Finite Group Databasebeta

← C47×#33910 #26073608

Subgroups — C47×#33910 #26073608

Order 12032.

504 conjugacy classes of subgroups.

The subgroup lattice has 470 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C47×#3336C211yesmaximal, characteristic, complemented
2C47×#3334C211yesmaximal, characteristic
3C47×#2255C211yesmaximal, characteristic, complemented
4C47×#2236C211yesmaximal, characteristic, complemented
5C47×#2235C211yesmaximal, characteristic, complemented
6C47×#2234C211yesmaximal, characteristic, complemented
7C47×#2232C211yesmaximal, characteristic, complemented
8C47×#2228C211yesmaximal, characteristic, complemented
9C47×#2227C211yesmaximal, 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×#552—21no—
17C47×#547—21no—
18C2×SD32×C47C2211yescharacteristic
19C2×M32×C47C2211yescharacteristic
20C22×C16×C47C2211yescharacteristic
21C47×#500C2211yescharacteristic
22C47×#499C2211yescharacteristic
23C47×#485—21no—
24C47×#483—21no—
25C47×#480—21no—
26C47×#480—21no—
27C47×#479—21no—
28C47×#474—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×#41×C47—41no—
60C2×Q16×C47C2311yescharacteristic
61C2×D8×C47C2311yescharacteristic
62C22×C8×C47C2311yescharacteristic
63C22×C8×C47C2311yescharacteristic
64C4⋊Q8×C47—21no—
65#126×C47—41no—
66#125×C47—21no—
67#125×C47—41no—
68#123×C47—41no—
69#123×C47—41no—
70#123×C47—41no—
71C22⋊Q8×C47—21no—
72C22⋊Q8×C47—21no—
73C22⋊Q8×C47—41no—
74#121×C47—21no—
75#121×C47—21no—
76C4×Q8×C47—21no—
77C4×D4×C47—21no—
78C4×D4×C47D411yescharacteristic
79#117×C47—21no—
80#117×C47—41no—
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
113#41×C47—84no—
114C2×Q8×C47—21no—
115C2×Q8×C47—41no—
116C2×D4×C47—21no—
117C2×D4×C47—41no—
118C2×D4×C47—41no—
119C2×D4×C47D811yescharacteristic
120C22×C4×C47—41no—
121C22×C4×C47—41no—
122C22×C4×C47—41no—
123C22×C4×C47—41no—
124C22×C4×C47C2×D411yescharacteristic
125C22×C4×C47C2×D411yescharacteristic
126Q16×C47—21no—
127Q16×C47—21no—
128D8×C47—21no—
129D8×C47—21no—
130C2×C8×C47—21no—
131C2×C8×C47—21no—
132C2×C8×C47—21no—
133C2×C8×C47—21no—
134C2×C8×C47C2×D411yescharacteristic
135C2×C8×C47C2×D411yescharacteristic
136C2×C8×C47C2×D411yescharacteristic
137C2×C8×C47C2411yescharacteristic
138C4⋊C4×C47—21no—
139C4⋊C4×C47—21no—
140C4⋊C4×C47—21no—
141C4⋊C4×C47—21no—
142C4⋊C4×C47—21no—
143C4⋊C4×C47—21no—
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×C47—41no—
153C4⋊C4×C47D811yescharacteristic
154C22⋊C4×C47—41no—
155C22⋊C4×C47—41no—
156C22⋊C4×C47—41no—
157C22⋊C4×C47—41no—
158C22⋊C4×C47—41no—
159C22⋊C4×C47—41no—
160C22⋊C4×C47D811yescharacteristic
161C22⋊C4×C47D811yescharacteristic
162C42×C47—41no—
163C42×C47—41no—
164C42×C47C2×D411yescharacteristic
165C16×C47—21no—
166C16×C47—21no—
167C16×C47—21no—
168C16×C47#4112yescomplemented
169C23×C47—41no—
170C23×C47C2×D811yescharacteristic
171C23×C47C2×D811yescharacteristic
172Q8×C47—41no—
173Q8×C47—41no—
174Q8×C47—82no—
175D4×C47—22no—
176D4×C47—41no—
177D4×C47—41no—
178D4×C47—82no—
179D4×C47—82no—
180C2×C4×C47—21no—
181C2×C4×C47—21no—
182C2×C4×C47—21no—
183C2×C4×C47—21no—
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—41no—
191C2×C4×C47—82no—
192C2×C4×C47—82no—
193C2×C4×C47—82no—
194C2×C4×C47—82no—
195C2×C4×C47C2×D811yescharacteristic
196C2×C4×C47C2×D811yescharacteristic
197C2×C4×C47C2×D811yescharacteristic
198C2×C4×C47C2×D811yescharacteristic
199C2×C4×C47C22×D411yescharacteristic
200C8×C47—21no—
201C8×C47—21no—
202C8×C47—21no—
203C8×C47C2×#4111yescharacteristic
204C8×C472−1+411yescharacteristic
205#33910C4711yesmaximal, characteristic, direct product factor, Sylow
206C22×C47—21no—
207C22×C47—21no—
208C22×C47—21no—
209C22×C47—21no—
210C22×C47—21no—
211C22×C47—81no—
212C22×C47—81no—
213C22×C47—81no—
214C22×C47#50912yes—
215C22×C47C22×D811yescharacteristic
216C4×C47—21no—
217C4×C47—21no—
218C4×C47—21no—
219C4×C47—21no—
220C4×C47—81no—
221C4×C47—81no—
222C4×C47—81no—
223C4×C47—81no—
224C4×C47—81no—
225C4×C47—81no—
226C4×C47—81no—
227C4×C47#54711yescharacteristic
228C4×C47#57811yescharacteristic
229#3336C2×C4711yescharacteristic, complemented
230#3334C2×C4711yescharacteristic
231#2255C2×C4711yescharacteristic, complemented
232#2236C2×C4711yescharacteristic, complemented
233#2235C2×C4711yescharacteristic, complemented
234#2234C2×C4711yescharacteristic, complemented
235#2232C2×C4711yescharacteristic, complemented
236#2228C2×C4711yescharacteristic, complemented
237#2227C2×C4711yescharacteristic, complemented
238#2220C2×C4711yescharacteristic, complemented
239#2217C2×C4711yescharacteristic, complemented
240#2175C2×C4711yescharacteristic, complemented
241#2168C2×C4711yescharacteristic, complemented
242#2159C2×C4711yescharacteristic, complemented
243C2×#366C2×C4711yescharacteristic, complemented
244C2×C47—22no—
245C2×C47—41no—
246C2×C47—161no—
247C2×C47#333411yescharacteristic
248C2×C47C2×#50911yescharacteristic
249C2×C47#341711yescharacteristic
250#552—21no—
251#547—21no—
252C2×SD32C22×C4711yescharacteristic
253C2×M32C22×C4711yescharacteristic
254C22×C16C22×C4711yescharacteristic
255#500C22×C4711yescharacteristic
256#499C22×C4711yescharacteristic
257#485—21no—
258#483—21no—
259#480—21no—
260#480—21no—
261#479—21no—
262#474—21no—
263#467C22×C4711yescharacteristic
264#467C22×C4711yescharacteristic
265#466C22×C4711yescharacteristic
266#466C22×C4711yescharacteristic
267C4×Q16C22×C4711yescharacteristic
268C4×D8C22×C4711yescharacteristic
269C8×D4C22×C4711yescharacteristic
270#427C22×C4711yescharacteristic
271C2×#107C22×C4711yescharacteristic
272C2×#107C22×C4711yescharacteristic
273C2×#107C22×C4711yescharacteristic
274#367C22×C4711yescharacteristic
275#367C22×C4711yescharacteristic
276#367C22×C4711yescharacteristic
277#366C22×C4711yescharacteristic
278#366C22×C4711yescharacteristic
279#366C22×C4711yescharacteristic
280#366C22×C4711yescharacteristic
281#366C22×C4711yescharacteristic
282#366C22×C4711yescharacteristic
283C4⋊C16C22×C4711yescharacteristic
284#358C22×C4711yescharacteristic
285#358C22×C4711yescharacteristic
286#358C22×C4711yescharacteristic
287#357C22×C4711yescharacteristic
288#357C22×C4711yescharacteristic
289#357C22×C4711yescharacteristic
290C22⋊C16C22×C4711yescharacteristic
291C22⋊C16C22×C4711yescharacteristic
292#346C22×C4711yescharacteristic
293C47#3391011yescharacteristic, direct product factor, Sylow
294C2×#41—41no—
295C2×Q16C23×C4711yescharacteristic
296C2×D8C23×C4711yescharacteristic
297C22×C8C23×C4711yescharacteristic
298C22×C8C23×C4711yescharacteristic
299C4⋊Q8—21no—
300#126—41no—
301#125—21no—
302#125—41no—
303#123—41no—
304#123—41no—
305#123—41no—
306C22⋊Q8—21no—
307C22⋊Q8—21no—
308C22⋊Q8—41no—
309#121—21no—
310#121—21no—
311C4×Q8—21no—
312C4×D4—21no—
313C4×D4D4×C4711yescharacteristic
314#117—21no—
315#117—41no—
316C2×C4⋊C4—21no—
317C2×C4⋊C4—21no—
318C2×C4⋊C4—21no—
319SD32—22no—
320M32—22no—
321C2×C16—22no—
322C2×C16C23×C4711yescharacteristic
323C2×C16C23×C4711yescharacteristic
324C2×C16C23×C4711yescharacteristic
325C2×C16C23×C4711yescharacteristic
326#107—21no—
327#107—21no—
328#107—21no—
329#107—21no—
330#107C23×C4711yescharacteristic
331#107C23×C4711yescharacteristic
332#107C23×C4711yescharacteristic
333#107C23×C4711yescharacteristic
334#107C23×C4711yescharacteristic
335#107C23×C4711yescharacteristic
336#106—21no—
337#106—21no—
338C4⋊C8D4×C4711yescharacteristic
339#103—21no—
340#103—21no—
341#103—21no—
342#102—21no—
343#102—21no—
344#102—21no—
345C22⋊C8D4×C4711yescharacteristic
346C22⋊C8D4×C4711yescharacteristic
347C4×C8C23×C4711yescharacteristic
348#41—84no—
349C2×Q8—21no—
350C2×Q8—41no—
351C2×D4—21no—
352C2×D4—41no—
353C2×D4—41no—
354C2×D4D8×C4711yescharacteristic
355C22×C4—41no—
356C22×C4—41no—
357C22×C4—41no—
358C22×C4—41no—
359C22×C4C2×D4×C4711yescharacteristic
360C22×C4C2×D4×C4711yescharacteristic
361Q16—21no—
362Q16—21no—
363D8—21no—
364D8—21no—
365C2×C8—21no—
366C2×C8—21no—
367C2×C8—21no—
368C2×C8—21no—
369C2×C8C2×D4×C4711yescharacteristic
370C2×C8C2×D4×C4711yescharacteristic
371C2×C8C2×D4×C4711yescharacteristic
372C2×C8C24×C4711yescharacteristic
373C4⋊C4—21no—
374C4⋊C4—21no—
375C4⋊C4—21no—
376C4⋊C4—21no—
377C4⋊C4—21no—
378C4⋊C4—21no—
379C4⋊C4—41no—
380C4⋊C4—41no—
381C4⋊C4—41no—
382C4⋊C4—41no—
383C4⋊C4—41no—
384C4⋊C4—41no—
385C4⋊C4—41no—
386C4⋊C4—41no—
387C4⋊C4—41no—
388C4⋊C4D8×C4711yescharacteristic
389C22⋊C4—41no—
390C22⋊C4—41no—
391C22⋊C4—41no—
392C22⋊C4—41no—
393C22⋊C4—41no—
394C22⋊C4—41no—
395C22⋊C4D8×C4711yescharacteristic
396C22⋊C4D8×C4711yescharacteristic
397C42—41no—
398C42—41no—
399C42C2×D4×C4711yescharacteristic
400C16—21no—
401C16—21no—
402C16—21no—
403C16#41×C4712yescomplemented
404C23—41no—
405C23C2×D8×C4711yescharacteristic
406C23C2×D8×C4711yescharacteristic
407Q8—41no—
408Q8—41no—
409Q8—82no—
410D4—22no—
411D4—41no—
412D4—41no—
413D4—82no—
414D4—82no—
415C2×C4—21no—
416C2×C4—21no—
417C2×C4—21no—
418C2×C4—21no—
419C2×C4—41no—
420C2×C4—41no—
421C2×C4—41no—
422C2×C4—41no—
423C2×C4—41no—
424C2×C4—41no—
425C2×C4—41no—
426C2×C4—82no—
427C2×C4—82no—
428C2×C4—82no—
429C2×C4—82no—
430C2×C4C2×D8×C4711yescharacteristic
431C2×C4C2×D8×C4711yescharacteristic
432C2×C4C2×D8×C4711yescharacteristic
433C2×C4C2×D8×C4711yescharacteristic
434C2×C4C22×D4×C4711yescharacteristic
435C8—21no—
436C8—21no—
437C8—21no—
438C8C2×#41×C4711yescharacteristic
439C82−1+4×C4711yescharacteristic
440C22—21no—
441C22—21no—
442C22—21no—
443C22—21no—
444C22—21no—
445C22—81no—
446C22—81no—
447C22—81no—
448C22C47×#50912yes—
449C22C22×D8×C4711yescharacteristic
450C4—21no—
451C4—21no—
452C4—21no—
453C4—21no—
454C4—81no—
455C4—81no—
456C4—81no—
457C4—81no—
458C4—81no—
459C4—81no—
460C4—81no—
461C4C47×#54711yescharacteristic
462C4C47×#57811yescharacteristic
463C2—22no—
464C2—41no—
465C2—161no—
466C2C47×#333411yescharacteristic
467C2C2×C47×#50911yescharacteristic
468C2C47×#341711yescharacteristic
subgroupG/H
center, socleC22×C47C22×D8
commutator, Frattini, cosocleC2×C8C24×C47
prime radicalC47×#3334C2
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
1. C47×#3336C2semidirect
3. C47×#2255C2semidirect
4. C47×#2236C2semidirect
5. C47×#2235C2semidirect
6. C47×#2234C2semidirect
7. C47×#2232C2semidirect
8. C47×#2228C2semidirect
9. C47×#2227C2semidirect
10. C47×#2220C2semidirect
11. C47×#2217C2semidirect
12. C47×#2175C2semidirect
13. C47×#2168C2semidirect
14. C47×#2159C2semidirect
15. C2×C47×#366C2semidirect
168. C16×C47#41semidirect
205. #33910C47direct (N × H)
229. #3336C2×C47semidirect
231. #2255C2×C47semidirect
232. #2236C2×C47semidirect
233. #2235C2×C47semidirect
234. #2234C2×C47semidirect
235. #2232C2×C47semidirect
236. #2228C2×C47semidirect
237. #2227C2×C47semidirect
238. #2220C2×C47semidirect
239. #2217C2×C47semidirect
240. #2175C2×C47semidirect
241. #2168C2×C47semidirect
242. #2159C2×C47semidirect
243. C2×#366C2×C47semidirect
293. C47#33910direct (N × H)
403. C16#41×C47semidirect

Maximal subgroups

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

subgroupindex
C47×#33362
C47×#33342
C47×#22552
C47×#22362
C47×#22352
C47×#22342
C47×#22322
C47×#22282
C47×#22272
C47×#22202
C47×#22172
C47×#21752
C47×#21682
C47×#21592
C2×C47×#3662
#3391047