Finite Group Databasebeta

← #25087558

Subgroups — #25087558

Order 11008.

594 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#19147579C211yesmaximal, characteristic, complemented
2#19147010C211yesmaximal, characteristic, complemented
3#19146523C211yesmaximal, characteristic
4#19134273C211yesmaximal, characteristic, complemented
5#19134094C211yesmaximal, characteristic, complemented
6#19134051C211yesmaximal, characteristic, complemented
7#19133981C211yesmaximal, characteristic, complemented
8#19133958C211yesmaximal, characteristic, complemented
9#19133850C211yesmaximal, characteristic, complemented
10#19133830C211yesmaximal, characteristic, complemented
11#19133822C211yesmaximal, characteristic, complemented
12#19133767C211yesmaximal, characteristic, complemented
13#19133422C211yesmaximal, characteristic, complemented
14SD16⋊(C43⋊C8)C211yesmaximal, characteristic, complemented
15C43×#3353C211yesmaximal, characteristic, complemented
16#14583622C2211yescharacteristic
17#14583614C2211yescharacteristic
18#14583302C2211yescharacteristic
19#14583297C2211yescharacteristic
20#14583281—21no—
21#14583278C2211yescharacteristic
22#14583251C2211yescharacteristic
23#14583249C2211yescharacteristic
24#14583238—21no—
25#14583237—21no—
26#14583222—21no—
27#14583194C2211yescharacteristic
28#14583189C2211yescharacteristic
29#14583179C2211yescharacteristic
30#14583130—21no—
31#14583125—21no—
32#14583121—21no—
33#14583118—21no—
34#14583104C2211yescharacteristic
35#14583101C2211yescharacteristic
36#14583101C2211yescharacteristic
37#14583044—21no—
38Q8×C43⋊C8C2211yescharacteristic
39C4×#10621885—21no—
40C4×#10621882C2211yescharacteristic
41C8×D172C2211yescharacteristic
42D4×C43⋊C8C2211yescharacteristic
43#14582934—21no—
44#14582895—21no—
45#14582652C2211yescharacteristic
46#14582651C2211yescharacteristic
47#14582647C2211yescharacteristic
48#14582645C2211yescharacteristic
49#14582645C2211yescharacteristic
50#14582644C2211yescharacteristic
51Q8⋊(C43⋊C8)C2211yescharacteristic
52D4⋊(C43⋊C8)C2211yescharacteristic
53D4⋊(C43⋊C8)C2211yescharacteristic
54#14582626C2211yescharacteristic
55#14582620C2211yescharacteristic
56C43×#556C2211yescharacteristic
57C43×#547C2211yescharacteristic
58C43×#500C2211yescharacteristic
59C43×#484—21no—
60C43×#482—21no—
61C43×#475C2211yescharacteristic
62C43×#474C2211yescharacteristic
63C43×#468—21no—
64C4×SD16×C43C2211yescharacteristic
65C43×#436C2211yescharacteristic
66C43×#428—21no—
67C2×#10621885—21no—
68C2×#10621885—21no—
69C2×#10621883—21no—
70C2×#10621884—21no—
71C2×#10621884—21no—
72C2×#10621882D411yescharacteristic
73C22×C43⋊C8—21no—
74C2×C8×D43—21no—
75#13063325C2311yescharacteristic
76#13063325C2311yescharacteristic
77#13063320—41no—
78#13063313—21no—
79#13063311—41no—
80#13063301—21no—
81#13063299—21no—
82#13063296—21no—
83C4×Dic86—21no—
84C4×D172C2311yescharacteristic
85#13063284—21no—
86#13063283—21no—
87#13063283—21no—
88#13063258—21no—
89#13063258—21no—
90#13063258—41no—
91#13063258D411yescharacteristic
92#13063257—21no—
93#13063257—21no—
94#13063256—21no—
95C4⋊(C43⋊C8)—21no—
96C4⋊(C43⋊C8)C2311yescharacteristic
97C4⋊(C43⋊C8)C2311yescharacteristic
98C4⋊(C43⋊C8)C2311yescharacteristic
99#13063249—21no—
100#13063249—21no—
101#13063249—21no—
102#13063249—21no—
103#13063249—21no—
104#13063248—21no—
105#13063248—41no—
106#13063246—21no—
107#13063246—21no—
108#13063246D411yescharacteristic
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×SD16×C43D411yescharacteristic
117C2×M16×C43—21no—
118C4⋊Q8×C43C2311yescharacteristic
119C4⋊Q8×C43C2311yescharacteristic
120#126×C43—41no—
121#124×C43—21no—
122#123×C43—41no—
123C22⋊Q8×C43—21no—
124C22⋊Q8×C43—21no—
125#121×C43—21no—
126C4×Q8×C43—21no—
127C4×Q8×C43C2311yescharacteristic
128C4×D4×C43C2311yescharacteristic
129C4×D4×C43C2311yescharacteristic
130#117×C43—21no—
131C2×C4⋊C4×C43—21no—
132#107×C43—21no—
133#107×C43—21no—
134#107×C43—21no—
135#106×C43—21no—
136#106×C43D411yescharacteristic
137C4⋊C8×C43C2311yescharacteristic
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—
156C2×D172C2×D411yescharacteristic
157C2×C4×D43—21no—
158C2×Dic86—21no—
159C2×Dic86—21no—
160SD16×C43—22no—
161M16×C43—42no—
162C2×C8×C43—21no—
163C2×C8×C43C2×D411yescharacteristic
164C2×C8×C43C2×D411yescharacteristic
165C4⋊C4×C43—21no—
166C4⋊C4×C43—21no—
167C4⋊C4×C43—21no—
168C4⋊C4×C43—21no—
169C4⋊C4×C43—21no—
170C4⋊C4×C43—41no—
171C4⋊C4×C43—41no—
172C4⋊C4×C43C2×D411yescharacteristic
173C4⋊C4×C43C2×D411yescharacteristic
174C4⋊C4×C43C2×D411yescharacteristic
175C22⋊C4×C43—21no—
176C22⋊C4×C43—21no—
177C22⋊C4×C43—41no—
178C22⋊C4×C43—41no—
179C22⋊C4×C43—41no—
180C42×C43—21no—
181C42×C43—41no—
182C42×C43C2411yescharacteristic
183C22⋊Dic43—41no—
184#10621885—42no—
185#10621885—81no—
186#10621884—81no—
187#10621884—81no—
188#10621883—81no—
189#10621882—41no—
190(C2×D43)⋊C4—21no—
191(C2×D43)⋊C4—41no—
192(C2×D43)⋊C4—41no—
193(C2×D43)⋊C4—41no—
194C4⋊Dic43—21no—
195C4⋊Dic43—21no—
196C4⋊Dic43—21no—
197C4⋊Dic43—21no—
198C4⋊Dic43C2×D411yescharacteristic
199Dic43⋊C4—41no—
200C4×Dic43—41no—
201C4×Dic43—41no—
202C2×C43⋊C8—21no—
203C2×C43⋊C8—21no—
204C2×C43⋊C8—21no—
205C2×C43⋊C8—21no—
206C2×C43⋊C8—81no—
207C2×C43⋊C8C2×D411yescharacteristic
208C2×C43⋊C8C2×D411yescharacteristic
209C8×D43—42no—
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—21no—
223D4×C43—82no—
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—161no—
239C2×Dic43—21no—
240C2×Dic43—41no—
241C2×Dic43—41no—
242D172—21no—
243D172—21no—
244C4×D43—41no—
245C4×D43—41no—
246Dic86—41no—
247Dic86—41no—
248Dic86—81no—
249C8×C43—21no—
250C8×C43—41no—
251C8×C43#13512yes—
252C43⋊C8—21no—
253C43⋊C8—21no—
254C43⋊C8—41no—
255C43⋊C8—41no—
256C43⋊C8—41no—
257C43⋊C8—41no—
258#19863—431nomaximal, Sylow
259C22×C43—41no—
260C22×C43—41no—
261C22×C43—41no—
262C22×C43—41no—
263C22×C43—41no—
264C22×C43—41no—
265C22×C43D4211yescharacteristic
266C2×D43—41no—
267C2×D43—41no—
268C2×D43—41no—
269C4×C43—21no—
270C4×C43—41no—
271C4×C43—41no—
272C4×C43—41no—
273C4×C43—41no—
274C4×C43—81no—
275C4×C43—81no—
276C4×C43C2×#13511yescharacteristic
277C4×C43#57511yescharacteristic
278C4×C43#57611yescharacteristic
279C4×C43#57811yescharacteristic
280Dic43—41no—
281Dic43—81no—
282Dic43—81no—
283#3393—431no—
284#3353D4311yescharacteristic, complemented
285#3340—431no—
286#3303—431no—
287#1723—431no—
288#1691—431no—
289#1684—431no—
290#1673—431no—
291#1669—431no—
292#1650—431no—
293#1647—431no—
294#1646—431no—
295#1638—431no—
296#1581—431no—
297SD16⋊C8—431no—
298C2×C43—81no—
299C2×C43—81no—
300C2×C43#326811yescharacteristic
301C2×C43#328311yescharacteristic
302C2×C43#328911yescharacteristic
303D43—81no—
304#556—431no—
305#556C2×D4311yescharacteristic
306#555—431no—
307#547C2×D4311yescharacteristic
308#500—431no—
309#500C2×D4311yescharacteristic
310#498—431no—
311#495—861no—
312#494—431no—
313#487—431no—
314#487—431no—
315#485—861no—
316#485—861no—
317#484—21no—
318#482—21no—
319#482—861no—
320#477—431no—
321#476—431no—
322#475C2×D4311yescharacteristic
323#474—431no—
324#474C2×D4311yescharacteristic
325#468—21no—
326#465—861no—
327#465—861no—
328#464—861no—
329#464—861no—
330#461—431no—
331#461—431no—
332#461—431no—
333#449—861no—
334C8×Q8—431no—
335C4×Q16—861no—
336C4×SD16C2×D4311yescharacteristic
337C4×D8—431no—
338#436C2×D4311yescharacteristic
339C8×D4—431no—
340C8×D4—431no—
341#428—21no—
342#427—861no—
343#416—861no—
344#335—431no—
345#335—431no—
346#333—431no—
347#332—431no—
348#332—431no—
349#332—431no—
350Q8⋊C8—431no—
351D4⋊C8—431no—
352D4⋊C8—431no—
353D4⋊C8—431no—
354#322—431no—
355C43#1986311yescharacteristic, complemented, Sylow
356C2×#41—21no—
357C2×Q16—861no—
358C2×Q16—861no—
359C2×SD16—861no—
360C2×SD16—861no—
361C2×SD16—861no—
362C2×SD16C22⋊D4311yescharacteristic
363C2×D8—431no—
364C2×M16—21no—
365C22×C8—861no—
366C22×C8—861no—
367C4⋊Q8—431no—
368C4⋊Q8—431no—
369C4⋊Q8C22×D4311yescharacteristic
370C4⋊Q8C22×D4311yescharacteristic
371#126—41no—
372#126—1721no—
373#124—21no—
374#124—861no—
375#124—1721no—
376#123—41no—
377C22⋊Q8—21no—
378C22⋊Q8—21no—
379C22⋊Q8—861no—
380#121—21no—
381#121—861no—
382#121—861no—
383C4×Q8—21no—
384C4×Q8—861no—
385C4×Q8C22×D4311yescharacteristic
386C4×D4—431no—
387C4×D4C22×D4311yescharacteristic
388C4×D4C22×D4311yescharacteristic
389#117—21no—
390#117—861no—
391#117—861no—
392#117—861no—
393C2×C4⋊C4—21no—
394#107—21no—
395#107—21no—
396#107—21no—
397#107—431no—
398#107—861no—
399#107—861no—
400#107—1721no—
401#106—21no—
402#106—861no—
403#106—861no—
404#106—861no—
405#106C22⋊D4311yescharacteristic
406C4⋊C8—431no—
407C4⋊C8—431no—
408C4⋊C8—431no—
409C4⋊C8—861no—
410C4⋊C8C22×D4311yescharacteristic
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#102C22⋊D4311yescharacteristic
426C22⋊C8—21no—
427C22⋊C8—861no—
428C22⋊C8—861no—
429C4×C8—431no—
430C4×C8—431no—
431C4×C8—861no—
432C4×C8C22×D4311yescharacteristic
433#41—42no—
434#41—81no—
435C2×Q8—21no—
436C2×Q8—21no—
437C2×Q8—861no—
438C2×Q8—861no—
439C2×Q8C2×C22⋊D4311yescharacteristic
440C2×D4—41no—
441C2×D4—431no—
442C2×D4—1721no—
443C2×D4D4×D4311yescharacteristic
444C2×D4C2×C22⋊D4311yescharacteristic
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—41no—
448C22×C4—861no—
449Q16—3441no—
450Q16—1722no—
451SD16—22no—
452SD16—3441no—
453SD16—3441no—
454SD16—3441no—
455D8—1721no—
456M16—42no—
457C2×C8—21no—
458C2×C8—431no—
459C2×C8—431no—
460C2×C8—861no—
461C2×C8—861no—
462C2×C8—861no—
463C2×C8—861no—
464C2×C8—3441no—
465C2×C8—1722no—
466C2×C8C2×C22⋊D4311yescharacteristic
467C2×C8C2×C22⋊D4311yescharacteristic
468C4⋊C4—21no—
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—21no—
472C4⋊C4—21no—
473C4⋊C4—41no—
474C4⋊C4—41no—
475C4⋊C4—431no—
476C4⋊C4—861no—
477C4⋊C4—861no—
478C4⋊C4—861no—
479C4⋊C4—861no—
480C4⋊C4—1721no—
481C4⋊C4D4×D4311yescharacteristic
482C4⋊C4C2×C22⋊D4311yescharacteristic
483C4⋊C4C2×C22⋊D4311yescharacteristic
484C22⋊C4—21no—
485C22⋊C4—21no—
486C22⋊C4—41no—
487C22⋊C4—41no—
488C22⋊C4—41no—
489C22⋊C4—861no—
490C22⋊C4—1721no—
491C22⋊C4—1721no—
492C22⋊C4—1721no—
493C22⋊C4—1721no—
494C42—21no—
495C42—41no—
496C42—1721no—
497C42—1721no—
498C42C23×D4311yescharacteristic
499C23—21no—
500C23—21no—
501C23—861no—
502Q8—21no—
503Q8—21no—
504Q8—41no—
505Q8—41no—
506Q8—41no—
507Q8—41no—
508Q8—3441no—
509Q8—1721no—
510Q8—1721no—
511D4—21no—
512D4—21no—
513D4—21no—
514D4—21no—
515D4—82no—
516D4—861no—
517D4—861no—
518D4—6881no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—82no—
530C2×C4—861no—
531C2×C4—1721no—
532C2×C4—1721no—
533C2×C4—1721no—
534C2×C4—1721no—
535C2×C4C2×D4×D4311yescharacteristic
536C2×C4C22×C22⋊D4311yescharacteristic
537C2×C4#1306337011yescharacteristic
538C8—21no—
539C8—41no—
540C8—861no—
541C8—861no—
542C8—1721no—
543C8—1721no—
544C8—1721no—
545C8—1721no—
546C8#1306334512yes—
547C22—41no—
548C22—41no—
549C22—41no—
550C22—41no—
551C22—41no—
552C22—41no—
553C22—1721no—
554C22—1721no—
555C22—1721no—
556C22D4×C22⋊D4311yescharacteristic
557C4—21no—
558C4—41no—
559C4—41no—
560C4—41no—
561C4—41no—
562C4—81no—
563C4—81no—
564C4—3441no—
565C4—3441no—
566C4—1721no—
567C4C2×#1306334511yescharacteristic
568C4#1458369511yescharacteristic
569C4#1458370311yescharacteristic
570C4#1458371411yescharacteristic
571C2—81no—
572C2—81no—
573C2—3441no—
574C2#1914612911yescharacteristic
575C2#1914631311yescharacteristic
576C2#1914636611yescharacteristic
subgroupG/H
centerC22D4×C22⋊D43
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#3353C2
socleC22×C43D42
prime radical#19146523C2
hypercenter#3353D43
hypocenterC43#19863
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #3353

Complements

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

NH ≅ G/Ntype
1. #19147579C2semidirect
2. #19147010C2semidirect
4. #19134273C2semidirect
5. #19134094C2semidirect
6. #19134051C2semidirect
7. #19133981C2semidirect
8. #19133958C2semidirect
9. #19133850C2semidirect
10. #19133830C2semidirect
11. #19133822C2semidirect
12. #19133767C2semidirect
13. #19133422C2semidirect
14. SD16⋊(C43⋊C8)C2semidirect
15. C43×#3353C2semidirect
284. #3353D43semidirect
355. C43#19863semidirect

Maximal subgroups

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

subgroupindex
#191475792
#191470102
#191465232
#191342732
#191340942
#191340512
#191339812
#191339582
#191338502
#191338302
#191338222
#191337672
#191334222
SD16⋊(C43⋊C8)2
C43×#33532
#1986343