Subgroups — #27088994

Order 12032.

1636 conjugacy classes of subgroups.

The subgroup lattice has 1072 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20257214	C₂	1	1	yes	maximal, characteristic, complemented
2	#20254680	C₂	1	2	yes	maximal, complemented
3	#20254665	C₂	1	2	yes	maximal, complemented
4	#20254650	C₂	1	2	yes	maximal, complemented
5	#20254650	C₂	1	2	yes	maximal, complemented
6	#20254624	C₂	1	2	yes	maximal, complemented
7	#20254590	C₂	1	2	yes	maximal, complemented
8	#20254552	C₂	1	2	yes	maximal, complemented
9	#20254543	C₂	1	2	yes	maximal, complemented
10	#20253922	C₂	1	1	yes	maximal, characteristic, complemented
11	#20253914	C₂	1	1	yes	maximal, characteristic, complemented
12	#20253753	C₂	1	1	yes	maximal, characteristic, complemented
13	#20253753	C₂	1	1	yes	maximal, characteristic, complemented
14	#20253373	C₂	1	1	yes	maximal, characteristic
15	#20253362	C₂	1	1	yes	maximal, characteristic
16	#20253351	C₂	1	1	yes	maximal, characteristic, complemented
17	#20253351	C₂	1	1	yes	maximal, characteristic, complemented
18	#20253210	C₂	1	1	yes	maximal, characteristic, complemented
19	#20253193	C₂	1	1	yes	maximal, characteristic, complemented
20	#20253176	C₂	1	1	yes	maximal, characteristic, complemented
21	C₂×#15689430	C₂	1	1	yes	maximal, characteristic, complemented
22	#20252054	C₂	1	1	yes	maximal, characteristic, complemented
23	C₄₇×#3461	C₂	1	1	yes	maximal, characteristic
24	#15689849	—	2	1	no	—
25	#15689849	—	2	1	no	—
26	#15689832	—	2	1	no	—
27	#15689832	—	2	2	no	—
28	#15689832	—	2	2	no	—
29	#15689832	—	2	1	no	—
30	#15689751	C₂²	1	1	yes	characteristic
31	#15689751	C₂²	1	1	yes	characteristic
32	#15689751	C₂²	1	2	yes	—
33	#15689751	C₂²	1	2	yes	—
34	#15689680	C₂²	1	1	yes	characteristic
35	#15689680	C₂²	1	2	yes	—
36	C₂×#13094016	C₂²	1	1	yes	characteristic
37	C₂×#13094016	C₂²	1	2	yes	—
38	#15689606	C₂²	1	1	yes	characteristic
39	#15689606	C₂²	1	1	yes	characteristic
40	#15689533	C₂²	1	2	yes	—
41	#15689533	C₂²	1	2	yes	—
42	#15689529	C₂²	1	2	yes	—
43	#15689529	C₂²	1	2	yes	—
44	#15689526	C₂²	1	2	yes	—
45	#15689522	C₂²	1	2	yes	—
46	#15689522	C₂²	1	2	yes	—
47	#15689519	C₂²	1	2	yes	—
48	#15689491	C₂²	1	2	yes	—
49	#15689491	C₂²	1	2	yes	—
50	#15689482	C₂²	1	2	yes	—
51	#15689482	C₂²	1	2	yes	—
52	#15689477	C₂²	1	2	yes	—
53	#15689477	C₂²	1	2	yes	—
54	#15689473	C₂²	1	2	yes	—
55	#15689473	C₂²	1	2	yes	—
56	#15689461	C₂²	1	2	yes	—
57	#15689461	C₂²	1	2	yes	—
58	#15689461	C₂²	1	2	yes	—
59	#15689461	C₂²	1	2	yes	—
60	#15689461	C₂²	1	2	yes	—
61	#15689461	C₂²	1	2	yes	—
62	#15689456	C₂²	1	2	yes	—
63	#15689456	C₂²	1	2	yes	—
64	#15689456	C₂²	1	2	yes	—
65	#15689451	C₂²	1	2	yes	—
66	#15689451	C₂²	1	2	yes	—
67	#15689451	C₂²	1	2	yes	—
68	#15689444	C₂²	1	2	yes	—
69	#15689444	C₂²	1	2	yes	—
70	#15689439	C₂²	1	2	yes	—
71	#15689434	C₂²	1	2	yes	—
72	#15689430	C₂²	1	2	yes	—
73	#15689430	C₂²	1	2	yes	—
74	#15689430	C₂²	1	2	yes	—
75	#15689430	C₂²	1	2	yes	—
76	#15689430	C₂²	1	1	yes	characteristic
77	#15689430	C₂²	1	2	yes	—
78	#15689430	C₂²	1	1	yes	characteristic
79	#15689430	C₂²	1	2	yes	—
80	#15689430	C₂²	1	2	yes	—
81	#15689430	C₂²	1	2	yes	—
82	#15689423	C₂²	1	2	yes	—
83	#15689423	C₂²	1	2	yes	—
84	#15689423	C₂²	1	1	yes	characteristic
85	#15689423	C₂²	1	1	yes	characteristic
86	#15689418	C₂²	1	2	yes	—
87	#15689418	C₂²	1	1	yes	characteristic
88	#15689413	C₂²	1	1	yes	characteristic
89	#15689408	C₂²	1	2	yes	—
90	#15689408	C₂²	1	1	yes	characteristic
91	#15689403	C₂²	1	1	yes	characteristic
92	#15689184	C₂²	1	2	yes	—
93	#15689184	C₂²	1	2	yes	—
94	#15689180	C₂²	1	2	yes	—
95	#15689176	C₂²	1	2	yes	—
96	#15689166	C₂²	1	1	yes	characteristic
97	#15689166	C₂²	1	1	yes	characteristic
98	#15689163	C₂²	1	1	yes	characteristic
99	#15689163	C₂²	1	1	yes	characteristic
100	#15689159	C₂²	1	1	yes	characteristic
101	#15689159	C₂²	1	1	yes	characteristic
102	C₂×#13093957	C₂²	1	1	yes	characteristic
103	C₂×#13093955	C₂²	1	1	yes	characteristic
104	#15689147	C₂²	1	1	yes	characteristic
105	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
106	#15689132	C₂²	1	1	yes	characteristic
107	#15689132	C₂²	1	1	yes	characteristic
108	#15689124	C₂²	1	1	yes	characteristic
109	#15689124	C₂²	1	1	yes	characteristic
110	#15689119	C₂²	1	1	yes	characteristic
111	#15689119	C₂²	1	1	yes	characteristic
112	C₂×#13093948	C₂²	1	1	yes	characteristic
113	C₂×#13093948	C₂²	1	1	yes	characteristic
114	#15689090	C₂²	1	1	yes	characteristic
115	#15689090	C₂²	1	1	yes	characteristic
116	#15689079	C₂²	1	1	yes	characteristic
117	#15689079	C₂²	1	1	yes	characteristic
118	C₄₇×#544	C₂²	1	1	yes	characteristic
119	C₄₇×#542	—	2	1	no	—
120	C₄₇×#542	C₂²	1	2	yes	—
121	C₄₇×#541	—	2	1	no	—
122	C₄₇×#541	C₂²	1	2	yes	—
123	C₄₇×#539	—	2	2	no	—
124	C₄₇×#537	C₂²	1	1	yes	characteristic
125	C₄₇×#536	C₂²	1	1	yes	characteristic
126	C₄₇×#536	C₂²	1	1	yes	characteristic
127	C₄₇×#533	—	2	1	no	—
128	C₄₇×#533	C₂²	1	2	yes	—
129	C₄₇×#529	—	2	2	no	—
130	C₄₇×#529	—	2	1	no	—
131	C₄₇×#529	C₂²	1	2	yes	—
132	C₄×#41×C₄₇	C₂²	1	1	yes	characteristic
133	C₄×#41×C₄₇	C₂²	1	1	yes	characteristic
134	C₂×C₄×Q₈×C₄₇	C₂²	1	1	yes	characteristic
135	C₂×#10625329	C₂³	1	1	yes	characteristic
136	C₂×#10625329	C₂³	1	1	yes	characteristic
137	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
138	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
139	#13094024	C₂³	1	2	yes	—
140	#13094024	C₂³	1	2	yes	—
141	#13094024	C₂³	1	1	yes	characteristic
142	#13094024	C₂³	1	1	yes	characteristic
143	#13094023	—	2	1	no	—
144	#13094023	—	2	2	no	—
145	#13094023	—	2	1	no	—
146	#13094023	—	2	2	no	—
147	#13094016	—	2	1	no	—
148	#13094016	—	2	1	no	—
149	#13094016	—	2	2	no	—
150	#13094016	—	2	2	no	—
151	#13094016	C₂³	1	2	yes	—
152	#13094016	C₂³	1	2	yes	—
153	#13094016	C₂³	1	2	yes	—
154	#13094016	C₂³	1	2	yes	—
155	#13094016	C₂³	1	1	yes	characteristic
156	#13094016	C₂³	1	1	yes	characteristic
157	#13094015	—	2	1	no	—
158	#13094015	—	2	2	no	—
159	#13094015	—	2	1	no	—
160	#13094015	—	2	2	no	—
161	#13094003	—	2	1	no	—
162	#13094003	—	2	1	no	—
163	#13094003	—	2	2	no	—
164	#13094003	—	2	2	no	—
165	#13094001	—	2	2	no	—
166	#13094001	—	2	2	no	—
167	#13094001	—	2	2	no	—
168	#13094001	—	2	2	no	—
169	#13094001	—	2	2	no	—
170	#13094001	—	2	2	no	—
171	Q₈×Dic₄₇	—	2	1	no	—
172	Q₈×Dic₄₇	—	2	1	no	—
173	C₄×Dic₉₄	—	2	1	no	—
174	C₄×Dic₉₄	—	2	1	no	—
175	C₄×Dic₉₄	—	2	2	no	—
176	C₄×Dic₉₄	—	2	2	no	—
177	D₄×Dic₄₇	—	2	2	no	—
178	D₄×Dic₄₇	—	2	2	no	—
179	D₄×Dic₄₇	—	2	1	no	—
180	D₄×Dic₄₇	—	2	1	no	—
181	#13093983	C₂³	1	1	yes	characteristic
182	#13093983	C₂³	1	1	yes	characteristic
183	#13093983	C₂³	1	2	yes	—
184	#13093983	C₂³	1	2	yes	—
185	C₂×C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic
186	C₂×C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic
187	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
188	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
189	C₂×Dic₄₇⋊C₄	—	2	1	no	—
190	C₂×Dic₄₇⋊C₄	—	2	1	no	—
191	C₂×Dic₄₇⋊C₄	—	2	2	no	—
192	C₂×Dic₄₇⋊C₄	—	2	2	no	—
193	#13093957	C₂³	1	1	yes	characteristic
194	#13093957	C₂³	1	2	yes	—
195	#13093957	C₂³	1	2	yes	—
196	#13093957	C₂³	1	2	yes	—
197	#13093957	C₂³	1	1	yes	characteristic
198	#13093957	C₂³	1	2	yes	—
199	#13093957	C₂³	1	2	yes	—
200	#13093957	C₂³	1	1	yes	characteristic
201	#13093957	C₂³	1	2	yes	—
202	#13093957	C₂³	1	1	yes	characteristic
203	#13093955	C₂³	1	1	yes	characteristic
204	#13093955	C₂³	1	2	yes	—
205	#13093955	C₂³	1	2	yes	—
206	#13093955	C₂³	1	2	yes	—
207	#13093955	C₂³	1	1	yes	characteristic
208	#13093955	C₂³	1	2	yes	—
209	#13093955	C₂³	1	2	yes	—
210	#13093955	C₂³	1	1	yes	characteristic
211	#13093955	C₂³	1	2	yes	—
212	#13093955	C₂³	1	1	yes	characteristic
213	C₄⋊(C₄₇⋊C₈)	C₂³	1	1	yes	characteristic
214	C₄⋊(C₄₇⋊C₈)	C₂³	1	1	yes	characteristic
215	C₄⋊(C₄₇⋊C₈)	C₂³	1	1	yes	characteristic
216	C₄⋊(C₄₇⋊C₈)	C₂³	1	1	yes	characteristic
217	C₄⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
218	C₄⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
219	#13093948	C₂³	1	1	yes	characteristic
220	#13093948	C₂³	1	1	yes	characteristic
221	#13093948	C₂³	1	2	yes	—
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	2	yes	—
228	#13093948	C₂³	1	2	yes	—
229	#13093948	C₂³	1	2	yes	—
230	#13093948	C₂³	1	2	yes	—
231	#13093948	C₂³	1	1	yes	characteristic
232	#13093948	C₂³	1	1	yes	characteristic
233	#13093945	C₂³	1	1	yes	characteristic
234	#13093945	C₂³	1	1	yes	characteristic
235	#13093945	C₂³	1	2	yes	—
236	#13093945	C₂³	1	2	yes	—
237	#13093945	C₂³	1	1	yes	characteristic
238	#13093945	C₂³	1	1	yes	characteristic
239	C₂²⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
240	C₂²⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
241	C₂²⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
242	C₂²⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
243	#13093935	C₂³	1	2	yes	—
244	#13093935	C₂³	1	2	yes	—
245	C₄×C₄₇⋊C₈	C₂³	1	2	yes	—
246	C₄×C₄₇⋊C₈	C₂³	1	2	yes	—
247	C₂×#41×C₄₇	C₂³	1	1	yes	characteristic
248	C₂×#41×C₄₇	C₂³	1	1	yes	characteristic
249	C₂²×Q₈×C₄₇	C₂³	1	1	yes	characteristic
250	C₄⋊Q₈×C₄₇	—	2	1	no	—
251	C₄⋊Q₈×C₄₇	—	2	1	no	—
252	C₄⋊Q₈×C₄₇	C₂³	1	2	yes	—
253	C₄⋊Q₈×C₄₇	C₂³	1	2	yes	—
254	#126×C₄₇	—	2	2	no	—
255	#126×C₄₇	—	2	2	no	—
256	#126×C₄₇	—	2	2	no	—
257	#126×C₄₇	—	2	2	no	—
258	#125×C₄₇	—	2	2	no	—
259	#125×C₄₇	—	2	1	no	—
260	#125×C₄₇	—	2	2	no	—
261	#125×C₄₇	—	2	2	no	—
262	#125×C₄₇	C₂³	1	2	yes	—
263	#124×C₄₇	—	2	1	no	—
264	#124×C₄₇	—	2	2	no	—
265	#124×C₄₇	C₂³	1	2	yes	—
266	#123×C₄₇	—	2	2	no	—
267	#123×C₄₇	—	2	2	no	—
268	#123×C₄₇	—	2	2	no	—
269	#123×C₄₇	—	2	2	no	—
270	C₂²⋊Q₈×C₄₇	—	2	1	no	—
271	C₂²⋊Q₈×C₄₇	—	2	2	no	—
272	C₂²⋊Q₈×C₄₇	—	2	1	no	—
273	C₂²⋊Q₈×C₄₇	—	2	1	no	—
274	C₂²⋊Q₈×C₄₇	—	2	2	no	—
275	C₂²⋊Q₈×C₄₇	—	2	2	no	—
276	C₂²⋊Q₈×C₄₇	C₂³	1	2	yes	—
277	C₂²⋊Q₈×C₄₇	C₂³	1	2	yes	—
278	C₂²⋊Q₈×C₄₇	C₂³	1	2	yes	—
279	#121×C₄₇	—	2	2	no	—
280	#121×C₄₇	—	2	1	no	—
281	#121×C₄₇	C₂³	1	2	yes	—
282	C₄×Q₈×C₄₇	—	2	1	no	—
283	C₄×Q₈×C₄₇	—	2	1	no	—
284	C₄×Q₈×C₄₇	—	2	2	no	—
285	C₄×Q₈×C₄₇	D₄	1	1	yes	characteristic
286	C₄×Q₈×C₄₇	D₄	1	1	yes	characteristic
287	C₄×Q₈×C₄₇	C₂³	1	2	yes	—
288	C₄×Q₈×C₄₇	C₂³	1	2	yes	—
289	C₄×Q₈×C₄₇	C₂³	1	1	yes	characteristic
290	C₄×Q₈×C₄₇	C₂³	1	1	yes	characteristic
291	C₄×D₄×C₄₇	—	2	1	no	—
292	C₄×D₄×C₄₇	—	2	1	no	—
293	C₄×D₄×C₄₇	—	2	2	no	—
294	C₄×D₄×C₄₇	D₄	1	1	yes	characteristic
295	C₄×D₄×C₄₇	D₄	1	2	yes	—
296	C₄×D₄×C₄₇	D₄	1	2	yes	—
297	C₄×D₄×C₄₇	D₄	1	1	yes	characteristic
298	C₄×D₄×C₄₇	C₂³	1	1	yes	characteristic
299	C₄×D₄×C₄₇	C₂³	1	1	yes	characteristic
300	#117×C₄₇	—	2	2	no	—
301	#117×C₄₇	—	2	1	no	—
302	#117×C₄₇	—	2	2	no	—
303	#117×C₄₇	C₂³	1	1	yes	characteristic
304	#117×C₄₇	C₂³	1	1	yes	characteristic
305	#117×C₄₇	C₂³	1	2	yes	—
306	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
307	C₂×C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
308	C₂×C₄²×C₄₇	—	2	1	no	—
309	C₂×C₄²×C₄₇	—	2	1	no	—
310	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
311	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
312	#41×C₄₇	—	2	2	no	—
313	#41×C₄₇	—	2	2	no	—
314	#41×C₄₇	—	2	2	no	—
315	#41×C₄₇	—	2	2	no	—
316	C₂×Q₈×C₄₇	—	2	1	no	—
317	C₂×Q₈×C₄₇	—	2	2	no	—
318	C₂×Q₈×C₄₇	—	2	2	no	—
319	C₂×Q₈×C₄₇	—	2	2	no	—
320	C₂×Q₈×C₄₇	C₂×D₄	1	1	yes	characteristic
321	C₂×Q₈×C₄₇	C₂⁴	1	2	yes	—
322	C₂×Q₈×C₄₇	C₂⁴	1	1	yes	characteristic
323	C₂×D₄×C₄₇	—	2	1	no	—
324	C₂×D₄×C₄₇	—	2	2	no	—
325	C₂×D₄×C₄₇	C₂×D₄	1	2	yes	—
326	C₂×D₄×C₄₇	C₂×D₄	1	1	yes	characteristic
327	C₂×D₄×C₄₇	C₂⁴	1	1	yes	characteristic
328	C₂²×C₄×C₄₇	—	2	1	no	—
329	C₂²×C₄×C₄₇	—	2	1	no	—
330	C₂²×C₄×C₄₇	—	2	1	no	—
331	C₂²×C₄×C₄₇	—	2	1	no	—
332	C₂²×C₄×C₄₇	—	2	1	no	—
333	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
334	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
335	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
336	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
337	C₂²×C₄×C₄₇	C₂⁴	1	2	yes	—
338	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
339	C₂²×Dic₄₇	—	2	2	no	—
340	C₂²×Dic₄₇	—	2	2	no	—
341	C₂²×Dic₄₇	—	2	1	no	—
342	C₂²×Dic₄₇	—	2	1	no	—
343	C₂×Dic₉₄	—	2	1	no	—
344	C₂×Dic₉₄	—	2	1	no	—
345	C₂×Dic₉₄	—	2	2	no	—
346	C₂×Dic₉₄	—	2	2	no	—
347	C₄⋊C₄×C₄₇	—	2	2	no	—
348	C₄⋊C₄×C₄₇	—	2	2	no	—
349	C₄⋊C₄×C₄₇	—	2	1	no	—
350	C₄⋊C₄×C₄₇	—	2	1	no	—
351	C₄⋊C₄×C₄₇	—	2	1	no	—
352	C₄⋊C₄×C₄₇	—	2	2	no	—
353	C₄⋊C₄×C₄₇	—	2	2	no	—
354	C₄⋊C₄×C₄₇	—	2	2	no	—
355	C₄⋊C₄×C₄₇	—	2	2	no	—
356	C₄⋊C₄×C₄₇	—	2	2	no	—
357	C₄⋊C₄×C₄₇	—	2	2	no	—
358	C₄⋊C₄×C₄₇	—	2	2	no	—
359	C₄⋊C₄×C₄₇	—	2	2	no	—
360	C₄⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
361	C₄⋊C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
362	C₄⋊C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
363	C₄⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
364	C₄⋊C₄×C₄₇	C₂⁴	1	2	yes	—
365	C₄⋊C₄×C₄₇	C₂⁴	1	1	yes	characteristic
366	C₄⋊C₄×C₄₇	C₂⁴	1	1	yes	characteristic
367	C₂²⋊C₄×C₄₇	—	2	2	no	—
368	C₂²⋊C₄×C₄₇	—	2	2	no	—
369	C₂²⋊C₄×C₄₇	—	2	1	no	—
370	C₂²⋊C₄×C₄₇	—	2	2	no	—
371	C₂²⋊C₄×C₄₇	—	2	1	no	—
372	C₂²⋊C₄×C₄₇	—	2	1	no	—
373	C₂²⋊C₄×C₄₇	—	2	2	no	—
374	C₂²⋊C₄×C₄₇	—	2	2	no	—
375	C₂²⋊C₄×C₄₇	—	2	2	no	—
376	C₂²⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
377	C₂²⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
378	C₂²⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
379	C₄²×C₄₇	—	2	2	no	—
380	C₄²×C₄₇	—	2	1	no	—
381	C₄²×C₄₇	—	2	1	no	—
382	C₄²×C₄₇	—	2	1	no	—
383	C₄²×C₄₇	—	2	2	no	—
384	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
385	C₄²×C₄₇	C₂×D₄	1	2	yes	—
386	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
387	C₄²×C₄₇	C₂×D₄	1	2	yes	—
388	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
389	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
390	C₄²×C₄₇	C₂⁴	1	2	yes	—
391	C₂²⋊Dic₄₇	—	2	2	no	—
392	C₂²⋊Dic₄₇	—	2	2	no	—
393	C₂²⋊Dic₄₇	—	2	1	no	—
394	C₂²⋊Dic₄₇	—	2	1	no	—
395	C₄⋊Dic₄₇	—	2	2	no	—
396	C₄⋊Dic₄₇	—	2	2	no	—
397	C₄⋊Dic₄₇	—	2	1	no	—
398	C₄⋊Dic₄₇	—	2	1	no	—
399	C₄⋊Dic₄₇	—	2	1	no	—
400	C₄⋊Dic₄₇	—	2	1	no	—
401	C₄⋊Dic₄₇	—	2	2	no	—
402	C₄⋊Dic₄₇	—	2	2	no	—
403	C₄⋊Dic₄₇	C₂⁴	1	1	yes	characteristic
404	C₄⋊Dic₄₇	C₂⁴	1	2	yes	—
405	C₄⋊Dic₄₇	C₂⁴	1	1	yes	characteristic
406	C₄⋊Dic₄₇	C₂⁴	1	1	yes	characteristic
407	C₄⋊Dic₄₇	C₂⁴	1	2	yes	—
408	C₄⋊Dic₄₇	C₂⁴	1	1	yes	characteristic
409	Dic₄₇⋊C₄	—	2	2	no	—
410	Dic₄₇⋊C₄	—	2	1	no	—
411	Dic₄₇⋊C₄	—	2	2	no	—
412	Dic₄₇⋊C₄	—	2	1	no	—
413	Dic₄₇⋊C₄	—	2	2	no	—
414	Dic₄₇⋊C₄	—	2	2	no	—
415	Dic₄₇⋊C₄	—	2	2	no	—
416	Dic₄₇⋊C₄	—	2	2	no	—
417	Dic₄₇⋊C₄	—	2	2	no	—
418	Dic₄₇⋊C₄	—	2	2	no	—
419	Dic₄₇⋊C₄	—	2	1	no	—
420	Dic₄₇⋊C₄	—	2	1	no	—
421	C₄×Dic₄₇	—	2	2	no	—
422	C₄×Dic₄₇	—	2	2	no	—
423	C₄×Dic₄₇	—	2	1	no	—
424	C₄×Dic₄₇	—	2	1	no	—
425	#10625329	—	2	2	no	—
426	#10625329	—	2	2	no	—
427	C₂×C₄₇⋊C₈	—	2	2	no	—
428	C₂×C₄₇⋊C₈	—	2	2	no	—
429	C₂×C₄₇⋊C₈	C₂⁴	1	1	yes	characteristic
430	C₂×C₄₇⋊C₈	C₂⁴	1	1	yes	characteristic
431	C₂×C₄₇⋊C₈	C₂⁴	1	2	yes	—
432	C₂×C₄₇⋊C₈	C₂⁴	1	2	yes	—
433	C₂×C₄₇⋊C₈	C₂⁴	1	1	yes	characteristic
434	C₂×C₄₇⋊C₈	C₂⁴	1	1	yes	characteristic
435	C₂³×C₄₇	—	2	1	no	—
436	C₂³×C₄₇	C₂²×D₄	1	2	yes	—
437	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
438	Q₈×C₄₇	—	2	2	no	—
439	Q₈×C₄₇	—	2	2	no	—
440	Q₈×C₄₇	—	2	2	no	—
441	Q₈×C₄₇	—	2	1	no	—
442	Q₈×C₄₇	—	2	1	no	—
443	Q₈×C₄₇	—	4	2	no	—
444	Q₈×C₄₇	—	8	2	no	—
445	D₄×C₄₇	—	2	4	no	—
446	D₄×C₄₇	—	2	2	no	—
447	D₄×C₄₇	—	2	1	no	—
448	D₄×C₄₇	—	2	1	no	—
449	D₄×C₄₇	—	4	2	no	—
450	D₄×C₄₇	—	8	2	no	—
451	C₂×C₄×C₄₇	—	2	2	no	—
452	C₂×C₄×C₄₇	—	2	2	no	—
453	C₂×C₄×C₄₇	—	2	1	no	—
454	C₂×C₄×C₄₇	—	2	2	no	—
455	C₂×C₄×C₄₇	—	2	1	no	—
456	C₂×C₄×C₄₇	—	2	1	no	—
457	C₂×C₄×C₄₇	—	2	2	no	—
458	C₂×C₄×C₄₇	—	4	1	no	—
459	C₂×C₄×C₄₇	—	4	2	no	—
460	C₂×C₄×C₄₇	—	4	1	no	—
461	C₂×C₄×C₄₇	—	4	2	no	—
462	C₂×C₄×C₄₇	—	4	2	no	—
463	C₂×C₄×C₄₇	—	4	2	no	—
464	C₂×C₄×C₄₇	—	4	2	no	—
465	C₂×C₄×C₄₇	—	8	1	no	—
466	C₂×C₄×C₄₇	—	8	1	no	—
467	C₂×C₄×C₄₇	C₂²×D₄	1	2	yes	—
468	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
469	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
470	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
471	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
472	C₂×C₄×C₄₇	C₂²×D₄	1	2	yes	—
473	C₂×C₄×C₄₇	C₂²×D₄	1	2	yes	—
474	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
475	C₂×C₄×C₄₇	2₋¹⁺⁴	1	2	yes	—
476	C₂×C₄×C₄₇	2₋¹⁺⁴	1	2	yes	—
477	C₂×C₄×C₄₇	C₂⁵	1	1	yes	characteristic
478	C₂×Dic₄₇	—	2	1	no	—
479	C₂×Dic₄₇	—	2	1	no	—
480	C₂×Dic₄₇	—	2	2	no	—
481	C₂×Dic₄₇	—	2	1	no	—
482	C₂×Dic₄₇	—	2	2	no	—
483	C₂×Dic₄₇	—	2	1	no	—
484	C₂×Dic₄₇	—	8	1	no	—
485	C₂×Dic₄₇	—	8	2	no	—
486	C₂×Dic₄₇	—	8	1	no	—
487	C₂×Dic₄₇	—	8	2	no	—
488	Dic₉₄	—	8	1	no	—
489	Dic₉₄	—	8	2	no	—
490	Dic₉₄	—	8	1	no	—
491	Dic₉₄	—	8	2	no	—
492	C₄₇⋊C₈	—	2	1	no	—
493	C₄₇⋊C₈	—	2	1	no	—
494	C₄₇⋊C₈	—	2	1	no	—
495	C₄₇⋊C₈	—	2	1	no	—
496	C₄₇⋊C₈	—	2	2	no	—
497	C₄₇⋊C₈	—	2	2	no	—
498	#60891	—	47	1	no	maximal, Sylow
499	C₂²×C₄₇	—	2	1	no	—
500	C₂²×C₄₇	—	2	1	no	—
501	C₂²×C₄₇	—	2	2	no	—
502	C₂²×C₄₇	—	2	2	no	—
503	C₂²×C₄₇	—	2	2	no	—
504	C₂²×C₄₇	—	4	1	no	—
505	C₂²×C₄₇	—	4	1	no	—
506	C₂²×C₄₇	—	4	1	no	—
507	C₂²×C₄₇	#536	1	2	yes	—
508	C₂²×C₄₇	C₂³×D₄	1	1	yes	characteristic
509	C₄×C₄₇	—	2	1	no	—
510	C₄×C₄₇	—	2	2	no	—
511	C₄×C₄₇	—	2	1	no	—
512	C₄×C₄₇	—	2	1	no	—
513	C₄×C₄₇	—	2	2	no	—
514	C₄×C₄₇	—	2	1	no	—
515	C₄×C₄₇	—	2	2	no	—
516	C₄×C₄₇	—	4	2	no	—
517	C₄×C₄₇	—	4	1	no	—
518	C₄×C₄₇	—	4	1	no	—
519	C₄×C₄₇	—	4	1	no	—
520	C₄×C₄₇	—	4	2	no	—
521	C₄×C₄₇	#536	1	2	yes	—
522	C₄×C₄₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
523	C₄×C₄₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
524	Dic₄₇	—	4	1	no	—
525	Dic₄₇	—	4	1	no	—
526	Dic₄₇	—	4	2	no	—
527	Dic₄₇	—	4	1	no	—
528	Dic₄₇	—	4	2	no	—
529	Dic₄₇	—	4	1	no	—
530	#3504	—	47	1	no	—
531	#3461	D₄₇	1	1	yes	characteristic
532	#3244	—	47	2	no	—
533	#3243	—	47	2	no	—
534	#3242	—	47	2	no	—
535	#3242	—	47	2	no	—
536	#3240	—	47	2	no	—
537	#3236	—	47	2	no	—
538	#3232	—	47	2	no	—
539	#3231	—	47	2	no	—
540	#3164	—	47	1	no	—
541	#3163	—	47	1	no	—
542	#3137	—	47	1	no	—
543	#3137	—	47	1	no	—
544	#3099	—	47	1	no	—
545	#3098	—	47	1	no	—
546	#3097	—	47	1	no	—
547	#3097	—	47	1	no	—
548	#3080	—	47	1	no	—
549	#3078	—	47	1	no	—
550	#3076	—	47	1	no	—
551	C₂×#479	—	47	1	no	—
552	#2925	—	47	1	no	—
553	C₂×C₄₇	—	2	2	no	—
554	C₂×C₄₇	—	4	2	no	—
555	C₂×C₄₇	—	8	1	no	—
556	C₂×C₄₇	C₂×#536	1	1	yes	characteristic
557	C₂×C₄₇	#3584	1	1	yes	characteristic
558	C₂×C₄₇	#3586	1	1	yes	characteristic
559	#557	—	94	1	no	—
560	#557	—	94	1	no	—
561	#554	—	94	2	no	—
562	#554	—	94	1	no	—
563	#554	—	94	2	no	—
564	#554	—	94	1	no	—
565	#544	—	47	1	no	—
566	#544	—	47	1	no	—
567	#544	—	47	2	no	—
568	#544	—	47	2	no	—
569	#544	C₂×D₄₇	1	1	yes	characteristic
570	#542	—	2	1	no	—
571	#542	C₂×D₄₇	1	2	yes	—
572	#541	—	2	1	no	—
573	#541	C₂×D₄₇	1	2	yes	—
574	#539	—	2	2	no	—
575	#537	C₂×D₄₇	1	1	yes	characteristic
576	#536	C₂×D₄₇	1	1	yes	characteristic
577	#536	C₂×D₄₇	1	1	yes	characteristic
578	#533	—	2	1	no	—
579	#533	—	47	1	no	—
580	#533	—	47	2	no	—
581	#533	C₂×D₄₇	1	2	yes	—
582	#529	—	2	2	no	—
583	#529	—	2	1	no	—
584	#529	C₂×D₄₇	1	2	yes	—
585	C₂×#125	—	47	1	no	—
586	C₂×#125	—	47	2	no	—
587	#520	—	47	1	no	—
588	#520	—	47	1	no	—
589	C₄×#41	C₂×D₄₇	1	1	yes	characteristic
590	C₄×#41	C₂×D₄₇	1	1	yes	characteristic
591	C₂×C₄×Q₈	C₂×D₄₇	1	1	yes	characteristic
592	#501	—	47	2	no	—
593	#501	—	47	2	no	—
594	#501	—	47	2	no	—
595	#501	—	47	2	no	—
596	#500	—	47	2	no	—
597	#499	—	47	2	no	—
598	#499	—	47	2	no	—
599	#498	—	47	2	no	—
600	#491	—	47	2	no	—
601	#491	—	47	2	no	—
602	#489	—	47	2	no	—
603	#489	—	47	2	no	—
604	#488	—	47	2	no	—
605	#488	—	47	2	no	—
606	#487	—	47	2	no	—
607	#487	—	47	2	no	—
608	#485	—	47	2	no	—
609	#485	—	47	2	no	—
610	#485	—	47	2	no	—
611	#485	—	47	2	no	—
612	#485	—	47	2	no	—
613	#485	—	47	2	no	—
614	#484	—	47	2	no	—
615	#484	—	47	2	no	—
616	#484	—	47	2	no	—
617	#483	—	47	2	no	—
618	#483	—	47	2	no	—
619	#483	—	47	2	no	—
620	#482	—	47	2	no	—
621	#482	—	47	2	no	—
622	#481	—	47	2	no	—
623	#480	—	47	2	no	—
624	#479	—	47	2	no	—
625	#479	—	47	2	no	—
626	#479	—	47	2	no	—
627	#479	—	47	2	no	—
628	#479	—	47	1	no	—
629	#479	—	47	1	no	—
630	#479	—	47	2	no	—
631	#479	—	47	2	no	—
632	#479	—	47	2	no	—
633	#479	—	47	2	no	—
634	#478	—	47	1	no	—
635	#478	—	47	1	no	—
636	#478	—	47	2	no	—
637	#478	—	47	2	no	—
638	#477	—	47	1	no	—
639	#477	—	47	2	no	—
640	#476	—	47	1	no	—
641	#475	—	47	1	no	—
642	#475	—	47	2	no	—
643	#474	—	47	1	no	—
644	#433	—	47	2	no	—
645	#433	—	47	2	no	—
646	#432	—	47	2	no	—
647	#431	—	47	2	no	—
648	#428	—	47	1	no	—
649	#428	—	47	1	no	—
650	#428	—	47	1	no	—
651	#428	—	47	1	no	—
652	#427	—	47	1	no	—
653	#427	—	47	1	no	—
654	C₂×#107	—	47	1	no	—
655	C₂×#106	—	47	1	no	—
656	#423	—	47	1	no	—
657	C₂×C₄⋊C₈	—	47	1	no	—
658	#419	—	47	1	no	—
659	#419	—	47	1	no	—
660	#417	—	47	1	no	—
661	#417	—	47	1	no	—
662	#416	—	47	1	no	—
663	#416	—	47	1	no	—
664	C₂×#103	—	47	1	no	—
665	C₂×#103	—	47	1	no	—
666	#408	—	47	1	no	—
667	#408	—	47	1	no	—
668	#405	—	47	1	no	—
669	#405	—	47	1	no	—
670	C₄₇	#60891	1	1	yes	characteristic, complemented, Sylow
671	C₂×#41	C₂²×D₄₇	1	1	yes	characteristic
672	C₂×#41	C₂²×D₄₇	1	1	yes	characteristic
673	C₂²×Q₈	C₂²×D₄₇	1	1	yes	characteristic
674	C₂×M₁₆	—	47	1	no	—
675	C₂×M₁₆	—	47	1	no	—
676	C₂²×C₈	—	47	1	no	—
677	C₂²×C₈	—	47	1	no	—
678	C₄⋊Q₈	—	2	1	no	—
679	C₄⋊Q₈	—	2	1	no	—
680	C₄⋊Q₈	—	47	1	no	—
681	C₄⋊Q₈	—	47	1	no	—
682	C₄⋊Q₈	—	47	2	no	—
683	C₄⋊Q₈	—	47	2	no	—
684	C₄⋊Q₈	—	94	1	no	—
685	C₄⋊Q₈	—	94	2	no	—
686	C₄⋊Q₈	—	94	1	no	—
687	C₄⋊Q₈	—	94	2	no	—
688	C₄⋊Q₈	C₂²×D₄₇	1	2	yes	—
689	C₄⋊Q₈	C₂²×D₄₇	1	2	yes	—
690	#126	—	2	2	no	—
691	#126	—	2	2	no	—
692	#126	—	2	2	no	—
693	#126	—	2	2	no	—
694	#125	—	2	2	no	—
695	#125	—	2	1	no	—
696	#125	—	2	2	no	—
697	#125	—	2	2	no	—
698	#125	—	47	2	no	—
699	#125	—	47	1	no	—
700	#125	—	47	2	no	—
701	#125	—	47	2	no	—
702	#125	—	47	2	no	—
703	#125	—	47	1	no	—
704	#125	—	94	1	no	—
705	#125	—	94	2	no	—
706	#125	—	94	1	no	—
707	#125	—	94	2	no	—
708	#125	—	94	1	no	—
709	#125	—	94	1	no	—
710	#125	—	94	2	no	—
711	#125	—	94	2	no	—
712	#125	C₂²×D₄₇	1	2	yes	—
713	#124	—	2	1	no	—
714	#124	—	2	2	no	—
715	#124	C₂²×D₄₇	1	2	yes	—
716	#123	—	2	2	no	—
717	#123	—	2	2	no	—
718	#123	—	2	2	no	—
719	#123	—	2	2	no	—
720	C₂²⋊Q₈	—	2	1	no	—
721	C₂²⋊Q₈	—	2	2	no	—
722	C₂²⋊Q₈	—	2	1	no	—
723	C₂²⋊Q₈	—	2	1	no	—
724	C₂²⋊Q₈	—	2	2	no	—
725	C₂²⋊Q₈	—	2	2	no	—
726	C₂²⋊Q₈	—	94	1	no	—
727	C₂²⋊Q₈	—	94	1	no	—
728	C₂²⋊Q₈	—	94	2	no	—
729	C₂²⋊Q₈	—	94	2	no	—
730	C₂²⋊Q₈	—	94	2	no	—
731	C₂²⋊Q₈	—	94	2	no	—
732	C₂²⋊Q₈	—	94	2	no	—
733	C₂²⋊Q₈	—	94	2	no	—
734	C₂²⋊Q₈	—	94	2	no	—
735	C₂²⋊Q₈	—	94	2	no	—
736	C₂²⋊Q₈	C₂²×D₄₇	1	2	yes	—
737	C₂²⋊Q₈	C₂²×D₄₇	1	2	yes	—
738	C₂²⋊Q₈	C₂²×D₄₇	1	2	yes	—
739	#121	—	2	2	no	—
740	#121	—	2	1	no	—
741	#121	C₂²×D₄₇	1	2	yes	—
742	C₄×Q₈	—	2	1	no	—
743	C₄×Q₈	—	2	1	no	—
744	C₄×Q₈	—	2	2	no	—
745	C₄×Q₈	—	94	1	no	—
746	C₄×Q₈	—	94	1	no	—
747	C₄×Q₈	—	94	1	no	—
748	C₄×Q₈	—	94	1	no	—
749	C₄×Q₈	—	94	2	no	—
750	C₄×Q₈	—	94	2	no	—
751	C₄×Q₈	C₂²⋊D₄₇	1	1	yes	characteristic
752	C₄×Q₈	C₂²⋊D₄₇	1	1	yes	characteristic
753	C₄×Q₈	C₂²×D₄₇	1	2	yes	—
754	C₄×Q₈	C₂²×D₄₇	1	2	yes	—
755	C₄×Q₈	C₂²×D₄₇	1	1	yes	characteristic
756	C₄×Q₈	C₂²×D₄₇	1	1	yes	characteristic
757	C₄×D₄	—	2	1	no	—
758	C₄×D₄	—	2	1	no	—
759	C₄×D₄	—	2	2	no	—
760	C₄×D₄	—	94	2	no	—
761	C₄×D₄	—	94	2	no	—
762	C₄×D₄	—	94	1	no	—
763	C₄×D₄	—	94	1	no	—
764	C₄×D₄	C₂²⋊D₄₇	1	1	yes	characteristic
765	C₄×D₄	C₂²⋊D₄₇	1	2	yes	—
766	C₄×D₄	C₂²⋊D₄₇	1	2	yes	—
767	C₄×D₄	C₂²⋊D₄₇	1	1	yes	characteristic
768	C₄×D₄	C₂²×D₄₇	1	1	yes	characteristic
769	C₄×D₄	C₂²×D₄₇	1	1	yes	characteristic
770	#117	—	2	2	no	—
771	#117	—	2	1	no	—
772	#117	—	2	2	no	—
773	#117	—	47	1	no	—
774	#117	—	47	1	no	—
775	#117	—	47	2	no	—
776	#117	—	47	2	no	—
777	#117	C₂²×D₄₇	1	1	yes	characteristic
778	#117	C₂²×D₄₇	1	1	yes	characteristic
779	#117	C₂²×D₄₇	1	2	yes	—
780	C₂×C₄⋊C₄	—	2	1	no	—
781	C₂×C₄⋊C₄	—	47	1	no	—
782	C₂×C₄⋊C₄	—	47	1	no	—
783	C₂×C₄⋊C₄	—	47	2	no	—
784	C₂×C₄⋊C₄	—	47	2	no	—
785	C₂×C₄⋊C₄	—	94	1	no	—
786	C₂×C₄⋊C₄	—	94	1	no	—
787	C₂×C₄⋊C₄	—	94	2	no	—
788	C₂×C₄⋊C₄	—	94	2	no	—
789	C₂×C₄⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
790	C₂×C₄²	—	2	1	no	—
791	C₂×C₄²	—	2	1	no	—
792	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
793	C₂×C₄²	C₂²×D₄₇	1	2	yes	—
794	#107	—	47	2	no	—
795	#107	—	47	2	no	—
796	#107	—	47	1	no	—
797	#107	—	47	1	no	—
798	#107	—	47	1	no	—
799	#107	—	47	1	no	—
800	#107	—	47	2	no	—
801	#107	—	47	2	no	—
802	#107	—	47	2	no	—
803	#107	—	47	2	no	—
804	#106	—	47	2	no	—
805	#106	—	47	2	no	—
806	#106	—	47	1	no	—
807	#106	—	47	1	no	—
808	#106	—	47	1	no	—
809	#106	—	47	1	no	—
810	#106	—	47	2	no	—
811	#106	—	47	2	no	—
812	#106	—	47	2	no	—
813	#106	—	47	2	no	—
814	C₄⋊C₈	—	47	1	no	—
815	C₄⋊C₈	—	47	1	no	—
816	C₄⋊C₈	—	47	1	no	—
817	C₄⋊C₈	—	47	1	no	—
818	C₄⋊C₈	—	47	2	no	—
819	C₄⋊C₈	—	47	2	no	—
820	#103	—	47	2	no	—
821	#103	—	47	2	no	—
822	#103	—	47	2	no	—
823	#103	—	47	2	no	—
824	#103	—	47	1	no	—
825	#103	—	47	1	no	—
826	#103	—	47	1	no	—
827	#103	—	47	1	no	—
828	#103	—	47	2	no	—
829	#103	—	47	2	no	—
830	#103	—	47	2	no	—
831	#103	—	47	2	no	—
832	#103	—	47	2	no	—
833	#103	—	47	2	no	—
834	#102	—	47	1	no	—
835	#102	—	47	1	no	—
836	#102	—	47	1	no	—
837	#102	—	47	1	no	—
838	#102	—	47	2	no	—
839	#102	—	47	2	no	—
840	C₂²⋊C₈	—	47	2	no	—
841	C₂²⋊C₈	—	47	2	no	—
842	C₂²⋊C₈	—	47	2	no	—
843	C₂²⋊C₈	—	47	2	no	—
844	#97	—	47	2	no	—
845	#97	—	47	2	no	—
846	C₄×C₈	—	47	2	no	—
847	C₄×C₈	—	47	2	no	—
848	#41	—	2	2	no	—
849	#41	—	2	2	no	—
850	#41	—	2	2	no	—
851	#41	—	2	2	no	—
852	C₂×Q₈	—	2	1	no	—
853	C₂×Q₈	—	2	2	no	—
854	C₂×Q₈	—	2	2	no	—
855	C₂×Q₈	—	2	2	no	—
856	C₂×Q₈	—	94	1	no	—
857	C₂×Q₈	—	94	1	no	—
858	C₂×Q₈	—	94	2	no	—
859	C₂×Q₈	—	94	2	no	—
860	C₂×Q₈	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
861	C₂×Q₈	C₂³×D₄₇	1	2	yes	—
862	C₂×Q₈	C₂³×D₄₇	1	1	yes	characteristic
863	C₂×D₄	—	2	1	no	—
864	C₂×D₄	—	2	2	no	—
865	C₂×D₄	C₂×C₂²⋊D₄₇	1	2	yes	—
866	C₂×D₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
867	C₂×D₄	C₂³×D₄₇	1	1	yes	characteristic
868	C₂²×C₄	—	2	1	no	—
869	C₂²×C₄	—	2	1	no	—
870	C₂²×C₄	—	2	1	no	—
871	C₂²×C₄	—	2	1	no	—
872	C₂²×C₄	—	2	1	no	—
873	C₂²×C₄	—	94	2	no	—
874	C₂²×C₄	—	94	2	no	—
875	C₂²×C₄	—	94	1	no	—
876	C₂²×C₄	—	94	1	no	—
877	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
878	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
879	C₂²×C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
880	C₂²×C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
881	C₂²×C₄	C₂³×D₄₇	1	2	yes	—
882	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
883	M₁₆	—	94	2	no	—
884	M₁₆	—	94	2	no	—
885	C₂×C₈	—	47	1	no	—
886	C₂×C₈	—	47	1	no	—
887	C₂×C₈	—	47	2	no	—
888	C₂×C₈	—	47	2	no	—
889	C₂×C₈	—	47	1	no	—
890	C₂×C₈	—	47	1	no	—
891	C₂×C₈	—	94	2	no	—
892	C₂×C₈	—	94	2	no	—
893	C₄⋊C₄	—	2	2	no	—
894	C₄⋊C₄	—	2	2	no	—
895	C₄⋊C₄	—	2	1	no	—
896	C₄⋊C₄	—	2	1	no	—
897	C₄⋊C₄	—	2	1	no	—
898	C₄⋊C₄	—	2	2	no	—
899	C₄⋊C₄	—	2	2	no	—
900	C₄⋊C₄	—	2	2	no	—
901	C₄⋊C₄	—	2	2	no	—
902	C₄⋊C₄	—	2	2	no	—
903	C₄⋊C₄	—	2	2	no	—
904	C₄⋊C₄	—	2	2	no	—
905	C₄⋊C₄	—	2	2	no	—
906	C₄⋊C₄	—	47	1	no	—
907	C₄⋊C₄	—	47	2	no	—
908	C₄⋊C₄	—	47	1	no	—
909	C₄⋊C₄	—	47	1	no	—
910	C₄⋊C₄	—	47	2	no	—
911	C₄⋊C₄	—	47	1	no	—
912	C₄⋊C₄	—	94	2	no	—
913	C₄⋊C₄	—	94	1	no	—
914	C₄⋊C₄	—	94	2	no	—
915	C₄⋊C₄	—	94	1	no	—
916	C₄⋊C₄	—	94	2	no	—
917	C₄⋊C₄	—	94	2	no	—
918	C₄⋊C₄	—	94	2	no	—
919	C₄⋊C₄	—	94	2	no	—
920	C₄⋊C₄	—	94	2	no	—
921	C₄⋊C₄	—	94	2	no	—
922	C₄⋊C₄	—	94	1	no	—
923	C₄⋊C₄	—	94	1	no	—
924	C₄⋊C₄	—	94	2	no	—
925	C₄⋊C₄	—	94	2	no	—
926	C₄⋊C₄	—	94	1	no	—
927	C₄⋊C₄	—	94	1	no	—
928	C₄⋊C₄	—	94	1	no	—
929	C₄⋊C₄	—	94	1	no	—
930	C₄⋊C₄	—	94	2	no	—
931	C₄⋊C₄	—	94	2	no	—
932	C₄⋊C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
933	C₄⋊C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
934	C₄⋊C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
935	C₄⋊C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
936	C₄⋊C₄	C₂³×D₄₇	1	2	yes	—
937	C₄⋊C₄	C₂³×D₄₇	1	1	yes	characteristic
938	C₄⋊C₄	C₂³×D₄₇	1	1	yes	characteristic
939	C₂²⋊C₄	—	2	2	no	—
940	C₂²⋊C₄	—	2	2	no	—
941	C₂²⋊C₄	—	2	1	no	—
942	C₂²⋊C₄	—	2	2	no	—
943	C₂²⋊C₄	—	2	1	no	—
944	C₂²⋊C₄	—	2	1	no	—
945	C₂²⋊C₄	—	2	2	no	—
946	C₂²⋊C₄	—	2	2	no	—
947	C₂²⋊C₄	—	2	2	no	—
948	C₂²⋊C₄	—	94	2	no	—
949	C₂²⋊C₄	—	94	2	no	—
950	C₂²⋊C₄	—	94	1	no	—
951	C₂²⋊C₄	—	94	1	no	—
952	C₂²⋊C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
953	C₂²⋊C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
954	C₂²⋊C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
955	C₄²	—	2	2	no	—
956	C₄²	—	2	1	no	—
957	C₄²	—	2	1	no	—
958	C₄²	—	2	1	no	—
959	C₄²	—	2	2	no	—
960	C₄²	—	94	2	no	—
961	C₄²	—	94	2	no	—
962	C₄²	—	94	1	no	—
963	C₄²	—	94	1	no	—
964	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
965	C₄²	C₂×C₂²⋊D₄₇	1	2	yes	—
966	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
967	C₄²	C₂×C₂²⋊D₄₇	1	2	yes	—
968	C₄²	C₂³×D₄₇	1	2	yes	—
969	C₄²	C₂³×D₄₇	1	1	yes	characteristic
970	C₄²	C₂³×D₄₇	1	1	yes	characteristic
971	C₂³	—	2	1	no	—
972	C₂³	C₂²×C₂²⋊D₄₇	1	2	yes	—
973	C₂³	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
974	Q₈	—	2	2	no	—
975	Q₈	—	2	2	no	—
976	Q₈	—	2	2	no	—
977	Q₈	—	2	1	no	—
978	Q₈	—	2	1	no	—
979	Q₈	—	4	2	no	—
980	Q₈	—	8	2	no	—
981	Q₈	—	376	1	no	—
982	Q₈	—	376	2	no	—
983	Q₈	—	376	1	no	—
984	Q₈	—	376	2	no	—
985	D₄	—	2	4	no	—
986	D₄	—	2	2	no	—
987	D₄	—	2	1	no	—
988	D₄	—	2	1	no	—
989	D₄	—	4	2	no	—
990	D₄	—	8	2	no	—
991	C₂×C₄	—	2	2	no	—
992	C₂×C₄	—	2	2	no	—
993	C₂×C₄	—	2	1	no	—
994	C₂×C₄	—	2	2	no	—
995	C₂×C₄	—	2	1	no	—
996	C₂×C₄	—	2	1	no	—
997	C₂×C₄	—	2	2	no	—
998	C₂×C₄	—	4	1	no	—
999	C₂×C₄	—	4	2	no	—
1000	C₂×C₄	—	4	1	no	—
1001	C₂×C₄	—	4	2	no	—
1002	C₂×C₄	—	4	2	no	—
1003	C₂×C₄	—	4	2	no	—
1004	C₂×C₄	—	4	2	no	—
1005	C₂×C₄	—	8	1	no	—
1006	C₂×C₄	—	8	1	no	—
1007	C₂×C₄	—	94	1	no	—
1008	C₂×C₄	—	94	1	no	—
1009	C₂×C₄	—	94	2	no	—
1010	C₂×C₄	—	94	1	no	—
1011	C₂×C₄	—	94	2	no	—
1012	C₂×C₄	—	94	1	no	—
1013	C₂×C₄	—	376	1	no	—
1014	C₂×C₄	—	376	2	no	—
1015	C₂×C₄	—	376	1	no	—
1016	C₂×C₄	—	376	2	no	—
1017	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
1018	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
1019	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
1020	C₂×C₄	C₂²×C₂²⋊D₄₇	1	2	yes	—
1021	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
1022	C₂×C₄	C₂²×C₂²⋊D₄₇	1	2	yes	—
1023	C₂×C₄	C₂²×C₂²⋊D₄₇	1	2	yes	—
1024	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
1025	C₂×C₄	#13094071	1	2	yes	—
1026	C₂×C₄	#13094071	1	2	yes	—
1027	C₂×C₄	C₂⁴×D₄₇	1	1	yes	characteristic
1028	C₈	—	94	1	no	—
1029	C₈	—	94	1	no	—
1030	C₈	—	94	1	no	—
1031	C₈	—	94	1	no	—
1032	C₈	—	94	2	no	—
1033	C₈	—	94	2	no	—
1034	C₂²	—	2	1	no	—
1035	C₂²	—	2	1	no	—
1036	C₂²	—	2	2	no	—
1037	C₂²	—	2	2	no	—
1038	C₂²	—	2	2	no	—
1039	C₂²	—	4	1	no	—
1040	C₂²	—	4	1	no	—
1041	C₂²	—	4	1	no	—
1042	C₂²	#15689694	1	2	yes	—
1043	C₂²	C₂³×C₂²⋊D₄₇	1	1	yes	characteristic
1044	C₄	—	2	1	no	—
1045	C₄	—	2	1	no	—
1046	C₄	—	2	2	no	—
1047	C₄	—	2	1	no	—
1048	C₄	—	2	1	no	—
1049	C₄	—	2	2	no	—
1050	C₄	—	2	2	no	—
1051	C₄	—	4	2	no	—
1052	C₄	—	4	1	no	—
1053	C₄	—	4	1	no	—
1054	C₄	—	4	1	no	—
1055	C₄	—	4	2	no	—
1056	C₄	—	188	2	no	—
1057	C₄	—	188	1	no	—
1058	C₄	—	188	1	no	—
1059	C₄	—	188	2	no	—
1060	C₄	—	188	1	no	—
1061	C₄	—	188	1	no	—
1062	C₄	#15689694	1	2	yes	—
1063	C₄	C₂×#13094071	1	1	yes	characteristic
1064	C₄	C₂×#13094071	1	1	yes	characteristic
1065	C₂	—	2	2	no	—
1066	C₂	—	4	2	no	—
1067	C₂	—	8	1	no	—
1068	C₂	C₂×#15689694	1	1	yes	characteristic
1069	C₂	#20258159	1	1	yes	characteristic
1070	C₂	#20258175	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂³×C₂²⋊D₄₇
commutator, cosocle	C₂×C₄×C₄₇	C₂⁵
Frattini	C₂×C₄	C₂⁴×D₄₇
Fitting	C₄₇×#3461	C₂
socle	C₂²×C₄₇	C₂³×D₄
prime radical	C₄₇×#537	C₂²
hypercenter	#3461	D₄₇
hypocenter	C₄₇	#60891
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₄×#41 ◁ #3461

Complements

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

N	H ≅ G/N	type
1. #20257214	C₂	semidirect
2. #20254680	C₂	semidirect
3. #20254665	C₂	semidirect
4. #20254650	C₂	semidirect
5. #20254650	C₂	semidirect
6. #20254624	C₂	semidirect
7. #20254590	C₂	semidirect
8. #20254552	C₂	semidirect
9. #20254543	C₂	semidirect
10. #20253922	C₂	semidirect
11. #20253914	C₂	semidirect
12. #20253753	C₂	semidirect
13. #20253753	C₂	semidirect
16. #20253351	C₂	semidirect
17. #20253351	C₂	semidirect
18. #20253210	C₂	semidirect
19. #20253193	C₂	semidirect
20. #20253176	C₂	semidirect
21. C₂×#15689430	C₂	semidirect
22. #20252054	C₂	semidirect
670. C₄₇	#60891	semidirect

Maximal subgroups

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

subgroup	index
#20257214	2
#20254680	2
#20254665	2
#20254650	2
#20254624	2
#20254590	2
#20254552	2
#20254543	2
#20253922	2
#20253914	2
#20253753	2
#20253373	2
#20253362	2
#20253351	2
#20253210	2
#20253193	2
#20253176	2
C₂×#15689430	2
#20252054	2
C₄₇×#3461	2
#60891	47