Finite Group Databasebeta

← #25087982

Subgroups — #25087982

Order 11008.

684 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#19147505C211yesmaximal, characteristic, complemented
2#19147264C211yesmaximal, characteristic, complemented
3#19146211C211yesmaximal, characteristic
4#19134186C211yesmaximal, characteristic, complemented
5#19134116C211yesmaximal, characteristic, complemented
6#19134077C211yesmaximal, characteristic, complemented
7#19134008C211yesmaximal, characteristic, complemented
8#19134004C211yesmaximal, characteristic, complemented
9#19133721C211yesmaximal, characteristic, complemented
10#19133711C211yesmaximal, characteristic, complemented
11#19133672C211yesmaximal, characteristic, complemented
12#19133667C211yesmaximal, characteristic, complemented
13#19133486C211yesmaximal, characteristic, complemented
14C8×#10621883C211yesmaximal, characteristic, complemented
15C43×#3295C211yesmaximal, characteristic, complemented
16C2×#13063351—21no—
17Q8×Dic86C2211yescharacteristic, complemented
18#14583570C2211yescharacteristic
19#14583309—21no—
20#14583302C2211yescharacteristic, complemented
21#14583275C2211yescharacteristic
22#14583273C2211yescharacteristic, complemented
23#14583271C2211yescharacteristic
24#14583246C2211yescharacteristic, complemented
25#14583244—21no—
26#14583203—21no—
27#14583191C2211yescharacteristic, complemented
28#14583189C2211yescharacteristic
29#14583189C2211yescharacteristic
30#14583188—21no—
31#14583179—21no—
32#14583150—21no—
33#14583099C2211yescharacteristic, complemented
34#14583097—21no—
35#14583096C2211yescharacteristic
36#14583094C2211yescharacteristic
37#14583042—21no—
38#14583033—21no—
39#14583030C2211yescharacteristic, complemented
40C8×Dic86C2211yescharacteristic, complemented
41#14582999—21no—
42C4×#10621883C2211yescharacteristic
43#14582984—21no—
44#14582977C2211yescharacteristic
45#14582650C2211yescharacteristic, complemented
46#14582649C2211yescharacteristic, complemented
47#14582648C2211yescharacteristic, complemented
48#14582647C2211yescharacteristic, complemented
49#14582643C2211yescharacteristic
50#14582642C2211yescharacteristic, complemented
51Q8⋊(C43⋊C8)C2211yescharacteristic, complemented
52#14582629C2211yescharacteristic, complemented
53D4⋊(C43⋊C8)C2211yescharacteristic
54D4⋊(C43⋊C8)C2211yescharacteristic
55C8×C43⋊C8C2211yescharacteristic, complemented
56C43×#554C2211yescharacteristic
57D42×C43C2211yescharacteristic
58C43×#486C2211yescharacteristic
59C43×#481—21no—
60C43×#476C2211yescharacteristic
61C43×#465—21no—
62C43×#460C2211yescharacteristic
63C43×#450—21no—
64C4×SD16×C43C2211yescharacteristic
65C8×D4×C43C2211yescharacteristic
66C2×#102×C43—21no—
67C2×#10621898—21no—
68#13063351—44no—
69C2×#10621883—21no—
70C2×#10621883—41no—
71C2×#10621883D411yescharacteristic
72C2×#10621884—21no—
73C2×#10621884—41no—
74C2×#10621882—21no—
75C2×#10621882—21no—
76C2×#10621882—21no—
77C2×#10621877—21no—
78#13063325—21no—
79#13063325C2311yescharacteristic
80#13063324—21no—
81#13063324—41no—
82#13063322C2311yescharacteristic
83#13063321—21no—
84#13063299—21no—
85#13063298—41no—
86Q8×Dic43—21no—
87C4×Dic86—21no—
88C4×Dic86C2311yescharacteristic
89#13063287—21no—
90#13063258—21no—
91#13063258—21no—
92#13063258—21no—
93#13063256—21no—
94#13063256—21no—
95#13063256D411yescharacteristic
96C4⋊(C43⋊C8)—21no—
97C4⋊(C43⋊C8)C2311yescharacteristic
98C4⋊(C43⋊C8)C2311yescharacteristic
99C4⋊(C43⋊C8)C2311yescharacteristic
100Dic43⋊C8—21no—
101#13063248—21no—
102#13063248D411yescharacteristic
103#13063247—21no—
104#13063247—21no—
105#13063246—21no—
106#13063246—21no—
107#13063246—21no—
108#13063246D411yescharacteristic
109#13063245—21no—
110#13063245—21no—
111C22⋊(C43⋊C8)—21no—
112#13063236—21no—
113C4×C43⋊C8C2311yescharacteristic
114C4×C43⋊C8C2311yescharacteristic
115C8×Dic43—21no—
116C22×D4×C43—21no—
117C22×D4×C43—21no—
118C2×SD16×C43—21no—
119C2×SD16×C43D411yescharacteristic
120C22×C8×C43—21no—
121C4⋊Q8×C43C2311yescharacteristic
122#127×C43C2311yescharacteristic
123#125×C43—21no—
124C22⋊Q8×C43—21no—
125C22⋊Q8×C43—41no—
126#121×C43—21no—
127#121×C43—21no—
128#120×C43—41no—
129C4×Q8×C43C2311yescharacteristic
130C4×D4×C43—21no—
131C4×D4×C43C2311yescharacteristic
132C4×D4×C43C2311yescharacteristic
133C2×C4⋊C4×C43—21no—
134#106×C43—21no—
135#106×C43D411yescharacteristic
136C4⋊C8×C43C2311yescharacteristic
137#103×C43D411yescharacteristic
138#102×C43—21no—
139#102×C43—21no—
140#102×C43—21no—
141#102×C43—21no—
142#102×C43D411yescharacteristic
143C22⋊C8×C43—21no—
144C4×C8×C43C2311yescharacteristic
145C24×C43—41no—
146C2×Q8×C43—21no—
147C2×Q8×C43C2×D411yescharacteristic
148C2×D4×C43—21no—
149C2×D4×C43—21no—
150C2×D4×C43—21no—
151C2×D4×C43—41no—
152C2×D4×C43—41no—
153C2×D4×C43—42no—
154C2×D4×C43—42no—
155C2×D4×C43—81no—
156C2×D4×C43—81no—
157C2×D4×C43C2×D411yescharacteristic
158C2×D4×C43C2×D411yescharacteristic
159C22×C4×C43—21no—
160C22×C4×C43—21no—
161C22×C4×C43—41no—
162C2×C22⋊D43—41no—
163C2×C22⋊D43—41no—
164#10621898—42no—
165#10621898—81no—
166C2×D172—21no—
167C2×D172—21no—
168C2×D172—21no—
169C2×C4×D43—41no—
170C2×Dic86—21no—
171C2×Dic86—41no—
172C2×Dic86C2×D411yescharacteristic
173SD16×C43—41no—
174SD16×C43—81no—
175C2×C8×C43—21no—
176C2×C8×C43—81no—
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×C43—41no—
184C4⋊C4×C43C2×D411yescharacteristic
185C4⋊C4×C43C2×D411yescharacteristic
186C4⋊C4×C43C2×D411yescharacteristic
187C22⋊C4×C43—21no—
188C22⋊C4×C43—21no—
189C22⋊C4×C43—41no—
190C22⋊C4×C43—41no—
191C42×C43—21no—
192C42×C43C2411yescharacteristic
193#10621884—42no—
194#10621884—82no—
195#10621883—42no—
196#10621883—82no—
197#10621883SD1614yescomplemented
198#10621882—42no—
199#10621882—42no—
200#10621882—81no—
201(C2×D43)⋊C4—41no—
202C4⋊Dic43—21no—
203C4⋊Dic43—21no—
204C4⋊Dic43—41no—
205C4⋊Dic43C2×D411yescharacteristic
206Dic43⋊C4—21no—
207Dic43⋊C4—41no—
208C4×Dic43—21no—
209C4×Dic43—41no—
210#10621877—42no—
211C2×C43⋊C8—21no—
212C2×C43⋊C8—21no—
213C2×C43⋊C8—21no—
214C2×C43⋊C8—21no—
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—81no—
227D4×C43—21no—
228D4×C43—21no—
229D4×C43—21no—
230D4×C43—41no—
231D4×C43—41no—
232D4×C43—41no—
233D4×C43—41no—
234D4×C43—81no—
235D4×C43—82no—
236D4×C43—82no—
237D4×C43C2×SD1612yes—
238C2×C4×C43—21no—
239C2×C4×C43—21no—
240C2×C4×C43—21no—
241C2×C4×C43—21no—
242C2×C4×C43—41no—
243C2×C4×C43—41no—
244C2×C4×C43—41no—
245C2×C4×C43—41no—
246C2×C4×C43—41no—
247C2×C4×C43—161no—
248C2×C4×C43C22×D411yescharacteristic
249C2×C4×C43C22×D411yescharacteristic
250C2×C4×C43H(5,𝔽2)11yescharacteristic
251C22⋊D43—82no—
252C22⋊D43—161no—
253C2×Dic43—21no—
254C2×Dic43—21no—
255C2×Dic43—41no—
256D172—41no—
257D172—41no—
258D172—41no—
259D172—41no—
260D172—81no—
261C4×D43—82no—
262Dic86—21no—
263Dic86—81no—
264Dic86—161no—
265Dic86C2×SD1612yes—
266C8×C43—21no—
267C8×C43—21no—
268C8×C43—41no—
269C43⋊C8—22no—
270C43⋊C8—21no—
271C43⋊C8—41no—
272C43⋊C8—41no—
273C43⋊C8—41no—
274C43⋊C8C2×SD1612yes—
275#19893—431nomaximal, Sylow
276C22×C43—22no—
277C22×C43—41no—
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×C43C22×SD1611yescharacteristic
297C4×C43#57511yescharacteristic
298C4×C43#57711yescharacteristic
299C4×C43#57711yescharacteristic
300Dic43—22no—
301Dic43—41no—
302Dic43—81no—
303#3385—431no—
304#3362—431no—
305#3295D4311yescharacteristic, complemented
306#3274—431no—
307#1706—431no—
308#1695—431no—
309#1688—431no—
310#1678—431no—
311#1677—431no—
312#1631—431no—
313#1629—431no—
314#1623—431no—
315#1622—431no—
316#1590—431no—
317C8×SD16—431no—
318C2×C43—42no—
319C2×C43—81no—
320C2×C43—161no—
321C2×C43#327511yescharacteristic
322C2×C43D4×SD1611yescharacteristic
323C2×C43#329211yescharacteristic
324D43—161no—
325C2×AGL(1,ℤ/8)—861no—
326Q82—431no—
327#554C2×D4311yescharacteristic
328#550—431no—
329D42C2×D4311yescharacteristic
330#501—861no—
331#500—431no—
332#493—431no—
333#492—431no—
334#492—431no—
335#486—431no—
336#486—861no—
337#486C2×D4311yescharacteristic
338#481—21no—
339#479—861no—
340#477—431no—
341#476—431no—
342#476—431no—
343#476—861no—
344#476C2×D4311yescharacteristic
345#474—861no—
346#469—861no—
347#465—21no—
348#460—431no—
349#460—431no—
350#460—861no—
351#460C2×D4311yescharacteristic
352#459—431no—
353#450—21no—
354#449—861no—
355#447—861no—
356#446—431no—
357C8×Q8—431no—
358#440—861no—
359C4×SD16—431no—
360C4×SD16—861no—
361C4×SD16C2×D4311yescharacteristic
362#436—431no—
363C8×D4C2×D4311yescharacteristic
364C2×#102—21no—
365#334—431no—
366#334—431no—
367#333—431no—
368#333—431no—
369#331—431no—
370#331—431no—
371Q8⋊C8—431no—
372Q8⋊C8—431no—
373D4⋊C8—431no—
374D4⋊C8—431no—
375C82—431no—
376C43#1989311yescharacteristic, complemented, Sylow
377C2×#41—861no—
378C22×D4—21no—
379C22×D4—21no—
380AGL(1,ℤ/8)—1724no—
381C2×SD16—21no—
382C2×SD16—431no—
383C2×SD16—861no—
384C2×SD16—861no—
385C2×SD16—1721no—
386C2×SD16—1721no—
387C2×SD16C22⋊D4311yescharacteristic
388C2×D8—861no—
389C2×D8—861no—
390C2×D8—861no—
391C2×M16—861no—
392C22×C8—21no—
393C4⋊Q8—431no—
394C4⋊Q8—861no—
395C4⋊Q8—861no—
396C4⋊Q8—1721no—
397C4⋊Q8C22×D4311yescharacteristic
398#127—431no—
399#127—861no—
400#127C22×D4311yescharacteristic
401#125—21no—
402C22⋊Q8—21no—
403C22⋊Q8—41no—
404#121—21no—
405#121—21no—
406#121—861no—
407#121—1721no—
408#120—41no—
409C4×Q8—431no—
410C4×Q8—861no—
411C4×Q8—861no—
412C4×Q8C22×D4311yescharacteristic
413C4×D4—21no—
414C4×D4—861no—
415C4×D4C22×D4311yescharacteristic
416C4×D4C22×D4311yescharacteristic
417C2×C4⋊C4—21no—
418#107—861no—
419#107—861no—
420#107—861no—
421#106—21no—
422#106—431no—
423#106—861no—
424#106—861no—
425#106C22⋊D4311yescharacteristic
426C4⋊C8—431no—
427C4⋊C8—431no—
428C4⋊C8—431no—
429C4⋊C8—861no—
430C4⋊C8—861no—
431C4⋊C8C22×D4311yescharacteristic
432#103—431no—
433#103—861no—
434#103C22⋊D4311yescharacteristic
435#102—21no—
436#102—21no—
437#102—21no—
438#102—21no—
439#102—431no—
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—
456#41—3441no—
457#41—1722no—
458C2×Q8—21no—
459C2×Q8—431no—
460C2×Q8—861no—
461C2×Q8—1721no—
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×D4—1721no—
476C2×D4—1721no—
477C2×D4D4×D4311yescharacteristic
478C2×D4C2×C22⋊D4311yescharacteristic
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—41no—
482C22×C4—1721no—
483SD16—41no—
484SD16—81no—
485SD16—434no—
486SD16—3442no—
487SD16—3442no—
488SD16—1722no—
489SD16—1722no—
490D8—3441no—
491D8—1722no—
492D8—1722no—
493M16—1722no—
494C2×C8—21no—
495C2×C8—81no—
496C2×C8—431no—
497C2×C8—431no—
498C2×C8—861no—
499C2×C8—861no—
500C2×C8—861no—
501C2×C8—861no—
502C2×C8C2×C22⋊D4311yescharacteristic
503C2×C8C2×C22⋊D4311yescharacteristic
504C4⋊C4—21no—
505C4⋊C4—21no—
506C4⋊C4—21no—
507C4⋊C4—41no—
508C4⋊C4—41no—
509C4⋊C4—431no—
510C4⋊C4—861no—
511C4⋊C4—861no—
512C4⋊C4—861no—
513C4⋊C4—1721no—
514C4⋊C4—1721no—
515C4⋊C4D4×D4311yescharacteristic
516C4⋊C4C2×C22⋊D4311yescharacteristic
517C4⋊C4C2×C22⋊D4311yescharacteristic
518C22⋊C4—21no—
519C22⋊C4—21no—
520C22⋊C4—41no—
521C22⋊C4—41no—
522C22⋊C4—1721no—
523C42—21no—
524C42—861no—
525C42—1721no—
526C42C23×D4311yescharacteristic
527C23—21no—
528C23—21no—
529C23—41no—
530C23—82no—
531C23—82no—
532C23—161no—
533C23—1721no—
534Q8—21no—
535Q8—21no—
536Q8—81no—
537Q8—432no—
538Q8—861no—
539Q8—3441no—
540Q8—6881no—
541D4—21no—
542D4—21no—
543D4—21no—
544D4—41no—
545D4—41no—
546D4—41no—
547D4—41no—
548D4—81no—
549D4—82no—
550D4—82no—
551D4—3441no—
552D4—3442no—
553D4—1721no—
554D4—1721no—
555D4—1721no—
556D4—1721no—
557D4—6881no—
558D4SD16×D4312yes—
559C2×C4—21no—
560C2×C4—21no—
561C2×C4—21no—
562C2×C4—21no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—161no—
569C2×C4—861no—
570C2×C4—861no—
571C2×C4—3442no—
572C2×C4—1721no—
573C2×C4C2×D4×D4311yescharacteristic
574C2×C4C22×C22⋊D4311yescharacteristic
575C2×C4#1306337011yescharacteristic
576C8—21no—
577C8—21no—
578C8—41no—
579C8—432no—
580C8—862no—
581C8—861no—
582C8—1721no—
583C8—1721no—
584C8—1721no—
585C22—22no—
586C22—41no—
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—862no—
606C4—3441no—
607C4—1721no—
608C4C2×SD16×D4311yescharacteristic
609C4#1458369711yescharacteristic
610C4#1458370511yescharacteristic
611C4#1458371011yescharacteristic
612C2—42no—
613C2—81no—
614C2—161no—
615C2—6881no—
616C2#1914622211yescharacteristic
617C2SD16×C22⋊D4311yescharacteristic
618C2#1914639211yescharacteristic
subgroupG/H
centerC22D4×C22⋊D43
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#3295C2
socleC22×C43D42
prime radical#19146211C2
hypercenter#3295D43
hypocenterC43#19893
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #3295

Complements

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

NH ≅ G/Ntype
1. #19147505C2semidirect
2. #19147264C2semidirect
4. #19134186C2semidirect
5. #19134116C2semidirect
6. #19134077C2semidirect
7. #19134008C2semidirect
8. #19134004C2semidirect
9. #19133721C2semidirect
10. #19133711C2semidirect
11. #19133672C2semidirect
12. #19133667C2semidirect
13. #19133486C2semidirect
14. C8×#10621883C2semidirect
15. C43×#3295C2semidirect
17. Q8×Dic86C22semidirect
20. #14583302C22semidirect
22. #14583273C22semidirect
24. #14583246C22semidirect
27. #14583191C22semidirect
33. #14583099C22semidirect
39. #14583030C22semidirect
40. C8×Dic86C22semidirect
45. #14582650C22semidirect
46. #14582649C22semidirect
47. #14582648C22semidirect
48. #14582647C22semidirect
50. #14582642C22semidirect
51. Q8⋊(C43⋊C8)C22semidirect
52. #14582629C22semidirect
55. C8×C43⋊C8C22semidirect
197. #10621883SD16semidirect
305. #3295D43semidirect
376. C43#19893semidirect

Maximal subgroups

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

subgroupindex
#191475052
#191472642
#191462112
#191341862
#191341162
#191340772
#191340082
#191340042
#191337212
#191337112
#191336722
#191336672
#191334862
C8×#106218832
C43×#32952
#1989343