Finite Group Databasebeta

← #25087995

Subgroups — #25087995

Order 11008.

640 conjugacy classes of subgroups.

The subgroup lattice has 586 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19147233C211yesmaximal, characteristic, complemented
2#19146460C211yesmaximal, characteristic
3#19146242C211yesmaximal, characteristic
4#19134193C211yesmaximal, characteristic, complemented
5#19134105C211yesmaximal, characteristic, complemented
6#19134089C211yesmaximal, characteristic, complemented
7#19134023C211yesmaximal, characteristic, complemented
8#19134016C211yesmaximal, characteristic, complemented
9#19133878C211yesmaximal, characteristic
10#19133872C211yesmaximal, characteristic, complemented
11#19133858C211yesmaximal, characteristic, complemented
12#19133857C211yesmaximal, characteristic, complemented
13#19133485C211yesmaximal, characteristic, complemented
14SD16×C43⋊C8C211yesmaximal, characteristic, complemented
15C43×#3386C211yesmaximal, characteristic, complemented
16C2×#13063354—21no—
17Q8×D172C2211yescharacteristic
18#14583553C2211yescharacteristic
19#14583295C2211yescharacteristic
20#14583295C2211yescharacteristic
21#14583279C2211yescharacteristic
22#14583249—21no—
23#14583249C2211yescharacteristic
24#14583249C2211yescharacteristic
25#14583227—21no—
26#14583184—21no—
27#14583184C2211yescharacteristic
28#14583184C2211yescharacteristic
29#14583158—21no—
30#14583130—21no—
31#14583109C2211yescharacteristic
32#14583104C2211yescharacteristic
33#14583101—21no—
34#14583101C2211yescharacteristic
35#14583101C2211yescharacteristic
36#14583062—21no—
37#14583056—21no—
38#14583038—21no—
39Q8×C43⋊C8C2211yescharacteristic
40C4×#10621884—21no—
41C4×#10621884C2211yescharacteristic
42#14582978C2211yescharacteristic
43D4×C43⋊C8C2211yescharacteristic
44C2×#13063249—21no—
45#14582650C2211yescharacteristic
46#14582649C2211yescharacteristic
47#14582646C2211yescharacteristic
48#14582646C2211yescharacteristic
49#14582645C2211yescharacteristic
50#14582645C2211yescharacteristic
51Q8⋊(C43⋊C8)C2211yescharacteristic
52Q8⋊(C43⋊C8)C2211yescharacteristic
53D4⋊(C43⋊C8)C2211yescharacteristic
54#14582626C2211yescharacteristic
55C8×C43⋊C8C2211yescharacteristic
56C43×#557C2211yescharacteristic
57D4×Q8×C43C2211yescharacteristic
58C43×#501—21no—
59C43×#500C2211yescharacteristic
60C43×#478—21no—
61C43×#477—21no—
62C43×#475C2211yescharacteristic
63C43×#474C2211yescharacteristic
64C43×#446C2211yescharacteristic
65C43×#440—21no—
66C4×SD16×C43C2211yescharacteristic
67C2×#10621900—21no—
68C2×Q8×D43—21no—
69#13063354—44no—
70C2×Dic172—21no—
71C2×Dic172—21no—
72C2×#10621885—21no—
73C2×#10621883—21no—
74C2×#10621884—21no—
75C2×#10621884—21no—
76C2×#10621884D411yescharacteristic
77C2×#10621872—21no—
78C22×C43⋊C8—21no—
79#13063325—21no—
80#13063325C2311yescharacteristic
81#13063325C2311yescharacteristic
82#13063309—41no—
83#13063305—21no—
84#13063305—21no—
85#13063305—41no—
86#13063299—21no—
87C4×D172—21no—
88C4×D172C2311yescharacteristic
89C2×C4⋊Dic43—21no—
90#13063256—21no—
91#13063256—21no—
92#13063256—41no—
93#13063256—41no—
94#13063256D411yescharacteristic
95C4⋊(C43⋊C8)—21no—
96C4⋊(C43⋊C8)C2311yescharacteristic
97C4⋊(C43⋊C8)C2311yescharacteristic
98C4⋊(C43⋊C8)C2311yescharacteristic
99#13063249—21no—
100#13063249—21no—
101#13063249—21no—
102#13063249—21no—
103#13063249—21no—
104#13063249—21no—
105#13063249—21no—
106#13063249—21no—
107#13063249D411yescharacteristic
108#13063248—21no—
109#13063248—21no—
110#13063245D411yescharacteristic
111C22⋊(C43⋊C8)—21no—
112(C2×D43)⋊C8—21no—
113C4×C43⋊C8—21no—
114C4×C43⋊C8C2311yescharacteristic
115C4×C43⋊C8C2311yescharacteristic
116C22×Q8×C43—21no—
117C2×SD16×C43D411yescharacteristic
118C4⋊Q8×C43—21no—
119C4⋊Q8×C43—21no—
120C4⋊Q8×C43C2311yescharacteristic
121C4⋊Q8×C43C2311yescharacteristic
122#125×C43—21no—
123#125×C43—41no—
124C22⋊Q8×C43—21no—
125C22⋊Q8×C43—41no—
126C4×Q8×C43—21no—
127C4×Q8×C43—21no—
128C4×Q8×C43C2311yescharacteristic
129C4×Q8×C43C2311yescharacteristic
130C4×D4×C43—21no—
131C4×D4×C43C2311yescharacteristic
132#107×C43—21no—
133#107×C43—21no—
134#107×C43—21no—
135#106×C43—21no—
136#106×C43D411yescharacteristic
137C4⋊C8×C43—21no—
138C4⋊C8×C43C2311yescharacteristic
139#103×C43—21no—
140#103×C43D411yescharacteristic
141#102×C43—21no—
142#102×C43D411yescharacteristic
143#97×C43—21no—
144C4×C8×C43C2311yescharacteristic
145C2×Q8×C43—21no—
146C2×Q8×C43—21no—
147C2×Q8×C43—41no—
148C2×Q8×C43—42no—
149C2×Q8×C43—81no—
150C2×Q8×C43C2×D411yescharacteristic
151C2×Q8×C43C2×D411yescharacteristic
152C2×D4×C43C2×D411yescharacteristic
153C22×C4×C43—21no—
154C22×C4×C43—41no—
155C2×C22⋊D43—41no—
156C22×Dic43—41no—
157Q8×D43—42no—
158Q8×D43—81no—
159#10621900—42no—
160#10621900—81no—
161C2×D172C2×D411yescharacteristic
162C2×C4×D43—21no—
163C2×C4×D43—41no—
164C2×Dic86—21no—
165C2×Dic86—21no—
166C2×Dic86—41no—
167SD16×C43SD1614yescomplemented
168C2×C8×C43—21no—
169C2×C8×C43C2×D411yescharacteristic
170C2×C8×C43C2×D411yescharacteristic
171C4⋊C4×C43—21no—
172C4⋊C4×C43—21no—
173C4⋊C4×C43—21no—
174C4⋊C4×C43—21no—
175C4⋊C4×C43—21no—
176C4⋊C4×C43—21no—
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—42no—
191#10621884—41no—
192#10621884—42no—
193#10621884—81no—
194#10621883—42no—
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⋊Dic43—41no—
204C4⋊Dic43C2×D411yescharacteristic
205C2×C43⋊C8—21no—
206C2×C43⋊C8—21no—
207C2×C43⋊C8—21no—
208C2×C43⋊C8—21no—
209C2×C43⋊C8—81no—
210C2×C43⋊C8C2×D411yescharacteristic
211C2×C43⋊C8C2×D411yescharacteristic
212Dic172—42no—
213Dic172—81no—
214#10621872—42no—
215C23×C43—21no—
216C22×D43—21no—
217Q8×C43—21no—
218Q8×C43—21no—
219Q8×C43—21no—
220Q8×C43—41no—
221Q8×C43—41no—
222Q8×C43—41no—
223Q8×C43—41no—
224Q8×C43—82no—
225Q8×C43C2×SD1612yes—
226D4×C43—21no—
227D4×C43C2×SD1612yes—
228C2×C4×C43—21no—
229C2×C4×C43—21no—
230C2×C4×C43—21no—
231C2×C4×C43—21no—
232C2×C4×C43—21no—
233C2×C4×C43—41no—
234C2×C4×C43—41no—
235C2×C4×C43—41no—
236C2×C4×C43—41no—
237C2×C4×C43—82no—
238C2×C4×C43C22×D411yescharacteristic
239C2×C4×C43C22×D411yescharacteristic
240C2×C4×C43H(5,𝔽2)11yescharacteristic
241C22⋊D43—82no—
242C2×Dic43—21no—
243C2×Dic43—41no—
244C2×Dic43—41no—
245C2×Dic43—82no—
246D172—21no—
247D172—21no—
248C4×D43—41no—
249C4×D43—41no—
250C4×D43—82no—
251Dic86—41no—
252Dic86—41no—
253Dic86—41no—
254Dic86—41no—
255Dic86—82no—
256C8×C43—21no—
257C8×C43—41no—
258C8×C43C2×SD1612yes—
259C43⋊C8—22no—
260C43⋊C8—21no—
261C43⋊C8—21no—
262C43⋊C8—41no—
263C43⋊C8—41no—
264C43⋊C8—41no—
265#19894—431nomaximal, Sylow
266C22×C43—22no—
267C22×C43—41no—
268C22×C43—41no—
269C22×C43D4211yescharacteristic
270C2×D43—41no—
271C2×D43—41no—
272C2×D43—41no—
273C4×C43—22no—
274C4×C43—21no—
275C4×C43—41no—
276C4×C43—41no—
277C4×C43—41no—
278C4×C43—41no—
279C4×C43—81no—
280C4×C43—81no—
281C4×C43C22×SD1611yescharacteristic
282C4×C43#57511yescharacteristic
283C4×C43#57711yescharacteristic
284C4×C43#57711yescharacteristic
285Dic43—41no—
286Dic43—81no—
287Dic43—81no—
288#3386D4311yescharacteristic, complemented
289#3359—431no—
290#3298—431no—
291#3276—431no—
292#1707—431no—
293#1693—431no—
294#1690—431no—
295#1680—431no—
296#1679—431no—
297#1654—431no—
298#1653—431no—
299#1651—431no—
300#1651—431no—
301#1590—431no—
302C8×SD16—431no—
303C2×C43—42no—
304C2×C43#327511yescharacteristic
305C2×C43D4×SD1611yescharacteristic
306C2×C43#329311yescharacteristic
307D43—81no—
308C2×#137—861no—
309#557C2×D4311yescharacteristic
310D4×Q8—431no—
311D4×Q8C2×D4311yescharacteristic
312#547—431no—
313#501—21no—
314#500C2×D4311yescharacteristic
315#498—431no—
316#498—431no—
317#494—431no—
318#487—431no—
319#487—431no—
320#487—861no—
321#483—861no—
322#478—21no—
323#477—21no—
324#475—431no—
325#475—431no—
326#475—861no—
327#475C2×D4311yescharacteristic
328#474C2×D4311yescharacteristic
329#470—861no—
330#465—861no—
331#462—431no—
332#461—431no—
333#461—431no—
334#461—431no—
335#461—861no—
336#452—861no—
337#451—861no—
338#448—861no—
339#446C2×D4311yescharacteristic
340C8×Q8—431no—
341#440—21no—
342C4×SD16—431no—
343C4×SD16—861no—
344C4×SD16C2×D4311yescharacteristic
345#436—431no—
346C8×D4—431no—
347C2×#103—861no—
348#334—431no—
349#334—431no—
350#332—431no—
351#332—431no—
352#332—431no—
353#332—431no—
354Q8⋊C8—431no—
355Q8⋊C8—431no—
356D4⋊C8—431no—
357D4⋊C8—431no—
358C82—431no—
359C43#1989411yescharacteristic, complemented, Sylow
360C2×#41—861no—
361C22×Q8—21no—
362C22×Q8—861no—
363#137—1724no—
364C2×Q16—861no—
365C2×Q16—861no—
366C2×Q16—861no—
367C2×SD16—431no—
368C2×SD16—861no—
369C2×SD16—861no—
370C2×SD16—861no—
371C2×SD16C22⋊D4311yescharacteristic
372C2×M16—861no—
373C22×C8—861no—
374C4⋊Q8—21no—
375C4⋊Q8—21no—
376C4⋊Q8—431no—
377C4⋊Q8—431no—
378C4⋊Q8—861no—
379C4⋊Q8C22×D4311yescharacteristic
380C4⋊Q8C22×D4311yescharacteristic
381#125—21no—
382#125—41no—
383#123—1721no—
384C22⋊Q8—21no—
385C22⋊Q8—41no—
386C22⋊Q8—861no—
387C22⋊Q8—861no—
388C22⋊Q8—1721no—
389#121—861no—
390C4×Q8—21no—
391C4×Q8—21no—
392C4×Q8C22×D4311yescharacteristic
393C4×Q8C22×D4311yescharacteristic
394C4×D4—21no—
395C4×D4—431no—
396C4×D4—861no—
397C4×D4C22×D4311yescharacteristic
398C2×C4⋊C4—861no—
399#107—21no—
400#107—21no—
401#107—21no—
402#106—21no—
403#106—431no—
404#106—861no—
405#106—861no—
406#106—1721no—
407#106—1721no—
408#106C22⋊D4311yescharacteristic
409C4⋊C8—21no—
410C4⋊C8—431no—
411C4⋊C8—431no—
412C4⋊C8—431no—
413C4⋊C8—861no—
414C4⋊C8C22×D4311yescharacteristic
415#103—21no—
416#103—431no—
417#103—861no—
418#103—861no—
419#103—861no—
420#103—861no—
421#103—861no—
422#103—861no—
423#103—861no—
424#103—861no—
425#103—861no—
426#103—861no—
427#103C22⋊D4311yescharacteristic
428#102—21no—
429#102—431no—
430#102C22⋊D4311yescharacteristic
431C22⋊C8—861no—
432C22⋊C8—861no—
433#97—21no—
434C4×C8—431no—
435C4×C8—431no—
436C4×C8—861no—
437C4×C8C22×D4311yescharacteristic
438#41—3441no—
439#41—1722no—
440C2×Q8—21no—
441C2×Q8—21no—
442C2×Q8—41no—
443C2×Q8—42no—
444C2×Q8—81no—
445C2×Q8—861no—
446C2×Q8—861no—
447C2×Q8—3441no—
448C2×Q8—1721no—
449C2×Q8—1722no—
450C2×Q8D4×D4311yescharacteristic
451C2×Q8C2×C22⋊D4311yescharacteristic
452C2×D4—431no—
453C2×D4—1721no—
454C2×D4C2×C22⋊D4311yescharacteristic
455C22×C4—21no—
456C22×C4—41no—
457C22×C4—861no—
458C22×C4—1721no—
459C22×C4—1721no—
460Q16—3441no—
461Q16—1722no—
462Q16—1722no—
463SD16—3441no—
464SD16—1721no—
465SD16—1722no—
466SD16—1722no—
467SD16#1062188414yescomplemented
468M16—1722no—
469C2×C8—21no—
470C2×C8—431no—
471C2×C8—431no—
472C2×C8—861no—
473C2×C8—861no—
474C2×C8—861no—
475C2×C8—861no—
476C2×C8—3441no—
477C2×C8C2×C22⋊D4311yescharacteristic
478C2×C8C2×C22⋊D4311yescharacteristic
479C4⋊C4—21no—
480C4⋊C4—21no—
481C4⋊C4—21no—
482C4⋊C4—21no—
483C4⋊C4—21no—
484C4⋊C4—21no—
485C4⋊C4—41no—
486C4⋊C4—41no—
487C4⋊C4—41no—
488C4⋊C4—41no—
489C4⋊C4—431no—
490C4⋊C4—861no—
491C4⋊C4—861no—
492C4⋊C4—861no—
493C4⋊C4—861no—
494C4⋊C4—1721no—
495C4⋊C4—1721no—
496C4⋊C4D4×D4311yescharacteristic
497C4⋊C4C2×C22⋊D4311yescharacteristic
498C4⋊C4C2×C22⋊D4311yescharacteristic
499C22⋊C4—21no—
500C22⋊C4—41no—
501C22⋊C4—861no—
502C22⋊C4—1721no—
503C22⋊C4—1721no—
504C42—21no—
505C42—21no—
506C42—41no—
507C42C23×D4311yescharacteristic
508C23—21no—
509C23—861no—
510Q8—21no—
511Q8—21no—
512Q8—21no—
513Q8—41no—
514Q8—41no—
515Q8—41no—
516Q8—41no—
517Q8—82no—
518Q8—3442no—
519Q8—1721no—
520Q8—1721no—
521Q8—1721no—
522Q8—1721no—
523Q8C2×#1062188412yes—
524D4—21no—
525D4—861no—
526D4—861no—
527D4—3442no—
528D4C2×#1062188412yes—
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—82no—
539C2×C4—861no—
540C2×C4—3442no—
541C2×C4—3442no—
542C2×C4—1721no—
543C2×C4—1721no—
544C2×C4—1721no—
545C2×C4—1721no—
546C2×C4C2×D4×D4311yescharacteristic
547C2×C4C22×C22⋊D4311yescharacteristic
548C2×C4#1306337011yescharacteristic
549C8—21no—
550C8—41no—
551C8—862no—
552C8—861no—
553C8—861no—
554C8—1721no—
555C8—1721no—
556C8—1721no—
557C8C2×#1062188412yes—
558C22—22no—
559C22—41no—
560C22—41no—
561C22—1721no—
562C22—1721no—
563C22—1721no—
564C22D4×C22⋊D4311yescharacteristic
565C4—22no—
566C4—21no—
567C4—41no—
568C4—41no—
569C4—41no—
570C4—41no—
571C4—81no—
572C4—81no—
573C4—3441no—
574C4—3441no—
575C4—1721no—
576C4C22×#1062188411yescharacteristic
577C4#1458369511yescharacteristic
578C4#1458370711yescharacteristic
579C4#1458370911yescharacteristic
580C2—42no—
581C2—3441no—
582C2#1914622611yescharacteristic
583C2D4×#1062188411yescharacteristic
584C2#1914639711yescharacteristic
subgroupG/H
centerC22D4×C22⋊D43
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#3386C2
socleC22×C43D42
prime radical#14583553C22
hypercenter#3386D43
hypocenterC43#19894
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #3386

Complements

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

NH ≅ G/Ntype
1. #19147233C2semidirect
4. #19134193C2semidirect
5. #19134105C2semidirect
6. #19134089C2semidirect
7. #19134023C2semidirect
8. #19134016C2semidirect
10. #19133872C2semidirect
11. #19133858C2semidirect
12. #19133857C2semidirect
13. #19133485C2semidirect
14. SD16×C43⋊C8C2semidirect
15. C43×#3386C2semidirect
167. SD16×C43SD16semidirect
288. #3386D43semidirect
359. C43#19894semidirect
467. SD16#10621884semidirect

Maximal subgroups

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

subgroupindex
#191472332
#191464602
#191462422
#191341932
#191341052
#191340892
#191340232
#191340162
#191338782
#191338722
#191338582
#191338572
#191334852
SD16×C43⋊C82
C43×#33862
#1989443