Subgroups — #27081318

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	#20256966	C₂	1	1	yes	maximal, characteristic
2	#20252492	C₂	1	2	yes	maximal, complemented
3	#20252491	C₂	1	2	yes	maximal, complemented
4	#20252490	C₂	1	1	yes	maximal, characteristic, complemented
5	#20252488	C₂	1	1	yes	maximal, characteristic, complemented
6	#20252484	C₂	1	1	yes	maximal, characteristic, complemented
7	#20252484	C₂	1	2	yes	maximal, complemented
8	#20252480	C₂	1	2	yes	maximal, complemented
9	#20252478	C₂	1	1	yes	maximal, characteristic, complemented
10	#20252476	C₂	1	1	yes	maximal, characteristic, complemented
11	#20252471	C₂	1	1	yes	maximal, characteristic, complemented
12	#20252470	C₂	1	1	yes	maximal, characteristic, complemented
13	Q₈×#10625324	C₂	1	1	yes	maximal, characteristic, complemented
14	#20252336	C₂	1	2	yes	maximal, complemented
15	#20252330	C₂	1	1	yes	maximal, characteristic, complemented
16	#20252324	C₂	1	2	yes	maximal, complemented
17	#20252319	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	#20252051	C₂	1	2	yes	maximal
21	#20252036	C₂	1	2	yes	maximal
22	#20252027	C₂	1	1	yes	maximal, characteristic
23	C₄₇×#2985	C₂	1	1	yes	maximal, characteristic, complemented
24	#15689853	C₄	1	1	yes	characteristic
25	#15689850	C₄	1	2	yes	—
26	#15689848	C₄	1	1	yes	characteristic
27	#15689834	C₄	1	1	yes	characteristic
28	#15689831	C₄	1	1	yes	characteristic
29	#15689831	C₄	1	1	yes	characteristic
30	#15689829	C₄	1	2	yes	—
31	#15689827	C₄	1	2	yes	—
32	#15689827	C₄	1	2	yes	—
33	#15689788	C₄	1	1	yes	characteristic
34	#15689786	C₄	1	1	yes	characteristic
35	#15689786	C₄	1	1	yes	characteristic
36	#15689677	C₂²	1	1	yes	characteristic
37	#15689677	C₂²	1	2	yes	—
38	#15689677	C₂²	1	1	yes	characteristic
39	#15689677	C₂²	1	2	yes	—
40	#15689676	C₂²	1	2	yes	—
41	C₄×#10625350	C₂²	1	1	yes	characteristic
42	#15689591	C₂²	1	2	yes	—
43	C₂×C₄×Dic₉₄	C₂²	1	1	yes	characteristic
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	2	yes	—
49	#15689253	C₂²	1	1	yes	characteristic
50	#15689253	C₂²	1	1	yes	characteristic
51	#15689253	C₂²	1	1	yes	characteristic
52	#15689253	C₂²	1	1	yes	characteristic
53	#15689253	C₂²	1	2	yes	—
54	#15689253	C₂²	1	2	yes	—
55	#15689253	C₂²	1	2	yes	—
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	#15689251	C₂²	1	2	yes	—
61	#15689251	C₂²	1	2	yes	—
62	#15689251	C₂²	1	2	yes	—
63	#15689251	C₂²	1	2	yes	—
64	#15689251	C₂²	1	2	yes	—
65	#15689251	C₂²	1	2	yes	—
66	#15689250	C₂²	1	1	yes	characteristic
67	#15689250	C₂²	1	2	yes	—
68	#15689250	C₂²	1	2	yes	—
69	#15689250	C₂²	1	1	yes	characteristic
70	#15689250	C₂²	1	2	yes	—
71	#15689250	C₂²	1	2	yes	—
72	#15689250	C₂²	1	2	yes	—
73	Q₈×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
74	Q₈×C₄₇⋊C₈	C₂²	1	2	yes	—
75	Q₈×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
76	C₈×Dic₉₄	C₂²	1	2	yes	—
77	#15689247	C₂²	1	1	yes	characteristic
78	#15689247	C₂²	1	1	yes	characteristic
79	#15689247	C₂²	1	2	yes	—
80	#15689185	C₂²	1	2	yes	—
81	#15689185	C₂²	1	2	yes	—
82	#15689184	C₂²	1	2	yes	—
83	#15689184	C₂²	1	2	yes	—
84	#15689183	C₂²	1	1	yes	characteristic
85	#15689183	C₂²	1	2	yes	—
86	#15689183	C₂²	1	2	yes	—
87	#15689183	C₂²	1	1	yes	characteristic
88	#15689182	C₂²	1	2	yes	—
89	#15689181	C₂²	1	1	yes	characteristic
90	#15689181	C₂²	1	2	yes	—
91	#15689181	C₂²	1	1	yes	characteristic
92	#15689179	C₂²	1	2	yes	—
93	#15689179	C₂²	1	1	yes	characteristic
94	#15689179	C₂²	1	2	yes	—
95	#15689178	C₂²	1	2	yes	—
96	#15689177	C₂²	1	2	yes	—
97	#15689177	C₂²	1	2	yes	—
98	#15689177	C₂²	1	2	yes	—
99	#15689176	C₂²	1	1	yes	characteristic
100	#15689176	C₂²	1	1	yes	characteristic
101	#15689175	C₂²	1	1	yes	characteristic
102	#15689174	C₂²	1	1	yes	characteristic
103	#15689174	C₂²	1	2	yes	—
104	#15689174	C₂²	1	1	yes	characteristic
105	#15689173	C₂²	1	2	yes	—
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	#15689080	C₂²	1	2	yes	—
119	#15689077	C₂²	1	2	yes	—
120	C₄×#10625324	C₂²	1	1	yes	characteristic
121	C₄×#10625324	C₂²	1	2	yes	—
122	#97×D₄₇	C₂²	1	2	yes	—
123	C₄×C₈×D₄₇	C₂²	1	1	yes	characteristic
124	C₄₇×#533	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×#433	C₂²	1	2	yes	—
132	C₄₇×#433	C₂²	1	2	yes	—
133	C₄₇×#432	C₂²	1	1	yes	characteristic
134	C₄₇×#431	C₂²	1	1	yes	characteristic
135	C₂×#10625350	C₂³	1	1	yes	characteristic
136	C₂²×Dic₉₄	C₂×C₄	1	1	yes	characteristic
137	C₂×Q₈×D₄₇	C₂×C₄	1	1	yes	characteristic
138	C₂×Q₈×D₄₇	C₂×C₄	1	1	yes	characteristic
139	C₂×#10625324	C₂³	1	1	yes	characteristic
140	C₂×#10625324	C₂³	1	1	yes	characteristic
141	C₂×#10625324	C₂³	1	2	yes	—
142	C₂×C₈×D₄₇	C₂³	1	1	yes	characteristic
143	C₂×C₈×D₄₇	C₂³	1	1	yes	characteristic
144	C₂×C₈×D₄₇	C₂³	1	2	yes	—
145	#13094023	C₂×C₄	1	2	yes	—
146	#13094023	C₂×C₄	1	2	yes	—
147	#13094023	C₂×C₄	1	2	yes	—
148	#13094023	C₂×C₄	1	2	yes	—
149	#13094023	C₂×C₄	1	1	yes	characteristic
150	#13094023	C₂×C₄	1	1	yes	characteristic
151	#13094022	C₂×C₄	1	1	yes	characteristic
152	#13094022	C₂×C₄	1	1	yes	characteristic
153	#13094022	C₂×C₄	1	2	yes	—
154	#13094022	C₂×C₄	1	2	yes	—
155	#13094015	C₂×C₄	1	2	yes	—
156	#13094015	C₂×C₄	1	2	yes	—
157	#13094014	C₂×C₄	1	2	yes	—
158	#13094014	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	#13094004	C₂×C₄	1	1	yes	characteristic
164	#13094004	C₂×C₄	1	1	yes	characteristic
165	#13094004	C₂×C₄	1	2	yes	—
166	#13094004	C₂×C₄	1	2	yes	—
167	#13094002	C₂×C₄	1	2	yes	—
168	#13094002	C₂×C₄	1	2	yes	—
169	#13094002	C₂×C₄	1	2	yes	—
170	#13094002	C₂×C₄	1	2	yes	—
171	#13094002	C₂×C₄	1	2	yes	—
172	#13094002	C₂×C₄	1	2	yes	—
173	#13094001	C₂×C₄	1	2	yes	—
174	#13094001	C₂×C₄	1	2	yes	—
175	#13094001	C₂×C₄	1	2	yes	—
176	#13094001	C₂×C₄	1	2	yes	—
177	#13094000	C₂×C₄	1	1	yes	characteristic
178	#13094000	C₂×C₄	1	1	yes	characteristic
179	#13094000	C₂×C₄	1	2	yes	—
180	#13094000	C₂×C₄	1	2	yes	—
181	Q₈×Dic₄₇	C₂×C₄	1	1	yes	characteristic
182	Q₈×Dic₄₇	C₂×C₄	1	1	yes	characteristic
183	C₄×Dic₉₄	C₂×C₄	1	1	yes	characteristic
184	C₄×Dic₉₄	C₂×C₄	1	2	yes	—
185	C₄×Dic₉₄	C₂×C₄	1	1	yes	characteristic
186	C₄×Dic₉₄	C₂×C₄	1	1	yes	characteristic
187	C₄×Dic₉₄	C₂×C₄	1	1	yes	characteristic
188	C₄×Dic₉₄	C₂³	1	1	yes	characteristic
189	C₄×Dic₉₄	C₂³	1	2	yes	—
190	C₄×Dic₉₄	C₂³	1	2	yes	—
191	C₄×Dic₉₄	C₂³	1	2	yes	—
192	C₄×Dic₉₄	C₂³	1	1	yes	characteristic
193	C₄×Dic₉₄	C₂³	1	2	yes	—
194	C₄×Dic₉₄	C₂³	1	2	yes	—
195	#13093989	C₂×C₄	1	1	yes	characteristic
196	#13093989	C₂×C₄	1	1	yes	characteristic
197	#13093989	C₂×C₄	1	2	yes	—
198	#13093989	C₂×C₄	1	2	yes	—
199	#13093989	C₂×C₄	1	2	yes	—
200	#13093989	C₂×C₄	1	2	yes	—
201	C₄×D₁₈₈	C₂×C₄	1	1	yes	characteristic
202	C₄×D₁₈₈	C₂×C₄	1	1	yes	characteristic
203	#13093986	C₂×C₄	1	2	yes	—
204	#13093986	C₂×C₄	1	2	yes	—
205	C₄×C₂²⋊D₄₇	C₂×C₄	1	1	yes	characteristic
206	C₄×C₂²⋊D₄₇	C₂×C₄	1	1	yes	characteristic
207	C₄×C₂²⋊D₄₇	C₂×C₄	1	1	yes	characteristic
208	C₄×C₂²⋊D₄₇	C₂×C₄	1	1	yes	characteristic
209	(C₂²⋊D₄₇)⋊C₄	C₂×C₄	1	2	yes	—
210	(C₂²⋊D₄₇)⋊C₄	C₂×C₄	1	2	yes	—
211	(C₂²⋊D₄₇)⋊C₄	C₂×C₄	1	2	yes	—
212	(C₂²⋊D₄₇)⋊C₄	C₂×C₄	1	2	yes	—
213	#13093983	C₂³	1	1	yes	characteristic
214	#13093981	C₂³	1	2	yes	—
215	#13093981	C₂³	1	2	yes	—
216	#13093981	C₂³	1	1	yes	characteristic
217	#13093981	C₂³	1	1	yes	characteristic
218	C₂×C₄⋊Dic₄₇	C₂×C₄	1	1	yes	characteristic
219	C₂×Dic₄₇⋊C₄	C₂×C₄	1	2	yes	—
220	C₄⋊C₄×D₄₇	C₂×C₄	1	2	yes	—
221	C₄⋊C₄×D₄₇	C₂×C₄	1	2	yes	—
222	C₄⋊C₄×D₄₇	C₂×C₄	1	1	yes	characteristic
223	C₄⋊C₄×D₄₇	C₂×C₄	1	1	yes	characteristic
224	C₂×C₄×Dic₄₇	C₂³	1	2	yes	—
225	C₄²×D₄₇	C₂³	1	1	yes	characteristic
226	C₄²×D₄₇	C₂³	1	2	yes	—
227	C₄²×D₄₇	C₂³	1	2	yes	—
228	C₄²×D₄₇	C₂³	1	1	yes	characteristic
229	C₄⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
230	C₄⋊(C₄₇⋊C₈)	C₂³	1	1	yes	characteristic
231	C₄⋊(C₄₇⋊C₈)	C₂³	1	1	yes	characteristic
232	C₄⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
233	C₄⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
234	C₄⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
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	1	yes	characteristic
245	Dic₄₇⋊C₈	C₂³	1	2	yes	—
246	Dic₄₇⋊C₈	C₂³	1	2	yes	—
247	Dic₄₇⋊C₈	C₂³	1	2	yes	—
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	#13093934	C₂³	1	2	yes	—
263	#13093934	C₂³	1	2	yes	—
264	#13093934	C₂³	1	2	yes	—
265	#13093934	C₂³	1	2	yes	—
266	#13093934	C₂³	1	1	yes	characteristic
267	#13093934	C₂³	1	2	yes	—
268	#13093934	C₂³	1	2	yes	—
269	#13093934	C₂³	1	2	yes	—
270	#13093934	C₂³	1	1	yes	characteristic
271	C₄×C₄₇⋊C₈	C₂³	1	2	yes	—
272	C₄×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
273	C₄×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
274	C₄×C₄₇⋊C₈	C₂³	1	2	yes	—
275	C₄×C₄₇⋊C₈	C₂³	1	2	yes	—
276	C₈×Dic₄₇	C₂³	1	2	yes	—
277	C₈×Dic₄₇	C₂³	1	1	yes	characteristic
278	C₈×Dic₄₇	C₂³	1	2	yes	—
279	C₈×Dic₄₇	C₂³	1	2	yes	—
280	C₈×Dic₄₇	C₂³	1	1	yes	characteristic
281	C₄⋊Q₈×C₄₇	C₂×C₄	1	1	yes	characteristic
282	C₄⋊Q₈×C₄₇	C₂×C₄	1	1	yes	characteristic
283	#125×C₄₇	C₂×C₄	1	2	yes	—
284	C₂²⋊Q₈×C₄₇	C₂×C₄	1	1	yes	characteristic
285	C₂²⋊Q₈×C₄₇	C₂×C₄	1	1	yes	characteristic
286	C₂²⋊Q₈×C₄₇	C₂×C₄	1	2	yes	—
287	C₄×Q₈×C₄₇	C₂³	1	1	yes	characteristic
288	C₄×Q₈×C₄₇	C₂³	1	1	yes	characteristic
289	C₄×Q₈×C₄₇	C₂³	1	2	yes	—
290	#117×C₄₇	C₂³	1	2	yes	—
291	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
292	C₄⋊C₈×C₄₇	C₂³	1	1	yes	characteristic
293	C₄⋊C₈×C₄₇	C₂³	1	1	yes	characteristic
294	C₄⋊C₈×C₄₇	C₂³	1	2	yes	—
295	C₄⋊C₈×C₄₇	C₂³	1	1	yes	characteristic
296	C₄⋊C₈×C₄₇	C₂³	1	1	yes	characteristic
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	2	yes	—
301	C₂²⋊C₈×C₄₇	C₂³	1	1	yes	characteristic
302	C₂²⋊C₈×C₄₇	C₂³	1	1	yes	characteristic
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	C₂²×C₄	1	1	yes	characteristic
311	C₂×Q₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
312	C₂×Q₈×C₄₇	C₂²×C₄	1	2	yes	—
313	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
314	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
315	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
316	C₂×C₂²⋊D₄₇	C₂²×C₄	1	1	yes	characteristic
317	C₂×C₂²⋊D₄₇	C₂²×C₄	1	1	yes	characteristic
318	C₂²×Dic₄₇	C₂²×C₄	1	2	yes	—
319	C₂²×Dic₄₇	C₂²×C₄	1	2	yes	—
320	Q₈×D₄₇	—	4	2	no	—
321	Q₈×D₄₇	—	4	2	no	—
322	#10625350	—	2	2	no	—
323	#10625350	—	2	2	no	—
324	C₂×D₁₈₈	C₂²×C₄	1	1	yes	characteristic
325	C₂×C₄×D₄₇	C₂²×C₄	1	1	yes	characteristic
326	C₂×C₄×D₄₇	C₂²×C₄	1	1	yes	characteristic
327	C₂×C₄×D₄₇	C₂²×C₄	1	2	yes	—
328	C₂×C₄×D₄₇	C₂²×C₄	1	2	yes	—
329	C₂×C₄×D₄₇	C₂²×C₄	1	1	yes	characteristic
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	C₂⁴	1	1	yes	characteristic
334	C₂×C₄×D₄₇	C₂⁴	1	1	yes	characteristic
335	C₂×Dic₉₄	—	4	2	no	—
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	2	yes	—
345	C₂×C₈×C₄₇	C₂⁴	1	2	yes	—
346	C₂×C₈×C₄₇	C₂⁴	1	1	yes	characteristic
347	C₂×C₈×C₄₇	C₂⁴	1	1	yes	characteristic
348	C₂×C₈×C₄₇	C₂⁴	1	1	yes	characteristic
349	C₂×C₈×C₄₇	C₂⁴	1	1	yes	characteristic
350	C₄⋊C₄×C₄₇	C₂²×C₄	1	2	yes	—
351	C₄⋊C₄×C₄₇	C₂²×C₄	1	2	yes	—
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	C₄⋊C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
358	C₄⋊C₄×C₄₇	C₂²×C₄	1	2	yes	—
359	C₂²⋊C₄×C₄₇	C₂²×C₄	1	2	yes	—
360	C₂²⋊C₄×C₄₇	C₂²×C₄	1	2	yes	—
361	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
362	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
363	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
364	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
365	C₄²×C₄₇	C₂⁴	1	2	yes	—
366	C₄²×C₄₇	C₂⁴	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	2	yes	—
371	(C₂×D₄₇)⋊C₄	C₂²×C₄	1	2	yes	—
372	(C₂×D₄₇)⋊C₄	C₂²×C₄	1	2	yes	—
373	(C₂×D₄₇)⋊C₄	C₂²×C₄	1	1	yes	characteristic
374	(C₂×D₄₇)⋊C₄	C₂²×C₄	1	1	yes	characteristic
375	(C₂×D₄₇)⋊C₄	C₂²×C₄	1	1	yes	characteristic
376	(C₂×D₄₇)⋊C₄	C₂²×C₄	1	1	yes	characteristic
377	C₄⋊Dic₄₇	C₂²×C₄	1	1	yes	characteristic
378	C₄⋊Dic₄₇	C₂²×C₄	1	2	yes	—
379	C₄⋊Dic₄₇	C₂²×C₄	1	2	yes	—
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	Dic₄₇⋊C₄	C₂²×C₄	1	2	yes	—
387	Dic₄₇⋊C₄	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	2	yes	—
396	Dic₄₇⋊C₄	C₂²×C₄	1	2	yes	—
397	Dic₄₇⋊C₄	C₂²×C₄	1	2	yes	—
398	Dic₄₇⋊C₄	C₂²×C₄	1	1	yes	characteristic
399	Dic₄₇⋊C₄	C₂²×C₄	1	1	yes	characteristic
400	Dic₄₇⋊C₄	C₂²×C₄	1	1	yes	characteristic
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	C₄×Dic₄₇	C₂²×C₄	1	2	yes	—
407	C₄×Dic₄₇	C₂²×C₄	1	2	yes	—
408	C₄×Dic₄₇	C₂²×C₄	1	2	yes	—
409	C₄×Dic₄₇	C₂²×C₄	1	2	yes	—
410	C₄×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
411	C₄×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
412	C₄×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
413	C₄×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
414	C₄×Dic₄₇	C₂²×C₄	1	2	yes	—
415	C₄×Dic₄₇	C₂²×C₄	1	2	yes	—
416	C₄×Dic₄₇	C₂⁴	1	1	yes	characteristic
417	C₄×Dic₄₇	C₂⁴	1	1	yes	characteristic
418	C₄×Dic₄₇	C₂⁴	1	2	yes	—
419	C₄×Dic₄₇	C₂⁴	1	2	yes	—
420	C₂×C₄₇⋊C₈	C₂⁴	1	1	yes	characteristic
421	C₂×C₄₇⋊C₈	C₂⁴	1	1	yes	characteristic
422	C₂×C₄₇⋊C₈	C₂⁴	1	2	yes	—
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	C₂³×C₄	1	1	yes	characteristic
443	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
444	C₂×C₄×C₄₇	C₂³×C₄	1	2	yes	—
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	2	yes	—
448	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
449	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
450	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
451	C₂×C₄×C₄₇	C₂⁵	1	1	yes	characteristic
452	C₂²⋊D₄₇	—	2	2	no	—
453	C₂²⋊D₄₇	—	2	2	no	—
454	C₂×Dic₄₇	—	4	2	no	—
455	C₂×Dic₄₇	—	4	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	2	yes	—
460	C₂×Dic₄₇	C₂³×C₄	1	2	yes	—
461	C₂×Dic₄₇	C₂³×C₄	1	1	yes	characteristic
462	C₂×Dic₄₇	C₂³×C₄	1	1	yes	characteristic
463	C₂×Dic₄₇	C₂³×C₄	1	1	yes	characteristic
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	1	no	—
473	C₄×D₄₇	—	4	2	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	2	no	—
491	C₈×C₄₇	—	2	1	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	1	no	—
512	C₄×C₄₇	—	2	2	no	—
513	C₄×C₄₇	—	2	2	no	—
514	C₄×C₄₇	—	2	2	no	—
515	C₄×C₄₇	—	2	2	no	—
516	C₄×C₄₇	—	2	1	no	—
517	C₄×C₄₇	—	2	1	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	1	no	—
527	Dic₄₇	—	2	1	no	—
528	Dic₄₇	—	2	2	no	—
529	Dic₄₇	—	2	2	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	1	no	—
537	#2985	—	47	2	no	—
538	#2985	—	47	2	no	—
539	#2985	D₄₇	1	1	yes	characteristic, complemented
540	#2984	—	47	1	no	—
541	#2984	—	47	1	no	—
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	2	no	—
551	#2925	—	47	1	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	2	no	—
566	#554	—	47	2	no	—
567	#554	—	47	1	no	—
568	#554	—	47	1	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	2	no	—
577	#533	C₂×D₄₇	1	1	yes	characteristic
578	C₄×#41	—	47	2	no	—
579	C₄×#41	—	47	1	no	—
580	C₂×C₄×Q₈	—	47	1	no	—
581	C₂×C₄×Q₈	—	47	1	no	—
582	C₂×C₄×Q₈	—	47	1	no	—
583	#446	—	47	1	no	—
584	#446	—	47	2	no	—
585	#446	—	47	1	no	—
586	#446	—	47	1	no	—
587	#446	—	47	2	no	—
588	#446	—	47	2	no	—
589	#446	—	47	2	no	—
590	#446	—	47	2	no	—
591	#446	—	47	1	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	1	no	—
604	#446	—	47	1	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	1	yes	characteristic
612	#446	C₂×D₄₇	1	2	yes	—
613	#446	C₂×D₄₇	1	2	yes	—
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	1	no	—
620	C₈×Q₈	—	47	2	no	—
621	C₈×Q₈	C₂×D₄₇	1	1	yes	characteristic
622	C₈×Q₈	C₂×D₄₇	1	1	yes	characteristic
623	#433	—	47	2	no	—
624	#433	—	47	2	no	—
625	#433	—	47	1	no	—
626	#433	—	47	1	no	—
627	#433	—	47	2	no	—
628	#433	—	47	2	no	—
629	#433	—	47	1	no	—
630	#433	—	47	1	no	—
631	#433	—	47	2	no	—
632	#433	—	47	2	no	—
633	#433	—	47	2	no	—
634	#433	—	47	2	no	—
635	#433	C₂×D₄₇	1	2	yes	—
636	#433	C₂×D₄₇	1	2	yes	—
637	#432	—	47	2	no	—
638	#432	—	47	2	no	—
639	#432	—	47	1	no	—
640	#432	—	47	2	no	—
641	#432	—	47	2	no	—
642	#432	—	47	2	no	—
643	#432	—	47	2	no	—
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	—	47	2	no	—
652	#431	C₂×D₄₇	1	1	yes	characteristic
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	1	no	—
668	C₄×M₁₆	—	47	2	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	—	47	1	no	—
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	2	no	—
687	C₄⋊Q₈	—	47	2	no	—
688	C₄⋊Q₈	—	47	2	no	—
689	C₄⋊Q₈	—	47	2	no	—
690	C₄⋊Q₈	—	47	1	no	—
691	C₄⋊Q₈	—	47	1	no	—
692	C₄⋊Q₈	C₄×D₄₇	1	1	yes	characteristic
693	C₄⋊Q₈	C₄×D₄₇	1	1	yes	characteristic
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	C₄×D₄₇	1	2	yes	—
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	2	no	—
708	C₂²⋊Q₈	—	47	2	no	—
709	C₂²⋊Q₈	—	47	2	no	—
710	C₂²⋊Q₈	—	47	2	no	—
711	C₂²⋊Q₈	—	47	1	no	—
712	C₂²⋊Q₈	—	47	1	no	—
713	C₂²⋊Q₈	—	47	2	no	—
714	C₂²⋊Q₈	—	47	2	no	—
715	C₂²⋊Q₈	—	47	2	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	C₄×D₄₇	1	1	yes	characteristic
722	C₂²⋊Q₈	C₄×D₄₇	1	1	yes	characteristic
723	C₂²⋊Q₈	C₄×D₄₇	1	2	yes	—
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	2	no	—
731	C₄×Q₈	—	47	2	no	—
732	C₄×Q₈	—	47	1	no	—
733	C₄×Q₈	—	47	1	no	—
734	C₄×Q₈	—	47	2	no	—
735	C₄×Q₈	—	47	1	no	—
736	C₄×Q₈	—	47	1	no	—
737	C₄×Q₈	—	47	1	no	—
738	C₄×Q₈	—	47	1	no	—
739	C₄×Q₈	—	47	2	no	—
740	C₄×Q₈	—	47	2	no	—
741	C₄×Q₈	—	47	2	no	—
742	C₄×Q₈	—	47	2	no	—
743	C₄×Q₈	—	47	2	no	—
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	1	no	—
750	C₄×D₄	—	47	1	no	—
751	C₄×D₄	—	47	2	no	—
752	C₄×D₄	—	47	2	no	—
753	C₄×D₄	—	47	2	no	—
754	C₄×D₄	—	47	2	no	—
755	C₄×D₄	—	47	2	no	—
756	C₄×D₄	—	47	2	no	—
757	C₄×D₄	—	47	1	no	—
758	C₄×D₄	—	47	1	no	—
759	#117	—	47	1	no	—
760	#117	—	47	1	no	—
761	#117	—	47	2	no	—
762	#117	—	47	1	no	—
763	#117	—	47	2	no	—
764	#117	C₂²×D₄₇	1	2	yes	—
765	C₂×C₄⋊C₄	—	47	2	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	—	47	1	no	—
770	C₂×C₄⋊C₄	—	47	1	no	—
771	C₂×C₄²	—	47	2	no	—
772	C₂×C₄²	—	47	1	no	—
773	C₂×C₄²	—	47	2	no	—
774	C₂×C₄²	—	47	1	no	—
775	C₂×C₄²	—	47	2	no	—
776	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
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	1	yes	characteristic
800	C₄⋊C₈	C₂²×D₄₇	1	2	yes	—
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	1	no	—
813	C₂²⋊C₈	—	47	2	no	—
814	C₂²⋊C₈	—	47	2	no	—
815	C₂²⋊C₈	—	47	1	no	—
816	C₂²⋊C₈	C₂²×D₄₇	1	2	yes	—
817	C₂²⋊C₈	C₂²×D₄₇	1	1	yes	characteristic
818	C₂²⋊C₈	C₂²×D₄₇	1	1	yes	characteristic
819	#97	—	47	2	no	—
820	#97	—	47	2	no	—
821	#97	—	47	2	no	—
822	#97	—	47	2	no	—
823	#97	—	47	1	no	—
824	#97	—	47	1	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	1	no	—
839	C₄×C₈	—	47	1	no	—
840	C₄×C₈	—	47	2	no	—
841	C₄×C₈	—	47	2	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	—	47	1	no	—
850	C₂×Q₈	—	47	1	no	—
851	C₂×Q₈	—	47	1	no	—
852	C₂×Q₈	—	47	2	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	—	188	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	2	no	—
868	C₂²×C₄	—	47	2	no	—
869	C₂²×C₄	—	47	1	no	—
870	C₂²×C₄	—	47	1	no	—
871	C₂²×C₄	—	47	1	no	—
872	C₂²×C₄	—	47	2	no	—
873	C₂²×C₄	—	47	2	no	—
874	C₂²×C₄	—	47	1	no	—
875	C₂²×C₄	—	47	1	no	—
876	C₂²×C₄	—	47	2	no	—
877	C₂²×C₄	—	47	2	no	—
878	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
879	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
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	1	no	—
886	C₂×C₈	—	47	1	no	—
887	C₂×C₈	—	47	2	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	2	yes	—
894	C₂×C₈	C₂³×D₄₇	1	1	yes	characteristic
895	C₂×C₈	C₂³×D₄₇	1	1	yes	characteristic
896	C₂×C₈	C₂³×D₄₇	1	2	yes	—
897	C₂×C₈	C₂³×D₄₇	1	1	yes	characteristic
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	2	no	—
906	C₄⋊C₄	—	47	2	no	—
907	C₄⋊C₄	—	47	2	no	—
908	C₄⋊C₄	—	47	2	no	—
909	C₄⋊C₄	—	47	1	no	—
910	C₄⋊C₄	—	47	1	no	—
911	C₄⋊C₄	—	47	2	no	—
912	C₄⋊C₄	—	47	2	no	—
913	C₄⋊C₄	—	47	1	no	—
914	C₄⋊C₄	—	47	1	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	1	no	—
920	C₄⋊C₄	—	47	2	no	—
921	C₄⋊C₄	—	47	2	no	—
922	C₄⋊C₄	—	47	2	no	—
923	C₄⋊C₄	—	47	1	no	—
924	C₄⋊C₄	—	47	1	no	—
925	C₄⋊C₄	—	47	1	no	—
926	C₄⋊C₄	—	47	2	no	—
927	C₄⋊C₄	—	47	2	no	—
928	C₄⋊C₄	C₂×C₄×D₄₇	1	2	yes	—
929	C₄⋊C₄	C₂×C₄×D₄₇	1	2	yes	—
930	C₄⋊C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
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	2	yes	—
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	2	no	—
942	C₂²⋊C₄	—	47	2	no	—
943	C₂²⋊C₄	—	47	1	no	—
944	C₂²⋊C₄	—	47	1	no	—
945	C₂²⋊C₄	—	47	1	no	—
946	C₂²⋊C₄	—	47	1	no	—
947	C₂²⋊C₄	C₂×C₄×D₄₇	1	2	yes	—
948	C₂²⋊C₄	C₂×C₄×D₄₇	1	2	yes	—
949	C₄²	—	47	2	no	—
950	C₄²	—	47	1	no	—
951	C₄²	—	47	2	no	—
952	C₄²	—	47	1	no	—
953	C₄²	—	47	2	no	—
954	C₄²	—	47	2	no	—
955	C₄²	—	47	1	no	—
956	C₄²	—	47	2	no	—
957	C₄²	—	47	1	no	—
958	C₄²	—	47	2	no	—
959	C₄²	—	47	1	no	—
960	C₄²	—	47	1	no	—
961	C₄²	—	47	2	no	—
962	C₄²	—	47	2	no	—
963	C₄²	C₂×C₄×D₄₇	1	1	yes	characteristic
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	—	47	1	no	—
991	C₂×C₄	—	47	2	no	—
992	C₂×C₄	—	47	2	no	—
993	C₂×C₄	—	47	1	no	—
994	C₂×C₄	—	47	2	no	—
995	C₂×C₄	—	47	2	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	1	no	—
1001	C₂×C₄	—	47	1	no	—
1002	C₂×C₄	—	94	2	no	—
1003	C₂×C₄	—	94	2	no	—
1004	C₂×C₄	—	94	1	no	—
1005	C₂×C₄	—	94	1	no	—
1006	C₂×C₄	—	188	1	no	—
1007	C₂×C₄	—	188	1	no	—
1008	C₂×C₄	—	188	2	no	—
1009	C₂×C₄	—	188	2	no	—
1010	C₂×C₄	—	188	2	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	1	yes	characteristic
1016	C₂×C₄	C₂²×C₄×D₄₇	1	2	yes	—
1017	C₂×C₄	C₂²×C₄×D₄₇	1	2	yes	—
1018	C₂×C₄	C₂²×C₄×D₄₇	1	2	yes	—
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	1	yes	characteristic
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	2	no	—
1028	C₈	—	2	1	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	1	no	—
1035	C₈	—	94	2	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	1	no	—
1051	C₄	—	2	2	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	1	no	—
1062	C₄	—	94	2	no	—
1063	C₄	—	94	1	no	—
1064	C₄	#15689888	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×#15689888	1	1	yes	characteristic
1072	C₂	#20258101	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂⁴×D₄₇
commutator, socle	C₂²×C₄₇	C₂⁴×C₄
Fitting	C₄₇×#2985	C₂
prime radical	C₂×#10625350	C₂³
cosocle	C₂×C₄×C₄₇	C₂⁵
hypercenter	#2985	D₄₇
hypocenter	C₄₇	#60254
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ #2985

Complements

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

N	H ≅ G/N	type
2. #20252492	C₂	semidirect
3. #20252491	C₂	semidirect
4. #20252490	C₂	semidirect
5. #20252488	C₂	semidirect
6. #20252484	C₂	semidirect
7. #20252484	C₂	semidirect
8. #20252480	C₂	semidirect
9. #20252478	C₂	semidirect
10. #20252476	C₂	semidirect
11. #20252471	C₂	semidirect
12. #20252470	C₂	semidirect
13. Q₈×#10625324	C₂	semidirect
14. #20252336	C₂	semidirect
15. #20252330	C₂	semidirect
16. #20252324	C₂	semidirect
17. #20252319	C₂	semidirect
18. #446×D₄₇	C₂	semidirect
23. C₄₇×#2985	C₂	semidirect
539. #2985	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
#20256966	2
#20252492	2
#20252491	2
#20252490	2
#20252488	2
#20252484	2
#20252480	2
#20252478	2
#20252476	2
#20252471	2
#20252470	2
Q₈×#10625324	2
#20252336	2
#20252330	2
#20252324	2
#20252319	2
#446×D₄₇	2
#20252055	2
#20252051	2
#20252036	2
#20252027	2
C₄₇×#2985	2
#60254	47