Finite Group Databasebeta

← #11858587

Subgroups — #11858587

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×#5504C211yesmaximal, characteristic
2#10594986C211yesmaximal, characteristic
3C2×#63814C211yesmaximal, characteristic
4#10592663C211yesmaximal, characteristic, complemented
5C2×C3×#807C211yesmaximal, characteristic, complemented
6#10591139C211yesmaximal, characteristic, complemented
7#10591122C211yesmaximal, characteristic, complemented
8#10590580C212yesmaximal, complemented
9#10590571C212yesmaximal, complemented
10D3×#807C212yesmaximal, complemented
11#10590436C212yesmaximal, complemented
12#82562—31nomaximal
13#79146—31nomaximal
14C2×C3×#235C2211yescharacteristic
15C2×C32×C4⋊C4C2211yescharacteristic
16#64135C2211yescharacteristic
17C2×#3748C2211yescharacteristic
18C3×C4×#67—22no—
19C3×#926C2211yescharacteristic
20C2×C3×C4⋊Dic3C2211yescharacteristic
21C22×C3×C3⋊C8C2211yescharacteristic
22C3×#893—21no—
23C3×#892C2212yes—
24C3×D3×C4⋊C4C2212yes—
25C3×#887—21no—
26Dic3×#67—22no—
27#63898—21no—
28D3×C4⋊Dic3C2212yes—
29#63843—21no—
30#63841C2212yes—
31C2×#3711C2212yes—
32#63814C418yescomplemented
33C2×D3×C3⋊C8C2212yes—
34#63635C2212yes—
35#63634C2212yes—
36C3×#807C2212yes—
37C3×#807C2212yes—
38#63576C2212yes—
39#63575C2211yescharacteristic
40#63575C2211yescharacteristic
41#63574C2212yes—
42#63573C2211yescharacteristic
43#63573C2211yescharacteristic
44C3×#520—31no—
45#5827—31no—
46C2×#948—31no—
47C2×#901—31no—
48#5504—31no—
49#5504D311yescharacteristic
50C2×C3×#107—31no—
51#5106—31no—
52#4998—31no—
53#4998—32no—
54#4995—31no—
55#4995—32no—
56#4964—31no—
57#4964—31no—
58#4964—31no—
59#4964—32no—
60#4964—61no—
61C2×#807—32no—
62C2×#807D311yescharacteristic, complemented
63#4881—32no—
64#4881—32no—
65#4880—32no—
66D3×#107—32no—
67C22×C32×C4—21no—
68C22×C32×C4C2311yescharacteristic
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⋊C4—21no—
79C32×C4⋊C4C2312yes—
80#3757—21no—
81C4⋊(C3⋊Dic3)C2311yescharacteristic
82C4⋊(C3⋊Dic3)C2311yescharacteristic
83C4×C3⋊Dic3—21no—
84#3748C2×C414yescomplemented
85C2×C3⋊(C3⋊C8)C2312yes—
86C3×#217—21no—
87C3×(C2×D3)⋊C4—22no—
88C3×C4⋊Dic3—21no—
89C3×C4⋊Dic3C2311yescharacteristic
90C3×C4⋊Dic3C2311yescharacteristic
91C3×C4⋊Dic3C2312yes—
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—31no—
111C3×#117—32no—
112C2×C3×C4⋊C4—21no—
113C2×C3×C4⋊C4—31no—
114C2×C3×C4⋊C4—32no—
115C2×C3×C4⋊C4C2×D311yescharacteristic
116C2×C3×C4⋊C4C2×D311yescharacteristic
117#948—38no—
118Q8×Dic3—61no—
119D4×Dic3—61no—
120D4×Dic3—62no—
121C4×#67—22no—
122C4×#67—62no—
123#926—31no—
124#926—31no—
125#926—32no—
126#926—61no—
127#926C2×D311yescharacteristic
128C2×C4⋊Dic3—32no—
129C2×C4⋊Dic3C2×D311yescharacteristic
130C2×#208—31no—
131C2×#208—31no—
132C2×#208—32no—
133C2×#208—61no—
134C22×C3⋊C8—32no—
135C22×C3⋊C8C2×D311yescharacteristic
136#901—38no—
137C2×ΓL(1,𝔽25)—32no—
138C2×D3×C8—32no—
139#893—21no—
140#893—61no—
141#892—32no—
142#892C2×D312yes—
143D3×C4⋊C4—32no—
144D3×C4⋊C4C2×D312yes—
145#887—21no—
146#887—61no—
147C3×#107—32no—
148C3×#107—32no—
149#818—31no—
150#818—31no—
151#817—31no—
152#817—31no—
153#808—32no—
154#808—32no—
155#808—32no—
156#808—32no—
157#808—31no—
158#808—31no—
159#808—62no—
160#807—32no—
161#807—32no—
162#807—32no—
163#807—32no—
164#807—31no—
165#807—31no—
166#807—62no—
167#807C2×D312yes—
168#807C2×D312yes—
169C23×C32C2×D411yescharacteristic
170C22×C3×D3C2×D412yes—
171C2×C32×C4—22no—
172C2×C32×C4—81no—
173C2×C32×C4C22×C412yes—
174C2×C32×C4C2×D411yescharacteristic
175C2×C32×C4C2×Q812yes—
176C2×C32×C4C2411yescharacteristic
177C2×C3⋊Dic3—21no—
178C2×C3⋊Dic3—21no—
179C3×#67C4⋊C418yes—
180C2×C3×Dic3—22no—
181C2×C3×Dic3—21no—
182C2×C3×Dic3—21no—
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—92no—
202#427—91no—
203C2×#107—31no—
204C2×#107—92no—
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—21no—
212C22×C3×C4—21no—
213C22×C3×C4—32no—
214C22×C3×C4—41no—
215C22×C3×C4—62no—
216C22×C3×C4—61no—
217C22×C3×C4C22×D311yescharacteristic
218C22×C3×C4C22×D311yescharacteristic
219C2×#67#6712yes—
220C22×Dic3—21no—
221C22×Dic3—62no—
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—22no—
235C3×C4⋊C4—31no—
236C3×C4⋊C4—31no—
237C3×C4⋊C4—32no—
238C3×C4⋊C4—41no—
239C3×C4⋊C4—62no—
240C3×C4⋊C4—61no—
241C3×C4⋊C4C22×D312yes—
242C3×C4⋊C4C22×D312yes—
243C3×C22⋊C4—62no—
244C3×C22⋊C4—61no—
245C3×C42—62no—
246C3×C42—61no—
247#217—21no—
248#217—62no—
249#217—61no—
250#217—61no—
251#217—121no—
252(C2×D3)⋊C4—22no—
253(C2×D3)⋊C4—62no—
254C4⋊Dic3—21no—
255C4⋊Dic3—31no—
256C4⋊Dic3—31no—
257C4⋊Dic3—31no—
258C4⋊Dic3—31no—
259C4⋊Dic3—61no—
260C4⋊Dic3—61no—
261C4⋊Dic3—62no—
262C4⋊Dic3C22×D311yescharacteristic
263C4⋊Dic3C22×D312yes—
264C4⋊Dic3C22×D311yescharacteristic
265Dic3⋊C4—22no—
266Dic3⋊C4—62no—
267C4×Dic3—21no—
268C4×Dic3—22no—
269C4×Dic3—62no—
270C4×Dic3—61no—
271C4×Dic3—61no—
272C4×Dic3—62no—
273C4×Dic3—121no—
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—42no—
295C32×C4C2×C4⋊C412yes—
296C32×C4C23×C411yescharacteristic
297C32×C4C22×Q811yescharacteristic
298C3⋊Dic3—41no—
299C3⋊Dic3—41no—
300C3×Dic3—42no—
301C3×Dic3—41no—
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#117—91no—
320C2×C4⋊C4—31no—
321C2×C4⋊C4—32no—
322C2×C4⋊C4—92no—
323C2×C4⋊C4D3211yescharacteristic
324#107—32no—
325#107—32no—
326#107—92no—
327#107—91no—
328#107—91no—
329#107—92no—
330#106—92no—
331#106—91no—
332#106—91no—
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—22no—
343C2×C3×C4—22no—
344C2×C3×C4—21no—
345C2×C3×C4—22no—
346C2×C3×C4—22no—
347C2×C3×C4—21no—
348C2×C3×C4—32no—
349C2×C3×C4—34no—
350C2×C3×C4—34no—
351C2×C3×C4—42no—
352C2×C3×C4—61no—
353C2×C3×C4—61no—
354C2×C3×C4—62no—
355C2×C3×C4—81no—
356C2×C3×C4—81no—
357C2×C3×C4—82no—
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—22no—
370C2×Dic3—21no—
371C2×Dic3—21no—
372C2×Dic3—61no—
373C2×Dic3—61no—
374C2×Dic3—61no—
375C2×Dic3—61no—
376C2×Dic3—81no—
377C2×Dic3—121no—
378C2×Dic3—121no—
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—21no—
405C22×C4—32no—
406C22×C4—62no—
407C22×C4—61no—
408C22×C4—182no—
409C22×C4C2×D3211yescharacteristic
410M16—98no—
411M16—94no—
412C2×C8—31no—
413C2×C8—31no—
414C2×C8—34no—
415C2×C8—98no—
416C2×C8—92no—
417C4⋊C4—21no—
418C4⋊C4—31no—
419C4⋊C4—32no—
420C4⋊C4—31no—
421C4⋊C4—62no—
422C4⋊C4—61no—
423C4⋊C4—91no—
424C4⋊C4—91no—
425C4⋊C4—182no—
426C4⋊C4C2×D3212yes—
427C22⋊C4—62no—
428C22⋊C4—61no—
429C22⋊C4—182no—
430C22⋊C4—181no—
431C42—62no—
432C42—61no—
433C42—182no—
434C42—181no—
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—42no—
458C3×C4—42no—
459C3×C4—82no—
460C3×C4—121no—
461C3×C4—121no—
462C3×C4—122no—
463C3×C4D3×C4⋊C412yes—
464C3×C4C2×Dic3⋊C412yes—
465C3×C4C22×Dic611yescharacteristic
466C3×C4C22×C4×D311yescharacteristic
467C3×C4C22×C4×D311yescharacteristic
468C3×C4C2×D3×Q811yescharacteristic
469Dic3—42no—
470Dic3—41no—
471Dic3—41no—
472Dic3—121no—
473Dic3—121no—
474Dic3—121no—
475Dic3—121no—
476Dic3—241no—
477Dic3—241no—
478Dic3C2×Dic3⋊C414yes—
479C32#291311yescharacteristic, complemented, Sylow
480C23—32no—
481C23D3×#6711yescharacteristic
482Q8—34no—
483D4—38no—
484D4—34no—
485C2×C4—22no—
486C2×C4—32no—
487C2×C4—34no—
488C2×C4—34no—
489C2×C4—61no—
490C2×C4—61no—
491C2×C4—62no—
492C2×C4—81no—
493C2×C4—181no—
494C2×C4—181no—
495C2×C4—242no—
496C2×C4—241no—
497C2×C4—722no—
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#575711yescharacteristic
514C2×C3#576611yescharacteristic
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—42no—
528C4—121no—
529C4—122no—
530C4—121no—
531C4—361no—
532C4—361no—
533C4D3×Dic3⋊C412yes—
534C4C2×D3×Dic611yescharacteristic
535C4C2×C4×D3211yescharacteristic
536C3—21no—
537C3#7914611yescharacteristic, complemented
538C3#8256211yescharacteristic, complemented
539C2—22no—
540C2—64no—
541C2C2×D3×Dic3⋊C411yescharacteristic
542C2#1059509611yescharacteristic
543C2#1059532711yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC2×C32×C4⋊C4C22
socleC22×C32C22×D4
prime radicalC2×C3×#235C22
cosocleC2×C32×C4C24
hypercenterC2×C4⋊C4D32
hypocenterC32#2913
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
4. #10592663C2semidirect
5. C2×C3×#807C2semidirect
6. #10591139C2semidirect
7. #10591122C2semidirect
8. #10590580C2semidirect
9. #10590571C2semidirect
10. D3×#807C2semidirect
11. #10590436C2semidirect
32. #63814C4semidirect
62. C2×#807D3semidirect
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#79146semidirect
538. C3#82562semidirect

Maximal subgroups

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

subgroupindex
C3×#55042
#105949862
C2×#638142
#105926632
C2×C3×#8072
#105911392
#105911222
#105905802
#105905712
D3×#8072
#105904362
#825623
#791463