Finite Group Databasebeta

← C47×#19252 #26058950

Subgroups — C47×#19252 #26058950

Order 12032.

602 conjugacy classes of subgroups.

The subgroup lattice has 586 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C47×#3248C211yesmaximal, characteristic, complemented
2C47×#3212C211yesmaximal, characteristic
3C47×#3182C211yesmaximal, characteristic, complemented
4C47×#2969C211yesmaximal, characteristic, complemented
5C47×#1702C211yesmaximal, characteristic, complemented
6C47×#1700C211yesmaximal, characteristic, complemented
7C47×#1693C211yesmaximal, characteristic, complemented
8C47×#1685C211yesmaximal, characteristic, complemented
9C47×#1681C211yesmaximal, characteristic, complemented
10C47×#1679C211yesmaximal, characteristic, complemented
11C47×#1674C211yesmaximal, characteristic, complemented
12C47×#1666C211yesmaximal, characteristic, complemented
13C47×#1565C211yesmaximal, characteristic, complemented
14C47×#1544C211yesmaximal, characteristic, complemented
15C47×#1540C211yesmaximal, characteristic, complemented
16C47×#533C2211yescharacteristic
17C47×#532C2211yescharacteristic
18C47×#529C2211yescharacteristic
19C47×#500C2211yescharacteristic
20C47×#495—21no—
21C47×#492C2211yescharacteristic
22C47×#488—21no—
23C47×#487C2211yescharacteristic
24C47×#486C2211yescharacteristic
25C47×#479—21no—
26C47×#475C2211yescharacteristic
27C47×#474C2211yescharacteristic
28C47×#468—21no—
29C47×#468—21no—
30C47×#467—21no—
31C47×#465—21no—
32C47×#464—21no—
33C47×#462C2211yescharacteristic
34C47×#462C2211yescharacteristic
35C47×#461C2211yescharacteristic
36C47×#461C2211yescharacteristic
37C47×#460C2211yescharacteristic
38C47×#459C2211yescharacteristic
39C47×#452—21no—
40C47×#449—21no—
41C47×#446C2211yescharacteristic
42C8×Q8×C47C2211yescharacteristic
43C47×#440—21no—
44C47×#440—21no—
45C47×#436—21no—
46C47×#436C2211yescharacteristic
47C47×#435—21no—
48C8×D4×C47C2211yescharacteristic
49C47×#433—21no—
50C47×#431C2211yescharacteristic
51C47×#431C2211yescharacteristic
52C2×C4⋊C8×C47C2211yescharacteristic
53C47×#405—21no—
54C4×M16×C47C2211yescharacteristic
55C47×#335C2211yescharacteristic
56C47×#335C2211yescharacteristic
57C47×#334C2211yescharacteristic
58C47×#334C2211yescharacteristic
59C47×#332C2211yescharacteristic
60C47×#332C2211yescharacteristic
61C47×#332C2211yescharacteristic
62C47×#332C2211yescharacteristic
63C47×#332C2211yescharacteristic
64C47×#332C2211yescharacteristic
65C47×#331C2211yescharacteristic
66C47×#331C2211yescharacteristic
67C2×#41×C47—21no—
68C2×Q16×C47—21no—
69C2×Q16×C47—21no—
70C2×SD16×C47—21no—
71C2×SD16×C47—21no—
72C2×SD16×C47—21no—
73C2×SD16×C47—21no—
74C2×SD16×C47—21no—
75C2×D8×C47—21no—
76C2×M16×C47—21no—
77C2×M16×C47D411yescharacteristic
78C2×M16×C47D411yescharacteristic
79C22×C8×C47—21no—
80C22×C8×C47—21no—
81C4⋊Q8×C47C2311yescharacteristic
82C4⋊Q8×C47C2311yescharacteristic
83C4⋊Q8×C47C2311yescharacteristic
84#127×C47C2311yescharacteristic
85#126×C47—21no—
86#125×C47—21no—
87#125×C47D411yescharacteristic
88#124×C47—21no—
89#124×C47D411yescharacteristic
90#123×C47—21no—
91C22⋊Q8×C47—21no—
92C22⋊Q8×C47—21no—
93C22⋊Q8×C47D411yescharacteristic
94#121×C47—21no—
95#121×C47—21no—
96#121×C47D411yescharacteristic
97C4×Q8×C47—21no—
98C4×Q8×C47—21no—
99C4×Q8×C47C2311yescharacteristic
100C4×D4×C47—21no—
101C4×D4×C47—21no—
102C4×D4×C47—21no—
103C4×D4×C47C2311yescharacteristic
104#117×C47—21no—
105#117×C47—21no—
106C2×C42×C47C2311yescharacteristic
107#107×C47—21no—
108#107×C47—21no—
109#107×C47—21no—
110#106×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
118C4⋊C8×C47C2311yescharacteristic
119C4⋊C8×C47C2311yescharacteristic
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#102×C47—21no—
128#102×C47—21no—
129#102×C47—21no—
130#102×C47—21no—
131#102×C47—21no—
132C22⋊C8×C47—21no—
133C22⋊C8×C47—21no—
134C22⋊C8×C47—21no—
135C22⋊C8×C47—21no—
136#97×C47—21no—
137#97×C47D411yescharacteristic
138#97×C47D411yescharacteristic
139C4×C8×C47—21no—
140C4×C8×C47—21no—
141C4×C8×C47—21no—
142C4×C8×C47C2311yescharacteristic
143C4×C8×C47C2311yescharacteristic
144#41×C47—81no—
145#41×C47—81no—
146C2×Q8×C47—21no—
147C2×Q8×C47—21no—
148C2×Q8×C47—21no—
149C2×Q8×C47C2×D411yescharacteristic
150C2×D4×C47—21no—
151C2×D4×C47—21no—
152C2×D4×C47—21no—
153C2×D4×C47—21no—
154C2×D4×C47—41no—
155C2×D4×C47C2×D411yescharacteristic
156C22×C4×C47—21no—
157C22×C4×C47—41no—
158C22×C4×C47C2×D411yescharacteristic
159C22×C4×C47C2×D411yescharacteristic
160C22×C4×C47#4111yescharacteristic
161Q16×C47—81no—
162Q16×C47—81no—
163SD16×C47—42no—
164SD16×C47—42no—
165SD16×C47—81no—
166SD16×C47—81no—
167SD16×C47—81no—
168D8×C47—81no—
169M16×C47—22no—
170M16×C47—41no—
171M16×C47—42no—
172C2×C8×C47—21no—
173C2×C8×C47—21no—
174C2×C8×C47—21no—
175C2×C8×C47—21no—
176C2×C8×C47—21no—
177C2×C8×C47—21no—
178C2×C8×C47—42no—
179C2×C8×C47—81no—
180C2×C8×C47C2×D411yescharacteristic
181C2×C8×C47C2×D411yescharacteristic
182C2×C8×C47C2×D411yescharacteristic
183C2×C8×C47C2×D411yescharacteristic
184C4⋊C4×C47—21no—
185C4⋊C4×C47—21no—
186C4⋊C4×C47—21no—
187C4⋊C4×C47—21no—
188C4⋊C4×C47—21no—
189C4⋊C4×C47—21no—
190C4⋊C4×C47—21no—
191C4⋊C4×C47—21no—
192C4⋊C4×C47—21no—
193C4⋊C4×C47—21no—
194C4⋊C4×C47—41no—
195C4⋊C4×C47—41no—
196C4⋊C4×C47C2×D411yescharacteristic
197C4⋊C4×C47C2×D411yescharacteristic
198C22⋊C4×C47—21no—
199C22⋊C4×C47—21no—
200C22⋊C4×C47—21no—
201C22⋊C4×C47—21no—
202C22⋊C4×C47—21no—
203C22⋊C4×C47—41no—
204C22⋊C4×C47—41no—
205C22⋊C4×C47—41no—
206C42×C47—21no—
207C42×C47—41no—
208C42×C47C2×D411yescharacteristic
209C42×C47C2×D411yescharacteristic
210C42×C47#4111yescharacteristic
211C42×C47C2411yescharacteristic
212C23×C47—21no—
213C23×C47—41no—
214C23×C47#12111yescharacteristic
215Q8×C47—21no—
216Q8×C47—21no—
217Q8×C47—41no—
218Q8×C47—41no—
219Q8×C47—41no—
220Q8×C47—41no—
221Q8×C47—41no—
222Q8×C47—41no—
223D4×C47—21no—
224D4×C47—21no—
225D4×C47—41no—
226D4×C47—41no—
227D4×C47—41no—
228D4×C47—41no—
229D4×C47—81no—
230D4×C47—81no—
231D4×C47—82no—
232C2×C4×C47—21no—
233C2×C4×C47—21no—
234C2×C4×C47—21no—
235C2×C4×C47—21no—
236C2×C4×C47—21no—
237C2×C4×C47—21no—
238C2×C4×C47—21no—
239C2×C4×C47—41no—
240C2×C4×C47—41no—
241C2×C4×C47—41no—
242C2×C4×C47—41no—
243C2×C4×C47—41no—
244C2×C4×C47—41no—
245C2×C4×C47—82no—
246C2×C4×C47#12111yescharacteristic
247C2×C4×C47#12111yescharacteristic
248C2×C4×C47#12111yescharacteristic
249C2×C4×C47C22×D411yescharacteristic
250C2×C4×C47C22×D411yescharacteristic
251C2×C4×C47C2×#4111yescharacteristic
252C8×C47—21no—
253C8×C47—21no—
254C8×C47—21no—
255C8×C47—41no—
256C8×C47—41no—
257C8×C47—41no—
258C8×C47—41no—
259C8×C47—41no—
260C8×C47—41no—
261C8×C47#13512yes—
262#19252C4711yesmaximal, characteristic, direct product factor, Sylow
263C22×C47—21no—
264C22×C47—21no—
265C22×C47—21no—
266C22×C47—41no—
267C22×C47—41no—
268C22×C47—41no—
269C22×C47—81no—
270C22×C47—81no—
271C22×C47—81no—
272C22×C47C2×#12111yescharacteristic
273C4×C47—21no—
274C4×C47—21no—
275C4×C47—21no—
276C4×C47—21no—
277C4×C47—41no—
278C4×C47—41no—
279C4×C47—41no—
280C4×C47—81no—
281C4×C47—81no—
282C4×C47—81no—
283C4×C47C2×#13511yescharacteristic
284C4×C47#57511yescharacteristic
285C4×C47#57611yescharacteristic
286C4×C47#57711yescharacteristic
287#3248C2×C4711yescharacteristic, complemented
288#3212C2×C4711yescharacteristic
289#3182C2×C4711yescharacteristic, complemented
290#2969C2×C4711yescharacteristic, complemented
291#1702C2×C4711yescharacteristic, complemented
292#1700C2×C4711yescharacteristic, complemented
293#1693C2×C4711yescharacteristic, complemented
294#1685C2×C4711yescharacteristic, complemented
295#1681C2×C4711yescharacteristic, complemented
296#1679C2×C4711yescharacteristic, complemented
297#1674C2×C4711yescharacteristic, complemented
298#1666C2×C4711yescharacteristic, complemented
299#1565C2×C4711yescharacteristic, complemented
300#1544C2×C4711yescharacteristic, complemented
301#1540C2×C4711yescharacteristic, complemented
302C2×C47—41no—
303C2×C47—81no—
304C2×C47—161no—
305C2×C47#303511yescharacteristic
306C2×C47#306211yescharacteristic
307C2×C47#306911yescharacteristic
308#533C22×C4711yescharacteristic
309#532C22×C4711yescharacteristic
310#529C22×C4711yescharacteristic
311#500C22×C4711yescharacteristic
312#495—21no—
313#492C22×C4711yescharacteristic
314#488—21no—
315#487C22×C4711yescharacteristic
316#486C22×C4711yescharacteristic
317#479—21no—
318#475C22×C4711yescharacteristic
319#474C22×C4711yescharacteristic
320#468—21no—
321#468—21no—
322#467—21no—
323#465—21no—
324#464—21no—
325#462C22×C4711yescharacteristic
326#462C22×C4711yescharacteristic
327#461C22×C4711yescharacteristic
328#461C22×C4711yescharacteristic
329#460C22×C4711yescharacteristic
330#459C22×C4711yescharacteristic
331#452—21no—
332#449—21no—
333#446C22×C4711yescharacteristic
334C8×Q8C22×C4711yescharacteristic
335#440—21no—
336#440—21no—
337#436—21no—
338#436C22×C4711yescharacteristic
339#435—21no—
340C8×D4C22×C4711yescharacteristic
341#433—21no—
342#431C22×C4711yescharacteristic
343#431C22×C4711yescharacteristic
344C2×C4⋊C8C22×C4711yescharacteristic
345#405—21no—
346C4×M16C22×C4711yescharacteristic
347#335C22×C4711yescharacteristic
348#335C22×C4711yescharacteristic
349#334C22×C4711yescharacteristic
350#334C22×C4711yescharacteristic
351#332C22×C4711yescharacteristic
352#332C22×C4711yescharacteristic
353#332C22×C4711yescharacteristic
354#332C22×C4711yescharacteristic
355#332C22×C4711yescharacteristic
356#332C22×C4711yescharacteristic
357#331C22×C4711yescharacteristic
358#331C22×C4711yescharacteristic
359C47#1925211yescharacteristic, direct product factor, Sylow
360C2×#41—21no—
361C2×Q16—21no—
362C2×Q16—21no—
363C2×SD16—21no—
364C2×SD16—21no—
365C2×SD16—21no—
366C2×SD16—21no—
367C2×SD16—21no—
368C2×D8—21no—
369C2×M16—21no—
370C2×M16D4×C4711yescharacteristic
371C2×M16D4×C4711yescharacteristic
372C22×C8—21no—
373C22×C8—21no—
374C4⋊Q8C23×C4711yescharacteristic
375C4⋊Q8C23×C4711yescharacteristic
376C4⋊Q8C23×C4711yescharacteristic
377#127C23×C4711yescharacteristic
378#126—21no—
379#125—21no—
380#125D4×C4711yescharacteristic
381#124—21no—
382#124D4×C4711yescharacteristic
383#123—21no—
384C22⋊Q8—21no—
385C22⋊Q8—21no—
386C22⋊Q8D4×C4711yescharacteristic
387#121—21no—
388#121—21no—
389#121D4×C4711yescharacteristic
390C4×Q8—21no—
391C4×Q8—21no—
392C4×Q8C23×C4711yescharacteristic
393C4×D4—21no—
394C4×D4—21no—
395C4×D4—21no—
396C4×D4C23×C4711yescharacteristic
397#117—21no—
398#117—21no—
399C2×C42C23×C4711yescharacteristic
400#107—21no—
401#107—21no—
402#107—21no—
403#106—21no—
404C4⋊C8—21no—
405C4⋊C8—21no—
406C4⋊C8—21no—
407C4⋊C8C23×C4711yescharacteristic
408C4⋊C8C23×C4711yescharacteristic
409C4⋊C8C23×C4711yescharacteristic
410C4⋊C8C23×C4711yescharacteristic
411C4⋊C8C23×C4711yescharacteristic
412C4⋊C8C23×C4711yescharacteristic
413#103—21no—
414#103—21no—
415#103—21no—
416#103—21no—
417#103—21no—
418#103—21no—
419#103—21no—
420#102—21no—
421#102—21no—
422#102—21no—
423#102—21no—
424#102—21no—
425C22⋊C8—21no—
426C22⋊C8—21no—
427C22⋊C8—21no—
428C22⋊C8—21no—
429#97—21no—
430#97D4×C4711yescharacteristic
431#97D4×C4711yescharacteristic
432C4×C8—21no—
433C4×C8—21no—
434C4×C8—21no—
435C4×C8C23×C4711yescharacteristic
436C4×C8C23×C4711yescharacteristic
437#41—81no—
438#41—81no—
439C2×Q8—21no—
440C2×Q8—21no—
441C2×Q8—21no—
442C2×Q8C2×D4×C4711yescharacteristic
443C2×D4—21no—
444C2×D4—21no—
445C2×D4—21no—
446C2×D4—21no—
447C2×D4—41no—
448C2×D4C2×D4×C4711yescharacteristic
449C22×C4—21no—
450C22×C4—41no—
451C22×C4C2×D4×C4711yescharacteristic
452C22×C4C2×D4×C4711yescharacteristic
453C22×C4#41×C4711yescharacteristic
454Q16—81no—
455Q16—81no—
456SD16—42no—
457SD16—42no—
458SD16—81no—
459SD16—81no—
460SD16—81no—
461D8—81no—
462M16—22no—
463M16—41no—
464M16—42no—
465C2×C8—21no—
466C2×C8—21no—
467C2×C8—21no—
468C2×C8—21no—
469C2×C8—21no—
470C2×C8—21no—
471C2×C8—42no—
472C2×C8—81no—
473C2×C8C2×D4×C4711yescharacteristic
474C2×C8C2×D4×C4711yescharacteristic
475C2×C8C2×D4×C4711yescharacteristic
476C2×C8C2×D4×C4711yescharacteristic
477C4⋊C4—21no—
478C4⋊C4—21no—
479C4⋊C4—21no—
480C4⋊C4—21no—
481C4⋊C4—21no—
482C4⋊C4—21no—
483C4⋊C4—21no—
484C4⋊C4—21no—
485C4⋊C4—21no—
486C4⋊C4—21no—
487C4⋊C4—41no—
488C4⋊C4—41no—
489C4⋊C4C2×D4×C4711yescharacteristic
490C4⋊C4C2×D4×C4711yescharacteristic
491C22⋊C4—21no—
492C22⋊C4—21no—
493C22⋊C4—21no—
494C22⋊C4—21no—
495C22⋊C4—21no—
496C22⋊C4—41no—
497C22⋊C4—41no—
498C22⋊C4—41no—
499C42—21no—
500C42—41no—
501C42C2×D4×C4711yescharacteristic
502C42C2×D4×C4711yescharacteristic
503C42#41×C4711yescharacteristic
504C42C24×C4711yescharacteristic
505C23—21no—
506C23—41no—
507C23#121×C4711yescharacteristic
508Q8—21no—
509Q8—21no—
510Q8—41no—
511Q8—41no—
512Q8—41no—
513Q8—41no—
514Q8—41no—
515Q8—41no—
516D4—21no—
517D4—21no—
518D4—41no—
519D4—41no—
520D4—41no—
521D4—41no—
522D4—81no—
523D4—81no—
524D4—82no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—82no—
539C2×C4#121×C4711yescharacteristic
540C2×C4#121×C4711yescharacteristic
541C2×C4#121×C4711yescharacteristic
542C2×C4C22×D4×C4711yescharacteristic
543C2×C4C22×D4×C4711yescharacteristic
544C2×C4C2×#41×C4711yescharacteristic
545C8—21no—
546C8—21no—
547C8—21no—
548C8—41no—
549C8—41no—
550C8—41no—
551C8—41no—
552C8—41no—
553C8—41no—
554C8#135×C4712yes—
555C22—21no—
556C22—21no—
557C22—21no—
558C22—41no—
559C22—41no—
560C22—41no—
561C22—81no—
562C22—81no—
563C22—81no—
564C22C2×#121×C4711yescharacteristic
565C4—21no—
566C4—21no—
567C4—21no—
568C4—21no—
569C4—41no—
570C4—41no—
571C4—41no—
572C4—81no—
573C4—81no—
574C4—81no—
575C4C2×#135×C4711yescharacteristic
576C4C47×#57511yescharacteristic
577C4C47×#57611yescharacteristic
578C4C47×#57711yescharacteristic
579C2—41no—
580C2—81no—
581C2—161no—
582C2C47×#303511yescharacteristic
583C2C47×#306211yescharacteristic
584C2C47×#306911yescharacteristic
subgroupG/H
center, socleC22×C47C2×#121
commutator, Frattini, cosocleC42C24×C47
prime radicalC47×#3212C2
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C47 ◁ C2×C42×C47 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C47×#3248C2semidirect
3. C47×#3182C2semidirect
4. C47×#2969C2semidirect
5. C47×#1702C2semidirect
6. C47×#1700C2semidirect
7. C47×#1693C2semidirect
8. C47×#1685C2semidirect
9. C47×#1681C2semidirect
10. C47×#1679C2semidirect
11. C47×#1674C2semidirect
12. C47×#1666C2semidirect
13. C47×#1565C2semidirect
14. C47×#1544C2semidirect
15. C47×#1540C2semidirect
262. #19252C47direct (N × H)
287. #3248C2×C47semidirect
289. #3182C2×C47semidirect
290. #2969C2×C47semidirect
291. #1702C2×C47semidirect
292. #1700C2×C47semidirect
293. #1693C2×C47semidirect
294. #1685C2×C47semidirect
295. #1681C2×C47semidirect
296. #1679C2×C47semidirect
297. #1674C2×C47semidirect
298. #1666C2×C47semidirect
299. #1565C2×C47semidirect
300. #1544C2×C47semidirect
301. #1540C2×C47semidirect
359. C47#19252direct (N × H)

Maximal subgroups

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

subgroupindex
C47×#32482
C47×#32122
C47×#31822
C47×#29692
C47×#17022
C47×#17002
C47×#16932
C47×#16852
C47×#16812
C47×#16792
C47×#16742
C47×#16662
C47×#15652
C47×#15442
C47×#15402
#1925247