Finite Group Databasebeta

← C47×#19770 #26059468

Subgroups — C47×#19770 #26059468

Order 12032.

650 conjugacy classes of subgroups.

The subgroup lattice has 602 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C47×#3392C211yesmaximal, characteristic, complemented
2C47×#3387C211yesmaximal, characteristic, complemented
3C47×#3362C211yesmaximal, characteristic, complemented
4C47×#3287C211yesmaximal, characteristic
5C47×#1715C211yesmaximal, characteristic, complemented
6C47×#1688C211yesmaximal, characteristic, complemented
7C47×#1678C211yesmaximal, characteristic, complemented
8C47×#1671C211yesmaximal, characteristic, complemented
9C47×#1666C211yesmaximal, characteristic, complemented
10C47×#1642C211yesmaximal, characteristic, complemented
11C47×#1631C211yesmaximal, characteristic, complemented
12C47×#1626C211yesmaximal, characteristic, complemented
13C47×#1623C211yesmaximal, characteristic, complemented
14C47×#1582C211yesmaximal, characteristic, complemented
15C47×#1579C211yesmaximal, characteristic, complemented
16C2×#135×C47—21no—
17Q82×C47C2211yescharacteristic
18C47×#557C2211yescharacteristic
19C47×#550C2211yescharacteristic
20C47×#550C2211yescharacteristic
21C47×#501—21no—
22C47×#498C2211yescharacteristic
23C47×#493C2211yescharacteristic
24C47×#492—21no—
25C47×#492C2211yescharacteristic
26C47×#492C2211yescharacteristic
27C47×#486—21no—
28C47×#486C2211yescharacteristic
29C47×#486C2211yescharacteristic
30C47×#479—21no—
31C47×#477C2211yescharacteristic
32C47×#476—21no—
33C47×#476C2211yescharacteristic
34C47×#475—21no—
35C47×#475C2211yescharacteristic
36C47×#466—21no—
37C47×#461—21no—
38C47×#461C2211yescharacteristic
39C47×#460—21no—
40C47×#460—21no—
41C47×#460C2211yescharacteristic
42C47×#460C2211yescharacteristic
43C47×#460C2211yescharacteristic
44C47×#460C2211yescharacteristic
45C47×#449—21no—
46C47×#449—21no—
47C47×#446C2211yescharacteristic
48C8×Q8×C47C2211yescharacteristic
49C8×Q8×C47C2211yescharacteristic
50C47×#441—21no—
51C4×Q16×C47C2211yescharacteristic
52C4×SD16×C47—21no—
53C4×SD16×C47—21no—
54C4×SD16×C47C2211yescharacteristic
55C8×D4×C47C2211yescharacteristic
56C47×#334C2211yescharacteristic
57C47×#334C2211yescharacteristic
58C47×#333C2211yescharacteristic
59C47×#332C2211yescharacteristic
60C47×#331C2211yescharacteristic
61C47×#331C2211yescharacteristic
62C47×Q8⋊C8C2211yescharacteristic
63C47×Q8⋊C8C2211yescharacteristic
64C47×Q8⋊C8C2211yescharacteristic
65C47×D4⋊C8C2211yescharacteristic
66C47×#322C2211yescharacteristic
67C2×#41×C47—21no—
68C2×#41×C47—21no—
69#135×C47—44no—
70C2×Q16×C47D411yescharacteristic
71C2×SD16×C47—21no—
72C2×SD16×C47—21no—
73C2×SD16×C47—21no—
74C2×SD16×C47—21no—
75C2×SD16×C47—21no—
76C2×SD16×C47—21no—
77C2×SD16×C47—21no—
78C2×SD16×C47—41no—
79C2×SD16×C47D411yescharacteristic
80C2×D8×C47—21no—
81C2×D8×C47—21no—
82C22×C8×C47—21no—
83C4⋊Q8×C47—21no—
84C4⋊Q8×C47—21no—
85C4⋊Q8×C47—21no—
86C4⋊Q8×C47—41no—
87C4⋊Q8×C47C2311yescharacteristic
88C4⋊Q8×C47C2311yescharacteristic
89#127×C47—21no—
90#127×C47—21no—
91#127×C47C2311yescharacteristic
92#127×C47C2311yescharacteristic
93#125×C47—21no—
94#125×C47—41no—
95#121×C47—21no—
96#121×C47—21no—
97#121×C47—41no—
98#121×C47—41no—
99C4×Q8×C47—21no—
100C4×Q8×C47—21no—
101C4×Q8×C47—21no—
102C4×Q8×C47—21no—
103C4×Q8×C47C2311yescharacteristic
104C4×Q8×C47C2311yescharacteristic
105C4×Q8×C47C2311yescharacteristic
106C4×D4×C47—21no—
107C4×D4×C47—21no—
108C4×D4×C47C2311yescharacteristic
109#107×C47—21no—
110#107×C47D411yescharacteristic
111#106×C47—21no—
112#106×C47—21no—
113#106×C47—21no—
114#106×C47—21no—
115#106×C47D411yescharacteristic
116C4⋊C8×C47—21no—
117C4⋊C8×C47—21no—
118C4⋊C8×C47—21no—
119C4⋊C8×C47C2311yescharacteristic
120C4⋊C8×C47C2311yescharacteristic
121C4⋊C8×C47C2311yescharacteristic
122C4⋊C8×C47C2311yescharacteristic
123#103×C47—21no—
124#103×C47—21no—
125#103×C47—21no—
126#103×C47D411yescharacteristic
127#103×C47D411yescharacteristic
128#103×C47D411yescharacteristic
129#102×C47—21no—
130#102×C47—21no—
131#102×C47—21no—
132#102×C47—21no—
133#102×C47—21no—
134#102×C47—21no—
135#102×C47—21no—
136#102×C47—41no—
137#102×C47D411yescharacteristic
138C22⋊C8×C47—21no—
139#97×C47—21no—
140C4×C8×C47—21no—
141C4×C8×C47—21no—
142C4×C8×C47C2311yescharacteristic
143C4×C8×C47C2311yescharacteristic
144C4×C8×C47C2311yescharacteristic
145#41×C47—42no—
146#41×C47—42no—
147#41×C47—81no—
148#41×C47—81no—
149C2×Q8×C47—21no—
150C2×Q8×C47—21no—
151C2×Q8×C47—41no—
152C2×Q8×C47C2×D411yescharacteristic
153C2×Q8×C47C2×D411yescharacteristic
154C2×Q8×C47C2×D411yescharacteristic
155C2×D4×C47—21no—
156C2×D4×C47—21no—
157C2×D4×C47—21no—
158C2×D4×C47—21no—
159C2×D4×C47—21no—
160C2×D4×C47—21no—
161C2×D4×C47—41no—
162C2×D4×C47—41no—
163C2×D4×C47—41no—
164C2×D4×C47—41no—
165C2×D4×C47C2×D411yescharacteristic
166C22×C4×C47—21no—
167C22×C4×C47—41no—
168C22×C4×C47—41no—
169Q16×C47SD1614yescomplemented
170SD16×C47—41no—
171SD16×C47—42no—
172SD16×C47—42no—
173SD16×C47—42no—
174SD16×C47—42no—
175SD16×C47—81no—
176SD16×C47—81no—
177SD16×C47—81no—
178SD16×C47—82no—
179D8×C47—42no—
180D8×C47—81no—
181C2×C8×C47—21no—
182C2×C8×C47—21no—
183C2×C8×C47—21no—
184C2×C8×C47—21no—
185C2×C8×C47—21no—
186C2×C8×C47—42no—
187C2×C8×C47C2×D411yescharacteristic
188C2×C8×C47C2×D411yescharacteristic
189C2×C8×C47C2×D411yescharacteristic
190C2×C8×C47C2×D411yescharacteristic
191C4⋊C4×C47—21no—
192C4⋊C4×C47—21no—
193C4⋊C4×C47—21no—
194C4⋊C4×C47—21no—
195C4⋊C4×C47—21no—
196C4⋊C4×C47—21no—
197C4⋊C4×C47—21no—
198C4⋊C4×C47—41no—
199C4⋊C4×C47—41no—
200C4⋊C4×C47—41no—
201C4⋊C4×C47—41no—
202C4⋊C4×C47—41no—
203C4⋊C4×C47C2×D411yescharacteristic
204C4⋊C4×C47C2×D411yescharacteristic
205C4⋊C4×C47C2×D411yescharacteristic
206C4⋊C4×C47C2×D411yescharacteristic
207C22⋊C4×C47—21no—
208C22⋊C4×C47—41no—
209C22⋊C4×C47—41no—
210C42×C47—21no—
211C42×C47—21no—
212C42×C47—21no—
213C42×C47—41no—
214C42×C47—41no—
215C42×C47C2411yescharacteristic
216C23×C47—21no—
217C23×C47—41no—
218C23×C47—41no—
219Q8×C47—21no—
220Q8×C47—21no—
221Q8×C47—21no—
222Q8×C47—21no—
223Q8×C47—41no—
224Q8×C47—41no—
225Q8×C47—81no—
226Q8×C47—161no—
227Q8×C47C2×SD1612yes—
228Q8×C47C2×SD1612yes—
229D4×C47—21no—
230D4×C47—21no—
231D4×C47—41no—
232D4×C47—41no—
233D4×C47—41no—
234D4×C47—41no—
235D4×C47—41no—
236D4×C47—41no—
237D4×C47—41no—
238D4×C47—41no—
239D4×C47—82no—
240D4×C47—82no—
241D4×C47—81no—
242D4×C47—81no—
243D4×C47—161no—
244D4×C47—161no—
245C2×C4×C47—21no—
246C2×C4×C47—21no—
247C2×C4×C47—21no—
248C2×C4×C47—21no—
249C2×C4×C47—21no—
250C2×C4×C47—21no—
251C2×C4×C47—21no—
252C2×C4×C47—41no—
253C2×C4×C47—41no—
254C2×C4×C47—41no—
255C2×C4×C47—41no—
256C2×C4×C47—82no—
257C2×C4×C47—82no—
258C2×C4×C47C22×D411yescharacteristic
259C2×C4×C47C22×D411yescharacteristic
260C2×C4×C47H(5,𝔽2)11yescharacteristic
261C8×C47—21no—
262C8×C47—21no—
263C8×C47—21no—
264C8×C47—41no—
265C8×C47—41no—
266C8×C47—41no—
267C8×C47—41no—
268C8×C47—41no—
269C8×C47C2×SD1612yes—
270#19770C4711yesmaximal, characteristic, direct product factor, Sylow
271C22×C47—41no—
272C22×C47—41no—
273C22×C47—41no—
274C22×C47—81no—
275C22×C47—81no—
276C22×C47—81no—
277C22×C47—81no—
278C22×C47—81no—
279C22×C47—81no—
280C22×C47D4211yescharacteristic
281C4×C47—22no—
282C4×C47—22no—
283C4×C47—21no—
284C4×C47—41no—
285C4×C47—41no—
286C4×C47—41no—
287C4×C47—41no—
288C4×C47—41no—
289C4×C47—81no—
290C4×C47—81no—
291C4×C47C22×SD1611yescharacteristic
292C4×C47#57511yescharacteristic
293C4×C47#57711yescharacteristic
294C4×C47#57711yescharacteristic
295#3392C2×C4711yescharacteristic, complemented
296#3387C2×C4711yescharacteristic, complemented
297#3362C2×C4711yescharacteristic, complemented
298#3287C2×C4711yescharacteristic
299#1715C2×C4711yescharacteristic, complemented
300#1688C2×C4711yescharacteristic, complemented
301#1678C2×C4711yescharacteristic, complemented
302#1671C2×C4711yescharacteristic, complemented
303#1666C2×C4711yescharacteristic, complemented
304#1642C2×C4711yescharacteristic, complemented
305#1631C2×C4711yescharacteristic, complemented
306#1626C2×C4711yescharacteristic, complemented
307#1623C2×C4711yescharacteristic, complemented
308#1582C2×C4711yescharacteristic, complemented
309#1579C2×C4711yescharacteristic, complemented
310C2×C47—81no—
311C2×C47—161no—
312C2×C47—161no—
313C2×C47#327111yescharacteristic
314C2×C47D4×SD1611yescharacteristic
315C2×C47#328811yescharacteristic
316C2×#135—21no—
317Q82C22×C4711yescharacteristic
318#557C22×C4711yescharacteristic
319#550C22×C4711yescharacteristic
320#550C22×C4711yescharacteristic
321#501—21no—
322#498C22×C4711yescharacteristic
323#493C22×C4711yescharacteristic
324#492—21no—
325#492C22×C4711yescharacteristic
326#492C22×C4711yescharacteristic
327#486—21no—
328#486C22×C4711yescharacteristic
329#486C22×C4711yescharacteristic
330#479—21no—
331#477C22×C4711yescharacteristic
332#476—21no—
333#476C22×C4711yescharacteristic
334#475—21no—
335#475C22×C4711yescharacteristic
336#466—21no—
337#461—21no—
338#461C22×C4711yescharacteristic
339#460—21no—
340#460—21no—
341#460C22×C4711yescharacteristic
342#460C22×C4711yescharacteristic
343#460C22×C4711yescharacteristic
344#460C22×C4711yescharacteristic
345#449—21no—
346#449—21no—
347#446C22×C4711yescharacteristic
348C8×Q8C22×C4711yescharacteristic
349C8×Q8C22×C4711yescharacteristic
350#441—21no—
351C4×Q16C22×C4711yescharacteristic
352C4×SD16—21no—
353C4×SD16—21no—
354C4×SD16C22×C4711yescharacteristic
355C8×D4C22×C4711yescharacteristic
356#334C22×C4711yescharacteristic
357#334C22×C4711yescharacteristic
358#333C22×C4711yescharacteristic
359#332C22×C4711yescharacteristic
360#331C22×C4711yescharacteristic
361#331C22×C4711yescharacteristic
362Q8⋊C8C22×C4711yescharacteristic
363Q8⋊C8C22×C4711yescharacteristic
364Q8⋊C8C22×C4711yescharacteristic
365D4⋊C8C22×C4711yescharacteristic
366#322C22×C4711yescharacteristic
367C47#1977011yescharacteristic, direct product factor, Sylow
368C2×#41—21no—
369C2×#41—21no—
370#135—44no—
371C2×Q16D4×C4711yescharacteristic
372C2×SD16—21no—
373C2×SD16—21no—
374C2×SD16—21no—
375C2×SD16—21no—
376C2×SD16—21no—
377C2×SD16—21no—
378C2×SD16—21no—
379C2×SD16—41no—
380C2×SD16D4×C4711yescharacteristic
381C2×D8—21no—
382C2×D8—21no—
383C22×C8—21no—
384C4⋊Q8—21no—
385C4⋊Q8—21no—
386C4⋊Q8—21no—
387C4⋊Q8—41no—
388C4⋊Q8C23×C4711yescharacteristic
389C4⋊Q8C23×C4711yescharacteristic
390#127—21no—
391#127—21no—
392#127C23×C4711yescharacteristic
393#127C23×C4711yescharacteristic
394#125—21no—
395#125—41no—
396#121—21no—
397#121—21no—
398#121—41no—
399#121—41no—
400C4×Q8—21no—
401C4×Q8—21no—
402C4×Q8—21no—
403C4×Q8—21no—
404C4×Q8C23×C4711yescharacteristic
405C4×Q8C23×C4711yescharacteristic
406C4×Q8C23×C4711yescharacteristic
407C4×D4—21no—
408C4×D4—21no—
409C4×D4C23×C4711yescharacteristic
410#107—21no—
411#107D4×C4711yescharacteristic
412#106—21no—
413#106—21no—
414#106—21no—
415#106—21no—
416#106D4×C4711yescharacteristic
417C4⋊C8—21no—
418C4⋊C8—21no—
419C4⋊C8—21no—
420C4⋊C8C23×C4711yescharacteristic
421C4⋊C8C23×C4711yescharacteristic
422C4⋊C8C23×C4711yescharacteristic
423C4⋊C8C23×C4711yescharacteristic
424#103—21no—
425#103—21no—
426#103—21no—
427#103D4×C4711yescharacteristic
428#103D4×C4711yescharacteristic
429#103D4×C4711yescharacteristic
430#102—21no—
431#102—21no—
432#102—21no—
433#102—21no—
434#102—21no—
435#102—21no—
436#102—21no—
437#102—41no—
438#102D4×C4711yescharacteristic
439C22⋊C8—21no—
440#97—21no—
441C4×C8—21no—
442C4×C8—21no—
443C4×C8C23×C4711yescharacteristic
444C4×C8C23×C4711yescharacteristic
445C4×C8C23×C4711yescharacteristic
446#41—42no—
447#41—42no—
448#41—81no—
449#41—81no—
450C2×Q8—21no—
451C2×Q8—21no—
452C2×Q8—41no—
453C2×Q8C2×D4×C4711yescharacteristic
454C2×Q8C2×D4×C4711yescharacteristic
455C2×Q8C2×D4×C4711yescharacteristic
456C2×D4—21no—
457C2×D4—21no—
458C2×D4—21no—
459C2×D4—21no—
460C2×D4—21no—
461C2×D4—21no—
462C2×D4—41no—
463C2×D4—41no—
464C2×D4—41no—
465C2×D4—41no—
466C2×D4C2×D4×C4711yescharacteristic
467C22×C4—21no—
468C22×C4—41no—
469C22×C4—41no—
470Q16SD16×C4714yescomplemented
471SD16—41no—
472SD16—42no—
473SD16—42no—
474SD16—42no—
475SD16—42no—
476SD16—81no—
477SD16—81no—
478SD16—81no—
479SD16—82no—
480D8—42no—
481D8—81no—
482C2×C8—21no—
483C2×C8—21no—
484C2×C8—21no—
485C2×C8—21no—
486C2×C8—21no—
487C2×C8—42no—
488C2×C8C2×D4×C4711yescharacteristic
489C2×C8C2×D4×C4711yescharacteristic
490C2×C8C2×D4×C4711yescharacteristic
491C2×C8C2×D4×C4711yescharacteristic
492C4⋊C4—21no—
493C4⋊C4—21no—
494C4⋊C4—21no—
495C4⋊C4—21no—
496C4⋊C4—21no—
497C4⋊C4—21no—
498C4⋊C4—21no—
499C4⋊C4—41no—
500C4⋊C4—41no—
501C4⋊C4—41no—
502C4⋊C4—41no—
503C4⋊C4—41no—
504C4⋊C4C2×D4×C4711yescharacteristic
505C4⋊C4C2×D4×C4711yescharacteristic
506C4⋊C4C2×D4×C4711yescharacteristic
507C4⋊C4C2×D4×C4711yescharacteristic
508C22⋊C4—21no—
509C22⋊C4—41no—
510C22⋊C4—41no—
511C42—21no—
512C42—21no—
513C42—21no—
514C42—41no—
515C42—41no—
516C42C24×C4711yescharacteristic
517C23—21no—
518C23—41no—
519C23—41no—
520Q8—21no—
521Q8—21no—
522Q8—21no—
523Q8—21no—
524Q8—41no—
525Q8—41no—
526Q8—81no—
527Q8—161no—
528Q8C2×SD16×C4712yes—
529Q8C2×SD16×C4712yes—
530D4—21no—
531D4—21no—
532D4—41no—
533D4—41no—
534D4—41no—
535D4—41no—
536D4—41no—
537D4—41no—
538D4—41no—
539D4—41no—
540D4—82no—
541D4—82no—
542D4—81no—
543D4—81no—
544D4—161no—
545D4—161no—
546C2×C4—21no—
547C2×C4—21no—
548C2×C4—21no—
549C2×C4—21no—
550C2×C4—21no—
551C2×C4—21no—
552C2×C4—21no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4—82no—
558C2×C4—82no—
559C2×C4C22×D4×C4711yescharacteristic
560C2×C4C22×D4×C4711yescharacteristic
561C2×C4H(5,𝔽2)×C4711yescharacteristic
562C8—21no—
563C8—21no—
564C8—21no—
565C8—41no—
566C8—41no—
567C8—41no—
568C8—41no—
569C8—41no—
570C8C2×SD16×C4712yes—
571C22—41no—
572C22—41no—
573C22—41no—
574C22—81no—
575C22—81no—
576C22—81no—
577C22—81no—
578C22—81no—
579C22—81no—
580C22D42×C4711yescharacteristic
581C4—21no—
582C4—22no—
583C4—22no—
584C4—41no—
585C4—41no—
586C4—41no—
587C4—41no—
588C4—41no—
589C4—81no—
590C4—81no—
591C4C22×SD16×C4711yescharacteristic
592C4C47×#57511yescharacteristic
593C4C47×#57711yescharacteristic
594C4C47×#57711yescharacteristic
595C2—81no—
596C2—161no—
597C2—161no—
598C2C47×#327111yescharacteristic
599C2D4×SD16×C4711yescharacteristic
600C2C47×#328811yescharacteristic
subgroupG/H
center, socleC22×C47D42
commutator, Frattini, cosocleC42C24×C47
prime radicalC47×#3287C2
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×#3392C2semidirect
2. C47×#3387C2semidirect
3. C47×#3362C2semidirect
5. C47×#1715C2semidirect
6. C47×#1688C2semidirect
7. C47×#1678C2semidirect
8. C47×#1671C2semidirect
9. C47×#1666C2semidirect
10. C47×#1642C2semidirect
11. C47×#1631C2semidirect
12. C47×#1626C2semidirect
13. C47×#1623C2semidirect
14. C47×#1582C2semidirect
15. C47×#1579C2semidirect
169. Q16×C47SD16semidirect
270. #19770C47direct (N × H)
295. #3392C2×C47semidirect
296. #3387C2×C47semidirect
297. #3362C2×C47semidirect
299. #1715C2×C47semidirect
300. #1688C2×C47semidirect
301. #1678C2×C47semidirect
302. #1671C2×C47semidirect
303. #1666C2×C47semidirect
304. #1642C2×C47semidirect
305. #1631C2×C47semidirect
306. #1626C2×C47semidirect
307. #1623C2×C47semidirect
308. #1582C2×C47semidirect
309. #1579C2×C47semidirect
367. C47#19770direct (N × H)
470. Q16SD16×C47semidirect

Maximal subgroups

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

subgroupindex
C47×#33922
C47×#33872
C47×#33622
C47×#32872
C47×#17152
C47×#16882
C47×#16782
C47×#16712
C47×#16662
C47×#16422
C47×#16312
C47×#16262
C47×#16232
C47×#15822
C47×#15792
#1977047