Finite Group Databasebeta

← #25082044

Subgroups — #25082044

Order 11008.

628 conjugacy classes of subgroups.

The subgroup lattice has 590 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19144740C211yesmaximal, characteristic
2#19144660C211yesmaximal, characteristic, complemented
3#19143703C211yesmaximal, characteristic, complemented
4#19134036C211yesmaximal, characteristic, complemented
5#19134029C211yesmaximal, characteristic, complemented
6#19134022C211yesmaximal, characteristic, complemented
7#19134015C211yesmaximal, characteristic, complemented
8#19133962C211yesmaximal, characteristic, complemented
9#19133957C211yesmaximal, characteristic, complemented
10#19133940C211yesmaximal, characteristic, complemented
11#19133933C211yesmaximal, characteristic, complemented
12#19133375C211yesmaximal, characteristic, complemented
13#19133295C211yesmaximal, characteristic, complemented
14#19133244C211yesmaximal, characteristic, complemented
15C43×#3210C211yesmaximal, characteristic, complemented
16C4×#10621898C2211yescharacteristic
17#14583237—21no—
18#14583220—21no—
19#14583181C2211yescharacteristic
20#14583181C2211yescharacteristic
21#14583176C2211yescharacteristic
22#14583176C2211yescharacteristic
23#14583106C2211yescharacteristic
24#14583101C2211yescharacteristic
25#14583096C2211yescharacteristic
26#14583091C2211yescharacteristic
27#14583059—21no—
28#14583042—21no—
29C8×Dic86C2211yescharacteristic
30C8×Dic86C2211yescharacteristic
31#14583009—21no—
32#14582999—21no—
33C4×#10621885—21no—
34C4×#10621884—21no—
35C8×D172C2211yescharacteristic
36C8×D172C2211yescharacteristic
37(C22⋊D43)⋊C8—21no—
38(C22⋊D43)⋊C8—21no—
39#14582956C2211yescharacteristic
40#14582952C2211yescharacteristic
41#14582951—21no—
42C2×C4⋊(C43⋊C8)C2211yescharacteristic
43C4⋊C8×D43—21no—
44#14582652C2211yescharacteristic
45#14582652C2211yescharacteristic
46#14582650C2211yescharacteristic
47#14582650C2211yescharacteristic
48#14582645C2211yescharacteristic
49#14582645C2211yescharacteristic
50#14582645C2211yescharacteristic
51#14582645C2211yescharacteristic
52#14582645C2211yescharacteristic
53#14582645C2211yescharacteristic
54#14582643C2211yescharacteristic
55#14582643C2211yescharacteristic
56C43×#533C2211yescharacteristic
57C43×#532C2211yescharacteristic
58C43×#494C2211yescharacteristic
59C43×#492C2211yescharacteristic
60C43×#487C2211yescharacteristic
61C43×#486C2211yescharacteristic
62C43×#464—21no—
63C43×#464—21no—
64C43×#452—21no—
65C43×#452—21no—
66C43×#431C2211yescharacteristic
67C2×#10621898D411yescharacteristic
68C2×#10621885—21no—
69C2×#10621883—21no—
70C2×#10621884—21no—
71C2×#10621882—21no—
72C22×C43⋊C8—21no—
73C2×C8×D43—21no—
74C2×C8×D43—21no—
75C4×Dic86D411yescharacteristic
76C4×Dic86C2311yescharacteristic
77C4×D172D411yescharacteristic
78C4×D172C2311yescharacteristic
79C4×C22⋊D43—21no—
80C4×C22⋊D43—21no—
81#13063284D411yescharacteristic
82#13063282—21no—
83C42×D43—21no—
84#13063258—21no—
85#13063258—21no—
86#13063256—21no—
87#13063256—21no—
88C4⋊(C43⋊C8)—21no—
89C4⋊(C43⋊C8)C2311yescharacteristic
90C4⋊(C43⋊C8)C2311yescharacteristic
91C4⋊(C43⋊C8)C2311yescharacteristic
92C4⋊(C43⋊C8)C2311yescharacteristic
93C4⋊(C43⋊C8)C2311yescharacteristic
94C4⋊(C43⋊C8)C2311yescharacteristic
95Dic43⋊C8—21no—
96Dic43⋊C8—21no—
97#13063249—21no—
98#13063249—21no—
99#13063248—21no—
100#13063248—21no—
101#13063246—21no—
102#13063246—21no—
103#13063245—21no—
104#13063245—21no—
105C22⋊(C43⋊C8)—21no—
106C22⋊(C43⋊C8)—21no—
107(C2×D43)⋊C8—21no—
108(C2×D43)⋊C8—21no—
109#13063236—21no—
110C4×C43⋊C8—21no—
111C8×Dic43—21no—
112C8×Dic43—21no—
113C2×#41×C43—21no—
114C2×Q16×C43—21no—
115C2×Q16×C43—21no—
116C2×SD16×C43—21no—
117C2×SD16×C43—21no—
118C4⋊Q8×C43C2311yescharacteristic
119C4⋊Q8×C43C2311yescharacteristic
120C4⋊Q8×C43C2311yescharacteristic
121#127×C43C2311yescharacteristic
122#125×C43—21no—
123#124×C43—21no—
124C22⋊Q8×C43—21no—
125C22⋊Q8×C43—21no—
126#121×C43—21no—
127#121×C43—21no—
128C4×Q8×C43—21no—
129C4×Q8×C43—21no—
130C4×D4×C43—21no—
131C4×D4×C43—21no—
132#117×C43—21no—
133C2×C42×C43C2311yescharacteristic
134C4⋊C8×C43D411yescharacteristic
135C4⋊C8×C43D411yescharacteristic
136#103×C43—21no—
137#103×C43—21no—
138#102×C43—21no—
139#102×C43—21no—
140C22⋊C8×C43D411yescharacteristic
141C22⋊C8×C43D411yescharacteristic
142C4×C8×C43C2311yescharacteristic
143C4×C8×C43C2311yescharacteristic
144#41×C43—81no—
145#41×C43—81no—
146C2×Q8×C43—21no—
147C2×Q8×C43—21no—
148C2×Q8×C43—21no—
149C2×D4×C43—21no—
150C2×D4×C43—21no—
151C2×D4×C43—21no—
152C2×D4×C43—41no—
153C22×C4×C43—41no—
154C22×C4×C43C2×D411yescharacteristic
155C22×C4×C43C2×D411yescharacteristic
156C22×C4×C43#4111yescharacteristic
157C2×C22⋊D43—21no—
158#10621898—22no—
159#10621898—22no—
160C2×D172C2×D411yescharacteristic
161C2×C4×D43—21no—
162C2×C4×D43—21no—
163C2×C4×D43—21no—
164C2×Dic86C2×D411yescharacteristic
165Q16×C43—81no—
166Q16×C43—81no—
167SD16×C43—81no—
168SD16×C43—81no—
169C2×C8×C43C2×D411yescharacteristic
170C2×C8×C43C2×D411yescharacteristic
171C2×C8×C43C2×D411yescharacteristic
172C2×C8×C43C2×D411yescharacteristic
173C4⋊C4×C43—21no—
174C4⋊C4×C43—21no—
175C4⋊C4×C43—21no—
176C4⋊C4×C43—21no—
177C4⋊C4×C43—21no—
178C4⋊C4×C43—21no—
179C4⋊C4×C43—41no—
180C4⋊C4×C43—41no—
181C22⋊C4×C43—41no—
182C22⋊C4×C43—41no—
183C22⋊C4×C43—41no—
184C42×C43—41no—
185C42×C43C2×D411yescharacteristic
186C42×C43C2×D411yescharacteristic
187C42×C43#4111yescharacteristic
188C42×C43C2411yescharacteristic
189C22⋊Dic43—21no—
190#10621885—42no—
191#10621884—42no—
192#10621883—42no—
193#10621882—42no—
194(C2×D43)⋊C4—21no—
195(C2×D43)⋊C4—21no—
196C4⋊Dic43C2×D411yescharacteristic
197C4⋊Dic43C2×D411yescharacteristic
198Dic43⋊C4—21no—
199Dic43⋊C4—21no—
200C4×Dic43—21no—
201C4×Dic43—21no—
202C4×Dic43—21no—
203C2×C43⋊C8—21no—
204C2×C43⋊C8—21no—
205C2×C43⋊C8—21no—
206C2×C43⋊C8—21no—
207C2×C43⋊C8—21no—
208C2×C43⋊C8—21no—
209C2×C43⋊C8—81no—
210C8×D43—81no—
211C8×D43—81no—
212C23×C43—41no—
213C23×C43#12111yescharacteristic
214C22×D43—21no—
215Q8×C43—41no—
216Q8×C43—41no—
217Q8×C43—41no—
218Q8×C43—41no—
219Q8×C43—41no—
220Q8×C43—41no—
221D4×C43—41no—
222D4×C43—41no—
223D4×C43—41no—
224D4×C43—41no—
225D4×C43—81no—
226D4×C43—82no—
227C2×C4×C43—21no—
228C2×C4×C43—21no—
229C2×C4×C43—21no—
230C2×C4×C43—21no—
231C2×C4×C43—41no—
232C2×C4×C43—41no—
233C2×C4×C43—41no—
234C2×C4×C43—41no—
235C2×C4×C43—82no—
236C2×C4×C43#12111yescharacteristic
237C2×C4×C43#12111yescharacteristic
238C2×C4×C43#12111yescharacteristic
239C2×C4×C43C22×D411yescharacteristic
240C2×C4×C43C22×D411yescharacteristic
241C2×C4×C43C2×#4111yescharacteristic
242C22⋊D43—24no—
243C2×Dic43—21no—
244C2×Dic43—21no—
245C2×Dic43—21no—
246D172—21no—
247D172#13512yes—
248C4×D43—24no—
249C4×D43—41no—
250C4×D43—41no—
251C4×D43—81no—
252Dic86—21no—
253Dic86#13512yes—
254C8×C43—21no—
255C8×C43—21no—
256C8×C43—21no—
257C8×C43—21no—
258C43⋊C8—41no—
259C43⋊C8—41no—
260C43⋊C8—41no—
261C43⋊C8—41no—
262C43⋊C8—41no—
263C43⋊C8—41no—
264#19413—431nomaximal, Sylow
265C22×C43—21no—
266C22×C43—21no—
267C22×C43—21no—
268C22×C43—81no—
269C22×C43—81no—
270C22×C43—81no—
271C22×C43C2×#12111yescharacteristic
272C2×D43—22no—
273C2×D43—41no—
274C2×D43—41no—
275C4×C43—21no—
276C4×C43—21no—
277C4×C43—21no—
278C4×C43—21no—
279C4×C43—81no—
280C4×C43—81no—
281C4×C43—81no—
282C4×C43C2×#13511yescharacteristic
283C4×C43C2×#13511yescharacteristic
284C4×C43#57611yescharacteristic
285C4×C43#57711yescharacteristic
286Dic43—22no—
287Dic43—41no—
288Dic43—41no—
289#3210D4311yescharacteristic, complemented
290#3115—431no—
291#3107—431no—
292#2988—431no—
293#1682—431no—
294#1681—431no—
295#1680—431no—
296#1679—431no—
297#1670—431no—
298#1669—431no—
299#1666—431no—
300#1665—431no—
301#1572—431no—
302#1552—431no—
303#1540—431no—
304C2×C43—41no—
305C2×C43—161no—
306C2×C43#304511yescharacteristic
307C2×C43#305011yescharacteristic
308C2×C43#306911yescharacteristic
309D43—42no—
310#533C2×D4311yescharacteristic
311#532C2×D4311yescharacteristic
312C4×#41—431no—
313#494C2×D4311yescharacteristic
314#492C2×D4311yescharacteristic
315#487C2×D4311yescharacteristic
316#486C2×D4311yescharacteristic
317#485—861no—
318#482—861no—
319#475—431no—
320#475—431no—
321#474—431no—
322#474—431no—
323#464—21no—
324#464—21no—
325#462—431no—
326#461—431no—
327#460—431no—
328#459—431no—
329#452—21no—
330#452—21no—
331#452—861no—
332#449—861no—
333C8×Q8—431no—
334C8×Q8—431no—
335#442—861no—
336#440—861no—
337C4×Q16—861no—
338C4×SD16—861no—
339C8×D4—431no—
340C8×D4—431no—
341C8×D4—861no—
342C8×D4—861no—
343#432—431no—
344#431—431no—
345#431—861no—
346#431C2×D4311yescharacteristic
347C2×C4⋊C8—431no—
348C2×C4⋊C8—861no—
349#335—431no—
350#335—431no—
351#334—431no—
352#334—431no—
353#332—431no—
354#332—431no—
355#332—431no—
356#332—431no—
357#332—431no—
358#332—431no—
359#331—431no—
360#331—431no—
361C43#1941311yescharacteristic, complemented, Sylow
362C2×#41—21no—
363C2×#41—431no—
364C2×Q16—21no—
365C2×Q16—21no—
366C2×Q16—861no—
367C2×SD16—21no—
368C2×SD16—21no—
369C2×SD16—861no—
370C2×SD16—861no—
371C2×D8—861no—
372C22×C8—861no—
373C22×C8—861no—
374C22×C8—861no—
375C4⋊Q8C22×D4311yescharacteristic
376C4⋊Q8C22×D4311yescharacteristic
377C4⋊Q8C22×D4311yescharacteristic
378#127C22×D4311yescharacteristic
379#125—21no—
380#124—21no—
381C22⋊Q8—21no—
382C22⋊Q8—21no—
383#121—21no—
384#121—21no—
385C4×Q8—21no—
386C4×Q8—21no—
387C4×Q8—431no—
388C4×Q8—431no—
389C4×D4—21no—
390C4×D4—21no—
391C4×D4—431no—
392C4×D4—431no—
393C4×D4—861no—
394C4×D4—861no—
395#117—21no—
396#117—431no—
397#117—861no—
398C2×C42—861no—
399C2×C42C22×D4311yescharacteristic
400#107—861no—
401#107—861no—
402#106—861no—
403#106—861no—
404C4⋊C8—431no—
405C4⋊C8—431no—
406C4⋊C8—431no—
407C4⋊C8—431no—
408C4⋊C8—431no—
409C4⋊C8—431no—
410C4⋊C8—861no—
411C4⋊C8—861no—
412C4⋊C8—861no—
413C4⋊C8C22⋊D4311yescharacteristic
414C4⋊C8C22⋊D4311yescharacteristic
415#103—21no—
416#103—21no—
417#103—861no—
418#103—861no—
419#103—861no—
420#103—861no—
421#102—21no—
422#102—21no—
423#102—861no—
424#102—861no—
425#102—861no—
426#102—861no—
427C22⋊C8—861no—
428C22⋊C8—861no—
429C22⋊C8—861no—
430C22⋊C8—861no—
431C22⋊C8C22⋊D4311yescharacteristic
432C22⋊C8C22⋊D4311yescharacteristic
433#97—861no—
434C4×C8—861no—
435C4×C8—861no—
436C4×C8—861no—
437C4×C8C22×D4311yescharacteristic
438C4×C8C22×D4311yescharacteristic
439#41—81no—
440#41—81no—
441#41—862no—
442#41—862no—
443C2×Q8—21no—
444C2×Q8—21no—
445C2×Q8—21no—
446C2×Q8—431no—
447C2×D4—21no—
448C2×D4—21no—
449C2×D4—21no—
450C2×D4—41no—
451C2×D4—431no—
452C2×D4—861no—
453C22×C4—41no—
454C22×C4—861no—
455C22×C4—861no—
456C22×C4—861no—
457C22×C4D4×D4311yescharacteristic
458C22×C4#1062190011yescharacteristic
459C22×C4C2×C22⋊D4311yescharacteristic
460Q16—81no—
461Q16—81no—
462Q16—1722no—
463SD16—81no—
464SD16—81no—
465SD16—1722no—
466SD16—1722no—
467D8—1722no—
468C2×C8—861no—
469C2×C8—861no—
470C2×C8—861no—
471C2×C8—861no—
472C2×C8—861no—
473C2×C8—861no—
474C2×C8—3441no—
475C2×C8—3441no—
476C2×C8—3441no—
477C2×C8C2×C22⋊D4311yescharacteristic
478C2×C8C2×C22⋊D4311yescharacteristic
479C2×C8C2×C22⋊D4311yescharacteristic
480C2×C8C2×C22⋊D4311yescharacteristic
481C4⋊C4—21no—
482C4⋊C4—21no—
483C4⋊C4—21no—
484C4⋊C4—21no—
485C4⋊C4—21no—
486C4⋊C4—21no—
487C4⋊C4—41no—
488C4⋊C4—41no—
489C4⋊C4—431no—
490C4⋊C4—431no—
491C4⋊C4—861no—
492C4⋊C4—861no—
493C22⋊C4—41no—
494C22⋊C4—41no—
495C22⋊C4—41no—
496C22⋊C4—861no—
497C22⋊C4—861no—
498C22⋊C4—861no—
499C42—41no—
500C42—861no—
501C42—861no—
502C42—861no—
503C42D4×D4311yescharacteristic
504C42#1062190011yescharacteristic
505C42C2×C22⋊D4311yescharacteristic
506C42C23×D4311yescharacteristic
507C23—41no—
508C23—861no—
509C23#1306329611yescharacteristic
510Q8—41no—
511Q8—41no—
512Q8—41no—
513Q8—41no—
514Q8—41no—
515Q8—41no—
516Q8—432no—
517Q8—861no—
518D4—41no—
519D4—41no—
520D4—41no—
521D4—41no—
522D4—81no—
523D4—82no—
524D4—432no—
525D4—864no—
526D4—861no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—82no—
536C2×C4—864no—
537C2×C4—861no—
538C2×C4—861no—
539C2×C4—861no—
540C2×C4—3441no—
541C2×C4—1721no—
542C2×C4—1721no—
543C2×C4#1306329611yescharacteristic
544C2×C4#1306329611yescharacteristic
545C2×C4#1306329611yescharacteristic
546C2×C4C2×D4×D4311yescharacteristic
547C2×C4C22×C22⋊D4311yescharacteristic
548C2×C4C2×#1062190011yescharacteristic
549C8—21no—
550C8—21no—
551C8—21no—
552C8—21no—
553C8—1721no—
554C8—1721no—
555C8—1721no—
556C8—1721no—
557C8—1721no—
558C8—1721no—
559C22—21no—
560C22—21no—
561C22—21no—
562C22—81no—
563C22—81no—
564C22—81no—
565C22—862no—
566C22—1721no—
567C22—1721no—
568C22C2×#1306329611yescharacteristic
569C4—21no—
570C4—21no—
571C4—21no—
572C4—21no—
573C4—81no—
574C4—81no—
575C4—81no—
576C4—862no—
577C4—1721no—
578C4—1721no—
579C4#135×D4311yescharacteristic
580C4#135×D4311yescharacteristic
581C4#1458370211yescharacteristic
582C4#1458371011yescharacteristic
583C2—41no—
584C2—161no—
585C2—1722no—
586C2#1914413011yescharacteristic
587C2#1914417211yescharacteristic
588C2#1914432811yescharacteristic
subgroupG/H
centerC22C2×#13063296
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#3210C2
socleC22×C43C2×#121
prime radical#19144740C2
hypercenter#3210D43
hypocenterC43#19413
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3210

Complements

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

NH ≅ G/Ntype
2. #19144660C2semidirect
3. #19143703C2semidirect
4. #19134036C2semidirect
5. #19134029C2semidirect
6. #19134022C2semidirect
7. #19134015C2semidirect
8. #19133962C2semidirect
9. #19133957C2semidirect
10. #19133940C2semidirect
11. #19133933C2semidirect
12. #19133375C2semidirect
13. #19133295C2semidirect
14. #19133244C2semidirect
15. C43×#3210C2semidirect
289. #3210D43semidirect
361. C43#19413semidirect

Maximal subgroups

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

subgroupindex
#191447402
#191446602
#191437032
#191340362
#191340292
#191340222
#191340152
#191339622
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