Subgroups — #27081483

Order 12032.

1786 conjugacy classes of subgroups.

The subgroup lattice has 1142 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20256773	C₂	1	1	yes	maximal, characteristic
2	#20252560	C₂	1	2	yes	maximal, complemented
3	#20252553	C₂	1	2	yes	maximal, complemented
4	#20252550	C₂	1	2	yes	maximal, complemented
5	#20252542	C₂	1	2	yes	maximal, complemented
6	#20252539	C₂	1	2	yes	maximal, complemented
7	#20252531	C₂	1	2	yes	maximal, complemented
8	#20252529	C₂	1	2	yes	maximal, complemented
9	#20252522	C₂	1	2	yes	maximal, complemented
10	#20252326	C₂	1	1	yes	maximal, characteristic, complemented
11	#20252320	C₂	1	1	yes	maximal, characteristic, complemented
12	#20252118	C₂	1	1	yes	maximal, characteristic, complemented
13	#20252118	C₂	1	1	yes	maximal, characteristic, complemented
14	#20252116	C₂	1	1	yes	maximal, characteristic, complemented
15	#20252116	C₂	1	1	yes	maximal, characteristic, complemented
16	#20252103	C₂	1	1	yes	maximal, characteristic, complemented
17	#20252096	C₂	1	1	yes	maximal, characteristic, complemented
18	#20252053	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂×#15689183	C₂	1	1	yes	maximal, characteristic, complemented
20	#20251957	C₂	1	1	yes	maximal, characteristic, complemented
21	#20251956	C₂	1	1	yes	maximal, characteristic, complemented
22	#20251950	C₂	1	1	yes	maximal, characteristic, complemented
23	C₄₇×#2925	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#13094032	C₂²	1	1	yes	characteristic
25	C₂×#13094032	C₂²	1	1	yes	characteristic
26	C₂×#13094031	C₂²	1	1	yes	characteristic
27	C₂×#13094031	C₂²	1	1	yes	characteristic
28	C₂×M₁₆×D₄₇	C₂²	1	1	yes	characteristic
29	C₂×M₁₆×D₄₇	C₂²	1	1	yes	characteristic
30	#15689745	C₄	1	1	yes	characteristic
31	#15689745	C₄	1	1	yes	characteristic
32	#15689738	C₄	1	1	yes	characteristic
33	#15689738	C₄	1	1	yes	characteristic
34	#15689731	C₄	1	1	yes	characteristic
35	#15689731	C₄	1	1	yes	characteristic
36	#15689724	C₄	1	1	yes	characteristic
37	#15689724	C₄	1	1	yes	characteristic
38	#15689715	C₄	1	2	yes	—
39	#15689715	C₄	1	2	yes	—
40	#15689706	C₄	1	2	yes	—
41	#15689706	C₄	1	2	yes	—
42	#15689676	C₂²	1	1	yes	characteristic
43	#15689669	C₂²	1	1	yes	characteristic
44	#15689657	C₂²	1	2	yes	—
45	#15689657	C₂²	1	2	yes	—
46	#15689651	C₂²	1	2	yes	—
47	#15689651	C₂²	1	2	yes	—
48	#15689635	C₂²	1	1	yes	characteristic
49	#15689630	C₂²	1	1	yes	characteristic
50	C₄×#10625350	C₂²	1	1	yes	characteristic
51	C₂×#13093981	C₂²	1	1	yes	characteristic
52	#15689253	C₂²	1	2	yes	complemented
53	#15689253	C₂²	1	2	yes	complemented
54	#15689251	C₂²	1	2	yes	complemented
55	#15689251	C₂²	1	2	yes	complemented
56	#15689251	C₂²	1	2	yes	complemented
57	#15689251	C₂²	1	2	yes	complemented
58	C₈×Dic₉₄	C₂²	1	2	yes	complemented
59	C₈×Dic₉₄	C₂²	1	2	yes	complemented
60	#15689202	C₂²	1	2	yes	—
61	#15689202	C₂²	1	2	yes	—
62	#15689198	C₂²	1	2	yes	—
63	#15689198	C₂²	1	2	yes	—
64	#15689198	C₂²	1	2	yes	complemented
65	#15689198	C₂²	1	2	yes	complemented
66	#15689197	C₂²	1	2	yes	—
67	#15689197	C₂²	1	2	yes	—
68	#15689197	C₂²	1	2	yes	complemented
69	#15689197	C₂²	1	2	yes	complemented
70	#15689196	C₂²	1	2	yes	—
71	#15689196	C₂²	1	2	yes	—
72	#15689196	C₂²	1	2	yes	—
73	#15689196	C₂²	1	2	yes	—
74	#15689191	C₂²	1	2	yes	—
75	#15689191	C₂²	1	2	yes	—
76	#15689191	C₂²	1	2	yes	complemented
77	#15689191	C₂²	1	2	yes	complemented
78	C₈×D₁₈₈	C₂²	1	2	yes	—
79	C₈×D₁₈₈	C₂²	1	2	yes	—
80	(C₂²⋊D₄₇)⋊C₈	C₂²	1	2	yes	—
81	(C₂²⋊D₄₇)⋊C₈	C₂²	1	2	yes	—
82	(C₂²⋊D₄₇)⋊C₈	C₂²	1	2	yes	complemented
83	(C₂²⋊D₄₇)⋊C₈	C₂²	1	2	yes	complemented
84	#15689183	C₂²	1	1	yes	characteristic
85	#15689183	C₂²	1	1	yes	characteristic
86	#15689183	C₂²	1	1	yes	characteristic
87	#15689183	C₂²	1	1	yes	characteristic
88	#15689183	C₂²	1	1	yes	characteristic
89	#15689183	C₂²	1	1	yes	characteristic
90	#15689183	C₂²	1	1	yes	characteristic
91	#15689183	C₂²	1	1	yes	characteristic
92	#15689183	C₂²	1	2	yes	complemented
93	#15689183	C₂²	1	2	yes	complemented
94	#15689179	C₂²	1	2	yes	complemented
95	#15689175	C₂²	1	2	yes	complemented
96	#15689151	C₂²	1	1	yes	characteristic
97	#15689151	C₂²	1	1	yes	characteristic
98	#15689150	C₂²	1	1	yes	characteristic
99	#15689150	C₂²	1	1	yes	characteristic
100	#15689150	C₂²	1	2	yes	complemented
101	#15689150	C₂²	1	2	yes	complemented
102	#15689148	C₂²	1	2	yes	—
103	#15689148	C₂²	1	2	yes	—
104	#15689148	C₂²	1	2	yes	—
105	#15689148	C₂²	1	2	yes	—
106	#15689148	C₂²	1	2	yes	complemented
107	#15689148	C₂²	1	2	yes	complemented
108	#15689147	C₂²	1	1	yes	characteristic
109	#15689147	C₂²	1	2	yes	complemented
110	#15689146	C₂²	1	1	yes	characteristic
111	#15689146	C₂²	1	1	yes	characteristic
112	#15689145	C₂²	1	2	yes	complemented
113	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
114	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	2	yes	complemented
115	C₄⋊C₈×D₄₇	C₂²	1	2	yes	complemented
116	#15689089	C₂²	1	1	yes	characteristic
117	#15689089	C₂²	1	1	yes	characteristic
118	C₂×(C₂×D₄₇)⋊C₈	C₂²	1	1	yes	characteristic
119	C₂×(C₂×D₄₇)⋊C₈	C₂²	1	1	yes	characteristic
120	#15689078	C₂²	1	1	yes	characteristic
121	#15689078	C₂²	1	1	yes	characteristic
122	C₂×#13093934	C₂²	1	1	yes	characteristic
123	C₂×C₈×Dic₄₇	C₂²	1	1	yes	characteristic
124	C₄×#41×C₄₇	C₂²	1	1	yes	characteristic
125	C₄₇×#433	C₂²	1	2	yes	complemented
126	C₄₇×#433	C₂²	1	2	yes	complemented
127	C₄₇×#432	C₂²	1	2	yes	complemented
128	C₄₇×#431	C₂²	1	2	yes	complemented
129	C₄₇×#423	C₂²	1	1	yes	characteristic
130	C₂×C₄⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
131	C₄₇×#408	C₂²	1	1	yes	characteristic
132	C₄₇×#408	C₂²	1	1	yes	characteristic
133	C₄₇×#405	C₂²	1	1	yes	characteristic
134	C₄₇×#405	C₂²	1	1	yes	characteristic
135	C₂×#10625350	C₂³	1	1	yes	characteristic
136	C₂²×C₄×D₄₇	C₂³	1	1	yes	characteristic
137	#13094032	—	4	2	no	—
138	#13094032	—	4	2	no	—
139	#13094031	—	4	2	no	—
140	#13094031	—	4	2	no	—
141	C₂×#10625329	C₂³	1	1	yes	characteristic
142	C₂×#10625329	C₂³	1	1	yes	characteristic
143	C₂×#10625329	C₂³	1	2	yes	—
144	C₂×#10625329	C₂³	1	2	yes	—
145	C₂×#10625324	C₂³	1	2	yes	—
146	C₂×#10625324	C₂³	1	2	yes	—
147	C₂×#10625324	C₂³	1	2	yes	—
148	C₂×#10625324	C₂³	1	2	yes	—
149	M₁₆×D₄₇	—	4	2	no	—
150	M₁₆×D₄₇	—	4	2	no	—
151	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
152	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
153	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
154	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
155	C₂×C₈×D₄₇	C₂³	1	2	yes	—
156	C₂×C₈×D₄₇	C₂³	1	2	yes	—
157	C₂×C₈×D₄₇	C₂³	1	2	yes	—
158	C₂×C₈×D₄₇	C₂³	1	2	yes	—
159	#13094023	C₂×C₄	1	1	yes	characteristic
160	#13094023	C₂×C₄	1	1	yes	characteristic
161	#13094022	C₂×C₄	1	1	yes	characteristic
162	#13094020	C₂×C₄	1	1	yes	characteristic
163	#13094019	C₂×C₄	1	2	yes	—
164	#13094019	C₂×C₄	1	2	yes	—
165	#13094018	C₂×C₄	1	2	yes	—
166	#13094018	C₂×C₄	1	2	yes	—
167	#13094018	C₂×C₄	1	2	yes	—
168	#13094018	C₂×C₄	1	2	yes	—
169	#13094017	C₂×C₄	1	2	yes	—
170	#13094017	C₂×C₄	1	2	yes	—
171	#13094016	C₂×C₄	1	2	yes	—
172	#13094016	C₂×C₄	1	2	yes	—
173	#13094015	C₂×C₄	1	1	yes	characteristic
174	#13094015	C₂×C₄	1	1	yes	characteristic
175	#13094014	C₂×C₄	1	2	yes	—
176	#13094014	C₂×C₄	1	2	yes	—
177	#13094013	C₂×C₄	1	1	yes	characteristic
178	#13094012	C₂×C₄	1	2	yes	—
179	#13094012	C₂×C₄	1	2	yes	—
180	#13094011	C₂×C₄	1	1	yes	characteristic
181	#13094010	C₂×C₄	1	2	yes	—
182	#13094010	C₂×C₄	1	2	yes	—
183	#13094009	C₂×C₄	1	2	yes	—
184	#13094009	C₂×C₄	1	2	yes	—
185	#13094008	C₂×C₄	1	2	yes	—
186	#13094007	C₂×C₄	1	2	yes	—
187	#13094007	C₂×C₄	1	2	yes	—
188	#13094007	C₂×C₄	1	2	yes	—
189	#13094007	C₂×C₄	1	2	yes	—
190	#13094006	C₂×C₄	1	2	yes	—
191	#13094006	C₂×C₄	1	2	yes	—
192	#13094005	C₂×C₄	1	2	yes	—
193	#13094004	C₂×C₄	1	1	yes	characteristic
194	#13094004	C₂×C₄	1	1	yes	characteristic
195	#13094003	C₂×C₄	1	2	yes	—
196	#13094003	C₂×C₄	1	2	yes	—
197	#13094002	C₂×C₄	1	2	yes	—
198	#13094002	C₂×C₄	1	2	yes	—
199	#13094001	C₂×C₄	1	2	yes	—
200	#13094001	C₂×C₄	1	2	yes	—
201	#13094000	C₂×C₄	1	1	yes	characteristic
202	#13094000	C₂×C₄	1	1	yes	characteristic
203	#13093999	C₂×C₄	1	1	yes	characteristic
204	#13093999	C₂×C₄	1	1	yes	characteristic
205	#13093998	C₂×C₄	1	2	yes	—
206	#13093998	C₂×C₄	1	2	yes	—
207	#13093997	C₂×C₄	1	2	yes	—
208	#13093997	C₂×C₄	1	2	yes	—
209	#13093996	C₂×C₄	1	2	yes	—
210	#13093996	C₂×C₄	1	2	yes	—
211	#13093995	C₂×C₄	1	1	yes	characteristic
212	#13093995	C₂×C₄	1	1	yes	characteristic
213	#13093994	C₂×C₄	1	2	yes	—
214	#13093992	C₂×C₄	1	2	yes	—
215	C₄×Dic₉₄	C₂×C₄	1	1	yes	characteristic
216	C₄×Dic₉₄	C₂×C₄	1	1	yes	characteristic
217	C₄×Dic₉₄	C₂³	1	2	yes	—
218	C₄×Dic₉₄	C₂³	1	2	yes	—
219	C₄×D₁₈₈	C₂×C₄	1	1	yes	characteristic
220	C₄×D₁₈₈	C₂×C₄	1	1	yes	characteristic
221	C₄×D₁₈₈	C₂³	1	2	yes	—
222	C₄×D₁₈₈	C₂³	1	2	yes	—
223	C₄×C₂²⋊D₄₇	C₂×C₄	1	2	yes	—
224	C₄×C₂²⋊D₄₇	C₂×C₄	1	2	yes	—
225	C₄×C₂²⋊D₄₇	C₂³	1	2	yes	—
226	C₄×C₂²⋊D₄₇	C₂³	1	2	yes	—
227	C₄×C₂²⋊D₄₇	C₂³	1	2	yes	—
228	C₄×C₂²⋊D₄₇	C₂³	1	2	yes	—
229	#13093983	C₂³	1	1	yes	characteristic
230	#13093981	C₂×C₄	1	1	yes	characteristic
231	#13093981	C₂×C₄	1	1	yes	characteristic
232	#13093981	C₂×C₄	1	1	yes	characteristic
233	#13093981	C₂×C₄	1	1	yes	characteristic
234	#13093981	C₂³	1	1	yes	characteristic
235	#13093981	C₂³	1	1	yes	characteristic
236	#13093981	C₂³	1	1	yes	characteristic
237	#13093981	C₂³	1	1	yes	characteristic
238	#13093981	C₂³	1	2	yes	—
239	C₂×Dic₄₇⋊C₄	C₂×C₄	1	1	yes	characteristic
240	C₂×Dic₄₇⋊C₄	C₂×C₄	1	1	yes	characteristic
241	C₂×(C₂×D₄₇)⋊C₄	C₂×C₄	1	1	yes	characteristic
242	C₂×(C₂×D₄₇)⋊C₄	C₂×C₄	1	1	yes	characteristic
243	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
244	C₄²×D₄₇	C₂³	1	2	yes	—
245	C₄⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
246	C₄⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
247	C₄⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
248	C₄⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
249	C₄⋊(C₄₇⋊C₈)	C₂³	1	1	yes	characteristic
250	C₄⋊(C₄₇⋊C₈)	C₂³	1	1	yes	characteristic
251	C₄⋊(C₄₇⋊C₈)	C₂³	1	1	yes	characteristic
252	C₄⋊(C₄₇⋊C₈)	C₂³	1	1	yes	characteristic
253	C₄⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
254	C₄⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
255	Dic₄₇⋊C₈	C₂³	1	2	yes	—
256	Dic₄₇⋊C₈	C₂³	1	2	yes	—
257	Dic₄₇⋊C₈	C₂³	1	2	yes	—
258	Dic₄₇⋊C₈	C₂³	1	2	yes	—
259	Dic₄₇⋊C₈	C₂³	1	2	yes	—
260	Dic₄₇⋊C₈	C₂³	1	2	yes	—
261	Dic₄₇⋊C₈	C₂³	1	2	yes	—
262	Dic₄₇⋊C₈	C₂³	1	2	yes	—
263	(C₂×D₄₇)⋊C₈	C₂³	1	1	yes	characteristic
264	(C₂×D₄₇)⋊C₈	C₂³	1	1	yes	characteristic
265	(C₂×D₄₇)⋊C₈	C₂³	1	1	yes	characteristic
266	(C₂×D₄₇)⋊C₈	C₂³	1	1	yes	characteristic
267	(C₂×D₄₇)⋊C₈	C₂³	1	1	yes	characteristic
268	(C₂×D₄₇)⋊C₈	C₂³	1	1	yes	characteristic
269	(C₂×D₄₇)⋊C₈	C₂³	1	1	yes	characteristic
270	(C₂×D₄₇)⋊C₈	C₂³	1	1	yes	characteristic
271	(C₂×D₄₇)⋊C₈	C₂³	1	2	yes	—
272	(C₂×D₄₇)⋊C₈	C₂³	1	2	yes	—
273	(C₂×D₄₇)⋊C₈	C₂³	1	2	yes	—
274	(C₂×D₄₇)⋊C₈	C₂³	1	2	yes	—
275	#13093934	C₂³	1	1	yes	characteristic
276	#13093934	C₂³	1	1	yes	characteristic
277	#13093934	C₂³	1	2	yes	—
278	#13093934	C₂³	1	1	yes	characteristic
279	#13093934	C₂³	1	1	yes	characteristic
280	#13093934	C₂³	1	2	yes	—
281	C₈×Dic₄₇	C₂³	1	1	yes	characteristic
282	C₈×Dic₄₇	C₂³	1	1	yes	characteristic
283	C₈×Dic₄₇	C₂³	1	2	yes	—
284	C₈×Dic₄₇	C₂³	1	1	yes	characteristic
285	C₈×Dic₄₇	C₂³	1	1	yes	characteristic
286	C₈×Dic₄₇	C₂³	1	2	yes	—
287	C₂×#41×C₄₇	C₂³	1	1	yes	characteristic
288	C₂×M₁₆×C₄₇	C₂³	1	1	yes	characteristic
289	C₂×M₁₆×C₄₇	C₂³	1	1	yes	characteristic
290	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
291	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
292	C₄×Q₈×C₄₇	C₂×C₄	1	1	yes	characteristic
293	C₄×Q₈×C₄₇	C₂×C₄	1	1	yes	characteristic
294	C₄×D₄×C₄₇	C₂×C₄	1	1	yes	characteristic
295	C₄×D₄×C₄₇	C₂×C₄	1	1	yes	characteristic
296	C₄×D₄×C₄₇	C₂×C₄	1	2	yes	—
297	C₄×D₄×C₄₇	C₂×C₄	1	2	yes	—
298	#117×C₄₇	C₂³	1	1	yes	characteristic
299	#117×C₄₇	C₂³	1	2	yes	—
300	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
301	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
302	C₄⋊C₈×C₄₇	C₂³	1	2	yes	—
303	C₄⋊C₈×C₄₇	C₂³	1	2	yes	—
304	C₄⋊C₈×C₄₇	C₂³	1	1	yes	characteristic
305	C₄⋊C₈×C₄₇	C₂³	1	1	yes	characteristic
306	C₄⋊C₈×C₄₇	C₂³	1	1	yes	characteristic
307	C₄⋊C₈×C₄₇	C₂³	1	1	yes	characteristic
308	C₂²⋊C₈×C₄₇	C₂³	1	2	yes	—
309	C₂²⋊C₈×C₄₇	C₂³	1	2	yes	—
310	C₂²⋊C₈×C₄₇	C₂³	1	2	yes	—
311	C₂²⋊C₈×C₄₇	C₂³	1	2	yes	—
312	#97×C₄₇	C₂³	1	2	yes	—
313	#97×C₄₇	C₂³	1	2	yes	—
314	C₄×C₈×C₄₇	C₂³	1	2	yes	—
315	C₄×C₈×C₄₇	C₂³	1	2	yes	—
316	C₂³×D₄₇	C₂²×C₄	1	1	yes	characteristic
317	#41×C₄₇	—	2	2	no	—
318	#41×C₄₇	—	2	2	no	—
319	C₂×Q₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
320	C₂×D₄×C₄₇	C₂²×C₄	1	2	yes	—
321	C₂×D₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
322	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
323	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
324	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
325	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
326	C₂²×C₄×C₄₇	C₂⁴	1	2	yes	—
327	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
328	C₂×C₂²⋊D₄₇	C₂²×C₄	1	2	yes	—
329	C₂×C₂²⋊D₄₇	C₂²×C₄	1	2	yes	—
330	C₂×C₂²⋊D₄₇	C₂²×C₄	1	2	yes	—
331	C₂×C₂²⋊D₄₇	C₂²×C₄	1	2	yes	—
332	C₂×C₂²⋊D₄₇	C₂²×C₄	1	2	yes	—
333	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
334	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
335	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
336	#10625350	—	2	2	no	—
337	#10625350	—	2	2	no	—
338	C₂×D₁₈₈	C₂²×C₄	1	1	yes	characteristic
339	C₂×D₁₈₈	C₂²×C₄	1	2	yes	—
340	C₂×D₁₈₈	C₂²×C₄	1	2	yes	—
341	C₂×C₄×D₄₇	—	2	2	no	—
342	C₂×C₄×D₄₇	—	2	2	no	—
343	C₂×C₄×D₄₇	C₂²×C₄	1	1	yes	characteristic
344	C₂×C₄×D₄₇	C₂²×C₄	1	1	yes	characteristic
345	C₂×C₄×D₄₇	C₂²×C₄	1	2	yes	—
346	C₂×C₄×D₄₇	C₂²×C₄	1	2	yes	—
347	C₂×C₄×D₄₇	C₂⁴	1	2	yes	—
348	C₂×C₄×D₄₇	C₂⁴	1	1	yes	characteristic
349	C₂×C₄×D₄₇	C₂⁴	1	1	yes	characteristic
350	C₂×Dic₉₄	C₂²×C₄	1	1	yes	characteristic
351	C₂×Dic₉₄	C₂²×C₄	1	2	yes	—
352	C₂×Dic₉₄	C₂²×C₄	1	2	yes	—
353	M₁₆×C₄₇	—	2	2	no	—
354	M₁₆×C₄₇	—	2	2	no	—
355	C₂×C₈×C₄₇	—	2	2	no	—
356	C₂×C₈×C₄₇	—	2	2	no	—
357	C₂×C₈×C₄₇	C₂⁴	1	1	yes	characteristic
358	C₂×C₈×C₄₇	C₂⁴	1	1	yes	characteristic
359	C₂×C₈×C₄₇	C₂⁴	1	1	yes	characteristic
360	C₂×C₈×C₄₇	C₂⁴	1	1	yes	characteristic
361	C₂×C₈×C₄₇	C₂⁴	1	2	yes	—
362	C₂×C₈×C₄₇	C₂⁴	1	2	yes	—
363	C₄⋊C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
364	C₄⋊C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
365	C₄⋊C₄×C₄₇	C₂²×C₄	1	2	yes	—
366	C₄⋊C₄×C₄₇	C₂²×C₄	1	2	yes	—
367	C₂²⋊C₄×C₄₇	C₂²×C₄	1	2	yes	—
368	C₂²⋊C₄×C₄₇	C₂²×C₄	1	2	yes	—
369	C₂²⋊C₄×C₄₇	C₂²×C₄	1	2	yes	—
370	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
371	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
372	C₄²×C₄₇	C₂²×C₄	1	2	yes	—
373	C₄²×C₄₇	C₂²×C₄	1	2	yes	—
374	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
375	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
376	C₄²×C₄₇	C₂⁴	1	2	yes	—
377	C₂²⋊Dic₄₇	C₂²×C₄	1	2	yes	—
378	C₂²⋊Dic₄₇	C₂²×C₄	1	2	yes	—
379	C₂²⋊Dic₄₇	C₂²×C₄	1	2	yes	—
380	C₂²⋊Dic₄₇	C₂²×C₄	1	2	yes	—
381	C₂²⋊Dic₄₇	C₂²×C₄	1	2	yes	—
382	(C₂×D₄₇)⋊C₄	C₂²×C₄	1	1	yes	characteristic
383	(C₂×D₄₇)⋊C₄	C₂²×C₄	1	1	yes	characteristic
384	(C₂×D₄₇)⋊C₄	C₂²×C₄	1	1	yes	characteristic
385	(C₂×D₄₇)⋊C₄	C₂²×C₄	1	1	yes	characteristic
386	(C₂×D₄₇)⋊C₄	C₂²×C₄	1	1	yes	characteristic
387	(C₂×D₄₇)⋊C₄	C₂²×C₄	1	1	yes	characteristic
388	(C₂×D₄₇)⋊C₄	C₂²×C₄	1	1	yes	characteristic
389	(C₂×D₄₇)⋊C₄	C₂²×C₄	1	1	yes	characteristic
390	(C₂×D₄₇)⋊C₄	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	C₄⋊Dic₄₇	C₂²×C₄	1	1	yes	characteristic
401	C₄⋊Dic₄₇	C₂²×C₄	1	1	yes	characteristic
402	C₄⋊Dic₄₇	C₂²×C₄	1	2	yes	—
403	C₄⋊Dic₄₇	C₂²×C₄	1	2	yes	—
404	C₄⋊Dic₄₇	C₂²×C₄	1	2	yes	—
405	C₄⋊Dic₄₇	C₂²×C₄	1	2	yes	—
406	Dic₄₇⋊C₄	C₂²×C₄	1	1	yes	characteristic
407	Dic₄₇⋊C₄	C₂²×C₄	1	1	yes	characteristic
408	Dic₄₇⋊C₄	C₂²×C₄	1	1	yes	characteristic
409	Dic₄₇⋊C₄	C₂²×C₄	1	1	yes	characteristic
410	Dic₄₇⋊C₄	C₂²×C₄	1	1	yes	characteristic
411	Dic₄₇⋊C₄	C₂²×C₄	1	1	yes	characteristic
412	Dic₄₇⋊C₄	C₂²×C₄	1	1	yes	characteristic
413	Dic₄₇⋊C₄	C₂²×C₄	1	1	yes	characteristic
414	Dic₄₇⋊C₄	C₂²×C₄	1	2	yes	—
415	Dic₄₇⋊C₄	C₂²×C₄	1	2	yes	—
416	Dic₄₇⋊C₄	C₂²×C₄	1	2	yes	—
417	Dic₄₇⋊C₄	C₂²×C₄	1	2	yes	—
418	Dic₄₇⋊C₄	C₂²×C₄	1	2	yes	—
419	Dic₄₇⋊C₄	C₂²×C₄	1	2	yes	—
420	Dic₄₇⋊C₄	C₂²×C₄	1	2	yes	—
421	Dic₄₇⋊C₄	C₂²×C₄	1	2	yes	—
422	Dic₄₇⋊C₄	C₂²×C₄	1	2	yes	—
423	Dic₄₇⋊C₄	C₂²×C₄	1	2	yes	—
424	C₄×Dic₄₇	C₂²×C₄	1	2	yes	—
425	C₄×Dic₄₇	C₂²×C₄	1	2	yes	—
426	C₄×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
427	C₄×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
428	C₄×Dic₄₇	C₂⁴	1	2	yes	—
429	C₄×Dic₄₇	C₂⁴	1	1	yes	characteristic
430	C₄×Dic₄₇	C₂⁴	1	1	yes	characteristic
431	#10625329	—	2	2	no	—
432	#10625329	—	2	2	no	—
433	#10625329	—	4	2	no	—
434	#10625329	—	4	2	no	—
435	C₂×C₄₇⋊C₈	—	2	2	no	—
436	C₂×C₄₇⋊C₈	—	2	2	no	—
437	C₂×C₄₇⋊C₈	—	4	2	no	—
438	C₂×C₄₇⋊C₈	—	4	2	no	—
439	C₂×C₄₇⋊C₈	C₂⁴	1	1	yes	characteristic
440	C₂×C₄₇⋊C₈	C₂⁴	1	1	yes	characteristic
441	C₂×C₄₇⋊C₈	C₂⁴	1	2	yes	—
442	C₂×C₄₇⋊C₈	C₂⁴	1	2	yes	—
443	C₂×C₄₇⋊C₈	C₂⁴	1	1	yes	characteristic
444	C₂×C₄₇⋊C₈	C₂⁴	1	1	yes	characteristic
445	#10625324	—	4	2	no	—
446	#10625324	—	4	2	no	—
447	#10625324	—	4	2	no	—
448	#10625324	—	4	2	no	—
449	C₈×D₄₇	—	4	2	no	—
450	C₈×D₄₇	—	4	2	no	—
451	C₈×D₄₇	—	4	2	no	—
452	C₈×D₄₇	—	4	2	no	—
453	C₂³×C₄₇	C₂³×C₄	1	2	yes	—
454	C₂³×C₄₇	C₂³×C₄	1	1	yes	characteristic
455	C₂²×D₄₇	—	2	2	no	—
456	C₂²×D₄₇	—	4	1	no	—
457	C₂²×D₄₇	—	4	1	no	—
458	C₂²×D₄₇	C₂³×C₄	1	1	yes	characteristic
459	C₂²×D₄₇	C₂³×C₄	1	1	yes	characteristic
460	C₂²×D₄₇	C₂³×C₄	1	2	yes	—
461	Q₈×C₄₇	—	2	2	no	—
462	D₄×C₄₇	—	2	4	no	—
463	D₄×C₄₇	—	2	2	no	—
464	C₂×C₄×C₄₇	—	2	2	no	—
465	C₂×C₄×C₄₇	—	2	2	no	—
466	C₂×C₄×C₄₇	—	4	2	no	—
467	C₂×C₄×C₄₇	—	4	2	no	—
468	C₂×C₄×C₄₇	—	4	1	no	—
469	C₂×C₄×C₄₇	—	4	1	no	—
470	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
471	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
472	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
473	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
474	C₂×C₄×C₄₇	C₂³×C₄	1	2	yes	—
475	C₂×C₄×C₄₇	C₂³×C₄	1	2	yes	—
476	C₂×C₄×C₄₇	C₂³×C₄	1	2	yes	—
477	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
478	C₂×C₄×C₄₇	H(5,𝔽₂)	1	2	yes	—
479	C₂×C₄×C₄₇	2₋¹⁺⁴	1	2	yes	—
480	C₂×C₄×C₄₇	C₂⁵	1	1	yes	characteristic
481	C₂²⋊D₄₇	—	2	4	no	—
482	C₂²⋊D₄₇	—	4	2	no	—
483	C₂²⋊D₄₇	—	4	2	no	—
484	C₂²⋊D₄₇	—	4	2	no	—
485	C₂²⋊D₄₇	—	4	2	no	—
486	C₂×Dic₄₇	—	2	2	no	—
487	C₂×Dic₄₇	—	4	1	no	—
488	C₂×Dic₄₇	—	4	1	no	—
489	C₂×Dic₄₇	C₂³×C₄	1	2	yes	—
490	C₂×Dic₄₇	C₂³×C₄	1	1	yes	characteristic
491	C₂×Dic₄₇	C₂³×C₄	1	1	yes	characteristic
492	C₂×Dic₄₇	C₂³×C₄	1	2	yes	—
493	C₂×Dic₄₇	C₂³×C₄	1	2	yes	—
494	C₂×Dic₄₇	C₂³×C₄	1	1	yes	characteristic
495	C₂×Dic₄₇	C₂³×C₄	1	1	yes	characteristic
496	C₂×Dic₄₇	C₂³×C₄	1	1	yes	characteristic
497	C₂×Dic₄₇	C₂³×C₄	1	1	yes	characteristic
498	D₁₈₈	—	2	2	no	—
499	D₁₈₈	—	4	2	no	—
500	D₁₈₈	—	4	2	no	—
501	C₄×D₄₇	—	2	2	no	—
502	C₄×D₄₇	—	2	2	no	—
503	C₄×D₄₇	—	2	1	no	—
504	C₄×D₄₇	—	2	1	no	—
505	C₄×D₄₇	—	2	2	no	—
506	C₄×D₄₇	—	2	1	no	—
507	C₄×D₄₇	—	2	1	no	—
508	C₄×D₄₇	—	2	2	no	—
509	C₄×D₄₇	—	4	2	no	—
510	C₄×D₄₇	—	4	2	no	—
511	Dic₉₄	—	2	2	no	—
512	Dic₉₄	—	4	2	no	—
513	Dic₉₄	—	4	2	no	—
514	C₈×C₄₇	—	2	2	no	—
515	C₈×C₄₇	—	2	2	no	—
516	C₈×C₄₇	—	2	1	no	—
517	C₈×C₄₇	—	2	1	no	—
518	C₈×C₄₇	—	2	1	no	—
519	C₈×C₄₇	—	2	1	no	—
520	C₄₇⋊C₈	—	2	1	no	—
521	C₄₇⋊C₈	—	2	1	no	—
522	C₄₇⋊C₈	—	2	2	no	—
523	C₄₇⋊C₈	—	2	2	no	—
524	C₄₇⋊C₈	—	2	1	no	—
525	C₄₇⋊C₈	—	2	1	no	—
526	#60270	—	47	1	no	maximal, Sylow
527	C₂²×C₄₇	—	2	1	no	—
528	C₂²×C₄₇	—	2	1	no	—
529	C₂²×C₄₇	—	2	2	no	—
530	C₂²×C₄₇	—	2	2	no	—
531	C₂²×C₄₇	—	2	2	no	—
532	C₂²×C₄₇	#520	1	2	yes	—
533	C₂²×C₄₇	C₂⁴×C₄	1	1	yes	characteristic
534	C₂×D₄₇	—	2	1	no	—
535	C₂×D₄₇	—	2	1	no	—
536	C₂×D₄₇	—	2	2	no	—
537	C₂×D₄₇	—	2	2	no	—
538	C₂×D₄₇	—	2	2	no	—
539	C₂×D₄₇	—	2	1	no	—
540	C₂×D₄₇	—	2	1	no	—
541	C₂×D₄₇	—	2	1	no	—
542	C₂×D₄₇	—	2	1	no	—
543	C₂×D₄₇	—	8	2	no	—
544	C₄×C₄₇	—	2	2	no	—
545	C₄×C₄₇	—	2	2	no	—
546	C₄×C₄₇	—	2	2	no	—
547	C₄×C₄₇	—	2	1	no	—
548	C₄×C₄₇	—	2	1	no	—
549	C₄×C₄₇	—	2	1	no	—
550	C₄×C₄₇	—	2	1	no	—
551	C₄×C₄₇	#520	1	2	yes	—
552	C₄×C₄₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
553	C₄×C₄₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
554	Dic₄₇	—	2	2	no	—
555	Dic₄₇	—	2	1	no	—
556	Dic₄₇	—	2	1	no	—
557	Dic₄₇	—	2	1	no	—
558	Dic₄₇	—	2	1	no	—
559	Dic₄₇	—	2	2	no	—
560	Dic₄₇	—	2	2	no	—
561	Dic₄₇	—	2	1	no	—
562	Dic₄₇	—	2	1	no	—
563	#3455	—	47	1	no	—
564	#2995	—	47	2	no	—
565	#2995	—	47	2	no	—
566	#2994	—	47	2	no	—
567	#2994	—	47	2	no	—
568	#2993	—	47	2	no	—
569	#2993	—	47	2	no	—
570	#2992	—	47	2	no	—
571	#2992	—	47	2	no	—
572	#2961	—	47	1	no	—
573	#2960	—	47	1	no	—
574	#2933	—	47	1	no	—
575	#2933	—	47	1	no	—
576	#2933	—	47	1	no	—
577	#2933	—	47	1	no	—
578	#2932	—	47	1	no	—
579	#2931	—	47	1	no	—
580	#2925	—	47	1	no	—
581	#2925	D₄₇	1	1	yes	characteristic, complemented
582	C₂×#433	—	47	1	no	—
583	#2906	—	47	1	no	—
584	#2906	—	47	1	no	—
585	#2905	—	47	1	no	—
586	C₂×C₄₇	—	2	2	no	—
587	C₂×C₄₇	—	4	2	no	—
588	C₂×C₄₇	C₂×#520	1	1	yes	characteristic
589	C₂×C₄₇	#3573	1	1	yes	characteristic
590	C₂×C₄₇	#3573	1	1	yes	characteristic
591	D₄₇	—	4	2	no	—
592	D₄₇	—	4	1	no	—
593	D₄₇	—	4	1	no	—
594	C₂×#131	—	47	1	no	—
595	C₂×#131	—	47	1	no	—
596	C₂×#131	—	47	1	no	—
597	C₂×#131	—	47	1	no	—
598	C₂²×M₁₆	—	47	1	no	—
599	C₂²×M₁₆	—	47	1	no	—
600	#542	—	47	1	no	—
601	#542	—	47	1	no	—
602	#542	—	47	1	no	—
603	#542	—	47	1	no	—
604	#541	—	47	1	no	—
605	#541	—	47	1	no	—
606	#540	—	47	1	no	—
607	#540	—	47	1	no	—
608	#539	—	47	2	no	—
609	#539	—	47	2	no	—
610	#538	—	47	2	no	—
611	#538	—	47	2	no	—
612	#533	—	47	1	no	—
613	#532	—	47	1	no	—
614	#529	—	47	2	no	—
615	#529	—	47	2	no	—
616	#529	—	47	2	no	—
617	#529	—	47	2	no	—
618	#525	—	47	1	no	—
619	#525	—	47	1	no	—
620	C₄×#41	—	47	1	no	—
621	C₄×#41	C₂×D₄₇	1	1	yes	characteristic
622	C₂×#117	—	47	1	no	—
623	#446	—	47	2	no	—
624	#446	—	47	2	no	—
625	#446	—	47	2	no	—
626	#446	—	47	2	no	—
627	#446	—	47	2	no	—
628	#446	—	47	2	no	—
629	C₈×Q₈	—	47	2	no	—
630	C₈×Q₈	—	47	2	no	—
631	#436	—	47	2	no	—
632	#436	—	47	2	no	—
633	#436	—	47	2	no	—
634	#436	—	47	2	no	—
635	#436	—	47	2	no	—
636	#436	—	47	2	no	—
637	#435	—	47	2	no	—
638	#435	—	47	2	no	—
639	#435	—	47	2	no	—
640	#435	—	47	2	no	—
641	#435	—	47	2	no	—
642	#435	—	47	2	no	—
643	#435	—	47	2	no	—
644	#435	—	47	2	no	—
645	#435	—	47	2	no	—
646	#435	—	47	2	no	—
647	#435	—	47	2	no	—
648	#435	—	47	2	no	—
649	C₈×D₄	—	47	2	no	—
650	C₈×D₄	—	47	2	no	—
651	C₈×D₄	—	47	2	no	—
652	C₈×D₄	—	47	2	no	—
653	C₈×D₄	—	47	2	no	—
654	C₈×D₄	—	47	2	no	—
655	#433	—	47	1	no	—
656	#433	—	47	1	no	—
657	#433	—	47	1	no	—
658	#433	—	47	1	no	—
659	#433	—	47	1	no	—
660	#433	—	47	1	no	—
661	#433	—	47	1	no	—
662	#433	—	47	1	no	—
663	#433	—	47	2	no	—
664	#433	—	47	2	no	—
665	#433	C₂×D₄₇	1	2	yes	complemented
666	#433	C₂×D₄₇	1	2	yes	complemented
667	#432	—	47	2	no	—
668	#432	C₂×D₄₇	1	2	yes	complemented
669	#431	—	47	2	no	—
670	#431	C₂×D₄₇	1	2	yes	complemented
671	#424	—	47	1	no	—
672	#424	—	47	1	no	—
673	#424	—	47	1	no	—
674	#424	—	47	1	no	—
675	#424	—	47	2	no	—
676	#424	—	47	2	no	—
677	#424	—	47	2	no	—
678	#424	—	47	2	no	—
679	#424	—	47	2	no	—
680	#424	—	47	2	no	—
681	#424	—	47	2	no	—
682	#424	—	47	2	no	—
683	#423	—	47	1	no	—
684	#423	—	47	1	no	—
685	#423	—	47	1	no	—
686	#423	—	47	2	no	—
687	#423	—	47	2	no	—
688	#423	C₂×D₄₇	1	1	yes	characteristic
689	C₂×C₄⋊C₈	—	47	1	no	—
690	C₂×C₄⋊C₈	—	47	2	no	—
691	C₂×C₄⋊C₈	—	47	2	no	—
692	C₂×C₄⋊C₈	C₂×D₄₇	1	1	yes	characteristic
693	#408	—	47	1	no	—
694	#408	—	47	1	no	—
695	#408	C₂×D₄₇	1	1	yes	characteristic
696	#408	C₂×D₄₇	1	1	yes	characteristic
697	C₂×C₂²⋊C₈	—	47	1	no	—
698	C₂×C₂²⋊C₈	—	47	1	no	—
699	#405	—	47	1	no	—
700	#405	—	47	1	no	—
701	#405	C₂×D₄₇	1	1	yes	characteristic
702	#405	C₂×D₄₇	1	1	yes	characteristic
703	C₂×#97	—	47	1	no	—
704	C₂×C₄×C₈	—	47	1	no	—
705	C₄₇	#60270	1	1	yes	characteristic, complemented, Sylow
706	C₂×#41	—	47	1	no	—
707	C₂×#41	C₂²×D₄₇	1	1	yes	characteristic
708	C₂³×C₄	—	47	1	no	—
709	#131	—	188	2	no	—
710	#131	—	188	2	no	—
711	#131	—	188	2	no	—
712	#131	—	188	2	no	—
713	C₂×M₁₆	—	47	1	no	—
714	C₂×M₁₆	—	47	1	no	—
715	C₂×M₁₆	—	47	2	no	—
716	C₂×M₁₆	—	47	2	no	—
717	C₂×M₁₆	—	47	2	no	—
718	C₂×M₁₆	—	47	2	no	—
719	C₂×M₁₆	—	47	2	no	—
720	C₂×M₁₆	—	47	2	no	—
721	C₂×M₁₆	—	188	2	no	—
722	C₂×M₁₆	—	188	2	no	—
723	C₂×M₁₆	C₂²×D₄₇	1	1	yes	characteristic
724	C₂×M₁₆	C₂²×D₄₇	1	1	yes	characteristic
725	C₂²×C₈	—	47	1	no	—
726	C₂²×C₈	—	47	1	no	—
727	C₂²×C₈	—	47	2	no	—
728	C₂²×C₈	—	47	2	no	—
729	C₂²×C₈	—	47	2	no	—
730	C₂²×C₈	—	47	2	no	—
731	C₂²×C₈	—	47	2	no	—
732	C₂²×C₈	—	47	2	no	—
733	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
734	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
735	C₄⋊Q₈	—	47	1	no	—
736	C₄⋊Q₈	—	47	1	no	—
737	C₄⋊Q₈	—	47	1	no	—
738	#127	—	47	1	no	—
739	#126	—	47	2	no	—
740	#126	—	47	2	no	—
741	#126	—	47	2	no	—
742	#126	—	47	2	no	—
743	#126	—	47	2	no	—
744	#126	—	47	2	no	—
745	#126	—	47	2	no	—
746	#126	—	47	2	no	—
747	#125	—	47	2	no	—
748	#125	—	47	2	no	—
749	#125	—	47	1	no	—
750	#125	—	47	1	no	—
751	#125	—	47	2	no	—
752	#125	—	47	2	no	—
753	#124	—	47	1	no	—
754	#124	—	47	1	no	—
755	#124	—	47	2	no	—
756	#124	—	47	2	no	—
757	#124	—	47	2	no	—
758	#124	—	47	2	no	—
759	#123	—	47	2	no	—
760	#123	—	47	2	no	—
761	#123	—	47	2	no	—
762	#123	—	47	2	no	—
763	#123	—	47	2	no	—
764	#123	—	47	2	no	—
765	#123	—	47	2	no	—
766	#123	—	47	2	no	—
767	#123	—	47	2	no	—
768	#123	—	47	2	no	—
769	C₂²⋊Q₈	—	47	1	no	—
770	C₂²⋊Q₈	—	47	1	no	—
771	C₂²⋊Q₈	—	47	2	no	—
772	C₂²⋊Q₈	—	47	2	no	—
773	C₂²⋊Q₈	—	47	1	no	—
774	C₂²⋊Q₈	—	47	1	no	—
775	C₂²⋊Q₈	—	47	2	no	—
776	C₂²⋊Q₈	—	47	2	no	—
777	C₂²⋊Q₈	—	47	2	no	—
778	C₂²⋊Q₈	—	47	2	no	—
779	#121	—	47	1	no	—
780	#121	—	47	1	no	—
781	#121	—	47	2	no	—
782	#121	—	47	2	no	—
783	#121	—	47	2	no	—
784	#121	—	47	2	no	—
785	#121	—	47	1	no	—
786	#121	—	47	1	no	—
787	#121	—	47	2	no	—
788	#121	—	47	2	no	—
789	#120	—	47	2	no	—
790	#120	—	47	2	no	—
791	C₄×Q₈	—	47	1	no	—
792	C₄×Q₈	—	47	1	no	—
793	C₄×Q₈	—	47	2	no	—
794	C₄×Q₈	—	47	2	no	—
795	C₄×Q₈	C₄×D₄₇	1	1	yes	characteristic
796	C₄×Q₈	C₄×D₄₇	1	1	yes	characteristic
797	C₄×D₄	—	47	2	no	—
798	C₄×D₄	—	47	2	no	—
799	C₄×D₄	—	47	2	no	—
800	C₄×D₄	—	47	2	no	—
801	C₄×D₄	—	47	2	no	—
802	C₄×D₄	—	47	2	no	—
803	C₄×D₄	—	47	1	no	—
804	C₄×D₄	—	47	1	no	—
805	C₄×D₄	—	47	2	no	—
806	C₄×D₄	—	47	2	no	—
807	C₄×D₄	C₄×D₄₇	1	2	yes	—
808	C₄×D₄	C₄×D₄₇	1	2	yes	—
809	C₄×D₄	C₄×D₄₇	1	1	yes	characteristic
810	C₄×D₄	C₄×D₄₇	1	1	yes	characteristic
811	#117	—	47	1	no	—
812	#117	—	47	1	no	—
813	#117	—	47	1	no	—
814	#117	—	47	1	no	—
815	#117	—	47	1	no	—
816	#117	—	47	1	no	—
817	#117	—	47	1	no	—
818	#117	—	47	1	no	—
819	#117	—	47	1	no	—
820	#117	—	47	2	no	—
821	#117	C₂²×D₄₇	1	1	yes	characteristic
822	#117	C₂²×D₄₇	1	2	yes	—
823	C₂×C₄⋊C₄	—	47	1	no	—
824	C₂×C₄⋊C₄	—	47	1	no	—
825	C₂×C₂²⋊C₄	—	47	1	no	—
826	C₂×C₂²⋊C₄	—	47	1	no	—
827	C₂×C₄²	—	47	1	no	—
828	C₂×C₄²	—	47	2	no	—
829	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
830	C₂×C₄²	C₂²×D₄₇	1	2	yes	—
831	C₄⋊C₈	—	47	2	no	—
832	C₄⋊C₈	—	47	2	no	—
833	C₄⋊C₈	—	47	2	no	—
834	C₄⋊C₈	—	47	2	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	1	no	—
840	C₄⋊C₈	—	47	1	no	—
841	C₄⋊C₈	—	47	1	no	—
842	C₄⋊C₈	—	47	1	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	2	no	—
849	C₄⋊C₈	C₂²×D₄₇	1	2	yes	—
850	C₄⋊C₈	C₂²×D₄₇	1	1	yes	characteristic
851	C₄⋊C₈	C₂²×D₄₇	1	1	yes	characteristic
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	C₂²⋊C₈	—	47	1	no	—
856	C₂²⋊C₈	—	47	1	no	—
857	C₂²⋊C₈	—	47	1	no	—
858	C₂²⋊C₈	—	47	1	no	—
859	C₂²⋊C₈	—	47	1	no	—
860	C₂²⋊C₈	—	47	1	no	—
861	C₂²⋊C₈	—	47	1	no	—
862	C₂²⋊C₈	—	47	1	no	—
863	C₂²⋊C₈	—	47	2	no	—
864	C₂²⋊C₈	—	47	2	no	—
865	C₂²⋊C₈	—	47	2	no	—
866	C₂²⋊C₈	—	47	2	no	—
867	C₂²⋊C₈	C₂²×D₄₇	1	2	yes	—
868	C₂²⋊C₈	C₂²×D₄₇	1	2	yes	—
869	C₂²⋊C₈	C₂²×D₄₇	1	2	yes	—
870	C₂²⋊C₈	C₂²×D₄₇	1	2	yes	—
871	#97	—	47	1	no	—
872	#97	—	47	1	no	—
873	#97	—	47	1	no	—
874	#97	—	47	1	no	—
875	#97	—	47	2	no	—
876	#97	—	47	2	no	—
877	#97	C₂²×D₄₇	1	2	yes	—
878	#97	C₂²×D₄₇	1	2	yes	—
879	C₄×C₈	—	47	1	no	—
880	C₄×C₈	—	47	1	no	—
881	C₄×C₈	—	47	1	no	—
882	C₄×C₈	—	47	1	no	—
883	C₄×C₈	—	47	2	no	—
884	C₄×C₈	—	47	2	no	—
885	C₄×C₈	C₂²×D₄₇	1	2	yes	—
886	C₄×C₈	C₂²×D₄₇	1	2	yes	—
887	C₂⁴	—	47	1	no	—
888	#41	—	2	2	no	—
889	#41	—	2	2	no	—
890	#41	—	94	2	no	—
891	#41	—	94	2	no	—
892	C₂×Q₈	—	47	1	no	—
893	C₂×Q₈	—	47	2	no	—
894	C₂×Q₈	—	47	2	no	—
895	C₂×Q₈	C₂×C₄×D₄₇	1	1	yes	characteristic
896	C₂×D₄	—	47	2	no	—
897	C₂×D₄	—	47	2	no	—
898	C₂×D₄	—	47	2	no	—
899	C₂×D₄	—	47	2	no	—
900	C₂×D₄	—	47	2	no	—
901	C₂×D₄	—	47	1	no	—
902	C₂×D₄	—	47	2	no	—
903	C₂×D₄	—	47	2	no	—
904	C₂×D₄	C₂×C₄×D₄₇	1	2	yes	—
905	C₂×D₄	C₂×C₄×D₄₇	1	1	yes	characteristic
906	C₂²×C₄	—	47	1	no	—
907	C₂²×C₄	—	47	1	no	—
908	C₂²×C₄	—	47	1	no	—
909	C₂²×C₄	—	47	1	no	—
910	C₂²×C₄	—	47	1	no	—
911	C₂²×C₄	—	47	2	no	—
912	C₂²×C₄	—	47	1	no	—
913	C₂²×C₄	—	47	1	no	—
914	C₂²×C₄	—	47	2	no	—
915	C₂²×C₄	—	47	2	no	—
916	C₂²×C₄	—	94	2	no	—
917	C₂²×C₄	—	94	2	no	—
918	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
919	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
920	C₂²×C₄	C₂×C₄×D₄₇	1	2	yes	—
921	C₂²×C₄	C₂×C₄×D₄₇	1	2	yes	—
922	C₂²×C₄	C₂³×D₄₇	1	2	yes	—
923	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
924	M₁₆	—	2	2	no	—
925	M₁₆	—	2	2	no	—
926	M₁₆	—	94	2	no	—
927	M₁₆	—	94	2	no	—
928	M₁₆	—	188	2	no	—
929	M₁₆	—	188	2	no	—
930	M₁₆	—	188	2	no	—
931	M₁₆	—	188	2	no	—
932	M₁₆	—	188	2	no	—
933	M₁₆	—	188	2	no	—
934	C₂×C₈	—	2	2	no	—
935	C₂×C₈	—	2	2	no	—
936	C₂×C₈	—	47	1	no	—
937	C₂×C₈	—	47	1	no	—
938	C₂×C₈	—	47	2	no	—
939	C₂×C₈	—	47	2	no	—
940	C₂×C₈	—	47	1	no	—
941	C₂×C₈	—	47	1	no	—
942	C₂×C₈	—	94	2	no	—
943	C₂×C₈	—	94	2	no	—
944	C₂×C₈	—	188	2	no	—
945	C₂×C₈	—	188	2	no	—
946	C₂×C₈	—	188	2	no	—
947	C₂×C₈	—	188	2	no	—
948	C₂×C₈	—	188	2	no	—
949	C₂×C₈	—	188	2	no	—
950	C₂×C₈	C₂³×D₄₇	1	1	yes	characteristic
951	C₂×C₈	C₂³×D₄₇	1	1	yes	characteristic
952	C₂×C₈	C₂³×D₄₇	1	1	yes	characteristic
953	C₂×C₈	C₂³×D₄₇	1	1	yes	characteristic
954	C₂×C₈	C₂³×D₄₇	1	2	yes	—
955	C₂×C₈	C₂³×D₄₇	1	2	yes	—
956	C₄⋊C₄	—	47	1	no	—
957	C₄⋊C₄	—	47	1	no	—
958	C₄⋊C₄	—	47	1	no	—
959	C₄⋊C₄	—	47	1	no	—
960	C₄⋊C₄	—	47	1	no	—
961	C₄⋊C₄	—	47	1	no	—
962	C₄⋊C₄	—	47	1	no	—
963	C₄⋊C₄	—	47	1	no	—
964	C₄⋊C₄	—	47	2	no	—
965	C₄⋊C₄	—	47	2	no	—
966	C₄⋊C₄	—	47	2	no	—
967	C₄⋊C₄	—	47	2	no	—
968	C₄⋊C₄	—	47	2	no	—
969	C₄⋊C₄	—	47	2	no	—
970	C₄⋊C₄	—	47	2	no	—
971	C₄⋊C₄	—	47	2	no	—
972	C₄⋊C₄	—	47	2	no	—
973	C₄⋊C₄	—	47	2	no	—
974	C₄⋊C₄	—	47	1	no	—
975	C₄⋊C₄	—	47	1	no	—
976	C₄⋊C₄	—	47	2	no	—
977	C₄⋊C₄	—	47	2	no	—
978	C₄⋊C₄	—	47	2	no	—
979	C₄⋊C₄	—	47	2	no	—
980	C₄⋊C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
981	C₄⋊C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
982	C₄⋊C₄	C₂×C₄×D₄₇	1	2	yes	—
983	C₄⋊C₄	C₂×C₄×D₄₇	1	2	yes	—
984	C₂²⋊C₄	—	47	2	no	—
985	C₂²⋊C₄	—	47	2	no	—
986	C₂²⋊C₄	—	47	2	no	—
987	C₂²⋊C₄	—	47	2	no	—
988	C₂²⋊C₄	—	47	2	no	—
989	C₂²⋊C₄	—	47	1	no	—
990	C₂²⋊C₄	—	47	1	no	—
991	C₂²⋊C₄	—	47	1	no	—
992	C₂²⋊C₄	—	47	1	no	—
993	C₂²⋊C₄	—	47	1	no	—
994	C₂²⋊C₄	—	47	1	no	—
995	C₂²⋊C₄	—	47	1	no	—
996	C₂²⋊C₄	—	47	1	no	—
997	C₂²⋊C₄	—	47	2	no	—
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	C₂×C₄×D₄₇	1	2	yes	—
1008	C₂²⋊C₄	C₂×C₄×D₄₇	1	2	yes	—
1009	C₂²⋊C₄	C₂×C₄×D₄₇	1	2	yes	—
1010	C₄²	—	47	1	no	—
1011	C₄²	—	47	1	no	—
1012	C₄²	—	47	2	no	—
1013	C₄²	—	47	2	no	—
1014	C₄²	—	47	1	no	—
1015	C₄²	—	47	1	no	—
1016	C₄²	—	47	2	no	—
1017	C₄²	C₂×C₄×D₄₇	1	1	yes	characteristic
1018	C₄²	C₂×C₄×D₄₇	1	1	yes	characteristic
1019	C₄²	C₂×C₄×D₄₇	1	2	yes	—
1020	C₄²	C₂×C₄×D₄₇	1	2	yes	—
1021	C₄²	C₂³×D₄₇	1	2	yes	—
1022	C₄²	C₂³×D₄₇	1	1	yes	characteristic
1023	C₄²	C₂³×D₄₇	1	1	yes	characteristic
1024	C₂³	—	47	1	no	—
1025	C₂³	—	47	1	no	—
1026	C₂³	—	47	2	no	—
1027	C₂³	—	94	2	no	—
1028	C₂³	—	188	1	no	—
1029	C₂³	—	188	1	no	—
1030	C₂³	C₂²×C₄×D₄₇	1	2	yes	—
1031	C₂³	C₂²×C₄×D₄₇	1	1	yes	characteristic
1032	Q₈	—	2	2	no	—
1033	Q₈	—	94	2	no	—
1034	Q₈	—	188	2	no	—
1035	Q₈	—	188	2	no	—
1036	D₄	—	2	4	no	—
1037	D₄	—	2	2	no	—
1038	D₄	—	94	4	no	—
1039	D₄	—	94	2	no	—
1040	D₄	—	188	2	no	—
1041	D₄	—	188	2	no	—
1042	D₄	—	188	2	no	—
1043	D₄	—	188	2	no	—
1044	D₄	—	188	2	no	—
1045	D₄	—	188	2	no	—
1046	C₂×C₄	—	2	2	no	—
1047	C₂×C₄	—	2	2	no	—
1048	C₂×C₄	—	4	1	no	—
1049	C₂×C₄	—	4	2	no	—
1050	C₂×C₄	—	4	1	no	—
1051	C₂×C₄	—	4	2	no	—
1052	C₂×C₄	—	47	1	no	—
1053	C₂×C₄	—	47	1	no	—
1054	C₂×C₄	—	47	2	no	—
1055	C₂×C₄	—	47	2	no	—
1056	C₂×C₄	—	47	2	no	—
1057	C₂×C₄	—	47	1	no	—
1058	C₂×C₄	—	47	1	no	—
1059	C₂×C₄	—	47	1	no	—
1060	C₂×C₄	—	47	1	no	—
1061	C₂×C₄	—	94	2	no	—
1062	C₂×C₄	—	94	2	no	—
1063	C₂×C₄	—	94	2	no	—
1064	C₂×C₄	—	94	1	no	—
1065	C₂×C₄	—	94	1	no	—
1066	C₂×C₄	—	94	2	no	—
1067	C₂×C₄	—	94	1	no	—
1068	C₂×C₄	—	94	1	no	—
1069	C₂×C₄	—	94	2	no	—
1070	C₂×C₄	—	188	2	no	—
1071	C₂×C₄	—	188	2	no	—
1072	C₂×C₄	—	188	1	no	—
1073	C₂×C₄	—	188	1	no	—
1074	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
1075	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
1076	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
1077	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
1078	C₂×C₄	C₂²×C₄×D₄₇	1	2	yes	—
1079	C₂×C₄	C₂²×C₄×D₄₇	1	2	yes	—
1080	C₂×C₄	C₂²×C₄×D₄₇	1	2	yes	—
1081	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
1082	C₂×C₄	#13094070	1	2	yes	—
1083	C₂×C₄	#13094071	1	2	yes	—
1084	C₂×C₄	C₂⁴×D₄₇	1	1	yes	characteristic
1085	C₈	—	2	2	no	—
1086	C₈	—	2	2	no	—
1087	C₈	—	2	1	no	—
1088	C₈	—	2	1	no	—
1089	C₈	—	2	1	no	—
1090	C₈	—	2	1	no	—
1091	C₈	—	94	1	no	—
1092	C₈	—	94	1	no	—
1093	C₈	—	94	1	no	—
1094	C₈	—	94	1	no	—
1095	C₈	—	94	2	no	—
1096	C₈	—	94	2	no	—
1097	C₂²	—	2	1	no	—
1098	C₂²	—	2	1	no	—
1099	C₂²	—	2	2	no	—
1100	C₂²	—	2	2	no	—
1101	C₂²	—	2	2	no	—
1102	C₂²	—	94	2	no	—
1103	C₂²	—	94	1	no	—
1104	C₂²	—	94	1	no	—
1105	C₂²	—	94	2	no	—
1106	C₂²	—	94	1	no	—
1107	C₂²	—	94	1	no	—
1108	C₂²	—	94	1	no	—
1109	C₂²	—	94	1	no	—
1110	C₂²	—	94	2	no	—
1111	C₂²	—	376	2	no	—
1112	C₂²	#15689603	1	2	yes	—
1113	C₂²	C₂³×C₄×D₄₇	1	1	yes	characteristic
1114	C₄	—	2	1	no	—
1115	C₄	—	2	1	no	—
1116	C₄	—	2	2	no	—
1117	C₄	—	2	1	no	—
1118	C₄	—	2	1	no	—
1119	C₄	—	2	2	no	—
1120	C₄	—	2	2	no	—
1121	C₄	—	94	1	no	—
1122	C₄	—	94	2	no	—
1123	C₄	—	94	1	no	—
1124	C₄	—	94	1	no	—
1125	C₄	—	94	2	no	—
1126	C₄	—	94	1	no	—
1127	C₄	—	94	1	no	—
1128	C₄	—	94	1	no	—
1129	C₄	—	94	2	no	—
1130	C₄	#15689603	1	2	yes	—
1131	C₄	C₂×#13094070	1	1	yes	characteristic
1132	C₄	C₂×#13094071	1	1	yes	characteristic
1133	C₂	—	2	2	no	—
1134	C₂	—	4	2	no	—
1135	C₂	—	188	1	no	—
1136	C₂	—	188	1	no	—
1137	C₂	—	188	2	no	—
1138	C₂	C₂×#15689603	1	1	yes	characteristic
1139	C₂	#20258099	1	1	yes	characteristic
1140	C₂	#20258101	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂⁴×D₄₇
commutator, socle	C₂²×C₄₇	C₂⁴×C₄
Fitting	C₄₇×#2925	C₂
prime radical	#20256773	C₂
cosocle	C₂×C₄×C₄₇	C₂⁵
hypercenter	#2925	D₄₇
hypocenter	C₄₇	#60270
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ #2925

Complements

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

N	H ≅ G/N	type
2. #20252560	C₂	semidirect
3. #20252553	C₂	semidirect
4. #20252550	C₂	semidirect
5. #20252542	C₂	semidirect
6. #20252539	C₂	semidirect
7. #20252531	C₂	semidirect
8. #20252529	C₂	semidirect
9. #20252522	C₂	semidirect
10. #20252326	C₂	semidirect
11. #20252320	C₂	semidirect
12. #20252118	C₂	semidirect
13. #20252118	C₂	semidirect
14. #20252116	C₂	semidirect
15. #20252116	C₂	semidirect
16. #20252103	C₂	semidirect
17. #20252096	C₂	semidirect
18. #20252053	C₂	semidirect
19. C₂×#15689183	C₂	semidirect
20. #20251957	C₂	semidirect
21. #20251956	C₂	semidirect
22. #20251950	C₂	semidirect
23. C₄₇×#2925	C₂	semidirect
52. #15689253	C₂²	semidirect
53. #15689253	C₂²	semidirect
54. #15689251	C₂²	semidirect
55. #15689251	C₂²	semidirect
56. #15689251	C₂²	semidirect
57. #15689251	C₂²	semidirect
58. C₈×Dic₉₄	C₂²	semidirect
59. C₈×Dic₉₄	C₂²	semidirect
64. #15689198	C₂²	semidirect
65. #15689198	C₂²	semidirect
68. #15689197	C₂²	semidirect
69. #15689197	C₂²	semidirect
76. #15689191	C₂²	semidirect
77. #15689191	C₂²	semidirect
82. (C₂²⋊D₄₇)⋊C₈	C₂²	semidirect
83. (C₂²⋊D₄₇)⋊C₈	C₂²	semidirect
92. #15689183	C₂²	semidirect
93. #15689183	C₂²	semidirect
94. #15689179	C₂²	semidirect
95. #15689175	C₂²	semidirect
100. #15689150	C₂²	semidirect
101. #15689150	C₂²	semidirect
106. #15689148	C₂²	semidirect
107. #15689148	C₂²	semidirect
109. #15689147	C₂²	semidirect
112. #15689145	C₂²	semidirect
114. C₂×C₄⋊(C₄₇⋊C₈)	C₂²	semidirect
115. C₄⋊C₈×D₄₇	C₂²	semidirect
125. C₄₇×#433	C₂²	semidirect
126. C₄₇×#433	C₂²	semidirect
127. C₄₇×#432	C₂²	semidirect
128. C₄₇×#431	C₂²	semidirect
581. #2925	D₄₇	semidirect
665. #433	C₂×D₄₇	semidirect
666. #433	C₂×D₄₇	semidirect
668. #432	C₂×D₄₇	semidirect
670. #431	C₂×D₄₇	semidirect
705. C₄₇	#60270	semidirect

Maximal subgroups

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

subgroup	index
#20256773	2
#20252560	2
#20252553	2
#20252550	2
#20252542	2
#20252539	2
#20252531	2
#20252529	2
#20252522	2
#20252326	2
#20252320	2
#20252118	2
#20252116	2
#20252103	2
#20252096	2
#20252053	2
C₂×#15689183	2
#20251957	2
#20251956	2
#20251950	2
C₄₇×#2925	2
#60270	47