Finite Group Databasebeta

← #25086210

Subgroups — #25086210

Order 11008.

712 conjugacy classes of subgroups.

The subgroup lattice has 642 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19147242C211yesmaximal, characteristic, complemented
2#19146826C211yesmaximal, characteristic, complemented
3#19146419C211yesmaximal, characteristic, complemented
4#19134233C211yesmaximal, characteristic, complemented
5#19134126C211yesmaximal, characteristic, complemented
6#19134046C211yesmaximal, characteristic, complemented
7#19134030C211yesmaximal, characteristic, complemented
8#19133952C211yesmaximal, characteristic, complemented
9#19133774C211yesmaximal, characteristic, complemented
10#19133711C211yesmaximal, characteristic, complemented
11#19133703C211yesmaximal, characteristic, complemented
12#19133665C211yesmaximal, characteristic, complemented
13#19133425C211yesmaximal, characteristic, complemented
14#19133407C211yesmaximal, characteristic, complemented
15D4×D8×C43C211yesmaximal, characteristic
16#14583619C2211yescharacteristic, complemented
17#14583606C2211yescharacteristic, complemented
18#14583271C2211yescharacteristic, complemented
19#14583252—21no—
20#14583250C2211yescharacteristic, complemented
21#14583245C2211yescharacteristic, complemented
22#14583245C2211yescharacteristic, complemented
23#14583245C2211yescharacteristic, complemented
24#14583220—21no—
25#14583215—21no—
26#14583205—21no—
27#14583189C2211yescharacteristic
28#14583189C2211yescharacteristic, complemented
29#14583179C2211yescharacteristic
30#14583143—21no—
31#14583126—21no—
32#14583112—21no—
33#14583104C2211yescharacteristic, complemented
34#14583096C2211yescharacteristic, complemented
35#14583096C2211yescharacteristic, complemented
36#14583050—21no—
37#14583050—21no—
38C8×Dic86C2211yescharacteristic, complemented
39#14582990—21no—
40C4×#10621883C2211yescharacteristic
41#14582977C2211yescharacteristic, complemented
42D4×C43⋊C8C2211yescharacteristic, complemented
43#14582904—21no—
44C2×#13063246—21no—
45#14582652C2211yescharacteristic, complemented
46#14582651C2211yescharacteristic, complemented
47#14582647C2211yescharacteristic, complemented
48#14582646C2211yescharacteristic, complemented
49#14582643C2211yescharacteristic, complemented
50#14582643C2211yescharacteristic, complemented
51#14582629C2211yescharacteristic, complemented
52D4⋊(C43⋊C8)C2211yescharacteristic
53D4⋊(C43⋊C8)C2211yescharacteristic, complemented
54D4⋊(C43⋊C8)C2211yescharacteristic, complemented
55#14582621C2211yescharacteristic, complemented
56C22×D8×C43—21no—
57D42×C43C2211yescharacteristic
58D42×C43C2211yescharacteristic
59C43×#493C2211yescharacteristic
60C43×#466—21no—
61C43×#459C2211yescharacteristic
62C43×#459C2211yescharacteristic
63C43×#447—21no—
64C43×#447—21no—
65C4×D8×C43C2211yescharacteristic
66C8×D4×C43C2211yescharacteristic
67C2×#10621883—21no—
68C2×#10621883—21no—
69C2×#10621883—21no—
70C2×#10621883—41no—
71C2×#10621883D411yescharacteristic
72C2×#10621877—21no—
73C22×C43⋊C8—21no—
74#13063325C2311yescharacteristic
75#13063325C2311yescharacteristic
76#13063318—41no—
77#13063316—21no—
78#13063312—21no—
79#13063304—21no—
80#13063304—21no—
81#13063302—41no—
82C4×Dic86C2311yescharacteristic
83#13063290—21no—
84D4×Dic43—21no—
85#13063284—21no—
86C2×C4⋊Dic43—21no—
87#13063258—21no—
88#13063256—21no—
89#13063256—21no—
90#13063256D411yescharacteristic
91C4⋊(C43⋊C8)C2311yescharacteristic
92C4⋊(C43⋊C8)C2311yescharacteristic
93C4⋊(C43⋊C8)C2311yescharacteristic
94Dic43⋊C8—21no—
95#13063250—21no—
96#13063250—21no—
97#13063248—21no—
98#13063248D411yescharacteristic
99#13063246—21no—
100#13063246—21no—
101#13063246—21no—
102#13063246—21no—
103#13063246—21no—
104#13063246—21no—
105#13063246—21no—
106#13063246—21no—
107#13063246—21no—
108#13063246—41no—
109#13063246D411yescharacteristic
110C22⋊(C43⋊C8)—21no—
111C22⋊(C43⋊C8)—21no—
112C4×C43⋊C8C2311yescharacteristic
113C4×C43⋊C8C2311yescharacteristic
114C8×Dic43—21no—
115C22×D4×C43—21no—
116C22×D4×C43—21no—
117C22×D4×C43—21no—
118C22×D4×C43—21no—
119C2×D8×C43—21no—
120C2×D8×C43—21no—
121C2×D8×C43—21no—
122C2×D8×C43—21no—
123C2×D8×C43—44no—
124C2×D8×C43D411yescharacteristic
125C22×C8×C43—21no—
126#127×C43C2311yescharacteristic
127#127×C43C2311yescharacteristic
128#121×C43—21no—
129#121×C43—21no—
130#121×C43—21no—
131#121×C43—21no—
132#120×C43—41no—
133#120×C43—41no—
134C4×D4×C43C2311yescharacteristic
135C4×D4×C43C2311yescharacteristic
136C4×D4×C43C2311yescharacteristic
137#107×C43D411yescharacteristic
138C4⋊C8×C43C2311yescharacteristic
139#102×C43—21no—
140#102×C43—21no—
141#102×C43D411yescharacteristic
142#102×C43D411yescharacteristic
143C22⋊C8×C43—21no—
144C4×C8×C43C2311yescharacteristic
145C24×C43—41no—
146C24×C43—41no—
147C2×D4×C43—21no—
148C2×D4×C43—21no—
149C2×D4×C43—21no—
150C2×D4×C43—21no—
151C2×D4×C43—21no—
152C2×D4×C43—21no—
153C2×D4×C43—41no—
154C2×D4×C43—41no—
155C2×D4×C43—41no—
156C2×D4×C43—41no—
157C2×D4×C43—42no—
158C2×D4×C43—42no—
159C2×D4×C43—42no—
160C2×D4×C43—42no—
161C2×D4×C43—81no—
162C2×D4×C43—81no—
163C2×D4×C43—81no—
164C2×D4×C43—81no—
165C2×D4×C43C2×D411yescharacteristic
166C2×D4×C43C2×D411yescharacteristic
167C2×D4×C43C2×D411yescharacteristic
168C22×C4×C43—21no—
169C22×C4×C43—21no—
170C22×C4×C43—21no—
171C22×Dic43—41no—
172C2×Dic86—21no—
173C2×Dic86—21no—
174C2×Dic86C2×D411yescharacteristic
175D8×C43—22no—
176D8×C43—42no—
177D8×C43—42no—
178D8×C43—42no—
179D8×C43—81no—
180C2×C8×C43—21no—
181C2×C8×C43—42no—
182C2×C8×C43C2×D411yescharacteristic
183C2×C8×C43C2×D411yescharacteristic
184C4⋊C4×C43C2×D411yescharacteristic
185C4⋊C4×C43C2×D411yescharacteristic
186C4⋊C4×C43C2×D411yescharacteristic
187C22⋊C4×C43—21no—
188C22⋊C4×C43—21no—
189C22⋊C4×C43—21no—
190C22⋊C4×C43—41no—
191C22⋊C4×C43—41no—
192C42×C43C2411yescharacteristic
193C22⋊Dic43—41no—
194C22⋊Dic43—41no—
195C22⋊Dic43—41no—
196#10621883—22no—
197#10621883—42no—
198#10621883—81no—
199#10621883—81no—
200#10621883—82no—
201C4⋊Dic43—21no—
202C4⋊Dic43—21no—
203C4⋊Dic43—21no—
204C4⋊Dic43—21no—
205C4⋊Dic43—41no—
206C4⋊Dic43C2×D411yescharacteristic
207Dic43⋊C4—21no—
208Dic43⋊C4—41no—
209Dic43⋊C4—41no—
210C4×Dic43—21no—
211C4×Dic43—41no—
212#10621877—81no—
213C2×C43⋊C8—21no—
214C2×C43⋊C8—21no—
215C2×C43⋊C8—21no—
216C2×C43⋊C8—21no—
217C2×C43⋊C8—81no—
218C2×C43⋊C8C2×D411yescharacteristic
219C2×C43⋊C8C2×D411yescharacteristic
220C23×C43—21no—
221C23×C43—21no—
222C23×C43—21no—
223C23×C43—41no—
224C23×C43—41no—
225C23×C43—82no—
226C23×C43—82no—
227C23×C43—82no—
228C23×C43—82no—
229C23×C43—161no—
230C23×C43—161no—
231D4×C43—21no—
232D4×C43—21no—
233D4×C43—21no—
234D4×C43—21no—
235D4×C43—41no—
236D4×C43—41no—
237D4×C43—41no—
238D4×C43—41no—
239D4×C43—41no—
240D4×C43—41no—
241D4×C43—41no—
242D4×C43—41no—
243D4×C43—81no—
244D4×C43—81no—
245D4×C43—82no—
246D4×C43—82no—
247D4×C43—82no—
248D4×C43—82no—
249D4×C43#13512yes—
250D4×C43AGL(1,ℤ/8)12yes—
251C2×C4×C43—21no—
252C2×C4×C43—21no—
253C2×C4×C43—21no—
254C2×C4×C43—41no—
255C2×C4×C43—41no—
256C2×C4×C43—41no—
257C2×C4×C43—41no—
258C2×C4×C43—41no—
259C2×C4×C43—41no—
260C2×C4×C43C22×D411yescharacteristic
261C2×C4×C43C22×D411yescharacteristic
262C2×C4×C43H(5,𝔽2)11yescharacteristic
263C2×Dic43—21no—
264C2×Dic43—21no—
265C2×Dic43—41no—
266C2×Dic43—41no—
267C2×Dic43—161no—
268Dic86—21no—
269Dic86—21no—
270Dic86—41no—
271Dic86—41no—
272Dic86—81no—
273C8×C43—21no—
274C8×C43—21no—
275C8×C43—41no—
276C43⋊C8—21no—
277C43⋊C8—21no—
278C43⋊C8—41no—
279C43⋊C8—41no—
280C43⋊C8—41no—
281C43⋊C8—41no—
282#19773—431nomaximal, Sylow
283C22×C43—22no—
284C22×C43—22no—
285C22×C43—41no—
286C22×C43—41no—
287C22×C43—41no—
288C22×C43—41no—
289C22×C43—41no—
290C22×C43—41no—
291C22×C43—41no—
292C22×C43—81no—
293C22×C43—81no—
294C22×C43—81no—
295C22×C43—81no—
296C22×C43—81no—
297C22×C43—81no—
298C22×C43—164no—
299C22×C43—164no—
300C22×C43D4211yescharacteristic
301C4×C43—21no—
302C4×C43—41no—
303C4×C43—41no—
304C4×C43—41no—
305C4×C43C2×#13511yescharacteristic
306C4×C43C2×AGL(1,ℤ/8)11yescharacteristic
307C4×C43#57611yescharacteristic
308C4×C43#57711yescharacteristic
309Dic43—41no—
310Dic43—41no—
311Dic43—81no—
312Dic43—81no—
313#3360—431no—
314#3324—431no—
315#3295—431no—
316D4×D8D4311yescharacteristic
317#1717—431no—
318#1697—431no—
319#1683—431no—
320#1681—431no—
321#1668—431no—
322#1639—431no—
323#1629—431no—
324#1628—431no—
325#1622—431no—
326#1581—431no—
327SD16⋊C8—431no—
328C2×C43—42no—
329C2×C43—42no—
330C2×C43—81no—
331C2×C43—161no—
332C2×C43—161no—
333C2×C43#326511yescharacteristic
334C2×C43#328011yescharacteristic
335C2×C43#328811yescharacteristic
336C22×D8—21no—
337#556—431no—
338#554—431no—
339D42C2×D4311yescharacteristic
340D42C2×D4311yescharacteristic
341#493C2×D4311yescharacteristic
342#492—431no—
343#488—861no—
344#487—431no—
345#486—431no—
346#486—431no—
347#486—431no—
348#482—861no—
349#481—861no—
350#479—861no—
351#476—431no—
352#476—431no—
353#474—431no—
354#468—861no—
355#466—21no—
356#465—861no—
357#463—861no—
358#461—431no—
359#460—431no—
360#460—431no—
361#459C2×D4311yescharacteristic
362#459C2×D4311yescharacteristic
363#450—861no—
364#450—861no—
365#447—21no—
366#447—21no—
367C8×Q8—431no—
368C4×SD16—431no—
369C4×SD16—861no—
370C4×D8C2×D4311yescharacteristic
371#436—431no—
372C8×D4—431no—
373C8×D4C2×D4311yescharacteristic
374#418—861no—
375C2×#102—861no—
376#335—431no—
377#335—431no—
378#333—431no—
379#332—431no—
380#331—431no—
381#331—431no—
382Q8⋊C8—431no—
383D4⋊C8—431no—
384D4⋊C8—431no—
385D4⋊C8—431no—
386#322—431no—
387C43#1977311yescharacteristic, complemented, Sylow
388C22×D4—21no—
389C22×D4—21no—
390C22×D4—21no—
391C22×D4—21no—
392C2×SD16—431no—
393C2×SD16—861no—
394C2×SD16—861no—
395C2×SD16—861no—
396C2×SD16—1721no—
397C2×D8—21no—
398C2×D8—21no—
399C2×D8—21no—
400C2×D8—21no—
401C2×D8—44no—
402C2×D8C22⋊D4311yescharacteristic
403C2×M16—861no—
404C22×C8—21no—
405C22×C8—861no—
406C4⋊Q8—431no—
407C4⋊Q8—431no—
408#127C22×D4311yescharacteristic
409#127C22×D4311yescharacteristic
410#126—1721no—
411#125—861no—
412#124—861no—
413C22⋊Q8—861no—
414C22⋊Q8—861no—
415C22⋊Q8—1721no—
416#121—21no—
417#121—21no—
418#121—21no—
419#121—21no—
420#120—41no—
421#120—41no—
422C4×Q8—431no—
423C4×Q8—861no—
424C4×D4—861no—
425C4×D4C22×D4311yescharacteristic
426C4×D4C22×D4311yescharacteristic
427C4×D4C22×D4311yescharacteristic
428#117—861no—
429C2×C4⋊C4—861no—
430#107—861no—
431#107C22⋊D4311yescharacteristic
432#106—431no—
433#106—861no—
434#106—861no—
435C4⋊C8—431no—
436C4⋊C8—431no—
437C4⋊C8—431no—
438C4⋊C8—861no—
439C4⋊C8C22×D4311yescharacteristic
440#103—431no—
441#103—861no—
442#103—861no—
443#103—861no—
444#102—21no—
445#102—21no—
446#102—431no—
447#102—861no—
448#102—861no—
449#102—861no—
450#102—861no—
451#102—861no—
452#102—861no—
453#102—861no—
454#102—861no—
455#102—861no—
456#102—1721no—
457#102C22⋊D4311yescharacteristic
458#102C22⋊D4311yescharacteristic
459C22⋊C8—21no—
460C22⋊C8—861no—
461C22⋊C8—861no—
462C4×C8—431no—
463C4×C8—431no—
464C4×C8—861no—
465C4×C8C22×D4311yescharacteristic
466C24—41no—
467C24—41no—
468C2×Q8—431no—
469C2×Q8—861no—
470C2×Q8—861no—
471C2×D4—21no—
472C2×D4—21no—
473C2×D4—21no—
474C2×D4—21no—
475C2×D4—21no—
476C2×D4—21no—
477C2×D4—41no—
478C2×D4—41no—
479C2×D4—41no—
480C2×D4—41no—
481C2×D4—42no—
482C2×D4—42no—
483C2×D4—42no—
484C2×D4—42no—
485C2×D4—81no—
486C2×D4—81no—
487C2×D4—81no—
488C2×D4—81no—
489C2×D4D4×D4311yescharacteristic
490C2×D4C2×C22⋊D4311yescharacteristic
491C2×D4C2×C22⋊D4311yescharacteristic
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—1721no—
496SD16—862no—
497SD16—3441no—
498SD16—3441no—
499SD16—3442no—
500SD16—1722no—
501D8—22no—
502D8—42no—
503D8—42no—
504D8—42no—
505D8—81no—
506M16—3441no—
507C2×C8—21no—
508C2×C8—42no—
509C2×C8—431no—
510C2×C8—431no—
511C2×C8—861no—
512C2×C8—861no—
513C2×C8—861no—
514C2×C8—861no—
515C2×C8—3441no—
516C2×C8C2×C22⋊D4311yescharacteristic
517C2×C8C2×C22⋊D4311yescharacteristic
518C4⋊C4—431no—
519C4⋊C4—861no—
520C4⋊C4—861no—
521C4⋊C4—861no—
522C4⋊C4—861no—
523C4⋊C4—861no—
524C4⋊C4—1721no—
525C4⋊C4—1721no—
526C4⋊C4—1721no—
527C4⋊C4D4×D4311yescharacteristic
528C4⋊C4C2×C22⋊D4311yescharacteristic
529C4⋊C4C2×C22⋊D4311yescharacteristic
530C22⋊C4—21no—
531C22⋊C4—21no—
532C22⋊C4—21no—
533C22⋊C4—41no—
534C22⋊C4—41no—
535C22⋊C4—1721no—
536C22⋊C4—1721no—
537C22⋊C4—1721no—
538C42—861no—
539C42—1721no—
540C42C23×D4311yescharacteristic
541C23—21no—
542C23—21no—
543C23—21no—
544C23—41no—
545C23—41no—
546C23—82no—
547C23—82no—
548C23—82no—
549C23—82no—
550C23—161no—
551C23—161no—
552Q8—861no—
553Q8—861no—
554Q8—3441no—
555Q8—1721no—
556Q8—1721no—
557D4—21no—
558D4—21no—
559D4—21no—
560D4—21no—
561D4—41no—
562D4—41no—
563D4—41no—
564D4—41no—
565D4—41no—
566D4—41no—
567D4—41no—
568D4—41no—
569D4—81no—
570D4—81no—
571D4—82no—
572D4—82no—
573D4—82no—
574D4—82no—
575D4#1306334412yes—
576D4#1306335112yes—
577C2×C4—21no—
578C2×C4—21no—
579C2×C4—21no—
580C2×C4—41no—
581C2×C4—41no—
582C2×C4—41no—
583C2×C4—41no—
584C2×C4—41no—
585C2×C4—41no—
586C2×C4—861no—
587C2×C4—861no—
588C2×C4—1721no—
589C2×C4—1721no—
590C2×C4—6881no—
591C2×C4C2×D4×D4311yescharacteristic
592C2×C4C22×C22⋊D4311yescharacteristic
593C2×C4#1306337011yescharacteristic
594C8—21no—
595C8—21no—
596C8—41no—
597C8—861no—
598C8—861no—
599C8—1721no—
600C8—1721no—
601C8—1721no—
602C8—1721no—
603C22—22no—
604C22—22no—
605C22—41no—
606C22—41no—
607C22—41no—
608C22—41no—
609C22—41no—
610C22—41no—
611C22—41no—
612C22—81no—
613C22—81no—
614C22—81no—
615C22—81no—
616C22—81no—
617C22—81no—
618C22—164no—
619C22—164no—
620C22D4×C22⋊D4311yescharacteristic
621C4—21no—
622C4—41no—
623C4—41no—
624C4—41no—
625C4—3441no—
626C4—3441no—
627C4—1721no—
628C4—1721no—
629C4C2×#1306334411yescharacteristic
630C4C2×#1306335111yescharacteristic
631C4#1458370011yescharacteristic
632C4#1458371011yescharacteristic
633C2—42no—
634C2—42no—
635C2—81no—
636C2—161no—
637C2—161no—
638C2#1914608611yescharacteristic
639C2#1914628011yescharacteristic
640C2#1914635911yescharacteristic
subgroupG/H
centerC22D4×C22⋊D43
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
Fitting, prime radicalD4×D8×C43C2
socleC22×C43D42
hypercenterD4×D8D43
hypocenterC43#19773
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ D4×D8

Complements

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

NH ≅ G/Ntype
1. #19147242C2semidirect
2. #19146826C2semidirect
3. #19146419C2semidirect
4. #19134233C2semidirect
5. #19134126C2semidirect
6. #19134046C2semidirect
7. #19134030C2semidirect
8. #19133952C2semidirect
9. #19133774C2semidirect
10. #19133711C2semidirect
11. #19133703C2semidirect
12. #19133665C2semidirect
13. #19133425C2semidirect
14. #19133407C2semidirect
16. #14583619C22semidirect
17. #14583606C22semidirect
18. #14583271C22semidirect
20. #14583250C22semidirect
21. #14583245C22semidirect
22. #14583245C22semidirect
23. #14583245C22semidirect
28. #14583189C22semidirect
33. #14583104C22semidirect
34. #14583096C22semidirect
35. #14583096C22semidirect
38. C8×Dic86C22semidirect
41. #14582977C22semidirect
42. D4×C43⋊C8C22semidirect
45. #14582652C22semidirect
46. #14582651C22semidirect
47. #14582647C22semidirect
48. #14582646C22semidirect
49. #14582643C22semidirect
50. #14582643C22semidirect
51. #14582629C22semidirect
53. D4⋊(C43⋊C8)C22semidirect
54. D4⋊(C43⋊C8)C22semidirect
55. #14582621C22semidirect
387. C43#19773semidirect

Maximal subgroups

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

subgroupindex
#191472422
#191468262
#191464192
#191342332
#191341262
#191340462
#191340302
#191339522
#191337742
#191337112
#191337032
#191336652
#191334252
#191334072
D4×D8×C432
#1977343