Finite Group Databasebeta

← #11857807

Subgroups — #11857807

Order 1152.

1665 conjugacy classes of subgroups.

The subgroup lattice has 598 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64319C211yesmaximal, characteristic
2C2×D32×C8C211yesmaximal, characteristic, complemented
3#10594602C211yesmaximal, characteristic, complemented
4C3⋊D3×#103C211yesmaximal, characteristic, complemented
5C3×#4804C212yesmaximal, complemented
6#10591556C212yesmaximal, complemented
7#10591552C211yesmaximal, characteristic, complemented
8#10590954C212yesmaximal, complemented
9#10590940C211yesmaximal, characteristic, complemented
10#10590608C212yesmaximal, complemented
11#10590593C211yesmaximal, characteristic, complemented
12D3×#416—32nomaximal
13C2×Q8×C3⋊D3C2211yescharacteristic
14C2×C3×#239C2212yes—
15#64319—24no—
16#64319C418yescomplemented
17C2×#3802—21no—
18C2×#3802C2211yescharacteristic
19C2×C4×D32—21no—
20C2×C4×D32C2211yescharacteristic
21C2×#3795—22no—
22C2×#3795C2212yes—
23C2×C8×C3⋊D3C2211yescharacteristic
24C4⋊C4×C3⋊D3C2211yescharacteristic
25C2×C3×D3×C8C2212yescomplemented
26C3×#892C2212yescomplemented
27#63921—21no—
28#63900C2211yescharacteristic
29C4×#624—21no—
30#63877—22no—
31#63841C2212yescomplemented
32C2×#3710C2211yescharacteristic
33C2×D3×C3⋊C8C2212yescomplemented
34D32×C8—24no—
35C32×#103C2211yescharacteristic, complemented
36#63662C2211yescharacteristic, complemented
37#63643C2211yescharacteristic, complemented
38#63637C2211yescharacteristic, complemented
39C3×#835C2212yescomplemented
40C3×#821C2212yescomplemented
41C3×#809C2212yescomplemented
42#63567C2212yescomplemented
43#63563C2212yescomplemented
44#63562C2212yescomplemented
45C2×D3×#41—32no—
46C22×D3×C8—32no—
47D3×#117—32no—
48C3×#416—32no—
49#5233—32no—
50#5113—32no—
51#5002—32no—
52#4804—32no—
53#4804D312yescomplemented
54D3×#103—32no—
55D3×#103—32no—
56D3×#103—61no—
57#4772—32no—
58#4772—32no—
59D3×#102—32no—
60D3×#102—32no—
61C22×D32—21no—
62C22×D32D411yescharacteristic
63C2×C32×Q8C2311yescharacteristic
64Q8×C3⋊D3—22no—
65Q8×C3⋊D3C2×C414yes—
66C2×C4×C3⋊D3—21no—
67C2×C4×C3⋊D3—21no—
68C2×C4×C3⋊D3C2311yescharacteristic
69C2×#634—21no—
70C2×#634C2311yescharacteristic
71C3×#239—24no—
72C3×#239C2×C418yescomplemented
73C2×C3×D12—22no—
74C2×C3×D12C2312yes—
75C2×C3×C4×D3—22no—
76C2×C3×C4×D3C2312yes—
77C2×#625—22no—
78C2×#625—21no—
79C2×#624—21no—
80C2×#624D411yescharacteristic
81C2×D3×Dic3—22no—
82C2×D3×Dic3D412yes—
83#3802—28no—
84#3802—22no—
85#3802C2×C414yes—
86C4×D32—28no—
87C4×D32C2×C414yes—
88C4×D32D414yes—
89#3795—24no—
90#3795—216no—
91#3795C2×C418yescomplemented
92C2×C32×C8C2311yescharacteristic
93C32×C4⋊C4C2311yescharacteristic
94C4⋊(C3⋊Dic3)C2311yescharacteristic
95#3750—21no—
96C2×C3⋊(C3⋊C8)C2311yescharacteristic
97C8×C3⋊D3—22no—
98C3×(C2×D3)⋊C4—22no—
99C3×C4⋊Dic3C2312yes—
100C3×C4×Dic3—22no—
101C2×C3×C3⋊C8C2312yes—
102C3×D3×C8—24no—
103#3724—21no—
104(C2×D3)⋊Dic3—22no—
105Dic32—22no—
106#3710—22no—
107D3×C3⋊C8—24no—
108C2×#416—91noSylow
109C2×C3×#41—32no—
110D3×#41—316no—
111D3×#41—68no—
112C2×#239C2×D312yes—
113C2×D3×Q8—32no—
114C2×D3×Q8—61no—
115C2×#237—32no—
116C2×#237—62no—
117C2×D3×D4—32no—
118C2×D3×D4—62no—
119C2×#235—32no—
120C2×#235—62no—
121C22×C4×D3—32no—
122C22×C4×D3—62no—
123C22×C3×C8—32no—
124C3×#117—32no—
125#926—32no—
126C22×C3⋊C8—32no—
127C2×D3×C8—32no—
128C2×D3×C8—32no—
129C2×D3×C8—32no—
130C2×D3×C8—61no—
131C2×D3×C8—68no—
132C2×D3×C8C2×D312yescomplemented
133#892—32no—
134#892C2×D312yescomplemented
135D3×C4⋊C4—32no—
136D3×C4⋊C4—32no—
137D3×C4⋊C4—61no—
138D3×C22⋊C4—62no—
139#877—62no—
140#872—62no—
141C42×D3—62no—
142C3×#103—21no—
143C3×#103—32no—
144C3×#103C2×D312yescomplemented
145C3×#102—32no—
146C3×#102—32no—
147#835—32no—
148#835—61no—
149#835C2×D312yescomplemented
150#832—32no—
151#832—32no—
152#821—32no—
153#821C2×D312yescomplemented
154#816—32no—
155#816—32no—
156#816—61no—
157#810—32no—
158#810—32no—
159#810—61no—
160#809—32no—
161#809C2×D312yescomplemented
162C22×C3⋊D3C2×D411yescharacteristic
163C22×C3×D3—22no—
164C22×C3×D3C2×D412yes—
165C2×D32—22no—
166C2×D32—22no—
167C2×D32—24no—
168C2×D32—42no—
169C2×D32—42no—
170C2×D32C22⋊C414yes—
171C32×Q8—21no—
172C32×Q8C22×C412yes—
173C2×C32×C4—21no—
174C2×C32×C4—21no—
175C2×C32×C4C2411yescharacteristic
176C2×C3⋊Dic3—21no—
177C2×C3⋊Dic3—21no—
178C2×C3⋊Dic3C2×D411yescharacteristic
179C4×C3⋊D3—24no—
180C4×C3⋊D3—42no—
181C4×C3⋊D3C22×C412yes—
182C4×C3⋊D3C2×D412yes—
183#634—21no—
184#634—24no—
185#634C22×C412yes—
186C2×C3×Dic3—22no—
187C2×C3×Dic3C2×D412yes—
188C3×D12—28no—
189C3×D12—22no—
190C3×D12C22×C414yes—
191C3×C4×D3—28no—
192C3×C4×D3C22×C414yes—
193C3×C4×D3C2×D414yes—
194#625—28no—
195#625—24no—
196#624—42no—
197#624C22⋊C414yes—
198D3×Dic3—28no—
199D3×Dic3C22⋊C418yes—
200C32×C8—21no—
201C3⋊(C3⋊C8)—21no—
202C3×C3⋊C8—22no—
203C22×#41—91no—
204C23×C8—91no—
205C2×#117—91no—
206#416—32no—
207#416—92no—
208#416—92no—
209#416—92no—
210C2×#103—91no—
211C2×#103—91no—
212C2×#102—91no—
213C2×#102—91no—
214C23×D3—32no—
215C23×D3—62no—
216C3×#41—38no—
217C3×#41—64no—
218C2×C3×Q8—21no—
219C2×C3×Q8C22×D312yes—
220C2×C3×D4—32no—
221C2×C3×D4—62no—
222C22×C3×C4—32no—
223C22×C3×C4—62no—
224C2×#67—62no—
225C2×#67—62no—
226C2×#67—62no—
227C22×Dic3—32no—
228C22×Dic3—62no—
229#239—24no—
230#239C4×D318yescomplemented
231D3×Q8—38no—
232D3×Q8—64no—
233D3×Q8—64no—
234D3×Q8—122no—
235#237—38no—
236#237—616no—
237#237—64no—
238D3×D4—38no—
239D3×D4—64no—
240D3×D4—616no—
241#235—38no—
242#235—616no—
243#235—64no—
244C2×D12—22no—
245C2×D12C22×D312yes—
246C2×C4×D3—22no—
247C2×C4×D3—32no—
248C2×C4×D3—32no—
249C2×C4×D3—32no—
250C2×C4×D3—38no—
251C2×C4×D3—38no—
252C2×C4×D3—61no—
253C2×C4×D3—616no—
254C2×C4×D3—62no—
255C2×C4×D3—62no—
256C2×C4×D3—62no—
257C2×C4×D3—62no—
258C2×C4×D3—121no—
259C2×C4×D3—121no—
260C2×C4×D3C22×D312yes—
261C2×Dic6—32no—
262C2×Dic6—61no—
263C2×Dic6—62no—
264C2×Dic6—121no—
265C2×C3×C8—21no—
266C2×C3×C8—32no—
267C2×C3×C8—64no—
268C2×C3×C8C22×D312yes—
269C3×C4⋊C4—21no—
270C3×C4⋊C4—32no—
271C3×C4⋊C4C22×D312yes—
272C3×C22⋊C4—62no—
273C3×C42—62no—
274#217—62no—
275(C2×D3)⋊C4—22no—
276(C2×D3)⋊C4—62no—
277C4⋊Dic3—32no—
278C4⋊Dic3—61no—
279C4⋊Dic3C22×D312yes—
280Dic3⋊C4—62no—
281Dic3⋊C4—62no—
282Dic3⋊C4—121no—
283C4×Dic3—22no—
284C4×Dic3—62no—
285C4×Dic3—62no—
286C2×C3⋊C8—32no—
287C2×C3⋊C8—61no—
288C2×C3⋊C8—64no—
289C2×C3⋊C8C22×D312yes—
290D3×C8—24no—
291D3×C8—64no—
292D3×C8—64no—
293D3×C8—64no—
294D3×C8—122no—
295C22×C32C22×D411yescharacteristic
296C2×C3⋊D3C2×C22⋊C412yes—
297C2×C3⋊D3#13512yes—
298C2×C3⋊D3#13512yes—
299C2×C3×D3—22no—
300C2×C3×D3—22no—
301C2×C3×D3—24no—
302C2×C3×D3—42no—
303C2×C3×D3—42no—
304C2×C3×D3C2×C22⋊C414yes—
305D32—28no—
306D32—48no—
307C32×C4—22no—
308C32×C4—41no—
309C32×C4C23×C411yescharacteristic
310C32×C4C22×D411yescharacteristic
311C3⋊Dic3—22no—
312C3⋊Dic3—41no—
313C3⋊Dic3C2×C22⋊C412yes—
314C3×Dic3—42no—
315C3×Dic3C2×C22⋊C414yes—
316C2×#41—32no—
317C2×#41—92no—
318C2×#41—98no—
319C2×#41—182no—
320C2×#41—184no—
321C22×Q8—91no—
322C22×D4—91no—
323C22×D4—181no—
324C23×C4—91no—
325C23×C4—181no—
326C22×C8—32no—
327C22×C8—91no—
328C22×C8—92no—
329C22×C8—91no—
330C22×C8—184no—
331#117—32no—
332#117—92no—
333#117—182no—
334C2×C4⋊C4—91no—
335C2×C4⋊C4—91no—
336C2×C22⋊C4—181no—
337C2×C42—181no—
338#103—32no—
339#103—92no—
340#103—91no—
341#103—91no—
342#103—91no—
343#103D3211yescharacteristic, complemented
344#102—32no—
345#102—32no—
346#102—92no—
347#102—92no—
348C23×C3—32no—
349C23×C3—62no—
350C22×D3—22no—
351C22×D3—32no—
352C22×D3—38no—
353C22×D3—61no—
354C22×D3—64no—
355C22×D3—64no—
356C22×D3—68no—
357C22×D3—124no—
358C22×D3—124no—
359C22×D3D3×D412yes—
360C3×Q8—22no—
361C3×Q8—22no—
362C3×Q8—41no—
363C3×Q8C2×C4×D314yes—
364C3×D4—34no—
365C3×D4—68no—
366C3×D4—62no—
367C2×C3×C4—22no—
368C2×C3×C4—22no—
369C2×C3×C4—21no—
370C2×C3×C4—32no—
371C2×C3×C4—34no—
372C2×C3×C4—34no—
373C2×C3×C4—41no—
374C2×C3×C4—41no—
375C2×C3×C4—68no—
376C2×C3×C4—62no—
377C2×C3×C4C23×D312yes—
378#67—68no—
379#67—68no—
380#67—68no—
381C2×Dic3—22no—
382C2×Dic3—32no—
383C2×Dic3—38no—
384C2×Dic3—61no—
385C2×Dic3—62no—
386C2×Dic3—68no—
387C2×Dic3—62no—
388C2×Dic3—121no—
389C2×Dic3—121no—
390C2×Dic3D3×D412yes—
391D12—28no—
392D12—22no—
393D12C2×C4×D314yes—
394C4×D3—28no—
395C4×D3—38no—
396C4×D3—34no—
397C4×D3—34no—
398C4×D3—38no—
399C4×D3—62no—
400C4×D3—62no—
401C4×D3—68no—
402C4×D3—68no—
403C4×D3—124no—
404C4×D3—124no—
405C4×D3—124no—
406C4×D3—242no—
407C4×D3C2×C4×D314yes—
408C4×D3D3×D414yes—
409Dic6—34no—
410Dic6—62no—
411Dic6—68no—
412Dic6—62no—
413Dic6—124no—
414Dic6—121no—
415C3×C8—22no—
416C3×C8—41no—
417C3×C8—62no—
418C3⋊C8—22no—
419C3⋊C8—62no—
420C3⋊C8—121no—
421C2×C32C22×C22⋊C411yescharacteristic
422C2×C32C2×#13511yescharacteristic
423C2×C32C2×#13511yescharacteristic
424C3⋊D3#41614yescomplemented
425C3×D3—24no—
426C3×D3—44no—
427C24—91no—
428C24—181no—
429#41—38no—
430#41—64no—
431#41—98no—
432#41—184no—
433#41—1816no—
434C2×Q8—94no—
435C2×Q8—91no—
436C2×Q8—181no—
437C2×Q8—182no—
438C2×Q8C2×D3211yescharacteristic
439C2×D4—32no—
440C2×D4—62no—
441C2×D4—94no—
442C2×D4—182no—
443C2×D4—181no—
444C2×D4—188no—
445C2×D4—182no—
446C22×C4—32no—
447C22×C4—62no—
448C22×C4—91no—
449C22×C4—94no—
450C22×C4—94no—
451C22×C4—92no—
452C22×C4—91no—
453C22×C4—181no—
454C22×C4—181no—
455C22×C4—182no—
456C22×C4—188no—
457C22×C4—181no—
458C2×C8—32no—
459C2×C8—64no—
460C2×C8—91no—
461C2×C8—182no—
462C2×C8—182no—
463C2×C8—184no—
464C2×C8C2×D3211yescharacteristic
465C4⋊C4—32no—
466C4⋊C4—91no—
467C4⋊C4—181no—
468C4⋊C4—181no—
469C4⋊C4C2×D3211yescharacteristic
470C22⋊C4—62no—
471C22⋊C4—182no—
472C42—62no—
473C42—182no—
474C22×C3—21no—
475C22×C3—34no—
476C22×C3—62no—
477C22×C3—62no—
478C22×C3—64no—
479C22×C3—122no—
480C22×C3—122no—
481C22×C3C2×D3×D412yes—
482C2×D3—22no—
483C2×D3—22no—
484C2×D3—24no—
485C2×D3—34no—
486C2×D3—34no—
487C2×D3—34no—
488C2×D3—42no—
489C2×D3—42no—
490C2×D3—62no—
491C2×D3—62no—
492C2×D3—62no—
493C2×D3—616no—
494C2×D3—1216no—
495C2×D3D3×C22⋊C414yes—
496C3×C4—24no—
497C3×C4—21no—
498C3×C4—21no—
499C3×C4—34no—
500C3×C4—42no—
501C3×C4—42no—
502C3×C4—81no—
503C3×C4—122no—
504C3×C4C22×C4×D312yes—
505C3×C4C2×D3×D412yes—
506Dic3—34no—
507Dic3—42no—
508Dic3—62no—
509Dic3—64no—
510Dic3—122no—
511Dic3—122no—
512Dic3—241no—
513Dic3D3×C22⋊C414yes—
514C32C2×#41611yescharacteristic, complemented, Sylow
515C23—32no—
516C23—62no—
517C23—94no—
518C23—91no—
519C23—182no—
520C23—182no—
521C23—184no—
522C23—362no—
523C23—362no—
524Q8—21no—
525Q8—92no—
526Q8—184no—
527Q8—181no—
528Q8C4×D3212yes—
529D4—34no—
530D4—68no—
531D4—62no—
532D4—184no—
533D4—188no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—32no—
537C2×C4—34no—
538C2×C4—34no—
539C2×C4—68no—
540C2×C4—62no—
541C2×C4—94no—
542C2×C4—98no—
543C2×C4—91no—
544C2×C4—92no—
545C2×C4—92no—
546C2×C4—184no—
547C2×C4—188no—
548C2×C4—181no—
549C2×C4—181no—
550C2×C4—362no—
551C2×C4—362no—
552C2×C4C22×D3211yescharacteristic
553C8—21no—
554C8—62no—
555C8—181no—
556C2×C3—21no—
557C2×C3—21no—
558C2×C3—21no—
559C2×C3—64no—
560C2×C3—124no—
561C2×C3C2×D3×C22⋊C412yes—
562C2×C3D3×#13512yes—
563C2×C3D3×#13512yes—
564D3—24no—
565D3—38no—
566D3—44no—
567D3—64no—
568C22—34no—
569C22—62no—
570C22—62no—
571C22—64no—
572C22—92no—
573C22—92no—
574C22—92no—
575C22—122no—
576C22—122no—
577C22—188no—
578C22—368no—
579C22D32×D411yescharacteristic
580C4—22no—
581C4—34no—
582C4—41no—
583C4—92no—
584C4—122no—
585C4—182no—
586C4—361no—
587C4C2×C4×D3211yescharacteristic
588C4D32×D411yescharacteristic
589C3—21no—
590C3D3×#41612yescomplemented
591C2—64no—
592C2—94no—
593C2—124no—
594C2D32×C22⋊C411yescharacteristic
595C2#1059474711yescharacteristic
596C2#1059476411yescharacteristic
subgroupG/H
centerC22D32×D4
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC32×#103C22
socleC22×C32C22×D4
prime radicalC2×#64319C2
cosocleC2×C32×C4C24
hypercenter#103D32
hypocenterC32C2×#416
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #103

Complements

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

NH ≅ G/Ntype
2. C2×D32×C8C2semidirect
3. #10594602C2semidirect
4. C3⋊D3×#103C2semidirect
5. C3×#4804C2semidirect
6. #10591556C2semidirect
7. #10591552C2semidirect
8. #10590954C2semidirect
9. #10590940C2semidirect
10. #10590608C2semidirect
11. #10590593C2semidirect
16. #64319C4semidirect
25. C2×C3×D3×C8C22semidirect
26. C3×#892C22semidirect
31. #63841C22semidirect
33. C2×D3×C3⋊C8C22semidirect
35. C32×#103C22semidirect
36. #63662C22semidirect
37. #63643C22semidirect
38. #63637C22semidirect
39. C3×#835C22semidirect
40. C3×#821C22semidirect
41. C3×#809C22semidirect
42. #63567C22semidirect
43. #63563C22semidirect
44. #63562C22semidirect
53. #4804D3semidirect
72. C3×#239C2×C4semidirect
91. #3795C2×C4semidirect
132. C2×D3×C8C2×D3semidirect
134. #892C2×D3semidirect
144. C3×#103C2×D3semidirect
149. #835C2×D3semidirect
153. #821C2×D3semidirect
161. #809C2×D3semidirect
230. #239C4×D3semidirect
343. #103D32semidirect
424. C3⋊D3#416semidirect
514. C32C2×#416semidirect
590. C3D3×#416semidirect

Maximal subgroups

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

subgroupindex
C2×#643192
C2×D32×C82
#105946022
C3⋊D3×#1032
C3×#48042
#105915562
#105915522
#105909542
#105909402
#105906082
#105905932
D3×#4163