Finite Group Databasebeta

← #25074170

Subgroups — #25074170

Order 11008.

1206 conjugacy classes of subgroups.

The subgroup lattice has 612 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145911C211yesmaximal, characteristic, complemented
2#19145150C211yesmaximal, characteristic, complemented
3#19144392C211yesmaximal, characteristic, complemented
4#19133879C212yesmaximal, complemented
5#19133774C212yesmaximal, complemented
6#19133746C212yesmaximal, complemented
7#19133711C212yesmaximal, complemented
8#19133272C211yesmaximal, characteristic, complemented
9#19133046C211yesmaximal, characteristic, complemented
10C2×D4⋊(C43⋊C8)C211yesmaximal, characteristic, complemented
11C43×#3496C211yesmaximal, characteristic
12#14583456C2211yescharacteristic, complemented
13#14583295C2211yescharacteristic, complemented
14#14583271C2211yescharacteristic, complemented
15#14583251C2211yescharacteristic, complemented
16#14583245C2211yescharacteristic, complemented
17#14583199—22no—
18#14583189C2212yescomplemented
19#14583189C2212yescomplemented
20#14583181—21no—
21#14583179C2212yescomplemented
22#14583126—22no—
23#14583126—22no—
24#14583104C2212yescomplemented
25#14583096—21no—
26C4×#10621883—22no—
27#14582939—21no—
28#14582923C2211yescharacteristic, complemented
29C2×C4⋊(C43⋊C8)C2211yescharacteristic, complemented
30#14582904—21no—
31C2×C4×C43⋊C8C2211yescharacteristic, complemented
32#14582645C2212yescomplemented
33#14582643C2212yescomplemented
34D4⋊(C43⋊C8)C2212yescomplemented
35D4⋊(C43⋊C8)C2212yescomplemented
36D4⋊(C43⋊C8)C2212yescomplemented
37D4⋊(C43⋊C8)C2212yescomplemented
38C2×H(5,𝔽2)×C43—21no—
39C43×#547—21no—
40C43×#547C2212yes—
41C43×#546—22no—
42C43×#546—22no—
43D42×C43—21no—
44D42×C43C2212yes—
45C43×#537—21no—
46C43×#534—22no—
47C43×#532C2211yescharacteristic
48C43×#532C2211yescharacteristic
49C2×#121×C43—22no—
50C2×C4×D4×C43C2211yescharacteristic
51C2×#10621883—22no—
52C2×#10621883—22no—
53C2×#10621877—21no—
54C22×C43⋊C8—21no—
55C22×C43⋊C8—21no—
56#13063325C2311yescharacteristic
57#13063325C2311yescharacteristic
58#13063317—21no—
59#13063304—21no—
60#13063304—21no—
61C4×Dic86—21no—
62C4×Dic86—21no—
63#13063284—21no—
64#13063258—22no—
65#13063256—22no—
66#13063256—22no—
67#13063256—22no—
68C4⋊(C43⋊C8)—21no—
69C4⋊(C43⋊C8)—21no—
70C4⋊(C43⋊C8)C2312yes—
71C4⋊(C43⋊C8)C2312yes—
72#13063248—22no—
73#13063248—22no—
74#13063246—22no—
75#13063246—22no—
76#13063246—22no—
77#13063246—22no—
78C4×C43⋊C8—21no—
79C4×C43⋊C8C2311yescharacteristic
80C4×C43⋊C8C2311yescharacteristic
81H(5,𝔽2)×C43—44no—
82H(5,𝔽2)×C43—44no—
83C2×#41×C43—22no—
84C2×#41×C43—22no—
85C2×#41×C43—21no—
86C2×#41×C43—21no—
87C22×D4×C43—24no—
88C22×D4×C43—22no—
89C22×D4×C43—22no—
90C22×D4×C43—22no—
91C22×D4×C43D411yescharacteristic
92C23×C4×C43—21no—
93C4⋊Q8×C43D411yescharacteristic
94C4⋊Q8×C43C2311yescharacteristic
95#127×C43D411yescharacteristic
96#127×C43C2311yescharacteristic
97#124×C43—21no—
98#124×C43—21no—
99#123×C43—24no—
100#123×C43—24no—
101C22⋊Q8×C43—22no—
102C22⋊Q8×C43—22no—
103#121×C43—24no—
104#121×C43—24no—
105#121×C43—22no—
106#121×C43—22no—
107#121×C43—21no—
108#121×C43—21no—
109#121×C43—22no—
110#121×C43—22no—
111#121×C43D412yes—
112#121×C43D412yes—
113#120×C43—24no—
114#120×C43—24no—
115C4×D4×C43—21no—
116C4×D4×C43—21no—
117C4×D4×C43—21no—
118C4×D4×C43—21no—
119C4×D4×C43D412yes—
120C4×D4×C43D412yes—
121C4×D4×C43C2312yes—
122C4×D4×C43C2312yes—
123C2×C4⋊C4×C43—22no—
124C2×C4⋊C4×C43D411yescharacteristic
125C2×C22⋊C4×C43—24no—
126C2×C22⋊C4×C43—21no—
127C2×C42×C43C2311yescharacteristic
128C24×C43—21no—
129C24×C43—24no—
130#41×C43—44no—
131#41×C43—48no—
132#41×C43—44no—
133#41×C43—42no—
134#41×C43—42no—
135#41×C43—42no—
136#41×C43—42no—
137C2×Q8×C43—21no—
138C2×Q8×C43—21no—
139C2×D4×C43—24no—
140C2×D4×C43—24no—
141C2×D4×C43—24no—
142C2×D4×C43—21no—
143C2×D4×C43—21no—
144C2×D4×C43—21no—
145C2×D4×C43—22no—
146C2×D4×C43—21no—
147C2×D4×C43—21no—
148C2×D4×C43—22no—
149C2×D4×C43—22no—
150C2×D4×C43—416no—
151C2×D4×C43—44no—
152C2×D4×C43—48no—
153C2×D4×C43—44no—
154C2×D4×C43—82no—
155C2×D4×C43—82no—
156C2×D4×C43SD1614yescomplemented
157C2×D4×C43C2×D412yes—
158C2×D4×C43C2×D412yes—
159C2×D4×C43C2×D412yes—
160C22×C4×C43—24no—
161C22×C4×C43—22no—
162C22×C4×C43—22no—
163C22×C4×C43—22no—
164C22×C4×C43—22no—
165C22×C4×C43—21no—
166C22×C4×C43—81no—
167C22×C4×C43—81no—
168C22×C4×C43C2×D411yescharacteristic
169C22×C4×C43C2×D411yescharacteristic
170C22×C4×C43C2×D411yescharacteristic
171C2×Dic86—21no—
172C2×Dic86—21no—
173C4⋊C4×C43—24no—
174C4⋊C4×C43—21no—
175C4⋊C4×C43—21no—
176C4⋊C4×C43—21no—
177C4⋊C4×C43C2×D412yes—
178C4⋊C4×C43C2×D412yes—
179C4⋊C4×C43C2×D412yes—
180C22⋊C4×C43—24no—
181C22⋊C4×C43—24no—
182C22⋊C4×C43—22no—
183C22⋊C4×C43—22no—
184C22⋊C4×C43—22no—
185C22⋊C4×C43—22no—
186C22⋊C4×C43—22no—
187C22⋊C4×C43—22no—
188C42×C43C2×D411yescharacteristic
189C42×C43C2×D411yescharacteristic
190C42×C43C2×D411yescharacteristic
191C42×C43C2411yescharacteristic
192C22⋊Dic43—41no—
193#10621883—44no—
194#10621883—82no—
195C4⋊Dic43—21no—
196C4⋊Dic43—21no—
197C4⋊Dic43—21no—
198C4⋊Dic43—21no—
199Dic43⋊C4—41no—
200Dic43⋊C4—41no—
201C4×Dic43—41no—
202#10621877—42no—
203C2×C43⋊C8—21no—
204C2×C43⋊C8—21no—
205C2×C43⋊C8—22no—
206C2×C43⋊C8—22no—
207C2×C43⋊C8—42no—
208C2×C43⋊C8—81no—
209C23×C43—22no—
210C23×C43—24no—
211C23×C43—22no—
212C23×C43—22no—
213C23×C43—48no—
214C23×C43—81no—
215C23×C43—81no—
216C23×C43—84no—
217C23×C43—84no—
218C23×C43#12011yescharacteristic
219Q8×C43—41no—
220Q8×C43—41no—
221Q8×C43—42no—
222D4×C43—22no—
223D4×C43—22no—
224D4×C43—22no—
225D4×C43—24no—
226D4×C43—42no—
227D4×C43—48no—
228D4×C43—48no—
229D4×C43—44no—
230D4×C43—44no—
231D4×C43—41no—
232D4×C43—41no—
233D4×C43—41no—
234D4×C43—41no—
235D4×C43—42no—
236D4×C43—81no—
237D4×C43—84no—
238D4×C43C2×SD1614yes—
239C2×C4×C43—21no—
240C2×C4×C43—21no—
241C2×C4×C43—22no—
242C2×C4×C43—22no—
243C2×C4×C43—22no—
244C2×C4×C43—41no—
245C2×C4×C43—48no—
246C2×C4×C43—42no—
247C2×C4×C43—42no—
248C2×C4×C43—42no—
249C2×C4×C43—42no—
250C2×C4×C43—44no—
251C2×C4×C43—82no—
252C2×C4×C43—81no—
253C2×C4×C43#12011yescharacteristic
254C2×C4×C43#12011yescharacteristic
255C2×C4×C43#12011yescharacteristic
256C2×C4×C43C2×SD1612yes—
257C2×C4×C43AGL(1,ℤ/8)12yes—
258C2×C4×C43C22×D411yescharacteristic
259C2×C4×C43C22×D411yescharacteristic
260C2×C4×C43C22×D411yescharacteristic
261C2×Dic43—41no—
262C2×Dic43—41no—
263Dic86—42no—
264Dic86—41no—
265Dic86—41no—
266C43⋊C8—22no—
267C43⋊C8—41no—
268C43⋊C8—42no—
269C43⋊C8—42no—
270#18663—431nomaximal, Sylow
271C22×C43—21no—
272C22×C43—21no—
273C22×C43—24no—
274C22×C43—42no—
275C22×C43—42no—
276C22×C43—42no—
277C22×C43—42no—
278C22×C43—42no—
279C22×C43—42no—
280C22×C43—42no—
281C22×C43—42no—
282C22×C43—84no—
283C22×C43—168no—
284C22×C43#45012yes—
285C22×C43C2×#12011yescharacteristic
286C4×C43—21no—
287C4×C43—21no—
288C4×C43—21no—
289C4×C43—42no—
290C4×C43—42no—
291C4×C43—42no—
292C4×C43#45012yes—
293C4×C43C22×SD1611yescharacteristic
294C4×C43C2×AGL(1,ℤ/8)11yescharacteristic
295C4×C43#57611yescharacteristic
296C4×C43#57711yescharacteristic
297Dic43—81no—
298Dic43—81no—
299#3496D4311yescharacteristic
300#3246—431no—
301#3167—431no—
302#3077—431no—
303#1654—432no—
304#1639—432no—
305#1635—432no—
306#1629—432no—
307#1547—431no—
308#1492—431no—
309C2×D4⋊C8—431no—
310C2×C43—22no—
311C2×C43—44no—
312C2×C43—82no—
313C2×C43—82no—
314C2×C43C2×#45011yescharacteristic
315C2×C43#301211yescharacteristic
316C2×C43#301811yescharacteristic
317C2×H(5,𝔽2)—21no—
318#547—21no—
319#547C2×D4312yes—
320#546—22no—
321#546—22no—
322D42—21no—
323D42C2×D4312yes—
324#537—21no—
325#534—22no—
326#533—431no—
327#532C2×D4311yescharacteristic
328#532C2×D4311yescharacteristic
329C2×#121—22no—
330C2×C4×D4C2×D4311yescharacteristic
331#498—431no—
332#492—431no—
333#487—431no—
334#486—431no—
335#478—862no—
336#476—432no—
337#476—432no—
338#475—861no—
339#474—432no—
340#465—862no—
341#465—862no—
342#461—432no—
343#460—861no—
344C4×SD16—862no—
345#428—861no—
346#423—431no—
347C2×C4⋊C8—431no—
348#418—861no—
349C2×C4×C8—431no—
350#332—432no—
351#331—432no—
352D4⋊C8—432no—
353D4⋊C8—432no—
354D4⋊C8—432no—
355D4⋊C8—432no—
356C43#1866311yescharacteristic, complemented, Sylow
357H(5,𝔽2)—44no—
358H(5,𝔽2)—44no—
359C2×#41—22no—
360C2×#41—22no—
361C2×#41—21no—
362C2×#41—21no—
363C22×D4—24no—
364C22×D4—22no—
365C22×D4—22no—
366C22×D4—22no—
367C22×D4C22⋊D4311yescharacteristic
368C23×C4—21no—
369C2×SD16—862no—
370C2×SD16—862no—
371C2×M16—861no—
372C22×C8—861no—
373C22×C8—861no—
374C4⋊Q8—431no—
375C4⋊Q8—431no—
376C4⋊Q8C22⋊D4311yescharacteristic
377C4⋊Q8C22×D4311yescharacteristic
378#127C22⋊D4311yescharacteristic
379#127C22×D4311yescharacteristic
380#125—861no—
381#124—21no—
382#124—21no—
383#123—24no—
384#123—24no—
385C22⋊Q8—22no—
386C22⋊Q8—22no—
387C22⋊Q8—861no—
388C22⋊Q8—861no—
389#121—24no—
390#121—24no—
391#121—22no—
392#121—22no—
393#121—21no—
394#121—21no—
395#121—22no—
396#121—22no—
397#121C22⋊D4312yes—
398#121C22⋊D4312yes—
399#120—24no—
400#120—24no—
401C4×Q8—861no—
402C4×Q8—861no—
403C4×D4—21no—
404C4×D4—21no—
405C4×D4—21no—
406C4×D4—21no—
407C4×D4C22⋊D4312yes—
408C4×D4C22⋊D4312yes—
409C4×D4C22×D4312yes—
410C4×D4C22×D4312yes—
411#117—861no—
412C2×C4⋊C4—22no—
413C2×C4⋊C4C22⋊D4311yescharacteristic
414C2×C22⋊C4—24no—
415C2×C22⋊C4—21no—
416C2×C42C22×D4311yescharacteristic
417#107—862no—
418#106—862no—
419#106—862no—
420#106—862no—
421C4⋊C8—432no—
422C4⋊C8—432no—
423C4⋊C8—861no—
424C4⋊C8—861no—
425#103—862no—
426#103—862no—
427#102—862no—
428#102—862no—
429#102—862no—
430#102—862no—
431C4×C8—431no—
432C4×C8—431no—
433C4×C8—861no—
434C24—21no—
435C24—24no—
436#41—48no—
437#41—44no—
438#41—44no—
439#41—42no—
440#41—42no—
441#41—42no—
442#41—42no—
443C2×Q8—21no—
444C2×Q8—21no—
445C2×Q8—861no—
446C2×Q8—861no—
447C2×D4—24no—
448C2×D4—24no—
449C2×D4—22no—
450C2×D4—22no—
451C2×D4—24no—
452C2×D4—21no—
453C2×D4—21no—
454C2×D4—21no—
455C2×D4—22no—
456C2×D4—21no—
457C2×D4—21no—
458C2×D4—48no—
459C2×D4—44no—
460C2×D4—416no—
461C2×D4—44no—
462C2×D4—82no—
463C2×D4—82no—
464C2×D4#1062188314yescomplemented
465C2×D4C2×C22⋊D4312yes—
466C2×D4C2×C22⋊D4312yes—
467C2×D4C2×C22⋊D4312yes—
468C22×C4—24no—
469C22×C4—21no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—81no—
475C22×C4—81no—
476C22×C4C2×C22⋊D4311yescharacteristic
477C22×C4C2×C22⋊D4311yescharacteristic
478C22×C4C2×C22⋊D4311yescharacteristic
479SD16—3442no—
480SD16—1724no—
481M16—1722no—
482C2×C8—861no—
483C2×C8—861no—
484C2×C8—862no—
485C2×C8—862no—
486C2×C8—3441no—
487C2×C8—1722no—
488C4⋊C4—24no—
489C4⋊C4—21no—
490C4⋊C4—21no—
491C4⋊C4—21no—
492C4⋊C4—861no—
493C4⋊C4—861no—
494C4⋊C4—861no—
495C4⋊C4—861no—
496C4⋊C4—1721no—
497C4⋊C4—1721no—
498C4⋊C4C2×C22⋊D4312yes—
499C4⋊C4C2×C22⋊D4312yes—
500C4⋊C4C2×C22⋊D4312yes—
501C22⋊C4—24no—
502C22⋊C4—24no—
503C22⋊C4—22no—
504C22⋊C4—22no—
505C22⋊C4—22no—
506C22⋊C4—22no—
507C22⋊C4—22no—
508C22⋊C4—22no—
509C22⋊C4—1721no—
510C42—1721no—
511C42C2×C22⋊D4311yescharacteristic
512C42C2×C22⋊D4311yescharacteristic
513C42C2×C22⋊D4311yescharacteristic
514C42C23×D4311yescharacteristic
515C23—22no—
516C23—24no—
517C23—22no—
518C23—22no—
519C23—48no—
520C23—81no—
521C23—81no—
522C23—84no—
523C23—84no—
524C23#1306329411yescharacteristic
525Q8—42no—
526Q8—41no—
527Q8—41no—
528Q8—1722no—
529Q8—1721no—
530Q8—1721no—
531D4—24no—
532D4—22no—
533D4—22no—
534D4—22no—
535D4—42no—
536D4—48no—
537D4—48no—
538D4—44no—
539D4—44no—
540D4—42no—
541D4—41no—
542D4—41no—
543D4—41no—
544D4—41no—
545D4—81no—
546D4—84no—
547D4C2×#1062188314yes—
548C2×C4—21no—
549C2×C4—21no—
550C2×C4—22no—
551C2×C4—22no—
552C2×C4—22no—
553C2×C4—41no—
554C2×C4—48no—
555C2×C4—44no—
556C2×C4—42no—
557C2×C4—42no—
558C2×C4—42no—
559C2×C4—42no—
560C2×C4—82no—
561C2×C4—81no—
562C2×C4—1721no—
563C2×C4—1721no—
564C2×C4#1306329411yescharacteristic
565C2×C4#1306329411yescharacteristic
566C2×C4#1306329411yescharacteristic
567C2×C4C2×#1062188312yes—
568C2×C4#1306335112yes—
569C2×C4C22×C22⋊D4311yescharacteristic
570C2×C4C22×C22⋊D4311yescharacteristic
571C2×C4C22×C22⋊D4311yescharacteristic
572C8—862no—
573C8—1721no—
574C8—1722no—
575C8—1722no—
576C22—21no—
577C22—21no—
578C22—24no—
579C22—42no—
580C22—42no—
581C22—42no—
582C22—42no—
583C22—42no—
584C22—42no—
585C22—42no—
586C22—42no—
587C22—84no—
588C22—168no—
589C22#1458305012yes—
590C22C2×#1306329411yescharacteristic
591C4—21no—
592C4—21no—
593C4—21no—
594C4—42no—
595C4—42no—
596C4—42no—
597C4—3441no—
598C4—3441no—
599C4#1458305012yes—
600C4C22×#1062188311yescharacteristic
601C4C2×#1306335111yescharacteristic
602C4#1458370211yescharacteristic
603C4#1458371011yescharacteristic
604C2—22no—
605C2—44no—
606C2—82no—
607C2—82no—
608C2C2×#1458305011yescharacteristic
609C2#1914389911yescharacteristic
610C2#1914394411yescharacteristic
subgroupG/H
centerC22C2×#13063294
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
Fitting, prime radicalC43×#3496C2
socleC22×C43C2×#120
hypercenter#3496D43
hypocenterC43#18663
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3496

Complements

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

NH ≅ G/Ntype
1. #19145911C2semidirect
2. #19145150C2semidirect
3. #19144392C2semidirect
4. #19133879C2semidirect
5. #19133774C2semidirect
6. #19133746C2semidirect
7. #19133711C2semidirect
8. #19133272C2semidirect
9. #19133046C2semidirect
10. C2×D4⋊(C43⋊C8)C2semidirect
12. #14583456C22semidirect
13. #14583295C22semidirect
14. #14583271C22semidirect
15. #14583251C22semidirect
16. #14583245C22semidirect
18. #14583189C22semidirect
19. #14583189C22semidirect
21. #14583179C22semidirect
24. #14583104C22semidirect
28. #14582923C22semidirect
29. C2×C4⋊(C43⋊C8)C22semidirect
31. C2×C4×C43⋊C8C22semidirect
32. #14582645C22semidirect
33. #14582643C22semidirect
34. D4⋊(C43⋊C8)C22semidirect
35. D4⋊(C43⋊C8)C22semidirect
36. D4⋊(C43⋊C8)C22semidirect
37. D4⋊(C43⋊C8)C22semidirect
156. C2×D4×C43SD16semidirect
356. C43#18663semidirect
464. C2×D4#10621883semidirect

Maximal subgroups

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

subgroupindex
#191459112
#191451502
#191443922
#191338792
#191337742
#191337462
#191337112
#191332722
#191330462
C2×D4⋊(C43⋊C8)2
C43×#34962
#1866343