Finite Group Databasebeta

← C47×#19836 #26059534

Subgroups — C47×#19836 #26059534

Order 12032.

670 conjugacy classes of subgroups.

The subgroup lattice has 618 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C47×#3366C211yesmaximal, characteristic, complemented
2C47×#3358C211yesmaximal, characteristic, complemented
3C47×#3299C211yesmaximal, characteristic, complemented
4C47×#3287C211yesmaximal, characteristic, complemented
5C47×#1717C211yesmaximal, characteristic, complemented
6C47×#1702C211yesmaximal, characteristic, complemented
7C47×#1683C211yesmaximal, characteristic, complemented
8C47×#1678C211yesmaximal, characteristic, complemented
9C47×#1667C211yesmaximal, characteristic, complemented
10C47×#1641C211yesmaximal, characteristic, complemented
11C47×#1631C211yesmaximal, characteristic, complemented
12C47×#1627C211yesmaximal, characteristic, complemented
13C47×#1622C211yesmaximal, characteristic, complemented
14C47×#1584C211yesmaximal, characteristic, complemented
15C47×#1580C211yesmaximal, characteristic, complemented
16C2×#135×C47—21no—
17C47×#554C2211yescharacteristic
18C47×#550C2211yescharacteristic
19C47×#550C2211yescharacteristic
20D4×Q8×C47C2211yescharacteristic
21C47×#493C2211yescharacteristic
22C47×#492C2211yescharacteristic
23C47×#490—21no—
24C47×#487C2211yescharacteristic
25C47×#486—21no—
26C47×#486C2211yescharacteristic
27C47×#486C2211yescharacteristic
28C47×#486C2211yescharacteristic
29C47×#484—21no—
30C47×#478—21no—
31C47×#477C2211yescharacteristic
32C47×#476C2211yescharacteristic
33C47×#474—21no—
34C47×#474C2211yescharacteristic
35C47×#467—21no—
36C47×#466—21no—
37C47×#462C2211yescharacteristic
38C47×#460C2211yescharacteristic
39C47×#460C2211yescharacteristic
40C47×#459—21no—
41C47×#459—21no—
42C47×#459C2211yescharacteristic
43C47×#459C2211yescharacteristic
44C47×#451—21no—
45C47×#449—21no—
46C47×#449—21no—
47C47×#446C2211yescharacteristic
48C8×Q8×C47C2211yescharacteristic
49C47×#442—21no—
50C4×Q16×C47C2211yescharacteristic
51C4×D8×C47—21no—
52C4×D8×C47C2211yescharacteristic
53C8×D4×C47C2211yescharacteristic
54C8×D4×C47C2211yescharacteristic
55C2×#103×C47—21no—
56C47×#335C2211yescharacteristic
57C47×#334C2211yescharacteristic
58C47×#333C2211yescharacteristic
59C47×#332C2211yescharacteristic
60C47×#331C2211yescharacteristic
61C47×#331C2211yescharacteristic
62C47×Q8⋊C8C2211yescharacteristic
63C47×Q8⋊C8C2211yescharacteristic
64C47×D4⋊C8C2211yescharacteristic
65C47×D4⋊C8C2211yescharacteristic
66C47×#322C2211yescharacteristic
67C2×#41×C47—21no—
68C2×#41×C47—21no—
69C22×Q8×C47—21no—
70#135×C47—44no—
71C2×Q16×C47—21no—
72C2×Q16×C47D411yescharacteristic
73C2×SD16×C47—21no—
74C2×SD16×C47—21no—
75C2×SD16×C47—41no—
76C2×D8×C47—21no—
77C2×D8×C47—21no—
78C2×D8×C47—21no—
79C2×D8×C47—21no—
80C2×D8×C47D411yescharacteristic
81C22×C8×C47—21no—
82C22×C8×C47—21no—
83C4⋊Q8×C47—21no—
84C4⋊Q8×C47C2311yescharacteristic
85C4⋊Q8×C47C2311yescharacteristic
86#127×C47—21no—
87#127×C47—21no—
88#127×C47C2311yescharacteristic
89#127×C47C2311yescharacteristic
90#125×C47—21no—
91C22⋊Q8×C47—21no—
92C22⋊Q8×C47—21no—
93C22⋊Q8×C47—41no—
94C22⋊Q8×C47—41no—
95#121×C47—21no—
96#121×C47—21no—
97#121×C47—41no—
98#121×C47—41no—
99C4×Q8×C47C2311yescharacteristic
100C4×Q8×C47C2311yescharacteristic
101C4×D4×C47—21no—
102C4×D4×C47—21no—
103C4×D4×C47—21no—
104C4×D4×C47—21no—
105C4×D4×C47C2311yescharacteristic
106C4×D4×C47C2311yescharacteristic
107C2×C4⋊C4×C47—21no—
108#107×C47—21no—
109#107×C47—21no—
110#107×C47D411yescharacteristic
111#107×C47D411yescharacteristic
112#106×C47—21no—
113C4⋊C8×C47—21no—
114C4⋊C8×C47—21no—
115C4⋊C8×C47C2311yescharacteristic
116C4⋊C8×C47C2311yescharacteristic
117C4⋊C8×C47C2311yescharacteristic
118C4⋊C8×C47C2311yescharacteristic
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—21no—
135#102×C47—41no—
136#102×C47D411yescharacteristic
137#102×C47D411yescharacteristic
138C22⋊C8×C47—21no—
139C22⋊C8×C47—21no—
140#97×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×C47—42no—
153C2×Q8×C47—81no—
154C2×Q8×C47C2×D411yescharacteristic
155C2×Q8×C47C2×D411yescharacteristic
156C2×D4×C47—21no—
157C2×D4×C47—21no—
158C2×D4×C47—21no—
159C2×D4×C47—21no—
160C2×D4×C47—21no—
161C2×D4×C47—21no—
162C2×D4×C47—41no—
163C2×D4×C47—41no—
164C2×D4×C47—41no—
165C2×D4×C47—41no—
166C2×D4×C47C2×D411yescharacteristic
167C2×D4×C47C2×D411yescharacteristic
168C22×C4×C47—21no—
169C22×C4×C47—21no—
170C22×C4×C47—41no—
171C22×C4×C47—41no—
172C22×C4×C47—41no—
173C22×C4×C47—41no—
174Q16×C47—22no—
175Q16×C47—81no—
176SD16×C47—42no—
177SD16×C47—42no—
178SD16×C47—82no—
179D8×C47—22no—
180D8×C47—42no—
181D8×C47—42no—
182D8×C47—42no—
183D8×C47—81no—
184C2×C8×C47—21no—
185C2×C8×C47—21no—
186C2×C8×C47—21no—
187C2×C8×C47—21no—
188C2×C8×C47—21no—
189C2×C8×C47—42no—
190C2×C8×C47—81no—
191C2×C8×C47C2×D411yescharacteristic
192C2×C8×C47C2×D411yescharacteristic
193C2×C8×C47C2×D411yescharacteristic
194C2×C8×C47C2×D411yescharacteristic
195C4⋊C4×C47—21no—
196C4⋊C4×C47—21no—
197C4⋊C4×C47—21no—
198C4⋊C4×C47—21no—
199C4⋊C4×C47—21no—
200C4⋊C4×C47—21no—
201C4⋊C4×C47—41no—
202C4⋊C4×C47—41no—
203C4⋊C4×C47—41no—
204C4⋊C4×C47C2×D411yescharacteristic
205C4⋊C4×C47C2×D411yescharacteristic
206C4⋊C4×C47C2×D411yescharacteristic
207C4⋊C4×C47C2×D411yescharacteristic
208C22⋊C4×C47—21no—
209C22⋊C4×C47—21no—
210C22⋊C4×C47—41no—
211C22⋊C4×C47—41no—
212C22⋊C4×C47—41no—
213C22⋊C4×C47—41no—
214C42×C47—21no—
215C42×C47—21no—
216C42×C47C2411yescharacteristic
217C23×C47—21no—
218C23×C47—21no—
219C23×C47—41no—
220C23×C47—41no—
221Q8×C47—21no—
222Q8×C47—21no—
223Q8×C47—21no—
224Q8×C47—41no—
225Q8×C47—41no—
226Q8×C47—82no—
227Q8×C47—81no—
228Q8×C47AGL(1,ℤ/8)12yes—
229D4×C47—21no—
230D4×C47—21no—
231D4×C47—21no—
232D4×C47—41no—
233D4×C47—41no—
234D4×C47—41no—
235D4×C47—41no—
236D4×C47—41no—
237D4×C47—41no—
238D4×C47—41no—
239D4×C47—41no—
240D4×C47—82no—
241D4×C47—81no—
242D4×C47—81no—
243D4×C47—82no—
244D4×C47—161no—
245D4×C47—161no—
246D4×C47#13512yescomplemented
247C2×C4×C47—21no—
248C2×C4×C47—21no—
249C2×C4×C47—21no—
250C2×C4×C47—21no—
251C2×C4×C47—21no—
252C2×C4×C47—21no—
253C2×C4×C47—41no—
254C2×C4×C47—41no—
255C2×C4×C47—41no—
256C2×C4×C47—41no—
257C2×C4×C47—41no—
258C2×C4×C47—41no—
259C2×C4×C47—82no—
260C2×C4×C47—82no—
261C2×C4×C47—82no—
262C2×C4×C47—161no—
263C2×C4×C47C22×D411yescharacteristic
264C2×C4×C47C22×D411yescharacteristic
265C2×C4×C47H(5,𝔽2)11yescharacteristic
266C8×C47—21no—
267C8×C47—21no—
268C8×C47—21no—
269C8×C47—21no—
270C8×C47—41no—
271C8×C47—41no—
272C8×C47—41no—
273C8×C47—41no—
274C8×C47—41no—
275#19836C4711yesmaximal, characteristic, direct product factor, Sylow
276C22×C47—22no—
277C22×C47—41no—
278C22×C47—41no—
279C22×C47—41no—
280C22×C47—41no—
281C22×C47—41no—
282C22×C47—81no—
283C22×C47—81no—
284C22×C47—81no—
285C22×C47—81no—
286C22×C47—81no—
287C22×C47—81no—
288C22×C47D4211yescharacteristic
289C4×C47—22no—
290C4×C47—21no—
291C4×C47—41no—
292C4×C47—41no—
293C4×C47—41no—
294C4×C47—41no—
295C4×C47—41no—
296C4×C47—81no—
297C4×C47—81no—
298C4×C47C2×#13511yescharacteristic
299C4×C47C2×AGL(1,ℤ/8)11yescharacteristic
300C4×C47#57611yescharacteristic
301C4×C47#57811yescharacteristic
302#3366C2×C4711yescharacteristic, complemented
303#3358C2×C4711yescharacteristic, complemented
304#3299C2×C4711yescharacteristic, complemented
305#3287C2×C4711yescharacteristic, complemented
306#1717C2×C4711yescharacteristic, complemented
307#1702C2×C4711yescharacteristic, complemented
308#1683C2×C4711yescharacteristic, complemented
309#1678C2×C4711yescharacteristic, complemented
310#1667C2×C4711yescharacteristic, complemented
311#1641C2×C4711yescharacteristic, complemented
312#1631C2×C4711yescharacteristic, complemented
313#1627C2×C4711yescharacteristic, complemented
314#1622C2×C4711yescharacteristic, complemented
315#1584C2×C4711yescharacteristic, complemented
316#1580C2×C4711yescharacteristic, complemented
317C2×C47—42no—
318C2×C47—81no—
319C2×C47—161no—
320C2×C47—161no—
321C2×C47#326411yescharacteristic
322C2×C47#328511yescharacteristic
323C2×C47#328811yescharacteristic
324C2×#135—21no—
325#554C22×C4711yescharacteristic
326#550C22×C4711yescharacteristic
327#550C22×C4711yescharacteristic
328D4×Q8C22×C4711yescharacteristic
329#493C22×C4711yescharacteristic
330#492C22×C4711yescharacteristic
331#490—21no—
332#487C22×C4711yescharacteristic
333#486—21no—
334#486C22×C4711yescharacteristic
335#486C22×C4711yescharacteristic
336#486C22×C4711yescharacteristic
337#484—21no—
338#478—21no—
339#477C22×C4711yescharacteristic
340#476C22×C4711yescharacteristic
341#474—21no—
342#474C22×C4711yescharacteristic
343#467—21no—
344#466—21no—
345#462C22×C4711yescharacteristic
346#460C22×C4711yescharacteristic
347#460C22×C4711yescharacteristic
348#459—21no—
349#459—21no—
350#459C22×C4711yescharacteristic
351#459C22×C4711yescharacteristic
352#451—21no—
353#449—21no—
354#449—21no—
355#446C22×C4711yescharacteristic
356C8×Q8C22×C4711yescharacteristic
357#442—21no—
358C4×Q16C22×C4711yescharacteristic
359C4×D8—21no—
360C4×D8C22×C4711yescharacteristic
361C8×D4C22×C4711yescharacteristic
362C8×D4C22×C4711yescharacteristic
363C2×#103—21no—
364#335C22×C4711yescharacteristic
365#334C22×C4711yescharacteristic
366#333C22×C4711yescharacteristic
367#332C22×C4711yescharacteristic
368#331C22×C4711yescharacteristic
369#331C22×C4711yescharacteristic
370Q8⋊C8C22×C4711yescharacteristic
371Q8⋊C8C22×C4711yescharacteristic
372D4⋊C8C22×C4711yescharacteristic
373D4⋊C8C22×C4711yescharacteristic
374#322C22×C4711yescharacteristic
375C47#1983611yescharacteristic, direct product factor, Sylow
376C2×#41—21no—
377C2×#41—21no—
378C22×Q8—21no—
379#135—44no—
380C2×Q16—21no—
381C2×Q16D4×C4711yescharacteristic
382C2×SD16—21no—
383C2×SD16—21no—
384C2×SD16—41no—
385C2×D8—21no—
386C2×D8—21no—
387C2×D8—21no—
388C2×D8—21no—
389C2×D8D4×C4711yescharacteristic
390C22×C8—21no—
391C22×C8—21no—
392C4⋊Q8—21no—
393C4⋊Q8C23×C4711yescharacteristic
394C4⋊Q8C23×C4711yescharacteristic
395#127—21no—
396#127—21no—
397#127C23×C4711yescharacteristic
398#127C23×C4711yescharacteristic
399#125—21no—
400C22⋊Q8—21no—
401C22⋊Q8—21no—
402C22⋊Q8—41no—
403C22⋊Q8—41no—
404#121—21no—
405#121—21no—
406#121—41no—
407#121—41no—
408C4×Q8C23×C4711yescharacteristic
409C4×Q8C23×C4711yescharacteristic
410C4×D4—21no—
411C4×D4—21no—
412C4×D4—21no—
413C4×D4—21no—
414C4×D4C23×C4711yescharacteristic
415C4×D4C23×C4711yescharacteristic
416C2×C4⋊C4—21no—
417#107—21no—
418#107—21no—
419#107D4×C4711yescharacteristic
420#107D4×C4711yescharacteristic
421#106—21no—
422C4⋊C8—21no—
423C4⋊C8—21no—
424C4⋊C8C23×C4711yescharacteristic
425C4⋊C8C23×C4711yescharacteristic
426C4⋊C8C23×C4711yescharacteristic
427C4⋊C8C23×C4711yescharacteristic
428#103—21no—
429#103—21no—
430#103—21no—
431#103—21no—
432#103D4×C4711yescharacteristic
433#103D4×C4711yescharacteristic
434#102—21no—
435#102—21no—
436#102—21no—
437#102—21no—
438#102—21no—
439#102—21no—
440#102—21no—
441#102—21no—
442#102—21no—
443#102—21no—
444#102—41no—
445#102D4×C4711yescharacteristic
446#102D4×C4711yescharacteristic
447C22⋊C8—21no—
448C22⋊C8—21no—
449#97—21no—
450C4×C8—21no—
451C4×C8C23×C4711yescharacteristic
452C4×C8C23×C4711yescharacteristic
453C4×C8C23×C4711yescharacteristic
454#41—42no—
455#41—42no—
456#41—81no—
457#41—81no—
458C2×Q8—21no—
459C2×Q8—21no—
460C2×Q8—41no—
461C2×Q8—42no—
462C2×Q8—81no—
463C2×Q8C2×D4×C4711yescharacteristic
464C2×Q8C2×D4×C4711yescharacteristic
465C2×D4—21no—
466C2×D4—21no—
467C2×D4—21no—
468C2×D4—21no—
469C2×D4—21no—
470C2×D4—21no—
471C2×D4—41no—
472C2×D4—41no—
473C2×D4—41no—
474C2×D4—41no—
475C2×D4C2×D4×C4711yescharacteristic
476C2×D4C2×D4×C4711yescharacteristic
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—41no—
480C22×C4—41no—
481C22×C4—41no—
482C22×C4—41no—
483Q16—22no—
484Q16—81no—
485SD16—42no—
486SD16—42no—
487SD16—82no—
488D8—22no—
489D8—42no—
490D8—42no—
491D8—42no—
492D8—81no—
493C2×C8—21no—
494C2×C8—21no—
495C2×C8—21no—
496C2×C8—21no—
497C2×C8—21no—
498C2×C8—42no—
499C2×C8—81no—
500C2×C8C2×D4×C4711yescharacteristic
501C2×C8C2×D4×C4711yescharacteristic
502C2×C8C2×D4×C4711yescharacteristic
503C2×C8C2×D4×C4711yescharacteristic
504C4⋊C4—21no—
505C4⋊C4—21no—
506C4⋊C4—21no—
507C4⋊C4—21no—
508C4⋊C4—21no—
509C4⋊C4—21no—
510C4⋊C4—41no—
511C4⋊C4—41no—
512C4⋊C4—41no—
513C4⋊C4C2×D4×C4711yescharacteristic
514C4⋊C4C2×D4×C4711yescharacteristic
515C4⋊C4C2×D4×C4711yescharacteristic
516C4⋊C4C2×D4×C4711yescharacteristic
517C22⋊C4—21no—
518C22⋊C4—21no—
519C22⋊C4—41no—
520C22⋊C4—41no—
521C22⋊C4—41no—
522C22⋊C4—41no—
523C42—21no—
524C42—21no—
525C42C24×C4711yescharacteristic
526C23—21no—
527C23—21no—
528C23—41no—
529C23—41no—
530Q8—21no—
531Q8—21no—
532Q8—21no—
533Q8—41no—
534Q8—41no—
535Q8—82no—
536Q8—81no—
537Q8AGL(1,ℤ/8)×C4712yes—
538D4—21no—
539D4—21no—
540D4—21no—
541D4—41no—
542D4—41no—
543D4—41no—
544D4—41no—
545D4—41no—
546D4—41no—
547D4—41no—
548D4—41no—
549D4—82no—
550D4—81no—
551D4—81no—
552D4—82no—
553D4—161no—
554D4—161no—
555D4#135×C4712yescomplemented
556C2×C4—21no—
557C2×C4—21no—
558C2×C4—21no—
559C2×C4—21no—
560C2×C4—21no—
561C2×C4—21no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—82no—
569C2×C4—82no—
570C2×C4—82no—
571C2×C4—161no—
572C2×C4C22×D4×C4711yescharacteristic
573C2×C4C22×D4×C4711yescharacteristic
574C2×C4H(5,𝔽2)×C4711yescharacteristic
575C8—21no—
576C8—21no—
577C8—21no—
578C8—21no—
579C8—41no—
580C8—41no—
581C8—41no—
582C8—41no—
583C8—41no—
584C22—22no—
585C22—41no—
586C22—41no—
587C22—41no—
588C22—41no—
589C22—41no—
590C22—81no—
591C22—81no—
592C22—81no—
593C22—81no—
594C22—81no—
595C22—81no—
596C22D42×C4711yescharacteristic
597C4—21no—
598C4—22no—
599C4—41no—
600C4—41no—
601C4—41no—
602C4—41no—
603C4—41no—
604C4—81no—
605C4—81no—
606C4C2×#135×C4711yescharacteristic
607C4C2×AGL(1,ℤ/8)×C4711yescharacteristic
608C4C47×#57611yescharacteristic
609C4C47×#57811yescharacteristic
610C2—42no—
611C2—81no—
612C2—161no—
613C2—161no—
614C2C47×#326411yescharacteristic
615C2C47×#328511yescharacteristic
616C2C47×#328811yescharacteristic
subgroupG/H
center, socleC22×C47D42
commutator, Frattini, cosocleC42C24×C47
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×#3366C2semidirect
2. C47×#3358C2semidirect
3. C47×#3299C2semidirect
4. C47×#3287C2semidirect
5. C47×#1717C2semidirect
6. C47×#1702C2semidirect
7. C47×#1683C2semidirect
8. C47×#1678C2semidirect
9. C47×#1667C2semidirect
10. C47×#1641C2semidirect
11. C47×#1631C2semidirect
12. C47×#1627C2semidirect
13. C47×#1622C2semidirect
14. C47×#1584C2semidirect
15. C47×#1580C2semidirect
246. D4×C47#135semidirect
275. #19836C47direct (N × H)
302. #3366C2×C47semidirect
303. #3358C2×C47semidirect
304. #3299C2×C47semidirect
305. #3287C2×C47semidirect
306. #1717C2×C47semidirect
307. #1702C2×C47semidirect
308. #1683C2×C47semidirect
309. #1678C2×C47semidirect
310. #1667C2×C47semidirect
311. #1641C2×C47semidirect
312. #1631C2×C47semidirect
313. #1627C2×C47semidirect
314. #1622C2×C47semidirect
315. #1584C2×C47semidirect
316. #1580C2×C47semidirect
375. C47#19836direct (N × H)
555. D4#135×C47semidirect

Maximal subgroups

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

subgroupindex
C47×#33662
C47×#33582
C47×#32992
C47×#32872
C47×#17172
C47×#17022
C47×#16832
C47×#16782
C47×#16672
C47×#16412
C47×#16312
C47×#16272
C47×#16222
C47×#15842
C47×#15802
#1983647