Finite Group Databasebeta

← #25251069

Subgroups — #25251069

Order 11008.

738 conjugacy classes of subgroups.

The subgroup lattice has 590 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583333C211yesmaximal, characteristic, complemented
2C2×M32×D43C211yesmaximal, characteristic, complemented
3#19144174C211yesmaximal, characteristic, complemented
4#466×D43C211yesmaximal, characteristic, complemented
5#19136708C211yesmaximal, characteristic, complemented
6#19136706C211yesmaximal, characteristic, complemented
7#19136696C211yesmaximal, characteristic, complemented
8#19136692C211yesmaximal, characteristic, complemented
9#19136690C211yesmaximal, characteristic, complemented
10#19136680C211yesmaximal, characteristic, complemented
11#19136678C211yesmaximal, characteristic, complemented
12#19136382C211yesmaximal, characteristic, complemented
13#19136309C211yesmaximal, characteristic, complemented
14#19136304C211yesmaximal, characteristic, complemented
15C43×#2218C211yesmaximal, characteristic, complemented
16C2×#13063344C2211yescharacteristic
17C2×D8×D43C2211yescharacteristic
18C22×C8×D43C2211yescharacteristic
19#14583409—21no—
20#121×D43—21no—
21#14583333—24no—
22C2×#13063270C2211yescharacteristic, complemented
23C2×#13063269C2211yescharacteristic, complemented
24C2×#13063266C2211yescharacteristic, complemented
25C2×#13063265C2211yescharacteristic, complemented
26C2×#13063264C2211yescharacteristic
27C2×#13063264C2211yescharacteristic
28M32×D43—24no—
29C2×C16×D43C2211yescharacteristic, complemented
30C2×C16×D43C2211yescharacteristic, complemented
31#14583141C2211yescharacteristic, complemented
32#14583140C2211yescharacteristic, complemented
33#14583136C2211yescharacteristic
34#14583135C2211yescharacteristic
35#14583134—21no—
36#14583133—21no—
37#14583132C2211yescharacteristic
38#14583132C2211yescharacteristic, complemented
39#14583127—21no—
40#14583126—21no—
41#14582936C2211yescharacteristic
42#107×D43C2211yescharacteristic
43#14582892—21no—
44#102×D43—21no—
45#14582726C2211yescharacteristic, complemented
46#14582725C2211yescharacteristic, complemented
47#14582724C2211yescharacteristic, complemented
48#14582704C2211yescharacteristic, complemented
49#14582702C2211yescharacteristic, complemented
50#14582701C2211yescharacteristic, complemented
51#14582700C2211yescharacteristic, complemented
52#14582700C2211yescharacteristic, complemented
53#14582699C2211yescharacteristic, complemented
54C2×D16×C43C2211yescharacteristic, complemented
55C2×M32×C43C2211yescharacteristic, complemented
56C43×#466C2211yescharacteristic
57C43×#466C2211yescharacteristic, complemented
58C43×#367C2211yescharacteristic, complemented
59C43×#357C2211yescharacteristic, complemented
60C43×#357C2211yescharacteristic, complemented
61C2×#10621900—21no—
62C2×D4×D43—21no—
63C2×D4×D43—41no—
64C22×C4×D43D411yescharacteristic
65#13063344—22no—
66#13063344—22no—
67C2×Dic172C2311yescharacteristic
68C2×#10621883—21no—
69C2×D344C2311yescharacteristic
70C2×#10621882—21no—
71D8×D43—22no—
72D8×D43—22no—
73C22×C43⋊C8D411yescharacteristic
74C2×C8×D43—22no—
75C2×C8×D43—22no—
76C2×C8×D43D411yescharacteristic
77C2×C8×D43D411yescharacteristic
78C2×C8×D43C2311yescharacteristic
79C2×C8×D43C2311yescharacteristic
80#13063307—41no—
81#13063305—21no—
82#13063304—21no—
83#13063300—21no—
84#13063299—21no—
85#13063298—41no—
86#13063297—41no—
87#13063296—21no—
88#13063296—21no—
89#13063293—41no—
90D4×Dic43—41no—
91(C22⋊D43)⋊C4—41no—
92#13063283—21no—
93C4⋊C4×D43—21no—
94C22⋊C4×D43—41no—
95#13063270—22no—
96#13063269—22no—
97#13063266—22no—
98#13063265—22no—
99#13063264—22no—
100#13063264D414yescomplemented
101C2×C43⋊C16C2311yescharacteristic
102C2×C43⋊C16C2311yescharacteristic
103C16×D43—22no—
104C16×D43—22no—
105#13063259C2311yescharacteristic
106#13063259C2311yescharacteristic
107#13063258—21no—
108#13063256—21no—
109#13063250—21no—
110#13063248—21no—
111#13063247—21no—
112#13063246—21no—
113#13063246—21no—
114#13063245—21no—
115C2×D8×C43C2311yescharacteristic
116C2×D8×C43C2311yescharacteristic
117C22×C8×C43C2311yescharacteristic
118#121×C43—21no—
119#121×C43—21no—
120D16×C43—22no—
121M32×C43—22no—
122C2×C16×C43C2311yescharacteristic
123C2×C16×C43C2311yescharacteristic
124#107×C43C2311yescharacteristic
125#107×C43C2311yescharacteristic
126#102×C43—21no—
127#102×C43—21no—
128C23×D43—41no—
129C23×D43D811yescharacteristic
130C2×D4×C43—21no—
131C2×D4×C43—21no—
132C2×D4×C43—41no—
133C2×D4×C43—41no—
134C22×C4×C43C2×D411yescharacteristic
135C2×C22⋊D43—41no—
136C2×C22⋊D43—41no—
137C2×C22⋊D43—41no—
138C2×C22⋊D43—41no—
139C2×C22⋊D43—41no—
140C22×Dic43—41no—
141C22×Dic43D811yescharacteristic
142#10621900—42no—
143#10621900—42no—
144D4×D43—42no—
145D4×D43—42no—
146D4×D43—84no—
147C2×D172—21no—
148C2×D172—41no—
149C2×C4×D43—22no—
150C2×C4×D43—22no—
151C2×C4×D43—41no—
152C2×C4×D43D811yescharacteristic
153C2×C4×D43D811yescharacteristic
154C2×C4×D43C2×D411yescharacteristic
155C2×C4×D43C2×D411yescharacteristic
156C2×Dic86—21no—
157D8×C43—21no—
158D8×C43—21no—
159D8×C43—21no—
160D8×C43—21no—
161C2×C8×C43—21no—
162C2×C8×C43—21no—
163C2×C8×C43C2×D411yescharacteristic
164C2×C8×C43C2411yescharacteristic
165C4⋊C4×C43—21no—
166C4⋊C4×C43—21no—
167C22⋊C4×C43—41no—
168C22⋊C4×C43—41no—
169C22⋊Dic43—41no—
170C22⋊Dic43—41no—
171C22⋊Dic43—41no—
172#10621883—42no—
173#10621882—42no—
174(C2×D43)⋊C4—41no—
175(C2×D43)⋊C4—41no—
176(C2×D43)⋊C4—41no—
177(C2×D43)⋊C4—41no—
178C4⋊Dic43—21no—
179C4⋊Dic43—21no—
180C4⋊Dic43—41no—
181Dic43⋊C4—41no—
182Dic43⋊C4—41no—
183C4×Dic43—41no—
184C2×C43⋊C8—22no—
185C2×C43⋊C8C2×D411yescharacteristic
186C2×C43⋊C8C2×D411yescharacteristic
187Dic172—21no—
188Dic172—21no—
189D344—21no—
190D344—21no—
191C8×D43—22no—
192C8×D43—21no—
193C8×D43—21no—
194C8×D43—22no—
195C8×D43C2×D412yes—
196C8×D43#4112yes—
197C16×C43—21no—
198C16×C43C2×D412yescomplemented
199C43⋊C16—21no—
200C43⋊C16C2×D412yescomplemented
201C23×C43—41no—
202C23×C43—41no—
203C23×C43C2×D811yescharacteristic
204C22×D43—22no—
205C22×D43—22no—
206C22×D43—41no—
207C22×D43—41no—
208C22×D43—82no—
209C22×D43—82no—
210C22×D43—82no—
211C22×D43C2×D811yescharacteristic
212C22×D43C2×D811yescharacteristic
213D4×C43—41no—
214D4×C43—41no—
215D4×C43—41no—
216D4×C43—41no—
217D4×C43—82no—
218D4×C43—82no—
219C2×C4×C43—21no—
220C2×C4×C43—21no—
221C2×C4×C43—41no—
222C2×C4×C43—41no—
223C2×C4×C43C2×D811yescharacteristic
224C2×C4×C43C22×D411yescharacteristic
225C22⋊D43—82no—
226C22⋊D43—82no—
227C22⋊D43—82no—
228C22⋊D43—82no—
229C22⋊D43—82no—
230C2×Dic43—22no—
231C2×Dic43—41no—
232C2×Dic43—41no—
233C2×Dic43—41no—
234C2×Dic43—82no—
235C2×Dic43C2×D811yescharacteristic
236C2×Dic43C2×D811yescharacteristic
237D172—41no—
238D172—41no—
239D172—82no—
240C4×D43—22no—
241C4×D43—21no—
242C4×D43—21no—
243C4×D43—22no—
244C4×D43—82no—
245C4×D43#12112yes—
246C4×D43#13512yes—
247Dic86—41no—
248Dic86—41no—
249C8×C43—21no—
250C8×C43C22×D411yescharacteristic
251C8×C43C2×#4111yescharacteristic
252C43⋊C8—21no—
253C43⋊C8#12112yes—
254#33605—431nomaximal, Sylow
255C22×C43—21no—
256C22×C43—21no—
257C22×C43—21no—
258C22×C43—81no—
259C22×C43—81no—
260C22×C43—81no—
261C22×C43—81no—
262C22×C43—81no—
263C22×C43—81no—
264C22×C43C22×D811yescharacteristic
265C2×D43—21no—
266C2×D43—21no—
267C2×D43—21no—
268C2×D43—21no—
269C2×D43—44no—
270C2×D43—81no—
271C2×D43—81no—
272C2×D43—81no—
273C2×D43—164no—
274C2×D43#46612yes—
275C2×D43#50912yescomplemented
276C4×C43—21no—
277C4×C43—81no—
278C4×C43—81no—
279C4×C43C2×#12111yescharacteristic
280C4×C43C2×#13511yescharacteristic
281Dic43—21no—
282Dic43—81no—
283Dic43—81no—
284Dic43—81no—
285Dic43#46612yes—
286C2×#509—431no—
287C22×M32—431no—
288#3050—431no—
289C2×#466—431no—
290#2220—431no—
291#2220—431no—
292#2218—431no—
293#2218D4311yescharacteristic, complemented
294#2217—431no—
295#2217—431no—
296#2215—431no—
297#2215—431no—
298#2159—431no—
299#2140—431no—
300#2139—431no—
301C2×C43—41no—
302C2×C43—161no—
303C2×C43—161no—
304C2×C43C2×#46611yescharacteristic
305C2×C43C2×#50911yescharacteristic
306C2×C43#341411yescharacteristic
307D43—22no—
308D43—22no—
309D43—161no—
310C2×#135—431no—
311C22×D8—431no—
312C23×C8—431no—
313#525—861no—
314C2×#121—861no—
315#509—864no—
316C2×SD32—431no—
317C2×SD32—431no—
318C2×D16—431no—
319C2×D16C2×D4311yescharacteristic, complemented
320C2×M32—431no—
321C2×M32—431no—
322C2×M32—431no—
323C2×M32—864no—
324C2×M32C2×D4311yescharacteristic, complemented
325C22×C16—431no—
326C22×C16—431no—
327#467—431no—
328#467—431no—
329#466—431no—
330#466—431no—
331#466—431no—
332#466—431no—
333#466—861no—
334#466—861no—
335#466C2×D4311yescharacteristic
336#466C2×D4311yescharacteristic, complemented
337#465—861no—
338#465—861no—
339#427—431no—
340C2×#107—431no—
341#416—861no—
342C2×#102—861no—
343#367—431no—
344#367C2×D4311yescharacteristic, complemented
345#366—431no—
346#366—431no—
347#358—431no—
348#358—431no—
349#357—431no—
350#357—431no—
351#357—431no—
352#357—431no—
353#357C2×D4311yescharacteristic, complemented
354#357C2×D4311yescharacteristic, complemented
355C43#3360511yescharacteristic, complemented, Sylow
356C2×#41—861no—
357C22×D4—861no—
358C22×D4—1721no—
359C23×C4—431no—
360#135—862no—
361#135—862no—
362C2×Q16—431no—
363C2×SD16—861no—
364C2×D8—431no—
365C2×D8—862no—
366C2×D8—862no—
367C2×D8—861no—
368C2×D8C22×D4311yescharacteristic
369C2×D8C22×D4311yescharacteristic
370C22×C8—431no—
371C22×C8—431no—
372C22×C8—431no—
373C22×C8—431no—
374C22×C8—431no—
375C22×C8—862no—
376C22×C8—862no—
377C22×C8C22×D4311yescharacteristic
378#123—1721no—
379C22⋊Q8—861no—
380C22⋊Q8—861no—
381#121—21no—
382#121—21no—
383#121—861no—
384#121—861no—
385#121—861no—
386#121—861no—
387#121—1721no—
388#121—1721no—
389#120—1721no—
390C4×D4—1721no—
391C4×D4—1721no—
392#117—861no—
393C2×C4⋊C4—861no—
394C2×C22⋊C4—1721no—
395SD32—862no—
396SD32—862no—
397D16—22no—
398D16—862no—
399M32—22no—
400M32—434no—
401M32—862no—
402M32—862no—
403C2×C16—431no—
404C2×C16—431no—
405C2×C16—862no—
406C2×C16—862no—
407C2×C16C22×D4311yescharacteristic
408C2×C16C22×D4311yescharacteristic
409#107—431no—
410#107—431no—
411#107—861no—
412#107C22×D4311yescharacteristic
413#107C22×D4311yescharacteristic
414#106—861no—
415#103—861no—
416#103—861no—
417#102—21no—
418#102—21no—
419#102—861no—
420#102—861no—
421#102—861no—
422#102—861no—
423C24—431no—
424C24—1721no—
425#41—1722no—
426#41—1722no—
427C2×Q8—861no—
428C2×D4—21no—
429C2×D4—21no—
430C2×D4—41no—
431C2×D4—41no—
432C2×D4—861no—
433C2×D4—3444no—
434C2×D4—1721no—
435C2×D4—1722no—
436C2×D4—1722no—
437C2×D4—1721no—
438C2×D4—1721no—
439C2×D4—1721no—
440C2×D4—1721no—
441C2×D4—1721no—
442C22×C4—431no—
443C22×C4—431no—
444C22×C4—431no—
445C22×C4—431no—
446C22×C4—431no—
447C22×C4—862no—
448C22×C4—862no—
449C22×C4—1721no—
450C22×C4—1721no—
451C22×C4D4×D4311yescharacteristic
452Q16—861no—
453Q16—861no—
454SD16—1722no—
455D8—21no—
456D8—21no—
457D8—21no—
458D8—21no—
459D8—861no—
460D8—861no—
461D8—1722no—
462C2×C8—21no—
463C2×C8—21no—
464C2×C8—431no—
465C2×C8—432no—
466C2×C8—432no—
467C2×C8—431no—
468C2×C8—862no—
469C2×C8—862no—
470C2×C8—862no—
471C2×C8—861no—
472C2×C8—861no—
473C2×C8D4×D4311yescharacteristic
474C2×C8C23×D4311yescharacteristic
475C4⋊C4—21no—
476C4⋊C4—21no—
477C4⋊C4—861no—
478C4⋊C4—861no—
479C4⋊C4—1721no—
480C4⋊C4—1721no—
481C4⋊C4—1721no—
482C22⋊C4—41no—
483C22⋊C4—41no—
484C22⋊C4—1721no—
485C22⋊C4—1721no—
486C22⋊C4—1721no—
487C22⋊C4—1721no—
488C22⋊C4—1721no—
489C22⋊C4—1721no—
490C22⋊C4—1721no—
491C42—1721no—
492C16—21no—
493C16—432no—
494C16—861no—
495C16D4×D4312yescomplemented
496C23—41no—
497C23—41no—
498C23—431no—
499C23—431no—
500C23—862no—
501C23—862no—
502C23—3442no—
503C23—3442no—
504C23—3442no—
505C23—1721no—
506C23—1721no—
507C23D8×D4311yescharacteristic
508Q8—1721no—
509Q8—1721no—
510D4—41no—
511D4—41no—
512D4—41no—
513D4—41no—
514D4—82no—
515D4—82no—
516D4—3442no—
517D4—3442no—
518D4—3442no—
519D4—3442no—
520D4—3442no—
521D4—3442no—
522D4—1721no—
523D4—1721no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—431no—
529C2×C4—432no—
530C2×C4—432no—
531C2×C4—431no—
532C2×C4—862no—
533C2×C4—862no—
534C2×C4—862no—
535C2×C4—861no—
536C2×C4—861no—
537C2×C4—3442no—
538C2×C4—3442no—
539C2×C4—1721no—
540C2×C4—1721no—
541C2×C4—1721no—
542C2×C4D8×D4311yescharacteristic
543C2×C4C2×D4×D4311yescharacteristic
544C8—21no—
545C8—432no—
546C8—861no—
547C8C2×D4×D4311yescharacteristic
548C8#41×D4311yescharacteristic
549C22—21no—
550C22—21no—
551C22—21no—
552C22—81no—
553C22—81no—
554C22—81no—
555C22—81no—
556C22—81no—
557C22—81no—
558C22—432no—
559C22—432no—
560C22—861no—
561C22—861no—
562C22—861no—
563C22—861no—
564C22—3441no—
565C22—3441no—
566C22—3441no—
567C22—1724no—
568C22—6884no—
569C22C2×D8×D4311yescharacteristic
570C4—21no—
571C4—81no—
572C4—81no—
573C4—432no—
574C4—861no—
575C4—3441no—
576C4—3441no—
577C4—3441no—
578C4#121×D4311yescharacteristic
579C4#135×D4311yescharacteristic
580C2—41no—
581C2—161no—
582C2—161no—
583C2—862no—
584C2—862no—
585C2—6881no—
586C2#466×D4311yescharacteristic
587C2#509×D4311yescharacteristic
588C2#1914772711yescharacteristic
subgroupG/H
centerC22C2×D8×D43
commutator, cosocleC2×C8×C43C24
FrattiniC2×C8C23×D43
FittingC43×#2218C2
socleC22×C43C22×D8
hypercenter#2218D43
hypocenterC43#33605
LCSG ▷ C2×C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2218

Complements

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

NH ≅ G/Ntype
1. C2×#14583333C2semidirect
2. C2×M32×D43C2semidirect
3. #19144174C2semidirect
4. #466×D43C2semidirect
5. #19136708C2semidirect
6. #19136706C2semidirect
7. #19136696C2semidirect
8. #19136692C2semidirect
9. #19136690C2semidirect
10. #19136680C2semidirect
11. #19136678C2semidirect
12. #19136382C2semidirect
13. #19136309C2semidirect
14. #19136304C2semidirect
15. C43×#2218C2semidirect
22. C2×#13063270C22semidirect
23. C2×#13063269C22semidirect
24. C2×#13063266C22semidirect
25. C2×#13063265C22semidirect
29. C2×C16×D43C22semidirect
30. C2×C16×D43C22semidirect
31. #14583141C22semidirect
32. #14583140C22semidirect
38. #14583132C22semidirect
45. #14582726C22semidirect
46. #14582725C22semidirect
47. #14582724C22semidirect
48. #14582704C22semidirect
49. #14582702C22semidirect
50. #14582701C22semidirect
51. #14582700C22semidirect
52. #14582700C22semidirect
53. #14582699C22semidirect
54. C2×D16×C43C22semidirect
55. C2×M32×C43C22semidirect
57. C43×#466C22semidirect
58. C43×#367C22semidirect
59. C43×#357C22semidirect
60. C43×#357C22semidirect
100. #13063264D4semidirect
198. C16×C43C2×D4semidirect
200. C43⋊C16C2×D4semidirect
275. C2×D43#509semidirect
293. #2218D43semidirect
319. C2×D16C2×D43semidirect
324. C2×M32C2×D43semidirect
336. #466C2×D43semidirect
344. #367C2×D43semidirect
353. #357C2×D43semidirect
354. #357C2×D43semidirect
355. C43#33605semidirect
495. C16D4×D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145833332
C2×M32×D432
#191441742
#466×D432
#191367082
#191367062
#191366962
#191366922
#191366902
#191366802
#191366782
#191363822
#191363092
#191363042
C43×#22182
#3360543