Finite Group Databasebeta

← #25086664

Subgroups — #25086664

Order 11008.

728 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#19146460C211yesmaximal, characteristic, complemented
2D4×#10621884C211yesmaximal, characteristic, complemented
3#19146196C211yesmaximal, characteristic
4#19134218C211yesmaximal, characteristic, complemented
5#19134105C211yesmaximal, characteristic, complemented
6#19134016C211yesmaximal, characteristic, complemented
7#19133943C211yesmaximal, characteristic, complemented
8#19133938C211yesmaximal, characteristic, complemented
9#19133878C211yesmaximal, characteristic, complemented
10#19133858C211yesmaximal, characteristic, complemented
11#19133773C211yesmaximal, characteristic, complemented
12#19133698C211yesmaximal, characteristic, complemented
13#19133438C211yesmaximal, characteristic, complemented
14#19133419C211yesmaximal, characteristic, complemented
15Q8×D8×C43C211yesmaximal, characteristic, complemented
16C2×#13063349—21no—
17C22×#10621884—21no—
18#14583553C2211yescharacteristic
19D4×D172C2211yescharacteristic
20#14583295C2211yescharacteristic, complemented
21#14583273C2211yescharacteristic
22#14583272C2211yescharacteristic
23#14583249C2211yescharacteristic, complemented
24#14583247C2211yescharacteristic
25#14583227—21no—
26#14583184C2211yescharacteristic, complemented
27#14583146—21no—
28#14583130—21no—
29#14583130—21no—
30#14583104C2211yescharacteristic
31#14583101C2211yescharacteristic
32#14583101C2211yescharacteristic
33#14583099C2211yescharacteristic
34#14583094C2211yescharacteristic
35#14583051—21no—
36#14583049—21no—
37#14583045—21no—
38#14583038—21no—
39#14583038—21no—
40C4×#10621884C2211yescharacteristic
41#14582978C2211yescharacteristic
42D4×C43⋊C8C2211yescharacteristic
43D4×C43⋊C8C2211yescharacteristic, complemented
44C2×#13063249—21no—
45#14582650C2211yescharacteristic, complemented
46#14582649C2211yescharacteristic, complemented
47#14582646C2211yescharacteristic, complemented
48#14582645C2211yescharacteristic, complemented
49#14582645C2211yescharacteristic, complemented
50#14582642C2211yescharacteristic
51Q8⋊(C43⋊C8)C2211yescharacteristic, complemented
52D4⋊(C43⋊C8)C2211yescharacteristic
53D4⋊(C43⋊C8)C2211yescharacteristic, complemented
54#14582626C2211yescharacteristic
55#14582620C2211yescharacteristic, complemented
56D4×Q8×C43C2211yescharacteristic
57D4×Q8×C43C2211yescharacteristic, complemented
58C43×#500—21no—
59C43×#500C2211yescharacteristic, complemented
60C43×#474—21no—
61C43×#474—21no—
62C43×#474C2211yescharacteristic
63C43×#474C2211yescharacteristic, complemented
64C8×Q8×C43C2211yescharacteristic, complemented
65C4×D8×C43—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—21no—
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—41no—
97#13063256D411yescharacteristic
98C4⋊(C43⋊C8)C2311yescharacteristic
99C4⋊(C43⋊C8)C2311yescharacteristic
100C4⋊(C43⋊C8)C2311yescharacteristic
101#13063249—21no—
102#13063249—21no—
103#13063249—21no—
104#13063249—21no—
105#13063249—21no—
106#13063249D411yescharacteristic
107#13063248—21no—
108#13063245—21no—
109#13063245—21no—
110#13063245—41no—
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—
118C22×Q8×C43—21no—
119C2×D8×C43D411yescharacteristic
120C4⋊Q8×C43—21no—
121C4⋊Q8×C43—21no—
122C4⋊Q8×C43C2311yescharacteristic
123C4⋊Q8×C43C2311yescharacteristic
124C22⋊Q8×C43—21no—
125C22⋊Q8×C43—21no—
126C22⋊Q8×C43—41no—
127C22⋊Q8×C43—41no—
128C4×Q8×C43C2311yescharacteristic
129C4×D4×C43—21no—
130C4×D4×C43—21no—
131C4×D4×C43C2311yescharacteristic
132C4×D4×C43C2311yescharacteristic
133#107×C43—21no—
134#107×C43—21no—
135#107×C43—21no—
136#107×C43—21no—
137#107×C43D411yescharacteristic
138C4⋊C8×C43—21no—
139C4⋊C8×C43C2311yescharacteristic
140#102×C43—21no—
141#102×C43—21no—
142#102×C43D411yescharacteristic
143#102×C43D411yescharacteristic
144C4×C8×C43—21no—
145C4×C8×C43C2311yescharacteristic
146C23×D43—41no—
147C2×Q8×C43—21no—
148C2×Q8×C43—21no—
149C2×Q8×C43—41no—
150C2×Q8×C43—41no—
151C2×Q8×C43—42no—
152C2×Q8×C43—42no—
153C2×Q8×C43—81no—
154C2×Q8×C43—81no—
155C2×Q8×C43C2×D411yescharacteristic
156C2×D4×C43C2×D411yescharacteristic
157C2×D4×C43C2×D411yescharacteristic
158C22×C4×C43—21no—
159C22×C4×C43—21no—
160C22×C4×C43—41no—
161C22×C4×C43—41no—
162C2×C22⋊D43—41no—
163C2×C22⋊D43—41no—
164C22×Dic43—41no—
165#10621900—42no—
166#10621900—81no—
167D4×D43—42no—
168D4×D43—81no—
169C2×D172—21no—
170C2×D172—21no—
171C2×D172—21no—
172C2×D172—41no—
173C2×D172—42no—
174C2×D172—81no—
175C2×D172C2×D411yescharacteristic
176C2×C4×D43—21no—
177C2×Dic86—21no—
178D8×C43SD1614yescomplemented
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×C43—21no—
187C4⋊C4×C43—41no—
188C4⋊C4×C43—41no—
189C4⋊C4×C43C2×D411yescharacteristic
190C4⋊C4×C43C2×D411yescharacteristic
191C4⋊C4×C43C2×D411yescharacteristic
192C22⋊C4×C43—21no—
193C22⋊C4×C43—21no—
194C22⋊C4×C43—41no—
195C22⋊C4×C43—41no—
196C42×C43—21no—
197C42×C43C2411yescharacteristic
198#10621884—22no—
199#10621884—42no—
200#10621884—42no—
201#10621884—42no—
202#10621884—81no—
203#10621884—81no—
204#10621883—42no—
205#10621882—42no—
206(C2×D43)⋊C4—21no—
207(C2×D43)⋊C4—41no—
208(C2×D43)⋊C4—41no—
209C4⋊Dic43—21no—
210C4⋊Dic43—21no—
211C4⋊Dic43—41no—
212C4⋊Dic43C2×D411yescharacteristic
213C2×C43⋊C8—21no—
214C2×C43⋊C8—21no—
215C2×C43⋊C8—21no—
216C2×C43⋊C8—21no—
217C2×C43⋊C8—42no—
218C2×C43⋊C8—81no—
219C2×C43⋊C8C2×D411yescharacteristic
220C2×C43⋊C8C2×D411yescharacteristic
221#10621873—42no—
222#10621873—81no—
223#10621872—42no—
224C23×C43—21no—
225C23×C43—21no—
226C22×D43—21no—
227C22×D43—41no—
228C22×D43—82no—
229C22×D43—82no—
230C22×D43—161no—
231Q8×C43—21no—
232Q8×C43—41no—
233Q8×C43—41no—
234Q8×C43—41no—
235Q8×C43—41no—
236Q8×C43—82no—
237Q8×C43—82no—
238Q8×C43AGL(1,ℤ/8)12yescomplemented
239D4×C43—21no—
240D4×C43—21no—
241D4×C43C2×SD1612yes—
242D4×C43C2×SD1612yescomplemented
243C2×C4×C43—21no—
244C2×C4×C43—21no—
245C2×C4×C43—21no—
246C2×C4×C43—21no—
247C2×C4×C43—41no—
248C2×C4×C43—41no—
249C2×C4×C43—41no—
250C2×C4×C43—41no—
251C2×C4×C43—41no—
252C2×C4×C43—41no—
253C2×C4×C43—82no—
254C2×C4×C43—82no—
255C2×C4×C43C22×D411yescharacteristic
256C2×C4×C43C22×D411yescharacteristic
257C2×C4×C43H(5,𝔽2)11yescharacteristic
258C22⋊D43—82no—
259C22⋊D43—82no—
260C2×Dic43—21no—
261C2×Dic43—41no—
262C2×Dic43—82no—
263D172—21no—
264D172—21no—
265D172—41no—
266D172—41no—
267D172—41no—
268D172—41no—
269D172—81no—
270D172—82no—
271C4×D43—41no—
272C4×D43—41no—
273Dic86—41no—
274Dic86—41no—
275C8×C43—21no—
276C8×C43—41no—
277C8×C43C2×SD1612yescomplemented
278C43⋊C8—21no—
279C43⋊C8—21no—
280C43⋊C8—41no—
281C43⋊C8—41no—
282C43⋊C8—41no—
283C43⋊C8—41no—
284#19803—431nomaximal, Sylow
285C22×C43—22no—
286C22×C43—22no—
287C22×C43—41no—
288C22×C43—41no—
289C22×C43—41no—
290C22×C43—41no—
291C22×C43D4211yescharacteristic
292C2×D43—41no—
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—81no—
305C4×C43—81no—
306C4×C43C22×SD1611yescharacteristic
307C4×C43C2×AGL(1,ℤ/8)11yescharacteristic
308C4×C43#57611yescharacteristic
309C4×C43#57711yescharacteristic
310Dic43—41no—
311Dic43—81no—
312Q8×D8D4311yescharacteristic, complemented
313#3298—431no—
314D4×SD16—431no—
315#3272—431no—
316#1714—431no—
317#1693—431no—
318#1679—431no—
319#1666—431no—
320#1665—431no—
321#1654—431no—
322#1651—431no—
323#1639—431no—
324#1627—431no—
325#1583—431no—
326#1580—431no—
327C2×C43—42no—
328C2×C43—42no—
329C2×C43#326411yescharacteristic
330C2×C43D4×SD1611yescharacteristic
331C2×C43#328911yescharacteristic
332D43—81no—
333D43—161no—
334C2×AGL(1,ℤ/8)—861no—
335C22×SD16—861no—
336D4×Q8C2×D4311yescharacteristic
337D4×Q8C2×D4311yescharacteristic, complemented
338#547—431no—
339D42—431no—
340#500—21no—
341#500C2×D4311yescharacteristic, complemented
342#498—431no—
343#492—431no—
344#492—431no—
345#487—431no—
346#486—431no—
347#483—861no—
348#475—431no—
349#474—21no—
350#474—21no—
351#474C2×D4311yescharacteristic
352#474C2×D4311yescharacteristic, complemented
353#468—861no—
354#465—861no—
355#465—861no—
356#461—431no—
357#461—431no—
358#461—431no—
359#460—431no—
360#459—431no—
361#450—861no—
362#450—861no—
363#449—861no—
364#448—861no—
365#448—861no—
366C8×Q8C2×D4311yescharacteristic, complemented
367C4×SD16—431no—
368C4×D8—21no—
369C4×D8C2×D4311yescharacteristic
370#436—431no—
371C8×D4—431no—
372C8×D4—431no—
373C2×#103—861no—
374#334—431no—
375#334—431no—
376#332—431no—
377#332—431no—
378#332—431no—
379#331—431no—
380Q8⋊C8—431no—
381D4⋊C8—431no—
382D4⋊C8—431no—
383D4⋊C8—431no—
384#322—431no—
385C43#1980311yescharacteristic, complemented, Sylow
386C2×#41—861no—
387C22×Q8—21no—
388C22×Q8—21no—
389C22×D4—861no—
390C22×D4—861no—
391AGL(1,ℤ/8)—1724no—
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×D8—861no—
403C2×D8C22⋊D4311yescharacteristic
404C2×M16—861no—
405C22×C8—861no—
406C22×C8—861no—
407C4⋊Q8—21no—
408C4⋊Q8—21no—
409C4⋊Q8—431no—
410C4⋊Q8C22×D4311yescharacteristic
411C4⋊Q8C22×D4311yescharacteristic
412#127—431no—
413#123—1721no—
414C22⋊Q8—21no—
415C22⋊Q8—21no—
416C22⋊Q8—41no—
417C22⋊Q8—41no—
418C22⋊Q8—861no—
419#121—861no—
420#121—861no—
421#121—861no—
422#120—1721no—
423C4×Q8C22×D4311yescharacteristic
424C4×D4—21no—
425C4×D4—21no—
426C4×D4—431no—
427C4×D4C22×D4311yescharacteristic
428C4×D4C22×D4311yescharacteristic
429C2×C4⋊C4—861no—
430#107—21no—
431#107—21no—
432#107—21no—
433#107—21no—
434#107C22⋊D4311yescharacteristic
435#106—431no—
436#106—861no—
437#106—1721no—
438C4⋊C8—21no—
439C4⋊C8—431no—
440C4⋊C8—431no—
441C4⋊C8—431no—
442C4⋊C8C22×D4311yescharacteristic
443#103—431no—
444#103—861no—
445#103—861no—
446#103—861no—
447#103—861no—
448#103—861no—
449#103—861no—
450#102—21no—
451#102—21no—
452#102—431no—
453#102—861no—
454#102—861no—
455#102—1721no—
456#102C22⋊D4311yescharacteristic
457#102C22⋊D4311yescharacteristic
458C22⋊C8—861no—
459C22⋊C8—861no—
460C22⋊C8—861no—
461C4×C8—21no—
462C4×C8—431no—
463C4×C8—431no—
464C4×C8C22×D4311yescharacteristic
465C24—1721no—
466#41—3441no—
467#41—1722no—
468C2×Q8—21no—
469C2×Q8—21no—
470C2×Q8—41no—
471C2×Q8—41no—
472C2×Q8—42no—
473C2×Q8—42no—
474C2×Q8—81no—
475C2×Q8—81no—
476C2×Q8—861no—
477C2×Q8D4×D4311yescharacteristic
478C2×D4—431no—
479C2×D4—861no—
480C2×D4—861no—
481C2×D4—861no—
482C2×D4—3441no—
483C2×D4—3441no—
484C2×D4—1721no—
485C2×D4—1722no—
486C2×D4—1721no—
487C2×D4—1721no—
488C2×D4—1722no—
489C2×D4C2×C22⋊D4311yescharacteristic
490C2×D4C2×C22⋊D4311yescharacteristic
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—41no—
494C22×C4—41no—
495C22×C4—861no—
496C22×C4—1721no—
497SD16—862no—
498SD16—3441no—
499SD16—3441no—
500SD16—3441no—
501SD16—1722no—
502SD16—1722no—
503SD16—1722no—
504SD16—1722no—
505SD16—1722no—
506D8—1722no—
507D8#1062188414yescomplemented
508M16—1722no—
509C2×C8—21no—
510C2×C8—431no—
511C2×C8—431no—
512C2×C8—861no—
513C2×C8—861no—
514C2×C8—861no—
515C2×C8—861no—
516C2×C8—3441no—
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—21no—
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—21no—
536C22⋊C4—41no—
537C22⋊C4—41no—
538C22⋊C4—861no—
539C22⋊C4—1721no—
540C22⋊C4—1721no—
541C42—21no—
542C42C23×D4311yescharacteristic
543C23—21no—
544C23—21no—
545C23—861no—
546C23—3442no—
547C23—3442no—
548C23—1721no—
549C23—6881no—
550Q8—21no—
551Q8—41no—
552Q8—41no—
553Q8—41no—
554Q8—41no—
555Q8—82no—
556Q8—82no—
557Q8—1721no—
558Q8—1721no—
559Q8#1306334912yescomplemented
560D4—21no—
561D4—21no—
562D4—861no—
563D4—861no—
564D4—3441no—
565D4—3442no—
566D4—3442no—
567D4—3442no—
568D4—1721no—
569D4—1721no—
570D4—1721no—
571D4—1721no—
572D4C2×#1062188412yes—
573D4C2×#1062188412yescomplemented
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—21no—
578C2×C4—41no—
579C2×C4—41no—
580C2×C4—41no—
581C2×C4—41no—
582C2×C4—41no—
583C2×C4—41no—
584C2×C4—82no—
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—861no—
597C8—861no—
598C8—1721no—
599C8—1721no—
600C8—1721no—
601C8—1721no—
602C8C2×#1062188412yescomplemented
603C22—22no—
604C22—22no—
605C22—41no—
606C22—41no—
607C22—41no—
608C22—41no—
609C22—3441no—
610C22—3441no—
611C22—3441no—
612C22—1721no—
613C22—1721no—
614C22—1721no—
615C22—6884no—
616C22D4×C22⋊D4311yescharacteristic
617C4—22no—
618C4—21no—
619C4—41no—
620C4—41no—
621C4—41no—
622C4—81no—
623C4—81no—
624C4—3441no—
625C4—1721no—
626C4C22×#1062188411yescharacteristic
627C4C2×#1306334911yescharacteristic
628C4#1458370011yescharacteristic
629C4#1458370711yescharacteristic
630C2—42no—
631C2—42no—
632C2—3441no—
633C2—6881no—
634C2#1914607511yescharacteristic
635C2D4×#1062188411yescharacteristic
636C2#1914636611yescharacteristic
subgroupG/H
centerC22D4×C22⋊D43
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingQ8×D8×C43C2
socleC22×C43D42
prime radical#19146196C2
hypercenterQ8×D8D43
hypocenterC43#19803
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ Q8×D8

Complements

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

NH ≅ G/Ntype
1. #19146460C2semidirect
2. D4×#10621884C2semidirect
4. #19134218C2semidirect
5. #19134105C2semidirect
6. #19134016C2semidirect
7. #19133943C2semidirect
8. #19133938C2semidirect
9. #19133878C2semidirect
10. #19133858C2semidirect
11. #19133773C2semidirect
12. #19133698C2semidirect
13. #19133438C2semidirect
14. #19133419C2semidirect
15. Q8×D8×C43C2semidirect
20. #14583295C22semidirect
23. #14583249C22semidirect
26. #14583184C22semidirect
43. D4×C43⋊C8C22semidirect
45. #14582650C22semidirect
46. #14582649C22semidirect
47. #14582646C22semidirect
48. #14582645C22semidirect
49. #14582645C22semidirect
51. Q8⋊(C43⋊C8)C22semidirect
53. D4⋊(C43⋊C8)C22semidirect
55. #14582620C22semidirect
57. D4×Q8×C43C22semidirect
59. C43×#500C22semidirect
63. C43×#474C22semidirect
64. C8×Q8×C43C22semidirect
178. D8×C43SD16semidirect
238. Q8×C43AGL(1,ℤ/8)semidirect
242. D4×C43C2×SD16semidirect
277. C8×C43C2×SD16semidirect
312. Q8×D8D43semidirect
337. D4×Q8C2×D43semidirect
341. #500C2×D43semidirect
352. #474C2×D43semidirect
366. C8×Q8C2×D43semidirect
385. C43#19803semidirect
507. D8#10621884semidirect
559. Q8#13063349semidirect
573. D4C2×#10621884semidirect
602. C8C2×#10621884semidirect

Maximal subgroups

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

subgroupindex
#191464602
D4×#106218842
#191461962
#191342182
#191341052
#191340162
#191339432
#191339382
#191338782
#191338582
#191337732
#191336982
#191334382
#191334192
Q8×D8×C432
#1980343