Subgroups — #27107003

Order 12032.

1662 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	#20257859	C₂	1	1	yes	maximal, characteristic
2	#20256327	C₂	1	2	yes	maximal, complemented
3	#20256316	C₂	1	1	yes	maximal, characteristic, complemented
4	#20256305	C₂	1	1	yes	maximal, characteristic, complemented
5	#20256275	C₂	1	1	yes	maximal, characteristic, complemented
6	#20256259	C₂	1	2	yes	maximal, complemented
7	Q₈×#10625336	C₂	1	1	yes	maximal, characteristic, complemented
8	#20256202	C₂	1	1	yes	maximal, characteristic, complemented
9	#20256156	C₂	1	2	yes	maximal, complemented
10	#20256117	C₂	1	1	yes	maximal, characteristic, complemented
11	#20256084	C₂	1	2	yes	maximal, complemented
12	#20256084	C₂	1	1	yes	maximal, characteristic, complemented
13	#20256059	C₂	1	1	yes	maximal, characteristic, complemented
14	#20254686	C₂	1	2	yes	maximal, complemented
15	#20254641	C₂	1	2	yes	maximal, complemented
16	#20254567	C₂	1	1	yes	maximal, characteristic, complemented
17	#20254524	C₂	1	1	yes	maximal, characteristic, complemented
18	#20253679	C₂	1	2	yes	maximal, complemented
19	#20253617	C₂	1	2	yes	maximal, complemented
20	#20253468	C₂	1	1	yes	maximal, characteristic, complemented
21	#20253419	C₂	1	1	yes	maximal, characteristic, complemented
22	#20252490	C₂	1	1	yes	maximal, characteristic, complemented
23	C₄₇×#3502	C₂	1	1	yes	maximal, characteristic, complemented
24	#15689869	—	2	2	no	—
25	#15689858	C₂²	1	2	yes	—
26	#15689858	C₂²	1	1	yes	characteristic
27	#15689851	C₂²	1	1	yes	characteristic
28	#15689833	C₂²	1	2	yes	—
29	#15689795	C₂²	1	1	yes	characteristic
30	Q₈×D₁₈₈	C₂²	1	1	yes	characteristic
31	#15689783	—	2	1	no	—
32	#15689775	—	2	1	no	—
33	#15689747	—	2	1	no	—
34	#15689744	C₂²	1	2	yes	—
35	#15689728	C₂²	1	2	yes	—
36	#15689721	—	2	2	no	—
37	#15689698	—	2	1	no	—
38	#15689673	C₂²	1	1	yes	characteristic
39	#15689657	C₂²	1	1	yes	characteristic
40	#15689533	C₂²	1	2	yes	—
41	#15689529	C₂²	1	2	yes	—
42	#15689526	C₂²	1	1	yes	characteristic
43	#15689522	C₂²	1	2	yes	—
44	#15689522	C₂²	1	2	yes	—
45	#15689519	C₂²	1	2	yes	—
46	#15689519	C₂²	1	1	yes	characteristic
47	#15689489	C₂²	1	2	yes	—
48	#15689485	C₂²	1	2	yes	—
49	#15689480	C₂²	1	2	yes	—
50	#15689480	C₂²	1	2	yes	—
51	#15689471	C₂²	1	1	yes	characteristic
52	#15689471	C₂²	1	2	yes	—
53	#15689471	C₂²	1	1	yes	characteristic
54	#15689464	C₂²	1	2	yes	—
55	#15689453	C₂²	1	1	yes	characteristic
56	#15689447	C₂²	1	2	yes	—
57	#15689447	C₂²	1	2	yes	—
58	#15689447	C₂²	1	2	yes	—
59	#15689441	C₂²	1	2	yes	—
60	#15689436	C₂²	1	1	yes	characteristic
61	#15689430	C₂²	1	1	yes	characteristic
62	#15689430	C₂²	1	2	yes	—
63	#15689430	C₂²	1	2	yes	—
64	#15689430	C₂²	1	1	yes	characteristic
65	#15689427	C₂²	1	2	yes	—
66	#15689420	C₂²	1	2	yes	—
67	#15689420	C₂²	1	2	yes	—
68	#15689420	C₂²	1	2	yes	—
69	#15689420	C₂²	1	2	yes	—
70	#15689420	C₂²	1	2	yes	—
71	#15689418	C₂²	1	2	yes	—
72	#15689415	C₂²	1	1	yes	characteristic
73	#15689410	C₂²	1	2	yes	—
74	#15689410	C₂²	1	1	yes	characteristic
75	#15689410	C₂²	1	2	yes	—
76	#15689408	C₂²	1	1	yes	characteristic
77	#15689408	C₂²	1	1	yes	characteristic
78	#15689408	C₂²	1	2	yes	—
79	#15689405	C₂²	1	1	yes	characteristic
80	#15689405	C₂²	1	2	yes	—
81	#15689400	C₂²	1	2	yes	—
82	#15689400	C₂²	1	1	yes	characteristic
83	#15689345	C₂²	1	1	yes	characteristic
84	#15689345	C₂²	1	1	yes	characteristic
85	#15689345	C₂²	1	2	yes	—
86	#15689345	C₂²	1	2	yes	—
87	#15689323	C₂²	1	1	yes	characteristic
88	#15689323	C₂²	1	2	yes	—
89	#15689323	C₂²	1	2	yes	—
90	#15689323	C₂²	1	1	yes	characteristic
91	#15689279	C₂²	1	1	yes	characteristic
92	#15689262	C₂²	1	1	yes	characteristic
93	#15689262	C₂²	1	2	yes	—
94	#15689254	C₂²	1	1	yes	characteristic
95	#15689254	C₂²	1	1	yes	characteristic
96	#15689254	C₂²	1	2	yes	—
97	Q₈×C₄₇⋊C₈	C₂²	1	2	yes	—
98	Q₈×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
99	Q₈×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
100	#15689228	C₂²	1	2	yes	—
101	#15689221	C₂²	1	2	yes	—
102	#15689221	C₂²	1	2	yes	—
103	#15689221	C₂²	1	2	yes	—
104	C₄×#10625337	C₂²	1	1	yes	characteristic
105	C₄×#10625337	C₂²	1	2	yes	—
106	C₄×#10625337	C₂²	1	1	yes	characteristic
107	C₄×#10625336	C₂²	1	2	yes	—
108	C₄×#10625336	C₂²	1	2	yes	—
109	C₄×#10625336	C₂²	1	2	yes	—
110	C₄×#10625336	C₂²	1	1	yes	characteristic
111	C₄×#10625336	C₂²	1	1	yes	characteristic
112	C₄×#10625336	C₂²	1	2	yes	—
113	C₄×#10625336	C₂²	1	2	yes	—
114	#15689184	C₂²	1	2	yes	—
115	#15689184	C₂²	1	2	yes	—
116	#15689176	C₂²	1	1	yes	characteristic
117	#15689176	C₂²	1	1	yes	characteristic
118	Q₈²×C₄₇	—	2	1	no	—
119	Q₈²×C₄₇	C₂²	1	1	yes	characteristic
120	Q₈²×C₄₇	C₂²	1	1	yes	characteristic
121	C₄₇×#557	—	2	1	no	—
122	C₄₇×#557	—	2	2	no	—
123	C₄₇×#557	C₂²	1	2	yes	—
124	C₄₇×#557	C₂²	1	1	yes	characteristic
125	C₄₇×#557	C₂²	1	1	yes	characteristic
126	C₄₇×#557	C₂²	1	2	yes	—
127	C₄₇×#544	—	2	2	no	—
128	C₄₇×#544	C₂²	1	2	yes	—
129	C₄₇×#533	—	2	1	no	—
130	C₄₇×#533	—	2	1	no	—
131	C₄₇×#533	C₂²	1	1	yes	characteristic
132	C₄₇×#533	C₂²	1	1	yes	characteristic
133	C₄₇×#519	C₂²	1	2	yes	—
134	C₂×C₄×Q₈×C₄₇	C₂²	1	1	yes	characteristic
135	C₂×#10625354	—	2	1	no	—
136	C₂×#10625350	—	2	1	no	—
137	C₂×Q₈×D₄₇	—	2	1	no	—
138	C₂×#10625337	C₂³	1	1	yes	characteristic
139	C₂×#10625337	C₂³	1	1	yes	characteristic
140	C₂×#10625336	C₂³	1	1	yes	characteristic
141	C₂×#10625336	C₂³	1	2	yes	—
142	C₂×#10625336	C₂³	1	1	yes	characteristic
143	C₂×#10625336	C₂³	1	2	yes	—
144	#13094024	C₂³	1	2	yes	—
145	#13094024	C₂³	1	1	yes	characteristic
146	#13094022	—	2	1	no	—
147	#13094021	C₂³	1	2	yes	—
148	#13094021	C₂³	1	1	yes	characteristic
149	#13094019	—	2	2	no	—
150	#13094018	—	2	1	no	—
151	#13094016	C₂³	1	2	yes	—
152	#13094016	C₂³	1	1	yes	characteristic
153	#13094014	—	2	2	no	—
154	#13094013	—	2	2	no	—
155	#13094013	—	2	1	no	—
156	#13094012	—	2	1	no	—
157	#13094012	C₂³	1	1	yes	characteristic
158	#13094012	C₂³	1	2	yes	—
159	#13094010	—	2	2	no	—
160	#13094009	—	2	2	no	—
161	#13094009	—	2	2	no	—
162	#13094009	—	2	2	no	—
163	#13094009	—	2	2	no	—
164	#13094009	—	2	2	no	—
165	#13094007	—	2	1	no	—
166	#13094006	—	2	2	no	—
167	#13094004	—	2	1	no	—
168	#13094004	—	2	2	no	—
169	#13094003	C₂³	1	1	yes	characteristic
170	#13094002	—	2	2	no	—
171	#13094002	—	2	2	no	—
172	#13094002	—	2	2	no	—
173	#13094000	—	2	2	no	—
174	#13093999	—	2	1	no	—
175	#13093999	—	2	2	no	—
176	#13093998	—	2	1	no	—
177	#13093998	C₂³	1	1	yes	characteristic
178	#13093998	C₂³	1	2	yes	—
179	#13093997	—	2	2	no	—
180	#13093997	—	2	2	no	—
181	C₄×Dic₉₄	C₂³	1	1	yes	characteristic
182	C₄×Dic₉₄	C₂³	1	2	yes	—
183	#13093989	—	2	1	no	—
184	C₄×D₁₈₈	—	2	1	no	—
185	C₄×D₁₈₈	C₂³	1	2	yes	—
186	C₄×D₁₈₈	C₂³	1	2	yes	—
187	C₄×D₁₈₈	C₂³	1	2	yes	—
188	C₄×D₁₈₈	C₂³	1	1	yes	characteristic
189	C₄×D₁₈₈	C₂³	1	2	yes	—
190	#13093986	—	2	1	no	—
191	#13093986	—	2	2	no	—
192	C₄×C₂²⋊D₄₇	—	2	1	no	—
193	#13093981	—	2	1	no	—
194	C₄⋊C₄×D₄₇	—	2	2	no	—
195	#13093957	C₂³	1	1	yes	characteristic
196	#13093957	C₂³	1	2	yes	—
197	#13093957	C₂³	1	1	yes	characteristic
198	#13093957	C₂³	1	2	yes	—
199	#13093957	C₂³	1	2	yes	—
200	#13093957	C₂³	1	2	yes	—
201	#13093955	C₂³	1	2	yes	—
202	#13093955	C₂³	1	2	yes	—
203	#13093955	C₂³	1	1	yes	characteristic
204	#13093955	C₂³	1	2	yes	—
205	#13093955	C₂³	1	2	yes	—
206	#13093955	C₂³	1	2	yes	—
207	#13093955	C₂³	1	2	yes	—
208	#13093955	C₂³	1	1	yes	characteristic
209	C₄⋊(C₄₇⋊C₈)	C₂³	1	1	yes	characteristic
210	C₄⋊(C₄₇⋊C₈)	C₂³	1	1	yes	characteristic
211	C₄⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
212	C₄⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
213	C₄⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
214	C₄⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
215	C₄⋊(C₄₇⋊C₈)	C₂³	1	1	yes	characteristic
216	C₄⋊(C₄₇⋊C₈)	C₂³	1	1	yes	characteristic
217	#13093948	C₂³	1	1	yes	characteristic
218	#13093948	C₂³	1	2	yes	—
219	#13093948	C₂³	1	1	yes	characteristic
220	#13093948	C₂³	1	1	yes	characteristic
221	#13093948	C₂³	1	2	yes	—
222	#13093948	C₂³	1	1	yes	characteristic
223	#13093947	C₂³	1	1	yes	characteristic
224	#13093947	C₂³	1	2	yes	—
225	#13093947	C₂³	1	1	yes	characteristic
226	#13093947	C₂³	1	2	yes	—
227	#13093944	C₂³	1	2	yes	—
228	#13093944	C₂³	1	2	yes	—
229	#13093944	C₂³	1	2	yes	—
230	#13093944	C₂³	1	2	yes	—
231	#13093944	C₂³	1	2	yes	—
232	#13093944	C₂³	1	2	yes	—
233	#13093944	C₂³	1	2	yes	—
234	#13093944	C₂³	1	1	yes	characteristic
235	#13093944	C₂³	1	2	yes	—
236	#13093944	C₂³	1	1	yes	characteristic
237	C₂²⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
238	C₂²⋊(C₄₇⋊C₈)	C₂³	1	1	yes	characteristic
239	C₂²⋊(C₄₇⋊C₈)	C₂³	1	1	yes	characteristic
240	#13093935	C₂³	1	2	yes	—
241	#13093935	C₂³	1	2	yes	—
242	C₄×C₄₇⋊C₈	C₂³	1	2	yes	—
243	C₄×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
244	C₄×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
245	C₄×C₄₇⋊C₈	C₂³	1	2	yes	—
246	C₄×C₄₇⋊C₈	C₂³	1	2	yes	—
247	C₂²×Q₈×C₄₇	C₂³	1	1	yes	characteristic
248	C₄⋊Q₈×C₄₇	—	2	1	no	—
249	C₄⋊Q₈×C₄₇	—	2	1	no	—
250	C₄⋊Q₈×C₄₇	—	2	2	no	—
251	C₄⋊Q₈×C₄₇	—	2	2	no	—
252	C₄⋊Q₈×C₄₇	—	2	1	no	—
253	C₄⋊Q₈×C₄₇	—	2	1	no	—
254	C₄⋊Q₈×C₄₇	—	2	2	no	—
255	C₄⋊Q₈×C₄₇	—	2	2	no	—
256	C₄⋊Q₈×C₄₇	—	2	2	no	—
257	C₄⋊Q₈×C₄₇	D₄	1	1	yes	characteristic
258	C₄⋊Q₈×C₄₇	D₄	1	1	yes	characteristic
259	C₄⋊Q₈×C₄₇	C₂³	1	2	yes	—
260	C₄⋊Q₈×C₄₇	C₂³	1	1	yes	characteristic
261	C₄⋊Q₈×C₄₇	C₂³	1	1	yes	characteristic
262	C₄⋊Q₈×C₄₇	C₂³	1	2	yes	—
263	#125×C₄₇	—	2	2	no	—
264	#125×C₄₇	—	2	2	no	—
265	#125×C₄₇	—	2	2	no	—
266	#125×C₄₇	—	2	2	no	—
267	#125×C₄₇	—	2	2	no	—
268	#125×C₄₇	—	2	2	no	—
269	#125×C₄₇	—	2	2	no	—
270	#125×C₄₇	D₄	1	2	yes	—
271	#125×C₄₇	C₂³	1	2	yes	—
272	#125×C₄₇	C₂³	1	2	yes	—
273	#125×C₄₇	C₂³	1	2	yes	—
274	C₂²⋊Q₈×C₄₇	—	2	1	no	—
275	C₂²⋊Q₈×C₄₇	—	2	1	no	—
276	C₂²⋊Q₈×C₄₇	—	2	2	no	—
277	C₂²⋊Q₈×C₄₇	—	2	2	no	—
278	C₂²⋊Q₈×C₄₇	D₄	1	1	yes	characteristic
279	C₂²⋊Q₈×C₄₇	D₄	1	1	yes	characteristic
280	C₂²⋊Q₈×C₄₇	D₄	1	2	yes	—
281	C₄×Q₈×C₄₇	—	2	1	no	—
282	C₄×Q₈×C₄₇	—	2	1	no	—
283	C₄×Q₈×C₄₇	—	2	2	no	—
284	C₄×Q₈×C₄₇	—	2	2	no	—
285	C₄×Q₈×C₄₇	—	2	2	no	—
286	C₄×Q₈×C₄₇	—	2	2	no	—
287	C₄×Q₈×C₄₇	—	2	1	no	—
288	C₄×Q₈×C₄₇	—	2	1	no	—
289	C₄×Q₈×C₄₇	—	2	1	no	—
290	C₄×Q₈×C₄₇	—	2	1	no	—
291	C₄×Q₈×C₄₇	—	2	1	no	—
292	C₄×Q₈×C₄₇	—	2	1	no	—
293	C₄×Q₈×C₄₇	C₂³	1	2	yes	—
294	C₄×Q₈×C₄₇	C₂³	1	1	yes	characteristic
295	C₄×Q₈×C₄₇	C₂³	1	1	yes	characteristic
296	C₄×Q₈×C₄₇	C₂³	1	2	yes	—
297	C₄×Q₈×C₄₇	C₂³	1	2	yes	—
298	C₄×Q₈×C₄₇	C₂³	1	2	yes	—
299	C₄×Q₈×C₄₇	C₂³	1	1	yes	characteristic
300	C₄×Q₈×C₄₇	C₂³	1	1	yes	characteristic
301	C₄×Q₈×C₄₇	C₂³	1	1	yes	characteristic
302	C₄×Q₈×C₄₇	C₂³	1	1	yes	characteristic
303	C₄×Q₈×C₄₇	C₂³	1	2	yes	—
304	#117×C₄₇	—	2	2	no	—
305	#117×C₄₇	—	2	2	no	—
306	#117×C₄₇	C₂³	1	2	yes	—
307	#117×C₄₇	C₂³	1	2	yes	—
308	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
309	C₂×C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
310	C₂×C₄²×C₄₇	—	2	1	no	—
311	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
312	C₂×Q₈×C₄₇	—	2	2	no	—
313	C₂×Q₈×C₄₇	—	2	2	no	—
314	C₂×Q₈×C₄₇	—	2	1	no	—
315	C₂×Q₈×C₄₇	—	2	1	no	—
316	C₂×Q₈×C₄₇	—	2	1	no	—
317	C₂×Q₈×C₄₇	—	2	2	no	—
318	C₂×Q₈×C₄₇	—	2	2	no	—
319	C₂×Q₈×C₄₇	C₂×D₄	1	1	yes	characteristic
320	C₂×Q₈×C₄₇	C₂×D₄	1	1	yes	characteristic
321	C₂×Q₈×C₄₇	C₂×D₄	1	2	yes	—
322	C₂×Q₈×C₄₇	C₂⁴	1	1	yes	characteristic
323	C₂×Q₈×C₄₇	C₂⁴	1	1	yes	characteristic
324	C₂²×C₄×C₄₇	—	2	1	no	—
325	C₂²×C₄×C₄₇	—	2	1	no	—
326	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
327	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
328	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
329	C₂×C₂²⋊D₄₇	—	2	1	no	—
330	C₂×C₂²⋊D₄₇	—	2	2	no	—
331	#10625354	—	8	2	no	—
332	Q₈×D₄₇	—	8	2	no	—
333	#10625350	—	8	2	no	—
334	C₂×D₁₈₈	—	2	1	no	—
335	C₂×D₁₈₈	—	2	2	no	—
336	C₂×D₁₈₈	—	2	1	no	—
337	C₂×D₁₈₈	—	2	2	no	—
338	C₂×D₁₈₈	C₂⁴	1	1	yes	characteristic
339	C₂×D₁₈₈	C₂⁴	1	2	yes	—
340	C₂×C₄×D₄₇	—	2	1	no	—
341	C₂×C₄×D₄₇	—	2	2	no	—
342	C₂×C₄×D₄₇	—	2	2	no	—
343	C₂×C₄×D₄₇	—	2	2	no	—
344	C₂×C₄×D₄₇	—	2	2	no	—
345	C₂×Dic₉₄	—	2	1	no	—
346	C₂×Dic₉₄	—	2	2	no	—
347	C₂×Dic₉₄	C₂⁴	1	1	yes	characteristic
348	C₄⋊C₄×C₄₇	—	2	1	no	—
349	C₄⋊C₄×C₄₇	—	2	1	no	—
350	C₄⋊C₄×C₄₇	—	2	1	no	—
351	C₄⋊C₄×C₄₇	—	2	1	no	—
352	C₄⋊C₄×C₄₇	—	2	1	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	—	2	1	no	—
359	C₄⋊C₄×C₄₇	—	2	1	no	—
360	C₄⋊C₄×C₄₇	—	2	2	no	—
361	C₄⋊C₄×C₄₇	—	2	2	no	—
362	C₄⋊C₄×C₄₇	—	2	2	no	—
363	C₄⋊C₄×C₄₇	—	2	2	no	—
364	C₄⋊C₄×C₄₇	—	2	2	no	—
365	C₄⋊C₄×C₄₇	—	2	2	no	—
366	C₄⋊C₄×C₄₇	—	2	2	no	—
367	C₄⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
368	C₄⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
369	C₄⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
370	C₄⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
371	C₄⋊C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
372	C₄⋊C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
373	C₄⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
374	C₄⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
375	C₄⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
376	C₄⋊C₄×C₄₇	C₂⁴	1	1	yes	characteristic
377	C₄⋊C₄×C₄₇	C₂⁴	1	1	yes	characteristic
378	C₄⋊C₄×C₄₇	C₂⁴	1	2	yes	—
379	C₄⋊C₄×C₄₇	C₂⁴	1	2	yes	—
380	C₂²⋊C₄×C₄₇	—	2	2	no	—
381	C₂²⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
382	C₂²⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
383	C₄²×C₄₇	—	2	1	no	—
384	C₄²×C₄₇	—	2	1	no	—
385	C₄²×C₄₇	—	2	1	no	—
386	C₄²×C₄₇	—	2	1	no	—
387	C₄²×C₄₇	—	2	2	no	—
388	C₄²×C₄₇	—	2	2	no	—
389	C₄²×C₄₇	—	2	2	no	—
390	C₄²×C₄₇	—	2	2	no	—
391	C₄²×C₄₇	—	2	2	no	—
392	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
393	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
394	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
395	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
396	C₄²×C₄₇	C₂⁴	1	2	yes	—
397	C₄²×C₄₇	C₂⁴	1	2	yes	—
398	C₂²⋊Dic₄₇	—	2	1	no	—
399	#10625337	—	2	2	no	—
400	#10625337	—	2	2	no	—
401	#10625336	—	2	2	no	—
402	#10625336	—	2	4	no	—
403	#10625336	—	2	2	no	—
404	#10625336	—	2	4	no	—
405	(C₂×D₄₇)⋊C₄	—	2	1	no	—
406	(C₂×D₄₇)⋊C₄	—	2	1	no	—
407	(C₂×D₄₇)⋊C₄	—	2	1	no	—
408	(C₂×D₄₇)⋊C₄	—	2	2	no	—
409	(C₂×D₄₇)⋊C₄	—	2	2	no	—
410	(C₂×D₄₇)⋊C₄	—	2	2	no	—
411	(C₂×D₄₇)⋊C₄	—	2	2	no	—
412	(C₂×D₄₇)⋊C₄	—	2	2	no	—
413	(C₂×D₄₇)⋊C₄	—	2	2	no	—
414	(C₂×D₄₇)⋊C₄	—	2	2	no	—
415	(C₂×D₄₇)⋊C₄	—	2	1	no	—
416	C₄⋊Dic₄₇	—	2	2	no	—
417	C₄⋊Dic₄₇	—	2	1	no	—
418	C₄⋊Dic₄₇	C₂⁴	1	1	yes	characteristic
419	C₄⋊Dic₄₇	C₂⁴	1	2	yes	—
420	C₄⋊Dic₄₇	C₂⁴	1	1	yes	characteristic
421	Dic₄₇⋊C₄	—	2	1	no	—
422	Dic₄₇⋊C₄	—	2	2	no	—
423	Dic₄₇⋊C₄	—	2	1	no	—
424	Dic₄₇⋊C₄	—	2	1	no	—
425	Dic₄₇⋊C₄	—	2	2	no	—
426	Dic₄₇⋊C₄	—	2	2	no	—
427	Dic₄₇⋊C₄	—	2	1	no	—
428	C₄×Dic₄₇	—	2	1	no	—
429	C₄×Dic₄₇	—	2	2	no	—
430	C₂×C₄₇⋊C₈	C₂⁴	1	1	yes	characteristic
431	C₂×C₄₇⋊C₈	C₂⁴	1	2	yes	—
432	C₂×C₄₇⋊C₈	C₂⁴	1	1	yes	characteristic
433	C₂×C₄₇⋊C₈	C₂⁴	1	1	yes	characteristic
434	C₂×C₄₇⋊C₈	C₂⁴	1	1	yes	characteristic
435	C₂×C₄₇⋊C₈	C₂⁴	1	2	yes	—
436	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
437	C₂²×D₄₇	—	2	2	no	—
438	C₂²×D₄₇	—	2	1	no	—
439	Q₈×C₄₇	—	2	4	no	—
440	Q₈×C₄₇	—	2	2	no	—
441	Q₈×C₄₇	—	2	2	no	—
442	Q₈×C₄₇	—	2	1	no	—
443	Q₈×C₄₇	—	2	1	no	—
444	Q₈×C₄₇	—	4	2	no	—
445	Q₈×C₄₇	—	4	2	no	—
446	Q₈×C₄₇	—	8	2	no	—
447	Q₈×C₄₇	—	8	1	no	—
448	Q₈×C₄₇	—	8	2	no	—
449	Q₈×C₄₇	2₋¹⁺⁴	1	2	yes	—
450	Q₈×C₄₇	2₋¹⁺⁴	1	2	yes	—
451	C₂×C₄×C₄₇	—	2	4	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	—	2	1	no	—
456	C₂×C₄×C₄₇	—	2	1	no	—
457	C₂×C₄×C₄₇	—	2	2	no	—
458	C₂×C₄×C₄₇	—	2	2	no	—
459	C₂×C₄×C₄₇	—	2	1	no	—
460	C₂×C₄×C₄₇	—	2	1	no	—
461	C₂×C₄×C₄₇	—	4	1	no	—
462	C₂×C₄×C₄₇	—	8	1	no	—
463	C₂×C₄×C₄₇	C₂²×D₄	1	2	yes	—
464	C₂×C₄×C₄₇	C₂²×D₄	1	2	yes	—
465	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
466	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
467	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
468	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
469	C₂×C₄×C₄₇	C₂²×D₄	1	2	yes	—
470	C₂×C₄×C₄₇	C₂²×D₄	1	2	yes	—
471	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
472	C₂×C₄×C₄₇	C₂⁵	1	1	yes	characteristic
473	C₂²⋊D₄₇	—	8	2	no	—
474	C₂²⋊D₄₇	—	8	1	no	—
475	C₂×Dic₄₇	—	2	1	no	—
476	C₂×Dic₄₇	—	2	1	no	—
477	C₂×Dic₄₇	—	2	2	no	—
478	C₂×Dic₄₇	—	2	1	no	—
479	D₁₈₈	—	2	1	no	—
480	D₁₈₈	—	2	2	no	—
481	D₁₈₈	—	2	1	no	—
482	D₁₈₈	—	2	2	no	—
483	D₁₈₈	—	4	2	no	—
484	D₁₈₈	—	8	1	no	—
485	D₁₈₈	—	8	2	no	—
486	D₁₈₈	—	8	2	no	—
487	C₄×D₄₇	—	4	2	no	—
488	C₄×D₄₇	—	8	2	no	—
489	C₄×D₄₇	—	8	2	no	—
490	C₄×D₄₇	—	8	2	no	—
491	C₄×D₄₇	—	8	2	no	—
492	Dic₉₄	—	2	1	no	—
493	Dic₉₄	—	2	1	no	—
494	Dic₉₄	—	4	2	no	—
495	Dic₉₄	—	8	2	no	—
496	C₄₇⋊C₈	—	2	2	no	—
497	C₄₇⋊C₈	—	2	1	no	—
498	C₄₇⋊C₈	—	2	1	no	—
499	C₄₇⋊C₈	—	2	2	no	—
500	C₄₇⋊C₈	—	2	1	no	—
501	C₄₇⋊C₈	—	2	1	no	—
502	#61865	—	47	1	no	maximal, Sylow
503	C₂²×C₄₇	—	2	1	no	—
504	C₂²×C₄₇	—	2	1	no	—
505	C₂²×C₄₇	—	2	1	no	—
506	C₂²×C₄₇	C₂³×D₄	1	1	yes	characteristic
507	C₂×D₄₇	—	4	2	no	—
508	C₂×D₄₇	—	4	1	no	—
509	C₂×D₄₇	—	4	2	no	—
510	C₂×D₄₇	—	4	1	no	—
511	C₂×D₄₇	—	4	1	no	—
512	C₂×D₄₇	—	4	2	no	—
513	C₄×C₄₇	—	2	2	no	—
514	C₄×C₄₇	—	2	1	no	—
515	C₄×C₄₇	—	2	2	no	—
516	C₄×C₄₇	—	2	1	no	—
517	C₄×C₄₇	—	2	2	no	—
518	C₄×C₄₇	—	2	2	no	—
519	C₄×C₄₇	—	2	1	no	—
520	C₄×C₄₇	—	2	2	no	—
521	C₄×C₄₇	—	2	1	no	—
522	C₄×C₄₇	—	2	2	no	—
523	C₄×C₄₇	—	4	1	no	—
524	C₄×C₄₇	—	4	1	no	—
525	C₄×C₄₇	—	4	2	no	—
526	C₄×C₄₇	—	4	2	no	—
527	C₄×C₄₇	#577	1	2	yes	—
528	C₄×C₄₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
529	C₄×C₄₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
530	Dic₄₇	—	4	1	no	—
531	Dic₄₇	—	4	1	no	—
532	Dic₄₇	—	4	2	no	—
533	Dic₄₇	—	4	1	no	—
534	#3554	—	47	1	no	—
535	#3502	D₄₇	1	1	yes	characteristic, complemented
536	#3388	—	47	2	no	—
537	#3387	—	47	1	no	—
538	#3386	—	47	1	no	—
539	#3383	—	47	1	no	—
540	#3381	—	47	2	no	—
541	Q₈×SD₁₆	—	47	1	no	—
542	#3375	—	47	1	no	—
543	#3371	—	47	2	no	—
544	#3368	—	47	1	no	—
545	#3365	—	47	1	no	—
546	#3365	—	47	2	no	—
547	#3362	—	47	1	no	—
548	#3244	—	47	2	no	—
549	#3241	—	47	2	no	—
550	#3233	—	47	1	no	—
551	#3228	—	47	1	no	—
552	#3126	—	47	2	no	—
553	#3121	—	47	2	no	—
554	#3108	—	47	1	no	—
555	#3103	—	47	1	no	—
556	#2986	—	47	1	no	—
557	C₂×C₄₇	—	4	1	no	—
558	C₂×C₄₇	#3486	1	1	yes	characteristic
559	C₂×C₄₇	C₂×#577	1	1	yes	characteristic
560	C₂×C₄₇	#3584	1	1	yes	characteristic
561	D₄₇	—	8	2	no	—
562	D₄₇	—	8	1	no	—
563	#562	—	94	2	no	—
564	#559	—	47	2	no	—
565	#559	—	47	1	no	—
566	Q₈²	—	2	1	no	—
567	Q₈²	C₂×D₄₇	1	1	yes	characteristic
568	Q₈²	C₂×D₄₇	1	1	yes	characteristic
569	#557	—	2	1	no	—
570	#557	—	2	2	no	—
571	#557	—	47	1	no	—
572	#557	C₂×D₄₇	1	1	yes	characteristic
573	#557	C₂×D₄₇	1	2	yes	—
574	#557	C₂×D₄₇	1	1	yes	characteristic
575	#557	C₂×D₄₇	1	2	yes	—
576	#554	—	47	2	no	—
577	#550	—	47	1	no	—
578	D₄×Q₈	—	47	1	no	—
579	#548	—	94	1	no	—
580	#547	—	94	1	no	—
581	#544	—	2	2	no	—
582	#544	C₂×D₄₇	1	2	yes	—
583	#542	—	47	2	no	—
584	#542	—	94	1	no	—
585	#540	—	47	2	no	—
586	#539	—	94	2	no	—
587	#536	—	94	1	no	—
588	#533	—	2	1	no	—
589	#533	—	2	1	no	—
590	#533	C₂×D₄₇	1	1	yes	characteristic
591	#533	C₂×D₄₇	1	1	yes	characteristic
592	#532	—	47	1	no	—
593	#529	—	47	1	no	—
594	#519	C₂×D₄₇	1	2	yes	—
595	C₂×C₄×Q₈	C₂×D₄₇	1	1	yes	characteristic
596	#501	—	47	2	no	—
597	#501	—	47	2	no	—
598	#500	—	47	1	no	—
599	#499	—	47	2	no	—
600	#499	—	47	2	no	—
601	#498	—	47	2	no	—
602	#498	—	47	1	no	—
603	#490	—	47	2	no	—
604	#489	—	47	2	no	—
605	#488	—	47	2	no	—
606	#488	—	47	2	no	—
607	#486	—	47	2	no	—
608	#486	—	47	1	no	—
609	#486	—	47	1	no	—
610	#485	—	47	2	no	—
611	#483	—	47	1	no	—
612	#482	—	47	2	no	—
613	#482	—	47	2	no	—
614	#482	—	47	2	no	—
615	#481	—	47	2	no	—
616	#480	—	47	1	no	—
617	#479	—	47	2	no	—
618	#479	—	47	1	no	—
619	#479	—	47	1	no	—
620	#479	—	47	2	no	—
621	#479	—	47	2	no	—
622	#478	—	47	2	no	—
623	#478	—	47	2	no	—
624	#478	—	47	2	no	—
625	#478	—	47	2	no	—
626	#478	—	47	2	no	—
627	#477	—	47	1	no	—
628	#477	—	47	2	no	—
629	#476	—	47	1	no	—
630	#476	—	47	2	no	—
631	#476	—	47	2	no	—
632	#475	—	47	1	no	—
633	#475	—	47	2	no	—
634	#475	—	47	1	no	—
635	#475	—	47	1	no	—
636	#475	—	47	2	no	—
637	#474	—	47	1	no	—
638	#474	—	47	2	no	—
639	#464	—	47	1	no	—
640	#464	—	47	1	no	—
641	#464	—	47	2	no	—
642	#464	—	47	2	no	—
643	#460	—	47	1	no	—
644	#460	—	47	1	no	—
645	#460	—	47	2	no	—
646	#460	—	47	2	no	—
647	#451	—	47	1	no	—
648	#448	—	47	2	no	—
649	#448	—	47	1	no	—
650	#446	—	47	1	no	—
651	#446	—	47	2	no	—
652	#446	—	47	1	no	—
653	C₈×Q₈	—	47	1	no	—
654	C₈×Q₈	—	47	1	no	—
655	C₈×Q₈	—	47	2	no	—
656	#441	—	47	2	no	—
657	#440	—	47	2	no	—
658	#440	—	47	2	no	—
659	#440	—	47	2	no	—
660	C₄×Q₁₆	—	47	1	no	—
661	C₄×Q₁₆	—	47	1	no	—
662	C₄×Q₁₆	—	47	2	no	—
663	C₄×SD₁₆	—	47	2	no	—
664	C₄×SD₁₆	—	47	2	no	—
665	C₄×SD₁₆	—	47	1	no	—
666	C₄×SD₁₆	—	47	2	no	—
667	C₄×SD₁₆	—	47	1	no	—
668	C₄×SD₁₆	—	47	2	no	—
669	C₄×SD₁₆	—	47	2	no	—
670	#433	—	47	2	no	—
671	#433	—	47	2	no	—
672	#431	—	47	1	no	—
673	#431	—	47	1	no	—
674	C₄₇	#61865	1	1	yes	characteristic, complemented, Sylow
675	C₂×#41	—	94	1	no	—
676	C₂×#41	—	94	1	no	—
677	C₂²×Q₈	—	94	1	no	—
678	C₂²×Q₈	C₂²×D₄₇	1	1	yes	characteristic
679	C₂×Q₁₆	—	47	1	no	—
680	C₂×Q₁₆	—	47	1	no	—
681	C₂×SD₁₆	—	47	2	no	—
682	C₂×SD₁₆	—	47	1	no	—
683	C₂×SD₁₆	—	47	2	no	—
684	C₂×SD₁₆	—	47	1	no	—
685	C₄⋊Q₈	—	2	1	no	—
686	C₄⋊Q₈	—	2	1	no	—
687	C₄⋊Q₈	—	2	2	no	—
688	C₄⋊Q₈	—	2	2	no	—
689	C₄⋊Q₈	—	2	1	no	—
690	C₄⋊Q₈	—	2	1	no	—
691	C₄⋊Q₈	—	2	2	no	—
692	C₄⋊Q₈	—	2	2	no	—
693	C₄⋊Q₈	—	2	2	no	—
694	C₄⋊Q₈	—	47	1	no	—
695	C₄⋊Q₈	—	47	2	no	—
696	C₄⋊Q₈	—	94	1	no	—
697	C₄⋊Q₈	C₂²⋊D₄₇	1	1	yes	characteristic
698	C₄⋊Q₈	C₂²⋊D₄₇	1	1	yes	characteristic
699	C₄⋊Q₈	C₂²×D₄₇	1	1	yes	characteristic
700	C₄⋊Q₈	C₂²×D₄₇	1	1	yes	characteristic
701	C₄⋊Q₈	C₂²×D₄₇	1	2	yes	—
702	C₄⋊Q₈	C₂²×D₄₇	1	2	yes	—
703	#127	—	47	1	no	—
704	#127	—	47	2	no	—
705	#126	—	94	2	no	—
706	#126	—	94	1	no	—
707	#125	—	2	2	no	—
708	#125	—	2	2	no	—
709	#125	—	2	2	no	—
710	#125	—	2	2	no	—
711	#125	—	2	2	no	—
712	#125	—	2	2	no	—
713	#125	—	2	2	no	—
714	#125	—	47	1	no	—
715	#125	—	47	2	no	—
716	#125	—	94	2	no	—
717	#125	C₂²⋊D₄₇	1	2	yes	—
718	#125	C₂²×D₄₇	1	2	yes	—
719	#125	C₂²×D₄₇	1	2	yes	—
720	#125	C₂²×D₄₇	1	2	yes	—
721	#124	—	47	1	no	—
722	#124	—	47	2	no	—
723	#124	—	94	1	no	—
724	#124	—	94	2	no	—
725	#124	—	94	2	no	—
726	#124	—	94	1	no	—
727	#123	—	94	1	no	—
728	#123	—	94	2	no	—
729	#123	—	94	2	no	—
730	#123	—	94	2	no	—
731	#123	—	94	2	no	—
732	#123	—	94	2	no	—
733	#123	—	94	2	no	—
734	C₂²⋊Q₈	—	2	1	no	—
735	C₂²⋊Q₈	—	2	1	no	—
736	C₂²⋊Q₈	—	2	2	no	—
737	C₂²⋊Q₈	—	2	2	no	—
738	C₂²⋊Q₈	—	47	1	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	1	no	—
745	C₂²⋊Q₈	C₂²⋊D₄₇	1	1	yes	characteristic
746	C₂²⋊Q₈	C₂²⋊D₄₇	1	1	yes	characteristic
747	C₂²⋊Q₈	C₂²⋊D₄₇	1	2	yes	—
748	#121	—	47	1	no	—
749	#121	—	47	2	no	—
750	#121	—	94	1	no	—
751	#121	—	94	2	no	—
752	#121	—	94	1	no	—
753	#121	—	94	2	no	—
754	#121	—	94	2	no	—
755	C₄×Q₈	—	2	1	no	—
756	C₄×Q₈	—	2	1	no	—
757	C₄×Q₈	—	2	2	no	—
758	C₄×Q₈	—	2	2	no	—
759	C₄×Q₈	—	2	2	no	—
760	C₄×Q₈	—	2	2	no	—
761	C₄×Q₈	—	2	1	no	—
762	C₄×Q₈	—	2	1	no	—
763	C₄×Q₈	—	2	1	no	—
764	C₄×Q₈	—	2	1	no	—
765	C₄×Q₈	—	2	1	no	—
766	C₄×Q₈	—	2	1	no	—
767	C₄×Q₈	—	47	1	no	—
768	C₄×Q₈	—	47	2	no	—
769	C₄×Q₈	—	94	1	no	—
770	C₄×Q₈	C₂²×D₄₇	1	1	yes	characteristic
771	C₄×Q₈	C₂²×D₄₇	1	1	yes	characteristic
772	C₄×Q₈	C₂²×D₄₇	1	1	yes	characteristic
773	C₄×Q₈	C₂²×D₄₇	1	1	yes	characteristic
774	C₄×Q₈	C₂²×D₄₇	1	2	yes	—
775	C₄×Q₈	C₂²×D₄₇	1	2	yes	—
776	C₄×Q₈	C₂²×D₄₇	1	2	yes	—
777	C₄×Q₈	C₂²×D₄₇	1	2	yes	—
778	C₄×Q₈	C₂²×D₄₇	1	1	yes	characteristic
779	C₄×Q₈	C₂²×D₄₇	1	1	yes	characteristic
780	C₄×Q₈	C₂²×D₄₇	1	2	yes	—
781	C₄×D₄	—	47	1	no	—
782	C₄×D₄	—	47	2	no	—
783	C₄×D₄	—	47	2	no	—
784	C₄×D₄	—	47	2	no	—
785	C₄×D₄	—	47	2	no	—
786	C₄×D₄	—	94	1	no	—
787	C₄×D₄	—	94	2	no	—
788	C₄×D₄	—	94	1	no	—
789	C₄×D₄	—	94	1	no	—
790	#117	—	2	2	no	—
791	#117	—	2	2	no	—
792	#117	—	94	1	no	—
793	#117	C₂²×D₄₇	1	2	yes	—
794	#117	C₂²×D₄₇	1	2	yes	—
795	C₂×C₄⋊C₄	—	2	1	no	—
796	C₂×C₄⋊C₄	—	94	2	no	—
797	C₂×C₄⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
798	C₂×C₄²	—	2	1	no	—
799	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
800	#107	—	47	1	no	—
801	#107	—	47	2	no	—
802	#107	—	47	1	no	—
803	#107	—	47	2	no	—
804	#107	—	47	2	no	—
805	#107	—	47	2	no	—
806	#106	—	47	2	no	—
807	#106	—	47	2	no	—
808	#106	—	47	2	no	—
809	#106	—	47	2	no	—
810	#106	—	47	2	no	—
811	#106	—	47	1	no	—
812	#106	—	47	1	no	—
813	#106	—	47	2	no	—
814	C₄⋊C₈	—	47	1	no	—
815	C₄⋊C₈	—	47	1	no	—
816	C₄⋊C₈	—	47	1	no	—
817	C₄⋊C₈	—	47	1	no	—
818	C₄⋊C₈	—	47	2	no	—
819	C₄⋊C₈	—	47	2	no	—
820	C₄⋊C₈	—	47	2	no	—
821	C₄⋊C₈	—	47	2	no	—
822	#103	—	47	1	no	—
823	#103	—	47	2	no	—
824	#103	—	47	1	no	—
825	#103	—	47	1	no	—
826	#103	—	47	2	no	—
827	#103	—	47	1	no	—
828	#103	—	47	1	no	—
829	#103	—	47	2	no	—
830	#103	—	47	1	no	—
831	#103	—	47	2	no	—
832	#102	—	47	2	no	—
833	#102	—	47	2	no	—
834	#102	—	47	2	no	—
835	#102	—	47	2	no	—
836	#102	—	47	2	no	—
837	#102	—	47	1	no	—
838	#102	—	47	1	no	—
839	#102	—	47	2	no	—
840	#102	—	47	2	no	—
841	#102	—	47	2	no	—
842	C₂²⋊C₈	—	47	2	no	—
843	C₂²⋊C₈	—	47	1	no	—
844	C₂²⋊C₈	—	47	1	no	—
845	#97	—	47	2	no	—
846	#97	—	47	2	no	—
847	C₄×C₈	—	47	2	no	—
848	C₄×C₈	—	47	1	no	—
849	C₄×C₈	—	47	1	no	—
850	C₄×C₈	—	47	2	no	—
851	C₄×C₈	—	47	2	no	—
852	#41	—	376	2	no	—
853	#41	—	376	2	no	—
854	C₂×Q₈	—	2	2	no	—
855	C₂×Q₈	—	2	2	no	—
856	C₂×Q₈	—	2	1	no	—
857	C₂×Q₈	—	2	1	no	—
858	C₂×Q₈	—	2	1	no	—
859	C₂×Q₈	—	2	2	no	—
860	C₂×Q₈	—	2	2	no	—
861	C₂×Q₈	—	47	1	no	—
862	C₂×Q₈	—	94	2	no	—
863	C₂×Q₈	—	94	1	no	—
864	C₂×Q₈	—	376	2	no	—
865	C₂×Q₈	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
866	C₂×Q₈	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
867	C₂×Q₈	C₂×C₂²⋊D₄₇	1	2	yes	—
868	C₂×Q₈	C₂³×D₄₇	1	1	yes	characteristic
869	C₂×Q₈	C₂³×D₄₇	1	1	yes	characteristic
870	C₂×D₄	—	47	2	no	—
871	C₂×D₄	—	47	1	no	—
872	C₂×D₄	—	94	1	no	—
873	C₂×D₄	—	94	2	no	—
874	C₂×D₄	—	94	1	no	—
875	C₂×D₄	—	94	2	no	—
876	C₂×D₄	—	94	2	no	—
877	C₂×D₄	—	94	1	no	—
878	C₂²×C₄	—	2	1	no	—
879	C₂²×C₄	—	2	1	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	—	94	1	no	—
885	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
886	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
887	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
888	Q₁₆	—	94	2	no	—
889	Q₁₆	—	94	2	no	—
890	SD₁₆	—	94	4	no	—
891	SD₁₆	—	94	2	no	—
892	SD₁₆	—	94	4	no	—
893	SD₁₆	—	94	2	no	—
894	C₂×C₈	—	47	1	no	—
895	C₂×C₈	—	47	2	no	—
896	C₂×C₈	—	47	1	no	—
897	C₂×C₈	—	47	1	no	—
898	C₂×C₈	—	47	2	no	—
899	C₂×C₈	—	47	1	no	—
900	C₄⋊C₄	—	2	1	no	—
901	C₄⋊C₄	—	2	1	no	—
902	C₄⋊C₄	—	2	1	no	—
903	C₄⋊C₄	—	2	1	no	—
904	C₄⋊C₄	—	2	1	no	—
905	C₄⋊C₄	—	2	2	no	—
906	C₄⋊C₄	—	2	2	no	—
907	C₄⋊C₄	—	2	2	no	—
908	C₄⋊C₄	—	2	2	no	—
909	C₄⋊C₄	—	2	2	no	—
910	C₄⋊C₄	—	2	1	no	—
911	C₄⋊C₄	—	2	1	no	—
912	C₄⋊C₄	—	2	2	no	—
913	C₄⋊C₄	—	2	2	no	—
914	C₄⋊C₄	—	2	2	no	—
915	C₄⋊C₄	—	2	2	no	—
916	C₄⋊C₄	—	2	2	no	—
917	C₄⋊C₄	—	2	2	no	—
918	C₄⋊C₄	—	2	2	no	—
919	C₄⋊C₄	—	47	1	no	—
920	C₄⋊C₄	—	47	2	no	—
921	C₄⋊C₄	—	47	1	no	—
922	C₄⋊C₄	—	94	1	no	—
923	C₄⋊C₄	—	94	2	no	—
924	C₄⋊C₄	—	94	1	no	—
925	C₄⋊C₄	—	94	1	no	—
926	C₄⋊C₄	—	94	2	no	—
927	C₄⋊C₄	—	94	1	no	—
928	C₄⋊C₄	—	94	2	no	—
929	C₄⋊C₄	—	94	2	no	—
930	C₄⋊C₄	—	94	1	no	—
931	C₄⋊C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
932	C₄⋊C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
933	C₄⋊C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
934	C₄⋊C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
935	C₄⋊C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
936	C₄⋊C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
937	C₄⋊C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
938	C₄⋊C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
939	C₄⋊C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
940	C₄⋊C₄	C₂³×D₄₇	1	1	yes	characteristic
941	C₄⋊C₄	C₂³×D₄₇	1	1	yes	characteristic
942	C₄⋊C₄	C₂³×D₄₇	1	2	yes	—
943	C₄⋊C₄	C₂³×D₄₇	1	2	yes	—
944	C₂²⋊C₄	—	2	2	no	—
945	C₂²⋊C₄	—	94	1	no	—
946	C₂²⋊C₄	—	94	1	no	—
947	C₂²⋊C₄	—	94	1	no	—
948	C₂²⋊C₄	—	94	1	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	1	no	—
954	C₂²⋊C₄	—	94	2	no	—
955	C₂²⋊C₄	—	94	2	no	—
956	C₂²⋊C₄	—	94	2	no	—
957	C₂²⋊C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
958	C₂²⋊C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
959	C₄²	—	2	1	no	—
960	C₄²	—	2	1	no	—
961	C₄²	—	2	1	no	—
962	C₄²	—	2	1	no	—
963	C₄²	—	2	2	no	—
964	C₄²	—	2	2	no	—
965	C₄²	—	2	2	no	—
966	C₄²	—	2	2	no	—
967	C₄²	—	2	2	no	—
968	C₄²	—	94	1	no	—
969	C₄²	—	94	2	no	—
970	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
971	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
972	C₄²	C₂³×D₄₇	1	1	yes	characteristic
973	C₄²	C₂³×D₄₇	1	1	yes	characteristic
974	C₄²	C₂³×D₄₇	1	2	yes	—
975	C₄²	C₂³×D₄₇	1	2	yes	—
976	C₂³	—	94	1	no	—
977	C₂³	—	94	2	no	—
978	C₂³	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
979	Q₈	—	2	4	no	—
980	Q₈	—	2	2	no	—
981	Q₈	—	2	2	no	—
982	Q₈	—	2	1	no	—
983	Q₈	—	2	1	no	—
984	Q₈	—	4	2	no	—
985	Q₈	—	4	2	no	—
986	Q₈	—	8	1	no	—
987	Q₈	—	8	2	no	—
988	Q₈	—	8	2	no	—
989	Q₈	—	94	1	no	—
990	Q₈	—	94	1	no	—
991	Q₈	—	376	2	no	—
992	Q₈	—	188	2	no	—
993	Q₈	#13094072	1	2	yes	—
994	Q₈	#13094072	1	2	yes	—
995	D₄	—	94	2	no	—
996	D₄	—	94	1	no	—
997	D₄	—	94	2	no	—
998	D₄	—	94	1	no	—
999	D₄	—	376	1	no	—
1000	D₄	—	376	2	no	—
1001	D₄	—	376	2	no	—
1002	D₄	—	376	1	no	—
1003	D₄	—	376	2	no	—
1004	D₄	—	188	2	no	—
1005	C₂×C₄	—	2	4	no	—
1006	C₂×C₄	—	2	1	no	—
1007	C₂×C₄	—	2	1	no	—
1008	C₂×C₄	—	2	2	no	—
1009	C₂×C₄	—	2	1	no	—
1010	C₂×C₄	—	2	1	no	—
1011	C₂×C₄	—	2	2	no	—
1012	C₂×C₄	—	2	2	no	—
1013	C₂×C₄	—	2	1	no	—
1014	C₂×C₄	—	2	1	no	—
1015	C₂×C₄	—	4	1	no	—
1016	C₂×C₄	—	8	1	no	—
1017	C₂×C₄	—	94	1	no	—
1018	C₂×C₄	—	94	1	no	—
1019	C₂×C₄	—	94	2	no	—
1020	C₂×C₄	—	94	1	no	—
1021	C₂×C₄	—	376	2	no	—
1022	C₂×C₄	—	376	2	no	—
1023	C₂×C₄	—	376	2	no	—
1024	C₂×C₄	—	376	2	no	—
1025	C₂×C₄	—	188	2	no	—
1026	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
1027	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
1028	C₂×C₄	C₂²×C₂²⋊D₄₇	1	2	yes	—
1029	C₂×C₄	C₂²×C₂²⋊D₄₇	1	2	yes	—
1030	C₂×C₄	C₂²×C₂²⋊D₄₇	1	2	yes	—
1031	C₂×C₄	C₂²×C₂²⋊D₄₇	1	2	yes	—
1032	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
1033	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
1034	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
1035	C₂×C₄	C₂⁴×D₄₇	1	1	yes	characteristic
1036	C₈	—	94	2	no	—
1037	C₈	—	94	1	no	—
1038	C₈	—	94	2	no	—
1039	C₈	—	94	1	no	—
1040	C₈	—	94	1	no	—
1041	C₈	—	94	1	no	—
1042	C₂²	—	2	1	no	—
1043	C₂²	—	2	1	no	—
1044	C₂²	—	2	1	no	—
1045	C₂²	—	188	1	no	—
1046	C₂²	—	188	2	no	—
1047	C₂²	—	188	1	no	—
1048	C₂²	—	188	2	no	—
1049	C₂²	—	188	2	no	—
1050	C₂²	—	188	1	no	—
1051	C₂²	C₂³×C₂²⋊D₄₇	1	1	yes	characteristic
1052	C₄	—	2	2	no	—
1053	C₄	—	2	2	no	—
1054	C₄	—	2	1	no	—
1055	C₄	—	2	1	no	—
1056	C₄	—	2	2	no	—
1057	C₄	—	2	2	no	—
1058	C₄	—	2	1	no	—
1059	C₄	—	2	1	no	—
1060	C₄	—	2	2	no	—
1061	C₄	—	2	2	no	—
1062	C₄	—	4	2	no	—
1063	C₄	—	4	1	no	—
1064	C₄	—	4	1	no	—
1065	C₄	—	4	2	no	—
1066	C₄	—	188	1	no	—
1067	C₄	—	188	1	no	—
1068	C₄	—	188	2	no	—
1069	C₄	—	188	1	no	—
1070	C₄	#15689931	1	2	yes	—
1071	C₄	C₂×#13094072	1	1	yes	characteristic
1072	C₄	C₂×#13094072	1	1	yes	characteristic
1073	C₂	—	4	1	no	—
1074	C₂	—	376	1	no	—
1075	C₂	—	376	2	no	—
1076	C₂	#20257039	1	1	yes	characteristic
1077	C₂	C₂×#15689931	1	1	yes	characteristic
1078	C₂	#20258159	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂³×C₂²⋊D₄₇
commutator, cosocle	C₂×C₄×C₄₇	C₂⁵
Frattini	C₂×C₄	C₂⁴×D₄₇
Fitting	C₄₇×#3502	C₂
socle	C₂²×C₄₇	C₂³×D₄
prime radical	#20257859	C₂
hypercenter	#3502	D₄₇
hypocenter	C₄₇	#61865
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ #533 ◁ #3502

Complements

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

N	H ≅ G/N	type
2. #20256327	C₂	semidirect
3. #20256316	C₂	semidirect
4. #20256305	C₂	semidirect
5. #20256275	C₂	semidirect
6. #20256259	C₂	semidirect
7. Q₈×#10625336	C₂	semidirect
8. #20256202	C₂	semidirect
9. #20256156	C₂	semidirect
10. #20256117	C₂	semidirect
11. #20256084	C₂	semidirect
12. #20256084	C₂	semidirect
13. #20256059	C₂	semidirect
14. #20254686	C₂	semidirect
15. #20254641	C₂	semidirect
16. #20254567	C₂	semidirect
17. #20254524	C₂	semidirect
18. #20253679	C₂	semidirect
19. #20253617	C₂	semidirect
20. #20253468	C₂	semidirect
21. #20253419	C₂	semidirect
22. #20252490	C₂	semidirect
23. C₄₇×#3502	C₂	semidirect
535. #3502	D₄₇	semidirect
674. C₄₇	#61865	semidirect

Maximal subgroups

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

subgroup	index
#20257859	2
#20256327	2
#20256316	2
#20256305	2
#20256275	2
#20256259	2
Q₈×#10625336	2
#20256202	2
#20256156	2
#20256117	2
#20256084	2
#20256059	2
#20254686	2
#20254641	2
#20254567	2
#20254524	2
#20253679	2
#20253617	2
#20253468	2
#20253419	2
#20252490	2
C₄₇×#3502	2
#61865	47