Finite Group Databasebeta

← #11857866

Subgroups — #11857866

Order 1152.

1585 conjugacy classes of subgroups.

The subgroup lattice has 577 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D32×Q8C211yesmaximal, characteristic
2C2×#63791C211yesmaximal, characteristic
3#10594602C211yesmaximal, characteristic
4C3⋊D3×#103C211yesmaximal, characteristic, complemented
5C3×#4802C212yesmaximal, complemented
6#10591557C212yesmaximal, complemented
7#10591552C211yesmaximal, characteristic, complemented
8#10590948C212yesmaximal, complemented
9#10590672C211yesmaximal, characteristic, complemented
10#10590601C211yesmaximal, characteristic, complemented
11#10590600C212yesmaximal, complemented
12D3×#419—32nomaximal
13C2×Q8×C3⋊D3C2211yescharacteristic
14C2×C3×D3×Q8C2212yes—
15D32×Q8—24no—
16D32×Q8C418yescomplemented
17C2×C4×D32—21no—
18C2×C4×D32C2211yescharacteristic
19C2×#3797—21no—
20C2×#3797C2211yescharacteristic
21C2×D3×Dic6—22no—
22C2×D3×Dic6C2212yes—
23C2×C8×C3⋊D3C2211yescharacteristic
24C4⋊C4×C3⋊D3C2211yescharacteristic
25C2×C3×ΓL(1,𝔽25)C2212yes—
26C3×#892C2212yes—
27#63921—21no—
28#63900C2211yescharacteristic
29C4×#624—21no—
30#63877—22no—
31#63841C2212yes—
32C2×#3711C2212yes—
33C2×#3710C2211yescharacteristic
34#63791—24no—
35C32×#103C2211yescharacteristic, complemented
36#63662C2211yescharacteristic, complemented
37#63643C2211yescharacteristic, complemented
38#63637C2211yescharacteristic, complemented
39C3×#835C2212yescomplemented
40C3×#816C2212yescomplemented
41C3×#810C2212yescomplemented
42#63567C2212yescomplemented
43#63566C2212yescomplemented
44#63565C2212yescomplemented
45C22×D3×Q8—32no—
46C2×D3×M16—32no—
47D3×#117—32no—
48C3×#419—32no—
49#5225—32no—
50#5120—32no—
51#5004—32no—
52#4802—32no—
53#4802—32no—
54#4802—32no—
55#4802D312yescomplemented
56D3×#103—32no—
57D3×#103—32no—
58D3×#103—32no—
59D3×#103—32no—
60D3×#103—61no—
61C22×D32D411yescharacteristic
62C2×C32×Q8C2311yescharacteristic
63Q8×C3⋊D3—22no—
64Q8×C3⋊D3C2×C414yes—
65C2×C4×C3⋊D3—21no—
66C2×C4×C3⋊D3—21no—
67C2×C4×C3⋊D3C2311yescharacteristic
68C2×#634—21no—
69C2×#634C2311yescharacteristic
70C3×D3×Q8—24no—
71C3×D3×Q8C2×C418yescomplemented
72C2×C3×C4×D3—22no—
73C2×C3×C4×D3C2312yes—
74C2×C3×Dic6—22no—
75C2×C3×Dic6C2312yes—
76C2×#627—21no—
77C2×#627—22no—
78C2×#624—21no—
79C2×#624—21no—
80C2×#624D411yescharacteristic
81C2×D3×Dic3—22no—
82C2×D3×Dic3D412yes—
83C4×D32—28no—
84C4×D32C2×C414yes—
85C4×D32D414yes—
86#3797—22no—
87#3797—28no—
88#3797C2×C414yes—
89D3×Dic6—24no—
90D3×Dic6—216no—
91D3×Dic6C2×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×ΓL(1,𝔽25)—24no—
103#3724—21no—
104(C2×D3)⋊Dic3—22no—
105Dic32—22no—
106#3711—24no—
107#3710—22no—
108C2×#419—91noSylow
109C22×C3×Q8—32no—
110C2×D3×Q8—32no—
111C2×D3×Q8—316no—
112C2×D3×Q8—32no—
113C2×D3×Q8—32no—
114C2×D3×Q8—61no—
115C2×D3×Q8—62no—
116C2×D3×Q8—62no—
117C2×D3×Q8—68no—
118C2×D3×Q8C2×D312yes—
119C22×C4×D3—32no—
120C22×C4×D3—62no—
121C22×Dic6—32no—
122C22×Dic6—62no—
123C2×C3×M16—32no—
124C3×#117—32no—
125#926—32no—
126C2×#208—32no—
127D3×M16—68no—
128C2×ΓL(1,𝔽25)—32no—
129C2×ΓL(1,𝔽25)C2×D312yes—
130C2×D3×C8—32no—
131C2×D3×C8—32no—
132C2×D3×C8—61no—
133#892—32no—
134#892C2×D312yes—
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×#103—32no—
145C3×#103—32no—
146C3×#103C2×D312yescomplemented
147#835—32no—
148#835—32no—
149#835—32no—
150#835—61no—
151#835C2×D312yescomplemented
152#816—32no—
153#816—32no—
154#816—32no—
155#816—61no—
156#816C2×D312yescomplemented
157#810—32no—
158#810—32no—
159#810—32no—
160#810—61no—
161#810C2×D312yescomplemented
162C22×C3⋊D3C2×D411yescharacteristic
163C22×C3×D3C2×D412yes—
164C2×D32—22no—
165C2×D32—22no—
166C2×D32C22⋊C414yes—
167C32×Q8—21no—
168C32×Q8C22×C412yes—
169C2×C32×C4—21no—
170C2×C32×C4—21no—
171C2×C32×C4C2411yescharacteristic
172C2×C3⋊Dic3—21no—
173C2×C3⋊Dic3—21no—
174C2×C3⋊Dic3C2×D411yescharacteristic
175C4×C3⋊D3—24no—
176C4×C3⋊D3—42no—
177C4×C3⋊D3C22×C412yes—
178C4×C3⋊D3C2×D412yes—
179#634—21no—
180#634—24no—
181#634C22×C412yes—
182C2×C3×Dic3—22no—
183C2×C3×Dic3—22no—
184C2×C3×Dic3C2×D412yes—
185C3×C4×D3—28no—
186C3×C4×D3C22×C414yes—
187C3×C4×D3C2×D414yes—
188C3×Dic6—22no—
189C3×Dic6—28no—
190C3×Dic6C22×C414yes—
191#627—24no—
192#627—28no—
193#624—24no—
194#624—42no—
195#624C22⋊C414yes—
196D3×Dic3—28no—
197D3×Dic3C22⋊C418yes—
198C32×C8—21no—
199C3⋊(C3⋊C8)—21no—
200C3×C3⋊C8—22no—
201C23×Q8—91no—
202C22×M16—91no—
203C2×#117—91no—
204#419—32no—
205#419—92no—
206#419—92no—
207#419—92no—
208C2×#103—91no—
209C2×#103—91no—
210C2×#103—91no—
211C2×#103—91no—
212C23×D3—32no—
213C2×C3×Q8—21no—
214C2×C3×Q8—38no—
215C2×C3×Q8—32no—
216C2×C3×Q8—62no—
217C2×C3×Q8—64no—
218C2×C3×Q8C22×D312yes—
219C22×C3×C4—32no—
220C22×C3×C4—62no—
221C22×Dic3—32no—
222C22×Dic3—62no—
223D3×Q8—24no—
224D3×Q8—38no—
225D3×Q8—38no—
226D3×Q8—38no—
227D3×Q8—64no—
228D3×Q8—64no—
229D3×Q8—616no—
230D3×Q8—616no—
231D3×Q8—64no—
232D3×Q8—64no—
233D3×Q8—122no—
234D3×Q8C4×D318yescomplemented
235C2×C4×D3—22no—
236C2×C4×D3—32no—
237C2×C4×D3—32no—
238C2×C4×D3—32no—
239C2×C4×D3—38no—
240C2×C4×D3—38no—
241C2×C4×D3—61no—
242C2×C4×D3—616no—
243C2×C4×D3—62no—
244C2×C4×D3—62no—
245C2×C4×D3—62no—
246C2×C4×D3—62no—
247C2×C4×D3—62no—
248C2×C4×D3—121no—
249C2×C4×D3—121no—
250C2×C4×D3C22×D312yes—
251C2×Dic6—22no—
252C2×Dic6—32no—
253C2×Dic6—38no—
254C2×Dic6—61no—
255C2×Dic6—616no—
256C2×Dic6—64no—
257C2×Dic6—62no—
258C2×Dic6—62no—
259C2×Dic6—62no—
260C2×Dic6—62no—
261C2×Dic6—121no—
262C2×Dic6C22×D312yes—
263C3×M16—64no—
264C2×C3×C8—21no—
265C2×C3×C8—32no—
266C2×C3×C8C22×D312yes—
267C3×C4⋊C4—21no—
268C3×C4⋊C4—32no—
269C3×C4⋊C4C22×D312yes—
270C3×C22⋊C4—62no—
271C3×C42—62no—
272#217—62no—
273(C2×D3)⋊C4—22no—
274(C2×D3)⋊C4—62no—
275C4⋊Dic3—32no—
276C4⋊Dic3—61no—
277C4⋊Dic3C22×D312yes—
278Dic3⋊C4—62no—
279Dic3⋊C4—62no—
280Dic3⋊C4—121no—
281C4×Dic3—22no—
282C4×Dic3—62no—
283C4×Dic3—62no—
284#208—64no—
285C2×C3⋊C8—32no—
286C2×C3⋊C8—61no—
287C2×C3⋊C8C22×D312yes—
288ΓL(1,𝔽25)—24no—
289ΓL(1,𝔽25)—64no—
290D3×C8—64no—
291D3×C8—64no—
292D3×C8—122no—
293C22×C32C22×D411yescharacteristic
294C2×C3⋊D3C2×C22⋊C412yes—
295C2×C3⋊D3#13712yes—
296C2×C3⋊D3#13712yes—
297C2×C3×D3—22no—
298C2×C3×D3—22no—
299C2×C3×D3C2×C22⋊C414yes—
300D32—28no—
301C32×C4—22no—
302C32×C4—41no—
303C32×C4C23×C411yescharacteristic
304C32×C4C22×D411yescharacteristic
305C3⋊Dic3—22no—
306C3⋊Dic3—41no—
307C3⋊Dic3C2×C22⋊C412yes—
308C3×Dic3—24no—
309C3×Dic3—42no—
310C3×Dic3C2×C22⋊C414yes—
311C22×Q8—32no—
312C22×Q8—92no—
313C22×Q8—91no—
314C22×Q8—98no—
315C22×Q8—91no—
316C22×Q8—182no—
317C22×Q8—181no—
318C22×Q8—184no—
319C23×C4—91no—
320C23×C4—181no—
321C2×M16—32no—
322C2×M16—92no—
323C2×M16—184no—
324C22×C8—91no—
325C22×C8—91no—
326#117—32no—
327#117—92no—
328#117—182no—
329C2×C4⋊C4—91no—
330C2×C4⋊C4—91no—
331C2×C22⋊C4—181no—
332C2×C42—181no—
333#103—32no—
334#103—32no—
335#103—32no—
336#103—92no—
337#103—92no—
338#103—92no—
339#103—91no—
340#103—91no—
341#103—91no—
342#103D3211yescharacteristic, complemented
343C23×C3—32no—
344C22×D3—32no—
345C22×D3—38no—
346C22×D3—61no—
347C22×D3—64no—
348C22×D3—64no—
349C22×D3D3×D412yes—
350C3×Q8—22no—
351C3×Q8—22no—
352C3×Q8—34no—
353C3×Q8—41no—
354C3×Q8—68no—
355C3×Q8—62no—
356C3×Q8C2×C4×D314yes—
357C2×C3×C4—22no—
358C2×C3×C4—22no—
359C2×C3×C4—21no—
360C2×C3×C4—32no—
361C2×C3×C4—34no—
362C2×C3×C4—34no—
363C2×C3×C4—41no—
364C2×C3×C4—41no—
365C2×C3×C4—68no—
366C2×C3×C4—62no—
367C2×C3×C4—62no—
368C2×C3×C4C23×D312yes—
369C2×Dic3—22no—
370C2×Dic3—22no—
371C2×Dic3—32no—
372C2×Dic3—38no—
373C2×Dic3—61no—
374C2×Dic3—68no—
375C2×Dic3—62no—
376C2×Dic3—62no—
377C2×Dic3—121no—
378C2×Dic3—121no—
379C2×Dic3D3×D412yes—
380C4×D3—28no—
381C4×D3—38no—
382C4×D3—34no—
383C4×D3—34no—
384C4×D3—38no—
385C4×D3—62no—
386C4×D3—62no—
387C4×D3—68no—
388C4×D3—68no—
389C4×D3—68no—
390C4×D3—124no—
391C4×D3—124no—
392C4×D3—124no—
393C4×D3—242no—
394C4×D3C2×C4×D314yes—
395C4×D3D3×D414yes—
396Dic6—22no—
397Dic6—28no—
398Dic6—34no—
399Dic6—62no—
400Dic6—68no—
401Dic6—68no—
402Dic6—68no—
403Dic6—62no—
404Dic6—68no—
405Dic6—124no—
406Dic6—121no—
407Dic6C2×C4×D314yes—
408C3×C8—22no—
409C3×C8—41no—
410C3×C8—62no—
411C3⋊C8—22no—
412C3⋊C8—62no—
413C3⋊C8—121no—
414C2×C32C22×C22⋊C411yescharacteristic
415C2×C32C2×#13711yescharacteristic
416C2×C32C2×#13711yescharacteristic
417C3⋊D3#41914yescomplemented
418C3×D3—24no—
419C24—91no—
420C2×Q8—38no—
421C2×Q8—32no—
422C2×Q8—62no—
423C2×Q8—64no—
424C2×Q8—98no—
425C2×Q8—94no—
426C2×Q8—94no—
427C2×Q8—91no—
428C2×Q8—181no—
429C2×Q8—182no—
430C2×Q8—184no—
431C2×Q8—181no—
432C2×Q8—1816no—
433C2×Q8—182no—
434C2×Q8—188no—
435C2×Q8—182no—
436C2×Q8C2×D3211yescharacteristic
437C22×C4—32no—
438C22×C4—62no—
439C22×C4—91no—
440C22×C4—94no—
441C22×C4—94no—
442C22×C4—92no—
443C22×C4—91no—
444C22×C4—181no—
445C22×C4—181no—
446C22×C4—188no—
447C22×C4—181no—
448C22×C4—181no—
449C22×C4—182no—
450M16—64no—
451M16—184no—
452C2×C8—32no—
453C2×C8—91no—
454C2×C8—182no—
455C2×C8—182no—
456C2×C8C2×D3211yescharacteristic
457C4⋊C4—32no—
458C4⋊C4—91no—
459C4⋊C4—181no—
460C4⋊C4—181no—
461C4⋊C4C2×D3211yescharacteristic
462C22⋊C4—62no—
463C22⋊C4—182no—
464C42—62no—
465C42—182no—
466C22×C3—21no—
467C22×C3—34no—
468C22×C3—62no—
469C22×C3—62no—
470C22×C3C2×D3×D412yes—
471C2×D3—22no—
472C2×D3—22no—
473C2×D3—34no—
474C2×D3—34no—
475C2×D3—34no—
476C2×D3—62no—
477C2×D3—62no—
478C2×D3—62no—
479C2×D3—616no—
480C2×D3D3×C22⋊C414yes—
481C3×C4—24no—
482C3×C4—21no—
483C3×C4—21no—
484C3×C4—34no—
485C3×C4—42no—
486C3×C4—42no—
487C3×C4—64no—
488C3×C4—81no—
489C3×C4—122no—
490C3×C4C22×C4×D312yes—
491C3×C4C2×D3×D412yes—
492Dic3—24no—
493Dic3—34no—
494Dic3—42no—
495Dic3—62no—
496Dic3—64no—
497Dic3—122no—
498Dic3—122no—
499Dic3—241no—
500Dic3D3×C22⋊C414yes—
501C32C2×#41911yescharacteristic, complemented, Sylow
502C23—32no—
503C23—94no—
504C23—91no—
505C23—182no—
506C23—182no—
507Q8—21no—
508Q8—34no—
509Q8—68no—
510Q8—62no—
511Q8—92no—
512Q8—184no—
513Q8—188no—
514Q8—184no—
515Q8—181no—
516Q8C4×D3212yes—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—32no—
520C2×C4—34no—
521C2×C4—34no—
522C2×C4—68no—
523C2×C4—62no—
524C2×C4—62no—
525C2×C4—94no—
526C2×C4—98no—
527C2×C4—91no—
528C2×C4—92no—
529C2×C4—92no—
530C2×C4—184no—
531C2×C4—184no—
532C2×C4—188no—
533C2×C4—181no—
534C2×C4—181no—
535C2×C4—362no—
536C2×C4—362no—
537C2×C4C22×D3211yescharacteristic
538C8—21no—
539C8—62no—
540C8—181no—
541C2×C3—21no—
542C2×C3—21no—
543C2×C3—21no—
544C2×C3—64no—
545C2×C3C2×D3×C22⋊C412yes—
546C2×C3D3×#13712yes—
547C2×C3D3×#13712yes—
548D3—24no—
549D3—38no—
550D3—64no—
551C22—34no—
552C22—62no—
553C22—62no—
554C22—92no—
555C22—92no—
556C22—92no—
557C22—188no—
558C22D32×D411yescharacteristic
559C4—22no—
560C4—34no—
561C4—41no—
562C4—64no—
563C4—92no—
564C4—122no—
565C4—182no—
566C4—361no—
567C4C2×C4×D3211yescharacteristic
568C4D32×D411yescharacteristic
569C3—21no—
570C3D3×#41912yescomplemented
571C2—64no—
572C2—94no—
573C2D32×C22⋊C411yescharacteristic
574C2#1059474211yescharacteristic
575C2#1059476011yescharacteristic
subgroupG/H
centerC22D32×D4
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC32×#103C22
socleC22×C32C22×D4
prime radicalC22×D32D4
cosocleC2×C32×C4C24
hypercenter#103D32
hypocenterC32C2×#419
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
4. C3⋊D3×#103C2semidirect
5. C3×#4802C2semidirect
6. #10591557C2semidirect
7. #10591552C2semidirect
8. #10590948C2semidirect
9. #10590672C2semidirect
10. #10590601C2semidirect
11. #10590600C2semidirect
16. D32×Q8C4semidirect
35. C32×#103C22semidirect
36. #63662C22semidirect
37. #63643C22semidirect
38. #63637C22semidirect
39. C3×#835C22semidirect
40. C3×#816C22semidirect
41. C3×#810C22semidirect
42. #63567C22semidirect
43. #63566C22semidirect
44. #63565C22semidirect
55. #4802D3semidirect
71. C3×D3×Q8C2×C4semidirect
91. D3×Dic6C2×C4semidirect
146. C3×#103C2×D3semidirect
151. #835C2×D3semidirect
156. #816C2×D3semidirect
161. #810C2×D3semidirect
234. D3×Q8C4×D3semidirect
342. #103D32semidirect
417. C3⋊D3#419semidirect
501. C32C2×#419semidirect
570. C3D3×#419semidirect

Maximal subgroups

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

subgroupindex
C2×D32×Q82
C2×#637912
#105946022
C3⋊D3×#1032
C3×#48022
#105915572
#105915522
#105909482
#105906722
#105906012
#105906002
D3×#4193