Finite Group Databasebeta

← #25123177

Subgroups — #25123177

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#19145057C211yesmaximal, characteristic
2#19135092C211yesmaximal, characteristic, complemented
3#19135090C211yesmaximal, characteristic, complemented
4#19135082C211yesmaximal, characteristic, complemented
5#19135077C211yesmaximal, characteristic, complemented
6#19135072C211yesmaximal, characteristic, complemented
7#19135067C211yesmaximal, characteristic, complemented
8#19135066C211yesmaximal, characteristic, complemented
9#19134995C211yesmaximal, characteristic, complemented
10#19134983C211yesmaximal, characteristic, complemented
11#19134976C211yesmaximal, characteristic, complemented
12#19134975C211yesmaximal, characteristic, complemented
13#19134743C211yesmaximal, characteristic, complemented
14#19134742C211yesmaximal, characteristic, complemented
15C43×#1904C211yesmaximal, characteristic, complemented
16C2×#13063358C2211yescharacteristic
17C2×#13063355C2211yescharacteristic
18C2×#13063351C2211yescharacteristic
19#14583666C2211yescharacteristic
20#14583665C2211yescharacteristic
21#14583445C2211yescharacteristic
22C2×#13063312C2211yescharacteristic
23#14583376C2211yescharacteristic
24#14583290C412yescomplemented
25#14583287C412yescomplemented
26#14583282C412yescomplemented
27#14583280C412yescomplemented
28#14582917C2211yescharacteristic
29#14582917C2211yescharacteristic
30#14582916C2211yescharacteristic
31#14582907C2211yescharacteristic
32#14582907C2211yescharacteristic
33#14582904C2211yescharacteristic
34C2×#13063243C2211yescharacteristic
35C2×#13063242C2211yescharacteristic
36#14582872C2211yescharacteristic
37M16×Dic43C2211yescharacteristic
38#14582670C2211yescharacteristic
39#14582669C2211yescharacteristic
40#14582669C2211yescharacteristic
41#14582660C2211yescharacteristic
42#14582658C2211yescharacteristic
43#14582658C2211yescharacteristic
44#14582658C2211yescharacteristic
45C43⋊#338C2211yescharacteristic
46C43⋊#338C2211yescharacteristic
47#14582655C2211yescharacteristic
48C2×AGL(1,ℤ/8)×C43C2211yescharacteristic
49C43×#518C2211yescharacteristic
50C43×#421C2211yescharacteristic
51C43×#418C2211yescharacteristic
52C43×#410C2211yescharacteristic
53C43×#344C2211yescharacteristic
54C43×H(3,ℤ/4)C2211yescharacteristic
55C2×#10621898C2311yescharacteristic
56C22×Dic86C2311yescharacteristic
57#13063358—41no—
58#13063358—41no—
59#13063355—41no—
60#13063355—41no—
61#13063351—41no—
62#13063351—41no—
63C2×Dic172C2×C412yescomplemented
64C2×#10621885C2×C412yescomplemented
65C2×#10621873C2×C412yescomplemented
66C2×#10621883C2×C412yes—
67C2×#10621883C2×C412yescomplemented
68C2×#10621882C2×C412yes—
69#13063333—41no—
70#13063332—41no—
71#13063332—41no—
72#13063331—41no—
73C2×#10621877—41no—
74C2×#10621877C2311yescharacteristic
75C2×#10621877C2311yescharacteristic
76C2×#10621877C2311yescharacteristic
77C2×#10621877C2311yescharacteristic
78M16×D43—41no—
79#13063323C2×C411yescharacteristic, complemented
80#13063321C2×C411yescharacteristic, complemented
81#13063314C2×C411yescharacteristic, complemented
82#13063312—41no—
83#13063312C2×C412yes—
84#13063312C2×C412yes—
85#13063312C2×C411yescharacteristic, complemented
86#13063297—41no—
87C4×Dic86—41no—
88#13063290—41no—
89C4×C22⋊D43—41no—
90#13063284C2311yescharacteristic
91#13063281—41no—
92C2×C22⋊Dic43—41no—
93C2×C4×Dic43C2311yescharacteristic
94#13063253—41no—
95#13063253—41no—
96#13063252—41no—
97#13063248—41no—
98#13063248—41no—
99#13063246—41no—
100#13063243—41no—
101#13063242—41no—
102#13063239—41no—
103#13063235C2×C412yescomplemented
104C8×Dic43C2×C412yescomplemented
105C2×#41×C43C2311yescharacteristic
106C22×D4×C43C2311yescharacteristic
107AGL(1,ℤ/8)×C43—41no—
108AGL(1,ℤ/8)×C43—41no—
109C2×SD16×C43C2×C412yes—
110C2×D8×C43C2×C412yes—
111C2×M16×C43C2311yescharacteristic
112C2×M16×C43C2311yescharacteristic
113C4×D4×C43—41no—
114C4×D4×C43—41no—
115#117×C43C2311yescharacteristic
116#117×C43C2311yescharacteristic
117#117×C43C2311yescharacteristic
118C2×C22⋊C4×C43—41no—
119#104×C43—41no—
120#102×C43—41no—
121#99×C43—41no—
122C24×C43—21no—
123#41×C43—21no—
124#41×C43—21no—
125#41×C43—21no—
126#41×C43—21no—
127C2×Q8×C43C22×C411yescharacteristic
128C2×D4×C43—21no—
129C2×D4×C43—21no—
130C2×D4×C43—21no—
131C2×D4×C43—21no—
132C2×D4×C43—21no—
133C2×D4×C43—21no—
134C2×D4×C43C22×C411yescharacteristic
135C2×D4×C43C22×C412yes—
136C22×C4×C43—21no—
137C22×C4×C43—42no—
138C22×C4×C43C2411yescharacteristic
139C2×C22⋊D43—21no—
140C2×C22⋊D43—41no—
141C22×Dic43—21no—
142C22×Dic43—21no—
143#10621898—21no—
144#10621898—21no—
145#10621898—21no—
146#10621898—21no—
147C2×D172C22×C411yescharacteristic
148C2×C4×D43—21no—
149C2×Dic86—21no—
150C2×Dic86—21no—
151C2×Dic86—21no—
152C2×Dic86—21no—
153C2×Dic86—21no—
154C2×Dic86C22×C412yes—
155C2×Dic86C22×C411yescharacteristic
156SD16×C43—42no—
157D8×C43—42no—
158M16×C43—21no—
159M16×C43—21no—
160M16×C43—21no—
161M16×C43—21no—
162C2×C8×C43—21no—
163C2×C8×C43C22×C412yes—
164C4⋊C4×C43—21no—
165C4⋊C4×C43—21no—
166C4⋊C4×C43—21no—
167C22⋊C4×C43—21no—
168C22⋊C4×C43—21no—
169C22⋊C4×C43—21no—
170C22⋊C4×C43—42no—
171C42×C43—21no—
172C42×C43—21no—
173C42×C43—21no—
174C22⋊Dic43—21no—
175C22⋊Dic43—42no—
176C22⋊Dic43—42no—
177C22⋊Dic43—41no—
178#10621885—42no—
179#10621883—42no—
180#10621883—42no—
181#10621882—42no—
182(C2×D43)⋊C4—41no—
183C4⋊Dic43—21no—
184Dic43⋊C4—41no—
185Dic43⋊C4—42no—
186C4×Dic43—21no—
187C4×Dic43—21no—
188C4×Dic43—42no—
189C4×Dic43C22×C411yescharacteristic
190C4×Dic43C22×C411yescharacteristic
191#10621877—21no—
192#10621877—21no—
193#10621877—21no—
194#10621877—21no—
195#10621877—21no—
196#10621877—21no—
197#10621877—21no—
198#10621877—21no—
199#10621877—42no—
200C2×C43⋊C8—21no—
201C2×C43⋊C8—21no—
202C2×C43⋊C8—21no—
203C2×C43⋊C8—42no—
204C2×C43⋊C8C22×C412yes—
205Dic172—42no—
206#10621873—42no—
207#10621872—42no—
208C8×D43—42no—
209C23×C43—22no—
210C23×C43—21no—
211C23×C43—41no—
212C23×C43—41no—
213C23×C43—82no—
214C23×C43H(5,𝔽2)11yescharacteristic
215C22×D43—21no—
216Q8×C43—21no—
217Q8×C43—21no—
218D4×C43—22no—
219D4×C43—21no—
220D4×C43—21no—
221D4×C43—22no—
222D4×C43—41no—
223D4×C43—41no—
224D4×C43—41no—
225D4×C43—41no—
226C2×C4×C43—21no—
227C2×C4×C43—41no—
228C2×C4×C43—41no—
229C2×C4×C43—41no—
230C2×C4×C43—41no—
231C2×C4×C43—41no—
232C2×C4×C43—162no—
233C2×C4×C43C23×C411yescharacteristic
234C2×C4×C43H(5,𝔽2)11yescharacteristic
235C2×C4×C43H(5,𝔽2)11yescharacteristic
236C2×C4×C43H(5,𝔽2)11yescharacteristic
237C2×C4×C43H(5,𝔽2)11yescharacteristic
238C2×C4×C43H(5,𝔽2)11yescharacteristic
239C22⋊D43—41no—
240C22⋊D43—41no—
241C22⋊D43—82no—
242C2×Dic43—21no—
243C2×Dic43—21no—
244C2×Dic43—21no—
245C2×Dic43—22no—
246C2×Dic43—41no—
247C2×Dic43—41no—
248C2×Dic43—41no—
249C2×Dic43—81no—
250D172—21no—
251D172—21no—
252C4×D43—41no—
253C4×D43—41no—
254Dic86—22no—
255Dic86—21no—
256Dic86—21no—
257Dic86—22no—
258Dic86—41no—
259Dic86—41no—
260C8×C43—22no—
261C8×C43—41no—
262C43⋊C8—22no—
263C43⋊C8—41no—
264C43⋊C8—41no—
265C43⋊C8—41no—
266#23362—431nomaximal, Sylow
267C22×C43—41no—
268C22×C43—42no—
269C22×C43—41no—
270C22×C43—82no—
271C22×C43—81no—
272C22×C43—82no—
273C22×C43—161no—
274C22×C43#51811yescharacteristic
275C22×C43#56011yescharacteristic
276C22×C43#56011yescharacteristic
277C2×D43—41no—
278C2×D43—81no—
279C4×C43—41no—
280C4×C43—81no—
281C4×C43—81no—
282C4×C43—81no—
283C4×C43#51811yescharacteristic
284C4×C43#51811yescharacteristic
285C4×C43#56011yescharacteristic
286C4×C43#56011yescharacteristic
287Dic43—41no—
288Dic43—41no—
289Dic43—42no—
290Dic43—41no—
291Dic43—81no—
292#3153—431no—
293#1905—431no—
294#1905—431no—
295#1904—431no—
296#1904D4311yescharacteristic, complemented
297#1903—431no—
298#1903—431no—
299#1902—431no—
300#1902—431no—
301#1888—431no—
302#1885—431no—
303#1884—431no—
304#1884—431no—
305#1841—431no—
306#1841—431no—
307C2×C43—21no—
308C2×C43—21no—
309C2×C43—21no—
310C2×C43—81no—
311C2×C43—82no—
312C2×C43#238011yescharacteristic
313D43—81no—
314C2×#137—431no—
315C2×#137—431no—
316C2×AGL(1,ℤ/8)—431no—
317C2×AGL(1,ℤ/8)C2×D4311yescharacteristic
318#568—431no—
319#568—431no—
320#532—431no—
321C2×#124—431no—
322#519—431no—
323#518C2×D4311yescharacteristic
324#497—432no—
325#496—432no—
326#495—432no—
327#495—432no—
328#421—431no—
329#421—431no—
330#421—431no—
331#421C2×D4311yescharacteristic
332#419—431no—
333#419—431no—
334#418—431no—
335#418C2×D4311yescharacteristic
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#344C2×D4311yescharacteristic
345#339—431no—
346#339—431no—
347#339—431no—
348#339—431no—
349#338—431no—
350#338—431no—
351H(3,ℤ/4)—431no—
352H(3,ℤ/4)C2×D4311yescharacteristic
353C43#2336211yescharacteristic, complemented, Sylow
354C2×#41—431no—
355C2×#41C22×D4311yescharacteristic
356C22×Q8—431no—
357C22×D4C22×D4311yescharacteristic
358#137—1721no—
359#137—1721no—
360#137—1721no—
361#137—1721no—
362AGL(1,ℤ/8)—41no—
363AGL(1,ℤ/8)—41no—
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×SD16C4×D4312yes—
372C2×D8—432no—
373C2×D8C4×D4312yes—
374#131—1721no—
375#131—1721no—
376#131—1721no—
377#131—1721no—
378C2×M16—431no—
379C2×M16—431no—
380C2×M16—431no—
381C2×M16—431no—
382C2×M16—1721no—
383C2×M16—1721no—
384C2×M16C22×D4311yescharacteristic
385C2×M16C22×D4311yescharacteristic
386C4⋊Q8—431no—
387#127—431no—
388#124—431no—
389#124—432no—
390#124—432no—
391#124—431no—
392#124—1721no—
393#121—1721no—
394C4×Q8—1721no—
395C4×Q8—1721no—
396C4×D4—41no—
397C4×D4—41no—
398C4×D4—1721no—
399#117—431no—
400#117—1721no—
401#117C22×D4311yescharacteristic
402#117C22×D4311yescharacteristic
403#117C22×D4311yescharacteristic
404C2×C22⋊C4—41no—
405C2×C22⋊C4—1721no—
406C2×C42—431no—
407#104—41no—
408#104—1721no—
409#104—1721no—
410#104—1721no—
411#103—1721no—
412#103—1721no—
413#102—41no—
414#102—1721no—
415#101—1721no—
416#100—1721no—
417#99—41no—
418#99—1721no—
419#97—432no—
420C4×C8—432no—
421C24—21no—
422#41—21no—
423#41—21no—
424#41—21no—
425#41—21no—
426#41—861no—
427#41—861no—
428#41—861no—
429#41—861no—
430C2×Q8—432no—
431C2×Q8—431no—
432C2×Q8—861no—
433C2×Q8—861no—
434C2×Q8—861no—
435C2×Q8—861no—
436C2×Q8—861no—
437C2×Q8C2×C4×D4311yescharacteristic
438C2×D4—21no—
439C2×D4—21no—
440C2×D4—21no—
441C2×D4—21no—
442C2×D4—21no—
443C2×D4—21no—
444C2×D4—431no—
445C2×D4—861no—
446C2×D4—1721no—
447C2×D4C2×C4×D4312yes—
448C2×D4C2×C4×D4311yescharacteristic
449C22×C4—21no—
450C22×C4—42no—
451C22×C4—861no—
452C22×C4—861no—
453C22×C4—861no—
454C22×C4C23×D4311yescharacteristic
455Q16—1722no—
456Q16—1722no—
457SD16—42no—
458SD16—1722no—
459SD16—1722no—
460SD16—1722no—
461D8—42no—
462D8—1722no—
463M16—21no—
464M16—21no—
465M16—21no—
466M16—21no—
467M16—861no—
468M16—861no—
469M16—861no—
470M16—861no—
471M16—861no—
472M16—861no—
473M16—861no—
474M16—861no—
475M16—1722no—
476M16—1722no—
477C2×C8—21no—
478C2×C8—432no—
479C2×C8—861no—
480C2×C8—861no—
481C2×C8—861no—
482C2×C8—1722no—
483C2×C8—1722no—
484C2×C8C2×C4×D4312yes—
485C4⋊C4—21no—
486C4⋊C4—21no—
487C4⋊C4—21no—
488C4⋊C4—861no—
489C4⋊C4—1721no—
490C4⋊C4—1722no—
491C22⋊C4—21no—
492C22⋊C4—21no—
493C22⋊C4—21no—
494C22⋊C4—42no—
495C22⋊C4—861no—
496C22⋊C4—1721no—
497C22⋊C4—1722no—
498C22⋊C4—1722no—
499C22⋊C4—1721no—
500C42—21no—
501C42—21no—
502C42—21no—
503C42—431no—
504C42—431no—
505C42—861no—
506C42—861no—
507C42—1722no—
508C23—22no—
509C23—21no—
510C23—41no—
511C23—41no—
512C23—82no—
513C23—861no—
514C23#1306337011yescharacteristic
515Q8—21no—
516Q8—21no—
517Q8—861no—
518Q8—862no—
519Q8—862no—
520Q8—861no—
521Q8—1721no—
522Q8—1721no—
523D4—22no—
524D4—21no—
525D4—21no—
526D4—22no—
527D4—41no—
528D4—41no—
529D4—41no—
530D4—41no—
531D4—861no—
532D4—861no—
533D4—3442no—
534D4—1721no—
535D4—1721no—
536C2×C4—21no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—162no—
543C2×C4—861no—
544C2×C4—861no—
545C2×C4—862no—
546C2×C4—861no—
547C2×C4—3441no—
548C2×C4—1721no—
549C2×C4—1721no—
550C2×C4—1721no—
551C2×C4—1721no—
552C2×C4—1721no—
553C2×C4C22×C4×D4311yescharacteristic
554C2×C4#1306337011yescharacteristic
555C2×C4#1306337011yescharacteristic
556C2×C4#1306337011yescharacteristic
557C2×C4#1306337111yescharacteristic
558C2×C4#1306337111yescharacteristic
559C8—22no—
560C8—41no—
561C8—862no—
562C8—1721no—
563C8—1721no—
564C8—1721no—
565C22—41no—
566C22—41no—
567C22—42no—
568C22—81no—
569C22—82no—
570C22—82no—
571C22—161no—
572C22—3441no—
573C22—1721no—
574C22#1458337111yescharacteristic
575C22#1458363711yescharacteristic
576C22#1458363811yescharacteristic
577C4—41no—
578C4—81no—
579C4—81no—
580C4—81no—
581C4—3441no—
582C4—1721no—
583C4—1721no—
584C4—1721no—
585C4—1722no—
586C4#1458337111yescharacteristic
587C4#1458337211yescharacteristic
588C4#1458363711yescharacteristic
589C4#1458363911yescharacteristic
590C2—21no—
591C2—21no—
592C2—21no—
593C2—82no—
594C2—81no—
595C2—3441no—
596C2#1913777011yescharacteristic
subgroupG/H
centerC2#19137770
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1904C2
socleC2×C43#2380
prime radical#19145057C2
cosocleC22×C4×C43C24
hypercenter#1904D43
hypocenterC43#23362
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2 ◁ C22×C4 ◁ #1904

Complements

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

NH ≅ G/Ntype
2. #19135092C2semidirect
3. #19135090C2semidirect
4. #19135082C2semidirect
5. #19135077C2semidirect
6. #19135072C2semidirect
7. #19135067C2semidirect
8. #19135066C2semidirect
9. #19134995C2semidirect
10. #19134983C2semidirect
11. #19134976C2semidirect
12. #19134975C2semidirect
13. #19134743C2semidirect
14. #19134742C2semidirect
15. C43×#1904C2semidirect
24. #14583290C4semidirect
25. #14583287C4semidirect
26. #14583282C4semidirect
27. #14583280C4semidirect
63. C2×Dic172C2×C4semidirect
64. C2×#10621885C2×C4semidirect
65. C2×#10621873C2×C4semidirect
67. C2×#10621883C2×C4semidirect
79. #13063323C2×C4semidirect
80. #13063321C2×C4semidirect
81. #13063314C2×C4semidirect
85. #13063312C2×C4semidirect
103. #13063235C2×C4semidirect
104. C8×Dic43C2×C4semidirect
296. #1904D43semidirect
353. C43#23362semidirect

Maximal subgroups

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

subgroupindex
#191450572
#191350922
#191350902
#191350822
#191350772
#191350722
#191350672
#191350662
#191349952
#191349832
#191349762
#191349752
#191347432
#191347422
C43×#19042
#2336243