Finite Group Databasebeta

← C47×#19780 #26059478

Subgroups — C47×#19780 #26059478

Order 12032.

622 conjugacy classes of subgroups.

The subgroup lattice has 590 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1Q8×D8×C47C211yesmaximal, characteristic, complemented
2C47×#3329C211yesmaximal, characteristic, complemented
3C47×#3303C211yesmaximal, characteristic
4C47×#3298C211yesmaximal, characteristic, complemented
5C47×#1718C211yesmaximal, characteristic, complemented
6C47×#1699C211yesmaximal, characteristic, complemented
7C47×#1684C211yesmaximal, characteristic, complemented
8C47×#1683C211yesmaximal, characteristic, complemented
9C47×#1673C211yesmaximal, characteristic, complemented
10C47×#1654C211yesmaximal, characteristic, complemented
11C47×#1651C211yesmaximal, characteristic, complemented
12C47×#1646C211yesmaximal, characteristic, complemented
13C47×#1637C211yesmaximal, characteristic, complemented
14C47×#1581C211yesmaximal, characteristic, complemented
15C47×SD16⋊C8C211yesmaximal, characteristic, complemented
16C47×#555C2211yescharacteristic
17D4×Q8×C47C2211yescharacteristic
18D4×Q8×C47C2211yescharacteristic
19C47×#547C2211yescharacteristic
20C47×#500—21no—
21C47×#500C2211yescharacteristic
22C47×#498C2211yescharacteristic
23C47×#487C2211yescharacteristic
24C47×#487C2211yescharacteristic
25C47×#487C2211yescharacteristic
26C47×#487C2211yescharacteristic
27C47×#485—21no—
28C47×#485—21no—
29C47×#483—21no—
30C47×#477C2211yescharacteristic
31C47×#476C2211yescharacteristic
32C47×#475C2211yescharacteristic
33C47×#474—21no—
34C47×#474—21no—
35C47×#474C2211yescharacteristic
36C47×#474C2211yescharacteristic
37C47×#468—21no—
38C47×#465—21no—
39C47×#465—21no—
40C47×#461C2211yescharacteristic
41C47×#461C2211yescharacteristic
42C47×#461C2211yescharacteristic
43C47×#449—21no—
44C47×#448—21no—
45C47×#448—21no—
46C8×Q8×C47C2211yescharacteristic
47C4×SD16×C47C2211yescharacteristic
48C4×D8×C47—21no—
49C4×D8×C47C2211yescharacteristic
50C47×#436C2211yescharacteristic
51C8×D4×C47C2211yescharacteristic
52C8×D4×C47C2211yescharacteristic
53C47×#419—21no—
54C47×#416—21no—
55C2×#103×C47—21no—
56C47×#335C2211yescharacteristic
57C47×#335C2211yescharacteristic
58C47×#333C2211yescharacteristic
59C47×#332C2211yescharacteristic
60C47×#332C2211yescharacteristic
61C47×#332C2211yescharacteristic
62C47×Q8⋊C8C2211yescharacteristic
63C47×D4⋊C8C2211yescharacteristic
64C47×D4⋊C8C2211yescharacteristic
65C47×D4⋊C8C2211yescharacteristic
66C47×#322C2211yescharacteristic
67C2×#41×C47—21no—
68C22×Q8×C47—21no—
69C22×Q8×C47—21no—
70C2×SD16×C47—21no—
71C2×SD16×C47—21no—
72C2×SD16×C47—21no—
73C2×SD16×C47D411yescharacteristic
74C2×D8×C47D411yescharacteristic
75C2×M16×C47—21no—
76C22×C8×C47—21no—
77C22×C8×C47—21no—
78C4⋊Q8×C47—21no—
79C4⋊Q8×C47—21no—
80C4⋊Q8×C47C2311yescharacteristic
81C4⋊Q8×C47C2311yescharacteristic
82C4⋊Q8×C47C2311yescharacteristic
83C4⋊Q8×C47C2311yescharacteristic
84#124×C47—41no—
85#123×C47—41no—
86C22⋊Q8×C47—21no—
87C22⋊Q8×C47—21no—
88C22⋊Q8×C47—21no—
89C22⋊Q8×C47—41no—
90C22⋊Q8×C47—41no—
91#121×C47—21no—
92#121×C47—21no—
93#121×C47—21no—
94C4×Q8×C47C2311yescharacteristic
95C4×D4×C47—21no—
96C4×D4×C47—21no—
97C4×D4×C47C2311yescharacteristic
98C4×D4×C47C2311yescharacteristic
99C4×D4×C47C2311yescharacteristic
100#117×C47—21no—
101#117×C47—21no—
102C2×C4⋊C4×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×C47—21no—
111#106×C47—41no—
112#106×C47D411yescharacteristic
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—41no—
130#103×C47D411yescharacteristic
131#102×C47—21no—
132#102×C47—21no—
133#102×C47—21no—
134#102×C47D411yescharacteristic
135#102×C47D411yescharacteristic
136#102×C47D411yescharacteristic
137C22⋊C8×C47—21no—
138C22⋊C8×C47—21no—
139C22⋊C8×C47—21no—
140C4×C8×C47—21no—
141C4×C8×C47C2311yescharacteristic
142C4×C8×C47C2311yescharacteristic
143C4×C8×C47C2311yescharacteristic
144#41×C47—42no—
145#41×C47—81no—
146C2×Q8×C47—21no—
147C2×Q8×C47—21no—
148C2×Q8×C47—21no—
149C2×Q8×C47—21no—
150C2×Q8×C47—41no—
151C2×Q8×C47—41no—
152C2×Q8×C47—42no—
153C2×Q8×C47—42no—
154C2×Q8×C47—81no—
155C2×Q8×C47—81no—
156C2×Q8×C47C2×D411yescharacteristic
157C2×D4×C47—41no—
158C2×D4×C47—41no—
159C2×D4×C47C2×D411yescharacteristic
160C2×D4×C47C2×D411yescharacteristic
161C2×D4×C47C2×D411yescharacteristic
162C22×C4×C47—21no—
163C22×C4×C47—21no—
164C22×C4×C47—21no—
165C22×C4×C47—41no—
166C22×C4×C47—41no—
167C22×C4×C47—41no—
168SD16×C47—22no—
169SD16×C47—81no—
170SD16×C47—81no—
171SD16×C47—81no—
172D8×C47—22no—
173M16×C47—81no—
174C2×C8×C47—21no—
175C2×C8×C47—21no—
176C2×C8×C47—21no—
177C2×C8×C47—21no—
178C2×C8×C47—21no—
179C2×C8×C47—81no—
180C2×C8×C47—81no—
181C2×C8×C47C2×D411yescharacteristic
182C2×C8×C47C2×D411yescharacteristic
183C2×C8×C47C2×D411yescharacteristic
184C2×C8×C47C2×D411yescharacteristic
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×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—21no—
204C22⋊C4×C47—41no—
205C22⋊C4×C47—41no—
206C22⋊C4×C47—41no—
207C22⋊C4×C47—41no—
208C22⋊C4×C47—41no—
209C42×C47—21no—
210C42×C47—41no—
211C42×C47C2411yescharacteristic
212C23×C47—21no—
213C23×C47—21no—
214C23×C47—21no—
215Q8×C47—21no—
216Q8×C47—41no—
217Q8×C47—41no—
218Q8×C47—41no—
219Q8×C47—41no—
220Q8×C47—41no—
221Q8×C47—41no—
222Q8×C47—82no—
223Q8×C47—82no—
224Q8×C47—81no—
225Q8×C47#13512yes—
226D4×C47—21no—
227D4×C47—21no—
228D4×C47—21no—
229D4×C47—21no—
230D4×C47—21no—
231D4×C47—82no—
232D4×C47—161no—
233D4×C47#13712yes—
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—41no—
246C2×C4×C47—41no—
247C2×C4×C47—41no—
248C2×C4×C47—41no—
249C2×C4×C47—82no—
250C2×C4×C47—82no—
251C2×C4×C47—82no—
252C2×C4×C47C22×D411yescharacteristic
253C2×C4×C47C22×D411yescharacteristic
254C2×C4×C47H(5,𝔽2)11yescharacteristic
255C8×C47—21no—
256C8×C47—21no—
257C8×C47—21no—
258C8×C47—21no—
259C8×C47—41no—
260C8×C47—41no—
261C8×C47—41no—
262C8×C47—41no—
263C8×C47—41no—
264#19780C4711yesmaximal, characteristic, direct product factor, Sylow
265C22×C47—22no—
266C22×C47—41no—
267C22×C47—41no—
268C22×C47—41no—
269C22×C47—41no—
270C22×C47—41no—
271C22×C47—41no—
272C22×C47—41no—
273C22×C47—41no—
274C22×C47D4211yescharacteristic
275C4×C47—22no—
276C4×C47—21no—
277C4×C47—41no—
278C4×C47—41no—
279C4×C47—41no—
280C4×C47—41no—
281C4×C47—81no—
282C4×C47—81no—
283C4×C47—81no—
284C4×C47—81no—
285C4×C47C2×#13511yescharacteristic
286C4×C47C2×#13711yescharacteristic
287C4×C47#57611yescharacteristic
288C4×C47#57711yescharacteristic
289Q8×D8C2×C4711yescharacteristic, complemented
290#3329C2×C4711yescharacteristic, complemented
291#3303C2×C4711yescharacteristic
292#3298C2×C4711yescharacteristic, complemented
293#1718C2×C4711yescharacteristic, complemented
294#1699C2×C4711yescharacteristic, complemented
295#1684C2×C4711yescharacteristic, complemented
296#1683C2×C4711yescharacteristic, complemented
297#1673C2×C4711yescharacteristic, complemented
298#1654C2×C4711yescharacteristic, complemented
299#1651C2×C4711yescharacteristic, complemented
300#1646C2×C4711yescharacteristic, complemented
301#1637C2×C4711yescharacteristic, complemented
302#1581C2×C4711yescharacteristic, complemented
303SD16⋊C8C2×C4711yescharacteristic, complemented
304C2×C47—42no—
305C2×C47—81no—
306C2×C47—81no—
307C2×C47#326611yescharacteristic
308C2×C47#328011yescharacteristic
309C2×C47#328911yescharacteristic
310#555C22×C4711yescharacteristic
311D4×Q8C22×C4711yescharacteristic
312D4×Q8C22×C4711yescharacteristic
313#547C22×C4711yescharacteristic
314#500—21no—
315#500C22×C4711yescharacteristic
316#498C22×C4711yescharacteristic
317#487C22×C4711yescharacteristic
318#487C22×C4711yescharacteristic
319#487C22×C4711yescharacteristic
320#487C22×C4711yescharacteristic
321#485—21no—
322#485—21no—
323#483—21no—
324#477C22×C4711yescharacteristic
325#476C22×C4711yescharacteristic
326#475C22×C4711yescharacteristic
327#474—21no—
328#474—21no—
329#474C22×C4711yescharacteristic
330#474C22×C4711yescharacteristic
331#468—21no—
332#465—21no—
333#465—21no—
334#461C22×C4711yescharacteristic
335#461C22×C4711yescharacteristic
336#461C22×C4711yescharacteristic
337#449—21no—
338#448—21no—
339#448—21no—
340C8×Q8C22×C4711yescharacteristic
341C4×SD16C22×C4711yescharacteristic
342C4×D8—21no—
343C4×D8C22×C4711yescharacteristic
344#436C22×C4711yescharacteristic
345C8×D4C22×C4711yescharacteristic
346C8×D4C22×C4711yescharacteristic
347#419—21no—
348#416—21no—
349C2×#103—21no—
350#335C22×C4711yescharacteristic
351#335C22×C4711yescharacteristic
352#333C22×C4711yescharacteristic
353#332C22×C4711yescharacteristic
354#332C22×C4711yescharacteristic
355#332C22×C4711yescharacteristic
356Q8⋊C8C22×C4711yescharacteristic
357D4⋊C8C22×C4711yescharacteristic
358D4⋊C8C22×C4711yescharacteristic
359D4⋊C8C22×C4711yescharacteristic
360#322C22×C4711yescharacteristic
361C47#1978011yescharacteristic, direct product factor, Sylow
362C2×#41—21no—
363C22×Q8—21no—
364C22×Q8—21no—
365C2×SD16—21no—
366C2×SD16—21no—
367C2×SD16—21no—
368C2×SD16D4×C4711yescharacteristic
369C2×D8D4×C4711yescharacteristic
370C2×M16—21no—
371C22×C8—21no—
372C22×C8—21no—
373C4⋊Q8—21no—
374C4⋊Q8—21no—
375C4⋊Q8C23×C4711yescharacteristic
376C4⋊Q8C23×C4711yescharacteristic
377C4⋊Q8C23×C4711yescharacteristic
378C4⋊Q8C23×C4711yescharacteristic
379#124—41no—
380#123—41no—
381C22⋊Q8—21no—
382C22⋊Q8—21no—
383C22⋊Q8—21no—
384C22⋊Q8—41no—
385C22⋊Q8—41no—
386#121—21no—
387#121—21no—
388#121—21no—
389C4×Q8C23×C4711yescharacteristic
390C4×D4—21no—
391C4×D4—21no—
392C4×D4C23×C4711yescharacteristic
393C4×D4C23×C4711yescharacteristic
394C4×D4C23×C4711yescharacteristic
395#117—21no—
396#117—21no—
397C2×C4⋊C4—21no—
398#107—21no—
399#107—21no—
400#107—21no—
401#107—21no—
402#107—21no—
403#107D4×C4711yescharacteristic
404#106—21no—
405#106—21no—
406#106—41no—
407#106D4×C4711yescharacteristic
408C4⋊C8—21no—
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#103—21no—
421#103—21no—
422#103—21no—
423#103—21no—
424#103—41no—
425#103D4×C4711yescharacteristic
426#102—21no—
427#102—21no—
428#102—21no—
429#102D4×C4711yescharacteristic
430#102D4×C4711yescharacteristic
431#102D4×C4711yescharacteristic
432C22⋊C8—21no—
433C22⋊C8—21no—
434C22⋊C8—21no—
435C4×C8—21no—
436C4×C8C23×C4711yescharacteristic
437C4×C8C23×C4711yescharacteristic
438C4×C8C23×C4711yescharacteristic
439#41—42no—
440#41—81no—
441C2×Q8—21no—
442C2×Q8—21no—
443C2×Q8—21no—
444C2×Q8—21no—
445C2×Q8—41no—
446C2×Q8—41no—
447C2×Q8—42no—
448C2×Q8—42no—
449C2×Q8—81no—
450C2×Q8—81no—
451C2×Q8C2×D4×C4711yescharacteristic
452C2×D4—41no—
453C2×D4—41no—
454C2×D4C2×D4×C4711yescharacteristic
455C2×D4C2×D4×C4711yescharacteristic
456C2×D4C2×D4×C4711yescharacteristic
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—41no—
461C22×C4—41no—
462C22×C4—41no—
463SD16—22no—
464SD16—81no—
465SD16—81no—
466SD16—81no—
467D8—22no—
468M16—81no—
469C2×C8—21no—
470C2×C8—21no—
471C2×C8—21no—
472C2×C8—21no—
473C2×C8—21no—
474C2×C8—81no—
475C2×C8—81no—
476C2×C8C2×D4×C4711yescharacteristic
477C2×C8C2×D4×C4711yescharacteristic
478C2×C8C2×D4×C4711yescharacteristic
479C2×C8C2×D4×C4711yescharacteristic
480C4⋊C4—21no—
481C4⋊C4—21no—
482C4⋊C4—21no—
483C4⋊C4—21no—
484C4⋊C4—21no—
485C4⋊C4—21no—
486C4⋊C4—21no—
487C4⋊C4—21no—
488C4⋊C4—21no—
489C4⋊C4—41no—
490C4⋊C4—41no—
491C4⋊C4—41no—
492C4⋊C4C2×D4×C4711yescharacteristic
493C4⋊C4C2×D4×C4711yescharacteristic
494C4⋊C4C2×D4×C4711yescharacteristic
495C4⋊C4C2×D4×C4711yescharacteristic
496C22⋊C4—21no—
497C22⋊C4—21no—
498C22⋊C4—21no—
499C22⋊C4—41no—
500C22⋊C4—41no—
501C22⋊C4—41no—
502C22⋊C4—41no—
503C22⋊C4—41no—
504C42—21no—
505C42—41no—
506C42C24×C4711yescharacteristic
507C23—21no—
508C23—21no—
509C23—21no—
510Q8—21no—
511Q8—41no—
512Q8—41no—
513Q8—41no—
514Q8—41no—
515Q8—41no—
516Q8—41no—
517Q8—82no—
518Q8—82no—
519Q8—81no—
520Q8#135×C4712yes—
521D4—21no—
522D4—21no—
523D4—21no—
524D4—21no—
525D4—21no—
526D4—82no—
527D4—161no—
528D4#137×C4712yes—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—82no—
545C2×C4—82no—
546C2×C4—82no—
547C2×C4C22×D4×C4711yescharacteristic
548C2×C4C22×D4×C4711yescharacteristic
549C2×C4H(5,𝔽2)×C4711yescharacteristic
550C8—21no—
551C8—21no—
552C8—21no—
553C8—21no—
554C8—41no—
555C8—41no—
556C8—41no—
557C8—41no—
558C8—41no—
559C22—22no—
560C22—41no—
561C22—41no—
562C22—41no—
563C22—41no—
564C22—41no—
565C22—41no—
566C22—41no—
567C22—41no—
568C22D42×C4711yescharacteristic
569C4—21no—
570C4—22no—
571C4—41no—
572C4—41no—
573C4—41no—
574C4—41no—
575C4—81no—
576C4—81no—
577C4—81no—
578C4—81no—
579C4C2×#135×C4711yescharacteristic
580C4C2×#137×C4711yescharacteristic
581C4C47×#57611yescharacteristic
582C4C47×#57711yescharacteristic
583C2—42no—
584C2—81no—
585C2—81no—
586C2C47×#326611yescharacteristic
587C2C47×#328011yescharacteristic
588C2C47×#328911yescharacteristic
subgroupG/H
center, socleC22×C47D42
commutator, Frattini, cosocleC42C24×C47
prime radicalC47×#3303C2
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. Q8×D8×C47C2semidirect
2. C47×#3329C2semidirect
4. C47×#3298C2semidirect
5. C47×#1718C2semidirect
6. C47×#1699C2semidirect
7. C47×#1684C2semidirect
8. C47×#1683C2semidirect
9. C47×#1673C2semidirect
10. C47×#1654C2semidirect
11. C47×#1651C2semidirect
12. C47×#1646C2semidirect
13. C47×#1637C2semidirect
14. C47×#1581C2semidirect
15. C47×SD16⋊C8C2semidirect
264. #19780C47direct (N × H)
289. Q8×D8C2×C47semidirect
290. #3329C2×C47semidirect
292. #3298C2×C47semidirect
293. #1718C2×C47semidirect
294. #1699C2×C47semidirect
295. #1684C2×C47semidirect
296. #1683C2×C47semidirect
297. #1673C2×C47semidirect
298. #1654C2×C47semidirect
299. #1651C2×C47semidirect
300. #1646C2×C47semidirect
301. #1637C2×C47semidirect
302. #1581C2×C47semidirect
303. SD16⋊C8C2×C47semidirect
361. C47#19780direct (N × H)

Maximal subgroups

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

subgroupindex
Q8×D8×C472
C47×#33292
C47×#33032
C47×#32982
C47×#17182
C47×#16992
C47×#16842
C47×#16832
C47×#16732
C47×#16542
C47×#16512
C47×#16462
C47×#16372
C47×#15812
C47×SD16⋊C82
#1978047