Finite Group Databasebeta

← #25155522

Subgroups — #25155522

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#19145135C211yesmaximal, characteristic, complemented
2#19144457C211yesmaximal, characteristic
3#19144446C211yesmaximal, characteristic
4#19136108C211yesmaximal, characteristic, complemented
5#19136103C211yesmaximal, characteristic, complemented
6#19135943C211yesmaximal, characteristic, complemented
7#19135938C211yesmaximal, characteristic, complemented
8#19135373C211yesmaximal, characteristic, complemented
9#19135349C211yesmaximal, characteristic, complemented
10#19134828C211yesmaximal, characteristic
11#19134821C211yesmaximal, characteristic
12#19134760C211yesmaximal, characteristic, complemented
13#19134659C211yesmaximal, characteristic
14#19134437C211yesmaximal, characteristic
15C43×#2912C211yesmaximal, characteristic
16#14583527C2211yescharacteristic
17#14583527C2211yescharacteristic
18#14583306—21no—
19#14583306—21no—
20#14583303—21no—
21#14583300—21no—
22#14583206—21no—
23#14583206—21no—
24#14583199—21no—
25#14583199—21no—
26#14583194—21no—
27#14583189—21no—
28#14583184—21no—
29#14583179—21no—
30C2×#13063261C2211yescharacteristic
31#14582942C2211yescharacteristic
32#14582942C2211yescharacteristic
33#14582939C2211yescharacteristic
34#14582939C2211yescharacteristic
35C2×#13063259C2211yescharacteristic
36C2×#13063258C2211yescharacteristic
37C2×#13063256C2211yescharacteristic
38#14582926C2211yescharacteristic
39#14582926C2211yescharacteristic
40C2×#13063252C2211yescharacteristic
41#14582900C2211yescharacteristic
42#14582900C2211yescharacteristic
43#14582895C2211yescharacteristic
44#14582854C2211yescharacteristic
45C2×#13063235C2211yescharacteristic
46#14582768C2211yescharacteristic
47#14582764C2211yescharacteristic
48#14582668C2211yescharacteristic
49#14582668C2211yescharacteristic
50#14582667C2211yescharacteristic
51#14582667C2211yescharacteristic
52#14582663C2211yescharacteristic
53#14582660C2211yescharacteristic
54#14582658C2211yescharacteristic
55#14582658C2211yescharacteristic
56C2×#131×C43C2211yescharacteristic
57C43×#520C2211yescharacteristic
58C43×#520C2211yescharacteristic
59C43×#428—21no—
60C43×#428—21no—
61C43×#428C2211yescharacteristic
62C43×#428C2211yescharacteristic
63C43×#427—21no—
64C43×#427C2211yescharacteristic
65C2×#106×C43—21no—
66C2×#106×C43C2211yescharacteristic
67C2×#10621877C2311yescharacteristic
68C2×#10621877C2311yescharacteristic
69C2×#10621877C2311yescharacteristic
70C22×C43⋊C8C2311yescharacteristic
71#13063325—21no—
72#13063325—21no—
73#13063324—21no—
74#13063324—21no—
75#13063317—21no—
76#13063317—21no—
77#13063316—21no—
78#13063316—21no—
79#13063302—41no—
80#13063302—41no—
81#13063284C2311yescharacteristic
82C2×C4⋊Dic43C2311yescharacteristic
83C2×C4⋊Dic43C2311yescharacteristic
84C2×Dic43⋊C4—41no—
85C2×C4×Dic43C2311yescharacteristic
86#13063261—22no—
87#13063259—21no—
88#13063259—21no—
89#13063258—21no—
90#13063258—21no—
91#13063258—21no—
92#13063258—21no—
93#13063258—21no—
94#13063258—21no—
95#13063256—21no—
96#13063256—21no—
97#13063256—21no—
98#13063256—21no—
99#13063256—21no—
100#13063256—21no—
101C4⋊(C43⋊C8)—21no—
102C4⋊(C43⋊C8)—21no—
103C4⋊(C43⋊C8)—21no—
104C4⋊(C43⋊C8)—21no—
105#13063252Q814yescomplemented
106#13063249—21no—
107#13063249—21no—
108#13063249D411yescharacteristic
109#13063249D411yescharacteristic
110#13063246—21no—
111#13063246—21no—
112#13063246D411yescharacteristic
113#13063246D411yescharacteristic
114#13063235—21no—
115#13063235—22no—
116C8×Dic43—21no—
117C43⋊#95—41no—
118C2×#41×C43C2311yescharacteristic
119#131×C43—22no—
120#131×C43Q814yescomplemented
121C2×M16×C43—21no—
122C2×M16×C43C2311yescharacteristic
123C22×C8×C43—21no—
124C22×C8×C43C2311yescharacteristic
125C4×Q8×C43—21no—
126C4×Q8×C43—21no—
127C4×D4×C43—21no—
128C4×D4×C43—21no—
129C4×D4×C43—41no—
130C4×D4×C43—41no—
131#117×C43—21no—
132#117×C43—21no—
133#117×C43C2311yescharacteristic
134#117×C43C2311yescharacteristic
135C2×C4⋊C4×C43—21no—
136C2×C4⋊C4×C43—21no—
137C2×C4⋊C4×C43C2311yescharacteristic
138C2×C4⋊C4×C43C2311yescharacteristic
139#107×C43—21no—
140#107×C43—21no—
141#107×C43D411yescharacteristic
142#107×C43D411yescharacteristic
143#106×C43—21no—
144#106×C43—21no—
145#106×C43—21no—
146#106×C43—21no—
147#106×C43D411yescharacteristic
148#106×C43D411yescharacteristic
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—41no—
160C22×C4×C43—41no—
161C22×C4×C43C2411yescharacteristic
162C22×Dic43—21no—
163C22×Dic43—21no—
164C22×Dic43—21no—
165C2×Dic86—41no—
166C2×Dic86—41no—
167M16×C43—21no—
168M16×C43—24no—
169M16×C43C2×Q812yes—
170C2×C8×C43—21no—
171C2×C8×C43—24no—
172C2×C8×C43C2×D411yescharacteristic
173C2×C8×C43C2×D411yescharacteristic
174C2×C8×C43C2×Q812yes—
175C2×C8×C43#4112yes—
176C4⋊C4×C43—21no—
177C4⋊C4×C43—21no—
178C4⋊C4×C43—21no—
179C4⋊C4×C43—21no—
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—
189C22⋊C4×C43—41no—
190C42×C43—21no—
191C42×C43—21no—
192C42×C43—41no—
193C42×C43—41no—
194C22⋊Dic43—21no—
195C4⋊Dic43—21no—
196C4⋊Dic43—21no—
197C4⋊Dic43—21no—
198C4⋊Dic43—21no—
199C4⋊Dic43—41no—
200C4⋊Dic43—41no—
201C4⋊Dic43C2×D411yescharacteristic
202C4⋊Dic43C2×D411yescharacteristic
203Dic43⋊C4—41no—
204Dic43⋊C4—41no—
205Dic43⋊C4—41no—
206Dic43⋊C4—41no—
207Dic43⋊C4—82no—
208C4×Dic43—21no—
209C4×Dic43—21no—
210C4×Dic43C2×Q812yes—
211#10621877—21no—
212#10621877—21no—
213#10621877—21no—
214#10621877—21no—
215#10621877—21no—
216#10621877C2×Q812yes—
217C2×C43⋊C8—21no—
218C2×C43⋊C8—21no—
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—21no—
236C2×C4×C43—21no—
237C2×C4×C43—21no—
238C2×C4×C43—21no—
239C2×C4×C43—41no—
240C2×C4×C43—41no—
241C2×C4×C43—81no—
242C2×C4×C43—81no—
243C2×C4×C43—161no—
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—
260Dic86—161no—
261Dic86—161no—
262C8×C43—22no—
263C8×C43C22⋊Q812yes—
264C8×C43C22⋊Q812yes—
265C43⋊C8—21no—
266C43⋊C8—21no—
267C43⋊C8—22no—
268C43⋊C8—41no—
269C43⋊C8—41no—
270#26084—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#3164—431no—
296#3084—431no—
297#3083—431no—
298#2912D4311yescharacteristic
299#2090—431no—
300#2089—431no—
301#2061—431no—
302#2060—431no—
303#1951—431no—
304#1946—431no—
305#1860—431no—
306#1859—431no—
307#1847—431no—
308#1816—431no—
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#520C2×D4311yescharacteristic
320#520C2×D4311yescharacteristic
321#501—861no—
322#501—861no—
323#500—861no—
324#499—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×#108—431no—
334#428—21no—
335#428—21no—
336#428—431no—
337#428—431no—
338#428—431no—
339#428—431no—
340#428C2×D4311yescharacteristic
341#428C2×D4311yescharacteristic
342#427—21no—
343#427C2×D4311yescharacteristic
344C2×#107—431no—
345C2×#107—431no—
346C2×#106—21no—
347C2×#106—431no—
348C2×#106C2×D4311yescharacteristic
349#424—431no—
350#424—431no—
351C2×#104—431no—
352#417—431no—
353#417—431no—
354#416—431no—
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#2608411yescharacteristic, complemented, Sylow
368C2×#41C22×D4311yescharacteristic
369#131—22no—
370#131Dic8614yescomplemented
371C2×M16—21no—
372C2×M16—431no—
373C2×M16—431no—
374C2×M16—431no—
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—21no—
390C4×Q8—21no—
391C4×D4—21no—
392C4×D4—21no—
393C4×D4—41no—
394C4×D4—41no—
395#117—21no—
396#117—21no—
397#117—431no—
398#117C22×D4311yescharacteristic
399#117C22×D4311yescharacteristic
400C2×C4⋊C4—21no—
401C2×C4⋊C4—21no—
402C2×C4⋊C4—431no—
403C2×C4⋊C4—431no—
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—861no—
412#107—861no—
413#107—861no—
414#107—861no—
415#107—861no—
416#107—861no—
417#107—861no—
418#107—861no—
419#107C22⋊D4311yescharacteristic
420#107C22⋊D4311yescharacteristic
421#106—21no—
422#106—21no—
423#106—21no—
424#106—21no—
425#106—861no—
426#106—861no—
427#106—861no—
428#106—861no—
429#106—861no—
430#106—861no—
431#106C22⋊D4311yescharacteristic
432#106C22⋊D4311yescharacteristic
433C4⋊C8—861no—
434C4⋊C8—861no—
435C4⋊C8—861no—
436C4⋊C8—861no—
437#104—434no—
438#103—431no—
439#103—431no—
440#103—861no—
441#103—861no—
442#102—431no—
443#102—431no—
444#102—861no—
445#102—861no—
446#97—862no—
447#97—861no—
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—41no—
463C22×C4—41no—
464C22×C4—861no—
465C22×C4—861no—
466C22×C4—861no—
467C22×C4C23×D4311yescharacteristic
468M16—21no—
469M16—24no—
470M16—432no—
471M16—861no—
472M16—861no—
473M16—861no—
474M16—861no—
475M16—861no—
476M16C2×Dic8612yes—
477C2×C8—21no—
478C2×C8—24no—
479C2×C8—431no—
480C2×C8—431no—
481C2×C8—861no—
482C2×C8—861no—
483C2×C8—861no—
484C2×C8—861no—
485C2×C8—861no—
486C2×C8C2×Dic8612yes—
487C2×C8#1062189812yes—
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—431no—
497C4⋊C4—431no—
498C4⋊C4—861no—
499C4⋊C4—861no—
500C4⋊C4—861no—
501C4⋊C4—861no—
502C4⋊C4—3442no—
503C4⋊C4—1721no—
504C4⋊C4—1721no—
505C4⋊C4—1721no—
506C4⋊C4—1721no—
507C4⋊C4—1721no—
508C4⋊C4—1721no—
509C4⋊C4C2×C22⋊D4311yescharacteristic
510C4⋊C4C2×C22⋊D4311yescharacteristic
511C4⋊C4C2×C22⋊D4311yescharacteristic
512C4⋊C4C2×C22⋊D4311yescharacteristic
513C22⋊C4—21no—
514C22⋊C4—21no—
515C22⋊C4—41no—
516C22⋊C4—41no—
517C22⋊C4—861no—
518C42—21no—
519C42—21no—
520C42—41no—
521C42—41no—
522C42—432no—
523C42—861no—
524C42—861no—
525C23—21no—
526C23#1306337011yescharacteristic
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—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—161no—
548C2×C4—862no—
549C2×C4—861no—
550C2×C4—861no—
551C2×C4—3441no—
552C2×C4—3441no—
553C2×C4—1721no—
554C2×C4—1721no—
555C2×C4—1721no—
556C2×C4—1721no—
557C2×C4C2×D4×D4311yescharacteristic
558C2×C4C22×C22⋊D4311yescharacteristic
559C2×C4C2×Q8×D4311yescharacteristic
560C2×C4C22×Dic8611yescharacteristic
561C2×C4C2×#1062189811yescharacteristic
562C2×C4#1306337311yescharacteristic
563C8—22no—
564C8—862no—
565C8—861no—
566C8—861no—
567C8—1721no—
568C8—1721no—
569C8#1306330412yes—
570C8#1306330412yes—
571C22—21no—
572C22—21no—
573C22—22no—
574C22—41no—
575C22—41no—
576C22#1458353011yescharacteristic
577C22D4×C22⋊D4311yescharacteristic
578C22#1458360411yescharacteristic
579C4—22no—
580C4—41no—
581C4—41no—
582C4—41no—
583C4—41no—
584C4—81no—
585C4—81no—
586C4—3441no—
587C4—3441no—
588C4—1722no—
589C4—1721no—
590C4—1721no—
591C4C2×#1306330411yescharacteristic
592C4C2×#1306332411yescharacteristic
593C4#1458355011yescharacteristic
594C4Q8×C22⋊D4311yescharacteristic
595C2—21no—
596C2—21no—
597C2—42no—
598C2#1913829111yescharacteristic
599C2#1914635711yescharacteristic
600C2#1914636811yescharacteristic
subgroupG/H
centerC22D4×C22⋊D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2912C2
socleC22×C43D42
prime radicalC2×#41×C43C23
hypercenter#2912D43
hypocenterC43#26084
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ #2912

Complements

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

NH ≅ G/Ntype
1. #19145135C2semidirect
4. #19136108C2semidirect
5. #19136103C2semidirect
6. #19135943C2semidirect
7. #19135938C2semidirect
8. #19135373C2semidirect
9. #19135349C2semidirect
12. #19134760C2semidirect
105. #13063252Q8semidirect
120. #131×C43Q8semidirect
367. C43#26084semidirect
370. #131Dic86semidirect

Maximal subgroups

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

subgroupindex
#191451352
#191444572
#191444462
#191361082
#191361032
#191359432
#191359382
#191353732
#191353492
#191348282
#191348212
#191347602
#191346592
#191344372
C43×#29122
#2608443