Finite Group Databasebeta

← #25080313

Subgroups — #25080313

Order 11008.

624 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#19145921C211yesmaximal, characteristic, complemented
2#19145329C211yesmaximal, characteristic, complemented
3#19143600C211yesmaximal, characteristic, complemented
4#19134165C211yesmaximal, characteristic, complemented
5#19134133C211yesmaximal, characteristic, complemented
6#19134092C211yesmaximal, characteristic, complemented
7#19134072C211yesmaximal, characteristic, complemented
8#19134034C211yesmaximal, characteristic, complemented
9#19134002C211yesmaximal, characteristic, complemented
10#19133975C211yesmaximal, characteristic, complemented
11#19133953C211yesmaximal, characteristic, complemented
12#19133348C211yesmaximal, characteristic, complemented
13#19133255C211yesmaximal, characteristic, complemented
14#19133244C211yesmaximal, characteristic, complemented
15C43×#3212C211yesmaximal, characteristic, complemented
16#14583449C2211yescharacteristic
17#14583295C2211yescharacteristic
18#14583275C2211yescharacteristic
19#14583247C2211yescharacteristic
20#14583245C2211yescharacteristic
21#14583196—21no—
22#14583194C2211yescharacteristic
23#14583189C2211yescharacteristic
24#14583150—21no—
25#14583150—21no—
26#14583133—21no—
27#14583130—21no—
28#14583111—21no—
29#14583099C2211yescharacteristic
30#14583094C2211yescharacteristic
31#14583030C2211yescharacteristic
32Q8×C43⋊C8C2211yescharacteristic
33#14583009—21no—
34#14583009—21no—
35#14582977—21no—
36#14582977C2211yescharacteristic
37#14582971—21no—
38D4×C43⋊C8C2211yescharacteristic
39#14582960—21no—
40#14582952C2211yescharacteristic
41C2×C4⋊(C43⋊C8)C2211yescharacteristic
42#14582855—21no—
43C4×#10621877C2211yescharacteristic
44#14582651C2211yescharacteristic
45#14582651C2211yescharacteristic
46#14582649C2211yescharacteristic
47#14582649C2211yescharacteristic
48#14582647C2211yescharacteristic
49#14582647C2211yescharacteristic
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×#10621884—21no—
69C2×#10621882—21no—
70C2×#10621882—21no—
71C2×#10621882—21no—
72C2×#10621877—21no—
73C2×#10621877D411yescharacteristic
74C2×#10621877D411yescharacteristic
75C22×C43⋊C8—21no—
76C22×C43⋊C8—21no—
77#13063325C2311yescharacteristic
78#13063322C2311yescharacteristic
79#13063313—21no—
80#13063299—21no—
81#13063299—21no—
82C4×D172—21no—
83C4×D172—21no—
84#13063258—21no—
85#13063256—21no—
86#13063256—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#13063236D411yescharacteristic
108#13063236D411yescharacteristic
109C4×C43⋊C8—21no—
110C4×C43⋊C8—21no—
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—82no—
161C2×D172—21no—
162C2×D172—21no—
163C2×D172—21no—
164C2×C4×D43—41no—
165C2×Dic86—21no—
166Q16×C43—81no—
167SD16×C43—81no—
168SD16×C43—81no—
169D8×C43—81no—
170C2×C8×C43—21no—
171C2×C8×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—21no—
178C4⋊C4×C43C2×D411yescharacteristic
179C4⋊C4×C43C2×D411yescharacteristic
180C22⋊C4×C43—21no—
181C22⋊C4×C43—21no—
182C22⋊C4×C43—21no—
183C22⋊C4×C43—21no—
184C22⋊C4×C43—21no—
185C22⋊C4×C43—41no—
186C22⋊C4×C43—41no—
187C42×C43—21no—
188C42×C43C2×D411yescharacteristic
189C42×C43C2×D411yescharacteristic
190C42×C43#4111yescharacteristic
191C42×C43C2411yescharacteristic
192#10621884—81no—
193#10621882—42no—
194#10621882—42no—
195#10621882—81no—
196(C2×D43)⋊C4—41no—
197(C2×D43)⋊C4—41no—
198C4⋊Dic43—21no—
199C4⋊Dic43—21no—
200#10621877—22no—
201#10621877—41no—
202#10621877—42no—
203C2×C43⋊C8—21no—
204C2×C43⋊C8—21no—
205C2×C43⋊C8—21no—
206C2×C43⋊C8—21no—
207C2×C43⋊C8—42no—
208C2×C43⋊C8—81no—
209C2×C43⋊C8C2×D411yescharacteristic
210C2×C43⋊C8C2×D411yescharacteristic
211C2×C43⋊C8C2×D411yescharacteristic
212C2×C43⋊C8C2×D411yescharacteristic
213C23×C43—21no—
214C23×C43—41no—
215C23×C43#12111yescharacteristic
216C22×D43—41no—
217Q8×C43—21no—
218Q8×C43—21no—
219Q8×C43—41no—
220Q8×C43—41no—
221D4×C43—21no—
222D4×C43—21no—
223D4×C43—41no—
224D4×C43—41no—
225D4×C43—41no—
226D4×C43—41no—
227D4×C43—81no—
228D4×C43—81no—
229D4×C43—82no—
230C2×C4×C43—21no—
231C2×C4×C43—21no—
232C2×C4×C43—21no—
233C2×C4×C43—21no—
234C2×C4×C43—21no—
235C2×C4×C43—21no—
236C2×C4×C43—21no—
237C2×C4×C43—41no—
238C2×C4×C43—41no—
239C2×C4×C43—41no—
240C2×C4×C43—41no—
241C2×C4×C43—82no—
242C2×C4×C43#12111yescharacteristic
243C2×C4×C43#12111yescharacteristic
244C2×C4×C43#12111yescharacteristic
245C2×C4×C43C22×D411yescharacteristic
246C2×C4×C43C22×D411yescharacteristic
247C2×C4×C43C2×#4111yescharacteristic
248C22⋊D43—82no—
249C2×Dic43—41no—
250D172—41no—
251D172—41no—
252D172—41no—
253D172—41no—
254D172—81no—
255C4×D43—82no—
256Dic86—81no—
257C8×C43—41no—
258C8×C43—41no—
259C43⋊C8—21no—
260C43⋊C8—21no—
261C43⋊C8—21no—
262C43⋊C8—41no—
263C43⋊C8—41no—
264C43⋊C8—41no—
265C43⋊C8—41no—
266C43⋊C8#13512yes—
267#19250—431nomaximal, Sylow
268C22×C43—21no—
269C22×C43—21no—
270C22×C43—21no—
271C22×C43—41no—
272C22×C43—41no—
273C22×C43—41no—
274C22×C43—81no—
275C22×C43—81no—
276C22×C43—81no—
277C22×C43C2×#12111yescharacteristic
278C2×D43—81no—
279C2×D43—81no—
280C2×D43—81no—
281C4×C43—21no—
282C4×C43—21no—
283C4×C43—21no—
284C4×C43—21no—
285C4×C43—41no—
286C4×C43—41no—
287C4×C43—41no—
288C4×C43—81no—
289C4×C43C2×#13511yescharacteristic
290C4×C43#57511yescharacteristic
291C4×C43#57611yescharacteristic
292C4×C43#57711yescharacteristic
293Dic43—81no—
294#3247—431no—
295#3212D4311yescharacteristic, complemented
296#3184—431no—
297#2969—431no—
298#1702—431no—
299#1698—431no—
300#1691—431no—
301#1687—431no—
302#1681—431no—
303#1677—431no—
304#1672—431no—
305#1668—431no—
306#1565—431no—
307#1543—431no—
308#1540—431no—
309C2×C43—41no—
310C2×C43—81no—
311C2×C43—161no—
312C2×C43#303511yescharacteristic
313C2×C43#306211yescharacteristic
314C2×C43#306811yescharacteristic
315D43—161no—
316#532—431no—
317#532C2×D4311yescharacteristic
318#529C2×D4311yescharacteristic
319#498—431no—
320#495—21no—
321#493—431no—
322#488—21no—
323#486—431no—
324#486—431no—
325#478—861no—
326#477—431no—
327#476—431no—
328#469—861no—
329#469—861no—
330#466—861no—
331#465—861no—
332#463—861no—
333#462C2×D4311yescharacteristic
334#461C2×D4311yescharacteristic
335#460—431no—
336#460C2×D4311yescharacteristic
337#459—431no—
338#459C2×D4311yescharacteristic
339#452—21no—
340#449—21no—
341#446—431no—
342C8×Q8—431no—
343#442—861no—
344#442—861no—
345#436—431no—
346#436—861no—
347#435—861no—
348C8×D4—431no—
349#433—861no—
350#431—431no—
351#431C2×D4311yescharacteristic
352C2×C4⋊C8—431no—
353#405—861no—
354C4×M16—431no—
355#335—431no—
356#335—431no—
357#334—431no—
358#334—431no—
359#333—431no—
360#333—431no—
361#332—431no—
362#332—431no—
363#331—431no—
364#331—431no—
365#331—431no—
366#331—431no—
367C43#1925011yescharacteristic, complemented, Sylow
368C2×#41—21no—
369C2×#41—861no—
370C2×Q16—21no—
371C2×SD16—21no—
372C2×SD16—21no—
373C2×SD16—861no—
374C2×D8—21no—
375C2×D8—861no—
376C2×D8—861no—
377C2×D8—861no—
378C2×M16—431no—
379C2×M16—431no—
380C2×M16—861no—
381C22×C8—861no—
382C22×C8—861no—
383C4⋊Q8—431no—
384C4⋊Q8C22×D4311yescharacteristic
385#127—431no—
386#127C22×D4311yescharacteristic
387#126—21no—
388#125C22⋊D4311yescharacteristic
389#124—21no—
390#124—861no—
391#124C22⋊D4311yescharacteristic
392#123—21no—
393C22⋊Q8C22⋊D4311yescharacteristic
394#121—21no—
395#121—21no—
396#121—861no—
397#121—861no—
398#121C22⋊D4311yescharacteristic
399C4×Q8C22×D4311yescharacteristic
400C4×D4—21no—
401C4×D4—21no—
402C4×D4—21no—
403C4×D4—861no—
404C4×D4—861no—
405C4×D4C22×D4311yescharacteristic
406#117—21no—
407C2×C42C22×D4311yescharacteristic
408#107—861no—
409#106—861no—
410#106—861no—
411#106—861no—
412C4⋊C8—431no—
413C4⋊C8—431no—
414C4⋊C8—431no—
415C4⋊C8—431no—
416C4⋊C8—861no—
417C4⋊C8—861no—
418C4⋊C8—861no—
419C4⋊C8C22×D4311yescharacteristic
420C4⋊C8C22×D4311yescharacteristic
421#103—21no—
422#103—21no—
423#103—861no—
424#102—21no—
425#102—21no—
426#102—861no—
427#102—861no—
428#102—861no—
429#102—861no—
430#102—861no—
431#102—861no—
432#102—861no—
433C22⋊C8—21no—
434C22⋊C8—861no—
435C22⋊C8—861no—
436C22⋊C8—861no—
437#97—431no—
438#97—431no—
439#97—861no—
440C4×C8—21no—
441C4×C8—431no—
442C4×C8—431no—
443C4×C8—861no—
444C4×C8—861no—
445#41—81no—
446#41—81no—
447#41—3442no—
448C2×Q8—21no—
449C2×Q8—861no—
450C2×Q8C2×C22⋊D4311yescharacteristic
451C2×D4—21no—
452C2×D4—21no—
453C2×D4—21no—
454C2×D4—21no—
455C2×D4—41no—
456C2×D4—861no—
457C2×D4—861no—
458C2×D4—861no—
459C2×D4—1721no—
460C2×D4C2×C22⋊D4311yescharacteristic
461C22×C4—21no—
462C22×C4—41no—
463C22×C4—1721no—
464C22×C4D4×D4311yescharacteristic
465C22×C4#1062190011yescharacteristic
466C22×C4C2×C22⋊D4311yescharacteristic
467Q16—81no—
468SD16—81no—
469SD16—81no—
470SD16—3441no—
471D8—81no—
472D8—3441no—
473D8—1722no—
474D8—1722no—
475M16—862no—
476M16—1722no—
477M16—1721no—
478C2×C8—21no—
479C2×C8—21no—
480C2×C8—431no—
481C2×C8—431no—
482C2×C8—431no—
483C2×C8—431no—
484C2×C8—861no—
485C2×C8—861no—
486C2×C8—861no—
487C2×C8—861no—
488C2×C8—3441no—
489C2×C8—1722no—
490C4⋊C4—21no—
491C4⋊C4—21no—
492C4⋊C4—21no—
493C4⋊C4—21no—
494C4⋊C4—21no—
495C4⋊C4—21no—
496C4⋊C4—861no—
497C4⋊C4—861no—
498C4⋊C4C2×C22⋊D4311yescharacteristic
499C4⋊C4C2×C22⋊D4311yescharacteristic
500C22⋊C4—21no—
501C22⋊C4—21no—
502C22⋊C4—21no—
503C22⋊C4—21no—
504C22⋊C4—21no—
505C22⋊C4—41no—
506C22⋊C4—41no—
507C22⋊C4—1721no—
508C22⋊C4—1721no—
509C42—21no—
510C42D4×D4311yescharacteristic
511C42#1062190011yescharacteristic
512C42C2×C22⋊D4311yescharacteristic
513C42C23×D4311yescharacteristic
514C23—21no—
515C23—41no—
516C23—1721no—
517C23#1306329711yescharacteristic
518Q8—21no—
519Q8—21no—
520Q8—41no—
521Q8—41no—
522Q8—3441no—
523D4—21no—
524D4—21no—
525D4—41no—
526D4—41no—
527D4—41no—
528D4—41no—
529D4—81no—
530D4—81no—
531D4—82no—
532D4—3441no—
533D4—3442no—
534D4—1721no—
535D4—1721no—
536D4—1721no—
537D4—1721no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—82no—
550C2×C4—3442no—
551C2×C4—1721no—
552C2×C4#1306329711yescharacteristic
553C2×C4#1306329711yescharacteristic
554C2×C4#1306329711yescharacteristic
555C2×C4C2×D4×D4311yescharacteristic
556C2×C4C22×C22⋊D4311yescharacteristic
557C2×C4C2×#1062190011yescharacteristic
558C8—41no—
559C8—41no—
560C8—432no—
561C8—861no—
562C8—861no—
563C8—861no—
564C8—1721no—
565C8—1721no—
566C8—1721no—
567C8—1721no—
568C22—21no—
569C22—21no—
570C22—21no—
571C22—41no—
572C22—41no—
573C22—41no—
574C22—81no—
575C22—81no—
576C22—81no—
577C22—3441no—
578C22—3441no—
579C22—3441no—
580C22C2×#1306329711yescharacteristic
581C4—21no—
582C4—21no—
583C4—21no—
584C4—21no—
585C4—41no—
586C4—41no—
587C4—41no—
588C4—81no—
589C4—3441no—
590C4#135×D4311yescharacteristic
591C4#1458369611yescharacteristic
592C4#1458370211yescharacteristic
593C4#1458371011yescharacteristic
594C2—41no—
595C2—81no—
596C2—161no—
597C2—6881no—
598C2#1914404611yescharacteristic
599C2#1914427111yescharacteristic
600C2#1914432511yescharacteristic
subgroupG/H
centerC22C2×#13063297
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#3212C2
socleC22×C43C2×#121
hypercenter#3212D43
hypocenterC43#19250
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. #19145921C2semidirect
2. #19145329C2semidirect
3. #19143600C2semidirect
4. #19134165C2semidirect
5. #19134133C2semidirect
6. #19134092C2semidirect
7. #19134072C2semidirect
8. #19134034C2semidirect
9. #19134002C2semidirect
10. #19133975C2semidirect
11. #19133953C2semidirect
12. #19133348C2semidirect
13. #19133255C2semidirect
14. #19133244C2semidirect
15. C43×#3212C2semidirect
295. #3212D43semidirect
367. C43#19250semidirect

Maximal subgroups

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

subgroupindex
#191459212
#191453292
#191436002
#191341652
#191341332
#191340922
#191340722
#191340342
#191340022
#191339752
#191339532
#191333482
#191332552
#191332442
C43×#32122
#1925043