Finite Group Databasebeta

← #11860637

Subgroups — #11860637

Order 1152.

1019 conjugacy classes of subgroups.

The subgroup lattice has 582 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5516C211yesmaximal, characteristic, complemented
2#10594990C211yesmaximal, characteristic
3C2×#63833C211yesmaximal, characteristic
4#10592701C211yesmaximal, characteristic
5C3×#4995C211yesmaximal, characteristic, complemented
6C2×#63565C211yesmaximal, characteristic, complemented
7#10591057C211yesmaximal, characteristic, complemented
8#10590481C212yesmaximal, complemented
9#10590480C212yesmaximal, complemented
10#10590458C212yesmaximal, complemented
11#10590457C212yesmaximal, complemented
12#82547—31nomaximal
13#79202—31nomaximal
14C2×#3828C2211yescharacteristic
15C22×C3×Dic6C2211yescharacteristic
16C32×#117C2211yescharacteristic
17C22×C3⋊(C3⋊C8)C2211yescharacteristic
18C3×#926C2211yescharacteristic
19C2×C3×C4⋊Dic3C2211yescharacteristic
20C2×C3×#208C2211yescharacteristic
21C3×#887C2212yes—
22C3×#887C2212yes—
23C3×#877—22no—
24C3×C4×Dic6—21no—
25C3×C4×Dic6—21no—
26#63952—22no—
27#63900—21no—
28#63894C2212yes—
29#63849—21no—
30#63844C2212yes—
31C2×#3719C2212yes—
32#63833C418yescomplemented
33C2×#3717C2212yes—
34#63637C2211yescharacteristic
35#63637C2211yescharacteristic
36#63636C2211yescharacteristic
37#63636C2211yescharacteristic
38C3×#808C2212yes—
39C3×#807C2212yes—
40#63565C2212yes—
41#63565C2212yes—
42#63554C2212yes—
43Dic3×C3⋊C8C2212yes—
44C3×#519—31no—
45C2×#942—31no—
46C2×#909—31no—
47#5523—31no—
48#5516D311yescharacteristic, complemented
49#5504—31no—
50C3×#428—31no—
51C2×#835—31no—
52#5122—31no—
53#5030—32no—
54C4×#216—32no—
55#5026—32no—
56C4×#215—32no—
57#5002—31no—
58#5002—31no—
59#5002—61no—
60#4997—31no—
61#4995D311yescharacteristic, complemented
62C2×#810—31no—
63#4889—32no—
64#4873—32no—
65#4853—32no—
66#4852—32no—
67C22×C32×C4C2311yescharacteristic
68C2×#638—21no—
69#3828—22no—
70#3828C2×C414yes—
71C2×C4⋊(C3⋊D3)C2311yescharacteristic
72C2×C4×C3⋊D3—21no—
73C2×#634C2311yescharacteristic
74C22×C3×Dic3—21no—
75C22×C3×Dic3—21no—
76C2×C3×Dic6—21no—
77C2×C3×Dic6—22no—
78C2×C3×Dic6C2×C414yescomplemented
79C2×C3×Dic6C2312yes—
80C2×#624—22no—
81C32×C4⋊C4C2311yescharacteristic
82C32×C4⋊C4C2311yescharacteristic
83C32×C22⋊C4—21no—
84C32×C42—21no—
85C2×C3⋊(C3⋊C8)—22no—
86C2×C3⋊(C3⋊C8)C2311yescharacteristic
87C2×C3⋊(C3⋊C8)C2311yescharacteristic
88C3×#217D412yes—
89C3×C4⋊Dic3—21no—
90C3×C4⋊Dic3D411yescharacteristic
91C3×C4⋊Dic3D411yescharacteristic
92C3×C4⋊Dic3C2312yes—
93C3×Dic3⋊C4—22no—
94C3×Dic3⋊C4—22no—
95C3×C4×Dic3—22no—
96C3×C4×Dic3—22no—
97C3×C4×Dic3C2312yes—
98C3×#208C2×C414yescomplemented
99C2×C3×C3⋊C8C2312yes—
100#3724—22no—
101#3722—22no—
102Dic32—22no—
103#3719C2×C418yescomplemented
104#3717C2×C418yescomplemented
105#2947—91noSylow
106C22×C3×Q8—31no—
107C2×#235—31no—
108C2×#235—31no—
109C2×#235—61no—
110C22×Dic6C2×D311yescharacteristic
111C2×C3×M16—31no—
112C3×C4×Q8—32no—
113C3×C4×Q8—32no—
114C3×C4×Q8—61no—
115C3×C4×Q8—61no—
116C3×#117—21no—
117C3×#117—31no—
118C3×#117—62no—
119C3×#117C2×D311yescharacteristic
120C3×#117C2×D311yescharacteristic
121C2×C3×C4⋊C4—31no—
122C2×#216—32no—
123#942—38no—
124C2×#215—32no—
125C4×#67—62no—
126#926C2×D311yescharacteristic
127C2×C4⋊Dic3C2×D311yescharacteristic
128C2×#208C2×D311yescharacteristic
129C22×C3⋊C8—31no—
130C22×C3⋊C8—31no—
131C22×C3⋊C8—61no—
132#909—38no—
133C2×Dic12—32no—
134C2×#204—32no—
135#893—32no—
136#892—61no—
137#892—61no—
138D3×C4⋊C4—61no—
139D3×C4⋊C4—61no—
140#887—32no—
141#887C2×D312yes—
142#887C2×D312yes—
143#67⋊C4—62no—
144#877—22no—
145C4×D12—32no—
146C4×Dic6—21no—
147C4×Dic6—21no—
148C4×Dic6—32no—
149C3×#107—32no—
150C3×#106—32no—
151#835—32no—
152#835—32no—
153#815—32no—
154C8×Dic3—32no—
155#810—32no—
156#810—32no—
157#810—31no—
158#810—31no—
159#810—31no—
160#810—31no—
161#810—61no—
162#810—61no—
163#809—31no—
164#809—31no—
165#809—31no—
166#809—31no—
167#809—61no—
168#809—61no—
169#808C2×D312yes—
170#807C2×D312yes—
171#803—32no—
172C4×C3⋊C8—32no—
173C23×C32C2×D411yescharacteristic
174C22×C3⋊D3—21no—
175C2×C32×C4—21no—
176C2×C32×C4—21no—
177C2×C32×C4C22×C412yes—
178C2×C32×C4C2×D411yescharacteristic
179C2×C32×C4#4112yes—
180C2×C32×C4C2411yescharacteristic
181#638—24no—
182C2×C3⋊Dic3—21no—
183C4⋊(C3⋊D3)—21no—
184C4⋊(C3⋊D3)C22×C412yes—
185C4×C3⋊D3—24no—
186#634—21no—
187#634C22×C412yes—
188C2×C3×Dic3—24no—
189C2×C3×Dic3—22no—
190C2×C3×Dic3—22no—
191C2×C3×Dic3—81no—
192C2×C3×Dic3C2×D412yes—
193C2×C3×Dic3C2×D412yes—
194C3×Dic6—24no—
195C3×Dic6—22no—
196C3×Dic6C22×C414yes—
197#624—82no—
198C3⋊(C3⋊C8)—21no—
199C3⋊(C3⋊C8)—21no—
200C3×C3⋊C8C22×C414yes—
201C2×#137—91no—
202#520—91no—
203#519—31no—
204#441—92no—
205#440—92no—
206C4×Q16—92no—
207C4×SD16—92no—
208#428—31no—
209#416—91no—
210C2×#103—91no—
211#405—91no—
212C2×C3×Q8—34no—
213C2×C3×Q8—32no—
214C2×C3×Q8—61no—
215C2×C3×Q8—62no—
216C22×C3×C4—21no—
217C22×C3×C4—61no—
218C22×C3×C4—61no—
219C22×C3×C4C22×D311yescharacteristic
220C22×C3×C4C22×D311yescharacteristic
221C2×#67—61no—
222C2×#67—61no—
223C2×#67—121no—
224C22×Dic3—21no—
225C22×Dic3—21no—
226#235—34no—
227#235—34no—
228#235—64no—
229#235—62no—
230#235—62no—
231#235—122no—
232C2×D12—31no—
233C2×D12—31no—
234C2×D12—61no—
235C2×C4×D3—61no—
236C2×C4×D3—61no—
237C2×C4×D3—62no—
238C2×C4×D3—62no—
239C2×C4×D3—121no—
240C2×Dic6—22no—
241C2×Dic6—21no—
242C2×Dic6—31no—
243C2×Dic6—31no—
244C2×Dic6—61no—
245C2×Dic6C4×D314yescomplemented
246C2×Dic6C22×D312yes—
247C3×M16—34no—
248C2×C3×C8—32no—
249C3×C4⋊C4—21no—
250C3×C4⋊C4—21no—
251C3×C4⋊C4—31no—
252C3×C4⋊C4—31no—
253C3×C4⋊C4—32no—
254C3×C4⋊C4—62no—
255C3×C4⋊C4—62no—
256C3×C4⋊C4—61no—
257C3×C4⋊C4C22×D311yescharacteristic
258C3×C4⋊C4C22×D311yescharacteristic
259C3×C4⋊C4C22×D311yescharacteristic
260C3×C4⋊C4C22×D311yescharacteristic
261C3×C22⋊C4—21no—
262C3×C22⋊C4—21no—
263C3×C22⋊C4—32no—
264C3×C22⋊C4—41no—
265C3×C42—21no—
266C3×C42—21no—
267C3×C42—32no—
268C3×C42—41no—
269C3×C42—62no—
270C3×C42—62no—
271#217#6712yes—
272#216—38no—
273#215—38no—
274(C2×D3)⋊C4—62no—
275(C2×D3)⋊C4—62no—
276C4⋊Dic3—21no—
277C4⋊Dic3#6711yescharacteristic
278C4⋊Dic3#6711yescharacteristic
279C4⋊Dic3C22×D312yes—
280Dic3⋊C4—22no—
281Dic3⋊C4—22no—
282Dic3⋊C4—62no—
283Dic3⋊C4—62no—
284C4×Dic3—22no—
285C4×Dic3—22no—
286C4×Dic3—62no—
287C4×Dic3—62no—
288C4×Dic3C22×D312yes—
289#208C4×D314yescomplemented
290C2×C3⋊C8—31no—
291C2×C3⋊C8—31no—
292C2×C3⋊C8—31no—
293C2×C3⋊C8—31no—
294C2×C3⋊C8—61no—
295C2×C3⋊C8—61no—
296C2×C3⋊C8—62no—
297C2×C3⋊C8—62no—
298C2×C3⋊C8—122no—
299C2×C3⋊C8C22×D312yes—
300Dic12—38no—
301#204—38no—
302C22×C32—21no—
303C22×C32—21no—
304C22×C32C4×D412yes—
305C22×C32C22×D411yescharacteristic
306C2×C3⋊D3—22no—
307C2×C3⋊D3—41no—
308C2×C3⋊D3—41no—
309C32×C4—41no—
310C32×C4—41no—
311C32×C4C4×D412yes—
312C32×C4C23×C411yescharacteristic
313C32×C4C2×#4111yescharacteristic
314C3⋊Dic3—22no—
315C3×Dic3—24no—
316C3×Dic3—22no—
317C3×Dic3—22no—
318C3×Dic3—42no—
319C2×#41—91no—
320C22×Q8—31no—
321#137—98no—
322C2×Q16—92no—
323C2×SD16—92no—
324C2×M16—31no—
325C22×C8—91no—
326C4×Q8—32no—
327C4×Q8—32no—
328C4×Q8—61no—
329C4×Q8—61no—
330C4×Q8—92no—
331C4×D4—92no—
332C4×D4—182no—
333#117—31no—
334#117—62no—
335#117—181no—
336#117D3211yescharacteristic
337C2×C4⋊C4—31no—
338C2×C4⋊C4—181no—
339#107—32no—
340#106—32no—
341#103—92no—
342#103—92no—
343#103—91no—
344#103—91no—
345#102—91no—
346#102—91no—
347#97—92no—
348C4×C8—92no—
349C23×C3—21no—
350C23×C3D3×D411yescharacteristic
351C23×C3C2×#6711yescharacteristic
352C22×D3—61no—
353C22×D3—61no—
354C22×D3—121no—
355C3×Q8—34no—
356C3×Q8—64no—
357C3×Q8—62no—
358C2×C3×C4—21no—
359C2×C3×C4—21no—
360C2×C3×C4—21no—
361C2×C3×C4—21no—
362C2×C3×C4—21no—
363C2×C3×C4—22no—
364C2×C3×C4—22no—
365C2×C3×C4—21no—
366C2×C3×C4—32no—
367C2×C3×C4—32no—
368C2×C3×C4—41no—
369C2×C3×C4—41no—
370C2×C3×C4—64no—
371C2×C3×C4—62no—
372C2×C3×C4—62no—
373C2×C3×C4—241no—
374C2×C3×C4C2×C4×D312yes—
375C2×C3×C4C2×C4×D312yes—
376C2×C3×C4#23512yes—
377C2×C3×C4D3×D411yescharacteristic
378C2×C3×C4#23912yes—
379C2×C3×C4C2×#6711yescharacteristic
380C2×C3×C4C23×D311yescharacteristic
381C2×C3×C4C23×D311yescharacteristic
382#67—64no—
383#67—64no—
384#67—124no—
385C2×Dic3—24no—
386C2×Dic3—22no—
387C2×Dic3—22no—
388C2×Dic3—61no—
389C2×Dic3—61no—
390C2×Dic3—81no—
391C2×Dic3—121no—
392C2×Dic3C2×#6712yes—
393C2×Dic3C2×#6712yes—
394D12—32no—
395D12—32no—
396D12—62no—
397D12—61no—
398D12—61no—
399D12—121no—
400C4×D3—64no—
401C4×D3—64no—
402C4×D3—124no—
403C4×D3—242no—
404C4×D3—242no—
405Dic6—24no—
406Dic6—22no—
407Dic6—32no—
408Dic6—32no—
409Dic6—62no—
410Dic6—61no—
411Dic6—61no—
412Dic6—121no—
413Dic6C2×C4×D314yes—
414C3×C8—34no—
415C3⋊C8—61no—
416C3⋊C8—61no—
417C3⋊C8—61no—
418C3⋊C8—61no—
419C3⋊C8—121no—
420C3⋊C8—121no—
421C3⋊C8C2×C4×D314yes—
422C2×C32—22no—
423C2×C32C2×C4×D411yescharacteristic
424C2×C32#57711yescharacteristic
425C2×C32#57811yescharacteristic
426C3⋊D3—42no—
427#41—94no—
428#41—182no—
429C2×Q8—32no—
430C2×Q8—34no—
431C2×Q8—62no—
432C2×Q8—61no—
433C2×Q8—91no—
434C2×D4—91no—
435C2×D4—181no—
436C22×C4—61no—
437C22×C4—61no—
438C22×C4—182no—
439C22×C4—181no—
440C22×C4C2×D3211yescharacteristic
441Q16—98no—
442SD16—98no—
443M16—34no—
444C2×C8—32no—
445C2×C8—91no—
446C2×C8—91no—
447C2×C8—182no—
448C4⋊C4—31no—
449C4⋊C4—31no—
450C4⋊C4—32no—
451C4⋊C4—62no—
452C4⋊C4—62no—
453C4⋊C4—61no—
454C4⋊C4—182no—
455C4⋊C4C2×D3211yescharacteristic
456C4⋊C4C2×D3211yescharacteristic
457C22⋊C4—21no—
458C22⋊C4—32no—
459C22⋊C4—182no—
460C42—21no—
461C42—32no—
462C42—62no—
463C42—62no—
464C42—182no—
465C22×C3—21no—
466C22×C3—21no—
467C22×C3—21no—
468C22×C3—21no—
469C22×C3—21no—
470C22×C3—22no—
471C22×C3—41no—
472C22×C3—41no—
473C22×C3#89312yes—
474C22×C3C4×#6712yes—
475C22×C3C2×D3×D411yescharacteristic
476C22×C3C22×#6711yescharacteristic
477C2×D3—62no—
478C2×D3—62no—
479C2×D3—122no—
480C2×D3—121no—
481C2×D3—121no—
482C2×D3—121no—
483C2×D3—121no—
484C2×D3—241no—
485C2×D3—241no—
486C3×C4—21no—
487C3×C4—21no—
488C3×C4—22no—
489C3×C4—41no—
490C3×C4—41no—
491C3×C4—41no—
492C3×C4—41no—
493C3×C4—64no—
494C3×C4—62no—
495C3×C4—62no—
496C3×C4—81no—
497C3×C4—81no—
498C3×C4—122no—
499C3×C4#89312yes—
500C3×C4C4×#6712yes—
501C3×C4C22×C4×D311yescharacteristic
502C3×C4C22×C4×D311yescharacteristic
503C3×C4C2×#23511yescharacteristic
504C3×C4C2×#23911yescharacteristic
505Dic3—24no—
506Dic3—22no—
507Dic3—22no—
508Dic3—42no—
509Dic3—62no—
510Dic3—62no—
511Dic3—122no—
512C32#294711yescharacteristic, complemented, Sylow
513C23—181no—
514C23D3×#6711yescharacteristic
515Q8—34no—
516Q8—62no—
517Q8—64no—
518Q8—92no—
519Q8—181no—
520D4—92no—
521D4—184no—
522D4—181no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—32no—
526C2×C4—32no—
527C2×C4—62no—
528C2×C4—64no—
529C2×C4—62no—
530C2×C4—181no—
531C2×C4—184no—
532C2×C4—241no—
533C2×C4—722no—
534C2×C4#379912yes—
535C2×C4C4×D3212yes—
536C2×C4D3×#6711yescharacteristic
537C2×C4C22×D3211yescharacteristic
538C8—34no—
539C8—181no—
540C8—181no—
541C2×C3—22no—
542C2×C3—22no—
543C2×C3—21no—
544C2×C3—21no—
545C2×C3—21no—
546C2×C3—42no—
547C2×C3C2×#89311yescharacteristic
548C2×C3#577511yescharacteristic
549C2×C3#577911yescharacteristic
550C2×C3C2×C4×#6711yescharacteristic
551C2×C3#583711yescharacteristic
552C2×C3#583811yescharacteristic
553D3—122no—
554D3—122no—
555D3—242no—
556C22—21no—
557C22—21no—
558C22—182no—
559C22—361no—
560C22—361no—
561C22#6390412yes—
562C22C2×D3×#6711yescharacteristic
563C4—41no—
564C4—41no—
565C4—62no—
566C4—62no—
567C4—64no—
568C4—122no—
569C4—182no—
570C4#6390412yes—
571C4C2×#379911yescharacteristic
572C4C2×C4×D3211yescharacteristic
573C3—21no—
574C3#7920211yescharacteristic, complemented
575C3#8254711yescharacteristic, complemented
576C2—22no—
577C2—362no—
578C2C2×#6390411yescharacteristic
579C2#1059545511yescharacteristic
580C2#1059546511yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC32×#117C22
socleC22×C32C22×D4
prime radicalC2×#3828C22
cosocleC2×C32×C4C24
hypercenter#117D32
hypocenterC32#2947
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
1. C3×#5516C2semidirect
5. C3×#4995C2semidirect
6. C2×#63565C2semidirect
7. #10591057C2semidirect
8. #10590481C2semidirect
9. #10590480C2semidirect
10. #10590458C2semidirect
11. #10590457C2semidirect
32. #63833C4semidirect
48. #5516D3semidirect
61. #4995D3semidirect
78. C2×C3×Dic6C2×C4semidirect
98. C3×#208C2×C4semidirect
103. #3719C2×C4semidirect
104. #3717C2×C4semidirect
245. C2×Dic6C4×D3semidirect
289. #208C4×D3semidirect
512. C32#2947semidirect
574. C3#79202semidirect
575. C3#82547semidirect

Maximal subgroups

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

subgroupindex
C3×#55162
#105949902
C2×#638332
#105927012
C3×#49952
C2×#635652
#105910572
#105904812
#105904802
#105904582
#105904572
#825473
#792023