Finite Group Databasebeta

← #25088205

Subgroups — #25088205

Order 11008.

668 conjugacy classes of subgroups.

The subgroup lattice has 614 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19147313C211yesmaximal, characteristic, complemented
2#19147010C211yesmaximal, characteristic, complemented
3#19146837C211yesmaximal, characteristic
4#19134194C211yesmaximal, characteristic, complemented
5#19134144C211yesmaximal, characteristic, complemented
6#19134133C211yesmaximal, characteristic, complemented
7#19133970C211yesmaximal, characteristic, complemented
8#19133933C211yesmaximal, characteristic, complemented
9#19133821C211yesmaximal, characteristic, complemented
10#19133774C211yesmaximal, characteristic, complemented
11#19133760C211yesmaximal, characteristic, complemented
12#19133704C211yesmaximal, characteristic, complemented
13#19133486C211yesmaximal, characteristic, complemented
14C8×#10621882C211yesmaximal, characteristic, complemented
15D4×SD16×C43C211yesmaximal, characteristic, complemented
16#14583622C2211yescharacteristic, complemented
17#14583614C2211yescharacteristic
18#14583297C2211yescharacteristic, complemented
19#14583261—21no—
20#14583251C2211yescharacteristic, complemented
21#14583251C2211yescharacteristic, complemented
22#14583245C2211yescharacteristic
23#14583245C2211yescharacteristic
24#14583238—21no—
25#14583222—21no—
26#14583220—21no—
27#14583194C2211yescharacteristic, complemented
28#14583191—21no—
29#14583189C2211yescharacteristic
30#14583179C2211yescharacteristic
31#14583176C2211yescharacteristic, complemented
32#14583150—21no—
33#14583125—21no—
34#14583114—21no—
35#14583104C2211yescharacteristic
36#14583091C2211yescharacteristic
37#14583033—21no—
38#14583030C2211yescharacteristic, complemented
39#14582999—21no—
40C4×#10621882C2211yescharacteristic
41#14582977C2211yescharacteristic
42C8×D172C2211yescharacteristic, complemented
43#14582934—21no—
44#14582904—21no—
45#14582651C2211yescharacteristic, complemented
46#14582650C2211yescharacteristic, complemented
47#14582647C2211yescharacteristic, complemented
48#14582645C2211yescharacteristic, complemented
49#14582644C2211yescharacteristic, complemented
50#14582643C2211yescharacteristic
51Q8⋊(C43⋊C8)C2211yescharacteristic, complemented
52D4⋊(C43⋊C8)C2211yescharacteristic
53D4⋊(C43⋊C8)C2211yescharacteristic
54#14582626C2211yescharacteristic, complemented
55C8×C43⋊C8C2211yescharacteristic, 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×#10621882—21no—
69C2×#10621882D411yescharacteristic
70C2×#10621877—21no—
71C2×C8×D43—21no—
72#13063325C2311yescharacteristic
73#13063325C2311yescharacteristic
74#13063320—41no—
75#13063313—21no—
76#13063311—41no—
77#13063301—21no—
78#13063299—21no—
79#13063296—21no—
80C4×Dic86—21no—
81C4×D172C2311yescharacteristic
82#13063284—21no—
83#13063283—21no—
84#13063283—21no—
85#13063258—21no—
86#13063258—21no—
87#13063258—21no—
88#13063258D411yescharacteristic
89#13063257—21no—
90#13063257—21no—
91#13063256—21no—
92C4⋊(C43⋊C8)—21no—
93C4⋊(C43⋊C8)C2311yescharacteristic
94C4⋊(C43⋊C8)C2311yescharacteristic
95C4⋊(C43⋊C8)C2311yescharacteristic
96#13063249—21no—
97#13063248—21no—
98#13063248—21no—
99#13063248—21no—
100#13063248—41no—
101#13063246—21no—
102#13063246—21no—
103#13063246—21no—
104#13063246—21no—
105#13063246—21no—
106#13063246—41no—
107#13063246D411yescharacteristic
108#13063245—21no—
109#13063245D411yescharacteristic
110C22⋊(C43⋊C8)—21no—
111(C2×D43)⋊C8—21no—
112#13063236—21no—
113C4×C43⋊C8C2311yescharacteristic
114C4×C43⋊C8C2311yescharacteristic
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—
165C2×C22⋊D43—41no—
166C2×D172C2×D411yescharacteristic
167C2×C4×D43—21no—
168C2×Dic86—21no—
169C2×Dic86—21no—
170SD16×C43—22no—
171SD16×C43—42no—
172SD16×C43—42no—
173SD16×C43—42no—
174SD16×C43—81no—
175C2×C8×C43—21no—
176C2×C8×C43—42no—
177C2×C8×C43C2×D411yescharacteristic
178C2×C8×C43C2×D411yescharacteristic
179C4⋊C4×C43—21no—
180C4⋊C4×C43—21no—
181C4⋊C4×C43—21no—
182C4⋊C4×C43—41no—
183C4⋊C4×C43C2×D411yescharacteristic
184C4⋊C4×C43C2×D411yescharacteristic
185C4⋊C4×C43C2×D411yescharacteristic
186C22⋊C4×C43—21no—
187C22⋊C4×C43—21no—
188C22⋊C4×C43—41no—
189C22⋊C4×C43—41no—
190C42×C43—21no—
191C42×C43C2411yescharacteristic
192C22⋊Dic43—41no—
193#10621883—42no—
194#10621882—22no—
195#10621882—81no—
196(C2×D43)⋊C4—21no—
197(C2×D43)⋊C4—41no—
198(C2×D43)⋊C4—41no—
199(C2×D43)⋊C4—41no—
200C4⋊Dic43—21no—
201C4⋊Dic43—21no—
202C4⋊Dic43—21no—
203C4⋊Dic43—21no—
204C4⋊Dic43C2×D411yescharacteristic
205Dic43⋊C4—41no—
206C4×Dic43—41no—
207C4×Dic43—41no—
208#10621877—81no—
209C2×C43⋊C8—21no—
210C2×C43⋊C8—21no—
211C2×C43⋊C8—21no—
212C2×C43⋊C8—21no—
213C2×C43⋊C8C2×D411yescharacteristic
214C2×C43⋊C8C2×D411yescharacteristic
215C8×D43—42no—
216C23×C43—21no—
217C23×C43—21no—
218C23×C43—41no—
219C23×C43—82no—
220C23×C43—82no—
221C23×C43—161no—
222C22×D43—21no—
223Q8×C43—21no—
224Q8×C43—21no—
225Q8×C43—41no—
226Q8×C43—41no—
227Q8×C43—82no—
228D4×C43—21no—
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—
239C2×C4×C43—21no—
240C2×C4×C43—21no—
241C2×C4×C43—21no—
242C2×C4×C43—21no—
243C2×C4×C43—41no—
244C2×C4×C43—41no—
245C2×C4×C43—41no—
246C2×C4×C43—41no—
247C2×C4×C43—41no—
248C2×C4×C43—82no—
249C2×C4×C43C22×D411yescharacteristic
250C2×C4×C43C22×D411yescharacteristic
251C2×C4×C43H(5,𝔽2)11yescharacteristic
252C22⋊D43—161no—
253C2×Dic43—21no—
254C2×Dic43—41no—
255C2×Dic43—41no—
256D172—21no—
257D172—21no—
258C4×D43—41no—
259C4×D43—41no—
260Dic86—41no—
261Dic86—41no—
262Dic86—81no—
263C8×C43—21no—
264C8×C43—41no—
265C8×C43AGL(1,ℤ/8)12yes—
266C43⋊C8—21no—
267C43⋊C8—21no—
268C43⋊C8—41no—
269C43⋊C8—41no—
270C43⋊C8—41no—
271C43⋊C8—41no—
272#19910—431nomaximal, Sylow
273C22×C43—22no—
274C22×C43—41no—
275C22×C43—41no—
276C22×C43—41no—
277C22×C43—41no—
278C22×C43—41no—
279C22×C43—81no—
280C22×C43—81no—
281C22×C43—81no—
282C22×C43—164no—
283C22×C43D4211yescharacteristic
284C2×D43—41no—
285C2×D43—41no—
286C2×D43—41no—
287C4×C43—21no—
288C4×C43—41no—
289C4×C43—41no—
290C4×C43—41no—
291C4×C43—41no—
292C4×C43—81no—
293C4×C43C2×#13511yescharacteristic
294C4×C43C2×AGL(1,ℤ/8)11yescharacteristic
295C4×C43#57711yescharacteristic
296C4×C43#57711yescharacteristic
297Dic43—41no—
298Dic43—81no—
299Dic43—81no—
300#3367—431no—
301#3340—431no—
302#3325—431no—
303D4×SD16D4311yescharacteristic, complemented
304#1708—431no—
305#1699—431no—
306#1698—431no—
307#1671—431no—
308#1665—431no—
309#1646—431no—
310#1639—431no—
311#1637—431no—
312#1628—431no—
313#1590—431no—
314C8×D8—431no—
315C2×C43—42no—
316C2×C43—81no—
317C2×C43—161no—
318C2×C43#327211yescharacteristic
319C2×C43#328211yescharacteristic
320C2×C43#329011yescharacteristic
321D43—81no—
322C22×SD16—21no—
323#556—431no—
324#555—431no—
325D4×Q8C2×D4311yescharacteristic
326D42C2×D4311yescharacteristic
327#498—431no—
328#492C2×D4311yescharacteristic
329#489—861no—
330#487—431no—
331#487—431no—
332#486—431no—
333#486—431no—
334#485—861no—
335#482—861no—
336#482—861no—
337#477—431no—
338#477—861no—
339#476—431no—
340#474—431no—
341#474—431no—
342#469—861no—
343#465—21no—
344#465—861no—
345#463—861no—
346#461—431no—
347#461C2×D4311yescharacteristic
348#460C2×D4311yescharacteristic
349#459—431no—
350#450—21no—
351#448—21no—
352#447—861no—
353#446—431no—
354#440—861no—
355C4×SD16C2×D4311yescharacteristic
356C4×D8—431no—
357#436—431no—
358C8×D4—431no—
359C8×D4C2×D4311yescharacteristic
360#427—861no—
361#418—861no—
362#335—431no—
363#334—431no—
364#333—431no—
365#332—431no—
366#332—431no—
367#331—431no—
368Q8⋊C8—431no—
369D4⋊C8—431no—
370D4⋊C8—431no—
371D4⋊C8—431no—
372C82—431no—
373C43#1991011yescharacteristic, complemented, Sylow
374C22×Q8—21no—
375C22×D4—21no—
376C22×D4—21no—
377C2×SD16—21no—
378C2×SD16—21no—
379C2×SD16—21no—
380C2×SD16—21no—
381C2×SD16—44no—
382C2×SD16—861no—
383C2×SD16C22⋊D4311yescharacteristic
384C2×D8—431no—
385C2×D8—861no—
386C2×M16—861no—
387C22×C8—21no—
388C22×C8—861no—
389C4⋊Q8—21no—
390C4⋊Q8—431no—
391C4⋊Q8—431no—
392C4⋊Q8C22×D4311yescharacteristic
393#127C22×D4311yescharacteristic
394#126—1721no—
395#124—861no—
396#124—1721no—
397C22⋊Q8—21no—
398C22⋊Q8—41no—
399C22⋊Q8—861no—
400#121—21no—
401#121—21no—
402#121—861no—
403#121—861no—
404#120—41no—
405C4×Q8—861no—
406C4×Q8C22×D4311yescharacteristic
407C4×D4—21no—
408C4×D4—431no—
409C4×D4C22×D4311yescharacteristic
410C4×D4C22×D4311yescharacteristic
411#117—861no—
412#117—861no—
413#117—861no—
414#107—431no—
415#107—861no—
416#107—861no—
417#107—861no—
418#106—861no—
419#106—861no—
420#106—861no—
421#106C22⋊D4311yescharacteristic
422C4⋊C8—431no—
423C4⋊C8—431no—
424C4⋊C8—431no—
425C4⋊C8—861no—
426C4⋊C8C22×D4311yescharacteristic
427#103—21no—
428#103—861no—
429#103—861no—
430#103—861no—
431#103—861no—
432#103—1721no—
433#103C22⋊D4311yescharacteristic
434#102—21no—
435#102—431no—
436#102—431no—
437#102—861no—
438#102—861no—
439#102—861no—
440#102—861no—
441#102—861no—
442#102—861no—
443#102—1721no—
444#102C22⋊D4311yescharacteristic
445C22⋊C8—21no—
446C22⋊C8—861no—
447C22⋊C8—861no—
448#97—861no—
449C4×C8—431no—
450C4×C8—431no—
451C4×C8C22×D4311yescharacteristic
452C24—41no—
453C2×Q8—21no—
454C2×Q8—41no—
455C2×Q8—42no—
456C2×Q8—81no—
457C2×Q8—861no—
458C2×Q8—861no—
459C2×Q8C2×C22⋊D4311yescharacteristic
460C2×D4—21no—
461C2×D4—21no—
462C2×D4—21no—
463C2×D4—41no—
464C2×D4—41no—
465C2×D4—42no—
466C2×D4—42no—
467C2×D4—81no—
468C2×D4—81no—
469C2×D4—431no—
470C2×D4—1721no—
471C2×D4D4×D4311yescharacteristic
472C2×D4C2×C22⋊D4311yescharacteristic
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—41no—
476C22×C4—861no—
477SD16—22no—
478SD16—42no—
479SD16—42no—
480SD16—42no—
481SD16—81no—
482SD16—1722no—
483D8—862no—
484D8—3441no—
485M16—3441no—
486C2×C8—21no—
487C2×C8—42no—
488C2×C8—431no—
489C2×C8—431no—
490C2×C8—861no—
491C2×C8—861no—
492C2×C8—861no—
493C2×C8—861no—
494C2×C8—1722no—
495C2×C8C2×C22⋊D4311yescharacteristic
496C2×C8C2×C22⋊D4311yescharacteristic
497C4⋊C4—21no—
498C4⋊C4—21no—
499C4⋊C4—21no—
500C4⋊C4—41no—
501C4⋊C4—431no—
502C4⋊C4—861no—
503C4⋊C4—861no—
504C4⋊C4—861no—
505C4⋊C4—861no—
506C4⋊C4—1721no—
507C4⋊C4D4×D4311yescharacteristic
508C4⋊C4C2×C22⋊D4311yescharacteristic
509C4⋊C4C2×C22⋊D4311yescharacteristic
510C22⋊C4—21no—
511C22⋊C4—21no—
512C22⋊C4—41no—
513C22⋊C4—41no—
514C22⋊C4—861no—
515C22⋊C4—1721no—
516C22⋊C4—1721no—
517C22⋊C4—1721no—
518C22⋊C4—1721no—
519C42—21no—
520C42—1721no—
521C42—1721no—
522C42C23×D4311yescharacteristic
523C23—21no—
524C23—21no—
525C23—41no—
526C23—82no—
527C23—82no—
528C23—161no—
529C23—861no—
530Q8—21no—
531Q8—21no—
532Q8—41no—
533Q8—41no—
534Q8—82no—
535Q8—3441no—
536Q8—1721no—
537Q8—1721no—
538D4—21no—
539D4—21no—
540D4—21no—
541D4—41no—
542D4—41no—
543D4—41no—
544D4—41no—
545D4—81no—
546D4—82no—
547D4—82no—
548D4—861no—
549D4—861no—
550D4—6881no—
551D4#1306334612yes—
552C2×C4—21no—
553C2×C4—21no—
554C2×C4—21no—
555C2×C4—21no—
556C2×C4—41no—
557C2×C4—41no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4—82no—
562C2×C4—861no—
563C2×C4—1721no—
564C2×C4—1721no—
565C2×C4—1721no—
566C2×C4—1721no—
567C2×C4C2×D4×D4311yescharacteristic
568C2×C4C22×C22⋊D4311yescharacteristic
569C2×C4#1306337011yescharacteristic
570C8—21no—
571C8—41no—
572C8—861no—
573C8—861no—
574C8—1721no—
575C8—1721no—
576C8—1721no—
577C8—1721no—
578C8#1306335112yes—
579C22—22no—
580C22—41no—
581C22—41no—
582C22—41no—
583C22—41no—
584C22—41no—
585C22—81no—
586C22—81no—
587C22—81no—
588C22—164no—
589C22—1721no—
590C22—1721no—
591C22—1721no—
592C22D4×C22⋊D4311yescharacteristic
593C4—21no—
594C4—41no—
595C4—41no—
596C4—41no—
597C4—41no—
598C4—81no—
599C4—3441no—
600C4—3441no—
601C4—1721no—
602C4C2×#1306334611yescharacteristic
603C4C2×#1306335111yescharacteristic
604C4#1458370511yescharacteristic
605C4#1458371011yescharacteristic
606C2—42no—
607C2—81no—
608C2—161no—
609C2—3441no—
610C2#1914619111yescharacteristic
611C2#1914630211yescharacteristic
612C2#1914637511yescharacteristic
subgroupG/H
centerC22D4×C22⋊D43
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingD4×SD16×C43C2
socleC22×C43D42
prime radical#19146837C2
hypercenterD4×SD16D43
hypocenterC43#19910
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. #19147313C2semidirect
2. #19147010C2semidirect
4. #19134194C2semidirect
5. #19134144C2semidirect
6. #19134133C2semidirect
7. #19133970C2semidirect
8. #19133933C2semidirect
9. #19133821C2semidirect
10. #19133774C2semidirect
11. #19133760C2semidirect
12. #19133704C2semidirect
13. #19133486C2semidirect
14. C8×#10621882C2semidirect
15. D4×SD16×C43C2semidirect
16. #14583622C22semidirect
18. #14583297C22semidirect
20. #14583251C22semidirect
21. #14583251C22semidirect
27. #14583194C22semidirect
31. #14583176C22semidirect
38. #14583030C22semidirect
42. C8×D172C22semidirect
45. #14582651C22semidirect
46. #14582650C22semidirect
47. #14582647C22semidirect
48. #14582645C22semidirect
49. #14582644C22semidirect
51. Q8⋊(C43⋊C8)C22semidirect
54. #14582626C22semidirect
55. C8×C43⋊C8C22semidirect
303. D4×SD16D43semidirect
373. C43#19910semidirect

Maximal subgroups

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

subgroupindex
#191473132
#191470102
#191468372
#191341942
#191341442
#191341332
#191339702
#191339332
#191338212
#191337742
#191337602
#191337042
#191334862
C8×#106218822
D4×SD16×C432
#1991043