Subgroups — #27108544

Order 12032.

1878 conjugacy classes of subgroups.

The subgroup lattice has 1160 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20257349	C₂	1	1	yes	maximal, characteristic, complemented
2	#20256384	C₂	1	1	yes	maximal, characteristic, complemented
3	#20256372	C₂	1	1	yes	maximal, characteristic, complemented
4	#20256084	C₂	1	1	yes	maximal, characteristic, complemented
5	#20256073	C₂	1	1	yes	maximal, characteristic, complemented
6	#20255269	C₂	1	2	yes	maximal, complemented
7	#20255247	C₂	1	1	yes	maximal, characteristic, complemented
8	#20255217	C₂	1	2	yes	maximal, complemented
9	#20255195	C₂	1	1	yes	maximal, characteristic, complemented
10	D₄×#10625337	C₂	1	1	yes	maximal, characteristic, complemented
11	#20255125	C₂	1	2	yes	maximal, complemented
12	#20255096	C₂	1	2	yes	maximal, complemented
13	D₄×#10625336	C₂	1	1	yes	maximal, characteristic, complemented
14	#20254735	C₂	1	2	yes	maximal, complemented
15	#20254719	C₂	1	1	yes	maximal, characteristic, complemented
16	#20254349	C₂	1	2	yes	maximal, complemented
17	#20254340	C₂	1	1	yes	maximal, characteristic, complemented
18	#20253468	C₂	1	2	yes	maximal, complemented
19	#20253406	C₂	1	1	yes	maximal, characteristic, complemented
20	#20252843	C₂	1	1	yes	maximal, characteristic, complemented
21	C₂×#15689345	C₂	1	2	yes	maximal, complemented
22	#20252499	C₂	1	1	yes	maximal, characteristic, complemented
23	C₄₇×#3482	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#13094044	C₂²	1	2	yes	complemented
25	C₂²×#10625337	C₂²	1	2	yes	complemented
26	C₂²×#10625336	C₂²	1	2	yes	—
27	#15689858	C₂²	1	1	yes	characteristic
28	#15689846	C₂²	1	1	yes	characteristic
29	#15689836	—	2	1	no	—
30	#15689797	—	2	2	no	—
31	D₄×Dic₉₄	C₂²	1	1	yes	characteristic
32	#15689782	C₂²	1	2	yes	—
33	#15689769	C₂²	1	2	yes	—
34	#15689761	—	2	1	no	—
35	D₄×D₁₈₈	C₂²	1	1	yes	characteristic
36	#15689745	—	2	1	no	—
37	#15689706	—	2	2	no	—
38	#15689673	C₂²	1	1	yes	characteristic
39	#15689657	C₂²	1	2	yes	—
40	#15689657	C₂²	1	1	yes	characteristic
41	C₂×#13094012	C₂²	1	2	yes	—
42	#15689595	—	2	1	no	—
43	#15689505	C₂²	1	2	yes	—
44	#15689505	C₂²	1	2	yes	complemented
45	#15689502	C₂²	1	1	yes	characteristic, complemented
46	#15689497	C₂²	1	1	yes	characteristic
47	#15689480	C₂²	1	2	yes	—
48	#15689480	C₂²	1	2	yes	complemented
49	#15689475	C₂²	1	1	yes	characteristic, complemented
50	#15689471	C₂²	1	1	yes	characteristic
51	#15689464	C₂²	1	1	yes	characteristic, complemented
52	#15689453	C₂²	1	2	yes	complemented
53	#15689447	C₂²	1	1	yes	characteristic
54	#15689436	C₂²	1	2	yes	—
55	#15689430	C₂²	1	2	yes	complemented
56	#15689430	C₂²	1	1	yes	characteristic, complemented
57	#15689427	C₂²	1	2	yes	complemented
58	#15689423	C₂²	1	1	yes	characteristic, complemented
59	#15689420	C₂²	1	2	yes	complemented
60	#15689405	C₂²	1	1	yes	characteristic, complemented
61	#15689400	C₂²	1	1	yes	characteristic
62	#15689362	C₂²	1	2	yes	complemented
63	#15689362	C₂²	1	2	yes	complemented
64	#15689357	C₂²	1	2	yes	—
65	#15689354	C₂²	1	2	yes	—
66	#15689354	C₂²	1	2	yes	—
67	#15689350	C₂²	1	2	yes	complemented
68	#15689345	C₂²	1	2	yes	—
69	#15689345	C₂²	1	2	yes	—
70	#15689345	C₂²	1	2	yes	—
71	#15689345	C₂²	1	1	yes	characteristic
72	#15689345	C₂²	1	2	yes	complemented
73	#15689345	C₂²	1	2	yes	complemented
74	#15689345	C₂²	1	2	yes	complemented
75	#15689345	C₂²	1	2	yes	complemented
76	#15689345	C₂²	1	2	yes	complemented
77	#15689342	C₂²	1	2	yes	complemented
78	#15689338	C₂²	1	1	yes	characteristic
79	#15689338	C₂²	1	2	yes	complemented
80	#15689335	C₂²	1	2	yes	complemented
81	#15689333	C₂²	1	1	yes	characteristic, complemented
82	#15689330	C₂²	1	1	yes	characteristic, complemented
83	#15689328	C₂²	1	1	yes	characteristic, complemented
84	#15689325	C₂²	1	1	yes	characteristic
85	#15689323	C₂²	1	1	yes	characteristic
86	#15689318	C₂²	1	1	yes	characteristic
87	#15689285	C₂²	1	1	yes	characteristic, complemented
88	#15689283	C₂²	1	2	yes	complemented
89	#15689283	C₂²	1	2	yes	complemented
90	#15689279	C₂²	1	2	yes	complemented
91	#15689278	C₂²	1	2	yes	complemented
92	#15689273	C₂²	1	2	yes	—
93	#15689268	C₂²	1	1	yes	characteristic
94	#15689262	C₂²	1	2	yes	—
95	#15689261	C₂²	1	2	yes	complemented
96	#15689256	C₂²	1	2	yes	—
97	Q₈×C₄₇⋊C₈	C₂²	1	1	yes	characteristic, complemented
98	Q₈×C₄₇⋊C₈	C₂²	1	1	yes	characteristic, complemented
99	C₄×#10625337	C₂²	1	2	yes	complemented
100	C₄×#10625337	C₂²	1	2	yes	complemented
101	C₄×#10625337	C₂²	1	1	yes	characteristic, complemented
102	C₄×#10625336	C₂²	1	1	yes	characteristic
103	C₄×#10625336	C₂²	1	2	yes	complemented
104	C₄×#10625336	C₂²	1	2	yes	complemented
105	C₄×#10625335	C₂²	1	1	yes	characteristic, complemented
106	C₄×#10625334	C₂²	1	1	yes	characteristic
107	D₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
108	D₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
109	D₄×C₄₇⋊C₈	C₂²	1	2	yes	complemented
110	D₄×C₄₇⋊C₈	C₂²	1	2	yes	complemented
111	#15689176	C₂²	1	2	yes	complemented
112	#15689176	C₂²	1	1	yes	characteristic, complemented
113	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	2	yes	complemented
114	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic, complemented
115	#15689117	C₂²	1	2	yes	complemented
116	C₂×#13093947	C₂²	1	2	yes	complemented
117	C₂×#13093944	C₂²	1	2	yes	—
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	C₂³	1	2	yes	—
136	C₂²×Dic₉₄	C₂³	1	2	yes	—
137	C₂²×D₁₈₈	C₂³	1	2	yes	—
138	C₂×D₄×D₄₇	—	2	1	no	—
139	#13094044	—	4	4	no	—
140	C₂×#10625337	—	4	4	no	—
141	C₂×#10625337	C₂³	1	2	yes	—
142	C₂×#10625337	C₂³	1	1	yes	characteristic
143	C₂×#10625337	C₂³	1	2	yes	—
144	C₂×#10625337	C₂³	1	2	yes	—
145	C₂×#10625337	C₂³	1	2	yes	—
146	C₂×#10625335	C₂³	1	2	yes	—
147	C₂×#10625335	C₂³	1	1	yes	characteristic
148	C₂×#10625336	—	4	4	no	—
149	C₂×#10625336	C₂³	1	2	yes	—
150	C₂×#10625336	C₂³	1	1	yes	characteristic
151	C₂×#10625336	C₂³	1	2	yes	—
152	C₂×#10625336	C₂³	1	2	yes	—
153	C₂×#10625336	C₂³	1	2	yes	—
154	C₂×#10625334	C₂³	1	1	yes	characteristic
155	C₂×#10625334	C₂³	1	2	yes	—
156	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
157	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
158	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
159	#13094024	C₂³	1	1	yes	characteristic
160	#13094023	—	2	1	no	—
161	#13094021	C₂³	1	1	yes	characteristic
162	#13094019	—	2	2	no	—
163	#13094018	—	2	2	no	—
164	#13094018	—	2	1	no	—
165	#13094016	C₂³	1	1	yes	characteristic
166	#13094013	—	2	1	no	—
167	#13094012	—	2	2	no	—
168	#13094012	—	2	2	no	—
169	#13094012	C₂³	1	2	yes	—
170	#13094012	C₂³	1	2	yes	—
171	#13094012	C₂³	1	1	yes	characteristic
172	#13094012	C₂³	1	2	yes	—
173	#13094010	—	2	2	no	—
174	#13094009	—	2	2	no	—
175	#13094009	—	2	2	no	—
176	#13094007	—	2	2	no	—
177	#13094007	—	2	1	no	—
178	#13094003	C₂³	1	2	yes	—
179	#13094003	C₂³	1	1	yes	characteristic
180	#13094002	—	2	2	no	—
181	#13094001	—	2	2	no	—
182	#13094000	—	2	1	no	—
183	#13093999	—	2	1	no	—
184	#13093998	—	2	1	no	—
185	#13093998	—	2	1	no	—
186	#13093998	C₂³	1	2	yes	—
187	#13093998	C₂³	1	1	yes	characteristic
188	#13093997	—	2	2	no	—
189	#13093996	—	2	2	no	—
190	#13093994	—	2	2	no	—
191	#13093992	—	2	2	no	—
192	C₄×Dic₉₄	C₂³	1	2	yes	—
193	C₄×Dic₉₄	C₂³	1	1	yes	characteristic
194	C₄×D₁₈₈	—	2	1	no	—
195	C₄×D₁₈₈	—	2	1	no	—
196	C₄×D₁₈₈	C₂³	1	1	yes	characteristic
197	C₄×D₁₈₈	C₂³	1	2	yes	—
198	D₄×Dic₄₇	—	2	1	no	—
199	#13093986	—	2	1	no	—
200	C₄×C₂²⋊D₄₇	—	2	1	no	—
201	C₄×C₂²⋊D₄₇	—	2	2	no	—
202	(C₂²⋊D₄₇)⋊C₄	—	2	2	no	—
203	#13093982	—	2	1	no	—
204	#13093981	—	2	1	no	—
205	#13093981	—	2	2	no	—
206	C₂×(C₂×D₄₇)⋊C₄	—	2	2	no	—
207	C₂×(C₂×D₄₇)⋊C₄	—	2	2	no	—
208	C₂²⋊C₄×D₄₇	—	2	2	no	—
209	#13093957	C₂³	1	1	yes	characteristic
210	#13093957	C₂³	1	2	yes	—
211	#13093957	C₂³	1	1	yes	characteristic
212	#13093955	C₂³	1	2	yes	—
213	#13093955	C₂³	1	1	yes	characteristic
214	#13093955	C₂³	1	1	yes	characteristic
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	C₄⋊(C₄₇⋊C₈)	C₂³	1	1	yes	characteristic
220	C₄⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
221	C₄⋊(C₄₇⋊C₈)	C₂³	1	1	yes	characteristic
222	#13093948	C₂³	1	1	yes	characteristic
223	#13093948	C₂³	1	2	yes	—
224	#13093948	C₂³	1	1	yes	characteristic
225	#13093948	C₂³	1	2	yes	—
226	#13093947	C₂³	1	2	yes	—
227	#13093947	C₂³	1	1	yes	characteristic
228	#13093947	C₂³	1	2	yes	—
229	#13093947	C₂³	1	2	yes	—
230	#13093947	C₂³	1	2	yes	—
231	#13093947	C₂³	1	2	yes	—
232	#13093947	C₂³	1	1	yes	characteristic
233	#13093945	C₂³	1	1	yes	characteristic
234	#13093945	C₂³	1	1	yes	characteristic
235	#13093944	C₂³	1	1	yes	characteristic
236	#13093944	C₂³	1	2	yes	—
237	#13093944	C₂³	1	2	yes	—
238	#13093944	C₂³	1	2	yes	—
239	#13093944	C₂³	1	2	yes	—
240	#13093944	C₂³	1	2	yes	—
241	#13093944	C₂³	1	1	yes	characteristic
242	C₂²⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
243	C₂²⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
244	C₂²⋊(C₄₇⋊C₈)	C₂³	1	1	yes	characteristic
245	C₂²⋊(C₄₇⋊C₈)	C₂³	1	1	yes	characteristic
246	C₄×C₄₇⋊C₈	C₂³	1	2	yes	—
247	C₄×C₄₇⋊C₈	C₂³	1	2	yes	—
248	C₄×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
249	C₄×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
250	C₂×#41×C₄₇	—	2	1	no	—
251	C₂×#41×C₄₇	D₄	1	1	yes	characteristic
252	C₂×#41×C₄₇	C₂³	1	1	yes	characteristic
253	C₂²×Q₈×C₄₇	C₂³	1	2	yes	—
254	C₄⋊Q₈×C₄₇	—	2	1	no	—
255	C₄⋊Q₈×C₄₇	—	2	1	no	—
256	C₄⋊Q₈×C₄₇	C₂³	1	1	yes	characteristic
257	C₄⋊Q₈×C₄₇	C₂³	1	1	yes	characteristic
258	#126×C₄₇	—	2	2	no	—
259	#126×C₄₇	—	2	2	no	—
260	#126×C₄₇	—	2	2	no	—
261	#125×C₄₇	—	2	2	no	—
262	#125×C₄₇	—	2	2	no	—
263	#125×C₄₇	—	2	1	no	—
264	#125×C₄₇	C₂³	1	2	yes	—
265	#124×C₄₇	—	2	2	no	—
266	#124×C₄₇	C₂³	1	2	yes	—
267	#123×C₄₇	—	2	2	no	—
268	#123×C₄₇	—	2	2	no	—
269	#123×C₄₇	—	2	2	no	—
270	C₂²⋊Q₈×C₄₇	—	2	1	no	—
271	C₂²⋊Q₈×C₄₇	—	2	1	no	—
272	C₂²⋊Q₈×C₄₇	—	2	1	no	—
273	C₂²⋊Q₈×C₄₇	—	2	2	no	—
274	C₂²⋊Q₈×C₄₇	—	2	2	no	—
275	C₂²⋊Q₈×C₄₇	C₂³	1	2	yes	—
276	C₂²⋊Q₈×C₄₇	C₂³	1	2	yes	—
277	#121×C₄₇	—	2	2	no	—
278	#121×C₄₇	C₂³	1	2	yes	—
279	C₄×Q₈×C₄₇	—	2	1	no	—
280	C₄×Q₈×C₄₇	—	2	2	no	—
281	C₄×Q₈×C₄₇	—	2	2	no	—
282	C₄×Q₈×C₄₇	—	2	1	no	—
283	C₄×Q₈×C₄₇	D₄	1	1	yes	characteristic
284	C₄×Q₈×C₄₇	C₂³	1	2	yes	—
285	C₄×Q₈×C₄₇	C₂³	1	2	yes	—
286	C₄×Q₈×C₄₇	C₂³	1	1	yes	characteristic
287	C₄×Q₈×C₄₇	C₂³	1	1	yes	characteristic
288	C₄×Q₈×C₄₇	C₂³	1	2	yes	—
289	C₄×Q₈×C₄₇	C₂³	1	1	yes	characteristic
290	C₄×D₄×C₄₇	—	2	1	no	—
291	C₄×D₄×C₄₇	—	2	2	no	—
292	C₄×D₄×C₄₇	—	2	1	no	—
293	C₄×D₄×C₄₇	—	2	1	no	—
294	C₄×D₄×C₄₇	—	2	2	no	—
295	C₄×D₄×C₄₇	D₄	1	1	yes	characteristic
296	C₄×D₄×C₄₇	D₄	1	2	yes	—
297	C₄×D₄×C₄₇	C₂³	1	1	yes	characteristic
298	C₄×D₄×C₄₇	C₂³	1	1	yes	characteristic
299	C₄×D₄×C₄₇	C₂³	1	1	yes	characteristic
300	C₄×D₄×C₄₇	C₂³	1	2	yes	—
301	#117×C₄₇	—	2	1	no	—
302	#117×C₄₇	—	2	1	no	—
303	#117×C₄₇	—	2	2	no	—
304	#117×C₄₇	—	2	1	no	—
305	#117×C₄₇	—	2	2	no	—
306	#117×C₄₇	D₄	1	2	yes	—
307	#117×C₄₇	D₄	1	1	yes	characteristic
308	#117×C₄₇	C₂³	1	1	yes	characteristic
309	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
310	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
311	C₂×C₄²×C₄₇	—	2	2	no	—
312	C₂×C₄²×C₄₇	—	2	1	no	—
313	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
314	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
315	C₂³×D₄₇	—	2	2	no	—
316	#41×C₄₇	—	2	4	no	—
317	#41×C₄₇	—	2	2	no	—
318	#41×C₄₇	—	4	1	no	—
319	#41×C₄₇	—	4	4	no	—
320	C₂×Q₈×C₄₇	—	2	2	no	—
321	C₂×Q₈×C₄₇	—	2	1	no	—
322	C₂×Q₈×C₄₇	—	2	4	no	—
323	C₂×Q₈×C₄₇	—	4	2	no	—
324	C₂×Q₈×C₄₇	C₂×D₄	1	1	yes	characteristic
325	C₂×Q₈×C₄₇	C₂⁴	1	2	yes	—
326	C₂×Q₈×C₄₇	C₂⁴	1	1	yes	characteristic
327	C₂×D₄×C₄₇	—	2	1	no	—
328	C₂×D₄×C₄₇	—	2	2	no	—
329	C₂×D₄×C₄₇	C₂×D₄	1	2	yes	—
330	C₂×D₄×C₄₇	C₂×D₄	1	1	yes	characteristic
331	C₂×D₄×C₄₇	C₂⁴	1	1	yes	characteristic
332	C₂²×C₄×C₄₇	—	2	2	no	—
333	C₂²×C₄×C₄₇	—	2	2	no	—
334	C₂²×C₄×C₄₇	—	2	1	no	—
335	C₂²×C₄×C₄₇	—	2	1	no	—
336	C₂²×C₄×C₄₇	—	2	1	no	—
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	2	yes	—
340	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
341	C₂²×C₄×C₄₇	C₂⁴	1	2	yes	—
342	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
343	C₂×C₂²⋊D₄₇	—	2	2	no	—
344	C₂×C₂²⋊D₄₇	—	2	1	no	—
345	C₂×C₂²⋊D₄₇	—	2	2	no	—
346	C₂²×Dic₄₇	—	2	2	no	—
347	D₄×D₄₇	—	4	4	no	—
348	#10625350	—	4	2	no	—
349	#10625350	—	4	2	no	—
350	C₂×D₁₈₈	—	2	1	no	—
351	C₂×D₁₈₈	—	2	1	no	—
352	C₂×D₁₈₈	—	2	2	no	—
353	C₂×D₁₈₈	—	4	2	no	—
354	C₂×D₁₈₈	—	4	2	no	—
355	C₂×D₁₈₈	C₂⁴	1	1	yes	characteristic
356	C₂×D₁₈₈	C₂⁴	1	2	yes	—
357	C₂×C₄×D₄₇	—	2	1	no	—
358	C₂×C₄×D₄₇	—	2	2	no	—
359	C₂×C₄×D₄₇	—	2	2	no	—
360	C₂×Dic₉₄	—	2	2	no	—
361	C₂×Dic₉₄	—	4	2	no	—
362	C₂×Dic₉₄	—	4	2	no	—
363	C₂×Dic₉₄	C₂⁴	1	1	yes	characteristic
364	C₂×Dic₉₄	C₂⁴	1	2	yes	—
365	C₄⋊C₄×C₄₇	—	2	1	no	—
366	C₄⋊C₄×C₄₇	—	2	2	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	1	no	—
371	C₄⋊C₄×C₄₇	—	2	2	no	—
372	C₄⋊C₄×C₄₇	—	2	2	no	—
373	C₄⋊C₄×C₄₇	—	2	1	no	—
374	C₄⋊C₄×C₄₇	—	2	1	no	—
375	C₄⋊C₄×C₄₇	—	2	2	no	—
376	C₄⋊C₄×C₄₇	—	2	1	no	—
377	C₄⋊C₄×C₄₇	—	2	2	no	—
378	C₄⋊C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
379	C₄⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
380	C₄⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
381	C₄⋊C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
382	C₄⋊C₄×C₄₇	C₂⁴	1	1	yes	characteristic
383	C₄⋊C₄×C₄₇	C₂⁴	1	2	yes	—
384	C₄⋊C₄×C₄₇	C₂⁴	1	1	yes	characteristic
385	C₂²⋊C₄×C₄₇	—	2	2	no	—
386	C₂²⋊C₄×C₄₇	—	2	2	no	—
387	C₂²⋊C₄×C₄₇	—	2	1	no	—
388	C₂²⋊C₄×C₄₇	—	2	2	no	—
389	C₂²⋊C₄×C₄₇	—	2	1	no	—
390	C₂²⋊C₄×C₄₇	—	2	1	no	—
391	C₂²⋊C₄×C₄₇	—	2	2	no	—
392	C₂²⋊C₄×C₄₇	—	2	2	no	—
393	C₂²⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
394	C₂²⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
395	C₂²⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
396	C₄²×C₄₇	—	2	1	no	—
397	C₄²×C₄₇	—	2	1	no	—
398	C₄²×C₄₇	—	2	2	no	—
399	C₄²×C₄₇	—	2	2	no	—
400	C₄²×C₄₇	—	2	1	no	—
401	C₄²×C₄₇	—	2	2	no	—
402	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
403	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
404	C₄²×C₄₇	C₂×D₄	1	2	yes	—
405	C₄²×C₄₇	C₂×D₄	1	2	yes	—
406	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
407	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
408	C₄²×C₄₇	C₂⁴	1	2	yes	—
409	C₂²⋊Dic₄₇	—	2	2	no	—
410	C₂²⋊Dic₄₇	—	2	1	no	—
411	#10625337	—	2	2	no	—
412	#10625337	—	2	4	no	—
413	#10625337	—	4	2	no	—
414	#10625337	—	4	2	no	—
415	#10625337	—	4	2	no	—
416	#10625336	—	2	2	no	—
417	#10625336	—	2	4	no	—
418	#10625336	—	4	2	no	—
419	#10625336	—	4	2	no	—
420	#10625336	—	4	2	no	—
421	#10625335	—	4	1	no	—
422	#10625335	—	4	2	no	—
423	#10625334	—	4	1	no	—
424	#10625334	—	4	2	no	—
425	(C₂×D₄₇)⋊C₄	—	2	1	no	—
426	(C₂×D₄₇)⋊C₄	—	2	2	no	—
427	(C₂×D₄₇)⋊C₄	—	2	1	no	—
428	(C₂×D₄₇)⋊C₄	—	2	1	no	—
429	(C₂×D₄₇)⋊C₄	—	2	2	no	—
430	(C₂×D₄₇)⋊C₄	—	2	2	no	—
431	(C₂×D₄₇)⋊C₄	—	2	2	no	—
432	(C₂×D₄₇)⋊C₄	—	2	2	no	—
433	(C₂×D₄₇)⋊C₄	—	2	2	no	—
434	(C₂×D₄₇)⋊C₄	—	2	2	no	—
435	(C₂×D₄₇)⋊C₄	—	2	2	no	—
436	(C₂×D₄₇)⋊C₄	—	2	1	no	—
437	C₄⋊Dic₄₇	—	2	1	no	—
438	C₄⋊Dic₄₇	—	2	1	no	—
439	C₄⋊Dic₄₇	C₂⁴	1	1	yes	characteristic
440	C₄⋊Dic₄₇	C₂⁴	1	1	yes	characteristic
441	Dic₄₇⋊C₄	—	2	1	no	—
442	Dic₄₇⋊C₄	—	2	1	no	—
443	Dic₄₇⋊C₄	—	2	1	no	—
444	Dic₄₇⋊C₄	—	2	2	no	—
445	Dic₄₇⋊C₄	—	2	2	no	—
446	Dic₄₇⋊C₄	—	2	1	no	—
447	C₄×Dic₄₇	—	2	2	no	—
448	C₄×Dic₄₇	—	2	1	no	—
449	C₂×C₄₇⋊C₈	—	4	2	no	—
450	C₂×C₄₇⋊C₈	—	4	2	no	—
451	C₂×C₄₇⋊C₈	—	4	2	no	—
452	C₂×C₄₇⋊C₈	C₂⁴	1	1	yes	characteristic
453	C₂×C₄₇⋊C₈	C₂⁴	1	1	yes	characteristic
454	C₂×C₄₇⋊C₈	C₂⁴	1	1	yes	characteristic
455	C₂×C₄₇⋊C₈	C₂⁴	1	2	yes	—
456	C₂×C₄₇⋊C₈	C₂⁴	1	2	yes	—
457	C₂×C₄₇⋊C₈	C₂⁴	1	1	yes	characteristic
458	C₂³×C₄₇	—	2	1	no	—
459	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
460	C₂³×C₄₇	C₂²×D₄	1	2	yes	—
461	C₂²×D₄₇	—	2	1	no	—
462	C₂²×D₄₇	—	2	2	no	—
463	C₂²×D₄₇	—	4	4	no	—
464	C₂²×D₄₇	—	8	2	no	—
465	C₂²×D₄₇	—	8	2	no	—
466	Q₈×C₄₇	—	2	2	no	—
467	Q₈×C₄₇	—	2	1	no	—
468	Q₈×C₄₇	—	2	2	no	—
469	Q₈×C₄₇	—	2	2	no	—
470	Q₈×C₄₇	—	4	4	no	—
471	Q₈×C₄₇	—	4	2	no	—
472	Q₈×C₄₇	H(5,𝔽₂)	1	2	yes	—
473	D₄×C₄₇	—	2	4	no	—
474	D₄×C₄₇	—	2	1	no	—
475	D₄×C₄₇	—	2	1	no	—
476	D₄×C₄₇	—	4	2	no	—
477	D₄×C₄₇	—	4	4	no	—
478	D₄×C₄₇	#135	1	4	yes	complemented
479	C₂×C₄×C₄₇	—	2	4	no	—
480	C₂×C₄×C₄₇	—	2	1	no	—
481	C₂×C₄×C₄₇	—	2	2	no	—
482	C₂×C₄×C₄₇	—	2	2	no	—
483	C₂×C₄×C₄₇	—	2	1	no	—
484	C₂×C₄×C₄₇	—	2	2	no	—
485	C₂×C₄×C₄₇	—	2	1	no	—
486	C₂×C₄×C₄₇	—	2	1	no	—
487	C₂×C₄×C₄₇	—	2	1	no	—
488	C₂×C₄×C₄₇	—	2	2	no	—
489	C₂×C₄×C₄₇	—	2	2	no	—
490	C₂×C₄×C₄₇	—	4	2	no	—
491	C₂×C₄×C₄₇	—	4	1	no	—
492	C₂×C₄×C₄₇	—	4	2	no	—
493	C₂×C₄×C₄₇	—	4	4	no	—
494	C₂×C₄×C₄₇	—	4	2	no	—
495	C₂×C₄×C₄₇	—	4	4	no	—
496	C₂×C₄×C₄₇	—	4	2	no	—
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	C₂²×D₄	1	2	yes	—
502	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
503	C₂×C₄×C₄₇	C₂²×D₄	1	2	yes	—
504	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
505	C₂×C₄×C₄₇	C₂⁵	1	1	yes	characteristic
506	C₂²⋊D₄₇	—	4	4	no	—
507	C₂²⋊D₄₇	—	8	2	no	—
508	C₂²⋊D₄₇	—	8	1	no	—
509	C₂×Dic₄₇	—	2	1	no	—
510	C₂×Dic₄₇	—	2	1	no	—
511	C₂×Dic₄₇	—	2	2	no	—
512	C₂×Dic₄₇	—	2	1	no	—
513	C₂×Dic₄₇	—	8	2	no	—
514	D₁₈₈	—	2	2	no	—
515	D₁₈₈	—	2	1	no	—
516	D₁₈₈	—	2	1	no	—
517	D₁₈₈	—	2	2	no	—
518	D₁₈₈	—	4	2	no	—
519	D₁₈₈	—	8	1	no	—
520	D₁₈₈	—	8	2	no	—
521	C₄×D₄₇	—	4	2	no	—
522	C₄×D₄₇	—	8	2	no	—
523	C₄×D₄₇	—	8	2	no	—
524	Dic₉₄	—	2	2	no	—
525	Dic₉₄	—	2	1	no	—
526	Dic₉₄	—	2	1	no	—
527	Dic₉₄	—	2	2	no	—
528	Dic₉₄	—	8	2	no	—
529	C₄₇⋊C₈	—	2	2	no	—
530	C₄₇⋊C₈	—	2	2	no	—
531	C₄₇⋊C₈	—	2	1	no	—
532	C₄₇⋊C₈	—	2	1	no	—
533	C₄₇⋊C₈	—	2	1	no	—
534	C₄₇⋊C₈	—	2	1	no	—
535	#61956	—	47	1	no	maximal, Sylow
536	C₂²×C₄₇	—	2	2	no	—
537	C₂²×C₄₇	—	2	2	no	—
538	C₂²×C₄₇	—	2	1	no	—
539	C₂²×C₄₇	—	2	1	no	—
540	C₂²×C₄₇	—	2	1	no	—
541	C₂²×C₄₇	—	4	1	no	—
542	C₂²×C₄₇	—	4	1	no	—
543	C₂²×C₄₇	—	4	1	no	—
544	C₂²×C₄₇	C₂×#135	1	4	yes	—
545	C₂²×C₄₇	C₂³×D₄	1	1	yes	characteristic
546	C₂×D₄₇	—	4	2	no	—
547	C₂×D₄₇	—	4	1	no	—
548	C₂×D₄₇	—	4	2	no	—
549	C₂×D₄₇	—	4	1	no	—
550	C₂×D₄₇	—	4	1	no	—
551	C₂×D₄₇	—	4	2	no	—
552	C₂×D₄₇	—	16	4	no	—
553	C₄×C₄₇	—	2	2	no	—
554	C₄×C₄₇	—	2	1	no	—
555	C₄×C₄₇	—	2	1	no	—
556	C₄×C₄₇	—	2	2	no	—
557	C₄×C₄₇	—	2	1	no	—
558	C₄×C₄₇	—	2	2	no	—
559	C₄×C₄₇	—	2	1	no	—
560	C₄×C₄₇	—	2	2	no	—
561	C₄×C₄₇	—	4	1	no	—
562	C₄×C₄₇	—	4	2	no	—
563	C₄×C₄₇	—	4	1	no	—
564	C₄×C₄₇	—	4	2	no	—
565	C₄×C₄₇	C₂×#135	1	2	yes	—
566	C₄×C₄₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
567	C₄×C₄₇	#585	1	1	yes	characteristic
568	Dic₄₇	—	4	1	no	—
569	Dic₄₇	—	4	1	no	—
570	Dic₄₇	—	4	2	no	—
571	Dic₄₇	—	4	1	no	—
572	#3514	—	47	1	no	—
573	#3482	D₄₇	1	1	yes	characteristic, complemented
574	#3394	—	47	1	no	—
575	#3393	—	47	1	no	—
576	#3365	—	47	1	no	—
577	#3364	—	47	1	no	—
578	#3300	—	47	2	no	—
579	#3298	—	47	1	no	—
580	#3296	—	47	2	no	—
581	#3294	—	47	1	no	—
582	D₄×Q₁₆	—	47	1	no	—
583	#3285	—	47	2	no	—
584	#3282	—	47	2	no	—
585	D₄×SD₁₆	—	47	1	no	—
586	#3250	—	47	2	no	—
587	#3248	—	47	1	no	—
588	#3211	—	47	2	no	—
589	#3210	—	47	1	no	—
590	#3108	—	47	2	no	—
591	#3102	—	47	1	no	—
592	#3035	—	47	1	no	—
593	C₂×#464	—	47	2	no	—
594	#2988	—	47	1	no	—
595	C₂×C₄₇	—	2	4	no	—
596	C₂×C₄₇	—	4	1	no	—
597	C₂×C₄₇	—	8	1	no	—
598	C₂×C₄₇	#3488	1	1	yes	characteristic
599	C₂×C₄₇	C₂²×#135	1	1	yes	characteristic
600	C₂×C₄₇	#3586	1	1	yes	characteristic
601	D₄₇	—	8	2	no	—
602	D₄₇	—	8	1	no	—
603	C₂×#135	—	47	2	no	—
604	C₂²×Q₁₆	—	47	2	no	—
605	C₂²×SD₁₆	—	47	2	no	—
606	#559	—	47	1	no	—
607	#557	C₂×D₄₇	1	1	yes	characteristic, complemented
608	#556	—	2	1	no	—
609	#556	—	47	1	no	—
610	#556	C₂×D₄₇	1	1	yes	characteristic, complemented
611	#555	—	94	1	no	—
612	#552	—	2	2	no	—
613	#552	C₂×D₄₇	1	2	yes	complemented
614	#551	—	94	2	no	—
615	D₄×Q₈	—	47	1	no	—
616	D₄×Q₈	C₂×D₄₇	1	1	yes	characteristic
617	#548	—	47	2	no	—
618	#548	C₂×D₄₇	1	2	yes	complemented
619	#547	—	2	1	no	—
620	#547	C₂×D₄₇	1	1	yes	characteristic
621	#546	—	47	2	no	—
622	#546	—	94	1	no	—
623	D₄²	—	47	1	no	—
624	#542	—	94	1	no	—
625	#538	—	94	2	no	—
626	#533	—	2	1	no	—
627	#533	C₂×D₄₇	1	1	yes	characteristic, complemented
628	#532	—	47	1	no	—
629	#529	—	2	2	no	—
630	#529	—	47	1	no	—
631	#529	—	47	2	no	—
632	#529	C₂×D₄₇	1	2	yes	complemented
633	C₂×#124	—	47	2	no	—
634	#518	—	94	1	no	—
635	C₄×#41	—	2	1	no	—
636	C₄×#41	C₂×D₄₇	1	1	yes	characteristic
637	C₄×#41	C₂×D₄₇	1	1	yes	characteristic, complemented
638	C₂×C₄×Q₈	C₂×D₄₇	1	2	yes	complemented
639	#495	—	47	2	no	—
640	#495	—	47	2	no	—
641	#494	—	47	1	no	—
642	#492	—	47	1	no	—
643	#488	—	47	2	no	—
644	#488	—	47	2	no	—
645	#487	—	47	1	no	—
646	#486	—	47	1	no	—
647	#485	—	47	1	no	—
648	#483	—	47	2	no	—
649	#482	—	47	1	no	—
650	#480	—	47	2	no	—
651	#479	—	47	2	no	—
652	#479	—	47	1	no	—
653	#479	—	47	2	no	—
654	#478	—	47	2	no	—
655	#478	—	47	1	no	—
656	#475	—	47	1	no	—
657	#474	—	47	1	no	—
658	#467	—	47	2	no	—
659	#467	—	47	2	no	—
660	#466	—	47	2	no	—
661	#465	—	47	2	no	—
662	#465	—	47	2	no	—
663	#465	—	47	2	no	—
664	#464	—	47	2	no	—
665	#464	—	47	1	no	—
666	#464	—	47	2	no	—
667	#464	—	47	2	no	—
668	#464	—	47	2	no	—
669	#464	—	47	2	no	—
670	#464	—	47	2	no	—
671	#464	—	47	2	no	—
672	#464	—	47	2	no	—
673	#464	—	47	2	no	—
674	#463	—	47	2	no	—
675	#463	—	47	1	no	—
676	#463	—	47	2	no	—
677	#462	—	47	1	no	—
678	#462	—	47	1	no	—
679	#461	—	47	1	no	—
680	#461	—	47	1	no	—
681	#460	—	47	1	no	—
682	#459	—	47	1	no	—
683	#452	—	47	1	no	—
684	#452	—	47	2	no	—
685	#452	—	47	2	no	—
686	#451	—	47	2	no	—
687	#451	—	47	2	no	—
688	#450	—	47	2	no	—
689	#449	—	47	1	no	—
690	#448	—	47	2	no	—
691	#448	—	47	2	no	—
692	#447	—	47	2	no	—
693	C₈×Q₈	—	47	1	no	—
694	C₈×Q₈	—	47	1	no	—
695	C₄×Q₁₆	—	47	1	no	—
696	C₄×Q₁₆	—	47	2	no	—
697	C₄×Q₁₆	—	47	2	no	—
698	C₄×SD₁₆	—	47	1	no	—
699	C₄×SD₁₆	—	47	2	no	—
700	C₄×SD₁₆	—	47	2	no	—
701	C₄×SD₁₆	—	47	1	no	—
702	C₄×D₈	—	47	1	no	—
703	C₈×D₄	—	47	1	no	—
704	C₈×D₄	—	47	2	no	—
705	C₈×D₄	—	47	2	no	—
706	C₈×D₄	—	47	1	no	—
707	#431	—	47	1	no	—
708	#431	—	47	2	no	—
709	C₂×C₄⋊C₈	—	47	1	no	—
710	C₂×C₄⋊C₈	—	47	2	no	—
711	#416	—	47	2	no	—
712	C₂×#103	—	47	2	no	—
713	C₂×#102	—	47	2	no	—
714	C₄₇	#61956	1	1	yes	characteristic, complemented, Sylow
715	C₂×#41	—	2	1	no	—
716	C₂×#41	—	47	2	no	—
717	C₂×#41	C₂²⋊D₄₇	1	1	yes	characteristic
718	C₂×#41	C₂²×D₄₇	1	1	yes	characteristic
719	C₂²×Q₈	—	47	2	no	—
720	C₂²×Q₈	C₂²×D₄₇	1	2	yes	—
721	C₂²×D₄	—	47	2	no	—
722	C₂²×D₄	—	94	1	no	—
723	#135	—	188	4	no	—
724	C₂×Q₁₆	—	47	1	no	—
725	C₂×Q₁₆	—	47	2	no	—
726	C₂×Q₁₆	—	47	2	no	—
727	C₂×Q₁₆	—	47	2	no	—
728	C₂×Q₁₆	—	47	2	no	—
729	C₂×Q₁₆	—	188	4	no	—
730	C₂×SD₁₆	—	47	1	no	—
731	C₂×SD₁₆	—	47	2	no	—
732	C₂×SD₁₆	—	47	2	no	—
733	C₂×SD₁₆	—	47	2	no	—
734	C₂×SD₁₆	—	47	2	no	—
735	C₂×SD₁₆	—	47	2	no	—
736	C₂×SD₁₆	—	47	1	no	—
737	C₂×SD₁₆	—	188	4	no	—
738	C₂×D₈	—	47	2	no	—
739	C₂×D₈	—	47	1	no	—
740	C₂²×C₈	—	47	2	no	—
741	C₂²×C₈	—	47	2	no	—
742	C₂²×C₈	—	47	2	no	—
743	C₄⋊Q₈	—	2	1	no	—
744	C₄⋊Q₈	—	2	1	no	—
745	C₄⋊Q₈	—	47	1	no	—
746	C₄⋊Q₈	—	94	1	no	—
747	C₄⋊Q₈	C₂²×D₄₇	1	1	yes	characteristic
748	C₄⋊Q₈	C₂²×D₄₇	1	1	yes	characteristic
749	#127	—	47	1	no	—
750	#126	—	2	2	no	—
751	#126	—	2	2	no	—
752	#126	—	2	2	no	—
753	#126	—	94	2	no	—
754	#126	—	94	2	no	—
755	#126	—	94	1	no	—
756	#125	—	2	2	no	—
757	#125	—	2	2	no	—
758	#125	—	2	1	no	—
759	#125	—	47	1	no	—
760	#125	C₂²×D₄₇	1	2	yes	—
761	#124	—	2	2	no	—
762	#124	—	47	1	no	—
763	#124	—	47	2	no	—
764	#124	—	47	2	no	—
765	#124	—	47	2	no	—
766	#124	—	94	1	no	—
767	#124	—	94	2	no	—
768	#124	—	94	2	no	—
769	#124	—	94	2	no	—
770	#124	C₂²×D₄₇	1	2	yes	—
771	#123	—	2	2	no	—
772	#123	—	2	2	no	—
773	#123	—	2	2	no	—
774	#123	—	94	1	no	—
775	#123	—	94	2	no	—
776	#123	—	94	2	no	—
777	#123	—	94	2	no	—
778	C₂²⋊Q₈	—	2	1	no	—
779	C₂²⋊Q₈	—	2	1	no	—
780	C₂²⋊Q₈	—	2	1	no	—
781	C₂²⋊Q₈	—	2	2	no	—
782	C₂²⋊Q₈	—	2	2	no	—
783	C₂²⋊Q₈	—	47	2	no	—
784	C₂²⋊Q₈	—	47	1	no	—
785	C₂²⋊Q₈	—	94	1	no	—
786	C₂²⋊Q₈	—	94	2	no	—
787	C₂²⋊Q₈	—	94	2	no	—
788	C₂²⋊Q₈	C₂²×D₄₇	1	2	yes	—
789	C₂²⋊Q₈	C₂²×D₄₇	1	2	yes	—
790	#121	—	2	2	no	—
791	#121	—	47	2	no	—
792	#121	—	47	1	no	—
793	#121	—	94	2	no	—
794	#121	—	94	1	no	—
795	#121	—	94	1	no	—
796	#121	—	94	1	no	—
797	#121	—	94	2	no	—
798	#121	C₂²×D₄₇	1	2	yes	—
799	#120	—	94	2	no	—
800	#120	—	94	2	no	—
801	C₄×Q₈	—	2	1	no	—
802	C₄×Q₈	—	2	2	no	—
803	C₄×Q₈	—	2	2	no	—
804	C₄×Q₈	—	2	1	no	—
805	C₄×Q₈	—	47	2	no	—
806	C₄×Q₈	—	47	1	no	—
807	C₄×Q₈	C₂²⋊D₄₇	1	1	yes	characteristic
808	C₄×Q₈	C₂²×D₄₇	1	1	yes	characteristic
809	C₄×Q₈	C₂²×D₄₇	1	2	yes	—
810	C₄×Q₈	C₂²×D₄₇	1	2	yes	—
811	C₄×Q₈	C₂²×D₄₇	1	2	yes	—
812	C₄×Q₈	C₂²×D₄₇	1	1	yes	characteristic
813	C₄×Q₈	C₂²×D₄₇	1	1	yes	characteristic
814	C₄×D₄	—	2	1	no	—
815	C₄×D₄	—	2	2	no	—
816	C₄×D₄	—	2	1	no	—
817	C₄×D₄	—	2	1	no	—
818	C₄×D₄	—	2	2	no	—
819	C₄×D₄	—	47	1	no	—
820	C₄×D₄	—	47	2	no	—
821	C₄×D₄	—	94	1	no	—
822	C₄×D₄	—	94	2	no	—
823	C₄×D₄	—	94	1	no	—
824	C₄×D₄	—	94	1	no	—
825	C₄×D₄	—	94	2	no	—
826	C₄×D₄	—	94	1	no	—
827	C₄×D₄	—	94	1	no	—
828	C₄×D₄	C₂²⋊D₄₇	1	1	yes	characteristic
829	C₄×D₄	C₂²⋊D₄₇	1	2	yes	—
830	C₄×D₄	C₂²×D₄₇	1	1	yes	characteristic
831	C₄×D₄	C₂²×D₄₇	1	1	yes	characteristic
832	C₄×D₄	C₂²×D₄₇	1	1	yes	characteristic
833	C₄×D₄	C₂²×D₄₇	1	2	yes	—
834	#117	—	2	1	no	—
835	#117	—	2	1	no	—
836	#117	—	2	2	no	—
837	#117	—	2	1	no	—
838	#117	—	2	2	no	—
839	#117	—	94	1	no	—
840	#117	—	94	1	no	—
841	#117	—	94	2	no	—
842	#117	C₂²⋊D₄₇	1	2	yes	—
843	#117	C₂²⋊D₄₇	1	1	yes	characteristic
844	#117	C₂²×D₄₇	1	1	yes	characteristic
845	C₂×C₄⋊C₄	—	2	2	no	—
846	C₂×C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
847	C₂×C₂²⋊C₄	—	94	2	no	—
848	C₂×C₂²⋊C₄	—	94	2	no	—
849	C₂×C₂²⋊C₄	—	94	2	no	—
850	C₂×C₄²	—	2	2	no	—
851	C₂×C₄²	—	2	1	no	—
852	C₂×C₄²	C₂²×D₄₇	1	2	yes	—
853	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
854	#107	—	47	1	no	—
855	#107	—	47	2	no	—
856	#107	—	47	1	no	—
857	#106	—	47	1	no	—
858	#106	—	47	2	no	—
859	#106	—	47	1	no	—
860	C₄⋊C₈	—	47	2	no	—
861	C₄⋊C₈	—	47	1	no	—
862	C₄⋊C₈	—	47	1	no	—
863	C₄⋊C₈	—	47	1	no	—
864	C₄⋊C₈	—	47	2	no	—
865	C₄⋊C₈	—	47	2	no	—
866	C₄⋊C₈	—	47	1	no	—
867	#103	—	47	1	no	—
868	#103	—	47	1	no	—
869	#103	—	47	2	no	—
870	#103	—	47	2	no	—
871	#103	—	47	1	no	—
872	#103	—	47	2	no	—
873	#103	—	47	2	no	—
874	#103	—	47	2	no	—
875	#103	—	47	2	no	—
876	#103	—	47	2	no	—
877	#103	—	47	1	no	—
878	#102	—	47	1	no	—
879	#102	—	47	1	no	—
880	#102	—	47	1	no	—
881	#102	—	47	2	no	—
882	#102	—	47	2	no	—
883	#102	—	47	2	no	—
884	#102	—	47	2	no	—
885	#102	—	47	2	no	—
886	#102	—	47	1	no	—
887	C₂²⋊C₈	—	47	2	no	—
888	C₂²⋊C₈	—	47	2	no	—
889	C₂²⋊C₈	—	47	1	no	—
890	C₂²⋊C₈	—	47	1	no	—
891	C₄×C₈	—	47	1	no	—
892	C₄×C₈	—	47	1	no	—
893	C₄×C₈	—	47	2	no	—
894	C₄×C₈	—	47	2	no	—
895	C₂⁴	—	94	2	no	—
896	#41	—	2	4	no	—
897	#41	—	2	2	no	—
898	#41	—	4	1	no	—
899	#41	—	4	4	no	—
900	#41	—	188	2	no	—
901	#41	—	188	2	no	—
902	C₂×Q₈	—	2	2	no	—
903	C₂×Q₈	—	2	1	no	—
904	C₂×Q₈	—	2	4	no	—
905	C₂×Q₈	—	4	2	no	—
906	C₂×Q₈	—	47	1	no	—
907	C₂×Q₈	—	47	2	no	—
908	C₂×Q₈	—	94	2	no	—
909	C₂×Q₈	—	188	2	no	—
910	C₂×Q₈	—	188	2	no	—
911	C₂×Q₈	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
912	C₂×Q₈	C₂³×D₄₇	1	2	yes	—
913	C₂×Q₈	C₂³×D₄₇	1	1	yes	characteristic
914	C₂×D₄	—	2	1	no	—
915	C₂×D₄	—	2	2	no	—
916	C₂×D₄	—	47	1	no	—
917	C₂×D₄	—	47	2	no	—
918	C₂×D₄	—	94	1	no	—
919	C₂×D₄	—	94	2	no	—
920	C₂×D₄	—	94	2	no	—
921	C₂×D₄	—	94	1	no	—
922	C₂×D₄	—	94	2	no	—
923	C₂×D₄	—	94	1	no	—
924	C₂×D₄	—	188	2	no	—
925	C₂×D₄	—	188	2	no	—
926	C₂×D₄	—	188	4	no	—
927	C₂×D₄	C₂×C₂²⋊D₄₇	1	2	yes	—
928	C₂×D₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
929	C₂×D₄	C₂³×D₄₇	1	1	yes	characteristic
930	C₂²×C₄	—	2	2	no	—
931	C₂²×C₄	—	2	2	no	—
932	C₂²×C₄	—	2	1	no	—
933	C₂²×C₄	—	2	1	no	—
934	C₂²×C₄	—	2	1	no	—
935	C₂²×C₄	—	94	2	no	—
936	C₂²×C₄	—	94	2	no	—
937	C₂²×C₄	—	94	2	no	—
938	C₂²×C₄	—	94	1	no	—
939	C₂²×C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
940	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
941	C₂²×C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
942	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
943	C₂²×C₄	C₂³×D₄₇	1	2	yes	—
944	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
945	Q₁₆	—	94	2	no	—
946	Q₁₆	—	94	4	no	—
947	Q₁₆	—	188	2	no	—
948	Q₁₆	—	188	2	no	—
949	Q₁₆	—	188	2	no	—
950	SD₁₆	—	94	2	no	—
951	SD₁₆	—	94	4	no	—
952	SD₁₆	—	188	1	no	—
953	SD₁₆	—	188	2	no	—
954	SD₁₆	—	188	2	no	—
955	SD₁₆	—	188	2	no	—
956	SD₁₆	—	188	2	no	—
957	D₈	—	188	1	no	—
958	D₈	—	188	2	no	—
959	C₂×C₈	—	47	1	no	—
960	C₂×C₈	—	47	1	no	—
961	C₂×C₈	—	47	1	no	—
962	C₂×C₈	—	47	2	no	—
963	C₂×C₈	—	47	2	no	—
964	C₂×C₈	—	47	1	no	—
965	C₂×C₈	—	188	2	no	—
966	C₂×C₈	—	188	2	no	—
967	C₂×C₈	—	188	2	no	—
968	C₄⋊C₄	—	2	1	no	—
969	C₄⋊C₄	—	2	2	no	—
970	C₄⋊C₄	—	2	2	no	—
971	C₄⋊C₄	—	2	2	no	—
972	C₄⋊C₄	—	2	2	no	—
973	C₄⋊C₄	—	2	1	no	—
974	C₄⋊C₄	—	2	2	no	—
975	C₄⋊C₄	—	2	2	no	—
976	C₄⋊C₄	—	2	1	no	—
977	C₄⋊C₄	—	2	1	no	—
978	C₄⋊C₄	—	2	2	no	—
979	C₄⋊C₄	—	2	1	no	—
980	C₄⋊C₄	—	2	2	no	—
981	C₄⋊C₄	—	47	1	no	—
982	C₄⋊C₄	—	47	1	no	—
983	C₄⋊C₄	—	94	1	no	—
984	C₄⋊C₄	—	94	1	no	—
985	C₄⋊C₄	—	94	1	no	—
986	C₄⋊C₄	—	94	2	no	—
987	C₄⋊C₄	—	94	2	no	—
988	C₄⋊C₄	—	94	1	no	—
989	C₄⋊C₄	—	94	1	no	—
990	C₄⋊C₄	—	94	1	no	—
991	C₄⋊C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
992	C₄⋊C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
993	C₄⋊C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
994	C₄⋊C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
995	C₄⋊C₄	C₂³×D₄₇	1	1	yes	characteristic
996	C₄⋊C₄	C₂³×D₄₇	1	2	yes	—
997	C₄⋊C₄	C₂³×D₄₇	1	1	yes	characteristic
998	C₂²⋊C₄	—	2	2	no	—
999	C₂²⋊C₄	—	2	2	no	—
1000	C₂²⋊C₄	—	2	1	no	—
1001	C₂²⋊C₄	—	2	2	no	—
1002	C₂²⋊C₄	—	2	1	no	—
1003	C₂²⋊C₄	—	2	1	no	—
1004	C₂²⋊C₄	—	2	2	no	—
1005	C₂²⋊C₄	—	2	2	no	—
1006	C₂²⋊C₄	—	94	2	no	—
1007	C₂²⋊C₄	—	94	1	no	—
1008	C₂²⋊C₄	—	94	1	no	—
1009	C₂²⋊C₄	—	94	2	no	—
1010	C₂²⋊C₄	—	94	1	no	—
1011	C₂²⋊C₄	—	94	1	no	—
1012	C₂²⋊C₄	—	94	2	no	—
1013	C₂²⋊C₄	—	94	2	no	—
1014	C₂²⋊C₄	—	94	2	no	—
1015	C₂²⋊C₄	—	94	2	no	—
1016	C₂²⋊C₄	—	94	2	no	—
1017	C₂²⋊C₄	—	94	2	no	—
1018	C₂²⋊C₄	—	94	1	no	—
1019	C₂²⋊C₄	—	94	2	no	—
1020	C₂²⋊C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
1021	C₂²⋊C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
1022	C₂²⋊C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
1023	C₄²	—	2	1	no	—
1024	C₄²	—	2	1	no	—
1025	C₄²	—	2	2	no	—
1026	C₄²	—	2	2	no	—
1027	C₄²	—	2	1	no	—
1028	C₄²	—	2	2	no	—
1029	C₄²	—	94	2	no	—
1030	C₄²	—	94	1	no	—
1031	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
1032	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
1033	C₄²	C₂×C₂²⋊D₄₇	1	2	yes	—
1034	C₄²	C₂×C₂²⋊D₄₇	1	2	yes	—
1035	C₄²	C₂³×D₄₇	1	1	yes	characteristic
1036	C₄²	C₂³×D₄₇	1	2	yes	—
1037	C₄²	C₂³×D₄₇	1	1	yes	characteristic
1038	C₂³	—	2	1	no	—
1039	C₂³	—	94	1	no	—
1040	C₂³	—	94	2	no	—
1041	C₂³	—	376	2	no	—
1042	C₂³	—	376	2	no	—
1043	C₂³	—	188	4	no	—
1044	C₂³	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
1045	C₂³	C₂²×C₂²⋊D₄₇	1	2	yes	—
1046	Q₈	—	2	2	no	—
1047	Q₈	—	2	1	no	—
1048	Q₈	—	2	2	no	—
1049	Q₈	—	2	2	no	—
1050	Q₈	—	4	4	no	—
1051	Q₈	—	4	2	no	—
1052	Q₈	—	94	2	no	—
1053	Q₈	—	94	1	no	—
1054	Q₈	—	94	1	no	—
1055	Q₈	—	94	2	no	—
1056	Q₈	—	376	2	no	—
1057	Q₈	#13094070	1	2	yes	—
1058	D₄	—	2	4	no	—
1059	D₄	—	2	1	no	—
1060	D₄	—	2	1	no	—
1061	D₄	—	4	2	no	—
1062	D₄	—	4	4	no	—
1063	D₄	—	94	2	no	—
1064	D₄	—	94	1	no	—
1065	D₄	—	94	1	no	—
1066	D₄	—	94	2	no	—
1067	D₄	—	376	1	no	—
1068	D₄	—	376	2	no	—
1069	D₄	—	376	1	no	—
1070	D₄	—	376	2	no	—
1071	D₄	—	188	4	no	—
1072	D₄	—	188	2	no	—
1073	D₄	#13094044	1	4	yes	complemented
1074	C₂×C₄	—	2	4	no	—
1075	C₂×C₄	—	2	1	no	—
1076	C₂×C₄	—	2	2	no	—
1077	C₂×C₄	—	2	2	no	—
1078	C₂×C₄	—	2	1	no	—
1079	C₂×C₄	—	2	2	no	—
1080	C₂×C₄	—	2	1	no	—
1081	C₂×C₄	—	2	1	no	—
1082	C₂×C₄	—	2	1	no	—
1083	C₂×C₄	—	2	2	no	—
1084	C₂×C₄	—	2	2	no	—
1085	C₂×C₄	—	4	2	no	—
1086	C₂×C₄	—	4	1	no	—
1087	C₂×C₄	—	4	2	no	—
1088	C₂×C₄	—	4	4	no	—
1089	C₂×C₄	—	4	2	no	—
1090	C₂×C₄	—	4	4	no	—
1091	C₂×C₄	—	4	2	no	—
1092	C₂×C₄	—	94	1	no	—
1093	C₂×C₄	—	94	1	no	—
1094	C₂×C₄	—	94	1	no	—
1095	C₂×C₄	—	94	2	no	—
1096	C₂×C₄	—	376	2	no	—
1097	C₂×C₄	—	376	2	no	—
1098	C₂×C₄	—	376	2	no	—
1099	C₂×C₄	—	188	2	no	—
1100	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
1101	C₂×C₄	C₂²×C₂²⋊D₄₇	1	2	yes	—
1102	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
1103	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
1104	C₂×C₄	C₂²×C₂²⋊D₄₇	1	2	yes	—
1105	C₂×C₄	C₂²×C₂²⋊D₄₇	1	2	yes	—
1106	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
1107	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
1108	C₂×C₄	C₂⁴×D₄₇	1	1	yes	characteristic
1109	C₈	—	94	2	no	—
1110	C₈	—	94	2	no	—
1111	C₈	—	94	1	no	—
1112	C₈	—	94	1	no	—
1113	C₈	—	94	1	no	—
1114	C₈	—	94	1	no	—
1115	C₂²	—	2	2	no	—
1116	C₂²	—	2	2	no	—
1117	C₂²	—	2	1	no	—
1118	C₂²	—	2	1	no	—
1119	C₂²	—	2	1	no	—
1120	C₂²	—	4	1	no	—
1121	C₂²	—	4	1	no	—
1122	C₂²	—	4	1	no	—
1123	C₂²	—	188	2	no	—
1124	C₂²	—	188	1	no	—
1125	C₂²	—	188	1	no	—
1126	C₂²	—	188	2	no	—
1127	C₂²	—	188	2	no	—
1128	C₂²	—	188	1	no	—
1129	C₂²	—	752	4	no	—
1130	C₂²	C₂×#13094044	1	4	yes	—
1131	C₂²	C₂³×C₂²⋊D₄₇	1	1	yes	characteristic
1132	C₄	—	2	1	no	—
1133	C₄	—	2	2	no	—
1134	C₄	—	2	2	no	—
1135	C₄	—	2	1	no	—
1136	C₄	—	2	2	no	—
1137	C₄	—	2	1	no	—
1138	C₄	—	2	2	no	—
1139	C₄	—	2	1	no	—
1140	C₄	—	4	2	no	—
1141	C₄	—	4	1	no	—
1142	C₄	—	4	2	no	—
1143	C₄	—	4	1	no	—
1144	C₄	—	188	2	no	—
1145	C₄	—	188	1	no	—
1146	C₄	—	188	1	no	—
1147	C₄	—	188	1	no	—
1148	C₄	C₂×#13094044	1	2	yes	—
1149	C₄	C₂×#13094070	1	1	yes	characteristic
1150	C₄	#15689959	1	1	yes	characteristic
1151	C₂	—	2	4	no	—
1152	C₂	—	4	1	no	—
1153	C₂	—	8	1	no	—
1154	C₂	—	376	1	no	—
1155	C₂	—	376	2	no	—
1156	C₂	#20257057	1	1	yes	characteristic
1157	C₂	C₂²×#13094044	1	1	yes	characteristic
1158	C₂	#20258175	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂³×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	#61956
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₄×#41 ◁ #3482

Complements

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

N	H ≅ G/N	type
1. #20257349	C₂	semidirect
2. #20256384	C₂	semidirect
3. #20256372	C₂	semidirect
4. #20256084	C₂	semidirect
5. #20256073	C₂	semidirect
6. #20255269	C₂	semidirect
7. #20255247	C₂	semidirect
8. #20255217	C₂	semidirect
9. #20255195	C₂	semidirect
10. D₄×#10625337	C₂	semidirect
11. #20255125	C₂	semidirect
12. #20255096	C₂	semidirect
13. D₄×#10625336	C₂	semidirect
14. #20254735	C₂	semidirect
15. #20254719	C₂	semidirect
16. #20254349	C₂	semidirect
17. #20254340	C₂	semidirect
18. #20253468	C₂	semidirect
19. #20253406	C₂	semidirect
20. #20252843	C₂	semidirect
21. C₂×#15689345	C₂	semidirect
22. #20252499	C₂	semidirect
23. C₄₇×#3482	C₂	semidirect
24. C₂×#13094044	C₂²	semidirect
25. C₂²×#10625337	C₂²	semidirect
44. #15689505	C₂²	semidirect
45. #15689502	C₂²	semidirect
48. #15689480	C₂²	semidirect
49. #15689475	C₂²	semidirect
51. #15689464	C₂²	semidirect
52. #15689453	C₂²	semidirect
55. #15689430	C₂²	semidirect
56. #15689430	C₂²	semidirect
57. #15689427	C₂²	semidirect
58. #15689423	C₂²	semidirect
59. #15689420	C₂²	semidirect
60. #15689405	C₂²	semidirect
62. #15689362	C₂²	semidirect
63. #15689362	C₂²	semidirect
67. #15689350	C₂²	semidirect
72. #15689345	C₂²	semidirect
73. #15689345	C₂²	semidirect
74. #15689345	C₂²	semidirect
75. #15689345	C₂²	semidirect
76. #15689345	C₂²	semidirect
77. #15689342	C₂²	semidirect
79. #15689338	C₂²	semidirect
80. #15689335	C₂²	semidirect
81. #15689333	C₂²	semidirect
82. #15689330	C₂²	semidirect
83. #15689328	C₂²	semidirect
87. #15689285	C₂²	semidirect
88. #15689283	C₂²	semidirect
89. #15689283	C₂²	semidirect
90. #15689279	C₂²	semidirect
91. #15689278	C₂²	semidirect
95. #15689261	C₂²	semidirect
97. Q₈×C₄₇⋊C₈	C₂²	semidirect
98. Q₈×C₄₇⋊C₈	C₂²	semidirect
99. C₄×#10625337	C₂²	semidirect
100. C₄×#10625337	C₂²	semidirect
101. C₄×#10625337	C₂²	semidirect
103. C₄×#10625336	C₂²	semidirect
104. C₄×#10625336	C₂²	semidirect
105. C₄×#10625335	C₂²	semidirect
109. D₄×C₄₇⋊C₈	C₂²	semidirect
110. D₄×C₄₇⋊C₈	C₂²	semidirect
111. #15689176	C₂²	semidirect
112. #15689176	C₂²	semidirect
113. C₂×C₄⋊(C₄₇⋊C₈)	C₂²	semidirect
114. C₂×C₄⋊(C₄₇⋊C₈)	C₂²	semidirect
115. #15689117	C₂²	semidirect
116. C₂×#13093947	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
478. D₄×C₄₇	#135	semidirect
573. #3482	D₄₇	semidirect
607. #557	C₂×D₄₇	semidirect
610. #556	C₂×D₄₇	semidirect
613. #552	C₂×D₄₇	semidirect
618. #548	C₂×D₄₇	semidirect
627. #533	C₂×D₄₇	semidirect
632. #529	C₂×D₄₇	semidirect
637. C₄×#41	C₂×D₄₇	semidirect
638. C₂×C₄×Q₈	C₂×D₄₇	semidirect
714. C₄₇	#61956	semidirect
1073. D₄	#13094044	semidirect

Maximal subgroups

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

subgroup	index
#20257349	2
#20256384	2
#20256372	2
#20256084	2
#20256073	2
#20255269	2
#20255247	2
#20255217	2
#20255195	2
D₄×#10625337	2
#20255125	2
#20255096	2
D₄×#10625336	2
#20254735	2
#20254719	2
#20254349	2
#20254340	2
#20253468	2
#20253406	2
#20252843	2
C₂×#15689345	2
#20252499	2
C₄₇×#3482	2
#61956	47