Finite Group Databasebeta

← #25086763

Subgroups — #25086763

Order 11008.

632 conjugacy classes of subgroups.

The subgroup lattice has 586 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19147576C211yesmaximal, characteristic
2#19147484C211yesmaximal, characteristic, complemented
3#19147237C211yesmaximal, characteristic, complemented
4#19134214C211yesmaximal, characteristic, complemented
5#19134108C211yesmaximal, characteristic, complemented
6#19134027C211yesmaximal, characteristic, complemented
7#19133941C211yesmaximal, characteristic, complemented
8#19133940C211yesmaximal, characteristic, complemented
9#19133870C211yesmaximal, characteristic, complemented
10#19133858C211yesmaximal, characteristic, complemented
11#19133795C211yesmaximal, characteristic
12#19133690C211yesmaximal, characteristic, complemented
13#19133436C211yesmaximal, characteristic, complemented
14#19133414C211yesmaximal, characteristic, complemented
15C43×#3278C211yesmaximal, characteristic
16#14583628C2211yescharacteristic
17#14583628C2211yescharacteristic
18#14583304C2211yescharacteristic
19#14583300—21no—
20#14583295C2211yescharacteristic
21#14583271—21no—
22#14583271C2211yescharacteristic
23#14583251—21no—
24#14583251C2211yescharacteristic
25#14583245C2211yescharacteristic
26#14583208—21no—
27#14583208—21no—
28#14583184C2211yescharacteristic
29#14583184C2211yescharacteristic
30#14583181—21no—
31#14583181C2211yescharacteristic
32#14583104—21no—
33#14583104—21no—
34#14583104C2211yescharacteristic
35#14583104C2211yescharacteristic
36#14583096—21no—
37#14583096C2211yescharacteristic
38Q8×C43⋊C8C2211yescharacteristic
39Q8×C43⋊C8C2211yescharacteristic
40C8×Dic86C2211yescharacteristic
41Q16×Dic43—21no—
42C4×#10621883—21no—
43C4×#10621883—21no—
44C4×#10621883C2211yescharacteristic
45#14582650C2211yescharacteristic
46#14582649C2211yescharacteristic
47#14582645C2211yescharacteristic
48#14582644C2211yescharacteristic
49#14582644C2211yescharacteristic
50#14582643C2211yescharacteristic
51Q8⋊(C43⋊C8)C2211yescharacteristic
52Q8⋊(C43⋊C8)C2211yescharacteristic
53#14582629C2211yescharacteristic
54D4⋊(C43⋊C8)C2211yescharacteristic
55#14582620C2211yescharacteristic
56C2×#137×C43—21no—
57C43×#550C2211yescharacteristic
58D4×Q8×C43C2211yescharacteristic
59C43×#492C2211yescharacteristic
60C43×#468—21no—
61C43×#462C2211yescharacteristic
62C43×#460C2211yescharacteristic
63C43×#452—21no—
64C43×#448—21no—
65C4×Q16×C43C2211yescharacteristic
66C43×#436C2211yescharacteristic
67C2×#10621883—21no—
68C2×#10621883—21no—
69C2×#10621883—21no—
70C2×#10621883—21no—
71C2×#10621883—21no—
72C2×#10621883D411yescharacteristic
73#13063325—21no—
74#13063325—21no—
75#13063325C2311yescharacteristic
76#13063325C2311yescharacteristic
77#13063316—21no—
78#13063316—21no—
79#13063316—41no—
80#13063316—41no—
81Q8×Dic43—21no—
82Q8×Dic43—21no—
83C4×Dic86—21no—
84C4×Dic86—21no—
85C4×Dic86C2311yescharacteristic
86#13063259—21no—
87#13063259—21no—
88#13063256—21no—
89#13063256—21no—
90#13063256—21no—
91#13063256—41no—
92#13063256D411yescharacteristic
93C4⋊(C43⋊C8)—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#13063248—21no—
102#13063248—21no—
103#13063248—21no—
104#13063248—21no—
105#13063248—21no—
106#13063248D411yescharacteristic
107#13063246—21no—
108#13063246—41no—
109#13063246D411yescharacteristic
110C4×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×C43D411yescharacteristic
120C2×SD16×C43—21no—
121C2×SD16×C43—21no—
122C2×SD16×C43—21no—
123C2×M16×C43—21no—
124C4⋊Q8×C43—21no—
125C4⋊Q8×C43C2311yescharacteristic
126#127×C43—21no—
127#127×C43C2311yescharacteristic
128C22⋊Q8×C43—21no—
129C22⋊Q8×C43—41no—
130#121×C43—21no—
131#121×C43—41no—
132C4×Q8×C43C2311yescharacteristic
133C4×Q8×C43C2311yescharacteristic
134C4×D4×C43—21no—
135C4×D4×C43—21no—
136C4×D4×C43C2311yescharacteristic
137#107×C43D411yescharacteristic
138C4⋊C8×C43C2311yescharacteristic
139#103×C43—21no—
140#103×C43D411yescharacteristic
141#103×C43D411yescharacteristic
142#102×C43—21no—
143C22⋊C8×C43—21no—
144C4×C8×C43C2311yescharacteristic
145#41×C43—42no—
146#41×C43—81no—
147C2×Q8×C43—21no—
148C2×Q8×C43—41no—
149C2×Q8×C43—42no—
150C2×Q8×C43—81no—
151C2×Q8×C43C2×D411yescharacteristic
152C2×Q8×C43C2×D411yescharacteristic
153C2×D4×C43—21no—
154C2×D4×C43—21no—
155C2×D4×C43—21no—
156C2×D4×C43—41no—
157C2×D4×C43—41no—
158C2×D4×C43C2×D411yescharacteristic
159C22×C4×C43—21no—
160C22×C4×C43—41no—
161C22×C4×C43—41no—
162C2×Dic86—21no—
163C2×Dic86—21no—
164C2×Dic86C2×D411yescharacteristic
165Q16×C43—42no—
166Q16×C43SD1614yescomplemented
167SD16×C43—42no—
168SD16×C43—42no—
169SD16×C43—81no—
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—41no—
179C4⋊C4×C43C2×D411yescharacteristic
180C4⋊C4×C43C2×D411yescharacteristic
181C4⋊C4×C43C2×D411yescharacteristic
182C22⋊C4×C43—21no—
183C22⋊C4×C43—41no—
184C22⋊C4×C43—41no—
185C42×C43—21no—
186C42×C43—21no—
187C42×C43C2411yescharacteristic
188#10621883—41no—
189#10621883—42no—
190#10621883—42no—
191#10621883—81no—
192#10621883—81no—
193#10621883—81no—
194C4⋊Dic43—21no—
195C4⋊Dic43—21no—
196C4⋊Dic43—21no—
197C4⋊Dic43—21no—
198C4⋊Dic43—41no—
199C4⋊Dic43—41no—
200C4⋊Dic43—41no—
201C4⋊Dic43—41no—
202C4⋊Dic43C2×D411yescharacteristic
203Dic43⋊C4—21no—
204Dic43⋊C4—41no—
205Dic43⋊C4—41no—
206C4×Dic43—21no—
207C4×Dic43—41no—
208C4×Dic43—41no—
209C2×C43⋊C8—21no—
210C2×C43⋊C8—21no—
211C2×C43⋊C8—21no—
212C2×C43⋊C8—21no—
213C2×C43⋊C8C2×D411yescharacteristic
214C2×C43⋊C8C2×D411yescharacteristic
215C23×C43—21no—
216C23×C43—41no—
217Q8×C43—21no—
218Q8×C43—21no—
219Q8×C43—41no—
220Q8×C43—41no—
221Q8×C43—82no—
222Q8×C43C2×SD1612yes—
223Q8×C43C2×SD1612yes—
224D4×C43—21no—
225D4×C43—21no—
226D4×C43—41no—
227D4×C43—41no—
228D4×C43—41no—
229D4×C43—41no—
230D4×C43—82no—
231D4×C43—81no—
232D4×C43—161no—
233C2×C4×C43—21no—
234C2×C4×C43—21no—
235C2×C4×C43—21no—
236C2×C4×C43—21no—
237C2×C4×C43—21no—
238C2×C4×C43—41no—
239C2×C4×C43—41no—
240C2×C4×C43—41no—
241C2×C4×C43—82no—
242C2×C4×C43—82no—
243C2×C4×C43C22×D411yescharacteristic
244C2×C4×C43C22×D411yescharacteristic
245C2×C4×C43H(5,𝔽2)11yescharacteristic
246C2×Dic43—21no—
247C2×Dic43—21no—
248C2×Dic43—41no—
249C2×Dic43—41no—
250Dic86—21no—
251Dic86—21no—
252Dic86—41no—
253Dic86—41no—
254Dic86—41no—
255Dic86—41no—
256C8×C43—21no—
257C8×C43—41no—
258C8×C43C2×SD1612yes—
259C43⋊C8—21no—
260C43⋊C8—21no—
261C43⋊C8—41no—
262C43⋊C8—41no—
263C43⋊C8—41no—
264C43⋊C8—41no—
265#19810—431nomaximal, Sylow
266C22×C43—41no—
267C22×C43—41no—
268C22×C43—41no—
269C22×C43—81no—
270C22×C43—81no—
271C22×C43—81no—
272C22×C43D4211yescharacteristic
273C4×C43—22no—
274C4×C43—22no—
275C4×C43—21no—
276C4×C43—41no—
277C4×C43—41no—
278C4×C43—41no—
279C4×C43—81no—
280C4×C43C22×SD1611yescharacteristic
281C4×C43#57511yescharacteristic
282C4×C43#57711yescharacteristic
283C4×C43#57711yescharacteristic
284Dic43—41no—
285Dic43—41no—
286Dic43—81no—
287Dic43—81no—
288#3392—431no—
289#3383—431no—
290#3359—431no—
291#3278D4311yescharacteristic
292#1714—431no—
293#1693—431no—
294#1680—431no—
295#1666—431no—
296#1666—431no—
297#1653—431no—
298#1651—431no—
299#1642—431no—
300#1626—431no—
301#1583—431no—
302#1579—431no—
303C2×C43—81no—
304C2×C43—161no—
305C2×C43#327111yescharacteristic
306C2×C43D4×SD1611yescharacteristic
307C2×C43#328911yescharacteristic
308C2×#137—21no—
309#557—431no—
310#557—431no—
311#550C2×D4311yescharacteristic
312D4×Q8C2×D4311yescharacteristic
313#500—431no—
314#499—861no—
315#498—431no—
316#492—431no—
317#492—861no—
318#492C2×D4311yescharacteristic
319#487—431no—
320#487—861no—
321#486—431no—
322#479—861no—
323#479—861no—
324#475—431no—
325#475—431no—
326#475—431no—
327#475—861no—
328#468—21no—
329#462C2×D4311yescharacteristic
330#461—431no—
331#461—431no—
332#461—861no—
333#461—861no—
334#460—431no—
335#460—861no—
336#460C2×D4311yescharacteristic
337#452—21no—
338#448—21no—
339C8×Q8—431no—
340C8×Q8—431no—
341C8×Q8—431no—
342C4×Q16—861no—
343C4×Q16C2×D4311yescharacteristic
344C4×SD16—431no—
345C4×SD16—861no—
346C4×SD16—861no—
347#436C2×D4311yescharacteristic
348#334—431no—
349#334—431no—
350#332—431no—
351#332—431no—
352#332—431no—
353#331—431no—
354Q8⋊C8—431no—
355Q8⋊C8—431no—
356Q8⋊C8—431no—
357D4⋊C8—431no—
358#322—431no—
359C43#1981011yescharacteristic, complemented, Sylow
360C2×#41—21no—
361C22×Q8—21no—
362#137—44no—
363C2×Q16—21no—
364C2×Q16C22⋊D4311yescharacteristic
365C2×SD16—21no—
366C2×SD16—21no—
367C2×SD16—21no—
368C2×SD16—431no—
369C2×SD16—861no—
370C2×SD16—861no—
371C2×SD16—861no—
372C2×SD16—861no—
373C2×SD16—861no—
374C2×M16—21no—
375C4⋊Q8—21no—
376C4⋊Q8—431no—
377C4⋊Q8—431no—
378C4⋊Q8—861no—
379C4⋊Q8—861no—
380C4⋊Q8C22×D4311yescharacteristic
381#127—21no—
382#127C22×D4311yescharacteristic
383#125—861no—
384#125—861no—
385#125—1721no—
386#125—1721no—
387C22⋊Q8—21no—
388C22⋊Q8—41no—
389#121—21no—
390#121—41no—
391C4×Q8—431no—
392C4×Q8—861no—
393C4×Q8—861no—
394C4×Q8—861no—
395C4×Q8—861no—
396C4×Q8C22×D4311yescharacteristic
397C4×Q8C22×D4311yescharacteristic
398C4×D4—21no—
399C4×D4—21no—
400C4×D4C22×D4311yescharacteristic
401#107—861no—
402#107—861no—
403#107C22⋊D4311yescharacteristic
404#106—431no—
405#106—861no—
406#106—861no—
407#106—861no—
408#106—1721no—
409C4⋊C8—431no—
410C4⋊C8—431no—
411C4⋊C8—431no—
412C4⋊C8—861no—
413C4⋊C8—861no—
414C4⋊C8—861no—
415C4⋊C8C22×D4311yescharacteristic
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—861no—
425#103C22⋊D4311yescharacteristic
426#103C22⋊D4311yescharacteristic
427#102—21no—
428#102—431no—
429#102—861no—
430#102—1721no—
431C22⋊C8—21no—
432C4×C8—431no—
433C4×C8—431no—
434C4×C8—861no—
435C4×C8—861no—
436C4×C8—861no—
437C4×C8C22×D4311yescharacteristic
438#41—42no—
439#41—81no—
440C2×Q8—21no—
441C2×Q8—41no—
442C2×Q8—42no—
443C2×Q8—81no—
444C2×Q8—431no—
445C2×Q8—861no—
446C2×Q8—861no—
447C2×Q8C2×C22⋊D4311yescharacteristic
448C2×Q8C2×C22⋊D4311yescharacteristic
449C2×D4—21no—
450C2×D4—21no—
451C2×D4—21no—
452C2×D4—41no—
453C2×D4—41no—
454C2×D4D4×D4311yescharacteristic
455C22×C4—21no—
456C22×C4—41no—
457C22×C4—41no—
458Q16—42no—
459Q16#1062188314yescomplemented
460SD16—42no—
461SD16—42no—
462SD16—81no—
463SD16—3441no—
464SD16—3441no—
465SD16—3441no—
466SD16—1721no—
467SD16—1722no—
468SD16—1722no—
469M16—42no—
470C2×C8—21no—
471C2×C8—431no—
472C2×C8—431no—
473C2×C8—861no—
474C2×C8—861no—
475C2×C8—861no—
476C2×C8—861no—
477C2×C8C2×C22⋊D4311yescharacteristic
478C2×C8C2×C22⋊D4311yescharacteristic
479C4⋊C4—21no—
480C4⋊C4—21no—
481C4⋊C4—21no—
482C4⋊C4—21no—
483C4⋊C4—41no—
484C4⋊C4—431no—
485C4⋊C4—861no—
486C4⋊C4—861no—
487C4⋊C4—861no—
488C4⋊C4—861no—
489C4⋊C4—861no—
490C4⋊C4—1721no—
491C4⋊C4—1721no—
492C4⋊C4—1721no—
493C4⋊C4—1721no—
494C4⋊C4—1721no—
495C4⋊C4—1721no—
496C4⋊C4D4×D4311yescharacteristic
497C4⋊C4C2×C22⋊D4311yescharacteristic
498C4⋊C4C2×C22⋊D4311yescharacteristic
499C22⋊C4—21no—
500C22⋊C4—41no—
501C22⋊C4—41no—
502C42—21no—
503C42—21no—
504C42—861no—
505C42—1721no—
506C42—1721no—
507C42C23×D4311yescharacteristic
508C23—21no—
509C23—41no—
510Q8—21no—
511Q8—21no—
512Q8—41no—
513Q8—41no—
514Q8—82no—
515Q8—861no—
516Q8—861no—
517Q8—1721no—
518Q8—1721no—
519Q8—1721no—
520Q8—1721no—
521Q8C2×#1062188312yes—
522Q8C2×#1062188312yes—
523D4—21no—
524D4—21no—
525D4—41no—
526D4—41no—
527D4—41no—
528D4—41no—
529D4—82no—
530D4—81no—
531D4—161no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—82no—
541C2×C4—82no—
542C2×C4—861no—
543C2×C4—861no—
544C2×C4—1721no—
545C2×C4—1721no—
546C2×C4C2×D4×D4311yescharacteristic
547C2×C4C22×C22⋊D4311yescharacteristic
548C2×C4#1306337011yescharacteristic
549C8—21no—
550C8—41no—
551C8—861no—
552C8—861no—
553C8—1721no—
554C8—1721no—
555C8—1721no—
556C8—1721no—
557C8C2×#1062188312yes—
558C22—41no—
559C22—41no—
560C22—41no—
561C22—81no—
562C22—81no—
563C22—81no—
564C22D4×C22⋊D4311yescharacteristic
565C4—22no—
566C4—22no—
567C4—21no—
568C4—41no—
569C4—41no—
570C4—41no—
571C4—81no—
572C4—3441no—
573C4—3441no—
574C4—1721no—
575C4—1721no—
576C4C22×#1062188311yescharacteristic
577C4#1458369811yescharacteristic
578C4#1458370811yescharacteristic
579C4#1458371011yescharacteristic
580C2—81no—
581C2—161no—
582C2#1914617411yescharacteristic
583C2D4×#1062188311yescharacteristic
584C2#1914636811yescharacteristic
subgroupG/H
centerC22D4×C22⋊D43
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#3278C2
socleC22×C43D42
prime radicalC43×#550C22
hypercenter#3278D43
hypocenterC43#19810
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #3278

Complements

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

NH ≅ G/Ntype
2. #19147484C2semidirect
3. #19147237C2semidirect
4. #19134214C2semidirect
5. #19134108C2semidirect
6. #19134027C2semidirect
7. #19133941C2semidirect
8. #19133940C2semidirect
9. #19133870C2semidirect
10. #19133858C2semidirect
12. #19133690C2semidirect
13. #19133436C2semidirect
14. #19133414C2semidirect
166. Q16×C43SD16semidirect
359. C43#19810semidirect
459. Q16#10621883semidirect

Maximal subgroups

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

subgroupindex
#191475762
#191474842
#191472372
#191342142
#191341082
#191340272
#191339412
#191339402
#191338702
#191338582
#191337952
#191336902
#191334362
#191334142
C43×#32782
#1981043