Finite Group Databasebeta

← C2×C47×AGL(1,ℤ/16) #26073165

Subgroups — C2×C47×AGL(1,ℤ/16) #26073165

Order 12032.

710 conjugacy classes of subgroups.

The subgroup lattice has 378 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C47×#509C211yesmaximal, characteristic
2C2×C47×#444C211yesmaximal, characteristic, complemented
3C2×C47×#442C211yesmaximal, characteristic, complemented
4C47×AGL(1,ℤ/16)C218yesmaximal, direct product factor
5C2×C47×#365C211yesmaximal, characteristic, complemented
6C2×C47×#361C211yesmaximal, characteristic, complemented
7C2×C47×#360C211yesmaximal, characteristic, complemented
8C2×C47×#347C211yesmaximal, characteristic, complemented
9C2×#135×C47C2211yescharacteristic
10C22×D8×C47C2211yescharacteristic
11C2×#131×C47—21no—
12C2×C4×D4×C47—21no—
13C47×#509C414yescomplemented
14C47×#509C2214yes—
15C2×SD32×C47C412yescomplemented
16C2×D16×C47C412yescomplemented
17C2×M32×C47C2211yescharacteristic
18C2×M32×C47C2211yescharacteristic
19C47×#444—22no—
20C47×#444C2214yescomplemented
21C47×#442—22no—
22C47×#442C2214yescomplemented
23C2×#108×C47C2211yescharacteristic
24C2×#106×C47C2211yescharacteristic
25C2×#104×C47—21no—
26C2×#102×C47—21no—
27C2×#97×C47C2211yescharacteristic
28C47×#365C2214yescomplemented
29C47×#361C2214yescomplemented
30C47×#360C2214yescomplemented
31C47×#347C2214yescomplemented
32C2×#41×C47—21no—
33C22×D4×C47—21no—
34C23×C4×C47—41no—
35#135×C47—21no—
36#135×C47—21no—
37#135×C47C2×C412yescomplemented
38#135×C47C2312yes—
39C2×Q16×C47C2×C411yescharacteristic, complemented
40C2×SD16×C47—21no—
41C2×D8×C47—21no—
42C2×D8×C47—21no—
43C2×D8×C47—21no—
44C2×D8×C47C2×C412yes—
45C2×D8×C47C2×C412yes—
46C2×D8×C47C2×C411yescharacteristic, complemented
47C2×D8×C47C2312yes—
48#131×C47—24no—
49#131×C47—42no—
50C2×M16×C47—21no—
51C2×M16×C47—41no—
52C22×C8×C47—41no—
53C22×C8×C47D411yescharacteristic
54C22×C8×C47C2311yescharacteristic
55C4×D4×C47—24no—
56C4×D4×C47—42no—
57C2×C4⋊C4×C47—21no—
58C2×C22⋊C4×C47—41no—
59C2×C42×C47D411yescharacteristic
60SD32×C47C2×C418yescomplemented
61D16×C47C2×C418yescomplemented
62M32×C47—21no—
63M32×C47C2×C412yescomplemented
64M32×C47C2312yes—
65M32×C47C2312yes—
66C2×C16×C47—21no—
67C2×C16×C47C2×C412yescomplemented
68#108×C47—21no—
69#108×C47C2312yes—
70#106×C47—21no—
71#106×C47C2312yes—
72#104×C47—24no—
73#102×C47—24no—
74#97×C47D412yes—
75#97×C47C2312yes—
76C24×C47—41no—
77#41×C47—22no—
78#41×C47—22no—
79#41×C47—41no—
80#41×C47—41no—
81C2×Q8×C47—21no—
82C2×D4×C47—22no—
83C2×D4×C47—22no—
84C2×D4×C47—21no—
85C2×D4×C47—22no—
86C2×D4×C47—41no—
87C2×D4×C47—41no—
88C2×D4×C47—41no—
89C2×D4×C47—41no—
90C22×C4×C47—21no—
91C22×C4×C47—44no—
92C22×C4×C47—41no—
93C22×C4×C47—41no—
94C22×C4×C47—84no—
95C22×C4×C47C2×D411yescharacteristic
96Q16×C47—21no—
97Q16×C47C22×C412yescomplemented
98SD16×C47—22no—
99SD16×C47—22no—
100D8×C47—22no—
101D8×C47—22no—
102D8×C47—21no—
103D8×C47—22no—
104D8×C47C22×C414yes—
105D8×C47C22×C412yescomplemented
106M16×C47—22no—
107M16×C47—44no—
108M16×C47—41no—
109C2×C8×C47—21no—
110C2×C8×C47—21no—
111C2×C8×C47—44no—
112C2×C8×C47—41no—
113C2×C8×C47C22×C411yescharacteristic
114C2×C8×C47C22×C411yescharacteristic
115C2×C8×C47C2×D412yes—
116C2×C8×C47C2×D411yescharacteristic
117C2×C8×C47#4111yescharacteristic
118C2×C8×C47#4111yescharacteristic
119C2×C8×C47C2411yescharacteristic
120C4⋊C4×C47—22no—
121C4⋊C4×C47—41no—
122C22⋊C4×C47—44no—
123C42×C47—21no—
124C42×C47C2×D412yes—
125C16×C47—22no—
126C16×C47C22×C414yescomplemented
127C23×C47—42no—
128C23×C47—42no—
129C23×C47—41no—
130C23×C47—42no—
131C23×C47—82no—
132C23×C47—82no—
133C23×C47AGL(1,ℤ/8)11yescharacteristic
134Q8×C47—22no—
135Q8×C47—41no—
136D4×C47—24no—
137D4×C47—22no—
138D4×C47—42no—
139D4×C47—42no—
140D4×C47—42no—
141D4×C47—42no—
142D4×C47—42no—
143D4×C47—41no—
144C2×C4×C47—22no—
145C2×C4×C47—42no—
146C2×C4×C47—41no—
147C2×C4×C47—42no—
148C2×C4×C47—42no—
149C2×C4×C47—42no—
150C2×C4×C47—88no—
151C2×C4×C47—82no—
152C2×C4×C47C4×D411yescharacteristic
153C2×C4×C47C4×D411yescharacteristic
154C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
155C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
156C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
157C2×C4×C47C22×D411yescharacteristic
158C8×C47—22no—
159C8×C47—42no—
160C8×C47C4×D411yescharacteristic
161C8×C47C4×D411yescharacteristic
162C8×C47C23×C411yescharacteristic
163C8×C47C2×#4111yescharacteristic
164C2×AGL(1,ℤ/16)C4711yesmaximal, characteristic, direct product factor, Sylow
165C22×C47—22no—
166C22×C47—42no—
167C22×C47—44no—
168C22×C47—82no—
169C22×C47—82no—
170C22×C47—84no—
171C22×C47—82no—
172C22×C47—84no—
173C22×C47#44211yescharacteristic
174C22×C47#44211yescharacteristic
175C22×C47C2×AGL(1,ℤ/8)11yescharacteristic
176C4×C47—42no—
177C4×C47—42no—
178C4×C47—82no—
179C4×C47#44211yescharacteristic
180C4×C47#44211yescharacteristic
181C4×C47C2×C4×D411yescharacteristic
182C4×C47C2×AGL(1,ℤ/8)11yescharacteristic
183C2×#509C2×C4711yescharacteristic
184C2×#444C2×C4711yescharacteristic, complemented
185C2×#442C2×C4711yescharacteristic, complemented
186AGL(1,ℤ/16)C2×C4718yesdirect product factor
187C2×#365C2×C4711yescharacteristic, complemented
188C2×#361C2×C4711yescharacteristic, complemented
189C2×#360C2×C4711yescharacteristic, complemented
190C2×#347C2×C4711yescharacteristic, complemented
191C2×C47—21no—
192C2×C47—21no—
193C2×C47—82no—
194C2×C47—84no—
195C2×C47AGL(1,ℤ/16)12yesdirect product factor
196C2×C47C2×#44211yescharacteristic
197C2×#135C22×C4711yescharacteristic
198C22×D8C22×C4711yescharacteristic
199C2×#131—21no—
200C2×C4×D4—21no—
201#509C4×C4714yescomplemented
202#509C22×C4714yes—
203C2×SD32C4×C4712yescomplemented
204C2×D16C4×C4712yescomplemented
205C2×M32C22×C4711yescharacteristic
206C2×M32C22×C4711yescharacteristic
207#444—22no—
208#444C22×C4714yescomplemented
209#442—22no—
210#442C22×C4714yescomplemented
211C2×#108C22×C4711yescharacteristic
212C2×#106C22×C4711yescharacteristic
213C2×#104—21no—
214C2×#102—21no—
215C2×#97C22×C4711yescharacteristic
216#365C22×C4714yescomplemented
217#361C22×C4714yescomplemented
218#360C22×C4714yescomplemented
219#347C22×C4714yescomplemented
220C47C2×AGL(1,ℤ/16)11yescharacteristic, direct product factor, Sylow
221C2×#41—21no—
222C22×D4—21no—
223C23×C4—41no—
224#135—21no—
225#135—21no—
226#135C2×C4×C4712yescomplemented
227#135C23×C4712yes—
228C2×Q16C2×C4×C4711yescharacteristic, complemented
229C2×SD16—21no—
230C2×D8—21no—
231C2×D8—21no—
232C2×D8—21no—
233C2×D8C2×C4×C4712yes—
234C2×D8C2×C4×C4712yes—
235C2×D8C2×C4×C4711yescharacteristic, complemented
236C2×D8C23×C4712yes—
237#131—24no—
238#131—42no—
239C2×M16—21no—
240C2×M16—41no—
241C22×C8—41no—
242C22×C8D4×C4711yescharacteristic
243C22×C8C23×C4711yescharacteristic
244C4×D4—24no—
245C4×D4—42no—
246C2×C4⋊C4—21no—
247C2×C22⋊C4—41no—
248C2×C42D4×C4711yescharacteristic
249SD32C2×C4×C4718yescomplemented
250D16C2×C4×C4718yescomplemented
251M32—21no—
252M32C2×C4×C4712yescomplemented
253M32C23×C4712yes—
254M32C23×C4712yes—
255C2×C16—21no—
256C2×C16C2×C4×C4712yescomplemented
257#108—21no—
258#108C23×C4712yes—
259#106—21no—
260#106C23×C4712yes—
261#104—24no—
262#102—24no—
263#97D4×C4712yes—
264#97C23×C4712yes—
265C24—41no—
266#41—22no—
267#41—22no—
268#41—41no—
269#41—41no—
270C2×Q8—21no—
271C2×D4—22no—
272C2×D4—22no—
273C2×D4—21no—
274C2×D4—22no—
275C2×D4—41no—
276C2×D4—41no—
277C2×D4—41no—
278C2×D4—41no—
279C22×C4—21no—
280C22×C4—44no—
281C22×C4—41no—
282C22×C4—41no—
283C22×C4—84no—
284C22×C4C2×D4×C4711yescharacteristic
285Q16—21no—
286Q16C22×C4×C4712yescomplemented
287SD16—22no—
288SD16—22no—
289D8—22no—
290D8—22no—
291D8—21no—
292D8—22no—
293D8C22×C4×C4714yes—
294D8C22×C4×C4712yescomplemented
295M16—22no—
296M16—44no—
297M16—41no—
298C2×C8—21no—
299C2×C8—21no—
300C2×C8—44no—
301C2×C8—41no—
302C2×C8C22×C4×C4711yescharacteristic
303C2×C8C22×C4×C4711yescharacteristic
304C2×C8C2×D4×C4712yes—
305C2×C8C2×D4×C4711yescharacteristic
306C2×C8#41×C4711yescharacteristic
307C2×C8#41×C4711yescharacteristic
308C2×C8C24×C4711yescharacteristic
309C4⋊C4—22no—
310C4⋊C4—41no—
311C22⋊C4—44no—
312C42—21no—
313C42C2×D4×C4712yes—
314C16—22no—
315C16C22×C4×C4714yescomplemented
316C23—42no—
317C23—41no—
318C23—42no—
319C23—42no—
320C23—82no—
321C23—82no—
322C23AGL(1,ℤ/8)×C4711yescharacteristic
323Q8—22no—
324Q8—41no—
325D4—24no—
326D4—22no—
327D4—42no—
328D4—42no—
329D4—42no—
330D4—42no—
331D4—42no—
332D4—41no—
333C2×C4—22no—
334C2×C4—42no—
335C2×C4—41no—
336C2×C4—42no—
337C2×C4—42no—
338C2×C4—42no—
339C2×C4—88no—
340C2×C4—82no—
341C2×C4C4×D4×C4711yescharacteristic
342C2×C4C4×D4×C4711yescharacteristic
343C2×C4AGL(1,ℤ/8)×C4711yescharacteristic
344C2×C4AGL(1,ℤ/8)×C4711yescharacteristic
345C2×C4AGL(1,ℤ/8)×C4711yescharacteristic
346C2×C4C22×D4×C4711yescharacteristic
347C8—22no—
348C8—42no—
349C8C4×D4×C4711yescharacteristic
350C8C4×D4×C4711yescharacteristic
351C8C23×C4×C4711yescharacteristic
352C8C2×#41×C4711yescharacteristic
353C22—22no—
354C22—42no—
355C22—44no—
356C22—82no—
357C22—82no—
358C22—84no—
359C22—84no—
360C22—82no—
361C22C47×#44211yescharacteristic
362C22C47×#44211yescharacteristic
363C22C2×AGL(1,ℤ/8)×C4711yescharacteristic
364C4—42no—
365C4—42no—
366C4—82no—
367C4C47×#44211yescharacteristic
368C4C47×#44211yescharacteristic
369C4C2×C4×D4×C4711yescharacteristic
370C4C2×AGL(1,ℤ/8)×C4711yescharacteristic
371C2—21no—
372C2—21no—
373C2—84no—
374C2—82no—
375C2C47×AGL(1,ℤ/16)12yesdirect product factor
376C2C2×C47×#44211yescharacteristic
subgroupG/H
center, socleC22×C47#442
commutatorC8C23×C4×C47
Frattini, cosocleC2×C8C24×C47
prime radicalC2×C47×#509C2
LCSG ▷ C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C47 ◁ C22×C4×C47 ◁ C2×#97×C47 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C47×#444C2semidirect
3. C2×C47×#442C2semidirect
4. C47×AGL(1,ℤ/16)C2direct (N × H)
5. C2×C47×#365C2semidirect
6. C2×C47×#361C2semidirect
7. C2×C47×#360C2semidirect
8. C2×C47×#347C2semidirect
13. C47×#509C4semidirect
15. C2×SD32×C47C4semidirect
16. C2×D16×C47C4semidirect
20. C47×#444C22semidirect
22. C47×#442C22semidirect
28. C47×#365C22semidirect
29. C47×#361C22semidirect
30. C47×#360C22semidirect
31. C47×#347C22semidirect
37. #135×C47C2×C4semidirect
39. C2×Q16×C47C2×C4semidirect
46. C2×D8×C47C2×C4semidirect
60. SD32×C47C2×C4semidirect
61. D16×C47C2×C4semidirect
63. M32×C47C2×C4semidirect
67. C2×C16×C47C2×C4semidirect
97. Q16×C47C22×C4semidirect
105. D8×C47C22×C4semidirect
126. C16×C47C22×C4semidirect
164. C2×AGL(1,ℤ/16)C47direct (N × H)
184. C2×#444C2×C47semidirect
185. C2×#442C2×C47semidirect
186. AGL(1,ℤ/16)C2×C47direct (N × H)
187. C2×#365C2×C47semidirect
188. C2×#361C2×C47semidirect
189. C2×#360C2×C47semidirect
190. C2×#347C2×C47semidirect
195. C2×C47AGL(1,ℤ/16)direct (N × H)
201. #509C4×C47semidirect
203. C2×SD32C4×C47semidirect
204. C2×D16C4×C47semidirect
208. #444C22×C47semidirect
210. #442C22×C47semidirect
216. #365C22×C47semidirect
217. #361C22×C47semidirect
218. #360C22×C47semidirect
219. #347C22×C47semidirect
220. C47C2×AGL(1,ℤ/16)direct (N × H)
226. #135C2×C4×C47semidirect
228. C2×Q16C2×C4×C47semidirect
235. C2×D8C2×C4×C47semidirect
249. SD32C2×C4×C47semidirect
250. D16C2×C4×C47semidirect
252. M32C2×C4×C47semidirect
256. C2×C16C2×C4×C47semidirect
286. Q16C22×C4×C47semidirect
294. D8C22×C4×C47semidirect
315. C16C22×C4×C47semidirect
375. C2C47×AGL(1,ℤ/16)direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C47×#5092
C2×C47×#4442
C2×C47×#4422
C47×AGL(1,ℤ/16)2
C2×C47×#3652
C2×C47×#3612
C2×C47×#3602
C2×C47×#3472
C2×AGL(1,ℤ/16)47