Finite Group Databasebeta

← #11887090

Subgroups — #11887090

Order 1152.

1386 conjugacy classes of subgroups.

The subgroup lattice has 594 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596080C211yesmaximal, characteristic
2#10595982C211yesmaximal, characteristic, complemented
3C32×#481C211yesmaximal, characteristic, complemented
4#10592740C211yesmaximal, characteristic, complemented
5C2×#63636C211yesmaximal, characteristic, complemented
6#10592569C211yesmaximal, characteristic, complemented
7#10592563C211yesmaximal, characteristic, complemented
8#10592562C211yesmaximal, characteristic, complemented
9#10592551C211yesmaximal, characteristic, complemented
10#10592475C211yesmaximal, characteristic, complemented
11C3⋊D3×#102C211yesmaximal, characteristic, complemented
12#10592461C211yesmaximal, characteristic, complemented
13#10592459C211yesmaximal, characteristic, complemented
14#10592430C211yesmaximal, characteristic, complemented
15#10592424C211yesmaximal, characteristic, complemented
16#81342—34nomaximal
17C2×D4×C3⋊D3—21no—
18C2×D4×C3⋊D3C2211yescharacteristic
19C22×C4⋊(C3⋊D3)C2211yescharacteristic
20C32×#121C2211yescharacteristic
21C2×C32×C4⋊C4C2211yescharacteristic, complemented
22#64149C2211yescharacteristic
23#64146—21no—
24C2×#3754C2211yescharacteristic, complemented
25C4×#638—21no—
26C4×#638C2211yescharacteristic
27#64133—21no—
28#64133C2211yescharacteristic, complemented
29C22×C3⋊(C3⋊C8)C2211yescharacteristic, complemented
30C2×#3744C2211yescharacteristic
31C2×#3744C2211yescharacteristic, complemented
32C2×C8×C3⋊D3C2211yescharacteristic, complemented
33#64106C2211yescharacteristic, complemented
34#64105—21no—
35#64104C2211yescharacteristic
36#64102C2211yescharacteristic
37C4⋊C4×C3⋊D3C2211yescharacteristic, complemented
38#64098—21no—
39#64097C2211yescharacteristic, complemented
40#64096C2211yescharacteristic, complemented
41#64093—21no—
42#64091—21no—
43C32×#106C2211yescharacteristic, complemented
44C32×#106C2211yescharacteristic, complemented
45C32×#102C2211yescharacteristic, complemented
46C32×#102C2211yescharacteristic, complemented
47C32×C22⋊C8C2211yescharacteristic, complemented
48#63659C2211yescharacteristic, complemented
49#63648C2211yescharacteristic
50#63648C2211yescharacteristic, complemented
51#63647C2211yescharacteristic, complemented
52#63641C2211yescharacteristic, complemented
53C8×C3⋊Dic3C2211yescharacteristic, complemented
54#63637C2211yescharacteristic, complemented
55#63636C2211yescharacteristic
56#63636C2211yescharacteristic
57#63636C2211yescharacteristic, complemented
58#63636C2211yescharacteristic, complemented
59#63635C2211yescharacteristic, complemented
60#5609—34no—
61#5511—34no—
62C3×#481D314yescomplemented
63#5041—34no—
64C2×#809—34no—
65#4870—34no—
66#4864—34no—
67#4863—34no—
68#4852—34no—
69#4776—34no—
70D3×#102—34no—
71#4762—34no—
72#4760—34no—
73#4731—34no—
74#67⋊C8—34no—
75C23×C3⋊D3—21no—
76C23×C3⋊D3—21no—
77C2×C32×D4—21no—
78C2×C32×D4C2311yescharacteristic
79C22×C32×C4—21no—
80C22×C32×C4C2311yescharacteristic
81C2×#638—21no—
82C2×#638—21no—
83C2×#638—21no—
84C2×#638D411yescharacteristic
85D4×C3⋊D3—22no—
86D4×C3⋊D3—41no—
87D4×C3⋊D3—44no—
88C2×C4⋊(C3⋊D3)—22no—
89C2×C4⋊(C3⋊D3)—21no—
90C2×C4⋊(C3⋊D3)—21no—
91C2×C4⋊(C3⋊D3)—41no—
92C2×C4⋊(C3⋊D3)C2311yescharacteristic
93C2×C4⋊(C3⋊D3)C2311yescharacteristic
94C2×C4×C3⋊D3—21no—
95C2×C4×C3⋊D3—21no—
96C2×C4×C3⋊D3C2311yescharacteristic
97C2×#634—21no—
98C2×#634C2311yescharacteristic
99C2×C32×C8C2311yescharacteristic
100C2×C32×C8C2311yescharacteristic
101C32×C4⋊C4—21no—
102C32×C4⋊C4C2311yescharacteristic
103C32×C4⋊C4C2311yescharacteristic
104C32×C4⋊C4C2311yescharacteristic
105C32×C22⋊C4—21no—
106#3757—21no—
107#3757D411yescharacteristic
108#3754—41no—
109#3752—21no—
110#3752—21no—
111#3752—21no—
112#3752D411yescharacteristic
113C4⋊(C3⋊Dic3)—21no—
114C4⋊(C3⋊Dic3)C2311yescharacteristic
115#3750—21no—
116#3750—21no—
117#3750—21no—
118#3750—21no—
119#3750D411yescharacteristic
120C4×C3⋊Dic3—21no—
121C4×C3⋊Dic3C2311yescharacteristic
122C2×C3⋊(C3⋊C8)—41no—
123C2×C3⋊(C3⋊C8)C2311yescharacteristic
124C2×C3⋊(C3⋊C8)C2311yescharacteristic
125#3744—22no—
126#3744—41no—
127C8×C3⋊D3—41no—
128#3295—91noSylow
129C2×D3×D4—34no—
130C2×D3×D4—64no—
131C22×D12—34no—
132C3×#121C2×D314yes—
133C2×C3×C4⋊C4C2×D314yescomplemented
134#940—34no—
135#937—64no—
136C2×#214—34no—
137C4×#67—34no—
138C4×#67—64no—
139#924—34no—
140#924—64no—
141C22×C3⋊C8—34no—
142C2×#204—34no—
143C2×#204—34no—
144C2×D3×C8—34no—
145#897—34no—
146#896—64no—
147#895—34no—
148#893—34no—
149D3×C4⋊C4—34no—
150#889—64no—
151#888—34no—
152#887—34no—
153#884—64no—
154#882—64no—
155C3×#106C2×D314yescomplemented
156C3×#106C2×D314yescomplemented
157C3×#102C2×D314yescomplemented
158C3×#102C2×D314yescomplemented
159C3×C22⋊C8C2×D314yescomplemented
160#832—34no—
161#821—34no—
162#821—34no—
163(C2×D3)⋊C8—34no—
164Dic3⋊C8—34no—
165C8×Dic3—34no—
166#810—34no—
167#809—34no—
168#809—34no—
169#809—34no—
170#809—34no—
171#808—34no—
172C23×C32—21no—
173C23×C32C2×D411yescharacteristic
174C22×C3⋊D3—21no—
175C22×C3⋊D3—21no—
176C22×C3⋊D3—42no—
177C22×C3⋊D3—42no—
178C22×C3⋊D3—42no—
179C22×C3⋊D3—42no—
180C22×C3⋊D3—81no—
181C22×C3⋊D3—81no—
182C22×C3⋊D3C2×D411yescharacteristic
183C32×D4—21no—
184C32×D4—21no—
185C32×D4—42no—
186C2×C32×C4—21no—
187C2×C32×C4—21no—
188C2×C32×C4—21no—
189C2×C32×C4—21no—
190C2×C32×C4—21no—
191C2×C32×C4—81no—
192C2×C32×C4C2×D411yescharacteristic
193C2×C32×C4C2411yescharacteristic
194#638—42no—
195#638—42no—
196#638—81no—
197#638SD1614yescomplemented
198C2×C3⋊Dic3—21no—
199C2×C3⋊Dic3—21no—
200C2×C3⋊Dic3C2×D411yescharacteristic
201C2×C3⋊Dic3C2×D411yescharacteristic
202C2×C3⋊Dic3C2×D411yescharacteristic
203C4⋊(C3⋊D3)—21no—
204C4⋊(C3⋊D3)—21no—
205C4⋊(C3⋊D3)—21no—
206C4⋊(C3⋊D3)—42no—
207C4⋊(C3⋊D3)—42no—
208C4⋊(C3⋊D3)#4112yes—
209C4×C3⋊D3—21no—
210C4×C3⋊D3—21no—
211C4×C3⋊D3—42no—
212C4×C3⋊D3—81no—
213#634—21no—
214#634—21no—
215#634—81no—
216C32×C8—21no—
217C32×C8—21no—
218C3⋊(C3⋊C8)—21no—
219C3⋊(C3⋊C8)—21no—
220#554—91no—
221D42—91no—
222#486—91no—
223#481—91no—
224#481C3⋊D311yescharacteristic, complemented
225#476—91no—
226#465—91no—
227#465—91no—
228#460—91no—
229#450—91no—
230#450—91no—
231C4×SD16—91no—
232C8×D4—91no—
233C2×#102—91no—
234C2×#102—91no—
235C23×D3—64no—
236C23×D3—64no—
237C2×C3×D4—24no—
238C2×C3×D4C22×D314yes—
239C22×C3×C4—24no—
240C22×C3×C4C22×D314yes—
241C2×#67—34no—
242C2×#67—64no—
243C2×#67—64no—
244C2×#67—64no—
245D3×D4—68no—
246D3×D4—124no—
247D3×D4—1216no—
248C2×D12—34no—
249C2×D12—34no—
250C2×D12—68no—
251C2×D12—64no—
252C2×D12—64no—
253C2×D12—124no—
254C2×C4×D3—34no—
255C2×C4×D3—64no—
256C2×C4×D3—64no—
257C2×Dic6—34no—
258C2×Dic6—64no—
259C2×C3×C8C22×D314yes—
260C2×C3×C8C22×D314yes—
261C3×C4⋊C4—24no—
262C3×C4⋊C4C22×D314yes—
263C3×C4⋊C4C22×D314yes—
264C3×C4⋊C4C22×D314yes—
265C3×C22⋊C4—24no—
266#217—34no—
267#217—64no—
268#214—124no—
269(C2×D3)⋊C4—34no—
270(C2×D3)⋊C4—64no—
271(C2×D3)⋊C4—64no—
272(C2×D3)⋊C4—64no—
273C4⋊Dic3—34no—
274C4⋊Dic3—64no—
275Dic3⋊C4—34no—
276Dic3⋊C4—64no—
277Dic3⋊C4—64no—
278Dic3⋊C4—64no—
279Dic3⋊C4—64no—
280C4×Dic3—34no—
281C4×Dic3—64no—
282C2×C3⋊C8—34no—
283C2×C3⋊C8—34no—
284C2×C3⋊C8—124no—
285#204—68no—
286#204—124no—
287D3×C8—124no—
288C22×C32—21no—
289C22×C32—21no—
290C22×C32—41no—
291C22×C32—41no—
292C22×C32—41no—
293C22×C32C2×SD1612yes—
294C22×C32C22×D411yescharacteristic
295C2×C3⋊D3—21no—
296C2×C3⋊D3—21no—
297C2×C3⋊D3—22no—
298C2×C3⋊D3—41no—
299C2×C3⋊D3—41no—
300C2×C3⋊D3—41no—
301C2×C3⋊D3—41no—
302C2×C3⋊D3—41no—
303C2×C3⋊D3—84no—
304C2×C3⋊D3—84no—
305C2×C3⋊D3C2×SD1612yes—
306C32×C4—21no—
307C32×C4—41no—
308C32×C4—41no—
309C32×C4—41no—
310C32×C4C2×#4111yescharacteristic
311C32×C4H(5,𝔽2)11yescharacteristic
312C3⋊Dic3—21no—
313C3⋊Dic3—21no—
314C3⋊Dic3—41no—
315C3⋊Dic3—41no—
316C3⋊Dic3C2×SD1612yes—
317C22×D4—91no—
318C22×D4—91no—
319C22×D4—181no—
320C2×SD16—91no—
321C2×SD16—91no—
322C2×SD16—91no—
323C22×C8—91no—
324C22×C8—91no—
325C4⋊Q8—91no—
326#127—91no—
327#125—181no—
328C22⋊Q8—91no—
329C22⋊Q8—91no—
330C22⋊Q8—181no—
331C22⋊Q8—181no—
332#121—91no—
333#121—181no—
334#121C2×C3⋊D311yescharacteristic
335#120—181no—
336#120—181no—
337C4×Q8—91no—
338C4×D4—91no—
339C4×D4—91no—
340C4×D4—181no—
341C2×C4⋊C4—91no—
342C2×C4⋊C4C2×C3⋊D311yescharacteristic, complemented
343#106—91no—
344#106C2×C3⋊D311yescharacteristic, complemented
345#106C2×C3⋊D311yescharacteristic, complemented
346C4⋊C8—91no—
347#103—91no—
348#102—91no—
349#102—91no—
350#102—91no—
351#102—91no—
352#102—91no—
353#102—91no—
354#102—91no—
355#102C2×C3⋊D311yescharacteristic, complemented
356#102C2×C3⋊D311yescharacteristic, complemented
357C22⋊C8—91no—
358C22⋊C8C2×C3⋊D311yescharacteristic, complemented
359C4×C8—91no—
360C23×C3—24no—
361C23×C3D3×D414yes—
362C22×D3—34no—
363C22×D3—64no—
364C22×D3—64no—
365C22×D3—128no—
366C22×D3—128no—
367C22×D3—128no—
368C22×D3—128no—
369C22×D3—244no—
370C22×D3—244no—
371C3×D4—24no—
372C3×D4—24no—
373C3×D4—48no—
374C2×C3×C4—24no—
375C2×C3×C4—24no—
376C2×C3×C4—24no—
377C2×C3×C4—24no—
378C2×C3×C4—24no—
379C2×C3×C4—84no—
380C2×C3×C4D3×D414yes—
381C2×C3×C4C23×D314yes—
382#67—316no—
383#67—128no—
384#67—128no—
385#67—244no—
386C2×Dic3—34no—
387C2×Dic3—34no—
388C2×Dic3—34no—
389C2×Dic3—64no—
390C2×Dic3—64no—
391D12—38no—
392D12—64no—
393D12—64no—
394D12—64no—
395D12—128no—
396D12—128no—
397C4×D3—64no—
398C4×D3—64no—
399C4×D3—128no—
400C4×D3—244no—
401Dic6—64no—
402Dic6—64no—
403Dic6—244no—
404C3×C8—24no—
405C3×C8—24no—
406C3⋊C8—64no—
407C3⋊C8—64no—
408C2×C32—22no—
409C2×C32—81no—
410C2×C32#54611yescharacteristic
411C2×C32C22×SD1611yescharacteristic
412C2×C32#57611yescharacteristic
413C3⋊D3—22no—
414C3⋊D3—42no—
415C3⋊D3—81no—
416C24—181no—
417C24—181no—
418C2×Q8—91no—
419C2×Q8—181no—
420C2×D4—21no—
421C2×D4—91no—
422C2×D4—91no—
423C2×D4—91no—
424C2×D4—182no—
425C2×D4—181no—
426C2×D4—181no—
427C2×D4—181no—
428C2×D4—181no—
429C2×D4—182no—
430C2×D4—181no—
431C2×D4—361no—
432C2×D4—361no—
433C2×D4—364no—
434C2×D4C22×C3⋊D311yescharacteristic
435C22×C4—21no—
436C22×C4—91no—
437C22×C4—181no—
438C22×C4—181no—
439C22×C4C22×C3⋊D311yescharacteristic
440SD16—182no—
441SD16—361no—
442SD16—361no—
443C2×C8—91no—
444C2×C8—91no—
445C2×C8—361no—
446C2×C8—361no—
447C2×C8C22×C3⋊D311yescharacteristic
448C2×C8C22×C3⋊D311yescharacteristic
449C4⋊C4—21no—
450C4⋊C4—91no—
451C4⋊C4—91no—
452C4⋊C4—181no—
453C4⋊C4—181no—
454C4⋊C4—181no—
455C4⋊C4—181no—
456C4⋊C4—181no—
457C4⋊C4C22×C3⋊D311yescharacteristic
458C4⋊C4C22×C3⋊D311yescharacteristic
459C4⋊C4C22×C3⋊D311yescharacteristic
460C22⋊C4—21no—
461C22⋊C4—91no—
462C22⋊C4—91no—
463C22⋊C4—181no—
464C22⋊C4—181no—
465C22⋊C4—181no—
466C22⋊C4—181no—
467C42—91no—
468C42—181no—
469C22×C3—24no—
470C22×C3—24no—
471C22×C3—44no—
472C22×C3—44no—
473C22×C3—44no—
474C22×C3D3×SD1618yes—
475C22×C3C2×D3×D414yes—
476C2×D3—38no—
477C2×D3—64no—
478C2×D3—64no—
479C2×D3—68no—
480C2×D3—124no—
481C2×D3—124no—
482C2×D3—124no—
483C2×D3—124no—
484C2×D3—124no—
485C2×D3—2416no—
486C2×D3—2416no—
487C3×C4—24no—
488C3×C4—44no—
489C3×C4—44no—
490C3×C4—44no—
491C3×C4D3×#4114yes—
492C3×C4#100914yes—
493Dic3—38no—
494Dic3—64no—
495Dic3—64no—
496Dic3—124no—
497Dic3—124no—
498C32#329511yescharacteristic, complemented, Sylow
499C23—21no—
500C23—91no—
501C23—181no—
502C23—181no—
503C23—362no—
504C23—362no—
505C23—362no—
506C23—362no—
507C23—721no—
508C23—721no—
509C23D4×C3⋊D311yescharacteristic
510Q8—181no—
511Q8—181no—
512Q8—721no—
513D4—21no—
514D4—21no—
515D4—42no—
516D4—94no—
517D4—92no—
518D4—181no—
519D4—181no—
520D4—181no—
521D4—362no—
522D4—362no—
523D4—362no—
524D4—362no—
525D4—721no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—81no—
532C2×C4—91no—
533C2×C4—91no—
534C2×C4—91no—
535C2×C4—181no—
536C2×C4—181no—
537C2×C4—181no—
538C2×C4—181no—
539C2×C4—362no—
540C2×C4—721no—
541C2×C4D4×C3⋊D311yescharacteristic
542C2×C4C23×C3⋊D311yescharacteristic
543C8—21no—
544C8—21no—
545C8—181no—
546C8—181no—
547C2×C3—28no—
548C2×C3—84no—
549C2×C3#565414yes—
550C2×C3C2×D3×SD1614yes—
551C2×C3#577414yes—
552D3—68no—
553D3—128no—
554D3—244no—
555C22—21no—
556C22—21no—
557C22—41no—
558C22—41no—
559C22—41no—
560C22—92no—
561C22—181no—
562C22—181no—
563C22—182no—
564C22—361no—
565C22—361no—
566C22—361no—
567C22—361no—
568C22—361no—
569C22—724no—
570C22—724no—
571C22SD16×C3⋊D312yes—
572C22C2×D4×C3⋊D311yescharacteristic
573C4—21no—
574C4—41no—
575C4—41no—
576C4—41no—
577C4—92no—
578C4—181no—
579C4—181no—
580C4—361no—
581C4—361no—
582C4#41×C3⋊D311yescharacteristic
583C4#6436611yescharacteristic
584C3#8134214yescomplemented
585C2—22no—
586C2—81no—
587C2—182no—
588C2—362no—
589C2—721no—
590C2#1059612511yescharacteristic
591C2C2×SD16×C3⋊D311yescharacteristic
592C2#1059624511yescharacteristic
subgroupG/H
centerC22C2×D4×C3⋊D3
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC32×#481C2
socleC22×C32C22×D4
prime radical#10596080C2
hypercenter#481C3⋊D3
hypocenterC32#3295
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #481

Complements

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

NH ≅ G/Ntype
2. #10595982C2semidirect
3. C32×#481C2semidirect
4. #10592740C2semidirect
5. C2×#63636C2semidirect
6. #10592569C2semidirect
7. #10592563C2semidirect
8. #10592562C2semidirect
9. #10592551C2semidirect
10. #10592475C2semidirect
11. C3⋊D3×#102C2semidirect
12. #10592461C2semidirect
13. #10592459C2semidirect
14. #10592430C2semidirect
15. #10592424C2semidirect
21. C2×C32×C4⋊C4C22semidirect
24. C2×#3754C22semidirect
28. #64133C22semidirect
29. C22×C3⋊(C3⋊C8)C22semidirect
31. C2×#3744C22semidirect
32. C2×C8×C3⋊D3C22semidirect
33. #64106C22semidirect
37. C4⋊C4×C3⋊D3C22semidirect
39. #64097C22semidirect
40. #64096C22semidirect
43. C32×#106C22semidirect
44. C32×#106C22semidirect
45. C32×#102C22semidirect
46. C32×#102C22semidirect
47. C32×C22⋊C8C22semidirect
48. #63659C22semidirect
50. #63648C22semidirect
51. #63647C22semidirect
52. #63641C22semidirect
53. C8×C3⋊Dic3C22semidirect
54. #63637C22semidirect
57. #63636C22semidirect
58. #63636C22semidirect
59. #63635C22semidirect
62. C3×#481D3semidirect
133. C2×C3×C4⋊C4C2×D3semidirect
155. C3×#106C2×D3semidirect
156. C3×#106C2×D3semidirect
157. C3×#102C2×D3semidirect
158. C3×#102C2×D3semidirect
159. C3×C22⋊C8C2×D3semidirect
197. #638SD16semidirect
224. #481C3⋊D3semidirect
342. C2×C4⋊C4C2×C3⋊D3semidirect
344. #106C2×C3⋊D3semidirect
345. #106C2×C3⋊D3semidirect
355. #102C2×C3⋊D3semidirect
356. #102C2×C3⋊D3semidirect
358. C22⋊C8C2×C3⋊D3semidirect
498. C32#3295semidirect
584. C3#81342semidirect

Maximal subgroups

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

subgroupindex
#105960802
#105959822
C32×#4812
#105927402
C2×#636362
#105925692
#105925632
#105925622
#105925512
#105924752
C3⋊D3×#1022
#105924612
#105924592
#105924302
#105924242
#813423