Finite Group Databasebeta

← #25088081

Subgroups — #25088081

Order 11008.

710 conjugacy classes of subgroups.

The subgroup lattice has 646 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19147579C211yesmaximal, characteristic, complemented
2#19146828C211yesmaximal, characteristic, complemented
3D4×#10621882C211yesmaximal, characteristic
4#19134199C211yesmaximal, characteristic, complemented
5#19134156C211yesmaximal, characteristic, complemented
6#19134153C211yesmaximal, characteristic, complemented
7#19133958C211yesmaximal, characteristic, complemented
8#19133953C211yesmaximal, characteristic, complemented
9#19133774C211yesmaximal, characteristic, complemented
10#19133773C211yesmaximal, characteristic, complemented
11#19133705C211yesmaximal, characteristic, complemented
12#19133704C211yesmaximal, characteristic, complemented
13#19133478C211yesmaximal, characteristic, complemented
14SD16×C43⋊C8C211yesmaximal, characteristic, complemented
15C43×#3324C211yesmaximal, characteristic, complemented
16C22×#10621882—21no—
17#14583622C2211yescharacteristic, complemented
18D4×D172C2211yescharacteristic
19#14583281—21no—
20#14583278C2211yescharacteristic, complemented
21#14583275C2211yescharacteristic
22#14583247C2211yescharacteristic, complemented
23#14583246C2211yescharacteristic, complemented
24#14583245C2211yescharacteristic, complemented
25#14583225—21no—
26#14583179C2211yescharacteristic
27#14583148—21no—
28#14583133—21no—
29#14583121—21no—
30#14583118—21no—
31#14583104C2211yescharacteristic, complemented
32#14583101C2211yescharacteristic, complemented
33#14583099C2211yescharacteristic, complemented
34#14583094C2211yescharacteristic
35#14583091C2211yescharacteristic
36#14583048—21no—
37#14583033—21no—
38#14583032—21no—
39Q8×C43⋊C8C2211yescharacteristic, complemented
40C4×#10621885—21no—
41C4×#10621882C2211yescharacteristic
42#14582978C2211yescharacteristic, complemented
43D4×C43⋊C8C2211yescharacteristic
44#14582902—21no—
45#14582651C2211yescharacteristic, complemented
46#14582650C2211yescharacteristic, complemented
47#14582645C2211yescharacteristic, complemented
48#14582644C2211yescharacteristic, complemented
49#14582643C2211yescharacteristic, complemented
50#14582642C2211yescharacteristic, complemented
51Q8⋊(C43⋊C8)C2211yescharacteristic, complemented
52D4⋊(C43⋊C8)C2211yescharacteristic
53D4⋊(C43⋊C8)C2211yescharacteristic, complemented
54#14582626C2211yescharacteristic, complemented
55C8×C43⋊C8C2211yescharacteristic, complemented
56C43×#556C2211yescharacteristic, complemented
57D42×C43C2211yescharacteristic
58C43×#486C2211yescharacteristic, complemented
59C43×#482—21no—
60C43×#474C2211yescharacteristic
61C43×#468—21no—
62C43×#460C2211yescharacteristic, complemented
63C43×#450—21no—
64C4×SD16×C43C2211yescharacteristic
65C43×#436C2211yescharacteristic, complemented
66C43×#418—21no—
67C22×D172—21no—
68C2×D4×D43—21no—
69C2×#10621885—21no—
70C2×#10621885—21no—
71C2×#10621883—21no—
72C2×#10621884—21no—
73C2×#10621884—21no—
74C2×#10621882—21no—
75C2×#10621882—21no—
76C2×#10621882—21no—
77C2×#10621882—21no—
78C2×#10621882—44no—
79C2×#10621882D411yescharacteristic
80C2×#10621872—21no—
81C22×C43⋊C8—21no—
82#13063325C2311yescharacteristic
83#13063322C2311yescharacteristic
84#13063320—41no—
85#13063313—21no—
86#13063301—21no—
87#13063300—21no—
88#13063299—21no—
89#13063295—41no—
90C4×Dic86—21no—
91C4×D172C2311yescharacteristic
92#13063283—21no—
93#13063258—21no—
94#13063258D411yescharacteristic
95C4⋊(C43⋊C8)—21no—
96C4⋊(C43⋊C8)C2311yescharacteristic
97C4⋊(C43⋊C8)C2311yescharacteristic
98C4⋊(C43⋊C8)C2311yescharacteristic
99#13063249—21no—
100#13063248—21no—
101#13063247—21no—
102#13063247—21no—
103#13063246—21no—
104#13063246—21no—
105#13063246—41no—
106#13063246D411yescharacteristic
107#13063245—21no—
108#13063245—21no—
109#13063245—41no—
110#13063245D411yescharacteristic
111C22⋊(C43⋊C8)—21no—
112(C2×D43)⋊C8—21no—
113C4×C43⋊C8—21no—
114C4×C43⋊C8C2311yescharacteristic
115C4×C43⋊C8C2311yescharacteristic
116C22×D4×C43—21no—
117C22×D4×C43—21no—
118C2×SD16×C43—21no—
119C2×SD16×C43D411yescharacteristic
120C2×M16×C43—21no—
121C4⋊Q8×C43C2311yescharacteristic
122#127×C43C2311yescharacteristic
123#126×C43—41no—
124#124×C43—21no—
125C22⋊Q8×C43—21no—
126#121×C43—21no—
127#121×C43—21no—
128#120×C43—41no—
129C4×Q8×C43—21no—
130C4×Q8×C43C2311yescharacteristic
131C4×D4×C43C2311yescharacteristic
132C4×D4×C43C2311yescharacteristic
133#117×C43—21no—
134#107×C43—21no—
135#106×C43D411yescharacteristic
136C4⋊C8×C43C2311yescharacteristic
137#103×C43D411yescharacteristic
138#102×C43—21no—
139#102×C43—21no—
140#102×C43—21no—
141#102×C43—21no—
142#102×C43D411yescharacteristic
143C22⋊C8×C43—21no—
144C4×C8×C43C2311yescharacteristic
145C24×C43—41no—
146C23×D43—41no—
147C2×Q8×C43—21no—
148C2×Q8×C43C2×D411yescharacteristic
149C2×D4×C43—21no—
150C2×D4×C43—21no—
151C2×D4×C43—21no—
152C2×D4×C43—41no—
153C2×D4×C43—41no—
154C2×D4×C43—42no—
155C2×D4×C43—42no—
156C2×D4×C43—81no—
157C2×D4×C43—81no—
158C2×D4×C43C2×D411yescharacteristic
159C2×D4×C43C2×D411yescharacteristic
160C22×C4×C43—21no—
161C22×C4×C43—21no—
162C2×C22⋊D43—41no—
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×Dic86—21no—
174SD16×C43—22no—
175SD16×C43—81no—
176M16×C43—81no—
177C2×C8×C43—21no—
178C2×C8×C43C2×D411yescharacteristic
179C2×C8×C43C2×D411yescharacteristic
180C4⋊C4×C43—21no—
181C4⋊C4×C43—21no—
182C4⋊C4×C43—21no—
183C4⋊C4×C43—41no—
184C4⋊C4×C43C2×D411yescharacteristic
185C4⋊C4×C43C2×D411yescharacteristic
186C4⋊C4×C43C2×D411yescharacteristic
187C22⋊C4×C43—21no—
188C22⋊C4×C43—21no—
189C22⋊C4×C43—41no—
190C22⋊C4×C43—41no—
191C22⋊C4×C43—41no—
192C42×C43—21no—
193C42×C43—41no—
194C42×C43C2411yescharacteristic
195#10621885—42no—
196#10621885—81no—
197#10621884—81no—
198#10621884—81no—
199#10621883—81no—
200#10621882—22no—
201#10621882—42no—
202#10621882—42no—
203#10621882—42no—
204#10621882—81no—
205(C2×D43)⋊C4—21no—
206(C2×D43)⋊C4—41no—
207(C2×D43)⋊C4—41no—
208(C2×D43)⋊C4—41no—
209C4⋊Dic43—21no—
210C4⋊Dic43—21no—
211C4⋊Dic43C2×D411yescharacteristic
212Dic43⋊C4—41no—
213C4×Dic43—41no—
214C2×C43⋊C8—21no—
215C2×C43⋊C8—21no—
216C2×C43⋊C8—21no—
217C2×C43⋊C8—21no—
218C2×C43⋊C8—42no—
219C2×C43⋊C8C2×D411yescharacteristic
220C2×C43⋊C8C2×D411yescharacteristic
221#10621872—81no—
222C23×C43—21no—
223C23×C43—21no—
224C23×C43—41no—
225C23×C43—82no—
226C23×C43—82no—
227C23×C43—161no—
228C22×D43—21no—
229C22×D43—41no—
230C22×D43—82no—
231C22×D43—82no—
232C22×D43—161no—
233Q8×C43—21no—
234Q8×C43—21no—
235Q8×C43—41no—
236Q8×C43—41no—
237D4×C43—21no—
238D4×C43—21no—
239D4×C43—21no—
240D4×C43—41no—
241D4×C43—41no—
242D4×C43—41no—
243D4×C43—41no—
244D4×C43—81no—
245D4×C43—82no—
246D4×C43—82no—
247D4×C43#13512yes—
248C2×C4×C43—21no—
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×C43C22×D411yescharacteristic
258C2×C4×C43C22×D411yescharacteristic
259C2×C4×C43H(5,𝔽2)11yescharacteristic
260C22⋊D43—82no—
261C2×Dic43—21no—
262C2×Dic43—41no—
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—21no—
277C8×C43—41no—
278C43⋊C8—21no—
279C43⋊C8—41no—
280C43⋊C8—41no—
281C43⋊C8—41no—
282C43⋊C8—41no—
283C43⋊C8AGL(1,ℤ/8)12yes—
284#19900—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—164no—
295C22×C43D4211yescharacteristic
296C2×D43—41no—
297C2×D43—41no—
298C2×D43—41no—
299C2×D43—81no—
300C2×D43—81no—
301C2×D43—81no—
302C2×D43—164no—
303C4×C43—21no—
304C4×C43—41no—
305C4×C43—41no—
306C4×C43—41no—
307C4×C43—41no—
308C4×C43—81no—
309C4×C43C2×#13511yescharacteristic
310C4×C43C2×AGL(1,ℤ/8)11yescharacteristic
311C4×C43#57611yescharacteristic
312C4×C43#57611yescharacteristic
313Dic43—41no—
314Dic43—81no—
315#3393—431no—
316#3324—431no—
317#3324D4311yescharacteristic, complemented
318D4×D8—431no—
319#1709—431no—
320#1701—431no—
321#1701—431no—
322#1669—431no—
323#1668—431no—
324#1639—431no—
325#1639—431no—
326#1628—431no—
327#1628—431no—
328#1589—431no—
329C8×SD16—431no—
330C2×C43—42no—
331C2×C43—81no—
332C2×C43—161no—
333C2×C43#327411yescharacteristic
334C2×C43#328011yescharacteristic
335C2×C43#329011yescharacteristic
336D43—81no—
337D43—161no—
338C22×D8—861no—
339#556—431no—
340#556C2×D4311yescharacteristic, complemented
341D42—431no—
342D42C2×D4311yescharacteristic
343#495—861no—
344#494—431no—
345#493—431no—
346#486—431no—
347#486—431no—
348#486—431no—
349#486C2×D4311yescharacteristic, complemented
350#482—21no—
351#482—861no—
352#474—431no—
353#474C2×D4311yescharacteristic
354#468—21no—
355#468—861no—
356#466—861no—
357#464—861no—
358#464—861no—
359#461—431no—
360#461—431no—
361#460—431no—
362#460C2×D4311yescharacteristic, complemented
363#459—431no—
364#459—431no—
365#450—21no—
366#450—861no—
367#447—861no—
368#447—861no—
369C8×Q8—431no—
370C4×Q16—861no—
371C4×SD16C2×D4311yescharacteristic
372C4×D8—431no—
373#436—431no—
374#436C2×D4311yescharacteristic, complemented
375C8×D4—431no—
376#418—21no—
377#418—861no—
378#335—431no—
379#334—431no—
380#332—431no—
381#332—431no—
382#331—431no—
383#331—431no—
384Q8⋊C8—431no—
385D4⋊C8—431no—
386D4⋊C8—431no—
387D4⋊C8—431no—
388C82—431no—
389C43#1990011yescharacteristic, complemented, Sylow
390C22×D4—21no—
391C22×D4—21no—
392C22×D4—861no—
393C22×D4—861no—
394C2×Q16—861no—
395C2×Q16—861no—
396C2×SD16—21no—
397C2×SD16—861no—
398C2×SD16—861no—
399C2×SD16—861no—
400C2×SD16C22⋊D4311yescharacteristic
401C2×D8—431no—
402C2×D8—861no—
403C2×D8—861no—
404C2×D8—861no—
405C2×D8—861no—
406C2×D8—1724no—
407C2×M16—21no—
408C2×M16—861no—
409C22×C8—861no—
410C4⋊Q8—431no—
411C4⋊Q8C22×D4311yescharacteristic
412#127—431no—
413#127C22×D4311yescharacteristic
414#126—41no—
415#126—1721no—
416#124—21no—
417#124—861no—
418C22⋊Q8—21no—
419C22⋊Q8—861no—
420#121—21no—
421#121—21no—
422#121—861no—
423#121—861no—
424#120—41no—
425#120—1721no—
426C4×Q8—21no—
427C4×Q8—861no—
428C4×Q8C22×D4311yescharacteristic
429C4×D4—431no—
430C4×D4C22×D4311yescharacteristic
431C4×D4C22×D4311yescharacteristic
432#117—21no—
433#117—861no—
434#107—21no—
435#107—431no—
436#107—861no—
437#106C22⋊D4311yescharacteristic
438C4⋊C8—431no—
439C4⋊C8—431no—
440C4⋊C8—431no—
441C4⋊C8—861no—
442C4⋊C8C22×D4311yescharacteristic
443#103—861no—
444#103—861no—
445#103C22⋊D4311yescharacteristic
446#102—21no—
447#102—21no—
448#102—21no—
449#102—21no—
450#102—431no—
451#102—431no—
452#102—861no—
453#102—861no—
454#102—861no—
455#102—861no—
456#102—861no—
457#102—861no—
458#102—1721no—
459#102—1721no—
460#102C22⋊D4311yescharacteristic
461C22⋊C8—21no—
462C22⋊C8—861no—
463C22⋊C8—861no—
464C4×C8—431no—
465C4×C8—431no—
466C4×C8—861no—
467C4×C8C22×D4311yescharacteristic
468C24—41no—
469C24—1721no—
470C2×Q8—21no—
471C2×Q8—861no—
472C2×Q8C2×C22⋊D4311yescharacteristic
473C2×D4—21no—
474C2×D4—21no—
475C2×D4—21no—
476C2×D4—41no—
477C2×D4—41no—
478C2×D4—42no—
479C2×D4—42no—
480C2×D4—81no—
481C2×D4—81no—
482C2×D4—431no—
483C2×D4—861no—
484C2×D4—861no—
485C2×D4—861no—
486C2×D4—3441no—
487C2×D4—3441no—
488C2×D4—1721no—
489C2×D4—1722no—
490C2×D4—1721no—
491C2×D4—1722no—
492C2×D4D4×D4311yescharacteristic
493C2×D4C2×C22⋊D4311yescharacteristic
494C22×C4—21no—
495C22×C4—21no—
496C22×C4—861no—
497Q16—3441no—
498Q16—1722no—
499SD16—22no—
500SD16—81no—
501SD16—3441no—
502SD16—3441no—
503SD16—3441no—
504D8—862no—
505D8—3441no—
506D8—1722no—
507D8—1722no—
508D8—1722no—
509M16—81no—
510M16—3441no—
511C2×C8—21no—
512C2×C8—431no—
513C2×C8—431no—
514C2×C8—861no—
515C2×C8—861no—
516C2×C8—861no—
517C2×C8—861no—
518C2×C8—1722no—
519C2×C8C2×C22⋊D4311yescharacteristic
520C2×C8C2×C22⋊D4311yescharacteristic
521C4⋊C4—21no—
522C4⋊C4—21no—
523C4⋊C4—21no—
524C4⋊C4—41no—
525C4⋊C4—431no—
526C4⋊C4—861no—
527C4⋊C4—861no—
528C4⋊C4—1721no—
529C4⋊C4D4×D4311yescharacteristic
530C4⋊C4C2×C22⋊D4311yescharacteristic
531C4⋊C4C2×C22⋊D4311yescharacteristic
532C22⋊C4—21no—
533C22⋊C4—21no—
534C22⋊C4—41no—
535C22⋊C4—41no—
536C22⋊C4—41no—
537C22⋊C4—861no—
538C22⋊C4—1721no—
539C22⋊C4—1721no—
540C22⋊C4—1721no—
541C42—21no—
542C42—41no—
543C42—1721no—
544C42C23×D4311yescharacteristic
545C23—21no—
546C23—21no—
547C23—41no—
548C23—82no—
549C23—82no—
550C23—161no—
551C23—861no—
552C23—3442no—
553C23—3442no—
554C23—1721no—
555C23—6881no—
556Q8—21no—
557Q8—21no—
558Q8—41no—
559Q8—41no—
560Q8—1721no—
561Q8—1721no—
562D4—21no—
563D4—21no—
564D4—21no—
565D4—41no—
566D4—41no—
567D4—41no—
568D4—41no—
569D4—81no—
570D4—82no—
571D4—82no—
572D4—861no—
573D4—861no—
574D4—3441no—
575D4—3442no—
576D4—3442no—
577D4—1721no—
578D4—1721no—
579D4—1721no—
580D4—1721no—
581D4#1306334512yes—
582C2×C4—21no—
583C2×C4—21no—
584C2×C4—21no—
585C2×C4—21no—
586C2×C4—41no—
587C2×C4—41no—
588C2×C4—41no—
589C2×C4—41no—
590C2×C4—41no—
591C2×C4—861no—
592C2×C4—1721no—
593C2×C4—1721no—
594C2×C4—1721no—
595C2×C4C2×D4×D4311yescharacteristic
596C2×C4C22×C22⋊D4311yescharacteristic
597C2×C4#1306337011yescharacteristic
598C8—21no—
599C8—21no—
600C8—41no—
601C8—432no—
602C8—861no—
603C8—1721no—
604C8—1721no—
605C8—1721no—
606C8—1721no—
607C22—22no—
608C22—41no—
609C22—41no—
610C22—41no—
611C22—41no—
612C22—41no—
613C22—81no—
614C22—81no—
615C22—81no—
616C22—164no—
617C22—3441no—
618C22—3441no—
619C22—3441no—
620C22—1721no—
621C22—1721no—
622C22—1721no—
623C22—6884no—
624C22D4×C22⋊D4311yescharacteristic
625C4—21no—
626C4—41no—
627C4—41no—
628C4—41no—
629C4—41no—
630C4—81no—
631C4—3441no—
632C4—1721no—
633C4C2×#1306334511yescharacteristic
634C4AGL(1,ℤ/8)×D4311yescharacteristic
635C4#1458370211yescharacteristic
636C4#1458370311yescharacteristic
637C2—42no—
638C2—81no—
639C2—161no—
640C2—3441no—
641C2—6881no—
642C2#1914620911yescharacteristic
643C2#1914627611yescharacteristic
644C2#1914637511yescharacteristic
subgroupG/H
centerC22D4×C22⋊D43
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#3324C2
socleC22×C43D42
prime radicalD4×#10621882C2
hypercenter#3324D43
hypocenterC43#19900
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #3324

Complements

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

NH ≅ G/Ntype
1. #19147579C2semidirect
2. #19146828C2semidirect
4. #19134199C2semidirect
5. #19134156C2semidirect
6. #19134153C2semidirect
7. #19133958C2semidirect
8. #19133953C2semidirect
9. #19133774C2semidirect
10. #19133773C2semidirect
11. #19133705C2semidirect
12. #19133704C2semidirect
13. #19133478C2semidirect
14. SD16×C43⋊C8C2semidirect
15. C43×#3324C2semidirect
17. #14583622C22semidirect
20. #14583278C22semidirect
22. #14583247C22semidirect
23. #14583246C22semidirect
24. #14583245C22semidirect
31. #14583104C22semidirect
32. #14583101C22semidirect
33. #14583099C22semidirect
39. Q8×C43⋊C8C22semidirect
42. #14582978C22semidirect
45. #14582651C22semidirect
46. #14582650C22semidirect
47. #14582645C22semidirect
48. #14582644C22semidirect
49. #14582643C22semidirect
50. #14582642C22semidirect
51. Q8⋊(C43⋊C8)C22semidirect
53. D4⋊(C43⋊C8)C22semidirect
54. #14582626C22semidirect
55. C8×C43⋊C8C22semidirect
56. C43×#556C22semidirect
58. C43×#486C22semidirect
62. C43×#460C22semidirect
65. C43×#436C22semidirect
317. #3324D43semidirect
340. #556C2×D43semidirect
349. #486C2×D43semidirect
362. #460C2×D43semidirect
374. #436C2×D43semidirect
389. C43#19900semidirect

Maximal subgroups

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

subgroupindex
#191475792
#191468282
D4×#106218822
#191341992
#191341562
#191341532
#191339582
#191339532
#191337742
#191337732
#191337052
#191337042
#191334782
SD16×C43⋊C82
C43×#33242
#1990043