Subgroups — #27081443

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	#20256773	C₂	1	1	yes	maximal, characteristic
2	#20252560	C₂	1	2	yes	maximal, complemented
3	#20252553	C₂	1	2	yes	maximal, complemented
4	#20252550	C₂	1	2	yes	maximal, complemented
5	#20252542	C₂	1	2	yes	maximal, complemented
6	#20252539	C₂	1	2	yes	maximal, complemented
7	#20252531	C₂	1	2	yes	maximal, complemented
8	#20252529	C₂	1	2	yes	maximal, complemented
9	#20252522	C₂	1	2	yes	maximal, complemented
10	#20252332	C₂	1	1	yes	maximal, characteristic, complemented
11	#20252332	C₂	1	1	yes	maximal, characteristic, complemented
12	#20252128	C₂	1	1	yes	maximal, characteristic, complemented
13	#20252128	C₂	1	1	yes	maximal, characteristic, complemented
14	#20252094	C₂	1	1	yes	maximal, characteristic, complemented
15	#20252093	C₂	1	1	yes	maximal, characteristic, complemented
16	#20252085	C₂	1	1	yes	maximal, characteristic, complemented
17	#20252084	C₂	1	1	yes	maximal, characteristic, complemented
18	#20252056	C₂	1	1	yes	maximal, characteristic, complemented
19	#20252025	C₂	1	1	yes	maximal, characteristic, complemented
20	#20251956	C₂	1	1	yes	maximal, characteristic, complemented
21	#20251953	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂×#15689148	C₂	1	1	yes	maximal, characteristic, complemented
23	C₄₇×#2925	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#13094031	C₂²	1	1	yes	characteristic
25	C₂×#13094031	C₂²	1	1	yes	characteristic
26	C₂×#13094030	C₂²	1	1	yes	characteristic
27	C₂×#13094030	C₂²	1	1	yes	characteristic
28	C₂²×#10625324	C₂²	1	1	yes	characteristic
29	C₂²×C₈×D₄₇	C₂²	1	1	yes	characteristic
30	#15689745	C₄	1	1	yes	characteristic
31	#15689745	C₄	1	1	yes	characteristic
32	#15689738	C₄	1	1	yes	characteristic
33	#15689738	C₄	1	1	yes	characteristic
34	#15689731	C₄	1	1	yes	characteristic
35	#15689731	C₄	1	1	yes	characteristic
36	#15689724	C₄	1	1	yes	characteristic
37	#15689724	C₄	1	1	yes	characteristic
38	#15689715	C₄	1	2	yes	—
39	#15689715	C₄	1	2	yes	—
40	#15689706	C₄	1	2	yes	—
41	#15689706	C₄	1	2	yes	—
42	#15689676	C₂²	1	1	yes	characteristic
43	#15689669	C₂²	1	1	yes	characteristic
44	#15689657	C₂²	1	2	yes	—
45	#15689657	C₂²	1	2	yes	—
46	#15689651	C₂²	1	2	yes	—
47	#15689651	C₂²	1	2	yes	—
48	#15689635	C₂²	1	1	yes	characteristic
49	#15689630	C₂²	1	1	yes	characteristic
50	C₄×#10625350	C₂²	1	1	yes	characteristic
51	C₂×#13093981	C₂²	1	1	yes	characteristic
52	#15689253	C₂²	1	2	yes	complemented
53	#15689253	C₂²	1	2	yes	complemented
54	#15689251	C₂²	1	2	yes	complemented
55	#15689251	C₂²	1	2	yes	complemented
56	#15689251	C₂²	1	2	yes	complemented
57	#15689251	C₂²	1	2	yes	complemented
58	C₈×Dic₉₄	C₂²	1	2	yes	complemented
59	C₈×Dic₉₄	C₂²	1	2	yes	complemented
60	#15689202	C₂²	1	2	yes	—
61	#15689202	C₂²	1	2	yes	—
62	#15689198	C₂²	1	2	yes	—
63	#15689198	C₂²	1	2	yes	—
64	#15689198	C₂²	1	2	yes	complemented
65	#15689198	C₂²	1	2	yes	complemented
66	#15689197	C₂²	1	2	yes	—
67	#15689197	C₂²	1	2	yes	—
68	#15689197	C₂²	1	2	yes	complemented
69	#15689197	C₂²	1	2	yes	complemented
70	#15689196	C₂²	1	2	yes	—
71	#15689196	C₂²	1	2	yes	—
72	#15689196	C₂²	1	2	yes	—
73	#15689196	C₂²	1	2	yes	—
74	#15689191	C₂²	1	2	yes	—
75	#15689191	C₂²	1	2	yes	—
76	#15689191	C₂²	1	2	yes	complemented
77	#15689191	C₂²	1	2	yes	complemented
78	C₈×D₁₈₈	C₂²	1	2	yes	—
79	C₈×D₁₈₈	C₂²	1	2	yes	—
80	(C₂²⋊D₄₇)⋊C₈	C₂²	1	2	yes	—
81	(C₂²⋊D₄₇)⋊C₈	C₂²	1	2	yes	—
82	(C₂²⋊D₄₇)⋊C₈	C₂²	1	2	yes	complemented
83	(C₂²⋊D₄₇)⋊C₈	C₂²	1	2	yes	complemented
84	#15689183	C₂²	1	2	yes	—
85	#15689183	C₂²	1	2	yes	—
86	#15689183	C₂²	1	2	yes	—
87	#15689183	C₂²	1	2	yes	—
88	#15689183	C₂²	1	2	yes	complemented
89	#15689183	C₂²	1	2	yes	complemented
90	#15689179	C₂²	1	2	yes	complemented
91	#15689175	C₂²	1	2	yes	complemented
92	#15689150	C₂²	1	1	yes	characteristic
93	#15689150	C₂²	1	1	yes	characteristic
94	#15689150	C₂²	1	2	yes	complemented
95	#15689150	C₂²	1	2	yes	complemented
96	#15689149	C₂²	1	1	yes	characteristic
97	#15689149	C₂²	1	1	yes	characteristic
98	#15689148	C₂²	1	1	yes	characteristic
99	#15689148	C₂²	1	1	yes	characteristic
100	#15689148	C₂²	1	1	yes	characteristic
101	#15689148	C₂²	1	1	yes	characteristic
102	#15689148	C₂²	1	1	yes	characteristic
103	#15689148	C₂²	1	1	yes	characteristic
104	#15689148	C₂²	1	1	yes	characteristic
105	#15689148	C₂²	1	1	yes	characteristic
106	#15689148	C₂²	1	2	yes	complemented
107	#15689148	C₂²	1	2	yes	complemented
108	#15689147	C₂²	1	1	yes	characteristic
109	#15689147	C₂²	1	2	yes	complemented
110	#15689145	C₂²	1	2	yes	complemented
111	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
112	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	2	yes	complemented
113	C₂×Dic₄₇⋊C₈	C₂²	1	1	yes	characteristic
114	C₂×Dic₄₇⋊C₈	C₂²	1	1	yes	characteristic
115	C₄⋊C₈×D₄₇	C₂²	1	2	yes	complemented
116	#15689091	C₂²	1	1	yes	characteristic
117	#15689091	C₂²	1	1	yes	characteristic
118	#15689086	C₂²	1	1	yes	characteristic
119	#15689086	C₂²	1	1	yes	characteristic
120	#15689081	C₂²	1	1	yes	characteristic
121	#15689081	C₂²	1	1	yes	characteristic
122	M₁₆×Dic₄₇	C₂²	1	1	yes	characteristic
123	M₁₆×Dic₄₇	C₂²	1	1	yes	characteristic
124	C₄×#41×C₄₇	C₂²	1	1	yes	characteristic
125	C₄₇×#433	C₂²	1	2	yes	complemented
126	C₄₇×#433	C₂²	1	2	yes	complemented
127	C₄₇×#432	C₂²	1	2	yes	complemented
128	C₄₇×#431	C₂²	1	2	yes	complemented
129	C₄₇×#423	C₂²	1	1	yes	characteristic
130	C₂×C₄⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
131	C₄₇×#408	C₂²	1	1	yes	characteristic
132	C₄₇×#408	C₂²	1	1	yes	characteristic
133	C₄₇×#405	C₂²	1	1	yes	characteristic
134	C₄₇×#405	C₂²	1	1	yes	characteristic
135	C₂×#10625350	C₂³	1	1	yes	characteristic
136	C₂²×C₄×D₄₇	C₂³	1	1	yes	characteristic
137	#13094031	—	4	2	no	—
138	#13094031	—	4	2	no	—
139	#13094030	—	4	2	no	—
140	#13094030	—	4	2	no	—
141	C₂×#10625329	C₂³	1	1	yes	characteristic
142	C₂×#10625329	C₂³	1	1	yes	characteristic
143	C₂×#10625329	C₂³	1	2	yes	—
144	C₂×#10625329	C₂³	1	2	yes	—
145	C₂×#10625324	—	4	2	no	—
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	1	yes	characteristic
150	C₂×#10625324	C₂³	1	2	yes	—
151	C₂×#10625324	C₂³	1	2	yes	—
152	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
153	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
154	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
155	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
156	C₂×C₈×D₄₇	—	4	2	no	—
157	C₂×C₈×D₄₇	C₂³	1	1	yes	characteristic
158	C₂×C₈×D₄₇	C₂³	1	1	yes	characteristic
159	C₂×C₈×D₄₇	C₂³	1	1	yes	characteristic
160	C₂×C₈×D₄₇	C₂³	1	1	yes	characteristic
161	C₂×C₈×D₄₇	C₂³	1	2	yes	—
162	C₂×C₈×D₄₇	C₂³	1	2	yes	—
163	#13094023	C₂×C₄	1	1	yes	characteristic
164	#13094023	C₂×C₄	1	1	yes	characteristic
165	#13094022	C₂×C₄	1	1	yes	characteristic
166	#13094020	C₂×C₄	1	1	yes	characteristic
167	#13094019	C₂×C₄	1	2	yes	—
168	#13094019	C₂×C₄	1	2	yes	—
169	#13094018	C₂×C₄	1	2	yes	—
170	#13094018	C₂×C₄	1	2	yes	—
171	#13094018	C₂×C₄	1	2	yes	—
172	#13094018	C₂×C₄	1	2	yes	—
173	#13094017	C₂×C₄	1	2	yes	—
174	#13094017	C₂×C₄	1	2	yes	—
175	#13094016	C₂×C₄	1	2	yes	—
176	#13094016	C₂×C₄	1	2	yes	—
177	#13094015	C₂×C₄	1	1	yes	characteristic
178	#13094015	C₂×C₄	1	1	yes	characteristic
179	#13094014	C₂×C₄	1	2	yes	—
180	#13094014	C₂×C₄	1	2	yes	—
181	#13094013	C₂×C₄	1	1	yes	characteristic
182	#13094012	C₂×C₄	1	2	yes	—
183	#13094012	C₂×C₄	1	2	yes	—
184	#13094011	C₂×C₄	1	1	yes	characteristic
185	#13094010	C₂×C₄	1	2	yes	—
186	#13094010	C₂×C₄	1	2	yes	—
187	#13094009	C₂×C₄	1	2	yes	—
188	#13094009	C₂×C₄	1	2	yes	—
189	#13094008	C₂×C₄	1	2	yes	—
190	#13094007	C₂×C₄	1	2	yes	—
191	#13094007	C₂×C₄	1	2	yes	—
192	#13094007	C₂×C₄	1	2	yes	—
193	#13094007	C₂×C₄	1	2	yes	—
194	#13094006	C₂×C₄	1	2	yes	—
195	#13094006	C₂×C₄	1	2	yes	—
196	#13094005	C₂×C₄	1	2	yes	—
197	#13094004	C₂×C₄	1	1	yes	characteristic
198	#13094004	C₂×C₄	1	1	yes	characteristic
199	#13094003	C₂×C₄	1	2	yes	—
200	#13094003	C₂×C₄	1	2	yes	—
201	#13094002	C₂×C₄	1	2	yes	—
202	#13094002	C₂×C₄	1	2	yes	—
203	#13094001	C₂×C₄	1	2	yes	—
204	#13094001	C₂×C₄	1	2	yes	—
205	#13094000	C₂×C₄	1	1	yes	characteristic
206	#13094000	C₂×C₄	1	1	yes	characteristic
207	#13093999	C₂×C₄	1	1	yes	characteristic
208	#13093999	C₂×C₄	1	1	yes	characteristic
209	#13093998	C₂×C₄	1	2	yes	—
210	#13093998	C₂×C₄	1	2	yes	—
211	#13093997	C₂×C₄	1	2	yes	—
212	#13093997	C₂×C₄	1	2	yes	—
213	#13093996	C₂×C₄	1	2	yes	—
214	#13093996	C₂×C₄	1	2	yes	—
215	#13093995	C₂×C₄	1	1	yes	characteristic
216	#13093995	C₂×C₄	1	1	yes	characteristic
217	#13093994	C₂×C₄	1	2	yes	—
218	#13093992	C₂×C₄	1	2	yes	—
219	C₄×Dic₉₄	C₂×C₄	1	1	yes	characteristic
220	C₄×Dic₉₄	C₂×C₄	1	1	yes	characteristic
221	C₄×Dic₉₄	C₂³	1	2	yes	—
222	C₄×Dic₉₄	C₂³	1	2	yes	—
223	C₄×D₁₈₈	C₂×C₄	1	1	yes	characteristic
224	C₄×D₁₈₈	C₂×C₄	1	1	yes	characteristic
225	C₄×D₁₈₈	C₂³	1	2	yes	—
226	C₄×D₁₈₈	C₂³	1	2	yes	—
227	C₄×C₂²⋊D₄₇	C₂×C₄	1	2	yes	—
228	C₄×C₂²⋊D₄₇	C₂×C₄	1	2	yes	—
229	C₄×C₂²⋊D₄₇	C₂³	1	2	yes	—
230	C₄×C₂²⋊D₄₇	C₂³	1	2	yes	—
231	C₄×C₂²⋊D₄₇	C₂³	1	2	yes	—
232	C₄×C₂²⋊D₄₇	C₂³	1	2	yes	—
233	#13093983	C₂³	1	1	yes	characteristic
234	#13093981	C₂×C₄	1	1	yes	characteristic
235	#13093981	C₂×C₄	1	1	yes	characteristic
236	#13093981	C₂×C₄	1	1	yes	characteristic
237	#13093981	C₂×C₄	1	1	yes	characteristic
238	#13093981	C₂³	1	1	yes	characteristic
239	#13093981	C₂³	1	1	yes	characteristic
240	#13093981	C₂³	1	1	yes	characteristic
241	#13093981	C₂³	1	1	yes	characteristic
242	#13093981	C₂³	1	2	yes	—
243	C₂×Dic₄₇⋊C₄	C₂×C₄	1	1	yes	characteristic
244	C₂×Dic₄₇⋊C₄	C₂×C₄	1	1	yes	characteristic
245	C₂×(C₂×D₄₇)⋊C₄	C₂×C₄	1	1	yes	characteristic
246	C₂×(C₂×D₄₇)⋊C₄	C₂×C₄	1	1	yes	characteristic
247	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
248	C₄²×D₄₇	C₂³	1	2	yes	—
249	C₄⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
250	C₄⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
251	C₄⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
252	C₄⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
253	C₄⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
254	C₄⋊(C₄₇⋊C₈)	C₂³	1	1	yes	characteristic
255	C₄⋊(C₄₇⋊C₈)	C₂³	1	1	yes	characteristic
256	C₄⋊(C₄₇⋊C₈)	C₂³	1	1	yes	characteristic
257	C₄⋊(C₄₇⋊C₈)	C₂³	1	1	yes	characteristic
258	C₄⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
259	Dic₄₇⋊C₈	C₂³	1	1	yes	characteristic
260	Dic₄₇⋊C₈	C₂³	1	1	yes	characteristic
261	Dic₄₇⋊C₈	C₂³	1	2	yes	—
262	Dic₄₇⋊C₈	C₂³	1	2	yes	—
263	Dic₄₇⋊C₈	C₂³	1	2	yes	—
264	Dic₄₇⋊C₈	C₂³	1	1	yes	characteristic
265	Dic₄₇⋊C₈	C₂³	1	1	yes	characteristic
266	Dic₄₇⋊C₈	C₂³	1	1	yes	characteristic
267	Dic₄₇⋊C₈	C₂³	1	1	yes	characteristic
268	Dic₄₇⋊C₈	C₂³	1	2	yes	—
269	Dic₄₇⋊C₈	C₂³	1	1	yes	characteristic
270	Dic₄₇⋊C₈	C₂³	1	1	yes	characteristic
271	(C₂×D₄₇)⋊C₈	C₂³	1	2	yes	—
272	(C₂×D₄₇)⋊C₈	C₂³	1	2	yes	—
273	(C₂×D₄₇)⋊C₈	C₂³	1	2	yes	—
274	(C₂×D₄₇)⋊C₈	C₂³	1	2	yes	—
275	(C₂×D₄₇)⋊C₈	C₂³	1	2	yes	—
276	(C₂×D₄₇)⋊C₈	C₂³	1	2	yes	—
277	(C₂×D₄₇)⋊C₈	C₂³	1	2	yes	—
278	(C₂×D₄₇)⋊C₈	C₂³	1	2	yes	—
279	#13093934	C₂³	1	2	yes	—
280	#13093934	C₂³	1	2	yes	—
281	#13093934	C₂³	1	2	yes	—
282	#13093934	C₂³	1	2	yes	—
283	C₈×Dic₄₇	C₂³	1	2	yes	—
284	C₈×Dic₄₇	C₂³	1	2	yes	—
285	C₈×Dic₄₇	C₂³	1	2	yes	—
286	C₈×Dic₄₇	C₂³	1	2	yes	—
287	C₂×#41×C₄₇	C₂³	1	1	yes	characteristic
288	C₂×M₁₆×C₄₇	C₂³	1	1	yes	characteristic
289	C₂×M₁₆×C₄₇	C₂³	1	1	yes	characteristic
290	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
291	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
292	C₄×Q₈×C₄₇	C₂×C₄	1	1	yes	characteristic
293	C₄×Q₈×C₄₇	C₂×C₄	1	1	yes	characteristic
294	C₄×D₄×C₄₇	C₂×C₄	1	1	yes	characteristic
295	C₄×D₄×C₄₇	C₂×C₄	1	1	yes	characteristic
296	C₄×D₄×C₄₇	C₂×C₄	1	2	yes	—
297	C₄×D₄×C₄₇	C₂×C₄	1	2	yes	—
298	#117×C₄₇	C₂³	1	1	yes	characteristic
299	#117×C₄₇	C₂³	1	2	yes	—
300	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
301	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
302	C₄⋊C₈×C₄₇	C₂³	1	1	yes	characteristic
303	C₄⋊C₈×C₄₇	C₂³	1	1	yes	characteristic
304	C₄⋊C₈×C₄₇	C₂³	1	1	yes	characteristic
305	C₄⋊C₈×C₄₇	C₂³	1	1	yes	characteristic
306	C₄⋊C₈×C₄₇	C₂³	1	2	yes	—
307	C₄⋊C₈×C₄₇	C₂³	1	2	yes	—
308	C₂²⋊C₈×C₄₇	C₂³	1	2	yes	—
309	C₂²⋊C₈×C₄₇	C₂³	1	2	yes	—
310	C₂²⋊C₈×C₄₇	C₂³	1	2	yes	—
311	C₂²⋊C₈×C₄₇	C₂³	1	2	yes	—
312	#97×C₄₇	C₂³	1	2	yes	—
313	#97×C₄₇	C₂³	1	2	yes	—
314	C₄×C₈×C₄₇	C₂³	1	2	yes	—
315	C₄×C₈×C₄₇	C₂³	1	2	yes	—
316	C₂³×D₄₇	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	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
323	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
324	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
325	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
326	C₂²×C₄×C₄₇	C₂⁴	1	2	yes	—
327	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
328	C₂×C₂²⋊D₄₇	C₂²×C₄	1	2	yes	—
329	C₂×C₂²⋊D₄₇	C₂²×C₄	1	2	yes	—
330	C₂×C₂²⋊D₄₇	C₂²×C₄	1	2	yes	—
331	C₂×C₂²⋊D₄₇	C₂²×C₄	1	2	yes	—
332	C₂×C₂²⋊D₄₇	C₂²×C₄	1	2	yes	—
333	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
334	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
335	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
336	#10625350	—	2	2	no	—
337	#10625350	—	2	2	no	—
338	C₂×D₁₈₈	C₂²×C₄	1	1	yes	characteristic
339	C₂×D₁₈₈	C₂²×C₄	1	2	yes	—
340	C₂×D₁₈₈	C₂²×C₄	1	2	yes	—
341	C₂×C₄×D₄₇	—	2	2	no	—
342	C₂×C₄×D₄₇	—	2	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	2	yes	—
346	C₂×C₄×D₄₇	C₂²×C₄	1	2	yes	—
347	C₂×C₄×D₄₇	C₂⁴	1	2	yes	—
348	C₂×C₄×D₄₇	C₂⁴	1	1	yes	characteristic
349	C₂×C₄×D₄₇	C₂⁴	1	1	yes	characteristic
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	C₂×C₈×C₄₇	—	2	2	no	—
356	C₂×C₈×C₄₇	—	2	2	no	—
357	C₂×C₈×C₄₇	C₂⁴	1	1	yes	characteristic
358	C₂×C₈×C₄₇	C₂⁴	1	1	yes	characteristic
359	C₂×C₈×C₄₇	C₂⁴	1	1	yes	characteristic
360	C₂×C₈×C₄₇	C₂⁴	1	1	yes	characteristic
361	C₂×C₈×C₄₇	C₂⁴	1	2	yes	—
362	C₂×C₈×C₄₇	C₂⁴	1	2	yes	—
363	C₄⋊C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
364	C₄⋊C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
365	C₄⋊C₄×C₄₇	C₂²×C₄	1	2	yes	—
366	C₄⋊C₄×C₄₇	C₂²×C₄	1	2	yes	—
367	C₂²⋊C₄×C₄₇	C₂²×C₄	1	2	yes	—
368	C₂²⋊C₄×C₄₇	C₂²×C₄	1	2	yes	—
369	C₂²⋊C₄×C₄₇	C₂²×C₄	1	2	yes	—
370	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
371	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
372	C₄²×C₄₇	C₂²×C₄	1	2	yes	—
373	C₄²×C₄₇	C₂²×C₄	1	2	yes	—
374	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
375	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
376	C₄²×C₄₇	C₂⁴	1	2	yes	—
377	C₂²⋊Dic₄₇	C₂²×C₄	1	2	yes	—
378	C₂²⋊Dic₄₇	C₂²×C₄	1	2	yes	—
379	C₂²⋊Dic₄₇	C₂²×C₄	1	2	yes	—
380	C₂²⋊Dic₄₇	C₂²×C₄	1	2	yes	—
381	C₂²⋊Dic₄₇	C₂²×C₄	1	2	yes	—
382	(C₂×D₄₇)⋊C₄	C₂²×C₄	1	1	yes	characteristic
383	(C₂×D₄₇)⋊C₄	C₂²×C₄	1	1	yes	characteristic
384	(C₂×D₄₇)⋊C₄	C₂²×C₄	1	1	yes	characteristic
385	(C₂×D₄₇)⋊C₄	C₂²×C₄	1	1	yes	characteristic
386	(C₂×D₄₇)⋊C₄	C₂²×C₄	1	1	yes	characteristic
387	(C₂×D₄₇)⋊C₄	C₂²×C₄	1	1	yes	characteristic
388	(C₂×D₄₇)⋊C₄	C₂²×C₄	1	1	yes	characteristic
389	(C₂×D₄₇)⋊C₄	C₂²×C₄	1	1	yes	characteristic
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	(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	2	yes	—
403	C₄⋊Dic₄₇	C₂²×C₄	1	2	yes	—
404	C₄⋊Dic₄₇	C₂²×C₄	1	2	yes	—
405	C₄⋊Dic₄₇	C₂²×C₄	1	2	yes	—
406	Dic₄₇⋊C₄	C₂²×C₄	1	1	yes	characteristic
407	Dic₄₇⋊C₄	C₂²×C₄	1	1	yes	characteristic
408	Dic₄₇⋊C₄	C₂²×C₄	1	1	yes	characteristic
409	Dic₄₇⋊C₄	C₂²×C₄	1	1	yes	characteristic
410	Dic₄₇⋊C₄	C₂²×C₄	1	1	yes	characteristic
411	Dic₄₇⋊C₄	C₂²×C₄	1	1	yes	characteristic
412	Dic₄₇⋊C₄	C₂²×C₄	1	1	yes	characteristic
413	Dic₄₇⋊C₄	C₂²×C₄	1	1	yes	characteristic
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	C₂⁴	1	2	yes	—
429	C₄×Dic₄₇	C₂⁴	1	1	yes	characteristic
430	C₄×Dic₄₇	C₂⁴	1	1	yes	characteristic
431	#10625329	—	2	2	no	—
432	#10625329	—	2	2	no	—
433	#10625329	—	4	2	no	—
434	#10625329	—	4	2	no	—
435	C₂×C₄₇⋊C₈	—	2	2	no	—
436	C₂×C₄₇⋊C₈	—	2	2	no	—
437	C₂×C₄₇⋊C₈	—	4	2	no	—
438	C₂×C₄₇⋊C₈	—	4	2	no	—
439	C₂×C₄₇⋊C₈	C₂⁴	1	1	yes	characteristic
440	C₂×C₄₇⋊C₈	C₂⁴	1	1	yes	characteristic
441	C₂×C₄₇⋊C₈	C₂⁴	1	2	yes	—
442	C₂×C₄₇⋊C₈	C₂⁴	1	2	yes	—
443	C₂×C₄₇⋊C₈	C₂⁴	1	1	yes	characteristic
444	C₂×C₄₇⋊C₈	C₂⁴	1	1	yes	characteristic
445	#10625324	—	4	1	no	—
446	#10625324	—	4	1	no	—
447	#10625324	—	4	1	no	—
448	#10625324	—	4	1	no	—
449	#10625324	—	4	2	no	—
450	#10625324	—	4	2	no	—
451	C₈×D₄₇	—	4	1	no	—
452	C₈×D₄₇	—	4	1	no	—
453	C₈×D₄₇	—	4	1	no	—
454	C₈×D₄₇	—	4	1	no	—
455	C₈×D₄₇	—	4	2	no	—
456	C₈×D₄₇	—	4	2	no	—
457	C₂³×C₄₇	C₂³×C₄	1	2	yes	—
458	C₂³×C₄₇	C₂³×C₄	1	1	yes	characteristic
459	C₂²×D₄₇	—	2	2	no	—
460	C₂²×D₄₇	—	4	1	no	—
461	C₂²×D₄₇	—	4	1	no	—
462	C₂²×D₄₇	C₂³×C₄	1	1	yes	characteristic
463	C₂²×D₄₇	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	C₂×C₄×C₄₇	—	2	2	no	—
469	C₂×C₄×C₄₇	—	2	2	no	—
470	C₂×C₄×C₄₇	—	4	2	no	—
471	C₂×C₄×C₄₇	—	4	2	no	—
472	C₂×C₄×C₄₇	—	4	1	no	—
473	C₂×C₄×C₄₇	—	4	1	no	—
474	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
475	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
476	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
477	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
478	C₂×C₄×C₄₇	C₂³×C₄	1	2	yes	—
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	1	yes	characteristic
482	C₂×C₄×C₄₇	H(5,𝔽₂)	1	2	yes	—
483	C₂×C₄×C₄₇	2₋¹⁺⁴	1	2	yes	—
484	C₂×C₄×C₄₇	C₂⁵	1	1	yes	characteristic
485	C₂²⋊D₄₇	—	2	4	no	—
486	C₂²⋊D₄₇	—	4	2	no	—
487	C₂²⋊D₄₇	—	4	2	no	—
488	C₂²⋊D₄₇	—	4	2	no	—
489	C₂²⋊D₄₇	—	4	2	no	—
490	C₂×Dic₄₇	—	2	2	no	—
491	C₂×Dic₄₇	—	4	1	no	—
492	C₂×Dic₄₇	—	4	1	no	—
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	C₂×Dic₄₇	C₂³×C₄	1	2	yes	—
497	C₂×Dic₄₇	C₂³×C₄	1	2	yes	—
498	C₂×Dic₄₇	C₂³×C₄	1	1	yes	characteristic
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	D₁₈₈	—	2	2	no	—
503	D₁₈₈	—	4	2	no	—
504	D₁₈₈	—	4	2	no	—
505	C₄×D₄₇	—	2	2	no	—
506	C₄×D₄₇	—	2	2	no	—
507	C₄×D₄₇	—	2	1	no	—
508	C₄×D₄₇	—	2	1	no	—
509	C₄×D₄₇	—	2	2	no	—
510	C₄×D₄₇	—	2	1	no	—
511	C₄×D₄₇	—	2	1	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	1	no	—
520	C₈×C₄₇	—	2	1	no	—
521	C₈×C₄₇	—	2	1	no	—
522	C₈×C₄₇	—	2	2	no	—
523	C₈×C₄₇	—	2	2	no	—
524	C₄₇⋊C₈	—	2	1	no	—
525	C₄₇⋊C₈	—	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	#60267	—	47	1	no	maximal, Sylow
531	C₂²×C₄₇	—	2	1	no	—
532	C₂²×C₄₇	—	2	1	no	—
533	C₂²×C₄₇	—	2	2	no	—
534	C₂²×C₄₇	—	2	2	no	—
535	C₂²×C₄₇	—	2	2	no	—
536	C₂²×C₄₇	#520	1	2	yes	—
537	C₂²×C₄₇	C₂⁴×C₄	1	1	yes	characteristic
538	C₂×D₄₇	—	2	1	no	—
539	C₂×D₄₇	—	2	1	no	—
540	C₂×D₄₇	—	2	2	no	—
541	C₂×D₄₇	—	2	2	no	—
542	C₂×D₄₇	—	2	2	no	—
543	C₂×D₄₇	—	2	1	no	—
544	C₂×D₄₇	—	2	1	no	—
545	C₂×D₄₇	—	2	1	no	—
546	C₂×D₄₇	—	2	1	no	—
547	C₂×D₄₇	—	4	4	no	—
548	C₄×C₄₇	—	2	2	no	—
549	C₄×C₄₇	—	2	2	no	—
550	C₄×C₄₇	—	2	2	no	—
551	C₄×C₄₇	—	2	1	no	—
552	C₄×C₄₇	—	2	1	no	—
553	C₄×C₄₇	—	2	1	no	—
554	C₄×C₄₇	—	2	1	no	—
555	C₄×C₄₇	#520	1	2	yes	—
556	C₄×C₄₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
557	C₄×C₄₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
558	Dic₄₇	—	2	2	no	—
559	Dic₄₇	—	2	1	no	—
560	Dic₄₇	—	2	1	no	—
561	Dic₄₇	—	2	1	no	—
562	Dic₄₇	—	2	1	no	—
563	Dic₄₇	—	2	2	no	—
564	Dic₄₇	—	2	2	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	—	47	1	no	—
584	#2925	—	47	1	no	—
585	#2925	D₄₇	1	1	yes	characteristic, complemented
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	C₂×#520	1	1	yes	characteristic
593	C₂×C₄₇	#3573	1	1	yes	characteristic
594	C₂×C₄₇	#3573	1	1	yes	characteristic
595	D₄₇	—	4	2	no	—
596	D₄₇	—	4	1	no	—
597	D₄₇	—	4	1	no	—
598	C₂×#131	—	47	1	no	—
599	C₂×#131	—	47	1	no	—
600	C₂×#131	—	47	1	no	—
601	C₂×#131	—	47	1	no	—
602	C₂²×M₁₆	—	47	1	no	—
603	C₂³×C₈	—	47	1	no	—
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	—	47	1	no	—
624	C₄×#41	—	47	1	no	—
625	C₄×#41	C₂×D₄₇	1	1	yes	characteristic
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	—	47	2	no	—
652	#435	—	47	2	no	—
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	—	47	2	no	—
658	C₈×D₄	—	47	2	no	—
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	C₂×D₄₇	1	2	yes	complemented
666	#433	C₂×D₄₇	1	2	yes	complemented
667	#432	—	47	2	no	—
668	#432	C₂×D₄₇	1	2	yes	complemented
669	#431	—	47	2	no	—
670	#431	C₂×D₄₇	1	2	yes	complemented
671	#424	—	47	1	no	—
672	#424	—	47	1	no	—
673	#424	—	47	1	no	—
674	#424	—	47	1	no	—
675	#424	—	47	2	no	—
676	#424	—	47	2	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	1	no	—
683	#424	—	47	1	no	—
684	#424	—	47	1	no	—
685	#424	—	47	2	no	—
686	#424	—	47	2	no	—
687	#423	—	47	1	no	—
688	#423	—	47	2	no	—
689	#423	—	47	2	no	—
690	#423	C₂×D₄₇	1	1	yes	characteristic
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	2	no	—
695	C₂×C₄⋊C₈	—	47	2	no	—
696	C₂×C₄⋊C₈	C₂×D₄₇	1	1	yes	characteristic
697	#408	—	47	1	no	—
698	#408	—	47	1	no	—
699	#408	C₂×D₄₇	1	1	yes	characteristic
700	#408	C₂×D₄₇	1	1	yes	characteristic
701	#407	—	47	1	no	—
702	#407	—	47	1	no	—
703	#405	—	47	1	no	—
704	#405	—	47	1	no	—
705	#405	C₂×D₄₇	1	1	yes	characteristic
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	—	47	1	no	—
713	#131	—	188	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	2	no	—
720	C₂×M₁₆	—	47	2	no	—
721	C₂×M₁₆	—	47	1	no	—
722	C₂×M₁₆	—	47	1	no	—
723	C₂×M₁₆	—	47	1	no	—
724	C₂×M₁₆	—	47	1	no	—
725	C₂×M₁₆	—	47	2	no	—
726	C₂×M₁₆	—	47	2	no	—
727	C₂×M₁₆	—	188	2	no	—
728	C₂×M₁₆	C₂²×D₄₇	1	1	yes	characteristic
729	C₂×M₁₆	C₂²×D₄₇	1	1	yes	characteristic
730	C₂²×C₈	—	47	1	no	—
731	C₂²×C₈	—	47	1	no	—
732	C₂²×C₈	—	47	2	no	—
733	C₂²×C₈	—	47	2	no	—
734	C₂²×C₈	—	47	1	no	—
735	C₂²×C₈	—	47	1	no	—
736	C₂²×C₈	—	47	1	no	—
737	C₂²×C₈	—	47	1	no	—
738	C₂²×C₈	—	47	2	no	—
739	C₂²×C₈	—	47	2	no	—
740	C₂²×C₈	—	188	2	no	—
741	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
742	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
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	1	no	—
758	#125	—	47	1	no	—
759	#125	—	47	2	no	—
760	#125	—	47	2	no	—
761	#124	—	47	1	no	—
762	#124	—	47	1	no	—
763	#124	—	47	2	no	—
764	#124	—	47	2	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	—	47	2	no	—
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	1	no	—
782	C₂²⋊Q₈	—	47	1	no	—
783	C₂²⋊Q₈	—	47	2	no	—
784	C₂²⋊Q₈	—	47	2	no	—
785	C₂²⋊Q₈	—	47	2	no	—
786	C₂²⋊Q₈	—	47	2	no	—
787	#121	—	47	1	no	—
788	#121	—	47	1	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	—	47	2	no	—
796	#121	—	47	2	no	—
797	#120	—	47	2	no	—
798	#120	—	47	2	no	—
799	C₄×Q₈	—	47	1	no	—
800	C₄×Q₈	—	47	1	no	—
801	C₄×Q₈	—	47	2	no	—
802	C₄×Q₈	—	47	2	no	—
803	C₄×Q₈	C₄×D₄₇	1	1	yes	characteristic
804	C₄×Q₈	C₄×D₄₇	1	1	yes	characteristic
805	C₄×D₄	—	47	2	no	—
806	C₄×D₄	—	47	2	no	—
807	C₄×D₄	—	47	2	no	—
808	C₄×D₄	—	47	2	no	—
809	C₄×D₄	—	47	2	no	—
810	C₄×D₄	—	47	2	no	—
811	C₄×D₄	—	47	1	no	—
812	C₄×D₄	—	47	1	no	—
813	C₄×D₄	—	47	2	no	—
814	C₄×D₄	—	47	2	no	—
815	C₄×D₄	C₄×D₄₇	1	2	yes	—
816	C₄×D₄	C₄×D₄₇	1	2	yes	—
817	C₄×D₄	C₄×D₄₇	1	1	yes	characteristic
818	C₄×D₄	C₄×D₄₇	1	1	yes	characteristic
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	C₂²×D₄₇	1	1	yes	characteristic
830	#117	C₂²×D₄₇	1	2	yes	—
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	2	no	—
837	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
838	C₂×C₄²	C₂²×D₄₇	1	2	yes	—
839	C₄⋊C₈	—	47	1	no	—
840	C₄⋊C₈	—	47	1	no	—
841	C₄⋊C₈	—	47	2	no	—
842	C₄⋊C₈	—	47	1	no	—
843	C₄⋊C₈	—	47	1	no	—
844	C₄⋊C₈	—	47	1	no	—
845	C₄⋊C₈	—	47	1	no	—
846	C₄⋊C₈	—	47	2	no	—
847	C₄⋊C₈	—	47	1	no	—
848	C₄⋊C₈	—	47	1	no	—
849	C₄⋊C₈	—	47	2	no	—
850	C₄⋊C₈	—	47	2	no	—
851	C₄⋊C₈	—	47	1	no	—
852	C₄⋊C₈	—	47	2	no	—
853	C₄⋊C₈	—	47	1	no	—
854	C₄⋊C₈	—	47	2	no	—
855	C₄⋊C₈	—	47	1	no	—
856	C₄⋊C₈	—	47	1	no	—
857	C₄⋊C₈	—	47	2	no	—
858	C₄⋊C₈	—	47	2	no	—
859	C₄⋊C₈	—	47	2	no	—
860	C₄⋊C₈	—	47	2	no	—
861	C₄⋊C₈	C₂²×D₄₇	1	1	yes	characteristic
862	C₄⋊C₈	C₂²×D₄₇	1	1	yes	characteristic
863	C₄⋊C₈	C₂²×D₄₇	1	1	yes	characteristic
864	C₄⋊C₈	C₂²×D₄₇	1	1	yes	characteristic
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	C₂²×D₄₇	1	2	yes	—
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	C₂²×D₄₇	1	2	yes	—
890	C₄×C₈	C₂²×D₄₇	1	2	yes	—
891	C₂⁴	—	47	1	no	—
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	—	47	2	no	—
907	C₂×D₄	—	47	2	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	1	no	—
917	C₂²×C₄	—	47	1	no	—
918	C₂²×C₄	—	47	2	no	—
919	C₂²×C₄	—	47	2	no	—
920	C₂²×C₄	—	94	2	no	—
921	C₂²×C₄	—	94	2	no	—
922	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
923	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
924	C₂²×C₄	C₂×C₄×D₄₇	1	2	yes	—
925	C₂²×C₄	C₂×C₄×D₄₇	1	2	yes	—
926	C₂²×C₄	C₂³×D₄₇	1	2	yes	—
927	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
928	M₁₆	—	2	2	no	—
929	M₁₆	—	2	2	no	—
930	M₁₆	—	94	2	no	—
931	M₁₆	—	94	2	no	—
932	M₁₆	—	188	1	no	—
933	M₁₆	—	188	1	no	—
934	M₁₆	—	188	1	no	—
935	M₁₆	—	188	1	no	—
936	M₁₆	—	188	2	no	—
937	M₁₆	—	188	2	no	—
938	M₁₆	—	188	2	no	—
939	M₁₆	—	188	2	no	—
940	C₂×C₈	—	2	2	no	—
941	C₂×C₈	—	2	2	no	—
942	C₂×C₈	—	47	1	no	—
943	C₂×C₈	—	47	1	no	—
944	C₂×C₈	—	47	2	no	—
945	C₂×C₈	—	47	2	no	—
946	C₂×C₈	—	47	1	no	—
947	C₂×C₈	—	47	1	no	—
948	C₂×C₈	—	94	2	no	—
949	C₂×C₈	—	94	2	no	—
950	C₂×C₈	—	188	1	no	—
951	C₂×C₈	—	188	1	no	—
952	C₂×C₈	—	188	1	no	—
953	C₂×C₈	—	188	1	no	—
954	C₂×C₈	—	188	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	2	yes	—
960	C₂×C₈	C₂³×D₄₇	1	1	yes	characteristic
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	1	no	—
965	C₄⋊C₄	—	47	1	no	—
966	C₄⋊C₄	—	47	1	no	—
967	C₄⋊C₄	—	47	1	no	—
968	C₄⋊C₄	—	47	1	no	—
969	C₄⋊C₄	—	47	1	no	—
970	C₄⋊C₄	—	47	1	no	—
971	C₄⋊C₄	—	47	1	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	2	no	—
979	C₄⋊C₄	—	47	2	no	—
980	C₄⋊C₄	—	47	2	no	—
981	C₄⋊C₄	—	47	2	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	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	1	no	—
998	C₂²⋊C₄	—	47	1	no	—
999	C₂²⋊C₄	—	47	1	no	—
1000	C₂²⋊C₄	—	47	1	no	—
1001	C₂²⋊C₄	—	47	1	no	—
1002	C₂²⋊C₄	—	47	1	no	—
1003	C₂²⋊C₄	—	47	1	no	—
1004	C₂²⋊C₄	—	47	1	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	—	47	2	no	—
1014	C₂²⋊C₄	—	47	2	no	—
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	2	no	—
1021	C₄²	—	47	2	no	—
1022	C₄²	—	47	1	no	—
1023	C₄²	—	47	1	no	—
1024	C₄²	—	47	2	no	—
1025	C₄²	C₂×C₄×D₄₇	1	1	yes	characteristic
1026	C₄²	C₂×C₄×D₄₇	1	1	yes	characteristic
1027	C₄²	C₂×C₄×D₄₇	1	2	yes	—
1028	C₄²	C₂×C₄×D₄₇	1	2	yes	—
1029	C₄²	C₂³×D₄₇	1	2	yes	—
1030	C₄²	C₂³×D₄₇	1	1	yes	characteristic
1031	C₄²	C₂³×D₄₇	1	1	yes	characteristic
1032	C₂³	—	47	1	no	—
1033	C₂³	—	47	1	no	—
1034	C₂³	—	47	2	no	—
1035	C₂³	—	94	2	no	—
1036	C₂³	—	188	1	no	—
1037	C₂³	—	188	1	no	—
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	—	94	4	no	—
1047	D₄	—	94	2	no	—
1048	D₄	—	188	2	no	—
1049	D₄	—	188	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	—	4	1	no	—
1057	C₂×C₄	—	4	2	no	—
1058	C₂×C₄	—	4	1	no	—
1059	C₂×C₄	—	4	2	no	—
1060	C₂×C₄	—	47	1	no	—
1061	C₂×C₄	—	47	1	no	—
1062	C₂×C₄	—	47	2	no	—
1063	C₂×C₄	—	47	2	no	—
1064	C₂×C₄	—	47	2	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	—	94	2	no	—
1070	C₂×C₄	—	94	2	no	—
1071	C₂×C₄	—	94	2	no	—
1072	C₂×C₄	—	94	1	no	—
1073	C₂×C₄	—	94	1	no	—
1074	C₂×C₄	—	94	2	no	—
1075	C₂×C₄	—	94	1	no	—
1076	C₂×C₄	—	94	1	no	—
1077	C₂×C₄	—	94	2	no	—
1078	C₂×C₄	—	188	2	no	—
1079	C₂×C₄	—	188	2	no	—
1080	C₂×C₄	—	188	1	no	—
1081	C₂×C₄	—	188	1	no	—
1082	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
1083	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
1084	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
1085	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
1086	C₂×C₄	C₂²×C₄×D₄₇	1	2	yes	—
1087	C₂×C₄	C₂²×C₄×D₄₇	1	2	yes	—
1088	C₂×C₄	C₂²×C₄×D₄₇	1	2	yes	—
1089	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
1090	C₂×C₄	#13094070	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	2	no	—
1110	C₂²	—	94	2	no	—
1111	C₂²	—	94	1	no	—
1112	C₂²	—	94	1	no	—
1113	C₂²	—	94	2	no	—
1114	C₂²	—	94	1	no	—
1115	C₂²	—	94	1	no	—
1116	C₂²	—	94	1	no	—
1117	C₂²	—	94	1	no	—
1118	C₂²	—	94	2	no	—
1119	C₂²	—	188	4	no	—
1120	C₂²	#15689603	1	2	yes	—
1121	C₂²	C₂³×C₄×D₄₇	1	1	yes	characteristic
1122	C₄	—	2	1	no	—
1123	C₄	—	2	1	no	—
1124	C₄	—	2	2	no	—
1125	C₄	—	2	1	no	—
1126	C₄	—	2	1	no	—
1127	C₄	—	2	2	no	—
1128	C₄	—	2	2	no	—
1129	C₄	—	94	1	no	—
1130	C₄	—	94	2	no	—
1131	C₄	—	94	1	no	—
1132	C₄	—	94	1	no	—
1133	C₄	—	94	2	no	—
1134	C₄	—	94	1	no	—
1135	C₄	—	94	1	no	—
1136	C₄	—	94	1	no	—
1137	C₄	—	94	2	no	—
1138	C₄	#15689603	1	2	yes	—
1139	C₄	C₂×#13094070	1	1	yes	characteristic
1140	C₄	C₂×#13094071	1	1	yes	characteristic
1141	C₂	—	2	2	no	—
1142	C₂	—	4	2	no	—
1143	C₂	—	188	1	no	—
1144	C₂	—	188	1	no	—
1145	C₂	—	188	2	no	—
1146	C₂	C₂×#15689603	1	1	yes	characteristic
1147	C₂	#20258099	1	1	yes	characteristic
1148	C₂	#20258101	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂⁴×D₄₇
commutator, socle	C₂²×C₄₇	C₂⁴×C₄
Fitting	C₄₇×#2925	C₂
prime radical	#20256773	C₂
cosocle	C₂×C₄×C₄₇	C₂⁵
hypercenter	#2925	D₄₇
hypocenter	C₄₇	#60267
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ #2925

Complements

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

N	H ≅ G/N	type
2. #20252560	C₂	semidirect
3. #20252553	C₂	semidirect
4. #20252550	C₂	semidirect
5. #20252542	C₂	semidirect
6. #20252539	C₂	semidirect
7. #20252531	C₂	semidirect
8. #20252529	C₂	semidirect
9. #20252522	C₂	semidirect
10. #20252332	C₂	semidirect
11. #20252332	C₂	semidirect
12. #20252128	C₂	semidirect
13. #20252128	C₂	semidirect
14. #20252094	C₂	semidirect
15. #20252093	C₂	semidirect
16. #20252085	C₂	semidirect
17. #20252084	C₂	semidirect
18. #20252056	C₂	semidirect
19. #20252025	C₂	semidirect
20. #20251956	C₂	semidirect
21. #20251953	C₂	semidirect
22. C₂×#15689148	C₂	semidirect
23. C₄₇×#2925	C₂	semidirect
52. #15689253	C₂²	semidirect
53. #15689253	C₂²	semidirect
54. #15689251	C₂²	semidirect
55. #15689251	C₂²	semidirect
56. #15689251	C₂²	semidirect
57. #15689251	C₂²	semidirect
58. C₈×Dic₉₄	C₂²	semidirect
59. C₈×Dic₉₄	C₂²	semidirect
64. #15689198	C₂²	semidirect
65. #15689198	C₂²	semidirect
68. #15689197	C₂²	semidirect
69. #15689197	C₂²	semidirect
76. #15689191	C₂²	semidirect
77. #15689191	C₂²	semidirect
82. (C₂²⋊D₄₇)⋊C₈	C₂²	semidirect
83. (C₂²⋊D₄₇)⋊C₈	C₂²	semidirect
88. #15689183	C₂²	semidirect
89. #15689183	C₂²	semidirect
90. #15689179	C₂²	semidirect
91. #15689175	C₂²	semidirect
94. #15689150	C₂²	semidirect
95. #15689150	C₂²	semidirect
106. #15689148	C₂²	semidirect
107. #15689148	C₂²	semidirect
109. #15689147	C₂²	semidirect
110. #15689145	C₂²	semidirect
112. C₂×C₄⋊(C₄₇⋊C₈)	C₂²	semidirect
115. C₄⋊C₈×D₄₇	C₂²	semidirect
125. C₄₇×#433	C₂²	semidirect
126. C₄₇×#433	C₂²	semidirect
127. C₄₇×#432	C₂²	semidirect
128. C₄₇×#431	C₂²	semidirect
585. #2925	D₄₇	semidirect
665. #433	C₂×D₄₇	semidirect
666. #433	C₂×D₄₇	semidirect
668. #432	C₂×D₄₇	semidirect
670. #431	C₂×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
#20256773	2
#20252560	2
#20252553	2
#20252550	2
#20252542	2
#20252539	2
#20252531	2
#20252529	2
#20252522	2
#20252332	2
#20252128	2
#20252094	2
#20252093	2
#20252085	2
#20252084	2
#20252056	2
#20252025	2
#20251956	2
#20251953	2
C₂×#15689148	2
C₄₇×#2925	2
#60267	47