Finite Group Databasebeta

← #11899689

Subgroups — #11899689

Order 1152.

874 conjugacy classes of subgroups.

The subgroup lattice has 583 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596240C211yesmaximal, characteristic, complemented
2#10594687C211yesmaximal, characteristic, complemented
3C3×#5194C211yesmaximal, characteristic, complemented
4C3×#5193C211yesmaximal, characteristic, complemented
5#10591049C212yesmaximal, complemented
6#10591040C212yesmaximal, complemented
7#10591036C212yesmaximal, complemented
8#10591025C212yesmaximal, complemented
9#10590634C211yesmaximal, characteristic, complemented
10C2×#63546C211yesmaximal, characteristic, complemented
11#10590624C211yesmaximal, characteristic, complemented
12#82036—31nomaximal
13#82031—31nomaximal
14#64366—21no—
15#64307—21no—
16C32×#135C2211yescharacteristic, complemented
17#64158—21no—
18#64128C2212yescomplemented
19#64123—22no—
20D8×C3⋊D3C2212yescomplemented
21C2×#3745C2211yescharacteristic, complemented
22#64110C2211yescharacteristic
23C3×#904C2211yescharacteristic, complemented
24C2×C3×D24C2211yescharacteristic, complemented
25#63823—21no—
26#63810C2212yescomplemented
27#63798—22no—
28#63797C2212yescomplemented
29C3×#829C2211yescharacteristic, complemented
30C3×#828C2212yescomplemented
31C3×#828C2211yescharacteristic, complemented
32C3×#827C2211yescharacteristic, complemented
33C3×#826C2212yescomplemented
34C3×#826C2211yescharacteristic, complemented
35C3×#812C2211yescharacteristic, complemented
36C2×C3×C3⋊C16C2211yescharacteristic, complemented
37#63549C2212yescomplemented
38#63546C2212yescomplemented
39#63546C2212yescomplemented
40#63546C2212yescomplemented
41#63544C2212yescomplemented
42#63542C2212yescomplemented
43#5769—31no—
44#5769—31no—
45#5769—31no—
46#5769—61no—
47#5757—31no—
48C3×#509—31no—
49C3×#508—31no—
50#5194D311yescharacteristic, complemented
51#5193—31no—
52#5193D311yescharacteristic, complemented
53C2×#826—31no—
54#4919—32no—
55#4916—32no—
56#4914—32no—
57#4914—32no—
58#4914—32no—
59#4911—32no—
60D3×D16—32no—
61D3×D16—32no—
62#4908—31no—
63#4907—31no—
64C2×D48—31no—
65#4901—31no—
66C32×#41—21no—
67#3832—22no—
68D4×C3⋊D3—22no—
69D4×C3⋊D3—42no—
70#3828—41no—
71#3828D411yescharacteristic
72C2×C4⋊(C3⋊D3)—21no—
73C2×C4⋊(C3⋊D3)—41no—
74C3×#235—21no—
75C2×C3×D12—21no—
76D3×#67—42no—
77#3802—22no—
78D3×D12—41no—
79#3796—22no—
80#3795—41no—
81C32×Q16C2311yescharacteristic
82C32×SD16—21no—
83C32×D8C2311yescharacteristic
84C2×C32×C8C2311yescharacteristic
85#3755—22no—
86#3753—22no—
87#3748D411yescharacteristic
88#3745—21no—
89#3745C2312yes—
90#3743D412yes—
91C8×C3⋊D3C2312yes—
92C3×Dic12C2311yescharacteristic
93C3×D24—21no—
94C3×D24C2312yes—
95C3×D24C2311yescharacteristic
96C3×#204—21no—
97#3715—22no—
98#3713—22no—
99C3×C3⋊C16C2311yescharacteristic
100C3×C3⋊C16C2312yes—
101C3×C3⋊C16C2311yescharacteristic
102#3415—91noSylow
103#1009—61no—
104#1009—61no—
105#1009—61no—
106#1009—62no—
107#1004—61no—
108C3×#135—21no—
109C3×#135—31no—
110C3×#135C2×D311yescharacteristic, complemented
111C3×#135C2×D311yescharacteristic, complemented
112C2×C3×D8—31no—
113#949—61no—
114#949—61no—
115#949—61no—
116#949—62no—
117#932—61no—
118#919—32no—
119#919—32no—
120#919—32no—
121#919—62no—
122#914—62no—
123#914—62no—
124#914—62no—
125#914—64no—
126#912—32no—
127#911—62no—
128D3×D8—32no—
129D3×D8—32no—
130D3×D8—32no—
131D3×D8—32no—
132D3×D8—62no—
133#904C2×D311yescharacteristic, complemented
134C2×D24—31no—
135C2×D24—31no—
136C2×D24—61no—
137C2×D24C2×D311yescharacteristic, complemented
138#901—31no—
139#901—31no—
140#901—61no—
141C3×Q32—31no—
142C3×SD32—31no—
143C3×SD32—32no—
144C3×SD32—31no—
145C3×D16—31no—
146C3×D16—32no—
147C3×M32—31no—
148C2×C3×C16—31no—
149#829C2×D311yescharacteristic, complemented
150#828—32no—
151#828C2×D311yescharacteristic, complemented
152#828C2×D312yescomplemented
153#827C2×D311yescharacteristic, complemented
154#826—32no—
155#826—32no—
156#826—32no—
157#826C2×D311yescharacteristic, complemented
158#826C2×D312yescomplemented
159#812C2×D311yescharacteristic, complemented
160C2×C3⋊C16C2×D311yescharacteristic, complemented
161#800—32no—
162D48—32no—
163D48—32no—
164D48—32no—
165#798—32no—
166#798—32no—
167D3×C16—32no—
168D3×C16—32no—
169C22×C3⋊D3—41no—
170C22×C3⋊D3—42no—
171C22×C3×D3—41no—
172C2×D32—42no—
173C32×Q8—21no—
174C32×D4—21no—
175C32×D4—41no—
176C2×C32×C4—41no—
177C2×C32×C4C2×D411yescharacteristic
178#638—42no—
179#638D812yes—
180C4⋊(C3⋊D3)—22no—
181C4⋊(C3⋊D3)—42no—
182C4⋊(C3⋊D3)—41no—
183C4⋊(C3⋊D3)D811yescharacteristic
184C4×C3⋊D3—42no—
185C4×C3⋊D3C2×D412yes—
186#634D811yescharacteristic
187C3×#67—41no—
188C3×D12—21no—
189C3×D12—22no—
190C3×D12—41no—
191C3×C4×D3—41no—
192C3×Dic6—21no—
193#626—42no—
194#625—42no—
195D3×Dic3—42no—
196C32×C8C2×D411yescharacteristic
197C32×C8C2411yescharacteristic
198C3⋊(C3⋊C8)C2×D412yes—
199#576—91no—
200#576—91no—
201#509—31no—
202#509—91no—
203#509—92no—
204#509—92no—
205#508—31no—
206#508—92no—
207C2×D16—91no—
208C2×D16—92no—
209#504—91no—
210C3×#41—22no—
211C3×#41—21no—
212C3×#41—21no—
213C3×#41—61no—
214C2×C3×D4—61no—
215C2×#67—122no—
216#239—62no—
217#239—62no—
218#239—62no—
219#239—64no—
220#237—62no—
221#237—121no—
222D3×D4—62no—
223D3×D4—62no—
224D3×D4—62no—
225D3×D4—62no—
226D3×D4—64no—
227D3×D4—121no—
228D3×D4—122no—
229D3×D4—122no—
230D3×D4—122no—
231D3×D4—124no—
232#235—21no—
233#235—31no—
234#235—31no—
235#235—61no—
236#235—121no—
237#235—121no—
238#235—121no—
239#235—122no—
240C2×D12—21no—
241C2×D12—62no—
242C2×D12—61no—
243C2×D12—61no—
244C2×D12—121no—
245C2×D12—121no—
246C2×D12—121no—
247C2×D12—122no—
248C3×Q16—21no—
249C3×Q16—31no—
250C3×Q16C22×D311yescharacteristic
251C3×Q16C22×D311yescharacteristic
252C3×SD16—22no—
253C3×SD16—21no—
254C3×SD16—21no—
255C3×SD16—61no—
256C3×D8—21no—
257C3×D8—31no—
258C3×D8—32no—
259C3×D8—61no—
260C3×D8C22×D311yescharacteristic
261C3×D8C22×D311yescharacteristic
262C2×C3×C8—21no—
263C2×C3×C8C22×D311yescharacteristic
264C2×C3×C8C22×D311yescharacteristic
265#215—62no—
266#215—62no—
267#215—62no—
268#215—64no—
269#214—62no—
270#213—62no—
271#213—62no—
272#213—62no—
273#213—62no—
274#213—64no—
275#208—31no—
276#208—31no—
277#208—61no—
278Dic12C22×D311yescharacteristic
279D24—21no—
280D24—32no—
281D24—32no—
282D24—62no—
283D24—62no—
284D24—61no—
285D24—61no—
286D24C22×D312yes—
287D24C22×D311yescharacteristic
288#204—21no—
289ΓL(1,𝔽25)—32no—
290ΓL(1,𝔽25)—32no—
291ΓL(1,𝔽25)—62no—
292D3×C8—32no—
293D3×C8—32no—
294D3×C8—62no—
295C3×C16—31no—
296C3×C16—32no—
297C3×C16—31no—
298C3⋊C16C22×D311yescharacteristic
299C3⋊C16C22×D312yes—
300C3⋊C16C22×D311yescharacteristic
301C22×C32—41no—
302C22×C32C2×D811yescharacteristic
303C2×C3⋊D3—42no—
304C2×C3⋊D3—162no—
305C2×C3⋊D3—161no—
306C2×C3⋊D3C2×D812yes—
307C2×C3×D3—42no—
308C2×C3×D3—41no—
309C2×C3×D3—161no—
310D32—162no—
311C32×C4—41no—
312C32×C4C2×D811yescharacteristic
313C32×C4C22×D411yescharacteristic
314C3⋊Dic3C2×D812yes—
315C3×Dic3—41no—
316H(5,𝔽2)—181no—
317H(5,𝔽2)—181no—
318AGL(1,ℤ/8)—182no—
319AGL(1,ℤ/8)—182no—
320AGL(1,ℤ/8)—181no—
321AGL(1,ℤ/8)—181no—
322#135—31no—
323#135—92no—
324#135—92no—
325#135D3211yescharacteristic, complemented
326C2×D8—31no—
327C2×D8—92no—
328C2×D8—92no—
329C2×D8—91no—
330#131—91no—
331Q32—31no—
332SD32—31no—
333SD32—32no—
334SD32—31no—
335SD32—92no—
336D16—31no—
337D16—32no—
338D16—92no—
339D16—92no—
340D16—92no—
341M32—31no—
342M32—92no—
343C2×C16—31no—
344C2×C16—92no—
345C23×C3—121no—
346C22×D3—41no—
347C22×D3—122no—
348C22×D3—122no—
349C22×D3—122no—
350C22×D3—122no—
351C22×D3—124no—
352C22×D3—122no—
353C22×D3—121no—
354C22×D3—121no—
355C3×Q8—22no—
356C3×Q8—21no—
357C3×Q8—21no—
358C3×Q8—61no—
359C3×D4—22no—
360C3×D4—21no—
361C3×D4—21no—
362C3×D4—42no—
363C3×D4—41no—
364C3×D4—41no—
365C3×D4—61no—
366C3×D4—62no—
367C3×D4—121no—
368C3×D4—121no—
369C2×C3×C4—21no—
370C2×C3×C4—42no—
371C2×C3×C4—41no—
372C2×C3×C4—41no—
373C2×C3×C4—121no—
374C2×C3×C4D3×D411yescharacteristic
375C2×C3×C4D3×D411yescharacteristic
376#67—32no—
377#67—32no—
378#67—41no—
379#67—62no—
380#67—122no—
381#67—122no—
382#67—122no—
383#67—122no—
384#67—122no—
385#67—124no—
386C2×Dic3—122no—
387D12—21no—
388D12—22no—
389D12—31no—
390D12—31no—
391D12—41no—
392D12—61no—
393D12—64no—
394D12—62no—
395D12—62no—
396D12—122no—
397D12—122no—
398D12—122no—
399D12—124no—
400D12—122no—
401D12—121no—
402D12—121no—
403C4×D3—32no—
404C4×D3—32no—
405C4×D3—41no—
406C4×D3—62no—
407C4×D3—122no—
408C4×D3—122no—
409C4×D3—122no—
410C4×D3—124no—
411Dic6—21no—
412Dic6—31no—
413Dic6—31no—
414Dic6—61no—
415C3×C8—21no—
416C3×C8—21no—
417C3×C8D3×D411yescharacteristic
418C3×C8D3×D411yescharacteristic
419C3×C8C23×D311yescharacteristic
420C3×C8C23×D311yescharacteristic
421C3⋊C8—32no—
422C3⋊C8—32no—
423C3⋊C8—62no—
424C2×C32—21no—
425C2×C32—81no—
426C2×C32C22×D811yescharacteristic
427C3⋊D3—22no—
428C3⋊D3—82no—
429C3×D3—81no—
430C3×D3—82no—
431#41—21no—
432#41—61no—
433#41—91no—
434#41—182no—
435#41—182no—
436#41—361no—
437#41—361no—
438C2×D4—61no—
439C2×D4—182no—
440C2×D4—182no—
441C2×D4—181no—
442C2×D4—361no—
443C2×D4—361no—
444C2×D4—362no—
445C2×D4—362no—
446Q16—31no—
447Q16C2×D3211yescharacteristic
448SD16—21no—
449SD16—61no—
450SD16—182no—
451SD16—182no—
452D8—32no—
453D8—31no—
454D8—61no—
455D8—92no—
456D8—182no—
457D8—182no—
458D8—181no—
459D8C2×D3211yescharacteristic
460M16—91no—
461M16—92no—
462C2×C8—92no—
463C2×C8C2×D3211yescharacteristic
464C16—31no—
465C16—31no—
466C16—32no—
467C22×C3—21no—
468C22×C3—42no—
469C22×C3—41no—
470C22×C3—41no—
471C22×C3—122no—
472C22×C3—121no—
473C22×C3—481no—
474C22×C3D3×D811yescharacteristic
475C22×C3D3×D811yescharacteristic
476C2×D3—32no—
477C2×D3—32no—
478C2×D3—41no—
479C2×D3—42no—
480C2×D3—62no—
481C2×D3—124no—
482C2×D3—122no—
483C2×D3—122no—
484C2×D3—161no—
485C2×D3—482no—
486C2×D3—482no—
487C2×D3—482no—
488C2×D3—482no—
489C2×D3—484no—
490C2×D3—481no—
491C2×D3—481no—
492C2×D3—482no—
493C3×C4—21no—
494C3×C4—21no—
495C3×C4—42no—
496C3×C4—41no—
497C3×C4—41no—
498C3×C4—121no—
499C3×C4D3×D811yescharacteristic
500C3×C4D3×D811yescharacteristic
501C3×C4C2×D3×D411yescharacteristic
502C3×C4C2×D3×D411yescharacteristic
503Dic3—32no—
504Dic3—32no—
505Dic3—41no—
506Dic3—62no—
507C32#341511yescharacteristic, complemented, Sylow
508C23—121no—
509C23—362no—
510C23—362no—
511C23—361no—
512Q8—21no—
513Q8—61no—
514Q8—91no—
515D4—21no—
516D4—41no—
517D4—62no—
518D4—61no—
519D4—92no—
520D4—91no—
521D4—121no—
522D4—121no—
523D4—182no—
524D4—362no—
525D4—362no—
526D4—362no—
527D4—362no—
528D4—361no—
529C2×C4—41no—
530C2×C4—92no—
531C2×C4—121no—
532C2×C4—362no—
533C2×C4—362no—
534C2×C4#381111yescharacteristic
535C8—92no—
536C8#381111yescharacteristic
537C8C22×D3211yescharacteristic
538C2×C3—21no—
539C2×C3—21no—
540C2×C3—21no—
541C2×C3—41no—
542C2×C3—82no—
543C2×C3—81no—
544C2×C3—81no—
545C2×C3—242no—
546C2×C3—241no—
547C2×C3C2×D3×D811yescharacteristic
548C2×C3C2×D3×D811yescharacteristic
549D3—62no—
550D3—62no—
551D3—81no—
552D3—82no—
553D3—122no—
554D3—244no—
555D3—242no—
556D3—242no—
557C22—41no—
558C22—92no—
559C22—121no—
560C22—122no—
561C22—362no—
562C22—481no—
563C22—1441no—
564C22—1442no—
565C22—1442no—
566C22#6392611yescharacteristic
567C4—41no—
568C4—92no—
569C4—121no—
570C4#6392611yescharacteristic
571C4C2×#381111yescharacteristic
572C3—21no—
573C3#8203111yescharacteristic, complemented
574C3#8203611yescharacteristic, complemented
575C2—21no—
576C2—81no—
577C2—182no—
578C2—242no—
579C2—241no—
580C2—722no—
581C2C2×#6392611yescharacteristic
subgroupG/H
centerC2C2×#63926
commutator, cosocleC32×C8C24
FrattiniC8C22×D32
FittingC32×#135C22
socleC2×C32C22×D8
hypercenter#135D32
hypocenterC32#3415
LCSG ▷ C32×C8 ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ #135

Complements

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

NH ≅ G/Ntype
1. #10596240C2semidirect
2. #10594687C2semidirect
3. C3×#5194C2semidirect
4. C3×#5193C2semidirect
5. #10591049C2semidirect
6. #10591040C2semidirect
7. #10591036C2semidirect
8. #10591025C2semidirect
9. #10590634C2semidirect
10. C2×#63546C2semidirect
11. #10590624C2semidirect
16. C32×#135C22semidirect
18. #64128C22semidirect
20. D8×C3⋊D3C22semidirect
21. C2×#3745C22semidirect
23. C3×#904C22semidirect
24. C2×C3×D24C22semidirect
26. #63810C22semidirect
28. #63797C22semidirect
29. C3×#829C22semidirect
30. C3×#828C22semidirect
31. C3×#828C22semidirect
32. C3×#827C22semidirect
33. C3×#826C22semidirect
34. C3×#826C22semidirect
35. C3×#812C22semidirect
36. C2×C3×C3⋊C16C22semidirect
37. #63549C22semidirect
38. #63546C22semidirect
39. #63546C22semidirect
40. #63546C22semidirect
41. #63544C22semidirect
42. #63542C22semidirect
50. #5194D3semidirect
52. #5193D3semidirect
110. C3×#135C2×D3semidirect
111. C3×#135C2×D3semidirect
133. #904C2×D3semidirect
137. C2×D24C2×D3semidirect
149. #829C2×D3semidirect
151. #828C2×D3semidirect
152. #828C2×D3semidirect
153. #827C2×D3semidirect
157. #826C2×D3semidirect
158. #826C2×D3semidirect
159. #812C2×D3semidirect
160. C2×C3⋊C16C2×D3semidirect
325. #135D32semidirect
507. C32#3415semidirect
573. C3#82031semidirect
574. C3#82036semidirect

Maximal subgroups

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

subgroupindex
#105962402
#105946872
C3×#51942
C3×#51932
#105910492
#105910402
#105910362
#105910252
#105906342
C2×#635462
#105906242
#820363
#820313