Finite Group Databasebeta

← #25086463

Subgroups — #25086463

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#19147466C211yesmaximal, characteristic, complemented
2#19146421C211yesmaximal, characteristic
3#19146413C211yesmaximal, characteristic
4#19134252C211yesmaximal, characteristic, complemented
5#19134135C211yesmaximal, characteristic, complemented
6#19134043C211yesmaximal, characteristic, complemented
7#19134013C211yesmaximal, characteristic, complemented
8#19133968C211yesmaximal, characteristic, complemented
9#19133772C211yesmaximal, characteristic
10#19133729C211yesmaximal, characteristic, complemented
11#19133728C211yesmaximal, characteristic, complemented
12#19133691C211yesmaximal, characteristic, complemented
13#19133429C211yesmaximal, characteristic, complemented
14SD16⋊(C43⋊C8)C211yesmaximal, characteristic, complemented
15C43×#3372C211yesmaximal, characteristic, complemented
16#14583609C2211yescharacteristic
17D4×D172C2211yescharacteristic
18#14583298—21no—
19#14583295C2211yescharacteristic, complemented
20#14583278C2211yescharacteristic, complemented
21#14583247C2211yescharacteristic
22#14583247C2211yescharacteristic
23#14583246C2211yescharacteristic
24#14583219—21no—
25#14583217—21no—
26#14583206—21no—
27#14583196—21no—
28#14583194C2211yescharacteristic, complemented
29#14583189C2211yescharacteristic
30#14583186C2211yescharacteristic
31#14583176C2211yescharacteristic
32#14583131—21no—
33#14583130—21no—
34#14583099C2211yescharacteristic
35#14583099C2211yescharacteristic
36#14583049—21no—
37#14583048—21no—
38Q8×C43⋊C8C2211yescharacteristic, complemented
39C4×#10621884—21no—
40C4×#10621884C2211yescharacteristic
41C8×D172C2211yescharacteristic
42D4×C43⋊C8C2211yescharacteristic
43C2×#13063245—21no—
44#102×D43—21no—
45#14582652C2211yescharacteristic, complemented
46#14582649C2211yescharacteristic, complemented
47#14582648C2211yescharacteristic, complemented
48#14582647C2211yescharacteristic, complemented
49#14582645C2211yescharacteristic, complemented
50#14582642C2211yescharacteristic
51Q8⋊(C43⋊C8)C2211yescharacteristic, complemented
52Q8⋊(C43⋊C8)C2211yescharacteristic, complemented
53D4⋊(C43⋊C8)C2211yescharacteristic
54#14582626C2211yescharacteristic
55#14582620C2211yescharacteristic, complemented
56C43×#557C2211yescharacteristic, complemented
57C43×#554C2211yescharacteristic
58C43×#491—21no—
59C43×#487C2211yescharacteristic, complemented
60C43×#479—21no—
61C43×#477C2211yescharacteristic, complemented
62C43×#461—21no—
63C43×#461C2211yescharacteristic
64C43×#446C2211yescharacteristic, complemented
65C43×#440—21no—
66C4×SD16×C43C2211yescharacteristic
67C22×D172—21no—
68C2×D4×D43—21no—
69C2×#10621885—41no—
70C2×#10621884—21no—
71C2×#10621884—21no—
72C2×#10621884D411yescharacteristic
73C22×C43⋊C8—21no—
74C2×C8×D43—21no—
75#13063325C2311yescharacteristic
76#13063322C2311yescharacteristic
77#13063317—21no—
78#13063303—41no—
79#13063301—21no—
80#13063300—21no—
81#13063299—21no—
82#13063295—41no—
83C4×D172—21no—
84C4×D172C2311yescharacteristic
85C4⋊C4×D43—21no—
86#13063258—21no—
87#13063258—21no—
88#13063256—21no—
89#13063256—21no—
90#13063256—21no—
91#13063256—21no—
92#13063256D411yescharacteristic
93C4⋊(C43⋊C8)—21no—
94C4⋊(C43⋊C8)C2311yescharacteristic
95C4⋊(C43⋊C8)C2311yescharacteristic
96C4⋊(C43⋊C8)C2311yescharacteristic
97#13063249—21no—
98#13063249D411yescharacteristic
99#13063247—21no—
100#13063247—21no—
101#13063246—21no—
102#13063245—21no—
103#13063245—21no—
104#13063245—21no—
105#13063245—21no—
106#13063245—21no—
107#13063245—21no—
108#13063245—41no—
109#13063245D411yescharacteristic
110C22⋊(C43⋊C8)—21no—
111(C2×D43)⋊C8—21no—
112C4×C43⋊C8—21no—
113C4×C43⋊C8C2311yescharacteristic
114C4×C43⋊C8C2311yescharacteristic
115C2×SD16×C43—21no—
116C2×SD16×C43D411yescharacteristic
117C4⋊Q8×C43—21no—
118C4⋊Q8×C43C2311yescharacteristic
119C4⋊Q8×C43C2311yescharacteristic
120#125×C43—21no—
121#125×C43—21no—
122#125×C43—41no—
123C22⋊Q8×C43—21no—
124C22⋊Q8×C43—41no—
125C4×Q8×C43—21no—
126C4×Q8×C43—21no—
127C4×Q8×C43C2311yescharacteristic
128C4×Q8×C43C2311yescharacteristic
129C4×D4×C43—21no—
130C4×D4×C43C2311yescharacteristic
131C2×C4⋊C4×C43—21no—
132#107×C43—21no—
133#106×C43D411yescharacteristic
134C4⋊C8×C43—21no—
135C4⋊C8×C43C2311yescharacteristic
136#103×C43—21no—
137#103×C43—21no—
138#103×C43—21no—
139#103×C43—21no—
140#103×C43D411yescharacteristic
141#102×C43D411yescharacteristic
142#97×C43—21no—
143C4×C8×C43C2311yescharacteristic
144C23×D43—41no—
145C2×Q8×C43—21no—
146C2×Q8×C43—21no—
147C2×Q8×C43C2×D411yescharacteristic
148C2×Q8×C43C2×D411yescharacteristic
149C2×D4×C43C2×D411yescharacteristic
150C22×C4×C43—21no—
151C22×C4×C43—41no—
152C2×C22⋊D43—41no—
153D4×D43—42no—
154D4×D43—81no—
155C2×D172—21no—
156C2×D172—21no—
157C2×D172—21no—
158C2×D172—41no—
159C2×D172—42no—
160C2×D172—81no—
161C2×D172C2×D411yescharacteristic
162C2×C4×D43—21no—
163C2×C4×D43—41no—
164C2×Dic86—21no—
165SD16×C43—22no—
166SD16×C43—42no—
167C2×C8×C43—21no—
168C2×C8×C43C2×D411yescharacteristic
169C2×C8×C43C2×D411yescharacteristic
170C4⋊C4×C43—21no—
171C4⋊C4×C43—21no—
172C4⋊C4×C43—21no—
173C4⋊C4×C43—21no—
174C4⋊C4×C43—21no—
175C4⋊C4×C43—21no—
176C4⋊C4×C43—41no—
177C4⋊C4×C43—41no—
178C4⋊C4×C43—41no—
179C4⋊C4×C43—41no—
180C4⋊C4×C43—41no—
181C4⋊C4×C43C2×D411yescharacteristic
182C4⋊C4×C43C2×D411yescharacteristic
183C4⋊C4×C43C2×D411yescharacteristic
184C22⋊C4×C43—21no—
185C22⋊C4×C43—41no—
186C42×C43—21no—
187C42×C43—21no—
188C42×C43—41no—
189C42×C43C2411yescharacteristic
190#10621885—82no—
191#10621884—22no—
192#10621884—81no—
193#10621884—81no—
194(C2×D43)⋊C4—21no—
195(C2×D43)⋊C4—41no—
196(C2×D43)⋊C4—41no—
197C4⋊Dic43—21no—
198C4⋊Dic43—21no—
199C4⋊Dic43C2×D411yescharacteristic
200Dic43⋊C4—41no—
201Dic43⋊C4—41no—
202C2×C43⋊C8—21no—
203C2×C43⋊C8—21no—
204C2×C43⋊C8—21no—
205C2×C43⋊C8—21no—
206C2×C43⋊C8—81no—
207C2×C43⋊C8C2×D411yescharacteristic
208C2×C43⋊C8C2×D411yescharacteristic
209C8×D43—81no—
210C23×C43—21no—
211C22×D43—21no—
212C22×D43—41no—
213C22×D43—82no—
214C22×D43—82no—
215C22×D43—161no—
216Q8×C43—21no—
217Q8×C43—21no—
218Q8×C43—21no—
219Q8×C43—21no—
220Q8×C43—41no—
221Q8×C43—41no—
222Q8×C43—81no—
223D4×C43—21no—
224D4×C43#13512yes—
225C2×C4×C43—21no—
226C2×C4×C43—21no—
227C2×C4×C43—21no—
228C2×C4×C43—21no—
229C2×C4×C43—21no—
230C2×C4×C43—41no—
231C2×C4×C43—41no—
232C2×C4×C43—41no—
233C2×C4×C43—41no—
234C2×C4×C43—161no—
235C2×C4×C43C22×D411yescharacteristic
236C2×C4×C43C22×D411yescharacteristic
237C2×C4×C43H(5,𝔽2)11yescharacteristic
238C22⋊D43—82no—
239C2×Dic43—21no—
240C2×Dic43—41no—
241D172—21no—
242D172—41no—
243D172—41no—
244D172—41no—
245D172—41no—
246D172—81no—
247D172—82no—
248D172#13712yes—
249C4×D43—41no—
250C4×D43—41no—
251C4×D43—161no—
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—41no—
265C22×C43—41no—
266C22×C43D4211yescharacteristic
267C2×D43—22no—
268C2×D43—41no—
269C2×D43—41no—
270C2×D43—81no—
271C2×D43—81no—
272C2×D43—81no—
273C2×D43—164no—
274C4×C43—21no—
275C4×C43—41no—
276C4×C43—41no—
277C4×C43—41no—
278C4×C43—41no—
279C4×C43—41no—
280C4×C43—81no—
281C4×C43—81no—
282C4×C43C2×#13511yescharacteristic
283C4×C43C2×#13711yescharacteristic
284C4×C43#57711yescharacteristic
285C4×C43#57711yescharacteristic
286Dic43—41no—
287Dic43—81no—
288#3381—431no—
289#3372D4311yescharacteristic, complemented
290#3295—431no—
291#3295—431no—
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#326611yescharacteristic
305C2×C43#328211yescharacteristic
306C2×C43#328811yescharacteristic
307D43—42no—
308D43—161no—
309#557C2×D4311yescharacteristic, complemented
310#554—431no—
311#554C2×D4311yescharacteristic
312D42—431no—
313#499—861no—
314#498—431no—
315#494—431no—
316#491—21no—
317#487C2×D4311yescharacteristic, complemented
318#486—431no—
319#486—431no—
320#486—431no—
321#481—861no—
322#481—861no—
323#479—21no—
324#479—861no—
325#478—861no—
326#477—431no—
327#477C2×D4311yescharacteristic, complemented
328#476—431no—
329#476—431no—
330#474—431no—
331#465—861no—
332#465—861no—
333#461—21no—
334#461C2×D4311yescharacteristic
335#460—431no—
336#460—431no—
337#450—861no—
338#450—861no—
339#446C2×D4311yescharacteristic, complemented
340C8×Q8—431no—
341#440—21no—
342C4×SD16—431no—
343C4×SD16—861no—
344C4×SD16C2×D4311yescharacteristic
345C8×D4—431no—
346C8×D4—431no—
347C2×#102—861no—
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—861no—
362C22×D4—861no—
363C2×Q16—1721no—
364C2×SD16—21no—
365C2×SD16—431no—
366C2×SD16—861no—
367C2×SD16—861no—
368C2×SD16C22⋊D4311yescharacteristic
369C22×C8—861no—
370C22×C8—861no—
371C4⋊Q8—21no—
372C4⋊Q8—431no—
373C4⋊Q8C22×D4311yescharacteristic
374C4⋊Q8C22×D4311yescharacteristic
375#127—431no—
376#125—21no—
377#125—21no—
378#125—41no—
379#125—861no—
380C22⋊Q8—21no—
381C22⋊Q8—41no—
382C22⋊Q8—861no—
383C22⋊Q8—1721no—
384#121—861no—
385#121—861no—
386#120—1721no—
387C4×Q8—21no—
388C4×Q8—21no—
389C4×Q8C22×D4311yescharacteristic
390C4×Q8C22×D4311yescharacteristic
391C4×D4—21no—
392C4×D4—431no—
393C4×D4—861no—
394C4×D4C22×D4311yescharacteristic
395C2×C4⋊C4—21no—
396C2×C4⋊C4—861no—
397#107—21no—
398#107—861no—
399#107—861no—
400#106—431no—
401#106—861no—
402#106—861no—
403#106—861no—
404#106—861no—
405#106C22⋊D4311yescharacteristic
406C4⋊C8—21no—
407C4⋊C8—431no—
408C4⋊C8—431no—
409C4⋊C8—431no—
410C4⋊C8—861no—
411C4⋊C8C22×D4311yescharacteristic
412#103—21no—
413#103—21no—
414#103—21no—
415#103—21no—
416#103—431no—
417#103—861no—
418#103C22⋊D4311yescharacteristic
419#102—431no—
420#102—861no—
421#102—861no—
422#102—861no—
423#102—861no—
424#102—861no—
425#102—861no—
426#102—861no—
427#102—861no—
428#102—861no—
429#102—1721no—
430#102C22⋊D4311yescharacteristic
431C22⋊C8—861no—
432C22⋊C8—861no—
433#97—21no—
434C4×C8—431no—
435C4×C8—431no—
436C4×C8—861no—
437C4×C8C22×D4311yescharacteristic
438C24—1721no—
439C2×Q8—21no—
440C2×Q8—21no—
441C2×Q8—861no—
442C2×Q8D4×D4311yescharacteristic
443C2×Q8C2×C22⋊D4311yescharacteristic
444C2×D4—431no—
445C2×D4—861no—
446C2×D4—861no—
447C2×D4—861no—
448C2×D4—3441no—
449C2×D4—3441no—
450C2×D4—1721no—
451C2×D4—1722no—
452C2×D4—1721no—
453C2×D4—1722no—
454C2×D4C2×C22⋊D4311yescharacteristic
455C22×C4—21no—
456C22×C4—41no—
457C22×C4—861no—
458C22×C4—1721no—
459Q16—3442no—
460SD16—22no—
461SD16—42no—
462SD16—862no—
463SD16—3441no—
464SD16—3441no—
465C2×C8—21no—
466C2×C8—431no—
467C2×C8—431no—
468C2×C8—861no—
469C2×C8—861no—
470C2×C8—861no—
471C2×C8—861no—
472C2×C8—3441no—
473C2×C8—3441no—
474C2×C8C2×C22⋊D4311yescharacteristic
475C2×C8C2×C22⋊D4311yescharacteristic
476C4⋊C4—21no—
477C4⋊C4—21no—
478C4⋊C4—21no—
479C4⋊C4—21no—
480C4⋊C4—21no—
481C4⋊C4—21no—
482C4⋊C4—41no—
483C4⋊C4—41no—
484C4⋊C4—41no—
485C4⋊C4—41no—
486C4⋊C4—41no—
487C4⋊C4—431no—
488C4⋊C4—861no—
489C4⋊C4—861no—
490C4⋊C4—1721no—
491C4⋊C4—1721no—
492C4⋊C4D4×D4311yescharacteristic
493C4⋊C4C2×C22⋊D4311yescharacteristic
494C4⋊C4C2×C22⋊D4311yescharacteristic
495C22⋊C4—21no—
496C22⋊C4—41no—
497C22⋊C4—861no—
498C22⋊C4—1721no—
499C22⋊C4—1721no—
500C42—21no—
501C42—21no—
502C42—41no—
503C42C23×D4311yescharacteristic
504C23—21no—
505C23—861no—
506C23—3442no—
507C23—3442no—
508C23—1721no—
509C23—6881no—
510Q8—21no—
511Q8—21no—
512Q8—21no—
513Q8—21no—
514Q8—41no—
515Q8—41no—
516Q8—81no—
517Q8—3441no—
518D4—21no—
519D4—432no—
520D4—861no—
521D4—3441no—
522D4—3442no—
523D4—3442no—
524D4—1721no—
525D4—1721no—
526D4—1721no—
527D4—1721no—
528D4#1306334512yes—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—161no—
539C2×C4—861no—
540C2×C4—1721no—
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—41no—
558C22—41no—
559C22—862no—
560C22—3441no—
561C22—3441no—
562C22—3441no—
563C22—1721no—
564C22—1721no—
565C22—6884no—
566C22D4×C22⋊D4311yescharacteristic
567C4—21no—
568C4—41no—
569C4—41no—
570C4—41no—
571C4—41no—
572C4—41no—
573C4—81no—
574C4—81no—
575C4—3441no—
576C4—1721no—
577C4C2×#1306334511yescharacteristic
578C4#137×D4311yescharacteristic
579C4#1458370711yescharacteristic
580C4#1458370811yescharacteristic
581C2—42no—
582C2—1722no—
583C2—6881no—
584C2#1914609911yescharacteristic
585C2#1914630311yescharacteristic
586C2#1914635711yescharacteristic
subgroupG/H
centerC22D4×C22⋊D43
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#3372C2
socleC22×C43D42
prime radicalD4×D172C22
hypercenter#3372D43
hypocenterC43#19790
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #3372

Complements

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

NH ≅ G/Ntype
1. #19147466C2semidirect
4. #19134252C2semidirect
5. #19134135C2semidirect
6. #19134043C2semidirect
7. #19134013C2semidirect
8. #19133968C2semidirect
10. #19133729C2semidirect
11. #19133728C2semidirect
12. #19133691C2semidirect
13. #19133429C2semidirect
14. SD16⋊(C43⋊C8)C2semidirect
15. C43×#3372C2semidirect
19. #14583295C22semidirect
20. #14583278C22semidirect
28. #14583194C22semidirect
38. Q8×C43⋊C8C22semidirect
45. #14582652C22semidirect
46. #14582649C22semidirect
47. #14582648C22semidirect
48. #14582647C22semidirect
49. #14582645C22semidirect
51. Q8⋊(C43⋊C8)C22semidirect
52. Q8⋊(C43⋊C8)C22semidirect
55. #14582620C22semidirect
56. C43×#557C22semidirect
59. C43×#487C22semidirect
61. C43×#477C22semidirect
64. C43×#446C22semidirect
289. #3372D43semidirect
309. #557C2×D43semidirect
317. #487C2×D43semidirect
327. #477C2×D43semidirect
339. #446C2×D43semidirect
360. C43#19790semidirect

Maximal subgroups

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

subgroupindex
#191474662
#191464212
#191464132
#191342522
#191341352
#191340432
#191340132
#191339682
#191337722
#191337292
#191337282
#191336912
#191334292
SD16⋊(C43⋊C8)2
C43×#33722
#1979043