Finite Group Databasebeta

← C47×#19832 #26059530

Subgroups — C47×#19832 #26059530

Order 12032.

580 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×#3364C211yesmaximal, characteristic, complemented
2C47×#3359C211yesmaximal, characteristic, complemented
3C47×#3340C211yesmaximal, characteristic
4C47×#3329C211yesmaximal, characteristic
5C47×#1718C211yesmaximal, characteristic, complemented
6C47×#1699C211yesmaximal, characteristic, complemented
7C47×#1684C211yesmaximal, characteristic, complemented
8C47×#1679C211yesmaximal, characteristic, complemented
9C47×#1672C211yesmaximal, characteristic, complemented
10C47×#1650C211yesmaximal, characteristic, complemented
11C47×#1649C211yesmaximal, characteristic, complemented
12C47×#1646C211yesmaximal, characteristic
13C47×#1636C211yesmaximal, characteristic, complemented
14C47×#1583C211yesmaximal, characteristic, complemented
15C47×SD16⋊C8C211yesmaximal, characteristic, complemented
16C47×#557C2211yescharacteristic
17C47×#556C2211yescharacteristic
18C47×#555C2211yescharacteristic
19D4×Q8×C47C2211yescharacteristic
20C47×#500C2211yescharacteristic
21C47×#498C2211yescharacteristic
22C47×#488—21no—
23C47×#487—21no—
24C47×#487C2211yescharacteristic
25C47×#487C2211yescharacteristic
26C47×#487C2211yescharacteristic
27C47×#487C2211yescharacteristic
28C47×#485—21no—
29C47×#485—21no—
30C47×#482—21no—
31C47×#479—21no—
32C47×#477C2211yescharacteristic
33C47×#477C2211yescharacteristic
34C47×#475—21no—
35C47×#475C2211yescharacteristic
36C47×#474C2211yescharacteristic
37C47×#474C2211yescharacteristic
38C47×#468—21no—
39C47×#465—21no—
40C47×#464—21no—
41C47×#462C2211yescharacteristic
42C47×#461—21no—
43C47×#461C2211yescharacteristic
44C47×#461C2211yescharacteristic
45C47×#448—21no—
46C8×Q8×C47C2211yescharacteristic
47C8×Q8×C47C2211yescharacteristic
48C4×Q16×C47—21no—
49C4×SD16×C47—21no—
50C4×SD16×C47C2211yescharacteristic
51C4×SD16×C47C2211yescharacteristic
52C47×#436C2211yescharacteristic
53C8×D4×C47C2211yescharacteristic
54C47×#427—21no—
55C47×#419—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
67C22×Q8×C47—21no—
68C2×Q16×C47—21no—
69C2×SD16×C47—21no—
70C2×SD16×C47—21no—
71C2×SD16×C47D411yescharacteristic
72C2×SD16×C47D411yescharacteristic
73C2×M16×C47—21no—
74C22×C8×C47—21no—
75C4⋊Q8×C47—21no—
76C4⋊Q8×C47—21no—
77C4⋊Q8×C47C2311yescharacteristic
78C4⋊Q8×C47C2311yescharacteristic
79C4⋊Q8×C47C2311yescharacteristic
80C4⋊Q8×C47C2311yescharacteristic
81#126×C47—41no—
82#125×C47—21no—
83#125×C47—41no—
84#124×C47—21no—
85#124×C47—41no—
86C22⋊Q8×C47—21no—
87C22⋊Q8×C47—21no—
88C22⋊Q8×C47—41no—
89#121×C47—21no—
90#121×C47—21no—
91C4×Q8×C47—21no—
92C4×Q8×C47—21no—
93C4×Q8×C47—21no—
94C4×Q8×C47C2311yescharacteristic
95C4×Q8×C47C2311yescharacteristic
96C4×D4×C47—21no—
97C4×D4×C47C2311yescharacteristic
98C4×D4×C47C2311yescharacteristic
99#117×C47—21no—
100#117×C47—21no—
101#117×C47—21no—
102#107×C47—21no—
103#107×C47—21no—
104#107×C47—21no—
105#107×C47—21no—
106#107×C47—41no—
107#106×C47—21no—
108#106×C47—21no—
109#106×C47—21no—
110#106×C47D411yescharacteristic
111#106×C47D411yescharacteristic
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—21no—
127#103×C47—21no—
128#103×C47—21no—
129#103×C47—21no—
130#103×C47—41no—
131#103×C47D411yescharacteristic
132#103×C47D411yescharacteristic
133#102×C47—21no—
134#102×C47—21no—
135#102×C47D411yescharacteristic
136#102×C47D411yescharacteristic
137C22⋊C8×C47—21no—
138C22⋊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—21no—
148C2×Q8×C47—41no—
149C2×Q8×C47—42no—
150C2×Q8×C47—81no—
151C2×Q8×C47C2×D411yescharacteristic
152C2×Q8×C47C2×D411yescharacteristic
153C2×D4×C47—41no—
154C2×D4×C47C2×D411yescharacteristic
155C2×D4×C47C2×D411yescharacteristic
156C22×C4×C47—21no—
157C22×C4×C47—21no—
158C22×C4×C47—41no—
159Q16×C47—42no—
160SD16×C47—22no—
161SD16×C47—41no—
162SD16×C47—42no—
163SD16×C47—81no—
164M16×C47—81no—
165C2×C8×C47—21no—
166C2×C8×C47—21no—
167C2×C8×C47—21no—
168C2×C8×C47—21no—
169C2×C8×C47—21no—
170C2×C8×C47—42no—
171C2×C8×C47C2×D411yescharacteristic
172C2×C8×C47C2×D411yescharacteristic
173C2×C8×C47C2×D411yescharacteristic
174C2×C8×C47C2×D411yescharacteristic
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—21no—
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—21no—
196C22⋊C4×C47—41no—
197C22⋊C4×C47—41no—
198C22⋊C4×C47—41no—
199C22⋊C4×C47—41no—
200C22⋊C4×C47—41no—
201C42×C47—21no—
202C42×C47—21no—
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—41no—
213Q8×C47—41no—
214Q8×C47—41no—
215Q8×C47—41no—
216Q8×C47—41no—
217Q8×C47—41no—
218Q8×C47—82no—
219Q8×C47—81no—
220Q8×C47#13512yes—
221D4×C47—21no—
222D4×C47—21no—
223D4×C47—21no—
224D4×C47—21no—
225D4×C47—161no—
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—41no—
239C2×C4×C47—41no—
240C2×C4×C47—82no—
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—21no—
248C8×C47—41no—
249C8×C47—41no—
250C8×C47—41no—
251C8×C47—41no—
252C8×C47—41no—
253#19832C4711yesmaximal, characteristic, direct product factor, Sylow
254C22×C47—41no—
255C22×C47—41no—
256C22×C47—41no—
257C22×C47—41no—
258C22×C47—41no—
259C22×C47—41no—
260C22×C47D4211yescharacteristic
261C4×C47—22no—
262C4×C47—21no—
263C4×C47—41no—
264C4×C47—41no—
265C4×C47—41no—
266C4×C47—41no—
267C4×C47—41no—
268C4×C47—81no—
269C4×C47—81no—
270C4×C47—81no—
271C4×C47—81no—
272C4×C47C2×#13511yescharacteristic
273C4×C47#57511yescharacteristic
274C4×C47#57711yescharacteristic
275C4×C47#57811yescharacteristic
276#3364C2×C4711yescharacteristic, complemented
277#3359C2×C4711yescharacteristic, complemented
278#3340C2×C4711yescharacteristic
279#3329C2×C4711yescharacteristic
280#1718C2×C4711yescharacteristic, complemented
281#1699C2×C4711yescharacteristic, complemented
282#1684C2×C4711yescharacteristic, complemented
283#1679C2×C4711yescharacteristic, complemented
284#1672C2×C4711yescharacteristic, complemented
285#1650C2×C4711yescharacteristic, complemented
286#1649C2×C4711yescharacteristic, complemented
287#1646C2×C4711yescharacteristic
288#1636C2×C4711yescharacteristic, complemented
289#1583C2×C4711yescharacteristic, complemented
290SD16⋊C8C2×C4711yescharacteristic, complemented
291C2×C47—81no—
292C2×C47—81no—
293C2×C47#326911yescharacteristic
294C2×C47#328211yescharacteristic
295C2×C47#328911yescharacteristic
296#557C22×C4711yescharacteristic
297#556C22×C4711yescharacteristic
298#555C22×C4711yescharacteristic
299D4×Q8C22×C4711yescharacteristic
300#500C22×C4711yescharacteristic
301#498C22×C4711yescharacteristic
302#488—21no—
303#487—21no—
304#487C22×C4711yescharacteristic
305#487C22×C4711yescharacteristic
306#487C22×C4711yescharacteristic
307#487C22×C4711yescharacteristic
308#485—21no—
309#485—21no—
310#482—21no—
311#479—21no—
312#477C22×C4711yescharacteristic
313#477C22×C4711yescharacteristic
314#475—21no—
315#475C22×C4711yescharacteristic
316#474C22×C4711yescharacteristic
317#474C22×C4711yescharacteristic
318#468—21no—
319#465—21no—
320#464—21no—
321#462C22×C4711yescharacteristic
322#461—21no—
323#461C22×C4711yescharacteristic
324#461C22×C4711yescharacteristic
325#448—21no—
326C8×Q8C22×C4711yescharacteristic
327C8×Q8C22×C4711yescharacteristic
328C4×Q16—21no—
329C4×SD16—21no—
330C4×SD16C22×C4711yescharacteristic
331C4×SD16C22×C4711yescharacteristic
332#436C22×C4711yescharacteristic
333C8×D4C22×C4711yescharacteristic
334#427—21no—
335#419—21no—
336#335C22×C4711yescharacteristic
337#334C22×C4711yescharacteristic
338#333C22×C4711yescharacteristic
339#332C22×C4711yescharacteristic
340#332C22×C4711yescharacteristic
341#332C22×C4711yescharacteristic
342Q8⋊C8C22×C4711yescharacteristic
343Q8⋊C8C22×C4711yescharacteristic
344D4⋊C8C22×C4711yescharacteristic
345D4⋊C8C22×C4711yescharacteristic
346#322C22×C4711yescharacteristic
347C47#1983211yescharacteristic, direct product factor, Sylow
348C22×Q8—21no—
349C2×Q16—21no—
350C2×SD16—21no—
351C2×SD16—21no—
352C2×SD16D4×C4711yescharacteristic
353C2×SD16D4×C4711yescharacteristic
354C2×M16—21no—
355C22×C8—21no—
356C4⋊Q8—21no—
357C4⋊Q8—21no—
358C4⋊Q8C23×C4711yescharacteristic
359C4⋊Q8C23×C4711yescharacteristic
360C4⋊Q8C23×C4711yescharacteristic
361C4⋊Q8C23×C4711yescharacteristic
362#126—41no—
363#125—21no—
364#125—41no—
365#124—21no—
366#124—41no—
367C22⋊Q8—21no—
368C22⋊Q8—21no—
369C22⋊Q8—41no—
370#121—21no—
371#121—21no—
372C4×Q8—21no—
373C4×Q8—21no—
374C4×Q8—21no—
375C4×Q8C23×C4711yescharacteristic
376C4×Q8C23×C4711yescharacteristic
377C4×D4—21no—
378C4×D4C23×C4711yescharacteristic
379C4×D4C23×C4711yescharacteristic
380#117—21no—
381#117—21no—
382#117—21no—
383#107—21no—
384#107—21no—
385#107—21no—
386#107—21no—
387#107—41no—
388#106—21no—
389#106—21no—
390#106—21no—
391#106D4×C4711yescharacteristic
392#106D4×C4711yescharacteristic
393C4⋊C8—21no—
394C4⋊C8—21no—
395C4⋊C8C23×C4711yescharacteristic
396C4⋊C8C23×C4711yescharacteristic
397C4⋊C8C23×C4711yescharacteristic
398C4⋊C8C23×C4711yescharacteristic
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#103—21no—
409#103—21no—
410#103—21no—
411#103—41no—
412#103D4×C4711yescharacteristic
413#103D4×C4711yescharacteristic
414#102—21no—
415#102—21no—
416#102D4×C4711yescharacteristic
417#102D4×C4711yescharacteristic
418C22⋊C8—21no—
419C22⋊C8—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×Q8—21no—
429C2×Q8—41no—
430C2×Q8—42no—
431C2×Q8—81no—
432C2×Q8C2×D4×C4711yescharacteristic
433C2×Q8C2×D4×C4711yescharacteristic
434C2×D4—41no—
435C2×D4C2×D4×C4711yescharacteristic
436C2×D4C2×D4×C4711yescharacteristic
437C22×C4—21no—
438C22×C4—21no—
439C22×C4—41no—
440Q16—42no—
441SD16—22no—
442SD16—41no—
443SD16—42no—
444SD16—81no—
445M16—81no—
446C2×C8—21no—
447C2×C8—21no—
448C2×C8—21no—
449C2×C8—21no—
450C2×C8—21no—
451C2×C8—42no—
452C2×C8C2×D4×C4711yescharacteristic
453C2×C8C2×D4×C4711yescharacteristic
454C2×C8C2×D4×C4711yescharacteristic
455C2×C8C2×D4×C4711yescharacteristic
456C4⋊C4—21no—
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⋊C4C2×D4×C4711yescharacteristic
472C4⋊C4C2×D4×C4711yescharacteristic
473C4⋊C4C2×D4×C4711yescharacteristic
474C4⋊C4C2×D4×C4711yescharacteristic
475C22⋊C4—21no—
476C22⋊C4—21no—
477C22⋊C4—41no—
478C22⋊C4—41no—
479C22⋊C4—41no—
480C22⋊C4—41no—
481C22⋊C4—41no—
482C42—21no—
483C42—21no—
484C42—41no—
485C42—41no—
486C42—41no—
487C42C24×C4711yescharacteristic
488C23—21no—
489C23—21no—
490Q8—21no—
491Q8—21no—
492Q8—21no—
493Q8—41no—
494Q8—41no—
495Q8—41no—
496Q8—41no—
497Q8—41no—
498Q8—41no—
499Q8—82no—
500Q8—81no—
501Q8#135×C4712yes—
502D4—21no—
503D4—21no—
504D4—21no—
505D4—21no—
506D4—161no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—82no—
522C2×C4C22×D4×C4711yescharacteristic
523C2×C4C22×D4×C4711yescharacteristic
524C2×C4H(5,𝔽2)×C4711yescharacteristic
525C8—21no—
526C8—21no—
527C8—21no—
528C8—21no—
529C8—41no—
530C8—41no—
531C8—41no—
532C8—41no—
533C8—41no—
534C22—41no—
535C22—41no—
536C22—41no—
537C22—41no—
538C22—41no—
539C22—41no—
540C22D42×C4711yescharacteristic
541C4—21no—
542C4—22no—
543C4—41no—
544C4—41no—
545C4—41no—
546C4—41no—
547C4—41no—
548C4—81no—
549C4—81no—
550C4—81no—
551C4—81no—
552C4C2×#135×C4711yescharacteristic
553C4C47×#57511yescharacteristic
554C4C47×#57711yescharacteristic
555C4C47×#57811yescharacteristic
556C2—81no—
557C2—81no—
558C2C47×#326911yescharacteristic
559C2C47×#328211yescharacteristic
560C2C47×#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×#3364C2semidirect
2. C47×#3359C2semidirect
5. C47×#1718C2semidirect
6. C47×#1699C2semidirect
7. C47×#1684C2semidirect
8. C47×#1679C2semidirect
9. C47×#1672C2semidirect
10. C47×#1650C2semidirect
11. C47×#1649C2semidirect
13. C47×#1636C2semidirect
14. C47×#1583C2semidirect
15. C47×SD16⋊C8C2semidirect
253. #19832C47direct (N × H)
276. #3364C2×C47semidirect
277. #3359C2×C47semidirect
280. #1718C2×C47semidirect
281. #1699C2×C47semidirect
282. #1684C2×C47semidirect
283. #1679C2×C47semidirect
284. #1672C2×C47semidirect
285. #1650C2×C47semidirect
286. #1649C2×C47semidirect
288. #1636C2×C47semidirect
289. #1583C2×C47semidirect
290. SD16⋊C8C2×C47semidirect
347. C47#19832direct (N × H)

Maximal subgroups

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

subgroupindex
C47×#33642
C47×#33592
C47×#33402
C47×#33292
C47×#17182
C47×#16992
C47×#16842
C47×#16792
C47×#16722
C47×#16502
C47×#16492
C47×#16462
C47×#16362
C47×#15832
C47×SD16⋊C82
#1983247