Finite Group Databasebeta

← #25085983

Subgroups — #25085983

Order 11008.

736 conjugacy classes of subgroups.

The subgroup lattice has 650 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19146938C211yesmaximal, characteristic, complemented
2#19146408C211yesmaximal, characteristic, complemented
3#19146316C211yesmaximal, characteristic, complemented
4#19134264C211yesmaximal, characteristic, complemented
5#19134084C211yesmaximal, characteristic, complemented
6#19134030C211yesmaximal, characteristic, complemented
7#19133982C211yesmaximal, characteristic, complemented
8#19133933C211yesmaximal, characteristic, complemented
9#19133830C211yesmaximal, characteristic, complemented
10#19133828C211yesmaximal, characteristic, complemented
11#19133774C211yesmaximal, characteristic, complemented
12#19133682C211yesmaximal, characteristic, complemented
13#19133422C211yesmaximal, characteristic, complemented
14#19133419C211yesmaximal, characteristic, complemented
15C43×#3272C211yesmaximal, characteristic, complemented
16C2×#13063344—21no—
17#14583553C2211yescharacteristic
18#14583553C2211yescharacteristic, complemented
19#14583302C2211yescharacteristic, complemented
20#14583302C2211yescharacteristic, complemented
21#14583279C2211yescharacteristic, complemented
22#14583245C2211yescharacteristic
23#14583245C2211yescharacteristic
24#14583212—21no—
25#14583210—21no—
26#14583210—21no—
27#14583179C2211yescharacteristic
28#14583179C2211yescharacteristic
29#14583176C2211yescharacteristic, complemented
30#14583141—21no—
31#14583133—21no—
32#14583133—21no—
33#14583104C2211yescharacteristic
34#14583104C2211yescharacteristic, complemented
35#14583091C2211yescharacteristic
36#14583062—21no—
37#14583062—21no—
38#14583033—21no—
39C4×#10621882C2211yescharacteristic
40C8×D172C2211yescharacteristic, complemented
41D4×C43⋊C8C2211yescharacteristic
42D4×C43⋊C8C2211yescharacteristic, complemented
43C2×#13063258—21no—
44C2×#13063246—21no—
45#14582651C2211yescharacteristic, complemented
46#14582650C2211yescharacteristic, complemented
47#14582646C2211yescharacteristic, complemented
48#14582646C2211yescharacteristic, complemented
49#14582645C2211yescharacteristic, complemented
50#14582643C2211yescharacteristic
51D4⋊(C43⋊C8)C2211yescharacteristic
52D4⋊(C43⋊C8)C2211yescharacteristic
53D4⋊(C43⋊C8)C2211yescharacteristic, complemented
54#14582626C2211yescharacteristic, complemented
55#14582620C2211yescharacteristic, complemented
56C2×AGL(1,ℤ/8)×C43—21no—
57C43×#547C2211yescharacteristic
58D42×C43C2211yescharacteristic
59C43×#492C2211yescharacteristic
60C43×#468—21no—
61C43×#461C2211yescharacteristic
62C43×#459C2211yescharacteristic
63C43×#450—21no—
64C43×#449—21no—
65C4×D8×C43C2211yescharacteristic
66C43×#436C2211yescharacteristic
67C2×#10621900—21no—
68C2×#10621900—21no—
69#13063344—44no—
70C2×Dic172—21no—
71C2×Dic172—21no—
72C2×#10621883—21no—
73C2×#10621883—21no—
74C2×#10621882—21no—
75C2×#10621882D411yescharacteristic
76C22×C43⋊C8—21no—
77C22×C43⋊C8—21no—
78C2×C8×D43—21no—
79#13063325C2311yescharacteristic
80#13063325C2311yescharacteristic
81#13063309—41no—
82#13063309—41no—
83#13063305—21no—
84#13063305—21no—
85#13063299—21no—
86#13063299—21no—
87C4×D172C2311yescharacteristic
88C2×C4⋊Dic43—21no—
89C2×C4⋊Dic43—21no—
90#13063258—21no—
91#13063258—21no—
92#13063258—21no—
93#13063258—21no—
94#13063258—21no—
95#13063258—41no—
96#13063258D411yescharacteristic
97C4⋊(C43⋊C8)C2311yescharacteristic
98C4⋊(C43⋊C8)C2311yescharacteristic
99C4⋊(C43⋊C8)C2311yescharacteristic
100#13063248—21no—
101#13063248—21no—
102#13063246—21no—
103#13063246—21no—
104#13063246—21no—
105#13063246—21no—
106#13063246—21no—
107#13063246—41no—
108#13063246D411yescharacteristic
109#13063245—21no—
110#13063245D411yescharacteristic
111C22⋊(C43⋊C8)—21no—
112C22⋊(C43⋊C8)—21no—
113(C2×D43)⋊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×C43—21no—
122C2×SD16×C43—21no—
123C2×D8×C43—21no—
124C2×D8×C43D411yescharacteristic
125C2×M16×C43—21no—
126C4⋊Q8×C43C2311yescharacteristic
127#127×C43C2311yescharacteristic
128#123×C43—41no—
129C22⋊Q8×C43—21no—
130#121×C43—21no—
131#121×C43—21no—
132#121×C43—21no—
133#120×C43—41no—
134C4×D4×C43C2311yescharacteristic
135C4×D4×C43C2311yescharacteristic
136C4×D4×C43C2311yescharacteristic
137C2×C4⋊C4×C43—21no—
138#107×C43D411yescharacteristic
139C4⋊C8×C43C2311yescharacteristic
140#103×C43—21no—
141#102×C43—21no—
142#102×C43D411yescharacteristic
143#102×C43D411yescharacteristic
144C22⋊C8×C43—21no—
145C4×C8×C43C2311yescharacteristic
146C24×C43—41no—
147#41×C43—42no—
148#41×C43—81no—
149C2×Q8×C43—21no—
150C2×D4×C43—21no—
151C2×D4×C43—21no—
152C2×D4×C43—21no—
153C2×D4×C43—41no—
154C2×D4×C43—41no—
155C2×D4×C43—41no—
156C2×D4×C43—42no—
157C2×D4×C43—42no—
158C2×D4×C43—81no—
159C2×D4×C43—81no—
160C2×D4×C43C2×D411yescharacteristic
161C2×D4×C43C2×D411yescharacteristic
162C2×D4×C43C2×D411yescharacteristic
163C22×C4×C43—21no—
164C22×C4×C43—21no—
165C22×C4×C43—21no—
166C22×C4×C43—41no—
167C2×C22⋊D43—41no—
168C2×C22⋊D43—41no—
169C22×Dic43—41no—
170C22×Dic43—41no—
171#10621900—42no—
172#10621900—42no—
173#10621900—81no—
174#10621900—81no—
175C2×D172C2×D411yescharacteristic
176C2×C4×D43—21no—
177C2×Dic86—21no—
178C2×Dic86—21no—
179SD16×C43—42no—
180SD16×C43—42no—
181SD16×C43—81no—
182D8×C43—42no—
183D8×C43D814yescomplemented
184M16×C43—42no—
185C2×C8×C43—21no—
186C2×C8×C43C2×D411yescharacteristic
187C2×C8×C43C2×D411yescharacteristic
188C4⋊C4×C43—21no—
189C4⋊C4×C43—21no—
190C4⋊C4×C43—41no—
191C4⋊C4×C43C2×D411yescharacteristic
192C4⋊C4×C43C2×D411yescharacteristic
193C4⋊C4×C43C2×D411yescharacteristic
194C22⋊C4×C43—21no—
195C22⋊C4×C43—21no—
196C22⋊C4×C43—21no—
197C22⋊C4×C43—41no—
198C22⋊C4×C43—41no—
199C42×C43C2411yescharacteristic
200#10621883—42no—
201#10621883—42no—
202#10621882—41no—
203#10621882—81no—
204(C2×D43)⋊C4—21no—
205(C2×D43)⋊C4—41no—
206(C2×D43)⋊C4—41no—
207C4⋊Dic43—21no—
208C4⋊Dic43—21no—
209C4⋊Dic43—21no—
210C4⋊Dic43—21no—
211C4⋊Dic43—41no—
212C4⋊Dic43—41no—
213C4⋊Dic43C2×D411yescharacteristic
214C2×C43⋊C8—21no—
215C2×C43⋊C8—21no—
216C2×C43⋊C8—21no—
217C2×C43⋊C8—21no—
218C2×C43⋊C8—42no—
219C2×C43⋊C8—81no—
220C2×C43⋊C8C2×D411yescharacteristic
221C2×C43⋊C8C2×D411yescharacteristic
222Dic172—42no—
223Dic172—81no—
224C8×D43—42no—
225C23×C43—21no—
226C23×C43—21no—
227C23×C43—21no—
228C23×C43—41no—
229C23×C43—82no—
230C23×C43—82no—
231C23×C43—161no—
232C22×D43—21no—
233Q8×C43—41no—
234Q8×C43—41no—
235D4×C43—21no—
236D4×C43—21no—
237D4×C43—21no—
238D4×C43—21no—
239D4×C43—41no—
240D4×C43—41no—
241D4×C43—41no—
242D4×C43—41no—
243D4×C43—81no—
244D4×C43—82no—
245D4×C43—82no—
246D4×C43—82no—
247D4×C43C2×D812yes—
248D4×C43C2×D812yes—
249C2×C4×C43—21no—
250C2×C4×C43—21no—
251C2×C4×C43—21no—
252C2×C4×C43—41no—
253C2×C4×C43—41no—
254C2×C4×C43—41no—
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
263C22⋊D43—82no—
264C22⋊D43—82no—
265C2×Dic43—21no—
266C2×Dic43—41no—
267C2×Dic43—41no—
268C2×Dic43—82no—
269C2×Dic43—82no—
270D172—21no—
271D172—21no—
272C4×D43—41no—
273C4×D43—41no—
274Dic86—41no—
275Dic86—41no—
276Dic86—41no—
277Dic86—41no—
278C8×C43—21no—
279C8×C43—41no—
280C8×C43C2×D812yes—
281C43⋊C8—21no—
282C43⋊C8—21no—
283C43⋊C8—41no—
284C43⋊C8—41no—
285C43⋊C8—41no—
286C43⋊C8—41no—
287#19758—431nomaximal, Sylow
288C22×C43—22no—
289C22×C43—22no—
290C22×C43—41no—
291C22×C43—41no—
292C22×C43—41no—
293C22×C43—41no—
294C22×C43—41no—
295C22×C43—41no—
296C22×C43—41no—
297C22×C43—81no—
298C22×C43—81no—
299C22×C43—81no—
300C22×C43—164no—
301C22×C43D4211yescharacteristic
302C2×D43—41no—
303C2×D43—41no—
304C2×D43—41no—
305C4×C43—21no—
306C4×C43—41no—
307C4×C43—41no—
308C4×C43—41no—
309C4×C43—81no—
310C4×C43C22×D811yescharacteristic
311C4×C43#57511yescharacteristic
312C4×C43#57611yescharacteristic
313C4×C43#57711yescharacteristic
314Dic43—41no—
315Dic43—81no—
316Dic43—81no—
317#3334—431no—
318#3294—431no—
319#3283—431no—
320#3272D4311yescharacteristic, complemented
321#1722—431no—
322#1689—431no—
323#1681—431no—
324#1673—431no—
325#1665—431no—
326#1647—431no—
327#1647—431no—
328#1639—431no—
329#1625—431no—
330#1581—431no—
331#1580—431no—
332C2×C43—42no—
333C2×C43—42no—
334C2×C43—81no—
335C2×C43—161no—
336C2×C43#326711yescharacteristic
337C2×C43D4×D811yescharacteristic
338C2×C43#328911yescharacteristic
339D43—81no—
340C2×AGL(1,ℤ/8)—21no—
341C2×#135—861no—
342#547—431no—
343#547—431no—
344#547C2×D4311yescharacteristic
345D42C2×D4311yescharacteristic
346#500—431no—
347#500—431no—
348#494—431no—
349#492C2×D4311yescharacteristic
350#486—431no—
351#486—431no—
352#480—861no—
353#480—861no—
354#480—861no—
355#474—431no—
356#474—431no—
357#474—431no—
358#468—21no—
359#467—861no—
360#466—861no—
361#466—861no—
362#461—431no—
363#461—431no—
364#461C2×D4311yescharacteristic
365#459—431no—
366#459C2×D4311yescharacteristic
367#452—861no—
368#452—861no—
369#450—21no—
370#449—21no—
371#447—861no—
372C4×D8—431no—
373C4×D8C2×D4311yescharacteristic
374#436C2×D4311yescharacteristic
375C8×D4—431no—
376C8×D4—431no—
377C8×D4—431no—
378C2×#107—861no—
379C2×#102—861no—
380#335—431no—
381#334—431no—
382#332—431no—
383#332—431no—
384#332—431no—
385#331—431no—
386D4⋊C8—431no—
387D4⋊C8—431no—
388D4⋊C8—431no—
389D4⋊C8—431no—
390#322—431no—
391C43#1975811yescharacteristic, complemented, Sylow
392C2×#41—21no—
393C2×#41—861no—
394C2×#41—861no—
395C22×D4—21no—
396C22×D4—21no—
397AGL(1,ℤ/8)—44no—
398#135—1724no—
399C2×Q16—861no—
400C2×Q16—861no—
401C2×SD16—21no—
402C2×SD16—21no—
403C2×SD16—21no—
404C2×SD16—861no—
405C2×SD16—861no—
406C2×D8—21no—
407C2×D8—431no—
408C2×D8—861no—
409C2×D8C22⋊D4311yescharacteristic
410C2×M16—21no—
411C22×C8—861no—
412C22×C8—861no—
413C22×C8—861no—
414C4⋊Q8—431no—
415C4⋊Q8—431no—
416C4⋊Q8C22×D4311yescharacteristic
417#127C22×D4311yescharacteristic
418#123—41no—
419#123—1721no—
420#123—1721no—
421C22⋊Q8—21no—
422C22⋊Q8—861no—
423C22⋊Q8—861no—
424#121—21no—
425#121—21no—
426#121—21no—
427#121—861no—
428#121—861no—
429#120—41no—
430C4×D4—431no—
431C4×D4C22×D4311yescharacteristic
432C4×D4C22×D4311yescharacteristic
433C4×D4C22×D4311yescharacteristic
434C2×C4⋊C4—21no—
435C2×C4⋊C4—861no—
436C2×C4⋊C4—861no—
437#107—431no—
438#107—861no—
439#107—861no—
440#107—861no—
441#107—861no—
442#107—861no—
443#107—1721no—
444#107C22⋊D4311yescharacteristic
445C4⋊C8—431no—
446C4⋊C8—431no—
447C4⋊C8—431no—
448C4⋊C8C22×D4311yescharacteristic
449#103—21no—
450#103—861no—
451#103—861no—
452#102—21no—
453#102—431no—
454#102—431no—
455#102—861no—
456#102—861no—
457#102—861no—
458#102—861no—
459#102—861no—
460#102—861no—
461#102—1721no—
462#102C22⋊D4311yescharacteristic
463#102C22⋊D4311yescharacteristic
464C22⋊C8—21no—
465C22⋊C8—861no—
466C22⋊C8—861no—
467C22⋊C8—861no—
468C4×C8—431no—
469C4×C8—431no—
470C4×C8C22×D4311yescharacteristic
471C24—41no—
472#41—42no—
473#41—81no—
474#41—3441no—
475#41—3441no—
476#41—1722no—
477#41—1722no—
478C2×Q8—21no—
479C2×Q8—861no—
480C2×Q8—861no—
481C2×D4—21no—
482C2×D4—21no—
483C2×D4—21no—
484C2×D4—41no—
485C2×D4—41no—
486C2×D4—42no—
487C2×D4—42no—
488C2×D4—41no—
489C2×D4—81no—
490C2×D4—81no—
491C2×D4—431no—
492C2×D4—1721no—
493C2×D4—1721no—
494C2×D4D4×D4311yescharacteristic
495C2×D4C2×C22⋊D4311yescharacteristic
496C2×D4C2×C22⋊D4311yescharacteristic
497C22×C4—21no—
498C22×C4—21no—
499C22×C4—21no—
500C22×C4—41no—
501C22×C4—861no—
502C22×C4—1721no—
503C22×C4—1721no—
504Q16—3441no—
505Q16—1722no—
506SD16—42no—
507SD16—42no—
508SD16—81no—
509SD16—1722no—
510SD16—1722no—
511D8—42no—
512D8—3441no—
513D8—1721no—
514D8#1062188214yescomplemented
515M16—42no—
516C2×C8—21no—
517C2×C8—431no—
518C2×C8—431no—
519C2×C8—861no—
520C2×C8—861no—
521C2×C8—861no—
522C2×C8—861no—
523C2×C8—3441no—
524C2×C8—1722no—
525C2×C8—1722no—
526C2×C8C2×C22⋊D4311yescharacteristic
527C2×C8C2×C22⋊D4311yescharacteristic
528C4⋊C4—21no—
529C4⋊C4—21no—
530C4⋊C4—41no—
531C4⋊C4—431no—
532C4⋊C4—861no—
533C4⋊C4—861no—
534C4⋊C4—861no—
535C4⋊C4—861no—
536C4⋊C4—1721no—
537C4⋊C4—1721no—
538C4⋊C4D4×D4311yescharacteristic
539C4⋊C4C2×C22⋊D4311yescharacteristic
540C4⋊C4C2×C22⋊D4311yescharacteristic
541C22⋊C4—21no—
542C22⋊C4—21no—
543C22⋊C4—21no—
544C22⋊C4—41no—
545C22⋊C4—41no—
546C22⋊C4—861no—
547C22⋊C4—1721no—
548C22⋊C4—1721no—
549C42C23×D4311yescharacteristic
550C23—21no—
551C23—21no—
552C23—21no—
553C23—41no—
554C23—82no—
555C23—82no—
556C23—161no—
557C23—861no—
558Q8—41no—
559Q8—41no—
560Q8—1721no—
561Q8—1721no—
562Q8—1721no—
563Q8—1721no—
564D4—21no—
565D4—21no—
566D4—21no—
567D4—21no—
568D4—41no—
569D4—41no—
570D4—41no—
571D4—41no—
572D4—81no—
573D4—82no—
574D4—82no—
575D4—82no—
576D4—861no—
577D4—861no—
578D4—3442no—
579D4—3442no—
580D4C2×#1062188212yes—
581D4C2×#1062188212yes—
582C2×C4—21no—
583C2×C4—21no—
584C2×C4—21no—
585C2×C4—41no—
586C2×C4—41no—
587C2×C4—41no—
588C2×C4—41no—
589C2×C4—41no—
590C2×C4—41no—
591C2×C4—41no—
592C2×C4—82no—
593C2×C4—861no—
594C2×C4—3442no—
595C2×C4—3442no—
596C2×C4—1721no—
597C2×C4—1721no—
598C2×C4—1721no—
599C2×C4—1721no—
600C2×C4C2×D4×D4311yescharacteristic
601C2×C4C22×C22⋊D4311yescharacteristic
602C2×C4#1306337011yescharacteristic
603C8—21no—
604C8—41no—
605C8—861no—
606C8—861no—
607C8—1721no—
608C8—1721no—
609C8—1721no—
610C8—1721no—
611C8C2×#1062188212yes—
612C22—22no—
613C22—22no—
614C22—41no—
615C22—41no—
616C22—41no—
617C22—41no—
618C22—41no—
619C22—41no—
620C22—41no—
621C22—81no—
622C22—81no—
623C22—81no—
624C22—164no—
625C22—1721no—
626C22—1721no—
627C22—1721no—
628C22D4×C22⋊D4311yescharacteristic
629C4—21no—
630C4—41no—
631C4—41no—
632C4—41no—
633C4—81no—
634C4—3441no—
635C4—3441no—
636C4—1721no—
637C4C22×#1062188211yescharacteristic
638C4#1458369511yescharacteristic
639C4#1458370211yescharacteristic
640C4#1458370911yescharacteristic
641C2—42no—
642C2—42no—
643C2—81no—
644C2—161no—
645C2—3441no—
646C2#1914611411yescharacteristic
647C2D4×#1062188211yescharacteristic
648C2#1914636811yescharacteristic
subgroupG/H
centerC22D4×C22⋊D43
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#3272C2
socleC22×C43D42
hypercenter#3272D43
hypocenterC43#19758
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #3272

Complements

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

NH ≅ G/Ntype
1. #19146938C2semidirect
2. #19146408C2semidirect
3. #19146316C2semidirect
4. #19134264C2semidirect
5. #19134084C2semidirect
6. #19134030C2semidirect
7. #19133982C2semidirect
8. #19133933C2semidirect
9. #19133830C2semidirect
10. #19133828C2semidirect
11. #19133774C2semidirect
12. #19133682C2semidirect
13. #19133422C2semidirect
14. #19133419C2semidirect
15. C43×#3272C2semidirect
18. #14583553C22semidirect
19. #14583302C22semidirect
20. #14583302C22semidirect
21. #14583279C22semidirect
29. #14583176C22semidirect
34. #14583104C22semidirect
40. C8×D172C22semidirect
42. D4×C43⋊C8C22semidirect
45. #14582651C22semidirect
46. #14582650C22semidirect
47. #14582646C22semidirect
48. #14582646C22semidirect
49. #14582645C22semidirect
53. D4⋊(C43⋊C8)C22semidirect
54. #14582626C22semidirect
55. #14582620C22semidirect
183. D8×C43D8semidirect
320. #3272D43semidirect
391. C43#19758semidirect
514. D8#10621882semidirect

Maximal subgroups

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

subgroupindex
#191469382
#191464082
#191463162
#191342642
#191340842
#191340302
#191339822
#191339332
#191338302
#191338282
#191337742
#191336822
#191334222
#191334192
C43×#32722
#1975843