Finite Group Databasebeta

← #25080040

Subgroups — #25080040

Order 11008.

628 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145921C211yesmaximal, characteristic, complemented
2#19145170C211yesmaximal, characteristic, complemented
3#19143571C211yesmaximal, characteristic, complemented
4#19134121C211yesmaximal, characteristic, complemented
5#19134116C211yesmaximal, characteristic, complemented
6#19134077C211yesmaximal, characteristic, complemented
7#19134072C211yesmaximal, characteristic, complemented
8#19134013C211yesmaximal, characteristic, complemented
9#19134009C211yesmaximal, characteristic, complemented
10#19134006C211yesmaximal, characteristic, complemented
11#19134002C211yesmaximal, characteristic, complemented
12C2×#14582649C211yesmaximal, characteristic, complemented
13#19133290C211yesmaximal, characteristic, complemented
14#19133288C211yesmaximal, characteristic, complemented
15C43×#3247C211yesmaximal, characteristic, complemented
16#14583449C2211yescharacteristic
17#14583302C2211yescharacteristic
18#14583275C2211yescharacteristic
19#14583247C2211yescharacteristic
20#14583245C2211yescharacteristic
21#14583196—21no—
22#14583194C2211yescharacteristic
23#14583189C2211yescharacteristic
24#14583133—21no—
25#14583133—21no—
26#14583133—21no—
27#14583130—21no—
28#14583111—21no—
29#14583099C2211yescharacteristic
30#14583094C2211yescharacteristic
31#14583030C2211yescharacteristic
32Q8×C43⋊C8C2211yescharacteristic
33C4×#10621882—21no—
34C4×#10621882—21no—
35#14582977C2211yescharacteristic
36#14582971—21no—
37D4×C43⋊C8—21no—
38D4×C43⋊C8C2211yescharacteristic
39#14582960—21no—
40#14582956C2211yescharacteristic
41C2×C4⋊(C43⋊C8)C2211yescharacteristic
42#14582855—21no—
43C2×C4×C43⋊C8C2211yescharacteristic
44#14582649C2211yescharacteristic
45#14582649C2211yescharacteristic
46#14582649C2211yescharacteristic
47#14582649C2211yescharacteristic
48#14582648C2211yescharacteristic
49#14582648C2211yescharacteristic
50#14582647C2211yescharacteristic
51#14582647C2211yescharacteristic
52#14582643C2211yescharacteristic
53#14582643C2211yescharacteristic
54#14582642C2211yescharacteristic
55#14582642C2211yescharacteristic
56C43×#532C2211yescharacteristic
57C43×#529C2211yescharacteristic
58C43×#478—21no—
59C43×#477C2211yescharacteristic
60C43×#476C2211yescharacteristic
61C43×#466—21no—
62C43×#465—21no—
63C43×#463—21no—
64C43×#460C2211yescharacteristic
65C43×#459C2211yescharacteristic
66C2×C4⋊C8×C43C2211yescharacteristic
67C2×#10621898—21no—
68C2×#10621884—21no—
69C2×#10621882—21no—
70C2×#10621882—21no—
71C2×#10621882—21no—
72C2×#10621877—21no—
73C22×C43⋊C8—21no—
74C22×C43⋊C8—21no—
75C22×C43⋊C8D411yescharacteristic
76C22×C43⋊C8D411yescharacteristic
77#13063325C2311yescharacteristic
78#13063322C2311yescharacteristic
79#13063313—21no—
80#13063299—21no—
81#13063299—21no—
82C4×D172—21no—
83C4×D172—21no—
84#13063258—21no—
85#13063258—21no—
86#13063258—21no—
87#13063256—21no—
88C4⋊(C43⋊C8)—21no—
89C4⋊(C43⋊C8)—21no—
90C4⋊(C43⋊C8)—21no—
91C4⋊(C43⋊C8)C2311yescharacteristic
92C4⋊(C43⋊C8)C2311yescharacteristic
93C4⋊(C43⋊C8)C2311yescharacteristic
94C4⋊(C43⋊C8)C2311yescharacteristic
95#13063249—21no—
96#13063246—21no—
97#13063246—21no—
98#13063246—21no—
99#13063245—21no—
100#13063245—21no—
101#13063245—21no—
102#13063245—21no—
103C22⋊(C43⋊C8)—21no—
104C22⋊(C43⋊C8)—21no—
105C22⋊(C43⋊C8)—21no—
106#13063236—21no—
107#13063236—21no—
108C4×C43⋊C8—21no—
109C4×C43⋊C8D411yescharacteristic
110C4×C43⋊C8D411yescharacteristic
111C4×C43⋊C8C2311yescharacteristic
112C4×C43⋊C8C2311yescharacteristic
113C2×#41×C43—21no—
114C2×SD16×C43—21no—
115C2×D8×C43—21no—
116C22×C8×C43—21no—
117C4⋊Q8×C43C2311yescharacteristic
118#127×C43C2311yescharacteristic
119#126×C43—21no—
120#125×C43D411yescharacteristic
121#124×C43—21no—
122#124×C43D411yescharacteristic
123#123×C43—21no—
124C22⋊Q8×C43D411yescharacteristic
125#121×C43—21no—
126#121×C43—21no—
127#121×C43D411yescharacteristic
128C4×Q8×C43C2311yescharacteristic
129C4×D4×C43—21no—
130C4×D4×C43—21no—
131C4×D4×C43—21no—
132C4×D4×C43C2311yescharacteristic
133#117×C43—21no—
134C2×C42×C43C2311yescharacteristic
135#107×C43—21no—
136#106×C43—21no—
137C4⋊C8×C43—21no—
138C4⋊C8×C43C2311yescharacteristic
139C4⋊C8×C43C2311yescharacteristic
140#103×C43—21no—
141#102×C43—21no—
142#102×C43—21no—
143#102×C43—21no—
144#41×C43—82no—
145C2×Q8×C43—21no—
146C2×Q8×C43C2×D411yescharacteristic
147C2×D4×C43—21no—
148C2×D4×C43—21no—
149C2×D4×C43—21no—
150C2×D4×C43—21no—
151C2×D4×C43—41no—
152C2×D4×C43C2×D411yescharacteristic
153C22×C4×C43—21no—
154C22×C4×C43—41no—
155C22×C4×C43C2×D411yescharacteristic
156C22×C4×C43C2×D411yescharacteristic
157C22×C4×C43#4111yescharacteristic
158C2×C22⋊D43—41no—
159#10621898—82no—
160C2×D172—21no—
161C2×D172—21no—
162C2×D172—21no—
163C2×C4×D43—41no—
164C2×Dic86—21no—
165SD16×C43—81no—
166D8×C43—81no—
167C2×C8×C43—21no—
168C2×C8×C43—21no—
169C2×C8×C43—81no—
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×C43C2×D411yescharacteristic
177C4⋊C4×C43C2×D411yescharacteristic
178C22⋊C4×C43—21no—
179C22⋊C4×C43—21no—
180C22⋊C4×C43—21no—
181C22⋊C4×C43—21no—
182C22⋊C4×C43—21no—
183C22⋊C4×C43—41no—
184C22⋊C4×C43—41no—
185C42×C43—21no—
186C42×C43C2×D411yescharacteristic
187C42×C43C2×D411yescharacteristic
188C42×C43#4111yescharacteristic
189C42×C43C2411yescharacteristic
190#10621884—81no—
191#10621882—42no—
192#10621882—42no—
193#10621882—81no—
194(C2×D43)⋊C4—41no—
195(C2×D43)⋊C4—41no—
196C4⋊Dic43—21no—
197C4⋊Dic43—21no—
198#10621877—42no—
199C2×C43⋊C8—22no—
200C2×C43⋊C8—21no—
201C2×C43⋊C8—21no—
202C2×C43⋊C8—21no—
203C2×C43⋊C8—21no—
204C2×C43⋊C8—41no—
205C2×C43⋊C8—42no—
206C2×C43⋊C8—81no—
207C2×C43⋊C8C2×D411yescharacteristic
208C2×C43⋊C8C2×D411yescharacteristic
209C2×C43⋊C8C2×D411yescharacteristic
210C2×C43⋊C8C2×D411yescharacteristic
211C23×C43—21no—
212C23×C43—41no—
213C23×C43#12111yescharacteristic
214C22×D43—41no—
215Q8×C43—21no—
216Q8×C43—21no—
217Q8×C43—81no—
218D4×C43—21no—
219D4×C43—21no—
220D4×C43—42no—
221D4×C43—41no—
222D4×C43—41no—
223D4×C43—41no—
224D4×C43—41no—
225D4×C43—81no—
226D4×C43—82no—
227C2×C4×C43—22no—
228C2×C4×C43—21no—
229C2×C4×C43—21no—
230C2×C4×C43—21no—
231C2×C4×C43—21no—
232C2×C4×C43—21no—
233C2×C4×C43—21no—
234C2×C4×C43—21no—
235C2×C4×C43—41no—
236C2×C4×C43—41no—
237C2×C4×C43—41no—
238C2×C4×C43—82no—
239C2×C4×C43#12111yescharacteristic
240C2×C4×C43#12111yescharacteristic
241C2×C4×C43#12111yescharacteristic
242C2×C4×C43C22×D411yescharacteristic
243C2×C4×C43C22×D411yescharacteristic
244C2×C4×C43C2×#4111yescharacteristic
245C22⋊D43—82no—
246C2×Dic43—41no—
247D172—41no—
248D172—41no—
249D172—41no—
250D172—41no—
251D172—81no—
252C4×D43—82no—
253Dic86—81no—
254C8×C43—41no—
255C8×C43—41no—
256C43⋊C8—21no—
257C43⋊C8—21no—
258C43⋊C8—21no—
259C43⋊C8—41no—
260C43⋊C8—41no—
261C43⋊C8—41no—
262C43⋊C8—41no—
263C43⋊C8#13512yes—
264#19227—431nomaximal, Sylow
265C22×C43—21no—
266C22×C43—21no—
267C22×C43—41no—
268C22×C43—41no—
269C22×C43—41no—
270C22×C43—81no—
271C22×C43—81no—
272C22×C43—81no—
273C22×C43#47212yes—
274C22×C43C2×#12111yescharacteristic
275C2×D43—81no—
276C2×D43—81no—
277C2×D43—81no—
278C4×C43—21no—
279C4×C43—21no—
280C4×C43—21no—
281C4×C43—21no—
282C4×C43—41no—
283C4×C43—41no—
284C4×C43—41no—
285C4×C43—81no—
286C4×C43C2×#13511yescharacteristic
287C4×C43#57511yescharacteristic
288C4×C43#57711yescharacteristic
289C4×C43#57711yescharacteristic
290Dic43—81no—
291#3247—431no—
292#3247D4311yescharacteristic, complemented
293#3169—431no—
294#2966—431no—
295#1696—431no—
296#1695—431no—
297#1688—431no—
298#1687—431no—
299#1678—431no—
300#1678—431no—
301#1677—431no—
302#1677—431no—
303C2×#334—431no—
304#1551—431no—
305#1551—431no—
306C2×C43—22no—
307C2×C43—81no—
308C2×C43—161no—
309C2×C43#303511yescharacteristic
310C2×C43#306011yescharacteristic
311C2×C43C2×#47211yescharacteristic
312D43—161no—
313#532—431no—
314#532C2×D4311yescharacteristic
315#529C2×D4311yescharacteristic
316#500—431no—
317#493—431no—
318#486—431no—
319#486—431no—
320#478—21no—
321#478—861no—
322#477—431no—
323#477C2×D4311yescharacteristic
324#476—431no—
325#476C2×D4311yescharacteristic
326#466—21no—
327#466—861no—
328#466—861no—
329#466—861no—
330#465—21no—
331#465—861no—
332#463—21no—
333#463—861no—
334#460—431no—
335#460C2×D4311yescharacteristic
336#459—431no—
337#459C2×D4311yescharacteristic
338#446—431no—
339C8×Q8—431no—
340C4×D8—861no—
341C4×D8—861no—
342#436—431no—
343#435—861no—
344C8×D4—431no—
345C8×D4—861no—
346#433—861no—
347#432—431no—
348C2×C4⋊C8—431no—
349C2×C4⋊C8C2×D4311yescharacteristic
350#405—861no—
351C2×C4×C8—431no—
352#334—431no—
353#334—431no—
354#334—431no—
355#334—431no—
356#333—431no—
357#333—431no—
358#333—431no—
359#333—431no—
360#331—431no—
361#331—431no—
362#331—431no—
363#331—431no—
364C43#1922711yescharacteristic, complemented, Sylow
365C2×#41—21no—
366C2×#41—861no—
367C2×SD16—21no—
368C2×SD16—861no—
369C2×D8—21no—
370C2×D8—861no—
371C2×D8—861no—
372C2×D8—861no—
373C2×M16—861no—
374C22×C8—21no—
375C22×C8—431no—
376C22×C8—431no—
377C22×C8—861no—
378C22×C8—861no—
379C4⋊Q8—431no—
380C4⋊Q8C22×D4311yescharacteristic
381#127—431no—
382#127C22×D4311yescharacteristic
383#126—21no—
384#125C22⋊D4311yescharacteristic
385#124—21no—
386#124—861no—
387#124C22⋊D4311yescharacteristic
388#123—21no—
389C22⋊Q8C22⋊D4311yescharacteristic
390#121—21no—
391#121—21no—
392#121—861no—
393#121—861no—
394#121C22⋊D4311yescharacteristic
395C4×Q8C22×D4311yescharacteristic
396C4×D4—21no—
397C4×D4—21no—
398C4×D4—21no—
399C4×D4—861no—
400C4×D4—861no—
401C4×D4C22×D4311yescharacteristic
402#117—21no—
403C2×C42C22×D4311yescharacteristic
404#107—21no—
405#107—861no—
406#107—861no—
407#107—861no—
408#106—21no—
409#106—861no—
410C4⋊C8—21no—
411C4⋊C8—431no—
412C4⋊C8—431no—
413C4⋊C8—431no—
414C4⋊C8—431no—
415C4⋊C8—861no—
416C4⋊C8—861no—
417C4⋊C8—861no—
418C4⋊C8C22×D4311yescharacteristic
419C4⋊C8C22×D4311yescharacteristic
420#103—21no—
421#103—861no—
422#102—21no—
423#102—21no—
424#102—21no—
425#102—861no—
426#102—861no—
427#102—861no—
428#102—861no—
429#102—861no—
430#102—861no—
431#102—861no—
432C22⋊C8—861no—
433C22⋊C8—861no—
434C22⋊C8—861no—
435#97—861no—
436#97—861no—
437C4×C8—431no—
438C4×C8—431no—
439C4×C8—431no—
440C4×C8—431no—
441C4×C8—861no—
442#41—82no—
443#41—3442no—
444C2×Q8—21no—
445C2×Q8—861no—
446C2×Q8C2×C22⋊D4311yescharacteristic
447C2×D4—21no—
448C2×D4—21no—
449C2×D4—21no—
450C2×D4—21no—
451C2×D4—41no—
452C2×D4—861no—
453C2×D4—861no—
454C2×D4—861no—
455C2×D4—1721no—
456C2×D4C2×C22⋊D4311yescharacteristic
457C22×C4—21no—
458C22×C4—41no—
459C22×C4—1721no—
460C22×C4D4×D4311yescharacteristic
461C22×C4#1062190011yescharacteristic
462C22×C4C2×C22⋊D4311yescharacteristic
463SD16—81no—
464SD16—3441no—
465D8—81no—
466D8—3441no—
467D8—1722no—
468D8—1722no—
469M16—1722no—
470C2×C8—21no—
471C2×C8—21no—
472C2×C8—81no—
473C2×C8—431no—
474C2×C8—431no—
475C2×C8—431no—
476C2×C8—431no—
477C2×C8—862no—
478C2×C8—861no—
479C2×C8—861no—
480C2×C8—861no—
481C2×C8—861no—
482C2×C8—3441no—
483C2×C8—1721no—
484C2×C8—1722no—
485C4⋊C4—21no—
486C4⋊C4—21no—
487C4⋊C4—21no—
488C4⋊C4—21no—
489C4⋊C4—21no—
490C4⋊C4—21no—
491C4⋊C4—861no—
492C4⋊C4—861no—
493C4⋊C4C2×C22⋊D4311yescharacteristic
494C4⋊C4C2×C22⋊D4311yescharacteristic
495C22⋊C4—21no—
496C22⋊C4—21no—
497C22⋊C4—21no—
498C22⋊C4—21no—
499C22⋊C4—21no—
500C22⋊C4—41no—
501C22⋊C4—41no—
502C22⋊C4—1721no—
503C22⋊C4—1721no—
504C42—21no—
505C42D4×D4311yescharacteristic
506C42#1062190011yescharacteristic
507C42C2×C22⋊D4311yescharacteristic
508C42C23×D4311yescharacteristic
509C23—21no—
510C23—41no—
511C23—1721no—
512C23#1306329711yescharacteristic
513Q8—21no—
514Q8—21no—
515Q8—81no—
516Q8—3441no—
517D4—21no—
518D4—21no—
519D4—42no—
520D4—41no—
521D4—41no—
522D4—41no—
523D4—41no—
524D4—81no—
525D4—82no—
526D4—3441no—
527D4—3442no—
528D4—1721no—
529D4—1721no—
530D4—1721no—
531D4—1721no—
532C2×C4—22no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—82no—
544C2×C4—3442no—
545C2×C4—1721no—
546C2×C4#1306329711yescharacteristic
547C2×C4#1306329711yescharacteristic
548C2×C4#1306329711yescharacteristic
549C2×C4C2×D4×D4311yescharacteristic
550C2×C4C22×C22⋊D4311yescharacteristic
551C2×C4C2×#1062190011yescharacteristic
552C8—41no—
553C8—41no—
554C8—432no—
555C8—861no—
556C8—861no—
557C8—861no—
558C8—1721no—
559C8—1721no—
560C8—1721no—
561C8—1721no—
562C22—21no—
563C22—21no—
564C22—41no—
565C22—41no—
566C22—41no—
567C22—81no—
568C22—81no—
569C22—81no—
570C22—3441no—
571C22—3441no—
572C22—3441no—
573C22#1458316712yes—
574C22C2×#1306329711yescharacteristic
575C4—21no—
576C4—21no—
577C4—21no—
578C4—21no—
579C4—41no—
580C4—41no—
581C4—41no—
582C4—81no—
583C4—3441no—
584C4#135×D4311yescharacteristic
585C4#1458369611yescharacteristic
586C4#1458370711yescharacteristic
587C4#1458371011yescharacteristic
588C2—22no—
589C2—81no—
590C2—161no—
591C2—6881no—
592C2#1914404611yescharacteristic
593C2#1914425411yescharacteristic
594C2C2×#1458316711yescharacteristic
subgroupG/H
centerC22C2×#13063297
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#3247C2
socleC22×C43C2×#121
hypercenter#3247D43
hypocenterC43#19227
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3247

Complements

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

NH ≅ G/Ntype
1. #19145921C2semidirect
2. #19145170C2semidirect
3. #19143571C2semidirect
4. #19134121C2semidirect
5. #19134116C2semidirect
6. #19134077C2semidirect
7. #19134072C2semidirect
8. #19134013C2semidirect
9. #19134009C2semidirect
10. #19134006C2semidirect
11. #19134002C2semidirect
12. C2×#14582649C2semidirect
13. #19133290C2semidirect
14. #19133288C2semidirect
15. C43×#3247C2semidirect
292. #3247D43semidirect
364. C43#19227semidirect

Maximal subgroups

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

subgroupindex
#191459212
#191451702
#191435712
#191341212
#191341162
#191340772
#191340722
#191340132
#191340092
#191340062
#191340022
C2×#145826492
#191332902
#191332882
C43×#32472
#1922743