Finite Group Databasebeta

← #25080004

Subgroups — #25080004

Order 11008.

596 conjugacy classes of subgroups.

The subgroup lattice has 578 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145772C211yesmaximal, characteristic, complemented
2#19145569C211yesmaximal, characteristic
3#19145152C211yesmaximal, characteristic, complemented
4#19143573C211yesmaximal, characteristic, complemented
5#19134102C211yesmaximal, characteristic, complemented
6#19134094C211yesmaximal, characteristic, complemented
7#19134064C211yesmaximal, characteristic, complemented
8#19134024C211yesmaximal, characteristic, complemented
9#19134016C211yesmaximal, characteristic, complemented
10#19134010C211yesmaximal, characteristic, complemented
11#19134002C211yesmaximal, characteristic, complemented
12#19133342C211yesmaximal, characteristic, complemented
13#19133302C211yesmaximal, characteristic, complemented
14#19133297C211yesmaximal, characteristic, complemented
15C43×#1685C211yesmaximal, characteristic, complemented
16#14583454C2211yescharacteristic
17#14583447C2211yescharacteristic
18#14583431C2211yescharacteristic
19#14583300—21no—
20#14583297C2211yescharacteristic
21#14583282—21no—
22#14583252—21no—
23#14583252—21no—
24#14583249C2211yescharacteristic
25#14583245C2211yescharacteristic
26#14583242—21no—
27#14583221—21no—
28#14583195C2211yescharacteristic
29#14583189C2211yescharacteristic
30#14583181C2211yescharacteristic
31#14583125—21no—
32#14583125—21no—
33#14583110C2211yescharacteristic
34#14583104C2211yescharacteristic
35#14583096C2211yescharacteristic
36#14583062—21no—
37#14583041—21no—
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
47#14582951C2211yescharacteristic
48#14582951C2211yescharacteristic
49#14582857—21no—
50C4×C8×D43C2211yescharacteristic
51#14582652C2211yescharacteristic
52#14582649C2211yescharacteristic
53#14582649C2211yescharacteristic
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×D43D411yescharacteristic
73C2×C8×D43D411yescharacteristic
74#13063325C2311yescharacteristic
75#13063325C2311yescharacteristic
76#13063318—21no—
77#13063316—21no—
78#13063316D411yescharacteristic
79#13063312—21no—
80#13063312D411yescharacteristic
81#13063307—21no—
82#13063305—21no—
83#13063305D411yescharacteristic
84#13063301—21no—
85#13063296—21no—
86#13063296—21no—
87#13063296D411yescharacteristic
88Q8×Dic43—21no—
89C4×Dic86C2311yescharacteristic
90#13063290—21no—
91D4×Dic43—21no—
92D4×Dic43—21no—
93C4×C22⋊D43—21no—
94#13063284—21no—
95#13063283—21no—
96C42×D43C2311yescharacteristic
97#13063259—21no—
98#13063257—21no—
99#13063257—21no—
100#13063256—21no—
101#13063256—21no—
102C4⋊(C43⋊C8)C2311yescharacteristic
103C4⋊(C43⋊C8)C2311yescharacteristic
104C4⋊(C43⋊C8)C2311yescharacteristic
105Dic43⋊C8—21no—
106Dic43⋊C8—21no—
107#13063250—21no—
108#13063250—21no—
109#13063249—21no—
110#13063249—21no—
111#13063248—21no—
112#13063248—21no—
113#13063246—21no—
114#13063246—21no—
115#13063246—21no—
116#13063246—21no—
117C22⋊(C43⋊C8)—21no—
118(C2×D43)⋊C8—21no—
119(C2×D43)⋊C8—21no—
120(C2×D43)⋊C8—21no—
121#13063235—21no—
122#13063235—21no—
123C4×C43⋊C8C2311yescharacteristic
124C8×Dic43—21no—
125C8×Dic43—21no—
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—81no—
154#10621900—81no—
155C2×C4×D43C2×D411yescharacteristic
156C2×C4×D43C2×D411yescharacteristic
157C2×C4×D43#4111yescharacteristic
158C2×Dic86—21no—
159C2×Dic86—21no—
160C2×Dic86C2×D411yescharacteristic
161SD16×C43—42no—
162SD16×C43—42no—
163D8×C43—81no—
164M16×C43—42no—
165C2×C8×C43—21no—
166C2×C8×C43—21no—
167C2×C8×C43—21no—
168C2×C8×C43C2×D411yescharacteristic
169C2×C8×C43C2×D411yescharacteristic
170C4⋊C4×C43—21no—
171C4⋊C4×C43—21no—
172C4⋊C4×C43C2×D411yescharacteristic
173C22⋊C4×C43—21no—
174C42×C43C2411yescharacteristic
175C22⋊Dic43—21no—
176C22⋊Dic43—21no—
177C22⋊Dic43—21no—
178C22⋊Dic43—41no—
179C22⋊Dic43—41no—
180#10621883—81no—
181#10621883—81no—
182(C2×D43)⋊C4—21no—
183(C2×D43)⋊C4—41no—
184C4⋊Dic43—21no—
185C4⋊Dic43—21no—
186C4⋊Dic43—21no—
187C4⋊Dic43—21no—
188C4⋊Dic43—21no—
189C4⋊Dic43—21no—
190C4⋊Dic43—41no—
191C4⋊Dic43C2×D411yescharacteristic
192Dic43⋊C4—21no—
193Dic43⋊C4—21no—
194Dic43⋊C4—41no—
195C4×Dic43—21no—
196C4×Dic43—41no—
197C4×Dic43C2×D411yescharacteristic
198C4×Dic43C2×D411yescharacteristic
199C4×Dic43#4111yescharacteristic
200C2×C43⋊C8—21no—
201C2×C43⋊C8—21no—
202C2×C43⋊C8—21no—
203C2×C43⋊C8—42no—
204C2×C43⋊C8C2×D411yescharacteristic
205C2×C43⋊C8C2×D411yescharacteristic
206Dic172—81no—
207C8×D43—22no—
208C8×D43—41no—
209C23×C43—21no—
210C23×C43—41no—
211C22×D43#12111yescharacteristic
212Q8×C43—41no—
213Q8×C43—41no—
214D4×C43—21no—
215D4×C43—21no—
216D4×C43—41no—
217D4×C43—41no—
218D4×C43—41no—
219D4×C43—41no—
220D4×C43—81no—
221C2×C4×C43—21no—
222C2×C4×C43—41no—
223C2×C4×C43—41no—
224C2×C4×C43—41no—
225C2×C4×C43C22×D411yescharacteristic
226C2×C4×C43C22×D411yescharacteristic
227C2×C4×C43C2×#4111yescharacteristic
228C22⋊D43—42no—
229C22⋊D43—82no—
230C2×Dic43—21no—
231C2×Dic43—21no—
232C2×Dic43—41no—
233C2×Dic43—41no—
234C2×Dic43—82no—
235C2×Dic43#12111yescharacteristic
236C2×Dic43#12111yescharacteristic
237C2×Dic43#12111yescharacteristic
238C4×D43—21no—
239C4×D43—21no—
240C4×D43—21no—
241C4×D43—21no—
242C4×D43—41no—
243Dic86—21no—
244Dic86—21no—
245Dic86—41no—
246Dic86—41no—
247Dic86—81no—
248C8×C43—21no—
249C8×C43—41no—
250C8×C43—41no—
251C8×C43—41no—
252C8×C43#13512yes—
253C43⋊C8—21no—
254C43⋊C8—21no—
255C43⋊C8—41no—
256C43⋊C8—41no—
257C43⋊C8—41no—
258#19224—431nomaximal, Sylow
259C22×C43—41no—
260C22×C43—41no—
261C22×C43—41no—
262C22×C43—81no—
263C22×C43—81no—
264C22×C43—81no—
265C22×C43C2×#12111yescharacteristic
266C2×D43—21no—
267C2×D43—21no—
268C2×D43—21no—
269C4×C43—21no—
270C4×C43—41no—
271C4×C43—81no—
272C4×C43C2×#13511yescharacteristic
273C4×C43#57511yescharacteristic
274C4×C43#57711yescharacteristic
275C4×C43#57711yescharacteristic
276Dic43—21no—
277Dic43—21no—
278Dic43—21no—
279Dic43—41no—
280Dic43—41no—
281Dic43—81no—
282Dic43—81no—
283#3233—431no—
284#3212—431no—
285#3167—431no—
286#2966—431no—
287#1692—431no—
288#1691—431no—
289#1686—431no—
290#1685D4311yescharacteristic, complemented
291#1680—431no—
292#1679—431no—
293#1678—431no—
294#1677—431no—
295#1564—431no—
296#1554—431no—
297#1553—431no—
298C2×C43—81no—
299C2×C43—161no—
300C2×C43#303511yescharacteristic
301C2×C43#305711yescharacteristic
302C2×C43#306711yescharacteristic
303D43—41no—
304#533—431no—
305#532—431no—
306#529—431no—
307#499—861no—
308#498—431no—
309#495—861no—
310#492C2×D4311yescharacteristic
311#488—861no—
312#488—861no—
313#487—431no—
314#486—431no—
315#485—861no—
316#482—861no—
317#477—431no—
318#476—431no—
319#475—431no—
320#474C2×D4311yescharacteristic
321#465—861no—
322#465—861no—
323#462—431no—
324#461—431no—
325#460—431no—
326#459C2×D4311yescharacteristic
327#452—861no—
328#449—861no—
329#446—431no—
330C8×Q8—431no—
331C4×SD16—861no—
332C4×SD16—861no—
333#436C2×D4311yescharacteristic
334#435—861no—
335C8×D4—431no—
336C8×D4—861no—
337#433—861no—
338#432—431no—
339#431—431no—
340#431—431no—
341#405—861no—
342C2×C4×C8—431no—
343#335—431no—
344#335C2×D4311yescharacteristic
345#334—431no—
346#334—431no—
347#333—431no—
348#333—431no—
349#332—431no—
350#332—431no—
351#332—431no—
352#332C2×D4311yescharacteristic
353#331—431no—
354#331C2×D4311yescharacteristic
355C43#1922411yescharacteristic, complemented, Sylow
356C2×#41—861no—
357C2×Q16—861no—
358C2×SD16—21no—
359C2×SD16—21no—
360C2×SD16—861no—
361C2×SD16—861no—
362C2×D8—21no—
363C2×M16—21no—
364C22×C8—431no—
365C22×C8—431no—
366C22×C8—861no—
367C4⋊Q8—431no—
368C4⋊Q8—431no—
369C4⋊Q8C22×D4311yescharacteristic
370#127C22×D4311yescharacteristic
371#126—861no—
372#125—431no—
373#125—861no—
374#124—431no—
375#124—861no—
376#123—861no—
377C22⋊Q8—431no—
378C22⋊Q8—861no—
379C22⋊Q8—861no—
380#121—431no—
381#121—861no—
382#121—861no—
383C4×Q8—431no—
384C4×Q8—861no—
385C4×Q8—861no—
386C4×D4—861no—
387C4×D4—861no—
388C4×D4—861no—
389C4×D4C22×D4311yescharacteristic
390#117—861no—
391#117—861no—
392C2×C42—431no—
393#107—21no—
394#107—861no—
395#106—861no—
396#106—861no—
397#106—861no—
398#106—861no—
399C4⋊C8—431no—
400C4⋊C8—431no—
401C4⋊C8—431no—
402C4⋊C8—861no—
403C4⋊C8—861no—
404C4⋊C8C22×D4311yescharacteristic
405C4⋊C8C22×D4311yescharacteristic
406C4⋊C8C22×D4311yescharacteristic
407#103—861no—
408#103—861no—
409#103—861no—
410#103—861no—
411#103—861no—
412#103—861no—
413#102—21no—
414#102—21no—
415#102—861no—
416#102—861no—
417#102—861no—
418#102—861no—
419C22⋊C8—21no—
420C22⋊C8—861no—
421C22⋊C8—861no—
422C22⋊C8—861no—
423C22⋊C8—861no—
424#97—861no—
425#97—861no—
426C4×C8—431no—
427C4×C8—431no—
428C4×C8—431no—
429C4×C8—861no—
430C4×C8—861no—
431C4×C8—861no—
432C4×C8C22×D4311yescharacteristic
433#41—3441no—
434#41—3441no—
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—1721no—
467C2×C8—1722no—
468C2×C8D4×D4311yescharacteristic
469C2×C8D4×D4311yescharacteristic
470C4⋊C4—21no—
471C4⋊C4—21no—
472C4⋊C4—431no—
473C4⋊C4—861no—
474C4⋊C4—861no—
475C4⋊C4—861no—
476C4⋊C4—861no—
477C4⋊C4—861no—
478C4⋊C4—861no—
479C4⋊C4—861no—
480C4⋊C4—861no—
481C4⋊C4—1721no—
482C4⋊C4—1721no—
483C4⋊C4D4×D4311yescharacteristic
484C22⋊C4—21no—
485C22⋊C4—861no—
486C22⋊C4—861no—
487C22⋊C4—861no—
488C22⋊C4—861no—
489C22⋊C4—1721no—
490C22⋊C4—1721no—
491C22⋊C4—1721no—
492C42—431no—
493C42—431no—
494C42—431no—
495C42—861no—
496C42—1721no—
497C42C23×D4311yescharacteristic
498C23—21no—
499C23—41no—
500C23—431no—
501Q8—41no—
502Q8—41no—
503Q8—861no—
504Q8—861no—
505Q8—3441no—
506Q8—1721no—
507Q8—1721no—
508D4—21no—
509D4—21no—
510D4—41no—
511D4—41no—
512D4—41no—
513D4—41no—
514D4—81no—
515D4—3442no—
516D4—1722no—
517C2×C4—21no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—431no—
522C2×C4—431no—
523C2×C4—431no—
524C2×C4—861no—
525C2×C4—861no—
526C2×C4—861no—
527C2×C4—861no—
528C2×C4—861no—
529C2×C4—861no—
530C2×C4—3442no—
531C2×C4—1721no—
532C2×C4—1721no—
533C2×C4—1721no—
534C2×C4C2×D4×D4311yescharacteristic
535C2×C4C2×D4×D4311yescharacteristic
536C2×C4#41×D4311yescharacteristic
537C8—21no—
538C8—41no—
539C8—41no—
540C8—41no—
541C8—861no—
542C8—861no—
543C8—1721no—
544C8—1721no—
545C8—1721no—
546C8#1306334412yes—
547C22—41no—
548C22—41no—
549C22—41no—
550C22—81no—
551C22—81no—
552C22—81no—
553C22—861no—
554C22—861no—
555C22—861no—
556C22#121×D4311yescharacteristic
557C4—21no—
558C4—41no—
559C4—81no—
560C4—861no—
561C4—861no—
562C4—861no—
563C4—3441no—
564C4—3441no—
565C4—1721no—
566C4—1721no—
567C4C2×#1306334411yescharacteristic
568C4#1458369511yescharacteristic
569C4#1458370811yescharacteristic
570C4#1458370911yescharacteristic
571C2—81no—
572C2—161no—
573C2—1721no—
574C2#1914404311yescharacteristic
575C2#1914423211yescharacteristic
576C2#1914431011yescharacteristic
subgroupG/H
centerC22#121×D43
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#1685C2
socleC22×C43C2×#121
prime radical#19145569C2
hypercenter#1685D43
hypocenterC43#19224
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. #19145772C2semidirect
3. #19145152C2semidirect
4. #19143573C2semidirect
5. #19134102C2semidirect
6. #19134094C2semidirect
7. #19134064C2semidirect
8. #19134024C2semidirect
9. #19134016C2semidirect
10. #19134010C2semidirect
11. #19134002C2semidirect
12. #19133342C2semidirect
13. #19133302C2semidirect
14. #19133297C2semidirect
15. C43×#1685C2semidirect
290. #1685D43semidirect
355. C43#19224semidirect

Maximal subgroups

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

subgroupindex
#191457722
#191455692
#191451522
#191435732
#191341022
#191340942
#191340642
#191340242
#191340162
#191340102
#191340022
#191333422
#191333022
#191332972
C43×#16852
#1922443