Finite Group Databasebeta

← #25079012

Subgroups — #25079012

Order 11008.

672 conjugacy classes of subgroups.

The subgroup lattice has 592 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145152C211yesmaximal, characteristic, complemented
2#19144376C211yesmaximal, characteristic, complemented
3#19144043C211yesmaximal, characteristic
4C8×#10621900C211yesmaximal, characteristic, complemented
5#19134024C211yesmaximal, characteristic, complemented
6#19134016C211yesmaximal, characteristic, complemented
7#19134010C211yesmaximal, characteristic, complemented
8#19134002C211yesmaximal, characteristic, complemented
9#19133978C211yesmaximal, characteristic, complemented
10#19133970C211yesmaximal, characteristic, complemented
11#19133940C211yesmaximal, characteristic, complemented
12#334×D43C211yesmaximal, characteristic, complemented
13#19133251C211yesmaximal, characteristic, complemented
14#19133241C211yesmaximal, characteristic, complemented
15C43×#1665C211yesmaximal, characteristic, complemented
16C2×#13063344—21no—
17#14583454C2211yescharacteristic
18#14583447C2211yescharacteristic
19C4×#10621900C2211yescharacteristic
20#14583297C2211yescharacteristic
21#14583249C2211yescharacteristic
22#14583245C2211yescharacteristic
23#14583205—21no—
24#14583197—21no—
25#14583195C2211yescharacteristic
26#14583189C2211yescharacteristic
27#14583181C2211yescharacteristic
28#14583125—21no—
29#14583125—21no—
30#14583120—21no—
31#14583112—21no—
32#14583110C2211yescharacteristic
33#14583104C2211yescharacteristic
34#14583096C2211yescharacteristic
35C8×Dic86C2211yescharacteristic
36#14583023C2211yescharacteristic
37SD16×Dic43—21no—
38SD16×Dic43—21no—
39D4×C43⋊C8C2211yescharacteristic
40C8×C22⋊D43—21no—
41(C22⋊D43)⋊C8—21no—
42#14582951C2211yescharacteristic
43#14582949—21no—
44#14582936—21no—
45C4⋊C8×D43C2211yescharacteristic
46C4⋊C8×D43C2211yescharacteristic
47#14582892—21no—
48#14582892—21no—
49C2×C8×Dic43—21no—
50C4×C8×D43C2211yescharacteristic
51#14582650C2211yescharacteristic
52#14582649C2211yescharacteristic
53#14582649C2211yescharacteristic
54#14582647C2211yescharacteristic
55#14582647C2211yescharacteristic
56#14582646C2211yescharacteristic
57#14582645C2211yescharacteristic
58#14582644C2211yescharacteristic
59#14582643C2211yescharacteristic
60C43×#492C2211yescharacteristic
61C43×#474C2211yescharacteristic
62C43×#459C2211yescharacteristic
63C8×D4×C43C2211yescharacteristic
64C43×#334C2211yescharacteristic
65C43×#332C2211yescharacteristic
66C43×#331C2211yescharacteristic
67C2×#10621900—21no—
68C2×#10621900D411yescharacteristic
69#13063344—44no—
70C2×Dic172—21no—
71C2×#10621883—21no—
72C2×#10621883—21no—
73C22×C43⋊C8—21no—
74C2×C8×D43—21no—
75C2×C8×D43—21no—
76C2×C8×D43D411yescharacteristic
77C2×C8×D43D411yescharacteristic
78#13063325C2311yescharacteristic
79#13063325C2311yescharacteristic
80#13063316—21no—
81#13063312—21no—
82#13063305—21no—
83#13063301—21no—
84#13063296—21no—
85#13063296—21no—
86Q8×Dic43—21no—
87C4×Dic86C2311yescharacteristic
88#13063290—21no—
89#13063290D411yescharacteristic
90D4×Dic43—21no—
91D4×Dic43—21no—
92D4×Dic43D411yescharacteristic
93C4×C22⋊D43—21no—
94(C22⋊D43)⋊C4—21no—
95#13063283—21no—
96#13063283D411yescharacteristic
97#13063281—21no—
98C2×C4×Dic43—21no—
99C42×D43C2311yescharacteristic
100#13063259—21no—
101#13063257—21no—
102#13063257—21no—
103#13063256—21no—
104#13063256—21no—
105C4⋊(C43⋊C8)C2311yescharacteristic
106C4⋊(C43⋊C8)C2311yescharacteristic
107C4⋊(C43⋊C8)C2311yescharacteristic
108Dic43⋊C8—21no—
109Dic43⋊C8—21no—
110Dic43⋊C8—21no—
111Dic43⋊C8—21no—
112#13063250—21no—
113#13063250—21no—
114#13063249—21no—
115#13063249—21no—
116#13063248—21no—
117#13063248—21no—
118#13063246—21no—
119#13063246—21no—
120#13063246—21no—
121#13063246—21no—
122C22⋊(C43⋊C8)—21no—
123(C2×D43)⋊C8—21no—
124C4×C43⋊C8C2311yescharacteristic
125C8×Dic43—21no—
126C8×Dic43—21no—
127C8×Dic43—21no—
128C8×Dic43D411yescharacteristic
129C8×Dic43D411yescharacteristic
130C2×SD16×C43—21no—
131C2×SD16×C43—21no—
132C2×D8×C43—21no—
133C22×C8×C43—21no—
134C4⋊Q8×C43C2311yescharacteristic
135#127×C43C2311yescharacteristic
136C4×D4×C43C2311yescharacteristic
137#107×C43—21no—
138C4⋊C8×C43C2311yescharacteristic
139C4⋊C8×C43C2311yescharacteristic
140C4⋊C8×C43C2311yescharacteristic
141#102×C43—21no—
142#102×C43—21no—
143C22⋊C8×C43—21no—
144C4×C8×C43C2311yescharacteristic
145C2×Q8×C43—21no—
146C2×D4×C43—21no—
147C2×D4×C43—21no—
148C2×D4×C43—21no—
149C2×D4×C43C2×D411yescharacteristic
150C22×C4×C43—21no—
151C2×C22⋊D43—21no—
152C2×C22⋊D43—41no—
153C22×Dic43—21no—
154C22×Dic43—21no—
155C22×Dic43—41no—
156#10621900—22no—
157#10621900—42no—
158#10621900—42no—
159#10621900SD1614yescomplemented
160C2×C4×D43C2×D411yescharacteristic
161C2×C4×D43C2×D411yescharacteristic
162C2×C4×D43#4111yescharacteristic
163C2×Dic86—21no—
164C2×Dic86—21no—
165C2×Dic86C2×D411yescharacteristic
166SD16×C43—42no—
167SD16×C43—42no—
168D8×C43—42no—
169C2×C8×C43—21no—
170C2×C8×C43—21no—
171C2×C8×C43—21no—
172C2×C8×C43—42no—
173C2×C8×C43C2×D411yescharacteristic
174C2×C8×C43C2×D411yescharacteristic
175C4⋊C4×C43—21no—
176C4⋊C4×C43—21no—
177C4⋊C4×C43C2×D411yescharacteristic
178C22⋊C4×C43—21no—
179C42×C43C2411yescharacteristic
180C22⋊Dic43—21no—
181C22⋊Dic43—41no—
182C22⋊Dic43—41no—
183#10621883—42no—
184#10621883—42no—
185(C2×D43)⋊C4—21no—
186(C2×D43)⋊C4—41no—
187C4⋊Dic43—21no—
188C4⋊Dic43—21no—
189C4⋊Dic43—21no—
190C4⋊Dic43—21no—
191C4⋊Dic43—41no—
192C4⋊Dic43C2×D411yescharacteristic
193Dic43⋊C4—21no—
194Dic43⋊C4—21no—
195Dic43⋊C4—41no—
196C4×Dic43—21no—
197C4×Dic43—21no—
198C4×Dic43—21no—
199C4×Dic43—41no—
200C4×Dic43C2×D411yescharacteristic
201C4×Dic43C2×D411yescharacteristic
202C4×Dic43#4111yescharacteristic
203C2×C43⋊C8—21no—
204C2×C43⋊C8—21no—
205C2×C43⋊C8—21no—
206C2×C43⋊C8—42no—
207C2×C43⋊C8C2×D411yescharacteristic
208C2×C43⋊C8C2×D411yescharacteristic
209Dic172—42no—
210C8×D43—22no—
211C8×D43—41no—
212C8×D43—42no—
213C8×D43—42no—
214C23×C43—21no—
215C23×C43—41no—
216C22×D43#12111yescharacteristic
217Q8×C43—41no—
218Q8×C43—41no—
219D4×C43—21no—
220D4×C43—41no—
221D4×C43—41no—
222D4×C43—41no—
223D4×C43—41no—
224D4×C43—81no—
225D4×C43C2×SD1612yes—
226C2×C4×C43—21no—
227C2×C4×C43—41no—
228C2×C4×C43—41no—
229C2×C4×C43—41no—
230C2×C4×C43C22×D411yescharacteristic
231C2×C4×C43C22×D411yescharacteristic
232C2×C4×C43C2×#4111yescharacteristic
233C22⋊D43—24no—
234C22⋊D43—82no—
235C2×Dic43—21no—
236C2×Dic43—24no—
237C2×Dic43—21no—
238C2×Dic43—42no—
239C2×Dic43—41no—
240C2×Dic43—41no—
241C2×Dic43—82no—
242C2×Dic43#12111yescharacteristic
243C2×Dic43#12111yescharacteristic
244C2×Dic43#12111yescharacteristic
245C4×D43—21no—
246C4×D43—21no—
247C4×D43—41no—
248C4×D43C2×SD1612yes—
249C4×D43#13512yes—
250Dic86—21no—
251Dic86—41no—
252Dic86—41no—
253Dic86—81no—
254Dic86C2×SD1612yes—
255C8×C43—21no—
256C8×C43—41no—
257C8×C43—41no—
258C8×C43—41no—
259C8×C43#13512yescomplemented
260C43⋊C8—21no—
261C43⋊C8—21no—
262C43⋊C8—41no—
263C43⋊C8—41no—
264C43⋊C8—41no—
265#19124—431nomaximal, Sylow
266C22×C43—22no—
267C22×C43—41no—
268C22×C43—41no—
269C22×C43—81no—
270C22×C43—81no—
271C22×C43—81no—
272C22×C43C2×#12111yescharacteristic
273C2×D43—21no—
274C2×D43—21no—
275C2×D43#46512yes—
276C4×C43—21no—
277C4×C43—41no—
278C4×C43—81no—
279C4×C43C22×SD1611yescharacteristic
280C4×C43C2×#13511yescharacteristic
281C4×C43C2×#13511yescharacteristic
282C4×C43#57511yescharacteristic
283Dic43—21no—
284Dic43—22no—
285Dic43—21no—
286Dic43—41no—
287Dic43—81no—
288Dic43—81no—
289Dic43#46512yes—
290#3167—431no—
291#3076—431no—
292#3035—431no—
293C8×#41—431no—
294#1680—431no—
295#1679—431no—
296#1678—431no—
297#1677—431no—
298#1672—431no—
299#1671—431no—
300#1666—431no—
301#1665D4311yescharacteristic, complemented
302C2×#334—431no—
303#1542—431no—
304#1540—431no—
305C2×C43—42no—
306C2×C43—161no—
307C2×C43#303511yescharacteristic
308C2×C43C2×#46511yescharacteristic
309C2×C43#306711yescharacteristic
310D43—22no—
311C2×#135—861no—
312#533—431no—
313#532—431no—
314C4×#41—431no—
315#498—431no—
316#492C2×D4311yescharacteristic
317#487—431no—
318#486—431no—
319#479—861no—
320#478—861no—
321#477—431no—
322#476—431no—
323#475—431no—
324#474C2×D4311yescharacteristic
325#465—861no—
326#465—861no—
327#464—861no—
328#463—861no—
329#462—431no—
330#461—431no—
331#460—431no—
332#459C2×D4311yescharacteristic
333C8×Q8—431no—
334C8×Q8—431no—
335C4×SD16—861no—
336C4×SD16—861no—
337C8×D4—431no—
338C8×D4—861no—
339C8×D4—861no—
340C8×D4C2×D4311yescharacteristic
341#431—431no—
342#431—861no—
343#427—861no—
344C2×C4⋊C8—431no—
345C2×C4⋊C8—431no—
346#416—861no—
347#416—861no—
348C2×C4×C8—431no—
349C2×C4×C8—861no—
350#334—431no—
351#334—431no—
352#334—431no—
353#334C2×D4311yescharacteristic
354#333—431no—
355#333—431no—
356#332—431no—
357#332—431no—
358#332—431no—
359#332C2×D4311yescharacteristic
360#331—431no—
361#331C2×D4311yescharacteristic
362C43#1912411yescharacteristic, complemented, Sylow
363C2×#41—431no—
364C2×#41—861no—
365#135—1724no—
366C2×Q16—861no—
367C2×SD16—21no—
368C2×SD16—21no—
369C2×SD16—861no—
370C2×SD16—861no—
371C2×D8—21no—
372C22×C8—21no—
373C22×C8—431no—
374C22×C8—431no—
375C22×C8—861no—
376C22×C8—861no—
377C22×C8—861no—
378C4⋊Q8—431no—
379C4⋊Q8—431no—
380C4⋊Q8C22×D4311yescharacteristic
381#127C22×D4311yescharacteristic
382#125—861no—
383#124—861no—
384C22⋊Q8—861no—
385C22⋊Q8—861no—
386#121—861no—
387#121—861no—
388C4×Q8—431no—
389C4×Q8—431no—
390C4×Q8—861no—
391C4×Q8—861no—
392C4×D4—431no—
393C4×D4—861no—
394C4×D4—861no—
395C4×D4—861no—
396C4×D4—861no—
397C4×D4C22×D4311yescharacteristic
398#117—431no—
399#117—861no—
400#117—861no—
401C2×C42—431no—
402C2×C42—861no—
403#107—21no—
404#107—861no—
405#106—861no—
406#106—861no—
407#106—861no—
408#106—861no—
409C4⋊C8—431no—
410C4⋊C8—431no—
411C4⋊C8—431no—
412C4⋊C8—861no—
413C4⋊C8—861no—
414C4⋊C8—861no—
415C4⋊C8—861no—
416C4⋊C8C22×D4311yescharacteristic
417C4⋊C8C22×D4311yescharacteristic
418C4⋊C8C22×D4311yescharacteristic
419#103—861no—
420#103—861no—
421#103—861no—
422#103—861no—
423#103—861no—
424#103—861no—
425#102—21no—
426#102—21no—
427#102—861no—
428#102—861no—
429#102—861no—
430#102—861no—
431C22⋊C8—21no—
432C22⋊C8—861no—
433C22⋊C8—861no—
434C4×C8—431no—
435C4×C8—431no—
436C4×C8—431no—
437C4×C8—861no—
438C4×C8—861no—
439C4×C8—861no—
440C4×C8C22×D4311yescharacteristic
441#41—434no—
442#41—862no—
443#41—1722no—
444#41—1722no—
445C2×Q8—21no—
446C2×Q8—431no—
447C2×Q8—861no—
448C2×Q8—861no—
449C2×D4—21no—
450C2×D4—21no—
451C2×D4—21no—
452C2×D4—861no—
453C2×D4—1721no—
454C2×D4D4×D4311yescharacteristic
455C22×C4—21no—
456C22×C4—431no—
457C22×C4—431no—
458C22×C4—431no—
459C22×C4—861no—
460C22×C4—861no—
461C22×C4—1721no—
462Q16—1722no—
463SD16—42no—
464SD16—42no—
465SD16—1722no—
466SD16—1722no—
467D8—42no—
468C2×C8—21no—
469C2×C8—21no—
470C2×C8—21no—
471C2×C8—42no—
472C2×C8—431no—
473C2×C8—431no—
474C2×C8—862no—
475C2×C8—861no—
476C2×C8—861no—
477C2×C8—861no—
478C2×C8—1721no—
479C2×C8—1722no—
480C2×C8—1722no—
481C2×C8—1722no—
482C2×C8D4×D4311yescharacteristic
483C2×C8D4×D4311yescharacteristic
484C4⋊C4—21no—
485C4⋊C4—21no—
486C4⋊C4—431no—
487C4⋊C4—861no—
488C4⋊C4—861no—
489C4⋊C4—861no—
490C4⋊C4—861no—
491C4⋊C4—861no—
492C4⋊C4—861no—
493C4⋊C4—1721no—
494C4⋊C4—1721no—
495C4⋊C4D4×D4311yescharacteristic
496C22⋊C4—21no—
497C22⋊C4—861no—
498C22⋊C4—861no—
499C22⋊C4—1721no—
500C22⋊C4—1721no—
501C22⋊C4—1721no—
502C42—431no—
503C42—431no—
504C42—431no—
505C42—861no—
506C42—861no—
507C42—861no—
508C42—1721no—
509C42C23×D4311yescharacteristic
510C23—21no—
511C23—41no—
512C23—431no—
513Q8—41no—
514Q8—41no—
515Q8—432no—
516Q8—861no—
517Q8—3441no—
518Q8—1721no—
519Q8—1721no—
520D4—21no—
521D4—41no—
522D4—41no—
523D4—41no—
524D4—41no—
525D4—81no—
526D4—864no—
527D4—3442no—
528D4SD16×D4312yes—
529C2×C4—21no—
530C2×C4—41no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4—431no—
534C2×C4—432no—
535C2×C4—432no—
536C2×C4—431no—
537C2×C4—431no—
538C2×C4—864no—
539C2×C4—861no—
540C2×C4—861no—
541C2×C4—861no—
542C2×C4—861no—
543C2×C4—3442no—
544C2×C4—1721no—
545C2×C4—1722no—
546C2×C4—1721no—
547C2×C4—1721no—
548C2×C4C2×D4×D4311yescharacteristic
549C2×C4C2×D4×D4311yescharacteristic
550C2×C4#41×D4311yescharacteristic
551C8—21no—
552C8—41no—
553C8—41no—
554C8—41no—
555C8—861no—
556C8—861no—
557C8—1721no—
558C8—1721no—
559C8—1721no—
560C8#1306334412yescomplemented
561C22—22no—
562C22—41no—
563C22—41no—
564C22—81no—
565C22—81no—
566C22—81no—
567C22—432no—
568C22—861no—
569C22—861no—
570C22#121×D4311yescharacteristic
571C4—21no—
572C4—41no—
573C4—81no—
574C4—432no—
575C4—861no—
576C4—861no—
577C4—862no—
578C4—3441no—
579C4—3441no—
580C4—1721no—
581C4C2×SD16×D4311yescharacteristic
582C4#135×D4311yescharacteristic
583C4C2×#1306334411yescharacteristic
584C4#1458369511yescharacteristic
585C2—42no—
586C2—161no—
587C2—862no—
588C2#1914404311yescharacteristic
589C2#465×D4311yescharacteristic
590C2#1914431011yescharacteristic
subgroupG/H
centerC22#121×D43
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#1665C2
socleC22×C43C2×#121
prime radical#19144043C2
hypercenter#1665D43
hypocenterC43#19124
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #1665

Complements

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

NH ≅ G/Ntype
1. #19145152C2semidirect
2. #19144376C2semidirect
4. C8×#10621900C2semidirect
5. #19134024C2semidirect
6. #19134016C2semidirect
7. #19134010C2semidirect
8. #19134002C2semidirect
9. #19133978C2semidirect
10. #19133970C2semidirect
11. #19133940C2semidirect
12. #334×D43C2semidirect
13. #19133251C2semidirect
14. #19133241C2semidirect
15. C43×#1665C2semidirect
159. #10621900SD16semidirect
259. C8×C43#135semidirect
301. #1665D43semidirect
362. C43#19124semidirect
560. C8#13063344semidirect

Maximal subgroups

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

subgroupindex
#191451522
#191443762
#191440432
C8×#106219002
#191340242
#191340162
#191340102
#191340022
#191339782
#191339702
#191339402
#334×D432
#191332512
#191332412
C43×#16652
#1912443