Subgroups — #27106945

Order 12032.

1730 conjugacy classes of subgroups.

The subgroup lattice has 1120 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20257189	C₂	1	1	yes	maximal, characteristic, complemented
2	#20256342	C₂	1	2	yes	maximal, complemented
3	#20256305	C₂	1	1	yes	maximal, characteristic, complemented
4	#20256283	C₂	1	1	yes	maximal, characteristic, complemented
5	#20256259	C₂	1	1	yes	maximal, characteristic, complemented
6	#20256251	C₂	1	2	yes	maximal, complemented
7	Q₈×#10625334	C₂	1	1	yes	maximal, characteristic, complemented
8	#20256176	C₂	1	1	yes	maximal, characteristic, complemented
9	#20256135	C₂	1	2	yes	maximal, complemented
10	#20256091	C₂	1	1	yes	maximal, characteristic, complemented
11	#20256044	C₂	1	1	yes	maximal, characteristic, complemented
12	#20256044	C₂	1	2	yes	maximal, complemented
13	#20256019	C₂	1	1	yes	maximal, characteristic, complemented
14	#20254665	C₂	1	2	yes	maximal, complemented
15	#20254635	C₂	1	2	yes	maximal, complemented
16	#20254563	C₂	1	1	yes	maximal, characteristic, complemented
17	#20254520	C₂	1	1	yes	maximal, characteristic, complemented
18	#20253626	C₂	1	2	yes	maximal, complemented
19	#20253566	C₂	1	2	yes	maximal, complemented
20	#20253431	C₂	1	1	yes	maximal, characteristic, complemented
21	#20253384	C₂	1	1	yes	maximal, characteristic, complemented
22	#20252490	C₂	1	1	yes	maximal, characteristic, complemented
23	C₄₇×#3554	C₂	1	1	yes	maximal, characteristic, complemented
24	#15689834	—	2	1	no	—
25	#15689833	C₂²	1	1	yes	characteristic
26	#15689833	C₂²	1	1	yes	characteristic
27	#15689833	C₂²	1	2	yes	—
28	#15689833	C₂²	1	2	yes	—
29	#15689829	—	2	2	no	—
30	Q₈×D₁₈₈	C₂²	1	1	yes	characteristic
31	Q₈×D₁₈₈	C₂²	1	1	yes	characteristic
32	#15689788	—	2	1	no	—
33	#15689751	C₂²	1	2	yes	—
34	#15689748	—	2	2	no	—
35	#15689680	C₂²	1	1	yes	characteristic
36	C₂²⋊Q₈×D₄₇	—	2	1	no	—
37	C₂²⋊Q₈×D₄₇	—	2	1	no	—
38	#15689597	C₂²	1	2	yes	—
39	C₂×C₄×D₁₈₈	C₂²	1	1	yes	characteristic
40	#15689533	C₂²	1	2	yes	complemented
41	#15689529	C₂²	1	2	yes	complemented
42	#15689526	C₂²	1	1	yes	characteristic, complemented
43	#15689526	C₂²	1	2	yes	complemented
44	#15689522	C₂²	1	2	yes	complemented
45	#15689522	C₂²	1	2	yes	complemented
46	#15689519	C₂²	1	1	yes	characteristic, complemented
47	#15689487	C₂²	1	2	yes	complemented
48	#15689482	C₂²	1	2	yes	complemented
49	#15689477	C₂²	1	2	yes	complemented
50	#15689477	C₂²	1	2	yes	complemented
51	#15689469	C₂²	1	2	yes	complemented
52	#15689469	C₂²	1	1	yes	characteristic, complemented
53	#15689469	C₂²	1	1	yes	characteristic, complemented
54	#15689461	C₂²	1	2	yes	—
55	#15689456	C₂²	1	1	yes	characteristic
56	#15689444	C₂²	1	2	yes	—
57	#15689444	C₂²	1	2	yes	—
58	#15689444	C₂²	1	2	yes	—
59	#15689439	C₂²	1	1	yes	characteristic
60	#15689434	C₂²	1	2	yes	—
61	#15689430	C₂²	1	2	yes	complemented
62	#15689423	C₂²	1	2	yes	complemented
63	#15689423	C₂²	1	2	yes	complemented
64	#15689423	C₂²	1	2	yes	complemented
65	#15689423	C₂²	1	2	yes	complemented
66	#15689423	C₂²	1	2	yes	complemented
67	#15689420	C₂²	1	2	yes	—
68	#15689420	C₂²	1	2	yes	—
69	#15689420	C₂²	1	1	yes	characteristic
70	#15689420	C₂²	1	1	yes	characteristic
71	#15689418	C₂²	1	1	yes	characteristic, complemented
72	#15689418	C₂²	1	2	yes	complemented
73	#15689413	C₂²	1	1	yes	characteristic, complemented
74	#15689413	C₂²	1	2	yes	complemented
75	#15689410	C₂²	1	2	yes	—
76	#15689408	C₂²	1	1	yes	characteristic, complemented
77	#15689403	C₂²	1	2	yes	complemented
78	#15689403	C₂²	1	1	yes	characteristic, complemented
79	#15689403	C₂²	1	2	yes	complemented
80	#15689400	C₂²	1	1	yes	characteristic
81	#15689400	C₂²	1	1	yes	characteristic
82	#15689400	C₂²	1	2	yes	—
83	#15689335	C₂²	1	1	yes	characteristic
84	#15689335	C₂²	1	2	yes	—
85	#15689335	C₂²	1	2	yes	—
86	#15689335	C₂²	1	1	yes	characteristic
87	#15689315	C₂²	1	1	yes	characteristic
88	#15689315	C₂²	1	2	yes	—
89	#15689315	C₂²	1	2	yes	—
90	#15689315	C₂²	1	1	yes	characteristic
91	#15689273	C₂²	1	1	yes	characteristic
92	#15689256	C₂²	1	2	yes	—
93	#15689256	C₂²	1	1	yes	characteristic
94	#15689254	C₂²	1	1	yes	characteristic, complemented
95	#15689254	C₂²	1	1	yes	characteristic, complemented
96	#15689254	C₂²	1	2	yes	complemented
97	Q₈×C₄₇⋊C₈	C₂²	1	1	yes	characteristic, complemented
98	Q₈×C₄₇⋊C₈	C₂²	1	1	yes	characteristic, complemented
99	Q₈×C₄₇⋊C₈	C₂²	1	2	yes	complemented
100	#15689233	C₂²	1	2	yes	—
101	#15689233	C₂²	1	2	yes	—
102	#15689233	C₂²	1	2	yes	—
103	#15689221	C₂²	1	2	yes	—
104	C₄×#10625336	C₂²	1	2	yes	—
105	C₄×#10625336	C₂²	1	1	yes	characteristic
106	C₄×#10625336	C₂²	1	1	yes	characteristic
107	C₄×#10625334	C₂²	1	1	yes	characteristic
108	C₄×#10625334	C₂²	1	2	yes	—
109	C₄×#10625334	C₂²	1	2	yes	—
110	C₄×#10625334	C₂²	1	2	yes	—
111	C₄×#10625334	C₂²	1	2	yes	—
112	C₄×#10625334	C₂²	1	1	yes	characteristic
113	C₄×#10625334	C₂²	1	2	yes	—
114	#15689184	C₂²	1	2	yes	—
115	#15689184	C₂²	1	2	yes	—
116	#15689176	C₂²	1	1	yes	characteristic
117	#15689176	C₂²	1	1	yes	characteristic
118	C₄₇×#562	—	2	2	no	—
119	C₄₇×#559	C₂²	1	2	yes	complemented
120	C₄₇×#559	C₂²	1	1	yes	characteristic, complemented
121	C₄₇×#557	C₂²	1	1	yes	characteristic, complemented
122	C₄₇×#554	C₂²	1	2	yes	complemented
123	C₄₇×#550	C₂²	1	1	yes	characteristic, complemented
124	D₄×Q₈×C₄₇	C₂²	1	1	yes	characteristic, complemented
125	C₄₇×#548	—	2	1	no	—
126	C₄₇×#547	—	2	1	no	—
127	C₄₇×#542	—	2	1	no	—
128	C₄₇×#542	C₂²	1	2	yes	—
129	C₄₇×#540	C₂²	1	2	yes	—
130	C₄₇×#539	—	2	2	no	—
131	C₄₇×#536	—	2	1	no	—
132	C₄₇×#533	C₂²	1	1	yes	characteristic
133	C₄₇×#532	C₂²	1	1	yes	characteristic
134	C₄₇×#529	C₂²	1	1	yes	characteristic
135	C₂×Q₈×D₄₇	—	2	1	no	—
136	C₂×Q₈×D₄₇	—	2	1	no	—
137	C₂²×D₁₈₈	C₂³	1	1	yes	characteristic
138	C₂²×C₄×D₄₇	—	2	1	no	—
139	C₂×#10625336	C₂³	1	1	yes	characteristic
140	C₂×#10625336	C₂³	1	1	yes	characteristic
141	C₂×#10625334	C₂³	1	1	yes	characteristic
142	C₂×#10625334	C₂³	1	2	yes	—
143	C₂×#10625334	C₂³	1	2	yes	—
144	C₂×#10625334	C₂³	1	1	yes	characteristic
145	#13094024	C₂³	1	2	yes	—
146	#13094024	C₂³	1	2	yes	—
147	#13094024	C₂³	1	1	yes	characteristic
148	#13094024	C₂³	1	1	yes	characteristic
149	#13094023	—	2	2	no	—
150	#13094016	C₂³	1	2	yes	—
151	#13094016	C₂³	1	2	yes	—
152	#13094016	C₂³	1	2	yes	—
153	#13094015	—	2	2	no	—
154	#13094004	—	2	2	no	—
155	#13094004	—	2	2	no	—
156	#13094004	—	2	1	no	—
157	#13094004	—	2	1	no	—
158	#13094003	—	2	1	no	—
159	#13094003	—	2	1	no	—
160	#13094002	—	2	2	no	—
161	#13094002	—	2	2	no	—
162	#13094002	—	2	2	no	—
163	#13094002	—	2	2	no	—
164	#13094002	—	2	2	no	—
165	#13094002	—	2	2	no	—
166	#13094001	—	2	2	no	—
167	#13094001	—	2	2	no	—
168	#13094000	—	2	2	no	—
169	#13094000	—	2	2	no	—
170	#13094000	—	2	1	no	—
171	#13094000	—	2	1	no	—
172	C₄×Dic₉₄	—	2	1	no	—
173	C₄×Dic₉₄	—	2	1	no	—
174	C₄×D₁₈₈	—	2	1	no	—
175	C₄×D₁₈₈	—	2	1	no	—
176	C₄×D₁₈₈	C₂³	1	2	yes	—
177	C₄×D₁₈₈	C₂³	1	2	yes	—
178	C₄×D₁₈₈	C₂³	1	2	yes	—
179	C₄×D₁₈₈	C₂³	1	2	yes	—
180	C₄×D₁₈₈	C₂³	1	1	yes	characteristic
181	C₄×D₁₈₈	C₂³	1	1	yes	characteristic
182	C₄×D₁₈₈	C₂³	1	1	yes	characteristic
183	C₄×D₁₈₈	C₂³	1	1	yes	characteristic
184	#13093986	—	2	2	no	—
185	#13093986	—	2	2	no	—
186	#13093983	C₂³	1	2	yes	—
187	C₂×C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic
188	C₄⋊C₄×D₄₇	—	2	2	no	—
189	C₄⋊C₄×D₄₇	—	2	2	no	—
190	C₄⋊C₄×D₄₇	—	2	1	no	—
191	C₄⋊C₄×D₄₇	—	2	1	no	—
192	C₂×(C₂×D₄₇)⋊C₄	—	2	1	no	—
193	C₂²⋊C₄×D₄₇	—	2	2	no	—
194	C₂²⋊C₄×D₄₇	—	2	2	no	—
195	#13093957	C₂³	1	2	yes	—
196	#13093957	C₂³	1	2	yes	—
197	#13093957	C₂³	1	2	yes	—
198	#13093957	C₂³	1	2	yes	—
199	#13093957	C₂³	1	2	yes	—
200	#13093957	C₂³	1	1	yes	characteristic
201	#13093957	C₂³	1	1	yes	characteristic
202	#13093957	C₂³	1	2	yes	—
203	#13093955	C₂³	1	2	yes	—
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	1	yes	characteristic
209	C₄⋊(C₄₇⋊C₈)	C₂³	1	1	yes	characteristic
210	C₄⋊(C₄₇⋊C₈)	C₂³	1	1	yes	characteristic
211	C₄⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
212	C₄⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
213	C₄⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
214	C₄⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
215	C₄⋊(C₄₇⋊C₈)	C₂³	1	1	yes	characteristic
216	C₄⋊(C₄₇⋊C₈)	C₂³	1	1	yes	characteristic
217	#13093948	C₂³	1	2	yes	—
218	#13093948	C₂³	1	1	yes	characteristic
219	#13093948	C₂³	1	2	yes	—
220	#13093948	C₂³	1	1	yes	characteristic
221	#13093945	C₂³	1	2	yes	—
222	#13093945	C₂³	1	2	yes	—
223	#13093945	C₂³	1	2	yes	—
224	#13093945	C₂³	1	2	yes	—
225	#13093945	C₂³	1	2	yes	—
226	#13093945	C₂³	1	2	yes	—
227	#13093945	C₂³	1	1	yes	characteristic
228	#13093945	C₂³	1	2	yes	—
229	#13093945	C₂³	1	2	yes	—
230	#13093945	C₂³	1	1	yes	characteristic
231	#13093944	C₂³	1	2	yes	—
232	#13093944	C₂³	1	1	yes	characteristic
233	#13093944	C₂³	1	1	yes	characteristic
234	#13093944	C₂³	1	2	yes	—
235	#13093944	C₂³	1	1	yes	characteristic
236	#13093944	C₂³	1	1	yes	characteristic
237	C₂²⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
238	C₂²⋊(C₄₇⋊C₈)	C₂³	1	1	yes	characteristic
239	C₂²⋊(C₄₇⋊C₈)	C₂³	1	1	yes	characteristic
240	#13093935	C₂³	1	2	yes	—
241	#13093935	C₂³	1	2	yes	—
242	C₄×C₄₇⋊C₈	C₂³	1	2	yes	—
243	C₄×C₄₇⋊C₈	C₂³	1	2	yes	—
244	C₄×C₄₇⋊C₈	C₂³	1	2	yes	—
245	C₄×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
246	C₄×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
247	C₂×#41×C₄₇	—	2	1	no	—
248	C₂×#41×C₄₇	—	2	1	no	—
249	C₂²×Q₈×C₄₇	—	2	1	no	—
250	C₄⋊Q₈×C₄₇	—	2	1	no	—
251	C₄⋊Q₈×C₄₇	D₄	1	1	yes	characteristic
252	C₄⋊Q₈×C₄₇	D₄	1	1	yes	characteristic
253	C₄⋊Q₈×C₄₇	C₂³	1	1	yes	characteristic
254	C₄⋊Q₈×C₄₇	C₂³	1	2	yes	—
255	#127×C₄₇	C₂³	1	2	yes	—
256	#127×C₄₇	C₂³	1	1	yes	characteristic
257	#126×C₄₇	—	2	2	no	—
258	#126×C₄₇	—	2	1	no	—
259	#125×C₄₇	—	2	2	no	—
260	#125×C₄₇	D₄	1	2	yes	—
261	#125×C₄₇	C₂³	1	1	yes	characteristic
262	#125×C₄₇	C₂³	1	2	yes	—
263	#124×C₄₇	—	2	1	no	—
264	#124×C₄₇	—	2	2	no	—
265	#124×C₄₇	—	2	2	no	—
266	#124×C₄₇	—	2	1	no	—
267	#124×C₄₇	C₂³	1	1	yes	characteristic
268	#124×C₄₇	C₂³	1	2	yes	—
269	#123×C₄₇	—	2	1	no	—
270	#123×C₄₇	—	2	2	no	—
271	#123×C₄₇	—	2	2	no	—
272	#123×C₄₇	—	2	2	no	—
273	#123×C₄₇	—	2	2	no	—
274	#123×C₄₇	—	2	2	no	—
275	#123×C₄₇	—	2	2	no	—
276	C₂²⋊Q₈×C₄₇	—	2	2	no	—
277	C₂²⋊Q₈×C₄₇	—	2	2	no	—
278	C₂²⋊Q₈×C₄₇	—	2	2	no	—
279	C₂²⋊Q₈×C₄₇	—	2	2	no	—
280	C₂²⋊Q₈×C₄₇	—	2	2	no	—
281	C₂²⋊Q₈×C₄₇	—	2	1	no	—
282	C₂²⋊Q₈×C₄₇	D₄	1	2	yes	—
283	C₂²⋊Q₈×C₄₇	D₄	1	1	yes	characteristic
284	C₂²⋊Q₈×C₄₇	D₄	1	1	yes	characteristic
285	C₂²⋊Q₈×C₄₇	C₂³	1	1	yes	characteristic
286	#121×C₄₇	—	2	1	no	—
287	#121×C₄₇	—	2	2	no	—
288	#121×C₄₇	—	2	1	no	—
289	#121×C₄₇	—	2	2	no	—
290	#121×C₄₇	—	2	2	no	—
291	#121×C₄₇	C₂³	1	1	yes	characteristic
292	#121×C₄₇	C₂³	1	2	yes	—
293	C₄×Q₈×C₄₇	—	2	1	no	—
294	C₄×Q₈×C₄₇	C₂³	1	2	yes	—
295	C₄×Q₈×C₄₇	C₂³	1	1	yes	characteristic
296	C₄×Q₈×C₄₇	C₂³	1	1	yes	characteristic
297	C₄×Q₈×C₄₇	C₂³	1	1	yes	characteristic
298	C₄×Q₈×C₄₇	C₂³	1	2	yes	—
299	C₄×D₄×C₄₇	—	2	1	no	—
300	C₄×D₄×C₄₇	—	2	2	no	—
301	C₄×D₄×C₄₇	—	2	1	no	—
302	C₄×D₄×C₄₇	—	2	1	no	—
303	C₄×D₄×C₄₇	C₂³	1	2	yes	—
304	C₄×D₄×C₄₇	C₂³	1	2	yes	—
305	C₄×D₄×C₄₇	C₂³	1	2	yes	—
306	C₄×D₄×C₄₇	C₂³	1	1	yes	characteristic
307	C₄×D₄×C₄₇	C₂³	1	2	yes	—
308	#117×C₄₇	—	2	1	no	—
309	#117×C₄₇	C₂³	1	2	yes	—
310	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
311	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
312	C₂³×D₄₇	—	2	1	no	—
313	#41×C₄₇	—	8	2	no	—
314	#41×C₄₇	—	8	2	no	—
315	C₂×Q₈×C₄₇	—	2	1	no	—
316	C₂×Q₈×C₄₇	—	2	2	no	—
317	C₂×Q₈×C₄₇	—	8	2	no	—
318	C₂×Q₈×C₄₇	C₂×D₄	1	1	yes	characteristic
319	C₂×Q₈×C₄₇	C₂×D₄	1	1	yes	characteristic
320	C₂×Q₈×C₄₇	C₂×D₄	1	2	yes	—
321	C₂×Q₈×C₄₇	C₂⁴	1	1	yes	characteristic
322	C₂×D₄×C₄₇	—	2	1	no	—
323	C₂×D₄×C₄₇	—	2	2	no	—
324	C₂×D₄×C₄₇	—	2	1	no	—
325	C₂×D₄×C₄₇	—	2	1	no	—
326	C₂×D₄×C₄₇	—	2	2	no	—
327	C₂×D₄×C₄₇	—	2	2	no	—
328	C₂×D₄×C₄₇	C₂⁴	1	1	yes	characteristic
329	C₂×D₄×C₄₇	C₂⁴	1	2	yes	—
330	C₂²×C₄×C₄₇	—	2	1	no	—
331	C₂²×C₄×C₄₇	—	2	2	no	—
332	C₂²×C₄×C₄₇	—	2	2	no	—
333	C₂²×C₄×C₄₇	—	2	2	no	—
334	C₂²×C₄×C₄₇	—	2	2	no	—
335	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
336	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
337	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
338	C₂²×Dic₄₇	—	2	1	no	—
339	Q₈×D₄₇	—	8	2	no	—
340	Q₈×D₄₇	—	8	2	no	—
341	C₂×D₁₈₈	—	2	1	no	—
342	C₂×D₁₈₈	—	2	2	no	—
343	C₂×D₁₈₈	—	2	2	no	—
344	C₂×D₁₈₈	C₂⁴	1	1	yes	characteristic
345	C₂×D₁₈₈	C₂⁴	1	1	yes	characteristic
346	C₂×C₄×D₄₇	—	2	1	no	—
347	C₂×C₄×D₄₇	—	2	1	no	—
348	C₂×C₄×D₄₇	—	2	2	no	—
349	C₂×C₄×D₄₇	—	2	2	no	—
350	C₂×C₄×D₄₇	—	2	2	no	—
351	C₂×C₄×D₄₇	—	2	2	no	—
352	C₂×C₄×D₄₇	—	2	1	no	—
353	C₂×C₄×D₄₇	—	2	1	no	—
354	C₂×C₄×D₄₇	—	8	2	no	—
355	C₂×Dic₉₄	—	2	1	no	—
356	C₂×Dic₉₄	—	2	1	no	—
357	C₂×Dic₉₄	—	2	2	no	—
358	C₂×Dic₉₄	—	2	2	no	—
359	C₄⋊C₄×C₄₇	—	2	1	no	—
360	C₄⋊C₄×C₄₇	—	2	2	no	—
361	C₄⋊C₄×C₄₇	—	2	2	no	—
362	C₄⋊C₄×C₄₇	—	2	1	no	—
363	C₄⋊C₄×C₄₇	—	2	1	no	—
364	C₄⋊C₄×C₄₇	—	2	1	no	—
365	C₄⋊C₄×C₄₇	—	2	2	no	—
366	C₄⋊C₄×C₄₇	—	2	2	no	—
367	C₄⋊C₄×C₄₇	—	2	1	no	—
368	C₄⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
369	C₄⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
370	C₄⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
371	C₄⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
372	C₄⋊C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
373	C₄⋊C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
374	C₄⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
375	C₄⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
376	C₄⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
377	C₄⋊C₄×C₄₇	C₂⁴	1	1	yes	characteristic
378	C₄⋊C₄×C₄₇	C₂⁴	1	1	yes	characteristic
379	C₄⋊C₄×C₄₇	C₂⁴	1	2	yes	—
380	C₂²⋊C₄×C₄₇	—	2	1	no	—
381	C₂²⋊C₄×C₄₇	—	2	1	no	—
382	C₂²⋊C₄×C₄₇	—	2	1	no	—
383	C₂²⋊C₄×C₄₇	—	2	1	no	—
384	C₂²⋊C₄×C₄₇	—	2	2	no	—
385	C₂²⋊C₄×C₄₇	—	2	2	no	—
386	C₂²⋊C₄×C₄₇	—	2	2	no	—
387	C₂²⋊C₄×C₄₇	—	2	1	no	—
388	C₂²⋊C₄×C₄₇	—	2	2	no	—
389	C₂²⋊C₄×C₄₇	—	2	2	no	—
390	C₂²⋊C₄×C₄₇	—	2	2	no	—
391	C₂²⋊C₄×C₄₇	—	2	2	no	—
392	C₂²⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
393	C₂²⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
394	C₄²×C₄₇	—	2	1	no	—
395	C₄²×C₄₇	—	2	2	no	—
396	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
397	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
398	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
399	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
400	C₄²×C₄₇	C₂⁴	1	2	yes	—
401	C₄²×C₄₇	C₂⁴	1	2	yes	—
402	C₂²⋊Dic₄₇	—	2	2	no	—
403	#10625336	—	2	2	no	—
404	#10625336	—	2	2	no	—
405	#10625334	—	2	2	no	—
406	#10625334	—	2	4	no	—
407	#10625334	—	2	4	no	—
408	#10625334	—	2	2	no	—
409	(C₂×D₄₇)⋊C₄	—	2	2	no	—
410	(C₂×D₄₇)⋊C₄	—	2	2	no	—
411	(C₂×D₄₇)⋊C₄	—	2	2	no	—
412	(C₂×D₄₇)⋊C₄	—	2	2	no	—
413	(C₂×D₄₇)⋊C₄	—	2	1	no	—
414	(C₂×D₄₇)⋊C₄	—	2	1	no	—
415	(C₂×D₄₇)⋊C₄	—	2	1	no	—
416	(C₂×D₄₇)⋊C₄	—	2	1	no	—
417	C₄⋊Dic₄₇	—	2	1	no	—
418	C₄⋊Dic₄₇	—	2	2	no	—
419	C₄⋊Dic₄₇	—	2	2	no	—
420	C₄⋊Dic₄₇	—	2	1	no	—
421	C₄⋊Dic₄₇	—	2	1	no	—
422	C₄⋊Dic₄₇	C₂⁴	1	2	yes	—
423	C₄⋊Dic₄₇	C₂⁴	1	1	yes	characteristic
424	C₄⋊Dic₄₇	C₂⁴	1	1	yes	characteristic
425	C₄⋊Dic₄₇	C₂⁴	1	2	yes	—
426	Dic₄₇⋊C₄	—	2	2	no	—
427	Dic₄₇⋊C₄	—	2	2	no	—
428	Dic₄₇⋊C₄	—	2	2	no	—
429	Dic₄₇⋊C₄	—	2	2	no	—
430	Dic₄₇⋊C₄	—	2	2	no	—
431	Dic₄₇⋊C₄	—	2	2	no	—
432	C₄×Dic₄₇	—	2	2	no	—
433	C₂×C₄₇⋊C₈	C₂⁴	1	1	yes	characteristic
434	C₂×C₄₇⋊C₈	C₂⁴	1	1	yes	characteristic
435	C₂×C₄₇⋊C₈	C₂⁴	1	2	yes	—
436	C₂×C₄₇⋊C₈	C₂⁴	1	1	yes	characteristic
437	C₂×C₄₇⋊C₈	C₂⁴	1	2	yes	—
438	C₂×C₄₇⋊C₈	C₂⁴	1	1	yes	characteristic
439	C₂³×C₄₇	—	2	2	no	—
440	C₂³×C₄₇	—	2	1	no	—
441	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
442	C₂²×D₄₇	—	2	1	no	—
443	C₂²×D₄₇	—	2	1	no	—
444	C₂²×D₄₇	—	2	4	no	—
445	C₂²×D₄₇	—	8	1	no	—
446	C₂²×D₄₇	—	8	1	no	—
447	Q₈×C₄₇	—	2	2	no	—
448	Q₈×C₄₇	—	2	2	no	—
449	Q₈×C₄₇	—	2	1	no	—
450	Q₈×C₄₇	—	2	1	no	—
451	Q₈×C₄₇	—	4	2	no	—
452	Q₈×C₄₇	—	4	2	no	—
453	Q₈×C₄₇	—	8	2	no	—
454	D₄×C₄₇	—	2	1	no	—
455	D₄×C₄₇	—	2	2	no	—
456	D₄×C₄₇	—	2	1	no	—
457	D₄×C₄₇	—	2	2	no	—
458	D₄×C₄₇	—	4	2	no	—
459	D₄×C₄₇	—	8	1	no	—
460	D₄×C₄₇	—	8	2	no	—
461	D₄×C₄₇	—	8	2	no	—
462	D₄×C₄₇	—	8	1	no	—
463	D₄×C₄₇	—	8	2	no	—
464	C₂×C₄×C₄₇	—	2	2	no	—
465	C₂×C₄×C₄₇	—	2	1	no	—
466	C₂×C₄×C₄₇	—	2	1	no	—
467	C₂×C₄×C₄₇	—	2	1	no	—
468	C₂×C₄×C₄₇	—	2	1	no	—
469	C₂×C₄×C₄₇	—	2	2	no	—
470	C₂×C₄×C₄₇	—	2	1	no	—
471	C₂×C₄×C₄₇	—	4	1	no	—
472	C₂×C₄×C₄₇	—	4	2	no	—
473	C₂×C₄×C₄₇	—	8	2	no	—
474	C₂×C₄×C₄₇	—	8	2	no	—
475	C₂×C₄×C₄₇	—	8	2	no	—
476	C₂×C₄×C₄₇	—	8	2	no	—
477	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
478	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
479	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
480	C₂×C₄×C₄₇	C₂²×D₄	1	2	yes	—
481	C₂×C₄×C₄₇	C₂²×D₄	1	2	yes	—
482	C₂×C₄×C₄₇	C₂²×D₄	1	2	yes	—
483	C₂×C₄×C₄₇	C₂²×D₄	1	2	yes	—
484	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
485	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
486	C₂×C₄×C₄₇	C₂⁵	1	1	yes	characteristic
487	C₂×Dic₄₇	—	2	2	no	—
488	C₂×Dic₄₇	—	2	2	no	—
489	C₂×Dic₄₇	—	2	1	no	—
490	C₂×Dic₄₇	—	2	1	no	—
491	C₂×Dic₄₇	—	8	1	no	—
492	D₁₈₈	—	2	4	no	—
493	D₁₈₈	—	2	1	no	—
494	D₁₈₈	—	2	1	no	—
495	D₁₈₈	2₋¹⁺⁴	1	2	yes	—
496	D₁₈₈	2₋¹⁺⁴	1	2	yes	—
497	C₄×D₄₇	—	4	2	no	—
498	C₄×D₄₇	—	4	2	no	—
499	C₄×D₄₇	—	8	2	no	—
500	C₄×D₄₇	—	8	2	no	—
501	C₄×D₄₇	—	8	1	no	—
502	C₄×D₄₇	—	8	1	no	—
503	C₄×D₄₇	—	8	2	no	—
504	C₄×D₄₇	—	8	2	no	—
505	Dic₉₄	—	4	2	no	—
506	Dic₉₄	—	8	1	no	—
507	Dic₉₄	—	8	2	no	—
508	Dic₉₄	—	8	2	no	—
509	C₄₇⋊C₈	—	2	1	no	—
510	C₄₇⋊C₈	—	2	2	no	—
511	C₄₇⋊C₈	—	2	2	no	—
512	C₄₇⋊C₈	—	2	1	no	—
513	C₄₇⋊C₈	—	2	1	no	—
514	C₄₇⋊C₈	—	2	1	no	—
515	#61863	—	47	1	no	maximal, Sylow
516	C₂²×C₄₇	—	2	1	no	—
517	C₂²×C₄₇	—	2	1	no	—
518	C₂²×C₄₇	—	2	1	no	—
519	C₂²×C₄₇	—	4	2	no	—
520	C₂²×C₄₇	—	4	1	no	—
521	C₂²×C₄₇	—	4	2	no	—
522	C₂²×C₄₇	—	4	1	no	—
523	C₂²×C₄₇	—	4	1	no	—
524	C₂²×C₄₇	—	4	2	no	—
525	C₂²×C₄₇	C₂³×D₄	1	1	yes	characteristic
526	C₂×D₄₇	—	2	2	no	—
527	C₂×D₄₇	—	2	2	no	—
528	C₂×D₄₇	—	4	1	no	—
529	C₂×D₄₇	—	4	1	no	—
530	C₂×D₄₇	—	4	1	no	—
531	C₂×D₄₇	—	4	1	no	—
532	C₂×D₄₇	—	8	4	no	—
533	C₄×C₄₇	—	2	1	no	—
534	C₄×C₄₇	—	2	2	no	—
535	C₄×C₄₇	—	2	2	no	—
536	C₄×C₄₇	—	2	1	no	—
537	C₄×C₄₇	—	2	1	no	—
538	C₄×C₄₇	—	2	2	no	—
539	C₄×C₄₇	—	2	2	no	—
540	C₄×C₄₇	—	2	1	no	—
541	C₄×C₄₇	—	4	1	no	—
542	C₄×C₄₇	—	4	1	no	—
543	C₄×C₄₇	—	4	1	no	—
544	C₄×C₄₇	—	4	2	no	—
545	C₄×C₄₇	#576	1	2	yes	—
546	C₄×C₄₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
547	C₄×C₄₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
548	Dic₄₇	—	4	2	no	—
549	Dic₄₇	—	4	2	no	—
550	Dic₄₇	—	4	1	no	—
551	Dic₄₇	—	4	1	no	—
552	#3554	D₄₇	1	1	yes	characteristic, complemented
553	#3501	—	47	1	no	—
554	#3389	—	47	2	no	—
555	#3386	—	47	1	no	—
556	#3384	—	47	1	no	—
557	#3381	—	47	1	no	—
558	#3380	—	47	2	no	—
559	Q₈×D₈	—	47	1	no	—
560	#3373	—	47	1	no	—
561	#3370	—	47	2	no	—
562	#3366	—	47	1	no	—
563	#3361	—	47	1	no	—
564	#3361	—	47	2	no	—
565	#3358	—	47	1	no	—
566	#3243	—	47	2	no	—
567	#3241	—	47	2	no	—
568	#3233	—	47	1	no	—
569	#3228	—	47	1	no	—
570	#3122	—	47	2	no	—
571	#3118	—	47	2	no	—
572	#3105	—	47	1	no	—
573	#3100	—	47	1	no	—
574	#2986	—	47	1	no	—
575	C₂×C₄₇	—	4	1	no	—
576	C₂×C₄₇	—	8	2	no	—
577	C₂×C₄₇	—	8	1	no	—
578	C₂×C₄₇	#3486	1	1	yes	characteristic
579	C₂×C₄₇	C₂×#576	1	1	yes	characteristic
580	C₂×C₄₇	#3584	1	1	yes	characteristic
581	D₄₇	—	4	2	no	—
582	D₄₇	—	4	2	no	—
583	#562	—	2	2	no	—
584	#559	C₂×D₄₇	1	2	yes	complemented
585	#559	C₂×D₄₇	1	1	yes	characteristic, complemented
586	#557	C₂×D₄₇	1	1	yes	characteristic, complemented
587	#554	—	47	1	no	—
588	#554	—	47	2	no	—
589	#554	—	47	1	no	—
590	#554	—	47	2	no	—
591	#554	—	94	1	no	—
592	#554	—	94	2	no	—
593	#554	C₂×D₄₇	1	2	yes	complemented
594	#550	C₂×D₄₇	1	1	yes	characteristic, complemented
595	D₄×Q₈	—	47	1	no	—
596	D₄×Q₈	—	47	1	no	—
597	D₄×Q₈	—	94	1	no	—
598	D₄×Q₈	C₂×D₄₇	1	1	yes	characteristic, complemented
599	#548	—	2	1	no	—
600	#547	—	2	1	no	—
601	#544	—	47	2	no	—
602	#543	—	94	2	no	—
603	#542	—	2	1	no	—
604	#542	C₂×D₄₇	1	2	yes	—
605	#540	C₂×D₄₇	1	2	yes	—
606	#539	—	2	2	no	—
607	#536	—	2	1	no	—
608	#533	—	47	1	no	—
609	#533	C₂×D₄₇	1	1	yes	characteristic
610	#532	C₂×D₄₇	1	1	yes	characteristic
611	#529	C₂×D₄₇	1	1	yes	characteristic
612	C₂×C₂²⋊Q₈	—	94	1	no	—
613	C₂×C₂²⋊Q₈	—	94	1	no	—
614	#518	—	47	2	no	—
615	C₂×C₄×D₄	—	47	1	no	—
616	#501	—	47	2	no	—
617	#501	—	47	2	no	—
618	#500	—	47	2	no	—
619	#500	—	47	1	no	—
620	#499	—	47	2	no	—
621	#499	—	47	2	no	—
622	#498	—	47	1	no	—
623	#490	—	47	2	no	—
624	#489	—	47	2	no	—
625	#488	—	47	2	no	—
626	#488	—	47	2	no	—
627	#486	—	47	2	no	—
628	#486	—	47	1	no	—
629	#486	—	47	1	no	—
630	#485	—	47	2	no	—
631	#484	—	47	1	no	—
632	#482	—	47	2	no	—
633	#482	—	47	2	no	—
634	#482	—	47	2	no	—
635	#481	—	47	1	no	—
636	#480	—	47	2	no	—
637	#479	—	47	2	no	—
638	#478	—	47	1	no	—
639	#478	—	47	1	no	—
640	#478	—	47	2	no	—
641	#478	—	47	2	no	—
642	#478	—	47	2	no	—
643	#478	—	47	2	no	—
644	#478	—	47	2	no	—
645	#478	—	47	2	no	—
646	#478	—	47	2	no	—
647	#477	—	47	1	no	—
648	#477	—	47	2	no	—
649	#476	—	47	2	no	—
650	#476	—	47	1	no	—
651	#476	—	47	2	no	—
652	#475	—	47	1	no	—
653	#474	—	47	1	no	—
654	#474	—	47	1	no	—
655	#474	—	47	2	no	—
656	#474	—	47	1	no	—
657	#474	—	47	2	no	—
658	#474	—	47	2	no	—
659	#463	—	47	1	no	—
660	#463	—	47	1	no	—
661	#463	—	47	2	no	—
662	#463	—	47	2	no	—
663	#459	—	47	1	no	—
664	#459	—	47	1	no	—
665	#459	—	47	2	no	—
666	#459	—	47	2	no	—
667	#450	—	47	1	no	—
668	#447	—	47	2	no	—
669	#447	—	47	1	no	—
670	#446	—	47	1	no	—
671	#446	—	47	2	no	—
672	#446	—	47	1	no	—
673	C₈×Q₈	—	47	1	no	—
674	C₈×Q₈	—	47	1	no	—
675	C₈×Q₈	—	47	2	no	—
676	#442	—	47	2	no	—
677	#442	—	47	2	no	—
678	#442	—	47	2	no	—
679	#440	—	47	2	no	—
680	C₄×SD₁₆	—	47	1	no	—
681	C₄×SD₁₆	—	47	1	no	—
682	C₄×SD₁₆	—	47	2	no	—
683	C₄×D₈	—	47	2	no	—
684	C₄×D₈	—	47	2	no	—
685	C₄×D₈	—	47	1	no	—
686	C₄×D₈	—	47	2	no	—
687	C₄×D₈	—	47	1	no	—
688	C₄×D₈	—	47	2	no	—
689	C₄×D₈	—	47	2	no	—
690	#433	—	47	2	no	—
691	#433	—	47	2	no	—
692	#431	—	47	1	no	—
693	#431	—	47	1	no	—
694	C₄₇	#61863	1	1	yes	characteristic, complemented, Sylow
695	C₂×#41	—	2	1	no	—
696	C₂×#41	—	2	1	no	—
697	C₂²×Q₈	—	2	1	no	—
698	C₂²×Q₈	—	94	1	no	—
699	C₂²×Q₈	—	94	1	no	—
700	C₂²×D₄	—	47	1	no	—
701	C₂³×C₄	—	94	1	no	—
702	C₂×SD₁₆	—	47	1	no	—
703	C₂×SD₁₆	—	47	1	no	—
704	C₂×D₈	—	47	2	no	—
705	C₂×D₈	—	47	1	no	—
706	C₂×D₈	—	47	2	no	—
707	C₂×D₈	—	47	1	no	—
708	C₄⋊Q₈	—	2	1	no	—
709	C₄⋊Q₈	—	47	1	no	—
710	C₄⋊Q₈	—	47	1	no	—
711	C₄⋊Q₈	—	47	2	no	—
712	C₄⋊Q₈	—	47	2	no	—
713	C₄⋊Q₈	—	94	2	no	—
714	C₄⋊Q₈	C₂²⋊D₄₇	1	1	yes	characteristic
715	C₄⋊Q₈	C₂²⋊D₄₇	1	1	yes	characteristic
716	C₄⋊Q₈	C₂²×D₄₇	1	1	yes	characteristic
717	C₄⋊Q₈	C₂²×D₄₇	1	2	yes	—
718	#127	C₂²×D₄₇	1	1	yes	characteristic
719	#127	C₂²×D₄₇	1	2	yes	—
720	#126	—	2	2	no	—
721	#126	—	2	1	no	—
722	#125	—	2	2	no	—
723	#125	—	47	2	no	—
724	#125	—	47	2	no	—
725	#125	—	47	2	no	—
726	#125	—	94	2	no	—
727	#125	C₂²⋊D₄₇	1	2	yes	—
728	#125	C₂²×D₄₇	1	1	yes	characteristic
729	#125	C₂²×D₄₇	1	2	yes	—
730	#124	—	2	1	no	—
731	#124	—	2	2	no	—
732	#124	—	2	2	no	—
733	#124	—	2	1	no	—
734	#124	C₂²×D₄₇	1	1	yes	characteristic
735	#124	C₂²×D₄₇	1	2	yes	—
736	#123	—	2	1	no	—
737	#123	—	2	2	no	—
738	#123	—	2	2	no	—
739	#123	—	2	2	no	—
740	#123	—	2	2	no	—
741	#123	—	2	2	no	—
742	#123	—	2	2	no	—
743	C₂²⋊Q₈	—	2	2	no	—
744	C₂²⋊Q₈	—	2	2	no	—
745	C₂²⋊Q₈	—	2	2	no	—
746	C₂²⋊Q₈	—	2	2	no	—
747	C₂²⋊Q₈	—	2	2	no	—
748	C₂²⋊Q₈	—	2	1	no	—
749	C₂²⋊Q₈	—	94	1	no	—
750	C₂²⋊Q₈	—	94	1	no	—
751	C₂²⋊Q₈	—	94	2	no	—
752	C₂²⋊Q₈	—	94	2	no	—
753	C₂²⋊Q₈	—	94	1	no	—
754	C₂²⋊Q₈	—	94	1	no	—
755	C₂²⋊Q₈	—	94	1	no	—
756	C₂²⋊Q₈	—	94	1	no	—
757	C₂²⋊Q₈	—	94	2	no	—
758	C₂²⋊Q₈	—	94	2	no	—
759	C₂²⋊Q₈	—	94	2	no	—
760	C₂²⋊Q₈	—	94	2	no	—
761	C₂²⋊Q₈	—	94	2	no	—
762	C₂²⋊Q₈	—	94	2	no	—
763	C₂²⋊Q₈	—	94	2	no	—
764	C₂²⋊Q₈	—	94	2	no	—
765	C₂²⋊Q₈	—	94	2	no	—
766	C₂²⋊Q₈	—	94	2	no	—
767	C₂²⋊Q₈	C₂²⋊D₄₇	1	1	yes	characteristic
768	C₂²⋊Q₈	C₂²⋊D₄₇	1	1	yes	characteristic
769	C₂²⋊Q₈	C₂²⋊D₄₇	1	2	yes	—
770	C₂²⋊Q₈	C₂²×D₄₇	1	1	yes	characteristic
771	#121	—	2	1	no	—
772	#121	—	2	2	no	—
773	#121	—	2	1	no	—
774	#121	—	2	2	no	—
775	#121	—	2	2	no	—
776	#121	C₂²×D₄₇	1	1	yes	characteristic
777	#121	C₂²×D₄₇	1	2	yes	—
778	C₄×Q₈	—	2	1	no	—
779	C₄×Q₈	—	94	1	no	—
780	C₄×Q₈	—	94	1	no	—
781	C₄×Q₈	C₂²×D₄₇	1	1	yes	characteristic
782	C₄×Q₈	C₂²×D₄₇	1	2	yes	—
783	C₄×Q₈	C₂²×D₄₇	1	1	yes	characteristic
784	C₄×Q₈	C₂²×D₄₇	1	1	yes	characteristic
785	C₄×Q₈	C₂²×D₄₇	1	2	yes	—
786	C₄×D₄	—	2	1	no	—
787	C₄×D₄	—	2	2	no	—
788	C₄×D₄	—	2	1	no	—
789	C₄×D₄	—	2	1	no	—
790	C₄×D₄	—	47	1	no	—
791	C₄×D₄	—	47	1	no	—
792	C₄×D₄	—	47	1	no	—
793	C₄×D₄	—	47	1	no	—
794	C₄×D₄	—	47	2	no	—
795	C₄×D₄	—	47	2	no	—
796	C₄×D₄	—	47	2	no	—
797	C₄×D₄	—	47	2	no	—
798	C₄×D₄	—	94	2	no	—
799	C₄×D₄	—	94	2	no	—
800	C₄×D₄	—	94	1	no	—
801	C₄×D₄	—	94	1	no	—
802	C₄×D₄	C₂²×D₄₇	1	1	yes	characteristic
803	C₄×D₄	C₂²×D₄₇	1	2	yes	—
804	C₄×D₄	C₂²×D₄₇	1	2	yes	—
805	C₄×D₄	C₂²×D₄₇	1	2	yes	—
806	C₄×D₄	C₂²×D₄₇	1	2	yes	—
807	#117	—	2	1	no	—
808	#117	—	47	2	no	—
809	#117	C₂²×D₄₇	1	2	yes	—
810	C₂×C₄⋊C₄	—	2	2	no	—
811	C₂×C₄⋊C₄	—	47	1	no	—
812	C₂×C₄⋊C₄	—	94	2	no	—
813	C₂×C₄⋊C₄	—	94	2	no	—
814	C₂×C₄⋊C₄	—	94	1	no	—
815	C₂×C₄⋊C₄	—	94	1	no	—
816	C₂×C₂²⋊C₄	—	94	1	no	—
817	C₂×C₂²⋊C₄	—	94	2	no	—
818	C₂×C₂²⋊C₄	—	94	2	no	—
819	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
820	#107	—	47	2	no	—
821	#107	—	47	1	no	—
822	#107	—	47	2	no	—
823	#107	—	47	2	no	—
824	#107	—	47	2	no	—
825	#107	—	47	2	no	—
826	#107	—	47	1	no	—
827	#107	—	47	2	no	—
828	#106	—	47	1	no	—
829	#106	—	47	2	no	—
830	#106	—	47	1	no	—
831	#106	—	47	2	no	—
832	#106	—	47	2	no	—
833	#106	—	47	2	no	—
834	C₄⋊C₈	—	47	1	no	—
835	C₄⋊C₈	—	47	1	no	—
836	C₄⋊C₈	—	47	1	no	—
837	C₄⋊C₈	—	47	1	no	—
838	C₄⋊C₈	—	47	2	no	—
839	C₄⋊C₈	—	47	2	no	—
840	C₄⋊C₈	—	47	2	no	—
841	C₄⋊C₈	—	47	2	no	—
842	#103	—	47	1	no	—
843	#103	—	47	2	no	—
844	#103	—	47	1	no	—
845	#103	—	47	2	no	—
846	#102	—	47	2	no	—
847	#102	—	47	2	no	—
848	#102	—	47	2	no	—
849	#102	—	47	2	no	—
850	#102	—	47	1	no	—
851	#102	—	47	2	no	—
852	#102	—	47	1	no	—
853	#102	—	47	2	no	—
854	#102	—	47	2	no	—
855	#102	—	47	2	no	—
856	#102	—	47	1	no	—
857	#102	—	47	2	no	—
858	#102	—	47	1	no	—
859	#102	—	47	2	no	—
860	#102	—	47	1	no	—
861	#102	—	47	1	no	—
862	C₂²⋊C₈	—	47	2	no	—
863	C₂²⋊C₈	—	47	1	no	—
864	C₂²⋊C₈	—	47	1	no	—
865	#97	—	47	2	no	—
866	#97	—	47	2	no	—
867	C₄×C₈	—	47	2	no	—
868	C₄×C₈	—	47	1	no	—
869	C₄×C₈	—	47	1	no	—
870	C₄×C₈	—	47	2	no	—
871	C₄×C₈	—	47	2	no	—
872	C₂⁴	—	94	1	no	—
873	#41	—	8	2	no	—
874	#41	—	8	2	no	—
875	C₂×Q₈	—	2	1	no	—
876	C₂×Q₈	—	2	2	no	—
877	C₂×Q₈	—	8	2	no	—
878	C₂×Q₈	—	94	1	no	—
879	C₂×Q₈	—	94	2	no	—
880	C₂×Q₈	—	94	2	no	—
881	C₂×Q₈	—	94	1	no	—
882	C₂×Q₈	—	376	2	no	—
883	C₂×Q₈	—	376	2	no	—
884	C₂×Q₈	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
885	C₂×Q₈	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
886	C₂×Q₈	C₂×C₂²⋊D₄₇	1	2	yes	—
887	C₂×Q₈	C₂³×D₄₇	1	1	yes	characteristic
888	C₂×D₄	—	2	1	no	—
889	C₂×D₄	—	2	2	no	—
890	C₂×D₄	—	2	1	no	—
891	C₂×D₄	—	2	1	no	—
892	C₂×D₄	—	2	2	no	—
893	C₂×D₄	—	2	2	no	—
894	C₂×D₄	—	47	1	no	—
895	C₂×D₄	—	47	1	no	—
896	C₂×D₄	—	94	2	no	—
897	C₂×D₄	—	94	2	no	—
898	C₂×D₄	—	94	1	no	—
899	C₂×D₄	C₂³×D₄₇	1	1	yes	characteristic
900	C₂×D₄	C₂³×D₄₇	1	2	yes	—
901	C₂²×C₄	—	2	1	no	—
902	C₂²×C₄	—	2	2	no	—
903	C₂²×C₄	—	2	2	no	—
904	C₂²×C₄	—	2	2	no	—
905	C₂²×C₄	—	2	2	no	—
906	C₂²×C₄	—	94	1	no	—
907	C₂²×C₄	—	94	2	no	—
908	C₂²×C₄	—	94	2	no	—
909	C₂²×C₄	—	94	2	no	—
910	C₂²×C₄	—	94	2	no	—
911	C₂²×C₄	—	94	1	no	—
912	C₂²×C₄	—	94	1	no	—
913	C₂²×C₄	—	94	1	no	—
914	C₂²×C₄	—	94	1	no	—
915	C₂²×C₄	—	376	2	no	—
916	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
917	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
918	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
919	SD₁₆	—	94	2	no	—
920	SD₁₆	—	94	2	no	—
921	D₈	—	94	4	no	—
922	D₈	—	94	2	no	—
923	D₈	—	94	4	no	—
924	D₈	—	94	2	no	—
925	C₂×C₈	—	47	1	no	—
926	C₂×C₈	—	47	2	no	—
927	C₂×C₈	—	47	1	no	—
928	C₂×C₈	—	47	1	no	—
929	C₂×C₈	—	47	2	no	—
930	C₂×C₈	—	47	1	no	—
931	C₄⋊C₄	—	2	1	no	—
932	C₄⋊C₄	—	2	2	no	—
933	C₄⋊C₄	—	2	2	no	—
934	C₄⋊C₄	—	2	1	no	—
935	C₄⋊C₄	—	2	1	no	—
936	C₄⋊C₄	—	2	1	no	—
937	C₄⋊C₄	—	2	2	no	—
938	C₄⋊C₄	—	2	2	no	—
939	C₄⋊C₄	—	2	1	no	—
940	C₄⋊C₄	—	47	2	no	—
941	C₄⋊C₄	—	47	1	no	—
942	C₄⋊C₄	—	47	1	no	—
943	C₄⋊C₄	—	47	2	no	—
944	C₄⋊C₄	—	94	2	no	—
945	C₄⋊C₄	—	94	2	no	—
946	C₄⋊C₄	—	94	2	no	—
947	C₄⋊C₄	—	94	2	no	—
948	C₄⋊C₄	—	94	2	no	—
949	C₄⋊C₄	—	94	2	no	—
950	C₄⋊C₄	—	94	1	no	—
951	C₄⋊C₄	—	94	1	no	—
952	C₄⋊C₄	—	94	2	no	—
953	C₄⋊C₄	—	94	2	no	—
954	C₄⋊C₄	—	94	1	no	—
955	C₄⋊C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
956	C₄⋊C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
957	C₄⋊C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
958	C₄⋊C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
959	C₄⋊C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
960	C₄⋊C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
961	C₄⋊C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
962	C₄⋊C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
963	C₄⋊C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
964	C₄⋊C₄	C₂³×D₄₇	1	1	yes	characteristic
965	C₄⋊C₄	C₂³×D₄₇	1	1	yes	characteristic
966	C₄⋊C₄	C₂³×D₄₇	1	2	yes	—
967	C₂²⋊C₄	—	2	1	no	—
968	C₂²⋊C₄	—	2	1	no	—
969	C₂²⋊C₄	—	2	1	no	—
970	C₂²⋊C₄	—	2	1	no	—
971	C₂²⋊C₄	—	2	2	no	—
972	C₂²⋊C₄	—	2	2	no	—
973	C₂²⋊C₄	—	2	2	no	—
974	C₂²⋊C₄	—	2	1	no	—
975	C₂²⋊C₄	—	2	2	no	—
976	C₂²⋊C₄	—	2	2	no	—
977	C₂²⋊C₄	—	2	2	no	—
978	C₂²⋊C₄	—	2	2	no	—
979	C₂²⋊C₄	—	94	2	no	—
980	C₂²⋊C₄	—	94	2	no	—
981	C₂²⋊C₄	—	94	2	no	—
982	C₂²⋊C₄	—	94	2	no	—
983	C₂²⋊C₄	—	94	2	no	—
984	C₂²⋊C₄	—	94	1	no	—
985	C₂²⋊C₄	—	94	1	no	—
986	C₂²⋊C₄	—	94	1	no	—
987	C₂²⋊C₄	—	94	1	no	—
988	C₂²⋊C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
989	C₂²⋊C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
990	C₄²	—	2	1	no	—
991	C₄²	—	2	2	no	—
992	C₄²	—	94	2	no	—
993	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
994	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
995	C₄²	C₂³×D₄₇	1	1	yes	characteristic
996	C₄²	C₂³×D₄₇	1	1	yes	characteristic
997	C₄²	C₂³×D₄₇	1	2	yes	—
998	C₄²	C₂³×D₄₇	1	2	yes	—
999	C₂³	—	2	1	no	—
1000	C₂³	—	2	2	no	—
1001	C₂³	—	94	4	no	—
1002	C₂³	—	94	1	no	—
1003	C₂³	—	94	1	no	—
1004	C₂³	—	376	1	no	—
1005	C₂³	—	376	1	no	—
1006	C₂³	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
1007	Q₈	—	2	2	no	—
1008	Q₈	—	2	2	no	—
1009	Q₈	—	2	1	no	—
1010	Q₈	—	2	1	no	—
1011	Q₈	—	4	2	no	—
1012	Q₈	—	4	2	no	—
1013	Q₈	—	8	2	no	—
1014	Q₈	—	376	1	no	—
1015	Q₈	—	376	2	no	—
1016	Q₈	—	376	2	no	—
1017	Q₈	—	188	2	no	—
1018	D₄	—	2	1	no	—
1019	D₄	—	2	2	no	—
1020	D₄	—	2	1	no	—
1021	D₄	—	2	2	no	—
1022	D₄	—	4	2	no	—
1023	D₄	—	8	1	no	—
1024	D₄	—	8	2	no	—
1025	D₄	—	8	2	no	—
1026	D₄	—	8	1	no	—
1027	D₄	—	8	2	no	—
1028	D₄	—	47	2	no	—
1029	D₄	—	47	2	no	—
1030	D₄	—	94	4	no	—
1031	D₄	—	94	1	no	—
1032	D₄	—	94	1	no	—
1033	C₂×C₄	—	2	2	no	—
1034	C₂×C₄	—	2	1	no	—
1035	C₂×C₄	—	2	1	no	—
1036	C₂×C₄	—	2	1	no	—
1037	C₂×C₄	—	2	1	no	—
1038	C₂×C₄	—	2	2	no	—
1039	C₂×C₄	—	2	1	no	—
1040	C₂×C₄	—	4	1	no	—
1041	C₂×C₄	—	4	2	no	—
1042	C₂×C₄	—	8	2	no	—
1043	C₂×C₄	—	8	2	no	—
1044	C₂×C₄	—	8	2	no	—
1045	C₂×C₄	—	8	2	no	—
1046	C₂×C₄	—	94	2	no	—
1047	C₂×C₄	—	94	2	no	—
1048	C₂×C₄	—	94	1	no	—
1049	C₂×C₄	—	94	1	no	—
1050	C₂×C₄	—	376	2	no	—
1051	C₂×C₄	—	376	2	no	—
1052	C₂×C₄	—	376	1	no	—
1053	C₂×C₄	—	376	1	no	—
1054	C₂×C₄	—	376	2	no	—
1055	C₂×C₄	—	376	2	no	—
1056	C₂×C₄	—	376	1	no	—
1057	C₂×C₄	—	188	2	no	—
1058	C₂×C₄	—	188	2	no	—
1059	C₂×C₄	C₂²×C₂²⋊D₄₇	1	2	yes	—
1060	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
1061	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
1062	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
1063	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
1064	C₂×C₄	C₂²×C₂²⋊D₄₇	1	2	yes	—
1065	C₂×C₄	C₂²×C₂²⋊D₄₇	1	2	yes	—
1066	C₂×C₄	C₂²×C₂²⋊D₄₇	1	2	yes	—
1067	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
1068	C₂×C₄	C₂⁴×D₄₇	1	1	yes	characteristic
1069	C₈	—	94	2	no	—
1070	C₈	—	94	1	no	—
1071	C₈	—	94	2	no	—
1072	C₈	—	94	1	no	—
1073	C₈	—	94	1	no	—
1074	C₈	—	94	1	no	—
1075	C₂²	—	2	1	no	—
1076	C₂²	—	2	1	no	—
1077	C₂²	—	2	1	no	—
1078	C₂²	—	4	1	no	—
1079	C₂²	—	4	2	no	—
1080	C₂²	—	4	1	no	—
1081	C₂²	—	4	2	no	—
1082	C₂²	—	4	2	no	—
1083	C₂²	—	4	1	no	—
1084	C₂²	—	94	2	no	—
1085	C₂²	—	94	2	no	—
1086	C₂²	—	376	4	no	—
1087	C₂²	—	188	1	no	—
1088	C₂²	—	188	1	no	—
1089	C₂²	—	188	1	no	—
1090	C₂²	—	188	1	no	—
1091	C₂²	C₂³×C₂²⋊D₄₇	1	1	yes	characteristic
1092	C₄	—	2	1	no	—
1093	C₄	—	2	1	no	—
1094	C₄	—	2	2	no	—
1095	C₄	—	2	2	no	—
1096	C₄	—	2	1	no	—
1097	C₄	—	2	1	no	—
1098	C₄	—	2	2	no	—
1099	C₄	—	2	2	no	—
1100	C₄	—	4	1	no	—
1101	C₄	—	4	1	no	—
1102	C₄	—	4	2	no	—
1103	C₄	—	4	1	no	—
1104	C₄	—	188	1	no	—
1105	C₄	—	188	1	no	—
1106	C₄	—	188	2	no	—
1107	C₄	—	188	2	no	—
1108	C₄	#15689926	1	2	yes	—
1109	C₄	2₋¹⁺⁴×D₄₇	1	1	yes	characteristic
1110	C₄	2₋¹⁺⁴×D₄₇	1	1	yes	characteristic
1111	C₂	—	4	1	no	—
1112	C₂	—	8	1	no	—
1113	C₂	—	8	2	no	—
1114	C₂	—	188	2	no	—
1115	C₂	—	188	2	no	—
1116	C₂	#20257036	1	1	yes	characteristic
1117	C₂	C₂×#15689926	1	1	yes	characteristic
1118	C₂	#20258159	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×#3554	C₂
socle	C₂²×C₄₇	C₂³×D₄
hypercenter	#3554	D₄₇
hypocenter	C₄₇	#61863
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ #533 ◁ #3554

Complements

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

N	H ≅ G/N	type
1. #20257189	C₂	semidirect
2. #20256342	C₂	semidirect
3. #20256305	C₂	semidirect
4. #20256283	C₂	semidirect
5. #20256259	C₂	semidirect
6. #20256251	C₂	semidirect
7. Q₈×#10625334	C₂	semidirect
8. #20256176	C₂	semidirect
9. #20256135	C₂	semidirect
10. #20256091	C₂	semidirect
11. #20256044	C₂	semidirect
12. #20256044	C₂	semidirect
13. #20256019	C₂	semidirect
14. #20254665	C₂	semidirect
15. #20254635	C₂	semidirect
16. #20254563	C₂	semidirect
17. #20254520	C₂	semidirect
18. #20253626	C₂	semidirect
19. #20253566	C₂	semidirect
20. #20253431	C₂	semidirect
21. #20253384	C₂	semidirect
22. #20252490	C₂	semidirect
23. C₄₇×#3554	C₂	semidirect
40. #15689533	C₂²	semidirect
41. #15689529	C₂²	semidirect
42. #15689526	C₂²	semidirect
43. #15689526	C₂²	semidirect
44. #15689522	C₂²	semidirect
45. #15689522	C₂²	semidirect
46. #15689519	C₂²	semidirect
47. #15689487	C₂²	semidirect
48. #15689482	C₂²	semidirect
49. #15689477	C₂²	semidirect
50. #15689477	C₂²	semidirect
51. #15689469	C₂²	semidirect
52. #15689469	C₂²	semidirect
53. #15689469	C₂²	semidirect
61. #15689430	C₂²	semidirect
62. #15689423	C₂²	semidirect
63. #15689423	C₂²	semidirect
64. #15689423	C₂²	semidirect
65. #15689423	C₂²	semidirect
66. #15689423	C₂²	semidirect
71. #15689418	C₂²	semidirect
72. #15689418	C₂²	semidirect
73. #15689413	C₂²	semidirect
74. #15689413	C₂²	semidirect
76. #15689408	C₂²	semidirect
77. #15689403	C₂²	semidirect
78. #15689403	C₂²	semidirect
79. #15689403	C₂²	semidirect
94. #15689254	C₂²	semidirect
95. #15689254	C₂²	semidirect
96. #15689254	C₂²	semidirect
97. Q₈×C₄₇⋊C₈	C₂²	semidirect
98. Q₈×C₄₇⋊C₈	C₂²	semidirect
99. Q₈×C₄₇⋊C₈	C₂²	semidirect
119. C₄₇×#559	C₂²	semidirect
120. C₄₇×#559	C₂²	semidirect
121. C₄₇×#557	C₂²	semidirect
122. C₄₇×#554	C₂²	semidirect
123. C₄₇×#550	C₂²	semidirect
124. D₄×Q₈×C₄₇	C₂²	semidirect
552. #3554	D₄₇	semidirect
584. #559	C₂×D₄₇	semidirect
585. #559	C₂×D₄₇	semidirect
586. #557	C₂×D₄₇	semidirect
593. #554	C₂×D₄₇	semidirect
594. #550	C₂×D₄₇	semidirect
598. D₄×Q₈	C₂×D₄₇	semidirect
694. C₄₇	#61863	semidirect

Maximal subgroups

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

subgroup	index
#20257189	2
#20256342	2
#20256305	2
#20256283	2
#20256259	2
#20256251	2
Q₈×#10625334	2
#20256176	2
#20256135	2
#20256091	2
#20256044	2
#20256019	2
#20254665	2
#20254635	2
#20254563	2
#20254520	2
#20253626	2
#20253566	2
#20253431	2
#20253384	2
#20252490	2
C₄₇×#3554	2
#61863	47