Finite Group Databasebeta

← #25087935

Subgroups — #25087935

Order 11008.

718 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#19146946C211yesmaximal, characteristic, complemented
2D4×#10621884C211yesmaximal, characteristic, complemented
3#19146196C211yesmaximal, characteristic
4#19134183C211yesmaximal, characteristic, complemented
5#19134091C211yesmaximal, characteristic, complemented
6#19134067C211yesmaximal, characteristic, complemented
7#19133972C211yesmaximal, characteristic, complemented
8#19133938C211yesmaximal, characteristic, complemented
9#19133878C211yesmaximal, characteristic, complemented
10#19133858C211yesmaximal, characteristic, complemented
11#19133710C211yesmaximal, characteristic, complemented
12#19133667C211yesmaximal, characteristic, complemented
13#19133485C211yesmaximal, characteristic, complemented
14D8×C43⋊C8C211yesmaximal, characteristic, complemented
15C43×#3384C211yesmaximal, characteristic, complemented
16C2×#13063349—21no—
17C22×#10621884—21no—
18#14583553C2211yescharacteristic
19D4×D172C2211yescharacteristic
20#14583295C2211yescharacteristic, complemented
21#14583295C2211yescharacteristic, complemented
22#14583273C2211yescharacteristic
23#14583273C2211yescharacteristic
24#14583272C2211yescharacteristic
25#14583227—21no—
26#14583217—21no—
27#14583186C2211yescharacteristic
28#14583184C2211yescharacteristic, complemented
29#14583146—21no—
30#14583130—21no—
31#14583130—21no—
32#14583104C2211yescharacteristic
33#14583101C2211yescharacteristic
34#14583099C2211yescharacteristic
35#14583094C2211yescharacteristic
36#14583051—21no—
37#14583049—21no—
38#14583045—21no—
39#14583038—21no—
40C4×#10621884C2211yescharacteristic
41#14582978C2211yescharacteristic
42D4×C43⋊C8C2211yescharacteristic
43D4×C43⋊C8C2211yescharacteristic, complemented
44C2×#13063256—21no—
45#14582652C2211yescharacteristic, complemented
46#14582649C2211yescharacteristic, complemented
47#14582648C2211yescharacteristic, complemented
48#14582646C2211yescharacteristic, complemented
49#14582645C2211yescharacteristic, complemented
50#14582642C2211yescharacteristic
51Q8⋊(C43⋊C8)C2211yescharacteristic, complemented
52D4⋊(C43⋊C8)C2211yescharacteristic
53D4⋊(C43⋊C8)C2211yescharacteristic, complemented
54#14582626C2211yescharacteristic
55C8×C43⋊C8C2211yescharacteristic, complemented
56C43×#554C2211yescharacteristic, complemented
57D4×Q8×C43C2211yescharacteristic
58C43×#501—21no—
59C43×#498C2211yescharacteristic, complemented
60C43×#478—21no—
61C43×#476—21no—
62C43×#476C2211yescharacteristic
63C43×#474C2211yescharacteristic, complemented
64C43×#446C2211yescharacteristic, complemented
65C43×#442—21no—
66C4×D8×C43C2211yescharacteristic
67C2×#10621900—21no—
68C22×D172—21no—
69C2×D4×D43—21no—
70#13063349—44no—
71C2×#10621873—21no—
72C2×#10621873—21no—
73C2×#10621883—21no—
74C2×#10621884—21no—
75C2×#10621884—21no—
76C2×#10621884—21no—
77C2×#10621884—21no—
78C2×#10621884—41no—
79C2×#10621884—44no—
80C2×#10621884D411yescharacteristic
81C2×#10621882—21no—
82C2×#10621872—21no—
83C22×C43⋊C8—21no—
84C22×C43⋊C8—21no—
85#13063325C2311yescharacteristic
86#13063322C2311yescharacteristic
87#13063309—41no—
88#13063305—21no—
89#13063300—21no—
90#13063299—21no—
91#13063299—21no—
92#13063295—41no—
93C4×D172C2311yescharacteristic
94C2×C4⋊Dic43—21no—
95#13063256—21no—
96#13063256—21no—
97#13063256—21no—
98#13063256—21no—
99#13063256—41no—
100#13063256D411yescharacteristic
101C4⋊(C43⋊C8)C2311yescharacteristic
102C4⋊(C43⋊C8)C2311yescharacteristic
103C4⋊(C43⋊C8)C2311yescharacteristic
104#13063249—21no—
105#13063249—21no—
106#13063249D411yescharacteristic
107#13063248—21no—
108#13063245—21no—
109#13063245—21no—
110#13063245—21no—
111#13063245D411yescharacteristic
112C22⋊(C43⋊C8)—21no—
113C22⋊(C43⋊C8)—21no—
114(C2×D43)⋊C8—21no—
115C4×C43⋊C8C2311yescharacteristic
116C4×C43⋊C8C2311yescharacteristic
117C22×Q8×C43—21no—
118C2×D8×C43D411yescharacteristic
119C4⋊Q8×C43—21no—
120C4⋊Q8×C43C2311yescharacteristic
121C4⋊Q8×C43C2311yescharacteristic
122#125×C43—21no—
123C22⋊Q8×C43—21no—
124C22⋊Q8×C43—21no—
125C22⋊Q8×C43—41no—
126C22⋊Q8×C43—41no—
127C4×Q8×C43C2311yescharacteristic
128C4×D4×C43—21no—
129C4×D4×C43—21no—
130C4×D4×C43C2311yescharacteristic
131C4×D4×C43C2311yescharacteristic
132C2×C4⋊C4×C43—21no—
133#107×C43—21no—
134#107×C43D411yescharacteristic
135#106×C43—21no—
136#106×C43—21no—
137#106×C43—21no—
138C4⋊C8×C43—21no—
139C4⋊C8×C43C2311yescharacteristic
140#102×C43—21no—
141#102×C43—21no—
142#102×C43D411yescharacteristic
143#102×C43D411yescharacteristic
144#97×C43—21no—
145C4×C8×C43C2311yescharacteristic
146C23×D43—41no—
147C2×Q8×C43—21no—
148C2×Q8×C43—21no—
149C2×Q8×C43—41no—
150C2×Q8×C43—42no—
151C2×Q8×C43—81no—
152C2×Q8×C43C2×D411yescharacteristic
153C2×D4×C43C2×D411yescharacteristic
154C2×D4×C43C2×D411yescharacteristic
155C22×C4×C43—21no—
156C22×C4×C43—21no—
157C22×C4×C43—41no—
158C22×C4×C43—41no—
159C2×C22⋊D43—41no—
160C2×C22⋊D43—41no—
161C22×Dic43—41no—
162#10621900—42no—
163#10621900—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×Dic86—21no—
175D8×C43SD1614yescomplemented
176C2×C8×C43—21no—
177C2×C8×C43C2×D411yescharacteristic
178C2×C8×C43C2×D411yescharacteristic
179C4⋊C4×C43—21no—
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—21no—
192C22⋊C4×C43—41no—
193C22⋊C4×C43—41no—
194C42×C43—21no—
195C42×C43C2411yescharacteristic
196#10621884—22no—
197#10621884—42no—
198#10621884—42no—
199#10621884—42no—
200#10621884—81no—
201#10621884—82no—
202#10621883—42no—
203#10621882—42no—
204(C2×D43)⋊C4—21no—
205(C2×D43)⋊C4—41no—
206(C2×D43)⋊C4—41no—
207C4⋊Dic43—21no—
208C4⋊Dic43—21no—
209C4⋊Dic43—41no—
210C4⋊Dic43C2×D411yescharacteristic
211C2×C43⋊C8—21no—
212C2×C43⋊C8—21no—
213C2×C43⋊C8—21no—
214C2×C43⋊C8—21no—
215C2×C43⋊C8—42no—
216C2×C43⋊C8—42no—
217C2×C43⋊C8C2×D411yescharacteristic
218C2×C43⋊C8C2×D411yescharacteristic
219#10621873—42no—
220#10621873—81no—
221#10621872—42no—
222C23×C43—21no—
223C23×C43—21no—
224C22×D43—21no—
225C22×D43—41no—
226C22×D43—82no—
227C22×D43—82no—
228C22×D43—161no—
229Q8×C43—21no—
230Q8×C43—21no—
231Q8×C43—41no—
232Q8×C43—41no—
233Q8×C43—81no—
234Q8×C43—82no—
235D4×C43—21no—
236D4×C43—21no—
237D4×C43C2×SD1612yes—
238D4×C43C2×SD1612yescomplemented
239C2×C4×C43—21no—
240C2×C4×C43—21no—
241C2×C4×C43—21no—
242C2×C4×C43—21no—
243C2×C4×C43—41no—
244C2×C4×C43—41no—
245C2×C4×C43—41no—
246C2×C4×C43—41no—
247C2×C4×C43—41no—
248C2×C4×C43—41no—
249C2×C4×C43—82no—
250C2×C4×C43—161no—
251C2×C4×C43C22×D411yescharacteristic
252C2×C4×C43C22×D411yescharacteristic
253C2×C4×C43H(5,𝔽2)11yescharacteristic
254C22⋊D43—82no—
255C22⋊D43—82no—
256C2×Dic43—21no—
257C2×Dic43—41no—
258C2×Dic43—82no—
259D172—21no—
260D172—21no—
261D172—41no—
262D172—41no—
263D172—41no—
264D172—41no—
265D172—81no—
266D172—82no—
267C4×D43—41no—
268C4×D43—41no—
269Dic86—41no—
270Dic86—41no—
271C8×C43—21no—
272C8×C43—41no—
273C8×C43C2×SD1612yescomplemented
274C43⋊C8—22no—
275C43⋊C8—21no—
276C43⋊C8—41no—
277C43⋊C8—41no—
278C43⋊C8—41no—
279C43⋊C8AGL(1,ℤ/8)12yescomplemented
280#19890—431nomaximal, Sylow
281C22×C43—22no—
282C22×C43—22no—
283C22×C43—41no—
284C22×C43—41no—
285C22×C43—41no—
286C22×C43—41no—
287C22×C43D4211yescharacteristic
288C2×D43—41no—
289C2×D43—41no—
290C2×D43—41no—
291C2×D43—81no—
292C2×D43—81no—
293C2×D43—81no—
294C2×D43—164no—
295C4×C43—21no—
296C4×C43—41no—
297C4×C43—41no—
298C4×C43—41no—
299C4×C43—41no—
300C4×C43—81no—
301C4×C43—81no—
302C4×C43C22×SD1611yescharacteristic
303C4×C43C2×AGL(1,ℤ/8)11yescharacteristic
304C4×C43#57711yescharacteristic
305C4×C43#57711yescharacteristic
306Dic43—41no—
307Dic43—81no—
308#3384D4311yescharacteristic, complemented
309#3335—431no—
310D4×SD16—431no—
311#3272—431no—
312#1705—431no—
313#1691—431no—
314#1686—431no—
315#1671—431no—
316#1665—431no—
317#1654—431no—
318#1651—431no—
319#1629—431no—
320#1622—431no—
321#1590—431no—
322C8×D8—431no—
323C2×C43—42no—
324C2×C43—42no—
325C2×C43#327211yescharacteristic
326C2×C43D4×SD1611yescharacteristic
327C2×C43#329111yescharacteristic
328D43—81no—
329D43—161no—
330C2×AGL(1,ℤ/8)—861no—
331C22×SD16—861no—
332#554C2×D4311yescharacteristic, complemented
333D4×Q8C2×D4311yescharacteristic
334#547—431no—
335D42—431no—
336#501—21no—
337#498—431no—
338#498—431no—
339#498C2×D4311yescharacteristic, complemented
340#492—431no—
341#492—431no—
342#492—431no—
343#483—861no—
344#481—861no—
345#478—21no—
346#476—21no—
347#476—431no—
348#476C2×D4311yescharacteristic
349#475—431no—
350#474C2×D4311yescharacteristic, complemented
351#468—861no—
352#465—861no—
353#465—861no—
354#461—431no—
355#461—431no—
356#460—431no—
357#459—431no—
358#450—861no—
359#450—861no—
360#449—861no—
361#448—861no—
362#446C2×D4311yescharacteristic, complemented
363#442—21no—
364C4×SD16—431no—
365C4×D8C2×D4311yescharacteristic
366#436—431no—
367C8×D4—431no—
368C8×D4—431no—
369C2×#106—861no—
370#335—431no—
371#334—431no—
372#333—431no—
373#332—431no—
374#332—431no—
375#331—431no—
376Q8⋊C8—431no—
377D4⋊C8—431no—
378D4⋊C8—431no—
379D4⋊C8—431no—
380C82—431no—
381C43#1989011yescharacteristic, complemented, Sylow
382C2×#41—861no—
383C22×Q8—21no—
384C22×D4—861no—
385C22×D4—861no—
386AGL(1,ℤ/8)—1724no—
387C2×SD16—431no—
388C2×SD16—861no—
389C2×SD16—861no—
390C2×SD16—861no—
391C2×SD16—861no—
392C2×SD16—861no—
393C2×SD16—861no—
394C2×SD16—861no—
395C2×SD16—1721no—
396C2×SD16—1724no—
397C2×D8—861no—
398C2×D8C22⋊D4311yescharacteristic
399C2×M16—861no—
400C22×C8—861no—
401C22×C8—861no—
402C4⋊Q8—21no—
403C4⋊Q8—431no—
404C4⋊Q8C22×D4311yescharacteristic
405C4⋊Q8C22×D4311yescharacteristic
406#127—431no—
407#125—21no—
408#123—1721no—
409C22⋊Q8—21no—
410C22⋊Q8—21no—
411C22⋊Q8—41no—
412C22⋊Q8—41no—
413C22⋊Q8—861no—
414#121—861no—
415#121—861no—
416#121—861no—
417#120—1721no—
418C4×Q8C22×D4311yescharacteristic
419C4×D4—21no—
420C4×D4—21no—
421C4×D4—431no—
422C4×D4C22×D4311yescharacteristic
423C4×D4C22×D4311yescharacteristic
424C2×C4⋊C4—21no—
425C2×C4⋊C4—861no—
426#107—21no—
427#107C22⋊D4311yescharacteristic
428#106—21no—
429#106—21no—
430#106—21no—
431#106—431no—
432#106—861no—
433#106—861no—
434#106—861no—
435#106—861no—
436#106—1721no—
437C4⋊C8—21no—
438C4⋊C8—431no—
439C4⋊C8—431no—
440C4⋊C8—431no—
441C4⋊C8C22×D4311yescharacteristic
442#103—431no—
443#103—861no—
444#103—861no—
445#103—861no—
446#102—21no—
447#102—21no—
448#102—431no—
449#102—861no—
450#102—861no—
451#102—861no—
452#102C22⋊D4311yescharacteristic
453#102C22⋊D4311yescharacteristic
454C22⋊C8—861no—
455C22⋊C8—861no—
456C22⋊C8—861no—
457#97—21no—
458C4×C8—431no—
459C4×C8—431no—
460C4×C8C22×D4311yescharacteristic
461C24—1721no—
462#41—3441no—
463#41—1722no—
464C2×Q8—21no—
465C2×Q8—21no—
466C2×Q8—41no—
467C2×Q8—42no—
468C2×Q8—81no—
469C2×Q8—861no—
470C2×Q8D4×D4311yescharacteristic
471C2×D4—431no—
472C2×D4—861no—
473C2×D4—861no—
474C2×D4—861no—
475C2×D4—3441no—
476C2×D4—3441no—
477C2×D4—1721no—
478C2×D4—1722no—
479C2×D4—1721no—
480C2×D4—1721no—
481C2×D4—1722no—
482C2×D4C2×C22⋊D4311yescharacteristic
483C2×D4C2×C22⋊D4311yescharacteristic
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—41no—
487C22×C4—41no—
488C22×C4—861no—
489C22×C4—1721no—
490SD16—862no—
491SD16—3441no—
492SD16—3442no—
493SD16—3441no—
494SD16—1722no—
495SD16—1722no—
496SD16—1722no—
497SD16—1722no—
498SD16—1722no—
499D8—1722no—
500D8#1062188414yescomplemented
501M16—1722no—
502C2×C8—21no—
503C2×C8—431no—
504C2×C8—431no—
505C2×C8—861no—
506C2×C8—861no—
507C2×C8—861no—
508C2×C8—861no—
509C2×C8—1722no—
510C2×C8—1722no—
511C2×C8C2×C22⋊D4311yescharacteristic
512C2×C8C2×C22⋊D4311yescharacteristic
513C4⋊C4—21no—
514C4⋊C4—21no—
515C4⋊C4—21no—
516C4⋊C4—21no—
517C4⋊C4—21no—
518C4⋊C4—41no—
519C4⋊C4—41no—
520C4⋊C4—41no—
521C4⋊C4—431no—
522C4⋊C4—861no—
523C4⋊C4—861no—
524C4⋊C4—1721no—
525C4⋊C4D4×D4311yescharacteristic
526C4⋊C4C2×C22⋊D4311yescharacteristic
527C4⋊C4C2×C22⋊D4311yescharacteristic
528C22⋊C4—21no—
529C22⋊C4—21no—
530C22⋊C4—41no—
531C22⋊C4—41no—
532C22⋊C4—861no—
533C22⋊C4—1721no—
534C22⋊C4—1721no—
535C42—21no—
536C42C23×D4311yescharacteristic
537C23—21no—
538C23—21no—
539C23—861no—
540C23—3442no—
541C23—3442no—
542C23—1721no—
543C23—6881no—
544Q8—21no—
545Q8—21no—
546Q8—41no—
547Q8—41no—
548Q8—81no—
549Q8—82no—
550Q8—1721no—
551Q8—1721no—
552D4—21no—
553D4—21no—
554D4—861no—
555D4—861no—
556D4—3441no—
557D4—3442no—
558D4—3442no—
559D4—3442no—
560D4—1721no—
561D4—1721no—
562D4—1721no—
563D4—1721no—
564D4C2×#1062188412yes—
565D4C2×#1062188412yescomplemented
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—21no—
569C2×C4—21no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—82no—
577C2×C4—161no—
578C2×C4—861no—
579C2×C4—3442no—
580C2×C4—1721no—
581C2×C4—1721no—
582C2×C4—1721no—
583C2×C4C2×D4×D4311yescharacteristic
584C2×C4C22×C22⋊D4311yescharacteristic
585C2×C4#1306337011yescharacteristic
586C8—21no—
587C8—41no—
588C8—432no—
589C8—862no—
590C8—861no—
591C8—1721no—
592C8—1721no—
593C8—1721no—
594C8C2×#1062188412yescomplemented
595C22—22no—
596C22—22no—
597C22—41no—
598C22—41no—
599C22—41no—
600C22—41no—
601C22—3441no—
602C22—3441no—
603C22—3441no—
604C22—1721no—
605C22—1721no—
606C22—1721no—
607C22—6884no—
608C22D4×C22⋊D4311yescharacteristic
609C4—21no—
610C4—41no—
611C4—41no—
612C4—41no—
613C4—41no—
614C4—81no—
615C4—81no—
616C4—3441no—
617C4—1721no—
618C4C22×#1062188411yescharacteristic
619C4AGL(1,ℤ/8)×D4311yescharacteristic
620C4#1458370711yescharacteristic
621C4#1458370911yescharacteristic
622C2—42no—
623C2—42no—
624C2—3441no—
625C2—6881no—
626C2#1914618911yescharacteristic
627C2D4×#1062188411yescharacteristic
628C2#1914638611yescharacteristic
subgroupG/H
centerC22D4×C22⋊D43
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#3384C2
socleC22×C43D42
prime radical#19146196C2
hypercenter#3384D43
hypocenterC43#19890
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #3384

Complements

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

NH ≅ G/Ntype
1. #19146946C2semidirect
2. D4×#10621884C2semidirect
4. #19134183C2semidirect
5. #19134091C2semidirect
6. #19134067C2semidirect
7. #19133972C2semidirect
8. #19133938C2semidirect
9. #19133878C2semidirect
10. #19133858C2semidirect
11. #19133710C2semidirect
12. #19133667C2semidirect
13. #19133485C2semidirect
14. D8×C43⋊C8C2semidirect
15. C43×#3384C2semidirect
20. #14583295C22semidirect
21. #14583295C22semidirect
28. #14583184C22semidirect
43. D4×C43⋊C8C22semidirect
45. #14582652C22semidirect
46. #14582649C22semidirect
47. #14582648C22semidirect
48. #14582646C22semidirect
49. #14582645C22semidirect
51. Q8⋊(C43⋊C8)C22semidirect
53. D4⋊(C43⋊C8)C22semidirect
55. C8×C43⋊C8C22semidirect
56. C43×#554C22semidirect
59. C43×#498C22semidirect
63. C43×#474C22semidirect
64. C43×#446C22semidirect
175. D8×C43SD16semidirect
238. D4×C43C2×SD16semidirect
273. C8×C43C2×SD16semidirect
279. C43⋊C8AGL(1,ℤ/8)semidirect
308. #3384D43semidirect
332. #554C2×D43semidirect
339. #498C2×D43semidirect
350. #474C2×D43semidirect
362. #446C2×D43semidirect
381. C43#19890semidirect
500. D8#10621884semidirect
565. D4C2×#10621884semidirect
594. C8C2×#10621884semidirect

Maximal subgroups

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

subgroupindex
#191469462
D4×#106218842
#191461962
#191341832
#191340912
#191340672
#191339722
#191339382
#191338782
#191338582
#191337102
#191336672
#191334852
D8×C43⋊C82
C43×#33842
#1989043