Subgroups — #27085946

Order 12032.

1798 conjugacy classes of subgroups.

The subgroup lattice has 1082 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20256792	C₂	1	1	yes	maximal, characteristic
2	#544×D₄₇	C₂	1	1	yes	maximal, characteristic
3	#20253939	C₂	1	2	yes	maximal, complemented
4	#20253936	C₂	1	2	yes	maximal, complemented
5	#20253933	C₂	1	2	yes	maximal, complemented
6	#20253931	C₂	1	2	yes	maximal, complemented
7	#20253926	C₂	1	1	yes	maximal, characteristic, complemented
8	#20253924	C₂	1	1	yes	maximal, characteristic, complemented
9	#20253923	C₂	1	2	yes	maximal, complemented
10	#20253922	C₂	1	1	yes	maximal, characteristic, complemented
11	#20253921	C₂	1	2	yes	maximal, complemented
12	#20253920	C₂	1	1	yes	maximal, characteristic, complemented
13	#20253919	C₂	1	1	yes	maximal, characteristic, complemented
14	#20253918	C₂	1	1	yes	maximal, characteristic, complemented
15	#20253917	C₂	1	2	yes	maximal, complemented
16	#20253915	C₂	1	2	yes	maximal, complemented
17	#20253914	C₂	1	1	yes	maximal, characteristic, complemented
18	#20251976	C₂	1	1	yes	maximal, characteristic
19	#20251975	C₂	1	1	yes	maximal, characteristic
20	C₂×#15689164	C₂	1	1	yes	maximal, characteristic
21	#428×D₄₇	C₂	1	1	yes	maximal, characteristic
22	#20251804	C₂	1	1	yes	maximal, characteristic
23	C₄₇×#3164	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂²×#10625324	C₂²	1	1	yes	characteristic
25	C₂×M₁₆×D₄₇	C₂²	1	1	yes	characteristic
26	#15689754	C₂²	1	1	yes	characteristic
27	#15689754	C₂²	1	1	yes	characteristic
28	#15689753	—	2	1	no	—
29	#15689753	—	2	1	no	—
30	#15689753	C₂²	1	2	yes	—
31	#15689753	C₂²	1	2	yes	—
32	#15689752	—	2	2	no	—
33	#15689751	C₂²	1	1	yes	characteristic
34	#15689751	C₂²	1	1	yes	characteristic
35	#15689751	C₂²	1	1	yes	characteristic
36	#15689751	C₂²	1	1	yes	characteristic
37	#15689750	—	2	1	no	—
38	#15689750	—	2	1	no	—
39	#15689750	C₂²	1	2	yes	—
40	#15689750	C₂²	1	2	yes	—
41	#15689748	—	2	2	no	—
42	#15689679	—	2	1	no	—
43	#15689679	C₂²	1	2	yes	—
44	#15689678	—	2	1	no	—
45	#15689678	C₂²	1	2	yes	—
46	#15689675	—	2	2	no	—
47	C₄⋊Q₈×D₄₇	—	2	1	no	—
48	C₄⋊Q₈×D₄₇	C₂²	1	2	yes	—
49	#125×D₄₇	—	2	1	no	—
50	#125×D₄₇	C₂²	1	2	yes	—
51	C₂²⋊Q₈×D₄₇	—	2	2	no	—
52	C₂×#13093982	C₂²	1	1	yes	characteristic
53	#117×D₄₇	C₂²	1	1	yes	characteristic
54	#117×D₄₇	C₂²	1	1	yes	characteristic
55	#117×D₄₇	C₂²	1	1	yes	characteristic
56	C₂×C₄⋊C₄×D₄₇	C₂²	1	1	yes	characteristic
57	#15689533	C₂²	1	2	yes	complemented
58	#15689533	C₂²	1	2	yes	complemented
59	#15689532	C₂²	1	2	yes	complemented
60	#15689532	C₂²	1	2	yes	complemented
61	#15689531	C₂²	1	2	yes	complemented
62	#15689531	C₂²	1	2	yes	complemented
63	#15689531	C₂²	1	2	yes	complemented
64	#15689531	C₂²	1	2	yes	complemented
65	#15689531	C₂²	1	2	yes	complemented
66	#15689531	C₂²	1	2	yes	complemented
67	#15689530	C₂²	1	2	yes	complemented
68	#15689530	C₂²	1	2	yes	complemented
69	#15689529	C₂²	1	2	yes	complemented
70	#15689529	C₂²	1	2	yes	complemented
71	#15689527	C₂²	1	2	yes	complemented
72	#15689527	C₂²	1	2	yes	complemented
73	#15689526	C₂²	1	2	yes	complemented
74	#15689525	C₂²	1	2	yes	complemented
75	#15689524	C₂²	1	2	yes	complemented
76	#15689524	C₂²	1	2	yes	complemented
77	#15689523	C₂²	1	2	yes	complemented
78	#15689523	C₂²	1	2	yes	complemented
79	#15689522	C₂²	1	2	yes	complemented
80	#15689522	C₂²	1	2	yes	complemented
81	#15689521	C₂²	1	2	yes	complemented
82	#15689520	C₂²	1	2	yes	complemented
83	#15689520	C₂²	1	2	yes	complemented
84	#15689519	C₂²	1	2	yes	complemented
85	#15689166	C₂²	1	1	yes	characteristic
86	#15689166	C₂²	1	1	yes	characteristic
87	#15689165	C₂²	1	1	yes	characteristic
88	#15689165	C₂²	1	1	yes	characteristic
89	#15689164	C₂²	1	2	yes	—
90	#15689164	C₂²	1	2	yes	—
91	#15689164	C₂²	1	2	yes	—
92	#15689164	C₂²	1	2	yes	—
93	#15689164	C₂²	1	2	yes	—
94	#15689164	C₂²	1	2	yes	—
95	#15689164	C₂²	1	1	yes	characteristic
96	#15689164	C₂²	1	1	yes	characteristic
97	#15689164	C₂²	1	1	yes	characteristic
98	#15689164	C₂²	1	1	yes	characteristic
99	#15689163	C₂²	1	1	yes	characteristic
100	#15689163	C₂²	1	1	yes	characteristic
101	#15689162	C₂²	1	2	yes	—
102	#15689162	C₂²	1	2	yes	—
103	#15689162	C₂²	1	1	yes	characteristic
104	#15689162	C₂²	1	1	yes	characteristic
105	#15689162	C₂²	1	1	yes	characteristic
106	#15689162	C₂²	1	1	yes	characteristic
107	#15689161	C₂²	1	1	yes	characteristic
108	#15689160	C₂²	1	2	yes	—
109	#15689159	C₂²	1	1	yes	characteristic
110	#15689159	C₂²	1	1	yes	characteristic
111	#15689158	C₂²	1	2	yes	—
112	C₂×#13093957	C₂²	1	1	yes	characteristic
113	#107×D₄₇	C₂²	1	2	yes	—
114	C₂×#13093956	C₂²	1	1	yes	characteristic
115	C₂×#13093955	C₂²	1	1	yes	characteristic
116	#106×D₄₇	C₂²	1	2	yes	—
117	#15689081	C₂²	1	1	yes	characteristic
118	#15689080	C₂²	1	2	yes	—
119	#15689079	C₂²	1	1	yes	characteristic
120	#15689078	C₂²	1	1	yes	characteristic
121	#15689077	C₂²	1	2	yes	—
122	#15689075	C₂²	1	2	yes	—
123	C₄×#10625324	C₂²	1	2	yes	—
124	C₄₇×#544	C₂²	1	1	yes	characteristic
125	C₄₇×#544	C₂²	1	1	yes	characteristic
126	C₄₇×#501	C₂²	1	2	yes	complemented
127	C₄₇×#501	C₂²	1	2	yes	complemented
128	C₄₇×#500	C₂²	1	2	yes	complemented
129	C₄₇×#499	C₂²	1	2	yes	complemented
130	C₄₇×#428	C₂²	1	1	yes	characteristic
131	C₄₇×#428	C₂²	1	1	yes	characteristic
132	C₄₇×#427	C₂²	1	1	yes	characteristic
133	C₂×#107×C₄₇	C₂²	1	1	yes	characteristic
134	C₄₇×#405	C₂²	1	1	yes	characteristic
135	C₂×Q₈×D₄₇	—	2	2	no	—
136	C₂²×C₄×D₄₇	—	2	1	no	—
137	C₂²×C₄×D₄₇	C₂³	1	1	yes	characteristic
138	C₂×#10625329	C₂³	1	1	yes	characteristic
139	C₂×#10625324	Q₈	1	8	yes	complemented
140	C₂×#10625324	C₂³	1	1	yes	characteristic
141	C₂×#10625324	C₂³	1	2	yes	—
142	C₂×#10625324	C₂³	1	1	yes	characteristic
143	C₂×#10625324	C₂³	1	1	yes	characteristic
144	C₂×#10625324	C₂³	1	1	yes	characteristic
145	M₁₆×D₄₇	Q₈	1	8	yes	complemented
146	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
147	C₂×C₈×D₄₇	C₂³	1	2	yes	—
148	#13094024	—	2	1	no	—
149	#13094024	—	2	1	no	—
150	#13094024	C₂³	1	2	yes	—
151	#13094024	C₂³	1	2	yes	—
152	#13094023	—	2	1	no	—
153	#13094023	—	2	1	no	—
154	#13094023	—	2	1	no	—
155	#13094023	—	2	1	no	—
156	#13094023	—	2	2	no	—
157	#13094023	—	2	2	no	—
158	#13094023	—	2	2	no	—
159	#13094023	C₂³	1	2	yes	—
160	#13094023	C₂³	1	2	yes	—
161	#13094023	C₂³	1	2	yes	—
162	#13094023	C₂³	1	2	yes	—
163	#13094022	—	2	2	no	—
164	#13094022	—	2	2	no	—
165	#13094022	—	2	2	no	—
166	#13094016	—	2	1	no	—
167	#13094016	—	2	1	no	—
168	#13094016	C₂³	1	2	yes	—
169	#13094016	C₂³	1	2	yes	—
170	#13094015	—	2	1	no	—
171	#13094015	—	2	1	no	—
172	#13094015	—	2	1	no	—
173	#13094015	—	2	1	no	—
174	#13094015	C₂³	1	2	yes	—
175	#13094015	C₂³	1	2	yes	—
176	#13094015	C₂³	1	2	yes	—
177	#13094015	C₂³	1	2	yes	—
178	#13094014	—	2	2	no	—
179	#13094014	—	2	2	no	—
180	#13094014	—	2	2	no	—
181	#13094014	—	2	2	no	—
182	#13094014	—	2	2	no	—
183	#13094014	—	2	2	no	—
184	#13094004	—	2	2	no	—
185	#13094004	—	2	2	no	—
186	#13094004	—	2	2	no	—
187	#13094003	—	2	2	no	—
188	#13094003	—	2	2	no	—
189	#13094002	—	2	2	no	—
190	#13094002	—	2	2	no	—
191	#13094002	—	2	2	no	—
192	#13094002	—	2	2	no	—
193	#13094002	—	2	2	no	—
194	#13094002	—	2	2	no	—
195	#13094001	—	2	2	no	—
196	#13094001	—	2	2	no	—
197	#13094001	—	2	2	no	—
198	#13094001	—	2	2	no	—
199	#13094000	—	2	2	no	—
200	#13094000	—	2	2	no	—
201	#13094000	—	2	2	no	—
202	Q₈×Dic₄₇	—	2	2	no	—
203	#13093989	—	2	2	no	—
204	#13093989	—	2	2	no	—
205	#13093989	—	2	2	no	—
206	#13093983	C₂³	1	1	yes	characteristic
207	#13093983	C₂³	1	1	yes	characteristic
208	#13093983	C₂³	1	1	yes	characteristic
209	#13093982	—	2	1	no	—
210	#13093982	—	2	1	no	—
211	#13093982	D₄	1	1	yes	characteristic
212	#13093982	D₄	1	1	yes	characteristic
213	#13093982	C₂³	1	1	yes	characteristic
214	#13093982	C₂³	1	2	yes	—
215	#13093982	C₂³	1	1	yes	characteristic
216	#13093982	C₂³	1	1	yes	characteristic
217	#13093982	C₂³	1	1	yes	characteristic
218	#13093982	C₂³	1	2	yes	—
219	#13093981	—	2	1	no	—
220	#13093981	—	2	1	no	—
221	#13093981	C₂³	1	2	yes	—
222	#13093980	—	2	1	no	—
223	#13093980	—	2	1	no	—
224	#13093980	D₄	1	2	yes	—
225	C₂×C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic
226	C₂×C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic
227	C₂×Dic₄₇⋊C₄	—	2	1	no	—
228	C₄⋊C₄×D₄₇	—	2	1	no	—
229	C₄⋊C₄×D₄₇	—	2	1	no	—
230	C₄⋊C₄×D₄₇	—	2	2	no	—
231	C₄⋊C₄×D₄₇	—	2	2	no	—
232	C₄⋊C₄×D₄₇	—	2	2	no	—
233	C₄⋊C₄×D₄₇	D₄	1	1	yes	characteristic
234	C₄⋊C₄×D₄₇	D₄	1	1	yes	characteristic
235	C₄⋊C₄×D₄₇	C₂³	1	1	yes	characteristic
236	C₄⋊C₄×D₄₇	C₂³	1	2	yes	—
237	C₄⋊C₄×D₄₇	C₂³	1	1	yes	characteristic
238	C₄⋊C₄×D₄₇	C₂³	1	2	yes	—
239	C₄⋊C₄×D₄₇	C₂³	1	1	yes	characteristic
240	C₄⋊C₄×D₄₇	C₂³	1	1	yes	characteristic
241	C₂×(C₂×D₄₇)⋊C₄	—	2	1	no	—
242	C₂²⋊C₄×D₄₇	—	2	1	no	—
243	C₂²⋊C₄×D₄₇	—	2	1	no	—
244	C₂²⋊C₄×D₄₇	D₄	1	2	yes	—
245	C₂×C₄×Dic₄₇	—	2	1	no	—
246	C₄²×D₄₇	—	2	1	no	—
247	C₄²×D₄₇	—	2	1	no	—
248	C₄²×D₄₇	C₂³	1	2	yes	—
249	#13093958	C₂³	1	1	yes	characteristic
250	#13093958	C₂³	1	2	yes	—
251	#13093958	C₂³	1	2	yes	—
252	#13093958	C₂³	1	1	yes	characteristic
253	#13093957	C₂³	1	1	yes	characteristic
254	#13093957	C₂³	1	2	yes	—
255	#13093957	C₂³	1	2	yes	—
256	#13093957	C₂³	1	2	yes	—
257	#13093957	C₂³	1	1	yes	characteristic
258	#13093957	C₂³	1	2	yes	—
259	#13093957	C₂³	1	2	yes	—
260	#13093957	C₂³	1	1	yes	characteristic
261	#13093957	C₂³	1	2	yes	—
262	#13093957	C₂³	1	1	yes	characteristic
263	#13093956	C₂³	1	2	yes	—
264	#13093956	C₂³	1	2	yes	—
265	#13093956	C₂³	1	1	yes	characteristic
266	#13093956	C₂³	1	2	yes	—
267	#13093956	C₂³	1	2	yes	—
268	#13093956	C₂³	1	1	yes	characteristic
269	#13093955	C₂³	1	1	yes	characteristic
270	#13093955	C₂³	1	2	yes	—
271	#13093955	C₂³	1	2	yes	—
272	#13093955	C₂³	1	2	yes	—
273	#13093955	C₂³	1	1	yes	characteristic
274	#13093955	C₂³	1	2	yes	—
275	#13093955	C₂³	1	2	yes	—
276	#13093955	C₂³	1	1	yes	characteristic
277	#13093955	C₂³	1	2	yes	—
278	#13093955	C₂³	1	1	yes	characteristic
279	#13093935	C₂³	1	2	yes	—
280	#13093934	C₂³	1	2	yes	—
281	#13093934	C₂³	1	2	yes	—
282	C₄×C₄₇⋊C₈	C₂³	1	2	yes	—
283	C₈×Dic₄₇	C₂³	1	2	yes	—
284	C₈×Dic₄₇	C₂³	1	2	yes	—
285	C₂×M₁₆×C₄₇	C₂³	1	1	yes	characteristic
286	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
287	C₄⋊Q₈×C₄₇	—	2	1	no	—
288	C₄⋊Q₈×C₄₇	—	2	1	no	—
289	C₄⋊Q₈×C₄₇	C₂³	1	2	yes	—
290	C₄⋊Q₈×C₄₇	C₂³	1	2	yes	—
291	#125×C₄₇	—	2	1	no	—
292	#125×C₄₇	—	2	1	no	—
293	#125×C₄₇	C₂³	1	2	yes	—
294	#125×C₄₇	C₂³	1	2	yes	—
295	C₂²⋊Q₈×C₄₇	—	2	2	no	—
296	C₂²⋊Q₈×C₄₇	—	2	2	no	—
297	#117×C₄₇	C₂³	1	1	yes	characteristic
298	#117×C₄₇	C₂³	1	1	yes	characteristic
299	#117×C₄₇	C₂³	1	1	yes	characteristic
300	C₂×C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
301	C₂×C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
302	#107×C₄₇	C₂³	1	1	yes	characteristic
303	#107×C₄₇	C₂³	1	2	yes	—
304	#107×C₄₇	C₂³	1	1	yes	characteristic
305	#107×C₄₇	C₂³	1	2	yes	—
306	#107×C₄₇	C₂³	1	2	yes	—
307	#107×C₄₇	C₂³	1	2	yes	—
308	#106×C₄₇	C₂³	1	1	yes	characteristic
309	#106×C₄₇	C₂³	1	2	yes	—
310	#106×C₄₇	C₂³	1	2	yes	—
311	#106×C₄₇	C₂³	1	1	yes	characteristic
312	#97×C₄₇	C₂³	1	2	yes	—
313	C₄×C₈×C₄₇	C₂³	1	2	yes	—
314	C₂³×D₄₇	C₂×D₄	1	1	yes	characteristic
315	C₂×Q₈×C₄₇	—	2	2	no	—
316	C₂×Q₈×C₄₇	—	2	2	no	—
317	C₂²×C₄×C₄₇	—	2	1	no	—
318	C₂²×C₄×C₄₇	—	2	1	no	—
319	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
320	C₂²×Dic₄₇	—	2	1	no	—
321	C₂²×Dic₄₇	—	2	1	no	—
322	C₂²×Dic₄₇	C₂×D₄	1	1	yes	characteristic
323	Q₈×D₄₇	—	8	4	no	—
324	C₂×C₄×D₄₇	—	2	1	no	—
325	C₂×C₄×D₄₇	—	2	1	no	—
326	C₂×C₄×D₄₇	—	2	2	no	—
327	C₂×C₄×D₄₇	—	2	1	no	—
328	C₂×C₄×D₄₇	—	2	1	no	—
329	C₂×C₄×D₄₇	—	2	2	no	—
330	C₂×C₄×D₄₇	—	8	2	no	—
331	C₂×C₄×D₄₇	C₂×D₄	1	2	yes	—
332	C₂×C₄×D₄₇	C₂×D₄	1	2	yes	—
333	C₂×C₄×D₄₇	C₂×D₄	1	1	yes	characteristic
334	C₂×C₄×D₄₇	C₂×D₄	1	1	yes	characteristic
335	C₂×C₄×D₄₇	C₂×Q₈	1	4	yes	—
336	C₂×C₄×D₄₇	C₂×Q₈	1	4	yes	—
337	C₂×C₄×D₄₇	C₂⁴	1	1	yes	characteristic
338	C₂×C₄×D₄₇	C₂⁴	1	1	yes	characteristic
339	C₂×Dic₉₄	—	2	2	no	—
340	C₂×Dic₉₄	—	2	2	no	—
341	C₂×Dic₉₄	—	2	2	no	—
342	C₂×Dic₉₄	—	2	2	no	—
343	C₂×Dic₉₄	—	2	2	no	—
344	C₂×Dic₉₄	—	2	2	no	—
345	M₁₆×C₄₇	C₂×Q₈	1	4	yes	complemented
346	C₂×C₈×C₄₇	C₂×Q₈	1	4	yes	complemented
347	C₂×C₈×C₄₇	C₂⁴	1	1	yes	characteristic
348	C₂×C₈×C₄₇	C₂⁴	1	2	yes	—
349	C₂×C₈×C₄₇	C₂⁴	1	1	yes	characteristic
350	C₄⋊C₄×C₄₇	—	2	1	no	—
351	C₄⋊C₄×C₄₇	—	2	1	no	—
352	C₄⋊C₄×C₄₇	—	2	2	no	—
353	C₄⋊C₄×C₄₇	—	2	2	no	—
354	C₄⋊C₄×C₄₇	—	2	2	no	—
355	C₄⋊C₄×C₄₇	—	2	2	no	—
356	C₄⋊C₄×C₄₇	—	2	2	no	—
357	C₄⋊C₄×C₄₇	—	2	2	no	—
358	C₄⋊C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
359	C₄⋊C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
360	C₄⋊C₄×C₄₇	C₂⁴	1	1	yes	characteristic
361	C₄⋊C₄×C₄₇	C₂⁴	1	1	yes	characteristic
362	C₄⋊C₄×C₄₇	C₂⁴	1	2	yes	—
363	C₄⋊C₄×C₄₇	C₂⁴	1	2	yes	—
364	C₄⋊C₄×C₄₇	C₂⁴	1	1	yes	characteristic
365	C₄⋊C₄×C₄₇	C₂⁴	1	1	yes	characteristic
366	C₂²⋊C₄×C₄₇	—	2	1	no	—
367	C₂²⋊C₄×C₄₇	—	2	1	no	—
368	C₂²⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
369	C₄²×C₄₇	—	2	1	no	—
370	C₄²×C₄₇	—	2	1	no	—
371	C₄²×C₄₇	C₂⁴	1	2	yes	—
372	C₂²⋊Dic₄₇	—	2	1	no	—
373	C₂²⋊Dic₄₇	—	2	1	no	—
374	C₂²⋊Dic₄₇	C₂×D₄	1	2	yes	—
375	(C₂×D₄₇)⋊C₄	—	2	1	no	—
376	(C₂×D₄₇)⋊C₄	—	2	1	no	—
377	(C₂×D₄₇)⋊C₄	—	2	1	no	—
378	(C₂×D₄₇)⋊C₄	—	2	1	no	—
379	(C₂×D₄₇)⋊C₄	—	2	2	no	—
380	(C₂×D₄₇)⋊C₄	—	2	2	no	—
381	(C₂×D₄₇)⋊C₄	C₂×D₄	1	2	yes	—
382	(C₂×D₄₇)⋊C₄	C₂×D₄	1	2	yes	—
383	C₄⋊Dic₄₇	—	2	1	no	—
384	C₄⋊Dic₄₇	—	2	2	no	—
385	C₄⋊Dic₄₇	—	2	1	no	—
386	C₄⋊Dic₄₇	—	2	2	no	—
387	C₄⋊Dic₄₇	—	2	2	no	—
388	C₄⋊Dic₄₇	—	2	2	no	—
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	1	yes	characteristic
394	C₄⋊Dic₄₇	C₂⁴	1	2	yes	—
395	C₄⋊Dic₄₇	C₂⁴	1	1	yes	characteristic
396	C₄⋊Dic₄₇	C₂⁴	1	2	yes	—
397	C₄⋊Dic₄₇	C₂⁴	1	1	yes	characteristic
398	C₄⋊Dic₄₇	C₂⁴	1	1	yes	characteristic
399	Dic₄₇⋊C₄	—	2	2	no	—
400	Dic₄₇⋊C₄	—	2	2	no	—
401	Dic₄₇⋊C₄	—	2	2	no	—
402	Dic₄₇⋊C₄	—	2	2	no	—
403	Dic₄₇⋊C₄	—	2	2	no	—
404	Dic₄₇⋊C₄	—	2	2	no	—
405	Dic₄₇⋊C₄	—	2	2	no	—
406	Dic₄₇⋊C₄	—	2	2	no	—
407	Dic₄₇⋊C₄	—	2	2	no	—
408	Dic₄₇⋊C₄	—	2	2	no	—
409	Dic₄₇⋊C₄	—	2	1	no	—
410	Dic₄₇⋊C₄	—	2	1	no	—
411	Dic₄₇⋊C₄	—	2	1	no	—
412	Dic₄₇⋊C₄	—	2	1	no	—
413	Dic₄₇⋊C₄	—	2	2	no	—
414	Dic₄₇⋊C₄	—	2	2	no	—
415	Dic₄₇⋊C₄	—	2	2	no	—
416	Dic₄₇⋊C₄	—	2	2	no	—
417	Dic₄₇⋊C₄	C₂×D₄	1	2	yes	—
418	Dic₄₇⋊C₄	C₂×D₄	1	2	yes	—
419	C₄×Dic₄₇	—	2	1	no	—
420	C₄×Dic₄₇	—	2	1	no	—
421	C₄×Dic₄₇	—	2	1	no	—
422	C₄×Dic₄₇	—	2	1	no	—
423	C₄×Dic₄₇	—	2	1	no	—
424	C₄×Dic₄₇	—	2	1	no	—
425	C₄×Dic₄₇	—	2	2	no	—
426	C₄×Dic₄₇	—	2	2	no	—
427	C₄×Dic₄₇	C₂×D₄	1	2	yes	—
428	C₄×Dic₄₇	C₂×D₄	1	2	yes	—
429	C₄×Dic₄₇	C₂⁴	1	2	yes	—
430	#10625329	C₂×Q₈	1	4	yes	complemented
431	C₂×C₄₇⋊C₈	C₂×Q₈	1	4	yes	complemented
432	C₂×C₄₇⋊C₈	C₂⁴	1	1	yes	characteristic
433	C₂×C₄₇⋊C₈	C₂⁴	1	2	yes	—
434	C₂×C₄₇⋊C₈	C₂⁴	1	1	yes	characteristic
435	#10625324	C₂×Q₈	1	8	yes	—
436	#10625324	C₂×Q₈	1	4	yes	—
437	#10625324	C₂×Q₈	1	4	yes	—
438	#10625324	C₂×Q₈	1	4	yes	complemented
439	#10625324	C₂×Q₈	1	4	yes	complemented
440	C₈×D₄₇	C₂×Q₈	1	8	yes	complemented
441	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
442	C₂²×D₄₇	—	4	1	no	—
443	C₂²×D₄₇	—	4	1	no	—
444	C₂²×D₄₇	C₄⋊Q₈	1	4	yes	—
445	C₂²×D₄₇	C₂²×D₄	1	1	yes	characteristic
446	C₂²×D₄₇	C₂²×D₄	1	1	yes	characteristic
447	Q₈×C₄₇	—	8	2	no	—
448	Q₈×C₄₇	—	8	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	1	no	—
453	C₂×C₄×C₄₇	—	2	1	no	—
454	C₂×C₄×C₄₇	—	2	2	no	—
455	C₂×C₄×C₄₇	—	8	1	no	—
456	C₂×C₄×C₄₇	—	8	1	no	—
457	C₂×C₄×C₄₇	C₂²×D₄	1	2	yes	—
458	C₂×C₄×C₄₇	C₂²×D₄	1	2	yes	—
459	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
460	C₂×C₄×C₄₇	C₂²×Q₈	1	2	yes	—
461	C₂×C₄×C₄₇	C₂²×Q₈	1	2	yes	—
462	C₂×C₄×C₄₇	C₂⁵	1	1	yes	characteristic
463	C₂×Dic₄₇	—	2	1	no	—
464	C₂×Dic₄₇	—	2	1	no	—
465	C₂×Dic₄₇	—	2	2	no	—
466	C₂×Dic₄₇	—	2	1	no	—
467	C₂×Dic₄₇	—	2	1	no	—
468	C₂×Dic₄₇	—	2	2	no	—
469	C₂×Dic₄₇	—	8	1	no	—
470	C₂×Dic₄₇	—	8	1	no	—
471	C₂×Dic₄₇	C₄⋊Q₈	1	4	yes	—
472	C₂×Dic₄₇	C₂²×D₄	1	2	yes	—
473	C₂×Dic₄₇	C₂²×D₄	1	2	yes	—
474	C₂×Dic₄₇	C₂²×D₄	1	1	yes	characteristic
475	C₂×Dic₄₇	C₂²×D₄	1	1	yes	characteristic
476	C₄×D₄₇	—	4	2	no	—
477	C₄×D₄₇	—	4	2	no	—
478	C₄×D₄₇	—	4	2	no	—
479	C₄×D₄₇	—	4	4	no	—
480	C₄×D₄₇	—	4	2	no	—
481	C₄×D₄₇	—	8	1	no	—
482	C₄×D₄₇	—	8	1	no	—
483	C₄×D₄₇	—	8	2	no	—
484	C₄×D₄₇	C₄⋊Q₈	1	4	yes	—
485	C₄×D₄₇	C₄⋊Q₈	1	4	yes	—
486	C₄×D₄₇	C₂²×Q₈	1	2	yes	—
487	C₄×D₄₇	C₂²×Q₈	1	2	yes	—
488	C₄×D₄₇	C₂²×Q₈	1	2	yes	—
489	C₄×D₄₇	C₂²×Q₈	1	2	yes	—
490	Dic₉₄	—	8	2	no	—
491	Dic₉₄	—	8	2	no	—
492	Dic₉₄	—	8	2	no	—
493	Dic₉₄	—	8	2	no	—
494	Dic₉₄	—	8	2	no	—
495	Dic₉₄	—	8	2	no	—
496	C₈×C₄₇	C₂²×Q₈	1	4	yes	—
497	C₈×C₄₇	C₂²×Q₈	1	2	yes	—
498	C₈×C₄₇	C₂²×Q₈	1	2	yes	—
499	C₄₇⋊C₈	C₂²×Q₈	1	4	yes	—
500	C₄₇⋊C₈	C₂²×Q₈	1	2	yes	—
501	C₄₇⋊C₈	C₂²×Q₈	1	2	yes	—
502	#60664	—	47	1	no	maximal, Sylow
503	C₂²×C₄₇	—	2	1	no	—
504	C₂²×C₄₇	—	2	1	no	—
505	C₂²×C₄₇	C₂×C₄⋊Q₈	1	2	yes	—
506	C₂²×C₄₇	C₂³×D₄	1	1	yes	characteristic
507	C₂×D₄₇	—	2	1	no	—
508	C₂×D₄₇	—	2	1	no	—
509	C₂×D₄₇	—	2	1	no	—
510	C₂×D₄₇	—	2	1	no	—
511	C₂×D₄₇	—	4	4	no	—
512	C₂×D₄₇	C₂×C₄⋊Q₈	1	2	yes	—
513	C₂×D₄₇	C₂×C₄⋊Q₈	1	2	yes	—
514	C₄×C₄₇	—	2	2	no	—
515	C₄×C₄₇	—	2	2	no	—
516	C₄×C₄₇	—	4	1	no	—
517	C₄×C₄₇	—	4	2	no	—
518	C₄×C₄₇	—	4	2	no	—
519	C₄×C₄₇	—	4	1	no	—
520	C₄×C₄₇	—	4	1	no	—
521	C₄×C₄₇	—	4	1	no	—
522	C₄×C₄₇	C₂×C₄⋊Q₈	1	2	yes	—
523	C₄×C₄₇	C₂³×Q₈	1	1	yes	characteristic
524	C₄×C₄₇	C₂³×Q₈	1	1	yes	characteristic
525	Dic₄₇	—	2	2	no	—
526	Dic₄₇	—	2	2	no	—
527	Dic₄₇	—	4	1	no	—
528	Dic₄₇	—	4	2	no	—
529	Dic₄₇	—	4	1	no	—
530	Dic₄₇	—	4	1	no	—
531	Dic₄₇	—	4	2	no	—
532	Dic₄₇	—	4	1	no	—
533	Dic₄₇	C₂×C₄⋊Q₈	1	2	yes	—
534	Dic₄₇	C₂×C₄⋊Q₈	1	2	yes	—
535	#3458	—	47	1	no	—
536	C₂×#544	—	47	1	no	—
537	#3166	—	47	2	no	—
538	#3166	—	47	2	no	—
539	#3165	—	47	2	no	—
540	#3165	—	47	2	no	—
541	#3164	—	47	2	no	—
542	#3164	—	47	2	no	—
543	#3164	—	47	1	no	—
544	#3164	—	47	1	no	—
545	#3164	—	47	1	no	—
546	#3164	D₄₇	1	1	yes	characteristic, complemented
547	#3163	—	47	2	no	—
548	#3163	—	47	2	no	—
549	#3163	—	47	1	no	—
550	#3163	—	47	1	no	—
551	#3163	—	47	1	no	—
552	#3163	—	47	1	no	—
553	#2911	—	47	1	no	—
554	#2911	—	47	1	no	—
555	C₂×#428	—	47	1	no	—
556	C₂×#428	—	47	1	no	—
557	#2873	—	47	1	no	—
558	C₂×C₄₇	—	2	2	no	—
559	C₂×C₄₇	C₂²×C₄⋊Q₈	1	1	yes	characteristic
560	C₂×C₄₇	#3585	1	1	yes	characteristic
561	C₂×C₄₇	#3586	1	1	yes	characteristic
562	D₄₇	—	2	2	no	—
563	D₄₇	—	2	2	no	—
564	C₂²×M₁₆	—	47	1	no	—
565	C₂²×M₁₆	—	47	1	no	—
566	#544	—	47	2	no	—
567	#544	—	47	2	no	—
568	#544	—	47	2	no	—
569	#544	—	47	2	no	—
570	#544	—	47	1	no	—
571	#544	—	47	1	no	—
572	#544	—	47	1	no	—
573	#544	—	47	1	no	—
574	#544	—	47	1	no	—
575	#544	—	47	1	no	—
576	#544	—	94	1	no	—
577	#544	—	94	1	no	—
578	#544	—	94	2	no	—
579	#544	—	94	1	no	—
580	#544	—	94	1	no	—
581	#544	C₂×D₄₇	1	1	yes	characteristic
582	#544	C₂×D₄₇	1	1	yes	characteristic
583	#543	—	94	2	no	—
584	#533	—	47	2	no	—
585	#533	—	47	2	no	—
586	#533	—	94	2	no	—
587	#533	—	94	1	no	—
588	#533	—	94	1	no	—
589	C₂×C₄⋊Q₈	—	47	2	no	—
590	C₂×C₄⋊Q₈	—	94	1	no	—
591	C₂×#125	—	47	2	no	—
592	C₂×#125	—	94	1	no	—
593	C₂×C₂²⋊Q₈	—	94	2	no	—
594	C₂×#117	—	47	1	no	—
595	C₂×#117	—	47	1	no	—
596	C₂×#117	—	47	1	no	—
597	C₂×#117	—	47	1	no	—
598	C₂²×C₄⋊C₄	—	47	1	no	—
599	#501	—	47	2	no	—
600	#501	—	47	2	no	—
601	#501	—	47	2	no	—
602	#501	—	47	2	no	—
603	#501	—	47	2	no	—
604	#501	—	47	2	no	—
605	#501	—	47	2	no	—
606	#501	—	47	2	no	—
607	#501	—	47	2	no	—
608	#501	—	47	2	no	—
609	#501	—	47	2	no	—
610	#501	—	47	2	no	—
611	#501	—	47	2	no	—
612	#501	—	47	2	no	—
613	#501	C₂×D₄₇	1	2	yes	complemented
614	#501	C₂×D₄₇	1	2	yes	complemented
615	#500	—	47	2	no	—
616	#500	—	47	2	no	—
617	#500	—	47	2	no	—
618	#500	C₂×D₄₇	1	2	yes	complemented
619	#499	—	47	2	no	—
620	#499	—	47	2	no	—
621	#499	—	47	2	no	—
622	#499	—	47	2	no	—
623	#499	—	47	2	no	—
624	#499	—	47	2	no	—
625	#499	—	47	2	no	—
626	#499	C₂×D₄₇	1	2	yes	complemented
627	#498	—	47	2	no	—
628	#498	—	47	2	no	—
629	#498	—	47	2	no	—
630	#498	—	47	2	no	—
631	#428	—	47	1	no	—
632	#428	—	47	1	no	—
633	#428	—	47	1	no	—
634	#428	—	47	1	no	—
635	#428	—	47	1	no	—
636	#428	—	47	1	no	—
637	#428	—	47	1	no	—
638	#428	—	47	2	no	—
639	#428	—	47	2	no	—
640	#428	—	47	1	no	—
641	#428	—	47	2	no	—
642	#428	—	47	1	no	—
643	#428	—	47	2	no	—
644	#428	—	47	2	no	—
645	#428	—	47	2	no	—
646	#428	—	47	1	no	—
647	#428	—	47	1	no	—
648	#428	—	47	1	no	—
649	#428	—	47	1	no	—
650	#428	—	47	2	no	—
651	#428	—	47	2	no	—
652	#428	—	47	1	no	—
653	#428	C₂×D₄₇	1	1	yes	characteristic
654	#428	C₂×D₄₇	1	1	yes	characteristic
655	#427	—	47	1	no	—
656	#427	—	47	1	no	—
657	#427	—	47	1	no	—
658	#427	—	47	2	no	—
659	#427	—	47	2	no	—
660	#427	C₂×D₄₇	1	1	yes	characteristic
661	C₂×#107	—	47	1	no	—
662	C₂×#107	—	47	2	no	—
663	C₂×#107	C₂×D₄₇	1	1	yes	characteristic
664	C₂×#106	—	47	1	no	—
665	C₂×#106	—	47	1	no	—
666	C₂×#106	—	47	2	no	—
667	#405	—	47	1	no	—
668	#405	—	47	1	no	—
669	#405	—	47	1	no	—
670	#405	—	47	2	no	—
671	#405	—	47	2	no	—
672	#405	C₂×D₄₇	1	1	yes	characteristic
673	C₄×M₁₆	—	47	2	no	—
674	C₄×M₁₆	—	47	2	no	—
675	C₄₇	#60664	1	1	yes	characteristic, complemented, Sylow
676	C₂²×Q₈	—	94	2	no	—
677	C₂³×C₄	—	47	1	no	—
678	C₂³×C₄	—	94	1	no	—
679	C₂×M₁₆	—	47	1	no	—
680	C₂×M₁₆	—	47	8	no	—
681	C₂×M₁₆	—	47	8	no	—
682	C₂×M₁₆	—	47	1	no	—
683	C₂×M₁₆	—	47	2	no	—
684	C₂×M₁₆	—	47	1	no	—
685	C₂×M₁₆	—	47	1	no	—
686	C₂×M₁₆	—	47	1	no	—
687	C₂×M₁₆	C₂²×D₄₇	1	1	yes	characteristic
688	C₂²×C₈	—	47	1	no	—
689	C₂²×C₈	—	47	2	no	—
690	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
691	C₄⋊Q₈	—	2	1	no	—
692	C₄⋊Q₈	—	2	1	no	—
693	C₄⋊Q₈	—	47	2	no	—
694	C₄⋊Q₈	—	47	2	no	—
695	C₄⋊Q₈	—	47	2	no	—
696	C₄⋊Q₈	—	47	2	no	—
697	C₄⋊Q₈	—	47	2	no	—
698	C₄⋊Q₈	—	47	2	no	—
699	C₄⋊Q₈	—	94	1	no	—
700	C₄⋊Q₈	—	94	1	no	—
701	C₄⋊Q₈	—	94	2	no	—
702	C₄⋊Q₈	—	94	2	no	—
703	C₄⋊Q₈	—	94	2	no	—
704	C₄⋊Q₈	—	94	1	no	—
705	C₄⋊Q₈	—	94	2	no	—
706	C₄⋊Q₈	—	94	1	no	—
707	C₄⋊Q₈	—	94	2	no	—
708	C₄⋊Q₈	—	94	2	no	—
709	C₄⋊Q₈	—	94	1	no	—
710	C₄⋊Q₈	—	94	1	no	—
711	C₄⋊Q₈	C₂²×D₄₇	1	2	yes	—
712	C₄⋊Q₈	C₂²×D₄₇	1	2	yes	—
713	#125	—	2	1	no	—
714	#125	—	2	1	no	—
715	#125	—	47	2	no	—
716	#125	—	47	2	no	—
717	#125	—	47	2	no	—
718	#125	—	47	2	no	—
719	#125	—	47	2	no	—
720	#125	—	47	2	no	—
721	#125	—	94	1	no	—
722	#125	—	94	1	no	—
723	#125	—	94	2	no	—
724	#125	—	94	2	no	—
725	#125	—	94	2	no	—
726	#125	—	94	2	no	—
727	#125	—	94	1	no	—
728	#125	—	94	2	no	—
729	#125	—	94	2	no	—
730	#125	—	94	1	no	—
731	#125	—	94	1	no	—
732	#125	—	94	1	no	—
733	#125	C₂²×D₄₇	1	2	yes	—
734	#125	C₂²×D₄₇	1	2	yes	—
735	C₂²⋊Q₈	—	2	2	no	—
736	C₂²⋊Q₈	—	2	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	C₂²⋊Q₈	—	94	2	no	—
750	C₂²⋊Q₈	—	94	2	no	—
751	C₂²⋊Q₈	—	94	2	no	—
752	C₂²⋊Q₈	—	94	2	no	—
753	C₂²⋊Q₈	—	94	2	no	—
754	C₂²⋊Q₈	—	94	2	no	—
755	C₄×Q₈	—	94	2	no	—
756	C₄×Q₈	—	94	2	no	—
757	C₄×Q₈	—	94	2	no	—
758	C₄×Q₈	—	94	2	no	—
759	#117	—	47	1	no	—
760	#117	—	47	1	no	—
761	#117	—	47	1	no	—
762	#117	—	47	2	no	—
763	#117	—	47	2	no	—
764	#117	—	47	1	no	—
765	#117	—	47	1	no	—
766	#117	—	47	1	no	—
767	#117	—	47	2	no	—
768	#117	—	47	1	no	—
769	#117	—	47	2	no	—
770	#117	—	47	1	no	—
771	#117	—	47	1	no	—
772	#117	—	94	1	no	—
773	#117	—	94	1	no	—
774	#117	—	94	1	no	—
775	#117	—	94	1	no	—
776	#117	—	94	1	no	—
777	#117	—	94	1	no	—
778	#117	C₂²×D₄₇	1	1	yes	characteristic
779	#117	C₂²×D₄₇	1	1	yes	characteristic
780	#117	C₂²×D₄₇	1	1	yes	characteristic
781	C₂×C₄⋊C₄	—	47	1	no	—
782	C₂×C₄⋊C₄	—	47	1	no	—
783	C₂×C₄⋊C₄	—	47	1	no	—
784	C₂×C₄⋊C₄	—	47	1	no	—
785	C₂×C₄⋊C₄	—	47	2	no	—
786	C₂×C₄⋊C₄	—	47	2	no	—
787	C₂×C₄⋊C₄	—	47	1	no	—
788	C₂×C₄⋊C₄	—	47	1	no	—
789	C₂×C₄⋊C₄	—	47	1	no	—
790	C₂×C₄⋊C₄	—	47	1	no	—
791	C₂×C₄⋊C₄	—	94	1	no	—
792	C₂×C₄⋊C₄	—	94	1	no	—
793	C₂×C₄⋊C₄	—	94	2	no	—
794	C₂×C₄⋊C₄	—	94	2	no	—
795	C₂×C₄⋊C₄	—	94	2	no	—
796	C₂×C₄⋊C₄	—	94	1	no	—
797	C₂×C₄⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
798	C₂×C₄⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
799	C₂×C₂²⋊C₄	—	47	2	no	—
800	C₂×C₂²⋊C₄	—	94	1	no	—
801	C₂×C₂²⋊C₄	—	94	1	no	—
802	C₂×C₂²⋊C₄	—	94	1	no	—
803	C₂×C₄²	—	47	2	no	—
804	C₂×C₄²	—	94	1	no	—
805	C₂×C₄²	—	94	1	no	—
806	C₂×C₄²	—	94	1	no	—
807	#107	—	47	2	no	—
808	#107	—	47	1	no	—
809	#107	—	47	2	no	—
810	#107	—	47	1	no	—
811	#107	—	47	2	no	—
812	#107	—	47	2	no	—
813	#107	—	47	2	no	—
814	#107	—	47	2	no	—
815	#107	—	47	2	no	—
816	#107	—	47	1	no	—
817	#107	—	47	1	no	—
818	#107	—	47	1	no	—
819	#107	—	47	2	no	—
820	#107	—	47	1	no	—
821	#107	C₂²×D₄₇	1	2	yes	—
822	#107	C₂²×D₄₇	1	2	yes	—
823	#107	C₂²×D₄₇	1	2	yes	—
824	#107	C₂²×D₄₇	1	2	yes	—
825	#107	C₂²×D₄₇	1	1	yes	characteristic
826	#107	C₂²×D₄₇	1	1	yes	characteristic
827	#106	—	47	2	no	—
828	#106	—	47	2	no	—
829	#106	—	47	2	no	—
830	#106	—	47	2	no	—
831	#106	—	47	1	no	—
832	#106	—	47	1	no	—
833	#106	—	47	2	no	—
834	#106	—	47	2	no	—
835	#106	—	47	2	no	—
836	#106	—	47	2	no	—
837	#106	—	47	1	no	—
838	#106	—	47	2	no	—
839	#106	—	47	1	no	—
840	#106	—	47	1	no	—
841	#106	—	47	2	no	—
842	#106	—	47	1	no	—
843	#106	C₂²×D₄₇	1	2	yes	—
844	#106	C₂²×D₄₇	1	2	yes	—
845	#106	C₂²×D₄₇	1	1	yes	characteristic
846	#106	C₂²×D₄₇	1	1	yes	characteristic
847	#97	—	47	2	no	—
848	#97	—	47	2	no	—
849	#97	—	47	2	no	—
850	#97	C₂²×D₄₇	1	2	yes	—
851	C₄×C₈	—	47	2	no	—
852	C₄×C₈	—	47	2	no	—
853	C₄×C₈	—	47	2	no	—
854	C₄×C₈	C₂²×D₄₇	1	2	yes	—
855	C₂⁴	—	47	1	no	—
856	C₂×Q₈	—	2	2	no	—
857	C₂×Q₈	—	2	2	no	—
858	C₂×Q₈	—	94	2	no	—
859	C₂×Q₈	—	94	2	no	—
860	C₂×Q₈	—	94	2	no	—
861	C₂×Q₈	—	94	2	no	—
862	C₂×Q₈	—	94	2	no	—
863	C₂×Q₈	—	94	2	no	—
864	C₂×Q₈	—	376	4	no	—
865	C₂²×C₄	—	2	1	no	—
866	C₂²×C₄	—	2	1	no	—
867	C₂²×C₄	—	47	1	no	—
868	C₂²×C₄	—	47	1	no	—
869	C₂²×C₄	—	47	1	no	—
870	C₂²×C₄	—	47	4	no	—
871	C₂²×C₄	—	47	4	no	—
872	C₂²×C₄	—	47	1	no	—
873	C₂²×C₄	—	47	1	no	—
874	C₂²×C₄	—	47	2	no	—
875	C₂²×C₄	—	47	2	no	—
876	C₂²×C₄	—	94	1	no	—
877	C₂²×C₄	—	94	1	no	—
878	C₂²×C₄	—	94	2	no	—
879	C₂²×C₄	—	94	1	no	—
880	C₂²×C₄	—	94	1	no	—
881	C₂²×C₄	—	94	2	no	—
882	C₂²×C₄	—	94	1	no	—
883	C₂²×C₄	—	94	1	no	—
884	C₂²×C₄	—	376	2	no	—
885	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
886	M₁₆	—	47	4	no	—
887	M₁₆	—	47	8	no	—
888	M₁₆	—	47	4	no	—
889	M₁₆	—	47	4	no	—
890	M₁₆	—	47	4	no	—
891	M₁₆	—	47	4	no	—
892	M₁₆	Q₈×D₄₇	1	4	yes	complemented
893	C₂×C₈	—	47	4	no	—
894	C₂×C₈	—	47	1	no	—
895	C₂×C₈	—	47	2	no	—
896	C₂×C₈	—	47	1	no	—
897	C₂×C₈	—	47	8	no	—
898	C₂×C₈	Q₈×D₄₇	1	4	yes	complemented
899	C₂×C₈	C₂³×D₄₇	1	1	yes	characteristic
900	C₂×C₈	C₂³×D₄₇	1	2	yes	—
901	C₂×C₈	C₂³×D₄₇	1	1	yes	characteristic
902	C₄⋊C₄	—	2	1	no	—
903	C₄⋊C₄	—	2	2	no	—
904	C₄⋊C₄	—	2	2	no	—
905	C₄⋊C₄	—	2	2	no	—
906	C₄⋊C₄	—	2	1	no	—
907	C₄⋊C₄	—	2	2	no	—
908	C₄⋊C₄	—	2	2	no	—
909	C₄⋊C₄	—	2	2	no	—
910	C₄⋊C₄	—	47	2	no	—
911	C₄⋊C₄	—	47	2	no	—
912	C₄⋊C₄	—	47	1	no	—
913	C₄⋊C₄	—	47	1	no	—
914	C₄⋊C₄	—	47	1	no	—
915	C₄⋊C₄	—	47	2	no	—
916	C₄⋊C₄	—	47	2	no	—
917	C₄⋊C₄	—	47	1	no	—
918	C₄⋊C₄	—	47	1	no	—
919	C₄⋊C₄	—	47	1	no	—
920	C₄⋊C₄	—	94	2	no	—
921	C₄⋊C₄	—	94	2	no	—
922	C₄⋊C₄	—	94	1	no	—
923	C₄⋊C₄	—	94	1	no	—
924	C₄⋊C₄	—	94	1	no	—
925	C₄⋊C₄	—	94	1	no	—
926	C₄⋊C₄	—	94	2	no	—
927	C₄⋊C₄	—	94	2	no	—
928	C₄⋊C₄	—	94	2	no	—
929	C₄⋊C₄	—	94	2	no	—
930	C₄⋊C₄	—	94	2	no	—
931	C₄⋊C₄	—	94	2	no	—
932	C₄⋊C₄	—	94	2	no	—
933	C₄⋊C₄	—	94	2	no	—
934	C₄⋊C₄	—	94	2	no	—
935	C₄⋊C₄	—	94	2	no	—
936	C₄⋊C₄	—	94	2	no	—
937	C₄⋊C₄	—	94	2	no	—
938	C₄⋊C₄	—	94	2	no	—
939	C₄⋊C₄	—	94	2	no	—
940	C₄⋊C₄	—	94	2	no	—
941	C₄⋊C₄	—	94	2	no	—
942	C₄⋊C₄	—	94	1	no	—
943	C₄⋊C₄	—	94	1	no	—
944	C₄⋊C₄	—	94	2	no	—
945	C₄⋊C₄	—	94	2	no	—
946	C₄⋊C₄	D₄×D₄₇	1	1	yes	characteristic
947	C₄⋊C₄	D₄×D₄₇	1	1	yes	characteristic
948	C₄⋊C₄	C₂³×D₄₇	1	1	yes	characteristic
949	C₄⋊C₄	C₂³×D₄₇	1	2	yes	—
950	C₄⋊C₄	C₂³×D₄₇	1	1	yes	characteristic
951	C₄⋊C₄	C₂³×D₄₇	1	1	yes	characteristic
952	C₄⋊C₄	C₂³×D₄₇	1	1	yes	characteristic
953	C₄⋊C₄	C₂³×D₄₇	1	2	yes	—
954	C₂²⋊C₄	—	2	1	no	—
955	C₂²⋊C₄	—	2	1	no	—
956	C₂²⋊C₄	—	47	2	no	—
957	C₂²⋊C₄	—	47	2	no	—
958	C₂²⋊C₄	—	47	2	no	—
959	C₂²⋊C₄	—	94	1	no	—
960	C₂²⋊C₄	—	94	1	no	—
961	C₂²⋊C₄	—	94	1	no	—
962	C₂²⋊C₄	—	94	1	no	—
963	C₂²⋊C₄	—	94	2	no	—
964	C₂²⋊C₄	—	94	2	no	—
965	C₂²⋊C₄	—	94	1	no	—
966	C₂²⋊C₄	—	94	1	no	—
967	C₂²⋊C₄	D₄×D₄₇	1	2	yes	—
968	C₄²	—	2	1	no	—
969	C₄²	—	2	1	no	—
970	C₄²	—	47	2	no	—
971	C₄²	—	47	2	no	—
972	C₄²	—	47	2	no	—
973	C₄²	—	94	1	no	—
974	C₄²	—	94	1	no	—
975	C₄²	—	94	2	no	—
976	C₄²	—	94	1	no	—
977	C₄²	—	94	1	no	—
978	C₄²	—	94	2	no	—
979	C₄²	—	94	1	no	—
980	C₄²	—	94	1	no	—
981	C₄²	C₂³×D₄₇	1	2	yes	—
982	C₂³	—	47	1	no	—
983	C₂³	—	47	1	no	—
984	C₂³	—	47	4	no	—
985	C₂³	—	188	1	no	—
986	C₂³	—	188	1	no	—
987	C₂³	C₂×D₄×D₄₇	1	1	yes	characteristic
988	Q₈	—	8	2	no	—
989	Q₈	—	8	2	no	—
990	Q₈	—	376	2	no	—
991	Q₈	—	376	2	no	—
992	Q₈	—	376	2	no	—
993	Q₈	—	376	2	no	—
994	Q₈	—	376	2	no	—
995	Q₈	—	376	2	no	—
996	C₂×C₄	—	2	1	no	—
997	C₂×C₄	—	2	1	no	—
998	C₂×C₄	—	2	1	no	—
999	C₂×C₄	—	2	1	no	—
1000	C₂×C₄	—	2	2	no	—
1001	C₂×C₄	—	2	2	no	—
1002	C₂×C₄	—	8	1	no	—
1003	C₂×C₄	—	8	1	no	—
1004	C₂×C₄	—	47	4	no	—
1005	C₂×C₄	—	47	1	no	—
1006	C₂×C₄	—	47	1	no	—
1007	C₂×C₄	—	47	4	no	—
1008	C₂×C₄	—	47	4	no	—
1009	C₂×C₄	—	47	2	no	—
1010	C₂×C₄	—	47	2	no	—
1011	C₂×C₄	—	47	2	no	—
1012	C₂×C₄	—	47	2	no	—
1013	C₂×C₄	—	47	2	no	—
1014	C₂×C₄	—	47	2	no	—
1015	C₂×C₄	—	94	1	no	—
1016	C₂×C₄	—	94	1	no	—
1017	C₂×C₄	—	94	2	no	—
1018	C₂×C₄	—	94	1	no	—
1019	C₂×C₄	—	94	1	no	—
1020	C₂×C₄	—	94	2	no	—
1021	C₂×C₄	—	376	1	no	—
1022	C₂×C₄	—	376	1	no	—
1023	C₂×C₄	—	376	2	no	—
1024	C₂×C₄	—	376	1	no	—
1025	C₂×C₄	—	376	1	no	—
1026	C₂×C₄	—	188	2	no	—
1027	C₂×C₄	—	188	2	no	—
1028	C₂×C₄	—	188	2	no	—
1029	C₂×C₄	—	188	4	no	—
1030	C₂×C₄	—	188	2	no	—
1031	C₂×C₄	C₂×D₄×D₄₇	1	2	yes	—
1032	C₂×C₄	C₂×D₄×D₄₇	1	2	yes	—
1033	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
1034	C₂×C₄	C₂×Q₈×D₄₇	1	2	yes	—
1035	C₂×C₄	C₂×Q₈×D₄₇	1	2	yes	—
1036	C₂×C₄	C₂⁴×D₄₇	1	1	yes	characteristic
1037	C₈	—	47	4	no	—
1038	C₈	—	47	2	no	—
1039	C₈	—	47	2	no	—
1040	C₈	C₂×Q₈×D₄₇	1	4	yes	—
1041	C₈	C₂×Q₈×D₄₇	1	2	yes	—
1042	C₈	C₂×Q₈×D₄₇	1	2	yes	—
1043	C₂²	—	2	1	no	—
1044	C₂²	—	2	1	no	—
1045	C₂²	—	47	2	no	—
1046	C₂²	—	47	2	no	—
1047	C₂²	—	94	1	no	—
1048	C₂²	—	94	1	no	—
1049	C₂²	—	94	1	no	—
1050	C₂²	—	94	1	no	—
1051	C₂²	—	188	4	no	—
1052	C₂²	C₄⋊Q₈×D₄₇	1	2	yes	—
1053	C₂²	C₂²×D₄×D₄₇	1	1	yes	characteristic
1054	C₄	—	2	2	no	—
1055	C₄	—	2	2	no	—
1056	C₄	—	4	2	no	—
1057	C₄	—	4	2	no	—
1058	C₄	—	4	1	no	—
1059	C₄	—	4	1	no	—
1060	C₄	—	4	1	no	—
1061	C₄	—	4	1	no	—
1062	C₄	—	47	2	no	—
1063	C₄	—	47	2	no	—
1064	C₄	—	94	2	no	—
1065	C₄	—	94	2	no	—
1066	C₄	—	188	2	no	—
1067	C₄	—	188	1	no	—
1068	C₄	—	188	1	no	—
1069	C₄	—	188	1	no	—
1070	C₄	—	188	2	no	—
1071	C₄	—	188	1	no	—
1072	C₄	C₄⋊Q₈×D₄₇	1	2	yes	—
1073	C₄	C₂²×Q₈×D₄₇	1	1	yes	characteristic
1074	C₄	C₂²×Q₈×D₄₇	1	1	yes	characteristic
1075	C₂	—	2	2	no	—
1076	C₂	—	94	2	no	—
1077	C₂	—	94	2	no	—
1078	C₂	C₂×C₄⋊Q₈×D₄₇	1	1	yes	characteristic
1079	C₂	#20258163	1	1	yes	characteristic
1080	C₂	#20258173	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×#3164	C₂
socle	C₂²×C₄₇	C₂³×D₄
prime radical	C₂³×D₄₇	C₂×D₄
hypercenter	#3164	D₄₇
hypocenter	C₄₇	#60664
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ #117 ◁ #3164

Complements

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

N	H ≅ G/N	type
3. #20253939	C₂	semidirect
4. #20253936	C₂	semidirect
5. #20253933	C₂	semidirect
6. #20253931	C₂	semidirect
7. #20253926	C₂	semidirect
8. #20253924	C₂	semidirect
9. #20253923	C₂	semidirect
10. #20253922	C₂	semidirect
11. #20253921	C₂	semidirect
12. #20253920	C₂	semidirect
13. #20253919	C₂	semidirect
14. #20253918	C₂	semidirect
15. #20253917	C₂	semidirect
16. #20253915	C₂	semidirect
17. #20253914	C₂	semidirect
23. C₄₇×#3164	C₂	semidirect
57. #15689533	C₂²	semidirect
58. #15689533	C₂²	semidirect
59. #15689532	C₂²	semidirect
60. #15689532	C₂²	semidirect
61. #15689531	C₂²	semidirect
62. #15689531	C₂²	semidirect
63. #15689531	C₂²	semidirect
64. #15689531	C₂²	semidirect
65. #15689531	C₂²	semidirect
66. #15689531	C₂²	semidirect
67. #15689530	C₂²	semidirect
68. #15689530	C₂²	semidirect
69. #15689529	C₂²	semidirect
70. #15689529	C₂²	semidirect
71. #15689527	C₂²	semidirect
72. #15689527	C₂²	semidirect
73. #15689526	C₂²	semidirect
74. #15689525	C₂²	semidirect
75. #15689524	C₂²	semidirect
76. #15689524	C₂²	semidirect
77. #15689523	C₂²	semidirect
78. #15689523	C₂²	semidirect
79. #15689522	C₂²	semidirect
80. #15689522	C₂²	semidirect
81. #15689521	C₂²	semidirect
82. #15689520	C₂²	semidirect
83. #15689520	C₂²	semidirect
84. #15689519	C₂²	semidirect
126. C₄₇×#501	C₂²	semidirect
127. C₄₇×#501	C₂²	semidirect
128. C₄₇×#500	C₂²	semidirect
129. C₄₇×#499	C₂²	semidirect
139. C₂×#10625324	Q₈	semidirect
145. M₁₆×D₄₇	Q₈	semidirect
345. M₁₆×C₄₇	C₂×Q₈	semidirect
346. C₂×C₈×C₄₇	C₂×Q₈	semidirect
430. #10625329	C₂×Q₈	semidirect
431. C₂×C₄₇⋊C₈	C₂×Q₈	semidirect
438. #10625324	C₂×Q₈	semidirect
439. #10625324	C₂×Q₈	semidirect
440. C₈×D₄₇	C₂×Q₈	semidirect
546. #3164	D₄₇	semidirect
613. #501	C₂×D₄₇	semidirect
614. #501	C₂×D₄₇	semidirect
618. #500	C₂×D₄₇	semidirect
626. #499	C₂×D₄₇	semidirect
675. C₄₇	#60664	semidirect
892. M₁₆	Q₈×D₄₇	semidirect
898. C₂×C₈	Q₈×D₄₇	semidirect

Maximal subgroups

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

subgroup	index
#20256792	2
#544×D₄₇	2
#20253939	2
#20253936	2
#20253933	2
#20253931	2
#20253926	2
#20253924	2
#20253923	2
#20253922	2
#20253921	2
#20253920	2
#20253919	2
#20253918	2
#20253917	2
#20253915	2
#20253914	2
#20251976	2
#20251975	2
C₂×#15689164	2
#428×D₄₇	2
#20251804	2
C₄₇×#3164	2
#60664	47