Finite Group Databasebeta

← #25964252

Subgroups — #25964252

Order 11008.

2090 conjugacy classes of subgroups.

The subgroup lattice has 628 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19148408C211yesmaximal, characteristic, complemented
2#19147801C211yesmaximal, characteristic
3#19144451C213yesmaximal, complemented
4#19144445C213yesmaximal, complemented
5#19144429C213yesmaximal, complemented
6#19144424C213yesmaximal, complemented
7#19144408C213yesmaximal, complemented
8#19144391C213yesmaximal, complemented
9#19144381C213yesmaximal, complemented
10C2×#14583178C213yesmaximal, complemented
11#19143193C211yesmaximal, characteristic, complemented
12#19143161C211yesmaximal, characteristic, complemented
13#19143122C211yesmaximal, characteristic
14#19143118C211yesmaximal, characteristic
15C43×#2913C211yesmaximal, characteristic, complemented
16C2×#13063371C2211yescharacteristic
17C2×#13063332C2211yescharacteristic
18Q8×Dic86—21no—
19#14583625—21no—
20#14583608—23no—
21D4×Dic86—23no—
22#14583530C2213yescomplemented
23#14583527C2213yescomplemented
24#14583452C2213yescomplemented
25C2×#13063324C2213yescomplemented
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#14583205C2213yescomplemented
38#14583202C2216yescomplemented
39#14583202C2213yescomplemented
40#14583198C2213yescomplemented
41#14583198C2216yescomplemented
42#14583193C2216yescomplemented
43#14583193C2211yescharacteristic, complemented
44#14583188C2213yescomplemented
45#14583188C2216yescomplemented
46#14583183C2213yescomplemented
47#14583178C2216yescomplemented
48#14583178C2213yescomplemented
49#14583178C2216yescomplemented
50#14583178C2216yescomplemented
51#14582942C2213yescomplemented
52#14582939C2213yescomplemented
53#14582935C2213yescomplemented
54C2×#13063258C2213yescomplemented
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×Dic86—23no—
79C22×D172C2313yes—
80C2×D4×D43—23no—
81C22×C4×D43—23no—
82#13063332—24no—
83C2×#10621877C2313yes—
84C22×C43⋊C8C2313yes—
85#13063325—23no—
86#13063324—23no—
87#13063324—23no—
88#13063324—23no—
89#13063324C2313yes—
90#13063324C2316yes—
91#13063324C2311yescharacteristic
92#13063317—23no—
93#13063316—23no—
94#13063316C2313yes—
95#13063316C2313yes—
96#13063304—26no—
97#13063302—23no—
98#13063302—23no—
99#13063302—26no—
100Q8×Dic43—21no—
101Q8×Dic43D411yescharacteristic
102Q8×Dic43D411yescharacteristic
103C4×Dic86—23no—
104C4×Dic86—23no—
105#13063290C2311yescharacteristic
106#13063290C2313yes—
107C4×D172—23no—
108C4×D172—23no—
109D4×Dic43—23no—
110D4×Dic43D413yes—
111D4×Dic43D413yes—
112#13063287—23no—
113#13063287—23no—
114#13063287C2313yes—
115#13063287C2316yes—
116#13063287C2313yes—
117C4×C22⋊D43—26no—
118(C22⋊D43)⋊C4—23no—
119(C22⋊D43)⋊C4—23no—
120#13063284C2313yes—
121#13063284C2313yes—
122#13063283—23no—
123#13063282—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#13063258C2316yes—
133#13063258C2311yescharacteristic
134#13063256C2313yes—
135#13063256C2313yes—
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×C43C2313yes—
164#107×C43C2316yes—
165#107×C43C2311yescharacteristic
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×Q8112yescomplemented
184C2×D172—23no—
185C2×D172—26no—
186C2×D172C2×Q8112yescomplemented
187C2×D172C2413yes—
188C2×C4×D43—23no—
189C2×C4×D43—23no—
190C2×C4×D43—23no—
191C2×C4×D43—26no—
192C2×C4×D43—86no—
193C2×Dic86—21no—
194C2×Dic86—23no—
195C2×Dic86—26no—
196C2×Dic86—86no—
197C2×Dic86C2411yescharacteristic
198M16×C43—26no—
199C2×C8×C43—26no—
200C2×C8×C43C2413yes—
201C2×C8×C43C2411yescharacteristic
202C4⋊C4×C43—23no—
203C4⋊C4×C43—23no—
204C4⋊C4×C43C2411yescharacteristic
205C4⋊C4×C43C2411yescharacteristic
206C4⋊C4×C43C2413yes—
207C4⋊C4×C43C2413yes—
208C22⋊C4×C43—23no—
209C22⋊C4×C43—23no—
210C42×C43—23no—
211C42×C43—23no—
212C22⋊Dic43—23no—
213C22⋊Dic43C2×D416yes—
214(C2×D43)⋊C4—23no—
215(C2×D43)⋊C4—26no—
216(C2×D43)⋊C4—23no—
217C4⋊Dic43—23no—
218C4⋊Dic43—23no—
219C4⋊Dic43—23no—
220C4⋊Dic43C2×D413yes—
221C4⋊Dic43C2×D413yes—
222C4⋊Dic43C2411yescharacteristic
223C4⋊Dic43C2413yes—
224Dic43⋊C4—23no—
225Dic43⋊C4—23no—
226Dic43⋊C4—26no—
227Dic43⋊C4—21no—
228Dic43⋊C4—21no—
229Dic43⋊C4—23no—
230Dic43⋊C4—23no—
231C4×Dic43—23no—
232C4×Dic43—21no—
233C4×Dic43—23no—
234C4×Dic43C2×D413yes—
235C4×Dic43C2×D413yes—
236C4×Dic43C2411yescharacteristic
237C4×Dic43C2413yes—
238#10621877—26no—
239C2×C43⋊C8—26no—
240C2×C43⋊C8C2413yes—
241C2×C43⋊C8C2411yescharacteristic
242C23×C43C22×D413yes—
243C22×D43—23no—
244C22×D43—212no—
245C22×D43—83no—
246C22×D43—83no—
247Q8×C43C22⋊Q814yes—
248D4×C43C22⋊Q8112yes—
249C2×C4×C43—21no—
250C2×C4×C43—23no—
251C2×C4×C43—21no—
252C2×C4×C43—23no—
253C2×C4×C43—83no—
254C2×C4×C43—83no—
255C2×C4×C43C22×D413yes—
256C2×C4×C43C22×Q816yes—
257C2×C4×C43C2×#4116yes—
258C2×C4×C43C2511yescharacteristic
259C22⋊D43—212no—
260C2×Dic43—21no—
261C2×Dic43—26no—
262C2×Dic43—21no—
263C2×Dic43—23no—
264C2×Dic43—43no—
265C2×Dic43—83no—
266C2×Dic43C22×D413yes—
267C2×Dic43C22×D411yescharacteristic
268C2×Dic43C22×D413yes—
269C2×Dic43C22×D411yescharacteristic
270D172—212no—
271D172—23no—
272D172C22×Q816yes—
273C4×D43—212no—
274C4×D43—46no—
275C4×D43—83no—
276C4×D43—86no—
277Dic86—21no—
278Dic86—42no—
279Dic86—46no—
280Dic86—86no—
281Dic86C22×Q812yes—
282C8×C43—21no—
283C8×C43—23no—
284C43⋊C8—21no—
285C43⋊C8—23no—
286#60494—431nomaximal, Sylow
287C22×C43—23no—
288C22×C43—23no—
289C22×C43C2×C22⋊Q816yes—
290C22×C43C23×D411yescharacteristic
291C2×D43—26no—
292C2×D43—43no—
293C2×D43—43no—
294C2×D43—812no—
295C4×C43—41no—
296C4×C43—41no—
297C4×C43—43no—
298C4×C43—43no—
299C4×C43C2×C22⋊Q816yes—
300C4×C43C23×Q811yescharacteristic
301C4×C43C22×#4111yescharacteristic
302Dic43—21no—
303Dic43—23no—
304Dic43—22no—
305Dic43—23no—
306Dic43—41no—
307Dic43—43no—
308Dic43#57612yes—
309#3503—431no—
310C4×H(5,𝔽2)—431no—
311#3083—433no—
312#3083—433no—
313#3081—433no—
314#3081—433no—
315#3079—433no—
316#3077—433no—
317#3076—433no—
318C2×#474—433no—
319#2913—431no—
320#2913D4311yescharacteristic, complemented
321#2906—431no—
322#2897—431no—
323#2897—431no—
324C2×C43—26no—
325C2×C43C22×C22⋊Q811yescharacteristic
326C2×C43C2×#57611yescharacteristic
327C2×C43#358611yescharacteristic
328D43—46no—
329C2×H(5,𝔽2)—431no—
330C2×#131—431no—
331C2×#131C2×D4311yescharacteristic
332Q82—861no—
333#557—861no—
334#554—863no—
335D4×Q8—863no—
336#544—433no—
337#544—433no—
338#533—433no—
339C2×C4⋊Q8—433no—
340#520—431no—
341#520—433no—
342#520—861no—
343#520C2×D4311yescharacteristic
344#520C2×D4311yescharacteristic
345#518—433no—
346#518—863no—
347C4×#41—431no—
348C4×#41—433no—
349C4×#41—861no—
350C2×C4×D4—433no—
351C2×C4×D4—863no—
352#479—433no—
353#479—433no—
354#478—433no—
355#478—436no—
356#478—433no—
357#478—436no—
358#477—431no—
359#477—436no—
360#476—433no—
361#476—436no—
362#475—433no—
363#474—433no—
364#474—436no—
365#474—436no—
366#474—436no—
367#428—433no—
368#428—433no—
369#428C2×D4313yescomplemented
370#428C2×D4313yescomplemented
371#427—433no—
372#427C2×D4313yescomplemented
373C2×#107—433no—
374C2×#107C2×D4313yescomplemented
375#424—433no—
376#424—433no—
377#423—433no—
378C2×C4⋊C8—433no—
379#418—433no—
380#418—433no—
381#417—433no—
382#417—433no—
383#416—433no—
384#416—433no—
385C2×#102—433no—
386C2×#102—433no—
387C43#6049411yescharacteristic, complemented, Sylow
388H(5,𝔽2)—438no—
389H(5,𝔽2)—864no—
390C2×#41—433no—
391C2×#41—861no—
392C2×#41C22×D4311yescharacteristic
393C22×Q8—863no—
394C22×D4—433no—
395C22×D4—863no—
396C23×C4—863no—
397#131—24no—
398#131—864no—
399C2×M16—433no—
400C2×M16C22×D4313yes—
401C22×C8—433no—
402C22×C8C22×D4313yes—
403C4⋊Q8—433no—
404C4⋊Q8—436no—
405C4⋊Q8—431no—
406C4⋊Q8—863no—
407C4⋊Q8—863no—
408C4⋊Q8—863no—
409C4⋊Q8—863no—
410#125—433no—
411#125—433no—
412#125—863no—
413#125—863no—
414C22⋊Q8—866no—
415C22⋊Q8—863no—
416C22⋊Q8—863no—
417C22⋊Q8—866no—
418C4×Q8—21no—
419C4×Q8—21no—
420C4×Q8—431no—
421C4×Q8—431no—
422C4×Q8—431no—
423C4×Q8—433no—
424C4×Q8—863no—
425C4×Q8—863no—
426C4×Q8—861no—
427C4×D4—23no—
428C4×D4—23no—
429C4×D4—433no—
430C4×D4—433no—
431C4×D4—433no—
432C4×D4—436no—
433C4×D4—433no—
434C4×D4—863no—
435C4×D4—863no—
436C4×D4—863no—
437C4×D4—863no—
438C4×D4—863no—
439C4×D4—863no—
440C4×D4—866no—
441C4×D4—863no—
442#117—433no—
443#117—433no—
444#117—863no—
445#117—863no—
446#117C22×D4313yes—
447#117C22×D4313yes—
448C2×C4⋊C4—433no—
449C2×C4⋊C4—863no—
450C2×C4⋊C4—863no—
451C2×C4⋊C4C22×D4313yes—
452C2×C4⋊C4C22×D4313yes—
453C2×C22⋊C4—866no—
454C2×C22⋊C4—863no—
455C2×C42—433no—
456C2×C42—863no—
457#107—433no—
458#107—436no—
459#107—431no—
460#107C22×D4313yes—
461#107C22×D4316yes—
462#107C22×D4311yescharacteristic
463#106—433no—
464#106—433no—
465#106C22×D4313yes—
466#106C22×D4313yes—
467C4⋊C8—431no—
468C4⋊C8—433no—
469C4⋊C8—433no—
470C4⋊C8—433no—
471C4⋊C8—436no—
472#103—431no—
473#103—433no—
474#103—431no—
475#103—433no—
476#102—433no—
477#102—436no—
478#102—433no—
479#102—433no—
480#102—436no—
481#102—433no—
482C24—863no—
483#41—4312no—
484#41—868no—
485#41—866no—
486#41#1062189814yes—
487#41Q8×D4314yes—
488C2×Q8—431no—
489C2×Q8—866no—
490C2×Q8—861no—
491C2×Q8—863no—
492C2×Q8—3446no—
493C2×Q8D4×D4311yescharacteristic
494C2×D4—4312no—
495C2×D4—433no—
496C2×D4—863no—
497C2×D4—8624no—
498C2×D4—863no—
499C2×D4—866no—
500C2×D4D4×D4313yes—
501C22×C4—23no—
502C22×C4—23no—
503C22×C4—433no—
504C22×C4—433no—
505C22×C4—863no—
506C22×C4—866no—
507C22×C4—863no—
508C22×C4—863no—
509C22×C4—863no—
510C22×C4—3446no—
511C22×C4C23×D4313yes—
512M16—26no—
513M16—866no—
514C2×C8—26no—
515C2×C8—433no—
516C2×C8—431no—
517C2×C8—866no—
518C2×C8C23×D4313yes—
519C2×C8C23×D4311yescharacteristic
520C4⋊C4—23no—
521C4⋊C4—23no—
522C4⋊C4—433no—
523C4⋊C4—433no—
524C4⋊C4—431no—
525C4⋊C4—433no—
526C4⋊C4—863no—
527C4⋊C4—863no—
528C4⋊C4—866no—
529C4⋊C4—861no—
530C4⋊C4—861no—
531C4⋊C4—863no—
532C4⋊C4—863no—
533C4⋊C4—863no—
534C4⋊C4—863no—
535C4⋊C4—863no—
536C4⋊C4C23×D4311yescharacteristic
537C4⋊C4C23×D4313yes—
538C4⋊C4C23×D4311yescharacteristic
539C4⋊C4C23×D4313yes—
540C22⋊C4—23no—
541C22⋊C4—23no—
542C22⋊C4—436no—
543C22⋊C4—863no—
544C22⋊C4—863no—
545C22⋊C4—866no—
546C22⋊C4—863no—
547C42—23no—
548C42—23no—
549C42—433no—
550C42—433no—
551C42—431no—
552C42—433no—
553C42—861no—
554C42—863no—
555C42—863no—
556C23—8612no—
557C23—863no—
558C23—3443no—
559C23—3443no—
560C23C2×D4×D4313yes—
561Q8—432no—
562Q8—861no—
563Q8—3446no—
564Q8—1726no—
565Q8—1722no—
566Q8#1306330314yes—
567D4—436no—
568D4—8612no—
569D4—8612no—
570D4—863no—
571D4#13063303112yes—
572C2×C4—21no—
573C2×C4—21no—
574C2×C4—23no—
575C2×C4—23no—
576C2×C4—83no—
577C2×C4—83no—
578C2×C4—431no—
579C2×C4—431no—
580C2×C4—433no—
581C2×C4—433no—
582C2×C4—866no—
583C2×C4—861no—
584C2×C4—8612no—
585C2×C4—861no—
586C2×C4—863no—
587C2×C4—3446no—
588C2×C4—3443no—
589C2×C4—3443no—
590C2×C4—1726no—
591C2×C4—1723no—
592C2×C4C2×D4×D4313yes—
593C2×C4C2×Q8×D4316yes—
594C2×C4C2×#1062189816yes—
595C2×C4C24×D4311yescharacteristic
596C8—21no—
597C8—23no—
598C8—861no—
599C8—863no—
600C22—23no—
601C22—23no—
602C22—866no—
603C22—34412no—
604C22—1723no—
605C22—1723no—
606C22C2×#1306330316yes—
607C22C22×D4×D4311yescharacteristic
608C4—43no—
609C4—43no—
610C4—41no—
611C4—41no—
612C4—432no—
613C4—863no—
614C4—862no—
615C4—863no—
616C4—861no—
617C4—1723no—
618C4—1721no—
619C4C2×#1306330316yes—
620C4C22×Q8×D4311yescharacteristic
621C4C22×#1062189811yescharacteristic
622C2—26no—
623C2—1726no—
624C2C22×#1306330311yescharacteristic
625C2#576×D4311yescharacteristic
626C2#1914938011yescharacteristic
subgroupG/H
centerC22C22×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC43×#2913C2
socleC22×C43C23×D4
prime radicalC2×#13063371C22
hypercenter#2913D43
hypocenterC43#60494
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. #19148408C2semidirect
3. #19144451C2semidirect
4. #19144445C2semidirect
5. #19144429C2semidirect
6. #19144424C2semidirect
7. #19144408C2semidirect
8. #19144391C2semidirect
9. #19144381C2semidirect
10. C2×#14583178C2semidirect
11. #19143193C2semidirect
12. #19143161C2semidirect
15. C43×#2913C2semidirect
22. #14583530C22semidirect
23. #14583527C22semidirect
24. #14583452C22semidirect
25. C2×#13063324C22semidirect
36. #14583209C22semidirect
37. #14583205C22semidirect
38. #14583202C22semidirect
39. #14583202C22semidirect
40. #14583198C22semidirect
41. #14583198C22semidirect
42. #14583193C22semidirect
43. #14583193C22semidirect
44. #14583188C22semidirect
45. #14583188C22semidirect
46. #14583183C22semidirect
47. #14583178C22semidirect
48. #14583178C22semidirect
49. #14583178C22semidirect
50. #14583178C22semidirect
51. #14582942C22semidirect
52. #14582939C22semidirect
53. #14582935C22semidirect
54. C2×#13063258C22semidirect
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
183. #10621898C2×Q8semidirect
186. C2×D172C2×Q8semidirect
320. #2913D43semidirect
369. #428C2×D43semidirect
370. #428C2×D43semidirect
372. #427C2×D43semidirect
374. C2×#107C2×D43semidirect
387. C43#60494semidirect

Maximal subgroups

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

subgroupindex
#191484082
#191478012
#191444512
#191444452
#191444292
#191444242
#191444082
#191443912
#191443812
C2×#145831782
#191431932
#191431612
#191431222
#191431182
C43×#29132
#6049443