Subgroups — C₄₇×#9715 #26049413

Order 12032.

764 conjugacy classes of subgroups.

The subgroup lattice has 414 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₇×#2856	C₂	1	1	yes	maximal, characteristic
2	C₄₇×#1797	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄₇×#327	C₂	1	4	yes	maximal, complemented
4	C₄₇×#1434	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#127×C₄₇	C₄	1	1	yes	characteristic, complemented
6	C₂×#121×C₄₇	—	2	1	no	—
7	C₂×#121×C₄₇	—	2	1	no	—
8	C₂×#121×C₄₇	C₂²	1	2	yes	—
9	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
10	C₂×C₄⋊C₈×C₄₇	—	2	1	no	—
11	C₂×C₂²⋊C₈×C₄₇	C₂²	1	2	yes	—
12	C₄₇×#390	—	2	1	no	—
13	C₄₇×#390	—	2	1	no	—
14	C₄₇×#390	C₄	1	2	yes	complemented
15	C₄₇×#384	C₄	1	1	yes	characteristic, complemented
16	C₂×#95×C₄₇	—	2	1	no	—
17	C₂×#95×C₄₇	—	2	1	no	—
18	C₂×#95×C₄₇	C₂²	1	2	yes	—
19	C₄₇×#336	—	2	1	no	—
20	C₄₇×#327	—	2	8	no	—
21	C₂²×D₄×C₄₇	—	2	2	no	—
22	C₂²×D₄×C₄₇	—	2	1	no	—
23	C₂²×D₄×C₄₇	—	2	1	no	—
24	C₂²×D₄×C₄₇	C₂×C₄	1	2	yes	—
25	C₂³×C₄×C₄₇	—	2	2	no	—
26	C₂³×C₄×C₄₇	D₄	1	1	yes	characteristic
27	C₂³×C₄×C₄₇	D₄	1	1	yes	characteristic
28	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
29	C₂²×C₈×C₄₇	—	2	2	no	—
30	#127×C₄₇	—	4	2	no	—
31	#121×C₄₇	—	2	4	no	—
32	#121×C₄₇	—	2	4	no	—
33	#121×C₄₇	—	4	4	no	—
34	#121×C₄₇	—	4	2	no	—
35	#121×C₄₇	—	4	2	no	—
36	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
37	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
38	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
39	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
40	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
41	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
42	C₂×C₄²×C₄₇	—	4	2	no	—
43	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
44	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
45	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
46	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
47	C₄⋊C₈×C₄₇	—	4	2	no	—
48	C₂²⋊C₈×C₄₇	—	2	4	no	—
49	#95×C₄₇	—	2	2	no	—
50	#95×C₄₇	—	4	2	no	—
51	#95×C₄₇	—	4	2	no	—
52	#95×C₄₇	D₄	1	4	yes	complemented
53	C₂⁴×C₄₇	—	2	2	no	—
54	C₂⁴×C₄₇	C₂×D₄	1	1	yes	characteristic
55	C₂×D₄×C₄₇	—	2	4	no	—
56	C₂×D₄×C₄₇	—	4	2	no	—
57	C₂×D₄×C₄₇	—	4	2	no	—
58	C₂×D₄×C₄₇	—	4	2	no	—
59	C₂×D₄×C₄₇	—	4	2	no	—
60	C₂×D₄×C₄₇	—	4	2	no	—
61	C₂×D₄×C₄₇	—	4	2	no	—
62	C₂×D₄×C₄₇	—	4	4	no	—
63	C₂×D₄×C₄₇	—	4	2	no	—
64	C₂×D₄×C₄₇	—	4	2	no	—
65	C₂×D₄×C₄₇	—	4	4	no	—
66	C₂×D₄×C₄₇	—	4	2	no	—
67	C₂×D₄×C₄₇	—	4	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	4	no	—
72	C₂²×C₄×C₄₇	—	4	1	no	—
73	C₂²×C₄×C₄₇	—	4	1	no	—
74	C₂²×C₄×C₄₇	—	4	1	no	—
75	C₂²×C₄×C₄₇	—	4	1	no	—
76	C₂²×C₄×C₄₇	—	4	1	no	—
77	C₂²×C₄×C₄₇	—	4	2	no	—
78	C₂²×C₄×C₄₇	—	4	2	no	—
79	C₂²×C₄×C₄₇	—	4	2	no	—
80	C₂²×C₄×C₄₇	—	4	2	no	—
81	C₂²×C₄×C₄₇	—	4	2	no	—
82	C₂²×C₄×C₄₇	—	4	2	no	—
83	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
84	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
85	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
86	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
87	C₂²×C₄×C₄₇	D₈	1	2	yes	—
88	C₂²×C₄×C₄₇	SD₁₆	1	2	yes	—
89	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
90	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
91	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
92	C₂²×C₄×C₄₇	#41	1	2	yes	—
93	C₂×C₈×C₄₇	—	4	2	no	—
94	C₂×C₈×C₄₇	—	4	2	no	—
95	C₂×C₈×C₄₇	—	4	2	no	—
96	C₄⋊C₄×C₄₇	—	2	4	no	—
97	C₄⋊C₄×C₄₇	—	4	2	no	—
98	C₄⋊C₄×C₄₇	—	4	2	no	—
99	C₂²⋊C₄×C₄₇	—	4	4	no	—
100	C₂²⋊C₄×C₄₇	—	4	4	no	—
101	C₂²⋊C₄×C₄₇	—	4	2	no	—
102	C₂²⋊C₄×C₄₇	—	4	2	no	—
103	C₄²×C₄₇	—	2	2	no	—
104	C₄²×C₄₇	—	2	2	no	—
105	C₄²×C₄₇	—	4	1	no	—
106	C₄²×C₄₇	—	4	1	no	—
107	C₂³×C₄₇	—	2	1	no	—
108	C₂³×C₄₇	—	2	1	no	—
109	C₂³×C₄₇	—	2	1	no	—
110	C₂³×C₄₇	—	2	1	no	—
111	C₂³×C₄₇	—	4	2	no	—
112	C₂³×C₄₇	—	4	2	no	—
113	C₂³×C₄₇	—	4	2	no	—
114	C₂³×C₄₇	—	4	2	no	—
115	C₂³×C₄₇	—	4	2	no	—
116	C₂³×C₄₇	—	4	2	no	—
117	C₂³×C₄₇	—	4	2	no	—
118	C₂³×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
119	C₂³×C₄₇	#121	1	2	yes	—
120	C₂³×C₄₇	C₂×D₈	1	1	yes	characteristic
121	C₂³×C₄₇	C₂×SD₁₆	1	1	yes	characteristic
122	C₂³×C₄₇	AGL(1,ℤ/8)	1	2	yes	—
123	D₄×C₄₇	—	8	4	no	—
124	D₄×C₄₇	—	8	4	no	—
125	D₄×C₄₇	—	8	4	no	—
126	D₄×C₄₇	—	8	4	no	—
127	D₄×C₄₇	—	8	4	no	—
128	C₂×C₄×C₄₇	—	2	1	no	—
129	C₂×C₄×C₄₇	—	2	1	no	—
130	C₂×C₄×C₄₇	—	2	1	no	—
131	C₂×C₄×C₄₇	—	2	1	no	—
132	C₂×C₄×C₄₇	—	2	1	no	—
133	C₂×C₄×C₄₇	—	2	1	no	—
134	C₂×C₄×C₄₇	—	2	1	no	—
135	C₂×C₄×C₄₇	—	2	1	no	—
136	C₂×C₄×C₄₇	—	2	1	no	—
137	C₂×C₄×C₄₇	—	2	1	no	—
138	C₂×C₄×C₄₇	—	2	1	no	—
139	C₂×C₄×C₄₇	—	2	1	no	—
140	C₂×C₄×C₄₇	—	2	1	no	—
141	C₂×C₄×C₄₇	—	4	2	no	—
142	C₂×C₄×C₄₇	—	4	2	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	4	no	—
147	C₂×C₄×C₄₇	—	4	4	no	—
148	C₂×C₄×C₄₇	—	4	2	no	—
149	C₂×C₄×C₄₇	—	4	2	no	—
150	C₂×C₄×C₄₇	—	4	2	no	—
151	C₂×C₄×C₄₇	—	4	4	no	—
152	C₂×C₄×C₄₇	—	8	2	no	—
153	C₂×C₄×C₄₇	—	8	2	no	—
154	C₂×C₄×C₄₇	—	8	2	no	—
155	C₂×C₄×C₄₇	—	8	2	no	—
156	C₂×C₄×C₄₇	#99	1	2	yes	—
157	C₂×C₄×C₄₇	#102	1	2	yes	—
158	C₂×C₄×C₄₇	#102	1	2	yes	—
159	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
160	C₂×C₄×C₄₇	#124	1	1	yes	characteristic
161	C₂×C₄×C₄₇	#127	1	1	yes	characteristic
162	C₈×C₄₇	—	8	2	no	—
163	#9715	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
164	C₂²×C₄₇	—	2	2	no	—
165	C₂²×C₄₇	—	2	2	no	—
166	C₂²×C₄₇	—	2	2	no	—
167	C₂²×C₄₇	—	2	2	no	—
168	C₂²×C₄₇	—	2	1	no	—
169	C₂²×C₄₇	—	2	1	no	—
170	C₂²×C₄₇	—	2	1	no	—
171	C₂²×C₄₇	—	2	1	no	—
172	C₂²×C₄₇	—	8	2	no	—
173	C₂²×C₄₇	—	8	2	no	—
174	C₂²×C₄₇	—	8	2	no	—
175	C₂²×C₄₇	—	8	2	no	—
176	C₂²×C₄₇	—	8	2	no	—
177	C₂²×C₄₇	—	8	2	no	—
178	C₂²×C₄₇	—	8	2	no	—
179	C₂²×C₄₇	#390	1	1	yes	characteristic
180	C₂²×C₄₇	C₂×#99	1	1	yes	characteristic
181	C₂²×C₄₇	#410	1	1	yes	characteristic
182	C₂²×C₄₇	C₂×#102	1	1	yes	characteristic
183	C₂²×C₄₇	#418	1	1	yes	characteristic
184	C₂²×C₄₇	#421	1	1	yes	characteristic
185	C₂²×C₄₇	#421	1	1	yes	characteristic
186	C₂²×C₄₇	#459	1	2	yes	—
187	C₂²×C₄₇	#460	1	2	yes	—
188	C₄×C₄₇	—	2	1	no	—
189	C₄×C₄₇	—	2	2	no	—
190	C₄×C₄₇	—	2	1	no	—
191	C₄×C₄₇	—	2	2	no	—
192	C₄×C₄₇	—	2	2	no	—
193	C₄×C₄₇	—	2	2	no	—
194	C₄×C₄₇	—	4	1	no	—
195	C₄×C₄₇	—	8	4	no	—
196	C₄×C₄₇	—	8	2	no	—
197	#2856	C₂×C₄₇	1	1	yes	characteristic
198	#1797	C₂×C₄₇	1	1	yes	characteristic, complemented
199	C₂×#327	C₂×C₄₇	1	4	yes	complemented
200	#1434	C₂×C₄₇	1	1	yes	characteristic, complemented
201	C₂×C₄₇	—	2	2	no	—
202	C₂×C₄₇	—	2	2	no	—
203	C₂×C₄₇	—	16	2	no	—
204	C₂×C₄₇	#1510	1	1	yes	characteristic
205	C₂×C₄₇	#1514	1	1	yes	characteristic
206	C₂×C₄₇	#1517	1	1	yes	characteristic
207	C₂×C₄₇	#1519	1	1	yes	characteristic
208	C₂×C₄₇	#1963	1	1	yes	characteristic
209	C₂×C₄₇	#1964	1	1	yes	characteristic
210	C₂×C₄₇	#1982	1	1	yes	characteristic
211	C₂×#127	C₄×C₄₇	1	1	yes	characteristic, complemented
212	C₂×#121	—	2	1	no	—
213	C₂×#121	—	2	1	no	—
214	C₂×#121	C₂²×C₄₇	1	2	yes	—
215	C₂²×C₄²	C₂²×C₄₇	1	1	yes	characteristic
216	C₂×C₄⋊C₈	—	2	1	no	—
217	C₂×C₂²⋊C₈	C₂²×C₄₇	1	2	yes	—
218	#390	—	2	1	no	—
219	#390	—	2	1	no	—
220	#390	C₄×C₄₇	1	2	yes	complemented
221	#384	C₄×C₄₇	1	1	yes	characteristic, complemented
222	C₂×#95	—	2	1	no	—
223	C₂×#95	—	2	1	no	—
224	C₂×#95	C₂²×C₄₇	1	2	yes	—
225	#336	—	2	1	no	—
226	#327	—	2	8	no	—
227	C₄₇	#9715	1	1	yes	characteristic, direct product factor, Sylow
228	C₂²×D₄	—	2	2	no	—
229	C₂²×D₄	—	2	1	no	—
230	C₂²×D₄	—	2	1	no	—
231	C₂²×D₄	C₂×C₄×C₄₇	1	2	yes	—
232	C₂³×C₄	—	2	2	no	—
233	C₂³×C₄	D₄×C₄₇	1	1	yes	characteristic
234	C₂³×C₄	D₄×C₄₇	1	1	yes	characteristic
235	C₂³×C₄	C₂³×C₄₇	1	1	yes	characteristic
236	C₂²×C₈	—	2	2	no	—
237	#127	—	4	2	no	—
238	#121	—	2	4	no	—
239	#121	—	2	4	no	—
240	#121	—	4	4	no	—
241	#121	—	4	2	no	—
242	#121	—	4	2	no	—
243	C₂×C₄⋊C₄	—	2	1	no	—
244	C₂×C₄⋊C₄	—	2	1	no	—
245	C₂×C₄⋊C₄	C₂×C₄×C₄₇	1	2	yes	—
246	C₂×C₂²⋊C₄	—	2	2	no	—
247	C₂×C₂²⋊C₄	—	2	2	no	—
248	C₂×C₂²⋊C₄	—	2	2	no	—
249	C₂×C₄²	—	4	2	no	—
250	C₂×C₄²	C₂×C₄×C₄₇	1	1	yes	characteristic
251	C₂×C₄²	C₂×C₄×C₄₇	1	1	yes	characteristic
252	C₂×C₄²	D₄×C₄₇	1	1	yes	characteristic
253	C₂×C₄²	D₄×C₄₇	1	1	yes	characteristic
254	C₄⋊C₈	—	4	2	no	—
255	C₂²⋊C₈	—	2	4	no	—
256	#95	—	2	2	no	—
257	#95	—	4	2	no	—
258	#95	—	4	2	no	—
259	#95	D₄×C₄₇	1	4	yes	complemented
260	C₂⁴	—	2	2	no	—
261	C₂⁴	C₂×D₄×C₄₇	1	1	yes	characteristic
262	C₂×D₄	—	2	4	no	—
263	C₂×D₄	—	4	2	no	—
264	C₂×D₄	—	4	2	no	—
265	C₂×D₄	—	4	2	no	—
266	C₂×D₄	—	4	2	no	—
267	C₂×D₄	—	4	2	no	—
268	C₂×D₄	—	4	2	no	—
269	C₂×D₄	—	4	4	no	—
270	C₂×D₄	—	4	2	no	—
271	C₂×D₄	—	4	2	no	—
272	C₂×D₄	—	4	4	no	—
273	C₂×D₄	—	4	2	no	—
274	C₂×D₄	—	4	2	no	—
275	C₂²×C₄	—	2	2	no	—
276	C₂²×C₄	—	2	2	no	—
277	C₂²×C₄	—	2	2	no	—
278	C₂²×C₄	—	2	4	no	—
279	C₂²×C₄	—	4	1	no	—
280	C₂²×C₄	—	4	1	no	—
281	C₂²×C₄	—	4	1	no	—
282	C₂²×C₄	—	4	1	no	—
283	C₂²×C₄	—	4	1	no	—
284	C₂²×C₄	—	4	2	no	—
285	C₂²×C₄	—	4	2	no	—
286	C₂²×C₄	—	4	2	no	—
287	C₂²×C₄	—	4	2	no	—
288	C₂²×C₄	—	4	2	no	—
289	C₂²×C₄	—	4	2	no	—
290	C₂²×C₄	C₂²⋊C₄×C₄₇	1	1	yes	characteristic
291	C₂²×C₄	C₂²⋊C₄×C₄₇	1	1	yes	characteristic
292	C₂²×C₄	C₂²⋊C₄×C₄₇	1	1	yes	characteristic
293	C₂²×C₄	C₂²⋊C₄×C₄₇	1	1	yes	characteristic
294	C₂²×C₄	D₈×C₄₇	1	2	yes	—
295	C₂²×C₄	SD₁₆×C₄₇	1	2	yes	—
296	C₂²×C₄	C₂²×C₄×C₄₇	1	1	yes	characteristic
297	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
298	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
299	C₂²×C₄	#41×C₄₇	1	2	yes	—
300	C₂×C₈	—	4	2	no	—
301	C₂×C₈	—	4	2	no	—
302	C₂×C₈	—	4	2	no	—
303	C₄⋊C₄	—	2	4	no	—
304	C₄⋊C₄	—	4	2	no	—
305	C₄⋊C₄	—	4	2	no	—
306	C₂²⋊C₄	—	4	4	no	—
307	C₂²⋊C₄	—	4	2	no	—
308	C₂²⋊C₄	—	4	2	no	—
309	C₂²⋊C₄	—	4	4	no	—
310	C₄²	—	2	2	no	—
311	C₄²	—	2	2	no	—
312	C₄²	—	4	1	no	—
313	C₄²	—	4	1	no	—
314	C₂³	—	2	1	no	—
315	C₂³	—	2	1	no	—
316	C₂³	—	2	1	no	—
317	C₂³	—	2	1	no	—
318	C₂³	—	4	2	no	—
319	C₂³	—	4	2	no	—
320	C₂³	—	4	2	no	—
321	C₂³	—	4	2	no	—
322	C₂³	—	4	2	no	—
323	C₂³	—	4	2	no	—
324	C₂³	—	4	2	no	—
325	C₂³	C₂×C₂²⋊C₄×C₄₇	1	1	yes	characteristic
326	C₂³	#121×C₄₇	1	2	yes	—
327	C₂³	C₂×D₈×C₄₇	1	1	yes	characteristic
328	C₂³	C₂×SD₁₆×C₄₇	1	1	yes	characteristic
329	C₂³	AGL(1,ℤ/8)×C₄₇	1	2	yes	—
330	D₄	—	8	4	no	—
331	D₄	—	8	4	no	—
332	D₄	—	8	4	no	—
333	D₄	—	8	4	no	—
334	D₄	—	8	4	no	—
335	C₂×C₄	—	2	1	no	—
336	C₂×C₄	—	2	1	no	—
337	C₂×C₄	—	2	1	no	—
338	C₂×C₄	—	2	1	no	—
339	C₂×C₄	—	2	1	no	—
340	C₂×C₄	—	2	1	no	—
341	C₂×C₄	—	2	1	no	—
342	C₂×C₄	—	2	1	no	—
343	C₂×C₄	—	2	1	no	—
344	C₂×C₄	—	2	1	no	—
345	C₂×C₄	—	2	1	no	—
346	C₂×C₄	—	2	1	no	—
347	C₂×C₄	—	2	1	no	—
348	C₂×C₄	—	4	2	no	—
349	C₂×C₄	—	4	2	no	—
350	C₂×C₄	—	4	2	no	—
351	C₂×C₄	—	4	2	no	—
352	C₂×C₄	—	4	4	no	—
353	C₂×C₄	—	4	4	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	—	8	2	no	—
360	C₂×C₄	—	8	2	no	—
361	C₂×C₄	—	8	2	no	—
362	C₂×C₄	—	8	2	no	—
363	C₂×C₄	#99×C₄₇	1	2	yes	—
364	C₂×C₄	#102×C₄₇	1	2	yes	—
365	C₂×C₄	#102×C₄₇	1	2	yes	—
366	C₂×C₄	C₄×D₄×C₄₇	1	2	yes	—
367	C₂×C₄	#124×C₄₇	1	1	yes	characteristic
368	C₂×C₄	#127×C₄₇	1	1	yes	characteristic
369	C₈	—	8	2	no	—
370	C₂²	—	2	2	no	—
371	C₂²	—	2	2	no	—
372	C₂²	—	2	1	no	—
373	C₂²	—	2	1	no	—
374	C₂²	—	2	1	no	—
375	C₂²	—	2	1	no	—
376	C₂²	—	2	2	no	—
377	C₂²	—	2	2	no	—
378	C₂²	—	8	2	no	—
379	C₂²	—	8	2	no	—
380	C₂²	—	8	2	no	—
381	C₂²	—	8	2	no	—
382	C₂²	—	8	2	no	—
383	C₂²	—	8	2	no	—
384	C₂²	—	8	2	no	—
385	C₂²	C₄₇×#390	1	1	yes	characteristic
386	C₂²	C₂×#99×C₄₇	1	1	yes	characteristic
387	C₂²	C₄₇×#410	1	1	yes	characteristic
388	C₂²	C₂×#102×C₄₇	1	1	yes	characteristic
389	C₂²	C₄₇×#418	1	1	yes	characteristic
390	C₂²	C₄₇×#421	1	1	yes	characteristic
391	C₂²	C₄₇×#421	1	1	yes	characteristic
392	C₂²	C₄₇×#459	1	2	yes	—
393	C₂²	C₄₇×#460	1	2	yes	—
394	C₄	—	2	2	no	—
395	C₄	—	2	2	no	—
396	C₄	—	2	2	no	—
397	C₄	—	2	1	no	—
398	C₄	—	2	2	no	—
399	C₄	—	2	1	no	—
400	C₄	—	4	1	no	—
401	C₄	—	8	4	no	—
402	C₄	—	8	2	no	—
403	C₂	—	2	2	no	—
404	C₂	—	2	2	no	—
405	C₂	—	16	2	no	—
406	C₂	C₄₇×#1510	1	1	yes	characteristic
407	C₂	C₄₇×#1514	1	1	yes	characteristic
408	C₂	C₄₇×#1517	1	1	yes	characteristic
409	C₂	C₄₇×#1519	1	1	yes	characteristic
410	C₂	C₄₇×#1963	1	1	yes	characteristic
411	C₂	C₄₇×#1964	1	1	yes	characteristic
412	C₂	C₄₇×#1982	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₄₇	C₂×C₂²⋊C₄
commutator	C₂²×C₄	C₂²×C₄×C₄₇
Frattini, cosocle	C₂³×C₄	C₂³×C₄₇
prime radical	C₄₇×#2856	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂² ▷ 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
2. C₄₇×#1797	C₂	semidirect
3. C₂×C₄₇×#327	C₂	semidirect
4. C₄₇×#1434	C₂	semidirect
5. C₂×#127×C₄₇	C₄	semidirect
14. C₄₇×#390	C₄	semidirect
15. C₄₇×#384	C₄	semidirect
52. #95×C₄₇	D₄	semidirect
163. #9715	C₄₇	direct (N × H)
198. #1797	C₂×C₄₇	semidirect
199. C₂×#327	C₂×C₄₇	semidirect
200. #1434	C₂×C₄₇	semidirect
211. C₂×#127	C₄×C₄₇	semidirect
220. #390	C₄×C₄₇	semidirect
221. #384	C₄×C₄₇	semidirect
227. C₄₇	#9715	direct (N × H)
259. #95	D₄×C₄₇	semidirect

Maximal subgroups

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

subgroup	index
C₄₇×#2856	2
C₄₇×#1797	2
C₂×C₄₇×#327	2
C₄₇×#1434	2
#9715	47

Subgroups — C47×#9715 #26049413

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₇×#9715 #26049413