Finite Group Databasebeta

← #11899739

Subgroups — #11899739

Order 1152.

854 conjugacy classes of subgroups.

The subgroup lattice has 571 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596240C211yesmaximal, characteristic, complemented
2#10594703C211yesmaximal, characteristic, complemented
3C3×#5195C211yesmaximal, characteristic, complemented
4C3×#5194C211yesmaximal, characteristic, complemented
5#10591049C212yesmaximal, complemented
6#10591044C212yesmaximal, complemented
7#10591036C212yesmaximal, complemented
8#10591029C212yesmaximal, complemented
9C2×#63549C211yesmaximal, characteristic, complemented
10#10590634C211yesmaximal, characteristic, complemented
11#10590624C211yesmaximal, characteristic, complemented
12#82040—31nomaximal
13#82032—31nomaximal
14#64366—21no—
15#64297—21no—
16C32×#135C2211yescharacteristic
17#64158—21no—
18#64128C2212yes—
19#64123—22no—
20D8×C3⋊D3C2212yes—
21C2×#3745C2211yescharacteristic
22#64110C2211yescharacteristic
23C2×C3×Dic12C2211yescharacteristic, complemented
24C3×#904C2211yescharacteristic, complemented
25#63827—21no—
26#63811—22no—
27#63810C2212yescomplemented
28#63802C2212yescomplemented
29C3×#829C2211yescharacteristic, complemented
30C3×#829C2212yescomplemented
31C3×#828C2211yescharacteristic, complemented
32C3×#827C2211yescharacteristic, complemented
33C3×#827C2212yescomplemented
34C3×#826C2211yescharacteristic, complemented
35C3×#812C2211yescharacteristic, complemented
36C2×C3×C3⋊C16C2211yescharacteristic, complemented
37#63549C2212yescomplemented
38#63549C2212yescomplemented
39#63549C2212yescomplemented
40#63546C2212yescomplemented
41#63544C2212yescomplemented
42#63542C2212yescomplemented
43#5771—31no—
44#5769—31no—
45#5769—31no—
46#5769—61no—
47#5766—31no—
48C3×#510—31no—
49C3×#508—31no—
50#5195D311yescharacteristic, complemented
51#5194D311yescharacteristic, complemented
52#5193—31no—
53C2×#828—31no—
54#4919—32no—
55#4918—32no—
56#4918—32no—
57#4916—32no—
58#4914—32no—
59D3×SD32—32no—
60D3×SD32—32no—
61#4911—32no—
62#4908—31no—
63#4907—31no—
64C2×#800—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×Dic6—21no—
76#3804—42no—
77#3799—41no—
78#3797—22no—
79#3796—22no—
80D3×Dic6—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×Dic12—21no—
93C3×Dic12C2311yescharacteristic
94C3×Dic12C2312yes—
95C3×D24C2311yescharacteristic
96C3×#204—21no—
97#3718—22no—
98#3715—22no—
99C3×C3⋊C16C2311yescharacteristic
100C3×C3⋊C16C2312yes—
101C3×C3⋊C16C2311yescharacteristic
102#3416—91noSylow
103#1010—61no—
104#1009—61no—
105#1009—61no—
106#1009—62no—
107#1007—61no—
108C3×#135—21no—
109C3×#135—31no—
110C3×#135C2×D311yescharacteristic
111C3×#135C2×D311yescharacteristic
112C2×C3×Q16—31no—
113#951—61no—
114#949—61no—
115#949—61no—
116#949—62no—
117#942—61no—
118#919—32no—
119#919—32no—
120#919—32no—
121#919—62no—
122#918—62no—
123D3×Q16—32no—
124D3×Q16—32no—
125#915—62no—
126#914—62no—
127#914—62no—
128#914—64no—
129#912—32no—
130D3×D8—32no—
131D3×D8—32no—
132D3×D8—62no—
133C2×Dic12C2×D311yescharacteristic, complemented
134#904C2×D311yescharacteristic, complemented
135C2×D24—31no—
136C2×D24—31no—
137C2×D24—61no—
138#901—31no—
139#901—31no—
140#901—61no—
141C3×Q32—31no—
142C3×Q32—32no—
143C3×SD32—31no—
144C3×SD32—31no—
145C3×SD32—32no—
146C3×D16—31no—
147C3×M32—31no—
148C2×C3×C16—31no—
149#829C2×D312yescomplemented
150#829C2×D311yescharacteristic, complemented
151#828—32no—
152#828—32no—
153#828—32no—
154#828C2×D311yescharacteristic, complemented
155#827C2×D312yescomplemented
156#827C2×D311yescharacteristic, complemented
157#826—32no—
158#826C2×D311yescharacteristic, complemented
159#812C2×D311yescharacteristic, complemented
160C2×C3⋊C16C2×D311yescharacteristic, complemented
161#800—32no—
162#800—32no—
163#800—32no—
164D48—32no—
165#798—32no—
166#798—32no—
167D3×C16—32no—
168D3×C16—32no—
169C22×C3⋊D3—41no—
170C22×C3⋊D3—42no—
171C32×Q8—21no—
172C32×D4—21no—
173C32×D4—41no—
174C2×C32×C4—41no—
175C2×C32×C4C2×D411yescharacteristic
176#638—42no—
177#638D812yes—
178C4⋊(C3⋊D3)—22no—
179C4⋊(C3⋊D3)—42no—
180C4⋊(C3⋊D3)—41no—
181C4⋊(C3⋊D3)D811yescharacteristic
182C4×C3⋊D3—42no—
183C4×C3⋊D3C2×D412yes—
184#634D811yescharacteristic
185C3×#67—41no—
186C2×C3×Dic3—41no—
187C3×D12—21no—
188C3×C4×D3—41no—
189C3×Dic6—22no—
190C3×Dic6—21no—
191C3×Dic6—41no—
192#627—42no—
193#626—42no—
194#624—42no—
195D3×Dic3—42no—
196C32×C8C2×D411yescharacteristic
197C32×C8C2411yescharacteristic
198C3⋊(C3⋊C8)C2×D412yes—
199#578—91no—
200#576—91no—
201#510—31no—
202#510—92no—
203#509—91no—
204#509—92no—
205#508—31no—
206#508—92no—
207C2×SD32—91no—
208C2×SD32—92no—
209#504—91no—
210C3×#41—22no—
211C3×#41—21no—
212C3×#41—21no—
213C3×#41—61no—
214C2×C3×Q8—61no—
215#239—62no—
216#239—62no—
217#239—62no—
218#239—64no—
219#239—121no—
220D3×Q8—62no—
221D3×Q8—62no—
222D3×Q8—121no—
223#237—62no—
224#237—122no—
225D3×D4—62no—
226D3×D4—62no—
227D3×D4—64no—
228D3×D4—122no—
229D3×D4—122no—
230D3×D4—124no—
231#235—21no—
232#235—31no—
233#235—31no—
234#235—61no—
235#235—121no—
236#235—121no—
237#235—121no—
238#235—122no—
239#235—122no—
240C2×D12—62no—
241C2×D12—61no—
242C2×D12—61no—
243C2×D12—121no—
244C2×D12—121no—
245C2×D12—122no—
246C2×Dic6—21no—
247C2×Dic6—121no—
248C3×Q16—21no—
249C3×Q16—31no—
250C3×Q16—32no—
251C3×Q16—61no—
252C3×Q16C22×D311yescharacteristic
253C3×Q16C22×D311yescharacteristic
254C3×SD16—22no—
255C3×SD16—21no—
256C3×SD16—21no—
257C3×SD16—61no—
258C3×D8—21no—
259C3×D8—31no—
260C3×D8C22×D311yescharacteristic
261C3×D8C22×D311yescharacteristic
262C2×C3×C8—21no—
263C2×C3×C8C22×D311yescharacteristic
264C2×C3×C8C22×D311yescharacteristic
265#216—62no—
266#216—62no—
267#215—62no—
268#215—62no—
269#215—62no—
270#215—64no—
271#214—62no—
272#213—62no—
273#213—62no—
274#213—64no—
275#208—31no—
276#208—31no—
277#208—61no—
278Dic12—21no—
279Dic12C22×D311yescharacteristic
280Dic12C22×D312yes—
281D24—32no—
282D24—32no—
283D24—62no—
284D24—62no—
285D24—61no—
286D24—61no—
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—41no—
308C32×C4—41no—
309C32×C4C2×D811yescharacteristic
310C32×C4C22×D411yescharacteristic
311C3⋊Dic3C2×D812yes—
312C3×Dic3—42no—
313C3×Dic3—41no—
3142−1+4—181no—
315H(5,𝔽2)—181no—
316#137—182no—
317#137—181no—
318AGL(1,ℤ/8)—182no—
319AGL(1,ℤ/8)—181no—
320#135—31no—
321#135—92no—
322#135—92no—
323#135D3211yescharacteristic
324C2×Q16—31no—
325C2×Q16—92no—
326C2×D8—92no—
327C2×D8—91no—
328#131—91no—
329Q32—31no—
330Q32—32no—
331SD32—31no—
332SD32—31no—
333SD32—32no—
334SD32—92no—
335SD32—92no—
336SD32—92no—
337D16—31no—
338D16—92no—
339M32—31no—
340M32—92no—
341C2×C16—31no—
342C2×C16—92no—
343C22×D3—122no—
344C22×D3—122no—
345C22×D3—124no—
346C22×D3—122no—
347C22×D3—121no—
348C22×D3—121no—
349C3×Q8—22no—
350C3×Q8—21no—
351C3×Q8—21no—
352C3×Q8—62no—
353C3×Q8—61no—
354C3×Q8—121no—
355C3×D4—22no—
356C3×D4—21no—
357C3×D4—21no—
358C3×D4—42no—
359C3×D4—41no—
360C3×D4—41no—
361C3×D4—61no—
362C3×D4—121no—
363C2×C3×C4—21no—
364C2×C3×C4—42no—
365C2×C3×C4—41no—
366C2×C3×C4—41no—
367C2×C3×C4—121no—
368C2×C3×C4—121no—
369C2×C3×C4D3×D411yescharacteristic
370C2×C3×C4D3×D411yescharacteristic
371#67—32no—
372#67—32no—
373#67—41no—
374#67—62no—
375#67—122no—
376#67—122no—
377#67—122no—
378#67—124no—
379C2×Dic3—41no—
380C2×Dic3—122no—
381D12—21no—
382D12—31no—
383D12—31no—
384D12—61no—
385D12—64no—
386D12—62no—
387D12—62no—
388D12—122no—
389D12—122no—
390D12—122no—
391D12—124no—
392D12—122no—
393D12—121no—
394D12—121no—
395C4×D3—32no—
396C4×D3—32no—
397C4×D3—41no—
398C4×D3—62no—
399C4×D3—122no—
400C4×D3—122no—
401C4×D3—122no—
402C4×D3—122no—
403C4×D3—122no—
404C4×D3—124no—
405Dic6—21no—
406Dic6—22no—
407Dic6—31no—
408Dic6—31no—
409Dic6—41no—
410Dic6—61no—
411Dic6—122no—
412Dic6—122no—
413C3×C8—21no—
414C3×C8—21no—
415C3×C8D3×D411yescharacteristic
416C3×C8D3×D411yescharacteristic
417C3×C8C23×D311yescharacteristic
418C3×C8C23×D311yescharacteristic
419C3⋊C8—32no—
420C3⋊C8—32no—
421C3⋊C8—62no—
422C2×C32—21no—
423C2×C32—81no—
424C2×C32C22×D811yescharacteristic
425C3⋊D3—22no—
426C3⋊D3—82no—
427C3×D3—81no—
428#41—21no—
429#41—61no—
430#41—91no—
431#41—182no—
432#41—182no—
433#41—361no—
434#41—362no—
435#41—361no—
436C2×Q8—61no—
437C2×Q8—182no—
438C2×Q8—361no—
439C2×D4—182no—
440C2×D4—181no—
441C2×D4—361no—
442C2×D4—362no—
443Q16—32no—
444Q16—31no—
445Q16—61no—
446Q16—182no—
447Q16C2×D3211yescharacteristic
448SD16—21no—
449SD16—61no—
450SD16—182no—
451SD16—182no—
452D8—31no—
453D8—92no—
454D8—182no—
455D8—181no—
456D8C2×D3211yescharacteristic
457M16—91no—
458M16—92no—
459C2×C8—92no—
460C2×C8C2×D3211yescharacteristic
461C16—31no—
462C16—31no—
463C16—32no—
464C22×C3—21no—
465C22×C3—42no—
466C22×C3—41no—
467C22×C3—41no—
468C22×C3—121no—
469C22×C3D3×D811yescharacteristic
470C22×C3D3×D811yescharacteristic
471C2×D3—32no—
472C2×D3—32no—
473C2×D3—41no—
474C2×D3—62no—
475C2×D3—124no—
476C2×D3—122no—
477C2×D3—122no—
478C2×D3—482no—
479C2×D3—482no—
480C2×D3—484no—
481C2×D3—481no—
482C2×D3—481no—
483C2×D3—482no—
484C3×C4—21no—
485C3×C4—21no—
486C3×C4—42no—
487C3×C4—41no—
488C3×C4—41no—
489C3×C4—121no—
490C3×C4—122no—
491C3×C4D3×D811yescharacteristic
492C3×C4D3×D811yescharacteristic
493C3×C4C2×D3×D411yescharacteristic
494C3×C4C2×D3×D411yescharacteristic
495Dic3—32no—
496Dic3—32no—
497Dic3—42no—
498Dic3—41no—
499Dic3—62no—
500C32#341611yescharacteristic, complemented, Sylow
501C23—362no—
502C23—361no—
503Q8—21no—
504Q8—61no—
505Q8—62no—
506Q8—91no—
507Q8—121no—
508Q8—362no—
509D4—21no—
510D4—41no—
511D4—61no—
512D4—92no—
513D4—91no—
514D4—121no—
515D4—182no—
516D4—362no—
517D4—362no—
518D4—362no—
519D4—361no—
520C2×C4—41no—
521C2×C4—92no—
522C2×C4—121no—
523C2×C4—121no—
524C2×C4—362no—
525C2×C4—362no—
526C2×C4—362no—
527C2×C4#381111yescharacteristic
528C8—92no—
529C8#381111yescharacteristic
530C8C22×D3211yescharacteristic
531C2×C3—21no—
532C2×C3—21no—
533C2×C3—21no—
534C2×C3—41no—
535C2×C3—82no—
536C2×C3—81no—
537C2×C3—81no—
538C2×C3—241no—
539C2×C3C2×D3×D811yescharacteristic
540C2×C3C2×D3×D811yescharacteristic
541D3—62no—
542D3—62no—
543D3—81no—
544D3—122no—
545D3—244no—
546D3—242no—
547D3—242no—
548C22—41no—
549C22—92no—
550C22—121no—
551C22—362no—
552C22—1441no—
553C22—1442no—
554C22#6392611yescharacteristic
555C4—41no—
556C4—92no—
557C4—121no—
558C4—122no—
559C4#6392611yescharacteristic
560C4C2×#381111yescharacteristic
561C3—21no—
562C3#8203211yescharacteristic, complemented
563C3#8204011yescharacteristic, complemented
564C2—21no—
565C2—81no—
566C2—182no—
567C2—241no—
568C2—722no—
569C2C2×#6392611yescharacteristic
subgroupG/H
centerC2C2×#63926
commutator, cosocleC32×C8C24
FrattiniC8C22×D32
FittingC32×#135C22
socleC2×C32C22×D8
hypercenter#135D32
hypocenterC32#3416
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. #10594703C2semidirect
3. C3×#5195C2semidirect
4. C3×#5194C2semidirect
5. #10591049C2semidirect
6. #10591044C2semidirect
7. #10591036C2semidirect
8. #10591029C2semidirect
9. C2×#63549C2semidirect
10. #10590634C2semidirect
11. #10590624C2semidirect
23. C2×C3×Dic12C22semidirect
24. C3×#904C22semidirect
27. #63810C22semidirect
28. #63802C22semidirect
29. C3×#829C22semidirect
30. C3×#829C22semidirect
31. C3×#828C22semidirect
32. C3×#827C22semidirect
33. C3×#827C22semidirect
34. C3×#826C22semidirect
35. C3×#812C22semidirect
36. C2×C3×C3⋊C16C22semidirect
37. #63549C22semidirect
38. #63549C22semidirect
39. #63549C22semidirect
40. #63546C22semidirect
41. #63544C22semidirect
42. #63542C22semidirect
50. #5195D3semidirect
51. #5194D3semidirect
133. C2×Dic12C2×D3semidirect
134. #904C2×D3semidirect
149. #829C2×D3semidirect
150. #829C2×D3semidirect
154. #828C2×D3semidirect
155. #827C2×D3semidirect
156. #827C2×D3semidirect
158. #826C2×D3semidirect
159. #812C2×D3semidirect
160. C2×C3⋊C16C2×D3semidirect
500. C32#3416semidirect
562. C3#82032semidirect
563. C3#82040semidirect

Maximal subgroups

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

subgroupindex
#105962402
#105947032
C3×#51952
C3×#51942
#105910492
#105910442
#105910362
#105910292
C2×#635492
#105906342
#105906242
#820403
#820323