Finite Group Databasebeta

← #25080343

Subgroups — #25080343

Order 11008.

602 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#19145932C211yesmaximal, characteristic, complemented
2#19145309C211yesmaximal, characteristic, complemented
3#19143600C211yesmaximal, characteristic, complemented
4#19134161C211yesmaximal, characteristic, complemented
5#19134151C211yesmaximal, characteristic, complemented
6#19134106C211yesmaximal, characteristic, complemented
7#19134058C211yesmaximal, characteristic, complemented
8#19134030C211yesmaximal, characteristic, complemented
9#19134020C211yesmaximal, characteristic, complemented
10#19133987C211yesmaximal, characteristic, complemented
11#19133941C211yesmaximal, characteristic, complemented
12#19133348C211yesmaximal, characteristic, complemented
13#19133259C211yesmaximal, characteristic, complemented
14#19133244C211yesmaximal, characteristic, complemented
15C43×#3212C211yesmaximal, characteristic
16#14583456C2211yescharacteristic
17#14583302C2211yescharacteristic
18#14583271C2211yescharacteristic
19#14583251C2211yescharacteristic
20#14583245C2211yescharacteristic
21#14583203—21no—
22#14583184C2211yescharacteristic
23#14583179C2211yescharacteristic
24#14583143—21no—
25#14583143—21no—
26#14583138—21no—
27#14583126—21no—
28#14583118—21no—
29#14583109C2211yescharacteristic
30#14583104C2211yescharacteristic
31#14583030C2211yescharacteristic
32Q8×C43⋊C8C2211yescharacteristic
33#14582999—21no—
34#14582999—21no—
35#14582977—21no—
36#14582977C2211yescharacteristic
37#14582971—21no—
38D4×C43⋊C8C2211yescharacteristic
39#14582960—21no—
40#14582952C2211yescharacteristic
41C2×C4⋊(C43⋊C8)C2211yescharacteristic
42#14582855—21no—
43C4×#10621877C2211yescharacteristic
44#14582651C2211yescharacteristic
45#14582651C2211yescharacteristic
46#14582649C2211yescharacteristic
47#14582649C2211yescharacteristic
48#14582646C2211yescharacteristic
49#14582646C2211yescharacteristic
50#14582645C2211yescharacteristic
51#14582645C2211yescharacteristic
52#14582644C2211yescharacteristic
53#14582644C2211yescharacteristic
54#14582643C2211yescharacteristic
55#14582643C2211yescharacteristic
56C43×#532C2211yescharacteristic
57C43×#529C2211yescharacteristic
58C43×#495—21no—
59C43×#488—21no—
60C43×#462C2211yescharacteristic
61C43×#461C2211yescharacteristic
62C43×#460C2211yescharacteristic
63C43×#459C2211yescharacteristic
64C43×#452—21no—
65C43×#449—21no—
66C43×#431C2211yescharacteristic
67C2×#10621885—21no—
68C2×#10621883—21no—
69C2×#10621883—21no—
70C2×#10621883—21no—
71C2×#10621877—21no—
72C2×#10621877D411yescharacteristic
73C2×#10621877D411yescharacteristic
74C22×C43⋊C8—21no—
75C22×C43⋊C8—21no—
76#13063325C2311yescharacteristic
77#13063325C2311yescharacteristic
78#13063317—21no—
79#13063304—21no—
80#13063304—21no—
81C4×Dic86—21no—
82C4×Dic86—21no—
83#13063284—21no—
84#13063258—21no—
85#13063258—21no—
86#13063258—21no—
87#13063256—21no—
88C4⋊(C43⋊C8)—21no—
89C4⋊(C43⋊C8)—21no—
90C4⋊(C43⋊C8)—21no—
91C4⋊(C43⋊C8)C2311yescharacteristic
92C4⋊(C43⋊C8)C2311yescharacteristic
93C4⋊(C43⋊C8)C2311yescharacteristic
94C4⋊(C43⋊C8)C2311yescharacteristic
95#13063249—21no—
96#13063248—21no—
97#13063248—21no—
98#13063248—21no—
99#13063248—21no—
100#13063246—21no—
101#13063246—21no—
102#13063246—21no—
103C22⋊(C43⋊C8)—21no—
104C22⋊(C43⋊C8)—21no—
105C22⋊(C43⋊C8)—21no—
106#13063236—21no—
107#13063236D411yescharacteristic
108#13063236D411yescharacteristic
109C4×C43⋊C8—21no—
110C4×C43⋊C8—21no—
111C4×C43⋊C8C2311yescharacteristic
112C4×C43⋊C8C2311yescharacteristic
113C2×#41×C43—21no—
114C2×Q16×C43—21no—
115C2×SD16×C43—21no—
116C2×SD16×C43—21no—
117C2×D8×C43—21no—
118C4⋊Q8×C43C2311yescharacteristic
119#127×C43C2311yescharacteristic
120#126×C43—21no—
121#125×C43D411yescharacteristic
122#124×C43—21no—
123#124×C43D411yescharacteristic
124#123×C43—21no—
125C22⋊Q8×C43D411yescharacteristic
126#121×C43—21no—
127#121×C43—21no—
128#121×C43D411yescharacteristic
129C4×Q8×C43C2311yescharacteristic
130C4×D4×C43—21no—
131C4×D4×C43—21no—
132C4×D4×C43—21no—
133C4×D4×C43C2311yescharacteristic
134#117×C43—21no—
135C2×C42×C43C2311yescharacteristic
136C4⋊C8×C43C2311yescharacteristic
137C4⋊C8×C43C2311yescharacteristic
138#103×C43—21no—
139#103×C43—21no—
140#102×C43—21no—
141#102×C43—21no—
142C22⋊C8×C43—21no—
143C4×C8×C43—21no—
144#41×C43—81no—
145#41×C43—81no—
146C2×Q8×C43—21no—
147C2×Q8×C43C2×D411yescharacteristic
148C2×D4×C43—21no—
149C2×D4×C43—21no—
150C2×D4×C43—21no—
151C2×D4×C43—21no—
152C2×D4×C43—41no—
153C2×D4×C43C2×D411yescharacteristic
154C22×C4×C43—21no—
155C22×C4×C43—41no—
156C22×C4×C43C2×D411yescharacteristic
157C22×C4×C43C2×D411yescharacteristic
158C22×C4×C43#4111yescharacteristic
159C2×Dic86—21no—
160C2×Dic86—21no—
161Q16×C43—81no—
162SD16×C43—81no—
163SD16×C43—81no—
164D8×C43—81no—
165C2×C8×C43—21no—
166C2×C8×C43—21no—
167C4⋊C4×C43—21no—
168C4⋊C4×C43—21no—
169C4⋊C4×C43—21no—
170C4⋊C4×C43—21no—
171C4⋊C4×C43—21no—
172C4⋊C4×C43—21no—
173C4⋊C4×C43C2×D411yescharacteristic
174C4⋊C4×C43C2×D411yescharacteristic
175C22⋊C4×C43—21no—
176C22⋊C4×C43—21no—
177C22⋊C4×C43—21no—
178C22⋊C4×C43—21no—
179C22⋊C4×C43—21no—
180C22⋊C4×C43—41no—
181C22⋊C4×C43—41no—
182C42×C43—21no—
183C42×C43C2×D411yescharacteristic
184C42×C43C2×D411yescharacteristic
185C42×C43#4111yescharacteristic
186C42×C43C2411yescharacteristic
187C22⋊Dic43—41no—
188#10621885—81no—
189#10621883—42no—
190#10621883—42no—
191#10621883—81no—
192C4⋊Dic43—21no—
193C4⋊Dic43—21no—
194C4⋊Dic43—21no—
195C4⋊Dic43—21no—
196Dic43⋊C4—41no—
197Dic43⋊C4—41no—
198C4×Dic43—41no—
199#10621877—22no—
200#10621877—41no—
201#10621877—42no—
202C2×C43⋊C8—21no—
203C2×C43⋊C8—21no—
204C2×C43⋊C8—21no—
205C2×C43⋊C8—21no—
206C2×C43⋊C8—42no—
207C2×C43⋊C8—81no—
208C2×C43⋊C8C2×D411yescharacteristic
209C2×C43⋊C8C2×D411yescharacteristic
210C2×C43⋊C8C2×D411yescharacteristic
211C2×C43⋊C8C2×D411yescharacteristic
212C23×C43—21no—
213C23×C43—41no—
214C23×C43#12111yescharacteristic
215Q8×C43—21no—
216Q8×C43—21no—
217Q8×C43—41no—
218Q8×C43—41no—
219D4×C43—21no—
220D4×C43—21no—
221D4×C43—41no—
222D4×C43—41no—
223D4×C43—41no—
224D4×C43—41no—
225D4×C43—81no—
226D4×C43—81no—
227D4×C43—82no—
228C2×C4×C43—21no—
229C2×C4×C43—21no—
230C2×C4×C43—21no—
231C2×C4×C43—21no—
232C2×C4×C43—21no—
233C2×C4×C43—21no—
234C2×C4×C43—21no—
235C2×C4×C43—41no—
236C2×C4×C43—41no—
237C2×C4×C43—41no—
238C2×C4×C43—41no—
239C2×C4×C43—82no—
240C2×C4×C43#12111yescharacteristic
241C2×C4×C43#12111yescharacteristic
242C2×C4×C43#12111yescharacteristic
243C2×C4×C43C22×D411yescharacteristic
244C2×C4×C43C22×D411yescharacteristic
245C2×C4×C43C2×#4111yescharacteristic
246C2×Dic43—41no—
247C2×Dic43—41no—
248Dic86—41no—
249Dic86—41no—
250Dic86—41no—
251Dic86—41no—
252C8×C43—41no—
253C8×C43—41no—
254C43⋊C8—21no—
255C43⋊C8—21no—
256C43⋊C8—21no—
257C43⋊C8—41no—
258C43⋊C8—41no—
259C43⋊C8—41no—
260C43⋊C8—41no—
261C43⋊C8#13512yes—
262#19252—431nomaximal, Sylow
263C22×C43—21no—
264C22×C43—21no—
265C22×C43—21no—
266C22×C43—41no—
267C22×C43—41no—
268C22×C43—41no—
269C22×C43—81no—
270C22×C43—81no—
271C22×C43—81no—
272C22×C43C2×#12111yescharacteristic
273C4×C43—21no—
274C4×C43—21no—
275C4×C43—21no—
276C4×C43—21no—
277C4×C43—41no—
278C4×C43—41no—
279C4×C43—41no—
280C4×C43—81no—
281C4×C43C2×#13511yescharacteristic
282C4×C43#57511yescharacteristic
283C4×C43#57611yescharacteristic
284C4×C43#57711yescharacteristic
285Dic43—81no—
286Dic43—81no—
287#3248—431no—
288#3212D4311yescharacteristic
289#3182—431no—
290#2969—431no—
291#1702—431no—
292#1700—431no—
293#1693—431no—
294#1685—431no—
295#1681—431no—
296#1679—431no—
297#1674—431no—
298#1666—431no—
299#1565—431no—
300#1544—431no—
301#1540—431no—
302C2×C43—41no—
303C2×C43—81no—
304C2×C43—161no—
305C2×C43#303511yescharacteristic
306C2×C43#306211yescharacteristic
307C2×C43#306911yescharacteristic
308#533—431no—
309#532C2×D4311yescharacteristic
310#529C2×D4311yescharacteristic
311#500—431no—
312#495—21no—
313#492—431no—
314#488—21no—
315#487—431no—
316#486—431no—
317#479—861no—
318#475—431no—
319#474—431no—
320#468—861no—
321#468—861no—
322#467—861no—
323#465—861no—
324#464—861no—
325#462—431no—
326#462C2×D4311yescharacteristic
327#461—431no—
328#461C2×D4311yescharacteristic
329#460C2×D4311yescharacteristic
330#459C2×D4311yescharacteristic
331#452—21no—
332#449—21no—
333#446—431no—
334C8×Q8—431no—
335#440—861no—
336#440—861no—
337#436—431no—
338#436—861no—
339#435—861no—
340C8×D4—431no—
341#433—861no—
342#431—431no—
343#431C2×D4311yescharacteristic
344C2×C4⋊C8—431no—
345#405—861no—
346C4×M16—431no—
347#335—431no—
348#335—431no—
349#334—431no—
350#334—431no—
351#332—431no—
352#332—431no—
353#332—431no—
354#332—431no—
355#332—431no—
356#332—431no—
357#331—431no—
358#331—431no—
359C43#1925211yescharacteristic, complemented, Sylow
360C2×#41—21no—
361C2×Q16—21no—
362C2×Q16—861no—
363C2×SD16—21no—
364C2×SD16—21no—
365C2×SD16—861no—
366C2×SD16—861no—
367C2×SD16—861no—
368C2×D8—21no—
369C2×M16—431no—
370C2×M16—431no—
371C2×M16—861no—
372C22×C8—861no—
373C22×C8—861no—
374C4⋊Q8—431no—
375C4⋊Q8—431no—
376C4⋊Q8C22×D4311yescharacteristic
377#127C22×D4311yescharacteristic
378#126—21no—
379#125—861no—
380#125C22⋊D4311yescharacteristic
381#124—21no—
382#124C22⋊D4311yescharacteristic
383#123—21no—
384C22⋊Q8—861no—
385C22⋊Q8—861no—
386C22⋊Q8C22⋊D4311yescharacteristic
387#121—21no—
388#121—21no—
389#121C22⋊D4311yescharacteristic
390C4×Q8—861no—
391C4×Q8—861no—
392C4×Q8C22×D4311yescharacteristic
393C4×D4—21no—
394C4×D4—21no—
395C4×D4—21no—
396C4×D4C22×D4311yescharacteristic
397#117—21no—
398#117—861no—
399C2×C42C22×D4311yescharacteristic
400#107—861no—
401#107—861no—
402#107—861no—
403#106—861no—
404C4⋊C8—431no—
405C4⋊C8—431no—
406C4⋊C8—431no—
407C4⋊C8—431no—
408C4⋊C8—861no—
409C4⋊C8—861no—
410C4⋊C8—861no—
411C4⋊C8C22×D4311yescharacteristic
412C4⋊C8C22×D4311yescharacteristic
413#103—21no—
414#103—21no—
415#103—861no—
416#103—861no—
417#103—861no—
418#103—861no—
419#103—861no—
420#102—21no—
421#102—21no—
422#102—861no—
423#102—861no—
424#102—861no—
425C22⋊C8—21no—
426C22⋊C8—861no—
427C22⋊C8—861no—
428C22⋊C8—861no—
429#97—431no—
430#97—431no—
431#97—861no—
432C4×C8—21no—
433C4×C8—431no—
434C4×C8—431no—
435C4×C8—861no—
436C4×C8—861no—
437#41—81no—
438#41—81no—
439C2×Q8—21no—
440C2×Q8—861no—
441C2×Q8—861no—
442C2×Q8C2×C22⋊D4311yescharacteristic
443C2×D4—21no—
444C2×D4—21no—
445C2×D4—21no—
446C2×D4—21no—
447C2×D4—41no—
448C2×D4C2×C22⋊D4311yescharacteristic
449C22×C4—21no—
450C22×C4—41no—
451C22×C4D4×D4311yescharacteristic
452C22×C4#1062190011yescharacteristic
453C22×C4C2×C22⋊D4311yescharacteristic
454Q16—81no—
455Q16—3441no—
456SD16—81no—
457SD16—81no—
458SD16—3441no—
459SD16—1722no—
460SD16—1722no—
461D8—81no—
462M16—862no—
463M16—1722no—
464M16—1721no—
465C2×C8—21no—
466C2×C8—21no—
467C2×C8—431no—
468C2×C8—431no—
469C2×C8—431no—
470C2×C8—431no—
471C2×C8—861no—
472C2×C8—861no—
473C2×C8—861no—
474C2×C8—861no—
475C2×C8—3441no—
476C2×C8—1722no—
477C4⋊C4—21no—
478C4⋊C4—21no—
479C4⋊C4—21no—
480C4⋊C4—21no—
481C4⋊C4—21no—
482C4⋊C4—21no—
483C4⋊C4—861no—
484C4⋊C4—861no—
485C4⋊C4—861no—
486C4⋊C4—861no—
487C4⋊C4—1721no—
488C4⋊C4—1721no—
489C4⋊C4C2×C22⋊D4311yescharacteristic
490C4⋊C4C2×C22⋊D4311yescharacteristic
491C22⋊C4—21no—
492C22⋊C4—21no—
493C22⋊C4—21no—
494C22⋊C4—21no—
495C22⋊C4—21no—
496C22⋊C4—41no—
497C22⋊C4—41no—
498C22⋊C4—1721no—
499C42—21no—
500C42—1721no—
501C42D4×D4311yescharacteristic
502C42#1062190011yescharacteristic
503C42C2×C22⋊D4311yescharacteristic
504C42C23×D4311yescharacteristic
505C23—21no—
506C23—41no—
507C23#1306329711yescharacteristic
508Q8—21no—
509Q8—21no—
510Q8—41no—
511Q8—41no—
512Q8—1721no—
513Q8—1721no—
514Q8—1721no—
515Q8—1721no—
516D4—21no—
517D4—21no—
518D4—41no—
519D4—41no—
520D4—41no—
521D4—41no—
522D4—81no—
523D4—81no—
524D4—82no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—82no—
537C2×C4—1721no—
538C2×C4—1721no—
539C2×C4#1306329711yescharacteristic
540C2×C4#1306329711yescharacteristic
541C2×C4#1306329711yescharacteristic
542C2×C4C2×D4×D4311yescharacteristic
543C2×C4C22×C22⋊D4311yescharacteristic
544C2×C4C2×#1062190011yescharacteristic
545C8—41no—
546C8—41no—
547C8—432no—
548C8—861no—
549C8—861no—
550C8—861no—
551C8—1721no—
552C8—1721no—
553C8—1721no—
554C8—1721no—
555C22—21no—
556C22—21no—
557C22—21no—
558C22—41no—
559C22—41no—
560C22—41no—
561C22—81no—
562C22—81no—
563C22—81no—
564C22C2×#1306329711yescharacteristic
565C4—21no—
566C4—21no—
567C4—21no—
568C4—21no—
569C4—41no—
570C4—41no—
571C4—41no—
572C4—81no—
573C4—3441no—
574C4—3441no—
575C4#135×D4311yescharacteristic
576C4#1458369611yescharacteristic
577C4#1458370211yescharacteristic
578C4#1458371011yescharacteristic
579C2—41no—
580C2—81no—
581C2—161no—
582C2#1914404611yescharacteristic
583C2#1914427111yescharacteristic
584C2#1914433411yescharacteristic
subgroupG/H
centerC22C2×#13063297
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
Fitting, prime radicalC43×#3212C2
socleC22×C43C2×#121
hypercenter#3212D43
hypocenterC43#19252
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3212

Complements

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

NH ≅ G/Ntype
1. #19145932C2semidirect
2. #19145309C2semidirect
3. #19143600C2semidirect
4. #19134161C2semidirect
5. #19134151C2semidirect
6. #19134106C2semidirect
7. #19134058C2semidirect
8. #19134030C2semidirect
9. #19134020C2semidirect
10. #19133987C2semidirect
11. #19133941C2semidirect
12. #19133348C2semidirect
13. #19133259C2semidirect
14. #19133244C2semidirect
359. C43#19252semidirect

Maximal subgroups

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

subgroupindex
#191459322
#191453092
#191436002
#191341612
#191341512
#191341062
#191340582
#191340302
#191340202
#191339872
#191339412
#191333482
#191332592
#191332442
C43×#32122
#1925243