Finite Group Databasebeta

← #25084459

Subgroups — #25084459

Order 11008.

848 conjugacy classes of subgroups.

The subgroup lattice has 566 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145532C211yesmaximal, characteristic, complemented
2#19145516C211yesmaximal, characteristic, complemented
3#19145153C211yesmaximal, characteristic, complemented
4#19145138C211yesmaximal, characteristic, complemented
5#19145046C211yesmaximal, characteristic
6#486×D43C211yesmaximal, characteristic, complemented
7#19134222C211yesmaximal, characteristic, complemented
8#19134221C211yesmaximal, characteristic, complemented
9#19134218C211yesmaximal, characteristic, complemented
10#19134215C211yesmaximal, characteristic, complemented
11#19134196C211yesmaximal, characteristic, complemented
12#19134195C211yesmaximal, characteristic, complemented
13#19134186C211yesmaximal, characteristic, complemented
14C8×#10621872C211yesmaximal, characteristic, complemented
15C43×#1706C211yesmaximal, characteristic, complemented
16C2×#13063349—22no—
17#14583454C2211yescharacteristic
18#14583447C2211yescharacteristic
19C4⋊Q8×D43C2211yescharacteristic
20#127×D43C2211yescharacteristic
21#14583307—22no—
22#14583302C2211yescharacteristic, complemented
23#14583297C2211yescharacteristic, complemented
24#14583295C2211yescharacteristic, complemented
25#14583295C2211yescharacteristic, complemented
26#14583287—22no—
27#14583275C2211yescharacteristic
28#14583273C2211yescharacteristic
29#14583272C2211yescharacteristic
30#14583271C2211yescharacteristic
31#14583271C2211yescharacteristic, complemented
32#14583271C2211yescharacteristic, complemented
33#14583250C2211yescharacteristic, complemented
34#14583250C2211yescharacteristic, complemented
35#14583249C2211yescharacteristic, complemented
36#14583247C2211yescharacteristic
37#14583246C2211yescharacteristic
38#14583246C2211yescharacteristic
39#14583245C2211yescharacteristic
40#14583245C2211yescharacteristic
41#14583244—22no—
42#14583127—22no—
43#14583102—22no—
44#14583097—22no—
45#14583048—22no—
46#14583036—22no—
47#14582990—22no—
48#14582950C2211yescharacteristic
49#14582940—22no—
50#102×D43—22no—
51C4×#10621872C2211yescharacteristic
52C4×C8×D43C2211yescharacteristic
53#14582621C2211yescharacteristic, complemented
54#14582620C2211yescharacteristic, complemented
55C8×C43⋊C8C2211yescharacteristic, complemented
56C43×#500C2211yescharacteristic, complemented
57C43×#493C2211yescharacteristic
58C43×#492C2211yescharacteristic
59C43×#492C2211yescharacteristic, complemented
60C43×#486C2211yescharacteristic
61C43×#486C2211yescharacteristic, complemented
62C82×C43C2211yescharacteristic, complemented
63C2×#10621900—21no—
64C2×Q8×D43—21no—
65C2×D4×D43—21no—
66C2×D4×D43—21no—
67C2×D4×D43—21no—
68#13063349—48no—
69C2×#10621873—22no—
70C2×#10621883—22no—
71C2×#10621883—22no—
72C2×#10621883—22no—
73C2×#10621884—22no—
74C2×#10621882—22no—
75C2×#10621872D412yes—
76C2×C8×D43D412yes—
77#13063325C2311yescharacteristic
78#13063325C2311yescharacteristic
79#13063325C2311yescharacteristic
80#13063324—21no—
81#13063324—21no—
82#13063323—21no—
83#13063322C2311yescharacteristic
84#13063321—21no—
85#13063321—21no—
86#13063321—21no—
87#13063316—21no—
88#13063312—21no—
89#13063305—21no—
90#13063301—21no—
91#13063296—21no—
92#13063296—21no—
93Q8×Dic43—21no—
94#13063290—21no—
95D4×Dic43—21no—
96D4×Dic43—21no—
97#13063283—21no—
98C4⋊C4×D43—21no—
99C4⋊C4×D43—21no—
100C42×D43C2311yescharacteristic
101#13063258—22no—
102#13063257—22no—
103#13063256—22no—
104#13063256—22no—
105Dic43⋊C8D412yes—
106#13063250—22no—
107#13063250—22no—
108#13063249—22no—
109#13063247—22no—
110#13063247—22no—
111#13063246—22no—
112#13063246—22no—
113#13063245—22no—
114(C2×D43)⋊C8D412yes—
115#13063235D412yes—
116C4×C43⋊C8C2311yescharacteristic
117C4×C43⋊C8C2311yescharacteristic
118C4×C43⋊C8C2311yescharacteristic
119C8×Dic43D412yes—
120C2×SD16×C43—22no—
121C2×SD16×C43—22no—
122C2×D8×C43—22no—
123C4⋊Q8×C43C2311yescharacteristic
124C4⋊Q8×C43C2311yescharacteristic
125#127×C43C2311yescharacteristic
126#127×C43C2311yescharacteristic
127#107×C43—22no—
128#102×C43—22no—
129#102×C43—22no—
130C4×C8×C43C2311yescharacteristic
131C4×C8×C43C2311yescharacteristic
132C4×C8×C43C2311yescharacteristic
133C23×D43—41no—
134C2×Q8×C43—21no—
135C2×Q8×C43—21no—
136C2×D4×C43—21no—
137C2×D4×C43—21no—
138C2×D4×C43—21no—
139C2×D4×C43—21no—
140C2×D4×C43—21no—
141C2×D4×C43—21no—
142C2×C22⋊D43—41no—
143C2×C22⋊D43—41no—
144C2×C22⋊D43—41no—
145C2×C22⋊D43—41no—
146C22×Dic43—41no—
147Q8×D43—82no—
148#10621900—44no—
149D4×D43—44no—
150D4×D43—44no—
151D4×D43—82no—
152C2×D172—21no—
153C2×D172—21no—
154C2×D172—21no—
155C2×C4×D43—41no—
156C2×C4×D43C2×D411yescharacteristic
157C2×C4×D43C2×D411yescharacteristic
158C2×C4×D43C2×D411yescharacteristic
159C2×Dic86—21no—
160C2×Dic86—21no—
161C2×Dic86—21no—
162C2×Dic86—41no—
163SD16×C43—82no—
164SD16×C43—82no—
165D8×C43—44no—
166C2×C8×C43C2×D412yes—
167C2×C8×C43C2×D412yes—
168C2×C8×C43C2×D412yes—
169C4⋊C4×C43—21no—
170C4⋊C4×C43—21no—
171C4⋊C4×C43—21no—
172C4⋊C4×C43—21no—
173C42×C43C2411yescharacteristic
174C22⋊Dic43—41no—
175C22⋊Dic43—41no—
176#10621884—82no—
177#10621883—44no—
178#10621883—44no—
179#10621883—82no—
180#10621882—44no—
181(C2×D43)⋊C4—41no—
182C4⋊Dic43—21no—
183C4⋊Dic43—21no—
184C4⋊Dic43—21no—
185C4⋊Dic43—21no—
186C4⋊Dic43—21no—
187C4⋊Dic43—21no—
188C4⋊Dic43—41no—
189Dic43⋊C4—41no—
190Dic43⋊C4—41no—
191Dic43⋊C4—41no—
192C4×Dic43—41no—
193C4×Dic43C2×D411yescharacteristic
194C4×Dic43C2×D411yescharacteristic
195C4×Dic43C2×D411yescharacteristic
196C2×C43⋊C8C2×D412yes—
197C2×C43⋊C8C2×D412yes—
198C2×C43⋊C8C2×D412yes—
199#10621873—44no—
200#10621872SD1618yescomplemented
201C8×D43—42no—
202C23×C43—41no—
203C23×C43—41no—
204C22×D43—41no—
205C22×D43—82no—
206C22×D43—82no—
207C22×D43—82no—
208C22×D43#12711yescharacteristic
209Q8×C43—42no—
210Q8×C43—42no—
211D4×C43—42no—
212D4×C43—42no—
213D4×C43—42no—
214D4×C43—42no—
215D4×C43—42no—
216D4×C43—42no—
217C2×C4×C43—41no—
218C2×C4×C43—41no—
219C2×C4×C43C22×D411yescharacteristic
220C2×C4×C43C22×D411yescharacteristic
221C2×C4×C43C22×D411yescharacteristic
222C22⋊D43—82no—
223C22⋊D43—82no—
224C22⋊D43—82no—
225C22⋊D43—82no—
226C2×Dic43—41no—
227C2×Dic43—41no—
228C2×Dic43—41no—
229C2×Dic43—82no—
230C2×Dic43#12711yescharacteristic
231C2×Dic43#12711yescharacteristic
232C2×Dic43#12711yescharacteristic
233D172—42no—
234D172—42no—
235D172—42no—
236C4×D43—22no—
237C4×D43—22no—
238C4×D43—82no—
239C4×D43C2×SD1614yes—
240Dic86—42no—
241Dic86—42no—
242Dic86—42no—
243Dic86—82no—
244C8×C43—22no—
245C8×C43—22no—
246C8×C43C2×SD1614yes—
247C43⋊C8—22no—
248C43⋊C8—22no—
249C43⋊C8C2×SD1614yes—
250#19623—431nomaximal, Sylow
251C22×C43—81no—
252C22×C43—81no—
253C22×C43—81no—
254C22×C43—81no—
255C22×C43—81no—
256C22×C43—81no—
257C22×C43C2×#12711yescharacteristic
258C2×D43—21no—
259C2×D43—21no—
260C2×D43—81no—
261C2×D43—81no—
262C2×D43—81no—
263C2×D43—164no—
264C2×D43#49212yes—
265C4×C43—81no—
266C4×C43—81no—
267C4×C43C22×SD1612yes—
268C4×C43#57512yes—
269C4×C43#57612yes—
270Dic43—21no—
271Dic43—21no—
272Dic43—81no—
273Dic43—81no—
274Dic43—81no—
275Dic43#49212yes—
276#3208—431no—
277#3206—431no—
278#3167—431no—
279#3165—431no—
280#3151—431no—
281C2×#486—431no—
282#1715—431no—
283#1715—431no—
284#1714—431no—
285#1714—431no—
286#1708—431no—
287#1708—431no—
288#1706—431no—
289#1706D4311yescharacteristic, complemented
290C8×M16—431no—
291C2×C43—161no—
292C2×C43—161no—
293C2×C43C2×#49211yescharacteristic
294C2×C43#315311yescharacteristic
295C2×C43#315511yescharacteristic
296D43—22no—
297D43—161no—
298C2×AGL(1,ℤ/8)—862no—
299#533—431no—
300#532—431no—
301C2×C4⋊Q8—431no—
302C2×#127—431no—
303#501—862no—
304#500—431no—
305#500C2×D4311yescharacteristic, complemented
306#498—431no—
307#498—431no—
308#498—431no—
309#496—862no—
310#493—431no—
311#493C2×D4311yescharacteristic
312#492—431no—
313#492—431no—
314#492—431no—
315#492—431no—
316#492—431no—
317#492C2×D4311yescharacteristic
318#492C2×D4311yescharacteristic, complemented
319#487—431no—
320#487—431no—
321#487—431no—
322#486—431no—
323#486—431no—
324#486—431no—
325#486—431no—
326#486—431no—
327#486—862no—
328#486C2×D4311yescharacteristic
329#486C2×D4311yescharacteristic, complemented
330#465—862no—
331#461—862no—
332#460—862no—
333#450—862no—
334#448—862no—
335C4×SD16—862no—
336#431—431no—
337#428—862no—
338C2×#102—862no—
339C4×M16—431no—
340C2×C4×C8—431no—
341#322—431no—
342#322—431no—
343C82—431no—
344C82C2×D4311yescharacteristic, complemented
345C43#1962311yescharacteristic, complemented, Sylow
346C2×#41—861no—
347C22×Q8—861no—
348C22×D4—861no—
349C22×D4—861no—
350C22×D4—861no—
351AGL(1,ℤ/8)—1728no—
352C2×SD16—22no—
353C2×SD16—22no—
354C2×SD16—862no—
355C2×SD16—862no—
356C2×SD16—862no—
357C2×SD16—862no—
358C2×SD16—862no—
359C2×D8—22no—
360C2×D8—862no—
361C2×M16—432no—
362C22×C8—432no—
363C4⋊Q8—431no—
364C4⋊Q8—431no—
365C4⋊Q8—431no—
366C4⋊Q8—861no—
367C4⋊Q8—861no—
368C4⋊Q8—861no—
369C4⋊Q8C22×D4311yescharacteristic
370C4⋊Q8C22×D4311yescharacteristic
371#127—431no—
372#127—861no—
373#127—861no—
374#127—861no—
375#127C22×D4311yescharacteristic
376#127C22×D4311yescharacteristic
377#125—861no—
378#124—861no—
379C22⋊Q8—861no—
380C22⋊Q8—861no—
381#121—861no—
382#121—861no—
383C4×Q8—861no—
384C4×Q8—861no—
385C4×D4—861no—
386C4×D4—861no—
387#117—861no—
388C2×C4⋊C4—861no—
389C2×C4⋊C4—861no—
390C2×C42—431no—
391#107—22no—
392#107—862no—
393#106—862no—
394#106—862no—
395#106—862no—
396C4⋊C8—432no—
397#103—862no—
398#103—862no—
399#103—862no—
400#102—22no—
401#102—22no—
402#102—862no—
403#102—862no—
404#102—862no—
405#102—862no—
406#102—862no—
407C22⋊C8—432no—
408#97—432no—
409C4×C8—432no—
410C4×C8—431no—
411C4×C8—431no—
412C4×C8—431no—
413C4×C8C22×D4311yescharacteristic
414C4×C8C22×D4311yescharacteristic
415C4×C8C22×D4311yescharacteristic
416C24—1721no—
417#41—1724no—
418C2×Q8—21no—
419C2×Q8—21no—
420C2×Q8—861no—
421C2×Q8—861no—
422C2×Q8—861no—
423C2×Q8—3442no—
424C2×Q8—1721no—
425C2×D4—21no—
426C2×D4—21no—
427C2×D4—21no—
428C2×D4—21no—
429C2×D4—21no—
430C2×D4—21no—
431C2×D4—861no—
432C2×D4—861no—
433C2×D4—861no—
434C2×D4—3442no—
435C2×D4—1724no—
436C2×D4—1721no—
437C2×D4—1721no—
438C2×D4—1721no—
439C2×D4—1724no—
440C2×D4—1721no—
441C22×C4—431no—
442C22×C4—431no—
443C22×C4—431no—
444C22×C4—1721no—
445C22×C4—1721no—
446SD16—82no—
447SD16—82no—
448SD16—3442no—
449SD16—3442no—
450SD16—1724no—
451SD16—1724no—
452SD16—1724no—
453D8—44no—
454D8—1724no—
455M16—438no—
456C2×C8—432no—
457C2×C8—432no—
458C2×C8—432no—
459C2×C8—1722no—
460C2×C8D4×D4312yes—
461C2×C8D4×D4312yes—
462C2×C8D4×D4312yes—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—861no—
468C4⋊C4—861no—
469C4⋊C4—861no—
470C4⋊C4—861no—
471C4⋊C4—861no—
472C4⋊C4—861no—
473C4⋊C4—1721no—
474C4⋊C4—1721no—
475C4⋊C4—1721no—
476C4⋊C4—1721no—
477C22⋊C4—1721no—
478C22⋊C4—1721no—
479C22⋊C4—1721no—
480C42—431no—
481C42—431no—
482C42—431no—
483C42—1721no—
484C42C23×D4311yescharacteristic
485C23—41no—
486C23—41no—
487C23—431no—
488C23—3442no—
489C23—3442no—
490C23—3442no—
491C23—1721no—
492Q8—42no—
493Q8—42no—
494Q8—3442no—
495Q8—1722no—
496Q8—1722no—
497Q8—1722no—
498D4—42no—
499D4—42no—
500D4—42no—
501D4—42no—
502D4—42no—
503D4—42no—
504D4—3442no—
505D4—3442no—
506D4—3442no—
507D4—3442no—
508D4—1722no—
509D4—1722no—
510D4—1722no—
511C2×C4—41no—
512C2×C4—41no—
513C2×C4—431no—
514C2×C4—434no—
515C2×C4—431no—
516C2×C4—431no—
517C2×C4—862no—
518C2×C4—862no—
519C2×C4—3442no—
520C2×C4—3442no—
521C2×C4—1721no—
522C2×C4—1721no—
523C2×C4—1721no—
524C2×C4C2×D4×D4311yescharacteristic
525C2×C4C2×D4×D4311yescharacteristic
526C2×C4C2×D4×D4311yescharacteristic
527C8—22no—
528C8—22no—
529C8—434no—
530C8—862no—
531C8—862no—
532C8SD16×D4314yes—
533C22—81no—
534C22—81no—
535C22—81no—
536C22—81no—
537C22—81no—
538C22—81no—
539C22—432no—
540C22—861no—
541C22—861no—
542C22—3441no—
543C22—3441no—
544C22—3441no—
545C22—6884no—
546C22#127×D4311yescharacteristic
547C4—81no—
548C4—81no—
549C4—432no—
550C4—861no—
551C4—861no—
552C4—3441no—
553C4—3441no—
554C4—3441no—
555C4C2×SD16×D4312yes—
556C4#1458369612yes—
557C4#1458370012yes—
558C2—161no—
559C2—161no—
560C2—862no—
561C2—6881no—
562C2#492×D4311yescharacteristic
563C2#1914505611yescharacteristic
564C2#1914507511yescharacteristic
subgroupG/H
centerC22#127×D43
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#1706C2
socleC22×C43C2×#127
prime radical#19145046C2
hypercenter#1706D43
hypocenterC43#19623
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #1706

Complements

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

NH ≅ G/Ntype
1. #19145532C2semidirect
2. #19145516C2semidirect
3. #19145153C2semidirect
4. #19145138C2semidirect
6. #486×D43C2semidirect
7. #19134222C2semidirect
8. #19134221C2semidirect
9. #19134218C2semidirect
10. #19134215C2semidirect
11. #19134196C2semidirect
12. #19134195C2semidirect
13. #19134186C2semidirect
14. C8×#10621872C2semidirect
15. C43×#1706C2semidirect
22. #14583302C22semidirect
23. #14583297C22semidirect
24. #14583295C22semidirect
25. #14583295C22semidirect
31. #14583271C22semidirect
32. #14583271C22semidirect
33. #14583250C22semidirect
34. #14583250C22semidirect
35. #14583249C22semidirect
53. #14582621C22semidirect
54. #14582620C22semidirect
55. C8×C43⋊C8C22semidirect
56. C43×#500C22semidirect
59. C43×#492C22semidirect
61. C43×#486C22semidirect
62. C82×C43C22semidirect
200. #10621872SD16semidirect
289. #1706D43semidirect
305. #500C2×D43semidirect
318. #492C2×D43semidirect
329. #486C2×D43semidirect
344. C82C2×D43semidirect
345. C43#19623semidirect

Maximal subgroups

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

subgroupindex
#191455322
#191455162
#191451532
#191451382
#191450462
#486×D432
#191342222
#191342212
#191342182
#191342152
#191341962
#191341952
#191341862
C8×#106218722
C43×#17062
#1962343