Subgroups — #27097790

Order 12032.

1926 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	#20256998	C₂	1	1	yes	maximal, characteristic, complemented
2	#20256384	C₂	1	1	yes	maximal, characteristic, complemented
3	#20256259	C₂	1	1	yes	maximal, characteristic, complemented
4	#20256084	C₂	1	1	yes	maximal, characteristic, complemented
5	#20256033	C₂	1	1	yes	maximal, characteristic, complemented
6	#20255767	C₂	1	2	yes	maximal, complemented
7	#20255745	C₂	1	1	yes	maximal, characteristic, complemented
8	#20255290	C₂	1	2	yes	maximal, complemented
9	#20255264	C₂	1	1	yes	maximal, characteristic, complemented
10	#20255217	C₂	1	2	yes	maximal, complemented
11	#20255195	C₂	1	1	yes	maximal, characteristic, complemented
12	#20255096	C₂	1	2	yes	maximal, complemented
13	D₄×#10625336	C₂	1	1	yes	maximal, characteristic, complemented
14	#20253952	C₂	1	2	yes	maximal, complemented
15	#20253948	C₂	1	1	yes	maximal, characteristic, complemented
16	#20253468	C₂	1	2	yes	maximal, complemented
17	#20253453	C₂	1	1	yes	maximal, characteristic, complemented
18	#20253448	C₂	1	1	yes	maximal, characteristic, complemented
19	#20253431	C₂	1	2	yes	maximal, complemented
20	#41×C₄₇⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
21	C₄×#13094044	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂×C₄×#10625336	C₂	1	2	yes	maximal, complemented
23	C₄₇×#3482	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#13094044	C₂²	1	1	yes	characteristic
25	C₂²×#10625336	C₂²	1	2	yes	—
26	#15689858	C₂²	1	1	yes	characteristic
27	#15689833	C₂²	1	1	yes	characteristic
28	#15689830	C₂²	1	1	yes	characteristic
29	#15689819	C₂²	1	2	yes	—
30	#15689817	—	2	1	no	—
31	#15689797	—	2	2	no	—
32	#15689769	C₂²	1	2	yes	—
33	#15689761	—	2	1	no	—
34	D₄×D₁₈₈	C₂²	1	1	yes	characteristic
35	#15689673	C₂²	1	1	yes	characteristic
36	#15689660	—	2	1	no	—
37	#15689657	C₂²	1	2	yes	—
38	#15689632	—	2	2	no	—
39	C₄×#10625350	C₂²	1	1	yes	characteristic
40	C₂×C₄×D₁₈₈	C₂²	1	2	yes	—
41	C₄×D₄×D₄₇	—	2	1	no	—
42	#15689522	C₂²	1	2	yes	complemented
43	#15689519	C₂²	1	1	yes	characteristic, complemented
44	#15689505	C₂²	1	2	yes	complemented
45	#15689497	C₂²	1	1	yes	characteristic
46	#15689480	C₂²	1	2	yes	complemented
47	#15689477	C₂²	1	2	yes	complemented
48	#15689473	C₂²	1	1	yes	characteristic, complemented
49	#15689471	C₂²	1	1	yes	characteristic
50	#15689461	C₂²	1	2	yes	complemented
51	#15689456	C₂²	1	2	yes	complemented
52	#15689453	C₂²	1	2	yes	complemented
53	#15689447	C₂²	1	2	yes	complemented
54	#15689439	C₂²	1	2	yes	complemented
55	#15689436	C₂²	1	2	yes	—
56	#15689430	C₂²	1	2	yes	complemented
57	#15689430	C₂²	1	2	yes	complemented
58	#15689420	C₂²	1	2	yes	—
59	#15689420	C₂²	1	2	yes	complemented
60	#15689418	C₂²	1	1	yes	characteristic, complemented
61	#15689413	C₂²	1	1	yes	characteristic, complemented
62	#15689405	C₂²	1	1	yes	characteristic, complemented
63	#15689400	C₂²	1	1	yes	characteristic
64	#15689362	C₂²	1	2	yes	complemented
65	#15689357	C₂²	1	2	yes	—
66	#15689354	C₂²	1	2	yes	—
67	#15689354	C₂²	1	2	yes	complemented
68	#15689354	C₂²	1	2	yes	complemented
69	#15689350	C₂²	1	2	yes	complemented
70	#15689345	C₂²	1	2	yes	complemented
71	#15689345	C₂²	1	2	yes	complemented
72	#15689335	C₂²	1	2	yes	—
73	#15689335	C₂²	1	2	yes	complemented
74	#15689330	C₂²	1	1	yes	characteristic, complemented
75	#15689325	C₂²	1	1	yes	characteristic
76	#15689323	C₂²	1	1	yes	characteristic
77	#15689318	C₂²	1	1	yes	characteristic
78	#15689283	C₂²	1	2	yes	—
79	#15689279	C₂²	1	2	yes	complemented
80	#15689273	C₂²	1	2	yes	—
81	#15689268	C₂²	1	2	yes	complemented
82	#15689262	C₂²	1	2	yes	—
83	#15689256	C₂²	1	2	yes	—
84	Q₈×C₄₇⋊C₈	C₂²	1	1	yes	characteristic, complemented
85	Q₈×C₄₇⋊C₈	C₂²	1	1	yes	characteristic, complemented
86	C₄×#10625337	C₂²	1	2	yes	complemented
87	C₄×#10625337	C₂²	1	1	yes	characteristic, complemented
88	C₄×#10625337	C₂²	1	1	yes	characteristic, complemented
89	C₄×#10625336	C₂²	1	1	yes	characteristic
90	C₄×#10625336	C₂²	1	2	yes	—
91	C₄×#10625336	C₂²	1	2	yes	—
92	C₄×#10625336	C₂²	1	2	yes	—
93	C₄×#10625336	C₂²	1	1	yes	characteristic
94	C₄×#10625336	C₂²	1	2	yes	complemented
95	C₄×#10625336	C₂²	1	2	yes	complemented
96	C₄×#10625336	C₂²	1	2	yes	complemented
97	C₄×#10625336	C₂²	1	2	yes	complemented
98	C₄×#10625336	C₂²	1	2	yes	complemented
99	C₄×#10625335	C₂²	1	1	yes	characteristic, complemented
100	C₄×#10625335	C₂²	1	1	yes	characteristic, complemented
101	C₄×#10625334	C₂²	1	1	yes	characteristic
102	C₄×#10625334	C₂²	1	1	yes	characteristic
103	C₄×#10625334	C₂²	1	2	yes	complemented
104	D₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
105	D₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
106	D₄×C₄₇⋊C₈	C₂²	1	2	yes	complemented
107	D₄×C₄₇⋊C₈	C₂²	1	2	yes	complemented
108	#15689176	C₂²	1	1	yes	characteristic, complemented
109	#15689176	C₂²	1	2	yes	complemented
110	#15689159	C₂²	1	1	yes	characteristic, complemented
111	C₂×#13093955	C₂²	1	2	yes	complemented
112	#15689119	C₂²	1	1	yes	characteristic, complemented
113	#15689117	C₂²	1	1	yes	characteristic
114	C₂×#13093948	C₂²	1	2	yes	complemented
115	C₂×#13093944	C₂²	1	2	yes	—
116	C₂×C₄×C₄₇⋊C₈	C₂²	1	2	yes	complemented
117	C₂×C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic, complemented
118	C₄₇×#557	C₂²	1	1	yes	characteristic, complemented
119	C₄₇×#556	—	2	1	no	—
120	C₄₇×#556	C₂²	1	1	yes	characteristic, complemented
121	C₄₇×#552	—	2	2	no	—
122	C₄₇×#552	C₂²	1	2	yes	complemented
123	D₄×Q₈×C₄₇	C₂²	1	1	yes	characteristic
124	C₄₇×#548	C₂²	1	2	yes	complemented
125	C₄₇×#547	—	2	1	no	—
126	C₄₇×#547	C₂²	1	1	yes	characteristic
127	C₄₇×#533	—	2	1	no	—
128	C₄₇×#533	C₂²	1	1	yes	characteristic, complemented
129	C₄₇×#529	—	2	2	no	—
130	C₄₇×#529	C₂²	1	2	yes	complemented
131	C₄×#41×C₄₇	—	2	1	no	—
132	C₄×#41×C₄₇	C₂²	1	1	yes	characteristic
133	C₄×#41×C₄₇	C₂²	1	1	yes	characteristic, complemented
134	C₂×C₄×Q₈×C₄₇	C₂²	1	2	yes	complemented
135	C₂×#10625350	—	2	1	no	—
136	C₂×#10625350	C₂³	1	1	yes	characteristic
137	C₂²×D₁₈₈	C₂³	1	2	yes	—
138	C₂×D₄×D₄₇	—	2	1	no	—
139	C₂²×C₄×D₄₇	—	2	2	no	—
140	#13094044	—	2	4	no	—
141	C₂×#10625337	C₂³	1	1	yes	characteristic
142	C₂×#10625337	C₂³	1	2	yes	—
143	C₂×#10625335	C₂³	1	1	yes	characteristic
144	C₂×#10625336	—	2	8	no	—
145	C₂×#10625336	C₂³	1	2	yes	—
146	C₂×#10625336	C₂³	1	2	yes	—
147	C₂×#10625336	C₂³	1	2	yes	—
148	C₂×#10625336	C₂³	1	2	yes	—
149	C₂×#10625336	C₂³	1	1	yes	characteristic
150	C₂×#10625334	C₂³	1	1	yes	characteristic
151	C₂×#10625334	C₂³	1	2	yes	—
152	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
153	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
154	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
155	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
156	#13094024	C₂³	1	1	yes	characteristic
157	#13094021	C₂³	1	1	yes	characteristic
158	#13094019	—	2	2	no	—
159	#13094018	—	2	2	no	—
160	#13094016	C₂³	1	2	yes	—
161	#13094015	—	2	1	no	—
162	#13094013	—	2	1	no	—
163	#13094012	—	2	1	no	—
164	#13094012	C₂³	1	2	yes	—
165	#13094009	—	2	2	no	—
166	#13094009	—	2	2	no	—
167	#13094007	—	2	2	no	—
168	#13094006	—	2	2	no	—
169	#13094003	C₂³	1	2	yes	—
170	#13094002	—	2	2	no	—
171	#13094001	—	2	2	no	—
172	#13094000	—	2	1	no	—
173	#13093999	—	2	1	no	—
174	#13093998	—	2	1	no	—
175	#13093998	C₂³	1	2	yes	—
176	#13093998	C₂³	1	2	yes	—
177	#13093997	—	2	2	no	—
178	#13093996	—	2	2	no	—
179	#13093994	—	2	2	no	—
180	#13093992	—	2	2	no	—
181	C₄×Dic₉₄	C₂³	1	1	yes	characteristic
182	C₄×Dic₉₄	C₂³	1	1	yes	characteristic
183	C₄×D₁₈₈	—	2	2	no	—
184	C₄×D₁₈₈	—	2	1	no	—
185	C₄×D₁₈₈	—	2	2	no	—
186	C₄×D₁₈₈	C₂³	1	1	yes	characteristic
187	C₄×D₁₈₈	C₂³	1	2	yes	—
188	C₄×D₁₈₈	C₂³	1	2	yes	—
189	C₄×D₁₈₈	C₂³	1	1	yes	characteristic
190	C₄×D₁₈₈	C₂³	1	2	yes	—
191	D₄×Dic₄₇	—	2	1	no	—
192	#13093986	—	2	1	no	—
193	C₄×C₂²⋊D₄₇	—	2	1	no	—
194	C₄×C₂²⋊D₄₇	—	2	2	no	—
195	C₄×C₂²⋊D₄₇	—	2	1	no	—
196	(C₂²⋊D₄₇)⋊C₄	—	2	2	no	—
197	#13093983	C₂³	1	1	yes	characteristic
198	#13093981	—	2	1	no	—
199	#13093981	—	2	2	no	—
200	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
201	C₄⋊C₄×D₄₇	—	2	1	no	—
202	C₂×(C₂×D₄₇)⋊C₄	—	2	2	no	—
203	C₂²⋊C₄×D₄₇	—	2	2	no	—
204	C₄²×D₄₇	—	2	1	no	—
205	#13093957	C₂³	1	2	yes	—
206	#13093957	C₂³	1	1	yes	characteristic
207	#13093957	C₂³	1	1	yes	characteristic
208	#13093957	C₂³	1	2	yes	—
209	#13093955	C₂³	1	2	yes	—
210	#13093955	C₂³	1	2	yes	—
211	#13093955	C₂³	1	1	yes	characteristic
212	#13093955	C₂³	1	2	yes	—
213	#13093955	C₂³	1	1	yes	characteristic
214	#13093955	C₂³	1	2	yes	—
215	C₄⋊(C₄₇⋊C₈)	C₂³	1	1	yes	characteristic
216	C₄⋊(C₄₇⋊C₈)	C₂³	1	1	yes	characteristic
217	C₄⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
218	C₄⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
219	#13093948	C₂³	1	2	yes	—
220	#13093948	C₂³	1	1	yes	characteristic
221	#13093948	C₂³	1	1	yes	characteristic
222	#13093948	C₂³	1	2	yes	—
223	#13093948	C₂³	1	2	yes	—
224	#13093948	C₂³	1	2	yes	—
225	#13093948	C₂³	1	2	yes	—
226	#13093947	C₂³	1	1	yes	characteristic
227	#13093947	C₂³	1	2	yes	—
228	#13093947	C₂³	1	1	yes	characteristic
229	#13093945	C₂³	1	1	yes	characteristic
230	#13093945	C₂³	1	2	yes	—
231	#13093945	C₂³	1	1	yes	characteristic
232	#13093944	C₂³	1	2	yes	—
233	#13093944	C₂³	1	2	yes	—
234	#13093944	C₂³	1	2	yes	—
235	#13093944	C₂³	1	2	yes	—
236	#13093944	C₂³	1	1	yes	characteristic
237	#13093944	C₂³	1	2	yes	—
238	#13093944	C₂³	1	1	yes	characteristic
239	C₂²⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
240	C₂²⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
241	C₂²⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
242	C₄×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
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	2	yes	—
248	C₄×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
249	C₂×#41×C₄₇	—	2	1	no	—
250	C₂×#41×C₄₇	D₄	1	1	yes	characteristic
251	C₂×#41×C₄₇	C₂³	1	1	yes	characteristic
252	C₂²×Q₈×C₄₇	C₂³	1	2	yes	—
253	C₄⋊Q₈×C₄₇	—	2	1	no	—
254	C₄⋊Q₈×C₄₇	—	2	1	no	—
255	C₄⋊Q₈×C₄₇	C₂³	1	1	yes	characteristic
256	C₄⋊Q₈×C₄₇	C₂³	1	1	yes	characteristic
257	#126×C₄₇	—	2	2	no	—
258	#126×C₄₇	—	2	2	no	—
259	#126×C₄₇	—	2	2	no	—
260	#125×C₄₇	—	2	2	no	—
261	#125×C₄₇	—	2	2	no	—
262	#125×C₄₇	—	2	1	no	—
263	#125×C₄₇	C₂³	1	2	yes	—
264	#124×C₄₇	—	2	2	no	—
265	#124×C₄₇	C₂³	1	2	yes	—
266	#123×C₄₇	—	2	2	no	—
267	#123×C₄₇	—	2	2	no	—
268	#123×C₄₇	—	2	2	no	—
269	C₂²⋊Q₈×C₄₇	—	2	1	no	—
270	C₂²⋊Q₈×C₄₇	—	2	1	no	—
271	C₂²⋊Q₈×C₄₇	—	2	1	no	—
272	C₂²⋊Q₈×C₄₇	—	2	2	no	—
273	C₂²⋊Q₈×C₄₇	—	2	2	no	—
274	C₂²⋊Q₈×C₄₇	C₂³	1	2	yes	—
275	C₂²⋊Q₈×C₄₇	C₂³	1	2	yes	—
276	#121×C₄₇	—	2	2	no	—
277	#121×C₄₇	C₂³	1	2	yes	—
278	C₄×Q₈×C₄₇	—	2	1	no	—
279	C₄×Q₈×C₄₇	—	2	2	no	—
280	C₄×Q₈×C₄₇	—	2	2	no	—
281	C₄×Q₈×C₄₇	—	2	1	no	—
282	C₄×Q₈×C₄₇	D₄	1	1	yes	characteristic
283	C₄×Q₈×C₄₇	C₂³	1	1	yes	characteristic
284	C₄×Q₈×C₄₇	C₂³	1	2	yes	—
285	C₄×Q₈×C₄₇	C₂³	1	1	yes	characteristic
286	C₄×Q₈×C₄₇	C₂³	1	2	yes	—
287	C₄×Q₈×C₄₇	C₂³	1	2	yes	—
288	C₄×Q₈×C₄₇	C₂³	1	1	yes	characteristic
289	C₄×D₄×C₄₇	—	2	1	no	—
290	C₄×D₄×C₄₇	—	2	2	no	—
291	C₄×D₄×C₄₇	—	2	1	no	—
292	C₄×D₄×C₄₇	—	2	1	no	—
293	C₄×D₄×C₄₇	—	2	2	no	—
294	C₄×D₄×C₄₇	D₄	1	1	yes	characteristic
295	C₄×D₄×C₄₇	D₄	1	2	yes	—
296	C₄×D₄×C₄₇	C₂³	1	1	yes	characteristic
297	C₄×D₄×C₄₇	C₂³	1	1	yes	characteristic
298	C₄×D₄×C₄₇	C₂³	1	1	yes	characteristic
299	C₄×D₄×C₄₇	C₂³	1	2	yes	—
300	#117×C₄₇	—	2	1	no	—
301	#117×C₄₇	—	2	1	no	—
302	#117×C₄₇	—	2	2	no	—
303	#117×C₄₇	—	2	1	no	—
304	#117×C₄₇	—	2	2	no	—
305	#117×C₄₇	D₄	1	2	yes	—
306	#117×C₄₇	D₄	1	1	yes	characteristic
307	#117×C₄₇	C₂³	1	1	yes	characteristic
308	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
309	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
310	C₂×C₄²×C₄₇	—	2	2	no	—
311	C₂×C₄²×C₄₇	—	2	1	no	—
312	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
313	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
314	C₂³×D₄₇	—	2	2	no	—
315	#41×C₄₇	—	2	4	no	—
316	#41×C₄₇	—	2	2	no	—
317	#41×C₄₇	—	4	1	no	—
318	#41×C₄₇	—	4	4	no	—
319	C₂×Q₈×C₄₇	—	2	2	no	—
320	C₂×Q₈×C₄₇	—	2	1	no	—
321	C₂×Q₈×C₄₇	—	2	4	no	—
322	C₂×Q₈×C₄₇	—	4	2	no	—
323	C₂×Q₈×C₄₇	C₂×D₄	1	1	yes	characteristic
324	C₂×Q₈×C₄₇	C₂⁴	1	2	yes	—
325	C₂×Q₈×C₄₇	C₂⁴	1	1	yes	characteristic
326	C₂×D₄×C₄₇	—	2	1	no	—
327	C₂×D₄×C₄₇	—	2	2	no	—
328	C₂×D₄×C₄₇	C₂×D₄	1	2	yes	—
329	C₂×D₄×C₄₇	C₂×D₄	1	1	yes	characteristic
330	C₂×D₄×C₄₇	C₂⁴	1	1	yes	characteristic
331	C₂²×C₄×C₄₇	—	2	2	no	—
332	C₂²×C₄×C₄₇	—	2	2	no	—
333	C₂²×C₄×C₄₇	—	2	1	no	—
334	C₂²×C₄×C₄₇	—	2	1	no	—
335	C₂²×C₄×C₄₇	—	2	1	no	—
336	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
337	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
338	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
339	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
340	C₂²×C₄×C₄₇	C₂⁴	1	2	yes	—
341	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
342	C₂×C₂²⋊D₄₇	—	2	2	no	—
343	C₂×C₂²⋊D₄₇	—	2	1	no	—
344	C₂×C₂²⋊D₄₇	—	2	2	no	—
345	C₂²×Dic₄₇	—	2	2	no	—
346	D₄×D₄₇	—	4	4	no	—
347	#10625350	—	2	2	no	—
348	#10625350	—	4	1	no	—
349	#10625350	—	8	2	no	—
350	C₂×D₁₈₈	—	2	4	no	—
351	C₂×D₁₈₈	—	2	1	no	—
352	C₂×D₁₈₈	—	2	2	no	—
353	C₂×D₁₈₈	—	2	1	no	—
354	C₂×D₁₈₈	—	4	2	no	—
355	C₂×D₁₈₈	C₂⁴	1	2	yes	—
356	C₂×D₁₈₈	C₂⁴	1	1	yes	characteristic
357	C₂×C₄×D₄₇	—	2	1	no	—
358	C₂×C₄×D₄₇	—	2	1	no	—
359	C₂×C₄×D₄₇	—	2	1	no	—
360	C₂×C₄×D₄₇	—	2	2	no	—
361	C₂×C₄×D₄₇	—	2	2	no	—
362	C₂×C₄×D₄₇	—	2	2	no	—
363	C₂×C₄×D₄₇	—	8	4	no	—
364	C₂×Dic₉₄	—	2	1	no	—
365	C₂×Dic₉₄	C₂⁴	1	1	yes	characteristic
366	C₄⋊C₄×C₄₇	—	2	1	no	—
367	C₄⋊C₄×C₄₇	—	2	2	no	—
368	C₄⋊C₄×C₄₇	—	2	2	no	—
369	C₄⋊C₄×C₄₇	—	2	2	no	—
370	C₄⋊C₄×C₄₇	—	2	2	no	—
371	C₄⋊C₄×C₄₇	—	2	1	no	—
372	C₄⋊C₄×C₄₇	—	2	2	no	—
373	C₄⋊C₄×C₄₇	—	2	2	no	—
374	C₄⋊C₄×C₄₇	—	2	1	no	—
375	C₄⋊C₄×C₄₇	—	2	1	no	—
376	C₄⋊C₄×C₄₇	—	2	2	no	—
377	C₄⋊C₄×C₄₇	—	2	1	no	—
378	C₄⋊C₄×C₄₇	—	2	2	no	—
379	C₄⋊C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
380	C₄⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
381	C₄⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
382	C₄⋊C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
383	C₄⋊C₄×C₄₇	C₂⁴	1	1	yes	characteristic
384	C₄⋊C₄×C₄₇	C₂⁴	1	2	yes	—
385	C₄⋊C₄×C₄₇	C₂⁴	1	1	yes	characteristic
386	C₂²⋊C₄×C₄₇	—	2	2	no	—
387	C₂²⋊C₄×C₄₇	—	2	2	no	—
388	C₂²⋊C₄×C₄₇	—	2	1	no	—
389	C₂²⋊C₄×C₄₇	—	2	2	no	—
390	C₂²⋊C₄×C₄₇	—	2	1	no	—
391	C₂²⋊C₄×C₄₇	—	2	1	no	—
392	C₂²⋊C₄×C₄₇	—	2	2	no	—
393	C₂²⋊C₄×C₄₇	—	2	2	no	—
394	C₂²⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
395	C₂²⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
396	C₂²⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
397	C₄²×C₄₇	—	2	1	no	—
398	C₄²×C₄₇	—	2	1	no	—
399	C₄²×C₄₇	—	2	2	no	—
400	C₄²×C₄₇	—	2	2	no	—
401	C₄²×C₄₇	—	2	1	no	—
402	C₄²×C₄₇	—	2	2	no	—
403	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
404	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
405	C₄²×C₄₇	C₂×D₄	1	2	yes	—
406	C₄²×C₄₇	C₂×D₄	1	2	yes	—
407	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
408	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
409	C₄²×C₄₇	C₂⁴	1	2	yes	—
410	C₂²⋊Dic₄₇	—	2	2	no	—
411	C₂²⋊Dic₄₇	—	2	1	no	—
412	#10625337	—	2	2	no	—
413	#10625337	—	4	2	no	—
414	#10625336	—	2	4	no	—
415	#10625336	—	2	4	no	—
416	#10625336	—	2	4	no	—
417	#10625336	—	4	2	no	—
418	#10625336	#41	1	4	yes	complemented
419	#10625335	—	2	2	no	—
420	#10625334	—	2	2	no	—
421	#10625334	—	4	2	no	—
422	(C₂×D₄₇)⋊C₄	—	2	2	no	—
423	(C₂×D₄₇)⋊C₄	—	2	2	no	—
424	(C₂×D₄₇)⋊C₄	—	2	1	no	—
425	(C₂×D₄₇)⋊C₄	—	2	2	no	—
426	(C₂×D₄₇)⋊C₄	—	2	2	no	—
427	(C₂×D₄₇)⋊C₄	—	2	2	no	—
428	(C₂×D₄₇)⋊C₄	—	2	1	no	—
429	(C₂×D₄₇)⋊C₄	—	2	2	no	—
430	(C₂×D₄₇)⋊C₄	—	2	2	no	—
431	C₄⋊Dic₄₇	—	2	1	no	—
432	C₄⋊Dic₄₇	—	2	2	no	—
433	C₄⋊Dic₄₇	C₂⁴	1	1	yes	characteristic
434	C₄⋊Dic₄₇	C₂⁴	1	2	yes	—
435	C₄⋊Dic₄₇	C₂⁴	1	1	yes	characteristic
436	Dic₄₇⋊C₄	—	2	2	no	—
437	Dic₄₇⋊C₄	—	2	1	no	—
438	Dic₄₇⋊C₄	—	2	1	no	—
439	Dic₄₇⋊C₄	—	2	2	no	—
440	Dic₄₇⋊C₄	—	2	2	no	—
441	C₄×Dic₄₇	—	2	1	no	—
442	C₄×Dic₄₇	—	2	1	no	—
443	C₄×Dic₄₇	—	2	1	no	—
444	C₂×C₄₇⋊C₈	—	2	4	no	—
445	C₂×C₄₇⋊C₈	—	2	2	no	—
446	C₂×C₄₇⋊C₈	—	4	2	no	—
447	C₂×C₄₇⋊C₈	—	4	1	no	—
448	C₂×C₄₇⋊C₈	C₂⁴	1	1	yes	characteristic
449	C₂×C₄₇⋊C₈	C₂⁴	1	1	yes	characteristic
450	C₂×C₄₇⋊C₈	C₂⁴	1	2	yes	—
451	C₂×C₄₇⋊C₈	C₂⁴	1	2	yes	—
452	C₂×C₄₇⋊C₈	C₂⁴	1	1	yes	characteristic
453	C₂×C₄₇⋊C₈	C₂⁴	1	1	yes	characteristic
454	C₂³×C₄₇	—	2	1	no	—
455	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
456	C₂³×C₄₇	C₂²×D₄	1	2	yes	—
457	C₂²×D₄₇	—	2	1	no	—
458	C₂²×D₄₇	—	2	2	no	—
459	C₂²×D₄₇	—	4	4	no	—
460	C₂²×D₄₇	—	4	4	no	—
461	C₂²×D₄₇	—	8	2	no	—
462	Q₈×C₄₇	—	2	2	no	—
463	Q₈×C₄₇	—	2	1	no	—
464	Q₈×C₄₇	—	2	2	no	—
465	Q₈×C₄₇	—	2	2	no	—
466	Q₈×C₄₇	—	4	4	no	—
467	Q₈×C₄₇	—	4	2	no	—
468	Q₈×C₄₇	C₂×#41	1	2	yes	—
469	D₄×C₄₇	—	2	4	no	—
470	D₄×C₄₇	—	2	1	no	—
471	D₄×C₄₇	—	2	1	no	—
472	D₄×C₄₇	—	4	2	no	—
473	D₄×C₄₇	—	4	4	no	—
474	D₄×C₄₇	#135	1	4	yes	complemented
475	C₂×C₄×C₄₇	—	2	4	no	—
476	C₂×C₄×C₄₇	—	2	1	no	—
477	C₂×C₄×C₄₇	—	2	2	no	—
478	C₂×C₄×C₄₇	—	2	4	no	—
479	C₂×C₄×C₄₇	—	2	2	no	—
480	C₂×C₄×C₄₇	—	2	2	no	—
481	C₂×C₄×C₄₇	—	2	1	no	—
482	C₂×C₄×C₄₇	—	2	2	no	—
483	C₂×C₄×C₄₇	—	2	1	no	—
484	C₂×C₄×C₄₇	—	2	1	no	—
485	C₂×C₄×C₄₇	—	2	1	no	—
486	C₂×C₄×C₄₇	—	2	2	no	—
487	C₂×C₄×C₄₇	—	2	2	no	—
488	C₂×C₄×C₄₇	—	4	2	no	—
489	C₂×C₄×C₄₇	—	4	4	no	—
490	C₂×C₄×C₄₇	—	4	4	no	—
491	C₂×C₄×C₄₇	—	4	2	no	—
492	C₂×C₄×C₄₇	—	4	2	no	—
493	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
494	C₂×C₄×C₄₇	C₂²×D₄	1	2	yes	—
495	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
496	C₂×C₄×C₄₇	C₂²×D₄	1	2	yes	—
497	C₂×C₄×C₄₇	C₂²×D₄	1	2	yes	—
498	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
499	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
500	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
501	C₂×C₄×C₄₇	C₂⁵	1	1	yes	characteristic
502	C₂²⋊D₄₇	—	4	2	no	—
503	C₂²⋊D₄₇	—	4	4	no	—
504	C₂²⋊D₄₇	—	8	2	no	—
505	C₂×Dic₄₇	—	2	1	no	—
506	C₂×Dic₄₇	—	2	1	no	—
507	C₂×Dic₄₇	—	2	1	no	—
508	C₂×Dic₄₇	—	2	2	no	—
509	C₂×Dic₄₇	—	8	2	no	—
510	D₁₈₈	—	2	2	no	—
511	D₁₈₈	—	2	1	no	—
512	D₁₈₈	—	2	2	no	—
513	D₁₈₈	—	4	4	no	—
514	D₁₈₈	—	4	2	no	—
515	D₁₈₈	—	8	1	no	—
516	D₁₈₈	C₂×#41	1	2	yes	—
517	C₄×D₄₇	—	4	2	no	—
518	C₄×D₄₇	—	4	2	no	—
519	C₄×D₄₇	—	4	2	no	—
520	C₄×D₄₇	—	4	4	no	—
521	C₄×D₄₇	—	8	2	no	—
522	C₄×D₄₇	—	8	2	no	—
523	Dic₉₄	—	2	1	no	—
524	Dic₉₄	—	2	1	no	—
525	Dic₉₄	—	8	1	no	—
526	C₄₇⋊C₈	—	2	1	no	—
527	C₄₇⋊C₈	—	2	2	no	—
528	C₄₇⋊C₈	—	2	1	no	—
529	C₄₇⋊C₈	—	2	2	no	—
530	C₄₇⋊C₈	—	2	1	no	—
531	C₄₇⋊C₈	C₂×#41	1	2	yes	—
532	#61432	—	47	1	no	maximal, Sylow
533	C₂²×C₄₇	—	2	2	no	—
534	C₂²×C₄₇	—	2	2	no	—
535	C₂²×C₄₇	—	2	1	no	—
536	C₂²×C₄₇	—	2	1	no	—
537	C₂²×C₄₇	—	2	1	no	—
538	C₂²×C₄₇	—	4	1	no	—
539	C₂²×C₄₇	—	4	1	no	—
540	C₂²×C₄₇	—	4	1	no	—
541	C₂²×C₄₇	C₂×#135	1	4	yes	—
542	C₂²×C₄₇	C₂³×D₄	1	1	yes	characteristic
543	C₂×D₄₇	—	2	2	no	—
544	C₂×D₄₇	—	4	1	no	—
545	C₂×D₄₇	—	4	1	no	—
546	C₂×D₄₇	—	4	2	no	—
547	C₂×D₄₇	—	4	2	no	—
548	C₂×D₄₇	—	4	2	no	—
549	C₂×D₄₇	—	8	8	no	—
550	C₄×C₄₇	—	2	1	no	—
551	C₄×C₄₇	—	2	2	no	—
552	C₄×C₄₇	—	2	2	no	—
553	C₄×C₄₇	—	2	1	no	—
554	C₄×C₄₇	—	2	2	no	—
555	C₄×C₄₇	—	2	1	no	—
556	C₄×C₄₇	—	2	2	no	—
557	C₄×C₄₇	—	4	2	no	—
558	C₄×C₄₇	—	4	1	no	—
559	C₄×C₄₇	—	4	2	no	—
560	C₄×C₄₇	—	4	1	no	—
561	C₄×C₄₇	C₂×#135	1	2	yes	—
562	C₄×C₄₇	#577	1	2	yes	—
563	C₄×C₄₇	C₂²×#41	1	1	yes	characteristic
564	C₄×C₄₇	#585	1	1	yes	characteristic
565	Dic₄₇	—	4	1	no	—
566	Dic₄₇	—	4	1	no	—
567	Dic₄₇	—	4	2	no	—
568	Dic₄₇	—	4	1	no	—
569	#3482	D₄₇	1	1	yes	characteristic, complemented
570	#3481	—	47	1	no	—
571	#3394	—	47	1	no	—
572	#3381	—	47	1	no	—
573	#3365	—	47	1	no	—
574	#3360	—	47	1	no	—
575	#3337	—	47	2	no	—
576	#3335	—	47	1	no	—
577	#3301	—	47	2	no	—
578	#3299	—	47	1	no	—
579	#3296	—	47	2	no	—
580	#3294	—	47	1	no	—
581	#3282	—	47	2	no	—
582	D₄×SD₁₆	—	47	1	no	—
583	#3168	—	47	2	no	—
584	#3167	—	47	1	no	—
585	#3108	—	47	2	no	—
586	#3107	—	47	1	no	—
587	#3106	—	47	1	no	—
588	#3105	—	47	2	no	—
589	C₈×#41	—	47	1	no	—
590	C₄×#135	—	47	1	no	—
591	C₂×C₄×SD₁₆	—	47	2	no	—
592	C₂×C₄₇	—	2	4	no	—
593	C₂×C₄₇	—	4	1	no	—
594	C₂×C₄₇	—	8	1	no	—
595	C₂×C₄₇	D₄×#41	1	1	yes	characteristic
596	C₂×C₄₇	C₂²×#135	1	1	yes	characteristic
597	C₂×C₄₇	C₂×#577	1	1	yes	characteristic
598	D₄₇	—	4	2	no	—
599	D₄₇	—	8	2	no	—
600	C₂×#135	—	47	1	no	—
601	C₂²×SD₁₆	—	47	2	no	—
602	#559	—	47	1	no	—
603	#557	C₂×D₄₇	1	1	yes	characteristic, complemented
604	#556	—	2	1	no	—
605	#556	C₂×D₄₇	1	1	yes	characteristic, complemented
606	#554	—	47	1	no	—
607	#554	—	47	1	no	—
608	#553	—	47	2	no	—
609	#553	—	94	1	no	—
610	#552	—	2	2	no	—
611	#552	C₂×D₄₇	1	2	yes	complemented
612	#551	—	94	2	no	—
613	D₄×Q₈	C₂×D₄₇	1	1	yes	characteristic
614	#548	C₂×D₄₇	1	2	yes	complemented
615	#547	—	2	1	no	—
616	#547	C₂×D₄₇	1	1	yes	characteristic
617	#546	—	47	2	no	—
618	#546	—	94	1	no	—
619	D₄²	—	47	1	no	—
620	#533	—	2	1	no	—
621	#533	C₂×D₄₇	1	1	yes	characteristic, complemented
622	#532	—	47	1	no	—
623	#529	—	2	2	no	—
624	#529	—	47	2	no	—
625	#529	—	94	1	no	—
626	#529	C₂×D₄₇	1	2	yes	complemented
627	#525	—	94	2	no	—
628	C₄×#41	—	2	1	no	—
629	C₄×#41	—	47	1	no	—
630	C₄×#41	C₂×D₄₇	1	1	yes	characteristic
631	C₄×#41	C₂×D₄₇	1	1	yes	characteristic, complemented
632	C₂×C₄×Q₈	C₂×D₄₇	1	2	yes	complemented
633	C₂×C₄×D₄	—	47	2	no	—
634	C₂×C₄×D₄	—	94	1	no	—
635	#499	—	47	2	no	—
636	#498	—	47	1	no	—
637	#495	—	47	2	no	—
638	#492	—	47	1	no	—
639	#488	—	47	2	no	—
640	#488	—	47	2	no	—
641	#487	—	47	1	no	—
642	#486	—	47	1	no	—
643	#485	—	47	2	no	—
644	#484	—	47	2	no	—
645	#483	—	47	2	no	—
646	#482	—	47	2	no	—
647	#481	—	47	2	no	—
648	#480	—	47	2	no	—
649	#479	—	47	2	no	—
650	#479	—	47	2	no	—
651	#478	—	47	2	no	—
652	#478	—	47	2	no	—
653	#477	—	47	1	no	—
654	#476	—	47	1	no	—
655	#475	—	47	1	no	—
656	#474	—	47	1	no	—
657	#467	—	47	2	no	—
658	#466	—	47	2	no	—
659	#465	—	47	2	no	—
660	#465	—	47	2	no	—
661	#465	—	47	2	no	—
662	#465	—	47	2	no	—
663	#464	—	47	2	no	—
664	#464	—	47	2	no	—
665	#463	—	47	2	no	—
666	#463	—	47	2	no	—
667	#462	—	47	1	no	—
668	#461	—	47	1	no	—
669	#460	—	47	1	no	—
670	#459	—	47	1	no	—
671	#452	—	47	2	no	—
672	#451	—	47	2	no	—
673	#450	—	47	2	no	—
674	#449	—	47	2	no	—
675	#448	—	47	2	no	—
676	#447	—	47	2	no	—
677	C₈×Q₈	—	47	1	no	—
678	C₈×Q₈	—	47	1	no	—
679	C₄×Q₁₆	—	47	2	no	—
680	C₄×Q₁₆	—	47	1	no	—
681	C₄×Q₁₆	—	47	1	no	—
682	C₄×SD₁₆	—	47	2	no	—
683	C₄×SD₁₆	—	47	2	no	—
684	C₄×SD₁₆	—	47	2	no	—
685	C₄×SD₁₆	—	47	2	no	—
686	C₄×SD₁₆	—	47	2	no	—
687	C₄×SD₁₆	—	47	2	no	—
688	C₄×SD₁₆	—	47	2	no	—
689	C₄×SD₁₆	—	47	1	no	—
690	C₄×SD₁₆	—	47	2	no	—
691	C₄×SD₁₆	—	47	1	no	—
692	C₄×SD₁₆	—	47	1	no	—
693	C₄×SD₁₆	—	47	1	no	—
694	C₄×D₈	—	47	1	no	—
695	C₄×D₈	—	47	1	no	—
696	C₄×D₈	—	47	2	no	—
697	C₈×D₄	—	47	1	no	—
698	C₈×D₄	—	47	2	no	—
699	C₈×D₄	—	47	1	no	—
700	C₈×D₄	—	47	2	no	—
701	#431	—	47	2	no	—
702	#431	—	47	1	no	—
703	#427	—	47	1	no	—
704	C₂×#106	—	47	2	no	—
705	#416	—	47	1	no	—
706	#416	—	47	1	no	—
707	C₂×#103	—	47	2	no	—
708	C₂×#102	—	47	2	no	—
709	C₂×C₄×C₈	—	47	1	no	—
710	C₂×C₄×C₈	—	47	2	no	—
711	C₄₇	#61432	1	1	yes	characteristic, complemented, Sylow
712	C₂×#41	—	2	1	no	—
713	C₂×#41	—	47	1	no	—
714	C₂×#41	—	94	1	no	—
715	C₂×#41	C₂²⋊D₄₇	1	1	yes	characteristic
716	C₂×#41	C₂²×D₄₇	1	1	yes	characteristic
717	C₂²×Q₈	C₂²×D₄₇	1	2	yes	—
718	C₂²×D₄	—	47	2	no	—
719	C₂²×D₄	—	94	1	no	—
720	C₂³×C₄	—	94	2	no	—
721	#135	—	94	4	no	—
722	C₂×Q₁₆	—	47	1	no	—
723	C₂×Q₁₆	—	47	2	no	—
724	C₂×SD₁₆	—	47	1	no	—
725	C₂×SD₁₆	—	47	2	no	—
726	C₂×SD₁₆	—	47	2	no	—
727	C₂×SD₁₆	—	47	2	no	—
728	C₂×SD₁₆	—	47	1	no	—
729	C₂×SD₁₆	—	47	2	no	—
730	C₂×SD₁₆	—	94	8	no	—
731	C₂×D₈	—	47	1	no	—
732	C₂×D₈	—	47	2	no	—
733	C₂²×C₈	—	47	2	no	—
734	C₂²×C₈	—	47	1	no	—
735	C₂²×C₈	—	47	2	no	—
736	C₂²×C₈	—	47	1	no	—
737	C₄⋊Q₈	—	2	1	no	—
738	C₄⋊Q₈	—	2	1	no	—
739	C₄⋊Q₈	—	47	1	no	—
740	C₄⋊Q₈	C₂²×D₄₇	1	1	yes	characteristic
741	C₄⋊Q₈	C₂²×D₄₇	1	1	yes	characteristic
742	#127	—	47	1	no	—
743	#126	—	2	2	no	—
744	#126	—	2	2	no	—
745	#126	—	2	2	no	—
746	#126	—	94	2	no	—
747	#126	—	94	2	no	—
748	#125	—	2	2	no	—
749	#125	—	2	2	no	—
750	#125	—	2	1	no	—
751	#125	—	47	2	no	—
752	#125	—	94	1	no	—
753	#125	C₂²×D₄₇	1	2	yes	—
754	#124	—	2	2	no	—
755	#124	—	47	2	no	—
756	#124	—	94	1	no	—
757	#124	—	94	1	no	—
758	#124	C₂²×D₄₇	1	2	yes	—
759	#123	—	2	2	no	—
760	#123	—	2	2	no	—
761	#123	—	2	2	no	—
762	#123	—	94	2	no	—
763	#123	—	94	2	no	—
764	#123	—	94	2	no	—
765	#123	—	94	2	no	—
766	C₂²⋊Q₈	—	2	1	no	—
767	C₂²⋊Q₈	—	2	1	no	—
768	C₂²⋊Q₈	—	2	1	no	—
769	C₂²⋊Q₈	—	2	2	no	—
770	C₂²⋊Q₈	—	2	2	no	—
771	C₂²⋊Q₈	—	47	2	no	—
772	C₂²⋊Q₈	—	94	1	no	—
773	C₂²⋊Q₈	—	94	2	no	—
774	C₂²⋊Q₈	—	94	2	no	—
775	C₂²⋊Q₈	C₂²×D₄₇	1	2	yes	—
776	C₂²⋊Q₈	C₂²×D₄₇	1	2	yes	—
777	#121	—	2	2	no	—
778	#121	—	47	2	no	—
779	#121	—	47	2	no	—
780	#121	—	94	2	no	—
781	#121	—	94	1	no	—
782	#121	—	94	1	no	—
783	#121	—	94	2	no	—
784	#121	C₂²×D₄₇	1	2	yes	—
785	#120	—	94	2	no	—
786	#120	—	94	2	no	—
787	C₄×Q₈	—	2	1	no	—
788	C₄×Q₈	—	2	2	no	—
789	C₄×Q₈	—	2	2	no	—
790	C₄×Q₈	—	2	1	no	—
791	C₄×Q₈	—	47	1	no	—
792	C₄×Q₈	—	47	1	no	—
793	C₄×Q₈	C₂²⋊D₄₇	1	1	yes	characteristic
794	C₄×Q₈	C₂²×D₄₇	1	1	yes	characteristic
795	C₄×Q₈	C₂²×D₄₇	1	2	yes	—
796	C₄×Q₈	C₂²×D₄₇	1	2	yes	—
797	C₄×Q₈	C₂²×D₄₇	1	2	yes	—
798	C₄×Q₈	C₂²×D₄₇	1	1	yes	characteristic
799	C₄×Q₈	C₂²×D₄₇	1	1	yes	characteristic
800	C₄×D₄	—	2	1	no	—
801	C₄×D₄	—	2	2	no	—
802	C₄×D₄	—	2	1	no	—
803	C₄×D₄	—	2	1	no	—
804	C₄×D₄	—	2	2	no	—
805	C₄×D₄	—	47	1	no	—
806	C₄×D₄	—	47	2	no	—
807	C₄×D₄	—	47	2	no	—
808	C₄×D₄	—	47	2	no	—
809	C₄×D₄	—	47	1	no	—
810	C₄×D₄	—	94	1	no	—
811	C₄×D₄	—	94	2	no	—
812	C₄×D₄	—	94	1	no	—
813	C₄×D₄	—	94	1	no	—
814	C₄×D₄	—	94	1	no	—
815	C₄×D₄	—	94	2	no	—
816	C₄×D₄	—	94	2	no	—
817	C₄×D₄	—	94	2	no	—
818	C₄×D₄	—	94	1	no	—
819	C₄×D₄	C₂²⋊D₄₇	1	1	yes	characteristic
820	C₄×D₄	C₂²⋊D₄₇	1	2	yes	—
821	C₄×D₄	C₂²×D₄₇	1	1	yes	characteristic
822	C₄×D₄	C₂²×D₄₇	1	1	yes	characteristic
823	C₄×D₄	C₂²×D₄₇	1	1	yes	characteristic
824	C₄×D₄	C₂²×D₄₇	1	2	yes	—
825	#117	—	2	1	no	—
826	#117	—	2	1	no	—
827	#117	—	2	2	no	—
828	#117	—	2	1	no	—
829	#117	—	2	2	no	—
830	#117	—	47	1	no	—
831	#117	—	94	1	no	—
832	#117	—	94	2	no	—
833	#117	C₂²⋊D₄₇	1	2	yes	—
834	#117	C₂²⋊D₄₇	1	1	yes	characteristic
835	#117	C₂²×D₄₇	1	1	yes	characteristic
836	C₂×C₄⋊C₄	—	2	2	no	—
837	C₂×C₄⋊C₄	—	47	2	no	—
838	C₂×C₄⋊C₄	—	94	1	no	—
839	C₂×C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
840	C₂×C₂²⋊C₄	—	94	2	no	—
841	C₂×C₂²⋊C₄	—	94	2	no	—
842	C₂×C₄²	—	2	2	no	—
843	C₂×C₄²	—	2	1	no	—
844	C₂×C₄²	—	94	1	no	—
845	C₂×C₄²	C₂²×D₄₇	1	2	yes	—
846	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
847	#107	—	47	1	no	—
848	#107	—	47	1	no	—
849	#107	—	47	2	no	—
850	#107	—	47	2	no	—
851	#106	—	47	1	no	—
852	#106	—	47	2	no	—
853	#106	—	47	2	no	—
854	#106	—	47	2	no	—
855	#106	—	47	1	no	—
856	#106	—	47	2	no	—
857	C₄⋊C₈	—	47	1	no	—
858	C₄⋊C₈	—	47	1	no	—
859	C₄⋊C₈	—	47	2	no	—
860	C₄⋊C₈	—	47	2	no	—
861	#103	—	47	1	no	—
862	#103	—	47	2	no	—
863	#103	—	47	2	no	—
864	#103	—	47	2	no	—
865	#103	—	47	1	no	—
866	#103	—	47	2	no	—
867	#103	—	47	2	no	—
868	#103	—	47	1	no	—
869	#103	—	47	1	no	—
870	#103	—	47	2	no	—
871	#102	—	47	1	no	—
872	#102	—	47	1	no	—
873	#102	—	47	2	no	—
874	#102	—	47	1	no	—
875	#102	—	47	2	no	—
876	#102	—	47	2	no	—
877	#102	—	47	2	no	—
878	#102	—	47	1	no	—
879	#102	—	47	2	no	—
880	#102	—	47	2	no	—
881	C₂²⋊C₈	—	47	2	no	—
882	C₂²⋊C₈	—	47	2	no	—
883	C₂²⋊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	—	47	1	no	—
888	C₄×C₈	—	47	2	no	—
889	C₄×C₈	—	47	1	no	—
890	C₄×C₈	—	47	2	no	—
891	C₂⁴	—	94	2	no	—
892	#41	—	2	4	no	—
893	#41	—	2	2	no	—
894	#41	—	4	1	no	—
895	#41	—	4	4	no	—
896	#41	—	94	2	no	—
897	#41	—	376	2	no	—
898	#41	—	188	1	no	—
899	C₂×Q₈	—	2	2	no	—
900	C₂×Q₈	—	2	1	no	—
901	C₂×Q₈	—	2	4	no	—
902	C₂×Q₈	—	4	2	no	—
903	C₂×Q₈	—	47	1	no	—
904	C₂×Q₈	—	94	1	no	—
905	C₂×Q₈	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
906	C₂×Q₈	C₂³×D₄₇	1	2	yes	—
907	C₂×Q₈	C₂³×D₄₇	1	1	yes	characteristic
908	C₂×D₄	—	2	1	no	—
909	C₂×D₄	—	2	2	no	—
910	C₂×D₄	—	47	1	no	—
911	C₂×D₄	—	47	2	no	—
912	C₂×D₄	—	94	4	no	—
913	C₂×D₄	—	94	2	no	—
914	C₂×D₄	—	94	1	no	—
915	C₂×D₄	—	94	2	no	—
916	C₂×D₄	—	94	1	no	—
917	C₂×D₄	—	94	2	no	—
918	C₂×D₄	—	94	1	no	—
919	C₂×D₄	—	188	2	no	—
920	C₂×D₄	—	188	4	no	—
921	C₂×D₄	C₂×C₂²⋊D₄₇	1	2	yes	—
922	C₂×D₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
923	C₂×D₄	C₂³×D₄₇	1	1	yes	characteristic
924	C₂²×C₄	—	2	2	no	—
925	C₂²×C₄	—	2	2	no	—
926	C₂²×C₄	—	2	1	no	—
927	C₂²×C₄	—	2	1	no	—
928	C₂²×C₄	—	2	1	no	—
929	C₂²×C₄	—	94	2	no	—
930	C₂²×C₄	—	94	2	no	—
931	C₂²×C₄	—	94	2	no	—
932	C₂²×C₄	—	94	1	no	—
933	C₂²×C₄	—	94	1	no	—
934	C₂²×C₄	—	94	1	no	—
935	C₂²×C₄	—	94	2	no	—
936	C₂²×C₄	—	376	4	no	—
937	C₂²×C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
938	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
939	C₂²×C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
940	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
941	C₂²×C₄	C₂³×D₄₇	1	2	yes	—
942	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
943	Q₁₆	—	94	2	no	—
944	Q₁₆	—	188	2	no	—
945	SD₁₆	—	47	4	no	—
946	SD₁₆	—	94	2	no	—
947	SD₁₆	—	94	4	no	—
948	SD₁₆	—	94	4	no	—
949	SD₁₆	—	94	4	no	—
950	SD₁₆	—	188	2	no	—
951	D₈	—	94	2	no	—
952	D₈	—	188	2	no	—
953	C₂×C₈	—	47	1	no	—
954	C₂×C₈	—	47	1	no	—
955	C₂×C₈	—	47	2	no	—
956	C₂×C₈	—	47	1	no	—
957	C₂×C₈	—	47	1	no	—
958	C₂×C₈	—	47	2	no	—
959	C₂×C₈	—	94	4	no	—
960	C₂×C₈	—	94	2	no	—
961	C₂×C₈	—	188	2	no	—
962	C₂×C₈	—	188	1	no	—
963	C₄⋊C₄	—	2	1	no	—
964	C₄⋊C₄	—	2	2	no	—
965	C₄⋊C₄	—	2	2	no	—
966	C₄⋊C₄	—	2	2	no	—
967	C₄⋊C₄	—	2	2	no	—
968	C₄⋊C₄	—	2	1	no	—
969	C₄⋊C₄	—	2	2	no	—
970	C₄⋊C₄	—	2	2	no	—
971	C₄⋊C₄	—	2	1	no	—
972	C₄⋊C₄	—	2	1	no	—
973	C₄⋊C₄	—	2	2	no	—
974	C₄⋊C₄	—	2	1	no	—
975	C₄⋊C₄	—	2	2	no	—
976	C₄⋊C₄	—	47	1	no	—
977	C₄⋊C₄	—	47	2	no	—
978	C₄⋊C₄	—	47	1	no	—
979	C₄⋊C₄	—	94	2	no	—
980	C₄⋊C₄	—	94	1	no	—
981	C₄⋊C₄	—	94	1	no	—
982	C₄⋊C₄	—	94	2	no	—
983	C₄⋊C₄	—	94	2	no	—
984	C₄⋊C₄	—	94	2	no	—
985	C₄⋊C₄	—	94	1	no	—
986	C₄⋊C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
987	C₄⋊C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
988	C₄⋊C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
989	C₄⋊C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
990	C₄⋊C₄	C₂³×D₄₇	1	1	yes	characteristic
991	C₄⋊C₄	C₂³×D₄₇	1	2	yes	—
992	C₄⋊C₄	C₂³×D₄₇	1	1	yes	characteristic
993	C₂²⋊C₄	—	2	2	no	—
994	C₂²⋊C₄	—	2	2	no	—
995	C₂²⋊C₄	—	2	1	no	—
996	C₂²⋊C₄	—	2	2	no	—
997	C₂²⋊C₄	—	2	1	no	—
998	C₂²⋊C₄	—	2	1	no	—
999	C₂²⋊C₄	—	2	2	no	—
1000	C₂²⋊C₄	—	2	2	no	—
1001	C₂²⋊C₄	—	94	2	no	—
1002	C₂²⋊C₄	—	94	1	no	—
1003	C₂²⋊C₄	—	94	1	no	—
1004	C₂²⋊C₄	—	94	2	no	—
1005	C₂²⋊C₄	—	94	2	no	—
1006	C₂²⋊C₄	—	94	2	no	—
1007	C₂²⋊C₄	—	94	2	no	—
1008	C₂²⋊C₄	—	94	2	no	—
1009	C₂²⋊C₄	—	94	1	no	—
1010	C₂²⋊C₄	—	94	2	no	—
1011	C₂²⋊C₄	—	94	2	no	—
1012	C₂²⋊C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
1013	C₂²⋊C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
1014	C₂²⋊C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
1015	C₄²	—	2	1	no	—
1016	C₄²	—	2	2	no	—
1017	C₄²	—	2	1	no	—
1018	C₄²	—	2	2	no	—
1019	C₄²	—	2	1	no	—
1020	C₄²	—	2	2	no	—
1021	C₄²	—	94	1	no	—
1022	C₄²	—	94	1	no	—
1023	C₄²	—	94	1	no	—
1024	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
1025	C₄²	C₂×C₂²⋊D₄₇	1	2	yes	—
1026	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
1027	C₄²	C₂×C₂²⋊D₄₇	1	2	yes	—
1028	C₄²	C₂³×D₄₇	1	2	yes	—
1029	C₄²	C₂³×D₄₇	1	1	yes	characteristic
1030	C₄²	C₂³×D₄₇	1	1	yes	characteristic
1031	C₂³	—	2	1	no	—
1032	C₂³	—	94	1	no	—
1033	C₂³	—	94	2	no	—
1034	C₂³	—	376	2	no	—
1035	C₂³	—	188	4	no	—
1036	C₂³	—	188	4	no	—
1037	C₂³	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
1038	C₂³	C₂²×C₂²⋊D₄₇	1	2	yes	—
1039	Q₈	—	2	2	no	—
1040	Q₈	—	2	1	no	—
1041	Q₈	—	2	2	no	—
1042	Q₈	—	2	2	no	—
1043	Q₈	—	4	4	no	—
1044	Q₈	—	4	2	no	—
1045	Q₈	—	94	1	no	—
1046	Q₈	—	94	1	no	—
1047	Q₈	—	376	1	no	—
1048	Q₈	#41×D₄₇	1	2	yes	—
1049	D₄	—	2	4	no	—
1050	D₄	—	2	1	no	—
1051	D₄	—	2	1	no	—
1052	D₄	—	4	2	no	—
1053	D₄	—	4	4	no	—
1054	D₄	—	47	2	no	—
1055	D₄	—	94	2	no	—
1056	D₄	—	94	1	no	—
1057	D₄	—	94	2	no	—
1058	D₄	—	376	1	no	—
1059	D₄	—	376	2	no	—
1060	D₄	—	188	4	no	—
1061	D₄	—	188	2	no	—
1062	D₄	—	188	4	no	—
1063	D₄	—	188	2	no	—
1064	D₄	#13094044	1	4	yes	complemented
1065	C₂×C₄	—	2	4	no	—
1066	C₂×C₄	—	2	1	no	—
1067	C₂×C₄	—	2	2	no	—
1068	C₂×C₄	—	2	4	no	—
1069	C₂×C₄	—	2	2	no	—
1070	C₂×C₄	—	2	2	no	—
1071	C₂×C₄	—	2	1	no	—
1072	C₂×C₄	—	2	2	no	—
1073	C₂×C₄	—	2	1	no	—
1074	C₂×C₄	—	2	1	no	—
1075	C₂×C₄	—	2	1	no	—
1076	C₂×C₄	—	2	2	no	—
1077	C₂×C₄	—	2	2	no	—
1078	C₂×C₄	—	4	2	no	—
1079	C₂×C₄	—	4	4	no	—
1080	C₂×C₄	—	4	4	no	—
1081	C₂×C₄	—	4	2	no	—
1082	C₂×C₄	—	4	2	no	—
1083	C₂×C₄	—	94	1	no	—
1084	C₂×C₄	—	94	1	no	—
1085	C₂×C₄	—	94	1	no	—
1086	C₂×C₄	—	94	2	no	—
1087	C₂×C₄	—	376	2	no	—
1088	C₂×C₄	—	376	2	no	—
1089	C₂×C₄	—	376	2	no	—
1090	C₂×C₄	—	188	2	no	—
1091	C₂×C₄	—	188	2	no	—
1092	C₂×C₄	—	188	2	no	—
1093	C₂×C₄	—	188	4	no	—
1094	C₂×C₄	C₂²×C₂²⋊D₄₇	1	2	yes	—
1095	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
1096	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
1097	C₂×C₄	C₂²×C₂²⋊D₄₇	1	2	yes	—
1098	C₂×C₄	C₂²×C₂²⋊D₄₇	1	2	yes	—
1099	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
1100	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
1101	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
1102	C₂×C₄	C₂⁴×D₄₇	1	1	yes	characteristic
1103	C₈	—	47	2	no	—
1104	C₈	—	94	1	no	—
1105	C₈	—	94	2	no	—
1106	C₈	—	94	1	no	—
1107	C₈	—	94	2	no	—
1108	C₈	—	94	1	no	—
1109	C₂²	—	2	2	no	—
1110	C₂²	—	2	2	no	—
1111	C₂²	—	2	1	no	—
1112	C₂²	—	2	1	no	—
1113	C₂²	—	2	1	no	—
1114	C₂²	—	4	1	no	—
1115	C₂²	—	4	1	no	—
1116	C₂²	—	4	1	no	—
1117	C₂²	—	94	2	no	—
1118	C₂²	—	376	8	no	—
1119	C₂²	—	188	2	no	—
1120	C₂²	—	188	2	no	—
1121	C₂²	—	188	2	no	—
1122	C₂²	—	188	1	no	—
1123	C₂²	—	188	1	no	—
1124	C₂²	C₂×#13094044	1	4	yes	—
1125	C₂²	C₂³×C₂²⋊D₄₇	1	1	yes	characteristic
1126	C₄	—	2	1	no	—
1127	C₄	—	2	2	no	—
1128	C₄	—	2	2	no	—
1129	C₄	—	2	1	no	—
1130	C₄	—	2	1	no	—
1131	C₄	—	2	2	no	—
1132	C₄	—	2	2	no	—
1133	C₄	—	4	1	no	—
1134	C₄	—	4	2	no	—
1135	C₄	—	4	1	no	—
1136	C₄	—	4	2	no	—
1137	C₄	—	188	1	no	—
1138	C₄	—	188	1	no	—
1139	C₄	—	188	2	no	—
1140	C₄	—	188	1	no	—
1141	C₄	C₂×#13094044	1	2	yes	—
1142	C₄	#15689931	1	2	yes	—
1143	C₄	C₂×#41×D₄₇	1	1	yes	characteristic
1144	C₄	#15689959	1	1	yes	characteristic
1145	C₂	—	2	4	no	—
1146	C₂	—	4	1	no	—
1147	C₂	—	8	1	no	—
1148	C₂	—	376	2	no	—
1149	C₂	—	188	2	no	—
1150	C₂	#41×C₂²⋊D₄₇	1	1	yes	characteristic
1151	C₂	C₂²×#13094044	1	1	yes	characteristic
1152	C₂	C₂×#15689931	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×C₂²⋊D₄₇
commutator, cosocle	C₂×C₄×C₄₇	C₂⁵
Frattini	C₂×C₄	C₂⁴×D₄₇
Fitting	C₄₇×#3482	C₂
socle	C₂²×C₄₇	C₂³×D₄
hypercenter	#3482	D₄₇
hypocenter	C₄₇	#61432
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ C₄×#41 ◁ #3482

Complements

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

N	H ≅ G/N	type
1. #20256998	C₂	semidirect
2. #20256384	C₂	semidirect
3. #20256259	C₂	semidirect
4. #20256084	C₂	semidirect
5. #20256033	C₂	semidirect
6. #20255767	C₂	semidirect
7. #20255745	C₂	semidirect
8. #20255290	C₂	semidirect
9. #20255264	C₂	semidirect
10. #20255217	C₂	semidirect
11. #20255195	C₂	semidirect
12. #20255096	C₂	semidirect
13. D₄×#10625336	C₂	semidirect
14. #20253952	C₂	semidirect
15. #20253948	C₂	semidirect
16. #20253468	C₂	semidirect
17. #20253453	C₂	semidirect
18. #20253448	C₂	semidirect
19. #20253431	C₂	semidirect
20. #41×C₄₇⋊C₈	C₂	semidirect
21. C₄×#13094044	C₂	semidirect
22. C₂×C₄×#10625336	C₂	semidirect
23. C₄₇×#3482	C₂	semidirect
42. #15689522	C₂²	semidirect
43. #15689519	C₂²	semidirect
44. #15689505	C₂²	semidirect
46. #15689480	C₂²	semidirect
47. #15689477	C₂²	semidirect
48. #15689473	C₂²	semidirect
50. #15689461	C₂²	semidirect
51. #15689456	C₂²	semidirect
52. #15689453	C₂²	semidirect
53. #15689447	C₂²	semidirect
54. #15689439	C₂²	semidirect
56. #15689430	C₂²	semidirect
57. #15689430	C₂²	semidirect
59. #15689420	C₂²	semidirect
60. #15689418	C₂²	semidirect
61. #15689413	C₂²	semidirect
62. #15689405	C₂²	semidirect
64. #15689362	C₂²	semidirect
67. #15689354	C₂²	semidirect
68. #15689354	C₂²	semidirect
69. #15689350	C₂²	semidirect
70. #15689345	C₂²	semidirect
71. #15689345	C₂²	semidirect
73. #15689335	C₂²	semidirect
74. #15689330	C₂²	semidirect
79. #15689279	C₂²	semidirect
81. #15689268	C₂²	semidirect
84. Q₈×C₄₇⋊C₈	C₂²	semidirect
85. Q₈×C₄₇⋊C₈	C₂²	semidirect
86. C₄×#10625337	C₂²	semidirect
87. C₄×#10625337	C₂²	semidirect
88. C₄×#10625337	C₂²	semidirect
94. C₄×#10625336	C₂²	semidirect
95. C₄×#10625336	C₂²	semidirect
96. C₄×#10625336	C₂²	semidirect
97. C₄×#10625336	C₂²	semidirect
98. C₄×#10625336	C₂²	semidirect
99. C₄×#10625335	C₂²	semidirect
100. C₄×#10625335	C₂²	semidirect
103. C₄×#10625334	C₂²	semidirect
106. D₄×C₄₇⋊C₈	C₂²	semidirect
107. D₄×C₄₇⋊C₈	C₂²	semidirect
108. #15689176	C₂²	semidirect
109. #15689176	C₂²	semidirect
110. #15689159	C₂²	semidirect
111. C₂×#13093955	C₂²	semidirect
112. #15689119	C₂²	semidirect
114. C₂×#13093948	C₂²	semidirect
116. C₂×C₄×C₄₇⋊C₈	C₂²	semidirect
117. C₂×C₄×C₄₇⋊C₈	C₂²	semidirect
118. C₄₇×#557	C₂²	semidirect
120. C₄₇×#556	C₂²	semidirect
122. C₄₇×#552	C₂²	semidirect
124. C₄₇×#548	C₂²	semidirect
128. C₄₇×#533	C₂²	semidirect
130. C₄₇×#529	C₂²	semidirect
133. C₄×#41×C₄₇	C₂²	semidirect
134. C₂×C₄×Q₈×C₄₇	C₂²	semidirect
418. #10625336	#41	semidirect
474. D₄×C₄₇	#135	semidirect
569. #3482	D₄₇	semidirect
603. #557	C₂×D₄₇	semidirect
605. #556	C₂×D₄₇	semidirect
611. #552	C₂×D₄₇	semidirect
614. #548	C₂×D₄₇	semidirect
621. #533	C₂×D₄₇	semidirect
626. #529	C₂×D₄₇	semidirect
631. C₄×#41	C₂×D₄₇	semidirect
632. C₂×C₄×Q₈	C₂×D₄₇	semidirect
711. C₄₇	#61432	semidirect
1064. D₄	#13094044	semidirect

Maximal subgroups

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

subgroup	index
#20256998	2
#20256384	2
#20256259	2
#20256084	2
#20256033	2
#20255767	2
#20255745	2
#20255290	2
#20255264	2
#20255217	2
#20255195	2
#20255096	2
D₄×#10625336	2
#20253952	2
#20253948	2
#20253468	2
#20253453	2
#20253448	2
#20253431	2
#41×C₄₇⋊C₈	2
C₄×#13094044	2
C₂×C₄×#10625336	2
C₄₇×#3482	2
#61432	47