Subgroups — #27085056

Order 12032.

2084 conjugacy classes of subgroups.

The subgroup lattice has 1198 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20257125	C₂	1	1	yes	maximal, characteristic, complemented
2	#20256589	C₂	1	1	yes	maximal, characteristic, complemented
3	#20253660	C₂	1	2	yes	maximal, complemented
4	#20253653	C₂	1	2	yes	maximal, complemented
5	#20253590	C₂	1	2	yes	maximal, complemented
6	#20253582	C₂	1	2	yes	maximal, complemented
7	#20253534	C₂	1	2	yes	maximal, complemented
8	#20253500	C₂	1	2	yes	maximal, complemented
9	#20253443	C₂	1	2	yes	maximal, complemented
10	#20253409	C₂	1	2	yes	maximal, complemented
11	#20253328	C₂	1	1	yes	maximal, characteristic, complemented
12	#20253233	C₂	1	1	yes	maximal, characteristic, complemented
13	#20253222	C₂	1	1	yes	maximal, characteristic, complemented
14	#20252912	C₂	1	1	yes	maximal, characteristic, complemented
15	#20252894	C₂	1	1	yes	maximal, characteristic, complemented
16	#20252628	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂×#15689270	C₂	1	1	yes	maximal, characteristic, complemented
18	#20252246	C₂	1	1	yes	maximal, characteristic, complemented
19	#20252239	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	#20252042	C₂	1	1	yes	maximal, characteristic, complemented
23	C₄₇×#3091	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂²×#10625350	C₂²	1	1	yes	characteristic
25	C₂×#13094054	C₂²	1	1	yes	characteristic
26	C₂×#13094049	C₂²	1	1	yes	characteristic
27	C₂²×#10625325	C₂²	1	1	yes	characteristic
28	C₂²×D₃₇₆	C₂²	1	1	yes	characteristic
29	#15689838	—	2	1	no	—
30	#15689819	—	2	1	no	—
31	#15689819	—	2	1	no	—
32	#15689796	—	2	2	no	—
33	#15689777	—	2	1	no	—
34	#15689760	—	2	2	no	—
35	#15689751	C₂²	1	1	yes	characteristic
36	#15689746	C₂²	1	2	yes	complemented
37	#15689726	C₂²	1	2	yes	complemented
38	#15689687	C₂²	1	1	yes	characteristic
39	#15689668	C₂²	1	2	yes	complemented
40	#15689659	C₂²	1	2	yes	complemented
41	C₂×#13093998	C₂²	1	1	yes	characteristic
42	#15689606	C₂²	1	1	yes	characteristic
43	#15689604	C₂²	1	2	yes	complemented
44	#15689604	C₂²	1	2	yes	complemented
45	#15689603	—	2	1	no	—
46	#15689603	—	2	1	no	—
47	#15689600	C₂²	1	1	yes	characteristic
48	#15689600	C₂²	1	1	yes	characteristic
49	#15689597	C₂²	1	1	yes	characteristic
50	#15689597	C₂²	1	1	yes	characteristic
51	#15689597	C₂²	1	1	yes	characteristic
52	#15689596	—	2	2	no	—
53	C₄×#10625350	—	2	1	no	—
54	C₄×#10625350	—	2	1	no	—
55	#15689591	C₂²	1	2	yes	complemented
56	#15689591	C₂²	1	2	yes	complemented
57	C₂×#13093983	C₂²	1	1	yes	characteristic
58	#117×D₄₇	—	2	2	no	—
59	#15689447	C₂²	1	2	yes	complemented
60	#15689447	C₂²	1	2	yes	complemented
61	#15689441	C₂²	1	2	yes	complemented
62	#15689436	C₂²	1	2	yes	complemented
63	#15689433	C₂²	1	2	yes	complemented
64	#15689429	C₂²	1	2	yes	complemented
65	#15689426	C₂²	1	2	yes	complemented
66	#15689422	C₂²	1	2	yes	complemented
67	#15689417	C₂²	1	2	yes	complemented
68	#15689412	C₂²	1	2	yes	complemented
69	#15689407	C₂²	1	2	yes	complemented
70	#15689402	C₂²	1	2	yes	complemented
71	#15689348	C₂²	1	2	yes	complemented
72	#15689348	C₂²	1	2	yes	complemented
73	#15689341	C₂²	1	2	yes	complemented
74	#15689341	C₂²	1	2	yes	complemented
75	#15689322	C₂²	1	2	yes	complemented
76	#15689322	C₂²	1	2	yes	complemented
77	#15689317	C₂²	1	2	yes	complemented
78	#15689317	C₂²	1	2	yes	complemented
79	#15689283	C₂²	1	2	yes	complemented
80	#15689283	C₂²	1	2	yes	complemented
81	#15689270	C₂²	1	2	yes	—
82	#15689270	C₂²	1	2	yes	—
83	#15689270	C₂²	1	2	yes	—
84	#15689270	C₂²	1	2	yes	—
85	#15689266	C₂²	1	2	yes	complemented
86	#15689266	C₂²	1	2	yes	complemented
87	#15689234	C₂²	1	2	yes	complemented
88	#15689234	C₂²	1	2	yes	complemented
89	#15689232	C₂²	1	2	yes	complemented
90	#15689227	C₂²	1	2	yes	complemented
91	#15689226	C₂²	1	2	yes	complemented
92	#15689222	C₂²	1	2	yes	complemented
93	#15689222	C₂²	1	2	yes	complemented
94	#15689220	C₂²	1	2	yes	complemented
95	#15689215	C₂²	1	2	yes	complemented
96	#15689214	C₂²	1	2	yes	complemented
97	#15689210	C₂²	1	2	yes	complemented
98	#15689210	C₂²	1	2	yes	complemented
99	#15689208	C₂²	1	2	yes	complemented
100	#15689205	C₂²	1	2	yes	complemented
101	#15689205	C₂²	1	2	yes	complemented
102	#15689203	C₂²	1	2	yes	complemented
103	#15689181	C₂²	1	2	yes	complemented
104	#15689181	C₂²	1	2	yes	complemented
105	#15689177	C₂²	1	2	yes	complemented
106	#15689173	C₂²	1	2	yes	complemented
107	#15689166	C₂²	1	1	yes	characteristic
108	#15689166	C₂²	1	1	yes	characteristic
109	#15689149	C₂²	1	1	yes	characteristic
110	#15689149	C₂²	1	1	yes	characteristic
111	#15689131	C₂²	1	1	yes	characteristic
112	#15689127	C₂²	1	1	yes	characteristic
113	#15689127	C₂²	1	1	yes	characteristic
114	#15689127	C₂²	1	1	yes	characteristic
115	C₂×#13093949	C₂²	1	1	yes	characteristic
116	C₂×#13093946	C₂²	1	1	yes	characteristic
117	#15689087	C₂²	1	1	yes	characteristic
118	#15689078	C₂²	1	1	yes	characteristic
119	#15689078	C₂²	1	1	yes	characteristic
120	C₄₇×#525	C₂²	1	1	yes	characteristic
121	C₂×#117×C₄₇	C₂²	1	1	yes	characteristic
122	C₄₇×#485	C₂²	1	1	yes	characteristic, complemented
123	C₄₇×#485	C₂²	1	1	yes	characteristic, complemented
124	C₄₇×#484	C₂²	1	1	yes	characteristic, complemented
125	C₄₇×#483	C₂²	1	1	yes	characteristic, complemented
126	C₄₇×#482	C₂²	1	1	yes	characteristic, complemented
127	C₄₇×#482	C₂²	1	1	yes	characteristic, complemented
128	C₄₇×#481	C₂²	1	1	yes	characteristic, complemented
129	C₄₇×#480	C₂²	1	1	yes	characteristic, complemented
130	C₄₇×#427	C₂²	1	1	yes	characteristic
131	C₄₇×#427	C₂²	1	1	yes	characteristic
132	C₄₇×#416	C₂²	1	1	yes	characteristic
133	C₄₇×#416	C₂²	1	1	yes	characteristic
134	C₂×C₂²⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
135	C₂×#10625350	—	2	1	no	—
136	C₂×#10625350	—	2	1	no	—
137	C₂×#10625350	—	2	4	no	—
138	C₂×#10625350	—	2	4	no	—
139	C₂×#10625350	C₂³	1	2	yes	—
140	C₂×#10625350	C₂³	1	2	yes	—
141	C₂×#10625352	—	2	2	no	—
142	C₂²×Dic₉₄	C₂³	1	1	yes	characteristic
143	C₂²×D₁₈₈	C₂³	1	1	yes	characteristic
144	C₂²×D₁₈₈	C₂³	1	1	yes	characteristic
145	C₂²×C₂²⋊D₄₇	—	2	1	no	—
146	C₂²×C₂²⋊D₄₇	—	2	1	no	—
147	C₂²×C₄×D₄₇	—	2	1	no	—
148	#13094054	—	2	4	no	—
149	#13094049	—	2	4	no	—
150	C₂×#10625337	C₂³	1	2	yes	—
151	C₂×#10625325	—	2	4	no	—
152	C₂×#10625325	C₂³	1	2	yes	—
153	C₂×#10625325	C₂³	1	2	yes	—
154	C₂×#10625335	C₂³	1	2	yes	—
155	C₂×#10625336	C₂³	1	2	yes	—
156	C₂×D₃₇₆	—	2	4	no	—
157	C₂×D₃₇₆	C₂³	1	2	yes	—
158	C₂×D₃₇₆	C₂³	1	2	yes	—
159	C₂×#10625334	C₂³	1	2	yes	—
160	C₂×#10625329	C₂³	1	1	yes	characteristic
161	C₂×#10625329	C₂³	1	1	yes	characteristic
162	#13094024	—	2	1	no	—
163	#13094023	C₂³	1	2	yes	—
164	#13094020	C₂³	1	2	yes	—
165	#13094019	—	2	2	no	—
166	#13094019	—	2	2	no	—
167	#13094016	—	2	1	no	—
168	#13094015	C₂³	1	2	yes	—
169	#13094013	C₂³	1	2	yes	—
170	#13094010	—	2	2	no	—
171	#13094010	—	2	2	no	—
172	#13094008	—	2	2	no	—
173	#13094008	—	2	2	no	—
174	#13094006	—	2	2	no	—
175	#13094006	—	2	2	no	—
176	#13094004	—	2	2	no	—
177	#13094001	—	2	2	no	—
178	#13093998	—	2	1	no	—
179	#13093998	—	2	1	no	—
180	#13093998	—	2	1	no	—
181	#13093998	—	2	1	no	—
182	#13093998	C₂³	1	2	yes	—
183	#13093998	C₂³	1	2	yes	—
184	#13093996	—	2	2	no	—
185	#13093996	—	2	2	no	—
186	#13093995	—	2	2	no	—
187	#13093992	—	2	2	no	—
188	Q₈×Dic₄₇	C₂³	1	2	yes	—
189	C₄×Dic₉₄	—	2	1	no	—
190	C₄×Dic₉₄	—	2	1	no	—
191	C₄×Dic₉₄	—	2	1	no	—
192	C₄×Dic₉₄	—	2	1	no	—
193	#13093989	C₂³	1	2	yes	—
194	#13093989	C₂³	1	2	yes	—
195	#13093989	C₂³	1	2	yes	—
196	#13093989	C₂³	1	2	yes	—
197	C₄×D₁₈₈	—	2	1	no	—
198	C₄×D₁₈₈	—	2	1	no	—
199	C₄×D₁₈₈	—	2	1	no	—
200	C₄×D₁₈₈	—	2	1	no	—
201	C₄×D₁₈₈	—	2	1	no	—
202	C₄×D₁₈₈	—	2	1	no	—
203	D₄×Dic₄₇	—	2	2	no	—
204	D₄×Dic₄₇	C₂³	1	2	yes	—
205	#13093986	C₂³	1	2	yes	—
206	#13093986	C₂³	1	2	yes	—
207	#13093986	C₂³	1	2	yes	—
208	#13093986	C₂³	1	2	yes	—
209	#13093986	C₂³	1	2	yes	—
210	#13093986	C₂³	1	2	yes	—
211	C₄×C₂²⋊D₄₇	—	2	2	no	—
212	C₄×C₂²⋊D₄₇	—	2	2	no	—
213	C₄×C₂²⋊D₄₇	—	2	2	no	—
214	C₄×C₂²⋊D₄₇	—	2	2	no	—
215	(C₂²⋊D₄₇)⋊C₄	—	2	2	no	—
216	(C₂²⋊D₄₇)⋊C₄	—	2	2	no	—
217	(C₂²⋊D₄₇)⋊C₄	—	2	2	no	—
218	(C₂²⋊D₄₇)⋊C₄	—	2	2	no	—
219	(C₂²⋊D₄₇)⋊C₄	—	2	2	no	—
220	(C₂²⋊D₄₇)⋊C₄	—	2	2	no	—
221	#13093983	—	2	1	no	—
222	#13093983	D₄	1	2	yes	—
223	#13093983	D₄	1	1	yes	characteristic
224	#13093983	D₄	1	1	yes	characteristic
225	#13093983	C₂³	1	2	yes	—
226	#13093983	C₂³	1	1	yes	characteristic
227	#13093983	C₂³	1	1	yes	characteristic
228	#13093982	—	2	2	no	—
229	#13093982	—	2	2	no	—
230	#13093982	—	2	2	no	—
231	#13093981	—	2	2	no	—
232	#13093981	—	2	2	no	—
233	#13093980	—	2	2	no	—
234	#13093980	—	2	2	no	—
235	C₂×C₄⋊Dic₄₇	—	2	1	no	—
236	C₂×C₄⋊Dic₄₇	D₄	1	1	yes	characteristic
237	C₂×C₄⋊Dic₄₇	D₄	1	1	yes	characteristic
238	C₂×C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic
239	C₄⋊C₄×D₄₇	—	2	2	no	—
240	C₄⋊C₄×D₄₇	—	2	2	no	—
241	C₂×C₂²⋊Dic₄₇	D₄	1	2	yes	—
242	C₂×(C₂×D₄₇)⋊C₄	—	2	1	no	—
243	C₂²⋊C₄×D₄₇	—	2	2	no	—
244	C₂²⋊C₄×D₄₇	—	2	2	no	—
245	C₂²⋊C₄×D₄₇	—	2	2	no	—
246	C₂×C₄×Dic₄₇	C₂³	1	2	yes	—
247	C₄²×D₄₇	—	2	2	no	—
248	C₄²×D₄₇	—	2	2	no	—
249	#13093957	C₂³	1	2	yes	—
250	#13093957	C₂³	1	2	yes	—
251	#13093955	C₂³	1	2	yes	—
252	#13093955	C₂³	1	2	yes	—
253	Dic₄₇⋊C₈	C₂³	1	2	yes	—
254	Dic₄₇⋊C₈	C₂³	1	2	yes	—
255	Dic₄₇⋊C₈	C₂³	1	2	yes	—
256	Dic₄₇⋊C₈	C₂³	1	2	yes	—
257	#13093949	C₂³	1	2	yes	—
258	#13093949	C₂³	1	2	yes	—
259	#13093947	C₂³	1	2	yes	—
260	#13093947	C₂³	1	2	yes	—
261	#13093946	C₂³	1	2	yes	—
262	#13093946	C₂³	1	2	yes	—
263	#13093944	C₂³	1	2	yes	—
264	#13093944	C₂³	1	2	yes	—
265	#13093944	C₂³	1	2	yes	—
266	#13093944	C₂³	1	2	yes	—
267	#13093944	C₂³	1	2	yes	—
268	#13093944	C₂³	1	2	yes	—
269	C₂²⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
270	C₂²⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
271	#13093934	C₂³	1	2	yes	—
272	#13093934	C₂³	1	2	yes	—
273	C₈×Dic₄₇	C₂³	1	2	yes	—
274	C₈×Dic₄₇	C₂³	1	2	yes	—
275	C₂×#41×C₄₇	C₂³	1	1	yes	characteristic
276	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
277	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
278	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
279	#123×C₄₇	—	2	1	no	—
280	C₂²⋊Q₈×C₄₇	C₂³	1	1	yes	characteristic
281	C₂²⋊Q₈×C₄₇	C₂³	1	1	yes	characteristic
282	#121×C₄₇	C₂³	1	1	yes	characteristic
283	#121×C₄₇	C₂³	1	1	yes	characteristic
284	#120×C₄₇	—	2	1	no	—
285	C₄×D₄×C₄₇	—	2	1	no	—
286	C₄×D₄×C₄₇	—	2	1	no	—
287	#117×C₄₇	—	2	1	no	—
288	#117×C₄₇	—	2	1	no	—
289	#117×C₄₇	C₂³	1	1	yes	characteristic
290	#117×C₄₇	C₂³	1	1	yes	characteristic
291	#117×C₄₇	C₂³	1	1	yes	characteristic
292	#117×C₄₇	C₂³	1	1	yes	characteristic
293	#117×C₄₇	C₂³	1	1	yes	characteristic
294	C₂×C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
295	C₂×C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
296	C₂×C₂²⋊C₄×C₄₇	—	2	1	no	—
297	C₂×C₄²×C₄₇	—	2	1	no	—
298	#107×C₄₇	C₂³	1	1	yes	characteristic
299	#107×C₄₇	C₂³	1	1	yes	characteristic
300	#107×C₄₇	C₂³	1	1	yes	characteristic
301	#107×C₄₇	C₂³	1	1	yes	characteristic
302	#106×C₄₇	C₂³	1	1	yes	characteristic
303	#106×C₄₇	C₂³	1	1	yes	characteristic
304	#106×C₄₇	C₂³	1	1	yes	characteristic
305	#106×C₄₇	C₂³	1	1	yes	characteristic
306	#103×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	#102×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	C₂²⋊C₈×C₄₇	C₂³	1	1	yes	characteristic
315	C₂²⋊C₈×C₄₇	C₂³	1	1	yes	characteristic
316	C₂²⋊C₈×C₄₇	C₂³	1	1	yes	characteristic
317	C₂²⋊C₈×C₄₇	C₂³	1	1	yes	characteristic
318	C₂⁴×C₄₇	C₂×D₄	1	1	yes	characteristic
319	C₂³×D₄₇	—	2	1	no	—
320	C₂³×D₄₇	—	2	1	no	—
321	#41×C₄₇	—	2	2	no	—
322	#41×C₄₇	—	2	2	no	—
323	C₂×Q₈×C₄₇	C₂⁴	1	1	yes	characteristic
324	C₂×D₄×C₄₇	—	2	1	no	—
325	C₂×D₄×C₄₇	—	2	1	no	—
326	C₂×D₄×C₄₇	—	2	1	no	—
327	C₂×D₄×C₄₇	C₂⁴	1	1	yes	characteristic
328	C₂²×C₄×C₄₇	—	2	2	no	—
329	C₂²×C₄×C₄₇	—	2	2	no	—
330	C₂²×C₄×C₄₇	—	2	1	no	—
331	C₂²×C₄×C₄₇	—	2	1	no	—
332	C₂²×C₄×C₄₇	—	2	1	no	—
333	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
334	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
335	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
336	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
337	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
338	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
339	C₂×C₂²⋊D₄₇	—	2	8	no	—
340	C₂×C₂²⋊D₄₇	—	2	2	no	—
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	C₂×C₂²⋊D₄₇	—	2	2	no	—
346	C₂×C₂²⋊D₄₇	—	8	2	no	—
347	C₂²×Dic₄₇	—	2	1	no	—
348	C₂²×Dic₄₇	—	2	1	no	—
349	C₂²×Dic₄₇	—	2	2	no	—
350	C₂²×Dic₄₇	C₂×D₄	1	2	yes	—
351	C₂²×Dic₄₇	C₂×D₄	1	2	yes	—
352	#10625352	—	8	4	no	—
353	#10625350	—	2	8	no	—
354	#10625350	—	2	8	no	—
355	#10625350	—	2	4	no	—
356	#10625350	—	2	4	no	—
357	#10625350	—	2	4	no	—
358	#10625350	—	2	4	no	—
359	C₂×D₁₈₈	—	2	1	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	#41	1	4	yes	complemented
365	C₂×D₁₈₈	C₂⁴	1	2	yes	—
366	C₂×D₁₈₈	C₂⁴	1	2	yes	—
367	C₂×C₄×D₄₇	—	2	8	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	—	2	2	no	—
372	C₂×C₄×D₄₇	—	2	2	no	—
373	C₂×C₄×D₄₇	—	2	2	no	—
374	C₂×C₄×D₄₇	—	2	2	no	—
375	C₂×C₄×D₄₇	—	2	2	no	—
376	C₂×Dic₉₄	—	2	1	no	—
377	C₂×Dic₉₄	—	2	2	no	—
378	C₂×Dic₉₄	—	2	2	no	—
379	C₂×Dic₉₄	#41	1	4	yes	complemented
380	C₂×Dic₉₄	C₂⁴	1	2	yes	—
381	C₂×C₈×C₄₇	—	2	2	no	—
382	C₂×C₈×C₄₇	—	2	2	no	—
383	C₂×C₈×C₄₇	C₂⁴	1	1	yes	characteristic
384	C₂×C₈×C₄₇	C₂⁴	1	1	yes	characteristic
385	C₂×C₈×C₄₇	C₂⁴	1	1	yes	characteristic
386	C₂×C₈×C₄₇	C₂⁴	1	1	yes	characteristic
387	C₄⋊C₄×C₄₇	—	2	1	no	—
388	C₄⋊C₄×C₄₇	—	2	1	no	—
389	C₄⋊C₄×C₄₇	—	2	1	no	—
390	C₄⋊C₄×C₄₇	—	2	1	no	—
391	C₄⋊C₄×C₄₇	C₂⁴	1	1	yes	characteristic
392	C₄⋊C₄×C₄₇	C₂⁴	1	1	yes	characteristic
393	C₄⋊C₄×C₄₇	C₂⁴	1	1	yes	characteristic
394	C₄⋊C₄×C₄₇	C₂⁴	1	1	yes	characteristic
395	C₄⋊C₄×C₄₇	C₂⁴	1	1	yes	characteristic
396	C₄⋊C₄×C₄₇	C₂⁴	1	1	yes	characteristic
397	C₂²⋊C₄×C₄₇	—	2	1	no	—
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	C₂²⋊C₄×C₄₇	—	2	1	no	—
406	C₄²×C₄₇	—	2	1	no	—
407	C₄²×C₄₇	—	2	1	no	—
408	C₄²×C₄₇	—	2	1	no	—
409	C₄²×C₄₇	—	2	1	no	—
410	C₄²×C₄₇	—	2	1	no	—
411	C₂²⋊Dic₄₇	—	2	2	no	—
412	C₂²⋊Dic₄₇	C₂×D₄	1	2	yes	—
413	C₂²⋊Dic₄₇	C₂×D₄	1	2	yes	—
414	C₂²⋊Dic₄₇	C₂×D₄	1	2	yes	—
415	C₂²⋊Dic₄₇	C₂×D₄	1	2	yes	—
416	#10625337	—	2	4	no	—
417	#10625336	—	2	4	no	—
418	#10625335	—	2	4	no	—
419	#10625334	—	2	4	no	—
420	(C₂×D₄₇)⋊C₄	—	2	2	no	—
421	(C₂×D₄₇)⋊C₄	—	2	2	no	—
422	(C₂×D₄₇)⋊C₄	—	2	2	no	—
423	(C₂×D₄₇)⋊C₄	—	2	2	no	—
424	(C₂×D₄₇)⋊C₄	—	2	2	no	—
425	(C₂×D₄₇)⋊C₄	—	2	2	no	—
426	(C₂×D₄₇)⋊C₄	—	2	2	no	—
427	(C₂×D₄₇)⋊C₄	—	2	2	no	—
428	(C₂×D₄₇)⋊C₄	—	2	2	no	—
429	(C₂×D₄₇)⋊C₄	—	2	2	no	—
430	C₄⋊Dic₄₇	—	2	1	no	—
431	C₄⋊Dic₄₇	—	2	2	no	—
432	C₄⋊Dic₄₇	—	2	2	no	—
433	C₄⋊Dic₄₇	C₂×D₄	1	2	yes	—
434	C₄⋊Dic₄₇	C₂×D₄	1	2	yes	—
435	C₄⋊Dic₄₇	C₂×D₄	1	1	yes	characteristic
436	C₄⋊Dic₄₇	C₂×D₄	1	1	yes	characteristic
437	C₄⋊Dic₄₇	C₂×D₄	1	1	yes	characteristic
438	C₄⋊Dic₄₇	C₂×D₄	1	1	yes	characteristic
439	C₄⋊Dic₄₇	C₂⁴	1	2	yes	—
440	Dic₄₇⋊C₄	—	2	2	no	—
441	Dic₄₇⋊C₄	—	2	2	no	—
442	Dic₄₇⋊C₄	—	2	2	no	—
443	Dic₄₇⋊C₄	—	2	2	no	—
444	Dic₄₇⋊C₄	—	2	2	no	—
445	Dic₄₇⋊C₄	—	2	2	no	—
446	C₄×Dic₄₇	—	2	2	no	—
447	C₄×Dic₄₇	—	2	2	no	—
448	C₄×Dic₄₇	—	2	2	no	—
449	C₄×Dic₄₇	—	2	2	no	—
450	C₄×Dic₄₇	—	2	2	no	—
451	C₄×Dic₄₇	C₂×D₄	1	2	yes	—
452	C₄×Dic₄₇	C₂×D₄	1	2	yes	—
453	C₄×Dic₄₇	C₂⁴	1	2	yes	—
454	C₄×Dic₄₇	C₂⁴	1	2	yes	—
455	#10625329	—	2	2	no	—
456	#10625329	—	2	2	no	—
457	C₂×C₄₇⋊C₈	C₂⁴	1	2	yes	—
458	C₂×C₄₇⋊C₈	C₂⁴	1	2	yes	—
459	D₃₇₆	—	2	4	no	—
460	D₃₇₆	—	2	4	no	—
461	#10625325	—	2	4	no	—
462	#10625325	—	2	4	no	—
463	C₂³×C₄₇	—	2	2	no	—
464	C₂³×C₄₇	—	2	1	no	—
465	C₂³×C₄₇	—	4	1	no	—
466	C₂³×C₄₇	—	4	1	no	—
467	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
468	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
469	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
470	C₂²×D₄₇	—	2	2	no	—
471	C₂²×D₄₇	—	2	4	no	—
472	C₂²×D₄₇	—	2	2	no	—
473	C₂²×D₄₇	—	4	2	no	—
474	C₂²×D₄₇	—	8	1	no	—
475	C₂²×D₄₇	—	8	1	no	—
476	C₂²×D₄₇	—	8	1	no	—
477	C₂²×D₄₇	—	8	1	no	—
478	Q₈×C₄₇	—	2	1	no	—
479	Q₈×C₄₇	—	2	1	no	—
480	D₄×C₄₇	—	2	1	no	—
481	D₄×C₄₇	—	2	1	no	—
482	D₄×C₄₇	—	4	2	no	—
483	D₄×C₄₇	—	4	2	no	—
484	D₄×C₄₇	—	8	1	no	—
485	C₂×C₄×C₄₇	—	2	2	no	—
486	C₂×C₄×C₄₇	—	2	2	no	—
487	C₂×C₄×C₄₇	—	2	2	no	—
488	C₂×C₄×C₄₇	—	2	1	no	—
489	C₂×C₄×C₄₇	—	2	1	no	—
490	C₂×C₄×C₄₇	—	2	1	no	—
491	C₂×C₄×C₄₇	—	2	1	no	—
492	C₂×C₄×C₄₇	—	2	1	no	—
493	C₂×C₄×C₄₇	—	2	1	no	—
494	C₂×C₄×C₄₇	—	2	1	no	—
495	C₂×C₄×C₄₇	—	2	1	no	—
496	C₂×C₄×C₄₇	—	2	1	no	—
497	C₂×C₄×C₄₇	—	2	1	no	—
498	C₂×C₄×C₄₇	—	2	1	no	—
499	C₂×C₄×C₄₇	—	4	2	no	—
500	C₂×C₄×C₄₇	—	8	1	no	—
501	C₂×C₄×C₄₇	—	8	1	no	—
502	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
503	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
504	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
505	C₂×C₄×C₄₇	C₂×#41	1	2	yes	—
506	C₂×C₄×C₄₇	C₂×#41	1	2	yes	—
507	C₂×C₄×C₄₇	C₂⁵	1	1	yes	characteristic
508	C₂²⋊D₄₇	—	2	8	no	—
509	C₂²⋊D₄₇	—	2	8	no	—
510	C₂²⋊D₄₇	—	4	4	no	—
511	C₂²⋊D₄₇	—	8	2	no	—
512	C₂²⋊D₄₇	—	8	2	no	—
513	C₂²⋊D₄₇	—	8	2	no	—
514	C₂×Dic₄₇	—	2	4	no	—
515	C₂×Dic₄₇	—	2	2	no	—
516	C₂×Dic₄₇	—	2	2	no	—
517	C₂×Dic₄₇	—	4	2	no	—
518	C₂×Dic₄₇	—	4	2	no	—
519	C₂×Dic₄₇	—	8	2	no	—
520	C₂×Dic₄₇	—	8	1	no	—
521	C₂×Dic₄₇	C₂²×D₄	1	2	yes	—
522	C₂×Dic₄₇	C₂²×D₄	1	2	yes	—
523	C₂×Dic₄₇	C₂²×D₄	1	2	yes	—
524	C₂×Dic₄₇	C₂²×D₄	1	2	yes	—
525	D₁₈₈	—	2	4	no	—
526	D₁₈₈	—	2	2	no	—
527	D₁₈₈	—	2	2	no	—
528	D₁₈₈	—	2	2	no	—
529	D₁₈₈	—	4	2	no	—
530	D₁₈₈	C₂×#41	1	4	yes	—
531	C₄×D₄₇	—	2	8	no	—
532	C₄×D₄₇	—	2	8	no	—
533	C₄×D₄₇	—	8	2	no	—
534	C₄×D₄₇	—	8	2	no	—
535	C₄×D₄₇	—	8	2	no	—
536	C₄×D₄₇	—	8	2	no	—
537	C₄×D₄₇	—	8	2	no	—
538	C₄×D₄₇	—	8	2	no	—
539	Dic₉₄	—	2	4	no	—
540	Dic₉₄	—	2	2	no	—
541	Dic₉₄	—	8	2	no	—
542	Dic₉₄	C₂×#41	1	4	yes	—
543	C₈×C₄₇	—	2	1	no	—
544	C₈×C₄₇	—	2	1	no	—
545	C₈×C₄₇	—	2	1	no	—
546	C₈×C₄₇	—	2	1	no	—
547	C₄₇⋊C₈	—	2	2	no	—
548	C₄₇⋊C₈	—	2	2	no	—
549	#60580	—	47	1	no	maximal, Sylow
550	C₂²×C₄₇	—	2	1	no	—
551	C₂²×C₄₇	—	2	1	no	—
552	C₂²×C₄₇	—	2	1	no	—
553	C₂²×C₄₇	—	2	1	no	—
554	C₂²×C₄₇	—	2	1	no	—
555	C₂²×C₄₇	—	2	1	no	—
556	C₂²×C₄₇	—	2	1	no	—
557	C₂²×C₄₇	—	2	1	no	—
558	C₂²×C₄₇	—	4	1	no	—
559	C₂²×C₄₇	—	4	1	no	—
560	C₂²×C₄₇	—	4	1	no	—
561	C₂²×C₄₇	—	8	2	no	—
562	C₂²×C₄₇	#525	1	2	yes	—
563	C₂²×C₄₇	C₂³×D₄	1	1	yes	characteristic
564	C₂×D₄₇	—	2	4	no	—
565	C₂×D₄₇	—	4	2	no	—
566	C₂×D₄₇	—	4	2	no	—
567	C₂×D₄₇	—	4	2	no	—
568	C₂×D₄₇	—	4	2	no	—
569	C₂×D₄₇	—	4	2	no	—
570	C₂×D₄₇	—	8	4	no	—
571	C₂×D₄₇	—	16	2	no	—
572	C₄×C₄₇	—	2	1	no	—
573	C₄×C₄₇	—	2	1	no	—
574	C₄×C₄₇	—	4	1	no	—
575	C₄×C₄₇	—	4	1	no	—
576	C₄×C₄₇	—	4	1	no	—
577	C₄×C₄₇	—	4	1	no	—
578	C₄×C₄₇	—	4	1	no	—
579	C₄×C₄₇	—	4	1	no	—
580	C₄×C₄₇	—	4	1	no	—
581	C₄×C₄₇	#525	1	2	yes	—
582	C₄×C₄₇	C₂²×#41	1	1	yes	characteristic
583	C₄×C₄₇	C₂²×#41	1	1	yes	characteristic
584	Dic₄₇	—	2	2	no	—
585	Dic₄₇	—	2	2	no	—
586	Dic₄₇	—	2	2	no	—
587	Dic₄₇	—	2	2	no	—
588	Dic₄₇	—	2	4	no	—
589	Dic₄₇	—	4	2	no	—
590	#3494	—	47	1	no	—
591	#3428	—	47	1	no	—
592	#3125	—	47	2	no	—
593	#3124	—	47	2	no	—
594	#3119	—	47	2	no	—
595	#3119	—	47	2	no	—
596	#3115	—	47	2	no	—
597	#3111	—	47	2	no	—
598	#3106	—	47	2	no	—
599	#3102	—	47	2	no	—
600	#3094	—	47	1	no	—
601	#3091	D₄₇	1	1	yes	characteristic, complemented
602	#3082	—	47	1	no	—
603	#3081	—	47	1	no	—
604	#3043	—	47	1	no	—
605	#3041	—	47	1	no	—
606	#3005	—	47	1	no	—
607	C₂×#449	—	47	1	no	—
608	#2949	—	47	1	no	—
609	#2948	—	47	1	no	—
610	#2947	—	47	1	no	—
611	#2946	—	47	1	no	—
612	#2924	—	47	1	no	—
613	C₂×C₄₇	—	2	2	no	—
614	C₂×C₄₇	—	4	1	no	—
615	C₂×C₄₇	—	4	1	no	—
616	C₂×C₄₇	—	8	1	no	—
617	C₂×C₄₇	C₂×#525	1	1	yes	characteristic
618	C₂×C₄₇	#3584	1	1	yes	characteristic
619	C₂×C₄₇	#3585	1	1	yes	characteristic
620	D₄₇	—	4	4	no	—
621	D₄₇	—	8	2	no	—
622	C₂²×#41	—	47	1	no	—
623	C₂×#137	—	47	1	no	—
624	C₂×AGL(1,ℤ/8)	—	47	1	no	—
625	C₂²×SD₁₆	—	47	1	no	—
626	C₂²×D₈	—	47	1	no	—
627	#555	—	94	1	no	—
628	#553	—	94	1	no	—
629	#553	—	94	1	no	—
630	#551	—	94	2	no	—
631	#547	—	94	1	no	—
632	#546	—	94	2	no	—
633	#544	—	47	1	no	—
634	#542	—	47	2	no	—
635	#540	—	47	2	no	—
636	#535	—	47	1	no	—
637	#532	—	47	2	no	—
638	#529	—	47	2	no	—
639	#525	C₂×D₄₇	1	1	yes	characteristic
640	C₂×#121	—	47	1	no	—
641	#520	—	47	1	no	—
642	#520	—	47	2	no	—
643	#520	—	47	2	no	—
644	#520	—	94	1	no	—
645	#520	—	94	1	no	—
646	#519	—	47	1	no	—
647	#519	—	47	1	no	—
648	#518	—	47	1	no	—
649	#518	—	47	1	no	—
650	#518	—	47	1	no	—
651	#518	—	94	2	no	—
652	C₄×#41	—	47	2	no	—
653	C₄×#41	—	47	2	no	—
654	C₄×#41	—	94	1	no	—
655	C₄×#41	—	94	1	no	—
656	C₂×#117	—	47	1	no	—
657	C₂×#117	—	94	2	no	—
658	C₂×#117	C₂×D₄₇	1	1	yes	characteristic
659	#485	C₂×D₄₇	1	1	yes	characteristic, complemented
660	#485	C₂×D₄₇	1	1	yes	characteristic, complemented
661	#484	C₂×D₄₇	1	1	yes	characteristic, complemented
662	#483	C₂×D₄₇	1	1	yes	characteristic, complemented
663	#482	—	47	2	no	—
664	#482	—	47	2	no	—
665	#482	C₂×D₄₇	1	1	yes	characteristic, complemented
666	#482	C₂×D₄₇	1	1	yes	characteristic, complemented
667	#481	—	47	2	no	—
668	#481	C₂×D₄₇	1	1	yes	characteristic, complemented
669	#480	—	47	2	no	—
670	#480	C₂×D₄₇	1	1	yes	characteristic, complemented
671	#479	—	47	2	no	—
672	#479	—	47	2	no	—
673	#478	—	47	2	no	—
674	#478	—	47	2	no	—
675	#477	—	47	2	no	—
676	#476	—	47	2	no	—
677	#475	—	47	2	no	—
678	#474	—	47	2	no	—
679	#464	—	47	2	no	—
680	#464	—	47	2	no	—
681	#463	—	47	2	no	—
682	#463	—	47	2	no	—
683	#460	—	47	2	no	—
684	#460	—	47	2	no	—
685	#459	—	47	2	no	—
686	#459	—	47	2	no	—
687	#452	—	47	2	no	—
688	#452	—	47	2	no	—
689	#449	—	47	2	no	—
690	#449	—	47	2	no	—
691	#449	—	47	2	no	—
692	#449	—	47	2	no	—
693	#449	—	47	2	no	—
694	#449	—	47	2	no	—
695	#442	—	47	2	no	—
696	#442	—	47	2	no	—
697	#442	—	47	2	no	—
698	#441	—	47	2	no	—
699	#440	—	47	2	no	—
700	#440	—	47	2	no	—
701	#440	—	47	2	no	—
702	#440	—	47	2	no	—
703	C₄×Q₁₆	—	47	2	no	—
704	C₄×SD₁₆	—	47	2	no	—
705	C₄×SD₁₆	—	47	2	no	—
706	C₄×SD₁₆	—	47	2	no	—
707	C₄×SD₁₆	—	47	2	no	—
708	C₄×D₈	—	47	2	no	—
709	C₄×D₈	—	47	2	no	—
710	C₄×D₈	—	47	2	no	—
711	#433	—	47	2	no	—
712	#433	—	47	2	no	—
713	#432	—	47	2	no	—
714	#431	—	47	2	no	—
715	#428	—	47	1	no	—
716	#428	—	47	1	no	—
717	#427	C₂×D₄₇	1	1	yes	characteristic
718	#427	C₂×D₄₇	1	1	yes	characteristic
719	#424	—	47	1	no	—
720	#424	—	47	1	no	—
721	#419	—	47	1	no	—
722	#418	—	47	1	no	—
723	#418	—	47	1	no	—
724	#418	—	47	1	no	—
725	#416	C₂×D₄₇	1	1	yes	characteristic
726	#416	C₂×D₄₇	1	1	yes	characteristic
727	C₂×#103	—	47	1	no	—
728	C₂×#102	—	47	1	no	—
729	#407	—	47	1	no	—
730	C₂×C₂²⋊C₈	C₂×D₄₇	1	1	yes	characteristic
731	#405	—	47	1	no	—
732	#405	—	47	1	no	—
733	C₄₇	#60580	1	1	yes	characteristic, complemented, Sylow
734	C₂×#41	—	47	2	no	—
735	C₂×#41	—	47	2	no	—
736	C₂×#41	—	94	4	no	—
737	C₂×#41	—	94	4	no	—
738	C₂×#41	—	94	2	no	—
739	C₂×#41	—	94	1	no	—
740	C₂×#41	—	94	1	no	—
741	C₂×#41	C₂²×D₄₇	1	1	yes	characteristic
742	C₂²×Q₈	—	47	1	no	—
743	C₂²×D₄	—	47	1	no	—
744	C₂²×D₄	—	47	1	no	—
745	C₂²×D₄	—	94	1	no	—
746	C₂²×D₄	—	94	1	no	—
747	C₂³×C₄	—	94	1	no	—
748	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
749	#137	—	94	4	no	—
750	AGL(1,ℤ/8)	—	94	4	no	—
751	C₂×Q₁₆	—	47	2	no	—
752	C₂×SD₁₆	—	47	2	no	—
753	C₂×SD₁₆	—	47	2	no	—
754	C₂×SD₁₆	—	47	2	no	—
755	C₂×SD₁₆	—	47	2	no	—
756	C₂×SD₁₆	—	94	4	no	—
757	C₂×D₈	—	47	2	no	—
758	C₂×D₈	—	47	2	no	—
759	C₂×D₈	—	47	2	no	—
760	C₂×D₈	—	94	4	no	—
761	C₂×M₁₆	—	47	1	no	—
762	C₂×M₁₆	—	47	1	no	—
763	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
764	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
765	C₄⋊Q₈	—	47	2	no	—
766	C₄⋊Q₈	—	94	1	no	—
767	#127	—	47	2	no	—
768	#126	—	94	2	no	—
769	#126	—	94	2	no	—
770	#125	—	47	2	no	—
771	#125	—	94	1	no	—
772	#124	—	47	2	no	—
773	#124	—	94	2	no	—
774	#124	—	94	2	no	—
775	#123	—	2	1	no	—
776	#123	—	94	2	no	—
777	#123	—	94	2	no	—
778	#123	—	94	2	no	—
779	#123	—	94	2	no	—
780	C₂²⋊Q₈	—	94	2	no	—
781	C₂²⋊Q₈	—	94	2	no	—
782	C₂²⋊Q₈	C₂²×D₄₇	1	1	yes	characteristic
783	C₂²⋊Q₈	C₂²×D₄₇	1	1	yes	characteristic
784	#121	—	47	2	no	—
785	#121	—	47	2	no	—
786	#121	—	94	2	no	—
787	#121	—	94	2	no	—
788	#121	—	94	1	no	—
789	#121	—	94	1	no	—
790	#121	—	94	2	no	—
791	#121	—	94	1	no	—
792	#121	—	94	1	no	—
793	#121	C₂²×D₄₇	1	1	yes	characteristic
794	#121	C₂²×D₄₇	1	1	yes	characteristic
795	#120	—	2	1	no	—
796	#120	—	94	2	no	—
797	C₄×Q₈	—	47	2	no	—
798	C₄×Q₈	—	47	2	no	—
799	C₄×Q₈	—	47	2	no	—
800	C₄×Q₈	—	47	2	no	—
801	C₄×Q₈	—	47	2	no	—
802	C₄×Q₈	—	94	1	no	—
803	C₄×Q₈	—	94	1	no	—
804	C₄×Q₈	—	94	1	no	—
805	C₄×Q₈	—	94	1	no	—
806	C₄×D₄	—	2	1	no	—
807	C₄×D₄	—	2	1	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	—	47	2	no	—
814	C₄×D₄	—	47	2	no	—
815	C₄×D₄	—	94	1	no	—
816	C₄×D₄	—	94	1	no	—
817	C₄×D₄	—	94	1	no	—
818	C₄×D₄	—	94	1	no	—
819	C₄×D₄	—	94	1	no	—
820	C₄×D₄	—	94	1	no	—
821	C₄×D₄	—	94	2	no	—
822	C₄×D₄	—	94	2	no	—
823	C₄×D₄	—	94	2	no	—
824	C₄×D₄	—	94	2	no	—
825	C₄×D₄	—	94	2	no	—
826	C₄×D₄	—	94	2	no	—
827	C₄×D₄	—	94	2	no	—
828	C₄×D₄	—	94	2	no	—
829	C₄×D₄	—	94	2	no	—
830	C₄×D₄	—	94	2	no	—
831	C₄×D₄	—	94	2	no	—
832	#117	—	2	1	no	—
833	#117	—	2	1	no	—
834	#117	—	47	2	no	—
835	#117	—	47	1	no	—
836	#117	—	47	1	no	—
837	#117	—	47	1	no	—
838	#117	—	47	1	no	—
839	#117	—	47	2	no	—
840	#117	—	94	2	no	—
841	#117	—	94	2	no	—
842	#117	—	94	2	no	—
843	#117	—	94	2	no	—
844	#117	—	94	2	no	—
845	#117	—	94	2	no	—
846	#117	—	94	2	no	—
847	#117	—	94	1	no	—
848	#117	C₂²×D₄₇	1	1	yes	characteristic
849	#117	C₂²×D₄₇	1	1	yes	characteristic
850	#117	C₂²×D₄₇	1	1	yes	characteristic
851	#117	C₂²×D₄₇	1	1	yes	characteristic
852	#117	C₂²×D₄₇	1	1	yes	characteristic
853	C₂×C₄⋊C₄	—	47	1	no	—
854	C₂×C₄⋊C₄	—	47	1	no	—
855	C₂×C₄⋊C₄	—	47	1	no	—
856	C₂×C₄⋊C₄	—	94	2	no	—
857	C₂×C₄⋊C₄	—	94	2	no	—
858	C₂×C₄⋊C₄	—	94	1	no	—
859	C₂×C₄⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
860	C₂×C₄⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
861	C₂×C₂²⋊C₄	—	2	1	no	—
862	C₂×C₂²⋊C₄	—	47	2	no	—
863	C₂×C₂²⋊C₄	—	94	2	no	—
864	C₂×C₂²⋊C₄	—	94	2	no	—
865	C₂×C₂²⋊C₄	—	94	2	no	—
866	C₂×C₂²⋊C₄	—	94	1	no	—
867	C₂×C₄²	—	2	1	no	—
868	C₂×C₄²	—	47	2	no	—
869	C₂×C₄²	—	94	2	no	—
870	C₂×C₄²	—	94	2	no	—
871	#107	—	47	2	no	—
872	#107	—	47	2	no	—
873	#107	C₂²×D₄₇	1	1	yes	characteristic
874	#107	C₂²×D₄₇	1	1	yes	characteristic
875	#107	C₂²×D₄₇	1	1	yes	characteristic
876	#107	C₂²×D₄₇	1	1	yes	characteristic
877	#106	—	47	2	no	—
878	#106	—	47	2	no	—
879	#106	C₂²×D₄₇	1	1	yes	characteristic
880	#106	C₂²×D₄₇	1	1	yes	characteristic
881	#106	C₂²×D₄₇	1	1	yes	characteristic
882	#106	C₂²×D₄₇	1	1	yes	characteristic
883	C₄⋊C₈	—	47	2	no	—
884	C₄⋊C₈	—	47	2	no	—
885	C₄⋊C₈	—	47	2	no	—
886	C₄⋊C₈	—	47	2	no	—
887	#103	—	47	2	no	—
888	#103	—	47	2	no	—
889	#103	—	47	2	no	—
890	#103	—	47	2	no	—
891	#103	C₂²×D₄₇	1	1	yes	characteristic
892	#103	C₂²×D₄₇	1	1	yes	characteristic
893	#103	C₂²×D₄₇	1	1	yes	characteristic
894	#103	C₂²×D₄₇	1	1	yes	characteristic
895	#102	—	47	2	no	—
896	#102	—	47	2	no	—
897	#102	—	47	2	no	—
898	#102	—	47	2	no	—
899	#102	—	47	2	no	—
900	#102	—	47	2	no	—
901	#102	—	47	2	no	—
902	#102	—	47	2	no	—
903	#102	C₂²×D₄₇	1	1	yes	characteristic
904	#102	C₂²×D₄₇	1	1	yes	characteristic
905	#102	C₂²×D₄₇	1	1	yes	characteristic
906	#102	C₂²×D₄₇	1	1	yes	characteristic
907	C₂²⋊C₈	—	47	2	no	—
908	C₂²⋊C₈	—	47	2	no	—
909	C₂²⋊C₈	C₂²×D₄₇	1	1	yes	characteristic
910	C₂²⋊C₈	C₂²×D₄₇	1	1	yes	characteristic
911	C₂²⋊C₈	C₂²×D₄₇	1	1	yes	characteristic
912	C₂²⋊C₈	C₂²×D₄₇	1	1	yes	characteristic
913	#97	—	47	2	no	—
914	#97	—	47	2	no	—
915	C₄×C₈	—	47	2	no	—
916	C₄×C₈	—	47	2	no	—
917	C₂⁴	—	94	1	no	—
918	C₂⁴	—	94	1	no	—
919	C₂⁴	D₄×D₄₇	1	1	yes	characteristic
920	#41	—	2	2	no	—
921	#41	—	2	2	no	—
922	#41	—	94	4	no	—
923	#41	—	94	4	no	—
924	#41	—	94	4	no	—
925	#41	—	94	4	no	—
926	#41	—	94	8	no	—
927	#41	—	94	8	no	—
928	#41	—	376	4	no	—
929	C₂×Q₈	—	47	4	no	—
930	C₂×Q₈	—	47	2	no	—
931	C₂×Q₈	—	94	2	no	—
932	C₂×Q₈	—	94	1	no	—
933	C₂×Q₈	—	94	2	no	—
934	C₂×Q₈	C₂³×D₄₇	1	1	yes	characteristic
935	C₂×D₄	—	2	1	no	—
936	C₂×D₄	—	2	1	no	—
937	C₂×D₄	—	2	1	no	—
938	C₂×D₄	—	47	4	no	—
939	C₂×D₄	—	47	2	no	—
940	C₂×D₄	—	47	2	no	—
941	C₂×D₄	—	94	2	no	—
942	C₂×D₄	—	94	2	no	—
943	C₂×D₄	—	94	8	no	—
944	C₂×D₄	—	94	2	no	—
945	C₂×D₄	—	94	2	no	—
946	C₂×D₄	—	94	2	no	—
947	C₂×D₄	—	94	2	no	—
948	C₂×D₄	—	94	1	no	—
949	C₂×D₄	—	94	1	no	—
950	C₂×D₄	—	94	2	no	—
951	C₂×D₄	—	94	2	no	—
952	C₂×D₄	—	94	2	no	—
953	C₂×D₄	—	376	2	no	—
954	C₂×D₄	C₂³×D₄₇	1	1	yes	characteristic
955	C₂²×C₄	—	2	2	no	—
956	C₂²×C₄	—	2	2	no	—
957	C₂²×C₄	—	2	1	no	—
958	C₂²×C₄	—	2	1	no	—
959	C₂²×C₄	—	2	1	no	—
960	C₂²×C₄	—	47	2	no	—
961	C₂²×C₄	—	47	2	no	—
962	C₂²×C₄	—	94	2	no	—
963	C₂²×C₄	—	94	2	no	—
964	C₂²×C₄	—	94	2	no	—
965	C₂²×C₄	—	94	2	no	—
966	C₂²×C₄	—	94	2	no	—
967	C₂²×C₄	—	94	2	no	—
968	C₂²×C₄	—	94	8	no	—
969	C₂²×C₄	—	94	2	no	—
970	C₂²×C₄	—	94	1	no	—
971	C₂²×C₄	—	94	2	no	—
972	C₂²×C₄	—	94	2	no	—
973	C₂²×C₄	—	94	1	no	—
974	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
975	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
976	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
977	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
978	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
979	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
980	Q₁₆	—	94	4	no	—
981	SD₁₆	—	94	4	no	—
982	SD₁₆	—	94	4	no	—
983	SD₁₆	—	94	4	no	—
984	SD₁₆	—	94	4	no	—
985	D₈	—	94	4	no	—
986	D₈	—	94	4	no	—
987	D₈	—	94	4	no	—
988	M₁₆	—	94	2	no	—
989	M₁₆	—	94	2	no	—
990	C₂×C₈	—	2	2	no	—
991	C₂×C₈	—	2	2	no	—
992	C₂×C₈	—	47	2	no	—
993	C₂×C₈	—	47	2	no	—
994	C₂×C₈	C₂³×D₄₇	1	1	yes	characteristic
995	C₂×C₈	C₂³×D₄₇	1	1	yes	characteristic
996	C₂×C₈	C₂³×D₄₇	1	1	yes	characteristic
997	C₂×C₈	C₂³×D₄₇	1	1	yes	characteristic
998	C₄⋊C₄	—	2	1	no	—
999	C₄⋊C₄	—	2	1	no	—
1000	C₄⋊C₄	—	2	1	no	—
1001	C₄⋊C₄	—	2	1	no	—
1002	C₄⋊C₄	—	47	2	no	—
1003	C₄⋊C₄	—	47	2	no	—
1004	C₄⋊C₄	—	47	1	no	—
1005	C₄⋊C₄	—	47	1	no	—
1006	C₄⋊C₄	—	47	1	no	—
1007	C₄⋊C₄	—	47	1	no	—
1008	C₄⋊C₄	—	47	2	no	—
1009	C₄⋊C₄	—	94	2	no	—
1010	C₄⋊C₄	—	94	2	no	—
1011	C₄⋊C₄	—	94	2	no	—
1012	C₄⋊C₄	—	94	2	no	—
1013	C₄⋊C₄	—	94	2	no	—
1014	C₄⋊C₄	—	94	2	no	—
1015	C₄⋊C₄	—	94	2	no	—
1016	C₄⋊C₄	—	94	2	no	—
1017	C₄⋊C₄	—	94	1	no	—
1018	C₄⋊C₄	C₂³×D₄₇	1	1	yes	characteristic
1019	C₄⋊C₄	C₂³×D₄₇	1	1	yes	characteristic
1020	C₄⋊C₄	C₂³×D₄₇	1	1	yes	characteristic
1021	C₄⋊C₄	C₂³×D₄₇	1	1	yes	characteristic
1022	C₄⋊C₄	C₂³×D₄₇	1	1	yes	characteristic
1023	C₄⋊C₄	C₂³×D₄₇	1	1	yes	characteristic
1024	C₂²⋊C₄	—	2	1	no	—
1025	C₂²⋊C₄	—	2	1	no	—
1026	C₂²⋊C₄	—	2	1	no	—
1027	C₂²⋊C₄	—	2	1	no	—
1028	C₂²⋊C₄	—	2	1	no	—
1029	C₂²⋊C₄	—	2	1	no	—
1030	C₂²⋊C₄	—	2	1	no	—
1031	C₂²⋊C₄	—	2	1	no	—
1032	C₂²⋊C₄	—	2	1	no	—
1033	C₂²⋊C₄	—	47	2	no	—
1034	C₂²⋊C₄	—	47	2	no	—
1035	C₂²⋊C₄	—	47	2	no	—
1036	C₂²⋊C₄	—	47	2	no	—
1037	C₂²⋊C₄	—	94	2	no	—
1038	C₂²⋊C₄	—	94	2	no	—
1039	C₂²⋊C₄	—	94	2	no	—
1040	C₂²⋊C₄	—	94	2	no	—
1041	C₂²⋊C₄	—	94	2	no	—
1042	C₂²⋊C₄	—	94	2	no	—
1043	C₂²⋊C₄	—	94	2	no	—
1044	C₂²⋊C₄	—	94	2	no	—
1045	C₂²⋊C₄	—	94	2	no	—
1046	C₂²⋊C₄	—	94	2	no	—
1047	C₂²⋊C₄	—	94	2	no	—
1048	C₄²	—	2	1	no	—
1049	C₄²	—	2	1	no	—
1050	C₄²	—	2	1	no	—
1051	C₄²	—	2	1	no	—
1052	C₄²	—	2	1	no	—
1053	C₄²	—	47	2	no	—
1054	C₄²	—	47	2	no	—
1055	C₄²	—	47	2	no	—
1056	C₄²	—	47	2	no	—
1057	C₄²	—	94	2	no	—
1058	C₄²	—	94	2	no	—
1059	C₄²	—	94	2	no	—
1060	C₄²	—	94	2	no	—
1061	C₄²	—	94	2	no	—
1062	C₂³	—	2	2	no	—
1063	C₂³	—	2	1	no	—
1064	C₂³	—	4	1	no	—
1065	C₂³	—	4	1	no	—
1066	C₂³	—	94	4	no	—
1067	C₂³	—	94	2	no	—
1068	C₂³	—	94	2	no	—
1069	C₂³	—	376	1	no	—
1070	C₂³	—	376	1	no	—
1071	C₂³	—	376	1	no	—
1072	C₂³	—	376	1	no	—
1073	C₂³	—	188	2	no	—
1074	C₂³	C₂×D₄×D₄₇	1	1	yes	characteristic
1075	C₂³	C₂×D₄×D₄₇	1	1	yes	characteristic
1076	C₂³	C₂×D₄×D₄₇	1	1	yes	characteristic
1077	Q₈	—	2	1	no	—
1078	Q₈	—	2	1	no	—
1079	Q₈	—	47	4	no	—
1080	Q₈	—	94	4	no	—
1081	Q₈	—	94	2	no	—
1082	Q₈	—	376	2	no	—
1083	D₄	—	2	1	no	—
1084	D₄	—	2	1	no	—
1085	D₄	—	4	2	no	—
1086	D₄	—	4	2	no	—
1087	D₄	—	8	1	no	—
1088	D₄	—	47	4	no	—
1089	D₄	—	94	8	no	—
1090	D₄	—	94	8	no	—
1091	D₄	—	94	4	no	—
1092	D₄	—	94	2	no	—
1093	D₄	—	94	2	no	—
1094	D₄	—	94	2	no	—
1095	D₄	—	376	2	no	—
1096	D₄	—	376	2	no	—
1097	D₄	—	376	2	no	—
1098	D₄	—	188	4	no	—
1099	D₄	—	188	2	no	—
1100	C₂×C₄	—	2	2	no	—
1101	C₂×C₄	—	2	2	no	—
1102	C₂×C₄	—	2	2	no	—
1103	C₂×C₄	—	2	1	no	—
1104	C₂×C₄	—	2	1	no	—
1105	C₂×C₄	—	2	1	no	—
1106	C₂×C₄	—	2	1	no	—
1107	C₂×C₄	—	2	1	no	—
1108	C₂×C₄	—	2	1	no	—
1109	C₂×C₄	—	2	1	no	—
1110	C₂×C₄	—	2	1	no	—
1111	C₂×C₄	—	2	1	no	—
1112	C₂×C₄	—	2	1	no	—
1113	C₂×C₄	—	2	1	no	—
1114	C₂×C₄	—	4	2	no	—
1115	C₂×C₄	—	8	1	no	—
1116	C₂×C₄	—	8	1	no	—
1117	C₂×C₄	—	47	2	no	—
1118	C₂×C₄	—	47	2	no	—
1119	C₂×C₄	—	47	2	no	—
1120	C₂×C₄	—	47	2	no	—
1121	C₂×C₄	—	94	8	no	—
1122	C₂×C₄	—	94	8	no	—
1123	C₂×C₄	—	94	4	no	—
1124	C₂×C₄	—	94	2	no	—
1125	C₂×C₄	—	94	2	no	—
1126	C₂×C₄	—	376	2	no	—
1127	C₂×C₄	—	376	2	no	—
1128	C₂×C₄	—	376	2	no	—
1129	C₂×C₄	—	376	2	no	—
1130	C₂×C₄	—	376	2	no	—
1131	C₂×C₄	—	376	2	no	—
1132	C₂×C₄	—	376	2	no	—
1133	C₂×C₄	—	376	1	no	—
1134	C₂×C₄	—	188	2	no	—
1135	C₂×C₄	—	188	2	no	—
1136	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
1137	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
1138	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
1139	C₂×C₄	#41×D₄₇	1	2	yes	—
1140	C₂×C₄	#41×D₄₇	1	2	yes	—
1141	C₂×C₄	C₂⁴×D₄₇	1	1	yes	characteristic
1142	C₈	—	2	1	no	—
1143	C₈	—	2	1	no	—
1144	C₈	—	2	1	no	—
1145	C₈	—	2	1	no	—
1146	C₈	—	94	2	no	—
1147	C₈	—	94	2	no	—
1148	C₂²	—	2	1	no	—
1149	C₂²	—	2	1	no	—
1150	C₂²	—	2	1	no	—
1151	C₂²	—	2	1	no	—
1152	C₂²	—	2	1	no	—
1153	C₂²	—	2	1	no	—
1154	C₂²	—	2	1	no	—
1155	C₂²	—	2	1	no	—
1156	C₂²	—	4	1	no	—
1157	C₂²	—	4	1	no	—
1158	C₂²	—	4	1	no	—
1159	C₂²	—	8	2	no	—
1160	C₂²	—	94	4	no	—
1161	C₂²	—	376	4	no	—
1162	C₂²	—	188	2	no	—
1163	C₂²	—	188	2	no	—
1164	C₂²	—	188	2	no	—
1165	C₂²	—	188	2	no	—
1166	C₂²	—	188	2	no	—
1167	C₂²	—	752	2	no	—
1168	C₂²	#15689631	1	2	yes	—
1169	C₂²	C₂²×D₄×D₄₇	1	1	yes	characteristic
1170	C₄	—	2	1	no	—
1171	C₄	—	2	1	no	—
1172	C₄	—	4	1	no	—
1173	C₄	—	4	1	no	—
1174	C₄	—	4	1	no	—
1175	C₄	—	4	1	no	—
1176	C₄	—	4	1	no	—
1177	C₄	—	4	1	no	—
1178	C₄	—	4	1	no	—
1179	C₄	—	94	2	no	—
1180	C₄	—	94	2	no	—
1181	C₄	—	94	4	no	—
1182	C₄	—	94	2	no	—
1183	C₄	—	94	2	no	—
1184	C₄	—	188	2	no	—
1185	C₄	#15689631	1	2	yes	—
1186	C₄	C₂×#41×D₄₇	1	1	yes	characteristic
1187	C₄	C₂×#41×D₄₇	1	1	yes	characteristic
1188	C₂	—	2	2	no	—
1189	C₂	—	4	1	no	—
1190	C₂	—	4	1	no	—
1191	C₂	—	8	1	no	—
1192	C₂	—	376	2	no	—
1193	C₂	—	188	4	no	—
1194	C₂	C₂×#15689631	1	1	yes	characteristic
1195	C₂	#20258157	1	1	yes	characteristic
1196	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×#3091	C₂
socle	C₂²×C₄₇	C₂³×D₄
hypercenter	#3091	D₄₇
hypocenter	C₄₇	#60580
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₂³×C₄ ◁ #3091

Complements

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

N	H ≅ G/N	type
1. #20257125	C₂	semidirect
2. #20256589	C₂	semidirect
3. #20253660	C₂	semidirect
4. #20253653	C₂	semidirect
5. #20253590	C₂	semidirect
6. #20253582	C₂	semidirect
7. #20253534	C₂	semidirect
8. #20253500	C₂	semidirect
9. #20253443	C₂	semidirect
10. #20253409	C₂	semidirect
11. #20253328	C₂	semidirect
12. #20253233	C₂	semidirect
13. #20253222	C₂	semidirect
14. #20252912	C₂	semidirect
15. #20252894	C₂	semidirect
16. #20252628	C₂	semidirect
17. C₂×#15689270	C₂	semidirect
18. #20252246	C₂	semidirect
19. #20252239	C₂	semidirect
20. #20252234	C₂	semidirect
21. #20252223	C₂	semidirect
22. #20252042	C₂	semidirect
23. C₄₇×#3091	C₂	semidirect
36. #15689746	C₂²	semidirect
37. #15689726	C₂²	semidirect
39. #15689668	C₂²	semidirect
40. #15689659	C₂²	semidirect
43. #15689604	C₂²	semidirect
44. #15689604	C₂²	semidirect
55. #15689591	C₂²	semidirect
56. #15689591	C₂²	semidirect
59. #15689447	C₂²	semidirect
60. #15689447	C₂²	semidirect
61. #15689441	C₂²	semidirect
62. #15689436	C₂²	semidirect
63. #15689433	C₂²	semidirect
64. #15689429	C₂²	semidirect
65. #15689426	C₂²	semidirect
66. #15689422	C₂²	semidirect
67. #15689417	C₂²	semidirect
68. #15689412	C₂²	semidirect
69. #15689407	C₂²	semidirect
70. #15689402	C₂²	semidirect
71. #15689348	C₂²	semidirect
72. #15689348	C₂²	semidirect
73. #15689341	C₂²	semidirect
74. #15689341	C₂²	semidirect
75. #15689322	C₂²	semidirect
76. #15689322	C₂²	semidirect
77. #15689317	C₂²	semidirect
78. #15689317	C₂²	semidirect
79. #15689283	C₂²	semidirect
80. #15689283	C₂²	semidirect
85. #15689266	C₂²	semidirect
86. #15689266	C₂²	semidirect
87. #15689234	C₂²	semidirect
88. #15689234	C₂²	semidirect
89. #15689232	C₂²	semidirect
90. #15689227	C₂²	semidirect
91. #15689226	C₂²	semidirect
92. #15689222	C₂²	semidirect
93. #15689222	C₂²	semidirect
94. #15689220	C₂²	semidirect
95. #15689215	C₂²	semidirect
96. #15689214	C₂²	semidirect
97. #15689210	C₂²	semidirect
98. #15689210	C₂²	semidirect
99. #15689208	C₂²	semidirect
100. #15689205	C₂²	semidirect
101. #15689205	C₂²	semidirect
102. #15689203	C₂²	semidirect
103. #15689181	C₂²	semidirect
104. #15689181	C₂²	semidirect
105. #15689177	C₂²	semidirect
106. #15689173	C₂²	semidirect
122. C₄₇×#485	C₂²	semidirect
123. C₄₇×#485	C₂²	semidirect
124. C₄₇×#484	C₂²	semidirect
125. C₄₇×#483	C₂²	semidirect
126. C₄₇×#482	C₂²	semidirect
127. C₄₇×#482	C₂²	semidirect
128. C₄₇×#481	C₂²	semidirect
129. C₄₇×#480	C₂²	semidirect
364. C₂×D₁₈₈	#41	semidirect
379. C₂×Dic₉₄	#41	semidirect
601. #3091	D₄₇	semidirect
659. #485	C₂×D₄₇	semidirect
660. #485	C₂×D₄₇	semidirect
661. #484	C₂×D₄₇	semidirect
662. #483	C₂×D₄₇	semidirect
665. #482	C₂×D₄₇	semidirect
666. #482	C₂×D₄₇	semidirect
668. #481	C₂×D₄₇	semidirect
670. #480	C₂×D₄₇	semidirect
733. C₄₇	#60580	semidirect

Maximal subgroups

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

subgroup	index
#20257125	2
#20256589	2
#20253660	2
#20253653	2
#20253590	2
#20253582	2
#20253534	2
#20253500	2
#20253443	2
#20253409	2
#20253328	2
#20253233	2
#20253222	2
#20252912	2
#20252894	2
#20252628	2
C₂×#15689270	2
#20252246	2
#20252239	2
#20252234	2
#20252223	2
#20252042	2
C₄₇×#3091	2
#60580	47