Subgroups — #27081442

Order 12032.

1790 conjugacy classes of subgroups.

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

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20256776	C₂	1	1	yes	maximal, characteristic
2	#20252559	C₂	1	2	yes	maximal, complemented
3	#20252554	C₂	1	2	yes	maximal, complemented
4	#20252545	C₂	1	2	yes	maximal, complemented
5	#20252543	C₂	1	2	yes	maximal, complemented
6	#20252538	C₂	1	2	yes	maximal, complemented
7	#20252530	C₂	1	2	yes	maximal, complemented
8	#20252523	C₂	1	2	yes	maximal, complemented
9	#20252521	C₂	1	2	yes	maximal, complemented
10	#20252334	C₂	1	1	yes	maximal, characteristic, complemented
11	#20252332	C₂	1	1	yes	maximal, characteristic, complemented
12	#20252130	C₂	1	1	yes	maximal, characteristic, complemented
13	#20252128	C₂	1	1	yes	maximal, characteristic, complemented
14	#20252092	C₂	1	1	yes	maximal, characteristic, complemented
15	#20252087	C₂	1	1	yes	maximal, characteristic, complemented
16	#20252082	C₂	1	1	yes	maximal, characteristic, complemented
17	#20252052	C₂	1	1	yes	maximal, characteristic, complemented
18	#20252050	C₂	1	1	yes	maximal, characteristic, complemented
19	#20252023	C₂	1	1	yes	maximal, characteristic, complemented
20	#20251955	C₂	1	1	yes	maximal, characteristic, complemented
21	#20251954	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂×#15689149	C₂	1	1	yes	maximal, characteristic, complemented
23	C₄₇×#2929	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#13094032	C₂²	1	1	yes	characteristic
25	C₂×#13094031	C₂²	1	1	yes	characteristic
26	C₂×#13094030	C₂²	1	1	yes	characteristic
27	C₂²×#10625329	C₂²	1	1	yes	characteristic
28	#15689746	C₄	1	1	yes	characteristic
29	#15689746	C₄	1	1	yes	characteristic
30	#15689740	C₄	1	1	yes	characteristic
31	#15689740	C₄	1	1	yes	characteristic
32	#15689733	C₄	1	1	yes	characteristic
33	#15689733	C₄	1	1	yes	characteristic
34	#15689726	C₄	1	1	yes	characteristic
35	#15689726	C₄	1	1	yes	characteristic
36	#15689717	C₄	1	2	yes	—
37	#15689717	C₄	1	2	yes	—
38	#15689708	C₄	1	2	yes	—
39	#15689708	C₄	1	2	yes	—
40	#15689676	C₂²	1	1	yes	characteristic
41	#15689669	C₂²	1	1	yes	characteristic
42	#15689655	C₂²	1	2	yes	—
43	#15689655	C₂²	1	2	yes	—
44	#15689653	C₂²	1	2	yes	—
45	#15689653	C₂²	1	2	yes	—
46	#15689634	C₂²	1	1	yes	characteristic
47	#41×Dic₄₇	C₂²	1	1	yes	characteristic
48	#15689591	C₂²	1	1	yes	characteristic
49	C₂×#13093983	C₂²	1	1	yes	characteristic
50	#15689253	C₂²	1	2	yes	complemented
51	#15689252	C₂²	1	2	yes	complemented
52	#15689252	C₂²	1	2	yes	complemented
53	#15689251	C₂²	1	2	yes	complemented
54	#15689251	C₂²	1	2	yes	complemented
55	#15689250	C₂²	1	2	yes	complemented
56	C₈×Dic₉₄	C₂²	1	2	yes	complemented
57	#15689247	C₂²	1	2	yes	complemented
58	#15689201	C₂²	1	2	yes	—
59	#15689201	C₂²	1	2	yes	—
60	#15689199	C₂²	1	2	yes	complemented
61	#15689198	C₂²	1	2	yes	—
62	#15689198	C₂²	1	2	yes	—
63	#15689198	C₂²	1	2	yes	complemented
64	#15689197	C₂²	1	2	yes	—
65	#15689197	C₂²	1	2	yes	—
66	#15689197	C₂²	1	2	yes	complemented
67	#15689195	C₂²	1	2	yes	—
68	#15689195	C₂²	1	2	yes	—
69	#15689194	C₂²	1	2	yes	—
70	#15689194	C₂²	1	2	yes	—
71	#15689194	C₂²	1	2	yes	complemented
72	#15689192	C₂²	1	2	yes	complemented
73	#15689191	C₂²	1	2	yes	complemented
74	C₈×C₂²⋊D₄₇	C₂²	1	2	yes	—
75	C₈×C₂²⋊D₄₇	C₂²	1	2	yes	—
76	C₈×C₂²⋊D₄₇	C₂²	1	2	yes	complemented
77	(C₂²⋊D₄₇)⋊C₈	C₂²	1	2	yes	complemented
78	#15689185	C₂²	1	2	yes	complemented
79	#15689182	C₂²	1	2	yes	complemented
80	#15689181	C₂²	1	2	yes	—
81	#15689181	C₂²	1	2	yes	—
82	#15689181	C₂²	1	2	yes	—
83	#15689181	C₂²	1	2	yes	—
84	#15689181	C₂²	1	2	yes	complemented
85	#15689181	C₂²	1	2	yes	complemented
86	#15689178	C₂²	1	2	yes	complemented
87	#15689177	C₂²	1	2	yes	complemented
88	#15689174	C₂²	1	2	yes	complemented
89	#15689173	C₂²	1	2	yes	complemented
90	#15689151	C₂²	1	1	yes	characteristic
91	#15689151	C₂²	1	2	yes	complemented
92	#15689150	C₂²	1	1	yes	characteristic
93	#15689149	C₂²	1	1	yes	characteristic
94	#15689149	C₂²	1	1	yes	characteristic
95	#15689149	C₂²	1	1	yes	characteristic
96	#15689149	C₂²	1	1	yes	characteristic
97	#15689149	C₂²	1	1	yes	characteristic
98	#15689149	C₂²	1	1	yes	characteristic
99	#15689149	C₂²	1	1	yes	characteristic
100	#15689149	C₂²	1	1	yes	characteristic
101	#15689149	C₂²	1	1	yes	characteristic
102	#15689149	C₂²	1	2	yes	complemented
103	#15689148	C₂²	1	2	yes	complemented
104	#15689148	C₂²	1	2	yes	complemented
105	#15689146	C₂²	1	1	yes	characteristic
106	#15689146	C₂²	1	1	yes	characteristic
107	#15689146	C₂²	1	2	yes	complemented
108	#15689145	C₂²	1	2	yes	complemented
109	C₂×Dic₄₇⋊C₈	C₂²	1	1	yes	characteristic
110	C₂×Dic₄₇⋊C₈	C₂²	1	1	yes	characteristic
111	C₂×Dic₄₇⋊C₈	C₂²	1	1	yes	characteristic
112	C₂×Dic₄₇⋊C₈	C₂²	1	1	yes	characteristic
113	C₂×Dic₄₇⋊C₈	C₂²	1	2	yes	complemented
114	C₄⋊C₈×D₄₇	C₂²	1	2	yes	complemented
115	#15689091	C₂²	1	1	yes	characteristic
116	#15689090	C₂²	1	1	yes	characteristic
117	#15689089	C₂²	1	1	yes	characteristic
118	#15689087	C₂²	1	1	yes	characteristic
119	#15689081	C₂²	1	1	yes	characteristic
120	#15689079	C₂²	1	1	yes	characteristic
121	#15689078	C₂²	1	1	yes	characteristic
122	M₁₆×Dic₄₇	C₂²	1	1	yes	characteristic
123	M₁₆×Dic₄₇	C₂²	1	1	yes	characteristic
124	C₂×#131×C₄₇	C₂²	1	1	yes	characteristic
125	C₂³×C₈×C₄₇	C₂²	1	1	yes	characteristic
126	C₄₇×#525	C₂²	1	1	yes	characteristic
127	C₄₇×#435	C₂²	1	2	yes	—
128	C₄₇×#435	C₂²	1	2	yes	—
129	C₈×D₄×C₄₇	C₂²	1	2	yes	—
130	C₈×D₄×C₄₇	C₂²	1	2	yes	—
131	C₄₇×#424	C₂²	1	1	yes	characteristic
132	C₄₇×#408	C₂²	1	1	yes	characteristic
133	C₄₇×#407	C₂²	1	1	yes	characteristic
134	C₄₇×#405	C₂²	1	1	yes	characteristic
135	C₂×#10625350	C₂³	1	1	yes	characteristic
136	#13094032	—	4	2	no	—
137	#13094031	—	4	2	no	—
138	#13094030	—	4	2	no	—
139	C₂×#10625329	—	4	2	no	—
140	C₂×#10625329	C₂³	1	1	yes	characteristic
141	C₂×#10625329	C₂³	1	1	yes	characteristic
142	C₂×#10625329	C₂³	1	1	yes	characteristic
143	C₂×#10625329	C₂³	1	1	yes	characteristic
144	C₂×#10625329	C₂³	1	1	yes	characteristic
145	C₂×#10625329	C₂³	1	1	yes	characteristic
146	C₂×#10625329	C₂³	1	2	yes	—
147	C₂×#10625324	C₂³	1	2	yes	—
148	C₂×#10625324	C₂³	1	2	yes	—
149	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
150	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
151	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
152	C₂×C₈×D₄₇	C₂³	1	2	yes	—
153	C₂×C₈×D₄₇	C₂³	1	2	yes	—
154	#13094023	C₂×C₄	1	1	yes	characteristic
155	#13094023	C₂×C₄	1	1	yes	characteristic
156	#13094022	C₂×C₄	1	1	yes	characteristic
157	#13094020	C₂×C₄	1	1	yes	characteristic
158	#13094019	C₂×C₄	1	2	yes	—
159	#13094019	C₂×C₄	1	2	yes	—
160	#13094017	C₂×C₄	1	2	yes	—
161	#13094017	C₂×C₄	1	2	yes	—
162	#13094017	C₂×C₄	1	2	yes	—
163	#13094017	C₂×C₄	1	2	yes	—
164	#13094017	C₂×C₄	1	2	yes	—
165	#13094017	C₂×C₄	1	2	yes	—
166	#13094015	C₂×C₄	1	2	yes	—
167	#13094015	C₂×C₄	1	2	yes	—
168	#13094015	C₂×C₄	1	1	yes	characteristic
169	#13094015	C₂×C₄	1	1	yes	characteristic
170	#13094014	C₂×C₄	1	2	yes	—
171	#13094014	C₂×C₄	1	2	yes	—
172	#13094013	C₂×C₄	1	1	yes	characteristic
173	#13094011	C₂×C₄	1	1	yes	characteristic
174	#13094011	C₂×C₄	1	2	yes	—
175	#13094011	C₂×C₄	1	2	yes	—
176	#13094010	C₂×C₄	1	2	yes	—
177	#13094010	C₂×C₄	1	2	yes	—
178	#13094008	C₂×C₄	1	2	yes	—
179	#13094008	C₂×C₄	1	2	yes	—
180	#13094007	C₂×C₄	1	2	yes	—
181	#13094006	C₂×C₄	1	2	yes	—
182	#13094006	C₂×C₄	1	2	yes	—
183	#13094006	C₂×C₄	1	2	yes	—
184	#13094006	C₂×C₄	1	2	yes	—
185	#13094005	C₂×C₄	1	2	yes	—
186	#13094005	C₂×C₄	1	2	yes	—
187	#13094004	C₂×C₄	1	2	yes	—
188	#13094004	C₂×C₄	1	2	yes	—
189	#13094003	C₂×C₄	1	1	yes	characteristic
190	#13094003	C₂×C₄	1	1	yes	characteristic
191	#13094001	C₂×C₄	1	2	yes	—
192	#13094001	C₂×C₄	1	2	yes	—
193	#13094001	C₂×C₄	1	2	yes	—
194	#13094001	C₂×C₄	1	2	yes	—
195	#13093998	C₂×C₄	1	1	yes	characteristic
196	#13093998	C₂×C₄	1	1	yes	characteristic
197	#13093996	C₂×C₄	1	2	yes	—
198	#13093996	C₂×C₄	1	2	yes	—
199	#13093996	C₂×C₄	1	2	yes	—
200	#13093996	C₂×C₄	1	2	yes	—
201	#13093995	C₂×C₄	1	2	yes	—
202	#13093995	C₂×C₄	1	2	yes	—
203	#13093993	C₂×C₄	1	2	yes	—
204	Q₈×Dic₄₇	C₂×C₄	1	1	yes	characteristic
205	Q₈×Dic₄₇	C₂×C₄	1	1	yes	characteristic
206	C₄×Dic₉₄	C₂³	1	2	yes	—
207	C₄×Dic₉₄	C₂³	1	2	yes	—
208	#13093989	C₂×C₄	1	1	yes	characteristic
209	#13093989	C₂×C₄	1	1	yes	characteristic
210	D₄×Dic₄₇	C₂×C₄	1	1	yes	characteristic
211	D₄×Dic₄₇	C₂×C₄	1	1	yes	characteristic
212	D₄×Dic₄₇	C₂×C₄	1	2	yes	—
213	D₄×Dic₄₇	C₂×C₄	1	2	yes	—
214	#13093986	C₂×C₄	1	1	yes	characteristic
215	#13093986	C₂×C₄	1	1	yes	characteristic
216	C₄×C₂²⋊D₄₇	C₂³	1	2	yes	—
217	C₄×C₂²⋊D₄₇	C₂³	1	2	yes	—
218	C₄×C₂²⋊D₄₇	C₂³	1	2	yes	—
219	C₄×C₂²⋊D₄₇	C₂³	1	2	yes	—
220	(C₂²⋊D₄₇)⋊C₄	C₂×C₄	1	2	yes	—
221	(C₂²⋊D₄₇)⋊C₄	C₂×C₄	1	2	yes	—
222	#13093983	C₂×C₄	1	1	yes	characteristic
223	#13093983	C₂×C₄	1	1	yes	characteristic
224	#13093983	C₂×C₄	1	1	yes	characteristic
225	#13093983	C₂×C₄	1	1	yes	characteristic
226	#13093983	C₂³	1	1	yes	characteristic
227	#13093983	C₂³	1	1	yes	characteristic
228	#13093983	C₂³	1	1	yes	characteristic
229	#13093983	C₂³	1	1	yes	characteristic
230	#13093983	C₂³	1	1	yes	characteristic
231	#13093983	C₂³	1	2	yes	—
232	#13093981	C₂³	1	2	yes	—
233	C₂×C₄⋊Dic₄₇	C₂×C₄	1	1	yes	characteristic
234	C₂×C₄⋊Dic₄₇	C₂×C₄	1	1	yes	characteristic
235	C₂×C₂²⋊Dic₄₇	C₂×C₄	1	1	yes	characteristic
236	C₂×C₂²⋊Dic₄₇	C₂×C₄	1	1	yes	characteristic
237	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
238	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
239	C₂×C₄×Dic₄₇	C₂³	1	2	yes	—
240	C₄²×D₄₇	C₂³	1	2	yes	—
241	C₄⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
242	C₄⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
243	Dic₄₇⋊C₈	C₂³	1	1	yes	characteristic
244	Dic₄₇⋊C₈	C₂³	1	2	yes	—
245	Dic₄₇⋊C₈	C₂³	1	1	yes	characteristic
246	Dic₄₇⋊C₈	C₂³	1	2	yes	—
247	Dic₄₇⋊C₈	C₂³	1	1	yes	characteristic
248	Dic₄₇⋊C₈	C₂³	1	1	yes	characteristic
249	Dic₄₇⋊C₈	C₂³	1	1	yes	characteristic
250	Dic₄₇⋊C₈	C₂³	1	2	yes	—
251	Dic₄₇⋊C₈	C₂³	1	1	yes	characteristic
252	Dic₄₇⋊C₈	C₂³	1	1	yes	characteristic
253	Dic₄₇⋊C₈	C₂³	1	2	yes	—
254	Dic₄₇⋊C₈	C₂³	1	1	yes	characteristic
255	Dic₄₇⋊C₈	C₂³	1	1	yes	characteristic
256	Dic₄₇⋊C₈	C₂³	1	2	yes	—
257	Dic₄₇⋊C₈	C₂³	1	1	yes	characteristic
258	Dic₄₇⋊C₈	C₂³	1	1	yes	characteristic
259	Dic₄₇⋊C₈	C₂³	1	1	yes	characteristic
260	Dic₄₇⋊C₈	C₂³	1	1	yes	characteristic
261	Dic₄₇⋊C₈	C₂³	1	1	yes	characteristic
262	Dic₄₇⋊C₈	C₂³	1	1	yes	characteristic
263	Dic₄₇⋊C₈	C₂³	1	1	yes	characteristic
264	Dic₄₇⋊C₈	C₂³	1	2	yes	—
265	Dic₄₇⋊C₈	C₂³	1	2	yes	—
266	Dic₄₇⋊C₈	C₂³	1	2	yes	—
267	C₂²⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
268	C₂²⋊(C₄₇⋊C₈)	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	#13093935	C₂³	1	2	yes	—
276	#13093934	C₂³	1	2	yes	—
277	#13093934	C₂³	1	2	yes	—
278	#13093934	C₂³	1	2	yes	—
279	#13093934	C₂³	1	2	yes	—
280	C₄×C₄₇⋊C₈	C₂³	1	2	yes	—
281	C₈×Dic₄₇	C₂³	1	2	yes	—
282	C₈×Dic₄₇	C₂³	1	2	yes	—
283	C₈×Dic₄₇	C₂³	1	2	yes	—
284	C₈×Dic₄₇	C₂³	1	2	yes	—
285	C₂×#41×C₄₇	C₂³	1	1	yes	characteristic
286	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
287	#131×C₄₇	—	4	2	no	—
288	C₂×M₁₆×C₄₇	C₂³	1	1	yes	characteristic
289	C₂×M₁₆×C₄₇	C₂³	1	1	yes	characteristic
290	C₂×M₁₆×C₄₇	C₂³	1	2	yes	—
291	C₂²×C₈×C₄₇	—	4	2	no	—
292	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
293	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
294	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
295	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
296	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
297	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
298	C₂²×C₈×C₄₇	C₂³	1	2	yes	—
299	#123×C₄₇	C₂×C₄	1	2	yes	—
300	C₂²⋊Q₈×C₄₇	C₂×C₄	1	1	yes	characteristic
301	C₂²⋊Q₈×C₄₇	C₂×C₄	1	1	yes	characteristic
302	#121×C₄₇	C₂×C₄	1	1	yes	characteristic
303	#121×C₄₇	C₂×C₄	1	1	yes	characteristic
304	#120×C₄₇	C₂×C₄	1	2	yes	—
305	C₄×D₄×C₄₇	C₂³	1	2	yes	—
306	C₄×D₄×C₄₇	C₂³	1	2	yes	—
307	#117×C₄₇	C₂³	1	1	yes	characteristic
308	C₄⋊C₈×C₄₇	C₂³	1	2	yes	—
309	C₄⋊C₈×C₄₇	C₂³	1	2	yes	—
310	C₂²⋊C₈×C₄₇	C₂³	1	2	yes	—
311	C₂²⋊C₈×C₄₇	C₂³	1	2	yes	—
312	C₂²⋊C₈×C₄₇	C₂³	1	2	yes	—
313	C₂²⋊C₈×C₄₇	C₂³	1	2	yes	—
314	#97×C₄₇	C₂³	1	2	yes	—
315	C₄×C₈×C₄₇	C₂³	1	2	yes	—
316	C₂⁴×C₄₇	C₂²×C₄	1	1	yes	characteristic
317	#41×C₄₇	—	2	2	no	—
318	#41×C₄₇	—	2	2	no	—
319	C₂×Q₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
320	C₂×D₄×C₄₇	C₂²×C₄	1	2	yes	—
321	C₂×D₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
322	C₂×D₄×C₄₇	C₂²×C₄	1	2	yes	—
323	C₂×D₄×C₄₇	C₂²×C₄	1	2	yes	—
324	C₂²×C₄×C₄₇	—	2	2	no	—
325	C₂²×C₄×C₄₇	—	2	2	no	—
326	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
327	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
328	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
329	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
330	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
331	C₂²×C₄×C₄₇	C₂⁴	1	2	yes	—
332	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
333	C₂×C₂²⋊D₄₇	C₂²×C₄	1	2	yes	—
334	C₂×C₂²⋊D₄₇	C₂²×C₄	1	2	yes	—
335	C₂×C₂²⋊D₄₇	C₂²×C₄	1	2	yes	—
336	C₂×C₂²⋊D₄₇	C₂²×C₄	1	2	yes	—
337	C₂×C₂²⋊D₄₇	C₂²×C₄	1	2	yes	—
338	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
339	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
340	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
341	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
342	C₂²×Dic₄₇	C₂²×C₄	1	2	yes	—
343	C₂²×Dic₄₇	C₂²×C₄	1	2	yes	—
344	#10625350	—	2	2	no	—
345	#10625350	—	2	2	no	—
346	C₂×D₁₈₈	C₂²×C₄	1	1	yes	characteristic
347	C₂×C₄×D₄₇	C₂²×C₄	1	2	yes	—
348	C₂×C₄×D₄₇	C₂²×C₄	1	2	yes	—
349	C₂×C₄×D₄₇	C₂⁴	1	2	yes	—
350	C₂×Dic₉₄	C₂²×C₄	1	1	yes	characteristic
351	C₂×Dic₉₄	C₂²×C₄	1	2	yes	—
352	C₂×Dic₉₄	C₂²×C₄	1	2	yes	—
353	M₁₆×C₄₇	—	2	2	no	—
354	M₁₆×C₄₇	—	2	2	no	—
355	M₁₆×C₄₇	—	4	2	no	—
356	C₂×C₈×C₄₇	—	2	2	no	—
357	C₂×C₈×C₄₇	—	2	2	no	—
358	C₂×C₈×C₄₇	—	4	1	no	—
359	C₂×C₈×C₄₇	—	4	1	no	—
360	C₂×C₈×C₄₇	—	4	1	no	—
361	C₂×C₈×C₄₇	—	4	1	no	—
362	C₂×C₈×C₄₇	—	4	2	no	—
363	C₂×C₈×C₄₇	C₂⁴	1	1	yes	characteristic
364	C₂×C₈×C₄₇	C₂⁴	1	1	yes	characteristic
365	C₂×C₈×C₄₇	C₂⁴	1	2	yes	—
366	C₂×C₈×C₄₇	C₂⁴	1	1	yes	characteristic
367	C₂×C₈×C₄₇	C₂⁴	1	1	yes	characteristic
368	C₂×C₈×C₄₇	C₂⁴	1	2	yes	—
369	C₄⋊C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
370	C₄⋊C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
371	C₄⋊C₄×C₄₇	C₂²×C₄	1	2	yes	—
372	C₄⋊C₄×C₄₇	C₂²×C₄	1	2	yes	—
373	C₂²⋊C₄×C₄₇	C₂²×C₄	1	2	yes	—
374	C₂²⋊C₄×C₄₇	C₂²×C₄	1	2	yes	—
375	C₂²⋊C₄×C₄₇	C₂²×C₄	1	2	yes	—
376	C₂²⋊C₄×C₄₇	C₂²×C₄	1	2	yes	—
377	C₂²⋊C₄×C₄₇	C₂²×C₄	1	2	yes	—
378	C₄²×C₄₇	C₂⁴	1	2	yes	—
379	C₂²⋊Dic₄₇	C₂²×C₄	1	1	yes	characteristic
380	C₂²⋊Dic₄₇	C₂²×C₄	1	1	yes	characteristic
381	C₂²⋊Dic₄₇	C₂²×C₄	1	1	yes	characteristic
382	C₂²⋊Dic₄₇	C₂²×C₄	1	1	yes	characteristic
383	C₂²⋊Dic₄₇	C₂²×C₄	1	1	yes	characteristic
384	C₂²⋊Dic₄₇	C₂²×C₄	1	1	yes	characteristic
385	C₂²⋊Dic₄₇	C₂²×C₄	1	1	yes	characteristic
386	C₂²⋊Dic₄₇	C₂²×C₄	1	1	yes	characteristic
387	C₂²⋊Dic₄₇	C₂²×C₄	1	2	yes	—
388	C₂²⋊Dic₄₇	C₂²×C₄	1	2	yes	—
389	C₂²⋊Dic₄₇	C₂²×C₄	1	2	yes	—
390	C₂²⋊Dic₄₇	C₂²×C₄	1	2	yes	—
391	C₂²⋊Dic₄₇	C₂²×C₄	1	2	yes	—
392	C₂²⋊Dic₄₇	C₂²×C₄	1	2	yes	—
393	C₂²⋊Dic₄₇	C₂²×C₄	1	2	yes	—
394	(C₂×D₄₇)⋊C₄	C₂²×C₄	1	2	yes	—
395	(C₂×D₄₇)⋊C₄	C₂²×C₄	1	2	yes	—
396	(C₂×D₄₇)⋊C₄	C₂²×C₄	1	2	yes	—
397	(C₂×D₄₇)⋊C₄	C₂²×C₄	1	2	yes	—
398	(C₂×D₄₇)⋊C₄	C₂²×C₄	1	2	yes	—
399	(C₂×D₄₇)⋊C₄	C₂²×C₄	1	2	yes	—
400	C₄⋊Dic₄₇	C₂²×C₄	1	1	yes	characteristic
401	C₄⋊Dic₄₇	C₂²×C₄	1	1	yes	characteristic
402	C₄⋊Dic₄₇	C₂²×C₄	1	1	yes	characteristic
403	C₄⋊Dic₄₇	C₂²×C₄	1	1	yes	characteristic
404	C₄⋊Dic₄₇	C₂²×C₄	1	1	yes	characteristic
405	C₄⋊Dic₄₇	C₂²×C₄	1	1	yes	characteristic
406	C₄⋊Dic₄₇	C₂²×C₄	1	1	yes	characteristic
407	C₄⋊Dic₄₇	C₂²×C₄	1	1	yes	characteristic
408	C₄⋊Dic₄₇	C₂²×C₄	1	1	yes	characteristic
409	C₄⋊Dic₄₇	C₂²×C₄	1	1	yes	characteristic
410	C₄⋊Dic₄₇	C₂²×C₄	1	2	yes	—
411	C₄⋊Dic₄₇	C₂²×C₄	1	2	yes	—
412	C₄⋊Dic₄₇	C₂²×C₄	1	2	yes	—
413	C₄⋊Dic₄₇	C₂²×C₄	1	2	yes	—
414	Dic₄₇⋊C₄	C₂²×C₄	1	2	yes	—
415	Dic₄₇⋊C₄	C₂²×C₄	1	2	yes	—
416	Dic₄₇⋊C₄	C₂²×C₄	1	2	yes	—
417	Dic₄₇⋊C₄	C₂²×C₄	1	2	yes	—
418	Dic₄₇⋊C₄	C₂²×C₄	1	2	yes	—
419	Dic₄₇⋊C₄	C₂²×C₄	1	2	yes	—
420	Dic₄₇⋊C₄	C₂²×C₄	1	2	yes	—
421	Dic₄₇⋊C₄	C₂²×C₄	1	2	yes	—
422	Dic₄₇⋊C₄	C₂²×C₄	1	2	yes	—
423	Dic₄₇⋊C₄	C₂²×C₄	1	2	yes	—
424	C₄×Dic₄₇	C₂²×C₄	1	2	yes	—
425	C₄×Dic₄₇	C₂²×C₄	1	2	yes	—
426	C₄×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
427	C₄×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
428	C₄×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
429	C₄×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
430	C₄×Dic₄₇	C₂²×C₄	1	2	yes	—
431	C₄×Dic₄₇	C₂²×C₄	1	2	yes	—
432	C₄×Dic₄₇	C₂⁴	1	1	yes	characteristic
433	C₄×Dic₄₇	C₂⁴	1	1	yes	characteristic
434	C₄×Dic₄₇	C₂⁴	1	2	yes	—
435	C₄×Dic₄₇	C₂⁴	1	1	yes	characteristic
436	C₄×Dic₄₇	C₂⁴	1	1	yes	characteristic
437	#10625329	—	2	2	no	—
438	#10625329	—	2	2	no	—
439	#10625329	—	4	1	no	—
440	#10625329	—	4	1	no	—
441	#10625329	—	4	1	no	—
442	#10625329	—	4	1	no	—
443	#10625329	—	4	2	no	—
444	C₂×C₄₇⋊C₈	—	2	2	no	—
445	C₂×C₄₇⋊C₈	—	2	2	no	—
446	C₂×C₄₇⋊C₈	—	4	2	no	—
447	C₂×C₄₇⋊C₈	C₂⁴	1	2	yes	—
448	C₂×C₄₇⋊C₈	C₂⁴	1	1	yes	characteristic
449	C₂×C₄₇⋊C₈	C₂⁴	1	2	yes	—
450	C₂×C₄₇⋊C₈	C₂⁴	1	1	yes	characteristic
451	C₂×C₄₇⋊C₈	C₂⁴	1	1	yes	characteristic
452	C₂×C₄₇⋊C₈	C₂⁴	1	1	yes	characteristic
453	#10625324	—	4	2	no	—
454	#10625324	—	4	2	no	—
455	C₈×D₄₇	—	4	2	no	—
456	C₈×D₄₇	—	4	2	no	—
457	C₂³×C₄₇	—	2	2	no	—
458	C₂³×C₄₇	—	4	1	no	—
459	C₂³×C₄₇	—	4	1	no	—
460	C₂³×C₄₇	C₂³×C₄	1	1	yes	characteristic
461	C₂³×C₄₇	C₂³×C₄	1	1	yes	characteristic
462	C₂³×C₄₇	C₂³×C₄	1	2	yes	—
463	C₂³×C₄₇	C₂³×C₄	1	1	yes	characteristic
464	C₂²×D₄₇	C₂³×C₄	1	2	yes	—
465	Q₈×C₄₇	—	2	2	no	—
466	D₄×C₄₇	—	2	4	no	—
467	D₄×C₄₇	—	2	2	no	—
468	D₄×C₄₇	—	4	2	no	—
469	D₄×C₄₇	—	4	2	no	—
470	C₂×C₄×C₄₇	—	2	2	no	—
471	C₂×C₄×C₄₇	—	2	2	no	—
472	C₂×C₄×C₄₇	—	2	2	no	—
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	2	no	—
479	C₂×C₄×C₄₇	C₂³×C₄	1	2	yes	—
480	C₂×C₄×C₄₇	C₂³×C₄	1	2	yes	—
481	C₂×C₄×C₄₇	C₂³×C₄	1	2	yes	—
482	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
483	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
484	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
485	C₂×C₄×C₄₇	H(5,𝔽₂)	1	2	yes	—
486	C₂×C₄×C₄₇	2₋¹⁺⁴	1	2	yes	—
487	C₂×C₄×C₄₇	C₂⁵	1	1	yes	characteristic
488	C₂²⋊D₄₇	—	2	4	no	—
489	C₂²⋊D₄₇	—	4	2	no	—
490	C₂²⋊D₄₇	—	4	2	no	—
491	C₂²⋊D₄₇	—	4	2	no	—
492	C₂²⋊D₄₇	—	4	2	no	—
493	C₂×Dic₄₇	—	4	1	no	—
494	C₂×Dic₄₇	—	4	1	no	—
495	C₂×Dic₄₇	—	4	2	no	—
496	C₂×Dic₄₇	—	4	2	no	—
497	C₂×Dic₄₇	—	4	1	no	—
498	C₂×Dic₄₇	—	4	1	no	—
499	C₂×Dic₄₇	C₂³×C₄	1	1	yes	characteristic
500	C₂×Dic₄₇	C₂³×C₄	1	1	yes	characteristic
501	C₂×Dic₄₇	C₂³×C₄	1	1	yes	characteristic
502	C₂×Dic₄₇	C₂³×C₄	1	1	yes	characteristic
503	C₂×Dic₄₇	C₂³×C₄	1	2	yes	—
504	C₂×Dic₄₇	C₂³×C₄	1	1	yes	characteristic
505	C₂×Dic₄₇	C₂³×C₄	1	1	yes	characteristic
506	C₂×Dic₄₇	C₂³×C₄	1	2	yes	—
507	C₂×Dic₄₇	C₂³×C₄	1	2	yes	—
508	C₂×Dic₄₇	C₂³×C₄	1	1	yes	characteristic
509	C₂×Dic₄₇	C₂³×C₄	1	1	yes	characteristic
510	D₁₈₈	—	2	2	no	—
511	C₄×D₄₇	—	2	2	no	—
512	C₄×D₄₇	—	2	2	no	—
513	C₄×D₄₇	—	4	2	no	—
514	C₄×D₄₇	—	4	2	no	—
515	Dic₉₄	—	2	2	no	—
516	Dic₉₄	—	4	2	no	—
517	Dic₉₄	—	4	2	no	—
518	C₈×C₄₇	—	2	1	no	—
519	C₈×C₄₇	—	2	2	no	—
520	C₈×C₄₇	—	2	1	no	—
521	C₈×C₄₇	—	2	1	no	—
522	C₈×C₄₇	—	2	1	no	—
523	C₈×C₄₇	—	2	2	no	—
524	C₄₇⋊C₈	—	2	1	no	—
525	C₄₇⋊C₈	—	2	2	no	—
526	C₄₇⋊C₈	—	2	1	no	—
527	C₄₇⋊C₈	—	2	1	no	—
528	C₄₇⋊C₈	—	2	1	no	—
529	C₄₇⋊C₈	—	2	2	no	—
530	#60267	—	47	1	no	maximal, Sylow
531	C₂²×C₄₇	—	2	1	no	—
532	C₂²×C₄₇	—	2	1	no	—
533	C₂²×C₄₇	—	2	1	no	—
534	C₂²×C₄₇	—	2	1	no	—
535	C₂²×C₄₇	—	2	2	no	—
536	C₂²×C₄₇	—	2	2	no	—
537	C₂²×C₄₇	—	2	2	no	—
538	C₂²×C₄₇	—	2	1	no	—
539	C₂²×C₄₇	—	2	1	no	—
540	C₂²×C₄₇	—	2	1	no	—
541	C₂²×C₄₇	—	2	1	no	—
542	C₂²×C₄₇	—	4	4	no	—
543	C₂²×C₄₇	#520	1	2	yes	—
544	C₂²×C₄₇	C₂⁴×C₄	1	1	yes	characteristic
545	C₂×D₄₇	—	2	2	no	—
546	C₂×D₄₇	—	2	2	no	—
547	C₂×D₄₇	—	2	2	no	—
548	C₄×C₄₇	—	2	1	no	—
549	C₄×C₄₇	—	2	1	no	—
550	C₄×C₄₇	—	2	2	no	—
551	C₄×C₄₇	—	2	2	no	—
552	C₄×C₄₇	—	2	2	no	—
553	C₄×C₄₇	#520	1	2	yes	—
554	C₄×C₄₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
555	C₄×C₄₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
556	Dic₄₇	—	2	2	no	—
557	Dic₄₇	—	2	1	no	—
558	Dic₄₇	—	2	1	no	—
559	Dic₄₇	—	2	2	no	—
560	Dic₄₇	—	2	2	no	—
561	Dic₄₇	—	2	1	no	—
562	Dic₄₇	—	2	1	no	—
563	Dic₄₇	—	2	1	no	—
564	Dic₄₇	—	2	1	no	—
565	Dic₄₇	—	2	1	no	—
566	Dic₄₇	—	2	1	no	—
567	#3455	—	47	1	no	—
568	#2995	—	47	2	no	—
569	#2995	—	47	2	no	—
570	#2994	—	47	2	no	—
571	#2994	—	47	2	no	—
572	#2993	—	47	2	no	—
573	#2993	—	47	2	no	—
574	#2992	—	47	2	no	—
575	#2992	—	47	2	no	—
576	#2962	—	47	1	no	—
577	#2962	—	47	1	no	—
578	#2935	—	47	1	no	—
579	#2935	—	47	1	no	—
580	#2930	—	47	1	no	—
581	#2930	—	47	1	no	—
582	#2929	—	47	1	no	—
583	#2929	D₄₇	1	1	yes	characteristic, complemented
584	#2925	—	47	1	no	—
585	#2925	—	47	1	no	—
586	#2921	—	47	1	no	—
587	#2906	—	47	1	no	—
588	#2906	—	47	1	no	—
589	C₂×#424	—	47	1	no	—
590	C₂×C₄₇	—	2	2	no	—
591	C₂×C₄₇	—	4	2	no	—
592	C₂×C₄₇	—	4	1	no	—
593	C₂×C₄₇	—	4	1	no	—
594	C₂×C₄₇	C₂×#520	1	1	yes	characteristic
595	C₂×C₄₇	#3573	1	1	yes	characteristic
596	C₂×C₄₇	#3573	1	1	yes	characteristic
597	D₄₇	—	4	2	no	—
598	C₂×#131	—	47	1	no	—
599	C₂×#131	—	47	1	no	—
600	C₂×#131	—	47	1	no	—
601	C₂×#131	C₂×D₄₇	1	1	yes	characteristic
602	C₂²×M₁₆	—	47	1	no	—
603	C₂³×C₈	C₂×D₄₇	1	1	yes	characteristic
604	#542	—	47	1	no	—
605	#542	—	47	1	no	—
606	#542	—	47	1	no	—
607	#542	—	47	1	no	—
608	#541	—	47	1	no	—
609	#541	—	47	1	no	—
610	#540	—	47	1	no	—
611	#540	—	47	1	no	—
612	#539	—	47	2	no	—
613	#539	—	47	2	no	—
614	#538	—	47	2	no	—
615	#538	—	47	2	no	—
616	#533	—	47	1	no	—
617	#532	—	47	1	no	—
618	#529	—	47	2	no	—
619	#529	—	47	2	no	—
620	#529	—	47	2	no	—
621	#529	—	47	2	no	—
622	#525	—	47	1	no	—
623	#525	C₂×D₄₇	1	1	yes	characteristic
624	C₄×#41	—	47	1	no	—
625	C₄×#41	—	47	1	no	—
626	C₂×#117	—	47	1	no	—
627	#446	—	47	2	no	—
628	#446	—	47	2	no	—
629	#446	—	47	2	no	—
630	#446	—	47	2	no	—
631	#446	—	47	2	no	—
632	#446	—	47	2	no	—
633	C₈×Q₈	—	47	2	no	—
634	C₈×Q₈	—	47	2	no	—
635	#436	—	47	2	no	—
636	#436	—	47	2	no	—
637	#436	—	47	2	no	—
638	#436	—	47	2	no	—
639	#436	—	47	2	no	—
640	#436	—	47	2	no	—
641	#435	—	47	2	no	—
642	#435	—	47	2	no	—
643	#435	—	47	2	no	—
644	#435	—	47	2	no	—
645	#435	—	47	2	no	—
646	#435	—	47	2	no	—
647	#435	—	47	2	no	—
648	#435	—	47	2	no	—
649	#435	—	47	2	no	—
650	#435	—	47	2	no	—
651	#435	C₂×D₄₇	1	2	yes	—
652	#435	C₂×D₄₇	1	2	yes	—
653	C₈×D₄	—	47	2	no	—
654	C₈×D₄	—	47	2	no	—
655	C₈×D₄	—	47	2	no	—
656	C₈×D₄	—	47	2	no	—
657	C₈×D₄	C₂×D₄₇	1	2	yes	—
658	C₈×D₄	C₂×D₄₇	1	2	yes	—
659	#433	—	47	2	no	—
660	#433	—	47	2	no	—
661	#433	—	47	2	no	—
662	#433	—	47	2	no	—
663	#433	—	47	2	no	—
664	#433	—	47	2	no	—
665	#433	—	47	2	no	—
666	#433	—	47	2	no	—
667	#432	—	47	2	no	—
668	#432	—	47	2	no	—
669	#431	—	47	2	no	—
670	#431	—	47	2	no	—
671	#424	—	47	1	no	—
672	#424	—	47	2	no	—
673	#424	—	47	1	no	—
674	#424	—	47	1	no	—
675	#424	—	47	1	no	—
676	#424	—	47	1	no	—
677	#424	—	47	1	no	—
678	#424	—	47	1	no	—
679	#424	—	47	1	no	—
680	#424	—	47	1	no	—
681	#424	—	47	1	no	—
682	#424	—	47	2	no	—
683	#424	—	47	1	no	—
684	#424	—	47	2	no	—
685	#424	—	47	2	no	—
686	#424	C₂×D₄₇	1	1	yes	characteristic
687	#423	—	47	1	no	—
688	#423	—	47	2	no	—
689	#423	—	47	1	no	—
690	#423	—	47	2	no	—
691	C₂×C₄⋊C₈	—	47	1	no	—
692	C₂×C₄⋊C₈	—	47	1	no	—
693	C₂×C₄⋊C₈	—	47	1	no	—
694	C₂×C₄⋊C₈	—	47	1	no	—
695	C₂×C₄⋊C₈	—	47	2	no	—
696	C₂×C₄⋊C₈	—	47	2	no	—
697	#408	—	47	1	no	—
698	#408	—	47	1	no	—
699	#408	—	47	1	no	—
700	#408	C₂×D₄₇	1	1	yes	characteristic
701	#407	—	47	1	no	—
702	#407	C₂×D₄₇	1	1	yes	characteristic
703	#405	—	47	1	no	—
704	#405	—	47	1	no	—
705	#405	—	47	1	no	—
706	#405	C₂×D₄₇	1	1	yes	characteristic
707	C₄×M₁₆	—	47	1	no	—
708	C₄×M₁₆	—	47	1	no	—
709	C₄₇	#60267	1	1	yes	characteristic, complemented, Sylow
710	C₂×#41	—	47	1	no	—
711	C₂×#41	C₂²×D₄₇	1	1	yes	characteristic
712	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
713	#131	—	4	2	no	—
714	#131	—	188	2	no	—
715	#131	—	188	2	no	—
716	#131	—	188	2	no	—
717	C₂×M₁₆	—	47	1	no	—
718	C₂×M₁₆	—	47	1	no	—
719	C₂×M₁₆	—	47	1	no	—
720	C₂×M₁₆	—	47	1	no	—
721	C₂×M₁₆	—	47	1	no	—
722	C₂×M₁₆	—	47	1	no	—
723	C₂×M₁₆	—	47	2	no	—
724	C₂×M₁₆	—	47	2	no	—
725	C₂×M₁₆	—	47	2	no	—
726	C₂×M₁₆	—	188	2	no	—
727	C₂×M₁₆	C₂²×D₄₇	1	1	yes	characteristic
728	C₂×M₁₆	C₂²×D₄₇	1	1	yes	characteristic
729	C₂×M₁₆	C₂²×D₄₇	1	2	yes	—
730	C₂²×C₈	—	4	2	no	—
731	C₂²×C₈	—	47	1	no	—
732	C₂²×C₈	—	47	1	no	—
733	C₂²×C₈	—	47	2	no	—
734	C₂²×C₈	—	47	2	no	—
735	C₂²×C₈	—	47	2	no	—
736	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
737	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
738	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
739	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
740	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
741	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
742	C₂²×C₈	C₂²×D₄₇	1	2	yes	—
743	C₄⋊Q₈	—	47	1	no	—
744	C₄⋊Q₈	—	47	1	no	—
745	C₄⋊Q₈	—	47	1	no	—
746	#127	—	47	1	no	—
747	#126	—	47	2	no	—
748	#126	—	47	2	no	—
749	#126	—	47	2	no	—
750	#126	—	47	2	no	—
751	#126	—	47	2	no	—
752	#126	—	47	2	no	—
753	#126	—	47	2	no	—
754	#126	—	47	2	no	—
755	#125	—	47	2	no	—
756	#125	—	47	2	no	—
757	#125	—	47	2	no	—
758	#125	—	47	2	no	—
759	#125	—	47	1	no	—
760	#125	—	47	1	no	—
761	#124	—	47	1	no	—
762	#124	—	47	2	no	—
763	#124	—	47	2	no	—
764	#124	—	47	1	no	—
765	#124	—	47	2	no	—
766	#124	—	47	2	no	—
767	#123	—	47	2	no	—
768	#123	—	47	2	no	—
769	#123	—	47	2	no	—
770	#123	—	47	2	no	—
771	#123	—	47	2	no	—
772	#123	—	47	2	no	—
773	#123	—	47	2	no	—
774	#123	—	47	2	no	—
775	#123	—	47	2	no	—
776	#123	C₄×D₄₇	1	2	yes	—
777	C₂²⋊Q₈	—	47	1	no	—
778	C₂²⋊Q₈	—	47	1	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	—	47	2	no	—
785	C₂²⋊Q₈	C₄×D₄₇	1	1	yes	characteristic
786	C₂²⋊Q₈	C₄×D₄₇	1	1	yes	characteristic
787	#121	—	47	2	no	—
788	#121	—	47	2	no	—
789	#121	—	47	2	no	—
790	#121	—	47	2	no	—
791	#121	—	47	2	no	—
792	#121	—	47	2	no	—
793	#121	—	47	1	no	—
794	#121	—	47	1	no	—
795	#121	C₄×D₄₇	1	1	yes	characteristic
796	#121	C₄×D₄₇	1	1	yes	characteristic
797	#120	—	47	2	no	—
798	#120	C₄×D₄₇	1	2	yes	—
799	C₄×Q₈	—	47	1	no	—
800	C₄×Q₈	—	47	1	no	—
801	C₄×Q₈	—	47	1	no	—
802	C₄×Q₈	—	47	1	no	—
803	C₄×Q₈	—	47	2	no	—
804	C₄×Q₈	—	47	2	no	—
805	C₄×D₄	—	47	2	no	—
806	C₄×D₄	—	47	2	no	—
807	C₄×D₄	—	47	1	no	—
808	C₄×D₄	—	47	1	no	—
809	C₄×D₄	—	47	2	no	—
810	C₄×D₄	—	47	2	no	—
811	C₄×D₄	—	47	2	no	—
812	C₄×D₄	—	47	2	no	—
813	C₄×D₄	—	47	1	no	—
814	C₄×D₄	—	47	1	no	—
815	C₄×D₄	—	47	2	no	—
816	C₄×D₄	—	47	2	no	—
817	C₄×D₄	C₂²×D₄₇	1	2	yes	—
818	C₄×D₄	C₂²×D₄₇	1	2	yes	—
819	#117	—	47	1	no	—
820	#117	—	47	1	no	—
821	#117	—	47	1	no	—
822	#117	—	47	1	no	—
823	#117	—	47	1	no	—
824	#117	—	47	1	no	—
825	#117	—	47	1	no	—
826	#117	—	47	1	no	—
827	#117	—	47	1	no	—
828	#117	—	47	2	no	—
829	#117	—	47	2	no	—
830	#117	C₂²×D₄₇	1	1	yes	characteristic
831	C₂×C₄⋊C₄	—	47	1	no	—
832	C₂×C₄⋊C₄	—	47	1	no	—
833	C₂×C₂²⋊C₄	—	47	1	no	—
834	C₂×C₂²⋊C₄	—	47	1	no	—
835	C₂×C₄²	—	47	1	no	—
836	C₂×C₄²	—	47	1	no	—
837	C₂×C₄²	—	47	2	no	—
838	C₂×C₄²	—	47	2	no	—
839	C₄⋊C₈	—	47	1	no	—
840	C₄⋊C₈	—	47	1	no	—
841	C₄⋊C₈	—	47	1	no	—
842	C₄⋊C₈	—	47	1	no	—
843	C₄⋊C₈	—	47	2	no	—
844	C₄⋊C₈	—	47	2	no	—
845	C₄⋊C₈	—	47	1	no	—
846	C₄⋊C₈	—	47	1	no	—
847	C₄⋊C₈	—	47	1	no	—
848	C₄⋊C₈	—	47	1	no	—
849	C₄⋊C₈	—	47	1	no	—
850	C₄⋊C₈	—	47	1	no	—
851	C₄⋊C₈	—	47	2	no	—
852	C₄⋊C₈	—	47	1	no	—
853	C₄⋊C₈	—	47	1	no	—
854	C₄⋊C₈	—	47	1	no	—
855	C₄⋊C₈	—	47	1	no	—
856	C₄⋊C₈	—	47	2	no	—
857	C₄⋊C₈	—	47	1	no	—
858	C₄⋊C₈	—	47	1	no	—
859	C₄⋊C₈	—	47	2	no	—
860	C₄⋊C₈	—	47	2	no	—
861	C₄⋊C₈	—	47	2	no	—
862	C₄⋊C₈	—	47	2	no	—
863	C₄⋊C₈	—	47	2	no	—
864	C₄⋊C₈	—	47	2	no	—
865	C₄⋊C₈	C₂²×D₄₇	1	2	yes	—
866	C₄⋊C₈	C₂²×D₄₇	1	2	yes	—
867	C₂²⋊C₈	—	47	2	no	—
868	C₂²⋊C₈	—	47	2	no	—
869	C₂²⋊C₈	—	47	2	no	—
870	C₂²⋊C₈	—	47	2	no	—
871	C₂²⋊C₈	—	47	2	no	—
872	C₂²⋊C₈	—	47	2	no	—
873	C₂²⋊C₈	—	47	2	no	—
874	C₂²⋊C₈	—	47	2	no	—
875	C₂²⋊C₈	C₂²×D₄₇	1	2	yes	—
876	C₂²⋊C₈	C₂²×D₄₇	1	2	yes	—
877	C₂²⋊C₈	C₂²×D₄₇	1	2	yes	—
878	C₂²⋊C₈	C₂²×D₄₇	1	2	yes	—
879	#97	—	47	2	no	—
880	#97	—	47	2	no	—
881	#97	—	47	2	no	—
882	#97	—	47	2	no	—
883	#97	—	47	2	no	—
884	#97	C₂²×D₄₇	1	2	yes	—
885	C₄×C₈	—	47	2	no	—
886	C₄×C₈	—	47	2	no	—
887	C₄×C₈	—	47	2	no	—
888	C₄×C₈	—	47	2	no	—
889	C₄×C₈	—	47	2	no	—
890	C₄×C₈	C₂²×D₄₇	1	2	yes	—
891	C₂⁴	C₂×C₄×D₄₇	1	1	yes	characteristic
892	#41	—	2	2	no	—
893	#41	—	2	2	no	—
894	#41	—	94	2	no	—
895	#41	—	94	2	no	—
896	C₂×Q₈	—	47	1	no	—
897	C₂×Q₈	—	47	2	no	—
898	C₂×Q₈	—	47	2	no	—
899	C₂×Q₈	C₂×C₄×D₄₇	1	1	yes	characteristic
900	C₂×D₄	—	47	2	no	—
901	C₂×D₄	—	47	2	no	—
902	C₂×D₄	—	47	2	no	—
903	C₂×D₄	—	47	2	no	—
904	C₂×D₄	—	47	2	no	—
905	C₂×D₄	—	47	1	no	—
906	C₂×D₄	C₂×C₄×D₄₇	1	2	yes	—
907	C₂×D₄	C₂×C₄×D₄₇	1	1	yes	characteristic
908	C₂×D₄	C₂×C₄×D₄₇	1	2	yes	—
909	C₂×D₄	C₂×C₄×D₄₇	1	2	yes	—
910	C₂²×C₄	—	2	2	no	—
911	C₂²×C₄	—	2	2	no	—
912	C₂²×C₄	—	47	1	no	—
913	C₂²×C₄	—	47	1	no	—
914	C₂²×C₄	—	47	1	no	—
915	C₂²×C₄	—	47	1	no	—
916	C₂²×C₄	—	47	2	no	—
917	C₂²×C₄	—	47	2	no	—
918	C₂²×C₄	—	47	2	no	—
919	C₂²×C₄	—	47	2	no	—
920	C₂²×C₄	—	47	2	no	—
921	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
922	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
923	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
924	C₂²×C₄	C₂³×D₄₇	1	2	yes	—
925	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
926	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
927	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
928	M₁₆	—	2	2	no	—
929	M₁₆	—	2	2	no	—
930	M₁₆	—	4	2	no	—
931	M₁₆	—	94	2	no	—
932	M₁₆	—	94	2	no	—
933	M₁₆	—	188	2	no	—
934	M₁₆	—	188	2	no	—
935	M₁₆	—	188	1	no	—
936	M₁₆	—	188	1	no	—
937	M₁₆	—	188	1	no	—
938	M₁₆	—	188	1	no	—
939	M₁₆	—	188	2	no	—
940	C₂×C₈	—	2	2	no	—
941	C₂×C₈	—	2	2	no	—
942	C₂×C₈	—	4	1	no	—
943	C₂×C₈	—	4	1	no	—
944	C₂×C₈	—	4	1	no	—
945	C₂×C₈	—	4	1	no	—
946	C₂×C₈	—	4	2	no	—
947	C₂×C₈	—	47	2	no	—
948	C₂×C₈	—	47	1	no	—
949	C₂×C₈	—	47	1	no	—
950	C₂×C₈	—	47	2	no	—
951	C₂×C₈	—	47	1	no	—
952	C₂×C₈	—	47	1	no	—
953	C₂×C₈	—	94	2	no	—
954	C₂×C₈	—	94	2	no	—
955	C₂×C₈	—	188	2	no	—
956	C₂×C₈	—	188	2	no	—
957	C₂×C₈	—	188	2	no	—
958	C₂×C₈	C₂³×D₄₇	1	2	yes	—
959	C₂×C₈	C₂³×D₄₇	1	1	yes	characteristic
960	C₂×C₈	C₂³×D₄₇	1	2	yes	—
961	C₂×C₈	C₂³×D₄₇	1	1	yes	characteristic
962	C₂×C₈	C₂³×D₄₇	1	1	yes	characteristic
963	C₂×C₈	C₂³×D₄₇	1	1	yes	characteristic
964	C₄⋊C₄	—	47	2	no	—
965	C₄⋊C₄	—	47	2	no	—
966	C₄⋊C₄	—	47	2	no	—
967	C₄⋊C₄	—	47	2	no	—
968	C₄⋊C₄	—	47	2	no	—
969	C₄⋊C₄	—	47	2	no	—
970	C₄⋊C₄	—	47	2	no	—
971	C₄⋊C₄	—	47	2	no	—
972	C₄⋊C₄	—	47	2	no	—
973	C₄⋊C₄	—	47	2	no	—
974	C₄⋊C₄	—	47	1	no	—
975	C₄⋊C₄	—	47	1	no	—
976	C₄⋊C₄	—	47	1	no	—
977	C₄⋊C₄	—	47	1	no	—
978	C₄⋊C₄	—	47	1	no	—
979	C₄⋊C₄	—	47	1	no	—
980	C₄⋊C₄	—	47	1	no	—
981	C₄⋊C₄	—	47	1	no	—
982	C₄⋊C₄	—	47	1	no	—
983	C₄⋊C₄	—	47	1	no	—
984	C₄⋊C₄	—	47	2	no	—
985	C₄⋊C₄	—	47	2	no	—
986	C₄⋊C₄	—	47	2	no	—
987	C₄⋊C₄	—	47	2	no	—
988	C₄⋊C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
989	C₄⋊C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
990	C₄⋊C₄	C₂×C₄×D₄₇	1	2	yes	—
991	C₄⋊C₄	C₂×C₄×D₄₇	1	2	yes	—
992	C₂²⋊C₄	—	47	1	no	—
993	C₂²⋊C₄	—	47	1	no	—
994	C₂²⋊C₄	—	47	1	no	—
995	C₂²⋊C₄	—	47	1	no	—
996	C₂²⋊C₄	—	47	1	no	—
997	C₂²⋊C₄	—	47	1	no	—
998	C₂²⋊C₄	—	47	1	no	—
999	C₂²⋊C₄	—	47	1	no	—
1000	C₂²⋊C₄	—	47	2	no	—
1001	C₂²⋊C₄	—	47	2	no	—
1002	C₂²⋊C₄	—	47	2	no	—
1003	C₂²⋊C₄	—	47	2	no	—
1004	C₂²⋊C₄	—	47	2	no	—
1005	C₂²⋊C₄	—	47	2	no	—
1006	C₂²⋊C₄	—	47	2	no	—
1007	C₂²⋊C₄	—	47	2	no	—
1008	C₂²⋊C₄	—	47	2	no	—
1009	C₂²⋊C₄	—	47	2	no	—
1010	C₂²⋊C₄	—	47	2	no	—
1011	C₂²⋊C₄	—	47	2	no	—
1012	C₂²⋊C₄	—	47	2	no	—
1013	C₂²⋊C₄	C₂×C₄×D₄₇	1	2	yes	—
1014	C₂²⋊C₄	C₂×C₄×D₄₇	1	2	yes	—
1015	C₂²⋊C₄	C₂×C₄×D₄₇	1	2	yes	—
1016	C₂²⋊C₄	C₂×C₄×D₄₇	1	2	yes	—
1017	C₂²⋊C₄	C₂×C₄×D₄₇	1	2	yes	—
1018	C₄²	—	47	1	no	—
1019	C₄²	—	47	1	no	—
1020	C₄²	—	47	1	no	—
1021	C₄²	—	47	1	no	—
1022	C₄²	—	47	2	no	—
1023	C₄²	—	47	2	no	—
1024	C₄²	—	47	2	no	—
1025	C₄²	—	47	2	no	—
1026	C₄²	—	47	1	no	—
1027	C₄²	—	47	1	no	—
1028	C₄²	—	47	2	no	—
1029	C₄²	—	47	1	no	—
1030	C₄²	—	47	1	no	—
1031	C₄²	C₂³×D₄₇	1	2	yes	—
1032	C₂³	—	2	2	no	—
1033	C₂³	—	4	1	no	—
1034	C₂³	—	4	1	no	—
1035	C₂³	—	47	2	no	—
1036	C₂³	C₂²×C₄×D₄₇	1	1	yes	characteristic
1037	C₂³	C₂²×C₄×D₄₇	1	1	yes	characteristic
1038	C₂³	C₂²×C₄×D₄₇	1	2	yes	—
1039	C₂³	C₂²×C₄×D₄₇	1	1	yes	characteristic
1040	Q₈	—	2	2	no	—
1041	Q₈	—	94	2	no	—
1042	Q₈	—	188	2	no	—
1043	Q₈	—	188	2	no	—
1044	D₄	—	2	4	no	—
1045	D₄	—	2	2	no	—
1046	D₄	—	4	2	no	—
1047	D₄	—	4	2	no	—
1048	D₄	—	94	4	no	—
1049	D₄	—	94	2	no	—
1050	D₄	—	188	2	no	—
1051	D₄	—	188	2	no	—
1052	D₄	—	188	2	no	—
1053	D₄	—	188	2	no	—
1054	C₂×C₄	—	2	2	no	—
1055	C₂×C₄	—	2	2	no	—
1056	C₂×C₄	—	2	2	no	—
1057	C₂×C₄	—	2	1	no	—
1058	C₂×C₄	—	2	1	no	—
1059	C₂×C₄	—	2	2	no	—
1060	C₂×C₄	—	2	1	no	—
1061	C₂×C₄	—	2	1	no	—
1062	C₂×C₄	—	2	2	no	—
1063	C₂×C₄	—	47	1	no	—
1064	C₂×C₄	—	47	1	no	—
1065	C₂×C₄	—	47	1	no	—
1066	C₂×C₄	—	47	1	no	—
1067	C₂×C₄	—	47	1	no	—
1068	C₂×C₄	—	47	1	no	—
1069	C₂×C₄	—	47	2	no	—
1070	C₂×C₄	—	47	2	no	—
1071	C₂×C₄	—	47	2	no	—
1072	C₂×C₄	—	47	1	no	—
1073	C₂×C₄	—	47	1	no	—
1074	C₂×C₄	—	94	2	no	—
1075	C₂×C₄	—	94	2	no	—
1076	C₂×C₄	—	188	2	no	—
1077	C₂×C₄	—	188	2	no	—
1078	C₂×C₄	—	188	1	no	—
1079	C₂×C₄	—	188	1	no	—
1080	C₂×C₄	—	188	2	no	—
1081	C₂×C₄	—	188	2	no	—
1082	C₂×C₄	—	188	1	no	—
1083	C₂×C₄	—	188	1	no	—
1084	C₂×C₄	C₂²×C₄×D₄₇	1	2	yes	—
1085	C₂×C₄	C₂²×C₄×D₄₇	1	2	yes	—
1086	C₂×C₄	C₂²×C₄×D₄₇	1	2	yes	—
1087	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
1088	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
1089	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
1090	C₂×C₄	#13094069	1	2	yes	—
1091	C₂×C₄	#13094071	1	2	yes	—
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	—	2	1	no	—
1097	C₈	—	2	2	no	—
1098	C₈	—	2	2	no	—
1099	C₈	—	94	1	no	—
1100	C₈	—	94	1	no	—
1101	C₈	—	94	1	no	—
1102	C₈	—	94	1	no	—
1103	C₈	—	94	2	no	—
1104	C₈	—	94	2	no	—
1105	C₂²	—	2	1	no	—
1106	C₂²	—	2	1	no	—
1107	C₂²	—	2	2	no	—
1108	C₂²	—	2	2	no	—
1109	C₂²	—	2	1	no	—
1110	C₂²	—	2	1	no	—
1111	C₂²	—	2	1	no	—
1112	C₂²	—	2	1	no	—
1113	C₂²	—	2	1	no	—
1114	C₂²	—	2	1	no	—
1115	C₂²	—	2	2	no	—
1116	C₂²	—	4	4	no	—
1117	C₂²	—	94	2	no	—
1118	C₂²	—	94	2	no	—
1119	C₂²	—	94	2	no	—
1120	C₂²	#15689602	1	2	yes	—
1121	C₂²	C₂³×C₄×D₄₇	1	1	yes	characteristic
1122	C₄	—	2	2	no	—
1123	C₄	—	2	2	no	—
1124	C₄	—	2	1	no	—
1125	C₄	—	2	1	no	—
1126	C₄	—	2	2	no	—
1127	C₄	—	94	1	no	—
1128	C₄	—	94	1	no	—
1129	C₄	—	94	1	no	—
1130	C₄	—	94	1	no	—
1131	C₄	—	94	1	no	—
1132	C₄	—	94	1	no	—
1133	C₄	—	94	2	no	—
1134	C₄	—	94	2	no	—
1135	C₄	—	94	1	no	—
1136	C₄	—	94	1	no	—
1137	C₄	—	94	2	no	—
1138	C₄	#15689602	1	2	yes	—
1139	C₄	C₂×#13094069	1	1	yes	characteristic
1140	C₄	C₂×#13094071	1	1	yes	characteristic
1141	C₂	—	2	2	no	—
1142	C₂	—	4	1	no	—
1143	C₂	—	4	1	no	—
1144	C₂	—	4	2	no	—
1145	C₂	—	188	2	no	—
1146	C₂	C₂×#15689602	1	1	yes	characteristic
1147	C₂	#20258099	1	1	yes	characteristic
1148	C₂	#20258099	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂⁴×D₄₇
commutator, socle	C₂²×C₄₇	C₂⁴×C₄
Fitting	C₄₇×#2929	C₂
prime radical	#20256776	C₂
cosocle	C₂×C₄×C₄₇	C₂⁵
hypercenter	#2929	D₄₇
hypocenter	C₄₇	#60267
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ #2929

Complements

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

N	H ≅ G/N	type
2. #20252559	C₂	semidirect
3. #20252554	C₂	semidirect
4. #20252545	C₂	semidirect
5. #20252543	C₂	semidirect
6. #20252538	C₂	semidirect
7. #20252530	C₂	semidirect
8. #20252523	C₂	semidirect
9. #20252521	C₂	semidirect
10. #20252334	C₂	semidirect
11. #20252332	C₂	semidirect
12. #20252130	C₂	semidirect
13. #20252128	C₂	semidirect
14. #20252092	C₂	semidirect
15. #20252087	C₂	semidirect
16. #20252082	C₂	semidirect
17. #20252052	C₂	semidirect
18. #20252050	C₂	semidirect
19. #20252023	C₂	semidirect
20. #20251955	C₂	semidirect
21. #20251954	C₂	semidirect
22. C₂×#15689149	C₂	semidirect
23. C₄₇×#2929	C₂	semidirect
50. #15689253	C₂²	semidirect
51. #15689252	C₂²	semidirect
52. #15689252	C₂²	semidirect
53. #15689251	C₂²	semidirect
54. #15689251	C₂²	semidirect
55. #15689250	C₂²	semidirect
56. C₈×Dic₉₄	C₂²	semidirect
57. #15689247	C₂²	semidirect
60. #15689199	C₂²	semidirect
63. #15689198	C₂²	semidirect
66. #15689197	C₂²	semidirect
71. #15689194	C₂²	semidirect
72. #15689192	C₂²	semidirect
73. #15689191	C₂²	semidirect
76. C₈×C₂²⋊D₄₇	C₂²	semidirect
77. (C₂²⋊D₄₇)⋊C₈	C₂²	semidirect
78. #15689185	C₂²	semidirect
79. #15689182	C₂²	semidirect
84. #15689181	C₂²	semidirect
85. #15689181	C₂²	semidirect
86. #15689178	C₂²	semidirect
87. #15689177	C₂²	semidirect
88. #15689174	C₂²	semidirect
89. #15689173	C₂²	semidirect
91. #15689151	C₂²	semidirect
102. #15689149	C₂²	semidirect
103. #15689148	C₂²	semidirect
104. #15689148	C₂²	semidirect
107. #15689146	C₂²	semidirect
108. #15689145	C₂²	semidirect
113. C₂×Dic₄₇⋊C₈	C₂²	semidirect
114. C₄⋊C₈×D₄₇	C₂²	semidirect
583. #2929	D₄₇	semidirect
709. C₄₇	#60267	semidirect

Maximal subgroups

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

subgroup	index
#20256776	2
#20252559	2
#20252554	2
#20252545	2
#20252543	2
#20252538	2
#20252530	2
#20252523	2
#20252521	2
#20252334	2
#20252332	2
#20252130	2
#20252128	2
#20252092	2
#20252087	2
#20252082	2
#20252052	2
#20252050	2
#20252023	2
#20251955	2
#20251954	2
C₂×#15689149	2
C₄₇×#2929	2
#60267	47