Finite Group Databasebeta

← #25086330

Subgroups — #25086330

Order 11008.

616 conjugacy classes of subgroups.

The subgroup lattice has 586 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19147460C211yesmaximal, characteristic, complemented
2#19146933C211yesmaximal, characteristic, complemented
3#19146471C211yesmaximal, characteristic, complemented
4#19134247C211yesmaximal, characteristic, complemented
5#19134168C211yesmaximal, characteristic, complemented
6#19134036C211yesmaximal, characteristic, complemented
7#19134002C211yesmaximal, characteristic, complemented
8#19133999C211yesmaximal, characteristic, complemented
9#19133808C211yesmaximal, characteristic, complemented
10#19133760C211yesmaximal, characteristic, complemented
11#19133722C211yesmaximal, characteristic, complemented
12#19133665C211yesmaximal, characteristic, complemented
13#19133425C211yesmaximal, characteristic, complemented
14#19133412C211yesmaximal, characteristic, complemented
15C43×#3358C211yesmaximal, characteristic
16#14583606C2211yescharacteristic
17#14583606C2211yescharacteristic
18#14583304C2211yescharacteristic
19#14583300—21no—
20#14583271C2211yescharacteristic
21#14583251C2211yescharacteristic
22#14583249C2211yescharacteristic
23#14583245C2211yescharacteristic
24#14583232—21no—
25#14583210—21no—
26#14583197—21no—
27#14583197—21no—
28#14583194C2211yescharacteristic
29#14583194C2211yescharacteristic
30#14583189C2211yescharacteristic
31#14583189C2211yescharacteristic
32#14583143—21no—
33#14583138—21no—
34#14583106C2211yescharacteristic
35#14583096C2211yescharacteristic
36#14583061—21no—
37#14583055—21no—
38C8×Dic86C2211yescharacteristic
39C4×#10621885C2211yescharacteristic
40D8×Dic43—21no—
41#14582977C2211yescharacteristic
42D4×C43⋊C8C2211yescharacteristic
43#14582900—21no—
44C2×#13063249—21no—
45#14582652C2211yescharacteristic
46#14582649C2211yescharacteristic
47#14582647C2211yescharacteristic
48#14582647C2211yescharacteristic
49#14582645C2211yescharacteristic
50#14582643C2211yescharacteristic
51Q8⋊(C43⋊C8)C2211yescharacteristic
52#14582629C2211yescharacteristic
53D4⋊(C43⋊C8)C2211yescharacteristic
54D4⋊(C43⋊C8)C2211yescharacteristic
55#14582621C2211yescharacteristic
56C43×#550C2211yescharacteristic
57D4×Q8×C43C2211yescharacteristic
58C43×#486—21no—
59C43×#486C2211yescharacteristic
60C43×#474—21no—
61C43×#474C2211yescharacteristic
62C43×#459—21no—
63C43×#459C2211yescharacteristic
64C8×Q8×C43C2211yescharacteristic
65C4×D8×C43—21no—
66C4×D8×C43C2211yescharacteristic
67C2×#10621885—21no—
68C2×#10621885D411yescharacteristic
69C2×#10621883—21no—
70C2×#10621883—41no—
71C2×#10621877—21no—
72C22×C43⋊C8—21no—
73#13063325C2311yescharacteristic
74#13063325C2311yescharacteristic
75#13063316—21no—
76#13063316—21no—
77#13063304—21no—
78#13063304—21no—
79#13063302—41no—
80#13063302—41no—
81C4×Dic86C2311yescharacteristic
82D4×Dic43—21no—
83D4×Dic43—21no—
84C2×C4⋊Dic43—21no—
85C2×C4⋊Dic43—21no—
86#13063259—21no—
87#13063259—21no—
88#13063258—21no—
89#13063258—21no—
90#13063258D411yescharacteristic
91#13063256—21no—
92#13063256—21no—
93C4⋊(C43⋊C8)C2311yescharacteristic
94C4⋊(C43⋊C8)C2311yescharacteristic
95C4⋊(C43⋊C8)C2311yescharacteristic
96Dic43⋊C8—21no—
97#13063249—21no—
98#13063249—21no—
99#13063249—21no—
100#13063249—21no—
101#13063249—21no—
102#13063249D411yescharacteristic
103#13063248—41no—
104#13063248D411yescharacteristic
105#13063246—21no—
106#13063246—21no—
107#13063246—21no—
108#13063246—21no—
109#13063246—21no—
110C22⋊(C43⋊C8)—21no—
111C22⋊(C43⋊C8)—21no—
112C4×C43⋊C8C2311yescharacteristic
113C4×C43⋊C8C2311yescharacteristic
114C8×Dic43—21no—
115C2×#41×C43—21no—
116C22×Q8×C43—21no—
117C2×D8×C43—21no—
118C2×D8×C43D411yescharacteristic
119C4⋊Q8×C43—21no—
120C4⋊Q8×C43C2311yescharacteristic
121#127×C43—21no—
122#127×C43C2311yescharacteristic
123C22⋊Q8×C43—21no—
124C22⋊Q8×C43—41no—
125#121×C43—21no—
126#121×C43—41no—
127C4×Q8×C43C2311yescharacteristic
128C4×D4×C43—21no—
129C4×D4×C43—21no—
130C4×D4×C43C2311yescharacteristic
131C4×D4×C43C2311yescharacteristic
132#107×C43—21no—
133#107×C43D411yescharacteristic
134C4⋊C8×C43—21no—
135C4⋊C8×C43C2311yescharacteristic
136#102×C43—21no—
137#102×C43—21no—
138#102×C43—21no—
139#102×C43—21no—
140#102×C43D411yescharacteristic
141#102×C43D411yescharacteristic
142C4×C8×C43—21no—
143C4×C8×C43C2311yescharacteristic
144#41×C43—42no—
145#41×C43—81no—
146C2×Q8×C43—21no—
147C2×Q8×C43—41no—
148C2×Q8×C43—42no—
149C2×Q8×C43—81no—
150C2×Q8×C43C2×D411yescharacteristic
151C2×D4×C43—21no—
152C2×D4×C43—21no—
153C2×D4×C43—21no—
154C2×D4×C43—41no—
155C2×D4×C43—41no—
156C2×D4×C43C2×D411yescharacteristic
157C2×D4×C43C2×D411yescharacteristic
158C22×C4×C43—21no—
159C22×C4×C43—21no—
160C22×C4×C43—41no—
161C22×C4×C43—41no—
162C22×Dic43—41no—
163C22×Dic43—41no—
164C2×Dic86—21no—
165C2×Dic86—21no—
166C2×Dic86C2×D411yescharacteristic
167D8×C43—22no—
168D8×C43—42no—
169C2×C8×C43—21no—
170C2×C8×C43C2×D411yescharacteristic
171C2×C8×C43C2×D411yescharacteristic
172C4⋊C4×C43—21no—
173C4⋊C4×C43—21no—
174C4⋊C4×C43—21no—
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—
183C42×C43—21no—
184C42×C43C2411yescharacteristic
185C22⋊Dic43—41no—
186C22⋊Dic43—41no—
187#10621885—22no—
188#10621885—81no—
189#10621883—81no—
190#10621883—82no—
191C4⋊Dic43—21no—
192C4⋊Dic43—21no—
193C4⋊Dic43—21no—
194C4⋊Dic43—21no—
195C4⋊Dic43—41no—
196C4⋊Dic43—41no—
197C4⋊Dic43C2×D411yescharacteristic
198Dic43⋊C4—21no—
199Dic43⋊C4—41no—
200Dic43⋊C4—41no—
201C4×Dic43—21no—
202#10621877—81no—
203C2×C43⋊C8—21no—
204C2×C43⋊C8—21no—
205C2×C43⋊C8—21no—
206C2×C43⋊C8—21no—
207C2×C43⋊C8—81no—
208C2×C43⋊C8C2×D411yescharacteristic
209C2×C43⋊C8C2×D411yescharacteristic
210C23×C43—21no—
211C23×C43—21no—
212C23×C43—41no—
213Q8×C43—21no—
214Q8×C43—41no—
215Q8×C43—41no—
216Q8×C43—82no—
217Q8×C43#13512yes—
218D4×C43—21no—
219D4×C43—21no—
220D4×C43—21no—
221D4×C43—41no—
222D4×C43—41no—
223D4×C43—41no—
224D4×C43—41no—
225D4×C43—82no—
226D4×C43—81no—
227D4×C43—161no—
228D4×C43#13712yes—
229C2×C4×C43—21no—
230C2×C4×C43—21no—
231C2×C4×C43—21no—
232C2×C4×C43—21no—
233C2×C4×C43—41no—
234C2×C4×C43—41no—
235C2×C4×C43—41no—
236C2×C4×C43—41no—
237C2×C4×C43—41no—
238C2×C4×C43—82no—
239C2×C4×C43—82no—
240C2×C4×C43C22×D411yescharacteristic
241C2×C4×C43C22×D411yescharacteristic
242C2×C4×C43H(5,𝔽2)11yescharacteristic
243C2×Dic43—21no—
244C2×Dic43—21no—
245C2×Dic43—41no—
246C2×Dic43—41no—
247C2×Dic43—161no—
248C2×Dic43—161no—
249Dic86—21no—
250Dic86—21no—
251Dic86—81no—
252Dic86—81no—
253C8×C43—21no—
254C8×C43—21no—
255C8×C43—41no—
256C43⋊C8—21no—
257C43⋊C8—21no—
258C43⋊C8—41no—
259C43⋊C8—41no—
260C43⋊C8—41no—
261C43⋊C8—41no—
262#19781—431nomaximal, Sylow
263C22×C43—22no—
264C22×C43—41no—
265C22×C43—41no—
266C22×C43—41no—
267C22×C43—41no—
268C22×C43—41no—
269C22×C43—81no—
270C22×C43—81no—
271C22×C43—81no—
272C22×C43D4211yescharacteristic
273C4×C43—22no—
274C4×C43—21no—
275C4×C43—41no—
276C4×C43—41no—
277C4×C43—41no—
278C4×C43—81no—
279C4×C43C2×#13511yescharacteristic
280C4×C43C2×#13711yescharacteristic
281C4×C43#57611yescharacteristic
282C4×C43#57811yescharacteristic
283Dic43—41no—
284Dic43—41no—
285Dic43—81no—
286Dic43—81no—
287#3380—431no—
288#3358D4311yescharacteristic
289#3333—431no—
290#3299—431no—
291#1719—431no—
292#1703—431no—
293#1682—431no—
294#1677—431no—
295#1676—431no—
296#1644—431no—
297#1637—431no—
298#1631—431no—
299#1622—431no—
300#1581—431no—
301#1579—431no—
302C2×C43—42no—
303C2×C43—81no—
304C2×C43—161no—
305C2×C43#327011yescharacteristic
306C2×C43#328011yescharacteristic
307C2×C43#328811yescharacteristic
308#554—431no—
309#554—431no—
310#550C2×D4311yescharacteristic
311D4×Q8C2×D4311yescharacteristic
312#500—431no—
313#499—861no—
314#492—431no—
315#487—431no—
316#487—431no—
317#486—21no—
318#486—431no—
319#486C2×D4311yescharacteristic
320#484—861no—
321#480—861no—
322#478—861no—
323#478—861no—
324#477—431no—
325#477—431no—
326#476—431no—
327#476—431no—
328#474—21no—
329#474C2×D4311yescharacteristic
330#468—861no—
331#467—861no—
332#462—431no—
333#460—431no—
334#459—21no—
335#459C2×D4311yescharacteristic
336#452—861no—
337#451—861no—
338C8×Q8—431no—
339C8×Q8C2×D4311yescharacteristic
340C4×Q16—431no—
341C4×D8—21no—
342C4×D8—861no—
343C4×D8C2×D4311yescharacteristic
344#436—431no—
345C8×D4—431no—
346#417—861no—
347C2×#103—861no—
348#335—431no—
349#334—431no—
350#333—431no—
351#333—431no—
352#332—431no—
353#331—431no—
354Q8⋊C8—431no—
355Q8⋊C8—431no—
356D4⋊C8—431no—
357D4⋊C8—431no—
358#322—431no—
359C43#1978111yescharacteristic, complemented, Sylow
360C2×#41—21no—
361C22×Q8—21no—
362C2×Q16—431no—
363C2×Q16—861no—
364C2×SD16—861no—
365C2×SD16—1721no—
366C2×D8—21no—
367C2×D8C22⋊D4311yescharacteristic
368C2×M16—861no—
369C22×C8—861no—
370C4⋊Q8—21no—
371C4⋊Q8—431no—
372C4⋊Q8—431no—
373C4⋊Q8C22×D4311yescharacteristic
374#127—21no—
375#127C22×D4311yescharacteristic
376#125—861no—
377#125—861no—
378C22⋊Q8—21no—
379C22⋊Q8—41no—
380C22⋊Q8—861no—
381C22⋊Q8—861no—
382C22⋊Q8—1721no—
383C22⋊Q8—1721no—
384#121—21no—
385#121—41no—
386C4×Q8—431no—
387C4×Q8C22×D4311yescharacteristic
388C4×D4—21no—
389C4×D4—21no—
390C4×D4—861no—
391C4×D4—861no—
392C4×D4C22×D4311yescharacteristic
393C4×D4C22×D4311yescharacteristic
394C2×C4⋊C4—861no—
395C2×C4⋊C4—861no—
396#107—21no—
397#107—431no—
398#107—861no—
399#107—861no—
400#107—861no—
401#107—861no—
402#107C22⋊D4311yescharacteristic
403#106—861no—
404#106—861no—
405C4⋊C8—21no—
406C4⋊C8—431no—
407C4⋊C8—431no—
408C4⋊C8—431no—
409C4⋊C8—861no—
410C4⋊C8C22×D4311yescharacteristic
411#103—431no—
412#103—431no—
413#103—861no—
414#103—861no—
415#103—861no—
416#103—861no—
417#103—861no—
418#103—1721no—
419#102—21no—
420#102—21no—
421#102—21no—
422#102—21no—
423#102—861no—
424#102—861no—
425#102—861no—
426#102—861no—
427#102—861no—
428#102C22⋊D4311yescharacteristic
429#102C22⋊D4311yescharacteristic
430C22⋊C8—861no—
431C22⋊C8—861no—
432C4×C8—21no—
433C4×C8—431no—
434C4×C8—431no—
435C4×C8—861no—
436C4×C8C22×D4311yescharacteristic
437#41—42no—
438#41—81no—
439C2×Q8—21no—
440C2×Q8—41no—
441C2×Q8—42no—
442C2×Q8—81no—
443C2×Q8—431no—
444C2×Q8—861no—
445C2×Q8—861no—
446C2×Q8D4×D4311yescharacteristic
447C2×D4—21no—
448C2×D4—21no—
449C2×D4—21no—
450C2×D4—41no—
451C2×D4—41no—
452C2×D4C2×C22⋊D4311yescharacteristic
453C2×D4C2×C22⋊D4311yescharacteristic
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—41no—
457C22×C4—41no—
458C22×C4—1721no—
459C22×C4—1721no—
460Q16—862no—
461Q16—3441no—
462SD16—3441no—
463SD16—3442no—
464D8—22no—
465D8—42no—
466M16—3441no—
467C2×C8—21no—
468C2×C8—431no—
469C2×C8—431no—
470C2×C8—861no—
471C2×C8—861no—
472C2×C8—861no—
473C2×C8—861no—
474C2×C8—3441no—
475C2×C8C2×C22⋊D4311yescharacteristic
476C2×C8C2×C22⋊D4311yescharacteristic
477C4⋊C4—21no—
478C4⋊C4—21no—
479C4⋊C4—21no—
480C4⋊C4—41no—
481C4⋊C4—431no—
482C4⋊C4—861no—
483C4⋊C4—861no—
484C4⋊C4—861no—
485C4⋊C4—861no—
486C4⋊C4—861no—
487C4⋊C4—1721no—
488C4⋊C4—1721no—
489C4⋊C4—1721no—
490C4⋊C4—1721no—
491C4⋊C4D4×D4311yescharacteristic
492C4⋊C4C2×C22⋊D4311yescharacteristic
493C4⋊C4C2×C22⋊D4311yescharacteristic
494C22⋊C4—21no—
495C22⋊C4—21no—
496C22⋊C4—41no—
497C22⋊C4—41no—
498C22⋊C4—1721no—
499C22⋊C4—1721no—
500C42—21no—
501C42—861no—
502C42C23×D4311yescharacteristic
503C23—21no—
504C23—21no—
505C23—41no—
506Q8—21no—
507Q8—41no—
508Q8—41no—
509Q8—82no—
510Q8—861no—
511Q8—861no—
512Q8—3441no—
513Q8—3441no—
514Q8#1306334412yes—
515D4—21no—
516D4—21no—
517D4—21no—
518D4—41no—
519D4—41no—
520D4—41no—
521D4—41no—
522D4—82no—
523D4—81no—
524D4—161no—
525D4#1306335512yes—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—41no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—82no—
536C2×C4—82no—
537C2×C4—861no—
538C2×C4—861no—
539C2×C4—1721no—
540C2×C4—1721no—
541C2×C4—6881no—
542C2×C4—6881no—
543C2×C4C2×D4×D4311yescharacteristic
544C2×C4C22×C22⋊D4311yescharacteristic
545C2×C4#1306337011yescharacteristic
546C8—21no—
547C8—21no—
548C8—41no—
549C8—861no—
550C8—861no—
551C8—1721no—
552C8—1721no—
553C8—1721no—
554C8—1721no—
555C22—22no—
556C22—41no—
557C22—41no—
558C22—41no—
559C22—41no—
560C22—41no—
561C22—81no—
562C22—81no—
563C22—81no—
564C22D4×C22⋊D4311yescharacteristic
565C4—22no—
566C4—21no—
567C4—41no—
568C4—41no—
569C4—41no—
570C4—81no—
571C4—3441no—
572C4—3441no—
573C4—1721no—
574C4—1721no—
575C4C2×#1306334411yescharacteristic
576C4C2×#1306335511yescharacteristic
577C4#1458370011yescharacteristic
578C4#1458371411yescharacteristic
579C2—42no—
580C2—81no—
581C2—161no—
582C2#1914616111yescharacteristic
583C2#1914628011yescharacteristic
584C2#1914635711yescharacteristic
subgroupG/H
centerC22D4×C22⋊D43
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
Fitting, prime radicalC43×#3358C2
socleC22×C43D42
hypercenter#3358D43
hypocenterC43#19781
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #3358

Complements

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

NH ≅ G/Ntype
1. #19147460C2semidirect
2. #19146933C2semidirect
3. #19146471C2semidirect
4. #19134247C2semidirect
5. #19134168C2semidirect
6. #19134036C2semidirect
7. #19134002C2semidirect
8. #19133999C2semidirect
9. #19133808C2semidirect
10. #19133760C2semidirect
11. #19133722C2semidirect
12. #19133665C2semidirect
13. #19133425C2semidirect
14. #19133412C2semidirect
359. C43#19781semidirect

Maximal subgroups

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

subgroupindex
#191474602
#191469332
#191464712
#191342472
#191341682
#191340362
#191340022
#191339992
#191338082
#191337602
#191337222
#191336652
#191334252
#191334122
C43×#33582
#1978143