Subgroups — #27097705

Order 12032.

1890 conjugacy classes of subgroups.

The subgroup lattice has 1162 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20256952	C₂	1	1	yes	maximal, characteristic, complemented
2	#20256372	C₂	1	1	yes	maximal, characteristic, complemented
3	#20256251	C₂	1	1	yes	maximal, characteristic, complemented
4	#20256037	C₂	1	1	yes	maximal, characteristic, complemented
5	#20256033	C₂	1	1	yes	maximal, characteristic, complemented
6	#20255806	C₂	1	1	yes	maximal, characteristic, complemented
7	#20255750	C₂	1	2	yes	maximal, complemented
8	#20255316	C₂	1	1	yes	maximal, characteristic, complemented
9	#20255310	C₂	1	1	yes	maximal, characteristic, complemented
10	#20255223	C₂	1	2	yes	maximal, complemented
11	#20255217	C₂	1	2	yes	maximal, complemented
12	#20255106	C₂	1	1	yes	maximal, characteristic, complemented
13	#20255069	C₂	1	2	yes	maximal, complemented
14	#20253970	C₂	1	1	yes	maximal, characteristic, complemented
15	#20253952	C₂	1	2	yes	maximal, complemented
16	#20253406	C₂	1	2	yes	maximal, complemented
17	#20253400	C₂	1	2	yes	maximal, complemented
18	#20253396	C₂	1	1	yes	maximal, characteristic, complemented
19	#20253392	C₂	1	1	yes	maximal, characteristic, complemented
20	#41×C₄₇⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
21	C₄×#13094044	C₂	1	2	yes	maximal, complemented
22	C₂×C₄×#10625334	C₂	1	1	yes	maximal, characteristic, complemented
23	C₄₇×#3475	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#13094044	C₂²	1	2	yes	—
25	C₂²×#10625334	C₂²	1	1	yes	characteristic
26	#15689846	C₂²	1	1	yes	characteristic, complemented
27	#15689838	C₂²	1	1	yes	characteristic, complemented
28	#15689833	C₂²	1	1	yes	characteristic, complemented
29	#15689823	—	2	1	no	—
30	#15689814	—	2	1	no	—
31	#15689813	C₂²	1	2	yes	—
32	#15689802	—	2	2	no	—
33	#15689778	C₂²	1	1	yes	characteristic, complemented
34	#15689769	C₂²	1	2	yes	—
35	#15689680	C₂²	1	1	yes	characteristic
36	#15689657	C₂²	1	2	yes	complemented
37	#15689651	—	2	2	no	—
38	#15689630	—	2	1	no	—
39	C₄×#10625350	C₂²	1	2	yes	complemented
40	C₂×C₄×D₁₈₈	C₂²	1	1	yes	characteristic
41	#117×D₄₇	—	2	1	no	—
42	#15689526	C₂²	1	1	yes	characteristic, complemented
43	#15689522	C₂²	1	2	yes	complemented
44	#15689505	C₂²	1	2	yes	—
45	#15689502	C₂²	1	1	yes	characteristic, complemented
46	#15689480	C₂²	1	2	yes	complemented
47	#15689477	C₂²	1	2	yes	complemented
48	#15689475	C₂²	1	1	yes	characteristic, complemented
49	#15689473	C₂²	1	1	yes	characteristic, complemented
50	#15689464	C₂²	1	2	yes	complemented
51	#15689461	C₂²	1	2	yes	complemented
52	#15689453	C₂²	1	2	yes	—
53	#15689451	C₂²	1	2	yes	—
54	#15689447	C₂²	1	2	yes	complemented
55	#15689444	C₂²	1	2	yes	complemented
56	#15689430	C₂²	1	2	yes	complemented
57	#15689427	C₂²	1	2	yes	complemented
58	#15689423	C₂²	1	2	yes	complemented
59	#15689420	C₂²	1	2	yes	complemented
60	#15689413	C₂²	1	1	yes	characteristic, complemented
61	#15689413	C₂²	1	1	yes	characteristic, complemented
62	#15689410	C₂²	1	1	yes	characteristic, complemented
63	#15689410	C₂²	1	1	yes	characteristic, complemented
64	#15689362	C₂²	1	2	yes	—
65	#15689362	C₂²	1	2	yes	—
66	#15689362	C₂²	1	2	yes	complemented
67	#15689357	C₂²	1	2	yes	—
68	#15689354	C₂²	1	2	yes	complemented
69	#15689350	C₂²	1	2	yes	complemented
70	#15689345	C₂²	1	2	yes	complemented
71	#15689342	C₂²	1	2	yes	complemented
72	#15689338	C₂²	1	2	yes	—
73	#15689335	C₂²	1	2	yes	—
74	#15689328	C₂²	1	1	yes	characteristic, complemented
75	#15689328	C₂²	1	1	yes	characteristic, complemented
76	#15689325	C₂²	1	1	yes	characteristic, complemented
77	#15689325	C₂²	1	1	yes	characteristic, complemented
78	#15689285	C₂²	1	2	yes	complemented
79	#15689283	C₂²	1	2	yes	complemented
80	#15689274	C₂²	1	2	yes	—
81	#15689273	C₂²	1	2	yes	—
82	#15689268	C₂²	1	2	yes	—
83	#15689266	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	2	yes	complemented
88	C₄×#10625337	C₂²	1	2	yes	complemented
89	C₄×#10625336	C₂²	1	2	yes	complemented
90	C₄×#10625336	C₂²	1	2	yes	complemented
91	C₄×#10625336	C₂²	1	2	yes	complemented
92	C₄×#10625335	C₂²	1	2	yes	complemented
93	C₄×#10625335	C₂²	1	2	yes	complemented
94	C₄×#10625335	C₂²	1	2	yes	complemented
95	C₄×#10625334	C₂²	1	1	yes	characteristic
96	C₄×#10625334	C₂²	1	1	yes	characteristic
97	C₄×#10625334	C₂²	1	1	yes	characteristic
98	C₄×#10625334	C₂²	1	1	yes	characteristic
99	C₄×#10625334	C₂²	1	2	yes	—
100	C₄×#10625334	C₂²	1	1	yes	characteristic
101	C₄×#10625334	C₂²	1	1	yes	characteristic
102	C₄×#10625334	C₂²	1	1	yes	characteristic
103	C₄×#10625334	C₂²	1	1	yes	characteristic
104	D₄×C₄₇⋊C₈	C₂²	1	2	yes	—
105	D₄×C₄₇⋊C₈	C₂²	1	2	yes	—
106	D₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic, complemented
107	D₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic, complemented
108	#15689176	C₂²	1	1	yes	characteristic
109	#15689176	C₂²	1	2	yes	complemented
110	#15689159	C₂²	1	2	yes	complemented
111	C₂×#13093957	C₂²	1	1	yes	characteristic
112	#15689119	C₂²	1	2	yes	complemented
113	#15689117	C₂²	1	2	yes	complemented
114	C₂×#13093945	C₂²	1	1	yes	characteristic
115	C₂×#13093944	C₂²	1	1	yes	characteristic
116	C₂×C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
117	C₂×C₄×C₄₇⋊C₈	C₂²	1	2	yes	complemented
118	C₄₇×#556	C₂²	1	1	yes	characteristic, complemented
119	C₄₇×#555	C₂²	1	1	yes	characteristic, complemented
120	C₄₇×#554	C₂²	1	1	yes	characteristic, complemented
121	C₄₇×#553	—	2	1	no	—
122	C₄₇×#552	—	2	1	no	—
123	C₄₇×#552	C₂²	1	2	yes	—
124	C₄₇×#551	—	2	2	no	—
125	C₄₇×#547	C₂²	1	1	yes	characteristic, complemented
126	C₄₇×#546	C₂²	1	2	yes	—
127	C₄₇×#533	C₂²	1	1	yes	characteristic
128	C₄₇×#529	—	2	2	no	—
129	C₄₇×#529	C₂²	1	2	yes	complemented
130	C₄₇×#525	—	2	1	no	—
131	C₄×#41×C₄₇	C₂²	1	1	yes	characteristic
132	C₄×#41×C₄₇	C₂²	1	2	yes	complemented
133	C₂×C₄×D₄×C₄₇	C₂²	1	1	yes	characteristic
134	C₂×#117×C₄₇	—	2	1	no	—
135	C₂×#10625350	C₂³	1	2	yes	—
136	C₂²×D₁₈₈	C₂³	1	1	yes	characteristic
137	C₂²×C₄×D₄₇	—	2	1	no	—
138	#13094044	—	2	8	no	—
139	C₂×#10625337	C₂³	1	2	yes	—
140	C₂×#10625337	C₂³	1	2	yes	—
141	C₂×#10625335	C₂³	1	2	yes	—
142	C₂×#10625335	C₂³	1	2	yes	—
143	C₂×#10625336	C₂³	1	2	yes	—
144	C₂×#10625336	C₂³	1	2	yes	—
145	C₂×#10625334	—	2	4	no	—
146	C₂×#10625334	C₂³	1	1	yes	characteristic
147	C₂×#10625334	C₂³	1	1	yes	characteristic
148	C₂×#10625334	C₂³	1	1	yes	characteristic
149	C₂×#10625334	C₂³	1	1	yes	characteristic
150	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
151	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
152	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
153	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
154	#13094024	C₂³	1	1	yes	characteristic
155	#13094024	C₂³	1	1	yes	characteristic
156	#13094019	—	2	2	no	—
157	#13094018	—	2	2	no	—
158	#13094017	—	2	2	no	—
159	#13094016	—	2	1	no	—
160	#13094016	C₂³	1	2	yes	—
161	#13094014	—	2	2	no	—
162	#13094012	C₂³	1	2	yes	—
163	#13094010	—	2	2	no	—
164	#13094009	—	2	2	no	—
165	#13094007	—	2	2	no	—
166	#13094006	—	2	2	no	—
167	#13094005	—	2	2	no	—
168	#13094003	—	2	1	no	—
169	#13094003	C₂³	1	2	yes	—
170	#13094003	C₂³	1	2	yes	—
171	#13094002	—	2	2	no	—
172	#13094000	—	2	1	no	—
173	#13094000	—	2	1	no	—
174	#13093998	C₂³	1	2	yes	—
175	#13093997	—	2	2	no	—
176	#13093995	—	2	1	no	—
177	#13093995	—	2	1	no	—
178	#13093992	—	2	2	no	—
179	C₄×Dic₉₄	—	2	1	no	—
180	C₄×Dic₉₄	C₂³	1	2	yes	—
181	C₄×Dic₉₄	C₂³	1	2	yes	—
182	C₄×D₁₈₈	—	2	1	no	—
183	C₄×D₁₈₈	—	2	1	no	—
184	C₄×D₁₈₈	C₂³	1	2	yes	—
185	C₄×D₁₈₈	C₂³	1	1	yes	characteristic
186	C₄×D₁₈₈	C₂³	1	1	yes	characteristic
187	C₄×D₁₈₈	C₂³	1	1	yes	characteristic
188	C₄×D₁₈₈	C₂³	1	1	yes	characteristic
189	C₄×C₂²⋊D₄₇	—	2	2	no	—
190	C₄×C₂²⋊D₄₇	—	2	2	no	—
191	C₄×C₂²⋊D₄₇	—	2	2	no	—
192	#13093983	—	2	1	no	—
193	#13093983	C₂³	1	2	yes	—
194	#13093982	—	2	1	no	—
195	#13093982	—	2	1	no	—
196	#13093981	—	2	2	no	—
197	#13093981	—	2	2	no	—
198	#13093980	—	2	2	no	—
199	C₂×C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic
200	C₄⋊C₄×D₄₇	—	2	1	no	—
201	C₄⋊C₄×D₄₇	—	2	1	no	—
202	C₂×(C₂×D₄₇)⋊C₄	—	2	1	no	—
203	C₂²⋊C₄×D₄₇	—	2	2	no	—
204	C₄²×D₄₇	—	2	2	no	—
205	#13093957	C₂³	1	1	yes	characteristic
206	#13093957	C₂³	1	2	yes	—
207	#13093957	C₂³	1	2	yes	—
208	#13093957	C₂³	1	1	yes	characteristic
209	#13093957	C₂³	1	1	yes	characteristic
210	#13093957	C₂³	1	1	yes	characteristic
211	#13093955	C₂³	1	2	yes	—
212	#13093955	C₂³	1	2	yes	—
213	#13093955	C₂³	1	2	yes	—
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	2	yes	—
221	#13093948	C₂³	1	2	yes	—
222	#13093948	C₂³	1	2	yes	—
223	#13093947	C₂³	1	2	yes	—
224	#13093947	C₂³	1	2	yes	—
225	#13093947	C₂³	1	2	yes	—
226	#13093947	C₂³	1	2	yes	—
227	#13093945	C₂³	1	1	yes	characteristic
228	#13093945	C₂³	1	2	yes	—
229	#13093945	C₂³	1	2	yes	—
230	#13093945	C₂³	1	1	yes	characteristic
231	#13093945	C₂³	1	1	yes	characteristic
232	#13093945	C₂³	1	1	yes	characteristic
233	#13093944	C₂³	1	1	yes	characteristic
234	#13093944	C₂³	1	2	yes	—
235	#13093944	C₂³	1	2	yes	—
236	#13093944	C₂³	1	1	yes	characteristic
237	#13093944	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
246	C₄×C₄₇⋊C₈	C₂³	1	2	yes	—
247	C₄×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
248	C₄×C₄₇⋊C₈	C₂³	1	2	yes	—
249	C₂×#41×C₄₇	D₄	1	1	yes	characteristic
250	C₂×#41×C₄₇	C₂³	1	2	yes	—
251	C₂²×D₄×C₄₇	C₂³	1	1	yes	characteristic
252	C₂³×C₄×C₄₇	—	2	1	no	—
253	C₄⋊Q₈×C₄₇	C₂³	1	1	yes	characteristic
254	C₄⋊Q₈×C₄₇	C₂³	1	1	yes	characteristic
255	#126×C₄₇	—	2	2	no	—
256	#126×C₄₇	—	2	2	no	—
257	#126×C₄₇	—	2	2	no	—
258	#125×C₄₇	—	2	2	no	—
259	#125×C₄₇	—	2	1	no	—
260	#125×C₄₇	C₂³	1	2	yes	—
261	#124×C₄₇	—	2	2	no	—
262	#124×C₄₇	C₂³	1	2	yes	—
263	#123×C₄₇	—	2	2	no	—
264	#123×C₄₇	—	2	2	no	—
265	#123×C₄₇	—	2	2	no	—
266	#123×C₄₇	—	2	2	no	—
267	C₂²⋊Q₈×C₄₇	—	2	1	no	—
268	C₂²⋊Q₈×C₄₇	—	2	1	no	—
269	C₂²⋊Q₈×C₄₇	—	2	1	no	—
270	C₂²⋊Q₈×C₄₇	—	2	2	no	—
271	C₂²⋊Q₈×C₄₇	C₂³	1	2	yes	—
272	C₂²⋊Q₈×C₄₇	C₂³	1	2	yes	—
273	#121×C₄₇	—	2	1	no	—
274	#121×C₄₇	—	2	1	no	—
275	#121×C₄₇	—	2	2	no	—
276	#121×C₄₇	C₂³	1	2	yes	—
277	#120×C₄₇	—	2	2	no	—
278	C₄×Q₈×C₄₇	—	2	1	no	—
279	C₄×Q₈×C₄₇	D₄	1	1	yes	characteristic
280	C₄×Q₈×C₄₇	C₂³	1	2	yes	—
281	C₄×Q₈×C₄₇	C₂³	1	2	yes	—
282	C₄×Q₈×C₄₇	C₂³	1	1	yes	characteristic
283	C₄×D₄×C₄₇	—	2	2	no	—
284	C₄×D₄×C₄₇	—	2	2	no	—
285	C₄×D₄×C₄₇	—	2	2	no	—
286	C₄×D₄×C₄₇	—	2	1	no	—
287	C₄×D₄×C₄₇	—	2	1	no	—
288	C₄×D₄×C₄₇	D₄	1	2	yes	—
289	C₄×D₄×C₄₇	D₄	1	1	yes	characteristic
290	C₄×D₄×C₄₇	C₂³	1	1	yes	characteristic
291	C₄×D₄×C₄₇	C₂³	1	1	yes	characteristic
292	C₄×D₄×C₄₇	C₂³	1	1	yes	characteristic
293	C₄×D₄×C₄₇	C₂³	1	1	yes	characteristic
294	C₄×D₄×C₄₇	C₂³	1	2	yes	—
295	C₄×D₄×C₄₇	C₂³	1	2	yes	—
296	C₄×D₄×C₄₇	C₂³	1	1	yes	characteristic
297	#117×C₄₇	—	2	1	no	—
298	#117×C₄₇	—	2	1	no	—
299	#117×C₄₇	—	2	1	no	—
300	#117×C₄₇	—	2	2	no	—
301	#117×C₄₇	—	2	2	no	—
302	#117×C₄₇	—	2	2	no	—
303	#117×C₄₇	D₄	1	1	yes	characteristic
304	#117×C₄₇	D₄	1	2	yes	—
305	#117×C₄₇	C₂³	1	2	yes	—
306	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
307	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
308	C₂×C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
309	C₂×C₂²⋊C₄×C₄₇	—	2	1	no	—
310	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
311	C₂×C₄²×C₄₇	—	2	2	no	—
312	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
313	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
314	C₂⁴×C₄₇	—	2	1	no	—
315	C₂³×D₄₇	—	2	1	no	—
316	#41×C₄₇	—	2	4	no	—
317	#41×C₄₇	—	2	4	no	—
318	#41×C₄₇	—	4	2	no	—
319	C₂×Q₈×C₄₇	—	2	1	no	—
320	C₂×Q₈×C₄₇	C₂×D₄	1	1	yes	characteristic
321	C₂×Q₈×C₄₇	C₂⁴	1	2	yes	—
322	C₂×D₄×C₄₇	—	2	2	no	—
323	C₂×D₄×C₄₇	—	2	2	no	—
324	C₂×D₄×C₄₇	—	2	2	no	—
325	C₂×D₄×C₄₇	—	2	1	no	—
326	C₂×D₄×C₄₇	—	4	1	no	—
327	C₂×D₄×C₄₇	C₂×D₄	1	2	yes	—
328	C₂×D₄×C₄₇	C₂×D₄	1	1	yes	characteristic
329	C₂×D₄×C₄₇	C₂⁴	1	1	yes	characteristic
330	C₂×D₄×C₄₇	C₂⁴	1	1	yes	characteristic
331	C₂²×C₄×C₄₇	—	2	1	no	—
332	C₂²×C₄×C₄₇	—	2	1	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	—	2	2	no	—
338	C₂²×C₄×C₄₇	—	4	4	no	—
339	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
340	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
341	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
342	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
343	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
344	C₂²×C₄×C₄₇	C₂⁴	1	2	yes	—
345	C₂×C₂²⋊D₄₇	—	2	2	no	—
346	C₂×C₂²⋊D₄₇	—	2	2	no	—
347	C₂²×Dic₄₇	—	2	1	no	—
348	#10625350	—	2	4	no	—
349	#10625350	—	4	2	no	—
350	C₂×D₁₈₈	—	2	2	no	—
351	C₂×D₁₈₈	—	2	1	no	—
352	C₂×D₁₈₈	—	4	1	no	—
353	C₂×D₁₈₈	C₂⁴	1	1	yes	characteristic
354	C₂×D₁₈₈	C₂⁴	1	1	yes	characteristic
355	C₂×C₄×D₄₇	—	2	1	no	—
356	C₂×C₄×D₄₇	—	2	2	no	—
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	—	4	4	no	—
362	C₂×Dic₉₄	—	2	1	no	—
363	C₂×Dic₉₄	C₂⁴	1	2	yes	—
364	C₄⋊C₄×C₄₇	—	2	1	no	—
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	1	no	—
369	C₄⋊C₄×C₄₇	—	2	2	no	—
370	C₄⋊C₄×C₄₇	—	2	2	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	C₂×D₄	1	1	yes	characteristic
375	C₄⋊C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
376	C₄⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
377	C₄⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
378	C₄⋊C₄×C₄₇	C₂⁴	1	1	yes	characteristic
379	C₄⋊C₄×C₄₇	C₂⁴	1	1	yes	characteristic
380	C₄⋊C₄×C₄₇	C₂⁴	1	2	yes	—
381	C₂²⋊C₄×C₄₇	—	2	2	no	—
382	C₂²⋊C₄×C₄₇	—	2	2	no	—
383	C₂²⋊C₄×C₄₇	—	2	2	no	—
384	C₂²⋊C₄×C₄₇	—	2	1	no	—
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	1	no	—
389	C₂²⋊C₄×C₄₇	—	2	1	no	—
390	C₂²⋊C₄×C₄₇	—	2	2	no	—
391	C₂²⋊C₄×C₄₇	—	2	2	no	—
392	C₂²⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
393	C₂²⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
394	C₂²⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
395	C₄²×C₄₇	—	2	2	no	—
396	C₄²×C₄₇	—	2	2	no	—
397	C₄²×C₄₇	—	2	2	no	—
398	C₄²×C₄₇	C₂×D₄	1	2	yes	—
399	C₄²×C₄₇	C₂×D₄	1	2	yes	—
400	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
401	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
402	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
403	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
404	C₄²×C₄₇	C₂⁴	1	2	yes	—
405	C₂²⋊Dic₄₇	—	2	2	no	—
406	C₂²⋊Dic₄₇	—	2	2	no	—
407	C₂²⋊Dic₄₇	—	2	2	no	—
408	#10625337	—	2	4	no	—
409	#10625337	—	4	2	no	—
410	#10625336	—	2	4	no	—
411	#10625336	—	4	2	no	—
412	#10625335	—	2	4	no	—
413	#10625335	—	4	2	no	—
414	#10625334	—	2	2	no	—
415	#10625334	—	2	2	no	—
416	#10625334	—	2	2	no	—
417	#10625334	#41	1	4	yes	complemented
418	(C₂×D₄₇)⋊C₄	—	2	2	no	—
419	(C₂×D₄₇)⋊C₄	—	2	2	no	—
420	(C₂×D₄₇)⋊C₄	—	2	1	no	—
421	(C₂×D₄₇)⋊C₄	—	2	1	no	—
422	(C₂×D₄₇)⋊C₄	—	2	1	no	—
423	(C₂×D₄₇)⋊C₄	—	2	1	no	—
424	(C₂×D₄₇)⋊C₄	—	2	2	no	—
425	(C₂×D₄₇)⋊C₄	—	2	2	no	—
426	C₄⋊Dic₄₇	—	2	1	no	—
427	C₄⋊Dic₄₇	—	2	1	no	—
428	C₄⋊Dic₄₇	—	2	1	no	—
429	C₄⋊Dic₄₇	—	2	1	no	—
430	C₄⋊Dic₄₇	C₂⁴	1	1	yes	characteristic
431	C₄⋊Dic₄₇	C₂⁴	1	1	yes	characteristic
432	C₄⋊Dic₄₇	C₂⁴	1	2	yes	—
433	Dic₄₇⋊C₄	—	2	2	no	—
434	Dic₄₇⋊C₄	—	2	2	no	—
435	Dic₄₇⋊C₄	—	2	2	no	—
436	Dic₄₇⋊C₄	—	2	2	no	—
437	Dic₄₇⋊C₄	—	2	2	no	—
438	Dic₄₇⋊C₄	—	2	2	no	—
439	C₄×Dic₄₇	—	2	2	no	—
440	C₄×Dic₄₇	—	2	2	no	—
441	C₄×Dic₄₇	—	2	2	no	—
442	C₂×C₄₇⋊C₈	—	2	2	no	—
443	C₂×C₄₇⋊C₈	—	2	4	no	—
444	C₂×C₄₇⋊C₈	—	4	2	no	—
445	C₂×C₄₇⋊C₈	—	4	1	no	—
446	C₂×C₄₇⋊C₈	C₂⁴	1	1	yes	characteristic
447	C₂×C₄₇⋊C₈	C₂⁴	1	1	yes	characteristic
448	C₂×C₄₇⋊C₈	C₂⁴	1	2	yes	—
449	C₂×C₄₇⋊C₈	C₂⁴	1	2	yes	—
450	C₂×C₄₇⋊C₈	C₂⁴	1	1	yes	characteristic
451	C₂×C₄₇⋊C₈	C₂⁴	1	1	yes	characteristic
452	C₂³×C₄₇	—	2	1	no	—
453	C₂³×C₄₇	—	2	1	no	—
454	C₂³×C₄₇	—	4	2	no	—
455	C₂³×C₄₇	—	4	2	no	—
456	C₂³×C₄₇	—	8	1	no	—
457	C₂³×C₄₇	C₂²×D₄	1	2	yes	—
458	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
459	C₂²×D₄₇	—	2	1	no	—
460	C₂²×D₄₇	—	2	1	no	—
461	C₂²×D₄₇	—	4	2	no	—
462	C₂²×D₄₇	—	4	2	no	—
463	C₂²×D₄₇	—	8	1	no	—
464	Q₈×C₄₇	—	2	2	no	—
465	Q₈×C₄₇	—	2	2	no	—
466	Q₈×C₄₇	—	2	2	no	—
467	Q₈×C₄₇	—	8	1	no	—
468	D₄×C₄₇	—	2	4	no	—
469	D₄×C₄₇	—	2	2	no	—
470	D₄×C₄₇	—	2	1	no	—
471	D₄×C₄₇	—	2	1	no	—
472	D₄×C₄₇	—	2	1	no	—
473	D₄×C₄₇	—	4	2	no	—
474	D₄×C₄₇	—	4	4	no	—
475	D₄×C₄₇	—	8	2	no	—
476	D₄×C₄₇	C₂×#41	1	2	yes	—
477	C₂×C₄×C₄₇	—	2	4	no	—
478	C₂×C₄×C₄₇	—	2	1	no	—
479	C₂×C₄×C₄₇	—	2	2	no	—
480	C₂×C₄×C₄₇	—	2	1	no	—
481	C₂×C₄×C₄₇	—	2	2	no	—
482	C₂×C₄×C₄₇	—	2	1	no	—
483	C₂×C₄×C₄₇	—	2	2	no	—
484	C₂×C₄×C₄₇	—	2	2	no	—
485	C₂×C₄×C₄₇	—	2	1	no	—
486	C₂×C₄×C₄₇	—	4	1	no	—
487	C₂×C₄×C₄₇	—	4	2	no	—
488	C₂×C₄×C₄₇	—	4	4	no	—
489	C₂×C₄×C₄₇	—	4	2	no	—
490	C₂×C₄×C₄₇	—	4	2	no	—
491	C₂×C₄×C₄₇	—	4	2	no	—
492	C₂×C₄×C₄₇	—	4	2	no	—
493	C₂×C₄×C₄₇	—	4	2	no	—
494	C₂×C₄×C₄₇	—	8	2	no	—
495	C₂×C₄×C₄₇	#135	1	4	yes	complemented
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	2	yes	—
501	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
502	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
503	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
504	C₂×C₄×C₄₇	C₂⁵	1	1	yes	characteristic
505	C₂²⋊D₄₇	—	4	4	no	—
506	C₂²⋊D₄₇	—	8	2	no	—
507	C₂×Dic₄₇	—	2	1	no	—
508	C₂×Dic₄₇	—	2	2	no	—
509	C₂×Dic₄₇	—	2	2	no	—
510	C₂×Dic₄₇	—	2	1	no	—
511	C₂×Dic₄₇	—	4	2	no	—
512	D₁₈₈	—	2	1	no	—
513	D₁₈₈	—	2	1	no	—
514	D₁₈₈	—	2	1	no	—
515	D₁₈₈	—	4	2	no	—
516	D₁₈₈	C₂×#41	1	2	yes	—
517	C₄×D₄₇	—	4	4	no	—
518	C₄×D₄₇	—	4	2	no	—
519	C₄×D₄₇	—	4	2	no	—
520	C₄×D₄₇	—	4	2	no	—
521	C₄×D₄₇	—	4	2	no	—
522	C₄×D₄₇	—	8	2	no	—
523	Dic₉₄	—	2	2	no	—
524	Dic₉₄	—	2	2	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	#61427	—	47	1	no	maximal, Sylow
533	C₂²×C₄₇	—	2	1	no	—
534	C₂²×C₄₇	—	2	1	no	—
535	C₂²×C₄₇	—	2	2	no	—
536	C₂²×C₄₇	—	2	2	no	—
537	C₂²×C₄₇	—	2	2	no	—
538	C₂²×C₄₇	—	2	2	no	—
539	C₂²×C₄₇	—	4	1	no	—
540	C₂²×C₄₇	—	4	1	no	—
541	C₂²×C₄₇	—	4	1	no	—
542	C₂²×C₄₇	—	4	1	no	—
543	C₂²×C₄₇	—	4	1	no	—
544	C₂²×C₄₇	—	8	4	no	—
545	C₂²×C₄₇	C₂×#135	1	2	yes	—
546	C₂²×C₄₇	C₂³×D₄	1	1	yes	characteristic
547	C₂×D₄₇	—	2	2	no	—
548	C₂×D₄₇	—	4	1	no	—
549	C₂×D₄₇	—	4	1	no	—
550	C₂×D₄₇	—	4	1	no	—
551	C₂×D₄₇	—	4	1	no	—
552	C₂×D₄₇	—	4	1	no	—
553	C₂×D₄₇	—	8	4	no	—
554	C₄×C₄₇	—	2	1	no	—
555	C₄×C₄₇	—	2	2	no	—
556	C₄×C₄₇	—	2	1	no	—
557	C₄×C₄₇	—	2	2	no	—
558	C₄×C₄₇	—	2	1	no	—
559	C₄×C₄₇	—	2	2	no	—
560	C₄×C₄₇	—	4	2	no	—
561	C₄×C₄₇	—	4	2	no	—
562	C₄×C₄₇	—	4	1	no	—
563	C₄×C₄₇	—	4	1	no	—
564	C₄×C₄₇	C₂×#135	1	2	yes	—
565	C₄×C₄₇	C₂×#135	1	2	yes	—
566	C₄×C₄₇	C₂²×#41	1	1	yes	characteristic
567	C₄×C₄₇	#585	1	1	yes	characteristic
568	Dic₄₇	—	4	2	no	—
569	Dic₄₇	—	4	2	no	—
570	Dic₄₇	—	4	1	no	—
571	Dic₄₇	—	4	1	no	—
572	#3475	—	47	1	no	—
573	#3475	D₄₇	1	1	yes	characteristic, complemented
574	#3393	—	47	1	no	—
575	#3380	—	47	1	no	—
576	#3360	—	47	1	no	—
577	#3360	—	47	1	no	—
578	#3341	—	47	1	no	—
579	#3336	—	47	2	no	—
580	#3303	—	47	1	no	—
581	#3303	—	47	1	no	—
582	#3296	—	47	2	no	—
583	#3296	—	47	2	no	—
584	#3283	—	47	1	no	—
585	#3280	—	47	2	no	—
586	#3170	—	47	1	no	—
587	#3168	—	47	2	no	—
588	#3102	—	47	2	no	—
589	#3102	—	47	2	no	—
590	#3101	—	47	1	no	—
591	#3101	—	47	1	no	—
592	C₈×#41	—	47	1	no	—
593	C₄×#135	—	47	2	no	—
594	C₂×C₄×D₈	—	47	1	no	—
595	C₂×C₄₇	—	2	2	no	—
596	C₂×C₄₇	—	4	2	no	—
597	C₂×C₄₇	—	4	2	no	—
598	C₂×C₄₇	—	8	1	no	—
599	C₂×C₄₇	D₄×#41	1	1	yes	characteristic
600	C₂×C₄₇	C₂²×#135	1	1	yes	characteristic
601	C₂×C₄₇	#3584	1	1	yes	characteristic
602	D₄₇	—	4	2	no	—
603	D₄₇	—	8	1	no	—
604	C₂×#135	—	47	2	no	—
605	C₂²×D₈	—	47	1	no	—
606	#556	—	47	1	no	—
607	#556	C₂×D₄₇	1	1	yes	characteristic, complemented
608	#555	—	47	1	no	—
609	#555	C₂×D₄₇	1	1	yes	characteristic, complemented
610	#554	—	47	1	no	—
611	#554	C₂×D₄₇	1	1	yes	characteristic, complemented
612	#553	—	2	1	no	—
613	#553	—	94	1	no	—
614	#552	—	2	1	no	—
615	#552	—	47	2	no	—
616	#552	—	94	1	no	—
617	#552	C₂×D₄₇	1	2	yes	—
618	#551	—	2	2	no	—
619	#551	—	94	2	no	—
620	#547	—	47	1	no	—
621	#547	C₂×D₄₇	1	1	yes	characteristic, complemented
622	#546	—	47	2	no	—
623	#546	C₂×D₄₇	1	2	yes	—
624	#533	—	47	1	no	—
625	#533	C₂×D₄₇	1	1	yes	characteristic
626	#529	—	2	2	no	—
627	#529	—	47	2	no	—
628	#529	—	94	2	no	—
629	#529	C₂×D₄₇	1	2	yes	complemented
630	#525	—	2	1	no	—
631	#525	—	94	1	no	—
632	C₄×#41	—	47	2	no	—
633	C₄×#41	C₂×D₄₇	1	1	yes	characteristic
634	C₄×#41	C₂×D₄₇	1	2	yes	complemented
635	C₂×C₄×D₄	—	47	1	no	—
636	C₂×C₄×D₄	C₂×D₄₇	1	1	yes	characteristic
637	C₂×#117	—	2	1	no	—
638	C₂×#117	—	94	1	no	—
639	#500	—	47	1	no	—
640	#499	—	47	2	no	—
641	#495	—	47	2	no	—
642	#494	—	47	1	no	—
643	#488	—	47	2	no	—
644	#488	—	47	2	no	—
645	#487	—	47	1	no	—
646	#487	—	47	1	no	—
647	#485	—	47	2	no	—
648	#485	—	47	2	no	—
649	#483	—	47	2	no	—
650	#483	—	47	2	no	—
651	#482	—	47	2	no	—
652	#482	—	47	2	no	—
653	#479	—	47	2	no	—
654	#479	—	47	2	no	—
655	#478	—	47	2	no	—
656	#478	—	47	2	no	—
657	#476	—	47	1	no	—
658	#476	—	47	1	no	—
659	#476	—	47	1	no	—
660	#476	—	47	1	no	—
661	#467	—	47	2	no	—
662	#467	—	47	2	no	—
663	#467	—	47	2	no	—
664	#466	—	47	2	no	—
665	#465	—	47	2	no	—
666	#465	—	47	2	no	—
667	#464	—	47	2	no	—
668	#464	—	47	2	no	—
669	#463	—	47	2	no	—
670	#463	—	47	2	no	—
671	#461	—	47	1	no	—
672	#461	—	47	1	no	—
673	#461	—	47	1	no	—
674	#461	—	47	1	no	—
675	#452	—	47	2	no	—
676	#452	—	47	2	no	—
677	#450	—	47	2	no	—
678	#450	—	47	2	no	—
679	#449	—	47	2	no	—
680	#449	—	47	2	no	—
681	C₈×Q₈	—	47	1	no	—
682	C₈×Q₈	—	47	1	no	—
683	C₄×Q₁₆	—	47	2	no	—
684	C₄×Q₁₆	—	47	2	no	—
685	C₄×Q₁₆	—	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	2	no	—
690	C₄×SD₁₆	—	47	2	no	—
691	C₄×SD₁₆	—	47	2	no	—
692	C₄×D₈	—	47	1	no	—
693	C₄×D₈	—	47	1	no	—
694	C₄×D₈	—	47	1	no	—
695	C₄×D₈	—	47	1	no	—
696	C₄×D₈	—	47	1	no	—
697	C₄×D₈	—	47	1	no	—
698	C₄×D₈	—	47	2	no	—
699	C₄×D₈	—	47	1	no	—
700	C₄×D₈	—	47	1	no	—
701	C₈×D₄	—	47	2	no	—
702	C₈×D₄	—	47	1	no	—
703	C₈×D₄	—	47	2	no	—
704	C₈×D₄	—	47	1	no	—
705	#431	—	47	1	no	—
706	#431	—	47	2	no	—
707	#427	—	47	2	no	—
708	C₂×#107	—	47	1	no	—
709	#416	—	47	2	no	—
710	#416	—	47	2	no	—
711	C₂×#102	—	47	1	no	—
712	C₂×#102	—	47	1	no	—
713	C₂×C₄×C₈	—	47	2	no	—
714	C₂×C₄×C₈	—	47	1	no	—
715	C₄₇	#61427	1	1	yes	characteristic, complemented, Sylow
716	C₂×#41	—	47	2	no	—
717	C₂×#41	C₂²⋊D₄₇	1	1	yes	characteristic
718	C₂×#41	C₂²×D₄₇	1	2	yes	—
719	C₂²×D₄	—	47	1	no	—
720	C₂²×D₄	C₂²×D₄₇	1	1	yes	characteristic
721	C₂³×C₄	—	2	1	no	—
722	C₂³×C₄	—	94	1	no	—
723	#135	—	94	8	no	—
724	C₂×Q₁₆	—	47	2	no	—
725	C₂×Q₁₆	—	47	2	no	—
726	C₂×SD₁₆	—	47	2	no	—
727	C₂×SD₁₆	—	47	2	no	—
728	C₂×SD₁₆	—	47	2	no	—
729	C₂×SD₁₆	—	47	2	no	—
730	C₂×D₈	—	47	1	no	—
731	C₂×D₈	—	47	1	no	—
732	C₂×D₈	—	47	1	no	—
733	C₂×D₈	—	47	1	no	—
734	C₂×D₈	—	94	4	no	—
735	C₂²×C₈	—	47	1	no	—
736	C₂²×C₈	—	47	2	no	—
737	C₂²×C₈	—	47	1	no	—
738	C₂²×C₈	—	47	2	no	—
739	C₄⋊Q₈	—	47	1	no	—
740	C₄⋊Q₈	—	47	1	no	—
741	C₄⋊Q₈	C₂²×D₄₇	1	1	yes	characteristic
742	C₄⋊Q₈	C₂²×D₄₇	1	1	yes	characteristic
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	#126	—	94	2	no	—
749	#125	—	2	2	no	—
750	#125	—	2	1	no	—
751	#125	—	47	2	no	—
752	#125	—	94	2	no	—
753	#125	—	94	1	no	—
754	#125	C₂²×D₄₇	1	2	yes	—
755	#124	—	2	2	no	—
756	#124	—	47	2	no	—
757	#124	—	94	2	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	—	2	2	no	—
763	#123	—	94	2	no	—
764	#123	—	94	2	no	—
765	#123	—	94	2	no	—
766	#123	—	94	2	no	—
767	C₂²⋊Q₈	—	2	1	no	—
768	C₂²⋊Q₈	—	2	1	no	—
769	C₂²⋊Q₈	—	2	1	no	—
770	C₂²⋊Q₈	—	2	2	no	—
771	C₂²⋊Q₈	—	47	2	no	—
772	C₂²⋊Q₈	—	47	2	no	—
773	C₂²⋊Q₈	—	94	1	no	—
774	C₂²⋊Q₈	—	94	1	no	—
775	C₂²⋊Q₈	—	94	1	no	—
776	C₂²⋊Q₈	—	94	2	no	—
777	C₂²⋊Q₈	C₂²×D₄₇	1	2	yes	—
778	C₂²⋊Q₈	C₂²×D₄₇	1	2	yes	—
779	#121	—	2	1	no	—
780	#121	—	2	1	no	—
781	#121	—	2	2	no	—
782	#121	—	47	2	no	—
783	#121	—	94	1	no	—
784	#121	—	94	1	no	—
785	#121	—	94	2	no	—
786	#121	C₂²×D₄₇	1	2	yes	—
787	#120	—	2	2	no	—
788	#120	—	94	2	no	—
789	C₄×Q₈	—	2	1	no	—
790	C₄×Q₈	—	47	2	no	—
791	C₄×Q₈	—	47	2	no	—
792	C₄×Q₈	—	94	1	no	—
793	C₄×Q₈	C₂²⋊D₄₇	1	1	yes	characteristic
794	C₄×Q₈	C₂²×D₄₇	1	2	yes	—
795	C₄×Q₈	C₂²×D₄₇	1	2	yes	—
796	C₄×Q₈	C₂²×D₄₇	1	1	yes	characteristic
797	C₄×D₄	—	2	2	no	—
798	C₄×D₄	—	2	2	no	—
799	C₄×D₄	—	2	2	no	—
800	C₄×D₄	—	2	1	no	—
801	C₄×D₄	—	2	1	no	—
802	C₄×D₄	—	47	1	no	—
803	C₄×D₄	—	47	1	no	—
804	C₄×D₄	—	47	1	no	—
805	C₄×D₄	—	47	1	no	—
806	C₄×D₄	—	47	2	no	—
807	C₄×D₄	—	94	2	no	—
808	C₄×D₄	—	94	2	no	—
809	C₄×D₄	—	94	2	no	—
810	C₄×D₄	—	94	1	no	—
811	C₄×D₄	—	94	1	no	—
812	C₄×D₄	C₂²⋊D₄₇	1	2	yes	—
813	C₄×D₄	C₂²⋊D₄₇	1	1	yes	characteristic
814	C₄×D₄	C₂²×D₄₇	1	1	yes	characteristic
815	C₄×D₄	C₂²×D₄₇	1	1	yes	characteristic
816	C₄×D₄	C₂²×D₄₇	1	1	yes	characteristic
817	C₄×D₄	C₂²×D₄₇	1	1	yes	characteristic
818	C₄×D₄	C₂²×D₄₇	1	2	yes	—
819	C₄×D₄	C₂²×D₄₇	1	2	yes	—
820	C₄×D₄	C₂²×D₄₇	1	1	yes	characteristic
821	#117	—	2	1	no	—
822	#117	—	2	1	no	—
823	#117	—	2	1	no	—
824	#117	—	2	2	no	—
825	#117	—	2	2	no	—
826	#117	—	2	2	no	—
827	#117	—	47	2	no	—
828	#117	—	94	1	no	—
829	#117	—	94	1	no	—
830	#117	—	94	1	no	—
831	#117	—	94	2	no	—
832	#117	—	94	2	no	—
833	#117	—	94	2	no	—
834	#117	C₂²⋊D₄₇	1	1	yes	characteristic
835	#117	C₂²⋊D₄₇	1	2	yes	—
836	#117	C₂²×D₄₇	1	2	yes	—
837	C₂×C₄⋊C₄	—	2	1	no	—
838	C₂×C₄⋊C₄	—	2	1	no	—
839	C₂×C₄⋊C₄	—	47	1	no	—
840	C₂×C₄⋊C₄	—	94	1	no	—
841	C₂×C₄⋊C₄	—	94	1	no	—
842	C₂×C₄⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
843	C₂×C₂²⋊C₄	—	2	1	no	—
844	C₂×C₂²⋊C₄	—	2	2	no	—
845	C₂×C₂²⋊C₄	—	94	1	no	—
846	C₂×C₂²⋊C₄	—	94	2	no	—
847	C₂×C₄²	—	2	2	no	—
848	C₂×C₄²	—	94	2	no	—
849	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
850	C₂×C₄²	C₂²×D₄₇	1	2	yes	—
851	#107	—	47	1	no	—
852	#107	—	47	1	no	—
853	#107	—	47	1	no	—
854	#107	—	47	1	no	—
855	#107	—	47	2	no	—
856	#107	—	47	2	no	—
857	#106	—	47	2	no	—
858	#106	—	47	2	no	—
859	#106	—	47	2	no	—
860	#106	—	47	2	no	—
861	C₄⋊C₈	—	47	1	no	—
862	C₄⋊C₈	—	47	1	no	—
863	C₄⋊C₈	—	47	2	no	—
864	C₄⋊C₈	—	47	2	no	—
865	#103	—	47	2	no	—
866	#103	—	47	2	no	—
867	#103	—	47	2	no	—
868	#103	—	47	2	no	—
869	#103	—	47	2	no	—
870	#103	—	47	2	no	—
871	#103	—	47	2	no	—
872	#103	—	47	2	no	—
873	#102	—	47	1	no	—
874	#102	—	47	1	no	—
875	#102	—	47	1	no	—
876	#102	—	47	1	no	—
877	#102	—	47	2	no	—
878	#102	—	47	2	no	—
879	#102	—	47	1	no	—
880	#102	—	47	1	no	—
881	#102	—	47	1	no	—
882	#102	—	47	1	no	—
883	#102	—	47	2	no	—
884	#102	—	47	2	no	—
885	C₂²⋊C₈	—	47	2	no	—
886	C₂²⋊C₈	—	47	2	no	—
887	C₂²⋊C₈	—	47	2	no	—
888	C₄×C₈	—	47	1	no	—
889	C₄×C₈	—	47	1	no	—
890	C₄×C₈	—	47	2	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	—	2	1	no	—
896	C₂⁴	—	94	1	no	—
897	#41	—	2	4	no	—
898	#41	—	2	4	no	—
899	#41	—	4	2	no	—
900	#41	—	94	4	no	—
901	#41	—	188	2	no	—
902	C₂×Q₈	—	2	1	no	—
903	C₂×Q₈	—	47	2	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×D₄	—	2	2	no	—
908	C₂×D₄	—	2	2	no	—
909	C₂×D₄	—	2	2	no	—
910	C₂×D₄	—	2	1	no	—
911	C₂×D₄	—	4	1	no	—
912	C₂×D₄	—	47	1	no	—
913	C₂×D₄	—	47	1	no	—
914	C₂×D₄	—	94	2	no	—
915	C₂×D₄	—	94	2	no	—
916	C₂×D₄	—	94	2	no	—
917	C₂×D₄	—	94	1	no	—
918	C₂×D₄	—	188	1	no	—
919	C₂×D₄	C₂×C₂²⋊D₄₇	1	2	yes	—
920	C₂×D₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
921	C₂×D₄	C₂³×D₄₇	1	1	yes	characteristic
922	C₂×D₄	C₂³×D₄₇	1	1	yes	characteristic
923	C₂²×C₄	—	2	1	no	—
924	C₂²×C₄	—	2	2	no	—
925	C₂²×C₄	—	2	1	no	—
926	C₂²×C₄	—	2	1	no	—
927	C₂²×C₄	—	2	1	no	—
928	C₂²×C₄	—	2	1	no	—
929	C₂²×C₄	—	2	2	no	—
930	C₂²×C₄	—	4	4	no	—
931	C₂²×C₄	—	94	1	no	—
932	C₂²×C₄	—	94	2	no	—
933	C₂²×C₄	—	94	2	no	—
934	C₂²×C₄	—	94	1	no	—
935	C₂²×C₄	—	94	1	no	—
936	C₂²×C₄	—	94	1	no	—
937	C₂²×C₄	—	94	1	no	—
938	C₂²×C₄	—	188	4	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	1	yes	characteristic
944	C₂²×C₄	C₂³×D₄₇	1	2	yes	—
945	Q₁₆	—	94	4	no	—
946	Q₁₆	—	188	2	no	—
947	SD₁₆	—	94	4	no	—
948	SD₁₆	—	94	4	no	—
949	SD₁₆	—	188	2	no	—
950	SD₁₆	—	188	2	no	—
951	D₈	—	47	4	no	—
952	D₈	—	94	2	no	—
953	D₈	—	94	2	no	—
954	D₈	—	94	2	no	—
955	C₂×C₈	—	47	1	no	—
956	C₂×C₈	—	47	1	no	—
957	C₂×C₈	—	47	1	no	—
958	C₂×C₈	—	47	2	no	—
959	C₂×C₈	—	47	2	no	—
960	C₂×C₈	—	47	1	no	—
961	C₂×C₈	—	94	2	no	—
962	C₂×C₈	—	94	4	no	—
963	C₂×C₈	—	188	2	no	—
964	C₂×C₈	—	188	1	no	—
965	C₄⋊C₄	—	2	1	no	—
966	C₄⋊C₄	—	2	1	no	—
967	C₄⋊C₄	—	2	2	no	—
968	C₄⋊C₄	—	2	2	no	—
969	C₄⋊C₄	—	2	1	no	—
970	C₄⋊C₄	—	2	2	no	—
971	C₄⋊C₄	—	2	2	no	—
972	C₄⋊C₄	—	2	2	no	—
973	C₄⋊C₄	—	2	2	no	—
974	C₄⋊C₄	—	2	1	no	—
975	C₄⋊C₄	—	47	1	no	—
976	C₄⋊C₄	—	47	1	no	—
977	C₄⋊C₄	—	47	2	no	—
978	C₄⋊C₄	—	94	2	no	—
979	C₄⋊C₄	—	94	2	no	—
980	C₄⋊C₄	—	94	2	no	—
981	C₄⋊C₄	—	94	2	no	—
982	C₄⋊C₄	—	94	2	no	—
983	C₄⋊C₄	—	94	2	no	—
984	C₄⋊C₄	—	94	1	no	—
985	C₄⋊C₄	—	94	1	no	—
986	C₄⋊C₄	—	94	1	no	—
987	C₄⋊C₄	—	94	1	no	—
988	C₄⋊C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
989	C₄⋊C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
990	C₄⋊C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
991	C₄⋊C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
992	C₄⋊C₄	C₂³×D₄₇	1	1	yes	characteristic
993	C₄⋊C₄	C₂³×D₄₇	1	1	yes	characteristic
994	C₄⋊C₄	C₂³×D₄₇	1	2	yes	—
995	C₂²⋊C₄	—	2	2	no	—
996	C₂²⋊C₄	—	2	2	no	—
997	C₂²⋊C₄	—	2	2	no	—
998	C₂²⋊C₄	—	2	1	no	—
999	C₂²⋊C₄	—	2	2	no	—
1000	C₂²⋊C₄	—	2	2	no	—
1001	C₂²⋊C₄	—	2	1	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	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	—	94	1	no	—
1013	C₂²⋊C₄	—	94	1	no	—
1014	C₂²⋊C₄	—	94	1	no	—
1015	C₂²⋊C₄	—	94	2	no	—
1016	C₂²⋊C₄	—	94	2	no	—
1017	C₂²⋊C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
1018	C₂²⋊C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
1019	C₂²⋊C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
1020	C₄²	—	2	2	no	—
1021	C₄²	—	2	2	no	—
1022	C₄²	—	2	2	no	—
1023	C₄²	—	94	2	no	—
1024	C₄²	—	94	2	no	—
1025	C₄²	—	94	2	no	—
1026	C₄²	C₂×C₂²⋊D₄₇	1	2	yes	—
1027	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
1028	C₄²	C₂×C₂²⋊D₄₇	1	2	yes	—
1029	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
1030	C₄²	C₂³×D₄₇	1	1	yes	characteristic
1031	C₄²	C₂³×D₄₇	1	2	yes	—
1032	C₄²	C₂³×D₄₇	1	1	yes	characteristic
1033	C₂³	—	2	1	no	—
1034	C₂³	—	2	1	no	—
1035	C₂³	—	4	2	no	—
1036	C₂³	—	4	2	no	—
1037	C₂³	—	8	1	no	—
1038	C₂³	—	94	1	no	—
1039	C₂³	—	94	1	no	—
1040	C₂³	—	376	1	no	—
1041	C₂³	—	188	2	no	—
1042	C₂³	—	188	2	no	—
1043	C₂³	C₂²×C₂²⋊D₄₇	1	2	yes	—
1044	C₂³	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
1045	Q₈	—	2	2	no	—
1046	Q₈	—	2	2	no	—
1047	Q₈	—	2	2	no	—
1048	Q₈	—	8	1	no	—
1049	Q₈	—	94	2	no	—
1050	Q₈	—	94	2	no	—
1051	Q₈	—	376	1	no	—
1052	D₄	—	2	4	no	—
1053	D₄	—	2	2	no	—
1054	D₄	—	2	1	no	—
1055	D₄	—	2	1	no	—
1056	D₄	—	2	1	no	—
1057	D₄	—	4	2	no	—
1058	D₄	—	4	4	no	—
1059	D₄	—	8	2	no	—
1060	D₄	—	47	2	no	—
1061	D₄	—	94	1	no	—
1062	D₄	—	94	1	no	—
1063	D₄	—	94	1	no	—
1064	D₄	—	376	2	no	—
1065	D₄	—	188	2	no	—
1066	D₄	—	188	4	no	—
1067	D₄	#41×D₄₇	1	2	yes	—
1068	C₂×C₄	—	2	4	no	—
1069	C₂×C₄	—	2	1	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	2	no	—
1075	C₂×C₄	—	2	2	no	—
1076	C₂×C₄	—	2	1	no	—
1077	C₂×C₄	—	4	2	no	—
1078	C₂×C₄	—	4	1	no	—
1079	C₂×C₄	—	4	4	no	—
1080	C₂×C₄	—	4	2	no	—
1081	C₂×C₄	—	4	2	no	—
1082	C₂×C₄	—	4	2	no	—
1083	C₂×C₄	—	4	2	no	—
1084	C₂×C₄	—	4	2	no	—
1085	C₂×C₄	—	8	2	no	—
1086	C₂×C₄	—	94	1	no	—
1087	C₂×C₄	—	94	2	no	—
1088	C₂×C₄	—	94	2	no	—
1089	C₂×C₄	—	94	1	no	—
1090	C₂×C₄	—	376	2	no	—
1091	C₂×C₄	—	188	4	no	—
1092	C₂×C₄	—	188	2	no	—
1093	C₂×C₄	—	188	2	no	—
1094	C₂×C₄	—	188	2	no	—
1095	C₂×C₄	—	188	2	no	—
1096	C₂×C₄	—	188	2	no	—
1097	C₂×C₄	#13094044	1	4	yes	complemented
1098	C₂×C₄	C₂²×C₂²⋊D₄₇	1	2	yes	—
1099	C₂×C₄	C₂²×C₂²⋊D₄₇	1	2	yes	—
1100	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
1101	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
1102	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
1103	C₂×C₄	C₂²×C₂²⋊D₄₇	1	2	yes	—
1104	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
1105	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
1106	C₂×C₄	C₂⁴×D₄₇	1	1	yes	characteristic
1107	C₈	—	47	2	no	—
1108	C₈	—	94	1	no	—
1109	C₈	—	94	2	no	—
1110	C₈	—	94	1	no	—
1111	C₈	—	94	2	no	—
1112	C₈	—	94	1	no	—
1113	C₂²	—	2	1	no	—
1114	C₂²	—	2	1	no	—
1115	C₂²	—	2	2	no	—
1116	C₂²	—	2	2	no	—
1117	C₂²	—	2	2	no	—
1118	C₂²	—	2	2	no	—
1119	C₂²	—	4	1	no	—
1120	C₂²	—	4	1	no	—
1121	C₂²	—	4	1	no	—
1122	C₂²	—	4	1	no	—
1123	C₂²	—	4	1	no	—
1124	C₂²	—	8	4	no	—
1125	C₂²	—	94	2	no	—
1126	C₂²	—	376	4	no	—
1127	C₂²	—	188	1	no	—
1128	C₂²	—	188	1	no	—
1129	C₂²	—	188	1	no	—
1130	C₂²	—	188	1	no	—
1131	C₂²	—	188	1	no	—
1132	C₂²	C₂×#13094044	1	2	yes	—
1133	C₂²	C₂³×C₂²⋊D₄₇	1	1	yes	characteristic
1134	C₄	—	2	2	no	—
1135	C₄	—	2	2	no	—
1136	C₄	—	2	1	no	—
1137	C₄	—	2	1	no	—
1138	C₄	—	2	2	no	—
1139	C₄	—	2	1	no	—
1140	C₄	—	4	1	no	—
1141	C₄	—	4	1	no	—
1142	C₄	—	4	2	no	—
1143	C₄	—	4	2	no	—
1144	C₄	—	188	1	no	—
1145	C₄	—	188	1	no	—
1146	C₄	—	188	2	no	—
1147	C₄	—	188	2	no	—
1148	C₄	C₂×#13094044	1	2	yes	—
1149	C₄	C₂×#13094044	1	2	yes	—
1150	C₄	C₂×#41×D₄₇	1	1	yes	characteristic
1151	C₄	#15689959	1	1	yes	characteristic
1152	C₂	—	2	2	no	—
1153	C₂	—	4	2	no	—
1154	C₂	—	4	2	no	—
1155	C₂	—	8	1	no	—
1156	C₂	—	376	1	no	—
1157	C₂	—	188	2	no	—
1158	C₂	#41×C₂²⋊D₄₇	1	1	yes	characteristic
1159	C₂	C₂²×#13094044	1	1	yes	characteristic
1160	C₂	#20258159	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×#3475	C₂
socle	C₂²×C₄₇	C₂³×D₄
hypercenter	#3475	D₄₇
hypocenter	C₄₇	#61427
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ C₄×#41 ◁ #3475

Complements

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

N	H ≅ G/N	type
1. #20256952	C₂	semidirect
2. #20256372	C₂	semidirect
3. #20256251	C₂	semidirect
4. #20256037	C₂	semidirect
5. #20256033	C₂	semidirect
6. #20255806	C₂	semidirect
7. #20255750	C₂	semidirect
8. #20255316	C₂	semidirect
9. #20255310	C₂	semidirect
10. #20255223	C₂	semidirect
11. #20255217	C₂	semidirect
12. #20255106	C₂	semidirect
13. #20255069	C₂	semidirect
14. #20253970	C₂	semidirect
15. #20253952	C₂	semidirect
16. #20253406	C₂	semidirect
17. #20253400	C₂	semidirect
18. #20253396	C₂	semidirect
19. #20253392	C₂	semidirect
20. #41×C₄₇⋊C₈	C₂	semidirect
21. C₄×#13094044	C₂	semidirect
22. C₂×C₄×#10625334	C₂	semidirect
23. C₄₇×#3475	C₂	semidirect
26. #15689846	C₂²	semidirect
27. #15689838	C₂²	semidirect
28. #15689833	C₂²	semidirect
33. #15689778	C₂²	semidirect
36. #15689657	C₂²	semidirect
39. C₄×#10625350	C₂²	semidirect
42. #15689526	C₂²	semidirect
43. #15689522	C₂²	semidirect
45. #15689502	C₂²	semidirect
46. #15689480	C₂²	semidirect
47. #15689477	C₂²	semidirect
48. #15689475	C₂²	semidirect
49. #15689473	C₂²	semidirect
50. #15689464	C₂²	semidirect
51. #15689461	C₂²	semidirect
54. #15689447	C₂²	semidirect
55. #15689444	C₂²	semidirect
56. #15689430	C₂²	semidirect
57. #15689427	C₂²	semidirect
58. #15689423	C₂²	semidirect
59. #15689420	C₂²	semidirect
60. #15689413	C₂²	semidirect
61. #15689413	C₂²	semidirect
62. #15689410	C₂²	semidirect
63. #15689410	C₂²	semidirect
66. #15689362	C₂²	semidirect
68. #15689354	C₂²	semidirect
69. #15689350	C₂²	semidirect
70. #15689345	C₂²	semidirect
71. #15689342	C₂²	semidirect
74. #15689328	C₂²	semidirect
75. #15689328	C₂²	semidirect
76. #15689325	C₂²	semidirect
77. #15689325	C₂²	semidirect
78. #15689285	C₂²	semidirect
79. #15689283	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
89. C₄×#10625336	C₂²	semidirect
90. C₄×#10625336	C₂²	semidirect
91. C₄×#10625336	C₂²	semidirect
92. C₄×#10625335	C₂²	semidirect
93. C₄×#10625335	C₂²	semidirect
94. C₄×#10625335	C₂²	semidirect
106. D₄×C₄₇⋊C₈	C₂²	semidirect
107. D₄×C₄₇⋊C₈	C₂²	semidirect
109. #15689176	C₂²	semidirect
110. #15689159	C₂²	semidirect
112. #15689119	C₂²	semidirect
113. #15689117	C₂²	semidirect
117. C₂×C₄×C₄₇⋊C₈	C₂²	semidirect
118. C₄₇×#556	C₂²	semidirect
119. C₄₇×#555	C₂²	semidirect
120. C₄₇×#554	C₂²	semidirect
125. C₄₇×#547	C₂²	semidirect
129. C₄₇×#529	C₂²	semidirect
132. C₄×#41×C₄₇	C₂²	semidirect
417. #10625334	#41	semidirect
495. C₂×C₄×C₄₇	#135	semidirect
573. #3475	D₄₇	semidirect
607. #556	C₂×D₄₇	semidirect
609. #555	C₂×D₄₇	semidirect
611. #554	C₂×D₄₇	semidirect
621. #547	C₂×D₄₇	semidirect
629. #529	C₂×D₄₇	semidirect
634. C₄×#41	C₂×D₄₇	semidirect
715. C₄₇	#61427	semidirect
1097. C₂×C₄	#13094044	semidirect

Maximal subgroups

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

subgroup	index
#20256952	2
#20256372	2
#20256251	2
#20256037	2
#20256033	2
#20255806	2
#20255750	2
#20255316	2
#20255310	2
#20255223	2
#20255217	2
#20255106	2
#20255069	2
#20253970	2
#20253952	2
#20253406	2
#20253400	2
#20253396	2
#20253392	2
#41×C₄₇⋊C₈	2
C₄×#13094044	2
C₂×C₄×#10625334	2
C₄₇×#3475	2
#61427	47