Finite Group Databasebeta

← #25080403

Subgroups — #25080403

Order 11008.

716 conjugacy classes of subgroups.

The subgroup lattice has 616 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145156C211yesmaximal, characteristic, complemented
2#19144693C211yesmaximal, characteristic, complemented
3#19144688C211yesmaximal, characteristic
4C8×D4×D43C211yesmaximal, characteristic, complemented
5#19134049C211yesmaximal, characteristic, complemented
6#19134048C211yesmaximal, characteristic, complemented
7#19134035C211yesmaximal, characteristic, complemented
8#19134034C211yesmaximal, characteristic, complemented
9#19133967C211yesmaximal, characteristic, complemented
10#19133937C211yesmaximal, characteristic, complemented
11#19133936C211yesmaximal, characteristic, complemented
12#19133355C211yesmaximal, characteristic, complemented
13#19133292C211yesmaximal, characteristic, complemented
14#19133289C211yesmaximal, characteristic, complemented
15C43×#1671C211yesmaximal, characteristic, complemented
16C22×C8×D43—21no—
17#14583454C2211yescharacteristic
18#14583450C2211yescharacteristic
19C4×D4×D43C2211yescharacteristic
20#14583272C2211yescharacteristic, complemented
21#14583251C2211yescharacteristic, complemented
22#14583247C2211yescharacteristic, complemented
23#14583233—21no—
24#14583219—21no—
25#14583186C2211yescharacteristic
26#14583180C2211yescharacteristic
27#14583179C2211yescharacteristic
28#14583129—21no—
29#14583129—21no—
30#14583101C2211yescharacteristic
31#14583095C2211yescharacteristic
32#14583094C2211yescharacteristic
33#14583048—21no—
34#14583034—21no—
35#14583010—21no—
36#14583008—21no—
37#14583002—21no—
38#14583000—21no—
39#14582986—21no—
40#14582986—21no—
41C8×D172C2211yescharacteristic
42D4×C43⋊C8C2211yescharacteristic
43#14582964C2211yescharacteristic
44C8×C22⋊D43—21no—
45(C22⋊D43)⋊C8—21no—
46#14582955C2211yescharacteristic
47#14582955C2211yescharacteristic
48C4⋊C8×D43C2211yescharacteristic
49C22⋊C8×D43—21no—
50C4×C8×D43C2211yescharacteristic
51#14582651C2211yescharacteristic, complemented
52#14582651C2211yescharacteristic, complemented
53#14582650C2211yescharacteristic, complemented
54#14582648C2211yescharacteristic, complemented
55#14582646C2211yescharacteristic, complemented
56#14582645C2211yescharacteristic, complemented
57#14582644C2211yescharacteristic, complemented
58#14582642C2211yescharacteristic, complemented
59#14582642C2211yescharacteristic, complemented
60C43×#498C2211yescharacteristic, complemented
61C43×#476C2211yescharacteristic
62C43×#461C2211yescharacteristic
63C8×D4×C43C2211yescharacteristic
64C43×#334C2211yescharacteristic, complemented
65C43×#333C2211yescharacteristic, complemented
66C43×#332C2211yescharacteristic, complemented
67C2×#10621902—21no—
68C2×D4×D43D411yescharacteristic
69C22×C4×D43—21no—
70C2×#10621873—21no—
71C2×#10621873—21no—
72C2×#10621884—21no—
73C2×D344—21no—
74C2×#10621882—21no—
75C22×C43⋊C8—21no—
76C2×C8×D43—21no—
77C2×C8×D43—21no—
78C2×C8×D43—21no—
79C2×C8×D43—44no—
80C2×C8×D43D411yescharacteristic
81C2×C8×D43D411yescharacteristic
82#13063325C2311yescharacteristic
83#13063322C2311yescharacteristic
84#13063316—21no—
85#13063314—21no—
86#13063305—21no—
87#13063301—21no—
88#13063300—21no—
89#13063300—21no—
90Q8×Dic43—21no—
91#13063290—21no—
92C4×D172C2311yescharacteristic
93D4×Dic43D411yescharacteristic
94#13063287—21no—
95#13063287—21no—
96#13063287D411yescharacteristic
97C4×C22⋊D43—21no—
98(C22⋊D43)⋊C4—21no—
99#13063283—21no—
100C4⋊C4×D43D411yescharacteristic
101C22⋊C4×D43—21no—
102C42×D43C2311yescharacteristic
103#13063259—21no—
104#13063258—21no—
105#13063256—21no—
106C4⋊(C43⋊C8)C2311yescharacteristic
107C4⋊(C43⋊C8)C2311yescharacteristic
108C4⋊(C43⋊C8)C2311yescharacteristic
109Dic43⋊C8—21no—
110#13063249—21no—
111#13063248—21no—
112#13063248—21no—
113#13063247—21no—
114#13063247—21no—
115#13063246—21no—
116#13063245—21no—
117#13063245—21no—
118#13063245—21no—
119#13063245—21no—
120C22⋊(C43⋊C8)—21no—
121(C2×D43)⋊C8—21no—
122(C2×D43)⋊C8—21no—
123(C2×D43)⋊C8—21no—
124(C2×D43)⋊C8—21no—
125#13063235—21no—
126#13063235—21no—
127C4×C43⋊C8C2311yescharacteristic
128C8×Dic43D411yescharacteristic
129C8×Dic43D411yescharacteristic
130C2×SD16×C43—21no—
131C22×C8×C43—21no—
132C4⋊Q8×C43C2311yescharacteristic
133C4⋊Q8×C43C2311yescharacteristic
134C4×D4×C43C2311yescharacteristic
135#106×C43—21no—
136#106×C43—21no—
137#106×C43—21no—
138C4⋊C8×C43C2311yescharacteristic
139C4⋊C8×C43C2311yescharacteristic
140C4⋊C8×C43C2311yescharacteristic
141#103×C43—21no—
142#102×C43—21no—
143C22⋊C8×C43—21no—
144C4×C8×C43C2311yescharacteristic
145C23×D43—21no—
146C2×Q8×C43—21no—
147C2×Q8×C43—21no—
148C2×D4×C43C2×D411yescharacteristic
149C22×C4×C43—21no—
150C2×C22⋊D43—21no—
151C22×Dic43—21no—
152#10621902—82no—
153D4×D43—22no—
154D4×D43—22no—
155C2×D172—21no—
156C2×D172—21no—
157C2×D172—21no—
158C2×D172—41no—
159C2×D172C2×D411yescharacteristic
160C2×C4×D43—21no—
161C2×C4×D43—21no—
162C2×C4×D43—21no—
163C2×C4×D43—42no—
164C2×C4×D43—42no—
165C2×C4×D43—41no—
166C2×C4×D43C2×D411yescharacteristic
167C2×C4×D43C2×D411yescharacteristic
168C2×C4×D43#4111yescharacteristic
169C2×Dic86—21no—
170SD16×C43—42no—
171C2×C8×C43—21no—
172C2×C8×C43—21no—
173C2×C8×C43—21no—
174C2×C8×C43—42no—
175C2×C8×C43C2×D411yescharacteristic
176C2×C8×C43C2×D411yescharacteristic
177C4⋊C4×C43—21no—
178C4⋊C4×C43—21no—
179C4⋊C4×C43—21no—
180C4⋊C4×C43—21no—
181C4⋊C4×C43C2×D411yescharacteristic
182C22⋊C4×C43—21no—
183C42×C43C2411yescharacteristic
184C22⋊Dic43—21no—
185#10621884—42no—
186#10621882—42no—
187(C2×D43)⋊C4—21no—
188(C2×D43)⋊C4—21no—
189(C2×D43)⋊C4—41no—
190(C2×D43)⋊C4—41no—
191(C2×D43)⋊C4—41no—
192C4⋊Dic43—21no—
193C4⋊Dic43—21no—
194C4⋊Dic43—41no—
195C4⋊Dic43C2×D411yescharacteristic
196Dic43⋊C4—21no—
197Dic43⋊C4—41no—
198C4×Dic43—41no—
199C4×Dic43C2×D411yescharacteristic
200C4×Dic43C2×D411yescharacteristic
201C4×Dic43#4111yescharacteristic
202C2×C43⋊C8—21no—
203C2×C43⋊C8—21no—
204C2×C43⋊C8—21no—
205C2×C43⋊C8—42no—
206C2×C43⋊C8C2×D411yescharacteristic
207C2×C43⋊C8C2×D411yescharacteristic
208D344—42no—
209#10621873—42no—
210#10621873—42no—
211C8×D43—22no—
212C8×D43—41no—
213C8×D43—42no—
214C8×D43—42no—
215C8×D43—42no—
216C23×C43—21no—
217C22×D43—24no—
218C22×D43—21no—
219C22×D43—42no—
220C22×D43—42no—
221C22×D43—41no—
222C22×D43#12111yescharacteristic
223Q8×C43—41no—
224Q8×C43—41no—
225Q8×C43—81no—
226D4×C43—21no—
227D4×C43#13512yes—
228C2×C4×C43—21no—
229C2×C4×C43—41no—
230C2×C4×C43—41no—
231C2×C4×C43—41no—
232C2×C4×C43—41no—
233C2×C4×C43C22×D411yescharacteristic
234C2×C4×C43C22×D411yescharacteristic
235C2×C4×C43C2×#4111yescharacteristic
236C22⋊D43—24no—
237C2×Dic43—21no—
238C2×Dic43—42no—
239C2×Dic43—41no—
240C2×Dic43#12111yescharacteristic
241C2×Dic43#12111yescharacteristic
242C2×Dic43#12111yescharacteristic
243D172—21no—
244D172—41no—
245D172—41no—
246D172—41no—
247D172—41no—
248D172—81no—
249D172—82no—
250D172#13512yes—
251C4×D43—22no—
252C4×D43—21no—
253C4×D43—21no—
254C4×D43—21no—
255C4×D43—21no—
256C4×D43—42no—
257C4×D43—42no—
258C4×D43—41no—
259C4×D43—41no—
260C4×D43—82no—
261Dic86—41no—
262Dic86—41no—
263C8×C43—21no—
264C8×C43—41no—
265C8×C43—41no—
266C8×C43—41no—
267C8×C43AGL(1,ℤ/8)12yes—
268C43⋊C8—21no—
269C43⋊C8—21no—
270C43⋊C8—41no—
271C43⋊C8—41no—
272C43⋊C8—41no—
273#19257—431nomaximal, Sylow
274C22×C43—22no—
275C22×C43—41no—
276C22×C43—41no—
277C22×C43C2×#12111yescharacteristic
278C2×D43—21no—
279C2×D43—21no—
280C2×D43—22no—
281C2×D43—48no—
282C2×D43—41no—
283C2×D43—41no—
284C2×D43—81no—
285C2×D43—81no—
286C2×D43—81no—
287C2×D43#47112yes—
288C4×C43—21no—
289C4×C43—41no—
290C4×C43—81no—
291C4×C43—81no—
292C4×C43C2×#13511yescharacteristic
293C4×C43C2×#13511yescharacteristic
294C4×C43C2×AGL(1,ℤ/8)11yescharacteristic
295C4×C43#57511yescharacteristic
296Dic43—21no—
297Dic43—21no—
298Dic43—21no—
299Dic43—41no—
300Dic43—81no—
301#3167—431no—
302#3110—431no—
303#3109—431no—
304C2×C8×D4—431no—
305#1683—431no—
306#1683—431no—
307#1681—431no—
308#1681—431no—
309#1671—431no—
310#1671D4311yescharacteristic, complemented
311#1665—431no—
312#1665—431no—
313#1568—431no—
314#1552—431no—
315#1551—431no—
316C2×C43—42no—
317C2×C43#303611yescharacteristic
318C2×C43#305011yescharacteristic
319C2×C43C2×#47111yescharacteristic
320D43—22no—
321D43—42no—
322D43—161no—
323C23×C8—861no—
324#533—431no—
325#532—431no—
326C2×C4×D4—431no—
327#498C2×D4311yescharacteristic, complemented
328#492—431no—
329#487—431no—
330#486—431no—
331#484—861no—
332#481—861no—
333#476—431no—
334#476C2×D4311yescharacteristic
335#474—431no—
336#474—431no—
337#465—861no—
338#465—861no—
339#461—431no—
340#461C2×D4311yescharacteristic
341#459—431no—
342#459—431no—
343#450—861no—
344#447—861no—
345#442—861no—
346#442—861no—
347#440—861no—
348#440—861no—
349C4×SD16—861no—
350C4×SD16—861no—
351C8×D4—431no—
352C8×D4—431no—
353C8×D4—431no—
354C8×D4—861no—
355C8×D4—861no—
356C8×D4C2×D4311yescharacteristic
357#432—431no—
358#432—431no—
359C2×C4⋊C8—431no—
360C2×C22⋊C8—861no—
361C2×C4×C8—431no—
362#335—431no—
363#335—431no—
364#334—431no—
365#334C2×D4311yescharacteristic, complemented
366#333—431no—
367#333C2×D4311yescharacteristic, complemented
368#332—431no—
369#332—431no—
370#332—431no—
371#332C2×D4311yescharacteristic, complemented
372#331—431no—
373#331—431no—
374C43#1925711yescharacteristic, complemented, Sylow
375C2×#41—861no—
376C22×D4—431no—
377C23×C4—861no—
378C2×SD16—21no—
379C2×SD16—861no—
380C2×SD16—861no—
381C2×SD16—861no—
382C2×D8—861no—
383C2×D8—861no—
384C22×C8—21no—
385C22×C8—431no—
386C22×C8—431no—
387C22×C8—861no—
388C22×C8—861no—
389C22×C8—861no—
390C22×C8—861no—
391C22×C8—1724no—
392C4⋊Q8—431no—
393C4⋊Q8C22×D4311yescharacteristic
394C4⋊Q8C22×D4311yescharacteristic
395#127—431no—
396#125—861no—
397#124—861no—
398C22⋊Q8—861no—
399C22⋊Q8—861no—
400#121—861no—
401#121—861no—
402C4×Q8—861no—
403C4×Q8—861no—
404C4×D4—431no—
405C4×D4—431no—
406C4×D4—431no—
407C4×D4—861no—
408C4×D4—861no—
409C4×D4—861no—
410C4×D4—861no—
411C4×D4C22×D4311yescharacteristic
412#117—861no—
413C2×C4⋊C4—431no—
414C2×C22⋊C4—861no—
415C2×C42—431no—
416#107—861no—
417#107—861no—
418#106—21no—
419#106—21no—
420#106—21no—
421#106—861no—
422C4⋊C8—431no—
423C4⋊C8—431no—
424C4⋊C8—431no—
425C4⋊C8—861no—
426C4⋊C8C22×D4311yescharacteristic
427C4⋊C8C22×D4311yescharacteristic
428C4⋊C8C22×D4311yescharacteristic
429#103—21no—
430#103—861no—
431#103—861no—
432#103—861no—
433#102—21no—
434#102—861no—
435#102—861no—
436#102—861no—
437#102—861no—
438#102—861no—
439#102—861no—
440#102—861no—
441C22⋊C8—21no—
442C22⋊C8—861no—
443C22⋊C8—861no—
444C22⋊C8—861no—
445C22⋊C8—861no—
446C22⋊C8—861no—
447#97—861no—
448#97—861no—
449C4×C8—431no—
450C4×C8—431no—
451C4×C8—431no—
452C4×C8C22×D4311yescharacteristic
453C24—861no—
454#41—3442no—
455C2×Q8—21no—
456C2×Q8—21no—
457C2×Q8—861no—
458C2×D4—431no—
459C2×D4—861no—
460C2×D4—862no—
461C2×D4—862no—
462C2×D4—861no—
463C2×D4—861no—
464C2×D4—861no—
465C2×D4—1721no—
466C2×D4D4×D4311yescharacteristic
467C22×C4—21no—
468C22×C4—431no—
469C22×C4—431no—
470C22×C4—431no—
471C22×C4—861no—
472C22×C4—861no—
473C22×C4—861no—
474C22×C4—861no—
475C22×C4—1721no—
476C22×C4—1722no—
477C22×C4—1722no—
478SD16—42no—
479SD16—1722no—
480SD16—1722no—
481SD16—1722no—
482D8—1722no—
483D8—1722no—
484C2×C8—21no—
485C2×C8—21no—
486C2×C8—21no—
487C2×C8—42no—
488C2×C8—431no—
489C2×C8—431no—
490C2×C8—862no—
491C2×C8—861no—
492C2×C8—861no—
493C2×C8—861no—
494C2×C8—1721no—
495C2×C8—1722no—
496C2×C8—1722no—
497C2×C8—1722no—
498C2×C8—1722no—
499C2×C8D4×D4311yescharacteristic
500C2×C8D4×D4311yescharacteristic
501C4⋊C4—21no—
502C4⋊C4—21no—
503C4⋊C4—21no—
504C4⋊C4—21no—
505C4⋊C4—431no—
506C4⋊C4—861no—
507C4⋊C4—861no—
508C4⋊C4—861no—
509C4⋊C4—1721no—
510C4⋊C4—1721no—
511C4⋊C4D4×D4311yescharacteristic
512C22⋊C4—21no—
513C22⋊C4—861no—
514C22⋊C4—861no—
515C22⋊C4—861no—
516C22⋊C4—1721no—
517C22⋊C4—1721no—
518C22⋊C4—1721no—
519C42—431no—
520C42—431no—
521C42—431no—
522C42—1721no—
523C42C23×D4311yescharacteristic
524C23—21no—
525C23—431no—
526C23—864no—
527C23—861no—
528C23—1722no—
529C23—1722no—
530C23—1721no—
531Q8—41no—
532Q8—41no—
533Q8—81no—
534Q8—1721no—
535Q8—1721no—
536D4—21no—
537D4—432no—
538D4—864no—
539D4—861no—
540D4—3441no—
541D4—3442no—
542D4—1721no—
543D4—1721no—
544D4—1721no—
545D4—1721no—
546D4#1306334612yes—
547C2×C4—21no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—431no—
553C2×C4—431no—
554C2×C4—431no—
555C2×C4—862no—
556C2×C4—861no—
557C2×C4—861no—
558C2×C4—861no—
559C2×C4—861no—
560C2×C4—861no—
561C2×C4—3442no—
562C2×C4—1722no—
563C2×C4—1722no—
564C2×C4—1722no—
565C2×C4—1721no—
566C2×C4—1721no—
567C2×C4—1721no—
568C2×C4C2×D4×D4311yescharacteristic
569C2×C4C2×D4×D4311yescharacteristic
570C2×C4#41×D4311yescharacteristic
571C8—21no—
572C8—41no—
573C8—41no—
574C8—41no—
575C8—861no—
576C8—861no—
577C8—1721no—
578C8—1721no—
579C8—1721no—
580C8#1306335212yes—
581C22—22no—
582C22—41no—
583C22—41no—
584C22—432no—
585C22—861no—
586C22—861no—
587C22—862no—
588C22—3441no—
589C22—3441no—
590C22—3441no—
591C22—1728no—
592C22—1721no—
593C22—1721no—
594C22#121×D4311yescharacteristic
595C4—21no—
596C4—41no—
597C4—81no—
598C4—81no—
599C4—861no—
600C4—861no—
601C4—861no—
602C4—3441no—
603C4—1721no—
604C4#135×D4311yescharacteristic
605C4C2×#1306334611yescharacteristic
606C4C2×#1306335211yescharacteristic
607C4#1458369811yescharacteristic
608C2—42no—
609C2—862no—
610C2—1722no—
611C2—6881no—
612C2#1914406011yescharacteristic
613C2#1914417111yescharacteristic
614C2#471×D4311yescharacteristic
subgroupG/H
centerC22#121×D43
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#1671C2
socleC22×C43C2×#121
prime radical#19144688C2
hypercenter#1671D43
hypocenterC43#19257
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #1671

Complements

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

NH ≅ G/Ntype
1. #19145156C2semidirect
2. #19144693C2semidirect
4. C8×D4×D43C2semidirect
5. #19134049C2semidirect
6. #19134048C2semidirect
7. #19134035C2semidirect
8. #19134034C2semidirect
9. #19133967C2semidirect
10. #19133937C2semidirect
11. #19133936C2semidirect
12. #19133355C2semidirect
13. #19133292C2semidirect
14. #19133289C2semidirect
15. C43×#1671C2semidirect
20. #14583272C22semidirect
21. #14583251C22semidirect
22. #14583247C22semidirect
51. #14582651C22semidirect
52. #14582651C22semidirect
53. #14582650C22semidirect
54. #14582648C22semidirect
55. #14582646C22semidirect
56. #14582645C22semidirect
57. #14582644C22semidirect
58. #14582642C22semidirect
59. #14582642C22semidirect
60. C43×#498C22semidirect
64. C43×#334C22semidirect
65. C43×#333C22semidirect
66. C43×#332C22semidirect
310. #1671D43semidirect
327. #498C2×D43semidirect
365. #334C2×D43semidirect
367. #333C2×D43semidirect
371. #332C2×D43semidirect
374. C43#19257semidirect

Maximal subgroups

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

subgroupindex
#191451562
#191446932
#191446882
C8×D4×D432
#191340492
#191340482
#191340352
#191340342
#191339672
#191339372
#191339362
#191333552
#191332922
#191332892
C43×#16712
#1925743