Finite Group Databasebeta

← #25088016

Subgroups — #25088016

Order 11008.

624 conjugacy classes of subgroups.

The subgroup lattice has 574 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19147503C211yesmaximal, characteristic, complemented
2Q8×#10621883C211yesmaximal, characteristic, complemented
3#19146952C211yesmaximal, characteristic
4#19134189C211yesmaximal, characteristic, complemented
5#19134118C211yesmaximal, characteristic, complemented
6#19134086C211yesmaximal, characteristic, complemented
7#19133975C211yesmaximal, characteristic, complemented
8#19133968C211yesmaximal, characteristic, complemented
9#19133814C211yesmaximal, characteristic, complemented
10#19133800C211yesmaximal, characteristic, complemented
11#19133760C211yesmaximal, characteristic, complemented
12#19133746C211yesmaximal, characteristic
13#19133483C211yesmaximal, characteristic, complemented
14SD16×C43⋊C8C211yesmaximal, characteristic, complemented
15C43×#3276C211yesmaximal, characteristic
16Q8×Dic86C2211yescharacteristic
17#14583606C2211yescharacteristic
18#14583306—21no—
19#14583304C2211yescharacteristic
20#14583295—21no—
21#14583295C2211yescharacteristic
22#14583295C2211yescharacteristic
23#14583251C2211yescharacteristic
24#14583251C2211yescharacteristic
25#14583229—21no—
26#14583215—21no—
27#14583208—21no—
28#14583194C2211yescharacteristic
29#14583189—21no—
30#14583189C2211yescharacteristic
31#14583189C2211yescharacteristic
32#14583189C2211yescharacteristic
33#14583181—21no—
34#14583181C2211yescharacteristic
35#14583181C2211yescharacteristic
36#14583177—21no—
37#14583126—21no—
38#14583029C2211yescharacteristic
39Q8×C43⋊C8C2211yescharacteristic
40#14583000—21no—
41C4×#10621883—21no—
42C4×#10621883C2211yescharacteristic
43D4×C43⋊C8C2211yescharacteristic
44C2×#13063256—21no—
45#14582650C2211yescharacteristic
46#14582649C2211yescharacteristic
47#14582647C2211yescharacteristic
48#14582647C2211yescharacteristic
49#14582645C2211yescharacteristic
50#14582645C2211yescharacteristic
51Q8⋊(C43⋊C8)C2211yescharacteristic
52#14582629C2211yescharacteristic
53D4⋊(C43⋊C8)C2211yescharacteristic
54D4⋊(C43⋊C8)C2211yescharacteristic
55C8×C43⋊C8C2211yescharacteristic
56C2×#137×C43—21no—
57D4×Q8×C43C2211yescharacteristic
58C43×#547C2211yescharacteristic
59C43×#494C2211yescharacteristic
60C43×#470—21no—
61C43×#462C2211yescharacteristic
62C43×#461C2211yescharacteristic
63C43×#452—21no—
64C43×#451—21no—
65C4×SD16×C43C2211yescharacteristic
66C43×#436C2211yescharacteristic
67C2×#10621883D411yescharacteristic
68C22×C43⋊C8—21no—
69#13063325—21no—
70#13063325C2311yescharacteristic
71#13063325C2311yescharacteristic
72#13063324—21no—
73#13063324—41no—
74#13063316—21no—
75#13063304—21no—
76#13063302—41no—
77Q8×Dic43—21no—
78C4×Dic86—21no—
79C4×Dic86C2311yescharacteristic
80D4×Dic43—21no—
81C2×C4⋊Dic43—21no—
82#13063259—21no—
83#13063259—21no—
84#13063258—21no—
85#13063256—21no—
86#13063256—21no—
87#13063256—21no—
88#13063256—21no—
89#13063256—21no—
90#13063256—21no—
91#13063256—21no—
92#13063256—21no—
93#13063256—21no—
94#13063256D411yescharacteristic
95C4⋊(C43⋊C8)—21no—
96C4⋊(C43⋊C8)C2311yescharacteristic
97C4⋊(C43⋊C8)C2311yescharacteristic
98C4⋊(C43⋊C8)C2311yescharacteristic
99Dic43⋊C8—21no—
100#13063249—21no—
101#13063248—21no—
102#13063248—21no—
103#13063248—41no—
104#13063248—41no—
105#13063248D411yescharacteristic
106#13063246—21no—
107#13063246—21no—
108#13063246—21no—
109#13063246D411yescharacteristic
110C22⋊(C43⋊C8)—21no—
111#13063235—21no—
112C4×C43⋊C8—21no—
113C4×C43⋊C8C2311yescharacteristic
114C4×C43⋊C8C2311yescharacteristic
115C2×#41×C43—21no—
116C22×Q8×C43—21no—
117#137×C43—44no—
118C2×Q16×C43—21no—
119C2×Q16×C43—21no—
120C2×Q16×C43—21no—
121C2×SD16×C43—21no—
122C2×SD16×C43D411yescharacteristic
123C2×M16×C43—21no—
124C4⋊Q8×C43—21no—
125C4⋊Q8×C43C2311yescharacteristic
126C4⋊Q8×C43C2311yescharacteristic
127#123×C43—41no—
128C22⋊Q8×C43—21no—
129C22⋊Q8×C43—21no—
130C22⋊Q8×C43—41no—
131#121×C43—21no—
132C4×Q8×C43C2311yescharacteristic
133C4×D4×C43—21no—
134C4×D4×C43C2311yescharacteristic
135C4×D4×C43C2311yescharacteristic
136C2×C4⋊C4×C43—21no—
137#106×C43D411yescharacteristic
138C4⋊C8×C43C2311yescharacteristic
139#103×C43—21no—
140#103×C43—21no—
141#103×C43D411yescharacteristic
142#102×C43D411yescharacteristic
143C22⋊C8×C43—21no—
144C4×C8×C43C2311yescharacteristic
145#41×C43—42no—
146#41×C43—81no—
147C2×Q8×C43—21no—
148C2×Q8×C43—21no—
149C2×Q8×C43—41no—
150C2×Q8×C43—42no—
151C2×Q8×C43—81no—
152C2×Q8×C43C2×D411yescharacteristic
153C2×D4×C43—41no—
154C2×D4×C43C2×D411yescharacteristic
155C2×D4×C43C2×D411yescharacteristic
156C22×C4×C43—21no—
157C22×C4×C43—21no—
158C22×C4×C43—41no—
159C22×C4×C43—41no—
160C22×Dic43—41no—
161C2×Dic86—21no—
162C2×Dic86—21no—
163C2×Dic86—41no—
164C2×Dic86C2×D411yescharacteristic
165Q16×C43—42no—
166Q16×C43—42no—
167Q16×C43—81no—
168SD16×C43—42no—
169SD16×C43SD1614yescomplemented
170M16×C43—42no—
171C2×C8×C43—21no—
172C2×C8×C43C2×D411yescharacteristic
173C2×C8×C43C2×D411yescharacteristic
174C4⋊C4×C43—21no—
175C4⋊C4×C43—21no—
176C4⋊C4×C43—21no—
177C4⋊C4×C43—21no—
178C4⋊C4×C43—21no—
179C4⋊C4×C43—41no—
180C4⋊C4×C43—41no—
181C4⋊C4×C43C2×D411yescharacteristic
182C4⋊C4×C43C2×D411yescharacteristic
183C4⋊C4×C43C2×D411yescharacteristic
184C22⋊C4×C43—21no—
185C22⋊C4×C43—21no—
186C22⋊C4×C43—41no—
187C22⋊C4×C43—41no—
188C42×C43—21no—
189C42×C43C2411yescharacteristic
190C22⋊Dic43—41no—
191#10621883—22no—
192C4⋊Dic43—21no—
193C4⋊Dic43—21no—
194C4⋊Dic43—21no—
195C4⋊Dic43—21no—
196C4⋊Dic43—41no—
197C4⋊Dic43—41no—
198C4⋊Dic43C2×D411yescharacteristic
199Dic43⋊C4—21no—
200Dic43⋊C4—41no—
201Dic43⋊C4—41no—
202C4×Dic43—21no—
203C4×Dic43—41no—
204C2×C43⋊C8—21no—
205C2×C43⋊C8—21no—
206C2×C43⋊C8—21no—
207C2×C43⋊C8—21no—
208C2×C43⋊C8—42no—
209C2×C43⋊C8C2×D411yescharacteristic
210C2×C43⋊C8C2×D411yescharacteristic
211C23×C43—21no—
212C23×C43—21no—
213Q8×C43—21no—
214Q8×C43—41no—
215Q8×C43—41no—
216Q8×C43—41no—
217Q8×C43—41no—
218Q8×C43—82no—
219Q8×C43C2×SD1612yes—
220D4×C43—21no—
221D4×C43—21no—
222D4×C43—21no—
223D4×C43—82no—
224D4×C43C2×SD1612yes—
225C2×C4×C43—21no—
226C2×C4×C43—21no—
227C2×C4×C43—21no—
228C2×C4×C43—21no—
229C2×C4×C43—41no—
230C2×C4×C43—41no—
231C2×C4×C43—41no—
232C2×C4×C43—41no—
233C2×C4×C43—41no—
234C2×C4×C43—41no—
235C2×C4×C43—82no—
236C2×C4×C43—82no—
237C2×C4×C43C22×D411yescharacteristic
238C2×C4×C43C22×D411yescharacteristic
239C2×C4×C43H(5,𝔽2)11yescharacteristic
240C2×Dic43—21no—
241C2×Dic43—21no—
242C2×Dic43—41no—
243C2×Dic43—41no—
244C2×Dic43—161no—
245Dic86—21no—
246Dic86—21no—
247Dic86—81no—
248Dic86—81no—
249Dic86—161no—
250C8×C43—21no—
251C8×C43—41no—
252C8×C43C2×SD1612yes—
253C43⋊C8—21no—
254C43⋊C8—41no—
255C43⋊C8—41no—
256C43⋊C8—41no—
257C43⋊C8—41no—
258C43⋊C8#13712yescomplemented
259#19895—431nomaximal, Sylow
260C22×C43—22no—
261C22×C43—41no—
262C22×C43—41no—
263C22×C43—41no—
264C22×C43—41no—
265C22×C43—41no—
266C22×C43D4211yescharacteristic
267C4×C43—22no—
268C4×C43—21no—
269C4×C43—41no—
270C4×C43—41no—
271C4×C43—41no—
272C4×C43—81no—
273C4×C43—81no—
274C4×C43C22×SD1611yescharacteristic
275C4×C43C2×#13711yescharacteristic
276C4×C43#57711yescharacteristic
277C4×C43#57811yescharacteristic
278Dic43—41no—
279Dic43—41no—
280Dic43—81no—
281Dic43—81no—
282#3385—431no—
283Q8×SD16—431no—
284#3335—431no—
285#3276D4311yescharacteristic
286#1707—431no—
287#1695—431no—
288#1690—431no—
289#1672—431no—
290#1671—431no—
291#1645—431no—
292#1643—431no—
293#1637—431no—
294#1635—431no—
295#1590—431no—
296C8×SD16—431no—
297C2×C43—42no—
298C2×C43—81no—
299C2×C43#327611yescharacteristic
300C2×C43D4×SD1611yescharacteristic
301C2×C43#329011yescharacteristic
302C2×#137—21no—
303Q82—431no—
304#554—431no—
305D4×Q8C2×D4311yescharacteristic
306#547C2×D4311yescharacteristic
307#501—861no—
308#500—431no—
309#498—431no—
310#498—431no—
311#498—861no—
312#494C2×D4311yescharacteristic
313#487—431no—
314#487—431no—
315#483—861no—
316#481—861no—
317#479—861no—
318#477—431no—
319#476—431no—
320#476—431no—
321#476—431no—
322#476—861no—
323#475—431no—
324#475—431no—
325#475—861no—
326#474—861no—
327#470—21no—
328#465—861no—
329#462C2×D4311yescharacteristic
330#461C2×D4311yescharacteristic
331#452—21no—
332#451—21no—
333#446—431no—
334C8×Q8—431no—
335#440—861no—
336C4×SD16—431no—
337C4×SD16—861no—
338C4×SD16C2×D4311yescharacteristic
339#436C2×D4311yescharacteristic
340C8×D4—431no—
341C2×#106—861no—
342#334—431no—
343#334—431no—
344#333—431no—
345#333—431no—
346#332—431no—
347#332—431no—
348Q8⋊C8—431no—
349Q8⋊C8—431no—
350D4⋊C8—431no—
351D4⋊C8—431no—
352C82—431no—
353C43#1989511yescharacteristic, complemented, Sylow
354C2×#41—21no—
355C22×Q8—21no—
356#137—44no—
357C2×Q16—21no—
358C2×Q16—21no—
359C2×Q16—21no—
360C2×SD16—21no—
361C2×SD16—431no—
362C2×SD16C22⋊D4311yescharacteristic
363C2×M16—21no—
364C22×C8—861no—
365C4⋊Q8—21no—
366C4⋊Q8—431no—
367C4⋊Q8—431no—
368C4⋊Q8—861no—
369C4⋊Q8—861no—
370C4⋊Q8—1721no—
371C4⋊Q8C22×D4311yescharacteristic
372C4⋊Q8C22×D4311yescharacteristic
373#125—861no—
374#123—41no—
375C22⋊Q8—21no—
376C22⋊Q8—21no—
377C22⋊Q8—41no—
378C22⋊Q8—861no—
379C22⋊Q8—1721no—
380#121—21no—
381C4×Q8—431no—
382C4×Q8—861no—
383C4×Q8—861no—
384C4×Q8C22×D4311yescharacteristic
385C4×D4—21no—
386C4×D4—861no—
387C4×D4C22×D4311yescharacteristic
388C4×D4C22×D4311yescharacteristic
389C2×C4⋊C4—21no—
390C2×C4⋊C4—861no—
391#107—861no—
392#107—861no—
393#107—861no—
394#106—431no—
395#106—861no—
396#106—861no—
397#106—861no—
398#106—861no—
399#106—861no—
400#106—861no—
401#106—861no—
402#106—861no—
403#106—861no—
404#106C22⋊D4311yescharacteristic
405C4⋊C8—431no—
406C4⋊C8—431no—
407C4⋊C8—431no—
408C4⋊C8—861no—
409C4⋊C8—861no—
410C4⋊C8C22×D4311yescharacteristic
411#103—21no—
412#103—21no—
413#103—431no—
414#103—861no—
415#103—861no—
416#103—861no—
417#103—1721no—
418#103—1721no—
419#103C22⋊D4311yescharacteristic
420#102—431no—
421#102—861no—
422#102—861no—
423#102—861no—
424#102C22⋊D4311yescharacteristic
425C22⋊C8—21no—
426C22⋊C8—861no—
427#97—861no—
428C4×C8—431no—
429C4×C8—431no—
430C4×C8—861no—
431C4×C8C22×D4311yescharacteristic
432#41—42no—
433#41—81no—
434C2×Q8—21no—
435C2×Q8—21no—
436C2×Q8—41no—
437C2×Q8—42no—
438C2×Q8—81no—
439C2×Q8—431no—
440C2×Q8—861no—
441C2×Q8—861no—
442C2×Q8—1721no—
443C2×Q8C2×C22⋊D4311yescharacteristic
444C2×D4—41no—
445C2×D4D4×D4311yescharacteristic
446C2×D4C2×C22⋊D4311yescharacteristic
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—41no—
450C22×C4—41no—
451C22×C4—1721no—
452Q16—42no—
453Q16—42no—
454Q16—81no—
455SD16—42no—
456SD16—862no—
457SD16#1062188314yescomplemented
458M16—42no—
459C2×C8—21no—
460C2×C8—431no—
461C2×C8—431no—
462C2×C8—861no—
463C2×C8—861no—
464C2×C8—861no—
465C2×C8—861no—
466C2×C8—1722no—
467C2×C8C2×C22⋊D4311yescharacteristic
468C2×C8C2×C22⋊D4311yescharacteristic
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—21no—
472C4⋊C4—21no—
473C4⋊C4—21no—
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—21no—
491C22⋊C4—41no—
492C22⋊C4—41no—
493C22⋊C4—1721no—
494C42—21no—
495C42—861no—
496C42—1721no—
497C42C23×D4311yescharacteristic
498C23—21no—
499C23—21no—
500Q8—21no—
501Q8—41no—
502Q8—41no—
503Q8—41no—
504Q8—41no—
505Q8—82no—
506Q8—861no—
507Q8—861no—
508Q8—3441no—
509Q8—3441no—
510Q8—6881no—
511Q8C2×#1062188312yes—
512D4—21no—
513D4—21no—
514D4—21no—
515D4—82no—
516D4C2×#1062188312yes—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—82no—
528C2×C4—82no—
529C2×C4—861no—
530C2×C4—861no—
531C2×C4—1721no—
532C2×C4—1721no—
533C2×C4—6881no—
534C2×C4C2×D4×D4311yescharacteristic
535C2×C4C22×C22⋊D4311yescharacteristic
536C2×C4#1306337011yescharacteristic
537C8—21no—
538C8—41no—
539C8—432no—
540C8—861no—
541C8—1721no—
542C8—1721no—
543C8—1721no—
544C8—1721no—
545C8C2×#1062188312yes—
546C22—22no—
547C22—41no—
548C22—41no—
549C22—41no—
550C22—41no—
551C22—41no—
552C22D4×C22⋊D4311yescharacteristic
553C4—22no—
554C4—21no—
555C4—41no—
556C4—41no—
557C4—41no—
558C4—81no—
559C4—81no—
560C4—3441no—
561C4—3441no—
562C4—1721no—
563C4—1721no—
564C4C22×#1062188311yescharacteristic
565C4#137×D4311yescharacteristic
566C4#1458371011yescharacteristic
567C4#1458371511yescharacteristic
568C2—42no—
569C2—81no—
570C2#1914623511yescharacteristic
571C2D4×#1062188311yescharacteristic
572C2#1914638111yescharacteristic
subgroupG/H
centerC22D4×C22⋊D43
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#3276C2
socleC22×C43D42
prime radicalC43×#547C22
hypercenter#3276D43
hypocenterC43#19895
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #3276

Complements

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

NH ≅ G/Ntype
1. #19147503C2semidirect
2. Q8×#10621883C2semidirect
4. #19134189C2semidirect
5. #19134118C2semidirect
6. #19134086C2semidirect
7. #19133975C2semidirect
8. #19133968C2semidirect
9. #19133814C2semidirect
10. #19133800C2semidirect
11. #19133760C2semidirect
13. #19133483C2semidirect
14. SD16×C43⋊C8C2semidirect
169. SD16×C43SD16semidirect
258. C43⋊C8#137semidirect
353. C43#19895semidirect
457. SD16#10621883semidirect

Maximal subgroups

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

subgroupindex
#191475032
Q8×#106218832
#191469522
#191341892
#191341182
#191340862
#191339752
#191339682
#191338142
#191338002
#191337602
#191337462
#191334832
SD16×C43⋊C82
C43×#32762
#1989543