Finite Group Databasebeta

← C47×#33595 #26073293

Subgroups — C47×#33595 #26073293

Order 12032.

706 conjugacy classes of subgroups.

The subgroup lattice has 454 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C47×#3414C211yesmaximal, characteristic, complemented
2C2×C47×#509C211yesmaximal, characteristic, complemented
3C47×#3155C211yesmaximal, characteristic, complemented
4C47×#2957C211yesmaximal, characteristic, complemented
5C47×#2213C214yesmaximal, complemented
6C47×#2212C214yesmaximal, complemented
7C47×#2153C211yesmaximal, characteristic, complemented
8C47×#2148C211yesmaximal, characteristic, complemented
9C2×C47×#361C211yesmaximal, characteristic, complemented
10C2×AGL(1,ℤ/8)×C47—21no—
11C2×#135×C47C2211yescharacteristic
12C2×#135×C47C2211yescharacteristic
13C22×D8×C47C2211yescharacteristic
14C47×#568—21no—
15C47×#535—21no—
16C47×#510—21no—
17C47×#510C2212yescomplemented
18C47×#509—22no—
19C47×#509—21no—
20C47×#509C2214yes—
21C47×#509C2212yescomplemented
22C47×#508—22no—
23C2×SD32×C47—21no—
24C2×D16×C47—21no—
25C2×M32×C47C2211yescharacteristic
26C2×M32×C47C2211yescharacteristic
27C47×#496—22no—
28C47×#495C2212yescomplemented
29C47×#493C2212yescomplemented
30C47×#444—22no—
31C47×#443C2214yescomplemented
32C2×#108×C47C2211yescharacteristic
33C47×#421—21no—
34C47×#405C2211yescharacteristic
35C47×#364C2214yescomplemented
36C47×#362C2212yescomplemented
37C47×#361C2214yescomplemented
38C47×#361C2212yescomplemented
39C2×#41×C47—21no—
40C2×#41×C47—21no—
41C22×D4×C47—21no—
42AGL(1,ℤ/8)×C47—42no—
43AGL(1,ℤ/8)×C47—42no—
44#135×C47—21no—
45#135×C47—21no—
46#135×C47—21no—
47#135×C47—21no—
48#135×C47—21no—
49#135×C47—21no—
50#135×C47D412yescomplemented
51#135×C47C2312yes—
52C2×Q16×C47D411yescharacteristic, complemented
53C2×Q16×C47C2311yescharacteristic
54C2×SD16×C47—22no—
55C2×SD16×C47—21no—
56C2×SD16×C47—21no—
57C2×D8×C47—21no—
58C2×D8×C47—21no—
59C2×D8×C47—22no—
60C2×D8×C47—21no—
61C2×D8×C47—21no—
62C2×D8×C47—21no—
63C2×D8×C47D411yescharacteristic, complemented
64C2×D8×C47C2311yescharacteristic
65C2×D8×C47C2312yes—
66#131×C47—24no—
67#131×C47—42no—
68C2×M16×C47—21no—
69C2×M16×C47—42no—
70C2×M16×C47D411yescharacteristic
71C22×C8×C47C2311yescharacteristic
72#127×C47—22no—
73#124×C47—22no—
74#121×C47—42no—
75#120×C47—42no—
76#117×C47D411yescharacteristic
77Q32×C47—22no—
78SD32×C47—24no—
79SD32×C47—22no—
80SD32×C47—22no—
81D16×C47—24no—
82D16×C47—22no—
83M32×C47—21no—
84M32×C47—21no—
85M32×C47C2312yes—
86M32×C47C2312yes—
87C2×C16×C47—21no—
88C2×C16×C47—21no—
89#108×C47—21no—
90#108×C47C2312yes—
91#104×C47—24no—
92#97×C47D412yes—
93C4×C8×C47C2312yes—
94C24×C47—41no—
95#41×C47—22no—
96#41×C47—22no—
97#41×C47—41no—
98#41×C47—41no—
99#41×C47—41no—
100#41×C47—41no—
101#41×C47—41no—
102#41×C47—41no—
103C2×Q8×C47—21no—
104C2×Q8×C47—21no—
105C2×D4×C47—21no—
106C2×D4×C47—22no—
107C2×D4×C47—21no—
108C2×D4×C47—44no—
109C2×D4×C47—41no—
110C2×D4×C47—41no—
111C2×D4×C47—41no—
112C2×D4×C47—41no—
113C2×D4×C47—41no—
114C2×D4×C47—41no—
115C2×D4×C47—41no—
116C22×C4×C47—41no—
117C22×C4×C47—41no—
118C22×C4×C47C2×D411yescharacteristic
119Q16×C47—21no—
120Q16×C47—21no—
121Q16×C47—21no—
122Q16×C47C2×D412yes—
123SD16×C47—22no—
124SD16×C47—22no—
125SD16×C47—41no—
126SD16×C47—41no—
127SD16×C47—44no—
128D8×C47—21no—
129D8×C47—22no—
130D8×C47—21no—
131D8×C47—22no—
132D8×C47—21no—
133D8×C47—41no—
134D8×C47—41no—
135D8×C47—44no—
136D8×C47C2×D412yes—
137M16×C47—22no—
138M16×C47—41no—
139M16×C47—44no—
140M16×C47D812yes—
141M16×C47D812yes—
142C2×C8×C47—41no—
143C2×C8×C47—44no—
144C2×C8×C47C2×D411yescharacteristic
145C2×C8×C47C2×D411yescharacteristic
146C2×C8×C47C2×D411yescharacteristic
147C2×C8×C47C2×D412yes—
148C2×C8×C47#4111yescharacteristic
149C2×C8×C47#4111yescharacteristic
150C2×C8×C47C2411yescharacteristic
151C4⋊C4×C47—21no—
152C22⋊C4×C47—21no—
153C22⋊C4×C47—44no—
154C42×C47C2×D412yes—
155C16×C47—22no—
156C16×C47—22no—
157C23×C47—41no—
158C23×C47—42no—
159C23×C47—41no—
160C23×C47—81no—
161C23×C47—81no—
162C23×C47—162no—
163C23×C47AGL(1,ℤ/8)11yescharacteristic
164Q8×C47—22no—
165Q8×C47—41no—
166Q8×C47—41no—
167Q8×C47—41no—
168D4×C47—22no—
169D4×C47—42no—
170D4×C47—42no—
171D4×C47—42no—
172D4×C47—41no—
173D4×C47—41no—
174D4×C47—42no—
175D4×C47—41no—
176D4×C47—81no—
177D4×C47—81no—
178D4×C47—81no—
179D4×C47—81no—
180D4×C47—164no—
181C2×C4×C47—22no—
182C2×C4×C47—41no—
183C2×C4×C47—42no—
184C2×C4×C47—42no—
185C2×C4×C47—41no—
186C2×C4×C47—81no—
187C2×C4×C47—81no—
188C2×C4×C47#12111yescharacteristic
189C2×C4×C47#12111yescharacteristic
190C2×C4×C47C2×D811yescharacteristic
191C2×C4×C47C2×D811yescharacteristic
192C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
193C2×C4×C47C22×D411yescharacteristic
194C8×C47—42no—
195C8×C47#12111yescharacteristic
196C8×C47#12111yescharacteristic
197C8×C47C2×D814yes—
198C8×C47C22×D411yescharacteristic
199C8×C47C2×#4111yescharacteristic
200#33595C4711yesmaximal, characteristic, direct product factor, Sylow
201C22×C47—41no—
202C22×C47—42no—
203C22×C47—82no—
204C22×C47—84no—
205C22×C47—81no—
206C22×C47—82no—
207C22×C47—161no—
208C22×C47—162no—
209C22×C47—162no—
210C22×C47#45911yescharacteristic
211C22×C47#45911yescharacteristic
212C22×C47C2×AGL(1,ℤ/8)11yescharacteristic
213C4×C47—42no—
214C4×C47—42no—
215C4×C47—81no—
216C4×C47#45911yescharacteristic
217C4×C47#45911yescharacteristic
218C4×C47C2×#12111yescharacteristic
219C4×C47C22×D811yescharacteristic
220#3414C2×C4711yescharacteristic, complemented
221C2×#509C2×C4711yescharacteristic, complemented
222#3155C2×C4711yescharacteristic, complemented
223#2957C2×C4711yescharacteristic, complemented
224#2213C2×C4714yescomplemented
225#2212C2×C4714yescomplemented
226#2153C2×C4711yescharacteristic, complemented
227#2148C2×C4711yescharacteristic, complemented
228C2×#361C2×C4711yescharacteristic, complemented
229C2×C47—21no—
230C2×C47—21no—
231C2×C47—21no—
232C2×C47—82no—
233C2×C47—161no—
234C2×C47—162no—
235C2×C47C2×#45911yescharacteristic
236C2×AGL(1,ℤ/8)—21no—
237C2×#135C22×C4711yescharacteristic
238C2×#135C22×C4711yescharacteristic
239C22×D8C22×C4711yescharacteristic
240#568—21no—
241#535—21no—
242#510—21no—
243#510C22×C4712yescomplemented
244#509—22no—
245#509—21no—
246#509C22×C4714yes—
247#509C22×C4712yescomplemented
248#508—22no—
249C2×SD32—21no—
250C2×D16—21no—
251C2×M32C22×C4711yescharacteristic
252C2×M32C22×C4711yescharacteristic
253#496—22no—
254#495C22×C4712yescomplemented
255#493C22×C4712yescomplemented
256#444—22no—
257#443C22×C4714yescomplemented
258C2×#108C22×C4711yescharacteristic
259#421—21no—
260#405C22×C4711yescharacteristic
261#364C22×C4714yescomplemented
262#362C22×C4712yescomplemented
263#361C22×C4714yescomplemented
264#361C22×C4712yescomplemented
265C47#3359511yescharacteristic, direct product factor, Sylow
266C2×#41—21no—
267C2×#41—21no—
268C22×D4—21no—
269AGL(1,ℤ/8)—42no—
270AGL(1,ℤ/8)—42no—
271#135—21no—
272#135—21no—
273#135—21no—
274#135—21no—
275#135—21no—
276#135—21no—
277#135D4×C4712yescomplemented
278#135C23×C4712yes—
279C2×Q16D4×C4711yescharacteristic, complemented
280C2×Q16C23×C4711yescharacteristic
281C2×SD16—21no—
282C2×SD16—22no—
283C2×SD16—21no—
284C2×D8—21no—
285C2×D8—21no—
286C2×D8—21no—
287C2×D8—22no—
288C2×D8—21no—
289C2×D8—21no—
290C2×D8D4×C4711yescharacteristic, complemented
291C2×D8C23×C4712yes—
292C2×D8C23×C4711yescharacteristic
293#131—24no—
294#131—42no—
295C2×M16—21no—
296C2×M16—42no—
297C2×M16D4×C4711yescharacteristic
298C22×C8C23×C4711yescharacteristic
299#127—22no—
300#124—22no—
301#121—42no—
302#120—42no—
303#117D4×C4711yescharacteristic
304Q32—22no—
305SD32—24no—
306SD32—22no—
307SD32—22no—
308D16—24no—
309D16—22no—
310M32—21no—
311M32—21no—
312M32C23×C4712yes—
313M32C23×C4712yes—
314C2×C16—21no—
315C2×C16—21no—
316#108—21no—
317#108C23×C4712yes—
318#104—24no—
319#97D4×C4712yes—
320C4×C8C23×C4712yes—
321C24—41no—
322#41—22no—
323#41—22no—
324#41—41no—
325#41—41no—
326#41—41no—
327#41—41no—
328#41—41no—
329#41—41no—
330C2×Q8—21no—
331C2×Q8—21no—
332C2×D4—21no—
333C2×D4—22no—
334C2×D4—21no—
335C2×D4—44no—
336C2×D4—41no—
337C2×D4—41no—
338C2×D4—41no—
339C2×D4—41no—
340C2×D4—41no—
341C2×D4—41no—
342C2×D4—41no—
343C22×C4—41no—
344C22×C4—41no—
345C22×C4C2×D4×C4711yescharacteristic
346Q16—21no—
347Q16—21no—
348Q16—21no—
349Q16C2×D4×C4712yes—
350SD16—22no—
351SD16—22no—
352SD16—41no—
353SD16—41no—
354SD16—44no—
355D8—21no—
356D8—22no—
357D8—21no—
358D8—22no—
359D8—21no—
360D8—41no—
361D8—41no—
362D8—44no—
363D8C2×D4×C4712yes—
364M16—22no—
365M16—41no—
366M16—44no—
367M16D8×C4712yes—
368M16D8×C4712yes—
369C2×C8—41no—
370C2×C8—44no—
371C2×C8C2×D4×C4711yescharacteristic
372C2×C8C2×D4×C4711yescharacteristic
373C2×C8C2×D4×C4711yescharacteristic
374C2×C8C2×D4×C4712yes—
375C2×C8#41×C4711yescharacteristic
376C2×C8#41×C4711yescharacteristic
377C2×C8C24×C4711yescharacteristic
378C4⋊C4—21no—
379C22⋊C4—21no—
380C22⋊C4—44no—
381C42C2×D4×C4712yes—
382C16—22no—
383C16—22no—
384C23—41no—
385C23—42no—
386C23—41no—
387C23—81no—
388C23—81no—
389C23—162no—
390C23AGL(1,ℤ/8)×C4711yescharacteristic
391Q8—22no—
392Q8—41no—
393Q8—41no—
394Q8—41no—
395D4—22no—
396D4—42no—
397D4—42no—
398D4—41no—
399D4—42no—
400D4—41no—
401D4—41no—
402D4—42no—
403D4—81no—
404D4—81no—
405D4—81no—
406D4—81no—
407D4—164no—
408C2×C4—22no—
409C2×C4—41no—
410C2×C4—42no—
411C2×C4—42no—
412C2×C4—41no—
413C2×C4—81no—
414C2×C4—81no—
415C2×C4#121×C4711yescharacteristic
416C2×C4#121×C4711yescharacteristic
417C2×C4C2×D8×C4711yescharacteristic
418C2×C4C2×D8×C4711yescharacteristic
419C2×C4AGL(1,ℤ/8)×C4711yescharacteristic
420C2×C4C22×D4×C4711yescharacteristic
421C8—42no—
422C8#121×C4711yescharacteristic
423C8#121×C4711yescharacteristic
424C8C2×D8×C4714yes—
425C8C22×D4×C4711yescharacteristic
426C8C2×#41×C4711yescharacteristic
427C22—41no—
428C22—42no—
429C22—82no—
430C22—84no—
431C22—81no—
432C22—82no—
433C22—161no—
434C22—162no—
435C22—162no—
436C22C47×#45911yescharacteristic
437C22C47×#45911yescharacteristic
438C22C2×AGL(1,ℤ/8)×C4711yescharacteristic
439C4—42no—
440C4—42no—
441C4—81no—
442C4C47×#45911yescharacteristic
443C4C47×#45911yescharacteristic
444C4C2×#121×C4711yescharacteristic
445C4C22×D8×C4711yescharacteristic
446C2—21no—
447C2—21no—
448C2—21no—
449C2—82no—
450C2—162no—
451C2—161no—
452C2C2×C47×#45911yescharacteristic
subgroupG/H
center, socleC2×C47C2×#459
commutator, Frattini, cosocleC2×C8C24×C47
LCSG ▷ C2×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
1. C47×#3414C2semidirect
2. C2×C47×#509C2semidirect
3. C47×#3155C2semidirect
4. C47×#2957C2semidirect
5. C47×#2213C2semidirect
6. C47×#2212C2semidirect
7. C47×#2153C2semidirect
8. C47×#2148C2semidirect
9. C2×C47×#361C2semidirect
17. C47×#510C22semidirect
21. C47×#509C22semidirect
28. C47×#495C22semidirect
29. C47×#493C22semidirect
31. C47×#443C22semidirect
35. C47×#364C22semidirect
36. C47×#362C22semidirect
37. C47×#361C22semidirect
38. C47×#361C22semidirect
50. #135×C47D4semidirect
52. C2×Q16×C47D4semidirect
63. C2×D8×C47D4semidirect
200. #33595C47direct (N × H)
220. #3414C2×C47semidirect
221. C2×#509C2×C47semidirect
222. #3155C2×C47semidirect
223. #2957C2×C47semidirect
224. #2213C2×C47semidirect
225. #2212C2×C47semidirect
226. #2153C2×C47semidirect
227. #2148C2×C47semidirect
228. C2×#361C2×C47semidirect
243. #510C22×C47semidirect
247. #509C22×C47semidirect
254. #495C22×C47semidirect
255. #493C22×C47semidirect
257. #443C22×C47semidirect
261. #364C22×C47semidirect
262. #362C22×C47semidirect
263. #361C22×C47semidirect
264. #361C22×C47semidirect
265. C47#33595direct (N × H)
277. #135D4×C47semidirect
279. C2×Q16D4×C47semidirect
290. C2×D8D4×C47semidirect

Maximal subgroups

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

subgroupindex
C47×#34142
C2×C47×#5092
C47×#31552
C47×#29572
C47×#22132
C47×#22122
C47×#21532
C47×#21482
C2×C47×#3612
#3359547