Finite Group Databasebeta

← #11861122

Subgroups — #11861122

Order 1152.

963 conjugacy classes of subgroups.

The subgroup lattice has 587 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10594707C212yesmaximal, complemented
2#10594685C211yesmaximal, characteristic
3#10592592C211yesmaximal, characteristic, complemented
4C3×#4895C211yesmaximal, characteristic, complemented
5C3×#4894C211yesmaximal, characteristic, complemented
6#10591009C212yesmaximal, complemented
7#10590976C212yesmaximal, complemented
8#10590975C212yesmaximal, complemented
9#10590916C211yesmaximal, characteristic, complemented
10#10590915C211yesmaximal, characteristic, complemented
11#10590910C211yesmaximal, characteristic, complemented
12#79897—31nomaximal
13#79888—31nomaximal
14#64306C2212yes—
15M16×C3⋊D3C2212yes—
16C2×#3743C2211yescharacteristic
17C3×#907C2212yescomplemented
18C3×#907C2212yescomplemented
19C3×#904C2211yescharacteristic
20C3×#904C2211yescharacteristic
21#63874C2211yescharacteristic
22#63822C2212yes—
23C2×#3710C2211yescharacteristic
24#63814C2212yescomplemented
25#63814C2212yescomplemented
26#63811C412yescomplemented
27#63811C412yescomplemented
28#63804—22no—
29#63804—22no—
30#63798C412yescomplemented
31#63798C412yescomplemented
32#63791—22no—
33D32×C8—22no—
34C32×#108C2211yescharacteristic, complemented
35#63649C2212yescomplemented
36#63646C2211yescharacteristic, complemented
37C3×#825C2212yescomplemented
38C3×#825C2212yescomplemented
39C3×#815C2211yescharacteristic, complemented
40C3×C8×Dic3C2211yescharacteristic, complemented
41#63569C2212yescomplemented
42#63569C2212yescomplemented
43#63554C2211yescharacteristic, complemented
44Dic3×C3⋊C8C2211yescharacteristic, complemented
45#5768—31no—
46#5768—31no—
47D3×#131—32no—
48D3×#131—32no—
49C3×#444—31no—
50C3×#443—31no—
51#5197—31no—
52#5196—31no—
53#5145—32no—
54#5144—32no—
55#4895D311yescharacteristic, complemented
56#4894D311yescharacteristic, complemented
57#4893—31no—
58#4893—31no—
59#4893—61no—
60#4824—32no—
61#4823—32no—
62#4821—32no—
63#4821—32no—
64#4717—31no—
65#4708—31no—
66#4700—31no—
67#4689—31no—
68C2×C4×C3⋊D3C2311yescharacteristic
69C3×#235C2312yes—
70C3×#235C2312yes—
71#3811—22no—
72#3805—22no—
73#3802C2×C412yes—
74C4×D32—22no—
75#3798—22no—
76#3797C2×C412yes—
77#3796C2×C412yes—
78#3796C2×C412yes—
79C32×M16C2312yes—
80C2×C32×C8C2311yescharacteristic
81#3748C2312yes—
82C2×C3⋊(C3⋊C8)C2311yescharacteristic
83#3743—22no—
84#3743C2×C412yes—
85#3743C2×C412yes—
86C8×C3⋊D3—22no—
87C3×C4×Dic3C2311yescharacteristic
88C3×C4×Dic3C2311yescharacteristic
89C2×C3×C3⋊C8C2311yescharacteristic
90C2×C3×C3⋊C8C2311yescharacteristic
91C3×Dic12C2×C411yescharacteristic
92C3×Dic12C2×C411yescharacteristic
93C3×D24C2×C411yescharacteristic
94C3×D24C2×C411yescharacteristic
95C3×#204C2×C412yes—
96C3×#204C2×C412yes—
97C3×ΓL(1,𝔽25)—22no—
98C3×ΓL(1,𝔽25)—22no—
99C3×D3×C8—22no—
100C3×D3×C8—22no—
101#3724—21no—
102#3722—21no—
103#3718C2×C412yes—
104#3715C2×C412yes—
105#3715C2×C412yes—
106#3713C2×C412yes—
107#3711—22no—
108#3711—22no—
109#3710D412yes—
110#3710D412yes—
111D3×C3⋊C8—22no—
112D3×C3⋊C8—22no—
113#2955—91noSylow
114D3×#41—32no—
115D3×#41—32no—
116C3×#135—31no—
117C3×#135—31no—
118C3×#131—32no—
119C3×#131—32no—
120#950—32no—
121#950—32no—
122#948—32no—
123#948—32no—
124#918—32no—
125#918—32no—
126#915—32no—
127#915—32no—
128#914—32no—
129#914—32no—
130#911—32no—
131#911—32no—
132#907—62no—
133#907—62no—
134#907C2×D312yescomplemented
135#907C2×D312yescomplemented
136D3×M16—32no—
137D3×M16—32no—
138D3×M16—62no—
139D3×M16—62no—
140D3×M16—62no—
141#904C2×D311yescharacteristic
142#904C2×D311yescharacteristic
143#901—32no—
144#901—32no—
145#901—62no—
146#901—62no—
147C2×ΓL(1,𝔽25)—31no—
148C2×ΓL(1,𝔽25)—31no—
149C2×ΓL(1,𝔽25)—61no—
150C2×D3×C8—31no—
151C2×D3×C8—31no—
152C2×D3×C8—62no—
153C2×D3×C8—62no—
154#872—31no—
155#872—31no—
156C3×#108—21no—
157C3×#108C2×D311yescharacteristic, complemented
158C3×#108C2×D311yescharacteristic, complemented
159C3×#104—32no—
160C3×#104—32no—
161C3×#97—31no—
162C3×C4×C8—31no—
163#837—32no—
164#837—32no—
165#825C2×D312yescomplemented
166#825C2×D312yescomplemented
167#822—32no—
168#822—32no—
169#822—62no—
170#819—31no—
171#819—31no—
172#819—61no—
173#815—31no—
174#815C2×D311yescharacteristic, complemented
175C8×Dic3—31no—
176C8×Dic3C2×D311yescharacteristic, complemented
177#805—32no—
178#805—32no—
179#803—31no—
180C4×C3⋊C8—31no—
181C22×C3⋊D3#4111yescharacteristic
182C2×D32—22no—
183C2×C32×C4C2411yescharacteristic
184C2×C3⋊Dic3#4111yescharacteristic
185C4×C3⋊D3C22×C412yes—
186C4×C3⋊D3C2×D412yes—
187C3×#67—22no—
188C3×#67—22no—
189C2×C3×Dic3—21no—
190C2×C3×Dic3—21no—
191C3×D12C22×C412yes—
192C3×D12C22×C412yes—
193C3×C4×D3—22no—
194C3×C4×D3—22no—
195C3×Dic6C22×C412yes—
196C3×Dic6C22×C412yes—
197#627—22no—
198#626—22no—
199#626—22no—
200#625—22no—
201#624—22no—
202D3×Dic3—22no—
203D3×Dic3—22no—
204C32×C8—22no—
205C32×C8C22×C411yescharacteristic
206C32×C8C22×C411yescharacteristic
207C3⋊(C3⋊C8)—22no—
208C3⋊(C3⋊C8)C22×C412yes—
209C3×C3⋊C8C2×D411yescharacteristic
210C3×C3⋊C8C2×D412yes—
211C3×C3⋊C8C2×D411yescharacteristic
212#575—91no—
213C2×#131—92no—
214#444—31no—
215#444—91no—
216#444—92no—
217#443—31no—
218#443—91no—
219#443—92no—
220#430—91no—
221#421—92no—
222#405—91no—
223C3×#41—32no—
224C3×#41—32no—
225#239—32no—
226#239—32no—
227D3×Q8—32no—
228D3×Q8—32no—
229#237—32no—
230#237—32no—
231#237—62no—
232#237—62no—
233D3×D4—32no—
234D3×D4—32no—
235D3×D4—62no—
236D3×D4—62no—
237#235—62no—
238#235—62no—
239#235C22×D312yes—
240#235C22×D312yes—
241C2×C4×D3—31no—
242C2×C4×D3—31no—
243C2×C4×D3—61no—
244C2×C4×D3—62no—
245C2×C4×D3—62no—
246C3×Q16—31no—
247C3×Q16—31no—
248C3×SD16—32no—
249C3×SD16—32no—
250C3×D8—31no—
251C3×D8—31no—
252C3×M16—22no—
253C3×M16—62no—
254C3×M16—62no—
255C3×M16C22×D312yes—
256C3×M16C22×D312yes—
257C2×C3×C8—21no—
258C2×C3×C8—31no—
259C2×C3×C8—31no—
260C2×C3×C8—62no—
261C2×C3×C8—62no—
262C2×C3×C8C22×D311yescharacteristic
263C2×C3×C8C22×D311yescharacteristic
264C3×C42—31no—
265C3×C42—31no—
266#216—32no—
267#216—32no—
268#215—32no—
269#215—32no—
270#214—32no—
271#214—32no—
272#213—32no—
273#213—32no—
274(C2×D3)⋊C4—61no—
275(C2×D3)⋊C4—61no—
276Dic3⋊C4—61no—
277Dic3⋊C4—61no—
278C4×Dic3C22×D311yescharacteristic
279C4×Dic3C22×D311yescharacteristic
280#208—32no—
281#208—32no—
282#208—62no—
283#208—62no—
284#208—62no—
285C2×C3⋊C8—31no—
286C2×C3⋊C8—31no—
287C2×C3⋊C8—61no—
288C2×C3⋊C8—62no—
289C2×C3⋊C8—62no—
290C2×C3⋊C8C22×D311yescharacteristic
291C2×C3⋊C8C22×D311yescharacteristic
292Dic12C4×D311yescharacteristic
293Dic12C4×D311yescharacteristic
294D24C4×D311yescharacteristic
295D24C4×D311yescharacteristic
296#204C4×D312yes—
297#204C4×D312yes—
298ΓL(1,𝔽25)—22no—
299ΓL(1,𝔽25)—22no—
300ΓL(1,𝔽25)—32no—
301ΓL(1,𝔽25)—32no—
302ΓL(1,𝔽25)—32no—
303ΓL(1,𝔽25)—32no—
304ΓL(1,𝔽25)—62no—
305ΓL(1,𝔽25)—62no—
306ΓL(1,𝔽25)—62no—
307ΓL(1,𝔽25)—62no—
308ΓL(1,𝔽25)—62no—
309ΓL(1,𝔽25)—62no—
310ΓL(1,𝔽25)—122no—
311D3×C8—22no—
312D3×C8—22no—
313D3×C8—32no—
314D3×C8—32no—
315D3×C8—32no—
316D3×C8—32no—
317D3×C8—62no—
318D3×C8—62no—
319D3×C8—62no—
320D3×C8—62no—
321D3×C8—122no—
322C22×C32C2×#4111yescharacteristic
323C2×C3⋊D3—41no—
324C2×C3⋊D3C4×D412yes—
325C2×C3×D3—22no—
326C2×C3×D3—22no—
327D32—44no—
328C32×C4C23×C411yescharacteristic
329C32×C4C22×D411yescharacteristic
330C3⋊Dic3C4×D412yes—
331C3×Dic3—22no—
332C3×Dic3—22no—
333C3×Dic3—41no—
334C3×Dic3—41no—
335C2×#41—92no—
336#137—92no—
337#137—92no—
338AGL(1,ℤ/8)—92no—
339AGL(1,ℤ/8)—92no—
340#135—31no—
341#135—31no—
342#135—92no—
343#131—32no—
344#131—32no—
345#131—92no—
346#131—92no—
347#131—182no—
348#131—182no—
349C2×M16—91no—
350C2×M16—92no—
351C2×M16—182no—
352C22×C8—91no—
353C22×C8—182no—
354#117—91no—
355#108—92no—
356#108—91no—
357#108D3211yescharacteristic, complemented
358#104—32no—
359#104—32no—
360#104—92no—
361#104—92no—
362#97—31no—
363#97—91no—
364C4×C8—31no—
365C4×C8—91no—
366C22×D3—31no—
367C22×D3—31no—
368C22×D3—61no—
369C22×D3—62no—
370C22×D3—62no—
371C3×Q8—32no—
372C3×Q8—32no—
373C3×D4—32no—
374C3×D4—32no—
375C3×D4—62no—
376C3×D4—62no—
377C2×C3×C4—21no—
378C2×C3×C4—62no—
379C2×C3×C4—62no—
380C2×C3×C4—61no—
381C2×C3×C4—61no—
382C2×C3×C4C23×D311yescharacteristic
383C2×C3×C4C23×D311yescharacteristic
384#67—22no—
385#67—22no—
386#67—62no—
387#67—62no—
388#67—62no—
389#67—62no—
390C2×Dic3—21no—
391C2×Dic3—21no—
392C2×Dic3—31no—
393C2×Dic3—31no—
394C2×Dic3—61no—
395C2×Dic3—62no—
396C2×Dic3—62no—
397D12—62no—
398D12—62no—
399D12C2×C4×D312yes—
400D12C2×C4×D312yes—
401C4×D3—22no—
402C4×D3—22no—
403C4×D3—32no—
404C4×D3—32no—
405C4×D3—32no—
406C4×D3—32no—
407C4×D3—62no—
408C4×D3—62no—
409C4×D3—62no—
410C4×D3—62no—
411C4×D3—62no—
412C4×D3—62no—
413Dic6—62no—
414Dic6—62no—
415Dic6C2×C4×D312yes—
416Dic6C2×C4×D312yes—
417C3×C8—22no—
418C3×C8—22no—
419C3×C8—21no—
420C3×C8—21no—
421C3×C8—31no—
422C3×C8—32no—
423C3×C8—31no—
424C3×C8—42no—
425C3×C8C2×C4×D311yescharacteristic
426C3×C8C2×C4×D311yescharacteristic
427C3×C8C2×C4×D311yescharacteristic
428C3×C8C2×C4×D311yescharacteristic
429C3⋊C8—32no—
430C3⋊C8—32no—
431C3⋊C8—62no—
432C3⋊C8—62no—
433C3⋊C8—62no—
434C3⋊C8—122no—
435C3⋊C8D3×D411yescharacteristic
436C3⋊C8D3×D412yes—
437C3⋊C8D3×D411yescharacteristic
438C2×C32—21no—
439C2×C32C2×C4×D411yescharacteristic
440C3⋊D3—22no—
441C3×D3—42no—
442C3×D3—42no—
443#41—32no—
444#41—32no—
445#41—92no—
446#41—92no—
447#41—182no—
448#41—182no—
449C2×Q8—92no—
450C2×D4—92no—
451C2×D4—182no—
452C22×C4—91no—
453C22×C4—182no—
454Q16—31no—
455Q16—31no—
456Q16—92no—
457SD16—32no—
458SD16—32no—
459SD16—92no—
460SD16—92no—
461D8—31no—
462D8—31no—
463D8—92no—
464M16—62no—
465M16—62no—
466M16—92no—
467M16—92no—
468M16—92no—
469M16—182no—
470M16—182no—
471M16—182no—
472M16C2×D3212yes—
473C2×C8—31no—
474C2×C8—31no—
475C2×C8—62no—
476C2×C8—62no—
477C2×C8—92no—
478C2×C8—92no—
479C2×C8—91no—
480C2×C8—182no—
481C2×C8—182no—
482C2×C8—182no—
483C2×C8C2×D3211yescharacteristic
484C4⋊C4—181no—
485C22⋊C4—181no—
486C42—31no—
487C42—31no—
488C22×C3—21no—
489C22×C3—62no—
490C22×C3—62no—
491C22×C3D3×#4111yescharacteristic
492C22×C3D3×#4111yescharacteristic
493C2×D3—22no—
494C2×D3—22no—
495C2×D3—32no—
496C2×D3—32no—
497C2×D3—62no—
498C2×D3—124no—
499C2×D3—124no—
500C2×D3—121no—
501C2×D3—121no—
502C2×D3—241no—
503C3×C4—21no—
504C3×C4—21no—
505C3×C4—62no—
506C3×C4—62no—
507C3×C4—121no—
508C3×C4—121no—
509C3×C4C22×C4×D311yescharacteristic
510C3×C4C22×C4×D311yescharacteristic
511C3×C4C2×D3×D411yescharacteristic
512C3×C4C2×D3×D411yescharacteristic
513Dic3—22no—
514Dic3—22no—
515Dic3—32no—
516Dic3—32no—
517Dic3—41no—
518Dic3—41no—
519Dic3—62no—
520C32#295511yescharacteristic, complemented, Sylow
521C23—91no—
522C23—182no—
523Q8—32no—
524Q8—32no—
525Q8—182no—
526D4—32no—
527D4—32no—
528D4—62no—
529D4—62no—
530D4—182no—
531D4—182no—
532D4—182no—
533C2×C4—62no—
534C2×C4—62no—
535C2×C4—61no—
536C2×C4—61no—
537C2×C4—91no—
538C2×C4—92no—
539C2×C4—92no—
540C2×C4—182no—
541C2×C4—182no—
542C2×C4—182no—
543C2×C4C22×D3211yescharacteristic
544C8—22no—
545C8—31no—
546C8—32no—
547C8—31no—
548C8—92no—
549C8—182no—
550C8C4×D3211yescharacteristic
551C8C4×D3211yescharacteristic
552C2×C3—21no—
553C2×C3—21no—
554C2×C3—21no—
555C2×C3—41no—
556C2×C3—122no—
557C2×C3—122no—
558C2×C3C4×D3×D411yescharacteristic
559C2×C3C4×D3×D411yescharacteristic
560D3—42no—
561D3—42no—
562D3—62no—
563D3—62no—
564D3—122no—
565C22—62no—
566C22—62no—
567C22—92no—
568C22—361no—
569C22—364no—
570C22#6431911yescharacteristic
571C4—62no—
572C4—62no—
573C4—92no—
574C4—121no—
575C4—121no—
576C4C2×C4×D3211yescharacteristic
577C4D32×D411yescharacteristic
578C3—21no—
579C3#7988811yescharacteristic, complemented
580C3#7989711yescharacteristic, complemented
581C2—21no—
582C2—122no—
583C2—122no—
584C2—182no—
585C2#1059460511yescharacteristic
subgroupG/H
centerC4D32×D4
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC32×#108C22
socleC2×C32C2×C4×D4
prime radical#10594685C2
cosocleC2×C32×C4C24
hypercenter#108D32
hypocenterC32#2955
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C4 ◁ C2×C4 ◁ #108

Complements

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

NH ≅ G/Ntype
1. #10594707C2semidirect
3. #10592592C2semidirect
4. C3×#4895C2semidirect
5. C3×#4894C2semidirect
6. #10591009C2semidirect
7. #10590976C2semidirect
8. #10590975C2semidirect
9. #10590916C2semidirect
10. #10590915C2semidirect
11. #10590910C2semidirect
17. C3×#907C22semidirect
18. C3×#907C22semidirect
24. #63814C22semidirect
25. #63814C22semidirect
26. #63811C4semidirect
27. #63811C4semidirect
30. #63798C4semidirect
31. #63798C4semidirect
34. C32×#108C22semidirect
35. #63649C22semidirect
36. #63646C22semidirect
37. C3×#825C22semidirect
38. C3×#825C22semidirect
39. C3×#815C22semidirect
40. C3×C8×Dic3C22semidirect
41. #63569C22semidirect
42. #63569C22semidirect
43. #63554C22semidirect
44. Dic3×C3⋊C8C22semidirect
55. #4895D3semidirect
56. #4894D3semidirect
134. #907C2×D3semidirect
135. #907C2×D3semidirect
157. C3×#108C2×D3semidirect
158. C3×#108C2×D3semidirect
165. #825C2×D3semidirect
166. #825C2×D3semidirect
174. #815C2×D3semidirect
176. C8×Dic3C2×D3semidirect
357. #108D32semidirect
520. C32#2955semidirect
579. C3#79888semidirect
580. C3#79897semidirect

Maximal subgroups

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

subgroupindex
#105947072
#105946852
#105925922
C3×#48952
C3×#48942
#105910092
#105909762
#105909752
#105909162
#105909152
#105909102
#798973
#798883