Finite Group Databasebeta

← #25087515

Subgroups — #25087515

Order 11008.

632 conjugacy classes of subgroups.

The subgroup lattice has 588 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19147242C211yesmaximal, characteristic, complemented
2#19147179C211yesmaximal, characteristic, complemented
3#19146952C211yesmaximal, characteristic, complemented
4#19134270C211yesmaximal, characteristic, complemented
5#19134092C211yesmaximal, characteristic, complemented
6#19134046C211yesmaximal, characteristic, complemented
7#19133982C211yesmaximal, characteristic, complemented
8#19133962C211yesmaximal, characteristic, complemented
9#19133849C211yesmaximal, characteristic, complemented
10#19133830C211yesmaximal, characteristic, complemented
11#19133800C211yesmaximal, characteristic, complemented
12#19133746C211yesmaximal, characteristic, complemented
13#19133425C211yesmaximal, characteristic, complemented
14#19133407C211yesmaximal, characteristic, complemented
15C43×#3283C211yesmaximal, characteristic
16#14583619C2211yescharacteristic
17#14583606C2211yescharacteristic
18#14583302C2211yescharacteristic
19#14583302C2211yescharacteristic
20#14583295C2211yescharacteristic
21#14583252—21no—
22#14583251C2211yescharacteristic
23#14583250C2211yescharacteristic
24#14583234—21no—
25#14583229—21no—
26#14583220—21no—
27#14583215—21no—
28#14583205—21no—
29#14583189C2211yescharacteristic
30#14583189C2211yescharacteristic
31#14583181C2211yescharacteristic
32#14583181C2211yescharacteristic
33#14583179C2211yescharacteristic
34#14583143—21no—
35#14583126—21no—
36#14583112—21no—
37#14583104C2211yescharacteristic
38C8×Dic86C2211yescharacteristic
39#14582990—21no—
40C4×#10621883C2211yescharacteristic
41#14582977C2211yescharacteristic
42D4×C43⋊C8C2211yescharacteristic
43#14582939—21no—
44C2×#13063256—21no—
45#14582652C2211yescharacteristic
46#14582651C2211yescharacteristic
47#14582647C2211yescharacteristic
48#14582646C2211yescharacteristic
49#14582645C2211yescharacteristic
50#14582645C2211yescharacteristic
51#14582629C2211yescharacteristic
52D4⋊(C43⋊C8)C2211yescharacteristic
53D4⋊(C43⋊C8)C2211yescharacteristic
54D4⋊(C43⋊C8)C2211yescharacteristic
55#14582621C2211yescharacteristic
56C2×#135×C43—21no—
57C43×#547C2211yescharacteristic
58C43×#547C2211yescharacteristic
59C43×#494C2211yescharacteristic
60C43×#467—21no—
61C43×#461C2211yescharacteristic
62C43×#461C2211yescharacteristic
63C43×#452—21no—
64C43×#452—21no—
65C4×D8×C43C2211yescharacteristic
66C8×D4×C43C2211yescharacteristic
67C2×#10621883—21no—
68C2×#10621883D411yescharacteristic
69C2×#10621877—21no—
70C22×C43⋊C8—21no—
71#13063325C2311yescharacteristic
72#13063325C2311yescharacteristic
73#13063318—41no—
74#13063316—21no—
75#13063312—21no—
76#13063304—21no—
77#13063304—21no—
78#13063302—41no—
79C4×Dic86C2311yescharacteristic
80#13063290—21no—
81D4×Dic43—21no—
82#13063284—21no—
83C2×C4⋊Dic43—21no—
84#13063258—21no—
85#13063258—21no—
86#13063258—21no—
87#13063258—41no—
88#13063256—21no—
89#13063256—21no—
90#13063256—21no—
91#13063256—21no—
92#13063256—21no—
93#13063256—21no—
94#13063256D411yescharacteristic
95C4⋊(C43⋊C8)C2311yescharacteristic
96C4⋊(C43⋊C8)C2311yescharacteristic
97C4⋊(C43⋊C8)C2311yescharacteristic
98Dic43⋊C8—21no—
99#13063250—21no—
100#13063250—21no—
101#13063248—21no—
102#13063248—21no—
103#13063248—21no—
104#13063248—41no—
105#13063248D411yescharacteristic
106#13063246—21no—
107#13063246—21no—
108#13063246—21no—
109#13063246D411yescharacteristic
110C22⋊(C43⋊C8)—21no—
111C22⋊(C43⋊C8)—21no—
112C4×C43⋊C8C2311yescharacteristic
113C4×C43⋊C8C2311yescharacteristic
114C8×Dic43—21no—
115C2×#41×C43—21no—
116C2×#41×C43—21no—
117#135×C43—44no—
118C2×Q16×C43—21no—
119C2×Q16×C43—21no—
120C2×SD16×C43—21no—
121C2×SD16×C43—21no—
122C2×D8×C43D411yescharacteristic
123C22×C8×C43—21no—
124C4⋊Q8×C43C2311yescharacteristic
125C4⋊Q8×C43C2311yescharacteristic
126#123×C43—41no—
127#123×C43—41no—
128C22⋊Q8×C43—21no—
129C22⋊Q8×C43—21no—
130#121×C43—21no—
131#121×C43—21no—
132C4×D4×C43C2311yescharacteristic
133C4×D4×C43C2311yescharacteristic
134C4×D4×C43C2311yescharacteristic
135C2×C4⋊C4×C43—21no—
136C2×C4⋊C4×C43—21no—
137#107×C43D411yescharacteristic
138C4⋊C8×C43C2311yescharacteristic
139#103×C43—21no—
140#103×C43—21no—
141#102×C43D411yescharacteristic
142#102×C43D411yescharacteristic
143C22⋊C8×C43—21no—
144C4×C8×C43C2311yescharacteristic
145#41×C43—42no—
146#41×C43—42no—
147#41×C43—81no—
148#41×C43—81no—
149C2×Q8×C43—21no—
150C2×Q8×C43—21no—
151C2×D4×C43—41no—
152C2×D4×C43—41no—
153C2×D4×C43C2×D411yescharacteristic
154C2×D4×C43C2×D411yescharacteristic
155C2×D4×C43C2×D411yescharacteristic
156C22×C4×C43—21no—
157C22×C4×C43—21no—
158C22×C4×C43—21no—
159C22×C4×C43—41no—
160C22×C4×C43—41no—
161C22×Dic43—41no—
162C2×Dic86—21no—
163C2×Dic86—21no—
164C2×Dic86C2×D411yescharacteristic
165Q16×C43—42no—
166Q16×C43—81no—
167SD16×C43—42no—
168SD16×C43—42no—
169D8×C43—22no—
170C2×C8×C43—21no—
171C2×C8×C43—42no—
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×C43—41no—
180C4⋊C4×C43C2×D411yescharacteristic
181C4⋊C4×C43C2×D411yescharacteristic
182C4⋊C4×C43C2×D411yescharacteristic
183C22⋊C4×C43—21no—
184C22⋊C4×C43—21no—
185C22⋊C4×C43—21no—
186C22⋊C4×C43—41no—
187C22⋊C4×C43—41no—
188C42×C43C2411yescharacteristic
189C22⋊Dic43—41no—
190C22⋊Dic43—41no—
191C22⋊Dic43—41no—
192#10621883—22no—
193#10621883—42no—
194C4⋊Dic43—21no—
195C4⋊Dic43—21no—
196C4⋊Dic43—21no—
197C4⋊Dic43—21no—
198C4⋊Dic43—41no—
199C4⋊Dic43C2×D411yescharacteristic
200Dic43⋊C4—21no—
201Dic43⋊C4—41no—
202Dic43⋊C4—41no—
203C4×Dic43—21no—
204C4×Dic43—41no—
205#10621877—42no—
206C2×C43⋊C8—21no—
207C2×C43⋊C8—21no—
208C2×C43⋊C8—21no—
209C2×C43⋊C8—21no—
210C2×C43⋊C8—42no—
211C2×C43⋊C8C2×D411yescharacteristic
212C2×C43⋊C8C2×D411yescharacteristic
213C23×C43—21no—
214C23×C43—21no—
215C23×C43—21no—
216Q8×C43—41no—
217Q8×C43—41no—
218Q8×C43—41no—
219Q8×C43—41no—
220D4×C43—21no—
221D4×C43—21no—
222D4×C43—21no—
223D4×C43—21no—
224D4×C43—21no—
225D4×C43—82no—
226D4×C43—82no—
227D4×C43AGL(1,ℤ/8)12yes—
228C2×C4×C43—21no—
229C2×C4×C43—21no—
230C2×C4×C43—21no—
231C2×C4×C43—41no—
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—41no—
239C2×C4×C43—82no—
240C2×C4×C43—82no—
241C2×C4×C43C22×D411yescharacteristic
242C2×C4×C43C22×D411yescharacteristic
243C2×C4×C43H(5,𝔽2)11yescharacteristic
244C2×Dic43—21no—
245C2×Dic43—21no—
246C2×Dic43—41no—
247C2×Dic43—41no—
248C2×Dic43—161no—
249Dic86—21no—
250Dic86—21no—
251Dic86—41no—
252Dic86—41no—
253Dic86—81no—
254C8×C43—21no—
255C8×C43—21no—
256C8×C43—41no—
257C43⋊C8—21no—
258C43⋊C8—41no—
259C43⋊C8—41no—
260C43⋊C8—41no—
261C43⋊C8—41no—
262C43⋊C8#13512yescomplemented
263#19860—431nomaximal, Sylow
264C22×C43—22no—
265C22×C43—41no—
266C22×C43—41no—
267C22×C43—41no—
268C22×C43—41no—
269C22×C43—41no—
270C22×C43—41no—
271C22×C43—41no—
272C22×C43—41no—
273C22×C43D4211yescharacteristic
274C4×C43—21no—
275C4×C43—41no—
276C4×C43—41no—
277C4×C43—41no—
278C4×C43—81no—
279C4×C43—81no—
280C4×C43C2×#13511yescharacteristic
281C4×C43C2×AGL(1,ℤ/8)11yescharacteristic
282C4×C43#57711yescharacteristic
283C4×C43#57811yescharacteristic
284Dic43—41no—
285Dic43—41no—
286Dic43—81no—
287Dic43—81no—
288#3360—431no—
289#3353—431no—
290#3335—431no—
291#3283D4311yescharacteristic
292#1723—431no—
293#1691—431no—
294#1683—431no—
295#1673—431no—
296#1670—431no—
297#1650—431no—
298#1647—431no—
299#1643—431no—
300#1635—431no—
301#1581—431no—
302SD16⋊C8—431no—
303C2×C43—42no—
304C2×C43—81no—
305C2×C43—81no—
306C2×C43#326511yescharacteristic
307C2×C43#328311yescharacteristic
308C2×C43#328911yescharacteristic
309C2×#135—21no—
310#556—431no—
311#554—431no—
312#547C2×D4311yescharacteristic
313#547C2×D4311yescharacteristic
314#500—431no—
315#500—431no—
316#498—431no—
317#494C2×D4311yescharacteristic
318#488—861no—
319#487—431no—
320#487—431no—
321#484—861no—
322#483—861no—
323#482—861no—
324#481—861no—
325#479—861no—
326#476—431no—
327#476—431no—
328#475—431no—
329#475—431no—
330#474—431no—
331#468—861no—
332#467—21no—
333#465—861no—
334#463—861no—
335#461—431no—
336#461C2×D4311yescharacteristic
337#461C2×D4311yescharacteristic
338#452—21no—
339#452—21no—
340C8×Q8—431no—
341C4×SD16—431no—
342C4×SD16—861no—
343C4×D8C2×D4311yescharacteristic
344#436—431no—
345C8×D4—431no—
346C8×D4C2×D4311yescharacteristic
347#428—861no—
348C2×#106—861no—
349#335—431no—
350#335—431no—
351#333—431no—
352#332—431no—
353#332—431no—
354#332—431no—
355Q8⋊C8—431no—
356D4⋊C8—431no—
357D4⋊C8—431no—
358D4⋊C8—431no—
359#322—431no—
360C43#1986011yescharacteristic, complemented, Sylow
361C2×#41—21no—
362C2×#41—21no—
363#135—44no—
364C2×Q16—21no—
365C2×Q16—21no—
366C2×SD16—21no—
367C2×SD16—21no—
368C2×SD16—431no—
369C2×SD16—861no—
370C2×D8C22⋊D4311yescharacteristic
371C2×M16—861no—
372C22×C8—21no—
373C22×C8—861no—
374C4⋊Q8—431no—
375C4⋊Q8—431no—
376C4⋊Q8C22×D4311yescharacteristic
377C4⋊Q8C22×D4311yescharacteristic
378#126—1721no—
379#125—861no—
380#124—861no—
381#123—41no—
382#123—41no—
383C22⋊Q8—21no—
384C22⋊Q8—21no—
385C22⋊Q8—861no—
386C22⋊Q8—861no—
387C22⋊Q8—1721no—
388#121—21no—
389#121—21no—
390C4×Q8—431no—
391C4×Q8—861no—
392C4×D4—861no—
393C4×D4C22×D4311yescharacteristic
394C4×D4C22×D4311yescharacteristic
395C4×D4C22×D4311yescharacteristic
396#117—861no—
397C2×C4⋊C4—21no—
398C2×C4⋊C4—21no—
399C2×C4⋊C4—861no—
400#107—861no—
401#107—861no—
402#107—861no—
403#107—1721no—
404#107C22⋊D4311yescharacteristic
405#106—431no—
406#106—861no—
407#106—861no—
408#106—861no—
409#106—861no—
410#106—861no—
411#106—861no—
412C4⋊C8—431no—
413C4⋊C8—431no—
414C4⋊C8—431no—
415C4⋊C8—861no—
416C4⋊C8C22×D4311yescharacteristic
417#103—21no—
418#103—21no—
419#103—431no—
420#103—861no—
421#103—861no—
422#103—861no—
423#103—861no—
424#103—861no—
425#103—1721no—
426#102—431no—
427#102—861no—
428#102—861no—
429#102—861no—
430#102C22⋊D4311yescharacteristic
431#102C22⋊D4311yescharacteristic
432C22⋊C8—21no—
433C22⋊C8—861no—
434C22⋊C8—861no—
435C4×C8—431no—
436C4×C8—431no—
437C4×C8—861no—
438C4×C8C22×D4311yescharacteristic
439#41—42no—
440#41—42no—
441#41—81no—
442#41—81no—
443C2×Q8—21no—
444C2×Q8—21no—
445C2×Q8—431no—
446C2×Q8—861no—
447C2×Q8—861no—
448C2×D4—41no—
449C2×D4—41no—
450C2×D4D4×D4311yescharacteristic
451C2×D4C2×C22⋊D4311yescharacteristic
452C2×D4C2×C22⋊D4311yescharacteristic
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—41no—
457C22×C4—41no—
458C22×C4—1721no—
459Q16—42no—
460Q16—81no—
461SD16—42no—
462SD16—42no—
463SD16—862no—
464SD16—1722no—
465D8—22no—
466M16—1722no—
467C2×C8—21no—
468C2×C8—42no—
469C2×C8—431no—
470C2×C8—431no—
471C2×C8—861no—
472C2×C8—861no—
473C2×C8—861no—
474C2×C8—861no—
475C2×C8—1722no—
476C2×C8C2×C22⋊D4311yescharacteristic
477C2×C8C2×C22⋊D4311yescharacteristic
478C4⋊C4—21no—
479C4⋊C4—21no—
480C4⋊C4—21no—
481C4⋊C4—21no—
482C4⋊C4—41no—
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⋊C4D4×D4311yescharacteristic
494C4⋊C4C2×C22⋊D4311yescharacteristic
495C4⋊C4C2×C22⋊D4311yescharacteristic
496C22⋊C4—21no—
497C22⋊C4—21no—
498C22⋊C4—21no—
499C22⋊C4—41no—
500C22⋊C4—41no—
501C22⋊C4—1721no—
502C22⋊C4—1721no—
503C22⋊C4—1721no—
504C42—861no—
505C42—1721no—
506C42C23×D4311yescharacteristic
507C23—21no—
508C23—21no—
509C23—21no—
510Q8—41no—
511Q8—41no—
512Q8—41no—
513Q8—41no—
514Q8—861no—
515Q8—861no—
516Q8—3441no—
517Q8—1721no—
518Q8—1721no—
519D4—21no—
520D4—21no—
521D4—21no—
522D4—21no—
523D4—21no—
524D4—82no—
525D4—82no—
526D4#1306335112yes—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—41no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—82no—
539C2×C4—82no—
540C2×C4—861no—
541C2×C4—861no—
542C2×C4—1721no—
543C2×C4—1721no—
544C2×C4—6881no—
545C2×C4C2×D4×D4311yescharacteristic
546C2×C4C22×C22⋊D4311yescharacteristic
547C2×C4#1306337011yescharacteristic
548C8—21no—
549C8—21no—
550C8—41no—
551C8—432no—
552C8—861no—
553C8—1721no—
554C8—1721no—
555C8—1721no—
556C8—1721no—
557C22—22no—
558C22—41no—
559C22—41no—
560C22—41no—
561C22—41no—
562C22—41no—
563C22—41no—
564C22—41no—
565C22—41no—
566C22D4×C22⋊D4311yescharacteristic
567C4—21no—
568C4—41no—
569C4—41no—
570C4—41no—
571C4—81no—
572C4—81no—
573C4—3441no—
574C4—3441no—
575C4—1721no—
576C4—1721no—
577C4#135×D4311yescharacteristic
578C4C2×#1306335111yescharacteristic
579C4#1458371011yescharacteristic
580C4#1458371311yescharacteristic
581C2—42no—
582C2—81no—
583C2—81no—
584C2#1914608611yescharacteristic
585C2#1914631111yescharacteristic
586C2#1914636611yescharacteristic
subgroupG/H
centerC22D4×C22⋊D43
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
Fitting, prime radicalC43×#3283C2
socleC22×C43D42
hypercenter#3283D43
hypocenterC43#19860
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #3283

Complements

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

NH ≅ G/Ntype
1. #19147242C2semidirect
2. #19147179C2semidirect
3. #19146952C2semidirect
4. #19134270C2semidirect
5. #19134092C2semidirect
6. #19134046C2semidirect
7. #19133982C2semidirect
8. #19133962C2semidirect
9. #19133849C2semidirect
10. #19133830C2semidirect
11. #19133800C2semidirect
12. #19133746C2semidirect
13. #19133425C2semidirect
14. #19133407C2semidirect
262. C43⋊C8#135semidirect
360. C43#19860semidirect

Maximal subgroups

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

subgroupindex
#191472422
#191471792
#191469522
#191342702
#191340922
#191340462
#191339822
#191339622
#191338492
#191338302
#191338002
#191337462
#191334252
#191334072
C43×#32832
#1986043