Finite Group Databasebeta

← #11858593

Subgroups — #11858593

Order 1152.

1011 conjugacy classes of subgroups.

The subgroup lattice has 545 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5523C211yesmaximal, characteristic
2#10594992C211yesmaximal, characteristic
3C2×#63814C211yesmaximal, characteristic
4#10592694C211yesmaximal, characteristic, complemented
5C3×#4998C211yesmaximal, characteristic, complemented
6#10591139C211yesmaximal, characteristic, complemented
7C2×#63575C211yesmaximal, characteristic, complemented
8#10590581C212yesmaximal, complemented
9#10590571C212yesmaximal, complemented
10D3×#807C212yesmaximal, complemented
11#10590437C212yesmaximal, complemented
12#82562—31nomaximal
13#79179—31nomaximal
14C2×C3×#235C2211yescharacteristic
15C32×#117C2211yescharacteristic
16C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
17C2×#3748C2211yescharacteristic
18C3×#926C2211yescharacteristic
19C2×C3×C4⋊Dic3C2211yescharacteristic
20C22×C3×C3⋊C8C2211yescharacteristic
21C3×#892C2212yes—
22C3×D3×C4⋊C4C2212yes—
23C3×#67⋊C4—22no—
24C3×C4×D12—21no—
25C3×C4×Dic6—21no—
26#67⋊Dic3—22no—
27Dic3×D12—21no—
28D3×C4⋊Dic3C2212yes—
29Dic3×Dic6—21no—
30#63841C2212yes—
31C2×#3711C2212yes—
32#63814C418yescomplemented
33C2×D3×C3⋊C8C2212yes—
34#63635C2212yes—
35#63634C2212yes—
36C3×#808C2211yescharacteristic
37C3×#808C2211yescharacteristic
38C3×#807C2211yescharacteristic
39C3×#807C2211yescharacteristic
40#63576C2212yes—
41#63575C2212yes—
42#63575C2212yes—
43#63574C2212yes—
44C3×#520—31no—
45#5827—31no—
46C2×#948—31no—
47C2×#901—31no—
48#5523—31no—
49#5523D311yescharacteristic
50C3×#427—31no—
51C2×#818—31no—
52#4998—32no—
53#4998D311yescharacteristic, complemented
54#4995—31no—
55#4995—31no—
56#4995—31no—
57#4995—32no—
58#4995—61no—
59#4964—31no—
60#4964—32no—
61C2×#807—31no—
62C2×#807—32no—
63#4880—32no—
64D3×#107—32no—
65#4861—32no—
66#4861—32no—
67C22×C32×C4C2311yescharacteristic
68C22×C3⋊Dic3—21no—
69C2×C3×#67D412yes—
70C22×C3×Dic3—21no—
71C3×#235C2×C414yes—
72C3×#235Q814yes—
73C2×C3×D12D411yescharacteristic
74C2×C3×C4×D3—22no—
75C2×C3×C4×D3C2312yes—
76C2×C3×Dic6D411yescharacteristic
77C2×D3×Dic3—22no—
78C32×C4⋊C4C2311yescharacteristic
79C32×C4⋊C4C2311yescharacteristic
80C32×C22⋊C4—21no—
81C32×C42—21no—
82C4⋊(C3⋊Dic3)—21no—
83C4⋊(C3⋊Dic3)C2312yes—
84#3748C2×C414yescomplemented
85C2×C3⋊(C3⋊C8)C2312yes—
86C3×#217—21no—
87C3×(C2×D3)⋊C4—22no—
88C3×C4⋊Dic3—21no—
89C3×C4⋊Dic3C2312yes—
90C3×C4⋊Dic3C2311yescharacteristic
91C3×C4⋊Dic3C2311yescharacteristic
92C3×Dic3⋊C4—22no—
93C3×C4×Dic3—21no—
94C3×C4×Dic3—22no—
95C2×C3×C3⋊C8C2×C414yescomplemented
96C2×C3×C3⋊C8C2311yescharacteristic
97C2×C3×C3⋊C8C2311yescharacteristic
98Dic3⋊Dic3—22no—
99(C2×D3)⋊Dic3—22no—
100Dic32—22no—
101#3711C2×C418yescomplemented
102D3×C3⋊C8C2×C418yescomplemented
103#2913—91noSylow
104C2×C3×#41—31no—
105C2×#235C2×D311yescharacteristic
106C22×C3×C8—31no—
107C3×C4×Q8—61no—
108C3×C4×D4—61no—
109C3×C4×D4—62no—
110C3×#117—21no—
111C3×#117—31no—
112C3×#117—32no—
113C3×#117C2×D311yescharacteristic
114C3×#117C2×D311yescharacteristic
115C2×C3×C4⋊C4—31no—
116C2×C3×C4⋊C4—32no—
117#948—38no—
118Q8×Dic3—61no—
119D4×Dic3—61no—
120D4×Dic3—62no—
121#926—32no—
122#926C2×D311yescharacteristic
123C2×C4⋊Dic3—31no—
124C2×C4⋊Dic3—31no—
125C2×C4⋊Dic3—32no—
126C2×C4⋊Dic3—61no—
127C2×C4⋊Dic3C2×D311yescharacteristic
128C2×#208—31no—
129C2×#208—31no—
130C2×#208—32no—
131C2×#208—61no—
132C22×C3⋊C8—32no—
133C22×C3⋊C8C2×D311yescharacteristic
134#901—38no—
135C2×ΓL(1,𝔽25)—32no—
136C2×D3×C8—32no—
137#892—32no—
138#892C2×D312yes—
139D3×C4⋊C4—32no—
140D3×C4⋊C4C2×D312yes—
141#67⋊C4—22no—
142#67⋊C4—62no—
143C4×D12—21no—
144C4×D12—61no—
145C4×Dic6—21no—
146C4×Dic6—61no—
147C3×#107—31no—
148C3×#107—31no—
149C3×#106—31no—
150C3×#106—31no—
151#818—32no—
152#818—32no—
153#808—32no—
154#808—32no—
155#808—32no—
156#808—32no—
157#808—62no—
158#808C2×D311yescharacteristic
159#808C2×D311yescharacteristic
160#807—32no—
161#807—32no—
162#807—32no—
163#807—32no—
164#807—32no—
165#807—32no—
166#807—62no—
167#807C2×D311yescharacteristic
168#807C2×D311yescharacteristic
169C23×C32C2×D411yescharacteristic
170C22×C3×D3C2×D412yes—
171C2×C32×C4—21no—
172C2×C32×C4—21no—
173C2×C32×C4C22×C412yes—
174C2×C32×C4C2×D411yescharacteristic
175C2×C32×C4C2×Q812yes—
176C2×C32×C4C2411yescharacteristic
177C2×C3⋊Dic3—22no—
178C2×C3⋊Dic3—81no—
179C3×#67C4⋊C418yes—
180C2×C3×Dic3—21no—
181C2×C3×Dic3—21no—
182C2×C3×Dic3—22no—
183C2×C3×Dic3—81no—
184C2×C3×Dic3C2×D412yes—
185C3×D12C4⋊C414yes—
186C3×C4×D3—82no—
187C3×C4×D3C22×C414yes—
188C3×C4×D3C2×Q814yes—
189C3×Dic6C4⋊C414yes—
190D3×Dic3—82no—
191C3⋊(C3⋊C8)C22×C414yes—
192C3×C3⋊C8C22×C412yes—
193C3×C3⋊C8C22×C412yes—
194C2×#131—91no—
195#520—31no—
196#520—91no—
197#428—92no—
198#428—92no—
199#428—91no—
200#428—91no—
201#427—31no—
202#427—92no—
203C2×#107—92no—
204C2×#107—91no—
205C3×#41—34no—
206C3×#41—34no—
207C2×C3×Q8—31no—
208C2×C3×D4—32no—
209C2×C3×D4—31no—
210C22×C3×C4—21no—
211C22×C3×C4—32no—
212C22×C3×C4—62no—
213C22×C3×C4—61no—
214C22×C3×C4C22×D311yescharacteristic
215C22×C3×C4C22×D311yescharacteristic
216C2×#67#6712yes—
217C22×Dic3—21no—
218C22×Dic3—62no—
219C22×Dic3—61no—
220C22×Dic3—61no—
221C22×Dic3—121no—
222#235Dic614yes—
223#235C4×D314yes—
224C2×D12#6711yescharacteristic
225C2×C4×D3—22no—
226C2×C4×D3—62no—
227C2×C4×D3C22×D312yes—
228C2×Dic6#6711yescharacteristic
229C2×C3×C8—34no—
230C2×C3×C8—31no—
231C2×C3×C8—31no—
232C3×C4⋊C4—21no—
233C3×C4⋊C4—21no—
234C3×C4⋊C4—32no—
235C3×C4⋊C4—31no—
236C3×C4⋊C4—31no—
237C3×C4⋊C4—62no—
238C3×C4⋊C4—61no—
239C3×C4⋊C4C22×D311yescharacteristic
240C3×C4⋊C4C22×D311yescharacteristic
241C3×C4⋊C4C22×D311yescharacteristic
242C3×C4⋊C4C22×D311yescharacteristic
243C3×C22⋊C4—21no—
244C3×C22⋊C4—21no—
245C3×C22⋊C4—41no—
246C3×C22⋊C4—62no—
247C3×C22⋊C4—61no—
248C3×C42—21no—
249C3×C42—21no—
250C3×C42—41no—
251C3×C42—62no—
252C3×C42—61no—
253#217—21no—
254#217—62no—
255(C2×D3)⋊C4—22no—
256(C2×D3)⋊C4—62no—
257C4⋊Dic3—21no—
258C4⋊Dic3—32no—
259C4⋊Dic3—32no—
260C4⋊Dic3—62no—
261C4⋊Dic3—62no—
262C4⋊Dic3—61no—
263C4⋊Dic3—61no—
264C4⋊Dic3—121no—
265C4⋊Dic3C22×D311yescharacteristic
266C4⋊Dic3C22×D312yes—
267C4⋊Dic3C22×D311yescharacteristic
268Dic3⋊C4—22no—
269Dic3⋊C4—62no—
270C4×Dic3—21no—
271C4×Dic3—22no—
272C4×Dic3—62no—
273C4×Dic3—62no—
274#208—34no—
275#208—34no—
276#208—38no—
277#208—64no—
278C2×C3⋊C8—32no—
279C2×C3⋊C8—32no—
280C2×C3⋊C8—38no—
281C2×C3⋊C8—62no—
282C2×C3⋊C8C4×D314yescomplemented
283C2×C3⋊C8C22×D311yescharacteristic
284C2×C3⋊C8C22×D311yescharacteristic
285ΓL(1,𝔽25)—38no—
286D3×C8—38no—
287C22×C32—21no—
288C22×C32—21no—
289C22×C32C2×C4⋊C412yes—
290C22×C32C22×D411yescharacteristic
291C2×C3×D3—22no—
292C2×C3×D3—22no—
293C2×C3×D3C2×C4⋊C414yes—
294C32×C4—41no—
295C32×C4—41no—
296C32×C4C2×C4⋊C412yes—
297C32×C4C23×C411yescharacteristic
298C32×C4C22×Q811yescharacteristic
299C3⋊Dic3—42no—
300C3×Dic3—41no—
301C3×Dic3—42no—
302C3×Dic3—41no—
303C3×Dic3C2×C4⋊C414yes—
304C2×#41—31no—
305#131—98no—
306C2×M16—92no—
307C2×M16—91no—
308C22×C8—31no—
309C22×C8—92no—
310C4×Q8—61no—
311C4×Q8—181no—
312C4×D4—61no—
313C4×D4—62no—
314C4×D4—181no—
315C4×D4—182no—
316#117—31no—
317#117—32no—
318#117—92no—
319#117D3211yescharacteristic
320C2×C4⋊C4—31no—
321C2×C4⋊C4—32no—
322C2×C4⋊C4—92no—
323C2×C4⋊C4—91no—
324#107—31no—
325#107—31no—
326#107—92no—
327#107—92no—
328#107—92no—
329#107—92no—
330#106—31no—
331#106—31no—
332#106—92no—
333#106—92no—
334C23×C3—21no—
335C23×C3—32no—
336C23×C3D3×D411yescharacteristic
337C23×C3C2×#6711yescharacteristic
338C22×D3C2×#6712yes—
339C3×Q8—34no—
340C3×D4—38no—
341C3×D4—34no—
342C2×C3×C4—21no—
343C2×C3×C4—21no—
344C2×C3×C4—21no—
345C2×C3×C4—21no—
346C2×C3×C4—21no—
347C2×C3×C4—22no—
348C2×C3×C4—22no—
349C2×C3×C4—21no—
350C2×C3×C4—32no—
351C2×C3×C4—34no—
352C2×C3×C4—34no—
353C2×C3×C4—41no—
354C2×C3×C4—41no—
355C2×C3×C4—62no—
356C2×C3×C4—61no—
357C2×C3×C4—61no—
358C2×C3×C4—242no—
359C2×C3×C4—241no—
360C2×C3×C4C2×Dic612yes—
361C2×C3×C4C2×C4×D312yes—
362C2×C3×C4C2×C4×D312yes—
363C2×C3×C4D3×D411yescharacteristic
364C2×C3×C4D3×Q812yes—
365C2×C3×C4C2×#6711yescharacteristic
366C2×C3×C4C23×D311yescharacteristic
367C2×C3×C4C23×D311yescharacteristic
368#67Dic3⋊C418yes—
369C2×Dic3—21no—
370C2×Dic3—21no—
371C2×Dic3—22no—
372C2×Dic3—62no—
373C2×Dic3—62no—
374C2×Dic3—81no—
375C2×Dic3—122no—
376C2×Dic3—242no—
377C2×Dic3—241no—
378C2×Dic3—241no—
379C2×Dic3—242no—
380C2×Dic3C2×#6712yes—
381D12Dic3⋊C414yes—
382C4×D3—82no—
383C4×D3—242no—
384C4×D3C2×Dic614yes—
385C4×D3C2×C4×D314yes—
386Dic6Dic3⋊C414yes—
387C3×C8—32no—
388C3×C8—32no—
389C3⋊C8—34no—
390C3⋊C8—34no—
391C3⋊C8—64no—
392C3⋊C8C2×C4×D312yes—
393C3⋊C8C2×C4×D312yes—
394C2×C32—22no—
395C2×C32C22×C4⋊C411yescharacteristic
396C2×C32#57611yescharacteristic
397C2×C32#57811yescharacteristic
398C3×D3—24no—
399#41—34no—
400#41—34no—
401C2×Q8—31no—
402C2×D4—32no—
403C2×D4—31no—
404C22×C4—32no—
405C22×C4—62no—
406C22×C4—61no—
407C22×C4—182no—
408C22×C4—181no—
409C22×C4C2×D3211yescharacteristic
410M16—98no—
411M16—94no—
412C2×C8—31no—
413C2×C8—31no—
414C2×C8—34no—
415C2×C8—98no—
416C2×C8—92no—
417C4⋊C4—31no—
418C4⋊C4—31no—
419C4⋊C4—32no—
420C4⋊C4—62no—
421C4⋊C4—61no—
422C4⋊C4—92no—
423C4⋊C4—182no—
424C4⋊C4—181no—
425C4⋊C4C2×D3211yescharacteristic
426C4⋊C4C2×D3211yescharacteristic
427C22⋊C4—21no—
428C22⋊C4—62no—
429C22⋊C4—61no—
430C22⋊C4—182no—
431C42—21no—
432C42—62no—
433C42—61no—
434C42—182no—
435C22×C3—21no—
436C22×C3—21no—
437C22×C3—21no—
438C22×C3—21no—
439C22×C3—21no—
440C22×C3—22no—
441C22×C3—34no—
442C22×C3—41no—
443C22×C3—41no—
444C22×C3—62no—
445C22×C3—62no—
446C22×C3D3×C4⋊C412yes—
447C22×C3C2×Dic3⋊C412yes—
448C22×C3C2×D3×D411yescharacteristic
449C22×C3C22×#6711yescharacteristic
450C2×D3—22no—
451C2×D3—22no—
452C2×D3C2×Dic3⋊C414yes—
453C3×C4—21no—
454C3×C4—21no—
455C3×C4—22no—
456C3×C4—34no—
457C3×C4—41no—
458C3×C4—41no—
459C3×C4—41no—
460C3×C4—41no—
461C3×C4—81no—
462C3×C4—81no—
463C3×C4—122no—
464C3×C4—121no—
465C3×C4—121no—
466C3×C4D3×C4⋊C412yes—
467C3×C4C2×Dic3⋊C412yes—
468C3×C4C22×Dic611yescharacteristic
469C3×C4C22×C4×D311yescharacteristic
470C3×C4C22×C4×D311yescharacteristic
471C3×C4C2×D3×Q811yescharacteristic
472Dic3—41no—
473Dic3—41no—
474Dic3—42no—
475Dic3—122no—
476Dic3—122no—
477Dic3—242no—
478Dic3C2×Dic3⋊C414yes—
479C32#291311yescharacteristic, complemented, Sylow
480C23—32no—
481C23D3×#6711yescharacteristic
482Q8—34no—
483D4—38no—
484D4—34no—
485C2×C4—21no—
486C2×C4—21no—
487C2×C4—32no—
488C2×C4—34no—
489C2×C4—34no—
490C2×C4—61no—
491C2×C4—62no—
492C2×C4—61no—
493C2×C4—182no—
494C2×C4—242no—
495C2×C4—241no—
496C2×C4—722no—
497C2×C4—721no—
498C2×C4D3×Dic612yes—
499C2×C4C4×D3212yes—
500C2×C4D3×#6711yescharacteristic
501C2×C4C22×D3211yescharacteristic
502C8—32no—
503C8—32no—
504C8—94no—
505C2×C3—22no—
506C2×C3—22no—
507C2×C3—21no—
508C2×C3—21no—
509C2×C3—21no—
510C2×C3—42no—
511C2×C3—64no—
512C2×C3C2×D3×C4⋊C411yescharacteristic
513C2×C3#576911yescharacteristic
514C2×C3#577111yescharacteristic
515C2×C3C22×Dic3⋊C411yescharacteristic
516C2×C3#583511yescharacteristic
517C2×C3#583811yescharacteristic
518D3—24no—
519C22—21no—
520C22—21no—
521C22—34no—
522C22—62no—
523C22—62no—
524C22D3×Dic3⋊C412yes—
525C22C2×D3×#6711yescharacteristic
526C4—34no—
527C4—41no—
528C4—41no—
529C4—122no—
530C4—121no—
531C4—121no—
532C4—362no—
533C4D3×Dic3⋊C412yes—
534C4C2×D3×Dic611yescharacteristic
535C4C2×C4×D3211yescharacteristic
536C3—21no—
537C3#7917911yescharacteristic, complemented
538C3#8256211yescharacteristic, complemented
539C2—22no—
540C2—64no—
541C2C2×D3×Dic3⋊C411yescharacteristic
542C2#1059545611yescharacteristic
543C2#1059546711yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC32×#117C22
socleC22×C32C22×D4
prime radicalC2×C3×#235C22
cosocleC2×C32×C4C24
hypercenter#117D32
hypocenterC32#2913
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #117

Complements

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

NH ≅ G/Ntype
4. #10592694C2semidirect
5. C3×#4998C2semidirect
6. #10591139C2semidirect
7. C2×#63575C2semidirect
8. #10590581C2semidirect
9. #10590571C2semidirect
10. D3×#807C2semidirect
11. #10590437C2semidirect
32. #63814C4semidirect
53. #4998D3semidirect
84. #3748C2×C4semidirect
95. C2×C3×C3⋊C8C2×C4semidirect
101. #3711C2×C4semidirect
102. D3×C3⋊C8C2×C4semidirect
282. C2×C3⋊C8C4×D3semidirect
479. C32#2913semidirect
537. C3#79179semidirect
538. C3#82562semidirect

Maximal subgroups

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

subgroupindex
C3×#55232
#105949922
C2×#638142
#105926942
C3×#49982
#105911392
C2×#635752
#105905812
#105905712
D3×#8072
#105904372
#825623
#791793