Finite Group Databasebeta

← #25086238

Subgroups — #25086238

Order 11008.

656 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#19147013C211yesmaximal, characteristic, complemented
2#19146525C211yesmaximal, characteristic, complemented
3#19146408C211yesmaximal, characteristic, complemented
4#19134245C211yesmaximal, characteristic, complemented
5#19134170C211yesmaximal, characteristic, complemented
6#19134030C211yesmaximal, characteristic, complemented
7#19134001C211yesmaximal, characteristic, complemented
8#19133992C211yesmaximal, characteristic, complemented
9#19133823C211yesmaximal, characteristic, complemented
10#19133744C211yesmaximal, characteristic, complemented
11#19133711C211yesmaximal, characteristic, complemented
12#19133677C211yesmaximal, characteristic, complemented
13#19133422C211yesmaximal, characteristic, complemented
14#19133419C211yesmaximal, characteristic, complemented
15C43×#3325C211yesmaximal, characteristic, complemented
16#14583614C2211yescharacteristic, complemented
17#14583553C2211yescharacteristic
18#14583302C2211yescharacteristic, complemented
19#14583271C2211yescharacteristic
20#14583250C2211yescharacteristic, complemented
21#14583249C2211yescharacteristic, complemented
22#14583245C2211yescharacteristic
23#14583242—21no—
24#14583223—21no—
25#14583220—21no—
26#14583210—21no—
27#14583189C2211yescharacteristic
28#14583189C2211yescharacteristic
29#14583186C2211yescharacteristic, complemented
30#14583179C2211yescharacteristic
31#14583133—21no—
32#14583133—21no—
33#14583127—21no—
34#14583104C2211yescharacteristic, complemented
35#14583091C2211yescharacteristic
36#14583041—21no—
37#14583033—21no—
38C4×#10621882C2211yescharacteristic
39C8×D172C2211yescharacteristic, complemented
40D4×C43⋊C8C2211yescharacteristic
41D4×C43⋊C8C2211yescharacteristic, complemented
42#14582935—21no—
43#14582892—21no—
44C2×#13063246—21no—
45#14582651C2211yescharacteristic, complemented
46#14582650C2211yescharacteristic, complemented
47#14582648C2211yescharacteristic, complemented
48#14582647C2211yescharacteristic, complemented
49#14582646C2211yescharacteristic, complemented
50#14582643C2211yescharacteristic
51D4⋊(C43⋊C8)C2211yescharacteristic
52D4⋊(C43⋊C8)C2211yescharacteristic
53D4⋊(C43⋊C8)C2211yescharacteristic, complemented
54#14582626C2211yescharacteristic, complemented
55#14582620C2211yescharacteristic, complemented
56C43×#555C2211yescharacteristic
57D42×C43C2211yescharacteristic
58C43×#486C2211yescharacteristic
59C43×#482—21no—
60C43×#476C2211yescharacteristic
61C43×#469—21no—
62C43×#459C2211yescharacteristic
63C43×#447—21no—
64C4×D8×C43C2211yescharacteristic
65C43×#436C2211yescharacteristic
66C43×#418—21no—
67C2×#10621900—21no—
68C2×#10621883—21no—
69C2×#10621883—41no—
70C2×#10621882—21no—
71C2×#10621882D411yescharacteristic
72C22×C43⋊C8—21no—
73C22×C43⋊C8—21no—
74C2×C8×D43—21no—
75#13063325C2311yescharacteristic
76#13063325C2311yescharacteristic
77#13063311—41no—
78#13063309—41no—
79#13063305—21no—
80#13063299—21no—
81#13063299—21no—
82#13063296—21no—
83C4×D172C2311yescharacteristic
84#13063284—21no—
85#13063283—21no—
86C2×C4⋊Dic43—21no—
87#13063258—21no—
88#13063258—21no—
89#13063258—21no—
90#13063258D411yescharacteristic
91#13063256—21no—
92#13063256—21no—
93#13063256—21no—
94C4⋊(C43⋊C8)C2311yescharacteristic
95C4⋊(C43⋊C8)C2311yescharacteristic
96C4⋊(C43⋊C8)C2311yescharacteristic
97#13063250—21no—
98#13063250—21no—
99#13063249—41no—
100#13063248—21no—
101#13063246—21no—
102#13063246—21no—
103#13063246—21no—
104#13063246—21no—
105#13063246—21no—
106#13063246—21no—
107#13063246D411yescharacteristic
108#13063245—21no—
109#13063245D411yescharacteristic
110C22⋊(C43⋊C8)—21no—
111C22⋊(C43⋊C8)—21no—
112(C2×D43)⋊C8—21no—
113C4×C43⋊C8C2311yescharacteristic
114C4×C43⋊C8C2311yescharacteristic
115C22×D4×C43—21no—
116C22×D4×C43—21no—
117C2×D8×C43—21no—
118C2×D8×C43D411yescharacteristic
119C2×M16×C43—21no—
120C4⋊Q8×C43C2311yescharacteristic
121#127×C43C2311yescharacteristic
122#124×C43—41no—
123#121×C43—21no—
124#121×C43—21no—
125#121×C43—21no—
126#121×C43—21no—
127#120×C43—41no—
128C4×D4×C43C2311yescharacteristic
129C4×D4×C43C2311yescharacteristic
130C4×D4×C43C2311yescharacteristic
131#117×C43—21no—
132#117×C43—21no—
133#107×C43D411yescharacteristic
134#106×C43—21no—
135C4⋊C8×C43C2311yescharacteristic
136#102×C43—21no—
137#102×C43—21no—
138#102×C43—21no—
139#102×C43—21no—
140#102×C43D411yescharacteristic
141#102×C43D411yescharacteristic
142C22⋊C8×C43—21no—
143C4×C8×C43C2311yescharacteristic
144C24×C43—41no—
145C2×Q8×C43—21no—
146C2×D4×C43—21no—
147C2×D4×C43—21no—
148C2×D4×C43—21no—
149C2×D4×C43—41no—
150C2×D4×C43—41no—
151C2×D4×C43—41no—
152C2×D4×C43—42no—
153C2×D4×C43—42no—
154C2×D4×C43—81no—
155C2×D4×C43—81no—
156C2×D4×C43C2×D411yescharacteristic
157C2×D4×C43C2×D411yescharacteristic
158C2×D4×C43C2×D411yescharacteristic
159C22×C4×C43—21no—
160C22×C4×C43—21no—
161C22×C4×C43—21no—
162C2×C22⋊D43—41no—
163C2×C22⋊D43—41no—
164C22×Dic43—41no—
165#10621900—42no—
166#10621900—81no—
167C2×D172C2×D411yescharacteristic
168C2×C4×D43—21no—
169C2×Dic86—21no—
170C2×Dic86—21no—
171D8×C43—22no—
172D8×C43—81no—
173M16×C43—81no—
174C2×C8×C43—21no—
175C2×C8×C43C2×D411yescharacteristic
176C2×C8×C43C2×D411yescharacteristic
177C4⋊C4×C43—21no—
178C4⋊C4×C43—21no—
179C4⋊C4×C43C2×D411yescharacteristic
180C4⋊C4×C43C2×D411yescharacteristic
181C4⋊C4×C43C2×D411yescharacteristic
182C22⋊C4×C43—21no—
183C22⋊C4×C43—21no—
184C22⋊C4×C43—21no—
185C22⋊C4×C43—41no—
186C22⋊C4×C43—41no—
187C22⋊C4×C43—41no—
188C42×C43—41no—
189C42×C43C2411yescharacteristic
190C22⋊Dic43—41no—
191#10621883—81no—
192#10621883—82no—
193#10621882—41no—
194#10621882—81no—
195(C2×D43)⋊C4—21no—
196(C2×D43)⋊C4—41no—
197(C2×D43)⋊C4—41no—
198C4⋊Dic43—21no—
199C4⋊Dic43—21no—
200C4⋊Dic43—21no—
201C4⋊Dic43—21no—
202C4⋊Dic43—41no—
203C4⋊Dic43C2×D411yescharacteristic
204C4×Dic43—41no—
205C2×C43⋊C8—21no—
206C2×C43⋊C8—21no—
207C2×C43⋊C8—21no—
208C2×C43⋊C8—21no—
209C2×C43⋊C8—42no—
210C2×C43⋊C8—81no—
211C2×C43⋊C8C2×D411yescharacteristic
212C2×C43⋊C8C2×D411yescharacteristic
213C8×D43—81no—
214C23×C43—21no—
215C23×C43—21no—
216C23×C43—21no—
217C23×C43—41no—
218C23×C43—82no—
219C23×C43—82no—
220C23×C43—161no—
221C22×D43—21no—
222Q8×C43—81no—
223D4×C43—21no—
224D4×C43—21no—
225D4×C43—21no—
226D4×C43—21no—
227D4×C43—21no—
228D4×C43—41no—
229D4×C43—41no—
230D4×C43—41no—
231D4×C43—41no—
232D4×C43—81no—
233D4×C43—82no—
234D4×C43—82no—
235D4×C43—161no—
236D4×C43#13512yes—
237C2×C4×C43—21no—
238C2×C4×C43—21no—
239C2×C4×C43—21no—
240C2×C4×C43—41no—
241C2×C4×C43—41no—
242C2×C4×C43—41no—
243C2×C4×C43—41no—
244C2×C4×C43—41no—
245C2×C4×C43—41no—
246C2×C4×C43—41no—
247C2×C4×C43C22×D411yescharacteristic
248C2×C4×C43C22×D411yescharacteristic
249C2×C4×C43H(5,𝔽2)11yescharacteristic
250C22⋊D43—82no—
251C22⋊D43—161no—
252C2×Dic43—21no—
253C2×Dic43—41no—
254C2×Dic43—41no—
255C2×Dic43—82no—
256D172—21no—
257D172—21no—
258C4×D43—41no—
259C4×D43—41no—
260Dic86—41no—
261Dic86—41no—
262Dic86—81no—
263C8×C43—21no—
264C8×C43—21no—
265C8×C43—41no—
266C43⋊C8—21no—
267C43⋊C8—21no—
268C43⋊C8—41no—
269C43⋊C8—41no—
270C43⋊C8—41no—
271C43⋊C8—41no—
272#19775—431nomaximal, Sylow
273C22×C43—22no—
274C22×C43—41no—
275C22×C43—41no—
276C22×C43—41no—
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—41no—
288C2×D43—41no—
289C2×D43—41no—
290C4×C43—21no—
291C4×C43—41no—
292C4×C43—41no—
293C4×C43—41no—
294C4×C43—81no—
295C4×C43C2×#13511yescharacteristic
296C4×C43#57511yescharacteristic
297C4×C43#57611yescharacteristic
298C4×C43#57711yescharacteristic
299Dic43—41no—
300Dic43—81no—
301Dic43—81no—
302#3341—431no—
303#3325D4311yescharacteristic, complemented
304#3303—431no—
305#3294—431no—
306#1719—431no—
307#1703—431no—
308#1681—431no—
309#1677—431no—
310#1675—431no—
311#1646—431no—
312#1635—431no—
313#1629—431no—
314#1624—431no—
315#1581—431no—
316#1580—431no—
317C2×C43—42no—
318C2×C43—81no—
319C2×C43—81no—
320C2×C43—161no—
321C2×C43#326711yescharacteristic
322C2×C43#328011yescharacteristic
323C2×C43#328811yescharacteristic
324D43—81no—
325#555—431no—
326#555C2×D4311yescharacteristic
327#547—431no—
328D42C2×D4311yescharacteristic
329#500—431no—
330#492—431no—
331#487—431no—
332#487—431no—
333#486—431no—
334#486C2×D4311yescharacteristic
335#485—861no—
336#482—21no—
337#482—861no—
338#482—861no—
339#480—861no—
340#476—431no—
341#476—431no—
342#476—431no—
343#476C2×D4311yescharacteristic
344#474—431no—
345#469—21no—
346#466—861no—
347#466—861no—
348#465—861no—
349#461—431no—
350#459—431no—
351#459C2×D4311yescharacteristic
352#449—861no—
353#447—21no—
354#447—861no—
355C4×D8—431no—
356C4×D8C2×D4311yescharacteristic
357#436C2×D4311yescharacteristic
358C8×D4—431no—
359C8×D4—431no—
360C8×D4—431no—
361#427—861no—
362#418—21no—
363#416—861no—
364C2×#102—861no—
365#335—431no—
366#334—431no—
367#333—431no—
368#333—431no—
369#332—431no—
370#331—431no—
371D4⋊C8—431no—
372D4⋊C8—431no—
373D4⋊C8—431no—
374D4⋊C8—431no—
375#322—431no—
376C43#1977511yescharacteristic, complemented, Sylow
377C2×#41—861no—
378C22×D4—21no—
379C22×D4—21no—
380C2×SD16—861no—
381C2×SD16—1721no—
382C2×D8—21no—
383C2×D8—431no—
384C2×D8—861no—
385C2×D8C22⋊D4311yescharacteristic
386C2×M16—21no—
387C22×C8—861no—
388C22×C8—861no—
389C22×C8—861no—
390C4⋊Q8—431no—
391C4⋊Q8—431no—
392C4⋊Q8C22×D4311yescharacteristic
393#127C22×D4311yescharacteristic
394#124—41no—
395#124—1721no—
396#123—1721no—
397C22⋊Q8—861no—
398#121—21no—
399#121—21no—
400#121—21no—
401#121—21no—
402#121—861no—
403#121—861no—
404#121—861no—
405#120—41no—
406C4×D4—431no—
407C4×D4C22×D4311yescharacteristic
408C4×D4C22×D4311yescharacteristic
409C4×D4C22×D4311yescharacteristic
410#117—21no—
411#117—21no—
412#117—861no—
413#117—861no—
414C2×C4⋊C4—861no—
415#107—431no—
416#107—861no—
417#107—861no—
418#107—861no—
419#107C22⋊D4311yescharacteristic
420#106—21no—
421#106—861no—
422#106—861no—
423#106—861no—
424C4⋊C8—431no—
425C4⋊C8—431no—
426C4⋊C8—431no—
427C4⋊C8C22×D4311yescharacteristic
428#103—861no—
429#103—861no—
430#103—861no—
431#103—1721no—
432#102—21no—
433#102—21no—
434#102—21no—
435#102—21no—
436#102—431no—
437#102—431no—
438#102—861no—
439#102—861no—
440#102—861no—
441#102—861no—
442#102—861no—
443#102—861no—
444#102—861no—
445#102C22⋊D4311yescharacteristic
446#102C22⋊D4311yescharacteristic
447C22⋊C8—21no—
448C22⋊C8—861no—
449C22⋊C8—861no—
450C22⋊C8—861no—
451C4×C8—431no—
452C4×C8—431no—
453C4×C8C22×D4311yescharacteristic
454C24—41no—
455#41—3441no—
456#41—1722no—
457C2×Q8—21no—
458C2×Q8—861no—
459C2×Q8—861no—
460C2×D4—21no—
461C2×D4—21no—
462C2×D4—21no—
463C2×D4—41no—
464C2×D4—41no—
465C2×D4—42no—
466C2×D4—42no—
467C2×D4—41no—
468C2×D4—81no—
469C2×D4—81no—
470C2×D4—431no—
471C2×D4—1721no—
472C2×D4—1721no—
473C2×D4D4×D4311yescharacteristic
474C2×D4C2×C22⋊D4311yescharacteristic
475C2×D4C2×C22⋊D4311yescharacteristic
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—861no—
480C22×C4—1721no—
481SD16—3441no—
482SD16—3442no—
483D8—22no—
484D8—81no—
485D8—3441no—
486D8—1721no—
487M16—81no—
488C2×C8—21no—
489C2×C8—431no—
490C2×C8—431no—
491C2×C8—861no—
492C2×C8—861no—
493C2×C8—861no—
494C2×C8—861no—
495C2×C8—3441no—
496C2×C8—3441no—
497C2×C8—1722no—
498C2×C8C2×C22⋊D4311yescharacteristic
499C2×C8C2×C22⋊D4311yescharacteristic
500C4⋊C4—21no—
501C4⋊C4—21no—
502C4⋊C4—431no—
503C4⋊C4—861no—
504C4⋊C4—861no—
505C4⋊C4—861no—
506C4⋊C4—861no—
507C4⋊C4—1721no—
508C4⋊C4D4×D4311yescharacteristic
509C4⋊C4C2×C22⋊D4311yescharacteristic
510C4⋊C4C2×C22⋊D4311yescharacteristic
511C22⋊C4—21no—
512C22⋊C4—21no—
513C22⋊C4—21no—
514C22⋊C4—41no—
515C22⋊C4—41no—
516C22⋊C4—41no—
517C22⋊C4—861no—
518C22⋊C4—1721no—
519C22⋊C4—1721no—
520C22⋊C4—1721no—
521C42—41no—
522C42—1721no—
523C42C23×D4311yescharacteristic
524C23—21no—
525C23—21no—
526C23—21no—
527C23—41no—
528C23—82no—
529C23—82no—
530C23—161no—
531C23—861no—
532Q8—81no—
533Q8—3441no—
534Q8—1721no—
535Q8—1721no—
536D4—21no—
537D4—21no—
538D4—21no—
539D4—21no—
540D4—21no—
541D4—41no—
542D4—41no—
543D4—41no—
544D4—41no—
545D4—81no—
546D4—82no—
547D4—82no—
548D4—161no—
549D4—861no—
550D4—861no—
551D4—3442no—
552D4—6881no—
553D4#1306334512yes—
554C2×C4—21no—
555C2×C4—21no—
556C2×C4—21no—
557C2×C4—41no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—861no—
565C2×C4—3442no—
566C2×C4—1721no—
567C2×C4—1721no—
568C2×C4—1721no—
569C2×C4—1721no—
570C2×C4C2×D4×D4311yescharacteristic
571C2×C4C22×C22⋊D4311yescharacteristic
572C2×C4#1306337011yescharacteristic
573C8—21no—
574C8—21no—
575C8—41no—
576C8—861no—
577C8—861no—
578C8—1721no—
579C8—1721no—
580C8—1721no—
581C8—1721no—
582C22—22no—
583C22—41no—
584C22—41no—
585C22—41no—
586C22—41no—
587C22—41no—
588C22—41no—
589C22—41no—
590C22—41no—
591C22—81no—
592C22—81no—
593C22—81no—
594C22—164no—
595C22—1721no—
596C22—1721no—
597C22—1721no—
598C22D4×C22⋊D4311yescharacteristic
599C4—21no—
600C4—41no—
601C4—41no—
602C4—41no—
603C4—81no—
604C4—3441no—
605C4—3441no—
606C4—1721no—
607C4C2×#1306334511yescharacteristic
608C4#1458369511yescharacteristic
609C4#1458370211yescharacteristic
610C4#1458370911yescharacteristic
611C2—42no—
612C2—81no—
613C2—81no—
614C2—161no—
615C2—3441no—
616C2#1914611411yescharacteristic
617C2#1914627611yescharacteristic
618C2#1914635911yescharacteristic
subgroupG/H
centerC22D4×C22⋊D43
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#3325C2
socleC22×C43D42
hypercenter#3325D43
hypocenterC43#19775
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #3325

Complements

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

NH ≅ G/Ntype
1. #19147013C2semidirect
2. #19146525C2semidirect
3. #19146408C2semidirect
4. #19134245C2semidirect
5. #19134170C2semidirect
6. #19134030C2semidirect
7. #19134001C2semidirect
8. #19133992C2semidirect
9. #19133823C2semidirect
10. #19133744C2semidirect
11. #19133711C2semidirect
12. #19133677C2semidirect
13. #19133422C2semidirect
14. #19133419C2semidirect
15. C43×#3325C2semidirect
16. #14583614C22semidirect
18. #14583302C22semidirect
20. #14583250C22semidirect
21. #14583249C22semidirect
29. #14583186C22semidirect
34. #14583104C22semidirect
39. C8×D172C22semidirect
41. D4×C43⋊C8C22semidirect
45. #14582651C22semidirect
46. #14582650C22semidirect
47. #14582648C22semidirect
48. #14582647C22semidirect
49. #14582646C22semidirect
53. D4⋊(C43⋊C8)C22semidirect
54. #14582626C22semidirect
55. #14582620C22semidirect
303. #3325D43semidirect
376. C43#19775semidirect

Maximal subgroups

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

subgroupindex
#191470132
#191465252
#191464082
#191342452
#191341702
#191340302
#191340012
#191339922
#191338232
#191337442
#191337112
#191336772
#191334222
#191334192
C43×#33252
#1977543