Subgroups — #27100919

Order 12032.

1820 conjugacy classes of subgroups.

The subgroup lattice has 1144 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20257437	C₂	1	1	yes	maximal, characteristic, complemented
2	#20257405	C₂	1	1	yes	maximal, characteristic, complemented
3	#20256374	C₂	1	1	yes	maximal, characteristic, complemented
4	SD₁₆×Dic₉₄	C₂	1	1	yes	maximal, characteristic, complemented
5	#20256126	C₂	1	1	yes	maximal, characteristic, complemented
6	#20256104	C₂	1	1	yes	maximal, characteristic, complemented
7	#20255999	C₂	1	2	yes	maximal, complemented
8	#20255985	C₂	1	1	yes	maximal, characteristic, complemented
9	#20255500	C₂	1	2	yes	maximal, complemented
10	#20255425	C₂	1	2	yes	maximal, complemented
11	#20255318	C₂	1	1	yes	maximal, characteristic, complemented
12	#20255255	C₂	1	1	yes	maximal, characteristic, complemented
13	#20255035	C₂	1	1	yes	maximal, characteristic, complemented
14	#20255019	C₂	1	2	yes	maximal, complemented
15	#20254133	C₂	1	1	yes	maximal, characteristic, complemented
16	#20254003	C₂	1	2	yes	maximal, complemented
17	#20253669	C₂	1	2	yes	maximal, complemented
18	#20253615	C₂	1	2	yes	maximal, complemented
19	#20253459	C₂	1	1	yes	maximal, characteristic, complemented
20	#20253396	C₂	1	1	yes	maximal, characteristic, complemented
21	#20252392	C₂	1	1	yes	maximal, characteristic, complemented
22	#20252228	C₂	1	2	yes	maximal, complemented
23	C₄×AGL(1,ℤ/8)×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#13094053	C₂²	1	2	yes	—
25	Q₈×Dic₉₄	C₂²	1	1	yes	characteristic, complemented
26	#15689843	—	2	1	no	—
27	#15689843	C₂²	1	1	yes	characteristic
28	#15689843	C₂²	1	1	yes	characteristic, complemented
29	#15689841	—	2	2	no	—
30	#15689841	C₂²	1	2	yes	—
31	#15689838	—	2	1	no	—
32	#15689838	C₂²	1	1	yes	characteristic, complemented
33	#15689828	C₂²	1	2	yes	—
34	#15689813	—	2	1	no	—
35	#15689799	—	2	2	no	—
36	Q₈×D₁₈₈	C₂²	1	1	yes	characteristic, complemented
37	D₄×Dic₉₄	C₂²	1	1	yes	characteristic
38	#15689782	—	2	1	no	—
39	#15689780	C₂²	1	2	yes	—
40	#15689778	C₂²	1	1	yes	characteristic
41	#15689777	C₂²	1	1	yes	characteristic
42	#15689767	C₂²	1	2	yes	—
43	#15689738	—	2	2	no	—
44	#15689738	C₂²	1	2	yes	—
45	#15689738	C₂²	1	2	yes	complemented
46	#15689715	—	2	2	no	—
47	#15689680	—	2	1	no	—
48	#15689680	C₂²	1	1	yes	characteristic
49	#15689680	C₂²	1	1	yes	characteristic
50	#15689657	—	2	1	no	—
51	#15689657	C₂²	1	1	yes	characteristic
52	#15689634	—	2	1	no	—
53	C₂×#13094003	—	2	1	no	—
54	#15689602	C₂²	1	2	yes	—
55	#15689599	C₂²	1	2	yes	complemented
56	#15689521	C₂²	1	1	yes	characteristic, complemented
57	#15689520	C₂²	1	2	yes	complemented
58	#15689506	C₂²	1	2	yes	—
59	#15689503	C₂²	1	1	yes	characteristic, complemented
60	#15689481	C₂²	1	2	yes	—
61	#15689481	C₂²	1	2	yes	complemented
62	#15689474	C₂²	1	1	yes	characteristic, complemented
63	#15689474	C₂²	1	1	yes	characteristic, complemented
64	#15689466	C₂²	1	2	yes	complemented
65	#15689464	C₂²	1	2	yes	—
66	#15689455	C₂²	1	2	yes	complemented
67	#15689453	C₂²	1	2	yes	—
68	#15689446	C₂²	1	2	yes	—
69	#15689440	C₂²	1	2	yes	complemented
70	#15689417	C₂²	1	2	yes	complemented
71	#15689413	C₂²	1	1	yes	characteristic
72	#15689413	C₂²	1	1	yes	characteristic
73	#15689411	C₂²	1	2	yes	—
74	#15689408	C₂²	1	1	yes	characteristic, complemented
75	#15689407	C₂²	1	2	yes	complemented
76	#15689406	C₂²	1	2	yes	complemented
77	#15689403	C₂²	1	1	yes	characteristic, complemented
78	#15689382	C₂²	1	2	yes	complemented
79	#15689381	C₂²	1	2	yes	—
80	#15689381	C₂²	1	2	yes	—
81	#15689373	C₂²	1	2	yes	—
82	#15689351	C₂²	1	2	yes	—
83	#15689351	C₂²	1	2	yes	complemented
84	#15689344	C₂²	1	2	yes	—
85	#15689344	C₂²	1	2	yes	complemented
86	#15689343	C₂²	1	2	yes	—
87	#15689336	C₂²	1	2	yes	—
88	#15689333	C₂²	1	1	yes	characteristic, complemented
89	#15689328	C₂²	1	1	yes	characteristic
90	#15689328	C₂²	1	1	yes	characteristic
91	#15689328	C₂²	1	1	yes	characteristic, complemented
92	#15689286	C₂²	1	2	yes	—
93	#15689285	C₂²	1	2	yes	—
94	#15689280	C₂²	1	2	yes	complemented
95	#15689274	C₂²	1	2	yes	—
96	#15689265	C₂²	1	2	yes	—
97	#15689260	C₂²	1	2	yes	—
98	#15689253	C₂²	1	1	yes	characteristic, complemented
99	C₈×Dic₉₄	C₂²	1	1	yes	characteristic, complemented
100	#15689231	C₂²	1	2	yes	complemented
101	#15689231	C₂²	1	2	yes	complemented
102	#15689227	C₂²	1	2	yes	complemented
103	#15689220	C₂²	1	2	yes	—
104	#15689217	C₂²	1	2	yes	complemented
105	C₄×#10625337	C₂²	1	2	yes	complemented
106	SD₁₆×Dic₄₇	C₂²	1	2	yes	—
107	C₄×#10625335	C₂²	1	2	yes	—
108	C₄×#10625335	C₂²	1	2	yes	—
109	C₄×#10625335	C₂²	1	2	yes	complemented
110	#15689202	C₂²	1	1	yes	characteristic, complemented
111	#15689199	C₂²	1	2	yes	—
112	#15689192	C₂²	1	2	yes	—
113	C₈×D₁₈₈	C₂²	1	1	yes	characteristic, complemented
114	#15689185	C₂²	1	2	yes	complemented
115	#15689176	C₂²	1	1	yes	characteristic
116	#15689164	C₂²	1	2	yes	complemented
117	#15689116	C₂²	1	2	yes	—
118	#103×D₄₇	C₂²	1	2	yes	complemented
119	#15689080	C₂²	1	2	yes	complemented
120	C₂×AGL(1,ℤ/8)×C₄₇	C₂²	1	1	yes	characteristic
121	C₄×#41×C₄₇	C₂²	1	1	yes	characteristic
122	C₂×C₄×D₄×C₄₇	C₂²	1	1	yes	characteristic
123	C₄₇×#442	C₂²	1	1	yes	characteristic
124	C₄₇×#442	C₂²	1	1	yes	characteristic
125	C₄₇×#440	C₂²	1	1	yes	characteristic
126	C₄₇×#440	C₂²	1	1	yes	characteristic
127	C₄×SD₁₆×C₄₇	C₂²	1	1	yes	characteristic
128	C₄×SD₁₆×C₄₇	C₂²	1	1	yes	characteristic
129	C₄×D₈×C₄₇	C₂²	1	1	yes	characteristic
130	C₄×D₈×C₄₇	C₂²	1	1	yes	characteristic
131	C₄₇×#428	C₂²	1	1	yes	characteristic
132	C₄₇×#418	C₂²	1	1	yes	characteristic
133	C₄₇×#417	C₂²	1	1	yes	characteristic
134	C₄×M₁₆×C₄₇	C₂²	1	1	yes	characteristic
135	C₂×#10625350	—	2	1	no	—
136	C₂×#10625352	C₂³	1	2	yes	—
137	C₂²×Dic₉₄	—	2	1	no	—
138	C₂×Q₈×D₄₇	C₂³	1	2	yes	—
139	#13094053	—	2	8	no	—
140	C₂×Dic₁₈₈	C₂³	1	2	yes	—
141	C₂×Dic₁₈₈	C₂³	1	2	yes	—
142	C₂×#10625337	C₂³	1	2	yes	—
143	C₂×#10625335	C₂³	1	2	yes	—
144	C₂×#10625335	C₂³	1	2	yes	—
145	C₂×#10625335	C₂³	1	2	yes	—
146	C₂×#10625324	C₂³	1	2	yes	—
147	C₂×C₈×D₄₇	C₂³	1	2	yes	—
148	#13094024	—	2	1	no	—
149	#13094024	—	2	1	no	—
150	#13094024	C₂³	1	1	yes	characteristic
151	#13094024	C₂³	1	1	yes	characteristic
152	#13094024	C₂³	1	1	yes	characteristic
153	#13094024	C₂³	1	1	yes	characteristic
154	#13094023	—	2	2	no	—
155	#13094023	C₂³	1	2	yes	—
156	#13094023	C₂³	1	2	yes	—
157	#13094018	—	2	2	no	—
158	#13094018	D₄	1	2	yes	—
159	#13094017	—	2	2	no	—
160	#13094017	—	2	2	no	—
161	#13094017	—	2	2	no	—
162	#13094017	—	2	2	no	—
163	#13094017	—	2	2	no	—
164	#13094016	—	2	1	no	—
165	#13094016	—	2	1	no	—
166	#13094016	D₄	1	1	yes	characteristic
167	#13094014	—	2	2	no	—
168	#13094012	D₄	1	1	yes	characteristic
169	#13094011	—	2	2	no	—
170	#13094011	C₂³	1	2	yes	—
171	#13094011	C₂³	1	2	yes	—
172	#13094010	—	2	2	no	—
173	#13094010	—	2	2	no	—
174	#13094010	—	2	2	no	—
175	#13094010	—	2	2	no	—
176	#13094008	—	2	2	no	—
177	#13094007	—	2	2	no	—
178	#13094007	—	2	2	no	—
179	#13094007	D₄	1	2	yes	—
180	#13094006	—	2	2	no	—
181	#13094005	—	2	2	no	—
182	#13094004	—	2	2	no	—
183	#13094004	C₂³	1	2	yes	—
184	#13094004	C₂³	1	2	yes	—
185	#13094003	—	2	1	no	—
186	#13094003	—	2	1	no	—
187	#13094003	—	2	1	no	—
188	#13094003	—	2	1	no	—
189	#13094003	—	2	2	no	—
190	#13094003	—	2	1	no	—
191	#13094003	—	2	1	no	—
192	#13094003	—	2	2	no	—
193	#13094003	—	2	2	no	—
194	#13094003	—	2	2	no	—
195	#13094003	D₄	1	1	yes	characteristic
196	#13094003	C₂³	1	2	yes	—
197	#13094003	C₂³	1	2	yes	—
198	#13094002	—	2	2	no	—
199	#13094001	—	2	2	no	—
200	#13093998	—	2	1	no	—
201	#13093998	—	2	1	no	—
202	#13093998	D₄	1	1	yes	characteristic
203	#13093996	—	2	2	no	—
204	#13093995	—	2	2	no	—
205	#13093995	C₂³	1	2	yes	—
206	#13093995	C₂³	1	2	yes	—
207	#13093993	—	2	2	no	—
208	Q₈×Dic₄₇	C₂³	1	2	yes	—
209	C₄×Dic₉₄	—	2	1	no	—
210	C₄×Dic₉₄	—	2	1	no	—
211	C₄×Dic₉₄	—	2	1	no	—
212	C₄×Dic₉₄	—	2	2	no	—
213	C₄×Dic₉₄	—	2	2	no	—
214	C₄×Dic₉₄	C₂³	1	2	yes	—
215	C₄×Dic₉₄	C₂³	1	2	yes	—
216	C₄×Dic₉₄	C₂³	1	1	yes	characteristic
217	#13093989	—	2	2	no	—
218	#13093989	C₂³	1	2	yes	—
219	#13093989	C₂³	1	2	yes	—
220	C₄×D₁₈₈	—	2	1	no	—
221	C₄×D₁₈₈	C₂³	1	1	yes	characteristic
222	D₄×Dic₄₇	C₂³	1	2	yes	—
223	C₄×C₂²⋊D₄₇	—	2	2	no	—
224	C₄×C₂²⋊D₄₇	—	2	2	no	—
225	C₄×C₂²⋊D₄₇	—	2	2	no	—
226	C₄×C₂²⋊D₄₇	C₂³	1	2	yes	—
227	(C₂²⋊D₄₇)⋊C₄	—	2	2	no	—
228	#13093983	—	2	1	no	—
229	#13093983	—	2	1	no	—
230	#13093983	—	2	1	no	—
231	#13093983	—	2	1	no	—
232	#13093983	—	2	1	no	—
233	#13093982	—	2	2	no	—
234	#13093982	C₂³	1	2	yes	—
235	#13093981	—	2	2	no	—
236	#13093981	C₂³	1	2	yes	—
237	#13093980	—	2	2	no	—
238	C₂×C₄⋊Dic₄₇	—	2	1	no	—
239	C₂×Dic₄₇⋊C₄	—	2	2	no	—
240	C₄⋊C₄×D₄₇	C₂³	1	2	yes	—
241	C₂×C₂²⋊Dic₄₇	—	2	2	no	—
242	#13093957	C₂³	1	2	yes	—
243	#13093956	C₂³	1	2	yes	—
244	#13093956	C₂³	1	2	yes	—
245	#13093955	C₂³	1	2	yes	—
246	#13093955	C₂³	1	2	yes	—
247	#13093955	C₂³	1	2	yes	—
248	C₄⋊(C₄₇⋊C₈)	C₂³	1	1	yes	characteristic
249	C₄⋊(C₄₇⋊C₈)	C₂³	1	1	yes	characteristic
250	Dic₄₇⋊C₈	C₂³	1	2	yes	—
251	Dic₄₇⋊C₈	C₂³	1	2	yes	—
252	#13093949	C₂³	1	2	yes	—
253	#13093949	C₂³	1	2	yes	—
254	#13093949	C₂³	1	2	yes	—
255	#13093949	C₂³	1	2	yes	—
256	#13093948	C₂³	1	2	yes	—
257	#13093947	C₂³	1	2	yes	—
258	#13093947	C₂³	1	2	yes	—
259	#13093947	C₂³	1	2	yes	—
260	#13093947	C₂³	1	2	yes	—
261	#13093945	C₂³	1	2	yes	—
262	#13093945	C₂³	1	2	yes	—
263	#13093945	C₂³	1	2	yes	—
264	C₂²⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
265	(C₂×D₄₇)⋊C₈	C₂³	1	2	yes	—
266	(C₂×D₄₇)⋊C₈	C₂³	1	2	yes	—
267	#13093934	C₂³	1	2	yes	—
268	C₄×C₄₇⋊C₈	C₂³	1	2	yes	—
269	C₈×Dic₄₇	C₂³	1	2	yes	—
270	C₂×#41×C₄₇	C₂³	1	1	yes	characteristic
271	C₂²×D₄×C₄₇	C₂³	1	1	yes	characteristic
272	C₂³×C₄×C₄₇	—	2	1	no	—
273	AGL(1,ℤ/8)×C₄₇	—	2	4	no	—
274	C₂×SD₁₆×C₄₇	C₂³	1	1	yes	characteristic
275	C₂×SD₁₆×C₄₇	C₂³	1	1	yes	characteristic
276	C₂×D₈×C₄₇	C₂³	1	1	yes	characteristic
277	C₂×D₈×C₄₇	C₂³	1	1	yes	characteristic
278	C₂×M₁₆×C₄₇	C₂³	1	1	yes	characteristic
279	C₂×M₁₆×C₄₇	C₂³	1	1	yes	characteristic
280	C₄×Q₈×C₄₇	C₂³	1	1	yes	characteristic
281	C₄×Q₈×C₄₇	C₂³	1	1	yes	characteristic
282	C₄×D₄×C₄₇	—	2	1	no	—
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	C₄×D₄×C₄₇	C₂³	1	1	yes	characteristic
292	#117×C₄₇	—	2	1	no	—
293	#117×C₄₇	C₂³	1	1	yes	characteristic
294	C₂×C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
295	C₂×C₂²⋊C₄×C₄₇	—	2	1	no	—
296	C₂×C₄²×C₄₇	—	2	1	no	—
297	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
298	#107×C₄₇	C₂³	1	1	yes	characteristic
299	#107×C₄₇	C₂³	1	1	yes	characteristic
300	#106×C₄₇	C₂³	1	1	yes	characteristic
301	#106×C₄₇	C₂³	1	1	yes	characteristic
302	#103×C₄₇	C₂³	1	1	yes	characteristic
303	#103×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	#102×C₄₇	C₂³	1	1	yes	characteristic
310	#97×C₄₇	C₂³	1	1	yes	characteristic
311	#97×C₄₇	C₂³	1	1	yes	characteristic
312	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
313	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
314	C₂⁴×C₄₇	—	2	1	no	—
315	#41×C₄₇	—	2	2	no	—
316	#41×C₄₇	—	4	1	no	—
317	C₂×Q₈×C₄₇	C₂⁴	1	1	yes	characteristic
318	C₂×D₄×C₄₇	—	2	2	no	—
319	C₂×D₄×C₄₇	—	2	1	no	—
320	C₂×D₄×C₄₇	—	2	1	no	—
321	C₂×D₄×C₄₇	—	4	1	no	—
322	C₂×D₄×C₄₇	C₂⁴	1	1	yes	characteristic
323	C₂×D₄×C₄₇	C₂⁴	1	1	yes	characteristic
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	1	no	—
331	C₂²×C₄×C₄₇	—	2	1	no	—
332	C₂²×C₄×C₄₇	—	2	1	no	—
333	C₂²×C₄×C₄₇	—	8	2	no	—
334	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
335	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
336	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
337	C₂×C₂²⋊D₄₇	—	2	2	no	—
338	C₂×C₂²⋊D₄₇	—	2	2	no	—
339	C₂×C₂²⋊D₄₇	—	2	2	no	—
340	C₂×C₂²⋊D₄₇	C₂×D₄	1	2	yes	—
341	C₂²×Dic₄₇	—	2	2	no	—
342	C₂²×Dic₄₇	—	2	2	no	—
343	Q₈×D₄₇	—	2	4	no	—
344	Q₈×D₄₇	—	4	2	no	—
345	#10625352	—	2	4	no	—
346	#10625352	—	4	2	no	—
347	#10625350	—	8	2	no	—
348	C₂×D₁₈₈	C₂×D₄	1	1	yes	characteristic
349	C₂×C₄×D₄₇	—	2	2	no	—
350	C₂×C₄×D₄₇	—	2	2	no	—
351	C₂×C₄×D₄₇	C₂⁴	1	2	yes	—
352	C₂×Dic₉₄	—	2	1	no	—
353	C₂×Dic₉₄	—	2	2	no	—
354	C₂×Dic₉₄	—	2	1	no	—
355	C₂×Dic₉₄	—	2	2	no	—
356	C₂×Dic₉₄	—	2	2	no	—
357	C₂×Dic₉₄	—	8	2	no	—
358	C₂×Dic₉₄	C₂×D₄	1	1	yes	characteristic
359	C₂×Dic₉₄	C₂⁴	1	2	yes	—
360	C₂×Dic₉₄	C₂⁴	1	2	yes	—
361	SD₁₆×C₄₇	—	2	2	no	—
362	SD₁₆×C₄₇	#41	1	4	yes	complemented
363	D₈×C₄₇	—	2	2	no	—
364	D₈×C₄₇	—	2	2	no	—
365	M₁₆×C₄₇	—	2	2	no	—
366	M₁₆×C₄₇	—	4	1	no	—
367	C₂×C₈×C₄₇	C₂⁴	1	1	yes	characteristic
368	C₂×C₈×C₄₇	C₂⁴	1	1	yes	characteristic
369	C₂×C₈×C₄₇	C₂⁴	1	1	yes	characteristic
370	C₂×C₈×C₄₇	C₂⁴	1	1	yes	characteristic
371	C₄⋊C₄×C₄₇	—	2	1	no	—
372	C₄⋊C₄×C₄₇	—	2	1	no	—
373	C₄⋊C₄×C₄₇	—	2	1	no	—
374	C₄⋊C₄×C₄₇	C₂⁴	1	1	yes	characteristic
375	C₄⋊C₄×C₄₇	C₂⁴	1	1	yes	characteristic
376	C₄⋊C₄×C₄₇	C₂⁴	1	1	yes	characteristic
377	C₄⋊C₄×C₄₇	C₂⁴	1	1	yes	characteristic
378	C₂²⋊C₄×C₄₇	—	2	1	no	—
379	C₂²⋊C₄×C₄₇	—	2	1	no	—
380	C₂²⋊C₄×C₄₇	—	2	1	no	—
381	C₂²⋊C₄×C₄₇	—	2	1	no	—
382	C₂²⋊C₄×C₄₇	—	2	1	no	—
383	C₂²⋊C₄×C₄₇	—	2	1	no	—
384	C₂²⋊C₄×C₄₇	—	2	1	no	—
385	C₄²×C₄₇	—	2	1	no	—
386	C₄²×C₄₇	—	2	1	no	—
387	C₄²×C₄₇	—	2	1	no	—
388	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
389	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
390	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
391	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
392	C₂²⋊Dic₄₇	—	2	2	no	—
393	C₂²⋊Dic₄₇	—	2	2	no	—
394	C₂²⋊Dic₄₇	—	2	2	no	—
395	C₂²⋊Dic₄₇	—	2	2	no	—
396	C₂²⋊Dic₄₇	—	2	2	no	—
397	C₂²⋊Dic₄₇	—	2	2	no	—
398	C₂²⋊Dic₄₇	—	2	2	no	—
399	C₂²⋊Dic₄₇	—	2	2	no	—
400	C₂²⋊Dic₄₇	—	2	2	no	—
401	C₂²⋊Dic₄₇	C₂×D₄	1	2	yes	—
402	#10625337	—	2	4	no	—
403	#10625335	—	2	4	no	—
404	#10625335	—	4	2	no	—
405	#10625335	—	4	2	no	—
406	(C₂×D₄₇)⋊C₄	—	2	2	no	—
407	(C₂×D₄₇)⋊C₄	—	2	2	no	—
408	(C₂×D₄₇)⋊C₄	—	2	2	no	—
409	(C₂×D₄₇)⋊C₄	C₂×D₄	1	2	yes	—
410	(C₂×D₄₇)⋊C₄	C₂×D₄	1	2	yes	—
411	(C₂×D₄₇)⋊C₄	C₂×D₄	1	2	yes	—
412	(C₂×D₄₇)⋊C₄	C₂×D₄	1	2	yes	—
413	C₄⋊Dic₄₇	—	2	1	no	—
414	C₄⋊Dic₄₇	—	2	1	no	—
415	C₄⋊Dic₄₇	—	2	1	no	—
416	C₄⋊Dic₄₇	—	2	1	no	—
417	C₄⋊Dic₄₇	—	2	1	no	—
418	C₄⋊Dic₄₇	—	2	1	no	—
419	C₄⋊Dic₄₇	—	2	2	no	—
420	C₄⋊Dic₄₇	—	2	2	no	—
421	C₄⋊Dic₄₇	—	2	2	no	—
422	C₄⋊Dic₄₇	C₂×D₄	1	1	yes	characteristic
423	C₄⋊Dic₄₇	C₂×D₄	1	1	yes	characteristic
424	C₄⋊Dic₄₇	C₂⁴	1	2	yes	—
425	C₄⋊Dic₄₇	C₂⁴	1	2	yes	—
426	Dic₄₇⋊C₄	—	2	2	no	—
427	Dic₄₇⋊C₄	—	2	2	no	—
428	Dic₄₇⋊C₄	—	2	2	no	—
429	Dic₄₇⋊C₄	—	2	2	no	—
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	C₂×D₄	1	2	yes	—
436	Dic₄₇⋊C₄	C₂×D₄	1	2	yes	—
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	—	2	2	no	—
444	C₄×Dic₄₇	—	2	2	no	—
445	C₄×Dic₄₇	C₂⁴	1	2	yes	—
446	C₂×C₄₇⋊C₈	C₂⁴	1	2	yes	—
447	C₂×C₄₇⋊C₈	C₂⁴	1	2	yes	—
448	Dic₁₈₈	—	2	4	no	—
449	Dic₁₈₈	—	4	2	no	—
450	#10625324	—	2	4	no	—
451	C₈×D₄₇	—	4	2	no	—
452	C₂³×C₄₇	—	2	1	no	—
453	C₂³×C₄₇	—	2	1	no	—
454	C₂³×C₄₇	—	2	1	no	—
455	C₂³×C₄₇	—	4	2	no	—
456	C₂³×C₄₇	—	4	2	no	—
457	C₂³×C₄₇	—	8	1	no	—
458	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
459	C₂²×D₄₇	C₂²×D₄	1	2	yes	—
460	Q₈×C₄₇	—	2	1	no	—
461	Q₈×C₄₇	C₂×#41	1	2	yes	—
462	D₄×C₄₇	—	2	1	no	—
463	D₄×C₄₇	—	2	1	no	—
464	D₄×C₄₇	—	2	1	no	—
465	D₄×C₄₇	—	2	1	no	—
466	D₄×C₄₇	—	2	1	no	—
467	D₄×C₄₇	—	4	2	no	—
468	D₄×C₄₇	—	4	2	no	—
469	D₄×C₄₇	C₂×#41	1	2	yes	—
470	C₂×C₄×C₄₇	—	2	1	no	—
471	C₂×C₄×C₄₇	—	2	2	no	—
472	C₂×C₄×C₄₇	—	2	1	no	—
473	C₂×C₄×C₄₇	—	2	1	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	—	4	1	no	—
479	C₂×C₄×C₄₇	—	4	2	no	—
480	C₂×C₄×C₄₇	—	4	2	no	—
481	C₂×C₄×C₄₇	—	4	2	no	—
482	C₂×C₄×C₄₇	—	4	2	no	—
483	C₂×C₄×C₄₇	—	8	1	no	—
484	C₂×C₄×C₄₇	—	8	1	no	—
485	C₂×C₄×C₄₇	—	8	1	no	—
486	C₂×C₄×C₄₇	—	8	1	no	—
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	C₂⁵	1	1	yes	characteristic
493	C₂²⋊D₄₇	—	4	2	no	—
494	C₂²⋊D₄₇	—	4	4	no	—
495	C₂²⋊D₄₇	—	8	2	no	—
496	C₂²⋊D₄₇	—	8	2	no	—
497	C₂×Dic₄₇	—	2	2	no	—
498	C₂×Dic₄₇	—	2	2	no	—
499	C₂×Dic₄₇	—	2	2	no	—
500	C₂×Dic₄₇	—	2	2	no	—
501	C₂×Dic₄₇	—	4	4	no	—
502	C₂×Dic₄₇	—	8	2	no	—
503	C₂×Dic₄₇	C₂²×D₄	1	2	yes	—
504	C₂×Dic₄₇	C₂²×D₄	1	2	yes	—
505	C₂×Dic₄₇	C₂²×D₄	1	2	yes	—
506	D₁₈₈	—	2	2	no	—
507	C₄×D₄₇	—	2	2	no	—
508	C₄×D₄₇	—	2	2	no	—
509	C₄×D₄₇	—	4	4	no	—
510	C₄×D₄₇	—	8	2	no	—
511	Dic₉₄	—	2	2	no	—
512	Dic₉₄	—	2	2	no	—
513	Dic₉₄	—	2	2	no	—
514	Dic₉₄	—	2	2	no	—
515	Dic₉₄	—	2	2	no	—
516	Dic₉₄	—	4	4	no	—
517	Dic₉₄	—	4	2	no	—
518	Dic₉₄	—	8	2	no	—
519	Dic₉₄	—	8	2	no	—
520	Dic₉₄	—	8	1	no	—
521	C₈×C₄₇	—	2	1	no	—
522	C₈×C₄₇	—	2	1	no	—
523	C₈×C₄₇	—	2	1	no	—
524	C₈×C₄₇	C₂×#41	1	2	yes	—
525	C₄₇⋊C₈	—	2	2	no	—
526	C₄₇⋊C₈	—	2	2	no	—
527	#61557	—	47	1	no	maximal, Sylow
528	C₂²×C₄₇	—	2	1	no	—
529	C₂²×C₄₇	—	2	2	no	—
530	C₂²×C₄₇	—	2	1	no	—
531	C₂²×C₄₇	—	2	1	no	—
532	C₂²×C₄₇	—	4	1	no	—
533	C₂²×C₄₇	—	4	1	no	—
534	C₂²×C₄₇	—	4	1	no	—
535	C₂²×C₄₇	—	4	1	no	—
536	C₂²×C₄₇	—	4	1	no	—
537	C₂²×C₄₇	—	4	1	no	—
538	C₂²×C₄₇	—	4	1	no	—
539	C₂²×C₄₇	—	4	1	no	—
540	C₂²×C₄₇	—	8	4	no	—
541	C₂²×C₄₇	C₂³×D₄	1	1	yes	characteristic
542	C₂×D₄₇	—	2	2	no	—
543	C₂×D₄₇	—	2	2	no	—
544	C₂×D₄₇	—	2	2	no	—
545	C₄×C₄₇	—	2	1	no	—
546	C₄×C₄₇	—	2	1	no	—
547	C₄×C₄₇	—	2	2	no	—
548	C₄×C₄₇	—	2	1	no	—
549	C₄×C₄₇	—	2	1	no	—
550	C₄×C₄₇	—	4	1	no	—
551	C₄×C₄₇	—	4	1	no	—
552	C₄×C₄₇	—	4	1	no	—
553	C₄×C₄₇	—	4	1	no	—
554	C₄×C₄₇	#577	1	2	yes	—
555	C₄×C₄₇	C₂²×#41	1	1	yes	characteristic
556	C₄×C₄₇	#585	1	1	yes	characteristic
557	Dic₄₇	—	2	2	no	—
558	Dic₄₇	—	2	2	no	—
559	Dic₄₇	—	2	2	no	—
560	Dic₄₇	—	4	2	no	—
561	Dic₄₇	—	4	2	no	—
562	Dic₄₇	—	4	2	no	—
563	Dic₄₇	—	4	2	no	—
564	#3520	—	47	1	no	—
565	#3518	—	47	1	no	—
566	#3393	—	47	1	no	—
567	Q₈×SD₁₆	—	47	1	no	—
568	#3369	—	47	1	no	—
569	#3367	—	47	1	no	—
570	#3356	—	47	2	no	—
571	#3354	—	47	1	no	—
572	#3316	—	47	2	no	—
573	#3311	—	47	2	no	—
574	#3303	—	47	1	no	—
575	#3298	—	47	1	no	—
576	#3276	—	47	1	no	—
577	#3275	—	47	2	no	—
578	#3185	—	47	1	no	—
579	#3173	—	47	2	no	—
580	#3125	—	47	2	no	—
581	#3121	—	47	2	no	—
582	#3107	—	47	1	no	—
583	#3101	—	47	1	no	—
584	#2969	—	47	1	no	—
585	#2947	—	47	2	no	—
586	C₄×AGL(1,ℤ/8)	D₄₇	1	1	yes	characteristic, complemented
587	C₂×C₄₇	—	4	1	no	—
588	C₂×C₄₇	—	4	2	no	—
589	C₂×C₄₇	—	8	1	no	—
590	C₂×C₄₇	—	8	1	no	—
591	C₂×C₄₇	D₄×#41	1	1	yes	characteristic
592	C₂×C₄₇	C₂×#577	1	1	yes	characteristic
593	C₂×C₄₇	#3586	1	1	yes	characteristic
594	D₄₇	—	4	2	no	—
595	C₂×#137	—	47	2	no	—
596	C₂×AGL(1,ℤ/8)	C₂×D₄₇	1	1	yes	characteristic
597	Q₈²	—	47	1	no	—
598	#556	—	47	2	no	—
599	#556	—	47	1	no	—
600	#556	—	47	1	no	—
601	#556	—	94	2	no	—
602	#556	—	94	1	no	—
603	#555	—	47	1	no	—
604	#555	—	94	1	no	—
605	#554	—	47	2	no	—
606	#552	—	94	1	no	—
607	#551	—	94	2	no	—
608	D₄×Q₈	—	47	1	no	—
609	D₄×Q₈	—	47	1	no	—
610	#548	—	47	2	no	—
611	#548	—	94	1	no	—
612	#547	—	47	1	no	—
613	#547	—	47	1	no	—
614	#546	—	47	2	no	—
615	#542	—	47	2	no	—
616	#542	—	47	2	no	—
617	#542	—	94	2	no	—
618	#539	—	94	2	no	—
619	#533	—	47	1	no	—
620	#533	—	47	1	no	—
621	#533	—	94	1	no	—
622	#529	—	47	1	no	—
623	#529	—	94	1	no	—
624	#525	—	94	1	no	—
625	C₂×C₂²⋊Q₈	—	94	1	no	—
626	#520	—	47	2	no	—
627	#519	—	47	2	no	—
628	C₄×#41	C₂×D₄₇	1	1	yes	characteristic
629	C₂×C₄×D₄	C₂×D₄₇	1	1	yes	characteristic
630	#498	—	47	2	no	—
631	#498	—	47	1	no	—
632	#495	—	47	2	no	—
633	#494	—	47	1	no	—
634	#489	—	47	2	no	—
635	#489	—	47	2	no	—
636	#487	—	47	1	no	—
637	#487	—	47	1	no	—
638	#485	—	47	2	no	—
639	#485	—	47	2	no	—
640	#483	—	47	2	no	—
641	#483	—	47	2	no	—
642	#482	—	47	2	no	—
643	#481	—	47	2	no	—
644	#477	—	47	2	no	—
645	#476	—	47	1	no	—
646	#476	—	47	1	no	—
647	#476	—	47	2	no	—
648	#475	—	47	1	no	—
649	#475	—	47	2	no	—
650	#475	—	47	2	no	—
651	#474	—	47	1	no	—
652	#470	—	47	2	no	—
653	#470	—	47	2	no	—
654	#470	—	47	2	no	—
655	#469	—	47	2	no	—
656	#465	—	47	2	no	—
657	#465	—	47	2	no	—
658	#464	—	47	2	no	—
659	#464	—	47	2	no	—
660	#464	—	47	2	no	—
661	#463	—	47	2	no	—
662	#462	—	47	1	no	—
663	#461	—	47	1	no	—
664	#461	—	47	1	no	—
665	#461	—	47	1	no	—
666	#452	—	47	2	no	—
667	#452	—	47	2	no	—
668	#451	—	47	2	no	—
669	#450	—	47	2	no	—
670	#449	—	47	2	no	—
671	#448	—	47	2	no	—
672	#446	—	47	1	no	—
673	C₈×Q₈	—	47	1	no	—
674	#442	C₂×D₄₇	1	1	yes	characteristic
675	#442	C₂×D₄₇	1	1	yes	characteristic
676	#441	—	47	2	no	—
677	#441	—	47	2	no	—
678	#441	—	47	2	no	—
679	#440	—	47	2	no	—
680	#440	C₂×D₄₇	1	1	yes	characteristic
681	#440	C₂×D₄₇	1	1	yes	characteristic
682	C₄×Q₁₆	—	47	2	no	—
683	C₄×Q₁₆	—	47	2	no	—
684	C₄×SD₁₆	—	47	2	no	—
685	C₄×SD₁₆	—	47	2	no	—
686	C₄×SD₁₆	—	47	2	no	—
687	C₄×SD₁₆	—	47	2	no	—
688	C₄×SD₁₆	C₂×D₄₇	1	1	yes	characteristic
689	C₄×SD₁₆	C₂×D₄₇	1	1	yes	characteristic
690	C₄×D₈	C₂×D₄₇	1	1	yes	characteristic
691	C₄×D₈	C₂×D₄₇	1	1	yes	characteristic
692	#436	—	47	2	no	—
693	#436	—	47	1	no	—
694	#435	—	47	2	no	—
695	C₈×D₄	—	47	1	no	—
696	#433	—	47	2	no	—
697	#431	—	47	1	no	—
698	#428	—	47	2	no	—
699	#428	C₂×D₄₇	1	1	yes	characteristic
700	#418	C₂×D₄₇	1	1	yes	characteristic
701	#417	C₂×D₄₇	1	1	yes	characteristic
702	#416	—	47	2	no	—
703	C₂×#103	—	47	2	no	—
704	#405	—	47	2	no	—
705	C₄×M₁₆	C₂×D₄₇	1	1	yes	characteristic
706	C₄₇	#61557	1	1	yes	characteristic, complemented, Sylow
707	C₂×#41	—	47	2	no	—
708	C₂×#41	—	94	1	no	—
709	C₂×#41	C₂²×D₄₇	1	1	yes	characteristic
710	C₂²×Q₈	—	47	2	no	—
711	C₂²×Q₈	—	94	1	no	—
712	C₂²×D₄	C₂²×D₄₇	1	1	yes	characteristic
713	C₂³×C₄	—	2	1	no	—
714	#137	—	94	8	no	—
715	AGL(1,ℤ/8)	—	2	4	no	—
716	C₂×Q₁₆	—	47	2	no	—
717	C₂×Q₁₆	—	47	2	no	—
718	C₂×Q₁₆	—	47	2	no	—
719	C₂×SD₁₆	—	47	2	no	—
720	C₂×SD₁₆	—	47	2	no	—
721	C₂×SD₁₆	—	47	2	no	—
722	C₂×SD₁₆	C₂²×D₄₇	1	1	yes	characteristic
723	C₂×SD₁₆	C₂²×D₄₇	1	1	yes	characteristic
724	C₂×D₈	C₂²×D₄₇	1	1	yes	characteristic
725	C₂×D₈	C₂²×D₄₇	1	1	yes	characteristic
726	C₂×M₁₆	—	47	2	no	—
727	C₂×M₁₆	C₂²×D₄₇	1	1	yes	characteristic
728	C₂×M₁₆	C₂²×D₄₇	1	1	yes	characteristic
729	C₂²×C₈	—	47	2	no	—
730	C₄⋊Q₈	—	47	2	no	—
731	C₄⋊Q₈	—	47	2	no	—
732	C₄⋊Q₈	—	47	1	no	—
733	C₄⋊Q₈	—	47	1	no	—
734	C₄⋊Q₈	—	47	1	no	—
735	C₄⋊Q₈	—	47	1	no	—
736	C₄⋊Q₈	—	94	1	no	—
737	C₄⋊Q₈	—	94	1	no	—
738	C₄⋊Q₈	—	94	2	no	—
739	#126	—	47	2	no	—
740	#126	—	94	2	no	—
741	#126	—	94	2	no	—
742	#126	—	94	2	no	—
743	#126	—	94	2	no	—
744	#126	—	94	2	no	—
745	#126	—	94	2	no	—
746	#125	—	47	1	no	—
747	#125	—	94	2	no	—
748	#125	—	94	1	no	—
749	#125	—	94	1	no	—
750	#124	—	47	2	no	—
751	#124	—	47	2	no	—
752	#124	—	47	1	no	—
753	#124	—	94	2	no	—
754	#124	—	94	2	no	—
755	#124	—	94	2	no	—
756	#124	—	94	2	no	—
757	#124	—	94	2	no	—
758	#123	—	47	2	no	—
759	#123	—	94	2	no	—
760	#123	—	94	2	no	—
761	#123	—	94	2	no	—
762	#123	—	94	2	no	—
763	#123	—	94	2	no	—
764	C₂²⋊Q₈	—	47	1	no	—
765	C₂²⋊Q₈	—	47	2	no	—
766	C₂²⋊Q₈	—	47	2	no	—
767	C₂²⋊Q₈	—	47	2	no	—
768	C₂²⋊Q₈	—	47	2	no	—
769	C₂²⋊Q₈	—	94	2	no	—
770	C₂²⋊Q₈	—	94	2	no	—
771	C₂²⋊Q₈	—	94	2	no	—
772	C₂²⋊Q₈	—	94	2	no	—
773	C₂²⋊Q₈	—	94	2	no	—
774	C₂²⋊Q₈	—	94	1	no	—
775	C₂²⋊Q₈	—	94	1	no	—
776	C₂²⋊Q₈	—	94	2	no	—
777	C₂²⋊Q₈	—	94	2	no	—
778	C₂²⋊Q₈	—	94	1	no	—
779	C₂²⋊Q₈	—	94	1	no	—
780	C₂²⋊Q₈	—	94	1	no	—
781	C₂²⋊Q₈	—	94	1	no	—
782	#121	—	47	1	no	—
783	#121	—	47	2	no	—
784	#121	—	47	2	no	—
785	#121	—	94	2	no	—
786	#121	—	94	1	no	—
787	#121	—	94	1	no	—
788	#121	—	94	2	no	—
789	#120	—	94	2	no	—
790	C₄×Q₈	—	47	1	no	—
791	C₄×Q₈	—	47	2	no	—
792	C₄×Q₈	—	47	2	no	—
793	C₄×Q₈	—	47	2	no	—
794	C₄×Q₈	—	47	2	no	—
795	C₄×Q₈	—	47	2	no	—
796	C₄×Q₈	—	94	2	no	—
797	C₄×Q₈	—	94	2	no	—
798	C₄×Q₈	—	94	1	no	—
799	C₄×Q₈	—	94	2	no	—
800	C₄×Q₈	—	94	1	no	—
801	C₄×Q₈	—	94	1	no	—
802	C₄×Q₈	C₂²×D₄₇	1	1	yes	characteristic
803	C₄×Q₈	C₂²×D₄₇	1	1	yes	characteristic
804	C₄×D₄	—	2	1	no	—
805	C₄×D₄	—	2	1	no	—
806	C₄×D₄	—	2	1	no	—
807	C₄×D₄	—	2	1	no	—
808	C₄×D₄	—	47	2	no	—
809	C₄×D₄	—	47	2	no	—
810	C₄×D₄	—	47	1	no	—
811	C₄×D₄	—	94	1	no	—
812	C₄×D₄	—	94	2	no	—
813	C₄×D₄	—	94	2	no	—
814	C₄×D₄	—	94	2	no	—
815	C₄×D₄	—	94	2	no	—
816	C₄×D₄	C₂²×D₄₇	1	1	yes	characteristic
817	C₄×D₄	C₂²×D₄₇	1	1	yes	characteristic
818	C₄×D₄	C₂²×D₄₇	1	1	yes	characteristic
819	C₄×D₄	C₂²×D₄₇	1	1	yes	characteristic
820	C₄×D₄	C₂²×D₄₇	1	1	yes	characteristic
821	C₄×D₄	C₂²×D₄₇	1	1	yes	characteristic
822	#117	—	2	1	no	—
823	#117	—	47	2	no	—
824	#117	—	47	2	no	—
825	#117	—	94	2	no	—
826	#117	—	94	2	no	—
827	#117	—	94	2	no	—
828	#117	—	94	1	no	—
829	#117	—	94	1	no	—
830	#117	—	94	1	no	—
831	#117	—	94	1	no	—
832	#117	—	94	1	no	—
833	#117	C₂²×D₄₇	1	1	yes	characteristic
834	C₂×C₄⋊C₄	—	47	2	no	—
835	C₂×C₄⋊C₄	—	94	2	no	—
836	C₂×C₄⋊C₄	—	94	1	no	—
837	C₂×C₄⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
838	C₂×C₂²⋊C₄	—	2	1	no	—
839	C₂×C₂²⋊C₄	—	94	2	no	—
840	C₂×C₄²	—	2	1	no	—
841	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
842	#107	—	47	2	no	—
843	#107	C₂²×D₄₇	1	1	yes	characteristic
844	#107	C₂²×D₄₇	1	1	yes	characteristic
845	#106	—	47	2	no	—
846	#106	—	47	2	no	—
847	#106	—	47	2	no	—
848	#106	—	47	2	no	—
849	#106	—	47	2	no	—
850	#106	C₂²×D₄₇	1	1	yes	characteristic
851	#106	C₂²×D₄₇	1	1	yes	characteristic
852	C₄⋊C₈	—	47	2	no	—
853	C₄⋊C₈	—	47	2	no	—
854	C₄⋊C₈	—	47	1	no	—
855	C₄⋊C₈	—	47	1	no	—
856	#103	—	47	2	no	—
857	#103	—	47	2	no	—
858	#103	—	47	2	no	—
859	#103	—	47	2	no	—
860	#103	—	47	2	no	—
861	#103	—	47	2	no	—
862	#103	—	47	2	no	—
863	#103	—	47	2	no	—
864	#103	—	47	2	no	—
865	#103	C₂²×D₄₇	1	1	yes	characteristic
866	#103	C₂²×D₄₇	1	1	yes	characteristic
867	#102	—	47	2	no	—
868	#102	—	47	2	no	—
869	#102	—	47	2	no	—
870	#102	C₂²×D₄₇	1	1	yes	characteristic
871	#102	C₂²×D₄₇	1	1	yes	characteristic
872	#102	C₂²×D₄₇	1	1	yes	characteristic
873	#102	C₂²×D₄₇	1	1	yes	characteristic
874	#102	C₂²×D₄₇	1	1	yes	characteristic
875	#102	C₂²×D₄₇	1	1	yes	characteristic
876	C₂²⋊C₈	—	47	2	no	—
877	C₂²⋊C₈	—	47	2	no	—
878	C₂²⋊C₈	—	47	2	no	—
879	#97	—	47	2	no	—
880	#97	C₂²×D₄₇	1	1	yes	characteristic
881	#97	C₂²×D₄₇	1	1	yes	characteristic
882	C₄×C₈	—	47	2	no	—
883	C₄×C₈	—	47	2	no	—
884	C₄×C₈	C₂²×D₄₇	1	1	yes	characteristic
885	C₄×C₈	C₂²×D₄₇	1	1	yes	characteristic
886	C₂⁴	—	2	1	no	—
887	#41	—	2	2	no	—
888	#41	—	4	1	no	—
889	#41	—	94	4	no	—
890	#41	—	376	2	no	—
891	#41	—	188	2	no	—
892	C₂×Q₈	—	47	1	no	—
893	C₂×Q₈	—	47	2	no	—
894	C₂×Q₈	—	47	2	no	—
895	C₂×Q₈	—	94	2	no	—
896	C₂×Q₈	—	94	2	no	—
897	C₂×Q₈	—	94	2	no	—
898	C₂×Q₈	—	94	1	no	—
899	C₂×Q₈	—	94	1	no	—
900	C₂×Q₈	—	94	4	no	—
901	C₂×Q₈	—	376	2	no	—
902	C₂×Q₈	—	188	2	no	—
903	C₂×Q₈	C₂³×D₄₇	1	1	yes	characteristic
904	C₂×D₄	—	2	2	no	—
905	C₂×D₄	—	2	1	no	—
906	C₂×D₄	—	2	1	no	—
907	C₂×D₄	—	4	1	no	—
908	C₂×D₄	—	47	2	no	—
909	C₂×D₄	—	47	1	no	—
910	C₂×D₄	—	94	2	no	—
911	C₂×D₄	—	94	2	no	—
912	C₂×D₄	—	94	2	no	—
913	C₂×D₄	C₂³×D₄₇	1	1	yes	characteristic
914	C₂×D₄	C₂³×D₄₇	1	1	yes	characteristic
915	C₂×D₄	C₂³×D₄₇	1	1	yes	characteristic
916	C₂²×C₄	—	2	1	no	—
917	C₂²×C₄	—	2	1	no	—
918	C₂²×C₄	—	2	1	no	—
919	C₂²×C₄	—	2	1	no	—
920	C₂²×C₄	—	2	1	no	—
921	C₂²×C₄	—	2	1	no	—
922	C₂²×C₄	—	2	1	no	—
923	C₂²×C₄	—	2	1	no	—
924	C₂²×C₄	—	8	2	no	—
925	C₂²×C₄	—	47	2	no	—
926	C₂²×C₄	—	94	2	no	—
927	C₂²×C₄	—	94	2	no	—
928	C₂²×C₄	—	94	2	no	—
929	C₂²×C₄	—	94	2	no	—
930	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
931	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
932	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
933	Q₁₆	—	94	4	no	—
934	Q₁₆	—	94	4	no	—
935	Q₁₆	—	188	2	no	—
936	SD₁₆	—	2	2	no	—
937	SD₁₆	—	94	4	no	—
938	SD₁₆	—	188	2	no	—
939	SD₁₆	—	188	2	no	—
940	SD₁₆	#10625350	1	4	yes	complemented
941	D₈	—	2	2	no	—
942	D₈	—	2	2	no	—
943	M₁₆	—	2	2	no	—
944	M₁₆	—	4	1	no	—
945	M₁₆	—	94	4	no	—
946	C₂×C₈	—	47	2	no	—
947	C₂×C₈	—	47	2	no	—
948	C₂×C₈	—	188	2	no	—
949	C₂×C₈	C₂³×D₄₇	1	1	yes	characteristic
950	C₂×C₈	C₂³×D₄₇	1	1	yes	characteristic
951	C₂×C₈	C₂³×D₄₇	1	1	yes	characteristic
952	C₂×C₈	C₂³×D₄₇	1	1	yes	characteristic
953	C₄⋊C₄	—	2	1	no	—
954	C₄⋊C₄	—	2	1	no	—
955	C₄⋊C₄	—	2	1	no	—
956	C₄⋊C₄	—	47	2	no	—
957	C₄⋊C₄	—	47	2	no	—
958	C₄⋊C₄	—	47	2	no	—
959	C₄⋊C₄	—	47	2	no	—
960	C₄⋊C₄	—	47	1	no	—
961	C₄⋊C₄	—	47	1	no	—
962	C₄⋊C₄	—	47	2	no	—
963	C₄⋊C₄	—	47	2	no	—
964	C₄⋊C₄	—	94	2	no	—
965	C₄⋊C₄	—	94	2	no	—
966	C₄⋊C₄	—	94	2	no	—
967	C₄⋊C₄	—	94	2	no	—
968	C₄⋊C₄	—	94	2	no	—
969	C₄⋊C₄	—	94	2	no	—
970	C₄⋊C₄	—	94	2	no	—
971	C₄⋊C₄	—	94	2	no	—
972	C₄⋊C₄	—	94	2	no	—
973	C₄⋊C₄	—	94	2	no	—
974	C₄⋊C₄	—	94	2	no	—
975	C₄⋊C₄	—	94	2	no	—
976	C₄⋊C₄	—	94	1	no	—
977	C₄⋊C₄	—	94	1	no	—
978	C₄⋊C₄	—	94	1	no	—
979	C₄⋊C₄	—	94	1	no	—
980	C₄⋊C₄	—	94	1	no	—
981	C₄⋊C₄	—	94	1	no	—
982	C₄⋊C₄	C₂³×D₄₇	1	1	yes	characteristic
983	C₄⋊C₄	C₂³×D₄₇	1	1	yes	characteristic
984	C₄⋊C₄	C₂³×D₄₇	1	1	yes	characteristic
985	C₄⋊C₄	C₂³×D₄₇	1	1	yes	characteristic
986	C₂²⋊C₄	—	2	1	no	—
987	C₂²⋊C₄	—	2	1	no	—
988	C₂²⋊C₄	—	2	1	no	—
989	C₂²⋊C₄	—	2	1	no	—
990	C₂²⋊C₄	—	2	1	no	—
991	C₂²⋊C₄	—	2	1	no	—
992	C₂²⋊C₄	—	2	1	no	—
993	C₂²⋊C₄	—	47	2	no	—
994	C₂²⋊C₄	—	47	2	no	—
995	C₂²⋊C₄	—	47	2	no	—
996	C₂²⋊C₄	—	47	2	no	—
997	C₂²⋊C₄	—	47	2	no	—
998	C₂²⋊C₄	—	94	2	no	—
999	C₂²⋊C₄	—	94	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	2	no	—
1007	C₂²⋊C₄	—	94	2	no	—
1008	C₂²⋊C₄	—	94	2	no	—
1009	C₂²⋊C₄	—	94	2	no	—
1010	C₄²	—	2	1	no	—
1011	C₄²	—	2	1	no	—
1012	C₄²	—	2	1	no	—
1013	C₄²	—	47	2	no	—
1014	C₄²	—	94	2	no	—
1015	C₄²	—	94	2	no	—
1016	C₄²	—	94	2	no	—
1017	C₄²	—	94	2	no	—
1018	C₄²	—	94	2	no	—
1019	C₄²	—	94	2	no	—
1020	C₄²	D₄×D₄₇	1	1	yes	characteristic
1021	C₄²	D₄×D₄₇	1	1	yes	characteristic
1022	C₄²	C₂³×D₄₇	1	1	yes	characteristic
1023	C₄²	C₂³×D₄₇	1	1	yes	characteristic
1024	C₂³	—	2	1	no	—
1025	C₂³	—	2	1	no	—
1026	C₂³	—	2	1	no	—
1027	C₂³	—	4	2	no	—
1028	C₂³	—	4	2	no	—
1029	C₂³	—	8	1	no	—
1030	C₂³	—	47	2	no	—
1031	C₂³	C₂×D₄×D₄₇	1	1	yes	characteristic
1032	Q₈	—	2	1	no	—
1033	Q₈	—	94	2	no	—
1034	Q₈	—	94	2	no	—
1035	Q₈	—	94	2	no	—
1036	Q₈	—	94	2	no	—
1037	Q₈	—	94	2	no	—
1038	Q₈	—	376	1	no	—
1039	Q₈	—	376	2	no	—
1040	Q₈	—	376	2	no	—
1041	Q₈	—	188	4	no	—
1042	Q₈	—	188	2	no	—
1043	Q₈	C₂×#10625350	1	2	yes	—
1044	D₄	—	2	1	no	—
1045	D₄	—	2	1	no	—
1046	D₄	—	2	1	no	—
1047	D₄	—	2	1	no	—
1048	D₄	—	2	1	no	—
1049	D₄	—	4	2	no	—
1050	D₄	—	4	2	no	—
1051	D₄	—	94	2	no	—
1052	D₄	—	376	2	no	—
1053	D₄	—	376	2	no	—
1054	D₄	—	188	2	no	—
1055	D₄	—	188	4	no	—
1056	D₄	C₂×#10625350	1	2	yes	—
1057	C₂×C₄	—	2	1	no	—
1058	C₂×C₄	—	2	2	no	—
1059	C₂×C₄	—	2	1	no	—
1060	C₂×C₄	—	2	1	no	—
1061	C₂×C₄	—	2	1	no	—
1062	C₂×C₄	—	2	1	no	—
1063	C₂×C₄	—	2	1	no	—
1064	C₂×C₄	—	2	1	no	—
1065	C₂×C₄	—	4	1	no	—
1066	C₂×C₄	—	4	2	no	—
1067	C₂×C₄	—	4	2	no	—
1068	C₂×C₄	—	4	2	no	—
1069	C₂×C₄	—	4	2	no	—
1070	C₂×C₄	—	8	1	no	—
1071	C₂×C₄	—	8	1	no	—
1072	C₂×C₄	—	8	1	no	—
1073	C₂×C₄	—	8	1	no	—
1074	C₂×C₄	—	47	2	no	—
1075	C₂×C₄	—	47	2	no	—
1076	C₂×C₄	—	47	2	no	—
1077	C₂×C₄	—	94	2	no	—
1078	C₂×C₄	—	94	2	no	—
1079	C₂×C₄	—	94	2	no	—
1080	C₂×C₄	—	94	2	no	—
1081	C₂×C₄	—	94	2	no	—
1082	C₂×C₄	—	94	2	no	—
1083	C₂×C₄	—	376	2	no	—
1084	C₂×C₄	—	376	2	no	—
1085	C₂×C₄	—	188	4	no	—
1086	C₂×C₄	—	188	4	no	—
1087	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
1088	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
1089	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
1090	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
1091	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
1092	C₂×C₄	C₂⁴×D₄₇	1	1	yes	characteristic
1093	C₈	—	2	1	no	—
1094	C₈	—	2	1	no	—
1095	C₈	—	2	1	no	—
1096	C₈	—	94	2	no	—
1097	C₈	—	94	2	no	—
1098	C₈	C₂×#10625350	1	2	yes	—
1099	C₂²	—	2	1	no	—
1100	C₂²	—	2	1	no	—
1101	C₂²	—	2	2	no	—
1102	C₂²	—	2	1	no	—
1103	C₂²	—	4	1	no	—
1104	C₂²	—	4	1	no	—
1105	C₂²	—	4	1	no	—
1106	C₂²	—	4	1	no	—
1107	C₂²	—	4	1	no	—
1108	C₂²	—	4	1	no	—
1109	C₂²	—	4	1	no	—
1110	C₂²	—	4	1	no	—
1111	C₂²	—	8	4	no	—
1112	C₂²	—	94	2	no	—
1113	C₂²	—	94	2	no	—
1114	C₂²	—	94	2	no	—
1115	C₂²	C₂²×D₄×D₄₇	1	1	yes	characteristic
1116	C₄	—	2	1	no	—
1117	C₄	—	2	1	no	—
1118	C₄	—	2	2	no	—
1119	C₄	—	2	1	no	—
1120	C₄	—	2	1	no	—
1121	C₄	—	4	1	no	—
1122	C₄	—	4	1	no	—
1123	C₄	—	4	1	no	—
1124	C₄	—	4	1	no	—
1125	C₄	—	94	2	no	—
1126	C₄	—	94	2	no	—
1127	C₄	—	94	2	no	—
1128	C₄	—	188	2	no	—
1129	C₄	—	188	2	no	—
1130	C₄	—	188	2	no	—
1131	C₄	—	188	2	no	—
1132	C₄	#15689933	1	2	yes	—
1133	C₄	C₂²×#10625350	1	1	yes	characteristic
1134	C₄	#15689959	1	1	yes	characteristic
1135	C₂	—	4	1	no	—
1136	C₂	—	4	2	no	—
1137	C₂	—	8	1	no	—
1138	C₂	—	8	1	no	—
1139	C₂	—	188	2	no	—
1140	C₂	D₄×#10625350	1	1	yes	characteristic
1141	C₂	C₂×#15689933	1	1	yes	characteristic
1142	C₂	#20258172	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂²×D₄×D₄₇
commutator, cosocle	C₂×C₄×C₄₇	C₂⁵
Frattini	C₂×C₄	C₂⁴×D₄₇
Fitting	C₄×AGL(1,ℤ/8)×C₄₇	C₂
socle	C₂²×C₄₇	C₂³×D₄
hypercenter	C₄×AGL(1,ℤ/8)	D₄₇
hypocenter	C₄₇	#61557
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ C₄×AGL(1,ℤ/8)

Complements

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

N	H ≅ G/N	type
1. #20257437	C₂	semidirect
2. #20257405	C₂	semidirect
3. #20256374	C₂	semidirect
4. SD₁₆×Dic₉₄	C₂	semidirect
5. #20256126	C₂	semidirect
6. #20256104	C₂	semidirect
7. #20255999	C₂	semidirect
8. #20255985	C₂	semidirect
9. #20255500	C₂	semidirect
10. #20255425	C₂	semidirect
11. #20255318	C₂	semidirect
12. #20255255	C₂	semidirect
13. #20255035	C₂	semidirect
14. #20255019	C₂	semidirect
15. #20254133	C₂	semidirect
16. #20254003	C₂	semidirect
17. #20253669	C₂	semidirect
18. #20253615	C₂	semidirect
19. #20253459	C₂	semidirect
20. #20253396	C₂	semidirect
21. #20252392	C₂	semidirect
22. #20252228	C₂	semidirect
23. C₄×AGL(1,ℤ/8)×C₄₇	C₂	semidirect
25. Q₈×Dic₉₄	C₂²	semidirect
28. #15689843	C₂²	semidirect
32. #15689838	C₂²	semidirect
36. Q₈×D₁₈₈	C₂²	semidirect
45. #15689738	C₂²	semidirect
55. #15689599	C₂²	semidirect
56. #15689521	C₂²	semidirect
57. #15689520	C₂²	semidirect
59. #15689503	C₂²	semidirect
61. #15689481	C₂²	semidirect
62. #15689474	C₂²	semidirect
63. #15689474	C₂²	semidirect
64. #15689466	C₂²	semidirect
66. #15689455	C₂²	semidirect
69. #15689440	C₂²	semidirect
70. #15689417	C₂²	semidirect
74. #15689408	C₂²	semidirect
75. #15689407	C₂²	semidirect
76. #15689406	C₂²	semidirect
77. #15689403	C₂²	semidirect
78. #15689382	C₂²	semidirect
83. #15689351	C₂²	semidirect
85. #15689344	C₂²	semidirect
88. #15689333	C₂²	semidirect
91. #15689328	C₂²	semidirect
94. #15689280	C₂²	semidirect
98. #15689253	C₂²	semidirect
99. C₈×Dic₉₄	C₂²	semidirect
100. #15689231	C₂²	semidirect
101. #15689231	C₂²	semidirect
102. #15689227	C₂²	semidirect
104. #15689217	C₂²	semidirect
105. C₄×#10625337	C₂²	semidirect
109. C₄×#10625335	C₂²	semidirect
110. #15689202	C₂²	semidirect
113. C₈×D₁₈₈	C₂²	semidirect
114. #15689185	C₂²	semidirect
116. #15689164	C₂²	semidirect
118. #103×D₄₇	C₂²	semidirect
119. #15689080	C₂²	semidirect
362. SD₁₆×C₄₇	#41	semidirect
586. C₄×AGL(1,ℤ/8)	D₄₇	semidirect
706. C₄₇	#61557	semidirect
940. SD₁₆	#10625350	semidirect

Maximal subgroups

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

subgroup	index
#20257437	2
#20257405	2
#20256374	2
SD₁₆×Dic₉₄	2
#20256126	2
#20256104	2
#20255999	2
#20255985	2
#20255500	2
#20255425	2
#20255318	2
#20255255	2
#20255035	2
#20255019	2
#20254133	2
#20254003	2
#20253669	2
#20253615	2
#20253459	2
#20253396	2
#20252392	2
#20252228	2
C₄×AGL(1,ℤ/8)×C₄₇	2
#61557	47