Subgroups — #27097777

Order 12032.

2000 conjugacy classes of subgroups.

The subgroup lattice has 1124 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20256992	C₂	1	2	yes	maximal, complemented
2	#20256400	C₂	1	1	yes	maximal, characteristic, complemented
3	#20256255	C₂	1	1	yes	maximal, characteristic, complemented
4	#20256049	C₂	1	2	yes	maximal, complemented
5	#20255792	C₂	1	1	yes	maximal, characteristic, complemented
6	#20255786	C₂	1	1	yes	maximal, characteristic, complemented
7	#20255778	C₂	1	1	yes	maximal, characteristic, complemented
8	#20255243	C₂	1	2	yes	maximal, complemented
9	#20255234	C₂	1	2	yes	maximal, complemented
10	#20255208	C₂	1	2	yes	maximal, complemented
11	#20255074	C₂	1	1	yes	maximal, characteristic, complemented
12	#20255073	C₂	1	1	yes	maximal, characteristic, complemented
13	D₈×C₂²⋊D₄₇	C₂	1	1	yes	maximal, characteristic, complemented
14	#20253964	C₂	1	1	yes	maximal, characteristic, complemented
15	#20253958	C₂	1	1	yes	maximal, characteristic, complemented
16	#20253956	C₂	1	1	yes	maximal, characteristic, complemented
17	#20253444	C₂	1	2	yes	maximal, complemented
18	#20253435	C₂	1	2	yes	maximal, complemented
19	#20253433	C₂	1	2	yes	maximal, complemented
20	C₈×#10625350	C₂	1	1	yes	maximal, characteristic, complemented
21	C₄×#13094043	C₂	1	1	yes	maximal, characteristic, complemented
22	C₄×D₈×D₄₇	C₂	1	1	yes	maximal, characteristic, complemented
23	C₂×C₄×D₈×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#13094043	C₂²	1	1	yes	characteristic
25	C₂×D₈×D₄₇	C₂²	1	1	yes	characteristic
26	#15689856	C₂²	1	2	yes	complemented
27	#15689832	C₂²	1	2	yes	complemented
28	#15689828	C₂²	1	2	yes	—
29	#15689823	C₂²	1	2	yes	complemented
30	#15689822	—	2	2	no	—
31	#15689821	C₂²	1	2	yes	complemented
32	#15689802	—	2	2	no	—
33	#15689799	—	2	2	no	—
34	#15689768	C₂²	1	2	yes	complemented
35	#15689767	C₂²	1	2	yes	complemented
36	#15689763	—	2	2	no	—
37	D₄×C₂²⋊D₄₇	C₂²	1	2	yes	—
38	#15689670	C₂²	1	2	yes	complemented
39	#15689657	C₂²	1	2	yes	complemented
40	#15689655	C₂²	1	2	yes	complemented
41	#15689653	—	2	2	no	—
42	#15689634	—	2	2	no	—
43	#15689632	—	2	2	no	—
44	C₄×#10625350	C₂²	1	1	yes	characteristic
45	C₄×#10625352	C₂²	1	2	yes	complemented
46	C₂×C₄×C₂²⋊D₄₇	—	2	2	no	—
47	C₄×D₄×D₄₇	C₂²	1	2	yes	complemented
48	#15689527	C₂²	1	1	yes	characteristic, complemented
49	#15689525	C₂²	1	1	yes	characteristic, complemented
50	#15689524	C₂²	1	1	yes	characteristic, complemented
51	#15689507	C₂²	1	1	yes	characteristic, complemented
52	#15689506	C₂²	1	1	yes	characteristic, complemented
53	#15689498	C₂²	1	1	yes	characteristic
54	#15689478	C₂²	1	2	yes	complemented
55	#15689476	C₂²	1	2	yes	complemented
56	#15689468	C₂²	1	2	yes	complemented
57	#15689460	C₂²	1	2	yes	complemented
58	#15689458	C₂²	1	2	yes	complemented
59	#15689450	C₂²	1	2	yes	complemented
60	#15689446	C₂²	1	2	yes	complemented
61	#15689441	C₂²	1	2	yes	complemented
62	#15689440	C₂²	1	2	yes	complemented
63	#15689426	C₂²	1	2	yes	complemented
64	#15689425	C₂²	1	2	yes	complemented
65	#15689423	C₂²	1	2	yes	complemented
66	#15689423	C₂²	1	2	yes	complemented
67	#15689417	C₂²	1	2	yes	complemented
68	#15689411	C₂²	1	2	yes	complemented
69	#15689365	C₂²	1	1	yes	characteristic, complemented
70	#15689364	C₂²	1	1	yes	characteristic, complemented
71	#15689360	C₂²	1	1	yes	characteristic, complemented
72	#15689359	C₂²	1	1	yes	characteristic
73	#15689358	C₂²	1	2	yes	complemented
74	#15689356	C₂²	1	1	yes	characteristic
75	#15689356	C₂²	1	1	yes	characteristic, complemented
76	#15689352	C₂²	1	2	yes	complemented
77	#15689351	C₂²	1	2	yes	complemented
78	#15689338	C₂²	1	2	yes	complemented
79	#15689338	C₂²	1	2	yes	complemented
80	#15689337	C₂²	1	2	yes	complemented
81	#15689336	C₂²	1	2	yes	complemented
82	#15689322	C₂²	1	2	yes	complemented
83	#15689316	C₂²	1	2	yes	—
84	#15689275	C₂²	1	2	yes	complemented
85	#15689274	C₂²	1	2	yes	complemented
86	#15689269	C₂²	1	2	yes	complemented
87	#15689265	C₂²	1	2	yes	complemented
88	#15689257	C₂²	1	2	yes	—
89	#15689255	C₂²	1	2	yes	—
90	C₈×Dic₉₄	C₂²	1	1	yes	characteristic, complemented
91	C₈×Dic₉₄	C₂²	1	1	yes	characteristic, complemented
92	C₄×Dic₁₈₈	C₂²	1	1	yes	characteristic, complemented
93	#15689217	C₂²	1	1	yes	characteristic, complemented
94	#15689214	C₂²	1	2	yes	complemented
95	C₄×#10625325	C₂²	1	2	yes	complemented
96	C₄×#10625335	C₂²	1	2	yes	complemented
97	C₄×#10625335	C₂²	1	2	yes	complemented
98	C₄×D₃₇₆	C₂²	1	1	yes	characteristic, complemented
99	D₈×Dic₄₇	C₂²	1	1	yes	characteristic
100	D₈×Dic₄₇	C₂²	1	1	yes	characteristic
101	#15689205	C₂²	1	1	yes	characteristic, complemented
102	C₄×#10625334	C₂²	1	2	yes	complemented
103	C₄×#10625334	C₂²	1	2	yes	complemented
104	#15689203	C₂²	1	2	yes	complemented
105	C₈×D₁₈₈	C₂²	1	1	yes	characteristic, complemented
106	C₈×D₁₈₈	C₂²	1	1	yes	characteristic, complemented
107	C₈×C₂²⋊D₄₇	C₂²	1	1	yes	characteristic
108	C₈×C₂²⋊D₄₇	C₂²	1	1	yes	characteristic
109	C₈×C₂²⋊D₄₇	C₂²	1	1	yes	characteristic, complemented
110	C₈×C₂²⋊D₄₇	C₂²	1	1	yes	characteristic, complemented
111	#15689176	C₂²	1	1	yes	characteristic, complemented
112	#15689174	C₂²	1	1	yes	characteristic, complemented
113	#15689174	C₂²	1	1	yes	characteristic, complemented
114	#15689160	C₂²	1	1	yes	characteristic, complemented
115	#107×D₄₇	C₂²	1	1	yes	characteristic, complemented
116	#15689116	C₂²	1	2	yes	complemented
117	#102×D₄₇	C₂²	1	2	yes	complemented
118	C₄×C₈×D₄₇	C₂²	1	1	yes	characteristic, complemented
119	C₄×C₈×D₄₇	C₂²	1	1	yes	characteristic, complemented
120	C₂²×D₈×C₄₇	C₂²	1	1	yes	characteristic
121	C₂×C₄×D₄×C₄₇	C₂²	1	2	yes	complemented
122	C₄×D₈×C₄₇	C₂²	1	1	yes	characteristic
123	C₄×D₈×C₄₇	C₂²	1	1	yes	characteristic
124	C₄×D₈×C₄₇	C₂²	1	2	yes	complemented
125	C₄×D₈×C₄₇	C₂²	1	1	yes	characteristic, complemented
126	C₄×D₈×C₄₇	C₂²	1	2	yes	complemented
127	C₄×D₈×C₄₇	C₂²	1	1	yes	characteristic, complemented
128	C₂×#107×C₄₇	C₂²	1	1	yes	characteristic, complemented
129	C₂×#102×C₄₇	C₂²	1	2	yes	complemented
130	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic, complemented
131	C₂×#10625350	—	2	2	no	—
132	C₂×#10625350	D₄	1	1	yes	characteristic
133	C₂×#10625352	C₂³	1	2	yes	—
134	C₂²×C₂²⋊D₄₇	—	2	2	no	—
135	C₂×D₄×D₄₇	C₂³	1	2	yes	—
136	C₂²×C₄×D₄₇	—	2	2	no	—
137	#13094043	—	2	4	no	—
138	C₂×Dic₁₈₈	C₂³	1	1	yes	characteristic
139	C₂×#10625325	C₂³	1	2	yes	—
140	C₂×#10625335	C₂³	1	2	yes	—
141	C₂×#10625335	C₂³	1	2	yes	—
142	C₂×D₃₇₆	C₂³	1	1	yes	characteristic
143	C₂×#10625334	C₂³	1	2	yes	—
144	C₂×#10625334	C₂³	1	2	yes	—
145	D₈×D₄₇	—	2	4	no	—
146	C₂×C₈×D₄₇	C₂³	1	1	yes	characteristic
147	C₂×C₈×D₄₇	C₂³	1	1	yes	characteristic
148	C₂×C₈×D₄₇	C₂³	1	1	yes	characteristic
149	C₂×C₈×D₄₇	C₂³	1	1	yes	characteristic
150	#13094023	C₂³	1	2	yes	—
151	#13094020	C₂³	1	2	yes	—
152	#13094019	—	2	2	no	—
153	#13094018	—	2	2	no	—
154	#13094017	—	2	2	no	—
155	#13094017	—	2	2	no	—
156	#13094016	C₂³	1	2	yes	—
157	#13094015	C₂³	1	2	yes	—
158	#13094014	—	2	2	no	—
159	#13094012	C₂³	1	2	yes	—
160	#13094011	C₂³	1	2	yes	—
161	#13094010	—	2	2	no	—
162	#13094010	—	2	2	no	—
163	#13094009	—	2	2	no	—
164	#13094008	—	2	2	no	—
165	#13094007	—	2	2	no	—
166	#13094007	—	2	2	no	—
167	#13094007	—	2	2	no	—
168	#13094006	—	2	2	no	—
169	#13094006	—	2	2	no	—
170	#13094005	—	2	2	no	—
171	#13094004	C₂³	1	2	yes	—
172	#13094003	—	2	2	no	—
173	#13094003	—	2	2	no	—
174	#13094003	C₂³	1	2	yes	—
175	#13094002	—	2	2	no	—
176	#13094001	—	2	2	no	—
177	#13094001	—	2	2	no	—
178	#13093999	C₂³	1	2	yes	—
179	#13093998	—	2	2	no	—
180	#13093998	—	2	2	no	—
181	#13093998	C₂³	1	2	yes	—
182	#13093997	—	2	2	no	—
183	#13093997	—	2	2	no	—
184	#13093996	—	2	2	no	—
185	#13093996	—	2	2	no	—
186	#13093995	C₂³	1	2	yes	—
187	#13093995	C₂³	1	2	yes	—
188	#13093994	—	2	2	no	—
189	#13093993	—	2	2	no	—
190	#13093993	—	2	2	no	—
191	#13093992	—	2	2	no	—
192	C₄×Dic₉₄	D₄	1	1	yes	characteristic
193	C₄×Dic₉₄	C₂³	1	2	yes	—
194	C₄×Dic₉₄	C₂³	1	1	yes	characteristic
195	#13093989	C₂³	1	2	yes	—
196	C₄×D₁₈₈	D₄	1	1	yes	characteristic
197	C₄×D₁₈₈	C₂³	1	1	yes	characteristic
198	C₄×D₁₈₈	C₂³	1	2	yes	—
199	D₄×Dic₄₇	C₂³	1	2	yes	—
200	D₄×Dic₄₇	C₂³	1	2	yes	—
201	#13093986	C₂³	1	2	yes	—
202	C₄×C₂²⋊D₄₇	—	2	2	no	—
203	C₄×C₂²⋊D₄₇	—	2	2	no	—
204	C₄×C₂²⋊D₄₇	—	2	2	no	—
205	C₄×C₂²⋊D₄₇	—	2	2	no	—
206	C₄×C₂²⋊D₄₇	—	2	2	no	—
207	C₄×C₂²⋊D₄₇	—	2	2	no	—
208	C₄×C₂²⋊D₄₇	—	2	2	no	—
209	C₄×C₂²⋊D₄₇	—	2	2	no	—
210	C₄×C₂²⋊D₄₇	—	2	2	no	—
211	C₄×C₂²⋊D₄₇	D₄	1	1	yes	characteristic
212	C₄×C₂²⋊D₄₇	D₄	1	1	yes	characteristic
213	C₄×C₂²⋊D₄₇	C₂³	1	1	yes	characteristic
214	C₄×C₂²⋊D₄₇	C₂³	1	1	yes	characteristic
215	(C₂²⋊D₄₇)⋊C₄	—	2	2	no	—
216	(C₂²⋊D₄₇)⋊C₄	—	2	2	no	—
217	#13093983	—	2	2	no	—
218	#13093983	D₄	1	1	yes	characteristic
219	#13093982	C₂³	1	2	yes	—
220	#13093981	—	2	2	no	—
221	#13093981	D₄	1	1	yes	characteristic
222	#13093981	D₄	1	1	yes	characteristic
223	#13093980	—	2	2	no	—
224	C₂×Dic₄₇⋊C₄	—	2	2	no	—
225	C₄⋊C₄×D₄₇	C₂³	1	2	yes	—
226	C₂×C₂²⋊Dic₄₇	—	2	2	no	—
227	C₂×(C₂×D₄₇)⋊C₄	—	2	2	no	—
228	C₂²⋊C₄×D₄₇	—	2	2	no	—
229	C₂×C₄×Dic₄₇	—	2	2	no	—
230	C₄²×D₄₇	C₂³	1	1	yes	characteristic
231	C₄²×D₄₇	C₂³	1	1	yes	characteristic
232	#13093958	C₂³	1	1	yes	characteristic
233	#13093958	C₂³	1	1	yes	characteristic
234	#13093957	C₂³	1	2	yes	—
235	#13093957	C₂³	1	2	yes	—
236	#13093956	C₂³	1	2	yes	—
237	#13093955	C₂³	1	2	yes	—
238	#13093955	C₂³	1	2	yes	—
239	C₄⋊(C₄₇⋊C₈)	C₂³	1	1	yes	characteristic
240	C₄⋊(C₄₇⋊C₈)	C₂³	1	1	yes	characteristic
241	Dic₄₇⋊C₈	C₂³	1	1	yes	characteristic
242	Dic₄₇⋊C₈	C₂³	1	1	yes	characteristic
243	Dic₄₇⋊C₈	C₂³	1	1	yes	characteristic
244	Dic₄₇⋊C₈	C₂³	1	1	yes	characteristic
245	#13093949	C₂³	1	2	yes	—
246	#13093949	C₂³	1	2	yes	—
247	#13093947	C₂³	1	2	yes	—
248	#13093947	C₂³	1	2	yes	—
249	#13093946	C₂³	1	2	yes	—
250	#13093946	C₂³	1	2	yes	—
251	#13093945	C₂³	1	2	yes	—
252	#13093945	C₂³	1	2	yes	—
253	#13093945	C₂³	1	2	yes	—
254	#13093945	C₂³	1	2	yes	—
255	#13093944	C₂³	1	2	yes	—
256	#13093944	C₂³	1	2	yes	—
257	C₂²⋊(C₄₇⋊C₈)	C₂³	1	1	yes	characteristic
258	C₂²⋊(C₄₇⋊C₈)	C₂³	1	1	yes	characteristic
259	(C₂×D₄₇)⋊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	C₄×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
264	C₄×C₄₇⋊C₈	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	C₈×Dic₄₇	C₂³	1	1	yes	characteristic
269	C₂²×D₄×C₄₇	C₂³	1	2	yes	—
270	C₂³×C₄×C₄₇	—	2	2	no	—
271	C₂×D₈×C₄₇	—	2	4	no	—
272	C₂×D₈×C₄₇	C₂³	1	1	yes	characteristic
273	C₂×D₈×C₄₇	C₂³	1	2	yes	—
274	C₂×D₈×C₄₇	C₂³	1	1	yes	characteristic
275	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
276	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
277	C₄×D₄×C₄₇	—	2	2	no	—
278	C₄×D₄×C₄₇	—	2	2	no	—
279	C₄×D₄×C₄₇	C₂³	1	2	yes	—
280	C₄×D₄×C₄₇	C₂³	1	2	yes	—
281	C₄×D₄×C₄₇	C₂³	1	2	yes	—
282	C₄×D₄×C₄₇	C₂³	1	2	yes	—
283	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
284	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
285	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
286	#107×C₄₇	C₂³	1	1	yes	characteristic
287	#107×C₄₇	C₂³	1	1	yes	characteristic
288	#107×C₄₇	C₂³	1	2	yes	—
289	#102×C₄₇	C₂³	1	2	yes	—
290	#102×C₄₇	C₂³	1	2	yes	—
291	#102×C₄₇	C₂³	1	2	yes	—
292	#102×C₄₇	C₂³	1	2	yes	—
293	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
294	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
295	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
296	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
297	C₂⁴×C₄₇	—	2	2	no	—
298	C₂³×D₄₇	—	2	2	no	—
299	C₂×D₄×C₄₇	—	2	4	no	—
300	C₂×D₄×C₄₇	—	2	2	no	—
301	C₂×D₄×C₄₇	—	4	2	no	—
302	C₂×D₄×C₄₇	C₂⁴	1	2	yes	—
303	C₂×D₄×C₄₇	C₂⁴	1	2	yes	—
304	C₂²×C₄×C₄₇	—	2	2	no	—
305	C₂²×C₄×C₄₇	—	2	2	no	—
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	—	8	4	no	—
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	C₂×C₂²⋊D₄₇	—	2	2	no	—
314	C₂×C₂²⋊D₄₇	—	2	2	no	—
315	C₂×C₂²⋊D₄₇	—	2	2	no	—
316	C₂×C₂²⋊D₄₇	—	2	2	no	—
317	C₂×C₂²⋊D₄₇	—	2	2	no	—
318	C₂×C₂²⋊D₄₇	—	2	2	no	—
319	C₂×C₂²⋊D₄₇	—	2	2	no	—
320	C₂×C₂²⋊D₄₇	—	4	8	no	—
321	C₂×C₂²⋊D₄₇	C₂×D₄	1	1	yes	characteristic
322	C₂×C₂²⋊D₄₇	C₂×D₄	1	1	yes	characteristic
323	C₂²×Dic₄₇	—	2	2	no	—
324	C₂²×Dic₄₇	—	2	2	no	—
325	C₂²×Dic₄₇	—	2	2	no	—
326	#10625352	—	2	4	no	—
327	#10625352	—	4	2	no	—
328	D₄×D₄₇	—	2	4	no	—
329	D₄×D₄₇	—	4	2	no	—
330	#10625350	—	2	4	no	—
331	#10625350	—	8	4	no	—
332	C₂×D₁₈₈	—	2	2	no	—
333	C₂×D₁₈₈	C₂×D₄	1	1	yes	characteristic
334	C₂×D₁₈₈	C₂⁴	1	2	yes	—
335	C₂×C₄×D₄₇	—	2	2	no	—
336	C₂×C₄×D₄₇	—	2	2	no	—
337	C₂×C₄×D₄₇	—	2	2	no	—
338	C₂×C₄×D₄₇	—	8	4	no	—
339	C₂×C₄×D₄₇	C₂×D₄	1	1	yes	characteristic
340	C₂×C₄×D₄₇	C₂×D₄	1	1	yes	characteristic
341	C₂×C₄×D₄₇	C₂×D₄	1	1	yes	characteristic
342	C₂×C₄×D₄₇	C₂×D₄	1	1	yes	characteristic
343	C₂×C₄×D₄₇	C₂⁴	1	1	yes	characteristic
344	C₂×C₄×D₄₇	C₂⁴	1	1	yes	characteristic
345	C₂×Dic₉₄	—	2	2	no	—
346	C₂×Dic₉₄	C₂×D₄	1	1	yes	characteristic
347	C₂×Dic₉₄	C₂⁴	1	2	yes	—
348	D₈×C₄₇	—	2	4	no	—
349	D₈×C₄₇	—	2	2	no	—
350	D₈×C₄₇	#41	1	4	yes	complemented
351	C₂×C₈×C₄₇	—	2	2	no	—
352	C₂×C₈×C₄₇	—	4	1	no	—
353	C₂×C₈×C₄₇	C₂⁴	1	1	yes	characteristic
354	C₂×C₈×C₄₇	C₂⁴	1	1	yes	characteristic
355	C₂×C₈×C₄₇	C₂⁴	1	1	yes	characteristic
356	C₂×C₈×C₄₇	C₂⁴	1	1	yes	characteristic
357	C₄⋊C₄×C₄₇	—	2	2	no	—
358	C₄⋊C₄×C₄₇	C₂⁴	1	2	yes	—
359	C₄⋊C₄×C₄₇	C₂⁴	1	2	yes	—
360	C₂²⋊C₄×C₄₇	—	2	2	no	—
361	C₂²⋊C₄×C₄₇	—	2	2	no	—
362	C₂²⋊C₄×C₄₇	—	2	2	no	—
363	C₂²⋊C₄×C₄₇	—	2	2	no	—
364	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
365	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
366	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
367	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
368	C₂²⋊Dic₄₇	—	2	2	no	—
369	C₂²⋊Dic₄₇	—	2	2	no	—
370	C₂²⋊Dic₄₇	—	2	2	no	—
371	C₂²⋊Dic₄₇	—	2	2	no	—
372	C₂²⋊Dic₄₇	—	2	2	no	—
373	C₂²⋊Dic₄₇	—	2	2	no	—
374	C₂²⋊Dic₄₇	—	2	2	no	—
375	C₂²⋊Dic₄₇	C₂×D₄	1	1	yes	characteristic
376	C₂²⋊Dic₄₇	C₂×D₄	1	1	yes	characteristic
377	#10625335	—	2	4	no	—
378	#10625335	—	4	2	no	—
379	#10625334	—	2	4	no	—
380	#10625334	—	4	2	no	—
381	(C₂×D₄₇)⋊C₄	—	2	2	no	—
382	(C₂×D₄₇)⋊C₄	—	2	2	no	—
383	(C₂×D₄₇)⋊C₄	—	2	2	no	—
384	(C₂×D₄₇)⋊C₄	—	2	2	no	—
385	(C₂×D₄₇)⋊C₄	—	2	2	no	—
386	(C₂×D₄₇)⋊C₄	—	2	2	no	—
387	(C₂×D₄₇)⋊C₄	—	2	2	no	—
388	(C₂×D₄₇)⋊C₄	—	2	2	no	—
389	(C₂×D₄₇)⋊C₄	C₂×D₄	1	1	yes	characteristic
390	(C₂×D₄₇)⋊C₄	C₂×D₄	1	1	yes	characteristic
391	(C₂×D₄₇)⋊C₄	C₂×D₄	1	1	yes	characteristic
392	(C₂×D₄₇)⋊C₄	C₂×D₄	1	1	yes	characteristic
393	C₄⋊Dic₄₇	—	2	2	no	—
394	C₄⋊Dic₄₇	—	2	2	no	—
395	C₄⋊Dic₄₇	C₂×D₄	1	1	yes	characteristic
396	C₄⋊Dic₄₇	C₂×D₄	1	1	yes	characteristic
397	C₄⋊Dic₄₇	C₂⁴	1	2	yes	—
398	C₄⋊Dic₄₇	C₂⁴	1	2	yes	—
399	Dic₄₇⋊C₄	—	2	2	no	—
400	Dic₄₇⋊C₄	—	2	2	no	—
401	Dic₄₇⋊C₄	—	2	2	no	—
402	Dic₄₇⋊C₄	—	2	2	no	—
403	Dic₄₇⋊C₄	—	2	2	no	—
404	Dic₄₇⋊C₄	—	2	2	no	—
405	Dic₄₇⋊C₄	—	2	2	no	—
406	Dic₄₇⋊C₄	—	2	2	no	—
407	Dic₄₇⋊C₄	C₂×D₄	1	1	yes	characteristic
408	Dic₄₇⋊C₄	C₂×D₄	1	1	yes	characteristic
409	Dic₄₇⋊C₄	C₂×D₄	1	1	yes	characteristic
410	Dic₄₇⋊C₄	C₂×D₄	1	1	yes	characteristic
411	C₄×Dic₄₇	—	2	2	no	—
412	C₄×Dic₄₇	—	2	2	no	—
413	C₄×Dic₄₇	—	2	2	no	—
414	C₄×Dic₄₇	C₂×D₄	1	1	yes	characteristic
415	C₄×Dic₄₇	C₂×D₄	1	1	yes	characteristic
416	C₄×Dic₄₇	C₂×D₄	1	1	yes	characteristic
417	C₄×Dic₄₇	C₂×D₄	1	1	yes	characteristic
418	C₄×Dic₄₇	C₂⁴	1	1	yes	characteristic
419	C₄×Dic₄₇	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	C₂×C₄₇⋊C₈	C₂⁴	1	1	yes	characteristic
424	Dic₁₈₈	—	2	2	no	—
425	D₃₇₆	—	2	2	no	—
426	#10625325	—	4	2	no	—
427	C₈×D₄₇	—	2	2	no	—
428	C₈×D₄₇	—	2	2	no	—
429	C₈×D₄₇	—	4	1	no	—
430	C₈×D₄₇	—	4	1	no	—
431	C₂³×C₄₇	—	2	2	no	—
432	C₂³×C₄₇	—	2	2	no	—
433	C₂³×C₄₇	—	4	4	no	—
434	C₂³×C₄₇	—	4	4	no	—
435	C₂³×C₄₇	—	8	2	no	—
436	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
437	C₂²×D₄₇	—	2	2	no	—
438	C₂²×D₄₇	—	4	4	no	—
439	C₂²×D₄₇	—	4	4	no	—
440	C₂²×D₄₇	—	8	2	no	—
441	C₂²×D₄₇	C₂²×D₄	1	1	yes	characteristic
442	C₂²×D₄₇	C₂²×D₄	1	1	yes	characteristic
443	D₄×C₄₇	—	2	2	no	—
444	D₄×C₄₇	—	2	2	no	—
445	D₄×C₄₇	—	2	2	no	—
446	D₄×C₄₇	—	4	4	no	—
447	D₄×C₄₇	C₂×#41	1	4	yes	—
448	C₂×C₄×C₄₇	—	2	2	no	—
449	C₂×C₄×C₄₇	—	2	2	no	—
450	C₂×C₄×C₄₇	—	2	1	no	—
451	C₂×C₄×C₄₇	—	2	1	no	—
452	C₂×C₄×C₄₇	—	2	2	no	—
453	C₂×C₄×C₄₇	—	2	2	no	—
454	C₂×C₄×C₄₇	—	4	4	no	—
455	C₂×C₄×C₄₇	—	4	4	no	—
456	C₂×C₄×C₄₇	—	8	2	no	—
457	C₂×C₄×C₄₇	—	8	2	no	—
458	C₂×C₄×C₄₇	—	8	2	no	—
459	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
460	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
461	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
462	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
463	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
464	C₂×C₄×C₄₇	C₂⁵	1	1	yes	characteristic
465	C₂²⋊D₄₇	—	2	2	no	—
466	C₂²⋊D₄₇	—	4	4	no	—
467	C₂²⋊D₄₇	—	4	4	no	—
468	C₂²⋊D₄₇	—	4	4	no	—
469	C₂²⋊D₄₇	—	4	4	no	—
470	C₂²⋊D₄₇	—	4	4	no	—
471	C₂²⋊D₄₇	—	8	2	no	—
472	C₂²⋊D₄₇	—	8	2	no	—
473	C₂²⋊D₄₇	#135	1	4	yes	complemented
474	C₂×Dic₄₇	—	2	2	no	—
475	C₂×Dic₄₇	—	2	2	no	—
476	C₂×Dic₄₇	—	2	2	no	—
477	C₂×Dic₄₇	—	4	4	no	—
478	C₂×Dic₄₇	—	4	4	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	D₁₈₈	—	2	2	no	—
487	D₁₈₈	—	2	2	no	—
488	D₁₈₈	—	2	2	no	—
489	D₁₈₈	—	8	2	no	—
490	C₄×D₄₇	—	2	2	no	—
491	C₄×D₄₇	—	2	2	no	—
492	C₄×D₄₇	—	2	2	no	—
493	C₄×D₄₇	—	2	1	no	—
494	C₄×D₄₇	—	2	1	no	—
495	C₄×D₄₇	—	2	1	no	—
496	C₄×D₄₇	—	2	1	no	—
497	C₄×D₄₇	—	2	2	no	—
498	C₄×D₄₇	—	4	4	no	—
499	C₄×D₄₇	—	8	2	no	—
500	C₄×D₄₇	—	8	2	no	—
501	Dic₉₄	—	2	2	no	—
502	Dic₉₄	—	2	2	no	—
503	Dic₉₄	—	2	2	no	—
504	Dic₉₄	—	8	2	no	—
505	C₈×C₄₇	—	2	1	no	—
506	C₈×C₄₇	—	2	1	no	—
507	C₈×C₄₇	—	2	1	no	—
508	C₈×C₄₇	C₂×#41	1	2	yes	—
509	C₄₇⋊C₈	—	2	1	no	—
510	C₄₇⋊C₈	—	2	1	no	—
511	C₄₇⋊C₈	—	2	1	no	—
512	C₄₇⋊C₈	—	2	1	no	—
513	#61431	—	47	1	no	maximal, Sylow
514	C₂²×C₄₇	—	2	1	no	—
515	C₂²×C₄₇	—	2	1	no	—
516	C₂²×C₄₇	—	2	4	no	—
517	C₂²×C₄₇	—	4	2	no	—
518	C₂²×C₄₇	—	4	2	no	—
519	C₂²×C₄₇	—	4	2	no	—
520	C₂²×C₄₇	—	4	2	no	—
521	C₂²×C₄₇	—	4	2	no	—
522	C₂²×C₄₇	—	8	8	no	—
523	C₂²×C₄₇	C₂×#135	1	2	yes	—
524	C₂²×C₄₇	C₂³×D₄	1	1	yes	characteristic
525	C₂×D₄₇	—	2	1	no	—
526	C₂×D₄₇	—	2	1	no	—
527	C₂×D₄₇	—	2	1	no	—
528	C₂×D₄₇	—	2	1	no	—
529	C₂×D₄₇	—	2	1	no	—
530	C₂×D₄₇	—	4	2	no	—
531	C₂×D₄₇	—	4	2	no	—
532	C₂×D₄₇	—	4	2	no	—
533	C₂×D₄₇	—	8	8	no	—
534	C₂×D₄₇	C₂×#135	1	2	yes	—
535	C₄×C₄₇	—	2	1	no	—
536	C₄×C₄₇	—	2	1	no	—
537	C₄×C₄₇	—	2	1	no	—
538	C₄×C₄₇	—	2	1	no	—
539	C₄×C₄₇	—	4	2	no	—
540	C₄×C₄₇	—	4	2	no	—
541	C₄×C₄₇	#576	1	2	yes	—
542	C₄×C₄₇	C₂²×#41	1	1	yes	characteristic
543	C₄×C₄₇	#585	1	1	yes	characteristic
544	Dic₄₇	—	2	1	no	—
545	Dic₄₇	—	2	1	no	—
546	Dic₄₇	—	2	1	no	—
547	Dic₄₇	—	2	1	no	—
548	Dic₄₇	—	2	1	no	—
549	Dic₄₇	—	4	2	no	—
550	Dic₄₇	—	4	2	no	—
551	Dic₄₇	—	4	2	no	—
552	Dic₄₇	C₂×#135	1	2	yes	—
553	#3481	—	47	2	no	—
554	#3396	—	47	1	no	—
555	#3380	—	47	1	no	—
556	#3361	—	47	2	no	—
557	#3339	—	47	1	no	—
558	#3339	—	47	1	no	—
559	#3338	—	47	1	no	—
560	#3297	—	47	2	no	—
561	#3297	—	47	2	no	—
562	#3295	—	47	2	no	—
563	#3280	—	47	1	no	—
564	#3280	—	47	1	no	—
565	D₄×D₈	—	47	1	no	—
566	#3169	—	47	1	no	—
567	#3168	—	47	1	no	—
568	#3168	—	47	1	no	—
569	#3106	—	47	2	no	—
570	#3105	—	47	2	no	—
571	#3105	—	47	2	no	—
572	C₈×#41	—	47	1	no	—
573	C₄×#135	—	47	1	no	—
574	C₂×C₄×D₈	—	47	1	no	—
575	C₂×C₄×D₈	D₄₇	1	1	yes	characteristic, complemented
576	C₂×C₄₇	—	2	2	no	—
577	C₂×C₄₇	—	4	4	no	—
578	C₂×C₄₇	—	8	2	no	—
579	C₂×C₄₇	D₄×#41	1	1	yes	characteristic
580	C₂×C₄₇	C₂²×#135	1	1	yes	characteristic
581	C₂×C₄₇	C₂×#576	1	1	yes	characteristic
582	D₄₇	—	2	2	no	—
583	D₄₇	—	4	1	no	—
584	D₄₇	—	8	2	no	—
585	C₂×#135	—	47	1	no	—
586	C₂²×D₈	—	47	1	no	—
587	C₂²×D₈	C₂×D₄₇	1	1	yes	characteristic
588	#559	—	47	2	no	—
589	#554	—	47	2	no	—
590	#554	—	47	2	no	—
591	#553	—	47	2	no	—
592	#553	—	47	2	no	—
593	#553	—	94	2	no	—
594	#551	—	94	2	no	—
595	#551	—	94	2	no	—
596	#546	—	47	2	no	—
597	#546	—	47	2	no	—
598	#546	—	94	2	no	—
599	D₄²	—	47	2	no	—
600	#532	—	47	2	no	—
601	#529	—	47	2	no	—
602	#529	—	47	2	no	—
603	#529	—	94	2	no	—
604	#525	—	94	2	no	—
605	#525	—	94	2	no	—
606	C₄×#41	—	47	1	no	—
607	C₄×#41	—	47	2	no	—
608	C₂×C₄×D₄	—	47	2	no	—
609	C₂×C₄×D₄	—	94	2	no	—
610	C₂×C₄×D₄	C₂×D₄₇	1	2	yes	complemented
611	#500	—	47	1	no	—
612	#499	—	47	1	no	—
613	#499	—	47	1	no	—
614	#495	—	47	1	no	—
615	#495	—	47	1	no	—
616	#493	—	47	1	no	—
617	#488	—	47	2	no	—
618	#488	—	47	2	no	—
619	#486	—	47	2	no	—
620	#484	—	47	2	no	—
621	#484	—	47	2	no	—
622	#482	—	47	2	no	—
623	#482	—	47	2	no	—
624	#481	—	47	2	no	—
625	#481	—	47	2	no	—
626	#478	—	47	2	no	—
627	#478	—	47	2	no	—
628	#478	—	47	2	no	—
629	#478	—	47	2	no	—
630	#477	—	47	2	no	—
631	#476	—	47	2	no	—
632	#467	—	47	1	no	—
633	#467	—	47	1	no	—
634	#466	—	47	1	no	—
635	#466	—	47	1	no	—
636	#466	—	47	1	no	—
637	#466	—	47	1	no	—
638	#466	—	47	2	no	—
639	#465	—	47	2	no	—
640	#465	—	47	2	no	—
641	#463	—	47	2	no	—
642	#463	—	47	2	no	—
643	#463	—	47	2	no	—
644	#463	—	47	2	no	—
645	#460	—	47	2	no	—
646	#459	—	47	2	no	—
647	#450	—	47	2	no	—
648	#450	—	47	2	no	—
649	#449	—	47	2	no	—
650	#449	—	47	2	no	—
651	#447	—	47	2	no	—
652	#447	—	47	2	no	—
653	C₈×Q₈	—	47	1	no	—
654	C₈×Q₈	—	47	1	no	—
655	C₄×Q₁₆	—	47	1	no	—
656	C₄×Q₁₆	—	47	1	no	—
657	C₄×SD₁₆	—	47	2	no	—
658	C₄×SD₁₆	—	47	2	no	—
659	C₄×SD₁₆	—	47	2	no	—
660	C₄×SD₁₆	—	47	2	no	—
661	C₄×D₈	—	47	1	no	—
662	C₄×D₈	—	47	1	no	—
663	C₄×D₈	—	47	2	no	—
664	C₄×D₈	—	47	2	no	—
665	C₄×D₈	—	47	1	no	—
666	C₄×D₈	—	47	2	no	—
667	C₄×D₈	—	47	1	no	—
668	C₄×D₈	C₂×D₄₇	1	1	yes	characteristic
669	C₄×D₈	C₂×D₄₇	1	1	yes	characteristic
670	C₄×D₈	C₂×D₄₇	1	1	yes	characteristic, complemented
671	C₄×D₈	C₂×D₄₇	1	2	yes	complemented
672	C₄×D₈	C₂×D₄₇	1	2	yes	complemented
673	C₄×D₈	C₂×D₄₇	1	1	yes	characteristic, complemented
674	C₈×D₄	—	47	1	no	—
675	C₈×D₄	—	47	1	no	—
676	C₈×D₄	—	47	1	no	—
677	C₈×D₄	—	47	1	no	—
678	C₈×D₄	—	47	1	no	—
679	C₈×D₄	—	47	1	no	—
680	#431	—	47	1	no	—
681	#431	—	47	1	no	—
682	#431	—	47	1	no	—
683	#427	—	47	1	no	—
684	C₂×#107	—	47	1	no	—
685	C₂×#107	C₂×D₄₇	1	1	yes	characteristic, complemented
686	#416	—	47	2	no	—
687	C₂×#102	—	47	2	no	—
688	C₂×#102	C₂×D₄₇	1	2	yes	complemented
689	C₂×C₄×C₈	—	47	1	no	—
690	C₂×C₄×C₈	—	47	1	no	—
691	C₂×C₄×C₈	C₂×D₄₇	1	1	yes	characteristic, complemented
692	C₄₇	#61431	1	1	yes	characteristic, complemented, Sylow
693	C₂×#41	—	47	1	no	—
694	C₂×#41	—	47	2	no	—
695	C₂×#41	—	94	2	no	—
696	C₂²×D₄	—	47	2	no	—
697	C₂²×D₄	—	94	2	no	—
698	C₂²×D₄	C₂²×D₄₇	1	2	yes	—
699	C₂³×C₄	—	2	2	no	—
700	C₂³×C₄	—	94	2	no	—
701	#135	—	94	4	no	—
702	C₂×Q₁₆	—	47	1	no	—
703	C₂×SD₁₆	—	47	2	no	—
704	C₂×SD₁₆	—	47	2	no	—
705	C₂×SD₁₆	—	47	2	no	—
706	C₂×D₈	—	2	4	no	—
707	C₂×D₈	—	47	2	no	—
708	C₂×D₈	—	47	2	no	—
709	C₂×D₈	—	47	1	no	—
710	C₂×D₈	—	94	4	no	—
711	C₂×D₈	C₂²×D₄₇	1	2	yes	—
712	C₂×D₈	C₂²×D₄₇	1	1	yes	characteristic
713	C₂×D₈	C₂²×D₄₇	1	1	yes	characteristic
714	C₂²×C₈	—	47	1	no	—
715	C₂²×C₈	—	47	1	no	—
716	C₂²×C₈	—	47	1	no	—
717	C₂²×C₈	—	47	1	no	—
718	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
719	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
720	C₄⋊Q₈	—	47	2	no	—
721	#127	—	47	2	no	—
722	#126	—	94	2	no	—
723	#126	—	94	2	no	—
724	#126	—	94	2	no	—
725	#126	—	94	2	no	—
726	#125	—	47	2	no	—
727	#125	—	47	2	no	—
728	#125	—	94	2	no	—
729	#124	—	47	2	no	—
730	#124	—	47	2	no	—
731	#124	—	94	2	no	—
732	#124	—	94	2	no	—
733	#123	—	94	2	no	—
734	#123	—	94	2	no	—
735	#123	—	94	2	no	—
736	#123	—	94	2	no	—
737	#123	—	94	2	no	—
738	#123	—	94	2	no	—
739	#123	—	94	2	no	—
740	#123	—	94	2	no	—
741	C₂²⋊Q₈	—	47	2	no	—
742	C₂²⋊Q₈	—	47	2	no	—
743	C₂²⋊Q₈	—	94	2	no	—
744	C₂²⋊Q₈	—	94	2	no	—
745	C₂²⋊Q₈	—	94	2	no	—
746	C₂²⋊Q₈	—	94	2	no	—
747	C₂²⋊Q₈	—	94	2	no	—
748	#121	—	47	2	no	—
749	#121	—	47	2	no	—
750	#121	—	47	2	no	—
751	#121	—	47	2	no	—
752	#121	—	94	2	no	—
753	#121	—	94	2	no	—
754	#121	—	94	2	no	—
755	#121	—	94	2	no	—
756	#121	—	94	2	no	—
757	#121	—	94	2	no	—
758	#120	—	94	2	no	—
759	#120	—	94	2	no	—
760	#120	—	94	2	no	—
761	#120	—	94	2	no	—
762	C₄×Q₈	—	47	1	no	—
763	C₄×Q₈	—	47	1	no	—
764	C₄×Q₈	—	47	2	no	—
765	C₄×Q₈	—	47	2	no	—
766	C₄×D₄	—	2	2	no	—
767	C₄×D₄	—	2	2	no	—
768	C₄×D₄	—	47	1	no	—
769	C₄×D₄	—	47	1	no	—
770	C₄×D₄	—	47	1	no	—
771	C₄×D₄	—	47	1	no	—
772	C₄×D₄	—	47	2	no	—
773	C₄×D₄	—	47	2	no	—
774	C₄×D₄	—	47	2	no	—
775	C₄×D₄	—	47	1	no	—
776	C₄×D₄	—	47	1	no	—
777	C₄×D₄	—	47	2	no	—
778	C₄×D₄	—	94	2	no	—
779	C₄×D₄	—	94	2	no	—
780	C₄×D₄	—	94	2	no	—
781	C₄×D₄	—	94	2	no	—
782	C₄×D₄	—	94	2	no	—
783	C₄×D₄	—	94	2	no	—
784	C₄×D₄	—	94	2	no	—
785	C₄×D₄	—	94	2	no	—
786	C₄×D₄	—	94	2	no	—
787	C₄×D₄	—	94	2	no	—
788	C₄×D₄	—	94	2	no	—
789	C₄×D₄	C₂²×D₄₇	1	2	yes	—
790	C₄×D₄	C₂²×D₄₇	1	2	yes	—
791	C₄×D₄	C₂²×D₄₇	1	2	yes	—
792	C₄×D₄	C₂²×D₄₇	1	2	yes	—
793	#117	—	47	1	no	—
794	#117	—	47	1	no	—
795	#117	—	47	1	no	—
796	#117	—	47	2	no	—
797	#117	—	94	2	no	—
798	#117	—	94	2	no	—
799	#117	—	94	2	no	—
800	C₂×C₄⋊C₄	—	47	2	no	—
801	C₂×C₄⋊C₄	—	94	2	no	—
802	C₂×C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
803	C₂×C₂²⋊C₄	—	2	2	no	—
804	C₂×C₂²⋊C₄	—	94	2	no	—
805	C₂×C₂²⋊C₄	—	94	2	no	—
806	C₂×C₂²⋊C₄	—	94	2	no	—
807	C₂×C₄²	—	47	1	no	—
808	C₂×C₄²	—	47	1	no	—
809	C₂×C₄²	—	94	2	no	—
810	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
811	#107	—	47	1	no	—
812	#107	—	47	1	no	—
813	#107	—	47	2	no	—
814	#107	—	47	2	no	—
815	#107	C₂²×D₄₇	1	1	yes	characteristic
816	#107	C₂²×D₄₇	1	1	yes	characteristic
817	#107	C₂²×D₄₇	1	2	yes	—
818	#106	—	47	2	no	—
819	#106	—	47	2	no	—
820	#106	—	47	2	no	—
821	C₄⋊C₈	—	47	1	no	—
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	C₄⋊C₈	—	47	1	no	—
827	#103	—	47	2	no	—
828	#103	—	47	2	no	—
829	#103	—	47	2	no	—
830	#103	—	47	2	no	—
831	#102	—	47	2	no	—
832	#102	—	47	2	no	—
833	#102	—	47	2	no	—
834	#102	—	47	2	no	—
835	#102	—	47	2	no	—
836	#102	—	47	2	no	—
837	#102	—	47	2	no	—
838	#102	—	47	2	no	—
839	#102	C₂²×D₄₇	1	2	yes	—
840	#102	C₂²×D₄₇	1	2	yes	—
841	#102	C₂²×D₄₇	1	2	yes	—
842	#102	C₂²×D₄₇	1	2	yes	—
843	C₂²⋊C₈	—	47	1	no	—
844	C₂²⋊C₈	—	47	1	no	—
845	C₂²⋊C₈	—	47	1	no	—
846	C₂²⋊C₈	—	47	1	no	—
847	C₂²⋊C₈	—	47	1	no	—
848	C₂²⋊C₈	—	47	1	no	—
849	C₄×C₈	—	47	1	no	—
850	C₄×C₈	—	47	1	no	—
851	C₄×C₈	—	47	1	no	—
852	C₄×C₈	—	47	1	no	—
853	C₄×C₈	—	47	1	no	—
854	C₄×C₈	—	47	1	no	—
855	C₄×C₈	C₂²×D₄₇	1	1	yes	characteristic
856	C₄×C₈	C₂²×D₄₇	1	1	yes	characteristic
857	C₄×C₈	C₂²×D₄₇	1	1	yes	characteristic
858	C₄×C₈	C₂²×D₄₇	1	1	yes	characteristic
859	C₂⁴	—	2	2	no	—
860	C₂⁴	—	94	2	no	—
861	#41	—	94	4	no	—
862	#41	—	94	4	no	—
863	#41	—	376	4	no	—
864	#41	—	188	2	no	—
865	C₂×Q₈	—	47	1	no	—
866	C₂×Q₈	—	47	2	no	—
867	C₂×Q₈	—	94	2	no	—
868	C₂×D₄	—	2	4	no	—
869	C₂×D₄	—	2	2	no	—
870	C₂×D₄	—	4	2	no	—
871	C₂×D₄	—	47	1	no	—
872	C₂×D₄	—	47	1	no	—
873	C₂×D₄	—	47	1	no	—
874	C₂×D₄	—	47	2	no	—
875	C₂×D₄	—	94	2	no	—
876	C₂×D₄	—	94	2	no	—
877	C₂×D₄	—	94	2	no	—
878	C₂×D₄	—	94	2	no	—
879	C₂×D₄	—	94	4	no	—
880	C₂×D₄	—	94	2	no	—
881	C₂×D₄	—	94	2	no	—
882	C₂×D₄	—	94	2	no	—
883	C₂×D₄	—	94	2	no	—
884	C₂×D₄	—	188	2	no	—
885	C₂×D₄	—	188	8	no	—
886	C₂×D₄	C₂³×D₄₇	1	2	yes	—
887	C₂×D₄	C₂³×D₄₇	1	2	yes	—
888	C₂²×C₄	—	2	2	no	—
889	C₂²×C₄	—	2	2	no	—
890	C₂²×C₄	—	2	2	no	—
891	C₂²×C₄	—	2	2	no	—
892	C₂²×C₄	—	2	2	no	—
893	C₂²×C₄	—	8	4	no	—
894	C₂²×C₄	—	47	1	no	—
895	C₂²×C₄	—	47	1	no	—
896	C₂²×C₄	—	47	1	no	—
897	C₂²×C₄	—	47	1	no	—
898	C₂²×C₄	—	47	1	no	—
899	C₂²×C₄	—	47	1	no	—
900	C₂²×C₄	—	94	2	no	—
901	C₂²×C₄	—	94	2	no	—
902	C₂²×C₄	—	94	2	no	—
903	C₂²×C₄	—	94	2	no	—
904	C₂²×C₄	—	94	2	no	—
905	C₂²×C₄	—	94	2	no	—
906	C₂²×C₄	—	376	4	no	—
907	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
908	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
909	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
910	Q₁₆	—	94	2	no	—
911	SD₁₆	—	94	4	no	—
912	SD₁₆	—	188	2	no	—
913	SD₁₆	—	188	2	no	—
914	D₈	—	2	4	no	—
915	D₈	—	2	2	no	—
916	D₈	—	94	4	no	—
917	D₈	—	94	2	no	—
918	D₈	—	188	2	no	—
919	D₈	#10625350	1	4	yes	complemented
920	C₂×C₈	—	2	2	no	—
921	C₂×C₈	—	4	1	no	—
922	C₂×C₈	—	47	1	no	—
923	C₂×C₈	—	47	1	no	—
924	C₂×C₈	—	47	1	no	—
925	C₂×C₈	—	47	1	no	—
926	C₂×C₈	—	94	2	no	—
927	C₂×C₈	—	94	2	no	—
928	C₂×C₈	—	188	1	no	—
929	C₂×C₈	—	188	1	no	—
930	C₂×C₈	C₂³×D₄₇	1	1	yes	characteristic
931	C₂×C₈	C₂³×D₄₇	1	1	yes	characteristic
932	C₂×C₈	C₂³×D₄₇	1	1	yes	characteristic
933	C₂×C₈	C₂³×D₄₇	1	1	yes	characteristic
934	C₄⋊C₄	—	2	2	no	—
935	C₄⋊C₄	—	47	1	no	—
936	C₄⋊C₄	—	47	1	no	—
937	C₄⋊C₄	—	47	1	no	—
938	C₄⋊C₄	—	47	1	no	—
939	C₄⋊C₄	—	47	1	no	—
940	C₄⋊C₄	—	47	1	no	—
941	C₄⋊C₄	—	47	2	no	—
942	C₄⋊C₄	—	47	2	no	—
943	C₄⋊C₄	—	94	2	no	—
944	C₄⋊C₄	—	94	2	no	—
945	C₄⋊C₄	—	94	2	no	—
946	C₄⋊C₄	—	94	2	no	—
947	C₄⋊C₄	—	94	2	no	—
948	C₄⋊C₄	—	94	2	no	—
949	C₄⋊C₄	—	94	2	no	—
950	C₄⋊C₄	—	94	2	no	—
951	C₄⋊C₄	—	94	2	no	—
952	C₄⋊C₄	—	94	2	no	—
953	C₄⋊C₄	C₂³×D₄₇	1	2	yes	—
954	C₄⋊C₄	C₂³×D₄₇	1	2	yes	—
955	C₂²⋊C₄	—	2	2	no	—
956	C₂²⋊C₄	—	2	2	no	—
957	C₂²⋊C₄	—	2	2	no	—
958	C₂²⋊C₄	—	2	2	no	—
959	C₂²⋊C₄	—	47	1	no	—
960	C₂²⋊C₄	—	47	1	no	—
961	C₂²⋊C₄	—	47	1	no	—
962	C₂²⋊C₄	—	47	1	no	—
963	C₂²⋊C₄	—	47	1	no	—
964	C₂²⋊C₄	—	47	1	no	—
965	C₂²⋊C₄	—	94	2	no	—
966	C₂²⋊C₄	—	94	2	no	—
967	C₂²⋊C₄	—	94	2	no	—
968	C₂²⋊C₄	—	94	2	no	—
969	C₂²⋊C₄	—	94	2	no	—
970	C₂²⋊C₄	—	94	2	no	—
971	C₂²⋊C₄	—	94	2	no	—
972	C₂²⋊C₄	—	94	2	no	—
973	C₂²⋊C₄	—	94	2	no	—
974	C₂²⋊C₄	—	94	2	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	2	no	—
980	C₄²	—	47	1	no	—
981	C₄²	—	47	1	no	—
982	C₄²	—	47	1	no	—
983	C₄²	—	47	1	no	—
984	C₄²	—	47	1	no	—
985	C₄²	—	47	1	no	—
986	C₄²	—	94	2	no	—
987	C₄²	—	94	2	no	—
988	C₄²	—	94	2	no	—
989	C₄²	D₄×D₄₇	1	1	yes	characteristic
990	C₄²	D₄×D₄₇	1	1	yes	characteristic
991	C₄²	C₂³×D₄₇	1	1	yes	characteristic
992	C₄²	C₂³×D₄₇	1	1	yes	characteristic
993	C₂³	—	2	2	no	—
994	C₂³	—	2	2	no	—
995	C₂³	—	4	4	no	—
996	C₂³	—	4	4	no	—
997	C₂³	—	8	2	no	—
998	C₂³	—	47	1	no	—
999	C₂³	—	47	1	no	—
1000	C₂³	—	94	2	no	—
1001	C₂³	—	376	2	no	—
1002	C₂³	—	188	4	no	—
1003	C₂³	—	188	4	no	—
1004	C₂³	C₂×D₄×D₄₇	1	1	yes	characteristic
1005	Q₈	—	94	2	no	—
1006	Q₈	—	94	2	no	—
1007	Q₈	—	94	2	no	—
1008	Q₈	—	376	2	no	—
1009	D₄	—	2	2	no	—
1010	D₄	—	2	2	no	—
1011	D₄	—	2	2	no	—
1012	D₄	—	4	4	no	—
1013	D₄	—	47	4	no	—
1014	D₄	—	94	2	no	—
1015	D₄	—	94	2	no	—
1016	D₄	—	94	2	no	—
1017	D₄	—	94	2	no	—
1018	D₄	—	376	2	no	—
1019	D₄	—	376	2	no	—
1020	D₄	—	376	2	no	—
1021	D₄	—	188	4	no	—
1022	D₄	—	188	4	no	—
1023	D₄	—	188	4	no	—
1024	D₄	—	188	4	no	—
1025	D₄	—	188	4	no	—
1026	D₄	C₂×#10625350	1	4	yes	—
1027	C₂×C₄	—	2	2	no	—
1028	C₂×C₄	—	2	2	no	—
1029	C₂×C₄	—	2	1	no	—
1030	C₂×C₄	—	2	1	no	—
1031	C₂×C₄	—	2	2	no	—
1032	C₂×C₄	—	2	2	no	—
1033	C₂×C₄	—	4	4	no	—
1034	C₂×C₄	—	4	4	no	—
1035	C₂×C₄	—	8	2	no	—
1036	C₂×C₄	—	8	2	no	—
1037	C₂×C₄	—	8	2	no	—
1038	C₂×C₄	—	47	1	no	—
1039	C₂×C₄	—	47	1	no	—
1040	C₂×C₄	—	47	1	no	—
1041	C₂×C₄	—	47	1	no	—
1042	C₂×C₄	—	47	1	no	—
1043	C₂×C₄	—	47	1	no	—
1044	C₂×C₄	—	94	2	no	—
1045	C₂×C₄	—	94	2	no	—
1046	C₂×C₄	—	94	2	no	—
1047	C₂×C₄	—	94	2	no	—
1048	C₂×C₄	—	94	1	no	—
1049	C₂×C₄	—	94	1	no	—
1050	C₂×C₄	—	94	1	no	—
1051	C₂×C₄	—	94	1	no	—
1052	C₂×C₄	—	94	2	no	—
1053	C₂×C₄	—	94	2	no	—
1054	C₂×C₄	—	94	2	no	—
1055	C₂×C₄	—	376	2	no	—
1056	C₂×C₄	—	376	2	no	—
1057	C₂×C₄	—	376	2	no	—
1058	C₂×C₄	—	188	4	no	—
1059	C₂×C₄	—	188	4	no	—
1060	C₂×C₄	—	188	4	no	—
1061	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
1062	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
1063	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
1064	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
1065	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
1066	C₂×C₄	C₂⁴×D₄₇	1	1	yes	characteristic
1067	C₈	—	2	1	no	—
1068	C₈	—	2	1	no	—
1069	C₈	—	2	1	no	—
1070	C₈	—	94	1	no	—
1071	C₈	—	94	1	no	—
1072	C₈	—	94	1	no	—
1073	C₈	—	94	1	no	—
1074	C₈	C₂×#10625350	1	2	yes	—
1075	C₂²	—	2	1	no	—
1076	C₂²	—	2	1	no	—
1077	C₂²	—	2	4	no	—
1078	C₂²	—	4	2	no	—
1079	C₂²	—	4	2	no	—
1080	C₂²	—	4	2	no	—
1081	C₂²	—	4	2	no	—
1082	C₂²	—	4	2	no	—
1083	C₂²	—	8	8	no	—
1084	C₂²	—	47	2	no	—
1085	C₂²	—	94	1	no	—
1086	C₂²	—	94	1	no	—
1087	C₂²	—	94	1	no	—
1088	C₂²	—	94	1	no	—
1089	C₂²	—	94	1	no	—
1090	C₂²	—	376	8	no	—
1091	C₂²	—	188	2	no	—
1092	C₂²	—	188	2	no	—
1093	C₂²	—	188	2	no	—
1094	C₂²	#135×D₄₇	1	2	yes	—
1095	C₂²	C₂²×D₄×D₄₇	1	1	yes	characteristic
1096	C₄	—	2	1	no	—
1097	C₄	—	2	1	no	—
1098	C₄	—	2	1	no	—
1099	C₄	—	2	1	no	—
1100	C₄	—	4	2	no	—
1101	C₄	—	4	2	no	—
1102	C₄	—	47	2	no	—
1103	C₄	—	94	1	no	—
1104	C₄	—	94	1	no	—
1105	C₄	—	94	1	no	—
1106	C₄	—	94	1	no	—
1107	C₄	—	94	1	no	—
1108	C₄	—	188	2	no	—
1109	C₄	—	188	2	no	—
1110	C₄	—	188	2	no	—
1111	C₄	#15689924	1	2	yes	—
1112	C₄	C₂²×#10625350	1	1	yes	characteristic
1113	C₄	#15689959	1	1	yes	characteristic
1114	C₂	—	2	2	no	—
1115	C₂	—	4	4	no	—
1116	C₂	—	8	2	no	—
1117	C₂	—	94	2	no	—
1118	C₂	—	376	2	no	—
1119	C₂	—	188	1	no	—
1120	C₂	D₄×#10625350	1	1	yes	characteristic
1121	C₂	C₂×#135×D₄₇	1	1	yes	characteristic
1122	C₂	C₂×#15689924	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	C₂×C₄×D₈×C₄₇	C₂
socle	C₂²×C₄₇	C₂³×D₄
hypercenter	C₂×C₄×D₈	D₄₇
hypocenter	C₄₇	#61431
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₂×C₄×D₈

Complements

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

N	H ≅ G/N	type
1. #20256992	C₂	semidirect
2. #20256400	C₂	semidirect
3. #20256255	C₂	semidirect
4. #20256049	C₂	semidirect
5. #20255792	C₂	semidirect
6. #20255786	C₂	semidirect
7. #20255778	C₂	semidirect
8. #20255243	C₂	semidirect
9. #20255234	C₂	semidirect
10. #20255208	C₂	semidirect
11. #20255074	C₂	semidirect
12. #20255073	C₂	semidirect
13. D₈×C₂²⋊D₄₇	C₂	semidirect
14. #20253964	C₂	semidirect
15. #20253958	C₂	semidirect
16. #20253956	C₂	semidirect
17. #20253444	C₂	semidirect
18. #20253435	C₂	semidirect
19. #20253433	C₂	semidirect
20. C₈×#10625350	C₂	semidirect
21. C₄×#13094043	C₂	semidirect
22. C₄×D₈×D₄₇	C₂	semidirect
23. C₂×C₄×D₈×C₄₇	C₂	semidirect
26. #15689856	C₂²	semidirect
27. #15689832	C₂²	semidirect
29. #15689823	C₂²	semidirect
31. #15689821	C₂²	semidirect
34. #15689768	C₂²	semidirect
35. #15689767	C₂²	semidirect
38. #15689670	C₂²	semidirect
39. #15689657	C₂²	semidirect
40. #15689655	C₂²	semidirect
45. C₄×#10625352	C₂²	semidirect
47. C₄×D₄×D₄₇	C₂²	semidirect
48. #15689527	C₂²	semidirect
49. #15689525	C₂²	semidirect
50. #15689524	C₂²	semidirect
51. #15689507	C₂²	semidirect
52. #15689506	C₂²	semidirect
54. #15689478	C₂²	semidirect
55. #15689476	C₂²	semidirect
56. #15689468	C₂²	semidirect
57. #15689460	C₂²	semidirect
58. #15689458	C₂²	semidirect
59. #15689450	C₂²	semidirect
60. #15689446	C₂²	semidirect
61. #15689441	C₂²	semidirect
62. #15689440	C₂²	semidirect
63. #15689426	C₂²	semidirect
64. #15689425	C₂²	semidirect
65. #15689423	C₂²	semidirect
66. #15689423	C₂²	semidirect
67. #15689417	C₂²	semidirect
68. #15689411	C₂²	semidirect
69. #15689365	C₂²	semidirect
70. #15689364	C₂²	semidirect
71. #15689360	C₂²	semidirect
73. #15689358	C₂²	semidirect
75. #15689356	C₂²	semidirect
76. #15689352	C₂²	semidirect
77. #15689351	C₂²	semidirect
78. #15689338	C₂²	semidirect
79. #15689338	C₂²	semidirect
80. #15689337	C₂²	semidirect
81. #15689336	C₂²	semidirect
82. #15689322	C₂²	semidirect
84. #15689275	C₂²	semidirect
85. #15689274	C₂²	semidirect
86. #15689269	C₂²	semidirect
87. #15689265	C₂²	semidirect
90. C₈×Dic₉₄	C₂²	semidirect
91. C₈×Dic₉₄	C₂²	semidirect
92. C₄×Dic₁₈₈	C₂²	semidirect
93. #15689217	C₂²	semidirect
94. #15689214	C₂²	semidirect
95. C₄×#10625325	C₂²	semidirect
96. C₄×#10625335	C₂²	semidirect
97. C₄×#10625335	C₂²	semidirect
98. C₄×D₃₇₆	C₂²	semidirect
101. #15689205	C₂²	semidirect
102. C₄×#10625334	C₂²	semidirect
103. C₄×#10625334	C₂²	semidirect
104. #15689203	C₂²	semidirect
105. C₈×D₁₈₈	C₂²	semidirect
106. C₈×D₁₈₈	C₂²	semidirect
109. C₈×C₂²⋊D₄₇	C₂²	semidirect
110. C₈×C₂²⋊D₄₇	C₂²	semidirect
111. #15689176	C₂²	semidirect
112. #15689174	C₂²	semidirect
113. #15689174	C₂²	semidirect
114. #15689160	C₂²	semidirect
115. #107×D₄₇	C₂²	semidirect
116. #15689116	C₂²	semidirect
117. #102×D₄₇	C₂²	semidirect
118. C₄×C₈×D₄₇	C₂²	semidirect
119. C₄×C₈×D₄₇	C₂²	semidirect
121. C₂×C₄×D₄×C₄₇	C₂²	semidirect
124. C₄×D₈×C₄₇	C₂²	semidirect
125. C₄×D₈×C₄₇	C₂²	semidirect
126. C₄×D₈×C₄₇	C₂²	semidirect
127. C₄×D₈×C₄₇	C₂²	semidirect
128. C₂×#107×C₄₇	C₂²	semidirect
129. C₂×#102×C₄₇	C₂²	semidirect
130. C₂×C₄×C₈×C₄₇	C₂²	semidirect
350. D₈×C₄₇	#41	semidirect
473. C₂²⋊D₄₇	#135	semidirect
575. C₂×C₄×D₈	D₄₇	semidirect
610. C₂×C₄×D₄	C₂×D₄₇	semidirect
670. C₄×D₈	C₂×D₄₇	semidirect
671. C₄×D₈	C₂×D₄₇	semidirect
672. C₄×D₈	C₂×D₄₇	semidirect
673. C₄×D₈	C₂×D₄₇	semidirect
685. C₂×#107	C₂×D₄₇	semidirect
688. C₂×#102	C₂×D₄₇	semidirect
691. C₂×C₄×C₈	C₂×D₄₇	semidirect
692. C₄₇	#61431	semidirect
919. D₈	#10625350	semidirect

Maximal subgroups

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

subgroup	index
#20256992	2
#20256400	2
#20256255	2
#20256049	2
#20255792	2
#20255786	2
#20255778	2
#20255243	2
#20255234	2
#20255208	2
#20255074	2
#20255073	2
D₈×C₂²⋊D₄₇	2
#20253964	2
#20253958	2
#20253956	2
#20253444	2
#20253435	2
#20253433	2
C₈×#10625350	2
C₄×#13094043	2
C₄×D₈×D₄₇	2
C₂×C₄×D₈×C₄₇	2
#61431	47