Finite Group Databasebeta

← C47×#19856 #26059554

Subgroups — C47×#19856 #26059554

Order 12032.

570 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×#3398C211yesmaximal, characteristic, complemented
2C47×#3364C211yesmaximal, characteristic, complemented
3C47×#3340C211yesmaximal, characteristic
4C47×#3340C211yesmaximal, characteristic
5C47×#1716C211yesmaximal, characteristic, complemented
6C47×#1692C211yesmaximal, characteristic, complemented
7C47×#1679C211yesmaximal, characteristic, complemented
8C47×#1672C211yesmaximal, characteristic, complemented
9C47×#1669C211yesmaximal, characteristic, complemented
10C47×#1652C211yesmaximal, characteristic, complemented
11C47×#1652C211yesmaximal, characteristic, complemented
12C47×#1646C211yesmaximal, characteristic
13C47×#1636C211yesmaximal, characteristic, complemented
14C47×#1582C211yesmaximal, characteristic, complemented
15C47×SD16⋊C8C211yesmaximal, characteristic, complemented
16C47×#557C2211yescharacteristic
17C47×#556C2211yescharacteristic
18C47×#556C2211yescharacteristic
19C47×#555C2211yescharacteristic
20C47×#498C2211yescharacteristic
21C47×#498C2211yescharacteristic
22C47×#498C2211yescharacteristic
23C47×#497—21no—
24C47×#494C2211yescharacteristic
25C47×#488—21no—
26C47×#487C2211yescharacteristic
27C47×#487C2211yescharacteristic
28C47×#485—21no—
29C47×#485—21no—
30C47×#482—21no—
31C47×#482—21no—
32C47×#479—21no—
33C47×#477C2211yescharacteristic
34C47×#477C2211yescharacteristic
35C47×#474C2211yescharacteristic
36C47×#474C2211yescharacteristic
37C47×#474C2211yescharacteristic
38C47×#465—21no—
39C47×#465—21no—
40C47×#464—21no—
41C47×#464—21no—
42C47×#462—21no—
43C47×#462C2211yescharacteristic
44C47×#462C2211yescharacteristic
45C47×#461C2211yescharacteristic
46C47×#446C2211yescharacteristic
47C8×Q8×C47C2211yescharacteristic
48C47×#441—21no—
49C4×Q16×C47—21no—
50C4×SD16×C47C2211yescharacteristic
51C4×SD16×C47C2211yescharacteristic
52C8×D4×C47C2211yescharacteristic
53C8×D4×C47C2211yescharacteristic
54C47×#427—21no—
55C47×#427—21no—
56C47×#335C2211yescharacteristic
57C47×#334C2211yescharacteristic
58C47×#333C2211yescharacteristic
59C47×#332C2211yescharacteristic
60C47×#332C2211yescharacteristic
61C47×#332C2211yescharacteristic
62C47×Q8⋊C8C2211yescharacteristic
63C47×Q8⋊C8C2211yescharacteristic
64C47×D4⋊C8C2211yescharacteristic
65C47×D4⋊C8C2211yescharacteristic
66C47×#322C2211yescharacteristic
67C2×Q16×C47—21no—
68C2×Q16×C47—21no—
69C2×Q16×C47—21no—
70C2×Q16×C47—21no—
71C2×SD16×C47—21no—
72C2×SD16×C47D411yescharacteristic
73C2×SD16×C47D411yescharacteristic
74C22×C8×C47—21no—
75C22×C8×C47—21no—
76C4⋊Q8×C47—21no—
77C4⋊Q8×C47C2311yescharacteristic
78C4⋊Q8×C47C2311yescharacteristic
79C4⋊Q8×C47C2311yescharacteristic
80C4⋊Q8×C47C2311yescharacteristic
81#126×C47—41no—
82#126×C47—41no—
83#125×C47—21no—
84#125×C47—41no—
85#124×C47—21no—
86#124×C47—21no—
87#124×C47—41no—
88C22⋊Q8×C47—21no—
89C22⋊Q8×C47—21no—
90#121×C47—21no—
91#121×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×D4×C47C2311yescharacteristic
99C4×D4×C47C2311yescharacteristic
100#117×C47—21no—
101#117×C47—21no—
102#117×C47—21no—
103#117×C47—21no—
104#107×C47—21no—
105#107×C47—21no—
106#107×C47—21no—
107#107×C47—21no—
108#107×C47—21no—
109#106×C47—21no—
110#106×C47—21no—
111#106×C47—21no—
112#106×C47—21no—
113#106×C47—41no—
114#106×C47D411yescharacteristic
115#106×C47D411yescharacteristic
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—21no—
128#103×C47—21no—
129#103×C47—41no—
130#103×C47D411yescharacteristic
131#103×C47D411yescharacteristic
132#102×C47—21no—
133#102×C47—21no—
134#102×C47—21no—
135#102×C47D411yescharacteristic
136#102×C47D411yescharacteristic
137C22⋊C8×C47—21no—
138C22⋊C8×C47—21no—
139#97×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×C47C2×D411yescharacteristic
149C2×Q8×C47C2×D411yescharacteristic
150C2×D4×C47—41no—
151C2×D4×C47C2×D411yescharacteristic
152C2×D4×C47C2×D411yescharacteristic
153C22×C4×C47—21no—
154C22×C4×C47—21no—
155Q16×C47—42no—
156Q16×C47—42no—
157Q16×C47—81no—
158Q16×C47—81no—
159SD16×C47—22no—
160SD16×C47—41no—
161SD16×C47—81no—
162C2×C8×C47—21no—
163C2×C8×C47—21no—
164C2×C8×C47—21no—
165C2×C8×C47—21no—
166C2×C8×C47—21no—
167C2×C8×C47—42no—
168C2×C8×C47—42no—
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—41no—
184C4⋊C4×C47—41no—
185C4⋊C4×C47—41no—
186C4⋊C4×C47—41no—
187C4⋊C4×C47—41no—
188C4⋊C4×C47C2×D411yescharacteristic
189C4⋊C4×C47C2×D411yescharacteristic
190C4⋊C4×C47C2×D411yescharacteristic
191C4⋊C4×C47C2×D411yescharacteristic
192C22⋊C4×C47—21no—
193C22⋊C4×C47—21no—
194C22⋊C4×C47—41no—
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—41no—
203C42×C47—41no—
204C42×C47—41no—
205C42×C47—41no—
206C42×C47C2411yescharacteristic
207C23×C47—21no—
208C23×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—81no—
220D4×C47—21no—
221D4×C47—21no—
222D4×C47—21no—
223D4×C47—21no—
224D4×C47—161no—
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—41no—
237C2×C4×C47—41no—
238C2×C4×C47—41no—
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—41no—
246C8×C47—41no—
247C8×C47—41no—
248C8×C47—41no—
249C8×C47—41no—
250C8×C47#13512yes—
251#19856C4711yesmaximal, characteristic, direct product factor, Sylow
252C22×C47—41no—
253C22×C47—41no—
254C22×C47—41no—
255C22×C47—41no—
256C22×C47—41no—
257C22×C47—41no—
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—81no—
267C4×C47—81no—
268C4×C47—81no—
269C4×C47—81no—
270C4×C47C2×#13511yescharacteristic
271C4×C47#57511yescharacteristic
272C4×C47#57711yescharacteristic
273C4×C47#57811yescharacteristic
274#3398C2×C4711yescharacteristic, complemented
275#3364C2×C4711yescharacteristic, complemented
276#3340C2×C4711yescharacteristic
277#3340C2×C4711yescharacteristic
278#1716C2×C4711yescharacteristic, complemented
279#1692C2×C4711yescharacteristic, complemented
280#1679C2×C4711yescharacteristic, complemented
281#1672C2×C4711yescharacteristic, complemented
282#1669C2×C4711yescharacteristic, complemented
283#1652C2×C4711yescharacteristic, complemented
284#1652C2×C4711yescharacteristic, complemented
285#1646C2×C4711yescharacteristic
286#1636C2×C4711yescharacteristic, complemented
287#1582C2×C4711yescharacteristic, complemented
288SD16⋊C8C2×C4711yescharacteristic, complemented
289C2×C47—81no—
290C2×C47—81no—
291C2×C47#326911yescharacteristic
292C2×C47#328411yescharacteristic
293C2×C47#328911yescharacteristic
294#557C22×C4711yescharacteristic
295#556C22×C4711yescharacteristic
296#556C22×C4711yescharacteristic
297#555C22×C4711yescharacteristic
298#498C22×C4711yescharacteristic
299#498C22×C4711yescharacteristic
300#498C22×C4711yescharacteristic
301#497—21no—
302#494C22×C4711yescharacteristic
303#488—21no—
304#487C22×C4711yescharacteristic
305#487C22×C4711yescharacteristic
306#485—21no—
307#485—21no—
308#482—21no—
309#482—21no—
310#479—21no—
311#477C22×C4711yescharacteristic
312#477C22×C4711yescharacteristic
313#474C22×C4711yescharacteristic
314#474C22×C4711yescharacteristic
315#474C22×C4711yescharacteristic
316#465—21no—
317#465—21no—
318#464—21no—
319#464—21no—
320#462—21no—
321#462C22×C4711yescharacteristic
322#462C22×C4711yescharacteristic
323#461C22×C4711yescharacteristic
324#446C22×C4711yescharacteristic
325C8×Q8C22×C4711yescharacteristic
326#441—21no—
327C4×Q16—21no—
328C4×SD16C22×C4711yescharacteristic
329C4×SD16C22×C4711yescharacteristic
330C8×D4C22×C4711yescharacteristic
331C8×D4C22×C4711yescharacteristic
332#427—21no—
333#427—21no—
334#335C22×C4711yescharacteristic
335#334C22×C4711yescharacteristic
336#333C22×C4711yescharacteristic
337#332C22×C4711yescharacteristic
338#332C22×C4711yescharacteristic
339#332C22×C4711yescharacteristic
340Q8⋊C8C22×C4711yescharacteristic
341Q8⋊C8C22×C4711yescharacteristic
342D4⋊C8C22×C4711yescharacteristic
343D4⋊C8C22×C4711yescharacteristic
344#322C22×C4711yescharacteristic
345C47#1985611yescharacteristic, direct product factor, Sylow
346C2×Q16—21no—
347C2×Q16—21no—
348C2×Q16—21no—
349C2×Q16—21no—
350C2×SD16—21no—
351C2×SD16D4×C4711yescharacteristic
352C2×SD16D4×C4711yescharacteristic
353C22×C8—21no—
354C22×C8—21no—
355C4⋊Q8—21no—
356C4⋊Q8C23×C4711yescharacteristic
357C4⋊Q8C23×C4711yescharacteristic
358C4⋊Q8C23×C4711yescharacteristic
359C4⋊Q8C23×C4711yescharacteristic
360#126—41no—
361#126—41no—
362#125—21no—
363#125—41no—
364#124—21no—
365#124—21no—
366#124—41no—
367C22⋊Q8—21no—
368C22⋊Q8—21no—
369#121—21no—
370#121—21no—
371C4×Q8—21no—
372C4×Q8—21no—
373C4×Q8—21no—
374C4×Q8—21no—
375C4×Q8C23×C4711yescharacteristic
376C4×Q8C23×C4711yescharacteristic
377C4×D4C23×C4711yescharacteristic
378C4×D4C23×C4711yescharacteristic
379#117—21no—
380#117—21no—
381#117—21no—
382#117—21no—
383#107—21no—
384#107—21no—
385#107—21no—
386#107—21no—
387#107—21no—
388#106—21no—
389#106—21no—
390#106—21no—
391#106—21no—
392#106—41no—
393#106D4×C4711yescharacteristic
394#106D4×C4711yescharacteristic
395C4⋊C8—21no—
396C4⋊C8—21no—
397C4⋊C8C23×C4711yescharacteristic
398C4⋊C8C23×C4711yescharacteristic
399C4⋊C8C23×C4711yescharacteristic
400C4⋊C8C23×C4711yescharacteristic
401#103—21no—
402#103—21no—
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#102—21no—
412#102—21no—
413#102—21no—
414#102D4×C4711yescharacteristic
415#102D4×C4711yescharacteristic
416C22⋊C8—21no—
417C22⋊C8—21no—
418#97—21no—
419C4×C8—21no—
420C4×C8C23×C4711yescharacteristic
421C4×C8C23×C4711yescharacteristic
422C4×C8C23×C4711yescharacteristic
423C2×Q8—21no—
424C2×Q8—21no—
425C2×Q8—21no—
426C2×Q8—21no—
427C2×Q8C2×D4×C4711yescharacteristic
428C2×Q8C2×D4×C4711yescharacteristic
429C2×D4—41no—
430C2×D4C2×D4×C4711yescharacteristic
431C2×D4C2×D4×C4711yescharacteristic
432C22×C4—21no—
433C22×C4—21no—
434Q16—42no—
435Q16—42no—
436Q16—81no—
437Q16—81no—
438SD16—22no—
439SD16—41no—
440SD16—81no—
441C2×C8—21no—
442C2×C8—21no—
443C2×C8—21no—
444C2×C8—21no—
445C2×C8—21no—
446C2×C8—42no—
447C2×C8—42no—
448C2×C8C2×D4×C4711yescharacteristic
449C2×C8C2×D4×C4711yescharacteristic
450C2×C8C2×D4×C4711yescharacteristic
451C2×C8C2×D4×C4711yescharacteristic
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—21no—
461C4⋊C4—21no—
462C4⋊C4—41no—
463C4⋊C4—41no—
464C4⋊C4—41no—
465C4⋊C4—41no—
466C4⋊C4—41no—
467C4⋊C4C2×D4×C4711yescharacteristic
468C4⋊C4C2×D4×C4711yescharacteristic
469C4⋊C4C2×D4×C4711yescharacteristic
470C4⋊C4C2×D4×C4711yescharacteristic
471C22⋊C4—21no—
472C22⋊C4—21no—
473C22⋊C4—41no—
474C22⋊C4—41no—
475C22⋊C4—41no—
476C22⋊C4—41no—
477C22⋊C4—41no—
478C22⋊C4—41no—
479C42—21no—
480C42—21no—
481C42—41no—
482C42—41no—
483C42—41no—
484C42—41no—
485C42C24×C4711yescharacteristic
486C23—21no—
487C23—21no—
488Q8—21no—
489Q8—21no—
490Q8—21no—
491Q8—21no—
492Q8—41no—
493Q8—41no—
494Q8—41no—
495Q8—41no—
496Q8—41no—
497Q8—41no—
498Q8—81no—
499D4—21no—
500D4—21no—
501D4—21no—
502D4—21no—
503D4—161no—
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—41no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4C22×D4×C4711yescharacteristic
519C2×C4C22×D4×C4711yescharacteristic
520C2×C4H(5,𝔽2)×C4711yescharacteristic
521C8—21no—
522C8—21no—
523C8—21no—
524C8—41no—
525C8—41no—
526C8—41no—
527C8—41no—
528C8—41no—
529C8#135×C4712yes—
530C22—41no—
531C22—41no—
532C22—41no—
533C22—41no—
534C22—41no—
535C22—41no—
536C22D42×C4711yescharacteristic
537C4—21no—
538C4—41no—
539C4—41no—
540C4—41no—
541C4—41no—
542C4—41no—
543C4—41no—
544C4—81no—
545C4—81no—
546C4—81no—
547C4—81no—
548C4C2×#135×C4711yescharacteristic
549C4C47×#57511yescharacteristic
550C4C47×#57711yescharacteristic
551C4C47×#57811yescharacteristic
552C2—81no—
553C2—81no—
554C2C47×#326911yescharacteristic
555C2C47×#328411yescharacteristic
556C2C47×#328911yescharacteristic
subgroupG/H
center, socleC22×C47D42
commutator, Frattini, cosocleC42C24×C47
prime radicalC47×#555C22
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×#3398C2semidirect
2. C47×#3364C2semidirect
5. C47×#1716C2semidirect
6. C47×#1692C2semidirect
7. C47×#1679C2semidirect
8. C47×#1672C2semidirect
9. C47×#1669C2semidirect
10. C47×#1652C2semidirect
11. C47×#1652C2semidirect
13. C47×#1636C2semidirect
14. C47×#1582C2semidirect
15. C47×SD16⋊C8C2semidirect
251. #19856C47direct (N × H)
274. #3398C2×C47semidirect
275. #3364C2×C47semidirect
278. #1716C2×C47semidirect
279. #1692C2×C47semidirect
280. #1679C2×C47semidirect
281. #1672C2×C47semidirect
282. #1669C2×C47semidirect
283. #1652C2×C47semidirect
284. #1652C2×C47semidirect
286. #1636C2×C47semidirect
287. #1582C2×C47semidirect
288. SD16⋊C8C2×C47semidirect
345. C47#19856direct (N × H)

Maximal subgroups

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

subgroupindex
C47×#33982
C47×#33642
C47×#33402
C47×#17162
C47×#16922
C47×#16792
C47×#16722
C47×#16692
C47×#16522
C47×#16462
C47×#16362
C47×#15822
C47×SD16⋊C82
#1985647