Finite Group Databasebeta

← C47×#19790 #26059488

Subgroups — C47×#19790 #26059488

Order 12032.

626 conjugacy classes of subgroups.

The subgroup lattice has 588 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C47×#3381C211yesmaximal, characteristic, complemented
2C47×#3372C211yesmaximal, characteristic, complemented
3C47×#3295C211yesmaximal, characteristic
4C47×#3295C211yesmaximal, characteristic
5C47×#1720C211yesmaximal, characteristic, complemented
6C47×#1698C211yesmaximal, characteristic, complemented
7C47×#1683C211yesmaximal, characteristic, complemented
8C47×#1678C211yesmaximal, characteristic, complemented
9C47×#1671C211yesmaximal, characteristic, complemented
10C47×#1639C211yesmaximal, characteristic
11C47×#1632C211yesmaximal, characteristic, complemented
12C47×#1632C211yesmaximal, characteristic, complemented
13C47×#1626C211yesmaximal, characteristic, complemented
14C47×#1582C211yesmaximal, characteristic, complemented
15C47×SD16⋊C8C211yesmaximal, characteristic, complemented
16C47×#557C2211yescharacteristic, complemented
17C47×#554C2211yescharacteristic
18C47×#554C2211yescharacteristic
19D42×C47C2211yescharacteristic
20C47×#499—21no—
21C47×#498C2211yescharacteristic, complemented
22C47×#494C2211yescharacteristic, complemented
23C47×#491—21no—
24C47×#487C2211yescharacteristic, complemented
25C47×#486C2211yescharacteristic
26C47×#486C2211yescharacteristic
27C47×#486C2211yescharacteristic
28C47×#481—21no—
29C47×#481—21no—
30C47×#479—21no—
31C47×#479—21no—
32C47×#478—21no—
33C47×#477C2211yescharacteristic, complemented
34C47×#477C2211yescharacteristic, complemented
35C47×#476C2211yescharacteristic
36C47×#476C2211yescharacteristic
37C47×#474C2211yescharacteristic
38C47×#465—21no—
39C47×#465—21no—
40C47×#461—21no—
41C47×#461C2211yescharacteristic
42C47×#460C2211yescharacteristic
43C47×#460C2211yescharacteristic
44C47×#450—21no—
45C47×#450—21no—
46C47×#446C2211yescharacteristic, complemented
47C8×Q8×C47C2211yescharacteristic, complemented
48C47×#440—21no—
49C4×SD16×C47—21no—
50C4×SD16×C47C2211yescharacteristic
51C4×SD16×C47C2211yescharacteristic
52C8×D4×C47C2211yescharacteristic
53C8×D4×C47C2211yescharacteristic
54C2×#102×C47—21no—
55C2×#102×C47—21no—
56C47×#335C2211yescharacteristic, complemented
57C47×#334C2211yescharacteristic, complemented
58C47×#333C2211yescharacteristic, complemented
59C47×#333C2211yescharacteristic, complemented
60C47×#332C2211yescharacteristic, complemented
61C47×#331C2211yescharacteristic
62C47×Q8⋊C8C2211yescharacteristic, complemented
63C47×Q8⋊C8C2211yescharacteristic, complemented
64C47×D4⋊C8C2211yescharacteristic
65C47×D4⋊C8C2211yescharacteristic
66C47×#322C2211yescharacteristic, complemented
67C22×D4×C47—21no—
68C22×D4×C47—21no—
69C2×Q16×C47—41no—
70C2×SD16×C47—21no—
71C2×SD16×C47—21no—
72C2×SD16×C47—21no—
73C2×SD16×C47D411yescharacteristic
74C2×SD16×C47D411yescharacteristic
75C22×C8×C47—21no—
76C22×C8×C47—21no—
77C4⋊Q8×C47—21no—
78C4⋊Q8×C47C2311yescharacteristic
79C4⋊Q8×C47C2311yescharacteristic
80C4⋊Q8×C47C2311yescharacteristic
81#127×C47C2311yescharacteristic
82#125×C47—21no—
83#125×C47—21no—
84#125×C47—21no—
85#125×C47—41no—
86C22⋊Q8×C47—21no—
87C22⋊Q8×C47—21no—
88C22⋊Q8×C47—41no—
89C22⋊Q8×C47—41no—
90#121×C47—21no—
91#121×C47—21no—
92#120×C47—41no—
93C4×Q8×C47—21no—
94C4×Q8×C47—21no—
95C4×Q8×C47C2311yescharacteristic
96C4×Q8×C47C2311yescharacteristic
97C4×D4×C47—21no—
98C4×D4×C47—21no—
99C4×D4×C47C2311yescharacteristic
100C4×D4×C47C2311yescharacteristic
101C2×C4⋊C4×C47—21no—
102C2×C4⋊C4×C47—21no—
103#107×C47—21no—
104#107×C47—21no—
105#107×C47—21no—
106#106×C47—21no—
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×C47D411yescharacteristic
124#103×C47D411yescharacteristic
125#102×C47—21no—
126#102×C47—21no—
127#102×C47—21no—
128#102×C47—21no—
129#102×C47—21no—
130#102×C47—21no—
131#102×C47—21no—
132#102×C47—21no—
133#102×C47—21no—
134#102×C47—41no—
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
144C24×C47—41no—
145C2×Q8×C47—21no—
146C2×Q8×C47—21no—
147C2×Q8×C47—21no—
148C2×Q8×C47C2×D411yescharacteristic
149C2×Q8×C47C2×D411yescharacteristic
150C2×D4×C47—21no—
151C2×D4×C47—21no—
152C2×D4×C47—21no—
153C2×D4×C47—41no—
154C2×D4×C47—41no—
155C2×D4×C47—42no—
156C2×D4×C47—42no—
157C2×D4×C47—81no—
158C2×D4×C47—81no—
159C2×D4×C47C2×D411yescharacteristic
160C2×D4×C47C2×D411yescharacteristic
161C22×C4×C47—21no—
162C22×C4×C47—21no—
163C22×C4×C47—41no—
164C22×C4×C47—41no—
165Q16×C47—82no—
166SD16×C47—22no—
167SD16×C47—22no—
168SD16×C47—42no—
169SD16×C47—81no—
170SD16×C47—81no—
171C2×C8×C47—21no—
172C2×C8×C47—21no—
173C2×C8×C47—21no—
174C2×C8×C47—21no—
175C2×C8×C47—21no—
176C2×C8×C47—81no—
177C2×C8×C47—81no—
178C2×C8×C47C2×D411yescharacteristic
179C2×C8×C47C2×D411yescharacteristic
180C2×C8×C47C2×D411yescharacteristic
181C2×C8×C47C2×D411yescharacteristic
182C4⋊C4×C47—21no—
183C4⋊C4×C47—21no—
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—41no—
191C4⋊C4×C47—41no—
192C4⋊C4×C47—41no—
193C4⋊C4×C47—41no—
194C4⋊C4×C47—41no—
195C4⋊C4×C47—41no—
196C4⋊C4×C47—41no—
197C4⋊C4×C47C2×D411yescharacteristic
198C4⋊C4×C47C2×D411yescharacteristic
199C4⋊C4×C47C2×D411yescharacteristic
200C4⋊C4×C47C2×D411yescharacteristic
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—21no—
208C42×C47—41no—
209C42×C47C2411yescharacteristic
210C23×C47—21no—
211C23×C47—21no—
212C23×C47—41no—
213C23×C47—82no—
214C23×C47—82no—
215C23×C47—161no—
216Q8×C47—21no—
217Q8×C47—21no—
218Q8×C47—21no—
219Q8×C47—21no—
220Q8×C47—41no—
221Q8×C47—41no—
222Q8×C47—81no—
223Q8×C47—81no—
224D4×C47—21no—
225D4×C47—21no—
226D4×C47—41no—
227D4×C47—41no—
228D4×C47—41no—
229D4×C47—41no—
230D4×C47—81no—
231D4×C47—82no—
232D4×C47—82no—
233D4×C47#13512yes—
234D4×C47#13712yes—
235C2×C4×C47—21no—
236C2×C4×C47—21no—
237C2×C4×C47—21no—
238C2×C4×C47—21no—
239C2×C4×C47—21no—
240C2×C4×C47—21no—
241C2×C4×C47—41no—
242C2×C4×C47—41no—
243C2×C4×C47—41no—
244C2×C4×C47—41no—
245C2×C4×C47—41no—
246C2×C4×C47—41no—
247C2×C4×C47—41no—
248C2×C4×C47—161no—
249C2×C4×C47—161no—
250C2×C4×C47C22×D411yescharacteristic
251C2×C4×C47C22×D411yescharacteristic
252C2×C4×C47H(5,𝔽2)11yescharacteristic
253C8×C47—21no—
254C8×C47—21no—
255C8×C47—21no—
256C8×C47—21no—
257C8×C47—41no—
258C8×C47—41no—
259C8×C47—41no—
260C8×C47—41no—
261C8×C47—41no—
262#19790C4711yesmaximal, characteristic, direct product factor, Sylow
263C22×C47—22no—
264C22×C47—22no—
265C22×C47—41no—
266C22×C47—41no—
267C22×C47—41no—
268C22×C47—41no—
269C22×C47—81no—
270C22×C47—81no—
271C22×C47—81no—
272C22×C47—164no—
273C22×C47D4211yescharacteristic
274C4×C47—21no—
275C4×C47—41no—
276C4×C47—41no—
277C4×C47—41no—
278C4×C47—41no—
279C4×C47—41no—
280C4×C47—41no—
281C4×C47—81no—
282C4×C47—81no—
283C4×C47—81no—
284C4×C47C2×#13511yescharacteristic
285C4×C47C2×#13711yescharacteristic
286C4×C47#57711yescharacteristic
287C4×C47#57711yescharacteristic
288#3381C2×C4711yescharacteristic, complemented
289#3372C2×C4711yescharacteristic, complemented
290#3295C2×C4711yescharacteristic
291#3295C2×C4711yescharacteristic
292#1720C2×C4711yescharacteristic, complemented
293#1698C2×C4711yescharacteristic, complemented
294#1683C2×C4711yescharacteristic, complemented
295#1678C2×C4711yescharacteristic, complemented
296#1671C2×C4711yescharacteristic, complemented
297#1639C2×C4711yescharacteristic
298#1632C2×C4711yescharacteristic, complemented
299#1632C2×C4711yescharacteristic, complemented
300#1626C2×C4711yescharacteristic, complemented
301#1582C2×C4711yescharacteristic, complemented
302SD16⋊C8C2×C4711yescharacteristic, complemented
303C2×C47—42no—
304C2×C47—42no—
305C2×C47—161no—
306C2×C47#326611yescharacteristic
307C2×C47#328211yescharacteristic
308C2×C47#328811yescharacteristic
309#557C22×C4711yescharacteristic, complemented
310#554C22×C4711yescharacteristic
311#554C22×C4711yescharacteristic
312D42C22×C4711yescharacteristic
313#499—21no—
314#498C22×C4711yescharacteristic, complemented
315#494C22×C4711yescharacteristic, complemented
316#491—21no—
317#487C22×C4711yescharacteristic, complemented
318#486C22×C4711yescharacteristic
319#486C22×C4711yescharacteristic
320#486C22×C4711yescharacteristic
321#481—21no—
322#481—21no—
323#479—21no—
324#479—21no—
325#478—21no—
326#477C22×C4711yescharacteristic, complemented
327#477C22×C4711yescharacteristic, complemented
328#476C22×C4711yescharacteristic
329#476C22×C4711yescharacteristic
330#474C22×C4711yescharacteristic
331#465—21no—
332#465—21no—
333#461—21no—
334#461C22×C4711yescharacteristic
335#460C22×C4711yescharacteristic
336#460C22×C4711yescharacteristic
337#450—21no—
338#450—21no—
339#446C22×C4711yescharacteristic, complemented
340C8×Q8C22×C4711yescharacteristic, complemented
341#440—21no—
342C4×SD16—21no—
343C4×SD16C22×C4711yescharacteristic
344C4×SD16C22×C4711yescharacteristic
345C8×D4C22×C4711yescharacteristic
346C8×D4C22×C4711yescharacteristic
347C2×#102—21no—
348C2×#102—21no—
349#335C22×C4711yescharacteristic, complemented
350#334C22×C4711yescharacteristic, complemented
351#333C22×C4711yescharacteristic, complemented
352#333C22×C4711yescharacteristic, complemented
353#332C22×C4711yescharacteristic, complemented
354#331C22×C4711yescharacteristic
355Q8⋊C8C22×C4711yescharacteristic, complemented
356Q8⋊C8C22×C4711yescharacteristic, complemented
357D4⋊C8C22×C4711yescharacteristic
358D4⋊C8C22×C4711yescharacteristic
359#322C22×C4711yescharacteristic, complemented
360C47#1979011yescharacteristic, direct product factor, Sylow
361C22×D4—21no—
362C22×D4—21no—
363C2×Q16—41no—
364C2×SD16—21no—
365C2×SD16—21no—
366C2×SD16—21no—
367C2×SD16D4×C4711yescharacteristic
368C2×SD16D4×C4711yescharacteristic
369C22×C8—21no—
370C22×C8—21no—
371C4⋊Q8—21no—
372C4⋊Q8C23×C4711yescharacteristic
373C4⋊Q8C23×C4711yescharacteristic
374C4⋊Q8C23×C4711yescharacteristic
375#127C23×C4711yescharacteristic
376#125—21no—
377#125—21no—
378#125—21no—
379#125—41no—
380C22⋊Q8—21no—
381C22⋊Q8—21no—
382C22⋊Q8—41no—
383C22⋊Q8—41no—
384#121—21no—
385#121—21no—
386#120—41no—
387C4×Q8—21no—
388C4×Q8—21no—
389C4×Q8C23×C4711yescharacteristic
390C4×Q8C23×C4711yescharacteristic
391C4×D4—21no—
392C4×D4—21no—
393C4×D4C23×C4711yescharacteristic
394C4×D4C23×C4711yescharacteristic
395C2×C4⋊C4—21no—
396C2×C4⋊C4—21no—
397#107—21no—
398#107—21no—
399#107—21no—
400#106—21no—
401#106—21no—
402#106—21no—
403#106—21no—
404#106D4×C4711yescharacteristic
405#106D4×C4711yescharacteristic
406C4⋊C8—21no—
407C4⋊C8—21no—
408C4⋊C8C23×C4711yescharacteristic
409C4⋊C8C23×C4711yescharacteristic
410C4⋊C8C23×C4711yescharacteristic
411C4⋊C8C23×C4711yescharacteristic
412#103—21no—
413#103—21no—
414#103—21no—
415#103—21no—
416#103—21no—
417#103D4×C4711yescharacteristic
418#103D4×C4711yescharacteristic
419#102—21no—
420#102—21no—
421#102—21no—
422#102—21no—
423#102—21no—
424#102—21no—
425#102—21no—
426#102—21no—
427#102—21no—
428#102—41no—
429#102D4×C4711yescharacteristic
430#102D4×C4711yescharacteristic
431C22⋊C8—21no—
432C22⋊C8—21no—
433#97—21no—
434C4×C8—21no—
435C4×C8C23×C4711yescharacteristic
436C4×C8C23×C4711yescharacteristic
437C4×C8C23×C4711yescharacteristic
438C24—41no—
439C2×Q8—21no—
440C2×Q8—21no—
441C2×Q8—21no—
442C2×Q8C2×D4×C4711yescharacteristic
443C2×Q8C2×D4×C4711yescharacteristic
444C2×D4—21no—
445C2×D4—21no—
446C2×D4—21no—
447C2×D4—41no—
448C2×D4—41no—
449C2×D4—42no—
450C2×D4—42no—
451C2×D4—81no—
452C2×D4—81no—
453C2×D4C2×D4×C4711yescharacteristic
454C2×D4C2×D4×C4711yescharacteristic
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—41no—
458C22×C4—41no—
459Q16—82no—
460SD16—22no—
461SD16—22no—
462SD16—42no—
463SD16—81no—
464SD16—81no—
465C2×C8—21no—
466C2×C8—21no—
467C2×C8—21no—
468C2×C8—21no—
469C2×C8—21no—
470C2×C8—81no—
471C2×C8—81no—
472C2×C8C2×D4×C4711yescharacteristic
473C2×C8C2×D4×C4711yescharacteristic
474C2×C8C2×D4×C4711yescharacteristic
475C2×C8C2×D4×C4711yescharacteristic
476C4⋊C4—21no—
477C4⋊C4—21no—
478C4⋊C4—21no—
479C4⋊C4—21no—
480C4⋊C4—21no—
481C4⋊C4—21no—
482C4⋊C4—21no—
483C4⋊C4—21no—
484C4⋊C4—41no—
485C4⋊C4—41no—
486C4⋊C4—41no—
487C4⋊C4—41no—
488C4⋊C4—41no—
489C4⋊C4—41no—
490C4⋊C4—41no—
491C4⋊C4C2×D4×C4711yescharacteristic
492C4⋊C4C2×D4×C4711yescharacteristic
493C4⋊C4C2×D4×C4711yescharacteristic
494C4⋊C4C2×D4×C4711yescharacteristic
495C22⋊C4—21no—
496C22⋊C4—21no—
497C22⋊C4—41no—
498C22⋊C4—41no—
499C22⋊C4—41no—
500C42—21no—
501C42—21no—
502C42—41no—
503C42C24×C4711yescharacteristic
504C23—21no—
505C23—21no—
506C23—41no—
507C23—82no—
508C23—82no—
509C23—161no—
510Q8—21no—
511Q8—21no—
512Q8—21no—
513Q8—21no—
514Q8—41no—
515Q8—41no—
516Q8—81no—
517Q8—81no—
518D4—21no—
519D4—21no—
520D4—41no—
521D4—41no—
522D4—41no—
523D4—41no—
524D4—81no—
525D4—82no—
526D4—82no—
527D4#135×C4712yes—
528D4#137×C4712yes—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—161no—
543C2×C4—161no—
544C2×C4C22×D4×C4711yescharacteristic
545C2×C4C22×D4×C4711yescharacteristic
546C2×C4H(5,𝔽2)×C4711yescharacteristic
547C8—21no—
548C8—21no—
549C8—21no—
550C8—21no—
551C8—41no—
552C8—41no—
553C8—41no—
554C8—41no—
555C8—41no—
556C22—22no—
557C22—22no—
558C22—41no—
559C22—41no—
560C22—41no—
561C22—41no—
562C22—81no—
563C22—81no—
564C22—81no—
565C22—164no—
566C22D42×C4711yescharacteristic
567C4—21no—
568C4—41no—
569C4—41no—
570C4—41no—
571C4—41no—
572C4—41no—
573C4—41no—
574C4—81no—
575C4—81no—
576C4—81no—
577C4C2×#135×C4711yescharacteristic
578C4C2×#137×C4711yescharacteristic
579C4C47×#57711yescharacteristic
580C4C47×#57711yescharacteristic
581C2—42no—
582C2—42no—
583C2—161no—
584C2C47×#326611yescharacteristic
585C2C47×#328211yescharacteristic
586C2C47×#328811yescharacteristic
subgroupG/H
center, socleC22×C47D42
commutator, Frattini, cosocleC42C24×C47
prime radicalD42×C47C22
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×#3381C2semidirect
2. C47×#3372C2semidirect
5. C47×#1720C2semidirect
6. C47×#1698C2semidirect
7. C47×#1683C2semidirect
8. C47×#1678C2semidirect
9. C47×#1671C2semidirect
11. C47×#1632C2semidirect
12. C47×#1632C2semidirect
13. C47×#1626C2semidirect
14. C47×#1582C2semidirect
15. C47×SD16⋊C8C2semidirect
16. C47×#557C22semidirect
21. C47×#498C22semidirect
22. C47×#494C22semidirect
24. C47×#487C22semidirect
33. C47×#477C22semidirect
34. C47×#477C22semidirect
46. C47×#446C22semidirect
47. C8×Q8×C47C22semidirect
56. C47×#335C22semidirect
57. C47×#334C22semidirect
58. C47×#333C22semidirect
59. C47×#333C22semidirect
60. C47×#332C22semidirect
62. C47×Q8⋊C8C22semidirect
63. C47×Q8⋊C8C22semidirect
66. C47×#322C22semidirect
262. #19790C47direct (N × H)
288. #3381C2×C47semidirect
289. #3372C2×C47semidirect
292. #1720C2×C47semidirect
293. #1698C2×C47semidirect
294. #1683C2×C47semidirect
295. #1678C2×C47semidirect
296. #1671C2×C47semidirect
298. #1632C2×C47semidirect
299. #1632C2×C47semidirect
300. #1626C2×C47semidirect
301. #1582C2×C47semidirect
302. SD16⋊C8C2×C47semidirect
309. #557C22×C47semidirect
314. #498C22×C47semidirect
315. #494C22×C47semidirect
317. #487C22×C47semidirect
326. #477C22×C47semidirect
327. #477C22×C47semidirect
339. #446C22×C47semidirect
340. C8×Q8C22×C47semidirect
349. #335C22×C47semidirect
350. #334C22×C47semidirect
351. #333C22×C47semidirect
352. #333C22×C47semidirect
353. #332C22×C47semidirect
355. Q8⋊C8C22×C47semidirect
356. Q8⋊C8C22×C47semidirect
359. #322C22×C47semidirect
360. C47#19790direct (N × H)

Maximal subgroups

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

subgroupindex
C47×#33812
C47×#33722
C47×#32952
C47×#17202
C47×#16982
C47×#16832
C47×#16782
C47×#16712
C47×#16392
C47×#16322
C47×#16262
C47×#15822
C47×SD16⋊C82
#1979047