Finite Group Databasebeta

← C47×#33807 #26073505

Subgroups — C47×#33807 #26073505

Order 12032.

466 conjugacy classes of subgroups.

The subgroup lattice has 460 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C47×#3176C211yesmaximal, characteristic
2C47×#3164C211yesmaximal, characteristic, complemented
3C47×#2255C211yesmaximal, characteristic, complemented
4C47×#2253C211yesmaximal, characteristic, complemented
5C47×#2244C211yesmaximal, characteristic, complemented
6C47×#2240C211yesmaximal, characteristic, complemented
7C47×#2234C211yesmaximal, characteristic, complemented
8C47×#2234C211yesmaximal, characteristic, complemented
9C47×#2233C211yesmaximal, characteristic, complemented
10C47×#2232C211yesmaximal, characteristic, complemented
11C47×#2228C211yesmaximal, characteristic, complemented
12C47×#2228C211yesmaximal, characteristic, complemented
13C47×#2226C211yesmaximal, characteristic, complemented
14C47×#2224C211yesmaximal, characteristic, complemented
15C47×#2164C211yesmaximal, characteristic, complemented
16C47×#544—21no—
17C47×#540—21no—
18C47×#501—21no—
19C47×#501—21no—
20C47×#500C2211yescharacteristic
21C47×#500C2211yescharacteristic
22C47×#499C2211yescharacteristic
23C47×#499C2211yescharacteristic
24C47×#499C2211yescharacteristic
25C47×#493C2211yescharacteristic
26C47×#490—21no—
27C47×#469—21no—
28C47×#466C2211yescharacteristic
29C47×#466C2211yescharacteristic
30C47×#442—21no—
31C4×D8×C47C2211yescharacteristic
32C4×D8×C47C2211yescharacteristic
33C47×#428—21no—
34C47×#427C2211yescharacteristic
35C2×#107×C47C2211yescharacteristic
36C47×#405C2211yescharacteristic
37C47×#367C2211yescharacteristic
38C47×#367C2211yescharacteristic
39C47×#367C2211yescharacteristic
40C47×#367C2211yescharacteristic
41C47×#366C2211yescharacteristic
42C47×#366C2211yescharacteristic
43C47×#366C2211yescharacteristic
44C47×#366C2211yescharacteristic
45C47×C4⋊C16C2211yescharacteristic
46C47×C4⋊C16C2211yescharacteristic
47C47×#357C2211yescharacteristic
48C47×#357C2211yescharacteristic
49C47×#357C2211yescharacteristic
50C47×#357C2211yescharacteristic
51C47×#357C2211yescharacteristic
52C47×#357C2211yescharacteristic
53C47×#357C2211yescharacteristic
54C47×#357C2211yescharacteristic
55C47×C22⋊C16C2211yescharacteristic
56C47×C22⋊C16C2211yescharacteristic
57C47×#346C2211yescharacteristic
58C4×C16×C47C2211yescharacteristic
59C2×D8×C47—21no—
60C2×D8×C47C2311yescharacteristic
61C2×D8×C47C2311yescharacteristic
62C2×M16×C47D411yescharacteristic
63C22×C8×C47C2311yescharacteristic
64C4⋊Q8×C47—21no—
65C4⋊Q8×C47—21no—
66C4⋊Q8×C47—41no—
67#127×C47—21no—
68#125×C47—21no—
69#125×C47—21no—
70#125×C47—21no—
71#125×C47—41no—
72#123×C47—41no—
73#123×C47—41no—
74C22⋊Q8×C47—41no—
75C22⋊Q8×C47—41no—
76#121×C47—21no—
77#121×C47—21no—
78#121×C47—41no—
79#121×C47—41no—
80C4×D4×C47—21no—
81C4×D4×C47—21no—
82#117×C47—21no—
83#117×C47D411yescharacteristic
84C2×C4⋊C4×C47—21no—
85C2×C16×C47C2311yescharacteristic
86C2×C16×C47C2311yescharacteristic
87C2×C16×C47C2311yescharacteristic
88C2×C16×C47C2311yescharacteristic
89#107×C47—21no—
90#107×C47—21no—
91#107×C47—21no—
92#107×C47C2311yescharacteristic
93#107×C47C2311yescharacteristic
94#107×C47C2311yescharacteristic
95#107×C47C2311yescharacteristic
96#107×C47C2311yescharacteristic
97#107×C47C2311yescharacteristic
98#106×C47—21no—
99#106×C47—21no—
100#106×C47—21no—
101#106×C47—21no—
102#102×C47—21no—
103#102×C47—21no—
104#102×C47—21no—
105#102×C47—21no—
106#97×C47D411yescharacteristic
107#97×C47D411yescharacteristic
108C4×C8×C47C2311yescharacteristic
109C4×C8×C47C2311yescharacteristic
110C2×Q8×C47—41no—
111C2×Q8×C47—41no—
112C2×D4×C47—21no—
113C2×D4×C47—21no—
114C2×D4×C47—41no—
115C2×D4×C47—41no—
116C2×D4×C47—41no—
117C2×D4×C47—41no—
118C22×C4×C47—41no—
119C22×C4×C47—41no—
120C22×C4×C47—41no—
121C22×C4×C47C2×D411yescharacteristic
122D8×C47—21no—
123D8×C47—21no—
124D8×C47—21no—
125D8×C47—21no—
126D8×C47—42no—
127M16×C47—22no—
128C2×C8×C47—21no—
129C2×C8×C47—21no—
130C2×C8×C47C2×D411yescharacteristic
131C2×C8×C47C2×D411yescharacteristic
132C2×C8×C47C2×D411yescharacteristic
133C2×C8×C47C2411yescharacteristic
134C4⋊C4×C47—21no—
135C4⋊C4×C47—21no—
136C4⋊C4×C47—21no—
137C4⋊C4×C47—21no—
138C4⋊C4×C47—21no—
139C4⋊C4×C47—21no—
140C4⋊C4×C47—41no—
141C4⋊C4×C47—41no—
142C4⋊C4×C47—41no—
143C4⋊C4×C47—41no—
144C4⋊C4×C47—41no—
145C4⋊C4×C47—41no—
146C4⋊C4×C47—41no—
147C4⋊C4×C47—41no—
148C4⋊C4×C47—41no—
149C4⋊C4×C47D811yescharacteristic
150C4⋊C4×C47D811yescharacteristic
151C22⋊C4×C47—41no—
152C22⋊C4×C47—41no—
153C22⋊C4×C47—41no—
154C22⋊C4×C47—41no—
155C22⋊C4×C47—41no—
156C22⋊C4×C47D811yescharacteristic
157C22⋊C4×C47D811yescharacteristic
158C42×C47—41no—
159C42×C47C2×D411yescharacteristic
160C42×C47C2×D411yescharacteristic
161C16×C47—21no—
162C16×C47—21no—
163C16×C47—21no—
164C16×C47—21no—
165C23×C47—41no—
166C23×C47—41no—
167C23×C47C2×D811yescharacteristic
168Q8×C47—161no—
169Q8×C47—161no—
170D4×C47—41no—
171D4×C47—41no—
172D4×C47—41no—
173D4×C47—41no—
174D4×C47—161no—
175D4×C47—161no—
176D4×C47—161no—
177D4×C47—161no—
178C2×C4×C47—21no—
179C2×C4×C47—21no—
180C2×C4×C47—41no—
181C2×C4×C47—41no—
182C2×C4×C47—41no—
183C2×C4×C47—41no—
184C2×C4×C47—41no—
185C2×C4×C47—41no—
186C2×C4×C47—161no—
187C2×C4×C47—161no—
188C2×C4×C47—161no—
189C2×C4×C47C2×D811yescharacteristic
190C2×C4×C47C2×D811yescharacteristic
191C2×C4×C47C2×D811yescharacteristic
192C2×C4×C47C2×D811yescharacteristic
193C2×C4×C47C2×D811yescharacteristic
194C2×C4×C47C22×D411yescharacteristic
195C8×C47—21no—
196C8×C47—21no—
197C8×C47#13712yes—
198C8×C472−1+411yescharacteristic
199C8×C472−1+411yescharacteristic
200#33807C4711yesmaximal, characteristic, direct product factor, Sylow
201C22×C47—21no—
202C22×C47—21no—
203C22×C47—21no—
204C22×C47—81no—
205C22×C47—81no—
206C22×C47—81no—
207C22×C47—81no—
208C22×C47—81no—
209C22×C47—81no—
210C22×C47C22×D811yescharacteristic
211C4×C47—21no—
212C4×C47—21no—
213C4×C47—21no—
214C4×C47—21no—
215C4×C47—21no—
216C4×C47—81no—
217C4×C47—81no—
218C4×C47—81no—
219C4×C47—81no—
220C4×C47—81no—
221C4×C47—81no—
222C4×C47#53611yescharacteristic
223C4×C47C2×#13711yescharacteristic
224#3176C2×C4711yescharacteristic
225#3164C2×C4711yescharacteristic, complemented
226#2255C2×C4711yescharacteristic, complemented
227#2253C2×C4711yescharacteristic, complemented
228#2244C2×C4711yescharacteristic, complemented
229#2240C2×C4711yescharacteristic, complemented
230#2234C2×C4711yescharacteristic, complemented
231#2234C2×C4711yescharacteristic, complemented
232#2233C2×C4711yescharacteristic, complemented
233#2232C2×C4711yescharacteristic, complemented
234#2228C2×C4711yescharacteristic, complemented
235#2228C2×C4711yescharacteristic, complemented
236#2226C2×C4711yescharacteristic, complemented
237#2224C2×C4711yescharacteristic, complemented
238#2164C2×C4711yescharacteristic, complemented
239C2×C47—41no—
240C2×C47—161no—
241C2×C47—161no—
242C2×C47#322611yescharacteristic
243C2×C47#341511yescharacteristic
244C2×C47#341611yescharacteristic
245#544—21no—
246#540—21no—
247#501—21no—
248#501—21no—
249#500C22×C4711yescharacteristic
250#500C22×C4711yescharacteristic
251#499C22×C4711yescharacteristic
252#499C22×C4711yescharacteristic
253#499C22×C4711yescharacteristic
254#493C22×C4711yescharacteristic
255#490—21no—
256#469—21no—
257#466C22×C4711yescharacteristic
258#466C22×C4711yescharacteristic
259#442—21no—
260C4×D8C22×C4711yescharacteristic
261C4×D8C22×C4711yescharacteristic
262#428—21no—
263#427C22×C4711yescharacteristic
264C2×#107C22×C4711yescharacteristic
265#405C22×C4711yescharacteristic
266#367C22×C4711yescharacteristic
267#367C22×C4711yescharacteristic
268#367C22×C4711yescharacteristic
269#367C22×C4711yescharacteristic
270#366C22×C4711yescharacteristic
271#366C22×C4711yescharacteristic
272#366C22×C4711yescharacteristic
273#366C22×C4711yescharacteristic
274C4⋊C16C22×C4711yescharacteristic
275C4⋊C16C22×C4711yescharacteristic
276#357C22×C4711yescharacteristic
277#357C22×C4711yescharacteristic
278#357C22×C4711yescharacteristic
279#357C22×C4711yescharacteristic
280#357C22×C4711yescharacteristic
281#357C22×C4711yescharacteristic
282#357C22×C4711yescharacteristic
283#357C22×C4711yescharacteristic
284C22⋊C16C22×C4711yescharacteristic
285C22⋊C16C22×C4711yescharacteristic
286#346C22×C4711yescharacteristic
287C4×C16C22×C4711yescharacteristic
288C47#3380711yescharacteristic, direct product factor, Sylow
289C2×D8—21no—
290C2×D8C23×C4711yescharacteristic
291C2×D8C23×C4711yescharacteristic
292C2×M16D4×C4711yescharacteristic
293C22×C8C23×C4711yescharacteristic
294C4⋊Q8—21no—
295C4⋊Q8—21no—
296C4⋊Q8—41no—
297#127—21no—
298#125—21no—
299#125—21no—
300#125—21no—
301#125—41no—
302#123—41no—
303#123—41no—
304C22⋊Q8—41no—
305C22⋊Q8—41no—
306#121—21no—
307#121—21no—
308#121—41no—
309#121—41no—
310C4×D4—21no—
311C4×D4—21no—
312#117—21no—
313#117D4×C4711yescharacteristic
314C2×C4⋊C4—21no—
315C2×C16C23×C4711yescharacteristic
316C2×C16C23×C4711yescharacteristic
317C2×C16C23×C4711yescharacteristic
318C2×C16C23×C4711yescharacteristic
319#107—21no—
320#107—21no—
321#107—21no—
322#107C23×C4711yescharacteristic
323#107C23×C4711yescharacteristic
324#107C23×C4711yescharacteristic
325#107C23×C4711yescharacteristic
326#107C23×C4711yescharacteristic
327#107C23×C4711yescharacteristic
328#106—21no—
329#106—21no—
330#106—21no—
331#106—21no—
332#102—21no—
333#102—21no—
334#102—21no—
335#102—21no—
336#97D4×C4711yescharacteristic
337#97D4×C4711yescharacteristic
338C4×C8C23×C4711yescharacteristic
339C4×C8C23×C4711yescharacteristic
340C2×Q8—41no—
341C2×Q8—41no—
342C2×D4—21no—
343C2×D4—21no—
344C2×D4—41no—
345C2×D4—41no—
346C2×D4—41no—
347C2×D4—41no—
348C22×C4—41no—
349C22×C4—41no—
350C22×C4—41no—
351C22×C4C2×D4×C4711yescharacteristic
352D8—21no—
353D8—21no—
354D8—21no—
355D8—21no—
356D8—42no—
357M16—22no—
358C2×C8—21no—
359C2×C8—21no—
360C2×C8C2×D4×C4711yescharacteristic
361C2×C8C2×D4×C4711yescharacteristic
362C2×C8C2×D4×C4711yescharacteristic
363C2×C8C24×C4711yescharacteristic
364C4⋊C4—21no—
365C4⋊C4—21no—
366C4⋊C4—21no—
367C4⋊C4—21no—
368C4⋊C4—21no—
369C4⋊C4—21no—
370C4⋊C4—41no—
371C4⋊C4—41no—
372C4⋊C4—41no—
373C4⋊C4—41no—
374C4⋊C4—41no—
375C4⋊C4—41no—
376C4⋊C4—41no—
377C4⋊C4—41no—
378C4⋊C4—41no—
379C4⋊C4D8×C4711yescharacteristic
380C4⋊C4D8×C4711yescharacteristic
381C22⋊C4—41no—
382C22⋊C4—41no—
383C22⋊C4—41no—
384C22⋊C4—41no—
385C22⋊C4—41no—
386C22⋊C4D8×C4711yescharacteristic
387C22⋊C4D8×C4711yescharacteristic
388C42—41no—
389C42C2×D4×C4711yescharacteristic
390C42C2×D4×C4711yescharacteristic
391C16—21no—
392C16—21no—
393C16—21no—
394C16—21no—
395C23—41no—
396C23—41no—
397C23C2×D8×C4711yescharacteristic
398Q8—161no—
399Q8—161no—
400D4—41no—
401D4—41no—
402D4—41no—
403D4—41no—
404D4—161no—
405D4—161no—
406D4—161no—
407D4—161no—
408C2×C4—21no—
409C2×C4—21no—
410C2×C4—41no—
411C2×C4—41no—
412C2×C4—41no—
413C2×C4—41no—
414C2×C4—41no—
415C2×C4—41no—
416C2×C4—161no—
417C2×C4—161no—
418C2×C4—161no—
419C2×C4C2×D8×C4711yescharacteristic
420C2×C4C2×D8×C4711yescharacteristic
421C2×C4C2×D8×C4711yescharacteristic
422C2×C4C2×D8×C4711yescharacteristic
423C2×C4C2×D8×C4711yescharacteristic
424C2×C4C22×D4×C4711yescharacteristic
425C8—21no—
426C8—21no—
427C8#137×C4712yes—
428C82−1+4×C4711yescharacteristic
429C82−1+4×C4711yescharacteristic
430C22—21no—
431C22—21no—
432C22—21no—
433C22—81no—
434C22—81no—
435C22—81no—
436C22—81no—
437C22—81no—
438C22—81no—
439C22C22×D8×C4711yescharacteristic
440C4—21no—
441C4—21no—
442C4—21no—
443C4—21no—
444C4—21no—
445C4—81no—
446C4—81no—
447C4—81no—
448C4—81no—
449C4—81no—
450C4—81no—
451C4C47×#53611yescharacteristic
452C4C2×#137×C4711yescharacteristic
453C2—41no—
454C2—161no—
455C2—161no—
456C2C47×#322611yescharacteristic
457C2C47×#341511yescharacteristic
458C2C47×#341611yescharacteristic
subgroupG/H
center, socleC22×C47C22×D8
commutator, Frattini, cosocleC2×C8C24×C47
prime radicalC47×#3176C2
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C47 ◁ #117×C47 ◁ C47×#405 ◁ G

Complements

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

NH ≅ G/Ntype
2. C47×#3164C2semidirect
3. C47×#2255C2semidirect
4. C47×#2253C2semidirect
5. C47×#2244C2semidirect
6. C47×#2240C2semidirect
7. C47×#2234C2semidirect
8. C47×#2234C2semidirect
9. C47×#2233C2semidirect
10. C47×#2232C2semidirect
11. C47×#2228C2semidirect
12. C47×#2228C2semidirect
13. C47×#2226C2semidirect
14. C47×#2224C2semidirect
15. C47×#2164C2semidirect
200. #33807C47direct (N × H)
225. #3164C2×C47semidirect
226. #2255C2×C47semidirect
227. #2253C2×C47semidirect
228. #2244C2×C47semidirect
229. #2240C2×C47semidirect
230. #2234C2×C47semidirect
231. #2234C2×C47semidirect
232. #2233C2×C47semidirect
233. #2232C2×C47semidirect
234. #2228C2×C47semidirect
235. #2228C2×C47semidirect
236. #2226C2×C47semidirect
237. #2224C2×C47semidirect
238. #2164C2×C47semidirect
288. C47#33807direct (N × H)

Maximal subgroups

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

subgroupindex
C47×#31762
C47×#31642
C47×#22552
C47×#22532
C47×#22442
C47×#22402
C47×#22342
C47×#22332
C47×#22322
C47×#22282
C47×#22262
C47×#22242
C47×#21642
#3380747