Finite Group Databasebeta

← C47×#33913 #26073611

Subgroups — C47×#33913 #26073611

Order 12032.

484 conjugacy classes of subgroups.

The subgroup lattice has 468 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C47×#3339C211yesmaximal, characteristic
2C47×#3338C211yesmaximal, characteristic, complemented
3C47×#2255C211yesmaximal, characteristic, complemented
4C47×#2237C211yesmaximal, characteristic, complemented
5C47×#2236C211yesmaximal, characteristic, complemented
6C47×#2233C211yesmaximal, characteristic, complemented
7C47×#2232C211yesmaximal, characteristic, complemented
8C47×#2229C211yesmaximal, characteristic, complemented
9C47×#2224C211yesmaximal, characteristic, complemented
10C47×#2220C211yesmaximal, characteristic, complemented
11C47×#2217C211yesmaximal, characteristic, complemented
12C47×#2175C211yesmaximal, characteristic, complemented
13C47×#2168C211yesmaximal, characteristic, complemented
14C47×#2159C211yesmaximal, characteristic, complemented
15C2×C47×#366C211yesmaximal, characteristic, complemented
16C47×#554—21no—
17C47×#553—21no—
18C2×SD32×C47C2211yescharacteristic
19C2×M32×C47C2211yescharacteristic
20C22×C16×C47C2211yescharacteristic
21C47×#500C2211yescharacteristic
22C47×#499C2211yescharacteristic
23C47×#484—21no—
24C47×#484—21no—
25C47×#482—21no—
26C47×#481—21no—
27C47×#478—21no—
28C47×#477—21no—
29C47×#467C2211yescharacteristic
30C47×#467C2211yescharacteristic
31C47×#466C2211yescharacteristic
32C47×#466C2211yescharacteristic
33C4×Q16×C47C2211yescharacteristic
34C4×D8×C47C2211yescharacteristic
35C8×D4×C47C2211yescharacteristic
36C47×#427C2211yescharacteristic
37C2×#107×C47C2211yescharacteristic
38C2×#107×C47C2211yescharacteristic
39C2×#107×C47C2211yescharacteristic
40C47×#367C2211yescharacteristic
41C47×#367C2211yescharacteristic
42C47×#367C2211yescharacteristic
43C47×#366C2211yescharacteristic
44C47×#366C2211yescharacteristic
45C47×#366C2211yescharacteristic
46C47×#366C2211yescharacteristic
47C47×#366C2211yescharacteristic
48C47×#366C2211yescharacteristic
49C47×C4⋊C16C2211yescharacteristic
50C47×#358C2211yescharacteristic
51C47×#358C2211yescharacteristic
52C47×#358C2211yescharacteristic
53C47×#357C2211yescharacteristic
54C47×#357C2211yescharacteristic
55C47×#357C2211yescharacteristic
56C47×C22⋊C16C2211yescharacteristic
57C47×C22⋊C16C2211yescharacteristic
58C47×#346C2211yescharacteristic
59C2×Q16×C47C2311yescharacteristic
60C2×D8×C47C2311yescharacteristic
61C22×C8×C47C2311yescharacteristic
62C22×C8×C47C2311yescharacteristic
63C4⋊Q8×C47—21no—
64#126×C47—41no—
65#125×C47—21no—
66#125×C47—41no—
67#123×C47—41no—
68C22⋊Q8×C47—21no—
69C22⋊Q8×C47—21no—
70C22⋊Q8×C47—41no—
71C22⋊Q8×C47—41no—
72#121×C47—21no—
73#121×C47—21no—
74#121×C47—41no—
75C4×Q8×C47—21no—
76C4×D4×C47—21no—
77C4×D4×C47—41no—
78C4×D4×C47—41no—
79C4×D4×C47D411yescharacteristic
80#117×C47—21no—
81C2×C4⋊C4×C47—21no—
82C2×C4⋊C4×C47—21no—
83C2×C4⋊C4×C47—21no—
84SD32×C47—22no—
85M32×C47—22no—
86C2×C16×C47—22no—
87C2×C16×C47C2311yescharacteristic
88C2×C16×C47C2311yescharacteristic
89C2×C16×C47C2311yescharacteristic
90C2×C16×C47C2311yescharacteristic
91#107×C47—21no—
92#107×C47—21no—
93#107×C47—21no—
94#107×C47—21no—
95#107×C47C2311yescharacteristic
96#107×C47C2311yescharacteristic
97#107×C47C2311yescharacteristic
98#107×C47C2311yescharacteristic
99#107×C47C2311yescharacteristic
100#107×C47C2311yescharacteristic
101#106×C47—21no—
102#106×C47—21no—
103C4⋊C8×C47D411yescharacteristic
104#103×C47—21no—
105#103×C47—21no—
106#103×C47—21no—
107#102×C47—21no—
108#102×C47—21no—
109#102×C47—21no—
110C22⋊C8×C47D411yescharacteristic
111C22⋊C8×C47D411yescharacteristic
112C4×C8×C47C2311yescharacteristic
113C2×Q8×C47—21no—
114C2×Q8×C47—41no—
115C2×D4×C47—21no—
116C2×D4×C47—41no—
117C2×D4×C47—41no—
118C2×D4×C47D811yescharacteristic
119C22×C4×C47—41no—
120C22×C4×C47—41no—
121C22×C4×C47—41no—
122C22×C4×C47—41no—
123C22×C4×C47C2×D411yescharacteristic
124C22×C4×C47C2×D411yescharacteristic
125Q16×C47—21no—
126Q16×C47—21no—
127D8×C47—21no—
128D8×C47—21no—
129C2×C8×C47—21no—
130C2×C8×C47—21no—
131C2×C8×C47—21no—
132C2×C8×C47—21no—
133C2×C8×C47C2×D411yescharacteristic
134C2×C8×C47C2×D411yescharacteristic
135C2×C8×C47C2×D411yescharacteristic
136C2×C8×C47C2411yescharacteristic
137C4⋊C4×C47—21no—
138C4⋊C4×C47—21no—
139C4⋊C4×C47—21no—
140C4⋊C4×C47—21no—
141C4⋊C4×C47—21no—
142C4⋊C4×C47—21no—
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×C47—41no—
150C4⋊C4×C47—41no—
151C4⋊C4×C47—41no—
152C4⋊C4×C47D811yescharacteristic
153C22⋊C4×C47—41no—
154C22⋊C4×C47—41no—
155C22⋊C4×C47—41no—
156C22⋊C4×C47—41no—
157C22⋊C4×C47—41no—
158C22⋊C4×C47—41no—
159C22⋊C4×C47D811yescharacteristic
160C22⋊C4×C47D811yescharacteristic
161C42×C47—41no—
162C42×C47—41no—
163C42×C47C2×D411yescharacteristic
164C16×C47—21no—
165C16×C47—21no—
166C16×C47—21no—
167C16×C47#4112yes—
168C23×C47—41no—
169C23×C47C2×D811yescharacteristic
170C23×C47C2×D811yescharacteristic
171Q8×C47—41no—
172Q8×C47—41no—
173Q8×C47—161no—
174D4×C47—22no—
175D4×C47—41no—
176D4×C47—41no—
177D4×C47—82no—
178D4×C47—161no—
179C2×C4×C47—21no—
180C2×C4×C47—21no—
181C2×C4×C47—21no—
182C2×C4×C47—21no—
183C2×C4×C47—41no—
184C2×C4×C47—41no—
185C2×C4×C47—41no—
186C2×C4×C47—41no—
187C2×C4×C47—41no—
188C2×C4×C47—41no—
189C2×C4×C47—41no—
190C2×C4×C47—161no—
191C2×C4×C47—161no—
192C2×C4×C47—161no—
193C2×C4×C47—161no—
194C2×C4×C47C2×D811yescharacteristic
195C2×C4×C47C2×D811yescharacteristic
196C2×C4×C47C2×D811yescharacteristic
197C2×C4×C47C2×D811yescharacteristic
198C2×C4×C47C22×D411yescharacteristic
199C8×C47—21no—
200C8×C47—21no—
201C8×C47—21no—
202C8×C47C2×#4111yescharacteristic
203C8×C472−1+411yescharacteristic
204#33913C4711yesmaximal, characteristic, direct product factor, Sylow
205C22×C47—21no—
206C22×C47—21no—
207C22×C47—21no—
208C22×C47—21no—
209C22×C47—21no—
210C22×C47—81no—
211C22×C47—81no—
212C22×C47—81no—
213C22×C47#51012yes—
214C22×C47C22×D811yescharacteristic
215C4×C47—21no—
216C4×C47—21no—
217C4×C47—21no—
218C4×C47—21no—
219C4×C47—81no—
220C4×C47—81no—
221C4×C47—81no—
222C4×C47—81no—
223C4×C47—81no—
224C4×C47—81no—
225C4×C47—81no—
226C4×C47#54711yescharacteristic
227C4×C47#57811yescharacteristic
228#3339C2×C4711yescharacteristic
229#3338C2×C4711yescharacteristic, complemented
230#2255C2×C4711yescharacteristic, complemented
231#2237C2×C4711yescharacteristic, complemented
232#2236C2×C4711yescharacteristic, complemented
233#2233C2×C4711yescharacteristic, complemented
234#2232C2×C4711yescharacteristic, complemented
235#2229C2×C4711yescharacteristic, complemented
236#2224C2×C4711yescharacteristic, complemented
237#2220C2×C4711yescharacteristic, complemented
238#2217C2×C4711yescharacteristic, complemented
239#2175C2×C4711yescharacteristic, complemented
240#2168C2×C4711yescharacteristic, complemented
241#2159C2×C4711yescharacteristic, complemented
242C2×#366C2×C4711yescharacteristic, complemented
243C2×C47—22no—
244C2×C47—41no—
245C2×C47—161no—
246C2×C47#333411yescharacteristic
247C2×C47C2×#51011yescharacteristic
248C2×C47#341511yescharacteristic
249#554—21no—
250#553—21no—
251C2×SD32C22×C4711yescharacteristic
252C2×M32C22×C4711yescharacteristic
253C22×C16C22×C4711yescharacteristic
254#500C22×C4711yescharacteristic
255#499C22×C4711yescharacteristic
256#484—21no—
257#484—21no—
258#482—21no—
259#481—21no—
260#478—21no—
261#477—21no—
262#467C22×C4711yescharacteristic
263#467C22×C4711yescharacteristic
264#466C22×C4711yescharacteristic
265#466C22×C4711yescharacteristic
266C4×Q16C22×C4711yescharacteristic
267C4×D8C22×C4711yescharacteristic
268C8×D4C22×C4711yescharacteristic
269#427C22×C4711yescharacteristic
270C2×#107C22×C4711yescharacteristic
271C2×#107C22×C4711yescharacteristic
272C2×#107C22×C4711yescharacteristic
273#367C22×C4711yescharacteristic
274#367C22×C4711yescharacteristic
275#367C22×C4711yescharacteristic
276#366C22×C4711yescharacteristic
277#366C22×C4711yescharacteristic
278#366C22×C4711yescharacteristic
279#366C22×C4711yescharacteristic
280#366C22×C4711yescharacteristic
281#366C22×C4711yescharacteristic
282C4⋊C16C22×C4711yescharacteristic
283#358C22×C4711yescharacteristic
284#358C22×C4711yescharacteristic
285#358C22×C4711yescharacteristic
286#357C22×C4711yescharacteristic
287#357C22×C4711yescharacteristic
288#357C22×C4711yescharacteristic
289C22⋊C16C22×C4711yescharacteristic
290C22⋊C16C22×C4711yescharacteristic
291#346C22×C4711yescharacteristic
292C47#3391311yescharacteristic, direct product factor, Sylow
293C2×Q16C23×C4711yescharacteristic
294C2×D8C23×C4711yescharacteristic
295C22×C8C23×C4711yescharacteristic
296C22×C8C23×C4711yescharacteristic
297C4⋊Q8—21no—
298#126—41no—
299#125—21no—
300#125—41no—
301#123—41no—
302C22⋊Q8—21no—
303C22⋊Q8—21no—
304C22⋊Q8—41no—
305C22⋊Q8—41no—
306#121—21no—
307#121—21no—
308#121—41no—
309C4×Q8—21no—
310C4×D4—21no—
311C4×D4—41no—
312C4×D4—41no—
313C4×D4D4×C4711yescharacteristic
314#117—21no—
315C2×C4⋊C4—21no—
316C2×C4⋊C4—21no—
317C2×C4⋊C4—21no—
318SD32—22no—
319M32—22no—
320C2×C16—22no—
321C2×C16C23×C4711yescharacteristic
322C2×C16C23×C4711yescharacteristic
323C2×C16C23×C4711yescharacteristic
324C2×C16C23×C4711yescharacteristic
325#107—21no—
326#107—21no—
327#107—21no—
328#107—21no—
329#107C23×C4711yescharacteristic
330#107C23×C4711yescharacteristic
331#107C23×C4711yescharacteristic
332#107C23×C4711yescharacteristic
333#107C23×C4711yescharacteristic
334#107C23×C4711yescharacteristic
335#106—21no—
336#106—21no—
337C4⋊C8D4×C4711yescharacteristic
338#103—21no—
339#103—21no—
340#103—21no—
341#102—21no—
342#102—21no—
343#102—21no—
344C22⋊C8D4×C4711yescharacteristic
345C22⋊C8D4×C4711yescharacteristic
346C4×C8C23×C4711yescharacteristic
347C2×Q8—21no—
348C2×Q8—41no—
349C2×D4—21no—
350C2×D4—41no—
351C2×D4—41no—
352C2×D4D8×C4711yescharacteristic
353C22×C4—41no—
354C22×C4—41no—
355C22×C4—41no—
356C22×C4—41no—
357C22×C4C2×D4×C4711yescharacteristic
358C22×C4C2×D4×C4711yescharacteristic
359Q16—21no—
360Q16—21no—
361D8—21no—
362D8—21no—
363C2×C8—21no—
364C2×C8—21no—
365C2×C8—21no—
366C2×C8—21no—
367C2×C8C2×D4×C4711yescharacteristic
368C2×C8C2×D4×C4711yescharacteristic
369C2×C8C2×D4×C4711yescharacteristic
370C2×C8C24×C4711yescharacteristic
371C4⋊C4—21no—
372C4⋊C4—21no—
373C4⋊C4—21no—
374C4⋊C4—21no—
375C4⋊C4—21no—
376C4⋊C4—21no—
377C4⋊C4—41no—
378C4⋊C4—41no—
379C4⋊C4—41no—
380C4⋊C4—41no—
381C4⋊C4—41no—
382C4⋊C4—41no—
383C4⋊C4—41no—
384C4⋊C4—41no—
385C4⋊C4—41no—
386C4⋊C4D8×C4711yescharacteristic
387C22⋊C4—41no—
388C22⋊C4—41no—
389C22⋊C4—41no—
390C22⋊C4—41no—
391C22⋊C4—41no—
392C22⋊C4—41no—
393C22⋊C4D8×C4711yescharacteristic
394C22⋊C4D8×C4711yescharacteristic
395C42—41no—
396C42—41no—
397C42C2×D4×C4711yescharacteristic
398C16—21no—
399C16—21no—
400C16—21no—
401C16#41×C4712yes—
402C23—41no—
403C23C2×D8×C4711yescharacteristic
404C23C2×D8×C4711yescharacteristic
405Q8—41no—
406Q8—41no—
407Q8—161no—
408D4—22no—
409D4—41no—
410D4—41no—
411D4—82no—
412D4—161no—
413C2×C4—21no—
414C2×C4—21no—
415C2×C4—21no—
416C2×C4—21no—
417C2×C4—41no—
418C2×C4—41no—
419C2×C4—41no—
420C2×C4—41no—
421C2×C4—41no—
422C2×C4—41no—
423C2×C4—41no—
424C2×C4—161no—
425C2×C4—161no—
426C2×C4—161no—
427C2×C4—161no—
428C2×C4C2×D8×C4711yescharacteristic
429C2×C4C2×D8×C4711yescharacteristic
430C2×C4C2×D8×C4711yescharacteristic
431C2×C4C2×D8×C4711yescharacteristic
432C2×C4C22×D4×C4711yescharacteristic
433C8—21no—
434C8—21no—
435C8—21no—
436C8C2×#41×C4711yescharacteristic
437C82−1+4×C4711yescharacteristic
438C22—21no—
439C22—21no—
440C22—21no—
441C22—21no—
442C22—21no—
443C22—81no—
444C22—81no—
445C22—81no—
446C22C47×#51012yes—
447C22C22×D8×C4711yescharacteristic
448C4—21no—
449C4—21no—
450C4—21no—
451C4—21no—
452C4—81no—
453C4—81no—
454C4—81no—
455C4—81no—
456C4—81no—
457C4—81no—
458C4—81no—
459C4C47×#54711yescharacteristic
460C4C47×#57811yescharacteristic
461C2—22no—
462C2—41no—
463C2—161no—
464C2C47×#333411yescharacteristic
465C2C2×C47×#51011yescharacteristic
466C2C47×#341511yescharacteristic
subgroupG/H
center, socleC22×C47C22×D8
commutator, Frattini, cosocleC2×C8C24×C47
prime radicalC47×#3339C2
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C47 ◁ C4×D4×C47 ◁ C8×D4×C47 ◁ G

Complements

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

NH ≅ G/Ntype
2. C47×#3338C2semidirect
3. C47×#2255C2semidirect
4. C47×#2237C2semidirect
5. C47×#2236C2semidirect
6. C47×#2233C2semidirect
7. C47×#2232C2semidirect
8. C47×#2229C2semidirect
9. C47×#2224C2semidirect
10. C47×#2220C2semidirect
11. C47×#2217C2semidirect
12. C47×#2175C2semidirect
13. C47×#2168C2semidirect
14. C47×#2159C2semidirect
15. C2×C47×#366C2semidirect
204. #33913C47direct (N × H)
229. #3338C2×C47semidirect
230. #2255C2×C47semidirect
231. #2237C2×C47semidirect
232. #2236C2×C47semidirect
233. #2233C2×C47semidirect
234. #2232C2×C47semidirect
235. #2229C2×C47semidirect
236. #2224C2×C47semidirect
237. #2220C2×C47semidirect
238. #2217C2×C47semidirect
239. #2175C2×C47semidirect
240. #2168C2×C47semidirect
241. #2159C2×C47semidirect
242. C2×#366C2×C47semidirect
292. C47#33913direct (N × H)

Maximal subgroups

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

subgroupindex
C47×#33392
C47×#33382
C47×#22552
C47×#22372
C47×#22362
C47×#22332
C47×#22322
C47×#22292
C47×#22242
C47×#22202
C47×#22172
C47×#21752
C47×#21682
C47×#21592
C2×C47×#3662
#3391347