Finite Group Databasebeta

← #25155548

Subgroups — #25155548

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#19145121C211yesmaximal, characteristic, complemented
2#19144455C211yesmaximal, characteristic
3#19143193C211yesmaximal, characteristic
4#19136105C211yesmaximal, characteristic, complemented
5#19136101C211yesmaximal, characteristic, complemented
6#19135943C211yesmaximal, characteristic, complemented
7#19135937C211yesmaximal, characteristic, complemented
8#19135377C211yesmaximal, characteristic, complemented
9#19135345C211yesmaximal, characteristic, complemented
10#19134828C211yesmaximal, characteristic
11#19134819C211yesmaximal, characteristic
12#19134762C211yesmaximal, characteristic, complemented
13#19134652C211yesmaximal, characteristic
14#19134442C211yesmaximal, characteristic
15C43×#3083C211yesmaximal, characteristic
16C2×#13063332C2211yescharacteristic
17#14583527C2211yescharacteristic
18#14583382C2211yescharacteristic
19#14583309—21no—
20#14583305—21no—
21#14583298—21no—
22#14583295—21no—
23#14583204—21no—
24#14583201—21no—
25#14583187—21no—
26#14583182—21no—
27C2×#13063260C2211yescharacteristic
28#14582942—21no—
29#14582942C2211yescharacteristic
30#14582942C2211yescharacteristic
31#14582942C2211yescharacteristic
32#14582939—21no—
33#14582939C2211yescharacteristic
34#14582939C2211yescharacteristic
35#14582935—21no—
36#14582935C2211yescharacteristic
37C2×#13063258—21no—
38C2×#13063258C2211yescharacteristic
39C2×#13063257C2211yescharacteristic
40C2×#13063256C2211yescharacteristic
41#14582925C2211yescharacteristic
42C2×#13063252C2211yescharacteristic
43#14582900C2211yescharacteristic
44#14582855C2211yescharacteristic
45C2×#13063235C2211yescharacteristic
46#14582768C2211yescharacteristic
47#14582764C2211yescharacteristic
48#14582668C2211yescharacteristic
49#14582668C2211yescharacteristic
50#14582667C2211yescharacteristic
51#14582667C2211yescharacteristic
52#14582664C2211yescharacteristic
53#14582660C2211yescharacteristic
54#14582658C2211yescharacteristic
55#14582658C2211yescharacteristic
56C43×#544C2211yescharacteristic
57C43×#520C2211yescharacteristic
58C43×#479—21no—
59C43×#478—21no—
60C43×#477—21no—
61C43×#474—21no—
62C43×#428C2211yescharacteristic
63C2×#107×C43C2211yescharacteristic
64C43×#424C2211yescharacteristic
65C43×#417C2211yescharacteristic
66C43×#416C2211yescharacteristic
67#13063332—22no—
68#13063332Q814yescomplemented
69C2×#10621877—21no—
70C2×#10621877C2311yescharacteristic
71C2×#10621877C2311yescharacteristic
72C2×#10621877C2311yescharacteristic
73C22×C43⋊C8—21no—
74C22×C43⋊C8C2311yescharacteristic
75#13063325—21no—
76#13063324—21no—
77#13063317—21no—
78#13063316—21no—
79#13063302—41no—
80Q8×Dic43—21no—
81D4×Dic43—21no—
82D4×Dic43—41no—
83#13063284—21no—
84#13063284C2311yescharacteristic
85C2×C4⋊Dic43—21no—
86C2×C4⋊Dic43C2311yescharacteristic
87C2×C4⋊Dic43C2311yescharacteristic
88C2×Dic43⋊C4—41no—
89C2×C4×Dic43C2311yescharacteristic
90#13063260—22no—
91#13063258—21no—
92#13063258—21no—
93#13063258—21no—
94#13063258—21no—
95#13063258—21no—
96#13063258—21no—
97#13063258—21no—
98#13063258D411yescharacteristic
99#13063258D411yescharacteristic
100#13063257—21no—
101#13063257—21no—
102#13063256—21no—
103#13063256—21no—
104#13063256—21no—
105#13063256—21no—
106#13063256—21no—
107#13063256—21no—
108#13063256—21no—
109#13063256D411yescharacteristic
110#13063256D411yescharacteristic
111Dic43⋊C8—21no—
112Dic43⋊C8—21no—
113#13063252Q814yescomplemented
114#13063249—21no—
115#13063246—21no—
116#13063236—21no—
117#13063235—22no—
118C4×C43⋊C8—21no—
119C43⋊#95—41no—
120C2×#41×C43C2311yescharacteristic
121C2×M16×C43C2311yescharacteristic
122C22×C8×C43C2311yescharacteristic
123C4⋊Q8×C43—21no—
124C4⋊Q8×C43—21no—
125#125×C43—21no—
126#125×C43—21no—
127C22⋊Q8×C43—41no—
128C4×Q8×C43—21no—
129C4×D4×C43—21no—
130C4×D4×C43—41no—
131#117×C43—21no—
132#117×C43C2311yescharacteristic
133#117×C43C2311yescharacteristic
134C2×C4⋊C4×C43—21no—
135C2×C4⋊C4×C43C2311yescharacteristic
136C2×C4⋊C4×C43C2311yescharacteristic
137#107×C43—21no—
138#107×C43—21no—
139#107×C43—21no—
140#106×C43—21no—
141C4⋊C8×C43—21no—
142C4⋊C8×C43—21no—
143#103×C43—21no—
144#103×C43D411yescharacteristic
145#103×C43D411yescharacteristic
146#102×C43—21no—
147#102×C43D411yescharacteristic
148#102×C43D411yescharacteristic
149#41×C43—21no—
150#41×C43—21no—
151#41×C43C2×Q812yes—
152#41×C43C2×Q812yes—
153C2×Q8×C43—41no—
154C2×Q8×C43C2×D411yescharacteristic
155C2×D4×C43—21no—
156C2×D4×C43C2×D411yescharacteristic
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—21no—
165C22×Dic43—41no—
166C2×Dic86—41no—
167M16×C43—21no—
168M16×C43—21no—
169C2×C8×C43—21no—
170C2×C8×C43—21no—
171C2×C8×C43—21no—
172C2×C8×C43C2×D411yescharacteristic
173C2×C8×C43C2×D411yescharacteristic
174C4⋊C4×C43—21no—
175C4⋊C4×C43—21no—
176C4⋊C4×C43—21no—
177C4⋊C4×C43—21no—
178C4⋊C4×C43—41no—
179C4⋊C4×C43—41no—
180C4⋊C4×C43—41no—
181C4⋊C4×C43—41no—
182C4⋊C4×C43C2×D411yescharacteristic
183C4⋊C4×C43C2×D411yescharacteristic
184C4⋊C4×C43C2×D411yescharacteristic
185C4⋊C4×C43C2×D411yescharacteristic
186C22⋊C4×C43—21no—
187C22⋊C4×C43—21no—
188C22⋊C4×C43—41no—
189C42×C43—21no—
190C42×C43—21no—
191C42×C43—41no—
192C22⋊Dic43—21no—
193C22⋊Dic43—41no—
194C4⋊Dic43—21no—
195C4⋊Dic43—21no—
196C4⋊Dic43—21no—
197C4⋊Dic43—21no—
198C4⋊Dic43—41no—
199C4⋊Dic43—41no—
200C4⋊Dic43C2×D411yescharacteristic
201C4⋊Dic43C2×D411yescharacteristic
202Dic43⋊C4—41no—
203Dic43⋊C4—41no—
204Dic43⋊C4—82no—
205C4×Dic43—21no—
206C4×Dic43—21no—
207C4×Dic43—41no—
208C4×Dic43C2×Q812yes—
209#10621877—21no—
210#10621877—21no—
211#10621877—24no—
212#10621877—21no—
213#10621877—21no—
214#10621877C2×Q812yes—
215#10621877C2×Q812yes—
216C2×C43⋊C8—21no—
217C2×C43⋊C8—21no—
218C2×C43⋊C8—24no—
219C2×C43⋊C8—21no—
220C2×C43⋊C8C2×D411yescharacteristic
221C2×C43⋊C8C2×D411yescharacteristic
222C2×C43⋊C8C2×Q812yes—
223C2×C43⋊C8#4112yes—
224C23×C43—21no—
225C23×C43H(5,𝔽2)11yescharacteristic
226Q8×C43—21no—
227Q8×C43—161no—
228Q8×C43C4⋊Q812yes—
229D4×C43—22no—
230D4×C43—22no—
231D4×C43—21no—
232D4×C43C4⋊Q812yes—
233C2×C4×C43—21no—
234C2×C4×C43—22no—
235C2×C4×C43—22no—
236C2×C4×C43—21no—
237C2×C4×C43—21no—
238C2×C4×C43—21no—
239C2×C4×C43—21no—
240C2×C4×C43—41no—
241C2×C4×C43—41no—
242C2×C4×C43—81no—
243C2×C4×C43—81no—
244C2×C4×C43—161no—
245C2×C4×C43C22×D411yescharacteristic
246C2×C4×C43C22×D411yescharacteristic
247C2×C4×C43C22×Q811yescharacteristic
248C2×C4×C43C22×Q811yescharacteristic
249C2×C4×C43C2×#4111yescharacteristic
250C2×C4×C432−1+411yescharacteristic
251C2×Dic43—21no—
252C2×Dic43—21no—
253C2×Dic43—22no—
254C2×Dic43—41no—
255C2×Dic43—41no—
256C2×Dic43—41no—
257C2×Dic43—41no—
258C2×Dic43—81no—
259C2×Dic43—81no—
260C2×Dic43—161no—
261Dic86—161no—
262C8×C43—21no—
263C8×C43—21no—
264C8×C43—41no—
265C43⋊C8—22no—
266C43⋊C8—22no—
267C43⋊C8—41no—
268C43⋊C8C22⋊Q812yes—
269C43⋊C8C22⋊Q812yes—
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—41no—
281C4×C43—41no—
282C4×C43—41no—
283C4×C43—41no—
284C4×C43—81no—
285C4×C43—81no—
286C4×C43C2×C22⋊Q811yescharacteristic
287C4×C43C2×C4⋊Q811yescharacteristic
288C4×C43#54711yescharacteristic
289C4×C43D4×Q811yescharacteristic
290Dic43—42no—
291Dic43—41no—
292Dic43—41no—
293Dic43—81no—
294Dic43—81no—
295#3163—431no—
296#3084—431no—
297#3083D4311yescharacteristic
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#1815—431no—
309#1765—431no—
310C2×C43—21no—
311C2×C43—21no—
312C2×C43—42no—
313C2×C43#244011yescharacteristic
314C2×C43#328811yescharacteristic
315C2×C43#328911yescharacteristic
316C2×#131—431no—
317#544—431no—
318#544C2×D4311yescharacteristic
319#520—431no—
320#520C2×D4311yescharacteristic
321#501—861no—
322#501—861no—
323#499—861no—
324#498—861no—
325#479—21no—
326#479—861no—
327#478—21no—
328#478—861no—
329#477—21no—
330#476—861no—
331#475—861no—
332#474—21no—
333C2×#108—431no—
334#428—431no—
335#428—431no—
336#428—431no—
337#428—431no—
338#428—431no—
339#428—861no—
340#428—861no—
341#428C2×D4311yescharacteristic
342#427—431no—
343#427—861no—
344C2×#107—431no—
345C2×#107—861no—
346C2×#107C2×D4311yescharacteristic
347C2×#106—431no—
348C2×#106—431no—
349#424—431no—
350#424C2×D4311yescharacteristic
351C2×#104—431no—
352#417—431no—
353#417C2×D4311yescharacteristic
354#416C2×D4311yescharacteristic
355#405—431no—
356C2×#97—431no—
357#384—431no—
358#382—431no—
359#343—431no—
360#343—431no—
361#343—431no—
362#343—431no—
363#341—431no—
364#339—431no—
365#339—431no—
366#339—431no—
367C43#2608511yescharacteristic, complemented, Sylow
368C2×#41C22×D4311yescharacteristic
369#131—434no—
370#131—862no—
371C2×M16—431no—
372C2×M16—431no—
373C2×M16—431no—
374C2×M16—861no—
375C2×M16C22×D4311yescharacteristic
376C22×C8—431no—
377C22×C8—861no—
378C22×C8C22×D4311yescharacteristic
379C4⋊Q8—21no—
380C4⋊Q8—21no—
381C4⋊Q8—861no—
382C4⋊Q8—861no—
383#125—21no—
384#125—21no—
385#125—861no—
386#125—861no—
387C22⋊Q8—41no—
388C22⋊Q8—1721no—
389C4×Q8—21no—
390C4×Q8—861no—
391C4×D4—21no—
392C4×D4—41no—
393C4×D4—861no—
394C4×D4—1721no—
395#117—21no—
396#117—431no—
397#117—861no—
398#117C22×D4311yescharacteristic
399#117C22×D4311yescharacteristic
400C2×C4⋊C4—21no—
401C2×C4⋊C4—431no—
402C2×C4⋊C4—431no—
403C2×C4⋊C4—861no—
404C2×C4⋊C4—1721no—
405C2×C4⋊C4C22×D4311yescharacteristic
406C2×C4⋊C4C22×D4311yescharacteristic
407C2×C42—431no—
408#108—862no—
409#107—21no—
410#107—21no—
411#107—21no—
412#107—431no—
413#107—431no—
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—431no—
423#106—431no—
424#106—861no—
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—21no—
434C4⋊C8—21no—
435C4⋊C8—861no—
436C4⋊C8—861no—
437#104—434no—
438#103—21no—
439#103—861no—
440#103C22⋊D4311yescharacteristic
441#103C22⋊D4311yescharacteristic
442#102—21no—
443#102—861no—
444#102C22⋊D4311yescharacteristic
445#102C22⋊D4311yescharacteristic
446#97—861no—
447#97—862no—
448C4×C8—861no—
449#95—1721no—
450#41—21no—
451#41—21no—
452#41Q8×D4312yes—
453#41Q8×D4312yes—
454C2×Q8—41no—
455C2×Q8—1721no—
456C2×Q8C2×C22⋊D4311yescharacteristic
457C2×D4—21no—
458C2×D4C2×C22⋊D4311yescharacteristic
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—41no—
463C22×C4—861no—
464C22×C4—861no—
465C22×C4—861no—
466C22×C4—1721no—
467C22×C4C23×D4311yescharacteristic
468M16—21no—
469M16—21no—
470M16—432no—
471M16—432no—
472M16—864no—
473M16—861no—
474M16—861no—
475M16—861no—
476M16—861no—
477C2×C8—21no—
478C2×C8—21no—
479C2×C8—21no—
480C2×C8—431no—
481C2×C8—431no—
482C2×C8—432no—
483C2×C8—432no—
484C2×C8—864no—
485C2×C8—861no—
486C2×C8—861no—
487C2×C8—861no—
488C2×C8C2×C22⋊D4311yescharacteristic
489C2×C8C2×C22⋊D4311yescharacteristic
490C4⋊C4—21no—
491C4⋊C4—21no—
492C4⋊C4—21no—
493C4⋊C4—21no—
494C4⋊C4—41no—
495C4⋊C4—41no—
496C4⋊C4—41no—
497C4⋊C4—41no—
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⋊C4D4×D4311yescharacteristic
510C4⋊C4D4×D4311yescharacteristic
511C4⋊C4C2×C22⋊D4311yescharacteristic
512C4⋊C4C2×C22⋊D4311yescharacteristic
513C22⋊C4—21no—
514C22⋊C4—21no—
515C22⋊C4—41no—
516C22⋊C4—861no—
517C22⋊C4—1721no—
518C42—21no—
519C42—21no—
520C42—41no—
521C42—432no—
522C42—861no—
523C42—861no—
524C42—1721no—
525C23—21no—
526C23#1306337011yescharacteristic
527Q8—21no—
528Q8—161no—
529Q8—6881no—
530Q8#1306332312yes—
531D4—22no—
532D4—22no—
533D4—21no—
534D4#1306332312yes—
535C2×C4—21no—
536C2×C4—22no—
537C2×C4—22no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—81no—
545C2×C4—81no—
546C2×C4—161no—
547C2×C4—862no—
548C2×C4—861no—
549C2×C4—861no—
550C2×C4—3441no—
551C2×C4—3441no—
552C2×C4—1721no—
553C2×C4—1721no—
554C2×C4—1721no—
555C2×C4—1721no—
556C2×C4—6881no—
557C2×C4C2×D4×D4311yescharacteristic
558C2×C4C22×C22⋊D4311yescharacteristic
559C2×C4C2×Q8×D4311yescharacteristic
560C2×C4C2×Q8×D4311yescharacteristic
561C2×C4#41×D4311yescharacteristic
562C2×C4#1306337211yescharacteristic
563C8—21no—
564C8—21no—
565C8—41no—
566C8—432no—
567C8—432no—
568C8—862no—
569C8—862no—
570C8—1721no—
571C22—21no—
572C22—21no—
573C22—22no—
574C22—41no—
575C22—41no—
576C22#1458352811yescharacteristic
577C22D4×C22⋊D4311yescharacteristic
578C22#1458360311yescharacteristic
579C4—22no—
580C4—41no—
581C4—41no—
582C4—41no—
583C4—41no—
584C4—81no—
585C4—81no—
586C4—3441no—
587C4—3441no—
588C4—1722no—
589C4—1721no—
590C4—1721no—
591C4C22⋊Q8×D4311yescharacteristic
592C4C2×#1306332311yescharacteristic
593C4#1458354811yescharacteristic
594C4#1458356211yescharacteristic
595C2—21no—
596C2—21no—
597C2—42no—
598C2#1913829411yescharacteristic
599C2#1914635911yescharacteristic
600C2#1914636611yescharacteristic
subgroupG/H
centerC22D4×C22⋊D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#3083C2
socleC22×C43D42
prime radicalC2×#41×C43C23
hypercenter#3083D43
hypocenterC43#26085
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ #3083

Complements

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

NH ≅ G/Ntype
1. #19145121C2semidirect
4. #19136105C2semidirect
5. #19136101C2semidirect
6. #19135943C2semidirect
7. #19135937C2semidirect
8. #19135377C2semidirect
9. #19135345C2semidirect
12. #19134762C2semidirect
68. #13063332Q8semidirect
113. #13063252Q8semidirect
367. C43#26085semidirect

Maximal subgroups

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

subgroupindex
#191451212
#191444552
#191431932
#191361052
#191361012
#191359432
#191359372
#191353772
#191353452
#191348282
#191348192
#191347622
#191346522
#191344422
C43×#30832
#2608543