Finite Group Databasebeta

← #11860628

Subgroups — #11860628

Order 1152.

1005 conjugacy classes of subgroups.

The subgroup lattice has 564 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5523C211yesmaximal, characteristic
2C3×#5516C211yesmaximal, characteristic, complemented
3C2×#63827C211yesmaximal, characteristic
4#10592696C211yesmaximal, characteristic, complemented
5#10591139C211yesmaximal, characteristic, complemented
6C2×#63565C211yesmaximal, characteristic, complemented
7#10591083C211yesmaximal, characteristic
8#10590381C212yesmaximal, complemented
9C4×#3718C212yesmaximal, complemented
10#10590358C212yesmaximal, complemented
11C4×#3715C212yesmaximal, complemented
12#82571—31nomaximal
13#82547—31nomaximal
14C2×C3×#235C2211yescharacteristic
15C22×C3×Dic6C2211yescharacteristic
16C32×#117C2211yescharacteristic
17C2×#3748C2211yescharacteristic
18C22×C3⋊(C3⋊C8)C2211yescharacteristic
19C3×#926C2211yescharacteristic
20C2×C3×C4⋊Dic3C2211yescharacteristic
21C3×#892—21no—
22C3×D3×C4⋊C4—21no—
23C3×#887—21no—
24C3×#887—21no—
25C3×#67⋊C4—22no—
26C3×#877—22no—
27C3×C4×D12C2212yes—
28C3×C4×Dic6C2212yes—
29C3×C4×Dic6C2212yes—
30C3×C4×Dic6C2212yes—
31C2×#3718C2212yes—
32#63827C418yescomplemented
33C2×#3715C2212yes—
34#63630C2212yes—
35C4×C3⋊(C3⋊C8)C2212yes—
36#63576C2212yes—
37#63574C2212yes—
38#63565C2211yescharacteristic
39#63565C2211yescharacteristic
40#63565C2212yes—
41#63565C2212yes—
42#63562C2211yescharacteristic
43#63562C2211yescharacteristic
44C3×#520—31no—
45C3×#519—31no—
46C2×#951—31no—
47C2×#942—31no—
48#5523D311yescharacteristic
49#5516D311yescharacteristic, complemented
50#5233—31no—
51C2×#835—31no—
52#5030—32no—
53#5030—32no—
54C4×#216—32no—
55C4×#216—32no—
56#5026—32no—
57C4×#215—32no—
58#5018—32no—
59C4×#214—32no—
60#5002—31no—
61#4997—31no—
62#4997—31no—
63#4997—61no—
64#4995—31no—
65C2×#810—31no—
66#4964—31no—
67C22×C32×C4C2311yescharacteristic
68C2×C3×#67—21no—
69C22×C3×Dic3—21no—
70C22×C3×Dic3—21no—
71C3×#235—22no—
72C3×#235C2×C414yes—
73C2×C3×D12C2311yescharacteristic
74C2×C3×C4×D3—21no—
75C2×C3×C4×D3—22no—
76C2×C3×Dic6—21no—
77C2×C3×Dic6—22no—
78C2×C3×Dic6C2×C414yescomplemented
79C2×C3×Dic6C2312yes—
80C2×C3×Dic6C2311yescharacteristic
81C32×C4⋊C4D411yescharacteristic
82C32×C4⋊C4D411yescharacteristic
83C32×C22⋊C4D412yes—
84C32×C42C2312yes—
85#3748C2×C414yescomplemented
86C2×C3⋊(C3⋊C8)—22no—
87C2×C3⋊(C3⋊C8)C2311yescharacteristic
88C2×C3⋊(C3⋊C8)C2311yescharacteristic
89C2×C3⋊(C3⋊C8)C2312yes—
90C3×#217—21no—
91C3×(C2×D3)⋊C4—22no—
92C3×C4⋊Dic3—21no—
93C3×C4⋊Dic3C2312yes—
94C3×C4⋊Dic3C2311yescharacteristic
95C3×C4⋊Dic3C2311yescharacteristic
96C3×Dic3⋊C4—22no—
97C3×Dic3⋊C4—22no—
98C3×Dic3⋊C4—22no—
99C3×C4×Dic3—22no—
100C3×C4×Dic3—22no—
101C3×C4×Dic3—22no—
102C3×C4×Dic3—21no—
103#3718C2×C418yescomplemented
104#3715C2×C418yescomplemented
105#2947—91noSylow
106C2×C3×#41—31no—
107C22×C3×Q8—31no—
108C2×#235C2×D311yescharacteristic
109C22×Dic6C2×D311yescharacteristic
110C3×C4×Q8—32no—
111C3×C4×Q8—32no—
112C3×C4×Q8—32no—
113C3×C4×Q8—61no—
114C3×C4×Q8—61no—
115C3×C4×D4—32no—
116C3×C4×D4—62no—
117C3×#117—21no—
118C3×#117—31no—
119C3×#117—61no—
120C3×#117—62no—
121C3×#117C2×D311yescharacteristic
122C3×#117C2×D311yescharacteristic
123C2×C3×C4⋊C4—31no—
124C2×C3×C4⋊C4—61no—
125#951—38no—
126C2×#216—32no—
127C2×#216—32no—
128#942—38no—
129C2×#215—32no—
130C2×#214—32no—
131#926C2×D311yescharacteristic
132C2×C4⋊Dic3C2×D311yescharacteristic
133C2×#208—31no—
134C2×#208—31no—
135C2×#208—61no—
136C22×C3⋊C8—31no—
137C22×C3⋊C8—31no—
138C22×C3⋊C8—61no—
139#892—21no—
140D3×C4⋊C4—21no—
141#887—21no—
142#887—21no—
143#67⋊C4—22no—
144#877—22no—
145C4×D12C2×D312yes—
146C4×Dic6C2×D312yes—
147C4×Dic6C2×D312yes—
148C4×Dic6C2×D312yes—
149#835—32no—
150#835—32no—
151#835—31no—
152#835—31no—
153#832—31no—
154#832—31no—
155#810—32no—
156#810—32no—
157#810—31no—
158#810—31no—
159#809—31no—
160#809—31no—
161#808—32no—
162#808—32no—
163#807—32no—
164#807—32no—
165#803—32no—
166#803—32no—
167#803—62no—
168C4×C3⋊C8—32no—
169C4×C3⋊C8—32no—
170C4×C3⋊C8—62no—
171C23×C32C2×D411yescharacteristic
172C22×C3×D3—21no—
173C2×C32×C4C22×C412yes—
174C2×C32×C4C2×D412yes—
175C2×C32×C4C2×D412yes—
176C2×C32×C4C2×D411yescharacteristic
177C2×C32×C4#4112yes—
178C2×C32×C4C2411yescharacteristic
179C3×#67—24no—
180C2×C3×Dic3—24no—
181C2×C3×Dic3—22no—
182C2×C3×Dic3—21no—
183C2×C3×Dic3—21no—
184C2×C3×Dic3—21no—
185C2×C3×Dic3—22no—
186C2×C3×Dic3—81no—
187C3×D12—21no—
188C3×D12C22×C412yes—
189C3×C4×D3—24no—
190C3×C4×D3—82no—
191C3×Dic6—24no—
192C3×Dic6—22no—
193C3×Dic6—21no—
194C3×Dic6C22×C414yes—
195C3×Dic6C22×C412yes—
196C3⋊(C3⋊C8)—21no—
197C3⋊(C3⋊C8)—21no—
198C3⋊(C3⋊C8)C22×C414yes—
199C2×#137—91no—
200#520—31no—
201#519—31no—
202#441—92no—
203#440—92no—
204C4×Q16—92no—
205C4×SD16—92no—
206#428—91no—
207#416—91no—
208C2×#103—91no—
209#405—91no—
210C3×#41—34no—
211C3×#41—62no—
212C2×C3×Q8—34no—
213C2×C3×Q8—32no—
214C2×C3×Q8—31no—
215C2×C3×Q8—62no—
216C2×C3×Q8—61no—
217C2×C3×D4—31no—
218C2×C3×D4—61no—
219C22×C3×C4—21no—
220C22×C3×C4—61no—
221C22×C3×C4—61no—
222C22×C3×C4—61no—
223C22×C3×C4—62no—
224C22×C3×C4C22×D311yescharacteristic
225C22×C3×C4C22×D311yescharacteristic
226C2×#67—21no—
227C22×Dic3—21no—
228C22×Dic3—21no—
229#235—22no—
230#235C4×D314yes—
231C2×D12C22×D311yescharacteristic
232C2×C4×D3—21no—
233C2×C4×D3—22no—
234C2×Dic6—22no—
235C2×Dic6—21no—
236C2×Dic6C4×D314yescomplemented
237C2×Dic6C22×D312yes—
238C2×Dic6C22×D311yescharacteristic
239C3×C4⋊C4—21no—
240C3×C4⋊C4—21no—
241C3×C4⋊C4—31no—
242C3×C4⋊C4—32no—
243C3×C4⋊C4—31no—
244C3×C4⋊C4—62no—
245C3×C4⋊C4—62no—
246C3×C4⋊C4—62no—
247C3×C4⋊C4—61no—
248C3×C4⋊C4#6711yescharacteristic
249C3×C4⋊C4#6711yescharacteristic
250C3×C4⋊C4#6711yescharacteristic
251C3×C4⋊C4#6711yescharacteristic
252C3×C22⋊C4—22no—
253C3×C22⋊C4—61no—
254C3×C22⋊C4—62no—
255C3×C22⋊C4#6712yes—
256C3×C22⋊C4#6712yes—
257C3×C42—22no—
258C3×C42—61no—
259C3×C42—62no—
260C3×C42—62no—
261C3×C42—62no—
262C3×C42C22×D312yes—
263C3×C42C22×D312yes—
264#217—21no—
265#216—38no—
266#216—38no—
267#215—38no—
268#214—38no—
269(C2×D3)⋊C4—22no—
270C4⋊Dic3—21no—
271C4⋊Dic3C22×D311yescharacteristic
272C4⋊Dic3C22×D312yes—
273C4⋊Dic3C22×D311yescharacteristic
274Dic3⋊C4—22no—
275Dic3⋊C4—22no—
276Dic3⋊C4—22no—
277C4×Dic3—22no—
278C4×Dic3—22no—
279C4×Dic3—22no—
280C4×Dic3—21no—
281#208—34no—
282#208—34no—
283#208—64no—
284C2×C3⋊C8—32no—
285C2×C3⋊C8—32no—
286C2×C3⋊C8—31no—
287C2×C3⋊C8—31no—
288C2×C3⋊C8—31no—
289C2×C3⋊C8—31no—
290C2×C3⋊C8—61no—
291C2×C3⋊C8—62no—
292C2×C3⋊C8—61no—
293C2×C3⋊C8—64no—
294C2×C3⋊C8—62no—
295C2×C3⋊C8—62no—
296C22×C32—21no—
297C22×C32—21no—
298C22×C32C4×D412yes—
299C22×C32C22×D411yescharacteristic
300C2×C3×D3—22no—
301C2×C3×D3—41no—
302C2×C3×D3—41no—
303C32×C4—22no—
304C32×C4—22no—
305C32×C4C4×D412yes—
306C32×C4C23×C411yescharacteristic
307C32×C4C2×#4111yescharacteristic
308C3×Dic3—24no—
309C3×Dic3—22no—
310C3×Dic3—42no—
311C3×Dic3—41no—
312C3×Dic3—41no—
313C2×#41—31no—
314C22×Q8—31no—
315#137—98no—
316C2×Q16—92no—
317C2×SD16—92no—
318C2×M16—91no—
319C22×C8—91no—
320C4×Q8—32no—
321C4×Q8—32no—
322C4×Q8—32no—
323C4×Q8—61no—
324C4×Q8—61no—
325C4×D4—32no—
326C4×D4—62no—
327#117—31no—
328#117—61no—
329#117—62no—
330#117D3211yescharacteristic
331C2×C4⋊C4—31no—
332C2×C4⋊C4—61no—
333#107—92no—
334#106—92no—
335#103—92no—
336#103—92no—
337#103—91no—
338#103—91no—
339#102—91no—
340#102—91no—
341#97—92no—
342C4×C8—92no—
343C23×C3—21no—
344C23×C3—61no—
345C23×C3C2×#6711yescharacteristic
346C23×C3C2×#6711yescharacteristic
347C22×D3—21no—
348C3×Q8—34no—
349C3×Q8—32no—
350C3×Q8—64no—
351C3×Q8—62no—
352C3×Q8—61no—
353C3×D4—32no—
354C3×D4—64no—
355C3×D4—61no—
356C2×C3×C4—21no—
357C2×C3×C4—22no—
358C2×C3×C4—22no—
359C2×C3×C4—21no—
360C2×C3×C4—22no—
361C2×C3×C4—22no—
362C2×C3×C4—64no—
363C2×C3×C4—61no—
364C2×C3×C4—62no—
365C2×C3×C4—64no—
366C2×C3×C4—61no—
367C2×C3×C4—61no—
368C2×C3×C4—62no—
369C2×C3×C4—242no—
370C2×C3×C4—241no—
371C2×C3×C4C2×C4×D312yes—
372C2×C3×C4C2×C4×D312yes—
373C2×C3×C4#23512yes—
374C2×C3×C4#23512yes—
375C2×C3×C4C2×#6712yes—
376C2×C3×C4C2×#6712yes—
377C2×C3×C4C2×#6712yes—
378C2×C3×C4C2×#6712yes—
379C2×C3×C4C2×#6711yescharacteristic
380C2×C3×C4C2×#6711yescharacteristic
381C2×C3×C4C23×D311yescharacteristic
382C2×C3×C4C23×D311yescharacteristic
383#67—24no—
384C2×Dic3—24no—
385C2×Dic3—22no—
386C2×Dic3—21no—
387C2×Dic3—21no—
388C2×Dic3—21no—
389C2×Dic3—22no—
390C2×Dic3—81no—
391D12—21no—
392D12C2×C4×D312yes—
393C4×D3—24no—
394C4×D3—82no—
395Dic6—24no—
396Dic6—22no—
397Dic6—21no—
398Dic6C2×C4×D314yes—
399Dic6C2×C4×D312yes—
400C3⋊C8—34no—
401C3⋊C8—34no—
402C3⋊C8—64no—
403C3⋊C8—62no—
404C3⋊C8—62no—
405C3⋊C8—61no—
406C3⋊C8—61no—
407C3⋊C8—61no—
408C3⋊C8—61no—
409C2×C32—22no—
410C2×C32C2×C4×D411yescharacteristic
411C2×C32#57711yescharacteristic
412C2×C32#57811yescharacteristic
413C3×D3—42no—
414#41—34no—
415#41—62no—
416C2×Q8—32no—
417C2×Q8—31no—
418C2×Q8—34no—
419C2×Q8—62no—
420C2×Q8—61no—
421C2×D4—31no—
422C2×D4—61no—
423C22×C4—61no—
424C22×C4—61no—
425C22×C4—61no—
426C22×C4—62no—
427C22×C4C2×D3211yescharacteristic
428Q16—98no—
429SD16—98no—
430M16—94no—
431C2×C8—92no—
432C2×C8—91no—
433C2×C8—91no—
434C2×C8—182no—
435C4⋊C4—31no—
436C4⋊C4—31no—
437C4⋊C4—32no—
438C4⋊C4—61no—
439C4⋊C4—62no—
440C4⋊C4—62no—
441C4⋊C4—62no—
442C4⋊C4#62511yescharacteristic
443C4⋊C4#62511yescharacteristic
444C22⋊C4—61no—
445C22⋊C4—62no—
446C22⋊C4#62512yes—
447C42—61no—
448C42—62no—
449C42—62no—
450C42—62no—
451C42C2×D3212yes—
452C22×C3—21no—
453C22×C3—21no—
454C22×C3—21no—
455C22×C3—21no—
456C22×C3—21no—
457C22×C3—22no—
458C22×C3—41no—
459C22×C3—41no—
460C22×C3—62no—
461C22×C3—121no—
462C22×C3—121no—
463C22×C3C4×#6712yes—
464C22×C3C4×#6712yes—
465C22×C3C22×#6711yescharacteristic
466C22×C3C22×#6711yescharacteristic
467C2×D3—22no—
468C2×D3—41no—
469C2×D3—41no—
470C3×C4—22no—
471C3×C4—22no—
472C3×C4—22no—
473C3×C4—22no—
474C3×C4—21no—
475C3×C4—21no—
476C3×C4—22no—
477C3×C4—42no—
478C3×C4—42no—
479C3×C4—62no—
480C3×C4—64no—
481C3×C4—121no—
482C3×C4—122no—
483C3×C4—121no—
484C3×C4C4×#6712yes—
485C3×C4C4×#6712yes—
486C3×C4C22×C4×D311yescharacteristic
487C3×C4C22×C4×D311yescharacteristic
488C3×C4C2×#23511yescharacteristic
489C3×C4C2×#23511yescharacteristic
490Dic3—24no—
491Dic3—22no—
492Dic3—42no—
493Dic3—41no—
494Dic3—41no—
495C32#294711yescharacteristic, complemented, Sylow
496C23—61no—
497C23C2×#62511yescharacteristic
498Q8—34no—
499Q8—32no—
500Q8—62no—
501Q8—61no—
502Q8—64no—
503D4—32no—
504D4—64no—
505D4—61no—
506C2×C4—61no—
507C2×C4—62no—
508C2×C4—64no—
509C2×C4—64no—
510C2×C4—61no—
511C2×C4—61no—
512C2×C4—62no—
513C2×C4—242no—
514C2×C4—241no—
515C2×C4#379812yes—
516C2×C4C4×D3212yes—
517C2×C4C2×#62512yes—
518C2×C4C2×#62512yes—
519C2×C4C2×#62511yescharacteristic
520C2×C4C22×D3211yescharacteristic
521C8—94no—
522C8—181no—
523C8—181no—
524C2×C3—22no—
525C2×C3—22no—
526C2×C3—21no—
527C2×C3—21no—
528C2×C3—21no—
529C2×C3—42no—
530C2×C3—122no—
531C2×C3C2×C4×#6711yescharacteristic
532C2×C3C2×C4×#6711yescharacteristic
533C2×C3#583611yescharacteristic
534C2×C3#583711yescharacteristic
535C2×C3#583811yescharacteristic
536C2×C3#583811yescharacteristic
537D3—42no—
538C22—21no—
539C22—21no—
540C22—62no—
541C22—121no—
542C22—121no—
543C22C4×#62512yes—
544C22C22×#62511yescharacteristic
545C4—22no—
546C4—22no—
547C4—62no—
548C4—64no—
549C4—121no—
550C4—122no—
551C4—121no—
552C4C4×#62512yes—
553C4C2×#379811yescharacteristic
554C4C2×C4×D3211yescharacteristic
555C3—21no—
556C3#8254711yescharacteristic, complemented
557C3#8257111yescharacteristic, complemented
558C2—22no—
559C2—122no—
560C2C2×C4×#62511yescharacteristic
561C2#1059544511yescharacteristic
562C2#1059544611yescharacteristic
subgroupG/H
centerC22C22×#625
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC32×#117C22
socleC22×C32C22×D4
prime radicalC2×C3×#235C22
cosocleC2×C32×C4C24
hypercenter#117D32
hypocenterC32#2947
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ #117

Complements

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

NH ≅ G/Ntype
2. C3×#5516C2semidirect
4. #10592696C2semidirect
5. #10591139C2semidirect
6. C2×#63565C2semidirect
8. #10590381C2semidirect
9. C4×#3718C2semidirect
10. #10590358C2semidirect
11. C4×#3715C2semidirect
32. #63827C4semidirect
49. #5516D3semidirect
78. C2×C3×Dic6C2×C4semidirect
85. #3748C2×C4semidirect
103. #3718C2×C4semidirect
104. #3715C2×C4semidirect
236. C2×Dic6C4×D3semidirect
495. C32#2947semidirect
556. C3#82547semidirect
557. C3#82571semidirect

Maximal subgroups

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

subgroupindex
C3×#55232
C3×#55162
C2×#638272
#105926962
#105911392
C2×#635652
#105910832
#105903812
C4×#37182
#105903582
C4×#37152
#825713
#825473