Subgroups — #27084231

Order 12032.

2116 conjugacy classes of subgroups.

The subgroup lattice has 1206 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20257060	C₂	1	1	yes	maximal, characteristic
2	#20256589	C₂	1	1	yes	maximal, characteristic, complemented
3	#20253378	C₂	1	2	yes	maximal, complemented
4	#20253375	C₂	1	1	yes	maximal, characteristic, complemented
5	#20253364	C₂	1	1	yes	maximal, characteristic, complemented
6	#20253361	C₂	1	2	yes	maximal, complemented
7	#20253360	C₂	1	1	yes	maximal, characteristic, complemented
8	#20253360	C₂	1	1	yes	maximal, characteristic, complemented
9	#20253356	C₂	1	2	yes	maximal, complemented
10	#20253350	C₂	1	2	yes	maximal, complemented
11	#20253336	C₂	1	1	yes	maximal, characteristic, complemented
12	#20253335	C₂	1	2	yes	maximal, complemented
13	#20253317	C₂	1	1	yes	maximal, characteristic, complemented
14	#20253316	C₂	1	2	yes	maximal, complemented
15	#20253300	C₂	1	2	yes	maximal, complemented
16	C₂×#15689465	C₂	1	1	yes	maximal, characteristic, complemented
17	#485×D₄₇	C₂	1	2	yes	maximal, complemented
18	#20251985	C₂	1	1	yes	maximal, characteristic, complemented
19	#20251980	C₂	1	1	yes	maximal, characteristic, complemented
20	#20251917	C₂	1	1	yes	maximal, characteristic, complemented
21	#20251917	C₂	1	1	yes	maximal, characteristic, complemented
22	#20251834	C₂	1	1	yes	maximal, characteristic, complemented
23	C₄₇×#3091	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#13094071	C₂²	1	1	yes	characteristic
25	C₂²×#10625350	C₂²	1	1	yes	characteristic
26	C₂×#13094030	C₂²	1	1	yes	characteristic
27	C₂×#13094030	C₂²	1	1	yes	characteristic
28	D₄×Dic₉₄	—	2	1	no	—
29	#15689782	—	2	1	no	—
30	#15689778	—	2	1	no	—
31	#15689771	—	2	2	no	—
32	#15689769	—	2	1	no	—
33	#15689760	—	2	2	no	—
34	#15689702	C₂²	1	2	yes	—
35	#15689701	C₂²	1	1	yes	characteristic
36	#15689699	C₂²	1	1	yes	characteristic
37	#15689696	C₂²	1	2	yes	—
38	#15689633	C₂²	1	2	yes	—
39	C₂×#13094003	C₂²	1	1	yes	characteristic
40	C₂²⋊Q₈×D₄₇	C₂²	1	2	yes	—
41	#15689604	C₂²	1	2	yes	—
42	#15689604	C₂²	1	2	yes	—
43	#15689603	C₂²	1	1	yes	characteristic
44	#15689603	C₂²	1	1	yes	characteristic
45	#15689603	C₂²	1	1	yes	characteristic
46	#15689603	C₂²	1	1	yes	characteristic
47	#15689603	C₂²	1	1	yes	characteristic
48	#15689600	—	2	1	no	—
49	#15689597	—	2	1	no	—
50	#15689596	—	2	2	no	—
51	C₄×#10625350	—	2	1	no	—
52	C₄×#10625350	—	2	1	no	—
53	#15689591	—	2	2	no	—
54	C₂×#13093983	C₂²	1	1	yes	characteristic
55	#117×D₄₇	C₂²	1	2	yes	—
56	#117×D₄₇	C₂²	1	2	yes	—
57	#15689467	C₂²	1	2	yes	complemented
58	#15689467	C₂²	1	2	yes	complemented
59	#15689466	C₂²	1	2	yes	complemented
60	#15689466	C₂²	1	2	yes	complemented
61	#15689465	C₂²	1	2	yes	—
62	#15689465	C₂²	1	2	yes	—
63	#15689465	C₂²	1	2	yes	complemented
64	#15689465	C₂²	1	2	yes	complemented
65	#15689464	C₂²	1	2	yes	—
66	#15689464	C₂²	1	2	yes	—
67	#15689463	C₂²	1	2	yes	complemented
68	#15689462	C₂²	1	2	yes	complemented
69	#15689461	C₂²	1	2	yes	—
70	#15689461	C₂²	1	2	yes	complemented
71	#15689460	C₂²	1	2	yes	complemented
72	#15689460	C₂²	1	2	yes	complemented
73	#15689458	C₂²	1	2	yes	complemented
74	#15689457	C₂²	1	2	yes	complemented
75	#15689455	C₂²	1	2	yes	complemented
76	#15689455	C₂²	1	2	yes	complemented
77	#15689453	C₂²	1	2	yes	complemented
78	#15689452	C₂²	1	2	yes	complemented
79	#15689446	C₂²	1	2	yes	complemented
80	#15689445	C₂²	1	2	yes	complemented
81	#15689444	C₂²	1	2	yes	—
82	#15689444	C₂²	1	2	yes	complemented
83	#15689440	C₂²	1	2	yes	complemented
84	#15689435	C₂²	1	2	yes	complemented
85	#15689166	C₂²	1	1	yes	characteristic, complemented
86	#15689166	C₂²	1	1	yes	characteristic, complemented
87	#15689166	C₂²	1	1	yes	characteristic, complemented
88	#15689166	C₂²	1	1	yes	characteristic, complemented
89	#15689164	C₂²	1	2	yes	complemented
90	#15689164	C₂²	1	2	yes	complemented
91	#15689162	C₂²	1	2	yes	complemented
92	#15689162	C₂²	1	2	yes	complemented
93	#15689160	C₂²	1	2	yes	complemented
94	#15689158	C₂²	1	2	yes	complemented
95	C₂×#13093958	C₂²	1	1	yes	characteristic, complemented
96	#107×D₄₇	C₂²	1	2	yes	complemented
97	C₂×#13093956	C₂²	1	1	yes	characteristic, complemented
98	#106×D₄₇	C₂²	1	2	yes	complemented
99	#15689131	C₂²	1	1	yes	characteristic, complemented
100	#15689131	C₂²	1	1	yes	characteristic, complemented
101	#15689130	C₂²	1	2	yes	complemented
102	#15689130	C₂²	1	2	yes	complemented
103	#15689124	C₂²	1	1	yes	characteristic, complemented
104	#15689124	C₂²	1	1	yes	characteristic, complemented
105	#15689121	C₂²	1	2	yes	complemented
106	#15689121	C₂²	1	2	yes	complemented
107	#15689116	C₂²	1	2	yes	complemented
108	#15689116	C₂²	1	2	yes	complemented
109	C₂×#13093949	C₂²	1	1	yes	characteristic, complemented
110	C₂×#13093949	C₂²	1	1	yes	characteristic, complemented
111	#103×D₄₇	C₂²	1	2	yes	complemented
112	#103×D₄₇	C₂²	1	2	yes	complemented
113	#15689089	C₂²	1	1	yes	characteristic
114	#15689089	C₂²	1	1	yes	characteristic
115	#15689088	C₂²	1	2	yes	—
116	#15689088	C₂²	1	2	yes	—
117	#15689087	C₂²	1	1	yes	characteristic
118	#15689085	C₂²	1	2	yes	—
119	C₂²⋊C₈×D₄₇	C₂²	1	2	yes	—
120	C₄₇×#525	C₂²	1	1	yes	characteristic
121	C₂×#117×C₄₇	C₂²	1	1	yes	characteristic
122	C₄₇×#485	C₂²	1	1	yes	characteristic
123	C₄₇×#485	C₂²	1	1	yes	characteristic
124	C₄₇×#484	C₂²	1	1	yes	characteristic, complemented
125	C₄₇×#483	C₂²	1	1	yes	characteristic, complemented
126	C₄₇×#482	C₂²	1	1	yes	characteristic
127	C₄₇×#482	C₂²	1	1	yes	characteristic
128	C₄₇×#481	C₂²	1	1	yes	characteristic, complemented
129	C₄₇×#480	C₂²	1	1	yes	characteristic, complemented
130	C₄₇×#427	C₂²	1	1	yes	characteristic, complemented
131	C₄₇×#427	C₂²	1	1	yes	characteristic, complemented
132	C₄₇×#416	C₂²	1	1	yes	characteristic, complemented
133	C₄₇×#416	C₂²	1	1	yes	characteristic, complemented
134	C₂×C₂²⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
135	#13094071	—	2	4	no	—
136	#13094071	—	2	4	no	—
137	C₂×#10625350	—	2	4	no	—
138	C₂×#10625350	—	2	4	no	—
139	C₂×#10625350	—	2	1	no	—
140	C₂×#10625350	D₄	1	2	yes	—
141	C₂×#10625350	D₄	1	1	yes	characteristic
142	C₂×#10625350	D₄	1	1	yes	characteristic
143	C₂×#10625350	C₂³	1	2	yes	—
144	C₂×#10625350	C₂³	1	1	yes	characteristic
145	C₂×#10625350	C₂³	1	1	yes	characteristic
146	C₂×#10625352	—	2	2	no	—
147	C₂×#10625352	C₂³	1	2	yes	—
148	C₂²×Dic₉₄	—	2	1	no	—
149	C₂²×Dic₉₄	D₄	1	1	yes	characteristic
150	C₂²×Dic₉₄	C₂³	1	1	yes	characteristic
151	C₂×Q₈×D₄₇	C₂³	1	2	yes	—
152	C₂²×D₁₈₈	D₄	1	1	yes	characteristic
153	C₂²×C₂²⋊D₄₇	D₄	1	2	yes	—
154	C₂²×C₄×D₄₇	C₂³	1	2	yes	—
155	#13094030	—	2	4	no	—
156	#13094030	—	2	4	no	—
157	C₂×#10625329	C₂³	1	1	yes	characteristic
158	C₂×#10625329	C₂³	1	1	yes	characteristic
159	C₂×#10625324	C₂³	1	2	yes	—
160	C₂×#10625324	C₂³	1	2	yes	—
161	C₂×C₈×D₄₇	C₂³	1	2	yes	—
162	C₂×C₈×D₄₇	C₂³	1	2	yes	—
163	#13094024	—	2	1	no	—
164	#13094023	—	2	2	no	—
165	#13094012	—	2	1	no	—
166	#13094010	—	2	2	no	—
167	#13094009	—	2	2	no	—
168	#13094008	—	2	2	no	—
169	#13094006	—	2	2	no	—
170	#13094006	—	2	2	no	—
171	#13094004	C₂³	1	2	yes	—
172	#13094004	C₂³	1	2	yes	—
173	#13094003	—	2	1	no	—
174	#13094003	—	2	1	no	—
175	#13094003	—	2	1	no	—
176	#13094003	C₂³	1	2	yes	—
177	#13094003	C₂³	1	2	yes	—
178	#13094002	—	2	2	no	—
179	#13094001	—	2	2	no	—
180	#13094001	—	2	2	no	—
181	#13094000	C₂³	1	2	yes	—
182	#13093998	—	2	1	no	—
183	#13093997	—	2	2	no	—
184	#13093996	—	2	2	no	—
185	#13093996	—	2	2	no	—
186	#13093995	—	2	2	no	—
187	#13093995	C₂³	1	2	yes	—
188	#13093992	—	2	2	no	—
189	C₄×Dic₉₄	—	2	1	no	—
190	C₄×Dic₉₄	—	2	1	no	—
191	C₄×Dic₉₄	—	2	1	no	—
192	C₄×Dic₉₄	—	2	1	no	—
193	C₄×Dic₉₄	—	2	1	no	—
194	#13093989	—	2	2	no	—
195	#13093989	—	2	2	no	—
196	C₄×D₁₈₈	—	2	1	no	—
197	C₄×D₁₈₈	—	2	1	no	—
198	C₄×D₁₈₈	—	2	1	no	—
199	C₄×D₁₈₈	—	2	1	no	—
200	C₄×D₁₈₈	—	2	1	no	—
201	D₄×Dic₄₇	—	2	2	no	—
202	#13093986	—	2	2	no	—
203	#13093986	—	2	2	no	—
204	C₄×C₂²⋊D₄₇	—	2	2	no	—
205	C₄×C₂²⋊D₄₇	—	2	2	no	—
206	C₄×C₂²⋊D₄₇	—	2	2	no	—
207	C₄×C₂²⋊D₄₇	—	2	2	no	—
208	(C₂²⋊D₄₇)⋊C₄	—	2	2	no	—
209	(C₂²⋊D₄₇)⋊C₄	—	2	2	no	—
210	(C₂²⋊D₄₇)⋊C₄	—	2	2	no	—
211	(C₂²⋊D₄₇)⋊C₄	—	2	2	no	—
212	(C₂²⋊D₄₇)⋊C₄	—	2	2	no	—
213	(C₂²⋊D₄₇)⋊C₄	—	2	2	no	—
214	#13093983	—	2	1	no	—
215	#13093983	—	2	1	no	—
216	#13093983	C₂³	1	2	yes	—
217	#13093983	C₂³	1	2	yes	—
218	#13093982	C₂³	1	2	yes	—
219	#13093982	C₂³	1	2	yes	—
220	#13093982	C₂³	1	2	yes	—
221	#13093982	C₂³	1	2	yes	—
222	#13093982	C₂³	1	2	yes	—
223	#13093981	—	2	2	no	—
224	#13093981	—	2	2	no	—
225	#13093980	—	2	2	no	—
226	#13093980	—	2	2	no	—
227	C₂×C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic
228	C₂×C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic
229	C₂×C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic
230	C₂×Dic₄₇⋊C₄	—	2	1	no	—
231	C₄⋊C₄×D₄₇	—	2	2	no	—
232	C₄⋊C₄×D₄₇	C₂³	1	2	yes	—
233	C₄⋊C₄×D₄₇	C₂³	1	2	yes	—
234	C₄⋊C₄×D₄₇	C₂³	1	2	yes	—
235	C₄⋊C₄×D₄₇	C₂³	1	2	yes	—
236	C₄⋊C₄×D₄₇	C₂³	1	2	yes	—
237	C₂×C₂²⋊Dic₄₇	—	2	1	no	—
238	C₂×C₂²⋊Dic₄₇	—	2	1	no	—
239	C₂²⋊C₄×D₄₇	—	2	2	no	—
240	C₂²⋊C₄×D₄₇	—	2	2	no	—
241	C₂²⋊C₄×D₄₇	—	2	2	no	—
242	C₂×C₄×Dic₄₇	—	2	1	no	—
243	C₄²×D₄₇	—	2	2	no	—
244	C₄²×D₄₇	—	2	2	no	—
245	#13093958	C₂³	1	2	yes	—
246	#13093958	C₂³	1	2	yes	—
247	#13093957	C₂³	1	2	yes	—
248	#13093957	C₂³	1	2	yes	—
249	#13093957	C₂³	1	2	yes	—
250	#13093957	C₂³	1	2	yes	—
251	#13093956	C₂³	1	2	yes	—
252	#13093956	C₂³	1	2	yes	—
253	#13093955	C₂³	1	2	yes	—
254	#13093955	C₂³	1	2	yes	—
255	#13093955	C₂³	1	2	yes	—
256	#13093955	C₂³	1	2	yes	—
257	#13093949	C₂³	1	2	yes	—
258	#13093949	C₂³	1	2	yes	—
259	#13093949	C₂³	1	2	yes	—
260	#13093949	C₂³	1	2	yes	—
261	#13093948	C₂³	1	2	yes	—
262	#13093948	C₂³	1	2	yes	—
263	#13093947	C₂³	1	2	yes	—
264	#13093947	C₂³	1	2	yes	—
265	#13093947	C₂³	1	2	yes	—
266	#13093947	C₂³	1	2	yes	—
267	#13093945	C₂³	1	2	yes	—
268	#13093945	C₂³	1	2	yes	—
269	C₂²⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
270	C₂²⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
271	(C₂×D₄₇)⋊C₈	C₂³	1	2	yes	—
272	(C₂×D₄₇)⋊C₈	C₂³	1	2	yes	—
273	(C₂×D₄₇)⋊C₈	C₂³	1	2	yes	—
274	(C₂×D₄₇)⋊C₈	C₂³	1	2	yes	—
275	C₂×#41×C₄₇	C₂³	1	1	yes	characteristic
276	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
277	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
278	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
279	#123×C₄₇	—	2	1	no	—
280	C₂²⋊Q₈×C₄₇	C₂³	1	1	yes	characteristic
281	C₂²⋊Q₈×C₄₇	C₂³	1	1	yes	characteristic
282	#121×C₄₇	C₂³	1	1	yes	characteristic
283	#121×C₄₇	C₂³	1	1	yes	characteristic
284	#120×C₄₇	—	2	1	no	—
285	C₄×D₄×C₄₇	—	2	1	no	—
286	C₄×D₄×C₄₇	—	2	1	no	—
287	#117×C₄₇	—	2	1	no	—
288	#117×C₄₇	—	2	1	no	—
289	#117×C₄₇	C₂³	1	1	yes	characteristic
290	#117×C₄₇	C₂³	1	1	yes	characteristic
291	#117×C₄₇	C₂³	1	1	yes	characteristic
292	#117×C₄₇	C₂³	1	1	yes	characteristic
293	#117×C₄₇	C₂³	1	1	yes	characteristic
294	C₂×C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
295	C₂×C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
296	C₂×C₂²⋊C₄×C₄₇	—	2	1	no	—
297	C₂×C₄²×C₄₇	—	2	1	no	—
298	#107×C₄₇	C₂³	1	1	yes	characteristic
299	#107×C₄₇	C₂³	1	1	yes	characteristic
300	#107×C₄₇	C₂³	1	1	yes	characteristic
301	#107×C₄₇	C₂³	1	1	yes	characteristic
302	#106×C₄₇	C₂³	1	1	yes	characteristic
303	#106×C₄₇	C₂³	1	1	yes	characteristic
304	#106×C₄₇	C₂³	1	1	yes	characteristic
305	#106×C₄₇	C₂³	1	1	yes	characteristic
306	#103×C₄₇	C₂³	1	1	yes	characteristic
307	#103×C₄₇	C₂³	1	1	yes	characteristic
308	#103×C₄₇	C₂³	1	1	yes	characteristic
309	#103×C₄₇	C₂³	1	1	yes	characteristic
310	#102×C₄₇	C₂³	1	1	yes	characteristic
311	#102×C₄₇	C₂³	1	1	yes	characteristic
312	#102×C₄₇	C₂³	1	1	yes	characteristic
313	#102×C₄₇	C₂³	1	1	yes	characteristic
314	C₂²⋊C₈×C₄₇	C₂³	1	1	yes	characteristic
315	C₂²⋊C₈×C₄₇	C₂³	1	1	yes	characteristic
316	C₂²⋊C₈×C₄₇	C₂³	1	1	yes	characteristic
317	C₂²⋊C₈×C₄₇	C₂³	1	1	yes	characteristic
318	C₂⁴×C₄₇	C₂×D₄	1	1	yes	characteristic
319	C₂³×D₄₇	C₂×D₄	1	2	yes	—
320	#41×C₄₇	—	2	2	no	—
321	#41×C₄₇	—	2	2	no	—
322	C₂×Q₈×C₄₇	C₂⁴	1	1	yes	characteristic
323	C₂×D₄×C₄₇	—	2	1	no	—
324	C₂×D₄×C₄₇	—	2	1	no	—
325	C₂×D₄×C₄₇	—	2	1	no	—
326	C₂×D₄×C₄₇	C₂⁴	1	1	yes	characteristic
327	C₂²×C₄×C₄₇	—	2	2	no	—
328	C₂²×C₄×C₄₇	—	2	2	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	C₂×D₄	1	1	yes	characteristic
333	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
334	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
335	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
336	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
337	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
338	C₂×C₂²⋊D₄₇	—	2	8	no	—
339	C₂×C₂²⋊D₄₇	—	2	2	no	—
340	C₂×C₂²⋊D₄₇	—	2	2	no	—
341	C₂×C₂²⋊D₄₇	C₂×D₄	1	2	yes	—
342	C₂×C₂²⋊D₄₇	C₂×D₄	1	2	yes	—
343	C₂×C₂²⋊D₄₇	C₂×D₄	1	2	yes	—
344	C₂×C₂²⋊D₄₇	C₂×D₄	1	2	yes	—
345	C₂²×Dic₄₇	—	2	1	no	—
346	C₂²×Dic₄₇	—	2	1	no	—
347	C₂²×Dic₄₇	—	2	1	no	—
348	C₂²×Dic₄₇	—	2	1	no	—
349	C₂²×Dic₄₇	—	2	2	no	—
350	C₂²×Dic₄₇	C₂×D₄	1	2	yes	—
351	Q₈×D₄₇	—	2	4	no	—
352	Q₈×D₄₇	—	2	4	no	—
353	#10625352	—	2	4	no	—
354	#10625352	—	2	4	no	—
355	#10625352	—	4	8	no	—
356	#10625350	—	2	2	no	—
357	#10625350	—	2	2	no	—
358	#10625350	—	2	8	no	—
359	#10625350	—	2	4	no	—
360	#10625350	—	2	4	no	—
361	#10625350	—	2	4	no	—
362	#10625350	—	2	4	no	—
363	#10625350	—	4	4	no	—
364	#10625350	#41	1	4	yes	—
365	#10625350	#41	1	4	yes	—
366	C₂×D₁₈₈	—	2	4	no	—
367	C₂×D₁₈₈	C₂×D₄	1	2	yes	—
368	C₂×D₁₈₈	C₂×D₄	1	1	yes	characteristic
369	C₂×D₁₈₈	C₂×D₄	1	1	yes	characteristic
370	C₂×C₄×D₄₇	—	2	4	no	—
371	C₂×C₄×D₄₇	—	2	4	no	—
372	C₂×C₄×D₄₇	—	2	2	no	—
373	C₂×C₄×D₄₇	—	2	2	no	—
374	C₂×C₄×D₄₇	—	2	2	no	—
375	C₂×C₄×D₄₇	—	2	2	no	—
376	C₂×C₄×D₄₇	—	2	2	no	—
377	C₂×C₄×D₄₇	—	2	2	no	—
378	C₂×C₄×D₄₇	C₂×D₄	1	2	yes	—
379	C₂×C₄×D₄₇	C₂×D₄	1	2	yes	—
380	C₂×C₄×D₄₇	C₂⁴	1	2	yes	—
381	C₂×C₄×D₄₇	C₂⁴	1	2	yes	—
382	C₂×Dic₉₄	—	2	4	no	—
383	C₂×Dic₉₄	—	2	2	no	—
384	C₂×Dic₉₄	—	2	2	no	—
385	C₂×Dic₉₄	—	2	1	no	—
386	C₂×Dic₉₄	—	2	2	no	—
387	C₂×Dic₉₄	—	4	4	no	—
388	C₂×Dic₉₄	C₂×D₄	1	2	yes	—
389	C₂×Dic₉₄	C₂×D₄	1	1	yes	characteristic
390	C₂×Dic₉₄	C₂×D₄	1	1	yes	characteristic
391	C₂×Dic₉₄	C₂⁴	1	2	yes	—
392	C₂×C₈×C₄₇	—	2	2	no	—
393	C₂×C₈×C₄₇	—	2	2	no	—
394	C₂×C₈×C₄₇	C₂⁴	1	1	yes	characteristic
395	C₂×C₈×C₄₇	C₂⁴	1	1	yes	characteristic
396	C₂×C₈×C₄₇	C₂⁴	1	1	yes	characteristic
397	C₂×C₈×C₄₇	C₂⁴	1	1	yes	characteristic
398	C₄⋊C₄×C₄₇	—	2	1	no	—
399	C₄⋊C₄×C₄₇	—	2	1	no	—
400	C₄⋊C₄×C₄₇	—	2	1	no	—
401	C₄⋊C₄×C₄₇	—	2	1	no	—
402	C₄⋊C₄×C₄₇	C₂⁴	1	1	yes	characteristic
403	C₄⋊C₄×C₄₇	C₂⁴	1	1	yes	characteristic
404	C₄⋊C₄×C₄₇	C₂⁴	1	1	yes	characteristic
405	C₄⋊C₄×C₄₇	C₂⁴	1	1	yes	characteristic
406	C₄⋊C₄×C₄₇	C₂⁴	1	1	yes	characteristic
407	C₄⋊C₄×C₄₇	C₂⁴	1	1	yes	characteristic
408	C₂²⋊C₄×C₄₇	—	2	1	no	—
409	C₂²⋊C₄×C₄₇	—	2	1	no	—
410	C₂²⋊C₄×C₄₇	—	2	1	no	—
411	C₂²⋊C₄×C₄₇	—	2	1	no	—
412	C₂²⋊C₄×C₄₇	—	2	1	no	—
413	C₂²⋊C₄×C₄₇	—	2	1	no	—
414	C₂²⋊C₄×C₄₇	—	2	1	no	—
415	C₂²⋊C₄×C₄₇	—	2	1	no	—
416	C₂²⋊C₄×C₄₇	—	2	1	no	—
417	C₄²×C₄₇	—	2	1	no	—
418	C₄²×C₄₇	—	2	1	no	—
419	C₄²×C₄₇	—	2	1	no	—
420	C₄²×C₄₇	—	2	1	no	—
421	C₄²×C₄₇	—	2	1	no	—
422	C₂²⋊Dic₄₇	—	2	2	no	—
423	C₂²⋊Dic₄₇	—	2	2	no	—
424	C₂²⋊Dic₄₇	—	2	2	no	—
425	C₂²⋊Dic₄₇	—	2	2	no	—
426	C₂²⋊Dic₄₇	—	2	2	no	—
427	(C₂×D₄₇)⋊C₄	—	2	2	no	—
428	(C₂×D₄₇)⋊C₄	—	2	2	no	—
429	(C₂×D₄₇)⋊C₄	—	2	2	no	—
430	(C₂×D₄₇)⋊C₄	—	2	2	no	—
431	(C₂×D₄₇)⋊C₄	—	2	2	no	—
432	(C₂×D₄₇)⋊C₄	—	2	2	no	—
433	(C₂×D₄₇)⋊C₄	—	2	2	no	—
434	(C₂×D₄₇)⋊C₄	—	2	2	no	—
435	C₄⋊Dic₄₇	—	2	1	no	—
436	C₄⋊Dic₄₇	—	2	1	no	—
437	C₄⋊Dic₄₇	—	2	1	no	—
438	C₄⋊Dic₄₇	—	2	2	no	—
439	C₄⋊Dic₄₇	—	2	2	no	—
440	C₄⋊Dic₄₇	C₂⁴	1	2	yes	—
441	C₄⋊Dic₄₇	C₂⁴	1	2	yes	—
442	C₄⋊Dic₄₇	C₂⁴	1	2	yes	—
443	Dic₄₇⋊C₄	—	2	2	no	—
444	Dic₄₇⋊C₄	—	2	2	no	—
445	Dic₄₇⋊C₄	—	2	2	no	—
446	Dic₄₇⋊C₄	—	2	2	no	—
447	Dic₄₇⋊C₄	—	2	2	no	—
448	Dic₄₇⋊C₄	—	2	2	no	—
449	Dic₄₇⋊C₄	—	2	2	no	—
450	Dic₄₇⋊C₄	—	2	2	no	—
451	C₄×Dic₄₇	—	2	2	no	—
452	C₄×Dic₄₇	—	2	2	no	—
453	C₄×Dic₄₇	—	2	2	no	—
454	C₄×Dic₄₇	—	2	2	no	—
455	C₄×Dic₄₇	—	2	2	no	—
456	C₄×Dic₄₇	—	2	2	no	—
457	C₄×Dic₄₇	—	2	2	no	—
458	#10625329	—	2	2	no	—
459	#10625329	—	2	2	no	—
460	C₂×C₄₇⋊C₈	C₂⁴	1	2	yes	—
461	C₂×C₄₇⋊C₈	C₂⁴	1	2	yes	—
462	#10625324	—	2	4	no	—
463	#10625324	—	2	4	no	—
464	C₈×D₄₇	—	2	4	no	—
465	C₈×D₄₇	—	2	4	no	—
466	C₂³×C₄₇	—	2	2	no	—
467	C₂³×C₄₇	—	2	1	no	—
468	C₂³×C₄₇	—	4	1	no	—
469	C₂³×C₄₇	—	4	1	no	—
470	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
471	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
472	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
473	C₂²×D₄₇	—	2	4	no	—
474	C₂²×D₄₇	—	4	2	no	—
475	C₂²×D₄₇	—	4	2	no	—
476	C₂²×D₄₇	C₂²×D₄	1	2	yes	—
477	C₂²×D₄₇	C₂²×D₄	1	2	yes	—
478	Q₈×C₄₇	—	2	1	no	—
479	Q₈×C₄₇	—	2	1	no	—
480	D₄×C₄₇	—	2	1	no	—
481	D₄×C₄₇	—	2	1	no	—
482	D₄×C₄₇	—	4	2	no	—
483	D₄×C₄₇	—	4	2	no	—
484	D₄×C₄₇	—	8	1	no	—
485	C₂×C₄×C₄₇	—	2	2	no	—
486	C₂×C₄×C₄₇	—	2	2	no	—
487	C₂×C₄×C₄₇	—	2	2	no	—
488	C₂×C₄×C₄₇	—	2	1	no	—
489	C₂×C₄×C₄₇	—	2	1	no	—
490	C₂×C₄×C₄₇	—	2	1	no	—
491	C₂×C₄×C₄₇	—	2	1	no	—
492	C₂×C₄×C₄₇	—	2	1	no	—
493	C₂×C₄×C₄₇	—	2	1	no	—
494	C₂×C₄×C₄₇	—	2	1	no	—
495	C₂×C₄×C₄₇	—	2	1	no	—
496	C₂×C₄×C₄₇	—	2	1	no	—
497	C₂×C₄×C₄₇	—	2	1	no	—
498	C₂×C₄×C₄₇	—	2	1	no	—
499	C₂×C₄×C₄₇	—	4	2	no	—
500	C₂×C₄×C₄₇	—	8	1	no	—
501	C₂×C₄×C₄₇	—	8	1	no	—
502	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
503	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
504	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
505	C₂×C₄×C₄₇	C₂×#41	1	2	yes	—
506	C₂×C₄×C₄₇	C₂×#41	1	2	yes	—
507	C₂×C₄×C₄₇	C₂⁵	1	1	yes	characteristic
508	C₂²⋊D₄₇	—	2	4	no	—
509	C₂²⋊D₄₇	—	2	4	no	—
510	C₂²⋊D₄₇	—	2	4	no	—
511	C₂²⋊D₄₇	—	4	4	no	—
512	C₂²⋊D₄₇	—	8	2	no	—
513	C₂²⋊D₄₇	#123	1	8	yes	—
514	C₂×Dic₄₇	—	2	4	no	—
515	C₂×Dic₄₇	—	2	2	no	—
516	C₂×Dic₄₇	—	2	2	no	—
517	C₂×Dic₄₇	—	2	2	no	—
518	C₂×Dic₄₇	—	2	2	no	—
519	C₂×Dic₄₇	—	4	2	no	—
520	C₂×Dic₄₇	—	4	4	no	—
521	C₂×Dic₄₇	—	8	1	no	—
522	C₂×Dic₄₇	—	8	1	no	—
523	C₂×Dic₄₇	—	8	1	no	—
524	C₂×Dic₄₇	C₂²×D₄	1	2	yes	—
525	C₂×Dic₄₇	C₂²×D₄	1	2	yes	—
526	D₁₈₈	—	2	4	no	—
527	D₁₈₈	—	2	2	no	—
528	D₁₈₈	#123	1	4	yes	—
529	C₄×D₄₇	—	2	4	no	—
530	C₄×D₄₇	—	2	2	no	—
531	C₄×D₄₇	—	2	2	no	—
532	C₄×D₄₇	—	2	4	no	—
533	C₄×D₄₇	—	4	4	no	—
534	C₄×D₄₇	—	8	2	no	—
535	C₄×D₄₇	—	8	2	no	—
536	C₄×D₄₇	—	8	2	no	—
537	C₄×D₄₇	—	8	2	no	—
538	C₄×D₄₇	—	8	2	no	—
539	C₄×D₄₇	C₂×#41	1	4	yes	—
540	C₄×D₄₇	C₂×#41	1	4	yes	—
541	Dic₉₄	—	2	2	no	—
542	Dic₉₄	—	2	4	no	—
543	Dic₉₄	—	2	2	no	—
544	Dic₉₄	—	2	2	no	—
545	Dic₉₄	—	4	2	no	—
546	Dic₉₄	—	4	4	no	—
547	Dic₉₄	#123	1	4	yes	—
548	C₈×C₄₇	—	2	1	no	—
549	C₈×C₄₇	—	2	1	no	—
550	C₈×C₄₇	—	2	1	no	—
551	C₈×C₄₇	—	2	1	no	—
552	C₄₇⋊C₈	—	2	2	no	—
553	C₄₇⋊C₈	—	2	2	no	—
554	#60524	—	47	1	no	maximal, Sylow
555	C₂²×C₄₇	—	2	1	no	—
556	C₂²×C₄₇	—	2	1	no	—
557	C₂²×C₄₇	—	2	1	no	—
558	C₂²×C₄₇	—	2	1	no	—
559	C₂²×C₄₇	—	2	1	no	—
560	C₂²×C₄₇	—	2	1	no	—
561	C₂²×C₄₇	—	2	1	no	—
562	C₂²×C₄₇	—	2	1	no	—
563	C₂²×C₄₇	—	4	1	no	—
564	C₂²×C₄₇	—	4	1	no	—
565	C₂²×C₄₇	—	4	1	no	—
566	C₂²×C₄₇	—	8	2	no	—
567	C₂²×C₄₇	C₂×#123	1	2	yes	—
568	C₂²×C₄₇	C₂³×D₄	1	1	yes	characteristic
569	C₂×D₄₇	—	2	2	no	—
570	C₂×D₄₇	—	2	2	no	—
571	C₂×D₄₇	—	2	2	no	—
572	C₂×D₄₇	—	2	2	no	—
573	C₂×D₄₇	—	2	2	no	—
574	C₂×D₄₇	—	8	4	no	—
575	C₂×D₄₇	C₂×#123	1	4	yes	—
576	C₄×C₄₇	—	2	1	no	—
577	C₄×C₄₇	—	2	1	no	—
578	C₄×C₄₇	—	4	1	no	—
579	C₄×C₄₇	—	4	1	no	—
580	C₄×C₄₇	—	4	1	no	—
581	C₄×C₄₇	—	4	1	no	—
582	C₄×C₄₇	—	4	1	no	—
583	C₄×C₄₇	—	4	1	no	—
584	C₄×C₄₇	—	4	1	no	—
585	C₄×C₄₇	C₂×#123	1	2	yes	—
586	C₄×C₄₇	C₂²×#41	1	1	yes	characteristic
587	C₄×C₄₇	C₂²×#41	1	1	yes	characteristic
588	Dic₄₇	—	2	2	no	—
589	Dic₄₇	—	4	2	no	—
590	Dic₄₇	—	4	2	no	—
591	Dic₄₇	—	4	2	no	—
592	Dic₄₇	—	4	2	no	—
593	Dic₄₇	C₂×#123	1	4	yes	—
594	#3489	—	47	1	no	—
595	#3428	—	47	1	no	—
596	#3099	—	47	2	no	—
597	#3099	—	47	1	no	—
598	#3098	—	47	2	no	—
599	#3098	—	47	1	no	—
600	#3097	—	47	2	no	—
601	#3097	—	47	2	no	—
602	#3097	—	47	1	no	—
603	#3097	—	47	1	no	—
604	#3095	—	47	2	no	—
605	#3095	—	47	1	no	—
606	#3093	—	47	2	no	—
607	#3093	—	47	1	no	—
608	#3091	—	47	2	no	—
609	#3091	D₄₇	1	1	yes	characteristic, complemented
610	C₂×#485	—	47	2	no	—
611	C₂×#485	—	47	1	no	—
612	#2913	—	47	1	no	—
613	#2912	—	47	1	no	—
614	#2898	—	47	1	no	—
615	#2898	—	47	1	no	—
616	#2880	—	47	1	no	—
617	C₂×C₄₇	—	2	2	no	—
618	C₂×C₄₇	—	4	1	no	—
619	C₂×C₄₇	—	4	1	no	—
620	C₂×C₄₇	—	8	1	no	—
621	C₂×C₄₇	C₂²×#123	1	1	yes	characteristic
622	C₂×C₄₇	#3584	1	1	yes	characteristic
623	C₂×C₄₇	#3586	1	1	yes	characteristic
624	D₄₇	—	2	4	no	—
625	D₄₇	—	4	2	no	—
626	C₂×2₋¹⁺⁴	—	47	1	no	—
627	C₂²×#41	—	47	1	no	—
628	C₂×#131	—	47	1	no	—
629	C₂×#131	—	47	1	no	—
630	D₄×Q₈	—	94	1	no	—
631	#548	—	94	1	no	—
632	#547	—	94	1	no	—
633	#547	—	94	2	no	—
634	#546	—	94	1	no	—
635	#546	—	94	2	no	—
636	#537	—	47	1	no	—
637	#537	—	47	2	no	—
638	#536	—	47	2	no	—
639	#536	—	47	1	no	—
640	#525	—	47	2	no	—
641	#525	C₂×D₄₇	1	1	yes	characteristic
642	C₂×C₂²⋊Q₈	—	47	1	no	—
643	C₂×C₂²⋊Q₈	—	47	2	no	—
644	#520	—	47	1	no	—
645	#520	—	47	1	no	—
646	#520	—	47	1	no	—
647	#520	—	47	1	no	—
648	#520	—	47	1	no	—
649	#520	—	47	2	no	—
650	#520	—	47	2	no	—
651	#519	—	94	1	no	—
652	#518	—	94	2	no	—
653	#518	—	94	1	no	—
654	C₄×#41	—	94	1	no	—
655	C₄×#41	—	94	1	no	—
656	C₄×#41	—	94	2	no	—
657	C₂×#117	—	47	1	no	—
658	C₂×#117	—	47	2	no	—
659	C₂×#117	—	47	2	no	—
660	C₂×#117	C₂×D₄₇	1	1	yes	characteristic
661	#485	—	47	2	no	—
662	#485	—	47	2	no	—
663	#485	—	47	2	no	—
664	#485	—	47	2	no	—
665	#485	—	47	2	no	—
666	#485	—	47	2	no	—
667	#485	—	47	2	no	—
668	#485	—	47	2	no	—
669	#485	—	47	2	no	—
670	#485	—	47	2	no	—
671	#485	—	47	2	no	—
672	#485	—	47	2	no	—
673	#485	—	47	2	no	—
674	#485	—	47	2	no	—
675	#485	C₂×D₄₇	1	1	yes	characteristic
676	#485	C₂×D₄₇	1	1	yes	characteristic
677	#484	—	47	2	no	—
678	#484	—	47	2	no	—
679	#484	—	47	2	no	—
680	#484	—	47	2	no	—
681	#484	C₂×D₄₇	1	1	yes	characteristic, complemented
682	#483	—	47	2	no	—
683	#483	—	47	2	no	—
684	#483	—	47	2	no	—
685	#483	—	47	2	no	—
686	#483	C₂×D₄₇	1	1	yes	characteristic, complemented
687	#482	—	47	2	no	—
688	#482	—	47	2	no	—
689	#482	—	47	2	no	—
690	#482	—	47	2	no	—
691	#482	C₂×D₄₇	1	1	yes	characteristic
692	#482	C₂×D₄₇	1	1	yes	characteristic
693	#481	—	47	2	no	—
694	#481	C₂×D₄₇	1	1	yes	characteristic, complemented
695	#480	—	47	2	no	—
696	#480	C₂×D₄₇	1	1	yes	characteristic, complemented
697	#428	—	47	1	no	—
698	#428	—	47	1	no	—
699	#428	—	47	1	no	—
700	#428	—	47	1	no	—
701	#428	—	47	2	no	—
702	#428	—	47	2	no	—
703	#428	—	47	2	no	—
704	#428	—	47	2	no	—
705	#427	—	47	2	no	—
706	#427	—	47	2	no	—
707	#427	C₂×D₄₇	1	1	yes	characteristic, complemented
708	#427	C₂×D₄₇	1	1	yes	characteristic, complemented
709	C₂×#107	—	47	1	no	—
710	C₂×#107	—	47	2	no	—
711	C₂×#106	—	47	1	no	—
712	C₂×#106	—	47	2	no	—
713	#419	—	47	1	no	—
714	#419	—	47	1	no	—
715	#419	—	47	2	no	—
716	#419	—	47	2	no	—
717	#417	—	47	1	no	—
718	#417	—	47	1	no	—
719	#417	—	47	2	no	—
720	#417	—	47	2	no	—
721	#416	—	47	2	no	—
722	#416	—	47	2	no	—
723	#416	C₂×D₄₇	1	1	yes	characteristic, complemented
724	#416	C₂×D₄₇	1	1	yes	characteristic, complemented
725	C₂×#103	—	47	1	no	—
726	C₂×#103	—	47	1	no	—
727	C₂×#103	—	47	2	no	—
728	C₂×#103	—	47	2	no	—
729	#408	—	47	1	no	—
730	#408	—	47	1	no	—
731	#408	—	47	2	no	—
732	#408	—	47	2	no	—
733	#407	—	47	1	no	—
734	#407	—	47	2	no	—
735	C₂×C₂²⋊C₈	—	47	2	no	—
736	C₂×C₂²⋊C₈	C₂×D₄₇	1	1	yes	characteristic
737	C₄₇	#60524	1	1	yes	characteristic, complemented, Sylow
738	2₋¹⁺⁴	—	94	4	no	—
739	2₋¹⁺⁴	—	94	4	no	—
740	C₂×#41	—	47	1	no	—
741	C₂×#41	—	47	2	no	—
742	C₂×#41	—	47	1	no	—
743	C₂×#41	—	47	1	no	—
744	C₂×#41	—	47	2	no	—
745	C₂×#41	—	47	1	no	—
746	C₂×#41	—	47	2	no	—
747	C₂×#41	—	94	1	no	—
748	C₂×#41	—	94	4	no	—
749	C₂×#41	—	94	4	no	—
750	C₂×#41	—	94	2	no	—
751	C₂×#41	C₂²×D₄₇	1	1	yes	characteristic
752	C₂²×Q₈	—	47	1	no	—
753	C₂²×Q₈	—	47	2	no	—
754	C₂²×Q₈	—	47	1	no	—
755	C₂²×Q₈	—	94	1	no	—
756	C₂²×D₄	—	47	2	no	—
757	C₂²×D₄	—	47	1	no	—
758	C₂³×C₄	—	47	2	no	—
759	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
760	#131	—	94	4	no	—
761	#131	—	94	4	no	—
762	C₂×M₁₆	—	47	1	no	—
763	C₂×M₁₆	—	47	1	no	—
764	C₂×M₁₆	—	47	2	no	—
765	C₂×M₁₆	—	47	2	no	—
766	C₂²×C₈	—	47	2	no	—
767	C₂²×C₈	—	47	2	no	—
768	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
769	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
770	C₄⋊Q₈	—	94	1	no	—
771	C₄⋊Q₈	—	94	2	no	—
772	#124	—	94	1	no	—
773	#124	—	94	2	no	—
774	#123	—	2	1	no	—
775	#123	—	94	2	no	—
776	#123	—	94	2	no	—
777	#123	—	94	2	no	—
778	#123	—	94	2	no	—
779	C₂²⋊Q₈	—	47	2	no	—
780	C₂²⋊Q₈	—	47	2	no	—
781	C₂²⋊Q₈	—	47	2	no	—
782	C₂²⋊Q₈	—	47	2	no	—
783	C₂²⋊Q₈	—	47	2	no	—
784	C₂²⋊Q₈	—	94	2	no	—
785	C₂²⋊Q₈	—	94	2	no	—
786	C₂²⋊Q₈	—	94	2	no	—
787	C₂²⋊Q₈	—	94	1	no	—
788	C₂²⋊Q₈	—	94	1	no	—
789	C₂²⋊Q₈	—	94	1	no	—
790	C₂²⋊Q₈	C₂²×D₄₇	1	1	yes	characteristic
791	C₂²⋊Q₈	C₂²×D₄₇	1	1	yes	characteristic
792	#121	—	47	2	no	—
793	#121	—	94	2	no	—
794	#121	—	94	1	no	—
795	#121	—	94	2	no	—
796	#121	—	94	2	no	—
797	#121	—	94	2	no	—
798	#121	C₂²×D₄₇	1	1	yes	characteristic
799	#121	C₂²×D₄₇	1	1	yes	characteristic
800	#120	—	2	1	no	—
801	#120	—	94	2	no	—
802	C₄×Q₈	—	94	1	no	—
803	C₄×Q₈	—	94	1	no	—
804	C₄×Q₈	—	94	1	no	—
805	C₄×Q₈	—	94	1	no	—
806	C₄×Q₈	—	94	1	no	—
807	C₄×Q₈	—	94	2	no	—
808	C₄×Q₈	—	94	2	no	—
809	C₄×D₄	—	2	1	no	—
810	C₄×D₄	—	2	1	no	—
811	C₄×D₄	—	94	1	no	—
812	C₄×D₄	—	94	1	no	—
813	C₄×D₄	—	94	1	no	—
814	C₄×D₄	—	94	1	no	—
815	C₄×D₄	—	94	1	no	—
816	C₄×D₄	—	94	2	no	—
817	C₄×D₄	—	94	2	no	—
818	C₄×D₄	—	94	2	no	—
819	C₄×D₄	—	94	2	no	—
820	C₄×D₄	—	94	2	no	—
821	C₄×D₄	—	94	2	no	—
822	C₄×D₄	—	94	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	2	no	—
828	C₄×D₄	—	94	2	no	—
829	#117	—	2	1	no	—
830	#117	—	2	1	no	—
831	#117	—	47	2	no	—
832	#117	—	47	2	no	—
833	#117	—	47	2	no	—
834	#117	—	47	2	no	—
835	#117	—	47	2	no	—
836	#117	—	47	2	no	—
837	#117	—	47	2	no	—
838	#117	—	94	2	no	—
839	#117	—	94	2	no	—
840	#117	—	94	2	no	—
841	#117	—	94	2	no	—
842	#117	—	94	1	no	—
843	#117	—	94	1	no	—
844	#117	C₂²×D₄₇	1	1	yes	characteristic
845	#117	C₂²×D₄₇	1	1	yes	characteristic
846	#117	C₂²×D₄₇	1	1	yes	characteristic
847	#117	C₂²×D₄₇	1	1	yes	characteristic
848	#117	C₂²×D₄₇	1	1	yes	characteristic
849	C₂×C₄⋊C₄	—	47	1	no	—
850	C₂×C₄⋊C₄	—	47	1	no	—
851	C₂×C₄⋊C₄	—	47	1	no	—
852	C₂×C₄⋊C₄	—	47	2	no	—
853	C₂×C₄⋊C₄	—	47	2	no	—
854	C₂×C₄⋊C₄	—	47	2	no	—
855	C₂×C₄⋊C₄	—	47	2	no	—
856	C₂×C₄⋊C₄	—	47	2	no	—
857	C₂×C₄⋊C₄	—	94	2	no	—
858	C₂×C₄⋊C₄	—	94	1	no	—
859	C₂×C₄⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
860	C₂×C₄⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
861	C₂×C₂²⋊C₄	—	2	1	no	—
862	C₂×C₂²⋊C₄	—	94	2	no	—
863	C₂×C₂²⋊C₄	—	94	2	no	—
864	C₂×C₂²⋊C₄	—	94	2	no	—
865	C₂×C₂²⋊C₄	—	94	1	no	—
866	C₂×C₂²⋊C₄	—	94	1	no	—
867	C₂×C₄²	—	2	1	no	—
868	C₂×C₄²	—	94	2	no	—
869	C₂×C₄²	—	94	2	no	—
870	C₂×C₄²	—	94	1	no	—
871	#107	—	47	2	no	—
872	#107	—	47	2	no	—
873	#107	—	47	2	no	—
874	#107	—	47	2	no	—
875	#107	—	47	2	no	—
876	#107	—	47	2	no	—
877	#107	C₂²×D₄₇	1	1	yes	characteristic
878	#107	C₂²×D₄₇	1	1	yes	characteristic
879	#107	C₂²×D₄₇	1	1	yes	characteristic
880	#107	C₂²×D₄₇	1	1	yes	characteristic
881	#106	—	47	2	no	—
882	#106	—	47	2	no	—
883	#106	—	47	2	no	—
884	#106	—	47	2	no	—
885	#106	—	47	2	no	—
886	#106	—	47	2	no	—
887	#106	C₂²×D₄₇	1	1	yes	characteristic
888	#106	C₂²×D₄₇	1	1	yes	characteristic
889	#106	C₂²×D₄₇	1	1	yes	characteristic
890	#106	C₂²×D₄₇	1	1	yes	characteristic
891	#103	—	47	2	no	—
892	#103	—	47	2	no	—
893	#103	—	47	2	no	—
894	#103	—	47	2	no	—
895	#103	—	47	2	no	—
896	#103	—	47	2	no	—
897	#103	—	47	2	no	—
898	#103	—	47	2	no	—
899	#103	—	47	2	no	—
900	#103	—	47	2	no	—
901	#103	C₂²×D₄₇	1	1	yes	characteristic
902	#103	C₂²×D₄₇	1	1	yes	characteristic
903	#103	C₂²×D₄₇	1	1	yes	characteristic
904	#103	C₂²×D₄₇	1	1	yes	characteristic
905	#102	—	47	2	no	—
906	#102	—	47	2	no	—
907	#102	C₂²×D₄₇	1	1	yes	characteristic
908	#102	C₂²×D₄₇	1	1	yes	characteristic
909	#102	C₂²×D₄₇	1	1	yes	characteristic
910	#102	C₂²×D₄₇	1	1	yes	characteristic
911	C₂²⋊C₈	—	47	2	no	—
912	C₂²⋊C₈	—	47	2	no	—
913	C₂²⋊C₈	—	47	2	no	—
914	C₂²⋊C₈	—	47	2	no	—
915	C₂²⋊C₈	—	47	2	no	—
916	C₂²⋊C₈	—	47	2	no	—
917	C₂²⋊C₈	C₂²×D₄₇	1	1	yes	characteristic
918	C₂²⋊C₈	C₂²×D₄₇	1	1	yes	characteristic
919	C₂²⋊C₈	C₂²×D₄₇	1	1	yes	characteristic
920	C₂²⋊C₈	C₂²×D₄₇	1	1	yes	characteristic
921	C₂⁴	—	47	2	no	—
922	C₂⁴	D₄×D₄₇	1	1	yes	characteristic
923	#41	—	2	2	no	—
924	#41	—	2	2	no	—
925	#41	—	47	4	no	—
926	#41	—	47	4	no	—
927	#41	—	94	4	no	—
928	#41	—	94	4	no	—
929	#41	—	94	8	no	—
930	#41	—	94	4	no	—
931	#41	—	94	4	no	—
932	#41	—	94	4	no	—
933	#41	—	94	4	no	—
934	#41	—	94	2	no	—
935	#41	—	94	2	no	—
936	#41	—	188	4	no	—
937	#41	—	188	8	no	—
938	C₂×Q₈	—	47	1	no	—
939	C₂×Q₈	—	47	2	no	—
940	C₂×Q₈	—	47	1	no	—
941	C₂×Q₈	—	47	2	no	—
942	C₂×Q₈	—	94	2	no	—
943	C₂×Q₈	—	94	4	no	—
944	C₂×Q₈	—	94	4	no	—
945	C₂×Q₈	—	94	4	no	—
946	C₂×Q₈	—	94	1	no	—
947	C₂×Q₈	—	94	2	no	—
948	C₂×Q₈	—	94	2	no	—
949	C₂×Q₈	—	188	4	no	—
950	C₂×Q₈	C₂³×D₄₇	1	1	yes	characteristic
951	C₂×D₄	—	2	1	no	—
952	C₂×D₄	—	2	1	no	—
953	C₂×D₄	—	2	1	no	—
954	C₂×D₄	—	47	2	no	—
955	C₂×D₄	—	47	2	no	—
956	C₂×D₄	—	47	2	no	—
957	C₂×D₄	—	47	2	no	—
958	C₂×D₄	—	47	1	no	—
959	C₂×D₄	—	47	2	no	—
960	C₂×D₄	—	47	1	no	—
961	C₂×D₄	—	94	4	no	—
962	C₂×D₄	—	94	8	no	—
963	C₂×D₄	—	94	2	no	—
964	C₂×D₄	—	94	2	no	—
965	C₂×D₄	C₂³×D₄₇	1	1	yes	characteristic
966	C₂²×C₄	—	2	2	no	—
967	C₂²×C₄	—	2	2	no	—
968	C₂²×C₄	—	2	1	no	—
969	C₂²×C₄	—	2	1	no	—
970	C₂²×C₄	—	2	1	no	—
971	C₂²×C₄	—	47	2	no	—
972	C₂²×C₄	—	47	2	no	—
973	C₂²×C₄	—	47	2	no	—
974	C₂²×C₄	—	47	2	no	—
975	C₂²×C₄	—	47	2	no	—
976	C₂²×C₄	—	94	4	no	—
977	C₂²×C₄	—	94	4	no	—
978	C₂²×C₄	—	94	2	no	—
979	C₂²×C₄	—	94	2	no	—
980	C₂²×C₄	—	94	2	no	—
981	C₂²×C₄	—	94	2	no	—
982	C₂²×C₄	—	94	2	no	—
983	C₂²×C₄	—	94	2	no	—
984	C₂²×C₄	—	94	2	no	—
985	C₂²×C₄	—	94	1	no	—
986	C₂²×C₄	—	94	1	no	—
987	C₂²×C₄	—	94	1	no	—
988	C₂²×C₄	—	94	1	no	—
989	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
990	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
991	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
992	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
993	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
994	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
995	M₁₆	—	94	4	no	—
996	M₁₆	—	94	4	no	—
997	M₁₆	—	94	2	no	—
998	M₁₆	—	94	2	no	—
999	C₂×C₈	—	2	2	no	—
1000	C₂×C₈	—	2	2	no	—
1001	C₂×C₈	—	47	2	no	—
1002	C₂×C₈	—	47	2	no	—
1003	C₂×C₈	—	94	4	no	—
1004	C₂×C₈	—	94	4	no	—
1005	C₂×C₈	C₂³×D₄₇	1	1	yes	characteristic
1006	C₂×C₈	C₂³×D₄₇	1	1	yes	characteristic
1007	C₂×C₈	C₂³×D₄₇	1	1	yes	characteristic
1008	C₂×C₈	C₂³×D₄₇	1	1	yes	characteristic
1009	C₄⋊C₄	—	2	1	no	—
1010	C₄⋊C₄	—	2	1	no	—
1011	C₄⋊C₄	—	2	1	no	—
1012	C₄⋊C₄	—	2	1	no	—
1013	C₄⋊C₄	—	47	2	no	—
1014	C₄⋊C₄	—	47	2	no	—
1015	C₄⋊C₄	—	47	2	no	—
1016	C₄⋊C₄	—	94	2	no	—
1017	C₄⋊C₄	—	94	2	no	—
1018	C₄⋊C₄	—	94	2	no	—
1019	C₄⋊C₄	—	94	2	no	—
1020	C₄⋊C₄	—	94	2	no	—
1021	C₄⋊C₄	—	94	2	no	—
1022	C₄⋊C₄	—	94	2	no	—
1023	C₄⋊C₄	—	94	2	no	—
1024	C₄⋊C₄	—	94	2	no	—
1025	C₄⋊C₄	—	94	2	no	—
1026	C₄⋊C₄	—	94	1	no	—
1027	C₄⋊C₄	—	94	1	no	—
1028	C₄⋊C₄	—	94	1	no	—
1029	C₄⋊C₄	C₂³×D₄₇	1	1	yes	characteristic
1030	C₄⋊C₄	C₂³×D₄₇	1	1	yes	characteristic
1031	C₄⋊C₄	C₂³×D₄₇	1	1	yes	characteristic
1032	C₄⋊C₄	C₂³×D₄₇	1	1	yes	characteristic
1033	C₄⋊C₄	C₂³×D₄₇	1	1	yes	characteristic
1034	C₄⋊C₄	C₂³×D₄₇	1	1	yes	characteristic
1035	C₂²⋊C₄	—	2	1	no	—
1036	C₂²⋊C₄	—	2	1	no	—
1037	C₂²⋊C₄	—	2	1	no	—
1038	C₂²⋊C₄	—	2	1	no	—
1039	C₂²⋊C₄	—	2	1	no	—
1040	C₂²⋊C₄	—	2	1	no	—
1041	C₂²⋊C₄	—	2	1	no	—
1042	C₂²⋊C₄	—	2	1	no	—
1043	C₂²⋊C₄	—	2	1	no	—
1044	C₂²⋊C₄	—	94	2	no	—
1045	C₂²⋊C₄	—	94	2	no	—
1046	C₂²⋊C₄	—	94	2	no	—
1047	C₂²⋊C₄	—	94	2	no	—
1048	C₂²⋊C₄	—	94	2	no	—
1049	C₂²⋊C₄	—	94	2	no	—
1050	C₂²⋊C₄	—	94	2	no	—
1051	C₂²⋊C₄	—	94	2	no	—
1052	C₂²⋊C₄	—	94	2	no	—
1053	C₂²⋊C₄	—	94	2	no	—
1054	C₂²⋊C₄	—	94	2	no	—
1055	C₂²⋊C₄	—	94	2	no	—
1056	C₂²⋊C₄	—	94	2	no	—
1057	C₄²	—	2	1	no	—
1058	C₄²	—	2	1	no	—
1059	C₄²	—	2	1	no	—
1060	C₄²	—	2	1	no	—
1061	C₄²	—	2	1	no	—
1062	C₄²	—	94	2	no	—
1063	C₄²	—	94	2	no	—
1064	C₄²	—	94	2	no	—
1065	C₄²	—	94	2	no	—
1066	C₄²	—	94	2	no	—
1067	C₄²	—	94	2	no	—
1068	C₄²	—	94	2	no	—
1069	C₂³	—	2	2	no	—
1070	C₂³	—	2	1	no	—
1071	C₂³	—	4	1	no	—
1072	C₂³	—	4	1	no	—
1073	C₂³	—	47	2	no	—
1074	C₂³	—	47	2	no	—
1075	C₂³	—	94	4	no	—
1076	C₂³	—	188	2	no	—
1077	C₂³	—	188	2	no	—
1078	C₂³	C₂×D₄×D₄₇	1	1	yes	characteristic
1079	C₂³	C₂×D₄×D₄₇	1	1	yes	characteristic
1080	C₂³	C₂×D₄×D₄₇	1	1	yes	characteristic
1081	Q₈	—	2	1	no	—
1082	Q₈	—	2	1	no	—
1083	Q₈	—	47	4	no	—
1084	Q₈	—	94	4	no	—
1085	Q₈	—	94	2	no	—
1086	Q₈	—	94	2	no	—
1087	Q₈	—	94	2	no	—
1088	Q₈	—	188	4	no	—
1089	Q₈	—	188	2	no	—
1090	D₄	—	2	1	no	—
1091	D₄	—	2	1	no	—
1092	D₄	—	4	2	no	—
1093	D₄	—	4	2	no	—
1094	D₄	—	8	1	no	—
1095	D₄	—	47	8	no	—
1096	D₄	—	47	4	no	—
1097	D₄	—	94	4	no	—
1098	D₄	—	94	4	no	—
1099	D₄	—	94	4	no	—
1100	D₄	—	94	4	no	—
1101	D₄	—	94	2	no	—
1102	D₄	—	376	2	no	—
1103	D₄	—	188	4	no	—
1104	C₂×C₄	—	2	2	no	—
1105	C₂×C₄	—	2	2	no	—
1106	C₂×C₄	—	2	2	no	—
1107	C₂×C₄	—	2	1	no	—
1108	C₂×C₄	—	2	1	no	—
1109	C₂×C₄	—	2	1	no	—
1110	C₂×C₄	—	2	1	no	—
1111	C₂×C₄	—	2	1	no	—
1112	C₂×C₄	—	2	1	no	—
1113	C₂×C₄	—	2	1	no	—
1114	C₂×C₄	—	2	1	no	—
1115	C₂×C₄	—	2	1	no	—
1116	C₂×C₄	—	2	1	no	—
1117	C₂×C₄	—	2	1	no	—
1118	C₂×C₄	—	4	2	no	—
1119	C₂×C₄	—	8	1	no	—
1120	C₂×C₄	—	8	1	no	—
1121	C₂×C₄	—	47	2	no	—
1122	C₂×C₄	—	47	4	no	—
1123	C₂×C₄	—	47	4	no	—
1124	C₂×C₄	—	47	2	no	—
1125	C₂×C₄	—	94	4	no	—
1126	C₂×C₄	—	94	4	no	—
1127	C₂×C₄	—	94	4	no	—
1128	C₂×C₄	—	94	2	no	—
1129	C₂×C₄	—	94	2	no	—
1130	C₂×C₄	—	94	2	no	—
1131	C₂×C₄	—	94	2	no	—
1132	C₂×C₄	—	94	2	no	—
1133	C₂×C₄	—	94	2	no	—
1134	C₂×C₄	—	376	2	no	—
1135	C₂×C₄	—	376	2	no	—
1136	C₂×C₄	—	376	2	no	—
1137	C₂×C₄	—	376	2	no	—
1138	C₂×C₄	—	376	2	no	—
1139	C₂×C₄	—	376	1	no	—
1140	C₂×C₄	—	376	1	no	—
1141	C₂×C₄	—	376	1	no	—
1142	C₂×C₄	—	188	4	no	—
1143	C₂×C₄	—	188	4	no	—
1144	C₂×C₄	—	188	2	no	—
1145	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
1146	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
1147	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
1148	C₂×C₄	#41×D₄₇	1	2	yes	—
1149	C₂×C₄	#41×D₄₇	1	2	yes	—
1150	C₂×C₄	C₂⁴×D₄₇	1	1	yes	characteristic
1151	C₈	—	2	1	no	—
1152	C₈	—	2	1	no	—
1153	C₈	—	2	1	no	—
1154	C₈	—	2	1	no	—
1155	C₈	—	94	2	no	—
1156	C₈	—	94	2	no	—
1157	C₂²	—	2	1	no	—
1158	C₂²	—	2	1	no	—
1159	C₂²	—	2	1	no	—
1160	C₂²	—	2	1	no	—
1161	C₂²	—	2	1	no	—
1162	C₂²	—	2	1	no	—
1163	C₂²	—	2	1	no	—
1164	C₂²	—	2	1	no	—
1165	C₂²	—	4	1	no	—
1166	C₂²	—	4	1	no	—
1167	C₂²	—	4	1	no	—
1168	C₂²	—	8	2	no	—
1169	C₂²	—	47	4	no	—
1170	C₂²	—	94	2	no	—
1171	C₂²	—	94	2	no	—
1172	C₂²	—	94	2	no	—
1173	C₂²	—	94	2	no	—
1174	C₂²	—	94	2	no	—
1175	C₂²	—	376	4	no	—
1176	C₂²	#123×D₄₇	1	2	yes	—
1177	C₂²	C₂²×D₄×D₄₇	1	1	yes	characteristic
1178	C₄	—	2	1	no	—
1179	C₄	—	2	1	no	—
1180	C₄	—	4	1	no	—
1181	C₄	—	4	1	no	—
1182	C₄	—	4	1	no	—
1183	C₄	—	4	1	no	—
1184	C₄	—	4	1	no	—
1185	C₄	—	4	1	no	—
1186	C₄	—	4	1	no	—
1187	C₄	—	47	4	no	—
1188	C₄	—	94	2	no	—
1189	C₄	—	188	2	no	—
1190	C₄	—	188	2	no	—
1191	C₄	—	188	2	no	—
1192	C₄	—	188	2	no	—
1193	C₄	#123×D₄₇	1	2	yes	—
1194	C₄	C₂×#41×D₄₇	1	1	yes	characteristic
1195	C₄	C₂×#41×D₄₇	1	1	yes	characteristic
1196	C₂	—	2	2	no	—
1197	C₂	—	4	1	no	—
1198	C₂	—	4	1	no	—
1199	C₂	—	8	1	no	—
1200	C₂	—	94	4	no	—
1201	C₂	—	188	2	no	—
1202	C₂	C₂×#123×D₄₇	1	1	yes	characteristic
1203	C₂	#20258157	1	1	yes	characteristic
1204	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	C₄₇×#3091	C₂
socle	C₂²×C₄₇	C₂³×D₄
prime radical	#20257060	C₂
hypercenter	#3091	D₄₇
hypocenter	C₄₇	#60524
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₂³×C₄ ◁ #3091

Complements

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

N	H ≅ G/N	type
2. #20256589	C₂	semidirect
3. #20253378	C₂	semidirect
4. #20253375	C₂	semidirect
5. #20253364	C₂	semidirect
6. #20253361	C₂	semidirect
7. #20253360	C₂	semidirect
8. #20253360	C₂	semidirect
9. #20253356	C₂	semidirect
10. #20253350	C₂	semidirect
11. #20253336	C₂	semidirect
12. #20253335	C₂	semidirect
13. #20253317	C₂	semidirect
14. #20253316	C₂	semidirect
15. #20253300	C₂	semidirect
16. C₂×#15689465	C₂	semidirect
17. #485×D₄₇	C₂	semidirect
18. #20251985	C₂	semidirect
19. #20251980	C₂	semidirect
20. #20251917	C₂	semidirect
21. #20251917	C₂	semidirect
22. #20251834	C₂	semidirect
23. C₄₇×#3091	C₂	semidirect
57. #15689467	C₂²	semidirect
58. #15689467	C₂²	semidirect
59. #15689466	C₂²	semidirect
60. #15689466	C₂²	semidirect
63. #15689465	C₂²	semidirect
64. #15689465	C₂²	semidirect
67. #15689463	C₂²	semidirect
68. #15689462	C₂²	semidirect
70. #15689461	C₂²	semidirect
71. #15689460	C₂²	semidirect
72. #15689460	C₂²	semidirect
73. #15689458	C₂²	semidirect
74. #15689457	C₂²	semidirect
75. #15689455	C₂²	semidirect
76. #15689455	C₂²	semidirect
77. #15689453	C₂²	semidirect
78. #15689452	C₂²	semidirect
79. #15689446	C₂²	semidirect
80. #15689445	C₂²	semidirect
82. #15689444	C₂²	semidirect
83. #15689440	C₂²	semidirect
84. #15689435	C₂²	semidirect
85. #15689166	C₂²	semidirect
86. #15689166	C₂²	semidirect
87. #15689166	C₂²	semidirect
88. #15689166	C₂²	semidirect
89. #15689164	C₂²	semidirect
90. #15689164	C₂²	semidirect
91. #15689162	C₂²	semidirect
92. #15689162	C₂²	semidirect
93. #15689160	C₂²	semidirect
94. #15689158	C₂²	semidirect
95. C₂×#13093958	C₂²	semidirect
96. #107×D₄₇	C₂²	semidirect
97. C₂×#13093956	C₂²	semidirect
98. #106×D₄₇	C₂²	semidirect
99. #15689131	C₂²	semidirect
100. #15689131	C₂²	semidirect
101. #15689130	C₂²	semidirect
102. #15689130	C₂²	semidirect
103. #15689124	C₂²	semidirect
104. #15689124	C₂²	semidirect
105. #15689121	C₂²	semidirect
106. #15689121	C₂²	semidirect
107. #15689116	C₂²	semidirect
108. #15689116	C₂²	semidirect
109. C₂×#13093949	C₂²	semidirect
110. C₂×#13093949	C₂²	semidirect
111. #103×D₄₇	C₂²	semidirect
112. #103×D₄₇	C₂²	semidirect
124. C₄₇×#484	C₂²	semidirect
125. C₄₇×#483	C₂²	semidirect
128. C₄₇×#481	C₂²	semidirect
129. C₄₇×#480	C₂²	semidirect
130. C₄₇×#427	C₂²	semidirect
131. C₄₇×#427	C₂²	semidirect
132. C₄₇×#416	C₂²	semidirect
133. C₄₇×#416	C₂²	semidirect
609. #3091	D₄₇	semidirect
681. #484	C₂×D₄₇	semidirect
686. #483	C₂×D₄₇	semidirect
694. #481	C₂×D₄₇	semidirect
696. #480	C₂×D₄₇	semidirect
707. #427	C₂×D₄₇	semidirect
708. #427	C₂×D₄₇	semidirect
723. #416	C₂×D₄₇	semidirect
724. #416	C₂×D₄₇	semidirect
737. C₄₇	#60524	semidirect

Maximal subgroups

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

subgroup	index
#20257060	2
#20256589	2
#20253378	2
#20253375	2
#20253364	2
#20253361	2
#20253360	2
#20253356	2
#20253350	2
#20253336	2
#20253335	2
#20253317	2
#20253316	2
#20253300	2
C₂×#15689465	2
#485×D₄₇	2
#20251985	2
#20251980	2
#20251917	2
#20251834	2
C₄₇×#3091	2
#60524	47