Finite Group Databasebeta

← #25088012

Subgroups — #25088012

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#19147505C211yesmaximal, characteristic, complemented
2SD16×Dic86C211yesmaximal, characteristic, complemented
3#19146237C211yesmaximal, characteristic
4#19134190C211yesmaximal, characteristic, complemented
5#19134116C211yesmaximal, characteristic, complemented
6#19134087C211yesmaximal, characteristic, complemented
7#19133974C211yesmaximal, characteristic, complemented
8#19133970C211yesmaximal, characteristic, complemented
9#19133815C211yesmaximal, characteristic, complemented
10#19133802C211yesmaximal, characteristic, complemented
11#19133759C211yesmaximal, characteristic, complemented
12#19133746C211yesmaximal, characteristic
13#19133486C211yesmaximal, characteristic, complemented
14C8×#10621883C211yesmaximal, characteristic, complemented
15C43×#3335C211yesmaximal, characteristic
16C2×#13063355—21no—
17Q8×Dic86C2211yescharacteristic
18D4×Dic86C2211yescharacteristic
19#14583309—21no—
20#14583302C2211yescharacteristic
21#14583297C2211yescharacteristic
22#14583296—21no—
23#14583278C2211yescharacteristic
24#14583251C2211yescharacteristic
25#14583249C2211yescharacteristic
26#14583203—21no—
27#14583191C2211yescharacteristic
28#14583189C2211yescharacteristic
29#14583189C2211yescharacteristic
30#14583187—21no—
31#14583184C2211yescharacteristic
32#14583182—21no—
33#14583179—21no—
34#14583155—21no—
35#14583106C2211yescharacteristic
36#14583104C2211yescharacteristic
37#14583061—21no—
38#14583054—21no—
39#14583030C2211yescharacteristic
40C8×Dic86C2211yescharacteristic
41#14582999—21no—
42SD16×Dic43—21no—
43C4×#10621883C2211yescharacteristic
44#14582977C2211yescharacteristic
45#14582650C2211yescharacteristic
46#14582649C2211yescharacteristic
47#14582648C2211yescharacteristic
48#14582647C2211yescharacteristic
49#14582645C2211yescharacteristic
50#14582644C2211yescharacteristic
51Q8⋊(C43⋊C8)C2211yescharacteristic
52#14582629C2211yescharacteristic
53D4⋊(C43⋊C8)C2211yescharacteristic
54D4⋊(C43⋊C8)C2211yescharacteristic
55C8×C43⋊C8C2211yescharacteristic
56C43×#554C2211yescharacteristic
57C43×#547C2211yescharacteristic
58C43×#498C2211yescharacteristic
59C43×#483—21no—
60C43×#481—21no—
61C43×#476C2211yescharacteristic
62C43×#475C2211yescharacteristic
63C43×#465—21no—
64C4×SD16×C43C2211yescharacteristic
65C8×D4×C43C2211yescharacteristic
66C2×#106×C43—21no—
67C22×Dic86—21no—
68#13063355—44no—
69C2×#10621885—21no—
70C2×#10621885—21no—
71C2×#10621885—21no—
72C2×#10621883—21no—
73C2×#10621883D411yescharacteristic
74C2×#10621877—21no—
75#13063325—21no—
76#13063325C2311yescharacteristic
77#13063325C2311yescharacteristic
78#13063324—21no—
79#13063324—21no—
80#13063324—41no—
81#13063304—21no—
82#13063302—41no—
83Q8×Dic43—21no—
84C4×Dic86—21no—
85C4×Dic86C2311yescharacteristic
86D4×Dic43—21no—
87#13063258—21no—
88#13063258—21no—
89#13063258—21no—
90#13063257—21no—
91#13063257—21no—
92#13063256—21no—
93#13063256—21no—
94#13063256—21no—
95#13063256D411yescharacteristic
96C4⋊(C43⋊C8)—21no—
97C4⋊(C43⋊C8)C2311yescharacteristic
98C4⋊(C43⋊C8)C2311yescharacteristic
99C4⋊(C43⋊C8)C2311yescharacteristic
100Dic43⋊C8—21no—
101#13063249—21no—
102#13063249—21no—
103#13063249—41no—
104#13063248—21no—
105#13063248—21no—
106#13063248—41no—
107#13063248D411yescharacteristic
108#13063246—21no—
109#13063246—21no—
110#13063246D411yescharacteristic
111C22⋊(C43⋊C8)—21no—
112#13063236—21no—
113C4×C43⋊C8C2311yescharacteristic
114C4×C43⋊C8C2311yescharacteristic
115C8×Dic43—21no—
116C2×#41×C43—21no—
117C2×SD16×C43D411yescharacteristic
118C22×C8×C43—21no—
119C4⋊Q8×C43C2311yescharacteristic
120C4⋊Q8×C43C2311yescharacteristic
121#125×C43—21no—
122#123×C43—41no—
123C22⋊Q8×C43—21no—
124C22⋊Q8×C43—21no—
125C22⋊Q8×C43—41no—
126#121×C43—21no—
127C4×Q8×C43C2311yescharacteristic
128C4×D4×C43—21no—
129C4×D4×C43C2311yescharacteristic
130C4×D4×C43C2311yescharacteristic
131C2×C4⋊C4×C43—21no—
132C2×C4⋊C4×C43—21no—
133#106×C43—21no—
134#106×C43—21no—
135#106×C43—21no—
136#106×C43—21no—
137#106×C43D411yescharacteristic
138C4⋊C8×C43C2311yescharacteristic
139#103×C43—21no—
140#103×C43D411yescharacteristic
141#102×C43—21no—
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×C43C2×D411yescharacteristic
150C2×D4×C43—41no—
151C2×D4×C43C2×D411yescharacteristic
152C2×D4×C43C2×D411yescharacteristic
153C22×C4×C43—21no—
154C22×C4×C43—21no—
155C22×C4×C43—41no—
156C22×C4×C43—41no—
157C22×Dic43—41no—
158C2×Dic86—21no—
159C2×Dic86—21no—
160C2×Dic86—42no—
161C2×Dic86—41no—
162C2×Dic86—41no—
163C2×Dic86—81no—
164C2×Dic86C2×D411yescharacteristic
165SD16×C43—22no—
166C2×C8×C43—21no—
167C2×C8×C43—42no—
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×C43—41no—
178C4⋊C4×C43C2×D411yescharacteristic
179C4⋊C4×C43C2×D411yescharacteristic
180C4⋊C4×C43C2×D411yescharacteristic
181C22⋊C4×C43—21no—
182C22⋊C4×C43—21no—
183C22⋊C4×C43—41no—
184C22⋊C4×C43—41no—
185C42×C43—21no—
186C42×C43C2411yescharacteristic
187C22⋊Dic43—41no—
188#10621885—42no—
189#10621885—42no—
190#10621885—81no—
191#10621883—42no—
192#10621883SD1614yescomplemented
193C4⋊Dic43—21no—
194C4⋊Dic43—21no—
195C4⋊Dic43—21no—
196C4⋊Dic43—21no—
197C4⋊Dic43—41no—
198C4⋊Dic43C2×D411yescharacteristic
199Dic43⋊C4—21no—
200Dic43⋊C4—41no—
201Dic43⋊C4—41no—
202C4×Dic43—21no—
203C4×Dic43—41no—
204#10621877—42no—
205C2×C43⋊C8—21no—
206C2×C43⋊C8—21no—
207C2×C43⋊C8—21no—
208C2×C43⋊C8—21no—
209C2×C43⋊C8C2×D411yescharacteristic
210C2×C43⋊C8C2×D411yescharacteristic
211C23×C43—21no—
212C23×C43—21no—
213Q8×C43—21no—
214Q8×C43—21no—
215Q8×C43—41no—
216Q8×C43—41no—
217Q8×C43—81no—
218D4×C43—21no—
219D4×C43—21no—
220D4×C43—21no—
221D4×C43—82no—
222D4×C43C2×SD1612yes—
223C2×C4×C43—21no—
224C2×C4×C43—21no—
225C2×C4×C43—21no—
226C2×C4×C43—21no—
227C2×C4×C43—41no—
228C2×C4×C43—41no—
229C2×C4×C43—41no—
230C2×C4×C43—41no—
231C2×C4×C43—41no—
232C2×C4×C43—41no—
233C2×C4×C43—82no—
234C2×C4×C43—161no—
235C2×C4×C43C22×D411yescharacteristic
236C2×C4×C43C22×D411yescharacteristic
237C2×C4×C43H(5,𝔽2)11yescharacteristic
238C2×Dic43—21no—
239C2×Dic43—21no—
240C2×Dic43—41no—
241C2×Dic43—41no—
242C2×Dic43—82no—
243Dic86—21no—
244Dic86—41no—
245Dic86—41no—
246Dic86—82no—
247Dic86—81no—
248Dic86—161no—
249Dic86C2×SD1612yes—
250C8×C43—21no—
251C8×C43—41no—
252C8×C43#13712yescomplemented
253C43⋊C8—21no—
254C43⋊C8—41no—
255C43⋊C8—41no—
256C43⋊C8—41no—
257C43⋊C8—41no—
258C43⋊C8C2×SD1612yes—
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—21no—
268C4×C43—41no—
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—22no—
279Dic43—41no—
280Dic43—81no—
281Dic43—81no—
282#3385—431no—
283Q8×SD16—431no—
284#3335D4311yescharacteristic
285#3276—431no—
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—861no—
303Q82—431no—
304#554C2×D4311yescharacteristic
305D4×Q8—431no—
306#547C2×D4311yescharacteristic
307#501—861no—
308#500—431no—
309#498—431no—
310#498—861no—
311#498C2×D4311yescharacteristic
312#494—431no—
313#487—431no—
314#487—431no—
315#483—21no—
316#481—21no—
317#479—861no—
318#477—431no—
319#476—431no—
320#476—431no—
321#476—861no—
322#476C2×D4311yescharacteristic
323#475—431no—
324#475—861no—
325#475C2×D4311yescharacteristic
326#474—861no—
327#470—861no—
328#465—21no—
329#462—431no—
330#461—431no—
331#452—861no—
332#451—861no—
333#446—431no—
334C8×Q8—431no—
335#440—861no—
336C4×SD16—431no—
337C4×SD16—861no—
338C4×SD16C2×D4311yescharacteristic
339#436—431no—
340C8×D4C2×D4311yescharacteristic
341C2×#106—21no—
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—861no—
356#137—1724no—
357C2×Q16—861no—
358C2×Q16—861no—
359C2×Q16—861no—
360C2×SD16—431no—
361C2×SD16—861no—
362C2×SD16C22⋊D4311yescharacteristic
363C2×M16—861no—
364C22×C8—21no—
365C4⋊Q8—431no—
366C4⋊Q8—431no—
367C4⋊Q8—861no—
368C4⋊Q8—861no—
369C4⋊Q8—861no—
370C4⋊Q8—1721no—
371C4⋊Q8C22×D4311yescharacteristic
372C4⋊Q8C22×D4311yescharacteristic
373#125—21no—
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—21no—
391#107—861no—
392#107—861no—
393#107—861no—
394#106—21no—
395#106—21no—
396#106—21no—
397#106—21no—
398#106—431no—
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—431no—
413#103—861no—
414#103—861no—
415#103—861no—
416#103—861no—
417#103—1721no—
418#103—1721no—
419#103C22⋊D4311yescharacteristic
420#102—21no—
421#102—431no—
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—431no—
437C2×Q8—861no—
438C2×Q8—861no—
439C2×Q8—3441no—
440C2×Q8—1721no—
441C2×Q8—1721no—
442C2×Q8—1722no—
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—3441no—
453Q16—1722no—
454Q16—1722no—
455SD16—22no—
456SD16—434no—
457SD16—1722no—
458M16—1722no—
459C2×C8—21no—
460C2×C8—42no—
461C2×C8—431no—
462C2×C8—431no—
463C2×C8—861no—
464C2×C8—861no—
465C2×C8—861no—
466C2×C8—861no—
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—41no—
477C4⋊C4—431no—
478C4⋊C4—861no—
479C4⋊C4—861no—
480C4⋊C4—861no—
481C4⋊C4—861no—
482C4⋊C4—861no—
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—21no—
502Q8—41no—
503Q8—41no—
504Q8—81no—
505Q8—432no—
506Q8—861no—
507Q8—3441no—
508Q8—3442no—
509Q8—1721no—
510Q8—1721no—
511Q8—6881no—
512D4—21no—
513D4—21no—
514D4—21no—
515D4—82no—
516D4SD16×D4312yes—
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—161no—
529C2×C4—861no—
530C2×C4—861no—
531C2×C4—3442no—
532C2×C4—1721no—
533C2×C4—1721no—
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—
545C8#1306335512yescomplemented
546C22—22no—
547C22—41no—
548C22—41no—
549C22—41no—
550C22—41no—
551C22—41no—
552C22D4×C22⋊D4311yescharacteristic
553C4—21no—
554C4—41no—
555C4—41no—
556C4—41no—
557C4—41no—
558C4—81no—
559C4—81no—
560C4—862no—
561C4—3441no—
562C4—3441no—
563C4—1721no—
564C4C2×SD16×D4311yescharacteristic
565C4C2×#1306335511yescharacteristic
566C4#1458370511yescharacteristic
567C4#1458371411yescharacteristic
568C2—42no—
569C2—81no—
570C2#1914623711yescharacteristic
571C2SD16×C22⋊D4311yescharacteristic
572C2#1914637511yescharacteristic
subgroupG/H
centerC22D4×C22⋊D43
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#3335C2
socleC22×C43D42
prime radicalC43×#547C22
hypercenter#3335D43
hypocenterC43#19895
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #3335

Complements

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

NH ≅ G/Ntype
1. #19147505C2semidirect
2. SD16×Dic86C2semidirect
4. #19134190C2semidirect
5. #19134116C2semidirect
6. #19134087C2semidirect
7. #19133974C2semidirect
8. #19133970C2semidirect
9. #19133815C2semidirect
10. #19133802C2semidirect
11. #19133759C2semidirect
13. #19133486C2semidirect
14. C8×#10621883C2semidirect
192. #10621883SD16semidirect
252. C8×C43#137semidirect
353. C43#19895semidirect
545. C8#13063355semidirect

Maximal subgroups

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

subgroupindex
#191475052
SD16×Dic862
#191462372
#191341902
#191341162
#191340872
#191339742
#191339702
#191338152
#191338022
#191337592
#191337462
#191334862
C8×#106218832
C43×#33352
#1989543