Finite Group Databasebeta

← #25155505

Subgroups — #25155505

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#19145133C211yesmaximal, characteristic, complemented
2#19144461C211yesmaximal, characteristic
3#19144457C211yesmaximal, characteristic
4#19143193C211yesmaximal, characteristic
5#19136109C211yesmaximal, characteristic, complemented
6#19136108C211yesmaximal, characteristic, complemented
7#19135945C211yesmaximal, characteristic, complemented
8#19135944C211yesmaximal, characteristic, complemented
9#19135379C211yesmaximal, characteristic, complemented
10#19135342C211yesmaximal, characteristic, complemented
11#19134830C211yesmaximal, characteristic
12#19134757C211yesmaximal, characteristic, complemented
13#19134657C211yesmaximal, characteristic
14#19134433C211yesmaximal, characteristic
15C43×#1860C211yesmaximal, characteristic
16C2×#13063332C2211yescharacteristic
17#14583530C2211yescharacteristic
18#14583527C2211yescharacteristic
19#14583382C2211yescharacteristic
20#14583307—21no—
21#14583306—21no—
22#14583303—21no—
23#14583299—21no—
24#14583208—21no—
25#14583206—21no—
26#14583199—21no—
27#14583197—21no—
28#14583189—21no—
29#14583187—21no—
30#14583184—21no—
31#14583182—21no—
32C2×#13063260C2211yescharacteristic
33#14582942—21no—
34#14582942C2211yescharacteristic
35#14582941C2211yescharacteristic
36#14582941C2211yescharacteristic
37#14582939—21no—
38#14582939C2211yescharacteristic
39#14582939C2211yescharacteristic
40#14582935—21no—
41#14582935C2211yescharacteristic
42C2×#13063258—21no—
43C2×#13063258C2211yescharacteristic
44C2×#13063258C2211yescharacteristic
45C2×#13063256C2211yescharacteristic
46C2×#13063256C2211yescharacteristic
47#14582927C2211yescharacteristic
48#14582926C2211yescharacteristic
49#14582900C2211yescharacteristic
50#14582895C2211yescharacteristic
51#14582857C2211yescharacteristic
52C2×C4×C43⋊C8C2211yescharacteristic
53#14582765C2211yescharacteristic
54#14582668C2211yescharacteristic
55#14582667C2211yescharacteristic
56#14582667C2211yescharacteristic
57#14582663C2211yescharacteristic
58#14582659C2211yescharacteristic
59#14582659C2211yescharacteristic
60C43×#520C2211yescharacteristic
61C43×#428C2211yescharacteristic
62C2×#104×C43C2211yescharacteristic
63C43×#417C2211yescharacteristic
64C43×#382C2211yescharacteristic
65C43×#343C2211yescharacteristic
66C43×#339C2211yescharacteristic
67#13063332—22no—
68#13063332Q814yescomplemented
69C2×#10621877—21no—
70C2×#10621877C2311yescharacteristic
71C2×#10621877C2311yescharacteristic
72C22×C43⋊C8—21no—
73C22×C43⋊C8C2311yescharacteristic
74C22×C43⋊C8C2311yescharacteristic
75#13063325—21no—
76#13063324—21no—
77#13063324—21no—
78#13063324—21no—
79#13063317—21no—
80#13063316—21no—
81#13063316—21no—
82#13063316—21no—
83#13063304—41no—
84#13063302—41no—
85Q8×Dic43—21no—
86D4×Dic43—21no—
87D4×Dic43—41no—
88#13063284—21no—
89#13063284C2311yescharacteristic
90#13063284C2311yescharacteristic
91C2×C4⋊Dic43—21no—
92C2×C4⋊Dic43C2311yescharacteristic
93C2×C4⋊Dic43C2311yescharacteristic
94#13063260—22no—
95#13063259—21no—
96#13063259—21no—
97#13063258—21no—
98#13063258—21no—
99#13063258—21no—
100#13063258—21no—
101#13063258—21no—
102#13063258—21no—
103#13063258—21no—
104#13063258D411yescharacteristic
105#13063258D411yescharacteristic
106#13063257—21no—
107#13063257—21no—
108#13063256—21no—
109#13063256—21no—
110#13063256—21no—
111#13063256—21no—
112#13063256—21no—
113#13063256—21no—
114#13063256—21no—
115#13063256D411yescharacteristic
116#13063256D411yescharacteristic
117C4⋊(C43⋊C8)—21no—
118C4⋊(C43⋊C8)—21no—
119Dic43⋊C8—21no—
120Dic43⋊C8—21no—
121#13063249—21no—
122#13063249D411yescharacteristic
123#13063249D411yescharacteristic
124#13063246—21no—
125#13063246D411yescharacteristic
126#13063246D411yescharacteristic
127#13063235—21no—
128C4×C43⋊C8—22no—
129C8×Dic43—21no—
130C43⋊#95—41no—
131C2×#41×C43C2311yescharacteristic
132C2×M16×C43C2311yescharacteristic
133C2×M16×C43C2311yescharacteristic
134C4×Q8×C43—21no—
135C4×D4×C43—21no—
136C4×D4×C43—41no—
137#117×C43—21no—
138#117×C43C2311yescharacteristic
139C2×C4⋊C4×C43—21no—
140C2×C4⋊C4×C43C2311yescharacteristic
141C2×C4⋊C4×C43C2311yescharacteristic
142C2×C42×C43C2311yescharacteristic
143#107×C43—21no—
144#106×C43—21no—
145#104×C43Q814yescomplemented
146#103×C43—21no—
147#102×C43—21no—
148#95×C43—41no—
149#41×C43—21no—
150#41×C43—21no—
151#41×C43C2×Q812yes—
152#41×C43C2×Q812yes—
153C2×Q8×C43C2×D411yescharacteristic
154C2×D4×C43—21no—
155C2×D4×C43C2×D411yescharacteristic
156C22×C4×C43—21no—
157C22×C4×C43—21no—
158C22×C4×C43—21no—
159C22×C4×C43—21no—
160C22×C4×C43—41no—
161C22×C4×C43C2411yescharacteristic
162C22×Dic43—21no—
163C22×Dic43—21no—
164C22×Dic43—41no—
165C2×Dic86—41no—
166C2×Dic86—41no—
167M16×C43—21no—
168M16×C43—21no—
169M16×C43—21no—
170M16×C43C2×Q812yes—
171C2×C8×C43—21no—
172C2×C8×C43—21no—
173C4⋊C4×C43—21no—
174C4⋊C4×C43—21no—
175C4⋊C4×C43—21no—
176C4⋊C4×C43—21no—
177C4⋊C4×C43—41no—
178C4⋊C4×C43C2×D411yescharacteristic
179C4⋊C4×C43C2×D411yescharacteristic
180C22⋊C4×C43—21no—
181C22⋊C4×C43—41no—
182C42×C43—21no—
183C42×C43—21no—
184C42×C43—41no—
185C42×C43C2×Q812yes—
186C22⋊Dic43—21no—
187C22⋊Dic43—21no—
188C22⋊Dic43—41no—
189C4⋊Dic43—21no—
190C4⋊Dic43—21no—
191C4⋊Dic43—21no—
192C4⋊Dic43—21no—
193C4⋊Dic43—41no—
194C4⋊Dic43—41no—
195C4⋊Dic43—41no—
196C4⋊Dic43C2×D411yescharacteristic
197C4⋊Dic43C2×D411yescharacteristic
198C4⋊Dic43C2×D411yescharacteristic
199C4⋊Dic43C2×D411yescharacteristic
200Dic43⋊C4—41no—
201Dic43⋊C4—41no—
202Dic43⋊C4—41no—
203Dic43⋊C4—41no—
204C4×Dic43—21no—
205C4×Dic43—21no—
206C4×Dic43—41no—
207#10621877—21no—
208#10621877—24no—
209#10621877—21no—
210#10621877—21no—
211#10621877C2×Q812yes—
212C2×C43⋊C8—21no—
213C2×C43⋊C8—21no—
214C2×C43⋊C8—21no—
215C2×C43⋊C8—24no—
216C2×C43⋊C8—21no—
217C2×C43⋊C8C2×D411yescharacteristic
218C2×C43⋊C8C2×D411yescharacteristic
219C2×C43⋊C8C2×D411yescharacteristic
220C2×C43⋊C8C2×D411yescharacteristic
221C2×C43⋊C8C2×Q812yes—
222C2×C43⋊C8#4112yes—
223C23×C43—21no—
224C23×C43H(5,𝔽2)11yescharacteristic
225Q8×C43—21no—
226Q8×C43C4⋊Q812yes—
227D4×C43—22no—
228D4×C43—22no—
229D4×C43—21no—
230D4×C43C4⋊Q812yes—
231C2×C4×C43—21no—
232C2×C4×C43—22no—
233C2×C4×C43—22no—
234C2×C4×C43—21no—
235C2×C4×C43—21no—
236C2×C4×C43—22no—
237C2×C4×C43—41no—
238C2×C4×C43—41no—
239C2×C4×C43—41no—
240C2×C4×C43—41no—
241C2×C4×C43—81no—
242C2×C4×C43—81no—
243C2×C4×C43—161no—
244C2×C4×C43C22×D411yescharacteristic
245C2×C4×C43C22×D411yescharacteristic
246C2×C4×C43C22×Q811yescharacteristic
247C2×C4×C43C22×Q811yescharacteristic
248C2×C4×C43C2×#4111yescharacteristic
249C2×C4×C432−1+411yescharacteristic
250C2×Dic43—21no—
251C2×Dic43—21no—
252C2×Dic43—21no—
253C2×Dic43—21no—
254C2×Dic43—41no—
255C2×Dic43—41no—
256C2×Dic43—81no—
257C2×Dic43—81no—
258C2×Dic43—161no—
259Dic86—161no—
260Dic86—161no—
261C8×C43—22no—
262C8×C43—41no—
263C43⋊C8—22no—
264C43⋊C8—21no—
265C43⋊C8—21no—
266C43⋊C8—41no—
267C43⋊C8C22⋊Q812yes—
268C43⋊C8C22⋊Q812yes—
269#26082—431nomaximal, Sylow
270C22×C43—21no—
271C22×C43—21no—
272C22×C43—22no—
273C22×C43—41no—
274C22×C43—41no—
275C22×C43#54411yescharacteristic
276C22×C43D4211yescharacteristic
277C22×C43#55411yescharacteristic
278C4×C43—22no—
279C4×C43—42no—
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—41no—
289Dic43—41no—
290Dic43—41no—
291Dic43—41no—
292Dic43—81no—
293Dic43—81no—
294#3164—431no—
295#3084—431no—
296#3084—431no—
297#2913—431no—
298#2090—431no—
299#2090—431no—
300#2061—431no—
301#2061—431no—
302#1952—431no—
303#1945—431no—
304#1860—431no—
305#1860D4311yescharacteristic
306#1846—431no—
307#1816—431no—
308#1764—431no—
309C2×C43—21no—
310C2×C43—21no—
311C2×C43—42no—
312C2×C43#244011yescharacteristic
313C2×C43#329011yescharacteristic
314C2×C43#329011yescharacteristic
315C2×#131—431no—
316#544—431no—
317#544—431no—
318#520—431no—
319#520C2×D4311yescharacteristic
320#501—861no—
321#501—861no—
322#500—861no—
323#499—861no—
324#479—861no—
325#479—861no—
326#478—861no—
327#478—861no—
328#476—861no—
329#476—861no—
330#475—861no—
331#475—861no—
332C2×#108—431no—
333#428—431no—
334#428—431no—
335#428—431no—
336#428—431no—
337#428—431no—
338#428—861no—
339#428—861no—
340#428C2×D4311yescharacteristic
341#427—431no—
342#427—861no—
343C2×#107—431no—
344C2×#107—431no—
345C2×#107—861no—
346C2×#106—431no—
347C2×#106—431no—
348#424—431no—
349#424—431no—
350C2×#104C2×D4311yescharacteristic
351#417—431no—
352#417C2×D4311yescharacteristic
353#416—431no—
354#405—431no—
355C2×C4×C8—431no—
356#382—431no—
357#382C2×D4311yescharacteristic
358#343—431no—
359#343—431no—
360#343—431no—
361#343C2×D4311yescharacteristic
362#341—431no—
363#339—431no—
364#339—431no—
365#339C2×D4311yescharacteristic
366C43#2608211yescharacteristic, complemented, Sylow
367C2×#41C22×D4311yescharacteristic
368#131—434no—
369#131—862no—
370C2×M16—431no—
371C2×M16—431no—
372C2×M16—861no—
373C2×M16C22×D4311yescharacteristic
374C2×M16C22×D4311yescharacteristic
375C22×C8—431no—
376C22×C8—431no—
377C22×C8—861no—
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—21no—
389C4×Q8—861no—
390C4×D4—21no—
391C4×D4—41no—
392C4×D4—861no—
393C4×D4—1721no—
394#117—21no—
395#117—431no—
396#117—431no—
397#117—861no—
398#117C22×D4311yescharacteristic
399C2×C4⋊C4—21no—
400C2×C4⋊C4—431no—
401C2×C4⋊C4—431no—
402C2×C4⋊C4—861no—
403C2×C4⋊C4C22×D4311yescharacteristic
404C2×C4⋊C4C22×D4311yescharacteristic
405C2×C42C22×D4311yescharacteristic
406#108—862no—
407#107—21no—
408#107—431no—
409#107—431no—
410#107—861no—
411#107—861no—
412#107—861no—
413#107—861no—
414#107—861no—
415#107—861no—
416#107—861no—
417#107—861no—
418#107—861no—
419#106—21no—
420#106—431no—
421#106—431no—
422#106—861no—
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—861no—
432C4⋊C8—861no—
433C4⋊C8—861no—
434C4⋊C8—861no—
435#104Dic8614yescomplemented
436#103—21no—
437#103—431no—
438#103—431no—
439#103—861no—
440#102—21no—
441#102—431no—
442#102—431no—
443#102—861no—
444#97—861no—
445C4×C8—862no—
446C4×C8—861no—
447#95—41no—
448#95—1721no—
449#41—21no—
450#41—21no—
451#41C2×Dic8612yes—
452#41Q8×D4312yes—
453C2×Q8—1721no—
454C2×Q8—1721no—
455C2×Q8D4×D4311yescharacteristic
456C2×D4—21no—
457C2×D4D4×D4311yescharacteristic
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—41no—
463C22×C4—861no—
464C22×C4—861no—
465C22×C4—1721no—
466C22×C4C23×D4311yescharacteristic
467M16—21no—
468M16—21no—
469M16—21no—
470M16—432no—
471M16—864no—
472M16—861no—
473M16—861no—
474M16—861no—
475M16C2×Dic8612yes—
476C2×C8—21no—
477C2×C8—21no—
478C2×C8—431no—
479C2×C8—431no—
480C2×C8—432no—
481C2×C8—432no—
482C2×C8—431no—
483C2×C8—431no—
484C2×C8—864no—
485C2×C8—861no—
486C2×C8—861no—
487C2×C8—861no—
488C2×C8—861no—
489C4⋊C4—21no—
490C4⋊C4—21no—
491C4⋊C4—21no—
492C4⋊C4—21no—
493C4⋊C4—41no—
494C4⋊C4—431no—
495C4⋊C4—431no—
496C4⋊C4—431no—
497C4⋊C4—431no—
498C4⋊C4—861no—
499C4⋊C4—861no—
500C4⋊C4—861no—
501C4⋊C4—861no—
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—41no—
513C22⋊C4—861no—
514C22⋊C4—861no—
515C22⋊C4—1721no—
516C42—21no—
517C42—21no—
518C42—41no—
519C42—861no—
520C42—861no—
521C42—1721no—
522C42C2×Dic8612yes—
523C23—21no—
524C23#1306337011yescharacteristic
525Q8—21no—
526Q8—6881no—
527Q8—6881no—
528Q8#1306332412yes—
529D4—22no—
530D4—22no—
531D4—21no—
532D4#1306332412yes—
533C2×C4—21no—
534C2×C4—22no—
535C2×C4—22no—
536C2×C4—22no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—81no—
544C2×C4—81no—
545C2×C4—161no—
546C2×C4—861no—
547C2×C4—861no—
548C2×C4—861no—
549C2×C4—861no—
550C2×C4—3441no—
551C2×C4—3441no—
552C2×C4—1721no—
553C2×C4—1721no—
554C2×C4—6881no—
555C2×C4C2×D4×D4311yescharacteristic
556C2×C4C2×D4×D4311yescharacteristic
557C2×C4C2×Q8×D4311yescharacteristic
558C2×C4C22×Dic8611yescharacteristic
559C2×C4#41×D4311yescharacteristic
560C2×C4#1306337211yescharacteristic
561C8—22no—
562C8—41no—
563C8—432no—
564C8—432no—
565C8—862no—
566C8—861no—
567C8—861no—
568C8—1721no—
569C22—21no—
570C22—21no—
571C22—22no—
572C22—41no—
573C22—41no—
574C22#1458352811yescharacteristic
575C22#1458353111yescharacteristic
576C22#1458360811yescharacteristic
577C4—22no—
578C4—42no—
579C4—41no—
580C4—41no—
581C4—81no—
582C4—81no—
583C4—3441no—
584C4—3441no—
585C4—1721no—
586C4—1721no—
587C4—1721no—
588C4—1721no—
589C4C22⋊Q8×D4311yescharacteristic
590C4C2×#1306332411yescharacteristic
591C4#1458354711yescharacteristic
592C4D4×Dic8611yescharacteristic
593C2—21no—
594C2—21no—
595C2—42no—
596C2#1913829611yescharacteristic
597C2#1914637411yescharacteristic
598C2#1914637911yescharacteristic
subgroupG/H
centerC22#14583531
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#1860C2
socleC22×C43D42
prime radicalC2×#41×C43C23
hypercenter#1860D43
hypocenterC43#26082
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ #1860

Complements

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

NH ≅ G/Ntype
1. #19145133C2semidirect
5. #19136109C2semidirect
6. #19136108C2semidirect
7. #19135945C2semidirect
8. #19135944C2semidirect
9. #19135379C2semidirect
10. #19135342C2semidirect
12. #19134757C2semidirect
68. #13063332Q8semidirect
145. #104×C43Q8semidirect
366. C43#26082semidirect
435. #104Dic86semidirect

Maximal subgroups

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

subgroupindex
#191451332
#191444612
#191444572
#191431932
#191361092
#191361082
#191359452
#191359442
#191353792
#191353422
#191348302
#191347572
#191346572
#191344332
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