Finite Group Databasebeta

← #25086289

Subgroups — #25086289

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#19147240C211yesmaximal, characteristic, complemented
2#19146938C211yesmaximal, characteristic
3#19146913C211yesmaximal, characteristic, complemented
4#19134242C211yesmaximal, characteristic, complemented
5#19134139C211yesmaximal, characteristic, complemented
6#19134046C211yesmaximal, characteristic, complemented
7#19134044C211yesmaximal, characteristic, complemented
8#19133987C211yesmaximal, characteristic, complemented
9#19133878C211yesmaximal, characteristic, complemented
10#19133865C211yesmaximal, characteristic, complemented
11#19133807C211yesmaximal, characteristic, complemented
12#19133746C211yesmaximal, characteristic, complemented
13#19133424C211yesmaximal, characteristic, complemented
14SD16⋊(C43⋊C8)C211yesmaximal, characteristic, complemented
15C43×#3302C211yesmaximal, characteristic, complemented
16#14583609C2211yescharacteristic
17#14583553C2211yescharacteristic
18#14583302C2211yescharacteristic
19#14583295C2211yescharacteristic
20#14583253—21no—
21#14583251C2211yescharacteristic
22#14583250C2211yescharacteristic
23#14583249C2211yescharacteristic
24#14583231—21no—
25#14583212—21no—
26#14583210—21no—
27#14583206—21no—
28#14583189C2211yescharacteristic
29#14583189C2211yescharacteristic
30#14583179C2211yescharacteristic
31#14583176C2211yescharacteristic
32#14583156—21no—
33#14583133—21no—
34#14583111—21no—
35#14583109C2211yescharacteristic
36#14583101C2211yescharacteristic
37#14583058—21no—
38Q8×C43⋊C8C2211yescharacteristic
39C4×#10621884—21no—
40C4×#10621882C2211yescharacteristic
41#14582978C2211yescharacteristic
42D4×C43⋊C8C2211yescharacteristic
43C2×#13063258—21no—
44#14582897—21no—
45#14582652C2211yescharacteristic
46#14582651C2211yescharacteristic
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
57C43×#547C2211yescharacteristic
58C43×#487C2211yescharacteristic
59C43×#485—21no—
60C43×#474C2211yescharacteristic
61C43×#467—21no—
62C43×#462C2211yescharacteristic
63C43×#452—21no—
64C4×SD16×C43C2211yescharacteristic
65C8×D4×C43C2211yescharacteristic
66C43×#416—21no—
67C2×#10621900—21no—
68C2×#10621885—21no—
69C2×#10621884—21no—
70C2×#10621882D411yescharacteristic
71C2×#10621872—21no—
72C22×C43⋊C8—21no—
73#13063325C2311yescharacteristic
74#13063325C2311yescharacteristic
75#13063317—21no—
76#13063309—41no—
77#13063305—21no—
78#13063303—41no—
79#13063301—21no—
80#13063299—21no—
81C4×D172—21no—
82C4×D172C2311yescharacteristic
83C2×C4⋊Dic43—21no—
84C4⋊C4×D43—21no—
85#13063258—21no—
86#13063258—21no—
87#13063258—21no—
88#13063258—21no—
89#13063258D411yescharacteristic
90#13063256—21no—
91#13063256—21no—
92#13063256—41no—
93C4⋊(C43⋊C8)—21no—
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#13063248—21no—
103#13063248—41no—
104#13063246—21no—
105#13063246—21no—
106#13063246—21no—
107#13063246D411yescharacteristic
108#13063245—21no—
109#13063245D411yescharacteristic
110C22⋊(C43⋊C8)—21no—
111(C2×D43)⋊C8—21no—
112C4×C43⋊C8—21no—
113C4×C43⋊C8C2311yescharacteristic
114C4×C43⋊C8C2311yescharacteristic
115C2×#41×C43—21no—
116C2×Q16×C43—21no—
117C2×SD16×C43D411yescharacteristic
118C22×C8×C43—21no—
119C4⋊Q8×C43C2311yescharacteristic
120C4⋊Q8×C43C2311yescharacteristic
121#126×C43—41no—
122#124×C43—21no—
123#123×C43—41no—
124C22⋊Q8×C43—21no—
125C22⋊Q8×C43—21no—
126#121×C43—21no—
127C4×Q8×C43—21no—
128C4×Q8×C43C2311yescharacteristic
129C4×D4×C43C2311yescharacteristic
130C4×D4×C43C2311yescharacteristic
131#117×C43—21no—
132C2×C4⋊C4×C43—21no—
133#107×C43—21no—
134#106×C43D411yescharacteristic
135C4⋊C8×C43C2311yescharacteristic
136#103×C43—21no—
137#103×C43—21no—
138#103×C43—21no—
139#103×C43D411yescharacteristic
140#102×C43—21no—
141#102×C43D411yescharacteristic
142C22⋊C8×C43—21no—
143C4×C8×C43C2311yescharacteristic
144#41×C43—42no—
145#41×C43—81no—
146C2×Q8×C43—21no—
147C2×Q8×C43—21no—
148C2×Q8×C43C2×D411yescharacteristic
149C2×D4×C43—41no—
150C2×D4×C43C2×D411yescharacteristic
151C2×D4×C43C2×D411yescharacteristic
152C22×C4×C43—21no—
153C22×C4×C43—21no—
154C22×C4×C43—41no—
155C2×C22⋊D43—41no—
156C22×Dic43—41no—
157#10621900—42no—
158#10621900—81no—
159C2×D172C2×D411yescharacteristic
160C2×C4×D43—21no—
161C2×C4×D43—41no—
162C2×Dic86—21no—
163C2×Dic86—21no—
164Q16×C43—81no—
165SD16×C43—22no—
166C2×C8×C43—21no—
167C2×C8×C43—81no—
168C2×C8×C43C2×D411yescharacteristic
169C2×C8×C43C2×D411yescharacteristic
170C4⋊C4×C43—21no—
171C4⋊C4×C43—21no—
172C4⋊C4×C43—21no—
173C4⋊C4×C43—21no—
174C4⋊C4×C43—21no—
175C4⋊C4×C43—41no—
176C4⋊C4×C43—41no—
177C4⋊C4×C43C2×D411yescharacteristic
178C4⋊C4×C43C2×D411yescharacteristic
179C4⋊C4×C43C2×D411yescharacteristic
180C22⋊C4×C43—21no—
181C22⋊C4×C43—21no—
182C22⋊C4×C43—41no—
183C22⋊C4×C43—41no—
184C22⋊C4×C43—41no—
185C42×C43—21no—
186C42×C43—41no—
187C42×C43C2411yescharacteristic
188#10621885—81no—
189#10621884—42no—
190#10621882—41no—
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
200Dic43⋊C4—41no—
201Dic43⋊C4—41no—
202C2×C43⋊C8—21no—
203C2×C43⋊C8—21no—
204C2×C43⋊C8—21no—
205C2×C43⋊C8—21no—
206C2×C43⋊C8—42no—
207C2×C43⋊C8C2×D411yescharacteristic
208C2×C43⋊C8C2×D411yescharacteristic
209#10621872—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—
219D4×C43—21no—
220D4×C43—21no—
221D4×C43—21no—
222D4×C43—82no—
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—
239C2×Dic43—21no—
240C2×Dic43—41no—
241C2×Dic43—41no—
242C2×Dic43—82no—
243D172—21no—
244D172—21no—
245C4×D43—41no—
246C4×D43—41no—
247C4×D43—161no—
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#19778—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#57611yescharacteristic
281C4×C43#57811yescharacteristic
282Dic43—41no—
283Dic43—81no—
284Dic43—81no—
285#3360—431no—
286#3334—431no—
287#3331—431no—
288#3302D4311yescharacteristic, complemented
289#1718—431no—
290#1699—431no—
291#1683—431no—
292#1683—431no—
293#1674—431no—
294#1654—431no—
295#1652—431no—
296#1644—431no—
297#1635—431no—
298#1581—431no—
299SD16⋊C8—431no—
300C2×C43—42no—
301C2×C43—81no—
302C2×C43#326911yescharacteristic
303C2×C43#328011yescharacteristic
304C2×C43#328911yescharacteristic
305D43—81no—
306#556C2×D4311yescharacteristic
307#554—431no—
308#547—431no—
309#547C2×D4311yescharacteristic
310#500—431no—
311#498—431no—
312#488—861no—
313#487—431no—
314#487—431no—
315#487—431no—
316#487C2×D4311yescharacteristic
317#485—21no—
318#483—861no—
319#480—861no—
320#480—861no—
321#479—861no—
322#476—431no—
323#476—431no—
324#474—431no—
325#474—431no—
326#474C2×D4311yescharacteristic
327#470—861no—
328#467—21no—
329#466—861no—
330#463—861no—
331#462—431no—
332#462C2×D4311yescharacteristic
333#461—431no—
334#452—21no—
335#452—861no—
336C8×Q8—431no—
337C4×SD16—861no—
338C4×SD16C2×D4311yescharacteristic
339C4×D8—431no—
340#436—431no—
341C8×D4—431no—
342C8×D4C2×D4311yescharacteristic
343C2×#107—861no—
344#417—861no—
345#416—21no—
346#335—431no—
347#335—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#1977811yescharacteristic, complemented, Sylow
358C2×#41—21no—
359C2×#41—861no—
360C2×Q16—21no—
361C2×Q16—861no—
362C2×SD16—861no—
363C2×SD16C22⋊D4311yescharacteristic
364C2×D8—431no—
365C2×M16—861no—
366C22×C8—21no—
367C22×C8—861no—
368C4⋊Q8—431no—
369C4⋊Q8—431no—
370C4⋊Q8C22×D4311yescharacteristic
371C4⋊Q8C22×D4311yescharacteristic
372#126—41no—
373#125—861no—
374#124—21no—
375#123—41no—
376#123—1721no—
377C22⋊Q8—21no—
378C22⋊Q8—21no—
379C22⋊Q8—861no—
380C22⋊Q8—861no—
381C22⋊Q8—1721no—
382#121—21no—
383#121—861no—
384C4×Q8—21no—
385C4×Q8C22×D4311yescharacteristic
386C4×D4—431no—
387C4×D4—861no—
388C4×D4C22×D4311yescharacteristic
389C4×D4C22×D4311yescharacteristic
390#117—21no—
391C2×C4⋊C4—21no—
392C2×C4⋊C4—861no—
393C2×C4⋊C4—861no—
394#107—21no—
395#107—431no—
396#107—861no—
397#107—861no—
398#107—861no—
399#107—861no—
400#106—861no—
401#106—861no—
402#106—1721no—
403#106C22⋊D4311yescharacteristic
404C4⋊C8—431no—
405C4⋊C8—431no—
406C4⋊C8—431no—
407C4⋊C8—861no—
408C4⋊C8C22×D4311yescharacteristic
409#103—21no—
410#103—21no—
411#103—21no—
412#103—861no—
413#103—861no—
414#103—861no—
415#103—861no—
416#103—861no—
417#103—861no—
418#103—1721no—
419#103C22⋊D4311yescharacteristic
420#102—21no—
421#102—431no—
422#102—431no—
423#102—861no—
424#102—861no—
425#102—861no—
426#102—861no—
427#102C22⋊D4311yescharacteristic
428C22⋊C8—21no—
429C22⋊C8—861no—
430C22⋊C8—861no—
431C4×C8—431no—
432C4×C8—431no—
433C4×C8—861no—
434C4×C8C22×D4311yescharacteristic
435#41—42no—
436#41—81no—
437#41—3441no—
438#41—1722no—
439C2×Q8—21no—
440C2×Q8—21no—
441C2×Q8—861no—
442C2×Q8—861no—
443C2×Q8C2×C22⋊D4311yescharacteristic
444C2×D4—41no—
445C2×D4—431no—
446C2×D4—1721no—
447C2×D4D4×D4311yescharacteristic
448C2×D4C2×C22⋊D4311yescharacteristic
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—41no—
452C22×C4—861no—
453C22×C4—1721no—
454C22×C4—1721no—
455Q16—81no—
456Q16—3441no—
457SD16—22no—
458SD16—1722no—
459D8—1721no—
460M16—3441no—
461C2×C8—21no—
462C2×C8—81no—
463C2×C8—431no—
464C2×C8—431no—
465C2×C8—861no—
466C2×C8—861no—
467C2×C8—861no—
468C2×C8—861no—
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⋊C4—1721no—
486C4⋊C4—1721no—
487C4⋊C4D4×D4311yescharacteristic
488C4⋊C4C2×C22⋊D4311yescharacteristic
489C4⋊C4C2×C22⋊D4311yescharacteristic
490C22⋊C4—21no—
491C22⋊C4—21no—
492C22⋊C4—41no—
493C22⋊C4—41no—
494C22⋊C4—41no—
495C22⋊C4—861no—
496C22⋊C4—1721no—
497C22⋊C4—1721no—
498C42—21no—
499C42—41no—
500C42C23×D4311yescharacteristic
501C23—21no—
502C23—21no—
503C23—861no—
504Q8—21no—
505Q8—21no—
506Q8—41no—
507Q8—41no—
508Q8—41no—
509Q8—41no—
510Q8—3441no—
511Q8—1721no—
512Q8—1721no—
513D4—21no—
514D4—21no—
515D4—21no—
516D4—82no—
517D4—861no—
518D4—861no—
519D4—3442no—
520D4#1306334512yes—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—41no—
531C2×C4—82no—
532C2×C4—861no—
533C2×C4—3442no—
534C2×C4—1721no—
535C2×C4—1721no—
536C2×C4—1721no—
537C2×C4—1721no—
538C2×C4—6881no—
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#1458369611yescharacteristic
573C4#1458370211yescharacteristic
574C4#1458371311yescharacteristic
575C2—42no—
576C2—81no—
577C2—3441no—
578C2#1914615011yescharacteristic
579C2#1914627611yescharacteristic
580C2#1914636611yescharacteristic
subgroupG/H
centerC22D4×C22⋊D43
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#3302C2
socleC22×C43D42
prime radical#19146938C2
hypercenter#3302D43
hypocenterC43#19778
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #3302

Complements

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

NH ≅ G/Ntype
1. #19147240C2semidirect
3. #19146913C2semidirect
4. #19134242C2semidirect
5. #19134139C2semidirect
6. #19134046C2semidirect
7. #19134044C2semidirect
8. #19133987C2semidirect
9. #19133878C2semidirect
10. #19133865C2semidirect
11. #19133807C2semidirect
12. #19133746C2semidirect
13. #19133424C2semidirect
14. SD16⋊(C43⋊C8)C2semidirect
15. C43×#3302C2semidirect
288. #3302D43semidirect
357. C43#19778semidirect

Maximal subgroups

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

subgroupindex
#191472402
#191469382
#191469132
#191342422
#191341392
#191340462
#191340442
#191339872
#191338782
#191338652
#191338072
#191337462
#191334242
SD16⋊(C43⋊C8)2
C43×#33022
#1977843