Finite Group Databasebeta

← C47×#33690 #26073388

Subgroups — C47×#33690 #26073388

Order 12032.

526 conjugacy classes of subgroups.

The subgroup lattice has 398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C47×#3183C211yesmaximal, characteristic, complemented
2C47×#2956C211yesmaximal, characteristic, complemented
3C47×#2239C211yesmaximal, characteristic, complemented
4C47×#2238C211yesmaximal, characteristic, complemented
5C47×#2231C212yesmaximal, complemented
6C47×#2212C212yesmaximal, complemented
7C47×#2191C211yesmaximal, characteristic, complemented
8C47×#2190C211yesmaximal, characteristic
9C47×AGL(1,ℤ/16)C212yesmaximal, complemented
10C47×#2180C212yesmaximal, complemented
11C47×#2165C211yesmaximal, characteristic, complemented
12C47×#575C2211yescharacteristic
13C47×#568—21no—
14C47×#529—21no—
15C47×#510C2212yes—
16C47×#509C2212yes—
17C47×#499C2211yescharacteristic, complemented
18C47×#495C2211yescharacteristic, complemented
19C47×#488—21no—
20C47×#470C2211yescharacteristic
21C47×#469C2211yescharacteristic
22C47×#468—21no—
23C47×#444—21no—
24C47×#444C2212yes—
25C47×#443—21no—
26C47×#443C2212yes—
27C47×#442C2211yescharacteristic, complemented
28C47×#441C2211yescharacteristic, complemented
29C47×#440—21no—
30C47×#430C2211yescharacteristic
31C2×#104×C47—21no—
32C4×M16×C47C2211yescharacteristic
33C47×#365C2212yescomplemented
34C47×#365C2212yescomplemented
35C47×#364C2212yescomplemented
36C47×#362C2212yescomplemented
37C47×#361C2212yescomplemented
38C47×#360C2212yes—
39C47×#360C2212yes—
40C47×#349C2211yescharacteristic
41C47×#349C2211yescharacteristic
42C47×#347C2212yescomplemented
43C2×#41×C47—21no—
44#137×C47—22no—
45AGL(1,ℤ/8)×C47—22no—
46#135×C47—21no—
47#135×C47C2312yes—
48C2×Q16×C47C2311yescharacteristic
49C2×SD16×C47—21no—
50C2×D8×C47C2311yescharacteristic
51#131×C47—22no—
52#131×C47—22no—
53#131×C47—42no—
54C2×M16×C47—21no—
55C2×M16×C47—42no—
56C2×M16×C47D411yescharacteristic
57C2×M16×C47C2311yescharacteristic
58#126×C47—41no—
59#125×C47—21no—
60#124×C47—21no—
61#123×C47—41no—
62C22⋊Q8×C47—21no—
63#121×C47—21no—
64C4×Q8×C47—21no—
65C4×D4×C47—21no—
66C4×D4×C47—41no—
67#117×C47—41no—
68C2×C42×C47D411yescharacteristic
69Q32×C47—22no—
70SD32×C47—22no—
71SD32×C47—22no—
72D16×C47—22no—
73M32×C47C2312yes—
74M32×C47C2312yes—
75#108×C47—21no—
76#108×C47C2312yes—
77#107×C47—21no—
78#106×C47C2311yescharacteristic
79#106×C47C2311yescharacteristic
80#104×C47—22no—
81#104×C47—22no—
82#103×C47—21no—
83#103×C47—21no—
84#102×C47—21no—
85#102×C47—21no—
86#97×C47D411yescharacteristic
87#97×C47C2311yescharacteristic
88C4×C8×C47D411yescharacteristic
89C4×C8×C47C2311yescharacteristic
90#41×C47—22no—
91#41×C47—22no—
92#41×C47—41no—
93#41×C47—41no—
94C2×Q8×C47—21no—
95C2×Q8×C47—21no—
96C2×D4×C47—21no—
97C2×D4×C47—21no—
98C2×D4×C47—41no—
99C2×D4×C47—41no—
100C22×C4×C47—21no—
101C22×C4×C47—41no—
102C22×C4×C47—41no—
103C22×C4×C47C2×D411yescharacteristic
104Q16×C47—21no—
105Q16×C47—22no—
106Q16×C47#4112yes—
107SD16×C47—22no—
108SD16×C47—22no—
109SD16×C47—42no—
110D8×C47—21no—
111D8×C47—22no—
112D8×C47#4112yes—
113M16×C47—22no—
114M16×C47—22no—
115M16×C47—22no—
116M16×C47—42no—
117M16×C47—41no—
118M16×C47—42no—
119C2×C8×C47—42no—
120C2×C8×C47—41no—
121C2×C8×C47—42no—
122C2×C8×C47C2×D411yescharacteristic
123C2×C8×C47C2×D411yescharacteristic
124C2×C8×C47C2×D411yescharacteristic
125C2×C8×C47C2411yescharacteristic
126C4⋊C4×C47—21no—
127C4⋊C4×C47—21no—
128C4⋊C4×C47—41no—
129C4⋊C4×C47—41no—
130C4⋊C4×C47—41no—
131C4⋊C4×C47—41no—
132C22⋊C4×C47—41no—
133C22⋊C4×C47—41no—
134C22⋊C4×C47—41no—
135C22⋊C4×C47—41no—
136C22⋊C4×C47—41no—
137C42×C47—21no—
138C42×C47—41no—
139C42×C47C2×D411yescharacteristic
140C42×C47C2×D411yescharacteristic
141C16×C47—22no—
142C16×C47—22no—
143C23×C47—41no—
144C23×C47—41no—
145C23×C47AGL(1,ℤ/8)11yescharacteristic
146Q8×C47—22no—
147Q8×C47—41no—
148Q8×C47—41no—
149Q8×C47—41no—
150D4×C47—22no—
151D4×C47—41no—
152D4×C47—42no—
153D4×C47—42no—
154D4×C47—41no—
155D4×C47—41no—
156D4×C47—82no—
157C2×C4×C47—21no—
158C2×C4×C47—21no—
159C2×C4×C47—21no—
160C2×C4×C47—21no—
161C2×C4×C47—42no—
162C2×C4×C47—41no—
163C2×C4×C47—42no—
164C2×C4×C47—41no—
165C2×C4×C47—41no—
166C2×C4×C47—41no—
167C2×C4×C47—81no—
168C2×C4×C47—82no—
169C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
170C2×C4×C47C22×D411yescharacteristic
171C8×C47—21no—
172C8×C47—21no—
173C8×C47—42no—
174C8×C47AGL(1,ℤ/8)12yes—
175C8×C47C2×#4112yes—
176#33690C4711yesmaximal, characteristic, direct product factor, Sylow
177C22×C47—21no—
178C22×C47—41no—
179C22×C47—42no—
180C22×C47—81no—
181C22×C47—81no—
182C22×C47—81no—
183C22×C47—161no—
184C22×C47C2×AGL(1,ℤ/8)11yescharacteristic
185C4×C47—21no—
186C4×C47—41no—
187C4×C47—41no—
188C4×C47—42no—
189C4×C47—81no—
190C4×C47—81no—
191C4×C47—81no—
192C4×C47#52511yescharacteristic
193C4×C47C2×AGL(1,ℤ/8)11yescharacteristic
194#3183C2×C4711yescharacteristic, complemented
195#2956C2×C4711yescharacteristic, complemented
196#2239C2×C4711yescharacteristic, complemented
197#2238C2×C4711yescharacteristic, complemented
198#2231C2×C4712yescomplemented
199#2212C2×C4712yescomplemented
200#2191C2×C4711yescharacteristic, complemented
201#2190C2×C4711yescharacteristic
202AGL(1,ℤ/16)C2×C4712yescomplemented
203#2180C2×C4712yescomplemented
204#2165C2×C4711yescharacteristic, complemented
205C2×C47—21no—
206C2×C47—41no—
207C2×C47—82no—
208C2×C47—161no—
209C2×C47#310911yescharacteristic
210#575C22×C4711yescharacteristic
211#568—21no—
212#529—21no—
213#510C22×C4712yes—
214#509C22×C4712yes—
215#499C22×C4711yescharacteristic, complemented
216#495C22×C4711yescharacteristic, complemented
217#488—21no—
218#470C22×C4711yescharacteristic
219#469C22×C4711yescharacteristic
220#468—21no—
221#444—21no—
222#444C22×C4712yes—
223#443—21no—
224#443C22×C4712yes—
225#442C22×C4711yescharacteristic, complemented
226#441C22×C4711yescharacteristic, complemented
227#440—21no—
228#430C22×C4711yescharacteristic
229C2×#104—21no—
230C4×M16C22×C4711yescharacteristic
231#365C22×C4712yescomplemented
232#365C22×C4712yescomplemented
233#364C22×C4712yescomplemented
234#362C22×C4712yescomplemented
235#361C22×C4712yescomplemented
236#360C22×C4712yes—
237#360C22×C4712yes—
238#349C22×C4711yescharacteristic
239#349C22×C4711yescharacteristic
240#347C22×C4712yescomplemented
241C47#3369011yescharacteristic, direct product factor, Sylow
242C2×#41—21no—
243#137—22no—
244AGL(1,ℤ/8)—22no—
245#135—21no—
246#135C23×C4712yes—
247C2×Q16C23×C4711yescharacteristic
248C2×SD16—21no—
249C2×D8C23×C4711yescharacteristic
250#131—22no—
251#131—22no—
252#131—42no—
253C2×M16—21no—
254C2×M16—42no—
255C2×M16D4×C4711yescharacteristic
256C2×M16C23×C4711yescharacteristic
257#126—41no—
258#125—21no—
259#124—21no—
260#123—41no—
261C22⋊Q8—21no—
262#121—21no—
263C4×Q8—21no—
264C4×D4—21no—
265C4×D4—41no—
266#117—41no—
267C2×C42D4×C4711yescharacteristic
268Q32—22no—
269SD32—22no—
270SD32—22no—
271D16—22no—
272M32C23×C4712yes—
273M32C23×C4712yes—
274#108—21no—
275#108C23×C4712yes—
276#107—21no—
277#106C23×C4711yescharacteristic
278#106C23×C4711yescharacteristic
279#104—22no—
280#104—22no—
281#103—21no—
282#103—21no—
283#102—21no—
284#102—21no—
285#97D4×C4711yescharacteristic
286#97C23×C4711yescharacteristic
287C4×C8D4×C4711yescharacteristic
288C4×C8C23×C4711yescharacteristic
289#41—22no—
290#41—22no—
291#41—41no—
292#41—41no—
293C2×Q8—21no—
294C2×Q8—21no—
295C2×D4—21no—
296C2×D4—21no—
297C2×D4—41no—
298C2×D4—41no—
299C22×C4—21no—
300C22×C4—41no—
301C22×C4—41no—
302C22×C4C2×D4×C4711yescharacteristic
303Q16—21no—
304Q16—22no—
305Q16#41×C4712yes—
306SD16—22no—
307SD16—22no—
308SD16—42no—
309D8—21no—
310D8—22no—
311D8#41×C4712yes—
312M16—22no—
313M16—22no—
314M16—22no—
315M16—42no—
316M16—41no—
317M16—42no—
318C2×C8—42no—
319C2×C8—41no—
320C2×C8—42no—
321C2×C8C2×D4×C4711yescharacteristic
322C2×C8C2×D4×C4711yescharacteristic
323C2×C8C2×D4×C4711yescharacteristic
324C2×C8C24×C4711yescharacteristic
325C4⋊C4—21no—
326C4⋊C4—21no—
327C4⋊C4—41no—
328C4⋊C4—41no—
329C4⋊C4—41no—
330C4⋊C4—41no—
331C22⋊C4—41no—
332C22⋊C4—41no—
333C22⋊C4—41no—
334C22⋊C4—41no—
335C22⋊C4—41no—
336C42—21no—
337C42—41no—
338C42C2×D4×C4711yescharacteristic
339C42C2×D4×C4711yescharacteristic
340C16—22no—
341C16—22no—
342C23—41no—
343C23—41no—
344C23AGL(1,ℤ/8)×C4711yescharacteristic
345Q8—22no—
346Q8—41no—
347Q8—41no—
348Q8—41no—
349D4—22no—
350D4—41no—
351D4—42no—
352D4—42no—
353D4—41no—
354D4—41no—
355D4—82no—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—42no—
361C2×C4—41no—
362C2×C4—42no—
363C2×C4—41no—
364C2×C4—41no—
365C2×C4—41no—
366C2×C4—81no—
367C2×C4—82no—
368C2×C4AGL(1,ℤ/8)×C4711yescharacteristic
369C2×C4C22×D4×C4711yescharacteristic
370C8—21no—
371C8—21no—
372C8—42no—
373C8AGL(1,ℤ/8)×C4712yes—
374C8C2×#41×C4712yes—
375C22—21no—
376C22—41no—
377C22—42no—
378C22—81no—
379C22—81no—
380C22—81no—
381C22—161no—
382C22C2×AGL(1,ℤ/8)×C4711yescharacteristic
383C4—21no—
384C4—41no—
385C4—41no—
386C4—42no—
387C4—81no—
388C4—81no—
389C4—81no—
390C4C47×#52511yescharacteristic
391C4C2×AGL(1,ℤ/8)×C4711yescharacteristic
392C2—21no—
393C2—41no—
394C2—82no—
395C2—161no—
396C2C47×#310911yescharacteristic
subgroupG/H
center, socleC2×C47#3109
commutator, Frattini, cosocleC2×C8C24×C47
prime radicalC47×#2190C2
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C47 ◁ C2×C4×C47 ◁ C4×M16×C47 ◁ G

Complements

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

NH ≅ G/Ntype
1. C47×#3183C2semidirect
2. C47×#2956C2semidirect
3. C47×#2239C2semidirect
4. C47×#2238C2semidirect
5. C47×#2231C2semidirect
6. C47×#2212C2semidirect
7. C47×#2191C2semidirect
9. C47×AGL(1,ℤ/16)C2semidirect
10. C47×#2180C2semidirect
11. C47×#2165C2semidirect
17. C47×#499C22semidirect
18. C47×#495C22semidirect
27. C47×#442C22semidirect
28. C47×#441C22semidirect
33. C47×#365C22semidirect
34. C47×#365C22semidirect
35. C47×#364C22semidirect
36. C47×#362C22semidirect
37. C47×#361C22semidirect
42. C47×#347C22semidirect
176. #33690C47direct (N × H)
194. #3183C2×C47semidirect
195. #2956C2×C47semidirect
196. #2239C2×C47semidirect
197. #2238C2×C47semidirect
198. #2231C2×C47semidirect
199. #2212C2×C47semidirect
200. #2191C2×C47semidirect
202. AGL(1,ℤ/16)C2×C47semidirect
203. #2180C2×C47semidirect
204. #2165C2×C47semidirect
215. #499C22×C47semidirect
216. #495C22×C47semidirect
225. #442C22×C47semidirect
226. #441C22×C47semidirect
231. #365C22×C47semidirect
232. #365C22×C47semidirect
233. #364C22×C47semidirect
234. #362C22×C47semidirect
235. #361C22×C47semidirect
240. #347C22×C47semidirect
241. C47#33690direct (N × H)

Maximal subgroups

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

subgroupindex
C47×#31832
C47×#29562
C47×#22392
C47×#22382
C47×#22312
C47×#22122
C47×#21912
C47×#21902
C47×AGL(1,ℤ/16)2
C47×#21802
C47×#21652
#3369047