Finite Group Databasebeta

← #25079693

Subgroups — #25079693

Order 11008.

662 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145722C211yesmaximal, characteristic
2#19145519C211yesmaximal, characteristic
3#498×D43C211yesmaximal, characteristic, complemented
4#19143302C211yesmaximal, characteristic
5#19134097C211yesmaximal, characteristic, complemented
6#19134096C211yesmaximal, characteristic, complemented
7#19134093C211yesmaximal, characteristic, complemented
8#19134092C211yesmaximal, characteristic, complemented
9#19133971C211yesmaximal, characteristic, complemented
10#19133970C211yesmaximal, characteristic, complemented
11#19133967C211yesmaximal, characteristic, complemented
12#19133340C211yesmaximal, characteristic, complemented
13#19133278C211yesmaximal, characteristic, complemented
14#19133274C211yesmaximal, characteristic, complemented
15C43×#1671C211yesmaximal, characteristic, complemented
16C2×#13063331—21no—
17#14583446C2211yescharacteristic
18C4⋊Q8×D43C2211yescharacteristic
19C4⋊Q8×D43C2211yescharacteristic
20#14583297C2211yescharacteristic
21#14583296—21no—
22#14583296—21no—
23#14583296—21no—
24#14583295C2211yescharacteristic
25#14583295C2211yescharacteristic
26#14583270—21no—
27#14583248—21no—
28#14583244—21no—
29#14583219—21no—
30#14583216—21no—
31#14583190C2211yescharacteristic
32#14583189C2211yescharacteristic
33#14583186C2211yescharacteristic
34#14583105C2211yescharacteristic
35#14583104C2211yescharacteristic
36#14583101C2211yescharacteristic
37#14583039—21no—
38#14583036—21no—
39#14582977C2211yescharacteristic
40#14582976C2211yescharacteristic
41#14582974—21no—
42C8×D172C2211yescharacteristic
43C8×C22⋊D43—21no—
44#14582951C2211yescharacteristic
45#14582951C2211yescharacteristic
46#106×D43—21no—
47#106×D43—21no—
48#14582921C2211yescharacteristic
49#14582864—21no—
50C4×C8×D43C2211yescharacteristic
51#14582651C2211yescharacteristic
52#14582651C2211yescharacteristic
53#14582650C2211yescharacteristic
54#14582648C2211yescharacteristic
55#14582647C2211yescharacteristic
56#14582647C2211yescharacteristic
57#14582646C2211yescharacteristic
58#14582645C2211yescharacteristic
59#14582644C2211yescharacteristic
60C43×#498C2211yescharacteristic
61C43×#476C2211yescharacteristic
62C43×#461C2211yescharacteristic
63C8×D4×C43C2211yescharacteristic
64C43×#334C2211yescharacteristic
65C43×#333C2211yescharacteristic
66C43×#332C2211yescharacteristic
67C2×#10621898—21no—
68C2×Q8×D43—21no—
69C2×Q8×D43—21no—
70C2×#10621873—21no—
71C2×#10621883—21no—
72C2×#10621884—21no—
73#13063331—44no—
74C2×#10621877—21no—
75C2×#10621872—21no—
76C2×#10621872—21no—
77C2×C8×D43—21no—
78C2×C8×D43D411yescharacteristic
79C2×C8×D43D411yescharacteristic
80#13063325C2311yescharacteristic
81#13063325C2311yescharacteristic
82#13063324—21no—
83#13063324—21no—
84#13063324—21no—
85#13063324—21no—
86#13063324D411yescharacteristic
87#13063323—21no—
88#13063323—21no—
89#13063321D411yescharacteristic
90#13063311—21no—
91#13063300D411yescharacteristic
92#13063298—21no—
93#13063296D411yescharacteristic
94C4×D172C2311yescharacteristic
95C4×C22⋊D43—21no—
96C4⋊C4×D43—21no—
97C4⋊C4×D43—21no—
98C4⋊C4×D43—21no—
99C4⋊C4×D43—21no—
100C42×D43C2311yescharacteristic
101#13063257—21no—
102#13063257—21no—
103#13063257—21no—
104#13063256—21no—
105#13063256—21no—
106#13063256—21no—
107#13063256—21no—
108#13063256—21no—
109#13063256—21no—
110C4⋊(C43⋊C8)C2311yescharacteristic
111C4⋊(C43⋊C8)C2311yescharacteristic
112C4⋊(C43⋊C8)C2311yescharacteristic
113Dic43⋊C8—21no—
114#13063250—21no—
115#13063249—21no—
116#13063248—21no—
117#13063247—21no—
118#13063246—21no—
119#13063245—21no—
120C22⋊(C43⋊C8)—21no—
121(C2×D43)⋊C8—21no—
122(C2×D43)⋊C8—21no—
123(C2×D43)⋊C8—21no—
124(C2×D43)⋊C8—21no—
125C4×C43⋊C8C2311yescharacteristic
126C8×Dic43—21no—
127C8×Dic43—21no—
128C8×Dic43D411yescharacteristic
129C8×Dic43D411yescharacteristic
130C2×SD16×C43—21no—
131C22×C8×C43—21no—
132C4⋊Q8×C43C2311yescharacteristic
133C4⋊Q8×C43C2311yescharacteristic
134C4×D4×C43C2311yescharacteristic
135#106×C43—21no—
136#106×C43—21no—
137#106×C43—21no—
138C4⋊C8×C43C2311yescharacteristic
139C4⋊C8×C43C2311yescharacteristic
140C4⋊C8×C43C2311yescharacteristic
141#103×C43—21no—
142#102×C43—21no—
143C22⋊C8×C43—21no—
144C4×C8×C43C2311yescharacteristic
145C2×Q8×C43—21no—
146C2×Q8×C43—21no—
147C2×D4×C43C2×D411yescharacteristic
148C22×C4×C43—21no—
149C2×C22⋊D43—21no—
150C2×C22⋊D43—21no—
151C2×C22⋊D43—21no—
152Q8×D43—81no—
153Q8×D43—81no—
154Q8×D43—82no—
155#10621898—42no—
156#10621898—42no—
157C2×D172—21no—
158C2×D172C2×D411yescharacteristic
159C2×C4×D43—21no—
160C2×C4×D43—41no—
161C2×C4×D43—41no—
162C2×C4×D43C2×D411yescharacteristic
163C2×C4×D43C2×D411yescharacteristic
164C2×C4×D43#4111yescharacteristic
165C2×Dic86—21no—
166C2×Dic86—21no—
167C2×Dic86—21no—
168C2×Dic86—41no—
169C2×Dic86—41no—
170SD16×C43—81no—
171C2×C8×C43—21no—
172C2×C8×C43—21no—
173C2×C8×C43—21no—
174C2×C8×C43—42no—
175C2×C8×C43C2×D411yescharacteristic
176C2×C8×C43C2×D411yescharacteristic
177C4⋊C4×C43—21no—
178C4⋊C4×C43—21no—
179C4⋊C4×C43—21no—
180C4⋊C4×C43—21no—
181C4⋊C4×C43C2×D411yescharacteristic
182C22⋊C4×C43—21no—
183C42×C43C2411yescharacteristic
184C22⋊Dic43—21no—
185#10621884—81no—
186#10621883—81no—
187(C2×D43)⋊C4—21no—
188(C2×D43)⋊C4—21no—
189C4⋊Dic43—21no—
190C4⋊Dic43—21no—
191C4⋊Dic43—21no—
192C4⋊Dic43—21no—
193C4⋊Dic43C2×D411yescharacteristic
194Dic43⋊C4—21no—
195Dic43⋊C4—41no—
196Dic43⋊C4—41no—
197Dic43⋊C4—41no—
198Dic43⋊C4—41no—
199C4×Dic43C2×D411yescharacteristic
200C4×Dic43C2×D411yescharacteristic
201C4×Dic43#4111yescharacteristic
202#10621877—42no—
203C2×C43⋊C8—21no—
204C2×C43⋊C8—21no—
205C2×C43⋊C8—21no—
206C2×C43⋊C8C2×D411yescharacteristic
207C2×C43⋊C8C2×D411yescharacteristic
208#10621873—81no—
209#10621872—42no—
210#10621872—42no—
211C8×D43—22no—
212C8×D43—42no—
213C8×D43SD1614yescomplemented
214C23×C43—21no—
215C22×D43—21no—
216C22×D43#12111yescharacteristic
217Q8×C43—41no—
218Q8×C43—41no—
219Q8×C43—81no—
220D4×C43—21no—
221D4×C43—21no—
222C2×C4×C43—21no—
223C2×C4×C43—41no—
224C2×C4×C43—41no—
225C2×C4×C43—41no—
226C2×C4×C43—41no—
227C2×C4×C43C22×D411yescharacteristic
228C2×C4×C43C22×D411yescharacteristic
229C2×C4×C43C2×#4111yescharacteristic
230C22⋊D43—42no—
231C22⋊D43—42no—
232C22⋊D43—42no—
233C2×Dic43—21no—
234C2×Dic43—41no—
235C2×Dic43—41no—
236C2×Dic43#12111yescharacteristic
237C2×Dic43#12111yescharacteristic
238C2×Dic43#12111yescharacteristic
239D172—21no—
240D172—21no—
241D172—42no—
242C4×D43—21no—
243C4×D43—21no—
244C4×D43—22no—
245C4×D43—41no—
246C4×D43—41no—
247C4×D43—82no—
248C4×D43—82no—
249C4×D43C2×SD1612yes—
250C4×D43#13712yes—
251Dic86—42no—
252Dic86—41no—
253Dic86—41no—
254Dic86—82no—
255Dic86—82no—
256Dic86—81no—
257C8×C43—21no—
258C8×C43—41no—
259C8×C43—41no—
260C8×C43—41no—
261C8×C43C2×SD1612yes—
262C43⋊C8—21no—
263C43⋊C8—41no—
264C43⋊C8—41no—
265C43⋊C8—41no—
266C43⋊C8C2×SD1612yes—
267#19191—431nomaximal, Sylow
268C22×C43—41no—
269C22×C43—41no—
270C22×C43—41no—
271C22×C43C2×#12111yescharacteristic
272C2×D43—21no—
273C2×D43—21no—
274C2×D43—41no—
275C2×D43—41no—
276C2×D43—41no—
277C2×D43#46112yes—
278C4×C43—21no—
279C4×C43—41no—
280C4×C43—81no—
281C4×C43—81no—
282C4×C43C22×SD1611yescharacteristic
283C4×C43C2×#13711yescharacteristic
284C4×C43#57711yescharacteristic
285C4×C43#57711yescharacteristic
286Dic43—21no—
287Dic43—41no—
288Dic43—81no—
289Dic43—81no—
290Dic43#46112yes—
291Dic43#47112yes—
292#3227—431no—
293#3206—431no—
294C2×#498—431no—
295#2931—431no—
296#1691—431no—
297#1691—431no—
298#1691—431no—
299#1691—431no—
300#1671—431no—
301#1671—431no—
302#1671—431no—
303#1671D4311yescharacteristic, complemented
304#1564—431no—
305#1549—431no—
306#1548—431no—
307C2×C43—81no—
308C2×C43C2×#46111yescharacteristic
309C2×C43#305711yescharacteristic
310C2×C43C2×#47111yescharacteristic
311D43—22no—
312D43—81no—
313C2×#131—861no—
314#532—431no—
315C2×C4⋊Q8—431no—
316C2×C4⋊Q8—431no—
317#498—431no—
318#498—431no—
319#498—431no—
320#498—861no—
321#498—861no—
322#498—861no—
323#498C2×D4311yescharacteristic
324#492—861no—
325#487—861no—
326#486—861no—
327#481—861no—
328#481—861no—
329#476—431no—
330#476—431no—
331#476—431no—
332#476C2×D4311yescharacteristic
333#461—431no—
334#461—431no—
335#461—431no—
336#461C2×D4311yescharacteristic
337#448—861no—
338#448—861no—
339#436—431no—
340#436—431no—
341#436—861no—
342C8×D4—431no—
343C8×D4—861no—
344C8×D4C2×D4311yescharacteristic
345#431—431no—
346#431—431no—
347C2×#106—861no—
348C2×#106—861no—
349#423—431no—
350#408—861no—
351C2×C4×C8—431no—
352#335—431no—
353#335—431no—
354#334—431no—
355#334C2×D4311yescharacteristic
356#333—431no—
357#333—431no—
358#333—431no—
359#333C2×D4311yescharacteristic
360#332—431no—
361#332—431no—
362#332—431no—
363#332C2×D4311yescharacteristic
364C43#1919111yescharacteristic, complemented, Sylow
365C2×#41—861no—
366C22×Q8—861no—
367C22×Q8—861no—
368C2×SD16—21no—
369C2×SD16—861no—
370C2×SD16—861no—
371C2×SD16—861no—
372#131—1724no—
373C2×M16—861no—
374C2×M16—861no—
375C2×M16—861no—
376C22×C8—21no—
377C22×C8—431no—
378C22×C8—431no—
379C22×C8—861no—
380C4⋊Q8—431no—
381C4⋊Q8—431no—
382C4⋊Q8—431no—
383C4⋊Q8—861no—
384C4⋊Q8—861no—
385C4⋊Q8—861no—
386C4⋊Q8—861no—
387C4⋊Q8—861no—
388C4⋊Q8—861no—
389C4⋊Q8C22×D4311yescharacteristic
390C4⋊Q8C22×D4311yescharacteristic
391#127—431no—
392#124—861no—
393#121—431no—
394#121—431no—
395#121—861no—
396C4×D4—431no—
397C4×D4—861no—
398C4×D4C22×D4311yescharacteristic
399C2×C4⋊C4—861no—
400C2×C4⋊C4—861no—
401C2×C4⋊C4—861no—
402C2×C4⋊C4—861no—
403C2×C42—431no—
404#106—21no—
405#106—21no—
406#106—21no—
407#106—861no—
408#106—861no—
409#106—861no—
410#106—861no—
411#106—861no—
412#106—861no—
413#106—861no—
414#106—861no—
415#106—861no—
416C4⋊C8—431no—
417C4⋊C8—431no—
418C4⋊C8—431no—
419C4⋊C8—861no—
420C4⋊C8C22×D4311yescharacteristic
421C4⋊C8C22×D4311yescharacteristic
422C4⋊C8C22×D4311yescharacteristic
423#103—21no—
424#103—861no—
425#103—861no—
426#103—861no—
427#102—21no—
428#102—861no—
429#102—861no—
430#102—861no—
431C22⋊C8—21no—
432C22⋊C8—861no—
433C22⋊C8—861no—
434C22⋊C8—861no—
435C22⋊C8—861no—
436C22⋊C8—861no—
437C4×C8—431no—
438C4×C8—431no—
439C4×C8—431no—
440C4×C8—861no—
441C4×C8—861no—
442C4×C8C22×D4311yescharacteristic
443#41—1722no—
444#41—1722no—
445C2×Q8—21no—
446C2×Q8—21no—
447C2×Q8—861no—
448C2×Q8—861no—
449C2×Q8—861no—
450C2×Q8—3441no—
451C2×Q8—3441no—
452C2×Q8—3442no—
453C2×Q8—1721no—
454C2×Q8—1721no—
455C2×D4—431no—
456C2×D4—861no—
457C2×D4—861no—
458C2×D4—861no—
459C2×D4—861no—
460C2×D4D4×D4311yescharacteristic
461C22×C4—21no—
462C22×C4—431no—
463C22×C4—431no—
464C22×C4—431no—
465C22×C4—861no—
466C22×C4—1721no—
467C22×C4—1721no—
468SD16—81no—
469SD16—3441no—
470SD16—3441no—
471SD16—3441no—
472M16—1722no—
473M16—1722no—
474M16—1722no—
475C2×C8—21no—
476C2×C8—21no—
477C2×C8—21no—
478C2×C8—42no—
479C2×C8—431no—
480C2×C8—434no—
481C2×C8—431no—
482C2×C8—862no—
483C2×C8—861no—
484C2×C8—861no—
485C2×C8—861no—
486C2×C8—1722no—
487C2×C8D4×D4311yescharacteristic
488C2×C8D4×D4311yescharacteristic
489C4⋊C4—21no—
490C4⋊C4—21no—
491C4⋊C4—21no—
492C4⋊C4—21no—
493C4⋊C4—431no—
494C4⋊C4—861no—
495C4⋊C4—861no—
496C4⋊C4—861no—
497C4⋊C4—861no—
498C4⋊C4—861no—
499C4⋊C4—1721no—
500C4⋊C4—1721no—
501C4⋊C4—1721no—
502C4⋊C4—1721no—
503C4⋊C4D4×D4311yescharacteristic
504C22⋊C4—21no—
505C22⋊C4—861no—
506C22⋊C4—861no—
507C22⋊C4—861no—
508C42—431no—
509C42—431no—
510C42—431no—
511C42C23×D4311yescharacteristic
512C23—21no—
513C23—431no—
514C23—861no—
515Q8—41no—
516Q8—41no—
517Q8—81no—
518Q8—3441no—
519Q8—3442no—
520Q8—3442no—
521Q8—1722no—
522Q8—1721no—
523Q8—1721no—
524D4—21no—
525D4—21no—
526D4—861no—
527D4—861no—
528D4—1722no—
529D4—1722no—
530D4—1722no—
531D4—1722no—
532C2×C4—21no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—431no—
538C2×C4—431no—
539C2×C4—432no—
540C2×C4—432no—
541C2×C4—431no—
542C2×C4—862no—
543C2×C4—861no—
544C2×C4—861no—
545C2×C4—861no—
546C2×C4—3442no—
547C2×C4—3442no—
548C2×C4—1721no—
549C2×C4—1721no—
550C2×C4—1721no—
551C2×C4—1721no—
552C2×C4C2×D4×D4311yescharacteristic
553C2×C4C2×D4×D4311yescharacteristic
554C2×C4#41×D4311yescharacteristic
555C8—21no—
556C8—41no—
557C8—41no—
558C8—41no—
559C8—432no—
560C8—861no—
561C8—1721no—
562C8—1721no—
563C8—1721no—
564C8SD16×D4312yes—
565C22—41no—
566C22—41no—
567C22—41no—
568C22—432no—
569C22—861no—
570C22—861no—
571C22—1721no—
572C22—1721no—
573C22—1721no—
574C22#121×D4311yescharacteristic
575C4—21no—
576C4—41no—
577C4—81no—
578C4—81no—
579C4—432no—
580C4—432no—
581C4—861no—
582C4—3441no—
583C4—3441no—
584C4—1721no—
585C4C2×SD16×D4311yescharacteristic
586C4#137×D4311yescharacteristic
587C4#1458370511yescharacteristic
588C4#1458370611yescharacteristic
589C2—81no—
590C2—862no—
591C2—3441no—
592C2#461×D4311yescharacteristic
593C2#1914422911yescharacteristic
594C2#471×D4311yescharacteristic
subgroupG/H
centerC22#121×D43
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#1671C2
socleC22×C43C2×#121
prime radical#14583446C22
hypercenter#1671D43
hypocenterC43#19191
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #1671

Complements

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

NH ≅ G/Ntype
3. #498×D43C2semidirect
5. #19134097C2semidirect
6. #19134096C2semidirect
7. #19134093C2semidirect
8. #19134092C2semidirect
9. #19133971C2semidirect
10. #19133970C2semidirect
11. #19133967C2semidirect
12. #19133340C2semidirect
13. #19133278C2semidirect
14. #19133274C2semidirect
15. C43×#1671C2semidirect
213. C8×D43SD16semidirect
303. #1671D43semidirect
364. C43#19191semidirect

Maximal subgroups

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

subgroupindex
#191457222
#191455192
#498×D432
#191433022
#191340972
#191340962
#191340932
#191340922
#191339712
#191339702
#191339672
#191333402
#191332782
#191332742
C43×#16712
#1919143