Subgroups — #27112879

Order 12032.

1986 conjugacy classes of subgroups.

The subgroup lattice has 1168 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20257403	C₂	1	1	yes	maximal, characteristic, complemented
2	D₄×#10625350	C₂	1	1	yes	maximal, characteristic, complemented
3	SD₁₆×Dic₉₄	C₂	1	1	yes	maximal, characteristic, complemented
4	D₈×Dic₉₄	C₂	1	1	yes	maximal, characteristic, complemented
5	#20256057	C₂	1	1	yes	maximal, characteristic, complemented
6	#20256021	C₂	1	1	yes	maximal, characteristic, complemented
7	#20255985	C₂	1	1	yes	maximal, characteristic, complemented
8	#20255976	C₂	1	2	yes	maximal, complemented
9	#20255974	C₂	1	1	yes	maximal, characteristic, complemented
10	#20255965	C₂	1	2	yes	maximal, complemented
11	#20255632	C₂	1	1	yes	maximal, characteristic, complemented
12	#20255623	C₂	1	2	yes	maximal, complemented
13	#20255621	C₂	1	1	yes	maximal, characteristic, complemented
14	#20255612	C₂	1	2	yes	maximal, complemented
15	#20254750	C₂	1	1	yes	maximal, characteristic, complemented
16	#20254747	C₂	1	2	yes	maximal, complemented
17	#20254526	C₂	1	1	yes	maximal, characteristic, complemented
18	#20254523	C₂	1	2	yes	maximal, complemented
19	#20253434	C₂	1	2	yes	maximal, complemented
20	#20253185	C₂	1	1	yes	maximal, characteristic, complemented
21	#20253183	C₂	1	2	yes	maximal, complemented
22	#20252517	C₂	1	1	yes	maximal, characteristic, complemented
23	C₄₇×#3105	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂²×#10625350	—	2	1	no	—
25	Q₈×Dic₉₄	C₂²	1	1	yes	characteristic, complemented
26	#15689846	C₂²	1	1	yes	characteristic, complemented
27	#15689844	C₂²	1	2	yes	complemented
28	#15689843	—	2	1	no	—
29	#15689840	—	2	2	no	—
30	#15689838	C₂²	1	1	yes	characteristic, complemented
31	#15689837	C₂²	1	2	yes	complemented
32	#15689794	C₂²	1	1	yes	characteristic
33	D₄×Dic₉₄	C₂²	1	1	yes	characteristic
34	D₄×Dic₉₄	C₂²	1	1	yes	characteristic, complemented
35	#15689782	—	2	1	no	—
36	#15689782	—	2	1	no	—
37	#15689778	C₂²	1	1	yes	characteristic
38	#15689774	C₂²	1	2	yes	—
39	#15689769	—	2	1	no	—
40	#15689763	—	2	2	no	—
41	D₄×D₁₈₈	C₂²	1	1	yes	characteristic
42	D₄×C₂²⋊D₄₇	C₂²	1	2	yes	—
43	#15689744	—	2	1	no	—
44	#15689741	—	2	2	no	—
45	#15689680	C₂²	1	1	yes	characteristic, complemented
46	#15689679	C₂²	1	2	yes	complemented
47	#15689673	C₂²	1	1	yes	characteristic
48	#15689670	C₂²	1	2	yes	—
49	#15689652	C₂²	1	2	yes	complemented
50	#15689634	—	2	1	no	—
51	#15689632	—	2	2	no	—
52	#15689600	—	2	1	no	—
53	C₄×#10625350	C₂²	1	1	yes	characteristic
54	C₄×D₄×D₄₇	C₂²	1	2	yes	—
55	#15689528	C₂²	1	1	yes	characteristic, complemented
56	#15689527	C₂²	1	2	yes	complemented
57	#15689521	C₂²	1	1	yes	characteristic, complemented
58	#15689520	C₂²	1	2	yes	complemented
59	#15689470	C₂²	1	1	yes	characteristic, complemented
60	#15689470	C₂²	1	1	yes	characteristic, complemented
61	#15689468	C₂²	1	2	yes	complemented
62	#15689468	C₂²	1	2	yes	complemented
63	#15689457	C₂²	1	2	yes	complemented
64	#15689450	C₂²	1	2	yes	complemented
65	#15689449	C₂²	1	2	yes	complemented
66	#15689448	C₂²	1	2	yes	complemented
67	#15689448	C₂²	1	2	yes	complemented
68	#15689446	C₂²	1	2	yes	complemented
69	#15689445	C₂²	1	2	yes	complemented
70	#15689440	C₂²	1	2	yes	complemented
71	#15689424	C₂²	1	2	yes	complemented
72	#15689424	C₂²	1	2	yes	complemented
73	#15689423	C₂²	1	2	yes	—
74	#15689423	C₂²	1	2	yes	complemented
75	#15689420	C₂²	1	2	yes	complemented
76	#15689413	C₂²	1	1	yes	characteristic
77	#15689413	C₂²	1	1	yes	characteristic, complemented
78	#15689412	C₂²	1	2	yes	complemented
79	#15689411	C₂²	1	2	yes	—
80	#15689408	C₂²	1	1	yes	characteristic, complemented
81	#15689406	C₂²	1	2	yes	complemented
82	#15689403	C₂²	1	1	yes	characteristic
83	#15689403	C₂²	1	1	yes	characteristic, complemented
84	#15689403	C₂²	1	1	yes	characteristic, complemented
85	#15689402	C₂²	1	2	yes	complemented
86	#15689401	C₂²	1	2	yes	—
87	#15689401	C₂²	1	2	yes	complemented
88	#15689375	C₂²	1	2	yes	complemented
89	#15689374	C₂²	1	2	yes	complemented
90	#15689373	C₂²	1	2	yes	complemented
91	#15689372	C₂²	1	2	yes	complemented
92	#15689371	C₂²	1	2	yes	complemented
93	#15689366	C₂²	1	2	yes	complemented
94	#15689335	C₂²	1	2	yes	complemented
95	#15689323	C₂²	1	1	yes	characteristic, complemented
96	#15689321	C₂²	1	2	yes	complemented
97	#15689318	C₂²	1	1	yes	characteristic, complemented
98	#15689316	C₂²	1	2	yes	complemented
99	#15689272	C₂²	1	2	yes	—
100	#15689255	C₂²	1	2	yes	—
101	C₈×Dic₉₄	C₂²	1	1	yes	characteristic, complemented
102	C₈×Dic₉₄	C₂²	1	1	yes	characteristic, complemented
103	SD₁₆×Dic₄₇	C₂²	1	2	yes	—
104	#15689208	C₂²	1	2	yes	complemented
105	D₈×Dic₄₇	C₂²	1	2	yes	—
106	#15689203	C₂²	1	2	yes	complemented
107	#15689202	C₂²	1	1	yes	characteristic, complemented
108	#15689202	C₂²	1	1	yes	characteristic, complemented
109	#15689198	C₂²	1	2	yes	complemented
110	#15689198	C₂²	1	2	yes	complemented
111	#15689175	C₂²	1	2	yes	complemented
112	#15689164	C₂²	1	2	yes	complemented
113	#15689163	C₂²	1	2	yes	complemented
114	#15689162	C₂²	1	2	yes	complemented
115	#15689147	C₂²	1	1	yes	characteristic, complemented
116	#15689145	C₂²	1	2	yes	complemented
117	#15689128	C₂²	1	2	yes	—
118	#15689126	C₂²	1	2	yes	—
119	#15689126	C₂²	1	2	yes	—
120	C₄₇×#529	C₂²	1	1	yes	characteristic, complemented
121	C₂×C₄×D₄×C₄₇	C₂²	1	1	yes	characteristic
122	C₄₇×#484	C₂²	1	1	yes	characteristic, complemented
123	C₄₇×#481	C₂²	1	1	yes	characteristic, complemented
124	C₄₇×#478	C₂²	1	1	yes	characteristic
125	C₄₇×#478	C₂²	1	1	yes	characteristic, complemented
126	C₄₇×#463	C₂²	1	1	yes	characteristic
127	C₄₇×#463	C₂²	1	1	yes	characteristic, complemented
128	C₄₇×#450	C₂²	1	1	yes	characteristic
129	C₄₇×#447	C₂²	1	1	yes	characteristic
130	C₄×SD₁₆×C₄₇	C₂²	1	1	yes	characteristic
131	C₄×SD₁₆×C₄₇	C₂²	1	1	yes	characteristic, complemented
132	C₄×D₈×C₄₇	C₂²	1	1	yes	characteristic
133	C₄×D₈×C₄₇	C₂²	1	1	yes	characteristic, complemented
134	C₄₇×#431	C₂²	1	1	yes	characteristic, complemented
135	C₂×#10625350	—	2	1	no	—
136	C₂×#10625350	—	2	2	no	—
137	C₂×#10625350	—	2	1	no	—
138	C₂×#10625350	—	2	2	no	—
139	C₂×#10625350	—	2	1	no	—
140	C₂×#10625350	—	4	8	no	—
141	C₂×#10625350	D₄	1	1	yes	characteristic
142	C₂²×Dic₉₄	—	2	1	no	—
143	C₂²×Dic₉₄	—	2	1	no	—
144	C₂²×D₁₈₈	—	2	1	no	—
145	C₂²×C₂²⋊D₄₇	—	2	2	no	—
146	C₂×D₄×D₄₇	C₂³	1	2	yes	—
147	C₂²×C₄×D₄₇	—	2	2	no	—
148	C₂×#10625336	C₂³	1	2	yes	—
149	C₂×#10625334	C₂³	1	2	yes	—
150	C₂×#10625329	C₂³	1	2	yes	—
151	C₂×#10625324	C₂³	1	2	yes	—
152	C₂×#10625324	C₂³	1	2	yes	—
153	#13094024	—	2	1	no	—
154	#13094024	C₂³	1	1	yes	characteristic
155	#13094024	C₂³	1	1	yes	characteristic
156	#13094024	C₂³	1	1	yes	characteristic
157	#13094023	—	2	2	no	—
158	#13094023	C₂³	1	2	yes	—
159	#13094023	C₂³	1	2	yes	—
160	#13094023	C₂³	1	2	yes	—
161	#13094021	C₂³	1	1	yes	characteristic
162	#13094020	C₂³	1	2	yes	—
163	#13094019	—	2	2	no	—
164	#13094019	—	2	2	no	—
165	#13094017	—	2	2	no	—
166	#13094017	—	2	2	no	—
167	#13094016	C₂³	1	2	yes	—
168	#13094012	—	2	1	no	—
169	#13094012	—	2	1	no	—
170	#13094011	—	2	2	no	—
171	#13094010	—	2	2	no	—
172	#13094010	—	2	2	no	—
173	#13094010	—	2	2	no	—
174	#13094010	—	2	2	no	—
175	#13094009	—	2	2	no	—
176	#13094007	—	2	2	no	—
177	#13094006	—	2	2	no	—
178	#13094006	—	2	2	no	—
179	#13094003	—	2	1	no	—
180	#13094003	—	2	1	no	—
181	#13094003	—	2	1	no	—
182	#13094003	—	2	1	no	—
183	#13094003	—	2	1	no	—
184	#13094002	—	2	2	no	—
185	#13094002	—	2	2	no	—
186	#13094002	—	2	2	no	—
187	#13094001	—	2	2	no	—
188	#13094001	—	2	2	no	—
189	#13094000	C₂³	1	2	yes	—
190	#13093999	C₂³	1	2	yes	—
191	#13093998	—	2	1	no	—
192	#13093998	—	2	1	no	—
193	#13093998	—	2	1	no	—
194	#13093998	—	2	1	no	—
195	#13093998	C₂³	1	2	yes	—
196	#13093997	—	2	2	no	—
197	#13093997	—	2	2	no	—
198	#13093996	—	2	2	no	—
199	#13093996	—	2	2	no	—
200	#13093995	C₂³	1	2	yes	—
201	#13093995	C₂³	1	2	yes	—
202	#13093994	—	2	2	no	—
203	#13093993	—	2	2	no	—
204	#13093992	—	2	2	no	—
205	Q₈×Dic₄₇	C₂³	1	2	yes	—
206	C₄×Dic₉₄	—	2	1	no	—
207	C₄×Dic₉₄	—	2	1	no	—
208	C₄×Dic₉₄	—	2	1	no	—
209	C₄×Dic₉₄	—	2	1	no	—
210	C₄×Dic₉₄	D₄	1	1	yes	characteristic
211	C₄×Dic₉₄	C₂³	1	1	yes	characteristic
212	#13093989	—	2	2	no	—
213	#13093989	—	2	2	no	—
214	#13093989	—	2	2	no	—
215	C₄×D₁₈₈	—	2	1	no	—
216	C₄×D₁₈₈	D₄	1	1	yes	characteristic
217	C₄×D₁₈₈	C₂³	1	1	yes	characteristic
218	C₄×D₁₈₈	C₂³	1	2	yes	—
219	D₄×Dic₄₇	C₂³	1	2	yes	—
220	D₄×Dic₄₇	C₂³	1	2	yes	—
221	#13093986	C₂³	1	2	yes	—
222	C₄×C₂²⋊D₄₇	—	2	2	no	—
223	C₄×C₂²⋊D₄₇	—	2	2	no	—
224	C₄×C₂²⋊D₄₇	D₄	1	2	yes	—
225	C₄×C₂²⋊D₄₇	C₂³	1	2	yes	—
226	(C₂²⋊D₄₇)⋊C₄	—	2	2	no	—
227	(C₂²⋊D₄₇)⋊C₄	—	2	2	no	—
228	#13093983	—	2	1	no	—
229	#13093983	D₄	1	1	yes	characteristic
230	#13093983	C₂³	1	2	yes	—
231	#13093982	C₂³	1	2	yes	—
232	#13093982	C₂³	1	2	yes	—
233	#13093981	D₄	1	2	yes	—
234	#13093980	—	2	2	no	—
235	#13093980	—	2	2	no	—
236	C₄⋊C₄×D₄₇	C₂³	1	2	yes	—
237	C₂²⋊C₄×D₄₇	—	2	2	no	—
238	C₄²×D₄₇	C₂³	1	2	yes	—
239	#13093958	C₂³	1	2	yes	—
240	#13093958	C₂³	1	2	yes	—
241	#13093957	C₂³	1	2	yes	—
242	#13093957	C₂³	1	2	yes	—
243	#13093957	C₂³	1	2	yes	—
244	#13093956	C₂³	1	2	yes	—
245	#13093956	C₂³	1	2	yes	—
246	#13093955	C₂³	1	2	yes	—
247	#13093955	C₂³	1	2	yes	—
248	#13093955	C₂³	1	2	yes	—
249	C₄⋊(C₄₇⋊C₈)	C₂³	1	1	yes	characteristic
250	C₄⋊(C₄₇⋊C₈)	C₂³	1	1	yes	characteristic
251	C₄⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
252	Dic₄₇⋊C₈	C₂³	1	2	yes	—
253	Dic₄₇⋊C₈	C₂³	1	2	yes	—
254	#13093948	C₂³	1	2	yes	—
255	#13093946	C₂³	1	2	yes	—
256	#13093946	C₂³	1	2	yes	—
257	#13093946	C₂³	1	2	yes	—
258	#13093946	C₂³	1	2	yes	—
259	#13093945	C₂³	1	2	yes	—
260	#13093945	C₂³	1	2	yes	—
261	#13093945	C₂³	1	2	yes	—
262	#13093945	C₂³	1	2	yes	—
263	#13093945	C₂³	1	2	yes	—
264	#13093944	C₂³	1	2	yes	—
265	#13093944	C₂³	1	2	yes	—
266	(C₂×D₄₇)⋊C₈	C₂³	1	2	yes	—
267	(C₂×D₄₇)⋊C₈	C₂³	1	2	yes	—
268	C₈×Dic₄₇	C₂³	1	2	yes	—
269	C₈×Dic₄₇	C₂³	1	2	yes	—
270	C₂²×D₄×C₄₇	C₂³	1	1	yes	characteristic
271	C₂³×C₄×C₄₇	—	2	1	no	—
272	C₂×SD₁₆×C₄₇	C₂³	1	1	yes	characteristic
273	C₂×SD₁₆×C₄₇	C₂³	1	1	yes	characteristic
274	C₂×D₈×C₄₇	C₂³	1	1	yes	characteristic
275	C₂×D₈×C₄₇	C₂³	1	1	yes	characteristic
276	#126×C₄₇	—	2	1	no	—
277	#125×C₄₇	C₂³	1	1	yes	characteristic
278	#124×C₄₇	C₂³	1	1	yes	characteristic
279	#123×C₄₇	—	2	1	no	—
280	C₂²⋊Q₈×C₄₇	C₂³	1	1	yes	characteristic
281	#121×C₄₇	C₂³	1	1	yes	characteristic
282	C₄×Q₈×C₄₇	C₂³	1	1	yes	characteristic
283	C₄×D₄×C₄₇	—	2	1	no	—
284	C₄×D₄×C₄₇	—	2	1	no	—
285	C₄×D₄×C₄₇	—	2	1	no	—
286	C₄×D₄×C₄₇	C₂³	1	1	yes	characteristic
287	C₄×D₄×C₄₇	C₂³	1	1	yes	characteristic
288	C₄×D₄×C₄₇	C₂³	1	1	yes	characteristic
289	C₄×D₄×C₄₇	C₂³	1	1	yes	characteristic
290	C₄×D₄×C₄₇	C₂³	1	1	yes	characteristic
291	#117×C₄₇	—	2	1	no	—
292	C₂×C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
293	C₂×C₂²⋊C₄×C₄₇	—	2	1	no	—
294	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
295	#107×C₄₇	C₂³	1	1	yes	characteristic
296	#107×C₄₇	C₂³	1	1	yes	characteristic
297	#106×C₄₇	C₂³	1	1	yes	characteristic
298	#106×C₄₇	C₂³	1	1	yes	characteristic
299	C₄⋊C₈×C₄₇	C₂³	1	1	yes	characteristic
300	C₄⋊C₈×C₄₇	C₂³	1	1	yes	characteristic
301	#103×C₄₇	C₂³	1	1	yes	characteristic
302	#103×C₄₇	C₂³	1	1	yes	characteristic
303	#102×C₄₇	C₂³	1	1	yes	characteristic
304	#102×C₄₇	C₂³	1	1	yes	characteristic
305	#102×C₄₇	C₂³	1	1	yes	characteristic
306	#102×C₄₇	C₂³	1	1	yes	characteristic
307	#102×C₄₇	C₂³	1	1	yes	characteristic
308	#102×C₄₇	C₂³	1	1	yes	characteristic
309	C₂²⋊C₈×C₄₇	C₂³	1	1	yes	characteristic
310	C₂²⋊C₈×C₄₇	C₂³	1	1	yes	characteristic
311	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
312	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
313	C₂⁴×C₄₇	—	2	1	no	—
314	C₂³×D₄₇	—	2	2	no	—
315	C₂×Q₈×C₄₇	C₂⁴	1	1	yes	characteristic
316	C₂×D₄×C₄₇	—	2	2	no	—
317	C₂×D₄×C₄₇	—	2	1	no	—
318	C₂×D₄×C₄₇	—	2	1	no	—
319	C₂×D₄×C₄₇	—	4	1	no	—
320	C₂×D₄×C₄₇	C₂⁴	1	1	yes	characteristic
321	C₂×D₄×C₄₇	C₂⁴	1	1	yes	characteristic
322	C₂×D₄×C₄₇	C₂⁴	1	1	yes	characteristic
323	C₂²×C₄×C₄₇	—	2	1	no	—
324	C₂²×C₄×C₄₇	—	2	1	no	—
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	—	4	4	no	—
330	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
331	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
332	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
333	C₂×C₂²⋊D₄₇	—	2	2	no	—
334	C₂×C₂²⋊D₄₇	—	2	2	no	—
335	C₂×C₂²⋊D₄₇	—	2	2	no	—
336	C₂×C₂²⋊D₄₇	—	2	2	no	—
337	C₂×C₂²⋊D₄₇	—	2	2	no	—
338	C₂×C₂²⋊D₄₇	—	2	2	no	—
339	C₂×C₂²⋊D₄₇	—	4	8	no	—
340	C₂×C₂²⋊D₄₇	C₂×D₄	1	2	yes	—
341	C₂²×Dic₄₇	—	2	2	no	—
342	C₂²×Dic₄₇	—	2	2	no	—
343	D₄×D₄₇	—	2	4	no	—
344	D₄×D₄₇	—	4	2	no	—
345	#10625350	—	2	4	no	—
346	#10625350	—	4	8	no	—
347	#10625350	—	4	4	no	—
348	#10625350	—	4	8	no	—
349	#10625350	—	4	4	no	—
350	#10625350	—	4	4	no	—
351	C₂×D₁₈₈	—	2	2	no	—
352	C₂×D₁₈₈	—	2	1	no	—
353	C₂×D₁₈₈	—	2	1	no	—
354	C₂×D₁₈₈	—	4	4	no	—
355	C₂×D₁₈₈	C₂×D₄	1	1	yes	characteristic
356	C₂×D₁₈₈	C₂⁴	1	2	yes	—
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	—	4	8	no	—
361	C₂×C₄×D₄₇	C₂×D₄	1	2	yes	—
362	C₂×C₄×D₄₇	C₂×D₄	1	2	yes	—
363	C₂×C₄×D₄₇	C₂⁴	1	2	yes	—
364	C₂×Dic₉₄	—	2	1	no	—
365	C₂×Dic₉₄	—	2	1	no	—
366	C₂×Dic₉₄	—	2	2	no	—
367	C₂×Dic₉₄	—	2	2	no	—
368	C₂×Dic₉₄	—	2	1	no	—
369	C₂×Dic₉₄	—	2	2	no	—
370	C₂×Dic₉₄	—	4	4	no	—
371	C₂×Dic₉₄	—	4	4	no	—
372	C₂×Dic₉₄	C₂×D₄	1	1	yes	characteristic
373	SD₁₆×C₄₇	—	2	2	no	—
374	SD₁₆×C₄₇	—	4	1	no	—
375	D₈×C₄₇	—	2	2	no	—
376	D₈×C₄₇	—	4	1	no	—
377	C₂×C₈×C₄₇	C₂⁴	1	1	yes	characteristic
378	C₂×C₈×C₄₇	C₂⁴	1	1	yes	characteristic
379	C₂×C₈×C₄₇	C₂⁴	1	1	yes	characteristic
380	C₂×C₈×C₄₇	C₂⁴	1	1	yes	characteristic
381	C₄⋊C₄×C₄₇	—	2	1	no	—
382	C₄⋊C₄×C₄₇	—	2	1	no	—
383	C₄⋊C₄×C₄₇	—	2	1	no	—
384	C₄⋊C₄×C₄₇	—	2	1	no	—
385	C₄⋊C₄×C₄₇	—	2	1	no	—
386	C₄⋊C₄×C₄₇	C₂⁴	1	1	yes	characteristic
387	C₄⋊C₄×C₄₇	C₂⁴	1	1	yes	characteristic
388	C₄⋊C₄×C₄₇	C₂⁴	1	1	yes	characteristic
389	C₄⋊C₄×C₄₇	C₂⁴	1	1	yes	characteristic
390	C₂²⋊C₄×C₄₇	—	2	1	no	—
391	C₂²⋊C₄×C₄₇	—	2	1	no	—
392	C₂²⋊C₄×C₄₇	—	2	1	no	—
393	C₂²⋊C₄×C₄₇	—	2	1	no	—
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	1	no	—
398	C₂²⋊C₄×C₄₇	—	2	1	no	—
399	C₄²×C₄₇	—	2	1	no	—
400	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
401	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
402	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
403	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
404	C₂²⋊Dic₄₇	—	2	2	no	—
405	C₂²⋊Dic₄₇	—	2	2	no	—
406	C₂²⋊Dic₄₇	—	2	2	no	—
407	C₂²⋊Dic₄₇	—	2	2	no	—
408	C₂²⋊Dic₄₇	—	2	2	no	—
409	C₂²⋊Dic₄₇	C₂×D₄	1	2	yes	—
410	#10625336	—	4	2	no	—
411	#10625334	—	4	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	2	no	—
416	(C₂×D₄₇)⋊C₄	—	2	2	no	—
417	(C₂×D₄₇)⋊C₄	—	2	2	no	—
418	(C₂×D₄₇)⋊C₄	—	2	2	no	—
419	(C₂×D₄₇)⋊C₄	C₂×D₄	1	2	yes	—
420	(C₂×D₄₇)⋊C₄	C₂×D₄	1	2	yes	—
421	C₄⋊Dic₄₇	—	2	1	no	—
422	C₄⋊Dic₄₇	—	2	1	no	—
423	C₄⋊Dic₄₇	—	2	1	no	—
424	C₄⋊Dic₄₇	—	2	2	no	—
425	C₄⋊Dic₄₇	C₂×D₄	1	1	yes	characteristic
426	C₄⋊Dic₄₇	C₂×D₄	1	1	yes	characteristic
427	C₄⋊Dic₄₇	C₂⁴	1	2	yes	—
428	C₄⋊Dic₄₇	C₂⁴	1	2	yes	—
429	C₄⋊Dic₄₇	C₂⁴	1	2	yes	—
430	Dic₄₇⋊C₄	—	2	2	no	—
431	Dic₄₇⋊C₄	—	2	2	no	—
432	Dic₄₇⋊C₄	—	2	2	no	—
433	Dic₄₇⋊C₄	—	2	2	no	—
434	Dic₄₇⋊C₄	—	2	2	no	—
435	Dic₄₇⋊C₄	—	2	2	no	—
436	Dic₄₇⋊C₄	—	2	2	no	—
437	Dic₄₇⋊C₄	C₂×D₄	1	2	yes	—
438	Dic₄₇⋊C₄	C₂×D₄	1	2	yes	—
439	C₄×Dic₄₇	—	2	2	no	—
440	C₄×Dic₄₇	—	2	2	no	—
441	C₄×Dic₄₇	—	2	2	no	—
442	C₄×Dic₄₇	—	2	2	no	—
443	C₄×Dic₄₇	C₂×D₄	1	2	yes	—
444	C₄×Dic₄₇	C₂×D₄	1	2	yes	—
445	C₄×Dic₄₇	C₂⁴	1	2	yes	—
446	#10625329	—	4	2	no	—
447	C₂×C₄₇⋊C₈	C₂⁴	1	2	yes	—
448	C₂×C₄₇⋊C₈	C₂⁴	1	2	yes	—
449	#10625324	—	4	2	no	—
450	#10625324	—	4	2	no	—
451	C₂³×C₄₇	—	2	1	no	—
452	C₂³×C₄₇	—	2	1	no	—
453	C₂³×C₄₇	—	2	1	no	—
454	C₂³×C₄₇	—	4	2	no	—
455	C₂³×C₄₇	—	4	2	no	—
456	C₂³×C₄₇	—	8	1	no	—
457	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
458	C₂²×D₄₇	—	2	2	no	—
459	C₂²×D₄₇	—	4	4	no	—
460	C₂²×D₄₇	—	4	4	no	—
461	C₂²×D₄₇	—	8	2	no	—
462	C₂²×D₄₇	C₂²×D₄	1	2	yes	—
463	Q₈×C₄₇	—	2	1	no	—
464	Q₈×C₄₇	—	2	1	no	—
465	D₄×C₄₇	—	2	1	no	—
466	D₄×C₄₇	—	2	1	no	—
467	D₄×C₄₇	—	2	1	no	—
468	D₄×C₄₇	—	2	1	no	—
469	D₄×C₄₇	—	2	1	no	—
470	D₄×C₄₇	—	4	2	no	—
471	D₄×C₄₇	—	8	1	no	—
472	D₄×C₄₇	2₋¹⁺⁴	1	2	yes	—
473	C₂×C₄×C₄₇	—	2	2	no	—
474	C₂×C₄×C₄₇	—	2	1	no	—
475	C₂×C₄×C₄₇	—	2	1	no	—
476	C₂×C₄×C₄₇	—	2	1	no	—
477	C₂×C₄×C₄₇	—	2	1	no	—
478	C₂×C₄×C₄₇	—	2	1	no	—
479	C₂×C₄×C₄₇	—	2	1	no	—
480	C₂×C₄×C₄₇	—	2	1	no	—
481	C₂×C₄×C₄₇	—	4	1	no	—
482	C₂×C₄×C₄₇	—	4	2	no	—
483	C₂×C₄×C₄₇	—	4	2	no	—
484	C₂×C₄×C₄₇	—	4	2	no	—
485	C₂×C₄×C₄₇	—	4	2	no	—
486	C₂×C₄×C₄₇	—	4	2	no	—
487	C₂×C₄×C₄₇	—	4	2	no	—
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	C₂²×D₄	1	1	yes	characteristic
493	C₂×C₄×C₄₇	C₂⁵	1	1	yes	characteristic
494	C₂²⋊D₄₇	—	2	4	no	—
495	C₂²⋊D₄₇	—	4	4	no	—
496	C₂²⋊D₄₇	—	4	4	no	—
497	C₂²⋊D₄₇	—	4	4	no	—
498	C₂²⋊D₄₇	—	4	4	no	—
499	C₂²⋊D₄₇	—	8	2	no	—
500	C₂²⋊D₄₇	—	8	2	no	—
501	C₂×Dic₄₇	—	2	2	no	—
502	C₂×Dic₄₇	—	2	2	no	—
503	C₂×Dic₄₇	—	2	2	no	—
504	C₂×Dic₄₇	—	4	4	no	—
505	C₂×Dic₄₇	—	4	4	no	—
506	C₂×Dic₄₇	C₂²×D₄	1	2	yes	—
507	C₂×Dic₄₇	C₂²×D₄	1	2	yes	—
508	C₂×Dic₄₇	C₂²×D₄	1	2	yes	—
509	D₁₈₈	—	2	2	no	—
510	D₁₈₈	—	2	2	no	—
511	D₁₈₈	—	2	2	no	—
512	D₁₈₈	—	4	4	no	—
513	D₁₈₈	—	4	2	no	—
514	D₁₈₈	—	8	1	no	—
515	C₄×D₄₇	—	2	2	no	—
516	C₄×D₄₇	—	2	2	no	—
517	C₄×D₄₇	—	2	4	no	—
518	C₄×D₄₇	—	4	2	no	—
519	C₄×D₄₇	—	4	4	no	—
520	C₄×D₄₇	—	4	4	no	—
521	C₄×D₄₇	—	4	4	no	—
522	Dic₉₄	—	4	2	no	—
523	Dic₉₄	—	4	2	no	—
524	Dic₉₄	—	4	4	no	—
525	Dic₉₄	—	4	4	no	—
526	Dic₉₄	—	8	2	no	—
527	Dic₉₄	—	8	1	no	—
528	Dic₉₄	AGL(1,ℤ/8)	1	4	yes	—
529	C₈×C₄₇	—	2	1	no	—
530	C₈×C₄₇	—	2	1	no	—
531	C₈×C₄₇	—	2	1	no	—
532	C₈×C₄₇	—	2	1	no	—
533	C₄₇⋊C₈	—	2	2	no	—
534	C₄₇⋊C₈	—	2	2	no	—
535	#62151	—	47	1	no	maximal, Sylow
536	C₂²×C₄₇	—	2	1	no	—
537	C₂²×C₄₇	—	2	2	no	—
538	C₂²×C₄₇	—	2	1	no	—
539	C₂²×C₄₇	—	2	1	no	—
540	C₂²×C₄₇	—	4	1	no	—
541	C₂²×C₄₇	—	4	1	no	—
542	C₂²×C₄₇	—	4	1	no	—
543	C₂²×C₄₇	—	4	1	no	—
544	C₂²×C₄₇	—	4	1	no	—
545	C₂²×C₄₇	—	4	1	no	—
546	C₂²×C₄₇	—	4	1	no	—
547	C₂²×C₄₇	—	4	1	no	—
548	C₂²×C₄₇	—	8	4	no	—
549	C₂²×C₄₇	C₂³×D₄	1	1	yes	characteristic
550	C₂×D₄₇	—	2	2	no	—
551	C₂×D₄₇	—	2	2	no	—
552	C₂×D₄₇	—	2	2	no	—
553	C₂×D₄₇	—	4	2	no	—
554	C₂×D₄₇	—	4	2	no	—
555	C₂×D₄₇	—	4	2	no	—
556	C₂×D₄₇	—	8	8	no	—
557	C₄×C₄₇	—	2	1	no	—
558	C₄×C₄₇	—	2	1	no	—
559	C₄×C₄₇	—	2	1	no	—
560	C₄×C₄₇	—	2	1	no	—
561	C₄×C₄₇	—	4	1	no	—
562	C₄×C₄₇	—	4	1	no	—
563	C₄×C₄₇	—	4	1	no	—
564	C₄×C₄₇	—	4	1	no	—
565	C₄×C₄₇	—	4	1	no	—
566	C₄×C₄₇	C₂×AGL(1,ℤ/8)	1	2	yes	—
567	C₄×C₄₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
568	C₄×C₄₇	#585	1	1	yes	characteristic
569	Dic₄₇	—	2	2	no	—
570	Dic₄₇	—	2	2	no	—
571	Dic₄₇	—	4	2	no	—
572	Dic₄₇	—	4	2	no	—
573	Dic₄₇	—	4	2	no	—
574	Dic₄₇	C₂×AGL(1,ℤ/8)	1	4	yes	—
575	#3518	—	47	1	no	—
576	D₄×#41	—	47	1	no	—
577	Q₈×SD₁₆	—	47	1	no	—
578	Q₈×D₈	—	47	1	no	—
579	#3362	—	47	1	no	—
580	#3358	—	47	1	no	—
581	#3354	—	47	2	no	—
582	#3354	—	47	1	no	—
583	#3353	—	47	2	no	—
584	#3353	—	47	1	no	—
585	#3325	—	47	2	no	—
586	#3325	—	47	1	no	—
587	#3324	—	47	2	no	—
588	#3324	—	47	1	no	—
589	#3251	—	47	2	no	—
590	#3251	—	47	1	no	—
591	#3228	—	47	2	no	—
592	#3228	—	47	1	no	—
593	#3105	—	47	2	no	—
594	#3105	D₄₇	1	1	yes	characteristic, complemented
595	#3077	—	47	2	no	—
596	#3077	—	47	1	no	—
597	#2991	—	47	1	no	—
598	C₂×C₄₇	—	4	2	no	—
599	C₂×C₄₇	—	4	1	no	—
600	C₂×C₄₇	—	8	1	no	—
601	C₂×C₄₇	—	8	1	no	—
602	C₂×C₄₇	#3489	1	1	yes	characteristic
603	C₂×C₄₇	C₂²×AGL(1,ℤ/8)	1	1	yes	characteristic
604	C₂×C₄₇	#3584	1	1	yes	characteristic
605	D₄₇	—	4	2	no	—
606	D₄₇	—	8	2	no	—
607	C₂²×#41	—	94	1	no	—
608	Q₈²	—	47	1	no	—
609	#556	—	47	2	no	—
610	#556	—	47	1	no	—
611	#556	—	94	1	no	—
612	#556	—	94	2	no	—
613	#555	—	47	2	no	—
614	#555	—	47	1	no	—
615	#550	—	47	1	no	—
616	D₄×Q₈	—	47	1	no	—
617	D₄×Q₈	—	47	1	no	—
618	#548	—	94	1	no	—
619	#548	—	94	1	no	—
620	#547	—	47	1	no	—
621	#547	—	47	2	no	—
622	#546	—	94	2	no	—
623	#546	—	94	1	no	—
624	D₄²	—	47	2	no	—
625	D₄²	—	47	1	no	—
626	#542	—	94	1	no	—
627	#542	—	94	2	no	—
628	#533	—	47	2	no	—
629	#533	—	47	1	no	—
630	#532	—	47	2	no	—
631	#532	—	47	1	no	—
632	#529	—	47	2	no	—
633	#529	C₂×D₄₇	1	1	yes	characteristic, complemented
634	#525	—	94	2	no	—
635	#525	—	94	1	no	—
636	#519	—	94	1	no	—
637	C₄×#41	—	47	1	no	—
638	C₂×C₄×D₄	—	47	2	no	—
639	C₂×C₄×D₄	C₂×D₄₇	1	1	yes	characteristic
640	#500	—	47	2	no	—
641	#500	—	47	1	no	—
642	#498	—	47	2	no	—
643	#498	—	47	1	no	—
644	#486	—	47	2	no	—
645	#486	—	47	2	no	—
646	#486	—	47	1	no	—
647	#486	—	47	1	no	—
648	#484	—	47	2	no	—
649	#484	C₂×D₄₇	1	1	yes	characteristic, complemented
650	#482	—	47	2	no	—
651	#482	—	47	2	no	—
652	#482	—	47	2	no	—
653	#482	—	47	2	no	—
654	#482	—	47	2	no	—
655	#482	—	47	2	no	—
656	#481	—	47	2	no	—
657	#481	C₂×D₄₇	1	1	yes	characteristic, complemented
658	#478	—	47	2	no	—
659	#478	—	47	2	no	—
660	#478	—	47	2	no	—
661	#478	—	47	2	no	—
662	#478	—	47	2	no	—
663	#478	C₂×D₄₇	1	1	yes	characteristic
664	#478	C₂×D₄₇	1	1	yes	characteristic, complemented
665	#476	—	47	1	no	—
666	#476	—	47	1	no	—
667	#476	—	47	2	no	—
668	#476	—	47	2	no	—
669	#475	—	47	1	no	—
670	#475	—	47	2	no	—
671	#474	—	47	1	no	—
672	#474	—	47	1	no	—
673	#474	—	47	1	no	—
674	#474	—	47	2	no	—
675	#474	—	47	2	no	—
676	#474	—	47	2	no	—
677	#469	—	47	2	no	—
678	#469	—	47	2	no	—
679	#469	—	47	2	no	—
680	#468	—	47	2	no	—
681	#468	—	47	2	no	—
682	#468	—	47	2	no	—
683	#463	—	47	2	no	—
684	#463	C₂×D₄₇	1	1	yes	characteristic
685	#463	C₂×D₄₇	1	1	yes	characteristic, complemented
686	#460	—	47	2	no	—
687	#460	—	47	1	no	—
688	#459	—	47	2	no	—
689	#459	—	47	1	no	—
690	#450	—	47	2	no	—
691	#450	C₂×D₄₇	1	1	yes	characteristic
692	#447	—	47	2	no	—
693	#447	C₂×D₄₇	1	1	yes	characteristic
694	C₈×Q₈	—	47	1	no	—
695	C₈×Q₈	—	47	1	no	—
696	C₄×SD₁₆	—	47	2	no	—
697	C₄×SD₁₆	—	47	2	no	—
698	C₄×SD₁₆	C₂×D₄₇	1	1	yes	characteristic
699	C₄×SD₁₆	C₂×D₄₇	1	1	yes	characteristic, complemented
700	C₄×D₈	—	47	2	no	—
701	C₄×D₈	—	47	2	no	—
702	C₄×D₈	C₂×D₄₇	1	1	yes	characteristic
703	C₄×D₈	C₂×D₄₇	1	1	yes	characteristic, complemented
704	#436	—	47	2	no	—
705	#436	—	47	2	no	—
706	#436	—	47	1	no	—
707	#436	—	47	1	no	—
708	#431	—	47	2	no	—
709	#431	C₂×D₄₇	1	1	yes	characteristic, complemented
710	#428	—	47	2	no	—
711	#428	—	47	2	no	—
712	#428	—	47	2	no	—
713	#423	—	47	1	no	—
714	#423	—	47	2	no	—
715	#418	—	47	2	no	—
716	#418	—	47	2	no	—
717	#418	—	47	2	no	—
718	C₄₇	#62151	1	1	yes	characteristic, complemented, Sylow
719	C₂×#41	—	47	1	no	—
720	C₂×#41	—	94	2	no	—
721	C₂×#41	—	94	2	no	—
722	C₂×#41	—	94	1	no	—
723	C₂×#41	—	94	1	no	—
724	C₂×#41	—	94	1	no	—
725	C₂×#41	—	188	8	no	—
726	C₂²×Q₈	—	94	1	no	—
727	C₂²×Q₈	—	94	1	no	—
728	C₂²×D₄	—	47	2	no	—
729	C₂²×D₄	—	94	1	no	—
730	C₂²×D₄	—	94	2	no	—
731	C₂²×D₄	C₂²×D₄₇	1	1	yes	characteristic
732	C₂³×C₄	—	2	1	no	—
733	C₂³×C₄	—	94	2	no	—
734	C₂×SD₁₆	—	47	2	no	—
735	C₂×SD₁₆	C₂²×D₄₇	1	1	yes	characteristic
736	C₂×SD₁₆	C₂²×D₄₇	1	1	yes	characteristic
737	C₂×D₈	—	47	2	no	—
738	C₂×D₈	C₂²×D₄₇	1	1	yes	characteristic
739	C₂×D₈	C₂²×D₄₇	1	1	yes	characteristic
740	C₂×M₁₆	—	47	2	no	—
741	C₂×M₁₆	—	47	2	no	—
742	C₂×M₁₆	—	47	2	no	—
743	C₄⋊Q₈	—	47	2	no	—
744	C₄⋊Q₈	—	47	2	no	—
745	C₄⋊Q₈	—	47	2	no	—
746	C₄⋊Q₈	—	47	1	no	—
747	C₄⋊Q₈	—	47	1	no	—
748	C₄⋊Q₈	—	47	1	no	—
749	C₄⋊Q₈	—	94	1	no	—
750	C₄⋊Q₈	—	94	2	no	—
751	#127	—	47	2	no	—
752	#127	—	47	1	no	—
753	#126	—	2	1	no	—
754	#126	—	94	2	no	—
755	#126	—	94	2	no	—
756	#126	—	94	2	no	—
757	#126	—	94	2	no	—
758	#125	—	47	2	no	—
759	#125	C₂²×D₄₇	1	1	yes	characteristic
760	#124	—	94	1	no	—
761	#124	—	94	2	no	—
762	#124	—	94	2	no	—
763	#124	—	94	2	no	—
764	#124	—	94	2	no	—
765	#124	—	94	2	no	—
766	#124	—	94	1	no	—
767	#124	C₂²×D₄₇	1	1	yes	characteristic
768	#123	—	2	1	no	—
769	#123	—	94	2	no	—
770	#123	—	94	2	no	—
771	#123	—	94	2	no	—
772	#123	—	94	2	no	—
773	C₂²⋊Q₈	—	47	2	no	—
774	C₂²⋊Q₈	—	94	2	no	—
775	C₂²⋊Q₈	—	94	2	no	—
776	C₂²⋊Q₈	—	94	2	no	—
777	C₂²⋊Q₈	—	94	2	no	—
778	C₂²⋊Q₈	—	94	2	no	—
779	C₂²⋊Q₈	—	94	1	no	—
780	C₂²⋊Q₈	—	94	1	no	—
781	C₂²⋊Q₈	—	94	1	no	—
782	C₂²⋊Q₈	—	94	1	no	—
783	C₂²⋊Q₈	—	94	1	no	—
784	C₂²⋊Q₈	C₂²×D₄₇	1	1	yes	characteristic
785	#121	—	47	2	no	—
786	#121	—	47	2	no	—
787	#121	—	47	2	no	—
788	#121	—	47	2	no	—
789	#121	—	94	2	no	—
790	#121	—	94	2	no	—
791	#121	—	94	1	no	—
792	#121	—	94	1	no	—
793	#121	—	94	2	no	—
794	#121	—	94	1	no	—
795	#121	—	94	2	no	—
796	#121	—	94	1	no	—
797	#121	C₂²×D₄₇	1	1	yes	characteristic
798	#120	—	94	2	no	—
799	#120	—	94	2	no	—
800	#120	—	94	2	no	—
801	C₄×Q₈	—	47	1	no	—
802	C₄×Q₈	—	47	1	no	—
803	C₄×Q₈	—	47	2	no	—
804	C₄×Q₈	—	94	1	no	—
805	C₄×Q₈	—	94	1	no	—
806	C₄×Q₈	—	94	2	no	—
807	C₄×Q₈	—	94	2	no	—
808	C₄×Q₈	—	94	2	no	—
809	C₄×Q₈	—	94	1	no	—
810	C₄×Q₈	—	94	1	no	—
811	C₄×Q₈	C₂²×D₄₇	1	1	yes	characteristic
812	C₄×D₄	—	2	1	no	—
813	C₄×D₄	—	2	1	no	—
814	C₄×D₄	—	2	1	no	—
815	C₄×D₄	—	47	2	no	—
816	C₄×D₄	—	47	2	no	—
817	C₄×D₄	—	47	2	no	—
818	C₄×D₄	—	47	2	no	—
819	C₄×D₄	—	47	2	no	—
820	C₄×D₄	—	47	1	no	—
821	C₄×D₄	—	47	1	no	—
822	C₄×D₄	—	47	2	no	—
823	C₄×D₄	—	94	2	no	—
824	C₄×D₄	—	94	2	no	—
825	C₄×D₄	—	94	2	no	—
826	C₄×D₄	—	94	2	no	—
827	C₄×D₄	—	94	1	no	—
828	C₄×D₄	C₂²×D₄₇	1	1	yes	characteristic
829	C₄×D₄	C₂²×D₄₇	1	1	yes	characteristic
830	C₄×D₄	C₂²×D₄₇	1	1	yes	characteristic
831	C₄×D₄	C₂²×D₄₇	1	1	yes	characteristic
832	C₄×D₄	C₂²×D₄₇	1	1	yes	characteristic
833	#117	—	2	1	no	—
834	#117	—	47	1	no	—
835	#117	—	47	2	no	—
836	#117	—	47	2	no	—
837	#117	—	47	2	no	—
838	#117	—	47	2	no	—
839	#117	—	94	2	no	—
840	#117	—	94	2	no	—
841	#117	—	94	1	no	—
842	C₂×C₄⋊C₄	—	47	2	no	—
843	C₂×C₄⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
844	C₂×C₂²⋊C₄	—	2	1	no	—
845	C₂×C₂²⋊C₄	—	94	2	no	—
846	C₂×C₄²	—	47	2	no	—
847	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
848	#107	—	47	2	no	—
849	#107	—	47	2	no	—
850	#107	—	47	2	no	—
851	#107	—	47	2	no	—
852	#107	—	47	2	no	—
853	#107	C₂²×D₄₇	1	1	yes	characteristic
854	#107	C₂²×D₄₇	1	1	yes	characteristic
855	#106	—	47	2	no	—
856	#106	—	47	2	no	—
857	#106	—	47	2	no	—
858	#106	—	47	2	no	—
859	#106	—	47	2	no	—
860	#106	C₂²×D₄₇	1	1	yes	characteristic
861	#106	C₂²×D₄₇	1	1	yes	characteristic
862	C₄⋊C₈	—	47	2	no	—
863	C₄⋊C₈	—	47	2	no	—
864	C₄⋊C₈	—	47	2	no	—
865	C₄⋊C₈	—	47	1	no	—
866	C₄⋊C₈	—	47	1	no	—
867	C₄⋊C₈	C₂²×D₄₇	1	1	yes	characteristic
868	C₄⋊C₈	C₂²×D₄₇	1	1	yes	characteristic
869	#103	—	47	2	no	—
870	#103	C₂²×D₄₇	1	1	yes	characteristic
871	#103	C₂²×D₄₇	1	1	yes	characteristic
872	#102	—	47	2	no	—
873	#102	—	47	2	no	—
874	#102	—	47	2	no	—
875	#102	—	47	2	no	—
876	#102	—	47	2	no	—
877	#102	—	47	2	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	C₂²×D₄₇	1	1	yes	characteristic
884	#102	C₂²×D₄₇	1	1	yes	characteristic
885	#102	C₂²×D₄₇	1	1	yes	characteristic
886	#102	C₂²×D₄₇	1	1	yes	characteristic
887	#102	C₂²×D₄₇	1	1	yes	characteristic
888	#102	C₂²×D₄₇	1	1	yes	characteristic
889	C₂²⋊C₈	—	47	2	no	—
890	C₂²⋊C₈	—	47	2	no	—
891	C₂²⋊C₈	C₂²×D₄₇	1	1	yes	characteristic
892	C₂²⋊C₈	C₂²×D₄₇	1	1	yes	characteristic
893	C₄×C₈	—	47	2	no	—
894	C₄×C₈	—	47	2	no	—
895	C₄×C₈	C₂²×D₄₇	1	1	yes	characteristic
896	C₄×C₈	C₂²×D₄₇	1	1	yes	characteristic
897	C₂⁴	—	2	1	no	—
898	C₂⁴	—	94	2	no	—
899	#41	—	94	4	no	—
900	#41	—	188	4	no	—
901	#41	—	188	8	no	—
902	#41	—	188	8	no	—
903	#41	—	188	4	no	—
904	#41	—	188	4	no	—
905	C₂×Q₈	—	47	1	no	—
906	C₂×Q₈	—	94	2	no	—
907	C₂×Q₈	—	94	2	no	—
908	C₂×Q₈	—	94	2	no	—
909	C₂×Q₈	—	94	1	no	—
910	C₂×Q₈	—	94	1	no	—
911	C₂×Q₈	—	94	1	no	—
912	C₂×Q₈	—	188	4	no	—
913	C₂×Q₈	—	188	4	no	—
914	C₂×Q₈	C₂³×D₄₇	1	1	yes	characteristic
915	C₂×D₄	—	2	2	no	—
916	C₂×D₄	—	2	1	no	—
917	C₂×D₄	—	2	1	no	—
918	C₂×D₄	—	4	1	no	—
919	C₂×D₄	—	47	2	no	—
920	C₂×D₄	—	47	1	no	—
921	C₂×D₄	—	47	2	no	—
922	C₂×D₄	—	94	2	no	—
923	C₂×D₄	—	94	2	no	—
924	C₂×D₄	—	94	2	no	—
925	C₂×D₄	—	94	2	no	—
926	C₂×D₄	—	94	4	no	—
927	C₂×D₄	—	94	2	no	—
928	C₂×D₄	—	94	2	no	—
929	C₂×D₄	—	94	2	no	—
930	C₂×D₄	—	94	1	no	—
931	C₂×D₄	—	94	1	no	—
932	C₂×D₄	—	188	4	no	—
933	C₂×D₄	—	188	2	no	—
934	C₂×D₄	—	188	8	no	—
935	C₂×D₄	C₂³×D₄₇	1	1	yes	characteristic
936	C₂×D₄	C₂³×D₄₇	1	1	yes	characteristic
937	C₂×D₄	C₂³×D₄₇	1	1	yes	characteristic
938	C₂²×C₄	—	2	1	no	—
939	C₂²×C₄	—	2	1	no	—
940	C₂²×C₄	—	2	1	no	—
941	C₂²×C₄	—	2	1	no	—
942	C₂²×C₄	—	2	1	no	—
943	C₂²×C₄	—	2	1	no	—
944	C₂²×C₄	—	4	4	no	—
945	C₂²×C₄	—	47	2	no	—
946	C₂²×C₄	—	47	2	no	—
947	C₂²×C₄	—	47	2	no	—
948	C₂²×C₄	—	94	2	no	—
949	C₂²×C₄	—	94	2	no	—
950	C₂²×C₄	—	94	2	no	—
951	C₂²×C₄	—	94	2	no	—
952	C₂²×C₄	—	94	2	no	—
953	C₂²×C₄	—	188	8	no	—
954	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
955	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
956	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
957	SD₁₆	—	2	2	no	—
958	SD₁₆	—	4	1	no	—
959	SD₁₆	—	188	2	no	—
960	D₈	—	2	2	no	—
961	D₈	—	4	1	no	—
962	D₈	—	188	2	no	—
963	M₁₆	—	188	2	no	—
964	M₁₆	—	188	2	no	—
965	M₁₆	—	188	2	no	—
966	C₂×C₈	—	47	2	no	—
967	C₂×C₈	—	47	2	no	—
968	C₂×C₈	C₂³×D₄₇	1	1	yes	characteristic
969	C₂×C₈	C₂³×D₄₇	1	1	yes	characteristic
970	C₂×C₈	C₂³×D₄₇	1	1	yes	characteristic
971	C₂×C₈	C₂³×D₄₇	1	1	yes	characteristic
972	C₄⋊C₄	—	2	1	no	—
973	C₄⋊C₄	—	2	1	no	—
974	C₄⋊C₄	—	2	1	no	—
975	C₄⋊C₄	—	2	1	no	—
976	C₄⋊C₄	—	2	1	no	—
977	C₄⋊C₄	—	47	2	no	—
978	C₄⋊C₄	—	47	2	no	—
979	C₄⋊C₄	—	47	1	no	—
980	C₄⋊C₄	—	47	1	no	—
981	C₄⋊C₄	—	47	2	no	—
982	C₄⋊C₄	—	47	2	no	—
983	C₄⋊C₄	—	47	2	no	—
984	C₄⋊C₄	—	94	2	no	—
985	C₄⋊C₄	—	94	2	no	—
986	C₄⋊C₄	—	94	2	no	—
987	C₄⋊C₄	—	94	2	no	—
988	C₄⋊C₄	—	94	2	no	—
989	C₄⋊C₄	—	94	2	no	—
990	C₄⋊C₄	—	94	2	no	—
991	C₄⋊C₄	—	94	2	no	—
992	C₄⋊C₄	—	94	1	no	—
993	C₄⋊C₄	—	94	1	no	—
994	C₄⋊C₄	—	94	1	no	—
995	C₄⋊C₄	C₂³×D₄₇	1	1	yes	characteristic
996	C₄⋊C₄	C₂³×D₄₇	1	1	yes	characteristic
997	C₄⋊C₄	C₂³×D₄₇	1	1	yes	characteristic
998	C₄⋊C₄	C₂³×D₄₇	1	1	yes	characteristic
999	C₂²⋊C₄	—	2	1	no	—
1000	C₂²⋊C₄	—	2	1	no	—
1001	C₂²⋊C₄	—	2	1	no	—
1002	C₂²⋊C₄	—	2	1	no	—
1003	C₂²⋊C₄	—	2	1	no	—
1004	C₂²⋊C₄	—	2	1	no	—
1005	C₂²⋊C₄	—	2	1	no	—
1006	C₂²⋊C₄	—	2	1	no	—
1007	C₂²⋊C₄	—	2	1	no	—
1008	C₂²⋊C₄	—	47	2	no	—
1009	C₂²⋊C₄	—	47	2	no	—
1010	C₂²⋊C₄	—	47	2	no	—
1011	C₂²⋊C₄	—	94	2	no	—
1012	C₂²⋊C₄	—	94	2	no	—
1013	C₂²⋊C₄	—	94	2	no	—
1014	C₂²⋊C₄	—	94	2	no	—
1015	C₂²⋊C₄	—	94	2	no	—
1016	C₂²⋊C₄	—	94	2	no	—
1017	C₂²⋊C₄	—	94	2	no	—
1018	C₂²⋊C₄	—	94	2	no	—
1019	C₂²⋊C₄	—	94	2	no	—
1020	C₂²⋊C₄	—	94	2	no	—
1021	C₂²⋊C₄	—	94	2	no	—
1022	C₂²⋊C₄	—	94	2	no	—
1023	C₄²	—	2	1	no	—
1024	C₄²	—	47	2	no	—
1025	C₄²	—	47	2	no	—
1026	C₄²	—	47	2	no	—
1027	C₄²	—	94	2	no	—
1028	C₄²	—	94	2	no	—
1029	C₄²	—	94	2	no	—
1030	C₄²	—	94	2	no	—
1031	C₄²	D₄×D₄₇	1	1	yes	characteristic
1032	C₄²	D₄×D₄₇	1	1	yes	characteristic
1033	C₄²	C₂³×D₄₇	1	1	yes	characteristic
1034	C₄²	C₂³×D₄₇	1	1	yes	characteristic
1035	C₂³	—	2	1	no	—
1036	C₂³	—	2	1	no	—
1037	C₂³	—	2	1	no	—
1038	C₂³	—	4	2	no	—
1039	C₂³	—	4	2	no	—
1040	C₂³	—	8	1	no	—
1041	C₂³	—	47	2	no	—
1042	C₂³	—	94	2	no	—
1043	C₂³	—	376	2	no	—
1044	C₂³	—	188	4	no	—
1045	C₂³	—	188	4	no	—
1046	C₂³	C₂×D₄×D₄₇	1	1	yes	characteristic
1047	Q₈	—	2	1	no	—
1048	Q₈	—	2	1	no	—
1049	Q₈	—	47	4	no	—
1050	Q₈	—	376	1	no	—
1051	Q₈	—	376	2	no	—
1052	Q₈	—	188	4	no	—
1053	Q₈	—	188	4	no	—
1054	Q₈	—	188	2	no	—
1055	Q₈	—	188	2	no	—
1056	D₄	—	2	1	no	—
1057	D₄	—	2	1	no	—
1058	D₄	—	2	1	no	—
1059	D₄	—	2	1	no	—
1060	D₄	—	2	1	no	—
1061	D₄	—	4	2	no	—
1062	D₄	—	8	1	no	—
1063	D₄	—	94	4	no	—
1064	D₄	—	94	2	no	—
1065	D₄	—	94	2	no	—
1066	D₄	—	94	2	no	—
1067	D₄	—	376	1	no	—
1068	D₄	—	376	2	no	—
1069	D₄	—	376	2	no	—
1070	D₄	—	188	4	no	—
1071	D₄	—	188	4	no	—
1072	D₄	—	188	4	no	—
1073	D₄	—	188	4	no	—
1074	D₄	—	188	4	no	—
1075	D₄	—	188	2	no	—
1076	D₄	#13094071	1	2	yes	—
1077	C₂×C₄	—	2	2	no	—
1078	C₂×C₄	—	2	1	no	—
1079	C₂×C₄	—	2	1	no	—
1080	C₂×C₄	—	2	1	no	—
1081	C₂×C₄	—	2	1	no	—
1082	C₂×C₄	—	2	1	no	—
1083	C₂×C₄	—	2	1	no	—
1084	C₂×C₄	—	2	1	no	—
1085	C₂×C₄	—	4	1	no	—
1086	C₂×C₄	—	4	2	no	—
1087	C₂×C₄	—	4	2	no	—
1088	C₂×C₄	—	4	2	no	—
1089	C₂×C₄	—	4	2	no	—
1090	C₂×C₄	—	4	2	no	—
1091	C₂×C₄	—	4	2	no	—
1092	C₂×C₄	—	47	2	no	—
1093	C₂×C₄	—	47	2	no	—
1094	C₂×C₄	—	47	2	no	—
1095	C₂×C₄	—	94	4	no	—
1096	C₂×C₄	—	94	2	no	—
1097	C₂×C₄	—	94	2	no	—
1098	C₂×C₄	—	94	2	no	—
1099	C₂×C₄	—	94	2	no	—
1100	C₂×C₄	—	94	2	no	—
1101	C₂×C₄	—	188	2	no	—
1102	C₂×C₄	—	188	4	no	—
1103	C₂×C₄	—	188	4	no	—
1104	C₂×C₄	—	188	4	no	—
1105	C₂×C₄	—	188	4	no	—
1106	C₂×C₄	—	188	4	no	—
1107	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
1108	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
1109	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
1110	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
1111	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
1112	C₂×C₄	C₂⁴×D₄₇	1	1	yes	characteristic
1113	C₈	—	2	1	no	—
1114	C₈	—	2	1	no	—
1115	C₈	—	2	1	no	—
1116	C₈	—	2	1	no	—
1117	C₈	—	94	2	no	—
1118	C₈	—	94	2	no	—
1119	C₂²	—	2	1	no	—
1120	C₂²	—	2	2	no	—
1121	C₂²	—	2	1	no	—
1122	C₂²	—	2	1	no	—
1123	C₂²	—	4	1	no	—
1124	C₂²	—	4	1	no	—
1125	C₂²	—	4	1	no	—
1126	C₂²	—	4	1	no	—
1127	C₂²	—	4	1	no	—
1128	C₂²	—	4	1	no	—
1129	C₂²	—	4	1	no	—
1130	C₂²	—	4	1	no	—
1131	C₂²	—	8	4	no	—
1132	C₂²	—	94	2	no	—
1133	C₂²	—	94	2	no	—
1134	C₂²	—	94	2	no	—
1135	C₂²	—	376	8	no	—
1136	C₂²	—	188	2	no	—
1137	C₂²	—	188	2	no	—
1138	C₂²	—	188	2	no	—
1139	C₂²	C₂²×D₄×D₄₇	1	1	yes	characteristic
1140	C₄	—	2	1	no	—
1141	C₄	—	2	1	no	—
1142	C₄	—	2	1	no	—
1143	C₄	—	2	1	no	—
1144	C₄	—	4	1	no	—
1145	C₄	—	4	1	no	—
1146	C₄	—	4	1	no	—
1147	C₄	—	4	1	no	—
1148	C₄	—	4	1	no	—
1149	C₄	—	47	4	no	—
1150	C₄	—	94	2	no	—
1151	C₄	—	94	2	no	—
1152	C₄	—	188	2	no	—
1153	C₄	—	188	2	no	—
1154	C₄	—	188	2	no	—
1155	C₄	AGL(1,ℤ/8)×D₄₇	1	2	yes	—
1156	C₄	C₂×#13094071	1	1	yes	characteristic
1157	C₄	#15689959	1	1	yes	characteristic
1158	C₂	—	4	1	no	—
1159	C₂	—	4	2	no	—
1160	C₂	—	8	1	no	—
1161	C₂	—	8	1	no	—
1162	C₂	—	376	2	no	—
1163	C₂	—	188	2	no	—
1164	C₂	#20257060	1	1	yes	characteristic
1165	C₂	C₂×AGL(1,ℤ/8)×D₄₇	1	1	yes	characteristic
1166	C₂	#20258157	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂²×D₄×D₄₇
commutator, cosocle	C₂×C₄×C₄₇	C₂⁵
Frattini	C₂×C₄	C₂⁴×D₄₇
Fitting	C₄₇×#3105	C₂
socle	C₂²×C₄₇	C₂³×D₄
hypercenter	#3105	D₄₇
hypocenter	C₄₇	#62151
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #3105

Complements

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

N	H ≅ G/N	type
1. #20257403	C₂	semidirect
2. D₄×#10625350	C₂	semidirect
3. SD₁₆×Dic₉₄	C₂	semidirect
4. D₈×Dic₉₄	C₂	semidirect
5. #20256057	C₂	semidirect
6. #20256021	C₂	semidirect
7. #20255985	C₂	semidirect
8. #20255976	C₂	semidirect
9. #20255974	C₂	semidirect
10. #20255965	C₂	semidirect
11. #20255632	C₂	semidirect
12. #20255623	C₂	semidirect
13. #20255621	C₂	semidirect
14. #20255612	C₂	semidirect
15. #20254750	C₂	semidirect
16. #20254747	C₂	semidirect
17. #20254526	C₂	semidirect
18. #20254523	C₂	semidirect
19. #20253434	C₂	semidirect
20. #20253185	C₂	semidirect
21. #20253183	C₂	semidirect
22. #20252517	C₂	semidirect
23. C₄₇×#3105	C₂	semidirect
25. Q₈×Dic₉₄	C₂²	semidirect
26. #15689846	C₂²	semidirect
27. #15689844	C₂²	semidirect
30. #15689838	C₂²	semidirect
31. #15689837	C₂²	semidirect
34. D₄×Dic₉₄	C₂²	semidirect
45. #15689680	C₂²	semidirect
46. #15689679	C₂²	semidirect
49. #15689652	C₂²	semidirect
55. #15689528	C₂²	semidirect
56. #15689527	C₂²	semidirect
57. #15689521	C₂²	semidirect
58. #15689520	C₂²	semidirect
59. #15689470	C₂²	semidirect
60. #15689470	C₂²	semidirect
61. #15689468	C₂²	semidirect
62. #15689468	C₂²	semidirect
63. #15689457	C₂²	semidirect
64. #15689450	C₂²	semidirect
65. #15689449	C₂²	semidirect
66. #15689448	C₂²	semidirect
67. #15689448	C₂²	semidirect
68. #15689446	C₂²	semidirect
69. #15689445	C₂²	semidirect
70. #15689440	C₂²	semidirect
71. #15689424	C₂²	semidirect
72. #15689424	C₂²	semidirect
74. #15689423	C₂²	semidirect
75. #15689420	C₂²	semidirect
77. #15689413	C₂²	semidirect
78. #15689412	C₂²	semidirect
80. #15689408	C₂²	semidirect
81. #15689406	C₂²	semidirect
83. #15689403	C₂²	semidirect
84. #15689403	C₂²	semidirect
85. #15689402	C₂²	semidirect
87. #15689401	C₂²	semidirect
88. #15689375	C₂²	semidirect
89. #15689374	C₂²	semidirect
90. #15689373	C₂²	semidirect
91. #15689372	C₂²	semidirect
92. #15689371	C₂²	semidirect
93. #15689366	C₂²	semidirect
94. #15689335	C₂²	semidirect
95. #15689323	C₂²	semidirect
96. #15689321	C₂²	semidirect
97. #15689318	C₂²	semidirect
98. #15689316	C₂²	semidirect
101. C₈×Dic₉₄	C₂²	semidirect
102. C₈×Dic₉₄	C₂²	semidirect
104. #15689208	C₂²	semidirect
106. #15689203	C₂²	semidirect
107. #15689202	C₂²	semidirect
108. #15689202	C₂²	semidirect
109. #15689198	C₂²	semidirect
110. #15689198	C₂²	semidirect
111. #15689175	C₂²	semidirect
112. #15689164	C₂²	semidirect
113. #15689163	C₂²	semidirect
114. #15689162	C₂²	semidirect
115. #15689147	C₂²	semidirect
116. #15689145	C₂²	semidirect
120. C₄₇×#529	C₂²	semidirect
122. C₄₇×#484	C₂²	semidirect
123. C₄₇×#481	C₂²	semidirect
125. C₄₇×#478	C₂²	semidirect
127. C₄₇×#463	C₂²	semidirect
131. C₄×SD₁₆×C₄₇	C₂²	semidirect
133. C₄×D₈×C₄₇	C₂²	semidirect
134. C₄₇×#431	C₂²	semidirect
594. #3105	D₄₇	semidirect
633. #529	C₂×D₄₇	semidirect
649. #484	C₂×D₄₇	semidirect
657. #481	C₂×D₄₇	semidirect
664. #478	C₂×D₄₇	semidirect
685. #463	C₂×D₄₇	semidirect
699. C₄×SD₁₆	C₂×D₄₇	semidirect
703. C₄×D₈	C₂×D₄₇	semidirect
709. #431	C₂×D₄₇	semidirect
718. C₄₇	#62151	semidirect

Maximal subgroups

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

subgroup	index
#20257403	2
D₄×#10625350	2
SD₁₆×Dic₉₄	2
D₈×Dic₉₄	2
#20256057	2
#20256021	2
#20255985	2
#20255976	2
#20255974	2
#20255965	2
#20255632	2
#20255623	2
#20255621	2
#20255612	2
#20254750	2
#20254747	2
#20254526	2
#20254523	2
#20253434	2
#20253185	2
#20253183	2
#20252517	2
C₄₇×#3105	2
#62151	47