Finite Group Databasebeta

← C47×#19842 #26059540

Subgroups — C47×#19842 #26059540

Order 12032.

576 conjugacy classes of subgroups.

The subgroup lattice has 558 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C47×#3372C211yesmaximal, characteristic, complemented
2C47×#3365C211yesmaximal, characteristic, complemented
3C47×#3361C211yesmaximal, characteristic
4C47×#3338C211yesmaximal, characteristic, complemented
5C47×#1719C211yesmaximal, characteristic, complemented
6C47×#1698C211yesmaximal, characteristic, complemented
7C47×#1684C211yesmaximal, characteristic, complemented
8C47×#1681C211yesmaximal, characteristic
9C47×#1676C211yesmaximal, characteristic, complemented
10C47×#1643C211yesmaximal, characteristic, complemented
11C47×#1636C211yesmaximal, characteristic, complemented
12C47×#1630C211yesmaximal, characteristic, complemented
13C47×#1622C211yesmaximal, characteristic
14C47×#1584C211yesmaximal, characteristic, complemented
15C47×SD16⋊C8C211yesmaximal, characteristic, complemented
16C47×#559C2211yescharacteristic
17C47×#557C2211yescharacteristic
18C47×#554C2211yescharacteristic
19C47×#554C2211yescharacteristic
20C47×#500C2211yescharacteristic
21C47×#492C2211yescharacteristic
22C47×#491—21no—
23C47×#488—21no—
24C47×#488—21no—
25C47×#487C2211yescharacteristic
26C47×#487C2211yescharacteristic
27C47×#486C2211yescharacteristic
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×#475C2211yescharacteristic
39C47×#467—21no—
40C47×#464—21no—
41C47×#463—21no—
42C47×#461—21no—
43C47×#461C2211yescharacteristic
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×#335C2211yescharacteristic
57C47×#335C2211yescharacteristic
58C47×#333C2211yescharacteristic
59C47×#333C2211yescharacteristic
60C47×#332C2211yescharacteristic
61C47×#331C2211yescharacteristic
62C47×Q8⋊C8C2211yescharacteristic
63C47×Q8⋊C8C2211yescharacteristic
64C47×Q8⋊C8C2211yescharacteristic
65C47×D4⋊C8C2211yescharacteristic
66C47×#322C2211yescharacteristic
67C2×Q16×C47D411yescharacteristic
68C2×SD16×C47—21no—
69C2×SD16×C47—21no—
70C2×SD16×C47—41no—
71C2×SD16×C47D411yescharacteristic
72C2×D8×C47—21no—
73C22×C8×C47—21no—
74C4⋊Q8×C47—21no—
75C4⋊Q8×C47C2311yescharacteristic
76C4⋊Q8×C47C2311yescharacteristic
77C4⋊Q8×C47C2311yescharacteristic
78#127×C47C2311yescharacteristic
79#125×C47—21no—
80#125×C47—21no—
81#125×C47—21no—
82#125×C47—41no—
83#124×C47—21no—
84#124×C47—21no—
85#123×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×C47C2311yescharacteristic
93C4×Q8×C47C2311yescharacteristic
94C4×Q8×C47C2311yescharacteristic
95C4×D4×C47—21no—
96C4×D4×C47—21no—
97C4×D4×C47—21no—
98C4×D4×C47—21no—
99C4×D4×C47C2311yescharacteristic
100C2×C4⋊C4×C47—21no—
101C2×C4⋊C4×C47—21no—
102#107×C47—21no—
103#107×C47—21no—
104#107×C47—21no—
105#107×C47—21no—
106#107×C47—21no—
107#107×C47—21no—
108#107×C47D411yescharacteristic
109#106×C47—21no—
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—41no—
127#103×C47D411yescharacteristic
128#103×C47D411yescharacteristic
129#103×C47D411yescharacteristic
130#102×C47—21no—
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—41no—
159SD16×C47—22no—
160SD16×C47—42no—
161SD16×C47—42no—
162SD16×C47—82no—
163D8×C47—42no—
164C2×C8×C47—21no—
165C2×C8×C47—21no—
166C2×C8×C47—21no—
167C2×C8×C47—21no—
168C2×C8×C47—21no—
169C2×C8×C47—42no—
170C2×C8×C47C2×D411yescharacteristic
171C2×C8×C47C2×D411yescharacteristic
172C2×C8×C47C2×D411yescharacteristic
173C2×C8×C47C2×D411yescharacteristic
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—41no—
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×C47C2×D411yescharacteristic
191C4⋊C4×C47C2×D411yescharacteristic
192C4⋊C4×C47C2×D411yescharacteristic
193C4⋊C4×C47C2×D411yescharacteristic
194C22⋊C4×C47—21no—
195C22⋊C4×C47—41no—
196C22⋊C4×C47—41no—
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×C47C2411yescharacteristic
205C23×C47—21no—
206C23×C47—41no—
207Q8×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—81no—
216Q8×C47—81no—
217D4×C47—21no—
218D4×C47—41no—
219D4×C47—41no—
220D4×C47—41no—
221D4×C47—41no—
222D4×C47—81no—
223D4×C47#13512yes—
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—41no—
232C2×C4×C47—41no—
233C2×C4×C47—41no—
234C2×C4×C47—41no—
235C2×C4×C47—41no—
236C2×C4×C47—161no—
237C2×C4×C47—161no—
238C2×C4×C47—161no—
239C2×C4×C47C22×D411yescharacteristic
240C2×C4×C47C22×D411yescharacteristic
241C2×C4×C47H(5,𝔽2)11yescharacteristic
242C8×C47—21no—
243C8×C47—21no—
244C8×C47—21no—
245C8×C47—21no—
246C8×C47—41no—
247C8×C47—41no—
248C8×C47—41no—
249C8×C47—41no—
250C8×C47—41no—
251#19842C4711yesmaximal, characteristic, direct product factor, Sylow
252C22×C47—22no—
253C22×C47—41no—
254C22×C47—41no—
255C22×C47—81no—
256C22×C47—81no—
257C22×C47—81no—
258C22×C47D4211yescharacteristic
259C4×C47—21no—
260C4×C47—41no—
261C4×C47—41no—
262C4×C47—41no—
263C4×C47—41no—
264C4×C47—41no—
265C4×C47—41no—
266C4×C47—41no—
267C4×C47—81no—
268C4×C47—81no—
269C4×C47—81no—
270C4×C47C2×#13511yescharacteristic
271C4×C47#57511yescharacteristic
272C4×C47#57811yescharacteristic
273C4×C47#57811yescharacteristic
274#3372C2×C4711yescharacteristic, complemented
275#3365C2×C4711yescharacteristic, complemented
276#3361C2×C4711yescharacteristic
277#3338C2×C4711yescharacteristic, complemented
278#1719C2×C4711yescharacteristic, complemented
279#1698C2×C4711yescharacteristic, complemented
280#1684C2×C4711yescharacteristic, complemented
281#1681C2×C4711yescharacteristic
282#1676C2×C4711yescharacteristic, complemented
283#1643C2×C4711yescharacteristic, complemented
284#1636C2×C4711yescharacteristic, complemented
285#1630C2×C4711yescharacteristic, complemented
286#1622C2×C4711yescharacteristic
287#1584C2×C4711yescharacteristic, complemented
288SD16⋊C8C2×C4711yescharacteristic, complemented
289C2×C47—42no—
290C2×C47—161no—
291C2×C47#326911yescharacteristic
292C2×C47#328511yescharacteristic
293C2×C47#328811yescharacteristic
294#559C22×C4711yescharacteristic
295#557C22×C4711yescharacteristic
296#554C22×C4711yescharacteristic
297#554C22×C4711yescharacteristic
298#500C22×C4711yescharacteristic
299#492C22×C4711yescharacteristic
300#491—21no—
301#488—21no—
302#488—21no—
303#487C22×C4711yescharacteristic
304#487C22×C4711yescharacteristic
305#486C22×C4711yescharacteristic
306#486C22×C4711yescharacteristic
307#484—21no—
308#484—21no—
309#479—21no—
310#478—21no—
311#478—21no—
312#477C22×C4711yescharacteristic
313#477C22×C4711yescharacteristic
314#477C22×C4711yescharacteristic
315#477C22×C4711yescharacteristic
316#475C22×C4711yescharacteristic
317#467—21no—
318#464—21no—
319#463—21no—
320#461—21no—
321#461C22×C4711yescharacteristic
322#460C22×C4711yescharacteristic
323#459C22×C4711yescharacteristic
324#446C22×C4711yescharacteristic
325C8×Q8C22×C4711yescharacteristic
326C8×Q8C22×C4711yescharacteristic
327#440—21no—
328C4×Q16C22×C4711yescharacteristic
329C4×SD16—21no—
330C4×SD16C22×C4711yescharacteristic
331C4×D8—21no—
332C8×D4C22×C4711yescharacteristic
333C2×#107—21no—
334#335C22×C4711yescharacteristic
335#335C22×C4711yescharacteristic
336#333C22×C4711yescharacteristic
337#333C22×C4711yescharacteristic
338#332C22×C4711yescharacteristic
339#331C22×C4711yescharacteristic
340Q8⋊C8C22×C4711yescharacteristic
341Q8⋊C8C22×C4711yescharacteristic
342Q8⋊C8C22×C4711yescharacteristic
343D4⋊C8C22×C4711yescharacteristic
344#322C22×C4711yescharacteristic
345C47#1984211yescharacteristic, direct product factor, Sylow
346C2×Q16D4×C4711yescharacteristic
347C2×SD16—21no—
348C2×SD16—21no—
349C2×SD16—41no—
350C2×SD16D4×C4711yescharacteristic
351C2×D8—21no—
352C22×C8—21no—
353C4⋊Q8—21no—
354C4⋊Q8C23×C4711yescharacteristic
355C4⋊Q8C23×C4711yescharacteristic
356C4⋊Q8C23×C4711yescharacteristic
357#127C23×C4711yescharacteristic
358#125—21no—
359#125—21no—
360#125—21no—
361#125—41no—
362#124—21no—
363#124—21no—
364#123—41no—
365C22⋊Q8—21no—
366C22⋊Q8—21no—
367C22⋊Q8—41no—
368C22⋊Q8—41no—
369C4×Q8—21no—
370C4×Q8—21no—
371C4×Q8C23×C4711yescharacteristic
372C4×Q8C23×C4711yescharacteristic
373C4×Q8C23×C4711yescharacteristic
374C4×D4—21no—
375C4×D4—21no—
376C4×D4—21no—
377C4×D4—21no—
378C4×D4C23×C4711yescharacteristic
379C2×C4⋊C4—21no—
380C2×C4⋊C4—21no—
381#107—21no—
382#107—21no—
383#107—21no—
384#107—21no—
385#107—21no—
386#107—21no—
387#107D4×C4711yescharacteristic
388#106—21no—
389#106D4×C4711yescharacteristic
390C4⋊C8—21no—
391C4⋊C8—21no—
392C4⋊C8—21no—
393C4⋊C8C23×C4711yescharacteristic
394C4⋊C8C23×C4711yescharacteristic
395C4⋊C8C23×C4711yescharacteristic
396C4⋊C8C23×C4711yescharacteristic
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—41no—
406#103D4×C4711yescharacteristic
407#103D4×C4711yescharacteristic
408#103D4×C4711yescharacteristic
409#102—21no—
410#102—21no—
411#102—21no—
412#102—21no—
413#102—21no—
414#102—21no—
415#102D4×C4711yescharacteristic
416C22⋊C8—21no—
417#97—21no—
418C4×C8—21no—
419C4×C8—21no—
420C4×C8C23×C4711yescharacteristic
421C4×C8C23×C4711yescharacteristic
422C4×C8C23×C4711yescharacteristic
423C2×Q8—21no—
424C2×Q8—21no—
425C2×Q8—21no—
426C2×Q8C2×D4×C4711yescharacteristic
427C2×Q8C2×D4×C4711yescharacteristic
428C2×Q8C2×D4×C4711yescharacteristic
429C2×D4—21no—
430C2×D4—21no—
431C2×D4—21no—
432C2×D4C2×D4×C4711yescharacteristic
433C22×C4—21no—
434C22×C4—41no—
435C22×C4—41no—
436C22×C4—41no—
437Q16—41no—
438SD16—22no—
439SD16—42no—
440SD16—42no—
441SD16—82no—
442D8—42no—
443C2×C8—21no—
444C2×C8—21no—
445C2×C8—21no—
446C2×C8—21no—
447C2×C8—21no—
448C2×C8—42no—
449C2×C8C2×D4×C4711yescharacteristic
450C2×C8C2×D4×C4711yescharacteristic
451C2×C8C2×D4×C4711yescharacteristic
452C2×C8C2×D4×C4711yescharacteristic
453C4⋊C4—21no—
454C4⋊C4—21no—
455C4⋊C4—21no—
456C4⋊C4—21no—
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—21no—
461C4⋊C4—21no—
462C4⋊C4—41no—
463C4⋊C4—41no—
464C4⋊C4—41no—
465C4⋊C4—41no—
466C4⋊C4—41no—
467C4⋊C4—41no—
468C4⋊C4—41no—
469C4⋊C4C2×D4×C4711yescharacteristic
470C4⋊C4C2×D4×C4711yescharacteristic
471C4⋊C4C2×D4×C4711yescharacteristic
472C4⋊C4C2×D4×C4711yescharacteristic
473C22⋊C4—21no—
474C22⋊C4—41no—
475C22⋊C4—41no—
476C22⋊C4—41no—
477C22⋊C4—41no—
478C22⋊C4—41no—
479C42—21no—
480C42—21no—
481C42—21no—
482C42—41no—
483C42C24×C4711yescharacteristic
484C23—21no—
485C23—41no—
486Q8—21no—
487Q8—21no—
488Q8—21no—
489Q8—21no—
490Q8—21no—
491Q8—21no—
492Q8—41no—
493Q8—41no—
494Q8—81no—
495Q8—81no—
496D4—21no—
497D4—41no—
498D4—41no—
499D4—41no—
500D4—41no—
501D4—81no—
502D4#135×C4712yes—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—41no—
511C2×C4—41no—
512C2×C4—41no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—161no—
516C2×C4—161no—
517C2×C4—161no—
518C2×C4C22×D4×C4711yescharacteristic
519C2×C4C22×D4×C4711yescharacteristic
520C2×C4H(5,𝔽2)×C4711yescharacteristic
521C8—21no—
522C8—21no—
523C8—21no—
524C8—21no—
525C8—41no—
526C8—41no—
527C8—41no—
528C8—41no—
529C8—41no—
530C22—22no—
531C22—41no—
532C22—41no—
533C22—81no—
534C22—81no—
535C22—81no—
536C22D42×C4711yescharacteristic
537C4—21no—
538C4—41no—
539C4—41no—
540C4—41no—
541C4—41no—
542C4—41no—
543C4—41no—
544C4—41no—
545C4—81no—
546C4—81no—
547C4—81no—
548C4C2×#135×C4711yescharacteristic
549C4C47×#57511yescharacteristic
550C4C47×#57811yescharacteristic
551C4C47×#57811yescharacteristic
552C2—42no—
553C2—161no—
554C2C47×#326911yescharacteristic
555C2C47×#328511yescharacteristic
556C2C47×#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×#3372C2semidirect
2. C47×#3365C2semidirect
4. C47×#3338C2semidirect
5. C47×#1719C2semidirect
6. C47×#1698C2semidirect
7. C47×#1684C2semidirect
9. C47×#1676C2semidirect
10. C47×#1643C2semidirect
11. C47×#1636C2semidirect
12. C47×#1630C2semidirect
14. C47×#1584C2semidirect
15. C47×SD16⋊C8C2semidirect
251. #19842C47direct (N × H)
274. #3372C2×C47semidirect
275. #3365C2×C47semidirect
277. #3338C2×C47semidirect
278. #1719C2×C47semidirect
279. #1698C2×C47semidirect
280. #1684C2×C47semidirect
282. #1676C2×C47semidirect
283. #1643C2×C47semidirect
284. #1636C2×C47semidirect
285. #1630C2×C47semidirect
287. #1584C2×C47semidirect
288. SD16⋊C8C2×C47semidirect
345. C47#19842direct (N × H)

Maximal subgroups

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

subgroupindex
C47×#33722
C47×#33652
C47×#33612
C47×#33382
C47×#17192
C47×#16982
C47×#16842
C47×#16812
C47×#16762
C47×#16432
C47×#16362
C47×#16302
C47×#16222
C47×#15842
C47×SD16⋊C82
#1984247