Subgroups — #27094789

Order 12032.

1874 conjugacy classes of subgroups.

The subgroup lattice has 1106 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20256948	C₂	1	2	yes	maximal, complemented
2	#20255815	C₂	1	1	yes	maximal, characteristic, complemented
3	#20255807	C₂	1	1	yes	maximal, characteristic, complemented
4	#20255796	C₂	1	2	yes	maximal, complemented
5	#20255793	C₂	1	1	yes	maximal, characteristic, complemented
6	#20255785	C₂	1	1	yes	maximal, characteristic, complemented
7	#20255777	C₂	1	1	yes	maximal, characteristic, complemented
8	#20255773	C₂	1	2	yes	maximal, complemented
9	#20255762	C₂	1	2	yes	maximal, complemented
10	#20255759	C₂	1	1	yes	maximal, characteristic, complemented
11	#20255751	C₂	1	1	yes	maximal, characteristic, complemented
12	#20255740	C₂	1	2	yes	maximal, complemented
13	#20255732	C₂	1	1	yes	maximal, characteristic, complemented
14	#20253900	C₂	1	1	yes	maximal, characteristic, complemented
15	#20253299	C₂	1	2	yes	maximal, complemented
16	#20253297	C₂	1	2	yes	maximal, complemented
17	#20253172	C₂	1	2	yes	maximal, complemented
18	#20252965	C₂	1	1	yes	maximal, characteristic, complemented
19	#135×Dic₄₇	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×C₈×C₂²⋊D₄₇	C₂	1	1	yes	maximal, characteristic, complemented
21	C₂×#15689161	C₂	1	1	yes	maximal, characteristic, complemented
22	#427×D₄₇	C₂	1	1	yes	maximal, characteristic, complemented
23	C₄₇×#3050	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂²×C₈×D₄₇	C₂²	1	1	yes	characteristic
25	#15689844	C₂²	1	2	yes	—
26	#15689837	C₂²	1	2	yes	—
27	#15689831	C₂²	1	2	yes	—
28	#15689825	C₂²	1	2	yes	—
29	#15689820	C₂²	1	2	yes	—
30	#15689815	C₂²	1	2	yes	—
31	#15689810	—	2	2	no	—
32	#15689807	C₂²	1	2	yes	—
33	#15689804	—	2	2	no	—
34	#15689796	—	2	2	no	—
35	#15689773	C₂²	1	2	yes	—
36	#15689760	—	2	2	no	—
37	#15689676	C₂²	1	2	yes	—
38	#15689655	—	2	2	no	—
39	#15689653	—	2	2	no	—
40	#15689653	—	2	2	no	—
41	#15689630	C₂²	1	2	yes	—
42	#41×Dic₄₇	C₂²	1	2	yes	—
43	C₄×#10625352	—	2	2	no	—
44	C₂×C₄×C₂²⋊D₄₇	C₂²	1	1	yes	characteristic
45	C₂×#13093983	C₂²	1	2	yes	—
46	#117×D₄₇	C₂²	1	2	yes	—
47	#15689527	C₂²	1	1	yes	characteristic, complemented
48	#15689527	C₂²	1	1	yes	characteristic, complemented
49	#15689524	C₂²	1	1	yes	characteristic, complemented
50	#15689524	C₂²	1	1	yes	characteristic, complemented
51	#15689523	C₂²	1	2	yes	complemented
52	#15689520	C₂²	1	2	yes	complemented
53	#15689463	C₂²	1	2	yes	complemented
54	#15689462	C₂²	1	2	yes	complemented
55	#15689461	C₂²	1	2	yes	complemented
56	#15689461	C₂²	1	2	yes	complemented
57	#15689457	C₂²	1	2	yes	complemented
58	#15689456	C₂²	1	2	yes	complemented
59	#15689452	C₂²	1	2	yes	complemented
60	#15689451	C₂²	1	2	yes	complemented
61	#15689446	C₂²	1	2	yes	complemented
62	#15689445	C₂²	1	2	yes	complemented
63	#15689444	C₂²	1	2	yes	complemented
64	#15689444	C₂²	1	2	yes	complemented
65	#15689440	C₂²	1	2	yes	complemented
66	#15689439	C₂²	1	2	yes	complemented
67	#15689435	C₂²	1	2	yes	complemented
68	#15689434	C₂²	1	2	yes	complemented
69	#15689432	C₂²	1	2	yes	complemented
70	#15689428	C₂²	1	2	yes	complemented
71	#15689425	C₂²	1	2	yes	complemented
72	#15689421	C₂²	1	2	yes	complemented
73	#15689416	C₂²	1	2	yes	complemented
74	#15689411	C₂²	1	2	yes	complemented
75	#15689406	C₂²	1	2	yes	complemented
76	#15689401	C₂²	1	2	yes	complemented
77	#15689361	C₂²	1	1	yes	characteristic, complemented
78	#15689361	C₂²	1	1	yes	characteristic, complemented
79	#15689356	C₂²	1	1	yes	characteristic, complemented
80	#15689356	C₂²	1	1	yes	characteristic, complemented
81	#15689349	C₂²	1	2	yes	complemented
82	#15689349	C₂²	1	2	yes	complemented
83	Q₁₆×Dic₄₇	C₂²	1	1	yes	characteristic, complemented
84	Q₁₆×Dic₄₇	C₂²	1	1	yes	characteristic, complemented
85	SD₁₆×Dic₄₇	C₂²	1	2	yes	complemented
86	SD₁₆×Dic₄₇	C₂²	1	2	yes	complemented
87	D₈×Dic₄₇	C₂²	1	1	yes	characteristic, complemented
88	D₈×Dic₄₇	C₂²	1	1	yes	characteristic, complemented
89	C₈×C₂²⋊D₄₇	C₂²	1	1	yes	characteristic
90	C₈×C₂²⋊D₄₇	C₂²	1	1	yes	characteristic
91	C₈×C₂²⋊D₄₇	C₂²	1	1	yes	characteristic
92	C₈×C₂²⋊D₄₇	C₂²	1	1	yes	characteristic
93	C₈×C₂²⋊D₄₇	C₂²	1	1	yes	characteristic
94	C₈×C₂²⋊D₄₇	C₂²	1	1	yes	characteristic
95	C₈×C₂²⋊D₄₇	C₂²	1	1	yes	characteristic
96	C₈×C₂²⋊D₄₇	C₂²	1	1	yes	characteristic
97	#15689161	C₂²	1	1	yes	characteristic
98	#15689161	C₂²	1	1	yes	characteristic
99	#15689161	C₂²	1	2	yes	—
100	#15689161	C₂²	1	1	yes	characteristic, complemented
101	#15689161	C₂²	1	2	yes	complemented
102	#15689161	C₂²	1	1	yes	characteristic, complemented
103	#15689160	C₂²	1	1	yes	characteristic, complemented
104	#15689160	C₂²	1	1	yes	characteristic, complemented
105	#15689159	C₂²	1	2	yes	—
106	#15689159	C₂²	1	2	yes	—
107	#15689158	C₂²	1	2	yes	complemented
108	C₂×#13093958	C₂²	1	1	yes	characteristic, complemented
109	C₂×#13093958	C₂²	1	1	yes	characteristic, complemented
110	#107×D₄₇	C₂²	1	1	yes	characteristic, complemented
111	#107×D₄₇	C₂²	1	1	yes	characteristic, complemented
112	C₂×#13093956	C₂²	1	2	yes	complemented
113	#106×D₄₇	C₂²	1	2	yes	complemented
114	C₂×Dic₄₇⋊C₈	C₂²	1	1	yes	characteristic
115	#15689119	C₂²	1	2	yes	—
116	#15689119	C₂²	1	2	yes	—
117	C₂×C₂²⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
118	C₂×(C₂×D₄₇)⋊C₈	C₂²	1	1	yes	characteristic
119	C₂×C₈×Dic₄₇	C₂²	1	1	yes	characteristic
120	C₂×#135×C₄₇	C₂²	1	1	yes	characteristic
121	C₂³×C₈×C₄₇	C₂²	1	1	yes	characteristic
122	C₄₇×#525	C₂²	1	2	yes	—
123	C₄₇×#467	C₂²	1	1	yes	characteristic, complemented
124	C₄₇×#467	C₂²	1	1	yes	characteristic, complemented
125	C₄₇×#466	C₂²	1	1	yes	characteristic, complemented
126	C₄₇×#466	C₂²	1	1	yes	characteristic, complemented
127	C₄₇×#465	C₂²	1	2	yes	complemented
128	C₄₇×#465	C₂²	1	2	yes	complemented
129	C₄₇×#427	C₂²	1	1	yes	characteristic
130	C₄₇×#416	C₂²	1	2	yes	—
131	C₂×#10625352	—	2	2	no	—
132	C₂²×C₂²⋊D₄₇	D₄	1	1	yes	characteristic
133	C₂²×C₄×D₄₇	C₂³	1	1	yes	characteristic
134	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
135	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
136	C₂×C₈×D₄₇	—	2	4	no	—
137	C₂×C₈×D₄₇	C₂³	1	1	yes	characteristic
138	C₂×C₈×D₄₇	C₂³	1	1	yes	characteristic
139	C₂×C₈×D₄₇	C₂³	1	1	yes	characteristic
140	C₂×C₈×D₄₇	C₂³	1	1	yes	characteristic
141	#13094023	C₂³	1	2	yes	—
142	#13094023	C₂³	1	2	yes	—
143	#13094019	—	2	2	no	—
144	#13094019	—	2	2	no	—
145	#13094017	—	2	2	no	—
146	#13094017	—	2	2	no	—
147	#13094017	—	2	2	no	—
148	#13094017	—	2	2	no	—
149	#13094015	—	2	2	no	—
150	#13094015	C₂³	1	2	yes	—
151	#13094015	C₂³	1	2	yes	—
152	#13094014	—	2	2	no	—
153	#13094014	—	2	2	no	—
154	#13094011	—	2	2	no	—
155	#13094010	—	2	2	no	—
156	#13094010	—	2	2	no	—
157	#13094008	—	2	2	no	—
158	#13094008	—	2	2	no	—
159	#13094006	—	2	2	no	—
160	#13094006	—	2	2	no	—
161	#13094005	—	2	2	no	—
162	#13094005	—	2	2	no	—
163	#13094005	—	2	2	no	—
164	#13094004	—	2	2	no	—
165	#13094001	—	2	2	no	—
166	#13094001	—	2	2	no	—
167	#13094001	—	2	2	no	—
168	#13094001	—	2	2	no	—
169	#13094000	C₂³	1	2	yes	—
170	#13094000	C₂³	1	2	yes	—
171	#13093996	—	2	2	no	—
172	#13093996	—	2	2	no	—
173	#13093995	—	2	2	no	—
174	#13093995	C₂³	1	2	yes	—
175	#13093995	C₂³	1	2	yes	—
176	#13093992	—	2	2	no	—
177	Q₈×Dic₄₇	C₂³	1	2	yes	—
178	Q₈×Dic₄₇	C₂³	1	2	yes	—
179	C₄×Dic₉₄	—	2	2	no	—
180	C₄×Dic₉₄	—	2	2	no	—
181	#13093989	—	2	2	no	—
182	D₄×Dic₄₇	—	2	2	no	—
183	D₄×Dic₄₇	—	2	2	no	—
184	D₄×Dic₄₇	—	2	2	no	—
185	D₄×Dic₄₇	C₂³	1	2	yes	—
186	D₄×Dic₄₇	C₂³	1	2	yes	—
187	C₄×C₂²⋊D₄₇	—	2	2	no	—
188	C₄×C₂²⋊D₄₇	—	2	2	no	—
189	C₄×C₂²⋊D₄₇	D₄	1	1	yes	characteristic
190	C₄×C₂²⋊D₄₇	D₄	1	1	yes	characteristic
191	C₄×C₂²⋊D₄₇	D₄	1	1	yes	characteristic
192	C₄×C₂²⋊D₄₇	D₄	1	1	yes	characteristic
193	C₄×C₂²⋊D₄₇	C₂³	1	1	yes	characteristic
194	C₄×C₂²⋊D₄₇	C₂³	1	1	yes	characteristic
195	C₄×C₂²⋊D₄₇	C₂³	1	1	yes	characteristic
196	C₄×C₂²⋊D₄₇	C₂³	1	1	yes	characteristic
197	(C₂²⋊D₄₇)⋊C₄	—	2	2	no	—
198	(C₂²⋊D₄₇)⋊C₄	—	2	2	no	—
199	#13093983	—	2	2	no	—
200	#13093983	—	2	2	no	—
201	#13093983	—	2	2	no	—
202	#13093983	C₂³	1	2	yes	—
203	#13093983	C₂³	1	2	yes	—
204	#13093983	C₂³	1	2	yes	—
205	#13093983	C₂³	1	2	yes	—
206	#13093982	—	2	2	no	—
207	#13093982	C₂³	1	2	yes	—
208	#13093982	C₂³	1	2	yes	—
209	#13093981	—	2	2	no	—
210	#13093980	—	2	2	no	—
211	#13093980	—	2	2	no	—
212	#13093980	—	2	2	no	—
213	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
214	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
215	C₂×Dic₄₇⋊C₄	D₄	1	1	yes	characteristic
216	C₄⋊C₄×D₄₇	C₂³	1	2	yes	—
217	C₄⋊C₄×D₄₇	C₂³	1	2	yes	—
218	C₂×C₂²⋊Dic₄₇	—	2	2	no	—
219	C₂×C₂²⋊Dic₄₇	D₄	1	1	yes	characteristic
220	C₂×(C₂×D₄₇)⋊C₄	D₄	1	1	yes	characteristic
221	C₂²⋊C₄×D₄₇	—	2	2	no	—
222	C₂×C₄×Dic₄₇	—	2	2	no	—
223	C₂×C₄×Dic₄₇	—	2	2	no	—
224	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
225	C₄²×D₄₇	—	2	2	no	—
226	#13093958	C₂³	1	1	yes	characteristic
227	#13093958	C₂³	1	1	yes	characteristic
228	#13093958	C₂³	1	1	yes	characteristic
229	#13093958	C₂³	1	1	yes	characteristic
230	#13093958	C₂³	1	2	yes	—
231	#13093958	C₂³	1	2	yes	—
232	#13093957	C₂³	1	2	yes	—
233	#13093957	C₂³	1	2	yes	—
234	#13093957	C₂³	1	2	yes	—
235	#13093957	C₂³	1	2	yes	—
236	#13093956	C₂³	1	2	yes	—
237	#13093956	C₂³	1	2	yes	—
238	#13093956	C₂³	1	2	yes	—
239	#13093956	C₂³	1	2	yes	—
240	#13093955	C₂³	1	2	yes	—
241	#13093955	C₂³	1	2	yes	—
242	#13093955	C₂³	1	2	yes	—
243	#13093955	C₂³	1	2	yes	—
244	Dic₄₇⋊C₈	C₂³	1	1	yes	characteristic
245	Dic₄₇⋊C₈	C₂³	1	1	yes	characteristic
246	Dic₄₇⋊C₈	C₂³	1	1	yes	characteristic
247	Dic₄₇⋊C₈	C₂³	1	1	yes	characteristic
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	#13093945	C₂³	1	2	yes	—
253	#13093945	C₂³	1	2	yes	—
254	#13093945	C₂³	1	2	yes	—
255	#13093945	C₂³	1	2	yes	—
256	C₂²⋊(C₄₇⋊C₈)	C₂³	1	1	yes	characteristic
257	C₂²⋊(C₄₇⋊C₈)	C₂³	1	1	yes	characteristic
258	C₂²⋊(C₄₇⋊C₈)	C₂³	1	1	yes	characteristic
259	C₂²⋊(C₄₇⋊C₈)	C₂³	1	1	yes	characteristic
260	(C₂×D₄₇)⋊C₈	C₂³	1	1	yes	characteristic
261	(C₂×D₄₇)⋊C₈	C₂³	1	1	yes	characteristic
262	(C₂×D₄₇)⋊C₈	C₂³	1	1	yes	characteristic
263	(C₂×D₄₇)⋊C₈	C₂³	1	1	yes	characteristic
264	C₈×Dic₄₇	C₂³	1	1	yes	characteristic
265	C₈×Dic₄₇	C₂³	1	1	yes	characteristic
266	C₈×Dic₄₇	C₂³	1	1	yes	characteristic
267	C₈×Dic₄₇	C₂³	1	1	yes	characteristic
268	C₂×#41×C₄₇	C₂³	1	2	yes	—
269	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
270	#135×C₄₇	—	2	4	no	—
271	C₂×Q₁₆×C₄₇	C₂³	1	1	yes	characteristic
272	C₂×SD₁₆×C₄₇	C₂³	1	2	yes	—
273	C₂×D₈×C₄₇	C₂³	1	1	yes	characteristic
274	C₂²×C₈×C₄₇	—	2	4	no	—
275	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
276	C₂²×C₈×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	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
280	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
281	#123×C₄₇	—	2	2	no	—
282	C₂²⋊Q₈×C₄₇	C₂³	1	2	yes	—
283	C₂²⋊Q₈×C₄₇	C₂³	1	2	yes	—
284	#121×C₄₇	C₂³	1	2	yes	—
285	#121×C₄₇	C₂³	1	2	yes	—
286	#120×C₄₇	—	2	2	no	—
287	C₄×D₄×C₄₇	—	2	2	no	—
288	C₄×D₄×C₄₇	—	2	2	no	—
289	#117×C₄₇	C₂³	1	2	yes	—
290	#107×C₄₇	C₂³	1	1	yes	characteristic
291	#107×C₄₇	C₂³	1	1	yes	characteristic
292	#106×C₄₇	C₂³	1	2	yes	—
293	#103×C₄₇	C₂³	1	2	yes	—
294	#103×C₄₇	C₂³	1	2	yes	—
295	#102×C₄₇	C₂³	1	2	yes	—
296	#102×C₄₇	C₂³	1	2	yes	—
297	C₂⁴×C₄₇	C₂×D₄	1	1	yes	characteristic
298	C₂³×D₄₇	C₂×D₄	1	1	yes	characteristic
299	#41×C₄₇	—	2	4	no	—
300	#41×C₄₇	—	2	4	no	—
301	C₂×Q₈×C₄₇	C₂⁴	1	2	yes	—
302	C₂×D₄×C₄₇	—	2	2	no	—
303	C₂×D₄×C₄₇	—	2	2	no	—
304	C₂×D₄×C₄₇	—	2	2	no	—
305	C₂×D₄×C₄₇	C₂⁴	1	2	yes	—
306	C₂²×C₄×C₄₇	—	2	2	no	—
307	C₂²×C₄×C₄₇	—	2	2	no	—
308	C₂²×C₄×C₄₇	—	2	2	no	—
309	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
310	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
311	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
312	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
313	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
314	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
315	C₂×C₂²⋊D₄₇	—	2	4	no	—
316	C₂×C₂²⋊D₄₇	—	2	2	no	—
317	C₂×C₂²⋊D₄₇	—	2	2	no	—
318	C₂×C₂²⋊D₄₇	C₂×D₄	1	1	yes	characteristic
319	C₂×C₂²⋊D₄₇	C₂×D₄	1	1	yes	characteristic
320	C₂×C₂²⋊D₄₇	C₂×D₄	1	1	yes	characteristic
321	C₂×C₂²⋊D₄₇	C₂×D₄	1	1	yes	characteristic
322	C₂²×Dic₄₇	—	2	2	no	—
323	C₂²×Dic₄₇	—	2	2	no	—
324	C₂²×Dic₄₇	—	2	2	no	—
325	C₂²×Dic₄₇	—	2	2	no	—
326	C₂²×Dic₄₇	C₂×D₄	1	1	yes	characteristic
327	C₂²×Dic₄₇	C₂×D₄	1	1	yes	characteristic
328	C₂²×Dic₄₇	C₂×D₄	1	1	yes	characteristic
329	#10625352	—	4	8	no	—
330	C₂×C₄×D₄₇	—	2	2	no	—
331	C₂×C₄×D₄₇	—	2	2	no	—
332	C₂×C₄×D₄₇	—	2	2	no	—
333	C₂×C₄×D₄₇	—	2	2	no	—
334	C₂×C₄×D₄₇	C₂×D₄	1	1	yes	characteristic
335	C₂×C₄×D₄₇	C₂×D₄	1	1	yes	characteristic
336	C₂×C₄×D₄₇	C₂⁴	1	1	yes	characteristic
337	C₂×C₄×D₄₇	C₂⁴	1	1	yes	characteristic
338	C₂×Dic₉₄	—	2	2	no	—
339	C₂×Dic₉₄	—	2	2	no	—
340	Q₁₆×C₄₇	—	2	2	no	—
341	SD₁₆×C₄₇	—	2	4	no	—
342	D₈×C₄₇	—	2	2	no	—
343	C₂×C₈×C₄₇	—	2	2	no	—
344	C₂×C₈×C₄₇	—	2	2	no	—
345	C₂×C₈×C₄₇	—	2	2	no	—
346	C₂×C₈×C₄₇	—	2	2	no	—
347	C₂×C₈×C₄₇	—	2	2	no	—
348	C₂×C₈×C₄₇	#41	1	4	yes	complemented
349	C₂×C₈×C₄₇	C₂⁴	1	1	yes	characteristic
350	C₂×C₈×C₄₇	C₂⁴	1	1	yes	characteristic
351	C₂×C₈×C₄₇	C₂⁴	1	1	yes	characteristic
352	C₂×C₈×C₄₇	C₂⁴	1	1	yes	characteristic
353	C₄⋊C₄×C₄₇	—	2	2	no	—
354	C₄⋊C₄×C₄₇	—	2	2	no	—
355	C₄⋊C₄×C₄₇	C₂⁴	1	2	yes	—
356	C₄⋊C₄×C₄₇	C₂⁴	1	2	yes	—
357	C₂²⋊C₄×C₄₇	—	2	2	no	—
358	C₂²⋊C₄×C₄₇	—	2	2	no	—
359	C₂²⋊C₄×C₄₇	—	2	2	no	—
360	C₂²⋊C₄×C₄₇	—	2	2	no	—
361	C₂²⋊C₄×C₄₇	—	2	2	no	—
362	C₄²×C₄₇	—	2	2	no	—
363	C₂²⋊Dic₄₇	—	2	2	no	—
364	C₂²⋊Dic₄₇	—	2	2	no	—
365	C₂²⋊Dic₄₇	—	2	2	no	—
366	C₂²⋊Dic₄₇	—	2	2	no	—
367	C₂²⋊Dic₄₇	—	2	2	no	—
368	C₂²⋊Dic₄₇	—	2	2	no	—
369	C₂²⋊Dic₄₇	—	2	2	no	—
370	C₂²⋊Dic₄₇	—	2	2	no	—
371	C₂²⋊Dic₄₇	C₂×D₄	1	1	yes	characteristic
372	C₂²⋊Dic₄₇	C₂×D₄	1	1	yes	characteristic
373	C₂²⋊Dic₄₇	C₂×D₄	1	1	yes	characteristic
374	C₂²⋊Dic₄₇	C₂×D₄	1	1	yes	characteristic
375	(C₂×D₄₇)⋊C₄	—	2	2	no	—
376	(C₂×D₄₇)⋊C₄	—	2	2	no	—
377	(C₂×D₄₇)⋊C₄	—	2	2	no	—
378	(C₂×D₄₇)⋊C₄	—	2	2	no	—
379	(C₂×D₄₇)⋊C₄	C₂×D₄	1	1	yes	characteristic
380	(C₂×D₄₇)⋊C₄	C₂×D₄	1	1	yes	characteristic
381	(C₂×D₄₇)⋊C₄	C₂×D₄	1	1	yes	characteristic
382	(C₂×D₄₇)⋊C₄	C₂×D₄	1	1	yes	characteristic
383	C₄⋊Dic₄₇	—	2	2	no	—
384	C₄⋊Dic₄₇	—	2	2	no	—
385	C₄⋊Dic₄₇	—	2	2	no	—
386	C₄⋊Dic₄₇	—	2	2	no	—
387	C₄⋊Dic₄₇	—	2	2	no	—
388	C₄⋊Dic₄₇	—	2	2	no	—
389	C₄⋊Dic₄₇	C₂⁴	1	2	yes	—
390	C₄⋊Dic₄₇	C₂⁴	1	2	yes	—
391	C₄⋊Dic₄₇	C₂⁴	1	2	yes	—
392	C₄⋊Dic₄₇	C₂⁴	1	2	yes	—
393	Dic₄₇⋊C₄	—	2	2	no	—
394	Dic₄₇⋊C₄	—	2	2	no	—
395	Dic₄₇⋊C₄	—	2	2	no	—
396	Dic₄₇⋊C₄	—	2	2	no	—
397	Dic₄₇⋊C₄	—	2	2	no	—
398	Dic₄₇⋊C₄	—	2	2	no	—
399	Dic₄₇⋊C₄	—	2	2	no	—
400	Dic₄₇⋊C₄	—	2	2	no	—
401	Dic₄₇⋊C₄	C₂×D₄	1	1	yes	characteristic
402	Dic₄₇⋊C₄	C₂×D₄	1	1	yes	characteristic
403	Dic₄₇⋊C₄	C₂×D₄	1	1	yes	characteristic
404	Dic₄₇⋊C₄	C₂×D₄	1	1	yes	characteristic
405	C₄×Dic₄₇	—	2	2	no	—
406	C₄×Dic₄₇	—	2	2	no	—
407	C₄×Dic₄₇	—	2	2	no	—
408	C₄×Dic₄₇	—	2	2	no	—
409	C₄×Dic₄₇	—	2	2	no	—
410	C₄×Dic₄₇	—	2	2	no	—
411	C₄×Dic₄₇	—	2	2	no	—
412	C₄×Dic₄₇	—	2	2	no	—
413	C₄×Dic₄₇	C₂×D₄	1	1	yes	characteristic
414	C₄×Dic₄₇	C₂×D₄	1	1	yes	characteristic
415	C₄×Dic₄₇	C₂⁴	1	1	yes	characteristic
416	C₄×Dic₄₇	C₂⁴	1	1	yes	characteristic
417	C₂×C₄₇⋊C₈	—	2	2	no	—
418	C₂×C₄₇⋊C₈	—	2	2	no	—
419	C₂×C₄₇⋊C₈	C₂⁴	1	1	yes	characteristic
420	C₂×C₄₇⋊C₈	C₂⁴	1	1	yes	characteristic
421	C₂×C₄₇⋊C₈	C₂⁴	1	1	yes	characteristic
422	C₂×C₄₇⋊C₈	C₂⁴	1	1	yes	characteristic
423	C₈×D₄₇	—	2	2	no	—
424	C₈×D₄₇	—	2	2	no	—
425	C₈×D₄₇	—	2	2	no	—
426	C₈×D₄₇	—	2	2	no	—
427	C₂³×C₄₇	—	2	2	no	—
428	C₂³×C₄₇	—	2	2	no	—
429	C₂³×C₄₇	—	2	2	no	—
430	C₂³×C₄₇	—	4	1	no	—
431	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
432	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
433	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
434	C₂²×D₄₇	—	2	2	no	—
435	C₂²×D₄₇	—	2	2	no	—
436	C₂²×D₄₇	—	4	1	no	—
437	C₂²×D₄₇	C₂²×D₄	1	1	yes	characteristic
438	C₂²×D₄₇	C₂²×D₄	1	1	yes	characteristic
439	Q₈×C₄₇	—	2	2	no	—
440	Q₈×C₄₇	—	2	2	no	—
441	D₄×C₄₇	—	2	2	no	—
442	D₄×C₄₇	—	2	2	no	—
443	D₄×C₄₇	—	4	4	no	—
444	D₄×C₄₇	—	4	4	no	—
445	D₄×C₄₇	—	8	2	no	—
446	C₂×C₄×C₄₇	—	2	2	no	—
447	C₂×C₄×C₄₇	—	2	2	no	—
448	C₂×C₄×C₄₇	—	2	2	no	—
449	C₂×C₄×C₄₇	—	2	1	no	—
450	C₂×C₄×C₄₇	—	2	1	no	—
451	C₂×C₄×C₄₇	—	2	1	no	—
452	C₂×C₄×C₄₇	—	2	1	no	—
453	C₂×C₄×C₄₇	—	2	2	no	—
454	C₂×C₄×C₄₇	—	2	2	no	—
455	C₂×C₄×C₄₇	—	2	2	no	—
456	C₂×C₄×C₄₇	—	4	4	no	—
457	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
458	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
459	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
460	C₂×C₄×C₄₇	C₂×#41	1	2	yes	—
461	C₂×C₄×C₄₇	2₋¹⁺⁴	1	2	yes	—
462	C₂×C₄×C₄₇	C₂⁵	1	1	yes	characteristic
463	C₂²⋊D₄₇	—	2	2	no	—
464	C₂²⋊D₄₇	—	2	2	no	—
465	C₂²⋊D₄₇	—	2	2	no	—
466	C₂²⋊D₄₇	—	4	4	no	—
467	C₂²⋊D₄₇	—	8	2	no	—
468	C₂²⋊D₄₇	#135	1	4	yes	complemented
469	C₂×Dic₄₇	—	2	2	no	—
470	C₂×Dic₄₇	—	2	2	no	—
471	C₂×Dic₄₇	—	2	2	no	—
472	C₂×Dic₄₇	—	2	2	no	—
473	C₂×Dic₄₇	—	2	2	no	—
474	C₂×Dic₄₇	—	2	2	no	—
475	C₂×Dic₄₇	—	4	1	no	—
476	C₂×Dic₄₇	—	4	4	no	—
477	C₂×Dic₄₇	—	4	4	no	—
478	C₂×Dic₄₇	—	8	2	no	—
479	C₂×Dic₄₇	—	8	2	no	—
480	C₂×Dic₄₇	C₂²×D₄	1	1	yes	characteristic
481	C₂×Dic₄₇	C₂²×D₄	1	1	yes	characteristic
482	C₂×Dic₄₇	C₂²×D₄	1	1	yes	characteristic
483	C₂×Dic₄₇	C₂²×D₄	1	1	yes	characteristic
484	C₂×Dic₄₇	C₂²×D₄	1	1	yes	characteristic
485	C₂×Dic₄₇	C₂²×D₄	1	1	yes	characteristic
486	C₄×D₄₇	—	2	2	no	—
487	C₄×D₄₇	—	2	2	no	—
488	C₄×D₄₇	—	2	1	no	—
489	C₄×D₄₇	—	2	1	no	—
490	C₄×D₄₇	—	2	1	no	—
491	C₄×D₄₇	—	2	1	no	—
492	C₄×D₄₇	—	4	4	no	—
493	C₄×D₄₇	—	8	2	no	—
494	Dic₉₄	—	4	4	no	—
495	Dic₉₄	—	8	2	no	—
496	C₈×C₄₇	—	2	1	no	—
497	C₈×C₄₇	—	2	1	no	—
498	C₈×C₄₇	C₂×#41	1	2	yes	—
499	C₈×C₄₇	C₂×#41	1	2	yes	—
500	C₄₇⋊C₈	—	2	1	no	—
501	C₄₇⋊C₈	—	2	1	no	—
502	C₄₇⋊C₈	—	2	1	no	—
503	C₄₇⋊C₈	—	2	1	no	—
504	#61234	—	47	1	no	maximal, Sylow
505	C₂²×C₄₇	—	2	1	no	—
506	C₂²×C₄₇	—	2	1	no	—
507	C₂²×C₄₇	—	2	1	no	—
508	C₂²×C₄₇	—	2	1	no	—
509	C₂²×C₄₇	—	2	1	no	—
510	C₂²×C₄₇	—	2	1	no	—
511	C₂²×C₄₇	—	2	1	no	—
512	C₂²×C₄₇	—	4	4	no	—
513	C₂²×C₄₇	—	4	2	no	—
514	C₂²×C₄₇	—	4	2	no	—
515	C₂²×C₄₇	—	4	2	no	—
516	C₂²×C₄₇	#547	1	2	yes	—
517	C₂²×C₄₇	C₂×#135	1	2	yes	—
518	C₂²×C₄₇	C₂³×D₄	1	1	yes	characteristic
519	C₂×D₄₇	—	2	1	no	—
520	C₂×D₄₇	—	2	1	no	—
521	C₂×D₄₇	—	2	1	no	—
522	C₂×D₄₇	—	2	1	no	—
523	C₂×D₄₇	—	2	1	no	—
524	C₂×D₄₇	—	4	4	no	—
525	C₂×D₄₇	C₂×#135	1	2	yes	—
526	C₄×C₄₇	—	2	1	no	—
527	C₄×C₄₇	—	2	1	no	—
528	C₄×C₄₇	—	4	2	no	—
529	C₄×C₄₇	—	4	2	no	—
530	C₄×C₄₇	—	4	2	no	—
531	C₄×C₄₇	#547	1	2	yes	—
532	C₄×C₄₇	C₂²×#41	1	1	yes	characteristic
533	C₄×C₄₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
534	Dic₄₇	—	2	1	no	—
535	Dic₄₇	—	2	1	no	—
536	Dic₄₇	—	2	1	no	—
537	Dic₄₇	—	2	1	no	—
538	Dic₄₇	—	2	1	no	—
539	Dic₄₇	—	4	2	no	—
540	Dic₄₇	—	4	2	no	—
541	Dic₄₇	—	4	2	no	—
542	Dic₄₇	—	4	2	no	—
543	Dic₄₇	C₂×#135	1	2	yes	—
544	#3475	—	47	2	no	—
545	#3342	—	47	1	no	—
546	#3341	—	47	1	no	—
547	#3340	—	47	2	no	—
548	#3339	—	47	1	no	—
549	#3339	—	47	1	no	—
550	#3338	—	47	1	no	—
551	#3337	—	47	2	no	—
552	#3337	—	47	2	no	—
553	#3336	—	47	1	no	—
554	#3336	—	47	1	no	—
555	#3335	—	47	2	no	—
556	#3334	—	47	1	no	—
557	#3160	—	47	1	no	—
558	#3091	—	47	2	no	—
559	#3091	—	47	2	no	—
560	#3076	—	47	2	no	—
561	#3050	—	47	1	no	—
562	#3050	D₄₇	1	1	yes	characteristic, complemented
563	C₄×#135	—	47	1	no	—
564	C₂×C₈×D₄	—	47	1	no	—
565	C₂×#427	—	47	1	no	—
566	C₂×#427	—	47	1	no	—
567	C₂×C₄₇	—	2	2	no	—
568	C₂×C₄₇	—	2	2	no	—
569	C₂×C₄₇	—	4	1	no	—
570	C₂×C₄₇	—	8	2	no	—
571	C₂×C₄₇	C₂×#547	1	1	yes	characteristic
572	C₂×C₄₇	C₂²×#135	1	1	yes	characteristic
573	C₂×C₄₇	#3584	1	1	yes	characteristic
574	D₄₇	—	2	2	no	—
575	D₄₇	—	4	1	no	—
576	C₂×#135	C₂×D₄₇	1	1	yes	characteristic
577	C₂³×C₈	—	47	1	no	—
578	C₂³×C₈	C₂×D₄₇	1	1	yes	characteristic
579	#556	—	47	2	no	—
580	#555	—	47	2	no	—
581	#554	—	47	2	no	—
582	#553	—	47	2	no	—
583	#553	—	47	2	no	—
584	#552	—	47	2	no	—
585	#552	—	47	2	no	—
586	#552	—	94	2	no	—
587	#551	—	94	2	no	—
588	#551	—	94	2	no	—
589	#547	—	47	2	no	—
590	#546	—	94	2	no	—
591	#533	—	47	2	no	—
592	#529	—	94	2	no	—
593	#529	—	94	2	no	—
594	#529	—	94	2	no	—
595	#525	—	47	2	no	—
596	#525	C₂×D₄₇	1	2	yes	—
597	C₄×#41	—	47	2	no	—
598	C₄×#41	—	94	2	no	—
599	C₂×C₄×D₄	—	47	1	no	—
600	C₂×#117	—	47	2	no	—
601	C₂×#117	—	47	2	no	—
602	#500	—	47	1	no	—
603	#500	—	47	1	no	—
604	#499	—	47	1	no	—
605	#499	—	47	1	no	—
606	#499	—	47	2	no	—
607	#498	—	47	2	no	—
608	#485	—	47	2	no	—
609	#485	—	47	2	no	—
610	#485	—	47	2	no	—
611	#485	—	47	2	no	—
612	#484	—	47	2	no	—
613	#484	—	47	2	no	—
614	#483	—	47	2	no	—
615	#483	—	47	2	no	—
616	#482	—	47	2	no	—
617	#482	—	47	2	no	—
618	#482	—	47	2	no	—
619	#482	—	47	2	no	—
620	#481	—	47	2	no	—
621	#481	—	47	2	no	—
622	#480	—	47	2	no	—
623	#480	—	47	2	no	—
624	#479	—	47	2	no	—
625	#479	—	47	2	no	—
626	#478	—	47	2	no	—
627	#478	—	47	2	no	—
628	#477	—	47	2	no	—
629	#476	—	47	2	no	—
630	#475	—	47	2	no	—
631	#474	—	47	2	no	—
632	#467	—	47	1	no	—
633	#467	—	47	1	no	—
634	#467	C₂×D₄₇	1	1	yes	characteristic, complemented
635	#467	C₂×D₄₇	1	1	yes	characteristic, complemented
636	#466	—	47	1	no	—
637	#466	—	47	1	no	—
638	#466	C₂×D₄₇	1	1	yes	characteristic, complemented
639	#466	C₂×D₄₇	1	1	yes	characteristic, complemented
640	#465	—	47	2	no	—
641	#465	—	47	2	no	—
642	#465	C₂×D₄₇	1	2	yes	complemented
643	#465	C₂×D₄₇	1	2	yes	complemented
644	C₄×Q₁₆	—	47	1	no	—
645	C₄×Q₁₆	—	47	1	no	—
646	C₄×SD₁₆	—	47	2	no	—
647	C₄×SD₁₆	—	47	2	no	—
648	C₄×D₈	—	47	1	no	—
649	C₄×D₈	—	47	1	no	—
650	C₈×D₄	—	47	1	no	—
651	C₈×D₄	—	47	1	no	—
652	C₈×D₄	—	47	1	no	—
653	C₈×D₄	—	47	1	no	—
654	C₈×D₄	—	47	1	no	—
655	C₈×D₄	—	47	1	no	—
656	C₈×D₄	—	47	1	no	—
657	C₈×D₄	—	47	1	no	—
658	#427	—	47	2	no	—
659	#427	—	47	1	no	—
660	#427	—	47	2	no	—
661	#427	—	47	1	no	—
662	#427	—	47	1	no	—
663	#427	—	47	1	no	—
664	#427	—	47	2	no	—
665	#427	—	47	2	no	—
666	#427	—	47	1	no	—
667	#427	—	47	1	no	—
668	#427	—	47	2	no	—
669	#427	C₂×D₄₇	1	1	yes	characteristic
670	C₂×#107	—	47	1	no	—
671	C₂×#107	—	47	1	no	—
672	C₂×#107	—	47	1	no	—
673	C₂×#107	—	47	1	no	—
674	C₂×#106	—	47	2	no	—
675	C₂×#106	—	47	2	no	—
676	C₂×C₄⋊C₈	—	47	1	no	—
677	#416	—	47	2	no	—
678	#416	—	47	2	no	—
679	#416	C₂×D₄₇	1	2	yes	—
680	C₂×C₂²⋊C₈	—	47	1	no	—
681	C₂×C₂²⋊C₈	—	47	1	no	—
682	C₂×C₄×C₈	—	47	1	no	—
683	C₄₇	#61234	1	1	yes	characteristic, complemented, Sylow
684	C₂×#41	—	94	2	no	—
685	C₂×#41	C₂²×D₄₇	1	2	yes	—
686	C₂²×D₄	—	47	1	no	—
687	C₂³×C₄	—	47	1	no	—
688	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
689	#135	—	2	4	no	—
690	C₂×Q₁₆	C₂²×D₄₇	1	1	yes	characteristic
691	C₂×SD₁₆	C₂²×D₄₇	1	2	yes	—
692	C₂×D₈	C₂²×D₄₇	1	1	yes	characteristic
693	C₂²×C₈	—	2	4	no	—
694	C₂²×C₈	—	47	1	no	—
695	C₂²×C₈	—	47	1	no	—
696	C₂²×C₈	—	47	1	no	—
697	C₂²×C₈	—	47	1	no	—
698	C₂²×C₈	—	47	1	no	—
699	C₂²×C₈	—	47	1	no	—
700	C₂²×C₈	—	94	4	no	—
701	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
702	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
703	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
704	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
705	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
706	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
707	C₄⋊Q₈	—	47	2	no	—
708	C₄⋊Q₈	—	47	2	no	—
709	#126	—	94	2	no	—
710	#126	—	94	2	no	—
711	#126	—	94	2	no	—
712	#126	—	94	2	no	—
713	#126	—	94	2	no	—
714	#126	—	94	2	no	—
715	#125	—	47	2	no	—
716	#125	—	47	2	no	—
717	#125	—	94	2	no	—
718	#125	—	94	2	no	—
719	#125	—	94	2	no	—
720	#124	—	94	2	no	—
721	#124	—	94	2	no	—
722	#124	—	94	2	no	—
723	#123	—	2	2	no	—
724	#123	—	94	2	no	—
725	#123	—	94	2	no	—
726	#123	—	94	2	no	—
727	#123	—	94	2	no	—
728	#123	—	94	2	no	—
729	#123	—	94	2	no	—
730	#123	—	94	2	no	—
731	C₂²⋊Q₈	—	47	2	no	—
732	C₂²⋊Q₈	—	47	2	no	—
733	C₂²⋊Q₈	—	94	2	no	—
734	C₂²⋊Q₈	—	94	2	no	—
735	C₂²⋊Q₈	—	94	2	no	—
736	C₂²⋊Q₈	—	94	2	no	—
737	C₂²⋊Q₈	—	94	2	no	—
738	C₂²⋊Q₈	C₂²×D₄₇	1	2	yes	—
739	C₂²⋊Q₈	C₂²×D₄₇	1	2	yes	—
740	#121	—	47	2	no	—
741	#121	—	47	2	no	—
742	#121	—	94	2	no	—
743	#121	—	94	2	no	—
744	#121	—	94	2	no	—
745	#121	C₂²×D₄₇	1	2	yes	—
746	#121	C₂²×D₄₇	1	2	yes	—
747	#120	—	2	2	no	—
748	#120	—	94	2	no	—
749	C₄×Q₈	—	47	2	no	—
750	C₄×Q₈	—	47	2	no	—
751	C₄×Q₈	—	94	2	no	—
752	C₄×Q₈	—	94	2	no	—
753	C₄×Q₈	—	94	2	no	—
754	C₄×D₄	—	2	2	no	—
755	C₄×D₄	—	2	2	no	—
756	C₄×D₄	—	47	1	no	—
757	C₄×D₄	—	47	1	no	—
758	C₄×D₄	—	47	1	no	—
759	C₄×D₄	—	47	1	no	—
760	C₄×D₄	—	47	1	no	—
761	C₄×D₄	—	47	1	no	—
762	C₄×D₄	—	47	1	no	—
763	C₄×D₄	—	47	1	no	—
764	C₄×D₄	—	47	2	no	—
765	C₄×D₄	—	47	2	no	—
766	C₄×D₄	—	94	2	no	—
767	C₄×D₄	—	94	2	no	—
768	C₄×D₄	—	94	2	no	—
769	C₄×D₄	—	94	2	no	—
770	C₄×D₄	—	94	2	no	—
771	C₄×D₄	—	94	2	no	—
772	C₄×D₄	—	94	2	no	—
773	#117	—	47	2	no	—
774	#117	—	47	2	no	—
775	#117	—	47	2	no	—
776	#117	—	47	2	no	—
777	#117	—	47	2	no	—
778	#117	—	47	2	no	—
779	#117	—	94	2	no	—
780	#117	—	94	2	no	—
781	#117	—	94	2	no	—
782	#117	—	94	2	no	—
783	#117	—	94	2	no	—
784	#117	—	94	2	no	—
785	#117	—	94	2	no	—
786	#117	—	94	2	no	—
787	#117	C₂²×D₄₇	1	2	yes	—
788	C₂×C₄⋊C₄	—	47	1	no	—
789	C₂×C₄⋊C₄	—	47	2	no	—
790	C₂×C₄⋊C₄	—	47	2	no	—
791	C₂×C₄⋊C₄	—	47	2	no	—
792	C₂×C₄⋊C₄	—	47	2	no	—
793	C₂×C₂²⋊C₄	—	47	1	no	—
794	C₂×C₂²⋊C₄	—	47	1	no	—
795	C₂×C₂²⋊C₄	—	94	2	no	—
796	C₂×C₂²⋊C₄	—	94	2	no	—
797	C₂×C₄²	—	47	1	no	—
798	C₂×C₄²	—	94	2	no	—
799	C₂×C₄²	—	94	2	no	—
800	C₂×C₄²	—	94	2	no	—
801	#107	—	47	1	no	—
802	#107	—	47	1	no	—
803	#107	—	47	1	no	—
804	#107	—	47	1	no	—
805	#107	—	47	2	no	—
806	#107	—	47	2	no	—
807	#107	—	47	2	no	—
808	#107	—	47	2	no	—
809	#107	—	47	2	no	—
810	#107	—	47	2	no	—
811	#107	C₂²×D₄₇	1	1	yes	characteristic
812	#107	C₂²×D₄₇	1	1	yes	characteristic
813	#106	—	47	2	no	—
814	#106	—	47	2	no	—
815	#106	—	47	2	no	—
816	#106	—	47	2	no	—
817	#106	—	47	2	no	—
818	#106	—	47	2	no	—
819	#106	—	47	2	no	—
820	#106	—	47	2	no	—
821	#106	C₂²×D₄₇	1	2	yes	—
822	C₄⋊C₈	—	47	1	no	—
823	C₄⋊C₈	—	47	1	no	—
824	C₄⋊C₈	—	47	1	no	—
825	C₄⋊C₈	—	47	1	no	—
826	#103	—	47	2	no	—
827	#103	—	47	2	no	—
828	#103	—	47	2	no	—
829	#103	—	47	2	no	—
830	#103	C₂²×D₄₇	1	2	yes	—
831	#103	C₂²×D₄₇	1	2	yes	—
832	#102	—	47	2	no	—
833	#102	—	47	2	no	—
834	#102	—	47	2	no	—
835	#102	—	47	2	no	—
836	#102	C₂²×D₄₇	1	2	yes	—
837	#102	C₂²×D₄₇	1	2	yes	—
838	C₂²⋊C₈	—	47	1	no	—
839	C₂²⋊C₈	—	47	1	no	—
840	C₂²⋊C₈	—	47	1	no	—
841	C₂²⋊C₈	—	47	1	no	—
842	C₂²⋊C₈	—	47	1	no	—
843	C₂²⋊C₈	—	47	1	no	—
844	C₂²⋊C₈	—	47	1	no	—
845	C₂²⋊C₈	—	47	1	no	—
846	C₄×C₈	—	47	1	no	—
847	C₄×C₈	—	47	1	no	—
848	C₄×C₈	—	47	1	no	—
849	C₄×C₈	—	47	1	no	—
850	C₂⁴	—	47	1	no	—
851	C₂⁴	D₄×D₄₇	1	1	yes	characteristic
852	#41	—	2	4	no	—
853	#41	—	2	4	no	—
854	#41	—	188	8	no	—
855	C₂×Q₈	—	94	2	no	—
856	C₂×Q₈	—	94	2	no	—
857	C₂×Q₈	C₂³×D₄₇	1	2	yes	—
858	C₂×D₄	—	2	2	no	—
859	C₂×D₄	—	2	2	no	—
860	C₂×D₄	—	2	2	no	—
861	C₂×D₄	—	47	1	no	—
862	C₂×D₄	—	47	1	no	—
863	C₂×D₄	—	47	1	no	—
864	C₂×D₄	—	47	1	no	—
865	C₂×D₄	—	94	4	no	—
866	C₂×D₄	—	94	2	no	—
867	C₂×D₄	—	94	2	no	—
868	C₂×D₄	C₂³×D₄₇	1	2	yes	—
869	C₂²×C₄	—	2	2	no	—
870	C₂²×C₄	—	2	2	no	—
871	C₂²×C₄	—	2	2	no	—
872	C₂²×C₄	—	47	1	no	—
873	C₂²×C₄	—	47	1	no	—
874	C₂²×C₄	—	47	1	no	—
875	C₂²×C₄	—	47	1	no	—
876	C₂²×C₄	—	47	1	no	—
877	C₂²×C₄	—	47	1	no	—
878	C₂²×C₄	—	47	1	no	—
879	C₂²×C₄	—	94	2	no	—
880	C₂²×C₄	—	94	2	no	—
881	C₂²×C₄	—	94	2	no	—
882	C₂²×C₄	—	94	2	no	—
883	C₂²×C₄	—	94	2	no	—
884	C₂²×C₄	—	94	2	no	—
885	C₂²×C₄	—	94	2	no	—
886	C₂²×C₄	—	94	2	no	—
887	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
888	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
889	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
890	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
891	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
892	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
893	Q₁₆	—	2	2	no	—
894	SD₁₆	—	2	4	no	—
895	D₈	—	2	2	no	—
896	C₂×C₈	—	2	2	no	—
897	C₂×C₈	—	2	2	no	—
898	C₂×C₈	—	2	2	no	—
899	C₂×C₈	—	2	2	no	—
900	C₂×C₈	—	2	2	no	—
901	C₂×C₈	—	47	1	no	—
902	C₂×C₈	—	47	1	no	—
903	C₂×C₈	—	47	1	no	—
904	C₂×C₈	—	47	1	no	—
905	C₂×C₈	—	94	2	no	—
906	C₂×C₈	—	94	2	no	—
907	C₂×C₈	—	94	2	no	—
908	C₂×C₈	—	94	2	no	—
909	C₂×C₈	—	94	2	no	—
910	C₂×C₈	—	94	2	no	—
911	C₂×C₈	#10625352	1	4	yes	complemented
912	C₂×C₈	C₂³×D₄₇	1	1	yes	characteristic
913	C₂×C₈	C₂³×D₄₇	1	1	yes	characteristic
914	C₂×C₈	C₂³×D₄₇	1	1	yes	characteristic
915	C₂×C₈	C₂³×D₄₇	1	1	yes	characteristic
916	C₄⋊C₄	—	2	2	no	—
917	C₄⋊C₄	—	2	2	no	—
918	C₄⋊C₄	—	47	1	no	—
919	C₄⋊C₄	—	47	1	no	—
920	C₄⋊C₄	—	47	1	no	—
921	C₄⋊C₄	—	47	1	no	—
922	C₄⋊C₄	—	47	2	no	—
923	C₄⋊C₄	—	47	2	no	—
924	C₄⋊C₄	—	47	2	no	—
925	C₄⋊C₄	—	47	2	no	—
926	C₄⋊C₄	—	94	2	no	—
927	C₄⋊C₄	—	94	2	no	—
928	C₄⋊C₄	—	94	2	no	—
929	C₄⋊C₄	—	94	2	no	—
930	C₄⋊C₄	—	94	2	no	—
931	C₄⋊C₄	—	94	2	no	—
932	C₄⋊C₄	—	94	2	no	—
933	C₄⋊C₄	—	94	2	no	—
934	C₄⋊C₄	—	94	2	no	—
935	C₄⋊C₄	—	94	2	no	—
936	C₄⋊C₄	—	94	2	no	—
937	C₄⋊C₄	—	94	2	no	—
938	C₄⋊C₄	—	94	2	no	—
939	C₄⋊C₄	—	94	2	no	—
940	C₄⋊C₄	C₂³×D₄₇	1	2	yes	—
941	C₄⋊C₄	C₂³×D₄₇	1	2	yes	—
942	C₂²⋊C₄	—	2	2	no	—
943	C₂²⋊C₄	—	2	2	no	—
944	C₂²⋊C₄	—	2	2	no	—
945	C₂²⋊C₄	—	2	2	no	—
946	C₂²⋊C₄	—	2	2	no	—
947	C₂²⋊C₄	—	47	1	no	—
948	C₂²⋊C₄	—	47	1	no	—
949	C₂²⋊C₄	—	47	1	no	—
950	C₂²⋊C₄	—	47	1	no	—
951	C₂²⋊C₄	—	47	1	no	—
952	C₂²⋊C₄	—	47	1	no	—
953	C₂²⋊C₄	—	47	1	no	—
954	C₂²⋊C₄	—	47	1	no	—
955	C₂²⋊C₄	—	94	2	no	—
956	C₂²⋊C₄	—	94	2	no	—
957	C₂²⋊C₄	—	94	2	no	—
958	C₂²⋊C₄	—	94	2	no	—
959	C₂²⋊C₄	—	94	2	no	—
960	C₂²⋊C₄	—	94	2	no	—
961	C₂²⋊C₄	—	94	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	C₄²	—	2	2	no	—
968	C₄²	—	47	1	no	—
969	C₄²	—	47	1	no	—
970	C₄²	—	47	1	no	—
971	C₄²	—	47	1	no	—
972	C₄²	—	94	2	no	—
973	C₄²	—	94	2	no	—
974	C₄²	—	94	2	no	—
975	C₄²	—	94	2	no	—
976	C₄²	—	94	2	no	—
977	C₄²	—	94	2	no	—
978	C₄²	—	94	2	no	—
979	C₄²	—	94	2	no	—
980	C₂³	—	2	2	no	—
981	C₂³	—	2	2	no	—
982	C₂³	—	2	2	no	—
983	C₂³	—	4	1	no	—
984	C₂³	—	47	1	no	—
985	C₂³	—	47	1	no	—
986	C₂³	—	94	2	no	—
987	C₂³	—	94	2	no	—
988	C₂³	—	188	1	no	—
989	C₂³	C₂×D₄×D₄₇	1	1	yes	characteristic
990	C₂³	C₂×D₄×D₄₇	1	1	yes	characteristic
991	C₂³	C₂×D₄×D₄₇	1	1	yes	characteristic
992	Q₈	—	2	2	no	—
993	Q₈	—	2	2	no	—
994	Q₈	—	376	2	no	—
995	Q₈	—	188	4	no	—
996	D₄	—	2	2	no	—
997	D₄	—	2	2	no	—
998	D₄	—	4	4	no	—
999	D₄	—	4	4	no	—
1000	D₄	—	8	2	no	—
1001	D₄	—	47	4	no	—
1002	D₄	—	94	2	no	—
1003	D₄	—	94	2	no	—
1004	D₄	—	94	2	no	—
1005	D₄	—	376	2	no	—
1006	D₄	—	188	4	no	—
1007	C₂×C₄	—	2	2	no	—
1008	C₂×C₄	—	2	2	no	—
1009	C₂×C₄	—	2	2	no	—
1010	C₂×C₄	—	2	1	no	—
1011	C₂×C₄	—	2	1	no	—
1012	C₂×C₄	—	2	1	no	—
1013	C₂×C₄	—	2	1	no	—
1014	C₂×C₄	—	2	2	no	—
1015	C₂×C₄	—	2	2	no	—
1016	C₂×C₄	—	2	2	no	—
1017	C₂×C₄	—	4	4	no	—
1018	C₂×C₄	—	47	1	no	—
1019	C₂×C₄	—	47	1	no	—
1020	C₂×C₄	—	47	1	no	—
1021	C₂×C₄	—	47	1	no	—
1022	C₂×C₄	—	47	1	no	—
1023	C₂×C₄	—	47	1	no	—
1024	C₂×C₄	—	94	2	no	—
1025	C₂×C₄	—	94	2	no	—
1026	C₂×C₄	—	94	2	no	—
1027	C₂×C₄	—	94	2	no	—
1028	C₂×C₄	—	94	1	no	—
1029	C₂×C₄	—	94	1	no	—
1030	C₂×C₄	—	94	1	no	—
1031	C₂×C₄	—	94	1	no	—
1032	C₂×C₄	—	94	2	no	—
1033	C₂×C₄	—	94	2	no	—
1034	C₂×C₄	—	94	2	no	—
1035	C₂×C₄	—	94	2	no	—
1036	C₂×C₄	—	376	2	no	—
1037	C₂×C₄	—	376	2	no	—
1038	C₂×C₄	—	376	2	no	—
1039	C₂×C₄	—	188	4	no	—
1040	C₂×C₄	—	188	4	no	—
1041	C₂×C₄	—	188	1	no	—
1042	C₂×C₄	—	188	4	no	—
1043	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
1044	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
1045	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
1046	C₂×C₄	C₂×#10625352	1	2	yes	—
1047	C₂×C₄	#13094071	1	2	yes	—
1048	C₂×C₄	C₂⁴×D₄₇	1	1	yes	characteristic
1049	C₈	—	2	1	no	—
1050	C₈	—	2	1	no	—
1051	C₈	—	94	1	no	—
1052	C₈	—	94	1	no	—
1053	C₈	—	94	1	no	—
1054	C₈	—	94	1	no	—
1055	C₈	C₂×#10625352	1	2	yes	—
1056	C₈	C₂×#10625352	1	2	yes	—
1057	C₂²	—	2	1	no	—
1058	C₂²	—	2	1	no	—
1059	C₂²	—	2	1	no	—
1060	C₂²	—	2	1	no	—
1061	C₂²	—	2	1	no	—
1062	C₂²	—	2	1	no	—
1063	C₂²	—	2	1	no	—
1064	C₂²	—	4	4	no	—
1065	C₂²	—	4	2	no	—
1066	C₂²	—	4	2	no	—
1067	C₂²	—	4	2	no	—
1068	C₂²	—	47	2	no	—
1069	C₂²	—	94	1	no	—
1070	C₂²	—	94	1	no	—
1071	C₂²	—	94	1	no	—
1072	C₂²	—	94	1	no	—
1073	C₂²	—	94	1	no	—
1074	C₂²	—	188	4	no	—
1075	C₂²	#15689773	1	2	yes	—
1076	C₂²	#135×D₄₇	1	2	yes	—
1077	C₂²	C₂²×D₄×D₄₇	1	1	yes	characteristic
1078	C₄	—	2	1	no	—
1079	C₄	—	2	1	no	—
1080	C₄	—	4	2	no	—
1081	C₄	—	4	2	no	—
1082	C₄	—	4	2	no	—
1083	C₄	—	47	2	no	—
1084	C₄	—	94	1	no	—
1085	C₄	—	94	1	no	—
1086	C₄	—	94	1	no	—
1087	C₄	—	94	1	no	—
1088	C₄	—	94	1	no	—
1089	C₄	—	188	2	no	—
1090	C₄	—	188	2	no	—
1091	C₄	—	188	2	no	—
1092	C₄	—	188	2	no	—
1093	C₄	#15689773	1	2	yes	—
1094	C₄	C₂²×#10625352	1	1	yes	characteristic
1095	C₄	C₂×#13094071	1	1	yes	characteristic
1096	C₂	—	2	2	no	—
1097	C₂	—	2	2	no	—
1098	C₂	—	4	1	no	—
1099	C₂	—	8	2	no	—
1100	C₂	—	94	2	no	—
1101	C₂	—	188	1	no	—
1102	C₂	C₂×#15689773	1	1	yes	characteristic
1103	C₂	C₂×#135×D₄₇	1	1	yes	characteristic
1104	C₂	#20258157	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₄₇
commutator, cosocle	C₂×C₄×C₄₇	C₂⁵
Frattini	C₂×C₄	C₂⁴×D₄₇
Fitting	C₄₇×#3050	C₂
socle	C₂²×C₄₇	C₂³×D₄
hypercenter	#3050	D₄₇
hypocenter	C₄₇	#61234
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂³×C₄ ◁ #3050

Complements

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

N	H ≅ G/N	type
1. #20256948	C₂	semidirect
2. #20255815	C₂	semidirect
3. #20255807	C₂	semidirect
4. #20255796	C₂	semidirect
5. #20255793	C₂	semidirect
6. #20255785	C₂	semidirect
7. #20255777	C₂	semidirect
8. #20255773	C₂	semidirect
9. #20255762	C₂	semidirect
10. #20255759	C₂	semidirect
11. #20255751	C₂	semidirect
12. #20255740	C₂	semidirect
13. #20255732	C₂	semidirect
14. #20253900	C₂	semidirect
15. #20253299	C₂	semidirect
16. #20253297	C₂	semidirect
17. #20253172	C₂	semidirect
18. #20252965	C₂	semidirect
19. #135×Dic₄₇	C₂	semidirect
20. C₂×C₈×C₂²⋊D₄₇	C₂	semidirect
21. C₂×#15689161	C₂	semidirect
22. #427×D₄₇	C₂	semidirect
23. C₄₇×#3050	C₂	semidirect
47. #15689527	C₂²	semidirect
48. #15689527	C₂²	semidirect
49. #15689524	C₂²	semidirect
50. #15689524	C₂²	semidirect
51. #15689523	C₂²	semidirect
52. #15689520	C₂²	semidirect
53. #15689463	C₂²	semidirect
54. #15689462	C₂²	semidirect
55. #15689461	C₂²	semidirect
56. #15689461	C₂²	semidirect
57. #15689457	C₂²	semidirect
58. #15689456	C₂²	semidirect
59. #15689452	C₂²	semidirect
60. #15689451	C₂²	semidirect
61. #15689446	C₂²	semidirect
62. #15689445	C₂²	semidirect
63. #15689444	C₂²	semidirect
64. #15689444	C₂²	semidirect
65. #15689440	C₂²	semidirect
66. #15689439	C₂²	semidirect
67. #15689435	C₂²	semidirect
68. #15689434	C₂²	semidirect
69. #15689432	C₂²	semidirect
70. #15689428	C₂²	semidirect
71. #15689425	C₂²	semidirect
72. #15689421	C₂²	semidirect
73. #15689416	C₂²	semidirect
74. #15689411	C₂²	semidirect
75. #15689406	C₂²	semidirect
76. #15689401	C₂²	semidirect
77. #15689361	C₂²	semidirect
78. #15689361	C₂²	semidirect
79. #15689356	C₂²	semidirect
80. #15689356	C₂²	semidirect
81. #15689349	C₂²	semidirect
82. #15689349	C₂²	semidirect
83. Q₁₆×Dic₄₇	C₂²	semidirect
84. Q₁₆×Dic₄₇	C₂²	semidirect
85. SD₁₆×Dic₄₇	C₂²	semidirect
86. SD₁₆×Dic₄₇	C₂²	semidirect
87. D₈×Dic₄₇	C₂²	semidirect
88. D₈×Dic₄₇	C₂²	semidirect
100. #15689161	C₂²	semidirect
101. #15689161	C₂²	semidirect
102. #15689161	C₂²	semidirect
103. #15689160	C₂²	semidirect
104. #15689160	C₂²	semidirect
107. #15689158	C₂²	semidirect
108. C₂×#13093958	C₂²	semidirect
109. C₂×#13093958	C₂²	semidirect
110. #107×D₄₇	C₂²	semidirect
111. #107×D₄₇	C₂²	semidirect
112. C₂×#13093956	C₂²	semidirect
113. #106×D₄₇	C₂²	semidirect
123. C₄₇×#467	C₂²	semidirect
124. C₄₇×#467	C₂²	semidirect
125. C₄₇×#466	C₂²	semidirect
126. C₄₇×#466	C₂²	semidirect
127. C₄₇×#465	C₂²	semidirect
128. C₄₇×#465	C₂²	semidirect
348. C₂×C₈×C₄₇	#41	semidirect
468. C₂²⋊D₄₇	#135	semidirect
562. #3050	D₄₇	semidirect
634. #467	C₂×D₄₇	semidirect
635. #467	C₂×D₄₇	semidirect
638. #466	C₂×D₄₇	semidirect
639. #466	C₂×D₄₇	semidirect
642. #465	C₂×D₄₇	semidirect
643. #465	C₂×D₄₇	semidirect
683. C₄₇	#61234	semidirect
911. C₂×C₈	#10625352	semidirect

Maximal subgroups

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

subgroup	index
#20256948	2
#20255815	2
#20255807	2
#20255796	2
#20255793	2
#20255785	2
#20255777	2
#20255773	2
#20255762	2
#20255759	2
#20255751	2
#20255740	2
#20255732	2
#20253900	2
#20253299	2
#20253297	2
#20253172	2
#20252965	2
#135×Dic₄₇	2
C₂×C₈×C₂²⋊D₄₇	2
C₂×#15689161	2
#427×D₄₇	2
C₄₇×#3050	2
#61234	47