Subgroups — #27081421

Order 12032.

1918 conjugacy classes of subgroups.

The subgroup lattice has 1154 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20256682	C₂	1	1	yes	maximal, characteristic
2	#20252550	C₂	1	1	yes	maximal, characteristic, complemented
3	#20252548	C₂	1	1	yes	maximal, characteristic, complemented
4	#20252544	C₂	1	1	yes	maximal, characteristic, complemented
5	#20252525	C₂	1	2	yes	maximal, complemented
6	#20252522	C₂	1	2	yes	maximal, complemented
7	#20252511	C₂	1	2	yes	maximal, complemented
8	#20252508	C₂	1	2	yes	maximal, complemented
9	#20252504	C₂	1	1	yes	maximal, characteristic, complemented
10	#20252503	C₂	1	1	yes	maximal, characteristic, complemented
11	#20252498	C₂	1	1	yes	maximal, characteristic, complemented
12	#20252495	C₂	1	1	yes	maximal, characteristic, complemented
13	#20252336	C₂	1	1	yes	maximal, characteristic, complemented
14	#20252330	C₂	1	1	yes	maximal, characteristic, complemented
15	#20252133	C₂	1	1	yes	maximal, characteristic, complemented
16	#20252127	C₂	1	1	yes	maximal, characteristic, complemented
17	#20252079	C₂	1	2	yes	maximal, complemented
18	#20252077	C₂	1	2	yes	maximal, complemented
19	#20252051	C₂	1	2	yes	maximal, complemented
20	#20252016	C₂	1	1	yes	maximal, characteristic, complemented
21	#20251955	C₂	1	2	yes	maximal, complemented
22	C₂×C₄⋊C₈×D₄₇	C₂	1	1	yes	maximal, characteristic, complemented
23	C₄₇×#2994	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#13094032	C₂²	1	2	yes	—
25	C₂×#13094030	C₂²	1	2	yes	—
26	C₂²×C₈×D₄₇	C₂²	1	2	yes	—
27	#15689679	C₄	1	1	yes	characteristic
28	#15689677	C₂²	1	1	yes	characteristic
29	#15689675	C₄	1	1	yes	characteristic
30	#15689672	C₄	1	1	yes	characteristic
31	#15689670	C₂²	1	1	yes	characteristic
32	#15689668	C₄	1	1	yes	characteristic
33	#15689658	C₄	1	1	yes	characteristic
34	#15689657	C₂²	1	1	yes	characteristic
35	#15689656	C₄	1	2	yes	—
36	#15689656	C₄	1	2	yes	—
37	#15689652	C₄	1	1	yes	characteristic
38	#15689651	C₂²	1	2	yes	—
39	#15689650	C₄	1	2	yes	—
40	#15689636	C₄	1	1	yes	characteristic
41	#15689633	C₄	1	1	yes	characteristic
42	#15689632	C₂²	1	2	yes	—
43	#15689631	C₄	1	2	yes	—
44	C₄×#10625354	C₂²	1	1	yes	characteristic
45	#15689591	C₂²	1	2	yes	—
46	C₄×#10625352	C₂²	1	1	yes	characteristic
47	C₄×#10625352	C₂²	1	2	yes	—
48	C₂×C₄²×D₄₇	C₂²	1	1	yes	characteristic
49	#15689254	C₂²	1	1	yes	characteristic, complemented
50	#15689253	C₂²	1	1	yes	characteristic, complemented
51	#15689253	C₂²	1	2	yes	complemented
52	#15689252	C₂²	1	2	yes	complemented
53	#15689251	C₂²	1	2	yes	complemented
54	#15689250	C₂²	1	1	yes	characteristic, complemented
55	#15689250	C₂²	1	2	yes	complemented
56	Q₈×C₄₇⋊C₈	C₂²	1	1	yes	characteristic, complemented
57	C₈×Dic₉₄	C₂²	1	1	yes	characteristic, complemented
58	#15689247	C₂²	1	1	yes	characteristic, complemented
59	#15689202	C₂²	1	1	yes	characteristic, complemented
60	#15689201	C₂²	1	1	yes	characteristic, complemented
61	#15689200	C₂²	1	1	yes	characteristic, complemented
62	#15689197	C₂²	1	2	yes	—
63	#15689197	C₂²	1	2	yes	complemented
64	#15689196	C₂²	1	2	yes	—
65	#15689195	C₂²	1	2	yes	—
66	#15689194	C₂²	1	2	yes	—
67	#15689194	C₂²	1	2	yes	complemented
68	#15689193	C₂²	1	2	yes	—
69	#15689192	C₂²	1	2	yes	—
70	#15689192	C₂²	1	2	yes	complemented
71	#15689191	C₂²	1	2	yes	—
72	#15689191	C₂²	1	2	yes	complemented
73	C₈×D₁₈₈	C₂²	1	2	yes	—
74	C₈×D₁₈₈	C₂²	1	1	yes	characteristic, complemented
75	D₄×C₄₇⋊C₈	C₂²	1	2	yes	—
76	D₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic, complemented
77	#15689188	C₂²	1	2	yes	—
78	#15689188	C₂²	1	1	yes	characteristic, complemented
79	C₈×C₂²⋊D₄₇	C₂²	1	2	yes	—
80	C₈×C₂²⋊D₄₇	C₂²	1	2	yes	—
81	(C₂²⋊D₄₇)⋊C₈	C₂²	1	2	yes	—
82	(C₂²⋊D₄₇)⋊C₈	C₂²	1	2	yes	—
83	#15689184	C₂²	1	2	yes	complemented
84	#15689183	C₂²	1	2	yes	complemented
85	#15689183	C₂²	1	2	yes	complemented
86	#15689179	C₂²	1	1	yes	characteristic
87	#15689179	C₂²	1	1	yes	characteristic
88	#15689178	C₂²	1	2	yes	complemented
89	#15689177	C₂²	1	1	yes	characteristic
90	#15689177	C₂²	1	1	yes	characteristic
91	#15689177	C₂²	1	2	yes	complemented
92	#15689176	C₂²	1	1	yes	characteristic
93	#15689174	C₂²	1	1	yes	characteristic
94	#15689174	C₂²	1	1	yes	characteristic
95	#15689174	C₂²	1	2	yes	complemented
96	#15689173	C₂²	1	2	yes	complemented
97	#15689150	C₂²	1	2	yes	complemented
98	#15689148	C₂²	1	2	yes	—
99	#15689148	C₂²	1	2	yes	—
100	#15689148	C₂²	1	2	yes	complemented
101	#15689148	C₂²	1	2	yes	complemented
102	#15689146	C₂²	1	2	yes	complemented
103	#15689145	C₂²	1	1	yes	characteristic
104	#15689145	C₂²	1	1	yes	characteristic
105	#15689145	C₂²	1	2	yes	complemented
106	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
107	C₂×Dic₄₇⋊C₈	C₂²	1	2	yes	—
108	C₂×Dic₄₇⋊C₈	C₂²	1	2	yes	complemented
109	C₄⋊C₈×D₄₇	C₂²	1	2	yes	—
110	C₄⋊C₈×D₄₇	C₂²	1	1	yes	characteristic
111	C₄⋊C₈×D₄₇	C₂²	1	1	yes	characteristic
112	C₄⋊C₈×D₄₇	C₂²	1	2	yes	—
113	C₄⋊C₈×D₄₇	C₂²	1	1	yes	characteristic
114	C₄⋊C₈×D₄₇	C₂²	1	1	yes	characteristic
115	C₄⋊C₈×D₄₇	C₂²	1	2	yes	complemented
116	#15689088	C₂²	1	2	yes	—
117	#15689088	C₂²	1	2	yes	—
118	#15689085	C₂²	1	1	yes	characteristic
119	#15689085	C₂²	1	1	yes	characteristic
120	#15689080	C₂²	1	2	yes	—
121	#15689077	C₂²	1	2	yes	—
122	C₄×#10625324	C₂²	1	1	yes	characteristic
123	C₄×#10625324	C₂²	1	1	yes	characteristic
124	C₄₇×#529	C₂²	1	1	yes	characteristic
125	C₄₇×#446	C₂²	1	1	yes	characteristic, complemented
126	C₈×Q₈×C₄₇	C₂²	1	1	yes	characteristic, complemented
127	C₄₇×#436	C₂²	1	1	yes	characteristic, complemented
128	C₄₇×#435	C₂²	1	2	yes	—
129	C₈×D₄×C₄₇	C₂²	1	2	yes	—
130	C₈×D₄×C₄₇	C₂²	1	1	yes	characteristic, complemented
131	C₄₇×#433	C₂²	1	2	yes	complemented
132	C₄₇×#431	C₂²	1	1	yes	characteristic
133	C₄₇×#424	C₂²	1	2	yes	complemented
134	C₂×C₄⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
135	C₂×#10625354	C₂×C₄	1	1	yes	characteristic
136	C₂×#10625350	C₂³	1	2	yes	—
137	C₂×#10625352	C₂×C₄	1	1	yes	characteristic
138	C₂×#10625352	C₂×C₄	1	2	yes	—
139	C₂²×C₄×D₄₇	C₂×C₄	1	1	yes	characteristic
140	C₂²×C₄×D₄₇	C₂×C₄	1	1	yes	characteristic
141	C₂²×C₄×D₄₇	C₂³	1	1	yes	characteristic
142	#13094032	—	4	4	no	—
143	#13094030	—	4	4	no	—
144	C₂×#10625329	C₂³	1	2	yes	—
145	C₂×#10625324	C₂³	1	1	yes	characteristic
146	C₂×#10625324	C₂³	1	1	yes	characteristic
147	C₂×#10625324	C₂³	1	1	yes	characteristic
148	C₂×#10625324	C₂³	1	1	yes	characteristic
149	C₂×#10625324	C₂³	1	2	yes	—
150	C₂×#10625324	C₂³	1	2	yes	—
151	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
152	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
153	C₂×C₈×D₄₇	—	4	4	no	—
154	C₂×C₈×D₄₇	C₂³	1	2	yes	—
155	C₂×C₈×D₄₇	C₂³	1	2	yes	—
156	C₂×C₈×D₄₇	C₂³	1	2	yes	—
157	C₂×C₈×D₄₇	C₂³	1	2	yes	—
158	C₂×C₈×D₄₇	C₂³	1	2	yes	—
159	C₂×C₈×D₄₇	C₂³	1	2	yes	—
160	#13094023	C₂×C₄	1	1	yes	characteristic
161	#13094023	C₂×C₄	1	1	yes	characteristic
162	#13094022	C₂×C₄	1	1	yes	characteristic
163	#13094020	C₂×C₄	1	1	yes	characteristic
164	#13094019	C₂×C₄	1	2	yes	—
165	#13094018	C₂×C₄	1	2	yes	—
166	#13094017	C₂×C₄	1	2	yes	—
167	#13094016	C₂×C₄	1	1	yes	characteristic
168	#13094014	C₂×C₄	1	2	yes	—
169	#13094014	C₂×C₄	1	2	yes	—
170	#13094012	C₂×C₄	1	1	yes	characteristic
171	#13094010	C₂×C₄	1	2	yes	—
172	#13094010	C₂×C₄	1	2	yes	—
173	#13094009	C₂×C₄	1	2	yes	—
174	#13094009	C₂×C₄	1	2	yes	—
175	#13094007	C₂×C₄	1	2	yes	—
176	#13094006	C₂×C₄	1	2	yes	—
177	#13094006	C₂×C₄	1	2	yes	—
178	#13094004	C₂×C₄	1	1	yes	characteristic
179	#13094003	C₂×C₄	1	1	yes	characteristic
180	#13094002	C₂×C₄	1	2	yes	—
181	#13094002	C₂×C₄	1	2	yes	—
182	#13094002	C₂×C₄	1	2	yes	—
183	#13094001	C₂×C₄	1	2	yes	—
184	#13094000	C₂×C₄	1	1	yes	characteristic
185	#13093999	C₂×C₄	1	1	yes	characteristic
186	#13093998	C₂×C₄	1	1	yes	characteristic
187	#13093997	C₂×C₄	1	2	yes	—
188	#13093997	C₂×C₄	1	2	yes	—
189	#13093997	C₂×C₄	1	2	yes	—
190	#13093996	C₂×C₄	1	2	yes	—
191	#13093995	C₂×C₄	1	1	yes	characteristic
192	#13093994	C₂×C₄	1	2	yes	—
193	#13093992	C₂×C₄	1	2	yes	—
194	Q₈×Dic₄₇	C₂×C₄	1	1	yes	characteristic
195	C₄×Dic₉₄	C₂³	1	1	yes	characteristic
196	C₄×Dic₉₄	C₂³	1	2	yes	—
197	#13093989	C₂×C₄	1	2	yes	—
198	#13093989	C₂×C₄	1	1	yes	characteristic
199	#13093989	C₂×C₄	1	2	yes	—
200	#13093989	C₂×C₄	1	2	yes	—
201	C₄×D₁₈₈	C₂³	1	2	yes	—
202	C₄×D₁₈₈	C₂³	1	1	yes	characteristic
203	D₄×Dic₄₇	C₂×C₄	1	2	yes	—
204	D₄×Dic₄₇	C₂×C₄	1	1	yes	characteristic
205	#13093986	C₂×C₄	1	2	yes	—
206	#13093986	C₂×C₄	1	2	yes	—
207	#13093986	C₂×C₄	1	2	yes	—
208	#13093986	C₂×C₄	1	1	yes	characteristic
209	C₄×C₂²⋊D₄₇	C₂³	1	2	yes	—
210	C₄×C₂²⋊D₄₇	C₂³	1	2	yes	—
211	C₄×C₂²⋊D₄₇	C₂³	1	2	yes	—
212	(C₂²⋊D₄₇)⋊C₄	C₂×C₄	1	2	yes	—
213	(C₂²⋊D₄₇)⋊C₄	C₂×C₄	1	2	yes	—
214	(C₂²⋊D₄₇)⋊C₄	C₂×C₄	1	2	yes	—
215	(C₂²⋊D₄₇)⋊C₄	C₂×C₄	1	2	yes	—
216	(C₂²⋊D₄₇)⋊C₄	C₂×C₄	1	2	yes	—
217	(C₂²⋊D₄₇)⋊C₄	C₂×C₄	1	2	yes	—
218	(C₂²⋊D₄₇)⋊C₄	C₂×C₄	1	2	yes	—
219	#13093982	C₂×C₄	1	1	yes	characteristic
220	#13093982	C₂×C₄	1	2	yes	—
221	#13093982	C₂×C₄	1	1	yes	characteristic
222	#13093982	C₂×C₄	1	2	yes	—
223	#13093981	C₂³	1	2	yes	—
224	#13093981	C₂³	1	2	yes	—
225	#13093980	C₂×C₄	1	2	yes	—
226	#13093980	C₂×C₄	1	2	yes	—
227	#13093980	C₂×C₄	1	2	yes	—
228	C₂×C₄×Dic₄₇	C₂×C₄	1	1	yes	characteristic
229	C₂×C₄×Dic₄₇	C₂×C₄	1	1	yes	characteristic
230	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
231	C₂×C₄×Dic₄₇	C₂³	1	2	yes	—
232	C₄²×D₄₇	C₂×C₄	1	1	yes	characteristic
233	C₄²×D₄₇	C₂×C₄	1	1	yes	characteristic
234	C₄²×D₄₇	C₂×C₄	1	1	yes	characteristic
235	C₄²×D₄₇	C₂×C₄	1	1	yes	characteristic
236	C₄²×D₄₇	C₂³	1	1	yes	characteristic
237	C₄²×D₄₇	C₂³	1	1	yes	characteristic
238	C₄²×D₄₇	C₂³	1	1	yes	characteristic
239	C₄²×D₄₇	C₂³	1	1	yes	characteristic
240	C₄²×D₄₇	C₂³	1	2	yes	—
241	C₄⋊(C₄₇⋊C₈)	C₂³	1	1	yes	characteristic
242	C₄⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
243	C₄⋊(C₄₇⋊C₈)	C₂³	1	1	yes	characteristic
244	C₄⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
245	C₄⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
246	C₄⋊(C₄₇⋊C₈)	C₂³	1	1	yes	characteristic
247	C₄⋊(C₄₇⋊C₈)	C₂³	1	1	yes	characteristic
248	Dic₄₇⋊C₈	C₂³	1	2	yes	—
249	Dic₄₇⋊C₈	C₂³	1	2	yes	—
250	Dic₄₇⋊C₈	C₂³	1	2	yes	—
251	Dic₄₇⋊C₈	C₂³	1	2	yes	—
252	Dic₄₇⋊C₈	C₂³	1	2	yes	—
253	Dic₄₇⋊C₈	C₂³	1	2	yes	—
254	Dic₄₇⋊C₈	C₂³	1	2	yes	—
255	Dic₄₇⋊C₈	C₂³	1	2	yes	—
256	Dic₄₇⋊C₈	C₂³	1	1	yes	characteristic
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	C₂²⋊(C₄₇⋊C₈)	C₂³	1	1	yes	characteristic
261	C₂²⋊(C₄₇⋊C₈)	C₂³	1	1	yes	characteristic
262	C₂²⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
263	C₂²⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
264	(C₂×D₄₇)⋊C₈	C₂³	1	1	yes	characteristic
265	(C₂×D₄₇)⋊C₈	C₂³	1	1	yes	characteristic
266	(C₂×D₄₇)⋊C₈	C₂³	1	1	yes	characteristic
267	(C₂×D₄₇)⋊C₈	C₂³	1	1	yes	characteristic
268	(C₂×D₄₇)⋊C₈	C₂³	1	2	yes	—
269	(C₂×D₄₇)⋊C₈	C₂³	1	2	yes	—
270	(C₂×D₄₇)⋊C₈	C₂³	1	2	yes	—
271	(C₂×D₄₇)⋊C₈	C₂³	1	2	yes	—
272	#13093935	C₂³	1	2	yes	—
273	#13093934	C₂³	1	1	yes	characteristic
274	#13093934	C₂³	1	2	yes	—
275	#13093934	C₂³	1	1	yes	characteristic
276	#13093934	C₂³	1	1	yes	characteristic
277	#13093934	C₂³	1	1	yes	characteristic
278	#13093934	C₂³	1	2	yes	—
279	C₄×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
280	C₄×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
281	C₄×C₄₇⋊C₈	C₂³	1	2	yes	—
282	C₈×Dic₄₇	C₂³	1	2	yes	—
283	C₈×Dic₄₇	C₂³	1	2	yes	—
284	C₂×M₁₆×C₄₇	C₂³	1	2	yes	—
285	C₂²×C₈×C₄₇	C₂³	1	2	yes	—
286	C₂²×C₈×C₄₇	C₂³	1	2	yes	—
287	#126×C₄₇	C₂×C₄	1	2	yes	—
288	#125×C₄₇	C₂×C₄	1	1	yes	characteristic
289	#124×C₄₇	C₂×C₄	1	1	yes	characteristic
290	#123×C₄₇	C₂×C₄	1	2	yes	—
291	C₂²⋊Q₈×C₄₇	C₂×C₄	1	1	yes	characteristic
292	#121×C₄₇	C₂×C₄	1	1	yes	characteristic
293	C₄×Q₈×C₄₇	C₂³	1	1	yes	characteristic
294	C₄×D₄×C₄₇	C₂³	1	2	yes	—
295	C₄×D₄×C₄₇	C₂³	1	1	yes	characteristic
296	#117×C₄₇	C₂³	1	2	yes	—
297	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
298	C₄⋊C₈×C₄₇	C₂³	1	1	yes	characteristic
299	C₄⋊C₈×C₄₇	C₂³	1	1	yes	characteristic
300	C₄⋊C₈×C₄₇	C₂³	1	2	yes	—
301	C₄⋊C₈×C₄₇	C₂³	1	2	yes	—
302	C₄⋊C₈×C₄₇	C₂³	1	2	yes	—
303	C₄⋊C₈×C₄₇	C₂³	1	1	yes	characteristic
304	C₄⋊C₈×C₄₇	C₂³	1	1	yes	characteristic
305	C₂²⋊C₈×C₄₇	C₂³	1	1	yes	characteristic
306	C₂²⋊C₈×C₄₇	C₂³	1	1	yes	characteristic
307	C₂²⋊C₈×C₄₇	C₂³	1	2	yes	—
308	C₂²⋊C₈×C₄₇	C₂³	1	2	yes	—
309	#97×C₄₇	C₂³	1	2	yes	—
310	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
311	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
312	C₄×C₈×C₄₇	C₂³	1	2	yes	—
313	C₂³×D₄₇	C₂²×C₄	1	1	yes	characteristic
314	C₂×Q₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
315	C₂×D₄×C₄₇	C₂²×C₄	1	2	yes	—
316	C₂×D₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
317	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
318	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
319	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
320	C₂²×C₄×C₄₇	C₂⁴	1	2	yes	—
321	C₂×C₂²⋊D₄₇	C₂²×C₄	1	2	yes	—
322	C₂×C₂²⋊D₄₇	C₂²×C₄	1	2	yes	—
323	C₂×C₂²⋊D₄₇	C₂²×C₄	1	2	yes	—
324	C₂×C₂²⋊D₄₇	C₂²×C₄	1	2	yes	—
325	C₂×C₂²⋊D₄₇	C₂²×C₄	1	2	yes	—
326	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
327	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
328	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
329	C₂²×Dic₄₇	C₂²×C₄	1	2	yes	—
330	C₂²×Dic₄₇	C₂²×C₄	1	2	yes	—
331	#10625354	—	2	4	no	—
332	#10625352	—	2	4	no	—
333	#10625352	—	4	4	no	—
334	#10625350	—	2	4	no	—
335	#10625350	—	2	4	no	—
336	C₂×D₁₈₈	C₂²×C₄	1	2	yes	—
337	C₂×D₁₈₈	C₂²×C₄	1	2	yes	—
338	C₂×D₁₈₈	C₂²×C₄	1	1	yes	characteristic
339	C₂×C₄×D₄₇	—	2	4	no	—
340	C₂×C₄×D₄₇	—	2	2	no	—
341	C₂×C₄×D₄₇	—	2	2	no	—
342	C₂×C₄×D₄₇	—	4	2	no	—
343	C₂×C₄×D₄₇	C₂²×C₄	1	1	yes	characteristic
344	C₂×C₄×D₄₇	C₂²×C₄	1	1	yes	characteristic
345	C₂×C₄×D₄₇	C₂²×C₄	1	1	yes	characteristic
346	C₂×C₄×D₄₇	C₂²×C₄	1	1	yes	characteristic
347	C₂×C₄×D₄₇	C₂²×C₄	1	1	yes	characteristic
348	C₂×C₄×D₄₇	C₂²×C₄	1	2	yes	—
349	C₂×C₄×D₄₇	C₂²×C₄	1	1	yes	characteristic
350	C₂×C₄×D₄₇	C₂²×C₄	1	1	yes	characteristic
351	C₂×C₄×D₄₇	C₂²×C₄	1	1	yes	characteristic
352	C₂×C₄×D₄₇	C₂²×C₄	1	1	yes	characteristic
353	C₂×C₄×D₄₇	C₂²×C₄	1	2	yes	—
354	C₂×C₄×D₄₇	C₂²×C₄	1	1	yes	characteristic
355	C₂×C₄×D₄₇	C₂⁴	1	1	yes	characteristic
356	C₂×C₄×D₄₇	C₂⁴	1	2	yes	—
357	C₂×C₄×D₄₇	C₂⁴	1	1	yes	characteristic
358	C₂×Dic₉₄	C₂²×C₄	1	2	yes	—
359	C₂×Dic₉₄	C₂²×C₄	1	1	yes	characteristic
360	C₂×Dic₉₄	C₂²×C₄	1	2	yes	—
361	M₁₆×C₄₇	—	4	2	no	—
362	C₂×C₈×C₄₇	—	4	2	no	—
363	C₂×C₈×C₄₇	—	4	2	no	—
364	C₂×C₈×C₄₇	C₂⁴	1	2	yes	—
365	C₂×C₈×C₄₇	C₂⁴	1	1	yes	characteristic
366	C₂×C₈×C₄₇	C₂⁴	1	2	yes	—
367	C₂×C₈×C₄₇	C₂⁴	1	1	yes	characteristic
368	C₂×C₈×C₄₇	C₂⁴	1	1	yes	characteristic
369	C₂×C₈×C₄₇	C₂⁴	1	1	yes	characteristic
370	C₄⋊C₄×C₄₇	C₂²×C₄	1	2	yes	—
371	C₄⋊C₄×C₄₇	C₂²×C₄	1	2	yes	—
372	C₄⋊C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
373	C₄⋊C₄×C₄₇	C₂²×C₄	1	2	yes	—
374	C₄⋊C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
375	C₄⋊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	C₂²⋊C₄×C₄₇	C₂²×C₄	1	2	yes	—
379	C₂²⋊C₄×C₄₇	C₂²×C₄	1	2	yes	—
380	C₂²⋊C₄×C₄₇	C₂²×C₄	1	2	yes	—
381	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
382	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
383	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
384	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
385	C₄²×C₄₇	C₂⁴	1	2	yes	—
386	C₂²⋊Dic₄₇	C₂²×C₄	1	2	yes	—
387	C₂²⋊Dic₄₇	C₂²×C₄	1	2	yes	—
388	C₂²⋊Dic₄₇	C₂²×C₄	1	2	yes	—
389	(C₂×D₄₇)⋊C₄	C₂²×C₄	1	2	yes	—
390	(C₂×D₄₇)⋊C₄	C₂²×C₄	1	2	yes	—
391	(C₂×D₄₇)⋊C₄	C₂²×C₄	1	2	yes	—
392	(C₂×D₄₇)⋊C₄	C₂²×C₄	1	2	yes	—
393	(C₂×D₄₇)⋊C₄	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	C₄⋊Dic₄₇	C₂²×C₄	1	1	yes	characteristic
400	C₄⋊Dic₄₇	C₂²×C₄	1	2	yes	—
401	C₄⋊Dic₄₇	C₂²×C₄	1	1	yes	characteristic
402	C₄⋊Dic₄₇	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	Dic₄₇⋊C₄	C₂²×C₄	1	2	yes	—
410	Dic₄₇⋊C₄	C₂²×C₄	1	2	yes	—
411	Dic₄₇⋊C₄	C₂²×C₄	1	2	yes	—
412	Dic₄₇⋊C₄	C₂²×C₄	1	2	yes	—
413	C₄×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
414	C₄×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
415	C₄×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
416	C₄×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
417	C₄×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
418	C₄×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
419	C₄×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
420	C₄×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
421	C₄×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
422	C₄×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
423	C₄×Dic₄₇	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	2	yes	—
427	C₄×Dic₄₇	C₂⁴	1	2	yes	—
428	C₄×Dic₄₇	C₂⁴	1	1	yes	characteristic
429	C₄×Dic₄₇	C₂⁴	1	1	yes	characteristic
430	#10625329	—	4	2	no	—
431	C₂×C₄₇⋊C₈	—	4	2	no	—
432	C₂×C₄₇⋊C₈	—	4	2	no	—
433	C₂×C₄₇⋊C₈	C₂⁴	1	1	yes	characteristic
434	C₂×C₄₇⋊C₈	C₂⁴	1	2	yes	—
435	C₂×C₄₇⋊C₈	C₂⁴	1	1	yes	characteristic
436	C₂×C₄₇⋊C₈	C₂⁴	1	1	yes	characteristic
437	C₂×C₄₇⋊C₈	C₂⁴	1	1	yes	characteristic
438	C₂×C₄₇⋊C₈	C₂⁴	1	2	yes	—
439	#10625324	—	2	2	no	—
440	#10625324	—	2	2	no	—
441	#10625324	—	2	2	no	—
442	#10625324	—	2	2	no	—
443	#10625324	—	4	2	no	—
444	#10625324	—	4	2	no	—
445	C₈×D₄₇	—	2	4	no	—
446	C₈×D₄₇	—	2	4	no	—
447	C₈×D₄₇	—	4	2	no	—
448	C₈×D₄₇	—	4	2	no	—
449	C₈×D₄₇	—	4	2	no	—
450	C₈×D₄₇	—	4	2	no	—
451	C₂³×C₄₇	C₂³×C₄	1	2	yes	—
452	C₂³×C₄₇	C₂³×C₄	1	1	yes	characteristic
453	C₂²×D₄₇	—	2	2	no	—
454	C₂²×D₄₇	—	2	2	no	—
455	C₂²×D₄₇	—	2	2	no	—
456	C₂²×D₄₇	C₂³×C₄	1	2	yes	—
457	C₂²×D₄₇	C₂³×C₄	1	1	yes	characteristic
458	C₂²×D₄₇	C₂³×C₄	1	1	yes	characteristic
459	Q₈×C₄₇	—	2	2	no	—
460	D₄×C₄₇	—	2	4	no	—
461	D₄×C₄₇	—	2	2	no	—
462	C₂×C₄×C₄₇	—	2	2	no	—
463	C₂×C₄×C₄₇	—	2	2	no	—
464	C₂×C₄×C₄₇	—	2	1	no	—
465	C₂×C₄×C₄₇	—	2	2	no	—
466	C₂×C₄×C₄₇	—	2	1	no	—
467	C₂×C₄×C₄₇	—	2	2	no	—
468	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
469	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
470	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
471	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
472	C₂×C₄×C₄₇	C₂³×C₄	1	2	yes	—
473	C₂×C₄×C₄₇	C₂³×C₄	1	2	yes	—
474	C₂×C₄×C₄₇	C₂³×C₄	1	2	yes	—
475	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
476	C₂×C₄×C₄₇	C₂⁵	1	1	yes	characteristic
477	C₂²⋊D₄₇	—	2	4	no	—
478	C₂²⋊D₄₇	—	2	4	no	—
479	C₂²⋊D₄₇	—	2	4	no	—
480	C₂²⋊D₄₇	—	2	4	no	—
481	C₂²⋊D₄₇	—	4	2	no	—
482	C₂×Dic₄₇	—	2	2	no	—
483	C₂×Dic₄₇	—	2	2	no	—
484	C₂×Dic₄₇	—	2	2	no	—
485	C₂×Dic₄₇	—	2	4	no	—
486	C₂×Dic₄₇	—	4	2	no	—
487	C₂×Dic₄₇	C₂³×C₄	1	1	yes	characteristic
488	C₂×Dic₄₇	C₂³×C₄	1	1	yes	characteristic
489	C₂×Dic₄₇	C₂³×C₄	1	1	yes	characteristic
490	C₂×Dic₄₇	C₂³×C₄	1	1	yes	characteristic
491	C₂×Dic₄₇	C₂³×C₄	1	2	yes	—
492	C₂×Dic₄₇	C₂³×C₄	1	2	yes	—
493	C₂×Dic₄₇	C₂³×C₄	1	2	yes	—
494	C₂×Dic₄₇	C₂³×C₄	1	1	yes	characteristic
495	C₂×Dic₄₇	C₂³×C₄	1	1	yes	characteristic
496	D₁₈₈	—	2	4	no	—
497	D₁₈₈	—	2	4	no	—
498	D₁₈₈	—	2	2	no	—
499	C₄×D₄₇	—	2	2	no	—
500	C₄×D₄₇	—	2	2	no	—
501	C₄×D₄₇	—	2	2	no	—
502	C₄×D₄₇	—	2	1	no	—
503	C₄×D₄₇	—	2	2	no	—
504	C₄×D₄₇	—	2	1	no	—
505	C₄×D₄₇	—	2	2	no	—
506	C₄×D₄₇	—	2	2	no	—
507	C₄×D₄₇	—	2	2	no	—
508	C₄×D₄₇	—	2	4	no	—
509	C₄×D₄₇	—	4	1	no	—
510	C₄×D₄₇	—	4	1	no	—
511	C₄×D₄₇	—	4	1	no	—
512	C₄×D₄₇	—	4	1	no	—
513	C₄×D₄₇	—	4	2	no	—
514	C₄×D₄₇	#131	1	4	yes	complemented
515	C₄×D₄₇	H(5,𝔽₂)	1	2	yes	—
516	C₄×D₄₇	2₋¹⁺⁴	1	2	yes	—
517	Dic₉₄	—	2	2	no	—
518	Dic₉₄	—	2	4	no	—
519	Dic₉₄	—	4	2	no	—
520	C₈×C₄₇	—	2	2	no	—
521	C₈×C₄₇	—	2	2	no	—
522	C₈×C₄₇	—	2	1	no	—
523	C₈×C₄₇	—	2	1	no	—
524	C₈×C₄₇	—	2	1	no	—
525	C₈×C₄₇	—	2	1	no	—
526	C₄₇⋊C₈	—	2	2	no	—
527	C₄₇⋊C₈	—	2	2	no	—
528	C₄₇⋊C₈	—	2	1	no	—
529	C₄₇⋊C₈	—	2	1	no	—
530	C₄₇⋊C₈	—	2	1	no	—
531	C₄₇⋊C₈	—	2	1	no	—
532	#60265	—	47	1	no	maximal, Sylow
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	#568	1	2	yes	—
539	C₂²×C₄₇	C₂⁴×C₄	1	1	yes	characteristic
540	C₂×D₄₇	—	2	8	no	—
541	C₂×D₄₇	—	2	1	no	—
542	C₂×D₄₇	—	2	1	no	—
543	C₂×D₄₇	—	2	1	no	—
544	C₂×D₄₇	—	2	1	no	—
545	C₂×D₄₇	—	2	2	no	—
546	C₂×D₄₇	—	2	2	no	—
547	C₂×D₄₇	—	2	2	no	—
548	C₂×D₄₇	#520	1	2	yes	—
549	C₂×D₄₇	C₂×#131	1	2	yes	—
550	C₄×C₄₇	—	2	2	no	—
551	C₄×C₄₇	—	2	1	no	—
552	C₄×C₄₇	—	2	1	no	—
553	C₄×C₄₇	—	2	2	no	—
554	C₄×C₄₇	—	2	2	no	—
555	C₄×C₄₇	—	2	1	no	—
556	C₄×C₄₇	—	2	1	no	—
557	C₄×C₄₇	C₂×#131	1	2	yes	—
558	C₄×C₄₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
559	C₄×C₄₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
560	Dic₄₇	—	2	2	no	—
561	Dic₄₇	—	2	1	no	—
562	Dic₄₇	—	2	2	no	—
563	Dic₄₇	—	2	1	no	—
564	Dic₄₇	—	2	1	no	—
565	Dic₄₇	—	2	2	no	—
566	Dic₄₇	—	2	1	no	—
567	Dic₄₇	#520	1	2	yes	—
568	Dic₄₇	C₂×#131	1	2	yes	—
569	#3444	—	47	1	no	—
570	#2994	—	47	1	no	—
571	#2994	—	47	1	no	—
572	#2994	—	47	1	no	—
573	#2994	D₄₇	1	1	yes	characteristic, complemented
574	#2992	—	47	2	no	—
575	#2992	—	47	2	no	—
576	#2990	—	47	2	no	—
577	#2990	—	47	2	no	—
578	#2989	—	47	1	no	—
579	#2989	—	47	1	no	—
580	#2988	—	47	1	no	—
581	#2988	—	47	1	no	—
582	#2962	—	47	1	no	—
583	#2962	—	47	1	no	—
584	#2935	—	47	1	no	—
585	#2935	—	47	1	no	—
586	#2929	—	47	2	no	—
587	#2929	—	47	2	no	—
588	#2925	—	47	2	no	—
589	#2920	—	47	1	no	—
590	#2906	—	47	2	no	—
591	C₂²×C₄⋊C₈	—	47	1	no	—
592	C₂×C₄₇	—	2	2	no	—
593	C₂×C₄₇	—	4	2	no	—
594	C₂×C₄₇	C₂×#520	1	1	yes	characteristic
595	C₂×C₄₇	C₂²×#131	1	1	yes	characteristic
596	C₂×C₄₇	C₂×#568	1	1	yes	characteristic
597	D₄₇	—	2	2	no	—
598	D₄₇	—	2	2	no	—
599	D₄₇	—	4	2	no	—
600	C₂×#131	—	47	2	no	—
601	C₂×#131	—	47	2	no	—
602	C₂³×C₈	—	47	2	no	—
603	#533	—	47	1	no	—
604	#533	—	47	1	no	—
605	#533	—	47	1	no	—
606	#532	—	47	1	no	—
607	#532	—	47	1	no	—
608	#532	—	47	1	no	—
609	#529	—	47	2	no	—
610	#529	—	47	2	no	—
611	#529	—	47	1	no	—
612	#529	—	47	1	no	—
613	#529	—	47	2	no	—
614	#529	—	47	2	no	—
615	#529	—	47	1	no	—
616	#529	C₂×D₄₇	1	1	yes	characteristic
617	#525	—	47	2	no	—
618	#525	—	47	1	no	—
619	#525	—	47	1	no	—
620	#525	—	47	2	no	—
621	C₄×#41	—	47	1	no	—
622	C₄×#41	—	47	1	no	—
623	C₄×#41	—	47	2	no	—
624	C₄×#41	—	47	2	no	—
625	C₂²×C₄²	—	47	1	no	—
626	#446	—	47	1	no	—
627	#446	—	47	1	no	—
628	#446	—	47	2	no	—
629	#446	—	47	2	no	—
630	#446	—	47	2	no	—
631	#446	—	47	1	no	—
632	#446	—	47	2	no	—
633	#446	C₂×D₄₇	1	1	yes	characteristic, complemented
634	C₈×Q₈	—	47	1	no	—
635	C₈×Q₈	—	47	1	no	—
636	C₈×Q₈	—	47	1	no	—
637	C₈×Q₈	C₂×D₄₇	1	1	yes	characteristic, complemented
638	#436	—	47	1	no	—
639	#436	—	47	1	no	—
640	#436	—	47	1	no	—
641	#436	C₂×D₄₇	1	1	yes	characteristic, complemented
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	—	47	2	no	—
652	#435	—	47	2	no	—
653	#435	C₂×D₄₇	1	2	yes	—
654	C₈×D₄	—	47	2	no	—
655	C₈×D₄	—	47	2	no	—
656	C₈×D₄	—	47	2	no	—
657	C₈×D₄	—	47	1	no	—
658	C₈×D₄	—	47	2	no	—
659	C₈×D₄	—	47	1	no	—
660	C₈×D₄	—	47	2	no	—
661	C₈×D₄	—	47	2	no	—
662	C₈×D₄	—	47	2	no	—
663	C₈×D₄	—	47	1	no	—
664	C₈×D₄	C₂×D₄₇	1	2	yes	—
665	C₈×D₄	C₂×D₄₇	1	1	yes	characteristic, complemented
666	#433	—	47	2	no	—
667	#433	—	47	2	no	—
668	#433	—	47	2	no	—
669	#433	C₂×D₄₇	1	2	yes	complemented
670	#432	—	47	1	no	—
671	#432	—	47	1	no	—
672	#432	—	47	1	no	—
673	#432	—	47	1	no	—
674	#432	—	47	2	no	—
675	#432	—	47	2	no	—
676	#431	—	47	1	no	—
677	#431	—	47	2	no	—
678	#431	—	47	1	no	—
679	#431	—	47	1	no	—
680	#431	—	47	2	no	—
681	#431	C₂×D₄₇	1	1	yes	characteristic
682	#424	—	47	2	no	—
683	#424	—	47	2	no	—
684	#424	—	47	2	no	—
685	#424	—	47	2	no	—
686	#424	—	47	2	no	—
687	#424	C₂×D₄₇	1	2	yes	complemented
688	#423	—	47	2	no	—
689	#423	—	47	1	no	—
690	#423	—	47	2	no	—
691	#423	—	47	1	no	—
692	C₂×C₄⋊C₈	—	47	2	no	—
693	C₂×C₄⋊C₈	—	47	2	no	—
694	C₂×C₄⋊C₈	—	47	1	no	—
695	C₂×C₄⋊C₈	—	47	2	no	—
696	C₂×C₄⋊C₈	—	47	1	no	—
697	C₂×C₄⋊C₈	—	47	1	no	—
698	C₂×C₄⋊C₈	—	47	1	no	—
699	C₂×C₄⋊C₈	—	47	1	no	—
700	C₂×C₄⋊C₈	—	47	2	no	—
701	C₂×C₄⋊C₈	—	47	2	no	—
702	C₂×C₄⋊C₈	C₂×D₄₇	1	1	yes	characteristic
703	#408	—	47	2	no	—
704	#408	—	47	2	no	—
705	#407	—	47	1	no	—
706	#407	—	47	1	no	—
707	#405	—	47	2	no	—
708	#405	—	47	2	no	—
709	C₄×M₁₆	—	47	1	no	—
710	C₄×M₁₆	—	47	1	no	—
711	C₄₇	#60265	1	1	yes	characteristic, complemented, Sylow
712	C₂×#41	—	47	1	no	—
713	C₂×#41	—	47	1	no	—
714	C₂×#41	—	47	2	no	—
715	C₂×#41	—	47	2	no	—
716	C₂³×C₄	—	47	1	no	—
717	C₂³×C₄	—	47	1	no	—
718	C₂³×C₄	—	47	1	no	—
719	#131	—	188	4	no	—
720	#131	—	188	4	no	—
721	C₂×M₁₆	—	47	2	no	—
722	C₂×M₁₆	—	47	1	no	—
723	C₂×M₁₆	—	47	1	no	—
724	C₂×M₁₆	—	47	1	no	—
725	C₂×M₁₆	—	47	1	no	—
726	C₂×M₁₆	—	47	2	no	—
727	C₂×M₁₆	—	47	2	no	—
728	C₂×M₁₆	C₂²×D₄₇	1	2	yes	—
729	C₂²×C₈	—	47	2	no	—
730	C₂²×C₈	—	47	2	no	—
731	C₂²×C₈	—	47	2	no	—
732	C₂²×C₈	—	47	2	no	—
733	C₂²×C₈	—	47	2	no	—
734	C₂²×C₈	—	47	2	no	—
735	C₂²×C₈	—	47	2	no	—
736	C₂²×C₈	—	47	2	no	—
737	C₂²×C₈	—	188	4	no	—
738	C₂²×C₈	C₂²×D₄₇	1	2	yes	—
739	C₂²×C₈	C₂²×D₄₇	1	2	yes	—
740	C₄⋊Q₈	—	47	1	no	—
741	C₄⋊Q₈	—	47	1	no	—
742	C₄⋊Q₈	—	47	1	no	—
743	#127	—	47	1	no	—
744	#126	—	47	2	no	—
745	#126	—	47	2	no	—
746	#126	—	47	2	no	—
747	#126	C₄×D₄₇	1	2	yes	—
748	#125	—	47	2	no	—
749	#125	—	47	2	no	—
750	#125	—	47	1	no	—
751	#125	C₄×D₄₇	1	1	yes	characteristic
752	#124	—	47	2	no	—
753	#124	—	47	2	no	—
754	#124	—	47	1	no	—
755	#124	C₄×D₄₇	1	1	yes	characteristic
756	#123	—	47	2	no	—
757	#123	—	47	2	no	—
758	#123	—	47	2	no	—
759	#123	—	47	2	no	—
760	#123	—	47	2	no	—
761	#123	C₄×D₄₇	1	2	yes	—
762	C₂²⋊Q₈	—	47	1	no	—
763	C₂²⋊Q₈	—	47	1	no	—
764	C₂²⋊Q₈	—	47	2	no	—
765	C₂²⋊Q₈	—	47	2	no	—
766	C₂²⋊Q₈	—	47	2	no	—
767	C₂²⋊Q₈	—	47	1	no	—
768	C₂²⋊Q₈	—	47	2	no	—
769	C₂²⋊Q₈	C₄×D₄₇	1	1	yes	characteristic
770	#121	—	47	1	no	—
771	#121	—	47	2	no	—
772	#121	—	47	1	no	—
773	#121	—	47	1	no	—
774	#121	—	47	2	no	—
775	#121	—	47	2	no	—
776	#121	—	47	2	no	—
777	#121	C₄×D₄₇	1	1	yes	characteristic
778	#120	—	47	2	no	—
779	#120	—	47	2	no	—
780	C₄×Q₈	—	47	1	no	—
781	C₄×Q₈	—	47	2	no	—
782	C₄×Q₈	—	47	2	no	—
783	C₄×Q₈	—	47	2	no	—
784	C₄×Q₈	—	47	1	no	—
785	C₄×Q₈	—	47	1	no	—
786	C₄×Q₈	—	47	2	no	—
787	C₄×Q₈	C₂²×D₄₇	1	1	yes	characteristic
788	C₄×D₄	—	47	2	no	—
789	C₄×D₄	—	47	1	no	—
790	C₄×D₄	—	47	2	no	—
791	C₄×D₄	—	47	2	no	—
792	C₄×D₄	—	47	2	no	—
793	C₄×D₄	—	47	2	no	—
794	C₄×D₄	—	47	2	no	—
795	C₄×D₄	—	47	2	no	—
796	C₄×D₄	—	47	1	no	—
797	C₄×D₄	—	47	2	no	—
798	C₄×D₄	—	47	2	no	—
799	C₄×D₄	—	47	2	no	—
800	C₄×D₄	—	47	2	no	—
801	C₄×D₄	—	47	2	no	—
802	C₄×D₄	—	47	2	no	—
803	C₄×D₄	—	47	2	no	—
804	C₄×D₄	—	47	2	no	—
805	C₄×D₄	—	47	1	no	—
806	C₄×D₄	C₂²×D₄₇	1	2	yes	—
807	C₄×D₄	C₂²×D₄₇	1	1	yes	characteristic
808	#117	—	47	1	no	—
809	#117	—	47	1	no	—
810	#117	—	47	2	no	—
811	#117	—	47	2	no	—
812	#117	—	47	2	no	—
813	#117	—	47	2	no	—
814	#117	—	47	2	no	—
815	#117	—	47	2	no	—
816	#117	—	47	2	no	—
817	#117	C₂²×D₄₇	1	2	yes	—
818	C₂×C₄²	—	47	1	no	—
819	C₂×C₄²	—	47	1	no	—
820	C₂×C₄²	—	47	2	no	—
821	C₂×C₄²	—	47	1	no	—
822	C₂×C₄²	—	47	1	no	—
823	C₂×C₄²	—	47	1	no	—
824	C₂×C₄²	—	47	1	no	—
825	C₂×C₄²	—	47	1	no	—
826	C₂×C₄²	—	47	2	no	—
827	C₂×C₄²	—	47	1	no	—
828	C₂×C₄²	—	47	1	no	—
829	C₂×C₄²	—	47	1	no	—
830	C₂×C₄²	—	47	1	no	—
831	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
832	C₄⋊C₈	—	47	2	no	—
833	C₄⋊C₈	—	47	2	no	—
834	C₄⋊C₈	—	47	2	no	—
835	C₄⋊C₈	—	47	2	no	—
836	C₄⋊C₈	—	47	1	no	—
837	C₄⋊C₈	—	47	1	no	—
838	C₄⋊C₈	—	47	2	no	—
839	C₄⋊C₈	—	47	2	no	—
840	C₄⋊C₈	—	47	2	no	—
841	C₄⋊C₈	—	47	2	no	—
842	C₄⋊C₈	—	47	1	no	—
843	C₄⋊C₈	—	47	1	no	—
844	C₄⋊C₈	—	47	2	no	—
845	C₄⋊C₈	—	47	1	no	—
846	C₄⋊C₈	—	47	1	no	—
847	C₄⋊C₈	—	47	2	no	—
848	C₄⋊C₈	—	47	1	no	—
849	C₄⋊C₈	—	47	2	no	—
850	C₄⋊C₈	—	47	1	no	—
851	C₄⋊C₈	C₂²×D₄₇	1	2	yes	—
852	C₄⋊C₈	C₂²×D₄₇	1	1	yes	characteristic
853	C₄⋊C₈	C₂²×D₄₇	1	1	yes	characteristic
854	C₄⋊C₈	C₂²×D₄₇	1	2	yes	—
855	C₄⋊C₈	C₂²×D₄₇	1	1	yes	characteristic
856	C₄⋊C₈	C₂²×D₄₇	1	2	yes	—
857	C₄⋊C₈	C₂²×D₄₇	1	1	yes	characteristic
858	C₂²⋊C₈	—	47	1	no	—
859	C₂²⋊C₈	—	47	1	no	—
860	C₂²⋊C₈	—	47	2	no	—
861	C₂²⋊C₈	—	47	2	no	—
862	C₂²⋊C₈	—	47	1	no	—
863	C₂²⋊C₈	—	47	1	no	—
864	C₂²⋊C₈	—	47	1	no	—
865	C₂²⋊C₈	—	47	1	no	—
866	C₂²⋊C₈	—	47	2	no	—
867	C₂²⋊C₈	—	47	2	no	—
868	C₂²⋊C₈	—	47	2	no	—
869	C₂²⋊C₈	—	47	2	no	—
870	C₂²⋊C₈	C₂²×D₄₇	1	1	yes	characteristic
871	C₂²⋊C₈	C₂²×D₄₇	1	1	yes	characteristic
872	C₂²⋊C₈	C₂²×D₄₇	1	2	yes	—
873	C₂²⋊C₈	C₂²×D₄₇	1	2	yes	—
874	#97	—	47	1	no	—
875	#97	—	47	1	no	—
876	#97	—	47	1	no	—
877	#97	—	47	1	no	—
878	#97	—	47	2	no	—
879	#97	—	47	2	no	—
880	#97	—	47	2	no	—
881	#97	C₂²×D₄₇	1	2	yes	—
882	C₄×C₈	—	47	2	no	—
883	C₄×C₈	—	47	2	no	—
884	C₄×C₈	—	47	1	no	—
885	C₄×C₈	—	47	1	no	—
886	C₄×C₈	—	47	2	no	—
887	C₄×C₈	C₂²×D₄₇	1	1	yes	characteristic
888	C₄×C₈	C₂²×D₄₇	1	1	yes	characteristic
889	C₄×C₈	C₂²×D₄₇	1	2	yes	—
890	C₂⁴	—	47	1	no	—
891	#41	—	94	4	no	—
892	#41	—	94	4	no	—
893	#41	—	94	4	no	—
894	#41	—	94	4	no	—
895	#41	—	188	4	no	—
896	C₂×Q₈	—	47	2	no	—
897	C₂×Q₈	—	47	1	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	2	no	—
906	C₂×D₄	—	47	2	no	—
907	C₂×D₄	—	47	1	no	—
908	C₂×D₄	C₂×C₄×D₄₇	1	2	yes	—
909	C₂×D₄	C₂×C₄×D₄₇	1	1	yes	characteristic
910	C₂²×C₄	—	47	1	no	—
911	C₂²×C₄	—	47	1	no	—
912	C₂²×C₄	—	47	1	no	—
913	C₂²×C₄	—	47	1	no	—
914	C₂²×C₄	—	47	1	no	—
915	C₂²×C₄	—	47	2	no	—
916	C₂²×C₄	—	47	2	no	—
917	C₂²×C₄	—	47	1	no	—
918	C₂²×C₄	—	47	1	no	—
919	C₂²×C₄	—	47	1	no	—
920	C₂²×C₄	—	47	1	no	—
921	C₂²×C₄	—	47	1	no	—
922	C₂²×C₄	—	47	2	no	—
923	C₂²×C₄	—	47	1	no	—
924	C₂²×C₄	—	47	2	no	—
925	C₂²×C₄	—	47	1	no	—
926	C₂²×C₄	—	47	1	no	—
927	C₂²×C₄	—	47	1	no	—
928	C₂²×C₄	—	47	1	no	—
929	C₂²×C₄	—	47	2	no	—
930	C₂²×C₄	—	94	2	no	—
931	C₂²×C₄	—	94	4	no	—
932	C₂²×C₄	—	94	2	no	—
933	C₂²×C₄	—	188	2	no	—
934	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
935	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
936	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
937	C₂²×C₄	C₂³×D₄₇	1	2	yes	—
938	M₁₆	—	4	2	no	—
939	M₁₆	—	94	2	no	—
940	M₁₆	—	94	2	no	—
941	M₁₆	—	94	2	no	—
942	M₁₆	—	94	2	no	—
943	M₁₆	—	188	2	no	—
944	M₁₆	—	188	2	no	—
945	M₁₆	—	188	2	no	—
946	C₂×C₈	—	4	2	no	—
947	C₂×C₈	—	4	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	—	47	2	no	—
954	C₂×C₈	—	94	4	no	—
955	C₂×C₈	—	94	4	no	—
956	C₂×C₈	—	188	2	no	—
957	C₂×C₈	—	188	2	no	—
958	C₂×C₈	—	188	2	no	—
959	C₂×C₈	—	188	2	no	—
960	C₂×C₈	—	188	2	no	—
961	C₂×C₈	—	188	2	no	—
962	C₂×C₈	C₂³×D₄₇	1	1	yes	characteristic
963	C₂×C₈	C₂³×D₄₇	1	2	yes	—
964	C₂×C₈	C₂³×D₄₇	1	1	yes	characteristic
965	C₂×C₈	C₂³×D₄₇	1	1	yes	characteristic
966	C₂×C₈	C₂³×D₄₇	1	1	yes	characteristic
967	C₂×C₈	C₂³×D₄₇	1	2	yes	—
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	2	no	—
975	C₄⋊C₄	—	47	2	no	—
976	C₄⋊C₄	—	47	2	no	—
977	C₄⋊C₄	—	47	2	no	—
978	C₄⋊C₄	—	47	1	no	—
979	C₄⋊C₄	—	47	1	no	—
980	C₄⋊C₄	—	47	2	no	—
981	C₄⋊C₄	—	47	2	no	—
982	C₄⋊C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
983	C₄⋊C₄	C₂×C₄×D₄₇	1	2	yes	—
984	C₄⋊C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
985	C₄⋊C₄	C₂×C₄×D₄₇	1	2	yes	—
986	C₄⋊C₄	C₂×C₄×D₄₇	1	2	yes	—
987	C₄⋊C₄	C₂×C₄×D₄₇	1	2	yes	—
988	C₂²⋊C₄	—	47	2	no	—
989	C₂²⋊C₄	—	47	2	no	—
990	C₂²⋊C₄	—	47	2	no	—
991	C₂²⋊C₄	—	47	2	no	—
992	C₂²⋊C₄	—	47	2	no	—
993	C₂²⋊C₄	—	47	2	no	—
994	C₂²⋊C₄	—	47	2	no	—
995	C₂²⋊C₄	—	47	2	no	—
996	C₂²⋊C₄	—	47	2	no	—
997	C₂²⋊C₄	—	47	2	no	—
998	C₂²⋊C₄	—	47	2	no	—
999	C₂²⋊C₄	—	47	2	no	—
1000	C₂²⋊C₄	—	47	2	no	—
1001	C₂²⋊C₄	C₂×C₄×D₄₇	1	2	yes	—
1002	C₂²⋊C₄	C₂×C₄×D₄₇	1	2	yes	—
1003	C₂²⋊C₄	C₂×C₄×D₄₇	1	2	yes	—
1004	C₂²⋊C₄	C₂×C₄×D₄₇	1	2	yes	—
1005	C₂²⋊C₄	C₂×C₄×D₄₇	1	2	yes	—
1006	C₄²	—	47	1	no	—
1007	C₄²	—	47	1	no	—
1008	C₄²	—	47	1	no	—
1009	C₄²	—	47	1	no	—
1010	C₄²	—	47	1	no	—
1011	C₄²	—	47	1	no	—
1012	C₄²	—	47	1	no	—
1013	C₄²	—	47	1	no	—
1014	C₄²	—	47	1	no	—
1015	C₄²	—	47	1	no	—
1016	C₄²	—	47	2	no	—
1017	C₄²	—	47	2	no	—
1018	C₄²	—	47	2	no	—
1019	C₄²	—	47	2	no	—
1020	C₄²	—	47	2	no	—
1021	C₄²	—	47	1	no	—
1022	C₄²	—	47	1	no	—
1023	C₄²	C₂×C₄×D₄₇	1	1	yes	characteristic
1024	C₄²	C₂×C₄×D₄₇	1	1	yes	characteristic
1025	C₄²	C₂³×D₄₇	1	1	yes	characteristic
1026	C₄²	C₂³×D₄₇	1	2	yes	—
1027	C₄²	C₂³×D₄₇	1	1	yes	characteristic
1028	C₂³	—	47	1	no	—
1029	C₂³	—	47	1	no	—
1030	C₂³	—	47	2	no	—
1031	C₂³	—	94	2	no	—
1032	C₂³	—	94	2	no	—
1033	C₂³	—	94	2	no	—
1034	C₂³	C₂²×C₄×D₄₇	1	2	yes	—
1035	C₂³	C₂²×C₄×D₄₇	1	1	yes	characteristic
1036	Q₈	—	2	2	no	—
1037	Q₈	—	94	4	no	—
1038	Q₈	—	94	2	no	—
1039	Q₈	—	188	2	no	—
1040	D₄	—	2	4	no	—
1041	D₄	—	2	2	no	—
1042	D₄	—	94	4	no	—
1043	D₄	—	94	4	no	—
1044	D₄	—	94	4	no	—
1045	D₄	—	94	4	no	—
1046	D₄	—	94	4	no	—
1047	D₄	—	94	4	no	—
1048	D₄	—	94	2	no	—
1049	D₄	—	188	2	no	—
1050	C₂×C₄	—	2	2	no	—
1051	C₂×C₄	—	2	2	no	—
1052	C₂×C₄	—	2	1	no	—
1053	C₂×C₄	—	2	2	no	—
1054	C₂×C₄	—	2	1	no	—
1055	C₂×C₄	—	2	2	no	—
1056	C₂×C₄	—	47	1	no	—
1057	C₂×C₄	—	47	1	no	—
1058	C₂×C₄	—	47	4	no	—
1059	C₂×C₄	—	47	2	no	—
1060	C₂×C₄	—	47	2	no	—
1061	C₂×C₄	—	47	1	no	—
1062	C₂×C₄	—	47	1	no	—
1063	C₂×C₄	—	47	1	no	—
1064	C₂×C₄	—	47	1	no	—
1065	C₂×C₄	—	47	2	no	—
1066	C₂×C₄	—	47	2	no	—
1067	C₂×C₄	—	47	2	no	—
1068	C₂×C₄	—	94	2	no	—
1069	C₂×C₄	—	94	2	no	—
1070	C₂×C₄	—	94	4	no	—
1071	C₂×C₄	—	94	2	no	—
1072	C₂×C₄	—	94	2	no	—
1073	C₂×C₄	—	94	2	no	—
1074	C₂×C₄	—	94	2	no	—
1075	C₂×C₄	—	94	4	no	—
1076	C₂×C₄	—	94	2	no	—
1077	C₂×C₄	—	94	2	no	—
1078	C₂×C₄	—	94	1	no	—
1079	C₂×C₄	—	94	2	no	—
1080	C₂×C₄	—	94	1	no	—
1081	C₂×C₄	—	94	2	no	—
1082	C₂×C₄	—	188	1	no	—
1083	C₂×C₄	—	188	1	no	—
1084	C₂×C₄	—	188	1	no	—
1085	C₂×C₄	—	188	1	no	—
1086	C₂×C₄	—	188	2	no	—
1087	C₂×C₄	—	188	2	no	—
1088	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
1089	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
1090	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
1091	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
1092	C₂×C₄	C₂²×C₄×D₄₇	1	2	yes	—
1093	C₂×C₄	C₂²×C₄×D₄₇	1	2	yes	—
1094	C₂×C₄	C₂²×C₄×D₄₇	1	2	yes	—
1095	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
1096	C₂×C₄	C₂⁴×D₄₇	1	1	yes	characteristic
1097	C₈	—	2	2	no	—
1098	C₈	—	2	1	no	—
1099	C₈	—	2	2	no	—
1100	C₈	—	2	1	no	—
1101	C₈	—	2	1	no	—
1102	C₈	—	2	1	no	—
1103	C₈	—	94	2	no	—
1104	C₈	—	94	2	no	—
1105	C₈	—	94	1	no	—
1106	C₈	—	94	1	no	—
1107	C₈	—	94	1	no	—
1108	C₈	—	94	1	no	—
1109	C₂²	—	2	1	no	—
1110	C₂²	—	2	1	no	—
1111	C₂²	—	2	2	no	—
1112	C₂²	—	2	2	no	—
1113	C₂²	—	2	2	no	—
1114	C₂²	—	47	2	no	—
1115	C₂²	—	47	2	no	—
1116	C₂²	—	94	8	no	—
1117	C₂²	—	94	1	no	—
1118	C₂²	—	94	1	no	—
1119	C₂²	—	94	1	no	—
1120	C₂²	—	94	1	no	—
1121	C₂²	—	94	2	no	—
1122	C₂²	—	94	2	no	—
1123	C₂²	—	94	2	no	—
1124	C₂²	#15689888	1	2	yes	—
1125	C₂²	C₂³×C₄×D₄₇	1	1	yes	characteristic
1126	C₄	—	2	1	no	—
1127	C₄	—	2	2	no	—
1128	C₄	—	2	1	no	—
1129	C₄	—	2	1	no	—
1130	C₄	—	2	2	no	—
1131	C₄	—	2	1	no	—
1132	C₄	—	2	2	no	—
1133	C₄	—	47	2	no	—
1134	C₄	—	47	2	no	—
1135	C₄	—	94	1	no	—
1136	C₄	—	94	2	no	—
1137	C₄	—	94	1	no	—
1138	C₄	—	94	1	no	—
1139	C₄	—	94	2	no	—
1140	C₄	—	94	1	no	—
1141	C₄	—	94	2	no	—
1142	C₄	#131×D₄₇	1	2	yes	—
1143	C₄	H(5,𝔽₂)×D₄₇	1	1	yes	characteristic
1144	C₄	2₋¹⁺⁴×D₄₇	1	1	yes	characteristic
1145	C₂	—	2	2	no	—
1146	C₂	—	4	2	no	—
1147	C₂	—	94	2	no	—
1148	C₂	—	94	2	no	—
1149	C₂	—	188	2	no	—
1150	C₂	#520×D₄₇	1	1	yes	characteristic
1151	C₂	C₂×#131×D₄₇	1	1	yes	characteristic
1152	C₂	C₂×#15689888	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂⁴×D₄₇
commutator, socle	C₂²×C₄₇	C₂⁴×C₄
Fitting	C₄₇×#2994	C₂
prime radical	#20256682	C₂
cosocle	C₂×C₄×C₄₇	C₂⁵
hypercenter	#2994	D₄₇
hypocenter	C₄₇	#60265
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ #2994

Complements

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

N	H ≅ G/N	type
2. #20252550	C₂	semidirect
3. #20252548	C₂	semidirect
4. #20252544	C₂	semidirect
5. #20252525	C₂	semidirect
6. #20252522	C₂	semidirect
7. #20252511	C₂	semidirect
8. #20252508	C₂	semidirect
9. #20252504	C₂	semidirect
10. #20252503	C₂	semidirect
11. #20252498	C₂	semidirect
12. #20252495	C₂	semidirect
13. #20252336	C₂	semidirect
14. #20252330	C₂	semidirect
15. #20252133	C₂	semidirect
16. #20252127	C₂	semidirect
17. #20252079	C₂	semidirect
18. #20252077	C₂	semidirect
19. #20252051	C₂	semidirect
20. #20252016	C₂	semidirect
21. #20251955	C₂	semidirect
22. C₂×C₄⋊C₈×D₄₇	C₂	semidirect
23. C₄₇×#2994	C₂	semidirect
49. #15689254	C₂²	semidirect
50. #15689253	C₂²	semidirect
51. #15689253	C₂²	semidirect
52. #15689252	C₂²	semidirect
53. #15689251	C₂²	semidirect
54. #15689250	C₂²	semidirect
55. #15689250	C₂²	semidirect
56. Q₈×C₄₇⋊C₈	C₂²	semidirect
57. C₈×Dic₉₄	C₂²	semidirect
58. #15689247	C₂²	semidirect
59. #15689202	C₂²	semidirect
60. #15689201	C₂²	semidirect
61. #15689200	C₂²	semidirect
63. #15689197	C₂²	semidirect
67. #15689194	C₂²	semidirect
70. #15689192	C₂²	semidirect
72. #15689191	C₂²	semidirect
74. C₈×D₁₈₈	C₂²	semidirect
76. D₄×C₄₇⋊C₈	C₂²	semidirect
78. #15689188	C₂²	semidirect
83. #15689184	C₂²	semidirect
84. #15689183	C₂²	semidirect
85. #15689183	C₂²	semidirect
88. #15689178	C₂²	semidirect
91. #15689177	C₂²	semidirect
95. #15689174	C₂²	semidirect
96. #15689173	C₂²	semidirect
97. #15689150	C₂²	semidirect
100. #15689148	C₂²	semidirect
101. #15689148	C₂²	semidirect
102. #15689146	C₂²	semidirect
105. #15689145	C₂²	semidirect
108. C₂×Dic₄₇⋊C₈	C₂²	semidirect
115. C₄⋊C₈×D₄₇	C₂²	semidirect
125. C₄₇×#446	C₂²	semidirect
126. C₈×Q₈×C₄₇	C₂²	semidirect
127. C₄₇×#436	C₂²	semidirect
130. C₈×D₄×C₄₇	C₂²	semidirect
131. C₄₇×#433	C₂²	semidirect
133. C₄₇×#424	C₂²	semidirect
514. C₄×D₄₇	#131	semidirect
573. #2994	D₄₇	semidirect
633. #446	C₂×D₄₇	semidirect
637. C₈×Q₈	C₂×D₄₇	semidirect
641. #436	C₂×D₄₇	semidirect
665. C₈×D₄	C₂×D₄₇	semidirect
669. #433	C₂×D₄₇	semidirect
687. #424	C₂×D₄₇	semidirect
711. C₄₇	#60265	semidirect

Maximal subgroups

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

subgroup	index
#20256682	2
#20252550	2
#20252548	2
#20252544	2
#20252525	2
#20252522	2
#20252511	2
#20252508	2
#20252504	2
#20252503	2
#20252498	2
#20252495	2
#20252336	2
#20252330	2
#20252133	2
#20252127	2
#20252079	2
#20252077	2
#20252051	2
#20252016	2
#20251955	2
C₂×C₄⋊C₈×D₄₇	2
C₄₇×#2994	2
#60265	47