Finite Group Databasebeta

← #25123176

Subgroups — #25123176

Order 11008.

706 conjugacy classes of subgroups.

The subgroup lattice has 598 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145063C211yesmaximal, characteristic
2#19135092C211yesmaximal, characteristic, complemented
3#19135086C211yesmaximal, characteristic, complemented
4#19135085C211yesmaximal, characteristic, complemented
5#19135079C211yesmaximal, characteristic, complemented
6#19135075C211yesmaximal, characteristic, complemented
7#19135073C211yesmaximal, characteristic, complemented
8#19135068C211yesmaximal, characteristic, complemented
9#19135066C211yesmaximal, characteristic, complemented
10#19134997C211yesmaximal, characteristic, complemented
11#19134982C211yesmaximal, characteristic, complemented
12#19134979C211yesmaximal, characteristic, complemented
13#19134741C211yesmaximal, characteristic, complemented
14#19134741C211yesmaximal, characteristic, complemented
15C43×#1884C211yesmaximal, characteristic, complemented
16C2×#13063355C2211yescharacteristic
17C2×#13063355C2211yescharacteristic
18C2×#13063350C2211yescharacteristic
19C2×#13063350C2211yescharacteristic
20#14583666C2211yescharacteristic
21C2×#13063313C2211yescharacteristic
22#14583376C2211yescharacteristic
23#14583373C2211yescharacteristic
24#14583291C412yescomplemented
25#14583286C412yescomplemented
26#14583281C412yescomplemented
27#14583281C412yescomplemented
28#14582916C2211yescharacteristic
29#14582916C2211yescharacteristic
30#14582909C2211yescharacteristic
31#14582907C2211yescharacteristic
32#14582905C2211yescharacteristic
33#14582903C2211yescharacteristic
34C2×#13063243C2211yescharacteristic
35C2×#13063241C2211yescharacteristic
36#14582873C2211yescharacteristic
37C4×#10621877C2211yescharacteristic
38#14582671C2211yescharacteristic
39#14582671C2211yescharacteristic
40#14582669C2211yescharacteristic
41#14582669C2211yescharacteristic
42#14582659C2211yescharacteristic
43#14582659C2211yescharacteristic
44C43⋊#338C2211yescharacteristic
45C43⋊#338C2211yescharacteristic
46#14582655C2211yescharacteristic
47#14582655C2211yescharacteristic
48C43×#568C2211yescharacteristic
49C43×#532C2211yescharacteristic
50C43×#421C2211yescharacteristic
51C43×#421C2211yescharacteristic
52C43×#410C2211yescharacteristic
53C43×#339C2211yescharacteristic
54C43×#339C2211yescharacteristic
55C22×Dic86C2311yescharacteristic
56C22×D172C2311yescharacteristic
57#13063355—41no—
58#13063355—41no—
59#13063355—41no—
60#13063355—41no—
61#13063350—41no—
62#13063350—41no—
63#13063350—41no—
64#13063350—41no—
65C2×#10621885C2×C412yescomplemented
66C2×#10621885C2×C412yescomplemented
67C2×#10621883C2×C412yescomplemented
68C2×#10621883C2×C412yescomplemented
69C2×#10621884C2×C412yes—
70C2×#10621884C2×C412yes—
71C2×#10621882C2×C412yes—
72C2×#10621882C2×C412yes—
73#13063332—41no—
74#13063332—41no—
75C2×#10621877—41no—
76C2×#10621877C2311yescharacteristic
77C2×#10621877C2311yescharacteristic
78C2×#10621877C2311yescharacteristic
79C2×#10621877C2311yescharacteristic
80#13063313—41no—
81#13063313C2×C412yes—
82#13063313C2×C412yes—
83C4×Dic86—41no—
84#13063290—41no—
85C4×D172—41no—
86#13063287—41no—
87#13063284C2311yescharacteristic
88#13063284C2311yescharacteristic
89#13063281—41no—
90C2×(C2×D43)⋊C4—41no—
91C22⋊C4×D43—41no—
92#13063252—41no—
93#13063252—41no—
94#13063250—41no—
95#13063248—41no—
96#13063247—41no—
97#13063245—41no—
98#13063243—41no—
99#13063241—41no—
100#13063240—41no—
101#13063236C2×C412yescomplemented
102C4×C43⋊C8C2×C412yescomplemented
103C2×#41×C43C2311yescharacteristic
104C2×#41×C43C2311yescharacteristic
105#131×C43—41no—
106#131×C43—41no—
107C2×M16×C43—41no—
108C2×M16×C43C2311yescharacteristic
109C2×M16×C43C2311yescharacteristic
110C4⋊Q8×C43C2×C411yescharacteristic, complemented
111#127×C43C2×C411yescharacteristic, complemented
112#124×C43C2×C411yescharacteristic, complemented
113#124×C43C2×C411yescharacteristic, complemented
114#121×C43—41no—
115C4×D4×C43—41no—
116#117×C43C2311yescharacteristic
117#117×C43C2311yescharacteristic
118C2×C42×C43C2311yescharacteristic
119#104×C43—41no—
120#104×C43—41no—
121#99×C43—41no—
122C23×D43—21no—
123#41×C43—21no—
124#41×C43—21no—
125#41×C43—21no—
126#41×C43—21no—
127#41×C43—21no—
128#41×C43—21no—
129#41×C43—21no—
130#41×C43—21no—
131C2×Q8×C43C22×C411yescharacteristic
132C2×Q8×C43C22×C411yescharacteristic
133C2×D4×C43—21no—
134C2×D4×C43—21no—
135C2×D4×C43—41no—
136C2×D4×C43C22×C411yescharacteristic
137C2×D4×C43C22×C411yescharacteristic
138C22×C4×C43—21no—
139C22×C4×C43—21no—
140C22×C4×C43—21no—
141C22×C4×C43C2411yescharacteristic
142C22×Dic43—21no—
143C2×D172—21no—
144C2×D172—21no—
145C2×D172—21no—
146C2×D172—21no—
147C2×D172—21no—
148C2×D172C22×C412yes—
149C2×C4×D43—42no—
150C2×Dic86—21no—
151C2×Dic86—21no—
152C2×Dic86—21no—
153C2×Dic86—21no—
154C2×Dic86—21no—
155C2×Dic86C22×C412yes—
156M16×C43—21no—
157M16×C43—21no—
158M16×C43—21no—
159M16×C43—21no—
160M16×C43—42no—
161C2×C8×C43—21no—
162C2×C8×C43—21no—
163C2×C8×C43—42no—
164C4⋊C4×C43—21no—
165C4⋊C4×C43—21no—
166C4⋊C4×C43—41no—
167C22⋊C4×C43—21no—
168C22⋊C4×C43—21no—
169C22⋊C4×C43—41no—
170C22⋊C4×C43—41no—
171C42×C43—21no—
172C42×C43—21no—
173C42×C43—21no—
174C42×C43C22×C411yescharacteristic
175C42×C43C22×C411yescharacteristic
176C22⋊Dic43—21no—
177C22⋊Dic43—21no—
178#10621885—42no—
179#10621885—42no—
180#10621884—42no—
181#10621884—42no—
182#10621883—42no—
183#10621883—42no—
184#10621882—42no—
185#10621882—42no—
186(C2×D43)⋊C4—42no—
187(C2×D43)⋊C4—42no—
188(C2×D43)⋊C4—42no—
189C4⋊Dic43—21no—
190C4⋊Dic43—21no—
191Dic43⋊C4—42no—
192C4×Dic43—21no—
193C4×Dic43—21no—
194C4×Dic43—42no—
195#10621877—21no—
196#10621877—21no—
197#10621877—21no—
198#10621877—21no—
199#10621877—21no—
200#10621877—21no—
201#10621877—21no—
202#10621877—21no—
203#10621877—42no—
204C2×C43⋊C8—21no—
205C2×C43⋊C8—21no—
206C2×C43⋊C8—42no—
207C2×C43⋊C8C22×C412yes—
208C2×C43⋊C8C22×C412yes—
209C23×C43—21no—
210C23×C43—21no—
211C23×C43H(5,𝔽2)11yescharacteristic
212C22×D43—22no—
213C22×D43—41no—
214C22×D43—41no—
215C22×D43—82no—
216Q8×C43—21no—
217Q8×C43—21no—
218Q8×C43—21no—
219Q8×C43—21no—
220D4×C43—21no—
221D4×C43—21no—
222D4×C43—21no—
223D4×C43—21no—
224D4×C43—41no—
225D4×C43—41no—
226D4×C43—41no—
227D4×C43—41no—
228D4×C43—82no—
229C2×C4×C43—21no—
230C2×C4×C43—21no—
231C2×C4×C43—21no—
232C2×C4×C43—21no—
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—81no—
240C2×C4×C43C23×C411yescharacteristic
241C2×C4×C43H(5,𝔽2)11yescharacteristic
242C2×C4×C43H(5,𝔽2)11yescharacteristic
243C2×C4×C43H(5,𝔽2)11yescharacteristic
244C2×C4×C43H(5,𝔽2)11yescharacteristic
245C2×C4×C43H(5,𝔽2)11yescharacteristic
246C2×Dic43—22no—
247C2×Dic43—41no—
248C2×Dic43—41no—
249C2×Dic43—41no—
250C2×Dic43—41no—
251D172—22no—
252D172—22no—
253D172—41no—
254D172—41no—
255C4×D43—162no—
256Dic86—22no—
257Dic86—22no—
258Dic86—41no—
259Dic86—41no—
260C8×C43—41no—
261C8×C43—41no—
262C43⋊C8—22no—
263C43⋊C8—22no—
264C43⋊C8—41no—
265C43⋊C8—41no—
266#23362—431nomaximal, Sylow
267C22×C43—41no—
268C22×C43—41no—
269C22×C43—41no—
270C22×C43—81no—
271C22×C43—81no—
272C22×C43#51811yescharacteristic
273C22×C43#56011yescharacteristic
274C22×C43#56011yescharacteristic
275C2×D43—42no—
276C2×D43—82no—
277C2×D43—82no—
278C2×D43—161no—
279C4×C43—41no—
280C4×C43—41no—
281C4×C43—41no—
282C4×C43—41no—
283C4×C43—81no—
284C4×C43—81no—
285C4×C43#51811yescharacteristic
286C4×C43#51811yescharacteristic
287C4×C43#56011yescharacteristic
288C4×C43#56011yescharacteristic
289Dic43—42no—
290Dic43—81no—
291Dic43—81no—
292#3153—431no—
293#1905—431no—
294#1905—431no—
295#1904—431no—
296#1904—431no—
297#1903—431no—
298#1903—431no—
299#1902—431no—
300#1902—431no—
301#1888—431no—
302#1885—431no—
303#1884—431no—
304#1884D4311yescharacteristic, complemented
305#1841—431no—
306#1841—431no—
307C2×C43—21no—
308C2×C43—21no—
309C2×C43—21no—
310C2×C43—81no—
311C2×C43—81no—
312C2×C43#238011yescharacteristic
313D43—82no—
314C2×#137—431no—
315C2×#137—431no—
316C2×AGL(1,ℤ/8)—431no—
317C2×AGL(1,ℤ/8)—431no—
318#568—431no—
319#568C2×D4311yescharacteristic
320#532C2×D4311yescharacteristic
321C2×#124—431no—
322#519—431no—
323#518—431no—
324#497—432no—
325#496—432no—
326#495—432no—
327#495—432no—
328#421—431no—
329#421—431no—
330#421C2×D4311yescharacteristic
331#421C2×D4311yescharacteristic
332#419—431no—
333#419—431no—
334#418—431no—
335#418—431no—
336C2×#101—431no—
337C2×#100—431no—
338#410—431no—
339#410C2×D4311yescharacteristic
340C4×M16—431no—
341#344—431no—
342#344—431no—
343#344—431no—
344#344—431no—
345#339—431no—
346#339—431no—
347#339C2×D4311yescharacteristic
348#339C2×D4311yescharacteristic
349#338—431no—
350#338—431no—
351H(3,ℤ/4)—431no—
352H(3,ℤ/4)—431no—
353C43#2336211yescharacteristic, complemented, Sylow
354C2×#41C22×D4311yescharacteristic
355C2×#41C22×D4311yescharacteristic
356C22×Q8—431no—
357C22×D4—431no—
358#137—1721no—
359#137—1721no—
360#137—1721no—
361#137—1721no—
362AGL(1,ℤ/8)—1721no—
363AGL(1,ℤ/8)—1721no—
364AGL(1,ℤ/8)—1721no—
365AGL(1,ℤ/8)—1721no—
366C2×Q16—432no—
367C2×Q16—432no—
368C2×SD16—432no—
369C2×SD16—432no—
370C2×SD16—432no—
371C2×SD16—432no—
372C2×D8—432no—
373C2×D8—432no—
374#131—41no—
375#131—41no—
376#131—1721no—
377#131—1721no—
378C2×M16—41no—
379C2×M16—431no—
380C2×M16—431no—
381C2×M16—431no—
382C2×M16—431no—
383C2×M16—1721no—
384C2×M16C22×D4311yescharacteristic
385C2×M16C22×D4311yescharacteristic
386C4⋊Q8C4×D4311yescharacteristic, complemented
387#127C4×D4311yescharacteristic, complemented
388#124—432no—
389#124—432no—
390#124—1721no—
391#124C4×D4311yescharacteristic, complemented
392#124C4×D4311yescharacteristic, complemented
393#121—41no—
394C4×Q8—1721no—
395C4×Q8—1721no—
396C4×D4—41no—
397C4×D4—1721no—
398C4×D4—1721no—
399#117—431no—
400#117—431no—
401#117—1721no—
402#117C22×D4311yescharacteristic
403#117C22×D4311yescharacteristic
404C2×C22⋊C4—1721no—
405C2×C22⋊C4—1721no—
406C2×C42C22×D4311yescharacteristic
407#104—41no—
408#104—41no—
409#104—1721no—
410#104—1721no—
411#103—1721no—
412#103—1721no—
413#102—1721no—
414#102—1721no—
415#101—1721no—
416#100—1721no—
417#99—41no—
418#99—1721no—
419#97—432no—
420C4×C8—432no—
421C24—861no—
422#41—21no—
423#41—21no—
424#41—21no—
425#41—21no—
426#41—21no—
427#41—21no—
428#41—21no—
429#41—21no—
430C2×Q8—432no—
431C2×Q8—861no—
432C2×Q8—861no—
433C2×Q8—861no—
434C2×Q8—861no—
435C2×Q8—861no—
436C2×Q8C2×C4×D4311yescharacteristic
437C2×Q8C2×C4×D4311yescharacteristic
438C2×D4—21no—
439C2×D4—21no—
440C2×D4—41no—
441C2×D4—432no—
442C2×D4—861no—
443C2×D4—861no—
444C2×D4—861no—
445C2×D4—861no—
446C2×D4—861no—
447C2×D4C2×C4×D4311yescharacteristic
448C2×D4C2×C4×D4311yescharacteristic
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—861no—
453C22×C4—1722no—
454C22×C4C23×D4311yescharacteristic
455Q16—1722no—
456Q16—1722no—
457SD16—1722no—
458SD16—1722no—
459SD16—1722no—
460SD16—1722no—
461D8—1722no—
462D8—1722no—
463M16—21no—
464M16—21no—
465M16—21no—
466M16—21no—
467M16—42no—
468M16—861no—
469M16—861no—
470M16—861no—
471M16—861no—
472M16—861no—
473M16—861no—
474M16—861no—
475M16—861no—
476M16—1722no—
477C2×C8—21no—
478C2×C8—21no—
479C2×C8—42no—
480C2×C8—432no—
481C2×C8—432no—
482C2×C8—861no—
483C2×C8—861no—
484C2×C8—1722no—
485C4⋊C4—21no—
486C4⋊C4—21no—
487C4⋊C4—41no—
488C4⋊C4—861no—
489C4⋊C4—861no—
490C4⋊C4—1722no—
491C22⋊C4—21no—
492C22⋊C4—21no—
493C22⋊C4—41no—
494C22⋊C4—41no—
495C22⋊C4—861no—
496C22⋊C4—861no—
497C22⋊C4—1722no—
498C22⋊C4—1722no—
499C22⋊C4—1722no—
500C42—21no—
501C42—21no—
502C42—21no—
503C42—861no—
504C42—861no—
505C42—1722no—
506C42C2×C4×D4311yescharacteristic
507C42C2×C4×D4311yescharacteristic
508C23—21no—
509C23—21no—
510C23—862no—
511C23—3442no—
512C23—1721no—
513C23—1721no—
514C23#1306337011yescharacteristic
515Q8—21no—
516Q8—21no—
517Q8—21no—
518Q8—21no—
519Q8—862no—
520Q8—862no—
521Q8—1721no—
522Q8—1721no—
523D4—21no—
524D4—21no—
525D4—21no—
526D4—21no—
527D4—41no—
528D4—41no—
529D4—41no—
530D4—41no—
531D4—82no—
532D4—862no—
533D4—862no—
534D4—1721no—
535D4—1721no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—81no—
547C2×C4—862no—
548C2×C4—1721no—
549C2×C4—1721no—
550C2×C4—1721no—
551C2×C4—1721no—
552C2×C4—6882no—
553C2×C4C22×C4×D4311yescharacteristic
554C2×C4#1306337011yescharacteristic
555C2×C4#1306337011yescharacteristic
556C2×C4#1306337011yescharacteristic
557C2×C4#1306337111yescharacteristic
558C2×C4#1306337111yescharacteristic
559C8—41no—
560C8—41no—
561C8—862no—
562C8—862no—
563C8—1721no—
564C8—1721no—
565C22—41no—
566C22—41no—
567C22—41no—
568C22—81no—
569C22—81no—
570C22—3442no—
571C22—3442no—
572C22—1722no—
573C22—6881no—
574C22#1458337211yescharacteristic
575C22#1458363711yescharacteristic
576C22#1458363711yescharacteristic
577C4—41no—
578C4—41no—
579C4—41no—
580C4—41no—
581C4—81no—
582C4—81no—
583C4—3441no—
584C4—3441no—
585C4—1722no—
586C4#1458337111yescharacteristic
587C4#1458337111yescharacteristic
588C4#1458363811yescharacteristic
589C4#1458363911yescharacteristic
590C2—21no—
591C2—21no—
592C2—21no—
593C2—81no—
594C2—81no—
595C2—3442no—
596C2#1913777011yescharacteristic
subgroupG/H
centerC2#19137770
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1884C2
socleC2×C43#2380
prime radical#19145063C2
cosocleC22×C4×C43C24
hypercenter#1884D43
hypocenterC43#23362
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2 ◁ C22×C4 ◁ #1884

Complements

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

NH ≅ G/Ntype
2. #19135092C2semidirect
3. #19135086C2semidirect
4. #19135085C2semidirect
5. #19135079C2semidirect
6. #19135075C2semidirect
7. #19135073C2semidirect
8. #19135068C2semidirect
9. #19135066C2semidirect
10. #19134997C2semidirect
11. #19134982C2semidirect
12. #19134979C2semidirect
13. #19134741C2semidirect
14. #19134741C2semidirect
15. C43×#1884C2semidirect
24. #14583291C4semidirect
25. #14583286C4semidirect
26. #14583281C4semidirect
27. #14583281C4semidirect
65. C2×#10621885C2×C4semidirect
66. C2×#10621885C2×C4semidirect
67. C2×#10621883C2×C4semidirect
68. C2×#10621883C2×C4semidirect
101. #13063236C2×C4semidirect
102. C4×C43⋊C8C2×C4semidirect
110. C4⋊Q8×C43C2×C4semidirect
111. #127×C43C2×C4semidirect
112. #124×C43C2×C4semidirect
113. #124×C43C2×C4semidirect
304. #1884D43semidirect
353. C43#23362semidirect
386. C4⋊Q8C4×D43semidirect
387. #127C4×D43semidirect
391. #124C4×D43semidirect
392. #124C4×D43semidirect

Maximal subgroups

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

subgroupindex
#191450632
#191350922
#191350862
#191350852
#191350792
#191350752
#191350732
#191350682
#191350662
#191349972
#191349822
#191349792
#191347412
C43×#18842
#2336243