Finite Group Databasebeta

← #25081822

Subgroups — #25081822

Order 11008.

696 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#19145719C211yesmaximal, characteristic, complemented
2#476×D43C211yesmaximal, characteristic, complemented
3#19144054C211yesmaximal, characteristic
4#19143616C211yesmaximal, characteristic, complemented
5#19134003C211yesmaximal, characteristic, complemented
6#19134002C211yesmaximal, characteristic, complemented
7#19134001C211yesmaximal, characteristic, complemented
8#19133973C211yesmaximal, characteristic, complemented
9#19133972C211yesmaximal, characteristic, complemented
10#19133971C211yesmaximal, characteristic, complemented
11#19133970C211yesmaximal, characteristic, complemented
12#19133364C211yesmaximal, characteristic, complemented
13#19133274C211yesmaximal, characteristic, complemented
14#19133241C211yesmaximal, characteristic, complemented
15C43×#1677C211yesmaximal, characteristic, complemented
16C2×#13063349—21no—
17#14583447C2211yescharacteristic
18C4⋊Q8×D43C2211yescharacteristic
19C4×D4×D43C2211yescharacteristic
20#14583297C2211yescharacteristic, complemented
21#14583295C2211yescharacteristic, complemented
22#14583245C2211yescharacteristic, complemented
23#14583216—21no—
24#14583216—21no—
25#14583190C2211yescharacteristic
26#14583189C2211yescharacteristic
27#14583188—21no—
28#14583187—21no—
29#14583187—21no—
30#14583187—21no—
31#14583186C2211yescharacteristic
32#14583113—21no—
33#14583112—21no—
34#14583105C2211yescharacteristic
35#14583104C2211yescharacteristic
36#14583091C2211yescharacteristic
37C8×D172C2211yescharacteristic
38D4×C43⋊C8C2211yescharacteristic
39#14582964C2211yescharacteristic
40C8×C22⋊D43—21no—
41(C22⋊D43)⋊C8—21no—
42#14582951C2211yescharacteristic
43#14582950C2211yescharacteristic
44#106×D43—21no—
45#14582921C2211yescharacteristic
46C4⋊C8×D43C2211yescharacteristic
47#14582897—21no—
48#102×D43—21no—
49C2×(C2×D43)⋊C8—21no—
50C22⋊C8×D43—21no—
51#14582650C2211yescharacteristic, complemented
52#14582649C2211yescharacteristic, complemented
53#14582649C2211yescharacteristic, complemented
54#14582648C2211yescharacteristic, complemented
55#14582647C2211yescharacteristic, complemented
56#14582647C2211yescharacteristic, complemented
57#14582646C2211yescharacteristic, complemented
58#14582644C2211yescharacteristic, complemented
59#14582643C2211yescharacteristic, complemented
60C43×#486C2211yescharacteristic, complemented
61C43×#476C2211yescharacteristic
62C43×#459C2211yescharacteristic
63C8×D4×C43C2211yescharacteristic
64C43×#334C2211yescharacteristic, complemented
65C43×#333C2211yescharacteristic, complemented
66C43×#331C2211yescharacteristic, complemented
67C2×#10621900—21no—
68C2×Q8×D43—21no—
69C2×D4×D43D411yescharacteristic
70C22×C4×D43—21no—
71#13063349—44no—
72C2×#10621873—21no—
73C2×#10621883—21no—
74C2×#10621882—21no—
75C2×#10621872—21no—
76C22×C43⋊C8—21no—
77C2×C8×D43—21no—
78C2×C8×D43—21no—
79C2×C8×D43—21no—
80#13063325C2311yescharacteristic
81#13063325C2311yescharacteristic
82#13063324—21no—
83#13063324—21no—
84#13063323—21no—
85#13063312—21no—
86#13063296—21no—
87#13063296—21no—
88C4×D172C2311yescharacteristic
89D4×Dic43—21no—
90D4×Dic43—21no—
91D4×Dic43D411yescharacteristic
92#13063287D411yescharacteristic
93C4×C22⋊D43—21no—
94(C22⋊D43)⋊C4—21no—
95C4⋊C4×D43—21no—
96C4⋊C4×D43—21no—
97C4⋊C4×D43D411yescharacteristic
98C22⋊C4×D43—21no—
99C42×D43C2311yescharacteristic
100#13063257—21no—
101#13063257—21no—
102#13063257—21no—
103#13063256—21no—
104#13063256—21no—
105#13063256—21no—
106#13063256—21no—
107C4⋊(C43⋊C8)C2311yescharacteristic
108C4⋊(C43⋊C8)C2311yescharacteristic
109C4⋊(C43⋊C8)C2311yescharacteristic
110Dic43⋊C8—21no—
111Dic43⋊C8—21no—
112Dic43⋊C8D411yescharacteristic
113Dic43⋊C8D411yescharacteristic
114#13063250—21no—
115#13063248—21no—
116#13063247—21no—
117#13063246—21no—
118#13063246—21no—
119#13063246—21no—
120#13063246—21no—
121#13063245—21no—
122C22⋊(C43⋊C8)—21no—
123(C2×D43)⋊C8—21no—
124(C2×D43)⋊C8—21no—
125(C2×D43)⋊C8—21no—
126(C2×D43)⋊C8D411yescharacteristic
127(C2×D43)⋊C8D411yescharacteristic
128C4×C43⋊C8C2311yescharacteristic
129C8×Dic43—21no—
130C2×D8×C43—21no—
131C22×C8×C43—21no—
132C4⋊Q8×C43C2311yescharacteristic
133#127×C43C2311yescharacteristic
134C4×D4×C43C2311yescharacteristic
135#106×C43—21no—
136C4⋊C8×C43C2311yescharacteristic
137C4⋊C8×C43C2311yescharacteristic
138C4⋊C8×C43C2311yescharacteristic
139#102×C43—21no—
140#102×C43—21no—
141#102×C43—21no—
142#102×C43—21no—
143C22⋊C8×C43—21no—
144C4×C8×C43C2311yescharacteristic
145C23×D43—21no—
146C2×Q8×C43—21no—
147C2×D4×C43—21no—
148C2×D4×C43—21no—
149C2×D4×C43—21no—
150C2×D4×C43C2×D411yescharacteristic
151C22×C4×C43—21no—
152C2×C22⋊D43—21no—
153C2×C22⋊D43—41no—
154C22×Dic43—21no—
155C22×Dic43—41no—
156Q8×D43—82no—
157#10621900—42no—
158#10621900—42no—
159D4×D43—22no—
160D4×D43SD1614yes—
161C2×D172C2×D411yescharacteristic
162C2×C4×D43—21no—
163C2×C4×D43—21no—
164C2×C4×D43—21no—
165C2×C4×D43—41no—
166C2×C4×D43—81no—
167C2×C4×D43—81no—
168C2×C4×D43C2×D411yescharacteristic
169C2×C4×D43C2×D411yescharacteristic
170C2×C4×D43#4111yescharacteristic
171C2×Dic86—21no—
172C2×Dic86—21no—
173C2×Dic86—41no—
174D8×C43—42no—
175C2×C8×C43—21no—
176C2×C8×C43—21no—
177C2×C8×C43—21no—
178C2×C8×C43—81no—
179C2×C8×C43C2×D411yescharacteristic
180C2×C8×C43C2×D411yescharacteristic
181C4⋊C4×C43—21no—
182C4⋊C4×C43—21no—
183C4⋊C4×C43C2×D411yescharacteristic
184C22⋊C4×C43—21no—
185C42×C43C2411yescharacteristic
186C22⋊Dic43—21no—
187C22⋊Dic43—41no—
188C22⋊Dic43—41no—
189#10621883—42no—
190#10621882—42no—
191(C2×D43)⋊C4—21no—
192(C2×D43)⋊C4—21no—
193C4⋊Dic43—21no—
194C4⋊Dic43—21no—
195C4⋊Dic43—21no—
196C4⋊Dic43—21no—
197C4⋊Dic43C2×D411yescharacteristic
198Dic43⋊C4—21no—
199Dic43⋊C4—41no—
200Dic43⋊C4—41no—
201C4×Dic43C2×D411yescharacteristic
202C4×Dic43C2×D411yescharacteristic
203C4×Dic43#4111yescharacteristic
204C2×C43⋊C8—21no—
205C2×C43⋊C8—21no—
206C2×C43⋊C8—21no—
207C2×C43⋊C8—81no—
208C2×C43⋊C8C2×D411yescharacteristic
209C2×C43⋊C8C2×D411yescharacteristic
210#10621873—42no—
211#10621872—42no—
212C8×D43—42no—
213C8×D43—81no—
214C8×D43—81no—
215C23×C43—21no—
216C23×C43—41no—
217C22×D43—21no—
218C22×D43—24no—
219C22×D43—81no—
220C22×D43—81no—
221C22×D43#12111yescharacteristic
222Q8×C43—81no—
223D4×C43—21no—
224D4×C43—41no—
225D4×C43—41no—
226D4×C43—41no—
227D4×C43—41no—
228D4×C43—81no—
229D4×C43C2×SD1612yes—
230C2×C4×C43—21no—
231C2×C4×C43—41no—
232C2×C4×C43—41no—
233C2×C4×C43—41no—
234C2×C4×C43C22×D411yescharacteristic
235C2×C4×C43C22×D411yescharacteristic
236C2×C4×C43C2×#4111yescharacteristic
237C22⋊D43—24no—
238C22⋊D43—82no—
239C2×Dic43—21no—
240C2×Dic43—41no—
241C2×Dic43—41no—
242C2×Dic43—81no—
243C2×Dic43—82no—
244C2×Dic43#12111yescharacteristic
245C2×Dic43#12111yescharacteristic
246C2×Dic43#12111yescharacteristic
247D172—21no—
248D172C2×SD1612yes—
249C4×D43—21no—
250C4×D43—21no—
251C4×D43—41no—
252C4×D43—41no—
253C4×D43—41no—
254C4×D43—81no—
255C4×D43—81no—
256C4×D43—82no—
257C4×D43C2×SD1612yes—
258C4×D43#13512yes—
259Dic86—41no—
260Dic86—41no—
261Dic86—82no—
262Dic86—81no—
263C8×C43—21no—
264C8×C43—21no—
265C8×C43—41no—
266C8×C43—41no—
267C8×C43—41no—
268C43⋊C8—21no—
269C43⋊C8—21no—
270C43⋊C8—41no—
271C43⋊C8—41no—
272C43⋊C8—41no—
273#19391—431nomaximal, Sylow
274C22×C43—22no—
275C22×C43—41no—
276C22×C43—41no—
277C22×C43—81no—
278C22×C43—81no—
279C22×C43—81no—
280C22×C43C2×#12111yescharacteristic
281C2×D43—21no—
282C2×D43—21no—
283C2×D43—22no—
284C2×D43—41no—
285C2×D43—41no—
286C2×D43—84no—
287C2×D43#46512yes—
288C4×C43—21no—
289C4×C43—41no—
290C4×C43—81no—
291C4×C43C22×SD1611yescharacteristic
292C4×C43C2×#13511yescharacteristic
293C4×C43#57711yescharacteristic
294C4×C43#57711yescharacteristic
295Dic43—21no—
296Dic43—21no—
297Dic43—41no—
298Dic43—81no—
299Dic43—81no—
300Dic43#46512yes—
301#3227—431no—
302C2×#476—431no—
303#3036—431no—
304#2972—431no—
305#1677—431no—
306#1677—431no—
307#1677—431no—
308#1677D4311yescharacteristic, complemented
309#1671—431no—
310#1671—431no—
311#1671—431no—
312#1671—431no—
313#1570—431no—
314#1548—431no—
315#1540—431no—
316C2×C43—42no—
317C2×C43—161no—
318C2×C43#304211yescharacteristic
319C2×C43C2×#46511yescharacteristic
320C2×C43#306811yescharacteristic
321D43—22no—
322D43—42no—
323C2×AGL(1,ℤ/8)—861no—
324#532—431no—
325C2×C4⋊Q8—431no—
326C2×C4×D4—431no—
327#498—431no—
328#498—431no—
329#486—431no—
330#486C2×D4311yescharacteristic, complemented
331#481—861no—
332#481—861no—
333#476—431no—
334#476—431no—
335#476—431no—
336#476—861no—
337#476—861no—
338#476—861no—
339#476—861no—
340#476C2×D4311yescharacteristic
341#463—861no—
342#463—861no—
343#461—431no—
344#461—431no—
345#459—431no—
346#459C2×D4311yescharacteristic
347C8×D4—431no—
348C8×D4—431no—
349C8×D4—431no—
350C8×D4—861no—
351C8×D4—861no—
352C8×D4C2×D4311yescharacteristic
353#431—431no—
354#431—431no—
355C2×#106—861no—
356#423—431no—
357C2×C4⋊C8—431no—
358#417—861no—
359C2×#102—861no—
360C2×C22⋊C8—861no—
361C2×C22⋊C8—861no—
362#334—431no—
363#334—431no—
364#334—431no—
365#334C2×D4311yescharacteristic, complemented
366#333—431no—
367#333—431no—
368#333—431no—
369#333C2×D4311yescharacteristic, complemented
370#332—431no—
371#332—431no—
372#331—431no—
373#331C2×D4311yescharacteristic, complemented
374C43#1939111yescharacteristic, complemented, Sylow
375C2×#41—861no—
376C22×Q8—861no—
377C22×D4—431no—
378C23×C4—861no—
379AGL(1,ℤ/8)—1724no—
380C2×SD16—861no—
381C2×SD16—861no—
382C2×D8—21no—
383C2×D8—861no—
384C2×M16—861no—
385C22×C8—21no—
386C22×C8—861no—
387C22×C8—861no—
388C22×C8—861no—
389C22×C8—861no—
390C4⋊Q8—431no—
391C4⋊Q8—431no—
392C4⋊Q8—861no—
393C4⋊Q8—861no—
394C4⋊Q8—861no—
395C4⋊Q8C22×D4311yescharacteristic
396#127C22×D4311yescharacteristic
397#124—861no—
398#121—861no—
399#121—861no—
400C4×D4—431no—
401C4×D4—431no—
402C4×D4—431no—
403C4×D4—861no—
404C4×D4—861no—
405C4×D4—861no—
406C4×D4—861no—
407C4×D4C22×D4311yescharacteristic
408C2×C4⋊C4—431no—
409C2×C4⋊C4—861no—
410C2×C4⋊C4—861no—
411C2×C22⋊C4—861no—
412C2×C42—431no—
413#106—21no—
414#106—861no—
415#106—861no—
416#106—861no—
417#106—861no—
418#106—861no—
419#106—861no—
420#106—861no—
421C4⋊C8—431no—
422C4⋊C8—431no—
423C4⋊C8—431no—
424C4⋊C8—431no—
425C4⋊C8—431no—
426C4⋊C8—861no—
427C4⋊C8—861no—
428C4⋊C8C22×D4311yescharacteristic
429C4⋊C8C22×D4311yescharacteristic
430C4⋊C8C22×D4311yescharacteristic
431#103—861no—
432#103—861no—
433#102—21no—
434#102—21no—
435#102—21no—
436#102—21no—
437#102—861no—
438#102—861no—
439#102—861no—
440#102—861no—
441#102—861no—
442#102—861no—
443C22⋊C8—21no—
444C22⋊C8—431no—
445C22⋊C8—431no—
446C22⋊C8—861no—
447C22⋊C8—861no—
448C22⋊C8—861no—
449C22⋊C8—861no—
450C4×C8—431no—
451C4×C8—861no—
452C4×C8C22×D4311yescharacteristic
453C24—861no—
454#41—1722no—
455#41—1722no—
456C2×Q8—21no—
457C2×Q8—861no—
458C2×Q8—861no—
459C2×Q8—3442no—
460C2×Q8—1721no—
461C2×D4—21no—
462C2×D4—21no—
463C2×D4—21no—
464C2×D4—434no—
465C2×D4—431no—
466C2×D4—862no—
467C2×D4—861no—
468C2×D4—1721no—
469C2×D4D4×D4311yescharacteristic
470C22×C4—21no—
471C22×C4—431no—
472C22×C4—431no—
473C22×C4—431no—
474C22×C4—861no—
475C22×C4—861no—
476C22×C4—861no—
477C22×C4—861no—
478C22×C4—3441no—
479C22×C4—3441no—
480C22×C4—1721no—
481C22×C4—1721no—
482SD16—1722no—
483SD16—1722no—
484D8—42no—
485D8—1722no—
486M16—1722no—
487C2×C8—21no—
488C2×C8—21no—
489C2×C8—21no—
490C2×C8—81no—
491C2×C8—431no—
492C2×C8—431no—
493C2×C8—861no—
494C2×C8—861no—
495C2×C8—861no—
496C2×C8—3441no—
497C2×C8—3441no—
498C2×C8—3441no—
499C2×C8—1722no—
500C2×C8D4×D4311yescharacteristic
501C2×C8D4×D4311yescharacteristic
502C4⋊C4—21no—
503C4⋊C4—21no—
504C4⋊C4—431no—
505C4⋊C4—861no—
506C4⋊C4—861no—
507C4⋊C4—861no—
508C4⋊C4—861no—
509C4⋊C4—861no—
510C4⋊C4—1721no—
511C4⋊C4—1721no—
512C4⋊C4D4×D4311yescharacteristic
513C22⋊C4—21no—
514C22⋊C4—861no—
515C22⋊C4—861no—
516C22⋊C4—861no—
517C22⋊C4—1721no—
518C22⋊C4—1721no—
519C42—431no—
520C42—431no—
521C42—431no—
522C42C23×D4311yescharacteristic
523C23—21no—
524C23—41no—
525C23—431no—
526C23—864no—
527C23—861no—
528C23—3441no—
529C23—3441no—
530Q8—81no—
531Q8—3441no—
532Q8—3442no—
533Q8—1721no—
534Q8—1721no—
535D4—21no—
536D4—41no—
537D4—41no—
538D4—41no—
539D4—41no—
540D4—81no—
541D4—432no—
542D4—864no—
543D4—861no—
544D4—3442no—
545D4SD16×D4312yes—
546C2×C4—21no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—431no—
551C2×C4—432no—
552C2×C4—432no—
553C2×C4—431no—
554C2×C4—431no—
555C2×C4—861no—
556C2×C4—861no—
557C2×C4—861no—
558C2×C4—3441no—
559C2×C4—3441no—
560C2×C4—3442no—
561C2×C4—3442no—
562C2×C4—3441no—
563C2×C4—1721no—
564C2×C4—1721no—
565C2×C4—1721no—
566C2×C4—1721no—
567C2×C4—1721no—
568C2×C4C2×D4×D4311yescharacteristic
569C2×C4C2×D4×D4311yescharacteristic
570C2×C4#41×D4311yescharacteristic
571C8—21no—
572C8—21no—
573C8—41no—
574C8—41no—
575C8—41no—
576C8—861no—
577C8—861no—
578C8—1721no—
579C8—1721no—
580C8—1721no—
581C22—22no—
582C22—41no—
583C22—41no—
584C22—81no—
585C22—81no—
586C22—81no—
587C22—432no—
588C22—861no—
589C22—861no—
590C22—862no—
591C22—3444no—
592C22—1721no—
593C22—1721no—
594C22#121×D4311yescharacteristic
595C4—21no—
596C4—41no—
597C4—81no—
598C4—432no—
599C4—861no—
600C4—861no—
601C4—3441no—
602C4—3441no—
603C4—1721no—
604C4C2×SD16×D4311yescharacteristic
605C4#135×D4311yescharacteristic
606C4#1458370611yescharacteristic
607C4#1458370911yescharacteristic
608C2—42no—
609C2—161no—
610C2—862no—
611C2—1722no—
612C2#1914410511yescharacteristic
613C2#465×D4311yescharacteristic
614C2#1914432111yescharacteristic
subgroupG/H
centerC22#121×D43
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#1677C2
socleC22×C43C2×#121
prime radical#19144054C2
hypercenter#1677D43
hypocenterC43#19391
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #1677

Complements

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

NH ≅ G/Ntype
1. #19145719C2semidirect
2. #476×D43C2semidirect
4. #19143616C2semidirect
5. #19134003C2semidirect
6. #19134002C2semidirect
7. #19134001C2semidirect
8. #19133973C2semidirect
9. #19133972C2semidirect
10. #19133971C2semidirect
11. #19133970C2semidirect
12. #19133364C2semidirect
13. #19133274C2semidirect
14. #19133241C2semidirect
15. C43×#1677C2semidirect
20. #14583297C22semidirect
21. #14583295C22semidirect
22. #14583245C22semidirect
51. #14582650C22semidirect
52. #14582649C22semidirect
53. #14582649C22semidirect
54. #14582648C22semidirect
55. #14582647C22semidirect
56. #14582647C22semidirect
57. #14582646C22semidirect
58. #14582644C22semidirect
59. #14582643C22semidirect
60. C43×#486C22semidirect
64. C43×#334C22semidirect
65. C43×#333C22semidirect
66. C43×#331C22semidirect
308. #1677D43semidirect
330. #486C2×D43semidirect
365. #334C2×D43semidirect
369. #333C2×D43semidirect
373. #331C2×D43semidirect
374. C43#19391semidirect

Maximal subgroups

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

subgroupindex
#191457192
#476×D432
#191440542
#191436162
#191340032
#191340022
#191340012
#191339732
#191339722
#191339712
#191339702
#191333642
#191332742
#191332412
C43×#16772
#1939143