Finite Group Databasebeta

← #25087654

Subgroups — #25087654

Order 11008.

596 conjugacy classes of subgroups.

The subgroup lattice has 576 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19147624C211yesmaximal, characteristic, complemented
2#19147482C211yesmaximal, characteristic, complemented
3#19146534C211yesmaximal, characteristic
4#19134264C211yesmaximal, characteristic, complemented
5#19134064C211yesmaximal, characteristic, complemented
6#19134037C211yesmaximal, characteristic, complemented
7#19133982C211yesmaximal, characteristic, complemented
8#19133965C211yesmaximal, characteristic, complemented
9#19133849C211yesmaximal, characteristic, complemented
10#19133837C211yesmaximal, characteristic, complemented
11#19133795C211yesmaximal, characteristic
12#19133689C211yesmaximal, characteristic, complemented
13#19133445C211yesmaximal, characteristic, complemented
14SD16⋊(C43⋊C8)C211yesmaximal, characteristic, complemented
15C43×#3392C211yesmaximal, characteristic
16#14583627C2211yescharacteristic
17#14583619C2211yescharacteristic
18#14583302C2211yescharacteristic
19#14583302C2211yescharacteristic
20#14583298—21no—
21#14583290—21no—
22#14583279C2211yescharacteristic
23#14583245C2211yescharacteristic
24#14583245C2211yescharacteristic
25#14583220—21no—
26#14583206—21no—
27#14583203—21no—
28#14583184C2211yescharacteristic
29#14583184C2211yescharacteristic
30#14583181C2211yescharacteristic
31#14583126—21no—
32#14583120—21no—
33#14583109C2211yescharacteristic
34#14583108—21no—
35#14583104C2211yescharacteristic
36#14583096C2211yescharacteristic
37#14583061—21no—
38#14583029C2211yescharacteristic
39Q8×C43⋊C8C2211yescharacteristic
40#14583005—21no—
41C4×#10621885—21no—
42C4×#10621885C2211yescharacteristic
43D4×C43⋊C8C2211yescharacteristic
44#14582895—21no—
45#14582652C2211yescharacteristic
46#14582651C2211yescharacteristic
47#14582646C2211yescharacteristic
48#14582646C2211yescharacteristic
49#14582645C2211yescharacteristic
50#14582643C2211yescharacteristic
51Q8⋊(C43⋊C8)C2211yescharacteristic
52Q8⋊(C43⋊C8)C2211yescharacteristic
53#14582629C2211yescharacteristic
54D4⋊(C43⋊C8)C2211yescharacteristic
55#14582620C2211yescharacteristic
56C43×#557C2211yescharacteristic
57C43×#550C2211yescharacteristic
58C43×#492—21no—
59C43×#492C2211yescharacteristic
60C43×#461—21no—
61C43×#461C2211yescharacteristic
62C43×#460—21no—
63C43×#460C2211yescharacteristic
64C8×Q8×C43C2211yescharacteristic
65C4×SD16×C43—21no—
66C4×SD16×C43C2211yescharacteristic
67C2×Dic172—21no—
68C2×Dic172—21no—
69C2×#10621885—21no—
70C2×#10621885D411yescharacteristic
71C2×#10621883—21no—
72C2×#10621883—21no—
73C22×C43⋊C8—21no—
74#13063325C2311yescharacteristic
75#13063325C2311yescharacteristic
76#13063323—21no—
77#13063318—41no—
78#13063317—21no—
79#13063315—41no—
80#13063312—21no—
81#13063304—21no—
82C4×Dic86—21no—
83C4×Dic86C2311yescharacteristic
84#13063290—21no—
85#13063290—21no—
86#13063284—21no—
87#13063258—21no—
88#13063258—21no—
89#13063258—41no—
90#13063258D411yescharacteristic
91#13063256—21no—
92#13063256—21no—
93#13063256—21no—
94C4⋊(C43⋊C8)—21no—
95C4⋊(C43⋊C8)C2311yescharacteristic
96C4⋊(C43⋊C8)C2311yescharacteristic
97C4⋊(C43⋊C8)C2311yescharacteristic
98Dic43⋊C8—21no—
99#13063249—21no—
100#13063249—21no—
101#13063249D411yescharacteristic
102#13063248—21no—
103#13063248—21no—
104#13063248—21no—
105#13063248D411yescharacteristic
106#13063246—21no—
107#13063246—21no—
108#13063246—21no—
109#13063246—41no—
110C22⋊(C43⋊C8)—21no—
111#13063235—21no—
112C4×C43⋊C8—21no—
113C4×C43⋊C8C2311yescharacteristic
114C4×C43⋊C8C2311yescharacteristic
115C2×#41×C43—21no—
116C2×SD16×C43—21no—
117C2×SD16×C43—21no—
118C2×SD16×C43—21no—
119C2×SD16×C43—21no—
120C2×SD16×C43D411yescharacteristic
121C4⋊Q8×C43—21no—
122C4⋊Q8×C43C2311yescharacteristic
123#127×C43—21no—
124#127×C43C2311yescharacteristic
125#125×C43—21no—
126#125×C43—41no—
127#121×C43—21no—
128#121×C43—41no—
129C4×Q8×C43—21no—
130C4×Q8×C43—21no—
131C4×Q8×C43C2311yescharacteristic
132C4×Q8×C43C2311yescharacteristic
133C4×D4×C43—21no—
134C4×D4×C43C2311yescharacteristic
135#106×C43D411yescharacteristic
136C4⋊C8×C43—21no—
137C4⋊C8×C43C2311yescharacteristic
138#103×C43—21no—
139#103×C43D411yescharacteristic
140#102×C43—21no—
141#102×C43D411yescharacteristic
142C4×C8×C43—21no—
143C4×C8×C43C2311yescharacteristic
144#41×C43—42no—
145#41×C43—81no—
146C2×Q8×C43—21no—
147C2×Q8×C43C2×D411yescharacteristic
148C2×Q8×C43C2×D411yescharacteristic
149C2×D4×C43—21no—
150C2×D4×C43—21no—
151C2×D4×C43—21no—
152C2×D4×C43—41no—
153C2×D4×C43—41no—
154C2×D4×C43C2×D411yescharacteristic
155C22×C4×C43—21no—
156C22×C4×C43—41no—
157C2×Dic86—21no—
158C2×Dic86—21no—
159C2×Dic86C2×D411yescharacteristic
160SD16×C43—22no—
161SD16×C43—42no—
162SD16×C43—81no—
163SD16×C43—81no—
164SD16×C43—81no—
165C2×C8×C43—21no—
166C2×C8×C43C2×D411yescharacteristic
167C2×C8×C43C2×D411yescharacteristic
168C4⋊C4×C43—21no—
169C4⋊C4×C43—21no—
170C4⋊C4×C43—21no—
171C4⋊C4×C43—21no—
172C4⋊C4×C43—41no—
173C4⋊C4×C43—41no—
174C4⋊C4×C43—41no—
175C4⋊C4×C43C2×D411yescharacteristic
176C4⋊C4×C43C2×D411yescharacteristic
177C4⋊C4×C43C2×D411yescharacteristic
178C22⋊C4×C43—21no—
179C22⋊C4×C43—41no—
180C42×C43—21no—
181C42×C43—21no—
182C42×C43—41no—
183C42×C43C2411yescharacteristic
184C22⋊Dic43—41no—
185C22⋊Dic43—41no—
186#10621885—22no—
187#10621885—81no—
188#10621883—81no—
189#10621883—81no—
190C4⋊Dic43—21no—
191C4⋊Dic43—21no—
192C4⋊Dic43—21no—
193C4⋊Dic43—21no—
194C4⋊Dic43C2×D411yescharacteristic
195Dic43⋊C4—21no—
196Dic43⋊C4—41no—
197Dic43⋊C4—41no—
198Dic43⋊C4—41no—
199Dic43⋊C4—41no—
200C4×Dic43—21no—
201C4×Dic43—41no—
202C4×Dic43—41no—
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
210Dic172—42no—
211Dic172—81no—
212C23×C43—21no—
213C23×C43—41no—
214Q8×C43—21no—
215Q8×C43—21no—
216Q8×C43—21no—
217Q8×C43—41no—
218Q8×C43—41no—
219Q8×C43#13712yes—
220D4×C43—21no—
221D4×C43—21no—
222D4×C43—41no—
223D4×C43—41no—
224D4×C43—41no—
225D4×C43—41no—
226D4×C43—82no—
227D4×C43—81no—
228D4×C43—161no—
229C2×C4×C43—21no—
230C2×C4×C43—21no—
231C2×C4×C43—21no—
232C2×C4×C43—21no—
233C2×C4×C43—21no—
234C2×C4×C43—41no—
235C2×C4×C43—41no—
236C2×C4×C43—41no—
237C2×C4×C43—82no—
238C2×C4×C43C22×D411yescharacteristic
239C2×C4×C43C22×D411yescharacteristic
240C2×C4×C43H(5,𝔽2)11yescharacteristic
241C2×Dic43—21no—
242C2×Dic43—21no—
243C2×Dic43—41no—
244C2×Dic43—41no—
245Dic86—21no—
246Dic86—21no—
247Dic86—41no—
248Dic86—41no—
249Dic86—41no—
250Dic86—41no—
251C8×C43—21no—
252C8×C43—41no—
253C8×C43#13512yes—
254C43⋊C8—21no—
255C43⋊C8—21no—
256C43⋊C8—41no—
257C43⋊C8—41no—
258C43⋊C8—41no—
259C43⋊C8—41no—
260#19869—431nomaximal, Sylow
261C22×C43—41no—
262C22×C43—41no—
263C22×C43—41no—
264C22×C43—81no—
265C22×C43—81no—
266C22×C43—81no—
267C22×C43D4211yescharacteristic
268C4×C43—22no—
269C4×C43—21no—
270C4×C43—41no—
271C4×C43—41no—
272C4×C43—41no—
273C4×C43—41no—
274C4×C43—81no—
275C4×C43C2×#13511yescharacteristic
276C4×C43C2×#13711yescharacteristic
277C4×C43#57611yescharacteristic
278C4×C43#57711yescharacteristic
279Dic43—41no—
280Dic43—41no—
281Dic43—81no—
282Dic43—81no—
283#3398—431no—
284#3392D4311yescharacteristic
285#3383—431no—
286#3304—431no—
287#1722—431no—
288#1686—431no—
289#1682—431no—
290#1673—431no—
291#1670—431no—
292#1650—431no—
293#1648—431no—
294#1642—431no—
295#1626—431no—
296#1584—431no—
297SD16⋊C8—431no—
298C2×C43—81no—
299C2×C43—161no—
300C2×C43#326611yescharacteristic
301C2×C43#328711yescharacteristic
302C2×C43#328911yescharacteristic
303#557—431no—
304#557C2×D4311yescharacteristic
305#556—431no—
306#550C2×D4311yescharacteristic
307#500—431no—
308#500—431no—
309#499—861no—
310#497—861no—
311#494—431no—
312#492—21no—
313#492C2×D4311yescharacteristic
314#486—431no—
315#486—431no—
316#482—861no—
317#479—861no—
318#479—861no—
319#475—431no—
320#475—431no—
321#475—431no—
322#465—861no—
323#464—861no—
324#462—431no—
325#462—861no—
326#461—21no—
327#461—431no—
328#461C2×D4311yescharacteristic
329#460—21no—
330#460—431no—
331#460C2×D4311yescharacteristic
332#452—861no—
333#446—431no—
334C8×Q8—431no—
335C8×Q8C2×D4311yescharacteristic
336#441—861no—
337C4×Q16—431no—
338C4×Q16—861no—
339C4×SD16—21no—
340C4×SD16C2×D4311yescharacteristic
341C8×D4—431no—
342#416—861no—
343#335—431no—
344#335—431no—
345#332—431no—
346#332—431no—
347#332—431no—
348#331—431no—
349Q8⋊C8—431no—
350Q8⋊C8—431no—
351Q8⋊C8—431no—
352D4⋊C8—431no—
353#322—431no—
354C43#1986911yescharacteristic, complemented, Sylow
355C2×#41—21no—
356C2×Q16—431no—
357C2×Q16—861no—
358C2×Q16—861no—
359C2×Q16—861no—
360C2×SD16—21no—
361C2×SD16—21no—
362C2×SD16—21no—
363C2×SD16—21no—
364C2×SD16—861no—
365C2×SD16—861no—
366C2×SD16C22⋊D4311yescharacteristic
367C22×C8—861no—
368C4⋊Q8—21no—
369C4⋊Q8—431no—
370C4⋊Q8—431no—
371C4⋊Q8—861no—
372C4⋊Q8C22×D4311yescharacteristic
373#127—21no—
374#127C22×D4311yescharacteristic
375#126—1721no—
376#125—21no—
377#125—41no—
378#125—861no—
379#125—1721no—
380#124—861no—
381C22⋊Q8—861no—
382#121—21no—
383#121—41no—
384C4×Q8—21no—
385C4×Q8—21no—
386C4×Q8—431no—
387C4×Q8—861no—
388C4×Q8—861no—
389C4×Q8—861no—
390C4×Q8C22×D4311yescharacteristic
391C4×Q8C22×D4311yescharacteristic
392C4×D4—21no—
393C4×D4C22×D4311yescharacteristic
394#117—861no—
395#107—431no—
396#107—861no—
397#107—861no—
398#107—1721no—
399#106—861no—
400#106—861no—
401#106—861no—
402#106C22⋊D4311yescharacteristic
403C4⋊C8—21no—
404C4⋊C8—431no—
405C4⋊C8—431no—
406C4⋊C8—431no—
407C4⋊C8—861no—
408C4⋊C8—861no—
409C4⋊C8C22×D4311yescharacteristic
410#103—21no—
411#103—431no—
412#103—431no—
413#103—861no—
414#103—861no—
415#103—861no—
416#103—861no—
417#103—861no—
418#103C22⋊D4311yescharacteristic
419#102—21no—
420#102—861no—
421#102—861no—
422#102—861no—
423#102—1721no—
424#102C22⋊D4311yescharacteristic
425C22⋊C8—861no—
426#97—861no—
427C4×C8—21no—
428C4×C8—431no—
429C4×C8—431no—
430C4×C8—861no—
431C4×C8C22×D4311yescharacteristic
432#41—42no—
433#41—81no—
434C2×Q8—21no—
435C2×Q8—431no—
436C2×Q8—861no—
437C2×Q8—861no—
438C2×Q8D4×D4311yescharacteristic
439C2×Q8C2×C22⋊D4311yescharacteristic
440C2×D4—21no—
441C2×D4—21no—
442C2×D4—21no—
443C2×D4—41no—
444C2×D4—41no—
445C2×D4C2×C22⋊D4311yescharacteristic
446C22×C4—21no—
447C22×C4—41no—
448Q16—862no—
449Q16—3441no—
450Q16—3441no—
451Q16—1722no—
452SD16—22no—
453SD16—42no—
454SD16—81no—
455SD16—81no—
456SD16—81no—
457SD16—3441no—
458SD16—3441no—
459C2×C8—21no—
460C2×C8—431no—
461C2×C8—431no—
462C2×C8—861no—
463C2×C8—861no—
464C2×C8—861no—
465C2×C8—861no—
466C2×C8—3441no—
467C2×C8C2×C22⋊D4311yescharacteristic
468C2×C8C2×C22⋊D4311yescharacteristic
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—21no—
472C4⋊C4—21no—
473C4⋊C4—41no—
474C4⋊C4—41no—
475C4⋊C4—41no—
476C4⋊C4—431no—
477C4⋊C4—861no—
478C4⋊C4—861no—
479C4⋊C4—861no—
480C4⋊C4—861no—
481C4⋊C4—861no—
482C4⋊C4—1721no—
483C4⋊C4—1721no—
484C4⋊C4—1721no—
485C4⋊C4—1721no—
486C4⋊C4D4×D4311yescharacteristic
487C4⋊C4C2×C22⋊D4311yescharacteristic
488C4⋊C4C2×C22⋊D4311yescharacteristic
489C22⋊C4—21no—
490C22⋊C4—41no—
491C22⋊C4—1721no—
492C22⋊C4—1721no—
493C42—21no—
494C42—21no—
495C42—41no—
496C42—861no—
497C42—1721no—
498C42—1721no—
499C42C23×D4311yescharacteristic
500C23—21no—
501C23—41no—
502Q8—21no—
503Q8—21no—
504Q8—21no—
505Q8—41no—
506Q8—41no—
507Q8—861no—
508Q8—861no—
509Q8—1721no—
510Q8—1721no—
511Q8—1721no—
512Q8—1721no—
513Q8#1306335412yes—
514D4—21no—
515D4—21no—
516D4—41no—
517D4—41no—
518D4—41no—
519D4—41no—
520D4—82no—
521D4—81no—
522D4—161no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—41no—
531C2×C4—82no—
532C2×C4—861no—
533C2×C4—861no—
534C2×C4—1721no—
535C2×C4—1721no—
536C2×C4C2×D4×D4311yescharacteristic
537C2×C4C22×C22⋊D4311yescharacteristic
538C2×C4#1306337011yescharacteristic
539C8—21no—
540C8—41no—
541C8—861no—
542C8—861no—
543C8—1721no—
544C8—1721no—
545C8—1721no—
546C8—1721no—
547C8#1306334512yes—
548C22—41no—
549C22—41no—
550C22—41no—
551C22—81no—
552C22—81no—
553C22—81no—
554C22D4×C22⋊D4311yescharacteristic
555C4—22no—
556C4—21no—
557C4—41no—
558C4—41no—
559C4—41no—
560C4—41no—
561C4—81no—
562C4—3441no—
563C4—3441no—
564C4—1721no—
565C4—1721no—
566C4C2×#1306334511yescharacteristic
567C4C2×#1306335411yescharacteristic
568C4#1458370211yescharacteristic
569C4#1458370511yescharacteristic
570C2—81no—
571C2—161no—
572C2#1914610511yescharacteristic
573C2#1914635111yescharacteristic
574C2#1914636811yescharacteristic
subgroupG/H
centerC22D4×C22⋊D43
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#3392C2
socleC22×C43D42
prime radicalC43×#550C22
hypercenter#3392D43
hypocenterC43#19869
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #3392

Complements

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

NH ≅ G/Ntype
1. #19147624C2semidirect
2. #19147482C2semidirect
4. #19134264C2semidirect
5. #19134064C2semidirect
6. #19134037C2semidirect
7. #19133982C2semidirect
8. #19133965C2semidirect
9. #19133849C2semidirect
10. #19133837C2semidirect
12. #19133689C2semidirect
13. #19133445C2semidirect
14. SD16⋊(C43⋊C8)C2semidirect
354. C43#19869semidirect

Maximal subgroups

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

subgroupindex
#191476242
#191474822
#191465342
#191342642
#191340642
#191340372
#191339822
#191339652
#191338492
#191338372
#191337952
#191336892
#191334452
SD16⋊(C43⋊C8)2
C43×#33922
#1986943