Finite Group Databasebeta

← #25964280

Subgroups — #25964280

Order 11008.

2054 conjugacy classes of subgroups.

The subgroup lattice has 624 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19148417C211yesmaximal, characteristic, complemented
2#19147801C211yesmaximal, characteristic
3#19144456C213yesmaximal, complemented
4#19144451C213yesmaximal, complemented
5#19144429C213yesmaximal, complemented
6#19144424C213yesmaximal, complemented
7#19144416C213yesmaximal, complemented
8#19144391C213yesmaximal, complemented
9#19144381C213yesmaximal, complemented
10C2×#14583202C213yesmaximal, complemented
11#19143188C211yesmaximal, characteristic, complemented
12#19143161C211yesmaximal, characteristic, complemented
13#19143122C211yesmaximal, characteristic
14#19143118C211yesmaximal, characteristic
15C43×#2913C211yesmaximal, characteristic, complemented
16C2×#13063371C2211yescharacteristic
17C2×#13063332C2211yescharacteristic
18#14583628—21no—
19#14583625—21no—
20#14583608—23no—
21#14583606—23no—
22#14583530C2213yescomplemented
23#14583527C2213yescomplemented
24#14583452C2213yescomplemented
25C2×#13063316C2213yescomplemented
26#14583382C2211yescharacteristic
27#14583381—21no—
28#14583380C2213yes—
29#14583373C2213yes—
30#14583371—23no—
31#41×Dic43C2211yescharacteristic
32C4×#10621902—21no—
33#14583367C2213yes—
34C2×#13063287C2213yes—
35C4×D4×D43—23no—
36#14583209C2213yescomplemented
37#14583205C2216yescomplemented
38#14583205C2211yescharacteristic, complemented
39#14583202C2216yescomplemented
40#14583202C2216yescomplemented
41#14583202C2213yescomplemented
42#14583202C2216yescomplemented
43#14583198C2213yescomplemented
44#14583198C2216yescomplemented
45#14583193C2213yescomplemented
46#14583188C2216yescomplemented
47#14583188C2213yescomplemented
48#14583183C2213yescomplemented
49#14583178C2216yescomplemented
50#14583178C2213yescomplemented
51#14582942C2213yescomplemented
52#14582939C2213yescomplemented
53#14582935C2213yescomplemented
54C2×#13063256C2213yescomplemented
55#14582927C2213yescomplemented
56#14582925C2213yescomplemented
57#14582922C2213yescomplemented
58C2×Dic43⋊C8C2213yescomplemented
59#14582905C2213yes—
60#14582903C2213yes—
61#14582901C2213yes—
62#14582898C2213yes—
63#14582896C2213yes—
64#14582893C2213yes—
65C2×#13063247C2213yes—
66C2×#13063245C2213yes—
67C2×#131×C43C2211yescharacteristic
68C43×#520C2211yescharacteristic
69C43×#520C2211yescharacteristic
70C43×#428C2213yescomplemented
71C43×#428C2213yescomplemented
72C43×#427C2213yescomplemented
73C2×#107×C43C2213yescomplemented
74#13063371—24no—
75#13063371Q818yescomplemented
76C2×#10621902—21no—
77C2×#10621898C2313yes—
78C22×D172C2313yes—
79C2×D4×D43—23no—
80C22×C4×D43—23no—
81#13063332—24no—
82C2×#10621877C2313yes—
83C22×C43⋊C8C2313yes—
84#13063325—23no—
85#13063324—23no—
86#13063324C2313yes—
87#13063324C2313yes—
88#13063317—23no—
89#13063316—23no—
90#13063316—23no—
91#13063316—23no—
92#13063316C2313yes—
93#13063316C2316yes—
94#13063316C2311yescharacteristic
95#13063304—26no—
96#13063302—23no—
97#13063302—23no—
98#13063302—26no—
99Q8×Dic43—21no—
100Q8×Dic43D411yescharacteristic
101Q8×Dic43D411yescharacteristic
102C4×Dic86—23no—
103C4×Dic86—23no—
104#13063290C2311yescharacteristic
105#13063290C2313yes—
106C4×D172—23no—
107C4×D172—23no—
108D4×Dic43—23no—
109D4×Dic43D413yes—
110D4×Dic43D413yes—
111#13063287—23no—
112#13063287—23no—
113#13063287C2313yes—
114#13063287C2316yes—
115#13063287C2313yes—
116C4×C22⋊D43—26no—
117(C22⋊D43)⋊C4—23no—
118(C22⋊D43)⋊C4—23no—
119#13063284C2313yes—
120#13063284C2313yes—
121#13063283—23no—
122#13063282—23no—
123C2×C4⋊Dic43—23no—
124C2×C4⋊Dic43C2313yes—
125C2×Dic43⋊C4—23no—
126C4⋊C4×D43—23no—
127C2×(C2×D43)⋊C4—23no—
128C22⋊C4×D43—26no—
129C2×C4×Dic43C2313yes—
130C42×D43—23no—
131#13063258C2313yes—
132#13063258C2313yes—
133#13063256C2313yes—
134#13063256C2316yes—
135#13063256C2311yescharacteristic
136Dic43⋊C8C2311yescharacteristic
137Dic43⋊C8C2313yes—
138Dic43⋊C8C2313yes—
139Dic43⋊C8C2313yes—
140Dic43⋊C8C2316yes—
141#13063250C2311yescharacteristic
142#13063250C2313yes—
143#13063248C2311yescharacteristic
144#13063248C2313yes—
145#13063247C2313yes—
146#13063247C2316yes—
147#13063247C2313yes—
148#13063245C2313yes—
149#13063245C2316yes—
150#13063245C2313yes—
151C2×#41×C43C2311yescharacteristic
152#131×C43—24no—
153C2×M16×C43C2313yes—
154C22×C8×C43C2313yes—
155C4×Q8×C43—21no—
156C4×Q8×C43—21no—
157C4×D4×C43—23no—
158C4×D4×C43—23no—
159#117×C43C2313yes—
160#117×C43C2313yes—
161C2×C4⋊C4×C43C2313yes—
162C2×C4⋊C4×C43C2313yes—
163#107×C43C2311yescharacteristic
164#107×C43C2316yes—
165#107×C43C2313yes—
166#106×C43C2313yes—
167#106×C43C2313yes—
168C23×D43—23no—
169#41×C43C2×Q814yes—
170#41×C43#4114yes—
171C2×Q8×C43C2×D411yescharacteristic
172C2×D4×C43C2×D413yes—
173C22×C4×C43—23no—
174C22×C4×C43—23no—
175C22×C4×C43C2413yes—
176C2×C22⋊D43—23no—
177C22×Dic43—23no—
178C22×Dic43C2×D413yes—
179C22×Dic43C2×D413yes—
180#10621902—28no—
181D4×D43—224no—
182#10621898—26no—
183#10621898C2×Q8112yes—
184C2×D172—23no—
185C2×D172—26no—
186C2×D172C2×Q8112yes—
187C2×D172C2413yes—
188C2×C4×D43—23no—
189C2×C4×D43—23no—
190C2×C4×D43—23no—
191C2×C4×D43—26no—
192C2×C4×D43—86no—
193C2×Dic86—23no—
194C2×Dic86—23no—
195C2×Dic86C2411yescharacteristic
196M16×C43—26no—
197C2×C8×C43—26no—
198C2×C8×C43C2413yes—
199C2×C8×C43C2411yescharacteristic
200C4⋊C4×C43—23no—
201C4⋊C4×C43—23no—
202C4⋊C4×C43C2411yescharacteristic
203C4⋊C4×C43C2411yescharacteristic
204C4⋊C4×C43C2413yes—
205C4⋊C4×C43C2413yes—
206C22⋊C4×C43—23no—
207C22⋊C4×C43—23no—
208C42×C43—23no—
209C42×C43—23no—
210C22⋊Dic43—23no—
211C22⋊Dic43C2×D416yes—
212(C2×D43)⋊C4—23no—
213(C2×D43)⋊C4—26no—
214(C2×D43)⋊C4—23no—
215C4⋊Dic43—23no—
216C4⋊Dic43—23no—
217C4⋊Dic43—26no—
218C4⋊Dic43—21no—
219C4⋊Dic43C2×D413yes—
220C4⋊Dic43C2×D413yes—
221C4⋊Dic43C2413yes—
222C4⋊Dic43C2411yescharacteristic
223Dic43⋊C4—23no—
224Dic43⋊C4—23no—
225Dic43⋊C4—26no—
226Dic43⋊C4—21no—
227Dic43⋊C4—21no—
228Dic43⋊C4—23no—
229Dic43⋊C4—23no—
230C4×Dic43—23no—
231C4×Dic43—21no—
232C4×Dic43—23no—
233C4×Dic43C2×D413yes—
234C4×Dic43C2×D413yes—
235C4×Dic43C2411yescharacteristic
236C4×Dic43C2413yes—
237#10621877—26no—
238C2×C43⋊C8—26no—
239C2×C43⋊C8C2411yescharacteristic
240C2×C43⋊C8C2413yes—
241C23×C43C22×D413yes—
242C22×D43—23no—
243C22×D43—212no—
244C22×D43—83no—
245C22×D43—83no—
246Q8×C43C22⋊Q814yes—
247D4×C43C22⋊Q8112yes—
248C2×C4×C43—21no—
249C2×C4×C43—23no—
250C2×C4×C43—23no—
251C2×C4×C43—21no—
252C2×C4×C43—83no—
253C2×C4×C43—83no—
254C2×C4×C43C22×D413yes—
255C2×C4×C43C22×Q816yes—
256C2×C4×C43C2×#4116yes—
257C2×C4×C43C2511yescharacteristic
258C22⋊D43—212no—
259C2×Dic43—21no—
260C2×Dic43—21no—
261C2×Dic43—23no—
262C2×Dic43—43no—
263C2×Dic43—43no—
264C2×Dic43—83no—
265C2×Dic43C22×D411yescharacteristic
266C2×Dic43C22×D413yes—
267C2×Dic43C22×D411yescharacteristic
268C2×Dic43C22×D413yes—
269D172—212no—
270D172—23no—
271D172C22×Q816yes—
272C4×D43—212no—
273C4×D43—46no—
274C4×D43—83no—
275C4×D43—86no—
276Dic86—21no—
277Dic86—83no—
278Dic86—83no—
279Dic86C22×Q812yes—
280C8×C43—21no—
281C8×C43—23no—
282C43⋊C8—21no—
283C43⋊C8—23no—
284#60496—431nomaximal, Sylow
285C22×C43—23no—
286C22×C43—23no—
287C22×C43C2×C22⋊Q816yes—
288C22×C43C23×D411yescharacteristic
289C2×D43—26no—
290C2×D43—43no—
291C2×D43—43no—
292C2×D43—812no—
293C4×C43—41no—
294C4×C43—41no—
295C4×C43—43no—
296C4×C43—43no—
297C4×C43C2×C22⋊Q816yes—
298C4×C43C23×Q811yescharacteristic
299C4×C43C22×#4111yescharacteristic
300Dic43—23no—
301Dic43—21no—
302Dic43—23no—
303Dic43—21no—
304Dic43—22no—
305Dic43—43no—
306Dic43—41no—
307#3504—431no—
308C4×H(5,𝔽2)—431no—
309#3084—433no—
310#3083—433no—
311#3081—433no—
312#3081—433no—
313#3080—433no—
314#3077—433no—
315#3076—433no—
316C2×#478—433no—
317#2913D4311yescharacteristic, complemented
318#2912—431no—
319#2906—431no—
320#2897—431no—
321#2897—431no—
322C2×C43—26no—
323C2×C43C22×C22⋊Q811yescharacteristic
324C2×C43#358411yescharacteristic
325C2×C43#358511yescharacteristic
326D43—46no—
327C2×H(5,𝔽2)—431no—
328C2×#131—431no—
329C2×#131C2×D4311yescharacteristic
330#557—861no—
331#557—861no—
332#554—863no—
333#554—863no—
334#544—433no—
335#544—433no—
336#533—433no—
337C2×#125—433no—
338#520—431no—
339#520—433no—
340#520—861no—
341#520C2×D4311yescharacteristic
342#520C2×D4311yescharacteristic
343#518—433no—
344#518—863no—
345C4×#41—431no—
346C4×#41—433no—
347C4×#41—861no—
348C2×C4×D4—433no—
349C2×C4×D4—863no—
350#479—431no—
351#479—436no—
352#479—433no—
353#478—433no—
354#478—436no—
355#478—436no—
356#478—436no—
357#478—433no—
358#478—436no—
359#477—433no—
360#476—433no—
361#476—436no—
362#475—433no—
363#474—433no—
364#474—436no—
365#428—433no—
366#428—433no—
367#428C2×D4313yescomplemented
368#428C2×D4313yescomplemented
369#427—433no—
370#427C2×D4313yescomplemented
371C2×#107C2×D4313yescomplemented
372C2×#106—433no—
373#424—433no—
374#424—433no—
375#423—433no—
376C2×C4⋊C8—433no—
377#418—433no—
378#418—433no—
379#417—433no—
380#417—433no—
381#416—433no—
382#416—433no—
383C2×#102—433no—
384C2×#102—433no—
385C43#6049611yescharacteristic, complemented, Sylow
386H(5,𝔽2)—438no—
387H(5,𝔽2)—864no—
388C2×#41—433no—
389C2×#41—861no—
390C2×#41C22×D4311yescharacteristic
391C22×D4—433no—
392C22×D4—863no—
393C23×C4—863no—
394#131—24no—
395#131—864no—
396C2×M16—433no—
397C2×M16C22×D4313yes—
398C22×C8—433no—
399C22×C8C22×D4313yes—
400C4⋊Q8—433no—
401C4⋊Q8—433no—
402C4⋊Q8—863no—
403C4⋊Q8—863no—
404#125—433no—
405#125—436no—
406#125—431no—
407#125—863no—
408#125—863no—
409#125—863no—
410#125—863no—
411C22⋊Q8—866no—
412C22⋊Q8—863no—
413C22⋊Q8—863no—
414C22⋊Q8—866no—
415C4×Q8—21no—
416C4×Q8—21no—
417C4×Q8—431no—
418C4×Q8—431no—
419C4×Q8—431no—
420C4×Q8—433no—
421C4×Q8—863no—
422C4×Q8—863no—
423C4×Q8—861no—
424C4×D4—23no—
425C4×D4—23no—
426C4×D4—433no—
427C4×D4—433no—
428C4×D4—433no—
429C4×D4—436no—
430C4×D4—433no—
431C4×D4—863no—
432C4×D4—863no—
433C4×D4—863no—
434C4×D4—863no—
435C4×D4—863no—
436C4×D4—863no—
437C4×D4—866no—
438C4×D4—863no—
439#117—433no—
440#117—433no—
441#117—863no—
442#117—863no—
443#117C22×D4313yes—
444#117C22×D4313yes—
445C2×C4⋊C4—433no—
446C2×C4⋊C4—863no—
447C2×C4⋊C4—863no—
448C2×C4⋊C4—863no—
449C2×C4⋊C4C22×D4313yes—
450C2×C4⋊C4C22×D4313yes—
451C2×C22⋊C4—866no—
452C2×C22⋊C4—863no—
453C2×C42—433no—
454C2×C42—863no—
455#107—433no—
456#107—433no—
457#107C22×D4313yes—
458#107C22×D4316yes—
459#107C22×D4311yescharacteristic
460#106—433no—
461#106—436no—
462#106—431no—
463#106C22×D4313yes—
464#106C22×D4313yes—
465C4⋊C8—431no—
466C4⋊C8—433no—
467C4⋊C8—433no—
468C4⋊C8—433no—
469C4⋊C8—436no—
470#103—431no—
471#103—433no—
472#103—431no—
473#103—433no—
474#102—433no—
475#102—436no—
476#102—433no—
477#102—433no—
478#102—436no—
479#102—433no—
480C24—863no—
481#41—4312no—
482#41—868no—
483#41—866no—
484#41#1062189814yes—
485#41Q8×D4314yes—
486C2×Q8—431no—
487C2×Q8—863no—
488C2×Q8—863no—
489C2×Q8D4×D4311yescharacteristic
490C2×D4—4312no—
491C2×D4—433no—
492C2×D4—863no—
493C2×D4—8624no—
494C2×D4—863no—
495C2×D4—866no—
496C2×D4D4×D4313yes—
497C22×C4—23no—
498C22×C4—23no—
499C22×C4—433no—
500C22×C4—433no—
501C22×C4—863no—
502C22×C4—866no—
503C22×C4—863no—
504C22×C4—863no—
505C22×C4—863no—
506C22×C4—3446no—
507C22×C4C23×D4313yes—
508M16—26no—
509M16—866no—
510C2×C8—26no—
511C2×C8—431no—
512C2×C8—433no—
513C2×C8—866no—
514C2×C8C23×D4313yes—
515C2×C8C23×D4311yescharacteristic
516C4⋊C4—23no—
517C4⋊C4—23no—
518C4⋊C4—433no—
519C4⋊C4—433no—
520C4⋊C4—433no—
521C4⋊C4—431no—
522C4⋊C4—863no—
523C4⋊C4—863no—
524C4⋊C4—863no—
525C4⋊C4—866no—
526C4⋊C4—866no—
527C4⋊C4—861no—
528C4⋊C4—861no—
529C4⋊C4—861no—
530C4⋊C4—863no—
531C4⋊C4—863no—
532C4⋊C4—863no—
533C4⋊C4C23×D4311yescharacteristic
534C4⋊C4C23×D4313yes—
535C4⋊C4C23×D4313yes—
536C4⋊C4C23×D4311yescharacteristic
537C22⋊C4—23no—
538C22⋊C4—23no—
539C22⋊C4—436no—
540C22⋊C4—863no—
541C22⋊C4—863no—
542C22⋊C4—866no—
543C22⋊C4—863no—
544C42—23no—
545C42—23no—
546C42—433no—
547C42—433no—
548C42—431no—
549C42—433no—
550C42—861no—
551C42—863no—
552C42—863no—
553C23—8612no—
554C23—863no—
555C23—3443no—
556C23—3443no—
557C23C2×D4×D4313yes—
558Q8—432no—
559Q8—861no—
560Q8—3443no—
561Q8—3443no—
562Q8#1306330314yes—
563D4—436no—
564D4—8612no—
565D4—8612no—
566D4—863no—
567D4#13063303112yes—
568C2×C4—21no—
569C2×C4—21no—
570C2×C4—23no—
571C2×C4—23no—
572C2×C4—83no—
573C2×C4—83no—
574C2×C4—431no—
575C2×C4—431no—
576C2×C4—433no—
577C2×C4—433no—
578C2×C4—861no—
579C2×C4—8612no—
580C2×C4—861no—
581C2×C4—863no—
582C2×C4—3446no—
583C2×C4—3443no—
584C2×C4—3443no—
585C2×C4—1726no—
586C2×C4—1723no—
587C2×C4—1723no—
588C2×C4C2×D4×D4313yes—
589C2×C4C2×Q8×D4316yes—
590C2×C4C2×#1062189816yes—
591C2×C4C24×D4311yescharacteristic
592C8—21no—
593C8—23no—
594C8—861no—
595C8—863no—
596C22—23no—
597C22—23no—
598C22—866no—
599C22—34412no—
600C22—1723no—
601C22—1723no—
602C22C2×#1306330316yes—
603C22C22×D4×D4311yescharacteristic
604C4—41no—
605C4—41no—
606C4—43no—
607C4—43no—
608C4—862no—
609C4—863no—
610C4—861no—
611C4—863no—
612C4—861no—
613C4—1723no—
614C4—1721no—
615C4C2×#1306330316yes—
616C4C22×Q8×D4311yescharacteristic
617C4C22×#1062189811yescharacteristic
618C2—26no—
619C2—1726no—
620C2C22×#1306330311yescharacteristic
621C2#1914936511yescharacteristic
622C2#1914937011yescharacteristic
subgroupG/H
centerC22C22×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC43×#2913C2
socleC22×C43C23×D4
prime radicalC2×#13063371C22
hypercenter#2913D43
hypocenterC43#60496
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×#41 ◁ #2913

Complements

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

NH ≅ G/Ntype
1. #19148417C2semidirect
3. #19144456C2semidirect
4. #19144451C2semidirect
5. #19144429C2semidirect
6. #19144424C2semidirect
7. #19144416C2semidirect
8. #19144391C2semidirect
9. #19144381C2semidirect
10. C2×#14583202C2semidirect
11. #19143188C2semidirect
12. #19143161C2semidirect
15. C43×#2913C2semidirect
22. #14583530C22semidirect
23. #14583527C22semidirect
24. #14583452C22semidirect
25. C2×#13063316C22semidirect
36. #14583209C22semidirect
37. #14583205C22semidirect
38. #14583205C22semidirect
39. #14583202C22semidirect
40. #14583202C22semidirect
41. #14583202C22semidirect
42. #14583202C22semidirect
43. #14583198C22semidirect
44. #14583198C22semidirect
45. #14583193C22semidirect
46. #14583188C22semidirect
47. #14583188C22semidirect
48. #14583183C22semidirect
49. #14583178C22semidirect
50. #14583178C22semidirect
51. #14582942C22semidirect
52. #14582939C22semidirect
53. #14582935C22semidirect
54. C2×#13063256C22semidirect
55. #14582927C22semidirect
56. #14582925C22semidirect
57. #14582922C22semidirect
58. C2×Dic43⋊C8C22semidirect
70. C43×#428C22semidirect
71. C43×#428C22semidirect
72. C43×#427C22semidirect
73. C2×#107×C43C22semidirect
75. #13063371Q8semidirect
317. #2913D43semidirect
367. #428C2×D43semidirect
368. #428C2×D43semidirect
370. #427C2×D43semidirect
371. C2×#107C2×D43semidirect
385. C43#60496semidirect

Maximal subgroups

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

subgroupindex
#191484172
#191478012
#191444562
#191444512
#191444292
#191444242
#191444162
#191443912
#191443812
C2×#145832022
#191431882
#191431612
#191431222
#191431182
C43×#29132
#6049643