Finite Group Databasebeta

← #25086450

Subgroups — #25086450

Order 11008.

680 conjugacy classes of subgroups.

The subgroup lattice has 620 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19147387C211yesmaximal, characteristic, complemented
2#19147253C211yesmaximal, characteristic, complemented
3#19146419C211yesmaximal, characteristic, complemented
4#19134232C211yesmaximal, characteristic, complemented
5#19134133C211yesmaximal, characteristic, complemented
6#19134034C211yesmaximal, characteristic, complemented
7#19134004C211yesmaximal, characteristic, complemented
8#19133940C211yesmaximal, characteristic, complemented
9#19133800C211yesmaximal, characteristic, complemented
10#19133760C211yesmaximal, characteristic, complemented
11#19133653C211yesmaximal, characteristic, complemented
12#19133649C211yesmaximal, characteristic
13#19133432C211yesmaximal, characteristic, complemented
14#19133407C211yesmaximal, characteristic, complemented
15D4×SD16×C43C211yesmaximal, characteristic, complemented
16#14583634C2211yescharacteristic, complemented
17#14583606C2211yescharacteristic
18#14583275C2211yescharacteristic
19#14583261—21no—
20#14583255—21no—
21#14583251C2211yescharacteristic, complemented
22#14583247C2211yescharacteristic, complemented
23#14583246C2211yescharacteristic, complemented
24#14583245C2211yescharacteristic
25#14583215—21no—
26#14583198—21no—
27#14583194C2211yescharacteristic, complemented
28#14583189C2211yescharacteristic
29#14583186—21no—
30#14583181C2211yescharacteristic, complemented
31#14583126—21no—
32#14583116—21no—
33#14583114—21no—
34#14583096C2211yescharacteristic
35#14583094C2211yescharacteristic
36#14583094C2211yescharacteristic
37#14583050—21no—
38#14583030C2211yescharacteristic, complemented
39C8×Dic86C2211yescharacteristic, complemented
40#14583009—21no—
41C4×#10621883C2211yescharacteristic
42#14582979—21no—
43D4×C43⋊C8C2211yescharacteristic
44C2×#13063246—21no—
45#14582651C2211yescharacteristic, complemented
46#14582650C2211yescharacteristic, complemented
47#14582647C2211yescharacteristic, complemented
48#14582645C2211yescharacteristic, complemented
49#14582643C2211yescharacteristic
50#14582642C2211yescharacteristic, complemented
51Q8⋊(C43⋊C8)C2211yescharacteristic, complemented
52#14582629C2211yescharacteristic, complemented
53D4⋊(C43⋊C8)C2211yescharacteristic
54D4⋊(C43⋊C8)C2211yescharacteristic
55#14582621C2211yescharacteristic, complemented
56C22×SD16×C43—21no—
57D4×Q8×C43C2211yescharacteristic
58D42×C43C2211yescharacteristic
59C43×#492C2211yescharacteristic
60C43×#465—21no—
61C43×#461C2211yescharacteristic
62C43×#460C2211yescharacteristic
63C43×#450—21no—
64C43×#448—21no—
65C4×SD16×C43C2211yescharacteristic
66C8×D4×C43C2211yescharacteristic
67C2×#10621883—21no—
68C2×#10621883D411yescharacteristic
69C2×#10621882—21no—
70C2×#10621882—21no—
71C2×#10621882—41no—
72C22×C43⋊C8—21no—
73#13063325C2311yescharacteristic
74#13063322C2311yescharacteristic
75#13063316—21no—
76#13063314—21no—
77#13063313—21no—
78#13063310—41no—
79#13063304—21no—
80#13063302—41no—
81C4×Dic86C2311yescharacteristic
82C4×D172—21no—
83D4×Dic43—21no—
84#13063287—21no—
85C2×C4⋊Dic43—21no—
86#13063258—21no—
87#13063256—21no—
88#13063256—21no—
89#13063256D411yescharacteristic
90C4⋊(C43⋊C8)—21no—
91C4⋊(C43⋊C8)C2311yescharacteristic
92C4⋊(C43⋊C8)C2311yescharacteristic
93C4⋊(C43⋊C8)C2311yescharacteristic
94Dic43⋊C8—21no—
95#13063249—21no—
96#13063248—21no—
97#13063248—41no—
98#13063248D411yescharacteristic
99#13063247—21no—
100#13063247—21no—
101#13063246—21no—
102#13063246—21no—
103#13063246—21no—
104#13063246—21no—
105#13063246D411yescharacteristic
106#13063245—21no—
107#13063245—21no—
108#13063245—21no—
109#13063245—21no—
110C22⋊(C43⋊C8)—21no—
111#13063236—21no—
112C4×C43⋊C8C2311yescharacteristic
113C4×C43⋊C8C2311yescharacteristic
114C8×Dic43—21no—
115C22×Q8×C43—21no—
116C22×D4×C43—21no—
117C22×D4×C43—21no—
118C2×SD16×C43—21no—
119C2×SD16×C43—21no—
120C2×SD16×C43—21no—
121C2×SD16×C43—21no—
122C2×SD16×C43—44no—
123C2×SD16×C43D411yescharacteristic
124C22×C8×C43—21no—
125C4⋊Q8×C43—21no—
126C4⋊Q8×C43C2311yescharacteristic
127#127×C43C2311yescharacteristic
128C22⋊Q8×C43—21no—
129C22⋊Q8×C43—41no—
130#121×C43—21no—
131#121×C43—21no—
132#120×C43—41no—
133C4×Q8×C43C2311yescharacteristic
134C4×D4×C43—21no—
135C4×D4×C43C2311yescharacteristic
136C4×D4×C43C2311yescharacteristic
137#106×C43D411yescharacteristic
138C4⋊C8×C43C2311yescharacteristic
139#103×C43—21no—
140#103×C43D411yescharacteristic
141#102×C43—21no—
142#102×C43D411yescharacteristic
143C22⋊C8×C43—21no—
144C4×C8×C43C2311yescharacteristic
145C24×C43—41no—
146C2×Q8×C43—21no—
147C2×Q8×C43—41no—
148C2×Q8×C43—42no—
149C2×Q8×C43—81no—
150C2×Q8×C43C2×D411yescharacteristic
151C2×D4×C43—21no—
152C2×D4×C43—21no—
153C2×D4×C43—21no—
154C2×D4×C43—41no—
155C2×D4×C43—41no—
156C2×D4×C43—42no—
157C2×D4×C43—42no—
158C2×D4×C43—81no—
159C2×D4×C43—81no—
160C2×D4×C43C2×D411yescharacteristic
161C2×D4×C43C2×D411yescharacteristic
162C22×C4×C43—21no—
163C22×C4×C43—21no—
164C22×C4×C43—41no—
165C22×Dic43—41no—
166C2×D172—21no—
167C2×D172—21no—
168C2×D172—21no—
169C2×C4×D43—41no—
170C2×Dic86—21no—
171C2×Dic86C2×D411yescharacteristic
172SD16×C43—22no—
173SD16×C43—42no—
174SD16×C43—42no—
175SD16×C43—42no—
176SD16×C43—81no—
177C2×C8×C43—21no—
178C2×C8×C43—42no—
179C2×C8×C43C2×D411yescharacteristic
180C2×C8×C43C2×D411yescharacteristic
181C4⋊C4×C43—21no—
182C4⋊C4×C43—21no—
183C4⋊C4×C43—21no—
184C4⋊C4×C43—41no—
185C4⋊C4×C43C2×D411yescharacteristic
186C4⋊C4×C43C2×D411yescharacteristic
187C4⋊C4×C43C2×D411yescharacteristic
188C22⋊C4×C43—21no—
189C22⋊C4×C43—21no—
190C22⋊C4×C43—41no—
191C22⋊C4×C43—41no—
192C42×C43—21no—
193C42×C43C2411yescharacteristic
194C22⋊Dic43—41no—
195#10621883—22no—
196#10621883—81no—
197#10621882—42no—
198#10621882—42no—
199#10621882—82no—
200(C2×D43)⋊C4—41no—
201(C2×D43)⋊C4—41no—
202(C2×D43)⋊C4—41no—
203C4⋊Dic43—21no—
204C4⋊Dic43—21no—
205C4⋊Dic43—41no—
206C4⋊Dic43C2×D411yescharacteristic
207Dic43⋊C4—21no—
208Dic43⋊C4—41no—
209C4×Dic43—21no—
210C2×C43⋊C8—21no—
211C2×C43⋊C8—21no—
212C2×C43⋊C8—21no—
213C2×C43⋊C8—21no—
214C2×C43⋊C8—81no—
215C2×C43⋊C8C2×D411yescharacteristic
216C2×C43⋊C8C2×D411yescharacteristic
217C23×C43—21no—
218C23×C43—21no—
219C23×C43—41no—
220C23×C43—82no—
221C23×C43—82no—
222C23×C43—161no—
223C22×D43—41no—
224Q8×C43—21no—
225Q8×C43—21no—
226Q8×C43—41no—
227Q8×C43—41no—
228Q8×C43—82no—
229D4×C43—21no—
230D4×C43—21no—
231D4×C43—41no—
232D4×C43—41no—
233D4×C43—41no—
234D4×C43—41no—
235D4×C43—81no—
236D4×C43—82no—
237D4×C43—82no—
238D4×C43#13512yes—
239D4×C43AGL(1,ℤ/8)12yes—
240C2×C4×C43—21no—
241C2×C4×C43—21no—
242C2×C4×C43—21no—
243C2×C4×C43—21no—
244C2×C4×C43—41no—
245C2×C4×C43—41no—
246C2×C4×C43—41no—
247C2×C4×C43—41no—
248C2×C4×C43—41no—
249C2×C4×C43—82no—
250C2×C4×C43C22×D411yescharacteristic
251C2×C4×C43C22×D411yescharacteristic
252C2×C4×C43H(5,𝔽2)11yescharacteristic
253C2×Dic43—21no—
254C2×Dic43—21no—
255C2×Dic43—41no—
256C2×Dic43—161no—
257D172—41no—
258D172—41no—
259D172—41no—
260D172—41no—
261D172—81no—
262C4×D43—161no—
263Dic86—21no—
264Dic86—21no—
265Dic86—81no—
266C8×C43—21no—
267C8×C43—21no—
268C8×C43—41no—
269C43⋊C8—21no—
270C43⋊C8—21no—
271C43⋊C8—41no—
272C43⋊C8—41no—
273C43⋊C8—41no—
274C43⋊C8—41no—
275#19789—431nomaximal, Sylow
276C22×C43—22no—
277C22×C43—22no—
278C22×C43—41no—
279C22×C43—41no—
280C22×C43—41no—
281C22×C43—41no—
282C22×C43—81no—
283C22×C43—81no—
284C22×C43—81no—
285C22×C43—164no—
286C22×C43D4211yescharacteristic
287C2×D43—81no—
288C2×D43—81no—
289C2×D43—81no—
290C4×C43—21no—
291C4×C43—41no—
292C4×C43—41no—
293C4×C43—41no—
294C4×C43—41no—
295C4×C43—81no—
296C4×C43C2×#13511yescharacteristic
297C4×C43C2×AGL(1,ℤ/8)11yescharacteristic
298C4×C43#57711yescharacteristic
299C4×C43#57711yescharacteristic
300Dic43—41no—
301Dic43—41no—
302Dic43—81no—
303#3373—431no—
304#3361—431no—
305#3295—431no—
306D4×SD16D4311yescharacteristic, complemented
307#1717—431no—
308#1698—431no—
309#1681—431no—
310#1677—431no—
311#1666—431no—
312#1643—431no—
313#1637—431no—
314#1620—431no—
315#1619—431no—
316#1582—431no—
317SD16⋊C8—431no—
318C2×C43—42no—
319C2×C43—42no—
320C2×C43—161no—
321C2×C43#326511yescharacteristic
322C2×C43#328211yescharacteristic
323C2×C43#328811yescharacteristic
324D43—161no—
325C22×SD16—21no—
326#559—431no—
327#554—431no—
328D4×Q8C2×D4311yescharacteristic
329D42C2×D4311yescharacteristic
330#493—431no—
331#492C2×D4311yescharacteristic
332#489—861no—
333#488—861no—
334#487—431no—
335#486—431no—
336#486—431no—
337#486—431no—
338#481—861no—
339#478—861no—
340#477—431no—
341#476—431no—
342#476—861no—
343#475—431no—
344#465—21no—
345#465—861no—
346#463—861no—
347#463—861no—
348#461C2×D4311yescharacteristic
349#460—431no—
350#460C2×D4311yescharacteristic
351#459—431no—
352#459—431no—
353#450—21no—
354#450—861no—
355#448—21no—
356#446—431no—
357C8×Q8—431no—
358#442—861no—
359C4×SD16—431no—
360C4×SD16C2×D4311yescharacteristic
361C4×D8—861no—
362C8×D4—431no—
363C8×D4C2×D4311yescharacteristic
364C2×#102—861no—
365#335—431no—
366#334—431no—
367#333—431no—
368#332—431no—
369#331—431no—
370#331—431no—
371Q8⋊C8—431no—
372Q8⋊C8—431no—
373D4⋊C8—431no—
374D4⋊C8—431no—
375#322—431no—
376C43#1978911yescharacteristic, complemented, Sylow
377C22×Q8—21no—
378C22×D4—21no—
379C22×D4—21no—
380C2×SD16—21no—
381C2×SD16—21no—
382C2×SD16—21no—
383C2×SD16—21no—
384C2×SD16—44no—
385C2×SD16—431no—
386C2×SD16—861no—
387C2×SD16C22⋊D4311yescharacteristic
388C2×D8—861no—
389C2×D8—861no—
390C2×D8—1721no—
391C22×C8—21no—
392C22×C8—861no—
393C4⋊Q8—21no—
394C4⋊Q8—431no—
395C4⋊Q8C22×D4311yescharacteristic
396#127—431no—
397#127C22×D4311yescharacteristic
398#125—861no—
399#124—861no—
400#124—861no—
401#123—1721no—
402C22⋊Q8—21no—
403C22⋊Q8—41no—
404C22⋊Q8—861no—
405C22⋊Q8—1721no—
406#121—21no—
407#121—21no—
408#120—41no—
409C4×Q8—431no—
410C4×Q8C22×D4311yescharacteristic
411C4×D4—21no—
412C4×D4—861no—
413C4×D4—861no—
414C4×D4—861no—
415C4×D4C22×D4311yescharacteristic
416C4×D4C22×D4311yescharacteristic
417C2×C4⋊C4—861no—
418#107—861no—
419#106—431no—
420#106—861no—
421#106—861no—
422#106C22⋊D4311yescharacteristic
423C4⋊C8—431no—
424C4⋊C8—431no—
425C4⋊C8—431no—
426C4⋊C8—861no—
427C4⋊C8—861no—
428C4⋊C8C22×D4311yescharacteristic
429#103—21no—
430#103—431no—
431#103—861no—
432#103—861no—
433#103—1721no—
434#103C22⋊D4311yescharacteristic
435#102—21no—
436#102—431no—
437#102—861no—
438#102—861no—
439#102—861no—
440#102—861no—
441#102—861no—
442#102—861no—
443#102—861no—
444#102—861no—
445#102—861no—
446#102—861no—
447#102C22⋊D4311yescharacteristic
448C22⋊C8—21no—
449C22⋊C8—861no—
450#97—861no—
451C4×C8—431no—
452C4×C8—431no—
453C4×C8—861no—
454C4×C8C22×D4311yescharacteristic
455C24—41no—
456C2×Q8—21no—
457C2×Q8—41no—
458C2×Q8—42no—
459C2×Q8—81no—
460C2×Q8—431no—
461C2×Q8—861no—
462C2×Q8C2×C22⋊D4311yescharacteristic
463C2×D4—21no—
464C2×D4—21no—
465C2×D4—21no—
466C2×D4—41no—
467C2×D4—41no—
468C2×D4—42no—
469C2×D4—42no—
470C2×D4—81no—
471C2×D4—81no—
472C2×D4—861no—
473C2×D4—861no—
474C2×D4—861no—
475C2×D4D4×D4311yescharacteristic
476C2×D4C2×C22⋊D4311yescharacteristic
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—41no—
480C22×C4—1721no—
481C22×C4—1721no—
482SD16—22no—
483SD16—42no—
484SD16—42no—
485SD16—42no—
486SD16—81no—
487SD16—862no—
488SD16—3441no—
489D8—3442no—
490D8—1722no—
491D8—1722no—
492C2×C8—21no—
493C2×C8—42no—
494C2×C8—431no—
495C2×C8—431no—
496C2×C8—861no—
497C2×C8—861no—
498C2×C8—861no—
499C2×C8—861no—
500C2×C8—3441no—
501C2×C8C2×C22⋊D4311yescharacteristic
502C2×C8C2×C22⋊D4311yescharacteristic
503C4⋊C4—21no—
504C4⋊C4—21no—
505C4⋊C4—21no—
506C4⋊C4—41no—
507C4⋊C4—431no—
508C4⋊C4—861no—
509C4⋊C4—861no—
510C4⋊C4—861no—
511C4⋊C4—1721no—
512C4⋊C4—1721no—
513C4⋊C4D4×D4311yescharacteristic
514C4⋊C4C2×C22⋊D4311yescharacteristic
515C4⋊C4C2×C22⋊D4311yescharacteristic
516C22⋊C4—21no—
517C22⋊C4—21no—
518C22⋊C4—41no—
519C22⋊C4—41no—
520C22⋊C4—1721no—
521C22⋊C4—1721no—
522C22⋊C4—1721no—
523C22⋊C4—1721no—
524C42—21no—
525C42—861no—
526C42C23×D4311yescharacteristic
527C23—21no—
528C23—21no—
529C23—41no—
530C23—82no—
531C23—82no—
532C23—161no—
533C23—1721no—
534Q8—21no—
535Q8—21no—
536Q8—41no—
537Q8—41no—
538Q8—82no—
539Q8—861no—
540Q8—861no—
541Q8—3441no—
542D4—21no—
543D4—21no—
544D4—41no—
545D4—41no—
546D4—41no—
547D4—41no—
548D4—81no—
549D4—82no—
550D4—82no—
551D4—3441no—
552D4—1721no—
553D4—1721no—
554D4—1721no—
555D4—1721no—
556D4#1306334612yes—
557D4#1306335112yes—
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—82no—
568C2×C4—861no—
569C2×C4—861no—
570C2×C4—1721no—
571C2×C4—6881no—
572C2×C4—6881no—
573C2×C4C2×D4×D4311yescharacteristic
574C2×C4C22×C22⋊D4311yescharacteristic
575C2×C4#1306337011yescharacteristic
576C8—21no—
577C8—21no—
578C8—41no—
579C8—861no—
580C8—861no—
581C8—1721no—
582C8—1721no—
583C8—1721no—
584C8—1721no—
585C22—22no—
586C22—22no—
587C22—41no—
588C22—41no—
589C22—41no—
590C22—41no—
591C22—81no—
592C22—81no—
593C22—81no—
594C22—164no—
595C22—3441no—
596C22—3441no—
597C22—3441no—
598C22D4×C22⋊D4311yescharacteristic
599C4—21no—
600C4—41no—
601C4—41no—
602C4—41no—
603C4—41no—
604C4—81no—
605C4—3441no—
606C4—1721no—
607C4—1721no—
608C4C2×#1306334611yescharacteristic
609C4C2×#1306335111yescharacteristic
610C4#1458370511yescharacteristic
611C4#1458371011yescharacteristic
612C2—42no—
613C2—42no—
614C2—161no—
615C2—6881no—
616C2#1914608611yescharacteristic
617C2#1914630211yescharacteristic
618C2#1914635711yescharacteristic
subgroupG/H
centerC22D4×C22⋊D43
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingD4×SD16×C43C2
socleC22×C43D42
prime radical#19133649C2
hypercenterD4×SD16D43
hypocenterC43#19789
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ D4×SD16

Complements

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

NH ≅ G/Ntype
1. #19147387C2semidirect
2. #19147253C2semidirect
3. #19146419C2semidirect
4. #19134232C2semidirect
5. #19134133C2semidirect
6. #19134034C2semidirect
7. #19134004C2semidirect
8. #19133940C2semidirect
9. #19133800C2semidirect
10. #19133760C2semidirect
11. #19133653C2semidirect
13. #19133432C2semidirect
14. #19133407C2semidirect
15. D4×SD16×C43C2semidirect
16. #14583634C22semidirect
21. #14583251C22semidirect
22. #14583247C22semidirect
23. #14583246C22semidirect
27. #14583194C22semidirect
30. #14583181C22semidirect
38. #14583030C22semidirect
39. C8×Dic86C22semidirect
45. #14582651C22semidirect
46. #14582650C22semidirect
47. #14582647C22semidirect
48. #14582645C22semidirect
50. #14582642C22semidirect
51. Q8⋊(C43⋊C8)C22semidirect
52. #14582629C22semidirect
55. #14582621C22semidirect
306. D4×SD16D43semidirect
376. C43#19789semidirect

Maximal subgroups

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

subgroupindex
#191473872
#191472532
#191464192
#191342322
#191341332
#191340342
#191340042
#191339402
#191338002
#191337602
#191336532
#191336492
#191334322
#191334072
D4×SD16×C432
#1978943