Finite Group Databasebeta

← #11899736

Subgroups — #11899736

Order 1152.

844 conjugacy classes of subgroups.

The subgroup lattice has 568 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596242C211yesmaximal, characteristic, complemented
2#10594687C211yesmaximal, characteristic, complemented
3C3×#5194C211yesmaximal, characteristic, complemented
4C3×#5193C211yesmaximal, characteristic, complemented
5#10591050C212yesmaximal, complemented
6#10591039C212yesmaximal, complemented
7#10591035C212yesmaximal, complemented
8#10591026C212yesmaximal, complemented
9#10590638C211yesmaximal, characteristic, complemented
10C2×#63548C211yesmaximal, characteristic, complemented
11#10590624C211yesmaximal, characteristic, complemented
12#82037—31nomaximal
13#82032—31nomaximal
14#64367—21no—
15#64307—21no—
16C32×#135C2211yescharacteristic, complemented
17#64160—21no—
18Q16×C3⋊D3C2212yescomplemented
19#64124—22no—
20#64121C2212yescomplemented
21C2×#3746C2211yescharacteristic, complemented
22#64110C2211yescharacteristic
23C3×#904C2211yescharacteristic
24C2×C3×D24C2211yescharacteristic
25#63823—21no—
26#63810C2212yes—
27#63798—22no—
28#63797C2212yes—
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#63551C2212yescomplemented
38#63548C2212yescomplemented
39#63548C2212yescomplemented
40#63548C2212yescomplemented
41#63544C2212yescomplemented
42#63542C2212yescomplemented
43#5771—31no—
44#5771—31no—
45#5771—61no—
46#5769—31no—
47#5757—31no—
48C3×#509—31no—
49C3×#508—31no—
50#5195—31no—
51#5194D311yescharacteristic, complemented
52#5193D311yescharacteristic, complemented
53C2×#827—31no—
54#4918—32no—
55#4916—32no—
56#4915—32no—
57D3×SD32—32no—
58D3×SD32—32no—
59#4912—32no—
60#4911—32no—
61#4911—32no—
62#4909—31no—
63#4907—31no—
64C2×#800—31no—
65#4901—31no—
66C32×#41—21no—
67Q8×C3⋊D3—22no—
68#3830—22no—
69#3830—42no—
70#3828—41no—
71#3828D411yescharacteristic
72C2×#634—21no—
73C2×#634—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#3756—22no—
86#3754—22no—
87#3748D411yescharacteristic
88#3746—21no—
89#3746C2312yes—
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#3416—91noSylow
103#1010—61no—
104#1010—61no—
105#1010—62no—
106#1009—61no—
107#1004—61no—
108C3×#135—21no—
109C3×#135—31no—
110C3×#135C2×D311yescharacteristic, complemented
111C3×#135C2×D311yescharacteristic, complemented
112C2×C3×D8—31no—
113#951—61no—
114#951—61no—
115#951—62no—
116#949—61no—
117#932—61no—
118#919—32no—
119D3×Q16—32no—
120D3×Q16—32no—
121D3×Q16—62no—
122#915—62no—
123#915—62no—
124#915—64no—
125#914—62no—
126#912—32no—
127#912—32no—
128#912—32no—
129#912—62no—
130#911—62no—
131D3×D8—32no—
132D3×D8—32no—
133C2×Dic12—31no—
134C2×Dic12—31no—
135C2×Dic12—61no—
136#904C2×D311yescharacteristic
137C2×D24C2×D311yescharacteristic
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#829—32no—
150#829C2×D311yescharacteristic, complemented
151#828C2×D311yescharacteristic, complemented
152#828C2×D312yescomplemented
153#827—32no—
154#827—32no—
155#827—32no—
156#827C2×D311yescharacteristic, complemented
157#826C2×D311yescharacteristic, complemented
158#826C2×D312yescomplemented
159#812C2×D311yescharacteristic, complemented
160C2×C3⋊C16C2×D311yescharacteristic, complemented
161Dic24—32no—
162#800—32no—
163#800—32no—
164#800—32no—
165#798—32no—
166#798—32no—
167D3×C16—32no—
168D3×C16—32no—
169C22×C3×D3—41no—
170C2×D32—42no—
171C32×Q8—21no—
172C32×D4—21no—
173C32×D4—41no—
174C2×C32×C4—41no—
175C2×C32×C4C2×D411yescharacteristic
176#638—42no—
177#638D812yes—
178C2×C3⋊Dic3—41no—
179C2×C3⋊Dic3—42no—
180C4⋊(C3⋊D3)D811yescharacteristic
181C4×C3⋊D3—42no—
182C4×C3⋊D3C2×D412yes—
183#634—22no—
184#634—41no—
185#634—42no—
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#578—91no—
200#576—91no—
201#510—91no—
202#510—92no—
203#509—31no—
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×D4—61no—
215C2×#67—122no—
216#239—62no—
217D3×Q8—62no—
218D3×Q8—62no—
219D3×Q8—64no—
220#237—62no—
221#237—62no—
222#237—62no—
223#237—64no—
224#237—121no—
225#237—122no—
226#237—122no—
227#237—124no—
228D3×D4—62no—
229D3×D4—62no—
230D3×D4—121no—
231D3×D4—122no—
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—121no—
242C2×Dic6—62no—
243C2×Dic6—61no—
244C2×Dic6—61no—
245C2×Dic6—121no—
246C2×Dic6—121no—
247C2×Dic6—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#216—62no—
266#216—62no—
267#216—64no—
268#215—62no—
269#214—62no—
270#214—62no—
271#214—62no—
272#214—64no—
273#213—62no—
274#213—62no—
275#208—31no—
276#208—31no—
277#208—61no—
278Dic12—32no—
279Dic12—32no—
280Dic12—62no—
281Dic12—62no—
282Dic12—61no—
283Dic12—61no—
284Dic12C22×D311yescharacteristic
285D24—21no—
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⋊D3C2×D812yes—
304C2×C3×D3—42no—
305C2×C3×D3—41no—
306C2×C3×D3—161no—
307D32—162no—
308C32×C4—41no—
309C32×C4C2×D811yescharacteristic
310C32×C4C22×D411yescharacteristic
311C3⋊Dic3—42no—
312C3⋊Dic3C2×D812yes—
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, complemented
324C2×Q16—92no—
325C2×Q16—91no—
326C2×D8—31no—
327C2×D8—92no—
328#131—91no—
329Q32—31no—
330Q32—92no—
331SD32—31no—
332SD32—32no—
333SD32—31no—
334SD32—92no—
335SD32—92no—
336SD32—92no—
337D16—31no—
338D16—32no—
339M32—31no—
340M32—92no—
341C2×C16—31no—
342C2×C16—92no—
343C23×C3—121no—
344C22×D3—41no—
345C22×D3—122no—
346C22×D3—122no—
347C3×Q8—22no—
348C3×Q8—21no—
349C3×Q8—21no—
350C3×Q8—61no—
351C3×D4—22no—
352C3×D4—21no—
353C3×D4—21no—
354C3×D4—42no—
355C3×D4—41no—
356C3×D4—41no—
357C3×D4—61no—
358C3×D4—62no—
359C3×D4—121no—
360C3×D4—121no—
361C2×C3×C4—21no—
362C2×C3×C4—42no—
363C2×C3×C4—41no—
364C2×C3×C4—41no—
365C2×C3×C4—121no—
366C2×C3×C4D3×D411yescharacteristic
367C2×C3×C4D3×D411yescharacteristic
368#67—32no—
369#67—32no—
370#67—41no—
371#67—62no—
372#67—122no—
373#67—122no—
374#67—122no—
375#67—122no—
376#67—122no—
377#67—124no—
378C2×Dic3—122no—
379C2×Dic3—122no—
380C2×Dic3—122no—
381C2×Dic3—124no—
382C2×Dic3—122no—
383C2×Dic3—121no—
384C2×Dic3—121no—
385D12—21no—
386D12—22no—
387D12—31no—
388D12—31no—
389D12—41no—
390D12—61no—
391D12—122no—
392C4×D3—32no—
393C4×D3—32no—
394C4×D3—41no—
395C4×D3—62no—
396C4×D3—122no—
397C4×D3—122no—
398C4×D3—122no—
399C4×D3—124no—
400Dic6—21no—
401Dic6—31no—
402Dic6—31no—
403Dic6—61no—
404Dic6—64no—
405Dic6—62no—
406Dic6—62no—
407Dic6—122no—
408Dic6—122no—
409Dic6—124no—
410Dic6—122no—
411Dic6—121no—
412Dic6—121no—
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—81no—
427C3×D3—82no—
428#41—21no—
429#41—61no—
430#41—91no—
431#41—182no—
432#41—182no—
433#41—361no—
434#41—361no—
435#41—362no—
436C2×Q8—182no—
437C2×Q8—181no—
438C2×Q8—361no—
439C2×D4—61no—
440C2×D4—182no—
441C2×D4—361no—
442C2×D4—362no—
443Q16—31no—
444Q16—92no—
445Q16—182no—
446Q16—181no—
447Q16C2×D3211yescharacteristic
448SD16—21no—
449SD16—61no—
450SD16—182no—
451SD16—182no—
452D8—32no—
453D8—31no—
454D8—61no—
455D8—182no—
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—122no—
469C22×C3—121no—
470C22×C3—481no—
471C22×C3D3×D811yescharacteristic
472C22×C3D3×D811yescharacteristic
473C2×D3—32no—
474C2×D3—32no—
475C2×D3—41no—
476C2×D3—42no—
477C2×D3—62no—
478C2×D3—161no—
479C2×D3—482no—
480C2×D3—482no—
481C3×C4—21no—
482C3×C4—21no—
483C3×C4—42no—
484C3×C4—41no—
485C3×C4—41no—
486C3×C4—121no—
487C3×C4D3×D811yescharacteristic
488C3×C4D3×D811yescharacteristic
489C3×C4C2×D3×D411yescharacteristic
490C3×C4C2×D3×D411yescharacteristic
491Dic3—32no—
492Dic3—32no—
493Dic3—41no—
494Dic3—62no—
495Dic3—124no—
496Dic3—122no—
497Dic3—122no—
498C32#341611yescharacteristic, complemented, Sylow
499C23—121no—
500C23—362no—
501Q8—21no—
502Q8—61no—
503Q8—91no—
504Q8—182no—
505Q8—362no—
506Q8—361no—
507D4—21no—
508D4—41no—
509D4—62no—
510D4—61no—
511D4—92no—
512D4—91no—
513D4—121no—
514D4—121no—
515D4—362no—
516D4—362no—
517D4—362no—
518C2×C4—41no—
519C2×C4—92no—
520C2×C4—121no—
521C2×C4—362no—
522C2×C4—362no—
523C2×C4—362no—
524C2×C4—361no—
525C2×C4#381111yescharacteristic
526C8—92no—
527C8#381111yescharacteristic
528C8C22×D3211yescharacteristic
529C2×C3—21no—
530C2×C3—21no—
531C2×C3—21no—
532C2×C3—41no—
533C2×C3—82no—
534C2×C3—81no—
535C2×C3—81no—
536C2×C3—242no—
537C2×C3—241no—
538C2×C3C2×D3×D811yescharacteristic
539C2×C3C2×D3×D811yescharacteristic
540D3—62no—
541D3—62no—
542D3—81no—
543D3—82no—
544D3—122no—
545C22—41no—
546C22—92no—
547C22—121no—
548C22—122no—
549C22—481no—
550C22—1442no—
551C22#6392611yescharacteristic
552C4—41no—
553C4—92no—
554C4—121no—
555C4—362no—
556C4#6392611yescharacteristic
557C4C2×#381111yescharacteristic
558C3—21no—
559C3#8203211yescharacteristic, complemented
560C3#8203711yescharacteristic, complemented
561C2—21no—
562C2—81no—
563C2—182no—
564C2—242no—
565C2—241no—
566C2C2×#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. #10596242C2semidirect
2. #10594687C2semidirect
3. C3×#5194C2semidirect
4. C3×#5193C2semidirect
5. #10591050C2semidirect
6. #10591039C2semidirect
7. #10591035C2semidirect
8. #10591026C2semidirect
9. #10590638C2semidirect
10. C2×#63548C2semidirect
11. #10590624C2semidirect
16. C32×#135C22semidirect
18. Q16×C3⋊D3C22semidirect
20. #64121C22semidirect
21. C2×#3746C22semidirect
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. #63551C22semidirect
38. #63548C22semidirect
39. #63548C22semidirect
40. #63548C22semidirect
41. #63544C22semidirect
42. #63542C22semidirect
51. #5194D3semidirect
52. #5193D3semidirect
110. C3×#135C2×D3semidirect
111. C3×#135C2×D3semidirect
150. #829C2×D3semidirect
151. #828C2×D3semidirect
152. #828C2×D3semidirect
156. #827C2×D3semidirect
157. #826C2×D3semidirect
158. #826C2×D3semidirect
159. #812C2×D3semidirect
160. C2×C3⋊C16C2×D3semidirect
323. #135D32semidirect
498. C32#3416semidirect
559. C3#82032semidirect
560. C3#82037semidirect

Maximal subgroups

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

subgroupindex
#105962422
#105946872
C3×#51942
C3×#51932
#105910502
#105910392
#105910352
#105910262
#105906382
C2×#635482
#105906242
#820373
#820323