Finite Group Databasebeta

← #25155545

Subgroups — #25155545

Order 11008.

678 conjugacy classes of subgroups.

The subgroup lattice has 602 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145123C211yesmaximal, characteristic, complemented
2#19144461C211yesmaximal, characteristic
3#19144450C211yesmaximal, characteristic
4#19143195C211yesmaximal, characteristic
5#19136109C211yesmaximal, characteristic, complemented
6#19136104C211yesmaximal, characteristic, complemented
7#19135946C211yesmaximal, characteristic, complemented
8#19135941C211yesmaximal, characteristic, complemented
9#19135381C211yesmaximal, characteristic, complemented
10#19135346C211yesmaximal, characteristic, complemented
11#19134826C211yesmaximal, characteristic
12#19134819C211yesmaximal, characteristic
13#19134760C211yesmaximal, characteristic, complemented
14#19134437C211yesmaximal, characteristic
15C43×#1815C211yesmaximal, characteristic
16#14583530C2211yescharacteristic
17#14583530C2211yescharacteristic
18#14583382C2211yescharacteristic
19#14583382C2211yescharacteristic
20#14583306—21no—
21#14583306—21no—
22#14583299—21no—
23#14583296—21no—
24#14583208—21no—
25#14583204—21no—
26#14583201—21no—
27#14583197—21no—
28#14583192—21no—
29#14583187—21no—
30#14583182—21no—
31#14583177—21no—
32#14582941—21no—
33#14582941—21no—
34#14582941C2211yescharacteristic
35#14582941C2211yescharacteristic
36#14582941C2211yescharacteristic
37#14582941C2211yescharacteristic
38#14582939C2211yescharacteristic
39#14582939C2211yescharacteristic
40#14582937—21no—
41#14582937C2211yescharacteristic
42C2×#13063259—21no—
43C2×#13063259C2211yescharacteristic
44C2×#13063258C2211yescharacteristic
45C2×#13063256C2211yescharacteristic
46#14582927C2211yescharacteristic
47#14582927C2211yescharacteristic
48C2×#13063252C2211yescharacteristic
49#14582895C2211yescharacteristic
50#14582854C2211yescharacteristic
51C2×#13063235C2211yescharacteristic
52#14582768C2211yescharacteristic
53#14582764C2211yescharacteristic
54#14582667C2211yescharacteristic
55#14582667C2211yescharacteristic
56#14582663C2211yescharacteristic
57#14582660C2211yescharacteristic
58#14582660C2211yescharacteristic
59#14582660C2211yescharacteristic
60C2×#131×C43C2211yescharacteristic
61C2×#108×C43C2211yescharacteristic
62C2×#106×C43C2211yescharacteristic
63C43×#417C2211yescharacteristic
64C43×#417C2211yescharacteristic
65C43×#343C2211yescharacteristic
66C43×#343C2211yescharacteristic
67C2×#10621877C2311yescharacteristic
68C22×C43⋊C8C2311yescharacteristic
69#13063324—21no—
70#13063324—21no—
71#13063324—21no—
72#13063324—21no—
73#13063316—21no—
74#13063316—21no—
75#13063316—21no—
76#13063316—21no—
77#13063304—41no—
78#13063304—41no—
79Q8×Dic43—21no—
80Q8×Dic43—21no—
81D4×Dic43—21no—
82D4×Dic43—21no—
83D4×Dic43—41no—
84D4×Dic43—41no—
85#13063284—21no—
86#13063284—21no—
87#13063284C2311yescharacteristic
88#13063284C2311yescharacteristic
89#13063284C2311yescharacteristic
90C2×C4⋊Dic43—21no—
91C2×C4⋊Dic43—21no—
92C2×C4⋊Dic43C2311yescharacteristic
93C2×C4⋊Dic43C2311yescharacteristic
94C2×Dic43⋊C4—41no—
95C2×C4×Dic43C2311yescharacteristic
96#13063259—21no—
97#13063259—21no—
98#13063259—21no—
99#13063259—21no—
100#13063259—21no—
101#13063259—21no—
102#13063259D411yescharacteristic
103#13063259D411yescharacteristic
104#13063258—21no—
105#13063258—21no—
106#13063258—21no—
107#13063258—21no—
108#13063257—21no—
109#13063257—21no—
110#13063257—21no—
111#13063257—21no—
112#13063257D411yescharacteristic
113#13063257D411yescharacteristic
114#13063256—21no—
115#13063256—21no—
116#13063256—21no—
117#13063256—21no—
118Dic43⋊C8—21no—
119Dic43⋊C8—21no—
120Dic43⋊C8—21no—
121Dic43⋊C8—21no—
122#13063252Q814yescomplemented
123#13063249D411yescharacteristic
124#13063249D411yescharacteristic
125#13063246D411yescharacteristic
126#13063246D411yescharacteristic
127#13063235—21no—
128#13063235—22no—
129C8×Dic43—21no—
130C43⋊#95—41no—
131C2×#41×C43C2311yescharacteristic
132#131×C43—22no—
133#131×C43Q814yescomplemented
134C2×M16×C43—21no—
135C2×M16×C43C2311yescharacteristic
136C2×M16×C43C2311yescharacteristic
137C2×M16×C43C2311yescharacteristic
138C22×C8×C43—21no—
139C22×C8×C43C2311yescharacteristic
140C2×C4⋊C4×C43C2311yescharacteristic
141C2×C4⋊C4×C43C2311yescharacteristic
142#108×C43—22no—
143#106×C43—21no—
144#106×C43—21no—
145#103×C43—21no—
146#103×C43—21no—
147#102×C43—21no—
148#102×C43—21no—
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×C43C2411yescharacteristic
160C22×Dic43—21no—
161C22×Dic43—21no—
162C22×Dic43—21no—
163C22×Dic43—41no—
164C22×Dic43—41no—
165C2×Dic86—41no—
166C2×Dic86—41no—
167M16×C43—21no—
168M16×C43—24no—
169M16×C43—21no—
170M16×C43—21no—
171M16×C43—21no—
172M16×C43—21no—
173M16×C43C2×Q812yes—
174C2×C8×C43—21no—
175C2×C8×C43—24no—
176C2×C8×C43—21no—
177C2×C8×C43—21no—
178C2×C8×C43C2×D411yescharacteristic
179C2×C8×C43C2×D411yescharacteristic
180C2×C8×C43C2×Q812yes—
181C2×C8×C43#4112yes—
182C4⋊C4×C43—21no—
183C4⋊C4×C43—21no—
184C4⋊C4×C43—21no—
185C4⋊C4×C43—21no—
186C22⋊Dic43—21no—
187C22⋊Dic43—21no—
188C22⋊Dic43—21no—
189C22⋊Dic43—41no—
190C22⋊Dic43—41no—
191C4⋊Dic43—21no—
192C4⋊Dic43—21no—
193C4⋊Dic43—21no—
194C4⋊Dic43—21no—
195C4⋊Dic43—41no—
196C4⋊Dic43—41no—
197C4⋊Dic43—41no—
198C4⋊Dic43—41no—
199C4⋊Dic43C2×D411yescharacteristic
200C4⋊Dic43C2×D411yescharacteristic
201C4⋊Dic43C2×D411yescharacteristic
202C4⋊Dic43C2×D411yescharacteristic
203C4⋊Dic43C2×D411yescharacteristic
204C4⋊Dic43C2×D411yescharacteristic
205Dic43⋊C4—41no—
206Dic43⋊C4—41no—
207Dic43⋊C4—41no—
208Dic43⋊C4—41no—
209Dic43⋊C4—82no—
210C4×Dic43—21no—
211C4×Dic43—21no—
212C4×Dic43—21no—
213C4×Dic43—21no—
214C4×Dic43—41no—
215C4×Dic43—41no—
216C4×Dic43C2×Q812yes—
217#10621877—21no—
218#10621877C2×Q812yes—
219C2×C43⋊C8—21no—
220C2×C43⋊C8—21no—
221C2×C43⋊C8—21no—
222C2×C43⋊C8C2×D411yescharacteristic
223C2×C43⋊C8C2×D411yescharacteristic
224C23×C43—21no—
225C23×C43H(5,𝔽2)11yescharacteristic
226Q8×C43—21no—
227Q8×C43C4⋊Q812yes—
228D4×C43—22no—
229D4×C43—22no—
230D4×C43—21no—
231D4×C43C4⋊Q812yes—
232C2×C4×C43—21no—
233C2×C4×C43—22no—
234C2×C4×C43—22no—
235C2×C4×C43—41no—
236C2×C4×C43—41no—
237C2×C4×C43—81no—
238C2×C4×C43—81no—
239C2×C4×C43C22×D411yescharacteristic
240C2×C4×C43C22×D411yescharacteristic
241C2×C4×C43C22×Q811yescharacteristic
242C2×C4×C43C22×Q811yescharacteristic
243C2×C4×C43C2×#4111yescharacteristic
244C2×C4×C432−1+411yescharacteristic
245C2×Dic43—21no—
246C2×Dic43—21no—
247C2×Dic43—21no—
248C2×Dic43—21no—
249C2×Dic43—21no—
250C2×Dic43—21no—
251C2×Dic43—22no—
252C2×Dic43—41no—
253C2×Dic43—41no—
254C2×Dic43—41no—
255C2×Dic43—41no—
256C2×Dic43—81no—
257C2×Dic43—81no—
258C2×Dic43—161no—
259C2×Dic43—161no—
260Dic86—161no—
261Dic86—161no—
262C8×C43—22no—
263C8×C43—41no—
264C8×C43—41no—
265C8×C43C22⋊Q812yes—
266C8×C43C22⋊Q812yes—
267C43⋊C8—21no—
268C43⋊C8—21no—
269C43⋊C8—22no—
270#26085—431nomaximal, Sylow
271C22×C43—21no—
272C22×C43—21no—
273C22×C43—22no—
274C22×C43—41no—
275C22×C43—41no—
276C22×C43#54411yescharacteristic
277C22×C43D4211yescharacteristic
278C22×C43#55411yescharacteristic
279C4×C43—22no—
280C4×C43—81no—
281C4×C43—81no—
282C4×C43C2×C22⋊Q811yescharacteristic
283C4×C43C2×C4⋊Q811yescharacteristic
284C4×C43#54711yescharacteristic
285C4×C43D4×Q811yescharacteristic
286Dic43—42no—
287Dic43—41no—
288Dic43—41no—
289Dic43—41no—
290Dic43—41no—
291Dic43—41no—
292Dic43—41no—
293Dic43—81no—
294Dic43—81no—
295#3163—431no—
296#3084—431no—
297#3083—431no—
298#2913—431no—
299#2090—431no—
300#2089—431no—
301#2061—431no—
302#2060—431no—
303#1952—431no—
304#1946—431no—
305#1860—431no—
306#1859—431no—
307#1847—431no—
308#1815D4311yescharacteristic
309#1765—431no—
310C2×C43—21no—
311C2×C43—21no—
312C2×C43—42no—
313C2×C43#244011yescharacteristic
314C2×C43#328811yescharacteristic
315C2×C43#328911yescharacteristic
316C2×#131C2×D4311yescharacteristic
317#544—431no—
318#544—431no—
319#520—431no—
320#520—431no—
321#501—861no—
322#501—861no—
323#499—861no—
324#498—861no—
325#479—861no—
326#479—861no—
327#478—861no—
328#478—861no—
329#477—861no—
330#476—861no—
331#475—861no—
332#474—861no—
333C2×#108C2×D4311yescharacteristic
334#428—431no—
335#428—431no—
336#428—431no—
337#428—431no—
338#428—431no—
339#428—431no—
340#428—861no—
341#428—861no—
342#427—431no—
343#427—861no—
344C2×#107—431no—
345C2×#107—431no—
346C2×#107—861no—
347C2×#106—431no—
348C2×#106C2×D4311yescharacteristic
349#424—431no—
350#424—431no—
351C2×#104—431no—
352#417C2×D4311yescharacteristic
353#417C2×D4311yescharacteristic
354#416—431no—
355#405—431no—
356C2×#97—431no—
357#384—431no—
358#382—431no—
359#343—431no—
360#343—431no—
361#343C2×D4311yescharacteristic
362#343C2×D4311yescharacteristic
363#341—431no—
364#339—431no—
365#339—431no—
366#339—431no—
367C43#2608511yescharacteristic, complemented, Sylow
368C2×#41C22×D4311yescharacteristic
369#131—22no—
370#131Dic8614yescomplemented
371C2×M16—21no—
372C2×M16—431no—
373C2×M16C22×D4311yescharacteristic
374C2×M16C22×D4311yescharacteristic
375C2×M16C22×D4311yescharacteristic
376C22×C8—21no—
377C22×C8—431no—
378C22×C8C22×D4311yescharacteristic
379C4⋊Q8—861no—
380C4⋊Q8—861no—
381C4⋊Q8—861no—
382C4⋊Q8—861no—
383#125—861no—
384#125—861no—
385#125—861no—
386#125—861no—
387C22⋊Q8—1721no—
388C22⋊Q8—1721no—
389C4×Q8—861no—
390C4×Q8—861no—
391C4×D4—861no—
392C4×D4—861no—
393C4×D4—1721no—
394C4×D4—1721no—
395#117—431no—
396#117—431no—
397#117—431no—
398#117—861no—
399#117—861no—
400C2×C4⋊C4—431no—
401C2×C4⋊C4—431no—
402C2×C4⋊C4—861no—
403C2×C4⋊C4—861no—
404C2×C4⋊C4—1721no—
405C2×C4⋊C4C22×D4311yescharacteristic
406C2×C4⋊C4C22×D4311yescharacteristic
407C2×C42—431no—
408#108—22no—
409#107—431no—
410#107—431no—
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#107—861no—
420#107—861no—
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—
433C4⋊C8—861no—
434C4⋊C8—861no—
435C4⋊C8—861no—
436C4⋊C8—861no—
437#104—434no—
438#103—21no—
439#103—21no—
440#103—431no—
441#103—431no—
442#102—21no—
443#102—21no—
444#102—431no—
445#102—431no—
446#97—861no—
447#97—862no—
448C4×C8—861no—
449#95—1721no—
450#41—21no—
451#41—21no—
452#41C2×Dic8612yes—
453#41Q8×D4312yes—
454C2×Q8—1721no—
455C2×Q8—1721no—
456C2×Q8D4×D4311yescharacteristic
457C2×D4—21no—
458C2×D4D4×D4311yescharacteristic
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—861no—
463C22×C4—861no—
464C22×C4—861no—
465C22×C4—1721no—
466C22×C4—1721no—
467C22×C4C23×D4311yescharacteristic
468M16—21no—
469M16—24no—
470M16—21no—
471M16—21no—
472M16—21no—
473M16—21no—
474M16—432no—
475M16—861no—
476M16C2×Dic8612yes—
477C2×C8—21no—
478C2×C8—24no—
479C2×C8—21no—
480C2×C8—21no—
481C2×C8—431no—
482C2×C8—431no—
483C2×C8—861no—
484C2×C8—861no—
485C2×C8—861no—
486C2×C8C2×Dic8612yes—
487C2×C8D4×D4311yescharacteristic
488C2×C8D4×D4311yescharacteristic
489C2×C8#1062190012yes—
490C4⋊C4—21no—
491C4⋊C4—21no—
492C4⋊C4—21no—
493C4⋊C4—21no—
494C4⋊C4—431no—
495C4⋊C4—431no—
496C4⋊C4—431no—
497C4⋊C4—431no—
498C4⋊C4—431no—
499C4⋊C4—431no—
500C4⋊C4—861no—
501C4⋊C4—861no—
502C4⋊C4—861no—
503C4⋊C4—861no—
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—
513C22⋊C4—861no—
514C22⋊C4—861no—
515C22⋊C4—861no—
516C22⋊C4—1721no—
517C22⋊C4—1721no—
518C42—432no—
519C42—861no—
520C42—861no—
521C42—861no—
522C42—861no—
523C42—1721no—
524C42—1721no—
525C23—21no—
526C23#1306337111yescharacteristic
527Q8—21no—
528Q8—6881no—
529Q8—6881no—
530Q8#1306332412yes—
531D4—22no—
532D4—22no—
533D4—21no—
534D4#1306332412yes—
535C2×C4—21no—
536C2×C4—22no—
537C2×C4—22no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—81no—
541C2×C4—81no—
542C2×C4—862no—
543C2×C4—861no—
544C2×C4—861no—
545C2×C4—861no—
546C2×C4—861no—
547C2×C4—861no—
548C2×C4—861no—
549C2×C4—3441no—
550C2×C4—3441no—
551C2×C4—1721no—
552C2×C4—1721no—
553C2×C4—1721no—
554C2×C4—1721no—
555C2×C4—6881no—
556C2×C4—6881no—
557C2×C4C2×D4×D4311yescharacteristic
558C2×C4C2×D4×D4311yescharacteristic
559C2×C4C2×Q8×D4311yescharacteristic
560C2×C4C22×Dic8611yescharacteristic
561C2×C4C2×#1062190011yescharacteristic
562C2×C4#1306337211yescharacteristic
563C8—22no—
564C8—41no—
565C8—41no—
566C8—862no—
567C8—861no—
568C8—861no—
569C8#1306330212yes—
570C8#1306330212yes—
571C22—21no—
572C22—21no—
573C22—22no—
574C22—41no—
575C22—41no—
576C22#1458352711yescharacteristic
577C22#1458353311yescharacteristic
578C22#1458360711yescharacteristic
579C4—22no—
580C4—81no—
581C4—81no—
582C4—3441no—
583C4—3441no—
584C4—1722no—
585C4—1721no—
586C4—1721no—
587C4—1721no—
588C4—1721no—
589C4—1721no—
590C4—1721no—
591C4C2×#1306330211yescharacteristic
592C4C2×#1306332411yescharacteristic
593C4#1458354911yescharacteristic
594C4#1458356211yescharacteristic
595C2—21no—
596C2—21no—
597C2—42no—
598C2#1913829811yescharacteristic
599C2#1914636011yescharacteristic
600C2#1914636711yescharacteristic
subgroupG/H
centerC22#14583533
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#1815C2
socleC22×C43D42
prime radicalC2×#41×C43C23
hypercenter#1815D43
hypocenterC43#26085
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ #1815

Complements

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

NH ≅ G/Ntype
1. #19145123C2semidirect
5. #19136109C2semidirect
6. #19136104C2semidirect
7. #19135946C2semidirect
8. #19135941C2semidirect
9. #19135381C2semidirect
10. #19135346C2semidirect
13. #19134760C2semidirect
122. #13063252Q8semidirect
133. #131×C43Q8semidirect
367. C43#26085semidirect
370. #131Dic86semidirect

Maximal subgroups

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

subgroupindex
#191451232
#191444612
#191444502
#191431952
#191361092
#191361042
#191359462
#191359412
#191353812
#191353462
#191348262
#191348192
#191347602
#191344372
C43×#18152
#2608543