Subgroups — #27081284

Order 12032.

1626 conjugacy classes of subgroups.

The subgroup lattice has 1066 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20256793	C₂	1	1	yes	maximal, characteristic
2	#20252493	C₂	1	2	yes	maximal, complemented
3	#20252492	C₂	1	2	yes	maximal, complemented
4	#20252489	C₂	1	2	yes	maximal, complemented
5	#20252487	C₂	1	2	yes	maximal, complemented
6	#20252485	C₂	1	2	yes	maximal, complemented
7	#20252482	C₂	1	2	yes	maximal, complemented
8	#20252480	C₂	1	2	yes	maximal, complemented
9	#20252480	C₂	1	2	yes	maximal, complemented
10	#20252334	C₂	1	1	yes	maximal, characteristic, complemented
11	#20252334	C₂	1	1	yes	maximal, characteristic, complemented
12	#20252332	C₂	1	1	yes	maximal, characteristic, complemented
13	#20252332	C₂	1	1	yes	maximal, characteristic, complemented
14	#20252327	C₂	1	1	yes	maximal, characteristic, complemented
15	#20252326	C₂	1	1	yes	maximal, characteristic, complemented
16	#20252321	C₂	1	1	yes	maximal, characteristic, complemented
17	#20252320	C₂	1	1	yes	maximal, characteristic, complemented
18	#20252048	C₂	1	1	yes	maximal, characteristic
19	#20252046	C₂	1	1	yes	maximal, characteristic
20	#20252042	C₂	1	1	yes	maximal, characteristic
21	#20252023	C₂	1	1	yes	maximal, characteristic
22	C₂×#15689181	C₂	1	1	yes	maximal, characteristic
23	C₄₇×#2924	C₂	1	1	yes	maximal, characteristic
24	#15689754	C₄	1	1	yes	characteristic
25	#15689754	C₄	1	1	yes	characteristic
26	#15689754	C₄	1	1	yes	characteristic
27	#15689754	C₄	1	1	yes	characteristic
28	#15689751	C₄	1	2	yes	—
29	#15689751	C₄	1	2	yes	—
30	#15689751	C₄	1	1	yes	characteristic
31	#15689751	C₄	1	1	yes	characteristic
32	#15689751	C₄	1	1	yes	characteristic
33	#15689751	C₄	1	1	yes	characteristic
34	#15689749	C₄	1	2	yes	—
35	#15689749	C₄	1	2	yes	—
36	#15689680	C₂²	1	2	yes	—
37	#15689680	C₂²	1	2	yes	—
38	#15689676	C₂²	1	2	yes	—
39	#15689676	C₂²	1	2	yes	—
40	#15689676	C₂²	1	1	yes	characteristic
41	#15689676	C₂²	1	1	yes	characteristic
42	#15689676	C₂²	1	1	yes	characteristic
43	#15689676	C₂²	1	1	yes	characteristic
44	C₂×#13093983	C₂²	1	1	yes	characteristic
45	C₂×#13093983	C₂²	1	1	yes	characteristic
46	#15689253	C₂²	1	2	yes	complemented
47	#15689253	C₂²	1	2	yes	complemented
48	#15689253	C₂²	1	2	yes	complemented
49	#15689253	C₂²	1	2	yes	complemented
50	#15689252	C₂²	1	2	yes	complemented
51	#15689252	C₂²	1	2	yes	complemented
52	#15689252	C₂²	1	2	yes	complemented
53	#15689252	C₂²	1	2	yes	complemented
54	#15689252	C₂²	1	2	yes	complemented
55	#15689252	C₂²	1	2	yes	complemented
56	#15689252	C₂²	1	2	yes	complemented
57	#15689252	C₂²	1	2	yes	complemented
58	#15689251	C₂²	1	2	yes	complemented
59	#15689251	C₂²	1	2	yes	complemented
60	#15689251	C₂²	1	2	yes	complemented
61	#15689251	C₂²	1	2	yes	complemented
62	#15689251	C₂²	1	2	yes	complemented
63	#15689251	C₂²	1	2	yes	complemented
64	#15689251	C₂²	1	2	yes	complemented
65	#15689251	C₂²	1	2	yes	complemented
66	#15689250	C₂²	1	2	yes	complemented
67	#15689250	C₂²	1	2	yes	complemented
68	#15689250	C₂²	1	2	yes	complemented
69	#15689250	C₂²	1	2	yes	complemented
70	C₈×Dic₉₄	C₂²	1	2	yes	complemented
71	C₈×Dic₉₄	C₂²	1	2	yes	complemented
72	C₈×Dic₉₄	C₂²	1	2	yes	complemented
73	C₈×Dic₉₄	C₂²	1	2	yes	complemented
74	#15689247	C₂²	1	2	yes	complemented
75	#15689247	C₂²	1	2	yes	complemented
76	#15689247	C₂²	1	2	yes	complemented
77	#15689247	C₂²	1	2	yes	complemented
78	#15689184	C₂²	1	2	yes	—
79	#15689184	C₂²	1	2	yes	—
80	#15689181	C₂²	1	1	yes	characteristic
81	#15689181	C₂²	1	1	yes	characteristic
82	#15689181	C₂²	1	2	yes	—
83	#15689181	C₂²	1	1	yes	characteristic
84	#15689181	C₂²	1	2	yes	—
85	#15689181	C₂²	1	2	yes	—
86	#15689181	C₂²	1	2	yes	—
87	#15689181	C₂²	1	1	yes	characteristic
88	#15689181	C₂²	1	2	yes	—
89	#15689181	C₂²	1	2	yes	—
90	#15689181	C₂²	1	1	yes	characteristic
91	#15689181	C₂²	1	2	yes	—
92	#15689181	C₂²	1	1	yes	characteristic
93	#15689181	C₂²	1	2	yes	—
94	#15689181	C₂²	1	1	yes	characteristic
95	#15689181	C₂²	1	1	yes	characteristic
96	#15689180	C₂²	1	2	yes	—
97	#15689177	C₂²	1	2	yes	—
98	#15689177	C₂²	1	2	yes	—
99	#15689176	C₂²	1	2	yes	—
100	#15689173	C₂²	1	2	yes	—
101	#15689173	C₂²	1	2	yes	—
102	#15689151	C₂²	1	1	yes	characteristic
103	#15689151	C₂²	1	1	yes	characteristic
104	#15689150	C₂²	1	1	yes	characteristic
105	#15689150	C₂²	1	1	yes	characteristic
106	#15689149	C₂²	1	1	yes	characteristic
107	#15689149	C₂²	1	1	yes	characteristic
108	#15689146	C₂²	1	1	yes	characteristic
109	#15689146	C₂²	1	1	yes	characteristic
110	C₂×Dic₄₇⋊C₈	C₂²	1	1	yes	characteristic
111	C₂×Dic₄₇⋊C₈	C₂²	1	1	yes	characteristic
112	#15689087	C₂²	1	1	yes	characteristic
113	C₂×C₂²⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
114	#15689081	C₂²	1	1	yes	characteristic
115	#15689081	C₂²	1	1	yes	characteristic
116	#15689079	C₂²	1	1	yes	characteristic
117	#15689079	C₂²	1	1	yes	characteristic
118	#15689078	C₂²	1	1	yes	characteristic
119	#15689078	C₂²	1	1	yes	characteristic
120	M₁₆×Dic₄₇	C₂²	1	1	yes	characteristic
121	M₁₆×Dic₄₇	C₂²	1	1	yes	characteristic
122	C₂×#13093934	C₂²	1	1	yes	characteristic
123	C₂×C₈×Dic₄₇	C₂²	1	1	yes	characteristic
124	C₂×#117×C₄₇	C₂²	1	1	yes	characteristic
125	C₄₇×#433	C₂²	1	2	yes	—
126	C₄₇×#433	C₂²	1	2	yes	—
127	C₄₇×#432	C₂²	1	2	yes	—
128	C₄₇×#431	C₂²	1	2	yes	—
129	C₄₇×#424	C₂²	1	1	yes	characteristic
130	C₄₇×#424	C₂²	1	1	yes	characteristic
131	C₄₇×#407	C₂²	1	1	yes	characteristic
132	C₂×C₂²⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
133	C₄₇×#405	C₂²	1	1	yes	characteristic
134	C₄₇×#405	C₂²	1	1	yes	characteristic
135	C₂×#10625329	C₂³	1	1	yes	characteristic
136	C₂×#10625329	C₂³	1	1	yes	characteristic
137	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
138	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
139	#13094024	C₂×C₄	1	2	yes	—
140	#13094024	C₂×C₄	1	2	yes	—
141	#13094024	C₂×C₄	1	2	yes	—
142	#13094024	C₂×C₄	1	2	yes	—
143	#13094023	C₂×C₄	1	2	yes	—
144	#13094023	C₂×C₄	1	2	yes	—
145	#13094023	C₂×C₄	1	2	yes	—
146	#13094023	C₂×C₄	1	2	yes	—
147	#13094023	C₂×C₄	1	1	yes	characteristic
148	#13094023	C₂×C₄	1	1	yes	characteristic
149	#13094023	C₂×C₄	1	1	yes	characteristic
150	#13094023	C₂×C₄	1	1	yes	characteristic
151	#13094023	C₂×C₄	1	1	yes	characteristic
152	#13094023	C₂×C₄	1	1	yes	characteristic
153	#13094023	C₂×C₄	1	1	yes	characteristic
154	#13094023	C₂×C₄	1	1	yes	characteristic
155	#13094016	C₂×C₄	1	2	yes	—
156	#13094016	C₂×C₄	1	2	yes	—
157	#13094016	C₂×C₄	1	2	yes	—
158	#13094016	C₂×C₄	1	2	yes	—
159	#13094015	C₂×C₄	1	2	yes	—
160	#13094015	C₂×C₄	1	2	yes	—
161	#13094015	C₂×C₄	1	2	yes	—
162	#13094015	C₂×C₄	1	2	yes	—
163	#13094015	C₂×C₄	1	1	yes	characteristic
164	#13094015	C₂×C₄	1	1	yes	characteristic
165	#13094015	C₂×C₄	1	1	yes	characteristic
166	#13094015	C₂×C₄	1	1	yes	characteristic
167	#13094015	C₂×C₄	1	1	yes	characteristic
168	#13094015	C₂×C₄	1	1	yes	characteristic
169	#13094015	C₂×C₄	1	1	yes	characteristic
170	#13094015	C₂×C₄	1	1	yes	characteristic
171	#13094003	C₂×C₄	1	2	yes	—
172	#13094003	C₂×C₄	1	2	yes	—
173	#13094003	C₂×C₄	1	2	yes	—
174	#13094003	C₂×C₄	1	2	yes	—
175	#13094003	C₂×C₄	1	2	yes	—
176	#13094003	C₂×C₄	1	2	yes	—
177	#13094003	C₂×C₄	1	2	yes	—
178	#13094003	C₂×C₄	1	2	yes	—
179	#13094001	C₂×C₄	1	2	yes	—
180	#13094001	C₂×C₄	1	2	yes	—
181	#13094001	C₂×C₄	1	2	yes	—
182	#13094001	C₂×C₄	1	2	yes	—
183	#13094001	C₂×C₄	1	2	yes	—
184	#13094001	C₂×C₄	1	2	yes	—
185	#13094001	C₂×C₄	1	2	yes	—
186	#13094001	C₂×C₄	1	2	yes	—
187	#13094001	C₂×C₄	1	2	yes	—
188	#13094001	C₂×C₄	1	2	yes	—
189	#13094001	C₂×C₄	1	2	yes	—
190	#13094001	C₂×C₄	1	2	yes	—
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	C₄×Dic₉₄	C₂³	1	2	yes	—
196	C₄×Dic₉₄	C₂³	1	2	yes	—
197	C₄×Dic₉₄	C₂³	1	2	yes	—
198	C₄×Dic₉₄	C₂³	1	2	yes	—
199	C₄×Dic₉₄	C₂³	1	2	yes	—
200	C₄×Dic₉₄	C₂³	1	2	yes	—
201	C₄×Dic₉₄	C₂³	1	2	yes	—
202	C₄×Dic₉₄	C₂³	1	2	yes	—
203	#13093983	C₂×C₄	1	1	yes	characteristic
204	#13093983	C₂×C₄	1	1	yes	characteristic
205	#13093983	C₂×C₄	1	2	yes	—
206	#13093983	C₂×C₄	1	1	yes	characteristic
207	#13093983	C₂×C₄	1	1	yes	characteristic
208	#13093983	C₂×C₄	1	1	yes	characteristic
209	#13093983	C₂×C₄	1	1	yes	characteristic
210	#13093983	C₂³	1	1	yes	characteristic
211	#13093983	C₂³	1	1	yes	characteristic
212	#13093983	C₂³	1	1	yes	characteristic
213	#13093983	C₂³	1	1	yes	characteristic
214	#13093983	C₂³	1	1	yes	characteristic
215	#13093983	C₂³	1	1	yes	characteristic
216	#13093983	C₂³	1	2	yes	—
217	C₂×C₄⋊Dic₄₇	C₂×C₄	1	1	yes	characteristic
218	C₂×C₄⋊Dic₄₇	C₂×C₄	1	1	yes	characteristic
219	C₂×C₄⋊Dic₄₇	C₂×C₄	1	1	yes	characteristic
220	C₂×C₄⋊Dic₄₇	C₂×C₄	1	1	yes	characteristic
221	C₂×C₂²⋊Dic₄₇	C₂×C₄	1	1	yes	characteristic
222	C₂×C₂²⋊Dic₄₇	C₂×C₄	1	1	yes	characteristic
223	C₂×C₂²⋊Dic₄₇	C₂×C₄	1	2	yes	—
224	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
225	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
226	C₂×C₄×Dic₄₇	C₂³	1	2	yes	—
227	C₄⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
228	C₄⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
229	C₄⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
230	C₄⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
231	Dic₄₇⋊C₈	C₂³	1	1	yes	characteristic
232	Dic₄₇⋊C₈	C₂³	1	1	yes	characteristic
233	Dic₄₇⋊C₈	C₂³	1	2	yes	—
234	Dic₄₇⋊C₈	C₂³	1	2	yes	—
235	Dic₄₇⋊C₈	C₂³	1	2	yes	—
236	Dic₄₇⋊C₈	C₂³	1	2	yes	—
237	Dic₄₇⋊C₈	C₂³	1	2	yes	—
238	Dic₄₇⋊C₈	C₂³	1	2	yes	—
239	Dic₄₇⋊C₈	C₂³	1	1	yes	characteristic
240	Dic₄₇⋊C₈	C₂³	1	1	yes	characteristic
241	Dic₄₇⋊C₈	C₂³	1	2	yes	—
242	Dic₄₇⋊C₈	C₂³	1	2	yes	—
243	Dic₄₇⋊C₈	C₂³	1	2	yes	—
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	2	yes	—
250	Dic₄₇⋊C₈	C₂³	1	1	yes	characteristic
251	C₂²⋊(C₄₇⋊C₈)	C₂³	1	1	yes	characteristic
252	C₂²⋊(C₄₇⋊C₈)	C₂³	1	1	yes	characteristic
253	C₂²⋊(C₄₇⋊C₈)	C₂³	1	1	yes	characteristic
254	C₂²⋊(C₄₇⋊C₈)	C₂³	1	1	yes	characteristic
255	C₂²⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
256	C₂²⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
257	#13093935	C₂³	1	2	yes	—
258	#13093935	C₂³	1	2	yes	—
259	#13093934	C₂³	1	1	yes	characteristic
260	#13093934	C₂³	1	2	yes	—
261	#13093934	C₂³	1	1	yes	characteristic
262	#13093934	C₂³	1	2	yes	—
263	#13093934	C₂³	1	2	yes	—
264	#13093934	C₂³	1	2	yes	—
265	#13093934	C₂³	1	2	yes	—
266	#13093934	C₂³	1	1	yes	characteristic
267	#13093934	C₂³	1	2	yes	—
268	#13093934	C₂³	1	1	yes	characteristic
269	C₄×C₄₇⋊C₈	C₂³	1	2	yes	—
270	C₄×C₄₇⋊C₈	C₂³	1	2	yes	—
271	C₈×Dic₄₇	C₂³	1	1	yes	characteristic
272	C₈×Dic₄₇	C₂³	1	2	yes	—
273	C₈×Dic₄₇	C₂³	1	1	yes	characteristic
274	C₈×Dic₄₇	C₂³	1	2	yes	—
275	C₈×Dic₄₇	C₂³	1	2	yes	—
276	C₈×Dic₄₇	C₂³	1	2	yes	—
277	C₈×Dic₄₇	C₂³	1	2	yes	—
278	C₈×Dic₄₇	C₂³	1	1	yes	characteristic
279	C₈×Dic₄₇	C₂³	1	2	yes	—
280	C₈×Dic₄₇	C₂³	1	1	yes	characteristic
281	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
282	C₂×M₁₆×C₄₇	C₂³	1	1	yes	characteristic
283	C₂×M₁₆×C₄₇	C₂³	1	1	yes	characteristic
284	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
285	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
286	#117×C₄₇	C₂×C₄	1	1	yes	characteristic
287	#117×C₄₇	C₂×C₄	1	1	yes	characteristic
288	#117×C₄₇	C₂×C₄	1	2	yes	—
289	#117×C₄₇	C₂³	1	1	yes	characteristic
290	#117×C₄₇	C₂³	1	1	yes	characteristic
291	#117×C₄₇	C₂³	1	2	yes	—
292	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
293	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
294	C₂×C₂²⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
295	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
296	C₄⋊C₈×C₄₇	C₂³	1	2	yes	—
297	C₄⋊C₈×C₄₇	C₂³	1	2	yes	—
298	C₄⋊C₈×C₄₇	C₂³	1	2	yes	—
299	C₄⋊C₈×C₄₇	C₂³	1	2	yes	—
300	C₂²⋊C₈×C₄₇	C₂³	1	1	yes	characteristic
301	C₂²⋊C₈×C₄₇	C₂³	1	1	yes	characteristic
302	C₂²⋊C₈×C₄₇	C₂³	1	1	yes	characteristic
303	C₂²⋊C₈×C₄₇	C₂³	1	1	yes	characteristic
304	C₂²⋊C₈×C₄₇	C₂³	1	2	yes	—
305	C₂²⋊C₈×C₄₇	C₂³	1	2	yes	—
306	#97×C₄₇	C₂³	1	2	yes	—
307	#97×C₄₇	C₂³	1	2	yes	—
308	C₄×C₈×C₄₇	C₂³	1	2	yes	—
309	C₄×C₈×C₄₇	C₂³	1	2	yes	—
310	C₂⁴×C₄₇	C₂²×C₄	1	1	yes	characteristic
311	C₂²×C₄×C₄₇	—	2	2	no	—
312	C₂²×C₄×C₄₇	—	2	2	no	—
313	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
314	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
315	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
316	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
317	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
318	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
319	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
320	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
321	C₂²×Dic₄₇	C₂²×C₄	1	2	yes	—
322	C₂²×Dic₄₇	C₂²×C₄	1	2	yes	—
323	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
324	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
325	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
326	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
327	C₂×Dic₉₄	C₂²×C₄	1	2	yes	—
328	C₂×Dic₉₄	C₂²×C₄	1	2	yes	—
329	C₂×Dic₉₄	C₂²×C₄	1	2	yes	—
330	C₂×Dic₉₄	C₂²×C₄	1	2	yes	—
331	C₂×Dic₉₄	C₂²×C₄	1	2	yes	—
332	C₂×Dic₉₄	C₂²×C₄	1	2	yes	—
333	C₂×Dic₉₄	C₂²×C₄	1	2	yes	—
334	C₂×Dic₉₄	C₂²×C₄	1	2	yes	—
335	M₁₆×C₄₇	—	2	2	no	—
336	M₁₆×C₄₇	—	2	2	no	—
337	C₂×C₈×C₄₇	—	2	2	no	—
338	C₂×C₈×C₄₇	—	2	2	no	—
339	C₂×C₈×C₄₇	C₂⁴	1	1	yes	characteristic
340	C₂×C₈×C₄₇	C₂⁴	1	1	yes	characteristic
341	C₂×C₈×C₄₇	C₂⁴	1	1	yes	characteristic
342	C₂×C₈×C₄₇	C₂⁴	1	1	yes	characteristic
343	C₂×C₈×C₄₇	C₂⁴	1	2	yes	—
344	C₂×C₈×C₄₇	C₂⁴	1	2	yes	—
345	C₄⋊C₄×C₄₇	C₂²×C₄	1	2	yes	—
346	C₄⋊C₄×C₄₇	C₂²×C₄	1	2	yes	—
347	C₄⋊C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
348	C₄⋊C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
349	C₄⋊C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
350	C₄⋊C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
351	C₂²⋊C₄×C₄₇	C₂²×C₄	1	2	yes	—
352	C₂²⋊C₄×C₄₇	C₂²×C₄	1	2	yes	—
353	C₂²⋊C₄×C₄₇	C₂²×C₄	1	2	yes	—
354	C₂²⋊C₄×C₄₇	C₂²×C₄	1	2	yes	—
355	C₄²×C₄₇	C₂²×C₄	1	2	yes	—
356	C₄²×C₄₇	C₂²×C₄	1	2	yes	—
357	C₄²×C₄₇	C₂⁴	1	2	yes	—
358	C₄²×C₄₇	C₂⁴	1	2	yes	—
359	C₂²⋊Dic₄₇	C₂²×C₄	1	1	yes	characteristic
360	C₂²⋊Dic₄₇	C₂²×C₄	1	1	yes	characteristic
361	C₂²⋊Dic₄₇	C₂²×C₄	1	1	yes	characteristic
362	C₂²⋊Dic₄₇	C₂²×C₄	1	1	yes	characteristic
363	C₂²⋊Dic₄₇	C₂²×C₄	1	2	yes	—
364	C₂²⋊Dic₄₇	C₂²×C₄	1	2	yes	—
365	C₂²⋊Dic₄₇	C₂²×C₄	1	1	yes	characteristic
366	C₂²⋊Dic₄₇	C₂²×C₄	1	1	yes	characteristic
367	C₂²⋊Dic₄₇	C₂²×C₄	1	1	yes	characteristic
368	C₂²⋊Dic₄₇	C₂²×C₄	1	1	yes	characteristic
369	C₂²⋊Dic₄₇	C₂²×C₄	1	2	yes	—
370	C₂²⋊Dic₄₇	C₂²×C₄	1	2	yes	—
371	C₄⋊Dic₄₇	C₂²×C₄	1	1	yes	characteristic
372	C₄⋊Dic₄₇	C₂²×C₄	1	1	yes	characteristic
373	C₄⋊Dic₄₇	C₂²×C₄	1	1	yes	characteristic
374	C₄⋊Dic₄₇	C₂²×C₄	1	1	yes	characteristic
375	C₄⋊Dic₄₇	C₂²×C₄	1	1	yes	characteristic
376	C₄⋊Dic₄₇	C₂²×C₄	1	1	yes	characteristic
377	C₄⋊Dic₄₇	C₂²×C₄	1	1	yes	characteristic
378	C₄⋊Dic₄₇	C₂²×C₄	1	1	yes	characteristic
379	C₄⋊Dic₄₇	C₂²×C₄	1	1	yes	characteristic
380	C₄⋊Dic₄₇	C₂²×C₄	1	1	yes	characteristic
381	C₄⋊Dic₄₇	C₂²×C₄	1	1	yes	characteristic
382	C₄⋊Dic₄₇	C₂²×C₄	1	1	yes	characteristic
383	C₄⋊Dic₄₇	C₂²×C₄	1	2	yes	—
384	C₄⋊Dic₄₇	C₂²×C₄	1	2	yes	—
385	C₄⋊Dic₄₇	C₂²×C₄	1	2	yes	—
386	C₄⋊Dic₄₇	C₂²×C₄	1	2	yes	—
387	C₄⋊Dic₄₇	C₂²×C₄	1	2	yes	—
388	C₄⋊Dic₄₇	C₂²×C₄	1	2	yes	—
389	C₄⋊Dic₄₇	C₂²×C₄	1	2	yes	—
390	C₄⋊Dic₄₇	C₂²×C₄	1	2	yes	—
391	C₄⋊Dic₄₇	C₂²×C₄	1	2	yes	—
392	C₄⋊Dic₄₇	C₂²×C₄	1	2	yes	—
393	Dic₄₇⋊C₄	C₂²×C₄	1	2	yes	—
394	Dic₄₇⋊C₄	C₂²×C₄	1	2	yes	—
395	Dic₄₇⋊C₄	C₂²×C₄	1	2	yes	—
396	Dic₄₇⋊C₄	C₂²×C₄	1	2	yes	—
397	Dic₄₇⋊C₄	C₂²×C₄	1	2	yes	—
398	Dic₄₇⋊C₄	C₂²×C₄	1	2	yes	—
399	Dic₄₇⋊C₄	C₂²×C₄	1	2	yes	—
400	Dic₄₇⋊C₄	C₂²×C₄	1	2	yes	—
401	Dic₄₇⋊C₄	C₂²×C₄	1	2	yes	—
402	Dic₄₇⋊C₄	C₂²×C₄	1	2	yes	—
403	Dic₄₇⋊C₄	C₂²×C₄	1	2	yes	—
404	Dic₄₇⋊C₄	C₂²×C₄	1	2	yes	—
405	Dic₄₇⋊C₄	C₂²×C₄	1	2	yes	—
406	Dic₄₇⋊C₄	C₂²×C₄	1	2	yes	—
407	Dic₄₇⋊C₄	C₂²×C₄	1	2	yes	—
408	Dic₄₇⋊C₄	C₂²×C₄	1	2	yes	—
409	C₄×Dic₄₇	C₂²×C₄	1	2	yes	—
410	C₄×Dic₄₇	C₂²×C₄	1	2	yes	—
411	C₄×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
412	C₄×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
413	C₄×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
414	C₄×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
415	C₄×Dic₄₇	C₂⁴	1	1	yes	characteristic
416	C₄×Dic₄₇	C₂⁴	1	2	yes	—
417	C₄×Dic₄₇	C₂⁴	1	1	yes	characteristic
418	C₄×Dic₄₇	C₂⁴	1	2	yes	—
419	C₄×Dic₄₇	C₂⁴	1	1	yes	characteristic
420	C₄×Dic₄₇	C₂⁴	1	1	yes	characteristic
421	#10625329	—	2	2	no	—
422	#10625329	—	2	2	no	—
423	C₂×C₄₇⋊C₈	—	2	2	no	—
424	C₂×C₄₇⋊C₈	—	2	2	no	—
425	C₂×C₄₇⋊C₈	C₂⁴	1	1	yes	characteristic
426	C₂×C₄₇⋊C₈	C₂⁴	1	2	yes	—
427	C₂×C₄₇⋊C₈	C₂⁴	1	2	yes	—
428	C₂×C₄₇⋊C₈	C₂⁴	1	1	yes	characteristic
429	C₂×C₄₇⋊C₈	C₂⁴	1	1	yes	characteristic
430	C₂×C₄₇⋊C₈	C₂⁴	1	1	yes	characteristic
431	C₂³×C₄₇	—	2	2	no	—
432	C₂³×C₄₇	—	4	1	no	—
433	C₂³×C₄₇	—	4	1	no	—
434	C₂³×C₄₇	C₂³×C₄	1	1	yes	characteristic
435	C₂³×C₄₇	C₂³×C₄	1	1	yes	characteristic
436	C₂³×C₄₇	C₂³×C₄	1	1	yes	characteristic
437	C₂×C₄×C₄₇	—	2	2	no	—
438	C₂×C₄×C₄₇	—	2	2	no	—
439	C₂×C₄×C₄₇	—	2	2	no	—
440	C₂×C₄×C₄₇	—	2	1	no	—
441	C₂×C₄×C₄₇	—	2	1	no	—
442	C₂×C₄×C₄₇	—	2	1	no	—
443	C₂×C₄×C₄₇	—	2	1	no	—
444	C₂×C₄×C₄₇	—	4	2	no	—
445	C₂×C₄×C₄₇	—	4	2	no	—
446	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
447	C₂×C₄×C₄₇	C₂³×C₄	1	2	yes	—
448	C₂×C₄×C₄₇	C₂³×C₄	1	2	yes	—
449	C₂×C₄×C₄₇	C₂³×C₄	1	2	yes	—
450	C₂×C₄×C₄₇	C₂³×C₄	1	2	yes	—
451	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
452	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
453	C₂×C₄×C₄₇	2₋¹⁺⁴	1	2	yes	—
454	C₂×C₄×C₄₇	2₋¹⁺⁴	1	2	yes	—
455	C₂×C₄×C₄₇	C₂⁵	1	1	yes	characteristic
456	C₂×Dic₄₇	—	4	1	no	—
457	C₂×Dic₄₇	—	4	1	no	—
458	C₂×Dic₄₇	—	4	1	no	—
459	C₂×Dic₄₇	—	4	1	no	—
460	C₂×Dic₄₇	—	4	2	no	—
461	C₂×Dic₄₇	—	4	2	no	—
462	C₂×Dic₄₇	C₂³×C₄	1	2	yes	—
463	C₂×Dic₄₇	C₂³×C₄	1	2	yes	—
464	C₂×Dic₄₇	C₂³×C₄	1	1	yes	characteristic
465	C₂×Dic₄₇	C₂³×C₄	1	1	yes	characteristic
466	C₂×Dic₄₇	C₂³×C₄	1	1	yes	characteristic
467	C₂×Dic₄₇	C₂³×C₄	1	1	yes	characteristic
468	C₂×Dic₄₇	C₂³×C₄	1	2	yes	—
469	C₂×Dic₄₇	C₂³×C₄	1	2	yes	—
470	C₂×Dic₄₇	C₂³×C₄	1	1	yes	characteristic
471	C₂×Dic₄₇	C₂³×C₄	1	1	yes	characteristic
472	C₂×Dic₄₇	C₂³×C₄	1	1	yes	characteristic
473	C₂×Dic₄₇	C₂³×C₄	1	1	yes	characteristic
474	Dic₉₄	—	4	2	no	—
475	Dic₉₄	—	4	2	no	—
476	Dic₉₄	—	4	2	no	—
477	Dic₉₄	—	4	2	no	—
478	Dic₉₄	—	4	2	no	—
479	Dic₉₄	—	4	2	no	—
480	Dic₉₄	—	4	2	no	—
481	Dic₉₄	—	4	2	no	—
482	C₈×C₄₇	—	2	1	no	—
483	C₈×C₄₇	—	2	1	no	—
484	C₈×C₄₇	—	2	1	no	—
485	C₈×C₄₇	—	2	1	no	—
486	C₈×C₄₇	—	2	2	no	—
487	C₈×C₄₇	—	2	2	no	—
488	C₄₇⋊C₈	—	2	1	no	—
489	C₄₇⋊C₈	—	2	1	no	—
490	C₄₇⋊C₈	—	2	1	no	—
491	C₄₇⋊C₈	—	2	1	no	—
492	C₄₇⋊C₈	—	2	2	no	—
493	C₄₇⋊C₈	—	2	2	no	—
494	#60252	—	47	1	no	maximal, Sylow
495	C₂²×C₄₇	—	2	1	no	—
496	C₂²×C₄₇	—	2	1	no	—
497	C₂²×C₄₇	—	2	1	no	—
498	C₂²×C₄₇	—	2	1	no	—
499	C₂²×C₄₇	—	2	1	no	—
500	C₂²×C₄₇	—	2	1	no	—
501	C₂²×C₄₇	—	2	1	no	—
502	C₂²×C₄₇	—	2	1	no	—
503	C₂²×C₄₇	—	8	2	no	—
504	C₂²×C₄₇	#519	1	2	yes	—
505	C₂²×C₄₇	C₂⁴×C₄	1	1	yes	characteristic
506	C₄×C₄₇	—	2	1	no	—
507	C₄×C₄₇	—	2	1	no	—
508	C₄×C₄₇	—	2	2	no	—
509	C₄×C₄₇	—	2	2	no	—
510	C₄×C₄₇	—	2	2	no	—
511	C₄×C₄₇	—	2	2	no	—
512	C₄×C₄₇	#519	1	2	yes	—
513	C₄×C₄₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
514	C₄×C₄₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
515	Dic₄₇	—	2	1	no	—
516	Dic₄₇	—	2	1	no	—
517	Dic₄₇	—	2	1	no	—
518	Dic₄₇	—	2	1	no	—
519	Dic₄₇	—	2	2	no	—
520	Dic₄₇	—	2	2	no	—
521	Dic₄₇	—	2	1	no	—
522	Dic₄₇	—	2	1	no	—
523	Dic₄₇	—	2	1	no	—
524	Dic₄₇	—	2	1	no	—
525	Dic₄₇	—	2	2	no	—
526	Dic₄₇	—	2	2	no	—
527	#3458	—	47	1	no	—
528	#2987	—	47	2	no	—
529	#2987	—	47	2	no	—
530	#2986	—	47	2	no	—
531	#2986	—	47	2	no	—
532	#2985	—	47	2	no	—
533	#2985	—	47	2	no	—
534	#2985	—	47	2	no	—
535	#2985	—	47	2	no	—
536	#2962	—	47	1	no	—
537	#2962	—	47	1	no	—
538	#2962	—	47	1	no	—
539	#2962	—	47	1	no	—
540	#2961	—	47	1	no	—
541	#2961	—	47	1	no	—
542	#2960	—	47	1	no	—
543	#2960	—	47	1	no	—
544	#2924	—	47	1	no	—
545	#2924	—	47	1	no	—
546	#2924	—	47	1	no	—
547	#2924	D₄₇	1	1	yes	characteristic
548	#2921	—	47	1	no	—
549	C₂×#433	—	47	1	no	—
550	C₂×C₄₇	—	2	2	no	—
551	C₂×C₄₇	—	4	1	no	—
552	C₂×C₄₇	—	4	1	no	—
553	C₂×C₄₇	C₂×#519	1	1	yes	characteristic
554	C₂×C₄₇	#3573	1	1	yes	characteristic
555	C₂×C₄₇	#3573	1	1	yes	characteristic
556	#544	—	47	2	no	—
557	#544	—	47	2	no	—
558	#544	—	47	1	no	—
559	#544	—	47	1	no	—
560	#544	—	47	1	no	—
561	#544	—	47	1	no	—
562	#544	—	47	1	no	—
563	#544	—	47	1	no	—
564	#544	—	47	1	no	—
565	#544	—	47	1	no	—
566	#543	—	47	2	no	—
567	#543	—	47	2	no	—
568	#533	—	47	1	no	—
569	#533	—	47	1	no	—
570	#533	—	47	1	no	—
571	#533	—	47	1	no	—
572	#533	—	47	2	no	—
573	#533	—	47	2	no	—
574	#533	—	47	2	no	—
575	#533	—	47	2	no	—
576	C₂×#117	—	47	1	no	—
577	C₂×#117	—	47	1	no	—
578	C₂×#117	C₂×D₄₇	1	1	yes	characteristic
579	#446	—	47	2	no	—
580	#446	—	47	2	no	—
581	#446	—	47	2	no	—
582	#446	—	47	2	no	—
583	#446	—	47	2	no	—
584	#446	—	47	2	no	—
585	#446	—	47	2	no	—
586	#446	—	47	2	no	—
587	#446	—	47	2	no	—
588	#446	—	47	2	no	—
589	#446	—	47	2	no	—
590	#446	—	47	2	no	—
591	#446	—	47	2	no	—
592	#446	—	47	2	no	—
593	#446	—	47	2	no	—
594	#446	—	47	2	no	—
595	#446	—	47	2	no	—
596	#446	—	47	2	no	—
597	#446	—	47	2	no	—
598	#446	—	47	2	no	—
599	#446	—	47	2	no	—
600	#446	—	47	2	no	—
601	#446	—	47	2	no	—
602	#446	—	47	2	no	—
603	C₈×Q₈	—	47	2	no	—
604	C₈×Q₈	—	47	2	no	—
605	C₈×Q₈	—	47	2	no	—
606	C₈×Q₈	—	47	2	no	—
607	C₈×Q₈	—	47	2	no	—
608	C₈×Q₈	—	47	2	no	—
609	C₈×Q₈	—	47	2	no	—
610	C₈×Q₈	—	47	2	no	—
611	#433	—	47	2	no	—
612	#433	—	47	2	no	—
613	#433	—	47	1	no	—
614	#433	—	47	1	no	—
615	#433	—	47	1	no	—
616	#433	—	47	1	no	—
617	#433	—	47	1	no	—
618	#433	—	47	1	no	—
619	#433	—	47	1	no	—
620	#433	—	47	1	no	—
621	#433	—	47	2	no	—
622	#433	—	47	2	no	—
623	#433	—	47	2	no	—
624	#433	—	47	2	no	—
625	#433	—	47	2	no	—
626	#433	—	47	2	no	—
627	#433	—	47	2	no	—
628	#433	—	47	2	no	—
629	#433	C₂×D₄₇	1	2	yes	—
630	#433	C₂×D₄₇	1	2	yes	—
631	#432	—	47	2	no	—
632	#432	—	47	2	no	—
633	#432	—	47	2	no	—
634	#432	C₂×D₄₇	1	2	yes	—
635	#431	—	47	2	no	—
636	#431	—	47	2	no	—
637	#431	—	47	2	no	—
638	#431	C₂×D₄₇	1	2	yes	—
639	#424	—	47	1	no	—
640	#424	—	47	1	no	—
641	#424	—	47	1	no	—
642	#424	—	47	1	no	—
643	#424	—	47	1	no	—
644	#424	—	47	1	no	—
645	#424	C₂×D₄₇	1	1	yes	characteristic
646	#424	C₂×D₄₇	1	1	yes	characteristic
647	#423	—	47	1	no	—
648	#423	—	47	1	no	—
649	C₂×C₄⋊C₈	—	47	1	no	—
650	C₂×C₄⋊C₈	—	47	1	no	—
651	#407	—	47	1	no	—
652	#407	C₂×D₄₇	1	1	yes	characteristic
653	C₂×C₂²⋊C₈	—	47	1	no	—
654	C₂×C₂²⋊C₈	C₂×D₄₇	1	1	yes	characteristic
655	#405	—	47	1	no	—
656	#405	—	47	1	no	—
657	#405	—	47	1	no	—
658	#405	—	47	1	no	—
659	#405	—	47	1	no	—
660	#405	—	47	1	no	—
661	#405	C₂×D₄₇	1	1	yes	characteristic
662	#405	C₂×D₄₇	1	1	yes	characteristic
663	C₄×M₁₆	—	47	1	no	—
664	C₄×M₁₆	—	47	1	no	—
665	C₂×#97	—	47	1	no	—
666	C₂×C₄×C₈	—	47	1	no	—
667	C₄₇	#60252	1	1	yes	characteristic, complemented, Sylow
668	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
669	C₂×M₁₆	—	47	1	no	—
670	C₂×M₁₆	—	47	1	no	—
671	C₂×M₁₆	C₂²×D₄₇	1	1	yes	characteristic
672	C₂×M₁₆	C₂²×D₄₇	1	1	yes	characteristic
673	C₂²×C₈	—	47	1	no	—
674	C₂²×C₈	—	47	1	no	—
675	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
676	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
677	C₄⋊Q₈	—	47	1	no	—
678	C₄⋊Q₈	—	47	1	no	—
679	C₄⋊Q₈	—	47	1	no	—
680	C₄⋊Q₈	—	47	1	no	—
681	C₄⋊Q₈	—	47	1	no	—
682	C₄⋊Q₈	—	47	1	no	—
683	C₄⋊Q₈	—	47	1	no	—
684	C₄⋊Q₈	—	47	1	no	—
685	C₄⋊Q₈	—	47	2	no	—
686	C₄⋊Q₈	—	47	2	no	—
687	C₄⋊Q₈	—	47	2	no	—
688	C₄⋊Q₈	—	47	2	no	—
689	C₄⋊Q₈	—	47	2	no	—
690	C₄⋊Q₈	—	47	2	no	—
691	C₄⋊Q₈	—	47	2	no	—
692	C₄⋊Q₈	—	47	2	no	—
693	#125	—	47	1	no	—
694	#125	—	47	1	no	—
695	#125	—	47	1	no	—
696	#125	—	47	1	no	—
697	#125	—	47	1	no	—
698	#125	—	47	1	no	—
699	#125	—	47	1	no	—
700	#125	—	47	1	no	—
701	#125	—	47	2	no	—
702	#125	—	47	2	no	—
703	#125	—	47	2	no	—
704	#125	—	47	2	no	—
705	#125	—	47	2	no	—
706	#125	—	47	2	no	—
707	#125	—	47	2	no	—
708	#125	—	47	2	no	—
709	C₂²⋊Q₈	—	47	2	no	—
710	C₂²⋊Q₈	—	47	2	no	—
711	C₂²⋊Q₈	—	47	2	no	—
712	C₂²⋊Q₈	—	47	2	no	—
713	C₂²⋊Q₈	—	47	2	no	—
714	C₂²⋊Q₈	—	47	2	no	—
715	C₂²⋊Q₈	—	47	2	no	—
716	C₂²⋊Q₈	—	47	2	no	—
717	C₂²⋊Q₈	—	47	2	no	—
718	C₂²⋊Q₈	—	47	2	no	—
719	C₂²⋊Q₈	—	47	2	no	—
720	C₂²⋊Q₈	—	47	2	no	—
721	C₂²⋊Q₈	—	47	2	no	—
722	C₂²⋊Q₈	—	47	2	no	—
723	C₂²⋊Q₈	—	47	2	no	—
724	C₂²⋊Q₈	—	47	2	no	—
725	C₂²⋊Q₈	—	47	2	no	—
726	C₂²⋊Q₈	—	47	2	no	—
727	C₂²⋊Q₈	—	47	2	no	—
728	C₂²⋊Q₈	—	47	2	no	—
729	C₂²⋊Q₈	—	47	2	no	—
730	C₂²⋊Q₈	—	47	2	no	—
731	C₂²⋊Q₈	—	47	2	no	—
732	C₂²⋊Q₈	—	47	2	no	—
733	C₄×Q₈	—	47	2	no	—
734	C₄×Q₈	—	47	2	no	—
735	C₄×Q₈	—	47	2	no	—
736	C₄×Q₈	—	47	2	no	—
737	C₄×Q₈	—	47	2	no	—
738	C₄×Q₈	—	47	2	no	—
739	C₄×Q₈	—	47	2	no	—
740	C₄×Q₈	—	47	2	no	—
741	#117	—	47	1	no	—
742	#117	—	47	1	no	—
743	#117	—	47	2	no	—
744	#117	—	47	1	no	—
745	#117	—	47	1	no	—
746	#117	—	47	1	no	—
747	#117	—	47	1	no	—
748	#117	—	47	1	no	—
749	#117	—	47	1	no	—
750	#117	—	47	1	no	—
751	#117	—	47	1	no	—
752	#117	—	47	1	no	—
753	#117	—	47	1	no	—
754	#117	—	47	2	no	—
755	#117	C₄×D₄₇	1	1	yes	characteristic
756	#117	C₄×D₄₇	1	1	yes	characteristic
757	#117	C₄×D₄₇	1	2	yes	—
758	#117	C₂²×D₄₇	1	1	yes	characteristic
759	#117	C₂²×D₄₇	1	1	yes	characteristic
760	#117	C₂²×D₄₇	1	2	yes	—
761	C₂×C₄⋊C₄	—	47	1	no	—
762	C₂×C₄⋊C₄	—	47	1	no	—
763	C₂×C₄⋊C₄	—	47	1	no	—
764	C₂×C₄⋊C₄	—	47	1	no	—
765	C₂×C₄⋊C₄	C₄×D₄₇	1	1	yes	characteristic
766	C₂×C₄⋊C₄	C₄×D₄₇	1	1	yes	characteristic
767	C₂×C₂²⋊C₄	—	47	1	no	—
768	C₂×C₂²⋊C₄	—	47	1	no	—
769	C₂×C₂²⋊C₄	—	47	2	no	—
770	C₂×C₂²⋊C₄	C₄×D₄₇	1	2	yes	—
771	C₂×C₄²	—	47	1	no	—
772	C₂×C₄²	—	47	1	no	—
773	C₂×C₄²	—	47	2	no	—
774	C₂×C₄²	C₂²×D₄₇	1	2	yes	—
775	C₄⋊C₈	—	47	1	no	—
776	C₄⋊C₈	—	47	1	no	—
777	C₄⋊C₈	—	47	1	no	—
778	C₄⋊C₈	—	47	1	no	—
779	C₄⋊C₈	—	47	1	no	—
780	C₄⋊C₈	—	47	1	no	—
781	C₄⋊C₈	—	47	1	no	—
782	C₄⋊C₈	—	47	1	no	—
783	C₄⋊C₈	—	47	2	no	—
784	C₄⋊C₈	—	47	2	no	—
785	C₄⋊C₈	—	47	2	no	—
786	C₄⋊C₈	—	47	2	no	—
787	C₄⋊C₈	—	47	2	no	—
788	C₄⋊C₈	—	47	2	no	—
789	C₄⋊C₈	—	47	2	no	—
790	C₄⋊C₈	—	47	2	no	—
791	C₄⋊C₈	—	47	2	no	—
792	C₄⋊C₈	—	47	2	no	—
793	C₄⋊C₈	—	47	2	no	—
794	C₄⋊C₈	—	47	2	no	—
795	C₄⋊C₈	—	47	2	no	—
796	C₄⋊C₈	—	47	2	no	—
797	C₄⋊C₈	—	47	2	no	—
798	C₄⋊C₈	—	47	2	no	—
799	C₄⋊C₈	C₂²×D₄₇	1	2	yes	—
800	C₄⋊C₈	C₂²×D₄₇	1	2	yes	—
801	C₄⋊C₈	C₂²×D₄₇	1	2	yes	—
802	C₄⋊C₈	C₂²×D₄₇	1	2	yes	—
803	C₂²⋊C₈	—	47	1	no	—
804	C₂²⋊C₈	—	47	1	no	—
805	C₂²⋊C₈	—	47	1	no	—
806	C₂²⋊C₈	—	47	1	no	—
807	C₂²⋊C₈	—	47	2	no	—
808	C₂²⋊C₈	—	47	2	no	—
809	C₂²⋊C₈	C₂²×D₄₇	1	1	yes	characteristic
810	C₂²⋊C₈	C₂²×D₄₇	1	1	yes	characteristic
811	C₂²⋊C₈	C₂²×D₄₇	1	1	yes	characteristic
812	C₂²⋊C₈	C₂²×D₄₇	1	1	yes	characteristic
813	C₂²⋊C₈	C₂²×D₄₇	1	2	yes	—
814	C₂²⋊C₈	C₂²×D₄₇	1	2	yes	—
815	#97	—	47	1	no	—
816	#97	—	47	1	no	—
817	#97	—	47	1	no	—
818	#97	—	47	1	no	—
819	#97	—	47	2	no	—
820	#97	—	47	2	no	—
821	#97	—	47	2	no	—
822	#97	—	47	2	no	—
823	#97	—	47	2	no	—
824	#97	—	47	2	no	—
825	#97	—	47	2	no	—
826	#97	—	47	2	no	—
827	#97	C₂²×D₄₇	1	2	yes	—
828	#97	C₂²×D₄₇	1	2	yes	—
829	C₄×C₈	—	47	1	no	—
830	C₄×C₈	—	47	1	no	—
831	C₄×C₈	—	47	1	no	—
832	C₄×C₈	—	47	1	no	—
833	C₄×C₈	—	47	2	no	—
834	C₄×C₈	—	47	2	no	—
835	C₄×C₈	—	47	2	no	—
836	C₄×C₈	—	47	2	no	—
837	C₄×C₈	—	47	2	no	—
838	C₄×C₈	—	47	2	no	—
839	C₄×C₈	—	47	2	no	—
840	C₄×C₈	—	47	2	no	—
841	C₄×C₈	C₂²×D₄₇	1	2	yes	—
842	C₄×C₈	C₂²×D₄₇	1	2	yes	—
843	C₂⁴	C₂×C₄×D₄₇	1	1	yes	characteristic
844	C₂×Q₈	—	47	2	no	—
845	C₂×Q₈	—	47	2	no	—
846	C₂×Q₈	—	47	2	no	—
847	C₂×Q₈	—	47	2	no	—
848	C₂×Q₈	—	47	2	no	—
849	C₂×Q₈	—	47	2	no	—
850	C₂×Q₈	—	47	2	no	—
851	C₂×Q₈	—	47	2	no	—
852	C₂²×C₄	—	2	2	no	—
853	C₂²×C₄	—	2	2	no	—
854	C₂²×C₄	—	47	2	no	—
855	C₂²×C₄	—	47	2	no	—
856	C₂²×C₄	—	47	1	no	—
857	C₂²×C₄	—	47	1	no	—
858	C₂²×C₄	—	47	1	no	—
859	C₂²×C₄	—	47	1	no	—
860	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
861	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
862	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
863	C₂²×C₄	C₂×C₄×D₄₇	1	2	yes	—
864	C₂²×C₄	C₂×C₄×D₄₇	1	2	yes	—
865	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
866	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
867	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
868	M₁₆	—	2	2	no	—
869	M₁₆	—	2	2	no	—
870	M₁₆	—	94	2	no	—
871	M₁₆	—	94	2	no	—
872	C₂×C₈	—	2	2	no	—
873	C₂×C₈	—	2	2	no	—
874	C₂×C₈	—	47	1	no	—
875	C₂×C₈	—	47	2	no	—
876	C₂×C₈	—	47	2	no	—
877	C₂×C₈	—	47	1	no	—
878	C₂×C₈	—	47	1	no	—
879	C₂×C₈	—	47	1	no	—
880	C₂×C₈	—	94	2	no	—
881	C₂×C₈	—	94	2	no	—
882	C₂×C₈	C₂³×D₄₇	1	1	yes	characteristic
883	C₂×C₈	C₂³×D₄₇	1	2	yes	—
884	C₂×C₈	C₂³×D₄₇	1	2	yes	—
885	C₂×C₈	C₂³×D₄₇	1	1	yes	characteristic
886	C₂×C₈	C₂³×D₄₇	1	1	yes	characteristic
887	C₂×C₈	C₂³×D₄₇	1	1	yes	characteristic
888	C₄⋊C₄	—	47	2	no	—
889	C₄⋊C₄	—	47	2	no	—
890	C₄⋊C₄	—	47	2	no	—
891	C₄⋊C₄	—	47	2	no	—
892	C₄⋊C₄	—	47	2	no	—
893	C₄⋊C₄	—	47	2	no	—
894	C₄⋊C₄	—	47	2	no	—
895	C₄⋊C₄	—	47	2	no	—
896	C₄⋊C₄	—	47	2	no	—
897	C₄⋊C₄	—	47	2	no	—
898	C₄⋊C₄	—	47	2	no	—
899	C₄⋊C₄	—	47	2	no	—
900	C₄⋊C₄	—	47	2	no	—
901	C₄⋊C₄	—	47	2	no	—
902	C₄⋊C₄	—	47	2	no	—
903	C₄⋊C₄	—	47	2	no	—
904	C₄⋊C₄	—	47	1	no	—
905	C₄⋊C₄	—	47	1	no	—
906	C₄⋊C₄	—	47	1	no	—
907	C₄⋊C₄	—	47	1	no	—
908	C₄⋊C₄	—	47	1	no	—
909	C₄⋊C₄	—	47	1	no	—
910	C₄⋊C₄	—	47	2	no	—
911	C₄⋊C₄	—	47	1	no	—
912	C₄⋊C₄	—	47	1	no	—
913	C₄⋊C₄	—	47	2	no	—
914	C₄⋊C₄	—	47	1	no	—
915	C₄⋊C₄	—	47	1	no	—
916	C₄⋊C₄	—	47	1	no	—
917	C₄⋊C₄	—	47	1	no	—
918	C₄⋊C₄	—	47	2	no	—
919	C₄⋊C₄	—	47	2	no	—
920	C₄⋊C₄	—	47	2	no	—
921	C₄⋊C₄	—	47	2	no	—
922	C₄⋊C₄	—	47	2	no	—
923	C₄⋊C₄	—	47	2	no	—
924	C₄⋊C₄	—	47	2	no	—
925	C₄⋊C₄	—	47	2	no	—
926	C₄⋊C₄	C₂×C₄×D₄₇	1	2	yes	—
927	C₄⋊C₄	C₂×C₄×D₄₇	1	2	yes	—
928	C₄⋊C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
929	C₄⋊C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
930	C₄⋊C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
931	C₄⋊C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
932	C₂²⋊C₄	—	47	1	no	—
933	C₂²⋊C₄	—	47	1	no	—
934	C₂²⋊C₄	—	47	1	no	—
935	C₂²⋊C₄	—	47	1	no	—
936	C₂²⋊C₄	—	47	2	no	—
937	C₂²⋊C₄	—	47	2	no	—
938	C₂²⋊C₄	—	47	1	no	—
939	C₂²⋊C₄	—	47	1	no	—
940	C₂²⋊C₄	—	47	1	no	—
941	C₂²⋊C₄	—	47	1	no	—
942	C₂²⋊C₄	—	47	2	no	—
943	C₂²⋊C₄	—	47	2	no	—
944	C₂²⋊C₄	C₂×C₄×D₄₇	1	2	yes	—
945	C₂²⋊C₄	C₂×C₄×D₄₇	1	2	yes	—
946	C₂²⋊C₄	C₂×C₄×D₄₇	1	2	yes	—
947	C₂²⋊C₄	C₂×C₄×D₄₇	1	2	yes	—
948	C₄²	—	47	2	no	—
949	C₄²	—	47	2	no	—
950	C₄²	—	47	1	no	—
951	C₄²	—	47	1	no	—
952	C₄²	—	47	1	no	—
953	C₄²	—	47	1	no	—
954	C₄²	—	47	1	no	—
955	C₄²	—	47	1	no	—
956	C₄²	—	47	1	no	—
957	C₄²	—	47	1	no	—
958	C₄²	—	47	2	no	—
959	C₄²	—	47	2	no	—
960	C₄²	C₂×C₄×D₄₇	1	2	yes	—
961	C₄²	C₂×C₄×D₄₇	1	2	yes	—
962	C₄²	C₂³×D₄₇	1	2	yes	—
963	C₄²	C₂³×D₄₇	1	2	yes	—
964	C₂³	—	2	2	no	—
965	C₂³	—	4	1	no	—
966	C₂³	—	4	1	no	—
967	C₂³	C₂²×C₄×D₄₇	1	1	yes	characteristic
968	C₂³	C₂²×C₄×D₄₇	1	1	yes	characteristic
969	C₂³	C₂²×C₄×D₄₇	1	1	yes	characteristic
970	Q₈	—	188	2	no	—
971	Q₈	—	188	2	no	—
972	Q₈	—	188	2	no	—
973	Q₈	—	188	2	no	—
974	Q₈	—	188	2	no	—
975	Q₈	—	188	2	no	—
976	Q₈	—	188	2	no	—
977	Q₈	—	188	2	no	—
978	C₂×C₄	—	2	2	no	—
979	C₂×C₄	—	2	2	no	—
980	C₂×C₄	—	2	2	no	—
981	C₂×C₄	—	2	1	no	—
982	C₂×C₄	—	2	1	no	—
983	C₂×C₄	—	2	1	no	—
984	C₂×C₄	—	2	1	no	—
985	C₂×C₄	—	4	2	no	—
986	C₂×C₄	—	4	2	no	—
987	C₂×C₄	—	47	2	no	—
988	C₂×C₄	—	47	2	no	—
989	C₂×C₄	—	47	1	no	—
990	C₂×C₄	—	47	1	no	—
991	C₂×C₄	—	47	1	no	—
992	C₂×C₄	—	47	1	no	—
993	C₂×C₄	—	47	2	no	—
994	C₂×C₄	—	47	2	no	—
995	C₂×C₄	—	47	1	no	—
996	C₂×C₄	—	47	1	no	—
997	C₂×C₄	—	47	1	no	—
998	C₂×C₄	—	47	1	no	—
999	C₂×C₄	—	188	1	no	—
1000	C₂×C₄	—	188	1	no	—
1001	C₂×C₄	—	188	2	no	—
1002	C₂×C₄	—	188	1	no	—
1003	C₂×C₄	—	188	1	no	—
1004	C₂×C₄	—	188	2	no	—
1005	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
1006	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
1007	C₂×C₄	C₂²×C₄×D₄₇	1	2	yes	—
1008	C₂×C₄	C₂²×C₄×D₄₇	1	2	yes	—
1009	C₂×C₄	C₂²×C₄×D₄₇	1	2	yes	—
1010	C₂×C₄	C₂²×C₄×D₄₇	1	2	yes	—
1011	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
1012	C₂×C₄	#13094071	1	2	yes	—
1013	C₂×C₄	#13094071	1	2	yes	—
1014	C₂×C₄	C₂⁴×D₄₇	1	1	yes	characteristic
1015	C₈	—	2	1	no	—
1016	C₈	—	2	1	no	—
1017	C₈	—	2	1	no	—
1018	C₈	—	2	1	no	—
1019	C₈	—	2	2	no	—
1020	C₈	—	2	2	no	—
1021	C₈	—	94	1	no	—
1022	C₈	—	94	1	no	—
1023	C₈	—	94	1	no	—
1024	C₈	—	94	1	no	—
1025	C₈	—	94	2	no	—
1026	C₈	—	94	2	no	—
1027	C₂²	—	2	1	no	—
1028	C₂²	—	2	1	no	—
1029	C₂²	—	2	1	no	—
1030	C₂²	—	2	1	no	—
1031	C₂²	—	2	1	no	—
1032	C₂²	—	2	1	no	—
1033	C₂²	—	2	1	no	—
1034	C₂²	—	2	1	no	—
1035	C₂²	—	8	2	no	—
1036	C₂²	#15689600	1	2	yes	—
1037	C₂²	C₂³×C₄×D₄₇	1	1	yes	characteristic
1038	C₄	—	2	2	no	—
1039	C₄	—	2	2	no	—
1040	C₄	—	2	2	no	—
1041	C₄	—	2	2	no	—
1042	C₄	—	2	1	no	—
1043	C₄	—	2	1	no	—
1044	C₄	—	94	1	no	—
1045	C₄	—	94	1	no	—
1046	C₄	—	94	1	no	—
1047	C₄	—	94	1	no	—
1048	C₄	—	94	2	no	—
1049	C₄	—	94	2	no	—
1050	C₄	—	94	1	no	—
1051	C₄	—	94	1	no	—
1052	C₄	—	94	1	no	—
1053	C₄	—	94	1	no	—
1054	C₄	—	94	2	no	—
1055	C₄	—	94	2	no	—
1056	C₄	#15689600	1	2	yes	—
1057	C₄	C₂×#13094071	1	1	yes	characteristic
1058	C₄	C₂×#13094071	1	1	yes	characteristic
1059	C₂	—	2	2	no	—
1060	C₂	—	4	1	no	—
1061	C₂	—	4	1	no	—
1062	C₂	C₂×#15689600	1	1	yes	characteristic
1063	C₂	#20258099	1	1	yes	characteristic
1064	C₂	#20258101	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂⁴×D₄₇
commutator, socle	C₂²×C₄₇	C₂⁴×C₄
Fitting	C₄₇×#2924	C₂
prime radical	C₂⁴×C₄₇	C₂²×C₄
cosocle	C₂×C₄×C₄₇	C₂⁵
hypercenter	#2924	D₄₇
hypocenter	C₄₇	#60252
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ #2924

Complements

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

N	H ≅ G/N	type
2. #20252493	C₂	semidirect
3. #20252492	C₂	semidirect
4. #20252489	C₂	semidirect
5. #20252487	C₂	semidirect
6. #20252485	C₂	semidirect
7. #20252482	C₂	semidirect
8. #20252480	C₂	semidirect
9. #20252480	C₂	semidirect
10. #20252334	C₂	semidirect
11. #20252334	C₂	semidirect
12. #20252332	C₂	semidirect
13. #20252332	C₂	semidirect
14. #20252327	C₂	semidirect
15. #20252326	C₂	semidirect
16. #20252321	C₂	semidirect
17. #20252320	C₂	semidirect
46. #15689253	C₂²	semidirect
47. #15689253	C₂²	semidirect
48. #15689253	C₂²	semidirect
49. #15689253	C₂²	semidirect
50. #15689252	C₂²	semidirect
51. #15689252	C₂²	semidirect
52. #15689252	C₂²	semidirect
53. #15689252	C₂²	semidirect
54. #15689252	C₂²	semidirect
55. #15689252	C₂²	semidirect
56. #15689252	C₂²	semidirect
57. #15689252	C₂²	semidirect
58. #15689251	C₂²	semidirect
59. #15689251	C₂²	semidirect
60. #15689251	C₂²	semidirect
61. #15689251	C₂²	semidirect
62. #15689251	C₂²	semidirect
63. #15689251	C₂²	semidirect
64. #15689251	C₂²	semidirect
65. #15689251	C₂²	semidirect
66. #15689250	C₂²	semidirect
67. #15689250	C₂²	semidirect
68. #15689250	C₂²	semidirect
69. #15689250	C₂²	semidirect
70. C₈×Dic₉₄	C₂²	semidirect
71. C₈×Dic₉₄	C₂²	semidirect
72. C₈×Dic₉₄	C₂²	semidirect
73. C₈×Dic₉₄	C₂²	semidirect
74. #15689247	C₂²	semidirect
75. #15689247	C₂²	semidirect
76. #15689247	C₂²	semidirect
77. #15689247	C₂²	semidirect
667. C₄₇	#60252	semidirect

Maximal subgroups

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

subgroup	index
#20256793	2
#20252493	2
#20252492	2
#20252489	2
#20252487	2
#20252485	2
#20252482	2
#20252480	2
#20252334	2
#20252332	2
#20252327	2
#20252326	2
#20252321	2
#20252320	2
#20252048	2
#20252046	2
#20252042	2
#20252023	2
C₂×#15689181	2
C₄₇×#2924	2
#60252	47