Finite Group Databasebeta

← #11866714

Subgroups — #11866714

Order 1152.

1229 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#10595282C211yesmaximal, characteristic
2C2×#63930C211yesmaximal, characteristic, complemented
3C2×D32×C8C211yesmaximal, characteristic, complemented
4#10594631C211yesmaximal, characteristic, complemented
5C3⋊D3×#102C211yesmaximal, characteristic, complemented
6C3×#4778C212yesmaximal, complemented
7#10591499C212yesmaximal, complemented
8#10590847C212yesmaximal, complemented
9#10590672C211yesmaximal, characteristic, complemented
10#10590577C212yesmaximal, complemented
11#10590575C211yesmaximal, characteristic, complemented
12D3×#465—32nomaximal
13C2×D4×C3⋊D3C2211yescharacteristic
14C2×#3811—21no—
15C2×C4×D32C2211yescharacteristic
16C2×#3797C2211yescharacteristic
17C2×C8×C3⋊D3C2211yescharacteristic
18C4⋊C4×C3⋊D3C2211yescharacteristic
19C3×#938C2212yes—
20C2×C3×#214C2212yescomplemented
21C2×C3×D3×C8C2212yescomplemented
22C3×#897C2212yescomplemented
23#63974—21no—
24#63971—22no—
25#63930—24no—
26#63921—21no—
27#63909C2212yes—
28#63900—21no—
29#63900C2211yescharacteristic
30#63899—22no—
31#63856C2212yescomplemented
32C2×#3717C2212yescomplemented
33C2×#3710C2211yescharacteristic
34C2×D3×C3⋊C8C2212yescomplemented
35D32×C8—24no—
36C32×#102C2211yescharacteristic, complemented
37#63659C2211yescharacteristic, complemented
38#63648C2211yescharacteristic, complemented
39#63636C2211yescharacteristic, complemented
40C3×#816C2212yescomplemented
41C3×#808C2212yescomplemented
42#63573C2212yescomplemented
43#63565C2212yescomplemented
44C2×D3×SD16—32no—
45C22×D3×C8—32no—
46D3×C22⋊Q8—32no—
47D3×#121—32no—
48C3×#465—32no—
49#5171—32no—
50#5114—32no—
51#5048—32no—
52#5041—32no—
53#4864—32no—
54D3×#106—32no—
55#4807—32no—
56D3×#103—32no—
57#4778D312yescomplemented
58D3×#102—32no—
59D3×#102—61no—
60C23×C3⋊D3—21no—
61C22×D32D411yescharacteristic
62C2×C32×D4C2311yescharacteristic
63C2×#638—21no—
64D4×C3⋊D3—22no—
65D4×C3⋊D3—22no—
66C2×C4⋊(C3⋊D3)C2311yescharacteristic
67C2×C4×C3⋊D3—21no—
68C2×C4×C3⋊D3C2311yescharacteristic
69C2×C3×#67—22no—
70C2×C3×C4×D3C2312yes—
71C2×C3×Dic6C2312yes—
72#3811—44no—
73C2×#627—21no—
74C2×#626—22no—
75C2×#624—21no—
76C2×#624—21no—
77C2×#624D411yescharacteristic
78C2×D3×Dic3D412yes—
79C4×D32—22no—
80C4×D32—22no—
81#3797—22no—
82#3797—22no—
83C2×C32×C8C2311yescharacteristic
84C32×C4⋊C4C2311yescharacteristic
85C4⋊(C3⋊Dic3)C2311yescharacteristic
86#3750—21no—
87C2×C3⋊(C3⋊C8)C2311yescharacteristic
88C8×C3⋊D3—22no—
89C3×#217—22no—
90C3×#214—24no—
91C3×(C2×D3)⋊C4—22no—
92C3×C4⋊Dic3—22no—
93C3×C4⋊Dic3C2312yes—
94C2×C3×C3⋊C8C2312yes—
95C3×D3×C8—24no—
96#3724—21no—
97#3724—22no—
98#3722—22no—
99(C2×D3)⋊Dic3—22no—
100#3717—24no—
101#3710D414yescomplemented
102D3×C3⋊C8—24no—
103C2×#465—91noSylow
104C2×D3×Q8—32no—
105C2×D3×D4—32no—
106C2×D3×D4—61no—
107C2×D3×D4—62no—
108C22×C4×D3—32no—
109C2×C3×SD16—32no—
110C22×C3×C8—32no—
111C3×C22⋊Q8—32no—
112C3×#121—32no—
113#946—32no—
114C2×#215—32no—
115#939—62no—
116#938C2×D312yes—
117C2×#214C2×D312yescomplemented
118#930—32no—
119#924—32no—
120C22×C3⋊C8—32no—
121D3×SD16—68no—
122C2×#204—32no—
123C2×D3×C8—32no—
124C2×D3×C8—32no—
125C2×D3×C8—32no—
126C2×D3×C8—61no—
127C2×D3×C8—68no—
128C2×D3×C8C2×D312yescomplemented
129#897C2×D312yescomplemented
130#896—62no—
131#895—32no—
132D3×C4⋊C4—32no—
133D3×C4⋊C4—32no—
134D3×C4⋊C4—61no—
135D3×C4⋊C4—62no—
136#884—62no—
137D3×C22⋊C4—62no—
138D3×C22⋊C4—62no—
139#878—62no—
140C3×#106—32no—
141C3×#103—32no—
142C3×#102—21no—
143C3×#102C2×D312yescomplemented
144#835—32no—
145#832—32no—
146#832—61no—
147#821—32no—
148#821—61no—
149#817—32no—
150#816C2×D312yescomplemented
151#810—32no—
152#809—32no—
153#809—61no—
154#808—32no—
155#808C2×D312yescomplemented
156C23×C32—21no—
157C22×C3⋊D3—21no—
158C22×C3⋊D3—42no—
159C22×C3⋊D3—42no—
160C22×C3⋊D3—42no—
161C22×C3⋊D3C2×D411yescharacteristic
162C22×C3×D3C2×D412yes—
163C2×D32—22no—
164C2×D32—22no—
165C2×D32SD1614yescomplemented
166C32×D4—21no—
167C32×D4—21no—
168C2×C32×C4—21no—
169C2×C32×C4C2411yescharacteristic
170#638—42no—
171C2×C3⋊Dic3—21no—
172C2×C3⋊Dic3C2×D411yescharacteristic
173C4⋊(C3⋊D3)—21no—
174C4⋊(C3⋊D3)—21no—
175C4×C3⋊D3—42no—
176C4×C3⋊D3C2×D412yes—
177C4×C3⋊D3#4112yes—
178C3×#67—44no—
179C2×C3×Dic3—22no—
180C2×C3×Dic3—22no—
181C2×C3×Dic3C2×D412yes—
182C3×C4×D3—22no—
183C3×C4×D3—22no—
184C3×Dic6—22no—
185C3×Dic6—22no—
186#627—42no—
187#626—44no—
188#624—22no—
189#624—42no—
190#624—42no—
191D3×Dic3—24no—
192C32×C8—21no—
193C3⋊(C3⋊C8)—21no—
194C3×C3⋊C8C2×D414yescomplemented
195C22×SD16—91no—
196C23×C8—91no—
197C2×C22⋊Q8—91no—
198C2×#121—91no—
199#465—32no—
200#465—92no—
201#465—92no—
202#465—92no—
203C2×#106—91no—
204C2×#103—91no—
205C2×#102—91no—
206C23×D3—32no—
207C23×D3—62no—
208C23×D3—121no—
209C2×C3×Q8—32no—
210C2×C3×D4—21no—
211C2×C3×D4—62no—
212C2×C3×D4C22×D312yes—
213C22×C3×C4—32no—
214C2×#67—22no—
215C2×#67—62no—
216C2×#67—62no—
217C2×#67—121no—
218C22×Dic3—32no—
219D3×Q8—64no—
220D3×Q8—64no—
221D3×D4—64no—
222D3×D4—64no—
223D3×D4—64no—
224D3×D4—122no—
225D3×D4—128no—
226C2×D12—32no—
227C2×D12—61no—
228C2×D12—62no—
229C2×C4×D3—32no—
230C2×C4×D3—32no—
231C2×C4×D3—32no—
232C2×C4×D3—61no—
233C2×C4×D3—64no—
234C2×C4×D3—64no—
235C2×C4×D3—62no—
236C2×C4×D3—62no—
237C2×C4×D3—62no—
238C2×C4×D3—121no—
239C2×C4×D3C22×D312yes—
240C2×Dic6—62no—
241C2×Dic6C22×D312yes—
242C3×SD16—64no—
243C2×C3×C8—21no—
244C2×C3×C8—32no—
245C2×C3×C8—64no—
246C2×C3×C8C22×D312yes—
247C3×C4⋊C4—21no—
248C3×C4⋊C4—32no—
249C3×C4⋊C4—62no—
250C3×C4⋊C4C22×D312yes—
251C3×C22⋊C4—62no—
252C3×C22⋊C4—62no—
253#217—22no—
254#217—62no—
255#215—64no—
256#214—24no—
257(C2×D3)⋊C4—22no—
258(C2×D3)⋊C4—62no—
259(C2×D3)⋊C4—62no—
260(C2×D3)⋊C4—62no—
261C4⋊Dic3—22no—
262C4⋊Dic3—32no—
263C4⋊Dic3—61no—
264C4⋊Dic3C22×D312yes—
265Dic3⋊C4—62no—
266Dic3⋊C4—62no—
267Dic3⋊C4—62no—
268Dic3⋊C4—62no—
269Dic3⋊C4—121no—
270C2×C3⋊C8—32no—
271C2×C3⋊C8—61no—
272C2×C3⋊C8—64no—
273C2×C3⋊C8C22×D312yes—
274#204—64no—
275D3×C8—24no—
276D3×C8—38no—
277D3×C8—64no—
278D3×C8—64no—
279D3×C8—122no—
280C22×C32—41no—
281C22×C32—41no—
282C22×C32—41no—
283C22×C32C22×D411yescharacteristic
284C2×C3⋊D3—41no—
285C2×C3⋊D3—41no—
286C2×C3⋊D3—41no—
287C2×C3⋊D3—84no—
288C2×C3⋊D3#12112yes—
289C2×C3⋊D3C2×SD1612yes—
290C2×C3⋊D3#13512yes—
291C2×C3×D3—22no—
292C2×C3×D3—22no—
293C2×C3×D3C2×SD1614yescomplemented
294D32—28no—
295C32×C4—41no—
296C32×C4C22×D411yescharacteristic
297C32×C4C2×#4111yescharacteristic
298C3⋊Dic3—41no—
299C3⋊Dic3#12112yes—
300C3×Dic3—22no—
301C3×Dic3—42no—
302C3×Dic3—42no—
303C22×Q8—91no—
304C22×D4—91no—
305C22×D4—181no—
306C23×C4—91no—
307C2×SD16—32no—
308C2×SD16—92no—
309C2×SD16—184no—
310C22×C8—32no—
311C22×C8—91no—
312C22×C8—92no—
313C22×C8—91no—
314C22×C8—184no—
315C22⋊Q8—32no—
316C22⋊Q8—92no—
317C22⋊Q8—182no—
318#121—32no—
319#121—92no—
320#121—182no—
321C2×C4⋊C4—91no—
322C2×C4⋊C4—91no—
323C2×C4⋊C4—181no—
324C2×C22⋊C4—181no—
325C2×C22⋊C4—181no—
326#106—32no—
327#106—92no—
328#103—32no—
329#103—92no—
330#102—91no—
331#102—91no—
332#102—91no—
333#102D3211yescharacteristic, complemented
334C23×C3—22no—
335C23×C3—32no—
336C23×C3—41no—
337C22×D3—32no—
338C22×D3—38no—
339C22×D3—61no—
340C22×D3—64no—
341C22×D3—64no—
342C22×D3—62no—
343C22×D3—121no—
344C22×D3—124no—
345C22×D3—124no—
346C22×D3—124no—
347C22×D3—124no—
348C22×D3—242no—
349C22×D3—242no—
350C22×D3D3×D412yes—
351C3×Q8—62no—
352C3×Q8—62no—
353C3×D4—22no—
354C3×D4—22no—
355C3×D4—22no—
356C3×D4—41no—
357C3×D4—124no—
358C2×C3×C4—22no—
359C2×C3×C4—21no—
360C2×C3×C4—32no—
361C2×C3×C4—41no—
362C2×C3×C4—62no—
363C2×C3×C4—62no—
364C2×C3×C4—62no—
365C2×C3×C4—62no—
366C2×C3×C4C23×D312yes—
367#67—44no—
368#67—124no—
369#67—124no—
370#67—124no—
371C2×Dic3—22no—
372C2×Dic3—22no—
373C2×Dic3—32no—
374C2×Dic3—61no—
375C2×Dic3—64no—
376C2×Dic3—62no—
377C2×Dic3—121no—
378C2×Dic3D3×D412yes—
379D12—62no—
380D12—62no—
381D12—62no—
382D12—121no—
383D12—124no—
384C4×D3—22no—
385C4×D3—22no—
386C4×D3—34no—
387C4×D3—34no—
388C4×D3—62no—
389C4×D3—62no—
390C4×D3—64no—
391C4×D3—64no—
392C4×D3—124no—
393C4×D3—124no—
394C4×D3—124no—
395C4×D3—242no—
396Dic6—22no—
397Dic6—22no—
398Dic6—124no—
399C3×C8—22no—
400C3×C8—34no—
401C3×C8—41no—
402C3⋊C8—62no—
403C3⋊C8—121no—
404C3⋊C8D3×D414yescomplemented
405C2×C32—81no—
406C2×C32C2×#12111yescharacteristic
407C2×C32C22×SD1611yescharacteristic
408C2×C32C2×#13511yescharacteristic
409C3⋊D3—81no—
410C3⋊D3#46514yescomplemented
411C3×D3—24no—
412C24—91no—
413C24—181no—
414C2×Q8—32no—
415C2×Q8—181no—
416C2×Q8—182no—
417C2×Q8—182no—
418C2×D4—62no—
419C2×D4—91no—
420C2×D4—182no—
421C2×D4—182no—
422C2×D4—182no—
423C2×D4—181no—
424C2×D4—364no—
425C2×D4C2×D3211yescharacteristic
426C22×C4—32no—
427C22×C4—91no—
428C22×C4—92no—
429C22×C4—91no—
430C22×C4—181no—
431C22×C4—182no—
432C22×C4—182no—
433C22×C4—181no—
434C22×C4—181no—
435SD16—64no—
436SD16—184no—
437C2×C8—32no—
438C2×C8—64no—
439C2×C8—94no—
440C2×C8—91no—
441C2×C8—182no—
442C2×C8—184no—
443C2×C8C2×D3211yescharacteristic
444C4⋊C4—32no—
445C4⋊C4—62no—
446C4⋊C4—91no—
447C4⋊C4—181no—
448C4⋊C4—182no—
449C4⋊C4—181no—
450C4⋊C4C2×D3211yescharacteristic
451C22⋊C4—62no—
452C22⋊C4—62no—
453C22⋊C4—182no—
454C22⋊C4—182no—
455C22×C3—21no—
456C22×C3—34no—
457C22×C3—42no—
458C22×C3—42no—
459C22×C3—42no—
460C22×C3—42no—
461C22×C3—62no—
462C22×C3—62no—
463C22×C3—81no—
464C22×C3—81no—
465C22×C3C2×D3×D412yes—
466C2×D3—22no—
467C2×D3—22no—
468C2×D3—34no—
469C2×D3—34no—
470C2×D3—34no—
471C2×D3—62no—
472C2×D3—62no—
473C2×D3—62no—
474C2×D3—616no—
475C2×D3—122no—
476C2×D3—122no—
477C2×D3—122no—
478C2×D3—122no—
479C2×D3—241no—
480C2×D3—241no—
481C2×D3—248no—
482C2×D3—248no—
483C2×D3D3×SD1614yescomplemented
484C3×C4—21no—
485C3×C4—21no—
486C3×C4—42no—
487C3×C4—62no—
488C3×C4—81no—
489C3×C4—122no—
490C3×C4—122no—
491C3×C4C2×D3×D412yes—
492C3×C4D3×#4112yes—
493Dic3—22no—
494Dic3—34no—
495Dic3—42no—
496Dic3—42no—
497Dic3—62no—
498Dic3—122no—
499Dic3—241no—
500C32C2×#46511yescharacteristic, complemented, Sylow
501C23—21no—
502C23—32no—
503C23—94no—
504C23—91no—
505C23—182no—
506C23—182no—
507C23—181no—
508C23—362no—
509C23—362no—
510C23—362no—
511Q8—62no—
512Q8—62no—
513Q8—362no—
514D4—21no—
515D4—21no—
516D4—124no—
517D4—181no—
518D4—181no—
519D4—362no—
520D4—364no—
521C2×C4—21no—
522C2×C4—32no—
523C2×C4—62no—
524C2×C4—62no—
525C2×C4—62no—
526C2×C4—62no—
527C2×C4—91no—
528C2×C4—92no—
529C2×C4—92no—
530C2×C4—182no—
531C2×C4—184no—
532C2×C4—181no—
533C2×C4—362no—
534C2×C4—362no—
535C2×C4—362no—
536C2×C4C22×D3211yescharacteristic
537C8—21no—
538C8—34no—
539C8—181no—
540C2×C3—21no—
541C2×C3—21no—
542C2×C3—21no—
543C2×C3—64no—
544C2×C3—82no—
545C2×C3—82no—
546C2×C3D3×#12112yes—
547C2×C3C2×D3×SD1612yes—
548C2×C3D3×#13512yes—
549D3—24no—
550D3—38no—
551D3—64no—
552D3—242no—
553D3—242no—
554C22—34no—
555C22—41no—
556C22—41no—
557C22—41no—
558C22—62no—
559C22—62no—
560C22—92no—
561C22—92no—
562C22—92no—
563C22—188no—
564C22—361no—
565C22—361no—
566C22—361no—
567C22—724no—
568C22D32×D411yescharacteristic
569C4—41no—
570C4—62no—
571C4—92no—
572C4—122no—
573C4—122no—
574C4—361no—
575C4#6430611yescharacteristic
576C4D32×D411yescharacteristic
577C3—21no—
578C3D3×#46512yescomplemented
579C2—64no—
580C2—81no—
581C2—94no—
582C2—721no—
583C2#1059426511yescharacteristic
584C2#1059473011yescharacteristic
585C2D32×SD1611yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#102C22
socleC22×C32C22×D4
prime radical#10595282C2
hypercenter#102D32
hypocenterC32C2×#465
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #102

Complements

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

NH ≅ G/Ntype
2. C2×#63930C2semidirect
3. C2×D32×C8C2semidirect
4. #10594631C2semidirect
5. C3⋊D3×#102C2semidirect
6. C3×#4778C2semidirect
7. #10591499C2semidirect
8. #10590847C2semidirect
9. #10590672C2semidirect
10. #10590577C2semidirect
11. #10590575C2semidirect
20. C2×C3×#214C22semidirect
21. C2×C3×D3×C8C22semidirect
22. C3×#897C22semidirect
31. #63856C22semidirect
32. C2×#3717C22semidirect
34. C2×D3×C3⋊C8C22semidirect
36. C32×#102C22semidirect
37. #63659C22semidirect
38. #63648C22semidirect
39. #63636C22semidirect
40. C3×#816C22semidirect
41. C3×#808C22semidirect
42. #63573C22semidirect
43. #63565C22semidirect
57. #4778D3semidirect
101. #3710D4semidirect
117. C2×#214C2×D3semidirect
128. C2×D3×C8C2×D3semidirect
129. #897C2×D3semidirect
143. C3×#102C2×D3semidirect
150. #816C2×D3semidirect
155. #808C2×D3semidirect
165. C2×D32SD16semidirect
194. C3×C3⋊C8C2×D4semidirect
293. C2×C3×D3C2×SD16semidirect
333. #102D32semidirect
404. C3⋊C8D3×D4semidirect
410. C3⋊D3#465semidirect
483. C2×D3D3×SD16semidirect
500. C32C2×#465semidirect
578. C3D3×#465semidirect

Maximal subgroups

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

subgroupindex
#105952822
C2×#639302
C2×D32×C82
#105946312
C3⋊D3×#1022
C3×#47782
#105914992
#105908472
#105906722
#105905772
#105905752
D3×#4653