Finite Group Databasebeta

← #11861123

Subgroups — #11861123

Order 1152.

964 conjugacy classes of subgroups.

The subgroup lattice has 588 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D3×#907C212yesmaximal, complemented
2#10594676C211yesmaximal, characteristic
3#10592593C211yesmaximal, characteristic, complemented
4C3×#4895C211yesmaximal, characteristic, complemented
5C3×#4893C211yesmaximal, characteristic, complemented
6#10591005C212yesmaximal, complemented
7#10590995C212yesmaximal, complemented
8#10590978C212yesmaximal, complemented
9#10590920C211yesmaximal, characteristic, complemented
10#10590917C211yesmaximal, characteristic, complemented
11#10590908C211yesmaximal, characteristic, complemented
12#79888—31nomaximal
13#79257—31nomaximal
14D3×#235C2212yes—
15#64116C2212yescomplemented
16#64113C2211yescharacteristic
17C3×#907C2212yescomplemented
18C3×D3×M16C2212yes—
19C3×#904C2211yescharacteristic
20C2×C3×ΓL(1,𝔽25)C2211yescharacteristic
21#63855C2211yescharacteristic
22#63829C2212yes—
23#63817C2212yescomplemented
24#63815C2212yescomplemented
25C2×D3×C3⋊C8C2211yescharacteristic
26#63805—22no—
27#63804—22no—
28#63801C412yescomplemented
29#63800C412yescomplemented
30#63795C412yescomplemented
31#63794C412yescomplemented
32D3×ΓL(1,𝔽25)—22no—
33D32×C8—22no—
34C32×#108C2211yescharacteristic, complemented
35#63652C2212yescomplemented
36#63642C2211yescharacteristic, complemented
37C3×#825C2212yescomplemented
38C3×#822C2212yescomplemented
39C3×#819C2211yescharacteristic, complemented
40C3×C8×Dic3C2211yescharacteristic, complemented
41#63570C2212yescomplemented
42#63568C2212yescomplemented
43#63554C2211yescharacteristic, complemented
44#63553C2211yescharacteristic, complemented
45#5768—31no—
46D3×#131—32no—
47#5748—31no—
48C2×#907—32no—
49C3×#443—31no—
50C3×#430—31no—
51#5197—31no—
52#5144—32no—
53#5139—32no—
54#5122—31no—
55#4895—32no—
56#4895—31no—
57#4895D311yescharacteristic, complemented
58#4894—31no—
59#4894—31no—
60#4894—31no—
61#4894—32no—
62#4894—61no—
63#4893D311yescharacteristic, complemented
64#4823—32no—
65#4821—32no—
66#4700—31no—
67#4689—31no—
68#3828C2312yes—
69C3×#235C2312yes—
70C2×C3×C4×D3C2311yescharacteristic
71D3×#67—22no—
72#3804—22no—
73D3×D12C2×C412yes—
74C4×D32—22no—
75#3799C2×C412yes—
76#3798—22no—
77#3795C2×C412yes—
78D3×Dic6C2×C412yes—
79C32×M16C2312yes—
80C2×C32×C8C2311yescharacteristic
81C4×C3⋊Dic3C2311yescharacteristic
82C2×C3⋊(C3⋊C8)C2311yescharacteristic
83#3746C2×C411yescharacteristic
84#3745C2×C411yescharacteristic
85#3744C2×C412yes—
86#3743—22no—
87C8×C3⋊D3—22no—
88C3×C4×Dic3C2311yescharacteristic
89C3×#208C2312yes—
90C2×C3×C3⋊C8C2311yescharacteristic
91C2×C3×C3⋊C8C2311yescharacteristic
92C3×Dic12C2×C411yescharacteristic
93C3×D24C2×C411yescharacteristic
94C3×#204C2×C412yes—
95C3×ΓL(1,𝔽25)—22no—
96C3×ΓL(1,𝔽25)—22no—
97C3×ΓL(1,𝔽25)C2×C412yes—
98C3×ΓL(1,𝔽25)C2×C412yes—
99C3×D3×C8—22no—
100C3×D3×C8—22no—
101Dic3⋊Dic3—21no—
102(C2×D3)⋊Dic3—21no—
103#3719C2×C412yes—
104#3717C2×C412yes—
105#3716C2×C412yes—
106#3714C2×C412yes—
107#3712—22no—
108#3711—22no—
109#3710—22no—
110D3×C3⋊C8—22no—
111D3×C3⋊C8D412yes—
112D3×C3⋊C8D412yes—
113#2955—91noSylow
114D3×#41—32no—
115C2×#235—32no—
116C3×#135—31no—
117C3×#131—32no—
118C2×C3×M16—31no—
119C2×C3×M16—32no—
120#950—32no—
121#948—32no—
122#926—31no—
123C22×C3⋊C8—31no—
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—32no—
134#907—32no—
135#907—32no—
136#907—62no—
137#907—62no—
138#907—62no—
139#907—62no—
140#907C2×D312yescomplemented
141D3×M16—62no—
142D3×M16C2×D312yes—
143#904—32no—
144#904—31no—
145#904—31no—
146#904—61no—
147#904C2×D311yescharacteristic
148#901—32no—
149#901—62no—
150C2×ΓL(1,𝔽25)—62no—
151C2×ΓL(1,𝔽25)C2×D311yescharacteristic
152C2×D3×C8—31no—
153C2×D3×C8—62no—
154C2×D3×C8—62no—
155#872—31no—
156C3×#108—21no—
157C3×#108—32no—
158C3×#108—31no—
159C3×#108C2×D311yescharacteristic, complemented
160C3×#108C2×D311yescharacteristic, complemented
161C3×#104—32no—
162C3×C4×C8—31no—
163#837—32no—
164#825—32no—
165#825—32no—
166#825—32no—
167#825—32no—
168#825—62no—
169#825C2×D312yescomplemented
170#822C2×D312yescomplemented
171#819C2×D311yescharacteristic, complemented
172#815—31no—
173#815—31no—
174#815—31no—
175#815—61no—
176C8×Dic3—31no—
177C8×Dic3—31no—
178C8×Dic3C2×D311yescharacteristic, complemented
179#805—32no—
180#803—31no—
181C22×C3×D3#4111yescharacteristic
182C2×D32—22no—
183C2×C32×C4C2411yescharacteristic
184#638—22no—
185C2×C3⋊Dic3—21no—
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×D3C22×C412yes—
195C3×C4×D3C2×D412yes—
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)C2×D412yes—
208C3×C3⋊C8—22no—
209C3×C3⋊C8C22×C412yes—
210C3×C3⋊C8C2×D411yescharacteristic
211C3×C3⋊C8C2×D411yescharacteristic
212#575—91no—
213C2×#131—92no—
214#444—92no—
215#444—91no—
216#444—91no—
217#443—31no—
218#443—91no—
219#443—92no—
220#430—31no—
221#421—92no—
222#405—91no—
223C3×#41—32no—
224C22×C3×C4—31no—
225C2×#67—62no—
226#239—32no—
227D3×Q8—32no—
228#237—32no—
229#237—62no—
230D3×D4—32no—
231D3×D4—62no—
232#235—32no—
233#235—32no—
234#235—32no—
235#235—32no—
236#235—62no—
237#235—62no—
238#235—62no—
239#235—62no—
240#235C22×D312yes—
241C2×D12—32no—
242C2×C4×D3—62no—
243C2×C4×D3—62no—
244C2×C4×D3C22×D311yescharacteristic
245C2×Dic6—32no—
246C3×Q16—31no—
247C3×SD16—32no—
248C3×D8—31no—
249C3×M16—22no—
250C3×M16—32no—
251C3×M16—32no—
252C3×M16—32no—
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—
265#217—61no—
266#216—32no—
267#215—32no—
268#214—32no—
269#213—32no—
270(C2×D3)⋊C4—61no—
271C4⋊Dic3—61no—
272Dic3⋊C4—61no—
273C4×Dic3—31no—
274C4×Dic3—31no—
275C4×Dic3—61no—
276C4×Dic3C22×D311yescharacteristic
277#208—62no—
278#208C22×D312yes—
279C2×C3⋊C8—31no—
280C2×C3⋊C8—31no—
281C2×C3⋊C8—32no—
282C2×C3⋊C8—32no—
283C2×C3⋊C8—61no—
284C2×C3⋊C8—62no—
285C2×C3⋊C8C22×D311yescharacteristic
286C2×C3⋊C8C22×D311yescharacteristic
287Dic12—32no—
288Dic12—31no—
289Dic12—31no—
290Dic12—61no—
291Dic12C4×D311yescharacteristic
292D24—32no—
293D24—31no—
294D24—31no—
295D24—61no—
296D24C4×D311yescharacteristic
297#204—32no—
298#204—32no—
299#204—32no—
300#204—32no—
301#204—62no—
302#204C4×D312yes—
303ΓL(1,𝔽25)—22no—
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)—122no—
311ΓL(1,𝔽25)C4×D312yes—
312ΓL(1,𝔽25)C4×D312yes—
313D3×C8—22no—
314D3×C8—22no—
315D3×C8—32no—
316D3×C8—32no—
317D3×C8—62no—
318D3×C8—62no—
319D3×C8—62no—
320D3×C8—62no—
321D3×C8—62no—
322D3×C8—122no—
323C22×C32C2×#4111yescharacteristic
324C2×C3⋊D3—22no—
325C2×C3×D3—22no—
326C2×C3×D3—41no—
327C2×C3×D3C4×D412yes—
328D32—44no—
329C32×C4C23×C411yescharacteristic
330C32×C4C22×D411yescharacteristic
331C3⋊Dic3—22no—
332C3⋊Dic3—41no—
333C3×Dic3—22no—
334C3×Dic3—41no—
335C3×Dic3C4×D412yes—
336C2×#41—92no—
337#137—92no—
338#137—92no—
339AGL(1,ℤ/8)—92no—
340AGL(1,ℤ/8)—92no—
341#135—31no—
342#135—92no—
343#135—91no—
344#131—32no—
345#131—92no—
346#131—92no—
347#131—92no—
348#131—182no—
349#131—182no—
350C2×M16—31no—
351C2×M16—32no—
352C2×M16—182no—
353C22×C8—91no—
354C22×C8—182no—
355#117—91no—
356#108—32no—
357#108—31no—
358#108D3211yescharacteristic, complemented
359#104—32no—
360#104—92no—
361#104—92no—
362#104—92no—
363#97—91no—
364#97—91no—
365C4×C8—31no—
366C4×C8—91no—
367C23×C3—31no—
368C22×D3—62no—
369C22×D3—62no—
370C22×D3#23911yescharacteristic
371C3×Q8—32no—
372C3×D4—32no—
373C3×D4—62no—
374C2×C3×C4—21no—
375C2×C3×C4—31no—
376C2×C3×C4—32no—
377C2×C3×C4—32no—
378C2×C3×C4—62no—
379C2×C3×C4—61no—
380C2×C3×C4C23×D311yescharacteristic
381C2×C3×C4C23×D311yescharacteristic
382#67—22no—
383#67—62no—
384#67—62no—
385#67—62no—
386#67—62no—
387#67—62no—
388#67—62no—
389#67—122no—
390C2×Dic3—21no—
391C2×Dic3—62no—
392C2×Dic3—62no—
393C2×Dic3—61no—
394C2×Dic3—61no—
395C2×Dic3—121no—
396C2×Dic3#23911yescharacteristic
397D12—32no—
398D12—32no—
399D12—62no—
400D12—62no—
401D12—62no—
402D12C2×C4×D312yes—
403C4×D3—22no—
404C4×D3—62no—
405C4×D3—62no—
406C4×D3—62no—
407C4×D3—62no—
408C4×D3—62no—
409C4×D3—62no—
410C4×D3—122no—
411C4×D3C2×C4×D312yes—
412C4×D3D3×D412yes—
413Dic6—32no—
414Dic6—32no—
415Dic6—62no—
416Dic6—62no—
417Dic6—62no—
418Dic6C2×C4×D312yes—
419C3×C8—22no—
420C3×C8—22no—
421C3×C8—21no—
422C3×C8—21no—
423C3×C8—32no—
424C3×C8—31no—
425C3×C8—31no—
426C3×C8—42no—
427C3×C8—62no—
428C3×C8C2×C4×D311yescharacteristic
429C3×C8C2×C4×D311yescharacteristic
430C3×C8C2×C4×D311yescharacteristic
431C3×C8C2×C4×D311yescharacteristic
432C3⋊C8—22no—
433C3⋊C8—32no—
434C3⋊C8—32no—
435C3⋊C8—62no—
436C3⋊C8C2×C4×D312yes—
437C3⋊C8D3×D411yescharacteristic
438C3⋊C8D3×D411yescharacteristic
439C2×C32—21no—
440C2×C32C2×C4×D411yescharacteristic
441C3⋊D3—42no—
442C3×D3—22no—
443C3×D3—42no—
444#41—32no—
445#41—92no—
446#41—92no—
447#41—92no—
448#41—182no—
449#41—182no—
450C2×Q8—92no—
451C2×D4—92no—
452C2×D4—182no—
453C22×C4—31no—
454C22×C4—182no—
455Q16—31no—
456Q16—92no—
457Q16—91no—
458SD16—32no—
459SD16—92no—
460SD16—92no—
461SD16—92no—
462D8—31no—
463D8—92no—
464D8—91no—
465M16—32no—
466M16—32no—
467M16—32no—
468M16—62no—
469M16—62no—
470M16—182no—
471M16—182no—
472M16—182no—
473M16C2×D3212yes—
474C2×C8—31no—
475C2×C8—31no—
476C2×C8—62no—
477C2×C8—62no—
478C2×C8—92no—
479C2×C8—92no—
480C2×C8—91no—
481C2×C8—182no—
482C2×C8—182no—
483C2×C8—182no—
484C2×C8C2×D3211yescharacteristic
485C4⋊C4—181no—
486C22⋊C4—181no—
487C42—31no—
488C42—91no—
489C22×C3—21no—
490C22×C3—32no—
491C22×C3—62no—
492C22×C3—121no—
493C22×C3C2×#23911yescharacteristic
494C22×C3D3×#4111yescharacteristic
495C2×D3—22no—
496C2×D3—41no—
497C2×D3—62no—
498C2×D3—62no—
499C2×D3—122no—
500C2×D3—124no—
501C2×D3—124no—
502C2×D3#89312yes—
503C3×C4—21no—
504C3×C4—21no—
505C3×C4—32no—
506C3×C4—62no—
507C3×C4—121no—
508C3×C4C22×C4×D311yescharacteristic
509C3×C4C22×C4×D311yescharacteristic
510C3×C4C2×D3×D411yescharacteristic
511C3×C4C2×D3×D411yescharacteristic
512Dic3—22no—
513Dic3—41no—
514Dic3—62no—
515Dic3—62no—
516Dic3—122no—
517Dic3—121no—
518Dic3—121no—
519Dic3—241no—
520Dic3#89312yes—
521C32#295511yescharacteristic, complemented, Sylow
522C23—31no—
523C23—182no—
524Q8—32no—
525Q8—92no—
526Q8—182no—
527D4—32no—
528D4—62no—
529D4—92no—
530D4—182no—
531D4—182no—
532D4—182no—
533D4—182no—
534C2×C4—31no—
535C2×C4—32no—
536C2×C4—32no—
537C2×C4—62no—
538C2×C4—61no—
539C2×C4—182no—
540C2×C4—182no—
541C2×C4—182no—
542C2×C4—182no—
543C2×C4—181no—
544C2×C4C22×D3211yescharacteristic
545C8—22no—
546C8—32no—
547C8—31no—
548C8—31no—
549C8—62no—
550C8—92no—
551C8C4×D3211yescharacteristic
552C8C4×D3211yescharacteristic
553C2×C3—21no—
554C2×C3—21no—
555C2×C3—21no—
556C2×C3—41no—
557C2×C3—62no—
558C2×C3—122no—
559C2×C3C2×#89311yescharacteristic
560C2×C3C4×D3×D411yescharacteristic
561D3—22no—
562D3—42no—
563D3—122no—
564D3—122no—
565D3—242no—
566C22—32no—
567C22—62no—
568C22—121no—
569C22—182no—
570C22—364no—
571C22D3×#23911yescharacteristic
572C4—32no—
573C4—62no—
574C4—121no—
575C4—182no—
576C4—361no—
577C4C2×C4×D3211yescharacteristic
578C4D32×D411yescharacteristic
579C3—21no—
580C3#7925711yescharacteristic, complemented
581C3#7988811yescharacteristic, complemented
582C2—21no—
583C2—62no—
584C2—122no—
585C2—362no—
586C2D3×#89311yescharacteristic
subgroupG/H
centerC4D32×D4
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC32×#108C22
socleC2×C32C2×C4×D4
prime radical#10594676C2
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. D3×#907C2semidirect
3. #10592593C2semidirect
4. C3×#4895C2semidirect
5. C3×#4893C2semidirect
6. #10591005C2semidirect
7. #10590995C2semidirect
8. #10590978C2semidirect
9. #10590920C2semidirect
10. #10590917C2semidirect
11. #10590908C2semidirect
15. #64116C22semidirect
17. C3×#907C22semidirect
23. #63817C22semidirect
24. #63815C22semidirect
28. #63801C4semidirect
29. #63800C4semidirect
30. #63795C4semidirect
31. #63794C4semidirect
34. C32×#108C22semidirect
35. #63652C22semidirect
36. #63642C22semidirect
37. C3×#825C22semidirect
38. C3×#822C22semidirect
39. C3×#819C22semidirect
40. C3×C8×Dic3C22semidirect
41. #63570C22semidirect
42. #63568C22semidirect
43. #63554C22semidirect
44. #63553C22semidirect
57. #4895D3semidirect
63. #4893D3semidirect
140. #907C2×D3semidirect
159. C3×#108C2×D3semidirect
160. C3×#108C2×D3semidirect
169. #825C2×D3semidirect
170. #822C2×D3semidirect
171. #819C2×D3semidirect
178. C8×Dic3C2×D3semidirect
358. #108D32semidirect
521. C32#2955semidirect
580. C3#79257semidirect
581. C3#79888semidirect

Maximal subgroups

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

subgroupindex
D3×#9072
#105946762
#105925932
C3×#48952
C3×#48932
#105910052
#105909952
#105909782
#105909202
#105909172
#105909082
#798883
#792573