Finite Group Databasebeta

← #25080060

Subgroups — #25080060

Order 11008.

606 conjugacy classes of subgroups.

The subgroup lattice has 580 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145926C211yesmaximal, characteristic, complemented
2#19145915C211yesmaximal, characteristic
3#19143570C211yesmaximal, characteristic, complemented
4#19134098C211yesmaximal, characteristic, complemented
5#19134091C211yesmaximal, characteristic, complemented
6#19134064C211yesmaximal, characteristic, complemented
7#19134057C211yesmaximal, characteristic, complemented
8#19134050C211yesmaximal, characteristic, complemented
9#19134043C211yesmaximal, characteristic, complemented
10#19134036C211yesmaximal, characteristic, complemented
11#19134029C211yesmaximal, characteristic, complemented
12C2×#14582652C211yesmaximal, characteristic, complemented
13#19133295C211yesmaximal, characteristic, complemented
14#19133290C211yesmaximal, characteristic, complemented
15C43×#3167C211yesmaximal, characteristic, complemented
16#14583433C2211yescharacteristic
17#14583206—21no—
18#14583199—21no—
19#14583191C2211yescharacteristic
20#14583186C2211yescharacteristic
21#14583181C2211yescharacteristic
22#14583176C2211yescharacteristic
23#14583138—21no—
24#14583133—21no—
25#14583130—21no—
26#14583126—21no—
27#14583121—21no—
28#14583114—21no—
29#14583106C2211yescharacteristic
30#14583101C2211yescharacteristic
31#14583096C2211yescharacteristic
32#14583091C2211yescharacteristic
33#14583029C2211yescharacteristic
34C8×Dic86C2211yescharacteristic
35#14582978C2211yescharacteristic
36#14582970—21no—
37C8×D172C2211yescharacteristic
38C8×C22⋊D43—21no—
39#14582958—21no—
40#14582956C2211yescharacteristic
41C2×C4⋊(C43⋊C8)C2211yescharacteristic
42C2×C4⋊(C43⋊C8)C2211yescharacteristic
43#14582853—21no—
44#14582652C2211yescharacteristic
45#14582652C2211yescharacteristic
46#14582652C2211yescharacteristic
47#14582652C2211yescharacteristic
48#14582648C2211yescharacteristic
49#14582648C2211yescharacteristic
50#14582645C2211yescharacteristic
51#14582645C2211yescharacteristic
52#14582645C2211yescharacteristic
53#14582645C2211yescharacteristic
54#14582643C2211yescharacteristic
55#14582643C2211yescharacteristic
56C43×#533C2211yescharacteristic
57C43×#532C2211yescharacteristic
58C43×#498C2211yescharacteristic
59C43×#492C2211yescharacteristic
60C43×#487C2211yescharacteristic
61C43×#486C2211yescharacteristic
62C43×#465—21no—
63C43×#465—21no—
64C4×SD16×C43—21no—
65C4×SD16×C43—21no—
66C2×C4×C8×C43C2211yescharacteristic
67C2×#10621885—21no—
68C2×#10621883—21no—
69C2×#10621884—21no—
70C2×#10621882—21no—
71C2×#10621872—21no—
72C22×C43⋊C8—21no—
73C22×C43⋊C8—21no—
74C2×C8×D43—21no—
75#13063319—21no—
76#13063317D411yescharacteristic
77#13063313D411yescharacteristic
78#13063308—21no—
79#13063304D411yescharacteristic
80#13063299D411yescharacteristic
81C4×Dic86C2311yescharacteristic
82C4×D172C2311yescharacteristic
83C4×C22⋊D43—21no—
84#13063282—21no—
85#13063258—21no—
86#13063258—21no—
87#13063256—21no—
88#13063256—21no—
89C4⋊(C43⋊C8)—21no—
90C4⋊(C43⋊C8)—21no—
91C4⋊(C43⋊C8)C2311yescharacteristic
92C4⋊(C43⋊C8)C2311yescharacteristic
93C4⋊(C43⋊C8)C2311yescharacteristic
94C4⋊(C43⋊C8)C2311yescharacteristic
95C4⋊(C43⋊C8)C2311yescharacteristic
96C4⋊(C43⋊C8)C2311yescharacteristic
97Dic43⋊C8—21no—
98Dic43⋊C8—21no—
99#13063249—21no—
100#13063249—21no—
101#13063248—21no—
102#13063248—21no—
103#13063246—21no—
104#13063246—21no—
105#13063245—21no—
106#13063245—21no—
107C22⋊(C43⋊C8)—21no—
108(C2×D43)⋊C8—21no—
109(C2×D43)⋊C8—21no—
110#13063236—21no—
111#13063235—21no—
112C8×Dic43—21no—
113C2×#41×C43—21no—
114C2×SD16×C43—21no—
115C2×SD16×C43—21no—
116C22×C8×C43D411yescharacteristic
117C22×C8×C43D411yescharacteristic
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
134#106×C43—21no—
135#106×C43—21no—
136#103×C43—21no—
137#103×C43—21no—
138#102×C43—21no—
139#102×C43—21no—
140C4×C8×C43D411yescharacteristic
141C4×C8×C43D411yescharacteristic
142C4×C8×C43C2311yescharacteristic
143C4×C8×C43C2311yescharacteristic
144#41×C43—82no—
145C2×Q8×C43—21no—
146C2×Q8×C43—21no—
147C2×Q8×C43—21no—
148C2×D4×C43—21no—
149C2×D4×C43—21no—
150C2×D4×C43—21no—
151C2×D4×C43—41no—
152C22×C4×C43—41no—
153C22×C4×C43C2×D411yescharacteristic
154C22×C4×C43C2×D411yescharacteristic
155C22×C4×C43#4111yescharacteristic
156C2×C22⋊D43—21no—
157C2×D172C2×D411yescharacteristic
158C2×C4×D43—21no—
159C2×Dic86C2×D411yescharacteristic
160SD16×C43—42no—
161SD16×C43—42no—
162C2×C8×C43—22no—
163C2×C8×C43—41no—
164C2×C8×C43C2×D411yescharacteristic
165C2×C8×C43C2×D411yescharacteristic
166C2×C8×C43C2×D411yescharacteristic
167C2×C8×C43C2×D411yescharacteristic
168C4⋊C4×C43—21no—
169C4⋊C4×C43—21no—
170C4⋊C4×C43—21no—
171C4⋊C4×C43—21no—
172C4⋊C4×C43—21no—
173C4⋊C4×C43—21no—
174C4⋊C4×C43—41no—
175C4⋊C4×C43—41no—
176C22⋊C4×C43—41no—
177C22⋊C4×C43—41no—
178C22⋊C4×C43—41no—
179C42×C43—41no—
180C42×C43C2×D411yescharacteristic
181C42×C43C2×D411yescharacteristic
182C42×C43#4111yescharacteristic
183C42×C43C2411yescharacteristic
184C22⋊Dic43—21no—
185#10621885—81no—
186#10621884—81no—
187#10621883—81no—
188#10621882—81no—
189(C2×D43)⋊C4—21no—
190(C2×D43)⋊C4—21no—
191(C2×D43)⋊C4—21no—
192(C2×D43)⋊C4—21no—
193C4⋊Dic43C2×D411yescharacteristic
194C4⋊Dic43C2×D411yescharacteristic
195Dic43⋊C4—21no—
196Dic43⋊C4—21no—
197Dic43⋊C4—21no—
198Dic43⋊C4—21no—
199C4×Dic43—21no—
200C2×C43⋊C8—21no—
201C2×C43⋊C8—21no—
202C2×C43⋊C8—21no—
203C2×C43⋊C8—21no—
204C2×C43⋊C8—21no—
205C2×C43⋊C8—21no—
206C2×C43⋊C8—81no—
207C2×C43⋊C8—81no—
208#10621872—42no—
209C8×D43—42no—
210C23×C43—41no—
211C23×C43#12111yescharacteristic
212C22×D43—21no—
213Q8×C43—41no—
214Q8×C43—41no—
215Q8×C43—41no—
216Q8×C43—41no—
217Q8×C43—81no—
218D4×C43—41no—
219D4×C43—41no—
220D4×C43—41no—
221D4×C43—41no—
222D4×C43—81no—
223D4×C43—82no—
224C2×C4×C43—22no—
225C2×C4×C43—21no—
226C2×C4×C43—21no—
227C2×C4×C43—21no—
228C2×C4×C43—21no—
229C2×C4×C43—41no—
230C2×C4×C43—41no—
231C2×C4×C43—41no—
232C2×C4×C43—82no—
233C2×C4×C43#12111yescharacteristic
234C2×C4×C43#12111yescharacteristic
235C2×C4×C43#12111yescharacteristic
236C2×C4×C43C22×D411yescharacteristic
237C2×C4×C43C22×D411yescharacteristic
238C2×C4×C43C2×#4111yescharacteristic
239C22⋊D43—42no—
240C2×Dic43—21no—
241C2×Dic43—21no—
242C2×Dic43—21no—
243D172—21no—
244D172—21no—
245C4×D43—41no—
246C4×D43—41no—
247Dic86—21no—
248Dic86—21no—
249C8×C43—21no—
250C8×C43—21no—
251C8×C43—21no—
252C8×C43#13512yes—
253C43⋊C8—41no—
254C43⋊C8—41no—
255C43⋊C8—41no—
256C43⋊C8—41no—
257C43⋊C8—41no—
258C43⋊C8—41no—
259#19229—431nomaximal, Sylow
260C22×C43—21no—
261C22×C43—21no—
262C22×C43—81no—
263C22×C43—81no—
264C22×C43—81no—
265C22×C43#47112yes—
266C22×C43C2×#12111yescharacteristic
267C2×D43—41no—
268C2×D43—41no—
269C2×D43—41no—
270C4×C43—21no—
271C4×C43—21no—
272C4×C43—21no—
273C4×C43—21no—
274C4×C43—81no—
275C4×C43—81no—
276C4×C43—81no—
277C4×C43C2×#13511yescharacteristic
278C4×C43#57511yescharacteristic
279C4×C43#57611yescharacteristic
280C4×C43#57811yescharacteristic
281Dic43—41no—
282Dic43—41no—
283Dic43—41no—
284#3248—431no—
285#3247—431no—
286#3167D4311yescharacteristic, complemented
287#2966—431no—
288#1692—431no—
289#1691—431no—
290#1686—431no—
291#1685—431no—
292#1684—431no—
293#1683—431no—
294#1682—431no—
295#1681—431no—
296C2×#335—431no—
297#1552—431no—
298#1551—431no—
299C2×C43—22no—
300C2×C43—161no—
301C2×C43#303511yescharacteristic
302C2×C43#306111yescharacteristic
303C2×C43C2×#47111yescharacteristic
304D43—81no—
305#533C2×D4311yescharacteristic
306#532C2×D4311yescharacteristic
307#529—431no—
308#498C2×D4311yescharacteristic
309#492C2×D4311yescharacteristic
310#487C2×D4311yescharacteristic
311#486C2×D4311yescharacteristic
312#479—861no—
313#478—861no—
314#477—431no—
315#476—431no—
316#475—431no—
317#474—431no—
318#467—861no—
319#466—861no—
320#465—21no—
321#465—21no—
322#465—861no—
323#465—861no—
324#464—861no—
325#463—861no—
326#462—431no—
327#461—431no—
328#460—431no—
329#459—431no—
330#446—431no—
331C8×Q8—431no—
332C4×SD16—21no—
333C4×SD16—21no—
334#436—431no—
335#435—861no—
336C8×D4—431no—
337C8×D4—861no—
338#433—861no—
339#432—431no—
340C2×C4⋊C8—431no—
341C2×C4⋊C8—431no—
342#405—861no—
343C2×C4×C8C2×D4311yescharacteristic
344#335—431no—
345#335—431no—
346#335—431no—
347#335—431no—
348#333—431no—
349#333—431no—
350#332—431no—
351#332—431no—
352#332—431no—
353#332—431no—
354#331—431no—
355#331—431no—
356C43#1922911yescharacteristic, complemented, Sylow
357C2×#41—21no—
358C2×Q16—861no—
359C2×SD16—21no—
360C2×SD16—21no—
361C2×SD16—861no—
362C2×SD16—861no—
363C2×D8—861no—
364C2×M16—861no—
365C22×C8—861no—
366C22×C8—861no—
367C22×C8—861no—
368C22×C8C22⋊D4311yescharacteristic
369C22×C8C22⋊D4311yescharacteristic
370C4⋊Q8C22×D4311yescharacteristic
371C4⋊Q8C22×D4311yescharacteristic
372C4⋊Q8C22×D4311yescharacteristic
373#127C22×D4311yescharacteristic
374#126—861no—
375#125—21no—
376#125—431no—
377#124—21no—
378#124—431no—
379#123—861no—
380C22⋊Q8—21no—
381C22⋊Q8—21no—
382C22⋊Q8—431no—
383#121—21no—
384#121—21no—
385#121—431no—
386C4×Q8—21no—
387C4×Q8—21no—
388C4×Q8—431no—
389C4×D4—21no—
390C4×D4—21no—
391C4×D4—431no—
392C4×D4—861no—
393#117—21no—
394#117—861no—
395C2×C42C22×D4311yescharacteristic
396#107—861no—
397#107—861no—
398#106—21no—
399#106—21no—
400#106—861no—
401#106—861no—
402C4⋊C8—431no—
403C4⋊C8—431no—
404C4⋊C8—431no—
405C4⋊C8—431no—
406C4⋊C8—431no—
407C4⋊C8—431no—
408C4⋊C8—861no—
409C4⋊C8—861no—
410C4⋊C8—861no—
411C4⋊C8—861no—
412#103—21no—
413#103—21no—
414#103—861no—
415#103—861no—
416#103—861no—
417#103—861no—
418#102—21no—
419#102—21no—
420#102—861no—
421#102—861no—
422#102—861no—
423#102—861no—
424C22⋊C8—861no—
425C22⋊C8—861no—
426C22⋊C8—861no—
427#97—861no—
428#97—861no—
429C4×C8—861no—
430C4×C8C22⋊D4311yescharacteristic
431C4×C8C22⋊D4311yescharacteristic
432C4×C8C22×D4311yescharacteristic
433C4×C8C22×D4311yescharacteristic
434#41—82no—
435C2×Q8—21no—
436C2×Q8—21no—
437C2×Q8—21no—
438C2×Q8—431no—
439C2×D4—21no—
440C2×D4—21no—
441C2×D4—21no—
442C2×D4—41no—
443C2×D4—431no—
444C2×D4—861no—
445C22×C4—41no—
446C22×C4—861no—
447C22×C4D4×D4311yescharacteristic
448C22×C4#1062190011yescharacteristic
449C22×C4C2×C22⋊D4311yescharacteristic
450Q16—3441no—
451SD16—42no—
452SD16—42no—
453SD16—3441no—
454SD16—3441no—
455D8—3441no—
456M16—1722no—
457C2×C8—22no—
458C2×C8—41no—
459C2×C8—861no—
460C2×C8—861no—
461C2×C8—861no—
462C2×C8—861no—
463C2×C8—861no—
464C2×C8—861no—
465C2×C8—3441no—
466C2×C8—3441no—
467C2×C8—1722no—
468C2×C8C2×C22⋊D4311yescharacteristic
469C2×C8C2×C22⋊D4311yescharacteristic
470C2×C8C2×C22⋊D4311yescharacteristic
471C2×C8C2×C22⋊D4311yescharacteristic
472C4⋊C4—21no—
473C4⋊C4—21no—
474C4⋊C4—21no—
475C4⋊C4—21no—
476C4⋊C4—21no—
477C4⋊C4—21no—
478C4⋊C4—41no—
479C4⋊C4—41no—
480C4⋊C4—431no—
481C4⋊C4—431no—
482C4⋊C4—861no—
483C4⋊C4—861no—
484C4⋊C4—861no—
485C4⋊C4—861no—
486C22⋊C4—41no—
487C22⋊C4—41no—
488C22⋊C4—41no—
489C22⋊C4—861no—
490C22⋊C4—861no—
491C22⋊C4—861no—
492C22⋊C4—861no—
493C22⋊C4—861no—
494C42—41no—
495C42—861no—
496C42D4×D4311yescharacteristic
497C42#1062190011yescharacteristic
498C42C2×C22⋊D4311yescharacteristic
499C42C23×D4311yescharacteristic
500C23—41no—
501C23—861no—
502C23#1306329611yescharacteristic
503Q8—41no—
504Q8—41no—
505Q8—41no—
506Q8—41no—
507Q8—81no—
508Q8—861no—
509Q8—861no—
510D4—41no—
511D4—41no—
512D4—41no—
513D4—41no—
514D4—81no—
515D4—82no—
516D4—861no—
517D4—861no—
518D4—1722no—
519C2×C4—22no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—41no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—82no—
528C2×C4—861no—
529C2×C4—861no—
530C2×C4—861no—
531C2×C4—1721no—
532C2×C4—1721no—
533C2×C4#1306329611yescharacteristic
534C2×C4#1306329611yescharacteristic
535C2×C4#1306329611yescharacteristic
536C2×C4C2×D4×D4311yescharacteristic
537C2×C4C22×C22⋊D4311yescharacteristic
538C2×C4C2×#1062190011yescharacteristic
539C8—21no—
540C8—21no—
541C8—21no—
542C8—1721no—
543C8—1721no—
544C8—1721no—
545C8—1721no—
546C8—1721no—
547C8—1721no—
548C8#1306334512yes—
549C22—21no—
550C22—21no—
551C22—81no—
552C22—81no—
553C22—81no—
554C22—1721no—
555C22—1721no—
556C22—1721no—
557C22#1458315912yes—
558C22C2×#1306329611yescharacteristic
559C4—21no—
560C4—21no—
561C4—21no—
562C4—21no—
563C4—81no—
564C4—81no—
565C4—81no—
566C4—1721no—
567C4—1721no—
568C4—1721no—
569C4C2×#1306334511yescharacteristic
570C4#1458369711yescharacteristic
571C4#1458370111yescharacteristic
572C4#1458371311yescharacteristic
573C2—22no—
574C2—161no—
575C2—3441no—
576C2#1914404411yescharacteristic
577C2#1914426111yescharacteristic
578C2C2×#1458315911yescharacteristic
subgroupG/H
centerC22C2×#13063296
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#3167C2
socleC22×C43C2×#121
prime radical#19145915C2
hypercenter#3167D43
hypocenterC43#19229
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3167

Complements

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

NH ≅ G/Ntype
1. #19145926C2semidirect
3. #19143570C2semidirect
4. #19134098C2semidirect
5. #19134091C2semidirect
6. #19134064C2semidirect
7. #19134057C2semidirect
8. #19134050C2semidirect
9. #19134043C2semidirect
10. #19134036C2semidirect
11. #19134029C2semidirect
12. C2×#14582652C2semidirect
13. #19133295C2semidirect
14. #19133290C2semidirect
15. C43×#3167C2semidirect
286. #3167D43semidirect
356. C43#19229semidirect

Maximal subgroups

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

subgroupindex
#191459262
#191459152
#191435702
#191340982
#191340912
#191340642
#191340572
#191340502
#191340432
#191340362
#191340292
C2×#145826522
#191332952
#191332902
C43×#31672
#1922943