Subgroups — C₄₇×#10928 #26050626

Order 12032.

1078 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#103×C₄₇	C₂	1	2	yes	maximal
2	C₂²×#97×C₄₇	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄₇×#391	C₂	1	1	yes	maximal, characteristic
4	C₂×C₄₇×#340	C₂	1	2	yes	maximal
5	C₄₇×C₄⋊#95	C₂	1	1	yes	maximal, characteristic
6	C₂³×Q₈×C₄₇	C₂²	1	1	yes	characteristic
7	C₂³×C₈×C₄₇	C₂²	1	2	yes	—
8	C₂²×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
9	C₂²×C₄⋊C₄×C₄₇	C₂²	1	2	yes	—
10	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
11	C₂×#103×C₄₇	—	2	4	no	—
12	C₂×#103×C₄₇	—	2	4	no	—
13	C₂×#103×C₄₇	C₄	1	8	yes	complemented
14	C₂×#97×C₄₇	—	2	4	no	—
15	C₂×#97×C₄₇	—	2	2	no	—
16	C₄₇×#391	—	2	2	no	—
17	C₄₇×#391	C₄	1	4	yes	complemented
18	C₂×#95×C₄₇	—	2	2	no	—
19	C₂×#95×C₄₇	—	2	2	no	—
20	C₄₇×#340	—	2	4	no	—
21	C₂²×Q₈×C₄₇	—	2	1	no	—
22	C₂²×Q₈×C₄₇	—	2	2	no	—
23	C₂²×Q₈×C₄₇	—	2	2	no	—
24	C₂²×Q₈×C₄₇	—	2	2	no	—
25	C₂²×Q₈×C₄₇	—	2	2	no	—
26	C₂²×Q₈×C₄₇	—	2	2	no	—
27	C₂²×Q₈×C₄₇	C₂×C₄	1	2	yes	—
28	C₂²×Q₈×C₄₇	C₂×C₄	1	4	yes	—
29	C₂³×C₄×C₄₇	—	2	1	no	—
30	C₂³×C₄×C₄₇	—	2	1	no	—
31	C₂³×C₄×C₄₇	—	2	2	no	—
32	C₂³×C₄×C₄₇	D₄	1	2	yes	—
33	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
34	C₂²×C₈×C₄₇	—	2	2	no	—
35	C₂²×C₈×C₄₇	—	2	2	no	—
36	C₂²×C₈×C₄₇	—	2	2	no	—
37	C₂²×C₈×C₄₇	—	2	2	no	—
38	C₂²×C₈×C₄₇	C₂×C₄	1	4	yes	—
39	C₂²×C₈×C₄₇	D₄	1	4	yes	—
40	C₂²×C₈×C₄₇	D₄	1	4	yes	—
41	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
42	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
43	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
44	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
45	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
46	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
47	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
48	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
49	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
50	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	4	yes	—
51	C₂×C₄²×C₄₇	—	2	2	no	—
52	C₂×C₄²×C₄₇	—	2	2	no	—
53	C₂×C₄²×C₄₇	C₂×C₄	1	2	yes	—
54	C₂×C₄²×C₄₇	D₄	1	2	yes	—
55	#103×C₄₇	—	2	16	no	—
56	#97×C₄₇	—	2	8	no	—
57	#95×C₄₇	—	2	8	no	—
58	#95×C₄₇	—	4	4	no	—
59	C₂⁴×C₄₇	C₂×D₄	1	1	yes	characteristic
60	C₂×Q₈×C₄₇	—	2	2	no	—
61	C₂×Q₈×C₄₇	—	2	4	no	—
62	C₂×Q₈×C₄₇	—	2	4	no	—
63	C₂×Q₈×C₄₇	—	2	4	no	—
64	C₂×Q₈×C₄₇	—	2	4	no	—
65	C₂×Q₈×C₄₇	—	2	4	no	—
66	C₂×Q₈×C₄₇	—	2	4	no	—
67	C₂×Q₈×C₄₇	—	2	4	no	—
68	C₂×Q₈×C₄₇	—	4	1	no	—
69	C₂×Q₈×C₄₇	—	4	2	no	—
70	C₂×Q₈×C₄₇	—	4	2	no	—
71	C₂×Q₈×C₄₇	—	4	1	no	—
72	C₂×Q₈×C₄₇	—	4	2	no	—
73	C₂×Q₈×C₄₇	—	4	2	no	—
74	C₂×Q₈×C₄₇	—	4	2	no	—
75	C₂×Q₈×C₄₇	C₄²	1	4	yes	—
76	C₂²×C₄×C₄₇	—	2	2	no	—
77	C₂²×C₄×C₄₇	—	2	4	no	—
78	C₂²×C₄×C₄₇	—	2	4	no	—
79	C₂²×C₄×C₄₇	—	2	2	no	—
80	C₂²×C₄×C₄₇	—	2	2	no	—
81	C₂²×C₄×C₄₇	—	2	4	no	—
82	C₂²×C₄×C₄₇	—	2	2	no	—
83	C₂²×C₄×C₄₇	—	2	4	no	—
84	C₂²×C₄×C₄₇	—	4	2	no	—
85	C₂²×C₄×C₄₇	—	4	1	no	—
86	C₂²×C₄×C₄₇	—	4	1	no	—
87	C₂²×C₄×C₄₇	—	4	2	no	—
88	C₂²×C₄×C₄₇	—	4	1	no	—
89	C₂²×C₄×C₄₇	—	4	1	no	—
90	C₂²×C₄×C₄₇	—	4	2	no	—
91	C₂²×C₄×C₄₇	—	4	2	no	—
92	C₂²×C₄×C₄₇	—	4	4	no	—
93	C₂²×C₄×C₄₇	—	4	2	no	—
94	C₂²×C₄×C₄₇	—	4	4	no	—
95	C₂²×C₄×C₄₇	C₂²⋊C₄	1	4	yes	—
96	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
97	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
98	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
99	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
100	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
101	C₂²×C₄×C₄₇	#41	1	2	yes	—
102	C₂²×C₄×C₄₇	#41	1	2	yes	—
103	C₂²×C₄×C₄₇	#41	1	2	yes	—
104	C₂×C₈×C₄₇	—	2	4	no	—
105	C₂×C₈×C₄₇	—	2	4	no	—
106	C₂×C₈×C₄₇	—	2	4	no	—
107	C₂×C₈×C₄₇	—	2	4	no	—
108	C₂×C₈×C₄₇	—	2	4	no	—
109	C₂×C₈×C₄₇	—	2	4	no	—
110	C₂×C₈×C₄₇	C₂²⋊C₄	1	8	yes	—
111	C₄⋊C₄×C₄₇	—	2	4	no	—
112	C₄⋊C₄×C₄₇	—	2	4	no	—
113	C₄⋊C₄×C₄₇	—	2	4	no	—
114	C₄⋊C₄×C₄₇	—	4	2	no	—
115	C₄⋊C₄×C₄₇	—	4	2	no	—
116	C₄⋊C₄×C₄₇	—	4	2	no	—
117	C₄²×C₄₇	—	2	4	no	—
118	C₄²×C₄₇	—	2	2	no	—
119	C₄²×C₄₇	—	2	2	no	—
120	C₂³×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
121	C₂³×C₄₇	C₄×D₄	1	2	yes	—
122	C₂³×C₄₇	#121	1	2	yes	—
123	C₂³×C₄₇	#124	1	1	yes	characteristic
124	C₂³×C₄₇	#127	1	1	yes	characteristic
125	C₂³×C₄₇	AGL(1,ℤ/8)	1	2	yes	—
126	C₂³×C₄₇	#137	1	2	yes	—
127	C₂³×C₄₇	#137	1	4	yes	—
128	Q₈×C₄₇	—	2	8	no	—
129	Q₈×C₄₇	—	4	4	no	—
130	Q₈×C₄₇	—	4	4	no	—
131	Q₈×C₄₇	—	4	4	no	—
132	C₂×C₄×C₄₇	—	2	4	no	—
133	C₂×C₄×C₄₇	—	2	4	no	—
134	C₂×C₄×C₄₇	—	2	4	no	—
135	C₂×C₄×C₄₇	—	2	4	no	—
136	C₂×C₄×C₄₇	—	4	2	no	—
137	C₂×C₄×C₄₇	—	4	4	no	—
138	C₂×C₄×C₄₇	—	4	2	no	—
139	C₂×C₄×C₄₇	—	4	4	no	—
140	C₂×C₄×C₄₇	—	4	4	no	—
141	C₂×C₄×C₄₇	—	4	4	no	—
142	C₂×C₄×C₄₇	—	4	2	no	—
143	C₂×C₄×C₄₇	—	4	4	no	—
144	C₂×C₄×C₄₇	—	4	4	no	—
145	C₂×C₄×C₄₇	—	4	8	no	—
146	C₂×C₄×C₄₇	—	8	4	no	—
147	C₂×C₄×C₄₇	—	8	2	no	—
148	C₂×C₄×C₄₇	—	8	1	no	—
149	C₂×C₄×C₄₇	—	8	2	no	—
150	C₂×C₄×C₄₇	—	8	1	no	—
151	C₂×C₄×C₄₇	—	8	2	no	—
152	C₂×C₄×C₄₇	C₂×C₄²	1	1	yes	characteristic
153	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
154	C₂×C₄×C₄₇	#117	1	2	yes	—
155	C₂×C₄×C₄₇	#117	1	1	yes	characteristic
156	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
157	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
158	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
159	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
160	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
161	C₂×C₄×C₄₇	#120	1	1	yes	characteristic
162	C₂×C₄×C₄₇	#121	1	2	yes	—
163	C₂×C₄×C₄₇	#121	1	2	yes	—
164	C₂×C₄×C₄₇	#123	1	2	yes	—
165	C₂×C₄×C₄₇	#123	1	1	yes	characteristic
166	C₂×C₄×C₄₇	#124	1	2	yes	—
167	C₂×C₄×C₄₇	#126	1	2	yes	—
168	C₈×C₄₇	—	2	8	no	—
169	#10928	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
170	C₂²×C₄₇	C₄×C₂²⋊C₄	1	1	yes	characteristic
171	C₂²×C₄₇	#386	1	1	yes	characteristic
172	C₂²×C₄₇	#388	1	2	yes	—
173	C₂²×C₄₇	#390	1	1	yes	characteristic
174	C₂²×C₄₇	#390	1	2	yes	—
175	C₂²×C₄₇	#417	1	2	yes	—
176	C₂²×C₄₇	#419	1	2	yes	—
177	C₂²×C₄₇	#440	1	4	yes	—
178	C₂²×C₄₇	#441	1	4	yes	—
179	C₂²×C₄₇	#468	1	4	yes	—
180	C₂²×C₄₇	#470	1	4	yes	—
181	C₂²×C₄₇	#489	1	2	yes	—
182	C₂²×C₄₇	#491	1	2	yes	—
183	C₂²×C₄₇	#496	1	1	yes	characteristic
184	C₂²×C₄₇	#497	1	1	yes	characteristic
185	C₂²×C₄₇	#497	1	2	yes	—
186	C₄×C₄₇	—	4	4	no	—
187	C₄×C₄₇	—	4	4	no	—
188	C₄×C₄₇	—	8	2	no	—
189	C₄×C₄₇	—	8	4	no	—
190	C₄×C₄₇	C₄×C₂²⋊C₄	1	2	yes	—
191	C₄×C₄₇	#386	1	2	yes	—
192	C₄×C₄₇	#388	1	2	yes	—
193	C₄×C₄₇	#388	1	2	yes	—
194	C₂²×#103	C₂×C₄₇	1	2	yes	—
195	C₂²×#97	C₂×C₄₇	1	1	yes	characteristic
196	C₂×#391	C₂×C₄₇	1	1	yes	characteristic
197	C₂×#340	C₂×C₄₇	1	2	yes	—
198	C₄⋊#95	C₂×C₄₇	1	1	yes	characteristic
199	C₂×C₄₇	#1437	1	1	yes	characteristic
200	C₂×C₄₇	#1763	1	2	yes	—
201	C₂×C₄₇	#1894	1	2	yes	—
202	C₂×C₄₇	#1935	1	4	yes	—
203	C₂×C₄₇	#1959	1	1	yes	characteristic
204	C₂×C₄₇	#1960	1	1	yes	characteristic
205	C₂×C₄₇	#1971	1	2	yes	—
206	C₂×C₄₇	#1973	1	2	yes	—
207	C₂³×Q₈	C₂²×C₄₇	1	1	yes	characteristic
208	C₂³×C₈	C₂²×C₄₇	1	2	yes	—
209	C₂²×C₄⋊C₄	C₂²×C₄₇	1	2	yes	—
210	C₂²×C₄⋊C₄	C₂²×C₄₇	1	1	yes	characteristic
211	C₂²×C₄²	C₂²×C₄₇	1	1	yes	characteristic
212	C₂×#103	—	2	4	no	—
213	C₂×#103	—	2	4	no	—
214	C₂×#103	C₄×C₄₇	1	8	yes	complemented
215	C₂×#97	—	2	4	no	—
216	C₂×#97	—	2	2	no	—
217	#391	—	2	2	no	—
218	#391	C₄×C₄₇	1	4	yes	complemented
219	C₂×#95	—	2	2	no	—
220	C₂×#95	—	2	2	no	—
221	#340	—	2	4	no	—
222	C₄₇	#10928	1	1	yes	characteristic, direct product factor, Sylow
223	C₂²×Q₈	—	2	1	no	—
224	C₂²×Q₈	—	2	2	no	—
225	C₂²×Q₈	—	2	2	no	—
226	C₂²×Q₈	—	2	2	no	—
227	C₂²×Q₈	—	2	2	no	—
228	C₂²×Q₈	—	2	2	no	—
229	C₂²×Q₈	C₂×C₄×C₄₇	1	2	yes	—
230	C₂²×Q₈	C₂×C₄×C₄₇	1	4	yes	—
231	C₂³×C₄	—	2	1	no	—
232	C₂³×C₄	—	2	1	no	—
233	C₂³×C₄	—	2	2	no	—
234	C₂³×C₄	D₄×C₄₇	1	2	yes	—
235	C₂³×C₄	C₂³×C₄₇	1	1	yes	characteristic
236	C₂²×C₈	—	2	2	no	—
237	C₂²×C₈	—	2	2	no	—
238	C₂²×C₈	—	2	2	no	—
239	C₂²×C₈	—	2	2	no	—
240	C₂²×C₈	C₂×C₄×C₄₇	1	4	yes	—
241	C₂²×C₈	D₄×C₄₇	1	4	yes	—
242	C₂²×C₈	D₄×C₄₇	1	4	yes	—
243	C₂×C₄⋊C₄	—	2	2	no	—
244	C₂×C₄⋊C₄	—	2	2	no	—
245	C₂×C₄⋊C₄	—	2	2	no	—
246	C₂×C₄⋊C₄	—	2	2	no	—
247	C₂×C₄⋊C₄	—	2	2	no	—
248	C₂×C₄⋊C₄	—	2	2	no	—
249	C₂×C₄⋊C₄	—	2	1	no	—
250	C₂×C₄⋊C₄	—	2	2	no	—
251	C₂×C₄⋊C₄	C₂×C₄×C₄₇	1	2	yes	—
252	C₂×C₄⋊C₄	C₂×C₄×C₄₇	1	4	yes	—
253	C₂×C₄²	—	2	2	no	—
254	C₂×C₄²	—	2	2	no	—
255	C₂×C₄²	C₂×C₄×C₄₇	1	2	yes	—
256	C₂×C₄²	D₄×C₄₇	1	2	yes	—
257	#103	—	2	16	no	—
258	#97	—	2	8	no	—
259	#95	—	2	8	no	—
260	#95	—	4	4	no	—
261	C₂⁴	C₂×D₄×C₄₇	1	1	yes	characteristic
262	C₂×Q₈	—	2	2	no	—
263	C₂×Q₈	—	2	4	no	—
264	C₂×Q₈	—	2	4	no	—
265	C₂×Q₈	—	2	4	no	—
266	C₂×Q₈	—	2	4	no	—
267	C₂×Q₈	—	2	4	no	—
268	C₂×Q₈	—	2	4	no	—
269	C₂×Q₈	—	2	4	no	—
270	C₂×Q₈	—	4	1	no	—
271	C₂×Q₈	—	4	2	no	—
272	C₂×Q₈	—	4	2	no	—
273	C₂×Q₈	—	4	1	no	—
274	C₂×Q₈	—	4	2	no	—
275	C₂×Q₈	—	4	2	no	—
276	C₂×Q₈	—	4	2	no	—
277	C₂×Q₈	C₄²×C₄₇	1	4	yes	—
278	C₂²×C₄	—	2	2	no	—
279	C₂²×C₄	—	2	4	no	—
280	C₂²×C₄	—	2	4	no	—
281	C₂²×C₄	—	2	2	no	—
282	C₂²×C₄	—	2	2	no	—
283	C₂²×C₄	—	2	4	no	—
284	C₂²×C₄	—	2	2	no	—
285	C₂²×C₄	—	2	4	no	—
286	C₂²×C₄	—	4	2	no	—
287	C₂²×C₄	—	4	1	no	—
288	C₂²×C₄	—	4	1	no	—
289	C₂²×C₄	—	4	2	no	—
290	C₂²×C₄	—	4	1	no	—
291	C₂²×C₄	—	4	1	no	—
292	C₂²×C₄	—	4	2	no	—
293	C₂²×C₄	—	4	4	no	—
294	C₂²×C₄	—	4	2	no	—
295	C₂²×C₄	—	4	2	no	—
296	C₂²×C₄	—	4	4	no	—
297	C₂²×C₄	C₂²⋊C₄×C₄₇	1	4	yes	—
298	C₂²×C₄	C₂²×C₄×C₄₇	1	2	yes	—
299	C₂²×C₄	C₂²×C₄×C₄₇	1	1	yes	characteristic
300	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
301	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
302	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
303	C₂²×C₄	#41×C₄₇	1	2	yes	—
304	C₂²×C₄	#41×C₄₇	1	2	yes	—
305	C₂²×C₄	#41×C₄₇	1	2	yes	—
306	C₂×C₈	—	2	4	no	—
307	C₂×C₈	—	2	4	no	—
308	C₂×C₈	—	2	4	no	—
309	C₂×C₈	—	2	4	no	—
310	C₂×C₈	—	2	4	no	—
311	C₂×C₈	—	2	4	no	—
312	C₂×C₈	C₂²⋊C₄×C₄₇	1	8	yes	—
313	C₄⋊C₄	—	2	4	no	—
314	C₄⋊C₄	—	2	4	no	—
315	C₄⋊C₄	—	2	4	no	—
316	C₄⋊C₄	—	4	2	no	—
317	C₄⋊C₄	—	4	2	no	—
318	C₄⋊C₄	—	4	2	no	—
319	C₄²	—	2	4	no	—
320	C₄²	—	2	2	no	—
321	C₄²	—	2	2	no	—
322	C₂³	C₂×C₂²⋊C₄×C₄₇	1	1	yes	characteristic
323	C₂³	C₄×D₄×C₄₇	1	2	yes	—
324	C₂³	#121×C₄₇	1	2	yes	—
325	C₂³	#124×C₄₇	1	1	yes	characteristic
326	C₂³	#127×C₄₇	1	1	yes	characteristic
327	C₂³	AGL(1,ℤ/8)×C₄₇	1	2	yes	—
328	C₂³	#137×C₄₇	1	4	yes	—
329	C₂³	#137×C₄₇	1	2	yes	—
330	Q₈	—	2	8	no	—
331	Q₈	—	4	4	no	—
332	Q₈	—	4	4	no	—
333	Q₈	—	4	4	no	—
334	C₂×C₄	—	2	4	no	—
335	C₂×C₄	—	2	4	no	—
336	C₂×C₄	—	2	4	no	—
337	C₂×C₄	—	2	4	no	—
338	C₂×C₄	—	4	4	no	—
339	C₂×C₄	—	4	4	no	—
340	C₂×C₄	—	4	2	no	—
341	C₂×C₄	—	4	4	no	—
342	C₂×C₄	—	4	2	no	—
343	C₂×C₄	—	4	4	no	—
344	C₂×C₄	—	4	2	no	—
345	C₂×C₄	—	4	4	no	—
346	C₂×C₄	—	4	4	no	—
347	C₂×C₄	—	4	8	no	—
348	C₂×C₄	—	8	4	no	—
349	C₂×C₄	—	8	2	no	—
350	C₂×C₄	—	8	1	no	—
351	C₂×C₄	—	8	2	no	—
352	C₂×C₄	—	8	1	no	—
353	C₂×C₄	—	8	2	no	—
354	C₂×C₄	C₂×C₄²×C₄₇	1	1	yes	characteristic
355	C₂×C₄	C₂×C₂²⋊C₄×C₄₇	1	2	yes	—
356	C₂×C₄	#117×C₄₇	1	2	yes	—
357	C₂×C₄	#117×C₄₇	1	1	yes	characteristic
358	C₂×C₄	C₄×D₄×C₄₇	1	2	yes	—
359	C₂×C₄	C₄×D₄×C₄₇	1	2	yes	—
360	C₂×C₄	C₄×D₄×C₄₇	1	2	yes	—
361	C₂×C₄	C₄×D₄×C₄₇	1	2	yes	—
362	C₂×C₄	C₄×D₄×C₄₇	1	2	yes	—
363	C₂×C₄	#120×C₄₇	1	1	yes	characteristic
364	C₂×C₄	#121×C₄₇	1	2	yes	—
365	C₂×C₄	#121×C₄₇	1	2	yes	—
366	C₂×C₄	#123×C₄₇	1	2	yes	—
367	C₂×C₄	#123×C₄₇	1	1	yes	characteristic
368	C₂×C₄	#124×C₄₇	1	2	yes	—
369	C₂×C₄	#126×C₄₇	1	2	yes	—
370	C₈	—	2	8	no	—
371	C₂²	C₄×C₂²⋊C₄×C₄₇	1	1	yes	characteristic
372	C₂²	C₄₇×#386	1	1	yes	characteristic
373	C₂²	C₄₇×#388	1	2	yes	—
374	C₂²	C₄₇×#390	1	1	yes	characteristic
375	C₂²	C₄₇×#390	1	2	yes	—
376	C₂²	C₄₇×#417	1	2	yes	—
377	C₂²	C₄₇×#419	1	2	yes	—
378	C₂²	C₄₇×#440	1	4	yes	—
379	C₂²	C₄₇×#441	1	4	yes	—
380	C₂²	C₄₇×#468	1	4	yes	—
381	C₂²	C₄₇×#470	1	4	yes	—
382	C₂²	C₄₇×#489	1	2	yes	—
383	C₂²	C₄₇×#491	1	2	yes	—
384	C₂²	C₄₇×#496	1	1	yes	characteristic
385	C₂²	C₄₇×#497	1	1	yes	characteristic
386	C₂²	C₄₇×#497	1	2	yes	—
387	C₄	—	4	4	no	—
388	C₄	—	4	4	no	—
389	C₄	—	8	2	no	—
390	C₄	—	8	4	no	—
391	C₄	C₄×C₂²⋊C₄×C₄₇	1	2	yes	—
392	C₄	C₄₇×#386	1	2	yes	—
393	C₄	C₄₇×#388	1	2	yes	—
394	C₄	C₄₇×#388	1	2	yes	—
395	C₂	C₄₇×#1437	1	1	yes	characteristic
396	C₂	C₄₇×#1763	1	2	yes	—
397	C₂	C₄₇×#1894	1	2	yes	—
398	C₂	C₄₇×#1935	1	4	yes	—
399	C₂	C₄₇×#1959	1	1	yes	characteristic
400	C₂	C₄₇×#1960	1	1	yes	characteristic
401	C₂	C₄₇×#1971	1	2	yes	—
402	C₂	C₄₇×#1973	1	2	yes	—

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

Complements

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

N	H ≅ G/N	type
13. C₂×#103×C₄₇	C₄	semidirect
17. C₄₇×#391	C₄	semidirect
169. #10928	C₄₇	direct (N × H)
214. C₂×#103	C₄×C₄₇	semidirect
218. #391	C₄×C₄₇	semidirect
222. C₄₇	#10928	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×#103×C₄₇	2
C₂²×#97×C₄₇	2
C₂×C₄₇×#391	2
C₂×C₄₇×#340	2
C₄₇×C₄⋊#95	2
#10928	47

Subgroups — C47×#10928 #26050626

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₇×#10928 #26050626