Finite Group Databasebeta

← #25155490

Subgroups — #25155490

Order 11008.

690 conjugacy classes of subgroups.

The subgroup lattice has 604 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145125C211yesmaximal, characteristic, complemented
2#19144462C211yesmaximal, characteristic
3#19144459C211yesmaximal, characteristic
4#19143189C211yesmaximal, characteristic
5#19136107C211yesmaximal, characteristic, complemented
6#19135941C211yesmaximal, characteristic, complemented
7#19135938C211yesmaximal, characteristic, complemented
8#19135374C211yesmaximal, characteristic, complemented
9#19135340C211yesmaximal, characteristic, complemented
10#19134824C211yesmaximal, characteristic
11#19134818C211yesmaximal, characteristic
12#19134750C211yesmaximal, characteristic, complemented
13#19134653C211yesmaximal, characteristic
14#19134431C211yesmaximal, characteristic
15C43×#2090C211yesmaximal, characteristic, complemented
16C2×#13063333C2211yescharacteristic
17#14583530C2211yescharacteristic
18#14583527C2211yescharacteristic
19#14583380C2211yescharacteristic
20#14583379C2211yescharacteristic
21#14583307—21no—
22#14583306—21no—
23#14583300—21no—
24#14583296—21no—
25#14583209—21no—
26#14583207—21no—
27#14583200—21no—
28#14583198—21no—
29#14583190—21no—
30#14583188—21no—
31#14583185—21no—
32#14583183—21no—
33C2×#13063260C2211yescharacteristic
34#14582941C2211yescharacteristic
35#14582941C2211yescharacteristic
36#14582941C2211yescharacteristic
37#14582940—21no—
38#14582939C2211yescharacteristic
39#14582938—21no—
40#14582936—21no—
41#14582935C2211yescharacteristic
42C2×#13063257C2211yescharacteristic
43C2×#13063256C2211yescharacteristic
44C2×#13063256C2211yescharacteristic
45#106×D43—21no—
46#14582925C2211yescharacteristic
47C2×#13063251C2211yescharacteristic
48#14582901C2211yescharacteristic
49#14582898C2211yescharacteristic
50#14582896C2211yescharacteristic
51#14582857C2211yescharacteristic
52C2×C8×Dic43C2211yescharacteristic
53#14582768C2211yescharacteristic
54#14582768C2211yescharacteristic
55#14582667C2211yescharacteristic
56#14582667C2211yescharacteristic
57#14582660C2211yescharacteristic
58#14582660C2211yescharacteristic
59#14582658C2211yescharacteristic
60C43×#428C2211yescharacteristic
61C43×#428C2211yescharacteristic
62C2×#106×C43C2211yescharacteristic
63C43×#424C2211yescharacteristic
64C43×#343C2211yescharacteristic
65C43×#343C2211yescharacteristic
66C43×#341C2211yescharacteristic
67C2×#10621898C2311yescharacteristic
68#13063333—22no—
69#13063333Q814yescomplemented
70C2×#10621877C2311yescharacteristic
71C2×#10621872—21no—
72C22×C43⋊C8C2311yescharacteristic
73C2×C8×D43—21no—
74#13063325—21no—
75#13063324—21no—
76#13063324—21no—
77#13063324—21no—
78#13063317—21no—
79#13063316—21no—
80#13063316—21no—
81#13063316—21no—
82#13063304—41no—
83#13063302—41no—
84C4×Dic86—21no—
85#13063290—21no—
86C4×D172—21no—
87#13063287—21no—
88C4×C22⋊D43—41no—
89(C22⋊D43)⋊C4—41no—
90#13063284C2311yescharacteristic
91#13063284C2311yescharacteristic
92#13063283—21no—
93#13063283—21no—
94C2×C4⋊Dic43C2311yescharacteristic
95C2×C4⋊Dic43C2311yescharacteristic
96C2×Dic43⋊C4—41no—
97C2×Dic43⋊C4—41no—
98C4⋊C4×D43—21no—
99C4⋊C4×D43—21no—
100C2×C4×Dic43C2311yescharacteristic
101#13063260—22no—
102#13063259—21no—
103#13063259—21no—
104#13063259—21no—
105#13063258—21no—
106#13063258D411yescharacteristic
107#13063258D411yescharacteristic
108#13063257—21no—
109#13063257—21no—
110#13063257—21no—
111#13063257—21no—
112#13063257—21no—
113#13063256—21no—
114#13063256—21no—
115#13063256—21no—
116#13063256—21no—
117#13063256—21no—
118#13063256D411yescharacteristic
119#13063256D411yescharacteristic
120Dic43⋊C8—21no—
121Dic43⋊C8—21no—
122#13063251Q814yescomplemented
123#13063250—21no—
124#13063250D411yescharacteristic
125#13063250D411yescharacteristic
126#13063248—21no—
127#13063247—21no—
128#13063247D411yescharacteristic
129#13063247D411yescharacteristic
130#13063245—21no—
131#13063235—21no—
132C8×Dic43—21no—
133C8×Dic43—22no—
134C2×M16×C43C2311yescharacteristic
135C2×M16×C43C2311yescharacteristic
136C2×M16×C43C2311yescharacteristic
137C22×C8×C43C2311yescharacteristic
138#117×C43C2311yescharacteristic
139C2×C4⋊C4×C43C2311yescharacteristic
140C2×C4⋊C4×C43C2311yescharacteristic
141#107×C43—21no—
142#107×C43—21no—
143#106×C43—21no—
144#106×C43—21no—
145#106×C43—21no—
146#106×C43—21no—
147C4⋊C8×C43—21no—
148C4⋊C8×C43—21no—
149C22×C4×C43—21no—
150C22×C4×C43—21no—
151C22×C4×C43C2411yescharacteristic
152C2×C22⋊D43—21no—
153C22×Dic43—21no—
154C22×Dic43—21no—
155C22×Dic43—21no—
156#10621898—21no—
157#10621898—21no—
158#10621898C2×Q812yes—
159#10621898C2×Q812yes—
160C2×D172C2×D411yescharacteristic
161C2×C4×D43—21no—
162C2×C4×D43—41no—
163C2×C4×D43—41no—
164C2×Dic86—41no—
165C2×Dic86—41no—
166C2×Dic86C2×D411yescharacteristic
167M16×C43—21no—
168M16×C43—21no—
169M16×C43—21no—
170M16×C43—21no—
171M16×C43C2×Q812yes—
172M16×C43C2×Q812yes—
173C2×C8×C43—21no—
174C2×C8×C43—21no—
175C2×C8×C43—21no—
176C2×C8×C43—21no—
177C2×C8×C43—21no—
178C2×C8×C43C2×D411yescharacteristic
179C2×C8×C43C2×D411yescharacteristic
180C4⋊C4×C43—21no—
181C4⋊C4×C43—21no—
182C4⋊C4×C43—21no—
183C4⋊C4×C43—21no—
184C4⋊C4×C43C2×D411yescharacteristic
185C4⋊C4×C43C2×D411yescharacteristic
186C22⋊C4×C43—21no—
187C42×C43—21no—
188C22⋊Dic43—21no—
189C22⋊Dic43—21no—
190(C2×D43)⋊C4—41no—
191(C2×D43)⋊C4—41no—
192C4⋊Dic43—21no—
193C4⋊Dic43—21no—
194C4⋊Dic43—21no—
195C4⋊Dic43—21no—
196C4⋊Dic43—41no—
197C4⋊Dic43—41no—
198C4⋊Dic43C2×D411yescharacteristic
199C4⋊Dic43C2×D411yescharacteristic
200C4⋊Dic43C2×D411yescharacteristic
201C4⋊Dic43C2×D411yescharacteristic
202Dic43⋊C4—41no—
203Dic43⋊C4—41no—
204Dic43⋊C4—41no—
205Dic43⋊C4—41no—
206Dic43⋊C4—41no—
207Dic43⋊C4—41no—
208Dic43⋊C4—82no—
209Dic43⋊C4—82no—
210C4×Dic43—21no—
211C4×Dic43—21no—
212C4×Dic43—21no—
213C4×Dic43—41no—
214C4×Dic43—41no—
215C4×Dic43C2×Q812yes—
216#10621877—21no—
217#10621877—21no—
218C2×C43⋊C8—21no—
219C2×C43⋊C8C2×D411yescharacteristic
220C2×C43⋊C8C2×D411yescharacteristic
221C2×C43⋊C8C2×Q812yes—
222C2×C43⋊C8#4112yes—
223#10621872—24no—
224C8×D43—24no—
225C23×C43H(5,𝔽2)11yescharacteristic
226C22×D43—21no—
227C2×C4×C43—21no—
228C2×C4×C43—21no—
229C2×C4×C43—41no—
230C2×C4×C43—41no—
231C2×C4×C43—81no—
232C2×C4×C43—81no—
233C2×C4×C43C22×D411yescharacteristic
234C2×C4×C43C22×D411yescharacteristic
235C2×C4×C43C22×Q811yescharacteristic
236C2×C4×C43C22×Q811yescharacteristic
237C2×C4×C43C2×#4111yescharacteristic
238C2×C4×C432−1+411yescharacteristic
239C22⋊D43—22no—
240C22⋊D43—22no—
241C2×Dic43—22no—
242C2×Dic43—22no—
243C2×Dic43—21no—
244C2×Dic43—22no—
245C2×Dic43—21no—
246C2×Dic43—21no—
247C2×Dic43—21no—
248C2×Dic43—21no—
249C2×Dic43—41no—
250C2×Dic43—41no—
251C2×Dic43—81no—
252C2×Dic43—81no—
253D172—21no—
254D172C4⋊Q812yes—
255C4×D43—22no—
256C4×D43—22no—
257C4×D43—161no—
258C4×D43—161no—
259Dic86—21no—
260Dic86—161no—
261Dic86—161no—
262Dic86C4⋊Q812yes—
263C8×C43—22no—
264C8×C43—21no—
265C8×C43—21no—
266C8×C43—22no—
267C8×C43—41no—
268C43⋊C8—41no—
269C43⋊C8C22⋊Q812yes—
270C43⋊C8C22⋊Q812yes—
271#26081—431nomaximal, Sylow
272C22×C43—21no—
273C22×C43—21no—
274C22×C43#54411yescharacteristic
275C22×C43D4211yescharacteristic
276C22×C43#55411yescharacteristic
277C2×D43—22no—
278C2×D43—41no—
279C2×D43—41no—
280C4×C43—41no—
281C4×C43—41no—
282C4×C43—81no—
283C4×C43—81no—
284C4×C43C2×C22⋊Q811yescharacteristic
285C4×C43C2×C4⋊Q811yescharacteristic
286C4×C43#54711yescharacteristic
287C4×C43D4×Q811yescharacteristic
288Dic43—24no—
289Dic43—22no—
290Dic43—41no—
291Dic43—41no—
292Dic43—41no—
293Dic43—41no—
294Dic43—81no—
295Dic43—81no—
296#3163—431no—
297#3084—431no—
298#3084—431no—
299#2912—431no—
300#2090—431no—
301#2090D4311yescharacteristic, complemented
302#2060—431no—
303#2060—431no—
304#1951—431no—
305#1945—431no—
306#1859—431no—
307#1859—431no—
308#1844—431no—
309#1815—431no—
310#1764—431no—
311C2×C43—21no—
312C2×C43—21no—
313C2×C43#244011yescharacteristic
314C2×C43#329111yescharacteristic
315C2×C43#329111yescharacteristic
316D43—42no—
317C2×#131—431no—
318#544—431no—
319#544—431no—
320#520—431no—
321#520—431no—
322#501—861no—
323#501—861no—
324#499—861no—
325#498—861no—
326#479—861no—
327#479—861no—
328#478—861no—
329#478—861no—
330#476—861no—
331#476—861no—
332#475—861no—
333#475—861no—
334C2×#108—431no—
335#428—431no—
336#428—431no—
337#428—431no—
338#428—431no—
339#428—861no—
340#428—861no—
341#428C2×D4311yescharacteristic
342#428C2×D4311yescharacteristic
343#427—431no—
344#427—861no—
345C2×#106—431no—
346C2×#106—431no—
347C2×#106—431no—
348C2×#106—861no—
349C2×#106C2×D4311yescharacteristic
350#424—431no—
351#424C2×D4311yescharacteristic
352C2×#104—431no—
353#417—431no—
354#417—431no—
355#416—431no—
356#405—431no—
357C2×C4×C8—431no—
358#384—431no—
359#384—431no—
360#343—431no—
361#343—431no—
362#343C2×D4311yescharacteristic
363#343C2×D4311yescharacteristic
364#341C2×D4311yescharacteristic
365#339—431no—
366#339—431no—
367#339—431no—
368C43#2608111yescharacteristic, complemented, Sylow
369C2×#41—431no—
370#131—434no—
371#131—862no—
372C2×M16—431no—
373C2×M16—861no—
374C2×M16C22×D4311yescharacteristic
375C2×M16C22×D4311yescharacteristic
376C2×M16C22×D4311yescharacteristic
377C22×C8—431no—
378C22×C8—861no—
379C22×C8C22×D4311yescharacteristic
380C4⋊Q8—861no—
381C4⋊Q8—861no—
382C4⋊Q8—861no—
383C4⋊Q8—861no—
384#125—861no—
385#125—861no—
386#125—861no—
387#125—861no—
388C22⋊Q8—1721no—
389C22⋊Q8—1721no—
390C4×Q8—861no—
391C4×Q8—861no—
392C4×D4—861no—
393C4×D4—861no—
394C4×D4—1721no—
395C4×D4—1721no—
396#117—431no—
397#117—431no—
398#117—861no—
399#117—861no—
400#117C22×D4311yescharacteristic
401C2×C4⋊C4—431no—
402C2×C4⋊C4—431no—
403C2×C4⋊C4—861no—
404C2×C4⋊C4—861no—
405C2×C4⋊C4—1721no—
406C2×C4⋊C4—1721no—
407C2×C4⋊C4C22×D4311yescharacteristic
408C2×C4⋊C4C22×D4311yescharacteristic
409C2×C42—431no—
410#108—862no—
411#107—21no—
412#107—21no—
413#107—431no—
414#107—431no—
415#107—861no—
416#107—861no—
417#107—861no—
418#107—861no—
419#106—21no—
420#106—21no—
421#106—21no—
422#106—21no—
423#106—431no—
424#106—431no—
425#106—861no—
426#106—861no—
427#106—861no—
428#106—861no—
429#106—861no—
430#106—861no—
431#106—861no—
432#106—861no—
433#106—861no—
434#106—861no—
435C4⋊C8—21no—
436C4⋊C8—21no—
437C4⋊C8—861no—
438C4⋊C8—861no—
439#104—434no—
440#103—431no—
441#103—431no—
442#103—861no—
443#103—861no—
444#102—431no—
445#102—431no—
446#102—861no—
447#102—861no—
448#97—861no—
449C4×C8—862no—
450C4×C8—861no—
451#41—432no—
452#41—432no—
453#41—861no—
454#41—861no—
455C2×Q8—431no—
456C2×Q8—1721no—
457C2×Q8—1721no—
458C2×D4—431no—
459C2×D4—861no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—861no—
463C22×C4—861no—
464C22×C4—861no—
465C22×C4—861no—
466C22×C4—1721no—
467C22×C4—1721no—
468C22×C4C23×D4311yescharacteristic
469M16—21no—
470M16—21no—
471M16—21no—
472M16—21no—
473M16—864no—
474M16—861no—
475M16—861no—
476M16Q8×D4312yes—
477M16Q8×D4312yes—
478C2×C8—21no—
479C2×C8—21no—
480C2×C8—21no—
481C2×C8—21no—
482C2×C8—21no—
483C2×C8—431no—
484C2×C8—431no—
485C2×C8—432no—
486C2×C8—432no—
487C2×C8—864no—
488C2×C8—861no—
489C2×C8D4×D4311yescharacteristic
490C2×C8D4×D4311yescharacteristic
491C4⋊C4—21no—
492C4⋊C4—21no—
493C4⋊C4—21no—
494C4⋊C4—21no—
495C4⋊C4—431no—
496C4⋊C4—431no—
497C4⋊C4—431no—
498C4⋊C4—431no—
499C4⋊C4—861no—
500C4⋊C4—861no—
501C4⋊C4—861no—
502C4⋊C4—861no—
503C4⋊C4—3442no—
504C4⋊C4—3442no—
505C4⋊C4—1721no—
506C4⋊C4—1721no—
507C4⋊C4—1721no—
508C4⋊C4—1721no—
509C4⋊C4—1721no—
510C4⋊C4—1721no—
511C4⋊C4—1721no—
512C4⋊C4—1721no—
513C4⋊C4D4×D4311yescharacteristic
514C4⋊C4D4×D4311yescharacteristic
515C22⋊C4—21no—
516C22⋊C4—861no—
517C22⋊C4—861no—
518C22⋊C4—1721no—
519C22⋊C4—1721no—
520C42—21no—
521C42—432no—
522C42—861no—
523C42—861no—
524C42—861no—
525C42—1721no—
526C42—1721no—
527C23—861no—
528C23#1306337111yescharacteristic
529Q8—432no—
530Q8—861no—
531Q8—6881no—
532Q8—6881no—
533D4—432no—
534D4—862no—
535D4—862no—
536D4—861no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—81no—
542C2×C4—81no—
543C2×C4—862no—
544C2×C4—862no—
545C2×C4—862no—
546C2×C4—861no—
547C2×C4—862no—
548C2×C4—862no—
549C2×C4—861no—
550C2×C4—861no—
551C2×C4—861no—
552C2×C4—861no—
553C2×C4—3441no—
554C2×C4—3441no—
555C2×C4—1721no—
556C2×C4—1721no—
557C2×C4—6881no—
558C2×C4—6881no—
559C2×C4C2×D4×D4311yescharacteristic
560C2×C4C2×D4×D4311yescharacteristic
561C2×C4C2×Q8×D4311yescharacteristic
562C2×C4C2×Q8×D4311yescharacteristic
563C2×C4#41×D4311yescharacteristic
564C2×C4#1306337211yescharacteristic
565C8—22no—
566C8—22no—
567C8—21no—
568C8—21no—
569C8—41no—
570C8—432no—
571C8—432no—
572C8—1721no—
573C22—21no—
574C22—21no—
575C22—862no—
576C22—1721no—
577C22—1721no—
578C22#1458352911yescharacteristic
579C22#1458353311yescharacteristic
580C22#1458360511yescharacteristic
581C4—41no—
582C4—41no—
583C4—81no—
584C4—81no—
585C4—864no—
586C4—862no—
587C4—3441no—
588C4—3441no—
589C4—1721no—
590C4—1721no—
591C4—1721no—
592C4—1721no—
593C4C22⋊Q8×D4311yescharacteristic
594C4C4⋊Q8×D4311yescharacteristic
595C4#1458354711yescharacteristic
596C4#1458356211yescharacteristic
597C2—21no—
598C2—21no—
599C2—1722no—
600C2#1913829211yescharacteristic
601C2#1914638711yescharacteristic
602C2#1914638711yescharacteristic
subgroupG/H
centerC22#14583533
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2090C2
socleC22×C43D42
prime radicalC2×#10621898C23
hypercenter#2090D43
hypocenterC43#26081
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ #2090

Complements

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

NH ≅ G/Ntype
1. #19145125C2semidirect
5. #19136107C2semidirect
6. #19135941C2semidirect
7. #19135938C2semidirect
8. #19135374C2semidirect
9. #19135340C2semidirect
12. #19134750C2semidirect
15. C43×#2090C2semidirect
69. #13063333Q8semidirect
122. #13063251Q8semidirect
301. #2090D43semidirect
368. C43#26081semidirect

Maximal subgroups

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

subgroupindex
#191451252
#191444622
#191444592
#191431892
#191361072
#191359412
#191359382
#191353742
#191353402
#191348242
#191348182
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C43×#20902
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