Finite Group Databasebeta

← #25086465

Subgroups — #25086465

Order 11008.

626 conjugacy classes of subgroups.

The subgroup lattice has 588 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19147468C211yesmaximal, characteristic, complemented
2#19147376C211yesmaximal, characteristic, complemented
3#19146419C211yesmaximal, characteristic
4#19134257C211yesmaximal, characteristic, complemented
5#19134133C211yesmaximal, characteristic, complemented
6#19134048C211yesmaximal, characteristic, complemented
7#19134008C211yesmaximal, characteristic, complemented
8#19133970C211yesmaximal, characteristic, complemented
9#19133774C211yesmaximal, characteristic
10#19133729C211yesmaximal, characteristic, complemented
11#19133727C211yesmaximal, characteristic, complemented
12#19133690C211yesmaximal, characteristic, complemented
13#19133432C211yesmaximal, characteristic, complemented
14#19133407C211yesmaximal, characteristic, complemented
15C43×#3295C211yesmaximal, characteristic
16#14583628C2211yescharacteristic, complemented
17#14583606C2211yescharacteristic
18#14583299—21no—
19#14583297C2211yescharacteristic, complemented
20#14583278C2211yescharacteristic, complemented
21#14583269—21no—
22#14583251C2211yescharacteristic, complemented
23#14583245C2211yescharacteristic
24#14583245C2211yescharacteristic
25#14583215—21no—
26#14583204—21no—
27#14583203—21no—
28#14583201—21no—
29#14583194C2211yescharacteristic, complemented
30#14583191C2211yescharacteristic, complemented
31#14583189C2211yescharacteristic
32#14583179C2211yescharacteristic
33#14583126—21no—
34#14583104—21no—
35#14583104C2211yescharacteristic
36#14583096C2211yescharacteristic
37#14583050—21no—
38#14583030C2211yescharacteristic, complemented
39C8×Dic86C2211yescharacteristic, complemented
40#14582999—21no—
41SD16×Dic43—21no—
42C4×#10621883C2211yescharacteristic
43D4×C43⋊C8C2211yescharacteristic
44C2×#13063246—21no—
45#14582651C2211yescharacteristic, complemented
46#14582650C2211yescharacteristic, complemented
47#14582648C2211yescharacteristic, complemented
48#14582647C2211yescharacteristic, complemented
49#14582644C2211yescharacteristic, complemented
50#14582643C2211yescharacteristic
51Q8⋊(C43⋊C8)C2211yescharacteristic, complemented
52#14582629C2211yescharacteristic, complemented
53D4⋊(C43⋊C8)C2211yescharacteristic
54D4⋊(C43⋊C8)C2211yescharacteristic
55#14582621C2211yescharacteristic, 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×#10621885—41no—
68C2×#10621883—21no—
69C2×#10621883—21no—
70C2×#10621883D411yescharacteristic
71C22×C43⋊C8—21no—
72#13063325—21no—
73#13063325C2311yescharacteristic
74#13063325C2311yescharacteristic
75#13063316—21no—
76#13063316—21no—
77#13063316—41no—
78#13063304—21no—
79#13063302—41no—
80Q8×Dic43—21no—
81C4×Dic86—21no—
82C4×Dic86C2311yescharacteristic
83D4×Dic43—21no—
84C2×C4⋊Dic43—21no—
85#13063258—21no—
86#13063258—21no—
87#13063258—21no—
88#13063257—21no—
89#13063257—21no—
90#13063256—21no—
91#13063256D411yescharacteristic
92C4⋊(C43⋊C8)—21no—
93C4⋊(C43⋊C8)C2311yescharacteristic
94C4⋊(C43⋊C8)C2311yescharacteristic
95C4⋊(C43⋊C8)C2311yescharacteristic
96Dic43⋊C8—21no—
97#13063249—21no—
98#13063248—21no—
99#13063248—21no—
100#13063248—21no—
101#13063248—21no—
102#13063248D411yescharacteristic
103#13063246—21no—
104#13063246—21no—
105#13063246—21no—
106#13063246—21no—
107#13063246—21no—
108#13063246—41no—
109#13063246D411yescharacteristic
110C22⋊(C43⋊C8)—21no—
111#13063236—21no—
112C4×C43⋊C8C2311yescharacteristic
113C4×C43⋊C8C2311yescharacteristic
114C8×Dic43—21no—
115C22×D4×C43—21no—
116C22×D4×C43—21no—
117C2×SD16×C43—21no—
118C2×SD16×C43D411yescharacteristic
119C22×C8×C43—21no—
120C4⋊Q8×C43C2311yescharacteristic
121#127×C43C2311yescharacteristic
122#125×C43—21no—
123C22⋊Q8×C43—21no—
124C22⋊Q8×C43—41no—
125#121×C43—21no—
126#121×C43—21no—
127#120×C43—41no—
128C4×Q8×C43C2311yescharacteristic
129C4×D4×C43—21no—
130C4×D4×C43C2311yescharacteristic
131C4×D4×C43C2311yescharacteristic
132C2×C4⋊C4×C43—21no—
133#106×C43—21no—
134#106×C43D411yescharacteristic
135C4⋊C8×C43C2311yescharacteristic
136#103×C43D411yescharacteristic
137#102×C43—21no—
138#102×C43—21no—
139#102×C43—21no—
140#102×C43—21no—
141#102×C43D411yescharacteristic
142C22⋊C8×C43—21no—
143C4×C8×C43C2311yescharacteristic
144C24×C43—41no—
145C2×Q8×C43—21no—
146C2×Q8×C43C2×D411yescharacteristic
147C2×D4×C43—21no—
148C2×D4×C43—21no—
149C2×D4×C43—21no—
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
158C22×C4×C43—21no—
159C22×C4×C43—21no—
160C22×C4×C43—41no—
161C22×Dic43—41no—
162C2×Dic86—21no—
163C2×Dic86—21no—
164C2×Dic86C2×D411yescharacteristic
165SD16×C43—22no—
166SD16×C43—81no—
167C2×C8×C43—21no—
168C2×C8×C43—81no—
169C2×C8×C43C2×D411yescharacteristic
170C2×C8×C43C2×D411yescharacteristic
171C4⋊C4×C43—21no—
172C4⋊C4×C43—21no—
173C4⋊C4×C43—21no—
174C4⋊C4×C43—41no—
175C4⋊C4×C43—41no—
176C4⋊C4×C43C2×D411yescharacteristic
177C4⋊C4×C43C2×D411yescharacteristic
178C4⋊C4×C43C2×D411yescharacteristic
179C22⋊C4×C43—21no—
180C22⋊C4×C43—21no—
181C22⋊C4×C43—41no—
182C22⋊C4×C43—41no—
183C42×C43—21no—
184C42×C43C2411yescharacteristic
185C22⋊Dic43—41no—
186#10621885—82no—
187#10621883—22no—
188#10621883—42no—
189#10621883—81no—
190C4⋊Dic43—21no—
191C4⋊Dic43—21no—
192C4⋊Dic43—21no—
193C4⋊Dic43—21no—
194C4⋊Dic43—41no—
195C4⋊Dic43—41no—
196C4⋊Dic43—41no—
197C4⋊Dic43C2×D411yescharacteristic
198Dic43⋊C4—21no—
199Dic43⋊C4—41no—
200Dic43⋊C4—41no—
201C4×Dic43—21no—
202C4×Dic43—41no—
203C2×C43⋊C8—21no—
204C2×C43⋊C8—21no—
205C2×C43⋊C8—21no—
206C2×C43⋊C8—21no—
207C2×C43⋊C8—81no—
208C2×C43⋊C8C2×D411yescharacteristic
209C2×C43⋊C8C2×D411yescharacteristic
210C23×C43—21no—
211C23×C43—21no—
212C23×C43—41no—
213C23×C43—82no—
214C23×C43—82no—
215C23×C43—161no—
216Q8×C43—21no—
217Q8×C43—21no—
218Q8×C43—81no—
219D4×C43—21no—
220D4×C43—21no—
221D4×C43—41no—
222D4×C43—41no—
223D4×C43—41no—
224D4×C43—41no—
225D4×C43—81no—
226D4×C43—82no—
227D4×C43—82no—
228D4×C43#13512yes—
229D4×C43#13712yes—
230C2×C4×C43—21no—
231C2×C4×C43—21no—
232C2×C4×C43—21no—
233C2×C4×C43—21no—
234C2×C4×C43—41no—
235C2×C4×C43—41no—
236C2×C4×C43—41no—
237C2×C4×C43—41no—
238C2×C4×C43—41no—
239C2×C4×C43—161no—
240C2×C4×C43C22×D411yescharacteristic
241C2×C4×C43C22×D411yescharacteristic
242C2×C4×C43H(5,𝔽2)11yescharacteristic
243C2×Dic43—21no—
244C2×Dic43—21no—
245C2×Dic43—41no—
246C2×Dic43—41no—
247C2×Dic43—161no—
248Dic86—21no—
249Dic86—21no—
250Dic86—41no—
251Dic86—41no—
252Dic86—81no—
253C8×C43—21no—
254C8×C43—21no—
255C8×C43—41no—
256C43⋊C8—21no—
257C43⋊C8—21no—
258C43⋊C8—41no—
259C43⋊C8—41no—
260C43⋊C8—41no—
261C43⋊C8—41no—
262#19790—431nomaximal, Sylow
263C22×C43—22no—
264C22×C43—22no—
265C22×C43—41no—
266C22×C43—41no—
267C22×C43—41no—
268C22×C43—41no—
269C22×C43—81no—
270C22×C43—81no—
271C22×C43—81no—
272C22×C43—164no—
273C22×C43D4211yescharacteristic
274C4×C43—21no—
275C4×C43—41no—
276C4×C43—41no—
277C4×C43—41no—
278C4×C43—41no—
279C4×C43—81no—
280C4×C43C2×#13511yescharacteristic
281C4×C43C2×#13711yescharacteristic
282C4×C43#57711yescharacteristic
283C4×C43#57711yescharacteristic
284Dic43—41no—
285Dic43—41no—
286Dic43—81no—
287Dic43—81no—
288#3381—431no—
289#3372—431no—
290#3295—431no—
291#3295D4311yescharacteristic
292#1720—431no—
293#1698—431no—
294#1683—431no—
295#1678—431no—
296#1671—431no—
297#1639—431no—
298#1632—431no—
299#1632—431no—
300#1626—431no—
301#1582—431no—
302SD16⋊C8—431no—
303C2×C43—42no—
304C2×C43—42no—
305C2×C43—161no—
306C2×C43#326611yescharacteristic
307C2×C43#328211yescharacteristic
308C2×C43#328811yescharacteristic
309#557—431no—
310#554—431no—
311#554C2×D4311yescharacteristic
312D42C2×D4311yescharacteristic
313#499—861no—
314#498—431no—
315#494—431no—
316#491—861no—
317#487—431no—
318#486—431no—
319#486—431no—
320#486C2×D4311yescharacteristic
321#481—21no—
322#481—861no—
323#479—861no—
324#479—861no—
325#478—861no—
326#477—431no—
327#477—431no—
328#476—431no—
329#476C2×D4311yescharacteristic
330#474—431no—
331#465—21no—
332#465—861no—
333#461—431no—
334#461—861no—
335#460—431no—
336#460C2×D4311yescharacteristic
337#450—21no—
338#450—861no—
339#446—431no—
340C8×Q8—431no—
341#440—861no—
342C4×SD16—431no—
343C4×SD16—861no—
344C4×SD16C2×D4311yescharacteristic
345C8×D4—431no—
346C8×D4C2×D4311yescharacteristic
347C2×#102—21no—
348C2×#102—861no—
349#335—431no—
350#334—431no—
351#333—431no—
352#333—431no—
353#332—431no—
354#331—431no—
355Q8⋊C8—431no—
356Q8⋊C8—431no—
357D4⋊C8—431no—
358D4⋊C8—431no—
359#322—431no—
360C43#1979011yescharacteristic, complemented, Sylow
361C22×D4—21no—
362C22×D4—21no—
363C2×Q16—1721no—
364C2×SD16—21no—
365C2×SD16—431no—
366C2×SD16—861no—
367C2×SD16—861no—
368C2×SD16C22⋊D4311yescharacteristic
369C22×C8—21no—
370C22×C8—861no—
371C4⋊Q8—431no—
372C4⋊Q8—431no—
373C4⋊Q8—861no—
374C4⋊Q8C22×D4311yescharacteristic
375#127C22×D4311yescharacteristic
376#125—21no—
377#125—861no—
378#125—861no—
379#125—1721no—
380C22⋊Q8—21no—
381C22⋊Q8—41no—
382C22⋊Q8—861no—
383C22⋊Q8—1721no—
384#121—21no—
385#121—21no—
386#120—41no—
387C4×Q8—431no—
388C4×Q8—861no—
389C4×Q8—861no—
390C4×Q8C22×D4311yescharacteristic
391C4×D4—21no—
392C4×D4—861no—
393C4×D4C22×D4311yescharacteristic
394C4×D4C22×D4311yescharacteristic
395C2×C4⋊C4—21no—
396C2×C4⋊C4—861no—
397#107—861no—
398#107—861no—
399#107—861no—
400#106—21no—
401#106—431no—
402#106—861no—
403#106—861no—
404#106—861no—
405#106C22⋊D4311yescharacteristic
406C4⋊C8—431no—
407C4⋊C8—431no—
408C4⋊C8—431no—
409C4⋊C8—861no—
410C4⋊C8—861no—
411C4⋊C8C22×D4311yescharacteristic
412#103—431no—
413#103—861no—
414#103—861no—
415#103—861no—
416#103—861no—
417#103—861no—
418#103C22⋊D4311yescharacteristic
419#102—21no—
420#102—21no—
421#102—21no—
422#102—21no—
423#102—431no—
424#102—861no—
425#102—861no—
426#102—861no—
427#102—861no—
428#102—861no—
429#102—1721no—
430#102C22⋊D4311yescharacteristic
431C22⋊C8—21no—
432C22⋊C8—861no—
433#97—861no—
434C4×C8—431no—
435C4×C8—431no—
436C4×C8—861no—
437C4×C8C22×D4311yescharacteristic
438C24—41no—
439C2×Q8—21no—
440C2×Q8—431no—
441C2×Q8—861no—
442C2×Q8—861no—
443C2×Q8C2×C22⋊D4311yescharacteristic
444C2×D4—21no—
445C2×D4—21no—
446C2×D4—21no—
447C2×D4—41no—
448C2×D4—41no—
449C2×D4—42no—
450C2×D4—42no—
451C2×D4—81no—
452C2×D4—81no—
453C2×D4D4×D4311yescharacteristic
454C2×D4C2×C22⋊D4311yescharacteristic
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—41no—
458C22×C4—1721no—
459Q16—3442no—
460SD16—22no—
461SD16—81no—
462SD16—862no—
463SD16—3441no—
464SD16—1722no—
465C2×C8—21no—
466C2×C8—81no—
467C2×C8—431no—
468C2×C8—431no—
469C2×C8—861no—
470C2×C8—861no—
471C2×C8—861no—
472C2×C8—861no—
473C2×C8—3441no—
474C2×C8C2×C22⋊D4311yescharacteristic
475C2×C8C2×C22⋊D4311yescharacteristic
476C4⋊C4—21no—
477C4⋊C4—21no—
478C4⋊C4—21no—
479C4⋊C4—41no—
480C4⋊C4—41no—
481C4⋊C4—431no—
482C4⋊C4—861no—
483C4⋊C4—861no—
484C4⋊C4—861no—
485C4⋊C4—861no—
486C4⋊C4—861no—
487C4⋊C4—1721no—
488C4⋊C4—1721no—
489C4⋊C4—1721no—
490C4⋊C4—1721no—
491C4⋊C4—1721no—
492C4⋊C4D4×D4311yescharacteristic
493C4⋊C4C2×C22⋊D4311yescharacteristic
494C4⋊C4C2×C22⋊D4311yescharacteristic
495C22⋊C4—21no—
496C22⋊C4—21no—
497C22⋊C4—41no—
498C22⋊C4—41no—
499C22⋊C4—1721no—
500C42—21no—
501C42—861no—
502C42—1721no—
503C42C23×D4311yescharacteristic
504C23—21no—
505C23—21no—
506C23—41no—
507C23—82no—
508C23—82no—
509C23—161no—
510Q8—21no—
511Q8—21no—
512Q8—81no—
513Q8—861no—
514Q8—861no—
515Q8—3441no—
516Q8—1721no—
517Q8—1721no—
518D4—21no—
519D4—21no—
520D4—41no—
521D4—41no—
522D4—41no—
523D4—41no—
524D4—81no—
525D4—82no—
526D4—82no—
527D4#1306334612yes—
528D4#1306335512yes—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—161no—
539C2×C4—861no—
540C2×C4—861no—
541C2×C4—1721no—
542C2×C4—1721no—
543C2×C4—6881no—
544C2×C4C2×D4×D4311yescharacteristic
545C2×C4C22×C22⋊D4311yescharacteristic
546C2×C4#1306337011yescharacteristic
547C8—21no—
548C8—21no—
549C8—41no—
550C8—861no—
551C8—861no—
552C8—1721no—
553C8—1721no—
554C8—1721no—
555C8—1721no—
556C22—22no—
557C22—22no—
558C22—41no—
559C22—41no—
560C22—41no—
561C22—41no—
562C22—81no—
563C22—81no—
564C22—81no—
565C22—164no—
566C22D4×C22⋊D4311yescharacteristic
567C4—21no—
568C4—41no—
569C4—41no—
570C4—41no—
571C4—41no—
572C4—81no—
573C4—3441no—
574C4—3441no—
575C4—1721no—
576C4—1721no—
577C4C2×#1306334611yescharacteristic
578C4C2×#1306335511yescharacteristic
579C4#1458370511yescharacteristic
580C4#1458371011yescharacteristic
581C2—42no—
582C2—42no—
583C2—161no—
584C2#1914610111yescharacteristic
585C2#1914630211yescharacteristic
586C2#1914635911yescharacteristic
subgroupG/H
centerC22D4×C22⋊D43
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#3295C2
socleC22×C43D42
prime radicalD42×C43C22
hypercenter#3295D43
hypocenterC43#19790
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. #19147468C2semidirect
2. #19147376C2semidirect
4. #19134257C2semidirect
5. #19134133C2semidirect
6. #19134048C2semidirect
7. #19134008C2semidirect
8. #19133970C2semidirect
10. #19133729C2semidirect
11. #19133727C2semidirect
12. #19133690C2semidirect
13. #19133432C2semidirect
14. #19133407C2semidirect
16. #14583628C22semidirect
19. #14583297C22semidirect
20. #14583278C22semidirect
22. #14583251C22semidirect
29. #14583194C22semidirect
30. #14583191C22semidirect
38. #14583030C22semidirect
39. C8×Dic86C22semidirect
45. #14582651C22semidirect
46. #14582650C22semidirect
47. #14582648C22semidirect
48. #14582647C22semidirect
49. #14582644C22semidirect
51. Q8⋊(C43⋊C8)C22semidirect
52. #14582629C22semidirect
55. #14582621C22semidirect
360. C43#19790semidirect

Maximal subgroups

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

subgroupindex
#191474682
#191473762
#191464192
#191342572
#191341332
#191340482
#191340082
#191339702
#191337742
#191337292
#191337272
#191336902
#191334322
#191334072
C43×#32952
#1979043