Subgroups — #27097662

Order 12032.

1932 conjugacy classes of subgroups.

The subgroup lattice has 1218 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20257284	C₂	1	1	yes	maximal, characteristic, complemented
2	#20257237	C₂	1	1	yes	maximal, characteristic, complemented
3	#20256476	C₂	1	2	yes	maximal, complemented
4	#20256462	C₂	1	2	yes	maximal, complemented
5	#20256461	C₂	1	2	yes	maximal, complemented
6	#20256458	C₂	1	2	yes	maximal, complemented
7	#20256433	C₂	1	2	yes	maximal, complemented
8	#20256403	C₂	1	2	yes	maximal, complemented
9	#20256395	C₂	1	2	yes	maximal, complemented
10	#20256379	C₂	1	2	yes	maximal, complemented
11	#20253875	C₂	1	1	yes	maximal, characteristic, complemented
12	#20253865	C₂	1	1	yes	maximal, characteristic, complemented
13	#20253856	C₂	1	1	yes	maximal, characteristic, complemented
14	#20252936	C₂	1	1	yes	maximal, characteristic, complemented
15	#20252925	C₂	1	1	yes	maximal, characteristic, complemented
16	#20252912	C₂	1	1	yes	maximal, characteristic, complemented
17	#20252894	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×#15689339	C₂	1	1	yes	maximal, characteristic, complemented
19	#20252331	C₂	1	1	yes	maximal, characteristic, complemented
20	#20252234	C₂	1	1	yes	maximal, characteristic, complemented
21	#20252223	C₂	1	1	yes	maximal, characteristic, complemented
22	C₄×#13094049	C₂	1	1	yes	maximal, characteristic, complemented
23	C₄₇×#3035	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#13094054	C₂²	1	1	yes	characteristic
25	C₂×#13094054	C₂²	1	1	yes	characteristic
26	C₂×#13094049	C₂²	1	1	yes	characteristic
27	C₂×#13094049	C₂²	1	1	yes	characteristic
28	C₂×#13094049	C₂²	1	1	yes	characteristic
29	C₂²×#10625325	C₂²	1	1	yes	characteristic
30	C₂²×D₃₇₆	C₂²	1	1	yes	characteristic
31	#15689856	C₂²	1	2	yes	complemented
32	#15689856	C₂²	1	2	yes	complemented
33	#15689855	C₂²	1	2	yes	complemented
34	#15689855	C₂²	1	2	yes	complemented
35	#15689847	C₂²	1	2	yes	complemented
36	#15689845	C₂²	1	2	yes	complemented
37	#15689845	C₂²	1	2	yes	complemented
38	#15689838	—	2	1	no	—
39	#15689819	—	2	1	no	—
40	#15689819	—	2	1	no	—
41	#15689802	—	2	2	no	—
42	#15689802	—	2	2	no	—
43	#15689793	C₂²	1	2	yes	complemented
44	#15689777	—	2	1	no	—
45	#15689744	—	2	1	no	—
46	#15689744	—	2	1	no	—
47	#15689710	—	2	2	no	—
48	#15689694	C₂²	1	1	yes	characteristic
49	#15689687	C₂²	1	1	yes	characteristic
50	#15689687	C₂²	1	1	yes	characteristic
51	#15689687	C₂²	1	1	yes	characteristic
52	#15689680	C₂²	1	1	yes	characteristic
53	#15689657	—	2	1	no	—
54	#15689657	—	2	1	no	—
55	C₂×#13094012	C₂²	1	1	yes	characteristic
56	#15689633	—	2	2	no	—
57	#15689606	C₂²	1	1	yes	characteristic
58	#15689606	C₂²	1	1	yes	characteristic
59	#15689600	C₂²	1	1	yes	characteristic
60	#15689597	C₂²	1	1	yes	characteristic
61	C₂×C₄×D₁₈₈	C₂²	1	1	yes	characteristic
62	#15689516	C₂²	1	2	yes	complemented
63	#15689515	C₂²	1	2	yes	complemented
64	#15689511	C₂²	1	2	yes	complemented
65	#15689510	C₂²	1	2	yes	complemented
66	#15689509	C₂²	1	2	yes	—
67	#15689509	C₂²	1	2	yes	—
68	#15689508	C₂²	1	2	yes	—
69	#15689505	C₂²	1	2	yes	complemented
70	#15689505	C₂²	1	2	yes	complemented
71	#15689504	C₂²	1	2	yes	complemented
72	#15689498	C₂²	1	2	yes	—
73	#15689494	C₂²	1	2	yes	complemented
74	#15689348	C₂²	1	2	yes	complemented
75	#15689348	C₂²	1	2	yes	complemented
76	#15689347	C₂²	1	2	yes	complemented
77	#15689343	C₂²	1	2	yes	complemented
78	#15689341	C₂²	1	2	yes	—
79	#15689341	C₂²	1	2	yes	—
80	#15689340	C₂²	1	2	yes	complemented
81	#15689339	C₂²	1	2	yes	—
82	#15689339	C₂²	1	2	yes	—
83	#15689339	C₂²	1	2	yes	—
84	#15689339	C₂²	1	2	yes	—
85	#15689336	C₂²	1	2	yes	complemented
86	#15689331	C₂²	1	2	yes	complemented
87	#15689326	C₂²	1	2	yes	complemented
88	#15689322	C₂²	1	2	yes	complemented
89	#15689322	C₂²	1	2	yes	complemented
90	#15689321	C₂²	1	2	yes	complemented
91	#15689317	C₂²	1	2	yes	—
92	#15689317	C₂²	1	2	yes	—
93	#15689316	C₂²	1	2	yes	complemented
94	#15689252	C₂²	1	2	yes	complemented
95	#15689252	C₂²	1	2	yes	complemented
96	#15689250	C₂²	1	2	yes	complemented
97	#15689247	C₂²	1	2	yes	complemented
98	#15689233	C₂²	1	2	yes	complemented
99	#15689232	C₂²	1	2	yes	complemented
100	#15689227	C₂²	1	2	yes	complemented
101	#15689226	C₂²	1	2	yes	complemented
102	#15689221	C₂²	1	2	yes	complemented
103	#15689220	C₂²	1	2	yes	complemented
104	#15689215	C₂²	1	2	yes	complemented
105	#15689214	C₂²	1	2	yes	complemented
106	C₄×#10625336	C₂²	1	2	yes	complemented
107	#15689208	C₂²	1	2	yes	complemented
108	C₄×#10625334	C₂²	1	2	yes	complemented
109	#15689203	C₂²	1	2	yes	complemented
110	#15689166	C₂²	1	1	yes	characteristic
111	#15689149	C₂²	1	1	yes	characteristic
112	#15689149	C₂²	1	1	yes	characteristic
113	#15689127	C₂²	1	1	yes	characteristic
114	#15689124	C₂²	1	1	yes	characteristic
115	C₂×#13093949	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×Dic₉₄	C₂³	1	1	yes	characteristic
137	C₂²×D₁₈₈	C₂³	1	1	yes	characteristic
138	C₂²×D₁₈₈	C₂³	1	1	yes	characteristic
139	C₂²×C₄×D₄₇	—	2	1	no	—
140	#13094054	—	2	4	no	—
141	#13094054	—	4	2	no	—
142	#13094049	—	2	4	no	—
143	#13094049	—	2	4	no	—
144	#13094049	—	4	2	no	—
145	C₂×#10625337	C₂³	1	2	yes	—
146	C₂×#10625337	C₂³	1	2	yes	—
147	C₂×#10625325	—	4	2	no	—
148	C₂×#10625325	C₂³	1	2	yes	—
149	C₂×#10625325	C₂³	1	2	yes	—
150	C₂×#10625335	C₂³	1	2	yes	—
151	C₂×#10625335	C₂³	1	2	yes	—
152	C₂×#10625336	C₂³	1	2	yes	—
153	C₂×#10625336	C₂³	1	2	yes	—
154	C₂×#10625336	C₂³	1	2	yes	—
155	C₂×D₃₇₆	—	4	2	no	—
156	C₂×D₃₇₆	C₂³	1	2	yes	—
157	C₂×D₃₇₆	C₂³	1	2	yes	—
158	C₂×#10625334	C₂³	1	2	yes	—
159	C₂×#10625334	C₂³	1	2	yes	—
160	C₂×#10625334	C₂³	1	2	yes	—
161	C₂×#10625329	C₂³	1	1	yes	characteristic
162	C₂×#10625329	C₂³	1	1	yes	characteristic
163	#13094024	D₄	1	1	yes	characteristic
164	#13094024	D₄	1	1	yes	characteristic
165	#13094022	C₂³	1	2	yes	—
166	#13094020	C₂³	1	2	yes	—
167	#13094020	C₂³	1	2	yes	—
168	#13094020	C₂³	1	2	yes	—
169	#13094019	—	2	2	no	—
170	#13094019	—	2	2	no	—
171	#13094019	—	2	2	no	—
172	#13094019	—	2	2	no	—
173	#13094018	—	2	2	no	—
174	#13094018	—	2	2	no	—
175	#13094016	D₄	1	1	yes	characteristic
176	#13094016	D₄	1	1	yes	characteristic
177	#13094013	C₂³	1	2	yes	—
178	#13094013	C₂³	1	2	yes	—
179	#13094013	C₂³	1	2	yes	—
180	#13094012	—	2	1	no	—
181	#13094012	—	2	1	no	—
182	#13094012	C₂³	1	2	yes	—
183	#13094012	C₂³	1	2	yes	—
184	#13094011	C₂³	1	2	yes	—
185	#13094010	—	2	2	no	—
186	#13094010	—	2	2	no	—
187	#13094010	—	2	2	no	—
188	#13094010	—	2	2	no	—
189	#13094008	—	2	2	no	—
190	#13094008	—	2	2	no	—
191	#13094007	—	2	2	no	—
192	#13094007	—	2	2	no	—
193	#13094006	—	2	2	no	—
194	#13094006	—	2	2	no	—
195	#13094006	—	2	2	no	—
196	#13094006	—	2	2	no	—
197	#13094005	—	2	2	no	—
198	#13094004	—	2	2	no	—
199	#13094003	—	2	1	no	—
200	#13094003	—	2	1	no	—
201	#13094003	D₄	1	2	yes	—
202	#13094003	D₄	1	2	yes	—
203	#13094002	—	2	2	no	—
204	#13094002	—	2	2	no	—
205	#13093998	—	2	1	no	—
206	#13093998	—	2	1	no	—
207	#13093998	—	2	1	no	—
208	#13093998	—	2	1	no	—
209	#13093998	—	2	1	no	—
210	#13093998	—	2	1	no	—
211	#13093996	—	2	2	no	—
212	#13093996	—	2	2	no	—
213	#13093995	—	2	2	no	—
214	#13093992	—	2	2	no	—
215	#13093992	—	2	2	no	—
216	#13093992	—	2	2	no	—
217	Q₈×Dic₄₇	C₂³	1	2	yes	—
218	Q₈×Dic₄₇	C₂³	1	2	yes	—
219	C₄×Dic₉₄	—	2	1	no	—
220	C₄×Dic₉₄	—	2	1	no	—
221	C₄×Dic₉₄	C₂³	1	2	yes	—
222	C₄×Dic₉₄	C₂³	1	2	yes	—
223	#13093989	C₂³	1	2	yes	—
224	#13093989	C₂³	1	2	yes	—
225	C₄×D₁₈₈	—	2	1	no	—
226	C₄×D₁₈₈	—	2	1	no	—
227	C₄×D₁₈₈	—	2	1	no	—
228	C₄×D₁₈₈	—	2	1	no	—
229	C₄×D₁₈₈	C₂³	1	2	yes	—
230	C₄×D₁₈₈	C₂³	1	2	yes	—
231	D₄×Dic₄₇	—	2	2	no	—
232	D₄×Dic₄₇	—	2	2	no	—
233	D₄×Dic₄₇	C₂³	1	2	yes	—
234	D₄×Dic₄₇	C₂³	1	2	yes	—
235	#13093986	C₂³	1	2	yes	—
236	#13093986	C₂³	1	2	yes	—
237	C₄×C₂²⋊D₄₇	—	2	2	no	—
238	C₄×C₂²⋊D₄₇	—	2	2	no	—
239	(C₂²⋊D₄₇)⋊C₄	—	2	2	no	—
240	(C₂²⋊D₄₇)⋊C₄	—	2	2	no	—
241	#13093983	—	2	1	no	—
242	#13093983	—	2	1	no	—
243	#13093983	C₂³	1	1	yes	characteristic
244	#13093983	C₂³	1	1	yes	characteristic
245	#13093982	—	2	2	no	—
246	#13093981	—	2	2	no	—
247	#13093981	—	2	2	no	—
248	#13093980	—	2	2	no	—
249	C₂×C₄⋊Dic₄₇	—	2	1	no	—
250	C₂×C₄⋊Dic₄₇	—	2	1	no	—
251	C₂×C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic
252	C₂×(C₂×D₄₇)⋊C₄	—	2	1	no	—
253	C₂×(C₂×D₄₇)⋊C₄	—	2	1	no	—
254	C₂×(C₂×D₄₇)⋊C₄	—	2	1	no	—
255	C₂²⋊C₄×D₄₇	—	2	2	no	—
256	#13093957	C₂³	1	2	yes	—
257	#13093955	C₂³	1	2	yes	—
258	Dic₄₇⋊C₈	C₂³	1	2	yes	—
259	Dic₄₇⋊C₈	C₂³	1	2	yes	—
260	Dic₄₇⋊C₈	C₂³	1	2	yes	—
261	Dic₄₇⋊C₈	C₂³	1	2	yes	—
262	#13093949	C₂³	1	2	yes	—
263	#13093949	C₂³	1	2	yes	—
264	#13093948	C₂³	1	2	yes	—
265	#13093946	C₂³	1	2	yes	—
266	#13093946	C₂³	1	2	yes	—
267	#13093945	C₂³	1	2	yes	—
268	#13093944	C₂³	1	2	yes	—
269	#13093944	C₂³	1	2	yes	—
270	#13093935	C₂³	1	2	yes	—
271	#13093934	C₂³	1	2	yes	—
272	#13093934	C₂³	1	2	yes	—
273	C₄×C₄₇⋊C₈	C₂³	1	2	yes	—
274	C₈×Dic₄₇	C₂³	1	2	yes	—
275	C₈×Dic₄₇	C₂³	1	2	yes	—
276	C₂×#41×C₄₇	C₂³	1	1	yes	characteristic
277	C₂×#41×C₄₇	C₂³	1	1	yes	characteristic
278	C₂×#41×C₄₇	C₂³	1	1	yes	characteristic
279	#135×C₄₇	—	4	2	no	—
280	#135×C₄₇	—	4	2	no	—
281	C₂×Q₁₆×C₄₇	C₂³	1	1	yes	characteristic
282	C₂×Q₁₆×C₄₇	C₂³	1	1	yes	characteristic
283	C₂×SD₁₆×C₄₇	C₂³	1	1	yes	characteristic
284	C₂×SD₁₆×C₄₇	C₂³	1	1	yes	characteristic
285	C₂×SD₁₆×C₄₇	C₂³	1	1	yes	characteristic
286	C₂×SD₁₆×C₄₇	C₂³	1	1	yes	characteristic
287	C₂×D₈×C₄₇	C₂³	1	1	yes	characteristic
288	C₂×D₈×C₄₇	C₂³	1	1	yes	characteristic
289	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
290	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
291	C₄⋊Q₈×C₄₇	C₂³	1	1	yes	characteristic
292	#127×C₄₇	C₂³	1	1	yes	characteristic
293	#124×C₄₇	C₂³	1	1	yes	characteristic
294	#124×C₄₇	C₂³	1	1	yes	characteristic
295	#121×C₄₇	—	2	1	no	—
296	#121×C₄₇	—	2	1	no	—
297	C₄×Q₈×C₄₇	C₂³	1	1	yes	characteristic
298	C₄×Q₈×C₄₇	C₂³	1	1	yes	characteristic
299	C₄×D₄×C₄₇	—	2	1	no	—
300	C₄×D₄×C₄₇	—	2	1	no	—
301	C₄×D₄×C₄₇	—	2	1	no	—
302	C₄×D₄×C₄₇	—	2	1	no	—
303	C₄×D₄×C₄₇	C₂³	1	1	yes	characteristic
304	C₄×D₄×C₄₇	C₂³	1	1	yes	characteristic
305	#117×C₄₇	—	2	1	no	—
306	#117×C₄₇	C₂³	1	1	yes	characteristic
307	C₂×C₄²×C₄₇	—	2	1	no	—
308	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
309	C₄⋊C₈×C₄₇	C₂³	1	1	yes	characteristic
310	C₄⋊C₈×C₄₇	C₂³	1	1	yes	characteristic
311	C₄⋊C₈×C₄₇	C₂³	1	1	yes	characteristic
312	C₄⋊C₈×C₄₇	C₂³	1	1	yes	characteristic
313	#103×C₄₇	C₂³	1	1	yes	characteristic
314	#103×C₄₇	C₂³	1	1	yes	characteristic
315	#103×C₄₇	C₂³	1	1	yes	characteristic
316	#103×C₄₇	C₂³	1	1	yes	characteristic
317	#102×C₄₇	C₂³	1	1	yes	characteristic
318	#102×C₄₇	C₂³	1	1	yes	characteristic
319	#102×C₄₇	C₂³	1	1	yes	characteristic
320	#102×C₄₇	C₂³	1	1	yes	characteristic
321	C₂³×D₄₇	—	2	1	no	—
322	C₂³×D₄₇	—	2	1	no	—
323	#41×C₄₇	—	2	2	no	—
324	#41×C₄₇	—	2	2	no	—
325	#41×C₄₇	—	2	2	no	—
326	#41×C₄₇	—	2	2	no	—
327	#41×C₄₇	—	2	2	no	—
328	#41×C₄₇	—	2	2	no	—
329	C₂×Q₈×C₄₇	C₂⁴	1	1	yes	characteristic
330	C₂×Q₈×C₄₇	C₂⁴	1	1	yes	characteristic
331	C₂×Q₈×C₄₇	C₂⁴	1	1	yes	characteristic
332	C₂×D₄×C₄₇	—	2	1	no	—
333	C₂×D₄×C₄₇	—	2	1	no	—
334	C₂×D₄×C₄₇	—	2	1	no	—
335	C₂×D₄×C₄₇	—	2	1	no	—
336	C₂×D₄×C₄₇	—	2	1	no	—
337	C₂×D₄×C₄₇	C₂⁴	1	1	yes	characteristic
338	C₂×D₄×C₄₇	C₂⁴	1	1	yes	characteristic
339	C₂×D₄×C₄₇	C₂⁴	1	1	yes	characteristic
340	C₂²×C₄×C₄₇	—	2	1	no	—
341	C₂²×C₄×C₄₇	—	2	1	no	—
342	C₂²×C₄×C₄₇	—	2	1	no	—
343	C₂²×C₄×C₄₇	—	2	1	no	—
344	C₂²×C₄×C₄₇	—	2	1	no	—
345	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
346	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
347	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
348	C₂×C₂²⋊D₄₇	—	2	2	no	—
349	C₂×C₂²⋊D₄₇	—	2	2	no	—
350	C₂×C₂²⋊D₄₇	—	2	2	no	—
351	C₂×C₂²⋊D₄₇	—	2	2	no	—
352	C₂×C₂²⋊D₄₇	—	2	2	no	—
353	C₂×C₂²⋊D₄₇	—	2	2	no	—
354	C₂²×Dic₄₇	—	2	1	no	—
355	C₂²×Dic₄₇	—	2	1	no	—
356	C₂²×Dic₄₇	—	2	2	no	—
357	C₂²×Dic₄₇	—	2	2	no	—
358	#10625352	—	8	4	no	—
359	C₂×D₁₈₈	—	2	2	no	—
360	C₂×D₁₈₈	—	2	2	no	—
361	C₂×D₁₈₈	—	2	2	no	—
362	C₂×D₁₈₈	—	2	2	no	—
363	C₂×D₁₈₈	—	2	1	no	—
364	C₂×D₁₈₈	—	2	1	no	—
365	C₂×D₁₈₈	C₂⁴	1	2	yes	—
366	C₂×D₁₈₈	C₂⁴	1	2	yes	—
367	C₂×C₄×D₄₇	—	2	2	no	—
368	C₂×C₄×D₄₇	—	2	2	no	—
369	C₂×C₄×D₄₇	—	2	2	no	—
370	C₂×C₄×D₄₇	—	2	2	no	—
371	C₂×C₄×D₄₇	—	8	2	no	—
372	C₂×Dic₉₄	—	2	2	no	—
373	C₂×Dic₉₄	—	2	2	no	—
374	C₂×Dic₉₄	—	2	1	no	—
375	C₂×Dic₉₄	C₂×D₄	1	2	yes	—
376	C₂×Dic₉₄	C₂×D₄	1	2	yes	—
377	C₂×Dic₉₄	C₂⁴	1	2	yes	—
378	Q₁₆×C₄₇	—	4	1	no	—
379	Q₁₆×C₄₇	—	4	1	no	—
380	SD₁₆×C₄₇	—	4	1	no	—
381	SD₁₆×C₄₇	—	4	1	no	—
382	SD₁₆×C₄₇	—	4	1	no	—
383	SD₁₆×C₄₇	—	4	1	no	—
384	D₈×C₄₇	—	4	1	no	—
385	D₈×C₄₇	—	4	1	no	—
386	C₂×C₈×C₄₇	—	2	2	no	—
387	C₂×C₈×C₄₇	—	2	2	no	—
388	C₂×C₈×C₄₇	C₂⁴	1	1	yes	characteristic
389	C₂×C₈×C₄₇	C₂⁴	1	1	yes	characteristic
390	C₂×C₈×C₄₇	C₂⁴	1	1	yes	characteristic
391	C₂×C₈×C₄₇	C₂⁴	1	1	yes	characteristic
392	C₄⋊C₄×C₄₇	—	2	1	no	—
393	C₄⋊C₄×C₄₇	—	2	1	no	—
394	C₄⋊C₄×C₄₇	—	2	1	no	—
395	C₄⋊C₄×C₄₇	—	2	1	no	—
396	C₄⋊C₄×C₄₇	C₂⁴	1	1	yes	characteristic
397	C₄⋊C₄×C₄₇	C₂⁴	1	1	yes	characteristic
398	C₂²⋊C₄×C₄₇	—	2	1	no	—
399	C₂²⋊C₄×C₄₇	—	2	1	no	—
400	C₂²⋊C₄×C₄₇	—	2	1	no	—
401	C₂²⋊C₄×C₄₇	—	2	1	no	—
402	C₂²⋊C₄×C₄₇	—	2	1	no	—
403	C₂²⋊C₄×C₄₇	—	2	1	no	—
404	C₂²⋊C₄×C₄₇	—	2	1	no	—
405	C₄²×C₄₇	—	2	1	no	—
406	C₄²×C₄₇	—	2	1	no	—
407	C₄²×C₄₇	—	2	1	no	—
408	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
409	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
410	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
411	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
412	C₂²⋊Dic₄₇	—	2	2	no	—
413	C₂²⋊Dic₄₇	—	2	2	no	—
414	C₂²⋊Dic₄₇	—	2	2	no	—
415	C₂²⋊Dic₄₇	—	2	2	no	—
416	C₂²⋊Dic₄₇	C₂×D₄	1	2	yes	—
417	C₂²⋊Dic₄₇	C₂×D₄	1	2	yes	—
418	#10625337	—	2	4	no	—
419	#10625337	—	4	2	no	—
420	#10625336	—	2	4	no	—
421	#10625336	—	2	4	no	—
422	#10625336	—	4	2	no	—
423	#10625335	—	2	4	no	—
424	#10625335	—	4	2	no	—
425	#10625334	—	2	4	no	—
426	#10625334	—	2	4	no	—
427	#10625334	—	4	2	no	—
428	(C₂×D₄₇)⋊C₄	—	2	2	no	—
429	(C₂×D₄₇)⋊C₄	—	2	2	no	—
430	(C₂×D₄₇)⋊C₄	—	2	2	no	—
431	(C₂×D₄₇)⋊C₄	—	2	2	no	—
432	(C₂×D₄₇)⋊C₄	—	2	2	no	—
433	(C₂×D₄₇)⋊C₄	—	2	2	no	—
434	(C₂×D₄₇)⋊C₄	—	2	2	no	—
435	(C₂×D₄₇)⋊C₄	—	2	2	no	—
436	(C₂×D₄₇)⋊C₄	—	2	2	no	—
437	(C₂×D₄₇)⋊C₄	—	2	2	no	—
438	(C₂×D₄₇)⋊C₄	—	2	2	no	—
439	(C₂×D₄₇)⋊C₄	—	2	2	no	—
440	(C₂×D₄₇)⋊C₄	—	2	2	no	—
441	(C₂×D₄₇)⋊C₄	—	2	2	no	—
442	C₄⋊Dic₄₇	—	2	1	no	—
443	C₄⋊Dic₄₇	—	2	2	no	—
444	C₄⋊Dic₄₇	—	2	2	no	—
445	C₄⋊Dic₄₇	C₂×D₄	1	1	yes	characteristic
446	C₄⋊Dic₄₇	C₂×D₄	1	1	yes	characteristic
447	C₄⋊Dic₄₇	C₂×D₄	1	2	yes	—
448	C₄⋊Dic₄₇	C₂×D₄	1	1	yes	characteristic
449	C₄⋊Dic₄₇	C₂×D₄	1	1	yes	characteristic
450	C₄⋊Dic₄₇	C₂×D₄	1	2	yes	—
451	C₄⋊Dic₄₇	C₂⁴	1	2	yes	—
452	Dic₄₇⋊C₄	—	2	2	no	—
453	Dic₄₇⋊C₄	—	2	2	no	—
454	Dic₄₇⋊C₄	—	2	2	no	—
455	Dic₄₇⋊C₄	—	2	2	no	—
456	Dic₄₇⋊C₄	C₂×D₄	1	2	yes	—
457	Dic₄₇⋊C₄	C₂×D₄	1	2	yes	—
458	Dic₄₇⋊C₄	C₂×D₄	1	2	yes	—
459	Dic₄₇⋊C₄	C₂×D₄	1	2	yes	—
460	C₄×Dic₄₇	—	2	2	no	—
461	C₄×Dic₄₇	—	2	2	no	—
462	C₄×Dic₄₇	—	2	2	no	—
463	C₄×Dic₄₇	—	2	2	no	—
464	C₄×Dic₄₇	C₂⁴	1	2	yes	—
465	C₄×Dic₄₇	C₂⁴	1	2	yes	—
466	#10625329	—	2	2	no	—
467	#10625329	#41	1	4	yes	complemented
468	C₂×C₄₇⋊C₈	C₂⁴	1	2	yes	—
469	C₂×C₄₇⋊C₈	C₂⁴	1	2	yes	—
470	D₃₇₆	—	4	2	no	—
471	D₃₇₆	—	4	2	no	—
472	#10625325	—	4	2	no	—
473	#10625325	—	4	2	no	—
474	C₂³×C₄₇	—	2	1	no	—
475	C₂³×C₄₇	—	2	1	no	—
476	C₂³×C₄₇	—	2	1	no	—
477	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
478	C₂²×D₄₇	—	2	2	no	—
479	C₂²×D₄₇	—	2	2	no	—
480	C₂²×D₄₇	—	4	2	no	—
481	C₂²×D₄₇	—	4	2	no	—
482	C₂²×D₄₇	—	8	1	no	—
483	C₂²×D₄₇	—	8	1	no	—
484	C₂²×D₄₇	—	8	1	no	—
485	C₂²×D₄₇	—	8	1	no	—
486	Q₈×C₄₇	—	2	1	no	—
487	Q₈×C₄₇	—	2	1	no	—
488	Q₈×C₄₇	—	2	1	no	—
489	Q₈×C₄₇	—	2	1	no	—
490	Q₈×C₄₇	—	2	1	no	—
491	Q₈×C₄₇	—	2	1	no	—
492	D₄×C₄₇	—	2	1	no	—
493	D₄×C₄₇	—	2	1	no	—
494	D₄×C₄₇	—	2	1	no	—
495	D₄×C₄₇	—	2	1	no	—
496	D₄×C₄₇	—	2	1	no	—
497	D₄×C₄₇	—	2	1	no	—
498	D₄×C₄₇	—	4	2	no	—
499	D₄×C₄₇	—	4	2	no	—
500	D₄×C₄₇	—	4	2	no	—
501	D₄×C₄₇	—	4	2	no	—
502	D₄×C₄₇	—	8	1	no	—
503	C₂×C₄×C₄₇	—	2	1	no	—
504	C₂×C₄×C₄₇	—	2	1	no	—
505	C₂×C₄×C₄₇	—	2	1	no	—
506	C₂×C₄×C₄₇	—	2	1	no	—
507	C₂×C₄×C₄₇	—	2	1	no	—
508	C₂×C₄×C₄₇	—	4	1	no	—
509	C₂×C₄×C₄₇	—	4	1	no	—
510	C₂×C₄×C₄₇	—	4	2	no	—
511	C₂×C₄×C₄₇	—	4	2	no	—
512	C₂×C₄×C₄₇	—	4	2	no	—
513	C₂×C₄×C₄₇	—	8	1	no	—
514	C₂×C₄×C₄₇	—	8	1	no	—
515	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
516	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
517	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
518	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
519	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
520	C₂×C₄×C₄₇	C₂×#41	1	2	yes	—
521	C₂×C₄×C₄₇	H(5,𝔽₂)	1	2	yes	—
522	C₂×C₄×C₄₇	C₂⁵	1	1	yes	characteristic
523	C₂²⋊D₄₇	—	8	2	no	—
524	C₂²⋊D₄₇	—	8	2	no	—
525	C₂²⋊D₄₇	—	8	2	no	—
526	C₂²⋊D₄₇	—	8	2	no	—
527	C₂²⋊D₄₇	—	8	2	no	—
528	C₂²⋊D₄₇	—	8	2	no	—
529	C₂×Dic₄₇	—	2	2	no	—
530	C₂×Dic₄₇	—	2	2	no	—
531	C₂×Dic₄₇	—	4	2	no	—
532	C₂×Dic₄₇	—	8	2	no	—
533	C₂×Dic₄₇	—	8	2	no	—
534	C₂×Dic₄₇	—	8	1	no	—
535	C₂×Dic₄₇	C₂²×D₄	1	2	yes	—
536	C₂×Dic₄₇	C₂²×D₄	1	2	yes	—
537	C₂×Dic₄₇	C₂²×D₄	1	2	yes	—
538	C₂×Dic₄₇	C₂²×D₄	1	2	yes	—
539	D₁₈₈	—	2	2	no	—
540	D₁₈₈	—	2	2	no	—
541	D₁₈₈	—	2	2	no	—
542	D₁₈₈	—	2	2	no	—
543	D₁₈₈	—	4	2	no	—
544	D₁₈₈	—	4	2	no	—
545	C₄×D₄₇	—	4	4	no	—
546	C₄×D₄₇	—	8	2	no	—
547	C₄×D₄₇	—	8	2	no	—
548	C₄×D₄₇	—	8	2	no	—
549	Dic₉₄	—	2	2	no	—
550	Dic₉₄	—	2	2	no	—
551	Dic₉₄	—	4	2	no	—
552	Dic₉₄	—	4	2	no	—
553	Dic₉₄	—	4	2	no	—
554	C₈×C₄₇	—	2	1	no	—
555	C₈×C₄₇	—	2	1	no	—
556	C₈×C₄₇	—	2	1	no	—
557	C₈×C₄₇	—	2	1	no	—
558	C₄₇⋊C₈	—	2	2	no	—
559	C₄₇⋊C₈	C₂×#41	1	4	yes	—
560	#61424	—	47	1	no	maximal, Sylow
561	C₂²×C₄₇	—	2	1	no	—
562	C₂²×C₄₇	—	2	1	no	—
563	C₂²×C₄₇	—	4	1	no	—
564	C₂²×C₄₇	—	4	1	no	—
565	C₂²×C₄₇	—	4	1	no	—
566	C₂²×C₄₇	—	4	1	no	—
567	C₂²×C₄₇	—	4	1	no	—
568	C₂²×C₄₇	—	4	1	no	—
569	C₂²×C₄₇	—	4	1	no	—
570	C₂²×C₄₇	—	4	1	no	—
571	C₂²×C₄₇	—	4	1	no	—
572	C₂²×C₄₇	#550	1	2	yes	—
573	C₂²×C₄₇	C₂³×D₄	1	1	yes	characteristic
574	C₂×D₄₇	—	4	2	no	—
575	C₂×D₄₇	—	4	2	no	—
576	C₂×D₄₇	—	4	2	no	—
577	C₂×D₄₇	—	4	2	no	—
578	C₂×D₄₇	—	4	2	no	—
579	C₂×D₄₇	—	4	2	no	—
580	C₂×D₄₇	—	8	4	no	—
581	C₂×D₄₇	—	16	2	no	—
582	C₄×C₄₇	—	2	1	no	—
583	C₄×C₄₇	—	2	1	no	—
584	C₄×C₄₇	—	2	1	no	—
585	C₄×C₄₇	—	2	1	no	—
586	C₄×C₄₇	—	4	1	no	—
587	C₄×C₄₇	—	4	1	no	—
588	C₄×C₄₇	—	4	1	no	—
589	C₄×C₄₇	—	4	1	no	—
590	C₄×C₄₇	—	4	1	no	—
591	C₄×C₄₇	#550	1	2	yes	—
592	C₄×C₄₇	C₂²×#41	1	1	yes	characteristic
593	C₄×C₄₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
594	Dic₄₇	—	2	2	no	—
595	Dic₄₇	—	2	2	no	—
596	Dic₄₇	—	2	2	no	—
597	Dic₄₇	—	2	2	no	—
598	Dic₄₇	—	4	2	no	—
599	Dic₄₇	—	4	2	no	—
600	#3510	—	47	1	no	—
601	#3506	—	47	1	no	—
602	#3403	—	47	2	no	—
603	#3402	—	47	2	no	—
604	#3401	—	47	2	no	—
605	#3401	—	47	2	no	—
606	#3399	—	47	2	no	—
607	#3397	—	47	2	no	—
608	#3396	—	47	2	no	—
609	#3394	—	47	2	no	—
610	#3155	—	47	1	no	—
611	#3154	—	47	1	no	—
612	#3153	—	47	1	no	—
613	#3046	—	47	1	no	—
614	#3045	—	47	1	no	—
615	#3043	—	47	1	no	—
616	#3041	—	47	1	no	—
617	#3035	D₄₇	1	1	yes	characteristic, complemented
618	C₂×#463	—	47	1	no	—
619	#2962	—	47	1	no	—
620	#2947	—	47	1	no	—
621	#2946	—	47	1	no	—
622	C₄×AGL(1,ℤ/8)	—	47	1	no	—
623	C₂×C₄₇	—	2	2	no	—
624	C₂×C₄₇	—	8	1	no	—
625	C₂×C₄₇	—	8	1	no	—
626	C₂×C₄₇	—	8	1	no	—
627	C₂×C₄₇	C₂×#550	1	1	yes	characteristic
628	C₂×C₄₇	#3584	1	1	yes	characteristic
629	C₂×C₄₇	#3585	1	1	yes	characteristic
630	D₄₇	—	8	2	no	—
631	D₄₇	—	8	2	no	—
632	C₂×#137	—	47	1	no	—
633	C₂×#137	—	47	1	no	—
634	C₂×AGL(1,ℤ/8)	—	47	1	no	—
635	C₂×AGL(1,ℤ/8)	—	47	1	no	—
636	C₂×AGL(1,ℤ/8)	—	47	1	no	—
637	C₂×#135	C₂×D₄₇	1	1	yes	characteristic
638	C₂×#135	C₂×D₄₇	1	1	yes	characteristic
639	C₂²×SD₁₆	—	47	1	no	—
640	C₂²×D₈	—	47	1	no	—
641	#559	—	47	2	no	—
642	#559	—	47	2	no	—
643	#559	—	47	2	no	—
644	#559	—	47	2	no	—
645	#556	—	47	2	no	—
646	#556	—	47	2	no	—
647	#556	—	47	2	no	—
648	#555	—	94	1	no	—
649	#553	—	94	1	no	—
650	#553	—	94	1	no	—
651	#551	—	94	2	no	—
652	#551	—	94	2	no	—
653	#550	—	47	2	no	—
654	#547	—	94	1	no	—
655	#542	—	94	1	no	—
656	#542	—	94	1	no	—
657	#538	—	94	2	no	—
658	#536	—	47	1	no	—
659	#535	—	47	1	no	—
660	#535	—	47	1	no	—
661	#535	—	47	1	no	—
662	#533	—	47	1	no	—
663	#532	C₂×D₄₇	1	1	yes	characteristic
664	#529	—	94	1	no	—
665	#529	—	94	1	no	—
666	C₂×#124	—	47	1	no	—
667	#525	—	94	2	no	—
668	#520	—	47	1	no	—
669	#520	—	47	1	no	—
670	#519	—	47	1	no	—
671	#518	—	47	1	no	—
672	C₄×#41	C₂×D₄₇	1	1	yes	characteristic
673	C₂×C₄×D₄	—	47	1	no	—
674	#497	—	47	2	no	—
675	#497	—	47	2	no	—
676	#496	—	47	2	no	—
677	#496	—	47	2	no	—
678	#496	—	47	2	no	—
679	#496	—	47	2	no	—
680	#495	—	47	2	no	—
681	#495	—	47	2	no	—
682	#495	—	47	2	no	—
683	#495	—	47	2	no	—
684	#493	—	47	2	no	—
685	#492	—	47	2	no	—
686	#464	—	47	2	no	—
687	#464	—	47	2	no	—
688	#464	—	47	2	no	—
689	#464	—	47	2	no	—
690	#464	C₂×D₄₇	1	1	yes	characteristic, complemented
691	#464	C₂×D₄₇	1	1	yes	characteristic, complemented
692	#463	—	47	2	no	—
693	#463	—	47	2	no	—
694	#463	—	47	2	no	—
695	#463	—	47	2	no	—
696	#463	—	47	2	no	—
697	#463	—	47	2	no	—
698	#463	—	47	2	no	—
699	#463	—	47	2	no	—
700	#463	C₂×D₄₇	1	1	yes	characteristic, complemented
701	#463	C₂×D₄₇	1	1	yes	characteristic, complemented
702	#462	—	47	2	no	—
703	#462	C₂×D₄₇	1	1	yes	characteristic, complemented
704	#461	—	47	2	no	—
705	#461	C₂×D₄₇	1	1	yes	characteristic, complemented
706	#460	—	47	2	no	—
707	#460	—	47	2	no	—
708	#460	—	47	2	no	—
709	#460	C₂×D₄₇	1	1	yes	characteristic, complemented
710	#459	—	47	2	no	—
711	#459	—	47	2	no	—
712	#459	—	47	2	no	—
713	#459	C₂×D₄₇	1	1	yes	characteristic, complemented
714	#446	—	47	2	no	—
715	#446	—	47	2	no	—
716	#446	—	47	2	no	—
717	C₈×Q₈	—	47	2	no	—
718	#442	—	47	2	no	—
719	#442	—	47	2	no	—
720	#441	—	47	2	no	—
721	#440	—	47	2	no	—
722	#440	—	47	2	no	—
723	#440	—	47	2	no	—
724	C₄×Q₁₆	—	47	2	no	—
725	C₄×SD₁₆	—	47	2	no	—
726	C₄×SD₁₆	—	47	2	no	—
727	C₄×SD₁₆	—	47	2	no	—
728	C₄×D₈	—	47	2	no	—
729	C₄×D₈	—	47	2	no	—
730	#428	—	47	1	no	—
731	#424	—	47	1	no	—
732	#424	—	47	1	no	—
733	C₂×C₄⋊C₈	C₂×D₄₇	1	1	yes	characteristic
734	#418	—	47	1	no	—
735	#417	—	47	1	no	—
736	#416	C₂×D₄₇	1	1	yes	characteristic
737	#416	C₂×D₄₇	1	1	yes	characteristic
738	C₂×#103	—	47	1	no	—
739	C₂×#102	—	47	1	no	—
740	#405	—	47	1	no	—
741	#405	—	47	1	no	—
742	C₄×M₁₆	—	47	1	no	—
743	C₄₇	#61424	1	1	yes	characteristic, complemented, Sylow
744	C₂×#41	—	94	2	no	—
745	C₂×#41	C₂²×D₄₇	1	1	yes	characteristic
746	C₂×#41	C₂²×D₄₇	1	1	yes	characteristic
747	C₂×#41	C₂²×D₄₇	1	1	yes	characteristic
748	C₂²×Q₈	—	47	1	no	—
749	C₂²×D₄	—	47	1	no	—
750	C₂²×D₄	—	47	1	no	—
751	C₂³×C₄	—	94	1	no	—
752	#137	—	94	4	no	—
753	#137	—	188	2	no	—
754	AGL(1,ℤ/8)	—	94	4	no	—
755	AGL(1,ℤ/8)	—	94	4	no	—
756	AGL(1,ℤ/8)	—	188	2	no	—
757	#135	—	4	2	no	—
758	#135	—	4	2	no	—
759	C₂×Q₁₆	—	47	2	no	—
760	C₂×Q₁₆	—	47	2	no	—
761	C₂×Q₁₆	C₂²×D₄₇	1	1	yes	characteristic
762	C₂×Q₁₆	C₂²×D₄₇	1	1	yes	characteristic
763	C₂×SD₁₆	—	47	2	no	—
764	C₂×SD₁₆	—	47	2	no	—
765	C₂×SD₁₆	—	47	2	no	—
766	C₂×SD₁₆	—	47	2	no	—
767	C₂×SD₁₆	—	47	2	no	—
768	C₂×SD₁₆	—	47	2	no	—
769	C₂×SD₁₆	—	47	2	no	—
770	C₂×SD₁₆	—	188	2	no	—
771	C₂×SD₁₆	C₂²×D₄₇	1	1	yes	characteristic
772	C₂×SD₁₆	C₂²×D₄₇	1	1	yes	characteristic
773	C₂×SD₁₆	C₂²×D₄₇	1	1	yes	characteristic
774	C₂×SD₁₆	C₂²×D₄₇	1	1	yes	characteristic
775	C₂×D₈	—	47	2	no	—
776	C₂×D₈	—	47	2	no	—
777	C₂×D₈	—	47	2	no	—
778	C₂×D₈	—	47	2	no	—
779	C₂×D₈	—	47	2	no	—
780	C₂×D₈	—	188	2	no	—
781	C₂×D₈	C₂²×D₄₇	1	1	yes	characteristic
782	C₂×D₈	C₂²×D₄₇	1	1	yes	characteristic
783	C₂×M₁₆	—	47	1	no	—
784	C₂×M₁₆	—	47	1	no	—
785	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
786	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
787	C₄⋊Q₈	—	47	2	no	—
788	C₄⋊Q₈	—	47	1	no	—
789	C₄⋊Q₈	—	47	1	no	—
790	C₄⋊Q₈	C₂²×D₄₇	1	1	yes	characteristic
791	#127	—	47	2	no	—
792	#127	—	47	2	no	—
793	#127	—	47	2	no	—
794	#127	C₂²×D₄₇	1	1	yes	characteristic
795	#126	—	94	2	no	—
796	#126	—	94	2	no	—
797	#126	—	94	2	no	—
798	#126	—	94	2	no	—
799	#126	—	94	2	no	—
800	#126	—	94	2	no	—
801	#125	—	47	1	no	—
802	#125	—	47	1	no	—
803	#124	—	47	2	no	—
804	#124	—	47	2	no	—
805	#124	—	47	2	no	—
806	#124	—	47	2	no	—
807	#124	—	47	2	no	—
808	#124	—	47	2	no	—
809	#124	—	94	2	no	—
810	#124	—	94	2	no	—
811	#124	—	94	2	no	—
812	#124	—	94	2	no	—
813	#124	—	94	1	no	—
814	#124	—	94	1	no	—
815	#124	C₂²×D₄₇	1	1	yes	characteristic
816	#124	C₂²×D₄₇	1	1	yes	characteristic
817	#123	—	94	2	no	—
818	#123	—	94	2	no	—
819	#123	—	94	2	no	—
820	#123	—	94	2	no	—
821	#123	—	94	2	no	—
822	#123	—	94	2	no	—
823	#123	—	94	2	no	—
824	#123	—	94	2	no	—
825	#123	—	94	2	no	—
826	C₂²⋊Q₈	—	47	2	no	—
827	C₂²⋊Q₈	—	47	2	no	—
828	C₂²⋊Q₈	—	94	2	no	—
829	C₂²⋊Q₈	—	94	2	no	—
830	C₂²⋊Q₈	—	94	2	no	—
831	C₂²⋊Q₈	—	94	1	no	—
832	C₂²⋊Q₈	—	94	1	no	—
833	#121	—	2	1	no	—
834	#121	—	2	1	no	—
835	#121	—	94	1	no	—
836	#121	—	94	1	no	—
837	#121	—	94	1	no	—
838	#121	—	94	1	no	—
839	#121	—	94	1	no	—
840	#121	—	94	1	no	—
841	#121	—	94	2	no	—
842	#121	—	94	2	no	—
843	#121	—	94	2	no	—
844	#120	—	94	2	no	—
845	#120	—	94	2	no	—
846	#120	—	94	2	no	—
847	C₄×Q₈	—	47	2	no	—
848	C₄×Q₈	—	47	2	no	—
849	C₄×Q₈	—	47	2	no	—
850	C₄×Q₈	—	47	2	no	—
851	C₄×Q₈	—	47	2	no	—
852	C₄×Q₈	—	47	2	no	—
853	C₄×Q₈	—	94	1	no	—
854	C₄×Q₈	—	94	1	no	—
855	C₄×Q₈	C₂²×D₄₇	1	1	yes	characteristic
856	C₄×Q₈	C₂²×D₄₇	1	1	yes	characteristic
857	C₄×D₄	—	2	1	no	—
858	C₄×D₄	—	2	1	no	—
859	C₄×D₄	—	2	1	no	—
860	C₄×D₄	—	2	1	no	—
861	C₄×D₄	—	47	2	no	—
862	C₄×D₄	—	47	2	no	—
863	C₄×D₄	—	47	2	no	—
864	C₄×D₄	—	47	2	no	—
865	C₄×D₄	—	47	2	no	—
866	C₄×D₄	—	47	2	no	—
867	C₄×D₄	—	94	1	no	—
868	C₄×D₄	—	94	1	no	—
869	C₄×D₄	—	94	2	no	—
870	C₄×D₄	—	94	2	no	—
871	C₄×D₄	—	94	2	no	—
872	C₄×D₄	—	94	2	no	—
873	C₄×D₄	—	94	2	no	—
874	C₄×D₄	—	94	2	no	—
875	C₄×D₄	—	94	1	no	—
876	C₄×D₄	—	94	1	no	—
877	C₄×D₄	C₂²×D₄₇	1	1	yes	characteristic
878	C₄×D₄	C₂²×D₄₇	1	1	yes	characteristic
879	#117	—	2	1	no	—
880	#117	—	47	1	no	—
881	#117	—	47	1	no	—
882	#117	—	94	2	no	—
883	#117	—	94	2	no	—
884	#117	—	94	2	no	—
885	#117	—	94	2	no	—
886	#117	—	94	1	no	—
887	#117	—	94	1	no	—
888	#117	C₂²×D₄₇	1	1	yes	characteristic
889	C₂×C₄⋊C₄	—	47	1	no	—
890	C₂×C₄⋊C₄	—	94	1	no	—
891	C₂×C₄⋊C₄	—	94	1	no	—
892	C₂×C₂²⋊C₄	—	94	2	no	—
893	C₂×C₂²⋊C₄	—	94	1	no	—
894	C₂×C₂²⋊C₄	—	94	1	no	—
895	C₂×C₂²⋊C₄	—	94	1	no	—
896	C₂×C₄²	—	2	1	no	—
897	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
898	#107	—	47	2	no	—
899	#106	—	47	2	no	—
900	C₄⋊C₈	—	47	2	no	—
901	C₄⋊C₈	—	47	2	no	—
902	C₄⋊C₈	—	47	2	no	—
903	C₄⋊C₈	—	47	2	no	—
904	C₄⋊C₈	C₂²×D₄₇	1	1	yes	characteristic
905	C₄⋊C₈	C₂²×D₄₇	1	1	yes	characteristic
906	C₄⋊C₈	C₂²×D₄₇	1	1	yes	characteristic
907	C₄⋊C₈	C₂²×D₄₇	1	1	yes	characteristic
908	#103	—	47	2	no	—
909	#103	—	47	2	no	—
910	#103	—	47	2	no	—
911	#103	C₂²×D₄₇	1	1	yes	characteristic
912	#103	C₂²×D₄₇	1	1	yes	characteristic
913	#103	C₂²×D₄₇	1	1	yes	characteristic
914	#103	C₂²×D₄₇	1	1	yes	characteristic
915	#102	—	47	2	no	—
916	#102	—	47	2	no	—
917	#102	—	47	2	no	—
918	#102	—	47	2	no	—
919	#102	—	47	2	no	—
920	#102	C₂²×D₄₇	1	1	yes	characteristic
921	#102	C₂²×D₄₇	1	1	yes	characteristic
922	#102	C₂²×D₄₇	1	1	yes	characteristic
923	#102	C₂²×D₄₇	1	1	yes	characteristic
924	#97	—	47	2	no	—
925	#97	—	47	2	no	—
926	#97	—	47	2	no	—
927	C₄×C₈	—	47	2	no	—
928	C₄×C₈	—	47	2	no	—
929	C₄×C₈	—	47	2	no	—
930	C₂⁴	—	94	1	no	—
931	C₂⁴	—	94	1	no	—
932	#41	—	2	2	no	—
933	#41	—	2	2	no	—
934	#41	—	2	2	no	—
935	#41	—	2	2	no	—
936	#41	—	2	2	no	—
937	#41	—	2	2	no	—
938	#41	—	376	4	no	—
939	C₂×Q₈	—	47	2	no	—
940	C₂×Q₈	—	47	2	no	—
941	C₂×Q₈	—	47	2	no	—
942	C₂×Q₈	—	94	1	no	—
943	C₂×Q₈	—	94	2	no	—
944	C₂×Q₈	—	94	2	no	—
945	C₂×Q₈	C₂³×D₄₇	1	1	yes	characteristic
946	C₂×Q₈	C₂³×D₄₇	1	1	yes	characteristic
947	C₂×Q₈	C₂³×D₄₇	1	1	yes	characteristic
948	C₂×D₄	—	2	1	no	—
949	C₂×D₄	—	2	1	no	—
950	C₂×D₄	—	2	1	no	—
951	C₂×D₄	—	2	1	no	—
952	C₂×D₄	—	2	1	no	—
953	C₂×D₄	—	47	2	no	—
954	C₂×D₄	—	47	2	no	—
955	C₂×D₄	—	94	2	no	—
956	C₂×D₄	—	94	2	no	—
957	C₂×D₄	—	94	2	no	—
958	C₂×D₄	—	94	2	no	—
959	C₂×D₄	—	94	2	no	—
960	C₂×D₄	—	94	2	no	—
961	C₂×D₄	—	94	1	no	—
962	C₂×D₄	—	94	1	no	—
963	C₂×D₄	—	94	2	no	—
964	C₂×D₄	—	94	2	no	—
965	C₂×D₄	—	94	2	no	—
966	C₂×D₄	—	94	2	no	—
967	C₂×D₄	C₂³×D₄₇	1	1	yes	characteristic
968	C₂×D₄	C₂³×D₄₇	1	1	yes	characteristic
969	C₂×D₄	C₂³×D₄₇	1	1	yes	characteristic
970	C₂²×C₄	—	2	1	no	—
971	C₂²×C₄	—	2	1	no	—
972	C₂²×C₄	—	2	1	no	—
973	C₂²×C₄	—	2	1	no	—
974	C₂²×C₄	—	2	1	no	—
975	C₂²×C₄	—	94	2	no	—
976	C₂²×C₄	—	94	2	no	—
977	C₂²×C₄	—	94	2	no	—
978	C₂²×C₄	—	94	2	no	—
979	C₂²×C₄	—	94	1	no	—
980	C₂²×C₄	—	94	1	no	—
981	C₂²×C₄	—	94	2	no	—
982	C₂²×C₄	—	94	2	no	—
983	C₂²×C₄	—	376	2	no	—
984	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
985	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
986	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
987	Q₁₆	—	4	1	no	—
988	Q₁₆	—	4	1	no	—
989	Q₁₆	—	94	4	no	—
990	Q₁₆	—	188	2	no	—
991	SD₁₆	—	4	1	no	—
992	SD₁₆	—	4	1	no	—
993	SD₁₆	—	4	1	no	—
994	SD₁₆	—	4	1	no	—
995	SD₁₆	—	94	4	no	—
996	SD₁₆	—	94	4	no	—
997	SD₁₆	—	94	4	no	—
998	SD₁₆	—	188	2	no	—
999	SD₁₆	—	188	2	no	—
1000	SD₁₆	—	188	2	no	—
1001	SD₁₆	—	188	2	no	—
1002	D₈	—	4	1	no	—
1003	D₈	—	4	1	no	—
1004	D₈	—	94	4	no	—
1005	D₈	—	94	4	no	—
1006	D₈	—	188	2	no	—
1007	D₈	—	188	2	no	—
1008	D₈	—	188	2	no	—
1009	M₁₆	—	47	4	no	—
1010	M₁₆	—	94	2	no	—
1011	C₂×C₈	—	2	2	no	—
1012	C₂×C₈	—	2	2	no	—
1013	C₂×C₈	—	47	2	no	—
1014	C₂×C₈	—	47	2	no	—
1015	C₂×C₈	C₂³×D₄₇	1	1	yes	characteristic
1016	C₂×C₈	C₂³×D₄₇	1	1	yes	characteristic
1017	C₂×C₈	C₂³×D₄₇	1	1	yes	characteristic
1018	C₂×C₈	C₂³×D₄₇	1	1	yes	characteristic
1019	C₄⋊C₄	—	2	1	no	—
1020	C₄⋊C₄	—	2	1	no	—
1021	C₄⋊C₄	—	2	1	no	—
1022	C₄⋊C₄	—	2	1	no	—
1023	C₄⋊C₄	—	47	2	no	—
1024	C₄⋊C₄	—	47	2	no	—
1025	C₄⋊C₄	—	47	2	no	—
1026	C₄⋊C₄	—	47	2	no	—
1027	C₄⋊C₄	—	47	1	no	—
1028	C₄⋊C₄	—	47	1	no	—
1029	C₄⋊C₄	—	47	1	no	—
1030	C₄⋊C₄	—	47	1	no	—
1031	C₄⋊C₄	—	47	2	no	—
1032	C₄⋊C₄	—	47	2	no	—
1033	C₄⋊C₄	—	47	2	no	—
1034	C₄⋊C₄	—	94	2	no	—
1035	C₄⋊C₄	—	94	2	no	—
1036	C₄⋊C₄	—	94	2	no	—
1037	C₄⋊C₄	—	94	2	no	—
1038	C₄⋊C₄	—	94	2	no	—
1039	C₄⋊C₄	—	94	2	no	—
1040	C₄⋊C₄	—	94	1	no	—
1041	C₄⋊C₄	C₂³×D₄₇	1	1	yes	characteristic
1042	C₄⋊C₄	C₂³×D₄₇	1	1	yes	characteristic
1043	C₂²⋊C₄	—	2	1	no	—
1044	C₂²⋊C₄	—	2	1	no	—
1045	C₂²⋊C₄	—	2	1	no	—
1046	C₂²⋊C₄	—	2	1	no	—
1047	C₂²⋊C₄	—	2	1	no	—
1048	C₂²⋊C₄	—	2	1	no	—
1049	C₂²⋊C₄	—	2	1	no	—
1050	C₂²⋊C₄	—	47	2	no	—
1051	C₂²⋊C₄	—	47	2	no	—
1052	C₂²⋊C₄	—	94	2	no	—
1053	C₂²⋊C₄	—	94	2	no	—
1054	C₂²⋊C₄	—	94	2	no	—
1055	C₂²⋊C₄	—	94	2	no	—
1056	C₂²⋊C₄	—	94	2	no	—
1057	C₂²⋊C₄	—	94	2	no	—
1058	C₂²⋊C₄	—	94	2	no	—
1059	C₂²⋊C₄	—	94	2	no	—
1060	C₂²⋊C₄	—	94	2	no	—
1061	C₂²⋊C₄	—	94	2	no	—
1062	C₂²⋊C₄	—	94	2	no	—
1063	C₂²⋊C₄	—	94	2	no	—
1064	C₂²⋊C₄	—	94	2	no	—
1065	C₂²⋊C₄	—	94	2	no	—
1066	C₂²⋊C₄	—	94	2	no	—
1067	C₂²⋊C₄	—	94	2	no	—
1068	C₂²⋊C₄	—	94	2	no	—
1069	C₂²⋊C₄	—	94	2	no	—
1070	C₄²	—	2	1	no	—
1071	C₄²	—	2	1	no	—
1072	C₄²	—	2	1	no	—
1073	C₄²	—	47	2	no	—
1074	C₄²	—	47	2	no	—
1075	C₄²	—	94	2	no	—
1076	C₄²	—	94	2	no	—
1077	C₄²	—	94	2	no	—
1078	C₄²	—	94	2	no	—
1079	C₄²	D₄×D₄₇	1	1	yes	characteristic
1080	C₄²	D₄×D₄₇	1	1	yes	characteristic
1081	C₄²	C₂³×D₄₇	1	1	yes	characteristic
1082	C₄²	C₂³×D₄₇	1	1	yes	characteristic
1083	C₂³	—	2	1	no	—
1084	C₂³	—	2	1	no	—
1085	C₂³	—	2	1	no	—
1086	C₂³	—	94	2	no	—
1087	C₂³	—	94	2	no	—
1088	C₂³	—	376	1	no	—
1089	C₂³	—	376	1	no	—
1090	C₂³	—	376	1	no	—
1091	C₂³	—	376	1	no	—
1092	C₂³	—	188	2	no	—
1093	C₂³	—	188	2	no	—
1094	C₂³	C₂×D₄×D₄₇	1	1	yes	characteristic
1095	Q₈	—	2	1	no	—
1096	Q₈	—	2	1	no	—
1097	Q₈	—	2	1	no	—
1098	Q₈	—	2	1	no	—
1099	Q₈	—	2	1	no	—
1100	Q₈	—	2	1	no	—
1101	Q₈	—	94	2	no	—
1102	Q₈	—	94	2	no	—
1103	Q₈	—	188	2	no	—
1104	Q₈	—	188	2	no	—
1105	Q₈	—	188	2	no	—
1106	D₄	—	2	1	no	—
1107	D₄	—	2	1	no	—
1108	D₄	—	2	1	no	—
1109	D₄	—	2	1	no	—
1110	D₄	—	2	1	no	—
1111	D₄	—	2	1	no	—
1112	D₄	—	4	2	no	—
1113	D₄	—	4	2	no	—
1114	D₄	—	4	2	no	—
1115	D₄	—	4	2	no	—
1116	D₄	—	8	1	no	—
1117	D₄	—	94	2	no	—
1118	D₄	—	94	2	no	—
1119	D₄	—	94	2	no	—
1120	D₄	—	94	2	no	—
1121	D₄	—	376	2	no	—
1122	D₄	—	376	2	no	—
1123	D₄	—	376	2	no	—
1124	D₄	—	376	2	no	—
1125	D₄	—	376	2	no	—
1126	D₄	—	376	2	no	—
1127	D₄	—	188	2	no	—
1128	D₄	—	188	2	no	—
1129	C₂×C₄	—	2	1	no	—
1130	C₂×C₄	—	2	1	no	—
1131	C₂×C₄	—	2	1	no	—
1132	C₂×C₄	—	2	1	no	—
1133	C₂×C₄	—	2	1	no	—
1134	C₂×C₄	—	4	1	no	—
1135	C₂×C₄	—	4	1	no	—
1136	C₂×C₄	—	4	2	no	—
1137	C₂×C₄	—	4	2	no	—
1138	C₂×C₄	—	4	2	no	—
1139	C₂×C₄	—	8	1	no	—
1140	C₂×C₄	—	8	1	no	—
1141	C₂×C₄	—	47	2	no	—
1142	C₂×C₄	—	47	2	no	—
1143	C₂×C₄	—	47	2	no	—
1144	C₂×C₄	—	47	2	no	—
1145	C₂×C₄	—	94	2	no	—
1146	C₂×C₄	—	94	2	no	—
1147	C₂×C₄	—	376	2	no	—
1148	C₂×C₄	—	376	2	no	—
1149	C₂×C₄	—	376	2	no	—
1150	C₂×C₄	—	376	2	no	—
1151	C₂×C₄	—	376	2	no	—
1152	C₂×C₄	—	376	1	no	—
1153	C₂×C₄	—	188	4	no	—
1154	C₂×C₄	—	188	2	no	—
1155	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
1156	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
1157	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
1158	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
1159	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
1160	C₂×C₄	#41×D₄₇	1	2	yes	—
1161	C₂×C₄	#13094069	1	2	yes	—
1162	C₂×C₄	C₂⁴×D₄₇	1	1	yes	characteristic
1163	C₈	—	2	1	no	—
1164	C₈	—	2	1	no	—
1165	C₈	—	2	1	no	—
1166	C₈	—	2	1	no	—
1167	C₈	—	47	4	no	—
1168	C₈	—	94	2	no	—
1169	C₂²	—	2	1	no	—
1170	C₂²	—	2	1	no	—
1171	C₂²	—	4	1	no	—
1172	C₂²	—	4	1	no	—
1173	C₂²	—	4	1	no	—
1174	C₂²	—	4	1	no	—
1175	C₂²	—	4	1	no	—
1176	C₂²	—	4	1	no	—
1177	C₂²	—	4	1	no	—
1178	C₂²	—	4	1	no	—
1179	C₂²	—	4	1	no	—
1180	C₂²	—	376	4	no	—
1181	C₂²	—	188	2	no	—
1182	C₂²	—	188	2	no	—
1183	C₂²	—	188	2	no	—
1184	C₂²	—	188	2	no	—
1185	C₂²	—	188	2	no	—
1186	C₂²	—	188	2	no	—
1187	C₂²	—	752	2	no	—
1188	C₂²	#15689791	1	2	yes	—
1189	C₂²	C₂²×D₄×D₄₇	1	1	yes	characteristic
1190	C₄	—	2	1	no	—
1191	C₄	—	2	1	no	—
1192	C₄	—	2	1	no	—
1193	C₄	—	2	1	no	—
1194	C₄	—	4	1	no	—
1195	C₄	—	4	1	no	—
1196	C₄	—	4	1	no	—
1197	C₄	—	4	1	no	—
1198	C₄	—	4	1	no	—
1199	C₄	—	94	2	no	—
1200	C₄	—	94	2	no	—
1201	C₄	—	94	2	no	—
1202	C₄	—	94	2	no	—
1203	C₄	—	188	2	no	—
1204	C₄	—	188	2	no	—
1205	C₄	#15689791	1	2	yes	—
1206	C₄	C₂×#41×D₄₇	1	1	yes	characteristic
1207	C₄	C₂×#13094069	1	1	yes	characteristic
1208	C₂	—	2	2	no	—
1209	C₂	—	8	1	no	—
1210	C₂	—	8	1	no	—
1211	C₂	—	8	1	no	—
1212	C₂	—	376	2	no	—
1213	C₂	—	376	2	no	—
1214	C₂	C₂×#15689791	1	1	yes	characteristic
1215	C₂	#20258157	1	1	yes	characteristic
1216	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	#61424
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. #20257284	C₂	semidirect
2. #20257237	C₂	semidirect
3. #20256476	C₂	semidirect
4. #20256462	C₂	semidirect
5. #20256461	C₂	semidirect
6. #20256458	C₂	semidirect
7. #20256433	C₂	semidirect
8. #20256403	C₂	semidirect
9. #20256395	C₂	semidirect
10. #20256379	C₂	semidirect
11. #20253875	C₂	semidirect
12. #20253865	C₂	semidirect
13. #20253856	C₂	semidirect
14. #20252936	C₂	semidirect
15. #20252925	C₂	semidirect
16. #20252912	C₂	semidirect
17. #20252894	C₂	semidirect
18. C₂×#15689339	C₂	semidirect
19. #20252331	C₂	semidirect
20. #20252234	C₂	semidirect
21. #20252223	C₂	semidirect
22. C₄×#13094049	C₂	semidirect
23. C₄₇×#3035	C₂	semidirect
31. #15689856	C₂²	semidirect
32. #15689856	C₂²	semidirect
33. #15689855	C₂²	semidirect
34. #15689855	C₂²	semidirect
35. #15689847	C₂²	semidirect
36. #15689845	C₂²	semidirect
37. #15689845	C₂²	semidirect
43. #15689793	C₂²	semidirect
62. #15689516	C₂²	semidirect
63. #15689515	C₂²	semidirect
64. #15689511	C₂²	semidirect
65. #15689510	C₂²	semidirect
69. #15689505	C₂²	semidirect
70. #15689505	C₂²	semidirect
71. #15689504	C₂²	semidirect
73. #15689494	C₂²	semidirect
74. #15689348	C₂²	semidirect
75. #15689348	C₂²	semidirect
76. #15689347	C₂²	semidirect
77. #15689343	C₂²	semidirect
80. #15689340	C₂²	semidirect
85. #15689336	C₂²	semidirect
86. #15689331	C₂²	semidirect
87. #15689326	C₂²	semidirect
88. #15689322	C₂²	semidirect
89. #15689322	C₂²	semidirect
90. #15689321	C₂²	semidirect
93. #15689316	C₂²	semidirect
94. #15689252	C₂²	semidirect
95. #15689252	C₂²	semidirect
96. #15689250	C₂²	semidirect
97. #15689247	C₂²	semidirect
98. #15689233	C₂²	semidirect
99. #15689232	C₂²	semidirect
100. #15689227	C₂²	semidirect
101. #15689226	C₂²	semidirect
102. #15689221	C₂²	semidirect
103. #15689220	C₂²	semidirect
104. #15689215	C₂²	semidirect
105. #15689214	C₂²	semidirect
106. C₄×#10625336	C₂²	semidirect
107. #15689208	C₂²	semidirect
108. C₄×#10625334	C₂²	semidirect
109. #15689203	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
467. #10625329	#41	semidirect
617. #3035	D₄₇	semidirect
690. #464	C₂×D₄₇	semidirect
691. #464	C₂×D₄₇	semidirect
700. #463	C₂×D₄₇	semidirect
701. #463	C₂×D₄₇	semidirect
703. #462	C₂×D₄₇	semidirect
705. #461	C₂×D₄₇	semidirect
709. #460	C₂×D₄₇	semidirect
713. #459	C₂×D₄₇	semidirect
743. C₄₇	#61424	semidirect

Maximal subgroups

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

subgroup	index
#20257284	2
#20257237	2
#20256476	2
#20256462	2
#20256461	2
#20256458	2
#20256433	2
#20256403	2
#20256395	2
#20256379	2
#20253875	2
#20253865	2
#20253856	2
#20252936	2
#20252925	2
#20252912	2
#20252894	2
C₂×#15689339	2
#20252331	2
#20252234	2
#20252223	2
C₄×#13094049	2
C₄₇×#3035	2
#61424	47