Finite Group Databasebeta

← #25086285

Subgroups — #25086285

Order 11008.

606 conjugacy classes of subgroups.

The subgroup lattice has 582 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19147242C211yesmaximal, characteristic, complemented
2#19146911C211yesmaximal, characteristic, complemented
3#19146512C211yesmaximal, characteristic, complemented
4#19134240C211yesmaximal, characteristic, complemented
5#19134140C211yesmaximal, characteristic, complemented
6#19134046C211yesmaximal, characteristic, complemented
7#19134044C211yesmaximal, characteristic, complemented
8#19133986C211yesmaximal, characteristic, complemented
9#19133879C211yesmaximal, characteristic, complemented
10#19133864C211yesmaximal, characteristic, complemented
11#19133808C211yesmaximal, characteristic, complemented
12#19133746C211yesmaximal, characteristic, complemented
13#19133425C211yesmaximal, characteristic, complemented
14#19133407C211yesmaximal, characteristic, complemented
15C43×#3334C211yesmaximal, characteristic
16#14583619C2211yescharacteristic
17#14583606C2211yescharacteristic
18#14583295C2211yescharacteristic
19#14583252—21no—
20#14583251C2211yescharacteristic
21#14583250C2211yescharacteristic
22#14583249C2211yescharacteristic
23#14583249C2211yescharacteristic
24#14583237—21no—
25#14583227—21no—
26#14583205—21no—
27#14583189C2211yescharacteristic
28#14583189C2211yescharacteristic
29#14583179C2211yescharacteristic
30#14583155—21no—
31#14583138—21no—
32#14583112—21no—
33#14583106C2211yescharacteristic
34#14583106C2211yescharacteristic
35#14583104C2211yescharacteristic
36#14583061—21no—
37#14583061—21no—
38C8×Dic86C2211yescharacteristic
39#14582990—21no—
40C4×#10621883C2211yescharacteristic
41#14582977C2211yescharacteristic
42D4×C43⋊C8C2211yescharacteristic
43#14582900—21no—
44#14582895—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
56C43×#547C2211yescharacteristic
57C43×#547C2211yescharacteristic
58C43×#500C2211yescharacteristic
59C43×#480—21no—
60C43×#480—21no—
61C43×#474C2211yescharacteristic
62C43×#474C2211yescharacteristic
63C43×#466—21no—
64C4×D8×C43C2211yescharacteristic
65C8×D4×C43C2211yescharacteristic
66C2×#107×C43—21no—
67C2×#10621885—21no—
68C2×#10621885—21no—
69C2×#10621883—21no—
70C2×#10621883D411yescharacteristic
71C2×#10621877—21no—
72C22×C43⋊C8—21no—
73#13063325C2311yescharacteristic
74#13063325C2311yescharacteristic
75#13063318—41no—
76#13063316—21no—
77#13063312—21no—
78#13063304—21no—
79#13063304—21no—
80#13063302—41no—
81C4×Dic86C2311yescharacteristic
82#13063290—21no—
83D4×Dic43—21no—
84#13063284—21no—
85C2×C4⋊Dic43—21no—
86#13063258—21no—
87#13063256—21no—
88#13063256—21no—
89#13063256—41no—
90#13063256D411yescharacteristic
91C4⋊(C43⋊C8)C2311yescharacteristic
92C4⋊(C43⋊C8)C2311yescharacteristic
93C4⋊(C43⋊C8)C2311yescharacteristic
94Dic43⋊C8—21no—
95#13063250—21no—
96#13063250—21no—
97#13063249—21no—
98#13063249—21no—
99#13063249—21no—
100#13063249—21no—
101#13063249—21no—
102#13063249—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—
117C2×D8×C43D411yescharacteristic
118C22×C8×C43—21no—
119C4⋊Q8×C43C2311yescharacteristic
120C4⋊Q8×C43C2311yescharacteristic
121#123×C43—41no—
122#123×C43—41no—
123C22⋊Q8×C43—21no—
124C22⋊Q8×C43—21no—
125#121×C43—21no—
126#121×C43—21no—
127C4×D4×C43C2311yescharacteristic
128C4×D4×C43C2311yescharacteristic
129C4×D4×C43C2311yescharacteristic
130C2×C4⋊C4×C43—21no—
131C2×C4⋊C4×C43—21no—
132#107×C43—21no—
133#107×C43—21no—
134#107×C43—21no—
135#107×C43—21no—
136#107×C43D411yescharacteristic
137C4⋊C8×C43C2311yescharacteristic
138#102×C43—21no—
139#102×C43—21no—
140#102×C43D411yescharacteristic
141#102×C43D411yescharacteristic
142C22⋊C8×C43—21no—
143C4×C8×C43C2311yescharacteristic
144#41×C43—42no—
145#41×C43—42no—
146#41×C43—81no—
147#41×C43—81no—
148C2×Q8×C43—21no—
149C2×Q8×C43—21no—
150C2×D4×C43—41no—
151C2×D4×C43—41no—
152C2×D4×C43C2×D411yescharacteristic
153C2×D4×C43C2×D411yescharacteristic
154C2×D4×C43C2×D411yescharacteristic
155C22×C4×C43—21no—
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×Dic86C2×D411yescharacteristic
164D8×C43—41no—
165C2×C8×C43—21no—
166C2×C8×C43—42no—
167C2×C8×C43C2×D411yescharacteristic
168C2×C8×C43C2×D411yescharacteristic
169C4⋊C4×C43—21no—
170C4⋊C4×C43—21no—
171C4⋊C4×C43—21no—
172C4⋊C4×C43—21no—
173C4⋊C4×C43—41no—
174C4⋊C4×C43—41no—
175C4⋊C4×C43C2×D411yescharacteristic
176C4⋊C4×C43C2×D411yescharacteristic
177C4⋊C4×C43C2×D411yescharacteristic
178C22⋊C4×C43—21no—
179C22⋊C4×C43—21no—
180C22⋊C4×C43—21no—
181C22⋊C4×C43—41no—
182C22⋊C4×C43—41no—
183C42×C43C2411yescharacteristic
184C22⋊Dic43—41no—
185C22⋊Dic43—41no—
186C22⋊Dic43—41no—
187#10621885—81no—
188#10621885—81no—
189#10621883—22no—
190#10621883—42no—
191C4⋊Dic43—21no—
192C4⋊Dic43—21no—
193C4⋊Dic43—21no—
194C4⋊Dic43—21no—
195C4⋊Dic43—41no—
196C4⋊Dic43C2×D411yescharacteristic
197Dic43⋊C4—21no—
198Dic43⋊C4—41no—
199Dic43⋊C4—41no—
200C4×Dic43—21no—
201C4×Dic43—41no—
202#10621877—81no—
203C2×C43⋊C8—21no—
204C2×C43⋊C8—21no—
205C2×C43⋊C8—21no—
206C2×C43⋊C8—21no—
207C2×C43⋊C8—81no—
208C2×C43⋊C8C2×D411yescharacteristic
209C2×C43⋊C8C2×D411yescharacteristic
210C23×C43—21no—
211C23×C43—21no—
212C23×C43—21no—
213Q8×C43—41no—
214Q8×C43—41no—
215Q8×C43—41no—
216Q8×C43—41no—
217D4×C43—21no—
218D4×C43—21no—
219D4×C43—21no—
220D4×C43—21no—
221D4×C43—21no—
222D4×C43—82no—
223D4×C43—82no—
224D4×C43#13512yes—
225C2×C4×C43—21no—
226C2×C4×C43—21no—
227C2×C4×C43—21no—
228C2×C4×C43—41no—
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—41no—
236C2×C4×C43—82no—
237C2×C4×C43—82no—
238C2×C4×C43C22×D411yescharacteristic
239C2×C4×C43C22×D411yescharacteristic
240C2×C4×C43H(5,𝔽2)11yescharacteristic
241C2×Dic43—21no—
242C2×Dic43—21no—
243C2×Dic43—41no—
244C2×Dic43—41no—
245C2×Dic43—161no—
246Dic86—21no—
247Dic86—21no—
248Dic86—41no—
249Dic86—41no—
250Dic86—81no—
251C8×C43—21no—
252C8×C43—21no—
253C8×C43—41no—
254C43⋊C8—21no—
255C43⋊C8—21no—
256C43⋊C8—41no—
257C43⋊C8—41no—
258C43⋊C8—41no—
259C43⋊C8—41no—
260#19778—431nomaximal, Sylow
261C22×C43—22no—
262C22×C43—41no—
263C22×C43—41no—
264C22×C43—41no—
265C22×C43—41no—
266C22×C43—41no—
267C22×C43—41no—
268C22×C43—41no—
269C22×C43—41no—
270C22×C43D4211yescharacteristic
271C4×C43—21no—
272C4×C43—41no—
273C4×C43—41no—
274C4×C43—41no—
275C4×C43—81no—
276C4×C43—81no—
277C4×C43C2×#13511yescharacteristic
278C4×C43#57511yescharacteristic
279C4×C43#57611yescharacteristic
280C4×C43#57811yescharacteristic
281Dic43—41no—
282Dic43—41no—
283Dic43—81no—
284Dic43—81no—
285#3360—431no—
286#3334D4311yescharacteristic
287#3331—431no—
288#3302—431no—
289#1718—431no—
290#1699—431no—
291#1683—431no—
292#1683—431no—
293#1674—431no—
294#1654—431no—
295#1652—431no—
296#1644—431no—
297#1635—431no—
298#1581—431no—
299SD16⋊C8—431no—
300C2×C43—42no—
301C2×C43—81no—
302C2×C43—81no—
303C2×C43#326911yescharacteristic
304C2×C43#328011yescharacteristic
305C2×C43#328911yescharacteristic
306#556—431no—
307#554—431no—
308#547C2×D4311yescharacteristic
309#547C2×D4311yescharacteristic
310#500C2×D4311yescharacteristic
311#498—431no—
312#488—861no—
313#487—431no—
314#487—431no—
315#487—431no—
316#487—431no—
317#485—861no—
318#483—861no—
319#480—21no—
320#480—21no—
321#479—861no—
322#476—431no—
323#476—431no—
324#474—431no—
325#474C2×D4311yescharacteristic
326#474C2×D4311yescharacteristic
327#470—861no—
328#467—861no—
329#466—21no—
330#463—861no—
331#462—431no—
332#462—431no—
333#461—431no—
334#452—861no—
335#452—861no—
336C8×Q8—431no—
337C4×SD16—431no—
338C4×SD16—861no—
339C4×D8C2×D4311yescharacteristic
340#436—431no—
341C8×D4—431no—
342C8×D4C2×D4311yescharacteristic
343C2×#107—21no—
344#417—861no—
345#416—861no—
346#335—431no—
347#335—431no—
348#333—431no—
349#332—431no—
350#332—431no—
351#332—431no—
352Q8⋊C8—431no—
353D4⋊C8—431no—
354D4⋊C8—431no—
355D4⋊C8—431no—
356#322—431no—
357C43#1977811yescharacteristic, complemented, Sylow
358C2×#41—21no—
359C2×#41—21no—
360C2×Q16—861no—
361C2×Q16—861no—
362C2×SD16—431no—
363C2×SD16—861no—
364C2×D8C22⋊D4311yescharacteristic
365C2×M16—861no—
366C22×C8—21no—
367C22×C8—861no—
368C4⋊Q8—431no—
369C4⋊Q8—431no—
370C4⋊Q8C22×D4311yescharacteristic
371C4⋊Q8C22×D4311yescharacteristic
372#126—1721no—
373#125—861no—
374#124—861no—
375#123—41no—
376#123—41no—
377C22⋊Q8—21no—
378C22⋊Q8—21no—
379C22⋊Q8—861no—
380C22⋊Q8—861no—
381C22⋊Q8—1721no—
382#121—21no—
383#121—21no—
384C4×Q8—431no—
385C4×Q8—861no—
386C4×D4—861no—
387C4×D4C22×D4311yescharacteristic
388C4×D4C22×D4311yescharacteristic
389C4×D4C22×D4311yescharacteristic
390#117—861no—
391C2×C4⋊C4—21no—
392C2×C4⋊C4—21no—
393C2×C4⋊C4—861no—
394#107—21no—
395#107—21no—
396#107—21no—
397#107—21no—
398#107—861no—
399#107C22⋊D4311yescharacteristic
400#106—431no—
401#106—861no—
402#106—861no—
403#106—1721no—
404C4⋊C8—431no—
405C4⋊C8—431no—
406C4⋊C8—431no—
407C4⋊C8—861no—
408C4⋊C8C22×D4311yescharacteristic
409#103—431no—
410#103—861no—
411#103—861no—
412#103—861no—
413#103—861no—
414#103—861no—
415#103—861no—
416#103—861no—
417#103—861no—
418#103—861no—
419#103—1721no—
420#102—21no—
421#102—21no—
422#102—431no—
423#102—861no—
424#102—861no—
425#102—861no—
426#102C22⋊D4311yescharacteristic
427#102C22⋊D4311yescharacteristic
428C22⋊C8—21no—
429C22⋊C8—861no—
430C22⋊C8—861no—
431C4×C8—431no—
432C4×C8—431no—
433C4×C8—861no—
434C4×C8C22×D4311yescharacteristic
435#41—42no—
436#41—42no—
437#41—81no—
438#41—81no—
439C2×Q8—21no—
440C2×Q8—21no—
441C2×Q8—431no—
442C2×Q8—861no—
443C2×Q8—861no—
444C2×D4—41no—
445C2×D4—41no—
446C2×D4D4×D4311yescharacteristic
447C2×D4C2×C22⋊D4311yescharacteristic
448C2×D4C2×C22⋊D4311yescharacteristic
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—41no—
453C22×C4—41no—
454C22×C4—1721no—
455Q16—3441no—
456Q16—3441no—
457SD16—862no—
458SD16—1722no—
459D8—41no—
460M16—3441no—
461C2×C8—21no—
462C2×C8—42no—
463C2×C8—431no—
464C2×C8—431no—
465C2×C8—861no—
466C2×C8—861no—
467C2×C8—861no—
468C2×C8—861no—
469C2×C8—3441no—
470C2×C8C2×C22⋊D4311yescharacteristic
471C2×C8C2×C22⋊D4311yescharacteristic
472C4⋊C4—21no—
473C4⋊C4—21no—
474C4⋊C4—21no—
475C4⋊C4—21no—
476C4⋊C4—41no—
477C4⋊C4—41no—
478C4⋊C4—431no—
479C4⋊C4—861no—
480C4⋊C4—861no—
481C4⋊C4—861no—
482C4⋊C4—861no—
483C4⋊C4—861no—
484C4⋊C4—1721no—
485C4⋊C4—1721no—
486C4⋊C4—1721no—
487C4⋊C4D4×D4311yescharacteristic
488C4⋊C4C2×C22⋊D4311yescharacteristic
489C4⋊C4C2×C22⋊D4311yescharacteristic
490C22⋊C4—21no—
491C22⋊C4—21no—
492C22⋊C4—21no—
493C22⋊C4—41no—
494C22⋊C4—41no—
495C22⋊C4—1721no—
496C22⋊C4—1721no—
497C22⋊C4—1721no—
498C42—861no—
499C42—1721no—
500C42C23×D4311yescharacteristic
501C23—21no—
502C23—21no—
503C23—21no—
504Q8—41no—
505Q8—41no—
506Q8—41no—
507Q8—41no—
508Q8—861no—
509Q8—861no—
510Q8—3441no—
511Q8—1721no—
512Q8—1721no—
513D4—21no—
514D4—21no—
515D4—21no—
516D4—21no—
517D4—21no—
518D4—82no—
519D4—82no—
520D4#1306334412yes—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—41no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—41no—
531C2×C4—41no—
532C2×C4—82no—
533C2×C4—82no—
534C2×C4—861no—
535C2×C4—861no—
536C2×C4—1721no—
537C2×C4—1721no—
538C2×C4—6881no—
539C2×C4C2×D4×D4311yescharacteristic
540C2×C4C22×C22⋊D4311yescharacteristic
541C2×C4#1306337011yescharacteristic
542C8—21no—
543C8—21no—
544C8—41no—
545C8—861no—
546C8—861no—
547C8—1721no—
548C8—1721no—
549C8—1721no—
550C8—1721no—
551C22—22no—
552C22—41no—
553C22—41no—
554C22—41no—
555C22—41no—
556C22—41no—
557C22—41no—
558C22—41no—
559C22—41no—
560C22D4×C22⋊D4311yescharacteristic
561C4—21no—
562C4—41no—
563C4—41no—
564C4—41no—
565C4—81no—
566C4—81no—
567C4—3441no—
568C4—3441no—
569C4—1721no—
570C4—1721no—
571C4C2×#1306334411yescharacteristic
572C4#1458369711yescharacteristic
573C4#1458370011yescharacteristic
574C4#1458371411yescharacteristic
575C2—42no—
576C2—81no—
577C2—81no—
578C2#1914614611yescharacteristic
579C2#1914628011yescharacteristic
580C2#1914636611yescharacteristic
subgroupG/H
centerC22D4×C22⋊D43
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
Fitting, prime radicalC43×#3334C2
socleC22×C43D42
hypercenter#3334D43
hypocenterC43#19778
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #3334

Complements

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

NH ≅ G/Ntype
1. #19147242C2semidirect
2. #19146911C2semidirect
3. #19146512C2semidirect
4. #19134240C2semidirect
5. #19134140C2semidirect
6. #19134046C2semidirect
7. #19134044C2semidirect
8. #19133986C2semidirect
9. #19133879C2semidirect
10. #19133864C2semidirect
11. #19133808C2semidirect
12. #19133746C2semidirect
13. #19133425C2semidirect
14. #19133407C2semidirect
357. C43#19778semidirect

Maximal subgroups

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

subgroupindex
#191472422
#191469112
#191465122
#191342402
#191341402
#191340462
#191340442
#191339862
#191338792
#191338642
#191338082
#191337462
#191334252
#191334072
C43×#33342
#1977843