Subgroups — #27085345

Order 12032.

2014 conjugacy classes of subgroups.

The subgroup lattice has 1154 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20257286	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄×#13094071	C₂	1	1	yes	maximal, characteristic, complemented
3	#20253670	C₂	1	2	yes	maximal, complemented
4	#20253655	C₂	1	2	yes	maximal, complemented
5	#20253624	C₂	1	2	yes	maximal, complemented
6	#20253622	C₂	1	2	yes	maximal, complemented
7	#20253564	C₂	1	2	yes	maximal, complemented
8	#20253502	C₂	1	2	yes	maximal, complemented
9	#20253473	C₂	1	2	yes	maximal, complemented
10	#20253411	C₂	1	2	yes	maximal, complemented
11	#20253360	C₂	1	1	yes	maximal, characteristic, complemented
12	#20253349	C₂	1	1	yes	maximal, characteristic, complemented
13	#20253189	C₂	1	1	yes	maximal, characteristic, complemented
14	#20252882	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×#15689346	C₂	1	1	yes	maximal, characteristic, complemented
16	#20252686	C₂	1	1	yes	maximal, characteristic, complemented
17	#20252677	C₂	1	1	yes	maximal, characteristic
18	#20252255	C₂	1	1	yes	maximal, characteristic, complemented
19	#20252246	C₂	1	1	yes	maximal, characteristic, complemented
20	#20252234	C₂	1	1	yes	maximal, characteristic, complemented
21	#20252223	C₂	1	1	yes	maximal, characteristic, complemented
22	#20252053	C₂	1	1	yes	maximal, characteristic, complemented
23	C₄₇×#3076	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#13094071	C₂²	1	1	yes	characteristic
25	C₂×#13094054	C₂²	1	1	yes	characteristic
26	C₂×#13094049	C₂²	1	1	yes	characteristic
27	C₂²×Dic₁₈₈	C₂²	1	1	yes	characteristic
28	C₂²×#10625325	C₂²	1	1	yes	characteristic
29	#15689858	—	2	1	no	—
30	#15689858	—	2	1	no	—
31	#15689846	—	2	1	no	—
32	#15689846	—	2	1	no	—
33	#15689800	—	2	2	no	—
34	#15689800	—	2	2	no	—
35	#15689747	C₂²	1	2	yes	—
36	#15689747	C₂²	1	2	yes	—
37	#15689699	C₂²	1	1	yes	characteristic
38	#15689692	C₂²	1	1	yes	characteristic
39	#15689658	C₂²	1	2	yes	—
40	#15689658	C₂²	1	2	yes	—
41	C₂×#13094012	C₂²	1	1	yes	characteristic
42	#15689606	C₂²	1	1	yes	characteristic
43	#15689603	—	2	1	no	—
44	#15689603	C₂²	1	1	yes	characteristic
45	#15689602	—	2	2	no	—
46	#15689602	C₂²	1	2	yes	complemented
47	#15689600	—	2	1	no	—
48	#15689600	C₂²	1	1	yes	characteristic
49	#15689600	C₂²	1	1	yes	characteristic
50	#15689599	C₂²	1	2	yes	complemented
51	#15689597	C₂²	1	1	yes	characteristic
52	C₄×#10625350	—	2	1	no	—
53	C₄×#10625350	C₂²	1	1	yes	characteristic
54	C₄×#10625352	—	2	2	no	—
55	C₄×#10625352	C₂²	1	2	yes	complemented
56	C₂×C₄×Dic₉₄	—	2	1	no	—
57	C₂×C₄×Dic₉₄	C₂²	1	1	yes	characteristic
58	C₄×Q₈×D₄₇	C₂²	1	2	yes	complemented
59	#15689467	C₂²	1	2	yes	complemented
60	#15689466	C₂²	1	2	yes	complemented
61	#15689460	C₂²	1	2	yes	complemented
62	#15689455	C₂²	1	2	yes	complemented
63	#15689450	C₂²	1	2	yes	—
64	#15689449	C₂²	1	2	yes	—
65	#15689443	C₂²	1	2	yes	—
66	#15689438	C₂²	1	2	yes	—
67	#15689427	C₂²	1	2	yes	complemented
68	#15689427	C₂²	1	2	yes	complemented
69	#15689415	C₂²	1	2	yes	complemented
70	#15689405	C₂²	1	2	yes	complemented
71	#15689346	C₂²	1	2	yes	—
72	#15689346	C₂²	1	2	yes	—
73	#15689346	C₂²	1	2	yes	—
74	#15689346	C₂²	1	2	yes	—
75	#15689345	C₂²	1	2	yes	—
76	#15689345	C₂²	1	2	yes	—
77	#15689338	C₂²	1	2	yes	—
78	#15689338	C₂²	1	2	yes	—
79	#15689286	C₂²	1	2	yes	complemented
80	#15689286	C₂²	1	2	yes	complemented
81	#15689280	C₂²	1	2	yes	complemented
82	#15689280	C₂²	1	2	yes	complemented
83	#15689269	C₂²	1	2	yes	—
84	#15689269	C₂²	1	2	yes	—
85	#15689263	C₂²	1	2	yes	—
86	#15689263	C₂²	1	2	yes	—
87	#15689232	C₂²	1	2	yes	—
88	#15689229	C₂²	1	2	yes	complemented
89	#15689229	C₂²	1	2	yes	complemented
90	#15689227	C₂²	1	2	yes	complemented
91	#15689226	C₂²	1	2	yes	—
92	#15689222	C₂²	1	2	yes	—
93	#15689222	C₂²	1	2	yes	—
94	#15689220	C₂²	1	2	yes	complemented
95	#15689217	C₂²	1	2	yes	complemented
96	#15689217	C₂²	1	2	yes	complemented
97	#15689215	C₂²	1	2	yes	complemented
98	#15689214	C₂²	1	2	yes	complemented
99	#15689210	C₂²	1	2	yes	—
100	#15689210	C₂²	1	2	yes	—
101	#15689208	C₂²	1	2	yes	—
102	#15689203	C₂²	1	2	yes	—
103	#15689183	C₂²	1	2	yes	complemented
104	#15689183	C₂²	1	2	yes	complemented
105	#15689179	C₂²	1	2	yes	complemented
106	#15689175	C₂²	1	2	yes	complemented
107	#15689166	C₂²	1	1	yes	characteristic
108	#15689166	C₂²	1	1	yes	characteristic
109	#15689147	C₂²	1	1	yes	characteristic
110	#15689131	C₂²	1	1	yes	characteristic
111	#15689131	C₂²	1	1	yes	characteristic
112	#15689131	C₂²	1	1	yes	characteristic
113	#15689127	C₂²	1	1	yes	characteristic
114	C₂×#13093949	C₂²	1	1	yes	characteristic
115	C₂×#13093946	C₂²	1	1	yes	characteristic
116	#15689089	C₂²	1	1	yes	characteristic
117	#15689089	C₂²	1	1	yes	characteristic
118	#15689078	C₂²	1	1	yes	characteristic
119	#15689078	C₂²	1	1	yes	characteristic
120	C₄₇×#533	C₂²	1	1	yes	characteristic
121	C₄×#41×C₄₇	C₂²	1	1	yes	characteristic
122	C₄₇×#479	C₂²	1	1	yes	characteristic, complemented
123	C₄₇×#479	C₂²	1	1	yes	characteristic, complemented
124	C₄₇×#478	C₂²	1	1	yes	characteristic, complemented
125	C₄₇×#478	C₂²	1	1	yes	characteristic, complemented
126	C₄₇×#477	C₂²	1	1	yes	characteristic, complemented
127	C₄₇×#476	C₂²	1	1	yes	characteristic, complemented
128	C₄₇×#475	C₂²	1	1	yes	characteristic, complemented
129	C₄₇×#474	C₂²	1	1	yes	characteristic, complemented
130	C₄₇×#427	C₂²	1	1	yes	characteristic
131	C₄₇×#427	C₂²	1	1	yes	characteristic
132	C₂×C₄⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
133	C₄₇×#416	C₂²	1	1	yes	characteristic
134	C₄₇×#416	C₂²	1	1	yes	characteristic
135	#13094071	—	2	4	no	—
136	#13094071	—	2	4	no	—
137	C₂×#10625350	—	2	1	no	—
138	C₂×#10625350	C₂³	1	1	yes	characteristic
139	C₂×#10625352	—	2	2	no	—
140	C₂×#10625352	C₂³	1	2	yes	—
141	C₂²×Dic₉₄	—	2	1	no	—
142	C₂²×Dic₉₄	C₂³	1	1	yes	characteristic
143	C₂²×Dic₉₄	C₂³	1	1	yes	characteristic
144	C₂×Q₈×D₄₇	C₂³	1	2	yes	—
145	C₂²×D₁₈₈	C₂³	1	1	yes	characteristic
146	#13094054	—	2	4	no	—
147	#13094049	—	2	4	no	—
148	C₂×Dic₁₈₈	—	2	4	no	—
149	C₂×Dic₁₈₈	C₂³	1	2	yes	—
150	C₂×Dic₁₈₈	C₂³	1	2	yes	—
151	C₂×#10625337	C₂³	1	2	yes	—
152	C₂×#10625325	—	2	4	no	—
153	C₂×#10625325	C₂³	1	2	yes	—
154	C₂×#10625325	C₂³	1	2	yes	—
155	C₂×#10625335	C₂³	1	2	yes	—
156	C₂×#10625336	C₂³	1	2	yes	—
157	C₂×#10625334	C₂³	1	2	yes	—
158	C₂×#10625329	C₂³	1	1	yes	characteristic
159	C₂×#10625329	C₂³	1	1	yes	characteristic
160	#13094024	—	2	1	no	—
161	#13094021	—	2	1	no	—
162	#13094019	—	2	2	no	—
163	#13094019	—	2	2	no	—
164	#13094019	—	2	2	no	—
165	#13094019	—	2	2	no	—
166	#13094013	—	2	2	no	—
167	#13094013	—	2	2	no	—
168	#13094012	—	2	1	no	—
169	#13094012	—	2	1	no	—
170	#13094012	—	2	1	no	—
171	#13094012	—	2	1	no	—
172	#13094012	C₂³	1	2	yes	—
173	#13094012	C₂³	1	2	yes	—
174	#13094009	—	2	2	no	—
175	#13094009	—	2	2	no	—
176	#13094009	—	2	2	no	—
177	#13094009	—	2	2	no	—
178	#13094008	—	2	2	no	—
179	#13094004	C₂³	1	2	yes	—
180	#13094004	C₂³	1	2	yes	—
181	#13094000	—	2	2	no	—
182	#13094000	—	2	2	no	—
183	#13093999	C₂³	1	2	yes	—
184	#13093999	C₂³	1	2	yes	—
185	#13093994	—	2	2	no	—
186	Q₈×Dic₄₇	C₂³	1	2	yes	—
187	C₄×Dic₉₄	—	2	1	no	—
188	C₄×Dic₉₄	—	2	1	no	—
189	C₄×Dic₉₄	—	2	1	no	—
190	C₄×Dic₉₄	—	2	1	no	—
191	C₄×Dic₉₄	—	2	1	no	—
192	C₄×Dic₉₄	—	2	1	no	—
193	C₄×Dic₉₄	—	2	1	no	—
194	C₄×Dic₉₄	—	2	2	no	—
195	C₄×Dic₉₄	—	2	2	no	—
196	C₄×Dic₉₄	D₄	1	1	yes	characteristic
197	C₄×Dic₉₄	D₄	1	1	yes	characteristic
198	C₄×Dic₉₄	C₂³	1	2	yes	—
199	C₄×Dic₉₄	C₂³	1	2	yes	—
200	#13093989	—	2	2	no	—
201	#13093989	—	2	2	no	—
202	#13093989	C₂³	1	2	yes	—
203	#13093989	C₂³	1	2	yes	—
204	#13093989	C₂³	1	2	yes	—
205	#13093989	C₂³	1	2	yes	—
206	C₄×D₁₈₈	—	2	1	no	—
207	C₄×D₁₈₈	—	2	1	no	—
208	C₄×D₁₈₈	—	2	1	no	—
209	C₄×D₁₈₈	D₄	1	1	yes	characteristic
210	C₄×D₁₈₈	D₄	1	1	yes	characteristic
211	D₄×Dic₄₇	—	2	2	no	—
212	D₄×Dic₄₇	C₂³	1	2	yes	—
213	#13093986	—	2	2	no	—
214	#13093986	—	2	2	no	—
215	#13093986	C₂³	1	2	yes	—
216	#13093986	C₂³	1	2	yes	—
217	C₄×C₂²⋊D₄₇	—	2	2	no	—
218	C₄×C₂²⋊D₄₇	—	2	2	no	—
219	C₄×C₂²⋊D₄₇	D₄	1	2	yes	—
220	C₄×C₂²⋊D₄₇	D₄	1	2	yes	—
221	(C₂²⋊D₄₇)⋊C₄	—	2	2	no	—
222	(C₂²⋊D₄₇)⋊C₄	—	2	2	no	—
223	(C₂²⋊D₄₇)⋊C₄	—	2	2	no	—
224	#13093983	—	2	1	no	—
225	#13093983	C₂³	1	1	yes	characteristic
226	#13093982	—	2	2	no	—
227	#13093982	—	2	2	no	—
228	#13093982	—	2	2	no	—
229	#13093982	C₂³	1	2	yes	—
230	#13093981	—	2	2	no	—
231	#13093981	C₂³	1	2	yes	—
232	#13093980	—	2	2	no	—
233	#13093980	—	2	2	no	—
234	#13093980	—	2	2	no	—
235	#13093980	—	2	2	no	—
236	C₂×C₄⋊Dic₄₇	—	2	1	no	—
237	C₂×C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic
238	C₂×Dic₄₇⋊C₄	—	2	1	no	—
239	C₂×Dic₄₇⋊C₄	—	2	2	no	—
240	C₄⋊C₄×D₄₇	—	2	2	no	—
241	C₄⋊C₄×D₄₇	C₂³	1	2	yes	—
242	C₂×(C₂×D₄₇)⋊C₄	—	2	1	no	—
243	C₂×(C₂×D₄₇)⋊C₄	—	2	1	no	—
244	C₂²⋊C₄×D₄₇	—	2	2	no	—
245	C₂×C₄×Dic₄₇	—	2	1	no	—
246	C₂×C₄×Dic₄₇	—	2	2	no	—
247	C₄²×D₄₇	—	2	2	no	—
248	C₄²×D₄₇	C₂³	1	2	yes	—
249	#13093957	C₂³	1	2	yes	—
250	#13093957	C₂³	1	2	yes	—
251	#13093955	C₂³	1	2	yes	—
252	#13093955	C₂³	1	2	yes	—
253	C₄⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
254	C₄⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
255	#13093949	C₂³	1	2	yes	—
256	#13093949	C₂³	1	2	yes	—
257	#13093947	C₂³	1	2	yes	—
258	#13093947	C₂³	1	2	yes	—
259	#13093947	C₂³	1	2	yes	—
260	#13093947	C₂³	1	2	yes	—
261	#13093947	C₂³	1	2	yes	—
262	#13093947	C₂³	1	2	yes	—
263	#13093946	C₂³	1	2	yes	—
264	#13093946	C₂³	1	2	yes	—
265	#13093944	C₂³	1	2	yes	—
266	#13093944	C₂³	1	2	yes	—
267	(C₂×D₄₇)⋊C₈	C₂³	1	2	yes	—
268	(C₂×D₄₇)⋊C₈	C₂³	1	2	yes	—
269	(C₂×D₄₇)⋊C₈	C₂³	1	2	yes	—
270	(C₂×D₄₇)⋊C₈	C₂³	1	2	yes	—
271	#13093934	C₂³	1	2	yes	—
272	#13093934	C₂³	1	2	yes	—
273	C₈×Dic₄₇	C₂³	1	2	yes	—
274	C₈×Dic₄₇	C₂³	1	2	yes	—
275	C₂×#41×C₄₇	C₂³	1	1	yes	characteristic
276	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
277	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
278	C₄⋊Q₈×C₄₇	C₂³	1	1	yes	characteristic
279	C₄⋊Q₈×C₄₇	C₂³	1	1	yes	characteristic
280	#125×C₄₇	C₂³	1	1	yes	characteristic
281	#125×C₄₇	C₂³	1	1	yes	characteristic
282	C₂²⋊Q₈×C₄₇	—	2	1	no	—
283	C₂²⋊Q₈×C₄₇	—	2	1	no	—
284	C₄×Q₈×C₄₇	—	2	1	no	—
285	C₄×Q₈×C₄₇	—	2	1	no	—
286	C₄×Q₈×C₄₇	C₂³	1	1	yes	characteristic
287	C₄×Q₈×C₄₇	C₂³	1	1	yes	characteristic
288	C₄×D₄×C₄₇	—	2	1	no	—
289	C₄×D₄×C₄₇	—	2	1	no	—
290	C₄×D₄×C₄₇	C₂³	1	1	yes	characteristic
291	C₄×D₄×C₄₇	C₂³	1	1	yes	characteristic
292	#117×C₄₇	—	2	1	no	—
293	#117×C₄₇	C₂³	1	1	yes	characteristic
294	#117×C₄₇	C₂³	1	1	yes	characteristic
295	#117×C₄₇	C₂³	1	1	yes	characteristic
296	C₂×C₄²×C₄₇	—	2	1	no	—
297	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
298	#107×C₄₇	C₂³	1	1	yes	characteristic
299	#107×C₄₇	C₂³	1	1	yes	characteristic
300	#107×C₄₇	C₂³	1	1	yes	characteristic
301	#107×C₄₇	C₂³	1	1	yes	characteristic
302	#106×C₄₇	C₂³	1	1	yes	characteristic
303	#106×C₄₇	C₂³	1	1	yes	characteristic
304	#106×C₄₇	C₂³	1	1	yes	characteristic
305	#106×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	C₄⋊C₈×C₄₇	C₂³	1	1	yes	characteristic
309	C₄⋊C₈×C₄₇	C₂³	1	1	yes	characteristic
310	#103×C₄₇	C₂³	1	1	yes	characteristic
311	#103×C₄₇	C₂³	1	1	yes	characteristic
312	#103×C₄₇	C₂³	1	1	yes	characteristic
313	#103×C₄₇	C₂³	1	1	yes	characteristic
314	#102×C₄₇	C₂³	1	1	yes	characteristic
315	#102×C₄₇	C₂³	1	1	yes	characteristic
316	#102×C₄₇	C₂³	1	1	yes	characteristic
317	#102×C₄₇	C₂³	1	1	yes	characteristic
318	C₂³×D₄₇	—	2	1	no	—
319	#41×C₄₇	—	2	2	no	—
320	#41×C₄₇	#41	1	4	yes	—
321	C₂×Q₈×C₄₇	—	2	1	no	—
322	C₂×Q₈×C₄₇	—	2	1	no	—
323	C₂×Q₈×C₄₇	C₂⁴	1	1	yes	characteristic
324	C₂×D₄×C₄₇	—	2	1	no	—
325	C₂×D₄×C₄₇	C₂⁴	1	1	yes	characteristic
326	C₂²×C₄×C₄₇	—	2	1	no	—
327	C₂²×C₄×C₄₇	—	2	1	no	—
328	C₂²×C₄×C₄₇	—	2	1	no	—
329	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
330	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
331	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
332	C₂×C₂²⋊D₄₇	—	2	2	no	—
333	C₂×C₂²⋊D₄₇	C₂×D₄	1	2	yes	—
334	C₂²×Dic₄₇	—	2	1	no	—
335	C₂²×Dic₄₇	—	2	2	no	—
336	C₂²×Dic₄₇	—	2	1	no	—
337	C₂²×Dic₄₇	—	2	1	no	—
338	C₂²×Dic₄₇	—	2	2	no	—
339	Q₈×D₄₇	—	2	4	no	—
340	Q₈×D₄₇	—	2	4	no	—
341	#10625352	—	2	16	no	—
342	#10625352	—	2	4	no	—
343	#10625352	—	2	4	no	—
344	#10625350	—	2	8	no	—
345	#10625350	—	2	2	no	—
346	#10625350	—	2	2	no	—
347	C₂×D₁₈₈	—	2	2	no	—
348	C₂×D₁₈₈	—	2	2	no	—
349	C₂×D₁₈₈	—	2	1	no	—
350	C₂×D₁₈₈	—	2	2	no	—
351	C₂×D₁₈₈	—	2	2	no	—
352	C₂×D₁₈₈	C₂×D₄	1	1	yes	characteristic
353	C₂×D₁₈₈	C₂⁴	1	2	yes	—
354	C₂×C₄×D₄₇	—	2	2	no	—
355	C₂×C₄×D₄₇	—	2	2	no	—
356	C₂×C₄×D₄₇	—	2	2	no	—
357	C₂×C₄×D₄₇	—	2	2	no	—
358	C₂×C₄×D₄₇	C₂×D₄	1	2	yes	—
359	C₂×C₄×D₄₇	C₂×D₄	1	2	yes	—
360	C₂×C₄×D₄₇	C₂⁴	1	2	yes	—
361	C₂×Dic₉₄	—	2	8	no	—
362	C₂×Dic₉₄	—	2	1	no	—
363	C₂×Dic₉₄	—	2	2	no	—
364	C₂×Dic₉₄	—	2	2	no	—
365	C₂×Dic₉₄	—	2	2	no	—
366	C₂×Dic₉₄	—	2	2	no	—
367	C₂×Dic₉₄	—	2	1	no	—
368	C₂×Dic₉₄	C₂×D₄	1	1	yes	characteristic
369	C₂×Dic₉₄	#41	1	4	yes	—
370	C₂×Dic₉₄	C₂⁴	1	2	yes	—
371	C₂×Dic₉₄	C₂⁴	1	2	yes	—
372	C₂×C₈×C₄₇	—	2	2	no	—
373	C₂×C₈×C₄₇	—	2	2	no	—
374	C₂×C₈×C₄₇	C₂⁴	1	1	yes	characteristic
375	C₂×C₈×C₄₇	C₂⁴	1	1	yes	characteristic
376	C₂×C₈×C₄₇	C₂⁴	1	1	yes	characteristic
377	C₂×C₈×C₄₇	C₂⁴	1	1	yes	characteristic
378	C₄⋊C₄×C₄₇	—	2	1	no	—
379	C₄⋊C₄×C₄₇	—	2	1	no	—
380	C₄⋊C₄×C₄₇	—	2	1	no	—
381	C₄⋊C₄×C₄₇	—	2	1	no	—
382	C₄⋊C₄×C₄₇	—	2	1	no	—
383	C₄⋊C₄×C₄₇	—	2	1	no	—
384	C₄⋊C₄×C₄₇	—	2	1	no	—
385	C₄⋊C₄×C₄₇	—	2	1	no	—
386	C₄⋊C₄×C₄₇	C₂⁴	1	1	yes	characteristic
387	C₄⋊C₄×C₄₇	C₂⁴	1	1	yes	characteristic
388	C₄⋊C₄×C₄₇	C₂⁴	1	1	yes	characteristic
389	C₄⋊C₄×C₄₇	C₂⁴	1	1	yes	characteristic
390	C₄⋊C₄×C₄₇	C₂⁴	1	1	yes	characteristic
391	C₄⋊C₄×C₄₇	C₂⁴	1	1	yes	characteristic
392	C₂²⋊C₄×C₄₇	—	2	1	no	—
393	C₂²⋊C₄×C₄₇	—	2	1	no	—
394	C₂²⋊C₄×C₄₇	—	2	1	no	—
395	C₂²⋊C₄×C₄₇	—	2	1	no	—
396	C₂²⋊C₄×C₄₇	—	2	1	no	—
397	C₄²×C₄₇	—	2	1	no	—
398	C₄²×C₄₇	—	2	1	no	—
399	C₄²×C₄₇	—	2	1	no	—
400	C₄²×C₄₇	—	2	1	no	—
401	C₄²×C₄₇	—	2	1	no	—
402	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
403	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
404	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
405	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
406	C₂²⋊Dic₄₇	—	2	2	no	—
407	C₂²⋊Dic₄₇	C₂×D₄	1	2	yes	—
408	#10625337	—	2	4	no	—
409	#10625336	—	2	4	no	—
410	#10625335	—	2	4	no	—
411	#10625334	—	2	4	no	—
412	(C₂×D₄₇)⋊C₄	—	2	2	no	—
413	(C₂×D₄₇)⋊C₄	—	2	2	no	—
414	(C₂×D₄₇)⋊C₄	—	2	2	no	—
415	(C₂×D₄₇)⋊C₄	—	2	2	no	—
416	(C₂×D₄₇)⋊C₄	—	2	2	no	—
417	(C₂×D₄₇)⋊C₄	—	2	2	no	—
418	(C₂×D₄₇)⋊C₄	—	2	2	no	—
419	(C₂×D₄₇)⋊C₄	—	2	2	no	—
420	(C₂×D₄₇)⋊C₄	—	2	2	no	—
421	(C₂×D₄₇)⋊C₄	—	2	2	no	—
422	(C₂×D₄₇)⋊C₄	—	2	2	no	—
423	(C₂×D₄₇)⋊C₄	C₂×D₄	1	2	yes	—
424	(C₂×D₄₇)⋊C₄	C₂×D₄	1	2	yes	—
425	C₄⋊Dic₄₇	—	2	1	no	—
426	C₄⋊Dic₄₇	—	2	2	no	—
427	C₄⋊Dic₄₇	—	2	2	no	—
428	C₄⋊Dic₄₇	—	2	2	no	—
429	C₄⋊Dic₄₇	C₂×D₄	1	1	yes	characteristic
430	C₄⋊Dic₄₇	C₂×D₄	1	1	yes	characteristic
431	C₄⋊Dic₄₇	C₂⁴	1	2	yes	—
432	Dic₄₇⋊C₄	—	2	2	no	—
433	Dic₄₇⋊C₄	—	2	2	no	—
434	Dic₄₇⋊C₄	—	2	2	no	—
435	Dic₄₇⋊C₄	—	2	2	no	—
436	Dic₄₇⋊C₄	—	2	2	no	—
437	Dic₄₇⋊C₄	—	2	2	no	—
438	Dic₄₇⋊C₄	—	2	2	no	—
439	Dic₄₇⋊C₄	C₂×D₄	1	2	yes	—
440	Dic₄₇⋊C₄	C₂×D₄	1	2	yes	—
441	C₄×Dic₄₇	—	2	2	no	—
442	C₄×Dic₄₇	—	2	2	no	—
443	C₄×Dic₄₇	—	2	2	no	—
444	C₄×Dic₄₇	—	2	2	no	—
445	C₄×Dic₄₇	—	2	2	no	—
446	C₄×Dic₄₇	—	2	2	no	—
447	C₄×Dic₄₇	—	2	2	no	—
448	C₄×Dic₄₇	—	2	2	no	—
449	C₄×Dic₄₇	C₂×D₄	1	2	yes	—
450	C₄×Dic₄₇	C₂×D₄	1	2	yes	—
451	C₄×Dic₄₇	C₂⁴	1	2	yes	—
452	#10625329	—	2	2	no	—
453	#10625329	—	2	2	no	—
454	C₂×C₄₇⋊C₈	C₂⁴	1	2	yes	—
455	C₂×C₄₇⋊C₈	C₂⁴	1	2	yes	—
456	Dic₁₈₈	—	2	4	no	—
457	Dic₁₈₈	—	2	4	no	—
458	#10625325	—	2	4	no	—
459	#10625325	—	2	4	no	—
460	C₂³×C₄₇	—	2	1	no	—
461	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
462	C₂²×D₄₇	—	2	2	no	—
463	C₂²×D₄₇	—	4	2	no	—
464	C₂²×D₄₇	—	8	1	no	—
465	C₂²×D₄₇	—	8	1	no	—
466	C₂²×D₄₇	C₂²×D₄	1	2	yes	—
467	Q₈×C₄₇	—	2	1	no	—
468	Q₈×C₄₇	—	8	1	no	—
469	Q₈×C₄₇	—	8	1	no	—
470	Q₈×C₄₇	C₂×#41	1	2	yes	—
471	D₄×C₄₇	—	2	4	no	—
472	D₄×C₄₇	—	2	1	no	—
473	D₄×C₄₇	C₂×#41	1	2	yes	—
474	C₂×C₄×C₄₇	—	2	1	no	—
475	C₂×C₄×C₄₇	—	2	4	no	—
476	C₂×C₄×C₄₇	—	2	1	no	—
477	C₂×C₄×C₄₇	—	2	1	no	—
478	C₂×C₄×C₄₇	—	2	1	no	—
479	C₂×C₄×C₄₇	—	2	1	no	—
480	C₂×C₄×C₄₇	—	2	1	no	—
481	C₂×C₄×C₄₇	—	2	1	no	—
482	C₂×C₄×C₄₇	—	4	1	no	—
483	C₂×C₄×C₄₇	—	4	1	no	—
484	C₂×C₄×C₄₇	—	4	2	no	—
485	C₂×C₄×C₄₇	—	8	1	no	—
486	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
487	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
488	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
489	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
490	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
491	C₂×C₄×C₄₇	C₂×#41	1	2	yes	—
492	C₂×C₄×C₄₇	C₂×#41	1	2	yes	—
493	C₂×C₄×C₄₇	C₂⁵	1	1	yes	characteristic
494	C₂²⋊D₄₇	—	2	8	no	—
495	C₂²⋊D₄₇	—	2	4	no	—
496	C₂×Dic₄₇	—	2	8	no	—
497	C₂×Dic₄₇	—	2	4	no	—
498	C₂×Dic₄₇	—	2	2	no	—
499	C₂×Dic₄₇	—	2	2	no	—
500	C₂×Dic₄₇	—	2	2	no	—
501	C₂×Dic₄₇	—	4	2	no	—
502	C₂×Dic₄₇	—	8	2	no	—
503	C₂×Dic₄₇	—	8	1	no	—
504	C₂×Dic₄₇	C₂²×D₄	1	2	yes	—
505	C₂×Dic₄₇	C₂²×D₄	1	2	yes	—
506	C₂×Dic₄₇	C₂²×D₄	1	2	yes	—
507	D₁₈₈	—	2	2	no	—
508	D₁₈₈	—	2	2	no	—
509	D₁₈₈	—	2	2	no	—
510	D₁₈₈	—	4	2	no	—
511	D₁₈₈	—	8	2	no	—
512	D₁₈₈	—	8	2	no	—
513	C₄×D₄₇	—	2	8	no	—
514	C₄×D₄₇	—	2	2	no	—
515	C₄×D₄₇	—	2	2	no	—
516	C₄×D₄₇	—	4	2	no	—
517	C₄×D₄₇	—	4	2	no	—
518	C₄×D₄₇	—	8	2	no	—
519	C₄×D₄₇	—	8	2	no	—
520	C₄×D₄₇	—	8	2	no	—
521	Dic₉₄	—	2	8	no	—
522	Dic₉₄	—	2	2	no	—
523	Dic₉₄	—	2	4	no	—
524	Dic₉₄	—	2	2	no	—
525	Dic₉₄	—	2	2	no	—
526	Dic₉₄	—	2	2	no	—
527	Dic₉₄	—	4	2	no	—
528	Dic₉₄	C₂×#41	1	4	yes	—
529	C₈×C₄₇	—	2	1	no	—
530	C₈×C₄₇	—	2	1	no	—
531	C₈×C₄₇	—	2	1	no	—
532	C₈×C₄₇	—	2	1	no	—
533	C₄₇⋊C₈	—	2	2	no	—
534	C₄₇⋊C₈	—	2	2	no	—
535	#60595	—	47	1	no	maximal, Sylow
536	C₂²×C₄₇	—	2	1	no	—
537	C₂²×C₄₇	—	2	1	no	—
538	C₂²×C₄₇	—	2	2	no	—
539	C₂²×C₄₇	—	4	1	no	—
540	C₂²×C₄₇	—	4	1	no	—
541	C₂²×C₄₇	#525	1	2	yes	—
542	C₂²×C₄₇	C₂³×D₄	1	1	yes	characteristic
543	C₂×D₄₇	—	2	2	no	—
544	C₂×D₄₇	—	2	2	no	—
545	C₂×D₄₇	—	2	2	no	—
546	C₂×D₄₇	—	4	2	no	—
547	C₂×D₄₇	—	4	2	no	—
548	C₂×D₄₇	—	4	2	no	—
549	C₂×D₄₇	—	16	2	no	—
550	C₄×C₄₇	—	2	1	no	—
551	C₄×C₄₇	—	2	1	no	—
552	C₄×C₄₇	—	2	1	no	—
553	C₄×C₄₇	—	2	1	no	—
554	C₄×C₄₇	—	2	2	no	—
555	C₄×C₄₇	—	4	1	no	—
556	C₄×C₄₇	—	4	1	no	—
557	C₄×C₄₇	—	4	1	no	—
558	C₄×C₄₇	—	4	1	no	—
559	C₄×C₄₇	—	4	1	no	—
560	C₄×C₄₇	—	4	1	no	—
561	C₄×C₄₇	#525	1	2	yes	—
562	C₄×C₄₇	C₂²×#41	1	1	yes	characteristic
563	C₄×C₄₇	C₂²×#41	1	1	yes	characteristic
564	Dic₄₇	—	2	2	no	—
565	Dic₄₇	—	2	2	no	—
566	Dic₄₇	—	2	2	no	—
567	Dic₄₇	—	2	4	no	—
568	Dic₄₇	—	4	2	no	—
569	Dic₄₇	—	4	2	no	—
570	#3510	—	47	1	no	—
571	C₄×2₋¹⁺⁴	—	47	1	no	—
572	#3125	—	47	2	no	—
573	#3124	—	47	2	no	—
574	#3121	—	47	2	no	—
575	#3121	—	47	2	no	—
576	#3117	—	47	2	no	—
577	#3111	—	47	2	no	—
578	#3108	—	47	2	no	—
579	#3102	—	47	2	no	—
580	#3097	—	47	1	no	—
581	#3096	—	47	1	no	—
582	#3078	—	47	1	no	—
583	#3076	D₄₇	1	1	yes	characteristic, complemented
584	#3040	—	47	1	no	—
585	C₂×#464	—	47	1	no	—
586	#3011	—	47	1	no	—
587	#3010	—	47	1	no	—
588	#2950	—	47	1	no	—
589	#2949	—	47	1	no	—
590	#2947	—	47	1	no	—
591	#2946	—	47	1	no	—
592	#2925	—	47	1	no	—
593	C₂×C₄₇	—	2	2	no	—
594	C₂×C₄₇	—	4	2	no	—
595	C₂×C₄₇	C₂×#525	1	1	yes	characteristic
596	C₂×C₄₇	#3584	1	1	yes	characteristic
597	C₂×C₄₇	#3586	1	1	yes	characteristic
598	D₄₇	—	4	2	no	—
599	D₄₇	—	8	2	no	—
600	C₂×2₋¹⁺⁴	—	47	1	no	—
601	C₂×#137	—	47	1	no	—
602	C₂×AGL(1,ℤ/8)	—	47	1	no	—
603	C₂²×Q₁₆	—	47	1	no	—
604	C₂²×SD₁₆	—	47	1	no	—
605	#559	—	94	1	no	—
606	#559	—	94	1	no	—
607	#556	—	94	1	no	—
608	#556	—	94	1	no	—
609	#551	—	94	2	no	—
610	#551	—	94	2	no	—
611	#542	—	47	2	no	—
612	#542	—	47	2	no	—
613	#536	—	47	1	no	—
614	#535	—	47	1	no	—
615	#533	C₂×D₄₇	1	1	yes	characteristic
616	#529	—	47	2	no	—
617	#529	—	47	2	no	—
618	C₂×#124	—	47	1	no	—
619	#520	—	47	1	no	—
620	#520	—	47	1	no	—
621	#520	—	47	2	no	—
622	#520	—	94	1	no	—
623	#520	—	94	2	no	—
624	#519	—	47	2	no	—
625	#519	—	47	1	no	—
626	#519	—	47	1	no	—
627	#519	—	94	1	no	—
628	#518	—	47	1	no	—
629	C₄×#41	—	47	1	no	—
630	C₄×#41	—	47	2	no	—
631	C₄×#41	—	94	1	no	—
632	C₄×#41	—	94	2	no	—
633	C₄×#41	C₂×D₄₇	1	1	yes	characteristic
634	C₂×C₄×Q₈	—	47	2	no	—
635	C₂×C₄×Q₈	—	47	1	no	—
636	C₂×C₄×Q₈	—	94	1	no	—
637	#485	—	47	2	no	—
638	#485	—	47	2	no	—
639	#484	—	47	2	no	—
640	#483	—	47	2	no	—
641	#482	—	47	2	no	—
642	#482	—	47	2	no	—
643	#481	—	47	2	no	—
644	#480	—	47	2	no	—
645	#479	—	47	2	no	—
646	#479	—	47	2	no	—
647	#479	C₂×D₄₇	1	1	yes	characteristic, complemented
648	#479	C₂×D₄₇	1	1	yes	characteristic, complemented
649	#478	C₂×D₄₇	1	1	yes	characteristic, complemented
650	#478	C₂×D₄₇	1	1	yes	characteristic, complemented
651	#477	—	47	2	no	—
652	#477	C₂×D₄₇	1	1	yes	characteristic, complemented
653	#476	C₂×D₄₇	1	1	yes	characteristic, complemented
654	#475	—	47	2	no	—
655	#475	C₂×D₄₇	1	1	yes	characteristic, complemented
656	#474	C₂×D₄₇	1	1	yes	characteristic, complemented
657	#464	—	47	2	no	—
658	#464	—	47	2	no	—
659	#464	—	47	2	no	—
660	#464	—	47	2	no	—
661	#464	—	47	2	no	—
662	#464	—	47	2	no	—
663	#463	—	47	2	no	—
664	#463	—	47	2	no	—
665	#452	—	47	2	no	—
666	#452	—	47	2	no	—
667	#451	—	47	2	no	—
668	#451	—	47	2	no	—
669	#449	—	47	2	no	—
670	#449	—	47	2	no	—
671	#448	—	47	2	no	—
672	#448	—	47	2	no	—
673	#442	—	47	2	no	—
674	#441	—	47	2	no	—
675	#441	—	47	2	no	—
676	#441	—	47	2	no	—
677	#440	—	47	2	no	—
678	#440	—	47	2	no	—
679	#440	—	47	2	no	—
680	#440	—	47	2	no	—
681	C₄×Q₁₆	—	47	2	no	—
682	C₄×Q₁₆	—	47	2	no	—
683	C₄×Q₁₆	—	47	2	no	—
684	C₄×SD₁₆	—	47	2	no	—
685	C₄×SD₁₆	—	47	2	no	—
686	C₄×SD₁₆	—	47	2	no	—
687	C₄×SD₁₆	—	47	2	no	—
688	C₄×D₈	—	47	2	no	—
689	#433	—	47	2	no	—
690	#433	—	47	2	no	—
691	#432	—	47	2	no	—
692	#431	—	47	2	no	—
693	#428	—	47	1	no	—
694	#428	—	47	1	no	—
695	#427	C₂×D₄₇	1	1	yes	characteristic
696	#427	C₂×D₄₇	1	1	yes	characteristic
697	#423	—	47	1	no	—
698	C₂×C₄⋊C₈	C₂×D₄₇	1	1	yes	characteristic
699	#419	—	47	1	no	—
700	#419	—	47	1	no	—
701	#419	—	47	1	no	—
702	#418	—	47	1	no	—
703	#416	C₂×D₄₇	1	1	yes	characteristic
704	#416	C₂×D₄₇	1	1	yes	characteristic
705	C₂×#103	—	47	1	no	—
706	C₂×#102	—	47	1	no	—
707	#408	—	47	1	no	—
708	#408	—	47	1	no	—
709	#405	—	47	1	no	—
710	#405	—	47	1	no	—
711	C₄₇	#60595	1	1	yes	characteristic, complemented, Sylow
712	2₋¹⁺⁴	—	94	4	no	—
713	2₋¹⁺⁴	—	94	4	no	—
714	C₂×#41	—	47	1	no	—
715	C₂×#41	—	47	2	no	—
716	C₂×#41	—	94	1	no	—
717	C₂×#41	—	94	2	no	—
718	C₂×#41	C₂²×D₄₇	1	1	yes	characteristic
719	C₂²×Q₈	—	47	2	no	—
720	C₂²×Q₈	—	47	1	no	—
721	C₂²×Q₈	—	47	1	no	—
722	C₂²×Q₈	—	94	1	no	—
723	C₂²×D₄	—	47	1	no	—
724	#137	—	94	4	no	—
725	AGL(1,ℤ/8)	—	94	4	no	—
726	C₂×Q₁₆	—	47	2	no	—
727	C₂×Q₁₆	—	47	2	no	—
728	C₂×Q₁₆	—	47	2	no	—
729	C₂×Q₁₆	—	94	4	no	—
730	C₂×SD₁₆	—	47	2	no	—
731	C₂×SD₁₆	—	47	2	no	—
732	C₂×SD₁₆	—	47	2	no	—
733	C₂×SD₁₆	—	47	2	no	—
734	C₂×SD₁₆	—	94	4	no	—
735	C₂×D₈	—	47	2	no	—
736	C₂×M₁₆	—	47	1	no	—
737	C₂×M₁₆	—	47	1	no	—
738	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
739	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
740	C₄⋊Q₈	—	94	1	no	—
741	C₄⋊Q₈	C₂²×D₄₇	1	1	yes	characteristic
742	C₄⋊Q₈	C₂²×D₄₇	1	1	yes	characteristic
743	#127	—	94	1	no	—
744	#126	—	94	2	no	—
745	#126	—	94	2	no	—
746	#126	—	94	2	no	—
747	#126	—	94	2	no	—
748	#125	C₂²×D₄₇	1	1	yes	characteristic
749	#125	C₂²×D₄₇	1	1	yes	characteristic
750	#124	—	47	2	no	—
751	#124	—	47	2	no	—
752	#124	—	94	1	no	—
753	#124	—	94	1	no	—
754	#124	—	94	2	no	—
755	#124	—	94	2	no	—
756	#124	—	94	1	no	—
757	#124	—	94	1	no	—
758	#123	—	94	2	no	—
759	#123	—	94	2	no	—
760	#123	—	94	2	no	—
761	#123	—	94	2	no	—
762	#123	—	94	2	no	—
763	C₂²⋊Q₈	—	2	1	no	—
764	C₂²⋊Q₈	—	2	1	no	—
765	C₂²⋊Q₈	—	47	2	no	—
766	C₂²⋊Q₈	—	47	2	no	—
767	C₂²⋊Q₈	—	94	2	no	—
768	C₂²⋊Q₈	—	94	2	no	—
769	#121	—	47	2	no	—
770	#121	—	47	2	no	—
771	#120	—	94	2	no	—
772	C₄×Q₈	—	2	1	no	—
773	C₄×Q₈	—	2	1	no	—
774	C₄×Q₈	—	47	1	no	—
775	C₄×Q₈	—	47	1	no	—
776	C₄×Q₈	—	47	2	no	—
777	C₄×Q₈	—	47	2	no	—
778	C₄×Q₈	—	47	2	no	—
779	C₄×Q₈	—	47	2	no	—
780	C₄×Q₈	—	47	2	no	—
781	C₄×Q₈	—	47	2	no	—
782	C₄×Q₈	—	47	2	no	—
783	C₄×Q₈	—	94	2	no	—
784	C₄×Q₈	—	94	1	no	—
785	C₄×Q₈	—	94	2	no	—
786	C₄×Q₈	—	94	1	no	—
787	C₄×Q₈	—	94	1	no	—
788	C₄×Q₈	—	94	1	no	—
789	C₄×Q₈	—	94	1	no	—
790	C₄×Q₈	—	94	2	no	—
791	C₄×Q₈	—	94	2	no	—
792	C₄×Q₈	—	94	1	no	—
793	C₄×Q₈	—	94	1	no	—
794	C₄×Q₈	C₂²×D₄₇	1	1	yes	characteristic
795	C₄×Q₈	C₂²×D₄₇	1	1	yes	characteristic
796	C₄×D₄	—	2	1	no	—
797	C₄×D₄	—	2	1	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	—	94	1	no	—
806	C₄×D₄	—	94	1	no	—
807	C₄×D₄	—	94	1	no	—
808	C₄×D₄	—	94	2	no	—
809	C₄×D₄	—	94	2	no	—
810	C₄×D₄	—	94	2	no	—
811	C₄×D₄	—	94	2	no	—
812	C₄×D₄	—	94	2	no	—
813	C₄×D₄	—	94	2	no	—
814	C₄×D₄	—	94	2	no	—
815	C₄×D₄	—	94	2	no	—
816	C₄×D₄	C₂²×D₄₇	1	1	yes	characteristic
817	C₄×D₄	C₂²×D₄₇	1	1	yes	characteristic
818	#117	—	2	1	no	—
819	#117	—	47	1	no	—
820	#117	—	47	2	no	—
821	#117	—	47	2	no	—
822	#117	—	94	2	no	—
823	#117	—	94	2	no	—
824	#117	—	94	2	no	—
825	#117	—	94	2	no	—
826	#117	—	94	2	no	—
827	#117	—	94	2	no	—
828	#117	—	94	2	no	—
829	#117	—	94	2	no	—
830	#117	—	94	1	no	—
831	#117	C₂²×D₄₇	1	1	yes	characteristic
832	#117	C₂²×D₄₇	1	1	yes	characteristic
833	#117	C₂²×D₄₇	1	1	yes	characteristic
834	C₂×C₄⋊C₄	—	47	1	no	—
835	C₂×C₄⋊C₄	—	47	2	no	—
836	C₂×C₄⋊C₄	—	94	2	no	—
837	C₂×C₄⋊C₄	—	94	2	no	—
838	C₂×C₄⋊C₄	—	94	1	no	—
839	C₂×C₄⋊C₄	—	94	1	no	—
840	C₂×C₂²⋊C₄	—	94	2	no	—
841	C₂×C₂²⋊C₄	—	94	1	no	—
842	C₂×C₂²⋊C₄	—	94	1	no	—
843	C₂×C₄²	—	2	1	no	—
844	C₂×C₄²	—	47	2	no	—
845	C₂×C₄²	—	94	2	no	—
846	C₂×C₄²	—	94	2	no	—
847	C₂×C₄²	—	94	1	no	—
848	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
849	#107	—	47	2	no	—
850	#107	—	47	2	no	—
851	#107	C₂²×D₄₇	1	1	yes	characteristic
852	#107	C₂²×D₄₇	1	1	yes	characteristic
853	#107	C₂²×D₄₇	1	1	yes	characteristic
854	#107	C₂²×D₄₇	1	1	yes	characteristic
855	#106	—	47	2	no	—
856	#106	—	47	2	no	—
857	#106	C₂²×D₄₇	1	1	yes	characteristic
858	#106	C₂²×D₄₇	1	1	yes	characteristic
859	#106	C₂²×D₄₇	1	1	yes	characteristic
860	#106	C₂²×D₄₇	1	1	yes	characteristic
861	C₄⋊C₈	—	47	2	no	—
862	C₄⋊C₈	—	47	2	no	—
863	C₄⋊C₈	C₂²×D₄₇	1	1	yes	characteristic
864	C₄⋊C₈	C₂²×D₄₇	1	1	yes	characteristic
865	C₄⋊C₈	C₂²×D₄₇	1	1	yes	characteristic
866	C₄⋊C₈	C₂²×D₄₇	1	1	yes	characteristic
867	#103	—	47	2	no	—
868	#103	—	47	2	no	—
869	#103	—	47	2	no	—
870	#103	—	47	2	no	—
871	#103	—	47	2	no	—
872	#103	—	47	2	no	—
873	#103	—	47	2	no	—
874	#103	—	47	2	no	—
875	#103	C₂²×D₄₇	1	1	yes	characteristic
876	#103	C₂²×D₄₇	1	1	yes	characteristic
877	#103	C₂²×D₄₇	1	1	yes	characteristic
878	#103	C₂²×D₄₇	1	1	yes	characteristic
879	#102	—	47	2	no	—
880	#102	—	47	2	no	—
881	#102	—	47	2	no	—
882	#102	—	47	2	no	—
883	#102	C₂²×D₄₇	1	1	yes	characteristic
884	#102	C₂²×D₄₇	1	1	yes	characteristic
885	#102	C₂²×D₄₇	1	1	yes	characteristic
886	#102	C₂²×D₄₇	1	1	yes	characteristic
887	C₂²⋊C₈	—	47	2	no	—
888	C₂²⋊C₈	—	47	2	no	—
889	C₂²⋊C₈	—	47	2	no	—
890	C₂²⋊C₈	—	47	2	no	—
891	#97	—	47	2	no	—
892	#97	—	47	2	no	—
893	C₄×C₈	—	47	2	no	—
894	C₄×C₈	—	47	2	no	—
895	C₂⁴	—	94	1	no	—
896	#41	—	2	2	no	—
897	#41	—	94	8	no	—
898	#41	—	94	4	no	—
899	#41	—	94	16	no	—
900	#41	—	94	4	no	—
901	#41	—	94	2	no	—
902	#41	—	94	2	no	—
903	#41	#10625354	1	4	yes	—
904	C₂×Q₈	—	2	1	no	—
905	C₂×Q₈	—	2	1	no	—
906	C₂×Q₈	—	47	1	no	—
907	C₂×Q₈	—	47	4	no	—
908	C₂×Q₈	—	47	2	no	—
909	C₂×Q₈	—	47	2	no	—
910	C₂×Q₈	—	94	2	no	—
911	C₂×Q₈	—	94	8	no	—
912	C₂×Q₈	—	94	4	no	—
913	C₂×Q₈	—	94	4	no	—
914	C₂×Q₈	—	94	1	no	—
915	C₂×Q₈	—	94	1	no	—
916	C₂×Q₈	—	94	2	no	—
917	C₂×Q₈	—	94	2	no	—
918	C₂×Q₈	—	94	2	no	—
919	C₂×Q₈	C₂³×D₄₇	1	1	yes	characteristic
920	C₂×D₄	—	2	1	no	—
921	C₂×D₄	—	47	2	no	—
922	C₂×D₄	—	47	1	no	—
923	C₂×D₄	—	47	2	no	—
924	C₂×D₄	—	94	2	no	—
925	C₂×D₄	—	94	2	no	—
926	C₂×D₄	—	94	2	no	—
927	C₂×D₄	—	94	1	no	—
928	C₂×D₄	—	94	2	no	—
929	C₂×D₄	—	94	2	no	—
930	C₂×D₄	C₂³×D₄₇	1	1	yes	characteristic
931	C₂²×C₄	—	2	1	no	—
932	C₂²×C₄	—	2	1	no	—
933	C₂²×C₄	—	2	1	no	—
934	C₂²×C₄	—	47	2	no	—
935	C₂²×C₄	—	47	2	no	—
936	C₂²×C₄	—	47	2	no	—
937	C₂²×C₄	—	94	2	no	—
938	C₂²×C₄	—	94	2	no	—
939	C₂²×C₄	—	94	2	no	—
940	C₂²×C₄	—	94	2	no	—
941	C₂²×C₄	—	94	2	no	—
942	C₂²×C₄	—	94	2	no	—
943	C₂²×C₄	—	94	1	no	—
944	C₂²×C₄	—	94	1	no	—
945	C₂²×C₄	—	94	1	no	—
946	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
947	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
948	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
949	Q₁₆	—	94	4	no	—
950	Q₁₆	—	94	4	no	—
951	Q₁₆	—	94	4	no	—
952	SD₁₆	—	94	4	no	—
953	SD₁₆	—	94	4	no	—
954	SD₁₆	—	94	4	no	—
955	SD₁₆	—	94	4	no	—
956	D₈	—	94	4	no	—
957	M₁₆	—	94	2	no	—
958	M₁₆	—	94	2	no	—
959	C₂×C₈	—	2	2	no	—
960	C₂×C₈	—	2	2	no	—
961	C₂×C₈	—	47	2	no	—
962	C₂×C₈	—	47	2	no	—
963	C₂×C₈	C₂³×D₄₇	1	1	yes	characteristic
964	C₂×C₈	C₂³×D₄₇	1	1	yes	characteristic
965	C₂×C₈	C₂³×D₄₇	1	1	yes	characteristic
966	C₂×C₈	C₂³×D₄₇	1	1	yes	characteristic
967	C₄⋊C₄	—	2	1	no	—
968	C₄⋊C₄	—	2	1	no	—
969	C₄⋊C₄	—	2	1	no	—
970	C₄⋊C₄	—	2	1	no	—
971	C₄⋊C₄	—	2	1	no	—
972	C₄⋊C₄	—	2	1	no	—
973	C₄⋊C₄	—	2	1	no	—
974	C₄⋊C₄	—	2	1	no	—
975	C₄⋊C₄	—	47	2	no	—
976	C₄⋊C₄	—	47	2	no	—
977	C₄⋊C₄	—	47	1	no	—
978	C₄⋊C₄	—	47	1	no	—
979	C₄⋊C₄	—	47	2	no	—
980	C₄⋊C₄	—	94	2	no	—
981	C₄⋊C₄	—	94	2	no	—
982	C₄⋊C₄	—	94	2	no	—
983	C₄⋊C₄	—	94	2	no	—
984	C₄⋊C₄	—	94	2	no	—
985	C₄⋊C₄	—	94	2	no	—
986	C₄⋊C₄	—	94	2	no	—
987	C₄⋊C₄	—	94	2	no	—
988	C₄⋊C₄	—	94	2	no	—
989	C₄⋊C₄	—	94	2	no	—
990	C₄⋊C₄	—	94	1	no	—
991	C₄⋊C₄	C₂³×D₄₇	1	1	yes	characteristic
992	C₄⋊C₄	C₂³×D₄₇	1	1	yes	characteristic
993	C₄⋊C₄	C₂³×D₄₇	1	1	yes	characteristic
994	C₄⋊C₄	C₂³×D₄₇	1	1	yes	characteristic
995	C₄⋊C₄	C₂³×D₄₇	1	1	yes	characteristic
996	C₄⋊C₄	C₂³×D₄₇	1	1	yes	characteristic
997	C₂²⋊C₄	—	2	1	no	—
998	C₂²⋊C₄	—	2	1	no	—
999	C₂²⋊C₄	—	2	1	no	—
1000	C₂²⋊C₄	—	2	1	no	—
1001	C₂²⋊C₄	—	2	1	no	—
1002	C₂²⋊C₄	—	47	2	no	—
1003	C₂²⋊C₄	—	47	2	no	—
1004	C₂²⋊C₄	—	47	2	no	—
1005	C₂²⋊C₄	—	94	2	no	—
1006	C₂²⋊C₄	—	94	2	no	—
1007	C₂²⋊C₄	—	94	2	no	—
1008	C₂²⋊C₄	—	94	2	no	—
1009	C₂²⋊C₄	—	94	2	no	—
1010	C₂²⋊C₄	—	94	2	no	—
1011	C₂²⋊C₄	—	94	2	no	—
1012	C₂²⋊C₄	—	94	2	no	—
1013	C₂²⋊C₄	—	94	2	no	—
1014	C₂²⋊C₄	—	94	2	no	—
1015	C₂²⋊C₄	—	94	2	no	—
1016	C₂²⋊C₄	—	94	2	no	—
1017	C₄²	—	2	1	no	—
1018	C₄²	—	2	1	no	—
1019	C₄²	—	2	1	no	—
1020	C₄²	—	2	1	no	—
1021	C₄²	—	2	1	no	—
1022	C₄²	—	47	2	no	—
1023	C₄²	—	47	2	no	—
1024	C₄²	—	47	2	no	—
1025	C₄²	—	94	2	no	—
1026	C₄²	—	94	2	no	—
1027	C₄²	—	94	2	no	—
1028	C₄²	—	94	2	no	—
1029	C₄²	—	94	2	no	—
1030	C₄²	—	94	2	no	—
1031	C₄²	—	94	2	no	—
1032	C₄²	—	94	2	no	—
1033	C₄²	D₄×D₄₇	1	1	yes	characteristic
1034	C₄²	D₄×D₄₇	1	1	yes	characteristic
1035	C₄²	C₂³×D₄₇	1	1	yes	characteristic
1036	C₄²	C₂³×D₄₇	1	1	yes	characteristic
1037	C₂³	—	2	1	no	—
1038	C₂³	—	47	2	no	—
1039	C₂³	—	94	2	no	—
1040	C₂³	—	376	1	no	—
1041	C₂³	—	376	1	no	—
1042	C₂³	—	188	2	no	—
1043	C₂³	C₂×D₄×D₄₇	1	1	yes	characteristic
1044	Q₈	—	2	1	no	—
1045	Q₈	—	8	1	no	—
1046	Q₈	—	8	1	no	—
1047	Q₈	—	47	4	no	—
1048	Q₈	—	94	8	no	—
1049	Q₈	—	94	2	no	—
1050	Q₈	—	94	4	no	—
1051	Q₈	—	94	2	no	—
1052	Q₈	—	94	2	no	—
1053	Q₈	—	94	2	no	—
1054	Q₈	—	188	2	no	—
1055	Q₈	C₂×#10625354	1	2	yes	—
1056	D₄	—	2	4	no	—
1057	D₄	—	2	1	no	—
1058	D₄	—	94	8	no	—
1059	D₄	—	94	4	no	—
1060	D₄	—	94	2	no	—
1061	D₄	—	94	2	no	—
1062	D₄	—	94	2	no	—
1063	D₄	—	376	2	no	—
1064	D₄	—	376	2	no	—
1065	D₄	—	188	2	no	—
1066	D₄	C₂×#10625354	1	2	yes	—
1067	C₂×C₄	—	2	1	no	—
1068	C₂×C₄	—	2	4	no	—
1069	C₂×C₄	—	2	1	no	—
1070	C₂×C₄	—	2	1	no	—
1071	C₂×C₄	—	2	1	no	—
1072	C₂×C₄	—	2	1	no	—
1073	C₂×C₄	—	2	1	no	—
1074	C₂×C₄	—	2	1	no	—
1075	C₂×C₄	—	4	1	no	—
1076	C₂×C₄	—	4	1	no	—
1077	C₂×C₄	—	4	2	no	—
1078	C₂×C₄	—	8	1	no	—
1079	C₂×C₄	—	47	2	no	—
1080	C₂×C₄	—	47	2	no	—
1081	C₂×C₄	—	47	2	no	—
1082	C₂×C₄	—	94	8	no	—
1083	C₂×C₄	—	94	8	no	—
1084	C₂×C₄	—	94	4	no	—
1085	C₂×C₄	—	94	2	no	—
1086	C₂×C₄	—	94	2	no	—
1087	C₂×C₄	—	94	2	no	—
1088	C₂×C₄	—	94	2	no	—
1089	C₂×C₄	—	94	2	no	—
1090	C₂×C₄	—	376	2	no	—
1091	C₂×C₄	—	376	2	no	—
1092	C₂×C₄	—	376	2	no	—
1093	C₂×C₄	—	376	2	no	—
1094	C₂×C₄	—	376	1	no	—
1095	C₂×C₄	—	188	2	no	—
1096	C₂×C₄	—	188	2	no	—
1097	C₂×C₄	—	188	2	no	—
1098	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
1099	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
1100	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
1101	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
1102	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
1103	C₂×C₄	#41×D₄₇	1	2	yes	—
1104	C₂×C₄	C₂×#10625354	1	2	yes	—
1105	C₂×C₄	C₂⁴×D₄₇	1	1	yes	characteristic
1106	C₈	—	2	1	no	—
1107	C₈	—	2	1	no	—
1108	C₈	—	2	1	no	—
1109	C₈	—	2	1	no	—
1110	C₈	—	94	2	no	—
1111	C₈	—	94	2	no	—
1112	C₂²	—	2	1	no	—
1113	C₂²	—	2	1	no	—
1114	C₂²	—	2	2	no	—
1115	C₂²	—	4	1	no	—
1116	C₂²	—	4	1	no	—
1117	C₂²	—	94	2	no	—
1118	C₂²	—	94	2	no	—
1119	C₂²	—	94	2	no	—
1120	C₂²	—	188	2	no	—
1121	C₂²	—	188	2	no	—
1122	C₂²	—	188	2	no	—
1123	C₂²	—	752	2	no	—
1124	C₂²	#15689636	1	2	yes	—
1125	C₂²	C₂²×D₄×D₄₇	1	1	yes	characteristic
1126	C₄	—	2	1	no	—
1127	C₄	—	2	1	no	—
1128	C₄	—	2	2	no	—
1129	C₄	—	2	1	no	—
1130	C₄	—	2	1	no	—
1131	C₄	—	4	1	no	—
1132	C₄	—	4	1	no	—
1133	C₄	—	4	1	no	—
1134	C₄	—	4	1	no	—
1135	C₄	—	4	1	no	—
1136	C₄	—	4	1	no	—
1137	C₄	—	94	2	no	—
1138	C₄	—	94	2	no	—
1139	C₄	—	94	4	no	—
1140	C₄	—	94	2	no	—
1141	C₄	—	188	2	no	—
1142	C₄	—	188	2	no	—
1143	C₄	#15689636	1	2	yes	—
1144	C₄	C₂×#41×D₄₇	1	1	yes	characteristic
1145	C₄	C₂²×#10625354	1	1	yes	characteristic
1146	C₂	—	2	2	no	—
1147	C₂	—	4	2	no	—
1148	C₂	—	376	2	no	—
1149	C₂	—	188	2	no	—
1150	C₂	C₂×#15689636	1	1	yes	characteristic
1151	C₂	#20258157	1	1	yes	characteristic
1152	C₂	#20258172	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂²×D₄×D₄₇
commutator, cosocle	C₂×C₄×C₄₇	C₂⁵
Frattini	C₂×C₄	C₂⁴×D₄₇
Fitting	C₄₇×#3076	C₂
socle	C₂²×C₄₇	C₂³×D₄
prime radical	#20252677	C₂
hypercenter	#3076	D₄₇
hypocenter	C₄₇	#60595
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #3076

Complements

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

N	H ≅ G/N	type
1. #20257286	C₂	semidirect
2. C₄×#13094071	C₂	semidirect
3. #20253670	C₂	semidirect
4. #20253655	C₂	semidirect
5. #20253624	C₂	semidirect
6. #20253622	C₂	semidirect
7. #20253564	C₂	semidirect
8. #20253502	C₂	semidirect
9. #20253473	C₂	semidirect
10. #20253411	C₂	semidirect
11. #20253360	C₂	semidirect
12. #20253349	C₂	semidirect
13. #20253189	C₂	semidirect
14. #20252882	C₂	semidirect
15. C₂×#15689346	C₂	semidirect
16. #20252686	C₂	semidirect
18. #20252255	C₂	semidirect
19. #20252246	C₂	semidirect
20. #20252234	C₂	semidirect
21. #20252223	C₂	semidirect
22. #20252053	C₂	semidirect
23. C₄₇×#3076	C₂	semidirect
46. #15689602	C₂²	semidirect
50. #15689599	C₂²	semidirect
55. C₄×#10625352	C₂²	semidirect
58. C₄×Q₈×D₄₇	C₂²	semidirect
59. #15689467	C₂²	semidirect
60. #15689466	C₂²	semidirect
61. #15689460	C₂²	semidirect
62. #15689455	C₂²	semidirect
67. #15689427	C₂²	semidirect
68. #15689427	C₂²	semidirect
69. #15689415	C₂²	semidirect
70. #15689405	C₂²	semidirect
79. #15689286	C₂²	semidirect
80. #15689286	C₂²	semidirect
81. #15689280	C₂²	semidirect
82. #15689280	C₂²	semidirect
88. #15689229	C₂²	semidirect
89. #15689229	C₂²	semidirect
90. #15689227	C₂²	semidirect
94. #15689220	C₂²	semidirect
95. #15689217	C₂²	semidirect
96. #15689217	C₂²	semidirect
97. #15689215	C₂²	semidirect
98. #15689214	C₂²	semidirect
103. #15689183	C₂²	semidirect
104. #15689183	C₂²	semidirect
105. #15689179	C₂²	semidirect
106. #15689175	C₂²	semidirect
122. C₄₇×#479	C₂²	semidirect
123. C₄₇×#479	C₂²	semidirect
124. C₄₇×#478	C₂²	semidirect
125. C₄₇×#478	C₂²	semidirect
126. C₄₇×#477	C₂²	semidirect
127. C₄₇×#476	C₂²	semidirect
128. C₄₇×#475	C₂²	semidirect
129. C₄₇×#474	C₂²	semidirect
583. #3076	D₄₇	semidirect
647. #479	C₂×D₄₇	semidirect
648. #479	C₂×D₄₇	semidirect
649. #478	C₂×D₄₇	semidirect
650. #478	C₂×D₄₇	semidirect
652. #477	C₂×D₄₇	semidirect
653. #476	C₂×D₄₇	semidirect
655. #475	C₂×D₄₇	semidirect
656. #474	C₂×D₄₇	semidirect
711. C₄₇	#60595	semidirect

Maximal subgroups

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

subgroup	index
#20257286	2
C₄×#13094071	2
#20253670	2
#20253655	2
#20253624	2
#20253622	2
#20253564	2
#20253502	2
#20253473	2
#20253411	2
#20253360	2
#20253349	2
#20253189	2
#20252882	2
C₂×#15689346	2
#20252686	2
#20252677	2
#20252255	2
#20252246	2
#20252234	2
#20252223	2
#20252053	2
C₄₇×#3076	2
#60595	47