⋊C₈	—	2	1	no	—
494	C₄₇⋊C₈	—	2	2	no	—
495	C₄₇⋊C₈	—	2	1	no	—
496	C₄₇⋊C₈	—	2	1	no	—
497	C₄₇⋊C₈	—	2	1	no	—
498	C₄₇⋊C₈	—	2	2	no	—
499	#60254	—	47	1	no	maximal, Sylow
500	C₂²×C₄₇	—	2	1	no	—
501	C₂²×C₄₇	—	2	1	no	—
502	C₂²×C₄₇	—	2	1	no	—
503	C₂²×C₄₇	C₂⁴×C₄	1	1	yes	characteristic
504	C₂×D₄₇	—	2	1	no	—
505	C₂×D₄₇	—	2	1	no	—
506	C₂×D₄₇	—	2	1	no	—
507	C₂×D₄₇	—	2	1	no	—
508	C₂×D₄₇	—	2	1	no	—
509	C₂×D₄₇	#519	1	2	yes	—
510	C₄×C₄₇	—	2	1	no	—
511	C₄×C₄₇	—	2	2	no	—
512	C₄×C₄₇	—	2	1	no	—
513	C₄×C₄₇	—	2	2	no	—
514	C₄×C₄₇	—	2	1	no	—
515	C₄×C₄₇	—	2	2	no	—
516	C₄×C₄₇	—	2	1	no	—
517	C₄×C₄₇	—	2	2	no	—
518	C₄×C₄₇	#568	1	2	yes	—
519	C₄×C₄₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
520	C₄×C₄₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
521	Dic₄₇	—	2	1	no	—
522	Dic₄₇	—	2	2	no	—
523	Dic₄₇	—	2	2	no	—
524	Dic₄₇	—	2	1	no	—
525	Dic₄₇	—	2	1	no	—
526	Dic₄₇	—	2	2	no	—
527	Dic₄₇	—	2	1	no	—
528	Dic₄₇	—	2	2	no	—
529	Dic₄₇	—	2	1	no	—
530	Dic₄₇	#519	1	2	yes	—
531	Q₈×#41	—	47	1	no	—
532	#2987	—	47	2	no	—
533	#2987	—	47	2	no	—
534	#2986	—	47	1	no	—
535	#2986	—	47	1	no	—
536	#2985	—	47	2	no	—
537	#2985	—	47	1	no	—
538	#2985	—	47	1	no	—
539	#2985	—	47	2	no	—
540	#2984	—	47	1	no	—
541	#2984	D₄₇	1	1	yes	characteristic, complemented
542	#2983	—	47	1	no	—
543	#2983	—	47	1	no	—
544	Q₈×M₁₆	—	47	1	no	—
545	#2962	—	47	2	no	—
546	#2962	—	47	1	no	—
547	#2961	—	47	2	no	—
548	#2960	—	47	1	no	—
549	C₂×#446	—	47	1	no	—
550	#2925	—	47	1	no	—
551	#2925	—	47	2	no	—
552	#2923	—	47	2	no	—
553	#2922	—	47	1	no	—
554	C₂×C₄₇	—	4	1	no	—
555	C₂×C₄₇	C₂×#519	1	1	yes	characteristic
556	C₂×C₄₇	C₂×#568	1	1	yes	characteristic
557	C₂×C₄₇	#3573	1	1	yes	characteristic
558	D₄₇	—	2	2	no	—
559	D₄₇	—	4	1	no	—
560	Q₈²	—	47	1	no	—
561	#557	—	47	1	no	—
562	#557	—	47	2	no	—
563	#554	—	47	1	no	—
564	#554	—	47	2	no	—
565	#554	—	47	1	no	—
566	#554	—	47	1	no	—
567	#554	—	47	2	no	—
568	#554	—	47	2	no	—
569	D₄×Q₈	—	47	1	no	—
570	D₄×Q₈	—	47	1	no	—
571	D₄×Q₈	—	47	1	no	—
572	#533	—	47	1	no	—
573	#533	—	47	2	no	—
574	#533	—	47	1	no	—
575	#533	—	47	2	no	—
576	#533	—	47	1	no	—
577	#533	—	47	2	no	—
578	C₄×#41	—	47	1	no	—
579	C₄×#41	—	47	2	no	—
580	C₂×C₄×Q₈	—	47	1	no	—
581	C₂×C₄×Q₈	—	47	1	no	—
582	C₂×C₄×Q₈	C₂×D₄₇	1	1	yes	characteristic
583	#446	—	47	1	no	—
584	#446	—	47	1	no	—
585	#446	—	47	2	no	—
586	#446	—	47	1	no	—
587	#446	—	47	2	no	—
588	#446	—	47	1	no	—
589	#446	—	47	1	no	—
590	#446	—	47	1	no	—
591	#446	—	47	2	no	—
592	#446	—	47	2	no	—
593	#446	—	47	2	no	—
594	#446	—	47	2	no	—
595	#446	—	47	2	no	—
596	#446	—	47	2	no	—
597	#446	—	47	2	no	—
598	#446	—	47	2	no	—
599	#446	—	47	2	no	—
600	#446	—	47	2	no	—
601	#446	—	47	2	no	—
602	#446	—	47	2	no	—
603	#446	—	47	2	no	—
604	#446	—	47	2	no	—
605	#446	—	47	2	no	—
606	#446	—	47	1	no	—
607	#446	—	47	2	no	—
608	#446	—	47	1	no	—
609	#446	—	47	2	no	—
610	#446	C₂×D₄₇	1	1	yes	characteristic
611	#446	C₂×D₄₇	1	2	yes	—
612	#446	C₂×D₄₇	1	2	yes	—
613	#446	C₂×D₄₇	1	1	yes	characteristic
614	C₈×Q₈	—	47	1	no	—
615	C₈×Q₈	—	47	2	no	—
616	C₈×Q₈	—	47	1	no	—
617	C₈×Q₈	—	47	1	no	—
618	C₈×Q₈	—	47	2	no	—
619	C₈×Q₈	—	47	2	no	—
620	C₈×Q₈	—	47	1	no	—
621	C₈×Q₈	C₂×D₄₇	1	1	yes	characteristic
622	C₈×Q₈	C₂×D₄₇	1	1	yes	characteristic
623	#433	—	47	1	no	—
624	#433	—	47	1	no	—
625	#433	—	47	2	no	—
626	#433	—	47	2	no	—
627	#433	—	47	1	no	—
628	#433	—	47	1	no	—
629	#433	—	47	2	no	—
630	#433	—	47	2	no	—
631	#433	—	47	2	no	—
632	#433	—	47	2	no	—
633	#433	—	47	2	no	—
634	#433	—	47	2	no	—
635	#433	—	47	2	no	—
636	#433	—	47	2	no	—
637	#432	—	47	2	no	—
638	#432	—	47	2	no	—
639	#432	—	47	2	no	—
640	#432	—	47	1	no	—
641	#432	—	47	2	no	—
642	#432	—	47	2	no	—
643	#432	C₂×D₄₇	1	2	yes	—
644	#432	C₂×D₄₇	1	1	yes	characteristic
645	#431	—	47	1	no	—
646	#431	—	47	1	no	—
647	#431	—	47	1	no	—
648	#431	—	47	2	no	—
649	#431	—	47	1	no	—
650	#431	—	47	1	no	—
651	#431	C₂×D₄₇	1	1	yes	characteristic
652	#431	C₂×D₄₇	1	2	yes	—
653	#424	—	47	1	no	—
654	#424	—	47	1	no	—
655	#424	—	47	2	no	—
656	#424	—	47	2	no	—
657	#423	—	47	1	no	—
658	#423	—	47	2	no	—
659	C₂×C₄⋊C₈	—	47	2	no	—
660	C₂×C₄⋊C₈	—	47	1	no	—
661	#408	—	47	1	no	—
662	#408	—	47	1	no	—
663	#408	—	47	2	no	—
664	#405	—	47	2	no	—
665	#405	—	47	2	no	—
666	#405	—	47	2	no	—
667	C₄×M₁₆	—	47	2	no	—
668	C₄×M₁₆	—	47	1	no	—
669	C₂×#97	—	47	2	no	—
670	C₂×C₄×C₈	—	47	1	no	—
671	C₄₇	#60254	1	1	yes	characteristic, complemented, Sylow
672	C₂×#41	—	47	1	no	—
673	C₂²×Q₈	—	47	1	no	—
674	C₂²×Q₈	—	47	1	no	—
675	C₂²×Q₈	C₄×D₄₇	1	1	yes	characteristic
676	C₂×M₁₆	—	47	1	no	—
677	C₂×M₁₆	—	47	2	no	—
678	C₂×M₁₆	—	47	1	no	—
679	C₂²×C₈	—	47	1	no	—
680	C₂²×C₈	—	47	1	no	—
681	C₂²×C₈	—	47	2	no	—
682	C₄⋊Q₈	—	47	1	no	—
683	C₄⋊Q₈	—	47	1	no	—
684	C₄⋊Q₈	—	47	2	no	—
685	C₄⋊Q₈	—	47	2	no	—
686	C₄⋊Q₈	—	47	1	no	—
687	C₄⋊Q₈	—	47	2	no	—
688	C₄⋊Q₈	—	47	1	no	—
689	C₄⋊Q₈	—	47	2	no	—
690	C₄⋊Q₈	—	47	1	no	—
691	C₄⋊Q₈	—	47	2	no	—
692	C₄⋊Q₈	—	47	1	no	—
693	C₄⋊Q₈	—	47	2	no	—
694	#125	—	47	2	no	—
695	#125	—	47	2	no	—
696	#125	—	47	2	no	—
697	#125	—	47	2	no	—
698	#125	—	47	2	no	—
699	#125	—	47	2	no	—
700	#125	—	47	2	no	—
701	#125	—	47	2	no	—
702	#125	—	47	2	no	—
703	C₂²⋊Q₈	—	47	1	no	—
704	C₂²⋊Q₈	—	47	1	no	—
705	C₂²⋊Q₈	—	47	2	no	—
706	C₂²⋊Q₈	—	47	2	no	—
707	C₂²⋊Q₈	—	47	1	no	—
708	C₂²⋊Q₈	—	47	1	no	—
709	C₂²⋊Q₈	—	47	2	no	—
710	C₂²⋊Q₈	—	47	2	no	—
711	C₂²⋊Q₈	—	47	2	no	—
712	C₂²⋊Q₈	—	47	2	no	—
713	C₂²⋊Q₈	—	47	2	no	—
714	C₂²⋊Q₈	—	47	1	no	—
715	C₂²⋊Q₈	—	47	1	no	—
716	C₂²⋊Q₈	—	47	2	no	—
717	C₂²⋊Q₈	—	47	2	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	—	47	2	no	—
723	C₂²⋊Q₈	—	47	2	no	—
724	C₄×Q₈	—	47	1	no	—
725	C₄×Q₈	—	47	1	no	—
726	C₄×Q₈	—	47	1	no	—
727	C₄×Q₈	—	47	1	no	—
728	C₄×Q₈	—	47	2	no	—
729	C₄×Q₈	—	47	2	no	—
730	C₄×Q₈	—	47	1	no	—
731	C₄×Q₈	—	47	2	no	—
732	C₄×Q₈	—	47	1	no	—
733	C₄×Q₈	—	47	2	no	—
734	C₄×Q₈	—	47	1	no	—
735	C₄×Q₈	—	47	1	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	—	47	2	no	—
741	C₄×Q₈	C₄×D₄₇	1	1	yes	characteristic
742	C₄×Q₈	C₄×D₄₇	1	1	yes	characteristic
743	C₄×Q₈	C₄×D₄₇	1	2	yes	—
744	C₄×Q₈	C₂²×D₄₇	1	1	yes	characteristic
745	C₄×Q₈	C₂²×D₄₇	1	1	yes	characteristic
746	C₄×Q₈	C₂²×D₄₇	1	2	yes	—
747	C₄×D₄	—	47	1	no	—
748	C₄×D₄	—	47	1	no	—
749	C₄×D₄	—	47	2	no	—
750	C₄×D₄	—	47	2	no	—
751	C₄×D₄	—	47	1	no	—
752	C₄×D₄	—	47	1	no	—
753	C₄×D₄	—	47	2	no	—
754	C₄×D₄	—	47	2	no	—
755	C₄×D₄	—	47	1	no	—
756	C₄×D₄	—	47	2	no	—
757	C₄×D₄	—	47	1	no	—
758	C₄×D₄	—	47	2	no	—
759	#117	—	47	1	no	—
760	#117	—	47	2	no	—
761	#117	—	47	1	no	—
762	#117	—	47	2	no	—
763	#117	—	47	1	no	—
764	#117	—	47	2	no	—
765	C₂×C₄⋊C₄	—	47	1	no	—
766	C₂×C₄⋊C₄	—	47	1	no	—
767	C₂×C₄⋊C₄	—	47	2	no	—
768	C₂×C₄⋊C₄	—	47	2	no	—
769	C₂×C₄⋊C₄	C₄×D₄₇	1	1	yes	characteristic
770	C₂×C₄⋊C₄	C₄×D₄₇	1	2	yes	—
771	C₂×C₄²	—	47	1	no	—
772	C₂×C₄²	—	47	2	no	—
773	C₂×C₄²	—	47	1	no	—
774	C₂×C₄²	—	47	2	no	—
775	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
776	C₂×C₄²	C₂²×D₄₇	1	2	yes	—
777	C₄⋊C₈	—	47	2	no	—
778	C₄⋊C₈	—	47	2	no	—
779	C₄⋊C₈	—	47	2	no	—
780	C₄⋊C₈	—	47	2	no	—
781	C₄⋊C₈	—	47	2	no	—
782	C₄⋊C₈	—	47	2	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	—	47	2	no	—
788	C₄⋊C₈	—	47	2	no	—
789	C₄⋊C₈	—	47	2	no	—
790	C₄⋊C₈	—	47	2	no	—
791	C₄⋊C₈	—	47	1	no	—
792	C₄⋊C₈	—	47	2	no	—
793	C₄⋊C₈	—	47	1	no	—
794	C₄⋊C₈	—	47	2	no	—
795	C₄⋊C₈	—	47	1	no	—
796	C₄⋊C₈	—	47	1	no	—
797	C₄⋊C₈	—	47	2	no	—
798	C₄⋊C₈	—	47	2	no	—
799	C₄⋊C₈	C₂²×D₄₇	1	2	yes	—
800	C₄⋊C₈	C₂²×D₄₇	1	1	yes	characteristic
801	C₄⋊C₈	C₂²×D₄₇	1	1	yes	characteristic
802	C₄⋊C₈	C₂²×D₄₇	1	2	yes	—
803	C₄⋊C₈	C₂²×D₄₇	1	1	yes	characteristic
804	C₄⋊C₈	C₂²×D₄₇	1	1	yes	characteristic
805	C₄⋊C₈	C₂²×D₄₇	1	2	yes	—
806	C₄⋊C₈	C₂²×D₄₇	1	2	yes	—
807	C₂²⋊C₈	—	47	1	no	—
808	C₂²⋊C₈	—	47	1	no	—
809	C₂²⋊C₈	—	47	2	no	—
810	C₂²⋊C₈	—	47	1	no	—
811	C₂²⋊C₈	—	47	1	no	—
812	C₂²⋊C₈	—	47	2	no	—
813	C₂²⋊C₈	—	47	1	no	—
814	C₂²⋊C₈	—	47	2	no	—
815	C₂²⋊C₈	—	47	1	no	—
816	C₂²⋊C₈	C₂²×D₄₇	1	1	yes	characteristic
817	C₂²⋊C₈	C₂²×D₄₇	1	1	yes	characteristic
818	C₂²⋊C₈	C₂²×D₄₇	1	2	yes	—
819	#97	—	47	2	no	—
820	#97	—	47	2	no	—
821	#97	—	47	1	no	—
822	#97	—	47	1	no	—
823	#97	—	47	2	no	—
824	#97	—	47	2	no	—
825	#97	—	47	2	no	—
826	#97	—	47	2	no	—
827	#97	—	47	2	no	—
828	#97	—	47	2	no	—
829	#97	—	47	2	no	—
830	#97	C₂²×D₄₇	1	2	yes	—
831	#97	C₂²×D₄₇	1	2	yes	—
832	#97	C₂²×D₄₇	1	2	yes	—
833	C₄×C₈	—	47	1	no	—
834	C₄×C₈	—	47	1	no	—
835	C₄×C₈	—	47	2	no	—
836	C₄×C₈	—	47	2	no	—
837	C₄×C₈	—	47	2	no	—
838	C₄×C₈	—	47	2	no	—
839	C₄×C₈	—	47	2	no	—
840	C₄×C₈	—	47	1	no	—
841	C₄×C₈	—	47	1	no	—
842	C₄×C₈	—	47	2	no	—
843	C₄×C₈	C₂²×D₄₇	1	1	yes	characteristic
844	C₄×C₈	C₂²×D₄₇	1	1	yes	characteristic
845	C₄×C₈	C₂²×D₄₇	1	2	yes	—
846	C₄×C₈	C₂²×D₄₇	1	2	yes	—
847	#41	—	94	2	no	—
848	#41	—	94	2	no	—
849	C₂×Q₈	—	4	2	no	—
850	C₂×Q₈	—	47	1	no	—
851	C₂×Q₈	—	47	1	no	—
852	C₂×Q₈	—	47	1	no	—
853	C₂×Q₈	—	47	2	no	—
854	C₂×Q₈	—	47	2	no	—
855	C₂×Q₈	—	47	2	no	—
856	C₂×Q₈	—	47	2	no	—
857	C₂×Q₈	—	47	2	no	—
858	C₂×Q₈	—	188	2	no	—
859	C₂×Q₈	—	188	2	no	—
860	C₂×Q₈	C₂×C₄×D₄₇	1	1	yes	characteristic
861	C₂×Q₈	C₂×C₄×D₄₇	1	1	yes	characteristic
862	C₂×Q₈	C₂×C₄×D₄₇	1	2	yes	—
863	C₂×D₄	—	47	1	no	—
864	C₂×D₄	—	47	1	no	—
865	C₂×D₄	—	47	1	no	—
866	C₂²×C₄	—	47	1	no	—
867	C₂²×C₄	—	47	1	no	—
868	C₂²×C₄	—	47	1	no	—
869	C₂²×C₄	—	47	1	no	—
870	C₂²×C₄	—	47	1	no	—
871	C₂²×C₄	—	47	2	no	—
872	C₂²×C₄	—	47	1	no	—
873	C₂²×C₄	—	47	2	no	—
874	C₂²×C₄	—	47	2	no	—
875	C₂²×C₄	—	47	2	no	—
876	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
877	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
878	C₂²×C₄	C₂×C₄×D₄₇	1	2	yes	—
879	C₂²×C₄	C₂×C₄×D₄₇	1	2	yes	—
880	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
881	M₁₆	—	94	2	no	—
882	M₁₆	—	94	4	no	—
883	M₁₆	—	94	2	no	—
884	C₂×C₈	—	47	1	no	—
885	C₂×C₈	—	47	2	no	—
886	C₂×C₈	—	47	1	no	—
887	C₂×C₈	—	47	1	no	—
888	C₂×C₈	—	47	1	no	—
889	C₂×C₈	—	47	2	no	—
890	C₂×C₈	—	94	2	no	—
891	C₂×C₈	—	94	4	no	—
892	C₂×C₈	—	94	2	no	—
893	C₂×C₈	C₂³×D₄₇	1	1	yes	characteristic
894	C₂×C₈	C₂³×D₄₇	1	1	yes	characteristic
895	C₂×C₈	C₂³×D₄₇	1	2	yes	—
896	C₂×C₈	C₂³×D₄₇	1	1	yes	characteristic
897	C₂×C₈	C₂³×D₄₇	1	2	yes	—
898	C₂×C₈	C₂³×D₄₇	1	1	yes	characteristic
899	C₄⋊C₄	—	47	2	no	—
900	C₄⋊C₄	—	47	2	no	—
901	C₄⋊C₄	—	47	2	no	—
902	C₄⋊C₄	—	47	2	no	—
903	C₄⋊C₄	—	47	2	no	—
904	C₄⋊C₄	—	47	2	no	—
905	C₄⋊C₄	—	47	1	no	—
906	C₄⋊C₄	—	47	2	no	—
907	C₄⋊C₄	—	47	1	no	—
908	C₄⋊C₄	—	47	2	no	—
909	C₄⋊C₄	—	47	1	no	—
910	C₄⋊C₄	—	47	2	no	—
911	C₄⋊C₄	—	47	1	no	—
912	C₄⋊C₄	—	47	2	no	—
913	C₄⋊C₄	—	47	2	no	—
914	C₄⋊C₄	—	47	2	no	—
915	C₄⋊C₄	—	47	2	no	—
916	C₄⋊C₄	—	47	2	no	—
917	C₄⋊C₄	—	47	2	no	—
918	C₄⋊C₄	—	47	2	no	—
919	C₄⋊C₄	—	47	2	no	—
920	C₄⋊C₄	—	47	2	no	—
921	C₄⋊C₄	—	47	1	no	—
922	C₄⋊C₄	—	47	1	no	—
923	C₄⋊C₄	—	47	1	no	—
924	C₄⋊C₄	—	47	2	no	—
925	C₄⋊C₄	—	47	1	no	—
926	C₄⋊C₄	—	47	2	no	—
927	C₄⋊C₄	—	47	2	no	—
928	C₄⋊C₄	—	47	2	no	—
929	C₄⋊C₄	—	47	2	no	—
930	C₄⋊C₄	C₂×C₄×D₄₇	1	2	yes	—
931	C₄⋊C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
932	C₄⋊C₄	C₂×C₄×D₄₇	1	2	yes	—
933	C₄⋊C₄	C₂×C₄×D₄₇	1	2	yes	—
934	C₄⋊C₄	C₂×C₄×D₄₇	1	2	yes	—
935	C₄⋊C₄	C₂×C₄×D₄₇	1	2	yes	—
936	C₄⋊C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
937	C₂²⋊C₄	—	47	1	no	—
938	C₂²⋊C₄	—	47	1	no	—
939	C₂²⋊C₄	—	47	2	no	—
940	C₂²⋊C₄	—	47	2	no	—
941	C₂²⋊C₄	—	47	1	no	—
942	C₂²⋊C₄	—	47	2	no	—
943	C₂²⋊C₄	—	47	1	no	—
944	C₂²⋊C₄	—	47	2	no	—
945	C₂²⋊C₄	—	47	1	no	—
946	C₂²⋊C₄	—	47	2	no	—
947	C₂²⋊C₄	—	47	1	no	—
948	C₂²⋊C₄	—	47	2	no	—
949	C₄²	—	47	1	no	—
950	C₄²	—	47	2	no	—
951	C₄²	—	47	1	no	—
952	C₄²	—	47	2	no	—
953	C₄²	—	47	2	no	—
954	C₄²	—	47	1	no	—
955	C₄²	—	47	2	no	—
956	C₄²	—	47	1	no	—
957	C₄²	—	47	1	no	—
958	C₄²	—	47	2	no	—
959	C₄²	—	47	2	no	—
960	C₄²	—	47	1	no	—
961	C₄²	C₂×C₄×D₄₇	1	1	yes	characteristic
962	C₄²	C₂×C₄×D₄₇	1	2	yes	—
963	C₄²	C₂×C₄×D₄₇	1	2	yes	—
964	C₄²	C₂×C₄×D₄₇	1	1	yes	characteristic
965	C₄²	C₂³×D₄₇	1	1	yes	characteristic
966	C₄²	C₂³×D₄₇	1	1	yes	characteristic
967	C₄²	C₂³×D₄₇	1	2	yes	—
968	C₄²	C₂³×D₄₇	1	2	yes	—
969	C₂³	—	47	1	no	—
970	C₂³	—	47	1	no	—
971	C₂³	C₂²×C₄×D₄₇	1	1	yes	characteristic
972	Q₈	—	2	2	no	—
973	Q₈	—	2	2	no	—
974	Q₈	—	4	2	no	—
975	Q₈	—	94	2	no	—
976	Q₈	—	94	2	no	—
977	Q₈	—	94	2	no	—
978	Q₈	—	188	2	no	—
979	Q₈	—	188	2	no	—
980	Q₈	—	188	2	no	—
981	Q₈	—	188	2	no	—
982	Q₈	—	188	2	no	—
983	D₄	—	94	2	no	—
984	D₄	—	94	2	no	—
985	D₄	—	94	2	no	—
986	C₂×C₄	—	2	2	no	—
987	C₂×C₄	—	2	1	no	—
988	C₂×C₄	—	2	1	no	—
989	C₂×C₄	—	4	1	no	—
990	C₂×C₄	—	4	2	no	—
991	C₂×C₄	—	4	2	no	—
992	C₂×C₄	—	47	1	no	—
993	C₂×C₄	—	47	2	no	—
994	C₂×C₄	—	47	2	no	—
995	C₂×C₄	—	47	1	no	—
996	C₂×C₄	—	47	1	no	—
997	C₂×C₄	—	47	1	no	—
998	C₂×C₄	—	47	2	no	—
999	C₂×C₄	—	47	2	no	—
1000	C₂×C₄	—	47	2	no	—
1001	C₂×C₄	—	47	1	no	—
1002	C₂×C₄	—	47	2	no	—
1003	C₂×C₄	—	47	1	no	—
1004	C₂×C₄	—	94	2	no	—
1005	C₂×C₄	—	94	2	no	—
1006	C₂×C₄	—	94	1	no	—
1007	C₂×C₄	—	94	1	no	—
1008	C₂×C₄	—	188	1	no	—
1009	C₂×C₄	—	188	2	no	—
1010	C₂×C₄	—	188	1	no	—
1011	C₂×C₄	—	188	2	no	—
1012	C₂×C₄	—	188	2	no	—
1013	C₂×C₄	—	188	2	no	—
1014	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
1015	C₂×C₄	C₂²×C₄×D₄₇	1	2	yes	—
1016	C₂×C₄	C₂²×C₄×D₄₇	1	2	yes	—
1017	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
1018	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
1019	C₂×C₄	C₂²×C₄×D₄₇	1	2	yes	—
1020	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
1021	C₂×C₄	C₂²×C₄×D₄₇	1	2	yes	—
1022	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
1023	C₂×C₄	C₂⁴×D₄₇	1	1	yes	characteristic
1024	C₈	—	2	1	no	—
1025	C₈	—	2	2	no	—
1026	C₈	—	2	1	no	—
1027	C₈	—	2	1	no	—
1028	C₈	—	2	2	no	—
1029	C₈	—	2	1	no	—
1030	C₈	—	94	1	no	—
1031	C₈	—	94	2	no	—
1032	C₈	—	94	1	no	—
1033	C₈	—	94	1	no	—
1034	C₈	—	94	2	no	—
1035	C₈	—	94	1	no	—
1036	C₂²	—	2	1	no	—
1037	C₂²	—	2	1	no	—
1038	C₂²	—	2	1	no	—
1039	C₂²	—	47	2	no	—
1040	C₂²	—	94	1	no	—
1041	C₂²	—	94	1	no	—
1042	C₂²	—	94	1	no	—
1043	C₂²	—	94	1	no	—
1044	C₂²	—	94	1	no	—
1045	C₂²	C₂³×C₄×D₄₇	1	1	yes	characteristic
1046	C₄	—	2	1	no	—
1047	C₄	—	2	2	no	—
1048	C₄	—	2	2	no	—
1049	C₄	—	2	1	no	—
1050	C₄	—	2	2	no	—
1051	C₄	—	2	1	no	—
1052	C₄	—	2	2	no	—
1053	C₄	—	2	1	no	—
1054	C₄	—	47	2	no	—
1055	C₄	—	94	1	no	—
1056	C₄	—	94	1	no	—
1057	C₄	—	94	2	no	—
1058	C₄	—	94	2	no	—
1059	C₄	—	94	2	no	—
1060	C₄	—	94	1	no	—
1061	C₄	—	94	2	no	—
1062	C₄	—	94	1	no	—
1063	C₄	—	94	1	no	—
1064	C₄	#15689889	1	2	yes	—
1065	C₄	2₋¹⁺⁴×D₄₇	1	1	yes	characteristic
1066	C₄	2₋¹⁺⁴×D₄₇	1	1	yes	characteristic
1067	C₂	—	4	1	no	—
1068	C₂	—	94	2	no	—
1069	C₂	—	188	1	no	—
1070	C₂	#519×D₄₇	1	1	yes	characteristic
1071	C₂	C₂×#15689889	1	1	yes	characteristic
1072	C₂	#20258099	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂⁴×D₄₇
commutator, socle	C₂²×C₄₇	C₂⁴×C₄
Fitting	C₄₇×#2984	C₂
prime radical	C₂×#10625350	C₂³
cosocle	C₂×C₄×C₄₇	C₂⁵
hypercenter	#2984	D₄₇
hypocenter	C₄₇	#60254
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ #2984

Complements

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

N	H ≅ G/N	type
2. #20252493	C₂	semidirect
3. #20252491	C₂	semidirect
4. #20252489	C₂	semidirect
5. #20252488	C₂	semidirect
6. #20252485	C₂	semidirect
7. #20252482	C₂	semidirect
8. #20252481	C₂	semidirect
9. #20252479	C₂	semidirect
10. #20252474	C₂	semidirect
11. #20252473	C₂	semidirect
12. #20252470	C₂	semidirect
13. #20252340	C₂	semidirect
14. #20252333	C₂	semidirect
15. #20252330	C₂	semidirect
16. #20252324	C₂	semidirect
17. #20252317	C₂	semidirect
18. #446×D₄₇	C₂	semidirect
23. C₄₇×#2984	C₂	semidirect
541. #2984	D₄₇	semidirect
671. C₄₇	#60254	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
#20252493	2
#20252491	2
#20252489	2
#20252488	2
#20252485	2
#20252482	2
#20252481	2
#20252479	2
#20252474	2
#20252473	2
#20252470	2
#20252340	2
#20252333	2
#20252330	2
#20252324	2
#20252317	2
#446×D₄₇	2
#20252055	2
#20252049	2
#20252034	2
#20252027	2
C₄₇×#2984	2
#60254	47