Finite Group Databasebeta

← #25087543

Subgroups — #25087543

Order 11008.

602 conjugacy classes of subgroups.

The subgroup lattice has 584 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19147019C211yesmaximal, characteristic, complemented
2#19147013C211yesmaximal, characteristic, complemented
3#19146523C211yesmaximal, characteristic, complemented
4#19134269C211yesmaximal, characteristic, complemented
5#19134118C211yesmaximal, characteristic, complemented
6#19134044C211yesmaximal, characteristic, complemented
7#19133992C211yesmaximal, characteristic, complemented
8#19133967C211yesmaximal, characteristic, complemented
9#19133822C211yesmaximal, characteristic, complemented
10#19133746C211yesmaximal, characteristic, complemented
11#19133740C211yesmaximal, characteristic, complemented
12#19133739C211yesmaximal, characteristic, complemented
13#19133422C211yesmaximal, characteristic, complemented
14#19133419C211yesmaximal, characteristic, complemented
15C43×#3354C211yesmaximal, characteristic, complemented
16#14583614C2211yescharacteristic
17#14583614C2211yescharacteristic
18#14583304C2211yescharacteristic
19#14583302C2211yescharacteristic
20#14583278C2211yescharacteristic
21#14583251C2211yescharacteristic
22#14583249C2211yescharacteristic
23#14583237—21no—
24#14583223—21no—
25#14583221—21no—
26#14583221—21no—
27#14583220—21no—
28#14583189C2211yescharacteristic
29#14583189C2211yescharacteristic
30#14583189C2211yescharacteristic
31#14583189C2211yescharacteristic
32#14583186C2211yescharacteristic
33#14583133—21no—
34#14583132—21no—
35#14583130—21no—
36#14583101C2211yescharacteristic
37#14583044—21no—
38C4×#10621882C2211yescharacteristic
39C8×D172C2211yescharacteristic
40D4×C43⋊C8C2211yescharacteristic
41D4×C43⋊C8C2211yescharacteristic
42#14582936—21no—
43#14582935—21no—
44#14582895—21no—
45#14582651C2211yescharacteristic
46#14582650C2211yescharacteristic
47#14582648C2211yescharacteristic
48#14582647C2211yescharacteristic
49#14582647C2211yescharacteristic
50#14582645C2211yescharacteristic
51D4⋊(C43⋊C8)C2211yescharacteristic
52D4⋊(C43⋊C8)C2211yescharacteristic
53D4⋊(C43⋊C8)C2211yescharacteristic
54#14582626C2211yescharacteristic
55#14582620C2211yescharacteristic
56C43×#555C2211yescharacteristic
57C43×#547C2211yescharacteristic
58C43×#498C2211yescharacteristic
59C43×#482—21no—
60C43×#481—21no—
61C43×#476C2211yescharacteristic
62C43×#474C2211yescharacteristic
63C43×#469—21no—
64C4×D8×C43C2211yescharacteristic
65C43×#436C2211yescharacteristic
66C43×#428—21no—
67C2×#10621885—41no—
68C2×#10621884—21no—
69C2×#10621882D411yescharacteristic
70C22×C43⋊C8—21no—
71C22×C43⋊C8—21no—
72C2×C8×D43—21no—
73#13063325C2311yescharacteristic
74#13063325C2311yescharacteristic
75#13063311—41no—
76#13063311—41no—
77#13063299—21no—
78#13063299—21no—
79#13063296—21no—
80#13063296—21no—
81C4×D172C2311yescharacteristic
82#13063284—21no—
83#13063284—21no—
84#13063283—21no—
85#13063283—21no—
86#13063259—21no—
87#13063259—21no—
88#13063258—21no—
89#13063258—21no—
90#13063258D411yescharacteristic
91#13063256—21no—
92#13063256—21no—
93#13063256—21no—
94#13063256—21no—
95#13063256—21no—
96C4⋊(C43⋊C8)C2311yescharacteristic
97C4⋊(C43⋊C8)C2311yescharacteristic
98C4⋊(C43⋊C8)C2311yescharacteristic
99#13063249—21no—
100#13063249—21no—
101#13063249—21no—
102#13063248—41no—
103#13063246—21no—
104#13063246—21no—
105#13063246—21no—
106#13063246—21no—
107#13063246D411yescharacteristic
108#13063245—21no—
109#13063245D411yescharacteristic
110C22⋊(C43⋊C8)—21no—
111C22⋊(C43⋊C8)—21no—
112(C2×D43)⋊C8—21no—
113C4×C43⋊C8C2311yescharacteristic
114C4×C43⋊C8C2311yescharacteristic
115C2×#41×C43—21no—
116C2×D8×C43D411yescharacteristic
117C2×M16×C43—21no—
118C4⋊Q8×C43C2311yescharacteristic
119C4⋊Q8×C43C2311yescharacteristic
120#124×C43—41no—
121#123×C43—41no—
122C22⋊Q8×C43—21no—
123#121×C43—21no—
124#121×C43—21no—
125#121×C43—21no—
126C4×D4×C43C2311yescharacteristic
127C4×D4×C43C2311yescharacteristic
128C4×D4×C43C2311yescharacteristic
129#117×C43—21no—
130#117×C43—21no—
131C2×C4⋊C4×C43—21no—
132#107×C43—21no—
133#107×C43D411yescharacteristic
134#106×C43—21no—
135#106×C43—21no—
136#106×C43—21no—
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—81no—
146C2×Q8×C43—21no—
147C2×Q8×C43—21no—
148C2×D4×C43—41no—
149C2×D4×C43—41no—
150C2×D4×C43C2×D411yescharacteristic
151C2×D4×C43C2×D411yescharacteristic
152C2×D4×C43C2×D411yescharacteristic
153C22×C4×C43—21no—
154C22×C4×C43—21no—
155C22×C4×C43—21no—
156C22×C4×C43—41no—
157C2×C22⋊D43—41no—
158C2×C22⋊D43—41no—
159C2×D172C2×D411yescharacteristic
160C2×C4×D43—21no—
161C2×Dic86—21no—
162C2×Dic86—21no—
163D8×C43—22no—
164M16×C43—42no—
165C2×C8×C43—21no—
166C2×C8×C43C2×D411yescharacteristic
167C2×C8×C43C2×D411yescharacteristic
168C4⋊C4×C43—21no—
169C4⋊C4×C43—21no—
170C4⋊C4×C43—21no—
171C4⋊C4×C43—21no—
172C4⋊C4×C43—41no—
173C4⋊C4×C43C2×D411yescharacteristic
174C4⋊C4×C43C2×D411yescharacteristic
175C4⋊C4×C43C2×D411yescharacteristic
176C22⋊C4×C43—21no—
177C22⋊C4×C43—21no—
178C22⋊C4×C43—21no—
179C22⋊C4×C43—41no—
180C22⋊C4×C43—41no—
181C22⋊C4×C43—41no—
182C42×C43—41no—
183C42×C43C2411yescharacteristic
184C22⋊Dic43—41no—
185C22⋊Dic43—41no—
186#10621885—82no—
187#10621884—81no—
188#10621882—41no—
189(C2×D43)⋊C4—21no—
190(C2×D43)⋊C4—41no—
191(C2×D43)⋊C4—41no—
192C4⋊Dic43—21no—
193C4⋊Dic43—21no—
194C4⋊Dic43—21no—
195C4⋊Dic43—21no—
196C4⋊Dic43C2×D411yescharacteristic
197C4×Dic43—41no—
198C4×Dic43—41no—
199C2×C43⋊C8—21no—
200C2×C43⋊C8—21no—
201C2×C43⋊C8—21no—
202C2×C43⋊C8—21no—
203C2×C43⋊C8—42no—
204C2×C43⋊C8—81no—
205C2×C43⋊C8C2×D411yescharacteristic
206C2×C43⋊C8C2×D411yescharacteristic
207C8×D43—42no—
208C23×C43—21no—
209C23×C43—21no—
210C23×C43—21no—
211C22×D43—21no—
212Q8×C43—41no—
213Q8×C43—41no—
214Q8×C43—81no—
215D4×C43—21no—
216D4×C43—21no—
217D4×C43—21no—
218D4×C43—21no—
219D4×C43—21no—
220D4×C43—21no—
221D4×C43—82no—
222D4×C43—161no—
223C2×C4×C43—21no—
224C2×C4×C43—21no—
225C2×C4×C43—21no—
226C2×C4×C43—41no—
227C2×C4×C43—41no—
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—82no—
235C2×C4×C43C22×D411yescharacteristic
236C2×C4×C43C22×D411yescharacteristic
237C2×C4×C43H(5,𝔽2)11yescharacteristic
238C22⋊D43—161no—
239C22⋊D43—161no—
240C2×Dic43—21no—
241C2×Dic43—41no—
242C2×Dic43—41no—
243D172—21no—
244D172—21no—
245C4×D43—41no—
246C4×D43—41no—
247Dic86—81no—
248Dic86—81no—
249C8×C43—21no—
250C8×C43—41no—
251C8×C43#13512yes—
252C43⋊C8—21no—
253C43⋊C8—21no—
254C43⋊C8—41no—
255C43⋊C8—41no—
256C43⋊C8—41no—
257C43⋊C8—41no—
258#19862—431nomaximal, Sylow
259C22×C43—41no—
260C22×C43—41no—
261C22×C43—41no—
262C22×C43—41no—
263C22×C43—41no—
264C22×C43—41no—
265C22×C43—41no—
266C22×C43—41no—
267C22×C43—41no—
268C22×C43D4211yescharacteristic
269C2×D43—41no—
270C2×D43—41no—
271C2×D43—41no—
272C4×C43—21no—
273C4×C43—41no—
274C4×C43—41no—
275C4×C43—41no—
276C4×C43—81no—
277C4×C43—81no—
278C4×C43C2×#13511yescharacteristic
279C4×C43#57511yescharacteristic
280C4×C43#57711yescharacteristic
281C4×C43#57811yescharacteristic
282Dic43—41no—
283Dic43—81no—
284Dic43—81no—
285#3354D4311yescharacteristic, complemented
286#3341—431no—
287#3341—431no—
288#3303—431no—
289#1723—431no—
290#1695—431no—
291#1683—431no—
292#1675—431no—
293#1671—431no—
294#1646—431no—
295#1635—431no—
296#1634—431no—
297#1634—431no—
298#1581—431no—
299#1580—431no—
300C2×C43—81no—
301C2×C43—81no—
302C2×C43—81no—
303C2×C43#326711yescharacteristic
304C2×C43#328311yescharacteristic
305C2×C43#328811yescharacteristic
306D43—81no—
307#555—431no—
308#555—431no—
309#555C2×D4311yescharacteristic
310#547C2×D4311yescharacteristic
311#500—431no—
312#500—431no—
313#498C2×D4311yescharacteristic
314#494—431no—
315#487—431no—
316#487—431no—
317#485—861no—
318#482—21no—
319#482—861no—
320#482—861no—
321#482—861no—
322#482—861no—
323#481—21no—
324#476—431no—
325#476—431no—
326#476—431no—
327#476—431no—
328#476—431no—
329#476C2×D4311yescharacteristic
330#474C2×D4311yescharacteristic
331#469—21no—
332#466—861no—
333#466—861no—
334#465—861no—
335#461—431no—
336#449—861no—
337C4×D8—431no—
338C4×D8C2×D4311yescharacteristic
339#436C2×D4311yescharacteristic
340C8×D4—431no—
341C8×D4—431no—
342C8×D4—431no—
343#428—21no—
344#427—861no—
345#427—861no—
346#416—861no—
347#335—431no—
348#334—431no—
349#333—431no—
350#333—431no—
351#333—431no—
352#332—431no—
353D4⋊C8—431no—
354D4⋊C8—431no—
355D4⋊C8—431no—
356D4⋊C8—431no—
357#322—431no—
358C43#1986211yescharacteristic, complemented, Sylow
359C2×#41—21no—
360C2×Q16—1721no—
361C2×SD16—861no—
362C2×D8—431no—
363C2×D8C22⋊D4311yescharacteristic
364C2×M16—21no—
365C22×C8—861no—
366C22×C8—861no—
367C22×C8—861no—
368C4⋊Q8—431no—
369C4⋊Q8—431no—
370C4⋊Q8C22×D4311yescharacteristic
371C4⋊Q8C22×D4311yescharacteristic
372#124—41no—
373#124—1721no—
374#124—1721no—
375#123—41no—
376C22⋊Q8—21no—
377#121—21no—
378#121—21no—
379#121—21no—
380#121—861no—
381#121—861no—
382#121—861no—
383#121—861no—
384C4×D4—431no—
385C4×D4C22×D4311yescharacteristic
386C4×D4C22×D4311yescharacteristic
387C4×D4C22×D4311yescharacteristic
388#117—21no—
389#117—21no—
390#117—861no—
391#117—861no—
392#117—861no—
393#117—861no—
394C2×C4⋊C4—21no—
395#107—21no—
396#107—431no—
397#107—861no—
398#107—861no—
399#107—861no—
400#107—861no—
401#107C22⋊D4311yescharacteristic
402#106—21no—
403#106—21no—
404#106—21no—
405#106—861no—
406#106—861no—
407#106—861no—
408#106—861no—
409#106—861no—
410C4⋊C8—431no—
411C4⋊C8—431no—
412C4⋊C8—431no—
413C4⋊C8C22×D4311yescharacteristic
414#103—861no—
415#103—861no—
416#103—861no—
417#103—1721no—
418#102—21no—
419#102—21no—
420#102—431no—
421#102—431no—
422#102—861no—
423#102—861no—
424#102—861no—
425#102—861no—
426#102—861no—
427#102C22⋊D4311yescharacteristic
428#102C22⋊D4311yescharacteristic
429C22⋊C8—21no—
430C22⋊C8—861no—
431C22⋊C8—861no—
432C22⋊C8—861no—
433C4×C8—431no—
434C4×C8—431no—
435C4×C8C22×D4311yescharacteristic
436#41—42no—
437#41—81no—
438C2×Q8—21no—
439C2×Q8—21no—
440C2×Q8—861no—
441C2×Q8—861no—
442C2×D4—41no—
443C2×D4—41no—
444C2×D4—431no—
445C2×D4—1721no—
446C2×D4—1721no—
447C2×D4D4×D4311yescharacteristic
448C2×D4C2×C22⋊D4311yescharacteristic
449C2×D4C2×C22⋊D4311yescharacteristic
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—41no—
454C22×C4—861no—
455Q16—3442no—
456SD16—3441no—
457D8—22no—
458D8—1721no—
459M16—42no—
460C2×C8—21no—
461C2×C8—431no—
462C2×C8—431no—
463C2×C8—861no—
464C2×C8—861no—
465C2×C8—861no—
466C2×C8—861no—
467C2×C8—3441no—
468C2×C8—1722no—
469C2×C8—1722no—
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—431no—
478C4⋊C4—861no—
479C4⋊C4—861no—
480C4⋊C4—861no—
481C4⋊C4—861no—
482C4⋊C4D4×D4311yescharacteristic
483C4⋊C4C2×C22⋊D4311yescharacteristic
484C4⋊C4C2×C22⋊D4311yescharacteristic
485C22⋊C4—21no—
486C22⋊C4—21no—
487C22⋊C4—21no—
488C22⋊C4—41no—
489C22⋊C4—41no—
490C22⋊C4—41no—
491C22⋊C4—861no—
492C22⋊C4—1721no—
493C22⋊C4—1721no—
494C22⋊C4—1721no—
495C22⋊C4—1721no—
496C42—41no—
497C42—1721no—
498C42—1721no—
499C42C23×D4311yescharacteristic
500C23—21no—
501C23—21no—
502C23—21no—
503C23—861no—
504Q8—41no—
505Q8—41no—
506Q8—81no—
507Q8—3441no—
508Q8—3441no—
509D4—21no—
510D4—21no—
511D4—21no—
512D4—21no—
513D4—21no—
514D4—21no—
515D4—82no—
516D4—161no—
517D4—861no—
518D4—861no—
519D4—6881no—
520D4—6881no—
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—861no—
534C2×C4—1721no—
535C2×C4—1721no—
536C2×C4—1721no—
537C2×C4—1721no—
538C2×C4C2×D4×D4311yescharacteristic
539C2×C4C22×C22⋊D4311yescharacteristic
540C2×C4#1306337011yescharacteristic
541C8—21no—
542C8—41no—
543C8—861no—
544C8—861no—
545C8—1721no—
546C8—1721no—
547C8—1721no—
548C8—1721no—
549C8#1306334512yes—
550C22—41no—
551C22—41no—
552C22—41no—
553C22—41no—
554C22—41no—
555C22—41no—
556C22—41no—
557C22—41no—
558C22—41no—
559C22—1721no—
560C22—1721no—
561C22—1721no—
562C22D4×C22⋊D4311yescharacteristic
563C4—21no—
564C4—41no—
565C4—41no—
566C4—41no—
567C4—81no—
568C4—81no—
569C4—3441no—
570C4—3441no—
571C4—1721no—
572C4C2×#1306334511yescharacteristic
573C4#1458369511yescharacteristic
574C4#1458370911yescharacteristic
575C4#1458371411yescharacteristic
576C2—81no—
577C2—81no—
578C2—81no—
579C2—3441no—
580C2#1914611411yescharacteristic
581C2#1914631311yescharacteristic
582C2#1914635711yescharacteristic
subgroupG/H
centerC22D4×C22⋊D43
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#3354C2
socleC22×C43D42
hypercenter#3354D43
hypocenterC43#19862
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #3354

Complements

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

NH ≅ G/Ntype
1. #19147019C2semidirect
2. #19147013C2semidirect
3. #19146523C2semidirect
4. #19134269C2semidirect
5. #19134118C2semidirect
6. #19134044C2semidirect
7. #19133992C2semidirect
8. #19133967C2semidirect
9. #19133822C2semidirect
10. #19133746C2semidirect
11. #19133740C2semidirect
12. #19133739C2semidirect
13. #19133422C2semidirect
14. #19133419C2semidirect
15. C43×#3354C2semidirect
285. #3354D43semidirect
358. C43#19862semidirect

Maximal subgroups

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

subgroupindex
#191470192
#191470132
#191465232
#191342692
#191341182
#191340442
#191339922
#191339672
#191338222
#191337462
#191337402
#191337392
#191334222
#191334192
C43×#33542
#1986243