Finite Group Databasebeta

← #11861103

Subgroups — #11861103

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
1C3×#5768C211yesmaximal, characteristic
2D3×#948C212yesmaximal, complemented
3#10592896C211yesmaximal, characteristic, complemented
4C3×#5196C211yesmaximal, characteristic, complemented
5#10591676C212yesmaximal, complemented
6#10591673C212yesmaximal, complemented
7#10591670C212yesmaximal, complemented
8#10590920C211yesmaximal, characteristic, complemented
9#10590915C211yesmaximal, characteristic, complemented
10#10590912C211yesmaximal, characteristic, complemented
11#10590908C211yesmaximal, characteristic, complemented
12#83999—31nomaximal
13#79888—31nomaximal
14C3×D3×#41C2212yes—
15C32×#135C2211yescharacteristic
16#64157C2212yescomplemented
17C3×#950C2212yes—
18C3×#948C2212yescomplemented
19C3×#918C412yescomplemented
20C3×#915C412yescomplemented
21C3×#914C412yescomplemented
22C3×#911C412yescomplemented
23C3×#904C2211yescharacteristic
24C2×C3×ΓL(1,𝔽25)C2211yescharacteristic
25#63855C2211yescharacteristic
26#63815—22no—
27#63815C2212yescomplemented
28#63814—22no—
29#63814C2212yescomplemented
30D3×#208—22no—
31D3×#208C2212yes—
32C2×D3×C3⋊C8—22no—
33C2×D3×C3⋊C8C2211yescharacteristic
34#63664C2212yescomplemented
35#63646C2211yescharacteristic, complemented
36#63642C2211yescharacteristic, complemented
37C3×#837C2212yescomplemented
38C3×#819C2211yescharacteristic, complemented
39C3×C8×Dic3C2211yescharacteristic, complemented
40#63577C2212yescomplemented
41#63569C2212yescomplemented
42#63568C2212yescomplemented
43#63554C2211yescharacteristic, complemented
44#63553C2211yescharacteristic, complemented
45C3×#575—31no—
46C2×#948—32no—
47#5768D311yescharacteristic
48D3×#131—32no—
49C3×#443—31no—
50#5236—32no—
51#5197—31no—
52#5197—31no—
53#5197—32no—
54#5197—31no—
55#5197—61no—
56#5196—32no—
57#5196—31no—
58#5196D311yescharacteristic, complemented
59#5144—32no—
60#5125—31no—
61#5122—31no—
62#4894—31no—
63#4893—31no—
64#4823—32no—
65#4821—32no—
66#4700—31no—
67#4689—31no—
68C32×#41C2312yes—
69C3×#239C2×C412yes—
70C3×D3×Q8C2×C412yes—
71C3×#237—22no—
72C3×#237C2×C412yes—
73C3×D3×D4—22no—
74C3×D3×D4C2×C412yes—
75C3×#235—22no—
76C3×#235C2312yes—
77C2×C3×C4×D3—22no—
78C2×C3×C4×D3C2311yescharacteristic
79C32×Q16C2×C411yescharacteristic
80C32×SD16C2×C412yes—
81C32×D8C2×C411yescharacteristic
82C2×C32×C8C2311yescharacteristic
83C4×C3⋊Dic3C2311yescharacteristic
84#3748—22no—
85#3748C2312yes—
86C2×C3⋊(C3⋊C8)—22no—
87C2×C3⋊(C3⋊C8)C2311yescharacteristic
88C3×#216C2×C412yes—
89C3×#215C2×C412yes—
90C3×#214C2×C412yes—
91C3×#213C2×C412yes—
92C3×C4×Dic3C2311yescharacteristic
93C3×#208—22no—
94C3×#208C2312yes—
95C2×C3×C3⋊C8—22no—
96C2×C3×C3⋊C8C2311yescharacteristic
97C2×C3×C3⋊C8C2311yescharacteristic
98C3×Dic12C2×C411yescharacteristic
99C3×D24C2×C411yescharacteristic
100C3×#204C2×C412yes—
101C3×ΓL(1,𝔽25)C2×C412yes—
102C3×ΓL(1,𝔽25)C2×C412yes—
103Dic3⋊Dic3—21no—
104(C2×D3)⋊Dic3—21no—
105#3711—22no—
106#3711—22no—
107#3711—22no—
108D3×C3⋊C8—22no—
109D3×C3⋊C8—22no—
110D3×C3⋊C8—22no—
111D3×C3⋊C8D412yes—
112D3×C3⋊C8D412yes—
113#2955—91noSylow
114C2×C3×#41—32no—
115D3×#41C2×D312yes—
116C3×#137—32no—
117C3×#137—32no—
118C3×AGL(1,ℤ/8)—32no—
119C3×AGL(1,ℤ/8)—32no—
120C3×#135—21no—
121C3×#135—32no—
122C3×#135—31no—
123C3×#135C2×D311yescharacteristic
124C3×#135C2×D311yescharacteristic
125C3×#131—32no—
126C2×C3×M16—31no—
127#950C2×D312yes—
128#948—32no—
129#948—32no—
130#948—32no—
131#948—32no—
132#948—62no—
133#948—62no—
134#948—62no—
135#948C2×D312yescomplemented
136#926—31no—
137C2×#208—32no—
138C2×#208—62no—
139C22×C3⋊C8—31no—
140C22×C3⋊C8—62no—
141#918Dic312yescomplemented
142#915Dic312yescomplemented
143#914Dic312yescomplemented
144#911Dic312yescomplemented
145#907—32no—
146#907—62no—
147D3×M16—32no—
148D3×M16—62no—
149#904C2×D311yescharacteristic
150#901—32no—
151#901—62no—
152C2×ΓL(1,𝔽25)C2×D311yescharacteristic
153C2×D3×C8—31no—
154C2×D3×C8—62no—
155#872—31no—
156C3×#108—31no—
157C3×#104—32no—
158C3×C4×C8—31no—
159#837—32no—
160#837—32no—
161#837—32no—
162#837—32no—
163#837—62no—
164#837C2×D312yescomplemented
165#825—32no—
166#822—32no—
167#819—31no—
168#819—31no—
169#819—32no—
170#819—61no—
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—22no—
182C22×C3×D3#4111yescharacteristic
183C32×Q8C22×C412yes—
184C32×D4—22no—
185C32×D4C22×C412yes—
186C2×C32×C4—22no—
187C2×C32×C4C2411yescharacteristic
188C2×C3⋊Dic3—21no—
189C3×#67—22no—
190C3×#67—22no—
191C3×#67—22no—
192C2×C3×Dic3—22no—
193C2×C3×Dic3—21no—
194C2×C3×Dic3#4111yescharacteristic
195C3×D12—22no—
196C3×D12C22×C412yes—
197C3×C4×D3—22no—
198C3×C4×D3—22no—
199C3×C4×D3—22no—
200C3×C4×D3C22×C412yes—
201C3×C4×D3C2×D412yes—
202C3×Dic6—22no—
203C3×Dic6C22×C412yes—
204C32×C8C22×C411yescharacteristic
205C32×C8C22×C411yescharacteristic
206C3⋊(C3⋊C8)—22no—
207C3⋊(C3⋊C8)C2×D412yes—
208C3×C3⋊C8—22no—
209C3×C3⋊C8C22×C412yes—
210C3×C3⋊C8C2×D411yescharacteristic
211C3×C3⋊C8C2×D411yescharacteristic
212#575—31no—
213C2×#131—92no—
214#444—92no—
215#444—91no—
216#444—91no—
217#443—31no—
218#443—91no—
219#443—92no—
220#430—91no—
221#421—92no—
222#405—91no—
223C3×#41—22no—
224C3×#41—32no—
225C3×#41—32no—
226C3×#41—32no—
227C3×#41—62no—
228C3×#41—62no—
229C3×#41C22×D312yes—
230C3×#41C22×D312yes—
231C2×C3×Q8—32no—
232C2×C3×D4—32no—
233C2×C3×D4—62no—
234C22×C3×C4—31no—
235C22×C3×C4—62no—
236#239C2×Dic312yes—
237D3×Q8C2×Dic312yes—
238#237—22no—
239#237C2×Dic312yes—
240D3×D4—22no—
241D3×D4C2×Dic312yes—
242#235—22no—
243#235C22×D312yes—
244C2×C4×D3—22no—
245C2×C4×D3C22×D311yescharacteristic
246C3×Q16—21no—
247C3×Q16—32no—
248C3×Q16—31no—
249C3×Q16C4×D311yescharacteristic
250C3×Q16C2×Dic311yescharacteristic
251C3×SD16—22no—
252C3×SD16—32no—
253C3×SD16—32no—
254C3×SD16—32no—
255C3×SD16C4×D312yes—
256C3×SD16C2×Dic312yes—
257C3×D8—21no—
258C3×D8—32no—
259C3×D8—31no—
260C3×D8C4×D311yescharacteristic
261C3×D8C2×Dic311yescharacteristic
262C3×M16—32no—
263C3×M16—32no—
264C3×M16—32no—
265C3×M16—62no—
266C2×C3×C8—21no—
267C2×C3×C8—31no—
268C2×C3×C8—31no—
269C2×C3×C8—62no—
270C2×C3×C8C22×D311yescharacteristic
271C2×C3×C8C22×D311yescharacteristic
272C3×C42—31no—
273#217—61no—
274#216C2×Dic312yes—
275#215C2×Dic312yes—
276#214C2×Dic312yes—
277#213C2×Dic312yes—
278(C2×D3)⋊C4—61no—
279C4⋊Dic3—61no—
280Dic3⋊C4—61no—
281C4×Dic3—31no—
282C4×Dic3—31no—
283C4×Dic3—61no—
284C4×Dic3C22×D311yescharacteristic
285#208—22no—
286#208—32no—
287#208—32no—
288#208—62no—
289#208—62no—
290#208—62no—
291#208—62no—
292#208—62no—
293#208—62no—
294#208—122no—
295#208C22×D312yes—
296C2×C3⋊C8—22no—
297C2×C3⋊C8—31no—
298C2×C3⋊C8—31no—
299C2×C3⋊C8—32no—
300C2×C3⋊C8—32no—
301C2×C3⋊C8—61no—
302C2×C3⋊C8—62no—
303C2×C3⋊C8—62no—
304C2×C3⋊C8—62no—
305C2×C3⋊C8—62no—
306C2×C3⋊C8—62no—
307C2×C3⋊C8—122no—
308C2×C3⋊C8C22×D311yescharacteristic
309C2×C3⋊C8C22×D311yescharacteristic
310Dic12C2×Dic311yescharacteristic
311D24C2×Dic311yescharacteristic
312#204C2×Dic312yes—
313ΓL(1,𝔽25)—62no—
314ΓL(1,𝔽25)—62no—
315ΓL(1,𝔽25)—62no—
316ΓL(1,𝔽25)C2×Dic312yes—
317ΓL(1,𝔽25)C2×Dic312yes—
318D3×C8—32no—
319D3×C8—32no—
320D3×C8—62no—
321D3×C8—62no—
322D3×C8—62no—
323C22×C32—22no—
324C22×C32C2×#4111yescharacteristic
325C2×C3×D3—22no—
326C2×C3×D3—41no—
327C2×C3×D3—44no—
328C2×C3×D3C4×D412yes—
329C32×C4—22no—
330C32×C4C23×C411yescharacteristic
331C32×C4C22×D411yescharacteristic
332C3⋊Dic3—41no—
333C3×Dic3—22no—
334C3×Dic3—41no—
335C3×Dic3C4×D412yes—
336C2×#41—32no—
337#137—32no—
338#137—32no—
339AGL(1,ℤ/8)—32no—
340AGL(1,ℤ/8)—32no—
341#135—32no—
342#135—31no—
343#135D3211yescharacteristic
344#131—32no—
345#131—92no—
346#131—92no—
347#131—92no—
348#131—182no—
349#131—182no—
350C2×M16—31no—
351C2×M16—92no—
352C2×M16—182no—
353C22×C8—91no—
354C22×C8—182no—
355#117—91no—
356#108—31no—
357#108—92no—
358#108—91no—
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—
368C23×C3—62no—
369C22×D3—22no—
370C22×D3#23711yescharacteristic
371C3×Q8—22no—
372C3×Q8—32no—
373C3×Q8—62no—
374C3×Q8C2×C4×D312yes—
375C3×Q8C22×Dic312yes—
376C3×D4—22no—
377C3×D4—22no—
378C3×D4—22no—
379C3×D4—32no—
380C3×D4—42no—
381C3×D4—62no—
382C3×D4—62no—
383C3×D4—62no—
384C3×D4—62no—
385C3×D4C2×C4×D312yes—
386C3×D4C22×Dic312yes—
387C2×C3×C4—22no—
388C2×C3×C4—22no—
389C2×C3×C4—21no—
390C2×C3×C4—31no—
391C2×C3×C4—32no—
392C2×C3×C4—32no—
393C2×C3×C4—42no—
394C2×C3×C4—62no—
395C2×C3×C4—62no—
396C2×C3×C4—62no—
397C2×C3×C4—62no—
398C2×C3×C4—61no—
399C2×C3×C4C23×D311yescharacteristic
400C2×C3×C4C23×D311yescharacteristic
401#67—22no—
402#67—22no—
403#67—22no—
404C2×Dic3—22no—
405C2×Dic3—21no—
406C2×Dic3—61no—
407C2×Dic3—61no—
408C2×Dic3—121no—
409C2×Dic3#23711yescharacteristic
410D12—22no—
411D12C22×Dic312yes—
412C4×D3—22no—
413C4×D3—22no—
414C4×D3—22no—
415C4×D3D3×D412yes—
416C4×D3C22×Dic312yes—
417Dic6—22no—
418Dic6C22×Dic312yes—
419C3×C8—21no—
420C3×C8—21no—
421C3×C8—32no—
422C3×C8—31no—
423C3×C8—31no—
424C3×C8—62no—
425C3×C8C2×C4×D311yescharacteristic
426C3×C8C2×C4×D311yescharacteristic
427C3×C8C22×Dic311yescharacteristic
428C3×C8C22×Dic311yescharacteristic
429C3⋊C8—22no—
430C3⋊C8—32no—
431C3⋊C8—32no—
432C3⋊C8—62no—
433C3⋊C8—62no—
434C3⋊C8—62no—
435C3⋊C8—122no—
436C3⋊C8D3×D411yescharacteristic
437C3⋊C8D3×D411yescharacteristic
438C3⋊C8C22×Dic312yes—
439C2×C32—21no—
440C2×C32—42no—
441C2×C32C2×C4×D411yescharacteristic
442C3×D3—22no—
443C3×D3—42no—
444#41—32no—
445#41—32no—
446#41—32no—
447#41—62no—
448#41—62no—
449#41C2×D3212yes—
450C2×Q8—32no—
451C2×D4—32no—
452C2×D4—62no—
453C22×C4—31no—
454C22×C4—62no—
455Q16—32no—
456Q16—31no—
457Q16D3×Dic311yescharacteristic
458SD16—32no—
459SD16—32no—
460SD16—32no—
461SD16D3×Dic312yes—
462D8—32no—
463D8—31no—
464D8D3×Dic311yescharacteristic
465M16—32no—
466M16—32no—
467M16—32no—
468M16—62no—
469M16—92no—
470M16—182no—
471M16—182no—
472M16—182no—
473M16—182no—
474C2×C8—31no—
475C2×C8—31no—
476C2×C8—62no—
477C2×C8—92no—
478C2×C8—92no—
479C2×C8—91no—
480C2×C8—182no—
481C2×C8—182no—
482C2×C8—182no—
483C2×C8—182no—
484C2×C8C2×D3211yescharacteristic
485C4⋊C4—181no—
486C22⋊C4—181no—
487C42—31no—
488C42—91no—
489C22×C3—22no—
490C22×C3—22no—
491C22×C3—21no—
492C22×C3—32no—
493C22×C3—42no—
494C22×C3—62no—
495C22×C3—121no—
496C22×C3—124no—
497C22×C3C2×#23711yescharacteristic
498C22×C3D3×#4111yescharacteristic
499C2×D3—22no—
500C2×D3—41no—
501C2×D3—44no—
502C2×D3D4×Dic312yes—
503C3×C4—22no—
504C3×C4—22no—
505C3×C4—21no—
506C3×C4—21no—
507C3×C4—32no—
508C3×C4—42no—
509C3×C4—62no—
510C3×C4—121no—
511C3×C4C22×C4×D311yescharacteristic
512C3×C4C2×D3×D411yescharacteristic
513C3×C4C2×D3×D411yescharacteristic
514C3×C4C23×Dic311yescharacteristic
515Dic3—22no—
516Dic3—41no—
517Dic3—121no—
518Dic3—121no—
519Dic3—241no—
520Dic3D4×Dic312yes—
521C32#295511yescharacteristic, complemented, Sylow
522C23—31no—
523C23—62no—
524Q8—32no—
525Q8—62no—
526Q8C2×D3×Dic312yes—
527D4—22no—
528D4—32no—
529D4—62no—
530D4—62no—
531D4—62no—
532D4—62no—
533D4C2×D3×Dic312yes—
534C2×C4—22no—
535C2×C4—31no—
536C2×C4—32no—
537C2×C4—32no—
538C2×C4—62no—
539C2×C4—62no—
540C2×C4—62no—
541C2×C4—62no—
542C2×C4—61no—
543C2×C4—181no—
544C2×C4C22×D3211yescharacteristic
545C8—31no—
546C8—31no—
547C8—32no—
548C8—62no—
549C8—92no—
550C8—182no—
551C8C2×D3×Dic311yescharacteristic
552C8C2×D3×Dic311yescharacteristic
553C2×C3—21no—
554C2×C3—21no—
555C2×C3—21no—
556C2×C3—41no—
557C2×C3—42no—
558C2×C3—42no—
559C2×C3—62no—
560C2×C3—82no—
561C2×C3—122no—
562C2×C3C4×D3×D411yescharacteristic
563C2×C3C2×D4×Dic311yescharacteristic
564D3—22no—
565D3—42no—
566C22—22no—
567C22—32no—
568C22—62no—
569C22—121no—
570C22—124no—
571C22D3×#23711yescharacteristic
572C4—22no—
573C4—32no—
574C4—62no—
575C4—121no—
576C4—361no—
577C4D32×D411yescharacteristic
578C4C22×D3×Dic311yescharacteristic
579C3—21no—
580C3#7988811yescharacteristic, complemented
581C3#8399911yescharacteristic, complemented
582C2—21no—
583C2—42no—
584C2—62no—
585C2—122no—
586C2D3×D4×Dic311yescharacteristic
subgroupG/H
centerC4D32×D4
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC32×#135C22
socleC2×C32C2×C4×D4
prime radicalC3×#5768C2
cosocleC2×C32×C4C24
hypercenter#135D32
hypocenterC32#2955
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C4 ◁ C2×C4 ◁ #135

Complements

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

NH ≅ G/Ntype
2. D3×#948C2semidirect
3. #10592896C2semidirect
4. C3×#5196C2semidirect
5. #10591676C2semidirect
6. #10591673C2semidirect
7. #10591670C2semidirect
8. #10590920C2semidirect
9. #10590915C2semidirect
10. #10590912C2semidirect
11. #10590908C2semidirect
16. #64157C22semidirect
18. C3×#948C22semidirect
19. C3×#918C4semidirect
20. C3×#915C4semidirect
21. C3×#914C4semidirect
22. C3×#911C4semidirect
27. #63815C22semidirect
29. #63814C22semidirect
34. #63664C22semidirect
35. #63646C22semidirect
36. #63642C22semidirect
37. C3×#837C22semidirect
38. C3×#819C22semidirect
39. C3×C8×Dic3C22semidirect
40. #63577C22semidirect
41. #63569C22semidirect
42. #63568C22semidirect
43. #63554C22semidirect
44. #63553C22semidirect
58. #5196D3semidirect
135. #948C2×D3semidirect
141. #918Dic3semidirect
142. #915Dic3semidirect
143. #914Dic3semidirect
144. #911Dic3semidirect
164. #837C2×D3semidirect
171. #819C2×D3semidirect
178. C8×Dic3C2×D3semidirect
521. C32#2955semidirect
580. C3#79888semidirect
581. C3#83999semidirect

Maximal subgroups

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

subgroupindex
C3×#57682
D3×#9482
#105928962
C3×#51962
#105916762
#105916732
#105916702
#105909202
#105909152
#105909122
#105909082
#839993
#798883