Finite Group Databasebeta

← #25084499

Subgroups — #25084499

Order 11008.

784 conjugacy classes of subgroups.

The subgroup lattice has 556 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145539C211yesmaximal, characteristic, complemented
2#19145509C211yesmaximal, characteristic
3#19145153C211yesmaximal, characteristic, complemented
4#19144985C211yesmaximal, characteristic, complemented
5#19144966C211yesmaximal, characteristic, complemented
6#486×D43C211yesmaximal, characteristic, complemented
7#19134258C211yesmaximal, characteristic, complemented
8#19134256C211yesmaximal, characteristic, complemented
9#19134233C211yesmaximal, characteristic, complemented
10#19134231C211yesmaximal, characteristic, complemented
11#19134207C211yesmaximal, characteristic, complemented
12#19134206C211yesmaximal, characteristic, complemented
13#19134199C211yesmaximal, characteristic, complemented
14C8×#10621872C211yesmaximal, characteristic, complemented
15C43×#1709C211yesmaximal, characteristic, complemented
16#14583454C2211yescharacteristic
17#14583447C2211yescharacteristic
18C4⋊Q8×D43C2211yescharacteristic
19#127×D43C2211yescharacteristic
20#14583295C2211yescharacteristic, complemented
21#14583278C2211yescharacteristic, complemented
22#14583275C2211yescharacteristic
23#14583271C2211yescharacteristic, complemented
24#14583262—22no—
25#14583257—22no—
26#14583251C2211yescharacteristic, complemented
27#14583250C2211yescharacteristic, complemented
28#14583250C2211yescharacteristic, complemented
29#14583250C2211yescharacteristic, complemented
30#14583249C2211yescharacteristic, complemented
31#14583247C2211yescharacteristic
32#14583247C2211yescharacteristic
33#14583246C2211yescharacteristic
34#14583246C2211yescharacteristic
35#14583246C2211yescharacteristic
36#14583245C2211yescharacteristic
37#14583245C2211yescharacteristic
38#14583245C2211yescharacteristic
39#14583245C2211yescharacteristic, complemented
40#14583244—22no—
41#14583127—22no—
42#14583107—22no—
43#14583092—22no—
44#14583053—22no—
45#14583031—22no—
46#14582990—22no—
47#14582950C2211yescharacteristic
48#14582902—22no—
49#14582897—22no—
50#102×D43—22no—
51C4×#10621872C2211yescharacteristic
52C4×C8×D43C2211yescharacteristic
53#14582621C2211yescharacteristic, complemented
54#14582620C2211yescharacteristic, complemented
55C8×C43⋊C8C2211yescharacteristic, complemented
56C43×#494C2211yescharacteristic, complemented
57C43×#493C2211yescharacteristic
58C43×#486C2211yescharacteristic
59C43×#486C2211yescharacteristic
60C43×#486C2211yescharacteristic, complemented
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—
68C2×#10621885—22no—
69C2×#10621883—22no—
70C2×#10621882—22no—
71C2×#10621872D412yes—
72C2×C8×D43D412yes—
73#13063325C2311yescharacteristic
74#13063325C2311yescharacteristic
75#13063325C2311yescharacteristic
76#13063324—21no—
77#13063324—21no—
78#13063323—21no—
79#13063322C2311yescharacteristic
80#13063321—21no—
81#13063321—21no—
82#13063321—21no—
83#13063316—21no—
84#13063312—21no—
85#13063305—21no—
86#13063301—21no—
87#13063296—21no—
88#13063296—21no—
89Q8×Dic43—21no—
90#13063290—21no—
91D4×Dic43—21no—
92D4×Dic43—21no—
93#13063283—21no—
94C4⋊C4×D43—21no—
95C4⋊C4×D43—21no—
96C42×D43C2311yescharacteristic
97#13063256—22no—
98Dic43⋊C8D412yes—
99#13063250—22no—
100#13063250—22no—
101#13063250—22no—
102#13063249—22no—
103#13063248—22no—
104#13063247—22no—
105#13063247—22no—
106#13063247—22no—
107#13063246—22no—
108#13063246—22no—
109#13063246—22no—
110#13063246—22no—
111#13063245—22no—
112#13063245—22no—
113(C2×D43)⋊C8D412yes—
114#13063235D412yes—
115C4×C43⋊C8C2311yescharacteristic
116C4×C43⋊C8C2311yescharacteristic
117C4×C43⋊C8C2311yescharacteristic
118C8×Dic43D412yes—
119C2×Q16×C43—22no—
120C2×D8×C43—22no—
121C4⋊Q8×C43C2311yescharacteristic
122C4⋊Q8×C43C2311yescharacteristic
123#127×C43C2311yescharacteristic
124#127×C43C2311yescharacteristic
125#102×C43—22no—
126#102×C43—22no—
127#102×C43—22no—
128#102×C43—22no—
129C4×C8×C43C2311yescharacteristic
130C4×C8×C43C2311yescharacteristic
131C4×C8×C43C2311yescharacteristic
132C23×D43—41no—
133C2×Q8×C43—21no—
134C2×Q8×C43—21no—
135C2×D4×C43—21no—
136C2×D4×C43—21no—
137C2×D4×C43—21no—
138C2×D4×C43—21no—
139C2×D4×C43—21no—
140C2×D4×C43—21no—
141C2×C22⋊D43—41no—
142C2×C22⋊D43—41no—
143C2×C22⋊D43—41no—
144C2×C22⋊D43—41no—
145C22×Dic43—41no—
146Q8×D43—82no—
147#10621900—44no—
148D4×D43—44no—
149D4×D43—44no—
150D4×D43—82no—
151C2×D172—21no—
152C2×D172—21no—
153C2×D172—21no—
154C2×C4×D43—41no—
155C2×C4×D43C2×D411yescharacteristic
156C2×C4×D43C2×D411yescharacteristic
157C2×C4×D43C2×D411yescharacteristic
158C2×Dic86—21no—
159C2×Dic86—21no—
160C2×Dic86—21no—
161C2×Dic86—41no—
162Q16×C43—82no—
163D8×C43—82no—
164C2×C8×C43C2×D412yes—
165C2×C8×C43C2×D412yes—
166C2×C8×C43C2×D412yes—
167C4⋊C4×C43—21no—
168C4⋊C4×C43—21no—
169C4⋊C4×C43—21no—
170C4⋊C4×C43—21no—
171C42×C43C2411yescharacteristic
172C22⋊Dic43—41no—
173C22⋊Dic43—41no—
174#10621885—82no—
175#10621883—44no—
176#10621882—82no—
177(C2×D43)⋊C4—41no—
178C4⋊Dic43—21no—
179C4⋊Dic43—21no—
180C4⋊Dic43—21no—
181C4⋊Dic43—21no—
182C4⋊Dic43—21no—
183C4⋊Dic43—21no—
184C4⋊Dic43—41no—
185Dic43⋊C4—41no—
186Dic43⋊C4—41no—
187Dic43⋊C4—41no—
188C4×Dic43—41no—
189C4×Dic43C2×D411yescharacteristic
190C4×Dic43C2×D411yescharacteristic
191C4×Dic43C2×D411yescharacteristic
192C2×C43⋊C8C2×D412yes—
193C2×C43⋊C8C2×D412yes—
194C2×C43⋊C8C2×D412yes—
195#10621872—24no—
196C8×D43—42no—
197C23×C43—41no—
198C23×C43—41no—
199C22×D43—41no—
200C22×D43—82no—
201C22×D43—82no—
202C22×D43—82no—
203C22×D43#12711yescharacteristic
204Q8×C43—42no—
205Q8×C43—42no—
206D4×C43—42no—
207D4×C43—42no—
208D4×C43—42no—
209D4×C43—42no—
210D4×C43—42no—
211D4×C43—42no—
212C2×C4×C43—41no—
213C2×C4×C43—41no—
214C2×C4×C43C22×D411yescharacteristic
215C2×C4×C43C22×D411yescharacteristic
216C2×C4×C43C22×D411yescharacteristic
217C22⋊D43—82no—
218C22⋊D43—82no—
219C22⋊D43—82no—
220C22⋊D43—82no—
221C2×Dic43—41no—
222C2×Dic43—41no—
223C2×Dic43—41no—
224C2×Dic43—82no—
225C2×Dic43#12711yescharacteristic
226C2×Dic43#12711yescharacteristic
227C2×Dic43#12711yescharacteristic
228D172—42no—
229D172—42no—
230D172—42no—
231C4×D43—22no—
232C4×D43—22no—
233C4×D43—82no—
234C4×D43#13514yes—
235Dic86—42no—
236Dic86—42no—
237Dic86—42no—
238Dic86—82no—
239C8×C43—22no—
240C8×C43—22no—
241C8×C43—22no—
242C43⋊C8—22no—
243C43⋊C8—22no—
244C43⋊C8—22no—
245#19627—431nomaximal, Sylow
246C22×C43—81no—
247C22×C43—81no—
248C22×C43—81no—
249C22×C43—81no—
250C22×C43—81no—
251C22×C43—81no—
252C22×C43C2×#12711yescharacteristic
253C2×D43—21no—
254C2×D43—21no—
255C2×D43—81no—
256C2×D43—81no—
257C2×D43—81no—
258C2×D43—164no—
259C2×D43#49512yes—
260C4×C43—81no—
261C4×C43—81no—
262C4×C43C2×#13512yes—
263C4×C43#57512yes—
264C4×C43#57612yes—
265Dic43—21no—
266Dic43—21no—
267Dic43—81no—
268Dic43—81no—
269Dic43—81no—
270Dic43#49512yes—
271#3209—431no—
272#3205—431no—
273#3167—431no—
274#3141—431no—
275#3138—431no—
276C2×#486—431no—
277#1720—431no—
278#1720—431no—
279#1717—431no—
280#1717—431no—
281#1711—431no—
282#1711—431no—
283#1709—431no—
284#1709D4311yescharacteristic, complemented
285C8×M16—431no—
286C2×C43—161no—
287C2×C43—161no—
288C2×C43C2×#49511yescharacteristic
289C2×C43#315311yescharacteristic
290C2×C43#315511yescharacteristic
291D43—22no—
292D43—161no—
293#533—431no—
294#532—431no—
295C2×C4⋊Q8—431no—
296C2×#127—431no—
297#498—431no—
298#494—431no—
299#494C2×D4311yescharacteristic, complemented
300#493—431no—
301#493C2×D4311yescharacteristic
302#492—431no—
303#490—862no—
304#489—862no—
305#487—431no—
306#487—431no—
307#487—431no—
308#487—431no—
309#487—431no—
310#486—431no—
311#486—431no—
312#486—431no—
313#486—431no—
314#486—431no—
315#486—431no—
316#486—431no—
317#486—431no—
318#486—431no—
319#486—862no—
320#486C2×D4311yescharacteristic
321#486C2×D4311yescharacteristic
322#486C2×D4311yescharacteristic, complemented
323#486C2×D4311yescharacteristic, complemented
324#465—862no—
325#462—862no—
326#459—862no—
327#451—862no—
328#447—862no—
329C4×SD16—862no—
330#431—431no—
331#418—862no—
332#417—862no—
333C2×#102—862no—
334C4×M16—431no—
335C2×C4×C8—431no—
336#322—431no—
337#322—431no—
338C82—431no—
339C82C2×D4311yescharacteristic, complemented
340C43#1962711yescharacteristic, complemented, Sylow
341C2×#41—861no—
342C22×Q8—861no—
343C22×D4—861no—
344C22×D4—861no—
345C22×D4—861no—
346C2×Q16—22no—
347C2×Q16—862no—
348C2×SD16—862no—
349C2×D8—22no—
350C2×D8—862no—
351C2×M16—432no—
352C22×C8—432no—
353C4⋊Q8—431no—
354C4⋊Q8—431no—
355C4⋊Q8—431no—
356C4⋊Q8—861no—
357C4⋊Q8—861no—
358C4⋊Q8—861no—
359C4⋊Q8C22×D4311yescharacteristic
360C4⋊Q8C22×D4311yescharacteristic
361#127—431no—
362#127—861no—
363#127—861no—
364#127—861no—
365#127C22×D4311yescharacteristic
366#127C22×D4311yescharacteristic
367#125—861no—
368#124—861no—
369C22⋊Q8—861no—
370C22⋊Q8—861no—
371#121—861no—
372#121—861no—
373C4×Q8—861no—
374C4×Q8—861no—
375C4×D4—861no—
376C4×D4—861no—
377#117—861no—
378C2×C4⋊C4—861no—
379C2×C4⋊C4—861no—
380C2×C42—431no—
381#106—862no—
382C4⋊C8—432no—
383#103—862no—
384#103—862no—
385#103—862no—
386#103—862no—
387#103—862no—
388#102—22no—
389#102—22no—
390#102—22no—
391#102—22no—
392#102—862no—
393#102—862no—
394#102—862no—
395#102—862no—
396#102—862no—
397#102—862no—
398#102—862no—
399#102—862no—
400#102—862no—
401C22⋊C8—432no—
402#97—432no—
403C4×C8—432no—
404C4×C8—431no—
405C4×C8—431no—
406C4×C8—431no—
407C4×C8C22×D4311yescharacteristic
408C4×C8C22×D4311yescharacteristic
409C4×C8C22×D4311yescharacteristic
410C24—1721no—
411#41—1724no—
412C2×Q8—21no—
413C2×Q8—21no—
414C2×Q8—861no—
415C2×Q8—861no—
416C2×Q8—861no—
417C2×Q8—3442no—
418C2×Q8—1721no—
419C2×D4—21no—
420C2×D4—21no—
421C2×D4—21no—
422C2×D4—21no—
423C2×D4—21no—
424C2×D4—21no—
425C2×D4—861no—
426C2×D4—861no—
427C2×D4—861no—
428C2×D4—3442no—
429C2×D4—1724no—
430C2×D4—1721no—
431C2×D4—1721no—
432C2×D4—1721no—
433C2×D4—1724no—
434C2×D4—1721no—
435C22×C4—431no—
436C22×C4—431no—
437C22×C4—431no—
438C22×C4—1721no—
439C22×C4—1721no—
440Q16—82no—
441Q16—3442no—
442SD16—1724no—
443D8—82no—
444D8—3442no—
445M16—864no—
446C2×C8—432no—
447C2×C8—432no—
448C2×C8—432no—
449C2×C8—1722no—
450C2×C8D4×D4312yes—
451C2×C8D4×D4312yes—
452C2×C8D4×D4312yes—
453C4⋊C4—21no—
454C4⋊C4—21no—
455C4⋊C4—21no—
456C4⋊C4—21no—
457C4⋊C4—861no—
458C4⋊C4—861no—
459C4⋊C4—861no—
460C4⋊C4—861no—
461C4⋊C4—861no—
462C4⋊C4—861no—
463C4⋊C4—1721no—
464C4⋊C4—1721no—
465C4⋊C4—1721no—
466C4⋊C4—1721no—
467C22⋊C4—1721no—
468C22⋊C4—1721no—
469C22⋊C4—1721no—
470C42—431no—
471C42—431no—
472C42—431no—
473C42—1721no—
474C42C23×D4311yescharacteristic
475C23—41no—
476C23—41no—
477C23—431no—
478C23—3442no—
479C23—3442no—
480C23—3442no—
481C23—1721no—
482Q8—42no—
483Q8—42no—
484Q8—3442no—
485Q8—1722no—
486Q8—1722no—
487Q8—1722no—
488D4—42no—
489D4—42no—
490D4—42no—
491D4—42no—
492D4—42no—
493D4—42no—
494D4—3442no—
495D4—3442no—
496D4—3442no—
497D4—3442no—
498D4—1722no—
499D4—1722no—
500D4—1722no—
501C2×C4—41no—
502C2×C4—41no—
503C2×C4—431no—
504C2×C4—434no—
505C2×C4—431no—
506C2×C4—431no—
507C2×C4—862no—
508C2×C4—862no—
509C2×C4—3442no—
510C2×C4—3442no—
511C2×C4—1721no—
512C2×C4—1721no—
513C2×C4—1721no—
514C2×C4C2×D4×D4311yescharacteristic
515C2×C4C2×D4×D4311yescharacteristic
516C2×C4C2×D4×D4311yescharacteristic
517C8—22no—
518C8—22no—
519C8—22no—
520C8—862no—
521C8—862no—
522C8—862no—
523C22—81no—
524C22—81no—
525C22—81no—
526C22—81no—
527C22—81no—
528C22—81no—
529C22—432no—
530C22—861no—
531C22—861no—
532C22—3441no—
533C22—3441no—
534C22—3441no—
535C22—6884no—
536C22#127×D4311yescharacteristic
537C4—81no—
538C4—81no—
539C4—432no—
540C4—861no—
541C4—861no—
542C4—3441no—
543C4—3441no—
544C4—3441no—
545C4#135×D4312yes—
546C4#1458369612yes—
547C4#1458370012yes—
548C2—161no—
549C2—161no—
550C2—862no—
551C2—6881no—
552C2#495×D4311yescharacteristic
553C2#1914505611yescharacteristic
554C2#1914507511yescharacteristic
subgroupG/H
centerC22#127×D43
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#1709C2
socleC22×C43C2×#127
prime radical#19145509C2
hypercenter#1709D43
hypocenterC43#19627
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #1709

Complements

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

NH ≅ G/Ntype
1. #19145539C2semidirect
3. #19145153C2semidirect
4. #19144985C2semidirect
5. #19144966C2semidirect
6. #486×D43C2semidirect
7. #19134258C2semidirect
8. #19134256C2semidirect
9. #19134233C2semidirect
10. #19134231C2semidirect
11. #19134207C2semidirect
12. #19134206C2semidirect
13. #19134199C2semidirect
14. C8×#10621872C2semidirect
15. C43×#1709C2semidirect
20. #14583295C22semidirect
21. #14583278C22semidirect
23. #14583271C22semidirect
26. #14583251C22semidirect
27. #14583250C22semidirect
28. #14583250C22semidirect
29. #14583250C22semidirect
30. #14583249C22semidirect
39. #14583245C22semidirect
53. #14582621C22semidirect
54. #14582620C22semidirect
55. C8×C43⋊C8C22semidirect
56. C43×#494C22semidirect
60. C43×#486C22semidirect
61. C43×#486C22semidirect
62. C82×C43C22semidirect
284. #1709D43semidirect
299. #494C2×D43semidirect
322. #486C2×D43semidirect
323. #486C2×D43semidirect
339. C82C2×D43semidirect
340. C43#19627semidirect

Maximal subgroups

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

subgroupindex
#191455392
#191455092
#191451532
#191449852
#191449662
#486×D432
#191342582
#191342562
#191342332
#191342312
#191342072
#191342062
#191341992
C8×#106218722
C43×#17092
#1962743