Finite Group Databasebeta

← #25086227

Subgroups — #25086227

Order 11008.

650 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#19147461C211yesmaximal, characteristic, complemented
2#19146911C211yesmaximal, characteristic, complemented
3#19146416C211yesmaximal, characteristic, complemented
4#19146402C211yesmaximal, characteristic
5#19134250C211yesmaximal, characteristic, complemented
6#19134130C211yesmaximal, characteristic, complemented
7#19134045C211yesmaximal, characteristic, complemented
8#19134042C211yesmaximal, characteristic, complemented
9#19133992C211yesmaximal, characteristic, complemented
10#19133806C211yesmaximal, characteristic, complemented
11#19133713C211yesmaximal, characteristic, complemented
12#19133669C211yesmaximal, characteristic, complemented
13#19133427C211yesmaximal, characteristic, complemented
14#19133404C211yesmaximal, characteristic, complemented
15C43×#1635C211yesmaximal, characteristic, complemented
16#14583610C2211yescharacteristic
17#14583606C2211yescharacteristic, complemented
18D4×D172C2211yescharacteristic
19#14583302C2211yescharacteristic, complemented
20#14583299—21no—
21#14583272C2211yescharacteristic
22#14583249C2211yescharacteristic, complemented
23#14583247C2211yescharacteristic
24#14583247C2211yescharacteristic
25#14583227—21no—
26#14583219—21no—
27#14583212—21no—
28#14583201—21no—
29#14583198—21no—
30#14583190C2211yescharacteristic
31#14583189C2211yescharacteristic
32#14583176C2211yescharacteristic
33#14583155—21no—
34#14583133—21no—
35#14583129—21no—
36#14583106C2211yescharacteristic, complemented
37#14583100C2211yescharacteristic
38#14583094C2211yescharacteristic
39#14583061—21no—
40#14583051—21no—
41#14583032—21no—
42#14583023C2211yescharacteristic, complemented
43C4×#10621883C2211yescharacteristic
44C4×#10621882C2211yescharacteristic
45#14582979—21no—
46#14582977C2211yescharacteristic, complemented
47D4×C43⋊C8C2211yescharacteristic
48#14582964C2211yescharacteristic
49#14582900—21no—
50C2×#13063245—21no—
51#102×D43—21no—
52#14582651C2211yescharacteristic, complemented
53#14582651C2211yescharacteristic, complemented
54#14582648C2211yescharacteristic, complemented
55#14582647C2211yescharacteristic, complemented
56#14582642C2211yescharacteristic
57#14582631C2211yescharacteristic, complemented
58#14582628C2211yescharacteristic
59#14582621C2211yescharacteristic, complemented
60C43×#547C2211yescharacteristic
61C43×#487C2211yescharacteristic, complemented
62C43×#476C2211yescharacteristic
63C43×#476C2211yescharacteristic, complemented
64C43×#332C2211yescharacteristic, complemented
65C43×D4⋊C8C2211yescharacteristic
66C43×D4⋊C8C2211yescharacteristic, complemented
67C22×D172—21no—
68C2×D4×D43—21no—
69C2×#10621885—21no—
70C2×#10621873—21no—
71C2×#10621873—41no—
72C2×#10621883D411yescharacteristic
73C2×#10621882—21no—
74C2×#10621882D411yescharacteristic
75C2×#10621877—21no—
76C22×C43⋊C8—21no—
77C2×C8×D43—21no—
78#13063325C2311yescharacteristic
79#13063322C2311yescharacteristic
80#13063316—21no—
81#13063316—21no—
82#13063305—21no—
83#13063304—21no—
84#13063302—41no—
85#13063301—41no—
86#13063300—21no—
87#13063299—21no—
88#13063295—41no—
89C4×Dic86C2311yescharacteristic
90C4×D172C2311yescharacteristic
91D4×Dic43—21no—
92#13063287—21no—
93C2×C4⋊Dic43—21no—
94C4⋊C4×D43—21no—
95#13063258—21no—
96#13063258—21no—
97#13063258—21no—
98#13063258D411yescharacteristic
99#13063257—21no—
100#13063256—21no—
101#13063256D411yescharacteristic
102C4⋊(C43⋊C8)C2311yescharacteristic
103C4⋊(C43⋊C8)C2311yescharacteristic
104Dic43⋊C8—21no—
105#13063249—21no—
106#13063249—21no—
107#13063249—21no—
108#13063248D411yescharacteristic
109#13063247—21no—
110#13063247—21no—
111#13063246—21no—
112#13063246D411yescharacteristic
113#13063246D411yescharacteristic
114#13063245—21no—
115#13063245—21no—
116#13063245—21no—
117#13063245—21no—
118#13063245—21no—
119#13063245—21no—
120#13063245D411yescharacteristic
121C22⋊(C43⋊C8)—21no—
122C22⋊(C43⋊C8)—21no—
123(C2×D43)⋊C8—21no—
124C4×C43⋊C8C2311yescharacteristic
125C4×C43⋊C8C2311yescharacteristic
126C8×Dic43—21no—
127C2×#41×C43—21no—
128C4⋊Q8×C43C2311yescharacteristic
129C4⋊Q8×C43C2311yescharacteristic
130#123×C43—41no—
131C22⋊Q8×C43—21no—
132#121×C43—21no—
133C4×D4×C43C2311yescharacteristic
134C4×D4×C43C2311yescharacteristic
135C2×C4⋊C4×C43—21no—
136#106×C43—21no—
137#106×C43—21no—
138C4⋊C8×C43C2311yescharacteristic
139C4⋊C8×C43C2311yescharacteristic
140#103×C43—41no—
141#102×C43—21no—
142#102×C43—21no—
143C4×C8×C43C2311yescharacteristic
144C23×D43—41no—
145#41×C43—42no—
146#41×C43—81no—
147C2×Q8×C43—21no—
148C2×Q8×C43—21no—
149C2×D4×C43—41no—
150C2×D4×C43C2×D411yescharacteristic
151C2×D4×C43C2×D411yescharacteristic
152C22×C4×C43—21no—
153C22×C4×C43—21no—
154C22×C4×C43—41no—
155C2×C22⋊D43—41no—
156C22×Dic43—41no—
157D4×D43—42no—
158D4×D43—81no—
159C2×D172—21no—
160C2×D172—21no—
161C2×D172—21no—
162C2×D172—41no—
163C2×D172—42no—
164C2×D172—81no—
165C2×D172C2×D411yescharacteristic
166C2×C4×D43—21no—
167C2×C4×D43—41no—
168C2×Dic86—21no—
169C2×Dic86C2×D411yescharacteristic
170C2×C8×C43—21no—
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—41no—
178C4⋊C4×C43C2×D411yescharacteristic
179C4⋊C4×C43C2×D411yescharacteristic
180C22⋊C4×C43—21no—
181C22⋊C4×C43—21no—
182C22⋊C4×C43—41no—
183C42×C43C2411yescharacteristic
184C22⋊Dic43—41no—
185#10621885—81no—
186#10621883—22no—
187#10621882—22no—
188#10621882—81no—
189(C2×D43)⋊C4—21no—
190(C2×D43)⋊C4—41no—
191(C2×D43)⋊C4—41no—
192C4⋊Dic43—21no—
193C4⋊Dic43—21no—
194C4⋊Dic43—41no—
195C4⋊Dic43—41no—
196C4⋊Dic43C2×D411yescharacteristic
197C4⋊Dic43C2×D411yescharacteristic
198Dic43⋊C4—21no—
199Dic43⋊C4—41no—
200Dic43⋊C4—41no—
201C4×Dic43—21no—
202#10621877—81no—
203C2×C43⋊C8—21no—
204C2×C43⋊C8—21no—
205C2×C43⋊C8—81no—
206C2×C43⋊C8C2×D411yescharacteristic
207C2×C43⋊C8C2×D411yescharacteristic
208C2×C43⋊C8C2×D411yescharacteristic
209C2×C43⋊C8C2×D411yescharacteristic
210#10621873—81no—
211#10621873—82no—
212C8×D43—81no—
213C23×C43—21no—
214C23×C43—21no—
215C22×D43—21no—
216C22×D43—41no—
217C22×D43—82no—
218C22×D43—82no—
219C22×D43—161no—
220Q8×C43—41no—
221Q8×C43—41no—
222Q8×C43—81no—
223D4×C43—21no—
224D4×C43—21no—
225D4×C43—21no—
226D4×C43—82no—
227D4×C43#13512yes—
228C2×C4×C43—21no—
229C2×C4×C43—21no—
230C2×C4×C43—41no—
231C2×C4×C43—41no—
232C2×C4×C43—41no—
233C2×C4×C43—41no—
234C2×C4×C43—41no—
235C2×C4×C43—41no—
236C2×C4×C43—82no—
237C2×C4×C43C22×D411yescharacteristic
238C2×C4×C43C22×D411yescharacteristic
239C2×C4×C43H(5,𝔽2)11yescharacteristic
240C22⋊D43—82no—
241C2×Dic43—21no—
242C2×Dic43—21no—
243C2×Dic43—21no—
244C2×Dic43—41no—
245C2×Dic43—161no—
246D172—21no—
247D172—41no—
248D172—41no—
249D172—41no—
250D172—41no—
251D172—81no—
252D172—82no—
253D172#13712yes—
254C4×D43—41no—
255C4×D43—41no—
256C4×D43—161no—
257Dic86—21no—
258Dic86—21no—
259Dic86—81no—
260C8×C43—41no—
261C8×C43—41no—
262C8×C43—41no—
263C43⋊C8—21no—
264C43⋊C8—21no—
265C43⋊C8—21no—
266C43⋊C8—21no—
267C43⋊C8—41no—
268C43⋊C8—41no—
269#19774—431nomaximal, Sylow
270C22×C43—22no—
271C22×C43—41no—
272C22×C43—41no—
273C22×C43—41no—
274C22×C43—41no—
275C22×C43—41no—
276C22×C43D4211yescharacteristic
277C2×D43—22no—
278C2×D43—41no—
279C2×D43—41no—
280C2×D43—81no—
281C2×D43—81no—
282C2×D43—81no—
283C2×D43—164no—
284C4×C43—21no—
285C4×C43—41no—
286C4×C43—41no—
287C4×C43—81no—
288C4×C43—81no—
289C4×C43C2×#13511yescharacteristic
290C4×C43C2×#13711yescharacteristic
291C4×C43#57611yescharacteristic
292C4×C43#57711yescharacteristic
293Dic43—41no—
294Dic43—41no—
295Dic43—41no—
296Dic43—81no—
297#3380—431no—
298#3331—431no—
299#3295—431no—
300#3294—431no—
301#1719—431no—
302#1697—431no—
303#1683—431no—
304#1682—431no—
305#1675—431no—
306#1644—431no—
307#1635D4311yescharacteristic, complemented
308#1629—431no—
309#1622—431no—
310#1581—431no—
311SD16⋊C8—431no—
312C2×C43—42no—
313C2×C43—81no—
314C2×C43#326611yescharacteristic
315C2×C43#328011yescharacteristic
316C2×C43#328811yescharacteristic
317D43—42no—
318D43—161no—
319#554—431no—
320#554—431no—
321#547C2×D4311yescharacteristic
322D42—431no—
323#500—431no—
324#499—861no—
325#492—431no—
326#487—431no—
327#487C2×D4311yescharacteristic, complemented
328#486—431no—
329#486—431no—
330#483—861no—
331#481—861no—
332#480—861no—
333#478—861no—
334#478—861no—
335#476—431no—
336#476—431no—
337#476C2×D4311yescharacteristic
338#476C2×D4311yescharacteristic, complemented
339#474—431no—
340#470—861no—
341#466—861no—
342#465—861no—
343#462—431no—
344#460—431no—
345#459—431no—
346#452—861no—
347#450—861no—
348#447—861no—
349C8×Q8—431no—
350C4×SD16—431no—
351C4×D8—431no—
352C4×D8—861no—
353#436—431no—
354C8×D4—431no—
355C8×D4—431no—
356#417—861no—
357C2×#102—861no—
358C2×#102—861no—
359#335—431no—
360#335—431no—
361#333—431no—
362#333—431no—
363#332C2×D4311yescharacteristic, complemented
364#331—431no—
365Q8⋊C8—431no—
366D4⋊C8—431no—
367D4⋊C8C2×D4311yescharacteristic
368D4⋊C8C2×D4311yescharacteristic, complemented
369#322—431no—
370C43#1977411yescharacteristic, complemented, Sylow
371C2×#41—21no—
372C22×D4—861no—
373C22×D4—861no—
374C2×Q16—861no—
375C2×SD16—431no—
376C2×SD16—861no—
377C2×SD16—1721no—
378C2×D8—431no—
379C2×D8—861no—
380C2×M16—861no—
381C22×C8—861no—
382C22×C8—861no—
383C4⋊Q8—431no—
384C4⋊Q8C22×D4311yescharacteristic
385C4⋊Q8C22×D4311yescharacteristic
386#127—431no—
387#125—861no—
388#125—861no—
389#123—41no—
390C22⋊Q8—21no—
391C22⋊Q8—861no—
392C22⋊Q8—861no—
393C22⋊Q8—1721no—
394C22⋊Q8—1721no—
395#121—21no—
396#121—861no—
397#121—861no—
398#120—1721no—
399C4×Q8—431no—
400C4×D4—431no—
401C4×D4—861no—
402C4×D4—861no—
403C4×D4C22×D4311yescharacteristic
404C4×D4C22×D4311yescharacteristic
405C2×C4⋊C4—21no—
406C2×C4⋊C4—861no—
407C2×C4⋊C4—861no—
408#107—431no—
409#107—861no—
410#107—861no—
411#107—861no—
412#106—21no—
413#106—21no—
414#106—431no—
415#106—861no—
416#106—861no—
417C4⋊C8—431no—
418C4⋊C8—431no—
419C4⋊C8—861no—
420C4⋊C8C22×D4311yescharacteristic
421C4⋊C8C22×D4311yescharacteristic
422#103—41no—
423#103—431no—
424#103—861no—
425#103—861no—
426#103—861no—
427#102—21no—
428#102—21no—
429#102—431no—
430#102—431no—
431#102—431no—
432#102—861no—
433#102—861no—
434#102—861no—
435#102—861no—
436#102—861no—
437#102—861no—
438#102—861no—
439#102—861no—
440#102—861no—
441C22⋊C8—861no—
442C22⋊C8—861no—
443C22⋊C8—861no—
444C4×C8—431no—
445C4×C8—431no—
446C4×C8—861no—
447C4×C8C22×D4311yescharacteristic
448C24—1721no—
449#41—42no—
450#41—81no—
451C2×Q8—21no—
452C2×Q8—21no—
453C2×Q8—431no—
454C2×Q8—861no—
455C2×D4—41no—
456C2×D4—431no—
457C2×D4—861no—
458C2×D4—861no—
459C2×D4—861no—
460C2×D4—3441no—
461C2×D4—3441no—
462C2×D4—1721no—
463C2×D4—1722no—
464C2×D4—1721no—
465C2×D4—1722no—
466C2×D4D4×D4311yescharacteristic
467C2×D4D4×D4311yescharacteristic
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—41no—
471C22×C4—861no—
472C22×C4—1721no—
473C22×C4—1721no—
474Q16—3441no—
475SD16—862no—
476SD16—3442no—
477SD16—3441no—
478D8—862no—
479D8—3441no—
480M16—3441no—
481C2×C8—21no—
482C2×C8—21no—
483C2×C8—21no—
484C2×C8—431no—
485C2×C8—431no—
486C2×C8—431no—
487C2×C8—431no—
488C2×C8—861no—
489C2×C8—861no—
490C2×C8—3441no—
491C2×C8—3441no—
492C4⋊C4—21no—
493C4⋊C4—21no—
494C4⋊C4—21no—
495C4⋊C4—21no—
496C4⋊C4—41no—
497C4⋊C4—431no—
498C4⋊C4—431no—
499C4⋊C4—861no—
500C4⋊C4—861no—
501C4⋊C4—861no—
502C4⋊C4—1721no—
503C4⋊C4—1721no—
504C4⋊C4—1721no—
505C4⋊C4—1721no—
506C4⋊C4D4×D4311yescharacteristic
507C4⋊C4D4×D4311yescharacteristic
508C22⋊C4—21no—
509C22⋊C4—21no—
510C22⋊C4—41no—
511C22⋊C4—861no—
512C22⋊C4—1721no—
513C22⋊C4—1721no—
514C22⋊C4—1721no—
515C42—861no—
516C42C23×D4311yescharacteristic
517C23—21no—
518C23—21no—
519C23—861no—
520C23—3442no—
521C23—3442no—
522C23—1721no—
523C23—6881no—
524Q8—41no—
525Q8—41no—
526Q8—81no—
527Q8—861no—
528Q8—861no—
529Q8—3441no—
530D4—21no—
531D4—21no—
532D4—21no—
533D4—82no—
534D4—432no—
535D4—861no—
536D4—3441no—
537D4—3442no—
538D4—3442no—
539D4—1721no—
540D4—1721no—
541D4—1721no—
542D4—1721no—
543D4#1306334612yes—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—82no—
553C2×C4—861no—
554C2×C4—861no—
555C2×C4—861no—
556C2×C4—1721no—
557C2×C4—1721no—
558C2×C4—1721no—
559C2×C4—6881no—
560C2×C4—6881no—
561C2×C4C2×D4×D4311yescharacteristic
562C2×C4C2×D4×D4311yescharacteristic
563C2×C4#1306337011yescharacteristic
564C8—41no—
565C8—41no—
566C8—41no—
567C8—861no—
568C8—861no—
569C8—861no—
570C8—861no—
571C8—1721no—
572C8—1721no—
573C22—22no—
574C22—41no—
575C22—41no—
576C22—41no—
577C22—41no—
578C22—41no—
579C22—862no—
580C22—3441no—
581C22—3441no—
582C22—3441no—
583C22—1721no—
584C22—1721no—
585C22—6884no—
586C22#1458353111yescharacteristic
587C4—21no—
588C4—41no—
589C4—41no—
590C4—81no—
591C4—81no—
592C4—3441no—
593C4—1721no—
594C4—1721no—
595C4—1721no—
596C4C2×#1306334611yescharacteristic
597C4#137×D4311yescharacteristic
598C4#1458370311yescharacteristic
599C4#1458370611yescharacteristic
600C2—42no—
601C2—81no—
602C2—1722no—
603C2—6881no—
604C2#1914610311yescharacteristic
605C2#1914627311yescharacteristic
606C2#1914636311yescharacteristic
subgroupG/H
centerC22#14583531
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#1635C2
socleC22×C43D42
prime radical#19146402C2
hypercenter#1635D43
hypocenterC43#19774
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #1635

Complements

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

NH ≅ G/Ntype
1. #19147461C2semidirect
2. #19146911C2semidirect
3. #19146416C2semidirect
5. #19134250C2semidirect
6. #19134130C2semidirect
7. #19134045C2semidirect
8. #19134042C2semidirect
9. #19133992C2semidirect
10. #19133806C2semidirect
11. #19133713C2semidirect
12. #19133669C2semidirect
13. #19133427C2semidirect
14. #19133404C2semidirect
15. C43×#1635C2semidirect
17. #14583606C22semidirect
19. #14583302C22semidirect
22. #14583249C22semidirect
36. #14583106C22semidirect
42. #14583023C22semidirect
46. #14582977C22semidirect
52. #14582651C22semidirect
53. #14582651C22semidirect
54. #14582648C22semidirect
55. #14582647C22semidirect
57. #14582631C22semidirect
59. #14582621C22semidirect
61. C43×#487C22semidirect
63. C43×#476C22semidirect
64. C43×#332C22semidirect
66. C43×D4⋊C8C22semidirect
307. #1635D43semidirect
327. #487C2×D43semidirect
338. #476C2×D43semidirect
363. #332C2×D43semidirect
368. D4⋊C8C2×D43semidirect
370. C43#19774semidirect

Maximal subgroups

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

subgroupindex
#191474612
#191469112
#191464162
#191464022
#191342502
#191341302
#191340452
#191340422
#191339922
#191338062
#191337132
#191336692
#191334272
#191334042
C43×#16352
#1977443