Finite Group Databasebeta

← C47×#19857 #26059555

Subgroups — C47×#19857 #26059555

Order 12032.

582 conjugacy classes of subgroups.

The subgroup lattice has 562 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C47×#3400C211yesmaximal, characteristic, complemented
2C47×#3381C211yesmaximal, characteristic, complemented
3C47×#3361C211yesmaximal, characteristic
4C47×#3338C211yesmaximal, characteristic, complemented
5C47×#1714C211yesmaximal, characteristic, complemented
6C47×#1696C211yesmaximal, characteristic, complemented
7C47×#1678C211yesmaximal, characteristic, complemented
8C47×#1672C211yesmaximal, characteristic, complemented
9C47×#1665C211yesmaximal, characteristic
10C47×#1644C211yesmaximal, characteristic, complemented
11C47×#1636C211yesmaximal, characteristic, complemented
12C47×#1630C211yesmaximal, characteristic, complemented
13C47×#1622C211yesmaximal, characteristic
14C47×#1582C211yesmaximal, characteristic, complemented
15C47×#1579C211yesmaximal, characteristic, complemented
16C47×#559C2211yescharacteristic
17C47×#557C2211yescharacteristic
18C47×#554C2211yescharacteristic
19C47×#554C2211yescharacteristic
20C47×#500C2211yescharacteristic
21C47×#499—21no—
22C47×#498C2211yescharacteristic
23C47×#497—21no—
24C47×#492C2211yescharacteristic
25C47×#492C2211yescharacteristic
26C47×#488—21no—
27C47×#487C2211yescharacteristic
28C47×#486C2211yescharacteristic
29C47×#484—21no—
30C47×#484—21no—
31C47×#479—21no—
32C47×#478—21no—
33C47×#478—21no—
34C47×#477C2211yescharacteristic
35C47×#477C2211yescharacteristic
36C47×#477C2211yescharacteristic
37C47×#477C2211yescharacteristic
38C47×#474C2211yescharacteristic
39C47×#467—21no—
40C47×#464—21no—
41C47×#463—21no—
42C47×#462C2211yescharacteristic
43C47×#461—21no—
44C47×#460C2211yescharacteristic
45C47×#459C2211yescharacteristic
46C47×#446C2211yescharacteristic
47C8×Q8×C47C2211yescharacteristic
48C8×Q8×C47C2211yescharacteristic
49C47×#440—21no—
50C4×Q16×C47C2211yescharacteristic
51C4×SD16×C47—21no—
52C4×SD16×C47C2211yescharacteristic
53C4×D8×C47—21no—
54C8×D4×C47C2211yescharacteristic
55C2×#107×C47—21no—
56C47×#334C2211yescharacteristic
57C47×#334C2211yescharacteristic
58C47×#333C2211yescharacteristic
59C47×#333C2211yescharacteristic
60C47×#332C2211yescharacteristic
61C47×#331C2211yescharacteristic
62C47×Q8⋊C8C2211yescharacteristic
63C47×Q8⋊C8C2211yescharacteristic
64C47×Q8⋊C8C2211yescharacteristic
65C47×D4⋊C8C2211yescharacteristic
66C47×#322C2211yescharacteristic
67C2×Q16×C47—21no—
68C2×Q16×C47D411yescharacteristic
69C2×SD16×C47—21no—
70C2×SD16×C47—21no—
71C2×SD16×C47—21no—
72C2×SD16×C47—41no—
73C2×SD16×C47D411yescharacteristic
74C2×D8×C47—21no—
75C22×C8×C47—21no—
76C4⋊Q8×C47—21no—
77C4⋊Q8×C47C2311yescharacteristic
78C4⋊Q8×C47C2311yescharacteristic
79C4⋊Q8×C47C2311yescharacteristic
80#127×C47C2311yescharacteristic
81#125×C47—21no—
82#125×C47—21no—
83#125×C47—21no—
84#125×C47—41no—
85#124×C47—21no—
86#124×C47—21no—
87#123×C47—41no—
88C22⋊Q8×C47—21no—
89C22⋊Q8×C47—21no—
90C22⋊Q8×C47—41no—
91C22⋊Q8×C47—41no—
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×C47—21no—
100C4×D4×C47—21no—
101C4×D4×C47C2311yescharacteristic
102C2×C4⋊C4×C47—21no—
103C2×C4⋊C4×C47—21no—
104#107×C47—21no—
105#107×C47—21no—
106#107×C47—21no—
107#107×C47—21no—
108#107×C47—21no—
109#107×C47—21no—
110#107×C47—21no—
111#107×C47D411yescharacteristic
112#106×C47—21no—
113#106×C47—21no—
114#106×C47D411yescharacteristic
115C4⋊C8×C47—21no—
116C4⋊C8×C47—21no—
117C4⋊C8×C47—21no—
118C4⋊C8×C47C2311yescharacteristic
119C4⋊C8×C47C2311yescharacteristic
120C4⋊C8×C47C2311yescharacteristic
121C4⋊C8×C47C2311yescharacteristic
122#103×C47—21no—
123#103×C47—21no—
124#103×C47—21no—
125#103×C47—21no—
126#103×C47—21no—
127#103×C47—41no—
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×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×C47C2×D411yescharacteristic
148C2×Q8×C47C2×D411yescharacteristic
149C2×Q8×C47C2×D411yescharacteristic
150C2×D4×C47—21no—
151C2×D4×C47—21no—
152C2×D4×C47—21no—
153C2×D4×C47C2×D411yescharacteristic
154C22×C4×C47—21no—
155C22×C4×C47—41no—
156C22×C4×C47—41no—
157C22×C4×C47—41no—
158Q16×C47—22no—
159Q16×C47—81no—
160SD16×C47—22no—
161SD16×C47—42no—
162SD16×C47—81no—
163SD16×C47—81no—
164SD16×C47—82no—
165D8×C47—42no—
166C2×C8×C47—21no—
167C2×C8×C47—21no—
168C2×C8×C47—21no—
169C2×C8×C47—21no—
170C2×C8×C47—21no—
171C2×C8×C47—42no—
172C2×C8×C47C2×D411yescharacteristic
173C2×C8×C47C2×D411yescharacteristic
174C2×C8×C47C2×D411yescharacteristic
175C2×C8×C47C2×D411yescharacteristic
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—21no—
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—
200C22⋊C4×C47—41no—
201C22⋊C4×C47—41no—
202C42×C47—21no—
203C42×C47—21no—
204C42×C47—21no—
205C42×C47—41no—
206C42×C47C2411yescharacteristic
207C23×C47—21no—
208C23×C47—41no—
209Q8×C47—21no—
210Q8×C47—21no—
211Q8×C47—21no—
212Q8×C47—21no—
213Q8×C47—21no—
214Q8×C47—21no—
215Q8×C47—41no—
216Q8×C47—41no—
217Q8×C47—81no—
218Q8×C47—81no—
219D4×C47—21no—
220D4×C47—41no—
221D4×C47—41no—
222D4×C47—41no—
223D4×C47—41no—
224D4×C47—81no—
225D4×C47#13712yes—
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—21no—
233C2×C4×C47—41no—
234C2×C4×C47—41no—
235C2×C4×C47—41no—
236C2×C4×C47—41no—
237C2×C4×C47—41no—
238C2×C4×C47—161no—
239C2×C4×C47—161no—
240C2×C4×C47—161no—
241C2×C4×C47C22×D411yescharacteristic
242C2×C4×C47C22×D411yescharacteristic
243C2×C4×C47H(5,𝔽2)11yescharacteristic
244C8×C47—21no—
245C8×C47—21no—
246C8×C47—21no—
247C8×C47—41no—
248C8×C47—41no—
249C8×C47—41no—
250C8×C47—41no—
251C8×C47—41no—
252C8×C47#13512yes—
253#19857C4711yesmaximal, characteristic, direct product factor, Sylow
254C22×C47—22no—
255C22×C47—41no—
256C22×C47—41no—
257C22×C47—81no—
258C22×C47—81no—
259C22×C47—81no—
260C22×C47D4211yescharacteristic
261C4×C47—21no—
262C4×C47—41no—
263C4×C47—41no—
264C4×C47—41no—
265C4×C47—41no—
266C4×C47—41no—
267C4×C47—41no—
268C4×C47—41no—
269C4×C47—81no—
270C4×C47—81no—
271C4×C47—81no—
272C4×C47C2×#13511yescharacteristic
273C4×C47C2×#13711yescharacteristic
274C4×C47#57711yescharacteristic
275C4×C47#57811yescharacteristic
276#3400C2×C4711yescharacteristic, complemented
277#3381C2×C4711yescharacteristic, complemented
278#3361C2×C4711yescharacteristic
279#3338C2×C4711yescharacteristic, complemented
280#1714C2×C4711yescharacteristic, complemented
281#1696C2×C4711yescharacteristic, complemented
282#1678C2×C4711yescharacteristic, complemented
283#1672C2×C4711yescharacteristic, complemented
284#1665C2×C4711yescharacteristic
285#1644C2×C4711yescharacteristic, complemented
286#1636C2×C4711yescharacteristic, complemented
287#1630C2×C4711yescharacteristic, complemented
288#1622C2×C4711yescharacteristic
289#1582C2×C4711yescharacteristic, complemented
290#1579C2×C4711yescharacteristic, complemented
291C2×C47—42no—
292C2×C47—161no—
293C2×C47#327011yescharacteristic
294C2×C47#328411yescharacteristic
295C2×C47#328811yescharacteristic
296#559C22×C4711yescharacteristic
297#557C22×C4711yescharacteristic
298#554C22×C4711yescharacteristic
299#554C22×C4711yescharacteristic
300#500C22×C4711yescharacteristic
301#499—21no—
302#498C22×C4711yescharacteristic
303#497—21no—
304#492C22×C4711yescharacteristic
305#492C22×C4711yescharacteristic
306#488—21no—
307#487C22×C4711yescharacteristic
308#486C22×C4711yescharacteristic
309#484—21no—
310#484—21no—
311#479—21no—
312#478—21no—
313#478—21no—
314#477C22×C4711yescharacteristic
315#477C22×C4711yescharacteristic
316#477C22×C4711yescharacteristic
317#477C22×C4711yescharacteristic
318#474C22×C4711yescharacteristic
319#467—21no—
320#464—21no—
321#463—21no—
322#462C22×C4711yescharacteristic
323#461—21no—
324#460C22×C4711yescharacteristic
325#459C22×C4711yescharacteristic
326#446C22×C4711yescharacteristic
327C8×Q8C22×C4711yescharacteristic
328C8×Q8C22×C4711yescharacteristic
329#440—21no—
330C4×Q16C22×C4711yescharacteristic
331C4×SD16—21no—
332C4×SD16C22×C4711yescharacteristic
333C4×D8—21no—
334C8×D4C22×C4711yescharacteristic
335C2×#107—21no—
336#334C22×C4711yescharacteristic
337#334C22×C4711yescharacteristic
338#333C22×C4711yescharacteristic
339#333C22×C4711yescharacteristic
340#332C22×C4711yescharacteristic
341#331C22×C4711yescharacteristic
342Q8⋊C8C22×C4711yescharacteristic
343Q8⋊C8C22×C4711yescharacteristic
344Q8⋊C8C22×C4711yescharacteristic
345D4⋊C8C22×C4711yescharacteristic
346#322C22×C4711yescharacteristic
347C47#1985711yescharacteristic, direct product factor, Sylow
348C2×Q16—21no—
349C2×Q16D4×C4711yescharacteristic
350C2×SD16—21no—
351C2×SD16—21no—
352C2×SD16—21no—
353C2×SD16—41no—
354C2×SD16D4×C4711yescharacteristic
355C2×D8—21no—
356C22×C8—21no—
357C4⋊Q8—21no—
358C4⋊Q8C23×C4711yescharacteristic
359C4⋊Q8C23×C4711yescharacteristic
360C4⋊Q8C23×C4711yescharacteristic
361#127C23×C4711yescharacteristic
362#125—21no—
363#125—21no—
364#125—21no—
365#125—41no—
366#124—21no—
367#124—21no—
368#123—41no—
369C22⋊Q8—21no—
370C22⋊Q8—21no—
371C22⋊Q8—41no—
372C22⋊Q8—41no—
373C4×Q8—21no—
374C4×Q8—21no—
375C4×Q8C23×C4711yescharacteristic
376C4×Q8C23×C4711yescharacteristic
377C4×Q8C23×C4711yescharacteristic
378C4×D4—21no—
379C4×D4—21no—
380C4×D4—21no—
381C4×D4—21no—
382C4×D4C23×C4711yescharacteristic
383C2×C4⋊C4—21no—
384C2×C4⋊C4—21no—
385#107—21no—
386#107—21no—
387#107—21no—
388#107—21no—
389#107—21no—
390#107—21no—
391#107—21no—
392#107D4×C4711yescharacteristic
393#106—21no—
394#106—21no—
395#106D4×C4711yescharacteristic
396C4⋊C8—21no—
397C4⋊C8—21no—
398C4⋊C8—21no—
399C4⋊C8C23×C4711yescharacteristic
400C4⋊C8C23×C4711yescharacteristic
401C4⋊C8C23×C4711yescharacteristic
402C4⋊C8C23×C4711yescharacteristic
403#103—21no—
404#103—21no—
405#103—21no—
406#103—21no—
407#103—21no—
408#103—41no—
409#103D4×C4711yescharacteristic
410#103D4×C4711yescharacteristic
411#103D4×C4711yescharacteristic
412#102—21no—
413#102—21no—
414#102—21no—
415#102—21no—
416#102—21no—
417#102D4×C4711yescharacteristic
418C22⋊C8—21no—
419#97—21no—
420C4×C8—21no—
421C4×C8—21no—
422C4×C8C23×C4711yescharacteristic
423C4×C8C23×C4711yescharacteristic
424C4×C8C23×C4711yescharacteristic
425C2×Q8—21no—
426C2×Q8—21no—
427C2×Q8—21no—
428C2×Q8C2×D4×C4711yescharacteristic
429C2×Q8C2×D4×C4711yescharacteristic
430C2×Q8C2×D4×C4711yescharacteristic
431C2×D4—21no—
432C2×D4—21no—
433C2×D4—21no—
434C2×D4C2×D4×C4711yescharacteristic
435C22×C4—21no—
436C22×C4—41no—
437C22×C4—41no—
438C22×C4—41no—
439Q16—22no—
440Q16—81no—
441SD16—22no—
442SD16—42no—
443SD16—81no—
444SD16—81no—
445SD16—82no—
446D8—42no—
447C2×C8—21no—
448C2×C8—21no—
449C2×C8—21no—
450C2×C8—21no—
451C2×C8—21no—
452C2×C8—42no—
453C2×C8C2×D4×C4711yescharacteristic
454C2×C8C2×D4×C4711yescharacteristic
455C2×C8C2×D4×C4711yescharacteristic
456C2×C8C2×D4×C4711yescharacteristic
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—21no—
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—41no—
467C4⋊C4—41no—
468C4⋊C4—41no—
469C4⋊C4—41no—
470C4⋊C4—41no—
471C4⋊C4—41no—
472C4⋊C4—41no—
473C4⋊C4C2×D4×C4711yescharacteristic
474C4⋊C4C2×D4×C4711yescharacteristic
475C4⋊C4C2×D4×C4711yescharacteristic
476C4⋊C4C2×D4×C4711yescharacteristic
477C22⋊C4—21no—
478C22⋊C4—41no—
479C22⋊C4—41no—
480C22⋊C4—41no—
481C22⋊C4—41no—
482C22⋊C4—41no—
483C42—21no—
484C42—21no—
485C42—21no—
486C42—41no—
487C42C24×C4711yescharacteristic
488C23—21no—
489C23—41no—
490Q8—21no—
491Q8—21no—
492Q8—21no—
493Q8—21no—
494Q8—21no—
495Q8—21no—
496Q8—41no—
497Q8—41no—
498Q8—81no—
499Q8—81no—
500D4—21no—
501D4—41no—
502D4—41no—
503D4—41no—
504D4—41no—
505D4—81no—
506D4#137×C4712yes—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—41no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—161no—
520C2×C4—161no—
521C2×C4—161no—
522C2×C4C22×D4×C4711yescharacteristic
523C2×C4C22×D4×C4711yescharacteristic
524C2×C4H(5,𝔽2)×C4711yescharacteristic
525C8—21no—
526C8—21no—
527C8—21no—
528C8—41no—
529C8—41no—
530C8—41no—
531C8—41no—
532C8—41no—
533C8#135×C4712yes—
534C22—22no—
535C22—41no—
536C22—41no—
537C22—81no—
538C22—81no—
539C22—81no—
540C22D42×C4711yescharacteristic
541C4—21no—
542C4—41no—
543C4—41no—
544C4—41no—
545C4—41no—
546C4—41no—
547C4—41no—
548C4—41no—
549C4—81no—
550C4—81no—
551C4—81no—
552C4C2×#135×C4711yescharacteristic
553C4C2×#137×C4711yescharacteristic
554C4C47×#57711yescharacteristic
555C4C47×#57811yescharacteristic
556C2—42no—
557C2—161no—
558C2C47×#327011yescharacteristic
559C2C47×#328411yescharacteristic
560C2C47×#328811yescharacteristic
subgroupG/H
center, socleC22×C47D42
commutator, Frattini, cosocleC42C24×C47
prime radicalC47×#459C22
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×#3400C2semidirect
2. C47×#3381C2semidirect
4. C47×#3338C2semidirect
5. C47×#1714C2semidirect
6. C47×#1696C2semidirect
7. C47×#1678C2semidirect
8. C47×#1672C2semidirect
10. C47×#1644C2semidirect
11. C47×#1636C2semidirect
12. C47×#1630C2semidirect
14. C47×#1582C2semidirect
15. C47×#1579C2semidirect
253. #19857C47direct (N × H)
276. #3400C2×C47semidirect
277. #3381C2×C47semidirect
279. #3338C2×C47semidirect
280. #1714C2×C47semidirect
281. #1696C2×C47semidirect
282. #1678C2×C47semidirect
283. #1672C2×C47semidirect
285. #1644C2×C47semidirect
286. #1636C2×C47semidirect
287. #1630C2×C47semidirect
289. #1582C2×C47semidirect
290. #1579C2×C47semidirect
347. C47#19857direct (N × H)

Maximal subgroups

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

subgroupindex
C47×#34002
C47×#33812
C47×#33612
C47×#33382
C47×#17142
C47×#16962
C47×#16782
C47×#16722
C47×#16652
C47×#16442
C47×#16362
C47×#16302
C47×#16222
C47×#15822
C47×#15792
#1985747