Finite Group Databasebeta

← #25086255

Subgroups — #25086255

Order 11008.

630 conjugacy classes of subgroups.

The subgroup lattice has 602 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19146900C211yesmaximal, characteristic, complemented
2#19146525C211yesmaximal, characteristic, complemented
3#19146523C211yesmaximal, characteristic, complemented
4#19134240C211yesmaximal, characteristic, complemented
5#19134168C211yesmaximal, characteristic, complemented
6#19134046C211yesmaximal, characteristic, complemented
7#19134016C211yesmaximal, characteristic, complemented
8#19133981C211yesmaximal, characteristic, complemented
9#19133879C211yesmaximal, characteristic, complemented
10#19133878C211yesmaximal, characteristic, complemented
11#19133822C211yesmaximal, characteristic, complemented
12#19133746C211yesmaximal, characteristic, complemented
13#19133425C211yesmaximal, characteristic, complemented
14#19133417C211yesmaximal, characteristic, complemented
15C43×#3334C211yesmaximal, characteristic, complemented
16#14583614C2211yescharacteristic
17#14583553C2211yescharacteristic
18#14583295C2211yescharacteristic
19#14583251C2211yescharacteristic
20#14583250C2211yescharacteristic
21#14583249C2211yescharacteristic
22#14583249C2211yescharacteristic
23#14583242—21no—
24#14583237—21no—
25#14583232—21no—
26#14583189C2211yescharacteristic
27#14583189C2211yescharacteristic
28#14583179C2211yescharacteristic
29#14583147—21no—
30#14583130—21no—
31#14583127—21no—
32#14583104C2211yescharacteristic
33#14583101C2211yescharacteristic
34#14583101C2211yescharacteristic
35#14583044—21no—
36#14583044—21no—
37#14583041—21no—
38C4×#10621882C2211yescharacteristic
39#14582977C2211yescharacteristic
40C8×D172C2211yescharacteristic
41D4×C43⋊C8C2211yescharacteristic
42#14582900—21no—
43#14582895—21no—
44#14582892—21no—
45#14582652C2211yescharacteristic
46#14582649C2211yescharacteristic
47#14582647C2211yescharacteristic
48#14582646C2211yescharacteristic
49#14582645C2211yescharacteristic
50#14582645C2211yescharacteristic
51D4⋊(C43⋊C8)C2211yescharacteristic
52D4⋊(C43⋊C8)C2211yescharacteristic
53D4⋊(C43⋊C8)C2211yescharacteristic
54#14582626C2211yescharacteristic
55#14582621C2211yescharacteristic
56C43×#547C2211yescharacteristic
57C43×#547C2211yescharacteristic
58C43×#500C2211yescharacteristic
59C43×#480—21no—
60C43×#480—21no—
61C43×#474C2211yescharacteristic
62C43×#474C2211yescharacteristic
63C43×#466—21no—
64C4×D8×C43C2211yescharacteristic
65C8×D4×C43C2211yescharacteristic
66C2×#107×C43—21no—
67C2×#10621900—21no—
68C2×#10621883—21no—
69C2×#10621884—21no—
70C2×#10621884—21no—
71C2×#10621882D411yescharacteristic
72C2×#10621877—21no—
73C22×C43⋊C8—21no—
74C2×C8×D43—21no—
75#13063325C2311yescharacteristic
76#13063325C2311yescharacteristic
77#13063311—41no—
78#13063309—41no—
79#13063305—21no—
80#13063299—21no—
81#13063299—21no—
82#13063296—21no—
83C4×D172C2311yescharacteristic
84#13063284—21no—
85#13063283—21no—
86C2×C4⋊Dic43—21no—
87#13063258—21no—
88#13063258D411yescharacteristic
89#13063256—21no—
90#13063256—21no—
91#13063256—41no—
92C4⋊(C43⋊C8)C2311yescharacteristic
93C4⋊(C43⋊C8)C2311yescharacteristic
94C4⋊(C43⋊C8)C2311yescharacteristic
95#13063250—21no—
96#13063250—21no—
97#13063249—21no—
98#13063249—21no—
99#13063249—21no—
100#13063249—21no—
101#13063249—21no—
102#13063249—21no—
103#13063248—21no—
104#13063248—41no—
105#13063246—21no—
106#13063246—21no—
107#13063246—21no—
108#13063246D411yescharacteristic
109#13063245D411yescharacteristic
110C22⋊(C43⋊C8)—21no—
111C22⋊(C43⋊C8)—21no—
112(C2×D43)⋊C8—21no—
113C4×C43⋊C8C2311yescharacteristic
114C4×C43⋊C8C2311yescharacteristic
115C2×#41×C43—21no—
116C2×#41×C43—21no—
117C2×D8×C43D411yescharacteristic
118C22×C8×C43—21no—
119C4⋊Q8×C43C2311yescharacteristic
120C4⋊Q8×C43C2311yescharacteristic
121#123×C43—41no—
122#123×C43—41no—
123C22⋊Q8×C43—21no—
124C22⋊Q8×C43—21no—
125#121×C43—21no—
126#121×C43—21no—
127C4×D4×C43C2311yescharacteristic
128C4×D4×C43C2311yescharacteristic
129C4×D4×C43C2311yescharacteristic
130C2×C4⋊C4×C43—21no—
131C2×C4⋊C4×C43—21no—
132#107×C43—21no—
133#107×C43—21no—
134#107×C43—21no—
135#107×C43—21no—
136#107×C43D411yescharacteristic
137C4⋊C8×C43C2311yescharacteristic
138#102×C43—21no—
139#102×C43—21no—
140#102×C43D411yescharacteristic
141#102×C43D411yescharacteristic
142C22⋊C8×C43—21no—
143C4×C8×C43C2311yescharacteristic
144#41×C43—42no—
145#41×C43—42no—
146#41×C43—81no—
147#41×C43—81no—
148C2×Q8×C43—21no—
149C2×Q8×C43—21no—
150C2×D4×C43—41no—
151C2×D4×C43—41no—
152C2×D4×C43C2×D411yescharacteristic
153C2×D4×C43C2×D411yescharacteristic
154C2×D4×C43C2×D411yescharacteristic
155C22×C4×C43—21no—
156C22×C4×C43—21no—
157C22×C4×C43—21no—
158C22×C4×C43—41no—
159C22×C4×C43—41no—
160C2×C22⋊D43—41no—
161C2×C22⋊D43—41no—
162C22×Dic43—41no—
163#10621900—42no—
164#10621900—81no—
165C2×D172C2×D411yescharacteristic
166C2×C4×D43—21no—
167C2×Dic86—21no—
168C2×Dic86—21no—
169D8×C43—41no—
170C2×C8×C43—21no—
171C2×C8×C43—42no—
172C2×C8×C43C2×D411yescharacteristic
173C2×C8×C43C2×D411yescharacteristic
174C4⋊C4×C43—21no—
175C4⋊C4×C43—21no—
176C4⋊C4×C43—21no—
177C4⋊C4×C43—21no—
178C4⋊C4×C43—41no—
179C4⋊C4×C43—41no—
180C4⋊C4×C43C2×D411yescharacteristic
181C4⋊C4×C43C2×D411yescharacteristic
182C4⋊C4×C43C2×D411yescharacteristic
183C22⋊C4×C43—21no—
184C22⋊C4×C43—21no—
185C22⋊C4×C43—21no—
186C22⋊C4×C43—41no—
187C22⋊C4×C43—41no—
188C42×C43C2411yescharacteristic
189C22⋊Dic43—41no—
190#10621884—81no—
191#10621884—81no—
192#10621883—81no—
193#10621882—22no—
194(C2×D43)⋊C4—21no—
195(C2×D43)⋊C4—41no—
196(C2×D43)⋊C4—41no—
197C4⋊Dic43—21no—
198C4⋊Dic43—21no—
199C4⋊Dic43—21no—
200C4⋊Dic43—21no—
201C4⋊Dic43—41no—
202C4⋊Dic43C2×D411yescharacteristic
203C4×Dic43—41no—
204#10621877—81no—
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
212C8×D43—81no—
213C23×C43—21no—
214C23×C43—21no—
215C23×C43—21no—
216C22×D43—21no—
217Q8×C43—41no—
218Q8×C43—41no—
219Q8×C43—41no—
220Q8×C43—41no—
221D4×C43—21no—
222D4×C43—21no—
223D4×C43—21no—
224D4×C43—21no—
225D4×C43—21no—
226D4×C43—82no—
227D4×C43—82no—
228D4×C43#13512yes—
229C2×C4×C43—21no—
230C2×C4×C43—21no—
231C2×C4×C43—21no—
232C2×C4×C43—41no—
233C2×C4×C43—41no—
234C2×C4×C43—41no—
235C2×C4×C43—41no—
236C2×C4×C43—41no—
237C2×C4×C43—41no—
238C2×C4×C43—41no—
239C2×C4×C43—41no—
240C2×C4×C43—82no—
241C2×C4×C43—82no—
242C2×C4×C43C22×D411yescharacteristic
243C2×C4×C43C22×D411yescharacteristic
244C2×C4×C43H(5,𝔽2)11yescharacteristic
245C22⋊D43—82no—
246C22⋊D43—161no—
247C2×Dic43—21no—
248C2×Dic43—41no—
249C2×Dic43—41no—
250C2×Dic43—82no—
251D172—21no—
252D172—21no—
253C4×D43—41no—
254C4×D43—41no—
255Dic86—41no—
256Dic86—41no—
257Dic86—81no—
258C8×C43—21no—
259C8×C43—21no—
260C8×C43—41no—
261C43⋊C8—21no—
262C43⋊C8—21no—
263C43⋊C8—41no—
264C43⋊C8—41no—
265C43⋊C8—41no—
266C43⋊C8—41no—
267#19776—431nomaximal, Sylow
268C22×C43—22no—
269C22×C43—41no—
270C22×C43—41no—
271C22×C43—41no—
272C22×C43—41no—
273C22×C43—41no—
274C22×C43—41no—
275C22×C43—41no—
276C22×C43—41no—
277C22×C43D4211yescharacteristic
278C2×D43—41no—
279C2×D43—41no—
280C2×D43—41no—
281C4×C43—21no—
282C4×C43—41no—
283C4×C43—41no—
284C4×C43—41no—
285C4×C43—81no—
286C4×C43—81no—
287C4×C43C2×#13511yescharacteristic
288C4×C43#57511yescharacteristic
289C4×C43#57611yescharacteristic
290C4×C43#57711yescharacteristic
291Dic43—41no—
292Dic43—81no—
293Dic43—81no—
294#3334D4311yescharacteristic, complemented
295#3330—431no—
296#3303—431no—
297#3303—431no—
298#1718—431no—
299#1703—431no—
300#1683—431no—
301#1679—431no—
302#1673—431no—
303#1654—431no—
304#1654—431no—
305#1646—431no—
306#1635—431no—
307#1581—431no—
308#1580—431no—
309C2×C43—42no—
310C2×C43—81no—
311C2×C43—81no—
312C2×C43#326711yescharacteristic
313C2×C43#328011yescharacteristic
314C2×C43#328911yescharacteristic
315D43—81no—
316#555—431no—
317#547—431no—
318#547C2×D4311yescharacteristic
319#547C2×D4311yescharacteristic
320#500C2×D4311yescharacteristic
321#498—431no—
322#487—431no—
323#487—431no—
324#487—431no—
325#487—431no—
326#485—861no—
327#485—861no—
328#484—861no—
329#480—21no—
330#480—21no—
331#476—431no—
332#476—431no—
333#474—431no—
334#474C2×D4311yescharacteristic
335#474C2×D4311yescharacteristic
336#468—861no—
337#466—21no—
338#465—861no—
339#465—861no—
340#461—431no—
341#461—431no—
342#461—431no—
343#449—861no—
344#449—861no—
345#449—861no—
346C4×D8—431no—
347C4×D8C2×D4311yescharacteristic
348#436—431no—
349C8×D4—431no—
350C8×D4—431no—
351C8×D4C2×D4311yescharacteristic
352C2×#107—21no—
353#417—861no—
354#416—861no—
355#416—861no—
356#335—431no—
357#334—431no—
358#333—431no—
359#332—431no—
360#332—431no—
361#332—431no—
362D4⋊C8—431no—
363D4⋊C8—431no—
364D4⋊C8—431no—
365D4⋊C8—431no—
366#322—431no—
367C43#1977611yescharacteristic, complemented, Sylow
368C2×#41—21no—
369C2×#41—21no—
370C2×#41—861no—
371C2×SD16—861no—
372C2×SD16—861no—
373C2×SD16—861no—
374C2×D8—431no—
375C2×D8C22⋊D4311yescharacteristic
376C2×M16—861no—
377C22×C8—21no—
378C22×C8—861no—
379C22×C8—861no—
380C4⋊Q8—431no—
381C4⋊Q8—431no—
382C4⋊Q8C22×D4311yescharacteristic
383C4⋊Q8C22×D4311yescharacteristic
384#124—1721no—
385#123—41no—
386#123—41no—
387#123—1721no—
388C22⋊Q8—21no—
389C22⋊Q8—21no—
390C22⋊Q8—861no—
391#121—21no—
392#121—21no—
393#121—861no—
394#121—861no—
395#121—861no—
396C4×D4—431no—
397C4×D4C22×D4311yescharacteristic
398C4×D4C22×D4311yescharacteristic
399C4×D4C22×D4311yescharacteristic
400#117—861no—
401#117—861no—
402C2×C4⋊C4—21no—
403C2×C4⋊C4—21no—
404C2×C4⋊C4—861no—
405#107—21no—
406#107—21no—
407#107—21no—
408#107—21no—
409#107—431no—
410#107—861no—
411#107C22⋊D4311yescharacteristic
412#106—861no—
413#106—861no—
414#106—1721no—
415C4⋊C8—431no—
416C4⋊C8—431no—
417C4⋊C8—431no—
418C4⋊C8C22×D4311yescharacteristic
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#103—861no—
428#103—1721no—
429#102—21no—
430#102—21no—
431#102—431no—
432#102—431no—
433#102—861no—
434#102—861no—
435#102—861no—
436#102C22⋊D4311yescharacteristic
437#102C22⋊D4311yescharacteristic
438C22⋊C8—21no—
439C22⋊C8—861no—
440C22⋊C8—861no—
441C22⋊C8—861no—
442C4×C8—431no—
443C4×C8—431no—
444C4×C8C22×D4311yescharacteristic
445#41—42no—
446#41—42no—
447#41—81no—
448#41—81no—
449#41—3441no—
450#41—1722no—
451C2×Q8—21no—
452C2×Q8—21no—
453C2×Q8—861no—
454C2×Q8—861no—
455C2×D4—41no—
456C2×D4—41no—
457C2×D4—431no—
458C2×D4—1721no—
459C2×D4—1721no—
460C2×D4D4×D4311yescharacteristic
461C2×D4C2×C22⋊D4311yescharacteristic
462C2×D4C2×C22⋊D4311yescharacteristic
463C22×C4—21no—
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—41no—
467C22×C4—41no—
468C22×C4—861no—
469C22×C4—1721no—
470SD16—3441no—
471SD16—3441no—
472SD16—3441no—
473D8—41no—
474D8—862no—
475M16—3441no—
476C2×C8—21no—
477C2×C8—42no—
478C2×C8—431no—
479C2×C8—431no—
480C2×C8—861no—
481C2×C8—861no—
482C2×C8—861no—
483C2×C8—861no—
484C2×C8—3441no—
485C2×C8—3441no—
486C2×C8C2×C22⋊D4311yescharacteristic
487C2×C8C2×C22⋊D4311yescharacteristic
488C4⋊C4—21no—
489C4⋊C4—21no—
490C4⋊C4—21no—
491C4⋊C4—21no—
492C4⋊C4—41no—
493C4⋊C4—41no—
494C4⋊C4—431no—
495C4⋊C4—861no—
496C4⋊C4—861no—
497C4⋊C4—861no—
498C4⋊C4—861no—
499C4⋊C4—1721no—
500C4⋊C4D4×D4311yescharacteristic
501C4⋊C4C2×C22⋊D4311yescharacteristic
502C4⋊C4C2×C22⋊D4311yescharacteristic
503C22⋊C4—21no—
504C22⋊C4—21no—
505C22⋊C4—21no—
506C22⋊C4—41no—
507C22⋊C4—41no—
508C22⋊C4—861no—
509C22⋊C4—1721no—
510C22⋊C4—1721no—
511C22⋊C4—1721no—
512C42—1721no—
513C42C23×D4311yescharacteristic
514C23—21no—
515C23—21no—
516C23—21no—
517C23—861no—
518Q8—41no—
519Q8—41no—
520Q8—41no—
521Q8—41no—
522Q8—3441no—
523Q8—1721no—
524Q8—1721no—
525D4—21no—
526D4—21no—
527D4—21no—
528D4—21no—
529D4—21no—
530D4—82no—
531D4—82no—
532D4—861no—
533D4—861no—
534D4—3442no—
535D4—6881no—
536D4#1306334412yes—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—82no—
549C2×C4—82no—
550C2×C4—861no—
551C2×C4—3442no—
552C2×C4—1721no—
553C2×C4—1721no—
554C2×C4—1721no—
555C2×C4—1721no—
556C2×C4C2×D4×D4311yescharacteristic
557C2×C4C22×C22⋊D4311yescharacteristic
558C2×C4#1306337011yescharacteristic
559C8—21no—
560C8—21no—
561C8—41no—
562C8—861no—
563C8—861no—
564C8—1721no—
565C8—1721no—
566C8—1721no—
567C8—1721no—
568C22—22no—
569C22—41no—
570C22—41no—
571C22—41no—
572C22—41no—
573C22—41no—
574C22—41no—
575C22—41no—
576C22—41no—
577C22—1721no—
578C22—1721no—
579C22—1721no—
580C22D4×C22⋊D4311yescharacteristic
581C4—21no—
582C4—41no—
583C4—41no—
584C4—41no—
585C4—81no—
586C4—81no—
587C4—3441no—
588C4—3441no—
589C4—1721no—
590C4C2×#1306334411yescharacteristic
591C4#1458369711yescharacteristic
592C4#1458370011yescharacteristic
593C4#1458370711yescharacteristic
594C2—42no—
595C2—81no—
596C2—81no—
597C2—3441no—
598C2#1914612111yescharacteristic
599C2#1914628011yescharacteristic
600C2#1914636611yescharacteristic
subgroupG/H
centerC22D4×C22⋊D43
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#3334C2
socleC22×C43D42
hypercenter#3334D43
hypocenterC43#19776
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #3334

Complements

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

NH ≅ G/Ntype
1. #19146900C2semidirect
2. #19146525C2semidirect
3. #19146523C2semidirect
4. #19134240C2semidirect
5. #19134168C2semidirect
6. #19134046C2semidirect
7. #19134016C2semidirect
8. #19133981C2semidirect
9. #19133879C2semidirect
10. #19133878C2semidirect
11. #19133822C2semidirect
12. #19133746C2semidirect
13. #19133425C2semidirect
14. #19133417C2semidirect
15. C43×#3334C2semidirect
294. #3334D43semidirect
367. C43#19776semidirect

Maximal subgroups

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

subgroupindex
#191469002
#191465252
#191465232
#191342402
#191341682
#191340462
#191340162
#191339812
#191338792
#191338782
#191338222
#191337462
#191334252
#191334172
C43×#33342
#1977643