Finite Group Databasebeta

← #25084188

Subgroups — #25084188

Order 11008.

602 conjugacy classes of subgroups.

The subgroup lattice has 584 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145915C211yesmaximal, characteristic
2#19145622C211yesmaximal, characteristic, complemented
3#19143757C211yesmaximal, characteristic, complemented
4#19134160C211yesmaximal, characteristic, complemented
5#19134153C211yesmaximal, characteristic, complemented
6#19134098C211yesmaximal, characteristic, complemented
7#19134091C211yesmaximal, characteristic, complemented
8#19134036C211yesmaximal, characteristic, complemented
9#19134029C211yesmaximal, characteristic, complemented
10#19133974C211yesmaximal, characteristic, complemented
11#19133967C211yesmaximal, characteristic, complemented
12#19133380C211yesmaximal, characteristic, complemented
13#19133290C211yesmaximal, characteristic, complemented
14C2×#14582645C211yesmaximal, characteristic, complemented
15C43×#3227C211yesmaximal, characteristic, complemented
16#14583433C2211yescharacteristic
17#14583291—21no—
18#14583267—21no—
19#14583199—21no—
20#14583191C2211yescharacteristic
21#14583186C2211yescharacteristic
22#14583133—21no—
23#14583126—21no—
24#14583114—21no—
25#14583106C2211yescharacteristic
26#14583106C2211yescharacteristic
27#14583101C2211yescharacteristic
28#14583101C2211yescharacteristic
29#14583096C2211yescharacteristic
30#14583091C2211yescharacteristic
31#14583055—21no—
32#14583038—21no—
33#14583029C2211yescharacteristic
34C8×Dic86C2211yescharacteristic
35#14582978C2211yescharacteristic
36#14582967—21no—
37C8×D172C2211yescharacteristic
38(C22⋊D43)⋊C8—21no—
39#14582959—21no—
40#14582956C2211yescharacteristic
41#14582924—21no—
42C2×C4⋊(C43⋊C8)C2211yescharacteristic
43C2×C4⋊(C43⋊C8)C2211yescharacteristic
44#14582652C2211yescharacteristic
45#14582652C2211yescharacteristic
46#14582650C2211yescharacteristic
47#14582650C2211yescharacteristic
48#14582648C2211yescharacteristic
49#14582648C2211yescharacteristic
50#14582645C2211yescharacteristic
51#14582645C2211yescharacteristic
52#14582645C2211yescharacteristic
53#14582645C2211yescharacteristic
54#14582643C2211yescharacteristic
55#14582643C2211yescharacteristic
56C43×#532C2211yescharacteristic
57C2×C4⋊Q8×C43C2211yescharacteristic
58C43×#498C2211yescharacteristic
59C43×#498C2211yescharacteristic
60C43×#486C2211yescharacteristic
61C43×#486C2211yescharacteristic
62C43×#481—21no—
63C43×#481—21no—
64C43×#476—21no—
65C43×#476—21no—
66C43×#431C2211yescharacteristic
67C2×#10621885—21no—
68C2×#10621885—21no—
69C2×#10621883—21no—
70C2×#10621884—21no—
71C2×#10621884—21no—
72C2×#10621882—21no—
73C2×#10621872—21no—
74C22×C43⋊C8—21no—
75C22×C43⋊C8—21no—
76C2×C8×D43—21no—
77#13063319—21no—
78#13063317D411yescharacteristic
79#13063313D411yescharacteristic
80#13063308—21no—
81#13063304D411yescharacteristic
82#13063299D411yescharacteristic
83C4×Dic86C2311yescharacteristic
84C4×D172C2311yescharacteristic
85C4×C22⋊D43—21no—
86#13063282—21no—
87#13063258—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#13063249—21no—
102#13063249—21no—
103#13063248—21no—
104#13063246—21no—
105#13063246—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—
114C22×Q8×C43—21no—
115C4⋊Q8×C43—21no—
116C4⋊Q8×C43—21no—
117C4⋊Q8×C43—21no—
118C4⋊Q8×C43C2311yescharacteristic
119C4⋊Q8×C43C2311yescharacteristic
120C4⋊Q8×C43C2311yescharacteristic
121#127×C43C2311yescharacteristic
122#124×C43—21no—
123#121×C43—21no—
124#121×C43—21no—
125C4×D4×C43—21no—
126C4×D4×C43—21no—
127C2×C4⋊C4×C43—21no—
128C2×C4⋊C4×C43—21no—
129C2×C42×C43C2311yescharacteristic
130#106×C43—21no—
131#106×C43—21no—
132#106×C43—21no—
133#106×C43—21no—
134C4⋊C8×C43D411yescharacteristic
135C4⋊C8×C43D411yescharacteristic
136#102×C43—21no—
137#102×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—82no—
145C2×Q8×C43—21no—
146C2×Q8×C43—21no—
147C2×Q8×C43—21no—
148C2×Q8×C43—41no—
149C2×Q8×C43—81no—
150C2×Q8×C43—81no—
151C2×D4×C43—21no—
152C2×D4×C43—21no—
153C2×D4×C43—21no—
154C2×D4×C43—41no—
155C22×C4×C43—41no—
156C22×C4×C43—41no—
157C22×C4×C43C2×D411yescharacteristic
158C22×C4×C43C2×D411yescharacteristic
159C22×C4×C43#4111yescharacteristic
160C2×C22⋊D43—21no—
161C2×D172C2×D411yescharacteristic
162C2×C4×D43—21no—
163C2×Dic86C2×D411yescharacteristic
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—
178C42×C43C2×D411yescharacteristic
179C42×C43C2×D411yescharacteristic
180C42×C43#4111yescharacteristic
181C42×C43C2411yescharacteristic
182C22⋊Dic43—21no—
183#10621885—81no—
184#10621885—81no—
185#10621884—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—81no—
209C8×D43—81no—
210C23×C43—41no—
211C23×C43#12111yescharacteristic
212C22×D43—21no—
213Q8×C43—41no—
214Q8×C43—41no—
215Q8×C43—41no—
216Q8×C43—41no—
217Q8×C43—81no—
218Q8×C43—82no—
219D4×C43—41no—
220D4×C43—41no—
221D4×C43—41no—
222D4×C43—41no—
223D4×C43—81no—
224D4×C43—82no—
225C2×C4×C43—22no—
226C2×C4×C43—21no—
227C2×C4×C43—21no—
228C2×C4×C43—21no—
229C2×C4×C43—21no—
230C2×C4×C43—41no—
231C2×C4×C43—41no—
232C2×C4×C43—41no—
233C2×C4×C43—82no—
234C2×C4×C43—82no—
235C2×C4×C43#12111yescharacteristic
236C2×C4×C43#12111yescharacteristic
237C2×C4×C43#12111yescharacteristic
238C2×C4×C43C22×D411yescharacteristic
239C2×C4×C43C22×D411yescharacteristic
240C2×C4×C43C2×#4111yescharacteristic
241C22⋊D43—42no—
242C2×Dic43—21no—
243C2×Dic43—21no—
244C2×Dic43—21no—
245D172—21no—
246D172—21no—
247C4×D43—41no—
248C4×D43—41no—
249Dic86—21no—
250Dic86—21no—
251C8×C43—21no—
252C8×C43—21no—
253C8×C43—21no—
254C8×C43—21no—
255C43⋊C8—41no—
256C43⋊C8—41no—
257C43⋊C8—41no—
258C43⋊C8—41no—
259C43⋊C8—41no—
260C43⋊C8—41no—
261#19589—431nomaximal, Sylow
262C22×C43—21no—
263C22×C43—21no—
264C22×C43—81no—
265C22×C43—81no—
266C22×C43—81no—
267C22×C43#47112yes—
268C22×C43C2×#12111yescharacteristic
269C2×D43—41no—
270C2×D43—41no—
271C2×D43—41no—
272C4×C43—21no—
273C4×C43—21no—
274C4×C43—21no—
275C4×C43—21no—
276C4×C43—81no—
277C4×C43—81no—
278C4×C43—81no—
279C4×C43#57611yescharacteristic
280C4×C43#57711yescharacteristic
281C4×C43#57711yescharacteristic
282C4×C43#57811yescharacteristic
283Dic43—41no—
284Dic43—41no—
285Dic43—41no—
286#3247—431no—
287#3227D4311yescharacteristic, complemented
288#3218—431no—
289#2994—431no—
290#1702—431no—
291#1701—431no—
292#1692—431no—
293#1691—431no—
294#1682—431no—
295#1681—431no—
296#1672—431no—
297#1671—431no—
298#1573—431no—
299#1551—431no—
300C2×#332—431no—
301C2×C43—22no—
302C2×C43—161no—
303C2×C43#304611yescharacteristic
304C2×C43#306211yescharacteristic
305C2×C43C2×#47111yescharacteristic
306D43—81no—
307#532C2×D4311yescharacteristic
308C2×C4⋊Q8C2×D4311yescharacteristic
309#529—431no—
310#498C2×D4311yescharacteristic
311#498C2×D4311yescharacteristic
312#497—861no—
313#491—861no—
314#486C2×D4311yescharacteristic
315#486C2×D4311yescharacteristic
316#481—21no—
317#481—21no—
318#478—861no—
319#477—431no—
320#476—21no—
321#476—21no—
322#476—431no—
323#466—861no—
324#465—861no—
325#463—861no—
326#462—431no—
327#462—431no—
328#461—431no—
329#461—431no—
330#460—431no—
331#459—431no—
332#451—861no—
333#448—861no—
334#446—431no—
335C8×Q8—431no—
336#436—431no—
337#435—861no—
338C8×D4—431no—
339C8×D4—861no—
340#433—861no—
341#432—431no—
342#431C2×D4311yescharacteristic
343#424—861no—
344C2×C4⋊C8—431no—
345C2×C4⋊C8—431no—
346#335—431no—
347#335—431no—
348#334—431no—
349#334—431no—
350#333—431no—
351#333—431no—
352#332—431no—
353#332—431no—
354#332—431no—
355#332—431no—
356#331—431no—
357#331—431no—
358C43#1958911yescharacteristic, complemented, Sylow
359C2×#41—21no—
360C22×Q8—21no—
361C2×Q16—861no—
362C2×Q16—861no—
363C2×SD16—861no—
364C2×SD16—861no—
365C2×SD16—861no—
366C2×D8—861no—
367C2×M16—861no—
368C22×C8—861no—
369C22×C8—861no—
370C22×C8—861no—
371C4⋊Q8—21no—
372C4⋊Q8—21no—
373C4⋊Q8—21no—
374C4⋊Q8C22×D4311yescharacteristic
375C4⋊Q8C22×D4311yescharacteristic
376C4⋊Q8C22×D4311yescharacteristic
377#127C22×D4311yescharacteristic
378#126—861no—
379#125—431no—
380#124—21no—
381#124—431no—
382#123—861no—
383C22⋊Q8—431no—
384#121—21no—
385#121—21no—
386#121—431no—
387C4×Q8—431no—
388C4×D4—21no—
389C4×D4—21no—
390C4×D4—431no—
391C4×D4—861no—
392#117—861no—
393C2×C4⋊C4—21no—
394C2×C4⋊C4—21no—
395C2×C42C22×D4311yescharacteristic
396#107—861no—
397#106—21no—
398#106—21no—
399#106—21no—
400#106—21no—
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—
412C4⋊C8C22⋊D4311yescharacteristic
413C4⋊C8C22⋊D4311yescharacteristic
414#103—861no—
415#103—861no—
416#103—861no—
417#103—861no—
418#103—861no—
419#102—21no—
420#102—21no—
421#102—21no—
422#102—21no—
423#102—861no—
424#102—861no—
425#102—861no—
426C22⋊C8—861no—
427C22⋊C8—861no—
428C22⋊C8—861no—
429C22⋊C8C22⋊D4311yescharacteristic
430C22⋊C8C22⋊D4311yescharacteristic
431#97—861no—
432#97—861no—
433C4×C8—861no—
434C4×C8C22×D4311yescharacteristic
435C4×C8C22×D4311yescharacteristic
436#41—82no—
437C2×Q8—21no—
438C2×Q8—21no—
439C2×Q8—21no—
440C2×Q8—41no—
441C2×Q8—81no—
442C2×Q8—81no—
443C2×Q8—431no—
444C2×D4—21no—
445C2×D4—21no—
446C2×D4—21no—
447C2×D4—41no—
448C2×D4—431no—
449C2×D4—861no—
450C22×C4—41no—
451C22×C4—41no—
452C22×C4—861no—
453C22×C4D4×D4311yescharacteristic
454C22×C4#1062190011yescharacteristic
455C22×C4C2×C22⋊D4311yescharacteristic
456Q16—3441no—
457Q16—3441no—
458SD16—3441no—
459SD16—3441no—
460SD16—3441no—
461D8—3441no—
462M16—3441no—
463C2×C8—861no—
464C2×C8—861no—
465C2×C8—861no—
466C2×C8—861no—
467C2×C8—861no—
468C2×C8—861no—
469C2×C8—3441no—
470C2×C8—3441no—
471C2×C8—3441no—
472C2×C8C2×C22⋊D4311yescharacteristic
473C2×C8C2×C22⋊D4311yescharacteristic
474C2×C8C2×C22⋊D4311yescharacteristic
475C2×C8C2×C22⋊D4311yescharacteristic
476C4⋊C4—21no—
477C4⋊C4—21no—
478C4⋊C4—21no—
479C4⋊C4—21no—
480C4⋊C4—21no—
481C4⋊C4—21no—
482C4⋊C4—41no—
483C4⋊C4—41no—
484C4⋊C4—431no—
485C4⋊C4—431no—
486C4⋊C4—861no—
487C4⋊C4—861no—
488C4⋊C4—861no—
489C4⋊C4—861no—
490C22⋊C4—41no—
491C22⋊C4—41no—
492C22⋊C4—861no—
493C22⋊C4—861no—
494C22⋊C4—861no—
495C22⋊C4—861no—
496C22⋊C4—861no—
497C42—861no—
498C42D4×D4311yescharacteristic
499C42#1062190011yescharacteristic
500C42C2×C22⋊D4311yescharacteristic
501C42C23×D4311yescharacteristic
502C23—41no—
503C23—861no—
504C23#1306329611yescharacteristic
505Q8—41no—
506Q8—41no—
507Q8—41no—
508Q8—41no—
509Q8—81no—
510Q8—82no—
511Q8—861no—
512Q8—861no—
513D4—41no—
514D4—41no—
515D4—41no—
516D4—41no—
517D4—81no—
518D4—82no—
519D4—861no—
520D4—861no—
521D4—1722no—
522C2×C4—22no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—82no—
531C2×C4—82no—
532C2×C4—861no—
533C2×C4—861no—
534C2×C4—861no—
535C2×C4—1721no—
536C2×C4—1721no—
537C2×C4#1306329611yescharacteristic
538C2×C4#1306329611yescharacteristic
539C2×C4#1306329611yescharacteristic
540C2×C4C2×D4×D4311yescharacteristic
541C2×C4C22×C22⋊D4311yescharacteristic
542C2×C4C2×#1062190011yescharacteristic
543C8—21no—
544C8—21no—
545C8—21no—
546C8—21no—
547C8—1721no—
548C8—1721no—
549C8—1721no—
550C8—1721no—
551C8—1721no—
552C8—1721no—
553C22—21no—
554C22—21no—
555C22—81no—
556C22—81no—
557C22—81no—
558C22—1721no—
559C22—1721no—
560C22—1721no—
561C22#1458315912yes—
562C22C2×#1306329611yescharacteristic
563C4—21no—
564C4—21no—
565C4—21no—
566C4—21no—
567C4—81no—
568C4—81no—
569C4—81no—
570C4—1721no—
571C4—1721no—
572C4—1721no—
573C4#1458370311yescharacteristic
574C4#1458370711yescharacteristic
575C4#1458370911yescharacteristic
576C4#1458371411yescharacteristic
577C2—22no—
578C2—161no—
579C2—3441no—
580C2#1914414111yescharacteristic
581C2#1914426911yescharacteristic
582C2C2×#1458315911yescharacteristic
subgroupG/H
centerC22C2×#13063296
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#3227C2
socleC22×C43C2×#121
prime radical#19145915C2
hypercenter#3227D43
hypocenterC43#19589
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3227

Complements

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

NH ≅ G/Ntype
2. #19145622C2semidirect
3. #19143757C2semidirect
4. #19134160C2semidirect
5. #19134153C2semidirect
6. #19134098C2semidirect
7. #19134091C2semidirect
8. #19134036C2semidirect
9. #19134029C2semidirect
10. #19133974C2semidirect
11. #19133967C2semidirect
12. #19133380C2semidirect
13. #19133290C2semidirect
14. C2×#14582645C2semidirect
15. C43×#3227C2semidirect
287. #3227D43semidirect
358. C43#19589semidirect

Maximal subgroups

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

subgroupindex
#191459152
#191456222
#191437572
#191341602
#191341532
#191340982
#191340912
#191340362
#191340292
#191339742
#191339672
#191333802
#191332902
C2×#145826452
C43×#32272
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