Subgroups — C₄₇×#17510 #26057208

Order 12032.

970 conjugacy classes of subgroups.

The subgroup lattice has 622 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₇×#3480	C₂	1	1	yes	maximal, characteristic
2	C₈×#41×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄₇×#2925	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄₇×#1494	C₂	1	2	yes	maximal, complemented
5	C₄₇×#1492	C₂	1	1	yes	maximal, characteristic, complemented
6	C₄₇×#1488	C₂	1	2	yes	maximal, complemented
7	C₄₇×#1487	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄₇×#1482	C₂	1	2	yes	maximal, complemented
9	C₄₇×#1480	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄₇×#1476	C₂	1	2	yes	maximal, complemented
11	C₂×C₄₇×Q₈⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
12	C₄₇×#559	—	2	1	no	—
13	C₄₇×#559	C₄	1	1	yes	characteristic
14	C₄₇×#557	C₄	1	1	yes	characteristic
15	C₄₇×#556	—	2	1	no	—
16	C₄₇×#556	C₄	1	1	yes	characteristic
17	C₄₇×#553	—	2	2	no	—
18	C₄₇×#553	C₄	1	2	yes	—
19	C₄₇×#550	C₄	1	1	yes	characteristic
20	C₄₇×#548	C₄	1	2	yes	—
21	C₄₇×#532	—	2	1	no	—
22	C₄₇×#532	C₂²	1	1	yes	characteristic
23	C₄₇×#529	—	2	2	no	—
24	C₄₇×#529	C₂²	1	2	yes	—
25	C₄×#41×C₄₇	—	2	1	no	—
26	C₄×#41×C₄₇	C₂²	1	2	yes	—
27	C₄×#41×C₄₇	C₂²	1	1	yes	characteristic
28	C₂×C₄×Q₈×C₄₇	C₂²	1	1	yes	characteristic
29	C₈×Q₈×C₄₇	—	2	1	no	—
30	C₈×D₄×C₄₇	—	2	2	no	—
31	C₈×D₄×C₄₇	—	2	1	no	—
32	C₄₇×#433	—	2	2	no	—
33	C₄₇×#432	C₂²	1	2	yes	—
34	C₄₇×#431	C₂²	1	1	yes	characteristic
35	C₄₇×#431	C₂²	1	2	yes	—
36	C₄₇×#431	C₂²	1	2	yes	—
37	C₄₇×#423	C₂²	1	1	yes	characteristic
38	C₂×C₄⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
39	C₄₇×#408	—	2	1	no	—
40	C₄₇×#405	—	2	1	no	—
41	C₂×C₄×C₈×C₄₇	C₂²	1	2	yes	—
42	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
43	C₄₇×Q₈⋊C₈	C₂²	1	1	yes	characteristic
44	C₄₇×Q₈⋊C₈	C₂²	1	2	yes	—
45	C₄₇×Q₈⋊C₈	C₂²	1	1	yes	characteristic
46	C₄₇×Q₈⋊C₈	C₂²	1	1	yes	characteristic
47	C₄₇×Q₈⋊C₈	C₂²	1	1	yes	characteristic
48	C₄₇×Q₈⋊C₈	C₂²	1	2	yes	—
49	C₄₇×D₄⋊C₈	C₂²	1	2	yes	—
50	C₄₇×D₄⋊C₈	C₂²	1	2	yes	—
51	C₄₇×D₄⋊C₈	C₂²	1	2	yes	—
52	C₄₇×D₄⋊C₈	C₂²	1	2	yes	—
53	C₂×#41×C₄₇	—	2	1	no	—
54	C₂×#41×C₄₇	C₂×C₄	1	2	yes	—
55	C₂×#41×C₄₇	D₄	1	1	yes	characteristic
56	C₂²×Q₈×C₄₇	C₂×C₄	1	1	yes	characteristic
57	C₂×M₁₆×C₄₇	—	2	1	no	—
58	C₂²×C₈×C₄₇	—	2	1	no	—
59	C₂²×C₈×C₄₇	—	2	2	no	—
60	C₂²×C₈×C₄₇	—	2	1	no	—
61	C₄⋊Q₈×C₄₇	—	2	1	no	—
62	C₄⋊Q₈×C₄₇	C₂×C₄	1	1	yes	characteristic
63	#127×C₄₇	—	2	1	no	—
64	#127×C₄₇	C₂×C₄	1	1	yes	characteristic
65	#126×C₄₇	—	2	2	no	—
66	#126×C₄₇	—	2	2	no	—
67	#126×C₄₇	—	2	2	no	—
68	#125×C₄₇	—	2	2	no	—
69	#125×C₄₇	C₂×C₄	1	2	yes	—
70	#124×C₄₇	—	2	1	no	—
71	#124×C₄₇	—	2	1	no	—
72	#124×C₄₇	—	2	2	no	—
73	#124×C₄₇	—	2	1	no	—
74	#124×C₄₇	C₂×C₄	1	2	yes	—
75	#123×C₄₇	—	2	2	no	—
76	#123×C₄₇	—	2	2	no	—
77	#123×C₄₇	—	2	2	no	—
78	C₂²⋊Q₈×C₄₇	—	2	2	no	—
79	C₂²⋊Q₈×C₄₇	C₂×C₄	1	2	yes	—
80	#121×C₄₇	—	2	2	no	—
81	#121×C₄₇	—	2	2	no	—
82	#121×C₄₇	—	2	1	no	—
83	#121×C₄₇	—	2	2	no	—
84	#121×C₄₇	C₂×C₄	1	2	yes	—
85	#121×C₄₇	C₂×C₄	1	2	yes	—
86	C₄×Q₈×C₄₇	—	2	1	no	—
87	C₄×Q₈×C₄₇	—	2	1	no	—
88	C₄×Q₈×C₄₇	—	2	1	no	—
89	C₄×Q₈×C₄₇	—	2	1	no	—
90	C₄×Q₈×C₄₇	C₂×C₄	1	1	yes	characteristic
91	C₄×Q₈×C₄₇	C₂×C₄	1	1	yes	characteristic
92	C₄×Q₈×C₄₇	C₂×C₄	1	2	yes	—
93	C₄×Q₈×C₄₇	C₂×C₄	1	1	yes	characteristic
94	C₄×Q₈×C₄₇	D₄	1	1	yes	characteristic
95	C₄×Q₈×C₄₇	C₂³	1	1	yes	characteristic
96	C₄×Q₈×C₄₇	C₂³	1	1	yes	characteristic
97	C₄×D₄×C₄₇	—	2	2	no	—
98	C₄×D₄×C₄₇	—	2	2	no	—
99	C₄×D₄×C₄₇	—	2	2	no	—
100	C₄×D₄×C₄₇	—	2	1	no	—
101	C₄×D₄×C₄₇	—	2	1	no	—
102	C₄×D₄×C₄₇	—	2	2	no	—
103	C₄×D₄×C₄₇	—	2	2	no	—
104	C₄×D₄×C₄₇	—	2	1	no	—
105	C₄×D₄×C₄₇	C₂×C₄	1	2	yes	—
106	C₄×D₄×C₄₇	C₂×C₄	1	2	yes	—
107	C₄×D₄×C₄₇	C₂×C₄	1	1	yes	characteristic
108	C₄×D₄×C₄₇	D₄	1	2	yes	—
109	C₄×D₄×C₄₇	D₄	1	1	yes	characteristic
110	C₄×D₄×C₄₇	C₂³	1	2	yes	—
111	#117×C₄₇	—	2	2	no	—
112	#117×C₄₇	—	2	2	no	—
113	#117×C₄₇	C₂×C₄	1	2	yes	—
114	#117×C₄₇	D₄	1	1	yes	characteristic
115	#117×C₄₇	D₄	1	2	yes	—
116	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
117	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
118	C₂×C₄²×C₄₇	—	2	1	no	—
119	C₂×C₄²×C₄₇	—	2	2	no	—
120	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
121	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
122	C₄⋊C₈×C₄₇	—	2	1	no	—
123	C₄⋊C₈×C₄₇	—	2	1	no	—
124	C₄⋊C₈×C₄₇	—	2	2	no	—
125	C₄⋊C₈×C₄₇	—	2	1	no	—
126	C₄⋊C₈×C₄₇	C₂³	1	1	yes	characteristic
127	C₄⋊C₈×C₄₇	C₂³	1	1	yes	characteristic
128	C₄⋊C₈×C₄₇	C₂³	1	2	yes	—
129	C₂²⋊C₈×C₄₇	—	2	2	no	—
130	C₂²⋊C₈×C₄₇	—	2	2	no	—
131	C₂²⋊C₈×C₄₇	—	2	1	no	—
132	C₂²⋊C₈×C₄₇	—	2	2	no	—
133	#97×C₄₇	—	2	2	no	—
134	C₄×C₈×C₄₇	—	2	2	no	—
135	C₄×C₈×C₄₇	—	2	1	no	—
136	C₄×C₈×C₄₇	—	2	2	no	—
137	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
138	C₄×C₈×C₄₇	C₂³	1	2	yes	—
139	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
140	#41×C₄₇	—	2	2	no	—
141	#41×C₄₇	—	2	2	no	—
142	#41×C₄₇	—	2	4	no	—
143	#41×C₄₇	—	4	2	no	—
144	#41×C₄₇	—	4	2	no	—
145	#41×C₄₇	—	4	2	no	—
146	C₂×Q₈×C₄₇	—	2	1	no	—
147	C₂×Q₈×C₄₇	—	2	1	no	—
148	C₂×Q₈×C₄₇	—	2	2	no	—
149	C₂×Q₈×C₄₇	—	4	1	no	—
150	C₂×Q₈×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
151	C₂×Q₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
152	C₂×Q₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
153	C₂×D₄×C₄₇	—	2	2	no	—
154	C₂×D₄×C₄₇	—	2	2	no	—
155	C₂×D₄×C₄₇	—	2	2	no	—
156	C₂×D₄×C₄₇	—	2	1	no	—
157	C₂×D₄×C₄₇	—	2	1	no	—
158	C₂×D₄×C₄₇	C₂²⋊C₄	1	2	yes	—
159	C₂×D₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
160	C₂×D₄×C₄₇	C₂²×C₄	1	2	yes	—
161	C₂²×C₄×C₄₇	—	2	1	no	—
162	C₂²×C₄×C₄₇	—	2	1	no	—
163	C₂²×C₄×C₄₇	—	2	2	no	—
164	C₂²×C₄×C₄₇	—	2	2	no	—
165	C₂²×C₄×C₄₇	—	2	2	no	—
166	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
167	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
168	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
169	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
170	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
171	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
172	M₁₆×C₄₇	—	4	2	no	—
173	C₂×C₈×C₄₇	—	2	1	no	—
174	C₂×C₈×C₄₇	—	2	1	no	—
175	C₂×C₈×C₄₇	—	2	2	no	—
176	C₂×C₈×C₄₇	—	2	1	no	—
177	C₂×C₈×C₄₇	—	2	1	no	—
178	C₂×C₈×C₄₇	—	2	2	no	—
179	C₂×C₈×C₄₇	—	4	4	no	—
180	C₂×C₈×C₄₇	—	4	2	no	—
181	C₂×C₈×C₄₇	—	4	2	no	—
182	C₄⋊C₄×C₄₇	—	2	1	no	—
183	C₄⋊C₄×C₄₇	—	2	1	no	—
184	C₄⋊C₄×C₄₇	—	2	1	no	—
185	C₄⋊C₄×C₄₇	—	2	2	no	—
186	C₄⋊C₄×C₄₇	—	2	2	no	—
187	C₄⋊C₄×C₄₇	—	2	2	no	—
188	C₄⋊C₄×C₄₇	—	2	1	no	—
189	C₄⋊C₄×C₄₇	—	2	2	no	—
190	C₄⋊C₄×C₄₇	—	2	1	no	—
191	C₄⋊C₄×C₄₇	—	2	1	no	—
192	C₄⋊C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
193	C₄⋊C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
194	C₄⋊C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
195	C₄⋊C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
196	C₄⋊C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
197	C₄⋊C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
198	C₄⋊C₄×C₄₇	C₂²×C₄	1	2	yes	—
199	C₂²⋊C₄×C₄₇	—	2	2	no	—
200	C₂²⋊C₄×C₄₇	—	2	2	no	—
201	C₂²⋊C₄×C₄₇	—	2	2	no	—
202	C₂²⋊C₄×C₄₇	—	2	2	no	—
203	C₂²⋊C₄×C₄₇	—	2	2	no	—
204	C₂²⋊C₄×C₄₇	—	2	2	no	—
205	C₂²⋊C₄×C₄₇	—	2	2	no	—
206	C₂²⋊C₄×C₄₇	—	2	2	no	—
207	C₂²⋊C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
208	C₂²⋊C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
209	C₂²⋊C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
210	C₄²×C₄₇	—	2	2	no	—
211	C₄²×C₄₇	—	2	2	no	—
212	C₄²×C₄₇	—	2	1	no	—
213	C₄²×C₄₇	—	2	1	no	—
214	C₄²×C₄₇	—	2	1	no	—
215	C₄²×C₄₇	—	2	1	no	—
216	C₄²×C₄₇	C₂²×C₄	1	2	yes	—
217	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
218	C₄²×C₄₇	C₂×D₄	1	2	yes	—
219	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
220	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
221	C₄²×C₄₇	C₂×D₄	1	2	yes	—
222	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
223	C₂³×C₄₇	—	2	2	no	—
224	C₂³×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
225	C₂³×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
226	Q₈×C₄₇	—	2	1	no	—
227	Q₈×C₄₇	—	2	2	no	—
228	Q₈×C₄₇	—	2	1	no	—
229	Q₈×C₄₇	—	2	1	no	—
230	Q₈×C₄₇	—	4	2	no	—
231	Q₈×C₄₇	—	4	2	no	—
232	Q₈×C₄₇	#131	1	2	yes	—
233	D₄×C₄₇	—	2	4	no	—
234	D₄×C₄₇	—	2	2	no	—
235	D₄×C₄₇	—	2	2	no	—
236	D₄×C₄₇	—	2	2	no	—
237	D₄×C₄₇	—	4	4	no	—
238	D₄×C₄₇	—	4	4	no	—
239	D₄×C₄₇	—	4	2	no	—
240	D₄×C₄₇	—	8	1	no	—
241	D₄×C₄₇	—	8	2	no	—
242	C₂×C₄×C₄₇	—	2	1	no	—
243	C₂×C₄×C₄₇	—	2	1	no	—
244	C₂×C₄×C₄₇	—	2	2	no	—
245	C₂×C₄×C₄₇	—	2	1	no	—
246	C₂×C₄×C₄₇	—	2	2	no	—
247	C₂×C₄×C₄₇	—	2	2	no	—
248	C₂×C₄×C₄₇	—	2	2	no	—
249	C₂×C₄×C₄₇	—	2	1	no	—
250	C₂×C₄×C₄₇	—	2	1	no	—
251	C₂×C₄×C₄₇	—	2	2	no	—
252	C₂×C₄×C₄₇	—	2	1	no	—
253	C₂×C₄×C₄₇	—	4	2	no	—
254	C₂×C₄×C₄₇	—	4	1	no	—
255	C₂×C₄×C₄₇	—	4	4	no	—
256	C₂×C₄×C₄₇	—	4	2	no	—
257	C₂×C₄×C₄₇	—	4	2	no	—
258	C₂×C₄×C₄₇	—	4	2	no	—
259	C₂×C₄×C₄₇	—	8	2	no	—
260	C₂×C₄×C₄₇	—	8	1	no	—
261	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
262	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
263	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
264	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
265	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
266	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
267	C₂×C₄×C₄₇	#135	1	2	yes	—
268	C₂×C₄×C₄₇	#135	1	2	yes	—
269	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
270	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
271	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
272	C₈×C₄₇	—	2	2	no	—
273	C₈×C₄₇	—	4	1	no	—
274	C₈×C₄₇	—	4	2	no	—
275	C₈×C₄₇	—	4	1	no	—
276	C₈×C₄₇	—	4	1	no	—
277	C₈×C₄₇	—	4	2	no	—
278	#17510	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
279	C₂²×C₄₇	—	2	1	no	—
280	C₂²×C₄₇	—	2	1	no	—
281	C₂²×C₄₇	—	2	2	no	—
282	C₂²×C₄₇	—	2	2	no	—
283	C₂²×C₄₇	—	2	2	no	—
284	C₂²×C₄₇	—	4	2	no	—
285	C₂²×C₄₇	—	4	2	no	—
286	C₂²×C₄₇	—	4	2	no	—
287	C₂²×C₄₇	#416	1	2	yes	—
288	C₂²×C₄₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
289	C₄×C₄₇	—	2	2	no	—
290	C₄×C₄₇	—	2	1	no	—
291	C₄×C₄₇	—	2	2	no	—
292	C₄×C₄₇	—	2	2	no	—
293	C₄×C₄₇	—	2	1	no	—
294	C₄×C₄₇	—	2	2	no	—
295	C₄×C₄₇	—	2	1	no	—
296	C₄×C₄₇	—	4	1	no	—
297	C₄×C₄₇	—	4	2	no	—
298	C₄×C₄₇	—	4	1	no	—
299	C₄×C₄₇	—	4	1	no	—
300	C₄×C₄₇	#416	1	2	yes	—
301	C₄×C₄₇	C₂×#131	1	1	yes	characteristic
302	C₄×C₄₇	#568	1	1	yes	characteristic
303	C₄×C₄₇	C₂×#135	1	1	yes	characteristic
304	C₄×C₄₇	C₂×#135	1	1	yes	characteristic
305	#3480	C₂×C₄₇	1	1	yes	characteristic
306	C₈×#41	C₂×C₄₇	1	1	yes	characteristic, complemented
307	#2925	C₂×C₄₇	1	1	yes	characteristic, complemented
308	#1494	C₂×C₄₇	1	2	yes	complemented
309	#1492	C₂×C₄₇	1	1	yes	characteristic, complemented
310	#1488	C₂×C₄₇	1	2	yes	complemented
311	#1487	C₂×C₄₇	1	1	yes	characteristic, complemented
312	#1482	C₂×C₄₇	1	2	yes	complemented
313	#1480	C₂×C₄₇	1	1	yes	characteristic, complemented
314	#1476	C₂×C₄₇	1	2	yes	complemented
315	C₂×Q₈⋊C₈	C₂×C₄₇	1	1	yes	characteristic, complemented
316	C₂×C₄₇	—	2	2	no	—
317	C₂×C₄₇	—	4	2	no	—
318	C₂×C₄₇	—	8	2	no	—
319	C₂×C₄₇	#2880	1	1	yes	characteristic
320	C₂×C₄₇	C₂×#416	1	1	yes	characteristic
321	C₂×C₄₇	#2901	1	1	yes	characteristic
322	#559	—	2	1	no	—
323	#559	C₄×C₄₇	1	1	yes	characteristic
324	#557	C₄×C₄₇	1	1	yes	characteristic
325	#556	—	2	1	no	—
326	#556	C₄×C₄₇	1	1	yes	characteristic
327	#553	—	2	2	no	—
328	#553	C₄×C₄₇	1	2	yes	—
329	#550	C₄×C₄₇	1	1	yes	characteristic
330	#548	C₄×C₄₇	1	2	yes	—
331	#532	—	2	1	no	—
332	#532	C₂²×C₄₇	1	1	yes	characteristic
333	#529	—	2	2	no	—
334	#529	C₂²×C₄₇	1	2	yes	—
335	C₄×#41	—	2	1	no	—
336	C₄×#41	C₂²×C₄₇	1	2	yes	—
337	C₄×#41	C₂²×C₄₇	1	1	yes	characteristic
338	C₂×C₄×Q₈	C₂²×C₄₇	1	1	yes	characteristic
339	C₈×Q₈	—	2	1	no	—
340	C₈×D₄	—	2	2	no	—
341	C₈×D₄	—	2	1	no	—
342	#433	—	2	2	no	—
343	#432	C₂²×C₄₇	1	2	yes	—
344	#431	C₂²×C₄₇	1	2	yes	—
345	#431	C₂²×C₄₇	1	1	yes	characteristic
346	#431	C₂²×C₄₇	1	2	yes	—
347	#423	C₂²×C₄₇	1	1	yes	characteristic
348	C₂×C₄⋊C₈	C₂²×C₄₇	1	1	yes	characteristic
349	#408	—	2	1	no	—
350	#405	—	2	1	no	—
351	C₂×C₄×C₈	C₂²×C₄₇	1	1	yes	characteristic
352	C₂×C₄×C₈	C₂²×C₄₇	1	2	yes	—
353	Q₈⋊C₈	C₂²×C₄₇	1	1	yes	characteristic
354	Q₈⋊C₈	C₂²×C₄₇	1	1	yes	characteristic
355	Q₈⋊C₈	C₂²×C₄₇	1	1	yes	characteristic
356	Q₈⋊C₈	C₂²×C₄₇	1	1	yes	characteristic
357	Q₈⋊C₈	C₂²×C₄₇	1	2	yes	—
358	Q₈⋊C₈	C₂²×C₄₇	1	2	yes	—
359	D₄⋊C₈	C₂²×C₄₇	1	2	yes	—
360	D₄⋊C₈	C₂²×C₄₇	1	2	yes	—
361	D₄⋊C₈	C₂²×C₄₇	1	2	yes	—
362	D₄⋊C₈	C₂²×C₄₇	1	2	yes	—
363	C₄₇	#17510	1	1	yes	characteristic, direct product factor, Sylow
364	C₂×#41	—	2	1	no	—
365	C₂×#41	C₂×C₄×C₄₇	1	2	yes	—
366	C₂×#41	D₄×C₄₇	1	1	yes	characteristic
367	C₂²×Q₈	C₂×C₄×C₄₇	1	1	yes	characteristic
368	C₂×M₁₆	—	2	1	no	—
369	C₂²×C₈	—	2	1	no	—
370	C₂²×C₈	—	2	2	no	—
371	C₂²×C₈	—	2	1	no	—
372	C₄⋊Q₈	—	2	1	no	—
373	C₄⋊Q₈	C₂×C₄×C₄₇	1	1	yes	characteristic
374	#127	—	2	1	no	—
375	#127	C₂×C₄×C₄₇	1	1	yes	characteristic
376	#126	—	2	2	no	—
377	#126	—	2	2	no	—
378	#126	—	2	2	no	—
379	#125	—	2	2	no	—
380	#125	C₂×C₄×C₄₇	1	2	yes	—
381	#124	—	2	1	no	—
382	#124	—	2	1	no	—
383	#124	—	2	2	no	—
384	#124	—	2	1	no	—
385	#124	C₂×C₄×C₄₇	1	2	yes	—
386	#123	—	2	2	no	—
387	#123	—	2	2	no	—
388	#123	—	2	2	no	—
389	C₂²⋊Q₈	—	2	2	no	—
390	C₂²⋊Q₈	C₂×C₄×C₄₇	1	2	yes	—
391	#121	—	2	2	no	—
392	#121	—	2	2	no	—
393	#121	—	2	1	no	—
394	#121	—	2	2	no	—
395	#121	C₂×C₄×C₄₇	1	2	yes	—
396	#121	C₂×C₄×C₄₇	1	2	yes	—
397	C₄×Q₈	—	2	1	no	—
398	C₄×Q₈	—	2	1	no	—
399	C₄×Q₈	—	2	1	no	—
400	C₄×Q₈	—	2	1	no	—
401	C₄×Q₈	C₂×C₄×C₄₇	1	1	yes	characteristic
402	C₄×Q₈	C₂×C₄×C₄₇	1	1	yes	characteristic
403	C₄×Q₈	C₂×C₄×C₄₇	1	2	yes	—
404	C₄×Q₈	C₂×C₄×C₄₇	1	1	yes	characteristic
405	C₄×Q₈	D₄×C₄₇	1	1	yes	characteristic
406	C₄×Q₈	C₂³×C₄₇	1	1	yes	characteristic
407	C₄×Q₈	C₂³×C₄₇	1	1	yes	characteristic
408	C₄×D₄	—	2	2	no	—
409	C₄×D₄	—	2	2	no	—
410	C₄×D₄	—	2	2	no	—
411	C₄×D₄	—	2	1	no	—
412	C₄×D₄	—	2	1	no	—
413	C₄×D₄	—	2	2	no	—
414	C₄×D₄	—	2	2	no	—
415	C₄×D₄	—	2	1	no	—
416	C₄×D₄	C₂×C₄×C₄₇	1	2	yes	—
417	C₄×D₄	C₂×C₄×C₄₇	1	2	yes	—
418	C₄×D₄	C₂×C₄×C₄₇	1	1	yes	characteristic
419	C₄×D₄	D₄×C₄₇	1	2	yes	—
420	C₄×D₄	D₄×C₄₇	1	1	yes	characteristic
421	C₄×D₄	C₂³×C₄₇	1	2	yes	—
422	#117	—	2	2	no	—
423	#117	—	2	2	no	—
424	#117	C₂×C₄×C₄₇	1	2	yes	—
425	#117	D₄×C₄₇	1	1	yes	characteristic
426	#117	D₄×C₄₇	1	2	yes	—
427	C₂×C₄⋊C₄	—	2	1	no	—
428	C₂×C₄⋊C₄	C₂×C₄×C₄₇	1	1	yes	characteristic
429	C₂×C₄²	—	2	1	no	—
430	C₂×C₄²	—	2	2	no	—
431	C₂×C₄²	C₂³×C₄₇	1	1	yes	characteristic
432	C₂×C₄²	C₂³×C₄₇	1	2	yes	—
433	C₄⋊C₈	—	2	1	no	—
434	C₄⋊C₈	—	2	1	no	—
435	C₄⋊C₈	—	2	2	no	—
436	C₄⋊C₈	—	2	1	no	—
437	C₄⋊C₈	C₂³×C₄₇	1	1	yes	characteristic
438	C₄⋊C₈	C₂³×C₄₇	1	1	yes	characteristic
439	C₄⋊C₈	C₂³×C₄₇	1	2	yes	—
440	C₂²⋊C₈	—	2	2	no	—
441	C₂²⋊C₈	—	2	2	no	—
442	C₂²⋊C₈	—	2	1	no	—
443	C₂²⋊C₈	—	2	2	no	—
444	#97	—	2	2	no	—
445	C₄×C₈	—	2	2	no	—
446	C₄×C₈	—	2	1	no	—
447	C₄×C₈	—	2	2	no	—
448	C₄×C₈	C₂³×C₄₇	1	1	yes	characteristic
449	C₄×C₈	C₂³×C₄₇	1	2	yes	—
450	C₄×C₈	C₂³×C₄₇	1	1	yes	characteristic
451	#41	—	2	2	no	—
452	#41	—	2	2	no	—
453	#41	—	2	4	no	—
454	#41	—	4	2	no	—
455	#41	—	4	2	no	—
456	#41	—	4	2	no	—
457	C₂×Q₈	—	2	1	no	—
458	C₂×Q₈	—	2	1	no	—
459	C₂×Q₈	—	2	2	no	—
460	C₂×Q₈	—	4	1	no	—
461	C₂×Q₈	C₂²⋊C₄×C₄₇	1	1	yes	characteristic
462	C₂×Q₈	C₂²×C₄×C₄₇	1	1	yes	characteristic
463	C₂×Q₈	C₂²×C₄×C₄₇	1	1	yes	characteristic
464	C₂×D₄	—	2	2	no	—
465	C₂×D₄	—	2	2	no	—
466	C₂×D₄	—	2	2	no	—
467	C₂×D₄	—	2	1	no	—
468	C₂×D₄	—	2	1	no	—
469	C₂×D₄	C₂²⋊C₄×C₄₇	1	2	yes	—
470	C₂×D₄	C₂²⋊C₄×C₄₇	1	1	yes	characteristic
471	C₂×D₄	C₂²×C₄×C₄₇	1	2	yes	—
472	C₂²×C₄	—	2	1	no	—
473	C₂²×C₄	—	2	1	no	—
474	C₂²×C₄	—	2	2	no	—
475	C₂²×C₄	—	2	2	no	—
476	C₂²×C₄	—	2	2	no	—
477	C₂²×C₄	C₂²×C₄×C₄₇	1	1	yes	characteristic
478	C₂²×C₄	C₂²×C₄×C₄₇	1	2	yes	—
479	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
480	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
481	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
482	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
483	M₁₆	—	4	2	no	—
484	C₂×C₈	—	2	1	no	—
485	C₂×C₈	—	2	1	no	—
486	C₂×C₈	—	2	2	no	—
487	C₂×C₈	—	2	1	no	—
488	C₂×C₈	—	2	2	no	—
489	C₂×C₈	—	2	1	no	—
490	C₂×C₈	—	4	4	no	—
491	C₂×C₈	—	4	2	no	—
492	C₂×C₈	—	4	2	no	—
493	C₄⋊C₄	—	2	1	no	—
494	C₄⋊C₄	—	2	1	no	—
495	C₄⋊C₄	—	2	1	no	—
496	C₄⋊C₄	—	2	2	no	—
497	C₄⋊C₄	—	2	2	no	—
498	C₄⋊C₄	—	2	2	no	—
499	C₄⋊C₄	—	2	1	no	—
500	C₄⋊C₄	—	2	2	no	—
501	C₄⋊C₄	—	2	1	no	—
502	C₄⋊C₄	—	2	1	no	—
503	C₄⋊C₄	C₂²⋊C₄×C₄₇	1	1	yes	characteristic
504	C₄⋊C₄	C₂²⋊C₄×C₄₇	1	1	yes	characteristic
505	C₄⋊C₄	C₂²⋊C₄×C₄₇	1	2	yes	—
506	C₄⋊C₄	C₂²⋊C₄×C₄₇	1	2	yes	—
507	C₄⋊C₄	C₂²×C₄×C₄₇	1	1	yes	characteristic
508	C₄⋊C₄	C₂²×C₄×C₄₇	1	1	yes	characteristic
509	C₄⋊C₄	C₂²×C₄×C₄₇	1	2	yes	—
510	C₂²⋊C₄	—	2	2	no	—
511	C₂²⋊C₄	—	2	2	no	—
512	C₂²⋊C₄	—	2	2	no	—
513	C₂²⋊C₄	—	2	2	no	—
514	C₂²⋊C₄	—	2	2	no	—
515	C₂²⋊C₄	—	2	2	no	—
516	C₂²⋊C₄	—	2	2	no	—
517	C₂²⋊C₄	—	2	2	no	—
518	C₂²⋊C₄	C₂²⋊C₄×C₄₇	1	2	yes	—
519	C₂²⋊C₄	C₂²⋊C₄×C₄₇	1	2	yes	—
520	C₂²⋊C₄	C₂²⋊C₄×C₄₇	1	2	yes	—
521	C₄²	—	2	2	no	—
522	C₄²	—	2	2	no	—
523	C₄²	—	2	1	no	—
524	C₄²	—	2	1	no	—
525	C₄²	—	2	1	no	—
526	C₄²	—	2	1	no	—
527	C₄²	C₂²×C₄×C₄₇	1	2	yes	—
528	C₄²	C₂²×C₄×C₄₇	1	1	yes	characteristic
529	C₄²	C₂×D₄×C₄₇	1	2	yes	—
530	C₄²	C₂×D₄×C₄₇	1	2	yes	—
531	C₄²	C₂×D₄×C₄₇	1	1	yes	characteristic
532	C₄²	C₂×D₄×C₄₇	1	1	yes	characteristic
533	C₄²	C₂⁴×C₄₇	1	1	yes	characteristic
534	C₂³	—	2	2	no	—
535	C₂³	C₂×C₂²⋊C₄×C₄₇	1	2	yes	—
536	C₂³	C₂×C₂²⋊C₄×C₄₇	1	1	yes	characteristic
537	Q₈	—	2	1	no	—
538	Q₈	—	2	2	no	—
539	Q₈	—	2	1	no	—
540	Q₈	—	2	1	no	—
541	Q₈	—	4	2	no	—
542	Q₈	—	4	2	no	—
543	Q₈	#131×C₄₇	1	2	yes	—
544	D₄	—	2	4	no	—
545	D₄	—	2	2	no	—
546	D₄	—	2	2	no	—
547	D₄	—	2	2	no	—
548	D₄	—	4	4	no	—
549	D₄	—	4	4	no	—
550	D₄	—	4	2	no	—
551	D₄	—	8	1	no	—
552	D₄	—	8	2	no	—
553	C₂×C₄	—	2	1	no	—
554	C₂×C₄	—	2	1	no	—
555	C₂×C₄	—	2	2	no	—
556	C₂×C₄	—	2	1	no	—
557	C₂×C₄	—	2	2	no	—
558	C₂×C₄	—	2	2	no	—
559	C₂×C₄	—	2	2	no	—
560	C₂×C₄	—	2	1	no	—
561	C₂×C₄	—	2	1	no	—
562	C₂×C₄	—	2	2	no	—
563	C₂×C₄	—	2	1	no	—
564	C₂×C₄	—	4	2	no	—
565	C₂×C₄	—	4	1	no	—
566	C₂×C₄	—	4	4	no	—
567	C₂×C₄	—	4	2	no	—
568	C₂×C₄	—	4	2	no	—
569	C₂×C₄	—	4	2	no	—
570	C₂×C₄	—	8	2	no	—
571	C₂×C₄	—	8	1	no	—
572	C₂×C₄	C₂×C₂²⋊C₄×C₄₇	1	2	yes	—
573	C₂×C₄	C₂×C₂²⋊C₄×C₄₇	1	2	yes	—
574	C₂×C₄	C₂×C₂²⋊C₄×C₄₇	1	2	yes	—
575	C₂×C₄	C₂×C₂²⋊C₄×C₄₇	1	1	yes	characteristic
576	C₂×C₄	C₂×C₂²⋊C₄×C₄₇	1	1	yes	characteristic
577	C₂×C₄	C₂×C₂²⋊C₄×C₄₇	1	1	yes	characteristic
578	C₂×C₄	#135×C₄₇	1	2	yes	—
579	C₂×C₄	#135×C₄₇	1	2	yes	—
580	C₂×C₄	C₂³×C₄×C₄₇	1	1	yes	characteristic
581	C₂×C₄	C₂²×D₄×C₄₇	1	1	yes	characteristic
582	C₂×C₄	C₂²×D₄×C₄₇	1	1	yes	characteristic
583	C₈	—	2	2	no	—
584	C₈	—	4	2	no	—
585	C₈	—	4	1	no	—
586	C₈	—	4	1	no	—
587	C₈	—	4	1	no	—
588	C₈	—	4	2	no	—
589	C₂²	—	2	1	no	—
590	C₂²	—	2	1	no	—
591	C₂²	—	2	2	no	—
592	C₂²	—	2	2	no	—
593	C₂²	—	2	2	no	—
594	C₂²	—	4	2	no	—
595	C₂²	—	4	2	no	—
596	C₂²	—	4	2	no	—
597	C₂²	C₄₇×#416	1	2	yes	—
598	C₂²	C₂²×C₂²⋊C₄×C₄₇	1	1	yes	characteristic
599	C₄	—	2	2	no	—
600	C₄	—	2	1	no	—
601	C₄	—	2	2	no	—
602	C₄	—	2	2	no	—
603	C₄	—	2	1	no	—
604	C₄	—	2	2	no	—
605	C₄	—	2	1	no	—
606	C₄	—	4	1	no	—
607	C₄	—	4	2	no	—
608	C₄	—	4	1	no	—
609	C₄	—	4	1	no	—
610	C₄	C₄₇×#416	1	2	yes	—
611	C₄	C₂×#131×C₄₇	1	1	yes	characteristic
612	C₄	C₄₇×#568	1	1	yes	characteristic
613	C₄	C₂×#135×C₄₇	1	1	yes	characteristic
614	C₄	C₂×#135×C₄₇	1	1	yes	characteristic
615	C₂	—	2	2	no	—
616	C₂	—	4	2	no	—
617	C₂	—	8	2	no	—
618	C₂	C₄₇×#2880	1	1	yes	characteristic
619	C₂	C₂×C₄₇×#416	1	1	yes	characteristic
620	C₂	C₄₇×#2901	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₄₇	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₄₇
Frattini, cosocle	C₄²	C₂⁴×C₄₇
socle	C₂²×C₄₇	C₂²×C₂²⋊C₄
prime radical	C₄₇×#3480	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₄₇ ◁ C₄×#41×C₄₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₈×#41×C₄₇	C₂	semidirect
3. C₄₇×#2925	C₂	semidirect
4. C₄₇×#1494	C₂	semidirect
5. C₄₇×#1492	C₂	semidirect
6. C₄₇×#1488	C₂	semidirect
7. C₄₇×#1487	C₂	semidirect
8. C₄₇×#1482	C₂	semidirect
9. C₄₇×#1480	C₂	semidirect
10. C₄₇×#1476	C₂	semidirect
11. C₂×C₄₇×Q₈⋊C₈	C₂	semidirect
278. #17510	C₄₇	direct (N × H)
306. C₈×#41	C₂×C₄₇	semidirect
307. #2925	C₂×C₄₇	semidirect
308. #1494	C₂×C₄₇	semidirect
309. #1492	C₂×C₄₇	semidirect
310. #1488	C₂×C₄₇	semidirect
311. #1487	C₂×C₄₇	semidirect
312. #1482	C₂×C₄₇	semidirect
313. #1480	C₂×C₄₇	semidirect
314. #1476	C₂×C₄₇	semidirect
315. C₂×Q₈⋊C₈	C₂×C₄₇	semidirect
363. C₄₇	#17510	direct (N × H)

Maximal subgroups

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

subgroup	index
C₄₇×#3480	2
C₈×#41×C₄₇	2
C₄₇×#2925	2
C₄₇×#1494	2
C₄₇×#1492	2
C₄₇×#1488	2
C₄₇×#1487	2
C₄₇×#1482	2
C₄₇×#1480	2
C₄₇×#1476	2
C₂×C₄₇×Q₈⋊C₈	2
#17510	47

Subgroups — C47×#17510 #26057208

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₇×#17510 #26057208