Finite Group Databasebeta

← #25138086

Subgroups — #25138086

Order 11008.

674 conjugacy classes of subgroups.

The subgroup lattice has 624 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19144408C211yesmaximal, characteristic
2C2×#14583183C211yesmaximal, characteristic, complemented
3#19143413C211yesmaximal, characteristic
4#19143259C211yesmaximal, characteristic
5#19136044C211yesmaximal, characteristic
6#19136041C211yesmaximal, characteristic
7#19135897C211yesmaximal, characteristic
8#19135896C211yesmaximal, characteristic
9#19135582C211yesmaximal, characteristic, complemented
10#19135372C211yesmaximal, characteristic, complemented
11#19135367C211yesmaximal, characteristic, complemented
12#19135250C211yesmaximal, characteristic, complemented
13#19135249C211yesmaximal, characteristic, complemented
14#19134590C211yesmaximal, characteristic, complemented
15C43×#1951C211yesmaximal, characteristic, complemented
16C2×#13063358C2211yescharacteristic
17C2×#13063324C2211yescharacteristic
18#14583367C2211yescharacteristic
19C2×#13063290C2211yescharacteristic
20#14583193—21no—
21#14583188—21no—
22#14583183—21no—
23#14583183—21no—
24#14583183—21no—
25#14583183—21no—
26#14583183—21no—
27#14583178—21no—
28#14583005—21no—
29#14582998—21no—
30#14582993—21no—
31#14582986—21no—
32#14582961—21no—
33#14582958—21no—
34#14582954—21no—
35#14582950—21no—
36C2×#13063260C2211yescharacteristic
37#14582942C2211yescharacteristic
38C2×#13063256C2211yescharacteristic
39#14582922C2211yescharacteristic
40#14582922C2211yescharacteristic
41C2×Dic43⋊C8C2211yescharacteristic
42#14582907C2211yescharacteristic
43#14582901C2211yescharacteristic
44#14582898C2211yescharacteristic
45#14582898C2211yescharacteristic
46C2×#13063250C2211yescharacteristic
47C2×#13063248C2211yescharacteristic
48C2×#13063243C2211yescharacteristic
49C2×#13063243C2211yescharacteristic
50#14582867C2211yescharacteristic
51#14582865C2211yescharacteristic
52#14582855C2211yescharacteristic
53M16×Dic43C2211yescharacteristic
54#14582668C2211yescharacteristic
55#14582668C2211yescharacteristic
56#14582667C2211yescharacteristic
57#14582667C2211yescharacteristic
58#14582664C2211yescharacteristic
59#14582663C2211yescharacteristic
60C2×#108×C43C2211yescharacteristic
61C43×#428C2211yescharacteristic
62C43×#428C2211yescharacteristic
63C2×#106×C43C2211yescharacteristic
64C43×#405C2211yescharacteristic
65C43×#343C2211yescharacteristic
66C43×#343C2211yescharacteristic
67C2×#10621898C2311yescharacteristic
68C22×Dic86—21no—
69C22×Dic86C2311yescharacteristic
70#13063358—22no—
71#13063358—22no—
72C2×Dic172—21no—
73C2×#10621873—21no—
74C2×#10621877C2311yescharacteristic
75C2×#10621877C2311yescharacteristic
76C2×#10621877C2311yescharacteristic
77C22×C43⋊C8C2311yescharacteristic
78#13063324—21no—
79#13063324—21no—
80#13063324—21no—
81#13063324—21no—
82#13063290—21no—
83#13063290—21no—
84#13063290—21no—
85#13063290—21no—
86#13063290D411yescharacteristic
87#13063290D411yescharacteristic
88#13063287D411yescharacteristic
89#13063287D411yescharacteristic
90(C22⋊D43)⋊C4—21no—
91(C22⋊D43)⋊C4—21no—
92#13063282—21no—
93C2×C4⋊Dic43C2311yescharacteristic
94C2×Dic43⋊C4—21no—
95C2×Dic43⋊C4—21no—
96C2×C4×Dic43—21no—
97C2×C4×Dic43C2311yescharacteristic
98C42×D43—21no—
99#13063260—22no—
100#13063258—21no—
101#13063256—21no—
102#13063256—21no—
103#13063256—21no—
104Dic43⋊C8—21no—
105Dic43⋊C8—21no—
106Dic43⋊C8—21no—
107Dic43⋊C8—21no—
108Dic43⋊C8D411yescharacteristic
109Dic43⋊C8D411yescharacteristic
110Dic43⋊C8D411yescharacteristic
111Dic43⋊C8D411yescharacteristic
112#13063250—21no—
113#13063250—21no—
114#13063250—21no—
115#13063248—21no—
116#13063248—21no—
117#13063248—21no—
118#13063248—21no—
119#13063248—21no—
120#13063248—21no—
121#13063247—21no—
122#13063245—21no—
123#13063245—21no—
124#13063243—22no—
125#13063243—22no—
126(C2×D43)⋊C8—21no—
127(C2×D43)⋊C8—21no—
128(C2×D43)⋊C8—21no—
129(C2×D43)⋊C8—21no—
130#13063236—21no—
131#13063235—21no—
132C4×C43⋊C8—21no—
133C8×Dic43—21no—
134C2×M16×C43C2311yescharacteristic
135C2×M16×C43C2311yescharacteristic
136C2×M16×C43C2311yescharacteristic
137C22×C8×C43C2311yescharacteristic
138#117×C43C2311yescharacteristic
139C2×C4⋊C4×C43C2311yescharacteristic
140C2×C4⋊C4×C43C2311yescharacteristic
141#108×C43—22no—
142#107×C43—21no—
143#107×C43—21no—
144#106×C43—21no—
145#106×C43—21no—
146#106×C43—21no—
147#106×C43—21no—
148#97×C43—21no—
149C4×C8×C43—21no—
150C22×C4×C43—21no—
151C22×C4×C43—21no—
152C22×C4×C43C2411yescharacteristic
153C2×C22⋊D43—21no—
154C22×Dic43—21no—
155C22×Dic43—21no—
156C22×Dic43#4111yescharacteristic
157C22×Dic43#4111yescharacteristic
158#10621898—21no—
159#10621898—21no—
160#10621898—21no—
161#10621898—21no—
162C2×D172C2×D411yescharacteristic
163C2×C4×D43—21no—
164C2×C4×D43—21no—
165C2×C4×D43—21no—
166C2×Dic86—21no—
167C2×Dic86—21no—
168C2×Dic86—21no—
169C2×Dic86—21no—
170C2×Dic86—21no—
171C2×Dic86—41no—
172C2×Dic86—41no—
173C2×Dic86—82no—
174C2×Dic86C2×D411yescharacteristic
175C2×Dic86#4112yes—
176M16×C43—21no—
177M16×C43—21no—
178M16×C43—21no—
179M16×C43—21no—
180M16×C43—21no—
181M16×C43#4112yes—
182C2×C8×C43—21no—
183C2×C8×C43—21no—
184C2×C8×C43—21no—
185C2×C8×C43—21no—
186C2×C8×C43—21no—
187C2×C8×C43C2×D411yescharacteristic
188C2×C8×C43C2×D411yescharacteristic
189C4⋊C4×C43—21no—
190C4⋊C4×C43—21no—
191C4⋊C4×C43—21no—
192C4⋊C4×C43—21no—
193C4⋊C4×C43C2×D411yescharacteristic
194C4⋊C4×C43C2×D411yescharacteristic
195C22⋊C4×C43—21no—
196C42×C43—21no—
197(C2×D43)⋊C4—21no—
198(C2×D43)⋊C4—21no—
199C4⋊Dic43—21no—
200C4⋊Dic43—21no—
201Dic43⋊C4—21no—
202Dic43⋊C4—21no—
203Dic43⋊C4—41no—
204Dic43⋊C4—41no—
205Dic43⋊C4—41no—
206Dic43⋊C4—41no—
207C4×Dic43—21no—
208C4×Dic43—21no—
209C4×Dic43—41no—
210C4×Dic43—41no—
211C4×Dic43C2×D411yescharacteristic
212C4×Dic43C2×D411yescharacteristic
213C4×Dic43C2×D411yescharacteristic
214C4×Dic43C2×D411yescharacteristic
215#10621877—21no—
216#10621877—21no—
217#10621877—21no—
218#10621877—21no—
219#10621877—21no—
220#10621877—21no—
221C2×C43⋊C8—21no—
222C2×C43⋊C8—21no—
223C2×C43⋊C8—21no—
224C2×C43⋊C8—21no—
225C2×C43⋊C8—21no—
226C2×C43⋊C8C2×D411yescharacteristic
227C2×C43⋊C8C2×D411yescharacteristic
228Dic172—24no—
229#10621873—24no—
230C23×C43C2×#4111yescharacteristic
231C22×D43—21no—
232C2×C4×C43—21no—
233C2×C4×C43—21no—
234C2×C4×C43—41no—
235C2×C4×C43—41no—
236C2×C4×C43—81no—
237C2×C4×C43—81no—
238C2×C4×C43C22×D411yescharacteristic
239C2×C4×C43C22×D411yescharacteristic
240C2×C4×C43C2×#4111yescharacteristic
241C2×C4×C43C2×#4111yescharacteristic
242C2×C4×C432−1+411yescharacteristic
243C2×C4×C432−1+411yescharacteristic
244C22⋊D43—41no—
245C22⋊D43—41no—
246C2×Dic43—22no—
247C2×Dic43—21no—
248C2×Dic43—22no—
249C2×Dic43—41no—
250C2×Dic43—41no—
251C2×Dic43—41no—
252C2×Dic43—41no—
253C2×Dic43—81no—
254C2×Dic43#12111yescharacteristic
255C2×Dic43#12111yescharacteristic
256C2×Dic43#12111yescharacteristic
257C2×Dic43#12111yescharacteristic
258D172—21no—
259D172—21no—
260C4×D43—41no—
261C4×D43—41no—
262C4×D43—42no—
263C4×D43—81no—
264Dic86—22no—
265Dic86—21no—
266Dic86—21no—
267Dic86—22no—
268Dic86—41no—
269Dic86—41no—
270Dic86—82no—
271Dic86—82no—
272C8×C43—22no—
273C8×C43—21no—
274C8×C43—21no—
275C8×C43—41no—
276C8×C43—41no—
277C43⋊C8—21no—
278C43⋊C8—21no—
279C43⋊C8—41no—
280C43⋊C8—41no—
281C43⋊C8—41no—
282#24723—431nomaximal, Sylow
283C22×C43—21no—
284C22×C43—21no—
285C22×C43C2×#12111yescharacteristic
286C22×C43#55211yescharacteristic
287C22×C43#55611yescharacteristic
288C2×D43—41no—
289C2×D43—41no—
290C2×D43—41no—
291C4×C43—41no—
292C4×C43—41no—
293C4×C43—81no—
294C4×C43—81no—
295C4×C43#52511yescharacteristic
296C4×C43#53611yescharacteristic
297C4×C43#54711yescharacteristic
298C4×C43#54811yescharacteristic
299Dic43—21no—
300Dic43—21no—
301Dic43—21no—
302Dic43—42no—
303Dic43—41no—
304Dic43—81no—
305Dic43#47112yes—
306#3079—431no—
307C2×#475—431no—
308C4×#137—431no—
309#2925—431no—
310#2079—431no—
311#2079—431no—
312#2052—431no—
313#2052—431no—
314#1997—431no—
315#1951—431no—
316#1951D4311yescharacteristic, complemented
317#1950—431no—
318#1930—431no—
319#1930—431no—
320#1801—431no—
321C2×C43—21no—
322C2×C43—21no—
323C2×C43#241511yescharacteristic
324C2×C43C2×#47111yescharacteristic
325C2×C43#306911yescharacteristic
326D43—81no—
327C2×#137—431no—
328C2×C4⋊Q8—431no—
329C4×#41—431no—
330C2×C4×Q8—431no—
331#477—861no—
332#476—861no—
333#475—861no—
334#475—861no—
335#475—861no—
336#475—861no—
337#475—861no—
338#474—861no—
339#441—861no—
340#440—861no—
341C4×Q16—861no—
342C4×SD16—861no—
343#433—861no—
344#433—861no—
345#432—861no—
346#431—861no—
347C2×#108—431no—
348C2×#108C2×D4311yescharacteristic
349#428—431no—
350#428C2×D4311yescharacteristic
351#428C2×D4311yescharacteristic
352C2×#106—431no—
353C2×#106C2×D4311yescharacteristic
354#423—431no—
355#423—431no—
356C2×C4⋊C8—431no—
357#419—431no—
358#417—431no—
359#417—431no—
360#417—431no—
361C2×#103—431no—
362C2×#103—431no—
363C2×#101—431no—
364C2×#101—431no—
365#408—431no—
366#408—431no—
367#405—431no—
368#405C2×D4311yescharacteristic
369C4×M16—431no—
370#343—431no—
371#343—431no—
372#343—431no—
373#343—431no—
374#343C2×D4311yescharacteristic
375#343C2×D4311yescharacteristic
376#341—431no—
377#341—431no—
378C43#2472311yescharacteristic, complemented, Sylow
379C2×#41—431no—
380C22×Q8—431no—
381C22×Q8—861no—
382#137—862no—
383#137—862no—
384C2×Q16—861no—
385C2×SD16—861no—
386C2×M16—431no—
387C2×M16—431no—
388C2×M16—431no—
389C2×M16C22×D4311yescharacteristic
390C2×M16C22×D4311yescharacteristic
391C2×M16C22×D4311yescharacteristic
392C22×C8—431no—
393C22×C8C22×D4311yescharacteristic
394C4⋊Q8—861no—
395C4⋊Q8—861no—
396C4⋊Q8—861no—
397C4⋊Q8—861no—
398C4×Q8—431no—
399C4×Q8—431no—
400C4×Q8—861no—
401C4×Q8—861no—
402C4×Q8—861no—
403C4×Q8—861no—
404C4×D4—431no—
405C4×D4—431no—
406C4×D4—861no—
407C4×D4—861no—
408#117—861no—
409#117C22×D4311yescharacteristic
410C2×C4⋊C4—431no—
411C2×C4⋊C4—861no—
412C2×C4⋊C4—861no—
413C2×C4⋊C4C22×D4311yescharacteristic
414C2×C4⋊C4C22×D4311yescharacteristic
415C2×C42—431no—
416C2×C42—861no—
417C2×C42—861no—
418#108—22no—
419#108—862no—
420#107—21no—
421#107—21no—
422#107—861no—
423#106—21no—
424#106—21no—
425#106—21no—
426#106—21no—
427#106—861no—
428#106—861no—
429#106—861no—
430C4⋊C8—431no—
431C4⋊C8—431no—
432C4⋊C8—431no—
433C4⋊C8—431no—
434C4⋊C8—861no—
435C4⋊C8—861no—
436C4⋊C8—861no—
437C4⋊C8—861no—
438#103—861no—
439#103—861no—
440#103—861no—
441#103—861no—
442#103—861no—
443#103—861no—
444#103—861no—
445#103—861no—
446#103—861no—
447#102—861no—
448#102—861no—
449#102—861no—
450#101—862no—
451#101—862no—
452C22⋊C8—861no—
453C22⋊C8—861no—
454C22⋊C8—861no—
455C22⋊C8—861no—
456#97—21no—
457#97—861no—
458#97—861no—
459C4×C8—21no—
460C4×C8—861no—
461C4×C8—861no—
462#41—861no—
463#41—861no—
464#41—861no—
465#41—861no—
466C2×Q8—431no—
467C2×Q8—432no—
468C2×Q8—861no—
469C2×Q8—861no—
470C2×Q8—861no—
471C2×Q8—861no—
472C2×Q8—861no—
473C2×Q8—3442no—
474C2×Q8—1721no—
475C2×Q8—1721no—
476C2×D4—431no—
477C2×D4—861no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—431no—
481C22×C4—431no—
482C22×C4—861no—
483C22×C4—861no—
484C22×C4—861no—
485C22×C4—861no—
486C22×C4—861no—
487C22×C4C23×D4311yescharacteristic
488Q16—864no—
489SD16—864no—
490M16—21no—
491M16—21no—
492M16—21no—
493M16—21no—
494M16—21no—
495M16—861no—
496M16—861no—
497M16—861no—
498M16—861no—
499M16—861no—
500M16—861no—
501M16#1062189812yes—
502C2×C8—21no—
503C2×C8—21no—
504C2×C8—21no—
505C2×C8—21no—
506C2×C8—21no—
507C2×C8—431no—
508C2×C8—431no—
509C2×C8—861no—
510C2×C8—861no—
511C2×C8—861no—
512C2×C8—861no—
513C2×C8—861no—
514C2×C8D4×D4311yescharacteristic
515C2×C8D4×D4311yescharacteristic
516C4⋊C4—21no—
517C4⋊C4—21no—
518C4⋊C4—21no—
519C4⋊C4—21no—
520C4⋊C4—861no—
521C4⋊C4—861no—
522C4⋊C4—861no—
523C4⋊C4—861no—
524C4⋊C4—1721no—
525C4⋊C4—1721no—
526C4⋊C4—1721no—
527C4⋊C4—1721no—
528C4⋊C4D4×D4311yescharacteristic
529C4⋊C4D4×D4311yescharacteristic
530C22⋊C4—21no—
531C22⋊C4—861no—
532C22⋊C4—861no—
533C42—21no—
534C42—431no—
535C42—431no—
536C42—431no—
537C42—431no—
538C42—861no—
539C42—861no—
540C42—1721no—
541C42—1721no—
542C23—861no—
543C23#41×D4311yescharacteristic
544Q8—862no—
545Q8—862no—
546Q8—861no—
547Q8—861no—
548Q8—3442no—
549Q8—3442no—
550Q8—1721no—
551Q8—1721no—
552D4—861no—
553D4—861no—
554D4—1721no—
555D4—1721no—
556C2×C4—21no—
557C2×C4—21no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—81no—
561C2×C4—81no—
562C2×C4—431no—
563C2×C4—431no—
564C2×C4—431no—
565C2×C4—431no—
566C2×C4—862no—
567C2×C4—862no—
568C2×C4—861no—
569C2×C4—3441no—
570C2×C4—3441no—
571C2×C4—1722no—
572C2×C4—1721no—
573C2×C4—1721no—
574C2×C4—1721no—
575C2×C4—1721no—
576C2×C4—1721no—
577C2×C4—1721no—
578C2×C4C2×D4×D4311yescharacteristic
579C2×C4C2×D4×D4311yescharacteristic
580C2×C4#41×D4311yescharacteristic
581C2×C4C2×#1062189811yescharacteristic
582C2×C4#1306337311yescharacteristic
583C2×C4#1306337311yescharacteristic
584C8—22no—
585C8—21no—
586C8—21no—
587C8—41no—
588C8—41no—
589C8—861no—
590C8—861no—
591C8—1721no—
592C8—1721no—
593C8—1721no—
594C22—21no—
595C22—21no—
596C22—1721no—
597C22—1721no—
598C22—1721no—
599C22#121×D4311yescharacteristic
600C22#1458358111yescharacteristic
601C22#1458362111yescharacteristic
602C4—41no—
603C4—41no—
604C4—81no—
605C4—81no—
606C4—432no—
607C4—861no—
608C4—861no—
609C4—861no—
610C4—3441no—
611C4—1721no—
612C4—1722no—
613C4#1458340811yescharacteristic
614C4#1458347411yescharacteristic
615C4#1458355011yescharacteristic
616C4#1458355911yescharacteristic
617C2—21no—
618C2—21no—
619C2—3441no—
620C2#1913802311yescharacteristic
621C2#471×D4311yescharacteristic
622C2#1914432711yescharacteristic
subgroupG/H
centerC22#121×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#1951C2
socleC22×C43C2×#121
prime radicalC2×#10621898C23
hypercenter#1951D43
hypocenterC43#24723
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ #1951

Complements

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

NH ≅ G/Ntype
2. C2×#14583183C2semidirect
9. #19135582C2semidirect
10. #19135372C2semidirect
11. #19135367C2semidirect
12. #19135250C2semidirect
13. #19135249C2semidirect
14. #19134590C2semidirect
15. C43×#1951C2semidirect
316. #1951D43semidirect
378. C43#24723semidirect

Maximal subgroups

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

subgroupindex
#191444082
C2×#145831832
#191434132
#191432592
#191360442
#191360412
#191358972
#191358962
#191355822
#191353722
#191353672
#191352502
#191352492
#191345902
C43×#19512
#2472343