Finite Group Databasebeta

← #11858517

Subgroups — #11858517

Order 1152.

1041 conjugacy classes of subgroups.

The subgroup lattice has 573 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×D3×#117C211yesmaximal, characteristic
2D3×#926C211yesmaximal, characteristic
3C22×#3711C211yesmaximal, characteristic
4#10592697C211yesmaximal, characteristic, complemented
5C3×#4998C211yesmaximal, characteristic, complemented
6#10591138C211yesmaximal, characteristic, complemented
7#10591122C211yesmaximal, characteristic, complemented
8#10590581C212yesmaximal, complemented
9#10590580C212yesmaximal, complemented
10#10590437C212yesmaximal, complemented
11#10590436C212yesmaximal, complemented
12#82207—31nomaximal
13#79177—31nomaximal
14C22×C3×C4×D3C2211yescharacteristic
15C32×#117C2211yescharacteristic
16#64135C2211yescharacteristic
17C22×C3⋊(C3⋊C8)C2211yescharacteristic
18C3×#926C2211yescharacteristic
19C3×#926C2211yescharacteristic
20C22×C3×C3⋊C8C2211yescharacteristic
21C3×#892C2212yes—
22C3×D3×C4⋊C4C2212yes—
23C3×D3×C22⋊C4—21no—
24C3×#877—21no—
25C3×#872—21no—
26C3×C42×D3—21no—
27D3×#217—21no—
28#63955—21no—
29D3×C4⋊Dic3C2212yes—
30C4×D3×Dic3—21no—
31#63855—21no—
32#63841C2212yes—
33C2×#3711C418yescomplemented
34C2×#3711C2211yescharacteristic
35C2×#3711C2211yescharacteristic
36C2×#3711C2211yescharacteristic
37C2×#3711C2211yescharacteristic
38#63635C2212yescomplemented
39#63634C2212yescomplemented
40C3×#808C2212yescomplemented
41C3×#807C2212yescomplemented
42#63576C2212yescomplemented
43#63575C2212yescomplemented
44#63574C2212yescomplemented
45#63573C2212yescomplemented
46C2×C3×#117—31no—
47C2×#926—31no—
48C22×#208—31no—
49C22×ΓL(1,𝔽25)—31no—
50D3×#117—31no—
51D3×#117D311yescharacteristic
52C3×#427—31no—
53#5106—31no—
54#4998—31no—
55#4998—31no—
56#4998—31no—
57#4998—31no—
58#4998—31no—
59#4998—61no—
60#4998D311yescharacteristic, complemented
61#4995—32no—
62#4995—32no—
63#4964—32no—
64#4964—32no—
65#4881—32no—
66#4881—32no—
67#4861—32no—
68#4861—32no—
69C23×C3×D3D411yescharacteristic
70C22×C32×C4C2311yescharacteristic
71C22×C3×Dic3D411yescharacteristic
72C2×C3×C4×D3—22no—
73C2×C3×C4×D3C2×C414yes—
74C2×C3×C4×D3D411yescharacteristic
75C2×C3×C4×D3D411yescharacteristic
76C2×C3×C4×D3Q814yes—
77C2×C3×C4×D3C2311yescharacteristic
78C2×C3×C4×D3C2311yescharacteristic
79C2×D3×Dic3—22no—
80C32×C4⋊C4C2312yes—
81C32×C22⋊C4—21no—
82C32×C42—21no—
83#3757—21no—
84C4⋊(C3⋊Dic3)C2312yes—
85C4×C3⋊Dic3—21no—
86C2×C3⋊(C3⋊C8)C2×C414yescomplemented
87C2×C3⋊(C3⋊C8)C2311yescharacteristic
88C2×C3⋊(C3⋊C8)C2311yescharacteristic
89C3×#217—21no—
90C3×#217—21no—
91C3×(C2×D3)⋊C4—22no—
92C3×C4⋊Dic3C2312yes—
93C3×C4⋊Dic3C2312yes—
94C3×Dic3⋊C4—22no—
95C3×C4×Dic3—21no—
96C3×C4×Dic3—21no—
97C3×C4×Dic3—22no—
98C2×C3×C3⋊C8C2×C414yescomplemented
99C2×C3×C3⋊C8C2311yescharacteristic
100C2×C3×C3⋊C8C2311yescharacteristic
101Dic3⋊Dic3—22no—
102(C2×D3)⋊Dic3—22no—
103Dic32—22no—
104#3711C2×C414yescomplemented
105#3711C2×C414yescomplemented
106#3711C2×C414yescomplemented
107#3711C2×C414yescomplemented
108#2911—91noSylow
109C23×C3×C4—31no—
110C22×C4×D3C2×D311yescharacteristic
111C22×C3×C8—31no—
112C3×#117—21no—
113C3×#117—31no—
114C3×#117—31no—
115C3×#117—32no—
116C3×#117—61no—
117C3×#117—61no—
118C3×#117C2×D311yescharacteristic
119C3×#117C2×D311yescharacteristic
120C2×C3×C4⋊C4—32no—
121C2×C3×C22⋊C4—61no—
122C2×C3×C42—61no—
123C2×#217—61no—
124#926—31no—
125#926—31no—
126#926—32no—
127#926—61no—
128#926—61no—
129#926—61no—
130#926C2×D311yescharacteristic
131#926C2×D311yescharacteristic
132C2×C4⋊Dic3—32no—
133C2×C4×Dic3—61no—
134C2×#208—38no—
135C2×#208—31no—
136C2×#208—31no—
137C2×#208—31no—
138C2×#208—31no—
139C22×C3⋊C8—31no—
140C22×C3⋊C8—31no—
141C22×C3⋊C8—61no—
142C22×C3⋊C8C2×D311yescharacteristic
143C2×ΓL(1,𝔽25)—38no—
144C2×ΓL(1,𝔽25)—31no—
145C2×ΓL(1,𝔽25)—31no—
146C2×ΓL(1,𝔽25)—31no—
147C2×ΓL(1,𝔽25)—31no—
148#892—32no—
149#892C2×D312yes—
150D3×C4⋊C4—32no—
151D3×C4⋊C4C2×D312yes—
152D3×C22⋊C4—21no—
153D3×C22⋊C4—61no—
154#877—21no—
155#877—61no—
156#872—21no—
157#872—61no—
158C42×D3—21no—
159C42×D3—61no—
160C3×#107—32no—
161C3×#106—32no—
162#818—32no—
163#817—32no—
164#808—32no—
165#808—32no—
166#808—32no—
167#808—32no—
168#808—32no—
169#808—62no—
170#808C2×D312yescomplemented
171#807—32no—
172#807—32no—
173#807—32no—
174#807—32no—
175#807—32no—
176#807—62no—
177#807C2×D312yescomplemented
178C23×C32C2×D411yescharacteristic
179C22×C3×D3—42no—
180C22×C3×D3C4⋊C414yes—
181C22×C3×D3C2×D411yescharacteristic
182C22×C3×D3C2×D411yescharacteristic
183C2×C32×C4—22no—
184C2×C32×C4C22×C412yes—
185C2×C32×C4C2×D411yescharacteristic
186C2×C32×C4C2×Q812yes—
187C2×C32×C4C2411yescharacteristic
188C2×C3⋊Dic3—22no—
189C2×C3×Dic3—22no—
190C2×C3×Dic3—22no—
191C2×C3×Dic3C4⋊C414yes—
192C2×C3×Dic3C2×D411yescharacteristic
193C2×C3×Dic3C2×D411yescharacteristic
194C3×C4×D3—44no—
195C3×C4×D3C4⋊C414yes—
196C3×C4×D3C4⋊C414yes—
197C3×C4×D3C22×C412yes—
198C3×C4×D3C22×C412yes—
199C3×C4×D3C2×Q812yes—
200C3×C4×D3C2×Q812yes—
201D3×Dic3—44no—
202C3⋊(C3⋊C8)C22×C412yes—
203C3⋊(C3⋊C8)C22×C412yes—
204C3×C3⋊C8C22×C412yes—
205C3×C3⋊C8C22×C412yes—
206C22×M16—91no—
207C2×#117—31no—
208C2×#117—91no—
209#428—92no—
210#428—92no—
211#428—92no—
212#428—92no—
213#427—31no—
214#427—91no—
215#427—91no—
216#427—91no—
217C24×C3—31no—
218C23×D3#6711yescharacteristic
219C22×C3×C4—21no—
220C22×C3×C4—31no—
221C22×C3×C4—34no—
222C22×C3×C4—31no—
223C22×C3×C4—31no—
224C22×C3×C4—34no—
225C22×C3×C4—31no—
226C22×C3×C4—31no—
227C22×C3×C4—62no—
228C22×C3×C4C22×D311yescharacteristic
229C22×C3×C4C22×D311yescharacteristic
230C22×Dic3—62no—
231C22×Dic3#6711yescharacteristic
232C2×C4×D3—22no—
233C2×C4×D3—62no—
234C2×C4×D3Dic614yes—
235C2×C4×D3C4×D314yes—
236C2×C4×D3#6711yescharacteristic
237C2×C4×D3#6711yescharacteristic
238C2×C4×D3C22×D311yescharacteristic
239C2×C4×D3C22×D311yescharacteristic
240C2×C3×C8—34no—
241C2×C3×C8—31no—
242C2×C3×C8—31no—
243C3×C4⋊C4—22no—
244C3×C4⋊C4—32no—
245C3×C4⋊C4—32no—
246C3×C4⋊C4—62no—
247C3×C4⋊C4C22×D312yes—
248C3×C4⋊C4C22×D312yes—
249C3×C22⋊C4—21no—
250C3×C22⋊C4—21no—
251C3×C22⋊C4—41no—
252C3×C22⋊C4—62no—
253C3×C22⋊C4—61no—
254C3×C22⋊C4—61no—
255C3×C42—21no—
256C3×C42—21no—
257C3×C42—41no—
258C3×C42—62no—
259C3×C42—61no—
260C3×C42—61no—
261#217—21no—
262#217—21no—
263#217—62no—
264#217—61no—
265#217—61no—
266#217—121no—
267(C2×D3)⋊C4—22no—
268(C2×D3)⋊C4—62no—
269C4⋊Dic3—32no—
270C4⋊Dic3—32no—
271C4⋊Dic3—62no—
272C4⋊Dic3—62no—
273C4⋊Dic3C22×D312yes—
274C4⋊Dic3C22×D312yes—
275Dic3⋊C4—22no—
276Dic3⋊C4—62no—
277C4×Dic3—21no—
278C4×Dic3—21no—
279C4×Dic3—22no—
280C4×Dic3—62no—
281C4×Dic3—61no—
282C4×Dic3—61no—
283C4×Dic3—62no—
284C4×Dic3—121no—
285#208—34no—
286#208—34no—
287#208—34no—
288#208—34no—
289C2×C3⋊C8—34no—
290C2×C3⋊C8—34no—
291C2×C3⋊C8—31no—
292C2×C3⋊C8—31no—
293C2×C3⋊C8—31no—
294C2×C3⋊C8—31no—
295C2×C3⋊C8—61no—
296C2×C3⋊C8—61no—
297C2×C3⋊C8—64no—
298C2×C3⋊C8C4×D314yescomplemented
299C2×C3⋊C8C22×D311yescharacteristic
300C2×C3⋊C8C22×D311yescharacteristic
301ΓL(1,𝔽25)—34no—
302ΓL(1,𝔽25)—34no—
303ΓL(1,𝔽25)—34no—
304ΓL(1,𝔽25)—34no—
305C22×C32—22no—
306C22×C32C2×C4⋊C412yes—
307C22×C32C22×D411yescharacteristic
308C2×C3×D3—22no—
309C2×C3×D3—22no—
310C2×C3×D3—44no—
311C2×C3×D3C2×C4⋊C412yes—
312C2×C3×D3C2×C4⋊C412yes—
313C32×C4—42no—
314C32×C4C2×C4⋊C412yes—
315C32×C4C23×C411yescharacteristic
316C32×C4C22×Q811yescharacteristic
317C3⋊Dic3—42no—
318C3×Dic3—42no—
319C3×Dic3—42no—
320C3×Dic3C2×C4⋊C412yes—
321C3×Dic3C2×C4⋊C412yes—
322C23×C4—31no—
323C2×M16—98no—
324C2×M16—91no—
325C2×M16—91no—
326C2×M16—91no—
327C2×M16—91no—
328C22×C8—31no—
329C22×C8—91no—
330#117—31no—
331#117—31no—
332#117—32no—
333#117—61no—
334#117—61no—
335#117—92no—
336#117—91no—
337#117—181no—
338#117—181no—
339#117D3211yescharacteristic
340C2×C4⋊C4—32no—
341C2×C4⋊C4—92no—
342C2×C22⋊C4—61no—
343C2×C22⋊C4—181no—
344C2×C42—61no—
345C2×C42—181no—
346#107—32no—
347#107—92no—
348#107—92no—
349#107—92no—
350#106—32no—
351#106—92no—
352#106—92no—
353#106—92no—
354C23×C3—21no—
355C23×C3—31no—
356C23×C3—31no—
357C23×C3—34no—
358C23×C3—122no—
359C23×C3D3×D411yescharacteristic
360C23×C3C2×#6711yescharacteristic
361C22×D3—42no—
362C22×D3Dic3⋊C414yes—
363C22×D3C2×#6711yescharacteristic
364C22×D3C2×#6711yescharacteristic
365C2×C3×C4—22no—
366C2×C3×C4—22no—
367C2×C3×C4—21no—
368C2×C3×C4—22no—
369C2×C3×C4—22no—
370C2×C3×C4—21no—
371C2×C3×C4—34no—
372C2×C3×C4—31no—
373C2×C3×C4—31no—
374C2×C3×C4—34no—
375C2×C3×C4—34no—
376C2×C3×C4—32no—
377C2×C3×C4—32no—
378C2×C3×C4—32no—
379C2×C3×C4—32no—
380C2×C3×C4—42no—
381C2×C3×C4—62no—
382C2×C3×C4—62no—
383C2×C3×C4—124no—
384C2×C3×C4C2×Dic612yes—
385C2×C3×C4C2×C4×D312yes—
386C2×C3×C4C2×C4×D312yes—
387C2×C3×C4D3×D411yescharacteristic
388C2×C3×C4D3×Q812yes—
389C2×C3×C4C2×#6711yescharacteristic
390C2×C3×C4C23×D311yescharacteristic
391C2×C3×C4C23×D311yescharacteristic
392C2×Dic3—22no—
393C2×Dic3—22no—
394C2×Dic3—62no—
395C2×Dic3—62no—
396C2×Dic3—122no—
397C2×Dic3—124no—
398C2×Dic3Dic3⋊C414yes—
399C2×Dic3C2×#6711yescharacteristic
400C2×Dic3C2×#6711yescharacteristic
401C4×D3—44no—
402C4×D3—124no—
403C4×D3Dic3⋊C414yes—
404C4×D3Dic3⋊C414yes—
405C4×D3C2×Dic612yes—
406C4×D3C2×Dic612yes—
407C4×D3C2×C4×D312yes—
408C4×D3C2×C4×D312yes—
409C3×C8—32no—
410C3×C8—32no—
411C3⋊C8—32no—
412C3⋊C8—32no—
413C3⋊C8—32no—
414C3⋊C8—32no—
415C3⋊C8—62no—
416C3⋊C8—62no—
417C3⋊C8C2×C4×D312yes—
418C3⋊C8C2×C4×D312yes—
419C2×C32—22no—
420C2×C32C22×C4⋊C411yescharacteristic
421C2×C32#57512yes—
422C3×D3—22no—
423C3×D3—22no—
424C24—31no—
425C22×C4—31no—
426C22×C4—31no—
427C22×C4—31no—
428C22×C4—34no—
429C22×C4—34no—
430C22×C4—31no—
431C22×C4—31no—
432C22×C4—62no—
433C22×C4—182no—
434C22×C4C2×D3211yescharacteristic
435M16—94no—
436M16—94no—
437M16—94no—
438M16—94no—
439C2×C8—31no—
440C2×C8—31no—
441C2×C8—34no—
442C2×C8—91no—
443C2×C8—91no—
444C2×C8—94no—
445C4⋊C4—32no—
446C4⋊C4—32no—
447C4⋊C4—62no—
448C4⋊C4—92no—
449C4⋊C4—182no—
450C4⋊C4C2×D3212yes—
451C22⋊C4—21no—
452C22⋊C4—62no—
453C22⋊C4—61no—
454C22⋊C4—61no—
455C22⋊C4—182no—
456C22⋊C4—181no—
457C42—21no—
458C42—62no—
459C42—61no—
460C42—61no—
461C42—182no—
462C42—181no—
463C22×C3—22no—
464C22×C3—22no—
465C22×C3—21no—
466C22×C3—22no—
467C22×C3—32no—
468C22×C3—32no—
469C22×C3—42no—
470C22×C3—62no—
471C22×C3—62no—
472C22×C3—124no—
473C22×C3D3×C4⋊C412yes—
474C22×C3C2×Dic3⋊C412yes—
475C22×C3C2×D3×D411yescharacteristic
476C22×C3C22×#6711yescharacteristic
477C2×D3—22no—
478C2×D3—22no—
479C2×D3—44no—
480C2×D3C2×Dic3⋊C412yes—
481C2×D3C2×Dic3⋊C412yes—
482C3×C4—21no—
483C3×C4—21no—
484C3×C4—22no—
485C3×C4—32no—
486C3×C4—32no—
487C3×C4—42no—
488C3×C4—42no—
489C3×C4—82no—
490C3×C4—122no—
491C3×C4—122no—
492C3×C4D3×C4⋊C412yes—
493C3×C4C2×Dic3⋊C412yes—
494C3×C4C22×Dic611yescharacteristic
495C3×C4C22×C4×D311yescharacteristic
496C3×C4C22×C4×D311yescharacteristic
497C3×C4C2×D3×Q811yescharacteristic
498Dic3—42no—
499Dic3—42no—
500Dic3—122no—
501Dic3—122no—
502Dic3—242no—
503Dic3C2×Dic3⋊C412yes—
504Dic3C2×Dic3⋊C412yes—
505C32#291111yescharacteristic, complemented, Sylow
506C23—31no—
507C23—31no—
508C23—34no—
509C23—122no—
510C23D3×#6711yescharacteristic
511C2×C4—22no—
512C2×C4—31no—
513C2×C4—31no—
514C2×C4—34no—
515C2×C4—32no—
516C2×C4—32no—
517C2×C4—32no—
518C2×C4—32no—
519C2×C4—34no—
520C2×C4—34no—
521C2×C4—62no—
522C2×C4—62no—
523C2×C4—124no—
524C2×C4—182no—
525C2×C4—364no—
526C2×C4D3×Dic612yes—
527C2×C4C4×D3212yes—
528C2×C4D3×#6711yescharacteristic
529C2×C4C22×D3211yescharacteristic
530C8—32no—
531C8—32no—
532C8—92no—
533C8—92no—
534C2×C3—22no—
535C2×C3—22no—
536C2×C3—21no—
537C2×C3—22no—
538C2×C3—42no—
539C2×C3—62no—
540C2×C3—62no—
541C2×C3C2×D3×C4⋊C411yescharacteristic
542C2×C3#576812yes—
543C2×C3C22×Dic3⋊C411yescharacteristic
544C2×C3#582212yes—
545D3—22no—
546D3—22no—
547C22—22no—
548C22—32no—
549C22—32no—
550C22—62no—
551C22—62no—
552C22—124no—
553C22D3×Dic3⋊C412yes—
554C22C2×D3×#6711yescharacteristic
555C4—32no—
556C4—32no—
557C4—42no—
558C4—122no—
559C4—122no—
560C4—362no—
561C4D3×Dic3⋊C412yes—
562C4C2×D3×Dic611yescharacteristic
563C4C2×C4×D3211yescharacteristic
564C3—21no—
565C3#7917711yescharacteristic, complemented
566C3#8220711yescharacteristic, complemented
567C2—22no—
568C2—62no—
569C2—62no—
570C2C2×D3×Dic3⋊C411yescharacteristic
571C2#1059545312yes—
subgroupG/H
centerC2×C4D3×#67
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC32×#117C22
socleC22×C32C22×D4
prime radicalC23×C3×D3D4
cosocleC2×C32×C4C24
hypercenter#117D32
hypocenterC32#2911
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ #117

Complements

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

NH ≅ G/Ntype
4. #10592697C2semidirect
5. C3×#4998C2semidirect
6. #10591138C2semidirect
7. #10591122C2semidirect
8. #10590581C2semidirect
9. #10590580C2semidirect
10. #10590437C2semidirect
11. #10590436C2semidirect
33. C2×#3711C4semidirect
38. #63635C22semidirect
39. #63634C22semidirect
40. C3×#808C22semidirect
41. C3×#807C22semidirect
42. #63576C22semidirect
43. #63575C22semidirect
44. #63574C22semidirect
45. #63573C22semidirect
60. #4998D3semidirect
86. C2×C3⋊(C3⋊C8)C2×C4semidirect
98. C2×C3×C3⋊C8C2×C4semidirect
104. #3711C2×C4semidirect
105. #3711C2×C4semidirect
106. #3711C2×C4semidirect
107. #3711C2×C4semidirect
170. #808C2×D3semidirect
177. #807C2×D3semidirect
298. C2×C3⋊C8C4×D3semidirect
505. C32#2911semidirect
565. C3#79177semidirect
566. C3#82207semidirect

Maximal subgroups

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

subgroupindex
C3×D3×#1172
D3×#9262
C22×#37112
#105926972
C3×#49982
#105911382
#105911222
#105905812
#105905802
#105904372
#105904362
#822073
#791773