Finite Group Databasebeta

← #25080018

Subgroups — #25080018

Order 11008.

630 conjugacy classes of subgroups.

The subgroup lattice has 608 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145567C211yesmaximal, characteristic, complemented
2#19145170C211yesmaximal, characteristic, complemented
3#19143571C211yesmaximal, characteristic, complemented
4#19134111C211yesmaximal, characteristic, complemented
5#19134106C211yesmaximal, characteristic, complemented
6#19134077C211yesmaximal, characteristic, complemented
7#19134072C211yesmaximal, characteristic, complemented
8#19134041C211yesmaximal, characteristic, complemented
9#19134037C211yesmaximal, characteristic, complemented
10#19134034C211yesmaximal, characteristic, complemented
11#19134030C211yesmaximal, characteristic, complemented
12#19133341C211yesmaximal, characteristic, complemented
13#19133300C211yesmaximal, characteristic, complemented
14#19133298C211yesmaximal, characteristic, complemented
15C43×#3212C211yesmaximal, characteristic, complemented
16#14583449C2211yescharacteristic
17#14583302C2211yescharacteristic
18#14583281—21no—
19#14583275C2211yescharacteristic
20#14583256—21no—
21#14583247C2211yescharacteristic
22#14583245C2211yescharacteristic
23#14583133—21no—
24#14583133—21no—
25#14583109C2211yescharacteristic
26#14583104C2211yescharacteristic
27#14583099C2211yescharacteristic
28#14583094C2211yescharacteristic
29#14583059—21no—
30#14583042—21no—
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
41#14582952C2211yescharacteristic
42#14582855—21no—
43C2×C4×C43⋊C8C2211yescharacteristic
44#14582651C2211yescharacteristic
45#14582651C2211yescharacteristic
46#14582649C2211yescharacteristic
47#14582649C2211yescharacteristic
48#14582646C2211yescharacteristic
49#14582646C2211yescharacteristic
50#14582645C2211yescharacteristic
51#14582645C2211yescharacteristic
52#14582643C2211yescharacteristic
53#14582643C2211yescharacteristic
54#14582642C2211yescharacteristic
55#14582642C2211yescharacteristic
56C43×#532C2211yescharacteristic
57C43×#529C2211yescharacteristic
58C43×#495—21no—
59C43×#488—21no—
60C43×#462C2211yescharacteristic
61C43×#461C2211yescharacteristic
62C43×#460C2211yescharacteristic
63C43×#459C2211yescharacteristic
64C43×#452—21no—
65C43×#449—21no—
66C43×#431C2211yescharacteristic
67C2×#10621898—21no—
68C2×#10621885—21no—
69C2×#10621883—21no—
70C2×#10621884—21no—
71C2×#10621882—21no—
72C2×#10621882—21no—
73C2×#10621882—21no—
74C2×#10621877—21no—
75C22×C43⋊C8—21no—
76C22×C43⋊C8D411yescharacteristic
77C22×C43⋊C8D411yescharacteristic
78#13063325C2311yescharacteristic
79#13063322C2311yescharacteristic
80#13063313—21no—
81#13063299—21no—
82#13063299—21no—
83C4×D172—21no—
84C4×D172—21no—
85#13063258—21no—
86#13063258—21no—
87C4⋊(C43⋊C8)—21no—
88C4⋊(C43⋊C8)—21no—
89C4⋊(C43⋊C8)C2311yescharacteristic
90C4⋊(C43⋊C8)C2311yescharacteristic
91C4⋊(C43⋊C8)C2311yescharacteristic
92C4⋊(C43⋊C8)C2311yescharacteristic
93#13063248—21no—
94#13063248—21no—
95#13063246—21no—
96#13063246—21no—
97#13063245—21no—
98#13063245—21no—
99#13063245—21no—
100#13063245—21no—
101C22⋊(C43⋊C8)—21no—
102C22⋊(C43⋊C8)—21no—
103C22⋊(C43⋊C8)—21no—
104C22⋊(C43⋊C8)—21no—
105#13063236—21no—
106#13063236—21no—
107C4×C43⋊C8—21no—
108C4×C43⋊C8—21no—
109C4×C43⋊C8D411yescharacteristic
110C4×C43⋊C8D411yescharacteristic
111C4×C43⋊C8C2311yescharacteristic
112C4×C43⋊C8C2311yescharacteristic
113C2×#41×C43—21no—
114C2×Q16×C43—21no—
115C2×SD16×C43—21no—
116C2×SD16×C43—21no—
117C2×D8×C43—21no—
118C4⋊Q8×C43C2311yescharacteristic
119#127×C43C2311yescharacteristic
120#126×C43—21no—
121#125×C43D411yescharacteristic
122#124×C43—21no—
123#124×C43D411yescharacteristic
124#123×C43—21no—
125C22⋊Q8×C43D411yescharacteristic
126#121×C43—21no—
127#121×C43—21no—
128#121×C43D411yescharacteristic
129C4×Q8×C43C2311yescharacteristic
130C4×D4×C43—21no—
131C4×D4×C43—21no—
132C4×D4×C43—21no—
133C4×D4×C43C2311yescharacteristic
134#117×C43—21no—
135C2×C42×C43C2311yescharacteristic
136C4⋊C8×C43C2311yescharacteristic
137C4⋊C8×C43C2311yescharacteristic
138#103×C43—21no—
139#103×C43—21no—
140#102×C43—21no—
141#102×C43—21no—
142C22⋊C8×C43—21no—
143C4×C8×C43—21no—
144#41×C43—81no—
145#41×C43—81no—
146C2×Q8×C43—21no—
147C2×Q8×C43C2×D411yescharacteristic
148C2×D4×C43—21no—
149C2×D4×C43—21no—
150C2×D4×C43—21no—
151C2×D4×C43—21no—
152C2×D4×C43—41no—
153C2×D4×C43C2×D411yescharacteristic
154C22×C4×C43—21no—
155C22×C4×C43—41no—
156C22×C4×C43C2×D411yescharacteristic
157C22×C4×C43C2×D411yescharacteristic
158C22×C4×C43#4111yescharacteristic
159C2×C22⋊D43—41no—
160#10621898—81no—
161#10621898—81no—
162C2×D172—21no—
163C2×D172—21no—
164C2×D172—21no—
165C2×C4×D43—41no—
166C2×Dic86—21no—
167Q16×C43—81no—
168SD16×C43—81no—
169SD16×C43—81no—
170D8×C43—81no—
171C2×C8×C43—21no—
172C2×C8×C43—21no—
173C4⋊C4×C43—21no—
174C4⋊C4×C43—21no—
175C4⋊C4×C43—21no—
176C4⋊C4×C43—21no—
177C4⋊C4×C43—21no—
178C4⋊C4×C43—21no—
179C4⋊C4×C43C2×D411yescharacteristic
180C4⋊C4×C43C2×D411yescharacteristic
181C22⋊C4×C43—21no—
182C22⋊C4×C43—21no—
183C22⋊C4×C43—21no—
184C22⋊C4×C43—21no—
185C22⋊C4×C43—21no—
186C22⋊C4×C43—41no—
187C22⋊C4×C43—41no—
188C42×C43—21no—
189C42×C43C2×D411yescharacteristic
190C42×C43C2×D411yescharacteristic
191C42×C43#4111yescharacteristic
192C42×C43C2411yescharacteristic
193#10621885—81no—
194#10621884—81no—
195#10621883—81no—
196#10621882—42no—
197#10621882—42no—
198#10621882—81no—
199(C2×D43)⋊C4—41no—
200(C2×D43)⋊C4—41no—
201C4⋊Dic43—21no—
202C4⋊Dic43—21no—
203#10621877—42no—
204C2×C43⋊C8—22no—
205C2×C43⋊C8—21no—
206C2×C43⋊C8—21no—
207C2×C43⋊C8—21no—
208C2×C43⋊C8—21no—
209C2×C43⋊C8—41no—
210C2×C43⋊C8—42no—
211C2×C43⋊C8C2×D411yescharacteristic
212C2×C43⋊C8C2×D411yescharacteristic
213C2×C43⋊C8C2×D411yescharacteristic
214C2×C43⋊C8C2×D411yescharacteristic
215C23×C43—21no—
216C23×C43—41no—
217C23×C43#12111yescharacteristic
218C22×D43—41no—
219Q8×C43—21no—
220Q8×C43—21no—
221Q8×C43—41no—
222Q8×C43—41no—
223D4×C43—21no—
224D4×C43—21no—
225D4×C43—42no—
226D4×C43—41no—
227D4×C43—41no—
228D4×C43—41no—
229D4×C43—41no—
230D4×C43—81no—
231D4×C43—82no—
232C2×C4×C43—21no—
233C2×C4×C43—21no—
234C2×C4×C43—21no—
235C2×C4×C43—21no—
236C2×C4×C43—21no—
237C2×C4×C43—21no—
238C2×C4×C43—21no—
239C2×C4×C43—41no—
240C2×C4×C43—41no—
241C2×C4×C43—41no—
242C2×C4×C43—41no—
243C2×C4×C43—82no—
244C2×C4×C43#12111yescharacteristic
245C2×C4×C43#12111yescharacteristic
246C2×C4×C43#12111yescharacteristic
247C2×C4×C43C22×D411yescharacteristic
248C2×C4×C43C22×D411yescharacteristic
249C2×C4×C43C2×#4111yescharacteristic
250C22⋊D43—82no—
251C2×Dic43—41no—
252D172—41no—
253D172—41no—
254D172—41no—
255D172—41no—
256D172—81no—
257C4×D43—82no—
258Dic86—41no—
259Dic86—41no—
260C8×C43—41no—
261C8×C43—41no—
262C43⋊C8—21no—
263C43⋊C8—21no—
264C43⋊C8—21no—
265C43⋊C8—41no—
266C43⋊C8—41no—
267C43⋊C8—41no—
268C43⋊C8—41no—
269C43⋊C8#13512yes—
270#19225—431nomaximal, Sylow
271C22×C43—21no—
272C22×C43—21no—
273C22×C43—21no—
274C22×C43—41no—
275C22×C43—41no—
276C22×C43—41no—
277C22×C43—81no—
278C22×C43—81no—
279C22×C43—81no—
280C22×C43C2×#12111yescharacteristic
281C2×D43—81no—
282C2×D43—81no—
283C2×D43—81no—
284C4×C43—21no—
285C4×C43—21no—
286C4×C43—21no—
287C4×C43—21no—
288C4×C43—41no—
289C4×C43—41no—
290C4×C43—41no—
291C4×C43—81no—
292C4×C43C2×#13511yescharacteristic
293C4×C43#57511yescharacteristic
294C4×C43#57611yescharacteristic
295C4×C43#57611yescharacteristic
296Dic43—81no—
297#3212—431no—
298#3212D4311yescharacteristic, complemented
299#3169—431no—
300#2966—431no—
301#1694—431no—
302#1693—431no—
303#1688—431no—
304#1687—431no—
305#1682—431no—
306#1682—431no—
307#1681—431no—
308#1681—431no—
309#1564—431no—
310#1553—431no—
311#1553—431no—
312C2×C43—41no—
313C2×C43—81no—
314C2×C43—161no—
315C2×C43#303511yescharacteristic
316C2×C43#305811yescharacteristic
317C2×C43#306711yescharacteristic
318D43—161no—
319#532—431no—
320#532C2×D4311yescharacteristic
321#529C2×D4311yescharacteristic
322#500—431no—
323#495—21no—
324#495—861no—
325#493—431no—
326#488—21no—
327#488—861no—
328#486—431no—
329#486—431no—
330#466—861no—
331#466—861no—
332#462—431no—
333#462C2×D4311yescharacteristic
334#461—431no—
335#461C2×D4311yescharacteristic
336#460—431no—
337#460C2×D4311yescharacteristic
338#459—431no—
339#459C2×D4311yescharacteristic
340#452—21no—
341#452—861no—
342#449—21no—
343#449—861no—
344#446—431no—
345C8×Q8—431no—
346C4×D8—861no—
347C4×D8—861no—
348#436—431no—
349#435—861no—
350C8×D4—431no—
351C8×D4—861no—
352#433—861no—
353#432—431no—
354#431—431no—
355#431C2×D4311yescharacteristic
356#405—861no—
357C2×C4×C8—431no—
358#335—431no—
359#335—431no—
360#334—431no—
361#334—431no—
362#332—431no—
363#332—431no—
364#332—431no—
365#332—431no—
366#331—431no—
367#331—431no—
368#331—431no—
369#331—431no—
370C43#1922511yescharacteristic, complemented, Sylow
371C2×#41—21no—
372C2×#41—861no—
373C2×Q16—21no—
374C2×Q16—861no—
375C2×SD16—21no—
376C2×SD16—21no—
377C2×SD16—861no—
378C2×SD16—861no—
379C2×D8—21no—
380C2×D8—861no—
381C2×D8—861no—
382C2×D8—861no—
383C2×M16—861no—
384C22×C8—431no—
385C22×C8—431no—
386C22×C8—861no—
387C4⋊Q8—431no—
388C4⋊Q8C22×D4311yescharacteristic
389#127—431no—
390#127C22×D4311yescharacteristic
391#126—21no—
392#125C22⋊D4311yescharacteristic
393#124—21no—
394#124—861no—
395#124C22⋊D4311yescharacteristic
396#123—21no—
397C22⋊Q8C22⋊D4311yescharacteristic
398#121—21no—
399#121—21no—
400#121—861no—
401#121—861no—
402#121C22⋊D4311yescharacteristic
403C4×Q8C22×D4311yescharacteristic
404C4×D4—21no—
405C4×D4—21no—
406C4×D4—21no—
407C4×D4—861no—
408C4×D4—861no—
409C4×D4C22×D4311yescharacteristic
410#117—21no—
411C2×C42C22×D4311yescharacteristic
412#107—861no—
413#107—861no—
414C4⋊C8—431no—
415C4⋊C8—431no—
416C4⋊C8—431no—
417C4⋊C8—431no—
418C4⋊C8—861no—
419C4⋊C8—861no—
420C4⋊C8C22×D4311yescharacteristic
421C4⋊C8C22×D4311yescharacteristic
422#103—21no—
423#103—21no—
424#103—861no—
425#103—861no—
426#102—21no—
427#102—21no—
428#102—861no—
429#102—861no—
430#102—861no—
431#102—861no—
432#102—861no—
433#102—861no—
434C22⋊C8—21no—
435C22⋊C8—861no—
436C22⋊C8—861no—
437C22⋊C8—861no—
438C22⋊C8—861no—
439#97—861no—
440#97—861no—
441C4×C8—21no—
442C4×C8—431no—
443C4×C8—431no—
444C4×C8—431no—
445C4×C8—431no—
446C4×C8—861no—
447C4×C8—861no—
448#41—81no—
449#41—81no—
450#41—3441no—
451#41—3441no—
452C2×Q8—21no—
453C2×Q8—861no—
454C2×Q8C2×C22⋊D4311yescharacteristic
455C2×D4—21no—
456C2×D4—21no—
457C2×D4—21no—
458C2×D4—21no—
459C2×D4—41no—
460C2×D4—861no—
461C2×D4—861no—
462C2×D4—861no—
463C2×D4—1721no—
464C2×D4C2×C22⋊D4311yescharacteristic
465C22×C4—21no—
466C22×C4—41no—
467C22×C4—1721no—
468C22×C4D4×D4311yescharacteristic
469C22×C4#1062190011yescharacteristic
470C22×C4C2×C22⋊D4311yescharacteristic
471Q16—81no—
472Q16—3441no—
473SD16—81no—
474SD16—81no—
475SD16—3441no—
476SD16—3441no—
477D8—81no—
478D8—3441no—
479D8—1722no—
480D8—1722no—
481M16—1722no—
482C2×C8—21no—
483C2×C8—21no—
484C2×C8—431no—
485C2×C8—431no—
486C2×C8—431no—
487C2×C8—431no—
488C2×C8—862no—
489C2×C8—861no—
490C2×C8—861no—
491C2×C8—861no—
492C2×C8—861no—
493C2×C8—1721no—
494C2×C8—1722no—
495C4⋊C4—21no—
496C4⋊C4—21no—
497C4⋊C4—21no—
498C4⋊C4—21no—
499C4⋊C4—21no—
500C4⋊C4—21no—
501C4⋊C4—861no—
502C4⋊C4—861no—
503C4⋊C4C2×C22⋊D4311yescharacteristic
504C4⋊C4C2×C22⋊D4311yescharacteristic
505C22⋊C4—21no—
506C22⋊C4—21no—
507C22⋊C4—21no—
508C22⋊C4—21no—
509C22⋊C4—21no—
510C22⋊C4—41no—
511C22⋊C4—41no—
512C22⋊C4—1721no—
513C22⋊C4—1721no—
514C42—21no—
515C42D4×D4311yescharacteristic
516C42#1062190011yescharacteristic
517C42C2×C22⋊D4311yescharacteristic
518C42C23×D4311yescharacteristic
519C23—21no—
520C23—41no—
521C23—1721no—
522C23#1306329711yescharacteristic
523Q8—21no—
524Q8—21no—
525Q8—41no—
526Q8—41no—
527Q8—1721no—
528Q8—1721no—
529D4—21no—
530D4—21no—
531D4—42no—
532D4—41no—
533D4—41no—
534D4—41no—
535D4—41no—
536D4—81no—
537D4—82no—
538D4—3441no—
539D4—3442no—
540D4—1721no—
541D4—1721no—
542D4—1721no—
543D4—1721no—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—21no—
547C2×C4—21no—
548C2×C4—21no—
549C2×C4—21no—
550C2×C4—21no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—82no—
556C2×C4—3442no—
557C2×C4—1721no—
558C2×C4#1306329711yescharacteristic
559C2×C4#1306329711yescharacteristic
560C2×C4#1306329711yescharacteristic
561C2×C4C2×D4×D4311yescharacteristic
562C2×C4C22×C22⋊D4311yescharacteristic
563C2×C4C2×#1062190011yescharacteristic
564C8—41no—
565C8—41no—
566C8—432no—
567C8—861no—
568C8—861no—
569C8—861no—
570C8—1721no—
571C8—1721no—
572C8—1721no—
573C8—1721no—
574C22—21no—
575C22—21no—
576C22—21no—
577C22—41no—
578C22—41no—
579C22—41no—
580C22—81no—
581C22—81no—
582C22—81no—
583C22—3441no—
584C22—3441no—
585C22—3441no—
586C22C2×#1306329711yescharacteristic
587C4—21no—
588C4—21no—
589C4—21no—
590C4—21no—
591C4—41no—
592C4—41no—
593C4—41no—
594C4—81no—
595C4—3441no—
596C4#135×D4311yescharacteristic
597C4#1458369611yescharacteristic
598C4#1458370211yescharacteristic
599C4#1458370211yescharacteristic
600C2—41no—
601C2—81no—
602C2—161no—
603C2—6881no—
604C2#1914404611yescharacteristic
605C2#1914424011yescharacteristic
606C2#1914431211yescharacteristic
subgroupG/H
centerC22C2×#13063297
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#3212C2
socleC22×C43C2×#121
hypercenter#3212D43
hypocenterC43#19225
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3212

Complements

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

NH ≅ G/Ntype
1. #19145567C2semidirect
2. #19145170C2semidirect
3. #19143571C2semidirect
4. #19134111C2semidirect
5. #19134106C2semidirect
6. #19134077C2semidirect
7. #19134072C2semidirect
8. #19134041C2semidirect
9. #19134037C2semidirect
10. #19134034C2semidirect
11. #19134030C2semidirect
12. #19133341C2semidirect
13. #19133300C2semidirect
14. #19133298C2semidirect
15. C43×#3212C2semidirect
298. #3212D43semidirect
370. C43#19225semidirect

Maximal subgroups

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

subgroupindex
#191455672
#191451702
#191435712
#191341112
#191341062
#191340772
#191340722
#191340412
#191340372
#191340342
#191340302
#191333412
#191333002
#191332982
C43×#32122
#1922543