Finite Group Databasebeta

← #25086688

Subgroups — #25086688

Order 11008.

640 conjugacy classes of subgroups.

The subgroup lattice has 584 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1Q8×#10621883C211yesmaximal, characteristic, complemented
2SD16×Dic86C211yesmaximal, characteristic, complemented
3#19146454C211yesmaximal, characteristic
4#19134226C211yesmaximal, characteristic, complemented
5#19134094C211yesmaximal, characteristic, complemented
6#19134027C211yesmaximal, characteristic, complemented
7#19133968C211yesmaximal, characteristic, complemented
8#19133962C211yesmaximal, characteristic, complemented
9#19133858C211yesmaximal, characteristic, complemented
10#19133856C211yesmaximal, characteristic, complemented
11#19133814C211yesmaximal, characteristic, complemented
12#19133746C211yesmaximal, characteristic
13#19133436C211yesmaximal, characteristic, complemented
14SD16⋊(C43⋊C8)C211yesmaximal, characteristic, complemented
15C43×#3276C211yesmaximal, characteristic
16Q8×Dic86C2211yescharacteristic
17D4×Dic86C2211yescharacteristic
18#14583297C2211yescharacteristic
19#14583296—21no—
20#14583295—21no—
21#14583295C2211yescharacteristic
22#14583295C2211yescharacteristic
23#14583251C2211yescharacteristic
24#14583251C2211yescharacteristic
25#14583229—21no—
26#14583189—21no—
27#14583189C2211yescharacteristic
28#14583189C2211yescharacteristic
29#14583187—21no—
30#14583184C2211yescharacteristic
31#14583182—21no—
32#14583181—21no—
33#14583181C2211yescharacteristic
34#14583181C2211yescharacteristic
35#14583126—21no—
36#14583104C2211yescharacteristic
37#14583037—21no—
38Q8×C43⋊C8C2211yescharacteristic
39C8×Dic86C2211yescharacteristic
40SD16×Dic43—21no—
41C4×#10621883—21no—
42C4×#10621883C2211yescharacteristic
43D4×C43⋊C8C2211yescharacteristic
44C2×#13063248—21no—
45#14582652C2211yescharacteristic
46#14582649C2211yescharacteristic
47#14582647C2211yescharacteristic
48#14582645C2211yescharacteristic
49#14582645C2211yescharacteristic
50#14582644C2211yescharacteristic
51Q8⋊(C43⋊C8)C2211yescharacteristic
52#14582629C2211yescharacteristic
53D4⋊(C43⋊C8)C2211yescharacteristic
54D4⋊(C43⋊C8)C2211yescharacteristic
55#14582620C2211yescharacteristic
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
67C22×Dic86—21no—
68C2×#10621883—21no—
69C2×#10621883D411yescharacteristic
70C22×C43⋊C8—21no—
71#13063325—21no—
72#13063325C2311yescharacteristic
73#13063325C2311yescharacteristic
74#13063324—21no—
75#13063324—21no—
76#13063324—41no—
77#13063304—21no—
78#13063302—41no—
79Q8×Dic43—21no—
80C4×Dic86—21no—
81C4×Dic86C2311yescharacteristic
82D4×Dic43—21no—
83#13063257—21no—
84#13063257—21no—
85#13063256—21no—
86#13063256—21no—
87#13063256—21no—
88#13063256—21no—
89#13063256—21no—
90#13063256—21no—
91#13063256—21no—
92#13063256—41no—
93#13063256D411yescharacteristic
94C4⋊(C43⋊C8)—21no—
95C4⋊(C43⋊C8)C2311yescharacteristic
96C4⋊(C43⋊C8)C2311yescharacteristic
97C4⋊(C43⋊C8)C2311yescharacteristic
98Dic43⋊C8—21no—
99#13063249—21no—
100#13063248—21no—
101#13063248—21no—
102#13063248—21no—
103#13063248—21no—
104#13063248—21no—
105#13063248—41no—
106#13063248D411yescharacteristic
107#13063246—21no—
108#13063246—21no—
109#13063246D411yescharacteristic
110C22⋊(C43⋊C8)—21no—
111C4×C43⋊C8—21no—
112C4×C43⋊C8C2311yescharacteristic
113C4×C43⋊C8C2311yescharacteristic
114C8×Dic43—21no—
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—42no—
164C2×Dic86—41no—
165C2×Dic86—41no—
166C2×Dic86—81no—
167C2×Dic86C2×D411yescharacteristic
168Q16×C43—42no—
169Q16×C43—42no—
170Q16×C43—81no—
171SD16×C43—42no—
172SD16×C43SD1614yescomplemented
173M16×C43—42no—
174C2×C8×C43—21no—
175C2×C8×C43C2×D411yescharacteristic
176C2×C8×C43C2×D411yescharacteristic
177C4⋊C4×C43—21no—
178C4⋊C4×C43—21no—
179C4⋊C4×C43—21no—
180C4⋊C4×C43—21no—
181C4⋊C4×C43—21no—
182C4⋊C4×C43—41no—
183C4⋊C4×C43—41no—
184C4⋊C4×C43C2×D411yescharacteristic
185C4⋊C4×C43C2×D411yescharacteristic
186C4⋊C4×C43C2×D411yescharacteristic
187C22⋊C4×C43—21no—
188C22⋊C4×C43—21no—
189C22⋊C4×C43—41no—
190C22⋊C4×C43—41no—
191C42×C43—21no—
192C42×C43C2411yescharacteristic
193C22⋊Dic43—41no—
194#10621883—22no—
195#10621883—81no—
196C4⋊Dic43—21no—
197C4⋊Dic43—21no—
198C4⋊Dic43—21no—
199C4⋊Dic43—21no—
200C4⋊Dic43—41no—
201C4⋊Dic43C2×D411yescharacteristic
202Dic43⋊C4—21no—
203Dic43⋊C4—41no—
204Dic43⋊C4—41no—
205C4×Dic43—21no—
206C4×Dic43—41no—
207C2×C43⋊C8—21no—
208C2×C43⋊C8—21no—
209C2×C43⋊C8—21no—
210C2×C43⋊C8—21no—
211C2×C43⋊C8—81no—
212C2×C43⋊C8C2×D411yescharacteristic
213C2×C43⋊C8C2×D411yescharacteristic
214C23×C43—21no—
215C23×C43—21no—
216Q8×C43—21no—
217Q8×C43—41no—
218Q8×C43—41no—
219Q8×C43—41no—
220Q8×C43—41no—
221Q8×C43—82no—
222Q8×C43C2×SD1612yes—
223D4×C43—21no—
224D4×C43—21no—
225D4×C43—21no—
226D4×C43—82no—
227D4×C43C2×SD1612yes—
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—41no—
236C2×C4×C43—41no—
237C2×C4×C43—41no—
238C2×C4×C43—82no—
239C2×C4×C43—82no—
240C2×C4×C43C22×D411yescharacteristic
241C2×C4×C43C22×D411yescharacteristic
242C2×C4×C43H(5,𝔽2)11yescharacteristic
243C2×Dic43—21no—
244C2×Dic43—21no—
245C2×Dic43—41no—
246C2×Dic43—41no—
247C2×Dic43—82no—
248Dic86—21no—
249Dic86—41no—
250Dic86—41no—
251Dic86—82no—
252Dic86—81no—
253Dic86—161no—
254Dic86#13712yescomplemented
255C8×C43—21no—
256C8×C43—41no—
257C8×C43C2×SD1612yes—
258C43⋊C8—21no—
259C43⋊C8—21no—
260C43⋊C8—41no—
261C43⋊C8—41no—
262C43⋊C8—41no—
263C43⋊C8—41no—
264#19805—431nomaximal, Sylow
265C22×C43—22no—
266C22×C43—41no—
267C22×C43—41no—
268C22×C43—41no—
269C22×C43—41no—
270C22×C43—41no—
271C22×C43D4211yescharacteristic
272C4×C43—22no—
273C4×C43—21no—
274C4×C43—41no—
275C4×C43—41no—
276C4×C43—41no—
277C4×C43—81no—
278C4×C43—81no—
279C4×C43C22×SD1611yescharacteristic
280C4×C43C2×#13711yescharacteristic
281C4×C43#57711yescharacteristic
282C4×C43#57711yescharacteristic
283Dic43—22no—
284Dic43—41no—
285Dic43—81no—
286Dic43—81no—
287Q8×SD16—431no—
288Q8×SD16—431no—
289#3298—431no—
290#3276D4311yescharacteristic
291#1716—431no—
292#1691—431no—
293#1680—431no—
294#1671—431no—
295#1670—431no—
296#1651—431no—
297#1651—431no—
298#1645—431no—
299#1635—431no—
300#1583—431no—
301SD16⋊C8—431no—
302C2×C43—42no—
303C2×C43—81no—
304C2×C43#326611yescharacteristic
305C2×C43D4×SD1611yescharacteristic
306C2×C43#328911yescharacteristic
307C2×#137—21no—
308Q82—431no—
309D4×Q8—431no—
310D4×Q8C2×D4311yescharacteristic
311#547C2×D4311yescharacteristic
312#498—431no—
313#498—431no—
314#498—431no—
315#498—861no—
316#498—861no—
317#494C2×D4311yescharacteristic
318#487—431no—
319#487—431no—
320#483—861no—
321#476—431no—
322#476—431no—
323#476—861no—
324#476—861no—
325#475—431no—
326#475—431no—
327#475—431no—
328#475—861no—
329#475—861no—
330#470—21no—
331#465—861no—
332#462C2×D4311yescharacteristic
333#461—431no—
334#461C2×D4311yescharacteristic
335#452—21no—
336#451—21no—
337#448—861no—
338C8×Q8—431no—
339C8×Q8—431no—
340C4×SD16—431no—
341C4×SD16—861no—
342C4×SD16—861no—
343C4×SD16C2×D4311yescharacteristic
344#436C2×D4311yescharacteristic
345C8×D4—431no—
346C2×#103—861no—
347#335—431no—
348#334—431no—
349#333—431no—
350#332—431no—
351#332—431no—
352#332—431no—
353Q8⋊C8—431no—
354Q8⋊C8—431no—
355D4⋊C8—431no—
356D4⋊C8—431no—
357#322—431no—
358C43#1980511yescharacteristic, complemented, Sylow
359C2×#41—21no—
360C22×Q8—21no—
361C22×Q8—861no—
362#137—44no—
363C2×Q16—21no—
364C2×Q16—21no—
365C2×Q16—21no—
366C2×SD16—21no—
367C2×SD16—431no—
368C2×SD16—861no—
369C2×SD16C22⋊D4311yescharacteristic
370C2×M16—21no—
371C22×C8—861no—
372C4⋊Q8—21no—
373C4⋊Q8—431no—
374C4⋊Q8—431no—
375C4⋊Q8—861no—
376C4⋊Q8—861no—
377C4⋊Q8—861no—
378C4⋊Q8—1721no—
379C4⋊Q8C22×D4311yescharacteristic
380C4⋊Q8C22×D4311yescharacteristic
381#123—41no—
382C22⋊Q8—21no—
383C22⋊Q8—21no—
384C22⋊Q8—41no—
385C22⋊Q8—861no—
386C22⋊Q8—1721no—
387#121—21no—
388C4×Q8—431no—
389C4×Q8—861no—
390C4×Q8—861no—
391C4×Q8C22×D4311yescharacteristic
392C4×D4—21no—
393C4×D4—861no—
394C4×D4C22×D4311yescharacteristic
395C4×D4C22×D4311yescharacteristic
396C2×C4⋊C4—21no—
397#106—431no—
398#106—861no—
399#106—861no—
400#106—861no—
401#106—861no—
402#106—861no—
403#106—861no—
404#106—861no—
405#106—861no—
406#106—861no—
407#106—1721no—
408#106C22⋊D4311yescharacteristic
409C4⋊C8—431no—
410C4⋊C8—431no—
411C4⋊C8—431no—
412C4⋊C8—861no—
413C4⋊C8—861no—
414C4⋊C8C22×D4311yescharacteristic
415#103—21no—
416#103—21no—
417#103—431no—
418#103—861no—
419#103—861no—
420#103—861no—
421#103—861no—
422#103—861no—
423#103—861no—
424#103—1721no—
425#103C22⋊D4311yescharacteristic
426#102—431no—
427#102—861no—
428#102—861no—
429#102C22⋊D4311yescharacteristic
430C22⋊C8—21no—
431C22⋊C8—861no—
432C4×C8—431no—
433C4×C8—431no—
434C4×C8—861no—
435C4×C8—861no—
436C4×C8C22×D4311yescharacteristic
437#41—42no—
438#41—81no—
439C2×Q8—21no—
440C2×Q8—21no—
441C2×Q8—41no—
442C2×Q8—42no—
443C2×Q8—81no—
444C2×Q8—431no—
445C2×Q8—861no—
446C2×Q8—861no—
447C2×Q8—3441no—
448C2×Q8—1721no—
449C2×Q8—1721no—
450C2×Q8—1722no—
451C2×Q8C2×C22⋊D4311yescharacteristic
452C2×D4—41no—
453C2×D4D4×D4311yescharacteristic
454C2×D4C2×C22⋊D4311yescharacteristic
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—41no—
458C22×C4—41no—
459C22×C4—1721no—
460Q16—42no—
461Q16—42no—
462Q16—81no—
463SD16—42no—
464SD16—862no—
465SD16—3441no—
466SD16#1062188314yescomplemented
467M16—42no—
468C2×C8—21no—
469C2×C8—431no—
470C2×C8—431no—
471C2×C8—861no—
472C2×C8—861no—
473C2×C8—861no—
474C2×C8—861no—
475C2×C8—3441no—
476C2×C8C2×C22⋊D4311yescharacteristic
477C2×C8C2×C22⋊D4311yescharacteristic
478C4⋊C4—21no—
479C4⋊C4—21no—
480C4⋊C4—21no—
481C4⋊C4—21no—
482C4⋊C4—21no—
483C4⋊C4—41no—
484C4⋊C4—41no—
485C4⋊C4—431no—
486C4⋊C4—861no—
487C4⋊C4—861no—
488C4⋊C4—861no—
489C4⋊C4—861no—
490C4⋊C4—861no—
491C4⋊C4—1721no—
492C4⋊C4—1721no—
493C4⋊C4—1721no—
494C4⋊C4D4×D4311yescharacteristic
495C4⋊C4C2×C22⋊D4311yescharacteristic
496C4⋊C4C2×C22⋊D4311yescharacteristic
497C22⋊C4—21no—
498C22⋊C4—21no—
499C22⋊C4—41no—
500C22⋊C4—41no—
501C22⋊C4—1721no—
502C42—21no—
503C42—861no—
504C42—1721no—
505C42C23×D4311yescharacteristic
506C23—21no—
507C23—21no—
508Q8—21no—
509Q8—41no—
510Q8—41no—
511Q8—41no—
512Q8—41no—
513Q8—82no—
514Q8—432no—
515Q8—861no—
516Q8—3441no—
517Q8—3442no—
518Q8—1721no—
519Q8—1721no—
520Q8—6881no—
521Q8C2×#1062188312yes—
522D4—21no—
523D4—21no—
524D4—21no—
525D4—82no—
526D4C2×#1062188312yes—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—82no—
538C2×C4—82no—
539C2×C4—861no—
540C2×C4—861no—
541C2×C4—3442no—
542C2×C4—1721no—
543C2×C4—1721no—
544C2×C4C2×D4×D4311yescharacteristic
545C2×C4C22×C22⋊D4311yescharacteristic
546C2×C4#1306337011yescharacteristic
547C8—21no—
548C8—41no—
549C8—861no—
550C8—861no—
551C8—1721no—
552C8—1721no—
553C8—1721no—
554C8—1721no—
555C8C2×#1062188312yes—
556C22—22no—
557C22—41no—
558C22—41no—
559C22—41no—
560C22—41no—
561C22—41no—
562C22D4×C22⋊D4311yescharacteristic
563C4—22no—
564C4—21no—
565C4—41no—
566C4—41no—
567C4—41no—
568C4—81no—
569C4—81no—
570C4—862no—
571C4—3441no—
572C4—3441no—
573C4—1721no—
574C4C22×#1062188311yescharacteristic
575C4#137×D4311yescharacteristic
576C4#1458370811yescharacteristic
577C4#1458371011yescharacteristic
578C2—42no—
579C2—81no—
580C2#1914609911yescharacteristic
581C2D4×#1062188311yescharacteristic
582C2#1914636611yescharacteristic
subgroupG/H
centerC22D4×C22⋊D43
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#3276C2
socleC22×C43D42
prime radicalC43×#547C22
hypercenter#3276D43
hypocenterC43#19805
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. Q8×#10621883C2semidirect
2. SD16×Dic86C2semidirect
4. #19134226C2semidirect
5. #19134094C2semidirect
6. #19134027C2semidirect
7. #19133968C2semidirect
8. #19133962C2semidirect
9. #19133858C2semidirect
10. #19133856C2semidirect
11. #19133814C2semidirect
13. #19133436C2semidirect
14. SD16⋊(C43⋊C8)C2semidirect
172. SD16×C43SD16semidirect
254. Dic86#137semidirect
358. C43#19805semidirect
466. SD16#10621883semidirect

Maximal subgroups

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

subgroupindex
Q8×#106218832
SD16×Dic862
#191464542
#191342262
#191340942
#191340272
#191339682
#191339622
#191338582
#191338562
#191338142
#191337462
#191334362
SD16⋊(C43⋊C8)2
C43×#32762
#1980543