Finite Group Databasebeta

← #25080347

Subgroups — #25080347

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#19145567C211yesmaximal, characteristic
3#19145313C211yesmaximal, characteristic, complemented
4#19134163C211yesmaximal, characteristic, complemented
5#19134149C211yesmaximal, characteristic, complemented
6#19134108C211yesmaximal, characteristic, complemented
7#19134060C211yesmaximal, characteristic, complemented
8#19134032C211yesmaximal, characteristic, complemented
9#19134018C211yesmaximal, characteristic, complemented
10#19133989C211yesmaximal, characteristic, complemented
11#19133943C211yesmaximal, characteristic, complemented
12#19133347C211yesmaximal, characteristic, complemented
13#19133259C211yesmaximal, characteristic, complemented
14#19133242C211yesmaximal, characteristic, complemented
15C43×#2969C211yesmaximal, characteristic, complemented
16#14583456C2211yescharacteristic
17#14583449C2211yescharacteristic
18#14583304C2211yescharacteristic
19#14583281—21no—
20#14583272C2211yescharacteristic
21#14583256—21no—
22#14583250C2211yescharacteristic
23#14583246C2211yescharacteristic
24#14583203—21no—
25#14583184C2211yescharacteristic
26#14583179C2211yescharacteristic
27#14583145—21no—
28#14583145—21no—
29#14583138—21no—
30#14583126—21no—
31#14583118—21no—
32#14583109C2211yescharacteristic
33#14583109C2211yescharacteristic
34#14583104C2211yescharacteristic
35#14583104C2211yescharacteristic
36#14583099C2211yescharacteristic
37#14583094C2211yescharacteristic
38#14583059—21no—
39#14583042—21no—
40#14583001—21no—
41#14583001—21no—
42#14582952C2211yescharacteristic
43C2×C4⋊(C43⋊C8)C2211yescharacteristic
44#14582652C2211yescharacteristic
45#14582652C2211yescharacteristic
46#14582650C2211yescharacteristic
47#14582650C2211yescharacteristic
48#14582646C2211yescharacteristic
49#14582646C2211yescharacteristic
50#14582644C2211yescharacteristic
51#14582644C2211yescharacteristic
52#14582644C2211yescharacteristic
53#14582644C2211yescharacteristic
54#14582642C2211yescharacteristic
55#14582642C2211yescharacteristic
56C43×#529C2211yescharacteristic
57C43×#446C2211yescharacteristic
58C8×Q8×C43C2211yescharacteristic
59C43×#436—21no—
60C43×#436C2211yescharacteristic
61C43×#435—21no—
62C8×D4×C43C2211yescharacteristic
63C43×#433—21no—
64C43×#431C2211yescharacteristic
65C43×#405—21no—
66C4×M16×C43C2211yescharacteristic
67C2×#10621898—21no—
68C2×#10621885—21no—
69C2×#10621885—21no—
70C2×#10621873—21no—
71C2×#10621873—21no—
72C2×#10621883—21no—
73C2×#10621883—21no—
74C2×#10621884—21no—
75C2×#10621882—21no—
76C22×C43⋊C8—21no—
77#13063325C2311yescharacteristic
78#13063325C2311yescharacteristic
79#13063325C2311yescharacteristic
80#13063322C2311yescharacteristic
81#13063317—21no—
82#13063313—21no—
83#13063304—21no—
84#13063304—21no—
85#13063299—21no—
86#13063299—21no—
87C4×Dic86—21no—
88C4×Dic86—21no—
89C4×D172—21no—
90C4×D172—21no—
91#13063284—21no—
92#13063259—21no—
93#13063259—21no—
94#13063258—21no—
95#13063256—21no—
96C4⋊(C43⋊C8)—21no—
97C4⋊(C43⋊C8)C2311yescharacteristic
98C4⋊(C43⋊C8)C2311yescharacteristic
99C4⋊(C43⋊C8)C2311yescharacteristic
100C4⋊(C43⋊C8)C2311yescharacteristic
101#13063250—21no—
102#13063250—21no—
103#13063249—21no—
104#13063248—21no—
105#13063248—21no—
106#13063248—21no—
107#13063248—21no—
108#13063247—21no—
109#13063247—21no—
110#13063246—21no—
111#13063245—21no—
112#13063245—21no—
113C22⋊(C43⋊C8)—21no—
114C4×C43⋊C8—21no—
115C2×M16×C43—21no—
116C2×M16×C43D411yescharacteristic
117C2×M16×C43D411yescharacteristic
118C22×C8×C43—21no—
119#126×C43—21no—
120#125×C43D411yescharacteristic
121#124×C43D411yescharacteristic
122#123×C43—21no—
123C22⋊Q8×C43D411yescharacteristic
124#121×C43D411yescharacteristic
125C4×Q8×C43C2311yescharacteristic
126C4×D4×C43—21no—
127C4×D4×C43C2311yescharacteristic
128#117×C43—21no—
129C2×C42×C43C2311yescharacteristic
130C4⋊C8×C43—21no—
131C4⋊C8×C43—21no—
132C4⋊C8×C43C2311yescharacteristic
133C4⋊C8×C43C2311yescharacteristic
134C22⋊C8×C43—21no—
135C22⋊C8×C43—21no—
136C22⋊C8×C43—21no—
137#97×C43—21no—
138#97×C43D411yescharacteristic
139#97×C43D411yescharacteristic
140C4×C8×C43—21no—
141C4×C8×C43—21no—
142C4×C8×C43C2311yescharacteristic
143C4×C8×C43C2311yescharacteristic
144C2×Q8×C43C2×D411yescharacteristic
145C2×D4×C43—21no—
146C2×D4×C43C2×D411yescharacteristic
147C22×C4×C43—21no—
148C22×C4×C43C2×D411yescharacteristic
149C22×C4×C43C2×D411yescharacteristic
150C22×C4×C43#4111yescharacteristic
151C2×C22⋊D43—41no—
152#10621898—81no—
153#10621898—81no—
154C2×D172—21no—
155C2×D172—21no—
156C2×D172—21no—
157C2×C4×D43—41no—
158C2×Dic86—21no—
159C2×Dic86—21no—
160C2×Dic86—21no—
161M16×C43—22no—
162M16×C43—41no—
163M16×C43—42no—
164C2×C8×C43—21no—
165C2×C8×C43—21no—
166C2×C8×C43—42no—
167C2×C8×C43C2×D411yescharacteristic
168C2×C8×C43C2×D411yescharacteristic
169C2×C8×C43C2×D411yescharacteristic
170C2×C8×C43C2×D411yescharacteristic
171C4⋊C4×C43—21no—
172C4⋊C4×C43—21no—
173C4⋊C4×C43—21no—
174C4⋊C4×C43—21no—
175C4⋊C4×C43C2×D411yescharacteristic
176C4⋊C4×C43C2×D411yescharacteristic
177C22⋊C4×C43—21no—
178C22⋊C4×C43—21no—
179C22⋊C4×C43—21no—
180C22⋊C4×C43—21no—
181C22⋊C4×C43—21no—
182C42×C43—21no—
183C42×C43C2×D411yescharacteristic
184C42×C43C2×D411yescharacteristic
185C42×C43#4111yescharacteristic
186C42×C43C2411yescharacteristic
187C22⋊Dic43—41no—
188#10621885—81no—
189#10621885—81no—
190#10621884—81no—
191#10621883—81no—
192#10621883—81no—
193#10621882—81no—
194(C2×D43)⋊C4—41no—
195(C2×D43)⋊C4—41no—
196C4⋊Dic43—21no—
197C4⋊Dic43—21no—
198C4⋊Dic43—21no—
199C4⋊Dic43—21no—
200C4⋊Dic43—21no—
201C4⋊Dic43—21no—
202Dic43⋊C4—41no—
203Dic43⋊C4—41no—
204C4×Dic43—41no—
205C2×C43⋊C8—21no—
206C2×C43⋊C8—21no—
207C2×C43⋊C8—21no—
208C2×C43⋊C8—21no—
209C2×C43⋊C8—81no—
210#10621873—42no—
211#10621873—42no—
212C23×C43—21no—
213C23×C43#12111yescharacteristic
214C22×D43—41no—
215Q8×C43—21no—
216Q8×C43—21no—
217D4×C43—21no—
218D4×C43—21no—
219D4×C43—81no—
220C2×C4×C43—21no—
221C2×C4×C43—21no—
222C2×C4×C43—21no—
223C2×C4×C43—21no—
224C2×C4×C43—21no—
225C2×C4×C43—21no—
226C2×C4×C43—21no—
227C2×C4×C43—41no—
228C2×C4×C43—41no—
229C2×C4×C43—41no—
230C2×C4×C43#12111yescharacteristic
231C2×C4×C43#12111yescharacteristic
232C2×C4×C43#12111yescharacteristic
233C2×C4×C43C22×D411yescharacteristic
234C2×C4×C43C22×D411yescharacteristic
235C2×C4×C43C2×#4111yescharacteristic
236C22⋊D43—82no—
237C2×Dic43—41no—
238C2×Dic43—41no—
239C2×Dic43—41no—
240D172—41no—
241D172—41no—
242D172—41no—
243D172—41no—
244D172—81no—
245C4×D43—82no—
246Dic86—41no—
247Dic86—41no—
248Dic86—41no—
249Dic86—41no—
250Dic86—41no—
251Dic86—41no—
252C8×C43—21no—
253C8×C43—21no—
254C8×C43—21no—
255C8×C43—41no—
256C8×C43—41no—
257C8×C43#13512yes—
258C43⋊C8—41no—
259C43⋊C8—41no—
260C43⋊C8—41no—
261C43⋊C8—41no—
262#19252—431nomaximal, Sylow
263C22×C43—21no—
264C22×C43—21no—
265C22×C43—21no—
266C22×C43—41no—
267C22×C43—41no—
268C22×C43—41no—
269C22×C43C2×#12111yescharacteristic
270C2×D43—81no—
271C2×D43—81no—
272C2×D43—81no—
273C4×C43—21no—
274C4×C43—21no—
275C4×C43—21no—
276C4×C43—21no—
277C4×C43—41no—
278C4×C43—41no—
279C4×C43—41no—
280C4×C43C2×#13511yescharacteristic
281C4×C43#57511yescharacteristic
282C4×C43#57611yescharacteristic
283C4×C43#57711yescharacteristic
284Dic43—81no—
285Dic43—81no—
286Dic43—81no—
287#3248—431no—
288#3212—431no—
289#3182—431no—
290#2969D4311yescharacteristic, complemented
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#303511yescharacteristic
305C2×C43#306211yescharacteristic
306C2×C43#306911yescharacteristic
307D43—161no—
308#533—431no—
309#532—431no—
310#529C2×D4311yescharacteristic
311#500—431no—
312#495—861no—
313#492—431no—
314#488—861no—
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#462—431no—
327#461—431no—
328#461—431no—
329#460—431no—
330#459—431no—
331#452—861no—
332#449—861no—
333#446C2×D4311yescharacteristic
334C8×Q8C2×D4311yescharacteristic
335#440—861no—
336#440—861no—
337#436—21no—
338#436C2×D4311yescharacteristic
339#435—21no—
340C8×D4C2×D4311yescharacteristic
341#433—21no—
342#431—431no—
343#431C2×D4311yescharacteristic
344C2×C4⋊C8—431no—
345#405—21no—
346C4×M16C2×D4311yescharacteristic
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—861no—
361C2×Q16—861no—
362C2×Q16—861no—
363C2×SD16—861no—
364C2×SD16—861no—
365C2×SD16—861no—
366C2×SD16—861no—
367C2×SD16—861no—
368C2×D8—861no—
369C2×M16—21no—
370C2×M16C22⋊D4311yescharacteristic
371C2×M16C22⋊D4311yescharacteristic
372C22×C8—21no—
373C22×C8—861no—
374C4⋊Q8—431no—
375C4⋊Q8—431no—
376C4⋊Q8—431no—
377#127—431no—
378#126—21no—
379#125—861no—
380#125D17211yescharacteristic
381#124—861no—
382#124D17211yescharacteristic
383#123—21no—
384C22⋊Q8—861no—
385C22⋊Q8—861no—
386C22⋊Q8D17211yescharacteristic
387#121—861no—
388#121—861no—
389#121D17211yescharacteristic
390C4×Q8—861no—
391C4×Q8—861no—
392C4×Q8C22×D4311yescharacteristic
393C4×D4—21no—
394C4×D4—861no—
395C4×D4—861no—
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—21no—
405C4⋊C8—21no—
406C4⋊C8—431no—
407C4⋊C8—431no—
408C4⋊C8—431no—
409C4⋊C8—431no—
410C4⋊C8—861no—
411C4⋊C8C22×D4311yescharacteristic
412C4⋊C8C22×D4311yescharacteristic
413#103—861no—
414#103—861no—
415#103—861no—
416#103—861no—
417#103—861no—
418#103—861no—
419#103—861no—
420#102—861no—
421#102—861no—
422#102—861no—
423#102—861no—
424#102—861no—
425C22⋊C8—21no—
426C22⋊C8—21no—
427C22⋊C8—21no—
428C22⋊C8—861no—
429#97—21no—
430#97C22⋊D4311yescharacteristic
431#97C22⋊D4311yescharacteristic
432C4×C8—21no—
433C4×C8—21no—
434C4×C8—861no—
435C4×C8C22×D4311yescharacteristic
436C4×C8C22×D4311yescharacteristic
437#41—3441no—
438#41—3441no—
439C2×Q8—861no—
440C2×Q8—861no—
441C2×Q8—861no—
442C2×Q8C2×D17211yescharacteristic
443C2×D4—21no—
444C2×D4—861no—
445C2×D4—861no—
446C2×D4—861no—
447C2×D4—1721no—
448C2×D4C2×D17211yescharacteristic
449C22×C4—21no—
450C22×C4—1721no—
451C22×C4C2×D17211yescharacteristic
452C22×C4#1062189811yescharacteristic
453C22×C4C2×C22⋊D4311yescharacteristic
454Q16—3441no—
455Q16—3441no—
456SD16—3441no—
457SD16—3441no—
458SD16—3441no—
459SD16—1722no—
460SD16—1722no—
461D8—3441no—
462M16—22no—
463M16—41no—
464M16—42no—
465C2×C8—21no—
466C2×C8—21no—
467C2×C8—42no—
468C2×C8—861no—
469C2×C8—861no—
470C2×C8—861no—
471C2×C8—861no—
472C2×C8—3441no—
473C2×C8C2×C22⋊D4311yescharacteristic
474C2×C8C2×C22⋊D4311yescharacteristic
475C2×C8C2×C22⋊D4311yescharacteristic
476C2×C8C2×C22⋊D4311yescharacteristic
477C4⋊C4—21no—
478C4⋊C4—21no—
479C4⋊C4—21no—
480C4⋊C4—21no—
481C4⋊C4—861no—
482C4⋊C4—861no—
483C4⋊C4—861no—
484C4⋊C4—861no—
485C4⋊C4—861no—
486C4⋊C4—861no—
487C4⋊C4—1721no—
488C4⋊C4—1721no—
489C4⋊C4C2×D17211yescharacteristic
490C4⋊C4C2×D17211yescharacteristic
491C22⋊C4—21no—
492C22⋊C4—21no—
493C22⋊C4—21no—
494C22⋊C4—21no—
495C22⋊C4—21no—
496C22⋊C4—1721no—
497C22⋊C4—1721no—
498C22⋊C4—1721no—
499C42—21no—
500C42—1721no—
501C42C2×D17211yescharacteristic
502C42#1062189811yescharacteristic
503C42C2×C22⋊D4311yescharacteristic
504C42C23×D4311yescharacteristic
505C23—21no—
506C23—1721no—
507C23#1306329911yescharacteristic
508Q8—21no—
509Q8—21no—
510Q8—1721no—
511Q8—1721no—
512Q8—1721no—
513Q8—1721no—
514Q8—1721no—
515Q8—1721no—
516D4—21no—
517D4—21no—
518D4—81no—
519D4—3441no—
520D4—3442no—
521D4—1721no—
522D4—1721no—
523D4—1721no—
524D4—1721no—
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—3442no—
536C2×C4—1721no—
537C2×C4—1721no—
538C2×C4—1721no—
539C2×C4#1306329911yescharacteristic
540C2×C4#1306329911yescharacteristic
541C2×C4#1306329911yescharacteristic
542C2×C4C22×C22⋊D4311yescharacteristic
543C2×C4C22×D17211yescharacteristic
544C2×C4C2×#1062189811yescharacteristic
545C8—21no—
546C8—21no—
547C8—21no—
548C8—41no—
549C8—41no—
550C8—1721no—
551C8—1721no—
552C8—1721no—
553C8—1721no—
554C8#1306334512yes—
555C22—21no—
556C22—21no—
557C22—21no—
558C22—41no—
559C22—41no—
560C22—41no—
561C22—3441no—
562C22—3441no—
563C22—3441no—
564C22C2×#1306329911yescharacteristic
565C4—21no—
566C4—21no—
567C4—21no—
568C4—21no—
569C4—41no—
570C4—41no—
571C4—41no—
572C4—3441no—
573C4—3441no—
574C4—3441no—
575C4C2×#1306334511yescharacteristic
576C4#1458369711yescharacteristic
577C4#1458370411yescharacteristic
578C4#1458371111yescharacteristic
579C2—41no—
580C2—81no—
581C2—6881no—
582C2#1914405011yescharacteristic
583C2#1914427511yescharacteristic
584C2#1914433211yescharacteristic
subgroupG/H
centerC22C2×#13063299
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#2969C2
socleC22×C43C2×#121
prime radical#19145567C2
hypercenter#2969D43
hypocenterC43#19252
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2969

Complements

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

NH ≅ G/Ntype
1. #19145932C2semidirect
3. #19145313C2semidirect
4. #19134163C2semidirect
5. #19134149C2semidirect
6. #19134108C2semidirect
7. #19134060C2semidirect
8. #19134032C2semidirect
9. #19134018C2semidirect
10. #19133989C2semidirect
11. #19133943C2semidirect
12. #19133347C2semidirect
13. #19133259C2semidirect
14. #19133242C2semidirect
15. C43×#2969C2semidirect
290. #2969D43semidirect
359. C43#19252semidirect

Maximal subgroups

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

subgroupindex
#191459322
#191455672
#191453132
#191341632
#191341492
#191341082
#191340602
#191340322
#191340182
#191339892
#191339432
#191333472
#191332592
#191332422
C43×#29692
#1925243