Subgroups — #27098989

Order 12032.

1800 conjugacy classes of subgroups.

The subgroup lattice has 1080 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20257456	C₂	1	2	yes	maximal, complemented
2	#20256376	C₂	1	1	yes	maximal, characteristic, complemented
3	#20256255	C₂	1	1	yes	maximal, characteristic, complemented
4	#20256211	C₂	1	2	yes	maximal, complemented
5	#20255816	C₂	1	1	yes	maximal, characteristic, complemented
6	#20255790	C₂	1	1	yes	maximal, characteristic, complemented
7	#20255758	C₂	1	1	yes	maximal, characteristic, complemented
8	#20255609	C₂	1	2	yes	maximal, complemented
9	#20255420	C₂	1	2	yes	maximal, complemented
10	#20255360	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	#20254043	C₂	1	1	yes	maximal, characteristic, complemented
15	#20254029	C₂	1	1	yes	maximal, characteristic, complemented
16	#20253958	C₂	1	1	yes	maximal, characteristic, complemented
17	#20253661	C₂	1	2	yes	maximal, complemented
18	#20253637	C₂	1	2	yes	maximal, complemented
19	#20253497	C₂	1	2	yes	maximal, complemented
20	#20252363	C₂	1	1	yes	maximal, characteristic, complemented
21	#20252258	C₂	1	1	yes	maximal, characteristic, complemented
22	#20252235	C₂	1	1	yes	maximal, characteristic, complemented
23	C₄×#135×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	#15689845	C₂²	1	2	yes	complemented
27	#15689841	C₂²	1	2	yes	—
28	#15689832	C₂²	1	2	yes	complemented
29	#15689822	—	2	2	no	—
30	#15689817	C₂²	1	2	yes	complemented
31	#15689814	C₂²	1	2	yes	—
32	#15689806	—	2	2	no	—
33	#15689802	—	2	2	no	—
34	#15689797	—	2	2	no	—
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	#15689731	C₂²	1	2	yes	—
40	#15689715	—	2	2	no	—
41	#15689706	—	2	2	no	—
42	#15689657	—	2	2	no	—
43	#15689657	C₂²	1	1	yes	characteristic
44	#15689657	C₂²	1	2	yes	complemented
45	C₂×#13094018	—	2	2	no	—
46	#15689602	C₂²	1	2	yes	complemented
47	#15689595	C₂²	1	2	yes	—
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	#15689508	C₂²	1	1	yes	characteristic
52	#15689507	C₂²	1	1	yes	characteristic
53	#15689501	C₂²	1	1	yes	characteristic, complemented
54	#15689490	C₂²	1	2	yes	complemented
55	#15689484	C₂²	1	2	yes	complemented
56	#15689478	C₂²	1	2	yes	complemented
57	#15689467	C₂²	1	2	yes	—
58	#15689464	C₂²	1	2	yes	complemented
59	#15689462	C₂²	1	2	yes	—
60	#15689452	C₂²	1	2	yes	complemented
61	#15689447	C₂²	1	2	yes	complemented
62	#15689443	C₂²	1	2	yes	complemented
63	#15689430	C₂²	1	2	yes	complemented
64	#15689425	C₂²	1	2	yes	complemented
65	#15689423	C₂²	1	2	yes	complemented
66	#15689422	C₂²	1	2	yes	complemented
67	#15689411	C₂²	1	2	yes	complemented
68	#15689407	C₂²	1	2	yes	complemented
69	#15689380	C₂²	1	2	yes	—
70	#15689372	C₂²	1	2	yes	complemented
71	#15689365	C₂²	1	1	yes	characteristic
72	#15689364	C₂²	1	1	yes	characteristic, complemented
73	#15689361	C₂²	1	1	yes	characteristic
74	#15689361	C₂²	1	1	yes	characteristic, complemented
75	#15689360	C₂²	1	1	yes	characteristic
76	#15689359	C₂²	1	1	yes	characteristic
77	#15689352	C₂²	1	2	yes	complemented
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	#15689253	C₂²	1	1	yes	characteristic, complemented
91	C₈×Dic₉₄	C₂²	1	1	yes	characteristic, complemented
92	#15689233	C₂²	1	2	yes	—
93	#15689232	C₂²	1	2	yes	—
94	#15689228	C₂²	1	2	yes	complemented
95	#15689223	C₂²	1	2	yes	complemented
96	#15689221	C₂²	1	2	yes	complemented
97	#15689220	C₂²	1	2	yes	complemented
98	C₄×Dic₁₈₈	C₂²	1	1	yes	characteristic, complemented
99	#15689217	C₂²	1	1	yes	characteristic, complemented
100	C₄×#10625325	C₂²	1	2	yes	complemented
101	C₄×D₃₇₆	C₂²	1	1	yes	characteristic
102	D₈×Dic₄₇	C₂²	1	1	yes	characteristic
103	D₈×Dic₄₇	C₂²	1	1	yes	characteristic
104	#15689205	C₂²	1	1	yes	characteristic
105	#15689202	C₂²	1	1	yes	characteristic
106	#15689194	C₂²	1	1	yes	characteristic
107	#15689194	C₂²	1	1	yes	characteristic, complemented
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	#15689182	C₂²	1	1	yes	characteristic
112	#15689182	C₂²	1	1	yes	characteristic, complemented
113	#15689180	C₂²	1	1	yes	characteristic, complemented
114	#15689160	C₂²	1	1	yes	characteristic
115	#107×D₄₇	C₂²	1	1	yes	characteristic, complemented
116	#15689126	C₂²	1	2	yes	—
117	#15689121	C₂²	1	2	yes	complemented
118	#15689077	C₂²	1	1	yes	characteristic
119	#15689077	C₂²	1	1	yes	characteristic, complemented
120	C₂×#135×C₄₇	C₂²	1	1	yes	characteristic
121	C₄×#41×C₄₇	C₂²	1	2	yes	complemented
122	C₄×Q₁₆×C₄₇	C₂²	1	1	yes	characteristic, complemented
123	C₄×Q₁₆×C₄₇	C₂²	1	1	yes	characteristic, complemented
124	C₄×SD₁₆×C₄₇	C₂²	1	2	yes	complemented
125	C₄×SD₁₆×C₄₇	C₂²	1	2	yes	complemented
126	C₄×D₈×C₄₇	C₂²	1	1	yes	characteristic
127	C₄×D₈×C₄₇	C₂²	1	1	yes	characteristic
128	C₄₇×#427	C₂²	1	1	yes	characteristic, complemented
129	C₄₇×#416	C₂²	1	2	yes	complemented
130	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic, complemented
131	C₂×#10625352	C₂³	1	2	yes	—
132	C₂×D₄×D₄₇	C₂³	1	2	yes	—
133	#13094043	—	2	4	no	—
134	C₂×Dic₁₈₈	C₂³	1	1	yes	characteristic
135	C₂×#10625337	C₂³	1	2	yes	—
136	C₂×#10625325	C₂³	1	2	yes	—
137	C₂×#10625335	C₂³	1	2	yes	—
138	C₂×#10625336	C₂³	1	2	yes	—
139	C₂×D₃₇₆	C₂³	1	1	yes	characteristic
140	C₂×#10625334	C₂³	1	2	yes	—
141	D₈×D₄₇	—	2	4	no	—
142	C₂×#10625324	C₂³	1	1	yes	characteristic
143	C₂×#10625324	C₂³	1	1	yes	characteristic
144	C₂×C₈×D₄₇	C₂³	1	1	yes	characteristic
145	C₂×C₈×D₄₇	C₂³	1	1	yes	characteristic
146	#13094023	C₂³	1	2	yes	—
147	#13094022	C₂³	1	2	yes	—
148	#13094019	—	2	2	no	—
149	#13094019	—	2	2	no	—
150	#13094018	—	2	2	no	—
151	#13094018	—	2	2	no	—
152	#13094018	—	2	2	no	—
153	#13094018	—	2	2	no	—
154	#13094018	—	2	2	no	—
155	#13094018	—	2	2	no	—
156	#13094018	—	2	2	no	—
157	#13094018	D₄	1	1	yes	characteristic
158	#13094018	D₄	1	1	yes	characteristic
159	#13094017	—	2	2	no	—
160	#13094016	—	2	2	no	—
161	#13094016	D₄	1	1	yes	characteristic
162	#13094016	C₂³	1	2	yes	—
163	#13094015	C₂³	1	2	yes	—
164	#13094014	—	2	2	no	—
165	#13094014	—	2	2	no	—
166	#13094013	C₂³	1	2	yes	—
167	#13094012	—	2	2	no	—
168	#13094012	D₄	1	1	yes	characteristic
169	#13094012	C₂³	1	2	yes	—
170	#13094010	—	2	2	no	—
171	#13094009	—	2	2	no	—
172	#13094009	—	2	2	no	—
173	#13094008	—	2	2	no	—
174	#13094007	—	2	2	no	—
175	#13094007	—	2	2	no	—
176	#13094007	—	2	2	no	—
177	#13094007	D₄	1	1	yes	characteristic
178	#13094007	D₄	1	1	yes	characteristic
179	#13094006	—	2	2	no	—
180	#13094005	—	2	2	no	—
181	#13094004	C₂³	1	2	yes	—
182	#13094003	—	2	2	no	—
183	#13094003	D₄	1	1	yes	characteristic
184	#13094003	C₂³	1	2	yes	—
185	#13094002	—	2	2	no	—
186	#13094002	—	2	2	no	—
187	#13094001	—	2	2	no	—
188	#13094001	—	2	2	no	—
189	#13094000	C₂³	1	2	yes	—
190	#13094000	C₂³	1	2	yes	—
191	#13093999	C₂³	1	2	yes	—
192	#13093998	—	2	2	no	—
193	#13093998	D₄	1	1	yes	characteristic
194	#13093998	C₂³	1	2	yes	—
195	#13093997	—	2	2	no	—
196	#13093996	—	2	2	no	—
197	#13093996	—	2	2	no	—
198	#13093994	—	2	2	no	—
199	#13093992	—	2	2	no	—
200	C₄×Dic₉₄	—	2	2	no	—
201	C₄×Dic₉₄	C₂³	1	2	yes	—
202	C₄×Dic₉₄	C₂³	1	1	yes	characteristic
203	#13093989	C₂³	1	2	yes	—
204	C₄×D₁₈₈	—	2	2	no	—
205	C₄×D₁₈₈	C₂³	1	1	yes	characteristic
206	C₄×D₁₈₈	C₂³	1	2	yes	—
207	D₄×Dic₄₇	C₂³	1	2	yes	—
208	D₄×Dic₄₇	C₂³	1	2	yes	—
209	#13093986	C₂³	1	2	yes	—
210	C₄×C₂²⋊D₄₇	—	2	2	no	—
211	C₄×C₂²⋊D₄₇	—	2	2	no	—
212	C₄×C₂²⋊D₄₇	—	2	2	no	—
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	#13093982	C₂³	1	2	yes	—
218	#13093981	—	2	2	no	—
219	#13093981	—	2	2	no	—
220	#13093981	—	2	2	no	—
221	#13093981	C₂³	1	1	yes	characteristic
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	C₂×Dic₄₇⋊C₄	—	2	2	no	—
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	C₂×(C₂×D₄₇)⋊C₄	—	2	2	no	—
231	C₂²⋊C₄×D₄₇	—	2	2	no	—
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	#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	#13093935	C₂³	1	1	yes	characteristic
265	#13093934	C₂³	1	1	yes	characteristic
266	#13093934	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	C₂²×C₈×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	2	yes	—
284	C₂×C₄²×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	#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	C₂×D₄	1	1	yes	characteristic
307	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
308	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
309	C₂×C₂²⋊D₄₇	—	2	2	no	—
310	C₂×C₂²⋊D₄₇	—	2	2	no	—
311	C₂×C₂²⋊D₄₇	—	2	2	no	—
312	C₂×C₂²⋊D₄₇	C₂×D₄	1	1	yes	characteristic
313	C₂×C₂²⋊D₄₇	C₂×D₄	1	1	yes	characteristic
314	C₂²×Dic₄₇	—	2	2	no	—
315	C₂²×Dic₄₇	—	2	2	no	—
316	C₂²×Dic₄₇	—	2	2	no	—
317	#10625352	—	2	4	no	—
318	#10625352	—	4	2	no	—
319	D₄×D₄₇	—	2	4	no	—
320	D₄×D₄₇	—	4	2	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	C₂⁴	1	1	yes	characteristic
328	C₂×C₄×D₄₇	C₂⁴	1	1	yes	characteristic
329	C₂×Dic₉₄	—	2	2	no	—
330	C₂×Dic₉₄	C₂×D₄	1	1	yes	characteristic
331	C₂×Dic₉₄	C₂⁴	1	2	yes	—
332	Q₁₆×C₄₇	—	2	2	no	—
333	SD₁₆×C₄₇	—	2	4	no	—
334	D₈×C₄₇	#41	1	4	yes	—
335	C₂×C₈×C₄₇	—	2	2	no	—
336	C₂×C₈×C₄₇	—	4	1	no	—
337	C₂×C₈×C₄₇	C₂⁴	1	1	yes	characteristic
338	C₂×C₈×C₄₇	C₂⁴	1	1	yes	characteristic
339	C₂×C₈×C₄₇	C₂⁴	1	1	yes	characteristic
340	C₂×C₈×C₄₇	C₂⁴	1	1	yes	characteristic
341	C₄⋊C₄×C₄₇	—	2	2	no	—
342	C₄⋊C₄×C₄₇	—	2	2	no	—
343	C₄⋊C₄×C₄₇	C₂⁴	1	2	yes	—
344	C₄⋊C₄×C₄₇	C₂⁴	1	2	yes	—
345	C₂²⋊C₄×C₄₇	—	2	2	no	—
346	C₂²⋊C₄×C₄₇	—	2	2	no	—
347	C₂²⋊C₄×C₄₇	—	2	2	no	—
348	C₄²×C₄₇	—	2	2	no	—
349	C₄²×C₄₇	—	2	2	no	—
350	C₄²×C₄₇	—	2	2	no	—
351	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
352	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
353	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
354	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
355	C₂²⋊Dic₄₇	—	2	2	no	—
356	C₂²⋊Dic₄₇	—	2	2	no	—
357	C₂²⋊Dic₄₇	—	2	2	no	—
358	C₂²⋊Dic₄₇	C₂×D₄	1	1	yes	characteristic
359	C₂²⋊Dic₄₇	C₂×D₄	1	1	yes	characteristic
360	#10625337	—	4	2	no	—
361	#10625336	—	4	2	no	—
362	#10625335	—	2	4	no	—
363	#10625334	—	2	4	no	—
364	(C₂×D₄₇)⋊C₄	—	2	2	no	—
365	(C₂×D₄₇)⋊C₄	—	2	2	no	—
366	(C₂×D₄₇)⋊C₄	—	2	2	no	—
367	(C₂×D₄₇)⋊C₄	—	2	2	no	—
368	(C₂×D₄₇)⋊C₄	—	2	2	no	—
369	(C₂×D₄₇)⋊C₄	—	2	2	no	—
370	(C₂×D₄₇)⋊C₄	—	2	2	no	—
371	(C₂×D₄₇)⋊C₄	—	2	2	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	C₂×D₄	1	1	yes	characteristic
377	(C₂×D₄₇)⋊C₄	C₂×D₄	1	1	yes	characteristic
378	(C₂×D₄₇)⋊C₄	C₂×D₄	1	1	yes	characteristic
379	(C₂×D₄₇)⋊C₄	C₂×D₄	1	1	yes	characteristic
380	(C₂×D₄₇)⋊C₄	C₂×D₄	1	1	yes	characteristic
381	(C₂×D₄₇)⋊C₄	C₂×D₄	1	1	yes	characteristic
382	(C₂×D₄₇)⋊C₄	C₂×D₄	1	1	yes	characteristic
383	(C₂×D₄₇)⋊C₄	C₂×D₄	1	1	yes	characteristic
384	C₄⋊Dic₄₇	—	2	2	no	—
385	C₄⋊Dic₄₇	—	2	2	no	—
386	C₄⋊Dic₄₇	C₂×D₄	1	1	yes	characteristic
387	C₄⋊Dic₄₇	C₂×D₄	1	1	yes	characteristic
388	C₄⋊Dic₄₇	C₂⁴	1	2	yes	—
389	C₄⋊Dic₄₇	C₂⁴	1	2	yes	—
390	Dic₄₇⋊C₄	—	2	2	no	—
391	Dic₄₇⋊C₄	—	2	2	no	—
392	Dic₄₇⋊C₄	—	2	2	no	—
393	Dic₄₇⋊C₄	—	2	2	no	—
394	Dic₄₇⋊C₄	—	2	2	no	—
395	Dic₄₇⋊C₄	—	2	2	no	—
396	Dic₄₇⋊C₄	—	2	2	no	—
397	Dic₄₇⋊C₄	—	2	2	no	—
398	Dic₄₇⋊C₄	—	2	2	no	—
399	Dic₄₇⋊C₄	—	2	2	no	—
400	Dic₄₇⋊C₄	—	2	2	no	—
401	Dic₄₇⋊C₄	—	2	2	no	—
402	Dic₄₇⋊C₄	C₂×D₄	1	1	yes	characteristic
403	Dic₄₇⋊C₄	C₂×D₄	1	1	yes	characteristic
404	Dic₄₇⋊C₄	C₂×D₄	1	1	yes	characteristic
405	Dic₄₇⋊C₄	C₂×D₄	1	1	yes	characteristic
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	C₄×Dic₄₇	—	2	2	no	—
411	C₄×Dic₄₇	—	2	2	no	—
412	C₄×Dic₄₇	—	2	2	no	—
413	C₄×Dic₄₇	C₂⁴	1	1	yes	characteristic
414	C₄×Dic₄₇	C₂⁴	1	1	yes	characteristic
415	C₂×C₄₇⋊C₈	C₂⁴	1	1	yes	characteristic
416	C₂×C₄₇⋊C₈	C₂⁴	1	1	yes	characteristic
417	C₂×C₄₇⋊C₈	C₂⁴	1	1	yes	characteristic
418	C₂×C₄₇⋊C₈	C₂⁴	1	1	yes	characteristic
419	Dic₁₈₈	—	2	2	no	—
420	D₃₇₆	—	2	2	no	—
421	#10625325	—	4	2	no	—
422	#10625324	—	4	1	no	—
423	#10625324	—	4	1	no	—
424	C₈×D₄₇	—	2	2	no	—
425	C₈×D₄₇	—	2	2	no	—
426	C₂³×C₄₇	—	2	2	no	—
427	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
428	C₂²×D₄₇	—	2	2	no	—
429	C₂²×D₄₇	—	4	4	no	—
430	C₂²×D₄₇	—	8	2	no	—
431	C₂²×D₄₇	—	8	2	no	—
432	C₂²×D₄₇	C₂²×D₄	1	1	yes	characteristic
433	C₂²×D₄₇	C₂²×D₄	1	1	yes	characteristic
434	Q₈×C₄₇	—	2	2	no	—
435	Q₈×C₄₇	—	2	2	no	—
436	D₄×C₄₇	—	2	2	no	—
437	D₄×C₄₇	—	4	4	no	—
438	D₄×C₄₇	C₂×#41	1	4	yes	—
439	C₂×C₄×C₄₇	—	2	1	no	—
440	C₂×C₄×C₄₇	—	2	1	no	—
441	C₂×C₄×C₄₇	—	2	2	no	—
442	C₂×C₄×C₄₇	—	2	2	no	—
443	C₂×C₄×C₄₇	—	2	2	no	—
444	C₂×C₄×C₄₇	—	4	1	no	—
445	C₂×C₄×C₄₇	—	4	1	no	—
446	C₂×C₄×C₄₇	—	4	4	no	—
447	C₂×C₄×C₄₇	—	8	2	no	—
448	C₂×C₄×C₄₇	—	8	2	no	—
449	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
450	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
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	C₂⁵	1	1	yes	characteristic
455	C₂²⋊D₄₇	—	4	1	no	—
456	C₂²⋊D₄₇	—	4	1	no	—
457	C₂²⋊D₄₇	—	4	4	no	—
458	C₂²⋊D₄₇	—	4	4	no	—
459	C₂²⋊D₄₇	—	8	2	no	—
460	C₂×Dic₄₇	—	2	2	no	—
461	C₂×Dic₄₇	—	2	2	no	—
462	C₂×Dic₄₇	—	2	2	no	—
463	C₂×Dic₄₇	—	4	4	no	—
464	C₂×Dic₄₇	—	8	2	no	—
465	C₂×Dic₄₇	—	8	2	no	—
466	C₂×Dic₄₇	C₂²×D₄	1	1	yes	characteristic
467	C₂×Dic₄₇	C₂²×D₄	1	1	yes	characteristic
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	D₁₈₈	—	2	2	no	—
473	D₁₈₈	—	2	2	no	—
474	D₁₈₈	—	4	1	no	—
475	D₁₈₈	—	8	2	no	—
476	C₄×D₄₇	—	2	1	no	—
477	C₄×D₄₇	—	2	1	no	—
478	C₄×D₄₇	—	2	1	no	—
479	C₄×D₄₇	—	2	1	no	—
480	C₄×D₄₇	—	8	2	no	—
481	C₄×D₄₇	—	8	2	no	—
482	C₄×D₄₇	—	8	2	no	—
483	Dic₉₄	—	2	2	no	—
484	Dic₉₄	—	2	2	no	—
485	Dic₉₄	—	4	1	no	—
486	Dic₉₄	—	8	2	no	—
487	C₈×C₄₇	—	2	1	no	—
488	C₈×C₄₇	—	2	1	no	—
489	C₈×C₄₇	—	2	1	no	—
490	C₈×C₄₇	C₂×#41	1	2	yes	—
491	C₄₇⋊C₈	—	2	1	no	—
492	C₄₇⋊C₈	—	2	1	no	—
493	C₄₇⋊C₈	—	2	1	no	—
494	C₄₇⋊C₈	—	2	1	no	—
495	#61487	—	47	1	no	maximal, Sylow
496	C₂²×C₄₇	—	2	1	no	—
497	C₂²×C₄₇	—	2	1	no	—
498	C₂²×C₄₇	—	2	4	no	—
499	C₂²×C₄₇	—	2	1	no	—
500	C₂²×C₄₇	—	4	2	no	—
501	C₂²×C₄₇	—	4	2	no	—
502	C₂²×C₄₇	C₂³×D₄	1	1	yes	characteristic
503	C₂×D₄₇	—	2	1	no	—
504	C₂×D₄₇	—	2	1	no	—
505	C₂×D₄₇	—	2	1	no	—
506	C₂×D₄₇	—	2	1	no	—
507	C₂×D₄₇	—	2	1	no	—
508	C₂×D₄₇	—	2	1	no	—
509	C₂×D₄₇	—	4	2	no	—
510	C₂×D₄₇	—	4	2	no	—
511	C₂×D₄₇	—	4	2	no	—
512	C₂×D₄₇	—	16	4	no	—
513	C₄×C₄₇	—	2	1	no	—
514	C₄×C₄₇	—	2	1	no	—
515	C₄×C₄₇	—	2	1	no	—
516	C₄×C₄₇	—	2	1	no	—
517	C₄×C₄₇	—	2	1	no	—
518	C₄×C₄₇	—	4	2	no	—
519	C₄×C₄₇	—	4	2	no	—
520	C₄×C₄₇	—	4	2	no	—
521	C₄×C₄₇	C₂²×#41	1	1	yes	characteristic
522	C₄×C₄₇	#585	1	1	yes	characteristic
523	Dic₄₇	—	2	1	no	—
524	Dic₄₇	—	2	1	no	—
525	Dic₄₇	—	2	1	no	—
526	Dic₄₇	—	2	1	no	—
527	Dic₄₇	—	2	1	no	—
528	Dic₄₇	—	2	1	no	—
529	Dic₄₇	—	4	2	no	—
530	Dic₄₇	—	4	2	no	—
531	Dic₄₇	—	4	2	no	—
532	#3521	—	47	2	no	—
533	#3393	—	47	1	no	—
534	#3380	—	47	1	no	—
535	#3376	—	47	2	no	—
536	#3342	—	47	1	no	—
537	#3339	—	47	1	no	—
538	#3336	—	47	1	no	—
539	#3323	—	47	2	no	—
540	#3311	—	47	2	no	—
541	#3307	—	47	2	no	—
542	#3283	—	47	1	no	—
543	#3280	—	47	1	no	—
544	#3280	—	47	1	no	—
545	#3177	—	47	1	no	—
546	#3175	—	47	1	no	—
547	#3168	—	47	1	no	—
548	#3125	—	47	2	no	—
549	#3123	—	47	2	no	—
550	#3111	—	47	2	no	—
551	#2966	—	47	1	no	—
552	#2951	—	47	1	no	—
553	#2948	—	47	1	no	—
554	C₄×#135	D₄₇	1	1	yes	characteristic, complemented
555	C₂×C₄₇	—	4	4	no	—
556	C₂×C₄₇	—	4	1	no	—
557	C₂×C₄₇	D₄×#41	1	1	yes	characteristic
558	C₂×C₄₇	#3584	1	1	yes	characteristic
559	C₂×C₄₇	#3584	1	1	yes	characteristic
560	D₄₇	—	4	1	no	—
561	D₄₇	—	4	1	no	—
562	D₄₇	—	8	2	no	—
563	C₂×#135	—	47	1	no	—
564	C₂×#135	C₂×D₄₇	1	1	yes	characteristic
565	C₂²×D₈	—	47	1	no	—
566	#556	—	47	2	no	—
567	#556	—	47	2	no	—
568	#554	—	47	2	no	—
569	#553	—	47	2	no	—
570	#553	—	94	2	no	—
571	#552	—	47	2	no	—
572	#552	—	94	2	no	—
573	#551	—	94	2	no	—
574	#551	—	94	2	no	—
575	#547	—	47	2	no	—
576	#546	—	47	2	no	—
577	#546	—	47	2	no	—
578	#542	—	47	2	no	—
579	#541	—	47	2	no	—
580	#539	—	94	2	no	—
581	#538	—	94	2	no	—
582	#529	—	47	1	no	—
583	#529	—	47	2	no	—
584	#529	—	94	2	no	—
585	C₂×#126	—	94	2	no	—
586	#520	—	47	2	no	—
587	#518	—	47	2	no	—
588	C₄×#41	C₂×D₄₇	1	2	yes	complemented
589	#500	—	47	1	no	—
590	#499	—	47	1	no	—
591	#499	—	47	1	no	—
592	#495	—	47	1	no	—
593	#495	—	47	1	no	—
594	#494	—	47	1	no	—
595	#491	—	47	2	no	—
596	#489	—	47	2	no	—
597	#488	—	47	2	no	—
598	#485	—	47	2	no	—
599	#485	—	47	2	no	—
600	#485	—	47	2	no	—
601	#483	—	47	2	no	—
602	#482	—	47	2	no	—
603	#481	—	47	2	no	—
604	#479	—	47	2	no	—
605	#478	—	47	2	no	—
606	#478	—	47	2	no	—
607	#478	—	47	2	no	—
608	#476	—	47	2	no	—
609	#475	—	47	2	no	—
610	#470	—	47	2	no	—
611	#468	—	47	2	no	—
612	#467	—	47	1	no	—
613	#467	—	47	1	no	—
614	#467	—	47	1	no	—
615	#467	—	47	1	no	—
616	#466	—	47	1	no	—
617	#466	—	47	1	no	—
618	#465	—	47	2	no	—
619	#464	—	47	2	no	—
620	#464	—	47	2	no	—
621	#463	—	47	2	no	—
622	#463	—	47	2	no	—
623	#461	—	47	2	no	—
624	#461	—	47	2	no	—
625	#452	—	47	2	no	—
626	#452	—	47	2	no	—
627	#450	—	47	2	no	—
628	#450	—	47	2	no	—
629	#449	—	47	2	no	—
630	#449	—	47	2	no	—
631	#446	—	47	1	no	—
632	C₈×Q₈	—	47	1	no	—
633	#442	—	47	2	no	—
634	#442	—	47	2	no	—
635	#441	—	47	2	no	—
636	#440	—	47	2	no	—
637	#440	—	47	2	no	—
638	#440	—	47	2	no	—
639	C₄×Q₁₆	—	47	1	no	—
640	C₄×Q₁₆	—	47	1	no	—
641	C₄×Q₁₆	C₂×D₄₇	1	1	yes	characteristic, complemented
642	C₄×Q₁₆	C₂×D₄₇	1	1	yes	characteristic, complemented
643	C₄×SD₁₆	—	47	2	no	—
644	C₄×SD₁₆	C₂×D₄₇	1	2	yes	complemented
645	C₄×SD₁₆	C₂×D₄₇	1	2	yes	complemented
646	C₄×D₈	—	47	1	no	—
647	C₄×D₈	—	47	1	no	—
648	C₄×D₈	—	47	1	no	—
649	C₄×D₈	—	47	1	no	—
650	C₄×D₈	C₂×D₄₇	1	1	yes	characteristic
651	C₄×D₈	C₂×D₄₇	1	1	yes	characteristic
652	#436	—	47	1	no	—
653	#435	—	47	1	no	—
654	#435	—	47	1	no	—
655	C₈×D₄	—	47	1	no	—
656	C₈×D₄	—	47	1	no	—
657	C₈×D₄	—	47	1	no	—
658	#433	—	47	1	no	—
659	#433	—	47	1	no	—
660	#432	—	47	1	no	—
661	#427	—	47	1	no	—
662	#427	C₂×D₄₇	1	1	yes	characteristic, complemented
663	C₂×#107	—	47	1	no	—
664	#418	—	47	2	no	—
665	#417	—	47	2	no	—
666	#416	C₂×D₄₇	1	2	yes	complemented
667	#405	—	47	1	no	—
668	#405	—	47	1	no	—
669	C₂×C₄×C₈	C₂×D₄₇	1	1	yes	characteristic, complemented
670	C₄₇	#61487	1	1	yes	characteristic, complemented, Sylow
671	C₂×#41	—	47	2	no	—
672	C₂×#41	C₂²×D₄₇	1	2	yes	—
673	C₂²×D₄	—	47	2	no	—
674	#135	—	2	4	no	—
675	#135	—	94	4	no	—
676	C₂×Q₁₆	—	47	2	no	—
677	C₂×Q₁₆	—	47	1	no	—
678	C₂×Q₁₆	C₂²×D₄₇	1	1	yes	characteristic
679	C₂×SD₁₆	—	47	2	no	—
680	C₂×SD₁₆	—	47	2	no	—
681	C₂×SD₁₆	—	47	2	no	—
682	C₂×SD₁₆	C₂²×D₄₇	1	2	yes	—
683	C₂×D₈	—	47	2	no	—
684	C₂×D₈	—	47	1	no	—
685	C₂×D₈	—	94	4	no	—
686	C₂×D₈	C₂²×D₄₇	1	1	yes	characteristic
687	C₂×M₁₆	—	47	1	no	—
688	C₂×M₁₆	—	47	1	no	—
689	C₂²×C₈	—	47	1	no	—
690	C₂²×C₈	—	47	1	no	—
691	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
692	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
693	C₄⋊Q₈	—	47	2	no	—
694	C₄⋊Q₈	—	47	2	no	—
695	#126	—	47	1	no	—
696	#126	—	47	1	no	—
697	#126	—	94	2	no	—
698	#126	—	94	2	no	—
699	#126	—	94	2	no	—
700	#126	—	94	2	no	—
701	#126	—	94	2	no	—
702	#126	—	94	2	no	—
703	#126	—	94	2	no	—
704	#126	—	94	2	no	—
705	#126	—	94	2	no	—
706	#126	—	94	2	no	—
707	#125	—	47	2	no	—
708	#125	—	47	1	no	—
709	#125	—	47	2	no	—
710	#125	—	94	2	no	—
711	#125	—	94	2	no	—
712	#125	—	94	2	no	—
713	#124	—	47	2	no	—
714	#124	—	47	1	no	—
715	#124	—	47	2	no	—
716	#124	—	94	2	no	—
717	#124	—	94	2	no	—
718	#123	—	47	1	no	—
719	#123	—	47	1	no	—
720	#123	—	94	2	no	—
721	#123	—	94	2	no	—
722	#123	—	94	2	no	—
723	#123	—	94	2	no	—
724	#123	—	94	2	no	—
725	#123	—	94	2	no	—
726	#123	—	94	2	no	—
727	#123	—	94	2	no	—
728	C₂²⋊Q₈	—	47	1	no	—
729	C₂²⋊Q₈	—	47	2	no	—
730	C₂²⋊Q₈	—	47	2	no	—
731	C₂²⋊Q₈	—	47	2	no	—
732	C₂²⋊Q₈	—	47	2	no	—
733	C₂²⋊Q₈	—	94	2	no	—
734	C₂²⋊Q₈	—	94	2	no	—
735	C₂²⋊Q₈	—	94	2	no	—
736	C₂²⋊Q₈	—	94	2	no	—
737	C₂²⋊Q₈	—	94	2	no	—
738	#121	—	47	1	no	—
739	#121	—	47	2	no	—
740	#121	—	47	2	no	—
741	#121	—	94	2	no	—
742	#121	—	94	2	no	—
743	#121	—	94	2	no	—
744	#121	—	94	2	no	—
745	#120	—	94	2	no	—
746	#120	—	94	2	no	—
747	C₄×Q₈	—	47	1	no	—
748	C₄×Q₈	—	47	2	no	—
749	C₄×Q₈	—	47	2	no	—
750	C₄×Q₈	—	94	2	no	—
751	C₄×Q₈	C₂²×D₄₇	1	2	yes	—
752	C₄×Q₈	C₂²×D₄₇	1	2	yes	—
753	C₄×D₄	—	2	2	no	—
754	C₄×D₄	—	2	2	no	—
755	C₄×D₄	—	47	1	no	—
756	C₄×D₄	—	47	1	no	—
757	C₄×D₄	—	47	2	no	—
758	C₄×D₄	—	47	2	no	—
759	C₄×D₄	—	47	2	no	—
760	C₄×D₄	—	47	1	no	—
761	C₄×D₄	—	47	2	no	—
762	C₄×D₄	—	94	2	no	—
763	C₄×D₄	—	94	2	no	—
764	C₄×D₄	—	94	2	no	—
765	C₄×D₄	—	94	2	no	—
766	C₄×D₄	—	94	2	no	—
767	C₄×D₄	—	94	2	no	—
768	C₄×D₄	C₂²×D₄₇	1	2	yes	—
769	C₄×D₄	C₂²×D₄₇	1	2	yes	—
770	#117	—	2	2	no	—
771	#117	—	47	1	no	—
772	#117	—	47	1	no	—
773	#117	—	47	2	no	—
774	#117	—	94	2	no	—
775	#117	—	94	2	no	—
776	#117	—	94	2	no	—
777	#117	—	94	2	no	—
778	#117	C₂²×D₄₇	1	2	yes	—
779	C₂×C₄⋊C₄	—	47	2	no	—
780	C₂×C₄⋊C₄	—	94	2	no	—
781	C₂×C₄⋊C₄	—	94	2	no	—
782	C₂×C₄⋊C₄	—	94	2	no	—
783	C₂×C₂²⋊C₄	—	94	2	no	—
784	C₂×C₂²⋊C₄	—	94	2	no	—
785	C₂×C₂²⋊C₄	—	94	2	no	—
786	C₂×C₂²⋊C₄	—	94	2	no	—
787	C₂×C₄²	—	2	2	no	—
788	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
789	#107	—	47	1	no	—
790	#107	—	47	1	no	—
791	#107	—	47	2	no	—
792	#107	—	47	2	no	—
793	#107	C₂²×D₄₇	1	1	yes	characteristic
794	#107	C₂²×D₄₇	1	1	yes	characteristic
795	#106	—	47	2	no	—
796	#106	—	47	2	no	—
797	#106	—	47	2	no	—
798	#106	C₂²×D₄₇	1	2	yes	—
799	C₄⋊C₈	—	47	1	no	—
800	C₄⋊C₈	—	47	1	no	—
801	C₄⋊C₈	—	47	1	no	—
802	C₄⋊C₈	—	47	1	no	—
803	C₄⋊C₈	—	47	1	no	—
804	C₄⋊C₈	—	47	1	no	—
805	#103	—	47	2	no	—
806	#103	—	47	2	no	—
807	#103	—	47	2	no	—
808	#103	—	47	2	no	—
809	#103	—	47	2	no	—
810	#103	—	47	2	no	—
811	#103	C₂²×D₄₇	1	2	yes	—
812	#103	C₂²×D₄₇	1	2	yes	—
813	#102	—	47	2	no	—
814	#102	—	47	2	no	—
815	#102	—	47	2	no	—
816	#102	—	47	2	no	—
817	#102	—	47	2	no	—
818	#102	—	47	2	no	—
819	#102	C₂²×D₄₇	1	2	yes	—
820	#102	C₂²×D₄₇	1	2	yes	—
821	C₂²⋊C₈	—	47	1	no	—
822	C₂²⋊C₈	—	47	1	no	—
823	C₂²⋊C₈	—	47	1	no	—
824	C₂²⋊C₈	—	47	1	no	—
825	C₂²⋊C₈	—	47	1	no	—
826	C₂²⋊C₈	—	47	1	no	—
827	#97	—	47	1	no	—
828	#97	—	47	1	no	—
829	#97	—	47	1	no	—
830	#97	—	47	1	no	—
831	C₄×C₈	—	47	1	no	—
832	C₄×C₈	—	47	1	no	—
833	C₄×C₈	C₂²×D₄₇	1	1	yes	characteristic
834	C₄×C₈	C₂²×D₄₇	1	1	yes	characteristic
835	C₄×C₈	C₂²×D₄₇	1	1	yes	characteristic
836	C₄×C₈	C₂²×D₄₇	1	1	yes	characteristic
837	C₂⁴	—	94	2	no	—
838	#41	—	2	4	no	—
839	#41	—	4	2	no	—
840	#41	—	94	4	no	—
841	#41	—	188	2	no	—
842	C₂×Q₈	—	47	1	no	—
843	C₂×Q₈	—	47	2	no	—
844	C₂×Q₈	—	94	2	no	—
845	C₂×Q₈	C₂³×D₄₇	1	2	yes	—
846	C₂×D₄	—	2	2	no	—
847	C₂×D₄	—	47	1	no	—
848	C₂×D₄	—	47	1	no	—
849	C₂×D₄	—	47	1	no	—
850	C₂×D₄	—	47	2	no	—
851	C₂×D₄	—	94	2	no	—
852	C₂×D₄	—	94	2	no	—
853	C₂×D₄	—	94	4	no	—
854	C₂×D₄	—	94	2	no	—
855	C₂×D₄	—	94	2	no	—
856	C₂×D₄	—	188	2	no	—
857	C₂×D₄	C₂³×D₄₇	1	2	yes	—
858	C₂²×C₄	—	2	2	no	—
859	C₂²×C₄	—	2	2	no	—
860	C₂²×C₄	—	2	2	no	—
861	C₂²×C₄	—	47	1	no	—
862	C₂²×C₄	—	47	1	no	—
863	C₂²×C₄	—	94	2	no	—
864	C₂²×C₄	—	94	2	no	—
865	C₂²×C₄	—	94	2	no	—
866	C₂²×C₄	—	94	2	no	—
867	C₂²×C₄	—	94	2	no	—
868	C₂²×C₄	—	94	2	no	—
869	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
870	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
871	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
872	Q₁₆	—	2	2	no	—
873	Q₁₆	—	94	2	no	—
874	Q₁₆	—	188	2	no	—
875	SD₁₆	—	2	4	no	—
876	SD₁₆	—	94	4	no	—
877	SD₁₆	—	188	2	no	—
878	SD₁₆	—	188	2	no	—
879	D₈	—	94	4	no	—
880	D₈	—	94	2	no	—
881	D₈	#10625350	1	4	yes	—
882	M₁₆	—	188	1	no	—
883	M₁₆	—	188	1	no	—
884	C₂×C₈	—	2	2	no	—
885	C₂×C₈	—	4	1	no	—
886	C₂×C₈	—	47	1	no	—
887	C₂×C₈	—	47	1	no	—
888	C₂×C₈	—	47	1	no	—
889	C₂×C₈	—	47	1	no	—
890	C₂×C₈	—	94	2	no	—
891	C₂×C₈	—	94	2	no	—
892	C₂×C₈	C₂³×D₄₇	1	1	yes	characteristic
893	C₂×C₈	C₂³×D₄₇	1	1	yes	characteristic
894	C₂×C₈	C₂³×D₄₇	1	1	yes	characteristic
895	C₂×C₈	C₂³×D₄₇	1	1	yes	characteristic
896	C₄⋊C₄	—	2	2	no	—
897	C₄⋊C₄	—	2	2	no	—
898	C₄⋊C₄	—	47	1	no	—
899	C₄⋊C₄	—	47	1	no	—
900	C₄⋊C₄	—	47	1	no	—
901	C₄⋊C₄	—	47	1	no	—
902	C₄⋊C₄	—	47	1	no	—
903	C₄⋊C₄	—	47	1	no	—
904	C₄⋊C₄	—	47	1	no	—
905	C₄⋊C₄	—	47	1	no	—
906	C₄⋊C₄	—	47	1	no	—
907	C₄⋊C₄	—	47	1	no	—
908	C₄⋊C₄	—	47	2	no	—
909	C₄⋊C₄	—	47	2	no	—
910	C₄⋊C₄	—	94	2	no	—
911	C₄⋊C₄	—	94	2	no	—
912	C₄⋊C₄	—	94	2	no	—
913	C₄⋊C₄	—	94	2	no	—
914	C₄⋊C₄	—	94	2	no	—
915	C₄⋊C₄	—	94	2	no	—
916	C₄⋊C₄	—	94	2	no	—
917	C₄⋊C₄	—	94	2	no	—
918	C₄⋊C₄	—	94	2	no	—
919	C₄⋊C₄	—	94	2	no	—
920	C₄⋊C₄	—	94	2	no	—
921	C₄⋊C₄	—	94	2	no	—
922	C₄⋊C₄	—	94	2	no	—
923	C₄⋊C₄	—	94	2	no	—
924	C₄⋊C₄	C₂³×D₄₇	1	2	yes	—
925	C₄⋊C₄	C₂³×D₄₇	1	2	yes	—
926	C₂²⋊C₄	—	2	2	no	—
927	C₂²⋊C₄	—	2	2	no	—
928	C₂²⋊C₄	—	2	2	no	—
929	C₂²⋊C₄	—	47	1	no	—
930	C₂²⋊C₄	—	47	1	no	—
931	C₂²⋊C₄	—	47	1	no	—
932	C₂²⋊C₄	—	47	1	no	—
933	C₂²⋊C₄	—	47	1	no	—
934	C₂²⋊C₄	—	47	1	no	—
935	C₂²⋊C₄	—	47	1	no	—
936	C₂²⋊C₄	—	47	1	no	—
937	C₂²⋊C₄	—	47	1	no	—
938	C₂²⋊C₄	—	47	1	no	—
939	C₂²⋊C₄	—	94	2	no	—
940	C₂²⋊C₄	—	94	2	no	—
941	C₂²⋊C₄	—	94	2	no	—
942	C₂²⋊C₄	—	94	2	no	—
943	C₂²⋊C₄	—	94	2	no	—
944	C₂²⋊C₄	—	94	2	no	—
945	C₂²⋊C₄	—	94	2	no	—
946	C₂²⋊C₄	—	94	2	no	—
947	C₂²⋊C₄	—	94	2	no	—
948	C₂²⋊C₄	—	94	2	no	—
949	C₂²⋊C₄	—	94	2	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	C₄²	—	2	2	no	—
955	C₄²	—	2	2	no	—
956	C₄²	—	2	2	no	—
957	C₄²	—	47	1	no	—
958	C₄²	—	47	1	no	—
959	C₄²	—	94	2	no	—
960	C₄²	—	94	2	no	—
961	C₄²	—	94	2	no	—
962	C₄²	D₄×D₄₇	1	1	yes	characteristic
963	C₄²	D₄×D₄₇	1	1	yes	characteristic
964	C₄²	C₂³×D₄₇	1	1	yes	characteristic
965	C₄²	C₂³×D₄₇	1	1	yes	characteristic
966	C₂³	—	2	2	no	—
967	C₂³	—	47	1	no	—
968	C₂³	—	47	1	no	—
969	C₂³	—	94	2	no	—
970	C₂³	—	376	2	no	—
971	C₂³	—	376	2	no	—
972	C₂³	—	188	4	no	—
973	C₂³	C₂×D₄×D₄₇	1	1	yes	characteristic
974	Q₈	—	2	2	no	—
975	Q₈	—	2	2	no	—
976	Q₈	—	94	2	no	—
977	Q₈	—	94	2	no	—
978	Q₈	—	376	2	no	—
979	Q₈	—	188	1	no	—
980	D₄	—	2	2	no	—
981	D₄	—	4	4	no	—
982	D₄	—	94	2	no	—
983	D₄	—	94	2	no	—
984	D₄	—	376	2	no	—
985	D₄	—	376	2	no	—
986	D₄	—	188	1	no	—
987	D₄	—	188	1	no	—
988	D₄	—	188	1	no	—
989	D₄	—	188	4	no	—
990	D₄	—	188	4	no	—
991	D₄	C₂×#10625350	1	4	yes	—
992	C₂×C₄	—	2	1	no	—
993	C₂×C₄	—	2	1	no	—
994	C₂×C₄	—	2	2	no	—
995	C₂×C₄	—	2	2	no	—
996	C₂×C₄	—	2	2	no	—
997	C₂×C₄	—	4	1	no	—
998	C₂×C₄	—	4	1	no	—
999	C₂×C₄	—	4	4	no	—
1000	C₂×C₄	—	8	2	no	—
1001	C₂×C₄	—	8	2	no	—
1002	C₂×C₄	—	47	1	no	—
1003	C₂×C₄	—	47	1	no	—
1004	C₂×C₄	—	47	1	no	—
1005	C₂×C₄	—	47	1	no	—
1006	C₂×C₄	—	47	1	no	—
1007	C₂×C₄	—	47	1	no	—
1008	C₂×C₄	—	94	1	no	—
1009	C₂×C₄	—	94	1	no	—
1010	C₂×C₄	—	94	1	no	—
1011	C₂×C₄	—	94	1	no	—
1012	C₂×C₄	—	94	2	no	—
1013	C₂×C₄	—	94	2	no	—
1014	C₂×C₄	—	94	2	no	—
1015	C₂×C₄	—	376	2	no	—
1016	C₂×C₄	—	376	2	no	—
1017	C₂×C₄	—	376	2	no	—
1018	C₂×C₄	—	376	2	no	—
1019	C₂×C₄	—	376	2	no	—
1020	C₂×C₄	—	188	4	no	—
1021	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
1022	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
1023	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
1024	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
1025	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
1026	C₂×C₄	C₂⁴×D₄₇	1	1	yes	characteristic
1027	C₈	—	2	1	no	—
1028	C₈	—	2	1	no	—
1029	C₈	—	2	1	no	—
1030	C₈	—	94	1	no	—
1031	C₈	—	94	1	no	—
1032	C₈	—	94	1	no	—
1033	C₈	—	94	1	no	—
1034	C₈	C₂×#10625350	1	2	yes	—
1035	C₂²	—	2	1	no	—
1036	C₂²	—	2	4	no	—
1037	C₂²	—	2	1	no	—
1038	C₂²	—	2	1	no	—
1039	C₂²	—	4	2	no	—
1040	C₂²	—	4	2	no	—
1041	C₂²	—	94	1	no	—
1042	C₂²	—	94	1	no	—
1043	C₂²	—	94	1	no	—
1044	C₂²	—	94	1	no	—
1045	C₂²	—	94	1	no	—
1046	C₂²	—	94	1	no	—
1047	C₂²	—	188	2	no	—
1048	C₂²	—	188	2	no	—
1049	C₂²	—	188	2	no	—
1050	C₂²	—	752	4	no	—
1051	C₂²	C₂²×D₄×D₄₇	1	1	yes	characteristic
1052	C₄	—	2	1	no	—
1053	C₄	—	2	1	no	—
1054	C₄	—	2	1	no	—
1055	C₄	—	2	1	no	—
1056	C₄	—	2	1	no	—
1057	C₄	—	4	2	no	—
1058	C₄	—	4	2	no	—
1059	C₄	—	4	2	no	—
1060	C₄	—	94	1	no	—
1061	C₄	—	94	1	no	—
1062	C₄	—	94	1	no	—
1063	C₄	—	94	1	no	—
1064	C₄	—	94	1	no	—
1065	C₄	—	94	1	no	—
1066	C₄	—	188	2	no	—
1067	C₄	—	188	2	no	—
1068	C₄	—	188	2	no	—
1069	C₄	C₂²×#10625350	1	1	yes	characteristic
1070	C₄	#15689959	1	1	yes	characteristic
1071	C₂	—	4	1	no	—
1072	C₂	—	4	4	no	—
1073	C₂	—	376	2	no	—
1074	C₂	—	188	1	no	—
1075	C₂	—	188	1	no	—
1076	C₂	D₄×#10625350	1	1	yes	characteristic
1077	C₂	#20258157	1	1	yes	characteristic
1078	C₂	#20258157	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂²×D₄×D₄₇
commutator, cosocle	C₂×C₄×C₄₇	C₂⁵
Frattini	C₂×C₄	C₂⁴×D₄₇
Fitting	C₄×#135×C₄₇	C₂
socle	C₂²×C₄₇	C₂³×D₄
hypercenter	C₄×#135	D₄₇
hypocenter	C₄₇	#61487
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ C₄×#135

Complements

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

N	H ≅ G/N	type
1. #20257456	C₂	semidirect
2. #20256376	C₂	semidirect
3. #20256255	C₂	semidirect
4. #20256211	C₂	semidirect
5. #20255816	C₂	semidirect
6. #20255790	C₂	semidirect
7. #20255758	C₂	semidirect
8. #20255609	C₂	semidirect
9. #20255420	C₂	semidirect
10. #20255360	C₂	semidirect
11. #20255104	C₂	semidirect
12. #20255074	C₂	semidirect
13. #20255067	C₂	semidirect
14. #20254043	C₂	semidirect
15. #20254029	C₂	semidirect
16. #20253958	C₂	semidirect
17. #20253661	C₂	semidirect
18. #20253637	C₂	semidirect
19. #20253497	C₂	semidirect
20. #20252363	C₂	semidirect
21. #20252258	C₂	semidirect
22. #20252235	C₂	semidirect
23. C₄×#135×C₄₇	C₂	semidirect
26. #15689845	C₂²	semidirect
28. #15689832	C₂²	semidirect
30. #15689817	C₂²	semidirect
35. #15689772	C₂²	semidirect
38. #15689745	C₂²	semidirect
44. #15689657	C₂²	semidirect
46. #15689602	C₂²	semidirect
48. #15689527	C₂²	semidirect
49. #15689525	C₂²	semidirect
50. #15689524	C₂²	semidirect
53. #15689501	C₂²	semidirect
54. #15689490	C₂²	semidirect
55. #15689484	C₂²	semidirect
56. #15689478	C₂²	semidirect
58. #15689464	C₂²	semidirect
60. #15689452	C₂²	semidirect
61. #15689447	C₂²	semidirect
62. #15689443	C₂²	semidirect
63. #15689430	C₂²	semidirect
64. #15689425	C₂²	semidirect
65. #15689423	C₂²	semidirect
66. #15689422	C₂²	semidirect
67. #15689411	C₂²	semidirect
68. #15689407	C₂²	semidirect
70. #15689372	C₂²	semidirect
72. #15689364	C₂²	semidirect
74. #15689361	C₂²	semidirect
77. #15689352	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. #15689253	C₂²	semidirect
91. C₈×Dic₉₄	C₂²	semidirect
94. #15689228	C₂²	semidirect
95. #15689223	C₂²	semidirect
96. #15689221	C₂²	semidirect
97. #15689220	C₂²	semidirect
98. C₄×Dic₁₈₈	C₂²	semidirect
99. #15689217	C₂²	semidirect
100. C₄×#10625325	C₂²	semidirect
107. #15689194	C₂²	semidirect
110. C₈×C₂²⋊D₄₇	C₂²	semidirect
112. #15689182	C₂²	semidirect
113. #15689180	C₂²	semidirect
115. #107×D₄₇	C₂²	semidirect
117. #15689121	C₂²	semidirect
119. #15689077	C₂²	semidirect
121. C₄×#41×C₄₇	C₂²	semidirect
122. C₄×Q₁₆×C₄₇	C₂²	semidirect
123. C₄×Q₁₆×C₄₇	C₂²	semidirect
124. C₄×SD₁₆×C₄₇	C₂²	semidirect
125. C₄×SD₁₆×C₄₇	C₂²	semidirect
128. C₄₇×#427	C₂²	semidirect
129. C₄₇×#416	C₂²	semidirect
130. C₂×C₄×C₈×C₄₇	C₂²	semidirect
554. C₄×#135	D₄₇	semidirect
588. C₄×#41	C₂×D₄₇	semidirect
641. C₄×Q₁₆	C₂×D₄₇	semidirect
642. C₄×Q₁₆	C₂×D₄₇	semidirect
644. C₄×SD₁₆	C₂×D₄₇	semidirect
645. C₄×SD₁₆	C₂×D₄₇	semidirect
662. #427	C₂×D₄₇	semidirect
666. #416	C₂×D₄₇	semidirect
669. C₂×C₄×C₈	C₂×D₄₇	semidirect
670. C₄₇	#61487	semidirect

Maximal subgroups

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

subgroup	index
#20257456	2
#20256376	2
#20256255	2
#20256211	2
#20255816	2
#20255790	2
#20255758	2
#20255609	2
#20255420	2
#20255360	2
#20255104	2
#20255074	2
#20255067	2
#20254043	2
#20254029	2
#20253958	2
#20253661	2
#20253637	2
#20253497	2
#20252363	2
#20252258	2
#20252235	2
C₄×#135×C₄₇	2
#61487	47