Finite Group Databasebeta

← #25160077

Subgroups — #25160077

Order 11008.

706 conjugacy classes of subgroups.

The subgroup lattice has 624 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19144457C211yesmaximal, characteristic
2#19144439C211yesmaximal, characteristic, complemented
3#19143439C211yesmaximal, characteristic
4#19143193C211yesmaximal, characteristic
5#19136143C211yesmaximal, characteristic, complemented
6#19136104C211yesmaximal, characteristic, complemented
7#19135962C211yesmaximal, characteristic, complemented
8#19135944C211yesmaximal, characteristic, complemented
9#19135374C211yesmaximal, characteristic, complemented
10#19135197C211yesmaximal, characteristic, complemented
11#19135112C211yesmaximal, characteristic
12#19134868C211yesmaximal, characteristic
13#19134830C211yesmaximal, characteristic
14#19134809C211yesmaximal, characteristic, complemented
15C43×#1882C211yesmaximal, characteristic
16C2×#13063332C2211yescharacteristic
17#14583527C2211yescharacteristic
18#14583382C2211yescharacteristic
19#14583377C2211yescharacteristic
20#14583208—21no—
21#14583206—21no—
22#14583204—21no—
23#14583199—21no—
24#14583192—21no—
25#14583189—21no—
26#14583184—21no—
27#14583182—21no—
28#14583006—21no—
29#14583000—21no—
30Q16×Dic43—21no—
31SD16×Dic43—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×#13063256C2211yescharacteristic
45#14582927C2211yescharacteristic
46#14582926C2211yescharacteristic
47#14582900C2211yescharacteristic
48#14582895C2211yescharacteristic
49C2×#13063249C2211yescharacteristic
50C2×#13063249C2211yescharacteristic
51C2×#13063244C2211yescharacteristic
52#14582857C2211yescharacteristic
53#14582765C2211yescharacteristic
54#14582667C2211yescharacteristic
55#14582667C2211yescharacteristic
56#14582663C2211yescharacteristic
57#14582659C2211yescharacteristic
58#14582659C2211yescharacteristic
59#14582654C2211yescharacteristic
60C2×#137×C43C2211yescharacteristic
61C43×#520C2211yescharacteristic
62C2×#104×C43C2211yescharacteristic
63C43×#419C2211yescharacteristic
64C43×#391C2211yescharacteristic
65C43×#343C2211yescharacteristic
66C43×#339C2211yescharacteristic
67#13063332—22no—
68#13063332—22no—
69C2×#10621877—21no—
70C2×#10621877C2311yescharacteristic
71C2×#10621877C2311yescharacteristic
72C22×C43⋊C8—21no—
73C22×C43⋊C8C2311yescharacteristic
74C22×C43⋊C8C2311yescharacteristic
75#13063325—21no—
76#13063324—21no—
77#13063317—21no—
78#13063316—21no—
79#13063302—41no—
80Q8×Dic43—21no—
81Q8×Dic43—21no—
82Q8×Dic43—21no—
83Q8×Dic43—21no—
84Q8×Dic43—21no—
85D4×Dic43—21no—
86D4×Dic43—41no—
87#13063284—21no—
88#13063284—41no—
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#13063258D411yescharacteristic
103#13063258D411yescharacteristic
104#13063257—21no—
105#13063257—21no—
106#13063256—21no—
107#13063256—21no—
108#13063256—21no—
109#13063256—21no—
110#13063256—21no—
111#13063256D411yescharacteristic
112#13063256D411yescharacteristic
113C4⋊(C43⋊C8)—21no—
114C4⋊(C43⋊C8)—21no—
115Dic43⋊C8—21no—
116Dic43⋊C8—21no—
117#13063249—21no—
118#13063249—21no—
119#13063249—21no—
120#13063249—21no—
121#13063249—21no—
122#13063249D411yescharacteristic
123#13063249D411yescharacteristic
124#13063246—21no—
125#13063246D411yescharacteristic
126#13063246D411yescharacteristic
127#13063244—22no—
128#13063235—21no—
129C8×Dic43—21no—
130C43⋊#95—41no—
131C2×#41×C43C2311yescharacteristic
132C22×Q8×C43C2311yescharacteristic
133#137×C43—22no—
134#137×C43Q814yescomplemented
135C2×Q16×C43—21no—
136C2×SD16×C43—21no—
137C2×M16×C43C2311yescharacteristic
138C2×M16×C43C2311yescharacteristic
139C4×Q8×C43—21no—
140C4×D4×C43—21no—
141C4×D4×C43—41no—
142#117×C43—21no—
143#117×C43C2311yescharacteristic
144C2×C4⋊C4×C43—21no—
145C2×C4⋊C4×C43C2311yescharacteristic
146C2×C42×C43C2311yescharacteristic
147#104×C43—22no—
148#103×C43—21no—
149#103×C43—21no—
150#95×C43—41no—
151#41×C43—21no—
152#41×C43—21no—
153#41×C43C2×Q812yes—
154#41×C43#4112yes—
155C2×Q8×C43—21no—
156C2×Q8×C43—21no—
157C2×Q8×C43—21no—
158C2×Q8×C43—21no—
159C2×Q8×C43—21no—
160C2×Q8×C43C2×D411yescharacteristic
161C2×Q8×C43C2×Q812yes—
162C2×D4×C43—21no—
163C2×D4×C43C2×D411yescharacteristic
164C22×C4×C43—21no—
165C22×C4×C43—21no—
166C22×C4×C43—21no—
167C22×C4×C43—21no—
168C22×C4×C43—41no—
169C22×C4×C43C2411yescharacteristic
170C22×Dic43—21no—
171C22×Dic43—21no—
172C22×Dic43—41no—
173C2×Dic86—41no—
174Q16×C43—24no—
175SD16×C43—24no—
176M16×C43—21no—
177M16×C43—21no—
178M16×C43—21no—
179M16×C43C2×Q812yes—
180C2×C8×C43—21no—
181C2×C8×C43—21no—
182C4⋊C4×C43—21no—
183C4⋊C4×C43—21no—
184C4⋊C4×C43—41no—
185C4⋊C4×C43C2×D411yescharacteristic
186C4⋊C4×C43C2×D411yescharacteristic
187C22⋊C4×C43—21no—
188C22⋊C4×C43—41no—
189C42×C43—21no—
190C42×C43—21no—
191C42×C43—21no—
192C42×C43—41no—
193C22⋊Dic43—21no—
194C22⋊Dic43—21no—
195C22⋊Dic43—41no—
196C4⋊Dic43—21no—
197C4⋊Dic43—21no—
198C4⋊Dic43—21no—
199C4⋊Dic43—21no—
200C4⋊Dic43—41no—
201C4⋊Dic43—41no—
202C4⋊Dic43—41no—
203C4⋊Dic43—41no—
204C4⋊Dic43C2×D411yescharacteristic
205C4⋊Dic43C2×D411yescharacteristic
206C4⋊Dic43C2×D411yescharacteristic
207C4⋊Dic43C2×D411yescharacteristic
208Dic43⋊C4—41no—
209Dic43⋊C4—41no—
210C4×Dic43—21no—
211C4×Dic43—21no—
212C4×Dic43—41no—
213C4×Dic43—41no—
214C4×Dic43—41no—
215#10621877—24no—
216#10621877—21no—
217#10621877—21no—
218#10621877—21no—
219#10621877#4112yes—
220C2×C43⋊C8—24no—
221C2×C43⋊C8—21no—
222C2×C43⋊C8—21no—
223C2×C43⋊C8—21no—
224C2×C43⋊C8—21no—
225C2×C43⋊C8—21no—
226C2×C43⋊C8—21no—
227C2×C43⋊C8C2×D411yescharacteristic
228C2×C43⋊C8C2×D411yescharacteristic
229C2×C43⋊C8C2×D411yescharacteristic
230C2×C43⋊C8C2×D411yescharacteristic
231C23×C43—21no—
232C23×C43H(5,𝔽2)11yescharacteristic
233Q8×C43—21no—
234Q8×C43—22no—
235Q8×C43—22no—
236Q8×C43—41no—
237Q8×C43—41no—
238Q8×C43C22⋊Q812yes—
239D4×C43—22no—
240D4×C43—22no—
241D4×C43—21no—
242D4×C43C22⋊Q812yes—
243C2×C4×C43—21no—
244C2×C4×C43—22no—
245C2×C4×C43—22no—
246C2×C4×C43—21no—
247C2×C4×C43—21no—
248C2×C4×C43—22no—
249C2×C4×C43—41no—
250C2×C4×C43—41no—
251C2×C4×C43—41no—
252C2×C4×C43—41no—
253C2×C4×C43—41no—
254C2×C4×C43—41no—
255C2×C4×C43—81no—
256C2×C4×C43—161no—
257C2×C4×C43C22×D411yescharacteristic
258C2×C4×C43C22×D411yescharacteristic
259C2×C4×C43C22×Q811yescharacteristic
260C2×C4×C43C2×#4111yescharacteristic
261C2×C4×C43C2×#4111yescharacteristic
262C2×C4×C432−1+411yescharacteristic
263C2×Dic43—21no—
264C2×Dic43—21no—
265C2×Dic43—21no—
266C2×Dic43—21no—
267C2×Dic43—41no—
268C2×Dic43—41no—
269C2×Dic43—81no—
270C2×Dic43—81no—
271C2×Dic43—161no—
272Dic86—161no—
273C8×C43—22no—
274C8×C43—41no—
275C43⋊C8—21no—
276C43⋊C8—22no—
277C43⋊C8—21no—
278C43⋊C8—21no—
279C43⋊C8—21no—
280C43⋊C8—41no—
281#26403—431nomaximal, Sylow
282C22×C43—21no—
283C22×C43—21no—
284C22×C43—22no—
285C22×C43—41no—
286C22×C43—41no—
287C22×C43#53911yescharacteristic
288C22×C43D4211yescharacteristic
289C22×C43#55411yescharacteristic
290C4×C43—22no—
291C4×C43—42no—
292C4×C43—41no—
293C4×C43—41no—
294C4×C43—81no—
295C4×C43—81no—
296C4×C43C2×C22⋊Q811yescharacteristic
297C4×C43#52511yescharacteristic
298C4×C43#54711yescharacteristic
299C4×C43D4×Q811yescharacteristic
300Dic43—41no—
301Dic43—41no—
302Dic43—41no—
303Dic43—41no—
304Dic43—81no—
305Dic43—81no—
306#3084—431no—
307#3082—431no—
308#2947—431no—
309#2913—431no—
310#2097—431no—
311#2089—431no—
312#2064—431no—
313#2061—431no—
314#1951—431no—
315#1922—431no—
316#1908—431no—
317#1882D4311yescharacteristic
318#1866—431no—
319#1860—431no—
320#1857—431no—
321C2×C43—21no—
322C2×C43—21no—
323C2×C43—42no—
324C2×C43#244911yescharacteristic
325C2×C43#328911yescharacteristic
326C2×C43#329011yescharacteristic
327C2×#137C2×D4311yescharacteristic
328C2×#131—431no—
329#544—431no—
330#520—431no—
331#520C2×D4311yescharacteristic
332#519—431no—
333#479—861no—
334#479—861no—
335#479—861no—
336#478—861no—
337#477—861no—
338#476—861no—
339#475—861no—
340#475—861no—
341#441—861no—
342#440—861no—
343C4×Q16—861no—
344C4×SD16—861no—
345C2×#108—431no—
346#428—431no—
347#428—431no—
348#428—431no—
349#428—431no—
350#428—431no—
351#428—861no—
352#428—861no—
353#427—431no—
354#427—861no—
355C2×#107—431no—
356C2×#107—861no—
357C2×#106—431no—
358#424—431no—
359#424—431no—
360C2×#104C2×D4311yescharacteristic
361#419C2×D4311yescharacteristic
362#417—431no—
363#416—431no—
364C2×#103—431no—
365C2×#103—431no—
366C2×#101—431no—
367#405—431no—
368#391C2×D4311yescharacteristic
369#382—431no—
370#343—431no—
371#343—431no—
372#343C2×D4311yescharacteristic
373#341—431no—
374#339—431no—
375#339—431no—
376#339C2×D4311yescharacteristic
377#336—431no—
378C43#2640311yescharacteristic, complemented, Sylow
379C2×#41C22×D4311yescharacteristic
380C22×Q8C22×D4311yescharacteristic
381#137—22no—
382#137Dic8614yescomplemented
383C2×Q16—21no—
384C2×SD16—21no—
385#131—862no—
386#131—862no—
387C2×M16—431no—
388C2×M16—431no—
389C2×M16—861no—
390C2×M16C22×D4311yescharacteristic
391C2×M16C22×D4311yescharacteristic
392C22×C8—431no—
393C22×C8—431no—
394C22×C8—861no—
395C4⋊Q8—861no—
396C4⋊Q8—861no—
397#125—861no—
398#125—861no—
399C22⋊Q8—1721no—
400C4×Q8—21no—
401C4×Q8—861no—
402C4×Q8—861no—
403C4×Q8—861no—
404C4×Q8—861no—
405C4×Q8—861no—
406C4×D4—21no—
407C4×D4—41no—
408C4×D4—861no—
409C4×D4—1721no—
410#117—21no—
411#117—431no—
412#117—431no—
413#117—861no—
414#117—1721no—
415#117C22×D4311yescharacteristic
416C2×C4⋊C4—21no—
417C2×C4⋊C4—431no—
418C2×C4⋊C4—431no—
419C2×C4⋊C4—861no—
420C2×C4⋊C4C22×D4311yescharacteristic
421C2×C42C22×D4311yescharacteristic
422#108—862no—
423#107—431no—
424#107—431no—
425#107—861no—
426#107—861no—
427#107—861no—
428#107—861no—
429#107—861no—
430#107—861no—
431#107—861no—
432#106—431no—
433#106—431no—
434#106—861no—
435#106—861no—
436#106—861no—
437#106—861no—
438#106—861no—
439#106—861no—
440#106—861no—
441C4⋊C8—861no—
442C4⋊C8—861no—
443C4⋊C8—861no—
444C4⋊C8—861no—
445#104—22no—
446#103—21no—
447#103—21no—
448#103—431no—
449#103—431no—
450#103—861no—
451#103—861no—
452#103—861no—
453#103—861no—
454#103—861no—
455#102—431no—
456#102—431no—
457#102—861no—
458#101—862no—
459#97—861no—
460C4×C8—861no—
461#95—41no—
462#95—1721no—
463#41—21no—
464#41—21no—
465#41C2×Dic8612yes—
466#41#1062190012yes—
467C2×Q8—21no—
468C2×Q8—21no—
469C2×Q8—21no—
470C2×Q8—21no—
471C2×Q8—21no—
472C2×Q8—1721no—
473C2×Q8C2×Dic8612yes—
474C2×Q8D4×D4311yescharacteristic
475C2×D4—21no—
476C2×D4D4×D4311yescharacteristic
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—41no—
482C22×C4—861no—
483C22×C4—861no—
484C22×C4—1721no—
485C22×C4C23×D4311yescharacteristic
486Q16—24no—
487SD16—24no—
488M16—21no—
489M16—21no—
490M16—21no—
491M16—432no—
492M16—864no—
493M16—861no—
494M16—861no—
495M16—861no—
496M16C2×Dic8612yes—
497C2×C8—21no—
498C2×C8—21no—
499C2×C8—431no—
500C2×C8—431no—
501C2×C8—431no—
502C2×C8—431no—
503C2×C8—864no—
504C2×C8—861no—
505C2×C8—861no—
506C2×C8—861no—
507C2×C8—861no—
508C2×C8—861no—
509C2×C8—861no—
510C4⋊C4—21no—
511C4⋊C4—21no—
512C4⋊C4—41no—
513C4⋊C4—431no—
514C4⋊C4—431no—
515C4⋊C4—431no—
516C4⋊C4—431no—
517C4⋊C4—861no—
518C4⋊C4—861no—
519C4⋊C4—861no—
520C4⋊C4—861no—
521C4⋊C4—1721no—
522C4⋊C4—1721no—
523C4⋊C4—1721no—
524C4⋊C4—1721no—
525C4⋊C4—1721no—
526C4⋊C4—1721no—
527C4⋊C4D4×D4311yescharacteristic
528C4⋊C4D4×D4311yescharacteristic
529C22⋊C4—21no—
530C22⋊C4—41no—
531C22⋊C4—861no—
532C22⋊C4—861no—
533C22⋊C4—1721no—
534C42—21no—
535C42—21no—
536C42—21no—
537C42—41no—
538C42—861no—
539C42—861no—
540C42—1721no—
541C42—1721no—
542C42—1721no—
543C23—21no—
544C23#1306337011yescharacteristic
545Q8—21no—
546Q8—22no—
547Q8—22no—
548Q8—41no—
549Q8—41no—
550Q8—6881no—
551Q8#1306330212yes—
552D4—22no—
553D4—22no—
554D4—21no—
555D4#1306330212yes—
556C2×C4—21no—
557C2×C4—22no—
558C2×C4—22no—
559C2×C4—22no—
560C2×C4—21no—
561C2×C4—21no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—81no—
569C2×C4—161no—
570C2×C4—861no—
571C2×C4—861no—
572C2×C4—861no—
573C2×C4—861no—
574C2×C4—3441no—
575C2×C4—3441no—
576C2×C4—1721no—
577C2×C4—1721no—
578C2×C4—6881no—
579C2×C4C2×D4×D4311yescharacteristic
580C2×C4C2×D4×D4311yescharacteristic
581C2×C4C22×Dic8611yescharacteristic
582C2×C4#41×D4311yescharacteristic
583C2×C4C2×#1062190011yescharacteristic
584C2×C4#1306337211yescharacteristic
585C8—22no—
586C8—41no—
587C8—861no—
588C8—861no—
589C8—862no—
590C8—861no—
591C8—861no—
592C8—1721no—
593C22—21no—
594C22—21no—
595C22—22no—
596C22—41no—
597C22—41no—
598C22#1458349411yescharacteristic
599C22#1458353111yescharacteristic
600C22#1458360811yescharacteristic
601C4—22no—
602C4—42no—
603C4—41no—
604C4—41no—
605C4—81no—
606C4—81no—
607C4—3441no—
608C4—3441no—
609C4—1721no—
610C4—1721no—
611C4—1721no—
612C4—1721no—
613C4C2×#1306330211yescharacteristic
614C4#1458340911yescharacteristic
615C4#1458354711yescharacteristic
616C4D4×Dic8611yescharacteristic
617C2—21no—
618C2—21no—
619C2—42no—
620C2#1913840811yescharacteristic
621C2#1914636511yescharacteristic
622C2#1914637911yescharacteristic
subgroupG/H
centerC22#14583531
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#1882C2
socleC22×C43D42
prime radicalC2×#41×C43C23
hypercenter#1882D43
hypocenterC43#26403
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ #1882

Complements

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

NH ≅ G/Ntype
2. #19144439C2semidirect
5. #19136143C2semidirect
6. #19136104C2semidirect
7. #19135962C2semidirect
8. #19135944C2semidirect
9. #19135374C2semidirect
10. #19135197C2semidirect
14. #19134809C2semidirect
134. #137×C43Q8semidirect
378. C43#26403semidirect
382. #137Dic86semidirect

Maximal subgroups

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

subgroupindex
#191444572
#191444392
#191434392
#191431932
#191361432
#191361042
#191359622
#191359442
#191353742
#191351972
#191351122
#191348682
#191348302
#191348092
C43×#18822
#2640343