Subgroups — #27096661

Order 12032.

1810 conjugacy classes of subgroups.

The subgroup lattice has 1150 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20257237	C₂	1	1	yes	maximal, characteristic, complemented
2	#20257214	C₂	1	1	yes	maximal, characteristic, complemented
3	#20256223	C₂	1	2	yes	maximal, complemented
4	#20256208	C₂	1	2	yes	maximal, complemented
5	#20256160	C₂	1	2	yes	maximal, complemented
6	#20256145	C₂	1	2	yes	maximal, complemented
7	#20256112	C₂	1	2	yes	maximal, complemented
8	#20256090	C₂	1	2	yes	maximal, complemented
9	#20256079	C₂	1	2	yes	maximal, complemented
10	#20256043	C₂	1	2	yes	maximal, complemented
11	#20253788	C₂	1	1	yes	maximal, characteristic, complemented
12	#20253746	C₂	1	1	yes	maximal, characteristic, complemented
13	#20253746	C₂	1	1	yes	maximal, characteristic, complemented
14	#20253248	C₂	1	1	yes	maximal, characteristic, complemented
15	#20253237	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#15689424	C₂	1	1	yes	maximal, characteristic, complemented
17	#20252925	C₂	1	1	yes	maximal, characteristic, complemented
18	#20252925	C₂	1	1	yes	maximal, characteristic, complemented
19	#20252331	C₂	1	1	yes	maximal, characteristic, complemented
20	#20252272	C₂	1	1	yes	maximal, characteristic, complemented
21	#20252264	C₂	1	1	yes	maximal, characteristic, complemented
22	C₄×#13094049	C₂	1	1	yes	maximal, characteristic, complemented
23	C₄₇×#3035	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#13094049	C₂²	1	1	yes	characteristic
25	#15689855	C₂²	1	2	yes	—
26	#15689855	C₂²	1	2	yes	—
27	#15689849	C₂²	1	2	yes	complemented
28	#15689849	C₂²	1	2	yes	complemented
29	#15689847	C₂²	1	2	yes	—
30	#15689838	—	2	1	no	—
31	#15689832	—	2	2	no	—
32	#15689832	—	2	2	no	—
33	#15689832	C₂²	1	2	yes	complemented
34	#15689832	C₂²	1	2	yes	complemented
35	#15689819	—	2	1	no	—
36	#15689819	—	2	1	no	—
37	#15689793	C₂²	1	2	yes	—
38	#15689777	—	2	1	no	—
39	#15689751	—	2	1	no	—
40	#15689751	—	2	1	no	—
41	#15689751	C₂²	1	1	yes	characteristic
42	#15689751	C₂²	1	1	yes	characteristic
43	#15689710	—	2	2	no	—
44	#15689687	C₂²	1	1	yes	characteristic
45	#15689687	C₂²	1	1	yes	characteristic
46	#15689680	—	2	1	no	—
47	#15689680	C₂²	1	1	yes	characteristic
48	C₂×#13094016	—	2	1	no	—
49	C₂×#13094016	C₂²	1	1	yes	characteristic
50	#15689633	—	2	2	no	—
51	#15689606	C₂²	1	1	yes	characteristic
52	#15689606	C₂²	1	1	yes	characteristic
53	#15689606	C₂²	1	1	yes	characteristic
54	#15689606	C₂²	1	1	yes	characteristic
55	C₂×C₄×D₁₈₈	C₂²	1	1	yes	characteristic
56	#15689491	C₂²	1	2	yes	complemented
57	#15689487	C₂²	1	2	yes	complemented
58	#15689486	C₂²	1	2	yes	—
59	#15689486	C₂²	1	2	yes	—
60	#15689484	C₂²	1	2	yes	—
61	#15689484	C₂²	1	2	yes	—
62	#15689479	C₂²	1	2	yes	—
63	#15689479	C₂²	1	2	yes	—
64	#15689477	C₂²	1	2	yes	complemented
65	#15689477	C₂²	1	2	yes	complemented
66	#15689468	C₂²	1	2	yes	—
67	#15689468	C₂²	1	2	yes	—
68	#15689432	C₂²	1	2	yes	complemented
69	#15689428	C₂²	1	2	yes	complemented
70	#15689425	C₂²	1	2	yes	complemented
71	#15689424	C₂²	1	2	yes	—
72	#15689424	C₂²	1	2	yes	—
73	#15689424	C₂²	1	2	yes	—
74	#15689424	C₂²	1	2	yes	—
75	#15689421	C₂²	1	2	yes	complemented
76	#15689416	C₂²	1	2	yes	complemented
77	#15689411	C₂²	1	2	yes	complemented
78	#15689406	C₂²	1	2	yes	complemented
79	#15689401	C₂²	1	2	yes	complemented
80	#15689347	C₂²	1	2	yes	—
81	#15689347	C₂²	1	2	yes	—
82	#15689340	C₂²	1	2	yes	—
83	#15689340	C₂²	1	2	yes	—
84	#15689321	C₂²	1	2	yes	—
85	#15689321	C₂²	1	2	yes	—
86	#15689316	C₂²	1	2	yes	—
87	#15689316	C₂²	1	2	yes	—
88	#15689252	C₂²	1	2	yes	complemented
89	#15689252	C₂²	1	2	yes	complemented
90	#15689250	C₂²	1	2	yes	complemented
91	#15689247	C₂²	1	2	yes	complemented
92	#15689235	C₂²	1	2	yes	complemented
93	#15689233	C₂²	1	2	yes	—
94	#15689230	C₂²	1	2	yes	complemented
95	#15689224	C₂²	1	2	yes	complemented
96	#15689224	C₂²	1	2	yes	complemented
97	#15689221	C₂²	1	2	yes	—
98	Q₁₆×Dic₄₇	C₂²	1	2	yes	complemented
99	SD₁₆×Dic₄₇	C₂²	1	2	yes	complemented
100	SD₁₆×Dic₄₇	C₂²	1	2	yes	complemented
101	C₄×#10625336	C₂²	1	2	yes	—
102	D₈×Dic₄₇	C₂²	1	2	yes	complemented
103	C₄×#10625334	C₂²	1	2	yes	—
104	#15689166	C₂²	1	1	yes	characteristic
105	C₂×#13093958	C₂²	1	1	yes	characteristic
106	C₂×#13093956	C₂²	1	1	yes	characteristic
107	#15689149	C₂²	1	1	yes	characteristic
108	#15689149	C₂²	1	1	yes	characteristic
109	#15689127	C₂²	1	1	yes	characteristic
110	#15689124	C₂²	1	1	yes	characteristic
111	#15689124	C₂²	1	1	yes	characteristic
112	#15689124	C₂²	1	1	yes	characteristic
113	#15689124	C₂²	1	1	yes	characteristic
114	#15689124	C₂²	1	1	yes	characteristic
115	C₂×#13093946	C₂²	1	1	yes	characteristic
116	C₂×#13093946	C₂²	1	1	yes	characteristic
117	#15689078	C₂²	1	1	yes	characteristic
118	#15689078	C₂²	1	1	yes	characteristic
119	C₄×#10625329	C₂²	1	1	yes	characteristic
120	C₂×#135×C₄₇	C₂²	1	1	yes	characteristic
121	C₂×#135×C₄₇	C₂²	1	1	yes	characteristic
122	C₄₇×#532	C₂²	1	1	yes	characteristic
123	C₄×#41×C₄₇	C₂²	1	1	yes	characteristic
124	C₄₇×#464	C₂²	1	1	yes	characteristic, complemented
125	C₄₇×#464	C₂²	1	1	yes	characteristic, complemented
126	C₄₇×#463	C₂²	1	1	yes	characteristic, complemented
127	C₄₇×#463	C₂²	1	1	yes	characteristic, complemented
128	C₄₇×#462	C₂²	1	1	yes	characteristic, complemented
129	C₄₇×#461	C₂²	1	1	yes	characteristic, complemented
130	C₄₇×#460	C₂²	1	1	yes	characteristic, complemented
131	C₄₇×#459	C₂²	1	1	yes	characteristic, complemented
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	C₂×#10625352	—	2	2	no	—
136	C₂²×D₁₈₈	C₂³	1	1	yes	characteristic
137	C₂²×C₄×D₄₇	—	2	1	no	—
138	#13094049	—	2	4	no	—
139	C₂×#10625336	C₂³	1	2	yes	—
140	C₂×#10625334	C₂³	1	2	yes	—
141	C₂×#10625329	C₂³	1	1	yes	characteristic
142	C₂×#10625329	C₂³	1	1	yes	characteristic
143	#13094024	—	2	1	no	—
144	#13094024	—	2	1	no	—
145	#13094024	D₄	1	1	yes	characteristic
146	#13094024	D₄	1	1	yes	characteristic
147	#13094023	—	2	2	no	—
148	#13094023	—	2	2	no	—
149	#13094023	C₂³	1	2	yes	—
150	#13094023	C₂³	1	2	yes	—
151	#13094020	C₂³	1	2	yes	—
152	#13094020	C₂³	1	2	yes	—
153	#13094019	—	2	2	no	—
154	#13094019	—	2	2	no	—
155	#13094016	—	2	1	no	—
156	#13094016	—	2	1	no	—
157	#13094016	—	2	1	no	—
158	#13094016	—	2	1	no	—
159	#13094016	—	2	2	no	—
160	#13094016	—	2	2	no	—
161	#13094016	D₄	1	1	yes	characteristic
162	#13094016	D₄	1	1	yes	characteristic
163	#13094016	C₂³	1	2	yes	—
164	#13094016	C₂³	1	2	yes	—
165	#13094015	—	2	2	no	—
166	#13094015	—	2	2	no	—
167	#13094015	C₂³	1	2	yes	—
168	#13094015	C₂³	1	2	yes	—
169	#13094013	C₂³	1	2	yes	—
170	#13094013	C₂³	1	2	yes	—
171	#13094010	—	2	2	no	—
172	#13094010	—	2	2	no	—
173	#13094008	—	2	2	no	—
174	#13094008	—	2	2	no	—
175	#13094006	—	2	2	no	—
176	#13094006	—	2	2	no	—
177	#13094004	—	2	2	no	—
178	#13094003	—	2	2	no	—
179	#13094003	—	2	2	no	—
180	#13094003	D₄	1	2	yes	—
181	#13094003	D₄	1	2	yes	—
182	#13094001	—	2	2	no	—
183	#13094001	—	2	2	no	—
184	#13094001	—	2	2	no	—
185	#13094001	—	2	2	no	—
186	#13094001	—	2	2	no	—
187	#13094001	—	2	2	no	—
188	#13093998	—	2	1	no	—
189	#13093998	—	2	1	no	—
190	#13093998	—	2	1	no	—
191	#13093998	—	2	1	no	—
192	#13093996	—	2	2	no	—
193	#13093996	—	2	2	no	—
194	#13093995	—	2	2	no	—
195	#13093992	—	2	2	no	—
196	#13093992	—	2	2	no	—
197	Q₈×Dic₄₇	C₂³	1	2	yes	—
198	Q₈×Dic₄₇	C₂³	1	2	yes	—
199	Q₈×Dic₄₇	C₂³	1	2	yes	—
200	Q₈×Dic₄₇	C₂³	1	2	yes	—
201	C₄×Dic₉₄	—	2	2	no	—
202	C₄×Dic₉₄	—	2	2	no	—
203	C₄×Dic₉₄	C₂³	1	2	yes	—
204	C₄×Dic₉₄	C₂³	1	2	yes	—
205	C₄×D₁₈₈	—	2	1	no	—
206	C₄×D₁₈₈	—	2	1	no	—
207	C₄×D₁₈₈	C₂³	1	2	yes	—
208	C₄×D₁₈₈	C₂³	1	2	yes	—
209	D₄×Dic₄₇	—	2	2	no	—
210	D₄×Dic₄₇	—	2	2	no	—
211	D₄×Dic₄₇	—	2	2	no	—
212	D₄×Dic₄₇	—	2	2	no	—
213	D₄×Dic₄₇	C₂³	1	2	yes	—
214	D₄×Dic₄₇	C₂³	1	2	yes	—
215	D₄×Dic₄₇	C₂³	1	2	yes	—
216	D₄×Dic₄₇	C₂³	1	2	yes	—
217	(C₂²⋊D₄₇)⋊C₄	—	2	2	no	—
218	(C₂²⋊D₄₇)⋊C₄	—	2	2	no	—
219	#13093983	—	2	1	no	—
220	#13093983	—	2	1	no	—
221	#13093983	—	2	1	no	—
222	#13093983	—	2	1	no	—
223	#13093983	C₂³	1	1	yes	characteristic
224	#13093983	C₂³	1	1	yes	characteristic
225	#13093982	—	2	2	no	—
226	C₂×C₄⋊Dic₄₇	—	2	1	no	—
227	C₂×C₄⋊Dic₄₇	—	2	1	no	—
228	C₂×C₄⋊Dic₄₇	—	2	1	no	—
229	C₂×C₄⋊Dic₄₇	—	2	1	no	—
230	C₂×C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic
231	C₂×C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic
232	C₂×C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic
233	C₂×Dic₄₇⋊C₄	—	2	1	no	—
234	C₂×Dic₄₇⋊C₄	—	2	1	no	—
235	C₂×Dic₄₇⋊C₄	—	2	2	no	—
236	C₂×Dic₄₇⋊C₄	—	2	2	no	—
237	C₂×(C₂×D₄₇)⋊C₄	—	2	1	no	—
238	#13093958	C₂³	1	2	yes	—
239	#13093958	C₂³	1	2	yes	—
240	#13093957	C₂³	1	2	yes	—
241	#13093956	C₂³	1	2	yes	—
242	#13093956	C₂³	1	2	yes	—
243	#13093955	C₂³	1	2	yes	—
244	Dic₄₇⋊C₈	C₂³	1	2	yes	—
245	Dic₄₇⋊C₈	C₂³	1	2	yes	—
246	Dic₄₇⋊C₈	C₂³	1	2	yes	—
247	Dic₄₇⋊C₈	C₂³	1	2	yes	—
248	#13093948	C₂³	1	2	yes	—
249	#13093948	C₂³	1	2	yes	—
250	#13093948	C₂³	1	2	yes	—
251	#13093948	C₂³	1	2	yes	—
252	#13093948	C₂³	1	2	yes	—
253	#13093946	C₂³	1	2	yes	—
254	#13093946	C₂³	1	2	yes	—
255	#13093946	C₂³	1	2	yes	—
256	#13093946	C₂³	1	2	yes	—
257	#13093945	C₂³	1	2	yes	—
258	#13093945	C₂³	1	2	yes	—
259	#13093945	C₂³	1	2	yes	—
260	#13093945	C₂³	1	2	yes	—
261	#13093945	C₂³	1	2	yes	—
262	#13093944	C₂³	1	2	yes	—
263	#13093944	C₂³	1	2	yes	—
264	#13093935	C₂³	1	2	yes	—
265	#13093934	C₂³	1	2	yes	—
266	#13093934	C₂³	1	2	yes	—
267	C₄×C₄₇⋊C₈	C₂³	1	2	yes	—
268	C₈×Dic₄₇	C₂³	1	2	yes	—
269	C₈×Dic₄₇	C₂³	1	2	yes	—
270	C₂×#41×C₄₇	C₂³	1	1	yes	characteristic
271	C₂×#41×C₄₇	C₂³	1	1	yes	characteristic
272	C₂×#41×C₄₇	C₂³	1	1	yes	characteristic
273	#135×C₄₇	—	2	4	no	—
274	#135×C₄₇	—	2	4	no	—
275	C₂×Q₁₆×C₄₇	C₂³	1	1	yes	characteristic
276	C₂×Q₁₆×C₄₇	C₂³	1	1	yes	characteristic
277	C₂×SD₁₆×C₄₇	C₂³	1	1	yes	characteristic
278	C₂×SD₁₆×C₄₇	C₂³	1	1	yes	characteristic
279	C₂×SD₁₆×C₄₇	C₂³	1	1	yes	characteristic
280	C₂×SD₁₆×C₄₇	C₂³	1	1	yes	characteristic
281	C₂×D₈×C₄₇	C₂³	1	1	yes	characteristic
282	C₂×D₈×C₄₇	C₂³	1	1	yes	characteristic
283	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
284	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
285	C₄⋊Q₈×C₄₇	C₂³	1	1	yes	characteristic
286	#127×C₄₇	C₂³	1	1	yes	characteristic
287	#124×C₄₇	C₂³	1	1	yes	characteristic
288	#124×C₄₇	C₂³	1	1	yes	characteristic
289	#121×C₄₇	—	2	1	no	—
290	#121×C₄₇	—	2	1	no	—
291	C₄×Q₈×C₄₇	C₂³	1	1	yes	characteristic
292	C₄×Q₈×C₄₇	C₂³	1	1	yes	characteristic
293	C₄×D₄×C₄₇	—	2	1	no	—
294	C₄×D₄×C₄₇	—	2	1	no	—
295	C₄×D₄×C₄₇	—	2	1	no	—
296	C₄×D₄×C₄₇	—	2	1	no	—
297	C₄×D₄×C₄₇	C₂³	1	1	yes	characteristic
298	C₄×D₄×C₄₇	C₂³	1	1	yes	characteristic
299	#117×C₄₇	—	2	1	no	—
300	#117×C₄₇	C₂³	1	1	yes	characteristic
301	C₂×C₄²×C₄₇	—	2	1	no	—
302	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
303	C₄⋊C₈×C₄₇	C₂³	1	1	yes	characteristic
304	C₄⋊C₈×C₄₇	C₂³	1	1	yes	characteristic
305	C₄⋊C₈×C₄₇	C₂³	1	1	yes	characteristic
306	C₄⋊C₈×C₄₇	C₂³	1	1	yes	characteristic
307	#103×C₄₇	C₂³	1	1	yes	characteristic
308	#103×C₄₇	C₂³	1	1	yes	characteristic
309	#103×C₄₇	C₂³	1	1	yes	characteristic
310	#103×C₄₇	C₂³	1	1	yes	characteristic
311	#102×C₄₇	C₂³	1	1	yes	characteristic
312	#102×C₄₇	C₂³	1	1	yes	characteristic
313	#102×C₄₇	C₂³	1	1	yes	characteristic
314	#102×C₄₇	C₂³	1	1	yes	characteristic
315	C₂³×D₄₇	—	2	1	no	—
316	#41×C₄₇	—	2	2	no	—
317	#41×C₄₇	—	2	2	no	—
318	#41×C₄₇	—	2	2	no	—
319	#41×C₄₇	—	2	2	no	—
320	#41×C₄₇	—	2	2	no	—
321	#41×C₄₇	#41	1	4	yes	complemented
322	C₂×Q₈×C₄₇	C₂⁴	1	1	yes	characteristic
323	C₂×Q₈×C₄₇	C₂⁴	1	1	yes	characteristic
324	C₂×Q₈×C₄₇	C₂⁴	1	1	yes	characteristic
325	C₂×D₄×C₄₇	—	2	1	no	—
326	C₂×D₄×C₄₇	—	2	1	no	—
327	C₂×D₄×C₄₇	—	2	1	no	—
328	C₂×D₄×C₄₇	—	2	1	no	—
329	C₂×D₄×C₄₇	—	2	1	no	—
330	C₂×D₄×C₄₇	C₂⁴	1	1	yes	characteristic
331	C₂×D₄×C₄₇	C₂⁴	1	1	yes	characteristic
332	C₂×D₄×C₄₇	C₂⁴	1	1	yes	characteristic
333	C₂²×C₄×C₄₇	—	2	1	no	—
334	C₂²×C₄×C₄₇	—	2	1	no	—
335	C₂²×C₄×C₄₇	—	2	1	no	—
336	C₂²×C₄×C₄₇	—	2	1	no	—
337	C₂²×C₄×C₄₇	—	2	1	no	—
338	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
339	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
340	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
341	C₂×C₂²⋊D₄₇	—	2	2	no	—
342	C₂×C₂²⋊D₄₇	—	2	2	no	—
343	C₂×C₂²⋊D₄₇	—	2	2	no	—
344	C₂×C₂²⋊D₄₇	—	2	2	no	—
345	C₂²×Dic₄₇	—	2	1	no	—
346	C₂²×Dic₄₇	—	2	1	no	—
347	C₂²×Dic₄₇	—	2	1	no	—
348	C₂²×Dic₄₇	—	2	2	no	—
349	C₂²×Dic₄₇	—	2	2	no	—
350	C₂²×Dic₄₇	—	2	2	no	—
351	C₂²×Dic₄₇	—	2	2	no	—
352	#10625352	—	8	4	no	—
353	C₂×D₁₈₈	—	2	2	no	—
354	C₂×D₁₈₈	—	2	2	no	—
355	C₂×D₁₈₈	—	2	1	no	—
356	C₂×D₁₈₈	C₂⁴	1	2	yes	—
357	C₂×C₄×D₄₇	—	2	2	no	—
358	C₂×C₄×D₄₇	—	2	2	no	—
359	C₂×C₄×D₄₇	—	8	2	no	—
360	C₂×Dic₉₄	—	2	2	no	—
361	C₂×Dic₉₄	—	2	2	no	—
362	C₂×Dic₉₄	C₂×D₄	1	2	yes	—
363	C₂×Dic₉₄	C₂×D₄	1	2	yes	—
364	Q₁₆×C₄₇	—	2	2	no	—
365	Q₁₆×C₄₇	—	2	2	no	—
366	SD₁₆×C₄₇	—	2	2	no	—
367	SD₁₆×C₄₇	—	2	2	no	—
368	SD₁₆×C₄₇	—	2	2	no	—
369	SD₁₆×C₄₇	—	2	2	no	—
370	D₈×C₄₇	—	2	2	no	—
371	D₈×C₄₇	—	2	2	no	—
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	C₂⁴	1	1	yes	characteristic
383	C₄⋊C₄×C₄₇	C₂⁴	1	1	yes	characteristic
384	C₂²⋊C₄×C₄₇	—	2	1	no	—
385	C₂²⋊C₄×C₄₇	—	2	1	no	—
386	C₂²⋊C₄×C₄₇	—	2	1	no	—
387	C₂²⋊C₄×C₄₇	—	2	1	no	—
388	C₂²⋊C₄×C₄₇	—	2	1	no	—
389	C₂²⋊C₄×C₄₇	—	2	1	no	—
390	C₂²⋊C₄×C₄₇	—	2	1	no	—
391	C₄²×C₄₇	—	2	1	no	—
392	C₄²×C₄₇	—	2	1	no	—
393	C₄²×C₄₇	—	2	1	no	—
394	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
395	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
396	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
397	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
398	C₂²⋊Dic₄₇	—	2	2	no	—
399	C₂²⋊Dic₄₇	—	2	2	no	—
400	C₂²⋊Dic₄₇	—	2	2	no	—
401	C₂²⋊Dic₄₇	—	2	2	no	—
402	C₂²⋊Dic₄₇	C₂×D₄	1	2	yes	—
403	C₂²⋊Dic₄₇	C₂×D₄	1	2	yes	—
404	#10625336	—	2	4	no	—
405	#10625334	—	2	4	no	—
406	(C₂×D₄₇)⋊C₄	—	2	2	no	—
407	(C₂×D₄₇)⋊C₄	—	2	2	no	—
408	(C₂×D₄₇)⋊C₄	—	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	C₄⋊Dic₄₇	—	2	1	no	—
413	C₄⋊Dic₄₇	—	2	1	no	—
414	C₄⋊Dic₄₇	—	2	1	no	—
415	C₄⋊Dic₄₇	—	2	2	no	—
416	C₄⋊Dic₄₇	—	2	2	no	—
417	C₄⋊Dic₄₇	—	2	2	no	—
418	C₄⋊Dic₄₇	—	2	2	no	—
419	C₄⋊Dic₄₇	—	2	2	no	—
420	C₄⋊Dic₄₇	—	2	2	no	—
421	C₄⋊Dic₄₇	C₂×D₄	1	1	yes	characteristic
422	C₄⋊Dic₄₇	C₂×D₄	1	1	yes	characteristic
423	C₄⋊Dic₄₇	C₂×D₄	1	1	yes	characteristic
424	C₄⋊Dic₄₇	C₂×D₄	1	2	yes	—
425	C₄⋊Dic₄₇	C₂×D₄	1	1	yes	characteristic
426	C₄⋊Dic₄₇	C₂×D₄	1	2	yes	—
427	C₄⋊Dic₄₇	C₂⁴	1	2	yes	—
428	C₄⋊Dic₄₇	C₂⁴	1	2	yes	—
429	C₄⋊Dic₄₇	C₂⁴	1	2	yes	—
430	Dic₄₇⋊C₄	—	2	2	no	—
431	Dic₄₇⋊C₄	—	2	2	no	—
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	C₂×D₄	1	2	yes	—
439	Dic₄₇⋊C₄	C₂×D₄	1	2	yes	—
440	Dic₄₇⋊C₄	C₂×D₄	1	2	yes	—
441	Dic₄₇⋊C₄	C₂×D₄	1	2	yes	—
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	C₂⁴	1	2	yes	—
447	C₄×Dic₄₇	C₂⁴	1	2	yes	—
448	#10625329	—	2	2	no	—
449	#10625329	—	2	2	no	—
450	C₂×C₄₇⋊C₈	C₂⁴	1	2	yes	—
451	C₂×C₄₇⋊C₈	C₂⁴	1	2	yes	—
452	C₂³×C₄₇	—	2	1	no	—
453	C₂³×C₄₇	—	2	1	no	—
454	C₂³×C₄₇	—	2	1	no	—
455	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
456	C₂²×D₄₇	—	2	2	no	—
457	C₂²×D₄₇	—	4	2	no	—
458	C₂²×D₄₇	—	8	1	no	—
459	C₂²×D₄₇	—	8	1	no	—
460	Q₈×C₄₇	—	2	1	no	—
461	Q₈×C₄₇	—	2	1	no	—
462	Q₈×C₄₇	—	2	1	no	—
463	Q₈×C₄₇	—	2	1	no	—
464	Q₈×C₄₇	—	2	1	no	—
465	Q₈×C₄₇	C₂×#41	1	2	yes	—
466	D₄×C₄₇	—	2	4	no	—
467	D₄×C₄₇	—	2	1	no	—
468	D₄×C₄₇	—	2	1	no	—
469	D₄×C₄₇	—	2	1	no	—
470	D₄×C₄₇	—	2	1	no	—
471	D₄×C₄₇	—	2	1	no	—
472	D₄×C₄₇	—	4	2	no	—
473	D₄×C₄₇	—	4	2	no	—
474	D₄×C₄₇	—	4	2	no	—
475	D₄×C₄₇	—	8	1	no	—
476	D₄×C₄₇	C₂×#41	1	2	yes	—
477	C₂×C₄×C₄₇	—	2	1	no	—
478	C₂×C₄×C₄₇	—	2	4	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	—	2	1	no	—
483	C₂×C₄×C₄₇	—	4	1	no	—
484	C₂×C₄×C₄₇	—	4	1	no	—
485	C₂×C₄×C₄₇	—	4	2	no	—
486	C₂×C₄×C₄₇	—	4	2	no	—
487	C₂×C₄×C₄₇	—	8	1	no	—
488	C₂×C₄×C₄₇	—	8	1	no	—
489	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
490	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
491	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
492	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
493	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
494	C₂×C₄×C₄₇	C₂×#41	1	2	yes	—
495	C₂×C₄×C₄₇	2₋¹⁺⁴	1	2	yes	—
496	C₂×C₄×C₄₇	C₂⁵	1	1	yes	characteristic
497	C₂²⋊D₄₇	—	8	2	no	—
498	C₂²⋊D₄₇	—	8	2	no	—
499	C₂²⋊D₄₇	—	8	2	no	—
500	C₂²⋊D₄₇	—	8	2	no	—
501	C₂×Dic₄₇	—	2	2	no	—
502	C₂×Dic₄₇	—	2	2	no	—
503	C₂×Dic₄₇	—	2	2	no	—
504	C₂×Dic₄₇	—	8	2	no	—
505	C₂×Dic₄₇	—	8	2	no	—
506	C₂×Dic₄₇	—	8	2	no	—
507	C₂×Dic₄₇	—	8	2	no	—
508	C₂×Dic₄₇	—	8	1	no	—
509	C₂×Dic₄₇	—	8	1	no	—
510	C₂×Dic₄₇	—	8	1	no	—
511	C₂×Dic₄₇	C₂²×D₄	1	2	yes	—
512	C₂×Dic₄₇	C₂²×D₄	1	2	yes	—
513	C₂×Dic₄₇	C₂²×D₄	1	2	yes	—
514	C₂×Dic₄₇	C₂²×D₄	1	2	yes	—
515	D₁₈₈	—	2	2	no	—
516	D₁₈₈	—	2	2	no	—
517	D₁₈₈	—	4	2	no	—
518	C₄×D₄₇	—	4	4	no	—
519	C₄×D₄₇	—	8	2	no	—
520	Dic₉₄	—	4	2	no	—
521	Dic₉₄	—	4	2	no	—
522	Dic₉₄	—	8	2	no	—
523	Dic₉₄	—	8	2	no	—
524	C₈×C₄₇	—	2	1	no	—
525	C₈×C₄₇	—	2	1	no	—
526	C₈×C₄₇	—	2	1	no	—
527	C₈×C₄₇	—	2	1	no	—
528	C₄₇⋊C₈	—	2	2	no	—
529	C₄₇⋊C₈	—	2	2	no	—
530	#61349	—	47	1	no	maximal, Sylow
531	C₂²×C₄₇	—	2	1	no	—
532	C₂²×C₄₇	—	2	1	no	—
533	C₂²×C₄₇	—	2	2	no	—
534	C₂²×C₄₇	—	4	1	no	—
535	C₂²×C₄₇	—	4	1	no	—
536	C₂²×C₄₇	—	4	1	no	—
537	C₂²×C₄₇	—	4	1	no	—
538	C₂²×C₄₇	—	4	1	no	—
539	C₂²×C₄₇	—	4	1	no	—
540	C₂²×C₄₇	—	4	1	no	—
541	C₂²×C₄₇	—	4	1	no	—
542	C₂²×C₄₇	#548	1	2	yes	—
543	C₂²×C₄₇	C₂³×D₄	1	1	yes	characteristic
544	C₂×D₄₇	—	4	2	no	—
545	C₂×D₄₇	—	4	2	no	—
546	C₂×D₄₇	—	4	2	no	—
547	C₂×D₄₇	—	8	4	no	—
548	C₄×C₄₇	—	2	1	no	—
549	C₄×C₄₇	—	2	1	no	—
550	C₄×C₄₇	—	2	1	no	—
551	C₄×C₄₇	—	2	1	no	—
552	C₄×C₄₇	—	2	2	no	—
553	C₄×C₄₇	—	4	1	no	—
554	C₄×C₄₇	—	4	1	no	—
555	C₄×C₄₇	—	4	1	no	—
556	C₄×C₄₇	—	4	1	no	—
557	C₄×C₄₇	#548	1	2	yes	—
558	C₄×C₄₇	C₂²×#41	1	1	yes	characteristic
559	C₄×C₄₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
560	Dic₄₇	—	2	2	no	—
561	Dic₄₇	—	2	2	no	—
562	Dic₄₇	—	2	2	no	—
563	Dic₄₇	—	2	2	no	—
564	Dic₄₇	—	4	2	no	—
565	Dic₄₇	—	4	2	no	—
566	Dic₄₇	—	4	2	no	—
567	#3506	—	47	1	no	—
568	#3504	—	47	1	no	—
569	#3377	—	47	2	no	—
570	#3376	—	47	2	no	—
571	#3371	—	47	2	no	—
572	#3370	—	47	2	no	—
573	#3368	—	47	2	no	—
574	#3366	—	47	2	no	—
575	#3365	—	47	2	no	—
576	#3361	—	47	2	no	—
577	#3142	—	47	1	no	—
578	#3136	—	47	1	no	—
579	#3136	—	47	1	no	—
580	#3084	—	47	1	no	—
581	#3083	—	47	1	no	—
582	C₂×#478	—	47	1	no	—
583	#3045	—	47	1	no	—
584	#3045	—	47	1	no	—
585	#3035	D₄₇	1	1	yes	characteristic, complemented
586	#2962	—	47	1	no	—
587	#2952	—	47	1	no	—
588	#2951	—	47	1	no	—
589	C₄×AGL(1,ℤ/8)	—	47	1	no	—
590	C₂×C₄₇	—	2	2	no	—
591	C₂×C₄₇	—	4	2	no	—
592	C₂×C₄₇	—	8	1	no	—
593	C₂×C₄₇	—	8	1	no	—
594	C₂×C₄₇	C₂×#548	1	1	yes	characteristic
595	C₂×C₄₇	#3584	1	1	yes	characteristic
596	C₂×C₄₇	#3585	1	1	yes	characteristic
597	D₄₇	—	8	2	no	—
598	C₂×AGL(1,ℤ/8)	—	47	1	no	—
599	C₂×#135	C₂×D₄₇	1	1	yes	characteristic
600	C₂×#135	C₂×D₄₇	1	1	yes	characteristic
601	#559	—	47	2	no	—
602	#559	—	47	2	no	—
603	#557	—	47	2	no	—
604	#557	—	47	2	no	—
605	#556	—	47	2	no	—
606	#555	—	94	1	no	—
607	#554	—	47	2	no	—
608	#554	—	47	2	no	—
609	#554	—	94	2	no	—
610	#554	—	94	2	no	—
611	#553	—	94	1	no	—
612	#553	—	94	1	no	—
613	#550	—	47	2	no	—
614	#547	—	94	1	no	—
615	#544	—	47	1	no	—
616	#544	—	47	1	no	—
617	#544	—	94	1	no	—
618	#544	—	94	1	no	—
619	#538	—	94	2	no	—
620	#535	—	47	1	no	—
621	#535	—	47	1	no	—
622	#533	—	47	1	no	—
623	#533	—	94	1	no	—
624	#532	C₂×D₄₇	1	1	yes	characteristic
625	C₂×#125	—	47	1	no	—
626	C₂×#125	—	94	1	no	—
627	#525	—	94	2	no	—
628	#520	—	47	1	no	—
629	#520	—	47	1	no	—
630	#520	—	47	1	no	—
631	#520	—	47	1	no	—
632	C₄×#41	C₂×D₄₇	1	1	yes	characteristic
633	C₂×C₄×D₄	—	47	1	no	—
634	#491	—	47	2	no	—
635	#490	—	47	2	no	—
636	#490	—	47	2	no	—
637	#490	—	47	2	no	—
638	#489	—	47	2	no	—
639	#489	—	47	2	no	—
640	#488	—	47	2	no	—
641	#488	—	47	2	no	—
642	#488	—	47	2	no	—
643	#488	—	47	2	no	—
644	#486	—	47	2	no	—
645	#486	—	47	2	no	—
646	#479	—	47	2	no	—
647	#479	—	47	2	no	—
648	#478	—	47	2	no	—
649	#478	—	47	2	no	—
650	#478	—	47	2	no	—
651	#478	—	47	2	no	—
652	#478	—	47	2	no	—
653	#478	—	47	2	no	—
654	#477	—	47	2	no	—
655	#476	—	47	2	no	—
656	#475	—	47	2	no	—
657	#474	—	47	2	no	—
658	#464	—	47	2	no	—
659	#464	—	47	2	no	—
660	#464	C₂×D₄₇	1	1	yes	characteristic, complemented
661	#464	C₂×D₄₇	1	1	yes	characteristic, complemented
662	#463	—	47	2	no	—
663	#463	—	47	2	no	—
664	#463	C₂×D₄₇	1	1	yes	characteristic, complemented
665	#463	C₂×D₄₇	1	1	yes	characteristic, complemented
666	#462	C₂×D₄₇	1	1	yes	characteristic, complemented
667	#461	C₂×D₄₇	1	1	yes	characteristic, complemented
668	#460	—	47	2	no	—
669	#460	—	47	2	no	—
670	#460	C₂×D₄₇	1	1	yes	characteristic, complemented
671	#459	—	47	2	no	—
672	#459	—	47	2	no	—
673	#459	C₂×D₄₇	1	1	yes	characteristic, complemented
674	#446	—	47	2	no	—
675	#446	—	47	2	no	—
676	#446	—	47	2	no	—
677	C₈×Q₈	—	47	2	no	—
678	#442	—	47	2	no	—
679	#442	—	47	2	no	—
680	#441	—	47	2	no	—
681	#440	—	47	2	no	—
682	#440	—	47	2	no	—
683	#440	—	47	2	no	—
684	C₄×Q₁₆	—	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	C₄×D₈	—	47	2	no	—
690	#428	—	47	1	no	—
691	C₂×#107	—	47	1	no	—
692	C₂×#106	—	47	1	no	—
693	#424	—	47	1	no	—
694	#424	—	47	1	no	—
695	C₂×C₄⋊C₈	C₂×D₄₇	1	1	yes	characteristic
696	#418	—	47	1	no	—
697	#417	—	47	1	no	—
698	#417	—	47	1	no	—
699	#417	—	47	1	no	—
700	#417	—	47	1	no	—
701	#417	—	47	1	no	—
702	#416	C₂×D₄₇	1	1	yes	characteristic
703	#416	C₂×D₄₇	1	1	yes	characteristic
704	C₂×#102	—	47	1	no	—
705	C₂×#102	—	47	1	no	—
706	#405	—	47	1	no	—
707	#405	—	47	1	no	—
708	C₄×M₁₆	—	47	1	no	—
709	C₄₇	#61349	1	1	yes	characteristic, complemented, Sylow
710	C₂×#41	—	94	2	no	—
711	C₂×#41	C₂²×D₄₇	1	1	yes	characteristic
712	C₂×#41	C₂²×D₄₇	1	1	yes	characteristic
713	C₂×#41	C₂²×D₄₇	1	1	yes	characteristic
714	C₂²×D₄	—	47	1	no	—
715	C₂³×C₄	—	94	1	no	—
716	AGL(1,ℤ/8)	—	94	4	no	—
717	#135	—	2	4	no	—
718	#135	—	2	4	no	—
719	C₂×Q₁₆	C₂²×D₄₇	1	1	yes	characteristic
720	C₂×Q₁₆	C₂²×D₄₇	1	1	yes	characteristic
721	C₂×SD₁₆	—	47	2	no	—
722	C₂×SD₁₆	C₂²×D₄₇	1	1	yes	characteristic
723	C₂×SD₁₆	C₂²×D₄₇	1	1	yes	characteristic
724	C₂×SD₁₆	C₂²×D₄₇	1	1	yes	characteristic
725	C₂×SD₁₆	C₂²×D₄₇	1	1	yes	characteristic
726	C₂×D₈	—	47	2	no	—
727	C₂×D₈	C₂²×D₄₇	1	1	yes	characteristic
728	C₂×D₈	C₂²×D₄₇	1	1	yes	characteristic
729	C₂×M₁₆	—	47	1	no	—
730	C₂×M₁₆	—	47	1	no	—
731	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
732	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
733	C₄⋊Q₈	—	47	2	no	—
734	C₄⋊Q₈	—	47	2	no	—
735	C₄⋊Q₈	—	47	1	no	—
736	C₄⋊Q₈	—	47	1	no	—
737	C₄⋊Q₈	—	94	1	no	—
738	C₄⋊Q₈	—	94	1	no	—
739	C₄⋊Q₈	—	94	2	no	—
740	C₄⋊Q₈	—	94	2	no	—
741	C₄⋊Q₈	C₂²×D₄₇	1	1	yes	characteristic
742	#127	—	47	2	no	—
743	#127	—	47	2	no	—
744	#127	C₂²×D₄₇	1	1	yes	characteristic
745	#126	—	94	2	no	—
746	#126	—	94	2	no	—
747	#125	—	47	2	no	—
748	#125	—	47	2	no	—
749	#125	—	47	1	no	—
750	#125	—	47	1	no	—
751	#125	—	47	2	no	—
752	#125	—	47	2	no	—
753	#125	—	94	1	no	—
754	#125	—	94	1	no	—
755	#125	—	94	2	no	—
756	#125	—	94	2	no	—
757	#125	—	94	2	no	—
758	#125	—	94	2	no	—
759	#125	—	94	1	no	—
760	#125	—	94	1	no	—
761	#124	—	47	2	no	—
762	#124	—	47	2	no	—
763	#124	—	94	2	no	—
764	#124	—	94	2	no	—
765	#124	C₂²×D₄₇	1	1	yes	characteristic
766	#124	C₂²×D₄₇	1	1	yes	characteristic
767	#123	—	94	2	no	—
768	#123	—	94	2	no	—
769	#123	—	94	2	no	—
770	#123	—	94	2	no	—
771	C₂²⋊Q₈	—	47	2	no	—
772	C₂²⋊Q₈	—	47	2	no	—
773	C₂²⋊Q₈	—	94	2	no	—
774	C₂²⋊Q₈	—	94	2	no	—
775	C₂²⋊Q₈	—	94	2	no	—
776	C₂²⋊Q₈	—	94	2	no	—
777	C₂²⋊Q₈	—	94	2	no	—
778	C₂²⋊Q₈	—	94	2	no	—
779	C₂²⋊Q₈	—	94	2	no	—
780	C₂²⋊Q₈	—	94	2	no	—
781	C₂²⋊Q₈	—	94	2	no	—
782	#121	—	2	1	no	—
783	#121	—	2	1	no	—
784	#121	—	94	1	no	—
785	#121	—	94	1	no	—
786	#121	—	94	1	no	—
787	#121	—	94	1	no	—
788	#121	—	94	2	no	—
789	#121	—	94	2	no	—
790	#121	—	94	2	no	—
791	#120	—	94	2	no	—
792	#120	—	94	2	no	—
793	C₄×Q₈	—	47	2	no	—
794	C₄×Q₈	—	47	2	no	—
795	C₄×Q₈	—	47	2	no	—
796	C₄×Q₈	—	47	2	no	—
797	C₄×Q₈	—	47	2	no	—
798	C₄×Q₈	—	47	2	no	—
799	C₄×Q₈	—	94	2	no	—
800	C₄×Q₈	—	94	2	no	—
801	C₄×Q₈	C₂²×D₄₇	1	1	yes	characteristic
802	C₄×Q₈	C₂²×D₄₇	1	1	yes	characteristic
803	C₄×D₄	—	2	1	no	—
804	C₄×D₄	—	2	1	no	—
805	C₄×D₄	—	2	1	no	—
806	C₄×D₄	—	2	1	no	—
807	C₄×D₄	—	47	2	no	—
808	C₄×D₄	—	47	2	no	—
809	C₄×D₄	—	47	2	no	—
810	C₄×D₄	—	47	2	no	—
811	C₄×D₄	—	47	2	no	—
812	C₄×D₄	—	47	2	no	—
813	C₄×D₄	—	94	2	no	—
814	C₄×D₄	—	94	2	no	—
815	C₄×D₄	—	94	2	no	—
816	C₄×D₄	—	94	2	no	—
817	C₄×D₄	—	94	2	no	—
818	C₄×D₄	—	94	2	no	—
819	C₄×D₄	—	94	1	no	—
820	C₄×D₄	—	94	1	no	—
821	C₄×D₄	C₂²×D₄₇	1	1	yes	characteristic
822	C₄×D₄	C₂²×D₄₇	1	1	yes	characteristic
823	#117	—	2	1	no	—
824	#117	—	47	1	no	—
825	#117	—	47	1	no	—
826	#117	—	94	2	no	—
827	#117	—	94	1	no	—
828	#117	—	94	1	no	—
829	#117	—	94	1	no	—
830	#117	—	94	1	no	—
831	#117	C₂²×D₄₇	1	1	yes	characteristic
832	C₂×C₄⋊C₄	—	47	1	no	—
833	C₂×C₄⋊C₄	—	47	1	no	—
834	C₂×C₄⋊C₄	—	47	1	no	—
835	C₂×C₄⋊C₄	—	94	1	no	—
836	C₂×C₄⋊C₄	—	94	1	no	—
837	C₂×C₄⋊C₄	—	94	1	no	—
838	C₂×C₄⋊C₄	—	94	1	no	—
839	C₂×C₄⋊C₄	—	94	2	no	—
840	C₂×C₄⋊C₄	—	94	2	no	—
841	C₂×C₄⋊C₄	—	94	1	no	—
842	C₂×C₄⋊C₄	—	94	1	no	—
843	C₂×C₂²⋊C₄	—	94	1	no	—
844	C₂×C₄²	—	2	1	no	—
845	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
846	#107	—	47	2	no	—
847	#107	—	47	2	no	—
848	#107	—	47	2	no	—
849	#106	—	47	2	no	—
850	#106	—	47	2	no	—
851	#106	—	47	2	no	—
852	C₄⋊C₈	—	47	2	no	—
853	C₄⋊C₈	—	47	2	no	—
854	C₄⋊C₈	—	47	2	no	—
855	C₄⋊C₈	—	47	2	no	—
856	C₄⋊C₈	C₂²×D₄₇	1	1	yes	characteristic
857	C₄⋊C₈	C₂²×D₄₇	1	1	yes	characteristic
858	C₄⋊C₈	C₂²×D₄₇	1	1	yes	characteristic
859	C₄⋊C₈	C₂²×D₄₇	1	1	yes	characteristic
860	#103	—	47	2	no	—
861	#103	—	47	2	no	—
862	#103	—	47	2	no	—
863	#103	—	47	2	no	—
864	#103	—	47	2	no	—
865	#103	C₂²×D₄₇	1	1	yes	characteristic
866	#103	C₂²×D₄₇	1	1	yes	characteristic
867	#103	C₂²×D₄₇	1	1	yes	characteristic
868	#103	C₂²×D₄₇	1	1	yes	characteristic
869	#102	—	47	2	no	—
870	#102	—	47	2	no	—
871	#102	—	47	2	no	—
872	#102	—	47	2	no	—
873	#102	—	47	2	no	—
874	#102	—	47	2	no	—
875	#102	—	47	2	no	—
876	#102	—	47	2	no	—
877	#102	—	47	2	no	—
878	#102	—	47	2	no	—
879	#102	—	47	2	no	—
880	#102	C₂²×D₄₇	1	1	yes	characteristic
881	#102	C₂²×D₄₇	1	1	yes	characteristic
882	#102	C₂²×D₄₇	1	1	yes	characteristic
883	#102	C₂²×D₄₇	1	1	yes	characteristic
884	#97	—	47	2	no	—
885	#97	—	47	2	no	—
886	#97	—	47	2	no	—
887	C₄×C₈	—	47	2	no	—
888	C₄×C₈	—	47	2	no	—
889	C₄×C₈	—	47	2	no	—
890	C₂⁴	—	94	1	no	—
891	#41	—	2	2	no	—
892	#41	—	2	2	no	—
893	#41	—	2	2	no	—
894	#41	—	2	2	no	—
895	#41	—	2	2	no	—
896	#41	—	376	4	no	—
897	#41	#10625352	1	4	yes	complemented
898	C₂×Q₈	—	47	2	no	—
899	C₂×Q₈	—	47	2	no	—
900	C₂×Q₈	—	94	2	no	—
901	C₂×Q₈	—	94	2	no	—
902	C₂×Q₈	C₂³×D₄₇	1	1	yes	characteristic
903	C₂×Q₈	C₂³×D₄₇	1	1	yes	characteristic
904	C₂×Q₈	C₂³×D₄₇	1	1	yes	characteristic
905	C₂×D₄	—	2	1	no	—
906	C₂×D₄	—	2	1	no	—
907	C₂×D₄	—	2	1	no	—
908	C₂×D₄	—	2	1	no	—
909	C₂×D₄	—	2	1	no	—
910	C₂×D₄	—	47	2	no	—
911	C₂×D₄	—	94	2	no	—
912	C₂×D₄	—	94	2	no	—
913	C₂×D₄	—	94	2	no	—
914	C₂×D₄	—	94	2	no	—
915	C₂×D₄	—	94	1	no	—
916	C₂×D₄	—	94	2	no	—
917	C₂×D₄	—	94	2	no	—
918	C₂×D₄	C₂³×D₄₇	1	1	yes	characteristic
919	C₂×D₄	C₂³×D₄₇	1	1	yes	characteristic
920	C₂×D₄	C₂³×D₄₇	1	1	yes	characteristic
921	C₂²×C₄	—	2	1	no	—
922	C₂²×C₄	—	2	1	no	—
923	C₂²×C₄	—	2	1	no	—
924	C₂²×C₄	—	2	1	no	—
925	C₂²×C₄	—	2	1	no	—
926	C₂²×C₄	—	94	2	no	—
927	C₂²×C₄	—	94	2	no	—
928	C₂²×C₄	—	94	2	no	—
929	C₂²×C₄	—	94	2	no	—
930	C₂²×C₄	—	94	1	no	—
931	C₂²×C₄	—	94	1	no	—
932	C₂²×C₄	—	94	1	no	—
933	C₂²×C₄	—	94	2	no	—
934	C₂²×C₄	—	94	2	no	—
935	C₂²×C₄	—	376	2	no	—
936	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
937	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
938	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
939	Q₁₆	—	2	2	no	—
940	Q₁₆	—	2	2	no	—
941	SD₁₆	—	2	2	no	—
942	SD₁₆	—	2	2	no	—
943	SD₁₆	—	2	2	no	—
944	SD₁₆	—	2	2	no	—
945	SD₁₆	—	94	4	no	—
946	D₈	—	2	2	no	—
947	D₈	—	2	2	no	—
948	D₈	—	94	4	no	—
949	M₁₆	—	94	2	no	—
950	M₁₆	—	94	2	no	—
951	C₂×C₈	—	2	2	no	—
952	C₂×C₈	—	2	2	no	—
953	C₂×C₈	—	47	2	no	—
954	C₂×C₈	—	47	2	no	—
955	C₂×C₈	C₂³×D₄₇	1	1	yes	characteristic
956	C₂×C₈	C₂³×D₄₇	1	1	yes	characteristic
957	C₂×C₈	C₂³×D₄₇	1	1	yes	characteristic
958	C₂×C₈	C₂³×D₄₇	1	1	yes	characteristic
959	C₄⋊C₄	—	2	1	no	—
960	C₄⋊C₄	—	2	1	no	—
961	C₄⋊C₄	—	2	1	no	—
962	C₄⋊C₄	—	2	1	no	—
963	C₄⋊C₄	—	47	2	no	—
964	C₄⋊C₄	—	47	2	no	—
965	C₄⋊C₄	—	47	2	no	—
966	C₄⋊C₄	—	47	2	no	—
967	C₄⋊C₄	—	47	1	no	—
968	C₄⋊C₄	—	47	1	no	—
969	C₄⋊C₄	—	47	1	no	—
970	C₄⋊C₄	—	47	1	no	—
971	C₄⋊C₄	—	47	2	no	—
972	C₄⋊C₄	—	47	2	no	—
973	C₄⋊C₄	—	47	2	no	—
974	C₄⋊C₄	—	47	2	no	—
975	C₄⋊C₄	—	47	2	no	—
976	C₄⋊C₄	—	94	2	no	—
977	C₄⋊C₄	—	94	2	no	—
978	C₄⋊C₄	—	94	2	no	—
979	C₄⋊C₄	—	94	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	—	94	1	no	—
992	C₄⋊C₄	—	94	1	no	—
993	C₄⋊C₄	C₂³×D₄₇	1	1	yes	characteristic
994	C₄⋊C₄	C₂³×D₄₇	1	1	yes	characteristic
995	C₂²⋊C₄	—	2	1	no	—
996	C₂²⋊C₄	—	2	1	no	—
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	—	94	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	C₄²	—	2	1	no	—
1015	C₄²	—	2	1	no	—
1016	C₄²	—	2	1	no	—
1017	C₄²	—	47	2	no	—
1018	C₄²	—	47	2	no	—
1019	C₄²	—	94	2	no	—
1020	C₄²	—	94	2	no	—
1021	C₄²	—	94	2	no	—
1022	C₄²	—	94	2	no	—
1023	C₄²	D₄×D₄₇	1	1	yes	characteristic
1024	C₄²	D₄×D₄₇	1	1	yes	characteristic
1025	C₄²	C₂³×D₄₇	1	1	yes	characteristic
1026	C₄²	C₂³×D₄₇	1	1	yes	characteristic
1027	C₂³	—	2	1	no	—
1028	C₂³	—	2	1	no	—
1029	C₂³	—	2	1	no	—
1030	C₂³	—	94	2	no	—
1031	C₂³	—	376	1	no	—
1032	C₂³	—	376	1	no	—
1033	C₂³	—	188	2	no	—
1034	C₂³	C₂×D₄×D₄₇	1	1	yes	characteristic
1035	Q₈	—	2	1	no	—
1036	Q₈	—	2	1	no	—
1037	Q₈	—	2	1	no	—
1038	Q₈	—	2	1	no	—
1039	Q₈	—	2	1	no	—
1040	Q₈	—	376	2	no	—
1041	Q₈	—	376	2	no	—
1042	Q₈	—	188	2	no	—
1043	Q₈	—	188	2	no	—
1044	Q₈	C₂×#10625352	1	2	yes	—
1045	D₄	—	2	4	no	—
1046	D₄	—	2	1	no	—
1047	D₄	—	2	1	no	—
1048	D₄	—	2	1	no	—
1049	D₄	—	2	1	no	—
1050	D₄	—	2	1	no	—
1051	D₄	—	4	2	no	—
1052	D₄	—	4	2	no	—
1053	D₄	—	4	2	no	—
1054	D₄	—	8	1	no	—
1055	D₄	—	94	2	no	—
1056	D₄	—	94	2	no	—
1057	D₄	—	376	2	no	—
1058	D₄	—	376	2	no	—
1059	D₄	—	376	2	no	—
1060	D₄	—	376	2	no	—
1061	D₄	—	188	2	no	—
1062	D₄	C₂×#10625352	1	2	yes	—
1063	C₂×C₄	—	2	1	no	—
1064	C₂×C₄	—	2	4	no	—
1065	C₂×C₄	—	2	1	no	—
1066	C₂×C₄	—	2	1	no	—
1067	C₂×C₄	—	2	1	no	—
1068	C₂×C₄	—	2	1	no	—
1069	C₂×C₄	—	4	1	no	—
1070	C₂×C₄	—	4	1	no	—
1071	C₂×C₄	—	4	2	no	—
1072	C₂×C₄	—	4	2	no	—
1073	C₂×C₄	—	8	1	no	—
1074	C₂×C₄	—	8	1	no	—
1075	C₂×C₄	—	47	2	no	—
1076	C₂×C₄	—	47	2	no	—
1077	C₂×C₄	—	47	2	no	—
1078	C₂×C₄	—	47	2	no	—
1079	C₂×C₄	—	94	2	no	—
1080	C₂×C₄	—	94	2	no	—
1081	C₂×C₄	—	94	2	no	—
1082	C₂×C₄	—	376	2	no	—
1083	C₂×C₄	—	376	2	no	—
1084	C₂×C₄	—	376	2	no	—
1085	C₂×C₄	—	376	2	no	—
1086	C₂×C₄	—	376	2	no	—
1087	C₂×C₄	—	376	1	no	—
1088	C₂×C₄	—	376	1	no	—
1089	C₂×C₄	—	376	1	no	—
1090	C₂×C₄	—	188	4	no	—
1091	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
1092	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
1093	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
1094	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
1095	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
1096	C₂×C₄	C₂×#10625352	1	2	yes	—
1097	C₂×C₄	#13094071	1	2	yes	—
1098	C₂×C₄	C₂⁴×D₄₇	1	1	yes	characteristic
1099	C₈	—	2	1	no	—
1100	C₈	—	2	1	no	—
1101	C₈	—	2	1	no	—
1102	C₈	—	2	1	no	—
1103	C₈	—	94	2	no	—
1104	C₈	—	94	2	no	—
1105	C₂²	—	2	1	no	—
1106	C₂²	—	2	1	no	—
1107	C₂²	—	2	2	no	—
1108	C₂²	—	4	1	no	—
1109	C₂²	—	4	1	no	—
1110	C₂²	—	4	1	no	—
1111	C₂²	—	4	1	no	—
1112	C₂²	—	4	1	no	—
1113	C₂²	—	4	1	no	—
1114	C₂²	—	4	1	no	—
1115	C₂²	—	4	1	no	—
1116	C₂²	—	376	4	no	—
1117	C₂²	—	188	2	no	—
1118	C₂²	—	188	2	no	—
1119	C₂²	—	188	2	no	—
1120	C₂²	#15689779	1	2	yes	—
1121	C₂²	C₂²×D₄×D₄₇	1	1	yes	characteristic
1122	C₄	—	2	2	no	—
1123	C₄	—	2	1	no	—
1124	C₄	—	2	1	no	—
1125	C₄	—	2	1	no	—
1126	C₄	—	2	1	no	—
1127	C₄	—	4	1	no	—
1128	C₄	—	4	1	no	—
1129	C₄	—	4	1	no	—
1130	C₄	—	4	1	no	—
1131	C₄	—	94	2	no	—
1132	C₄	—	94	2	no	—
1133	C₄	—	94	2	no	—
1134	C₄	—	94	2	no	—
1135	C₄	—	188	2	no	—
1136	C₄	—	188	2	no	—
1137	C₄	—	188	2	no	—
1138	C₄	#15689779	1	2	yes	—
1139	C₄	C₂²×#10625352	1	1	yes	characteristic
1140	C₄	C₂×#13094071	1	1	yes	characteristic
1141	C₂	—	2	2	no	—
1142	C₂	—	4	2	no	—
1143	C₂	—	8	1	no	—
1144	C₂	—	8	1	no	—
1145	C₂	—	376	2	no	—
1146	C₂	C₂×#15689779	1	1	yes	characteristic
1147	C₂	#20258157	1	1	yes	characteristic
1148	C₂	#20258165	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×#3035	C₂
socle	C₂²×C₄₇	C₂³×D₄
hypercenter	#3035	D₄₇
hypocenter	C₄₇	#61349
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #3035

Complements

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

N	H ≅ G/N	type
1. #20257237	C₂	semidirect
2. #20257214	C₂	semidirect
3. #20256223	C₂	semidirect
4. #20256208	C₂	semidirect
5. #20256160	C₂	semidirect
6. #20256145	C₂	semidirect
7. #20256112	C₂	semidirect
8. #20256090	C₂	semidirect
9. #20256079	C₂	semidirect
10. #20256043	C₂	semidirect
11. #20253788	C₂	semidirect
12. #20253746	C₂	semidirect
13. #20253746	C₂	semidirect
14. #20253248	C₂	semidirect
15. #20253237	C₂	semidirect
16. C₂×#15689424	C₂	semidirect
17. #20252925	C₂	semidirect
18. #20252925	C₂	semidirect
19. #20252331	C₂	semidirect
20. #20252272	C₂	semidirect
21. #20252264	C₂	semidirect
22. C₄×#13094049	C₂	semidirect
23. C₄₇×#3035	C₂	semidirect
27. #15689849	C₂²	semidirect
28. #15689849	C₂²	semidirect
33. #15689832	C₂²	semidirect
34. #15689832	C₂²	semidirect
56. #15689491	C₂²	semidirect
57. #15689487	C₂²	semidirect
64. #15689477	C₂²	semidirect
65. #15689477	C₂²	semidirect
68. #15689432	C₂²	semidirect
69. #15689428	C₂²	semidirect
70. #15689425	C₂²	semidirect
75. #15689421	C₂²	semidirect
76. #15689416	C₂²	semidirect
77. #15689411	C₂²	semidirect
78. #15689406	C₂²	semidirect
79. #15689401	C₂²	semidirect
88. #15689252	C₂²	semidirect
89. #15689252	C₂²	semidirect
90. #15689250	C₂²	semidirect
91. #15689247	C₂²	semidirect
92. #15689235	C₂²	semidirect
94. #15689230	C₂²	semidirect
95. #15689224	C₂²	semidirect
96. #15689224	C₂²	semidirect
98. Q₁₆×Dic₄₇	C₂²	semidirect
99. SD₁₆×Dic₄₇	C₂²	semidirect
100. SD₁₆×Dic₄₇	C₂²	semidirect
102. D₈×Dic₄₇	C₂²	semidirect
124. C₄₇×#464	C₂²	semidirect
125. C₄₇×#464	C₂²	semidirect
126. C₄₇×#463	C₂²	semidirect
127. C₄₇×#463	C₂²	semidirect
128. C₄₇×#462	C₂²	semidirect
129. C₄₇×#461	C₂²	semidirect
130. C₄₇×#460	C₂²	semidirect
131. C₄₇×#459	C₂²	semidirect
321. #41×C₄₇	#41	semidirect
585. #3035	D₄₇	semidirect
660. #464	C₂×D₄₇	semidirect
661. #464	C₂×D₄₇	semidirect
664. #463	C₂×D₄₇	semidirect
665. #463	C₂×D₄₇	semidirect
666. #462	C₂×D₄₇	semidirect
667. #461	C₂×D₄₇	semidirect
670. #460	C₂×D₄₇	semidirect
673. #459	C₂×D₄₇	semidirect
709. C₄₇	#61349	semidirect
897. #41	#10625352	semidirect

Maximal subgroups

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

subgroup	index
#20257237	2
#20257214	2
#20256223	2
#20256208	2
#20256160	2
#20256145	2
#20256112	2
#20256090	2
#20256079	2
#20256043	2
#20253788	2
#20253746	2
#20253248	2
#20253237	2
C₂×#15689424	2
#20252925	2
#20252331	2
#20252272	2
#20252264	2
C₄×#13094049	2
C₄₇×#3035	2
#61349	47