Finite Group Databasebeta

← #25086630

Subgroups — #25086630

Order 11008.

590 conjugacy classes of subgroups.

The subgroup lattice has 572 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19147398C211yesmaximal, characteristic, complemented
2#19147278C211yesmaximal, characteristic, complemented
3#19146534C211yesmaximal, characteristic
4#19134246C211yesmaximal, characteristic, complemented
5#19134161C211yesmaximal, characteristic, complemented
6#19134025C211yesmaximal, characteristic, complemented
7#19134020C211yesmaximal, characteristic, complemented
8#19133940C211yesmaximal, characteristic, complemented
9#19133849C211yesmaximal, characteristic, complemented
10#19133837C211yesmaximal, characteristic, complemented
11#19133788C211yesmaximal, characteristic
12#19133690C211yesmaximal, characteristic, complemented
13#19133432C211yesmaximal, characteristic, complemented
14#19133412C211yesmaximal, characteristic, complemented
15C43×#3392C211yesmaximal, characteristic
16#14583628C2211yescharacteristic
17#14583619C2211yescharacteristic
18#14583302C2211yescharacteristic
19#14583269—21no—
20#14583252—21no—
21#14583251C2211yescharacteristic
22#14583250C2211yescharacteristic
23#14583245C2211yescharacteristic
24#14583245C2211yescharacteristic
25#14583220—21no—
26#14583209—21no—
27#14583203—21no—
28#14583184C2211yescharacteristic
29#14583181C2211yescharacteristic
30#14583179C2211yescharacteristic
31#14583126—21no—
32#14583119—21no—
33#14583109—21no—
34#14583109C2211yescharacteristic
35#14583109C2211yescharacteristic
36#14583096C2211yescharacteristic
37#14583061—21no—
38#14583030C2211yescharacteristic
39C8×Dic86C2211yescharacteristic
40#14583004—21no—
41C4×#10621885C2211yescharacteristic
42#14582991—21no—
43D4×C43⋊C8C2211yescharacteristic
44#14582895—21no—
45#14582650C2211yescharacteristic
46#14582649C2211yescharacteristic
47#14582646C2211yescharacteristic
48#14582645C2211yescharacteristic
49#14582644C2211yescharacteristic
50#14582643C2211yescharacteristic
51Q8⋊(C43⋊C8)C2211yescharacteristic
52Q8⋊(C43⋊C8)C2211yescharacteristic
53#14582629C2211yescharacteristic
54D4⋊(C43⋊C8)C2211yescharacteristic
55#14582621C2211yescharacteristic
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×#10621885—21no—
68C2×#10621885—21no—
69C2×#10621885D411yescharacteristic
70C2×#10621883—21no—
71C22×C43⋊C8—21no—
72#13063325—21no—
73#13063325C2311yescharacteristic
74#13063325C2311yescharacteristic
75#13063318—41no—
76#13063316—21no—
77#13063316—41no—
78#13063312—21no—
79#13063304—21no—
80Q8×Dic43—21no—
81C4×Dic86—21no—
82C4×Dic86C2311yescharacteristic
83#13063290—21no—
84#13063284—21no—
85#13063258—21no—
86#13063258—41no—
87#13063258D411yescharacteristic
88#13063256—21no—
89#13063256—21no—
90C4⋊(C43⋊C8)—21no—
91C4⋊(C43⋊C8)C2311yescharacteristic
92C4⋊(C43⋊C8)C2311yescharacteristic
93C4⋊(C43⋊C8)C2311yescharacteristic
94Dic43⋊C8—21no—
95#13063250—21no—
96#13063250—21no—
97#13063249—21no—
98#13063249D411yescharacteristic
99#13063248—21no—
100#13063248—21no—
101#13063248—21no—
102#13063248—21no—
103#13063248—21no—
104#13063248D411yescharacteristic
105#13063246—21no—
106#13063246—21no—
107#13063246—21no—
108#13063246—21no—
109#13063246—41no—
110C22⋊(C43⋊C8)—21no—
111#13063236—21no—
112C4×C43⋊C8C2311yescharacteristic
113C4×C43⋊C8C2311yescharacteristic
114C8×Dic43—21no—
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—41no—
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—42no—
188#10621885—42no—
189#10621883—81no—
190C4⋊Dic43—21no—
191C4⋊Dic43—21no—
192C4⋊Dic43—21no—
193C4⋊Dic43—21no—
194C4⋊Dic43—41no—
195C4⋊Dic43—41no—
196C4⋊Dic43C2×D411yescharacteristic
197Dic43⋊C4—21no—
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
210C23×C43—21no—
211C23×C43—41no—
212Q8×C43—21no—
213Q8×C43—21no—
214Q8×C43—21no—
215Q8×C43—41no—
216Q8×C43—41no—
217Q8×C43#13512yes—
218D4×C43—21no—
219D4×C43—21no—
220D4×C43—41no—
221D4×C43—41no—
222D4×C43—41no—
223D4×C43—41no—
224D4×C43—82no—
225D4×C43—81no—
226D4×C43—161no—
227C2×C4×C43—21no—
228C2×C4×C43—21no—
229C2×C4×C43—21no—
230C2×C4×C43—21no—
231C2×C4×C43—21no—
232C2×C4×C43—41no—
233C2×C4×C43—41no—
234C2×C4×C43—41no—
235C2×C4×C43—82no—
236C2×C4×C43C22×D411yescharacteristic
237C2×C4×C43C22×D411yescharacteristic
238C2×C4×C43H(5,𝔽2)11yescharacteristic
239C2×Dic43—21no—
240C2×Dic43—21no—
241C2×Dic43—41no—
242C2×Dic43—41no—
243Dic86—21no—
244Dic86—21no—
245Dic86—41no—
246Dic86—41no—
247Dic86—41no—
248Dic86—41no—
249C8×C43—21no—
250C8×C43—21no—
251C8×C43—41no—
252C43⋊C8—21no—
253C43⋊C8—21no—
254C43⋊C8—41no—
255C43⋊C8—41no—
256C43⋊C8—41no—
257C43⋊C8—41no—
258#19801—431nomaximal, Sylow
259C22×C43—41no—
260C22×C43—41no—
261C22×C43—41no—
262C22×C43—81no—
263C22×C43—81no—
264C22×C43—81no—
265C22×C43D4211yescharacteristic
266C4×C43—22no—
267C4×C43—21no—
268C4×C43—41no—
269C4×C43—41no—
270C4×C43—41no—
271C4×C43—41no—
272C4×C43—81no—
273C4×C43C2×#13511yescharacteristic
274C4×C43#57511yescharacteristic
275C4×C43#57711yescharacteristic
276C4×C43#57711yescharacteristic
277Dic43—41no—
278Dic43—41no—
279Dic43—81no—
280Dic43—81no—
281#3392D4311yescharacteristic
282#3374—431no—
283#3364—431no—
284#3304—431no—
285#1719—431no—
286#1702—431no—
287#1680—431no—
288#1679—431no—
289#1666—431no—
290#1650—431no—
291#1648—431no—
292#1641—431no—
293#1626—431no—
294#1582—431no—
295#1579—431no—
296C2×C43—81no—
297C2×C43—161no—
298C2×C43#327111yescharacteristic
299C2×C43#328211yescharacteristic
300C2×C43#328911yescharacteristic
301#557—431no—
302#557C2×D4311yescharacteristic
303#556—431no—
304#550C2×D4311yescharacteristic
305#500—431no—
306#492—21no—
307#492C2×D4311yescharacteristic
308#491—861no—
309#488—861no—
310#487—431no—
311#487—431no—
312#486—431no—
313#486—431no—
314#482—861no—
315#479—861no—
316#479—861no—
317#475—431no—
318#475—431no—
319#474—431no—
320#465—861no—
321#464—861no—
322#462—431no—
323#462—431no—
324#462—861no—
325#461—21no—
326#461C2×D4311yescharacteristic
327#460—21no—
328#460—431no—
329#460C2×D4311yescharacteristic
330#452—861no—
331#446—431no—
332C8×Q8—431no—
333C8×Q8C2×D4311yescharacteristic
334#441—861no—
335C4×Q16—431no—
336C4×Q16—861no—
337C4×SD16—21no—
338C4×SD16C2×D4311yescharacteristic
339C8×D4—431no—
340#416—861no—
341#334—431no—
342#334—431no—
343#332—431no—
344#332—431no—
345#332—431no—
346#331—431no—
347Q8⋊C8—431no—
348Q8⋊C8—431no—
349Q8⋊C8—431no—
350D4⋊C8—431no—
351#322—431no—
352C43#1980111yescharacteristic, complemented, Sylow
353C2×#41—21no—
354C2×Q16—431no—
355C2×Q16—861no—
356C2×Q16—861no—
357C2×SD16—21no—
358C2×SD16—21no—
359C2×SD16—21no—
360C2×SD16—21no—
361C2×SD16—861no—
362C2×SD16C22⋊D4311yescharacteristic
363C22×C8—861no—
364C4⋊Q8—21no—
365C4⋊Q8—431no—
366C4⋊Q8—431no—
367C4⋊Q8—861no—
368C4⋊Q8C22×D4311yescharacteristic
369#127—21no—
370#127C22×D4311yescharacteristic
371#126—1721no—
372#125—21no—
373#125—41no—
374#125—861no—
375#125—1721no—
376#124—861no—
377C22⋊Q8—861no—
378#121—21no—
379#121—41no—
380C4×Q8—21no—
381C4×Q8—21no—
382C4×Q8—431no—
383C4×Q8—861no—
384C4×Q8—861no—
385C4×Q8—861no—
386C4×Q8C22×D4311yescharacteristic
387C4×Q8C22×D4311yescharacteristic
388C4×D4—21no—
389C4×D4C22×D4311yescharacteristic
390#117—861no—
391#107—431no—
392#107—861no—
393#107—1721no—
394#106—861no—
395#106—861no—
396#106C22⋊D4311yescharacteristic
397C4⋊C8—21no—
398C4⋊C8—431no—
399C4⋊C8—431no—
400C4⋊C8—431no—
401C4⋊C8—861no—
402C4⋊C8—861no—
403C4⋊C8C22×D4311yescharacteristic
404#103—21no—
405#103—431no—
406#103—431no—
407#103—861no—
408#103—861no—
409#103—861no—
410#103—861no—
411#103—861no—
412#103—861no—
413#103—861no—
414#103—861no—
415#103C22⋊D4311yescharacteristic
416#102—21no—
417#102—861no—
418#102—861no—
419#102—861no—
420#102—861no—
421#102—1721no—
422#102C22⋊D4311yescharacteristic
423C22⋊C8—861no—
424#97—861no—
425C4×C8—21no—
426C4×C8—431no—
427C4×C8—431no—
428C4×C8—861no—
429C4×C8C22×D4311yescharacteristic
430#41—42no—
431#41—81no—
432C2×Q8—21no—
433C2×Q8—431no—
434C2×Q8—861no—
435C2×Q8—861no—
436C2×Q8D4×D4311yescharacteristic
437C2×Q8C2×C22⋊D4311yescharacteristic
438C2×D4—21no—
439C2×D4—21no—
440C2×D4—21no—
441C2×D4—41no—
442C2×D4—41no—
443C2×D4C2×C22⋊D4311yescharacteristic
444C22×C4—21no—
445C22×C4—41no—
446Q16—862no—
447Q16—1722no—
448Q16—1722no—
449SD16—41no—
450SD16—42no—
451SD16—81no—
452SD16—81no—
453SD16—81no—
454SD16—3441no—
455C2×C8—21no—
456C2×C8—431no—
457C2×C8—431no—
458C2×C8—861no—
459C2×C8—861no—
460C2×C8—861no—
461C2×C8—861no—
462C2×C8—3441no—
463C2×C8C2×C22⋊D4311yescharacteristic
464C2×C8C2×C22⋊D4311yescharacteristic
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—41no—
470C4⋊C4—41no—
471C4⋊C4—41no—
472C4⋊C4—431no—
473C4⋊C4—861no—
474C4⋊C4—861no—
475C4⋊C4—861no—
476C4⋊C4—861no—
477C4⋊C4—861no—
478C4⋊C4—1721no—
479C4⋊C4—1721no—
480C4⋊C4—1721no—
481C4⋊C4—1721no—
482C4⋊C4D4×D4311yescharacteristic
483C4⋊C4C2×C22⋊D4311yescharacteristic
484C4⋊C4C2×C22⋊D4311yescharacteristic
485C22⋊C4—21no—
486C22⋊C4—41no—
487C22⋊C4—1721no—
488C22⋊C4—1721no—
489C42—21no—
490C42—21no—
491C42—41no—
492C42—861no—
493C42—1721no—
494C42—1721no—
495C42C23×D4311yescharacteristic
496C23—21no—
497C23—41no—
498Q8—21no—
499Q8—21no—
500Q8—21no—
501Q8—41no—
502Q8—41no—
503Q8—861no—
504Q8—861no—
505Q8—1721no—
506Q8—1721no—
507Q8—1721no—
508Q8—1721no—
509Q8#1306334612yes—
510D4—21no—
511D4—21no—
512D4—41no—
513D4—41no—
514D4—41no—
515D4—41no—
516D4—82no—
517D4—81no—
518D4—161no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—41no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—82no—
528C2×C4—861no—
529C2×C4—861no—
530C2×C4—1721no—
531C2×C4—1721no—
532C2×C4C2×D4×D4311yescharacteristic
533C2×C4C22×C22⋊D4311yescharacteristic
534C2×C4#1306337011yescharacteristic
535C8—21no—
536C8—21no—
537C8—41no—
538C8—861no—
539C8—861no—
540C8—1721no—
541C8—1721no—
542C8—1721no—
543C8—1721no—
544C22—41no—
545C22—41no—
546C22—41no—
547C22—81no—
548C22—81no—
549C22—81no—
550C22D4×C22⋊D4311yescharacteristic
551C4—22no—
552C4—21no—
553C4—41no—
554C4—41no—
555C4—41no—
556C4—41no—
557C4—81no—
558C4—3441no—
559C4—3441no—
560C4—1721no—
561C4—1721no—
562C4C2×#1306334611yescharacteristic
563C4#1458369711yescharacteristic
564C4#1458370511yescharacteristic
565C4#1458371011yescharacteristic
566C2—81no—
567C2—161no—
568C2#1914617611yescharacteristic
569C2#1914630211yescharacteristic
570C2#1914636811yescharacteristic
subgroupG/H
centerC22D4×C22⋊D43
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#3392C2
socleC22×C43D42
prime radicalC43×#550C22
hypercenter#3392D43
hypocenterC43#19801
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. #19147398C2semidirect
2. #19147278C2semidirect
4. #19134246C2semidirect
5. #19134161C2semidirect
6. #19134025C2semidirect
7. #19134020C2semidirect
8. #19133940C2semidirect
9. #19133849C2semidirect
10. #19133837C2semidirect
12. #19133690C2semidirect
13. #19133432C2semidirect
14. #19133412C2semidirect
352. C43#19801semidirect

Maximal subgroups

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

subgroupindex
#191473982
#191472782
#191465342
#191342462
#191341612
#191340252
#191340202
#191339402
#191338492
#191338372
#191337882
#191336902
#191334322
#191334122
C43×#33922
#1980143