Finite Group Databasebeta

← #25086405

Subgroups — #25086405

Order 11008.

614 conjugacy classes of subgroups.

The subgroup lattice has 592 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19147581C211yesmaximal, characteristic, complemented
2#19146878C211yesmaximal, characteristic, complemented
3#19146534C211yesmaximal, characteristic, complemented
4#19134254C211yesmaximal, characteristic, complemented
5#19134154C211yesmaximal, characteristic, complemented
6#19134036C211yesmaximal, characteristic, complemented
7#19134016C211yesmaximal, characteristic, complemented
8#19133965C211yesmaximal, characteristic, complemented
9#19133864C211yesmaximal, characteristic, complemented
10#19133858C211yesmaximal, characteristic, complemented
11#19133795C211yesmaximal, characteristic, complemented
12#19133703C211yesmaximal, characteristic, complemented
13#19133425C211yesmaximal, characteristic, complemented
14#19133412C211yesmaximal, characteristic, complemented
15C43×#3358C211yesmaximal, characteristic
16#14583619C2211yescharacteristic
17#14583619C2211yescharacteristic
18#14583295C2211yescharacteristic
19#14583282—21no—
20#14583279C2211yescharacteristic
21#14583249C2211yescharacteristic
22#14583245C2211yescharacteristic
23#14583245C2211yescharacteristic
24#14583237—21no—
25#14583220—21no—
26#14583184C2211yescharacteristic
27#14583184C2211yescharacteristic
28#14583155—21no—
29#14583126—21no—
30#14583120—21no—
31#14583120—21no—
32#14583106C2211yescharacteristic
33#14583104C2211yescharacteristic
34#14583104C2211yescharacteristic
35#14583096C2211yescharacteristic
36#14583061—21no—
37#14583055—21no—
38C8×Dic86C2211yescharacteristic
39#14582993—21no—
40C4×#10621885C2211yescharacteristic
41#14582977C2211yescharacteristic
42D4×C43⋊C8C2211yescharacteristic
43#14582908—21no—
44#14582895—21no—
45#14582652C2211yescharacteristic
46#14582649C2211yescharacteristic
47#14582646C2211yescharacteristic
48#14582646C2211yescharacteristic
49#14582645C2211yescharacteristic
50#14582643C2211yescharacteristic
51Q8⋊(C43⋊C8)C2211yescharacteristic
52#14582629C2211yescharacteristic
53D4⋊(C43⋊C8)C2211yescharacteristic
54D4⋊(C43⋊C8)C2211yescharacteristic
55#14582621C2211yescharacteristic
56C43×#550C2211yescharacteristic
57D4×Q8×C43C2211yescharacteristic
58C43×#486—21no—
59C43×#486C2211yescharacteristic
60C43×#474—21no—
61C43×#474C2211yescharacteristic
62C43×#459—21no—
63C43×#459C2211yescharacteristic
64C8×Q8×C43C2211yescharacteristic
65C4×D8×C43—21no—
66C4×D8×C43C2211yescharacteristic
67C2×Dic172—21no—
68C2×Dic172—21no—
69C2×#10621885—21no—
70C2×#10621885D411yescharacteristic
71C2×#10621883—21no—
72C2×#10621883—21no—
73C2×#10621883—21no—
74C2×#10621877—21no—
75C22×C43⋊C8—21no—
76#13063325C2311yescharacteristic
77#13063325C2311yescharacteristic
78#13063318—41no—
79#13063318—41no—
80#13063312—21no—
81#13063312—21no—
82#13063304—21no—
83#13063304—21no—
84C4×Dic86C2311yescharacteristic
85#13063290—21no—
86#13063290—21no—
87#13063284—21no—
88#13063284—21no—
89#13063258D411yescharacteristic
90#13063256—21no—
91#13063256—21no—
92#13063256—41no—
93C4⋊(C43⋊C8)C2311yescharacteristic
94C4⋊(C43⋊C8)C2311yescharacteristic
95C4⋊(C43⋊C8)C2311yescharacteristic
96Dic43⋊C8—21no—
97#13063249—21no—
98#13063249—21no—
99#13063249—21no—
100#13063249—21no—
101#13063249—21no—
102#13063249D411yescharacteristic
103#13063248—21no—
104#13063248—21no—
105#13063248D411yescharacteristic
106#13063246—21no—
107#13063246—21no—
108#13063246—21no—
109#13063246—41no—
110C22⋊(C43⋊C8)—21no—
111C22⋊(C43⋊C8)—21no—
112C4×C43⋊C8C2311yescharacteristic
113C4×C43⋊C8C2311yescharacteristic
114C8×Dic43—21no—
115C2×#41×C43—21no—
116C22×Q8×C43—21no—
117C2×D8×C43—21no—
118C2×D8×C43D411yescharacteristic
119C4⋊Q8×C43—21no—
120C4⋊Q8×C43C2311yescharacteristic
121#127×C43—21no—
122#127×C43C2311yescharacteristic
123C22⋊Q8×C43—21no—
124C22⋊Q8×C43—41no—
125#121×C43—21no—
126#121×C43—41no—
127C4×Q8×C43C2311yescharacteristic
128C4×D4×C43—21no—
129C4×D4×C43—21no—
130C4×D4×C43C2311yescharacteristic
131C4×D4×C43C2311yescharacteristic
132#107×C43—21no—
133#107×C43D411yescharacteristic
134C4⋊C8×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
142C4×C8×C43—21no—
143C4×C8×C43C2311yescharacteristic
144#41×C43—42no—
145#41×C43—81no—
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×C43C2×D411yescharacteristic
157C2×D4×C43C2×D411yescharacteristic
158C22×C4×C43—21no—
159C22×C4×C43—21no—
160C22×C4×C43—41no—
161C22×C4×C43—41no—
162C2×Dic86—21no—
163C2×Dic86—21no—
164C2×Dic86C2×D411yescharacteristic
165D8×C43—41no—
166D8×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—41no—
174C4⋊C4×C43C2×D411yescharacteristic
175C4⋊C4×C43C2×D411yescharacteristic
176C4⋊C4×C43C2×D411yescharacteristic
177C22⋊C4×C43—21no—
178C22⋊C4×C43—21no—
179C22⋊C4×C43—41no—
180C22⋊C4×C43—41no—
181C42×C43—21no—
182C42×C43C2411yescharacteristic
183C22⋊Dic43—41no—
184C22⋊Dic43—41no—
185C22⋊Dic43—41no—
186C22⋊Dic43—41no—
187#10621885—22no—
188#10621885—81no—
189#10621883—81no—
190#10621883—81no—
191#10621883—81no—
192C4⋊Dic43—21no—
193C4⋊Dic43—21no—
194C4⋊Dic43—21no—
195C4⋊Dic43—21no—
196C4⋊Dic43C2×D411yescharacteristic
197Dic43⋊C4—21no—
198Dic43⋊C4—41no—
199Dic43⋊C4—41no—
200C4×Dic43—21no—
201C4×Dic43—41no—
202C4×Dic43—41no—
203#10621877—81no—
204C2×C43⋊C8—21no—
205C2×C43⋊C8—21no—
206C2×C43⋊C8—21no—
207C2×C43⋊C8—21no—
208C2×C43⋊C8—81no—
209C2×C43⋊C8C2×D411yescharacteristic
210C2×C43⋊C8C2×D411yescharacteristic
211Dic172—42no—
212Dic172—81no—
213C23×C43—21no—
214C23×C43—21no—
215C23×C43—41no—
216Q8×C43—21no—
217Q8×C43—41no—
218Q8×C43—41no—
219Q8×C43—82no—
220Q8×C43#13512yes—
221D4×C43—21no—
222D4×C43—21no—
223D4×C43—21no—
224D4×C43—21no—
225D4×C43—41no—
226D4×C43—41no—
227D4×C43—41no—
228D4×C43—41no—
229D4×C43—82no—
230D4×C43—81no—
231D4×C43—161no—
232C2×C4×C43—21no—
233C2×C4×C43—21no—
234C2×C4×C43—21no—
235C2×C4×C43—21no—
236C2×C4×C43—41no—
237C2×C4×C43—41no—
238C2×C4×C43—41no—
239C2×C4×C43—41no—
240C2×C4×C43—41no—
241C2×C4×C43—82no—
242C2×C4×C43—82no—
243C2×C4×C43C22×D411yescharacteristic
244C2×C4×C43C22×D411yescharacteristic
245C2×C4×C43H(5,𝔽2)11yescharacteristic
246C2×Dic43—21no—
247C2×Dic43—21no—
248C2×Dic43—41no—
249C2×Dic43—41no—
250Dic86—21no—
251Dic86—21no—
252Dic86—41no—
253Dic86—41no—
254Dic86—41no—
255Dic86—41no—
256C8×C43—21no—
257C8×C43—21no—
258C8×C43—41no—
259C43⋊C8—21no—
260C43⋊C8—21no—
261C43⋊C8—41no—
262C43⋊C8—41no—
263C43⋊C8—41no—
264C43⋊C8—41no—
265#19786—431nomaximal, Sylow
266C22×C43—41no—
267C22×C43—41no—
268C22×C43—41no—
269C22×C43—41no—
270C22×C43—41no—
271C22×C43—41no—
272C22×C43—81no—
273C22×C43—81no—
274C22×C43—81no—
275C22×C43D4211yescharacteristic
276C4×C43—22no—
277C4×C43—21no—
278C4×C43—41no—
279C4×C43—41no—
280C4×C43—41no—
281C4×C43—81no—
282C4×C43C2×#13511yescharacteristic
283C4×C43#57511yescharacteristic
284C4×C43#57611yescharacteristic
285C4×C43#57711yescharacteristic
286Dic43—41no—
287Dic43—41no—
288Dic43—81no—
289Dic43—81no—
290#3393—431no—
291#3358D4311yescharacteristic
292#3328—431no—
293#3304—431no—
294#1720—431no—
295#1701—431no—
296#1682—431no—
297#1679—431no—
298#1670—431no—
299#1652—431no—
300#1651—431no—
301#1642—431no—
302#1628—431no—
303#1581—431no—
304#1579—431no—
305C2×C43—81no—
306C2×C43—81no—
307C2×C43—161no—
308C2×C43#327111yescharacteristic
309C2×C43#328011yescharacteristic
310C2×C43#328911yescharacteristic
311#556—431no—
312#556—431no—
313#550C2×D4311yescharacteristic
314D4×Q8C2×D4311yescharacteristic
315#498—431no—
316#495—861no—
317#494—431no—
318#487—431no—
319#486—21no—
320#486—431no—
321#486—431no—
322#486C2×D4311yescharacteristic
323#485—861no—
324#482—861no—
325#475—431no—
326#475—431no—
327#474—21no—
328#474C2×D4311yescharacteristic
329#470—861no—
330#465—861no—
331#464—861no—
332#464—861no—
333#462—431no—
334#461—431no—
335#461—431no—
336#460—431no—
337#459—21no—
338#459C2×D4311yescharacteristic
339#452—861no—
340#451—861no—
341C8×Q8—431no—
342C8×Q8C2×D4311yescharacteristic
343C4×Q16—431no—
344C4×Q16—861no—
345C4×D8—21no—
346C4×D8C2×D4311yescharacteristic
347#436—431no—
348C8×D4—431no—
349#419—861no—
350#416—861no—
351#335—431no—
352#334—431no—
353#332—431no—
354#332—431no—
355#332—431no—
356#331—431no—
357Q8⋊C8—431no—
358Q8⋊C8—431no—
359D4⋊C8—431no—
360D4⋊C8—431no—
361#322—431no—
362C43#1978611yescharacteristic, complemented, Sylow
363C2×#41—21no—
364C22×Q8—21no—
365C2×Q16—431no—
366C2×Q16—861no—
367C2×Q16—861no—
368C2×Q16—861no—
369C2×SD16—861no—
370C2×SD16—861no—
371C2×SD16—861no—
372C2×D8—21no—
373C2×D8C22⋊D4311yescharacteristic
374C2×M16—861no—
375C22×C8—861no—
376C4⋊Q8—21no—
377C4⋊Q8—431no—
378C4⋊Q8—431no—
379C4⋊Q8C22×D4311yescharacteristic
380#127—21no—
381#127C22×D4311yescharacteristic
382#126—1721no—
383#126—1721no—
384#124—861no—
385#124—861no—
386C22⋊Q8—21no—
387C22⋊Q8—41no—
388C22⋊Q8—861no—
389C22⋊Q8—861no—
390#121—21no—
391#121—41no—
392C4×Q8—431no—
393C4×Q8—861no—
394C4×Q8—861no—
395C4×Q8C22×D4311yescharacteristic
396C4×D4—21no—
397C4×D4—21no—
398C4×D4C22×D4311yescharacteristic
399C4×D4C22×D4311yescharacteristic
400#117—861no—
401#117—861no—
402#107—21no—
403#107—431no—
404#107C22⋊D4311yescharacteristic
405#106—861no—
406#106—861no—
407#106—1721no—
408C4⋊C8—21no—
409C4⋊C8—431no—
410C4⋊C8—431no—
411C4⋊C8—431no—
412C4⋊C8—861no—
413C4⋊C8C22×D4311yescharacteristic
414#103—431no—
415#103—431no—
416#103—861no—
417#103—861no—
418#103—861no—
419#103—861no—
420#103—861no—
421#103—861no—
422#103—861no—
423#102—21no—
424#102—21no—
425#102—21no—
426#102—21no—
427#102—861no—
428#102—861no—
429#102—861no—
430#102—1721no—
431#102C22⋊D4311yescharacteristic
432#102C22⋊D4311yescharacteristic
433C22⋊C8—861no—
434C22⋊C8—861no—
435C4×C8—21no—
436C4×C8—431no—
437C4×C8—431no—
438C4×C8—861no—
439C4×C8C22×D4311yescharacteristic
440#41—42no—
441#41—81no—
442C2×Q8—21no—
443C2×Q8—41no—
444C2×Q8—42no—
445C2×Q8—81no—
446C2×Q8—431no—
447C2×Q8—861no—
448C2×Q8—861no—
449C2×Q8D4×D4311yescharacteristic
450C2×D4—21no—
451C2×D4—21no—
452C2×D4—21no—
453C2×D4—41no—
454C2×D4—41no—
455C2×D4C2×C22⋊D4311yescharacteristic
456C2×D4C2×C22⋊D4311yescharacteristic
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—41no—
460C22×C4—41no—
461Q16—862no—
462Q16—3441no—
463Q16—3441no—
464Q16—1722no—
465SD16—3441no—
466SD16—3441no—
467SD16—3441no—
468D8—41no—
469D8—42no—
470M16—3441no—
471C2×C8—21no—
472C2×C8—431no—
473C2×C8—431no—
474C2×C8—861no—
475C2×C8—861no—
476C2×C8—861no—
477C2×C8—861no—
478C2×C8—3441no—
479C2×C8C2×C22⋊D4311yescharacteristic
480C2×C8C2×C22⋊D4311yescharacteristic
481C4⋊C4—21no—
482C4⋊C4—21no—
483C4⋊C4—21no—
484C4⋊C4—41no—
485C4⋊C4—431no—
486C4⋊C4—861no—
487C4⋊C4—861no—
488C4⋊C4—861no—
489C4⋊C4—861no—
490C4⋊C4—861no—
491C4⋊C4—1721no—
492C4⋊C4—1721no—
493C4⋊C4D4×D4311yescharacteristic
494C4⋊C4C2×C22⋊D4311yescharacteristic
495C4⋊C4C2×C22⋊D4311yescharacteristic
496C22⋊C4—21no—
497C22⋊C4—21no—
498C22⋊C4—41no—
499C22⋊C4—41no—
500C22⋊C4—1721no—
501C22⋊C4—1721no—
502C22⋊C4—1721no—
503C22⋊C4—1721no—
504C42—21no—
505C42—861no—
506C42—1721no—
507C42—1721no—
508C42C23×D4311yescharacteristic
509C23—21no—
510C23—21no—
511C23—41no—
512Q8—21no—
513Q8—41no—
514Q8—41no—
515Q8—82no—
516Q8—861no—
517Q8—861no—
518Q8—1721no—
519Q8—1721no—
520Q8—1721no—
521Q8—1721no—
522Q8#1306334412yes—
523D4—21no—
524D4—21no—
525D4—21no—
526D4—21no—
527D4—41no—
528D4—41no—
529D4—41no—
530D4—41no—
531D4—82no—
532D4—81no—
533D4—161no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—82no—
544C2×C4—82no—
545C2×C4—861no—
546C2×C4—861no—
547C2×C4—1721no—
548C2×C4—1721no—
549C2×C4C2×D4×D4311yescharacteristic
550C2×C4C22×C22⋊D4311yescharacteristic
551C2×C4#1306337011yescharacteristic
552C8—21no—
553C8—21no—
554C8—41no—
555C8—861no—
556C8—861no—
557C8—1721no—
558C8—1721no—
559C8—1721no—
560C8—1721no—
561C22—41no—
562C22—41no—
563C22—41no—
564C22—41no—
565C22—41no—
566C22—41no—
567C22—81no—
568C22—81no—
569C22—81no—
570C22D4×C22⋊D4311yescharacteristic
571C4—22no—
572C4—21no—
573C4—41no—
574C4—41no—
575C4—41no—
576C4—81no—
577C4—3441no—
578C4—3441no—
579C4—1721no—
580C4—1721no—
581C4C2×#1306334411yescharacteristic
582C4#1458369711yescharacteristic
583C4#1458370011yescharacteristic
584C4#1458370711yescharacteristic
585C2—81no—
586C2—81no—
587C2—161no—
588C2#1914618111yescharacteristic
589C2#1914628011yescharacteristic
590C2#1914636811yescharacteristic
subgroupG/H
centerC22D4×C22⋊D43
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
Fitting, prime radicalC43×#3358C2
socleC22×C43D42
hypercenter#3358D43
hypocenterC43#19786
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #3358

Complements

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

NH ≅ G/Ntype
1. #19147581C2semidirect
2. #19146878C2semidirect
3. #19146534C2semidirect
4. #19134254C2semidirect
5. #19134154C2semidirect
6. #19134036C2semidirect
7. #19134016C2semidirect
8. #19133965C2semidirect
9. #19133864C2semidirect
10. #19133858C2semidirect
11. #19133795C2semidirect
12. #19133703C2semidirect
13. #19133425C2semidirect
14. #19133412C2semidirect
362. C43#19786semidirect

Maximal subgroups

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

subgroupindex
#191475812
#191468782
#191465342
#191342542
#191341542
#191340362
#191340162
#191339652
#191338642
#191338582
#191337952
#191337032
#191334252
#191334122
C43×#33582
#1978643