Subgroups — D₄₇×#3173 #27086068

Order 12032.

1970 conjugacy classes of subgroups.

The subgroup lattice has 1054 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#542×D₄₇	C₂	1	2	yes	maximal, complemented
2	#20254008	C₂	1	1	yes	maximal, characteristic, complemented
3	#20254007	C₂	1	1	yes	maximal, characteristic, complemented
4	#20254006	C₂	1	1	yes	maximal, characteristic, complemented
5	#20254005	C₂	1	1	yes	maximal, characteristic, complemented
6	#20254004	C₂	1	2	yes	maximal, complemented
7	#20254003	C₂	1	1	yes	maximal, characteristic, complemented
8	#20254002	C₂	1	1	yes	maximal, characteristic, complemented
9	#20254001	C₂	1	2	yes	maximal, complemented
10	#20254000	C₂	1	1	yes	maximal, characteristic, complemented
11	#20253999	C₂	1	2	yes	maximal, complemented
12	#20253998	C₂	1	2	yes	maximal, complemented
13	#498×D₄₇	C₂	1	1	yes	maximal, characteristic, complemented
14	#495×D₄₇	C₂	1	1	yes	maximal, characteristic, complemented
15	#489×D₄₇	C₂	1	2	yes	maximal, complemented
16	#470×D₄₇	C₂	1	1	yes	maximal, characteristic, complemented
17	#469×D₄₇	C₂	1	1	yes	maximal, characteristic
18	#465×D₄₇	C₂	1	2	yes	maximal, complemented
19	#442×D₄₇	C₂	1	1	yes	maximal, characteristic, complemented
20	#441×D₄₇	C₂	1	1	yes	maximal, characteristic, complemented
21	C₄×SD₁₆×D₄₇	C₂	1	2	yes	maximal, complemented
22	#405×D₄₇	C₂	1	1	yes	maximal, characteristic, complemented
23	C₄₇×#3173	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×Q₁₆×D₄₇	C₂²	1	1	yes	characteristic
25	C₂×SD₁₆×D₄₇	C₂²	1	2	yes	—
26	C₂×D₈×D₄₇	C₂²	1	1	yes	characteristic
27	C₂×M₁₆×D₄₇	C₂²	1	1	yes	characteristic
28	C₂²×C₈×D₄₇	C₂²	1	1	yes	characteristic
29	#15689747	C₂²	1	2	yes	complemented
30	#15689746	C₂²	1	2	yes	complemented
31	#15689745	C₂²	1	2	yes	complemented
32	#15689744	C₂²	1	2	yes	complemented
33	#15689743	—	2	2	no	—
34	#15689742	C₂²	1	2	yes	complemented
35	#15689741	—	2	2	no	—
36	#15689740	C₂²	1	2	yes	complemented
37	#15689739	—	2	2	no	—
38	#15689738	C₂²	1	2	yes	complemented
39	#15689737	—	2	2	no	—
40	C₄⋊Q₈×D₄₇	C₂²	1	2	yes	—
41	#126×D₄₇	—	2	2	no	—
42	#124×D₄₇	—	2	2	no	—
43	#124×D₄₇	C₂²	1	2	yes	—
44	#123×D₄₇	—	2	2	no	—
45	C₂²⋊Q₈×D₄₇	—	2	2	no	—
46	C₂²⋊Q₈×D₄₇	C₂²	1	2	yes	—
47	#121×D₄₇	C₂²	1	2	yes	—
48	C₄×Q₈×D₄₇	C₂²	1	2	yes	—
49	C₄×D₄×D₄₇	C₂²	1	2	yes	—
50	#117×D₄₇	C₂²	1	1	yes	characteristic
51	#15689521	C₂²	1	1	yes	characteristic, complemented
52	#15689520	C₂²	1	2	yes	complemented
53	#15689520	C₂²	1	1	yes	characteristic, complemented
54	#15689520	C₂²	1	1	yes	characteristic, complemented
55	#15689519	C₂²	1	2	yes	complemented
56	#15689508	C₂²	1	1	yes	characteristic, complemented
57	#15689507	C₂²	1	1	yes	characteristic, complemented
58	#15689506	C₂²	1	1	yes	characteristic, complemented
59	#15689505	C₂²	1	2	yes	complemented
60	#15689504	C₂²	1	2	yes	complemented
61	#15689485	C₂²	1	2	yes	complemented
62	#15689484	C₂²	1	2	yes	complemented
63	#15689484	C₂²	1	2	yes	complemented
64	#15689483	C₂²	1	2	yes	complemented
65	#15689482	C₂²	1	2	yes	complemented
66	#15689481	C₂²	1	2	yes	complemented
67	#15689481	C₂²	1	2	yes	complemented
68	#15689382	C₂²	1	1	yes	characteristic, complemented
69	#15689381	C₂²	1	1	yes	characteristic, complemented
70	#15689380	C₂²	1	2	yes	complemented
71	#15689379	C₂²	1	2	yes	complemented
72	#15689378	C₂²	1	1	yes	characteristic, complemented
73	#15689377	C₂²	1	1	yes	characteristic
74	#15689376	C₂²	1	1	yes	characteristic
75	#15689375	C₂²	1	2	yes	—
76	#15689374	C₂²	1	2	yes	—
77	#15689373	C₂²	1	1	yes	characteristic
78	#15689355	C₂²	1	2	yes	complemented
79	#15689354	C₂²	1	2	yes	complemented
80	#15689353	C₂²	1	2	yes	complemented
81	#15689352	C₂²	1	2	yes	complemented
82	#15689351	C₂²	1	2	yes	complemented
83	#15689350	C₂²	1	2	yes	complemented
84	#15689349	C₂²	1	2	yes	complemented
85	#15689236	C₂²	1	1	yes	characteristic, complemented
86	#15689235	C₂²	1	1	yes	characteristic, complemented
87	#15689234	C₂²	1	1	yes	characteristic, complemented
88	#15689233	C₂²	1	2	yes	complemented
89	#15689232	C₂²	1	2	yes	complemented
90	#15689231	C₂²	1	1	yes	characteristic, complemented
91	#15689230	C₂²	1	1	yes	characteristic, complemented
92	#15689229	C₂²	1	1	yes	characteristic, complemented
93	#15689228	C₂²	1	2	yes	complemented
94	#15689227	C₂²	1	2	yes	complemented
95	#15689214	C₂²	1	2	yes	complemented
96	C₄×#10625325	C₂²	1	2	yes	complemented
97	SD₁₆×Dic₄₇	C₂²	1	2	yes	complemented
98	C₄×#10625336	C₂²	1	2	yes	complemented
99	#15689210	C₂²	1	2	yes	complemented
100	C₄×#10625335	C₂²	1	2	yes	complemented
101	#15689208	C₂²	1	2	yes	complemented
102	#106×D₄₇	C₂²	1	1	yes	characteristic
103	#106×D₄₇	C₂²	1	2	yes	—
104	#106×D₄₇	C₂²	1	1	yes	characteristic
105	#103×D₄₇	C₂²	1	2	yes	—
106	#103×D₄₇	C₂²	1	2	yes	—
107	#102×D₄₇	C₂²	1	2	yes	—
108	#102×D₄₇	C₂²	1	2	yes	—
109	#15689081	C₂²	1	1	yes	characteristic, complemented
110	#15689080	C₂²	1	1	yes	characteristic, complemented
111	#15689080	C₂²	1	1	yes	characteristic, complemented
112	#15689079	C₂²	1	1	yes	characteristic, complemented
113	#15689078	C₂²	1	1	yes	characteristic, complemented
114	#15689077	C₂²	1	1	yes	characteristic, complemented
115	#15689077	C₂²	1	1	yes	characteristic, complemented
116	#97×D₄₇	C₂²	1	1	yes	characteristic
117	#97×D₄₇	C₂²	1	1	yes	characteristic
118	C₄×C₈×D₄₇	C₂²	1	1	yes	characteristic
119	C₄×C₈×D₄₇	C₂²	1	1	yes	characteristic
120	C₄₇×#542	C₂²	1	2	yes	complemented
121	C₄₇×#498	C₂²	1	1	yes	characteristic, complemented
122	C₄₇×#495	C₂²	1	1	yes	characteristic, complemented
123	C₄₇×#489	C₂²	1	2	yes	complemented
124	C₄₇×#470	C₂²	1	1	yes	characteristic, complemented
125	C₄₇×#469	C₂²	1	1	yes	characteristic
126	C₄₇×#465	C₂²	1	2	yes	complemented
127	C₄₇×#442	C₂²	1	1	yes	characteristic, complemented
128	C₄₇×#441	C₂²	1	1	yes	characteristic, complemented
129	C₄×SD₁₆×C₄₇	C₂²	1	2	yes	complemented
130	C₄₇×#405	C₂²	1	1	yes	characteristic, complemented
131	C₂×Q₈×D₄₇	—	2	2	no	—
132	C₂×Q₈×D₄₇	C₂³	1	2	yes	—
133	C₂×D₄×D₄₇	—	2	2	no	—
134	C₂×D₄×D₄₇	C₂³	1	2	yes	—
135	C₂²×C₄×D₄₇	—	2	2	no	—
136	C₂²×C₄×D₄₇	C₂³	1	1	yes	characteristic
137	C₂×Dic₁₈₈	C₂³	1	1	yes	characteristic
138	C₂×#10625337	C₂³	1	2	yes	—
139	Q₁₆×D₄₇	—	2	4	no	—
140	C₂×#10625325	C₂³	1	2	yes	—
141	C₂×#10625335	C₂³	1	2	yes	—
142	C₂×#10625336	C₂³	1	2	yes	—
143	SD₁₆×D₄₇	—	2	8	no	—
144	C₂×D₃₇₆	C₂³	1	1	yes	characteristic
145	C₂×#10625334	C₂³	1	2	yes	—
146	D₈×D₄₇	—	2	4	no	—
147	C₂×#10625329	C₂³	1	1	yes	characteristic
148	C₂×#10625324	C₂³	1	1	yes	characteristic
149	C₂×#10625324	C₂³	1	1	yes	characteristic
150	M₁₆×D₄₇	—	2	4	no	—
151	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
152	C₂×C₈×D₄₇	—	2	4	no	—
153	C₂×C₈×D₄₇	C₂³	1	1	yes	characteristic
154	C₂×C₈×D₄₇	C₂³	1	1	yes	characteristic
155	C₂×C₈×D₄₇	C₂³	1	1	yes	characteristic
156	C₂×C₈×D₄₇	C₂³	1	1	yes	characteristic
157	C₂×C₈×D₄₇	C₂³	1	1	yes	characteristic
158	C₂×C₈×D₄₇	C₂³	1	1	yes	characteristic
159	#13094024	C₂³	1	2	yes	—
160	#13094023	—	2	2	no	—
161	#13094023	C₂³	1	2	yes	—
162	#13094023	C₂³	1	2	yes	—
163	#13094022	—	2	2	no	—
164	#13094019	—	2	2	no	—
165	#13094019	—	2	2	no	—
166	#13094019	—	2	2	no	—
167	#13094018	—	2	2	no	—
168	#13094017	—	2	2	no	—
169	#13094017	—	2	2	no	—
170	#13094017	—	2	2	no	—
171	#13094013	—	2	2	no	—
172	#13094013	C₂³	1	2	yes	—
173	#13094012	—	2	2	no	—
174	#13094012	C₂³	1	2	yes	—
175	#13094011	—	2	2	no	—
176	#13094011	C₂³	1	2	yes	—
177	#13094010	—	2	2	no	—
178	#13094010	—	2	2	no	—
179	#13094010	—	2	2	no	—
180	#13094010	—	2	2	no	—
181	#13094010	—	2	2	no	—
182	#13094010	—	2	2	no	—
183	#13094009	—	2	2	no	—
184	#13094009	—	2	2	no	—
185	#13094008	—	2	2	no	—
186	#13094007	—	2	2	no	—
187	#13094006	—	2	2	no	—
188	#13094006	—	2	2	no	—
189	#13094005	—	2	2	no	—
190	#13094004	—	2	2	no	—
191	#13094004	C₂³	1	2	yes	—
192	#13094003	—	2	2	no	—
193	#13094003	C₂³	1	2	yes	—
194	#13094002	—	2	2	no	—
195	#13094002	—	2	2	no	—
196	#13094002	—	2	2	no	—
197	#13094001	—	2	2	no	—
198	#13094001	—	2	2	no	—
199	#13094001	—	2	2	no	—
200	#13094000	—	2	2	no	—
201	#13094000	C₂³	1	2	yes	—
202	#13093999	C₂³	1	2	yes	—
203	#13093998	C₂³	1	2	yes	—
204	#13093997	—	2	2	no	—
205	#13093996	—	2	2	no	—
206	#13093995	C₂³	1	2	yes	—
207	Q₈×Dic₄₇	C₂³	1	2	yes	—
208	C₄×Dic₉₄	—	2	2	no	—
209	C₄×Dic₉₄	C₂³	1	2	yes	—
210	#13093989	—	2	2	no	—
211	#13093989	C₂³	1	2	yes	—
212	C₄×D₁₈₈	C₂³	1	2	yes	—
213	D₄×Dic₄₇	C₂³	1	2	yes	—
214	#13093986	C₂³	1	2	yes	—
215	C₄×C₂²⋊D₄₇	—	2	2	no	—
216	(C₂²⋊D₄₇)⋊C₄	—	2	2	no	—
217	#13093983	C₂³	1	1	yes	characteristic
218	#13093982	D₄	1	2	yes	—
219	#13093981	C₂³	1	1	yes	characteristic
220	#13093981	C₂³	1	1	yes	characteristic
221	#13093980	D₄	1	2	yes	—
222	C₄⋊C₄×D₄₇	—	2	2	no	—
223	C₄⋊C₄×D₄₇	—	2	2	no	—
224	C₄⋊C₄×D₄₇	—	2	2	no	—
225	C₄⋊C₄×D₄₇	D₄	1	2	yes	—
226	C₄⋊C₄×D₄₇	C₂³	1	2	yes	—
227	C₄⋊C₄×D₄₇	C₂³	1	2	yes	—
228	C₂²⋊C₄×D₄₇	—	2	2	no	—
229	C₂²⋊C₄×D₄₇	—	2	2	no	—
230	C₂²⋊C₄×D₄₇	—	2	2	no	—
231	C₂²⋊C₄×D₄₇	—	2	2	no	—
232	C₂²⋊C₄×D₄₇	—	2	2	no	—
233	C₂²⋊C₄×D₄₇	D₄	1	2	yes	—
234	C₄²×D₄₇	—	2	2	no	—
235	C₄²×D₄₇	C₂³	1	1	yes	characteristic
236	C₄²×D₄₇	C₂³	1	1	yes	characteristic
237	#13093956	C₂³	1	1	yes	characteristic
238	#13093956	C₂³	1	1	yes	characteristic
239	#13093956	C₂³	1	2	yes	—
240	#13093955	C₂³	1	2	yes	—
241	#13093955	C₂³	1	2	yes	—
242	#13093955	C₂³	1	2	yes	—
243	#13093955	C₂³	1	2	yes	—
244	#13093949	C₂³	1	2	yes	—
245	#13093949	C₂³	1	2	yes	—
246	#13093948	C₂³	1	2	yes	—
247	#13093948	C₂³	1	2	yes	—
248	#13093947	C₂³	1	2	yes	—
249	#13093947	C₂³	1	2	yes	—
250	#13093946	C₂³	1	2	yes	—
251	#13093946	C₂³	1	2	yes	—
252	#13093945	C₂³	1	2	yes	—
253	#13093945	C₂³	1	2	yes	—
254	#13093944	C₂³	1	2	yes	—
255	#13093944	C₂³	1	2	yes	—
256	#13093935	C₂³	1	1	yes	characteristic
257	#13093935	C₂³	1	1	yes	characteristic
258	#13093934	C₂³	1	1	yes	characteristic
259	#13093934	C₂³	1	1	yes	characteristic
260	#13093934	C₂³	1	1	yes	characteristic
261	#13093934	C₂³	1	1	yes	characteristic
262	C₄×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
263	C₄×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
264	C₈×Dic₄₇	C₂³	1	1	yes	characteristic
265	C₈×Dic₄₇	C₂³	1	1	yes	characteristic
266	C₈×Dic₄₇	C₂³	1	1	yes	characteristic
267	C₈×Dic₄₇	C₂³	1	1	yes	characteristic
268	C₂×Q₁₆×C₄₇	C₂³	1	1	yes	characteristic
269	C₂×SD₁₆×C₄₇	C₂³	1	2	yes	—
270	C₂×D₈×C₄₇	C₂³	1	1	yes	characteristic
271	C₂×M₁₆×C₄₇	C₂³	1	1	yes	characteristic
272	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
273	C₄⋊Q₈×C₄₇	C₂³	1	2	yes	—
274	#126×C₄₇	—	2	2	no	—
275	#124×C₄₇	—	2	2	no	—
276	#124×C₄₇	C₂³	1	2	yes	—
277	#123×C₄₇	—	2	2	no	—
278	C₂²⋊Q₈×C₄₇	—	2	2	no	—
279	C₂²⋊Q₈×C₄₇	C₂³	1	2	yes	—
280	#121×C₄₇	C₂³	1	2	yes	—
281	C₄×Q₈×C₄₇	C₂³	1	2	yes	—
282	C₄×D₄×C₄₇	C₂³	1	2	yes	—
283	#117×C₄₇	C₂³	1	1	yes	characteristic
284	#106×C₄₇	C₂³	1	1	yes	characteristic
285	#106×C₄₇	C₂³	1	2	yes	—
286	#106×C₄₇	C₂³	1	1	yes	characteristic
287	#103×C₄₇	C₂³	1	2	yes	—
288	#103×C₄₇	C₂³	1	2	yes	—
289	#102×C₄₇	C₂³	1	2	yes	—
290	#102×C₄₇	C₂³	1	2	yes	—
291	#97×C₄₇	C₂³	1	1	yes	characteristic
292	#97×C₄₇	C₂³	1	1	yes	characteristic
293	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
294	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
295	C₂³×D₄₇	—	2	2	no	—
296	C₂³×D₄₇	C₂×D₄	1	1	yes	characteristic
297	C₂×Q₈×C₄₇	—	2	2	no	—
298	C₂×Q₈×C₄₇	C₂⁴	1	2	yes	—
299	C₂×D₄×C₄₇	—	2	2	no	—
300	C₂×D₄×C₄₇	C₂⁴	1	2	yes	—
301	C₂²×C₄×C₄₇	—	2	2	no	—
302	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
303	C₂×C₂²⋊D₄₇	—	2	2	no	—
304	C₂×C₂²⋊D₄₇	—	2	2	no	—
305	C₂×C₂²⋊D₄₇	—	2	2	no	—
306	C₂²×Dic₄₇	—	2	2	no	—
307	C₂²×Dic₄₇	C₂×D₄	1	1	yes	characteristic
308	Q₈×D₄₇	—	2	4	no	—
309	Q₈×D₄₇	—	2	4	no	—
310	Q₈×D₄₇	—	8	4	no	—
311	D₄×D₄₇	—	2	4	no	—
312	D₄×D₄₇	—	2	4	no	—
313	D₄×D₄₇	—	8	4	no	—
314	C₂×D₁₈₈	—	2	2	no	—
315	C₂×D₁₈₈	C₂⁴	1	2	yes	—
316	C₂×C₄×D₄₇	—	2	2	no	—
317	C₂×C₄×D₄₇	—	2	2	no	—
318	C₂×C₄×D₄₇	—	2	2	no	—
319	C₂×C₄×D₄₇	—	2	2	no	—
320	C₂×C₄×D₄₇	—	2	2	no	—
321	C₂×C₄×D₄₇	—	2	2	no	—
322	C₂×C₄×D₄₇	—	2	2	no	—
323	C₂×C₄×D₄₇	—	8	4	no	—
324	C₂×C₄×D₄₇	C₂×D₄	1	2	yes	—
325	C₂×C₄×D₄₇	C₂×D₄	1	2	yes	—
326	C₂×C₄×D₄₇	C₂×D₄	1	1	yes	characteristic
327	C₂×C₄×D₄₇	C₂×D₄	1	1	yes	characteristic
328	C₂×C₄×D₄₇	C₂⁴	1	1	yes	characteristic
329	C₂×C₄×D₄₇	C₂⁴	1	1	yes	characteristic
330	C₂×Dic₉₄	—	2	2	no	—
331	C₂×Dic₉₄	—	2	2	no	—
332	C₂×Dic₉₄	—	2	2	no	—
333	C₂×Dic₉₄	—	2	2	no	—
334	C₂×Dic₉₄	C₂⁴	1	2	yes	—
335	Q₁₆×C₄₇	—	2	2	no	—
336	SD₁₆×C₄₇	—	2	4	no	—
337	D₈×C₄₇	—	2	2	no	—
338	M₁₆×C₄₇	—	2	2	no	—
339	C₂×C₈×C₄₇	—	2	2	no	—
340	C₂×C₈×C₄₇	C₂⁴	1	1	yes	characteristic
341	C₂×C₈×C₄₇	C₂⁴	1	1	yes	characteristic
342	C₂×C₈×C₄₇	C₂⁴	1	1	yes	characteristic
343	C₂×C₈×C₄₇	C₂⁴	1	1	yes	characteristic
344	C₄⋊C₄×C₄₇	—	2	2	no	—
345	C₄⋊C₄×C₄₇	—	2	2	no	—
346	C₄⋊C₄×C₄₇	—	2	2	no	—
347	C₄⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
348	C₄⋊C₄×C₄₇	C₂⁴	1	2	yes	—
349	C₄⋊C₄×C₄₇	C₂⁴	1	2	yes	—
350	C₂²⋊C₄×C₄₇	—	2	2	no	—
351	C₂²⋊C₄×C₄₇	—	2	2	no	—
352	C₂²⋊C₄×C₄₇	—	2	2	no	—
353	C₂²⋊C₄×C₄₇	—	2	2	no	—
354	C₂²⋊C₄×C₄₇	—	2	2	no	—
355	C₂²⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
356	C₄²×C₄₇	—	2	2	no	—
357	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
358	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
359	C₂²⋊Dic₄₇	—	2	2	no	—
360	C₂²⋊Dic₄₇	—	2	2	no	—
361	C₂²⋊Dic₄₇	—	2	2	no	—
362	C₂²⋊Dic₄₇	—	2	2	no	—
363	C₂²⋊Dic₄₇	—	2	2	no	—
364	C₂²⋊Dic₄₇	C₂×D₄	1	2	yes	—
365	#10625337	—	2	4	no	—
366	#10625336	—	2	4	no	—
367	#10625335	—	2	4	no	—
368	#10625334	—	2	4	no	—
369	(C₂×D₄₇)⋊C₄	—	2	2	no	—
370	(C₂×D₄₇)⋊C₄	—	2	2	no	—
371	(C₂×D₄₇)⋊C₄	—	2	2	no	—
372	(C₂×D₄₇)⋊C₄	—	2	2	no	—
373	(C₂×D₄₇)⋊C₄	—	2	2	no	—
374	(C₂×D₄₇)⋊C₄	—	2	2	no	—
375	(C₂×D₄₇)⋊C₄	—	2	2	no	—
376	(C₂×D₄₇)⋊C₄	—	2	2	no	—
377	(C₂×D₄₇)⋊C₄	—	2	2	no	—
378	(C₂×D₄₇)⋊C₄	—	2	2	no	—
379	(C₂×D₄₇)⋊C₄	C₂×D₄	1	2	yes	—
380	(C₂×D₄₇)⋊C₄	C₂×D₄	1	2	yes	—
381	C₄⋊Dic₄₇	—	2	2	no	—
382	C₄⋊Dic₄₇	—	2	2	no	—
383	C₄⋊Dic₄₇	—	2	2	no	—
384	C₄⋊Dic₄₇	C₂×D₄	1	2	yes	—
385	C₄⋊Dic₄₇	C₂⁴	1	2	yes	—
386	C₄⋊Dic₄₇	C₂⁴	1	2	yes	—
387	Dic₄₇⋊C₄	—	2	2	no	—
388	Dic₄₇⋊C₄	—	2	2	no	—
389	Dic₄₇⋊C₄	—	2	2	no	—
390	Dic₄₇⋊C₄	—	2	2	no	—
391	Dic₄₇⋊C₄	—	2	2	no	—
392	Dic₄₇⋊C₄	—	2	2	no	—
393	Dic₄₇⋊C₄	—	2	2	no	—
394	Dic₄₇⋊C₄	—	2	2	no	—
395	Dic₄₇⋊C₄	C₂×D₄	1	2	yes	—
396	Dic₄₇⋊C₄	C₂×D₄	1	2	yes	—
397	C₄×Dic₄₇	—	2	2	no	—
398	C₄×Dic₄₇	—	2	2	no	—
399	C₄×Dic₄₇	—	2	2	no	—
400	C₄×Dic₄₇	C₂×D₄	1	2	yes	—
401	C₄×Dic₄₇	C₂×D₄	1	2	yes	—
402	C₄×Dic₄₇	C₂⁴	1	1	yes	characteristic
403	C₄×Dic₄₇	C₂⁴	1	1	yes	characteristic
404	#10625329	—	2	2	no	—
405	C₂×C₄₇⋊C₈	—	2	2	no	—
406	C₂×C₄₇⋊C₈	C₂⁴	1	1	yes	characteristic
407	C₂×C₄₇⋊C₈	C₂⁴	1	1	yes	characteristic
408	C₂×C₄₇⋊C₈	C₂⁴	1	1	yes	characteristic
409	C₂×C₄₇⋊C₈	C₂⁴	1	1	yes	characteristic
410	Dic₁₈₈	—	2	2	no	—
411	D₃₇₆	—	2	2	no	—
412	#10625325	—	2	4	no	—
413	#10625324	—	2	2	no	—
414	#10625324	—	2	2	no	—
415	C₈×D₄₇	—	2	2	no	—
416	C₈×D₄₇	—	2	2	no	—
417	C₈×D₄₇	—	2	2	no	—
418	C₈×D₄₇	—	2	2	no	—
419	C₈×D₄₇	#41	1	4	yes	—
420	C₈×D₄₇	#41	1	4	yes	—
421	C₂³×C₄₇	—	2	2	no	—
422	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
423	C₂²×D₄₇	—	2	2	no	—
424	C₂²×D₄₇	—	2	4	no	—
425	C₂²×D₄₇	—	2	2	no	—
426	C₂²×D₄₇	—	4	4	no	—
427	C₂²×D₄₇	—	4	4	no	—
428	C₂²×D₄₇	—	4	4	no	—
429	C₂²×D₄₇	C₂²×D₄	1	1	yes	characteristic
430	C₂²×D₄₇	C₂²×D₄	1	1	yes	characteristic
431	Q₈×C₄₇	—	2	2	no	—
432	Q₈×C₄₇	—	2	2	no	—
433	Q₈×C₄₇	—	8	2	no	—
434	D₄×C₄₇	—	2	2	no	—
435	D₄×C₄₇	—	2	2	no	—
436	D₄×C₄₇	—	8	2	no	—
437	C₂×C₄×C₄₇	—	2	1	no	—
438	C₂×C₄×C₄₇	—	2	1	no	—
439	C₂×C₄×C₄₇	—	2	2	no	—
440	C₂×C₄×C₄₇	—	2	2	no	—
441	C₂×C₄×C₄₇	—	2	2	no	—
442	C₂×C₄×C₄₇	—	8	2	no	—
443	C₂×C₄×C₄₇	C₂²×D₄	1	2	yes	—
444	C₂×C₄×C₄₇	C₂²×D₄	1	2	yes	—
445	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
446	C₂×C₄×C₄₇	C₂⁵	1	1	yes	characteristic
447	C₂²⋊D₄₇	—	4	4	no	—
448	C₂²⋊D₄₇	—	8	2	no	—
449	C₂²⋊D₄₇	—	8	2	no	—
450	C₂×Dic₄₇	—	2	2	no	—
451	C₂×Dic₄₇	—	2	2	no	—
452	C₂×Dic₄₇	—	2	2	no	—
453	C₂×Dic₄₇	—	2	2	no	—
454	C₂×Dic₄₇	—	8	2	no	—
455	C₂×Dic₄₇	C₂²×D₄	1	2	yes	—
456	C₂×Dic₄₇	C₂²×D₄	1	2	yes	—
457	C₂×Dic₄₇	C₂²×D₄	1	1	yes	characteristic
458	C₂×Dic₄₇	C₂²×D₄	1	1	yes	characteristic
459	D₁₈₈	—	2	2	no	—
460	D₁₈₈	—	2	2	no	—
461	D₁₈₈	—	8	2	no	—
462	C₄×D₄₇	—	2	2	no	—
463	C₄×D₄₇	—	2	4	no	—
464	C₄×D₄₇	—	2	4	no	—
465	C₄×D₄₇	—	2	1	no	—
466	C₄×D₄₇	—	2	1	no	—
467	C₄×D₄₇	—	2	2	no	—
468	C₄×D₄₇	—	4	4	no	—
469	C₄×D₄₇	—	4	4	no	—
470	C₄×D₄₇	—	4	4	no	—
471	C₄×D₄₇	—	8	2	no	—
472	C₄×D₄₇	—	8	2	no	—
473	C₄×D₄₇	C₂×#41	1	2	yes	—
474	C₄×D₄₇	C₂×#41	1	2	yes	—
475	Dic₉₄	—	2	2	no	—
476	Dic₉₄	—	2	2	no	—
477	Dic₉₄	—	4	4	no	—
478	Dic₉₄	—	8	2	no	—
479	Dic₉₄	—	8	2	no	—
480	Dic₉₄	—	8	2	no	—
481	C₈×C₄₇	—	2	1	no	—
482	C₈×C₄₇	—	2	1	no	—
483	C₈×C₄₇	C₂×#41	1	2	yes	—
484	C₈×C₄₇	C₂×#41	1	2	yes	—
485	C₄₇⋊C₈	—	2	1	no	—
486	C₄₇⋊C₈	—	2	1	no	—
487	C₄₇⋊C₈	C₂×#41	1	2	yes	—
488	C₄₇⋊C₈	C₂×#41	1	2	yes	—
489	C₂×#3173	—	47	1	no	maximal, Sylow
490	C₂²×C₄₇	—	2	1	no	—
491	C₂²×C₄₇	—	2	2	no	—
492	C₂²×C₄₇	—	4	2	no	—
493	C₂²×C₄₇	—	4	2	no	—
494	C₂²×C₄₇	—	4	2	no	—
495	C₂²×C₄₇	C₂³×D₄	1	1	yes	characteristic
496	C₂×D₄₇	—	2	1	no	—
497	C₂×D₄₇	—	2	2	no	—
498	C₂×D₄₇	—	4	4	no	—
499	C₂×D₄₇	—	4	2	no	—
500	C₂×D₄₇	—	4	2	no	—
501	C₂×D₄₇	—	4	2	no	—
502	C₂×D₄₇	—	8	8	no	—
503	C₂×D₄₇	#532	1	2	yes	—
504	C₂×D₄₇	#577	1	4	yes	—
505	C₄×C₄₇	—	2	1	no	—
506	C₄×C₄₇	—	2	2	no	—
507	C₄×C₄₇	—	2	2	no	—
508	C₄×C₄₇	—	4	2	no	—
509	C₄×C₄₇	—	4	2	no	—
510	C₄×C₄₇	—	4	2	no	—
511	C₄×C₄₇	C₂²×#41	1	1	yes	characteristic
512	C₄×C₄₇	C₂²×#41	1	1	yes	characteristic
513	Dic₄₇	—	2	1	no	—
514	Dic₄₇	—	2	2	no	—
515	Dic₄₇	—	2	2	no	—
516	Dic₄₇	—	4	2	no	—
517	Dic₄₇	—	4	2	no	—
518	Dic₄₇	—	4	2	no	—
519	Dic₄₇	#532	1	2	yes	—
520	C₂×#542	—	47	2	no	—
521	#3173	—	47	1	no	—
522	#3173	—	47	1	no	—
523	#3173	—	47	2	no	—
524	#3173	—	47	1	no	—
525	#3173	—	47	1	no	—
526	#3173	—	47	2	no	—
527	#3173	—	47	1	no	—
528	#3173	—	47	1	no	—
529	#3173	—	47	2	no	—
530	#3173	—	47	1	no	—
531	#3173	—	47	2	no	—
532	#3173	D₄₇	1	1	yes	characteristic, direct product factor
533	C₂×#498	—	47	1	no	—
534	C₂×#495	—	47	1	no	—
535	C₂×#489	—	47	2	no	—
536	C₂×#470	—	47	1	no	—
537	C₂×#469	—	47	1	no	—
538	C₂×#465	—	47	2	no	—
539	C₂×#442	—	47	1	no	—
540	C₂×#441	—	47	1	no	—
541	C₂×C₄×SD₁₆	—	47	2	no	—
542	C₂×#405	—	47	1	no	—
543	C₂×C₄₇	—	4	1	no	—
544	C₂×C₄₇	—	8	2	no	—
545	C₂×C₄₇	C₂×#532	1	1	yes	characteristic
546	C₂×C₄₇	C₂×#577	1	2	yes	—
547	D₄₇	—	4	1	no	—
548	D₄₇	—	8	2	no	—
549	D₄₇	#3173	1	4	yes	direct product factor
550	C₂²×Q₁₆	—	47	1	no	—
551	C₂²×SD₁₆	—	47	2	no	—
552	C₂²×D₈	—	47	1	no	—
553	C₂²×M₁₆	—	47	1	no	—
554	C₂³×C₈	—	47	1	no	—
555	#542	—	47	2	no	—
556	#542	—	47	2	no	—
557	#542	—	47	2	no	—
558	#542	—	47	2	no	—
559	#542	—	47	2	no	—
560	#542	—	47	2	no	—
561	#542	—	47	2	no	—
562	#542	—	94	2	no	—
563	#542	—	94	2	no	—
564	#542	—	94	2	no	—
565	#542	—	94	2	no	—
566	#542	C₂×D₄₇	1	2	yes	complemented
567	C₂×C₄⋊Q₈	—	47	2	no	—
568	C₂×#126	—	94	2	no	—
569	C₂×#124	—	47	2	no	—
570	C₂×#124	—	94	2	no	—
571	C₂×#123	—	94	2	no	—
572	C₂×C₂²⋊Q₈	—	47	2	no	—
573	C₂×C₂²⋊Q₈	—	94	2	no	—
574	C₂×#121	—	47	2	no	—
575	C₂×C₄×Q₈	—	47	2	no	—
576	C₂×C₄×D₄	—	47	2	no	—
577	C₂×#117	—	47	1	no	—
578	#498	—	47	2	no	—
579	#498	—	47	2	no	—
580	#498	—	47	1	no	—
581	#498	—	47	1	no	—
582	#498	—	47	1	no	—
583	#498	C₂×D₄₇	1	1	yes	characteristic, complemented
584	#495	—	47	1	no	—
585	#495	—	47	2	no	—
586	#495	—	47	1	no	—
587	#495	—	47	2	no	—
588	#495	—	47	1	no	—
589	#495	C₂×D₄₇	1	1	yes	characteristic, complemented
590	#489	—	47	2	no	—
591	#489	—	47	2	no	—
592	#489	—	47	2	no	—
593	#489	—	47	2	no	—
594	#489	—	47	2	no	—
595	#489	—	47	2	no	—
596	#489	—	47	2	no	—
597	#489	C₂×D₄₇	1	2	yes	complemented
598	#470	—	47	1	no	—
599	#470	—	47	1	no	—
600	#470	—	47	2	no	—
601	#470	—	47	1	no	—
602	#470	—	47	2	no	—
603	#470	C₂×D₄₇	1	1	yes	characteristic, complemented
604	#469	—	47	1	no	—
605	#469	—	47	1	no	—
606	#469	—	47	2	no	—
607	#469	—	47	1	no	—
608	#469	—	47	2	no	—
609	#469	C₂×D₄₇	1	1	yes	characteristic
610	#465	—	47	2	no	—
611	#465	—	47	2	no	—
612	#465	—	47	2	no	—
613	#465	—	47	2	no	—
614	#465	—	47	2	no	—
615	#465	—	47	2	no	—
616	#465	—	47	2	no	—
617	#465	C₂×D₄₇	1	2	yes	complemented
618	#442	—	47	1	no	—
619	#442	—	47	2	no	—
620	#442	—	47	1	no	—
621	#442	—	47	2	no	—
622	#442	—	47	1	no	—
623	#442	C₂×D₄₇	1	1	yes	characteristic, complemented
624	#441	—	47	1	no	—
625	#441	—	47	2	no	—
626	#441	—	47	1	no	—
627	#441	—	47	2	no	—
628	#441	—	47	1	no	—
629	#441	C₂×D₄₇	1	1	yes	characteristic, complemented
630	C₄×SD₁₆	—	47	2	no	—
631	C₄×SD₁₆	—	47	2	no	—
632	C₄×SD₁₆	—	47	2	no	—
633	C₄×SD₁₆	—	47	2	no	—
634	C₄×SD₁₆	—	47	2	no	—
635	C₄×SD₁₆	—	47	2	no	—
636	C₄×SD₁₆	—	47	2	no	—
637	C₄×SD₁₆	C₂×D₄₇	1	2	yes	complemented
638	C₂×#106	—	47	2	no	—
639	C₂×#106	—	47	1	no	—
640	C₂×#106	—	47	1	no	—
641	C₂×#103	—	47	2	no	—
642	C₂×#103	—	47	2	no	—
643	C₂×#102	—	47	2	no	—
644	C₂×#102	—	47	2	no	—
645	#405	—	47	1	no	—
646	#405	—	47	1	no	—
647	#405	—	47	1	no	—
648	#405	—	47	1	no	—
649	#405	—	47	1	no	—
650	#405	—	47	1	no	—
651	#405	—	47	1	no	—
652	#405	C₂×D₄₇	1	1	yes	characteristic, complemented
653	C₂×#97	—	47	1	no	—
654	C₂×#97	—	47	1	no	—
655	C₂×C₄×C₈	—	47	1	no	—
656	C₂×C₄×C₈	—	47	1	no	—
657	C₄₇	C₂×#3173	1	1	yes	characteristic, complemented, Sylow
658	C₂²×Q₈	—	47	2	no	—
659	C₂²×Q₈	—	94	2	no	—
660	C₂²×D₄	—	47	2	no	—
661	C₂²×D₄	—	94	2	no	—
662	C₂³×C₄	—	47	1	no	—
663	C₂³×C₄	—	94	2	no	—
664	C₂×Q₁₆	—	47	2	no	—
665	C₂×Q₁₆	—	47	1	no	—
666	C₂×Q₁₆	—	94	4	no	—
667	C₂×Q₁₆	C₂²×D₄₇	1	1	yes	characteristic
668	C₂×SD₁₆	—	47	2	no	—
669	C₂×SD₁₆	—	47	2	no	—
670	C₂×SD₁₆	—	47	2	no	—
671	C₂×SD₁₆	—	94	8	no	—
672	C₂×SD₁₆	C₂²×D₄₇	1	2	yes	—
673	C₂×D₈	—	47	2	no	—
674	C₂×D₈	—	47	1	no	—
675	C₂×D₈	—	94	4	no	—
676	C₂×D₈	C₂²×D₄₇	1	1	yes	characteristic
677	C₂×M₁₆	—	47	1	no	—
678	C₂×M₁₆	—	47	1	no	—
679	C₂×M₁₆	—	47	1	no	—
680	C₂×M₁₆	—	94	4	no	—
681	C₂×M₁₆	C₂²×D₄₇	1	1	yes	characteristic
682	C₂²×C₈	—	47	1	no	—
683	C₂²×C₈	—	47	1	no	—
684	C₂²×C₈	—	47	1	no	—
685	C₂²×C₈	—	47	1	no	—
686	C₂²×C₈	—	47	1	no	—
687	C₂²×C₈	—	47	1	no	—
688	C₂²×C₈	—	47	1	no	—
689	C₂²×C₈	—	94	4	no	—
690	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
691	C₄⋊Q₈	—	47	2	no	—
692	C₄⋊Q₈	—	47	2	no	—
693	C₄⋊Q₈	—	47	2	no	—
694	C₄⋊Q₈	—	94	2	no	—
695	C₄⋊Q₈	—	94	2	no	—
696	C₄⋊Q₈	C₂²×D₄₇	1	2	yes	—
697	#126	—	2	2	no	—
698	#126	—	94	2	no	—
699	#126	—	94	2	no	—
700	#126	—	94	2	no	—
701	#126	—	94	2	no	—
702	#126	—	94	2	no	—
703	#126	—	94	2	no	—
704	#126	—	94	2	no	—
705	#124	—	2	2	no	—
706	#124	—	47	2	no	—
707	#124	—	47	2	no	—
708	#124	—	47	2	no	—
709	#124	—	94	2	no	—
710	#124	—	94	2	no	—
711	#124	—	94	2	no	—
712	#124	—	94	2	no	—
713	#124	—	94	2	no	—
714	#124	—	94	2	no	—
715	#124	—	94	2	no	—
716	#124	—	94	2	no	—
717	#124	—	94	2	no	—
718	#124	C₂²×D₄₇	1	2	yes	—
719	#123	—	2	2	no	—
720	#123	—	94	2	no	—
721	#123	—	94	2	no	—
722	#123	—	94	2	no	—
723	#123	—	94	2	no	—
724	#123	—	94	2	no	—
725	#123	—	94	2	no	—
726	#123	—	94	2	no	—
727	C₂²⋊Q₈	—	2	2	no	—
728	C₂²⋊Q₈	—	47	2	no	—
729	C₂²⋊Q₈	—	47	2	no	—
730	C₂²⋊Q₈	—	47	2	no	—
731	C₂²⋊Q₈	—	94	2	no	—
732	C₂²⋊Q₈	—	94	2	no	—
733	C₂²⋊Q₈	—	94	2	no	—
734	C₂²⋊Q₈	—	94	2	no	—
735	C₂²⋊Q₈	—	94	2	no	—
736	C₂²⋊Q₈	—	94	2	no	—
737	C₂²⋊Q₈	—	94	2	no	—
738	C₂²⋊Q₈	—	94	2	no	—
739	C₂²⋊Q₈	—	94	2	no	—
740	C₂²⋊Q₈	C₂²×D₄₇	1	2	yes	—
741	#121	—	47	2	no	—
742	#121	—	47	2	no	—
743	#121	—	47	2	no	—
744	#121	—	94	2	no	—
745	#121	—	94	2	no	—
746	#121	C₂²×D₄₇	1	2	yes	—
747	C₄×Q₈	—	47	2	no	—
748	C₄×Q₈	—	47	2	no	—
749	C₄×Q₈	—	47	2	no	—
750	C₄×Q₈	—	94	2	no	—
751	C₄×Q₈	—	94	2	no	—
752	C₄×Q₈	C₂²×D₄₇	1	2	yes	—
753	C₄×D₄	—	47	2	no	—
754	C₄×D₄	—	47	2	no	—
755	C₄×D₄	—	47	2	no	—
756	C₄×D₄	—	94	2	no	—
757	C₄×D₄	—	94	2	no	—
758	C₄×D₄	C₂²×D₄₇	1	2	yes	—
759	#117	—	47	1	no	—
760	#117	—	47	2	no	—
761	#117	—	47	2	no	—
762	#117	—	47	1	no	—
763	#117	—	47	1	no	—
764	#117	C₂²×D₄₇	1	1	yes	characteristic
765	C₂×C₄⋊C₄	—	47	2	no	—
766	C₂×C₄⋊C₄	—	47	2	no	—
767	C₂×C₄⋊C₄	—	47	2	no	—
768	C₂×C₄⋊C₄	—	94	2	no	—
769	C₂×C₄⋊C₄	—	94	2	no	—
770	C₂×C₄⋊C₄	—	94	2	no	—
771	C₂×C₂²⋊C₄	—	47	2	no	—
772	C₂×C₂²⋊C₄	—	94	2	no	—
773	C₂×C₂²⋊C₄	—	94	2	no	—
774	C₂×C₂²⋊C₄	—	94	2	no	—
775	C₂×C₂²⋊C₄	—	94	2	no	—
776	C₂×C₂²⋊C₄	—	94	2	no	—
777	C₂×C₄²	—	47	1	no	—
778	C₂×C₄²	—	47	1	no	—
779	C₂×C₄²	—	94	2	no	—
780	#106	—	47	2	no	—
781	#106	—	47	1	no	—
782	#106	—	47	1	no	—
783	#106	—	47	2	no	—
784	#106	—	47	2	no	—
785	#106	—	47	2	no	—
786	#106	—	47	2	no	—
787	#106	C₂²×D₄₇	1	2	yes	—
788	#106	C₂²×D₄₇	1	1	yes	characteristic
789	#106	C₂²×D₄₇	1	1	yes	characteristic
790	#103	—	47	2	no	—
791	#103	—	47	2	no	—
792	#103	—	47	2	no	—
793	#103	—	47	2	no	—
794	#103	—	47	2	no	—
795	#103	—	47	2	no	—
796	#103	C₂²×D₄₇	1	2	yes	—
797	#103	C₂²×D₄₇	1	2	yes	—
798	#102	—	47	2	no	—
799	#102	—	47	2	no	—
800	#102	—	47	2	no	—
801	#102	—	47	2	no	—
802	#102	—	47	2	no	—
803	#102	—	47	2	no	—
804	#102	C₂²×D₄₇	1	2	yes	—
805	#102	C₂²×D₄₇	1	2	yes	—
806	#97	—	47	1	no	—
807	#97	—	47	1	no	—
808	#97	—	47	1	no	—
809	#97	—	47	1	no	—
810	#97	—	47	1	no	—
811	#97	—	47	1	no	—
812	#97	C₂²×D₄₇	1	1	yes	characteristic
813	#97	C₂²×D₄₇	1	1	yes	characteristic
814	C₄×C₈	—	47	1	no	—
815	C₄×C₈	—	47	1	no	—
816	C₄×C₈	—	47	1	no	—
817	C₄×C₈	—	47	1	no	—
818	C₄×C₈	—	47	1	no	—
819	C₄×C₈	—	47	1	no	—
820	C₄×C₈	C₂²×D₄₇	1	1	yes	characteristic
821	C₄×C₈	C₂²×D₄₇	1	1	yes	characteristic
822	C₂⁴	—	47	1	no	—
823	C₂⁴	—	94	2	no	—
824	C₂×Q₈	—	2	2	no	—
825	C₂×Q₈	—	47	2	no	—
826	C₂×Q₈	—	94	2	no	—
827	C₂×Q₈	—	94	2	no	—
828	C₂×Q₈	—	94	2	no	—
829	C₂×Q₈	—	94	4	no	—
830	C₂×Q₈	—	94	4	no	—
831	C₂×Q₈	—	94	2	no	—
832	C₂×Q₈	—	376	4	no	—
833	C₂×Q₈	C₂³×D₄₇	1	2	yes	—
834	C₂×D₄	—	2	2	no	—
835	C₂×D₄	—	47	2	no	—
836	C₂×D₄	—	94	2	no	—
837	C₂×D₄	—	94	4	no	—
838	C₂×D₄	—	94	4	no	—
839	C₂×D₄	—	94	2	no	—
840	C₂×D₄	—	94	2	no	—
841	C₂×D₄	—	94	2	no	—
842	C₂×D₄	—	376	4	no	—
843	C₂×D₄	C₂³×D₄₇	1	2	yes	—
844	C₂²×C₄	—	2	2	no	—
845	C₂²×C₄	—	47	1	no	—
846	C₂²×C₄	—	47	1	no	—
847	C₂²×C₄	—	47	2	no	—
848	C₂²×C₄	—	47	2	no	—
849	C₂²×C₄	—	47	1	no	—
850	C₂²×C₄	—	47	1	no	—
851	C₂²×C₄	—	47	1	no	—
852	C₂²×C₄	—	94	2	no	—
853	C₂²×C₄	—	94	2	no	—
854	C₂²×C₄	—	94	2	no	—
855	C₂²×C₄	—	94	2	no	—
856	C₂²×C₄	—	94	2	no	—
857	C₂²×C₄	—	94	2	no	—
858	C₂²×C₄	—	94	2	no	—
859	C₂²×C₄	—	94	2	no	—
860	C₂²×C₄	—	376	4	no	—
861	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
862	Q₁₆	—	2	2	no	—
863	Q₁₆	—	94	4	no	—
864	Q₁₆	—	94	2	no	—
865	SD₁₆	—	2	4	no	—
866	SD₁₆	—	94	4	no	—
867	SD₁₆	—	94	4	no	—
868	SD₁₆	—	94	4	no	—
869	D₈	—	2	2	no	—
870	D₈	—	94	4	no	—
871	D₈	—	94	2	no	—
872	M₁₆	—	2	2	no	—
873	M₁₆	—	94	2	no	—
874	M₁₆	—	94	2	no	—
875	M₁₆	—	94	2	no	—
876	C₂×C₈	—	2	2	no	—
877	C₂×C₈	—	47	1	no	—
878	C₂×C₈	—	47	1	no	—
879	C₂×C₈	—	47	4	no	—
880	C₂×C₈	—	47	4	no	—
881	C₂×C₈	—	47	1	no	—
882	C₂×C₈	—	47	1	no	—
883	C₂×C₈	—	94	2	no	—
884	C₂×C₈	—	94	2	no	—
885	C₂×C₈	—	94	2	no	—
886	C₂×C₈	—	94	2	no	—
887	C₂×C₈	—	94	2	no	—
888	C₂×C₈	C₂³×D₄₇	1	1	yes	characteristic
889	C₂×C₈	C₂³×D₄₇	1	1	yes	characteristic
890	C₂×C₈	C₂³×D₄₇	1	1	yes	characteristic
891	C₂×C₈	C₂³×D₄₇	1	1	yes	characteristic
892	C₄⋊C₄	—	2	2	no	—
893	C₄⋊C₄	—	2	2	no	—
894	C₄⋊C₄	—	2	2	no	—
895	C₄⋊C₄	—	47	2	no	—
896	C₄⋊C₄	—	47	2	no	—
897	C₄⋊C₄	—	47	2	no	—
898	C₄⋊C₄	—	47	2	no	—
899	C₄⋊C₄	—	47	2	no	—
900	C₄⋊C₄	—	94	2	no	—
901	C₄⋊C₄	—	94	2	no	—
902	C₄⋊C₄	—	94	2	no	—
903	C₄⋊C₄	—	94	2	no	—
904	C₄⋊C₄	—	94	2	no	—
905	C₄⋊C₄	—	94	2	no	—
906	C₄⋊C₄	—	94	2	no	—
907	C₄⋊C₄	—	94	2	no	—
908	C₄⋊C₄	—	94	2	no	—
909	C₄⋊C₄	—	94	2	no	—
910	C₄⋊C₄	—	94	2	no	—
911	C₄⋊C₄	D₄×D₄₇	1	2	yes	—
912	C₄⋊C₄	C₂³×D₄₇	1	2	yes	—
913	C₄⋊C₄	C₂³×D₄₇	1	2	yes	—
914	C₂²⋊C₄	—	2	2	no	—
915	C₂²⋊C₄	—	2	2	no	—
916	C₂²⋊C₄	—	2	2	no	—
917	C₂²⋊C₄	—	2	2	no	—
918	C₂²⋊C₄	—	2	2	no	—
919	C₂²⋊C₄	—	47	2	no	—
920	C₂²⋊C₄	—	47	2	no	—
921	C₂²⋊C₄	—	47	2	no	—
922	C₂²⋊C₄	—	94	2	no	—
923	C₂²⋊C₄	—	94	2	no	—
924	C₂²⋊C₄	—	94	2	no	—
925	C₂²⋊C₄	—	94	2	no	—
926	C₂²⋊C₄	—	94	2	no	—
927	C₂²⋊C₄	—	94	2	no	—
928	C₂²⋊C₄	—	94	2	no	—
929	C₂²⋊C₄	—	94	2	no	—
930	C₂²⋊C₄	—	94	2	no	—
931	C₂²⋊C₄	—	94	2	no	—
932	C₂²⋊C₄	—	94	2	no	—
933	C₂²⋊C₄	—	94	2	no	—
934	C₂²⋊C₄	—	94	2	no	—
935	C₂²⋊C₄	—	94	2	no	—
936	C₂²⋊C₄	—	94	2	no	—
937	C₂²⋊C₄	D₄×D₄₇	1	2	yes	—
938	C₄²	—	2	2	no	—
939	C₄²	—	47	2	no	—
940	C₄²	—	47	2	no	—
941	C₄²	—	47	1	no	—
942	C₄²	—	47	1	no	—
943	C₄²	—	94	2	no	—
944	C₄²	—	94	2	no	—
945	C₄²	—	94	2	no	—
946	C₄²	C₂³×D₄₇	1	1	yes	characteristic
947	C₄²	C₂³×D₄₇	1	1	yes	characteristic
948	C₂³	—	2	2	no	—
949	C₂³	—	47	1	no	—
950	C₂³	—	47	1	no	—
951	C₂³	—	94	2	no	—
952	C₂³	—	94	4	no	—
953	C₂³	—	94	2	no	—
954	C₂³	—	188	4	no	—
955	C₂³	—	188	4	no	—
956	C₂³	—	188	4	no	—
957	C₂³	C₂×D₄×D₄₇	1	1	yes	characteristic
958	Q₈	—	2	2	no	—
959	Q₈	—	2	2	no	—
960	Q₈	—	8	2	no	—
961	Q₈	—	94	2	no	—
962	Q₈	—	94	2	no	—
963	Q₈	—	376	2	no	—
964	Q₈	—	376	2	no	—
965	Q₈	—	376	2	no	—
966	Q₈	—	188	4	no	—
967	D₄	—	2	2	no	—
968	D₄	—	2	2	no	—
969	D₄	—	8	2	no	—
970	D₄	—	94	2	no	—
971	D₄	—	94	2	no	—
972	D₄	—	376	2	no	—
973	D₄	—	376	2	no	—
974	D₄	—	376	2	no	—
975	D₄	—	188	4	no	—
976	C₂×C₄	—	2	1	no	—
977	C₂×C₄	—	2	1	no	—
978	C₂×C₄	—	2	2	no	—
979	C₂×C₄	—	2	2	no	—
980	C₂×C₄	—	2	2	no	—
981	C₂×C₄	—	8	2	no	—
982	C₂×C₄	—	47	1	no	—
983	C₂×C₄	—	47	2	no	—
984	C₂×C₄	—	47	2	no	—
985	C₂×C₄	—	47	2	no	—
986	C₂×C₄	—	47	2	no	—
987	C₂×C₄	—	47	1	no	—
988	C₂×C₄	—	94	2	no	—
989	C₂×C₄	—	94	2	no	—
990	C₂×C₄	—	94	4	no	—
991	C₂×C₄	—	94	4	no	—
992	C₂×C₄	—	94	2	no	—
993	C₂×C₄	—	94	1	no	—
994	C₂×C₄	—	94	1	no	—
995	C₂×C₄	—	94	2	no	—
996	C₂×C₄	—	94	2	no	—
997	C₂×C₄	—	94	2	no	—
998	C₂×C₄	—	376	2	no	—
999	C₂×C₄	—	376	2	no	—
1000	C₂×C₄	—	376	2	no	—
1001	C₂×C₄	—	188	4	no	—
1002	C₂×C₄	—	188	4	no	—
1003	C₂×C₄	—	188	4	no	—
1004	C₂×C₄	C₂×D₄×D₄₇	1	2	yes	—
1005	C₂×C₄	C₂×D₄×D₄₇	1	2	yes	—
1006	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
1007	C₂×C₄	C₂⁴×D₄₇	1	1	yes	characteristic
1008	C₈	—	2	1	no	—
1009	C₈	—	2	1	no	—
1010	C₈	—	47	2	no	—
1011	C₈	—	47	2	no	—
1012	C₈	—	94	1	no	—
1013	C₈	—	94	1	no	—
1014	C₈	#41×D₄₇	1	2	yes	—
1015	C₈	#41×D₄₇	1	2	yes	—
1016	C₂²	—	2	2	no	—
1017	C₂²	—	2	1	no	—
1018	C₂²	—	4	2	no	—
1019	C₂²	—	4	2	no	—
1020	C₂²	—	4	2	no	—
1021	C₂²	—	47	4	no	—
1022	C₂²	—	47	2	no	—
1023	C₂²	—	94	2	no	—
1024	C₂²	—	94	1	no	—
1025	C₂²	—	376	8	no	—
1026	C₂²	—	188	4	no	—
1027	C₂²	—	188	2	no	—
1028	C₂²	—	188	2	no	—
1029	C₂²	—	188	2	no	—
1030	C₂²	C₂²×D₄×D₄₇	1	1	yes	characteristic
1031	C₄	—	2	2	no	—
1032	C₄	—	2	2	no	—
1033	C₄	—	2	1	no	—
1034	C₄	—	4	2	no	—
1035	C₄	—	4	2	no	—
1036	C₄	—	4	2	no	—
1037	C₄	—	47	2	no	—
1038	C₄	—	94	2	no	—
1039	C₄	—	94	2	no	—
1040	C₄	—	94	1	no	—
1041	C₄	—	188	2	no	—
1042	C₄	—	188	2	no	—
1043	C₄	—	188	2	no	—
1044	C₄	C₂×#41×D₄₇	1	1	yes	characteristic
1045	C₄	C₂×#41×D₄₇	1	1	yes	characteristic
1046	C₂	—	4	1	no	—
1047	C₂	—	8	2	no	—
1048	C₂	—	47	4	no	—
1049	C₂	—	376	2	no	—
1050	C₂	—	188	1	no	—
1051	C₂	#532×D₄₇	1	1	yes	characteristic
1052	C₂	#577×D₄₇	1	2	yes	—

	subgroup	G/H
center	C₂²	C₂²×D₄×D₄₇
commutator, cosocle	C₂×C₄×C₄₇	C₂⁵
Frattini	C₂×C₄	C₂⁴×D₄₇
Fitting	C₄₇×#3173	C₂
socle	C₂²×C₄₇	C₂³×D₄
prime radical	#469×D₄₇	C₂
hypercenter	#3173	D₄₇
hypocenter	C₄₇	C₂×#3173
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ #117 ◁ #3173

Complements

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

N	H ≅ G/N	type
1. #542×D₄₇	C₂	semidirect
2. #20254008	C₂	semidirect
3. #20254007	C₂	semidirect
4. #20254006	C₂	semidirect
5. #20254005	C₂	semidirect
6. #20254004	C₂	semidirect
7. #20254003	C₂	semidirect
8. #20254002	C₂	semidirect
9. #20254001	C₂	semidirect
10. #20254000	C₂	semidirect
11. #20253999	C₂	semidirect
12. #20253998	C₂	semidirect
13. #498×D₄₇	C₂	semidirect
14. #495×D₄₇	C₂	semidirect
15. #489×D₄₇	C₂	semidirect
16. #470×D₄₇	C₂	semidirect
18. #465×D₄₇	C₂	semidirect
19. #442×D₄₇	C₂	semidirect
20. #441×D₄₇	C₂	semidirect
21. C₄×SD₁₆×D₄₇	C₂	semidirect
22. #405×D₄₇	C₂	semidirect
23. C₄₇×#3173	C₂	semidirect
29. #15689747	C₂²	semidirect
30. #15689746	C₂²	semidirect
31. #15689745	C₂²	semidirect
32. #15689744	C₂²	semidirect
34. #15689742	C₂²	semidirect
36. #15689740	C₂²	semidirect
38. #15689738	C₂²	semidirect
51. #15689521	C₂²	semidirect
52. #15689520	C₂²	semidirect
53. #15689520	C₂²	semidirect
54. #15689520	C₂²	semidirect
55. #15689519	C₂²	semidirect
56. #15689508	C₂²	semidirect
57. #15689507	C₂²	semidirect
58. #15689506	C₂²	semidirect
59. #15689505	C₂²	semidirect
60. #15689504	C₂²	semidirect
61. #15689485	C₂²	semidirect
62. #15689484	C₂²	semidirect
63. #15689484	C₂²	semidirect
64. #15689483	C₂²	semidirect
65. #15689482	C₂²	semidirect
66. #15689481	C₂²	semidirect
67. #15689481	C₂²	semidirect
68. #15689382	C₂²	semidirect
69. #15689381	C₂²	semidirect
70. #15689380	C₂²	semidirect
71. #15689379	C₂²	semidirect
72. #15689378	C₂²	semidirect
78. #15689355	C₂²	semidirect
79. #15689354	C₂²	semidirect
80. #15689353	C₂²	semidirect
81. #15689352	C₂²	semidirect
82. #15689351	C₂²	semidirect
83. #15689350	C₂²	semidirect
84. #15689349	C₂²	semidirect
85. #15689236	C₂²	semidirect
86. #15689235	C₂²	semidirect
87. #15689234	C₂²	semidirect
88. #15689233	C₂²	semidirect
89. #15689232	C₂²	semidirect
90. #15689231	C₂²	semidirect
91. #15689230	C₂²	semidirect
92. #15689229	C₂²	semidirect
93. #15689228	C₂²	semidirect
94. #15689227	C₂²	semidirect
95. #15689214	C₂²	semidirect
96. C₄×#10625325	C₂²	semidirect
97. SD₁₆×Dic₄₇	C₂²	semidirect
98. C₄×#10625336	C₂²	semidirect
99. #15689210	C₂²	semidirect
100. C₄×#10625335	C₂²	semidirect
101. #15689208	C₂²	semidirect
109. #15689081	C₂²	semidirect
110. #15689080	C₂²	semidirect
111. #15689080	C₂²	semidirect
112. #15689079	C₂²	semidirect
113. #15689078	C₂²	semidirect
114. #15689077	C₂²	semidirect
115. #15689077	C₂²	semidirect
120. C₄₇×#542	C₂²	semidirect
121. C₄₇×#498	C₂²	semidirect
122. C₄₇×#495	C₂²	semidirect
123. C₄₇×#489	C₂²	semidirect
124. C₄₇×#470	C₂²	semidirect
126. C₄₇×#465	C₂²	semidirect
127. C₄₇×#442	C₂²	semidirect
128. C₄₇×#441	C₂²	semidirect
129. C₄×SD₁₆×C₄₇	C₂²	semidirect
130. C₄₇×#405	C₂²	semidirect
532. #3173	D₄₇	direct (N × H)
549. D₄₇	#3173	direct (N × H)
566. #542	C₂×D₄₇	semidirect
583. #498	C₂×D₄₇	semidirect
589. #495	C₂×D₄₇	semidirect
597. #489	C₂×D₄₇	semidirect
603. #470	C₂×D₄₇	semidirect
617. #465	C₂×D₄₇	semidirect
623. #442	C₂×D₄₇	semidirect
629. #441	C₂×D₄₇	semidirect
637. C₄×SD₁₆	C₂×D₄₇	semidirect
652. #405	C₂×D₄₇	semidirect
657. C₄₇	C₂×#3173	semidirect

Maximal subgroups

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

subgroup	index
#542×D₄₇	2
#20254008	2
#20254007	2
#20254006	2
#20254005	2
#20254004	2
#20254003	2
#20254002	2
#20254001	2
#20254000	2
#20253999	2
#20253998	2
#498×D₄₇	2
#495×D₄₇	2
#489×D₄₇	2
#470×D₄₇	2
#469×D₄₇	2
#465×D₄₇	2
#442×D₄₇	2
#441×D₄₇	2
C₄×SD₁₆×D₄₇	2
#405×D₄₇	2
C₄₇×#3173	2
C₂×#3173	47

Subgroups — D47×#3173 #27086068

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₄₇×#3173 #27086068