Subgroups — C₄₇×#20735 #26060433

Order 12032.

1326 conjugacy classes of subgroups.

The subgroup lattice has 366 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄×Q₈×C₄₇	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄₇×#431	C₂	1	1	yes	maximal, characteristic
3	C₄₇×#2283	C₂	1	1	yes	maximal, characteristic
4	C₄₇×#1823	C₂	1	2	yes	maximal
5	C₄₇×#1805	C₂	1	4	yes	maximal, complemented
6	C₄₇×#1787	C₂	1	2	yes	maximal
7	C₄×#103×C₄₇	C₂	1	4	yes	maximal, complemented
8	C₂³×Q₈×C₄₇	C₂²	1	1	yes	characteristic
9	C₂×C₄×Q₈×C₄₇	—	2	4	no	—
10	C₂×C₄×Q₈×C₄₇	—	2	1	no	—
11	C₂×C₄×Q₈×C₄₇	—	2	1	no	—
12	C₂×C₄×Q₈×C₄₇	C₄	1	8	yes	complemented
13	C₂×C₄×Q₈×C₄₇	C₂²	1	2	yes	—
14	C₂×C₄×Q₈×C₄₇	C₂²	1	2	yes	—
15	C₂²×C₄⋊C₄×C₄₇	—	2	1	no	—
16	C₂²×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
17	C₂²×C₄²×C₄₇	—	2	1	no	—
18	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
19	C₄₇×#431	—	2	4	no	—
20	C₂×C₄⋊C₈×C₄₇	C₂²	1	2	yes	—
21	C₂×#103×C₄₇	C₂²	1	8	yes	—
22	C₂×C₂²⋊C₈×C₄₇	C₂²	1	2	yes	—
23	C₂×C₄×C₈×C₄₇	C₂²	1	2	yes	—
24	C₄₇×#383	—	2	1	no	—
25	C₄₇×#382	C₂²	1	2	yes	—
26	C₄₇×#381	—	2	1	no	—
27	C₄₇×#380	C₂²	1	2	yes	—
28	C₄×C₄⋊C₄×C₄₇	C₂²	1	2	yes	—
29	C₄×C₂²⋊C₄×C₄₇	—	2	1	no	—
30	C₄₇×#376	—	2	1	no	—
31	C₄₇×#340	C₂²	1	8	yes	—
32	C₂²×Q₈×C₄₇	—	2	8	no	—
33	C₂²×Q₈×C₄₇	—	2	2	no	—
34	C₂²×Q₈×C₄₇	—	2	1	no	—
35	C₂²×Q₈×C₄₇	C₂×C₄	1	4	yes	—
36	C₂²×Q₈×C₄₇	C₂³	1	2	yes	—
37	C₂³×C₄×C₄₇	—	2	1	no	—
38	C₂³×C₄×C₄₇	—	2	1	no	—
39	C₂³×C₄×C₄₇	D₄	1	1	yes	characteristic
40	C₂³×C₄×C₄₇	D₄	1	1	yes	characteristic
41	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
42	C₂²×C₈×C₄₇	C₂³	1	4	yes	—
43	C₄×Q₈×C₄₇	—	2	8	no	—
44	C₄×Q₈×C₄₇	—	2	8	no	—
45	C₄×Q₈×C₄₇	—	2	4	no	—
46	C₄×Q₈×C₄₇	—	2	4	no	—
47	C₄×Q₈×C₄₇	C₂×C₄	1	8	yes	—
48	C₄×Q₈×C₄₇	C₂×C₄	1	8	yes	—
49	C₂×C₄⋊C₄×C₄₇	—	2	8	no	—
50	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
51	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
52	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
53	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
54	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	4	yes	—
55	C₂×C₄⋊C₄×C₄₇	C₂³	1	4	yes	—
56	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
57	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
58	C₂×C₄²×C₄₇	—	2	8	no	—
59	C₂×C₄²×C₄₇	—	2	2	no	—
60	C₂×C₄²×C₄₇	—	2	2	no	—
61	C₂×C₄²×C₄₇	—	2	2	no	—
62	C₂×C₄²×C₄₇	C₂×C₄	1	4	yes	—
63	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
64	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
65	C₂×C₄²×C₄₇	D₄	1	4	yes	—
66	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
67	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
68	C₄⋊C₈×C₄₇	—	2	4	no	—
69	#103×C₄₇	—	2	16	no	—
70	C₂²⋊C₈×C₄₇	—	2	4	no	—
71	C₄×C₈×C₄₇	—	2	4	no	—
72	#95×C₄₇	—	2	2	no	—
73	#95×C₄₇	—	2	2	no	—
74	#95×C₄₇	—	2	2	no	—
75	#95×C₄₇	—	2	2	no	—
76	C₂⁴×C₄₇	C₂×D₄	1	1	yes	characteristic
77	C₂×Q₈×C₄₇	—	2	16	no	—
78	C₂×Q₈×C₄₇	—	2	8	no	—
79	C₂×Q₈×C₄₇	—	2	16	no	—
80	C₂×Q₈×C₄₇	—	2	4	no	—
81	C₂×Q₈×C₄₇	—	2	2	no	—
82	C₂×Q₈×C₄₇	—	2	4	no	—
83	C₂×Q₈×C₄₇	C₂²×C₄	1	4	yes	—
84	C₂×Q₈×C₄₇	#41	1	8	yes	—
85	C₂²×C₄×C₄₇	—	2	8	no	—
86	C₂²×C₄×C₄₇	—	2	4	no	—
87	C₂²×C₄×C₄₇	—	2	4	no	—
88	C₂²×C₄×C₄₇	—	2	2	no	—
89	C₂²×C₄×C₄₇	—	2	4	no	—
90	C₂²×C₄×C₄₇	—	2	4	no	—
91	C₂²×C₄×C₄₇	—	2	4	no	—
92	C₂²×C₄×C₄₇	—	2	2	no	—
93	C₂²×C₄×C₄₇	—	2	4	no	—
94	C₂²×C₄×C₄₇	—	4	4	no	—
95	C₂²×C₄×C₄₇	C₂²⋊C₄	1	4	yes	—
96	C₂²×C₄×C₄₇	C₂²⋊C₄	1	4	yes	—
97	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
98	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
99	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
100	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
101	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
102	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
103	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
104	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
105	C₂×C₈×C₄₇	—	2	4	no	—
106	C₂×C₈×C₄₇	—	2	8	no	—
107	C₄⋊C₄×C₄₇	—	2	8	no	—
108	C₄⋊C₄×C₄₇	—	2	8	no	—
109	C₄⋊C₄×C₄₇	—	2	4	no	—
110	C₄⋊C₄×C₄₇	—	2	2	no	—
111	C₄⋊C₄×C₄₇	—	2	8	no	—
112	C₄⋊C₄×C₄₇	C₂²×C₄	1	4	yes	—
113	C₂²⋊C₄×C₄₇	—	4	4	no	—
114	C₄²×C₄₇	—	2	8	no	—
115	C₄²×C₄₇	—	2	8	no	—
116	C₄²×C₄₇	—	4	4	no	—
117	C₄²×C₄₇	C₂²⋊C₄	1	4	yes	—
118	C₄²×C₄₇	C₂²⋊C₄	1	4	yes	—
119	C₄²×C₄₇	C₂²×C₄	1	2	yes	—
120	C₄²×C₄₇	C₂²×C₄	1	2	yes	—
121	C₄²×C₄₇	C₂×D₄	1	2	yes	—
122	C₄²×C₄₇	C₂×D₄	1	2	yes	—
123	C₂³×C₄₇	—	2	2	no	—
124	C₂³×C₄₇	—	2	2	no	—
125	C₂³×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
126	C₂³×C₄₇	#135	1	4	yes	—
127	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
128	Q₈×C₄₇	—	2	16	no	—
129	Q₈×C₄₇	—	2	4	no	—
130	Q₈×C₄₇	—	2	8	no	—
131	Q₈×C₄₇	#117	1	8	yes	—
132	C₂×C₄×C₄₇	—	2	16	no	—
133	C₂×C₄×C₄₇	—	2	4	no	—
134	C₂×C₄×C₄₇	—	2	8	no	—
135	C₂×C₄×C₄₇	—	2	2	no	—
136	C₂×C₄×C₄₇	—	2	2	no	—
137	C₂×C₄×C₄₇	—	2	2	no	—
138	C₂×C₄×C₄₇	—	2	2	no	—
139	C₂×C₄×C₄₇	—	2	8	no	—
140	C₂×C₄×C₄₇	—	2	4	no	—
141	C₂×C₄×C₄₇	—	2	4	no	—
142	C₂×C₄×C₄₇	—	2	8	no	—
143	C₂×C₄×C₄₇	—	2	4	no	—
144	C₂×C₄×C₄₇	—	4	4	no	—
145	C₂×C₄×C₄₇	—	4	8	no	—
146	C₂×C₄×C₄₇	—	4	4	no	—
147	C₂×C₄×C₄₇	—	4	4	no	—
148	C₂×C₄×C₄₇	—	4	4	no	—
149	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
150	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
151	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
152	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
153	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
154	C₂×C₄×C₄₇	#137	1	4	yes	—
155	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
156	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
157	C₂×C₄×C₄₇	C₂×#41	1	4	yes	—
158	C₈×C₄₇	—	4	4	no	—
159	#20735	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
160	C₂²×C₄₇	—	2	8	no	—
161	C₂²×C₄₇	—	2	2	no	—
162	C₂²×C₄₇	—	2	2	no	—
163	C₂²×C₄₇	#416	1	4	yes	—
164	C₂²×C₄₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
165	C₂²×C₄₇	#525	1	2	yes	—
166	C₂²×C₄₇	C₂×#135	1	2	yes	—
167	C₂²×C₄₇	C₂×#137	1	2	yes	—
168	C₄×C₄₇	—	2	2	no	—
169	C₄×C₄₇	—	2	2	no	—
170	C₄×C₄₇	—	2	2	no	—
171	C₄×C₄₇	—	2	8	no	—
172	C₄×C₄₇	—	2	2	no	—
173	C₄×C₄₇	—	4	4	no	—
174	C₄×C₄₇	—	8	4	no	—
175	C₄×C₄₇	#419	1	4	yes	—
176	C₄×C₄₇	C₂×#117	1	2	yes	—
177	C₄×C₄₇	#525	1	2	yes	—
178	C₂²×C₄×Q₈	C₂×C₄₇	1	1	yes	characteristic
179	C₂×#431	C₂×C₄₇	1	1	yes	characteristic
180	#2283	C₂×C₄₇	1	1	yes	characteristic
181	#1823	C₂×C₄₇	1	2	yes	—
182	#1805	C₂×C₄₇	1	4	yes	complemented
183	#1787	C₂×C₄₇	1	2	yes	—
184	C₄×#103	C₂×C₄₇	1	4	yes	complemented
185	C₂×C₄₇	—	2	4	no	—
186	C₂×C₄₇	#2280	1	1	yes	characteristic
187	C₂×C₄₇	C₂×#416	1	1	yes	characteristic
188	C₂×C₄₇	C₂×#419	1	1	yes	characteristic
189	C₂×C₄₇	#3108	1	4	yes	—
190	C₂³×Q₈	C₂²×C₄₇	1	1	yes	characteristic
191	C₂×C₄×Q₈	—	2	4	no	—
192	C₂×C₄×Q₈	—	2	1	no	—
193	C₂×C₄×Q₈	—	2	1	no	—
194	C₂×C₄×Q₈	C₄×C₄₇	1	8	yes	complemented
195	C₂×C₄×Q₈	C₂²×C₄₇	1	2	yes	—
196	C₂×C₄×Q₈	C₂²×C₄₇	1	2	yes	—
197	C₂²×C₄⋊C₄	—	2	1	no	—
198	C₂²×C₄⋊C₄	C₂²×C₄₇	1	1	yes	characteristic
199	C₂²×C₄²	—	2	1	no	—
200	C₂²×C₄²	C₂²×C₄₇	1	1	yes	characteristic
201	#431	—	2	4	no	—
202	C₂×C₄⋊C₈	C₂²×C₄₇	1	2	yes	—
203	C₂×#103	C₂²×C₄₇	1	8	yes	—
204	C₂×C₂²⋊C₈	C₂²×C₄₇	1	2	yes	—
205	C₂×C₄×C₈	C₂²×C₄₇	1	2	yes	—
206	#383	—	2	1	no	—
207	#382	C₂²×C₄₇	1	2	yes	—
208	#381	—	2	1	no	—
209	#380	C₂²×C₄₇	1	2	yes	—
210	C₄×C₄⋊C₄	C₂²×C₄₇	1	2	yes	—
211	C₄×C₂²⋊C₄	—	2	1	no	—
212	#376	—	2	1	no	—
213	#340	C₂²×C₄₇	1	8	yes	—
214	C₄₇	#20735	1	1	yes	characteristic, direct product factor, Sylow
215	C₂²×Q₈	—	2	8	no	—
216	C₂²×Q₈	—	2	2	no	—
217	C₂²×Q₈	—	2	1	no	—
218	C₂²×Q₈	C₂×C₄×C₄₇	1	4	yes	—
219	C₂²×Q₈	C₂³×C₄₇	1	2	yes	—
220	C₂³×C₄	—	2	1	no	—
221	C₂³×C₄	—	2	1	no	—
222	C₂³×C₄	D₄×C₄₇	1	1	yes	characteristic
223	C₂³×C₄	D₄×C₄₇	1	1	yes	characteristic
224	C₂³×C₄	C₂³×C₄₇	1	1	yes	characteristic
225	C₂²×C₈	C₂³×C₄₇	1	4	yes	—
226	C₄×Q₈	—	2	8	no	—
227	C₄×Q₈	—	2	8	no	—
228	C₄×Q₈	—	2	4	no	—
229	C₄×Q₈	—	2	4	no	—
230	C₄×Q₈	C₂×C₄×C₄₇	1	8	yes	—
231	C₄×Q₈	C₂×C₄×C₄₇	1	8	yes	—
232	C₂×C₄⋊C₄	—	2	8	no	—
233	C₂×C₄⋊C₄	—	2	2	no	—
234	C₂×C₄⋊C₄	—	2	2	no	—
235	C₂×C₄⋊C₄	—	2	1	no	—
236	C₂×C₄⋊C₄	—	2	2	no	—
237	C₂×C₄⋊C₄	C₂×C₄×C₄₇	1	4	yes	—
238	C₂×C₄⋊C₄	C₂³×C₄₇	1	4	yes	—
239	C₂×C₄⋊C₄	C₂³×C₄₇	1	2	yes	—
240	C₂×C₂²⋊C₄	—	2	2	no	—
241	C₂×C₄²	—	2	8	no	—
242	C₂×C₄²	—	2	2	no	—
243	C₂×C₄²	—	2	2	no	—
244	C₂×C₄²	—	2	2	no	—
245	C₂×C₄²	C₂×C₄×C₄₇	1	4	yes	—
246	C₂×C₄²	D₄×C₄₇	1	1	yes	characteristic
247	C₂×C₄²	D₄×C₄₇	1	1	yes	characteristic
248	C₂×C₄²	D₄×C₄₇	1	4	yes	—
249	C₂×C₄²	C₂³×C₄₇	1	1	yes	characteristic
250	C₂×C₄²	C₂³×C₄₇	1	1	yes	characteristic
251	C₄⋊C₈	—	2	4	no	—
252	#103	—	2	16	no	—
253	C₂²⋊C₈	—	2	4	no	—
254	C₄×C₈	—	2	4	no	—
255	#95	—	2	2	no	—
256	#95	—	2	2	no	—
257	#95	—	2	2	no	—
258	#95	—	2	2	no	—
259	C₂⁴	C₂×D₄×C₄₇	1	1	yes	characteristic
260	C₂×Q₈	—	2	16	no	—
261	C₂×Q₈	—	2	8	no	—
262	C₂×Q₈	—	2	16	no	—
263	C₂×Q₈	—	2	4	no	—
264	C₂×Q₈	—	2	2	no	—
265	C₂×Q₈	—	2	4	no	—
266	C₂×Q₈	C₂²×C₄×C₄₇	1	4	yes	—
267	C₂×Q₈	#41×C₄₇	1	8	yes	—
268	C₂²×C₄	—	2	8	no	—
269	C₂²×C₄	—	2	4	no	—
270	C₂²×C₄	—	2	4	no	—
271	C₂²×C₄	—	2	2	no	—
272	C₂²×C₄	—	2	4	no	—
273	C₂²×C₄	—	2	4	no	—
274	C₂²×C₄	—	2	4	no	—
275	C₂²×C₄	—	2	2	no	—
276	C₂²×C₄	—	2	4	no	—
277	C₂²×C₄	—	4	4	no	—
278	C₂²×C₄	C₂²⋊C₄×C₄₇	1	4	yes	—
279	C₂²×C₄	C₂²⋊C₄×C₄₇	1	4	yes	—
280	C₂²×C₄	C₂²×C₄×C₄₇	1	2	yes	—
281	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
282	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
283	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
284	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
285	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
286	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
287	C₂²×C₄	C₂⁴×C₄₇	1	1	yes	characteristic
288	C₂×C₈	—	2	4	no	—
289	C₂×C₈	—	2	8	no	—
290	C₄⋊C₄	—	2	8	no	—
291	C₄⋊C₄	—	2	8	no	—
292	C₄⋊C₄	—	2	4	no	—
293	C₄⋊C₄	—	2	2	no	—
294	C₄⋊C₄	—	2	8	no	—
295	C₄⋊C₄	C₂²×C₄×C₄₇	1	4	yes	—
296	C₂²⋊C₄	—	4	4	no	—
297	C₄²	—	2	8	no	—
298	C₄²	—	2	8	no	—
299	C₄²	—	4	4	no	—
300	C₄²	C₂²⋊C₄×C₄₇	1	4	yes	—
301	C₄²	C₂²⋊C₄×C₄₇	1	4	yes	—
302	C₄²	C₂²×C₄×C₄₇	1	2	yes	—
303	C₄²	C₂²×C₄×C₄₇	1	2	yes	—
304	C₄²	C₂×D₄×C₄₇	1	2	yes	—
305	C₄²	C₂×D₄×C₄₇	1	2	yes	—
306	C₂³	—	2	2	no	—
307	C₂³	—	2	2	no	—
308	C₂³	C₂×C₂²⋊C₄×C₄₇	1	2	yes	—
309	C₂³	#135×C₄₇	1	4	yes	—
310	C₂³	C₂²×D₄×C₄₇	1	1	yes	characteristic
311	Q₈	—	2	16	no	—
312	Q₈	—	2	4	no	—
313	Q₈	—	2	8	no	—
314	Q₈	#117×C₄₇	1	8	yes	—
315	C₂×C₄	—	2	16	no	—
316	C₂×C₄	—	2	4	no	—
317	C₂×C₄	—	2	8	no	—
318	C₂×C₄	—	2	2	no	—
319	C₂×C₄	—	2	2	no	—
320	C₂×C₄	—	2	2	no	—
321	C₂×C₄	—	2	2	no	—
322	C₂×C₄	—	2	8	no	—
323	C₂×C₄	—	2	4	no	—
324	C₂×C₄	—	2	4	no	—
325	C₂×C₄	—	2	8	no	—
326	C₂×C₄	—	2	4	no	—
327	C₂×C₄	—	4	4	no	—
328	C₂×C₄	—	4	8	no	—
329	C₂×C₄	—	4	4	no	—
330	C₂×C₄	—	4	4	no	—
331	C₂×C₄	—	4	4	no	—
332	C₂×C₄	C₂×C₂²⋊C₄×C₄₇	1	2	yes	—
333	C₂×C₄	C₂×C₂²⋊C₄×C₄₇	1	2	yes	—
334	C₂×C₄	C₂×C₂²⋊C₄×C₄₇	1	2	yes	—
335	C₂×C₄	C₂×C₂²⋊C₄×C₄₇	1	2	yes	—
336	C₂×C₄	C₂×C₂²⋊C₄×C₄₇	1	2	yes	—
337	C₂×C₄	#137×C₄₇	1	4	yes	—
338	C₂×C₄	C₂³×C₄×C₄₇	1	1	yes	characteristic
339	C₂×C₄	C₂²×D₄×C₄₇	1	1	yes	characteristic
340	C₂×C₄	C₂×#41×C₄₇	1	4	yes	—
341	C₈	—	4	4	no	—
342	C₂²	—	2	2	no	—
343	C₂²	—	2	8	no	—
344	C₂²	—	2	2	no	—
345	C₂²	C₄₇×#416	1	4	yes	—
346	C₂²	C₂²×C₂²⋊C₄×C₄₇	1	1	yes	characteristic
347	C₂²	C₄₇×#525	1	2	yes	—
348	C₂²	C₂×#135×C₄₇	1	2	yes	—
349	C₂²	C₂×#137×C₄₇	1	2	yes	—
350	C₄	—	2	8	no	—
351	C₄	—	2	2	no	—
352	C₄	—	2	2	no	—
353	C₄	—	2	2	no	—
354	C₄	—	2	2	no	—
355	C₄	—	4	4	no	—
356	C₄	—	8	4	no	—
357	C₄	C₄₇×#419	1	4	yes	—
358	C₄	C₂×#117×C₄₇	1	2	yes	—
359	C₄	C₄₇×#525	1	2	yes	—
360	C₂	—	2	4	no	—
361	C₂	C₄₇×#2280	1	1	yes	characteristic
362	C₂	C₂×C₄₇×#416	1	1	yes	characteristic
363	C₂	C₂×C₄₇×#419	1	1	yes	characteristic
364	C₂	C₄₇×#3108	1	4	yes	—

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

Complements

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

N	H ≅ G/N	type
5. C₄₇×#1805	C₂	semidirect
7. C₄×#103×C₄₇	C₂	semidirect
12. C₂×C₄×Q₈×C₄₇	C₄	semidirect
159. #20735	C₄₇	direct (N × H)
182. #1805	C₂×C₄₇	semidirect
184. C₄×#103	C₂×C₄₇	semidirect
194. C₂×C₄×Q₈	C₄×C₄₇	semidirect
214. C₄₇	#20735	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×C₄×Q₈×C₄₇	2
C₂×C₄₇×#431	2
C₄₇×#2283	2
C₄₇×#1823	2
C₄₇×#1805	2
C₄₇×#1787	2
C₄×#103×C₄₇	2
#20735	47

Subgroups — C47×#20735 #26060433

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₇×#20735 #26060433