Finite Group Databasebeta

← #25087971

Subgroups — #25087971

Order 11008.

720 conjugacy classes of subgroups.

The subgroup lattice has 638 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19147576C211yesmaximal, characteristic, complemented
2#19147514C211yesmaximal, characteristic, complemented
3D4×#10621883C211yesmaximal, characteristic, complemented
4#19134184C211yesmaximal, characteristic, complemented
5#19134108C211yesmaximal, characteristic, complemented
6#19134076C211yesmaximal, characteristic, complemented
7#19133941C211yesmaximal, characteristic, complemented
8#19133934C211yesmaximal, characteristic, complemented
9#19133795C211yesmaximal, characteristic, complemented
10#19133774C211yesmaximal, characteristic, complemented
11#19133697C211yesmaximal, characteristic, complemented
12#19133690C211yesmaximal, characteristic, complemented
13#19133483C211yesmaximal, characteristic, complemented
14SD16×C43⋊C8C211yesmaximal, characteristic, complemented
15C43×#3274C211yesmaximal, characteristic
16C22×#10621883—21no—
17#14583628C2211yescharacteristic, complemented
18D4×Dic86C2211yescharacteristic
19#14583306—21no—
20#14583304C2211yescharacteristic, complemented
21#14583271—21no—
22#14583271C2211yescharacteristic
23#14583271C2211yescharacteristic, complemented
24#14583245C2211yescharacteristic
25#14583245C2211yescharacteristic, complemented
26#14583197—21no—
27#14583192—21no—
28#14583184C2211yescharacteristic, complemented
29#14583179C2211yescharacteristic
30#14583126—21no—
31#14583104—21no—
32#14583104C2211yescharacteristic
33#14583104C2211yescharacteristic
34#14583096—21no—
35#14583096C2211yescharacteristic
36#14583096C2211yescharacteristic, complemented
37#14583050—21no—
38#14583037—21no—
39#14583029C2211yescharacteristic, complemented
40Q8×C43⋊C8C2211yescharacteristic, complemented
41#14583000—21no—
42C4×#10621883—21no—
43C4×#10621883C2211yescharacteristic
44D4×C43⋊C8C2211yescharacteristic
45#14582650C2211yescharacteristic, complemented
46#14582649C2211yescharacteristic, complemented
47#14582644C2211yescharacteristic, complemented
48#14582644C2211yescharacteristic, complemented
49#14582643C2211yescharacteristic
50#14582643C2211yescharacteristic, complemented
51Q8⋊(C43⋊C8)C2211yescharacteristic, complemented
52#14582629C2211yescharacteristic, complemented
53D4⋊(C43⋊C8)C2211yescharacteristic
54D4⋊(C43⋊C8)C2211yescharacteristic
55C8×C43⋊C8C2211yescharacteristic, complemented
56C2×AGL(1,ℤ/8)×C43—21no—
57C43×#550C2211yescharacteristic
58D42×C43C2211yescharacteristic
59C43×#493C2211yescharacteristic
60C43×#469—21no—
61C43×#460C2211yescharacteristic
62C43×#459C2211yescharacteristic
63C43×#449—21no—
64C43×#447—21no—
65C4×SD16×C43C2211yescharacteristic
66C43×#436C2211yescharacteristic
67C22×Dic86—21no—
68C2×#10621883—21no—
69C2×#10621883—21no—
70C2×#10621883—21no—
71C2×#10621883—21no—
72C2×#10621883—21no—
73C2×#10621883—21no—
74C2×#10621883—21no—
75C2×#10621883—21no—
76C2×#10621883—44no—
77C2×#10621883D411yescharacteristic
78C22×C43⋊C8—21no—
79#13063325—21no—
80#13063325C2311yescharacteristic
81#13063325C2311yescharacteristic
82#13063324—21no—
83#13063316—21no—
84#13063316—41no—
85#13063304—21no—
86#13063302—41no—
87Q8×Dic43—21no—
88C4×Dic86—21no—
89C4×Dic86C2311yescharacteristic
90D4×Dic43—21no—
91#13063259—21no—
92#13063259—21no—
93#13063258—21no—
94#13063256—21no—
95#13063256D411yescharacteristic
96C4⋊(C43⋊C8)—21no—
97C4⋊(C43⋊C8)C2311yescharacteristic
98C4⋊(C43⋊C8)C2311yescharacteristic
99C4⋊(C43⋊C8)C2311yescharacteristic
100Dic43⋊C8—21no—
101#13063249—21no—
102#13063248—21no—
103#13063248—21no—
104#13063248D411yescharacteristic
105#13063246—21no—
106#13063246—21no—
107#13063246—21no—
108#13063246—41no—
109#13063246—41no—
110#13063246D411yescharacteristic
111C22⋊(C43⋊C8)—21no—
112#13063235—21no—
113C4×C43⋊C8—21no—
114C4×C43⋊C8C2311yescharacteristic
115C4×C43⋊C8C2311yescharacteristic
116C2×#41×C43—21no—
117C22×D4×C43—21no—
118C22×D4×C43—21no—
119AGL(1,ℤ/8)×C43—44no—
120C2×SD16×C43—21no—
121C2×SD16×C43D411yescharacteristic
122C2×D8×C43—21no—
123C2×D8×C43—21no—
124C2×D8×C43—21no—
125C2×M16×C43—21no—
126#127×C43—21no—
127#127×C43C2311yescharacteristic
128#127×C43C2311yescharacteristic
129#121×C43—21no—
130#121×C43—21no—
131#121×C43—21no—
132#121×C43—41no—
133#120×C43—41no—
134C4×Q8×C43C2311yescharacteristic
135C4×D4×C43—21no—
136C4×D4×C43C2311yescharacteristic
137C4×D4×C43C2311yescharacteristic
138#106×C43D411yescharacteristic
139C4⋊C8×C43C2311yescharacteristic
140#103×C43D411yescharacteristic
141#102×C43—21no—
142#102×C43—21no—
143#102×C43D411yescharacteristic
144C22⋊C8×C43—21no—
145C4×C8×C43C2311yescharacteristic
146C24×C43—41no—
147#41×C43—42no—
148#41×C43—81no—
149C2×Q8×C43C2×D411yescharacteristic
150C2×D4×C43—21no—
151C2×D4×C43—21no—
152C2×D4×C43—21no—
153C2×D4×C43—21no—
154C2×D4×C43—21no—
155C2×D4×C43—21no—
156C2×D4×C43—41no—
157C2×D4×C43—41no—
158C2×D4×C43—41no—
159C2×D4×C43—41no—
160C2×D4×C43—42no—
161C2×D4×C43—42no—
162C2×D4×C43—81no—
163C2×D4×C43—81no—
164C2×D4×C43C2×D411yescharacteristic
165C2×D4×C43C2×D411yescharacteristic
166C22×C4×C43—21no—
167C22×C4×C43—21no—
168C22×C4×C43—41no—
169C22×Dic43—41no—
170C2×Dic86—21no—
171C2×Dic86—21no—
172C2×Dic86—42no—
173C2×Dic86—41no—
174C2×Dic86—81no—
175C2×Dic86C2×D411yescharacteristic
176SD16×C43—42no—
177SD16×C43SD1614yescomplemented
178D8×C43—42no—
179D8×C43—42no—
180D8×C43—81no—
181M16×C43—42no—
182C2×C8×C43—21no—
183C2×C8×C43C2×D411yescharacteristic
184C2×C8×C43C2×D411yescharacteristic
185C4⋊C4×C43—21no—
186C4⋊C4×C43C2×D411yescharacteristic
187C4⋊C4×C43C2×D411yescharacteristic
188C4⋊C4×C43C2×D411yescharacteristic
189C22⋊C4×C43—21no—
190C22⋊C4×C43—21no—
191C22⋊C4×C43—41no—
192C22⋊C4×C43—41no—
193C42×C43—21no—
194C42×C43C2411yescharacteristic
195C22⋊Dic43—41no—
196#10621883—22no—
197#10621883—42no—
198#10621883—42no—
199#10621883—42no—
200#10621883—42no—
201#10621883—81no—
202#10621883—81no—
203#10621883—81no—
204#10621883—81no—
205C4⋊Dic43—21no—
206C4⋊Dic43—21no—
207C4⋊Dic43—21no—
208C4⋊Dic43—21no—
209C4⋊Dic43—41no—
210C4⋊Dic43—41no—
211C4⋊Dic43C2×D411yescharacteristic
212Dic43⋊C4—21no—
213Dic43⋊C4—41no—
214Dic43⋊C4—41no—
215C4×Dic43—21no—
216C4×Dic43—41no—
217C2×C43⋊C8—21no—
218C2×C43⋊C8—21no—
219C2×C43⋊C8—21no—
220C2×C43⋊C8—21no—
221C2×C43⋊C8—42no—
222C2×C43⋊C8C2×D411yescharacteristic
223C2×C43⋊C8C2×D411yescharacteristic
224C23×C43—21no—
225C23×C43—21no—
226C23×C43—41no—
227C23×C43—41no—
228C23×C43—82no—
229C23×C43—82no—
230C23×C43—161no—
231Q8×C43—21no—
232Q8×C43C2×SD1612yescomplemented
233D4×C43—21no—
234D4×C43—21no—
235D4×C43—21no—
236D4×C43—41no—
237D4×C43—41no—
238D4×C43—41no—
239D4×C43—41no—
240D4×C43—41no—
241D4×C43—41no—
242D4×C43—41no—
243D4×C43—41no—
244D4×C43—82no—
245D4×C43—81no—
246D4×C43—81no—
247D4×C43—82no—
248D4×C43—82no—
249D4×C43—161no—
250D4×C43C2×SD1612yes—
251C2×C4×C43—21no—
252C2×C4×C43—21no—
253C2×C4×C43—21no—
254C2×C4×C43—21no—
255C2×C4×C43—41no—
256C2×C4×C43—41no—
257C2×C4×C43—41no—
258C2×C4×C43—41no—
259C2×C4×C43—82no—
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—82no—
268Dic86—21no—
269Dic86—21no—
270Dic86—41no—
271Dic86—41no—
272Dic86—41no—
273Dic86—41no—
274Dic86—82no—
275C8×C43—21no—
276C8×C43—41no—
277C8×C43C2×SD1612yescomplemented
278C43⋊C8—21no—
279C43⋊C8—41no—
280C43⋊C8—41no—
281C43⋊C8—41no—
282C43⋊C8—41no—
283C43⋊C8AGL(1,ℤ/8)12yescomplemented
284#19892—431nomaximal, Sylow
285C22×C43—22no—
286C22×C43—41no—
287C22×C43—41no—
288C22×C43—41no—
289C22×C43—41no—
290C22×C43—41no—
291C22×C43—81no—
292C22×C43—81no—
293C22×C43—81no—
294C22×C43—81no—
295C22×C43—81no—
296C22×C43—81no—
297C22×C43—164no—
298C22×C43D4211yescharacteristic
299C4×C43—22no—
300C4×C43—21no—
301C4×C43—41no—
302C4×C43—41no—
303C4×C43—41no—
304C4×C43C22×SD1611yescharacteristic
305C4×C43C2×AGL(1,ℤ/8)11yescharacteristic
306C4×C43#57611yescharacteristic
307C4×C43#57711yescharacteristic
308Dic43—41no—
309Dic43—41no—
310Dic43—81no—
311Dic43—81no—
312#3392—431no—
313#3386—431no—
314D4×SD16—431no—
315#3274D4311yescharacteristic
316#1706—431no—
317#1693—431no—
318#1688—431no—
319#1666—431no—
320#1665—431no—
321#1642—431no—
322#1639—431no—
323#1627—431no—
324#1626—431no—
325#1590—431no—
326C8×SD16—431no—
327C2×C43—42no—
328C2×C43—81no—
329C2×C43—161no—
330C2×C43—161no—
331C2×C43#327411yescharacteristic
332C2×C43D4×SD1611yescharacteristic
333C2×C43#329011yescharacteristic
334C2×AGL(1,ℤ/8)—21no—
335C22×SD16—861no—
336#557—431no—
337#550C2×D4311yescharacteristic
338D4×Q8—431no—
339D42C2×D4311yescharacteristic
340#501—861no—
341#500—431no—
342#493C2×D4311yescharacteristic
343#492—431no—
344#492—431no—
345#492—861no—
346#486—431no—
347#486—431no—
348#478—861no—
349#477—861no—
350#475—431no—
351#474—431no—
352#469—21no—
353#465—861no—
354#461—431no—
355#461—431no—
356#461—861no—
357#460—431no—
358#460—431no—
359#460—861no—
360#460C2×D4311yescharacteristic
361#459C2×D4311yescharacteristic
362#450—861no—
363#449—21no—
364#448—861no—
365#447—21no—
366#446—431no—
367C8×Q8—431no—
368#440—861no—
369C4×SD16—431no—
370C4×SD16—861no—
371C4×SD16C2×D4311yescharacteristic
372#436C2×D4311yescharacteristic
373C8×D4—431no—
374#334—431no—
375#334—431no—
376#332—431no—
377#332—431no—
378#331—431no—
379#331—431no—
380Q8⋊C8—431no—
381Q8⋊C8—431no—
382D4⋊C8—431no—
383D4⋊C8—431no—
384C82—431no—
385C43#1989211yescharacteristic, complemented, Sylow
386C2×#41—21no—
387C22×Q8—861no—
388C22×D4—21no—
389C22×D4—21no—
390AGL(1,ℤ/8)—44no—
391C2×SD16—21no—
392C2×SD16—431no—
393C2×SD16—861no—
394C2×SD16—861no—
395C2×SD16—861no—
396C2×SD16—861no—
397C2×SD16—861no—
398C2×SD16—861no—
399C2×SD16—861no—
400C2×SD16—861no—
401C2×SD16—1724no—
402C2×SD16C22⋊D4311yescharacteristic
403C2×D8—21no—
404C2×D8—21no—
405C2×D8—21no—
406C2×M16—21no—
407C22×C8—861no—
408C4⋊Q8—431no—
409C4⋊Q8—431no—
410C4⋊Q8—861no—
411C4⋊Q8—861no—
412#127—21no—
413#127C22×D4311yescharacteristic
414#127C22×D4311yescharacteristic
415#125—861no—
416#125—1721no—
417C22⋊Q8—861no—
418C22⋊Q8—1721no—
419#121—21no—
420#121—21no—
421#121—21no—
422#121—41no—
423#120—41no—
424C4×Q8—431no—
425C4×Q8—861no—
426C4×Q8—861no—
427C4×Q8C22×D4311yescharacteristic
428C4×D4—21no—
429C4×D4—861no—
430C4×D4C22×D4311yescharacteristic
431C4×D4C22×D4311yescharacteristic
432#107—861no—
433#107—861no—
434#107—861no—
435#106—431no—
436#106—861no—
437#106C22⋊D4311yescharacteristic
438C4⋊C8—431no—
439C4⋊C8—431no—
440C4⋊C8—431no—
441C4⋊C8—861no—
442C4⋊C8—861no—
443C4⋊C8C22×D4311yescharacteristic
444#103—431no—
445#103—861no—
446#103—861no—
447#103—861no—
448#103C22⋊D4311yescharacteristic
449#102—21no—
450#102—21no—
451#102—431no—
452#102—861no—
453#102—861no—
454#102—861no—
455#102—1721no—
456#102—1721no—
457#102C22⋊D4311yescharacteristic
458C22⋊C8—21no—
459C22⋊C8—861no—
460#97—861no—
461C4×C8—431no—
462C4×C8—431no—
463C4×C8—861no—
464C4×C8C22×D4311yescharacteristic
465C24—41no—
466#41—42no—
467#41—81no—
468C2×Q8—431no—
469C2×Q8—861no—
470C2×Q8—861no—
471C2×Q8—3441no—
472C2×Q8—1721no—
473C2×Q8—1722no—
474C2×Q8C2×C22⋊D4311yescharacteristic
475C2×D4—21no—
476C2×D4—21no—
477C2×D4—21no—
478C2×D4—21no—
479C2×D4—21no—
480C2×D4—21no—
481C2×D4—41no—
482C2×D4—41no—
483C2×D4—41no—
484C2×D4—41no—
485C2×D4—42no—
486C2×D4—42no—
487C2×D4—81no—
488C2×D4—81no—
489C2×D4D4×D4311yescharacteristic
490C2×D4C2×C22⋊D4311yescharacteristic
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—41no—
494C22×C4—1721no—
495SD16—42no—
496SD16—862no—
497SD16—3441no—
498SD16—3441no—
499SD16—3441no—
500SD16—3441no—
501SD16—1722no—
502SD16—1722no—
503SD16—1722no—
504SD16—1722no—
505SD16#1062188314yescomplemented
506D8—42no—
507D8—42no—
508D8—81no—
509M16—42no—
510C2×C8—21no—
511C2×C8—431no—
512C2×C8—431no—
513C2×C8—861no—
514C2×C8—861no—
515C2×C8—861no—
516C2×C8—861no—
517C2×C8—1722no—
518C2×C8C2×C22⋊D4311yescharacteristic
519C2×C8C2×C22⋊D4311yescharacteristic
520C4⋊C4—21no—
521C4⋊C4—431no—
522C4⋊C4—861no—
523C4⋊C4—861no—
524C4⋊C4—861no—
525C4⋊C4—861no—
526C4⋊C4—861no—
527C4⋊C4—1721no—
528C4⋊C4—1721no—
529C4⋊C4—1721no—
530C4⋊C4—1721no—
531C4⋊C4D4×D4311yescharacteristic
532C4⋊C4C2×C22⋊D4311yescharacteristic
533C4⋊C4C2×C22⋊D4311yescharacteristic
534C22⋊C4—21no—
535C22⋊C4—21no—
536C22⋊C4—41no—
537C22⋊C4—41no—
538C22⋊C4—1721no—
539C42—21no—
540C42—861no—
541C42—1721no—
542C42C23×D4311yescharacteristic
543C23—21no—
544C23—21no—
545C23—41no—
546C23—41no—
547C23—82no—
548C23—82no—
549C23—161no—
550Q8—21no—
551Q8—861no—
552Q8—861no—
553Q8—3442no—
554Q8—1721no—
555Q8—1721no—
556Q8—1721no—
557Q8—1721no—
558Q8C2×#1062188312yescomplemented
559D4—21no—
560D4—21no—
561D4—21no—
562D4—41no—
563D4—41no—
564D4—41no—
565D4—41no—
566D4—41no—
567D4—41no—
568D4—41no—
569D4—41no—
570D4—82no—
571D4—81no—
572D4—81no—
573D4—82no—
574D4—82no—
575D4—161no—
576D4C2×#1062188312yes—
577C2×C4—21no—
578C2×C4—21no—
579C2×C4—21no—
580C2×C4—21no—
581C2×C4—41no—
582C2×C4—41no—
583C2×C4—41no—
584C2×C4—41no—
585C2×C4—82no—
586C2×C4—861no—
587C2×C4—861no—
588C2×C4—3442no—
589C2×C4—1721no—
590C2×C4—1721no—
591C2×C4C2×D4×D4311yescharacteristic
592C2×C4C22×C22⋊D4311yescharacteristic
593C2×C4#1306337011yescharacteristic
594C8—21no—
595C8—41no—
596C8—432no—
597C8—861no—
598C8—1721no—
599C8—1721no—
600C8—1721no—
601C8—1721no—
602C8C2×#1062188312yescomplemented
603C22—22no—
604C22—41no—
605C22—41no—
606C22—41no—
607C22—41no—
608C22—41no—
609C22—81no—
610C22—81no—
611C22—81no—
612C22—81no—
613C22—81no—
614C22—81no—
615C22—164no—
616C22D4×C22⋊D4311yescharacteristic
617C4—22no—
618C4—21no—
619C4—41no—
620C4—41no—
621C4—41no—
622C4—3441no—
623C4—3441no—
624C4—1721no—
625C4—1721no—
626C4C22×#1062188311yescharacteristic
627C4AGL(1,ℤ/8)×D4311yescharacteristic
628C4#1458370311yescharacteristic
629C4#1458371011yescharacteristic
630C2—42no—
631C2—81no—
632C2—161no—
633C2—161no—
634C2#1914620911yescharacteristic
635C2D4×#1062188311yescharacteristic
636C2#1914637711yescharacteristic
subgroupG/H
centerC22D4×C22⋊D43
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
Fitting, prime radicalC43×#3274C2
socleC22×C43D42
hypercenter#3274D43
hypocenterC43#19892
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #3274

Complements

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

NH ≅ G/Ntype
1. #19147576C2semidirect
2. #19147514C2semidirect
3. D4×#10621883C2semidirect
4. #19134184C2semidirect
5. #19134108C2semidirect
6. #19134076C2semidirect
7. #19133941C2semidirect
8. #19133934C2semidirect
9. #19133795C2semidirect
10. #19133774C2semidirect
11. #19133697C2semidirect
12. #19133690C2semidirect
13. #19133483C2semidirect
14. SD16×C43⋊C8C2semidirect
17. #14583628C22semidirect
20. #14583304C22semidirect
23. #14583271C22semidirect
25. #14583245C22semidirect
28. #14583184C22semidirect
36. #14583096C22semidirect
39. #14583029C22semidirect
40. Q8×C43⋊C8C22semidirect
45. #14582650C22semidirect
46. #14582649C22semidirect
47. #14582644C22semidirect
48. #14582644C22semidirect
50. #14582643C22semidirect
51. Q8⋊(C43⋊C8)C22semidirect
52. #14582629C22semidirect
55. C8×C43⋊C8C22semidirect
177. SD16×C43SD16semidirect
232. Q8×C43C2×SD16semidirect
277. C8×C43C2×SD16semidirect
283. C43⋊C8AGL(1,ℤ/8)semidirect
385. C43#19892semidirect
505. SD16#10621883semidirect
558. Q8C2×#10621883semidirect
602. C8C2×#10621883semidirect

Maximal subgroups

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

subgroupindex
#191475762
#191475142
D4×#106218832
#191341842
#191341082
#191340762
#191339412
#191339342
#191337952
#191337742
#191336972
#191336902
#191334832
SD16×C43⋊C82
C43×#32742
#1989243