Finite Group Databasebeta

← #25086725

Subgroups — #25086725

Order 11008.

684 conjugacy classes of subgroups.

The subgroup lattice has 624 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19147466C211yesmaximal, characteristic, complemented
2#19146421C211yesmaximal, characteristic, complemented
3#19146215C211yesmaximal, characteristic
4#19134222C211yesmaximal, characteristic, complemented
5#19134092C211yesmaximal, characteristic, complemented
6#19134011C211yesmaximal, characteristic, complemented
7#19133953C211yesmaximal, characteristic, complemented
8#19133933C211yesmaximal, characteristic, complemented
9#19133772C211yesmaximal, characteristic, complemented
10#19133722C211yesmaximal, characteristic, complemented
11#19133691C211yesmaximal, characteristic, complemented
12#19133666C211yesmaximal, characteristic, complemented
13#19133439C211yesmaximal, characteristic, complemented
14#19133405C211yesmaximal, characteristic, complemented
15C43×#3392C211yesmaximal, characteristic, complemented
16C2×#13063350—21no—
17#14583609C2211yescharacteristic
18D4×D172C2211yescharacteristic
19#14583298—21no—
20#14583295C2211yescharacteristic, complemented
21#14583275C2211yescharacteristic
22#14583271C2211yescharacteristic, complemented
23#14583247C2211yescharacteristic
24#14583246C2211yescharacteristic
25#14583219—21no—
26#14583206—21no—
27#14583196—21no—
28#14583194C2211yescharacteristic, complemented
29#14583189C2211yescharacteristic
30#14583176C2211yescharacteristic
31#14583150—21no—
32#14583131—21no—
33#14583099C2211yescharacteristic
34#14583099C2211yescharacteristic
35#14583091C2211yescharacteristic
36#14583048—21no—
37#14583044—21no—
38#14583032—21no—
39Q8×C43⋊C8C2211yescharacteristic, complemented
40C4×#10621884—21no—
41C4×#10621884C2211yescharacteristic
42#14582977C2211yescharacteristic
43C8×D172C2211yescharacteristic
44#102×D43—21no—
45#14582651C2211yescharacteristic, complemented
46#14582650C2211yescharacteristic, complemented
47#14582647C2211yescharacteristic, complemented
48#14582645C2211yescharacteristic, 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
56C43×#557C2211yescharacteristic, complemented
57C43×#550C2211yescharacteristic
58C43×#492—21no—
59C43×#492C2211yescharacteristic, complemented
60C43×#461—21no—
61C43×#461C2211yescharacteristic
62C43×#460—21no—
63C43×#460C2211yescharacteristic, complemented
64C8×Q8×C43C2211yescharacteristic, complemented
65C4×SD16×C43—21no—
66C4×SD16×C43C2211yescharacteristic
67C22×D172—21no—
68C2×D4×D43—21no—
69#13063350—44no—
70C2×#10621883—41no—
71C2×#10621884—21no—
72C2×#10621884—21no—
73C2×#10621884D411yescharacteristic
74C2×#10621882—21no—
75C2×#10621882—21no—
76C2×#10621882—21no—
77C2×#10621877—21no—
78C2×C8×D43—21no—
79#13063325C2311yescharacteristic
80#13063322C2311yescharacteristic
81#13063317—21no—
82#13063303—41no—
83#13063301—21no—
84#13063300—21no—
85#13063299—21no—
86#13063295—41no—
87C4×D172—21no—
88C4×D172C2311yescharacteristic
89C4⋊C4×D43—21no—
90#13063258—21no—
91#13063258—21no—
92#13063256—21no—
93#13063256—21no—
94#13063256—21no—
95#13063256D411yescharacteristic
96C4⋊(C43⋊C8)—21no—
97C4⋊(C43⋊C8)C2311yescharacteristic
98C4⋊(C43⋊C8)C2311yescharacteristic
99C4⋊(C43⋊C8)C2311yescharacteristic
100#13063249—21no—
101#13063249D411yescharacteristic
102#13063247—21no—
103#13063247—21no—
104#13063246—21no—
105#13063246—21no—
106#13063245—21no—
107#13063245—21no—
108#13063245—21no—
109#13063245—41no—
110#13063245D411yescharacteristic
111C22⋊(C43⋊C8)—21no—
112(C2×D43)⋊C8—21no—
113C4×C43⋊C8—21no—
114C4×C43⋊C8C2311yescharacteristic
115C4×C43⋊C8C2311yescharacteristic
116C2×#41×C43—21no—
117C2×SD16×C43—21no—
118C2×SD16×C43—21no—
119C2×SD16×C43—21no—
120C2×SD16×C43—21no—
121C2×SD16×C43D411yescharacteristic
122C4⋊Q8×C43—21no—
123C4⋊Q8×C43C2311yescharacteristic
124#127×C43—21no—
125#127×C43C2311yescharacteristic
126#125×C43—21no—
127#125×C43—41no—
128#121×C43—21no—
129#121×C43—41no—
130C4×Q8×C43—21no—
131C4×Q8×C43—21no—
132C4×Q8×C43C2311yescharacteristic
133C4×Q8×C43C2311yescharacteristic
134C4×D4×C43—21no—
135C4×D4×C43C2311yescharacteristic
136#106×C43D411yescharacteristic
137C4⋊C8×C43—21no—
138C4⋊C8×C43C2311yescharacteristic
139#103×C43—21no—
140#103×C43D411yescharacteristic
141#102×C43—21no—
142#102×C43D411yescharacteristic
143C4×C8×C43—21no—
144C4×C8×C43C2311yescharacteristic
145C23×D43—41no—
146#41×C43—42no—
147#41×C43—81no—
148C2×Q8×C43—21no—
149C2×Q8×C43C2×D411yescharacteristic
150C2×Q8×C43C2×D411yescharacteristic
151C2×D4×C43—21no—
152C2×D4×C43—21no—
153C2×D4×C43—21no—
154C2×D4×C43—41no—
155C2×D4×C43—41no—
156C2×D4×C43C2×D411yescharacteristic
157C22×C4×C43—21no—
158C22×C4×C43—41no—
159C2×C22⋊D43—41no—
160D4×D43—42no—
161D4×D43—81no—
162C2×D172—21no—
163C2×D172—21no—
164C2×D172—21no—
165C2×D172—41no—
166C2×D172—42no—
167C2×D172—81no—
168C2×D172C2×D411yescharacteristic
169C2×C4×D43—21no—
170C2×C4×D43—41no—
171C2×Dic86—21no—
172SD16×C43—41no—
173SD16×C43—42no—
174SD16×C43—81no—
175SD16×C43—81no—
176SD16×C43—81no—
177C2×C8×C43—21no—
178C2×C8×C43C2×D411yescharacteristic
179C2×C8×C43C2×D411yescharacteristic
180C4⋊C4×C43—21no—
181C4⋊C4×C43—21no—
182C4⋊C4×C43—21no—
183C4⋊C4×C43—21no—
184C4⋊C4×C43—41no—
185C4⋊C4×C43—41no—
186C4⋊C4×C43—41no—
187C4⋊C4×C43C2×D411yescharacteristic
188C4⋊C4×C43C2×D411yescharacteristic
189C4⋊C4×C43C2×D411yescharacteristic
190C22⋊C4×C43—21no—
191C22⋊C4×C43—41no—
192C42×C43—21no—
193C42×C43—21no—
194C42×C43—41no—
195C42×C43C2411yescharacteristic
196#10621884—42no—
197#10621884—81no—
198#10621884SD1614yescomplemented
199#10621883—82no—
200#10621882—42no—
201#10621882—42no—
202#10621882—81no—
203(C2×D43)⋊C4—21no—
204(C2×D43)⋊C4—41no—
205(C2×D43)⋊C4—41no—
206C4⋊Dic43—21no—
207C4⋊Dic43—21no—
208C4⋊Dic43C2×D411yescharacteristic
209Dic43⋊C4—41no—
210Dic43⋊C4—41no—
211#10621877—42no—
212C2×C43⋊C8—21no—
213C2×C43⋊C8—21no—
214C2×C43⋊C8—21no—
215C2×C43⋊C8—21no—
216C2×C43⋊C8C2×D411yescharacteristic
217C2×C43⋊C8C2×D411yescharacteristic
218C8×D43—81no—
219C23×C43—21no—
220C23×C43—41no—
221C22×D43—21no—
222C22×D43—41no—
223C22×D43—82no—
224C22×D43—82no—
225C22×D43—161no—
226Q8×C43—21no—
227Q8×C43—21no—
228Q8×C43—21no—
229Q8×C43—41no—
230Q8×C43—41no—
231Q8×C43C2×SD1612yes—
232D4×C43—21no—
233D4×C43—21no—
234D4×C43—41no—
235D4×C43—41no—
236D4×C43—41no—
237D4×C43—41no—
238D4×C43—82no—
239D4×C43—81no—
240D4×C43—161no—
241C2×C4×C43—21no—
242C2×C4×C43—21no—
243C2×C4×C43—21no—
244C2×C4×C43—21no—
245C2×C4×C43—21no—
246C2×C4×C43—41no—
247C2×C4×C43—41no—
248C2×C4×C43—41no—
249C2×C4×C43—82no—
250C2×C4×C43C22×D411yescharacteristic
251C2×C4×C43C22×D411yescharacteristic
252C2×C4×C43H(5,𝔽2)11yescharacteristic
253C22⋊D43—82no—
254C2×Dic43—21no—
255C2×Dic43—41no—
256D172—21no—
257D172—41no—
258D172—41no—
259D172—41no—
260D172—41no—
261D172—81no—
262D172—82no—
263D172C2×SD1612yes—
264C4×D43—41no—
265C4×D43—41no—
266C4×D43—161no—
267Dic86—81no—
268C8×C43—21no—
269C8×C43—21no—
270C8×C43—41no—
271C43⋊C8—21no—
272C43⋊C8—41no—
273C43⋊C8—41no—
274C43⋊C8—41no—
275C43⋊C8—41no—
276C43⋊C8C2×SD1612yes—
277#19807—431nomaximal, Sylow
278C22×C43—41no—
279C22×C43—41no—
280C22×C43—41no—
281C22×C43—81no—
282C22×C43—81no—
283C22×C43—81no—
284C22×C43D4211yescharacteristic
285C2×D43—22no—
286C2×D43—41no—
287C2×D43—41no—
288C2×D43—81no—
289C2×D43—81no—
290C2×D43—81no—
291C2×D43—164no—
292C4×C43—22no—
293C4×C43—21no—
294C4×C43—41no—
295C4×C43—41no—
296C4×C43—41no—
297C4×C43—41no—
298C4×C43—81no—
299C4×C43C22×SD1611yescharacteristic
300C4×C43#57511yescharacteristic
301C4×C43#57611yescharacteristic
302C4×C43#57711yescharacteristic
303Dic43—41no—
304Dic43—81no—
305#3392D4311yescharacteristic, complemented
306#3381—431no—
307#3295—431no—
308#3274—431no—
309#1715—431no—
310#1691—431no—
311#1678—431no—
312#1668—431no—
313#1665—431no—
314#1639—431no—
315#1631—431no—
316#1626—431no—
317#1622—431no—
318#1583—431no—
319SD16⋊C8—431no—
320C2×C43—81no—
321C2×C43—161no—
322C2×C43#326811yescharacteristic
323C2×C43D4×SD1611yescharacteristic
324C2×C43#328811yescharacteristic
325D43—42no—
326D43—161no—
327C2×AGL(1,ℤ/8)—861no—
328#557C2×D4311yescharacteristic, complemented
329#554—431no—
330#550C2×D4311yescharacteristic
331D42—431no—
332#499—861no—
333#498—431no—
334#493—431no—
335#492—21no—
336#492—431no—
337#492C2×D4311yescharacteristic, complemented
338#486—431no—
339#486—431no—
340#481—861no—
341#479—861no—
342#478—861no—
343#477—431no—
344#476—431no—
345#474—431no—
346#469—861no—
347#465—861no—
348#461—21no—
349#461C2×D4311yescharacteristic
350#460—21no—
351#460—431no—
352#460—431no—
353#460C2×D4311yescharacteristic, complemented
354#459—431no—
355#450—861no—
356#449—861no—
357#447—861no—
358C8×Q8—431no—
359C8×Q8C2×D4311yescharacteristic, complemented
360C4×SD16—21no—
361C4×SD16—431no—
362C4×SD16—861no—
363C4×SD16C2×D4311yescharacteristic
364#436—431no—
365C8×D4—431no—
366C2×#102—861no—
367#335—431no—
368#334—431no—
369#333—431no—
370#332—431no—
371#331—431no—
372#331—431no—
373Q8⋊C8—431no—
374Q8⋊C8—431no—
375D4⋊C8—431no—
376D4⋊C8—431no—
377#322—431no—
378C43#1980711yescharacteristic, complemented, Sylow
379C2×#41—21no—
380C22×D4—861no—
381C22×D4—861no—
382AGL(1,ℤ/8)—1724no—
383C2×SD16—21no—
384C2×SD16—21no—
385C2×SD16—21no—
386C2×SD16—21no—
387C2×SD16—431no—
388C2×SD16—861no—
389C2×SD16—861no—
390C2×SD16—1721no—
391C2×SD16C22⋊D4311yescharacteristic
392C2×D8—861no—
393C2×D8—861no—
394C2×D8—861no—
395C2×M16—861no—
396C22×C8—861no—
397C4⋊Q8—21no—
398C4⋊Q8—431no—
399C4⋊Q8C22×D4311yescharacteristic
400#127—21no—
401#127—431no—
402#127C22×D4311yescharacteristic
403#125—21no—
404#125—41no—
405#125—861no—
406C22⋊Q8—861no—
407C22⋊Q8—1721no—
408#121—21no—
409#121—41no—
410#121—861no—
411#121—861no—
412#120—1721no—
413C4×Q8—21no—
414C4×Q8—21no—
415C4×Q8C22×D4311yescharacteristic
416C4×Q8C22×D4311yescharacteristic
417C4×D4—21no—
418C4×D4—431no—
419C4×D4—861no—
420C4×D4C22×D4311yescharacteristic
421C2×C4⋊C4—861no—
422#107—861no—
423#107—861no—
424#106—431no—
425#106—861no—
426#106—861no—
427#106—861no—
428#106C22⋊D4311yescharacteristic
429C4⋊C8—21no—
430C4⋊C8—431no—
431C4⋊C8—431no—
432C4⋊C8—431no—
433C4⋊C8—861no—
434C4⋊C8C22×D4311yescharacteristic
435#103—21no—
436#103—431no—
437#103—861no—
438#103C22⋊D4311yescharacteristic
439#102—21no—
440#102—431no—
441#102—861no—
442#102—861no—
443#102—861no—
444#102—861no—
445#102—861no—
446#102—861no—
447#102—861no—
448#102—1721no—
449#102C22⋊D4311yescharacteristic
450C22⋊C8—861no—
451C22⋊C8—861no—
452C4×C8—21no—
453C4×C8—431no—
454C4×C8—431no—
455C4×C8—861no—
456C4×C8C22×D4311yescharacteristic
457C24—1721no—
458#41—42no—
459#41—81no—
460C2×Q8—21no—
461C2×Q8—861no—
462C2×Q8D4×D4311yescharacteristic
463C2×Q8C2×C22⋊D4311yescharacteristic
464C2×D4—21no—
465C2×D4—21no—
466C2×D4—21no—
467C2×D4—41no—
468C2×D4—41no—
469C2×D4—431no—
470C2×D4—861no—
471C2×D4—861no—
472C2×D4—861no—
473C2×D4—3441no—
474C2×D4—3441no—
475C2×D4—1721no—
476C2×D4—1722no—
477C2×D4—1721no—
478C2×D4—1722no—
479C2×D4C2×C22⋊D4311yescharacteristic
480C22×C4—21no—
481C22×C4—41no—
482C22×C4—861no—
483C22×C4—1721no—
484SD16—41no—
485SD16—42no—
486SD16—81no—
487SD16—81no—
488SD16—81no—
489SD16—434no—
490SD16—3442no—
491SD16—3441no—
492SD16—1722no—
493D8—3441no—
494D8—1722no—
495D8—1722no—
496M16—1722no—
497C2×C8—21no—
498C2×C8—431no—
499C2×C8—431no—
500C2×C8—861no—
501C2×C8—861no—
502C2×C8—861no—
503C2×C8—861no—
504C2×C8—3441no—
505C2×C8C2×C22⋊D4311yescharacteristic
506C2×C8C2×C22⋊D4311yescharacteristic
507C4⋊C4—21no—
508C4⋊C4—21no—
509C4⋊C4—21no—
510C4⋊C4—21no—
511C4⋊C4—41no—
512C4⋊C4—41no—
513C4⋊C4—41no—
514C4⋊C4—431no—
515C4⋊C4—861no—
516C4⋊C4—861no—
517C4⋊C4—1721no—
518C4⋊C4—1721no—
519C4⋊C4D4×D4311yescharacteristic
520C4⋊C4C2×C22⋊D4311yescharacteristic
521C4⋊C4C2×C22⋊D4311yescharacteristic
522C22⋊C4—21no—
523C22⋊C4—41no—
524C22⋊C4—861no—
525C22⋊C4—1721no—
526C22⋊C4—1721no—
527C42—21no—
528C42—21no—
529C42—41no—
530C42C23×D4311yescharacteristic
531C23—21no—
532C23—41no—
533C23—861no—
534C23—3442no—
535C23—3442no—
536C23—1721no—
537C23—6881no—
538Q8—21no—
539Q8—21no—
540Q8—21no—
541Q8—41no—
542Q8—41no—
543Q8—3441no—
544Q8SD16×D4312yes—
545D4—21no—
546D4—21no—
547D4—41no—
548D4—41no—
549D4—41no—
550D4—41no—
551D4—82no—
552D4—81no—
553D4—161no—
554D4—432no—
555D4—861no—
556D4—3441no—
557D4—3442no—
558D4—3442no—
559D4—1721no—
560D4—1721no—
561D4—1721no—
562D4—1721no—
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—82no—
572C2×C4—861no—
573C2×C4—1721no—
574C2×C4—1721no—
575C2×C4—1721no—
576C2×C4—6881no—
577C2×C4C2×D4×D4311yescharacteristic
578C2×C4C22×C22⋊D4311yescharacteristic
579C2×C4#1306337011yescharacteristic
580C8—21no—
581C8—21no—
582C8—41no—
583C8—432no—
584C8—861no—
585C8—1721no—
586C8—1721no—
587C8—1721no—
588C8—1721no—
589C22—41no—
590C22—41no—
591C22—41no—
592C22—81no—
593C22—81no—
594C22—81no—
595C22—862no—
596C22—3441no—
597C22—3441no—
598C22—3441no—
599C22—1721no—
600C22—1721no—
601C22—6884no—
602C22D4×C22⋊D4311yescharacteristic
603C4—22no—
604C4—21no—
605C4—41no—
606C4—41no—
607C4—41no—
608C4—41no—
609C4—81no—
610C4—3441no—
611C4—1721no—
612C4C2×SD16×D4311yescharacteristic
613C4#1458369711yescharacteristic
614C4#1458370211yescharacteristic
615C4#1458370511yescharacteristic
616C2—81no—
617C2—161no—
618C2—1722no—
619C2—6881no—
620C2#1914613611yescharacteristic
621C2SD16×C22⋊D4311yescharacteristic
622C2#1914635711yescharacteristic
subgroupG/H
centerC22D4×C22⋊D43
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#3392C2
socleC22×C43D42
prime radical#19146215C2
hypercenter#3392D43
hypocenterC43#19807
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #3392

Complements

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

NH ≅ G/Ntype
1. #19147466C2semidirect
2. #19146421C2semidirect
4. #19134222C2semidirect
5. #19134092C2semidirect
6. #19134011C2semidirect
7. #19133953C2semidirect
8. #19133933C2semidirect
9. #19133772C2semidirect
10. #19133722C2semidirect
11. #19133691C2semidirect
12. #19133666C2semidirect
13. #19133439C2semidirect
14. #19133405C2semidirect
15. C43×#3392C2semidirect
20. #14583295C22semidirect
22. #14583271C22semidirect
28. #14583194C22semidirect
39. Q8×C43⋊C8C22semidirect
45. #14582651C22semidirect
46. #14582650C22semidirect
47. #14582647C22semidirect
48. #14582645C22semidirect
49. #14582643C22semidirect
51. Q8⋊(C43⋊C8)C22semidirect
52. Q8⋊(C43⋊C8)C22semidirect
55. #14582621C22semidirect
56. C43×#557C22semidirect
59. C43×#492C22semidirect
63. C43×#460C22semidirect
64. C8×Q8×C43C22semidirect
198. #10621884SD16semidirect
305. #3392D43semidirect
328. #557C2×D43semidirect
337. #492C2×D43semidirect
353. #460C2×D43semidirect
359. C8×Q8C2×D43semidirect
378. C43#19807semidirect

Maximal subgroups

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

subgroupindex
#191474662
#191464212
#191462152
#191342222
#191340922
#191340112
#191339532
#191339332
#191337722
#191337222
#191336912
#191336662
#191334392
#191334052
C43×#33922
#1980743