Finite Group Databasebeta

← #25087972

Subgroups — #25087972

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#19147512C211yesmaximal, characteristic, complemented
2SD16×D172C211yesmaximal, characteristic, complemented
3#19146215C211yesmaximal, characteristic
4#19134185C211yesmaximal, characteristic, complemented
5#19134106C211yesmaximal, characteristic, complemented
6#19134077C211yesmaximal, characteristic, complemented
7#19133943C211yesmaximal, characteristic, complemented
8#19133933C211yesmaximal, characteristic, complemented
9#19133795C211yesmaximal, characteristic, complemented
10#19133772C211yesmaximal, characteristic, complemented
11#19133696C211yesmaximal, characteristic, complemented
12#19133691C211yesmaximal, characteristic, complemented
13#19133486C211yesmaximal, characteristic, complemented
14C8×#10621884C211yesmaximal, characteristic, complemented
15C43×#3392C211yesmaximal, characteristic, complemented
16C2×#13063350—21no—
17C2×SD16×D43—21no—
18Q8×D172C2211yescharacteristic
19D4×D172C2211yescharacteristic
20#14583309—21no—
21#14583302C2211yescharacteristic, complemented
22#14583275C2211yescharacteristic
23#14583272C2211yescharacteristic
24#14583247C2211yescharacteristic
25#14583245C2211yescharacteristic, complemented
26#14583196—21no—
27#14583194—21no—
28#14583184C2211yescharacteristic, complemented
29#14583176C2211yescharacteristic
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—
40#14583030C2211yescharacteristic, complemented
41#14582997—21no—
42C4×#10621884C2211yescharacteristic
43#14582977C2211yescharacteristic
44C8×D172C2211yescharacteristic
45#14582650C2211yescharacteristic, complemented
46#14582649C2211yescharacteristic, complemented
47#14582646C2211yescharacteristic, 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
55C8×C43⋊C8C2211yescharacteristic, 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
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×#10621884D411yescharacteristic
77SD16×D43—44no—
78C2×#10621882—21no—
79C2×#10621882—21no—
80C2×#10621882—21no—
81C2×#10621877—21no—
82C2×C8×D43—21no—
83#13063325—21no—
84#13063325C2311yescharacteristic
85#13063322C2311yescharacteristic
86#13063305—21no—
87#13063305—41no—
88#13063300—21no—
89#13063299—21no—
90#13063295—41no—
91C4×D172—21no—
92C4×D172C2311yescharacteristic
93#13063258—21no—
94#13063258—21no—
95#13063258—21no—
96#13063256—21no—
97#13063256D411yescharacteristic
98C4⋊(C43⋊C8)—21no—
99C4⋊(C43⋊C8)C2311yescharacteristic
100C4⋊(C43⋊C8)C2311yescharacteristic
101C4⋊(C43⋊C8)C2311yescharacteristic
102#13063249—21no—
103#13063249D411yescharacteristic
104#13063248—21no—
105#13063246—21no—
106#13063246—41no—
107#13063245—21no—
108#13063245—21no—
109#13063245—21no—
110#13063245—41no—
111#13063245D411yescharacteristic
112C22⋊(C43⋊C8)—21no—
113(C2×D43)⋊C8—21no—
114#13063236—21no—
115C4×C43⋊C8C2311yescharacteristic
116C4×C43⋊C8C2311yescharacteristic
117C2×#41×C43—21no—
118C2×SD16×C43—21no—
119C2×SD16×C43—21no—
120C2×SD16×C43—21no—
121C2×SD16×C43—21no—
122C2×SD16×C43D411yescharacteristic
123C4⋊Q8×C43—21no—
124C4⋊Q8×C43C2311yescharacteristic
125#127×C43—21no—
126#127×C43C2311yescharacteristic
127#125×C43—21no—
128#125×C43—41no—
129#121×C43—21no—
130#121×C43—41no—
131C4×Q8×C43—21no—
132C4×Q8×C43—21no—
133C4×Q8×C43C2311yescharacteristic
134C4×Q8×C43C2311yescharacteristic
135C4×D4×C43—21no—
136C4×D4×C43C2311yescharacteristic
137#106×C43D411yescharacteristic
138C4⋊C8×C43—21no—
139C4⋊C8×C43C2311yescharacteristic
140#103×C43—21no—
141#103×C43D411yescharacteristic
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×C43C2×D411yescharacteristic
151C2×Q8×C43C2×D411yescharacteristic
152C2×D4×C43—21no—
153C2×D4×C43—21no—
154C2×D4×C43—21no—
155C2×D4×C43—41no—
156C2×D4×C43—41no—
157C2×D4×C43C2×D411yescharacteristic
158C22×C4×C43—21no—
159C22×C4×C43—41no—
160C2×C22⋊D43—41no—
161Q8×D43—42no—
162Q8×D43—81no—
163D4×D43—42no—
164D4×D43—81no—
165C2×D172—21no—
166C2×D172—21no—
167C2×D172—21no—
168C2×D172—41no—
169C2×D172—42no—
170C2×D172—81no—
171C2×D172C2×D411yescharacteristic
172C2×C4×D43—21no—
173C2×C4×D43—41no—
174C2×Dic86—21no—
175C2×Dic86—41no—
176SD16×C43—22no—
177SD16×C43—42no—
178SD16×C43—81no—
179SD16×C43—81no—
180SD16×C43—81no—
181C2×C8×C43—21no—
182C2×C8×C43C2×D411yescharacteristic
183C2×C8×C43C2×D411yescharacteristic
184C4⋊C4×C43—21no—
185C4⋊C4×C43—21no—
186C4⋊C4×C43—21no—
187C4⋊C4×C43—21no—
188C4⋊C4×C43—41no—
189C4⋊C4×C43—41no—
190C4⋊C4×C43—41no—
191C4⋊C4×C43C2×D411yescharacteristic
192C4⋊C4×C43C2×D411yescharacteristic
193C4⋊C4×C43C2×D411yescharacteristic
194C22⋊C4×C43—21no—
195C22⋊C4×C43—41no—
196C42×C43—21no—
197C42×C43—21no—
198C42×C43—41no—
199C42×C43C2411yescharacteristic
200#10621884—42no—
201#10621884—42no—
202#10621884SD1614yescomplemented
203#10621883—42no—
204#10621882—42no—
205#10621882—42no—
206#10621882—81no—
207(C2×D43)⋊C4—21no—
208(C2×D43)⋊C4—41no—
209(C2×D43)⋊C4—41no—
210C4⋊Dic43—21no—
211C4⋊Dic43—21no—
212C4⋊Dic43—41no—
213C4⋊Dic43C2×D411yescharacteristic
214#10621877—42no—
215C2×C43⋊C8—21no—
216C2×C43⋊C8—21no—
217C2×C43⋊C8—21no—
218C2×C43⋊C8—21no—
219C2×C43⋊C8C2×D411yescharacteristic
220C2×C43⋊C8C2×D411yescharacteristic
221#10621873—42no—
222#10621873—81no—
223C8×D43—42no—
224C23×C43—21no—
225C23×C43—41no—
226C22×D43—21no—
227C22×D43—41no—
228C22×D43—82no—
229C22×D43—82no—
230C22×D43—161no—
231Q8×C43—21no—
232Q8×C43—21no—
233Q8×C43—21no—
234Q8×C43—41no—
235Q8×C43—41no—
236Q8×C43C2×SD1612yescomplemented
237D4×C43—21no—
238D4×C43—21no—
239D4×C43—41no—
240D4×C43—41no—
241D4×C43—41no—
242D4×C43—41no—
243D4×C43—82no—
244D4×C43—81no—
245D4×C43—161no—
246C2×C4×C43—21no—
247C2×C4×C43—21no—
248C2×C4×C43—21no—
249C2×C4×C43—21no—
250C2×C4×C43—21no—
251C2×C4×C43—41no—
252C2×C4×C43—41no—
253C2×C4×C43—41no—
254C2×C4×C43—82no—
255C2×C4×C43C22×D411yescharacteristic
256C2×C4×C43C22×D411yescharacteristic
257C2×C4×C43H(5,𝔽2)11yescharacteristic
258C22⋊D43—82no—
259C2×Dic43—21no—
260C2×Dic43—41no—
261D172—21no—
262D172—41no—
263D172—41no—
264D172—41no—
265D172—41no—
266D172—81no—
267D172—82no—
268D172C2×SD1612yes—
269C4×D43—41no—
270C4×D43—41no—
271C4×D43—82no—
272Dic86—41no—
273Dic86—41no—
274Dic86—82no—
275C8×C43—21no—
276C8×C43—41no—
277C8×C43AGL(1,ℤ/8)12yescomplemented
278C43⋊C8—21no—
279C43⋊C8—41no—
280C43⋊C8—41no—
281C43⋊C8—41no—
282C43⋊C8—41no—
283C43⋊C8C2×SD1612yescomplemented
284#19892—431nomaximal, Sylow
285C22×C43—41no—
286C22×C43—41no—
287C22×C43—41no—
288C22×C43—81no—
289C22×C43—81no—
290C22×C43—81no—
291C22×C43D4211yescharacteristic
292C2×D43—22no—
293C2×D43—41no—
294C2×D43—41no—
295C2×D43—81no—
296C2×D43—81no—
297C2×D43—81no—
298C2×D43—164no—
299C4×C43—22no—
300C4×C43—21no—
301C4×C43—41no—
302C4×C43—41no—
303C4×C43—41no—
304C4×C43—41no—
305C4×C43—81no—
306C4×C43C22×SD1611yescharacteristic
307C4×C43C2×AGL(1,ℤ/8)11yescharacteristic
308C4×C43#57611yescharacteristic
309C4×C43#57711yescharacteristic
310Dic43—41no—
311Dic43—81no—
312#3392D4311yescharacteristic, complemented
313#3386—431no—
314D4×SD16—431no—
315#3274—431no—
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—81no—
328C2×C43—161no—
329C2×C43#327411yescharacteristic
330C2×C43D4×SD1611yescharacteristic
331C2×C43#329011yescharacteristic
332D43—42no—
333D43—161no—
334C2×AGL(1,ℤ/8)—861no—
335C22×SD16—861no—
336#557C2×D4311yescharacteristic, complemented
337#550C2×D4311yescharacteristic
338D4×Q8—431no—
339D42—431no—
340#501—861no—
341#500—431no—
342#493—431no—
343#492—21no—
344#492—431no—
345#492C2×D4311yescharacteristic, complemented
346#486—431no—
347#486—431no—
348#478—861no—
349#477—861no—
350#475—431no—
351#474—431no—
352#469—861no—
353#465—861no—
354#461—21no—
355#461—431no—
356#461C2×D4311yescharacteristic
357#460—21no—
358#460—431no—
359#460—431no—
360#460C2×D4311yescharacteristic, complemented
361#459—431no—
362#450—861no—
363#449—861no—
364#448—861no—
365#447—861no—
366#446—431no—
367C8×Q8C2×D4311yescharacteristic, complemented
368#440—861no—
369C4×SD16—21no—
370C4×SD16—431no—
371C4×SD16C2×D4311yescharacteristic
372#436—431no—
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—861no—
389C22×D4—861no—
390AGL(1,ℤ/8)—1724no—
391C2×SD16—21no—
392C2×SD16—21no—
393C2×SD16—21no—
394C2×SD16—21no—
395C2×SD16—431no—
396C2×SD16—861no—
397C2×SD16—861no—
398C2×SD16—861no—
399C2×SD16—861no—
400C2×SD16—861no—
401C2×SD16—1724no—
402C2×SD16C22⋊D4311yescharacteristic
403C2×D8—861no—
404C2×D8—861no—
405C2×D8—861no—
406C2×M16—861no—
407C22×C8—861no—
408C4⋊Q8—21no—
409C4⋊Q8—431no—
410C4⋊Q8—861no—
411C4⋊Q8C22×D4311yescharacteristic
412#127—21no—
413#127—431no—
414#127C22×D4311yescharacteristic
415#125—21no—
416#125—41no—
417C22⋊Q8—861no—
418C22⋊Q8—1721no—
419#121—21no—
420#121—41no—
421#121—861no—
422#121—861no—
423#120—1721no—
424C4×Q8—21no—
425C4×Q8—21no—
426C4×Q8C22×D4311yescharacteristic
427C4×Q8C22×D4311yescharacteristic
428C4×D4—21no—
429C4×D4—431no—
430C4×D4—861no—
431C4×D4C22×D4311yescharacteristic
432#107—861no—
433#107—861no—
434#107—861no—
435#106—431no—
436#106—861no—
437#106C22⋊D4311yescharacteristic
438C4⋊C8—21no—
439C4⋊C8—431no—
440C4⋊C8—431no—
441C4⋊C8—431no—
442C4⋊C8—861no—
443C4⋊C8C22×D4311yescharacteristic
444#103—21no—
445#103—431no—
446#103—861no—
447#103—861no—
448#103C22⋊D4311yescharacteristic
449#102—21no—
450#102—431no—
451#102—861no—
452#102—861no—
453#102—861no—
454#102—861no—
455#102—1721no—
456#102—1721no—
457#102C22⋊D4311yescharacteristic
458C22⋊C8—861no—
459C22⋊C8—861no—
460#97—861no—
461C4×C8—21no—
462C4×C8—431no—
463C4×C8—431no—
464C4×C8C22×D4311yescharacteristic
465C24—1721no—
466#41—42no—
467#41—81no—
468C2×Q8—21no—
469C2×Q8—861no—
470C2×Q8—3441no—
471C2×Q8—1721no—
472C2×Q8—1722no—
473C2×Q8D4×D4311yescharacteristic
474C2×Q8C2×C22⋊D4311yescharacteristic
475C2×D4—21no—
476C2×D4—21no—
477C2×D4—21no—
478C2×D4—41no—
479C2×D4—41no—
480C2×D4—431no—
481C2×D4—861no—
482C2×D4—861no—
483C2×D4—861no—
484C2×D4—3441no—
485C2×D4—3441no—
486C2×D4—1721no—
487C2×D4—1722no—
488C2×D4—1721no—
489C2×D4—1722no—
490C2×D4C2×C22⋊D4311yescharacteristic
491C22×C4—21no—
492C22×C4—41no—
493C22×C4—861no—
494C22×C4—1721no—
495SD16—22no—
496SD16—42no—
497SD16—81no—
498SD16—81no—
499SD16—81no—
500SD16—434no—
501SD16—3441no—
502SD16—1722no—
503SD16—1722no—
504SD16—1722no—
505SD16—1722no—
506D8—3441no—
507D8—1722no—
508D8—1722no—
509M16—1722no—
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—21no—
522C4⋊C4—21no—
523C4⋊C4—21no—
524C4⋊C4—41no—
525C4⋊C4—41no—
526C4⋊C4—41no—
527C4⋊C4—431no—
528C4⋊C4—861no—
529C4⋊C4—861no—
530C4⋊C4—1721no—
531C4⋊C4D4×D4311yescharacteristic
532C4⋊C4C2×C22⋊D4311yescharacteristic
533C4⋊C4C2×C22⋊D4311yescharacteristic
534C22⋊C4—21no—
535C22⋊C4—41no—
536C22⋊C4—861no—
537C22⋊C4—1721no—
538C22⋊C4—1721no—
539C42—21no—
540C42—21no—
541C42—41no—
542C42C23×D4311yescharacteristic
543C23—21no—
544C23—41no—
545C23—861no—
546C23—3442no—
547C23—3442no—
548C23—1721no—
549C23—6881no—
550Q8—21no—
551Q8—21no—
552Q8—21no—
553Q8—41no—
554Q8—41no—
555Q8—3442no—
556Q8—1721no—
557Q8—1721no—
558Q8SD16×D4312yescomplemented
559D4—21no—
560D4—21no—
561D4—41no—
562D4—41no—
563D4—41no—
564D4—41no—
565D4—82no—
566D4—81no—
567D4—161no—
568D4—432no—
569D4—861no—
570D4—3441no—
571D4—3442no—
572D4—3442no—
573D4—1721no—
574D4—1721no—
575D4—1721no—
576D4—1721no—
577C2×C4—21no—
578C2×C4—21no—
579C2×C4—21no—
580C2×C4—21no—
581C2×C4—21no—
582C2×C4—41no—
583C2×C4—41no—
584C2×C4—41no—
585C2×C4—82no—
586C2×C4—861no—
587C2×C4—3442no—
588C2×C4—1721no—
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—
602C8#1306335012yescomplemented
603C22—41no—
604C22—41no—
605C22—41no—
606C22—81no—
607C22—81no—
608C22—81no—
609C22—862no—
610C22—3441no—
611C22—3441no—
612C22—3441no—
613C22—1721no—
614C22—1721no—
615C22—6884no—
616C22D4×C22⋊D4311yescharacteristic
617C4—22no—
618C4—21no—
619C4—41no—
620C4—41no—
621C4—41no—
622C4—41no—
623C4—81no—
624C4—3441no—
625C4—1721no—
626C4C2×SD16×D4311yescharacteristic
627C4C2×#1306335011yescharacteristic
628C4#1458370211yescharacteristic
629C4#1458370511yescharacteristic
630C2—81no—
631C2—161no—
632C2—1722no—
633C2—6881no—
634C2#1914621511yescharacteristic
635C2SD16×C22⋊D4311yescharacteristic
636C2#1914637511yescharacteristic
subgroupG/H
centerC22D4×C22⋊D43
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#3392C2
socleC22×C43D42
prime radical#19146215C2
hypercenter#3392D43
hypocenterC43#19892
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. #19147512C2semidirect
2. SD16×D172C2semidirect
4. #19134185C2semidirect
5. #19134106C2semidirect
6. #19134077C2semidirect
7. #19133943C2semidirect
8. #19133933C2semidirect
9. #19133795C2semidirect
10. #19133772C2semidirect
11. #19133696C2semidirect
12. #19133691C2semidirect
13. #19133486C2semidirect
14. C8×#10621884C2semidirect
15. C43×#3392C2semidirect
21. #14583302C22semidirect
25. #14583245C22semidirect
28. #14583184C22semidirect
40. #14583030C22semidirect
45. #14582650C22semidirect
46. #14582649C22semidirect
47. #14582646C22semidirect
48. #14582645C22semidirect
49. #14582643C22semidirect
51. Q8⋊(C43⋊C8)C22semidirect
52. Q8⋊(C43⋊C8)C22semidirect
55. C8×C43⋊C8C22semidirect
56. C43×#557C22semidirect
59. C43×#492C22semidirect
63. C43×#460C22semidirect
64. C8×Q8×C43C22semidirect
202. #10621884SD16semidirect
236. Q8×C43C2×SD16semidirect
277. C8×C43AGL(1,ℤ/8)semidirect
283. C43⋊C8C2×SD16semidirect
312. #3392D43semidirect
336. #557C2×D43semidirect
345. #492C2×D43semidirect
360. #460C2×D43semidirect
367. C8×Q8C2×D43semidirect
385. C43#19892semidirect
558. Q8SD16×D43semidirect
602. C8#13063350semidirect

Maximal subgroups

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

subgroupindex
#191475122
SD16×D1722
#191462152
#191341852
#191341062
#191340772
#191339432
#191339332
#191337952
#191337722
#191336962
#191336912
#191334862
C8×#106218842
C43×#33922
#1989243