Finite Group Databasebeta

← #11861163

Subgroups — #11861163

Order 1152.

969 conjugacy classes of subgroups.

The subgroup lattice has 593 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10594676C211yesmaximal, characteristic
2#10594668C212yesmaximal, complemented
3#10592399C211yesmaximal, characteristic, complemented
4C3×#4700C211yesmaximal, characteristic, complemented
5C3×C4×ΓL(1,𝔽25)C211yesmaximal, characteristic, complemented
6#10590924C212yesmaximal, complemented
7#10590918C211yesmaximal, characteristic, complemented
8#10590916C211yesmaximal, characteristic, complemented
9#10590912C211yesmaximal, characteristic, complemented
10D3×#805C212yesmaximal, complemented
11#10590341C212yesmaximal, complemented
12#79889—31nomaximal
13#78541—31nomaximal
14D3×#235C2212yes—
15#64113C2211yescharacteristic
16#64110C2212yescomplemented
17C3×#904C2211yescharacteristic
18C3×#901C2212yescomplemented
19C2×C3×ΓL(1,𝔽25)C2211yescharacteristic
20C2×C3×ΓL(1,𝔽25)C2211yescharacteristic
21C3×C42×D3C2211yescharacteristic
22#63829C2212yes—
23#63817C2212yescomplemented
24#63814C2212yescomplemented
25D3×#208C2212yes—
26#63805—22no—
27#63804—22no—
28#63801C412yescomplemented
29#63800C412yescomplemented
30#63795C412yescomplemented
31#63794C412yescomplemented
32#63791—22no—
33D3×ΓL(1,𝔽25)—22no—
34C32×C4×C8C2211yescharacteristic, complemented
35#63646C2211yescharacteristic, complemented
36#63632C2212yescomplemented
37C3×#819C2211yescharacteristic, complemented
38C3×#815C2211yescharacteristic, complemented
39C3×#815C2211yescharacteristic, complemented
40C3×#805C2212yescomplemented
41C3×C4×C3⋊C8C2211yescharacteristic, complemented
42#63577C2212yescomplemented
43#63570C2212yescomplemented
44#63569C2212yescomplemented
45#5768—31no—
46#5750—32no—
47#5748—31no—
48#5745—32no—
49C3×#443—31no—
50C3×C4×M16—31no—
51#5197—31no—
52#5145—32no—
53#5125—31no—
54C2×#805—32no—
55#4894—31no—
56#4893—31no—
57#4824—32no—
58D3×#104—32no—
59#4717—31no—
60#4717—32no—
61#4717—31no—
62#4700—31no—
63#4700—31no—
64#4700—32no—
65#4700—61no—
66#4700D311yescharacteristic, complemented
67C4×ΓL(1,𝔽25)D311yescharacteristic, complemented
68#3828C2312yes—
69C3×#235C2312yes—
70C2×C3×C4×D3—21no—
71C2×C3×C4×D3C2311yescharacteristic
72D3×#67—22no—
73#3804—22no—
74D3×D12C2×C412yes—
75C4×D32—22no—
76#3799C2×C412yes—
77#3798—22no—
78#3795C2×C412yes—
79D3×Dic6C2×C412yes—
80C2×C32×C8C2311yescharacteristic
81C2×C32×C8C2311yescharacteristic
82C32×C42C2311yescharacteristic
83#3748C2312yes—
84#3746C2×C411yescharacteristic, complemented
85#3745C2×C411yescharacteristic, complemented
86#3744C2×C412yescomplemented
87#3743—22no—
88C8×C3⋊D3—22no—
89C3×C4×Dic3—21no—
90C3×C4×Dic3C2311yescharacteristic
91C3×#208C2312yes—
92C2×C3×C3⋊C8C2311yescharacteristic
93C2×C3×C3⋊C8C2311yescharacteristic
94C3×Dic12C2×C411yescharacteristic, complemented
95C3×D24C2×C411yescharacteristic, complemented
96C3×#204C2×C412yescomplemented
97C3×ΓL(1,𝔽25)—22no—
98C3×ΓL(1,𝔽25)C2×C412yes—
99C3×ΓL(1,𝔽25)C2×C412yes—
100C3×ΓL(1,𝔽25)D412yes—
101C3×ΓL(1,𝔽25)D412yes—
102C3×D3×C8—22no—
103#3719C2×C412yescomplemented
104#3717C2×C412yescomplemented
105#3716C2×C412yescomplemented
106#3714C2×C412yescomplemented
107#3712—22no—
108#3711—22no—
109#3711—22no—
110#3710—22no—
111D3×C3⋊C8—22no—
112D3×C3⋊C8—22no—
113#2956—91noSylow
114D3×#41—32no—
115C2×#235—32no—
116C3×#135—31no—
117C3×#131—32no—
118C2×C3×M16—31no—
119C2×C3×M16—31no—
120C2×C3×C42—31no—
121#950—32no—
122#948—32no—
123C2×#208—32no—
124#918—32no—
125#915—32no—
126#914—32no—
127#911—32no—
128#909—32no—
129#909—32no—
130#908—32no—
131#908—32no—
132#907—32no—
133#907—62no—
134#907—62no—
135#907—62no—
136D3×M16—32no—
137D3×M16—62no—
138D3×M16—62no—
139D3×M16—62no—
140#904—32no—
141#904—31no—
142#904—31no—
143#904—61no—
144#904C2×D311yescharacteristic
145#901—32no—
146#901—32no—
147#901—32no—
148#901—32no—
149#901—62no—
150#901—62no—
151#901C2×D312yescomplemented
152C2×ΓL(1,𝔽25)—62no—
153C2×ΓL(1,𝔽25)C2×D311yescharacteristic
154C2×ΓL(1,𝔽25)C2×D311yescharacteristic
155C42×D3C2×D311yescharacteristic
156C3×#108—31no—
157C3×#104—32no—
158C3×#97—31no—
159C3×#97—31no—
160C3×C4×C8—21no—
161C3×C4×C8—31no—
162C3×C4×C8C2×D311yescharacteristic, complemented
163C3×C4×C8C2×D311yescharacteristic, complemented
164#837—32no—
165#825—32no—
166#822—32no—
167#819—31no—
168#819—31no—
169#819—32no—
170#819—61no—
171#819C2×D311yescharacteristic, complemented
172#815C2×D311yescharacteristic, complemented
173#815C2×D311yescharacteristic, complemented
174#805—32no—
175#805—32no—
176#805—32no—
177#805—32no—
178#805—62no—
179#805C2×D312yescomplemented
180C4×C3⋊C8C2×D311yescharacteristic, complemented
181C22×C3×D3#4111yescharacteristic
182C2×D32—22no—
183C2×C32×C4—21no—
184C2×C32×C4C2411yescharacteristic
185#638—22no—
186C4⋊(C3⋊D3)C22×C412yes—
187C4×C3⋊D3—22no—
188#634C22×C412yes—
189C3×#67—22no—
190C2×C3×Dic3—21no—
191C2×C3×Dic3#4111yescharacteristic
192C3×D12C22×C412yes—
193C3×C4×D3—22no—
194C3×C4×D3—42no—
195C3×C4×D3C22×C412yes—
196C3×C4×D3C2×D412yes—
197C3×Dic6C22×C412yes—
198#627—22no—
199#626—22no—
200#626—22no—
201#625—22no—
202#624—22no—
203D3×Dic3—22no—
204D3×Dic3—22no—
205C32×C8C22×C411yescharacteristic
206C32×C8C22×C411yescharacteristic
207C32×C8C2×D411yescharacteristic
208C32×C8C2×D411yescharacteristic
209C3⋊(C3⋊C8)—22no—
210C3×C3⋊C8—22no—
211C3×C3⋊C8C22×C412yes—
212C3×C3⋊C8C2×D412yes—
213#575—91no—
214#568—92no—
215#444—91no—
216#444—92no—
217#444—91no—
218#443—31no—
219#443—92no—
220#443—91no—
221#430—91no—
222C2×#104—92no—
223C4×M16—31no—
224C3×#41—32no—
225C22×C3×C4—31no—
226C22×C3×C4—61no—
227C2×#67—62no—
228#239—32no—
229D3×Q8—32no—
230#237—32no—
231#237—62no—
232D3×D4—32no—
233D3×D4—62no—
234#235—32no—
235#235—32no—
236#235—32no—
237#235—32no—
238#235—62no—
239#235—62no—
240#235—62no—
241#235—62no—
242#235C22×D312yes—
243C2×D12—32no—
244C2×C4×D3—21no—
245C2×C4×D3—62no—
246C2×C4×D3—62no—
247C2×C4×D3C22×D311yescharacteristic
248C2×Dic6—32no—
249C3×Q16—31no—
250C3×SD16—32no—
251C3×D8—31no—
252C3×M16—32no—
253C3×M16—32no—
254C3×M16—32no—
255C3×M16—32no—
256C3×M16—32no—
257C3×M16—62no—
258C2×C3×C8—21no—
259C2×C3×C8—21no—
260C2×C3×C8—31no—
261C2×C3×C8—31no—
262C2×C3×C8—62no—
263C2×C3×C8C22×D311yescharacteristic
264C2×C3×C8C22×D311yescharacteristic
265C2×C3×C8C22×D311yescharacteristic
266C2×C3×C8C22×D311yescharacteristic
267C3×C42—21no—
268C3×C42—31no—
269C3×C42—61no—
270C3×C42C22×D311yescharacteristic
271C3×C42C22×D311yescharacteristic
272#216—32no—
273#215—32no—
274#214—32no—
275#213—32no—
276C4×Dic3—21no—
277C4×Dic3C22×D311yescharacteristic
278#208—32no—
279#208—32no—
280#208—62no—
281#208—62no—
282#208—62no—
283#208C22×D312yes—
284C2×C3⋊C8—62no—
285C2×C3⋊C8—62no—
286C2×C3⋊C8C22×D311yescharacteristic
287C2×C3⋊C8C22×D311yescharacteristic
288Dic12—32no—
289Dic12—31no—
290Dic12—31no—
291Dic12—61no—
292Dic12C4×D311yescharacteristic, complemented
293D24—32no—
294D24—31no—
295D24—31no—
296D24—61no—
297D24C4×D311yescharacteristic, complemented
298#204—32no—
299#204—32no—
300#204—32no—
301#204—32no—
302#204—62no—
303#204C4×D312yescomplemented
304ΓL(1,𝔽25)—22no—
305ΓL(1,𝔽25)—62no—
306ΓL(1,𝔽25)—62no—
307ΓL(1,𝔽25)—62no—
308ΓL(1,𝔽25)—62no—
309ΓL(1,𝔽25)—62no—
310ΓL(1,𝔽25)—62no—
311ΓL(1,𝔽25)—122no—
312ΓL(1,𝔽25)C4×D312yes—
313ΓL(1,𝔽25)C4×D312yes—
314ΓL(1,𝔽25)D1212yes—
315ΓL(1,𝔽25)D1212yes—
316D3×C8—22no—
317D3×C8—62no—
318D3×C8—62no—
319D3×C8—62no—
320D3×C8—62no—
321D3×C8—62no—
322D3×C8—62no—
323D3×C8—122no—
324C22×C32C2×#4111yescharacteristic
325C2×C3⋊D3—22no—
326C2×C3×D3—22no—
327C2×C3×D3—41no—
328C2×C3×D3C4×D412yes—
329D32—82no—
330C32×C4—22no—
331C32×C4C23×C411yescharacteristic
332C32×C4C22×D411yescharacteristic
333C3⋊Dic3—22no—
334C3×Dic3—22no—
335C3×Dic3—41no—
336C3×Dic3C4×D412yes—
337C2×#41—92no—
338#137—92no—
339#137—92no—
340AGL(1,ℤ/8)—92no—
341AGL(1,ℤ/8)—92no—
342#135—31no—
343#135—92no—
344#135—91no—
345#131—32no—
346#131—92no—
347#131—92no—
348#131—92no—
349#131—182no—
350#131—182no—
351C2×M16—31no—
352C2×M16—31no—
353C2×M16—92no—
354C2×M16—182no—
355C2×M16—182no—
356C2×C42—31no—
357#108—31no—
358#108—92no—
359#108—91no—
360#104—32no—
361#104—92no—
362#104—92no—
363#104—92no—
364#97—31no—
365#97—31no—
366C4×C8—31no—
367C4×C8D3211yescharacteristic, complemented
368C23×C3—31no—
369C22×D3—62no—
370C22×D3—62no—
371C22×D3#23511yescharacteristic
372C3×Q8—32no—
373C3×D4—32no—
374C3×D4—62no—
375C2×C3×C4—21no—
376C2×C3×C4—21no—
377C2×C3×C4—21no—
378C2×C3×C4—31no—
379C2×C3×C4—32no—
380C2×C3×C4—32no—
381C2×C3×C4—41no—
382C2×C3×C4—62no—
383C2×C3×C4—61no—
384C2×C3×C4—122no—
385C2×C3×C4C23×D311yescharacteristic
386C2×C3×C4C23×D311yescharacteristic
387#67—22no—
388#67—62no—
389#67—62no—
390#67—62no—
391#67—62no—
392#67—62no—
393#67—62no—
394#67—122no—
395C2×Dic3—21no—
396C2×Dic3—62no—
397C2×Dic3—62no—
398C2×Dic3#23511yescharacteristic
399D12—32no—
400D12—32no—
401D12—62no—
402D12—62no—
403D12—62no—
404D12C2×C4×D312yes—
405C4×D3—22no—
406C4×D3—42no—
407C4×D3—62no—
408C4×D3—62no—
409C4×D3—62no—
410C4×D3—62no—
411C4×D3—62no—
412C4×D3—62no—
413C4×D3—122no—
414C4×D3C2×C4×D312yes—
415C4×D3C2×D1212yes—
416Dic6—32no—
417Dic6—32no—
418Dic6—62no—
419Dic6—62no—
420Dic6—62no—
421Dic6C2×C4×D312yes—
422C3×C8—21no—
423C3×C8—21no—
424C3×C8—21no—
425C3×C8—21no—
426C3×C8—32no—
427C3×C8—32no—
428C3×C8—62no—
429C3×C8C2×C4×D311yescharacteristic
430C3×C8C2×C4×D311yescharacteristic
431C3×C8C2×C4×D311yescharacteristic
432C3×C8C2×C4×D311yescharacteristic
433C3×C8C2×D1211yescharacteristic
434C3×C8C2×D1211yescharacteristic
435C3×C8D3×D411yescharacteristic
436C3×C8D3×D411yescharacteristic
437C3⋊C8—22no—
438C3⋊C8—62no—
439C3⋊C8—62no—
440C3⋊C8—122no—
441C3⋊C8C2×C4×D312yes—
442C3⋊C8C2×D1212yes—
443C2×C32—21no—
444C2×C32C2×C4×D411yescharacteristic
445C3⋊D3—42no—
446C3×D3—22no—
447C3×D3—42no—
448#41—32no—
449#41—92no—
450#41—92no—
451#41—92no—
452#41—182no—
453#41—182no—
454C2×Q8—92no—
455C2×D4—92no—
456C2×D4—182no—
457C22×C4—31no—
458C22×C4—61no—
459C22×C4—182no—
460Q16—31no—
461Q16—92no—
462Q16—91no—
463SD16—32no—
464SD16—92no—
465SD16—92no—
466SD16—92no—
467D8—31no—
468D8—92no—
469D8—91no—
470M16—32no—
471M16—32no—
472M16—32no—
473M16—32no—
474M16—32no—
475M16—62no—
476M16—92no—
477M16—182no—
478M16—182no—
479M16—182no—
480M16—182no—
481C2×C8—31no—
482C2×C8—31no—
483C2×C8—62no—
484C2×C8—182no—
485C2×C8—182no—
486C2×C8—182no—
487C2×C8—182no—
488C2×C8C2×D3211yescharacteristic
489C2×C8C2×D3211yescharacteristic
490C42—31no—
491C42—61no—
492C42C2×D3211yescharacteristic
493C22×C3—21no—
494C22×C3—32no—
495C22×C3—62no—
496C22×C3—121no—
497C22×C3C2×#23511yescharacteristic
498C22×C3D3×#4111yescharacteristic
499C2×D3—22no—
500C2×D3—41no—
501C2×D3—62no—
502C2×D3—62no—
503C2×D3—122no—
504C2×D3—242no—
505C2×D3—242no—
506C2×D3C4×D1212yes—
507C3×C4—22no—
508C3×C4—22no—
509C3×C4—21no—
510C3×C4—21no—
511C3×C4—32no—
512C3×C4—42no—
513C3×C4—62no—
514C3×C4—121no—
515C3×C4C22×C4×D311yescharacteristic
516C3×C4C22×C4×D311yescharacteristic
517C3×C4C22×D1211yescharacteristic
518C3×C4C2×D3×D411yescharacteristic
519Dic3—22no—
520Dic3—41no—
521Dic3—62no—
522Dic3—62no—
523Dic3—122no—
524Dic3C4×D1212yes—
525C32#295611yescharacteristic, complemented, Sylow
526C23—31no—
527C23—182no—
528Q8—32no—
529Q8—92no—
530Q8—182no—
531D4—32no—
532D4—62no—
533D4—92no—
534D4—182no—
535D4—182no—
536D4—182no—
537D4—182no—
538C2×C4—21no—
539C2×C4—31no—
540C2×C4—32no—
541C2×C4—32no—
542C2×C4—62no—
543C2×C4—61no—
544C2×C4—122no—
545C2×C4—182no—
546C2×C4—182no—
547C2×C4—182no—
548C2×C4—182no—
549C2×C4C22×D3211yescharacteristic
550C8—32no—
551C8—32no—
552C8—62no—
553C8—182no—
554C8C4×D3211yescharacteristic
555C8C4×D3211yescharacteristic
556C8D3×D1211yescharacteristic
557C8D3×D1211yescharacteristic
558C2×C3—21no—
559C2×C3—21no—
560C2×C3—21no—
561C2×C3—41no—
562C2×C3—62no—
563C2×C3—122no—
564C2×C3C2×C4×D1211yescharacteristic
565C2×C3C4×D3×D411yescharacteristic
566D3—22no—
567D3—42no—
568D3—122no—
569D3—122no—
570D3—242no—
571C22—32no—
572C22—62no—
573C22—121no—
574C22—182no—
575C22—722no—
576C22D3×#23511yescharacteristic
577C4—22no—
578C4—32no—
579C4—62no—
580C4—121no—
581C4—182no—
582C4C2×C4×D3211yescharacteristic
583C4C2×D3×D1211yescharacteristic
584C3—21no—
585C3#7854111yescharacteristic, complemented
586C3#7988911yescharacteristic, complemented
587C2—21no—
588C2—62no—
589C2—122no—
590C2—362no—
591C2C4×D3×D1211yescharacteristic
subgroupG/H
centerC4C2×D3×D12
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC32×C4×C8C22
socleC2×C32C2×C4×D4
prime radical#10594676C2
cosocleC2×C32×C4C24
hypercenterC4×C8D32
hypocenterC32#2956
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C4 ◁ C2×C8 ◁ C4×C8

Complements

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

NH ≅ G/Ntype
2. #10594668C2semidirect
3. #10592399C2semidirect
4. C3×#4700C2semidirect
5. C3×C4×ΓL(1,𝔽25)C2semidirect
6. #10590924C2semidirect
7. #10590918C2semidirect
8. #10590916C2semidirect
9. #10590912C2semidirect
10. D3×#805C2semidirect
11. #10590341C2semidirect
16. #64110C22semidirect
18. C3×#901C22semidirect
23. #63817C22semidirect
24. #63814C22semidirect
28. #63801C4semidirect
29. #63800C4semidirect
30. #63795C4semidirect
31. #63794C4semidirect
34. C32×C4×C8C22semidirect
35. #63646C22semidirect
36. #63632C22semidirect
37. C3×#819C22semidirect
38. C3×#815C22semidirect
39. C3×#815C22semidirect
40. C3×#805C22semidirect
41. C3×C4×C3⋊C8C22semidirect
42. #63577C22semidirect
43. #63570C22semidirect
44. #63569C22semidirect
66. #4700D3semidirect
67. C4×ΓL(1,𝔽25)D3semidirect
84. #3746C2×C4semidirect
85. #3745C2×C4semidirect
86. #3744C2×C4semidirect
94. C3×Dic12C2×C4semidirect
95. C3×D24C2×C4semidirect
96. C3×#204C2×C4semidirect
103. #3719C2×C4semidirect
104. #3717C2×C4semidirect
105. #3716C2×C4semidirect
106. #3714C2×C4semidirect
151. #901C2×D3semidirect
162. C3×C4×C8C2×D3semidirect
163. C3×C4×C8C2×D3semidirect
171. #819C2×D3semidirect
172. #815C2×D3semidirect
173. #815C2×D3semidirect
179. #805C2×D3semidirect
180. C4×C3⋊C8C2×D3semidirect
292. Dic12C4×D3semidirect
297. D24C4×D3semidirect
303. #204C4×D3semidirect
367. C4×C8D32semidirect
525. C32#2956semidirect
585. C3#78541semidirect
586. C3#79889semidirect

Maximal subgroups

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

subgroupindex
#105946762
#105946682
#105923992
C3×#47002
C3×C4×ΓL(1,𝔽25)2
#105909242
#105909182
#105909162
#105909122
D3×#8052
#105903412
#798893
#785413