Subgroups — C₄₇×#15106 #26054804

Order 12032.

1310 conjugacy classes of subgroups.

The subgroup lattice has 400 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₇×#398	C₂	1	2	yes	maximal
2	C₂×C₄₇×#389	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄×C₄⋊C₄×C₄₇	C₂	1	1	yes	maximal, characteristic
4	C₄₇×#1445	C₂	1	2	yes	maximal
5	C₄₇×#1444	C₂	1	2	yes	maximal
6	C₄₇×#1441	C₂	1	2	yes	maximal
7	C₄₇×#1436	C₂	1	4	yes	maximal
8	C₄₇×#1434	C₂	1	1	yes	maximal, characteristic
9	C₂²×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
10	C₂²×C₄⋊C₄×C₄₇	C₂²	1	2	yes	—
11	C₂²×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
12	C₂²×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
13	C₂²×C₄⋊C₄×C₄₇	C₂²	1	4	yes	—
14	C₂²×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
15	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
16	C₂²×C₄²×C₄₇	C₂²	1	2	yes	—
17	C₄₇×#398	—	2	8	no	—
18	C₄₇×#389	—	2	4	no	—
19	C₄×C₄⋊C₄×C₄₇	—	2	4	no	—
20	C₂×#95×C₄₇	C₂²	1	2	yes	—
21	C₂×#95×C₄₇	C₂²	1	2	yes	—
22	C₂×#95×C₄₇	C₂²	1	2	yes	—
23	C₂×#95×C₄₇	C₂²	1	4	yes	—
24	C₂×#95×C₄₇	C₂²	1	2	yes	—
25	C₂×#95×C₄₇	C₂²	1	4	yes	—
26	C₂×#95×C₄₇	C₂²	1	4	yes	—
27	C₂×#95×C₄₇	C₂²	1	2	yes	—
28	C₂³×C₄×C₄₇	C₂³	1	2	yes	—
29	C₂³×C₄×C₄₇	C₂³	1	2	yes	—
30	C₂³×C₄×C₄₇	C₂³	1	4	yes	—
31	C₂³×C₄×C₄₇	C₂³	1	2	yes	—
32	C₂³×C₄×C₄₇	C₂³	1	2	yes	—
33	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
34	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
35	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
36	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
37	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
38	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
39	C₂×C₄⋊C₄×C₄₇	—	2	4	no	—
40	C₂×C₄⋊C₄×C₄₇	—	2	4	no	—
41	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
42	C₂×C₄⋊C₄×C₄₇	—	2	4	no	—
43	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
44	C₂×C₄⋊C₄×C₄₇	—	2	8	no	—
45	C₂×C₄⋊C₄×C₄₇	—	2	4	no	—
46	C₂×C₄⋊C₄×C₄₇	—	2	8	no	—
47	C₂×C₄⋊C₄×C₄₇	—	2	4	no	—
48	C₂×C₄⋊C₄×C₄₇	—	2	4	no	—
49	C₂×C₄⋊C₄×C₄₇	—	4	4	no	—
50	C₂×C₄⋊C₄×C₄₇	D₄	1	4	yes	—
51	C₂×C₄²×C₄₇	—	2	4	no	—
52	C₂×C₄²×C₄₇	—	2	4	no	—
53	C₂×C₄²×C₄₇	—	4	4	no	—
54	C₂×C₄²×C₄₇	D₄	1	4	yes	—
55	#95×C₄₇	—	2	4	no	—
56	#95×C₄₇	—	2	4	no	—
57	#95×C₄₇	—	2	4	no	—
58	#95×C₄₇	—	2	8	no	—
59	#95×C₄₇	—	2	4	no	—
60	#95×C₄₇	—	2	8	no	—
61	#95×C₄₇	—	4	4	no	—
62	#95×C₄₇	Q₈	1	8	yes	—
63	C₂⁴×C₄₇	C₂⁴	1	1	yes	characteristic
64	C₂²×C₄×C₄₇	—	2	2	no	—
65	C₂²×C₄×C₄₇	—	2	2	no	—
66	C₂²×C₄×C₄₇	—	2	2	no	—
67	C₂²×C₄×C₄₇	—	2	2	no	—
68	C₂²×C₄×C₄₇	—	2	2	no	—
69	C₂²×C₄×C₄₇	—	2	2	no	—
70	C₂²×C₄×C₄₇	—	2	2	no	—
71	C₂²×C₄×C₄₇	—	2	2	no	—
72	C₂²×C₄×C₄₇	—	2	2	no	—
73	C₂²×C₄×C₄₇	—	2	2	no	—
74	C₂²×C₄×C₄₇	—	2	4	no	—
75	C₂²×C₄×C₄₇	—	2	2	no	—
76	C₂²×C₄×C₄₇	—	2	2	no	—
77	C₂²×C₄×C₄₇	—	2	2	no	—
78	C₂²×C₄×C₄₇	—	2	4	no	—
79	C₂²×C₄×C₄₇	—	2	4	no	—
80	C₂²×C₄×C₄₇	—	2	2	no	—
81	C₂²×C₄×C₄₇	—	2	4	no	—
82	C₂²×C₄×C₄₇	—	2	4	no	—
83	C₂²×C₄×C₄₇	—	2	4	no	—
84	C₂²×C₄×C₄₇	—	2	4	no	—
85	C₂²×C₄×C₄₇	—	2	2	no	—
86	C₂²×C₄×C₄₇	—	2	4	no	—
87	C₂²×C₄×C₄₇	—	2	2	no	—
88	C₂²×C₄×C₄₇	—	2	4	no	—
89	C₂²×C₄×C₄₇	—	2	4	no	—
90	C₂²×C₄×C₄₇	—	2	2	no	—
91	C₂²×C₄×C₄₇	—	2	2	no	—
92	C₂²×C₄×C₄₇	—	2	2	no	—
93	C₂²×C₄×C₄₇	—	2	4	no	—
94	C₂²×C₄×C₄₇	—	2	4	no	—
95	C₂²×C₄×C₄₇	C₂×D₄	1	4	yes	—
96	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
97	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
98	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
99	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
100	C₂²×C₄×C₄₇	C₂×Q₈	1	8	yes	—
101	C₂²×C₄×C₄₇	C₂×Q₈	1	4	yes	—
102	C₂²×C₄×C₄₇	#41	1	4	yes	—
103	C₂²×C₄×C₄₇	#41	1	4	yes	—
104	C₂²×C₄×C₄₇	#41	1	2	yes	—
105	C₂²×C₄×C₄₇	#41	1	4	yes	—
106	C₄⋊C₄×C₄₇	—	2	8	no	—
107	C₄⋊C₄×C₄₇	—	2	8	no	—
108	C₄⋊C₄×C₄₇	—	2	8	no	—
109	C₄⋊C₄×C₄₇	—	4	16	no	—
110	C₄⋊C₄×C₄₇	—	4	8	no	—
111	C₄⋊C₄×C₄₇	—	4	4	no	—
112	C₄²×C₄₇	—	2	8	no	—
113	C₄²×C₄₇	—	4	8	no	—
114	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
115	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
116	C₂³×C₄₇	C₂²×Q₈	1	2	yes	—
117	C₂³×C₄₇	C₂×#41	1	1	yes	characteristic
118	C₂³×C₄₇	C₂×#41	1	2	yes	—
119	C₂³×C₄₇	C₂×#41	1	2	yes	—
120	C₂³×C₄₇	C₂×#41	1	2	yes	—
121	C₂³×C₄₇	H(5,𝔽₂)	1	2	yes	—
122	C₂³×C₄₇	2₋¹⁺⁴	1	2	yes	—
123	C₂×C₄×C₄₇	—	2	2	no	—
124	C₂×C₄×C₄₇	—	2	2	no	—
125	C₂×C₄×C₄₇	—	2	2	no	—
126	C₂×C₄×C₄₇	—	2	2	no	—
127	C₂×C₄×C₄₇	—	2	4	no	—
128	C₂×C₄×C₄₇	—	2	4	no	—
129	C₂×C₄×C₄₇	—	2	2	no	—
130	C₂×C₄×C₄₇	—	2	2	no	—
131	C₂×C₄×C₄₇	—	2	8	no	—
132	C₂×C₄×C₄₇	—	2	8	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	—	2	8	no	—
137	C₂×C₄×C₄₇	—	2	8	no	—
138	C₂×C₄×C₄₇	—	2	4	no	—
139	C₂×C₄×C₄₇	—	2	8	no	—
140	C₂×C₄×C₄₇	—	2	8	no	—
141	C₂×C₄×C₄₇	—	2	4	no	—
142	C₂×C₄×C₄₇	—	2	8	no	—
143	C₂×C₄×C₄₇	—	4	2	no	—
144	C₂×C₄×C₄₇	—	4	2	no	—
145	C₂×C₄×C₄₇	—	4	4	no	—
146	C₂×C₄×C₄₇	—	4	2	no	—
147	C₂×C₄×C₄₇	—	4	2	no	—
148	C₂×C₄×C₄₇	—	4	2	no	—
149	C₂×C₄×C₄₇	—	4	2	no	—
150	C₂×C₄×C₄₇	—	4	4	no	—
151	C₂×C₄×C₄₇	—	4	4	no	—
152	C₂×C₄×C₄₇	—	4	4	no	—
153	C₂×C₄×C₄₇	—	4	2	no	—
154	C₂×C₄×C₄₇	—	4	4	no	—
155	C₂×C₄×C₄₇	—	4	4	no	—
156	C₂×C₄×C₄₇	—	4	2	no	—
157	C₂×C₄×C₄₇	—	4	2	no	—
158	C₂×C₄×C₄₇	—	4	2	no	—
159	C₂×C₄×C₄₇	—	4	2	no	—
160	C₂×C₄×C₄₇	—	4	4	no	—
161	C₂×C₄×C₄₇	—	4	4	no	—
162	C₂×C₄×C₄₇	#121	1	4	yes	—
163	C₂×C₄×C₄₇	#123	1	4	yes	—
164	C₂×C₄×C₄₇	C₄⋊Q₈	1	4	yes	—
165	#15106	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
166	C₂²×C₄₇	C₂×#121	1	1	yes	characteristic
167	C₂²×C₄₇	C₂×#123	1	1	yes	characteristic
168	C₂²×C₄₇	#525	1	1	yes	characteristic
169	C₂²×C₄₇	#525	1	1	yes	characteristic
170	C₂²×C₄₇	#529	1	2	yes	—
171	C₂²×C₄₇	C₂×C₄⋊Q₈	1	1	yes	characteristic
172	C₂²×C₄₇	#532	1	2	yes	—
173	C₂²×C₄₇	#533	1	4	yes	—
174	C₂²×C₄₇	#535	1	1	yes	characteristic
175	C₂²×C₄₇	#536	1	1	yes	characteristic
176	C₂²×C₄₇	#539	1	4	yes	—
177	C₂²×C₄₇	#546	1	2	yes	—
178	C₂²×C₄₇	D₄×Q₈	1	2	yes	—
179	C₂²×C₄₇	#552	1	4	yes	—
180	C₂²×C₄₇	#553	1	2	yes	—
181	C₂²×C₄₇	#554	1	4	yes	—
182	C₂²×C₄₇	#557	1	2	yes	—
183	C₄×C₄₇	—	2	4	no	—
184	C₄×C₄₇	—	2	4	no	—
185	C₄×C₄₇	—	2	4	no	—
186	C₄×C₄₇	—	4	4	no	—
187	C₄×C₄₇	—	4	4	no	—
188	C₄×C₄₇	—	4	4	no	—
189	C₄×C₄₇	—	4	8	no	—
190	C₄×C₄₇	—	8	2	no	—
191	C₂×#398	C₂×C₄₇	1	2	yes	—
192	C₂×#389	C₂×C₄₇	1	1	yes	characteristic
193	C₂×C₄×C₄⋊C₄	C₂×C₄₇	1	1	yes	characteristic
194	#1445	C₂×C₄₇	1	2	yes	—
195	#1444	C₂×C₄₇	1	2	yes	—
196	#1441	C₂×C₄₇	1	2	yes	—
197	#1436	C₂×C₄₇	1	4	yes	—
198	#1434	C₂×C₄₇	1	1	yes	characteristic
199	C₂×C₄₇	#2399	1	1	yes	characteristic
200	C₂×C₄₇	#2484	1	1	yes	characteristic
201	C₂×C₄₇	#2502	1	1	yes	characteristic
202	C₂×C₄₇	#2535	1	1	yes	characteristic
203	C₂×C₄₇	#2546	1	1	yes	characteristic
204	C₂×C₄₇	#2556	1	4	yes	—
205	C₂×C₄₇	#2590	1	4	yes	—
206	C₂×C₄₇	#2633	1	1	yes	characteristic
207	C₂×C₄₇	#2854	1	1	yes	characteristic
208	C₂²×C₄⋊C₄	C₂²×C₄₇	1	2	yes	—
209	C₂²×C₄⋊C₄	C₂²×C₄₇	1	1	yes	characteristic
210	C₂²×C₄⋊C₄	C₂²×C₄₇	1	1	yes	characteristic
211	C₂²×C₄⋊C₄	C₂²×C₄₇	1	1	yes	characteristic
212	C₂²×C₄⋊C₄	C₂²×C₄₇	1	4	yes	—
213	C₂²×C₄⋊C₄	C₂²×C₄₇	1	1	yes	characteristic
214	C₂²×C₄²	C₂²×C₄₇	1	1	yes	characteristic
215	C₂²×C₄²	C₂²×C₄₇	1	2	yes	—
216	#398	—	2	8	no	—
217	#389	—	2	4	no	—
218	C₄×C₄⋊C₄	—	2	4	no	—
219	C₂×#95	C₂²×C₄₇	1	2	yes	—
220	C₂×#95	C₂²×C₄₇	1	4	yes	—
221	C₂×#95	C₂²×C₄₇	1	2	yes	—
222	C₂×#95	C₂²×C₄₇	1	2	yes	—
223	C₂×#95	C₂²×C₄₇	1	4	yes	—
224	C₂×#95	C₂²×C₄₇	1	2	yes	—
225	C₂×#95	C₂²×C₄₇	1	4	yes	—
226	C₂×#95	C₂²×C₄₇	1	2	yes	—
227	C₄₇	#15106	1	1	yes	characteristic, direct product factor, Sylow
228	C₂³×C₄	C₂³×C₄₇	1	2	yes	—
229	C₂³×C₄	C₂³×C₄₇	1	2	yes	—
230	C₂³×C₄	C₂³×C₄₇	1	4	yes	—
231	C₂³×C₄	C₂³×C₄₇	1	2	yes	—
232	C₂³×C₄	C₂³×C₄₇	1	2	yes	—
233	C₂³×C₄	C₂³×C₄₇	1	1	yes	characteristic
234	C₂³×C₄	C₂³×C₄₇	1	1	yes	characteristic
235	C₂³×C₄	C₂³×C₄₇	1	1	yes	characteristic
236	C₂×C₄⋊C₄	—	2	2	no	—
237	C₂×C₄⋊C₄	—	2	2	no	—
238	C₂×C₄⋊C₄	—	2	2	no	—
239	C₂×C₄⋊C₄	—	2	4	no	—
240	C₂×C₄⋊C₄	—	2	4	no	—
241	C₂×C₄⋊C₄	—	2	2	no	—
242	C₂×C₄⋊C₄	—	2	4	no	—
243	C₂×C₄⋊C₄	—	2	2	no	—
244	C₂×C₄⋊C₄	—	2	8	no	—
245	C₂×C₄⋊C₄	—	2	4	no	—
246	C₂×C₄⋊C₄	—	2	8	no	—
247	C₂×C₄⋊C₄	—	2	4	no	—
248	C₂×C₄⋊C₄	—	2	4	no	—
249	C₂×C₄⋊C₄	—	4	4	no	—
250	C₂×C₄⋊C₄	D₄×C₄₇	1	4	yes	—
251	C₂×C₄²	—	2	4	no	—
252	C₂×C₄²	—	2	4	no	—
253	C₂×C₄²	—	4	4	no	—
254	C₂×C₄²	D₄×C₄₇	1	4	yes	—
255	#95	—	2	4	no	—
256	#95	—	2	4	no	—
257	#95	—	2	4	no	—
258	#95	—	2	8	no	—
259	#95	—	2	4	no	—
260	#95	—	2	8	no	—
261	#95	—	4	4	no	—
262	#95	Q₈×C₄₇	1	8	yes	—
263	C₂⁴	C₂⁴×C₄₇	1	1	yes	characteristic
264	C₂²×C₄	—	2	2	no	—
265	C₂²×C₄	—	2	2	no	—
266	C₂²×C₄	—	2	2	no	—
267	C₂²×C₄	—	2	2	no	—
268	C₂²×C₄	—	2	2	no	—
269	C₂²×C₄	—	2	2	no	—
270	C₂²×C₄	—	2	4	no	—
271	C₂²×C₄	—	2	2	no	—
272	C₂²×C₄	—	2	2	no	—
273	C₂²×C₄	—	2	2	no	—
274	C₂²×C₄	—	2	2	no	—
275	C₂²×C₄	—	2	4	no	—
276	C₂²×C₄	—	2	4	no	—
277	C₂²×C₄	—	2	2	no	—
278	C₂²×C₄	—	2	2	no	—
279	C₂²×C₄	—	2	2	no	—
280	C₂²×C₄	—	2	4	no	—
281	C₂²×C₄	—	2	4	no	—
282	C₂²×C₄	—	2	2	no	—
283	C₂²×C₄	—	2	2	no	—
284	C₂²×C₄	—	2	4	no	—
285	C₂²×C₄	—	2	4	no	—
286	C₂²×C₄	—	2	4	no	—
287	C₂²×C₄	—	2	2	no	—
288	C₂²×C₄	—	2	4	no	—
289	C₂²×C₄	—	2	4	no	—
290	C₂²×C₄	—	2	2	no	—
291	C₂²×C₄	—	2	2	no	—
292	C₂²×C₄	—	2	4	no	—
293	C₂²×C₄	—	2	2	no	—
294	C₂²×C₄	—	2	4	no	—
295	C₂²×C₄	C₂×D₄×C₄₇	1	4	yes	—
296	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
297	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
298	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
299	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
300	C₂²×C₄	C₂×Q₈×C₄₇	1	8	yes	—
301	C₂²×C₄	C₂×Q₈×C₄₇	1	4	yes	—
302	C₂²×C₄	#41×C₄₇	1	4	yes	—
303	C₂²×C₄	#41×C₄₇	1	4	yes	—
304	C₂²×C₄	#41×C₄₇	1	2	yes	—
305	C₂²×C₄	#41×C₄₇	1	4	yes	—
306	C₄⋊C₄	—	2	8	no	—
307	C₄⋊C₄	—	2	8	no	—
308	C₄⋊C₄	—	2	8	no	—
309	C₄⋊C₄	—	4	16	no	—
310	C₄⋊C₄	—	4	8	no	—
311	C₄⋊C₄	—	4	4	no	—
312	C₄²	—	2	8	no	—
313	C₄²	—	4	8	no	—
314	C₂³	C₂²×D₄×C₄₇	1	1	yes	characteristic
315	C₂³	C₂²×D₄×C₄₇	1	1	yes	characteristic
316	C₂³	C₂²×Q₈×C₄₇	1	2	yes	—
317	C₂³	C₂×#41×C₄₇	1	1	yes	characteristic
318	C₂³	C₂×#41×C₄₇	1	2	yes	—
319	C₂³	C₂×#41×C₄₇	1	2	yes	—
320	C₂³	C₂×#41×C₄₇	1	2	yes	—
321	C₂³	H(5,𝔽₂)×C₄₇	1	2	yes	—
322	C₂³	2₋¹⁺⁴×C₄₇	1	2	yes	—
323	C₂×C₄	—	2	2	no	—
324	C₂×C₄	—	2	2	no	—
325	C₂×C₄	—	2	2	no	—
326	C₂×C₄	—	2	2	no	—
327	C₂×C₄	—	2	4	no	—
328	C₂×C₄	—	2	4	no	—
329	C₂×C₄	—	2	2	no	—
330	C₂×C₄	—	2	2	no	—
331	C₂×C₄	—	2	8	no	—
332	C₂×C₄	—	2	8	no	—
333	C₂×C₄	—	2	4	no	—
334	C₂×C₄	—	2	4	no	—
335	C₂×C₄	—	2	4	no	—
336	C₂×C₄	—	2	8	no	—
337	C₂×C₄	—	2	8	no	—
338	C₂×C₄	—	2	4	no	—
339	C₂×C₄	—	2	8	no	—
340	C₂×C₄	—	2	8	no	—
341	C₂×C₄	—	2	4	no	—
342	C₂×C₄	—	2	8	no	—
343	C₂×C₄	—	4	2	no	—
344	C₂×C₄	—	4	2	no	—
345	C₂×C₄	—	4	4	no	—
346	C₂×C₄	—	4	2	no	—
347	C₂×C₄	—	4	2	no	—
348	C₂×C₄	—	4	2	no	—
349	C₂×C₄	—	4	2	no	—
350	C₂×C₄	—	4	4	no	—
351	C₂×C₄	—	4	4	no	—
352	C₂×C₄	—	4	4	no	—
353	C₂×C₄	—	4	2	no	—
354	C₂×C₄	—	4	4	no	—
355	C₂×C₄	—	4	4	no	—
356	C₂×C₄	—	4	2	no	—
357	C₂×C₄	—	4	2	no	—
358	C₂×C₄	—	4	2	no	—
359	C₂×C₄	—	4	2	no	—
360	C₂×C₄	—	4	4	no	—
361	C₂×C₄	—	4	4	no	—
362	C₂×C₄	#121×C₄₇	1	4	yes	—
363	C₂×C₄	#123×C₄₇	1	4	yes	—
364	C₂×C₄	C₄⋊Q₈×C₄₇	1	4	yes	—
365	C₂²	C₂×#121×C₄₇	1	1	yes	characteristic
366	C₂²	C₂×#123×C₄₇	1	1	yes	characteristic
367	C₂²	C₄₇×#525	1	1	yes	characteristic
368	C₂²	C₄₇×#525	1	1	yes	characteristic
369	C₂²	C₄₇×#529	1	2	yes	—
370	C₂²	C₂×C₄⋊Q₈×C₄₇	1	1	yes	characteristic
371	C₂²	C₄₇×#532	1	2	yes	—
372	C₂²	C₄₇×#533	1	4	yes	—
373	C₂²	C₄₇×#535	1	1	yes	characteristic
374	C₂²	C₄₇×#536	1	1	yes	characteristic
375	C₂²	C₄₇×#539	1	4	yes	—
376	C₂²	C₄₇×#546	1	2	yes	—
377	C₂²	D₄×Q₈×C₄₇	1	2	yes	—
378	C₂²	C₄₇×#552	1	4	yes	—
379	C₂²	C₄₇×#553	1	2	yes	—
380	C₂²	C₄₇×#554	1	4	yes	—
381	C₂²	C₄₇×#557	1	2	yes	—
382	C₄	—	2	4	no	—
383	C₄	—	2	4	no	—
384	C₄	—	2	4	no	—
385	C₄	—	4	4	no	—
386	C₄	—	4	4	no	—
387	C₄	—	4	8	no	—
388	C₄	—	4	4	no	—
389	C₄	—	8	2	no	—
390	C₂	C₄₇×#2399	1	1	yes	characteristic
391	C₂	C₄₇×#2484	1	1	yes	characteristic
392	C₂	C₄₇×#2502	1	1	yes	characteristic
393	C₂	C₄₇×#2535	1	1	yes	characteristic
394	C₂	C₄₇×#2546	1	1	yes	characteristic
395	C₂	C₄₇×#2556	1	4	yes	—
396	C₂	C₄₇×#2590	1	4	yes	—
397	C₂	C₄₇×#2633	1	1	yes	characteristic
398	C₂	C₄₇×#2854	1	1	yes	characteristic

	subgroup	G/H
center, socle, prime radical	C₂⁴×C₄₇	C₂⁴
commutator, Frattini, cosocle	C₂⁴	C₂⁴×C₄₇
LCS	G ▷ C₂⁴ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₄₇ ◁ G

Complements

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

N	H ≅ G/N	type
165. #15106	C₄₇	direct (N × H)
227. C₄₇	#15106	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₄₇×#398	2
C₂×C₄₇×#389	2
C₂×C₄×C₄⋊C₄×C₄₇	2
C₄₇×#1445	2
C₄₇×#1444	2
C₄₇×#1441	2
C₄₇×#1436	2
C₄₇×#1434	2
#15106	47

Subgroups — C47×#15106 #26054804

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₇×#15106 #26054804