Finite Group Databasebeta

← C47×#33469 #26073167

Subgroups — C47×#33469 #26073167

Order 12032.

646 conjugacy classes of subgroups.

The subgroup lattice has 400 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C47×#3414C211yesmaximal, characteristic
2C47×#2957C211yesmaximal, characteristic, complemented
3C47×#2952C211yesmaximal, characteristic, complemented
4C47×AGL(1,ℤ/16)C214yesmaximal, complemented
5C47×#2180C214yesmaximal, complemented
6C2×C47×#365C211yesmaximal, characteristic, complemented
7C47×#2148C211yesmaximal, characteristic, complemented
8C2×C47×#360C211yesmaximal, characteristic, complemented
9C47×#2110C211yesmaximal, characteristic, complemented
10C2×#135×C47C2211yescharacteristic
11C2×#135×C47C2211yescharacteristic
12C47×#568—21no—
13C47×#520—21no—
14C47×#510C412yescomplemented
15C47×#510C2212yes—
16C47×#509C412yescomplemented
17C47×#509C2212yes—
18C47×#508C414yescomplemented
19C2×M32×C47C2211yescharacteristic
20C2×M32×C47C2211yescharacteristic
21C47×#444C2214yes—
22C47×#443—22no—
23C47×#442C2212yescomplemented
24C47×#441C2212yescomplemented
25C4×SD16×C47—22no—
26C2×#108×C47C2211yescharacteristic
27C2×#106×C47C2211yescharacteristic
28C47×#421—21no—
29C47×#417—21no—
30C47×#405C2211yescharacteristic
31C47×#365C2214yescomplemented
32C47×#362C2212yescomplemented
33C47×#361C2212yescomplemented
34C47×#360C2214yes—
35C47×#347C2214yescomplemented
36C2×#41×C47—21no—
37C2×#41×C47—21no—
38#135×C47—21no—
39#135×C47—21no—
40#135×C47—21no—
41#135×C47—21no—
42#135×C47C2×C412yes—
43#135×C47C2×C412yes—
44#135×C47C2×C412yescomplemented
45#135×C47C2312yes—
46C2×Q16×C47C2×C411yescharacteristic, complemented
47C2×Q16×C47C2311yescharacteristic
48C2×SD16×C47—21no—
49C2×SD16×C47—21no—
50C2×D8×C47C2×C411yescharacteristic, complemented
51C2×D8×C47C2311yescharacteristic
52#131×C47—24no—
53#131×C47—42no—
54C2×M16×C47—21no—
55C2×M16×C47—42no—
56C2×M16×C47D411yescharacteristic
57C22×C8×C47C2311yescharacteristic
58C4×Q8×C47—22no—
59C4×D4×C47—22no—
60C4×D4×C47—42no—
61#117×C47—41no—
62#117×C47D411yescharacteristic
63C2×C4⋊C4×C47—21no—
64C2×C4⋊C4×C47—41no—
65Q32×C47C2×C414yescomplemented
66SD32×C47C2×C414yescomplemented
67SD32×C47C2×C414yescomplemented
68D16×C47C2×C414yescomplemented
69M32×C47—21no—
70M32×C47C2×C412yescomplemented
71M32×C47C2312yes—
72M32×C47C2312yes—
73C2×C16×C47—21no—
74C2×C16×C47C2×C412yescomplemented
75#108×C47—21no—
76#108×C47C2312yes—
77#106×C47—21no—
78#106×C47C2312yes—
79#104×C47—24no—
80#103×C47—22no—
81#102×C47—22no—
82#97×C47C2312yes—
83C4×C8×C47D412yes—
84#41×C47—22no—
85#41×C47—22no—
86#41×C47—22no—
87#41×C47—22no—
88#41×C47—41no—
89#41×C47—41no—
90#41×C47—41no—
91#41×C47—41no—
92C2×Q8×C47—21no—
93C2×Q8×C47—21no—
94C2×D4×C47—21no—
95C2×D4×C47—21no—
96C2×D4×C47—41no—
97C2×D4×C47—41no—
98C22×C4×C47—42no—
99C22×C4×C47—41no—
100C22×C4×C47—41no—
101C22×C4×C47—41no—
102C22×C4×C47C2×D411yescharacteristic
103Q16×C47—21no—
104Q16×C47—21no—
105Q16×C47C22×C412yes—
106Q16×C47C22×C412yes—
107SD16×C47—22no—
108SD16×C47—22no—
109SD16×C47—22no—
110SD16×C47—22no—
111D8×C47—21no—
112D8×C47—21no—
113D8×C47C22×C412yes—
114D8×C47C22×C412yes—
115M16×C47—21no—
116M16×C47—21no—
117M16×C47—22no—
118M16×C47—44no—
119M16×C47—41no—
120C2×C8×C47—44no—
121C2×C8×C47—41no—
122C2×C8×C47C22×C411yescharacteristic
123C2×C8×C47C22×C411yescharacteristic
124C2×C8×C47C2×D412yes—
125C2×C8×C47C2×D411yescharacteristic
126C2×C8×C47#4111yescharacteristic
127C2×C8×C47#4111yescharacteristic
128C2×C8×C47C2411yescharacteristic
129C4⋊C4×C47—21no—
130C4⋊C4×C47—22no—
131C4⋊C4×C47—42no—
132C4⋊C4×C47—41no—
133C22⋊C4×C47—21no—
134C22⋊C4×C47—42no—
135C42×C47—42no—
136C42×C47C2×D412yes—
137C16×C47—22no—
138C16×C47C22×C414yes—
139C23×C47—41no—
140C23×C47—41no—
141C23×C47AGL(1,ℤ/8)11yescharacteristic
142Q8×C47—22no—
143Q8×C47—22no—
144Q8×C47—41no—
145Q8×C47—41no—
146D4×C47—22no—
147D4×C47—22no—
148D4×C47—42no—
149D4×C47—42no—
150D4×C47—42no—
151D4×C47—42no—
152D4×C47—41no—
153D4×C47—41no—
154C2×C4×C47—22no—
155C2×C4×C47—41no—
156C2×C4×C47—41no—
157C2×C4×C47—42no—
158C2×C4×C47—42no—
159C2×C4×C47—42no—
160C2×C4×C47—42no—
161C2×C4×C47—42no—
162C2×C4×C47—162no—
163C2×C4×C47—161no—
164C2×C4×C47C4×D411yescharacteristic
165C2×C4×C47C4×D411yescharacteristic
166C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
167C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
168C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
169C2×C4×C47C22×D411yescharacteristic
170C8×C47—22no—
171C8×C47—42no—
172C8×C47C4×D411yescharacteristic
173C8×C47C4×D411yescharacteristic
174C8×C47C23×C411yescharacteristic
175C8×C47C2×#4111yescharacteristic
176#33469C4711yesmaximal, characteristic, direct product factor, Sylow
177C22×C47—41no—
178C22×C47—42no—
179C22×C47—42no—
180C22×C47—81no—
181C22×C47—81no—
182C22×C47—161no—
183C22×C47#44211yescharacteristic
184C22×C47#44211yescharacteristic
185C22×C47C2×AGL(1,ℤ/8)11yescharacteristic
186C4×C47—42no—
187C4×C47—42no—
188C4×C47—42no—
189C4×C47—82no—
190C4×C47#44211yescharacteristic
191C4×C47#44211yescharacteristic
192C4×C47C2×C4×D411yescharacteristic
193C4×C47C2×AGL(1,ℤ/8)11yescharacteristic
194#3414C2×C4711yescharacteristic
195#2957C2×C4711yescharacteristic, complemented
196#2952C2×C4711yescharacteristic, complemented
197AGL(1,ℤ/16)C2×C4714yescomplemented
198#2180C2×C4714yescomplemented
199C2×#365C2×C4711yescharacteristic, complemented
200#2148C2×C4711yescharacteristic, complemented
201C2×#360C2×C4711yescharacteristic, complemented
202#2110C2×C4711yescharacteristic, complemented
203C2×C47—21no—
204C2×C47—21no—
205C2×C47—21no—
206C2×C47—82no—
207C2×C47—82no—
208C2×C47C2×#44211yescharacteristic
209C2×#135C22×C4711yescharacteristic
210C2×#135C22×C4711yescharacteristic
211#568—21no—
212#520—21no—
213#510C4×C4712yescomplemented
214#510C22×C4712yes—
215#509C4×C4712yescomplemented
216#509C22×C4712yes—
217#508C4×C4714yescomplemented
218C2×M32C22×C4711yescharacteristic
219C2×M32C22×C4711yescharacteristic
220#444C22×C4714yes—
221#443—22no—
222#442C22×C4712yescomplemented
223#441C22×C4712yescomplemented
224C4×SD16—22no—
225C2×#108C22×C4711yescharacteristic
226C2×#106C22×C4711yescharacteristic
227#421—21no—
228#417—21no—
229#405C22×C4711yescharacteristic
230#365C22×C4714yescomplemented
231#362C22×C4712yescomplemented
232#361C22×C4712yescomplemented
233#360C22×C4714yes—
234#347C22×C4714yescomplemented
235C47#3346911yescharacteristic, direct product factor, Sylow
236C2×#41—21no—
237C2×#41—21no—
238#135—21no—
239#135—21no—
240#135—21no—
241#135—21no—
242#135C2×C4×C4712yes—
243#135C2×C4×C4712yes—
244#135C2×C4×C4712yescomplemented
245#135C23×C4712yes—
246C2×Q16C2×C4×C4711yescharacteristic, complemented
247C2×Q16C23×C4711yescharacteristic
248C2×SD16—21no—
249C2×SD16—21no—
250C2×D8C2×C4×C4711yescharacteristic, complemented
251C2×D8C23×C4711yescharacteristic
252#131—24no—
253#131—42no—
254C2×M16—21no—
255C2×M16—42no—
256C2×M16D4×C4711yescharacteristic
257C22×C8C23×C4711yescharacteristic
258C4×Q8—22no—
259C4×D4—22no—
260C4×D4—42no—
261#117—41no—
262#117D4×C4711yescharacteristic
263C2×C4⋊C4—21no—
264C2×C4⋊C4—41no—
265Q32C2×C4×C4714yescomplemented
266SD32C2×C4×C4714yescomplemented
267SD32C2×C4×C4714yescomplemented
268D16C2×C4×C4714yescomplemented
269M32—21no—
270M32C2×C4×C4712yescomplemented
271M32C23×C4712yes—
272M32C23×C4712yes—
273C2×C16—21no—
274C2×C16C2×C4×C4712yescomplemented
275#108—21no—
276#108C23×C4712yes—
277#106—21no—
278#106C23×C4712yes—
279#104—24no—
280#103—22no—
281#102—22no—
282#97C23×C4712yes—
283C4×C8D4×C4712yes—
284#41—22no—
285#41—22no—
286#41—22no—
287#41—22no—
288#41—41no—
289#41—41no—
290#41—41no—
291#41—41no—
292C2×Q8—21no—
293C2×Q8—21no—
294C2×D4—21no—
295C2×D4—21no—
296C2×D4—41no—
297C2×D4—41no—
298C22×C4—42no—
299C22×C4—41no—
300C22×C4—41no—
301C22×C4—41no—
302C22×C4C2×D4×C4711yescharacteristic
303Q16—21no—
304Q16—21no—
305Q16C22×C4×C4712yes—
306Q16C22×C4×C4712yes—
307SD16—22no—
308SD16—22no—
309SD16—22no—
310SD16—22no—
311D8—21no—
312D8—21no—
313D8C22×C4×C4712yes—
314D8C22×C4×C4712yes—
315M16—21no—
316M16—21no—
317M16—22no—
318M16—44no—
319M16—41no—
320C2×C8—44no—
321C2×C8—41no—
322C2×C8C22×C4×C4711yescharacteristic
323C2×C8C22×C4×C4711yescharacteristic
324C2×C8C2×D4×C4712yes—
325C2×C8C2×D4×C4711yescharacteristic
326C2×C8#41×C4711yescharacteristic
327C2×C8#41×C4711yescharacteristic
328C2×C8C24×C4711yescharacteristic
329C4⋊C4—21no—
330C4⋊C4—22no—
331C4⋊C4—42no—
332C4⋊C4—41no—
333C22⋊C4—21no—
334C22⋊C4—42no—
335C42—42no—
336C42C2×D4×C4712yes—
337C16—22no—
338C16C22×C4×C4714yes—
339C23—41no—
340C23—41no—
341C23AGL(1,ℤ/8)×C4711yescharacteristic
342Q8—22no—
343Q8—22no—
344Q8—41no—
345Q8—41no—
346D4—22no—
347D4—22no—
348D4—42no—
349D4—42no—
350D4—42no—
351D4—42no—
352D4—41no—
353D4—41no—
354C2×C4—22no—
355C2×C4—41no—
356C2×C4—41no—
357C2×C4—42no—
358C2×C4—42no—
359C2×C4—42no—
360C2×C4—42no—
361C2×C4—42no—
362C2×C4—162no—
363C2×C4—161no—
364C2×C4C4×D4×C4711yescharacteristic
365C2×C4C4×D4×C4711yescharacteristic
366C2×C4AGL(1,ℤ/8)×C4711yescharacteristic
367C2×C4AGL(1,ℤ/8)×C4711yescharacteristic
368C2×C4AGL(1,ℤ/8)×C4711yescharacteristic
369C2×C4C22×D4×C4711yescharacteristic
370C8—22no—
371C8—42no—
372C8C4×D4×C4711yescharacteristic
373C8C4×D4×C4711yescharacteristic
374C8C23×C4×C4711yescharacteristic
375C8C2×#41×C4711yescharacteristic
376C22—41no—
377C22—42no—
378C22—42no—
379C22—81no—
380C22—81no—
381C22—161no—
382C22C47×#44211yescharacteristic
383C22C47×#44211yescharacteristic
384C22C2×AGL(1,ℤ/8)×C4711yescharacteristic
385C4—42no—
386C4—42no—
387C4—42no—
388C4—82no—
389C4C47×#44211yescharacteristic
390C4C47×#44211yescharacteristic
391C4C2×C4×D4×C4711yescharacteristic
392C4C2×AGL(1,ℤ/8)×C4711yescharacteristic
393C2—21no—
394C2—21no—
395C2—21no—
396C2—82no—
397C2—82no—
398C2C2×C47×#44211yescharacteristic
subgroupG/H
center, socleC2×C47C2×#442
commutatorC8C23×C4×C47
Frattini, cosocleC2×C8C24×C47
prime radicalC47×#3414C2
LCSG ▷ C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C47 ◁ C22×C4×C47 ◁ C47×#405 ◁ G

Complements

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

NH ≅ G/Ntype
2. C47×#2957C2semidirect
3. C47×#2952C2semidirect
4. C47×AGL(1,ℤ/16)C2semidirect
5. C47×#2180C2semidirect
6. C2×C47×#365C2semidirect
7. C47×#2148C2semidirect
8. C2×C47×#360C2semidirect
9. C47×#2110C2semidirect
14. C47×#510C4semidirect
16. C47×#509C4semidirect
18. C47×#508C4semidirect
23. C47×#442C22semidirect
24. C47×#441C22semidirect
31. C47×#365C22semidirect
32. C47×#362C22semidirect
33. C47×#361C22semidirect
35. C47×#347C22semidirect
44. #135×C47C2×C4semidirect
46. C2×Q16×C47C2×C4semidirect
50. C2×D8×C47C2×C4semidirect
65. Q32×C47C2×C4semidirect
66. SD32×C47C2×C4semidirect
67. SD32×C47C2×C4semidirect
68. D16×C47C2×C4semidirect
70. M32×C47C2×C4semidirect
74. C2×C16×C47C2×C4semidirect
176. #33469C47direct (N × H)
195. #2957C2×C47semidirect
196. #2952C2×C47semidirect
197. AGL(1,ℤ/16)C2×C47semidirect
198. #2180C2×C47semidirect
199. C2×#365C2×C47semidirect
200. #2148C2×C47semidirect
201. C2×#360C2×C47semidirect
202. #2110C2×C47semidirect
213. #510C4×C47semidirect
215. #509C4×C47semidirect
217. #508C4×C47semidirect
222. #442C22×C47semidirect
223. #441C22×C47semidirect
230. #365C22×C47semidirect
231. #362C22×C47semidirect
232. #361C22×C47semidirect
234. #347C22×C47semidirect
235. C47#33469direct (N × H)
244. #135C2×C4×C47semidirect
246. C2×Q16C2×C4×C47semidirect
250. C2×D8C2×C4×C47semidirect
265. Q32C2×C4×C47semidirect
266. SD32C2×C4×C47semidirect
267. SD32C2×C4×C47semidirect
268. D16C2×C4×C47semidirect
270. M32C2×C4×C47semidirect
274. C2×C16C2×C4×C47semidirect

Maximal subgroups

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

subgroupindex
C47×#34142
C47×#29572
C47×#29522
C47×AGL(1,ℤ/16)2
C47×#21802
C2×C47×#3652
C47×#21482
C2×C47×#3602
C47×#21102
#3346947