Subgroups — #27098888

Order 12032.

1882 conjugacy classes of subgroups.

The subgroup lattice has 1094 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20257427	C₂	1	2	yes	maximal, complemented
2	#20256376	C₂	1	1	yes	maximal, characteristic, complemented
3	D₈×Dic₉₄	C₂	1	1	yes	maximal, characteristic, complemented
4	#20256107	C₂	1	2	yes	maximal, complemented
5	#20255782	C₂	1	1	yes	maximal, characteristic, complemented
6	#20255778	C₂	1	1	yes	maximal, characteristic, complemented
7	#20255733	C₂	1	1	yes	maximal, characteristic, complemented
8	#20255689	C₂	1	2	yes	maximal, complemented
9	#20255474	C₂	1	2	yes	maximal, complemented
10	#20255470	C₂	1	2	yes	maximal, complemented
11	#20255104	C₂	1	1	yes	maximal, characteristic, complemented
12	#20255074	C₂	1	1	yes	maximal, characteristic, complemented
13	#20255067	C₂	1	1	yes	maximal, characteristic, complemented
14	#20254029	C₂	1	1	yes	maximal, characteristic, complemented
15	#20254027	C₂	1	1	yes	maximal, characteristic, complemented
16	#20253971	C₂	1	1	yes	maximal, characteristic, complemented
17	#20253654	C₂	1	2	yes	maximal, complemented
18	#20253650	C₂	1	2	yes	maximal, complemented
19	#20253485	C₂	1	2	yes	maximal, complemented
20	#20252359	C₂	1	1	yes	maximal, characteristic, complemented
21	#20252258	C₂	1	1	yes	maximal, characteristic, complemented
22	C₄×D₈×D₄₇	C₂	1	1	yes	maximal, characteristic, complemented
23	C₄₇×#2951	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	#15689845	C₂²	1	2	yes	complemented
27	#15689833	C₂²	1	2	yes	—
28	#15689828	C₂²	1	2	yes	—
29	#15689806	—	2	2	no	—
30	#15689802	—	2	2	no	—
31	#15689797	—	2	2	no	—
32	D₄×Dic₉₄	C₂²	1	2	yes	complemented
33	#15689782	—	2	2	no	—
34	#15689774	C₂²	1	2	yes	complemented
35	#15689772	C₂²	1	2	yes	complemented
36	#15689768	C₂²	1	2	yes	—
37	#15689761	C₂²	1	2	yes	—
38	#15689745	C₂²	1	2	yes	complemented
39	#15689744	C₂²	1	2	yes	complemented
40	#15689720	—	2	2	no	—
41	#15689715	—	2	2	no	—
42	#15689677	C₂²	1	2	yes	—
43	#15689651	C₂²	1	1	yes	characteristic
44	#15689632	—	2	2	no	—
45	C₂×#13094002	—	2	2	no	—
46	#15689602	C₂²	1	2	yes	complemented
47	C₄×D₄×D₄₇	C₂²	1	2	yes	—
48	#15689528	C₂²	1	1	yes	characteristic, complemented
49	#15689527	C₂²	1	1	yes	characteristic, complemented
50	#15689527	C₂²	1	1	yes	characteristic, complemented
51	#15689508	C₂²	1	1	yes	characteristic
52	#15689507	C₂²	1	1	yes	characteristic
53	#15689501	C₂²	1	1	yes	characteristic, complemented
54	#15689484	C₂²	1	2	yes	complemented
55	#15689483	C₂²	1	2	yes	complemented
56	#15689472	C₂²	1	2	yes	complemented
57	#15689460	C₂²	1	2	yes	—
58	#15689458	C₂²	1	2	yes	complemented
59	#15689457	C₂²	1	2	yes	—
60	#15689457	C₂²	1	2	yes	complemented
61	#15689438	C₂²	1	2	yes	complemented
62	#15689436	C₂²	1	2	yes	complemented
63	#15689418	C₂²	1	2	yes	complemented
64	#15689417	C₂²	1	2	yes	complemented
65	#15689403	C₂²	1	2	yes	complemented
66	#15689402	C₂²	1	2	yes	complemented
67	#15689401	C₂²	1	2	yes	complemented
68	#15689401	C₂²	1	2	yes	complemented
69	#15689372	C₂²	1	2	yes	complemented
70	#15689369	C₂²	1	2	yes	complemented
71	#15689365	C₂²	1	1	yes	characteristic
72	#15689364	C₂²	1	1	yes	characteristic, complemented
73	#15689363	C₂²	1	2	yes	—
74	#15689361	C₂²	1	1	yes	characteristic
75	#15689361	C₂²	1	1	yes	characteristic, complemented
76	#15689360	C₂²	1	1	yes	characteristic
77	#15689359	C₂²	1	1	yes	characteristic
78	#15689348	C₂²	1	2	yes	complemented
79	#15689345	C₂²	1	2	yes	complemented
80	#15689340	C₂²	1	2	yes	—
81	#15689338	C₂²	1	2	yes	—
82	#15689327	C₂²	1	2	yes	complemented
83	#15689326	C₂²	1	2	yes	complemented
84	#15689285	C₂²	1	2	yes	complemented
85	#15689282	C₂²	1	2	yes	complemented
86	#15689275	C₂²	1	2	yes	—
87	#15689272	C₂²	1	2	yes	—
88	#15689269	C₂²	1	2	yes	—
89	#15689268	C₂²	1	2	yes	—
90	#15689251	C₂²	1	1	yes	characteristic, complemented
91	C₈×Dic₉₄	C₂²	1	1	yes	characteristic, complemented
92	#15689225	C₂²	1	2	yes	complemented
93	#15689223	C₂²	1	2	yes	complemented
94	#15689221	C₂²	1	2	yes	complemented
95	#15689220	C₂²	1	2	yes	complemented
96	C₄×Dic₁₈₈	C₂²	1	1	yes	characteristic, complemented
97	#15689217	C₂²	1	1	yes	characteristic, complemented
98	C₄×#10625337	C₂²	1	2	yes	complemented
99	C₄×D₃₇₆	C₂²	1	1	yes	characteristic
100	D₈×Dic₄₇	C₂²	1	1	yes	characteristic
101	D₈×Dic₄₇	C₂²	1	1	yes	characteristic
102	#15689205	C₂²	1	1	yes	characteristic
103	C₄×#10625334	C₂²	1	2	yes	—
104	#15689203	C₂²	1	2	yes	—
105	#15689199	C₂²	1	1	yes	characteristic, complemented
106	#15689196	C₂²	1	1	yes	characteristic
107	#15689192	C₂²	1	1	yes	characteristic
108	C₈×D₁₈₈	C₂²	1	1	yes	characteristic
109	C₈×C₂²⋊D₄₇	C₂²	1	1	yes	characteristic
110	C₈×C₂²⋊D₄₇	C₂²	1	1	yes	characteristic, complemented
111	#15689185	C₂²	1	1	yes	characteristic, complemented
112	#15689184	C₂²	1	1	yes	characteristic, complemented
113	#15689178	C₂²	1	1	yes	characteristic
114	#107×D₄₇	C₂²	1	1	yes	characteristic
115	#107×D₄₇	C₂²	1	1	yes	characteristic, complemented
116	#15689121	C₂²	1	2	yes	complemented
117	#102×D₄₇	C₂²	1	2	yes	—
118	#15689077	C₂²	1	1	yes	characteristic, complemented
119	C₄×C₈×D₄₇	C₂²	1	1	yes	characteristic
120	C₂×#135×C₄₇	C₂²	1	1	yes	characteristic
121	C₄₇×#520	C₂²	1	2	yes	complemented
122	C₄₇×#440	C₂²	1	2	yes	complemented
123	C₄₇×#440	C₂²	1	2	yes	complemented
124	C₄×Q₁₆×C₄₇	C₂²	1	1	yes	characteristic, complemented
125	C₄×Q₁₆×C₄₇	C₂²	1	1	yes	characteristic, complemented
126	C₄×D₈×C₄₇	C₂²	1	1	yes	characteristic
127	C₄×D₈×C₄₇	C₂²	1	1	yes	characteristic
128	C₂×#107×C₄₇	C₂²	1	1	yes	characteristic, complemented
129	C₄₇×#417	C₂²	1	2	yes	complemented
130	C₄₇×#405	C₂²	1	1	yes	characteristic, complemented
131	C₂×#10625350	—	2	2	no	—
132	C₂×#10625352	C₂³	1	2	yes	—
133	C₂²×Dic₉₄	—	2	2	no	—
134	C₂×D₄×D₄₇	C₂³	1	2	yes	—
135	C₂²×C₄×D₄₇	—	2	2	no	—
136	#13094043	—	2	4	no	—
137	C₂×Dic₁₈₈	C₂³	1	1	yes	characteristic
138	C₂×#10625337	C₂³	1	2	yes	—
139	C₂×#10625325	C₂³	1	2	yes	—
140	C₂×#10625335	C₂³	1	2	yes	—
141	C₂×#10625336	C₂³	1	2	yes	—
142	C₂×D₃₇₆	C₂³	1	1	yes	characteristic
143	C₂×#10625334	C₂³	1	2	yes	—
144	D₈×D₄₇	—	2	4	no	—
145	C₂×#10625324	C₂³	1	1	yes	characteristic
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	#13094024	C₂³	1	2	yes	—
150	#13094023	C₂³	1	2	yes	—
151	#13094023	C₂³	1	2	yes	—
152	#13094022	C₂³	1	2	yes	—
153	#13094019	—	2	2	no	—
154	#13094019	—	2	2	no	—
155	#13094019	D₄	1	1	yes	characteristic
156	#13094018	—	2	2	no	—
157	#13094018	—	2	2	no	—
158	#13094017	D₄	1	1	yes	characteristic
159	#13094016	—	2	2	no	—
160	#13094014	—	2	2	no	—
161	#13094014	—	2	2	no	—
162	#13094014	D₄	1	1	yes	characteristic
163	#13094013	C₂³	1	2	yes	—
164	#13094012	—	2	2	no	—
165	#13094012	C₂³	1	2	yes	—
166	#13094010	—	2	2	no	—
167	#13094010	D₄	1	1	yes	characteristic
168	#13094009	—	2	2	no	—
169	#13094009	—	2	2	no	—
170	#13094009	D₄	1	1	yes	characteristic
171	#13094008	—	2	2	no	—
172	#13094007	—	2	2	no	—
173	#13094007	—	2	2	no	—
174	#13094007	—	2	2	no	—
175	#13094006	—	2	2	no	—
176	#13094006	D₄	1	1	yes	characteristic
177	#13094005	—	2	2	no	—
178	#13094004	C₂³	1	2	yes	—
179	#13094003	—	2	2	no	—
180	#13094003	—	2	2	no	—
181	#13094003	C₂³	1	2	yes	—
182	#13094002	—	2	2	no	—
183	#13094002	—	2	2	no	—
184	#13094002	—	2	2	no	—
185	#13094002	—	2	2	no	—
186	#13094002	—	2	2	no	—
187	#13094002	—	2	2	no	—
188	#13094002	—	2	2	no	—
189	#13094002	—	2	2	no	—
190	#13094002	D₄	1	1	yes	characteristic
191	#13094001	—	2	2	no	—
192	#13094001	—	2	2	no	—
193	#13094000	C₂³	1	2	yes	—
194	#13094000	C₂³	1	2	yes	—
195	#13093999	C₂³	1	2	yes	—
196	#13093998	—	2	2	no	—
197	#13093998	C₂³	1	2	yes	—
198	#13093997	D₄	1	1	yes	characteristic
199	#13093996	—	2	2	no	—
200	#13093996	—	2	2	no	—
201	#13093994	—	2	2	no	—
202	#13093992	—	2	2	no	—
203	C₄×Dic₉₄	—	2	2	no	—
204	C₄×Dic₉₄	C₂³	1	2	yes	—
205	C₄×Dic₉₄	C₂³	1	1	yes	characteristic
206	#13093989	C₂³	1	2	yes	—
207	C₄×D₁₈₈	—	2	2	no	—
208	C₄×D₁₈₈	C₂³	1	1	yes	characteristic
209	C₄×D₁₈₈	C₂³	1	2	yes	—
210	D₄×Dic₄₇	C₂³	1	2	yes	—
211	D₄×Dic₄₇	C₂³	1	2	yes	—
212	#13093986	C₂³	1	2	yes	—
213	C₄×C₂²⋊D₄₇	—	2	2	no	—
214	C₄×C₂²⋊D₄₇	—	2	2	no	—
215	C₄×C₂²⋊D₄₇	—	2	2	no	—
216	C₄×C₂²⋊D₄₇	C₂³	1	1	yes	characteristic
217	C₄×C₂²⋊D₄₇	C₂³	1	1	yes	characteristic
218	(C₂²⋊D₄₇)⋊C₄	—	2	2	no	—
219	(C₂²⋊D₄₇)⋊C₄	—	2	2	no	—
220	#13093981	—	2	2	no	—
221	#13093981	—	2	2	no	—
222	#13093981	C₂³	1	1	yes	characteristic
223	#13093980	—	2	2	no	—
224	C₂×Dic₄₇⋊C₄	—	2	2	no	—
225	C₂×Dic₄₇⋊C₄	—	2	2	no	—
226	C₄⋊C₄×D₄₇	C₂³	1	2	yes	—
227	C₄⋊C₄×D₄₇	C₂³	1	2	yes	—
228	C₂×(C₂×D₄₇)⋊C₄	—	2	2	no	—
229	C₂×(C₂×D₄₇)⋊C₄	—	2	2	no	—
230	C₂²⋊C₄×D₄₇	—	2	2	no	—
231	C₄²×D₄₇	C₂³	1	1	yes	characteristic
232	#13093958	C₂³	1	1	yes	characteristic
233	#13093958	C₂³	1	2	yes	—
234	#13093958	C₂³	1	1	yes	characteristic
235	#13093957	C₂³	1	2	yes	—
236	#13093957	C₂³	1	2	yes	—
237	#13093957	C₂³	1	2	yes	—
238	#13093957	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	#13093948	C₂³	1	2	yes	—
248	#13093948	C₂³	1	2	yes	—
249	#13093947	C₂³	1	2	yes	—
250	#13093947	C₂³	1	2	yes	—
251	#13093946	C₂³	1	2	yes	—
252	#13093946	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	#13093935	C₂³	1	1	yes	characteristic
264	#13093934	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	C₂×#41×C₄₇	C₂³	1	2	yes	—
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	C₂×M₁₆×C₄₇	C₂³	1	1	yes	characteristic
275	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
276	C₄×Q₈×C₄₇	C₂³	1	2	yes	—
277	C₄×Q₈×C₄₇	C₂³	1	2	yes	—
278	C₄×D₄×C₄₇	—	2	2	no	—
279	C₄×D₄×C₄₇	—	2	2	no	—
280	C₄×D₄×C₄₇	C₂³	1	2	yes	—
281	C₄×D₄×C₄₇	C₂³	1	2	yes	—
282	#117×C₄₇	—	2	2	no	—
283	#117×C₄₇	C₂³	1	1	yes	characteristic
284	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
285	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
286	#107×C₄₇	C₂³	1	1	yes	characteristic
287	#107×C₄₇	C₂³	1	1	yes	characteristic
288	#107×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	#97×C₄₇	C₂³	1	1	yes	characteristic
294	#97×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	#41×C₄₇	—	2	4	no	—
299	#41×C₄₇	—	4	2	no	—
300	C₂×Q₈×C₄₇	C₂⁴	1	2	yes	—
301	C₂×D₄×C₄₇	—	2	2	no	—
302	C₂×D₄×C₄₇	C₂⁴	1	2	yes	—
303	C₂²×C₄×C₄₇	—	2	2	no	—
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	C₂⁴	1	1	yes	characteristic
308	C₂×C₂²⋊D₄₇	—	2	2	no	—
309	C₂×C₂²⋊D₄₇	—	2	2	no	—
310	C₂×C₂²⋊D₄₇	—	2	2	no	—
311	C₂×C₂²⋊D₄₇	C₂×D₄	1	1	yes	characteristic
312	C₂×C₂²⋊D₄₇	C₂×D₄	1	1	yes	characteristic
313	C₂²×Dic₄₇	—	2	2	no	—
314	C₂²×Dic₄₇	—	2	2	no	—
315	C₂²×Dic₄₇	—	2	2	no	—
316	#10625352	—	2	4	no	—
317	#10625352	—	4	2	no	—
318	D₄×D₄₇	—	2	4	no	—
319	D₄×D₄₇	—	4	2	no	—
320	#10625350	—	8	4	no	—
321	C₂×D₁₈₈	—	2	2	no	—
322	C₂×D₁₈₈	C₂×D₄	1	1	yes	characteristic
323	C₂×D₁₈₈	C₂⁴	1	2	yes	—
324	C₂×C₄×D₄₇	—	2	2	no	—
325	C₂×C₄×D₄₇	—	2	2	no	—
326	C₂×C₄×D₄₇	—	2	2	no	—
327	C₂×C₄×D₄₇	—	2	2	no	—
328	C₂×C₄×D₄₇	—	8	4	no	—
329	C₂×C₄×D₄₇	C₂×D₄	1	1	yes	characteristic
330	C₂×C₄×D₄₇	C₂×D₄	1	1	yes	characteristic
331	C₂×C₄×D₄₇	C₂⁴	1	1	yes	characteristic
332	C₂×C₄×D₄₇	C₂⁴	1	1	yes	characteristic
333	C₂×Dic₉₄	—	2	2	no	—
334	C₂×Dic₉₄	—	2	2	no	—
335	C₂×Dic₉₄	—	2	2	no	—
336	C₂×Dic₉₄	—	8	4	no	—
337	C₂×Dic₉₄	C₂×D₄	1	1	yes	characteristic
338	C₂×Dic₉₄	C₂⁴	1	2	yes	—
339	Q₁₆×C₄₇	—	2	2	no	—
340	SD₁₆×C₄₇	—	2	4	no	—
341	D₈×C₄₇	#41	1	4	yes	complemented
342	M₁₆×C₄₇	—	4	1	no	—
343	C₂×C₈×C₄₇	—	2	2	no	—
344	C₂×C₈×C₄₇	C₂⁴	1	1	yes	characteristic
345	C₂×C₈×C₄₇	C₂⁴	1	1	yes	characteristic
346	C₂×C₈×C₄₇	C₂⁴	1	1	yes	characteristic
347	C₂×C₈×C₄₇	C₂⁴	1	1	yes	characteristic
348	C₄⋊C₄×C₄₇	—	2	2	no	—
349	C₄⋊C₄×C₄₇	—	2	2	no	—
350	C₄⋊C₄×C₄₇	—	2	2	no	—
351	C₄⋊C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
352	C₄⋊C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
353	C₄⋊C₄×C₄₇	C₂⁴	1	2	yes	—
354	C₄⋊C₄×C₄₇	C₂⁴	1	2	yes	—
355	C₂²⋊C₄×C₄₇	—	2	2	no	—
356	C₂²⋊C₄×C₄₇	—	2	2	no	—
357	C₂²⋊C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
358	C₂²⋊C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
359	C₄²×C₄₇	—	2	2	no	—
360	C₄²×C₄₇	—	2	2	no	—
361	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
362	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
363	C₂²⋊Dic₄₇	—	2	2	no	—
364	C₂²⋊Dic₄₇	—	2	2	no	—
365	C₂²⋊Dic₄₇	—	2	2	no	—
366	C₂²⋊Dic₄₇	C₂×D₄	1	1	yes	characteristic
367	C₂²⋊Dic₄₇	C₂×D₄	1	1	yes	characteristic
368	#10625337	—	4	2	no	—
369	#10625336	—	4	2	no	—
370	#10625335	—	2	4	no	—
371	#10625334	—	2	4	no	—
372	(C₂×D₄₇)⋊C₄	—	2	2	no	—
373	(C₂×D₄₇)⋊C₄	—	2	2	no	—
374	(C₂×D₄₇)⋊C₄	—	2	2	no	—
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	—	2	2	no	—
380	(C₂×D₄₇)⋊C₄	—	2	2	no	—
381	(C₂×D₄₇)⋊C₄	—	2	2	no	—
382	(C₂×D₄₇)⋊C₄	—	2	2	no	—
383	(C₂×D₄₇)⋊C₄	C₂×D₄	1	1	yes	characteristic
384	(C₂×D₄₇)⋊C₄	C₂×D₄	1	1	yes	characteristic
385	(C₂×D₄₇)⋊C₄	C₂×D₄	1	1	yes	characteristic
386	(C₂×D₄₇)⋊C₄	C₂×D₄	1	1	yes	characteristic
387	(C₂×D₄₇)⋊C₄	C₂×D₄	1	1	yes	characteristic
388	(C₂×D₄₇)⋊C₄	C₂×D₄	1	1	yes	characteristic
389	C₄⋊Dic₄₇	—	2	2	no	—
390	C₄⋊Dic₄₇	—	2	2	no	—
391	C₄⋊Dic₄₇	C₂×D₄	1	1	yes	characteristic
392	C₄⋊Dic₄₇	C₂×D₄	1	1	yes	characteristic
393	C₄⋊Dic₄₇	C₂⁴	1	2	yes	—
394	C₄⋊Dic₄₇	C₂⁴	1	2	yes	—
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	—	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	C₂×D₄	1	1	yes	characteristic
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	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	C₂⁴	1	1	yes	characteristic
417	C₄×Dic₄₇	C₂⁴	1	1	yes	characteristic
418	C₂×C₄₇⋊C₈	C₂⁴	1	1	yes	characteristic
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	Dic₁₈₈	—	2	2	no	—
423	D₃₇₆	—	2	2	no	—
424	#10625325	—	4	2	no	—
425	#10625324	—	4	1	no	—
426	C₈×D₄₇	—	2	2	no	—
427	C₈×D₄₇	—	2	2	no	—
428	C₈×D₄₇	—	4	1	no	—
429	C₂³×C₄₇	—	2	2	no	—
430	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
431	C₂²×D₄₇	—	2	2	no	—
432	C₂²×D₄₇	—	4	4	no	—
433	C₂²×D₄₇	—	4	4	no	—
434	C₂²×D₄₇	—	8	2	no	—
435	C₂²×D₄₇	C₂²×D₄	1	1	yes	characteristic
436	C₂²×D₄₇	C₂²×D₄	1	1	yes	characteristic
437	Q₈×C₄₇	—	2	2	no	—
438	Q₈×C₄₇	—	2	2	no	—
439	D₄×C₄₇	—	2	2	no	—
440	D₄×C₄₇	—	4	4	no	—
441	D₄×C₄₇	C₂×#41	1	4	yes	—
442	C₂×C₄×C₄₇	—	2	1	no	—
443	C₂×C₄×C₄₇	—	2	1	no	—
444	C₂×C₄×C₄₇	—	2	2	no	—
445	C₂×C₄×C₄₇	—	2	2	no	—
446	C₂×C₄×C₄₇	—	2	2	no	—
447	C₂×C₄×C₄₇	—	4	4	no	—
448	C₂×C₄×C₄₇	—	8	2	no	—
449	C₂×C₄×C₄₇	—	8	2	no	—
450	C₂×C₄×C₄₇	—	8	2	no	—
451	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
452	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
453	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
454	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
455	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
456	C₂×C₄×C₄₇	C₂⁵	1	1	yes	characteristic
457	C₂²⋊D₄₇	—	2	2	no	—
458	C₂²⋊D₄₇	—	2	2	no	—
459	C₂²⋊D₄₇	—	4	4	no	—
460	C₂²⋊D₄₇	—	4	4	no	—
461	C₂²⋊D₄₇	—	8	2	no	—
462	C₂×Dic₄₇	—	2	2	no	—
463	C₂×Dic₄₇	—	2	2	no	—
464	C₂×Dic₄₇	—	2	2	no	—
465	C₂×Dic₄₇	—	4	4	no	—
466	C₂×Dic₄₇	—	4	4	no	—
467	C₂×Dic₄₇	—	8	2	no	—
468	C₂×Dic₄₇	C₂²×D₄	1	1	yes	characteristic
469	C₂×Dic₄₇	C₂²×D₄	1	1	yes	characteristic
470	C₂×Dic₄₇	C₂²×D₄	1	1	yes	characteristic
471	C₂×Dic₄₇	C₂²×D₄	1	1	yes	characteristic
472	C₂×Dic₄₇	C₂²×D₄	1	1	yes	characteristic
473	C₂×Dic₄₇	C₂²×D₄	1	1	yes	characteristic
474	D₁₈₈	—	2	2	no	—
475	D₁₈₈	—	2	2	no	—
476	D₁₈₈	—	2	2	no	—
477	D₁₈₈	—	8	2	no	—
478	C₄×D₄₇	—	2	2	no	—
479	C₄×D₄₇	—	2	1	no	—
480	C₄×D₄₇	—	2	1	no	—
481	C₄×D₄₇	—	2	1	no	—
482	C₄×D₄₇	—	2	1	no	—
483	C₄×D₄₇	—	2	2	no	—
484	C₄×D₄₇	—	4	4	no	—
485	C₄×D₄₇	—	8	2	no	—
486	C₄×D₄₇	—	8	2	no	—
487	C₄×D₄₇	—	8	2	no	—
488	Dic₉₄	—	2	2	no	—
489	Dic₉₄	—	2	2	no	—
490	Dic₉₄	—	2	2	no	—
491	Dic₉₄	—	4	4	no	—
492	Dic₉₄	—	8	2	no	—
493	Dic₉₄	—	8	2	no	—
494	C₈×C₄₇	—	2	1	no	—
495	C₈×C₄₇	—	2	1	no	—
496	C₈×C₄₇	—	2	1	no	—
497	C₈×C₄₇	C₂×#41	1	2	yes	—
498	C₄₇⋊C₈	—	2	1	no	—
499	C₄₇⋊C₈	—	2	1	no	—
500	C₄₇⋊C₈	—	2	1	no	—
501	C₄₇⋊C₈	—	2	1	no	—
502	#61482	—	47	1	no	maximal, Sylow
503	C₂²×C₄₇	—	2	4	no	—
504	C₂²×C₄₇	—	2	1	no	—
505	C₂²×C₄₇	—	2	1	no	—
506	C₂²×C₄₇	—	2	1	no	—
507	C₂²×C₄₇	—	4	2	no	—
508	C₂²×C₄₇	—	4	2	no	—
509	C₂²×C₄₇	C₂³×D₄	1	1	yes	characteristic
510	C₂×D₄₇	—	2	1	no	—
511	C₂×D₄₇	—	2	1	no	—
512	C₂×D₄₇	—	2	1	no	—
513	C₂×D₄₇	—	2	1	no	—
514	C₂×D₄₇	—	2	1	no	—
515	C₂×D₄₇	—	4	2	no	—
516	C₂×D₄₇	—	4	2	no	—
517	C₂×D₄₇	—	4	2	no	—
518	C₂×D₄₇	—	8	8	no	—
519	C₂×D₄₇	#578	1	2	yes	—
520	C₄×C₄₇	—	2	1	no	—
521	C₄×C₄₇	—	2	1	no	—
522	C₄×C₄₇	—	2	1	no	—
523	C₄×C₄₇	—	2	1	no	—
524	C₄×C₄₇	—	2	1	no	—
525	C₄×C₄₇	—	4	2	no	—
526	C₄×C₄₇	—	4	2	no	—
527	C₄×C₄₇	—	4	2	no	—
528	C₄×C₄₇	C₂²×#41	1	1	yes	characteristic
529	C₄×C₄₇	#585	1	1	yes	characteristic
530	Dic₄₇	—	2	1	no	—
531	Dic₄₇	—	2	1	no	—
532	Dic₄₇	—	2	1	no	—
533	Dic₄₇	—	2	1	no	—
534	Dic₄₇	—	2	1	no	—
535	Dic₄₇	—	4	2	no	—
536	Dic₄₇	—	4	2	no	—
537	Dic₄₇	—	4	2	no	—
538	Dic₄₇	#576	1	2	yes	—
539	#3520	—	47	2	no	—
540	#3393	—	47	1	no	—
541	Q₈×D₈	—	47	1	no	—
542	#3367	—	47	2	no	—
543	#3338	—	47	1	no	—
544	#3338	—	47	1	no	—
545	#3334	—	47	1	no	—
546	#3330	—	47	2	no	—
547	#3314	—	47	2	no	—
548	#3314	—	47	2	no	—
549	#3283	—	47	1	no	—
550	#3280	—	47	1	no	—
551	#3280	—	47	1	no	—
552	#3175	—	47	1	no	—
553	#3175	—	47	1	no	—
554	#3170	—	47	1	no	—
555	#3124	—	47	2	no	—
556	#3124	—	47	2	no	—
557	#3110	—	47	2	no	—
558	#2966	—	47	1	no	—
559	#2951	—	47	1	no	—
560	#2951	D₄₇	1	1	yes	characteristic, complemented
561	C₂×C₄×D₈	—	47	1	no	—
562	C₂×C₄₇	—	4	4	no	—
563	C₂×C₄₇	—	4	1	no	—
564	C₂×C₄₇	D₄×#41	1	1	yes	characteristic
565	C₂×C₄₇	C₂×#576	1	1	yes	characteristic
566	C₂×C₄₇	C₂×#578	1	1	yes	characteristic
567	D₄₇	—	2	2	no	—
568	D₄₇	—	4	1	no	—
569	D₄₇	—	8	2	no	—
570	C₂×#135	—	47	1	no	—
571	C₂×#135	C₂×D₄₇	1	1	yes	characteristic
572	C₂²×D₈	—	47	1	no	—
573	#556	—	47	2	no	—
574	#554	—	47	2	no	—
575	#554	—	47	2	no	—
576	#552	—	94	2	no	—
577	#551	—	94	2	no	—
578	#551	—	94	2	no	—
579	D₄×Q₈	—	47	2	no	—
580	#548	—	94	2	no	—
581	#547	—	47	2	no	—
582	#547	—	47	2	no	—
583	#546	—	47	2	no	—
584	#546	—	47	2	no	—
585	#542	—	47	2	no	—
586	#542	—	47	2	no	—
587	#539	—	94	2	no	—
588	#539	—	94	2	no	—
589	#533	—	47	2	no	—
590	#529	—	47	1	no	—
591	#525	—	94	2	no	—
592	C₂×C₂²⋊Q₈	—	94	2	no	—
593	#520	—	47	2	no	—
594	#520	C₂×D₄₇	1	2	yes	complemented
595	C₂×C₄×D₄	—	47	2	no	—
596	#500	—	47	1	no	—
597	#500	—	47	1	no	—
598	#500	—	47	1	no	—
599	#495	—	47	1	no	—
600	#495	—	47	1	no	—
601	#494	—	47	1	no	—
602	#489	—	47	2	no	—
603	#489	—	47	2	no	—
604	#487	—	47	2	no	—
605	#484	—	47	2	no	—
606	#484	—	47	2	no	—
607	#484	—	47	2	no	—
608	#484	—	47	2	no	—
609	#480	—	47	2	no	—
610	#480	—	47	2	no	—
611	#477	—	47	2	no	—
612	#477	—	47	2	no	—
613	#474	—	47	2	no	—
614	#474	—	47	2	no	—
615	#474	—	47	2	no	—
616	#474	—	47	2	no	—
617	#468	—	47	2	no	—
618	#468	—	47	2	no	—
619	#467	—	47	1	no	—
620	#467	—	47	1	no	—
621	#467	—	47	1	no	—
622	#467	—	47	1	no	—
623	#467	—	47	2	no	—
624	#466	—	47	1	no	—
625	#466	—	47	1	no	—
626	#464	—	47	2	no	—
627	#464	—	47	2	no	—
628	#463	—	47	2	no	—
629	#463	—	47	2	no	—
630	#461	—	47	2	no	—
631	#461	—	47	2	no	—
632	#452	—	47	2	no	—
633	#452	—	47	2	no	—
634	#450	—	47	2	no	—
635	#450	—	47	2	no	—
636	#449	—	47	2	no	—
637	#449	—	47	2	no	—
638	#446	—	47	1	no	—
639	C₈×Q₈	—	47	1	no	—
640	#440	—	47	2	no	—
641	#440	—	47	2	no	—
642	#440	—	47	2	no	—
643	#440	—	47	2	no	—
644	#440	C₂×D₄₇	1	2	yes	complemented
645	#440	C₂×D₄₇	1	2	yes	complemented
646	C₄×Q₁₆	—	47	2	no	—
647	C₄×Q₁₆	—	47	1	no	—
648	C₄×Q₁₆	—	47	1	no	—
649	C₄×Q₁₆	C₂×D₄₇	1	1	yes	characteristic, complemented
650	C₄×Q₁₆	C₂×D₄₇	1	1	yes	characteristic, complemented
651	C₄×D₈	—	47	1	no	—
652	C₄×D₈	—	47	1	no	—
653	C₄×D₈	—	47	2	no	—
654	C₄×D₈	—	47	1	no	—
655	C₄×D₈	—	47	2	no	—
656	C₄×D₈	—	47	1	no	—
657	C₄×D₈	C₂×D₄₇	1	1	yes	characteristic
658	C₄×D₈	C₂×D₄₇	1	1	yes	characteristic
659	#436	—	47	1	no	—
660	#435	—	47	1	no	—
661	#435	—	47	1	no	—
662	C₈×D₄	—	47	1	no	—
663	C₈×D₄	—	47	1	no	—
664	C₈×D₄	—	47	1	no	—
665	#433	—	47	1	no	—
666	#433	—	47	1	no	—
667	#432	—	47	1	no	—
668	C₂×#107	—	47	1	no	—
669	C₂×#107	—	47	1	no	—
670	C₂×#107	C₂×D₄₇	1	1	yes	characteristic, complemented
671	#417	—	47	2	no	—
672	#417	C₂×D₄₇	1	2	yes	complemented
673	C₂×#102	—	47	2	no	—
674	#405	—	47	1	no	—
675	#405	C₂×D₄₇	1	1	yes	characteristic, complemented
676	C₂×C₄×C₈	—	47	1	no	—
677	C₄₇	#61482	1	1	yes	characteristic, complemented, Sylow
678	C₂×#41	—	47	2	no	—
679	C₂×#41	—	94	2	no	—
680	C₂×#41	C₂²×D₄₇	1	2	yes	—
681	C₂²×Q₈	—	94	2	no	—
682	C₂²×D₄	—	47	2	no	—
683	C₂³×C₄	—	94	2	no	—
684	#135	—	2	4	no	—
685	#135	—	94	4	no	—
686	C₂×Q₁₆	—	47	2	no	—
687	C₂×Q₁₆	—	47	1	no	—
688	C₂×Q₁₆	C₂²×D₄₇	1	1	yes	characteristic
689	C₂×SD₁₆	—	47	2	no	—
690	C₂×SD₁₆	—	47	2	no	—
691	C₂×SD₁₆	—	47	2	no	—
692	C₂×SD₁₆	C₂²×D₄₇	1	2	yes	—
693	C₂×D₈	—	47	2	no	—
694	C₂×D₈	—	47	1	no	—
695	C₂×D₈	—	94	4	no	—
696	C₂×D₈	C₂²×D₄₇	1	1	yes	characteristic
697	C₂×M₁₆	—	47	1	no	—
698	C₂×M₁₆	C₂²×D₄₇	1	1	yes	characteristic
699	C₂²×C₈	—	47	1	no	—
700	C₂²×C₈	—	47	1	no	—
701	C₂²×C₈	—	47	1	no	—
702	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
703	C₄⋊Q₈	—	47	2	no	—
704	C₄⋊Q₈	—	47	2	no	—
705	C₄⋊Q₈	—	47	2	no	—
706	C₄⋊Q₈	—	47	2	no	—
707	#126	—	47	1	no	—
708	#126	—	47	1	no	—
709	#126	—	94	2	no	—
710	#126	—	94	2	no	—
711	#126	—	94	2	no	—
712	#126	—	94	2	no	—
713	#125	—	47	1	no	—
714	#125	—	94	2	no	—
715	#125	—	94	2	no	—
716	#125	—	94	2	no	—
717	#124	—	47	1	no	—
718	#124	—	47	2	no	—
719	#124	—	47	2	no	—
720	#124	—	94	2	no	—
721	#124	—	94	2	no	—
722	#123	—	47	1	no	—
723	#123	—	47	1	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	#123	—	94	2	no	—
732	C₂²⋊Q₈	—	47	1	no	—
733	C₂²⋊Q₈	—	47	2	no	—
734	C₂²⋊Q₈	—	47	2	no	—
735	C₂²⋊Q₈	—	47	2	no	—
736	C₂²⋊Q₈	—	47	2	no	—
737	C₂²⋊Q₈	—	94	2	no	—
738	C₂²⋊Q₈	—	94	2	no	—
739	C₂²⋊Q₈	—	94	2	no	—
740	C₂²⋊Q₈	—	94	2	no	—
741	C₂²⋊Q₈	—	94	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	—	94	2	no	—
748	C₂²⋊Q₈	—	94	2	no	—
749	#121	—	47	1	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	#120	—	94	2	no	—
756	#120	—	94	2	no	—
757	C₄×Q₈	—	47	1	no	—
758	C₄×Q₈	—	47	2	no	—
759	C₄×Q₈	—	47	2	no	—
760	C₄×Q₈	—	94	2	no	—
761	C₄×Q₈	C₂²×D₄₇	1	2	yes	—
762	C₄×Q₈	C₂²×D₄₇	1	2	yes	—
763	C₄×D₄	—	2	2	no	—
764	C₄×D₄	—	2	2	no	—
765	C₄×D₄	—	47	1	no	—
766	C₄×D₄	—	47	1	no	—
767	C₄×D₄	—	47	2	no	—
768	C₄×D₄	—	47	2	no	—
769	C₄×D₄	—	47	2	no	—
770	C₄×D₄	—	47	1	no	—
771	C₄×D₄	—	47	2	no	—
772	C₄×D₄	—	94	2	no	—
773	C₄×D₄	—	94	2	no	—
774	C₄×D₄	—	94	2	no	—
775	C₄×D₄	—	94	2	no	—
776	C₄×D₄	—	94	2	no	—
777	C₄×D₄	—	94	2	no	—
778	C₄×D₄	C₂²×D₄₇	1	2	yes	—
779	C₄×D₄	C₂²×D₄₇	1	2	yes	—
780	#117	—	2	2	no	—
781	#117	—	47	1	no	—
782	#117	—	94	2	no	—
783	#117	—	94	2	no	—
784	#117	—	94	2	no	—
785	#117	C₂²×D₄₇	1	1	yes	characteristic
786	C₂×C₄⋊C₄	—	2	2	no	—
787	C₂×C₄⋊C₄	—	47	2	no	—
788	C₂×C₄⋊C₄	—	47	2	no	—
789	C₂×C₄⋊C₄	—	94	2	no	—
790	C₂×C₄⋊C₄	—	94	2	no	—
791	C₂×C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
792	C₂×C₂²⋊C₄	—	94	2	no	—
793	C₂×C₂²⋊C₄	—	94	2	no	—
794	C₂×C₂²⋊C₄	—	94	2	no	—
795	C₂×C₄²	—	47	1	no	—
796	#107	—	47	1	no	—
797	#107	—	47	1	no	—
798	#107	—	47	2	no	—
799	#107	—	47	2	no	—
800	#107	—	47	2	no	—
801	#107	—	47	2	no	—
802	#107	—	47	2	no	—
803	#107	C₂²×D₄₇	1	1	yes	characteristic
804	#107	C₂²×D₄₇	1	1	yes	characteristic
805	#107	C₂²×D₄₇	1	2	yes	—
806	C₄⋊C₈	—	47	1	no	—
807	C₄⋊C₈	—	47	1	no	—
808	C₄⋊C₈	—	47	1	no	—
809	C₄⋊C₈	—	47	1	no	—
810	C₄⋊C₈	—	47	1	no	—
811	C₄⋊C₈	—	47	1	no	—
812	#103	—	47	2	no	—
813	#103	—	47	2	no	—
814	#103	—	47	2	no	—
815	#103	—	47	2	no	—
816	#103	—	47	2	no	—
817	#103	—	47	2	no	—
818	#103	C₂²×D₄₇	1	2	yes	—
819	#103	C₂²×D₄₇	1	2	yes	—
820	#102	—	47	2	no	—
821	#102	—	47	2	no	—
822	#102	—	47	2	no	—
823	#102	—	47	2	no	—
824	#102	—	47	2	no	—
825	#102	—	47	2	no	—
826	#102	C₂²×D₄₇	1	2	yes	—
827	#102	C₂²×D₄₇	1	2	yes	—
828	C₂²⋊C₈	—	47	1	no	—
829	C₂²⋊C₈	—	47	1	no	—
830	C₂²⋊C₈	—	47	1	no	—
831	C₂²⋊C₈	—	47	1	no	—
832	C₂²⋊C₈	—	47	1	no	—
833	C₂²⋊C₈	—	47	1	no	—
834	#97	—	47	1	no	—
835	#97	—	47	1	no	—
836	#97	C₂²×D₄₇	1	1	yes	characteristic
837	#97	C₂²×D₄₇	1	1	yes	characteristic
838	C₄×C₈	—	47	1	no	—
839	C₄×C₈	—	47	1	no	—
840	C₄×C₈	—	47	1	no	—
841	C₄×C₈	—	47	1	no	—
842	C₄×C₈	C₂²×D₄₇	1	1	yes	characteristic
843	C₄×C₈	C₂²×D₄₇	1	1	yes	characteristic
844	C₂⁴	—	94	2	no	—
845	#41	—	2	4	no	—
846	#41	—	4	2	no	—
847	#41	—	94	4	no	—
848	#41	—	376	4	no	—
849	#41	—	188	2	no	—
850	C₂×Q₈	—	47	1	no	—
851	C₂×Q₈	—	47	2	no	—
852	C₂×Q₈	—	94	2	no	—
853	C₂×Q₈	—	94	2	no	—
854	C₂×Q₈	—	94	2	no	—
855	C₂×Q₈	—	376	4	no	—
856	C₂×Q₈	C₂³×D₄₇	1	2	yes	—
857	C₂×D₄	—	2	2	no	—
858	C₂×D₄	—	47	1	no	—
859	C₂×D₄	—	47	1	no	—
860	C₂×D₄	—	47	1	no	—
861	C₂×D₄	—	47	2	no	—
862	C₂×D₄	—	94	2	no	—
863	C₂×D₄	—	94	2	no	—
864	C₂×D₄	—	94	4	no	—
865	C₂×D₄	—	94	2	no	—
866	C₂×D₄	—	94	2	no	—
867	C₂×D₄	—	188	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	—	2	2	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	—	94	2	no	—
878	C₂²×C₄	—	94	2	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	—	376	4	no	—
885	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
886	Q₁₆	—	2	2	no	—
887	Q₁₆	—	94	2	no	—
888	Q₁₆	—	188	2	no	—
889	SD₁₆	—	2	4	no	—
890	SD₁₆	—	94	4	no	—
891	SD₁₆	—	188	2	no	—
892	SD₁₆	—	188	2	no	—
893	D₈	—	94	4	no	—
894	D₈	—	94	2	no	—
895	D₈	#10625350	1	4	yes	complemented
896	M₁₆	—	4	1	no	—
897	M₁₆	—	188	1	no	—
898	C₂×C₈	—	2	2	no	—
899	C₂×C₈	—	47	1	no	—
900	C₂×C₈	—	47	1	no	—
901	C₂×C₈	—	47	1	no	—
902	C₂×C₈	—	47	1	no	—
903	C₂×C₈	—	94	2	no	—
904	C₂×C₈	—	94	2	no	—
905	C₂×C₈	—	188	1	no	—
906	C₂×C₈	C₂³×D₄₇	1	1	yes	characteristic
907	C₂×C₈	C₂³×D₄₇	1	1	yes	characteristic
908	C₂×C₈	C₂³×D₄₇	1	1	yes	characteristic
909	C₂×C₈	C₂³×D₄₇	1	1	yes	characteristic
910	C₄⋊C₄	—	2	2	no	—
911	C₄⋊C₄	—	2	2	no	—
912	C₄⋊C₄	—	2	2	no	—
913	C₄⋊C₄	—	47	1	no	—
914	C₄⋊C₄	—	47	1	no	—
915	C₄⋊C₄	—	47	1	no	—
916	C₄⋊C₄	—	47	1	no	—
917	C₄⋊C₄	—	47	1	no	—
918	C₄⋊C₄	—	47	1	no	—
919	C₄⋊C₄	—	47	1	no	—
920	C₄⋊C₄	—	47	1	no	—
921	C₄⋊C₄	—	47	2	no	—
922	C₄⋊C₄	—	47	2	no	—
923	C₄⋊C₄	—	94	2	no	—
924	C₄⋊C₄	—	94	2	no	—
925	C₄⋊C₄	—	94	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	D₄×D₄₇	1	1	yes	characteristic
937	C₄⋊C₄	D₄×D₄₇	1	1	yes	characteristic
938	C₄⋊C₄	C₂³×D₄₇	1	2	yes	—
939	C₄⋊C₄	C₂³×D₄₇	1	2	yes	—
940	C₂²⋊C₄	—	2	2	no	—
941	C₂²⋊C₄	—	2	2	no	—
942	C₂²⋊C₄	—	47	1	no	—
943	C₂²⋊C₄	—	47	1	no	—
944	C₂²⋊C₄	—	47	1	no	—
945	C₂²⋊C₄	—	47	1	no	—
946	C₂²⋊C₄	—	47	1	no	—
947	C₂²⋊C₄	—	47	1	no	—
948	C₂²⋊C₄	—	47	1	no	—
949	C₂²⋊C₄	—	47	1	no	—
950	C₂²⋊C₄	—	94	2	no	—
951	C₂²⋊C₄	—	94	2	no	—
952	C₂²⋊C₄	—	94	2	no	—
953	C₂²⋊C₄	—	94	2	no	—
954	C₂²⋊C₄	—	94	2	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	D₄×D₄₇	1	1	yes	characteristic
965	C₂²⋊C₄	D₄×D₄₇	1	1	yes	characteristic
966	C₄²	—	2	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	C₂³×D₄₇	1	1	yes	characteristic
975	C₄²	C₂³×D₄₇	1	1	yes	characteristic
976	C₂³	—	2	2	no	—
977	C₂³	—	47	1	no	—
978	C₂³	—	47	1	no	—
979	C₂³	—	94	2	no	—
980	C₂³	—	376	2	no	—
981	C₂³	—	188	4	no	—
982	C₂³	—	188	4	no	—
983	C₂³	C₂×D₄×D₄₇	1	1	yes	characteristic
984	Q₈	—	2	2	no	—
985	Q₈	—	2	2	no	—
986	Q₈	—	94	2	no	—
987	Q₈	—	94	2	no	—
988	Q₈	—	94	2	no	—
989	Q₈	—	376	2	no	—
990	Q₈	—	376	2	no	—
991	Q₈	—	188	4	no	—
992	D₄	—	2	2	no	—
993	D₄	—	4	4	no	—
994	D₄	—	94	2	no	—
995	D₄	—	94	2	no	—
996	D₄	—	94	2	no	—
997	D₄	—	94	2	no	—
998	D₄	—	94	2	no	—
999	D₄	—	376	2	no	—
1000	D₄	—	376	2	no	—
1001	D₄	—	188	4	no	—
1002	D₄	—	188	4	no	—
1003	D₄	C₂×#10625350	1	4	yes	—
1004	C₂×C₄	—	2	1	no	—
1005	C₂×C₄	—	2	1	no	—
1006	C₂×C₄	—	2	2	no	—
1007	C₂×C₄	—	2	2	no	—
1008	C₂×C₄	—	2	2	no	—
1009	C₂×C₄	—	4	4	no	—
1010	C₂×C₄	—	8	2	no	—
1011	C₂×C₄	—	8	2	no	—
1012	C₂×C₄	—	8	2	no	—
1013	C₂×C₄	—	47	1	no	—
1014	C₂×C₄	—	47	1	no	—
1015	C₂×C₄	—	47	1	no	—
1016	C₂×C₄	—	47	1	no	—
1017	C₂×C₄	—	47	1	no	—
1018	C₂×C₄	—	47	1	no	—
1019	C₂×C₄	—	94	2	no	—
1020	C₂×C₄	—	94	2	no	—
1021	C₂×C₄	—	94	1	no	—
1022	C₂×C₄	—	94	1	no	—
1023	C₂×C₄	—	94	1	no	—
1024	C₂×C₄	—	94	1	no	—
1025	C₂×C₄	—	94	2	no	—
1026	C₂×C₄	—	94	2	no	—
1027	C₂×C₄	—	94	2	no	—
1028	C₂×C₄	—	376	2	no	—
1029	C₂×C₄	—	376	2	no	—
1030	C₂×C₄	—	376	2	no	—
1031	C₂×C₄	—	376	2	no	—
1032	C₂×C₄	—	188	4	no	—
1033	C₂×C₄	—	188	4	no	—
1034	C₂×C₄	—	188	4	no	—
1035	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
1036	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
1037	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
1038	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
1039	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
1040	C₂×C₄	C₂⁴×D₄₇	1	1	yes	characteristic
1041	C₈	—	2	1	no	—
1042	C₈	—	2	1	no	—
1043	C₈	—	2	1	no	—
1044	C₈	—	94	1	no	—
1045	C₈	—	94	1	no	—
1046	C₈	—	94	1	no	—
1047	C₈	—	94	1	no	—
1048	C₈	C₂×#10625350	1	2	yes	—
1049	C₂²	—	2	1	no	—
1050	C₂²	—	2	1	no	—
1051	C₂²	—	2	1	no	—
1052	C₂²	—	2	4	no	—
1053	C₂²	—	4	2	no	—
1054	C₂²	—	4	2	no	—
1055	C₂²	—	47	2	no	—
1056	C₂²	—	94	1	no	—
1057	C₂²	—	94	1	no	—
1058	C₂²	—	94	1	no	—
1059	C₂²	—	94	1	no	—
1060	C₂²	—	94	1	no	—
1061	C₂²	—	376	8	no	—
1062	C₂²	—	188	2	no	—
1063	C₂²	—	188	2	no	—
1064	C₂²	—	188	2	no	—
1065	C₂²	C₂²×D₄×D₄₇	1	1	yes	characteristic
1066	C₄	—	2	1	no	—
1067	C₄	—	2	1	no	—
1068	C₄	—	2	1	no	—
1069	C₄	—	2	1	no	—
1070	C₄	—	2	1	no	—
1071	C₄	—	4	2	no	—
1072	C₄	—	4	2	no	—
1073	C₄	—	4	2	no	—
1074	C₄	—	47	2	no	—
1075	C₄	—	94	1	no	—
1076	C₄	—	94	1	no	—
1077	C₄	—	94	1	no	—
1078	C₄	—	94	1	no	—
1079	C₄	—	94	1	no	—
1080	C₄	—	188	2	no	—
1081	C₄	—	188	2	no	—
1082	C₄	—	188	2	no	—
1083	C₄	C₂²×#10625350	1	1	yes	characteristic
1084	C₄	#15689959	1	1	yes	characteristic
1085	C₂	—	4	1	no	—
1086	C₂	—	4	4	no	—
1087	C₂	—	94	2	no	—
1088	C₂	—	376	2	no	—
1089	C₂	—	188	1	no	—
1090	C₂	D₄×#10625350	1	1	yes	characteristic
1091	C₂	#576×D₄₇	1	1	yes	characteristic
1092	C₂	#578×D₄₇	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂²×D₄×D₄₇
commutator, cosocle	C₂×C₄×C₄₇	C₂⁵
Frattini	C₂×C₄	C₂⁴×D₄₇
Fitting	C₄₇×#2951	C₂
socle	C₂²×C₄₇	C₂³×D₄
hypercenter	#2951	D₄₇
hypocenter	C₄₇	#61482
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ #117 ◁ #2951

Complements

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

N	H ≅ G/N	type
1. #20257427	C₂	semidirect
2. #20256376	C₂	semidirect
3. D₈×Dic₉₄	C₂	semidirect
4. #20256107	C₂	semidirect
5. #20255782	C₂	semidirect
6. #20255778	C₂	semidirect
7. #20255733	C₂	semidirect
8. #20255689	C₂	semidirect
9. #20255474	C₂	semidirect
10. #20255470	C₂	semidirect
11. #20255104	C₂	semidirect
12. #20255074	C₂	semidirect
13. #20255067	C₂	semidirect
14. #20254029	C₂	semidirect
15. #20254027	C₂	semidirect
16. #20253971	C₂	semidirect
17. #20253654	C₂	semidirect
18. #20253650	C₂	semidirect
19. #20253485	C₂	semidirect
20. #20252359	C₂	semidirect
21. #20252258	C₂	semidirect
22. C₄×D₈×D₄₇	C₂	semidirect
23. C₄₇×#2951	C₂	semidirect
26. #15689845	C₂²	semidirect
32. D₄×Dic₉₄	C₂²	semidirect
34. #15689774	C₂²	semidirect
35. #15689772	C₂²	semidirect
38. #15689745	C₂²	semidirect
39. #15689744	C₂²	semidirect
46. #15689602	C₂²	semidirect
48. #15689528	C₂²	semidirect
49. #15689527	C₂²	semidirect
50. #15689527	C₂²	semidirect
53. #15689501	C₂²	semidirect
54. #15689484	C₂²	semidirect
55. #15689483	C₂²	semidirect
56. #15689472	C₂²	semidirect
58. #15689458	C₂²	semidirect
60. #15689457	C₂²	semidirect
61. #15689438	C₂²	semidirect
62. #15689436	C₂²	semidirect
63. #15689418	C₂²	semidirect
64. #15689417	C₂²	semidirect
65. #15689403	C₂²	semidirect
66. #15689402	C₂²	semidirect
67. #15689401	C₂²	semidirect
68. #15689401	C₂²	semidirect
69. #15689372	C₂²	semidirect
70. #15689369	C₂²	semidirect
72. #15689364	C₂²	semidirect
75. #15689361	C₂²	semidirect
78. #15689348	C₂²	semidirect
79. #15689345	C₂²	semidirect
82. #15689327	C₂²	semidirect
83. #15689326	C₂²	semidirect
84. #15689285	C₂²	semidirect
85. #15689282	C₂²	semidirect
90. #15689251	C₂²	semidirect
91. C₈×Dic₉₄	C₂²	semidirect
92. #15689225	C₂²	semidirect
93. #15689223	C₂²	semidirect
94. #15689221	C₂²	semidirect
95. #15689220	C₂²	semidirect
96. C₄×Dic₁₈₈	C₂²	semidirect
97. #15689217	C₂²	semidirect
98. C₄×#10625337	C₂²	semidirect
105. #15689199	C₂²	semidirect
110. C₈×C₂²⋊D₄₇	C₂²	semidirect
111. #15689185	C₂²	semidirect
112. #15689184	C₂²	semidirect
115. #107×D₄₇	C₂²	semidirect
116. #15689121	C₂²	semidirect
118. #15689077	C₂²	semidirect
121. C₄₇×#520	C₂²	semidirect
122. C₄₇×#440	C₂²	semidirect
123. C₄₇×#440	C₂²	semidirect
124. C₄×Q₁₆×C₄₇	C₂²	semidirect
125. C₄×Q₁₆×C₄₇	C₂²	semidirect
128. C₂×#107×C₄₇	C₂²	semidirect
129. C₄₇×#417	C₂²	semidirect
130. C₄₇×#405	C₂²	semidirect
341. D₈×C₄₇	#41	semidirect
560. #2951	D₄₇	semidirect
594. #520	C₂×D₄₇	semidirect
644. #440	C₂×D₄₇	semidirect
645. #440	C₂×D₄₇	semidirect
649. C₄×Q₁₆	C₂×D₄₇	semidirect
650. C₄×Q₁₆	C₂×D₄₇	semidirect
670. C₂×#107	C₂×D₄₇	semidirect
672. #417	C₂×D₄₇	semidirect
675. #405	C₂×D₄₇	semidirect
677. C₄₇	#61482	semidirect
895. D₈	#10625350	semidirect

Maximal subgroups

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

subgroup	index
#20257427	2
#20256376	2
D₈×Dic₉₄	2
#20256107	2
#20255782	2
#20255778	2
#20255733	2
#20255689	2
#20255474	2
#20255470	2
#20255104	2
#20255074	2
#20255067	2
#20254029	2
#20254027	2
#20253971	2
#20253654	2
#20253650	2
#20253485	2
#20252359	2
#20252258	2
C₄×D₈×D₄₇	2
C₄₇×#2951	2
#61482	47