Finite Group Databasebeta

← C47×#18439 #26058137

Subgroups — C47×#18439 #26058137

Order 12032.

964 conjugacy classes of subgroups.

The subgroup lattice has 580 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C47×#3561C211yesmaximal, characteristic
2C47×#3239C211yesmaximal, characteristic, complemented
3C47×#3230C211yesmaximal, characteristic, complemented
4C47×#2658C211yesmaximal, characteristic, complemented
5C47×#1618C214yesmaximal, complemented
6C47×#1614C214yesmaximal, complemented
7C47×#1506C211yesmaximal, characteristic, complemented
8C47×#1500C211yesmaximal, characteristic, complemented
9C47×#1469C211yesmaximal, characteristic, complemented
10C47×#563—21no—
11C47×#562—21no—
12C47×#556—21no—
13C47×#551—22no—
14D4×Q8×C47—21no—
15C47×#548—21no—
16C47×#546—21no—
17C47×#543C2212yes—
18C47×#542—21no—
19C47×#542—22no—
20C47×#538C2212yes—
21C47×#536—21no—
22C47×#533C2211yescharacteristic
23C2×C4⋊Q8×C47—21no—
24C2×C4⋊Q8×C47C2211yescharacteristic
25C47×#529C2211yescharacteristic
26C2×#124×C47—21no—
27C2×#124×C47C2211yescharacteristic
28C47×#501—21no—
29C47×#500—21no—
30C47×#489—21no—
31C47×#487—21no—
32C47×#484C2212yes—
33C47×#484C2214yes—
34C47×#481C2212yes—
35C47×#477—22no—
36C47×#475—21no—
37C47×#474—21no—
38C47×#432C2211yescharacteristic
39C47×#431C2211yescharacteristic
40C47×#399—22no—
41C47×#399C2214yes—
42C47×#376C2211yescharacteristic
43C47×#328C2212yes—
44C47×#328C2214yes—
45C47×#327C2212yes—
46C47×#323C2214yes—
47C2×#41×C47—21no—
48C22×Q8×C47—21no—
49C22×Q8×C47—21no—
50C22×Q8×C47D411yescharacteristic
51C22×D4×C47D411yescharacteristic
52C4⋊Q8×C47—21no—
53C4⋊Q8×C47—22no—
54C4⋊Q8×C47—21no—
55C4⋊Q8×C47—21no—
56C4⋊Q8×C47—21no—
57C4⋊Q8×C47—21no—
58C4⋊Q8×C47—44no—
59C4⋊Q8×C47D411yescharacteristic
60C4⋊Q8×C47D411yescharacteristic
61#126×C47—22no—
62#126×C47—22no—
63#126×C47—22no—
64#126×C47—21no—
65#125×C47—21no—
66#125×C47D411yescharacteristic
67#124×C47—21no—
68#124×C47—22no—
69#124×C47—22no—
70#124×C47—21no—
71#124×C47—21no—
72#124×C47—21no—
73#124×C47—21no—
74#124×C47—44no—
75#124×C47D411yescharacteristic
76#123×C47—22no—
77#123×C47—22no—
78#123×C47—22no—
79#123×C47—21no—
80#123×C47—22no—
81C22⋊Q8×C47—22no—
82C22⋊Q8×C47—21no—
83C22⋊Q8×C47—22no—
84C22⋊Q8×C47—22no—
85C22⋊Q8×C47—22no—
86C22⋊Q8×C47—21no—
87C22⋊Q8×C47—22no—
88C22⋊Q8×C47—22no—
89C22⋊Q8×C47—22no—
90C22⋊Q8×C47C2311yescharacteristic
91C22⋊Q8×C47C2312yes—
92#121×C47—21no—
93#121×C47—22no—
94#121×C47—22no—
95#121×C47C2311yescharacteristic
96#120×C47—22no—
97C4×Q8×C47—21no—
98C4×Q8×C47—21no—
99C4×Q8×C47D411yescharacteristic
100C4×Q8×C47D412yes—
101C4×D4×C47—21no—
102C4×D4×C47—22no—
103C4×D4×C47—21no—
104C4×D4×C47—22no—
105C4×D4×C47D411yescharacteristic
106#117×C47—22no—
107#117×C47—21no—
108#117×C47—21no—
109C2×C4⋊C4×C47—24no—
110C2×C4⋊C4×C47—21no—
111C2×C4⋊C4×C47C2312yes—
112C2×C22⋊C4×C47—22no—
113C2×C22⋊C4×C47—24no—
114C2×C22⋊C4×C47D412yes—
115C2×C22⋊C4×C47C2312yes—
116C2×C42×C47—21no—
117C2×C42×C47C2311yescharacteristic
118#107×C47—22no—
119#107×C47—24no—
120#106×C47—22no—
121C4⋊C8×C47—21no—
122C4⋊C8×C47—21no—
123#103×C47—22no—
124#103×C47—24no—
125#102×C47—22no—
126C22⋊C8×C47C2312yes—
127C22⋊C8×C47C2312yes—
128#97×C47—21no—
129C4×C8×C47—21no—
130#95×C47—21no—
131#95×C47C2312yes—
132C24×C47C2×D412yes—
133#41×C47—82no—
134C2×Q8×C47—22no—
135C2×Q8×C47—21no—
136C2×Q8×C47—21no—
137C2×Q8×C47—21no—
138C2×Q8×C47—42no—
139C2×Q8×C47—42no—
140C2×Q8×C47—42no—
141C2×Q8×C47—41no—
142C2×Q8×C47—41no—
143C2×Q8×C47—82no—
144C2×Q8×C47C2×D411yescharacteristic
145C2×Q8×C47C2×D412yes—
146C2×D4×C47—21no—
147C2×D4×C47—22no—
148C2×D4×C47—22no—
149C2×D4×C47—21no—
150C2×D4×C47—21no—
151C2×D4×C47—42no—
152C2×D4×C47C2×D411yescharacteristic
153C22×C4×C47—22no—
154C22×C4×C47—22no—
155C22×C4×C47—22no—
156C22×C4×C47—22no—
157C22×C4×C47—21no—
158C22×C4×C47—22no—
159C22×C4×C47C2×D411yescharacteristic
160C22×C4×C47C2×D411yescharacteristic
161C22×C4×C47C2×D412yes—
162C22×C4×C47C2411yescharacteristic
163C2×C8×C47—22no—
164C2×C8×C47—22no—
165C4⋊C4×C47—22no—
166C4⋊C4×C47—22no—
167C4⋊C4×C47—22no—
168C4⋊C4×C47—22no—
169C4⋊C4×C47—21no—
170C4⋊C4×C47—21no—
171C4⋊C4×C47—21no—
172C4⋊C4×C47—21no—
173C4⋊C4×C47—21no—
174C4⋊C4×C47—21no—
175C4⋊C4×C47—22no—
176C4⋊C4×C47—21no—
177C4⋊C4×C47—22no—
178C4⋊C4×C47—22no—
179C4⋊C4×C47—22no—
180C4⋊C4×C47—48no—
181C4⋊C4×C47—41no—
182C4⋊C4×C47—41no—
183C4⋊C4×C47C2×D411yescharacteristic
184C4⋊C4×C47C2×D411yescharacteristic
185C4⋊C4×C47C2×D412yes—
186C22⋊C4×C47—22no—
187C22⋊C4×C47—22no—
188C22⋊C4×C47—22no—
189C22⋊C4×C47—22no—
190C22⋊C4×C47—22no—
191C22⋊C4×C47—21no—
192C22⋊C4×C47—22no—
193C22⋊C4×C47—22no—
194C22⋊C4×C47—22no—
195C22⋊C4×C47—21no—
196C22⋊C4×C47—21no—
197C22⋊C4×C47—21no—
198C22⋊C4×C47—22no—
199C22⋊C4×C47—22no—
200C22⋊C4×C47—21no—
201C22⋊C4×C47—48no—
202C42×C47—24no—
203C42×C47—22no—
204C42×C47—22no—
205C42×C47—21no—
206C42×C47C2×D411yescharacteristic
207C42×C47C2×D411yescharacteristic
208C42×C47C2×D411yescharacteristic
209C42×C47C2×D411yescharacteristic
210C23×C47—22no—
211C23×C47—21no—
212C23×C47—24no—
213C23×C47—42no—
214C23×C47—42no—
215C23×C47C22×D411yescharacteristic
216Q8×C47—41no—
217Q8×C47—42no—
218Q8×C47—42no—
219Q8×C47—42no—
220Q8×C47—81no—
221Q8×C47—82no—
222Q8×C47—82no—
223Q8×C47—82no—
224D4×C47—41no—
225D4×C47—42no—
226D4×C47—42no—
227D4×C47—81no—
228D4×C47—82no—
229D4×C47—82no—
230C2×C4×C47—22no—
231C2×C4×C47—22no—
232C2×C4×C47—24no—
233C2×C4×C47—21no—
234C2×C4×C47—22no—
235C2×C4×C47—21no—
236C2×C4×C47—22no—
237C2×C4×C47—22no—
238C2×C4×C47—21no—
239C2×C4×C47—41no—
240C2×C4×C47—42no—
241C2×C4×C47—42no—
242C2×C4×C47—42no—
243C2×C4×C47—42no—
244C2×C4×C47—42no—
245C2×C4×C47—42no—
246C2×C4×C47—42no—
247C2×C4×C47—82no—
248C2×C4×C47—82no—
249C2×C4×C47—82no—
250C2×C4×C47#12011yescharacteristic
251C2×C4×C47#12011yescharacteristic
252C2×C4×C47#12011yescharacteristic
253C2×C4×C47#12011yescharacteristic
254C2×C4×C47C22×D411yescharacteristic
255C2×C4×C47C22×D411yescharacteristic
256C8×C47—42no—
257C8×C47—42no—
258#18439C4711yesmaximal, characteristic, direct product factor, Sylow
259C22×C47—21no—
260C22×C47—21no—
261C22×C47—41no—
262C22×C47—42no—
263C22×C47—41no—
264C22×C47—42no—
265C22×C47—42no—
266C22×C47—41no—
267C22×C47—84no—
268C22×C47C2×#12011yescharacteristic
269C22×C47#57812yes—
270C4×C47—21no—
271C4×C47—21no—
272C4×C47—21no—
273C4×C47—21no—
274C4×C47—21no—
275C4×C47—44no—
276C4×C47—41no—
277C4×C47—41no—
278C4×C47—42no—
279C4×C47—42no—
280C4×C47—41no—
281C4×C47—42no—
282C4×C47—82no—
283C4×C47#45312yes—
284#3561C2×C4711yescharacteristic
285#3239C2×C4711yescharacteristic, complemented
286#3230C2×C4711yescharacteristic, complemented
287#2658C2×C4711yescharacteristic, complemented
288#1618C2×C4714yescomplemented
289#1614C2×C4714yescomplemented
290#1506C2×C4711yescharacteristic, complemented
291#1500C2×C4711yescharacteristic, complemented
292#1469C2×C4711yescharacteristic, complemented
293C2×C47—22no—
294C2×C47—81no—
295C2×C47—82no—
296C2×C47#301111yescharacteristic
297C2×C47C2×#45311yescharacteristic
298C2×C47#302811yescharacteristic
299#563—21no—
300#562—21no—
301#556—21no—
302#551—22no—
303D4×Q8—21no—
304#548—21no—
305#546—21no—
306#543C22×C4712yes—
307#542—21no—
308#542—22no—
309#538C22×C4712yes—
310#536—21no—
311#533C22×C4711yescharacteristic
312C2×C4⋊Q8—21no—
313C2×C4⋊Q8C22×C4711yescharacteristic
314#529C22×C4711yescharacteristic
315C2×#124—21no—
316C2×#124C22×C4711yescharacteristic
317#501—21no—
318#500—21no—
319#489—21no—
320#487—21no—
321#484C22×C4712yes—
322#484C22×C4714yes—
323#481C22×C4712yes—
324#477—22no—
325#475—21no—
326#474—21no—
327#432C22×C4711yescharacteristic
328#431C22×C4711yescharacteristic
329#399—22no—
330#399C22×C4714yes—
331#376C22×C4711yescharacteristic
332#328C22×C4712yes—
333#328C22×C4714yes—
334#327C22×C4712yes—
335#323C22×C4714yes—
336C47#1843911yescharacteristic, direct product factor, Sylow
337C2×#41—21no—
338C22×Q8—21no—
339C22×Q8—21no—
340C22×Q8D4×C4711yescharacteristic
341C22×D4D4×C4711yescharacteristic
342C4⋊Q8—21no—
343C4⋊Q8—22no—
344C4⋊Q8—21no—
345C4⋊Q8—21no—
346C4⋊Q8—21no—
347C4⋊Q8—21no—
348C4⋊Q8—44no—
349C4⋊Q8D4×C4711yescharacteristic
350C4⋊Q8D4×C4711yescharacteristic
351#126—22no—
352#126—22no—
353#126—22no—
354#126—21no—
355#125—21no—
356#125D4×C4711yescharacteristic
357#124—21no—
358#124—22no—
359#124—22no—
360#124—21no—
361#124—21no—
362#124—21no—
363#124—21no—
364#124—44no—
365#124D4×C4711yescharacteristic
366#123—22no—
367#123—22no—
368#123—22no—
369#123—21no—
370#123—22no—
371C22⋊Q8—22no—
372C22⋊Q8—21no—
373C22⋊Q8—22no—
374C22⋊Q8—22no—
375C22⋊Q8—22no—
376C22⋊Q8—21no—
377C22⋊Q8—22no—
378C22⋊Q8—22no—
379C22⋊Q8—22no—
380C22⋊Q8C23×C4711yescharacteristic
381C22⋊Q8C23×C4712yes—
382#121—21no—
383#121—22no—
384#121—22no—
385#121C23×C4711yescharacteristic
386#120—22no—
387C4×Q8—21no—
388C4×Q8—21no—
389C4×Q8D4×C4711yescharacteristic
390C4×Q8D4×C4712yes—
391C4×D4—21no—
392C4×D4—22no—
393C4×D4—21no—
394C4×D4—22no—
395C4×D4D4×C4711yescharacteristic
396#117—22no—
397#117—21no—
398#117—21no—
399C2×C4⋊C4—24no—
400C2×C4⋊C4—21no—
401C2×C4⋊C4C23×C4712yes—
402C2×C22⋊C4—22no—
403C2×C22⋊C4—24no—
404C2×C22⋊C4D4×C4712yes—
405C2×C22⋊C4C23×C4712yes—
406C2×C42—21no—
407C2×C42C23×C4711yescharacteristic
408#107—22no—
409#107—24no—
410#106—22no—
411C4⋊C8—21no—
412C4⋊C8—21no—
413#103—22no—
414#103—24no—
415#102—22no—
416C22⋊C8C23×C4712yes—
417C22⋊C8C23×C4712yes—
418#97—21no—
419C4×C8—21no—
420#95—21no—
421#95C23×C4712yes—
422C24C2×D4×C4712yes—
423#41—82no—
424C2×Q8—22no—
425C2×Q8—21no—
426C2×Q8—21no—
427C2×Q8—21no—
428C2×Q8—42no—
429C2×Q8—42no—
430C2×Q8—42no—
431C2×Q8—41no—
432C2×Q8—41no—
433C2×Q8—82no—
434C2×Q8C2×D4×C4711yescharacteristic
435C2×Q8C2×D4×C4712yes—
436C2×D4—21no—
437C2×D4—22no—
438C2×D4—22no—
439C2×D4—21no—
440C2×D4—21no—
441C2×D4—42no—
442C2×D4C2×D4×C4711yescharacteristic
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—21no—
448C22×C4—22no—
449C22×C4C2×D4×C4711yescharacteristic
450C22×C4C2×D4×C4711yescharacteristic
451C22×C4C2×D4×C4712yes—
452C22×C4C24×C4711yescharacteristic
453C2×C8—22no—
454C2×C8—22no—
455C4⋊C4—22no—
456C4⋊C4—22no—
457C4⋊C4—22no—
458C4⋊C4—22no—
459C4⋊C4—21no—
460C4⋊C4—21no—
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—22no—
466C4⋊C4—21no—
467C4⋊C4—22no—
468C4⋊C4—22no—
469C4⋊C4—22no—
470C4⋊C4—48no—
471C4⋊C4—41no—
472C4⋊C4—41no—
473C4⋊C4C2×D4×C4711yescharacteristic
474C4⋊C4C2×D4×C4711yescharacteristic
475C4⋊C4C2×D4×C4712yes—
476C22⋊C4—22no—
477C22⋊C4—22no—
478C22⋊C4—22no—
479C22⋊C4—22no—
480C22⋊C4—22no—
481C22⋊C4—21no—
482C22⋊C4—22no—
483C22⋊C4—22no—
484C22⋊C4—22no—
485C22⋊C4—21no—
486C22⋊C4—21no—
487C22⋊C4—21no—
488C22⋊C4—22no—
489C22⋊C4—22no—
490C22⋊C4—21no—
491C22⋊C4—48no—
492C42—24no—
493C42—22no—
494C42—22no—
495C42—21no—
496C42C2×D4×C4711yescharacteristic
497C42C2×D4×C4711yescharacteristic
498C42C2×D4×C4711yescharacteristic
499C42C2×D4×C4711yescharacteristic
500C23—22no—
501C23—21no—
502C23—24no—
503C23—42no—
504C23—42no—
505C23C22×D4×C4711yescharacteristic
506Q8—41no—
507Q8—42no—
508Q8—42no—
509Q8—42no—
510Q8—81no—
511Q8—82no—
512Q8—82no—
513Q8—82no—
514D4—41no—
515D4—42no—
516D4—42no—
517D4—81no—
518D4—82no—
519D4—82no—
520C2×C4—22no—
521C2×C4—22no—
522C2×C4—24no—
523C2×C4—21no—
524C2×C4—22no—
525C2×C4—21no—
526C2×C4—22no—
527C2×C4—22no—
528C2×C4—21no—
529C2×C4—41no—
530C2×C4—42no—
531C2×C4—42no—
532C2×C4—42no—
533C2×C4—42no—
534C2×C4—42no—
535C2×C4—42no—
536C2×C4—42no—
537C2×C4—82no—
538C2×C4—82no—
539C2×C4—82no—
540C2×C4#120×C4711yescharacteristic
541C2×C4#120×C4711yescharacteristic
542C2×C4#120×C4711yescharacteristic
543C2×C4#120×C4711yescharacteristic
544C2×C4C22×D4×C4711yescharacteristic
545C2×C4C22×D4×C4711yescharacteristic
546C8—42no—
547C8—42no—
548C22—21no—
549C22—21no—
550C22—41no—
551C22—42no—
552C22—41no—
553C22—42no—
554C22—42no—
555C22—41no—
556C22—84no—
557C22C2×#120×C4711yescharacteristic
558C22C47×#57812yes—
559C4—21no—
560C4—21no—
561C4—21no—
562C4—21no—
563C4—21no—
564C4—44no—
565C4—41no—
566C4—41no—
567C4—42no—
568C4—42no—
569C4—41no—
570C4—42no—
571C4—82no—
572C4C47×#45312yes—
573C2—22no—
574C2—82no—
575C2—81no—
576C2C47×#301111yescharacteristic
577C2C2×C47×#45311yescharacteristic
578C2C47×#302811yescharacteristic
subgroupG/H
center, socleC22×C47C2×#120
commutator, Frattini, cosocleC22×C4C24×C47
prime radicalC47×#3561C2
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C47 ◁ C2×C42×C47 ◁ G

Complements

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

NH ≅ G/Ntype
2. C47×#3239C2semidirect
3. C47×#3230C2semidirect
4. C47×#2658C2semidirect
5. C47×#1618C2semidirect
6. C47×#1614C2semidirect
7. C47×#1506C2semidirect
8. C47×#1500C2semidirect
9. C47×#1469C2semidirect
258. #18439C47direct (N × H)
285. #3239C2×C47semidirect
286. #3230C2×C47semidirect
287. #2658C2×C47semidirect
288. #1618C2×C47semidirect
289. #1614C2×C47semidirect
290. #1506C2×C47semidirect
291. #1500C2×C47semidirect
292. #1469C2×C47semidirect
336. C47#18439direct (N × H)

Maximal subgroups

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

subgroupindex
C47×#35612
C47×#32392
C47×#32302
C47×#26582
C47×#16182
C47×#16142
C47×#15062
C47×#15002
C47×#14692
#1843947