Subgroups — C₄₇×#9089 #26048787

Order 12032.

564 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₇×#2972	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₄₇×#442	C₂	1	1	yes	maximal, characteristic
3	C₄₇×#1478	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄₇×#1478	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₇×#1460	C₂	1	1	yes	maximal, characteristic, complemented
6	C₄₇×#1281	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄₇×#1275	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×D₈×C₄₇	C₄	1	1	yes	characteristic
9	C₂×C₄×D₄×C₄₇	C₂²	1	1	yes	characteristic
10	C₂×C₄×D₄×C₄₇	C₂²	1	1	yes	characteristic
11	C₄₇×#442	—	2	2	no	—
12	C₄₇×#442	—	2	2	no	—
13	C₈×D₄×C₄₇	—	2	2	no	—
14	C₈×D₄×C₄₇	—	2	2	no	—
15	C₄₇×#431	C₂²	1	1	yes	characteristic
16	C₄₇×#431	C₂²	1	1	yes	characteristic
17	C₄₇×#431	C₂²	1	1	yes	characteristic
18	C₄₇×#431	C₂²	1	1	yes	characteristic
19	C₂×#106×C₄₇	C₄	1	1	yes	characteristic
20	C₂×#102×C₄₇	C₄	1	1	yes	characteristic
21	C₂×#102×C₄₇	C₄	1	1	yes	characteristic
22	C₂×C₂²⋊C₈×C₄₇	—	2	2	no	—
23	C₂×#97×C₄₇	C₂²	1	1	yes	characteristic
24	C₄₇×D₄⋊C₈	—	2	2	no	—
25	C₄₇×D₄⋊C₈	—	2	2	no	—
26	C₄₇×#323	—	2	2	no	—
27	C₂²×D₄×C₄₇	C₂×C₄	1	1	yes	characteristic
28	C₂²×D₄×C₄₇	C₂×C₄	1	1	yes	characteristic
29	C₂³×C₄×C₄₇	—	2	1	no	—
30	C₂³×C₄×C₄₇	—	2	1	no	—
31	C₂×D₈×C₄₇	—	2	2	no	—
32	C₂×D₈×C₄₇	—	2	2	no	—
33	C₂×D₈×C₄₇	C₈	1	4	yes	complemented
34	C₂²×C₈×C₄₇	—	2	4	no	—
35	C₂²×C₈×C₄₇	C₂×C₄	1	1	yes	characteristic
36	C₂²×C₈×C₄₇	C₂×C₄	1	1	yes	characteristic
37	C₄×D₄×C₄₇	—	2	1	no	—
38	C₄×D₄×C₄₇	—	2	1	no	—
39	C₄×D₄×C₄₇	—	2	1	no	—
40	C₄×D₄×C₄₇	—	2	1	no	—
41	C₄×D₄×C₄₇	—	2	1	no	—
42	C₄×D₄×C₄₇	—	2	1	no	—
43	C₄×D₄×C₄₇	D₄	1	2	yes	—
44	C₄×D₄×C₄₇	D₄	1	2	yes	—
45	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
46	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
47	C₂×C₂²⋊C₄×C₄₇	—	2	1	no	—
48	C₂×C₂²⋊C₄×C₄₇	—	2	1	no	—
49	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
50	#106×C₄₇	—	2	2	no	—
51	C₄⋊C₈×C₄₇	—	2	1	no	—
52	C₄⋊C₈×C₄₇	—	2	1	no	—
53	C₄⋊C₈×C₄₇	—	2	1	no	—
54	C₄⋊C₈×C₄₇	—	2	1	no	—
55	#102×C₄₇	—	2	2	no	—
56	#102×C₄₇	—	2	2	no	—
57	C₂²⋊C₈×C₄₇	—	2	4	no	—
58	C₂²⋊C₈×C₄₇	—	2	1	no	—
59	C₂²⋊C₈×C₄₇	—	2	1	no	—
60	C₂²⋊C₈×C₄₇	—	2	1	no	—
61	C₂²⋊C₈×C₄₇	D₄	1	2	yes	—
62	#97×C₄₇	—	2	1	no	—
63	#97×C₄₇	—	2	1	no	—
64	C₄×C₈×C₄₇	—	2	1	no	—
65	C₄×C₈×C₄₇	—	2	1	no	—
66	C₄×C₈×C₄₇	—	2	1	no	—
67	C₄×C₈×C₄₇	D₄	1	2	yes	—
68	C₂⁴×C₄₇	—	2	1	no	—
69	C₂⁴×C₄₇	—	2	1	no	—
70	C₂×D₄×C₄₇	—	2	1	no	—
71	C₂×D₄×C₄₇	—	2	1	no	—
72	C₂×D₄×C₄₇	—	2	1	no	—
73	C₂×D₄×C₄₇	—	2	1	no	—
74	C₂×D₄×C₄₇	—	2	1	no	—
75	C₂×D₄×C₄₇	—	2	1	no	—
76	C₂×D₄×C₄₇	—	2	1	no	—
77	C₂×D₄×C₄₇	—	2	1	no	—
78	C₂×D₄×C₄₇	C₂²⋊C₄	1	2	yes	—
79	C₂×D₄×C₄₇	C₂×C₈	1	2	yes	—
80	C₂×D₄×C₄₇	C₂×C₈	1	2	yes	complemented
81	C₂×D₄×C₄₇	M₁₆	1	2	yes	—
82	C₂²×C₄×C₄₇	—	2	1	no	—
83	C₂²×C₄×C₄₇	—	2	2	no	—
84	C₂²×C₄×C₄₇	—	2	2	no	—
85	C₂²×C₄×C₄₇	—	2	1	no	—
86	C₂²×C₄×C₄₇	—	4	1	no	—
87	C₂²×C₄×C₄₇	—	4	1	no	—
88	C₂²×C₄×C₄₇	—	8	2	no	—
89	C₂²×C₄×C₄₇	—	8	2	no	—
90	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
91	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
92	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
93	D₈×C₄₇	—	2	8	no	—
94	C₂×C₈×C₄₇	—	2	1	no	—
95	C₂×C₈×C₄₇	—	2	1	no	—
96	C₂×C₈×C₄₇	—	2	1	no	—
97	C₂×C₈×C₄₇	—	2	2	no	—
98	C₂×C₈×C₄₇	—	2	2	no	—
99	C₂×C₈×C₄₇	—	2	1	no	—
100	C₂×C₈×C₄₇	—	2	1	no	—
101	C₂×C₈×C₄₇	—	4	1	no	—
102	C₂×C₈×C₄₇	—	4	1	no	—
103	C₂×C₈×C₄₇	—	8	4	no	—
104	C₂×C₈×C₄₇	C₂×C₈	1	2	yes	complemented
105	C₄⋊C₄×C₄₇	—	2	1	no	—
106	C₄⋊C₄×C₄₇	—	2	1	no	—
107	C₄⋊C₄×C₄₇	—	2	1	no	—
108	C₄⋊C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
109	C₂²⋊C₄×C₄₇	—	2	2	no	—
110	C₂²⋊C₄×C₄₇	—	2	2	no	—
111	C₂²⋊C₄×C₄₇	—	4	1	no	—
112	C₂²⋊C₄×C₄₇	—	4	1	no	—
113	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
114	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
115	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
116	C₄²×C₄₇	#41	1	1	yes	characteristic
117	C₂³×C₄₇	—	2	2	no	—
118	C₂³×C₄₇	—	2	2	no	—
119	C₂³×C₄₇	—	2	2	no	—
120	C₂³×C₄₇	—	2	2	no	—
121	C₂³×C₄₇	—	4	1	no	—
122	C₂³×C₄₇	—	4	1	no	—
123	C₂³×C₄₇	—	8	1	no	—
124	C₂³×C₄₇	—	8	1	no	—
125	C₂³×C₄₇	—	8	1	no	—
126	C₂³×C₄₇	—	8	1	no	—
127	C₂³×C₄₇	C₄×D₄	1	1	yes	characteristic
128	D₄×C₄₇	—	2	2	no	—
129	D₄×C₄₇	—	2	2	no	—
130	D₄×C₄₇	—	2	2	no	—
131	D₄×C₄₇	—	2	2	no	—
132	D₄×C₄₇	—	2	2	no	—
133	D₄×C₄₇	—	4	1	no	—
134	D₄×C₄₇	—	4	1	no	—
135	D₄×C₄₇	C₂²⋊C₈	1	4	yes	—
136	C₂×C₄×C₄₇	—	2	2	no	—
137	C₂×C₄×C₄₇	—	4	1	no	—
138	C₂×C₄×C₄₇	—	4	1	no	—
139	C₂×C₄×C₄₇	—	4	4	no	—
140	C₂×C₄×C₄₇	—	4	1	no	—
141	C₂×C₄×C₄₇	—	8	2	no	—
142	C₂×C₄×C₄₇	—	8	2	no	—
143	C₂×C₄×C₄₇	—	8	2	no	—
144	C₂×C₄×C₄₇	—	8	1	no	—
145	C₂×C₄×C₄₇	—	8	1	no	—
146	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
147	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
148	C₂×C₄×C₄₇	#120	1	1	yes	characteristic
149	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
150	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
151	C₂×C₄×C₄₇	#123	1	1	yes	characteristic
152	C₂×C₄×C₄₇	C₂²×C₈	1	1	yes	characteristic
153	C₂×C₄×C₄₇	C₂×M₁₆	1	1	yes	characteristic
154	C₂×C₄×C₄₇	#131	1	1	yes	characteristic
155	C₂×C₄×C₄₇	#131	1	1	yes	characteristic
156	C₈×C₄₇	—	2	2	no	—
157	C₈×C₄₇	—	4	2	no	—
158	C₈×C₄₇	—	4	2	no	—
159	C₈×C₄₇	—	4	1	no	—
160	C₈×C₄₇	—	8	1	no	—
161	C₈×C₄₇	—	8	1	no	—
162	#9089	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
163	C₂²×C₄₇	—	2	1	no	—
164	C₂²×C₄₇	—	2	1	no	—
165	C₂²×C₄₇	—	2	4	no	—
166	C₂²×C₄₇	—	4	2	no	—
167	C₂²×C₄₇	—	4	2	no	—
168	C₂²×C₄₇	—	4	2	no	—
169	C₂²×C₄₇	—	8	2	no	—
170	C₂²×C₄₇	—	8	2	no	—
171	C₂²×C₄₇	—	8	2	no	—
172	C₂²×C₄₇	—	8	2	no	—
173	C₂²×C₄₇	—	8	1	no	—
174	C₂²×C₄₇	—	8	1	no	—
175	C₂²×C₄₇	#386	1	1	yes	characteristic
176	C₂²×C₄₇	C₈×D₄	1	1	yes	characteristic
177	C₂²×C₄₇	#435	1	1	yes	characteristic
178	C₄×C₄₇	—	2	1	no	—
179	C₄×C₄₇	—	2	1	no	—
180	C₄×C₄₇	—	2	1	no	—
181	C₄×C₄₇	—	2	1	no	—
182	C₄×C₄₇	—	4	2	no	—
183	C₄×C₄₇	—	8	1	no	—
184	C₄×C₄₇	C₂×C₂²⋊C₈	1	1	yes	characteristic
185	C₄×C₄₇	#408	1	1	yes	characteristic
186	C₄×C₄₇	C₈×D₄	1	1	yes	characteristic
187	C₄×C₄₇	#435	1	1	yes	characteristic
188	#2972	C₂×C₄₇	1	1	yes	characteristic, complemented
189	C₂×#442	C₂×C₄₇	1	1	yes	characteristic
190	#1478	C₂×C₄₇	1	1	yes	characteristic, complemented
191	#1478	C₂×C₄₇	1	1	yes	characteristic, complemented
192	#1460	C₂×C₄₇	1	1	yes	characteristic, complemented
193	#1281	C₂×C₄₇	1	1	yes	characteristic, complemented
194	#1275	C₂×C₄₇	1	1	yes	characteristic, complemented
195	C₂×C₄₇	—	2	1	no	—
196	C₂×C₄₇	—	2	1	no	—
197	C₂×C₄₇	—	4	4	no	—
198	C₂×C₄₇	—	8	2	no	—
199	C₂×C₄₇	#1869	1	1	yes	characteristic
200	C₂×C₄₇	#1903	1	1	yes	characteristic
201	C₂×C₄₇	#1904	1	1	yes	characteristic
202	C₂²×D₈	C₄×C₄₇	1	1	yes	characteristic
203	C₂×C₄×D₄	C₂²×C₄₇	1	1	yes	characteristic
204	C₂×C₄×D₄	C₂²×C₄₇	1	1	yes	characteristic
205	#442	—	2	2	no	—
206	#442	—	2	2	no	—
207	C₈×D₄	—	2	2	no	—
208	C₈×D₄	—	2	2	no	—
209	#431	C₂²×C₄₇	1	1	yes	characteristic
210	#431	C₂²×C₄₇	1	1	yes	characteristic
211	#431	C₂²×C₄₇	1	1	yes	characteristic
212	#431	C₂²×C₄₇	1	1	yes	characteristic
213	C₂×#106	C₄×C₄₇	1	1	yes	characteristic
214	C₂×#102	C₄×C₄₇	1	1	yes	characteristic
215	C₂×#102	C₄×C₄₇	1	1	yes	characteristic
216	C₂×C₂²⋊C₈	—	2	2	no	—
217	C₂×#97	C₂²×C₄₇	1	1	yes	characteristic
218	D₄⋊C₈	—	2	2	no	—
219	D₄⋊C₈	—	2	2	no	—
220	#323	—	2	2	no	—
221	C₄₇	#9089	1	1	yes	characteristic, direct product factor, Sylow
222	C₂²×D₄	C₂×C₄×C₄₇	1	1	yes	characteristic
223	C₂²×D₄	C₂×C₄×C₄₇	1	1	yes	characteristic
224	C₂³×C₄	—	2	1	no	—
225	C₂³×C₄	—	2	1	no	—
226	C₂×D₈	—	2	2	no	—
227	C₂×D₈	—	2	2	no	—
228	C₂×D₈	C₈×C₄₇	1	4	yes	complemented
229	C₂²×C₈	—	2	4	no	—
230	C₂²×C₈	C₂×C₄×C₄₇	1	1	yes	characteristic
231	C₂²×C₈	C₂×C₄×C₄₇	1	1	yes	characteristic
232	C₄×D₄	—	2	1	no	—
233	C₄×D₄	—	2	1	no	—
234	C₄×D₄	—	2	1	no	—
235	C₄×D₄	—	2	1	no	—
236	C₄×D₄	—	2	1	no	—
237	C₄×D₄	—	2	1	no	—
238	C₄×D₄	D₄×C₄₇	1	2	yes	—
239	C₄×D₄	D₄×C₄₇	1	2	yes	—
240	C₂×C₄⋊C₄	C₂×C₄×C₄₇	1	1	yes	characteristic
241	C₂×C₄⋊C₄	C₂×C₄×C₄₇	1	1	yes	characteristic
242	C₂×C₂²⋊C₄	—	2	1	no	—
243	C₂×C₂²⋊C₄	—	2	1	no	—
244	C₂×C₄²	C₂³×C₄₇	1	1	yes	characteristic
245	#106	—	2	2	no	—
246	C₄⋊C₈	—	2	1	no	—
247	C₄⋊C₈	—	2	1	no	—
248	C₄⋊C₈	—	2	1	no	—
249	C₄⋊C₈	—	2	1	no	—
250	#102	—	2	2	no	—
251	#102	—	2	2	no	—
252	C₂²⋊C₈	—	2	4	no	—
253	C₂²⋊C₈	—	2	1	no	—
254	C₂²⋊C₈	—	2	1	no	—
255	C₂²⋊C₈	—	2	1	no	—
256	C₂²⋊C₈	D₄×C₄₇	1	2	yes	—
257	#97	—	2	1	no	—
258	#97	—	2	1	no	—
259	C₄×C₈	—	2	1	no	—
260	C₄×C₈	—	2	1	no	—
261	C₄×C₈	—	2	1	no	—
262	C₄×C₈	D₄×C₄₇	1	2	yes	—
263	C₂⁴	—	2	1	no	—
264	C₂⁴	—	2	1	no	—
265	C₂×D₄	—	2	1	no	—
266	C₂×D₄	—	2	1	no	—
267	C₂×D₄	—	2	1	no	—
268	C₂×D₄	—	2	1	no	—
269	C₂×D₄	—	2	1	no	—
270	C₂×D₄	—	2	1	no	—
271	C₂×D₄	—	2	1	no	—
272	C₂×D₄	—	2	1	no	—
273	C₂×D₄	C₂²⋊C₄×C₄₇	1	2	yes	—
274	C₂×D₄	C₂×C₈×C₄₇	1	2	yes	—
275	C₂×D₄	C₂×C₈×C₄₇	1	2	yes	complemented
276	C₂×D₄	M₁₆×C₄₇	1	2	yes	—
277	C₂²×C₄	—	2	1	no	—
278	C₂²×C₄	—	2	2	no	—
279	C₂²×C₄	—	2	2	no	—
280	C₂²×C₄	—	2	1	no	—
281	C₂²×C₄	—	4	1	no	—
282	C₂²×C₄	—	4	1	no	—
283	C₂²×C₄	—	8	2	no	—
284	C₂²×C₄	—	8	2	no	—
285	C₂²×C₄	C₂²×C₄×C₄₇	1	1	yes	characteristic
286	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
287	C₂²×C₄	#41×C₄₇	1	1	yes	characteristic
288	D₈	—	2	8	no	—
289	C₂×C₈	—	2	1	no	—
290	C₂×C₈	—	2	1	no	—
291	C₂×C₈	—	2	1	no	—
292	C₂×C₈	—	2	2	no	—
293	C₂×C₈	—	2	2	no	—
294	C₂×C₈	—	2	1	no	—
295	C₂×C₈	—	2	1	no	—
296	C₂×C₈	—	4	1	no	—
297	C₂×C₈	—	4	1	no	—
298	C₂×C₈	—	8	4	no	—
299	C₂×C₈	C₂×C₈×C₄₇	1	2	yes	complemented
300	C₄⋊C₄	—	2	1	no	—
301	C₄⋊C₄	—	2	1	no	—
302	C₄⋊C₄	—	2	1	no	—
303	C₄⋊C₄	C₂²⋊C₄×C₄₇	1	2	yes	—
304	C₂²⋊C₄	—	2	2	no	—
305	C₂²⋊C₄	—	2	2	no	—
306	C₂²⋊C₄	—	4	1	no	—
307	C₂²⋊C₄	—	4	1	no	—
308	C₄²	C₂×D₄×C₄₇	1	1	yes	characteristic
309	C₄²	C₂×D₄×C₄₇	1	1	yes	characteristic
310	C₄²	C₂×D₄×C₄₇	1	1	yes	characteristic
311	C₄²	#41×C₄₇	1	1	yes	characteristic
312	C₂³	—	2	2	no	—
313	C₂³	—	2	2	no	—
314	C₂³	—	2	2	no	—
315	C₂³	—	2	2	no	—
316	C₂³	—	4	1	no	—
317	C₂³	—	4	1	no	—
318	C₂³	—	8	1	no	—
319	C₂³	—	8	1	no	—
320	C₂³	—	8	1	no	—
321	C₂³	—	8	1	no	—
322	C₂³	C₄×D₄×C₄₇	1	1	yes	characteristic
323	D₄	—	2	2	no	—
324	D₄	—	2	2	no	—
325	D₄	—	2	2	no	—
326	D₄	—	2	2	no	—
327	D₄	—	2	2	no	—
328	D₄	—	4	1	no	—
329	D₄	—	4	1	no	—
330	D₄	C₂²⋊C₈×C₄₇	1	4	yes	—
331	C₂×C₄	—	2	2	no	—
332	C₂×C₄	—	4	1	no	—
333	C₂×C₄	—	4	1	no	—
334	C₂×C₄	—	4	4	no	—
335	C₂×C₄	—	4	1	no	—
336	C₂×C₄	—	8	2	no	—
337	C₂×C₄	—	8	2	no	—
338	C₂×C₄	—	8	2	no	—
339	C₂×C₄	—	8	1	no	—
340	C₂×C₄	—	8	1	no	—
341	C₂×C₄	C₂×C₂²⋊C₄×C₄₇	1	1	yes	characteristic
342	C₂×C₄	C₄×D₄×C₄₇	1	1	yes	characteristic
343	C₂×C₄	#120×C₄₇	1	1	yes	characteristic
344	C₂×C₄	#121×C₄₇	1	1	yes	characteristic
345	C₂×C₄	#121×C₄₇	1	1	yes	characteristic
346	C₂×C₄	#123×C₄₇	1	1	yes	characteristic
347	C₂×C₄	C₂²×C₈×C₄₇	1	1	yes	characteristic
348	C₂×C₄	C₂×M₁₆×C₄₇	1	1	yes	characteristic
349	C₂×C₄	#131×C₄₇	1	1	yes	characteristic
350	C₂×C₄	#131×C₄₇	1	1	yes	characteristic
351	C₈	—	2	2	no	—
352	C₈	—	4	2	no	—
353	C₈	—	4	2	no	—
354	C₈	—	4	1	no	—
355	C₈	—	8	1	no	—
356	C₈	—	8	1	no	—
357	C₂²	—	2	1	no	—
358	C₂²	—	2	1	no	—
359	C₂²	—	2	4	no	—
360	C₂²	—	4	2	no	—
361	C₂²	—	4	2	no	—
362	C₂²	—	4	2	no	—
363	C₂²	—	8	2	no	—
364	C₂²	—	8	2	no	—
365	C₂²	—	8	2	no	—
366	C₂²	—	8	2	no	—
367	C₂²	—	8	1	no	—
368	C₂²	—	8	1	no	—
369	C₂²	C₄₇×#386	1	1	yes	characteristic
370	C₂²	C₈×D₄×C₄₇	1	1	yes	characteristic
371	C₂²	C₄₇×#435	1	1	yes	characteristic
372	C₄	—	2	1	no	—
373	C₄	—	2	1	no	—
374	C₄	—	2	1	no	—
375	C₄	—	2	1	no	—
376	C₄	—	4	2	no	—
377	C₄	—	8	1	no	—
378	C₄	C₂×C₂²⋊C₈×C₄₇	1	1	yes	characteristic
379	C₄	C₄₇×#408	1	1	yes	characteristic
380	C₄	C₈×D₄×C₄₇	1	1	yes	characteristic
381	C₄	C₄₇×#435	1	1	yes	characteristic
382	C₂	—	2	1	no	—
383	C₂	—	2	1	no	—
384	C₂	—	4	4	no	—
385	C₂	—	8	2	no	—
386	C₂	C₄₇×#1869	1	1	yes	characteristic
387	C₂	C₄₇×#1903	1	1	yes	characteristic
388	C₂	C₄₇×#1904	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₄₇	#386
commutator	C₂×C₄	C₂²×C₈×C₄₇
Frattini, cosocle	C₂×C₄²	C₂³×C₄₇
prime radical	C₂²×D₈×C₄₇	C₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄₇ ◁ C₂×C₄²×C₄₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₄₇×#2972	C₂	semidirect
3. C₄₇×#1478	C₂	semidirect
4. C₄₇×#1478	C₂	semidirect
5. C₄₇×#1460	C₂	semidirect
6. C₄₇×#1281	C₂	semidirect
7. C₄₇×#1275	C₂	semidirect
33. C₂×D₈×C₄₇	C₈	semidirect
80. C₂×D₄×C₄₇	C₂×C₈	semidirect
104. C₂×C₈×C₄₇	C₂×C₈	semidirect
162. #9089	C₄₇	direct (N × H)
188. #2972	C₂×C₄₇	semidirect
190. #1478	C₂×C₄₇	semidirect
191. #1478	C₂×C₄₇	semidirect
192. #1460	C₂×C₄₇	semidirect
193. #1281	C₂×C₄₇	semidirect
194. #1275	C₂×C₄₇	semidirect
221. C₄₇	#9089	direct (N × H)
228. C₂×D₈	C₈×C₄₇	semidirect
275. C₂×D₄	C₂×C₈×C₄₇	semidirect
299. C₂×C₈	C₂×C₈×C₄₇	semidirect

Maximal subgroups

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

subgroup	index
C₄₇×#2972	2
C₂×C₄₇×#442	2
C₄₇×#1478	2
C₄₇×#1460	2
C₄₇×#1281	2
C₄₇×#1275	2
#9089	47

Subgroups — C47×#9089 #26048787

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₇×#9089 #26048787