Finite Group Databasebeta

← C47×#19920 #26059618

Subgroups — C47×#19920 #26059618

Order 12032.

572 conjugacy classes of subgroups.

The subgroup lattice has 552 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C47×#3374C211yesmaximal, characteristic, complemented
2C47×#3364C211yesmaximal, characteristic
3C47×#3359C211yesmaximal, characteristic
4C47×#3328C211yesmaximal, characteristic
5C47×#1710C211yesmaximal, characteristic, complemented
6C47×#1700C211yesmaximal, characteristic, complemented
7C47×#1699C211yesmaximal, characteristic
8C47×#1680C211yesmaximal, characteristic, complemented
9C47×#1680C211yesmaximal, characteristic, complemented
10C47×#1650C211yesmaximal, characteristic
11C47×#1649C211yesmaximal, characteristic
12C47×#1648C211yesmaximal, characteristic, complemented
13C47×#1648C211yesmaximal, characteristic, complemented
14C47×#1590C211yesmaximal, characteristic
15C8×Q16×C47C211yesmaximal, characteristic, complemented
16C47×#557C2211yescharacteristic
17C47×#557C2211yescharacteristic
18C47×#556C2211yescharacteristic
19D4×Q8×C47C2211yescharacteristic
20C47×#500C2211yescharacteristic
21C47×#500C2211yescharacteristic
22C47×#491—21no—
23C47×#488—21no—
24C47×#487—21no—
25C47×#487C2211yescharacteristic
26C47×#487C2211yescharacteristic
27C47×#487C2211yescharacteristic
28C47×#487C2211yescharacteristic
29C47×#485—21no—
30C47×#479—21no—
31C47×#479—21no—
32C47×#475—21no—
33C47×#475C2211yescharacteristic
34C47×#475C2211yescharacteristic
35C47×#475C2211yescharacteristic
36C47×#474C2211yescharacteristic
37C47×#470—21no—
38C47×#464—21no—
39C47×#462—21no—
40C47×#462C2211yescharacteristic
41C47×#462C2211yescharacteristic
42C47×#462C2211yescharacteristic
43C47×#461—21no—
44C47×#461C2211yescharacteristic
45C47×#451—21no—
46C47×#446C2211yescharacteristic
47C8×Q8×C47C2211yescharacteristic
48C8×Q8×C47C2211yescharacteristic
49C47×#441—21no—
50C4×Q16×C47—21no—
51C4×Q16×C47C2211yescharacteristic
52C4×SD16×C47—21no—
53C4×SD16×C47C2211yescharacteristic
54C47×#436C2211yescharacteristic
55C47×#419—21no—
56C47×#335C2211yescharacteristic
57C47×#334C2211yescharacteristic
58C47×#332C2211yescharacteristic
59C47×#332C2211yescharacteristic
60C47×#332C2211yescharacteristic
61C47×#332C2211yescharacteristic
62C47×Q8⋊C8C2211yescharacteristic
63C47×Q8⋊C8C2211yescharacteristic
64C47×Q8⋊C8C2211yescharacteristic
65C47×D4⋊C8C2211yescharacteristic
66C82×C47C2211yescharacteristic
67C22×Q8×C47—21no—
68C2×Q16×C47—21no—
69C2×Q16×C47—21no—
70C2×Q16×C47—21no—
71C2×Q16×C47D411yescharacteristic
72C2×SD16×C47—21no—
73C2×SD16×C47D411yescharacteristic
74C2×M16×C47—21no—
75C4⋊Q8×C47—21no—
76C4⋊Q8×C47—21no—
77C4⋊Q8×C47—21no—
78C4⋊Q8×C47C2311yescharacteristic
79C4⋊Q8×C47C2311yescharacteristic
80C4⋊Q8×C47C2311yescharacteristic
81C4⋊Q8×C47C2311yescharacteristic
82#126×C47—41no—
83#125×C47—21no—
84#125×C47—21no—
85#125×C47—41no—
86#125×C47—41no—
87#124×C47—21no—
88C22⋊Q8×C47—21no—
89C22⋊Q8×C47—21no—
90C22⋊Q8×C47—41no—
91C4×Q8×C47—21no—
92C4×Q8×C47—21no—
93C4×Q8×C47—21no—
94C4×Q8×C47—21no—
95C4×Q8×C47—21no—
96C4×Q8×C47C2311yescharacteristic
97C4×Q8×C47C2311yescharacteristic
98C4×Q8×C47C2311yescharacteristic
99C4×D4×C47—21no—
100C4×D4×C47C2311yescharacteristic
101#117×C47—21no—
102#107×C47—21no—
103#107×C47—41no—
104#107×C47—41no—
105#107×C47D411yescharacteristic
106#106×C47—21no—
107#106×C47—21no—
108#106×C47—21no—
109#106×C47D411yescharacteristic
110C4⋊C8×C47—21no—
111C4⋊C8×C47—21no—
112C4⋊C8×C47—21no—
113C4⋊C8×C47C2311yescharacteristic
114C4⋊C8×C47C2311yescharacteristic
115C4⋊C8×C47C2311yescharacteristic
116C4⋊C8×C47C2311yescharacteristic
117#103×C47—21no—
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×C47D411yescharacteristic
133#103×C47D411yescharacteristic
134#103×C47D411yescharacteristic
135#102×C47—21no—
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—
157Q16×C47—22no—
158Q16×C47—42no—
159Q16×C47—42no—
160Q16×C47—81no—
161SD16×C47—41no—
162SD16×C47—42no—
163M16×C47—81no—
164C2×C8×C47—21no—
165C2×C8×C47—21no—
166C2×C8×C47—21no—
167C2×C8×C47—21no—
168C2×C8×C47—21no—
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×C47C2×D411yescharacteristic
193C4⋊C4×C47C2×D411yescharacteristic
194C4⋊C4×C47C2×D411yescharacteristic
195C4⋊C4×C47C2×D411yescharacteristic
196C22⋊C4×C47—21no—
197C22⋊C4×C47—41no—
198C22⋊C4×C47—41no—
199C22⋊C4×C47—41no—
200C42×C47—21no—
201C42×C47—21no—
202C42×C47—21no—
203C42×C47—41no—
204C42×C47—41no—
205C42×C47—41no—
206C42×C47C2411yescharacteristic
207C23×C47—21no—
208Q8×C47—21no—
209Q8×C47—21no—
210Q8×C47—21no—
211Q8×C47—21no—
212Q8×C47—21no—
213Q8×C47—41no—
214Q8×C47—41no—
215Q8×C47—41no—
216Q8×C47—41no—
217Q8×C47—41no—
218Q8×C47—41no—
219Q8×C47—41no—
220Q8×C47—41no—
221Q8×C47—82no—
222Q8×C47#13512yes—
223D4×C47—21no—
224D4×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—21no—
231C2×C4×C47—21no—
232C2×C4×C47—41no—
233C2×C4×C47—41no—
234C2×C4×C47—41no—
235C2×C4×C47—41no—
236C2×C4×C47—41no—
237C2×C4×C47—41no—
238C2×C4×C47—82no—
239C2×C4×C47C22×D411yescharacteristic
240C2×C4×C47C22×D411yescharacteristic
241C2×C4×C47H(5,𝔽2)11yescharacteristic
242C8×C47—22no—
243C8×C47—21no—
244C8×C47—21no—
245C8×C47—21no—
246C8×C47—21no—
247C8×C47—41no—
248C8×C47—41no—
249C8×C47—41no—
250C8×C47—41no—
251#19920C4711yesmaximal, characteristic, direct product factor, Sylow
252C22×C47—41no—
253C22×C47—41no—
254C22×C47—41no—
255C22×C47D4211yescharacteristic
256C4×C47—22no—
257C4×C47—21no—
258C4×C47—41no—
259C4×C47—41no—
260C4×C47—41no—
261C4×C47—41no—
262C4×C47—41no—
263C4×C47—41no—
264C4×C47—81no—
265C4×C47—81no—
266C4×C47—81no—
267C4×C47—81no—
268C4×C47C2×#13511yescharacteristic
269C4×C47#57511yescharacteristic
270C4×C47#57711yescharacteristic
271C4×C47#57811yescharacteristic
272#3374C2×C4711yescharacteristic, complemented
273#3364C2×C4711yescharacteristic
274#3359C2×C4711yescharacteristic
275#3328C2×C4711yescharacteristic
276#1710C2×C4711yescharacteristic, complemented
277#1700C2×C4711yescharacteristic, complemented
278#1699C2×C4711yescharacteristic
279#1680C2×C4711yescharacteristic, complemented
280#1680C2×C4711yescharacteristic, complemented
281#1650C2×C4711yescharacteristic
282#1649C2×C4711yescharacteristic
283#1648C2×C4711yescharacteristic, complemented
284#1648C2×C4711yescharacteristic, complemented
285#1590C2×C4711yescharacteristic
286C8×Q16C2×C4711yescharacteristic, complemented
287C2×C47—81no—
288C2×C47#327711yescharacteristic
289C2×C47#328211yescharacteristic
290C2×C47#329311yescharacteristic
291#557C22×C4711yescharacteristic
292#557C22×C4711yescharacteristic
293#556C22×C4711yescharacteristic
294D4×Q8C22×C4711yescharacteristic
295#500C22×C4711yescharacteristic
296#500C22×C4711yescharacteristic
297#491—21no—
298#488—21no—
299#487—21no—
300#487C22×C4711yescharacteristic
301#487C22×C4711yescharacteristic
302#487C22×C4711yescharacteristic
303#487C22×C4711yescharacteristic
304#485—21no—
305#479—21no—
306#479—21no—
307#475—21no—
308#475C22×C4711yescharacteristic
309#475C22×C4711yescharacteristic
310#475C22×C4711yescharacteristic
311#474C22×C4711yescharacteristic
312#470—21no—
313#464—21no—
314#462—21no—
315#462C22×C4711yescharacteristic
316#462C22×C4711yescharacteristic
317#462C22×C4711yescharacteristic
318#461—21no—
319#461C22×C4711yescharacteristic
320#451—21no—
321#446C22×C4711yescharacteristic
322C8×Q8C22×C4711yescharacteristic
323C8×Q8C22×C4711yescharacteristic
324#441—21no—
325C4×Q16—21no—
326C4×Q16C22×C4711yescharacteristic
327C4×SD16—21no—
328C4×SD16C22×C4711yescharacteristic
329#436C22×C4711yescharacteristic
330#419—21no—
331#335C22×C4711yescharacteristic
332#334C22×C4711yescharacteristic
333#332C22×C4711yescharacteristic
334#332C22×C4711yescharacteristic
335#332C22×C4711yescharacteristic
336#332C22×C4711yescharacteristic
337Q8⋊C8C22×C4711yescharacteristic
338Q8⋊C8C22×C4711yescharacteristic
339Q8⋊C8C22×C4711yescharacteristic
340D4⋊C8C22×C4711yescharacteristic
341C82C22×C4711yescharacteristic
342C47#1992011yescharacteristic, direct product factor, Sylow
343C22×Q8—21no—
344C2×Q16—21no—
345C2×Q16—21no—
346C2×Q16—21no—
347C2×Q16D4×C4711yescharacteristic
348C2×SD16—21no—
349C2×SD16D4×C4711yescharacteristic
350C2×M16—21no—
351C4⋊Q8—21no—
352C4⋊Q8—21no—
353C4⋊Q8—21no—
354C4⋊Q8C23×C4711yescharacteristic
355C4⋊Q8C23×C4711yescharacteristic
356C4⋊Q8C23×C4711yescharacteristic
357C4⋊Q8C23×C4711yescharacteristic
358#126—41no—
359#125—21no—
360#125—21no—
361#125—41no—
362#125—41no—
363#124—21no—
364C22⋊Q8—21no—
365C22⋊Q8—21no—
366C22⋊Q8—41no—
367C4×Q8—21no—
368C4×Q8—21no—
369C4×Q8—21no—
370C4×Q8—21no—
371C4×Q8—21no—
372C4×Q8C23×C4711yescharacteristic
373C4×Q8C23×C4711yescharacteristic
374C4×Q8C23×C4711yescharacteristic
375C4×D4—21no—
376C4×D4C23×C4711yescharacteristic
377#117—21no—
378#107—21no—
379#107—41no—
380#107—41no—
381#107D4×C4711yescharacteristic
382#106—21no—
383#106—21no—
384#106—21no—
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—21no—
408#103D4×C4711yescharacteristic
409#103D4×C4711yescharacteristic
410#103D4×C4711yescharacteristic
411#102—21no—
412#102D4×C4711yescharacteristic
413C22⋊C8—21no—
414#97—21no—
415C4×C8—21no—
416C4×C8—21no—
417C4×C8C23×C4711yescharacteristic
418C4×C8C23×C4711yescharacteristic
419C4×C8C23×C4711yescharacteristic
420C2×Q8—21no—
421C2×Q8—21no—
422C2×Q8—21no—
423C2×Q8—21no—
424C2×Q8—41no—
425C2×Q8—42no—
426C2×Q8—81no—
427C2×Q8C2×D4×C4711yescharacteristic
428C2×Q8C2×D4×C4711yescharacteristic
429C2×Q8C2×D4×C4711yescharacteristic
430C2×D4C2×D4×C4711yescharacteristic
431C22×C4—21no—
432C22×C4—41no—
433Q16—22no—
434Q16—42no—
435Q16—42no—
436Q16—81no—
437SD16—41no—
438SD16—42no—
439M16—81no—
440C2×C8—21no—
441C2×C8—21no—
442C2×C8—21no—
443C2×C8—21no—
444C2×C8—21no—
445C2×C8C2×D4×C4711yescharacteristic
446C2×C8C2×D4×C4711yescharacteristic
447C2×C8C2×D4×C4711yescharacteristic
448C2×C8C2×D4×C4711yescharacteristic
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—21no—
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—
475C22⋊C4—41no—
476C42—21no—
477C42—21no—
478C42—21no—
479C42—41no—
480C42—41no—
481C42—41no—
482C42C24×C4711yescharacteristic
483C23—21no—
484Q8—21no—
485Q8—21no—
486Q8—21no—
487Q8—21no—
488Q8—21no—
489Q8—41no—
490Q8—41no—
491Q8—41no—
492Q8—41no—
493Q8—41no—
494Q8—41no—
495Q8—41no—
496Q8—41no—
497Q8—82no—
498Q8#135×C4712yes—
499D4—21no—
500D4—21no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—41no—
509C2×C4—41no—
510C2×C4—41no—
511C2×C4—41no—
512C2×C4—41no—
513C2×C4—41no—
514C2×C4—82no—
515C2×C4C22×D4×C4711yescharacteristic
516C2×C4C22×D4×C4711yescharacteristic
517C2×C4H(5,𝔽2)×C4711yescharacteristic
518C8—22no—
519C8—21no—
520C8—21no—
521C8—21no—
522C8—21no—
523C8—41no—
524C8—41no—
525C8—41no—
526C8—41no—
527C22—41no—
528C22—41no—
529C22—41no—
530C22D42×C4711yescharacteristic
531C4—21no—
532C4—22no—
533C4—41no—
534C4—41no—
535C4—41no—
536C4—41no—
537C4—41no—
538C4—41no—
539C4—81no—
540C4—81no—
541C4—81no—
542C4—81no—
543C4C2×#135×C4711yescharacteristic
544C4C47×#57511yescharacteristic
545C4C47×#57711yescharacteristic
546C4C47×#57811yescharacteristic
547C2—81no—
548C2C47×#327711yescharacteristic
549C2C47×#328211yescharacteristic
550C2C47×#329311yescharacteristic
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×#3374C2semidirect
5. C47×#1710C2semidirect
6. C47×#1700C2semidirect
8. C47×#1680C2semidirect
9. C47×#1680C2semidirect
12. C47×#1648C2semidirect
13. C47×#1648C2semidirect
15. C8×Q16×C47C2semidirect
251. #19920C47direct (N × H)
272. #3374C2×C47semidirect
276. #1710C2×C47semidirect
277. #1700C2×C47semidirect
279. #1680C2×C47semidirect
280. #1680C2×C47semidirect
283. #1648C2×C47semidirect
284. #1648C2×C47semidirect
286. C8×Q16C2×C47semidirect
342. C47#19920direct (N × H)

Maximal subgroups

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

subgroupindex
C47×#33742
C47×#33642
C47×#33592
C47×#33282
C47×#17102
C47×#17002
C47×#16992
C47×#16802
C47×#16502
C47×#16492
C47×#16482
C47×#15902
C8×Q16×C472
#1992047