Finite Group Databasebeta

← #25086680

Subgroups — #25086680

Order 11008.

720 conjugacy classes of subgroups.

The subgroup lattice has 634 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1Q8×#10621884C211yesmaximal, characteristic, complemented
2SD16×D172C211yesmaximal, characteristic, complemented
3#19146215C211yesmaximal, characteristic
4#19134225C211yesmaximal, characteristic, complemented
5#19134096C211yesmaximal, characteristic, complemented
6#19134001C211yesmaximal, characteristic, complemented
7#19133953C211yesmaximal, characteristic, complemented
8#19133943C211yesmaximal, characteristic, complemented
9#19133795C211yesmaximal, characteristic, complemented
10#19133710C211yesmaximal, characteristic, complemented
11#19133696C211yesmaximal, characteristic, complemented
12#19133673C211yesmaximal, characteristic, complemented
13#19133439C211yesmaximal, characteristic, complemented
14#19133405C211yesmaximal, characteristic, complemented
15C43×#3362C211yesmaximal, characteristic, complemented
16C2×#13063350—21no—
17C2×SD16×D43—21no—
18Q8×D172C2211yescharacteristic
19D4×D172C2211yescharacteristic
20#14583295—21no—
21#14583295C2211yescharacteristic, complemented
22#14583275C2211yescharacteristic
23#14583273C2211yescharacteristic
24#14583272C2211yescharacteristic
25#14583245C2211yescharacteristic, complemented
26#14583186—21no—
27#14583186C2211yescharacteristic
28#14583184—21no—
29#14583184C2211yescharacteristic, complemented
30#14583150—21no—
31#14583129—21no—
32#14583104C2211yescharacteristic
33#14583099C2211yescharacteristic
34#14583099C2211yescharacteristic
35#14583091C2211yescharacteristic
36#14583051—21no—
37#14583044—21no—
38#14583039—21no—
39#14583032—21no—
40Q8×C43⋊C8C2211yescharacteristic, complemented
41C4×#10621884—21no—
42C4×#10621884C2211yescharacteristic
43#14582977C2211yescharacteristic
44C8×D172C2211yescharacteristic
45#14582651C2211yescharacteristic, complemented
46#14582650C2211yescharacteristic, complemented
47#14582648C2211yescharacteristic, complemented
48#14582646C2211yescharacteristic, complemented
49#14582643C2211yescharacteristic, complemented
50#14582642C2211yescharacteristic
51Q8⋊(C43⋊C8)C2211yescharacteristic, complemented
52Q8⋊(C43⋊C8)C2211yescharacteristic, complemented
53D4⋊(C43⋊C8)C2211yescharacteristic
54#14582626C2211yescharacteristic
55#14582621C2211yescharacteristic, complemented
56Q82×C43C2211yescharacteristic, complemented
57C43×#550C2211yescharacteristic
58C43×#486—21no—
59C43×#486C2211yescharacteristic, complemented
60C43×#476—21no—
61C43×#476C2211yescharacteristic
62C43×#460—21no—
63C43×#460C2211yescharacteristic, complemented
64C8×Q8×C43C2211yescharacteristic, complemented
65C4×SD16×C43—21no—
66C4×SD16×C43C2211yescharacteristic
67C2×Q8×D43—21no—
68C22×D172—21no—
69C2×D4×D43—21no—
70#13063350—44no—
71C2×#10621873—21no—
72C2×#10621873—21no—
73C2×#10621883—21no—
74C2×#10621884—21no—
75C2×#10621884—21no—
76C2×#10621884—41no—
77C2×#10621884D411yescharacteristic
78SD16×D43—44no—
79C2×#10621882—21no—
80C2×#10621882—21no—
81C2×#10621882—21no—
82C2×#10621877—21no—
83C2×C8×D43—21no—
84#13063325—21no—
85#13063325C2311yescharacteristic
86#13063322C2311yescharacteristic
87#13063305—21no—
88#13063305—41no—
89#13063300—21no—
90#13063299—21no—
91#13063295—41no—
92C4×D172—21no—
93C4×D172C2311yescharacteristic
94#13063256—21no—
95#13063256—21no—
96#13063256—21no—
97#13063256—21no—
98#13063256D411yescharacteristic
99C4⋊(C43⋊C8)—21no—
100C4⋊(C43⋊C8)C2311yescharacteristic
101C4⋊(C43⋊C8)C2311yescharacteristic
102C4⋊(C43⋊C8)C2311yescharacteristic
103#13063249—21no—
104#13063249D411yescharacteristic
105#13063248—21no—
106#13063246—21no—
107#13063246—41no—
108#13063245—21no—
109#13063245—21no—
110#13063245—21no—
111#13063245D411yescharacteristic
112C22⋊(C43⋊C8)—21no—
113(C2×D43)⋊C8—21no—
114C4×C43⋊C8—21no—
115C4×C43⋊C8C2311yescharacteristic
116C4×C43⋊C8C2311yescharacteristic
117C2×#41×C43—21no—
118C2×SD16×C43—21no—
119C2×SD16×C43D411yescharacteristic
120C4⋊Q8×C43—21no—
121C4⋊Q8×C43—21no—
122C4⋊Q8×C43—41no—
123C4⋊Q8×C43C2311yescharacteristic
124#127×C43—21no—
125#127×C43C2311yescharacteristic
126#121×C43—21no—
127#121×C43—41no—
128C4×Q8×C43—21no—
129C4×Q8×C43—21no—
130C4×Q8×C43C2311yescharacteristic
131C4×Q8×C43C2311yescharacteristic
132C4×D4×C43—21no—
133C4×D4×C43C2311yescharacteristic
134#106×C43—21no—
135#106×C43D411yescharacteristic
136C4⋊C8×C43—21no—
137C4⋊C8×C43C2311yescharacteristic
138#103×C43D411yescharacteristic
139#102×C43—21no—
140#102×C43—21no—
141#102×C43—21no—
142#102×C43—21no—
143#102×C43D411yescharacteristic
144C4×C8×C43—21no—
145C4×C8×C43C2311yescharacteristic
146C23×D43—41no—
147#41×C43—42no—
148#41×C43—81no—
149C2×Q8×C43—21no—
150C2×Q8×C43—41no—
151C2×Q8×C43C2×D411yescharacteristic
152C2×Q8×C43C2×D411yescharacteristic
153C2×D4×C43—21no—
154C2×D4×C43—21no—
155C2×D4×C43—21no—
156C2×D4×C43—41no—
157C2×D4×C43—41no—
158C2×D4×C43C2×D411yescharacteristic
159C22×C4×C43—21no—
160C22×C4×C43—41no—
161C2×C22⋊D43—41no—
162Q8×D43—42no—
163Q8×D43—81no—
164D4×D43—42no—
165D4×D43—81no—
166C2×D172—21no—
167C2×D172—21no—
168C2×D172—21no—
169C2×D172—41no—
170C2×D172—42no—
171C2×D172—81no—
172C2×D172C2×D411yescharacteristic
173C2×C4×D43—21no—
174C2×C4×D43—41no—
175C2×Dic86—21no—
176C2×Dic86—41no—
177SD16×C43—22no—
178SD16×C43—42no—
179C2×C8×C43—21no—
180C2×C8×C43C2×D411yescharacteristic
181C2×C8×C43C2×D411yescharacteristic
182C4⋊C4×C43—21no—
183C4⋊C4×C43—21no—
184C4⋊C4×C43—21no—
185C4⋊C4×C43—21no—
186C4⋊C4×C43—41no—
187C4⋊C4×C43—41no—
188C4⋊C4×C43C2×D411yescharacteristic
189C4⋊C4×C43C2×D411yescharacteristic
190C4⋊C4×C43C2×D411yescharacteristic
191C22⋊C4×C43—21no—
192C22⋊C4×C43—41no—
193C42×C43—21no—
194C42×C43—21no—
195C42×C43—41no—
196C42×C43C2411yescharacteristic
197#10621884—42no—
198#10621884—42no—
199#10621884—82no—
200#10621884SD1614yescomplemented
201#10621883—42no—
202#10621882—42no—
203#10621882—42no—
204#10621882—81no—
205(C2×D43)⋊C4—21no—
206(C2×D43)⋊C4—41no—
207(C2×D43)⋊C4—41no—
208C4⋊Dic43—21no—
209C4⋊Dic43—21no—
210C4⋊Dic43—41no—
211C4⋊Dic43C2×D411yescharacteristic
212#10621877—42no—
213C2×C43⋊C8—21no—
214C2×C43⋊C8—21no—
215C2×C43⋊C8—21no—
216C2×C43⋊C8—21no—
217C2×C43⋊C8C2×D411yescharacteristic
218C2×C43⋊C8C2×D411yescharacteristic
219#10621873—42no—
220#10621873—81no—
221C8×D43—42no—
222C23×C43—21no—
223C23×C43—41no—
224C22×D43—21no—
225C22×D43—41no—
226C22×D43—82no—
227C22×D43—82no—
228C22×D43—161no—
229Q8×C43—21no—
230Q8×C43—21no—
231Q8×C43—81no—
232Q8×C43—161no—
233Q8×C43C2×SD1612yescomplemented
234Q8×C43AGL(1,ℤ/8)12yescomplemented
235D4×C43—21no—
236D4×C43—21no—
237D4×C43—41no—
238D4×C43—41no—
239D4×C43—41no—
240D4×C43—41no—
241D4×C43—82no—
242D4×C43—81no—
243D4×C43—161no—
244C2×C4×C43—21no—
245C2×C4×C43—21no—
246C2×C4×C43—21no—
247C2×C4×C43—21no—
248C2×C4×C43—21no—
249C2×C4×C43—41no—
250C2×C4×C43—41no—
251C2×C4×C43—41no—
252C2×C4×C43—82no—
253C2×C4×C43C22×D411yescharacteristic
254C2×C4×C43C22×D411yescharacteristic
255C2×C4×C43H(5,𝔽2)11yescharacteristic
256C22⋊D43—82no—
257C2×Dic43—21no—
258C2×Dic43—41no—
259D172—21no—
260D172—41no—
261D172—41no—
262D172—41no—
263D172—41no—
264D172—81no—
265D172—82no—
266D172C2×SD1612yes—
267C4×D43—41no—
268C4×D43—41no—
269C4×D43—82no—
270Dic86—41no—
271Dic86—41no—
272Dic86—82no—
273C8×C43—21no—
274C8×C43—21no—
275C8×C43—41no—
276C43⋊C8—21no—
277C43⋊C8—41no—
278C43⋊C8—41no—
279C43⋊C8—41no—
280C43⋊C8—41no—
281C43⋊C8C2×SD1612yescomplemented
282#19804—431nomaximal, Sylow
283C22×C43—41no—
284C22×C43—41no—
285C22×C43—41no—
286C22×C43—81no—
287C22×C43—81no—
288C22×C43—81no—
289C22×C43D4211yescharacteristic
290C2×D43—22no—
291C2×D43—41no—
292C2×D43—41no—
293C2×D43—81no—
294C2×D43—81no—
295C2×D43—81no—
296C2×D43—164no—
297C4×C43—22no—
298C4×C43—22no—
299C4×C43—21no—
300C4×C43—41no—
301C4×C43—41no—
302C4×C43—41no—
303C4×C43—81no—
304C4×C43C22×SD1611yescharacteristic
305C4×C43C2×AGL(1,ℤ/8)11yescharacteristic
306C4×C43#57711yescharacteristic
307C4×C43#57711yescharacteristic
308Dic43—41no—
309Dic43—81no—
310Q8×SD16—431no—
311#3362D4311yescharacteristic, complemented
312D4×SD16—431no—
313#3274—431no—
314#1715—431no—
315#1691—431no—
316#1677—431no—
317#1668—431no—
318#1666—431no—
319#1642—431no—
320#1629—431no—
321#1627—431no—
322#1623—431no—
323#1583—431no—
324SD16⋊C8—431no—
325C2×C43—81no—
326C2×C43—161no—
327C2×C43#326511yescharacteristic
328C2×C43D4×SD1611yescharacteristic
329C2×C43#328811yescharacteristic
330D43—42no—
331D43—161no—
332C2×AGL(1,ℤ/8)—861no—
333C22×SD16—861no—
334Q82C2×D4311yescharacteristic, complemented
335#550C2×D4311yescharacteristic
336D4×Q8—431no—
337D42—431no—
338#498—431no—
339#498—861no—
340#493—431no—
341#492—431no—
342#492—431no—
343#486—21no—
344#486—431no—
345#486C2×D4311yescharacteristic, complemented
346#476—21no—
347#476—431no—
348#476—861no—
349#476C2×D4311yescharacteristic
350#475—431no—
351#475—861no—
352#469—861no—
353#465—861no—
354#461—431no—
355#460—21no—
356#460—431no—
357#460—431no—
358#460C2×D4311yescharacteristic, complemented
359#459—431no—
360#450—861no—
361#449—861no—
362#448—861no—
363#447—861no—
364C8×Q8—431no—
365C8×Q8C2×D4311yescharacteristic, complemented
366C4×SD16—21no—
367C4×SD16—431no—
368C4×SD16—861no—
369C4×SD16C2×D4311yescharacteristic
370#436—431no—
371C8×D4—431no—
372#335—431no—
373#334—431no—
374#333—431no—
375#332—431no—
376#331—431no—
377#331—431no—
378Q8⋊C8—431no—
379Q8⋊C8—431no—
380D4⋊C8—431no—
381D4⋊C8—431no—
382#322—431no—
383C43#1980411yescharacteristic, complemented, Sylow
384C2×#41—21no—
385C22×Q8—861no—
386C22×D4—861no—
387C22×D4—861no—
388AGL(1,ℤ/8)—1724no—
389C2×SD16—21no—
390C2×SD16—431no—
391C2×SD16—861no—
392C2×SD16—861no—
393C2×SD16—861no—
394C2×SD16—861no—
395C2×SD16—861no—
396C2×SD16—1721no—
397C2×SD16—1724no—
398C2×SD16C22⋊D4311yescharacteristic
399C2×D8—861no—
400C2×D8—861no—
401C2×D8—861no—
402C2×M16—861no—
403C22×C8—861no—
404C4⋊Q8—21no—
405C4⋊Q8—21no—
406C4⋊Q8—41no—
407C4⋊Q8—431no—
408C4⋊Q8—861no—
409C4⋊Q8C22×D4311yescharacteristic
410#127—21no—
411#127—431no—
412#127C22×D4311yescharacteristic
413C22⋊Q8—861no—
414C22⋊Q8—1721no—
415#121—21no—
416#121—41no—
417#121—861no—
418#121—861no—
419#120—1721no—
420C4×Q8—21no—
421C4×Q8—21no—
422C4×Q8C22×D4311yescharacteristic
423C4×Q8C22×D4311yescharacteristic
424C4×D4—21no—
425C4×D4—431no—
426C4×D4—861no—
427C4×D4C22×D4311yescharacteristic
428#106—21no—
429#106—431no—
430#106—861no—
431#106—861no—
432#106—861no—
433#106—861no—
434#106C22⋊D4311yescharacteristic
435C4⋊C8—21no—
436C4⋊C8—431no—
437C4⋊C8—431no—
438C4⋊C8—431no—
439C4⋊C8—861no—
440C4⋊C8C22×D4311yescharacteristic
441#103—431no—
442#103—861no—
443#103—861no—
444#103C22⋊D4311yescharacteristic
445#102—21no—
446#102—21no—
447#102—21no—
448#102—21no—
449#102—431no—
450#102—861no—
451#102—861no—
452#102—861no—
453#102—861no—
454#102—1721no—
455#102C22⋊D4311yescharacteristic
456C22⋊C8—861no—
457C22⋊C8—861no—
458C4×C8—21no—
459C4×C8—431no—
460C4×C8—431no—
461C4×C8—861no—
462C4×C8C22×D4311yescharacteristic
463C24—1721no—
464#41—42no—
465#41—81no—
466C2×Q8—21no—
467C2×Q8—41no—
468C2×Q8—861no—
469C2×Q8—3441no—
470C2×Q8—1721no—
471C2×Q8—1722no—
472C2×Q8D4×D4311yescharacteristic
473C2×Q8C2×C22⋊D4311yescharacteristic
474C2×D4—21no—
475C2×D4—21no—
476C2×D4—21no—
477C2×D4—41no—
478C2×D4—41no—
479C2×D4—431no—
480C2×D4—861no—
481C2×D4—861no—
482C2×D4—861no—
483C2×D4—3441no—
484C2×D4—3441no—
485C2×D4—1721no—
486C2×D4—1722no—
487C2×D4—1721no—
488C2×D4—1722no—
489C2×D4C2×C22⋊D4311yescharacteristic
490C22×C4—21no—
491C22×C4—41no—
492C22×C4—861no—
493C22×C4—1721no—
494SD16—22no—
495SD16—42no—
496SD16—434no—
497SD16—3441no—
498SD16—3442no—
499SD16—1722no—
500SD16—1722no—
501SD16—1722no—
502SD16—1722no—
503D8—3441no—
504D8—1722no—
505D8—1722no—
506M16—1722no—
507C2×C8—21no—
508C2×C8—431no—
509C2×C8—431no—
510C2×C8—861no—
511C2×C8—861no—
512C2×C8—861no—
513C2×C8—861no—
514C2×C8—1722no—
515C2×C8C2×C22⋊D4311yescharacteristic
516C2×C8C2×C22⋊D4311yescharacteristic
517C4⋊C4—21no—
518C4⋊C4—21no—
519C4⋊C4—21no—
520C4⋊C4—21no—
521C4⋊C4—41no—
522C4⋊C4—41no—
523C4⋊C4—431no—
524C4⋊C4—861no—
525C4⋊C4—861no—
526C4⋊C4—1721no—
527C4⋊C4D4×D4311yescharacteristic
528C4⋊C4C2×C22⋊D4311yescharacteristic
529C4⋊C4C2×C22⋊D4311yescharacteristic
530C22⋊C4—21no—
531C22⋊C4—41no—
532C22⋊C4—861no—
533C22⋊C4—1721no—
534C22⋊C4—1721no—
535C42—21no—
536C42—21no—
537C42—41no—
538C42C23×D4311yescharacteristic
539C23—21no—
540C23—41no—
541C23—861no—
542C23—3442no—
543C23—3442no—
544C23—1721no—
545C23—6881no—
546Q8—21no—
547Q8—21no—
548Q8—81no—
549Q8—161no—
550Q8—3442no—
551Q8—1721no—
552Q8—1721no—
553Q8SD16×D4312yescomplemented
554Q8#1306335012yescomplemented
555D4—21no—
556D4—21no—
557D4—41no—
558D4—41no—
559D4—41no—
560D4—41no—
561D4—82no—
562D4—81no—
563D4—161no—
564D4—432no—
565D4—861no—
566D4—3441no—
567D4—3442no—
568D4—3442no—
569D4—1721no—
570D4—1721no—
571D4—1721no—
572D4—1721no—
573C2×C4—21no—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—21no—
578C2×C4—41no—
579C2×C4—41no—
580C2×C4—41no—
581C2×C4—82no—
582C2×C4—861no—
583C2×C4—3442no—
584C2×C4—1721no—
585C2×C4—1721no—
586C2×C4—1721no—
587C2×C4C2×D4×D4311yescharacteristic
588C2×C4C22×C22⋊D4311yescharacteristic
589C2×C4#1306337011yescharacteristic
590C8—21no—
591C8—21no—
592C8—41no—
593C8—432no—
594C8—861no—
595C8—1721no—
596C8—1721no—
597C8—1721no—
598C8—1721no—
599C22—41no—
600C22—41no—
601C22—41no—
602C22—81no—
603C22—81no—
604C22—81no—
605C22—862no—
606C22—3441no—
607C22—3441no—
608C22—3441no—
609C22—1721no—
610C22—1721no—
611C22—6884no—
612C22D4×C22⋊D4311yescharacteristic
613C4—22no—
614C4—22no—
615C4—21no—
616C4—41no—
617C4—41no—
618C4—41no—
619C4—81no—
620C4—3441no—
621C4—1721no—
622C4C2×SD16×D4311yescharacteristic
623C4C2×#1306335011yescharacteristic
624C4#1458370511yescharacteristic
625C4#1458370711yescharacteristic
626C2—81no—
627C2—161no—
628C2—1722no—
629C2—6881no—
630C2#1914609111yescharacteristic
631C2SD16×C22⋊D4311yescharacteristic
632C2#1914635911yescharacteristic
subgroupG/H
centerC22D4×C22⋊D43
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#3362C2
socleC22×C43D42
prime radical#19146215C2
hypercenter#3362D43
hypocenterC43#19804
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #3362

Complements

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

NH ≅ G/Ntype
1. Q8×#10621884C2semidirect
2. SD16×D172C2semidirect
4. #19134225C2semidirect
5. #19134096C2semidirect
6. #19134001C2semidirect
7. #19133953C2semidirect
8. #19133943C2semidirect
9. #19133795C2semidirect
10. #19133710C2semidirect
11. #19133696C2semidirect
12. #19133673C2semidirect
13. #19133439C2semidirect
14. #19133405C2semidirect
15. C43×#3362C2semidirect
21. #14583295C22semidirect
25. #14583245C22semidirect
29. #14583184C22semidirect
40. Q8×C43⋊C8C22semidirect
45. #14582651C22semidirect
46. #14582650C22semidirect
47. #14582648C22semidirect
48. #14582646C22semidirect
49. #14582643C22semidirect
51. Q8⋊(C43⋊C8)C22semidirect
52. Q8⋊(C43⋊C8)C22semidirect
55. #14582621C22semidirect
56. Q82×C43C22semidirect
59. C43×#486C22semidirect
63. C43×#460C22semidirect
64. C8×Q8×C43C22semidirect
200. #10621884SD16semidirect
233. Q8×C43C2×SD16semidirect
234. Q8×C43AGL(1,ℤ/8)semidirect
281. C43⋊C8C2×SD16semidirect
311. #3362D43semidirect
334. Q82C2×D43semidirect
345. #486C2×D43semidirect
358. #460C2×D43semidirect
365. C8×Q8C2×D43semidirect
383. C43#19804semidirect
553. Q8SD16×D43semidirect
554. Q8#13063350semidirect

Maximal subgroups

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

subgroupindex
Q8×#106218842
SD16×D1722
#191462152
#191342252
#191340962
#191340012
#191339532
#191339432
#191337952
#191337102
#191336962
#191336732
#191334392
#191334052
C43×#33622
#1980443