Subgroups — #27080825

Order 12032.

1950 conjugacy classes of subgroups.

The subgroup lattice has 1164 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20256682	C₂	1	1	yes	maximal, characteristic
2	#20252407	C₂	1	1	yes	maximal, characteristic, complemented
3	#20252404	C₂	1	1	yes	maximal, characteristic, complemented
4	#20252404	C₂	1	2	yes	maximal, complemented
5	#20252401	C₂	1	1	yes	maximal, characteristic, complemented
6	#20252398	C₂	1	2	yes	maximal, complemented
7	#20252396	C₂	1	1	yes	maximal, characteristic, complemented
8	#20252393	C₂	1	1	yes	maximal, characteristic, complemented
9	#20252392	C₂	1	1	yes	maximal, characteristic, complemented
10	#20252390	C₂	1	2	yes	maximal, complemented
11	#20252388	C₂	1	2	yes	maximal, complemented
12	#20252386	C₂	1	1	yes	maximal, characteristic, complemented
13	#20252319	C₂	1	1	yes	maximal, characteristic, complemented
14	#20252317	C₂	1	1	yes	maximal, characteristic, complemented
15	#20252097	C₂	1	1	yes	maximal, characteristic, complemented
16	#20252095	C₂	1	1	yes	maximal, characteristic, complemented
17	#20252088	C₂	1	2	yes	maximal, complemented
18	#20252086	C₂	1	2	yes	maximal, complemented
19	#20252036	C₂	1	2	yes	maximal, complemented
20	#20252016	C₂	1	1	yes	maximal, characteristic, complemented
21	#20251815	C₂	1	2	yes	maximal, complemented
22	C₄×M₁₆×D₄₇	C₂	1	1	yes	maximal, characteristic, complemented
23	C₄₇×#2969	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#13094032	C₂²	1	2	yes	—
25	C₂×#13094030	C₂²	1	2	yes	—
26	C₂×M₁₆×D₄₇	C₂²	1	1	yes	characteristic
27	C₂×M₁₆×D₄₇	C₂²	1	1	yes	characteristic
28	#15689679	C₄	1	1	yes	characteristic
29	#15689677	C₂²	1	1	yes	characteristic
30	#15689675	C₄	1	1	yes	characteristic
31	#15689672	C₄	1	1	yes	characteristic
32	#15689670	C₂²	1	1	yes	characteristic
33	#15689668	C₄	1	1	yes	characteristic
34	#15689658	C₄	1	1	yes	characteristic
35	#15689657	C₂²	1	1	yes	characteristic
36	#15689656	C₄	1	2	yes	—
37	#15689656	C₄	1	2	yes	—
38	#15689652	C₄	1	1	yes	characteristic
39	#15689651	C₂²	1	2	yes	—
40	#15689650	C₄	1	2	yes	—
41	#15689636	C₄	1	1	yes	characteristic
42	#15689633	C₄	1	1	yes	characteristic
43	#15689632	C₂²	1	2	yes	—
44	#15689631	C₄	1	2	yes	—
45	C₄×#10625354	C₂²	1	1	yes	characteristic
46	#15689591	C₂²	1	2	yes	—
47	C₄×#10625352	C₂²	1	1	yes	characteristic
48	C₄×#10625352	C₂²	1	2	yes	—
49	C₂×C₄²×D₄₇	C₂²	1	1	yes	characteristic
50	#15689254	C₂²	1	1	yes	characteristic, complemented
51	#15689253	C₂²	1	1	yes	characteristic, complemented
52	#15689252	C₂²	1	2	yes	complemented
53	#15689251	C₂²	1	2	yes	complemented
54	#15689250	C₂²	1	1	yes	characteristic, complemented
55	Q₈×C₄₇⋊C₈	C₂²	1	1	yes	characteristic, complemented
56	C₈×Dic₉₄	C₂²	1	2	yes	complemented
57	C₈×Dic₉₄	C₂²	1	1	yes	characteristic, complemented
58	#15689247	C₂²	1	1	yes	characteristic, complemented
59	#15689247	C₂²	1	2	yes	complemented
60	#15689202	C₂²	1	2	yes	—
61	#15689202	C₂²	1	1	yes	characteristic, complemented
62	#15689201	C₂²	1	2	yes	—
63	#15689201	C₂²	1	1	yes	characteristic, complemented
64	#15689200	C₂²	1	2	yes	—
65	#15689200	C₂²	1	1	yes	characteristic, complemented
66	#15689199	C₂²	1	2	yes	—
67	#15689199	C₂²	1	2	yes	—
68	#15689199	C₂²	1	2	yes	complemented
69	#15689198	C₂²	1	2	yes	—
70	#15689198	C₂²	1	2	yes	—
71	#15689198	C₂²	1	2	yes	complemented
72	#15689197	C₂²	1	2	yes	—
73	#15689196	C₂²	1	2	yes	—
74	#15689195	C₂²	1	2	yes	—
75	#15689194	C₂²	1	2	yes	—
76	#15689193	C₂²	1	2	yes	—
77	#15689192	C₂²	1	2	yes	—
78	#15689191	C₂²	1	2	yes	—
79	C₈×D₁₈₈	C₂²	1	1	yes	characteristic, complemented
80	D₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic, complemented
81	#15689188	C₂²	1	1	yes	characteristic, complemented
82	C₈×C₂²⋊D₄₇	C₂²	1	2	yes	complemented
83	(C₂²⋊D₄₇)⋊C₈	C₂²	1	2	yes	complemented
84	#15689185	C₂²	1	2	yes	complemented
85	#15689184	C₂²	1	2	yes	complemented
86	#15689182	C₂²	1	2	yes	complemented
87	#15689179	C₂²	1	1	yes	characteristic
88	#15689179	C₂²	1	1	yes	characteristic
89	#15689179	C₂²	1	2	yes	complemented
90	#15689179	C₂²	1	2	yes	complemented
91	#15689177	C₂²	1	2	yes	—
92	#15689177	C₂²	1	2	yes	complemented
93	#15689177	C₂²	1	2	yes	complemented
94	#15689176	C₂²	1	1	yes	characteristic
95	#15689174	C₂²	1	2	yes	—
96	#15689148	C₂²	1	2	yes	—
97	#15689148	C₂²	1	2	yes	—
98	#15689145	C₂²	1	1	yes	characteristic
99	#15689145	C₂²	1	1	yes	characteristic
100	#15689088	C₂²	1	2	yes	—
101	#15689088	C₂²	1	2	yes	—
102	#15689085	C₂²	1	2	yes	—
103	#15689080	C₂²	1	2	yes	—
104	#15689080	C₂²	1	2	yes	complemented
105	#15689079	C₂²	1	2	yes	complemented
106	#15689077	C₂²	1	2	yes	—
107	#15689077	C₂²	1	2	yes	complemented
108	C₄×#10625329	C₂²	1	1	yes	characteristic
109	#15689075	C₂²	1	1	yes	characteristic
110	#15689075	C₂²	1	1	yes	characteristic
111	M₁₆×Dic₄₇	C₂²	1	1	yes	characteristic
112	M₁₆×Dic₄₇	C₂²	1	1	yes	characteristic
113	M₁₆×Dic₄₇	C₂²	1	2	yes	complemented
114	C₄×#10625324	C₂²	1	2	yes	—
115	C₄×#10625324	C₂²	1	1	yes	characteristic
116	C₄×#10625324	C₂²	1	1	yes	characteristic
117	C₄×#10625324	C₂²	1	2	yes	complemented
118	C₂×#13093934	C₂²	1	2	yes	complemented
119	#97×D₄₇	C₂²	1	1	yes	characteristic
120	#97×D₄₇	C₂²	1	1	yes	characteristic
121	#97×D₄₇	C₂²	1	2	yes	complemented
122	C₄×C₈×D₄₇	C₂²	1	1	yes	characteristic
123	C₄×C₈×D₄₇	C₂²	1	1	yes	characteristic
124	C₄₇×#529	C₂²	1	1	yes	characteristic
125	C₄₇×#446	C₂²	1	1	yes	characteristic, complemented
126	C₈×Q₈×C₄₇	C₂²	1	1	yes	characteristic, complemented
127	C₄₇×#436	C₂²	1	2	yes	—
128	C₄₇×#436	C₂²	1	1	yes	characteristic, complemented
129	C₄₇×#435	C₂²	1	2	yes	—
130	C₈×D₄×C₄₇	C₂²	1	1	yes	characteristic, complemented
131	C₄₇×#433	C₂²	1	2	yes	complemented
132	C₄₇×#431	C₂²	1	1	yes	characteristic
133	C₄₇×#405	C₂²	1	2	yes	complemented
134	C₄×M₁₆×C₄₇	C₂²	1	1	yes	characteristic
135	C₂×#10625354	C₂×C₄	1	1	yes	characteristic
136	C₂×#10625350	C₂³	1	2	yes	—
137	C₂×#10625352	C₂×C₄	1	2	yes	—
138	C₂×#10625352	C₂×C₄	1	1	yes	characteristic
139	C₂²×C₄×D₄₇	C₂×C₄	1	1	yes	characteristic
140	C₂²×C₄×D₄₇	C₂×C₄	1	1	yes	characteristic
141	C₂²×C₄×D₄₇	C₂³	1	1	yes	characteristic
142	#13094032	—	2	8	no	—
143	#13094030	—	2	8	no	—
144	C₂×#10625329	C₂³	1	1	yes	characteristic
145	C₂×#10625329	C₂³	1	1	yes	characteristic
146	C₂×#10625329	C₂³	1	2	yes	—
147	C₂×#10625324	C₂³	1	1	yes	characteristic
148	C₂×#10625324	C₂³	1	1	yes	characteristic
149	C₂×#10625324	C₂³	1	1	yes	characteristic
150	C₂×#10625324	C₂³	1	1	yes	characteristic
151	C₂×#10625324	C₂³	1	2	yes	—
152	C₂×#10625324	C₂³	1	2	yes	—
153	C₂×#10625324	C₂³	1	2	yes	—
154	C₂×#10625324	C₂³	1	2	yes	—
155	M₁₆×D₄₇	—	2	4	no	—
156	M₁₆×D₄₇	—	2	4	no	—
157	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
158	C₂×C₈×D₄₇	C₂³	1	1	yes	characteristic
159	C₂×C₈×D₄₇	C₂³	1	1	yes	characteristic
160	C₂×C₈×D₄₇	C₂³	1	2	yes	—
161	C₂×C₈×D₄₇	C₂³	1	2	yes	—
162	C₂×C₈×D₄₇	C₂³	1	1	yes	characteristic
163	C₂×C₈×D₄₇	C₂³	1	1	yes	characteristic
164	#13094023	C₂×C₄	1	1	yes	characteristic
165	#13094023	C₂×C₄	1	1	yes	characteristic
166	#13094022	C₂×C₄	1	1	yes	characteristic
167	#13094020	C₂×C₄	1	1	yes	characteristic
168	#13094019	C₂×C₄	1	2	yes	—
169	#13094018	C₂×C₄	1	2	yes	—
170	#13094017	C₂×C₄	1	2	yes	—
171	#13094016	C₂×C₄	1	1	yes	characteristic
172	#13094014	C₂×C₄	1	2	yes	—
173	#13094014	C₂×C₄	1	2	yes	—
174	#13094012	C₂×C₄	1	1	yes	characteristic
175	#13094010	C₂×C₄	1	2	yes	—
176	#13094010	C₂×C₄	1	2	yes	—
177	#13094009	C₂×C₄	1	2	yes	—
178	#13094009	C₂×C₄	1	2	yes	—
179	#13094007	C₂×C₄	1	2	yes	—
180	#13094006	C₂×C₄	1	2	yes	—
181	#13094006	C₂×C₄	1	2	yes	—
182	#13094004	C₂×C₄	1	1	yes	characteristic
183	#13094003	C₂×C₄	1	1	yes	characteristic
184	#13094002	C₂×C₄	1	2	yes	—
185	#13094002	C₂×C₄	1	2	yes	—
186	#13094002	C₂×C₄	1	2	yes	—
187	#13094001	C₂×C₄	1	2	yes	—
188	#13094000	C₂×C₄	1	1	yes	characteristic
189	#13093999	C₂×C₄	1	1	yes	characteristic
190	#13093998	C₂×C₄	1	1	yes	characteristic
191	#13093997	C₂×C₄	1	2	yes	—
192	#13093997	C₂×C₄	1	2	yes	—
193	#13093997	C₂×C₄	1	2	yes	—
194	#13093996	C₂×C₄	1	2	yes	—
195	#13093995	C₂×C₄	1	1	yes	characteristic
196	#13093994	C₂×C₄	1	2	yes	—
197	#13093992	C₂×C₄	1	2	yes	—
198	Q₈×Dic₄₇	C₂×C₄	1	1	yes	characteristic
199	C₄×Dic₉₄	C₂³	1	1	yes	characteristic
200	C₄×Dic₉₄	C₂³	1	2	yes	—
201	#13093989	C₂×C₄	1	2	yes	—
202	#13093989	C₂×C₄	1	1	yes	characteristic
203	#13093989	C₂×C₄	1	2	yes	—
204	#13093989	C₂×C₄	1	2	yes	—
205	C₄×D₁₈₈	C₂³	1	2	yes	—
206	C₄×D₁₈₈	C₂³	1	1	yes	characteristic
207	D₄×Dic₄₇	C₂×C₄	1	2	yes	—
208	D₄×Dic₄₇	C₂×C₄	1	1	yes	characteristic
209	#13093986	C₂×C₄	1	2	yes	—
210	#13093986	C₂×C₄	1	2	yes	—
211	#13093986	C₂×C₄	1	2	yes	—
212	#13093986	C₂×C₄	1	1	yes	characteristic
213	C₄×C₂²⋊D₄₇	C₂³	1	2	yes	—
214	C₄×C₂²⋊D₄₇	C₂³	1	2	yes	—
215	C₄×C₂²⋊D₄₇	C₂³	1	2	yes	—
216	(C₂²⋊D₄₇)⋊C₄	C₂×C₄	1	2	yes	—
217	(C₂²⋊D₄₇)⋊C₄	C₂×C₄	1	2	yes	—
218	(C₂²⋊D₄₇)⋊C₄	C₂×C₄	1	2	yes	—
219	(C₂²⋊D₄₇)⋊C₄	C₂×C₄	1	2	yes	—
220	(C₂²⋊D₄₇)⋊C₄	C₂×C₄	1	2	yes	—
221	(C₂²⋊D₄₇)⋊C₄	C₂×C₄	1	2	yes	—
222	(C₂²⋊D₄₇)⋊C₄	C₂×C₄	1	2	yes	—
223	#13093982	C₂×C₄	1	1	yes	characteristic
224	#13093982	C₂×C₄	1	2	yes	—
225	#13093982	C₂×C₄	1	1	yes	characteristic
226	#13093982	C₂×C₄	1	2	yes	—
227	#13093981	C₂³	1	2	yes	—
228	#13093981	C₂³	1	2	yes	—
229	#13093980	C₂×C₄	1	2	yes	—
230	#13093980	C₂×C₄	1	2	yes	—
231	#13093980	C₂×C₄	1	2	yes	—
232	C₂×C₄×Dic₄₇	C₂×C₄	1	1	yes	characteristic
233	C₂×C₄×Dic₄₇	C₂×C₄	1	1	yes	characteristic
234	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
235	C₂×C₄×Dic₄₇	C₂³	1	2	yes	—
236	C₄²×D₄₇	C₂×C₄	1	1	yes	characteristic
237	C₄²×D₄₇	C₂×C₄	1	1	yes	characteristic
238	C₄²×D₄₇	C₂×C₄	1	1	yes	characteristic
239	C₄²×D₄₇	C₂×C₄	1	1	yes	characteristic
240	C₄²×D₄₇	C₂³	1	1	yes	characteristic
241	C₄²×D₄₇	C₂³	1	1	yes	characteristic
242	C₄²×D₄₇	C₂³	1	1	yes	characteristic
243	C₄²×D₄₇	C₂³	1	1	yes	characteristic
244	C₄²×D₄₇	C₂³	1	2	yes	—
245	C₄⋊(C₄₇⋊C₈)	C₂³	1	1	yes	characteristic
246	C₄⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
247	C₄⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
248	C₄⋊(C₄₇⋊C₈)	C₂³	1	1	yes	characteristic
249	Dic₄₇⋊C₈	C₂³	1	2	yes	—
250	Dic₄₇⋊C₈	C₂³	1	2	yes	—
251	Dic₄₇⋊C₈	C₂³	1	2	yes	—
252	Dic₄₇⋊C₈	C₂³	1	2	yes	—
253	Dic₄₇⋊C₈	C₂³	1	2	yes	—
254	Dic₄₇⋊C₈	C₂³	1	2	yes	—
255	C₂²⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
256	C₂²⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
257	C₂²⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
258	(C₂×D₄₇)⋊C₈	C₂³	1	2	yes	—
259	(C₂×D₄₇)⋊C₈	C₂³	1	2	yes	—
260	(C₂×D₄₇)⋊C₈	C₂³	1	2	yes	—
261	(C₂×D₄₇)⋊C₈	C₂³	1	2	yes	—
262	(C₂×D₄₇)⋊C₈	C₂³	1	2	yes	—
263	(C₂×D₄₇)⋊C₈	C₂³	1	2	yes	—
264	#13093935	C₂³	1	2	yes	—
265	#13093935	C₂³	1	1	yes	characteristic
266	#13093935	C₂³	1	1	yes	characteristic
267	#13093934	C₂³	1	2	yes	—
268	#13093934	C₂³	1	2	yes	—
269	#13093934	C₂³	1	1	yes	characteristic
270	#13093934	C₂³	1	1	yes	characteristic
271	#13093934	C₂³	1	1	yes	characteristic
272	#13093934	C₂³	1	1	yes	characteristic
273	#13093934	C₂³	1	2	yes	—
274	#13093934	C₂³	1	2	yes	—
275	C₄×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
276	C₄×C₄₇⋊C₈	C₂³	1	2	yes	—
277	C₄×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
278	C₄×C₄₇⋊C₈	C₂³	1	2	yes	—
279	C₈×Dic₄₇	C₂³	1	1	yes	characteristic
280	C₈×Dic₄₇	C₂³	1	2	yes	—
281	C₈×Dic₄₇	C₂³	1	1	yes	characteristic
282	C₈×Dic₄₇	C₂³	1	2	yes	—
283	C₈×Dic₄₇	C₂³	1	1	yes	characteristic
284	C₈×Dic₄₇	C₂³	1	1	yes	characteristic
285	C₂×M₁₆×C₄₇	C₂³	1	1	yes	characteristic
286	C₂×M₁₆×C₄₇	C₂³	1	1	yes	characteristic
287	C₂×M₁₆×C₄₇	C₂³	1	2	yes	—
288	C₂²×C₈×C₄₇	C₂³	1	2	yes	—
289	#126×C₄₇	C₂×C₄	1	2	yes	—
290	#125×C₄₇	C₂×C₄	1	1	yes	characteristic
291	#124×C₄₇	C₂×C₄	1	1	yes	characteristic
292	#123×C₄₇	C₂×C₄	1	2	yes	—
293	C₂²⋊Q₈×C₄₇	C₂×C₄	1	1	yes	characteristic
294	#121×C₄₇	C₂×C₄	1	1	yes	characteristic
295	C₄×Q₈×C₄₇	C₂³	1	1	yes	characteristic
296	C₄×D₄×C₄₇	C₂³	1	2	yes	—
297	C₄×D₄×C₄₇	C₂³	1	1	yes	characteristic
298	#117×C₄₇	C₂³	1	2	yes	—
299	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
300	C₄⋊C₈×C₄₇	C₂³	1	1	yes	characteristic
301	C₄⋊C₈×C₄₇	C₂³	1	2	yes	—
302	C₄⋊C₈×C₄₇	C₂³	1	1	yes	characteristic
303	C₄⋊C₈×C₄₇	C₂³	1	2	yes	—
304	C₂²⋊C₈×C₄₇	C₂³	1	2	yes	—
305	C₂²⋊C₈×C₄₇	C₂³	1	2	yes	—
306	C₂²⋊C₈×C₄₇	C₂³	1	2	yes	—
307	#97×C₄₇	C₂³	1	2	yes	—
308	#97×C₄₇	C₂³	1	1	yes	characteristic
309	#97×C₄₇	C₂³	1	1	yes	characteristic
310	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
311	C₄×C₈×C₄₇	C₂³	1	2	yes	—
312	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
313	C₄×C₈×C₄₇	C₂³	1	2	yes	—
314	C₂³×D₄₇	C₂²×C₄	1	1	yes	characteristic
315	C₂×Q₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
316	C₂×D₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
317	C₂×D₄×C₄₇	C₂²×C₄	1	2	yes	—
318	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
319	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
320	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
321	C₂²×C₄×C₄₇	C₂⁴	1	2	yes	—
322	C₂×C₂²⋊D₄₇	C₂²×C₄	1	2	yes	—
323	C₂×C₂²⋊D₄₇	C₂²×C₄	1	2	yes	—
324	C₂×C₂²⋊D₄₇	C₂²×C₄	1	2	yes	—
325	C₂×C₂²⋊D₄₇	C₂²×C₄	1	2	yes	—
326	C₂×C₂²⋊D₄₇	C₂²×C₄	1	2	yes	—
327	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
328	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
329	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
330	C₂²×Dic₄₇	C₂²×C₄	1	2	yes	—
331	C₂²×Dic₄₇	C₂²×C₄	1	2	yes	—
332	#10625354	—	4	2	no	—
333	#10625352	—	4	2	no	—
334	#10625352	—	4	4	no	—
335	#10625350	—	2	4	no	—
336	#10625350	—	2	4	no	—
337	C₂×D₁₈₈	C₂²×C₄	1	2	yes	—
338	C₂×D₁₈₈	C₂²×C₄	1	1	yes	characteristic
339	C₂×D₁₈₈	C₂²×C₄	1	2	yes	—
340	C₂×C₄×D₄₇	—	2	2	no	—
341	C₂×C₄×D₄₇	—	2	2	no	—
342	C₂×C₄×D₄₇	—	4	2	no	—
343	C₂×C₄×D₄₇	—	4	2	no	—
344	C₂×C₄×D₄₇	C₂²×C₄	1	1	yes	characteristic
345	C₂×C₄×D₄₇	C₂²×C₄	1	1	yes	characteristic
346	C₂×C₄×D₄₇	C₂²×C₄	1	1	yes	characteristic
347	C₂×C₄×D₄₇	C₂²×C₄	1	1	yes	characteristic
348	C₂×C₄×D₄₇	C₂²×C₄	1	1	yes	characteristic
349	C₂×C₄×D₄₇	C₂²×C₄	1	1	yes	characteristic
350	C₂×C₄×D₄₇	C₂²×C₄	1	1	yes	characteristic
351	C₂×C₄×D₄₇	C₂²×C₄	1	1	yes	characteristic
352	C₂×C₄×D₄₇	C₂²×C₄	1	1	yes	characteristic
353	C₂×C₄×D₄₇	C₂²×C₄	1	1	yes	characteristic
354	C₂×C₄×D₄₇	C₂²×C₄	1	2	yes	—
355	C₂×C₄×D₄₇	C₂²×C₄	1	2	yes	—
356	C₂×C₄×D₄₇	C₂⁴	1	1	yes	characteristic
357	C₂×C₄×D₄₇	C₂⁴	1	2	yes	—
358	C₂×C₄×D₄₇	C₂⁴	1	1	yes	characteristic
359	C₂×Dic₉₄	C₂²×C₄	1	2	yes	—
360	C₂×Dic₉₄	C₂²×C₄	1	2	yes	—
361	C₂×Dic₉₄	C₂²×C₄	1	1	yes	characteristic
362	M₁₆×C₄₇	—	2	2	no	—
363	M₁₆×C₄₇	—	2	2	no	—
364	M₁₆×C₄₇	—	2	4	no	—
365	C₂×C₈×C₄₇	—	2	4	no	—
366	C₂×C₈×C₄₇	C₂⁴	1	2	yes	—
367	C₂×C₈×C₄₇	C₂⁴	1	2	yes	—
368	C₂×C₈×C₄₇	C₂⁴	1	1	yes	characteristic
369	C₂×C₈×C₄₇	C₂⁴	1	1	yes	characteristic
370	C₂×C₈×C₄₇	C₂⁴	1	1	yes	characteristic
371	C₂×C₈×C₄₇	C₂⁴	1	1	yes	characteristic
372	C₄⋊C₄×C₄₇	C₂²×C₄	1	2	yes	—
373	C₄⋊C₄×C₄₇	C₂²×C₄	1	2	yes	—
374	C₄⋊C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
375	C₄⋊C₄×C₄₇	C₂²×C₄	1	2	yes	—
376	C₄⋊C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
377	C₄⋊C₄×C₄₇	C₂²×C₄	1	2	yes	—
378	C₂²⋊C₄×C₄₇	C₂²×C₄	1	2	yes	—
379	C₂²⋊C₄×C₄₇	C₂²×C₄	1	2	yes	—
380	C₂²⋊C₄×C₄₇	C₂²×C₄	1	2	yes	—
381	C₂²⋊C₄×C₄₇	C₂²×C₄	1	2	yes	—
382	C₂²⋊C₄×C₄₇	C₂²×C₄	1	2	yes	—
383	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
384	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
385	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
386	C₄²×C₄₇	C₂⁴	1	2	yes	—
387	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
388	C₂²⋊Dic₄₇	C₂²×C₄	1	2	yes	—
389	C₂²⋊Dic₄₇	C₂²×C₄	1	2	yes	—
390	C₂²⋊Dic₄₇	C₂²×C₄	1	2	yes	—
391	(C₂×D₄₇)⋊C₄	C₂²×C₄	1	2	yes	—
392	(C₂×D₄₇)⋊C₄	C₂²×C₄	1	2	yes	—
393	(C₂×D₄₇)⋊C₄	C₂²×C₄	1	2	yes	—
394	(C₂×D₄₇)⋊C₄	C₂²×C₄	1	2	yes	—
395	(C₂×D₄₇)⋊C₄	C₂²×C₄	1	2	yes	—
396	(C₂×D₄₇)⋊C₄	C₂²×C₄	1	2	yes	—
397	(C₂×D₄₇)⋊C₄	C₂²×C₄	1	2	yes	—
398	(C₂×D₄₇)⋊C₄	C₂²×C₄	1	2	yes	—
399	(C₂×D₄₇)⋊C₄	C₂²×C₄	1	2	yes	—
400	(C₂×D₄₇)⋊C₄	C₂²×C₄	1	2	yes	—
401	C₄⋊Dic₄₇	C₂²×C₄	1	1	yes	characteristic
402	C₄⋊Dic₄₇	C₂²×C₄	1	2	yes	—
403	C₄⋊Dic₄₇	C₂²×C₄	1	1	yes	characteristic
404	C₄⋊Dic₄₇	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	Dic₄₇⋊C₄	C₂²×C₄	1	2	yes	—
409	Dic₄₇⋊C₄	C₂²×C₄	1	2	yes	—
410	Dic₄₇⋊C₄	C₂²×C₄	1	2	yes	—
411	Dic₄₇⋊C₄	C₂²×C₄	1	2	yes	—
412	Dic₄₇⋊C₄	C₂²×C₄	1	2	yes	—
413	Dic₄₇⋊C₄	C₂²×C₄	1	2	yes	—
414	Dic₄₇⋊C₄	C₂²×C₄	1	2	yes	—
415	C₄×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
416	C₄×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
417	C₄×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
418	C₄×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
419	C₄×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
420	C₄×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
421	C₄×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
422	C₄×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
423	C₄×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
424	C₄×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
425	C₄×Dic₄₇	C₂²×C₄	1	2	yes	—
426	C₄×Dic₄₇	C₂²×C₄	1	2	yes	—
427	C₄×Dic₄₇	C₂²×C₄	1	2	yes	—
428	C₄×Dic₄₇	C₂²×C₄	1	2	yes	—
429	C₄×Dic₄₇	C₂⁴	1	1	yes	characteristic
430	C₄×Dic₄₇	C₂⁴	1	2	yes	—
431	C₄×Dic₄₇	C₂⁴	1	1	yes	characteristic
432	#10625329	—	2	2	no	—
433	#10625329	—	2	2	no	—
434	#10625329	—	2	4	no	—
435	C₂×C₄₇⋊C₈	—	2	4	no	—
436	C₂×C₄₇⋊C₈	C₂⁴	1	1	yes	characteristic
437	C₂×C₄₇⋊C₈	C₂⁴	1	2	yes	—
438	C₂×C₄₇⋊C₈	C₂⁴	1	1	yes	characteristic
439	C₂×C₄₇⋊C₈	C₂⁴	1	2	yes	—
440	C₂×C₄₇⋊C₈	C₂⁴	1	1	yes	characteristic
441	C₂×C₄₇⋊C₈	C₂⁴	1	1	yes	characteristic
442	#10625324	—	2	4	no	—
443	#10625324	—	2	4	no	—
444	#10625324	—	2	2	no	—
445	#10625324	—	2	2	no	—
446	#10625324	—	2	4	no	—
447	#10625324	—	2	2	no	—
448	#10625324	—	2	2	no	—
449	#10625324	—	2	4	no	—
450	C₈×D₄₇	—	2	2	no	—
451	C₈×D₄₇	—	2	2	no	—
452	C₈×D₄₇	—	2	4	no	—
453	C₈×D₄₇	—	2	4	no	—
454	C₈×D₄₇	#41	1	4	yes	complemented
455	C₈×D₄₇	#41	1	4	yes	complemented
456	C₂³×C₄₇	C₂³×C₄	1	2	yes	—
457	C₂³×C₄₇	C₂³×C₄	1	1	yes	characteristic
458	C₂²×D₄₇	—	2	2	no	—
459	C₂²×D₄₇	—	4	1	no	—
460	C₂²×D₄₇	—	4	1	no	—
461	C₂²×D₄₇	C₂³×C₄	1	2	yes	—
462	C₂²×D₄₇	C₂³×C₄	1	1	yes	characteristic
463	C₂²×D₄₇	C₂³×C₄	1	1	yes	characteristic
464	Q₈×C₄₇	—	2	2	no	—
465	D₄×C₄₇	—	2	2	no	—
466	D₄×C₄₇	—	4	2	no	—
467	C₂×C₄×C₄₇	—	2	2	no	—
468	C₂×C₄×C₄₇	—	2	2	no	—
469	C₂×C₄×C₄₇	—	2	2	no	—
470	C₂×C₄×C₄₇	—	2	1	no	—
471	C₂×C₄×C₄₇	—	2	1	no	—
472	C₂×C₄×C₄₇	—	4	1	no	—
473	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
474	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
475	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
476	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
477	C₂×C₄×C₄₇	C₂³×C₄	1	2	yes	—
478	C₂×C₄×C₄₇	C₂³×C₄	1	2	yes	—
479	C₂×C₄×C₄₇	C₂³×C₄	1	2	yes	—
480	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
481	C₂×C₄×C₄₇	C₂⁵	1	1	yes	characteristic
482	C₂²⋊D₄₇	—	2	4	no	—
483	C₂²⋊D₄₇	—	2	4	no	—
484	C₂²⋊D₄₇	—	2	4	no	—
485	C₂²⋊D₄₇	—	4	2	no	—
486	C₂²⋊D₄₇	—	4	2	no	—
487	C₂×Dic₄₇	—	2	2	no	—
488	C₂×Dic₄₇	—	2	2	no	—
489	C₂×Dic₄₇	—	4	1	no	—
490	C₂×Dic₄₇	—	4	2	no	—
491	C₂×Dic₄₇	—	4	2	no	—
492	C₂×Dic₄₇	C₂³×C₄	1	1	yes	characteristic
493	C₂×Dic₄₇	C₂³×C₄	1	1	yes	characteristic
494	C₂×Dic₄₇	C₂³×C₄	1	1	yes	characteristic
495	C₂×Dic₄₇	C₂³×C₄	1	1	yes	characteristic
496	C₂×Dic₄₇	C₂³×C₄	1	2	yes	—
497	C₂×Dic₄₇	C₂³×C₄	1	2	yes	—
498	C₂×Dic₄₇	C₂³×C₄	1	2	yes	—
499	C₂×Dic₄₇	C₂³×C₄	1	1	yes	characteristic
500	C₂×Dic₄₇	C₂³×C₄	1	1	yes	characteristic
501	D₁₈₈	—	2	4	no	—
502	D₁₈₈	—	2	2	no	—
503	D₁₈₈	—	4	2	no	—
504	C₄×D₄₇	—	2	2	no	—
505	C₄×D₄₇	—	2	2	no	—
506	C₄×D₄₇	—	2	2	no	—
507	C₄×D₄₇	—	2	2	no	—
508	C₄×D₄₇	—	2	2	no	—
509	C₄×D₄₇	—	2	1	no	—
510	C₄×D₄₇	—	2	1	no	—
511	C₄×D₄₇	—	2	2	no	—
512	C₄×D₄₇	—	2	2	no	—
513	C₄×D₄₇	—	2	2	no	—
514	C₄×D₄₇	—	4	1	no	—
515	C₄×D₄₇	—	4	1	no	—
516	C₄×D₄₇	—	4	1	no	—
517	C₄×D₄₇	—	4	1	no	—
518	C₄×D₄₇	—	4	2	no	—
519	C₄×D₄₇	—	4	2	no	—
520	C₄×D₄₇	C₂×#41	1	2	yes	—
521	C₄×D₄₇	C₂×#41	1	2	yes	—
522	Dic₉₄	—	2	2	no	—
523	Dic₉₄	—	2	4	no	—
524	Dic₉₄	—	2	4	no	—
525	C₈×C₄₇	—	2	1	no	—
526	C₈×C₄₇	—	2	1	no	—
527	C₈×C₄₇	—	2	2	no	—
528	C₈×C₄₇	—	2	2	no	—
529	C₈×C₄₇	C₂×#41	1	2	yes	—
530	C₈×C₄₇	C₂×#41	1	2	yes	—
531	C₄₇⋊C₈	—	2	1	no	—
532	C₄₇⋊C₈	—	2	1	no	—
533	C₄₇⋊C₈	—	2	2	no	—
534	C₄₇⋊C₈	—	2	2	no	—
535	C₄₇⋊C₈	C₂×#41	1	2	yes	—
536	C₄₇⋊C₈	C₂×#41	1	2	yes	—
537	#60208	—	47	1	no	maximal, Sylow
538	C₂²×C₄₇	—	2	1	no	—
539	C₂²×C₄₇	—	2	2	no	—
540	C₂²×C₄₇	—	2	1	no	—
541	C₂²×C₄₇	—	2	2	no	—
542	C₂²×C₄₇	—	2	2	no	—
543	C₂²×C₄₇	—	2	1	no	—
544	C₂²×C₄₇	C₂⁴×C₄	1	1	yes	characteristic
545	C₂×D₄₇	—	2	1	no	—
546	C₂×D₄₇	—	2	1	no	—
547	C₂×D₄₇	—	2	1	no	—
548	C₂×D₄₇	—	2	2	no	—
549	C₂×D₄₇	—	2	1	no	—
550	C₂×D₄₇	—	2	1	no	—
551	C₂×D₄₇	—	2	2	no	—
552	C₂×D₄₇	—	2	2	no	—
553	C₂×D₄₇	—	4	4	no	—
554	C₂×D₄₇	C₄×#41	1	2	yes	—
555	C₄×C₄₇	—	2	2	no	—
556	C₄×C₄₇	—	2	1	no	—
557	C₄×C₄₇	—	2	2	no	—
558	C₄×C₄₇	—	2	1	no	—
559	C₄×C₄₇	—	2	1	no	—
560	C₄×C₄₇	—	2	1	no	—
561	C₄×C₄₇	—	2	2	no	—
562	C₄×C₄₇	#568	1	2	yes	—
563	C₄×C₄₇	C₂²×#41	1	1	yes	characteristic
564	C₄×C₄₇	C₂²×#41	1	1	yes	characteristic
565	Dic₄₇	—	2	2	no	—
566	Dic₄₇	—	2	1	no	—
567	Dic₄₇	—	2	2	no	—
568	Dic₄₇	—	2	2	no	—
569	Dic₄₇	—	2	1	no	—
570	Dic₄₇	—	2	1	no	—
571	Dic₄₇	—	2	1	no	—
572	Dic₄₇	C₄×#41	1	2	yes	—
573	Dic₄₇	#568	1	2	yes	—
574	#3444	—	47	1	no	—
575	#2971	—	47	1	no	—
576	#2971	—	47	2	no	—
577	#2971	—	47	1	no	—
578	#2970	—	47	1	no	—
579	#2970	—	47	2	no	—
580	#2970	—	47	1	no	—
581	#2969	—	47	2	no	—
582	#2969	—	47	1	no	—
583	#2969	—	47	2	no	—
584	#2969	—	47	1	no	—
585	#2969	—	47	1	no	—
586	#2969	D₄₇	1	1	yes	characteristic, complemented
587	#2960	—	47	1	no	—
588	#2960	—	47	1	no	—
589	#2931	—	47	1	no	—
590	#2931	—	47	1	no	—
591	#2930	—	47	2	no	—
592	#2930	—	47	2	no	—
593	#2923	—	47	2	no	—
594	#2920	—	47	1	no	—
595	#2875	—	47	2	no	—
596	C₂×C₄×M₁₆	—	47	1	no	—
597	C₂×C₄₇	—	4	1	no	—
598	C₂×C₄₇	—	4	2	no	—
599	C₂×C₄₇	C₂×C₄×#41	1	1	yes	characteristic
600	C₂×C₄₇	C₂×#568	1	1	yes	characteristic
601	C₂×C₄₇	C₂×#568	1	1	yes	characteristic
602	D₄₇	—	2	2	no	—
603	D₄₇	—	4	2	no	—
604	D₄₇	—	4	1	no	—
605	C₂×#131	—	47	2	no	—
606	C₂×#131	—	47	2	no	—
607	C₂²×M₁₆	—	47	1	no	—
608	C₂²×M₁₆	—	47	1	no	—
609	#533	—	47	1	no	—
610	#533	—	47	1	no	—
611	#533	—	47	1	no	—
612	#532	—	47	1	no	—
613	#532	—	47	1	no	—
614	#532	—	47	1	no	—
615	#529	—	47	2	no	—
616	#529	—	47	2	no	—
617	#529	—	47	1	no	—
618	#529	—	47	1	no	—
619	#529	—	47	2	no	—
620	#529	—	47	2	no	—
621	#529	—	47	1	no	—
622	#529	C₂×D₄₇	1	1	yes	characteristic
623	#525	—	47	2	no	—
624	#525	—	47	1	no	—
625	#525	—	47	1	no	—
626	#525	—	47	2	no	—
627	C₄×#41	—	47	1	no	—
628	C₄×#41	—	47	1	no	—
629	C₄×#41	—	47	2	no	—
630	C₄×#41	—	47	2	no	—
631	C₂²×C₄²	—	47	1	no	—
632	#446	—	47	1	no	—
633	#446	—	47	1	no	—
634	#446	—	47	2	no	—
635	#446	—	47	2	no	—
636	#446	—	47	1	no	—
637	#446	C₂×D₄₇	1	1	yes	characteristic, complemented
638	C₈×Q₈	—	47	1	no	—
639	C₈×Q₈	—	47	2	no	—
640	C₈×Q₈	—	47	1	no	—
641	C₈×Q₈	—	47	2	no	—
642	C₈×Q₈	—	47	1	no	—
643	C₈×Q₈	C₂×D₄₇	1	1	yes	characteristic, complemented
644	#436	—	47	2	no	—
645	#436	—	47	2	no	—
646	#436	—	47	2	no	—
647	#436	—	47	2	no	—
648	#436	—	47	1	no	—
649	#436	—	47	2	no	—
650	#436	—	47	1	no	—
651	#436	—	47	2	no	—
652	#436	—	47	2	no	—
653	#436	—	47	2	no	—
654	#436	—	47	2	no	—
655	#436	—	47	1	no	—
656	#436	C₂×D₄₇	1	2	yes	—
657	#436	C₂×D₄₇	1	1	yes	characteristic, complemented
658	#435	—	47	2	no	—
659	#435	—	47	2	no	—
660	#435	—	47	2	no	—
661	#435	—	47	2	no	—
662	#435	—	47	2	no	—
663	#435	—	47	2	no	—
664	#435	—	47	2	no	—
665	#435	C₂×D₄₇	1	2	yes	—
666	C₈×D₄	—	47	2	no	—
667	C₈×D₄	—	47	1	no	—
668	C₈×D₄	—	47	1	no	—
669	C₈×D₄	—	47	2	no	—
670	C₈×D₄	—	47	1	no	—
671	C₈×D₄	C₂×D₄₇	1	1	yes	characteristic, complemented
672	#433	—	47	2	no	—
673	#433	—	47	2	no	—
674	#433	—	47	2	no	—
675	#433	C₂×D₄₇	1	2	yes	complemented
676	#432	—	47	1	no	—
677	#432	—	47	1	no	—
678	#432	—	47	2	no	—
679	#432	—	47	2	no	—
680	#432	—	47	2	no	—
681	#432	—	47	2	no	—
682	#432	—	47	2	no	—
683	#431	—	47	1	no	—
684	#431	—	47	2	no	—
685	#431	C₂×D₄₇	1	1	yes	characteristic
686	#424	—	47	2	no	—
687	#424	—	47	2	no	—
688	#423	—	47	1	no	—
689	#423	—	47	1	no	—
690	#408	—	47	2	no	—
691	#408	—	47	2	no	—
692	#407	—	47	2	no	—
693	#405	—	47	2	no	—
694	#405	—	47	2	no	—
695	#405	—	47	2	no	—
696	#405	—	47	2	no	—
697	#405	—	47	2	no	—
698	#405	C₂×D₄₇	1	2	yes	complemented
699	C₄×M₁₆	—	47	1	no	—
700	C₄×M₁₆	—	47	1	no	—
701	C₄×M₁₆	—	47	2	no	—
702	C₄×M₁₆	—	47	1	no	—
703	C₄×M₁₆	—	47	1	no	—
704	C₄×M₁₆	—	47	1	no	—
705	C₄×M₁₆	—	47	1	no	—
706	C₄×M₁₆	—	47	1	no	—
707	C₄×M₁₆	—	47	2	no	—
708	C₄×M₁₆	—	47	2	no	—
709	C₄×M₁₆	C₂×D₄₇	1	1	yes	characteristic
710	C₂×#97	—	47	2	no	—
711	C₂×#97	—	47	1	no	—
712	C₂×#97	—	47	1	no	—
713	C₂×#97	—	47	2	no	—
714	C₂×C₄×C₈	—	47	1	no	—
715	C₂×C₄×C₈	—	47	1	no	—
716	C₄₇	#60208	1	1	yes	characteristic, complemented, Sylow
717	C₂×#41	—	47	1	no	—
718	C₂×#41	—	47	2	no	—
719	C₂×#41	—	47	1	no	—
720	C₂×#41	—	47	2	no	—
721	C₂³×C₄	—	47	1	no	—
722	C₂³×C₄	—	47	1	no	—
723	C₂³×C₄	—	47	1	no	—
724	#131	—	94	8	no	—
725	#131	—	94	8	no	—
726	C₂×M₁₆	—	47	1	no	—
727	C₂×M₁₆	—	47	1	no	—
728	C₂×M₁₆	—	47	2	no	—
729	C₂×M₁₆	—	47	1	no	—
730	C₂×M₁₆	—	47	1	no	—
731	C₂×M₁₆	—	47	1	no	—
732	C₂×M₁₆	—	47	1	no	—
733	C₂×M₁₆	—	47	2	no	—
734	C₂×M₁₆	—	47	2	no	—
735	C₂×M₁₆	—	47	2	no	—
736	C₂×M₁₆	—	47	2	no	—
737	C₂×M₁₆	—	94	4	no	—
738	C₂×M₁₆	—	94	4	no	—
739	C₂×M₁₆	C₂²×D₄₇	1	1	yes	characteristic
740	C₂×M₁₆	C₂²×D₄₇	1	1	yes	characteristic
741	C₂×M₁₆	C₂²×D₄₇	1	2	yes	—
742	C₂²×C₈	—	47	1	no	—
743	C₂²×C₈	—	47	1	no	—
744	C₂²×C₈	—	47	2	no	—
745	C₂²×C₈	—	47	1	no	—
746	C₂²×C₈	—	47	1	no	—
747	C₂²×C₈	—	47	2	no	—
748	C₂²×C₈	—	47	2	no	—
749	C₂²×C₈	C₂²×D₄₇	1	2	yes	—
750	C₄⋊Q₈	—	47	1	no	—
751	C₄⋊Q₈	—	47	1	no	—
752	C₄⋊Q₈	—	47	1	no	—
753	#127	—	47	1	no	—
754	#126	—	47	2	no	—
755	#126	—	47	2	no	—
756	#126	—	47	2	no	—
757	#126	C₄×D₄₇	1	2	yes	—
758	#125	—	47	2	no	—
759	#125	—	47	2	no	—
760	#125	—	47	1	no	—
761	#125	C₄×D₄₇	1	1	yes	characteristic
762	#124	—	47	2	no	—
763	#124	—	47	2	no	—
764	#124	—	47	1	no	—
765	#124	C₄×D₄₇	1	1	yes	characteristic
766	#123	—	47	2	no	—
767	#123	—	47	2	no	—
768	#123	—	47	2	no	—
769	#123	—	47	2	no	—
770	#123	—	47	2	no	—
771	#123	C₄×D₄₇	1	2	yes	—
772	C₂²⋊Q₈	—	47	1	no	—
773	C₂²⋊Q₈	—	47	1	no	—
774	C₂²⋊Q₈	—	47	2	no	—
775	C₂²⋊Q₈	—	47	2	no	—
776	C₂²⋊Q₈	—	47	2	no	—
777	C₂²⋊Q₈	—	47	1	no	—
778	C₂²⋊Q₈	—	47	2	no	—
779	C₂²⋊Q₈	C₄×D₄₇	1	1	yes	characteristic
780	#121	—	47	1	no	—
781	#121	—	47	2	no	—
782	#121	—	47	1	no	—
783	#121	—	47	1	no	—
784	#121	—	47	2	no	—
785	#121	—	47	2	no	—
786	#121	—	47	2	no	—
787	#121	C₄×D₄₇	1	1	yes	characteristic
788	#120	—	47	2	no	—
789	#120	—	47	2	no	—
790	C₄×Q₈	—	47	1	no	—
791	C₄×Q₈	—	47	2	no	—
792	C₄×Q₈	—	47	2	no	—
793	C₄×Q₈	—	47	2	no	—
794	C₄×Q₈	—	47	1	no	—
795	C₄×Q₈	—	47	2	no	—
796	C₄×Q₈	—	47	1	no	—
797	C₄×Q₈	C₂²×D₄₇	1	1	yes	characteristic
798	C₄×D₄	—	47	2	no	—
799	C₄×D₄	—	47	1	no	—
800	C₄×D₄	—	47	2	no	—
801	C₄×D₄	—	47	2	no	—
802	C₄×D₄	—	47	2	no	—
803	C₄×D₄	—	47	2	no	—
804	C₄×D₄	—	47	2	no	—
805	C₄×D₄	—	47	2	no	—
806	C₄×D₄	—	47	1	no	—
807	C₄×D₄	—	47	2	no	—
808	C₄×D₄	—	47	2	no	—
809	C₄×D₄	—	47	2	no	—
810	C₄×D₄	—	47	2	no	—
811	C₄×D₄	—	47	2	no	—
812	C₄×D₄	—	47	2	no	—
813	C₄×D₄	—	47	2	no	—
814	C₄×D₄	—	47	2	no	—
815	C₄×D₄	—	47	1	no	—
816	C₄×D₄	C₂²×D₄₇	1	2	yes	—
817	C₄×D₄	C₂²×D₄₇	1	1	yes	characteristic
818	#117	—	47	1	no	—
819	#117	—	47	1	no	—
820	#117	—	47	2	no	—
821	#117	—	47	2	no	—
822	#117	—	47	2	no	—
823	#117	—	47	2	no	—
824	#117	—	47	2	no	—
825	#117	—	47	2	no	—
826	#117	—	47	2	no	—
827	#117	C₂²×D₄₇	1	2	yes	—
828	C₂×C₄²	—	47	1	no	—
829	C₂×C₄²	—	47	1	no	—
830	C₂×C₄²	—	47	2	no	—
831	C₂×C₄²	—	47	1	no	—
832	C₂×C₄²	—	47	1	no	—
833	C₂×C₄²	—	47	1	no	—
834	C₂×C₄²	—	47	1	no	—
835	C₂×C₄²	—	47	1	no	—
836	C₂×C₄²	—	47	2	no	—
837	C₂×C₄²	—	47	1	no	—
838	C₂×C₄²	—	47	1	no	—
839	C₂×C₄²	—	47	1	no	—
840	C₂×C₄²	—	47	1	no	—
841	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
842	C₄⋊C₈	—	47	2	no	—
843	C₄⋊C₈	—	47	2	no	—
844	C₄⋊C₈	—	47	2	no	—
845	C₄⋊C₈	—	47	2	no	—
846	C₄⋊C₈	—	47	2	no	—
847	C₄⋊C₈	—	47	2	no	—
848	C₄⋊C₈	—	47	1	no	—
849	C₄⋊C₈	—	47	1	no	—
850	C₄⋊C₈	—	47	2	no	—
851	C₄⋊C₈	—	47	2	no	—
852	C₄⋊C₈	C₂²×D₄₇	1	1	yes	characteristic
853	C₄⋊C₈	C₂²×D₄₇	1	1	yes	characteristic
854	C₄⋊C₈	C₂²×D₄₇	1	2	yes	—
855	C₄⋊C₈	C₂²×D₄₇	1	2	yes	—
856	C₂²⋊C₈	—	47	2	no	—
857	C₂²⋊C₈	—	47	2	no	—
858	C₂²⋊C₈	—	47	2	no	—
859	C₂²⋊C₈	—	47	2	no	—
860	C₂²⋊C₈	—	47	2	no	—
861	C₂²⋊C₈	—	47	2	no	—
862	C₂²⋊C₈	—	47	2	no	—
863	C₂²⋊C₈	—	47	2	no	—
864	C₂²⋊C₈	—	47	2	no	—
865	C₂²⋊C₈	C₂²×D₄₇	1	2	yes	—
866	C₂²⋊C₈	C₂²×D₄₇	1	2	yes	—
867	C₂²⋊C₈	C₂²×D₄₇	1	2	yes	—
868	#97	—	47	1	no	—
869	#97	—	47	1	no	—
870	#97	—	47	1	no	—
871	#97	—	47	1	no	—
872	#97	—	47	2	no	—
873	#97	—	47	2	no	—
874	#97	—	47	2	no	—
875	#97	—	47	2	no	—
876	#97	—	47	1	no	—
877	#97	—	47	1	no	—
878	#97	—	47	2	no	—
879	#97	C₂²×D₄₇	1	1	yes	characteristic
880	#97	C₂²×D₄₇	1	1	yes	characteristic
881	#97	C₂²×D₄₇	1	2	yes	—
882	C₄×C₈	—	47	1	no	—
883	C₄×C₈	—	47	1	no	—
884	C₄×C₈	—	47	1	no	—
885	C₄×C₈	—	47	1	no	—
886	C₄×C₈	—	47	2	no	—
887	C₄×C₈	—	47	2	no	—
888	C₄×C₈	—	47	1	no	—
889	C₄×C₈	—	47	1	no	—
890	C₄×C₈	—	47	2	no	—
891	C₄×C₈	—	47	2	no	—
892	C₄×C₈	C₂²×D₄₇	1	1	yes	characteristic
893	C₄×C₈	C₂²×D₄₇	1	1	yes	characteristic
894	C₄×C₈	C₂²×D₄₇	1	2	yes	—
895	C₄×C₈	C₂²×D₄₇	1	2	yes	—
896	C₂⁴	—	47	1	no	—
897	#41	—	94	4	no	—
898	#41	—	94	4	no	—
899	#41	—	188	2	no	—
900	#41	—	188	4	no	—
901	#41	—	188	2	no	—
902	C₂×Q₈	—	47	2	no	—
903	C₂×Q₈	—	47	2	no	—
904	C₂×Q₈	—	47	1	no	—
905	C₂×Q₈	C₂×C₄×D₄₇	1	1	yes	characteristic
906	C₂×D₄	—	47	2	no	—
907	C₂×D₄	—	47	2	no	—
908	C₂×D₄	—	47	2	no	—
909	C₂×D₄	—	47	2	no	—
910	C₂×D₄	—	47	2	no	—
911	C₂×D₄	—	47	2	no	—
912	C₂×D₄	—	47	1	no	—
913	C₂×D₄	—	47	2	no	—
914	C₂×D₄	C₂×C₄×D₄₇	1	1	yes	characteristic
915	C₂×D₄	C₂×C₄×D₄₇	1	2	yes	—
916	C₂²×C₄	—	47	1	no	—
917	C₂²×C₄	—	47	1	no	—
918	C₂²×C₄	—	47	1	no	—
919	C₂²×C₄	—	47	1	no	—
920	C₂²×C₄	—	47	2	no	—
921	C₂²×C₄	—	47	2	no	—
922	C₂²×C₄	—	47	1	no	—
923	C₂²×C₄	—	47	1	no	—
924	C₂²×C₄	—	47	1	no	—
925	C₂²×C₄	—	47	1	no	—
926	C₂²×C₄	—	47	1	no	—
927	C₂²×C₄	—	47	1	no	—
928	C₂²×C₄	—	47	1	no	—
929	C₂²×C₄	—	47	2	no	—
930	C₂²×C₄	—	47	1	no	—
931	C₂²×C₄	—	47	1	no	—
932	C₂²×C₄	—	47	1	no	—
933	C₂²×C₄	—	47	1	no	—
934	C₂²×C₄	—	47	2	no	—
935	C₂²×C₄	—	47	2	no	—
936	C₂²×C₄	—	94	2	no	—
937	C₂²×C₄	—	94	2	no	—
938	C₂²×C₄	—	188	2	no	—
939	C₂²×C₄	—	188	2	no	—
940	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
941	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
942	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
943	C₂²×C₄	C₂³×D₄₇	1	2	yes	—
944	M₁₆	—	2	2	no	—
945	M₁₆	—	2	2	no	—
946	M₁₆	—	2	4	no	—
947	M₁₆	—	94	2	no	—
948	M₁₆	—	94	2	no	—
949	M₁₆	—	94	4	no	—
950	M₁₆	—	94	4	no	—
951	M₁₆	—	94	4	no	—
952	M₁₆	—	94	2	no	—
953	M₁₆	—	94	2	no	—
954	M₁₆	—	94	4	no	—
955	M₁₆	—	94	2	no	—
956	M₁₆	—	94	2	no	—
957	M₁₆	—	94	4	no	—
958	C₂×C₈	—	2	4	no	—
959	C₂×C₈	—	47	1	no	—
960	C₂×C₈	—	47	1	no	—
961	C₂×C₈	—	47	4	no	—
962	C₂×C₈	—	47	4	no	—
963	C₂×C₈	—	47	1	no	—
964	C₂×C₈	—	47	1	no	—
965	C₂×C₈	—	47	2	no	—
966	C₂×C₈	—	47	2	no	—
967	C₂×C₈	—	94	4	no	—
968	C₂×C₈	—	94	2	no	—
969	C₂×C₈	—	94	2	no	—
970	C₂×C₈	—	94	4	no	—
971	C₂×C₈	—	94	4	no	—
972	C₂×C₈	C₂³×D₄₇	1	1	yes	characteristic
973	C₂×C₈	C₂³×D₄₇	1	1	yes	characteristic
974	C₂×C₈	C₂³×D₄₇	1	2	yes	—
975	C₂×C₈	C₂³×D₄₇	1	2	yes	—
976	C₂×C₈	C₂³×D₄₇	1	1	yes	characteristic
977	C₂×C₈	C₂³×D₄₇	1	1	yes	characteristic
978	C₄⋊C₄	—	47	2	no	—
979	C₄⋊C₄	—	47	2	no	—
980	C₄⋊C₄	—	47	2	no	—
981	C₄⋊C₄	—	47	2	no	—
982	C₄⋊C₄	—	47	2	no	—
983	C₄⋊C₄	—	47	2	no	—
984	C₄⋊C₄	—	47	2	no	—
985	C₄⋊C₄	—	47	2	no	—
986	C₄⋊C₄	—	47	2	no	—
987	C₄⋊C₄	—	47	2	no	—
988	C₄⋊C₄	—	47	1	no	—
989	C₄⋊C₄	—	47	1	no	—
990	C₄⋊C₄	—	47	2	no	—
991	C₄⋊C₄	—	47	2	no	—
992	C₄⋊C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
993	C₄⋊C₄	C₂×C₄×D₄₇	1	2	yes	—
994	C₄⋊C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
995	C₄⋊C₄	C₂×C₄×D₄₇	1	2	yes	—
996	C₄⋊C₄	C₂×C₄×D₄₇	1	2	yes	—
997	C₄⋊C₄	C₂×C₄×D₄₇	1	2	yes	—
998	C₂²⋊C₄	—	47	2	no	—
999	C₂²⋊C₄	—	47	2	no	—
1000	C₂²⋊C₄	—	47	2	no	—
1001	C₂²⋊C₄	—	47	2	no	—
1002	C₂²⋊C₄	—	47	2	no	—
1003	C₂²⋊C₄	—	47	2	no	—
1004	C₂²⋊C₄	—	47	2	no	—
1005	C₂²⋊C₄	—	47	2	no	—
1006	C₂²⋊C₄	—	47	2	no	—
1007	C₂²⋊C₄	—	47	2	no	—
1008	C₂²⋊C₄	—	47	2	no	—
1009	C₂²⋊C₄	—	47	2	no	—
1010	C₂²⋊C₄	—	47	2	no	—
1011	C₂²⋊C₄	C₂×C₄×D₄₇	1	2	yes	—
1012	C₂²⋊C₄	C₂×C₄×D₄₇	1	2	yes	—
1013	C₂²⋊C₄	C₂×C₄×D₄₇	1	2	yes	—
1014	C₂²⋊C₄	C₂×C₄×D₄₇	1	2	yes	—
1015	C₂²⋊C₄	C₂×C₄×D₄₇	1	2	yes	—
1016	C₄²	—	47	1	no	—
1017	C₄²	—	47	1	no	—
1018	C₄²	—	47	1	no	—
1019	C₄²	—	47	1	no	—
1020	C₄²	—	47	1	no	—
1021	C₄²	—	47	1	no	—
1022	C₄²	—	47	1	no	—
1023	C₄²	—	47	1	no	—
1024	C₄²	—	47	1	no	—
1025	C₄²	—	47	1	no	—
1026	C₄²	—	47	2	no	—
1027	C₄²	—	47	2	no	—
1028	C₄²	—	47	2	no	—
1029	C₄²	—	47	2	no	—
1030	C₄²	—	47	1	no	—
1031	C₄²	—	47	2	no	—
1032	C₄²	—	47	1	no	—
1033	C₄²	C₂×C₄×D₄₇	1	1	yes	characteristic
1034	C₄²	C₂×C₄×D₄₇	1	1	yes	characteristic
1035	C₄²	C₂³×D₄₇	1	1	yes	characteristic
1036	C₄²	C₂³×D₄₇	1	1	yes	characteristic
1037	C₄²	C₂³×D₄₇	1	2	yes	—
1038	C₂³	—	47	1	no	—
1039	C₂³	—	47	2	no	—
1040	C₂³	—	47	1	no	—
1041	C₂³	—	94	2	no	—
1042	C₂³	—	188	1	no	—
1043	C₂³	—	188	1	no	—
1044	C₂³	C₂²×C₄×D₄₇	1	2	yes	—
1045	C₂³	C₂²×C₄×D₄₇	1	1	yes	characteristic
1046	Q₈	—	2	2	no	—
1047	Q₈	—	94	4	no	—
1048	Q₈	—	94	4	no	—
1049	Q₈	—	94	2	no	—
1050	D₄	—	2	2	no	—
1051	D₄	—	4	2	no	—
1052	D₄	—	94	4	no	—
1053	D₄	—	94	4	no	—
1054	D₄	—	94	4	no	—
1055	D₄	—	94	4	no	—
1056	D₄	—	94	2	no	—
1057	D₄	—	188	2	no	—
1058	D₄	—	188	2	no	—
1059	D₄	—	188	2	no	—
1060	C₂×C₄	—	2	2	no	—
1061	C₂×C₄	—	2	2	no	—
1062	C₂×C₄	—	2	2	no	—
1063	C₂×C₄	—	2	1	no	—
1064	C₂×C₄	—	2	1	no	—
1065	C₂×C₄	—	4	1	no	—
1066	C₂×C₄	—	47	1	no	—
1067	C₂×C₄	—	47	1	no	—
1068	C₂×C₄	—	47	2	no	—
1069	C₂×C₄	—	47	2	no	—
1070	C₂×C₄	—	47	1	no	—
1071	C₂×C₄	—	47	1	no	—
1072	C₂×C₄	—	47	1	no	—
1073	C₂×C₄	—	47	1	no	—
1074	C₂×C₄	—	47	2	no	—
1075	C₂×C₄	—	47	2	no	—
1076	C₂×C₄	—	47	2	no	—
1077	C₂×C₄	—	94	2	no	—
1078	C₂×C₄	—	94	2	no	—
1079	C₂×C₄	—	94	2	no	—
1080	C₂×C₄	—	94	2	no	—
1081	C₂×C₄	—	94	2	no	—
1082	C₂×C₄	—	94	2	no	—
1083	C₂×C₄	—	94	2	no	—
1084	C₂×C₄	—	94	2	no	—
1085	C₂×C₄	—	94	2	no	—
1086	C₂×C₄	—	94	2	no	—
1087	C₂×C₄	—	94	1	no	—
1088	C₂×C₄	—	94	1	no	—
1089	C₂×C₄	—	188	1	no	—
1090	C₂×C₄	—	188	1	no	—
1091	C₂×C₄	—	188	1	no	—
1092	C₂×C₄	—	188	1	no	—
1093	C₂×C₄	—	188	2	no	—
1094	C₂×C₄	—	188	2	no	—
1095	C₂×C₄	—	188	1	no	—
1096	C₂×C₄	—	188	2	no	—
1097	C₂×C₄	—	188	2	no	—
1098	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
1099	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
1100	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
1101	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
1102	C₂×C₄	C₂²×C₄×D₄₇	1	2	yes	—
1103	C₂×C₄	C₂²×C₄×D₄₇	1	2	yes	—
1104	C₂×C₄	C₂²×C₄×D₄₇	1	2	yes	—
1105	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
1106	C₂×C₄	C₂⁴×D₄₇	1	1	yes	characteristic
1107	C₈	—	2	2	no	—
1108	C₈	—	2	2	no	—
1109	C₈	—	2	1	no	—
1110	C₈	—	2	1	no	—
1111	C₈	—	47	2	no	—
1112	C₈	—	47	2	no	—
1113	C₈	—	94	1	no	—
1114	C₈	—	94	1	no	—
1115	C₈	—	94	2	no	—
1116	C₈	—	94	2	no	—
1117	C₈	#41×D₄₇	1	2	yes	—
1118	C₈	#41×D₄₇	1	2	yes	—
1119	C₂²	—	2	1	no	—
1120	C₂²	—	2	2	no	—
1121	C₂²	—	2	1	no	—
1122	C₂²	—	2	2	no	—
1123	C₂²	—	2	1	no	—
1124	C₂²	—	2	2	no	—
1125	C₂²	—	47	2	no	—
1126	C₂²	—	94	1	no	—
1127	C₂²	—	94	1	no	—
1128	C₂²	—	94	1	no	—
1129	C₂²	—	94	2	no	—
1130	C₂²	—	94	1	no	—
1131	C₂²	—	94	2	no	—
1132	C₂²	—	94	1	no	—
1133	C₂²	—	94	2	no	—
1134	C₂²	—	188	4	no	—
1135	C₂²	C₂³×C₄×D₄₇	1	1	yes	characteristic
1136	C₄	—	2	1	no	—
1137	C₄	—	2	1	no	—
1138	C₄	—	2	2	no	—
1139	C₄	—	2	1	no	—
1140	C₄	—	2	2	no	—
1141	C₄	—	2	1	no	—
1142	C₄	—	2	2	no	—
1143	C₄	—	47	2	no	—
1144	C₄	—	47	2	no	—
1145	C₄	—	94	1	no	—
1146	C₄	—	94	2	no	—
1147	C₄	—	94	1	no	—
1148	C₄	—	94	1	no	—
1149	C₄	—	94	2	no	—
1150	C₄	—	94	1	no	—
1151	C₄	—	94	2	no	—
1152	C₄	#15689888	1	2	yes	—
1153	C₄	C₂×#41×D₄₇	1	1	yes	characteristic
1154	C₄	C₂×#41×D₄₇	1	1	yes	characteristic
1155	C₂	—	4	1	no	—
1156	C₂	—	4	2	no	—
1157	C₂	—	94	2	no	—
1158	C₂	—	188	1	no	—
1159	C₂	—	188	2	no	—
1160	C₂	C₄×#41×D₄₇	1	1	yes	characteristic
1161	C₂	#568×D₄₇	1	1	yes	characteristic
1162	C₂	C₂×#15689888	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂⁴×D₄₇
commutator, socle	C₂²×C₄₇	C₂⁴×C₄
Fitting	C₄₇×#2969	C₂
prime radical	#20256682	C₂
cosocle	C₂×C₄×C₄₇	C₂⁵
hypercenter	#2969	D₄₇
hypocenter	C₄₇	#60208
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ #2969

Complements

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

N	H ≅ G/N	type
2. #20252407	C₂	semidirect
3. #20252404	C₂	semidirect
4. #20252404	C₂	semidirect
5. #20252401	C₂	semidirect
6. #20252398	C₂	semidirect
7. #20252396	C₂	semidirect
8. #20252393	C₂	semidirect
9. #20252392	C₂	semidirect
10. #20252390	C₂	semidirect
11. #20252388	C₂	semidirect
12. #20252386	C₂	semidirect
13. #20252319	C₂	semidirect
14. #20252317	C₂	semidirect
15. #20252097	C₂	semidirect
16. #20252095	C₂	semidirect
17. #20252088	C₂	semidirect
18. #20252086	C₂	semidirect
19. #20252036	C₂	semidirect
20. #20252016	C₂	semidirect
21. #20251815	C₂	semidirect
22. C₄×M₁₆×D₄₇	C₂	semidirect
23. C₄₇×#2969	C₂	semidirect
50. #15689254	C₂²	semidirect
51. #15689253	C₂²	semidirect
52. #15689252	C₂²	semidirect
53. #15689251	C₂²	semidirect
54. #15689250	C₂²	semidirect
55. Q₈×C₄₇⋊C₈	C₂²	semidirect
56. C₈×Dic₉₄	C₂²	semidirect
57. C₈×Dic₉₄	C₂²	semidirect
58. #15689247	C₂²	semidirect
59. #15689247	C₂²	semidirect
61. #15689202	C₂²	semidirect
63. #15689201	C₂²	semidirect
65. #15689200	C₂²	semidirect
68. #15689199	C₂²	semidirect
71. #15689198	C₂²	semidirect
79. C₈×D₁₈₈	C₂²	semidirect
80. D₄×C₄₇⋊C₈	C₂²	semidirect
81. #15689188	C₂²	semidirect
82. C₈×C₂²⋊D₄₇	C₂²	semidirect
83. (C₂²⋊D₄₇)⋊C₈	C₂²	semidirect
84. #15689185	C₂²	semidirect
85. #15689184	C₂²	semidirect
86. #15689182	C₂²	semidirect
89. #15689179	C₂²	semidirect
90. #15689179	C₂²	semidirect
92. #15689177	C₂²	semidirect
93. #15689177	C₂²	semidirect
104. #15689080	C₂²	semidirect
105. #15689079	C₂²	semidirect
107. #15689077	C₂²	semidirect
113. M₁₆×Dic₄₇	C₂²	semidirect
117. C₄×#10625324	C₂²	semidirect
118. C₂×#13093934	C₂²	semidirect
121. #97×D₄₇	C₂²	semidirect
125. C₄₇×#446	C₂²	semidirect
126. C₈×Q₈×C₄₇	C₂²	semidirect
128. C₄₇×#436	C₂²	semidirect
130. C₈×D₄×C₄₇	C₂²	semidirect
131. C₄₇×#433	C₂²	semidirect
133. C₄₇×#405	C₂²	semidirect
454. C₈×D₄₇	#41	semidirect
455. C₈×D₄₇	#41	semidirect
586. #2969	D₄₇	semidirect
637. #446	C₂×D₄₇	semidirect
643. C₈×Q₈	C₂×D₄₇	semidirect
657. #436	C₂×D₄₇	semidirect
671. C₈×D₄	C₂×D₄₇	semidirect
675. #433	C₂×D₄₇	semidirect
698. #405	C₂×D₄₇	semidirect
716. C₄₇	#60208	semidirect

Maximal subgroups

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

subgroup	index
#20256682	2
#20252407	2
#20252404	2
#20252401	2
#20252398	2
#20252396	2
#20252393	2
#20252392	2
#20252390	2
#20252388	2
#20252386	2
#20252319	2
#20252317	2
#20252097	2
#20252095	2
#20252088	2
#20252086	2
#20252036	2
#20252016	2
#20251815	2
C₄×M₁₆×D₄₇	2
C₄₇×#2969	2
#60208	47