Subgroups — C₄₇×#29113 #26068811

Order 12032.

910 conjugacy classes of subgroups.

The subgroup lattice has 532 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₇×#2857	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄₇×#2297	C₂	1	1	yes	maximal, characteristic
3	C₄₇×#2072	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄₇×#2071	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₇×#2024	C₂	1	1	yes	maximal, characteristic, complemented
6	C₄₇×#2023	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄₇×#1936	C₂	1	2	yes	maximal, complemented
8	C₄₇×#1935	C₂	1	2	yes	maximal, complemented
9	C₄₇×#1825	C₂	1	2	yes	maximal, complemented
10	C₄₇×#1788	C₂	1	2	yes	maximal
11	C₄₇×#1749	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×#41×C₄₇	C₂²	1	1	yes	characteristic
13	C₂×C₄⋊Q₈×C₄₇	C₂²	1	1	yes	characteristic
14	C₂×C₂²⋊Q₈×C₄₇	—	2	1	no	—
15	C₂×#117×C₄₇	C₂²	1	1	yes	characteristic
16	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
17	C₂×#103×C₄₇	C₂²	1	2	yes	—
18	C₂×#103×C₄₇	C₂²	1	2	yes	—
19	C₂×#102×C₄₇	C₂²	1	2	yes	—
20	C₂×#102×C₄₇	C₂²	1	2	yes	—
21	C₂×C₂²⋊C₈×C₄₇	C₂²	1	2	yes	—
22	C₂×#97×C₄₇	C₂²	1	2	yes	—
23	C₄₇×#391	—	2	1	no	—
24	C₄₇×#391	C₂²	1	1	yes	characteristic
25	C₄₇×#391	C₂²	1	1	yes	characteristic
26	C₄₇×#390	C₂²	1	1	yes	characteristic
27	C₄₇×#390	C₂²	1	1	yes	characteristic
28	C₄₇×#389	—	2	1	no	—
29	C₄₇×#389	C₂²	1	2	yes	—
30	C₄₇×#386	—	2	1	no	—
31	C₄₇×#386	—	2	1	no	—
32	C₄₇×#384	C₂²	1	1	yes	characteristic
33	C₄₇×#380	—	2	1	no	—
34	C₄₇×#380	C₂²	1	2	yes	—
35	C₄×C₂²⋊C₄×C₄₇	—	2	1	no	—
36	C₄×C₂²⋊C₄×C₄₇	—	2	1	no	—
37	C₄₇×#340	C₂²	1	2	yes	—
38	C₄₇×#340	C₂²	1	2	yes	—
39	C₄₇×#340	C₂²	1	2	yes	—
40	C₄₇×#340	C₂²	1	2	yes	—
41	C₄₇×#336	C₂²	1	1	yes	characteristic
42	C₄₇×#336	C₂²	1	1	yes	characteristic
43	C₂×#41×C₄₇	—	2	2	no	—
44	C₂×#41×C₄₇	—	2	2	no	—
45	C₂×#41×C₄₇	—	2	4	no	—
46	C₂×#41×C₄₇	—	4	2	no	—
47	C₂²×Q₈×C₄₇	—	2	1	no	—
48	C₂²×Q₈×C₄₇	C₂³	1	1	yes	characteristic
49	C₂²×D₄×C₄₇	—	2	1	no	—
50	C₂²×D₄×C₄₇	C₂³	1	1	yes	characteristic
51	C₂³×C₄×C₄₇	—	2	1	no	—
52	C₂³×C₄×C₄₇	D₄	1	1	yes	characteristic
53	C₂³×C₄×C₄₇	D₄	1	1	yes	characteristic
54	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
55	C₂²×C₈×C₄₇	C₂³	1	2	yes	—
56	C₂²×C₈×C₄₇	C₂³	1	2	yes	—
57	C₄⋊Q₈×C₄₇	—	4	2	no	—
58	C₂²⋊Q₈×C₄₇	—	4	4	no	—
59	#117×C₄₇	—	2	4	no	—
60	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
61	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
62	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
63	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
64	C₂×C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
65	C₂×C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
66	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
67	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
68	C₂×C₂²⋊C₄×C₄₇	—	2	1	no	—
69	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
70	C₂×C₂²⋊C₄×C₄₇	—	2	1	no	—
71	C₂×C₂²⋊C₄×C₄₇	—	2	1	no	—
72	C₂×C₂²⋊C₄×C₄₇	—	2	1	no	—
73	C₂×C₂²⋊C₄×C₄₇	—	2	1	no	—
74	C₂×C₄²×C₄₇	—	2	1	no	—
75	C₂×C₄²×C₄₇	—	4	2	no	—
76	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
77	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
78	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
79	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
80	#103×C₄₇	—	2	4	no	—
81	#103×C₄₇	—	4	2	no	—
82	#102×C₄₇	—	2	4	no	—
83	#102×C₄₇	—	4	2	no	—
84	C₂²⋊C₈×C₄₇	—	2	4	no	—
85	#97×C₄₇	—	4	2	no	—
86	#95×C₄₇	—	2	1	no	—
87	#95×C₄₇	—	2	1	no	—
88	#95×C₄₇	—	2	1	no	—
89	#95×C₄₇	—	2	1	no	—
90	#95×C₄₇	—	2	2	no	—
91	#95×C₄₇	—	2	2	no	—
92	C₂⁴×C₄₇	—	2	1	no	—
93	C₂⁴×C₄₇	C₂×D₄	1	1	yes	characteristic
94	#41×C₄₇	—	4	8	no	—
95	#41×C₄₇	—	4	8	no	—
96	C₂×Q₈×C₄₇	—	2	1	no	—
97	C₂×Q₈×C₄₇	—	2	2	no	—
98	C₂×Q₈×C₄₇	—	2	2	no	—
99	C₂×Q₈×C₄₇	—	4	2	no	—
100	C₂×Q₈×C₄₇	—	4	2	no	—
101	C₂×Q₈×C₄₇	—	4	2	no	—
102	C₂×Q₈×C₄₇	#41	1	2	yes	—
103	C₂×D₄×C₄₇	—	2	4	no	—
104	C₂×D₄×C₄₇	—	2	2	no	—
105	C₂×D₄×C₄₇	—	2	1	no	—
106	C₂×D₄×C₄₇	—	2	2	no	—
107	C₂×D₄×C₄₇	—	4	2	no	—
108	C₂×D₄×C₄₇	—	4	2	no	—
109	C₂×D₄×C₄₇	#41	1	2	yes	—
110	C₂²×C₄×C₄₇	—	2	1	no	—
111	C₂²×C₄×C₄₇	—	2	1	no	—
112	C₂²×C₄×C₄₇	—	2	2	no	—
113	C₂²×C₄×C₄₇	—	2	4	no	—
114	C₂²×C₄×C₄₇	—	2	1	no	—
115	C₂²×C₄×C₄₇	—	2	2	no	—
116	C₂²×C₄×C₄₇	—	2	2	no	—
117	C₂²×C₄×C₄₇	—	2	1	no	—
118	C₂²×C₄×C₄₇	—	2	1	no	—
119	C₂²×C₄×C₄₇	—	2	2	no	—
120	C₂²×C₄×C₄₇	—	2	2	no	—
121	C₂²×C₄×C₄₇	—	4	1	no	—
122	C₂²×C₄×C₄₇	—	4	1	no	—
123	C₂²×C₄×C₄₇	—	4	1	no	—
124	C₂²×C₄×C₄₇	—	4	1	no	—
125	C₂²×C₄×C₄₇	—	4	2	no	—
126	C₂²×C₄×C₄₇	—	4	2	no	—
127	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
128	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
129	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
130	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
131	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
132	C₂²×C₄×C₄₇	#41	1	4	yes	—
133	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
134	C₂×C₈×C₄₇	—	2	2	no	—
135	C₂×C₈×C₄₇	—	2	2	no	—
136	C₂×C₈×C₄₇	—	2	2	no	—
137	C₂×C₈×C₄₇	—	2	2	no	—
138	C₂×C₈×C₄₇	—	2	2	no	—
139	C₂×C₈×C₄₇	—	2	2	no	—
140	C₄⋊C₄×C₄₇	—	2	2	no	—
141	C₄⋊C₄×C₄₇	—	2	2	no	—
142	C₄⋊C₄×C₄₇	—	2	2	no	—
143	C₄⋊C₄×C₄₇	—	2	2	no	—
144	C₄⋊C₄×C₄₇	—	2	2	no	—
145	C₄⋊C₄×C₄₇	—	2	2	no	—
146	C₄⋊C₄×C₄₇	—	4	2	no	—
147	C₄⋊C₄×C₄₇	—	4	4	no	—
148	C₄⋊C₄×C₄₇	—	4	2	no	—
149	C₄⋊C₄×C₄₇	—	4	2	no	—
150	C₂²⋊C₄×C₄₇	—	4	2	no	—
151	C₂²⋊C₄×C₄₇	—	4	2	no	—
152	C₂²⋊C₄×C₄₇	—	4	4	no	—
153	C₂²⋊C₄×C₄₇	—	4	2	no	—
154	C₂²⋊C₄×C₄₇	—	4	2	no	—
155	C₂²⋊C₄×C₄₇	—	4	2	no	—
156	C₄²×C₄₇	—	2	2	no	—
157	C₄²×C₄₇	—	2	2	no	—
158	C₄²×C₄₇	—	4	1	no	—
159	C₄²×C₄₇	—	4	1	no	—
160	C₄²×C₄₇	—	4	2	no	—
161	C₂³×C₄₇	—	2	1	no	—
162	C₂³×C₄₇	—	2	1	no	—
163	C₂³×C₄₇	—	2	1	no	—
164	C₂³×C₄₇	—	2	1	no	—
165	C₂³×C₄₇	—	2	1	no	—
166	C₂³×C₄₇	—	2	1	no	—
167	C₂³×C₄₇	—	2	2	no	—
168	C₂³×C₄₇	—	4	1	no	—
169	C₂³×C₄₇	—	4	1	no	—
170	C₂³×C₄₇	—	4	1	no	—
171	C₂³×C₄₇	—	4	1	no	—
172	C₂³×C₄₇	—	4	1	no	—
173	C₂³×C₄₇	—	4	1	no	—
174	C₂³×C₄₇	#124	1	2	yes	—
175	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
176	Q₈×C₄₇	—	2	4	no	—
177	Q₈×C₄₇	—	4	2	no	—
178	Q₈×C₄₇	—	8	4	no	—
179	D₄×C₄₇	—	2	4	no	—
180	D₄×C₄₇	—	4	8	no	—
181	D₄×C₄₇	—	4	2	no	—
182	C₂×C₄×C₄₇	—	2	1	no	—
183	C₂×C₄×C₄₇	—	2	1	no	—
184	C₂×C₄×C₄₇	—	2	1	no	—
185	C₂×C₄×C₄₇	—	2	1	no	—
186	C₂×C₄×C₄₇	—	2	1	no	—
187	C₂×C₄×C₄₇	—	2	1	no	—
188	C₂×C₄×C₄₇	—	2	4	no	—
189	C₂×C₄×C₄₇	—	2	4	no	—
190	C₂×C₄×C₄₇	—	2	2	no	—
191	C₂×C₄×C₄₇	—	2	1	no	—
192	C₂×C₄×C₄₇	—	2	1	no	—
193	C₂×C₄×C₄₇	—	2	1	no	—
194	C₂×C₄×C₄₇	—	2	1	no	—
195	C₂×C₄×C₄₇	—	2	1	no	—
196	C₂×C₄×C₄₇	—	2	1	no	—
197	C₂×C₄×C₄₇	—	4	4	no	—
198	C₂×C₄×C₄₇	—	4	4	no	—
199	C₂×C₄×C₄₇	—	4	8	no	—
200	C₂×C₄×C₄₇	—	4	1	no	—
201	C₂×C₄×C₄₇	—	4	1	no	—
202	C₂×C₄×C₄₇	—	4	2	no	—
203	C₂×C₄×C₄₇	—	4	1	no	—
204	C₂×C₄×C₄₇	—	4	1	no	—
205	C₂×C₄×C₄₇	—	4	2	no	—
206	C₂×C₄×C₄₇	—	4	2	no	—
207	C₂×C₄×C₄₇	—	4	2	no	—
208	C₂×C₄×C₄₇	—	4	1	no	—
209	C₂×C₄×C₄₇	—	4	1	no	—
210	C₂×C₄×C₄₇	—	4	1	no	—
211	C₂×C₄×C₄₇	—	4	1	no	—
212	C₂×C₄×C₄₇	—	4	2	no	—
213	C₂×C₄×C₄₇	—	4	2	no	—
214	C₂×C₄×C₄₇	#124	1	2	yes	—
215	C₂×C₄×C₄₇	AGL(1,ℤ/8)	1	2	yes	—
216	C₂×C₄×C₄₇	#137	1	2	yes	—
217	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
218	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
219	C₂×C₄×C₄₇	C₂×#41	1	2	yes	—
220	C₂×C₄×C₄₇	H(5,𝔽₂)	1	2	yes	—
221	C₈×C₄₇	—	4	2	no	—
222	C₈×C₄₇	—	4	2	no	—
223	#29113	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
224	C₂²×C₄₇	—	2	2	no	—
225	C₂²×C₄₇	—	2	2	no	—
226	C₂²×C₄₇	—	2	2	no	—
227	C₂²×C₄₇	—	4	1	no	—
228	C₂²×C₄₇	—	4	1	no	—
229	C₂²×C₄₇	—	4	1	no	—
230	C₂²×C₄₇	—	4	1	no	—
231	C₂²×C₄₇	—	4	2	no	—
232	C₂²×C₄₇	—	4	2	no	—
233	C₂²×C₄₇	—	4	2	no	—
234	C₂²×C₄₇	—	8	1	no	—
235	C₂²×C₄₇	—	8	1	no	—
236	C₂²×C₄₇	—	8	1	no	—
237	C₂²×C₄₇	—	8	1	no	—
238	C₂²×C₄₇	#525	1	1	yes	characteristic
239	C₂²×C₄₇	C₂×#124	1	1	yes	characteristic
240	C₂²×C₄₇	#534	1	1	yes	characteristic
241	C₂²×C₄₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
242	C₂²×C₄₇	C₂×#137	1	1	yes	characteristic
243	C₂²×C₄₇	#575	1	1	yes	characteristic
244	C₂²×C₄₇	#575	1	1	yes	characteristic
245	C₄×C₄₇	—	2	2	no	—
246	C₄×C₄₇	—	2	2	no	—
247	C₄×C₄₇	—	2	2	no	—
248	C₄×C₄₇	—	4	2	no	—
249	C₄×C₄₇	—	4	1	no	—
250	C₄×C₄₇	—	4	1	no	—
251	C₄×C₄₇	—	8	2	no	—
252	C₄×C₄₇	—	8	1	no	—
253	C₄×C₄₇	—	8	1	no	—
254	C₄×C₄₇	—	8	2	no	—
255	C₄×C₄₇	#551	1	2	yes	—
256	C₄×C₄₇	#551	1	2	yes	—
257	#2857	C₂×C₄₇	1	1	yes	characteristic, complemented
258	#2297	C₂×C₄₇	1	1	yes	characteristic
259	#2072	C₂×C₄₇	1	1	yes	characteristic, complemented
260	#2071	C₂×C₄₇	1	1	yes	characteristic, complemented
261	#2024	C₂×C₄₇	1	1	yes	characteristic, complemented
262	#2023	C₂×C₄₇	1	1	yes	characteristic, complemented
263	#1936	C₂×C₄₇	1	2	yes	complemented
264	#1935	C₂×C₄₇	1	2	yes	complemented
265	#1825	C₂×C₄₇	1	2	yes	complemented
266	#1788	C₂×C₄₇	1	2	yes	—
267	#1749	C₂×C₄₇	1	1	yes	characteristic, complemented
268	C₂×C₄₇	—	4	2	no	—
269	C₂×C₄₇	—	8	2	no	—
270	C₂×C₄₇	#2561	1	1	yes	characteristic
271	C₂×C₄₇	#3115	1	1	yes	characteristic
272	C₂×C₄₇	#3116	1	1	yes	characteristic
273	C₂×C₄₇	#3135	1	1	yes	characteristic
274	C₂×C₄₇	#3141	1	1	yes	characteristic
275	C₂×C₄₇	#3194	1	1	yes	characteristic
276	C₂×C₄₇	#3196	1	1	yes	characteristic
277	C₂²×#41	C₂²×C₄₇	1	1	yes	characteristic
278	C₂×C₄⋊Q₈	C₂²×C₄₇	1	1	yes	characteristic
279	C₂×C₂²⋊Q₈	—	2	1	no	—
280	C₂×#117	C₂²×C₄₇	1	1	yes	characteristic
281	C₂²×C₄²	C₂²×C₄₇	1	1	yes	characteristic
282	C₂×#103	C₂²×C₄₇	1	2	yes	—
283	C₂×#103	C₂²×C₄₇	1	2	yes	—
284	C₂×#102	C₂²×C₄₇	1	2	yes	—
285	C₂×#102	C₂²×C₄₇	1	2	yes	—
286	C₂×C₂²⋊C₈	C₂²×C₄₇	1	2	yes	—
287	C₂×#97	C₂²×C₄₇	1	2	yes	—
288	#391	—	2	1	no	—
289	#391	C₂²×C₄₇	1	1	yes	characteristic
290	#391	C₂²×C₄₇	1	1	yes	characteristic
291	#390	C₂²×C₄₇	1	1	yes	characteristic
292	#390	C₂²×C₄₇	1	1	yes	characteristic
293	#389	—	2	1	no	—
294	#389	C₂²×C₄₇	1	2	yes	—
295	#386	—	2	1	no	—
296	#386	—	2	1	no	—
297	#384	C₂²×C₄₇	1	1	yes	characteristic
298	#380	—	2	1	no	—
299	#380	C₂²×C₄₇	1	2	yes	—
300	C₄×C₂²⋊C₄	—	2	1	no	—
301	C₄×C₂²⋊C₄	—	2	1	no	—
302	#340	C₂²×C₄₇	1	2	yes	—
303	#340	C₂²×C₄₇	1	2	yes	—
304	#340	C₂²×C₄₇	1	2	yes	—
305	#340	C₂²×C₄₇	1	2	yes	—
306	#336	C₂²×C₄₇	1	1	yes	characteristic
307	#336	C₂²×C₄₇	1	1	yes	characteristic
308	C₄₇	#29113	1	1	yes	characteristic, direct product factor, Sylow
309	C₂×#41	—	2	2	no	—
310	C₂×#41	—	2	2	no	—
311	C₂×#41	—	2	4	no	—
312	C₂×#41	—	4	2	no	—
313	C₂²×Q₈	—	2	1	no	—
314	C₂²×Q₈	C₂³×C₄₇	1	1	yes	characteristic
315	C₂²×D₄	—	2	1	no	—
316	C₂²×D₄	C₂³×C₄₇	1	1	yes	characteristic
317	C₂³×C₄	—	2	1	no	—
318	C₂³×C₄	D₄×C₄₇	1	1	yes	characteristic
319	C₂³×C₄	D₄×C₄₇	1	1	yes	characteristic
320	C₂³×C₄	C₂³×C₄₇	1	1	yes	characteristic
321	C₂²×C₈	C₂³×C₄₇	1	2	yes	—
322	C₂²×C₈	C₂³×C₄₇	1	2	yes	—
323	C₄⋊Q₈	—	4	2	no	—
324	C₂²⋊Q₈	—	4	4	no	—
325	#117	—	2	4	no	—
326	C₂×C₄⋊C₄	—	2	1	no	—
327	C₂×C₄⋊C₄	—	2	2	no	—
328	C₂×C₄⋊C₄	—	2	1	no	—
329	C₂×C₄⋊C₄	—	2	1	no	—
330	C₂×C₄⋊C₄	C₂³×C₄₇	1	1	yes	characteristic
331	C₂×C₄⋊C₄	C₂³×C₄₇	1	1	yes	characteristic
332	C₂×C₄⋊C₄	C₂³×C₄₇	1	2	yes	—
333	C₂×C₄⋊C₄	C₂³×C₄₇	1	2	yes	—
334	C₂×C₂²⋊C₄	—	2	1	no	—
335	C₂×C₂²⋊C₄	—	2	2	no	—
336	C₂×C₂²⋊C₄	—	2	1	no	—
337	C₂×C₂²⋊C₄	—	2	1	no	—
338	C₂×C₂²⋊C₄	—	2	1	no	—
339	C₂×C₂²⋊C₄	—	2	1	no	—
340	C₂×C₄²	—	2	1	no	—
341	C₂×C₄²	—	4	2	no	—
342	C₂×C₄²	D₄×C₄₇	1	1	yes	characteristic
343	C₂×C₄²	D₄×C₄₇	1	1	yes	characteristic
344	C₂×C₄²	C₂³×C₄₇	1	1	yes	characteristic
345	C₂×C₄²	C₂³×C₄₇	1	1	yes	characteristic
346	#103	—	2	4	no	—
347	#103	—	4	2	no	—
348	#102	—	2	4	no	—
349	#102	—	4	2	no	—
350	C₂²⋊C₈	—	2	4	no	—
351	#97	—	4	2	no	—
352	#95	—	2	1	no	—
353	#95	—	2	1	no	—
354	#95	—	2	1	no	—
355	#95	—	2	1	no	—
356	#95	—	2	2	no	—
357	#95	—	2	2	no	—
358	C₂⁴	—	2	1	no	—
359	C₂⁴	C₂×D₄×C₄₇	1	1	yes	characteristic
360	#41	—	4	8	no	—
361	#41	—	4	8	no	—
362	C₂×Q₈	—	2	1	no	—
363	C₂×Q₈	—	2	2	no	—
364	C₂×Q₈	—	2	2	no	—
365	C₂×Q₈	—	4	2	no	—
366	C₂×Q₈	—	4	2	no	—
367	C₂×Q₈	—	4	2	no	—
368	C₂×Q₈	#41×C₄₇	1	2	yes	—
369	C₂×D₄	—	2	4	no	—
370	C₂×D₄	—	2	2	no	—
371	C₂×D₄	—	2	1	no	—
372	C₂×D₄	—	2	2	no	—
373	C₂×D₄	—	4	2	no	—
374	C₂×D₄	—	4	2	no	—
375	C₂×D₄	#41×C₄₇	1	2	yes	—
376	C₂²×C₄	—	2	1	no	—
377	C₂²×C₄	—	2	1	no	—
378	C₂²×C₄	—	2	2	no	—
379	C₂²×C₄	—	2	4	no	—
380	C₂²×C₄	—	2	1	no	—
381	C₂²×C₄	—	2	2	no	—
382	C₂²×C₄	—	2	2	no	—
383	C₂²×C₄	—	2	1	no	—
384	C₂²×C₄	—	2	1	no	—
385	C₂²×C₄	—	2	2	no	—
386	C₂²×C₄	—	2	2	no	—
387	C₂²×C₄	—	4	1	no	—
388	C₂²×C₄	—	4	1	no	—
389	C₂²×C₄	—	4	1	no	—
390	C₂²×C₄	—	4	1	no	—
391	C₂²×C₄	—	4	2	no	—
392	C₂²×C₄	—	4	2	no	—
393	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
394	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
395	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
396	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
397	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
398	C₂²×C₄	#41×C₄₇	1	4	yes	—
399	C₂²×C₄	C₂⁴×C₄₇	1	1	yes	characteristic
400	C₂×C₈	—	2	2	no	—
401	C₂×C₈	—	2	2	no	—
402	C₂×C₈	—	2	2	no	—
403	C₂×C₈	—	2	2	no	—
404	C₂×C₈	—	2	2	no	—
405	C₂×C₈	—	2	2	no	—
406	C₄⋊C₄	—	2	2	no	—
407	C₄⋊C₄	—	2	2	no	—
408	C₄⋊C₄	—	2	2	no	—
409	C₄⋊C₄	—	2	2	no	—
410	C₄⋊C₄	—	2	2	no	—
411	C₄⋊C₄	—	2	2	no	—
412	C₄⋊C₄	—	4	2	no	—
413	C₄⋊C₄	—	4	4	no	—
414	C₄⋊C₄	—	4	2	no	—
415	C₄⋊C₄	—	4	2	no	—
416	C₂²⋊C₄	—	4	2	no	—
417	C₂²⋊C₄	—	4	2	no	—
418	C₂²⋊C₄	—	4	4	no	—
419	C₂²⋊C₄	—	4	2	no	—
420	C₂²⋊C₄	—	4	2	no	—
421	C₂²⋊C₄	—	4	2	no	—
422	C₄²	—	2	2	no	—
423	C₄²	—	2	2	no	—
424	C₄²	—	4	1	no	—
425	C₄²	—	4	1	no	—
426	C₄²	—	4	2	no	—
427	C₂³	—	2	1	no	—
428	C₂³	—	2	1	no	—
429	C₂³	—	2	1	no	—
430	C₂³	—	2	1	no	—
431	C₂³	—	2	1	no	—
432	C₂³	—	2	1	no	—
433	C₂³	—	2	2	no	—
434	C₂³	—	4	1	no	—
435	C₂³	—	4	1	no	—
436	C₂³	—	4	1	no	—
437	C₂³	—	4	1	no	—
438	C₂³	—	4	1	no	—
439	C₂³	—	4	1	no	—
440	C₂³	#124×C₄₇	1	2	yes	—
441	C₂³	C₂²×D₄×C₄₇	1	1	yes	characteristic
442	Q₈	—	2	4	no	—
443	Q₈	—	4	2	no	—
444	Q₈	—	8	4	no	—
445	D₄	—	2	4	no	—
446	D₄	—	4	8	no	—
447	D₄	—	4	2	no	—
448	C₂×C₄	—	2	1	no	—
449	C₂×C₄	—	2	1	no	—
450	C₂×C₄	—	2	1	no	—
451	C₂×C₄	—	2	1	no	—
452	C₂×C₄	—	2	1	no	—
453	C₂×C₄	—	2	1	no	—
454	C₂×C₄	—	2	4	no	—
455	C₂×C₄	—	2	4	no	—
456	C₂×C₄	—	2	2	no	—
457	C₂×C₄	—	2	1	no	—
458	C₂×C₄	—	2	1	no	—
459	C₂×C₄	—	2	1	no	—
460	C₂×C₄	—	2	1	no	—
461	C₂×C₄	—	2	1	no	—
462	C₂×C₄	—	2	1	no	—
463	C₂×C₄	—	4	4	no	—
464	C₂×C₄	—	4	4	no	—
465	C₂×C₄	—	4	8	no	—
466	C₂×C₄	—	4	1	no	—
467	C₂×C₄	—	4	1	no	—
468	C₂×C₄	—	4	2	no	—
469	C₂×C₄	—	4	1	no	—
470	C₂×C₄	—	4	1	no	—
471	C₂×C₄	—	4	2	no	—
472	C₂×C₄	—	4	2	no	—
473	C₂×C₄	—	4	2	no	—
474	C₂×C₄	—	4	1	no	—
475	C₂×C₄	—	4	1	no	—
476	C₂×C₄	—	4	1	no	—
477	C₂×C₄	—	4	1	no	—
478	C₂×C₄	—	4	2	no	—
479	C₂×C₄	—	4	2	no	—
480	C₂×C₄	#124×C₄₇	1	2	yes	—
481	C₂×C₄	AGL(1,ℤ/8)×C₄₇	1	2	yes	—
482	C₂×C₄	#137×C₄₇	1	2	yes	—
483	C₂×C₄	C₂×#41×C₄₇	1	1	yes	characteristic
484	C₂×C₄	C₂×#41×C₄₇	1	1	yes	characteristic
485	C₂×C₄	C₂×#41×C₄₇	1	2	yes	—
486	C₂×C₄	H(5,𝔽₂)×C₄₇	1	2	yes	—
487	C₈	—	4	2	no	—
488	C₈	—	4	2	no	—
489	C₂²	—	2	2	no	—
490	C₂²	—	2	2	no	—
491	C₂²	—	2	2	no	—
492	C₂²	—	4	1	no	—
493	C₂²	—	4	1	no	—
494	C₂²	—	4	1	no	—
495	C₂²	—	4	1	no	—
496	C₂²	—	4	2	no	—
497	C₂²	—	4	2	no	—
498	C₂²	—	4	2	no	—
499	C₂²	—	8	1	no	—
500	C₂²	—	8	1	no	—
501	C₂²	—	8	1	no	—
502	C₂²	—	8	1	no	—
503	C₂²	C₄₇×#525	1	1	yes	characteristic
504	C₂²	C₂×#124×C₄₇	1	1	yes	characteristic
505	C₂²	C₄₇×#534	1	1	yes	characteristic
506	C₂²	C₂×AGL(1,ℤ/8)×C₄₇	1	1	yes	characteristic
507	C₂²	C₂×#137×C₄₇	1	1	yes	characteristic
508	C₂²	C₄₇×#575	1	1	yes	characteristic
509	C₂²	C₄₇×#575	1	1	yes	characteristic
510	C₄	—	2	2	no	—
511	C₄	—	2	2	no	—
512	C₄	—	2	2	no	—
513	C₄	—	4	2	no	—
514	C₄	—	4	1	no	—
515	C₄	—	4	1	no	—
516	C₄	—	8	2	no	—
517	C₄	—	8	1	no	—
518	C₄	—	8	1	no	—
519	C₄	—	8	2	no	—
520	C₄	C₄₇×#551	1	2	yes	—
521	C₄	C₄₇×#551	1	2	yes	—
522	C₂	—	4	2	no	—
523	C₂	—	8	2	no	—
524	C₂	C₄₇×#2561	1	1	yes	characteristic
525	C₂	C₄₇×#3115	1	1	yes	characteristic
526	C₂	C₄₇×#3116	1	1	yes	characteristic
527	C₂	C₄₇×#3135	1	1	yes	characteristic
528	C₂	C₄₇×#3141	1	1	yes	characteristic
529	C₂	C₄₇×#3194	1	1	yes	characteristic
530	C₂	C₄₇×#3196	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. C₄₇×#2857	C₂	semidirect
3. C₄₇×#2072	C₂	semidirect
4. C₄₇×#2071	C₂	semidirect
5. C₄₇×#2024	C₂	semidirect
6. C₄₇×#2023	C₂	semidirect
7. C₄₇×#1936	C₂	semidirect
8. C₄₇×#1935	C₂	semidirect
9. C₄₇×#1825	C₂	semidirect
11. C₄₇×#1749	C₂	semidirect
223. #29113	C₄₇	direct (N × H)
257. #2857	C₂×C₄₇	semidirect
259. #2072	C₂×C₄₇	semidirect
260. #2071	C₂×C₄₇	semidirect
261. #2024	C₂×C₄₇	semidirect
262. #2023	C₂×C₄₇	semidirect
263. #1936	C₂×C₄₇	semidirect
264. #1935	C₂×C₄₇	semidirect
265. #1825	C₂×C₄₇	semidirect
267. #1749	C₂×C₄₇	semidirect
308. C₄₇	#29113	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×#2857	2
C₄₇×#2297	2
C₄₇×#2072	2
C₄₇×#2071	2
C₄₇×#2024	2
C₄₇×#2023	2
C₄₇×#1936	2
C₄₇×#1935	2
C₄₇×#1825	2
C₄₇×#1788	2
C₄₇×#1749	2
#29113	47

Subgroups — C47×#29113 #26068811

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₇×#29113 #26068811