Subgroups — C₄₇×#10963 #26050661

Order 12032.

978 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	C₂²×#101×C₄₇	C₂	1	2	yes	maximal
2	C₂×C₄×M₁₆×C₄₇	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄₇×#391	C₂	1	1	yes	maximal, characteristic
4	C₂×C₄₇×#343	C₂	1	2	yes	maximal
5	C₄₇×#1728	C₂	1	1	yes	maximal, characteristic
6	C₂³×Q₈×C₄₇	C₂²	1	1	yes	characteristic
7	C₂²×M₁₆×C₄₇	C₂²	1	2	yes	—
8	C₂²×M₁₆×C₄₇	C₂²	1	2	yes	—
9	C₂²×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
10	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
11	C₂×#101×C₄₇	—	2	4	no	—
12	C₂×#101×C₄₇	—	2	4	no	—
13	C₂×#101×C₄₇	C₄	1	8	yes	complemented
14	C₄×M₁₆×C₄₇	—	2	4	no	—
15	C₂×#97×C₄₇	—	2	1	no	—
16	C₂×C₄×C₈×C₄₇	—	2	1	no	—
17	C₄₇×#391	—	2	2	no	—
18	C₄₇×#391	—	2	1	no	—
19	C₄₇×#391	—	2	1	no	—
20	C₂×#95×C₄₇	C₄	1	4	yes	—
21	C₄₇×#343	—	2	4	no	—
22	C₄₇×#336	—	2	2	no	—
23	C₂²×Q₈×C₄₇	—	2	1	no	—
24	C₂²×Q₈×C₄₇	—	2	1	no	—
25	C₂²×Q₈×C₄₇	—	2	2	no	—
26	C₂²×Q₈×C₄₇	—	2	2	no	—
27	C₂²×Q₈×C₄₇	—	2	2	no	—
28	C₂²×Q₈×C₄₇	—	2	2	no	—
29	C₂²×Q₈×C₄₇	—	2	2	no	—
30	C₂²×Q₈×C₄₇	C₂×C₄	1	4	yes	—
31	C₂³×C₄×C₄₇	C₂×C₄	1	2	yes	—
32	C₂³×C₄×C₄₇	C₂×C₄	1	2	yes	—
33	C₂³×C₄×C₄₇	C₂×C₄	1	2	yes	—
34	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
35	C₂×M₁₆×C₄₇	—	2	2	no	—
36	C₂×M₁₆×C₄₇	—	2	2	no	—
37	C₂×M₁₆×C₄₇	—	2	2	no	—
38	C₂×M₁₆×C₄₇	—	2	2	no	—
39	C₂×M₁₆×C₄₇	—	2	2	no	—
40	C₂×M₁₆×C₄₇	—	2	2	no	—
41	C₂×M₁₆×C₄₇	—	2	2	no	—
42	C₂×M₁₆×C₄₇	—	2	2	no	—
43	C₂×M₁₆×C₄₇	C₂×C₄	1	4	yes	—
44	C₂×M₁₆×C₄₇	C₂×C₄	1	4	yes	—
45	C₂×M₁₆×C₄₇	D₄	1	4	yes	—
46	C₂×M₁₆×C₄₇	D₄	1	4	yes	—
47	C₂²×C₈×C₄₇	—	2	2	no	—
48	C₂²×C₈×C₄₇	—	2	2	no	—
49	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
50	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
51	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
52	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
53	C₂×C₄²×C₄₇	—	2	2	no	—
54	C₂×C₄²×C₄₇	—	2	2	no	—
55	C₂×C₄²×C₄₇	D₄	1	2	yes	—
56	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
57	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
58	#101×C₄₇	—	2	16	no	—
59	#97×C₄₇	—	2	4	no	—
60	C₄×C₈×C₄₇	—	2	4	no	—
61	#95×C₄₇	—	2	4	no	—
62	#95×C₄₇	—	2	4	no	—
63	C₂⁴×C₄₇	C₂²×C₄	1	1	yes	characteristic
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	—	2	4	no	—
69	C₂×Q₈×C₄₇	—	2	4	no	—
70	C₂×Q₈×C₄₇	—	4	1	no	—
71	C₂×Q₈×C₄₇	—	4	2	no	—
72	C₂×Q₈×C₄₇	—	4	2	no	—
73	C₂×Q₈×C₄₇	—	4	2	no	—
74	C₂×Q₈×C₄₇	—	4	1	no	—
75	C₂×Q₈×C₄₇	—	4	2	no	—
76	C₂×Q₈×C₄₇	—	4	2	no	—
77	C₂×Q₈×C₄₇	—	4	1	no	—
78	C₂×Q₈×C₄₇	—	4	2	no	—
79	C₂×Q₈×C₄₇	—	4	1	no	—
80	C₂²×C₄×C₄₇	—	2	2	no	—
81	C₂²×C₄×C₄₇	—	2	2	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	4	no	—
86	C₂²×C₄×C₄₇	—	2	2	no	—
87	C₂²×C₄×C₄₇	—	2	4	no	—
88	C₂²×C₄×C₄₇	—	4	2	no	—
89	C₂²×C₄×C₄₇	—	4	4	no	—
90	C₂²×C₄×C₄₇	C₄²	1	4	yes	—
91	C₂²×C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
92	C₂²×C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
93	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
94	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
95	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
96	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
97	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
98	C₂²×C₄×C₄₇	#41	1	2	yes	—
99	C₂²×C₄×C₄₇	#41	1	2	yes	—
100	C₂²×C₄×C₄₇	#41	1	2	yes	—
101	M₁₆×C₄₇	—	2	4	no	—
102	M₁₆×C₄₇	—	2	4	no	—
103	M₁₆×C₄₇	—	2	4	no	—
104	M₁₆×C₄₇	—	2	4	no	—
105	M₁₆×C₄₇	—	2	4	no	—
106	M₁₆×C₄₇	—	4	2	no	—
107	M₁₆×C₄₇	—	4	2	no	—
108	M₁₆×C₄₇	C₂²⋊C₄	1	8	yes	—
109	C₂×C₈×C₄₇	—	2	4	no	—
110	C₂×C₈×C₄₇	—	2	4	no	—
111	C₂×C₈×C₄₇	—	2	4	no	—
112	C₂×C₈×C₄₇	—	2	4	no	—
113	C₂×C₈×C₄₇	—	4	2	no	—
114	C₂×C₈×C₄₇	—	4	2	no	—
115	C₄⋊C₄×C₄₇	—	4	2	no	—
116	C₄⋊C₄×C₄₇	—	4	1	no	—
117	C₄⋊C₄×C₄₇	—	4	1	no	—
118	C₄²×C₄₇	—	2	1	no	—
119	C₄²×C₄₇	—	2	1	no	—
120	C₄²×C₄₇	—	2	4	no	—
121	C₄²×C₄₇	—	2	1	no	—
122	C₄²×C₄₇	—	2	1	no	—
123	C₂³×C₄₇	—	2	2	no	—
124	C₂³×C₄₇	—	2	2	no	—
125	C₂³×C₄₇	C₂×C₄²	1	1	yes	characteristic
126	C₂³×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
127	C₂³×C₄₇	#117	1	1	yes	characteristic
128	C₂³×C₄₇	C₄×D₄	1	2	yes	—
129	C₂³×C₄₇	C₄×D₄	1	2	yes	—
130	Q₈×C₄₇	—	4	4	no	—
131	Q₈×C₄₇	—	4	4	no	—
132	Q₈×C₄₇	—	4	4	no	—
133	Q₈×C₄₇	—	4	4	no	—
134	C₂×C₄×C₄₇	—	2	2	no	—
135	C₂×C₄×C₄₇	—	2	2	no	—
136	C₂×C₄×C₄₇	—	2	8	no	—
137	C₂×C₄×C₄₇	—	2	4	no	—
138	C₂×C₄×C₄₇	—	2	2	no	—
139	C₂×C₄×C₄₇	—	2	2	no	—
140	C₂×C₄×C₄₇	—	2	2	no	—
141	C₂×C₄×C₄₇	—	4	8	no	—
142	C₂×C₄×C₄₇	—	4	2	no	—
143	C₂×C₄×C₄₇	—	4	4	no	—
144	C₂×C₄×C₄₇	—	4	2	no	—
145	C₂×C₄×C₄₇	—	4	2	no	—
146	C₂×C₄×C₄₇	—	4	4	no	—
147	C₂×C₄×C₄₇	—	8	4	no	—
148	C₂×C₄×C₄₇	#101	1	4	yes	complemented
149	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
150	C₂×C₄×C₄₇	#117	1	2	yes	—
151	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
152	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
153	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
154	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
155	C₂×C₄×C₄₇	#120	1	1	yes	characteristic
156	C₂×C₄×C₄₇	#121	1	2	yes	—
157	C₂×C₄×C₄₇	#121	1	2	yes	—
158	C₂×C₄×C₄₇	#121	1	2	yes	—
159	C₂×C₄×C₄₇	#123	1	2	yes	—
160	C₂×C₄×C₄₇	#123	1	1	yes	characteristic
161	C₂×C₄×C₄₇	#124	1	1	yes	characteristic
162	C₂×C₄×C₄₇	#124	1	2	yes	—
163	C₂×C₄×C₄₇	#126	1	2	yes	—
164	C₂×C₄×C₄₇	#127	1	1	yes	characteristic
165	C₈×C₄₇	—	2	8	no	—
166	C₈×C₄₇	—	4	4	no	—
167	#10963	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
168	C₂²×C₄₇	—	2	4	no	—
169	C₂²×C₄₇	—	2	2	no	—
170	C₂²×C₄₇	—	2	2	no	—
171	C₂²×C₄₇	—	2	2	no	—
172	C₂²×C₄₇	—	2	2	no	—
173	C₂²×C₄₇	C₄×C₂²⋊C₄	1	2	yes	—
174	C₂²×C₄₇	C₄×C₂²⋊C₄	1	1	yes	characteristic
175	C₂²×C₄₇	#386	1	1	yes	characteristic
176	C₂²×C₄₇	#388	1	2	yes	—
177	C₂²×C₄₇	#390	1	1	yes	characteristic
178	C₂²×C₄₇	C₂×#101	1	2	yes	—
179	C₂²×C₄₇	#413	1	2	yes	—
180	C₄×C₄₇	—	2	4	no	—
181	C₄×C₄₇	—	4	2	no	—
182	C₄×C₄₇	—	4	4	no	—
183	C₄×C₄₇	—	8	2	no	—
184	C₄×C₄₇	#386	1	2	yes	—
185	C₄×C₄₇	#388	1	2	yes	—
186	C₄×C₄₇	#388	1	2	yes	—
187	C₄×C₄₇	#390	1	2	yes	—
188	C₂²×#101	C₂×C₄₇	1	2	yes	—
189	C₂×C₄×M₁₆	C₂×C₄₇	1	1	yes	characteristic
190	C₂×#391	C₂×C₄₇	1	1	yes	characteristic
191	C₂×#343	C₂×C₄₇	1	2	yes	—
192	#1728	C₂×C₄₇	1	1	yes	characteristic
193	C₂×C₄₇	—	2	2	no	—
194	C₂×C₄₇	—	2	2	no	—
195	C₂×C₄₇	#1437	1	1	yes	characteristic
196	C₂×C₄₇	C₄×#101	1	2	yes	—
197	C₂×C₄₇	#1901	1	2	yes	—
198	C₂×C₄₇	#1966	1	1	yes	characteristic
199	C₂×C₄₇	#1967	1	1	yes	characteristic
200	C₂³×Q₈	C₂²×C₄₇	1	1	yes	characteristic
201	C₂²×M₁₆	C₂²×C₄₇	1	2	yes	—
202	C₂²×M₁₆	C₂²×C₄₇	1	2	yes	—
203	C₂²×C₄⋊C₄	C₂²×C₄₇	1	1	yes	characteristic
204	C₂²×C₄²	C₂²×C₄₇	1	1	yes	characteristic
205	C₂×#101	—	2	4	no	—
206	C₂×#101	—	2	4	no	—
207	C₂×#101	C₄×C₄₇	1	8	yes	complemented
208	C₄×M₁₆	—	2	4	no	—
209	C₂×#97	—	2	1	no	—
210	C₂×C₄×C₈	—	2	1	no	—
211	#391	—	2	2	no	—
212	#391	—	2	1	no	—
213	#391	—	2	1	no	—
214	C₂×#95	C₄×C₄₇	1	4	yes	—
215	#343	—	2	4	no	—
216	#336	—	2	2	no	—
217	C₄₇	#10963	1	1	yes	characteristic, direct product factor, Sylow
218	C₂²×Q₈	—	2	1	no	—
219	C₂²×Q₈	—	2	1	no	—
220	C₂²×Q₈	—	2	2	no	—
221	C₂²×Q₈	—	2	2	no	—
222	C₂²×Q₈	—	2	2	no	—
223	C₂²×Q₈	—	2	2	no	—
224	C₂²×Q₈	—	2	2	no	—
225	C₂²×Q₈	C₂×C₄×C₄₇	1	4	yes	—
226	C₂³×C₄	C₂×C₄×C₄₇	1	2	yes	—
227	C₂³×C₄	C₂×C₄×C₄₇	1	2	yes	—
228	C₂³×C₄	C₂×C₄×C₄₇	1	2	yes	—
229	C₂³×C₄	C₂³×C₄₇	1	1	yes	characteristic
230	C₂×M₁₆	—	2	2	no	—
231	C₂×M₁₆	—	2	2	no	—
232	C₂×M₁₆	—	2	2	no	—
233	C₂×M₁₆	—	2	2	no	—
234	C₂×M₁₆	—	2	2	no	—
235	C₂×M₁₆	—	2	2	no	—
236	C₂×M₁₆	—	2	2	no	—
237	C₂×M₁₆	—	2	2	no	—
238	C₂×M₁₆	C₂×C₄×C₄₇	1	4	yes	—
239	C₂×M₁₆	C₂×C₄×C₄₇	1	4	yes	—
240	C₂×M₁₆	D₄×C₄₇	1	4	yes	—
241	C₂×M₁₆	D₄×C₄₇	1	4	yes	—
242	C₂²×C₈	—	2	2	no	—
243	C₂²×C₈	—	2	2	no	—
244	C₂×C₄⋊C₄	—	2	2	no	—
245	C₂×C₄⋊C₄	—	2	1	no	—
246	C₂×C₄⋊C₄	—	2	1	no	—
247	C₂×C₄⋊C₄	—	2	2	no	—
248	C₂×C₄²	—	2	2	no	—
249	C₂×C₄²	—	2	2	no	—
250	C₂×C₄²	D₄×C₄₇	1	2	yes	—
251	C₂×C₄²	D₄×C₄₇	1	1	yes	characteristic
252	C₂×C₄²	D₄×C₄₇	1	1	yes	characteristic
253	#101	—	2	16	no	—
254	#97	—	2	4	no	—
255	C₄×C₈	—	2	4	no	—
256	#95	—	2	4	no	—
257	#95	—	2	4	no	—
258	C₂⁴	C₂²×C₄×C₄₇	1	1	yes	characteristic
259	C₂×Q₈	—	2	4	no	—
260	C₂×Q₈	—	2	4	no	—
261	C₂×Q₈	—	2	4	no	—
262	C₂×Q₈	—	2	4	no	—
263	C₂×Q₈	—	2	4	no	—
264	C₂×Q₈	—	2	4	no	—
265	C₂×Q₈	—	4	1	no	—
266	C₂×Q₈	—	4	2	no	—
267	C₂×Q₈	—	4	2	no	—
268	C₂×Q₈	—	4	2	no	—
269	C₂×Q₈	—	4	1	no	—
270	C₂×Q₈	—	4	2	no	—
271	C₂×Q₈	—	4	2	no	—
272	C₂×Q₈	—	4	1	no	—
273	C₂×Q₈	—	4	2	no	—
274	C₂×Q₈	—	4	1	no	—
275	C₂²×C₄	—	2	2	no	—
276	C₂²×C₄	—	2	2	no	—
277	C₂²×C₄	—	2	4	no	—
278	C₂²×C₄	—	2	4	no	—
279	C₂²×C₄	—	2	4	no	—
280	C₂²×C₄	—	2	4	no	—
281	C₂²×C₄	—	2	2	no	—
282	C₂²×C₄	—	2	4	no	—
283	C₂²×C₄	—	4	2	no	—
284	C₂²×C₄	—	4	4	no	—
285	C₂²×C₄	C₄²×C₄₇	1	4	yes	—
286	C₂²×C₄	C₂²⋊C₄×C₄₇	1	2	yes	—
287	C₂²×C₄	C₂²⋊C₄×C₄₇	1	2	yes	—
288	C₂²×C₄	C₂²×C₄×C₄₇	1	2	yes	—
289	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
290	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
291	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
292	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
293	C₂²×C₄	#41×C₄₇	1	2	yes	—
294	C₂²×C₄	#41×C₄₇	1	2	yes	—
295	C₂²×C₄	#41×C₄₇	1	2	yes	—
296	M₁₆	—	2	4	no	—
297	M₁₆	—	2	4	no	—
298	M₁₆	—	2	4	no	—
299	M₁₆	—	2	4	no	—
300	M₁₆	—	2	4	no	—
301	M₁₆	—	4	2	no	—
302	M₁₆	—	4	2	no	—
303	M₁₆	C₂²⋊C₄×C₄₇	1	8	yes	—
304	C₂×C₈	—	2	4	no	—
305	C₂×C₈	—	2	4	no	—
306	C₂×C₈	—	2	4	no	—
307	C₂×C₈	—	2	4	no	—
308	C₂×C₈	—	4	2	no	—
309	C₂×C₈	—	4	2	no	—
310	C₄⋊C₄	—	4	2	no	—
311	C₄⋊C₄	—	4	1	no	—
312	C₄⋊C₄	—	4	1	no	—
313	C₄²	—	2	1	no	—
314	C₄²	—	2	1	no	—
315	C₄²	—	2	4	no	—
316	C₄²	—	2	1	no	—
317	C₄²	—	2	1	no	—
318	C₂³	—	2	2	no	—
319	C₂³	—	2	2	no	—
320	C₂³	C₂×C₄²×C₄₇	1	1	yes	characteristic
321	C₂³	C₂×C₂²⋊C₄×C₄₇	1	1	yes	characteristic
322	C₂³	#117×C₄₇	1	1	yes	characteristic
323	C₂³	C₄×D₄×C₄₇	1	2	yes	—
324	C₂³	C₄×D₄×C₄₇	1	2	yes	—
325	Q₈	—	4	4	no	—
326	Q₈	—	4	4	no	—
327	Q₈	—	4	4	no	—
328	Q₈	—	4	4	no	—
329	C₂×C₄	—	2	2	no	—
330	C₂×C₄	—	2	2	no	—
331	C₂×C₄	—	2	8	no	—
332	C₂×C₄	—	2	4	no	—
333	C₂×C₄	—	2	2	no	—
334	C₂×C₄	—	2	2	no	—
335	C₂×C₄	—	2	2	no	—
336	C₂×C₄	—	4	8	no	—
337	C₂×C₄	—	4	2	no	—
338	C₂×C₄	—	4	4	no	—
339	C₂×C₄	—	4	2	no	—
340	C₂×C₄	—	4	2	no	—
341	C₂×C₄	—	4	4	no	—
342	C₂×C₄	—	8	4	no	—
343	C₂×C₄	#101×C₄₇	1	4	yes	complemented
344	C₂×C₄	C₂×C₂²⋊C₄×C₄₇	1	2	yes	—
345	C₂×C₄	#117×C₄₇	1	2	yes	—
346	C₂×C₄	C₄×D₄×C₄₇	1	2	yes	—
347	C₂×C₄	C₄×D₄×C₄₇	1	2	yes	—
348	C₂×C₄	C₄×D₄×C₄₇	1	2	yes	—
349	C₂×C₄	C₄×D₄×C₄₇	1	2	yes	—
350	C₂×C₄	#120×C₄₇	1	1	yes	characteristic
351	C₂×C₄	#121×C₄₇	1	2	yes	—
352	C₂×C₄	#121×C₄₇	1	2	yes	—
353	C₂×C₄	#121×C₄₇	1	2	yes	—
354	C₂×C₄	#123×C₄₇	1	2	yes	—
355	C₂×C₄	#123×C₄₇	1	1	yes	characteristic
356	C₂×C₄	#124×C₄₇	1	1	yes	characteristic
357	C₂×C₄	#124×C₄₇	1	2	yes	—
358	C₂×C₄	#126×C₄₇	1	2	yes	—
359	C₂×C₄	#127×C₄₇	1	1	yes	characteristic
360	C₈	—	2	8	no	—
361	C₈	—	4	4	no	—
362	C₂²	—	2	2	no	—
363	C₂²	—	2	2	no	—
364	C₂²	—	2	4	no	—
365	C₂²	—	2	2	no	—
366	C₂²	—	2	2	no	—
367	C₂²	C₄×C₂²⋊C₄×C₄₇	1	2	yes	—
368	C₂²	C₄×C₂²⋊C₄×C₄₇	1	1	yes	characteristic
369	C₂²	C₄₇×#386	1	1	yes	characteristic
370	C₂²	C₄₇×#388	1	2	yes	—
371	C₂²	C₄₇×#390	1	1	yes	characteristic
372	C₂²	C₂×#101×C₄₇	1	2	yes	—
373	C₂²	C₄₇×#413	1	2	yes	—
374	C₄	—	2	4	no	—
375	C₄	—	4	2	no	—
376	C₄	—	4	4	no	—
377	C₄	—	8	2	no	—
378	C₄	C₄₇×#386	1	2	yes	—
379	C₄	C₄₇×#388	1	2	yes	—
380	C₄	C₄₇×#388	1	2	yes	—
381	C₄	C₄₇×#390	1	2	yes	—
382	C₂	—	2	2	no	—
383	C₂	—	2	2	no	—
384	C₂	C₄₇×#1437	1	1	yes	characteristic
385	C₂	C₄×#101×C₄₇	1	2	yes	—
386	C₂	C₄₇×#1901	1	2	yes	—
387	C₂	C₄₇×#1966	1	1	yes	characteristic
388	C₂	C₄₇×#1967	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₄₇	C₂×C₂²⋊C₄
commutator	C₂³	C₂×C₄²×C₄₇
Frattini, cosocle	C₂³×C₄	C₂³×C₄₇
prime radical	C₂⁴×C₄₇	C₂²×C₄
LCS	G ▷ C₂³ ▷ C₂ ▷ 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
13. C₂×#101×C₄₇	C₄	semidirect
148. C₂×C₄×C₄₇	#101	semidirect
167. #10963	C₄₇	direct (N × H)
207. C₂×#101	C₄×C₄₇	semidirect
217. C₄₇	#10963	direct (N × H)
343. C₂×C₄	#101×C₄₇	semidirect

Maximal subgroups

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

subgroup	index
C₂²×#101×C₄₇	2
C₂×C₄×M₁₆×C₄₇	2
C₂×C₄₇×#391	2
C₂×C₄₇×#343	2
C₄₇×#1728	2
#10963	47

Subgroups — C47×#10963 #26050661

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₇×#10963 #26050661