Finite Group Databasebeta

← #25196555

Subgroups — #25196555

Order 11008.

608 conjugacy classes of subgroups.

The subgroup lattice has 600 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145117C211yesmaximal, characteristic, complemented
2C2×#14583018C211yesmaximal, characteristic
3#19135768C211yesmaximal, characteristic, complemented
4#19135767C211yesmaximal, characteristic, complemented
5#19135764C211yesmaximal, characteristic, complemented
6#19135492C211yesmaximal, characteristic
7#19135490C211yesmaximal, characteristic
8#19134717C211yesmaximal, characteristic, complemented
9#19134716C211yesmaximal, characteristic, complemented
10#19134648C211yesmaximal, characteristic, complemented
11#19134647C211yesmaximal, characteristic, complemented
12#19134640C211yesmaximal, characteristic, complemented
13#19134639C211yesmaximal, characteristic, complemented
14#19134478C211yesmaximal, characteristic, complemented
15C43×#2031C211yesmaximal, characteristic, complemented
16C2×#13063345C2211yescharacteristic
17C2×#13063333C2211yescharacteristic
18C2×#13063332C2211yescharacteristic
19#14583456C2211yescharacteristic
20#14583309—21no—
21#14583309—21no—
22#14583305—21no—
23#14583305—21no—
24#14583018—21no—
25#14583018—21no—
26#14583018—21no—
27#14583018—21no—
28C2×#13063260C2211yescharacteristic
29C2×#13063260C2211yescharacteristic
30#14582935C2211yescharacteristic
31#14582935C2211yescharacteristic
32#14582935C2211yescharacteristic
33#14582935C2211yescharacteristic
34#14582935C2211yescharacteristic
35#14582917C2211yescharacteristic
36#14582916C2211yescharacteristic
37#14582915C2211yescharacteristic
38C2×#13063253C2211yescharacteristic
39#14582873C2211yescharacteristic
40#14582872C2211yescharacteristic
41#14582872C2211yescharacteristic
42#14582857C2211yescharacteristic
43#14582855C2211yescharacteristic
44C2×#13063236C2211yescharacteristic
45#14582671C2211yescharacteristic
46#14582670C2211yescharacteristic
47#14582669C2211yescharacteristic
48#14582659C2211yescharacteristic
49#14582656C2211yescharacteristic
50#14582655C2211yescharacteristic
51#14582655C2211yescharacteristic
52C43×#533C2211yescharacteristic
53C43×#421C2211yescharacteristic
54C2×#104×C43C2211yescharacteristic
55C43×#410C2211yescharacteristic
56C43×#344C2211yescharacteristic
57C43×#339C2211yescharacteristic
58C43×H(3,ℤ/4)C2211yescharacteristic
59C2×#10621898C2311yescharacteristic
60#13063345—21no—
61#13063345—21no—
62#13063345—21no—
63#13063345—21no—
64C2×#10621885Q811yescharacteristic, complemented
65C2×#10621883Q811yescharacteristic, complemented
66C2×#10621884Q811yescharacteristic, complemented
67C2×#10621882Q811yescharacteristic, complemented
68#13063333—21no—
69#13063333—21no—
70#13063333—21no—
71#13063333—21no—
72#13063332—21no—
73#13063332—21no—
74#13063332—21no—
75#13063332—21no—
76C2×#10621877—21no—
77C2×#10621877C2311yescharacteristic
78C2×#10621877C2311yescharacteristic
79C2×#10621872—21no—
80C22×C43⋊C8—21no—
81C22×C43⋊C8C2311yescharacteristic
82C22×C43⋊C8C2311yescharacteristic
83C2×C8×D43—21no—
84#13063325—21no—
85#13063317—21no—
86#13063304—41no—
87C4×Dic86—41no—
88#13063284C2311yescharacteristic
89#13063284C2311yescharacteristic
90#13063284C2311yescharacteristic
91#13063260—21no—
92#13063260—21no—
93#13063260—21no—
94#13063260—21no—
95#13063258—21no—
96#13063258—21no—
97#13063258—21no—
98#13063258—21no—
99#13063258—21no—
100#13063256—21no—
101#13063256—21no—
102#13063256—21no—
103#13063256—21no—
104#13063256—21no—
105#13063253—21no—
106#13063253—21no—
107#13063253—41no—
108#13063252—41no—
109#13063251—41no—
110#13063240—41no—
111#13063239—41no—
112#13063239—41no—
113#13063236—21no—
114#13063236D411yescharacteristic
115#13063236D411yescharacteristic
116#13063236D411yescharacteristic
117#13063236D411yescharacteristic
118#13063235—21no—
119C4×C43⋊C8—21no—
120C8×Dic43—21no—
121C2×#41×C43C2311yescharacteristic
122C2×M16×C43C2311yescharacteristic
123C2×M16×C43C2311yescharacteristic
124C4⋊Q8×C43—21no—
125#125×C43—21no—
126C22⋊Q8×C43—41no—
127C4×Q8×C43—41no—
128#117×C43C2311yescharacteristic
129#117×C43C2311yescharacteristic
130#117×C43C2311yescharacteristic
131C2×C42×C43C2311yescharacteristic
132#104×C43—21no—
133#104×C43—21no—
134#104×C43—41no—
135#99×C43—41no—
136#41×C43—21no—
137#41×C43—21no—
138#41×C43—21no—
139#41×C43—21no—
140C2×Q8×C43—41no—
141C2×Q8×C43C2×Q811yescharacteristic
142C2×D4×C43—21no—
143C2×D4×C43C2×Q811yescharacteristic
144C22×C4×C43—21no—
145C22×C4×C43—21no—
146C22×C4×C43C2411yescharacteristic
147C2×C22⋊D43—21no—
148#10621898—21no—
149#10621898—21no—
150#10621898—21no—
151#10621898—21no—
152C2×D172C2×Q811yescharacteristic
153C2×C4×D43—21no—
154C2×Dic86—41no—
155C2×Dic86C2×Q811yescharacteristic
156M16×C43—21no—
157M16×C43—21no—
158M16×C43—21no—
159M16×C43—21no—
160C2×C8×C43—21no—
161C2×C8×C43—21no—
162C4⋊C4×C43—21no—
163C4⋊C4×C43—21no—
164C4⋊C4×C43—21no—
165C4⋊C4×C43—42no—
166C4⋊C4×C43—41no—
167C22⋊C4×C43—21no—
168C22⋊C4×C43—21no—
169C22⋊C4×C43—21no—
170C42×C43—21no—
171C42×C43—21no—
172C42×C43—21no—
173C42×C43—21no—
174C42×C43C2×D411yescharacteristic
175C42×C43C2×D411yescharacteristic
176C22⋊Dic43—21no—
177C22⋊Dic43—21no—
178C22⋊Dic43—21no—
179#10621885—21no—
180#10621885—21no—
181#10621884—21no—
182#10621884—21no—
183#10621883—21no—
184#10621883—21no—
185#10621882—21no—
186#10621882—21no—
187C4⋊Dic43—21no—
188C4⋊Dic43—21no—
189C4⋊Dic43—21no—
190C4⋊Dic43—41no—
191Dic43⋊C4—42no—
192C4×Dic43—21no—
193C4×Dic43—21no—
194C4×Dic43—21no—
195#10621877—21no—
196#10621877—21no—
197#10621877—21no—
198#10621877—21no—
199#10621877—41no—
200#10621877—41no—
201C2×C43⋊C8—21no—
202C2×C43⋊C8—21no—
203C2×C43⋊C8—41no—
204C2×C43⋊C8—41no—
205C2×C43⋊C8C2×D411yescharacteristic
206C2×C43⋊C8C2×D411yescharacteristic
207C2×C43⋊C8C2×D411yescharacteristic
208C2×C43⋊C8C2×D411yescharacteristic
209C2×C43⋊C8C2×Q811yescharacteristic
210C2×C43⋊C8C2×Q811yescharacteristic
211C2×C43⋊C8#4111yescharacteristic
212C2×C43⋊C8#4111yescharacteristic
213C2×C43⋊C8#4111yescharacteristic
214C2×C43⋊C8#4111yescharacteristic
215C2×C43⋊C8#4111yescharacteristic
216C2×C43⋊C8#4111yescharacteristic
217#10621872—41no—
218#10621872—41no—
219C8×D43—41no—
220C8×D43—41no—
221C23×C43—21no—
222C23×C43H(5,𝔽2)11yescharacteristic
223C22×D43—21no—
224Q8×C43—21no—
225Q8×C43—21no—
226Q8×C43—82no—
227D4×C43—21no—
228D4×C43—21no—
229D4×C43—41no—
230D4×C43—41no—
231C2×C4×C43—21no—
232C2×C4×C43—21no—
233C2×C4×C43—21no—
234C2×C4×C43—41no—
235C2×C4×C43—41no—
236C2×C4×C43—41no—
237C2×C4×C43—41no—
238C2×C4×C43—41no—
239C2×C4×C43—81no—
240C2×C4×C43C22×D411yescharacteristic
241C2×C4×C43C22×Q811yescharacteristic
242C2×C4×C43C2×#4111yescharacteristic
243C2×C4×C43C2×#4111yescharacteristic
244C2×C4×C43C2×#4111yescharacteristic
245C2×C4×C43H(5,𝔽2)11yescharacteristic
246C22⋊D43—41no—
247C22⋊D43—41no—
248C2×Dic43—21no—
249C2×Dic43—41no—
250C2×Dic43—41no—
251C2×Dic43—41no—
252D172—21no—
253D172—21no—
254C4×D43—41no—
255C4×D43—41no—
256Dic86—21no—
257Dic86—21no—
258Dic86—82no—
259C8×C43—41no—
260C8×C43—41no—
261C43⋊C8—41no—
262C43⋊C8—41no—
263C43⋊C8C22⋊Q811yescharacteristic
264C43⋊C8C22⋊Q811yescharacteristic
265C43⋊C8C22⋊Q811yescharacteristic
266C43⋊C8C22⋊Q811yescharacteristic
267C43⋊C8#12411yescharacteristic
268C43⋊C8#12411yescharacteristic
269C43⋊C8#12411yescharacteristic
270C43⋊C8#12411yescharacteristic
271#29155—431nomaximal, Sylow
272C22×C43—41no—
273C22×C43—41no—
274C22×C43—81no—
275C22×C43#53511yescharacteristic
276C22×C43#55411yescharacteristic
277C22×C43#55511yescharacteristic
278C2×D43—41no—
279C2×D43—81no—
280C4×C43—41no—
281C4×C43—41no—
282C4×C43—41no—
283C4×C43—81no—
284C4×C43—81no—
285C4×C43—81no—
286C4×C43C2×C22⋊Q811yescharacteristic
287C4×C43C2×#12411yescharacteristic
288C4×C43#55411yescharacteristic
289C4×C43#55511yescharacteristic
290Dic43—41no—
291Dic43—81no—
292Dic43—81no—
293Dic43—81no—
294#3162—431no—
295C2×#444—431no—
296#2031—431no—
297#2031—431no—
298#2031—431no—
299#2031D4311yescharacteristic, complemented
300#1976—431no—
301#1976—431no—
302#1833—431no—
303#1833—431no—
304#1814—431no—
305#1814—431no—
306#1812—431no—
307#1812—431no—
308#1773—431no—
309C2×C43—21no—
310C2×C43—21no—
311C2×C43—21no—
312C2×C43—81no—
313C2×C43#256311yescharacteristic
314D43—81no—
315C2×#135—431no—
316C2×#131—431no—
317C2×#131—431no—
318#533—431no—
319#533C2×D4311yescharacteristic
320#501—861no—
321#501—861no—
322#501—861no—
323#501—861no—
324#444—861no—
325#444—861no—
326#444—861no—
327#444—861no—
328C2×#108—431no—
329C2×#108—431no—
330#427—431no—
331#427—431no—
332#427—431no—
333#427—431no—
334#427—431no—
335#421—431no—
336#421—431no—
337#421—431no—
338#421C2×D4311yescharacteristic
339C2×#104—431no—
340C2×#104C2×D4311yescharacteristic
341#410—431no—
342#410—431no—
343#410—431no—
344#410C2×D4311yescharacteristic
345#405—431no—
346#405—431no—
347C2×#97—431no—
348#344—431no—
349#344—431no—
350#344—431no—
351#344C2×D4311yescharacteristic
352#339—431no—
353#339C2×D4311yescharacteristic
354H(3,ℤ/4)—431no—
355H(3,ℤ/4)—431no—
356H(3,ℤ/4)—431no—
357H(3,ℤ/4)C2×D4311yescharacteristic
358C43#2915511yescharacteristic, complemented, Sylow
359C2×#41—431no—
360C2×#41C22×D4311yescharacteristic
361#135—861no—
362#135—861no—
363#135—861no—
364#135—861no—
365C2×Q16—431no—
366C2×SD16—431no—
367C2×SD16—431no—
368C2×D8—431no—
369#131—861no—
370#131—861no—
371#131—861no—
372#131—861no—
373#131—861no—
374#131—861no—
375#131—861no—
376#131—861no—
377C2×M16—431no—
378C2×M16—431no—
379C2×M16—861no—
380C2×M16—861no—
381C2×M16C22×D4311yescharacteristic
382C2×M16C22×D4311yescharacteristic
383C22×C8—431no—
384C22×C8—431no—
385C22×C8—861no—
386C22×C8—861no—
387C4⋊Q8—21no—
388C4⋊Q8—861no—
389#125—21no—
390#125—861no—
391C22⋊Q8—41no—
392C22⋊Q8—1721no—
393C4×Q8—41no—
394C4×Q8—1721no—
395#117—431no—
396#117—431no—
397#117—431no—
398#117C22×D4311yescharacteristic
399#117C22×D4311yescharacteristic
400#117C22×D4311yescharacteristic
401C2×C42C22×D4311yescharacteristic
402#108—861no—
403#108—861no—
404#108—861no—
405#108—861no—
406#107—861no—
407#107—861no—
408#107—861no—
409#107—861no—
410#107—861no—
411#106—861no—
412#106—861no—
413#106—861no—
414#106—861no—
415#106—861no—
416#104—21no—
417#104—21no—
418#104—41no—
419#104—861no—
420#104—861no—
421#104—1721no—
422#104—1721no—
423#104—1721no—
424#99—41no—
425#99—1721no—
426#99—1721no—
427#99—1721no—
428#97—431no—
429#97—431no—
430#97—431no—
431#97—431no—
432#97—861no—
433#97—861no—
434C4×C8—861no—
435C4×C8—861no—
436#41—21no—
437#41—21no—
438#41—21no—
439#41—21no—
440#41—861no—
441#41—861no—
442#41—861no—
443#41—861no—
444C2×Q8—41no—
445C2×Q8—431no—
446C2×Q8—1721no—
447C2×Q8Q8×D4311yescharacteristic
448C2×D4—21no—
449C2×D4—431no—
450C2×D4—861no—
451C2×D4Q8×D4311yescharacteristic
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—861no—
455C22×C4C23×D4311yescharacteristic
456Q16—861no—
457Q16—861no—
458SD16—861no—
459SD16—861no—
460SD16—861no—
461SD16—861no—
462D8—861no—
463D8—861no—
464M16—21no—
465M16—21no—
466M16—21no—
467M16—21no—
468M16—861no—
469M16—861no—
470M16—861no—
471M16—861no—
472M16—1721no—
473M16—1721no—
474M16—1721no—
475M16—1721no—
476C2×C8—21no—
477C2×C8—21no—
478C2×C8—431no—
479C2×C8—431no—
480C2×C8—431no—
481C2×C8—431no—
482C2×C8—431no—
483C2×C8—431no—
484C2×C8—431no—
485C2×C8—431no—
486C2×C8—431no—
487C2×C8—431no—
488C2×C8—431no—
489C2×C8—431no—
490C2×C8—861no—
491C2×C8—861no—
492C2×C8—1721no—
493C2×C8—1721no—
494C2×C8—1721no—
495C2×C8—1721no—
496C4⋊C4—21no—
497C4⋊C4—21no—
498C4⋊C4—21no—
499C4⋊C4—42no—
500C4⋊C4—41no—
501C4⋊C4—861no—
502C4⋊C4—861no—
503C4⋊C4—861no—
504C4⋊C4—1722no—
505C4⋊C4—1721no—
506C22⋊C4—21no—
507C22⋊C4—21no—
508C22⋊C4—21no—
509C22⋊C4—861no—
510C22⋊C4—861no—
511C22⋊C4—861no—
512C42—21no—
513C42—21no—
514C42—21no—
515C42—21no—
516C42—861no—
517C42—861no—
518C42—861no—
519C42D4×D4311yescharacteristic
520C42D4×D4311yescharacteristic
521C23—21no—
522C23—861no—
523C23#1306337011yescharacteristic
524Q8—21no—
525Q8—21no—
526Q8—82no—
527Q8—861no—
528Q8—861no—
529Q8—3442no—
530D4—21no—
531D4—21no—
532D4—41no—
533D4—41no—
534D4—861no—
535D4—861no—
536D4—1721no—
537D4—1721no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—81no—
547C2×C4—861no—
548C2×C4—1721no—
549C2×C4—1721no—
550C2×C4—1721no—
551C2×C4—1721no—
552C2×C4—1721no—
553C2×C4C2×D4×D4311yescharacteristic
554C2×C4C2×Q8×D4311yescharacteristic
555C2×C4#41×D4311yescharacteristic
556C2×C4#41×D4311yescharacteristic
557C2×C4#41×D4311yescharacteristic
558C2×C4#1306337011yescharacteristic
559C8—41no—
560C8—41no—
561C8—431no—
562C8—431no—
563C8—431no—
564C8—431no—
565C8—431no—
566C8—431no—
567C8—431no—
568C8—431no—
569C8—1721no—
570C8—1721no—
571C22—41no—
572C22—41no—
573C22—81no—
574C22—3441no—
575C22—1721no—
576C22#1458346411yescharacteristic
577C22#1458360311yescharacteristic
578C22#1458361111yescharacteristic
579C4—41no—
580C4—41no—
581C4—41no—
582C4—81no—
583C4—81no—
584C4—81no—
585C4—3441no—
586C4—3441no—
587C4—3441no—
588C4—1721no—
589C4C22⋊Q8×D4311yescharacteristic
590C4#124×D4311yescharacteristic
591C4#1458360311yescharacteristic
592C4#1458361111yescharacteristic
593C2—21no—
594C2—21no—
595C2—21no—
596C2—81no—
597C2—3441no—
598C2#1913976311yescharacteristic
subgroupG/H
centerC4#14583611
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2031C2
socleC2×C43#2563
prime radicalC2×#13063345C22
hypercenter#2031D43
hypocenterC43#29155
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C4 ◁ C22×C4 ◁ #2031

Complements

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

NH ≅ G/Ntype
1. #19145117C2semidirect
3. #19135768C2semidirect
4. #19135767C2semidirect
5. #19135764C2semidirect
8. #19134717C2semidirect
9. #19134716C2semidirect
10. #19134648C2semidirect
11. #19134647C2semidirect
12. #19134640C2semidirect
13. #19134639C2semidirect
14. #19134478C2semidirect
15. C43×#2031C2semidirect
64. C2×#10621885Q8semidirect
65. C2×#10621883Q8semidirect
66. C2×#10621884Q8semidirect
67. C2×#10621882Q8semidirect
299. #2031D43semidirect
358. C43#29155semidirect

Maximal subgroups

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

subgroupindex
#191451172
C2×#145830182
#191357682
#191357672
#191357642
#191354922
#191354902
#191347172
#191347162
#191346482
#191346472
#191346402
#191346392
#191344782
C43×#20312
#2915543