Finite Group Databasebeta

← #25086478

Subgroups — #25086478

Order 11008.

606 conjugacy classes of subgroups.

The subgroup lattice has 582 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19147002C211yesmaximal, characteristic, complemented
2#19146525C211yesmaximal, characteristic
3#19146460C211yesmaximal, characteristic, complemented
4#19134238C211yesmaximal, characteristic, complemented
5#19134177C211yesmaximal, characteristic, complemented
6#19134016C211yesmaximal, characteristic, complemented
7#19134015C211yesmaximal, characteristic, complemented
8#19133968C211yesmaximal, characteristic, complemented
9#19133851C211yesmaximal, characteristic, complemented
10#19133828C211yesmaximal, characteristic, complemented
11#19133822C211yesmaximal, characteristic, complemented
12#19133760C211yesmaximal, characteristic, complemented
13#19133429C211yesmaximal, characteristic, complemented
14#19133419C211yesmaximal, characteristic, complemented
15C43×#3367C211yesmaximal, characteristic, complemented
16#14583614C2211yescharacteristic
17#14583553C2211yescharacteristic
18#14583302C2211yescharacteristic
19#14583295C2211yescharacteristic
20#14583251C2211yescharacteristic
21#14583250C2211yescharacteristic
22#14583249C2211yescharacteristic
23#14583242—21no—
24#14583237—21no—
25#14583227—21no—
26#14583223—21no—
27#14583194C2211yescharacteristic
28#14583189C2211yescharacteristic
29#14583184C2211yescharacteristic
30#14583176C2211yescharacteristic
31#14583130—21no—
32#14583130—21no—
33#14583127—21no—
34#14583104C2211yescharacteristic
35#14583101C2211yescharacteristic
36#14583041—21no—
37#14583038—21no—
38C4×#10621884C2211yescharacteristic
39C8×D172C2211yescharacteristic
40D4×C43⋊C8C2211yescharacteristic
41D4×C43⋊C8C2211yescharacteristic
42#14582935—21no—
43#14582892—21no—
44C2×#13063249—21no—
45#14582650C2211yescharacteristic
46#14582649C2211yescharacteristic
47#14582647C2211yescharacteristic
48#14582646C2211yescharacteristic
49#14582645C2211yescharacteristic
50#14582645C2211yescharacteristic
51Q8⋊(C43⋊C8)C2211yescharacteristic
52D4⋊(C43⋊C8)C2211yescharacteristic
53D4⋊(C43⋊C8)C2211yescharacteristic
54#14582626C2211yescharacteristic
55#14582620C2211yescharacteristic
56C43×#556C2211yescharacteristic
57D4×Q8×C43C2211yescharacteristic
58C43×#489—21no—
59C43×#487C2211yescharacteristic
60C43×#477—21no—
61C43×#474C2211yescharacteristic
62C43×#463—21no—
63C43×#461C2211yescharacteristic
64C43×#446C2211yescharacteristic
65C43×#440—21no—
66C4×D8×C43C2211yescharacteristic
67C2×#10621900—21no—
68C2×#10621883—21no—
69C2×#10621884—21no—
70C2×#10621884D411yescharacteristic
71C22×C43⋊C8—21no—
72C22×C43⋊C8—21no—
73C2×C8×D43—21no—
74#13063325C2311yescharacteristic
75#13063325C2311yescharacteristic
76#13063311—41no—
77#13063309—41no—
78#13063305—21no—
79#13063299—21no—
80#13063299—21no—
81#13063296—21no—
82C4×D172C2311yescharacteristic
83#13063284—21no—
84#13063283—21no—
85C2×C4⋊Dic43—21no—
86#13063258—21no—
87#13063258—21no—
88#13063258—41no—
89#13063256—21no—
90#13063256—21no—
91#13063256—21no—
92#13063256—21no—
93#13063256D411yescharacteristic
94C4⋊(C43⋊C8)C2311yescharacteristic
95C4⋊(C43⋊C8)C2311yescharacteristic
96C4⋊(C43⋊C8)C2311yescharacteristic
97#13063250—21no—
98#13063250—21no—
99#13063249—21no—
100#13063249—21no—
101#13063249—21no—
102#13063249—21no—
103#13063249—21no—
104#13063249D411yescharacteristic
105#13063248—21no—
106#13063248—41no—
107#13063246—21no—
108#13063245—21no—
109#13063245D411yescharacteristic
110C22⋊(C43⋊C8)—21no—
111C22⋊(C43⋊C8)—21no—
112(C2×D43)⋊C8—21no—
113C4×C43⋊C8C2311yescharacteristic
114C4×C43⋊C8C2311yescharacteristic
115C22×Q8×C43—21no—
116C2×SD16×C43—21no—
117C2×D8×C43D411yescharacteristic
118C4⋊Q8×C43—21no—
119C4⋊Q8×C43C2311yescharacteristic
120C4⋊Q8×C43C2311yescharacteristic
121#126×C43—41no—
122#124×C43—21no—
123C22⋊Q8×C43—21no—
124C22⋊Q8×C43—21no—
125C22⋊Q8×C43—41no—
126C4×Q8×C43—21no—
127C4×Q8×C43C2311yescharacteristic
128C4×D4×C43—21no—
129C4×D4×C43C2311yescharacteristic
130C4×D4×C43C2311yescharacteristic
131#117×C43—21no—
132#107×C43—21no—
133#107×C43D411yescharacteristic
134C4⋊C8×C43—21no—
135C4⋊C8×C43C2311yescharacteristic
136#103×C43—21no—
137#103×C43—21no—
138#103×C43—21no—
139#102×C43—21no—
140#102×C43D411yescharacteristic
141#102×C43D411yescharacteristic
142#97×C43—21no—
143C4×C8×C43C2311yescharacteristic
144C2×Q8×C43—21no—
145C2×Q8×C43—21no—
146C2×Q8×C43—41no—
147C2×Q8×C43—42no—
148C2×Q8×C43—81no—
149C2×Q8×C43C2×D411yescharacteristic
150C2×D4×C43C2×D411yescharacteristic
151C2×D4×C43C2×D411yescharacteristic
152C22×C4×C43—21no—
153C22×C4×C43—21no—
154C22×C4×C43—41no—
155C2×C22⋊D43—41no—
156C2×C22⋊D43—41no—
157C22×Dic43—41no—
158#10621900—42no—
159#10621900—81no—
160C2×D172C2×D411yescharacteristic
161C2×C4×D43—21no—
162C2×Dic86—21no—
163C2×Dic86—21no—
164SD16×C43—42no—
165D8×C43—22no—
166C2×C8×C43—21no—
167C2×C8×C43C2×D411yescharacteristic
168C2×C8×C43C2×D411yescharacteristic
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—
176C4⋊C4×C43C2×D411yescharacteristic
177C4⋊C4×C43C2×D411yescharacteristic
178C4⋊C4×C43C2×D411yescharacteristic
179C22⋊C4×C43—21no—
180C22⋊C4×C43—21no—
181C22⋊C4×C43—41no—
182C22⋊C4×C43—41no—
183C22⋊C4×C43—41no—
184C42×C43—21no—
185C42×C43—41no—
186C42×C43C2411yescharacteristic
187C22⋊Dic43—41no—
188#10621884—41no—
189#10621884—81no—
190#10621883—81no—
191(C2×D43)⋊C4—21no—
192(C2×D43)⋊C4—41no—
193(C2×D43)⋊C4—41no—
194C4⋊Dic43—21no—
195C4⋊Dic43—21no—
196C4⋊Dic43—21no—
197C4⋊Dic43—21no—
198C4⋊Dic43—41no—
199C4⋊Dic43C2×D411yescharacteristic
200C4×Dic43—41no—
201C2×C43⋊C8—21no—
202C2×C43⋊C8—21no—
203C2×C43⋊C8—21no—
204C2×C43⋊C8—21no—
205C2×C43⋊C8—42no—
206C2×C43⋊C8—81no—
207C2×C43⋊C8C2×D411yescharacteristic
208C2×C43⋊C8C2×D411yescharacteristic
209C8×D43—81no—
210C23×C43—21no—
211C23×C43—21no—
212C22×D43—21no—
213Q8×C43—21no—
214Q8×C43—21no—
215Q8×C43—41no—
216Q8×C43—41no—
217Q8×C43—41no—
218Q8×C43—41no—
219Q8×C43—82no—
220D4×C43—21no—
221D4×C43—21no—
222D4×C43—21no—
223D4×C43#13512yes—
224C2×C4×C43—21no—
225C2×C4×C43—21no—
226C2×C4×C43—21no—
227C2×C4×C43—21no—
228C2×C4×C43—41no—
229C2×C4×C43—41no—
230C2×C4×C43—41no—
231C2×C4×C43—41no—
232C2×C4×C43—41no—
233C2×C4×C43—41no—
234C2×C4×C43—82no—
235C2×C4×C43C22×D411yescharacteristic
236C2×C4×C43C22×D411yescharacteristic
237C2×C4×C43H(5,𝔽2)11yescharacteristic
238C22⋊D43—82no—
239C22⋊D43—161no—
240C2×Dic43—21no—
241C2×Dic43—41no—
242C2×Dic43—41no—
243C2×Dic43—82no—
244D172—21no—
245D172—21no—
246C4×D43—41no—
247C4×D43—41no—
248Dic86—41no—
249Dic86—41no—
250Dic86—81no—
251C8×C43—21no—
252C8×C43—21no—
253C8×C43—41no—
254C43⋊C8—21no—
255C43⋊C8—21no—
256C43⋊C8—41no—
257C43⋊C8—41no—
258C43⋊C8—41no—
259C43⋊C8—41no—
260#19791—431nomaximal, Sylow
261C22×C43—22no—
262C22×C43—41no—
263C22×C43—41no—
264C22×C43—41no—
265C22×C43—41no—
266C22×C43—41no—
267C22×C43D4211yescharacteristic
268C2×D43—41no—
269C2×D43—41no—
270C2×D43—41no—
271C4×C43—21no—
272C4×C43—41no—
273C4×C43—41no—
274C4×C43—41no—
275C4×C43—41no—
276C4×C43—81no—
277C4×C43—81no—
278C4×C43C2×#13511yescharacteristic
279C4×C43#57511yescharacteristic
280C4×C43#57711yescharacteristic
281C4×C43#57711yescharacteristic
282Dic43—41no—
283Dic43—81no—
284Dic43—81no—
285#3367D4311yescharacteristic, complemented
286#3340—431no—
287#3303—431no—
288#3298—431no—
289#1718—431no—
290#1704—431no—
291#1679—431no—
292#1679—431no—
293#1671—431no—
294#1650—431no—
295#1647—431no—
296#1646—431no—
297#1637—431no—
298#1582—431no—
299#1580—431no—
300C2×C43—42no—
301C2×C43—81no—
302C2×C43#326711yescharacteristic
303C2×C43#328211yescharacteristic
304C2×C43#328911yescharacteristic
305D43—81no—
306#556C2×D4311yescharacteristic
307#555—431no—
308D4×Q8C2×D4311yescharacteristic
309#547—431no—
310#500—431no—
311#498—431no—
312#489—21no—
313#487—431no—
314#487—431no—
315#487—431no—
316#487C2×D4311yescharacteristic
317#485—861no—
318#485—861no—
319#483—861no—
320#482—861no—
321#477—21no—
322#477—431no—
323#476—431no—
324#475—431no—
325#474—431no—
326#474C2×D4311yescharacteristic
327#465—861no—
328#465—861no—
329#465—861no—
330#463—21no—
331#461—431no—
332#461—431no—
333#461C2×D4311yescharacteristic
334#449—861no—
335#448—861no—
336#446C2×D4311yescharacteristic
337#440—21no—
338C4×SD16—431no—
339C4×D8C2×D4311yescharacteristic
340C8×D4—431no—
341C8×D4—431no—
342C8×D4—431no—
343#427—861no—
344#416—861no—
345C2×#103—861no—
346#334—431no—
347#334—431no—
348#333—431no—
349#332—431no—
350#332—431no—
351#332—431no—
352Q8⋊C8—431no—
353D4⋊C8—431no—
354D4⋊C8—431no—
355D4⋊C8—431no—
356#322—431no—
357C43#1979111yescharacteristic, complemented, Sylow
358C2×#41—861no—
359C22×Q8—21no—
360C2×SD16—21no—
361C2×SD16—431no—
362C2×SD16—861no—
363C2×SD16—861no—
364C2×D8C22⋊D4311yescharacteristic
365C22×C8—861no—
366C22×C8—861no—
367C22×C8—861no—
368C4⋊Q8—21no—
369C4⋊Q8—431no—
370C4⋊Q8—431no—
371C4⋊Q8C22×D4311yescharacteristic
372C4⋊Q8C22×D4311yescharacteristic
373#126—41no—
374#124—21no—
375#124—1721no—
376#123—1721no—
377C22⋊Q8—21no—
378C22⋊Q8—21no—
379C22⋊Q8—41no—
380C22⋊Q8—861no—
381#121—861no—
382#121—861no—
383#121—861no—
384C4×Q8—21no—
385C4×Q8C22×D4311yescharacteristic
386C4×D4—21no—
387C4×D4—431no—
388C4×D4C22×D4311yescharacteristic
389C4×D4C22×D4311yescharacteristic
390#117—21no—
391#117—861no—
392#117—861no—
393C2×C4⋊C4—861no—
394#107—21no—
395#107—861no—
396#107—861no—
397#107—1721no—
398#107C22⋊D4311yescharacteristic
399#106—431no—
400#106—861no—
401#106—861no—
402#106—861no—
403#106—861no—
404C4⋊C8—21no—
405C4⋊C8—431no—
406C4⋊C8—431no—
407C4⋊C8—431no—
408C4⋊C8C22×D4311yescharacteristic
409#103—21no—
410#103—21no—
411#103—21no—
412#103—431no—
413#103—861no—
414#103—861no—
415#103—861no—
416#103—861no—
417#103—861no—
418#103—861no—
419#103—861no—
420#103—861no—
421#103—1721no—
422#102—21no—
423#102—431no—
424#102—861no—
425#102—861no—
426#102C22⋊D4311yescharacteristic
427#102C22⋊D4311yescharacteristic
428C22⋊C8—861no—
429C22⋊C8—861no—
430C22⋊C8—861no—
431#97—21no—
432C4×C8—431no—
433C4×C8—431no—
434C4×C8C22×D4311yescharacteristic
435#41—3441no—
436#41—1722no—
437C2×Q8—21no—
438C2×Q8—21no—
439C2×Q8—41no—
440C2×Q8—42no—
441C2×Q8—81no—
442C2×Q8—861no—
443C2×Q8—861no—
444C2×Q8D4×D4311yescharacteristic
445C2×D4—431no—
446C2×D4—1721no—
447C2×D4—1721no—
448C2×D4C2×C22⋊D4311yescharacteristic
449C2×D4C2×C22⋊D4311yescharacteristic
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—41no—
453C22×C4—861no—
454C22×C4—1721no—
455SD16—42no—
456SD16—3441no—
457SD16—3441no—
458SD16—1721no—
459D8—22no—
460C2×C8—21no—
461C2×C8—431no—
462C2×C8—431no—
463C2×C8—861no—
464C2×C8—861no—
465C2×C8—861no—
466C2×C8—861no—
467C2×C8—3441no—
468C2×C8—3441no—
469C2×C8—1722no—
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—41no—
478C4⋊C4—41no—
479C4⋊C4—431no—
480C4⋊C4—861no—
481C4⋊C4—861no—
482C4⋊C4—861no—
483C4⋊C4—861no—
484C4⋊C4—1721no—
485C4⋊C4D4×D4311yescharacteristic
486C4⋊C4C2×C22⋊D4311yescharacteristic
487C4⋊C4C2×C22⋊D4311yescharacteristic
488C22⋊C4—21no—
489C22⋊C4—21no—
490C22⋊C4—41no—
491C22⋊C4—41no—
492C22⋊C4—41no—
493C22⋊C4—861no—
494C22⋊C4—1721no—
495C22⋊C4—1721no—
496C22⋊C4—1721no—
497C42—21no—
498C42—41no—
499C42—1721no—
500C42C23×D4311yescharacteristic
501C23—21no—
502C23—21no—
503C23—861no—
504Q8—21no—
505Q8—21no—
506Q8—41no—
507Q8—41no—
508Q8—41no—
509Q8—41no—
510Q8—82no—
511Q8—3441no—
512Q8—1721no—
513Q8—1721no—
514D4—21no—
515D4—21no—
516D4—21no—
517D4—861no—
518D4—861no—
519D4—3442no—
520D4—6881no—
521D4#1306334512yes—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—41no—
531C2×C4—41no—
532C2×C4—82no—
533C2×C4—861no—
534C2×C4—3442no—
535C2×C4—1721no—
536C2×C4—1721no—
537C2×C4—1721no—
538C2×C4—1721no—
539C2×C4C2×D4×D4311yescharacteristic
540C2×C4C22×C22⋊D4311yescharacteristic
541C2×C4#1306337011yescharacteristic
542C8—21no—
543C8—21no—
544C8—41no—
545C8—861no—
546C8—861no—
547C8—1721no—
548C8—1721no—
549C8—1721no—
550C8—1721no—
551C22—22no—
552C22—41no—
553C22—41no—
554C22—41no—
555C22—41no—
556C22—41no—
557C22—1721no—
558C22—1721no—
559C22—1721no—
560C22D4×C22⋊D4311yescharacteristic
561C4—21no—
562C4—41no—
563C4—41no—
564C4—41no—
565C4—41no—
566C4—81no—
567C4—81no—
568C4—3441no—
569C4—3441no—
570C4—1721no—
571C4C2×#1306334511yescharacteristic
572C4#1458369511yescharacteristic
573C4#1458370711yescharacteristic
574C4#1458370911yescharacteristic
575C2—42no—
576C2—81no—
577C2—3441no—
578C2#1914611411yescharacteristic
579C2#1914630311yescharacteristic
580C2#1914636611yescharacteristic
subgroupG/H
centerC22D4×C22⋊D43
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#3367C2
socleC22×C43D42
prime radical#19146525C2
hypercenter#3367D43
hypocenterC43#19791
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #3367

Complements

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

NH ≅ G/Ntype
1. #19147002C2semidirect
3. #19146460C2semidirect
4. #19134238C2semidirect
5. #19134177C2semidirect
6. #19134016C2semidirect
7. #19134015C2semidirect
8. #19133968C2semidirect
9. #19133851C2semidirect
10. #19133828C2semidirect
11. #19133822C2semidirect
12. #19133760C2semidirect
13. #19133429C2semidirect
14. #19133419C2semidirect
15. C43×#3367C2semidirect
285. #3367D43semidirect
357. C43#19791semidirect

Maximal subgroups

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

subgroupindex
#191470022
#191465252
#191464602
#191342382
#191341772
#191340162
#191340152
#191339682
#191338512
#191338282
#191338222
#191337602
#191334292
#191334192
C43×#33672
#1979143