Finite Group Databasebeta

← #25160045

Subgroups — #25160045

Order 11008.

714 conjugacy classes of subgroups.

The subgroup lattice has 626 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19144461C211yesmaximal, characteristic
2#19144435C211yesmaximal, characteristic, complemented
3#19143434C211yesmaximal, characteristic
4#19143188C211yesmaximal, characteristic
5#19136139C211yesmaximal, characteristic, complemented
6#19136109C211yesmaximal, characteristic, complemented
7#19135963C211yesmaximal, characteristic, complemented
8#19135940C211yesmaximal, characteristic, complemented
9#19135372C211yesmaximal, characteristic, complemented
10#19135192C211yesmaximal, characteristic, complemented
11#19135108C211yesmaximal, characteristic
12#19134962C211yesmaximal, characteristic
13#19134868C211yesmaximal, characteristic
14#19134811C211yesmaximal, characteristic, complemented
15C43×#1859C211yesmaximal, characteristic
16C2×#13063355C2211yescharacteristic
17C2×#13063332C2211yescharacteristic
18#14583530C2211yescharacteristic
19#14583382C2211yescharacteristic
20#14583376C2211yescharacteristic
21#14583209—21no—
22#14583208—21no—
23#14583205—21no—
24#14583197—21no—
25#14583193—21no—
26#14583187—21no—
27#14583183—21no—
28#14583182—21no—
29#14583004—21no—
30#14582999—21no—
31C4×#10621885—21no—
32C4×#10621883—21no—
33C2×#13063260C2211yescharacteristic
34#14582942—21no—
35#14582942C2211yescharacteristic
36#14582941C2211yescharacteristic
37#14582939—21no—
38#14582939C2211yescharacteristic
39#14582939C2211yescharacteristic
40#14582935—21no—
41#14582935C2211yescharacteristic
42C2×#13063256—21no—
43C2×#13063256C2211yescharacteristic
44C2×#13063256C2211yescharacteristic
45#14582927C2211yescharacteristic
46#14582927C2211yescharacteristic
47#14582909C2211yescharacteristic
48#14582895C2211yescharacteristic
49C2×#13063248C2211yescharacteristic
50C2×#13063248C2211yescharacteristic
51C2×#13063243C2211yescharacteristic
52#14582855C2211yescharacteristic
53#14582805C2211yescharacteristic
54#14582668C2211yescharacteristic
55#14582667C2211yescharacteristic
56#14582663C2211yescharacteristic
57#14582659C2211yescharacteristic
58#14582659C2211yescharacteristic
59#14582654C2211yescharacteristic
60C43×#520C2211yescharacteristic
61C43×#428C2211yescharacteristic
62C2×#104×C43C2211yescharacteristic
63C43×#417C2211yescharacteristic
64C43×#384C2211yescharacteristic
65C43×#343C2211yescharacteristic
66C43×#339C2211yescharacteristic
67C22×Dic86C2311yescharacteristic
68#13063355—22no—
69#13063355Q814yescomplemented
70C2×#10621885—21no—
71C2×#10621883—21no—
72#13063332—22no—
73#13063332—22no—
74C2×#10621877—21no—
75C2×#10621877C2311yescharacteristic
76C2×#10621877C2311yescharacteristic
77C22×C43⋊C8—21no—
78C22×C43⋊C8C2311yescharacteristic
79C22×C43⋊C8C2311yescharacteristic
80#13063324—21no—
81#13063324—21no—
82#13063316—21no—
83#13063316—21no—
84#13063304—41no—
85Q8×Dic43—21no—
86C4×Dic86—21no—
87C4×Dic86—21no—
88#13063290—21no—
89#13063290—21no—
90D4×Dic43—21no—
91D4×Dic43—41no—
92#13063284—21no—
93#13063284C2311yescharacteristic
94#13063284C2311yescharacteristic
95#13063281—41no—
96C2×C4⋊Dic43—21no—
97C2×C4⋊Dic43C2311yescharacteristic
98#13063260—22no—
99#13063259—21no—
100#13063258—21no—
101#13063258—21no—
102#13063258—21no—
103#13063258D411yescharacteristic
104#13063258D411yescharacteristic
105#13063257—21no—
106#13063256—21no—
107#13063256—21no—
108#13063256—21no—
109#13063256—21no—
110#13063256—21no—
111#13063256—21no—
112#13063256—21no—
113#13063256D411yescharacteristic
114#13063256D411yescharacteristic
115Dic43⋊C8—21no—
116Dic43⋊C8—21no—
117Dic43⋊C8—21no—
118Dic43⋊C8—21no—
119#13063250—21no—
120#13063250—21no—
121#13063249D411yescharacteristic
122#13063249D411yescharacteristic
123#13063248—21no—
124#13063248—21no—
125#13063248—21no—
126#13063248—21no—
127#13063246D411yescharacteristic
128#13063246D411yescharacteristic
129#13063243—22no—
130#13063236—21no—
131C4×C43⋊C8—21no—
132C43⋊#95—41no—
133C2×#41×C43C2311yescharacteristic
134C2×M16×C43C2311yescharacteristic
135C2×M16×C43C2311yescharacteristic
136C4×Q8×C43—21no—
137C4×D4×C43—21no—
138C4×D4×C43—41no—
139#117×C43—21no—
140#117×C43C2311yescharacteristic
141C2×C4⋊C4×C43—21no—
142C2×C4⋊C4×C43—41no—
143C2×C4⋊C4×C43C2311yescharacteristic
144C2×C4⋊C4×C43C2311yescharacteristic
145C2×C42×C43C2311yescharacteristic
146#107×C43—21no—
147#106×C43—21no—
148#104×C43—22no—
149#103×C43—21no—
150#102×C43—21no—
151#41×C43—21no—
152#41×C43—21no—
153#41×C43C2×Q812yes—
154#41×C43#4112yes—
155C2×Q8×C43C2×D411yescharacteristic
156C2×D4×C43—21no—
157C2×D4×C43C2×D411yescharacteristic
158C22×C4×C43—21no—
159C22×C4×C43—21no—
160C22×C4×C43—21no—
161C22×C4×C43—21no—
162C22×C4×C43—41no—
163C22×C4×C43C2411yescharacteristic
164C22×Dic43—21no—
165C22×Dic43—21no—
166C22×Dic43—41no—
167C2×Dic86—21no—
168C2×Dic86—21no—
169C2×Dic86—21no—
170C2×Dic86—21no—
171C2×Dic86—21no—
172C2×Dic86—41no—
173C2×Dic86C2×Q812yes—
174M16×C43—21no—
175M16×C43—21no—
176M16×C43—21no—
177M16×C43—21no—
178C2×C8×C43—21no—
179C2×C8×C43—21no—
180C4⋊C4×C43—21no—
181C4⋊C4×C43—21no—
182C4⋊C4×C43—21no—
183C4⋊C4×C43—21no—
184C4⋊C4×C43—41no—
185C4⋊C4×C43—82no—
186C4⋊C4×C43C2×D411yescharacteristic
187C4⋊C4×C43C2×D411yescharacteristic
188C22⋊C4×C43—21no—
189C22⋊C4×C43—41no—
190C42×C43—21no—
191C42×C43—21no—
192C42×C43—21no—
193C42×C43—41no—
194C22⋊Dic43—21no—
195C22⋊Dic43—21no—
196C22⋊Dic43—41no—
197#10621885—24no—
198#10621883—24no—
199C4⋊Dic43—21no—
200C4⋊Dic43—21no—
201C4⋊Dic43—41no—
202C4⋊Dic43—41no—
203C4⋊Dic43C2×D411yescharacteristic
204C4⋊Dic43C2×D411yescharacteristic
205C4⋊Dic43C2×D411yescharacteristic
206C4⋊Dic43C2×D411yescharacteristic
207Dic43⋊C4—41no—
208Dic43⋊C4—41no—
209Dic43⋊C4—41no—
210Dic43⋊C4—41no—
211C4×Dic43—21no—
212C4×Dic43—21no—
213C4×Dic43—41no—
214C4×Dic43—41no—
215C4×Dic43—41no—
216#10621877—24no—
217#10621877—21no—
218#10621877—21no—
219#10621877C2×Q812yes—
220#10621877#4112yes—
221C2×C43⋊C8—24no—
222C2×C43⋊C8—21no—
223C2×C43⋊C8—21no—
224C2×C43⋊C8—21no—
225C2×C43⋊C8—21no—
226C2×C43⋊C8—21no—
227C2×C43⋊C8—21no—
228C2×C43⋊C8C2×D411yescharacteristic
229C2×C43⋊C8C2×D411yescharacteristic
230C2×C43⋊C8C2×D411yescharacteristic
231C2×C43⋊C8C2×D411yescharacteristic
232C23×C43—21no—
233C23×C43H(5,𝔽2)11yescharacteristic
234Q8×C43—21no—
235Q8×C43C22⋊Q812yes—
236D4×C43—22no—
237D4×C43—22no—
238D4×C43—21no—
239D4×C43C22⋊Q812yes—
240C2×C4×C43—21no—
241C2×C4×C43—22no—
242C2×C4×C43—22no—
243C2×C4×C43—22no—
244C2×C4×C43—21no—
245C2×C4×C43—21no—
246C2×C4×C43—41no—
247C2×C4×C43—41no—
248C2×C4×C43—41no—
249C2×C4×C43—41no—
250C2×C4×C43—81no—
251C2×C4×C43—81no—
252C2×C4×C43—161no—
253C2×C4×C43C22×D411yescharacteristic
254C2×C4×C43C22×D411yescharacteristic
255C2×C4×C43C22×Q811yescharacteristic
256C2×C4×C43C2×#4111yescharacteristic
257C2×C4×C43C2×#4111yescharacteristic
258C2×C4×C432−1+411yescharacteristic
259C2×Dic43—21no—
260C2×Dic43—21no—
261C2×Dic43—21no—
262C2×Dic43—21no—
263C2×Dic43—22no—
264C2×Dic43—41no—
265C2×Dic43—41no—
266C2×Dic43—41no—
267C2×Dic43—81no—
268C2×Dic43—161no—
269Dic86—22no—
270Dic86—22no—
271Dic86—41no—
272Dic86—41no—
273Dic86—161no—
274C8×C43—41no—
275C8×C43—41no—
276C43⋊C8—22no—
277C43⋊C8—21no—
278C43⋊C8—22no—
279C43⋊C8—21no—
280C43⋊C8—21no—
281C43⋊C8—21no—
282#26401—431nomaximal, Sylow
283C22×C43—21no—
284C22×C43—21no—
285C22×C43—22no—
286C22×C43—41no—
287C22×C43—41no—
288C22×C43#53911yescharacteristic
289C22×C43D4211yescharacteristic
290C22×C43#55411yescharacteristic
291C4×C43—22no—
292C4×C43—42no—
293C4×C43—41no—
294C4×C43—41no—
295C4×C43—81no—
296C4×C43—81no—
297C4×C43C2×C22⋊Q811yescharacteristic
298C4×C43#52511yescharacteristic
299C4×C43#54711yescharacteristic
300C4×C43D4×Q811yescharacteristic
301Dic43—42no—
302Dic43—41no—
303Dic43—41no—
304Dic43—41no—
305Dic43—41no—
306Dic43—81no—
307#3084—431no—
308#3082—431no—
309#2947—431no—
310#2912—431no—
311#2096—431no—
312#2090—431no—
313#2064—431no—
314#2060—431no—
315#1951—431no—
316#1922—431no—
317#1908—431no—
318#1882—431no—
319#1866—431no—
320#1859D4311yescharacteristic
321#1857—431no—
322C2×C43—21no—
323C2×C43—21no—
324C2×C43—42no—
325C2×C43#244911yescharacteristic
326C2×C43#328911yescharacteristic
327C2×C43#329111yescharacteristic
328C2×#137—431no—
329C2×#131—431no—
330#544—431no—
331#520—431no—
332#520C2×D4311yescharacteristic
333#519—431no—
334#479—861no—
335#479—861no—
336#479—861no—
337#478—861no—
338#477—861no—
339#476—861no—
340#475—861no—
341#475—861no—
342#441—861no—
343#440—861no—
344C4×Q16—861no—
345C4×SD16—861no—
346C2×#108—431no—
347#428—431no—
348#428—431no—
349#428—431no—
350#428—431no—
351#428—861no—
352#428—861no—
353#428C2×D4311yescharacteristic
354#427—431no—
355#427—861no—
356C2×#106—431no—
357C2×#106—431no—
358C2×#106—861no—
359#424—431no—
360#424—431no—
361C2×#104C2×D4311yescharacteristic
362#419—431no—
363#417C2×D4311yescharacteristic
364#416—431no—
365C2×#103—431no—
366C2×#103—431no—
367C2×#101—431no—
368#405—431no—
369#391—431no—
370#384C2×D4311yescharacteristic
371#343—431no—
372#343—431no—
373#343C2×D4311yescharacteristic
374#341—431no—
375#339—431no—
376#339—431no—
377#339C2×D4311yescharacteristic
378#336—431no—
379C43#2640111yescharacteristic, complemented, Sylow
380C2×#41C22×D4311yescharacteristic
381C22×Q8—431no—
382#137—434no—
383#137—862no—
384C2×Q16—861no—
385C2×SD16—861no—
386#131—862no—
387#131—862no—
388C2×M16—431no—
389C2×M16—431no—
390C2×M16—861no—
391C2×M16C22×D4311yescharacteristic
392C2×M16C22×D4311yescharacteristic
393C22×C8—431no—
394C22×C8—431no—
395C22×C8—861no—
396C4⋊Q8—861no—
397C4⋊Q8—861no—
398#125—861no—
399#125—861no—
400C22⋊Q8—1721no—
401C4×Q8—21no—
402C4×Q8—861no—
403C4×Q8—861no—
404C4×Q8—861no—
405C4×Q8—861no—
406C4×Q8—861no—
407C4×D4—21no—
408C4×D4—41no—
409C4×D4—861no—
410C4×D4—1721no—
411#117—21no—
412#117—431no—
413#117—431no—
414#117—861no—
415#117—1721no—
416#117C22×D4311yescharacteristic
417C2×C4⋊C4—21no—
418C2×C4⋊C4—41no—
419C2×C4⋊C4—431no—
420C2×C4⋊C4—861no—
421C2×C4⋊C4C22×D4311yescharacteristic
422C2×C4⋊C4C22×D4311yescharacteristic
423C2×C42C22×D4311yescharacteristic
424#108—862no—
425#107—21no—
426#107—431no—
427#107—431no—
428#107—861no—
429#107—861no—
430#107—861no—
431#107—861no—
432#106—21no—
433#106—431no—
434#106—431no—
435#106—861no—
436#106—861no—
437#106—861no—
438#106—861no—
439#106—861no—
440#106—861no—
441#106—861no—
442#106—861no—
443C4⋊C8—861no—
444C4⋊C8—861no—
445C4⋊C8—861no—
446C4⋊C8—861no—
447#104—22no—
448#103—21no—
449#103—431no—
450#103—431no—
451#103—861no—
452#103—861no—
453#103—861no—
454#103—861no—
455#103—861no—
456#103—861no—
457#102—21no—
458#102—431no—
459#102—431no—
460#101—862no—
461#97—861no—
462C4×C8—861no—
463#95—1721no—
464#41—21no—
465#41—21no—
466#41#1062189812yes—
467#41Q8×D4312yes—
468C2×Q8—432no—
469C2×Q8—861no—
470C2×Q8—861no—
471C2×Q8—861no—
472C2×Q8—861no—
473C2×Q8—861no—
474C2×Q8—1721no—
475C2×Q8D4×D4311yescharacteristic
476C2×D4—21no—
477C2×D4D4×D4311yescharacteristic
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—41no—
483C22×C4—861no—
484C22×C4—861no—
485C22×C4—1721no—
486C22×C4C23×D4311yescharacteristic
487Q16—864no—
488SD16—864no—
489M16—21no—
490M16—21no—
491M16—21no—
492M16—21no—
493M16—432no—
494M16—432no—
495M16—864no—
496M16—861no—
497M16—861no—
498C2×C8—21no—
499C2×C8—21no—
500C2×C8—431no—
501C2×C8—431no—
502C2×C8—431no—
503C2×C8—431no—
504C2×C8—864no—
505C2×C8—861no—
506C2×C8—861no—
507C2×C8—861no—
508C2×C8—861no—
509C2×C8—861no—
510C2×C8—861no—
511C4⋊C4—21no—
512C4⋊C4—21no—
513C4⋊C4—21no—
514C4⋊C4—21no—
515C4⋊C4—41no—
516C4⋊C4—82no—
517C4⋊C4—431no—
518C4⋊C4—431no—
519C4⋊C4—431no—
520C4⋊C4—431no—
521C4⋊C4—861no—
522C4⋊C4—861no—
523C4⋊C4—1721no—
524C4⋊C4—1721no—
525C4⋊C4—1721no—
526C4⋊C4—1721no—
527C4⋊C4—1721no—
528C4⋊C4—1721no—
529C4⋊C4D4×D4311yescharacteristic
530C4⋊C4D4×D4311yescharacteristic
531C22⋊C4—21no—
532C22⋊C4—41no—
533C22⋊C4—861no—
534C22⋊C4—861no—
535C22⋊C4—1721no—
536C42—21no—
537C42—21no—
538C42—21no—
539C42—41no—
540C42—861no—
541C42—861no—
542C42—1721no—
543C42—1721no—
544C42—1721no—
545C23—21no—
546C23#1306337011yescharacteristic
547Q8—21no—
548Q8—862no—
549Q8—862no—
550Q8—1721no—
551Q8—1721no—
552Q8—6881no—
553Q8#1306330312yes—
554D4—22no—
555D4—22no—
556D4—21no—
557D4#1306330312yes—
558C2×C4—21no—
559C2×C4—22no—
560C2×C4—22no—
561C2×C4—22no—
562C2×C4—21no—
563C2×C4—21no—
564C2×C4—41no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—81no—
569C2×C4—81no—
570C2×C4—161no—
571C2×C4—862no—
572C2×C4—861no—
573C2×C4—861no—
574C2×C4—861no—
575C2×C4—861no—
576C2×C4—3441no—
577C2×C4—1721no—
578C2×C4—1721no—
579C2×C4—1721no—
580C2×C4—6881no—
581C2×C4C2×D4×D4311yescharacteristic
582C2×C4C2×D4×D4311yescharacteristic
583C2×C4C2×Q8×D4311yescharacteristic
584C2×C4#41×D4311yescharacteristic
585C2×C4C2×#1062189811yescharacteristic
586C2×C4#1306337211yescharacteristic
587C8—41no—
588C8—41no—
589C8—862no—
590C8—861no—
591C8—861no—
592C8—862no—
593C8—861no—
594C8—861no—
595C22—21no—
596C22—21no—
597C22—22no—
598C22—41no—
599C22—41no—
600C22#1458349111yescharacteristic
601C22#1458353111yescharacteristic
602C22#1458360311yescharacteristic
603C4—22no—
604C4—42no—
605C4—41no—
606C4—41no—
607C4—81no—
608C4—81no—
609C4—3441no—
610C4—1722no—
611C4—1721no—
612C4—1721no—
613C4—1721no—
614C4—1721no—
615C4C2×#1306330311yescharacteristic
616C4#1458340811yescharacteristic
617C4#1458354711yescharacteristic
618C4#1458356211yescharacteristic
619C2—21no—
620C2—21no—
621C2—42no—
622C2#1913840611yescharacteristic
623C2#1914636511yescharacteristic
624C2#1914639011yescharacteristic
subgroupG/H
centerC22#14583531
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#1859C2
socleC22×C43D42
prime radicalC2×#41×C43C23
hypercenter#1859D43
hypocenterC43#26401
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ #1859

Complements

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

NH ≅ G/Ntype
2. #19144435C2semidirect
5. #19136139C2semidirect
6. #19136109C2semidirect
7. #19135963C2semidirect
8. #19135940C2semidirect
9. #19135372C2semidirect
10. #19135192C2semidirect
14. #19134811C2semidirect
69. #13063355Q8semidirect
379. C43#26401semidirect

Maximal subgroups

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

subgroupindex
#191444612
#191444352
#191434342
#191431882
#191361392
#191361092
#191359632
#191359402
#191353722
#191351922
#191351082
#191349622
#191348682
#191348112
C43×#18592
#2640143