Finite Group Databasebeta

← C47×#19846 #26059544

Subgroups — C47×#19846 #26059544

Order 12032.

566 conjugacy classes of subgroups.

The subgroup lattice has 546 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1Q8×Q16×C47C211yesmaximal, characteristic, complemented
2C47×#3375C211yesmaximal, characteristic
3C47×#3365C211yesmaximal, characteristic
4C47×#3363C211yesmaximal, characteristic, complemented
5C47×#1719C211yesmaximal, characteristic
6C47×#1704C211yesmaximal, characteristic, complemented
7C47×#1682C211yesmaximal, characteristic
8C47×#1678C211yesmaximal, characteristic
9C47×#1676C211yesmaximal, characteristic, complemented
10C47×#1645C211yesmaximal, characteristic, complemented
11C47×#1636C211yesmaximal, characteristic, complemented
12C47×#1630C211yesmaximal, characteristic
13C47×#1623C211yesmaximal, characteristic
14C47×#1584C211yesmaximal, characteristic, complemented
15C47×#1579C211yesmaximal, characteristic, complemented
16C47×#559C2211yescharacteristic
17Q82×C47C2211yescharacteristic
18Q82×C47C2211yescharacteristic
19C47×#557C2211yescharacteristic
20C47×#500—21no—
21C47×#500C2211yescharacteristic
22C47×#492C2211yescharacteristic
23C47×#489—21no—
24C47×#488—21no—
25C47×#487—21no—
26C47×#487C2211yescharacteristic
27C47×#487C2211yescharacteristic
28C47×#486C2211yescharacteristic
29C47×#486C2211yescharacteristic
30C47×#478—21no—
31C47×#477—21no—
32C47×#477—21no—
33C47×#477—21no—
34C47×#477C2211yescharacteristic
35C47×#477C2211yescharacteristic
36C47×#477C2211yescharacteristic
37C47×#477C2211yescharacteristic
38C47×#475C2211yescharacteristic
39C47×#474—21no—
40C47×#464—21no—
41C47×#464—21no—
42C47×#462—21no—
43C47×#462C2211yescharacteristic
44C47×#460C2211yescharacteristic
45C47×#460C2211yescharacteristic
46C47×#446C2211yescharacteristic
47C8×Q8×C47C2211yescharacteristic
48C8×Q8×C47C2211yescharacteristic
49C8×Q8×C47C2211yescharacteristic
50C47×#440—21no—
51C4×Q16×C47—21no—
52C4×Q16×C47—21no—
53C4×Q16×C47C2211yescharacteristic
54C4×Q16×C47C2211yescharacteristic
55C4×SD16×C47—21no—
56C47×#335C2211yescharacteristic
57C47×#334C2211yescharacteristic
58C47×#333C2211yescharacteristic
59C47×#333C2211yescharacteristic
60C47×#332C2211yescharacteristic
61C47×#331C2211yescharacteristic
62C47×Q8⋊C8C2211yescharacteristic
63C47×Q8⋊C8C2211yescharacteristic
64C47×Q8⋊C8C2211yescharacteristic
65C47×Q8⋊C8C2211yescharacteristic
66C47×#322C2211yescharacteristic
67C2×Q16×C47—21no—
68C2×Q16×C47D411yescharacteristic
69C2×Q16×C47D411yescharacteristic
70C2×SD16×C47—21no—
71C2×SD16×C47—21no—
72C2×SD16×C47—41no—
73C4⋊Q8×C47—21no—
74C4⋊Q8×C47—21no—
75C4⋊Q8×C47—21no—
76C4⋊Q8×C47—21no—
77C4⋊Q8×C47—21no—
78C4⋊Q8×C47—41no—
79C4⋊Q8×C47—41no—
80C4⋊Q8×C47C2311yescharacteristic
81C4⋊Q8×C47C2311yescharacteristic
82C4⋊Q8×C47C2311yescharacteristic
83#127×C47C2311yescharacteristic
84#125×C47—21no—
85#125×C47—41no—
86#124×C47—21no—
87#124×C47—21no—
88#123×C47—41no—
89C4×Q8×C47—21no—
90C4×Q8×C47—21no—
91C4×Q8×C47—21no—
92C4×Q8×C47—21no—
93C4×Q8×C47—21no—
94C4×Q8×C47—21no—
95C4×Q8×C47C2311yescharacteristic
96C4×Q8×C47C2311yescharacteristic
97C4×Q8×C47C2311yescharacteristic
98C4×Q8×C47C2311yescharacteristic
99C4×D4×C47—21no—
100C4×D4×C47—21no—
101#107×C47—21no—
102#107×C47—21no—
103#107×C47—21no—
104#107×C47—21no—
105#107×C47—21no—
106#107×C47—21no—
107#107×C47D411yescharacteristic
108#107×C47D411yescharacteristic
109#106×C47—21no—
110C4⋊C8×C47—21no—
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—41no—
127#103×C47D411yescharacteristic
128#103×C47D411yescharacteristic
129#103×C47D411yescharacteristic
130#103×C47D411yescharacteristic
131#102×C47—21no—
132#102×C47—21no—
133#102×C47—21no—
134#102×C47—21no—
135#102×C47—21no—
136#102×C47—21no—
137#97×C47—21no—
138C4×C8×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—41no—
148C2×Q8×C47—41no—
149C2×Q8×C47C2×D411yescharacteristic
150C2×Q8×C47C2×D411yescharacteristic
151C2×Q8×C47C2×D411yescharacteristic
152C2×Q8×C47C2×D411yescharacteristic
153C2×D4×C47—21no—
154C2×D4×C47—21no—
155C2×D4×C47—21no—
156C22×C4×C47—41no—
157Q16×C47—22no—
158Q16×C47—22no—
159Q16×C47—42no—
160SD16×C47—42no—
161SD16×C47—42no—
162SD16×C47—82no—
163C2×C8×C47—21no—
164C2×C8×C47—21no—
165C2×C8×C47—21no—
166C2×C8×C47—21no—
167C2×C8×C47—21no—
168C2×C8×C47C2×D411yescharacteristic
169C2×C8×C47C2×D411yescharacteristic
170C2×C8×C47C2×D411yescharacteristic
171C2×C8×C47C2×D411yescharacteristic
172C4⋊C4×C47—21no—
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—41no—
183C4⋊C4×C47—41no—
184C4⋊C4×C47—41no—
185C4⋊C4×C47—41no—
186C4⋊C4×C47—41no—
187C4⋊C4×C47—41no—
188C4⋊C4×C47—41no—
189C4⋊C4×C47C2×D411yescharacteristic
190C4⋊C4×C47C2×D411yescharacteristic
191C4⋊C4×C47C2×D411yescharacteristic
192C4⋊C4×C47C2×D411yescharacteristic
193C22⋊C4×C47—41no—
194C22⋊C4×C47—41no—
195C22⋊C4×C47—41no—
196C42×C47—21no—
197C42×C47—21no—
198C42×C47—21no—
199C42×C47—21no—
200C42×C47—41no—
201C42×C47—41no—
202C42×C47—41no—
203C42×C47C2411yescharacteristic
204C23×C47—41no—
205Q8×C47—21no—
206Q8×C47—21no—
207Q8×C47—21no—
208Q8×C47—21no—
209Q8×C47—21no—
210Q8×C47—21no—
211Q8×C47—41no—
212Q8×C47—41no—
213Q8×C47—81no—
214Q8×C47—81no—
215Q8×C47—161no—
216Q8×C47—161no—
217Q8×C47#13512yes—
218Q8×C47#13712yes—
219D4×C47—41no—
220D4×C47—41no—
221D4×C47—41no—
222D4×C47—41no—
223D4×C47—81no—
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—21no—
231C2×C4×C47—21no—
232C2×C4×C47—41no—
233C2×C4×C47—41no—
234C2×C4×C47—41no—
235C2×C4×C47—161no—
236C2×C4×C47C22×D411yescharacteristic
237C2×C4×C47C22×D411yescharacteristic
238C2×C4×C47H(5,𝔽2)11yescharacteristic
239C8×C47—21no—
240C8×C47—21no—
241C8×C47—21no—
242C8×C47—21no—
243C8×C47—41no—
244C8×C47—41no—
245C8×C47—41no—
246C8×C47—41no—
247C8×C47—41no—
248#19846C4711yesmaximal, characteristic, direct product factor, Sylow
249C22×C47—81no—
250C22×C47—81no—
251C22×C47—81no—
252C22×C47D4211yescharacteristic
253C4×C47—22no—
254C4×C47—22no—
255C4×C47—21no—
256C4×C47—41no—
257C4×C47—41no—
258C4×C47—41no—
259C4×C47—41no—
260C4×C47—41no—
261C4×C47—41no—
262C4×C47—81no—
263C4×C47—81no—
264C4×C47—81no—
265C4×C47C2×#13511yescharacteristic
266C4×C47C2×#13711yescharacteristic
267C4×C47#57811yescharacteristic
268C4×C47#57811yescharacteristic
269Q8×Q16C2×C4711yescharacteristic, complemented
270#3375C2×C4711yescharacteristic
271#3365C2×C4711yescharacteristic
272#3363C2×C4711yescharacteristic, complemented
273#1719C2×C4711yescharacteristic
274#1704C2×C4711yescharacteristic, complemented
275#1682C2×C4711yescharacteristic
276#1678C2×C4711yescharacteristic
277#1676C2×C4711yescharacteristic, complemented
278#1645C2×C4711yescharacteristic, complemented
279#1636C2×C4711yescharacteristic, complemented
280#1630C2×C4711yescharacteristic
281#1623C2×C4711yescharacteristic
282#1584C2×C4711yescharacteristic, complemented
283#1579C2×C4711yescharacteristic, complemented
284C2×C47—161no—
285C2×C47#327011yescharacteristic
286C2×C47#328511yescharacteristic
287C2×C47#328811yescharacteristic
288#559C22×C4711yescharacteristic
289Q82C22×C4711yescharacteristic
290Q82C22×C4711yescharacteristic
291#557C22×C4711yescharacteristic
292#500—21no—
293#500C22×C4711yescharacteristic
294#492C22×C4711yescharacteristic
295#489—21no—
296#488—21no—
297#487—21no—
298#487C22×C4711yescharacteristic
299#487C22×C4711yescharacteristic
300#486C22×C4711yescharacteristic
301#486C22×C4711yescharacteristic
302#478—21no—
303#477—21no—
304#477—21no—
305#477—21no—
306#477C22×C4711yescharacteristic
307#477C22×C4711yescharacteristic
308#477C22×C4711yescharacteristic
309#477C22×C4711yescharacteristic
310#475C22×C4711yescharacteristic
311#474—21no—
312#464—21no—
313#464—21no—
314#462—21no—
315#462C22×C4711yescharacteristic
316#460C22×C4711yescharacteristic
317#460C22×C4711yescharacteristic
318#446C22×C4711yescharacteristic
319C8×Q8C22×C4711yescharacteristic
320C8×Q8C22×C4711yescharacteristic
321C8×Q8C22×C4711yescharacteristic
322#440—21no—
323C4×Q16—21no—
324C4×Q16—21no—
325C4×Q16C22×C4711yescharacteristic
326C4×Q16C22×C4711yescharacteristic
327C4×SD16—21no—
328#335C22×C4711yescharacteristic
329#334C22×C4711yescharacteristic
330#333C22×C4711yescharacteristic
331#333C22×C4711yescharacteristic
332#332C22×C4711yescharacteristic
333#331C22×C4711yescharacteristic
334Q8⋊C8C22×C4711yescharacteristic
335Q8⋊C8C22×C4711yescharacteristic
336Q8⋊C8C22×C4711yescharacteristic
337Q8⋊C8C22×C4711yescharacteristic
338#322C22×C4711yescharacteristic
339C47#1984611yescharacteristic, direct product factor, Sylow
340C2×Q16—21no—
341C2×Q16D4×C4711yescharacteristic
342C2×Q16D4×C4711yescharacteristic
343C2×SD16—21no—
344C2×SD16—21no—
345C2×SD16—41no—
346C4⋊Q8—21no—
347C4⋊Q8—21no—
348C4⋊Q8—21no—
349C4⋊Q8—21no—
350C4⋊Q8—21no—
351C4⋊Q8—41no—
352C4⋊Q8—41no—
353C4⋊Q8C23×C4711yescharacteristic
354C4⋊Q8C23×C4711yescharacteristic
355C4⋊Q8C23×C4711yescharacteristic
356#127C23×C4711yescharacteristic
357#125—21no—
358#125—41no—
359#124—21no—
360#124—21no—
361#123—41no—
362C4×Q8—21no—
363C4×Q8—21no—
364C4×Q8—21no—
365C4×Q8—21no—
366C4×Q8—21no—
367C4×Q8—21no—
368C4×Q8C23×C4711yescharacteristic
369C4×Q8C23×C4711yescharacteristic
370C4×Q8C23×C4711yescharacteristic
371C4×Q8C23×C4711yescharacteristic
372C4×D4—21no—
373C4×D4—21no—
374#107—21no—
375#107—21no—
376#107—21no—
377#107—21no—
378#107—21no—
379#107—21no—
380#107D4×C4711yescharacteristic
381#107D4×C4711yescharacteristic
382#106—21no—
383C4⋊C8—21no—
384C4⋊C8—21no—
385C4⋊C8—21no—
386C4⋊C8—21no—
387C4⋊C8C23×C4711yescharacteristic
388C4⋊C8C23×C4711yescharacteristic
389C4⋊C8C23×C4711yescharacteristic
390C4⋊C8C23×C4711yescharacteristic
391#103—21no—
392#103—21no—
393#103—21no—
394#103—21no—
395#103—21no—
396#103—21no—
397#103—21no—
398#103—21no—
399#103—41no—
400#103D4×C4711yescharacteristic
401#103D4×C4711yescharacteristic
402#103D4×C4711yescharacteristic
403#103D4×C4711yescharacteristic
404#102—21no—
405#102—21no—
406#102—21no—
407#102—21no—
408#102—21no—
409#102—21no—
410#97—21no—
411C4×C8—21no—
412C4×C8—21no—
413C4×C8—21no—
414C4×C8C23×C4711yescharacteristic
415C4×C8C23×C4711yescharacteristic
416C4×C8C23×C4711yescharacteristic
417C2×Q8—21no—
418C2×Q8—21no—
419C2×Q8—21no—
420C2×Q8—41no—
421C2×Q8—41no—
422C2×Q8C2×D4×C4711yescharacteristic
423C2×Q8C2×D4×C4711yescharacteristic
424C2×Q8C2×D4×C4711yescharacteristic
425C2×Q8C2×D4×C4711yescharacteristic
426C2×D4—21no—
427C2×D4—21no—
428C2×D4—21no—
429C22×C4—41no—
430Q16—22no—
431Q16—22no—
432Q16—42no—
433SD16—42no—
434SD16—42no—
435SD16—82no—
436C2×C8—21no—
437C2×C8—21no—
438C2×C8—21no—
439C2×C8—21no—
440C2×C8—21no—
441C2×C8C2×D4×C4711yescharacteristic
442C2×C8C2×D4×C4711yescharacteristic
443C2×C8C2×D4×C4711yescharacteristic
444C2×C8C2×D4×C4711yescharacteristic
445C4⋊C4—21no—
446C4⋊C4—21no—
447C4⋊C4—21no—
448C4⋊C4—21no—
449C4⋊C4—21no—
450C4⋊C4—21no—
451C4⋊C4—21no—
452C4⋊C4—21no—
453C4⋊C4—21no—
454C4⋊C4—21no—
455C4⋊C4—41no—
456C4⋊C4—41no—
457C4⋊C4—41no—
458C4⋊C4—41no—
459C4⋊C4—41no—
460C4⋊C4—41no—
461C4⋊C4—41no—
462C4⋊C4C2×D4×C4711yescharacteristic
463C4⋊C4C2×D4×C4711yescharacteristic
464C4⋊C4C2×D4×C4711yescharacteristic
465C4⋊C4C2×D4×C4711yescharacteristic
466C22⋊C4—41no—
467C22⋊C4—41no—
468C22⋊C4—41no—
469C42—21no—
470C42—21no—
471C42—21no—
472C42—21no—
473C42—41no—
474C42—41no—
475C42—41no—
476C42C24×C4711yescharacteristic
477C23—41no—
478Q8—21no—
479Q8—21no—
480Q8—21no—
481Q8—21no—
482Q8—21no—
483Q8—21no—
484Q8—41no—
485Q8—41no—
486Q8—81no—
487Q8—81no—
488Q8—161no—
489Q8—161no—
490Q8#135×C4712yes—
491Q8#137×C4712yes—
492D4—41no—
493D4—41no—
494D4—41no—
495D4—41no—
496D4—81no—
497C2×C4—21no—
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—161no—
509C2×C4C22×D4×C4711yescharacteristic
510C2×C4C22×D4×C4711yescharacteristic
511C2×C4H(5,𝔽2)×C4711yescharacteristic
512C8—21no—
513C8—21no—
514C8—21no—
515C8—21no—
516C8—41no—
517C8—41no—
518C8—41no—
519C8—41no—
520C8—41no—
521C22—81no—
522C22—81no—
523C22—81no—
524C22D42×C4711yescharacteristic
525C4—21no—
526C4—22no—
527C4—22no—
528C4—41no—
529C4—41no—
530C4—41no—
531C4—41no—
532C4—41no—
533C4—41no—
534C4—81no—
535C4—81no—
536C4—81no—
537C4C2×#135×C4711yescharacteristic
538C4C2×#137×C4711yescharacteristic
539C4C47×#57811yescharacteristic
540C4C47×#57811yescharacteristic
541C2—161no—
542C2C47×#327011yescharacteristic
543C2C47×#328511yescharacteristic
544C2C47×#328811yescharacteristic
subgroupG/H
center, socleC22×C47D42
commutator, Frattini, cosocleC42C24×C47
prime radical#127×C47C23
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. Q8×Q16×C47C2semidirect
4. C47×#3363C2semidirect
6. C47×#1704C2semidirect
9. C47×#1676C2semidirect
10. C47×#1645C2semidirect
11. C47×#1636C2semidirect
14. C47×#1584C2semidirect
15. C47×#1579C2semidirect
248. #19846C47direct (N × H)
269. Q8×Q16C2×C47semidirect
272. #3363C2×C47semidirect
274. #1704C2×C47semidirect
277. #1676C2×C47semidirect
278. #1645C2×C47semidirect
279. #1636C2×C47semidirect
282. #1584C2×C47semidirect
283. #1579C2×C47semidirect
339. C47#19846direct (N × H)

Maximal subgroups

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

subgroupindex
Q8×Q16×C472
C47×#33752
C47×#33652
C47×#33632
C47×#17192
C47×#17042
C47×#16822
C47×#16782
C47×#16762
C47×#16452
C47×#16362
C47×#16302
C47×#16232
C47×#15842
C47×#15792
#1984647