Subgroups — #27095035

Order 12032.

1842 conjugacy classes of subgroups.

The subgroup lattice has 1132 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20256946	C₂	1	1	yes	maximal, characteristic, complemented
2	#20256014	C₂	1	1	yes	maximal, characteristic, complemented
3	#20256008	C₂	1	1	yes	maximal, characteristic, complemented
4	#20256003	C₂	1	1	yes	maximal, characteristic, complemented
5	#20255997	C₂	1	1	yes	maximal, characteristic, complemented
6	#20255988	C₂	1	2	yes	maximal, complemented
7	#20255983	C₂	1	1	yes	maximal, characteristic, complemented
8	#20255977	C₂	1	1	yes	maximal, characteristic, complemented
9	#20255972	C₂	1	1	yes	maximal, characteristic, complemented
10	#20255966	C₂	1	1	yes	maximal, characteristic, complemented
11	#20255957	C₂	1	2	yes	maximal, complemented
12	#20255948	C₂	1	2	yes	maximal, complemented
13	#20255942	C₂	1	2	yes	maximal, complemented
14	#20253898	C₂	1	1	yes	maximal, characteristic, complemented
15	#20253301	C₂	1	2	yes	maximal, complemented
16	#20253297	C₂	1	2	yes	maximal, complemented
17	#20253176	C₂	1	1	yes	maximal, characteristic, complemented
18	#20253170	C₂	1	1	yes	maximal, characteristic, complemented
19	#20252994	C₂	1	2	yes	maximal, complemented
20	C₄×#13094044	C₂	1	1	yes	maximal, characteristic, complemented
21	C₂×#15689201	C₂	1	1	yes	maximal, characteristic, complemented
22	#20251977	C₂	1	2	yes	maximal, complemented
23	C₄₇×#3475	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#13094044	C₂²	1	1	yes	characteristic
25	C₂²×#10625329	C₂²	1	2	yes	—
26	#15689843	C₂²	1	1	yes	characteristic
27	#15689838	C₂²	1	1	yes	characteristic
28	#15689830	C₂²	1	1	yes	characteristic
29	#15689819	C₂²	1	2	yes	—
30	#15689813	C₂²	1	2	yes	—
31	#15689808	—	2	1	no	—
32	#15689799	—	2	2	no	—
33	#15689777	C₂²	1	1	yes	characteristic
34	#15689767	—	2	1	no	—
35	#15689680	C₂²	1	1	yes	characteristic
36	#15689655	—	2	1	no	—
37	#15689653	—	2	2	no	—
38	#15689634	C₂²	1	2	yes	—
39	C₄×#10625350	C₂²	1	1	yes	characteristic
40	C₄×#10625352	—	2	1	no	—
41	C₂×#13093983	C₂²	1	2	yes	—
42	#15689526	C₂²	1	1	yes	characteristic, complemented
43	#15689526	C₂²	1	1	yes	characteristic, complemented
44	#15689522	C₂²	1	2	yes	complemented
45	#15689522	C₂²	1	2	yes	complemented
46	#15689519	C₂²	1	1	yes	characteristic, complemented
47	#15689519	C₂²	1	1	yes	characteristic, complemented
48	#15689464	C₂²	1	2	yes	complemented
49	#15689464	C₂²	1	2	yes	complemented
50	#15689461	C₂²	1	2	yes	complemented
51	#15689461	C₂²	1	2	yes	complemented
52	#15689458	C₂²	1	2	yes	complemented
53	#15689456	C₂²	1	2	yes	complemented
54	#15689453	C₂²	1	2	yes	complemented
55	#15689451	C₂²	1	2	yes	complemented
56	#15689447	C₂²	1	2	yes	complemented
57	#15689447	C₂²	1	2	yes	complemented
58	#15689444	C₂²	1	2	yes	complemented
59	#15689444	C₂²	1	2	yes	complemented
60	#15689441	C₂²	1	2	yes	complemented
61	#15689439	C₂²	1	2	yes	complemented
62	#15689436	C₂²	1	2	yes	complemented
63	#15689434	C₂²	1	2	yes	complemented
64	#15689430	C₂²	1	2	yes	complemented
65	#15689427	C₂²	1	2	yes	complemented
66	#15689423	C₂²	1	2	yes	complemented
67	#15689420	C₂²	1	2	yes	complemented
68	#15689418	C₂²	1	1	yes	characteristic, complemented
69	#15689415	C₂²	1	1	yes	characteristic, complemented
70	#15689413	C₂²	1	1	yes	characteristic, complemented
71	#15689410	C₂²	1	1	yes	characteristic, complemented
72	#15689408	C₂²	1	1	yes	characteristic, complemented
73	#15689405	C₂²	1	1	yes	characteristic, complemented
74	#15689403	C₂²	1	1	yes	characteristic, complemented
75	#15689400	C₂²	1	1	yes	characteristic, complemented
76	#15689379	C₂²	1	2	yes	complemented
77	#15689379	C₂²	1	2	yes	complemented
78	#15689374	C₂²	1	2	yes	complemented
79	#15689374	C₂²	1	2	yes	complemented
80	#15689371	C₂²	1	2	yes	complemented
81	#15689371	C₂²	1	2	yes	complemented
82	#15689367	C₂²	1	2	yes	complemented
83	#15689367	C₂²	1	2	yes	complemented
84	C₄×#10625337	C₂²	1	1	yes	characteristic, complemented
85	C₄×#10625337	C₂²	1	1	yes	characteristic, complemented
86	C₄×#10625336	C₂²	1	1	yes	characteristic, complemented
87	C₄×#10625336	C₂²	1	1	yes	characteristic, complemented
88	C₄×#10625335	C₂²	1	1	yes	characteristic, complemented
89	C₄×#10625335	C₂²	1	1	yes	characteristic, complemented
90	C₄×#10625334	C₂²	1	1	yes	characteristic, complemented
91	C₄×#10625334	C₂²	1	1	yes	characteristic, complemented
92	#15689201	C₂²	1	1	yes	characteristic
93	#15689201	C₂²	1	1	yes	characteristic
94	#15689201	C₂²	1	1	yes	characteristic
95	#15689201	C₂²	1	2	yes	—
96	#15689201	C₂²	1	2	yes	—
97	#15689201	C₂²	1	1	yes	characteristic
98	#15689166	C₂²	1	2	yes	complemented
99	#15689166	C₂²	1	2	yes	complemented
100	#15689166	C₂²	1	2	yes	complemented
101	#15689166	C₂²	1	2	yes	complemented
102	#15689163	C₂²	1	2	yes	complemented
103	#15689163	C₂²	1	2	yes	complemented
104	#15689163	C₂²	1	2	yes	complemented
105	#15689163	C₂²	1	2	yes	complemented
106	#15689159	C₂²	1	2	yes	—
107	#15689159	C₂²	1	1	yes	characteristic
108	#15689159	C₂²	1	2	yes	—
109	#15689159	C₂²	1	2	yes	—
110	#15689159	C₂²	1	2	yes	—
111	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
112	#15689119	C₂²	1	2	yes	—
113	#15689119	C₂²	1	1	yes	characteristic
114	#15689117	C₂²	1	2	yes	—
115	#15689117	C₂²	1	1	yes	characteristic
116	C₂×C₂²⋊(C₄₇⋊C₈)	C₂²	1	2	yes	—
117	C₂×C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
118	C₄₇×#556	C₂²	1	1	yes	characteristic
119	C₄₇×#555	C₂²	1	1	yes	characteristic
120	C₄₇×#554	C₂²	1	1	yes	characteristic
121	C₄₇×#553	C₂²	1	2	yes	—
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
126	C₄₇×#546	—	2	1	no	—
127	C₄₇×#533	C₂²	1	1	yes	characteristic
128	C₄₇×#529	—	2	2	no	—
129	C₄₇×#529	—	2	1	no	—
130	C₄₇×#525	C₂²	1	2	yes	—
131	C₄×#41×C₄₇	—	2	1	no	—
132	C₄×#41×C₄₇	C₂²	1	1	yes	characteristic
133	C₂×C₄×D₄×C₄₇	C₂²	1	1	yes	characteristic
134	C₂×#117×C₄₇	C₂²	1	2	yes	—
135	C₂×#10625350	C₂³	1	1	yes	characteristic
136	C₂×#10625352	—	2	1	no	—
137	#13094044	—	2	4	no	—
138	C₂×#10625337	C₂³	1	1	yes	characteristic
139	C₂×#10625335	C₂³	1	1	yes	characteristic
140	C₂×#10625336	C₂³	1	1	yes	characteristic
141	C₂×#10625334	C₂³	1	1	yes	characteristic
142	C₂×#10625329	—	2	8	no	—
143	C₂×#10625329	C₂³	1	2	yes	—
144	C₂×#10625329	C₂³	1	2	yes	—
145	C₂×#10625329	C₂³	1	2	yes	—
146	C₂×#10625329	C₂³	1	2	yes	—
147	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
148	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
149	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
150	#13094024	C₂³	1	1	yes	characteristic
151	#13094024	C₂³	1	1	yes	characteristic
152	#13094019	—	2	2	no	—
153	#13094017	—	2	2	no	—
154	#13094017	—	2	2	no	—
155	#13094016	C₂³	1	2	yes	—
156	#13094015	—	2	1	no	—
157	#13094014	—	2	2	no	—
158	#13094011	—	2	1	no	—
159	#13094010	—	2	2	no	—
160	#13094008	—	2	2	no	—
161	#13094007	—	2	2	no	—
162	#13094006	—	2	2	no	—
163	#13094005	—	2	2	no	—
164	#13094004	—	2	1	no	—
165	#13094003	—	2	1	no	—
166	#13094003	—	2	1	no	—
167	#13094003	C₂³	1	2	yes	—
168	#13094003	C₂³	1	2	yes	—
169	#13094001	—	2	2	no	—
170	#13093998	C₂³	1	2	yes	—
171	#13093998	C₂³	1	2	yes	—
172	#13093996	—	2	2	no	—
173	#13093995	—	2	1	no	—
174	#13093993	—	2	2	no	—
175	C₄×Dic₉₄	—	2	1	no	—
176	C₄×Dic₉₄	—	2	1	no	—
177	C₄×Dic₉₄	C₂³	1	1	yes	characteristic
178	C₄×Dic₉₄	C₂³	1	1	yes	characteristic
179	#13093989	—	2	1	no	—
180	C₄×D₁₈₈	C₂³	1	1	yes	characteristic
181	C₄×D₁₈₈	C₂³	1	1	yes	characteristic
182	D₄×Dic₄₇	—	2	1	no	—
183	C₄×C₂²⋊D₄₇	—	2	1	no	—
184	C₄×C₂²⋊D₄₇	—	2	1	no	—
185	C₄×C₂²⋊D₄₇	—	2	2	no	—
186	C₄×C₂²⋊D₄₇	—	2	2	no	—
187	(C₂²⋊D₄₇)⋊C₄	—	2	2	no	—
188	#13093983	—	2	2	no	—
189	#13093983	—	2	2	no	—
190	#13093983	C₂³	1	2	yes	—
191	#13093983	C₂³	1	2	yes	—
192	#13093983	C₂³	1	1	yes	characteristic
193	#13093983	C₂³	1	2	yes	—
194	#13093982	—	2	1	no	—
195	#13093981	—	2	1	no	—
196	#13093980	—	2	2	no	—
197	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
198	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
199	C₂×C₂²⋊Dic₄₇	—	2	2	no	—
200	C₂×C₄×Dic₄₇	—	2	2	no	—
201	C₄²×D₄₇	—	2	1	no	—
202	#13093957	C₂³	1	1	yes	characteristic
203	#13093957	C₂³	1	1	yes	characteristic
204	#13093957	C₂³	1	2	yes	—
205	#13093957	C₂³	1	2	yes	—
206	#13093957	C₂³	1	2	yes	—
207	#13093957	C₂³	1	2	yes	—
208	#13093957	C₂³	1	2	yes	—
209	#13093957	C₂³	1	2	yes	—
210	#13093957	C₂³	1	2	yes	—
211	#13093957	C₂³	1	2	yes	—
212	#13093955	C₂³	1	2	yes	—
213	#13093955	C₂³	1	2	yes	—
214	#13093955	C₂³	1	2	yes	—
215	#13093955	C₂³	1	2	yes	—
216	#13093955	C₂³	1	2	yes	—
217	#13093955	C₂³	1	2	yes	—
218	#13093955	C₂³	1	2	yes	—
219	#13093955	C₂³	1	2	yes	—
220	#13093955	C₂³	1	1	yes	characteristic
221	#13093955	C₂³	1	1	yes	characteristic
222	C₄⋊(C₄₇⋊C₈)	C₂³	1	1	yes	characteristic
223	C₄⋊(C₄₇⋊C₈)	C₂³	1	1	yes	characteristic
224	C₄⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
225	#13093948	C₂³	1	1	yes	characteristic
226	#13093948	C₂³	1	1	yes	characteristic
227	#13093948	C₂³	1	2	yes	—
228	#13093948	C₂³	1	2	yes	—
229	#13093947	C₂³	1	1	yes	characteristic
230	#13093947	C₂³	1	1	yes	characteristic
231	#13093947	C₂³	1	2	yes	—
232	#13093947	C₂³	1	2	yes	—
233	#13093945	C₂³	1	2	yes	—
234	#13093945	C₂³	1	2	yes	—
235	#13093945	C₂³	1	1	yes	characteristic
236	#13093945	C₂³	1	1	yes	characteristic
237	#13093944	C₂³	1	2	yes	—
238	#13093944	C₂³	1	2	yes	—
239	#13093944	C₂³	1	1	yes	characteristic
240	#13093944	C₂³	1	1	yes	characteristic
241	C₂²⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
242	C₂²⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
243	C₂²⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
244	C₂²⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
245	C₄×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
246	C₄×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
247	C₄×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
248	C₄×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
249	C₂×#41×C₄₇	—	2	1	no	—
250	C₂×#41×C₄₇	C₂³	1	1	yes	characteristic
251	C₂²×D₄×C₄₇	D₄	1	1	yes	characteristic
252	C₂³×C₄×C₄₇	C₂³	1	2	yes	—
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	1	no	—
262	#124×C₄₇	—	2	2	no	—
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	2	no	—
274	#121×C₄₇	—	2	1	no	—
275	#121×C₄₇	C₂³	1	2	yes	—
276	#121×C₄₇	C₂³	1	2	yes	—
277	#120×C₄₇	—	2	2	no	—
278	C₄×Q₈×C₄₇	—	2	1	no	—
279	C₄×Q₈×C₄₇	—	2	1	no	—
280	C₄×Q₈×C₄₇	—	2	1	no	—
281	C₄×Q₈×C₄₇	C₂³	1	1	yes	characteristic
282	C₄×Q₈×C₄₇	C₂³	1	1	yes	characteristic
283	C₄×D₄×C₄₇	—	2	1	no	—
284	C₄×D₄×C₄₇	—	2	2	no	—
285	C₄×D₄×C₄₇	—	2	1	no	—
286	C₄×D₄×C₄₇	—	2	1	no	—
287	C₄×D₄×C₄₇	—	2	2	no	—
288	C₄×D₄×C₄₇	—	2	2	no	—
289	C₄×D₄×C₄₇	D₄	1	1	yes	characteristic
290	C₄×D₄×C₄₇	D₄	1	1	yes	characteristic
291	C₄×D₄×C₄₇	D₄	1	2	yes	—
292	C₄×D₄×C₄₇	C₂³	1	1	yes	characteristic
293	C₄×D₄×C₄₇	C₂³	1	1	yes	characteristic
294	C₄×D₄×C₄₇	C₂³	1	1	yes	characteristic
295	C₄×D₄×C₄₇	C₂³	1	2	yes	—
296	C₄×D₄×C₄₇	C₂³	1	1	yes	characteristic
297	#117×C₄₇	—	2	2	no	—
298	#117×C₄₇	—	2	2	no	—
299	#117×C₄₇	—	2	1	no	—
300	#117×C₄₇	—	2	2	no	—
301	#117×C₄₇	—	2	1	no	—
302	#117×C₄₇	C₂³	1	1	yes	characteristic
303	#117×C₄₇	C₂³	1	2	yes	—
304	#117×C₄₇	C₂³	1	2	yes	—
305	#117×C₄₇	C₂³	1	2	yes	—
306	C₂×C₄⋊C₄×C₄₇	D₄	1	1	yes	characteristic
307	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
308	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
309	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
310	C₂×C₂²⋊C₄×C₄₇	D₄	1	2	yes	—
311	C₂×C₄²×C₄₇	—	2	2	no	—
312	C₂×C₄²×C₄₇	—	2	1	no	—
313	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
314	C₂⁴×C₄₇	C₂×D₄	1	2	yes	—
315	#41×C₄₇	—	2	2	no	—
316	#41×C₄₇	—	2	2	no	—
317	#41×C₄₇	—	4	4	no	—
318	C₂×Q₈×C₄₇	—	2	1	no	—
319	C₂×Q₈×C₄₇	—	2	1	no	—
320	C₂×Q₈×C₄₇	C₂⁴	1	1	yes	characteristic
321	C₂×D₄×C₄₇	—	2	1	no	—
322	C₂×D₄×C₄₇	—	2	2	no	—
323	C₂×D₄×C₄₇	—	2	2	no	—
324	C₂×D₄×C₄₇	—	4	2	no	—
325	C₂×D₄×C₄₇	C₂×D₄	1	1	yes	characteristic
326	C₂×D₄×C₄₇	C₂×D₄	1	1	yes	characteristic
327	C₂×D₄×C₄₇	C₂×D₄	1	2	yes	—
328	C₂×D₄×C₄₇	C₂⁴	1	1	yes	characteristic
329	C₂²×C₄×C₄₇	—	2	4	no	—
330	C₂²×C₄×C₄₇	—	2	4	no	—
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	1	yes	characteristic
338	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
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	2	yes	—
343	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
344	C₂×C₂²⋊D₄₇	—	2	2	no	—
345	C₂×C₂²⋊D₄₇	—	2	1	no	—
346	C₂×C₂²⋊D₄₇	—	2	2	no	—
347	C₂²×Dic₄₇	—	2	2	no	—
348	C₂²×Dic₄₇	—	2	2	no	—
349	#10625352	—	4	4	no	—
350	#10625350	—	2	2	no	—
351	#10625350	—	2	2	no	—
352	C₂×D₁₈₈	C₂⁴	1	1	yes	characteristic
353	C₂×C₄×D₄₇	—	2	1	no	—
354	C₂×C₄×D₄₇	—	2	1	no	—
355	C₂×C₄×D₄₇	—	2	1	no	—
356	C₂×Dic₉₄	—	2	1	no	—
357	C₂×Dic₉₄	—	2	1	no	—
358	C₂×Dic₉₄	C₂⁴	1	1	yes	characteristic
359	C₄⋊C₄×C₄₇	—	2	2	no	—
360	C₄⋊C₄×C₄₇	—	2	2	no	—
361	C₄⋊C₄×C₄₇	—	2	1	no	—
362	C₄⋊C₄×C₄₇	—	2	2	no	—
363	C₄⋊C₄×C₄₇	—	2	2	no	—
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	C₂×D₄	1	1	yes	characteristic
370	C₄⋊C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
371	C₄⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
372	C₄⋊C₄×C₄₇	C₂⁴	1	1	yes	characteristic
373	C₄⋊C₄×C₄₇	C₂⁴	1	1	yes	characteristic
374	C₄⋊C₄×C₄₇	C₂⁴	1	2	yes	—
375	C₄⋊C₄×C₄₇	C₂⁴	1	2	yes	—
376	C₂²⋊C₄×C₄₇	—	2	1	no	—
377	C₂²⋊C₄×C₄₇	—	2	2	no	—
378	C₂²⋊C₄×C₄₇	—	2	2	no	—
379	C₂²⋊C₄×C₄₇	—	2	2	no	—
380	C₂²⋊C₄×C₄₇	—	2	2	no	—
381	C₂²⋊C₄×C₄₇	—	2	2	no	—
382	C₂²⋊C₄×C₄₇	—	2	2	no	—
383	C₂²⋊C₄×C₄₇	—	2	1	no	—
384	C₂²⋊C₄×C₄₇	—	2	1	no	—
385	C₂²⋊C₄×C₄₇	—	2	2	no	—
386	C₂²⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
387	C₂²⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
388	C₂²⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
389	C₂²⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
390	C₄²×C₄₇	—	2	1	no	—
391	C₄²×C₄₇	—	2	2	no	—
392	C₄²×C₄₇	—	2	1	no	—
393	C₄²×C₄₇	—	2	2	no	—
394	C₄²×C₄₇	—	2	2	no	—
395	C₄²×C₄₇	—	2	1	no	—
396	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
397	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
398	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
399	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
400	C₂²⋊Dic₄₇	—	2	1	no	—
401	C₂²⋊Dic₄₇	—	2	2	no	—
402	C₂²⋊Dic₄₇	—	2	2	no	—
403	C₂²⋊Dic₄₇	—	2	2	no	—
404	C₂²⋊Dic₄₇	—	2	2	no	—
405	C₂²⋊Dic₄₇	—	2	2	no	—
406	#10625337	—	2	2	no	—
407	#10625336	—	2	2	no	—
408	#10625335	—	2	2	no	—
409	#10625334	—	2	2	no	—
410	(C₂×D₄₇)⋊C₄	—	2	1	no	—
411	(C₂×D₄₇)⋊C₄	—	2	1	no	—
412	(C₂×D₄₇)⋊C₄	—	2	2	no	—
413	(C₂×D₄₇)⋊C₄	—	2	2	no	—
414	C₄⋊Dic₄₇	—	2	2	no	—
415	C₄⋊Dic₄₇	—	2	2	no	—
416	C₄⋊Dic₄₇	—	2	1	no	—
417	C₄⋊Dic₄₇	—	2	1	no	—
418	C₄⋊Dic₄₇	C₂⁴	1	1	yes	characteristic
419	C₄⋊Dic₄₇	C₂⁴	1	1	yes	characteristic
420	C₄⋊Dic₄₇	C₂⁴	1	2	yes	—
421	C₄⋊Dic₄₇	C₂⁴	1	2	yes	—
422	Dic₄₇⋊C₄	—	2	2	no	—
423	Dic₄₇⋊C₄	—	2	2	no	—
424	Dic₄₇⋊C₄	—	2	1	no	—
425	Dic₄₇⋊C₄	—	2	1	no	—
426	Dic₄₇⋊C₄	—	2	2	no	—
427	Dic₄₇⋊C₄	—	2	2	no	—
428	C₄×Dic₄₇	—	2	1	no	—
429	C₄×Dic₄₇	—	2	1	no	—
430	C₄×Dic₄₇	—	2	1	no	—
431	C₄×Dic₄₇	—	2	2	no	—
432	C₄×Dic₄₇	—	2	2	no	—
433	C₄×Dic₄₇	—	2	2	no	—
434	#10625329	—	2	4	no	—
435	#10625329	—	2	4	no	—
436	#10625329	—	2	4	no	—
437	#10625329	—	2	4	no	—
438	C₂×C₄₇⋊C₈	—	2	4	no	—
439	C₂×C₄₇⋊C₈	—	2	2	no	—
440	C₂×C₄₇⋊C₈	#41	1	4	yes	complemented
441	C₂×C₄₇⋊C₈	C₂⁴	1	1	yes	characteristic
442	C₂×C₄₇⋊C₈	C₂⁴	1	1	yes	characteristic
443	C₂×C₄₇⋊C₈	C₂⁴	1	2	yes	—
444	C₂×C₄₇⋊C₈	C₂⁴	1	2	yes	—
445	C₂×C₄₇⋊C₈	C₂⁴	1	1	yes	characteristic
446	C₂×C₄₇⋊C₈	C₂⁴	1	1	yes	characteristic
447	C₂³×C₄₇	—	2	4	no	—
448	C₂³×C₄₇	—	2	1	no	—
449	C₂³×C₄₇	—	4	2	no	—
450	C₂³×C₄₇	—	4	2	no	—
451	C₂³×C₄₇	C₂²×D₄	1	2	yes	—
452	C₂³×C₄₇	C₂²×D₄	1	2	yes	—
453	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
454	C₂²×D₄₇	—	2	1	no	—
455	Q₈×C₄₇	—	2	1	no	—
456	Q₈×C₄₇	—	2	1	no	—
457	Q₈×C₄₇	—	4	2	no	—
458	Q₈×C₄₇	—	8	1	no	—
459	D₄×C₄₇	—	2	2	no	—
460	D₄×C₄₇	—	2	2	no	—
461	D₄×C₄₇	—	2	1	no	—
462	D₄×C₄₇	—	2	1	no	—
463	D₄×C₄₇	—	4	2	no	—
464	D₄×C₄₇	—	4	4	no	—
465	D₄×C₄₇	—	4	2	no	—
466	D₄×C₄₇	—	8	2	no	—
467	C₂×C₄×C₄₇	—	2	4	no	—
468	C₂×C₄×C₄₇	—	2	4	no	—
469	C₂×C₄×C₄₇	—	2	4	no	—
470	C₂×C₄×C₄₇	—	2	2	no	—
471	C₂×C₄×C₄₇	—	2	2	no	—
472	C₂×C₄×C₄₇	—	2	2	no	—
473	C₂×C₄×C₄₇	—	2	2	no	—
474	C₂×C₄×C₄₇	—	2	2	no	—
475	C₂×C₄×C₄₇	—	2	1	no	—
476	C₂×C₄×C₄₇	—	2	1	no	—
477	C₂×C₄×C₄₇	—	2	1	no	—
478	C₂×C₄×C₄₇	—	2	2	no	—
479	C₂×C₄×C₄₇	—	2	2	no	—
480	C₂×C₄×C₄₇	—	4	1	no	—
481	C₂×C₄×C₄₇	—	4	4	no	—
482	C₂×C₄×C₄₇	—	4	2	no	—
483	C₂×C₄×C₄₇	—	4	2	no	—
484	C₂×C₄×C₄₇	—	8	1	no	—
485	C₂×C₄×C₄₇	—	8	2	no	—
486	C₂×C₄×C₄₇	C₂²×D₄	1	2	yes	—
487	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
488	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
489	C₂×C₄×C₄₇	C₂²×D₄	1	2	yes	—
490	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
491	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
492	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
493	C₂×C₄×C₄₇	C₂×#41	1	2	yes	—
494	C₂×C₄×C₄₇	2₋¹⁺⁴	1	2	yes	—
495	C₂×C₄×C₄₇	C₂⁵	1	1	yes	characteristic
496	C₂²⋊D₄₇	—	4	4	no	—
497	C₂²⋊D₄₇	—	4	2	no	—
498	C₂²⋊D₄₇	—	8	2	no	—
499	C₂×Dic₄₇	—	2	1	no	—
500	C₂×Dic₄₇	—	2	1	no	—
501	C₂×Dic₄₇	—	2	1	no	—
502	C₂×Dic₄₇	—	2	2	no	—
503	C₂×Dic₄₇	—	2	2	no	—
504	C₂×Dic₄₇	—	4	4	no	—
505	C₂×Dic₄₇	—	8	2	no	—
506	D₁₈₈	—	2	1	no	—
507	D₁₈₈	—	2	1	no	—
508	C₄×D₄₇	—	4	2	no	—
509	C₄×D₄₇	—	4	2	no	—
510	C₄×D₄₇	—	8	1	no	—
511	Dic₉₄	—	2	1	no	—
512	Dic₉₄	—	2	1	no	—
513	Dic₉₄	—	4	2	no	—
514	Dic₉₄	—	8	1	no	—
515	C₄₇⋊C₈	—	2	2	no	—
516	C₄₇⋊C₈	—	2	2	no	—
517	C₄₇⋊C₈	—	2	1	no	—
518	C₄₇⋊C₈	—	2	1	no	—
519	C₄₇⋊C₈	C₂×#41	1	2	yes	—
520	C₄₇⋊C₈	C₂×#41	1	2	yes	—
521	#61251	—	47	1	no	maximal, Sylow
522	C₂²×C₄₇	—	2	1	no	—
523	C₂²×C₄₇	—	2	1	no	—
524	C₂²×C₄₇	—	2	2	no	—
525	C₂²×C₄₇	—	2	2	no	—
526	C₂²×C₄₇	—	2	2	no	—
527	C₂²×C₄₇	—	2	2	no	—
528	C₂²×C₄₇	—	2	2	no	—
529	C₂²×C₄₇	—	2	2	no	—
530	C₂²×C₄₇	—	4	1	no	—
531	C₂²×C₄₇	—	4	1	no	—
532	C₂²×C₄₇	—	4	1	no	—
533	C₂²×C₄₇	—	8	4	no	—
534	C₂²×C₄₇	#547	1	2	yes	—
535	C₂²×C₄₇	C₂³×D₄	1	1	yes	characteristic
536	C₂×D₄₇	—	4	1	no	—
537	C₂×D₄₇	—	4	1	no	—
538	C₂×D₄₇	—	4	1	no	—
539	C₄×C₄₇	—	2	1	no	—
540	C₄×C₄₇	—	2	1	no	—
541	C₄×C₄₇	—	2	2	no	—
542	C₄×C₄₇	—	2	2	no	—
543	C₄×C₄₇	—	2	1	no	—
544	C₄×C₄₇	—	4	1	no	—
545	C₄×C₄₇	—	4	2	no	—
546	C₄×C₄₇	—	4	1	no	—
547	C₄×C₄₇	—	4	1	no	—
548	C₄×C₄₇	—	4	2	no	—
549	C₄×C₄₇	#547	1	2	yes	—
550	C₄×C₄₇	#575	1	2	yes	—
551	C₄×C₄₇	C₂²×#41	1	1	yes	characteristic
552	C₄×C₄₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
553	Dic₄₇	—	4	2	no	—
554	Dic₄₇	—	4	1	no	—
555	Dic₄₇	—	4	1	no	—
556	Dic₄₇	—	4	2	no	—
557	Dic₄₇	—	4	1	no	—
558	#3475	—	47	1	no	—
559	#3475	D₄₇	1	1	yes	characteristic, complemented
560	#3357	—	47	1	no	—
561	#3357	—	47	1	no	—
562	#3356	—	47	1	no	—
563	#3356	—	47	1	no	—
564	#3355	—	47	2	no	—
565	#3354	—	47	1	no	—
566	#3354	—	47	1	no	—
567	#3353	—	47	1	no	—
568	#3353	—	47	1	no	—
569	#3352	—	47	2	no	—
570	#3351	—	47	2	no	—
571	#3351	—	47	2	no	—
572	#3160	—	47	1	no	—
573	#3091	—	47	2	no	—
574	#3091	—	47	2	no	—
575	#3076	—	47	1	no	—
576	#3076	—	47	1	no	—
577	#3054	—	47	2	no	—
578	C₄×#135	—	47	1	no	—
579	C₂×#436	—	47	1	no	—
580	#2911	—	47	2	no	—
581	C₂×C₄₇	—	2	2	no	—
582	C₂×C₄₇	—	4	2	no	—
583	C₂×C₄₇	—	4	2	no	—
584	C₂×C₄₇	—	8	1	no	—
585	C₂×C₄₇	C₂×#547	1	1	yes	characteristic
586	C₂×C₄₇	C₂×#575	1	1	yes	characteristic
587	C₂×C₄₇	#3584	1	1	yes	characteristic
588	D₄₇	—	8	1	no	—
589	C₂×#135	—	47	1	no	—
590	C₂²×M₁₆	—	47	2	no	—
591	#556	—	47	1	no	—
592	#556	C₂×D₄₇	1	1	yes	characteristic
593	#555	—	47	1	no	—
594	#555	C₂×D₄₇	1	1	yes	characteristic
595	#554	—	47	1	no	—
596	#554	C₂×D₄₇	1	1	yes	characteristic
597	#553	—	47	2	no	—
598	#553	C₂×D₄₇	1	2	yes	—
599	#552	—	2	1	no	—
600	#552	—	47	2	no	—
601	#552	—	94	1	no	—
602	#552	C₂×D₄₇	1	2	yes	—
603	#551	—	2	2	no	—
604	#551	—	94	2	no	—
605	#547	—	47	1	no	—
606	#547	C₂×D₄₇	1	1	yes	characteristic
607	#546	—	2	1	no	—
608	#546	—	94	1	no	—
609	#533	—	47	1	no	—
610	#533	C₂×D₄₇	1	1	yes	characteristic
611	#529	—	2	2	no	—
612	#529	—	2	1	no	—
613	#529	—	94	2	no	—
614	#529	—	94	1	no	—
615	#525	—	47	2	no	—
616	#525	C₂×D₄₇	1	2	yes	—
617	C₄×#41	—	2	1	no	—
618	C₄×#41	—	47	1	no	—
619	C₄×#41	—	94	1	no	—
620	C₄×#41	C₂×D₄₇	1	1	yes	characteristic
621	C₂×C₄×D₄	C₂×D₄₇	1	1	yes	characteristic
622	C₂×#117	—	47	2	no	—
623	C₂×#117	C₂×D₄₇	1	2	yes	—
624	#500	—	47	1	no	—
625	#500	—	47	1	no	—
626	#499	—	47	2	no	—
627	#499	—	47	2	no	—
628	#498	—	47	1	no	—
629	#498	—	47	1	no	—
630	#485	—	47	2	no	—
631	#485	—	47	2	no	—
632	#485	—	47	2	no	—
633	#485	—	47	2	no	—
634	#484	—	47	2	no	—
635	#484	—	47	2	no	—
636	#483	—	47	2	no	—
637	#483	—	47	2	no	—
638	#482	—	47	2	no	—
639	#482	—	47	2	no	—
640	#482	—	47	2	no	—
641	#482	—	47	2	no	—
642	#481	—	47	2	no	—
643	#481	—	47	2	no	—
644	#480	—	47	2	no	—
645	#480	—	47	2	no	—
646	#479	—	47	2	no	—
647	#479	—	47	2	no	—
648	#478	—	47	2	no	—
649	#478	—	47	2	no	—
650	#477	—	47	1	no	—
651	#477	—	47	1	no	—
652	#476	—	47	1	no	—
653	#476	—	47	1	no	—
654	#475	—	47	1	no	—
655	#475	—	47	1	no	—
656	#474	—	47	1	no	—
657	#474	—	47	1	no	—
658	#470	—	47	2	no	—
659	#470	—	47	2	no	—
660	#469	—	47	2	no	—
661	#469	—	47	2	no	—
662	#468	—	47	2	no	—
663	#468	—	47	2	no	—
664	#468	—	47	2	no	—
665	#468	—	47	2	no	—
666	C₄×Q₁₆	—	47	1	no	—
667	C₄×Q₁₆	—	47	1	no	—
668	C₄×SD₁₆	—	47	1	no	—
669	C₄×SD₁₆	—	47	1	no	—
670	C₄×SD₁₆	—	47	1	no	—
671	C₄×SD₁₆	—	47	1	no	—
672	C₄×D₈	—	47	1	no	—
673	C₄×D₈	—	47	1	no	—
674	#436	—	47	2	no	—
675	#436	—	47	2	no	—
676	#436	—	47	1	no	—
677	#436	—	47	1	no	—
678	#436	—	47	1	no	—
679	#436	—	47	1	no	—
680	#428	—	47	2	no	—
681	#428	—	47	2	no	—
682	#428	—	47	2	no	—
683	#428	—	47	2	no	—
684	#428	—	47	2	no	—
685	#428	—	47	2	no	—
686	#428	—	47	2	no	—
687	#428	—	47	2	no	—
688	#427	—	47	2	no	—
689	#427	—	47	2	no	—
690	#427	—	47	2	no	—
691	#427	—	47	2	no	—
692	#427	—	47	1	no	—
693	C₂×C₄⋊C₈	—	47	1	no	—
694	#416	—	47	2	no	—
695	#416	—	47	1	no	—
696	#416	—	47	2	no	—
697	#416	—	47	1	no	—
698	C₂×C₂²⋊C₈	—	47	2	no	—
699	C₂×C₄×C₈	—	47	1	no	—
700	C₄₇	#61251	1	1	yes	characteristic, complemented, Sylow
701	C₂×#41	—	2	1	no	—
702	C₂×#41	—	47	1	no	—
703	C₂×#41	—	94	1	no	—
704	C₂×#41	C₂²×D₄₇	1	1	yes	characteristic
705	C₂²×D₄	C₂²⋊D₄₇	1	1	yes	characteristic
706	C₂³×C₄	C₂²×D₄₇	1	2	yes	—
707	#135	—	94	4	no	—
708	C₂×Q₁₆	—	47	1	no	—
709	C₂×SD₁₆	—	47	1	no	—
710	C₂×SD₁₆	—	47	1	no	—
711	C₂×D₈	—	47	1	no	—
712	C₂×M₁₆	—	47	2	no	—
713	C₂×M₁₆	—	47	2	no	—
714	C₂×M₁₆	—	47	2	no	—
715	C₂×M₁₆	—	47	2	no	—
716	C₂×M₁₆	—	94	8	no	—
717	C₂²×C₈	—	47	1	no	—
718	C₂²×C₈	—	47	2	no	—
719	C₂²×C₈	—	47	1	no	—
720	C₄⋊Q₈	—	47	1	no	—
721	C₄⋊Q₈	—	47	1	no	—
722	C₄⋊Q₈	C₂²×D₄₇	1	1	yes	characteristic
723	C₄⋊Q₈	C₂²×D₄₇	1	1	yes	characteristic
724	#126	—	2	2	no	—
725	#126	—	2	2	no	—
726	#126	—	2	2	no	—
727	#126	—	94	2	no	—
728	#126	—	94	2	no	—
729	#126	—	94	2	no	—
730	#125	—	2	2	no	—
731	#125	—	2	1	no	—
732	#125	—	47	2	no	—
733	#125	—	94	2	no	—
734	#125	—	94	1	no	—
735	#125	C₂²×D₄₇	1	2	yes	—
736	#124	—	2	1	no	—
737	#124	—	2	2	no	—
738	#124	—	94	1	no	—
739	#124	—	94	2	no	—
740	#123	—	2	2	no	—
741	#123	—	2	2	no	—
742	#123	—	2	2	no	—
743	#123	—	2	2	no	—
744	#123	—	94	2	no	—
745	#123	—	94	2	no	—
746	#123	—	94	2	no	—
747	#123	—	94	2	no	—
748	C₂²⋊Q₈	—	2	1	no	—
749	C₂²⋊Q₈	—	2	1	no	—
750	C₂²⋊Q₈	—	2	1	no	—
751	C₂²⋊Q₈	—	2	2	no	—
752	C₂²⋊Q₈	—	47	2	no	—
753	C₂²⋊Q₈	—	47	2	no	—
754	C₂²⋊Q₈	—	94	1	no	—
755	C₂²⋊Q₈	—	94	1	no	—
756	C₂²⋊Q₈	—	94	1	no	—
757	C₂²⋊Q₈	—	94	2	no	—
758	C₂²⋊Q₈	C₂²×D₄₇	1	2	yes	—
759	C₂²⋊Q₈	C₂²×D₄₇	1	2	yes	—
760	#121	—	2	2	no	—
761	#121	—	2	1	no	—
762	#121	—	47	2	no	—
763	#121	—	47	2	no	—
764	#121	—	94	2	no	—
765	#121	—	94	1	no	—
766	#121	C₂²×D₄₇	1	2	yes	—
767	#121	C₂²×D₄₇	1	2	yes	—
768	#120	—	2	2	no	—
769	#120	—	94	2	no	—
770	C₄×Q₈	—	2	1	no	—
771	C₄×Q₈	—	2	1	no	—
772	C₄×Q₈	—	2	1	no	—
773	C₄×Q₈	—	47	1	no	—
774	C₄×Q₈	—	47	1	no	—
775	C₄×Q₈	—	94	1	no	—
776	C₄×Q₈	—	94	1	no	—
777	C₄×Q₈	—	94	1	no	—
778	C₄×Q₈	C₂²×D₄₇	1	1	yes	characteristic
779	C₄×Q₈	C₂²×D₄₇	1	1	yes	characteristic
780	C₄×D₄	—	2	1	no	—
781	C₄×D₄	—	2	2	no	—
782	C₄×D₄	—	2	1	no	—
783	C₄×D₄	—	2	1	no	—
784	C₄×D₄	—	2	2	no	—
785	C₄×D₄	—	2	2	no	—
786	C₄×D₄	—	47	1	no	—
787	C₄×D₄	—	47	1	no	—
788	C₄×D₄	—	94	1	no	—
789	C₄×D₄	—	94	1	no	—
790	C₄×D₄	—	94	1	no	—
791	C₄×D₄	—	94	2	no	—
792	C₄×D₄	—	94	2	no	—
793	C₄×D₄	—	94	2	no	—
794	C₄×D₄	C₂²⋊D₄₇	1	1	yes	characteristic
795	C₄×D₄	C₂²⋊D₄₇	1	1	yes	characteristic
796	C₄×D₄	C₂²⋊D₄₇	1	2	yes	—
797	C₄×D₄	C₂²×D₄₇	1	1	yes	characteristic
798	C₄×D₄	C₂²×D₄₇	1	1	yes	characteristic
799	C₄×D₄	C₂²×D₄₇	1	1	yes	characteristic
800	C₄×D₄	C₂²×D₄₇	1	1	yes	characteristic
801	C₄×D₄	C₂²×D₄₇	1	2	yes	—
802	#117	—	2	2	no	—
803	#117	—	2	2	no	—
804	#117	—	2	1	no	—
805	#117	—	2	2	no	—
806	#117	—	2	1	no	—
807	#117	—	47	1	no	—
808	#117	—	47	2	no	—
809	#117	—	47	2	no	—
810	#117	—	47	2	no	—
811	#117	—	94	2	no	—
812	#117	—	94	2	no	—
813	#117	—	94	1	no	—
814	#117	—	94	2	no	—
815	#117	—	94	1	no	—
816	#117	C₂²×D₄₇	1	1	yes	characteristic
817	#117	C₂²×D₄₇	1	2	yes	—
818	#117	C₂²×D₄₇	1	2	yes	—
819	#117	C₂²×D₄₇	1	2	yes	—
820	C₂×C₄⋊C₄	—	47	2	no	—
821	C₂×C₄⋊C₄	—	47	2	no	—
822	C₂×C₄⋊C₄	C₂²⋊D₄₇	1	1	yes	characteristic
823	C₂×C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
824	C₂×C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
825	C₂×C₂²⋊C₄	—	2	2	no	—
826	C₂×C₂²⋊C₄	—	94	2	no	—
827	C₂×C₂²⋊C₄	C₂²⋊D₄₇	1	2	yes	—
828	C₂×C₄²	—	2	2	no	—
829	C₂×C₄²	—	2	1	no	—
830	C₂×C₄²	—	94	2	no	—
831	C₂×C₄²	—	94	1	no	—
832	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
833	#107	—	47	1	no	—
834	#107	—	47	1	no	—
835	#107	—	47	2	no	—
836	#107	—	47	2	no	—
837	#107	—	47	2	no	—
838	#107	—	47	2	no	—
839	#107	—	47	2	no	—
840	#107	—	47	2	no	—
841	#107	—	47	2	no	—
842	#107	—	47	2	no	—
843	#106	—	47	1	no	—
844	#106	—	47	1	no	—
845	#106	—	47	2	no	—
846	#106	—	47	2	no	—
847	#106	—	47	2	no	—
848	#106	—	47	2	no	—
849	#106	—	47	2	no	—
850	#106	—	47	2	no	—
851	#106	—	47	2	no	—
852	#106	—	47	2	no	—
853	C₄⋊C₈	—	47	1	no	—
854	C₄⋊C₈	—	47	1	no	—
855	C₄⋊C₈	—	47	2	no	—
856	#103	—	47	1	no	—
857	#103	—	47	1	no	—
858	#103	—	47	2	no	—
859	#103	—	47	2	no	—
860	#103	—	47	1	no	—
861	#103	—	47	1	no	—
862	#103	—	47	2	no	—
863	#103	—	47	2	no	—
864	#102	—	47	1	no	—
865	#102	—	47	1	no	—
866	#102	—	47	2	no	—
867	#102	—	47	2	no	—
868	#102	—	47	1	no	—
869	#102	—	47	1	no	—
870	#102	—	47	2	no	—
871	#102	—	47	2	no	—
872	C₂²⋊C₈	—	47	2	no	—
873	C₂²⋊C₈	—	47	2	no	—
874	C₂²⋊C₈	—	47	2	no	—
875	C₂²⋊C₈	—	47	2	no	—
876	C₄×C₈	—	47	1	no	—
877	C₄×C₈	—	47	1	no	—
878	C₄×C₈	—	47	1	no	—
879	C₄×C₈	—	47	1	no	—
880	C₂⁴	C₂×C₂²⋊D₄₇	1	2	yes	—
881	#41	—	2	2	no	—
882	#41	—	2	2	no	—
883	#41	—	4	4	no	—
884	#41	—	94	2	no	—
885	#41	—	94	2	no	—
886	#41	—	188	4	no	—
887	C₂×Q₈	—	2	1	no	—
888	C₂×Q₈	—	2	1	no	—
889	C₂×Q₈	—	47	1	no	—
890	C₂×Q₈	—	94	1	no	—
891	C₂×Q₈	—	94	1	no	—
892	C₂×Q₈	C₂³×D₄₇	1	1	yes	characteristic
893	C₂×D₄	—	2	1	no	—
894	C₂×D₄	—	2	2	no	—
895	C₂×D₄	—	2	2	no	—
896	C₂×D₄	—	4	2	no	—
897	C₂×D₄	—	47	1	no	—
898	C₂×D₄	—	94	2	no	—
899	C₂×D₄	—	94	1	no	—
900	C₂×D₄	—	94	2	no	—
901	C₂×D₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
902	C₂×D₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
903	C₂×D₄	C₂×C₂²⋊D₄₇	1	2	yes	—
904	C₂×D₄	C₂³×D₄₇	1	1	yes	characteristic
905	C₂²×C₄	—	2	4	no	—
906	C₂²×C₄	—	2	4	no	—
907	C₂²×C₄	—	2	2	no	—
908	C₂²×C₄	—	2	2	no	—
909	C₂²×C₄	—	2	1	no	—
910	C₂²×C₄	—	2	1	no	—
911	C₂²×C₄	—	2	1	no	—
912	C₂²×C₄	—	94	2	no	—
913	C₂²×C₄	—	94	2	no	—
914	C₂²×C₄	—	94	1	no	—
915	C₂²×C₄	—	94	1	no	—
916	C₂²×C₄	—	94	1	no	—
917	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
918	C₂²×C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
919	C₂²×C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
920	C₂²×C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
921	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
922	C₂²×C₄	C₂³×D₄₇	1	2	yes	—
923	C₂²×C₄	C₂³×D₄₇	1	2	yes	—
924	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
925	Q₁₆	—	94	2	no	—
926	SD₁₆	—	94	2	no	—
927	SD₁₆	—	94	2	no	—
928	D₈	—	94	2	no	—
929	M₁₆	—	94	4	no	—
930	M₁₆	—	94	4	no	—
931	M₁₆	—	94	4	no	—
932	M₁₆	—	94	4	no	—
933	C₂×C₈	—	47	4	no	—
934	C₂×C₈	—	47	1	no	—
935	C₂×C₈	—	47	1	no	—
936	C₂×C₈	—	47	1	no	—
937	C₂×C₈	—	47	1	no	—
938	C₂×C₈	—	47	2	no	—
939	C₂×C₈	—	47	2	no	—
940	C₂×C₈	—	94	4	no	—
941	C₂×C₈	—	94	2	no	—
942	C₄⋊C₄	—	2	2	no	—
943	C₄⋊C₄	—	2	2	no	—
944	C₄⋊C₄	—	2	1	no	—
945	C₄⋊C₄	—	2	2	no	—
946	C₄⋊C₄	—	2	2	no	—
947	C₄⋊C₄	—	2	1	no	—
948	C₄⋊C₄	—	2	1	no	—
949	C₄⋊C₄	—	2	2	no	—
950	C₄⋊C₄	—	2	2	no	—
951	C₄⋊C₄	—	2	1	no	—
952	C₄⋊C₄	—	47	1	no	—
953	C₄⋊C₄	—	47	1	no	—
954	C₄⋊C₄	—	47	2	no	—
955	C₄⋊C₄	—	47	2	no	—
956	C₄⋊C₄	—	94	1	no	—
957	C₄⋊C₄	—	94	1	no	—
958	C₄⋊C₄	—	94	2	no	—
959	C₄⋊C₄	—	94	2	no	—
960	C₄⋊C₄	—	94	2	no	—
961	C₄⋊C₄	—	94	2	no	—
962	C₄⋊C₄	—	94	2	no	—
963	C₄⋊C₄	—	94	2	no	—
964	C₄⋊C₄	—	94	1	no	—
965	C₄⋊C₄	—	94	1	no	—
966	C₄⋊C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
967	C₄⋊C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
968	C₄⋊C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
969	C₄⋊C₄	C₂³×D₄₇	1	1	yes	characteristic
970	C₄⋊C₄	C₂³×D₄₇	1	1	yes	characteristic
971	C₄⋊C₄	C₂³×D₄₇	1	2	yes	—
972	C₄⋊C₄	C₂³×D₄₇	1	2	yes	—
973	C₂²⋊C₄	—	2	1	no	—
974	C₂²⋊C₄	—	2	2	no	—
975	C₂²⋊C₄	—	2	2	no	—
976	C₂²⋊C₄	—	2	2	no	—
977	C₂²⋊C₄	—	2	2	no	—
978	C₂²⋊C₄	—	2	2	no	—
979	C₂²⋊C₄	—	2	2	no	—
980	C₂²⋊C₄	—	2	1	no	—
981	C₂²⋊C₄	—	2	1	no	—
982	C₂²⋊C₄	—	2	2	no	—
983	C₂²⋊C₄	—	94	1	no	—
984	C₂²⋊C₄	—	94	2	no	—
985	C₂²⋊C₄	—	94	2	no	—
986	C₂²⋊C₄	—	94	2	no	—
987	C₂²⋊C₄	—	94	2	no	—
988	C₂²⋊C₄	—	94	2	no	—
989	C₂²⋊C₄	—	94	1	no	—
990	C₂²⋊C₄	—	94	1	no	—
991	C₂²⋊C₄	—	94	2	no	—
992	C₂²⋊C₄	—	94	2	no	—
993	C₂²⋊C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
994	C₂²⋊C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
995	C₂²⋊C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
996	C₂²⋊C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
997	C₄²	—	2	2	no	—
998	C₄²	—	2	1	no	—
999	C₄²	—	2	2	no	—
1000	C₄²	—	2	1	no	—
1001	C₄²	—	2	1	no	—
1002	C₄²	—	2	2	no	—
1003	C₄²	—	94	2	no	—
1004	C₄²	—	94	2	no	—
1005	C₄²	—	94	1	no	—
1006	C₄²	—	94	1	no	—
1007	C₄²	—	94	1	no	—
1008	C₄²	—	94	2	no	—
1009	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
1010	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
1011	C₄²	C₂³×D₄₇	1	1	yes	characteristic
1012	C₄²	C₂³×D₄₇	1	1	yes	characteristic
1013	C₂³	—	2	4	no	—
1014	C₂³	—	2	1	no	—
1015	C₂³	—	4	2	no	—
1016	C₂³	—	4	2	no	—
1017	C₂³	—	94	1	no	—
1018	C₂³	C₂²×C₂²⋊D₄₇	1	2	yes	—
1019	C₂³	C₂²×C₂²⋊D₄₇	1	2	yes	—
1020	C₂³	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
1021	Q₈	—	2	1	no	—
1022	Q₈	—	2	1	no	—
1023	Q₈	—	4	2	no	—
1024	Q₈	—	8	1	no	—
1025	Q₈	—	94	1	no	—
1026	Q₈	—	94	1	no	—
1027	Q₈	—	376	1	no	—
1028	Q₈	—	188	2	no	—
1029	D₄	—	2	2	no	—
1030	D₄	—	2	2	no	—
1031	D₄	—	2	1	no	—
1032	D₄	—	2	1	no	—
1033	D₄	—	4	2	no	—
1034	D₄	—	4	4	no	—
1035	D₄	—	4	2	no	—
1036	D₄	—	8	2	no	—
1037	D₄	—	94	1	no	—
1038	D₄	—	94	1	no	—
1039	D₄	—	376	2	no	—
1040	D₄	—	188	4	no	—
1041	D₄	—	188	2	no	—
1042	C₂×C₄	—	2	4	no	—
1043	C₂×C₄	—	2	4	no	—
1044	C₂×C₄	—	2	4	no	—
1045	C₂×C₄	—	2	2	no	—
1046	C₂×C₄	—	2	2	no	—
1047	C₂×C₄	—	2	2	no	—
1048	C₂×C₄	—	2	2	no	—
1049	C₂×C₄	—	2	2	no	—
1050	C₂×C₄	—	2	1	no	—
1051	C₂×C₄	—	2	1	no	—
1052	C₂×C₄	—	2	1	no	—
1053	C₂×C₄	—	2	2	no	—
1054	C₂×C₄	—	2	2	no	—
1055	C₂×C₄	—	4	1	no	—
1056	C₂×C₄	—	4	4	no	—
1057	C₂×C₄	—	4	2	no	—
1058	C₂×C₄	—	4	2	no	—
1059	C₂×C₄	—	8	1	no	—
1060	C₂×C₄	—	8	2	no	—
1061	C₂×C₄	—	94	1	no	—
1062	C₂×C₄	—	94	1	no	—
1063	C₂×C₄	—	94	2	no	—
1064	C₂×C₄	—	94	2	no	—
1065	C₂×C₄	—	94	1	no	—
1066	C₂×C₄	—	376	1	no	—
1067	C₂×C₄	—	376	2	no	—
1068	C₂×C₄	—	188	4	no	—
1069	C₂×C₄	—	188	2	no	—
1070	C₂×C₄	—	188	2	no	—
1071	C₂×C₄	C₂²×C₂²⋊D₄₇	1	2	yes	—
1072	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
1073	C₂×C₄	C₂²×C₂²⋊D₄₇	1	2	yes	—
1074	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
1075	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
1076	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
1077	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
1078	C₂×C₄	#41×D₄₇	1	2	yes	—
1079	C₂×C₄	#13094071	1	2	yes	—
1080	C₂×C₄	C₂⁴×D₄₇	1	1	yes	characteristic
1081	C₈	—	47	2	no	—
1082	C₈	—	47	2	no	—
1083	C₈	—	94	2	no	—
1084	C₈	—	94	2	no	—
1085	C₈	—	94	1	no	—
1086	C₈	—	94	1	no	—
1087	C₂²	—	2	1	no	—
1088	C₂²	—	2	1	no	—
1089	C₂²	—	2	2	no	—
1090	C₂²	—	2	2	no	—
1091	C₂²	—	2	2	no	—
1092	C₂²	—	2	2	no	—
1093	C₂²	—	2	2	no	—
1094	C₂²	—	2	2	no	—
1095	C₂²	—	4	1	no	—
1096	C₂²	—	4	1	no	—
1097	C₂²	—	4	1	no	—
1098	C₂²	—	8	4	no	—
1099	C₂²	—	188	1	no	—
1100	C₂²	—	188	1	no	—
1101	C₂²	—	188	1	no	—
1102	C₂²	#15689772	1	2	yes	—
1103	C₂²	C₂³×C₂²⋊D₄₇	1	1	yes	characteristic
1104	C₄	—	2	2	no	—
1105	C₄	—	2	2	no	—
1106	C₄	—	2	1	no	—
1107	C₄	—	2	1	no	—
1108	C₄	—	2	1	no	—
1109	C₄	—	4	1	no	—
1110	C₄	—	4	1	no	—
1111	C₄	—	4	2	no	—
1112	C₄	—	4	1	no	—
1113	C₄	—	4	2	no	—
1114	C₄	—	188	1	no	—
1115	C₄	—	188	1	no	—
1116	C₄	—	188	2	no	—
1117	C₄	—	188	1	no	—
1118	C₄	—	188	2	no	—
1119	C₄	#15689772	1	2	yes	—
1120	C₄	#15689921	1	2	yes	—
1121	C₄	C₂×#41×D₄₇	1	1	yes	characteristic
1122	C₄	C₂×#13094071	1	1	yes	characteristic
1123	C₂	—	2	2	no	—
1124	C₂	—	4	2	no	—
1125	C₂	—	4	2	no	—
1126	C₂	—	8	1	no	—
1127	C₂	—	376	1	no	—
1128	C₂	C₂×#15689772	1	1	yes	characteristic
1129	C₂	C₂×#15689921	1	1	yes	characteristic
1130	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	#61251
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄×D₄ ◁ #3475

Complements

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

N	H ≅ G/N	type
1. #20256946	C₂	semidirect
2. #20256014	C₂	semidirect
3. #20256008	C₂	semidirect
4. #20256003	C₂	semidirect
5. #20255997	C₂	semidirect
6. #20255988	C₂	semidirect
7. #20255983	C₂	semidirect
8. #20255977	C₂	semidirect
9. #20255972	C₂	semidirect
10. #20255966	C₂	semidirect
11. #20255957	C₂	semidirect
12. #20255948	C₂	semidirect
13. #20255942	C₂	semidirect
14. #20253898	C₂	semidirect
15. #20253301	C₂	semidirect
16. #20253297	C₂	semidirect
17. #20253176	C₂	semidirect
18. #20253170	C₂	semidirect
19. #20252994	C₂	semidirect
20. C₄×#13094044	C₂	semidirect
21. C₂×#15689201	C₂	semidirect
22. #20251977	C₂	semidirect
23. C₄₇×#3475	C₂	semidirect
42. #15689526	C₂²	semidirect
43. #15689526	C₂²	semidirect
44. #15689522	C₂²	semidirect
45. #15689522	C₂²	semidirect
46. #15689519	C₂²	semidirect
47. #15689519	C₂²	semidirect
48. #15689464	C₂²	semidirect
49. #15689464	C₂²	semidirect
50. #15689461	C₂²	semidirect
51. #15689461	C₂²	semidirect
52. #15689458	C₂²	semidirect
53. #15689456	C₂²	semidirect
54. #15689453	C₂²	semidirect
55. #15689451	C₂²	semidirect
56. #15689447	C₂²	semidirect
57. #15689447	C₂²	semidirect
58. #15689444	C₂²	semidirect
59. #15689444	C₂²	semidirect
60. #15689441	C₂²	semidirect
61. #15689439	C₂²	semidirect
62. #15689436	C₂²	semidirect
63. #15689434	C₂²	semidirect
64. #15689430	C₂²	semidirect
65. #15689427	C₂²	semidirect
66. #15689423	C₂²	semidirect
67. #15689420	C₂²	semidirect
68. #15689418	C₂²	semidirect
69. #15689415	C₂²	semidirect
70. #15689413	C₂²	semidirect
71. #15689410	C₂²	semidirect
72. #15689408	C₂²	semidirect
73. #15689405	C₂²	semidirect
74. #15689403	C₂²	semidirect
75. #15689400	C₂²	semidirect
76. #15689379	C₂²	semidirect
77. #15689379	C₂²	semidirect
78. #15689374	C₂²	semidirect
79. #15689374	C₂²	semidirect
80. #15689371	C₂²	semidirect
81. #15689371	C₂²	semidirect
82. #15689367	C₂²	semidirect
83. #15689367	C₂²	semidirect
84. C₄×#10625337	C₂²	semidirect
85. C₄×#10625337	C₂²	semidirect
86. C₄×#10625336	C₂²	semidirect
87. C₄×#10625336	C₂²	semidirect
88. C₄×#10625335	C₂²	semidirect
89. C₄×#10625335	C₂²	semidirect
90. C₄×#10625334	C₂²	semidirect
91. C₄×#10625334	C₂²	semidirect
98. #15689166	C₂²	semidirect
99. #15689166	C₂²	semidirect
100. #15689166	C₂²	semidirect
101. #15689166	C₂²	semidirect
102. #15689163	C₂²	semidirect
103. #15689163	C₂²	semidirect
104. #15689163	C₂²	semidirect
105. #15689163	C₂²	semidirect
440. C₂×C₄₇⋊C₈	#41	semidirect
559. #3475	D₄₇	semidirect
700. C₄₇	#61251	semidirect

Maximal subgroups

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

subgroup	index
#20256946	2
#20256014	2
#20256008	2
#20256003	2
#20255997	2
#20255988	2
#20255983	2
#20255977	2
#20255972	2
#20255966	2
#20255957	2
#20255948	2
#20255942	2
#20253898	2
#20253301	2
#20253297	2
#20253176	2
#20253170	2
#20252994	2
C₄×#13094044	2
C₂×#15689201	2
#20251977	2
C₄₇×#3475	2
#61251	47