Finite Group Databasebeta

← #25084199

Subgroups — #25084199

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#19145917C211yesmaximal, characteristic
2#19145719C211yesmaximal, characteristic, complemented
3#19145621C211yesmaximal, characteristic, complemented
4#19143756C211yesmaximal, characteristic, complemented
5#19134162C211yesmaximal, characteristic, complemented
6#19134100C211yesmaximal, characteristic, complemented
7#19134094C211yesmaximal, characteristic, complemented
8#19134036C211yesmaximal, characteristic, complemented
9#19134030C211yesmaximal, characteristic, complemented
10#19133978C211yesmaximal, characteristic, complemented
11#19133968C211yesmaximal, characteristic, complemented
12#19133377C211yesmaximal, characteristic, complemented
13#19133287C211yesmaximal, characteristic, complemented
14#332×D43C211yesmaximal, characteristic, complemented
15C43×#1701C211yesmaximal, characteristic, complemented
16#14583447C2211yescharacteristic
17C4⋊Q8×D43C2211yescharacteristic
18#14583431C2211yescharacteristic
19#14583297C2211yescharacteristic
20#14583295C2211yescharacteristic
21#14583290—21no—
22#14583266—21no—
23#14583245C2211yescharacteristic
24#14583216—21no—
25#14583216—21no—
26#14583197—21no—
27#14583195C2211yescharacteristic
28#14583189C2211yescharacteristic
29#14583187—21no—
30#14583187—21no—
31#14583132—21no—
32#14583127—21no—
33#14583112—21no—
34#14583110C2211yescharacteristic
35#14583106C2211yescharacteristic
36#14583104C2211yescharacteristic
37#14583096C2211yescharacteristic
38#14583056—21no—
39#14583036—21no—
40#14583026C2211yescharacteristic
41C8×Dic86C2211yescharacteristic
42#14582968—21no—
43D4×C43⋊C8C2211yescharacteristic
44(C22⋊D43)⋊C8—21no—
45#14582957—21no—
46#14582955C2211yescharacteristic
47#14582950C2211yescharacteristic
48#14582927—21no—
49C4⋊C8×D43C2211yescharacteristic
50C4⋊C8×D43C2211yescharacteristic
51#14582652C2211yescharacteristic
52#14582651C2211yescharacteristic
53#14582649C2211yescharacteristic
54#14582647C2211yescharacteristic
55#14582647C2211yescharacteristic
56#14582646C2211yescharacteristic
57#14582645C2211yescharacteristic
58#14582644C2211yescharacteristic
59#14582643C2211yescharacteristic
60C43×#486C2211yescharacteristic
61C43×#461C2211yescharacteristic
62C43×#459C2211yescharacteristic
63C43×#436C2211yescharacteristic
64C43×#334C2211yescharacteristic
65C43×#332C2211yescharacteristic
66C43×#331C2211yescharacteristic
67C2×#10621900—21no—
68C2×Q8×D43—21no—
69C2×Dic172—21no—
70C2×#10621885—21no—
71C2×#10621883—21no—
72C2×#10621883—21no—
73C22×C43⋊C8—21no—
74C2×C8×D43—21no—
75C2×C8×D43—21no—
76#13063325C2311yescharacteristic
77#13063325C2311yescharacteristic
78#13063324—21no—
79#13063324—21no—
80#13063323—21no—
81#13063318—21no—
82#13063316D411yescharacteristic
83#13063312—21no—
84#13063312D411yescharacteristic
85#13063307—21no—
86#13063305D411yescharacteristic
87#13063296—21no—
88#13063296—21no—
89#13063296D411yescharacteristic
90C4×Dic86C2311yescharacteristic
91D4×Dic43—21no—
92D4×Dic43—21no—
93C4×C22⋊D43—21no—
94#13063284—21no—
95C4⋊C4×D43—21no—
96C4⋊C4×D43—21no—
97C42×D43C2311yescharacteristic
98#13063259—21no—
99#13063257—21no—
100#13063257—21no—
101#13063256—21no—
102#13063256—21no—
103#13063256—21no—
104C4⋊(C43⋊C8)C2311yescharacteristic
105C4⋊(C43⋊C8)C2311yescharacteristic
106C4⋊(C43⋊C8)C2311yescharacteristic
107Dic43⋊C8—21no—
108Dic43⋊C8—21no—
109Dic43⋊C8—21no—
110Dic43⋊C8—21no—
111Dic43⋊C8D411yescharacteristic
112Dic43⋊C8D411yescharacteristic
113#13063250—21no—
114#13063250—21no—
115#13063249—21no—
116#13063248—21no—
117#13063246—21no—
118#13063246—21no—
119#13063246—21no—
120#13063246—21no—
121C22⋊(C43⋊C8)—21no—
122(C2×D43)⋊C8—21no—
123(C2×D43)⋊C8D411yescharacteristic
124(C2×D43)⋊C8D411yescharacteristic
125#13063235—21no—
126#13063235—21no—
127C4×C43⋊C8C2311yescharacteristic
128C8×Dic43—21no—
129C2×SD16×C43—21no—
130C2×D8×C43—21no—
131C2×M16×C43—21no—
132C4⋊Q8×C43C2311yescharacteristic
133#127×C43C2311yescharacteristic
134C4×D4×C43C2311yescharacteristic
135C4⋊C8×C43C2311yescharacteristic
136C4⋊C8×C43C2311yescharacteristic
137C4⋊C8×C43C2311yescharacteristic
138#103×C43—21no—
139#102×C43—21no—
140#102×C43—21no—
141#102×C43—21no—
142C22⋊C8×C43—21no—
143C4×C8×C43C2311yescharacteristic
144C2×Q8×C43—21no—
145C2×D4×C43—21no—
146C2×D4×C43—21no—
147C2×D4×C43—21no—
148C2×D4×C43C2×D411yescharacteristic
149C22×C4×C43—21no—
150C2×C22⋊D43—21no—
151C2×C22⋊D43—41no—
152C22×Dic43—41no—
153Q8×D43—81no—
154Q8×D43—81no—
155#10621900—82no—
156C2×C4×D43—41no—
157C2×C4×D43C2×D411yescharacteristic
158C2×C4×D43C2×D411yescharacteristic
159C2×C4×D43#4111yescharacteristic
160C2×Dic86—21no—
161C2×Dic86—21no—
162C2×Dic86—41no—
163C2×Dic86C2×D411yescharacteristic
164SD16×C43—81no—
165D8×C43—81no—
166M16×C43—81no—
167C2×C8×C43—21no—
168C2×C8×C43—21no—
169C2×C8×C43—21no—
170C2×C8×C43C2×D411yescharacteristic
171C2×C8×C43C2×D411yescharacteristic
172C4⋊C4×C43—21no—
173C4⋊C4×C43—21no—
174C4⋊C4×C43C2×D411yescharacteristic
175C22⋊C4×C43—21no—
176C42×C43C2411yescharacteristic
177C22⋊Dic43—21no—
178C22⋊Dic43—21no—
179C22⋊Dic43—21no—
180C22⋊Dic43—41no—
181C22⋊Dic43—41no—
182#10621885—81no—
183#10621883—81no—
184#10621883—81no—
185(C2×D43)⋊C4—21no—
186C4⋊Dic43—21no—
187C4⋊Dic43—21no—
188C4⋊Dic43—21no—
189C4⋊Dic43—21no—
190C4⋊Dic43—21no—
191C4⋊Dic43—21no—
192C4⋊Dic43C2×D411yescharacteristic
193Dic43⋊C4—21no—
194Dic43⋊C4—21no—
195Dic43⋊C4—41no—
196Dic43⋊C4—41no—
197C4×Dic43—21no—
198C4×Dic43C2×D411yescharacteristic
199C4×Dic43C2×D411yescharacteristic
200C4×Dic43#4111yescharacteristic
201C2×C43⋊C8—21no—
202C2×C43⋊C8—21no—
203C2×C43⋊C8—21no—
204C2×C43⋊C8—81no—
205C2×C43⋊C8C2×D411yescharacteristic
206C2×C43⋊C8C2×D411yescharacteristic
207Dic172—81no—
208C8×D43—81no—
209C8×D43—81no—
210C23×C43—21no—
211C23×C43—41no—
212C22×D43#12111yescharacteristic
213Q8×C43—41no—
214Q8×C43—41no—
215D4×C43—21no—
216D4×C43—21no—
217D4×C43—41no—
218D4×C43—41no—
219D4×C43—41no—
220D4×C43—41no—
221D4×C43—81no—
222C2×C4×C43—21no—
223C2×C4×C43—41no—
224C2×C4×C43—41no—
225C2×C4×C43—41no—
226C2×C4×C43C22×D411yescharacteristic
227C2×C4×C43C22×D411yescharacteristic
228C2×C4×C43C2×#4111yescharacteristic
229C22⋊D43—42no—
230C22⋊D43—82no—
231C2×Dic43—21no—
232C2×Dic43—21no—
233C2×Dic43—41no—
234C2×Dic43—41no—
235C2×Dic43—82no—
236C2×Dic43#12111yescharacteristic
237C2×Dic43#12111yescharacteristic
238C2×Dic43#12111yescharacteristic
239C4×D43—22no—
240C4×D43—21no—
241C4×D43—21no—
242C4×D43—21no—
243C4×D43—21no—
244C4×D43—82no—
245Dic86—21no—
246Dic86—21no—
247Dic86—41no—
248Dic86—41no—
249Dic86—82no—
250Dic86—81no—
251C8×C43—21no—
252C8×C43—21no—
253C8×C43—41no—
254C8×C43—41no—
255C8×C43—41no—
256C43⋊C8—21no—
257C43⋊C8—21no—
258C43⋊C8—41no—
259C43⋊C8—41no—
260C43⋊C8—41no—
261#19589—431nomaximal, Sylow
262C22×C43—41no—
263C22×C43—41no—
264C22×C43—41no—
265C22×C43—81no—
266C22×C43—81no—
267C22×C43—81no—
268C22×C43C2×#12111yescharacteristic
269C2×D43—21no—
270C2×D43—21no—
271C2×D43#47112yes—
272C4×C43—21no—
273C4×C43—41no—
274C4×C43—81no—
275C4×C43#57611yescharacteristic
276C4×C43#57711yescharacteristic
277C4×C43#57711yescharacteristic
278C4×C43#57811yescharacteristic
279Dic43—21no—
280Dic43—21no—
281Dic43—21no—
282Dic43—41no—
283Dic43—41no—
284Dic43—81no—
285Dic43—81no—
286#3247—431no—
287#3227—431no—
288#3218—431no—
289#2994—431no—
290#1702—431no—
291#1701D4311yescharacteristic, complemented
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—81no—
302C2×C43—161no—
303C2×C43#304611yescharacteristic
304C2×C43#306211yescharacteristic
305C2×C43C2×#47111yescharacteristic
306D43—22no—
307#532—431no—
308C2×C4⋊Q8—431no—
309#529—431no—
310#498—431no—
311#498—431no—
312#497—861no—
313#491—861no—
314#486—431no—
315#486C2×D4311yescharacteristic
316#481—861no—
317#481—861no—
318#478—861no—
319#477—431no—
320#476—431no—
321#476—861no—
322#476—861no—
323#466—861no—
324#465—861no—
325#463—861no—
326#462—431no—
327#462—431no—
328#461—431no—
329#461C2×D4311yescharacteristic
330#460—431no—
331#459C2×D4311yescharacteristic
332#451—861no—
333#448—861no—
334#446—431no—
335C8×Q8—431no—
336#436C2×D4311yescharacteristic
337#435—861no—
338C8×D4—431no—
339C8×D4—861no—
340#433—861no—
341#432—431no—
342#431—431no—
343#424—861no—
344C2×C4⋊C8—431no—
345C2×C4⋊C8—431no—
346#335—431no—
347#335—431no—
348#334—431no—
349#334C2×D4311yescharacteristic
350#333—431no—
351#333—431no—
352#332—431no—
353#332—431no—
354#332—431no—
355#332C2×D4311yescharacteristic
356#331—431no—
357#331C2×D4311yescharacteristic
358C43#1958911yescharacteristic, complemented, Sylow
359C2×#41—861no—
360C22×Q8—861no—
361C2×Q16—861no—
362C2×Q16—861no—
363C2×SD16—21no—
364C2×SD16—861no—
365C2×SD16—861no—
366C2×D8—21no—
367C2×M16—21no—
368C22×C8—861no—
369C22×C8—861no—
370C22×C8—861no—
371C4⋊Q8—431no—
372C4⋊Q8—431no—
373C4⋊Q8—861no—
374C4⋊Q8—861no—
375C4⋊Q8—861no—
376C4⋊Q8C22×D4311yescharacteristic
377#127C22×D4311yescharacteristic
378#126—861no—
379#125—431no—
380#124—431no—
381#124—861no—
382#123—861no—
383C22⋊Q8—431no—
384#121—431no—
385#121—861no—
386#121—861no—
387C4×Q8—431no—
388C4×D4—861no—
389C4×D4—861no—
390C4×D4—861no—
391C4×D4C22×D4311yescharacteristic
392#117—861no—
393C2×C4⋊C4—861no—
394C2×C4⋊C4—861no—
395C2×C42—431no—
396#107—861no—
397#106—861no—
398#106—861no—
399#106—861no—
400#106—861no—
401#106—861no—
402C4⋊C8—431no—
403C4⋊C8—431no—
404C4⋊C8—431no—
405C4⋊C8—431no—
406C4⋊C8—431no—
407C4⋊C8—861no—
408C4⋊C8—861no—
409C4⋊C8—861no—
410C4⋊C8—861no—
411C4⋊C8C22×D4311yescharacteristic
412C4⋊C8C22×D4311yescharacteristic
413C4⋊C8C22×D4311yescharacteristic
414#103—21no—
415#103—861no—
416#103—861no—
417#103—861no—
418#103—861no—
419#102—21no—
420#102—21no—
421#102—21no—
422#102—861no—
423#102—861no—
424#102—861no—
425#102—861no—
426C22⋊C8—21no—
427C22⋊C8—431no—
428C22⋊C8—431no—
429C22⋊C8—861no—
430C22⋊C8—861no—
431#97—861no—
432#97—861no—
433C4×C8—431no—
434C4×C8—861no—
435C4×C8C22×D4311yescharacteristic
436#41—3442no—
437C2×Q8—21no—
438C2×Q8—431no—
439C2×Q8—861no—
440C2×Q8—861no—
441C2×Q8—3441no—
442C2×Q8—3441no—
443C2×Q8—1721no—
444C2×D4—21no—
445C2×D4—21no—
446C2×D4—21no—
447C2×D4—861no—
448C2×D4—1721no—
449C2×D4D4×D4311yescharacteristic
450C22×C4—21no—
451C22×C4—431no—
452C22×C4—431no—
453C22×C4—431no—
454C22×C4—1721no—
455C22×C4—1721no—
456Q16—3441no—
457Q16—3441no—
458SD16—81no—
459SD16—3441no—
460SD16—3441no—
461D8—81no—
462M16—81no—
463C2×C8—21no—
464C2×C8—21no—
465C2×C8—21no—
466C2×C8—431no—
467C2×C8—431no—
468C2×C8—861no—
469C2×C8—861no—
470C2×C8—861no—
471C2×C8—3441no—
472C2×C8—3441no—
473C2×C8—3441no—
474C2×C8D4×D4311yescharacteristic
475C2×C8D4×D4311yescharacteristic
476C4⋊C4—21no—
477C4⋊C4—21no—
478C4⋊C4—431no—
479C4⋊C4—861no—
480C4⋊C4—861no—
481C4⋊C4—861no—
482C4⋊C4—861no—
483C4⋊C4—861no—
484C4⋊C4—861no—
485C4⋊C4—861no—
486C4⋊C4—861no—
487C4⋊C4—1721no—
488C4⋊C4—1721no—
489C4⋊C4D4×D4311yescharacteristic
490C22⋊C4—21no—
491C22⋊C4—861no—
492C22⋊C4—861no—
493C22⋊C4—861no—
494C22⋊C4—861no—
495C22⋊C4—1721no—
496C22⋊C4—1721no—
497C42—431no—
498C42—431no—
499C42—431no—
500C42—861no—
501C42C23×D4311yescharacteristic
502C23—21no—
503C23—41no—
504C23—431no—
505Q8—41no—
506Q8—41no—
507Q8—861no—
508Q8—861no—
509Q8—3441no—
510Q8—3442no—
511Q8—1721no—
512Q8—1721no—
513D4—21no—
514D4—21no—
515D4—41no—
516D4—41no—
517D4—41no—
518D4—41no—
519D4—81no—
520D4—3442no—
521D4—1722no—
522C2×C4—21no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4—41no—
526C2×C4—431no—
527C2×C4—431no—
528C2×C4—431no—
529C2×C4—862no—
530C2×C4—861no—
531C2×C4—861no—
532C2×C4—861no—
533C2×C4—861no—
534C2×C4—861no—
535C2×C4—861no—
536C2×C4—3442no—
537C2×C4—3442no—
538C2×C4—1721no—
539C2×C4—1721no—
540C2×C4C2×D4×D4311yescharacteristic
541C2×C4C2×D4×D4311yescharacteristic
542C2×C4#41×D4311yescharacteristic
543C8—21no—
544C8—21no—
545C8—41no—
546C8—41no—
547C8—41no—
548C8—861no—
549C8—861no—
550C8—1721no—
551C8—1721no—
552C8—1721no—
553C22—41no—
554C22—41no—
555C22—41no—
556C22—81no—
557C22—81no—
558C22—81no—
559C22—432no—
560C22—861no—
561C22—861no—
562C22#121×D4311yescharacteristic
563C4—21no—
564C4—41no—
565C4—81no—
566C4—861no—
567C4—861no—
568C4—861no—
569C4—3441no—
570C4—3441no—
571C4—1721no—
572C4—1721no—
573C4#1458370311yescharacteristic
574C4#1458370911yescharacteristic
575C4#1458370911yescharacteristic
576C4#1458371311yescharacteristic
577C2—81no—
578C2—161no—
579C2—862no—
580C2#1914414611yescharacteristic
581C2#1914427211yescharacteristic
582C2#471×D4311yescharacteristic
subgroupG/H
centerC22#121×D43
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#1701C2
socleC22×C43C2×#121
prime radical#19145917C2
hypercenter#1701D43
hypocenterC43#19589
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #1701

Complements

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

NH ≅ G/Ntype
2. #19145719C2semidirect
3. #19145621C2semidirect
4. #19143756C2semidirect
5. #19134162C2semidirect
6. #19134100C2semidirect
7. #19134094C2semidirect
8. #19134036C2semidirect
9. #19134030C2semidirect
10. #19133978C2semidirect
11. #19133968C2semidirect
12. #19133377C2semidirect
13. #19133287C2semidirect
14. #332×D43C2semidirect
15. C43×#1701C2semidirect
291. #1701D43semidirect
358. C43#19589semidirect

Maximal subgroups

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

subgroupindex
#191459172
#191457192
#191456212
#191437562
#191341622
#191341002
#191340942
#191340362
#191340302
#191339782
#191339682
#191333772
#191332872
#332×D432
C43×#17012
#1958943