Finite Group Databasebeta

← #11858591

Subgroups — #11858591

Order 1152.

1009 conjugacy classes of subgroups.

The subgroup lattice has 551 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5523C211yesmaximal, characteristic
2#10594986C211yesmaximal, characteristic
3C2×#63815C211yesmaximal, characteristic
4#10592697C211yesmaximal, characteristic, complemented
5C3×#4995C211yesmaximal, characteristic, complemented
6C2×#63576C211yesmaximal, characteristic, complemented
7#10591130C211yesmaximal, characteristic, complemented
8#10590580C212yesmaximal, complemented
9#10590572C212yesmaximal, complemented
10D3×#807C212yesmaximal, complemented
11#10590437C212yesmaximal, complemented
12#82562—31nomaximal
13#79210—31nomaximal
14C2×C3×#235C2211yescharacteristic
15C32×#117C2211yescharacteristic
16#64135C2211yescharacteristic
17C22×C3⋊(C3⋊C8)C2211yescharacteristic
18C2×C3×C4⋊Dic3C2211yescharacteristic
19C2×C3×C4⋊Dic3C2211yescharacteristic
20C2×C3×#208C2211yescharacteristic
21C3×#892C2212yes—
22C3×D3×C4⋊C4C2212yes—
23C3×#67⋊C4—22no—
24C3×C4×D12—21no—
25C3×C4×Dic6—21no—
26Dic3×#67—22no—
27#63898—21no—
28D3×C4⋊Dic3C2212yes—
29#63843—21no—
30#63841C2212yes—
31C2×#3711C2212yes—
32#63815C418yescomplemented
33C2×D3×C3⋊C8C2212yes—
34#63635C2211yescharacteristic
35#63635C2211yescharacteristic
36#63634C2211yescharacteristic
37#63634C2211yescharacteristic
38C3×#808C2212yes—
39C3×#807C2212yes—
40#63576C2212yes—
41#63576C2212yes—
42#63575C2212yes—
43#63573C2212yes—
44C3×#520—31no—
45#5827—31no—
46C2×#948—31no—
47C2×#907—31no—
48#5523D311yescharacteristic
49#5504—31no—
50C3×#428—31no—
51#5121—31no—
52#4998—31no—
53#4998—31no—
54#4998—32no—
55#4998—61no—
56#4995—32no—
57#4995D311yescharacteristic, complemented
58#4964—31no—
59#4964—32no—
60C2×#807—31no—
61C2×#807—31no—
62C2×#807—32no—
63#4881—32no—
64D3×#107—32no—
65#4861—32no—
66#4860—32no—
67C22×C32×C4C2311yescharacteristic
68C2×C3×#67D412yes—
69C22×C3×Dic3—21no—
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—
82#3757—21no—
83C4⋊(C3⋊Dic3)C2311yescharacteristic
84C4⋊(C3⋊Dic3)C2311yescharacteristic
85C4×C3⋊Dic3—21no—
86C2×C3⋊(C3⋊C8)C2×C414yescomplemented
87C2×C3⋊(C3⋊C8)C2311yescharacteristic
88C2×C3⋊(C3⋊C8)C2311yescharacteristic
89C3×(C2×D3)⋊C4—22no—
90C3×C4⋊Dic3—21no—
91C3×C4⋊Dic3—21no—
92C3×C4⋊Dic3C2312yes—
93C3×C4⋊Dic3C2312yes—
94C3×Dic3⋊C4—22no—
95C3×C4×Dic3—22no—
96C3×#208C2×C414yescomplemented
97C2×C3×C3⋊C8C2312yes—
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
106C2×C3×M16—31no—
107C3×C4×Q8—61no—
108C3×C4×D4—61no—
109C3×C4×D4—62no—
110C3×#117—21no—
111C3×#117—32no—
112C3×#117C2×D311yescharacteristic
113C3×#117C2×D311yescharacteristic
114C2×C3×C4⋊C4—31no—
115C2×C3×C4⋊C4—31no—
116C2×C3×C4⋊C4—32no—
117#948—38no—
118Q8×Dic3—61no—
119D4×Dic3—61no—
120D4×Dic3—62no—
121C4×#67—62no—
122#926—31no—
123#926—31no—
124#926—32no—
125#926—61no—
126C2×C4⋊Dic3—32no—
127C2×C4⋊Dic3C2×D311yescharacteristic
128C2×C4⋊Dic3C2×D311yescharacteristic
129C2×#208—32no—
130C2×#208C2×D311yescharacteristic
131C22×C3⋊C8—31no—
132C22×C3⋊C8—31no—
133C22×C3⋊C8—32no—
134C22×C3⋊C8—61no—
135#907—38no—
136C2×ΓL(1,𝔽25)—32no—
137C2×D3×C8—32no—
138#893—61no—
139#892—32no—
140#892C2×D312yes—
141D3×C4⋊C4—32no—
142D3×C4⋊C4C2×D312yes—
143#887—61no—
144#67⋊C4—22no—
145C4×D12—21no—
146C4×Dic6—21no—
147C3×#107—32no—
148C3×#106—32no—
149#818—32no—
150#817—32no—
151#808—31no—
152#808—31no—
153#808—31no—
154#808—31no—
155#808—32no—
156#808—61no—
157#808—61no—
158#808C2×D312yes—
159#807—31no—
160#807—31no—
161#807—31no—
162#807—31no—
163#807—32no—
164#807—32no—
165#807—32no—
166#807—32no—
167#807—32no—
168#807—61no—
169#807—61no—
170#807C2×D312yes—
171C23×C32C2×D411yescharacteristic
172C22×C3×D3C2×D412yes—
173C2×C32×C4—21no—
174C2×C32×C4—21no—
175C2×C32×C4C22×C412yes—
176C2×C32×C4C2×D411yescharacteristic
177C2×C32×C4C2×Q812yes—
178C2×C32×C4C2411yescharacteristic
179C2×C3⋊Dic3—21no—
180C2×C3⋊Dic3—21no—
181C3×#67C4⋊C418yes—
182C2×C3×Dic3—22no—
183C2×C3×Dic3—22no—
184C2×C3×Dic3—81no—
185C2×C3×Dic3—81no—
186C2×C3×Dic3C2×D412yes—
187C3×D12C4⋊C414yes—
188C3×C4×D3—82no—
189C3×C4×D3C22×C414yes—
190C3×C4×D3C2×Q814yes—
191C3×Dic6C4⋊C414yes—
192D3×Dic3—82no—
193C3⋊(C3⋊C8)C22×C412yes—
194C3⋊(C3⋊C8)C22×C412yes—
195C3×C3⋊C8C22×C414yes—
196C2×#131—91no—
197#520—31no—
198#520—91no—
199#428—31no—
200#428—92no—
201#428—92no—
202#428—91no—
203#427—92no—
204#427—91no—
205C2×#107—92no—
206C2×#107—91no—
207C3×#41—34no—
208C3×#41—34no—
209C2×C3×Q8—31no—
210C2×C3×D4—32no—
211C2×C3×D4—31no—
212C22×C3×C4—21no—
213C22×C3×C4—32no—
214C22×C3×C4—62no—
215C22×C3×C4—61no—
216C22×C3×C4—61no—
217C22×C3×C4C22×D311yescharacteristic
218C22×C3×C4C22×D311yescharacteristic
219C2×#67#6712yes—
220C22×Dic3—21no—
221C22×Dic3—21no—
222C22×Dic3—62no—
223#235Dic614yes—
224#235C4×D314yes—
225C2×D12#6711yescharacteristic
226C2×C4×D3—22no—
227C2×C4×D3—62no—
228C2×C4×D3C22×D312yes—
229C2×Dic6#6711yescharacteristic
230C3×M16—34no—
231C2×C3×C8—32no—
232C3×C4⋊C4—21no—
233C3×C4⋊C4—21no—
234C3×C4⋊C4—32no—
235C3×C4⋊C4—32no—
236C3×C4⋊C4—62no—
237C3×C4⋊C4—61no—
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×C42—21no—
248C3×C42—21no—
249C3×C42—41no—
250C3×C42—62no—
251#217—62no—
252#217—61no—
253#217—61no—
254#217—121no—
255(C2×D3)⋊C4—22no—
256(C2×D3)⋊C4—62no—
257C4⋊Dic3—21no—
258C4⋊Dic3—21no—
259C4⋊Dic3—31no—
260C4⋊Dic3—31no—
261C4⋊Dic3—31no—
262C4⋊Dic3—31no—
263C4⋊Dic3—61no—
264C4⋊Dic3—61no—
265C4⋊Dic3—62no—
266C4⋊Dic3C22×D312yes—
267C4⋊Dic3C22×D312yes—
268Dic3⋊C4—22no—
269Dic3⋊C4—62no—
270C4×Dic3—22no—
271C4×Dic3—62no—
272C4×Dic3—61no—
273C4×Dic3—61no—
274C4×Dic3—62no—
275C4×Dic3—121no—
276#208—38no—
277#208C4×D314yescomplemented
278C2×C3⋊C8—34no—
279C2×C3⋊C8—34no—
280C2×C3⋊C8—31no—
281C2×C3⋊C8—31no—
282C2×C3⋊C8—31no—
283C2×C3⋊C8—31no—
284C2×C3⋊C8—38no—
285C2×C3⋊C8—61no—
286C2×C3⋊C8—61no—
287C2×C3⋊C8—64no—
288C2×C3⋊C8C22×D312yes—
289ΓL(1,𝔽25)—38no—
290D3×C8—38no—
291C22×C32—21no—
292C22×C32—21no—
293C22×C32C2×C4⋊C412yes—
294C22×C32C22×D411yescharacteristic
295C2×C3×D3—22no—
296C2×C3×D3—22no—
297C2×C3×D3C2×C4⋊C414yes—
298C32×C4—41no—
299C32×C4—41no—
300C32×C4C2×C4⋊C412yes—
301C32×C4C23×C411yescharacteristic
302C32×C4C22×Q811yescharacteristic
303C3⋊Dic3—41no—
304C3⋊Dic3—41no—
305C3×Dic3—42no—
306C3×Dic3—42no—
307C3×Dic3C2×C4⋊C414yes—
308C2×#41—31no—
309#131—98no—
310C2×M16—31no—
311C2×M16—92no—
312C22×C8—92no—
313C22×C8—91no—
314C4×Q8—61no—
315C4×Q8—181no—
316C4×D4—61no—
317C4×D4—62no—
318C4×D4—181no—
319C4×D4—182no—
320#117—32no—
321#117—92no—
322#117—91no—
323#117D3211yescharacteristic
324C2×C4⋊C4—31no—
325C2×C4⋊C4—31no—
326C2×C4⋊C4—32no—
327C2×C4⋊C4—92no—
328#107—32no—
329#107—92no—
330#107—92no—
331#107—92no—
332#107—91no—
333#107—91no—
334#106—32no—
335#106—92no—
336#106—91no—
337#106—91no—
338C23×C3—21no—
339C23×C3—32no—
340C23×C3D3×D411yescharacteristic
341C23×C3C2×#6711yescharacteristic
342C22×D3C2×#6712yes—
343C3×Q8—34no—
344C3×D4—38no—
345C3×D4—34no—
346C2×C3×C4—21no—
347C2×C3×C4—21no—
348C2×C3×C4—21no—
349C2×C3×C4—21no—
350C2×C3×C4—21no—
351C2×C3×C4—22no—
352C2×C3×C4—22no—
353C2×C3×C4—21no—
354C2×C3×C4—32no—
355C2×C3×C4—34no—
356C2×C3×C4—34no—
357C2×C3×C4—41no—
358C2×C3×C4—41no—
359C2×C3×C4—62no—
360C2×C3×C4—62no—
361C2×C3×C4—242no—
362C2×C3×C4—241no—
363C2×C3×C4—241no—
364C2×C3×C4C2×Dic612yes—
365C2×C3×C4C2×C4×D312yes—
366C2×C3×C4C2×C4×D312yes—
367C2×C3×C4D3×D411yescharacteristic
368C2×C3×C4D3×Q812yes—
369C2×C3×C4C2×#6711yescharacteristic
370C2×C3×C4C23×D311yescharacteristic
371C2×C3×C4C23×D311yescharacteristic
372#67Dic3⋊C418yes—
373C2×Dic3—22no—
374C2×Dic3—22no—
375C2×Dic3—61no—
376C2×Dic3—61no—
377C2×Dic3—61no—
378C2×Dic3—61no—
379C2×Dic3—81no—
380C2×Dic3—81no—
381C2×Dic3—121no—
382C2×Dic3—121no—
383C2×Dic3—242no—
384C2×Dic3C2×#6712yes—
385D12Dic3⋊C414yes—
386C4×D3—82no—
387C4×D3—242no—
388C4×D3C2×Dic614yes—
389C4×D3C2×C4×D314yes—
390Dic6Dic3⋊C414yes—
391C3×C8—34no—
392C3⋊C8—32no—
393C3⋊C8—32no—
394C3⋊C8—32no—
395C3⋊C8—32no—
396C3⋊C8—62no—
397C3⋊C8—62no—
398C3⋊C8C2×C4×D314yes—
399C2×C32—22no—
400C2×C32C22×C4⋊C411yescharacteristic
401C2×C32#57611yescharacteristic
402C2×C32#57811yescharacteristic
403C3×D3—24no—
404#41—34no—
405#41—34no—
406C2×Q8—31no—
407C2×D4—32no—
408C2×D4—31no—
409C22×C4—32no—
410C22×C4—62no—
411C22×C4—61no—
412C22×C4—61no—
413C22×C4—182no—
414C22×C4C2×D3211yescharacteristic
415M16—34no—
416M16—98no—
417C2×C8—32no—
418C2×C8—98no—
419C2×C8—91no—
420C2×C8—91no—
421C2×C8—94no—
422C4⋊C4—32no—
423C4⋊C4—32no—
424C4⋊C4—62no—
425C4⋊C4—61no—
426C4⋊C4—61no—
427C4⋊C4—91no—
428C4⋊C4—91no—
429C4⋊C4—182no—
430C4⋊C4C2×D3211yescharacteristic
431C4⋊C4C2×D3211yescharacteristic
432C22⋊C4—21no—
433C22⋊C4—62no—
434C22⋊C4—182no—
435C22⋊C4—181no—
436C42—21no—
437C42—62no—
438C42—182no—
439C42—181no—
440C22×C3—21no—
441C22×C3—21no—
442C22×C3—21no—
443C22×C3—21no—
444C22×C3—21no—
445C22×C3—22no—
446C22×C3—34no—
447C22×C3—41no—
448C22×C3—41no—
449C22×C3—62no—
450C22×C3—62no—
451C22×C3D3×C4⋊C412yes—
452C22×C3C2×Dic3⋊C412yes—
453C22×C3C2×D3×D411yescharacteristic
454C22×C3C22×#6711yescharacteristic
455C2×D3—22no—
456C2×D3—22no—
457C2×D3C2×Dic3⋊C414yes—
458C3×C4—21no—
459C3×C4—21no—
460C3×C4—22no—
461C3×C4—34no—
462C3×C4—41no—
463C3×C4—41no—
464C3×C4—41no—
465C3×C4—41no—
466C3×C4—81no—
467C3×C4—81no—
468C3×C4—122no—
469C3×C4—122no—
470C3×C4D3×C4⋊C412yes—
471C3×C4C2×Dic3⋊C412yes—
472C3×C4C22×Dic611yescharacteristic
473C3×C4C22×C4×D311yescharacteristic
474C3×C4C22×C4×D311yescharacteristic
475C3×C4C2×D3×Q811yescharacteristic
476Dic3—42no—
477Dic3—42no—
478Dic3—121no—
479Dic3—121no—
480Dic3—121no—
481Dic3—121no—
482Dic3—241no—
483Dic3—241no—
484Dic3C2×Dic3⋊C414yes—
485C32#291311yescharacteristic, complemented, Sylow
486C23—32no—
487C23D3×#6711yescharacteristic
488Q8—34no—
489D4—38no—
490D4—34no—
491C2×C4—21no—
492C2×C4—21no—
493C2×C4—32no—
494C2×C4—34no—
495C2×C4—34no—
496C2×C4—62no—
497C2×C4—62no—
498C2×C4—181no—
499C2×C4—181no—
500C2×C4—242no—
501C2×C4—241no—
502C2×C4—241no—
503C2×C4—722no—
504C2×C4D3×Dic612yes—
505C2×C4C4×D3212yes—
506C2×C4D3×#6711yescharacteristic
507C2×C4C22×D3211yescharacteristic
508C8—34no—
509C8—92no—
510C8—92no—
511C2×C3—22no—
512C2×C3—22no—
513C2×C3—21no—
514C2×C3—21no—
515C2×C3—21no—
516C2×C3—42no—
517C2×C3—64no—
518C2×C3C2×D3×C4⋊C411yescharacteristic
519C2×C3#577411yescharacteristic
520C2×C3#577911yescharacteristic
521C2×C3C22×Dic3⋊C411yescharacteristic
522C2×C3#583511yescharacteristic
523C2×C3#583811yescharacteristic
524D3—24no—
525C22—21no—
526C22—21no—
527C22—34no—
528C22—62no—
529C22—62no—
530C22D3×Dic3⋊C412yes—
531C22C2×D3×#6711yescharacteristic
532C4—34no—
533C4—41no—
534C4—41no—
535C4—122no—
536C4—122no—
537C4—361no—
538C4—361no—
539C4D3×Dic3⋊C412yes—
540C4C2×D3×Dic611yescharacteristic
541C4C2×C4×D3211yescharacteristic
542C3—21no—
543C3#7921011yescharacteristic, complemented
544C3#8256211yescharacteristic, complemented
545C2—22no—
546C2—64no—
547C2C2×D3×Dic3⋊C411yescharacteristic
548C2#1059545411yescharacteristic
549C2#1059546511yescharacteristic
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. #10592697C2semidirect
5. C3×#4995C2semidirect
6. C2×#63576C2semidirect
7. #10591130C2semidirect
8. #10590580C2semidirect
9. #10590572C2semidirect
10. D3×#807C2semidirect
11. #10590437C2semidirect
32. #63815C4semidirect
57. #4995D3semidirect
86. C2×C3⋊(C3⋊C8)C2×C4semidirect
96. C3×#208C2×C4semidirect
101. #3711C2×C4semidirect
102. D3×C3⋊C8C2×C4semidirect
277. #208C4×D3semidirect
485. C32#2913semidirect
543. C3#79210semidirect
544. C3#82562semidirect

Maximal subgroups

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

subgroupindex
C3×#55232
#105949862
C2×#638152
#105926972
C3×#49952
C2×#635762
#105911302
#105905802
#105905722
D3×#8072
#105904372
#825623
#792103