Finite Group Databasebeta

← #25080063

Subgroups — #25080063

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#19145934C211yesmaximal, characteristic, complemented
2#19145917C211yesmaximal, characteristic
3#19145152C211yesmaximal, characteristic, complemented
4#19143573C211yesmaximal, characteristic, complemented
5#19134102C211yesmaximal, characteristic, complemented
6#19134094C211yesmaximal, characteristic, complemented
7#19134064C211yesmaximal, characteristic, complemented
8#19134052C211yesmaximal, characteristic, complemented
9#19134044C211yesmaximal, characteristic, complemented
10#19134038C211yesmaximal, characteristic, complemented
11#19134030C211yesmaximal, characteristic, complemented
12#335×D43C211yesmaximal, characteristic, complemented
13#19133292C211yesmaximal, characteristic, complemented
14#19133287C211yesmaximal, characteristic, complemented
15C43×#1685C211yesmaximal, characteristic, complemented
16#14583454C2211yescharacteristic
17#14583447C2211yescharacteristic
18#14583431C2211yescharacteristic
19#14583297C2211yescharacteristic
20#14583249C2211yescharacteristic
21#14583245C2211yescharacteristic
22#14583205—21no—
23#14583197—21no—
24#14583195C2211yescharacteristic
25#14583189C2211yescharacteristic
26#14583181C2211yescharacteristic
27#14583141—21no—
28#14583132—21no—
29#14583127—21no—
30#14583127—21no—
31#14583125—21no—
32#14583125—21no—
33#14583120—21no—
34#14583112—21no—
35#14583110C2211yescharacteristic
36#14583104C2211yescharacteristic
37#14583096C2211yescharacteristic
38#14583029C2211yescharacteristic
39#14583023C2211yescharacteristic
40SD16×Dic43—21no—
41SD16×Dic43—21no—
42#14582968—21no—
43D4×C43⋊C8C2211yescharacteristic
44(C22⋊D43)⋊C8—21no—
45#14582957—21no—
46#14582955C2211yescharacteristic
47C4⋊C8×D43C2211yescharacteristic
48C4⋊C8×D43C2211yescharacteristic
49#14582857—21no—
50C4×C8×D43C2211yescharacteristic
51#14582652C2211yescharacteristic
52#14582651C2211yescharacteristic
53#14582651C2211yescharacteristic
54#14582647C2211yescharacteristic
55#14582647C2211yescharacteristic
56#14582646C2211yescharacteristic
57#14582645C2211yescharacteristic
58#14582644C2211yescharacteristic
59#14582643C2211yescharacteristic
60C43×#492C2211yescharacteristic
61C43×#474C2211yescharacteristic
62C43×#459C2211yescharacteristic
63C43×#436C2211yescharacteristic
64C43×#335C2211yescharacteristic
65C43×#332C2211yescharacteristic
66C43×#331C2211yescharacteristic
67C2×#10621900—21no—
68C2×Dic172—21no—
69C2×#10621883—21no—
70C2×#10621883—21no—
71C22×C43⋊C8—21no—
72C2×C8×D43—21no—
73C2×C8×D43—21no—
74C2×C8×D43D411yescharacteristic
75C2×C8×D43D411yescharacteristic
76#13063325C2311yescharacteristic
77#13063325C2311yescharacteristic
78#13063318—21no—
79#13063316—21no—
80#13063316D411yescharacteristic
81#13063312—21no—
82#13063312D411yescharacteristic
83#13063307—21no—
84#13063305—21no—
85#13063305D411yescharacteristic
86#13063301—21no—
87#13063296—21no—
88#13063296—21no—
89#13063296D411yescharacteristic
90Q8×Dic43—21no—
91C4×Dic86C2311yescharacteristic
92#13063290—21no—
93D4×Dic43—21no—
94D4×Dic43—21no—
95C4×C22⋊D43—21no—
96#13063284—21no—
97#13063283—21no—
98C42×D43C2311yescharacteristic
99#13063259—21no—
100#13063257—21no—
101#13063257—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—
111#13063250—21no—
112#13063250—21no—
113#13063249—21no—
114#13063249—21no—
115#13063248—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#13063235—21no—
124#13063235—21no—
125C4×C43⋊C8C2311yescharacteristic
126C8×Dic43—21no—
127C8×Dic43D411yescharacteristic
128C8×Dic43D411yescharacteristic
129C2×SD16×C43—21no—
130C2×SD16×C43—21no—
131C2×D8×C43—21no—
132C2×M16×C43—21no—
133C4⋊Q8×C43C2311yescharacteristic
134#127×C43C2311yescharacteristic
135C4×D4×C43C2311yescharacteristic
136#107×C43—21no—
137C4⋊C8×C43C2311yescharacteristic
138C4⋊C8×C43C2311yescharacteristic
139C4⋊C8×C43C2311yescharacteristic
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—
153#10621900—82no—
154C2×C4×D43C2×D411yescharacteristic
155C2×C4×D43C2×D411yescharacteristic
156C2×C4×D43#4111yescharacteristic
157C2×Dic86—21no—
158C2×Dic86—21no—
159C2×Dic86C2×D411yescharacteristic
160SD16×C43—42no—
161SD16×C43—42no—
162D8×C43—81no—
163M16×C43—42no—
164C2×C8×C43—21no—
165C2×C8×C43—21no—
166C2×C8×C43—21no—
167C2×C8×C43C2×D411yescharacteristic
168C2×C8×C43C2×D411yescharacteristic
169C4⋊C4×C43—21no—
170C4⋊C4×C43—21no—
171C4⋊C4×C43C2×D411yescharacteristic
172C22⋊C4×C43—21no—
173C42×C43C2411yescharacteristic
174C22⋊Dic43—21no—
175C22⋊Dic43—21no—
176C22⋊Dic43—21no—
177C22⋊Dic43—41no—
178C22⋊Dic43—41no—
179#10621883—81no—
180#10621883—81no—
181(C2×D43)⋊C4—21no—
182(C2×D43)⋊C4—41no—
183C4⋊Dic43—21no—
184C4⋊Dic43—21no—
185C4⋊Dic43—21no—
186C4⋊Dic43—21no—
187C4⋊Dic43—21no—
188C4⋊Dic43—21no—
189C4⋊Dic43—41no—
190C4⋊Dic43C2×D411yescharacteristic
191Dic43⋊C4—21no—
192Dic43⋊C4—21no—
193Dic43⋊C4—41no—
194C4×Dic43—21no—
195C4×Dic43—41no—
196C4×Dic43C2×D411yescharacteristic
197C4×Dic43C2×D411yescharacteristic
198C4×Dic43#4111yescharacteristic
199C2×C43⋊C8—21no—
200C2×C43⋊C8—21no—
201C2×C43⋊C8—21no—
202C2×C43⋊C8—42no—
203C2×C43⋊C8C2×D411yescharacteristic
204C2×C43⋊C8C2×D411yescharacteristic
205Dic172—81no—
206C8×D43—22no—
207C8×D43—41no—
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—
244Dic86—21no—
245Dic86—21no—
246Dic86—41no—
247Dic86—41no—
248Dic86—81no—
249C8×C43—21no—
250C8×C43—41no—
251C8×C43—41no—
252C8×C43—41no—
253C8×C43#13512yes—
254C43⋊C8—21no—
255C43⋊C8—21no—
256C43⋊C8—41no—
257C43⋊C8—41no—
258C43⋊C8—41no—
259#19229—431nomaximal, Sylow
260C22×C43—41no—
261C22×C43—41no—
262C22×C43—41no—
263C22×C43—81no—
264C22×C43—81no—
265C22×C43—81no—
266C22×C43C2×#12111yescharacteristic
267C2×D43—21no—
268C2×D43—21no—
269C2×D43#47112yes—
270C4×C43—21no—
271C4×C43—41no—
272C4×C43—81no—
273C4×C43C2×#13511yescharacteristic
274C4×C43#57511yescharacteristic
275C4×C43#57611yescharacteristic
276C4×C43#57811yescharacteristic
277Dic43—21no—
278Dic43—21no—
279Dic43—21no—
280Dic43—41no—
281Dic43—41no—
282Dic43—81no—
283Dic43—81no—
284#3248—431no—
285#3247—431no—
286#3167—431no—
287#2966—431no—
288#1692—431no—
289#1691—431no—
290#1686—431no—
291#1685D4311yescharacteristic, complemented
292#1684—431no—
293#1683—431no—
294#1682—431no—
295#1681—431no—
296C2×#335—431no—
297#1552—431no—
298#1551—431no—
299C2×C43—81no—
300C2×C43—161no—
301C2×C43#303511yescharacteristic
302C2×C43#306111yescharacteristic
303C2×C43C2×#47111yescharacteristic
304D43—22no—
305#533—431no—
306#532—431no—
307#529—431no—
308#498—431no—
309#492C2×D4311yescharacteristic
310#487—431no—
311#486—431no—
312#479—861no—
313#478—861no—
314#477—431no—
315#476—431no—
316#475—431no—
317#474C2×D4311yescharacteristic
318#467—861no—
319#466—861no—
320#465—861no—
321#465—861no—
322#465—861no—
323#465—861no—
324#464—861no—
325#463—861no—
326#462—431no—
327#461—431no—
328#460—431no—
329#459C2×D4311yescharacteristic
330#446—431no—
331C8×Q8—431no—
332C4×SD16—861no—
333C4×SD16—861no—
334#436C2×D4311yescharacteristic
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×C8—431no—
344#335—431no—
345#335—431no—
346#335—431no—
347#335C2×D4311yescharacteristic
348#333—431no—
349#333—431no—
350#332—431no—
351#332—431no—
352#332—431no—
353#332C2×D4311yescharacteristic
354#331—431no—
355#331C2×D4311yescharacteristic
356C43#1922911yescharacteristic, complemented, Sylow
357C2×#41—861no—
358C2×Q16—861no—
359C2×SD16—21no—
360C2×SD16—21no—
361C2×SD16—861no—
362C2×SD16—861no—
363C2×D8—21no—
364C2×M16—21no—
365C22×C8—431no—
366C22×C8—431no—
367C22×C8—861no—
368C22×C8—861no—
369C22×C8—861no—
370C4⋊Q8—431no—
371C4⋊Q8—431no—
372C4⋊Q8C22×D4311yescharacteristic
373#127C22×D4311yescharacteristic
374#126—861no—
375#125—431no—
376#125—861no—
377#124—431no—
378#124—861no—
379#123—861no—
380C22⋊Q8—431no—
381C22⋊Q8—861no—
382C22⋊Q8—861no—
383#121—431no—
384#121—861no—
385#121—861no—
386C4×Q8—431no—
387C4×Q8—861no—
388C4×Q8—861no—
389C4×D4—861no—
390C4×D4—861no—
391C4×D4—861no—
392C4×D4C22×D4311yescharacteristic
393#117—861no—
394#117—861no—
395C2×C42—431no—
396#107—21no—
397#107—861no—
398#106—861no—
399#106—861no—
400#106—861no—
401#106—861no—
402C4⋊C8—431no—
403C4⋊C8—431no—
404C4⋊C8—431no—
405C4⋊C8—861no—
406C4⋊C8—861no—
407C4⋊C8—861no—
408C4⋊C8—861no—
409C4⋊C8C22×D4311yescharacteristic
410C4⋊C8C22×D4311yescharacteristic
411C4⋊C8C22×D4311yescharacteristic
412#103—861no—
413#103—861no—
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—21no—
425C22⋊C8—861no—
426C22⋊C8—861no—
427#97—861no—
428#97—861no—
429C4×C8—431no—
430C4×C8—431no—
431C4×C8—431no—
432C4×C8—861no—
433C4×C8C22×D4311yescharacteristic
434#41—3442no—
435C2×Q8—21no—
436C2×Q8—431no—
437C2×Q8—861no—
438C2×Q8—861no—
439C2×D4—21no—
440C2×D4—21no—
441C2×D4—21no—
442C2×D4—861no—
443C2×D4—1721no—
444C2×D4D4×D4311yescharacteristic
445C22×C4—21no—
446C22×C4—431no—
447C22×C4—431no—
448C22×C4—431no—
449C22×C4—1721no—
450Q16—3441no—
451SD16—42no—
452SD16—42no—
453SD16—3441no—
454SD16—3441no—
455D8—81no—
456M16—42no—
457C2×C8—21no—
458C2×C8—21no—
459C2×C8—21no—
460C2×C8—431no—
461C2×C8—431no—
462C2×C8—862no—
463C2×C8—861no—
464C2×C8—861no—
465C2×C8—861no—
466C2×C8—3441no—
467C2×C8—3441no—
468C2×C8—1721no—
469C2×C8—1722no—
470C2×C8D4×D4311yescharacteristic
471C2×C8D4×D4311yescharacteristic
472C4⋊C4—21no—
473C4⋊C4—21no—
474C4⋊C4—431no—
475C4⋊C4—861no—
476C4⋊C4—861no—
477C4⋊C4—861no—
478C4⋊C4—861no—
479C4⋊C4—861no—
480C4⋊C4—861no—
481C4⋊C4—861no—
482C4⋊C4—861no—
483C4⋊C4—1721no—
484C4⋊C4—1721no—
485C4⋊C4D4×D4311yescharacteristic
486C22⋊C4—21no—
487C22⋊C4—861no—
488C22⋊C4—861no—
489C22⋊C4—861no—
490C22⋊C4—861no—
491C22⋊C4—1721no—
492C22⋊C4—1721no—
493C22⋊C4—1721no—
494C42—431no—
495C42—431no—
496C42—431no—
497C42—861no—
498C42—1721no—
499C42C23×D4311yescharacteristic
500C23—21no—
501C23—41no—
502C23—431no—
503Q8—41no—
504Q8—41no—
505Q8—861no—
506Q8—861no—
507Q8—3441no—
508Q8—1721no—
509Q8—1721no—
510D4—21no—
511D4—21no—
512D4—41no—
513D4—41no—
514D4—41no—
515D4—41no—
516D4—81no—
517D4—3442no—
518D4—1722no—
519C2×C4—21no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—431no—
524C2×C4—431no—
525C2×C4—431no—
526C2×C4—862no—
527C2×C4—861no—
528C2×C4—861no—
529C2×C4—861no—
530C2×C4—861no—
531C2×C4—861no—
532C2×C4—861no—
533C2×C4—3442no—
534C2×C4—1721no—
535C2×C4—1721no—
536C2×C4C2×D4×D4311yescharacteristic
537C2×C4C2×D4×D4311yescharacteristic
538C2×C4#41×D4311yescharacteristic
539C8—21no—
540C8—41no—
541C8—41no—
542C8—41no—
543C8—861no—
544C8—861no—
545C8—1721no—
546C8—1721no—
547C8—1721no—
548C8#1306334412yes—
549C22—41no—
550C22—41no—
551C22—41no—
552C22—81no—
553C22—81no—
554C22—81no—
555C22—432no—
556C22—861no—
557C22—861no—
558C22#121×D4311yescharacteristic
559C4—21no—
560C4—41no—
561C4—81no—
562C4—861no—
563C4—861no—
564C4—861no—
565C4—3441no—
566C4—3441no—
567C4—1721no—
568C4—1721no—
569C4C2×#1306334411yescharacteristic
570C4#1458369511yescharacteristic
571C4#1458370311yescharacteristic
572C4#1458371511yescharacteristic
573C2—81no—
574C2—161no—
575C2—862no—
576C2#1914404311yescharacteristic
577C2#1914426311yescharacteristic
578C2#471×D4311yescharacteristic
subgroupG/H
centerC22#121×D43
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#1685C2
socleC22×C43C2×#121
prime radical#19145917C2
hypercenter#1685D43
hypocenterC43#19229
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #1685

Complements

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

NH ≅ G/Ntype
1. #19145934C2semidirect
3. #19145152C2semidirect
4. #19143573C2semidirect
5. #19134102C2semidirect
6. #19134094C2semidirect
7. #19134064C2semidirect
8. #19134052C2semidirect
9. #19134044C2semidirect
10. #19134038C2semidirect
11. #19134030C2semidirect
12. #335×D43C2semidirect
13. #19133292C2semidirect
14. #19133287C2semidirect
15. C43×#1685C2semidirect
291. #1685D43semidirect
356. C43#19229semidirect

Maximal subgroups

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

subgroupindex
#191459342
#191459172
#191451522
#191435732
#191341022
#191340942
#191340642
#191340522
#191340442
#191340382
#191340302
#335×D432
#191332922
#191332872
C43×#16852
#1922943