Finite Group Databasebeta

← #25082144

Subgroups — #25082144

Order 11008.

684 conjugacy classes of subgroups.

The subgroup lattice has 630 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145521C211yesmaximal, characteristic, complemented
2#474×D43C211yesmaximal, characteristic, complemented
3#19144060C211yesmaximal, characteristic
4#19143633C211yesmaximal, characteristic, complemented
5#19134145C211yesmaximal, characteristic, complemented
6#19134144C211yesmaximal, characteristic, complemented
7#19134139C211yesmaximal, characteristic, complemented
8#19134063C211yesmaximal, characteristic, complemented
9#19134062C211yesmaximal, characteristic, complemented
10#19134061C211yesmaximal, characteristic, complemented
11#19134060C211yesmaximal, characteristic, complemented
12#19133368C211yesmaximal, characteristic, complemented
13#19133278C211yesmaximal, characteristic, complemented
14#19133243C211yesmaximal, characteristic, complemented
15C43×#1699C211yesmaximal, characteristic, complemented
16C2×#13063352—21no—
17#14583450C2211yescharacteristic
18C4⋊Q8×D43C2211yescharacteristic
19C4×D4×D43C2211yescharacteristic
20#14583273C2211yescharacteristic, complemented
21#14583272C2211yescharacteristic, complemented
22#14583251C2211yescharacteristic, complemented
23#14583180C2211yescharacteristic
24#14583179C2211yescharacteristic
25#14583178—21no—
26#14583177—21no—
27#14583176C2211yescharacteristic
28#14583117—21no—
29#14583116—21no—
30#14583103—21no—
31#14583103—21no—
32#14583101C2211yescharacteristic
33#14583095C2211yescharacteristic
34#14583094C2211yescharacteristic
35#14583039—21no—
36#14583039—21no—
37#14582978C2211yescharacteristic
38#14582977C2211yescharacteristic
39#14582976C2211yescharacteristic
40#14582975—21no—
41#14582974—21no—
42#14582951C2211yescharacteristic
43#14582950C2211yescharacteristic
44#107×D43—21no—
45#14582921C2211yescharacteristic
46C4⋊C8×D43C2211yescharacteristic
47#14582899—21no—
48#102×D43—21no—
49#14582862—21no—
50#14582861—21no—
51#14582652C2211yescharacteristic, complemented
52#14582651C2211yescharacteristic, complemented
53#14582651C2211yescharacteristic, complemented
54#14582646C2211yescharacteristic, complemented
55#14582645C2211yescharacteristic, complemented
56#14582645C2211yescharacteristic, complemented
57#14582644C2211yescharacteristic, complemented
58#14582642C2211yescharacteristic, complemented
59#14582642C2211yescharacteristic, complemented
60C43×#487C2211yescharacteristic, complemented
61C43×#474C2211yescharacteristic
62C43×#461C2211yescharacteristic
63C43×#436C2211yescharacteristic
64C43×#335C2211yescharacteristic, complemented
65C43×#332C2211yescharacteristic, complemented
66C43×#332C2211yescharacteristic, complemented
67C2×#10621902—21no—
68C2×Q8×D43—21no—
69C2×D4×D43D411yescharacteristic
70C22×C4×D43—21no—
71#13063352—44no—
72C2×#10621873—21no—
73C2×#10621873—21no—
74C2×#10621884—21no—
75C2×#10621884—21no—
76C2×#10621884—21no—
77C2×D344—21no—
78C2×#10621882—21no—
79C2×#10621877—21no—
80C2×#10621872—21no—
81C2×#10621872—21no—
82C2×#10621872—21no—
83C2×C8×D43—21no—
84#13063325C2311yescharacteristic
85#13063324—21no—
86#13063324—21no—
87#13063323—21no—
88#13063322C2311yescharacteristic
89#13063314—21no—
90#13063300—21no—
91#13063300—21no—
92C4×D172C2311yescharacteristic
93D4×Dic43D411yescharacteristic
94#13063287—21no—
95#13063287—21no—
96#13063287D411yescharacteristic
97C4×C22⋊D43—21no—
98(C22⋊D43)⋊C4—21no—
99C4⋊C4×D43—21no—
100C4⋊C4×D43—21no—
101C4⋊C4×D43D411yescharacteristic
102C22⋊C4×D43—21no—
103C42×D43C2311yescharacteristic
104#13063259—21no—
105#13063258—21no—
106#13063258—21no—
107C4⋊(C43⋊C8)C2311yescharacteristic
108C4⋊(C43⋊C8)C2311yescharacteristic
109C4⋊(C43⋊C8)C2311yescharacteristic
110Dic43⋊C8—21no—
111Dic43⋊C8—21no—
112Dic43⋊C8D411yescharacteristic
113Dic43⋊C8D411yescharacteristic
114#13063249—21no—
115#13063248—21no—
116#13063248—21no—
117#13063247—21no—
118#13063247—21no—
119#13063246—21no—
120#13063245—21no—
121#13063245—21no—
122C22⋊(C43⋊C8)—21no—
123(C2×D43)⋊C8—21no—
124(C2×D43)⋊C8—21no—
125(C2×D43)⋊C8—21no—
126(C2×D43)⋊C8D411yescharacteristic
127(C2×D43)⋊C8D411yescharacteristic
128C4×C43⋊C8C2311yescharacteristic
129C8×Dic43—21no—
130C2×SD16×C43—21no—
131C2×M16×C43—21no—
132C4⋊Q8×C43C2311yescharacteristic
133C4⋊Q8×C43C2311yescharacteristic
134C4×D4×C43C2311yescharacteristic
135#107×C43—21no—
136C4⋊C8×C43C2311yescharacteristic
137C4⋊C8×C43C2311yescharacteristic
138C4⋊C8×C43C2311yescharacteristic
139#103×C43—21no—
140#103×C43—21no—
141#103×C43—21no—
142#102×C43—21no—
143C22⋊C8×C43—21no—
144C4×C8×C43C2311yescharacteristic
145C23×D43—21no—
146C2×Q8×C43—21no—
147C2×Q8×C43—21no—
148C2×D4×C43C2×D411yescharacteristic
149C22×C4×C43—21no—
150C2×C22⋊D43—21no—
151C22×Dic43—21no—
152#10621902—42no—
153#10621902—42no—
154Q8×D43—81no—
155Q8×D43—81no—
156D4×D43—22no—
157D4×D43—22no—
158C2×D172—21no—
159C2×D172—21no—
160C2×D172—21no—
161C2×D172—41no—
162C2×D172C2×D411yescharacteristic
163C2×C4×D43—21no—
164C2×C4×D43—21no—
165C2×C4×D43—21no—
166C2×C4×D43—41no—
167C2×C4×D43—41no—
168C2×C4×D43—81no—
169C2×C4×D43—81no—
170C2×C4×D43C2×D411yescharacteristic
171C2×C4×D43C2×D411yescharacteristic
172C2×C4×D43#4111yescharacteristic
173C2×Dic86—21no—
174C2×Dic86—41no—
175SD16×C43—42no—
176M16×C43—81no—
177C2×C8×C43—21no—
178C2×C8×C43—21no—
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×C43C2×D411yescharacteristic
187C22⋊C4×C43—21no—
188C42×C43C2411yescharacteristic
189C22⋊Dic43—21no—
190#10621884—42no—
191#10621884—81no—
192#10621884—81no—
193#10621882—42no—
194(C2×D43)⋊C4—21no—
195(C2×D43)⋊C4—21no—
196(C2×D43)⋊C4—41no—
197(C2×D43)⋊C4—41no—
198C4⋊Dic43—21no—
199C4⋊Dic43—21no—
200C4⋊Dic43C2×D411yescharacteristic
201Dic43⋊C4—21no—
202Dic43⋊C4—41no—
203Dic43⋊C4—41no—
204C4×Dic43C2×D411yescharacteristic
205C4×Dic43C2×D411yescharacteristic
206C4×Dic43#4111yescharacteristic
207#10621877—81no—
208C2×C43⋊C8—21no—
209C2×C43⋊C8—21no—
210C2×C43⋊C8—21no—
211C2×C43⋊C8C2×D411yescharacteristic
212C2×C43⋊C8C2×D411yescharacteristic
213D344—42no—
214#10621873—81no—
215#10621873—81no—
216#10621872—42no—
217#10621872—81no—
218#10621872—81no—
219C8×D43—42no—
220C23×C43—21no—
221C22×D43—21no—
222C22×D43—42no—
223C22×D43—41no—
224C22×D43—81no—
225C22×D43—81no—
226C22×D43#12111yescharacteristic
227Q8×C43—41no—
228Q8×C43—41no—
229Q8×C43—41no—
230Q8×C43—41no—
231D4×C43—21no—
232D4×C43—21no—
233C2×C4×C43—21no—
234C2×C4×C43—41no—
235C2×C4×C43—41no—
236C2×C4×C43—41no—
237C2×C4×C43—41no—
238C2×C4×C43C22×D411yescharacteristic
239C2×C4×C43C22×D411yescharacteristic
240C2×C4×C43C2×#4111yescharacteristic
241C22⋊D43—42no—
242C2×Dic43—21no—
243C2×Dic43—41no—
244C2×Dic43—81no—
245C2×Dic43#12111yescharacteristic
246C2×Dic43#12111yescharacteristic
247C2×Dic43#12111yescharacteristic
248D172—21no—
249D172—21no—
250D172—41no—
251D172—41no—
252D172—41no—
253D172—41no—
254D172—81no—
255D172—82no—
256C4×D43—21no—
257C4×D43—21no—
258C4×D43—41no—
259C4×D43—41no—
260C4×D43—41no—
261C4×D43—81no—
262C4×D43—81no—
263C4×D43—82no—
264C4×D43—82no—
265C4×D43AGL(1,ℤ/8)12yes—
266C4×D43#13712yes—
267Dic86—41no—
268Dic86—41no—
269Dic86—82no—
270C8×C43—21no—
271C8×C43—21no—
272C8×C43—41no—
273C8×C43—41no—
274C8×C43—41no—
275C43⋊C8—21no—
276C43⋊C8—21no—
277C43⋊C8—41no—
278C43⋊C8—41no—
279C43⋊C8—41no—
280#19421—431nomaximal, Sylow
281C22×C43—41no—
282C22×C43—41no—
283C22×C43—41no—
284C22×C43C2×#12111yescharacteristic
285C2×D43—21no—
286C2×D43—21no—
287C2×D43—41no—
288C2×D43—41no—
289C2×D43—41no—
290C2×D43—84no—
291C2×D43—81no—
292C2×D43—81no—
293C2×D43—81no—
294C2×D43#46812yes—
295C4×C43—21no—
296C4×C43—41no—
297C4×C43—81no—
298C4×C43—81no—
299C4×C43C2×AGL(1,ℤ/8)11yescharacteristic
300C4×C43C2×#13711yescharacteristic
301C4×C43#57611yescharacteristic
302C4×C43#57611yescharacteristic
303Dic43—21no—
304Dic43—21no—
305Dic43—41no—
306Dic43—81no—
307Dic43#46812yes—
308#3206—431no—
309C2×#474—431no—
310#3036—431no—
311#2975—431no—
312#1699—431no—
313#1699—431no—
314#1699—431no—
315#1699D4311yescharacteristic, complemented
316#1685—431no—
317#1685—431no—
318#1685—431no—
319#1685—431no—
320#1571—431no—
321#1549—431no—
322#1540—431no—
323C2×C43—81no—
324C2×C43#304111yescharacteristic
325C2×C43C2×#46811yescharacteristic
326C2×C43#306911yescharacteristic
327D43—22no—
328D43—81no—
329D43—161no—
330C2×AGL(1,ℤ/8)—861no—
331#532—431no—
332C2×C4⋊Q8—431no—
333C2×C4×D4—431no—
334#492—431no—
335#492—431no—
336#487—431no—
337#487C2×D4311yescharacteristic, complemented
338#474—431no—
339#474—431no—
340#474—431no—
341#474—861no—
342#474—861no—
343#474C2×D4311yescharacteristic
344#463—861no—
345#463—861no—
346#461—431no—
347#461—861no—
348#461—861no—
349#461C2×D4311yescharacteristic
350#459—431no—
351#459—431no—
352#448—861no—
353#448—861no—
354#436—431no—
355#436—431no—
356#436—431no—
357#436—861no—
358#436—861no—
359#436C2×D4311yescharacteristic
360#431—431no—
361#431—431no—
362C2×#107—861no—
363#423—431no—
364C2×C4⋊C8—431no—
365#417—861no—
366C2×#102—861no—
367#407—861no—
368#407—861no—
369#335—431no—
370#335—431no—
371#335—431no—
372#335C2×D4311yescharacteristic, complemented
373#332—431no—
374#332—431no—
375#332—431no—
376#332—431no—
377#332C2×D4311yescharacteristic, complemented
378#332C2×D4311yescharacteristic, complemented
379#331—431no—
380#331—431no—
381C43#1942111yescharacteristic, complemented, Sylow
382C2×#41—861no—
383C22×Q8—861no—
384C22×D4—431no—
385C23×C4—861no—
386AGL(1,ℤ/8)—1724no—
387C2×SD16—21no—
388C2×SD16—861no—
389C2×SD16—861no—
390C2×SD16—861no—
391C2×SD16—861no—
392C2×SD16—861no—
393C2×D8—861no—
394C2×D8—861no—
395C2×M16—21no—
396C2×M16—861no—
397C2×M16—861no—
398C2×M16—861no—
399C2×M16—861no—
400C22×C8—861no—
401C4⋊Q8—431no—
402C4⋊Q8—861no—
403C4⋊Q8—861no—
404C4⋊Q8—861no—
405C4⋊Q8C22×D4311yescharacteristic
406C4⋊Q8C22×D4311yescharacteristic
407#127—431no—
408#124—861no—
409#121—861no—
410#121—861no—
411C4×D4—431no—
412C4×D4—431no—
413C4×D4—431no—
414C4×D4—861no—
415C4×D4—861no—
416C4×D4—861no—
417C4×D4—861no—
418C4×D4C22×D4311yescharacteristic
419C2×C4⋊C4—431no—
420C2×C4⋊C4—861no—
421C2×C4⋊C4—861no—
422C2×C22⋊C4—861no—
423C2×C42—431no—
424#107—21no—
425#107—861no—
426#107—861no—
427#107—861no—
428C4⋊C8—431no—
429C4⋊C8—431no—
430C4⋊C8—431no—
431C4⋊C8—431no—
432C4⋊C8—431no—
433C4⋊C8—861no—
434C4⋊C8—861no—
435C4⋊C8C22×D4311yescharacteristic
436C4⋊C8C22×D4311yescharacteristic
437C4⋊C8C22×D4311yescharacteristic
438#103—21no—
439#103—21no—
440#103—21no—
441#103—861no—
442#103—861no—
443#103—861no—
444#102—21no—
445#102—861no—
446#102—861no—
447#102—861no—
448#102—861no—
449#102—861no—
450C22⋊C8—21no—
451C22⋊C8—431no—
452C22⋊C8—431no—
453C22⋊C8—861no—
454C22⋊C8—861no—
455C22⋊C8—861no—
456C22⋊C8—861no—
457C4×C8—431no—
458C4×C8—861no—
459C4×C8C22×D4311yescharacteristic
460C24—861no—
461#41—1722no—
462#41—1722no—
463C2×Q8—21no—
464C2×Q8—21no—
465C2×Q8—861no—
466C2×Q8—3441no—
467C2×Q8—3441no—
468C2×Q8—1721no—
469C2×D4—431no—
470C2×D4—862no—
471C2×D4—862no—
472C2×D4—861no—
473C2×D4—861no—
474C2×D4—861no—
475C2×D4—861no—
476C2×D4—1721no—
477C2×D4D4×D4311yescharacteristic
478C22×C4—21no—
479C22×C4—431no—
480C22×C4—431no—
481C22×C4—431no—
482C22×C4—861no—
483C22×C4—861no—
484C22×C4—861no—
485C22×C4—861no—
486C22×C4—3441no—
487C22×C4—3441no—
488C22×C4—1721no—
489C22×C4—1721no—
490SD16—42no—
491SD16—3441no—
492SD16—3441no—
493SD16—3441no—
494SD16—3441no—
495SD16—1722no—
496D8—1722no—
497D8—1722no—
498M16—81no—
499M16—3441no—
500M16—3441no—
501M16—3441no—
502M16—1722no—
503C2×C8—21no—
504C2×C8—21no—
505C2×C8—21no—
506C2×C8—431no—
507C2×C8—431no—
508C2×C8—861no—
509C2×C8—861no—
510C2×C8—861no—
511C2×C8—1722no—
512C2×C8D4×D4311yescharacteristic
513C2×C8D4×D4311yescharacteristic
514C4⋊C4—21no—
515C4⋊C4—21no—
516C4⋊C4—21no—
517C4⋊C4—21no—
518C4⋊C4—431no—
519C4⋊C4—861no—
520C4⋊C4—861no—
521C4⋊C4—861no—
522C4⋊C4—1721no—
523C4⋊C4—1721no—
524C4⋊C4D4×D4311yescharacteristic
525C22⋊C4—21no—
526C22⋊C4—861no—
527C22⋊C4—861no—
528C22⋊C4—861no—
529C22⋊C4—1721no—
530C22⋊C4—1721no—
531C42—431no—
532C42—431no—
533C42—431no—
534C42C23×D4311yescharacteristic
535C23—21no—
536C23—431no—
537C23—861no—
538C23—3441no—
539C23—3441no—
540C23—1722no—
541C23—1721no—
542Q8—41no—
543Q8—41no—
544Q8—41no—
545Q8—41no—
546Q8—3442no—
547Q8—1721no—
548Q8—1721no—
549D4—21no—
550D4—21no—
551D4—861no—
552D4—861no—
553D4—3441no—
554D4—3442no—
555D4—1722no—
556D4—1721no—
557D4—1721no—
558D4—1721no—
559D4—1721no—
560C2×C4—21no—
561C2×C4—41no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—431no—
566C2×C4—432no—
567C2×C4—432no—
568C2×C4—431no—
569C2×C4—431no—
570C2×C4—861no—
571C2×C4—861no—
572C2×C4—861no—
573C2×C4—3441no—
574C2×C4—3441no—
575C2×C4—3442no—
576C2×C4—3442no—
577C2×C4—3441no—
578C2×C4—1721no—
579C2×C4—1721no—
580C2×C4—1721no—
581C2×C4—1721no—
582C2×C4C2×D4×D4311yescharacteristic
583C2×C4C2×D4×D4311yescharacteristic
584C2×C4#41×D4311yescharacteristic
585C8—21no—
586C8—21no—
587C8—41no—
588C8—41no—
589C8—41no—
590C8—861no—
591C8—861no—
592C8—1721no—
593C8—1721no—
594C8—1721no—
595C22—41no—
596C22—41no—
597C22—41no—
598C22—432no—
599C22—861no—
600C22—861no—
601C22—3444no—
602C22—3441no—
603C22—3441no—
604C22—3441no—
605C22—1721no—
606C22—1721no—
607C22—1721no—
608C22#121×D4311yescharacteristic
609C4—21no—
610C4—41no—
611C4—81no—
612C4—81no—
613C4—432no—
614C4—861no—
615C4—861no—
616C4—3441no—
617C4—1721no—
618C4AGL(1,ℤ/8)×D4311yescharacteristic
619C4#137×D4311yescharacteristic
620C4#1458370111yescharacteristic
621C4#1458370311yescharacteristic
622C2—81no—
623C2—862no—
624C2—3441no—
625C2—6881no—
626C2#1914409611yescharacteristic
627C2#468×D4311yescharacteristic
628C2#1914433011yescharacteristic
subgroupG/H
centerC22#121×D43
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#1699C2
socleC22×C43C2×#121
prime radical#19144060C2
hypercenter#1699D43
hypocenterC43#19421
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #1699

Complements

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

NH ≅ G/Ntype
1. #19145521C2semidirect
2. #474×D43C2semidirect
4. #19143633C2semidirect
5. #19134145C2semidirect
6. #19134144C2semidirect
7. #19134139C2semidirect
8. #19134063C2semidirect
9. #19134062C2semidirect
10. #19134061C2semidirect
11. #19134060C2semidirect
12. #19133368C2semidirect
13. #19133278C2semidirect
14. #19133243C2semidirect
15. C43×#1699C2semidirect
20. #14583273C22semidirect
21. #14583272C22semidirect
22. #14583251C22semidirect
51. #14582652C22semidirect
52. #14582651C22semidirect
53. #14582651C22semidirect
54. #14582646C22semidirect
55. #14582645C22semidirect
56. #14582645C22semidirect
57. #14582644C22semidirect
58. #14582642C22semidirect
59. #14582642C22semidirect
60. C43×#487C22semidirect
64. C43×#335C22semidirect
65. C43×#332C22semidirect
66. C43×#332C22semidirect
315. #1699D43semidirect
337. #487C2×D43semidirect
372. #335C2×D43semidirect
377. #332C2×D43semidirect
378. #332C2×D43semidirect
381. C43#19421semidirect

Maximal subgroups

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

subgroupindex
#191455212
#474×D432
#191440602
#191436332
#191341452
#191341442
#191341392
#191340632
#191340622
#191340612
#191340602
#191333682
#191332782
#191332432
C43×#16992
#1942143