Subgroups — #27094373

Order 12032.

2046 conjugacy classes of subgroups.

The subgroup lattice has 1208 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20257250	C₂	1	1	yes	maximal, characteristic, complemented
2	#20255656	C₂	1	2	yes	maximal, complemented
3	#20255604	C₂	1	2	yes	maximal, complemented
4	#20255499	C₂	1	2	yes	maximal, complemented
5	#20255469	C₂	1	2	yes	maximal, complemented
6	#20255454	C₂	1	2	yes	maximal, complemented
7	#20255424	C₂	1	2	yes	maximal, complemented
8	#20255275	C₂	1	2	yes	maximal, complemented
9	#20255223	C₂	1	2	yes	maximal, complemented
10	#20253774	C₂	1	1	yes	maximal, characteristic, complemented
11	#20253351	C₂	1	1	yes	maximal, characteristic, complemented
12	#20253340	C₂	1	1	yes	maximal, characteristic, complemented
13	#20253176	C₂	1	1	yes	maximal, characteristic, complemented
14	#20253040	C₂	1	1	yes	maximal, characteristic, complemented
15	#20253024	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#15689342	C₂	1	1	yes	maximal, characteristic, complemented
17	#20252683	C₂	1	1	yes	maximal, characteristic, complemented
18	#20252665	C₂	1	1	yes	maximal, characteristic, complemented
19	C₄×#13094054	C₂	1	1	yes	maximal, characteristic, complemented
20	#20252132	C₂	1	1	yes	maximal, characteristic, complemented
21	#20251921	C₂	1	1	yes	maximal, characteristic, complemented
22	#20251914	C₂	1	1	yes	maximal, characteristic, complemented
23	C₄₇×#3500	C₂	1	1	yes	maximal, characteristic
24	C₂×#13094054	C₂²	1	1	yes	characteristic
25	C₂²×#10625337	C₂²	1	1	yes	characteristic, complemented
26	C₂²×#10625335	C₂²	1	1	yes	characteristic
27	C₂×#13094031	C₂²	1	1	yes	characteristic
28	C₂×#13094031	C₂²	1	1	yes	characteristic, complemented
29	#15689859	—	2	1	no	—
30	#15689848	—	2	1	no	—
31	#15689843	C₂²	1	2	yes	complemented
32	#15689842	—	2	1	no	—
33	#15689842	—	2	1	no	—
34	#15689830	C₂²	1	2	yes	complemented
35	#15689813	C₂²	1	2	yes	complemented
36	#15689813	C₂²	1	2	yes	complemented
37	#15689718	—	2	2	no	—
38	#15689694	C₂²	1	1	yes	characteristic
39	#15689694	C₂²	1	1	yes	characteristic, complemented
40	#15689680	C₂²	1	1	yes	characteristic, complemented
41	#15689654	—	2	2	no	—
42	#15689606	C₂²	1	1	yes	characteristic
43	#15689606	C₂²	1	1	yes	characteristic, complemented
44	C₂×C₄×Dic₉₄	C₂²	1	1	yes	characteristic, complemented
45	#15689482	C₂²	1	2	yes	complemented
46	#15689482	C₂²	1	2	yes	complemented
47	#15689477	C₂²	1	2	yes	complemented
48	#15689477	C₂²	1	2	yes	complemented
49	#15689461	C₂²	1	2	yes	complemented
50	#15689461	C₂²	1	2	yes	complemented
51	#15689456	C₂²	1	2	yes	complemented
52	#15689451	C₂²	1	2	yes	complemented
53	#15689444	C₂²	1	2	yes	complemented
54	#15689444	C₂²	1	2	yes	complemented
55	#15689439	C₂²	1	2	yes	complemented
56	#15689434	C₂²	1	2	yes	complemented
57	#15689430	C₂²	1	1	yes	characteristic, complemented
58	#15689430	C₂²	1	1	yes	characteristic, complemented
59	#15689423	C₂²	1	1	yes	characteristic, complemented
60	#15689423	C₂²	1	1	yes	characteristic, complemented
61	#15689418	C₂²	1	1	yes	characteristic, complemented
62	#15689413	C₂²	1	1	yes	characteristic, complemented
63	#15689408	C₂²	1	1	yes	characteristic, complemented
64	#15689403	C₂²	1	1	yes	characteristic, complemented
65	#15689379	C₂²	1	2	yes	complemented
66	#15689379	C₂²	1	2	yes	complemented
67	#15689367	C₂²	1	2	yes	complemented
68	#15689367	C₂²	1	2	yes	complemented
69	#15689362	C₂²	1	2	yes	complemented
70	#15689362	C₂²	1	2	yes	complemented
71	#15689350	C₂²	1	2	yes	complemented
72	#15689350	C₂²	1	2	yes	complemented
73	#15689342	C₂²	1	2	yes	complemented
74	#15689342	C₂²	1	2	yes	complemented
75	#15689342	C₂²	1	2	yes	complemented
76	#15689342	C₂²	1	2	yes	complemented
77	#15689285	C₂²	1	2	yes	—
78	#15689285	C₂²	1	2	yes	—
79	#15689285	C₂²	1	2	yes	complemented
80	#15689285	C₂²	1	2	yes	complemented
81	#15689279	C₂²	1	2	yes	complemented
82	#15689279	C₂²	1	2	yes	complemented
83	#15689274	C₂²	1	2	yes	—
84	#15689274	C₂²	1	2	yes	—
85	#15689228	C₂²	1	2	yes	complemented
86	#15689223	C₂²	1	2	yes	complemented
87	C₄×#10625337	C₂²	1	2	yes	complemented
88	C₄×#10625335	C₂²	1	2	yes	complemented
89	#15689201	C₂²	1	2	yes	complemented
90	#15689195	C₂²	1	2	yes	complemented
91	#15689195	C₂²	1	2	yes	complemented
92	D₄×C₄₇⋊C₈	C₂²	1	2	yes	complemented
93	#15689166	C₂²	1	1	yes	characteristic, complemented
94	#15689159	C₂²	1	1	yes	characteristic, complemented
95	#15689159	C₂²	1	1	yes	characteristic, complemented
96	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic, complemented
97	#15689132	C₂²	1	1	yes	characteristic, complemented
98	#15689132	C₂²	1	1	yes	characteristic, complemented
99	#15689132	C₂²	1	2	yes	complemented
100	#15689131	C₂²	1	1	yes	characteristic, complemented
101	#15689128	C₂²	1	1	yes	characteristic
102	#15689128	C₂²	1	2	yes	—
103	#15689128	C₂²	1	1	yes	characteristic
104	#15689124	C₂²	1	2	yes	—
105	#15689124	C₂²	1	1	yes	characteristic
106	#15689124	C₂²	1	2	yes	complemented
107	#15689119	C₂²	1	1	yes	characteristic
108	#15689119	C₂²	1	2	yes	—
109	#15689119	C₂²	1	1	yes	characteristic
110	#15689119	C₂²	1	2	yes	complemented
111	C₂×#13093948	C₂²	1	2	yes	complemented
112	C₂×#13093948	C₂²	1	1	yes	characteristic, complemented
113	C₂×#13093945	C₂²	1	1	yes	characteristic
114	C₂×#13093945	C₂²	1	2	yes	—
115	#15689090	C₂²	1	1	yes	characteristic
116	#15689090	C₂²	1	1	yes	characteristic, complemented
117	C₄×#10625329	C₂²	1	1	yes	characteristic, complemented
118	C₂×2₋¹⁺⁴×C₄₇	C₂²	1	1	yes	characteristic
119	C₂×H(5,𝔽₂)×C₄₇	C₂²	1	1	yes	characteristic
120	C₄₇×#548	C₂²	1	2	yes	—
121	C₄₇×#548	C₂²	1	2	yes	—
122	C₄₇×#546	—	2	2	no	—
123	C₄₇×#546	—	2	2	no	—
124	C₄₇×#546	C₂²	1	2	yes	—
125	C₄₇×#546	C₂²	1	2	yes	—
126	C₄₇×#536	—	2	1	no	—
127	C₄₇×#536	C₂²	1	1	yes	characteristic
128	C₄₇×#535	—	2	1	no	—
129	C₄₇×#535	C₂²	1	1	yes	characteristic
130	C₄₇×#532	—	2	1	no	—
131	C₄₇×#532	C₂²	1	1	yes	characteristic
132	C₂×#124×C₄₇	—	2	1	no	—
133	C₂×#124×C₄₇	C₂²	1	1	yes	characteristic
134	C₄×#41×C₄₇	C₂²	1	1	yes	characteristic
135	C₂²×Dic₉₄	C₂³	1	1	yes	characteristic
136	#13094054	—	2	4	no	—
137	C₂×#10625337	—	4	2	no	—
138	C₂×#10625337	C₂³	1	2	yes	—
139	C₂×#10625337	C₂³	1	2	yes	—
140	C₂×#10625337	C₂³	1	2	yes	—
141	C₂×#10625335	—	4	2	no	—
142	C₂×#10625335	C₂³	1	2	yes	—
143	C₂×#10625335	C₂³	1	2	yes	—
144	C₂×#10625335	C₂³	1	2	yes	—
145	#13094031	—	4	2	no	—
146	#13094031	—	4	2	no	—
147	C₂×#10625329	C₂³	1	1	yes	characteristic
148	C₂×#10625329	C₂³	1	1	yes	characteristic
149	C₂×#10625329	C₂³	1	2	yes	—
150	C₂×#10625329	C₂³	1	2	yes	—
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	#13094024	C₂³	1	1	yes	characteristic
156	#13094024	C₂³	1	1	yes	characteristic
157	#13094022	—	2	1	no	—
158	#13094022	—	2	1	no	—
159	#13094017	—	2	2	no	—
160	#13094017	—	2	2	no	—
161	#13094017	—	2	2	no	—
162	#13094017	—	2	2	no	—
163	#13094016	C₂³	1	1	yes	characteristic
164	#13094016	C₂³	1	1	yes	characteristic
165	#13094015	—	2	2	no	—
166	#13094014	—	2	2	no	—
167	#13094014	—	2	2	no	—
168	#13094011	—	2	1	no	—
169	#13094011	—	2	1	no	—
170	#13094011	—	2	2	no	—
171	#13094005	—	2	2	no	—
172	#13094005	—	2	2	no	—
173	#13094005	—	2	2	no	—
174	#13094005	—	2	2	no	—
175	#13094003	—	2	1	no	—
176	#13094003	—	2	1	no	—
177	#13094003	C₂³	1	2	yes	—
178	#13094003	C₂³	1	2	yes	—
179	#13094003	C₂³	1	2	yes	—
180	#13094003	C₂³	1	2	yes	—
181	#13094001	—	2	2	no	—
182	#13094001	—	2	2	no	—
183	Q₈×Dic₄₇	—	2	1	no	—
184	Q₈×Dic₄₇	—	2	1	no	—
185	C₄×Dic₉₄	—	2	1	no	—
186	C₄×Dic₉₄	—	2	1	no	—
187	C₄×Dic₉₄	—	2	1	no	—
188	C₄×Dic₉₄	—	2	1	no	—
189	C₄×Dic₉₄	C₂³	1	2	yes	—
190	C₄×Dic₉₄	C₂³	1	2	yes	—
191	#13093989	—	2	2	no	—
192	D₄×Dic₄₇	—	2	2	no	—
193	D₄×Dic₄₇	—	2	1	no	—
194	D₄×Dic₄₇	—	2	1	no	—
195	D₄×Dic₄₇	—	2	2	no	—
196	D₄×Dic₄₇	—	2	2	no	—
197	#13093983	C₂³	1	2	yes	—
198	#13093983	C₂³	1	2	yes	—
199	#13093983	C₂³	1	1	yes	characteristic
200	#13093983	C₂³	1	1	yes	characteristic
201	#13093980	—	2	2	no	—
202	#13093980	—	2	2	no	—
203	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
204	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
205	C₂×C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic
206	C₂×Dic₄₇⋊C₄	—	2	1	no	—
207	C₂×C₄×Dic₄₇	—	2	1	no	—
208	#13093957	C₂³	1	2	yes	—
209	#13093957	C₂³	1	1	yes	characteristic
210	#13093957	C₂³	1	1	yes	characteristic
211	#13093957	C₂³	1	1	yes	characteristic
212	#13093957	C₂³	1	1	yes	characteristic
213	#13093955	C₂³	1	2	yes	—
214	#13093955	C₂³	1	1	yes	characteristic
215	#13093955	C₂³	1	1	yes	characteristic
216	#13093955	C₂³	1	1	yes	characteristic
217	#13093955	C₂³	1	1	yes	characteristic
218	C₄⋊(C₄₇⋊C₈)	C₂³	1	1	yes	characteristic
219	C₄⋊(C₄₇⋊C₈)	C₂³	1	1	yes	characteristic
220	C₄⋊(C₄₇⋊C₈)	C₂³	1	1	yes	characteristic
221	C₄⋊(C₄₇⋊C₈)	C₂³	1	1	yes	characteristic
222	#13093948	C₂³	1	2	yes	—
223	#13093948	C₂³	1	2	yes	—
224	#13093948	C₂³	1	2	yes	—
225	#13093948	C₂³	1	2	yes	—
226	#13093948	C₂³	1	2	yes	—
227	#13093948	C₂³	1	1	yes	characteristic
228	#13093948	C₂³	1	1	yes	characteristic
229	#13093948	C₂³	1	1	yes	characteristic
230	#13093948	C₂³	1	1	yes	characteristic
231	#13093948	C₂³	1	2	yes	—
232	#13093948	C₂³	1	2	yes	—
233	#13093947	C₂³	1	2	yes	—
234	#13093947	C₂³	1	2	yes	—
235	#13093945	C₂³	1	2	yes	—
236	#13093945	C₂³	1	2	yes	—
237	#13093945	C₂³	1	2	yes	—
238	#13093945	C₂³	1	2	yes	—
239	#13093945	C₂³	1	2	yes	—
240	#13093945	C₂³	1	1	yes	characteristic
241	#13093945	C₂³	1	1	yes	characteristic
242	#13093945	C₂³	1	1	yes	characteristic
243	#13093945	C₂³	1	1	yes	characteristic
244	#13093945	C₂³	1	2	yes	—
245	#13093945	C₂³	1	2	yes	—
246	C₂²⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
247	C₂²⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
248	C₂²⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
249	C₂²⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
250	#13093935	C₂³	1	2	yes	—
251	C₄×C₄₇⋊C₈	C₂³	1	2	yes	—
252	2₋¹⁺⁴×C₄₇	—	2	4	no	—
253	2₋¹⁺⁴×C₄₇	—	4	2	no	—
254	H(5,𝔽₂)×C₄₇	—	2	4	no	—
255	H(5,𝔽₂)×C₄₇	—	4	2	no	—
256	C₂×#41×C₄₇	—	2	1	no	—
257	C₂×#41×C₄₇	—	2	1	no	—
258	C₂×#41×C₄₇	—	2	2	no	—
259	C₂×#41×C₄₇	C₂³	1	2	yes	—
260	C₂×#41×C₄₇	C₂³	1	2	yes	—
261	C₂×#41×C₄₇	C₂³	1	1	yes	characteristic
262	C₂×#41×C₄₇	C₂³	1	1	yes	characteristic
263	C₂×#41×C₄₇	C₂³	1	1	yes	characteristic
264	C₂²×Q₈×C₄₇	—	2	1	no	—
265	C₂²×Q₈×C₄₇	C₂³	1	1	yes	characteristic
266	C₂²×Q₈×C₄₇	C₂³	1	2	yes	—
267	C₂²×D₄×C₄₇	—	2	1	no	—
268	C₂²×D₄×C₄₇	—	2	2	no	—
269	C₂²×D₄×C₄₇	C₂³	1	1	yes	characteristic
270	C₂²×D₄×C₄₇	C₂³	1	2	yes	—
271	C₄⋊Q₈×C₄₇	—	2	1	no	—
272	C₄⋊Q₈×C₄₇	D₄	1	1	yes	characteristic
273	#127×C₄₇	—	2	1	no	—
274	#127×C₄₇	D₄	1	1	yes	characteristic
275	#124×C₄₇	—	2	1	no	—
276	#124×C₄₇	—	2	1	no	—
277	#124×C₄₇	—	2	2	no	—
278	#124×C₄₇	—	2	2	no	—
279	#124×C₄₇	—	2	1	no	—
280	#124×C₄₇	—	2	1	no	—
281	#124×C₄₇	D₄	1	1	yes	characteristic
282	#124×C₄₇	D₄	1	1	yes	characteristic
283	#124×C₄₇	C₂³	1	2	yes	—
284	#124×C₄₇	C₂³	1	2	yes	—
285	#123×C₄₇	—	2	2	no	—
286	#123×C₄₇	—	2	2	no	—
287	#123×C₄₇	—	2	2	no	—
288	C₂²⋊Q₈×C₄₇	—	2	2	no	—
289	C₂²⋊Q₈×C₄₇	—	2	2	no	—
290	C₂²⋊Q₈×C₄₇	C₂³	1	2	yes	—
291	C₂²⋊Q₈×C₄₇	C₂³	1	2	yes	—
292	#121×C₄₇	—	2	2	no	—
293	#121×C₄₇	—	2	2	no	—
294	#121×C₄₇	—	2	2	no	—
295	#121×C₄₇	—	2	2	no	—
296	#121×C₄₇	D₄	1	2	yes	—
297	#121×C₄₇	D₄	1	2	yes	—
298	#121×C₄₇	C₂³	1	2	yes	—
299	#121×C₄₇	C₂³	1	2	yes	—
300	#120×C₄₇	—	2	2	no	—
301	#120×C₄₇	—	2	2	no	—
302	#120×C₄₇	—	2	2	no	—
303	C₄×Q₈×C₄₇	C₂³	1	1	yes	characteristic
304	C₄×Q₈×C₄₇	C₂³	1	1	yes	characteristic
305	C₄×D₄×C₄₇	—	2	1	no	—
306	C₄×D₄×C₄₇	—	2	1	no	—
307	C₄×D₄×C₄₇	—	2	2	no	—
308	C₄×D₄×C₄₇	—	2	2	no	—
309	C₄×D₄×C₄₇	C₂³	1	1	yes	characteristic
310	C₄×D₄×C₄₇	C₂³	1	1	yes	characteristic
311	C₄×D₄×C₄₇	C₂³	1	2	yes	—
312	C₄×D₄×C₄₇	C₂³	1	2	yes	—
313	#117×C₄₇	—	2	1	no	—
314	#117×C₄₇	C₂³	1	1	yes	characteristic
315	C₂×C₂²⋊C₄×C₄₇	—	2	1	no	—
316	C₂×C₂²⋊C₄×C₄₇	—	2	1	no	—
317	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
318	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
319	C₂×C₄²×C₄₇	—	2	1	no	—
320	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
321	C₂⁴×C₄₇	—	2	2	no	—
322	C₂⁴×C₄₇	—	2	1	no	—
323	#41×C₄₇	—	2	2	no	—
324	#41×C₄₇	—	2	2	no	—
325	#41×C₄₇	—	2	2	no	—
326	#41×C₄₇	—	2	2	no	—
327	#41×C₄₇	—	2	2	no	—
328	#41×C₄₇	—	2	4	no	—
329	#41×C₄₇	—	2	4	no	—
330	#41×C₄₇	—	4	2	no	—
331	#41×C₄₇	—	4	2	no	—
332	#41×C₄₇	—	4	4	no	—
333	#41×C₄₇	—	4	4	no	—
334	#41×C₄₇	—	4	8	no	—
335	#41×C₄₇	#41	1	4	yes	—
336	C₂×Q₈×C₄₇	—	2	2	no	—
337	C₂×Q₈×C₄₇	—	2	1	no	—
338	C₂×Q₈×C₄₇	—	2	4	no	—
339	C₂×Q₈×C₄₇	—	2	2	no	—
340	C₂×Q₈×C₄₇	—	2	2	no	—
341	C₂×Q₈×C₄₇	—	4	2	no	—
342	C₂×Q₈×C₄₇	—	4	4	no	—
343	C₂×Q₈×C₄₇	C₂×D₄	1	1	yes	characteristic
344	C₂×Q₈×C₄₇	C₂×D₄	1	1	yes	characteristic
345	C₂×Q₈×C₄₇	C₂⁴	1	2	yes	—
346	C₂×Q₈×C₄₇	C₂⁴	1	1	yes	characteristic
347	C₂×D₄×C₄₇	—	2	1	no	—
348	C₂×D₄×C₄₇	—	2	4	no	—
349	C₂×D₄×C₄₇	—	2	2	no	—
350	C₂×D₄×C₄₇	—	2	2	no	—
351	C₂×D₄×C₄₇	—	2	2	no	—
352	C₂×D₄×C₄₇	—	2	2	no	—
353	C₂×D₄×C₄₇	—	2	2	no	—
354	C₂×D₄×C₄₇	—	2	1	no	—
355	C₂×D₄×C₄₇	—	2	2	no	—
356	C₂×D₄×C₄₇	—	2	2	no	—
357	C₂×D₄×C₄₇	—	4	2	no	—
358	C₂×D₄×C₄₇	—	4	4	no	—
359	C₂×D₄×C₄₇	—	4	8	no	—
360	C₂×D₄×C₄₇	C₂×D₄	1	2	yes	—
361	C₂×D₄×C₄₇	C₂×D₄	1	2	yes	—
362	C₂×D₄×C₄₇	C₂×D₄	1	1	yes	characteristic
363	C₂×D₄×C₄₇	C₂×D₄	1	1	yes	characteristic
364	C₂×D₄×C₄₇	C₂×D₄	1	2	yes	—
365	C₂×D₄×C₄₇	C₂×D₄	1	2	yes	—
366	C₂×D₄×C₄₇	C₂⁴	1	2	yes	—
367	C₂×D₄×C₄₇	C₂⁴	1	1	yes	characteristic
368	C₂²×C₄×C₄₇	—	2	1	no	—
369	C₂²×C₄×C₄₇	—	2	1	no	—
370	C₂²×C₄×C₄₇	—	2	2	no	—
371	C₂²×C₄×C₄₇	—	2	2	no	—
372	C₂²×C₄×C₄₇	—	2	2	no	—
373	C₂²×C₄×C₄₇	—	2	1	no	—
374	C₂²×C₄×C₄₇	—	2	1	no	—
375	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
376	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
377	C₂²×C₄×C₄₇	C₂⁴	1	2	yes	—
378	C₂²×C₄×C₄₇	C₂⁴	1	2	yes	—
379	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
380	C₂²×Dic₄₇	—	2	1	no	—
381	C₂²×Dic₄₇	—	2	1	no	—
382	C₂²×Dic₄₇	—	2	2	no	—
383	C₂²×Dic₄₇	—	2	2	no	—
384	C₂×Dic₉₄	—	2	2	no	—
385	C₂×Dic₉₄	—	2	2	no	—
386	C₂×Dic₉₄	—	2	1	no	—
387	C₂×Dic₉₄	—	2	1	no	—
388	C₂×Dic₉₄	—	2	1	no	—
389	C₂×Dic₉₄	C₂⁴	1	2	yes	—
390	C₄⋊C₄×C₄₇	—	2	1	no	—
391	C₄⋊C₄×C₄₇	—	2	1	no	—
392	C₄⋊C₄×C₄₇	—	2	2	no	—
393	C₄⋊C₄×C₄₇	—	2	2	no	—
394	C₄⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
395	C₄⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
396	C₄⋊C₄×C₄₇	C₂⁴	1	1	yes	characteristic
397	C₄⋊C₄×C₄₇	C₂⁴	1	1	yes	characteristic
398	C₂²⋊C₄×C₄₇	—	2	2	no	—
399	C₂²⋊C₄×C₄₇	—	2	2	no	—
400	C₂²⋊C₄×C₄₇	—	2	1	no	—
401	C₂²⋊C₄×C₄₇	—	2	2	no	—
402	C₂²⋊C₄×C₄₇	—	2	2	no	—
403	C₂²⋊C₄×C₄₇	—	2	2	no	—
404	C₂²⋊C₄×C₄₇	—	2	2	no	—
405	C₂²⋊C₄×C₄₇	—	2	2	no	—
406	C₂²⋊C₄×C₄₇	—	2	2	no	—
407	C₂²⋊C₄×C₄₇	—	2	1	no	—
408	C₂²⋊C₄×C₄₇	—	2	1	no	—
409	C₂²⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
410	C₂²⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
411	C₂²⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
412	C₂²⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
413	C₄²×C₄₇	—	2	1	no	—
414	C₄²×C₄₇	—	2	1	no	—
415	C₄²×C₄₇	—	2	1	no	—
416	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
417	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
418	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
419	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
420	C₂²⋊Dic₄₇	—	2	2	no	—
421	C₂²⋊Dic₄₇	—	2	2	no	—
422	C₂²⋊Dic₄₇	—	2	1	no	—
423	C₂²⋊Dic₄₇	—	2	1	no	—
424	C₂²⋊Dic₄₇	—	2	2	no	—
425	C₂²⋊Dic₄₇	—	2	2	no	—
426	C₂²⋊Dic₄₇	—	2	2	no	—
427	C₂²⋊Dic₄₇	—	2	2	no	—
428	#10625337	—	2	4	no	—
429	#10625337	—	4	2	no	—
430	#10625337	—	4	2	no	—
431	#10625335	—	2	4	no	—
432	#10625335	—	4	2	no	—
433	#10625335	—	4	2	no	—
434	C₄⋊Dic₄₇	—	2	1	no	—
435	C₄⋊Dic₄₇	—	2	2	no	—
436	C₄⋊Dic₄₇	—	2	2	no	—
437	C₄⋊Dic₄₇	—	2	1	no	—
438	C₄⋊Dic₄₇	—	2	1	no	—
439	C₄⋊Dic₄₇	C₂⁴	1	2	yes	—
440	C₄⋊Dic₄₇	C₂⁴	1	1	yes	characteristic
441	C₄⋊Dic₄₇	C₂⁴	1	1	yes	characteristic
442	C₄⋊Dic₄₇	C₂⁴	1	1	yes	characteristic
443	C₄⋊Dic₄₇	C₂⁴	1	1	yes	characteristic
444	Dic₄₇⋊C₄	—	2	2	no	—
445	Dic₄₇⋊C₄	—	2	2	no	—
446	Dic₄₇⋊C₄	—	2	1	no	—
447	Dic₄₇⋊C₄	—	2	1	no	—
448	Dic₄₇⋊C₄	—	2	2	no	—
449	Dic₄₇⋊C₄	—	2	2	no	—
450	Dic₄₇⋊C₄	—	2	2	no	—
451	Dic₄₇⋊C₄	—	2	2	no	—
452	Dic₄₇⋊C₄	—	2	1	no	—
453	Dic₄₇⋊C₄	—	2	1	no	—
454	C₄×Dic₄₇	—	2	2	no	—
455	C₄×Dic₄₇	—	2	2	no	—
456	C₄×Dic₄₇	—	2	2	no	—
457	C₄×Dic₄₇	—	2	2	no	—
458	C₄×Dic₄₇	—	2	1	no	—
459	C₄×Dic₄₇	—	2	1	no	—
460	#10625329	—	2	2	no	—
461	#10625329	—	2	2	no	—
462	#10625329	—	4	2	no	—
463	#10625329	—	4	2	no	—
464	C₂×C₄₇⋊C₈	—	2	2	no	—
465	C₂×C₄₇⋊C₈	—	2	2	no	—
466	C₂×C₄₇⋊C₈	—	4	2	no	—
467	C₂×C₄₇⋊C₈	—	4	2	no	—
468	C₂×C₄₇⋊C₈	C₂⁴	1	2	yes	—
469	C₂×C₄₇⋊C₈	C₂⁴	1	2	yes	—
470	C₂×C₄₇⋊C₈	C₂⁴	1	1	yes	characteristic
471	C₂×C₄₇⋊C₈	C₂⁴	1	1	yes	characteristic
472	C₂×C₄₇⋊C₈	C₂⁴	1	1	yes	characteristic
473	C₂×C₄₇⋊C₈	C₂⁴	1	1	yes	characteristic
474	C₂³×C₄₇	—	2	1	no	—
475	C₂³×C₄₇	—	2	2	no	—
476	C₂³×C₄₇	—	4	4	no	—
477	C₂³×C₄₇	—	4	2	no	—
478	C₂³×C₄₇	—	8	1	no	—
479	C₂³×C₄₇	—	8	1	no	—
480	C₂³×C₄₇	—	8	2	no	—
481	C₂³×C₄₇	—	8	2	no	—
482	C₂³×C₄₇	C₂²×D₄	1	2	yes	—
483	C₂³×C₄₇	C₂²×D₄	1	2	yes	—
484	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
485	Q₈×C₄₇	—	2	2	no	—
486	Q₈×C₄₇	—	2	2	no	—
487	Q₈×C₄₇	—	2	1	no	—
488	Q₈×C₄₇	—	2	2	no	—
489	Q₈×C₄₇	—	2	2	no	—
490	Q₈×C₄₇	—	4	4	no	—
491	Q₈×C₄₇	—	4	2	no	—
492	Q₈×C₄₇	C₂×#41	1	2	yes	—
493	D₄×C₄₇	—	2	4	no	—
494	D₄×C₄₇	—	2	4	no	—
495	D₄×C₄₇	—	2	4	no	—
496	D₄×C₄₇	—	2	2	no	—
497	D₄×C₄₇	—	2	2	no	—
498	D₄×C₄₇	—	2	2	no	—
499	D₄×C₄₇	—	2	1	no	—
500	D₄×C₄₇	—	2	2	no	—
501	D₄×C₄₇	—	4	2	no	—
502	D₄×C₄₇	—	4	2	no	—
503	D₄×C₄₇	—	4	4	no	—
504	D₄×C₄₇	—	4	4	no	—
505	D₄×C₄₇	—	4	4	no	—
506	D₄×C₄₇	—	4	2	no	—
507	D₄×C₄₇	—	8	2	no	—
508	D₄×C₄₇	—	8	2	no	—
509	D₄×C₄₇	C₂×#41	1	2	yes	—
510	C₂×C₄×C₄₇	—	2	1	no	—
511	C₂×C₄×C₄₇	—	2	4	no	—
512	C₂×C₄×C₄₇	—	2	2	no	—
513	C₂×C₄×C₄₇	—	2	2	no	—
514	C₂×C₄×C₄₇	—	2	2	no	—
515	C₂×C₄×C₄₇	—	2	2	no	—
516	C₂×C₄×C₄₇	—	2	1	no	—
517	C₂×C₄×C₄₇	—	2	1	no	—
518	C₂×C₄×C₄₇	—	2	2	no	—
519	C₂×C₄×C₄₇	—	4	1	no	—
520	C₂×C₄×C₄₇	—	4	1	no	—
521	C₂×C₄×C₄₇	—	4	4	no	—
522	C₂×C₄×C₄₇	—	4	4	no	—
523	C₂×C₄×C₄₇	—	4	4	no	—
524	C₂×C₄×C₄₇	—	4	2	no	—
525	C₂×C₄×C₄₇	—	8	1	no	—
526	C₂×C₄×C₄₇	—	8	1	no	—
527	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
528	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
529	C₂×C₄×C₄₇	C₂²×D₄	1	2	yes	—
530	C₂×C₄×C₄₇	C₂²×D₄	1	2	yes	—
531	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
532	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
533	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
534	C₂×C₄×C₄₇	C₂×#41	1	2	yes	—
535	C₂×C₄×C₄₇	H(5,𝔽₂)	1	2	yes	—
536	C₂×C₄×C₄₇	C₂⁵	1	1	yes	characteristic
537	C₂×Dic₄₇	—	2	2	no	—
538	C₂×Dic₄₇	—	2	1	no	—
539	C₂×Dic₄₇	—	2	1	no	—
540	C₂×Dic₄₇	—	2	2	no	—
541	C₂×Dic₄₇	—	2	1	no	—
542	C₂×Dic₄₇	—	2	1	no	—
543	C₂×Dic₄₇	—	4	2	no	—
544	C₂×Dic₄₇	—	8	2	no	—
545	C₂×Dic₄₇	—	8	2	no	—
546	C₂×Dic₄₇	—	8	1	no	—
547	Dic₉₄	—	2	2	no	—
548	Dic₉₄	—	2	2	no	—
549	Dic₉₄	—	4	2	no	—
550	Dic₉₄	—	4	2	no	—
551	Dic₉₄	—	8	1	no	—
552	C₄₇⋊C₈	—	2	2	no	—
553	C₄₇⋊C₈	—	2	1	no	—
554	C₄₇⋊C₈	—	2	1	no	—
555	C₄₇⋊C₈	—	2	1	no	—
556	C₄₇⋊C₈	—	2	1	no	—
557	C₄₇⋊C₈	—	2	2	no	—
558	#61207	—	47	1	no	maximal, Sylow
559	C₂²×C₄₇	—	2	1	no	—
560	C₂²×C₄₇	—	2	1	no	—
561	C₂²×C₄₇	—	2	2	no	—
562	C₂²×C₄₇	—	2	2	no	—
563	C₂²×C₄₇	—	2	2	no	—
564	C₂²×C₄₇	—	2	2	no	—
565	C₂²×C₄₇	—	2	2	no	—
566	C₂²×C₄₇	—	2	2	no	—
567	C₂²×C₄₇	—	2	2	no	—
568	C₂²×C₄₇	—	4	1	no	—
569	C₂²×C₄₇	—	4	1	no	—
570	C₂²×C₄₇	—	4	2	no	—
571	C₂²×C₄₇	—	4	2	no	—
572	C₂²×C₄₇	—	4	2	no	—
573	C₂²×C₄₇	—	16	2	no	—
574	C₂²×C₄₇	—	16	4	no	—
575	C₂²×C₄₇	#546	1	2	yes	—
576	C₂²×C₄₇	C₂³×D₄	1	1	yes	characteristic
577	C₄×C₄₇	—	2	1	no	—
578	C₄×C₄₇	—	2	1	no	—
579	C₄×C₄₇	—	2	1	no	—
580	C₄×C₄₇	—	2	1	no	—
581	C₄×C₄₇	—	2	2	no	—
582	C₄×C₄₇	—	2	2	no	—
583	C₄×C₄₇	—	2	2	no	—
584	C₄×C₄₇	—	4	1	no	—
585	C₄×C₄₇	—	4	1	no	—
586	C₄×C₄₇	—	4	2	no	—
587	C₄×C₄₇	#546	1	2	yes	—
588	C₄×C₄₇	C₂²×#41	1	1	yes	characteristic
589	C₄×C₄₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
590	Dic₄₇	—	4	1	no	—
591	Dic₄₇	—	4	1	no	—
592	Dic₄₇	—	4	2	no	—
593	Dic₄₇	—	4	1	no	—
594	Dic₄₇	—	4	1	no	—
595	Dic₄₇	—	4	2	no	—
596	#3507	—	47	1	no	—
597	#3500	D₄₇	1	1	yes	characteristic
598	#3327	—	47	2	no	—
599	#3323	—	47	2	no	—
600	#3316	—	47	2	no	—
601	#3314	—	47	2	no	—
602	#3313	—	47	2	no	—
603	#3311	—	47	2	no	—
604	#3300	—	47	2	no	—
605	#3296	—	47	2	no	—
606	#3140	—	47	1	no	—
607	#3097	—	47	1	no	—
608	#3096	—	47	1	no	—
609	#3076	—	47	1	no	—
610	#3059	—	47	1	no	—
611	#3057	—	47	1	no	—
612	C₂×#464	—	47	1	no	—
613	#3011	—	47	1	no	—
614	#3009	—	47	1	no	—
615	C₄×#137	—	47	1	no	—
616	#2935	—	47	1	no	—
617	#2898	—	47	1	no	—
618	#2897	—	47	1	no	—
619	C₂×C₄₇	—	2	2	no	—
620	C₂×C₄₇	—	4	2	no	—
621	C₂×C₄₇	—	4	2	no	—
622	C₂×C₄₇	—	4	2	no	—
623	C₂×C₄₇	—	8	2	no	—
624	C₂×C₄₇	C₂×#546	1	1	yes	characteristic
625	C₂×C₄₇	#3584	1	1	yes	characteristic
626	C₂×C₄₇	#3586	1	1	yes	characteristic
627	C₂×2₋¹⁺⁴	C₂×D₄₇	1	1	yes	characteristic
628	C₂×H(5,𝔽₂)	C₂×D₄₇	1	1	yes	characteristic
629	C₂×#137	—	47	1	no	—
630	C₂²×Q₁₆	—	47	1	no	—
631	C₂²×SD₁₆	—	47	1	no	—
632	C₂×#131	—	47	1	no	—
633	C₂×#131	—	47	1	no	—
634	#559	—	94	1	no	—
635	#557	—	94	1	no	—
636	#556	—	47	2	no	—
637	#556	—	94	1	no	—
638	#556	—	94	1	no	—
639	#554	—	47	2	no	—
640	#552	—	47	2	no	—
641	#552	—	47	2	no	—
642	#548	C₂×D₄₇	1	2	yes	—
643	#548	C₂×D₄₇	1	2	yes	—
644	#546	—	2	2	no	—
645	#546	—	2	2	no	—
646	#546	C₂×D₄₇	1	2	yes	—
647	#546	C₂×D₄₇	1	2	yes	—
648	#539	—	94	2	no	—
649	#536	—	2	1	no	—
650	#536	—	47	1	no	—
651	#536	—	47	1	no	—
652	#536	C₂×D₄₇	1	1	yes	characteristic
653	#535	—	2	1	no	—
654	#535	C₂×D₄₇	1	1	yes	characteristic
655	#533	—	47	1	no	—
656	#532	—	2	1	no	—
657	#532	C₂×D₄₇	1	1	yes	characteristic
658	#529	—	94	2	no	—
659	C₂×#124	—	2	1	no	—
660	C₂×#124	C₂×D₄₇	1	1	yes	characteristic
661	#520	—	47	1	no	—
662	#520	—	47	1	no	—
663	C₄×#41	C₂×D₄₇	1	1	yes	characteristic
664	C₂×C₄×Q₈	—	47	1	no	—
665	#489	—	47	2	no	—
666	#489	—	47	2	no	—
667	#488	—	47	2	no	—
668	#488	—	47	2	no	—
669	#485	—	47	2	no	—
670	#485	—	47	2	no	—
671	#484	—	47	2	no	—
672	#483	—	47	2	no	—
673	#482	—	47	2	no	—
674	#482	—	47	2	no	—
675	#481	—	47	2	no	—
676	#480	—	47	2	no	—
677	#479	—	47	1	no	—
678	#479	—	47	1	no	—
679	#478	—	47	1	no	—
680	#478	—	47	1	no	—
681	#477	—	47	1	no	—
682	#476	—	47	1	no	—
683	#475	—	47	1	no	—
684	#474	—	47	1	no	—
685	#470	—	47	2	no	—
686	#470	—	47	2	no	—
687	#468	—	47	2	no	—
688	#468	—	47	2	no	—
689	#467	—	47	2	no	—
690	#467	—	47	2	no	—
691	#465	—	47	2	no	—
692	#465	—	47	2	no	—
693	#464	—	47	2	no	—
694	#464	—	47	2	no	—
695	#464	—	47	2	no	—
696	#464	—	47	2	no	—
697	#452	—	47	2	no	—
698	#452	—	47	2	no	—
699	#452	—	47	2	no	—
700	#452	—	47	2	no	—
701	#451	—	47	2	no	—
702	#451	—	47	2	no	—
703	#450	—	47	2	no	—
704	#450	—	47	2	no	—
705	#441	—	47	2	no	—
706	#440	—	47	2	no	—
707	C₄×Q₁₆	—	47	2	no	—
708	C₄×SD₁₆	—	47	2	no	—
709	#436	—	47	2	no	—
710	#435	—	47	2	no	—
711	#435	—	47	2	no	—
712	C₈×D₄	—	47	2	no	—
713	#428	—	47	1	no	—
714	#427	—	47	1	no	—
715	#427	—	47	1	no	—
716	C₂×C₄⋊C₈	—	47	1	no	—
717	#419	—	47	1	no	—
718	#419	—	47	1	no	—
719	#419	—	47	2	no	—
720	#419	—	47	1	no	—
721	#418	—	47	1	no	—
722	#418	—	47	1	no	—
723	#418	—	47	2	no	—
724	#417	—	47	1	no	—
725	#417	—	47	2	no	—
726	#417	—	47	2	no	—
727	#416	—	47	1	no	—
728	#416	—	47	1	no	—
729	#416	—	47	2	no	—
730	#416	—	47	2	no	—
731	C₂×#103	—	47	1	no	—
732	C₂×#103	—	47	2	no	—
733	C₂×#102	—	47	1	no	—
734	C₂×#102	—	47	2	no	—
735	#408	—	47	1	no	—
736	#408	—	47	1	no	—
737	C₄×M₁₆	—	47	1	no	—
738	C₄₇	#61207	1	1	yes	characteristic, complemented, Sylow
739	2₋¹⁺⁴	—	2	4	no	—
740	2₋¹⁺⁴	—	4	2	no	—
741	H(5,𝔽₂)	—	2	4	no	—
742	H(5,𝔽₂)	—	4	2	no	—
743	C₂×#41	—	2	1	no	—
744	C₂×#41	—	2	1	no	—
745	C₂×#41	—	2	2	no	—
746	C₂×#41	C₂²×D₄₇	1	2	yes	—
747	C₂×#41	C₂²×D₄₇	1	2	yes	—
748	C₂×#41	C₂²×D₄₇	1	1	yes	characteristic
749	C₂×#41	C₂²×D₄₇	1	1	yes	characteristic
750	C₂×#41	C₂²×D₄₇	1	1	yes	characteristic
751	C₂²×Q₈	—	2	1	no	—
752	C₂²×Q₈	—	47	1	no	—
753	C₂²×Q₈	C₂²×D₄₇	1	1	yes	characteristic
754	C₂²×Q₈	C₂²×D₄₇	1	2	yes	—
755	C₂²×D₄	—	2	1	no	—
756	C₂²×D₄	—	2	2	no	—
757	C₂²×D₄	C₂²×D₄₇	1	1	yes	characteristic
758	C₂²×D₄	C₂²×D₄₇	1	2	yes	—
759	#137	—	94	4	no	—
760	C₂×Q₁₆	—	47	2	no	—
761	C₂×Q₁₆	—	47	2	no	—
762	C₂×Q₁₆	—	47	2	no	—
763	C₂×Q₁₆	—	188	2	no	—
764	C₂×SD₁₆	—	47	2	no	—
765	C₂×SD₁₆	—	47	2	no	—
766	C₂×SD₁₆	—	47	2	no	—
767	C₂×SD₁₆	—	188	2	no	—
768	#131	—	188	2	no	—
769	#131	—	188	2	no	—
770	C₂×M₁₆	—	47	1	no	—
771	C₂×M₁₆	—	47	1	no	—
772	C₂×M₁₆	—	47	2	no	—
773	C₂×M₁₆	—	47	2	no	—
774	C₂²×C₈	—	47	1	no	—
775	C₂²×C₈	—	47	1	no	—
776	C₂²×C₈	—	47	2	no	—
777	C₂²×C₈	—	47	2	no	—
778	C₄⋊Q₈	—	2	1	no	—
779	C₄⋊Q₈	—	47	1	no	—
780	C₄⋊Q₈	—	47	1	no	—
781	C₄⋊Q₈	—	94	1	no	—
782	C₄⋊Q₈	—	94	1	no	—
783	C₄⋊Q₈	C₂²⋊D₄₇	1	1	yes	characteristic
784	#127	—	2	1	no	—
785	#127	C₂²⋊D₄₇	1	1	yes	characteristic
786	#126	—	94	2	no	—
787	#126	—	94	2	no	—
788	#126	—	94	2	no	—
789	#126	—	94	2	no	—
790	#125	—	47	1	no	—
791	#125	—	47	1	no	—
792	#125	—	94	2	no	—
793	#125	—	94	2	no	—
794	#125	—	94	2	no	—
795	#124	—	2	1	no	—
796	#124	—	2	1	no	—
797	#124	—	2	2	no	—
798	#124	—	2	2	no	—
799	#124	—	2	1	no	—
800	#124	—	2	1	no	—
801	#124	—	94	2	no	—
802	#124	—	94	1	no	—
803	#124	—	94	1	no	—
804	#124	C₂²⋊D₄₇	1	1	yes	characteristic
805	#124	C₂²⋊D₄₇	1	1	yes	characteristic
806	#124	C₂²×D₄₇	1	2	yes	—
807	#124	C₂²×D₄₇	1	2	yes	—
808	#123	—	2	2	no	—
809	#123	—	2	2	no	—
810	#123	—	2	2	no	—
811	#123	—	94	2	no	—
812	#123	—	94	2	no	—
813	#123	—	94	2	no	—
814	#123	—	94	2	no	—
815	C₂²⋊Q₈	—	2	2	no	—
816	C₂²⋊Q₈	—	2	2	no	—
817	C₂²⋊Q₈	—	47	2	no	—
818	C₂²⋊Q₈	—	47	2	no	—
819	C₂²⋊Q₈	—	47	2	no	—
820	C₂²⋊Q₈	—	47	2	no	—
821	C₂²⋊Q₈	—	94	1	no	—
822	C₂²⋊Q₈	—	94	1	no	—
823	C₂²⋊Q₈	—	94	2	no	—
824	C₂²⋊Q₈	—	94	2	no	—
825	C₂²⋊Q₈	C₂²×D₄₇	1	2	yes	—
826	C₂²⋊Q₈	C₂²×D₄₇	1	2	yes	—
827	#121	—	2	2	no	—
828	#121	—	2	2	no	—
829	#121	—	2	2	no	—
830	#121	—	2	2	no	—
831	#121	C₂²⋊D₄₇	1	2	yes	—
832	#121	C₂²⋊D₄₇	1	2	yes	—
833	#121	C₂²×D₄₇	1	2	yes	—
834	#121	C₂²×D₄₇	1	2	yes	—
835	#120	—	2	2	no	—
836	#120	—	2	2	no	—
837	#120	—	2	2	no	—
838	C₄×Q₈	—	47	2	no	—
839	C₄×Q₈	—	47	2	no	—
840	C₄×Q₈	—	94	1	no	—
841	C₄×Q₈	—	94	1	no	—
842	C₄×Q₈	—	94	2	no	—
843	C₄×Q₈	—	94	1	no	—
844	C₄×Q₈	—	94	1	no	—
845	C₄×Q₈	—	94	1	no	—
846	C₄×Q₈	—	94	1	no	—
847	C₄×Q₈	C₂²×D₄₇	1	1	yes	characteristic
848	C₄×Q₈	C₂²×D₄₇	1	1	yes	characteristic
849	C₄×D₄	—	2	1	no	—
850	C₄×D₄	—	2	1	no	—
851	C₄×D₄	—	2	2	no	—
852	C₄×D₄	—	2	2	no	—
853	C₄×D₄	—	94	2	no	—
854	C₄×D₄	—	94	2	no	—
855	C₄×D₄	—	94	1	no	—
856	C₄×D₄	—	94	1	no	—
857	C₄×D₄	—	94	2	no	—
858	C₄×D₄	C₂²×D₄₇	1	1	yes	characteristic
859	C₄×D₄	C₂²×D₄₇	1	1	yes	characteristic
860	C₄×D₄	C₂²×D₄₇	1	2	yes	—
861	C₄×D₄	C₂²×D₄₇	1	2	yes	—
862	#117	—	2	1	no	—
863	#117	—	47	1	no	—
864	#117	—	47	1	no	—
865	#117	—	47	2	no	—
866	#117	—	47	2	no	—
867	#117	—	94	2	no	—
868	#117	—	94	2	no	—
869	#117	C₂²×D₄₇	1	1	yes	characteristic
870	C₂×C₄⋊C₄	—	47	1	no	—
871	C₂×C₄⋊C₄	—	47	2	no	—
872	C₂×C₄⋊C₄	—	47	2	no	—
873	C₂×C₄⋊C₄	—	94	1	no	—
874	C₂×C₂²⋊C₄	—	2	1	no	—
875	C₂×C₂²⋊C₄	—	2	1	no	—
876	C₂×C₂²⋊C₄	—	2	2	no	—
877	C₂×C₂²⋊C₄	—	2	2	no	—
878	C₂×C₄²	—	2	1	no	—
879	C₂×C₄²	—	94	1	no	—
880	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
881	#107	—	47	1	no	—
882	#107	—	47	1	no	—
883	#107	—	47	1	no	—
884	#107	—	47	1	no	—
885	#107	—	47	2	no	—
886	#106	—	47	1	no	—
887	#106	—	47	1	no	—
888	#106	—	47	1	no	—
889	#106	—	47	1	no	—
890	#106	—	47	2	no	—
891	C₄⋊C₈	—	47	1	no	—
892	C₄⋊C₈	—	47	1	no	—
893	C₄⋊C₈	—	47	1	no	—
894	C₄⋊C₈	—	47	1	no	—
895	#103	—	47	1	no	—
896	#103	—	47	2	no	—
897	#103	—	47	2	no	—
898	#103	—	47	2	no	—
899	#103	—	47	2	no	—
900	#103	—	47	1	no	—
901	#103	—	47	1	no	—
902	#103	—	47	1	no	—
903	#103	—	47	2	no	—
904	#103	—	47	2	no	—
905	#103	—	47	2	no	—
906	#103	—	47	2	no	—
907	#103	—	47	2	no	—
908	#102	—	47	1	no	—
909	#102	—	47	2	no	—
910	#102	—	47	2	no	—
911	#102	—	47	2	no	—
912	#102	—	47	2	no	—
913	#102	—	47	1	no	—
914	#102	—	47	1	no	—
915	#102	—	47	1	no	—
916	#102	—	47	2	no	—
917	#102	—	47	2	no	—
918	#102	—	47	2	no	—
919	C₂²⋊C₈	—	47	2	no	—
920	C₂²⋊C₈	—	47	2	no	—
921	C₂²⋊C₈	—	47	2	no	—
922	C₂²⋊C₈	—	47	2	no	—
923	#97	—	47	2	no	—
924	C₄×C₈	—	47	2	no	—
925	C₂⁴	—	2	2	no	—
926	C₂⁴	—	2	1	no	—
927	#41	—	2	2	no	—
928	#41	—	2	2	no	—
929	#41	—	2	2	no	—
930	#41	—	2	2	no	—
931	#41	—	2	2	no	—
932	#41	—	2	4	no	—
933	#41	—	2	4	no	—
934	#41	—	4	2	no	—
935	#41	—	4	2	no	—
936	#41	—	4	4	no	—
937	#41	—	4	4	no	—
938	#41	—	4	8	no	—
939	#41	#10625352	1	4	yes	—
940	C₂×Q₈	—	2	2	no	—
941	C₂×Q₈	—	2	1	no	—
942	C₂×Q₈	—	2	4	no	—
943	C₂×Q₈	—	2	2	no	—
944	C₂×Q₈	—	2	2	no	—
945	C₂×Q₈	—	4	2	no	—
946	C₂×Q₈	—	4	4	no	—
947	C₂×Q₈	—	47	2	no	—
948	C₂×Q₈	—	94	1	no	—
949	C₂×Q₈	—	94	1	no	—
950	C₂×Q₈	—	94	1	no	—
951	C₂×Q₈	—	94	2	no	—
952	C₂×Q₈	—	94	2	no	—
953	C₂×Q₈	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
954	C₂×Q₈	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
955	C₂×Q₈	C₂³×D₄₇	1	2	yes	—
956	C₂×Q₈	C₂³×D₄₇	1	1	yes	characteristic
957	C₂×D₄	—	2	1	no	—
958	C₂×D₄	—	2	4	no	—
959	C₂×D₄	—	2	2	no	—
960	C₂×D₄	—	2	2	no	—
961	C₂×D₄	—	2	2	no	—
962	C₂×D₄	—	2	2	no	—
963	C₂×D₄	—	2	2	no	—
964	C₂×D₄	—	2	1	no	—
965	C₂×D₄	—	2	2	no	—
966	C₂×D₄	—	2	2	no	—
967	C₂×D₄	—	4	2	no	—
968	C₂×D₄	—	4	4	no	—
969	C₂×D₄	—	4	8	no	—
970	C₂×D₄	C₂×C₂²⋊D₄₇	1	2	yes	—
971	C₂×D₄	C₂×C₂²⋊D₄₇	1	2	yes	—
972	C₂×D₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
973	C₂×D₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
974	C₂×D₄	C₂×C₂²⋊D₄₇	1	2	yes	—
975	C₂×D₄	C₂×C₂²⋊D₄₇	1	2	yes	—
976	C₂×D₄	C₂³×D₄₇	1	2	yes	—
977	C₂×D₄	C₂³×D₄₇	1	1	yes	characteristic
978	C₂²×C₄	—	2	1	no	—
979	C₂²×C₄	—	2	1	no	—
980	C₂²×C₄	—	2	2	no	—
981	C₂²×C₄	—	2	2	no	—
982	C₂²×C₄	—	2	2	no	—
983	C₂²×C₄	—	2	1	no	—
984	C₂²×C₄	—	2	1	no	—
985	C₂²×C₄	—	94	1	no	—
986	C₂²×C₄	—	94	2	no	—
987	C₂²×C₄	—	94	2	no	—
988	C₂²×C₄	—	94	1	no	—
989	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
990	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
991	C₂²×C₄	C₂³×D₄₇	1	2	yes	—
992	C₂²×C₄	C₂³×D₄₇	1	2	yes	—
993	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
994	Q₁₆	—	94	4	no	—
995	Q₁₆	—	188	2	no	—
996	Q₁₆	—	188	2	no	—
997	SD₁₆	—	94	4	no	—
998	SD₁₆	—	188	2	no	—
999	SD₁₆	—	188	2	no	—
1000	M₁₆	—	94	2	no	—
1001	M₁₆	—	94	2	no	—
1002	M₁₆	—	188	2	no	—
1003	M₁₆	—	188	2	no	—
1004	C₂×C₈	—	47	2	no	—
1005	C₂×C₈	—	47	2	no	—
1006	C₂×C₈	—	47	1	no	—
1007	C₂×C₈	—	47	1	no	—
1008	C₂×C₈	—	47	1	no	—
1009	C₂×C₈	—	47	1	no	—
1010	C₂×C₈	—	94	2	no	—
1011	C₂×C₈	—	94	2	no	—
1012	C₂×C₈	—	188	2	no	—
1013	C₂×C₈	—	188	2	no	—
1014	C₄⋊C₄	—	2	1	no	—
1015	C₄⋊C₄	—	2	1	no	—
1016	C₄⋊C₄	—	2	2	no	—
1017	C₄⋊C₄	—	2	2	no	—
1018	C₄⋊C₄	—	47	2	no	—
1019	C₄⋊C₄	—	47	1	no	—
1020	C₄⋊C₄	—	47	1	no	—
1021	C₄⋊C₄	—	47	1	no	—
1022	C₄⋊C₄	—	47	1	no	—
1023	C₄⋊C₄	—	94	2	no	—
1024	C₄⋊C₄	—	94	2	no	—
1025	C₄⋊C₄	—	94	1	no	—
1026	C₄⋊C₄	—	94	1	no	—
1027	C₄⋊C₄	—	94	2	no	—
1028	C₄⋊C₄	—	94	2	no	—
1029	C₄⋊C₄	—	94	2	no	—
1030	C₄⋊C₄	—	94	2	no	—
1031	C₄⋊C₄	—	94	1	no	—
1032	C₄⋊C₄	—	94	1	no	—
1033	C₄⋊C₄	—	94	1	no	—
1034	C₄⋊C₄	—	94	2	no	—
1035	C₄⋊C₄	—	94	2	no	—
1036	C₄⋊C₄	—	94	1	no	—
1037	C₄⋊C₄	—	94	1	no	—
1038	C₄⋊C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
1039	C₄⋊C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
1040	C₄⋊C₄	C₂³×D₄₇	1	1	yes	characteristic
1041	C₄⋊C₄	C₂³×D₄₇	1	1	yes	characteristic
1042	C₂²⋊C₄	—	2	2	no	—
1043	C₂²⋊C₄	—	2	2	no	—
1044	C₂²⋊C₄	—	2	1	no	—
1045	C₂²⋊C₄	—	2	2	no	—
1046	C₂²⋊C₄	—	2	2	no	—
1047	C₂²⋊C₄	—	2	2	no	—
1048	C₂²⋊C₄	—	2	2	no	—
1049	C₂²⋊C₄	—	2	2	no	—
1050	C₂²⋊C₄	—	2	2	no	—
1051	C₂²⋊C₄	—	2	1	no	—
1052	C₂²⋊C₄	—	2	1	no	—
1053	C₂²⋊C₄	—	94	1	no	—
1054	C₂²⋊C₄	—	94	1	no	—
1055	C₂²⋊C₄	—	94	2	no	—
1056	C₂²⋊C₄	—	94	2	no	—
1057	C₂²⋊C₄	—	94	2	no	—
1058	C₂²⋊C₄	—	94	2	no	—
1059	C₂²⋊C₄	—	94	2	no	—
1060	C₂²⋊C₄	—	94	2	no	—
1061	C₂²⋊C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
1062	C₂²⋊C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
1063	C₂²⋊C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
1064	C₂²⋊C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
1065	C₄²	—	2	1	no	—
1066	C₄²	—	2	1	no	—
1067	C₄²	—	2	1	no	—
1068	C₄²	—	94	2	no	—
1069	C₄²	—	94	2	no	—
1070	C₄²	—	94	2	no	—
1071	C₄²	—	94	2	no	—
1072	C₄²	—	94	1	no	—
1073	C₄²	—	94	1	no	—
1074	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
1075	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
1076	C₄²	C₂³×D₄₇	1	1	yes	characteristic
1077	C₄²	C₂³×D₄₇	1	1	yes	characteristic
1078	C₂³	—	2	1	no	—
1079	C₂³	—	2	2	no	—
1080	C₂³	—	4	4	no	—
1081	C₂³	—	4	2	no	—
1082	C₂³	—	8	1	no	—
1083	C₂³	—	8	1	no	—
1084	C₂³	—	8	2	no	—
1085	C₂³	—	8	2	no	—
1086	C₂³	C₂²×C₂²⋊D₄₇	1	2	yes	—
1087	C₂³	C₂²×C₂²⋊D₄₇	1	2	yes	—
1088	C₂³	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
1089	Q₈	—	2	2	no	—
1090	Q₈	—	2	2	no	—
1091	Q₈	—	2	1	no	—
1092	Q₈	—	2	2	no	—
1093	Q₈	—	2	2	no	—
1094	Q₈	—	4	4	no	—
1095	Q₈	—	4	2	no	—
1096	Q₈	—	94	2	no	—
1097	Q₈	—	94	2	no	—
1098	Q₈	—	376	1	no	—
1099	Q₈	—	188	2	no	—
1100	Q₈	—	188	2	no	—
1101	Q₈	C₂×#10625352	1	2	yes	—
1102	D₄	—	2	4	no	—
1103	D₄	—	2	4	no	—
1104	D₄	—	2	4	no	—
1105	D₄	—	2	2	no	—
1106	D₄	—	2	2	no	—
1107	D₄	—	2	2	no	—
1108	D₄	—	2	1	no	—
1109	D₄	—	2	2	no	—
1110	D₄	—	4	2	no	—
1111	D₄	—	4	2	no	—
1112	D₄	—	4	4	no	—
1113	D₄	—	4	4	no	—
1114	D₄	—	4	4	no	—
1115	D₄	—	4	2	no	—
1116	D₄	—	8	2	no	—
1117	D₄	—	8	2	no	—
1118	D₄	C₂×#10625352	1	2	yes	—
1119	C₂×C₄	—	2	1	no	—
1120	C₂×C₄	—	2	4	no	—
1121	C₂×C₄	—	2	2	no	—
1122	C₂×C₄	—	2	2	no	—
1123	C₂×C₄	—	2	2	no	—
1124	C₂×C₄	—	2	2	no	—
1125	C₂×C₄	—	2	1	no	—
1126	C₂×C₄	—	2	1	no	—
1127	C₂×C₄	—	2	2	no	—
1128	C₂×C₄	—	4	1	no	—
1129	C₂×C₄	—	4	1	no	—
1130	C₂×C₄	—	4	4	no	—
1131	C₂×C₄	—	4	4	no	—
1132	C₂×C₄	—	4	4	no	—
1133	C₂×C₄	—	4	2	no	—
1134	C₂×C₄	—	8	1	no	—
1135	C₂×C₄	—	8	1	no	—
1136	C₂×C₄	—	94	2	no	—
1137	C₂×C₄	—	94	1	no	—
1138	C₂×C₄	—	94	1	no	—
1139	C₂×C₄	—	94	2	no	—
1140	C₂×C₄	—	94	1	no	—
1141	C₂×C₄	—	94	1	no	—
1142	C₂×C₄	—	376	1	no	—
1143	C₂×C₄	—	376	2	no	—
1144	C₂×C₄	—	376	2	no	—
1145	C₂×C₄	—	188	2	no	—
1146	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
1147	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
1148	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
1149	C₂×C₄	C₂²×C₂²⋊D₄₇	1	2	yes	—
1150	C₂×C₄	C₂²×C₂²⋊D₄₇	1	2	yes	—
1151	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
1152	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
1153	C₂×C₄	C₂×#10625352	1	2	yes	—
1154	C₂×C₄	#13094069	1	2	yes	—
1155	C₂×C₄	C₂⁴×D₄₇	1	1	yes	characteristic
1156	C₈	—	94	2	no	—
1157	C₈	—	94	1	no	—
1158	C₈	—	94	1	no	—
1159	C₈	—	94	1	no	—
1160	C₈	—	94	1	no	—
1161	C₈	—	94	2	no	—
1162	C₂²	—	2	1	no	—
1163	C₂²	—	2	1	no	—
1164	C₂²	—	2	2	no	—
1165	C₂²	—	2	2	no	—
1166	C₂²	—	2	2	no	—
1167	C₂²	—	2	2	no	—
1168	C₂²	—	2	2	no	—
1169	C₂²	—	2	2	no	—
1170	C₂²	—	2	2	no	—
1171	C₂²	—	4	1	no	—
1172	C₂²	—	4	1	no	—
1173	C₂²	—	4	2	no	—
1174	C₂²	—	4	2	no	—
1175	C₂²	—	4	2	no	—
1176	C₂²	—	16	2	no	—
1177	C₂²	—	16	4	no	—
1178	C₂²	#15689767	1	2	yes	—
1179	C₂²	C₂³×C₂²⋊D₄₇	1	1	yes	characteristic
1180	C₄	—	2	2	no	—
1181	C₄	—	2	2	no	—
1182	C₄	—	2	2	no	—
1183	C₄	—	2	1	no	—
1184	C₄	—	2	1	no	—
1185	C₄	—	2	1	no	—
1186	C₄	—	2	1	no	—
1187	C₄	—	4	2	no	—
1188	C₄	—	4	1	no	—
1189	C₄	—	4	1	no	—
1190	C₄	—	188	2	no	—
1191	C₄	—	188	2	no	—
1192	C₄	—	188	1	no	—
1193	C₄	—	188	1	no	—
1194	C₄	—	188	1	no	—
1195	C₄	—	188	1	no	—
1196	C₄	#15689767	1	2	yes	—
1197	C₄	C₂²×#10625352	1	1	yes	characteristic
1198	C₄	C₂×#13094069	1	1	yes	characteristic
1199	C₂	—	2	2	no	—
1200	C₂	—	4	2	no	—
1201	C₂	—	4	2	no	—
1202	C₂	—	4	2	no	—
1203	C₂	—	8	2	no	—
1204	C₂	C₂×#15689767	1	1	yes	characteristic
1205	C₂	#20258159	1	1	yes	characteristic
1206	C₂	#20258174	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂³×C₂²⋊D₄₇
commutator, cosocle	C₂×C₄×C₄₇	C₂⁵
Frattini	C₂×C₄	C₂⁴×D₄₇
Fitting, prime radical	C₄₇×#3500	C₂
socle	C₂²×C₄₇	C₂³×D₄
hypercenter	#3500	D₄₇
hypocenter	C₄₇	#61207
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ #532 ◁ #3500

Complements

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

N	H ≅ G/N	type
1. #20257250	C₂	semidirect
2. #20255656	C₂	semidirect
3. #20255604	C₂	semidirect
4. #20255499	C₂	semidirect
5. #20255469	C₂	semidirect
6. #20255454	C₂	semidirect
7. #20255424	C₂	semidirect
8. #20255275	C₂	semidirect
9. #20255223	C₂	semidirect
10. #20253774	C₂	semidirect
11. #20253351	C₂	semidirect
12. #20253340	C₂	semidirect
13. #20253176	C₂	semidirect
14. #20253040	C₂	semidirect
15. #20253024	C₂	semidirect
16. C₂×#15689342	C₂	semidirect
17. #20252683	C₂	semidirect
18. #20252665	C₂	semidirect
19. C₄×#13094054	C₂	semidirect
20. #20252132	C₂	semidirect
21. #20251921	C₂	semidirect
22. #20251914	C₂	semidirect
25. C₂²×#10625337	C₂²	semidirect
28. C₂×#13094031	C₂²	semidirect
31. #15689843	C₂²	semidirect
34. #15689830	C₂²	semidirect
35. #15689813	C₂²	semidirect
36. #15689813	C₂²	semidirect
39. #15689694	C₂²	semidirect
40. #15689680	C₂²	semidirect
43. #15689606	C₂²	semidirect
44. C₂×C₄×Dic₉₄	C₂²	semidirect
45. #15689482	C₂²	semidirect
46. #15689482	C₂²	semidirect
47. #15689477	C₂²	semidirect
48. #15689477	C₂²	semidirect
49. #15689461	C₂²	semidirect
50. #15689461	C₂²	semidirect
51. #15689456	C₂²	semidirect
52. #15689451	C₂²	semidirect
53. #15689444	C₂²	semidirect
54. #15689444	C₂²	semidirect
55. #15689439	C₂²	semidirect
56. #15689434	C₂²	semidirect
57. #15689430	C₂²	semidirect
58. #15689430	C₂²	semidirect
59. #15689423	C₂²	semidirect
60. #15689423	C₂²	semidirect
61. #15689418	C₂²	semidirect
62. #15689413	C₂²	semidirect
63. #15689408	C₂²	semidirect
64. #15689403	C₂²	semidirect
65. #15689379	C₂²	semidirect
66. #15689379	C₂²	semidirect
67. #15689367	C₂²	semidirect
68. #15689367	C₂²	semidirect
69. #15689362	C₂²	semidirect
70. #15689362	C₂²	semidirect
71. #15689350	C₂²	semidirect
72. #15689350	C₂²	semidirect
73. #15689342	C₂²	semidirect
74. #15689342	C₂²	semidirect
75. #15689342	C₂²	semidirect
76. #15689342	C₂²	semidirect
79. #15689285	C₂²	semidirect
80. #15689285	C₂²	semidirect
81. #15689279	C₂²	semidirect
82. #15689279	C₂²	semidirect
85. #15689228	C₂²	semidirect
86. #15689223	C₂²	semidirect
87. C₄×#10625337	C₂²	semidirect
88. C₄×#10625335	C₂²	semidirect
89. #15689201	C₂²	semidirect
90. #15689195	C₂²	semidirect
91. #15689195	C₂²	semidirect
92. D₄×C₄₇⋊C₈	C₂²	semidirect
93. #15689166	C₂²	semidirect
94. #15689159	C₂²	semidirect
95. #15689159	C₂²	semidirect
96. C₂×C₄⋊(C₄₇⋊C₈)	C₂²	semidirect
97. #15689132	C₂²	semidirect
98. #15689132	C₂²	semidirect
99. #15689132	C₂²	semidirect
100. #15689131	C₂²	semidirect
106. #15689124	C₂²	semidirect
110. #15689119	C₂²	semidirect
111. C₂×#13093948	C₂²	semidirect
112. C₂×#13093948	C₂²	semidirect
116. #15689090	C₂²	semidirect
117. C₄×#10625329	C₂²	semidirect
738. C₄₇	#61207	semidirect

Maximal subgroups

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

subgroup	index
#20257250	2
#20255656	2
#20255604	2
#20255499	2
#20255469	2
#20255454	2
#20255424	2
#20255275	2
#20255223	2
#20253774	2
#20253351	2
#20253340	2
#20253176	2
#20253040	2
#20253024	2
C₂×#15689342	2
#20252683	2
#20252665	2
C₄×#13094054	2
#20252132	2
#20251921	2
#20251914	2
C₄₇×#3500	2
#61207	47