Finite Group Databasebeta

← #25155479

Subgroups — #25155479

Order 11008.

674 conjugacy classes of subgroups.

The subgroup lattice has 600 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145125C211yesmaximal, characteristic, complemented
2#19144451C211yesmaximal, characteristic
3#19144448C211yesmaximal, characteristic
4#19143189C211yesmaximal, characteristic
5#19136102C211yesmaximal, characteristic, complemented
6#19135946C211yesmaximal, characteristic, complemented
7#19135943C211yesmaximal, characteristic, complemented
8#19135374C211yesmaximal, characteristic, complemented
9#19135340C211yesmaximal, characteristic, complemented
10#19134831C211yesmaximal, characteristic
11#19134825C211yesmaximal, characteristic
12#19134758C211yesmaximal, characteristic, complemented
13#19134653C211yesmaximal, characteristic
14#19134431C211yesmaximal, characteristic
15C43×#2089C211yesmaximal, 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#14583207—21no—
26#14583205—21no—
27#14583202—21no—
28#14583200—21no—
29#14583195—21no—
30#14583193—21no—
31#14583180—21no—
32#14583178—21no—
33C2×#13063260C2211yescharacteristic
34#14582941C2211yescharacteristic
35#14582941C2211yescharacteristic
36#14582941C2211yescharacteristic
37#14582940—21no—
38#14582939C2211yescharacteristic
39#14582938—21no—
40#14582936—21no—
41#14582935C2211yescharacteristic
42C2×#13063259C2211yescharacteristic
43C2×#13063256C2211yescharacteristic
44C2×#13063256C2211yescharacteristic
45#106×D43—21no—
46#14582925C2211yescharacteristic
47C2×#13063251C2211yescharacteristic
48#14582901C2211yescharacteristic
49#14582898C2211yescharacteristic
50#14582896C2211yescharacteristic
51#14582857C2211yescharacteristic
52C2×C8×Dic43C2211yescharacteristic
53#14582764C2211yescharacteristic
54#14582764C2211yescharacteristic
55#14582667C2211yescharacteristic
56#14582667C2211yescharacteristic
57#14582660C2211yescharacteristic
58#14582660C2211yescharacteristic
59#14582658C2211yescharacteristic
60C43×#428C2211yescharacteristic
61C43×#428C2211yescharacteristic
62C2×#107×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
96C4⋊C4×D43—21no—
97C4⋊C4×D43—21no—
98C2×C4×Dic43C2311yescharacteristic
99#13063260—22no—
100#13063259—21no—
101#13063259—21no—
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#13063256—21no—
112#13063256—21no—
113#13063256—21no—
114#13063256—21no—
115#13063256—21no—
116#13063256D411yescharacteristic
117#13063256D411yescharacteristic
118Dic43⋊C8—21no—
119Dic43⋊C8—21no—
120#13063251Q814yescomplemented
121#13063250—21no—
122#13063250D411yescharacteristic
123#13063250D411yescharacteristic
124#13063248—21no—
125#13063247—21no—
126#13063247D411yescharacteristic
127#13063247D411yescharacteristic
128#13063245—21no—
129#13063235—21no—
130C8×Dic43—21no—
131C8×Dic43—22no—
132C43⋊#95—41no—
133C43⋊#95—41no—
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#107×C43—21no—
144#107×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—
208C4×Dic43—21no—
209C4×Dic43—21no—
210C4×Dic43—21no—
211C4×Dic43—41no—
212C4×Dic43—41no—
213C4×Dic43C2×Q812yes—
214#10621877—21no—
215#10621877—21no—
216C2×C43⋊C8—21no—
217C2×C43⋊C8C2×D411yescharacteristic
218C2×C43⋊C8C2×D411yescharacteristic
219C2×C43⋊C8C2×Q812yes—
220C2×C43⋊C8#4112yes—
221#10621872—24no—
222C8×D43—24no—
223C23×C43H(5,𝔽2)11yescharacteristic
224C22×D43—21no—
225C2×C4×C43—21no—
226C2×C4×C43—21no—
227C2×C4×C43—41no—
228C2×C4×C43—41no—
229C2×C4×C43—81no—
230C2×C4×C43—81no—
231C2×C4×C43C22×D411yescharacteristic
232C2×C4×C43C22×D411yescharacteristic
233C2×C4×C43C22×Q811yescharacteristic
234C2×C4×C43C22×Q811yescharacteristic
235C2×C4×C43C2×#4111yescharacteristic
236C2×C4×C432−1+411yescharacteristic
237C22⋊D43—22no—
238C22⋊D43—22no—
239C2×Dic43—21no—
240C2×Dic43—21no—
241C2×Dic43—21no—
242C2×Dic43—21no—
243C2×Dic43—21no—
244C2×Dic43—22no—
245C2×Dic43—41no—
246C2×Dic43—41no—
247C2×Dic43—41no—
248C2×Dic43—41no—
249C2×Dic43—81no—
250C2×Dic43—81no—
251D172—21no—
252D172C4⋊Q812yes—
253C4×D43—22no—
254C4×D43—22no—
255C4×D43—161no—
256C4×D43—161no—
257Dic86—21no—
258Dic86—161no—
259Dic86—161no—
260Dic86C4⋊Q812yes—
261C8×C43—22no—
262C8×C43—21no—
263C8×C43—21no—
264C8×C43—22no—
265C8×C43—41no—
266C43⋊C8—41no—
267C43⋊C8C22⋊Q812yes—
268C43⋊C8C22⋊Q812yes—
269#26080—431nomaximal, Sylow
270C22×C43—21no—
271C22×C43—21no—
272C22×C43#54411yescharacteristic
273C22×C43D4211yescharacteristic
274C22×C43#55411yescharacteristic
275C2×D43—22no—
276C2×D43—41no—
277C2×D43—41no—
278C4×C43—41no—
279C4×C43—41no—
280C4×C43—81no—
281C4×C43—81no—
282C4×C43C2×C22⋊Q811yescharacteristic
283C4×C43C2×C4⋊Q811yescharacteristic
284C4×C43#54711yescharacteristic
285C4×C43D4×Q811yescharacteristic
286Dic43—22no—
287Dic43—42no—
288Dic43—41no—
289Dic43—41no—
290Dic43—41no—
291Dic43—41no—
292Dic43—81no—
293Dic43—81no—
294#3163—431no—
295#3083—431no—
296#3083—431no—
297#2912—431no—
298#2089—431no—
299#2089D4311yescharacteristic, complemented
300#2061—431no—
301#2061—431no—
302#1951—431no—
303#1945—431no—
304#1860—431no—
305#1860—431no—
306#1846—431no—
307#1815—431no—
308#1764—431no—
309C2×C43—21no—
310C2×C43—21no—
311C2×C43#244011yescharacteristic
312C2×C43#329011yescharacteristic
313C2×C43#329011yescharacteristic
314D43—42no—
315C2×#131—431no—
316#544—431no—
317#544—431no—
318#520—431no—
319#520—431no—
320#501—861no—
321#501—861no—
322#499—861no—
323#498—861no—
324#479—861no—
325#479—861no—
326#478—861no—
327#478—861no—
328#477—861no—
329#477—861no—
330#474—861no—
331#474—861no—
332C2×#108—431no—
333#428—431no—
334#428—431no—
335#428—431no—
336#428—431no—
337#428—861no—
338#428—861no—
339#428C2×D4311yescharacteristic
340#428C2×D4311yescharacteristic
341#427—431no—
342#427—861no—
343C2×#107—431no—
344C2×#107C2×D4311yescharacteristic
345C2×#106—431no—
346C2×#106—431no—
347C2×#106—861no—
348#424—431no—
349#424C2×D4311yescharacteristic
350C2×#104—431no—
351#417—431no—
352#417—431no—
353#416—431no—
354#405—431no—
355C2×C4×C8—431no—
356#382—431no—
357#382—431no—
358#343—431no—
359#343—431no—
360#343C2×D4311yescharacteristic
361#343C2×D4311yescharacteristic
362#341C2×D4311yescharacteristic
363#339—431no—
364#339—431no—
365#339—431no—
366C43#2608011yescharacteristic, complemented, Sylow
367C2×#41—431no—
368#131—434no—
369#131—862no—
370C2×M16—431no—
371C2×M16—861no—
372C2×M16C22×D4311yescharacteristic
373C2×M16C22×D4311yescharacteristic
374C2×M16C22×D4311yescharacteristic
375C22×C8—431no—
376C22×C8—861no—
377C22×C8C22×D4311yescharacteristic
378C4⋊Q8—861no—
379C4⋊Q8—861no—
380C4⋊Q8—861no—
381C4⋊Q8—861no—
382#125—861no—
383#125—861no—
384#125—861no—
385#125—861no—
386C22⋊Q8—1721no—
387C22⋊Q8—1721no—
388C4×Q8—861no—
389C4×Q8—861no—
390C4×D4—861no—
391C4×D4—861no—
392C4×D4—1721no—
393C4×D4—1721no—
394#117—431no—
395#117—431no—
396#117—861no—
397#117—861no—
398#117C22×D4311yescharacteristic
399C2×C4⋊C4—431no—
400C2×C4⋊C4—431no—
401C2×C4⋊C4—861no—
402C2×C4⋊C4—861no—
403C2×C4⋊C4C22×D4311yescharacteristic
404C2×C4⋊C4C22×D4311yescharacteristic
405C2×C42—431no—
406#108—862no—
407#107—21no—
408#107—21no—
409#107—21no—
410#107—21no—
411#107—431no—
412#107—431no—
413#107—861no—
414#107—861no—
415#107—861no—
416#107—861no—
417#107—861no—
418#107—861no—
419#106—21no—
420#106—21no—
421#106—431no—
422#106—431no—
423#106—861no—
424#106—861no—
425#106—861no—
426#106—861no—
427#106—861no—
428#106—861no—
429#106—861no—
430#106—861no—
431C4⋊C8—21no—
432C4⋊C8—21no—
433C4⋊C8—861no—
434C4⋊C8—861no—
435#104—434no—
436#103—431no—
437#103—431no—
438#103—861no—
439#103—861no—
440#102—431no—
441#102—431no—
442#102—861no—
443#102—861no—
444#97—861no—
445C4×C8—862no—
446C4×C8—861no—
447#95—1721no—
448#95—1721no—
449#41—432no—
450#41—432no—
451#41—861no—
452#41—861no—
453C2×Q8—431no—
454C2×Q8—1721no—
455C2×Q8—1721no—
456C2×D4—431no—
457C2×D4—861no—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—861no—
461C22×C4—861no—
462C22×C4—861no—
463C22×C4—861no—
464C22×C4—1721no—
465C22×C4—1721no—
466C22×C4C23×D4311yescharacteristic
467M16—21no—
468M16—21no—
469M16—21no—
470M16—21no—
471M16—864no—
472M16—861no—
473M16—861no—
474M16Q8×D4312yes—
475M16Q8×D4312yes—
476C2×C8—21no—
477C2×C8—21no—
478C2×C8—21no—
479C2×C8—21no—
480C2×C8—21no—
481C2×C8—431no—
482C2×C8—431no—
483C2×C8—432no—
484C2×C8—432no—
485C2×C8—864no—
486C2×C8—861no—
487C2×C8D4×D4311yescharacteristic
488C2×C8D4×D4311yescharacteristic
489C4⋊C4—21no—
490C4⋊C4—21no—
491C4⋊C4—21no—
492C4⋊C4—21no—
493C4⋊C4—431no—
494C4⋊C4—431no—
495C4⋊C4—431no—
496C4⋊C4—431no—
497C4⋊C4—861no—
498C4⋊C4—861no—
499C4⋊C4—861no—
500C4⋊C4—861no—
501C4⋊C4—1721no—
502C4⋊C4—1721no—
503C4⋊C4—1721no—
504C4⋊C4—1721no—
505C4⋊C4—1721no—
506C4⋊C4—1721no—
507C4⋊C4—1721no—
508C4⋊C4—1721no—
509C4⋊C4D4×D4311yescharacteristic
510C4⋊C4D4×D4311yescharacteristic
511C22⋊C4—21no—
512C22⋊C4—861no—
513C22⋊C4—861no—
514C22⋊C4—1721no—
515C22⋊C4—1721no—
516C42—21no—
517C42—432no—
518C42—861no—
519C42—861no—
520C42—861no—
521C42—1721no—
522C42—1721no—
523C23—861no—
524C23#1306337111yescharacteristic
525Q8—432no—
526Q8—861no—
527Q8—6881no—
528Q8—6881no—
529D4—432no—
530D4—862no—
531D4—862no—
532D4—861no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—81no—
538C2×C4—81no—
539C2×C4—861no—
540C2×C4—862no—
541C2×C4—862no—
542C2×C4—862no—
543C2×C4—861no—
544C2×C4—861no—
545C2×C4—861no—
546C2×C4—861no—
547C2×C4—3441no—
548C2×C4—3441no—
549C2×C4—1721no—
550C2×C4—1721no—
551C2×C4—1721no—
552C2×C4—1721no—
553C2×C4—6881no—
554C2×C4—6881no—
555C2×C4C2×D4×D4311yescharacteristic
556C2×C4C2×D4×D4311yescharacteristic
557C2×C4C2×Q8×D4311yescharacteristic
558C2×C4C2×Q8×D4311yescharacteristic
559C2×C4#41×D4311yescharacteristic
560C2×C4#1306337211yescharacteristic
561C8—22no—
562C8—22no—
563C8—21no—
564C8—21no—
565C8—41no—
566C8—432no—
567C8—432no—
568C8—1721no—
569C22—21no—
570C22—21no—
571C22—862no—
572C22—1721no—
573C22—1721no—
574C22#1458352911yescharacteristic
575C22#1458353311yescharacteristic
576C22#1458360511yescharacteristic
577C4—41no—
578C4—41no—
579C4—81no—
580C4—81no—
581C4—862no—
582C4—3441no—
583C4—3441no—
584C4—1722no—
585C4—1721no—
586C4—1721no—
587C4—1721no—
588C4—1721no—
589C4C22⋊Q8×D4311yescharacteristic
590C4C4⋊Q8×D4311yescharacteristic
591C4#1458354711yescharacteristic
592C4#1458356211yescharacteristic
593C2—21no—
594C2—21no—
595C2—1722no—
596C2#1913829211yescharacteristic
597C2#1914637611yescharacteristic
598C2#1914638411yescharacteristic
subgroupG/H
centerC22#14583533
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2089C2
socleC22×C43D42
prime radicalC2×#10621898C23
hypercenter#2089D43
hypocenterC43#26080
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ #2089

Complements

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

NH ≅ G/Ntype
1. #19145125C2semidirect
5. #19136102C2semidirect
6. #19135946C2semidirect
7. #19135943C2semidirect
8. #19135374C2semidirect
9. #19135340C2semidirect
12. #19134758C2semidirect
15. C43×#2089C2semidirect
69. #13063333Q8semidirect
120. #13063251Q8semidirect
299. #2089D43semidirect
366. C43#26080semidirect

Maximal subgroups

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

subgroupindex
#191451252
#191444512
#191444482
#191431892
#191361022
#191359462
#191359432
#191353742
#191353402
#191348312
#191348252
#191347582
#191346532
#191344312
C43×#20892
#2608043