Subgroups — #27096657

Order 12032.

1810 conjugacy classes of subgroups.

The subgroup lattice has 1150 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20257242	C₂	1	1	yes	maximal, characteristic, complemented
2	#20256230	C₂	1	2	yes	maximal, complemented
3	#20256215	C₂	1	2	yes	maximal, complemented
4	#20256156	C₂	1	2	yes	maximal, complemented
5	#20256141	C₂	1	2	yes	maximal, complemented
6	#20256117	C₂	1	2	yes	maximal, complemented
7	#20256095	C₂	1	2	yes	maximal, complemented
8	#20256084	C₂	1	2	yes	maximal, complemented
9	#20256048	C₂	1	2	yes	maximal, complemented
10	#20253791	C₂	1	1	yes	maximal, characteristic, complemented
11	#20253747	C₂	1	1	yes	maximal, characteristic, complemented
12	#20253747	C₂	1	1	yes	maximal, characteristic, complemented
13	#20253246	C₂	1	1	yes	maximal, characteristic, complemented
14	#20253235	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×#15689420	C₂	1	1	yes	maximal, characteristic, complemented
16	#20252927	C₂	1	1	yes	maximal, characteristic, complemented
17	#20252927	C₂	1	1	yes	maximal, characteristic, complemented
18	#20252843	C₂	1	1	yes	maximal, characteristic, complemented
19	#20252337	C₂	1	1	yes	maximal, characteristic, complemented
20	#20252269	C₂	1	1	yes	maximal, characteristic, complemented
21	#20252261	C₂	1	1	yes	maximal, characteristic, complemented
22	C₄×#13094049	C₂	1	1	yes	maximal, characteristic, complemented
23	C₄₇×#3504	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#13094049	C₂²	1	1	yes	characteristic
25	C₂×#13094044	C₂²	1	1	yes	characteristic
26	C₂×#13094044	C₂²	1	1	yes	characteristic
27	#15689858	C₂²	1	2	yes	—
28	#15689858	C₂²	1	2	yes	—
29	#15689846	C₂²	1	2	yes	—
30	#15689839	—	2	1	no	—
31	#15689826	—	2	1	no	—
32	#15689826	—	2	1	no	—
33	#15689795	C₂²	1	2	yes	—
34	#15689776	—	2	1	no	—
35	#15689713	—	2	2	no	—
36	#15689692	C₂²	1	1	yes	characteristic
37	#15689692	C₂²	1	1	yes	characteristic
38	#15689673	C₂²	1	1	yes	characteristic
39	#15689636	—	2	2	no	—
40	#15689603	C₂²	1	1	yes	characteristic
41	#15689603	C₂²	1	1	yes	characteristic
42	C₂×C₄×D₁₈₈	C₂²	1	1	yes	characteristic
43	#15689493	C₂²	1	2	yes	complemented
44	#15689489	C₂²	1	2	yes	—
45	#15689489	C₂²	1	2	yes	—
46	#15689489	C₂²	1	2	yes	complemented
47	#15689485	C₂²	1	2	yes	—
48	#15689485	C₂²	1	2	yes	—
49	#15689480	C₂²	1	2	yes	—
50	#15689480	C₂²	1	2	yes	—
51	#15689480	C₂²	1	2	yes	complemented
52	#15689480	C₂²	1	2	yes	complemented
53	#15689471	C₂²	1	2	yes	—
54	#15689471	C₂²	1	2	yes	—
55	#15689427	C₂²	1	2	yes	complemented
56	#15689427	C₂²	1	2	yes	complemented
57	#15689420	C₂²	1	2	yes	—
58	#15689420	C₂²	1	2	yes	—
59	#15689420	C₂²	1	2	yes	—
60	#15689420	C₂²	1	2	yes	—
61	#15689420	C₂²	1	2	yes	complemented
62	#15689420	C₂²	1	2	yes	complemented
63	#15689415	C₂²	1	2	yes	complemented
64	#15689410	C₂²	1	2	yes	complemented
65	#15689405	C₂²	1	2	yes	complemented
66	#15689400	C₂²	1	2	yes	complemented
67	#15689345	C₂²	1	2	yes	—
68	#15689345	C₂²	1	2	yes	—
69	#15689345	C₂²	1	1	yes	characteristic, complemented
70	#15689345	C₂²	1	1	yes	characteristic, complemented
71	#15689338	C₂²	1	2	yes	—
72	#15689338	C₂²	1	2	yes	—
73	#15689338	C₂²	1	1	yes	characteristic, complemented
74	#15689338	C₂²	1	1	yes	characteristic, complemented
75	#15689333	C₂²	1	1	yes	characteristic, complemented
76	#15689328	C₂²	1	1	yes	characteristic, complemented
77	#15689323	C₂²	1	2	yes	—
78	#15689323	C₂²	1	2	yes	—
79	#15689323	C₂²	1	1	yes	characteristic, complemented
80	#15689318	C₂²	1	2	yes	—
81	#15689318	C₂²	1	2	yes	—
82	#15689318	C₂²	1	1	yes	characteristic, complemented
83	#15689254	C₂²	1	2	yes	complemented
84	#15689254	C₂²	1	2	yes	complemented
85	#15689254	C₂²	1	2	yes	complemented
86	Q₈×C₄₇⋊C₈	C₂²	1	2	yes	complemented
87	#15689233	C₂²	1	2	yes	—
88	#15689233	C₂²	1	2	yes	complemented
89	#15689228	C₂²	1	2	yes	complemented
90	#15689223	C₂²	1	2	yes	complemented
91	#15689221	C₂²	1	2	yes	—
92	#15689221	C₂²	1	2	yes	complemented
93	C₄×#10625337	C₂²	1	2	yes	complemented
94	C₄×#10625336	C₂²	1	2	yes	—
95	C₄×#10625336	C₂²	1	2	yes	complemented
96	C₄×#10625335	C₂²	1	2	yes	complemented
97	C₄×#10625334	C₂²	1	2	yes	—
98	C₄×#10625334	C₂²	1	2	yes	complemented
99	#15689166	C₂²	1	1	yes	characteristic
100	C₂×#13093957	C₂²	1	1	yes	characteristic
101	C₂×#13093955	C₂²	1	1	yes	characteristic
102	#15689150	C₂²	1	1	yes	characteristic
103	#15689150	C₂²	1	1	yes	characteristic
104	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
105	#15689127	C₂²	1	1	yes	characteristic
106	#15689124	C₂²	1	1	yes	characteristic
107	#15689122	C₂²	1	1	yes	characteristic
108	#15689122	C₂²	1	1	yes	characteristic
109	#15689122	C₂²	1	1	yes	characteristic
110	#15689122	C₂²	1	1	yes	characteristic
111	#15689117	C₂²	1	1	yes	characteristic
112	#15689117	C₂²	1	1	yes	characteristic
113	C₂×#13093944	C₂²	1	1	yes	characteristic
114	C₂×#13093944	C₂²	1	1	yes	characteristic
115	#15689079	C₂²	1	1	yes	characteristic
116	#15689079	C₂²	1	1	yes	characteristic
117	C₄×#10625329	C₂²	1	1	yes	characteristic
118	C₄₇×#557	C₂²	1	2	yes	complemented
119	C₄₇×#557	C₂²	1	2	yes	complemented
120	C₄₇×#554	—	2	2	no	—
121	C₄₇×#554	—	2	2	no	—
122	C₄₇×#554	C₂²	1	2	yes	complemented
123	C₄₇×#554	C₂²	1	2	yes	complemented
124	C₄₇×#544	—	2	1	no	—
125	C₄₇×#544	—	2	1	no	—
126	C₄₇×#544	C₂²	1	1	yes	characteristic
127	C₄₇×#544	C₂²	1	1	yes	characteristic
128	C₄₇×#533	—	2	1	no	—
129	C₄₇×#533	C₂²	1	1	yes	characteristic
130	C₂×#125×C₄₇	—	2	1	no	—
131	C₂×#125×C₄₇	C₂²	1	1	yes	characteristic
132	C₄₇×#520	C₂²	1	1	yes	characteristic
133	C₄₇×#520	C₂²	1	1	yes	characteristic
134	C₄×#41×C₄₇	C₂²	1	1	yes	characteristic
135	C₂×#10625354	—	2	2	no	—
136	C₂×#10625350	C₂³	1	1	yes	characteristic
137	C₂×#10625350	C₂³	1	1	yes	characteristic
138	C₂²×D₁₈₈	C₂³	1	1	yes	characteristic
139	C₂²×C₄×D₄₇	—	2	1	no	—
140	#13094049	—	2	4	no	—
141	#13094044	—	2	4	no	—
142	#13094044	—	2	4	no	—
143	C₂×#10625337	C₂³	1	1	yes	characteristic
144	C₂×#10625337	C₂³	1	1	yes	characteristic
145	C₂×#10625335	C₂³	1	1	yes	characteristic
146	C₂×#10625335	C₂³	1	1	yes	characteristic
147	C₂×#10625336	C₂³	1	2	yes	—
148	C₂×#10625336	C₂³	1	1	yes	characteristic
149	C₂×#10625336	C₂³	1	1	yes	characteristic
150	C₂×#10625334	C₂³	1	2	yes	—
151	C₂×#10625334	C₂³	1	1	yes	characteristic
152	C₂×#10625334	C₂³	1	1	yes	characteristic
153	C₂×#10625329	C₂³	1	1	yes	characteristic
154	C₂×#10625329	C₂³	1	1	yes	characteristic
155	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
156	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
157	#13094024	C₂³	1	1	yes	characteristic
158	#13094021	C₂³	1	2	yes	—
159	#13094021	C₂³	1	2	yes	—
160	#13094021	C₂³	1	1	yes	characteristic
161	#13094019	—	2	2	no	—
162	#13094019	—	2	2	no	—
163	#13094013	—	2	2	no	—
164	#13094013	—	2	2	no	—
165	#13094012	C₂³	1	2	yes	—
166	#13094012	C₂³	1	2	yes	—
167	#13094012	C₂³	1	1	yes	characteristic
168	#13094012	C₂³	1	1	yes	characteristic
169	#13094009	—	2	2	no	—
170	#13094009	—	2	2	no	—
171	#13094009	—	2	2	no	—
172	#13094009	—	2	2	no	—
173	#13094000	—	2	2	no	—
174	#13093999	—	2	1	no	—
175	#13093999	—	2	1	no	—
176	#13093999	—	2	2	no	—
177	#13093999	—	2	2	no	—
178	#13093999	—	2	2	no	—
179	#13093999	—	2	1	no	—
180	#13093999	—	2	1	no	—
181	#13093998	—	2	1	no	—
182	#13093998	—	2	1	no	—
183	#13093994	—	2	2	no	—
184	#13093994	—	2	2	no	—
185	C₄×Dic₉₄	C₂³	1	2	yes	—
186	C₄×Dic₉₄	C₂³	1	2	yes	—
187	C₄×D₁₈₈	—	2	1	no	—
188	C₄×D₁₈₈	—	2	1	no	—
189	C₄×D₁₈₈	—	2	1	no	—
190	C₄×D₁₈₈	—	2	1	no	—
191	C₄×D₁₈₈	C₂³	1	2	yes	—
192	C₄×D₁₈₈	C₂³	1	2	yes	—
193	C₄×D₁₈₈	C₂³	1	2	yes	—
194	C₄×D₁₈₈	C₂³	1	2	yes	—
195	#13093986	—	2	2	no	—
196	#13093986	—	2	2	no	—
197	(C₂²⋊D₄₇)⋊C₄	—	2	2	no	—
198	(C₂²⋊D₄₇)⋊C₄	—	2	2	no	—
199	#13093982	—	2	1	no	—
200	#13093982	—	2	1	no	—
201	#13093982	—	2	2	no	—
202	C₂×C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic
203	C₄⋊C₄×D₄₇	—	2	1	no	—
204	C₄⋊C₄×D₄₇	—	2	1	no	—
205	C₂×(C₂×D₄₇)⋊C₄	—	2	1	no	—
206	#13093957	C₂³	1	2	yes	—
207	#13093957	C₂³	1	2	yes	—
208	#13093957	C₂³	1	2	yes	—
209	#13093955	C₂³	1	2	yes	—
210	#13093955	C₂³	1	2	yes	—
211	#13093955	C₂³	1	2	yes	—
212	C₄⋊(C₄₇⋊C₈)	C₂³	1	1	yes	characteristic
213	C₄⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
214	C₄⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
215	C₄⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
216	C₄⋊(C₄₇⋊C₈)	C₂³	1	1	yes	characteristic
217	C₄⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
218	C₄⋊(C₄₇⋊C₈)	C₂³	1	1	yes	characteristic
219	C₄⋊(C₄₇⋊C₈)	C₂³	1	1	yes	characteristic
220	#13093948	C₂³	1	2	yes	—
221	#13093947	C₂³	1	2	yes	—
222	#13093947	C₂³	1	1	yes	characteristic
223	#13093947	C₂³	1	1	yes	characteristic
224	#13093947	C₂³	1	2	yes	—
225	#13093947	C₂³	1	2	yes	—
226	#13093947	C₂³	1	2	yes	—
227	#13093947	C₂³	1	1	yes	characteristic
228	#13093947	C₂³	1	1	yes	characteristic
229	#13093945	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	2	yes	—
235	#13093944	C₂³	1	2	yes	—
236	#13093944	C₂³	1	2	yes	—
237	#13093944	C₂³	1	2	yes	—
238	#13093944	C₂³	1	2	yes	—
239	#13093944	C₂³	1	2	yes	—
240	#13093944	C₂³	1	1	yes	characteristic
241	#13093944	C₂³	1	1	yes	characteristic
242	#13093944	C₂³	1	1	yes	characteristic
243	#13093944	C₂³	1	1	yes	characteristic
244	#13093935	C₂³	1	2	yes	—
245	#13093935	C₂³	1	2	yes	—
246	#13093935	C₂³	1	2	yes	—
247	C₄×C₄₇⋊C₈	C₂³	1	2	yes	—
248	C₄×C₄₇⋊C₈	C₂³	1	2	yes	—
249	C₄×C₄₇⋊C₈	C₂³	1	2	yes	—
250	C₂×#41×C₄₇	C₂³	1	1	yes	characteristic
251	C₄⋊Q₈×C₄₇	—	2	2	no	—
252	C₄⋊Q₈×C₄₇	—	2	2	no	—
253	C₄⋊Q₈×C₄₇	—	2	1	no	—
254	C₄⋊Q₈×C₄₇	—	2	1	no	—
255	C₄⋊Q₈×C₄₇	D₄	1	1	yes	characteristic
256	C₄⋊Q₈×C₄₇	D₄	1	1	yes	characteristic
257	C₄⋊Q₈×C₄₇	C₂³	1	2	yes	—
258	C₄⋊Q₈×C₄₇	C₂³	1	2	yes	—
259	#125×C₄₇	—	2	1	no	—
260	#125×C₄₇	—	2	1	no	—
261	#125×C₄₇	—	2	2	no	—
262	#125×C₄₇	—	2	2	no	—
263	#125×C₄₇	—	2	2	no	—
264	#125×C₄₇	—	2	2	no	—
265	#125×C₄₇	—	2	1	no	—
266	#125×C₄₇	—	2	1	no	—
267	#125×C₄₇	D₄	1	1	yes	characteristic
268	#125×C₄₇	D₄	1	1	yes	characteristic
269	#125×C₄₇	C₂³	1	2	yes	—
270	#125×C₄₇	C₂³	1	2	yes	—
271	#125×C₄₇	C₂³	1	2	yes	—
272	#125×C₄₇	C₂³	1	2	yes	—
273	C₂²⋊Q₈×C₄₇	—	2	2	no	—
274	C₂²⋊Q₈×C₄₇	—	2	2	no	—
275	C₂²⋊Q₈×C₄₇	—	2	2	no	—
276	C₂²⋊Q₈×C₄₇	—	2	2	no	—
277	C₂²⋊Q₈×C₄₇	—	2	2	no	—
278	C₂²⋊Q₈×C₄₇	—	2	2	no	—
279	C₂²⋊Q₈×C₄₇	—	2	2	no	—
280	C₂²⋊Q₈×C₄₇	—	2	2	no	—
281	C₂²⋊Q₈×C₄₇	D₄	1	2	yes	—
282	C₂²⋊Q₈×C₄₇	D₄	1	2	yes	—
283	C₄×Q₈×C₄₇	—	2	2	no	—
284	C₄×Q₈×C₄₇	—	2	2	no	—
285	C₄×Q₈×C₄₇	C₂³	1	2	yes	—
286	C₄×Q₈×C₄₇	C₂³	1	1	yes	characteristic
287	C₄×Q₈×C₄₇	C₂³	1	2	yes	—
288	C₄×Q₈×C₄₇	C₂³	1	1	yes	characteristic
289	C₄×Q₈×C₄₇	C₂³	1	2	yes	—
290	C₄×Q₈×C₄₇	C₂³	1	2	yes	—
291	C₄×D₄×C₄₇	—	2	1	no	—
292	C₄×D₄×C₄₇	—	2	1	no	—
293	C₄×D₄×C₄₇	—	2	2	no	—
294	C₄×D₄×C₄₇	—	2	2	no	—
295	C₄×D₄×C₄₇	C₂³	1	2	yes	—
296	C₄×D₄×C₄₇	C₂³	1	1	yes	characteristic
297	C₄×D₄×C₄₇	C₂³	1	2	yes	—
298	C₄×D₄×C₄₇	C₂³	1	1	yes	characteristic
299	#117×C₄₇	—	2	1	no	—
300	#117×C₄₇	—	2	1	no	—
301	#117×C₄₇	—	2	1	no	—
302	#117×C₄₇	C₂³	1	1	yes	characteristic
303	#117×C₄₇	C₂³	1	1	yes	characteristic
304	#117×C₄₇	C₂³	1	1	yes	characteristic
305	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
306	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
307	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
308	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
309	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
310	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
311	C₂×C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
312	C₂×C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
313	C₂×C₄²×C₄₇	—	2	1	no	—
314	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
315	C₂³×D₄₇	—	2	1	no	—
316	#41×C₄₇	—	2	2	no	—
317	#41×C₄₇	#41	1	4	yes	complemented
318	C₂×Q₈×C₄₇	—	2	2	no	—
319	C₂×Q₈×C₄₇	—	2	2	no	—
320	C₂×Q₈×C₄₇	C₂×D₄	1	2	yes	—
321	C₂×Q₈×C₄₇	C₂×D₄	1	2	yes	—
322	C₂×Q₈×C₄₇	C₂⁴	1	1	yes	characteristic
323	C₂×D₄×C₄₇	—	2	1	no	—
324	C₂×D₄×C₄₇	C₂⁴	1	1	yes	characteristic
325	C₂²×C₄×C₄₇	—	2	1	no	—
326	C₂²×C₄×C₄₇	—	2	1	no	—
327	C₂²×C₄×C₄₇	—	2	1	no	—
328	C₂²×C₄×C₄₇	—	2	1	no	—
329	C₂²×C₄×C₄₇	—	2	1	no	—
330	C₂²×C₄×C₄₇	—	2	2	no	—
331	C₂²×C₄×C₄₇	—	2	2	no	—
332	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
333	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
334	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
335	C₂×C₂²⋊D₄₇	—	2	1	no	—
336	C₂×C₂²⋊D₄₇	—	2	1	no	—
337	C₂²×Dic₄₇	—	2	1	no	—
338	#10625354	—	8	4	no	—
339	#10625350	—	2	2	no	—
340	#10625350	—	2	2	no	—
341	#10625350	—	2	2	no	—
342	#10625350	—	2	2	no	—
343	C₂×D₁₈₈	—	2	2	no	—
344	C₂×D₁₈₈	—	2	2	no	—
345	C₂×D₁₈₈	—	2	1	no	—
346	C₂×D₁₈₈	—	2	1	no	—
347	C₂×D₁₈₈	—	2	2	no	—
348	C₂×D₁₈₈	—	2	2	no	—
349	C₂×D₁₈₈	—	2	1	no	—
350	C₂×D₁₈₈	—	2	2	no	—
351	C₂×D₁₈₈	—	2	2	no	—
352	C₂×D₁₈₈	C₂⁴	1	2	yes	—
353	C₂×D₁₈₈	C₂⁴	1	1	yes	characteristic
354	C₂×D₁₈₈	C₂⁴	1	1	yes	characteristic
355	C₂×C₄×D₄₇	—	2	1	no	—
356	C₂×C₄×D₄₇	—	2	1	no	—
357	C₂×C₄×D₄₇	—	2	2	no	—
358	C₂×C₄×D₄₇	—	2	2	no	—
359	C₂×C₄×D₄₇	—	2	2	no	—
360	C₂×C₄×D₄₇	—	2	2	no	—
361	C₂×C₄×D₄₇	—	8	2	no	—
362	C₂×Dic₉₄	C₂⁴	1	1	yes	characteristic
363	C₂×Dic₉₄	C₂⁴	1	1	yes	characteristic
364	C₄⋊C₄×C₄₇	—	2	2	no	—
365	C₄⋊C₄×C₄₇	—	2	2	no	—
366	C₄⋊C₄×C₄₇	—	2	1	no	—
367	C₄⋊C₄×C₄₇	—	2	1	no	—
368	C₄⋊C₄×C₄₇	—	2	2	no	—
369	C₄⋊C₄×C₄₇	—	2	2	no	—
370	C₄⋊C₄×C₄₇	—	2	2	no	—
371	C₄⋊C₄×C₄₇	—	2	2	no	—
372	C₄⋊C₄×C₄₇	—	2	2	no	—
373	C₄⋊C₄×C₄₇	—	2	2	no	—
374	C₄⋊C₄×C₄₇	—	2	2	no	—
375	C₄⋊C₄×C₄₇	—	2	2	no	—
376	C₄⋊C₄×C₄₇	—	2	1	no	—
377	C₄⋊C₄×C₄₇	—	2	1	no	—
378	C₄⋊C₄×C₄₇	—	2	2	no	—
379	C₄⋊C₄×C₄₇	—	2	2	no	—
380	C₄⋊C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
381	C₄⋊C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
382	C₄⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
383	C₄⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
384	C₄⋊C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
385	C₄⋊C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
386	C₄⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
387	C₄⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
388	C₄⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
389	C₄⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
390	C₄⋊C₄×C₄₇	C₂⁴	1	2	yes	—
391	C₄⋊C₄×C₄₇	C₂⁴	1	2	yes	—
392	C₄⋊C₄×C₄₇	C₂⁴	1	1	yes	characteristic
393	C₄⋊C₄×C₄₇	C₂⁴	1	1	yes	characteristic
394	C₂²⋊C₄×C₄₇	—	2	1	no	—
395	C₂²⋊C₄×C₄₇	—	2	1	no	—
396	C₂²⋊C₄×C₄₇	—	2	1	no	—
397	C₂²⋊C₄×C₄₇	—	2	2	no	—
398	C₂²⋊C₄×C₄₇	—	2	2	no	—
399	C₂²⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
400	C₂²⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
401	C₄²×C₄₇	—	2	1	no	—
402	C₄²×C₄₇	—	2	1	no	—
403	C₄²×C₄₇	—	2	1	no	—
404	C₄²×C₄₇	—	2	2	no	—
405	C₄²×C₄₇	—	2	2	no	—
406	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
407	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
408	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
409	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
410	C₄²×C₄₇	C₂⁴	1	2	yes	—
411	C₄²×C₄₇	C₂⁴	1	2	yes	—
412	#10625337	—	2	2	no	—
413	#10625337	—	2	2	no	—
414	#10625336	—	2	2	no	—
415	#10625336	—	2	2	no	—
416	#10625336	—	2	4	no	—
417	#10625335	—	2	2	no	—
418	#10625335	—	2	2	no	—
419	#10625334	—	2	2	no	—
420	#10625334	—	2	2	no	—
421	#10625334	—	2	4	no	—
422	(C₂×D₄₇)⋊C₄	—	2	2	no	—
423	(C₂×D₄₇)⋊C₄	—	2	2	no	—
424	(C₂×D₄₇)⋊C₄	—	2	2	no	—
425	(C₂×D₄₇)⋊C₄	—	2	2	no	—
426	(C₂×D₄₇)⋊C₄	—	2	2	no	—
427	(C₂×D₄₇)⋊C₄	—	2	2	no	—
428	(C₂×D₄₇)⋊C₄	—	2	1	no	—
429	(C₂×D₄₇)⋊C₄	—	2	1	no	—
430	(C₂×D₄₇)⋊C₄	—	2	2	no	—
431	(C₂×D₄₇)⋊C₄	—	2	2	no	—
432	(C₂×D₄₇)⋊C₄	—	2	1	no	—
433	(C₂×D₄₇)⋊C₄	—	2	1	no	—
434	C₄⋊Dic₄₇	—	2	1	no	—
435	C₄⋊Dic₄₇	—	2	1	no	—
436	C₄⋊Dic₄₇	—	2	1	no	—
437	C₄⋊Dic₄₇	C₂⁴	1	2	yes	—
438	Dic₄₇⋊C₄	—	2	2	no	—
439	Dic₄₇⋊C₄	—	2	2	no	—
440	C₄×Dic₄₇	—	2	2	no	—
441	C₄×Dic₄₇	—	2	2	no	—
442	#10625329	—	2	2	no	—
443	#10625329	—	2	2	no	—
444	C₂×C₄₇⋊C₈	—	2	2	no	—
445	C₂×C₄₇⋊C₈	—	2	2	no	—
446	C₂×C₄₇⋊C₈	C₂⁴	1	2	yes	—
447	C₂×C₄₇⋊C₈	C₂⁴	1	1	yes	characteristic
448	C₂×C₄₇⋊C₈	C₂⁴	1	1	yes	characteristic
449	C₂×C₄₇⋊C₈	C₂⁴	1	2	yes	—
450	C₂×C₄₇⋊C₈	C₂⁴	1	1	yes	characteristic
451	C₂×C₄₇⋊C₈	C₂⁴	1	1	yes	characteristic
452	C₂³×C₄₇	—	2	1	no	—
453	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
454	C₂²×D₄₇	—	2	2	no	—
455	C₂²×D₄₇	—	2	1	no	—
456	C₂²×D₄₇	—	2	1	no	—
457	C₂²×D₄₇	—	4	2	no	—
458	C₂²×D₄₇	—	8	1	no	—
459	C₂²×D₄₇	—	8	1	no	—
460	Q₈×C₄₇	—	2	1	no	—
461	Q₈×C₄₇	—	4	2	no	—
462	Q₈×C₄₇	—	4	2	no	—
463	Q₈×C₄₇	—	8	2	no	—
464	Q₈×C₄₇	—	8	2	no	—
465	Q₈×C₄₇	C₂×#41	1	2	yes	—
466	D₄×C₄₇	—	2	4	no	—
467	D₄×C₄₇	—	2	1	no	—
468	D₄×C₄₇	C₂×#41	1	2	yes	—
469	C₂×C₄×C₄₇	—	2	1	no	—
470	C₂×C₄×C₄₇	—	2	4	no	—
471	C₂×C₄×C₄₇	—	2	1	no	—
472	C₂×C₄×C₄₇	—	2	1	no	—
473	C₂×C₄×C₄₇	—	2	2	no	—
474	C₂×C₄×C₄₇	—	2	2	no	—
475	C₂×C₄×C₄₇	—	4	1	no	—
476	C₂×C₄×C₄₇	—	4	1	no	—
477	C₂×C₄×C₄₇	—	8	1	no	—
478	C₂×C₄×C₄₇	—	8	2	no	—
479	C₂×C₄×C₄₇	—	8	1	no	—
480	C₂×C₄×C₄₇	—	8	2	no	—
481	C₂×C₄×C₄₇	—	8	1	no	—
482	C₂×C₄×C₄₇	—	8	1	no	—
483	C₂×C₄×C₄₇	C₂²×D₄	1	2	yes	—
484	C₂×C₄×C₄₇	C₂²×D₄	1	2	yes	—
485	C₂×C₄×C₄₇	C₂²×D₄	1	2	yes	—
486	C₂×C₄×C₄₇	C₂²×D₄	1	2	yes	—
487	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
488	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
489	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
490	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
491	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
492	C₂×C₄×C₄₇	C₂×#41	1	2	yes	—
493	C₂×C₄×C₄₇	2₋¹⁺⁴	1	2	yes	—
494	C₂×C₄×C₄₇	C₂⁵	1	1	yes	characteristic
495	C₂²⋊D₄₇	—	4	2	no	—
496	C₂²⋊D₄₇	—	4	2	no	—
497	C₂×Dic₄₇	—	2	1	no	—
498	C₂×Dic₄₇	—	2	1	no	—
499	C₂×Dic₄₇	—	2	2	no	—
500	C₂×Dic₄₇	—	8	1	no	—
501	D₁₈₈	—	2	2	no	—
502	D₁₈₈	—	2	1	no	—
503	D₁₈₈	—	2	1	no	—
504	D₁₈₈	—	2	2	no	—
505	D₁₈₈	—	2	1	no	—
506	D₁₈₈	—	2	1	no	—
507	D₁₈₈	—	4	2	no	—
508	D₁₈₈	—	4	2	no	—
509	D₁₈₈	—	8	1	no	—
510	D₁₈₈	—	8	2	no	—
511	D₁₈₈	—	8	2	no	—
512	D₁₈₈	—	8	2	no	—
513	D₁₈₈	—	8	2	no	—
514	C₄×D₄₇	—	4	4	no	—
515	C₄×D₄₇	—	4	2	no	—
516	C₄×D₄₇	—	4	2	no	—
517	C₄×D₄₇	—	8	2	no	—
518	C₄×D₄₇	—	8	2	no	—
519	C₄×D₄₇	—	8	2	no	—
520	Dic₉₄	—	2	1	no	—
521	Dic₉₄	—	2	1	no	—
522	Dic₉₄	—	2	1	no	—
523	Dic₉₄	—	2	1	no	—
524	C₄₇⋊C₈	—	2	1	no	—
525	C₄₇⋊C₈	—	2	1	no	—
526	C₄₇⋊C₈	—	2	1	no	—
527	C₄₇⋊C₈	—	2	1	no	—
528	C₄₇⋊C₈	—	2	2	no	—
529	C₄₇⋊C₈	—	2	2	no	—
530	#61349	—	47	1	no	maximal, Sylow
531	C₂²×C₄₇	—	2	1	no	—
532	C₂²×C₄₇	—	2	1	no	—
533	C₂²×C₄₇	—	2	2	no	—
534	C₂²×C₄₇	—	4	1	no	—
535	C₂²×C₄₇	—	4	1	no	—
536	C₂²×C₄₇	#548	1	2	yes	—
537	C₂²×C₄₇	C₂³×D₄	1	1	yes	characteristic
538	C₂×D₄₇	—	4	1	no	—
539	C₂×D₄₇	—	4	1	no	—
540	C₂×D₄₇	—	4	2	no	—
541	C₂×D₄₇	—	4	2	no	—
542	C₂×D₄₇	—	4	1	no	—
543	C₂×D₄₇	—	4	1	no	—
544	C₂×D₄₇	—	4	1	no	—
545	C₂×D₄₇	—	4	1	no	—
546	C₂×D₄₇	—	4	2	no	—
547	C₂×D₄₇	—	8	4	no	—
548	C₄×C₄₇	—	2	1	no	—
549	C₄×C₄₇	—	2	2	no	—
550	C₄×C₄₇	—	2	2	no	—
551	C₄×C₄₇	—	2	1	no	—
552	C₄×C₄₇	—	2	1	no	—
553	C₄×C₄₇	—	2	1	no	—
554	C₄×C₄₇	—	2	2	no	—
555	C₄×C₄₇	—	2	2	no	—
556	C₄×C₄₇	—	2	2	no	—
557	C₄×C₄₇	—	4	2	no	—
558	C₄×C₄₇	—	4	1	no	—
559	C₄×C₄₇	—	4	2	no	—
560	C₄×C₄₇	—	4	1	no	—
561	C₄×C₄₇	#548	1	2	yes	—
562	C₄×C₄₇	C₂²×#41	1	1	yes	characteristic
563	C₄×C₄₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
564	Dic₄₇	—	4	2	no	—
565	Dic₄₇	—	4	1	no	—
566	Dic₄₇	—	4	1	no	—
567	#3506	—	47	1	no	—
568	#3504	D₄₇	1	1	yes	characteristic, complemented
569	#3377	—	47	2	no	—
570	#3376	—	47	2	no	—
571	#3371	—	47	2	no	—
572	#3370	—	47	2	no	—
573	#3368	—	47	2	no	—
574	#3366	—	47	2	no	—
575	#3365	—	47	2	no	—
576	#3361	—	47	2	no	—
577	#3142	—	47	1	no	—
578	#3136	—	47	1	no	—
579	#3136	—	47	1	no	—
580	#3084	—	47	1	no	—
581	#3083	—	47	1	no	—
582	C₂×#478	—	47	1	no	—
583	#3045	—	47	1	no	—
584	#3045	—	47	1	no	—
585	#3035	—	47	1	no	—
586	#2962	—	47	1	no	—
587	#2952	—	47	1	no	—
588	#2951	—	47	1	no	—
589	C₄×AGL(1,ℤ/8)	—	47	1	no	—
590	C₂×C₄₇	—	2	2	no	—
591	C₂×C₄₇	—	4	2	no	—
592	C₂×C₄₇	C₂×#548	1	1	yes	characteristic
593	C₂×C₄₇	#3584	1	1	yes	characteristic
594	C₂×C₄₇	#3585	1	1	yes	characteristic
595	D₄₇	—	8	1	no	—
596	D₄₇	—	8	1	no	—
597	D₄₇	—	8	2	no	—
598	C₂×AGL(1,ℤ/8)	—	47	1	no	—
599	C₂×#135	—	47	1	no	—
600	C₂×#135	—	47	1	no	—
601	#559	—	47	2	no	—
602	#559	—	47	2	no	—
603	#557	C₂×D₄₇	1	2	yes	complemented
604	#557	C₂×D₄₇	1	2	yes	complemented
605	#556	—	47	2	no	—
606	#555	—	94	1	no	—
607	#554	—	2	2	no	—
608	#554	—	2	2	no	—
609	#554	C₂×D₄₇	1	2	yes	complemented
610	#554	C₂×D₄₇	1	2	yes	complemented
611	#553	—	94	1	no	—
612	#553	—	94	1	no	—
613	#550	—	47	2	no	—
614	#547	—	94	1	no	—
615	#544	—	2	1	no	—
616	#544	—	2	1	no	—
617	#544	C₂×D₄₇	1	1	yes	characteristic
618	#544	C₂×D₄₇	1	1	yes	characteristic
619	#538	—	94	2	no	—
620	#535	—	47	1	no	—
621	#535	—	47	1	no	—
622	#533	—	2	1	no	—
623	#533	C₂×D₄₇	1	1	yes	characteristic
624	#532	—	47	1	no	—
625	C₂×#125	—	2	1	no	—
626	C₂×#125	C₂×D₄₇	1	1	yes	characteristic
627	#525	—	94	2	no	—
628	#520	—	47	1	no	—
629	#520	—	47	1	no	—
630	#520	C₂×D₄₇	1	1	yes	characteristic
631	#520	C₂×D₄₇	1	1	yes	characteristic
632	C₄×#41	C₂×D₄₇	1	1	yes	characteristic
633	C₂×C₄×D₄	—	47	1	no	—
634	#491	—	47	2	no	—
635	#490	—	47	2	no	—
636	#490	—	47	2	no	—
637	#490	—	47	2	no	—
638	#489	—	47	2	no	—
639	#489	—	47	2	no	—
640	#488	—	47	2	no	—
641	#488	—	47	2	no	—
642	#488	—	47	2	no	—
643	#488	—	47	2	no	—
644	#486	—	47	2	no	—
645	#486	—	47	2	no	—
646	#479	—	47	2	no	—
647	#479	—	47	2	no	—
648	#478	—	47	2	no	—
649	#478	—	47	2	no	—
650	#478	—	47	2	no	—
651	#478	—	47	2	no	—
652	#478	—	47	2	no	—
653	#478	—	47	2	no	—
654	#477	—	47	2	no	—
655	#476	—	47	2	no	—
656	#475	—	47	2	no	—
657	#474	—	47	2	no	—
658	#464	—	47	1	no	—
659	#464	—	47	2	no	—
660	#464	—	47	1	no	—
661	#464	—	47	2	no	—
662	#463	—	47	1	no	—
663	#463	—	47	2	no	—
664	#463	—	47	1	no	—
665	#463	—	47	2	no	—
666	#462	—	47	1	no	—
667	#461	—	47	1	no	—
668	#460	—	47	2	no	—
669	#460	—	47	1	no	—
670	#460	—	47	2	no	—
671	#459	—	47	2	no	—
672	#459	—	47	1	no	—
673	#459	—	47	2	no	—
674	#446	—	47	2	no	—
675	#446	—	47	2	no	—
676	#446	—	47	2	no	—
677	C₈×Q₈	—	47	2	no	—
678	#442	—	47	2	no	—
679	#442	—	47	2	no	—
680	#441	—	47	2	no	—
681	#440	—	47	2	no	—
682	#440	—	47	2	no	—
683	#440	—	47	2	no	—
684	C₄×Q₁₆	—	47	2	no	—
685	C₄×SD₁₆	—	47	2	no	—
686	C₄×SD₁₆	—	47	2	no	—
687	C₄×SD₁₆	—	47	2	no	—
688	C₄×D₈	—	47	2	no	—
689	C₄×D₈	—	47	2	no	—
690	#428	—	47	1	no	—
691	C₂×#107	—	47	1	no	—
692	C₂×#106	—	47	1	no	—
693	#424	—	47	1	no	—
694	#424	—	47	1	no	—
695	C₂×C₄⋊C₈	—	47	1	no	—
696	#418	—	47	1	no	—
697	#417	—	47	1	no	—
698	#417	—	47	1	no	—
699	#417	—	47	1	no	—
700	#417	—	47	1	no	—
701	#417	—	47	1	no	—
702	#416	—	47	1	no	—
703	#416	—	47	1	no	—
704	C₂×#102	—	47	1	no	—
705	C₂×#102	—	47	1	no	—
706	#405	—	47	1	no	—
707	#405	—	47	1	no	—
708	C₄×M₁₆	—	47	1	no	—
709	C₄₇	#61349	1	1	yes	characteristic, complemented, Sylow
710	C₂×#41	—	47	1	no	—
711	C₂×#41	—	47	1	no	—
712	C₂×#41	—	94	2	no	—
713	C₂×#41	C₂²×D₄₇	1	1	yes	characteristic
714	C₂²×D₄	—	47	1	no	—
715	C₂³×C₄	—	94	1	no	—
716	AGL(1,ℤ/8)	—	94	4	no	—
717	#135	—	94	4	no	—
718	#135	—	94	4	no	—
719	C₂×Q₁₆	—	47	1	no	—
720	C₂×Q₁₆	—	47	1	no	—
721	C₂×SD₁₆	—	47	1	no	—
722	C₂×SD₁₆	—	47	1	no	—
723	C₂×SD₁₆	—	47	2	no	—
724	C₂×SD₁₆	—	47	1	no	—
725	C₂×SD₁₆	—	47	1	no	—
726	C₂×D₈	—	47	1	no	—
727	C₂×D₈	—	47	1	no	—
728	C₂×D₈	—	47	2	no	—
729	C₂×M₁₆	—	47	1	no	—
730	C₂×M₁₆	—	47	1	no	—
731	C₂²×C₈	—	47	1	no	—
732	C₂²×C₈	—	47	1	no	—
733	C₄⋊Q₈	—	2	2	no	—
734	C₄⋊Q₈	—	2	2	no	—
735	C₄⋊Q₈	—	2	1	no	—
736	C₄⋊Q₈	—	2	1	no	—
737	C₄⋊Q₈	—	47	1	no	—
738	C₄⋊Q₈	C₂²⋊D₄₇	1	1	yes	characteristic
739	C₄⋊Q₈	C₂²⋊D₄₇	1	1	yes	characteristic
740	C₄⋊Q₈	C₂²×D₄₇	1	2	yes	—
741	C₄⋊Q₈	C₂²×D₄₇	1	2	yes	—
742	#127	—	47	1	no	—
743	#127	—	47	2	no	—
744	#127	—	47	2	no	—
745	#126	—	94	2	no	—
746	#126	—	94	2	no	—
747	#125	—	2	1	no	—
748	#125	—	2	1	no	—
749	#125	—	2	2	no	—
750	#125	—	2	2	no	—
751	#125	—	2	2	no	—
752	#125	—	2	2	no	—
753	#125	—	2	1	no	—
754	#125	—	2	1	no	—
755	#125	C₂²⋊D₄₇	1	1	yes	characteristic
756	#125	C₂²⋊D₄₇	1	1	yes	characteristic
757	#125	C₂²×D₄₇	1	2	yes	—
758	#125	C₂²×D₄₇	1	2	yes	—
759	#125	C₂²×D₄₇	1	2	yes	—
760	#125	C₂²×D₄₇	1	2	yes	—
761	#124	—	47	1	no	—
762	#124	—	47	1	no	—
763	#124	—	47	2	no	—
764	#124	—	47	2	no	—
765	#124	—	94	2	no	—
766	#124	—	94	2	no	—
767	#123	—	94	2	no	—
768	#123	—	94	2	no	—
769	#123	—	94	2	no	—
770	#123	—	94	2	no	—
771	C₂²⋊Q₈	—	2	2	no	—
772	C₂²⋊Q₈	—	2	2	no	—
773	C₂²⋊Q₈	—	2	2	no	—
774	C₂²⋊Q₈	—	2	2	no	—
775	C₂²⋊Q₈	—	2	2	no	—
776	C₂²⋊Q₈	—	2	2	no	—
777	C₂²⋊Q₈	—	2	2	no	—
778	C₂²⋊Q₈	—	2	2	no	—
779	C₂²⋊Q₈	—	94	2	no	—
780	C₂²⋊Q₈	C₂²⋊D₄₇	1	2	yes	—
781	C₂²⋊Q₈	C₂²⋊D₄₇	1	2	yes	—
782	#121	—	94	1	no	—
783	#121	—	94	1	no	—
784	#121	—	94	2	no	—
785	#121	—	94	1	no	—
786	#121	—	94	1	no	—
787	#121	—	94	1	no	—
788	#121	—	94	1	no	—
789	#121	—	94	2	no	—
790	#121	—	94	2	no	—
791	#120	—	94	2	no	—
792	#120	—	94	2	no	—
793	C₄×Q₈	—	2	2	no	—
794	C₄×Q₈	—	2	2	no	—
795	C₄×Q₈	—	47	2	no	—
796	C₄×Q₈	—	47	2	no	—
797	C₄×Q₈	C₂²×D₄₇	1	1	yes	characteristic
798	C₄×Q₈	C₂²×D₄₇	1	1	yes	characteristic
799	C₄×Q₈	C₂²×D₄₇	1	2	yes	—
800	C₄×Q₈	C₂²×D₄₇	1	2	yes	—
801	C₄×Q₈	C₂²×D₄₇	1	2	yes	—
802	C₄×Q₈	C₂²×D₄₇	1	2	yes	—
803	C₄×D₄	—	2	1	no	—
804	C₄×D₄	—	2	1	no	—
805	C₄×D₄	—	2	2	no	—
806	C₄×D₄	—	2	2	no	—
807	C₄×D₄	—	47	2	no	—
808	C₄×D₄	—	47	2	no	—
809	C₄×D₄	—	47	2	no	—
810	C₄×D₄	—	47	2	no	—
811	C₄×D₄	—	94	2	no	—
812	C₄×D₄	—	94	2	no	—
813	C₄×D₄	—	94	2	no	—
814	C₄×D₄	—	94	2	no	—
815	C₄×D₄	—	94	1	no	—
816	C₄×D₄	—	94	1	no	—
817	C₄×D₄	—	94	1	no	—
818	C₄×D₄	—	94	1	no	—
819	C₄×D₄	C₂²×D₄₇	1	1	yes	characteristic
820	C₄×D₄	C₂²×D₄₇	1	1	yes	characteristic
821	C₄×D₄	C₂²×D₄₇	1	2	yes	—
822	C₄×D₄	C₂²×D₄₇	1	2	yes	—
823	#117	—	2	1	no	—
824	#117	—	2	1	no	—
825	#117	—	2	1	no	—
826	#117	—	94	1	no	—
827	#117	—	94	1	no	—
828	#117	—	94	2	no	—
829	#117	C₂²×D₄₇	1	1	yes	characteristic
830	#117	C₂²×D₄₇	1	1	yes	characteristic
831	#117	C₂²×D₄₇	1	1	yes	characteristic
832	C₂×C₄⋊C₄	—	2	1	no	—
833	C₂×C₄⋊C₄	—	2	1	no	—
834	C₂×C₄⋊C₄	—	2	1	no	—
835	C₂×C₄⋊C₄	—	2	1	no	—
836	C₂×C₄⋊C₄	—	2	2	no	—
837	C₂×C₄⋊C₄	—	2	2	no	—
838	C₂×C₄⋊C₄	—	47	1	no	—
839	C₂×C₄⋊C₄	—	94	1	no	—
840	C₂×C₄⋊C₄	—	94	1	no	—
841	C₂×C₄⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
842	C₂×C₄⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
843	C₂×C₂²⋊C₄	—	94	1	no	—
844	C₂×C₄²	—	2	1	no	—
845	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
846	#107	—	47	2	no	—
847	#107	—	47	2	no	—
848	#107	—	47	2	no	—
849	#106	—	47	2	no	—
850	#106	—	47	2	no	—
851	#106	—	47	2	no	—
852	C₄⋊C₈	—	47	1	no	—
853	C₄⋊C₈	—	47	1	no	—
854	C₄⋊C₈	—	47	1	no	—
855	C₄⋊C₈	—	47	1	no	—
856	C₄⋊C₈	—	47	2	no	—
857	C₄⋊C₈	—	47	2	no	—
858	C₄⋊C₈	—	47	2	no	—
859	C₄⋊C₈	—	47	2	no	—
860	#103	—	47	2	no	—
861	#103	—	47	1	no	—
862	#103	—	47	1	no	—
863	#103	—	47	1	no	—
864	#103	—	47	1	no	—
865	#103	—	47	2	no	—
866	#103	—	47	2	no	—
867	#103	—	47	2	no	—
868	#103	—	47	2	no	—
869	#102	—	47	2	no	—
870	#102	—	47	2	no	—
871	#102	—	47	2	no	—
872	#102	—	47	2	no	—
873	#102	—	47	2	no	—
874	#102	—	47	1	no	—
875	#102	—	47	1	no	—
876	#102	—	47	1	no	—
877	#102	—	47	1	no	—
878	#102	—	47	2	no	—
879	#102	—	47	2	no	—
880	#102	—	47	2	no	—
881	#102	—	47	2	no	—
882	#102	—	47	2	no	—
883	#102	—	47	2	no	—
884	#97	—	47	2	no	—
885	#97	—	47	2	no	—
886	#97	—	47	2	no	—
887	C₄×C₈	—	47	2	no	—
888	C₄×C₈	—	47	2	no	—
889	C₄×C₈	—	47	2	no	—
890	C₂⁴	—	94	1	no	—
891	#41	—	2	2	no	—
892	#41	—	94	2	no	—
893	#41	—	94	2	no	—
894	#41	—	94	2	no	—
895	#41	—	94	2	no	—
896	#41	—	376	4	no	—
897	#41	#10625354	1	4	yes	complemented
898	C₂×Q₈	—	2	2	no	—
899	C₂×Q₈	—	2	2	no	—
900	C₂×Q₈	—	47	1	no	—
901	C₂×Q₈	—	47	1	no	—
902	C₂×Q₈	C₂×C₂²⋊D₄₇	1	2	yes	—
903	C₂×Q₈	C₂×C₂²⋊D₄₇	1	2	yes	—
904	C₂×Q₈	C₂³×D₄₇	1	1	yes	characteristic
905	C₂×D₄	—	2	1	no	—
906	C₂×D₄	—	47	2	no	—
907	C₂×D₄	—	47	1	no	—
908	C₂×D₄	—	47	1	no	—
909	C₂×D₄	—	94	1	no	—
910	C₂×D₄	—	94	1	no	—
911	C₂×D₄	—	94	2	no	—
912	C₂×D₄	—	94	2	no	—
913	C₂×D₄	—	94	1	no	—
914	C₂×D₄	—	94	2	no	—
915	C₂×D₄	—	94	2	no	—
916	C₂×D₄	—	94	1	no	—
917	C₂×D₄	—	94	1	no	—
918	C₂×D₄	—	94	2	no	—
919	C₂×D₄	—	94	2	no	—
920	C₂×D₄	C₂³×D₄₇	1	1	yes	characteristic
921	C₂²×C₄	—	2	1	no	—
922	C₂²×C₄	—	2	1	no	—
923	C₂²×C₄	—	2	1	no	—
924	C₂²×C₄	—	2	1	no	—
925	C₂²×C₄	—	2	1	no	—
926	C₂²×C₄	—	2	2	no	—
927	C₂²×C₄	—	2	2	no	—
928	C₂²×C₄	—	94	1	no	—
929	C₂²×C₄	—	94	2	no	—
930	C₂²×C₄	—	94	2	no	—
931	C₂²×C₄	—	94	2	no	—
932	C₂²×C₄	—	94	1	no	—
933	C₂²×C₄	—	94	1	no	—
934	C₂²×C₄	—	94	2	no	—
935	C₂²×C₄	—	376	2	no	—
936	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
937	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
938	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
939	Q₁₆	—	94	2	no	—
940	Q₁₆	—	94	2	no	—
941	SD₁₆	—	94	2	no	—
942	SD₁₆	—	94	2	no	—
943	SD₁₆	—	94	4	no	—
944	SD₁₆	—	94	2	no	—
945	SD₁₆	—	94	2	no	—
946	D₈	—	94	2	no	—
947	D₈	—	94	2	no	—
948	D₈	—	94	4	no	—
949	M₁₆	—	94	2	no	—
950	M₁₆	—	94	2	no	—
951	C₂×C₈	—	47	2	no	—
952	C₂×C₈	—	47	1	no	—
953	C₂×C₈	—	47	1	no	—
954	C₂×C₈	—	47	2	no	—
955	C₂×C₈	—	47	1	no	—
956	C₂×C₈	—	47	1	no	—
957	C₂×C₈	—	94	2	no	—
958	C₂×C₈	—	94	2	no	—
959	C₄⋊C₄	—	2	2	no	—
960	C₄⋊C₄	—	2	2	no	—
961	C₄⋊C₄	—	2	1	no	—
962	C₄⋊C₄	—	2	1	no	—
963	C₄⋊C₄	—	2	2	no	—
964	C₄⋊C₄	—	2	2	no	—
965	C₄⋊C₄	—	2	2	no	—
966	C₄⋊C₄	—	2	2	no	—
967	C₄⋊C₄	—	2	2	no	—
968	C₄⋊C₄	—	2	2	no	—
969	C₄⋊C₄	—	2	2	no	—
970	C₄⋊C₄	—	2	2	no	—
971	C₄⋊C₄	—	2	1	no	—
972	C₄⋊C₄	—	2	1	no	—
973	C₄⋊C₄	—	2	2	no	—
974	C₄⋊C₄	—	2	2	no	—
975	C₄⋊C₄	—	47	2	no	—
976	C₄⋊C₄	—	94	2	no	—
977	C₄⋊C₄	—	94	2	no	—
978	C₄⋊C₄	—	94	1	no	—
979	C₄⋊C₄	—	94	1	no	—
980	C₄⋊C₄	—	94	1	no	—
981	C₄⋊C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
982	C₄⋊C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
983	C₄⋊C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
984	C₄⋊C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
985	C₄⋊C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
986	C₄⋊C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
987	C₄⋊C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
988	C₄⋊C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
989	C₄⋊C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
990	C₄⋊C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
991	C₄⋊C₄	C₂³×D₄₇	1	2	yes	—
992	C₄⋊C₄	C₂³×D₄₇	1	1	yes	characteristic
993	C₄⋊C₄	C₂³×D₄₇	1	2	yes	—
994	C₄⋊C₄	C₂³×D₄₇	1	1	yes	characteristic
995	C₂²⋊C₄	—	2	1	no	—
996	C₂²⋊C₄	—	2	1	no	—
997	C₂²⋊C₄	—	2	1	no	—
998	C₂²⋊C₄	—	2	2	no	—
999	C₂²⋊C₄	—	2	2	no	—
1000	C₂²⋊C₄	—	94	2	no	—
1001	C₂²⋊C₄	—	94	2	no	—
1002	C₂²⋊C₄	—	94	2	no	—
1003	C₂²⋊C₄	—	94	2	no	—
1004	C₂²⋊C₄	—	94	2	no	—
1005	C₂²⋊C₄	—	94	2	no	—
1006	C₂²⋊C₄	—	94	1	no	—
1007	C₂²⋊C₄	—	94	1	no	—
1008	C₂²⋊C₄	—	94	2	no	—
1009	C₂²⋊C₄	—	94	2	no	—
1010	C₂²⋊C₄	—	94	1	no	—
1011	C₂²⋊C₄	—	94	1	no	—
1012	C₂²⋊C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
1013	C₂²⋊C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
1014	C₄²	—	2	1	no	—
1015	C₄²	—	2	1	no	—
1016	C₄²	—	2	1	no	—
1017	C₄²	—	2	2	no	—
1018	C₄²	—	2	2	no	—
1019	C₄²	—	94	2	no	—
1020	C₄²	—	94	2	no	—
1021	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
1022	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
1023	C₄²	C₂³×D₄₇	1	1	yes	characteristic
1024	C₄²	C₂³×D₄₇	1	2	yes	—
1025	C₄²	C₂³×D₄₇	1	2	yes	—
1026	C₄²	C₂³×D₄₇	1	1	yes	characteristic
1027	C₂³	—	2	1	no	—
1028	C₂³	—	94	2	no	—
1029	C₂³	—	94	1	no	—
1030	C₂³	—	94	1	no	—
1031	C₂³	—	376	1	no	—
1032	C₂³	—	376	1	no	—
1033	C₂³	—	188	2	no	—
1034	C₂³	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
1035	Q₈	—	2	1	no	—
1036	Q₈	—	4	2	no	—
1037	Q₈	—	4	2	no	—
1038	Q₈	—	8	2	no	—
1039	Q₈	—	8	2	no	—
1040	Q₈	—	94	1	no	—
1041	Q₈	—	94	1	no	—
1042	Q₈	—	94	1	no	—
1043	Q₈	—	94	1	no	—
1044	Q₈	C₂×#10625354	1	2	yes	—
1045	D₄	—	2	4	no	—
1046	D₄	—	2	1	no	—
1047	D₄	—	94	2	no	—
1048	D₄	—	94	1	no	—
1049	D₄	—	94	1	no	—
1050	D₄	—	94	2	no	—
1051	D₄	—	94	1	no	—
1052	D₄	—	94	1	no	—
1053	D₄	—	376	1	no	—
1054	D₄	—	376	2	no	—
1055	D₄	—	376	2	no	—
1056	D₄	—	376	2	no	—
1057	D₄	—	376	2	no	—
1058	D₄	—	188	2	no	—
1059	D₄	—	188	2	no	—
1060	D₄	—	188	2	no	—
1061	D₄	—	188	2	no	—
1062	D₄	C₂×#10625354	1	2	yes	—
1063	C₂×C₄	—	2	1	no	—
1064	C₂×C₄	—	2	4	no	—
1065	C₂×C₄	—	2	1	no	—
1066	C₂×C₄	—	2	1	no	—
1067	C₂×C₄	—	2	2	no	—
1068	C₂×C₄	—	2	2	no	—
1069	C₂×C₄	—	4	1	no	—
1070	C₂×C₄	—	4	1	no	—
1071	C₂×C₄	—	8	1	no	—
1072	C₂×C₄	—	8	2	no	—
1073	C₂×C₄	—	8	1	no	—
1074	C₂×C₄	—	8	2	no	—
1075	C₂×C₄	—	8	1	no	—
1076	C₂×C₄	—	8	1	no	—
1077	C₂×C₄	—	94	1	no	—
1078	C₂×C₄	—	94	1	no	—
1079	C₂×C₄	—	94	2	no	—
1080	C₂×C₄	—	376	2	no	—
1081	C₂×C₄	—	376	2	no	—
1082	C₂×C₄	—	376	2	no	—
1083	C₂×C₄	—	376	1	no	—
1084	C₂×C₄	—	188	4	no	—
1085	C₂×C₄	—	188	2	no	—
1086	C₂×C₄	—	188	2	no	—
1087	C₂×C₄	C₂²×C₂²⋊D₄₇	1	2	yes	—
1088	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
1089	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
1090	C₂×C₄	C₂²×C₂²⋊D₄₇	1	2	yes	—
1091	C₂×C₄	C₂²×C₂²⋊D₄₇	1	2	yes	—
1092	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
1093	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
1094	C₂×C₄	C₂²×C₂²⋊D₄₇	1	2	yes	—
1095	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
1096	C₂×C₄	C₂×#10625354	1	2	yes	—
1097	C₂×C₄	#13094072	1	2	yes	—
1098	C₂×C₄	C₂⁴×D₄₇	1	1	yes	characteristic
1099	C₈	—	94	1	no	—
1100	C₈	—	94	1	no	—
1101	C₈	—	94	1	no	—
1102	C₈	—	94	1	no	—
1103	C₈	—	94	2	no	—
1104	C₈	—	94	2	no	—
1105	C₂²	—	2	1	no	—
1106	C₂²	—	2	1	no	—
1107	C₂²	—	2	2	no	—
1108	C₂²	—	4	1	no	—
1109	C₂²	—	4	1	no	—
1110	C₂²	—	376	4	no	—
1111	C₂²	—	188	1	no	—
1112	C₂²	—	188	1	no	—
1113	C₂²	—	188	2	no	—
1114	C₂²	—	188	1	no	—
1115	C₂²	—	188	1	no	—
1116	C₂²	—	188	2	no	—
1117	C₂²	—	188	1	no	—
1118	C₂²	—	188	1	no	—
1119	C₂²	—	188	2	no	—
1120	C₂²	#15689784	1	2	yes	—
1121	C₂²	C₂³×C₂²⋊D₄₇	1	1	yes	characteristic
1122	C₄	—	2	2	no	—
1123	C₄	—	2	1	no	—
1124	C₄	—	2	1	no	—
1125	C₄	—	2	2	no	—
1126	C₄	—	2	2	no	—
1127	C₄	—	2	1	no	—
1128	C₄	—	2	1	no	—
1129	C₄	—	2	2	no	—
1130	C₄	—	2	2	no	—
1131	C₄	—	4	2	no	—
1132	C₄	—	4	1	no	—
1133	C₄	—	4	2	no	—
1134	C₄	—	4	1	no	—
1135	C₄	—	188	1	no	—
1136	C₄	—	188	1	no	—
1137	C₄	—	188	2	no	—
1138	C₄	#15689784	1	2	yes	—
1139	C₄	C₂²×#10625354	1	1	yes	characteristic
1140	C₄	C₂×#13094072	1	1	yes	characteristic
1141	C₂	—	2	2	no	—
1142	C₂	—	4	2	no	—
1143	C₂	—	376	2	no	—
1144	C₂	—	376	1	no	—
1145	C₂	—	376	1	no	—
1146	C₂	C₂×#15689784	1	1	yes	characteristic
1147	C₂	#20258159	1	1	yes	characteristic
1148	C₂	#20258167	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×#3504	C₂
socle	C₂²×C₄₇	C₂³×D₄
hypercenter	#3504	D₄₇
hypocenter	C₄₇	#61349
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ #533 ◁ #3504

Complements

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

N	H ≅ G/N	type
1. #20257242	C₂	semidirect
2. #20256230	C₂	semidirect
3. #20256215	C₂	semidirect
4. #20256156	C₂	semidirect
5. #20256141	C₂	semidirect
6. #20256117	C₂	semidirect
7. #20256095	C₂	semidirect
8. #20256084	C₂	semidirect
9. #20256048	C₂	semidirect
10. #20253791	C₂	semidirect
11. #20253747	C₂	semidirect
12. #20253747	C₂	semidirect
13. #20253246	C₂	semidirect
14. #20253235	C₂	semidirect
15. C₂×#15689420	C₂	semidirect
16. #20252927	C₂	semidirect
17. #20252927	C₂	semidirect
18. #20252843	C₂	semidirect
19. #20252337	C₂	semidirect
20. #20252269	C₂	semidirect
21. #20252261	C₂	semidirect
22. C₄×#13094049	C₂	semidirect
23. C₄₇×#3504	C₂	semidirect
43. #15689493	C₂²	semidirect
46. #15689489	C₂²	semidirect
51. #15689480	C₂²	semidirect
52. #15689480	C₂²	semidirect
55. #15689427	C₂²	semidirect
56. #15689427	C₂²	semidirect
61. #15689420	C₂²	semidirect
62. #15689420	C₂²	semidirect
63. #15689415	C₂²	semidirect
64. #15689410	C₂²	semidirect
65. #15689405	C₂²	semidirect
66. #15689400	C₂²	semidirect
69. #15689345	C₂²	semidirect
70. #15689345	C₂²	semidirect
73. #15689338	C₂²	semidirect
74. #15689338	C₂²	semidirect
75. #15689333	C₂²	semidirect
76. #15689328	C₂²	semidirect
79. #15689323	C₂²	semidirect
82. #15689318	C₂²	semidirect
83. #15689254	C₂²	semidirect
84. #15689254	C₂²	semidirect
85. #15689254	C₂²	semidirect
86. Q₈×C₄₇⋊C₈	C₂²	semidirect
88. #15689233	C₂²	semidirect
89. #15689228	C₂²	semidirect
90. #15689223	C₂²	semidirect
92. #15689221	C₂²	semidirect
93. C₄×#10625337	C₂²	semidirect
95. C₄×#10625336	C₂²	semidirect
96. C₄×#10625335	C₂²	semidirect
98. C₄×#10625334	C₂²	semidirect
118. C₄₇×#557	C₂²	semidirect
119. C₄₇×#557	C₂²	semidirect
122. C₄₇×#554	C₂²	semidirect
123. C₄₇×#554	C₂²	semidirect
317. #41×C₄₇	#41	semidirect
568. #3504	D₄₇	semidirect
603. #557	C₂×D₄₇	semidirect
604. #557	C₂×D₄₇	semidirect
609. #554	C₂×D₄₇	semidirect
610. #554	C₂×D₄₇	semidirect
709. C₄₇	#61349	semidirect
897. #41	#10625354	semidirect

Maximal subgroups

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

subgroup	index
#20257242	2
#20256230	2
#20256215	2
#20256156	2
#20256141	2
#20256117	2
#20256095	2
#20256084	2
#20256048	2
#20253791	2
#20253747	2
#20253246	2
#20253235	2
C₂×#15689420	2
#20252927	2
#20252843	2
#20252337	2
#20252269	2
#20252261	2
C₄×#13094049	2
C₄₇×#3504	2
#61349	47