Subgroups — #27097775

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	#20256994	C₂	1	2	yes	maximal, complemented
2	#20256397	C₂	1	1	yes	maximal, characteristic, complemented
3	#20256252	C₂	1	1	yes	maximal, characteristic, complemented
4	#20256045	C₂	1	2	yes	maximal, complemented
5	#20255793	C₂	1	1	yes	maximal, characteristic, complemented
6	#20255789	C₂	1	1	yes	maximal, characteristic, complemented
7	#20255777	C₂	1	1	yes	maximal, characteristic, complemented
8	#20255244	C₂	1	2	yes	maximal, complemented
9	#20255237	C₂	1	2	yes	maximal, complemented
10	#20255207	C₂	1	2	yes	maximal, complemented
11	#20255072	C₂	1	1	yes	maximal, characteristic, complemented
12	#20255070	C₂	1	1	yes	maximal, characteristic, complemented
13	#20255062	C₂	1	1	yes	maximal, characteristic, complemented
14	#20253964	C₂	1	1	yes	maximal, characteristic, complemented
15	#20253961	C₂	1	1	yes	maximal, characteristic, complemented
16	#20253446	C₂	1	2	yes	maximal, complemented
17	#20253439	C₂	1	2	yes	maximal, complemented
18	#20253431	C₂	1	2	yes	maximal, complemented
19	C₈×#10625350	C₂	1	1	yes	maximal, characteristic, complemented
20	C₄×#13094047	C₂	1	1	yes	maximal, characteristic, complemented
21	C₂×C₄×D₃₇₆	C₂	1	1	yes	maximal, characteristic, complemented
22	C₄×D₈×D₄₇	C₂	1	1	yes	maximal, characteristic, complemented
23	C₄₇×#3168	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#13094047	C₂²	1	1	yes	characteristic
25	C₂²×D₃₇₆	C₂²	1	1	yes	characteristic
26	C₂×D₈×D₄₇	C₂²	1	1	yes	characteristic
27	#15689855	C₂²	1	2	yes	complemented
28	#15689831	C₂²	1	2	yes	—
29	#15689829	C₂²	1	2	yes	complemented
30	#15689826	C₂²	1	2	yes	complemented
31	#15689825	C₂²	1	2	yes	complemented
32	#15689824	—	2	2	no	—
33	#15689798	—	2	2	no	—
34	#15689796	—	2	2	no	—
35	#15689766	C₂²	1	2	yes	complemented
36	#15689765	—	2	2	no	—
37	#15689764	C₂²	1	2	yes	complemented
38	#15689757	C₂²	1	2	yes	—
39	#15689670	C₂²	1	2	yes	complemented
40	#15689660	C₂²	1	2	yes	complemented
41	#15689651	—	2	2	no	—
42	#15689635	—	2	2	no	—
43	#15689632	—	2	2	no	—
44	C₄×#10625354	C₂²	1	2	yes	complemented
45	C₄×#10625350	C₂²	1	1	yes	characteristic
46	C₂×C₄×D₁₈₈	C₂²	1	2	yes	complemented
47	C₄×D₄×D₄₇	—	2	2	no	—
48	C₄×D₄×D₄₇	C₂²	1	2	yes	complemented
49	#15689527	C₂²	1	1	yes	characteristic, complemented
50	#15689524	C₂²	1	1	yes	characteristic, complemented
51	#15689508	C₂²	1	1	yes	characteristic, complemented
52	#15689498	C₂²	1	1	yes	characteristic
53	#15689479	C₂²	1	2	yes	complemented
54	#15689468	C₂²	1	2	yes	complemented
55	#15689457	C₂²	1	2	yes	complemented
56	#15689456	C₂²	1	2	yes	complemented
57	#15689449	C₂²	1	2	yes	complemented
58	#15689445	C₂²	1	2	yes	complemented
59	#15689443	C₂²	1	2	yes	complemented
60	#15689439	C₂²	1	2	yes	complemented
61	#15689422	C₂²	1	2	yes	complemented
62	#15689421	C₂²	1	2	yes	complemented
63	#15689420	C₂²	1	2	yes	complemented
64	#15689420	C₂²	1	2	yes	complemented
65	#15689416	C₂²	1	2	yes	complemented
66	#15689412	C₂²	1	2	yes	complemented
67	#15689361	C₂²	1	1	yes	characteristic, complemented
68	#15689360	C₂²	1	1	yes	characteristic
69	#15689360	C₂²	1	1	yes	characteristic, complemented
70	#15689358	C₂²	1	2	yes	complemented
71	#15689356	C₂²	1	1	yes	characteristic, complemented
72	#15689355	C₂²	1	2	yes	complemented
73	#15689341	C₂²	1	2	yes	complemented
74	#15689340	C₂²	1	2	yes	complemented
75	#15689335	C₂²	1	2	yes	complemented
76	#15689335	C₂²	1	2	yes	complemented
77	#15689321	C₂²	1	2	yes	complemented
78	#15689317	C₂²	1	2	yes	—
79	#15689273	C₂²	1	2	yes	complemented
80	#15689272	C₂²	1	2	yes	complemented
81	#15689271	C₂²	1	2	yes	complemented
82	#15689267	C₂²	1	2	yes	complemented
83	#15689258	C₂²	1	2	yes	—
84	#15689256	C₂²	1	2	yes	—
85	C₈×Dic₉₄	C₂²	1	1	yes	characteristic, complemented
86	C₈×Dic₉₄	C₂²	1	1	yes	characteristic, complemented
87	Q₁₆×Dic₄₇	C₂²	1	1	yes	characteristic, complemented
88	C₄×#10625336	C₂²	1	2	yes	complemented
89	C₄×#10625336	C₂²	1	2	yes	complemented
90	#15689208	C₂²	1	2	yes	complemented
91	C₄×D₃₇₆	C₂²	1	1	yes	characteristic
92	C₄×D₃₇₆	C₂²	1	1	yes	characteristic
93	C₄×D₃₇₆	C₂²	1	2	yes	complemented
94	C₄×D₃₇₆	C₂²	1	2	yes	complemented
95	C₄×D₃₇₆	C₂²	1	1	yes	characteristic, complemented
96	C₄×D₃₇₆	C₂²	1	1	yes	characteristic, complemented
97	D₈×Dic₄₇	C₂²	1	1	yes	characteristic, complemented
98	#15689205	C₂²	1	1	yes	characteristic
99	#15689205	C₂²	1	1	yes	characteristic
100	C₄×#10625334	C₂²	1	2	yes	complemented
101	C₄×#10625334	C₂²	1	2	yes	complemented
102	#15689203	C₂²	1	2	yes	complemented
103	C₈×D₁₈₈	C₂²	1	1	yes	characteristic, complemented
104	C₈×D₁₈₈	C₂²	1	1	yes	characteristic, complemented
105	C₈×C₂²⋊D₄₇	C₂²	1	1	yes	characteristic
106	C₈×C₂²⋊D₄₇	C₂²	1	1	yes	characteristic
107	C₈×C₂²⋊D₄₇	C₂²	1	1	yes	characteristic, complemented
108	C₈×C₂²⋊D₄₇	C₂²	1	1	yes	characteristic, complemented
109	#15689176	C₂²	1	1	yes	characteristic, complemented
110	#15689174	C₂²	1	1	yes	characteristic, complemented
111	#15689174	C₂²	1	1	yes	characteristic, complemented
112	#15689160	C₂²	1	1	yes	characteristic, complemented
113	C₂×#13093958	C₂²	1	1	yes	characteristic, complemented
114	#107×D₄₇	C₂²	1	1	yes	characteristic, complemented
115	#15689118	C₂²	1	2	yes	complemented
116	C₂×#13093946	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	C₄₇×#529	C₂²	1	2	yes	complemented
121	C₄₇×#499	C₂²	1	1	yes	characteristic, complemented
122	C₄₇×#495	C₂²	1	1	yes	characteristic, complemented
123	C₄₇×#488	C₂²	1	2	yes	complemented
124	C₄₇×#467	C₂²	1	1	yes	characteristic, complemented
125	C₄₇×#466	C₂²	1	1	yes	characteristic
126	C₄₇×#465	C₂²	1	2	yes	complemented
127	C₄×Q₁₆×C₄₇	C₂²	1	1	yes	characteristic, complemented
128	C₄×SD₁₆×C₄₇	C₂²	1	2	yes	complemented
129	C₄×D₈×C₄₇	C₂²	1	1	yes	characteristic, complemented
130	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic, complemented
131	C₂×#10625354	C₂³	1	2	yes	—
132	C₂×#10625350	—	2	2	no	—
133	C₂×#10625350	D₄	1	1	yes	characteristic
134	C₂²×D₁₈₈	C₂³	1	2	yes	—
135	C₂×D₄×D₄₇	—	2	2	no	—
136	C₂×D₄×D₄₇	C₂³	1	2	yes	—
137	C₂²×C₄×D₄₇	—	2	2	no	—
138	C₂²×C₄×D₄₇	—	2	2	no	—
139	#13094047	—	2	4	no	—
140	C₂×#10625336	C₂³	1	2	yes	—
141	C₂×#10625336	C₂³	1	2	yes	—
142	C₂×D₃₇₆	—	2	4	no	—
143	C₂×D₃₇₆	C₂³	1	1	yes	characteristic
144	C₂×D₃₇₆	C₂³	1	2	yes	—
145	C₂×D₃₇₆	C₂³	1	1	yes	characteristic
146	C₂×#10625334	C₂³	1	2	yes	—
147	C₂×#10625334	C₂³	1	2	yes	—
148	D₈×D₄₇	—	2	4	no	—
149	C₂×C₈×D₄₇	C₂³	1	1	yes	characteristic
150	C₂×C₈×D₄₇	C₂³	1	1	yes	characteristic
151	C₂×C₈×D₄₇	C₂³	1	1	yes	characteristic
152	C₂×C₈×D₄₇	C₂³	1	1	yes	characteristic
153	#13094023	C₂³	1	2	yes	—
154	#13094020	C₂³	1	2	yes	—
155	#13094019	—	2	2	no	—
156	#13094019	—	2	2	no	—
157	#13094017	—	2	2	no	—
158	#13094015	C₂³	1	2	yes	—
159	#13094014	—	2	2	no	—
160	#13094013	C₂³	1	2	yes	—
161	#13094010	—	2	2	no	—
162	#13094010	—	2	2	no	—
163	#13094009	—	2	2	no	—
164	#13094009	—	2	2	no	—
165	#13094009	—	2	2	no	—
166	#13094008	—	2	2	no	—
167	#13094008	—	2	2	no	—
168	#13094006	—	2	2	no	—
169	#13094006	—	2	2	no	—
170	#13094004	—	2	2	no	—
171	#13094004	—	2	2	no	—
172	#13094002	—	2	2	no	—
173	#13094002	—	2	2	no	—
174	#13094001	—	2	2	no	—
175	#13094000	C₂³	1	2	yes	—
176	#13093999	—	2	2	no	—
177	#13093999	—	2	2	no	—
178	#13093999	C₂³	1	2	yes	—
179	#13093999	C₂³	1	2	yes	—
180	#13093997	—	2	2	no	—
181	#13093997	—	2	2	no	—
182	#13093997	—	2	2	no	—
183	#13093996	—	2	2	no	—
184	#13093995	C₂³	1	2	yes	—
185	#13093994	—	2	2	no	—
186	#13093994	—	2	2	no	—
187	#13093994	—	2	2	no	—
188	#13093992	—	2	2	no	—
189	Q₈×Dic₄₇	C₂³	1	2	yes	—
190	C₄×Dic₉₄	D₄	1	1	yes	characteristic
191	C₄×Dic₉₄	C₂³	1	1	yes	characteristic
192	C₄×D₁₈₈	—	2	2	no	—
193	C₄×D₁₈₈	—	2	2	no	—
194	C₄×D₁₈₈	—	2	2	no	—
195	C₄×D₁₈₈	—	2	2	no	—
196	C₄×D₁₈₈	D₄	1	1	yes	characteristic
197	C₄×D₁₈₈	C₂³	1	1	yes	characteristic
198	C₄×D₁₈₈	C₂³	1	2	yes	—
199	C₄×D₁₈₈	C₂³	1	2	yes	—
200	C₄×D₁₈₈	C₂³	1	2	yes	—
201	C₄×D₁₈₈	C₂³	1	2	yes	—
202	D₄×Dic₄₇	—	2	2	no	—
203	D₄×Dic₄₇	C₂³	1	2	yes	—
204	#13093986	—	2	2	no	—
205	#13093986	—	2	2	no	—
206	#13093986	C₂³	1	2	yes	—
207	#13093986	C₂³	1	2	yes	—
208	C₄×C₂²⋊D₄₇	—	2	2	no	—
209	C₄×C₂²⋊D₄₇	—	2	2	no	—
210	C₄×C₂²⋊D₄₇	D₄	1	1	yes	characteristic
211	C₄×C₂²⋊D₄₇	D₄	1	1	yes	characteristic
212	C₄×C₂²⋊D₄₇	C₂³	1	1	yes	characteristic
213	C₄×C₂²⋊D₄₇	C₂³	1	1	yes	characteristic
214	(C₂²⋊D₄₇)⋊C₄	—	2	2	no	—
215	(C₂²⋊D₄₇)⋊C₄	—	2	2	no	—
216	(C₂²⋊D₄₇)⋊C₄	—	2	2	no	—
217	#13093983	D₄	1	1	yes	characteristic
218	#13093982	—	2	2	no	—
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	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
224	C₄⋊C₄×D₄₇	—	2	2	no	—
225	C₄⋊C₄×D₄₇	C₂³	1	2	yes	—
226	C₂×(C₂×D₄₇)⋊C₄	—	2	2	no	—
227	C₂²⋊C₄×D₄₇	—	2	2	no	—
228	C₂²⋊C₄×D₄₇	—	2	2	no	—
229	C₂²⋊C₄×D₄₇	—	2	2	no	—
230	C₄²×D₄₇	—	2	2	no	—
231	C₄²×D₄₇	C₂³	1	1	yes	characteristic
232	C₄²×D₄₇	C₂³	1	1	yes	characteristic
233	#13093958	C₂³	1	1	yes	characteristic
234	#13093958	C₂³	1	1	yes	characteristic
235	#13093958	C₂³	1	2	yes	—
236	#13093957	C₂³	1	2	yes	—
237	#13093957	C₂³	1	2	yes	—
238	#13093955	C₂³	1	2	yes	—
239	#13093955	C₂³	1	2	yes	—
240	C₄⋊(C₄₇⋊C₈)	C₂³	1	1	yes	characteristic
241	C₄⋊(C₄₇⋊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	Dic₄₇⋊C₈	C₂³	1	1	yes	characteristic
246	#13093948	C₂³	1	2	yes	—
247	#13093948	C₂³	1	2	yes	—
248	#13093946	C₂³	1	2	yes	—
249	#13093946	C₂³	1	2	yes	—
250	#13093946	C₂³	1	2	yes	—
251	#13093946	C₂³	1	2	yes	—
252	#13093945	C₂³	1	2	yes	—
253	#13093945	C₂³	1	2	yes	—
254	#13093944	C₂³	1	2	yes	—
255	#13093944	C₂³	1	2	yes	—
256	#13093944	C₂³	1	2	yes	—
257	#13093944	C₂³	1	2	yes	—
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	C₄×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
265	C₄×C₄₇⋊C₈	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	C₈×Dic₄₇	C₂³	1	1	yes	characteristic
270	C₂×Q₁₆×C₄₇	C₂³	1	1	yes	characteristic
271	C₂×SD₁₆×C₄₇	C₂³	1	2	yes	—
272	C₂×D₈×C₄₇	C₂³	1	1	yes	characteristic
273	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
274	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
275	#126×C₄₇	—	2	2	no	—
276	#125×C₄₇	C₂³	1	2	yes	—
277	#124×C₄₇	C₂³	1	2	yes	—
278	#123×C₄₇	—	2	2	no	—
279	C₂²⋊Q₈×C₄₇	C₂³	1	2	yes	—
280	#121×C₄₇	C₂³	1	2	yes	—
281	C₄×Q₈×C₄₇	C₂³	1	2	yes	—
282	C₄×D₄×C₄₇	—	2	2	no	—
283	C₄×D₄×C₄₇	C₂³	1	2	yes	—
284	#117×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	#106×C₄₇	C₂³	1	2	yes	—
289	#103×C₄₇	C₂³	1	2	yes	—
290	#103×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	C₂³×D₄₇	—	2	2	no	—
298	C₂³×D₄₇	—	2	2	no	—
299	C₂×Q₈×C₄₇	C₂⁴	1	2	yes	—
300	C₂×D₄×C₄₇	—	2	2	no	—
301	C₂×D₄×C₄₇	C₂⁴	1	2	yes	—
302	C₂²×C₄×C₄₇	—	2	2	no	—
303	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
304	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
305	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
306	C₂×C₂²⋊D₄₇	—	2	2	no	—
307	C₂×C₂²⋊D₄₇	—	2	2	no	—
308	C₂×C₂²⋊D₄₇	—	2	2	no	—
309	C₂×C₂²⋊D₄₇	—	2	2	no	—
310	C₂×C₂²⋊D₄₇	C₂×D₄	1	1	yes	characteristic
311	C₂×C₂²⋊D₄₇	C₂×D₄	1	1	yes	characteristic
312	C₂²×Dic₄₇	—	2	2	no	—
313	C₂²×Dic₄₇	—	2	2	no	—
314	#10625354	—	2	4	no	—
315	#10625354	—	4	2	no	—
316	D₄×D₄₇	—	2	4	no	—
317	D₄×D₄₇	—	4	2	no	—
318	D₄×D₄₇	—	4	8	no	—
319	#10625350	—	2	4	no	—
320	#10625350	—	8	4	no	—
321	C₂×D₁₈₈	—	2	4	no	—
322	C₂×D₁₈₈	—	2	2	no	—
323	C₂×D₁₈₈	—	2	2	no	—
324	C₂×D₁₈₈	—	2	2	no	—
325	C₂×D₁₈₈	—	2	2	no	—
326	C₂×D₁₈₈	—	4	2	no	—
327	C₂×D₁₈₈	C₂×D₄	1	1	yes	characteristic
328	C₂×D₁₈₈	C₂⁴	1	2	yes	—
329	C₂×D₁₈₈	C₂⁴	1	2	yes	—
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	—	2	2	no	—
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	—	8	4	no	—
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	C₂×D₄	1	1	yes	characteristic
344	C₂×C₄×D₄₇	C₂⁴	1	1	yes	characteristic
345	C₂×C₄×D₄₇	C₂⁴	1	1	yes	characteristic
346	C₂×Dic₉₄	—	2	2	no	—
347	C₂×Dic₉₄	C₂×D₄	1	1	yes	characteristic
348	Q₁₆×C₄₇	—	2	2	no	—
349	SD₁₆×C₄₇	—	4	2	no	—
350	D₈×C₄₇	—	2	2	no	—
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	—	2	2	no	—
359	C₄⋊C₄×C₄₇	—	2	2	no	—
360	C₄⋊C₄×C₄₇	—	2	2	no	—
361	C₄⋊C₄×C₄₇	C₂⁴	1	2	yes	—
362	C₄⋊C₄×C₄₇	C₂⁴	1	2	yes	—
363	C₂²⋊C₄×C₄₇	—	2	2	no	—
364	C₂²⋊C₄×C₄₇	—	2	2	no	—
365	C₂²⋊C₄×C₄₇	—	2	2	no	—
366	C₂²⋊C₄×C₄₇	—	2	2	no	—
367	C₂²⋊C₄×C₄₇	—	2	2	no	—
368	C₄²×C₄₇	—	2	2	no	—
369	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
370	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
371	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
372	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
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	#10625336	—	2	4	no	—
378	#10625336	—	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	—	2	2	no	—
390	(C₂×D₄₇)⋊C₄	—	2	2	no	—
391	(C₂×D₄₇)⋊C₄	—	2	2	no	—
392	(C₂×D₄₇)⋊C₄	—	2	2	no	—
393	(C₂×D₄₇)⋊C₄	C₂×D₄	1	1	yes	characteristic
394	(C₂×D₄₇)⋊C₄	C₂×D₄	1	1	yes	characteristic
395	(C₂×D₄₇)⋊C₄	C₂×D₄	1	1	yes	characteristic
396	(C₂×D₄₇)⋊C₄	C₂×D₄	1	1	yes	characteristic
397	C₄⋊Dic₄₇	—	2	2	no	—
398	C₄⋊Dic₄₇	—	2	2	no	—
399	C₄⋊Dic₄₇	—	2	2	no	—
400	C₄⋊Dic₄₇	C₂×D₄	1	1	yes	characteristic
401	C₄⋊Dic₄₇	C₂×D₄	1	1	yes	characteristic
402	C₄⋊Dic₄₇	C₂⁴	1	2	yes	—
403	C₄⋊Dic₄₇	C₂⁴	1	2	yes	—
404	Dic₄₇⋊C₄	—	2	2	no	—
405	Dic₄₇⋊C₄	—	2	2	no	—
406	Dic₄₇⋊C₄	—	2	2	no	—
407	Dic₄₇⋊C₄	—	2	2	no	—
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	Dic₄₇⋊C₄	C₂×D₄	1	1	yes	characteristic
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	D₃₇₆	—	2	4	no	—
425	D₃₇₆	—	2	2	no	—
426	D₃₇₆	#41	1	4	yes	complemented
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	C₂²×D₄	1	1	yes	characteristic
433	C₂²×D₄₇	—	2	2	no	—
434	C₂²×D₄₇	—	2	2	no	—
435	C₂²×D₄₇	—	4	4	no	—
436	C₂²×D₄₇	—	4	4	no	—
437	C₂²×D₄₇	—	4	4	no	—
438	C₂²×D₄₇	—	4	4	no	—
439	C₂²×D₄₇	—	8	2	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	Q₈×C₄₇	—	2	2	no	—
444	Q₈×C₄₇	—	2	2	no	—
445	D₄×C₄₇	—	2	2	no	—
446	D₄×C₄₇	—	2	2	no	—
447	D₄×C₄₇	—	4	4	no	—
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	—	2	2	no	—
455	C₂×C₄×C₄₇	—	4	4	no	—
456	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
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	C₂²×D₄	1	1	yes	characteristic
461	C₂×C₄×C₄₇	C₂⁵	1	1	yes	characteristic
462	C₂²⋊D₄₇	—	2	2	no	—
463	C₂²⋊D₄₇	—	4	4	no	—
464	C₂²⋊D₄₇	—	4	4	no	—
465	C₂²⋊D₄₇	—	8	2	no	—
466	C₂²⋊D₄₇	—	8	2	no	—
467	C₂²⋊D₄₇	#135	1	4	yes	complemented
468	C₂×Dic₄₇	—	2	2	no	—
469	C₂×Dic₄₇	—	2	2	no	—
470	C₂×Dic₄₇	—	8	2	no	—
471	C₂×Dic₄₇	—	8	2	no	—
472	C₂×Dic₄₇	C₂²×D₄	1	1	yes	characteristic
473	C₂×Dic₄₇	C₂²×D₄	1	1	yes	characteristic
474	C₂×Dic₄₇	C₂²×D₄	1	1	yes	characteristic
475	C₂×Dic₄₇	C₂²×D₄	1	1	yes	characteristic
476	C₂×Dic₄₇	C₂²×D₄	1	1	yes	characteristic
477	C₂×Dic₄₇	C₂²×D₄	1	1	yes	characteristic
478	D₁₈₈	—	2	2	no	—
479	D₁₈₈	—	2	2	no	—
480	D₁₈₈	—	2	2	no	—
481	D₁₈₈	—	2	2	no	—
482	D₁₈₈	—	4	4	no	—
483	D₁₈₈	—	4	4	no	—
484	D₁₈₈	—	4	4	no	—
485	D₁₈₈	—	8	2	no	—
486	D₁₈₈	C₂×#41	1	4	yes	—
487	C₄×D₄₇	—	2	2	no	—
488	C₄×D₄₇	—	2	2	no	—
489	C₄×D₄₇	—	2	2	no	—
490	C₄×D₄₇	—	2	1	no	—
491	C₄×D₄₇	—	2	1	no	—
492	C₄×D₄₇	—	2	1	no	—
493	C₄×D₄₇	—	2	1	no	—
494	C₄×D₄₇	—	2	2	no	—
495	C₄×D₄₇	—	4	4	no	—
496	C₄×D₄₇	—	4	4	no	—
497	C₄×D₄₇	—	4	4	no	—
498	C₄×D₄₇	—	4	4	no	—
499	C₄×D₄₇	—	8	2	no	—
500	C₄×D₄₇	—	8	2	no	—
501	C₄×D₄₇	—	8	2	no	—
502	C₄×D₄₇	—	8	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	—	4	2	no	—
517	C₂²×C₄₇	—	4	2	no	—
518	C₂²×C₄₇	—	4	2	no	—
519	C₂²×C₄₇	C₂×#135	1	2	yes	—
520	C₂²×C₄₇	C₂³×D₄	1	1	yes	characteristic
521	C₂×D₄₇	—	2	1	no	—
522	C₂×D₄₇	—	2	1	no	—
523	C₂×D₄₇	—	2	1	no	—
524	C₂×D₄₇	—	2	4	no	—
525	C₂×D₄₇	—	2	1	no	—
526	C₂×D₄₇	—	2	1	no	—
527	C₂×D₄₇	—	4	2	no	—
528	C₂×D₄₇	—	4	2	no	—
529	C₂×D₄₇	—	4	2	no	—
530	C₂×D₄₇	—	4	2	no	—
531	C₂×D₄₇	—	4	2	no	—
532	C₂×D₄₇	—	8	8	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	—	4	2	no	—
542	C₄×C₄₇	#576	1	2	yes	—
543	C₄×C₄₇	C₂²×#41	1	1	yes	characteristic
544	C₄×C₄₇	#585	1	1	yes	characteristic
545	Dic₄₇	—	2	1	no	—
546	Dic₄₇	—	2	1	no	—
547	Dic₄₇	—	2	1	no	—
548	Dic₄₇	—	2	1	no	—
549	Dic₄₇	—	2	1	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	D₄₇	1	1	yes	characteristic, complemented
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	—	47	1	no	—
576	C₂×C₄₇	—	2	2	no	—
577	C₂×C₄₇	—	8	2	no	—
578	C₂×C₄₇	D₄×#41	1	1	yes	characteristic
579	C₂×C₄₇	C₂²×#135	1	1	yes	characteristic
580	C₂×C₄₇	C₂×#576	1	1	yes	characteristic
581	D₄₇	—	2	2	no	—
582	D₄₇	—	4	1	no	—
583	D₄₇	—	4	4	no	—
584	D₄₇	—	8	2	no	—
585	C₂×#135	—	47	1	no	—
586	C₂²×D₈	—	47	1	no	—
587	C₂²×D₈	—	47	1	no	—
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	—	94	2	no	—
603	#529	C₂×D₄₇	1	2	yes	complemented
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	—	47	2	no	—
610	C₂×C₄×D₄	—	94	2	no	—
611	#500	—	47	1	no	—
612	#499	—	47	1	no	—
613	#499	C₂×D₄₇	1	1	yes	characteristic, complemented
614	#495	—	47	1	no	—
615	#495	C₂×D₄₇	1	1	yes	characteristic, complemented
616	#493	—	47	1	no	—
617	#488	—	47	2	no	—
618	#488	C₂×D₄₇	1	2	yes	complemented
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	C₂×D₄₇	1	1	yes	characteristic, complemented
634	#466	—	47	1	no	—
635	#466	—	47	1	no	—
636	#466	—	47	1	no	—
637	#466	—	47	2	no	—
638	#466	C₂×D₄₇	1	1	yes	characteristic
639	#465	—	47	2	no	—
640	#465	C₂×D₄₇	1	2	yes	complemented
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	C₂×D₄₇	1	1	yes	characteristic, complemented
657	C₄×SD₁₆	—	47	2	no	—
658	C₄×SD₁₆	—	47	2	no	—
659	C₄×SD₁₆	—	47	2	no	—
660	C₄×SD₁₆	C₂×D₄₇	1	2	yes	complemented
661	C₄×D₈	—	47	1	no	—
662	C₄×D₈	—	47	2	no	—
663	C₄×D₈	—	47	2	no	—
664	C₄×D₈	—	47	1	no	—
665	C₄×D₈	—	47	1	no	—
666	C₄×D₈	—	47	2	no	—
667	C₄×D₈	—	47	1	no	—
668	C₄×D₈	—	47	2	no	—
669	C₄×D₈	—	47	2	no	—
670	C₄×D₈	—	47	1	no	—
671	C₄×D₈	—	47	1	no	—
672	C₄×D₈	—	47	1	no	—
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	—	47	1	no	—
686	#416	—	47	2	no	—
687	C₂×#102	—	47	2	no	—
688	C₂×#102	—	47	2	no	—
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	—	47	2	no	—
698	C₂²×D₄	—	94	2	no	—
699	C₂³×C₄	—	94	2	no	—
700	C₂³×C₄	—	94	2	no	—
701	#135	—	94	4	no	—
702	C₂×Q₁₆	C₂²×D₄₇	1	1	yes	characteristic
703	C₂×SD₁₆	—	47	2	no	—
704	C₂×SD₁₆	—	47	2	no	—
705	C₂×SD₁₆	C₂²×D₄₇	1	2	yes	—
706	C₂×D₈	—	47	2	no	—
707	C₂×D₈	—	47	2	no	—
708	C₂×D₈	—	47	1	no	—
709	C₂×D₈	—	47	2	no	—
710	C₂×D₈	—	47	1	no	—
711	C₂×D₈	—	94	4	no	—
712	C₂×D₈	—	94	4	no	—
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	—	2	2	no	—
723	#126	—	94	2	no	—
724	#126	—	94	2	no	—
725	#126	—	94	2	no	—
726	#125	—	47	2	no	—
727	#125	—	94	2	no	—
728	#125	C₂²×D₄₇	1	2	yes	—
729	#124	—	47	2	no	—
730	#124	—	94	2	no	—
731	#124	—	94	2	no	—
732	#124	C₂²×D₄₇	1	2	yes	—
733	#123	—	2	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	—	94	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	C₂²×D₄₇	1	2	yes	—
748	#121	—	47	2	no	—
749	#121	—	47	2	no	—
750	#121	—	47	2	no	—
751	#121	—	94	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	C₂²×D₄₇	1	2	yes	—
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	C₂²×D₄₇	1	2	yes	—
766	C₄×D₄	—	2	2	no	—
767	C₄×D₄	—	47	1	no	—
768	C₄×D₄	—	47	1	no	—
769	C₄×D₄	—	47	1	no	—
770	C₄×D₄	—	47	1	no	—
771	C₄×D₄	—	47	2	no	—
772	C₄×D₄	—	47	2	no	—
773	C₄×D₄	—	47	2	no	—
774	C₄×D₄	—	47	1	no	—
775	C₄×D₄	—	47	1	no	—
776	C₄×D₄	—	47	2	no	—
777	C₄×D₄	—	47	2	no	—
778	C₄×D₄	—	47	2	no	—
779	C₄×D₄	—	47	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	—	94	2	no	—
790	C₄×D₄	—	94	2	no	—
791	C₄×D₄	—	94	2	no	—
792	C₄×D₄	C₂²×D₄₇	1	2	yes	—
793	#117	—	2	2	no	—
794	#117	—	47	1	no	—
795	#117	—	47	1	no	—
796	#117	—	47	1	no	—
797	#117	—	47	2	no	—
798	#117	—	94	2	no	—
799	#117	—	94	2	no	—
800	C₂×C₄⋊C₄	—	47	2	no	—
801	C₂×C₄⋊C₄	—	47	2	no	—
802	C₂×C₄⋊C₄	—	94	2	no	—
803	C₂×C₂²⋊C₄	—	94	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	—	47	2	no	—
816	#107	C₂²×D₄₇	1	1	yes	characteristic
817	#107	C₂²×D₄₇	1	1	yes	characteristic
818	#106	—	47	2	no	—
819	#106	—	47	2	no	—
820	#106	C₂²×D₄₇	1	2	yes	—
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	C₂²×D₄₇	1	2	yes	—
830	#103	C₂²×D₄₇	1	2	yes	—
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	—	47	2	no	—
840	#102	—	47	2	no	—
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	—	94	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	—	94	2	no	—
867	C₂×Q₈	C₂³×D₄₇	1	2	yes	—
868	C₂×D₄	—	2	2	no	—
869	C₂×D₄	—	47	1	no	—
870	C₂×D₄	—	47	1	no	—
871	C₂×D₄	—	47	1	no	—
872	C₂×D₄	—	47	2	no	—
873	C₂×D₄	—	47	2	no	—
874	C₂×D₄	—	94	4	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	2	no	—
880	C₂×D₄	—	94	2	no	—
881	C₂×D₄	—	94	4	no	—
882	C₂×D₄	—	94	2	no	—
883	C₂×D₄	—	94	2	no	—
884	C₂×D₄	—	188	2	no	—
885	C₂×D₄	—	188	2	no	—
886	C₂×D₄	—	188	8	no	—
887	C₂×D₄	C₂³×D₄₇	1	2	yes	—
888	C₂²×C₄	—	2	2	no	—
889	C₂²×C₄	—	47	1	no	—
890	C₂²×C₄	—	47	1	no	—
891	C₂²×C₄	—	47	1	no	—
892	C₂²×C₄	—	47	1	no	—
893	C₂²×C₄	—	47	1	no	—
894	C₂²×C₄	—	47	1	no	—
895	C₂²×C₄	—	94	2	no	—
896	C₂²×C₄	—	94	2	no	—
897	C₂²×C₄	—	94	2	no	—
898	C₂²×C₄	—	94	2	no	—
899	C₂²×C₄	—	94	2	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	—	376	4	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	—	2	2	no	—
911	SD₁₆	—	4	2	no	—
912	SD₁₆	—	94	4	no	—
913	SD₁₆	—	188	2	no	—
914	D₈	—	2	2	no	—
915	D₈	—	47	4	no	—
916	D₈	—	94	4	no	—
917	D₈	—	94	4	no	—
918	D₈	—	94	2	no	—
919	D₈	—	188	2	no	—
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	—	2	2	no	—
936	C₄⋊C₄	—	2	2	no	—
937	C₄⋊C₄	—	2	2	no	—
938	C₄⋊C₄	—	47	1	no	—
939	C₄⋊C₄	—	47	1	no	—
940	C₄⋊C₄	—	47	1	no	—
941	C₄⋊C₄	—	47	1	no	—
942	C₄⋊C₄	—	47	1	no	—
943	C₄⋊C₄	—	47	1	no	—
944	C₄⋊C₄	—	47	2	no	—
945	C₄⋊C₄	—	47	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	—	2	2	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	—	47	1	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	—	2	2	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	—	47	1	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	—	47	1	no	—
995	C₂³	—	47	1	no	—
996	C₂³	—	94	2	no	—
997	C₂³	—	94	2	no	—
998	C₂³	—	376	2	no	—
999	C₂³	—	376	2	no	—
1000	C₂³	—	188	4	no	—
1001	C₂³	—	188	4	no	—
1002	C₂³	—	188	4	no	—
1003	C₂³	—	188	4	no	—
1004	C₂³	C₂×D₄×D₄₇	1	1	yes	characteristic
1005	Q₈	—	2	2	no	—
1006	Q₈	—	2	2	no	—
1007	Q₈	—	94	2	no	—
1008	Q₈	—	376	2	no	—
1009	D₄	—	2	2	no	—
1010	D₄	—	2	2	no	—
1011	D₄	—	4	4	no	—
1012	D₄	—	47	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	—	94	2	no	—
1019	D₄	—	376	2	no	—
1020	D₄	—	376	2	no	—
1021	D₄	—	376	2	no	—
1022	D₄	—	188	4	no	—
1023	D₄	—	188	4	no	—
1024	D₄	—	188	4	no	—
1025	D₄	—	188	4	no	—
1026	D₄	—	188	4	no	—
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	—	2	2	no	—
1034	C₂×C₄	—	4	4	no	—
1035	C₂×C₄	—	47	1	no	—
1036	C₂×C₄	—	47	1	no	—
1037	C₂×C₄	—	47	1	no	—
1038	C₂×C₄	—	47	1	no	—
1039	C₂×C₄	—	47	1	no	—
1040	C₂×C₄	—	47	1	no	—
1041	C₂×C₄	—	94	2	no	—
1042	C₂×C₄	—	94	2	no	—
1043	C₂×C₄	—	94	2	no	—
1044	C₂×C₄	—	94	2	no	—
1045	C₂×C₄	—	94	1	no	—
1046	C₂×C₄	—	94	1	no	—
1047	C₂×C₄	—	94	1	no	—
1048	C₂×C₄	—	94	1	no	—
1049	C₂×C₄	—	94	2	no	—
1050	C₂×C₄	—	94	2	no	—
1051	C₂×C₄	—	376	2	no	—
1052	C₂×C₄	—	376	2	no	—
1053	C₂×C₄	—	376	2	no	—
1054	C₂×C₄	—	376	2	no	—
1055	C₂×C₄	—	376	2	no	—
1056	C₂×C₄	—	376	2	no	—
1057	C₂×C₄	—	188	4	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	#41×D₄₇	1	2	yes	—
1075	C₂²	—	2	1	no	—
1076	C₂²	—	2	1	no	—
1077	C₂²	—	4	2	no	—
1078	C₂²	—	4	2	no	—
1079	C₂²	—	4	2	no	—
1080	C₂²	—	47	2	no	—
1081	C₂²	—	94	1	no	—
1082	C₂²	—	94	1	no	—
1083	C₂²	—	94	1	no	—
1084	C₂²	—	94	1	no	—
1085	C₂²	—	94	1	no	—
1086	C₂²	—	94	4	no	—
1087	C₂²	—	376	8	no	—
1088	C₂²	—	376	8	no	—
1089	C₂²	—	188	2	no	—
1090	C₂²	—	188	2	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	—	4	2	no	—
1103	C₄	—	47	2	no	—
1104	C₄	—	94	1	no	—
1105	C₄	—	94	1	no	—
1106	C₄	—	94	1	no	—
1107	C₄	—	94	1	no	—
1108	C₄	—	94	1	no	—
1109	C₄	—	188	2	no	—
1110	C₄	—	188	2	no	—
1111	C₄	#15689925	1	2	yes	—
1112	C₄	C₂×#41×D₄₇	1	1	yes	characteristic
1113	C₄	#15689959	1	1	yes	characteristic
1114	C₂	—	2	2	no	—
1115	C₂	—	8	2	no	—
1116	C₂	—	94	2	no	—
1117	C₂	—	376	2	no	—
1118	C₂	—	188	1	no	—
1119	C₂	—	188	4	no	—
1120	C₂	#20256874	1	1	yes	characteristic
1121	C₂	C₂×#135×D₄₇	1	1	yes	characteristic
1122	C₂	C₂×#15689925	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×#3168	C₂
socle	C₂²×C₄₇	C₂³×D₄
hypercenter	#3168	D₄₇
hypocenter	C₄₇	#61431
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #3168

Complements

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

N	H ≅ G/N	type
1. #20256994	C₂	semidirect
2. #20256397	C₂	semidirect
3. #20256252	C₂	semidirect
4. #20256045	C₂	semidirect
5. #20255793	C₂	semidirect
6. #20255789	C₂	semidirect
7. #20255777	C₂	semidirect
8. #20255244	C₂	semidirect
9. #20255237	C₂	semidirect
10. #20255207	C₂	semidirect
11. #20255072	C₂	semidirect
12. #20255070	C₂	semidirect
13. #20255062	C₂	semidirect
14. #20253964	C₂	semidirect
15. #20253961	C₂	semidirect
16. #20253446	C₂	semidirect
17. #20253439	C₂	semidirect
18. #20253431	C₂	semidirect
19. C₈×#10625350	C₂	semidirect
20. C₄×#13094047	C₂	semidirect
21. C₂×C₄×D₃₇₆	C₂	semidirect
22. C₄×D₈×D₄₇	C₂	semidirect
23. C₄₇×#3168	C₂	semidirect
27. #15689855	C₂²	semidirect
29. #15689829	C₂²	semidirect
30. #15689826	C₂²	semidirect
31. #15689825	C₂²	semidirect
35. #15689766	C₂²	semidirect
37. #15689764	C₂²	semidirect
39. #15689670	C₂²	semidirect
40. #15689660	C₂²	semidirect
44. C₄×#10625354	C₂²	semidirect
46. C₂×C₄×D₁₈₈	C₂²	semidirect
48. C₄×D₄×D₄₇	C₂²	semidirect
49. #15689527	C₂²	semidirect
50. #15689524	C₂²	semidirect
51. #15689508	C₂²	semidirect
53. #15689479	C₂²	semidirect
54. #15689468	C₂²	semidirect
55. #15689457	C₂²	semidirect
56. #15689456	C₂²	semidirect
57. #15689449	C₂²	semidirect
58. #15689445	C₂²	semidirect
59. #15689443	C₂²	semidirect
60. #15689439	C₂²	semidirect
61. #15689422	C₂²	semidirect
62. #15689421	C₂²	semidirect
63. #15689420	C₂²	semidirect
64. #15689420	C₂²	semidirect
65. #15689416	C₂²	semidirect
66. #15689412	C₂²	semidirect
67. #15689361	C₂²	semidirect
69. #15689360	C₂²	semidirect
70. #15689358	C₂²	semidirect
71. #15689356	C₂²	semidirect
72. #15689355	C₂²	semidirect
73. #15689341	C₂²	semidirect
74. #15689340	C₂²	semidirect
75. #15689335	C₂²	semidirect
76. #15689335	C₂²	semidirect
77. #15689321	C₂²	semidirect
79. #15689273	C₂²	semidirect
80. #15689272	C₂²	semidirect
81. #15689271	C₂²	semidirect
82. #15689267	C₂²	semidirect
85. C₈×Dic₉₄	C₂²	semidirect
86. C₈×Dic₉₄	C₂²	semidirect
87. Q₁₆×Dic₄₇	C₂²	semidirect
88. C₄×#10625336	C₂²	semidirect
89. C₄×#10625336	C₂²	semidirect
90. #15689208	C₂²	semidirect
93. C₄×D₃₇₆	C₂²	semidirect
94. C₄×D₃₇₆	C₂²	semidirect
95. C₄×D₃₇₆	C₂²	semidirect
96. C₄×D₃₇₆	C₂²	semidirect
97. D₈×Dic₄₇	C₂²	semidirect
100. C₄×#10625334	C₂²	semidirect
101. C₄×#10625334	C₂²	semidirect
102. #15689203	C₂²	semidirect
103. C₈×D₁₈₈	C₂²	semidirect
104. C₈×D₁₈₈	C₂²	semidirect
107. C₈×C₂²⋊D₄₇	C₂²	semidirect
108. C₈×C₂²⋊D₄₇	C₂²	semidirect
109. #15689176	C₂²	semidirect
110. #15689174	C₂²	semidirect
111. #15689174	C₂²	semidirect
112. #15689160	C₂²	semidirect
113. C₂×#13093958	C₂²	semidirect
114. #107×D₄₇	C₂²	semidirect
115. #15689118	C₂²	semidirect
116. C₂×#13093946	C₂²	semidirect
117. #102×D₄₇	C₂²	semidirect
118. C₄×C₈×D₄₇	C₂²	semidirect
119. C₄×C₈×D₄₇	C₂²	semidirect
120. C₄₇×#529	C₂²	semidirect
121. C₄₇×#499	C₂²	semidirect
122. C₄₇×#495	C₂²	semidirect
123. C₄₇×#488	C₂²	semidirect
124. C₄₇×#467	C₂²	semidirect
126. C₄₇×#465	C₂²	semidirect
127. C₄×Q₁₆×C₄₇	C₂²	semidirect
128. C₄×SD₁₆×C₄₇	C₂²	semidirect
129. C₄×D₈×C₄₇	C₂²	semidirect
130. C₂×C₄×C₈×C₄₇	C₂²	semidirect
426. D₃₇₆	#41	semidirect
467. C₂²⋊D₄₇	#135	semidirect
568. #3168	D₄₇	semidirect
603. #529	C₂×D₄₇	semidirect
613. #499	C₂×D₄₇	semidirect
615. #495	C₂×D₄₇	semidirect
618. #488	C₂×D₄₇	semidirect
633. #467	C₂×D₄₇	semidirect
640. #465	C₂×D₄₇	semidirect
656. C₄×Q₁₆	C₂×D₄₇	semidirect
660. C₄×SD₁₆	C₂×D₄₇	semidirect
673. C₄×D₈	C₂×D₄₇	semidirect
691. C₂×C₄×C₈	C₂×D₄₇	semidirect
692. C₄₇	#61431	semidirect

Maximal subgroups

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

subgroup	index
#20256994	2
#20256397	2
#20256252	2
#20256045	2
#20255793	2
#20255789	2
#20255777	2
#20255244	2
#20255237	2
#20255207	2
#20255072	2
#20255070	2
#20255062	2
#20253964	2
#20253961	2
#20253446	2
#20253439	2
#20253431	2
C₈×#10625350	2
C₄×#13094047	2
C₂×C₄×D₃₇₆	2
C₄×D₈×D₄₇	2
C₄₇×#3168	2
#61431	47