Subgroups — #20257147

Order 6016.

1660 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#13094069	C₂	1	1	yes	maximal, characteristic, complemented
2	#15689772	C₂	1	4	yes	maximal, complemented
3	#15689767	C₂	1	4	yes	maximal, complemented
4	#15689761	C₂	1	4	yes	maximal, complemented
5	D₄×C₂²⋊D₄₇	C₂	1	4	yes	maximal, complemented
6	#15689701	C₂	1	2	yes	maximal, complemented
7	#15689682	C₂	1	4	yes	maximal, complemented
8	#15689669	C₂	1	2	yes	maximal, complemented
9	C₂×#13093996	C₂	1	4	yes	maximal, complemented
10	C₂×D₄×Dic₄₇	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×H(5,𝔽₂)×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
12	#13094069	—	2	8	no	—
13	C₂×#10625350	C₂²	1	2	yes	complemented
14	C₂×#10625352	C₂²	1	4	yes	complemented
15	C₂²×C₂²⋊D₄₇	C₂²	1	4	yes	complemented
16	C₂²×C₂²⋊D₄₇	C₂²	1	4	yes	complemented
17	C₂×D₄×D₄₇	C₂²	1	4	yes	complemented
18	C₂³×Dic₄₇	C₂²	1	2	yes	complemented
19	#13094022	C₂²	1	2	yes	complemented
20	#13094020	C₂²	1	2	yes	complemented
21	#13094013	C₂²	1	2	yes	complemented
22	#13094011	C₂²	1	2	yes	complemented
23	#13094007	C₂²	1	8	yes	complemented
24	#13094005	C₂²	1	8	yes	complemented
25	#13094003	C₂²	1	4	yes	complemented
26	#13094000	C₂²	1	4	yes	complemented
27	#13093998	C₂²	1	4	yes	complemented
28	#13093996	C₂²	1	8	yes	complemented
29	#13093996	C₂²	1	8	yes	complemented
30	#13093996	C₂²	1	4	yes	complemented
31	#13093996	C₂²	1	8	yes	complemented
32	#13093996	C₂²	1	4	yes	complemented
33	#13093995	C₂²	1	4	yes	complemented
34	#13093993	C₂²	1	8	yes	complemented
35	#13093992	C₂²	1	8	yes	complemented
36	D₄×Dic₄₇	C₂²	1	4	yes	complemented
37	D₄×Dic₄₇	C₂²	1	4	yes	complemented
38	C₄×C₂²⋊D₄₇	C₂²	1	4	yes	complemented
39	C₄×C₂²⋊D₄₇	C₂²	1	4	yes	complemented
40	C₂×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic, complemented
41	C₂×Dic₄₇⋊C₄	C₂²	1	4	yes	complemented
42	C₂×C₂²⋊Dic₄₇	C₂²	1	4	yes	complemented
43	C₂×C₂²⋊Dic₄₇	C₂²	1	2	yes	complemented
44	C₂×(C₂×D₄₇)⋊C₄	C₂²	1	4	yes	complemented
45	C₂×C₄×Dic₄₇	C₂²	1	1	yes	characteristic, complemented
46	H(5,𝔽₂)×C₄₇	—	2	8	no	—
47	C₂×#41×C₄₇	C₂²	1	4	yes	complemented
48	C₂×#41×C₄₇	C₂²	1	2	yes	complemented
49	C₂²×D₄×C₄₇	C₂²	1	1	yes	characteristic
50	C₂²×D₄×C₄₇	C₂²	1	4	yes	complemented
51	C₂²×D₄×C₄₇	C₂²	1	4	yes	complemented
52	C₂⁴×C₄₇	C₂³	1	4	yes	—
53	C₂⁴×C₄₇	C₂³	1	2	yes	—
54	C₂³×D₄₇	C₂³	1	4	yes	—
55	#41×C₄₇	—	2	16	no	—
56	#41×C₄₇	—	2	8	no	—
57	C₂×Q₈×C₄₇	C₂³	1	2	yes	—
58	C₂×D₄×C₄₇	—	2	16	no	—
59	C₂×D₄×C₄₇	—	2	16	no	—
60	C₂×D₄×C₄₇	D₄	1	8	yes	complemented
61	C₂×D₄×C₄₇	C₂³	1	8	yes	—
62	C₂×D₄×C₄₇	C₂³	1	2	yes	—
63	C₂×D₄×C₄₇	C₂³	1	4	yes	—
64	C₂×D₄×C₄₇	C₂³	1	4	yes	—
65	C₂²×C₄×C₄₇	C₂³	1	4	yes	—
66	C₂²×C₄×C₄₇	C₂³	1	4	yes	—
67	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
68	C₂×C₂²⋊D₄₇	—	2	16	no	—
69	C₂×C₂²⋊D₄₇	—	4	8	no	—
70	C₂×C₂²⋊D₄₇	C₂³	1	4	yes	—
71	C₂×C₂²⋊D₄₇	C₂³	1	8	yes	—
72	C₂×C₂²⋊D₄₇	C₂³	1	4	yes	—
73	C₂×C₂²⋊D₄₇	C₂³	1	4	yes	—
74	C₂×C₂²⋊D₄₇	C₂³	1	8	yes	—
75	C₂²×Dic₄₇	—	4	4	no	—
76	C₂²×Dic₄₇	C₂³	1	1	yes	characteristic
77	C₂²×Dic₄₇	C₂³	1	4	yes	—
78	C₂²×Dic₄₇	C₂³	1	4	yes	—
79	C₂²×Dic₄₇	C₂³	1	1	yes	characteristic
80	C₂²×Dic₄₇	C₂³	1	4	yes	—
81	C₂²×Dic₄₇	C₂³	1	2	yes	—
82	#10625352	—	2	16	no	—
83	D₄×D₄₇	—	2	16	no	—
84	#10625350	—	2	8	no	—
85	C₂×D₁₈₈	C₂³	1	2	yes	—
86	C₂×C₄×D₄₇	C₂³	1	4	yes	—
87	C₂×Dic₉₄	C₂³	1	2	yes	—
88	C₂²⋊Dic₄₇	C₂³	1	4	yes	—
89	C₂²⋊Dic₄₇	C₂³	1	8	yes	—
90	C₂²⋊Dic₄₇	C₂³	1	8	yes	—
91	C₂²⋊Dic₄₇	C₂³	1	4	yes	—
92	(C₂×D₄₇)⋊C₄	C₂³	1	4	yes	—
93	(C₂×D₄₇)⋊C₄	C₂³	1	8	yes	—
94	(C₂×D₄₇)⋊C₄	C₂³	1	4	yes	—
95	C₄⋊Dic₄₇	C₂³	1	4	yes	—
96	Dic₄₇⋊C₄	C₂³	1	4	yes	—
97	Dic₄₇⋊C₄	C₂³	1	8	yes	—
98	Dic₄₇⋊C₄	C₂³	1	4	yes	—
99	C₄×Dic₄₇	C₂³	1	2	yes	—
100	C₄×Dic₄₇	C₂³	1	2	yes	—
101	C₂³×C₄₇	—	2	8	no	—
102	C₂³×C₄₇	—	4	2	no	—
103	C₂³×C₄₇	—	4	2	no	—
104	C₂³×C₄₇	—	4	4	no	—
105	C₂³×C₄₇	—	4	4	no	—
106	C₂³×C₄₇	C₂×D₄	1	8	yes	complemented
107	C₂³×C₄₇	C₂⁴	1	4	yes	—
108	C₂³×C₄₇	C₂⁴	1	4	yes	—
109	C₂³×C₄₇	C₂⁴	1	1	yes	characteristic
110	C₂²×D₄₇	—	2	8	no	—
111	C₂²×D₄₇	—	4	4	no	—
112	C₂²×D₄₇	—	4	4	no	—
113	C₂²×D₄₇	C₂⁴	1	4	yes	—
114	Q₈×C₄₇	—	2	4	no	—
115	D₄×C₄₇	—	2	16	no	—
116	D₄×C₄₇	—	2	8	no	—
117	D₄×C₄₇	—	2	4	no	—
118	D₄×C₄₇	C₂×D₄	1	16	yes	complemented
119	C₂×C₄×C₄₇	—	2	8	no	—
120	C₂×C₄×C₄₇	—	2	8	no	—
121	C₂×C₄×C₄₇	C₂×D₄	1	4	yes	complemented
122	C₂×C₄×C₄₇	C₂⁴	1	4	yes	—
123	C₂×C₄×C₄₇	C₂⁴	1	2	yes	—
124	C₂²⋊D₄₇	—	2	8	no	—
125	C₂²⋊D₄₇	—	2	16	no	—
126	C₂²⋊D₄₇	—	2	8	no	—
127	C₂²⋊D₄₇	—	4	8	no	—
128	C₂²⋊D₄₇	—	4	4	no	—
129	C₂×Dic₄₇	—	2	8	no	—
130	C₂×Dic₄₇	—	2	2	no	—
131	C₂×Dic₄₇	—	2	8	no	—
132	C₂×Dic₄₇	—	4	4	no	—
133	C₂×Dic₄₇	—	4	2	no	—
134	C₂×Dic₄₇	—	4	1	no	—
135	C₂×Dic₄₇	C₂⁴	1	2	yes	—
136	C₂×Dic₄₇	C₂⁴	1	1	yes	characteristic
137	C₂×Dic₄₇	C₂⁴	1	4	yes	—
138	C₂×Dic₄₇	C₂⁴	1	4	yes	—
139	C₂×Dic₄₇	C₂⁴	1	1	yes	characteristic
140	D₁₈₈	—	2	4	no	—
141	C₄×D₄₇	—	2	8	no	—
142	Dic₉₄	—	2	4	no	—
143	C₂²×C₄₇	—	2	1	no	—
144	C₂²×C₄₇	—	2	4	no	—
145	C₂²×C₄₇	—	2	1	no	—
146	C₂²×C₄₇	—	2	4	no	—
147	C₂²×C₄₇	—	2	4	no	—
148	C₂²×C₄₇	—	2	4	no	—
149	C₂²×C₄₇	—	2	4	no	—
150	C₂²×C₄₇	—	4	8	no	—
151	C₂²×C₄₇	—	8	8	no	—
152	C₂²×C₄₇	C₂²×D₄	1	8	yes	—
153	C₂²×C₄₇	C₂²×D₄	1	2	yes	—
154	C₂²×C₄₇	C₂⁵	1	1	yes	characteristic
155	C₂×D₄₇	—	2	4	no	—
156	C₂×D₄₇	—	2	4	no	—
157	C₂×D₄₇	—	2	4	no	—
158	C₂×D₄₇	—	8	8	no	—
159	C₄×C₄₇	—	2	4	no	—
160	C₄×C₄₇	C₂²×D₄	1	4	yes	—
161	Dic₄₇	—	2	4	no	—
162	Dic₄₇	—	2	1	no	—
163	Dic₄₇	—	2	4	no	—
164	Dic₄₇	—	2	2	no	—
165	Dic₄₇	H(5,𝔽₂)	1	2	yes	complemented
166	#3496	—	47	1	no	maximal, Sylow
167	C₂×C₄₇	—	2	8	no	—
168	C₂×C₄₇	—	2	2	no	—
169	C₂×C₄₇	—	4	4	no	—
170	C₂×C₄₇	C₂³×D₄	1	1	yes	characteristic
171	C₂×C₄₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
172	C₂×C₄₇	#585	1	1	yes	characteristic
173	D₄₇	—	4	4	no	—
174	C₂×H(5,𝔽₂)	—	47	1	no	—
175	C₂×H(5,𝔽₂)	D₄₇	1	1	yes	characteristic, complemented
176	#547	—	47	4	no	—
177	#546	—	47	4	no	—
178	#546	—	47	4	no	—
179	D₄²	—	47	4	no	—
180	#537	—	47	2	no	—
181	#534	—	47	4	no	—
182	#532	—	47	2	no	—
183	C₂×#121	—	47	4	no	—
184	C₂×C₄×D₄	—	47	1	no	—
185	C₄₇	#3496	1	1	yes	characteristic, complemented, Sylow
186	H(5,𝔽₂)	—	2	8	no	—
187	H(5,𝔽₂)	—	94	8	no	—
188	C₂×#41	—	47	4	no	—
189	C₂×#41	—	47	2	no	—
190	C₂×#41	C₂×D₄₇	1	2	yes	complemented
191	C₂×#41	C₂×D₄₇	1	4	yes	complemented
192	C₂²×D₄	—	47	4	no	—
193	C₂²×D₄	—	47	4	no	—
194	C₂²×D₄	—	47	4	no	—
195	C₂²×D₄	C₂×D₄₇	1	1	yes	characteristic
196	C₂²×D₄	C₂×D₄₇	1	4	yes	complemented
197	C₂²×D₄	C₂×D₄₇	1	4	yes	complemented
198	C₂³×C₄	—	47	2	no	—
199	C₄⋊Q₈	—	47	2	no	—
200	#127	—	47	2	no	—
201	#124	—	47	2	no	—
202	#124	—	47	2	no	—
203	#123	—	47	8	no	—
204	#123	—	47	8	no	—
205	C₂²⋊Q₈	—	47	4	no	—
206	C₂²⋊Q₈	—	47	4	no	—
207	#121	—	47	4	no	—
208	#121	—	47	8	no	—
209	#121	—	47	8	no	—
210	#121	—	47	8	no	—
211	#121	—	47	4	no	—
212	#121	—	47	4	no	—
213	#121	—	47	4	no	—
214	#120	—	47	8	no	—
215	#120	—	47	8	no	—
216	C₄×D₄	—	47	4	no	—
217	C₄×D₄	—	47	4	no	—
218	C₄×D₄	—	47	4	no	—
219	C₄×D₄	—	47	4	no	—
220	C₂×C₄⋊C₄	—	47	1	no	—
221	C₂×C₄⋊C₄	—	47	4	no	—
222	C₂×C₂²⋊C₄	—	47	2	no	—
223	C₂×C₂²⋊C₄	—	47	4	no	—
224	C₂×C₂²⋊C₄	—	47	4	no	—
225	C₂×C₄²	—	47	1	no	—
226	C₂⁴	—	47	4	no	—
227	C₂⁴	C₂²×D₄₇	1	4	yes	—
228	C₂⁴	C₂²×D₄₇	1	2	yes	—
229	#41	—	2	16	no	—
230	#41	—	2	8	no	—
231	#41	—	94	16	no	—
232	#41	—	94	8	no	—
233	C₂×Q₈	—	47	2	no	—
234	C₂×Q₈	C₂²×D₄₇	1	2	yes	—
235	C₂×D₄	—	2	16	no	—
236	C₂×D₄	—	2	16	no	—
237	C₂×D₄	—	47	4	no	—
238	C₂×D₄	—	47	8	no	—
239	C₂×D₄	—	47	4	no	—
240	C₂×D₄	—	47	4	no	—
241	C₂×D₄	—	47	8	no	—
242	C₂×D₄	—	47	2	no	—
243	C₂×D₄	—	94	16	no	—
244	C₂×D₄	—	94	16	no	—
245	C₂×D₄	—	188	8	no	—
246	C₂×D₄	C₂²⋊D₄₇	1	8	yes	complemented
247	C₂×D₄	C₂²×D₄₇	1	8	yes	—
248	C₂×D₄	C₂²×D₄₇	1	4	yes	—
249	C₂×D₄	C₂²×D₄₇	1	2	yes	—
250	C₂×D₄	C₂²×D₄₇	1	4	yes	—
251	C₂²×C₄	—	47	1	no	—
252	C₂²×C₄	—	47	4	no	—
253	C₂²×C₄	—	47	4	no	—
254	C₂²×C₄	—	47	1	no	—
255	C₂²×C₄	—	47	4	no	—
256	C₂²×C₄	—	47	2	no	—
257	C₂²×C₄	—	47	4	no	—
258	C₂²×C₄	—	188	4	no	—
259	C₂²×C₄	C₂²×D₄₇	1	4	yes	—
260	C₂²×C₄	C₂²×D₄₇	1	4	yes	—
261	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
262	C₄⋊C₄	—	47	4	no	—
263	C₄⋊C₄	—	47	8	no	—
264	C₄⋊C₄	—	47	4	no	—
265	C₄⋊C₄	—	47	4	no	—
266	C₂²⋊C₄	—	47	4	no	—
267	C₂²⋊C₄	—	47	8	no	—
268	C₂²⋊C₄	—	47	8	no	—
269	C₂²⋊C₄	—	47	4	no	—
270	C₂²⋊C₄	—	47	4	no	—
271	C₂²⋊C₄	—	47	8	no	—
272	C₂²⋊C₄	—	47	4	no	—
273	C₄²	—	47	2	no	—
274	C₄²	—	47	2	no	—
275	C₂³	—	2	8	no	—
276	C₂³	—	4	2	no	—
277	C₂³	—	4	2	no	—
278	C₂³	—	4	4	no	—
279	C₂³	—	4	4	no	—
280	C₂³	—	47	4	no	—
281	C₂³	—	94	8	no	—
282	C₂³	—	188	4	no	—
283	C₂³	—	188	4	no	—
284	C₂³	C₂×C₂²⋊D₄₇	1	8	yes	complemented
285	C₂³	C₂³×D₄₇	1	4	yes	—
286	C₂³	C₂³×D₄₇	1	4	yes	—
287	C₂³	C₂³×D₄₇	1	1	yes	characteristic
288	Q₈	—	2	4	no	—
289	Q₈	—	94	4	no	—
290	D₄	—	2	16	no	—
291	D₄	—	2	8	no	—
292	D₄	—	2	4	no	—
293	D₄	—	94	8	no	—
294	D₄	—	94	16	no	—
295	D₄	—	94	8	no	—
296	D₄	—	94	4	no	—
297	D₄	—	188	4	no	—
298	D₄	—	188	8	no	—
299	D₄	C₂×C₂²⋊D₄₇	1	16	yes	complemented
300	C₂×C₄	—	2	8	no	—
301	C₂×C₄	—	2	8	no	—
302	C₂×C₄	—	47	1	no	—
303	C₂×C₄	—	47	2	no	—
304	C₂×C₄	—	47	1	no	—
305	C₂×C₄	—	47	4	no	—
306	C₂×C₄	—	47	4	no	—
307	C₂×C₄	—	94	2	no	—
308	C₂×C₄	—	94	8	no	—
309	C₂×C₄	—	94	8	no	—
310	C₂×C₄	—	94	8	no	—
311	C₂×C₄	—	188	1	no	—
312	C₂×C₄	—	188	4	no	—
313	C₂×C₄	—	188	2	no	—
314	C₂×C₄	C₂×C₂²⋊D₄₇	1	4	yes	complemented
315	C₂×C₄	C₂³×D₄₇	1	4	yes	—
316	C₂×C₄	C₂³×D₄₇	1	2	yes	—
317	C₂²	—	2	1	no	—
318	C₂²	—	2	4	no	—
319	C₂²	—	2	1	no	—
320	C₂²	—	2	4	no	—
321	C₂²	—	2	4	no	—
322	C₂²	—	2	4	no	—
323	C₂²	—	2	4	no	—
324	C₂²	—	4	8	no	—
325	C₂²	—	8	8	no	—
326	C₂²	—	94	4	no	—
327	C₂²	—	94	4	no	—
328	C₂²	—	94	4	no	—
329	C₂²	—	376	8	no	—
330	C₂²	C₂²×C₂²⋊D₄₇	1	8	yes	—
331	C₂²	C₂²×C₂²⋊D₄₇	1	2	yes	—
332	C₂²	C₂⁴×D₄₇	1	1	yes	characteristic
333	C₄	—	2	4	no	—
334	C₄	—	47	2	no	—
335	C₄	—	94	4	no	—
336	C₄	—	94	1	no	—
337	C₄	—	94	4	no	—
338	C₄	—	94	2	no	—
339	C₄	C₂²×C₂²⋊D₄₇	1	4	yes	—
340	C₂	—	2	2	no	—
341	C₂	—	2	8	no	—
342	C₂	—	4	4	no	—
343	C₂	—	188	4	no	—
344	C₂	C₂³×C₂²⋊D₄₇	1	1	yes	characteristic
345	C₂	H(5,𝔽₂)×D₄₇	1	1	yes	characteristic
346	C₂	#15689958	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₄₇
commutator, socle	C₂²×C₄₇	C₂⁵
Fitting	C₂×H(5,𝔽₂)×C₄₇	C₂
hypercenter	C₂×H(5,𝔽₂)	D₄₇
hypocenter	C₄₇	#3496
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₂×H(5,𝔽₂)

Complements

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

N	H ≅ G/N	type
1. C₂×#13094069	C₂	semidirect
2. #15689772	C₂	semidirect
3. #15689767	C₂	semidirect
4. #15689761	C₂	semidirect
5. D₄×C₂²⋊D₄₇	C₂	semidirect
6. #15689701	C₂	semidirect
7. #15689682	C₂	semidirect
8. #15689669	C₂	semidirect
9. C₂×#13093996	C₂	semidirect
10. C₂×D₄×Dic₄₇	C₂	semidirect
11. C₂×H(5,𝔽₂)×C₄₇	C₂	semidirect
13. C₂×#10625350	C₂²	semidirect
14. C₂×#10625352	C₂²	semidirect
15. C₂²×C₂²⋊D₄₇	C₂²	semidirect
16. C₂²×C₂²⋊D₄₇	C₂²	semidirect
17. C₂×D₄×D₄₇	C₂²	semidirect
18. C₂³×Dic₄₇	C₂²	semidirect
19. #13094022	C₂²	semidirect
20. #13094020	C₂²	semidirect
21. #13094013	C₂²	semidirect
22. #13094011	C₂²	semidirect
23. #13094007	C₂²	semidirect
24. #13094005	C₂²	semidirect
25. #13094003	C₂²	semidirect
26. #13094000	C₂²	semidirect
27. #13093998	C₂²	semidirect
28. #13093996	C₂²	semidirect
29. #13093996	C₂²	semidirect
30. #13093996	C₂²	semidirect
31. #13093996	C₂²	semidirect
32. #13093996	C₂²	semidirect
33. #13093995	C₂²	semidirect
34. #13093993	C₂²	semidirect
35. #13093992	C₂²	semidirect
36. D₄×Dic₄₇	C₂²	semidirect
37. D₄×Dic₄₇	C₂²	semidirect
38. C₄×C₂²⋊D₄₇	C₂²	semidirect
39. C₄×C₂²⋊D₄₇	C₂²	semidirect
40. C₂×C₄⋊Dic₄₇	C₂²	semidirect
41. C₂×Dic₄₇⋊C₄	C₂²	semidirect
42. C₂×C₂²⋊Dic₄₇	C₂²	semidirect
43. C₂×C₂²⋊Dic₄₇	C₂²	semidirect
44. C₂×(C₂×D₄₇)⋊C₄	C₂²	semidirect
45. C₂×C₄×Dic₄₇	C₂²	semidirect
47. C₂×#41×C₄₇	C₂²	semidirect
48. C₂×#41×C₄₇	C₂²	semidirect
50. C₂²×D₄×C₄₇	C₂²	semidirect
51. C₂²×D₄×C₄₇	C₂²	semidirect
60. C₂×D₄×C₄₇	D₄	semidirect
106. C₂³×C₄₇	C₂×D₄	semidirect
118. D₄×C₄₇	C₂×D₄	semidirect
121. C₂×C₄×C₄₇	C₂×D₄	semidirect
165. Dic₄₇	H(5,𝔽₂)	semidirect
175. C₂×H(5,𝔽₂)	D₄₇	semidirect
185. C₄₇	#3496	semidirect
190. C₂×#41	C₂×D₄₇	semidirect
191. C₂×#41	C₂×D₄₇	semidirect
196. C₂²×D₄	C₂×D₄₇	semidirect
197. C₂²×D₄	C₂×D₄₇	semidirect
246. C₂×D₄	C₂²⋊D₄₇	semidirect
284. C₂³	C₂×C₂²⋊D₄₇	semidirect
299. D₄	C₂×C₂²⋊D₄₇	semidirect
314. C₂×C₄	C₂×C₂²⋊D₄₇	semidirect