Finite Group Databasebeta

← #25087663

Subgroups — #25087663

Order 11008.

604 conjugacy classes of subgroups.

The subgroup lattice has 588 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19147581C211yesmaximal, characteristic, complemented
2#19147021C211yesmaximal, characteristic, complemented
3#19146534C211yesmaximal, characteristic, complemented
4#19134264C211yesmaximal, characteristic, complemented
5#19134089C211yesmaximal, characteristic, complemented
6#19134030C211yesmaximal, characteristic, complemented
7#19133982C211yesmaximal, characteristic, complemented
8#19133940C211yesmaximal, characteristic, complemented
9#19133851C211yesmaximal, characteristic, complemented
10#19133849C211yesmaximal, characteristic, complemented
11#19133795C211yesmaximal, characteristic, complemented
12#19133703C211yesmaximal, characteristic, complemented
13#19133443C211yesmaximal, characteristic, complemented
14#19133419C211yesmaximal, characteristic, complemented
15C43×#3397C211yesmaximal, characteristic
16#14583619C2211yescharacteristic
17#14583619C2211yescharacteristic
18#14583302C2211yescharacteristic
19#14583302C2211yescharacteristic
20#14583282—21no—
21#14583279C2211yescharacteristic
22#14583245C2211yescharacteristic
23#14583245C2211yescharacteristic
24#14583240—21no—
25#14583237—21no—
26#14583220—21no—
27#14583184C2211yescharacteristic
28#14583184C2211yescharacteristic
29#14583181C2211yescharacteristic
30#14583138—21no—
31#14583126—21no—
32#14583120—21no—
33#14583120—21no—
34#14583104C2211yescharacteristic
35#14583104C2211yescharacteristic
36#14583096C2211yescharacteristic
37#14583061—21no—
38C8×Dic86C2211yescharacteristic
39#14582993—21no—
40C4×#10621885C2211yescharacteristic
41D4×C43⋊C8C2211yescharacteristic
42D4×C43⋊C8C2211yescharacteristic
43#14582935—21no—
44#14582895—21no—
45#14582651C2211yescharacteristic
46#14582650C2211yescharacteristic
47#14582646C2211yescharacteristic
48#14582646C2211yescharacteristic
49#14582645C2211yescharacteristic
50#14582643C2211yescharacteristic
51Q8⋊(C43⋊C8)C2211yescharacteristic
52#14582629C2211yescharacteristic
53D4⋊(C43⋊C8)C2211yescharacteristic
54D4⋊(C43⋊C8)C2211yescharacteristic
55#14582620C2211yescharacteristic
56C43×#556C2211yescharacteristic
57C43×#550C2211yescharacteristic
58C43×#496—21no—
59C43×#492C2211yescharacteristic
60C43×#463—21no—
61C43×#461C2211yescharacteristic
62C43×#460—21no—
63C43×#459C2211yescharacteristic
64C43×#446C2211yescharacteristic
65C43×#440—21no—
66C4×D8×C43C2211yescharacteristic
67C2×Dic172—21no—
68C2×Dic172—21no—
69C2×#10621885D411yescharacteristic
70C2×#10621883—21no—
71C2×#10621883—21no—
72C2×#10621883—21no—
73C22×C43⋊C8—21no—
74C22×C43⋊C8—21no—
75#13063325C2311yescharacteristic
76#13063325C2311yescharacteristic
77#13063318—41no—
78#13063318—41no—
79#13063312—21no—
80#13063312—21no—
81#13063304—21no—
82#13063304—21no—
83C4×Dic86C2311yescharacteristic
84#13063290—21no—
85#13063290—21no—
86#13063284—21no—
87#13063284—21no—
88#13063258—21no—
89#13063258—21no—
90#13063258—41no—
91#13063258D411yescharacteristic
92#13063256—21no—
93#13063256—21no—
94#13063256—21no—
95C4⋊(C43⋊C8)C2311yescharacteristic
96C4⋊(C43⋊C8)C2311yescharacteristic
97C4⋊(C43⋊C8)C2311yescharacteristic
98Dic43⋊C8—21no—
99#13063249—21no—
100#13063249—21no—
101#13063249D411yescharacteristic
102#13063248—21no—
103#13063248—21no—
104#13063248—21no—
105#13063248D411yescharacteristic
106#13063246—21no—
107#13063246—21no—
108#13063246—21no—
109#13063246—41no—
110C22⋊(C43⋊C8)—21no—
111C22⋊(C43⋊C8)—21no—
112C4×C43⋊C8C2311yescharacteristic
113C4×C43⋊C8C2311yescharacteristic
114C8×Dic43—21no—
115C2×#41×C43—21no—
116C2×SD16×C43—21no—
117C2×SD16×C43—21no—
118C2×SD16×C43—21no—
119C2×D8×C43—21no—
120C2×D8×C43D411yescharacteristic
121C4⋊Q8×C43C2311yescharacteristic
122#127×C43—21no—
123#127×C43C2311yescharacteristic
124#126×C43—41no—
125#124×C43—21no—
126C22⋊Q8×C43—21no—
127#121×C43—21no—
128#121×C43—41no—
129C4×Q8×C43—21no—
130C4×Q8×C43C2311yescharacteristic
131C4×D4×C43—21no—
132C4×D4×C43C2311yescharacteristic
133C4×D4×C43C2311yescharacteristic
134#117×C43—21no—
135#107×C43D411yescharacteristic
136C4⋊C8×C43—21no—
137C4⋊C8×C43C2311yescharacteristic
138#103×C43—21no—
139#102×C43—21no—
140#102×C43D411yescharacteristic
141#102×C43D411yescharacteristic
142#97×C43—21no—
143C4×C8×C43C2311yescharacteristic
144#41×C43—42no—
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—41no—
152C2×D4×C43—41no—
153C2×D4×C43C2×D411yescharacteristic
154C2×D4×C43C2×D411yescharacteristic
155C22×C4×C43—21no—
156C22×C4×C43—21no—
157C22×C4×C43—41no—
158C2×Dic86—21no—
159C2×Dic86—21no—
160C2×Dic86C2×D411yescharacteristic
161SD16×C43—42no—
162SD16×C43—81no—
163SD16×C43—81no—
164D8×C43—22no—
165D8×C43—81no—
166C2×C8×C43—21no—
167C2×C8×C43C2×D411yescharacteristic
168C2×C8×C43C2×D411yescharacteristic
169C4⋊C4×C43—21no—
170C4⋊C4×C43—21no—
171C4⋊C4×C43—21no—
172C4⋊C4×C43—41no—
173C4⋊C4×C43C2×D411yescharacteristic
174C4⋊C4×C43C2×D411yescharacteristic
175C4⋊C4×C43C2×D411yescharacteristic
176C22⋊C4×C43—21no—
177C22⋊C4×C43—21no—
178C22⋊C4×C43—41no—
179C22⋊C4×C43—41no—
180C22⋊C4×C43—41no—
181C42×C43—21no—
182C42×C43—41no—
183C42×C43C2411yescharacteristic
184C22⋊Dic43—41no—
185C22⋊Dic43—41no—
186C22⋊Dic43—41no—
187C22⋊Dic43—41no—
188#10621885—41no—
189#10621883—81no—
190#10621883—81no—
191#10621883—81no—
192C4⋊Dic43—21no—
193C4⋊Dic43—21no—
194C4⋊Dic43—21no—
195C4⋊Dic43—21no—
196C4⋊Dic43C2×D411yescharacteristic
197Dic43⋊C4—21no—
198Dic43⋊C4—41no—
199Dic43⋊C4—41no—
200C4×Dic43—21no—
201C4×Dic43—41no—
202C4×Dic43—41no—
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
211Dic172—42no—
212Dic172—81no—
213C23×C43—21no—
214C23×C43—21no—
215C23×C43—41no—
216Q8×C43—21no—
217Q8×C43—21no—
218Q8×C43—41no—
219Q8×C43—41no—
220D4×C43—21no—
221D4×C43—21no—
222D4×C43—21no—
223D4×C43—21no—
224D4×C43—41no—
225D4×C43—41no—
226D4×C43—41no—
227D4×C43—41no—
228D4×C43—81no—
229D4×C43—82no—
230D4×C43—161no—
231C2×C4×C43—21no—
232C2×C4×C43—21no—
233C2×C4×C43—21no—
234C2×C4×C43—21no—
235C2×C4×C43—41no—
236C2×C4×C43—41no—
237C2×C4×C43—41no—
238C2×C4×C43—41no—
239C2×C4×C43—41no—
240C2×C4×C43—82no—
241C2×C4×C43C22×D411yescharacteristic
242C2×C4×C43C22×D411yescharacteristic
243C2×C4×C43H(5,𝔽2)11yescharacteristic
244C2×Dic43—21no—
245C2×Dic43—21no—
246C2×Dic43—41no—
247C2×Dic43—41no—
248Dic86—21no—
249Dic86—21no—
250Dic86—41no—
251Dic86—41no—
252Dic86—41no—
253Dic86—41no—
254C8×C43—21no—
255C8×C43—41no—
256C8×C43#13512yes—
257C43⋊C8—21no—
258C43⋊C8—21no—
259C43⋊C8—41no—
260C43⋊C8—41no—
261C43⋊C8—41no—
262C43⋊C8—41no—
263#19870—431nomaximal, Sylow
264C22×C43—41no—
265C22×C43—41no—
266C22×C43—41no—
267C22×C43—41no—
268C22×C43—41no—
269C22×C43—41no—
270C22×C43—81no—
271C22×C43—81no—
272C22×C43—81no—
273C22×C43D4211yescharacteristic
274C4×C43—21no—
275C4×C43—41no—
276C4×C43—41no—
277C4×C43—41no—
278C4×C43—41no—
279C4×C43—81no—
280C4×C43C2×#13511yescharacteristic
281C4×C43#57511yescharacteristic
282C4×C43#57611yescharacteristic
283C4×C43#57711yescharacteristic
284Dic43—41no—
285Dic43—41no—
286Dic43—81no—
287Dic43—81no—
288#3397D4311yescharacteristic
289#3393—431no—
290#3342—431no—
291#3304—431no—
292#1722—431no—
293#1690—431no—
294#1681—431no—
295#1673—431no—
296#1666—431no—
297#1650—431no—
298#1650—431no—
299#1642—431no—
300#1628—431no—
301#1584—431no—
302#1580—431no—
303C2×C43—81no—
304C2×C43—81no—
305C2×C43—161no—
306C2×C43#326711yescharacteristic
307C2×C43#328711yescharacteristic
308C2×C43#328911yescharacteristic
309#556—431no—
310#556—431no—
311#556C2×D4311yescharacteristic
312#550C2×D4311yescharacteristic
313#500—431no—
314#500—431no—
315#496—21no—
316#495—861no—
317#494—431no—
318#492C2×D4311yescharacteristic
319#486—431no—
320#486—431no—
321#485—861no—
322#485—861no—
323#482—861no—
324#475—431no—
325#475—431no—
326#475—431no—
327#467—861no—
328#465—861no—
329#464—861no—
330#464—861no—
331#463—21no—
332#461—431no—
333#461—431no—
334#461C2×D4311yescharacteristic
335#460—21no—
336#460—431no—
337#459C2×D4311yescharacteristic
338#452—861no—
339#446C2×D4311yescharacteristic
340C8×Q8—431no—
341#440—21no—
342C4×Q16—431no—
343C4×Q16—861no—
344C4×D8C2×D4311yescharacteristic
345C8×D4—431no—
346C8×D4—431no—
347#427—861no—
348#416—861no—
349#335—431no—
350#334—431no—
351#332—431no—
352#332—431no—
353#332—431no—
354#331—431no—
355Q8⋊C8—431no—
356Q8⋊C8—431no—
357D4⋊C8—431no—
358D4⋊C8—431no—
359#322—431no—
360C43#1987011yescharacteristic, complemented, Sylow
361C2×#41—21no—
362C2×Q16—431no—
363C2×Q16—861no—
364C2×Q16—861no—
365C2×SD16—21no—
366C2×SD16—21no—
367C2×SD16—21no—
368C2×SD16—861no—
369C2×SD16—861no—
370C2×SD16—861no—
371C2×D8—21no—
372C2×D8C22⋊D4311yescharacteristic
373C22×C8—861no—
374C22×C8—861no—
375C4⋊Q8—431no—
376C4⋊Q8—431no—
377C4⋊Q8C22×D4311yescharacteristic
378#127—21no—
379#127C22×D4311yescharacteristic
380#126—41no—
381#126—1721no—
382#126—1721no—
383#124—21no—
384#124—861no—
385#124—861no—
386C22⋊Q8—21no—
387C22⋊Q8—861no—
388C22⋊Q8—861no—
389#121—21no—
390#121—41no—
391C4×Q8—21no—
392C4×Q8—431no—
393C4×Q8—861no—
394C4×Q8—861no—
395C4×Q8C22×D4311yescharacteristic
396C4×D4—21no—
397C4×D4C22×D4311yescharacteristic
398C4×D4C22×D4311yescharacteristic
399#117—21no—
400#117—861no—
401#117—861no—
402#107—431no—
403#107—861no—
404#107—861no—
405#107—1721no—
406#107C22⋊D4311yescharacteristic
407#106—861no—
408#106—861no—
409#106—861no—
410C4⋊C8—21no—
411C4⋊C8—431no—
412C4⋊C8—431no—
413C4⋊C8—431no—
414C4⋊C8—861no—
415C4⋊C8C22×D4311yescharacteristic
416#103—21no—
417#103—431no—
418#103—431no—
419#103—861no—
420#103—861no—
421#103—861no—
422#103—861no—
423#103—861no—
424#102—21no—
425#102—861no—
426#102—861no—
427#102—861no—
428#102—1721no—
429#102C22⋊D4311yescharacteristic
430#102C22⋊D4311yescharacteristic
431C22⋊C8—861no—
432C22⋊C8—861no—
433#97—21no—
434C4×C8—431no—
435C4×C8—431no—
436C4×C8—861no—
437C4×C8C22×D4311yescharacteristic
438#41—42no—
439#41—81no—
440C2×Q8—21no—
441C2×Q8—431no—
442C2×Q8—861no—
443C2×Q8—861no—
444C2×Q8D4×D4311yescharacteristic
445C2×D4—21no—
446C2×D4—21no—
447C2×D4—21no—
448C2×D4—41no—
449C2×D4—41no—
450C2×D4C2×C22⋊D4311yescharacteristic
451C2×D4C2×C22⋊D4311yescharacteristic
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—41no—
455Q16—3441no—
456Q16—1721no—
457Q16—1722no—
458SD16—42no—
459SD16—81no—
460SD16—81no—
461SD16—3441no—
462SD16—3441no—
463SD16—3441no—
464D8—22no—
465D8—81no—
466C2×C8—21no—
467C2×C8—431no—
468C2×C8—431no—
469C2×C8—861no—
470C2×C8—861no—
471C2×C8—861no—
472C2×C8—861no—
473C2×C8—3441no—
474C2×C8—1722no—
475C2×C8C2×C22⋊D4311yescharacteristic
476C2×C8C2×C22⋊D4311yescharacteristic
477C4⋊C4—21no—
478C4⋊C4—21no—
479C4⋊C4—21no—
480C4⋊C4—41no—
481C4⋊C4—431no—
482C4⋊C4—861no—
483C4⋊C4—861no—
484C4⋊C4—861no—
485C4⋊C4—861no—
486C4⋊C4—861no—
487C4⋊C4—1721no—
488C4⋊C4—1721no—
489C4⋊C4D4×D4311yescharacteristic
490C4⋊C4C2×C22⋊D4311yescharacteristic
491C4⋊C4C2×C22⋊D4311yescharacteristic
492C22⋊C4—21no—
493C22⋊C4—21no—
494C22⋊C4—41no—
495C22⋊C4—41no—
496C22⋊C4—41no—
497C22⋊C4—1721no—
498C22⋊C4—1721no—
499C22⋊C4—1721no—
500C22⋊C4—1721no—
501C42—21no—
502C42—41no—
503C42—861no—
504C42—1721no—
505C42—1721no—
506C42C23×D4311yescharacteristic
507C23—21no—
508C23—21no—
509C23—41no—
510Q8—21no—
511Q8—21no—
512Q8—41no—
513Q8—41no—
514Q8—861no—
515Q8—861no—
516Q8—1721no—
517Q8—1721no—
518Q8—1721no—
519Q8—1721no—
520D4—21no—
521D4—21no—
522D4—21no—
523D4—21no—
524D4—41no—
525D4—41no—
526D4—41no—
527D4—41no—
528D4—81no—
529D4—82no—
530D4—161no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—82no—
541C2×C4—861no—
542C2×C4—861no—
543C2×C4—1721no—
544C2×C4—1721no—
545C2×C4C2×D4×D4311yescharacteristic
546C2×C4C22×C22⋊D4311yescharacteristic
547C2×C4#1306337011yescharacteristic
548C8—21no—
549C8—41no—
550C8—861no—
551C8—861no—
552C8—1721no—
553C8—1721no—
554C8—1721no—
555C8—1721no—
556C8#1306334512yes—
557C22—41no—
558C22—41no—
559C22—41no—
560C22—41no—
561C22—41no—
562C22—41no—
563C22—81no—
564C22—81no—
565C22—81no—
566C22D4×C22⋊D4311yescharacteristic
567C4—21no—
568C4—41no—
569C4—41no—
570C4—41no—
571C4—41no—
572C4—81no—
573C4—3441no—
574C4—3441no—
575C4—1721no—
576C4—1721no—
577C4C2×#1306334511yescharacteristic
578C4#1458369511yescharacteristic
579C4#1458370211yescharacteristic
580C4#1458370911yescharacteristic
581C2—81no—
582C2—81no—
583C2—161no—
584C2#1914611411yescharacteristic
585C2#1914635111yescharacteristic
586C2#1914636811yescharacteristic
subgroupG/H
centerC22D4×C22⋊D43
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
Fitting, prime radicalC43×#3397C2
socleC22×C43D42
hypercenter#3397D43
hypocenterC43#19870
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #3397

Complements

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

NH ≅ G/Ntype
1. #19147581C2semidirect
2. #19147021C2semidirect
3. #19146534C2semidirect
4. #19134264C2semidirect
5. #19134089C2semidirect
6. #19134030C2semidirect
7. #19133982C2semidirect
8. #19133940C2semidirect
9. #19133851C2semidirect
10. #19133849C2semidirect
11. #19133795C2semidirect
12. #19133703C2semidirect
13. #19133443C2semidirect
14. #19133419C2semidirect
360. C43#19870semidirect

Maximal subgroups

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

subgroupindex
#191475812
#191470212
#191465342
#191342642
#191340892
#191340302
#191339822
#191339402
#191338512
#191338492
#191337952
#191337032
#191334432
#191334192
C43×#33972
#1987043