Finite Group Databasebeta

← C47×#19838 #26059536

Subgroups — C47×#19838 #26059536

Order 12032.

574 conjugacy classes of subgroups.

The subgroup lattice has 550 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C47×#3383C211yesmaximal, characteristic, complemented
2C47×#3372C211yesmaximal, characteristic
3C47×#3359C211yesmaximal, characteristic
4C47×#3299C211yesmaximal, characteristic
5C47×#1718C211yesmaximal, characteristic, complemented
6C47×#1700C211yesmaximal, characteristic, complemented
7C47×#1684C211yesmaximal, characteristic, complemented
8C47×#1684C211yesmaximal, characteristic, complemented
9C47×#1673C211yesmaximal, characteristic
10C47×#1653C211yesmaximal, characteristic, complemented
11C47×#1651C211yesmaximal, characteristic
12C47×#1643C211yesmaximal, characteristic
13C47×#1636C211yesmaximal, characteristic, complemented
14C47×#1584C211yesmaximal, characteristic, complemented
15C47×SD16⋊C8C211yesmaximal, characteristic
16C47×#557C2211yescharacteristic
17C47×#557C2211yescharacteristic
18C47×#554C2211yescharacteristic
19D4×Q8×C47C2211yescharacteristic
20C47×#500C2211yescharacteristic
21C47×#499—21no—
22C47×#498C2211yescharacteristic
23C47×#491—21no—
24C47×#487—21no—
25C47×#487C2211yescharacteristic
26C47×#487C2211yescharacteristic
27C47×#487C2211yescharacteristic
28C47×#487C2211yescharacteristic
29C47×#484—21no—
30C47×#479—21no—
31C47×#479—21no—
32C47×#479—21no—
33C47×#477C2211yescharacteristic
34C47×#477C2211yescharacteristic
35C47×#475—21no—
36C47×#475C2211yescharacteristic
37C47×#475C2211yescharacteristic
38C47×#475C2211yescharacteristic
39C47×#467—21no—
40C47×#462C2211yescharacteristic
41C47×#461—21no—
42C47×#461—21no—
43C47×#461C2211yescharacteristic
44C47×#461C2211yescharacteristic
45C47×#451—21no—
46C47×#446C2211yescharacteristic
47C8×Q8×C47C2211yescharacteristic
48C8×Q8×C47C2211yescharacteristic
49C47×#440—21no—
50C4×Q16×C47—21no—
51C4×Q16×C47C2211yescharacteristic
52C4×SD16×C47—21no—
53C4×SD16×C47C2211yescharacteristic
54C8×D4×C47C2211yescharacteristic
55C2×#103×C47—21no—
56C47×#335C2211yescharacteristic
57C47×#335C2211yescharacteristic
58C47×#333C2211yescharacteristic
59C47×#332C2211yescharacteristic
60C47×#332C2211yescharacteristic
61C47×#332C2211yescharacteristic
62C47×Q8⋊C8C2211yescharacteristic
63C47×Q8⋊C8C2211yescharacteristic
64C47×Q8⋊C8C2211yescharacteristic
65C47×D4⋊C8C2211yescharacteristic
66C47×#322C2211yescharacteristic
67C22×Q8×C47—21no—
68C2×Q16×C47—21no—
69C2×Q16×C47D411yescharacteristic
70C2×SD16×C47—21no—
71C2×SD16×C47—21no—
72C2×SD16×C47D411yescharacteristic
73C22×C8×C47—21no—
74C4⋊Q8×C47—21no—
75C4⋊Q8×C47—21no—
76C4⋊Q8×C47—21no—
77C4⋊Q8×C47C2311yescharacteristic
78C4⋊Q8×C47C2311yescharacteristic
79C4⋊Q8×C47C2311yescharacteristic
80C4⋊Q8×C47C2311yescharacteristic
81#125×C47—21no—
82#125×C47—21no—
83#125×C47—21no—
84#125×C47—41no—
85#125×C47—41no—
86C22⋊Q8×C47—21no—
87C22⋊Q8×C47—21no—
88C22⋊Q8×C47—41no—
89C22⋊Q8×C47—41no—
90C4×Q8×C47—21no—
91C4×Q8×C47—21no—
92C4×Q8×C47—21no—
93C4×Q8×C47—21no—
94C4×Q8×C47C2311yescharacteristic
95C4×Q8×C47C2311yescharacteristic
96C4×Q8×C47C2311yescharacteristic
97C4×D4×C47—21no—
98C4×D4×C47—21no—
99C4×D4×C47C2311yescharacteristic
100C2×C4⋊C4×C47—21no—
101#107×C47—21no—
102#107×C47—21no—
103#107×C47—21no—
104#107×C47—21no—
105#107×C47D411yescharacteristic
106#106×C47—21no—
107#106×C47—21no—
108#106×C47—21no—
109#106×C47—41no—
110#106×C47D411yescharacteristic
111C4⋊C8×C47—21no—
112C4⋊C8×C47—21no—
113C4⋊C8×C47—21no—
114C4⋊C8×C47C2311yescharacteristic
115C4⋊C8×C47C2311yescharacteristic
116C4⋊C8×C47C2311yescharacteristic
117C4⋊C8×C47C2311yescharacteristic
118#103×C47—21no—
119#103×C47—21no—
120#103×C47—21no—
121#103×C47—21no—
122#103×C47—21no—
123#103×C47—21no—
124#103×C47—21no—
125#103×C47—21no—
126#103×C47—21no—
127#103×C47—21no—
128#103×C47—21no—
129#103×C47—21no—
130#103×C47—21no—
131#103×C47—21no—
132#103×C47—41no—
133#103×C47D411yescharacteristic
134#103×C47D411yescharacteristic
135#103×C47D411yescharacteristic
136#102×C47D411yescharacteristic
137C22⋊C8×C47—21no—
138#97×C47—21no—
139C4×C8×C47—21no—
140C4×C8×C47—21no—
141C4×C8×C47C2311yescharacteristic
142C4×C8×C47C2311yescharacteristic
143C4×C8×C47C2311yescharacteristic
144C2×Q8×C47—21no—
145C2×Q8×C47—21no—
146C2×Q8×C47—21no—
147C2×Q8×C47—21no—
148C2×Q8×C47—41no—
149C2×Q8×C47—42no—
150C2×Q8×C47—81no—
151C2×Q8×C47C2×D411yescharacteristic
152C2×Q8×C47C2×D411yescharacteristic
153C2×Q8×C47C2×D411yescharacteristic
154C2×D4×C47C2×D411yescharacteristic
155C22×C4×C47—21no—
156C22×C4×C47—41no—
157C22×C4×C47—41no—
158Q16×C47—22no—
159Q16×C47—81no—
160SD16×C47—22no—
161SD16×C47—42no—
162SD16×C47—42no—
163C2×C8×C47—21no—
164C2×C8×C47—21no—
165C2×C8×C47—21no—
166C2×C8×C47—21no—
167C2×C8×C47—21no—
168C2×C8×C47—81no—
169C2×C8×C47C2×D411yescharacteristic
170C2×C8×C47C2×D411yescharacteristic
171C2×C8×C47C2×D411yescharacteristic
172C2×C8×C47C2×D411yescharacteristic
173C4⋊C4×C47—21no—
174C4⋊C4×C47—21no—
175C4⋊C4×C47—21no—
176C4⋊C4×C47—21no—
177C4⋊C4×C47—21no—
178C4⋊C4×C47—21no—
179C4⋊C4×C47—21no—
180C4⋊C4×C47—21no—
181C4⋊C4×C47—21no—
182C4⋊C4×C47—21no—
183C4⋊C4×C47—21no—
184C4⋊C4×C47—41no—
185C4⋊C4×C47—41no—
186C4⋊C4×C47—41no—
187C4⋊C4×C47—41no—
188C4⋊C4×C47—41no—
189C4⋊C4×C47—41no—
190C4⋊C4×C47—41no—
191C4⋊C4×C47—41no—
192C4⋊C4×C47—41no—
193C4⋊C4×C47C2×D411yescharacteristic
194C4⋊C4×C47C2×D411yescharacteristic
195C4⋊C4×C47C2×D411yescharacteristic
196C4⋊C4×C47C2×D411yescharacteristic
197C22⋊C4×C47—21no—
198C22⋊C4×C47—41no—
199C22⋊C4×C47—41no—
200C42×C47—21no—
201C42×C47—21no—
202C42×C47—21no—
203C42×C47—41no—
204C42×C47—41no—
205C42×C47C2411yescharacteristic
206C23×C47—21no—
207Q8×C47—21no—
208Q8×C47—21no—
209Q8×C47—21no—
210Q8×C47—21no—
211Q8×C47—21no—
212Q8×C47—41no—
213Q8×C47—41no—
214Q8×C47—41no—
215Q8×C47—41no—
216Q8×C47—41no—
217Q8×C47—41no—
218Q8×C47—82no—
219Q8×C47—81no—
220Q8×C47#13712yes—
221D4×C47—21no—
222D4×C47#13512yes—
223C2×C4×C47—21no—
224C2×C4×C47—21no—
225C2×C4×C47—21no—
226C2×C4×C47—21no—
227C2×C4×C47—21no—
228C2×C4×C47—21no—
229C2×C4×C47—21no—
230C2×C4×C47—41no—
231C2×C4×C47—41no—
232C2×C4×C47—41no—
233C2×C4×C47—41no—
234C2×C4×C47—41no—
235C2×C4×C47—41no—
236C2×C4×C47—82no—
237C2×C4×C47—161no—
238C2×C4×C47C22×D411yescharacteristic
239C2×C4×C47C22×D411yescharacteristic
240C2×C4×C47H(5,𝔽2)11yescharacteristic
241C8×C47—21no—
242C8×C47—21no—
243C8×C47—21no—
244C8×C47—21no—
245C8×C47—41no—
246C8×C47—41no—
247C8×C47—41no—
248C8×C47—41no—
249C8×C47—41no—
250#19838C4711yesmaximal, characteristic, direct product factor, Sylow
251C22×C47—22no—
252C22×C47—41no—
253C22×C47—41no—
254C22×C47D4211yescharacteristic
255C4×C47—22no—
256C4×C47—21no—
257C4×C47—41no—
258C4×C47—41no—
259C4×C47—41no—
260C4×C47—41no—
261C4×C47—41no—
262C4×C47—41no—
263C4×C47—81no—
264C4×C47—81no—
265C4×C47—81no—
266C4×C47—81no—
267C4×C47C2×#13511yescharacteristic
268C4×C47C2×#13711yescharacteristic
269C4×C47#57711yescharacteristic
270C4×C47#57811yescharacteristic
271#3383C2×C4711yescharacteristic, complemented
272#3372C2×C4711yescharacteristic
273#3359C2×C4711yescharacteristic
274#3299C2×C4711yescharacteristic
275#1718C2×C4711yescharacteristic, complemented
276#1700C2×C4711yescharacteristic, complemented
277#1684C2×C4711yescharacteristic, complemented
278#1684C2×C4711yescharacteristic, complemented
279#1673C2×C4711yescharacteristic
280#1653C2×C4711yescharacteristic, complemented
281#1651C2×C4711yescharacteristic
282#1643C2×C4711yescharacteristic
283#1636C2×C4711yescharacteristic, complemented
284#1584C2×C4711yescharacteristic, complemented
285SD16⋊C8C2×C4711yescharacteristic
286C2×C47—42no—
287C2×C47#326611yescharacteristic
288C2×C47#328511yescharacteristic
289C2×C47#328911yescharacteristic
290#557C22×C4711yescharacteristic
291#557C22×C4711yescharacteristic
292#554C22×C4711yescharacteristic
293D4×Q8C22×C4711yescharacteristic
294#500C22×C4711yescharacteristic
295#499—21no—
296#498C22×C4711yescharacteristic
297#491—21no—
298#487—21no—
299#487C22×C4711yescharacteristic
300#487C22×C4711yescharacteristic
301#487C22×C4711yescharacteristic
302#487C22×C4711yescharacteristic
303#484—21no—
304#479—21no—
305#479—21no—
306#479—21no—
307#477C22×C4711yescharacteristic
308#477C22×C4711yescharacteristic
309#475—21no—
310#475C22×C4711yescharacteristic
311#475C22×C4711yescharacteristic
312#475C22×C4711yescharacteristic
313#467—21no—
314#462C22×C4711yescharacteristic
315#461—21no—
316#461—21no—
317#461C22×C4711yescharacteristic
318#461C22×C4711yescharacteristic
319#451—21no—
320#446C22×C4711yescharacteristic
321C8×Q8C22×C4711yescharacteristic
322C8×Q8C22×C4711yescharacteristic
323#440—21no—
324C4×Q16—21no—
325C4×Q16C22×C4711yescharacteristic
326C4×SD16—21no—
327C4×SD16C22×C4711yescharacteristic
328C8×D4C22×C4711yescharacteristic
329C2×#103—21no—
330#335C22×C4711yescharacteristic
331#335C22×C4711yescharacteristic
332#333C22×C4711yescharacteristic
333#332C22×C4711yescharacteristic
334#332C22×C4711yescharacteristic
335#332C22×C4711yescharacteristic
336Q8⋊C8C22×C4711yescharacteristic
337Q8⋊C8C22×C4711yescharacteristic
338Q8⋊C8C22×C4711yescharacteristic
339D4⋊C8C22×C4711yescharacteristic
340#322C22×C4711yescharacteristic
341C47#1983811yescharacteristic, direct product factor, Sylow
342C22×Q8—21no—
343C2×Q16—21no—
344C2×Q16D4×C4711yescharacteristic
345C2×SD16—21no—
346C2×SD16—21no—
347C2×SD16D4×C4711yescharacteristic
348C22×C8—21no—
349C4⋊Q8—21no—
350C4⋊Q8—21no—
351C4⋊Q8—21no—
352C4⋊Q8C23×C4711yescharacteristic
353C4⋊Q8C23×C4711yescharacteristic
354C4⋊Q8C23×C4711yescharacteristic
355C4⋊Q8C23×C4711yescharacteristic
356#125—21no—
357#125—21no—
358#125—21no—
359#125—41no—
360#125—41no—
361C22⋊Q8—21no—
362C22⋊Q8—21no—
363C22⋊Q8—41no—
364C22⋊Q8—41no—
365C4×Q8—21no—
366C4×Q8—21no—
367C4×Q8—21no—
368C4×Q8—21no—
369C4×Q8C23×C4711yescharacteristic
370C4×Q8C23×C4711yescharacteristic
371C4×Q8C23×C4711yescharacteristic
372C4×D4—21no—
373C4×D4—21no—
374C4×D4C23×C4711yescharacteristic
375C2×C4⋊C4—21no—
376#107—21no—
377#107—21no—
378#107—21no—
379#107—21no—
380#107D4×C4711yescharacteristic
381#106—21no—
382#106—21no—
383#106—21no—
384#106—41no—
385#106D4×C4711yescharacteristic
386C4⋊C8—21no—
387C4⋊C8—21no—
388C4⋊C8—21no—
389C4⋊C8C23×C4711yescharacteristic
390C4⋊C8C23×C4711yescharacteristic
391C4⋊C8C23×C4711yescharacteristic
392C4⋊C8C23×C4711yescharacteristic
393#103—21no—
394#103—21no—
395#103—21no—
396#103—21no—
397#103—21no—
398#103—21no—
399#103—21no—
400#103—21no—
401#103—21no—
402#103—21no—
403#103—21no—
404#103—21no—
405#103—21no—
406#103—21no—
407#103—41no—
408#103D4×C4711yescharacteristic
409#103D4×C4711yescharacteristic
410#103D4×C4711yescharacteristic
411#102D4×C4711yescharacteristic
412C22⋊C8—21no—
413#97—21no—
414C4×C8—21no—
415C4×C8—21no—
416C4×C8C23×C4711yescharacteristic
417C4×C8C23×C4711yescharacteristic
418C4×C8C23×C4711yescharacteristic
419C2×Q8—21no—
420C2×Q8—21no—
421C2×Q8—21no—
422C2×Q8—21no—
423C2×Q8—41no—
424C2×Q8—42no—
425C2×Q8—81no—
426C2×Q8C2×D4×C4711yescharacteristic
427C2×Q8C2×D4×C4711yescharacteristic
428C2×Q8C2×D4×C4711yescharacteristic
429C2×D4C2×D4×C4711yescharacteristic
430C22×C4—21no—
431C22×C4—41no—
432C22×C4—41no—
433Q16—22no—
434Q16—81no—
435SD16—22no—
436SD16—42no—
437SD16—42no—
438C2×C8—21no—
439C2×C8—21no—
440C2×C8—21no—
441C2×C8—21no—
442C2×C8—21no—
443C2×C8—81no—
444C2×C8C2×D4×C4711yescharacteristic
445C2×C8C2×D4×C4711yescharacteristic
446C2×C8C2×D4×C4711yescharacteristic
447C2×C8C2×D4×C4711yescharacteristic
448C4⋊C4—21no—
449C4⋊C4—21no—
450C4⋊C4—21no—
451C4⋊C4—21no—
452C4⋊C4—21no—
453C4⋊C4—21no—
454C4⋊C4—21no—
455C4⋊C4—21no—
456C4⋊C4—21no—
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—41no—
460C4⋊C4—41no—
461C4⋊C4—41no—
462C4⋊C4—41no—
463C4⋊C4—41no—
464C4⋊C4—41no—
465C4⋊C4—41no—
466C4⋊C4—41no—
467C4⋊C4—41no—
468C4⋊C4C2×D4×C4711yescharacteristic
469C4⋊C4C2×D4×C4711yescharacteristic
470C4⋊C4C2×D4×C4711yescharacteristic
471C4⋊C4C2×D4×C4711yescharacteristic
472C22⋊C4—21no—
473C22⋊C4—41no—
474C22⋊C4—41no—
475C42—21no—
476C42—21no—
477C42—21no—
478C42—41no—
479C42—41no—
480C42C24×C4711yescharacteristic
481C23—21no—
482Q8—21no—
483Q8—21no—
484Q8—21no—
485Q8—21no—
486Q8—21no—
487Q8—41no—
488Q8—41no—
489Q8—41no—
490Q8—41no—
491Q8—41no—
492Q8—41no—
493Q8—82no—
494Q8—81no—
495Q8#137×C4712yes—
496D4—21no—
497D4#135×C4712yes—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—41no—
506C2×C4—41no—
507C2×C4—41no—
508C2×C4—41no—
509C2×C4—41no—
510C2×C4—41no—
511C2×C4—82no—
512C2×C4—161no—
513C2×C4C22×D4×C4711yescharacteristic
514C2×C4C22×D4×C4711yescharacteristic
515C2×C4H(5,𝔽2)×C4711yescharacteristic
516C8—21no—
517C8—21no—
518C8—21no—
519C8—21no—
520C8—41no—
521C8—41no—
522C8—41no—
523C8—41no—
524C8—41no—
525C22—22no—
526C22—41no—
527C22—41no—
528C22D42×C4711yescharacteristic
529C4—21no—
530C4—22no—
531C4—41no—
532C4—41no—
533C4—41no—
534C4—41no—
535C4—41no—
536C4—41no—
537C4—81no—
538C4—81no—
539C4—81no—
540C4—81no—
541C4C2×#135×C4711yescharacteristic
542C4C2×#137×C4711yescharacteristic
543C4C47×#57711yescharacteristic
544C4C47×#57811yescharacteristic
545C2—42no—
546C2C47×#326611yescharacteristic
547C2C47×#328511yescharacteristic
548C2C47×#328911yescharacteristic
subgroupG/H
center, socleC22×C47D42
commutator, Frattini, cosocleC42C24×C47
prime radicalC2×D4×C47C2×D4
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C47 ◁ C42×C47 ◁ G

Complements

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

NH ≅ G/Ntype
1. C47×#3383C2semidirect
5. C47×#1718C2semidirect
6. C47×#1700C2semidirect
7. C47×#1684C2semidirect
8. C47×#1684C2semidirect
10. C47×#1653C2semidirect
13. C47×#1636C2semidirect
14. C47×#1584C2semidirect
250. #19838C47direct (N × H)
271. #3383C2×C47semidirect
275. #1718C2×C47semidirect
276. #1700C2×C47semidirect
277. #1684C2×C47semidirect
278. #1684C2×C47semidirect
280. #1653C2×C47semidirect
283. #1636C2×C47semidirect
284. #1584C2×C47semidirect
341. C47#19838direct (N × H)

Maximal subgroups

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

subgroupindex
C47×#33832
C47×#33722
C47×#33592
C47×#32992
C47×#17182
C47×#17002
C47×#16842
C47×#16732
C47×#16532
C47×#16512
C47×#16432
C47×#16362
C47×#15842
C47×SD16⋊C82
#1983847