Finite Group Databasebeta

← #14722246

Subgroups — #14722246

Order 2816.

1004 conjugacy classes of subgroups.

The subgroup lattice has 540 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082493C211yesmaximal, characteristic
2#13077725C211yesmaximal, characteristic, complemented
3#13077284C211yesmaximal, characteristic, complemented
4#13067320C212yesmaximal, complemented
5#13067310C212yesmaximal, complemented
6#13067285C211yesmaximal, characteristic, complemented
7#13067277C212yesmaximal, complemented
8#13067273C211yesmaximal, characteristic, complemented
9#13067264C212yesmaximal, complemented
10C2×#10622123C211yesmaximal, characteristic, complemented
11C11×#1550C211yesmaximal, characteristic, complemented
12C11×#533C2211yescharacteristic
13#10623256C2212yes—
14#10623256C2212yes—
15#10623229—22no—
16#10623161—22no—
17#10623161C414yes—
18#10623116—21no—
19#10623116C412yes—
20#10623108—21no—
21#10623108C412yes—
22#10623056—21no—
23#10623052—21no—
24C2×#66927C2211yescharacteristic
25C4×#4339C2211yescharacteristic
26C11×#423C2211yescharacteristic
27C2×C11×C4⋊C8C2211yescharacteristic
28#10622742—21no—
29#10622735—21no—
30C8×C22⋊D11—22no—
31#10622538C2211yescharacteristic
32C2×C4⋊(C11⋊C8)C2211yescharacteristic
33#10622453—22no—
34#10622448C2212yescomplemented
35#10622447—21no—
36#10622446C2212yescomplemented
37#10622446C2212yescomplemented
38D11×C4⋊C8C2212yescomplemented
39#10622443—21no—
40C11×#333C2212yescomplemented
41C11×#332C2212yescomplemented
42#10622185C2211yescharacteristic, complemented
43#10622185C2211yescharacteristic, complemented
44#10622184C2211yescharacteristic, complemented
45#10622184C2211yescharacteristic, complemented
46#10622123C2212yes—
47#10622123C2212yes—
48#10622123C2212yes—
49#10622123C2212yes—
50C2×#4343—22no—
51C2×#4343C2×C414yes—
52C2×#4339D411yescharacteristic
53C22×D44—21no—
54C22×D44—21no—
55C22×D44C2×C412yes—
56C2×C11×M16—21no—
57C22×C8×C11—21no—
58C11×C4⋊Q8C2311yescharacteristic
59C11×C4⋊Q8C2311yescharacteristic
60C11×#125—21no—
61C11×C22⋊Q8—21no—
62C11×C22⋊Q8C2×C412yes—
63C4×Q8×C11—21no—
64C4×Q8×C11C2×C412yes—
65C11×#117—21no—
66C2×C42×C11C2311yescharacteristic
67#67000—22no—
68#67000C2×C414yes—
69C4×C22⋊D11C2×C412yes—
70C4×C22⋊D11D412yes—
71#66979D411yescharacteristic
72C22×C11⋊C8—21no—
73C2×C8×D11—22no—
74#66948—22no—
75#66948—22no—
76#66948—22no—
77#66948—24no—
78#66948—24no—
79#66948C2×C414yes—
80#66947—24no—
81#66947—24no—
82#66946—22no—
83#66946—22no—
84#66946—22no—
85#66946C2×C414yes—
86#66935—24no—
87C22⋊C4×D11—24no—
88#66928—22no—
89#66927—22no—
90#66927—21no—
91#66927—21no—
92#66927C2×C412yes—
93#66927C2312yes—
94C4×D44—22no—
95C4×D44—22no—
96C4×D44C2×C411yescharacteristic
97C4×D44D411yescharacteristic
98#66925D412yes—
99C42×D11C2312yes—
100C4×Dic22C2×C411yescharacteristic
101C4×Dic22D411yescharacteristic
102C11×C4⋊C8—21no—
103C11×C4⋊C8—21no—
104C11×C4⋊C8C2312yes—
105C11×C4⋊C8C2312yes—
106C22⋊(C11⋊C8)—21no—
107(C2×D11)⋊C8—22no—
108(C2×D11)⋊C8—22no—
109(C2×D11)⋊C8—22no—
110#66879—22no—
111Dic11⋊C8—22no—
112C8×Dic11—22no—
113C8×Dic11—22no—
114C4⋊(C11⋊C8)—21no—
115C4⋊(C11⋊C8)C2311yescharacteristic
116C4⋊(C11⋊C8)C2311yescharacteristic
117C4⋊(C11⋊C8)C2311yescharacteristic
118C4⋊(C11⋊C8)C2311yescharacteristic
119C4×C11⋊C8—21no—
120#17724—111nomaximal, Sylow
121C23×D11—22no—
122C2×Q8×C11—21no—
123C2×Q8×C11C22×C412yes—
124C22×C4×C11C22×C411yescharacteristic
125C22×C4×C11C2×D411yescharacteristic
126C22×C4×C11C2×D411yescharacteristic
127C2×C22⋊D11C22⋊C412yes—
128#4343—82no—
129#4343—82no—
130#4343—84no—
131#4339—22no—
132#4339—22no—
133C2×D44—24no—
134C2×D44—24no—
135C2×D44—22no—
136C2×D44—22no—
137C2×D44—22no—
138C2×D44—22no—
139C2×D44—22no—
140C2×D44—42no—
141C2×D44—42no—
142C2×D44—81no—
143C2×D44—81no—
144C2×D44—82no—
145C2×D44C22⋊C411yescharacteristic
146C2×D44C22×C414yes—
147C2×C4×D11—24no—
148C2×C4×D11—24no—
149C2×C4×D11C22×C412yes—
150C2×C4×D11C2×D412yes—
151C2×C4×D11C2×D412yes—
152C2×Dic22C22⋊C411yescharacteristic
153C11×M16—42no—
154C2×C8×C11—22no—
155C2×C8×C11—22no—
156C2×C8×C11—81no—
157C11×C4⋊C4—22no—
158C11×C4⋊C4—22no—
159C11×C4⋊C4—21no—
160C11×C4⋊C4—21no—
161C11×C4⋊C4—21no—
162C11×C4⋊C4C22×C412yes—
163C11×C22⋊C4—22no—
164C42×C11—22no—
165C42×C11C22×C411yescharacteristic
166C42×C11C2×D411yescharacteristic
167C42×C11C2×D411yescharacteristic
168C42×C11C2411yescharacteristic
169C22⋊Dic11C22⋊C412yes—
170(C2×D11)⋊C4—24no—
171(C2×D11)⋊C4—24no—
172(C2×D11)⋊C4—24no—
173(C2×D11)⋊C4—24no—
174(C2×D11)⋊C4C22⋊C412yes—
175(C2×D11)⋊C4C22⋊C412yes—
176C4⋊Dic11C22⋊C411yescharacteristic
177C4⋊Dic11C22⋊C411yescharacteristic
178Dic11⋊C4C22⋊C412yes—
179Dic11⋊C4C22⋊C412yes—
180C4×Dic11C22×C412yes—
181C4×Dic11C2×D412yes—
182C4×Dic11C2×D412yes—
183C2×C11⋊C8—21no—
184C2×C11⋊C8—21no—
185C2×C11⋊C8—21no—
186C2×C11⋊C8—21no—
187C2×C11⋊C8—42no—
188C8×D11—82no—
189#3508—111no—
190#2988—111no—
191#2925—111no—
192#1553—112no—
193#1551—112no—
194#1550D1111yescharacteristic, complemented
195#1545—111no—
196#1543—112no—
197#1542—111no—
198#1540—112no—
199C2×#331—111no—
200C23×C11C2×C22⋊C411yescharacteristic
201C22×D11—24no—
202C22×D11—44no—
203C22×D11—82no—
204C22×D11—82no—
205C22×D11C2×C22⋊C412yes—
206Q8×C11—42no—
207Q8×C11—41no—
208Q8×C11—41no—
209C2×C4×C11—21no—
210C2×C4×C11—21no—
211C2×C4×C11—22no—
212C2×C4×C11—22no—
213C2×C4×C11—41no—
214C2×C4×C11C2×C22⋊C411yescharacteristic
215C2×C4×C11C2×C22⋊C411yescharacteristic
216C2×C4×C11C2×C22⋊C411yescharacteristic
217C2×C4×C11#13512yes—
218C2×C4×C11#13512yes—
219C2×C4×C11C23×C411yescharacteristic
220C2×C4×C11C22×D411yescharacteristic
221C2×C4×C11C22×D411yescharacteristic
222C22⋊D11—24no—
223C2×Dic11C2×C22⋊C412yes—
224C2×Dic11C2×C22⋊C412yes—
225C2×Dic11C2×C22⋊C412yes—
226D44—22no—
227D44—44no—
228D44—42no—
229D44—42no—
230D44—42no—
231D44—42no—
232D44—44no—
233D44—82no—
234D44—82no—
235D44—84no—
236D44—84no—
237C4×D11—22no—
238C4×D11—22no—
239C4×D11—22no—
240C4×D11—22no—
241C4×D11—42no—
242C4×D11—84no—
243C4×D11—84no—
244Dic22—22no—
245C8×C11—42no—
246C8×C11—42no—
247C11⋊C8—41no—
248C11⋊C8—41no—
249C11⋊C8—41no—
250C11⋊C8—41no—
251#559—112no—
252#559—221no—
253#550—112no—
254#550—221no—
255#546—114no—
256#546—222no—
257#540—222no—
258#535—221no—
259#533C2×D1111yescharacteristic
260#532—112no—
261#532—112no—
262C2×#127—111no—
263#518—221no—
264C4×#41—111no—
265C8×Q8—221no—
266C8×D4—221no—
267C8×D4—222no—
268#433—222no—
269#432—112no—
270#431—111no—
271#431—112no—
272#431—112no—
273#423C2×D1111yescharacteristic
274C2×C4⋊C8—111no—
275C2×C4⋊C8—112no—
276C2×C4⋊C8C2×D1111yescharacteristic
277#408—221no—
278#405—221no—
279#333—111no—
280#333—111no—
281#333C2×D1112yescomplemented
282#332—111no—
283#332—111no—
284#332C2×D1112yescomplemented
285#331—112no—
286#331—112no—
287#331—112no—
288#331—112no—
289C22×C11—21no—
290C22×C11—21no—
291C22×C11#41612yes—
292C22×C11C22×C22⋊C411yescharacteristic
293C2×D11—22no—
294C2×D11—22no—
295C2×D11—22no—
296C2×D11—44no—
297C2×D11—44no—
298C2×D11—44no—
299C2×D11—164no—
300C4×C11—21no—
301C4×C11—21no—
302C4×C11—21no—
303C4×C11—42no—
304C4×C11—42no—
305C4×C11#41612yes—
306C4×C11C2×#13511yescharacteristic
307C4×C11C2×#13511yescharacteristic
308C4×C11#57611yescharacteristic
309C4×C11#57711yescharacteristic
310Dic11—22no—
311Dic11—22no—
312Dic11—22no—
313C2×#41—111no—
314C2×#41—114no—
315C2×#41—222no—
316C22×D4—112no—
317C22×D4—221no—
318C22×D4—221no—
319C2×M16—21no—
320C22×C8—21no—
321C22×C8—222no—
322C22×C8—221no—
323C4⋊Q8C22×D1111yescharacteristic
324C4⋊Q8C22×D1111yescharacteristic
325#127—112no—
326#127—112no—
327#127—222no—
328#127—221no—
329#127—221no—
330#125—21no—
331#124—114no—
332#124—222no—
333#124—222no—
334#123—224no—
335#123—224no—
336C22⋊Q8—21no—
337C22⋊Q8C4×D1112yes—
338#121—114no—
339#121—224no—
340#121—224no—
341#121—222no—
342#121—222no—
343#121—222no—
344#120—224no—
345C4×Q8—21no—
346C4×Q8—111no—
347C4×Q8—111no—
348C4×Q8C4×D1112yes—
349C4×D4—112no—
350C4×D4—112no—
351C4×D4—114no—
352C4×D4—111no—
353C4×D4—111no—
354C4×D4—222no—
355C4×D4—222no—
356C4×D4—222no—
357C4×D4—222no—
358C4×D4—222no—
359#117—21no—
360#117—111no—
361#117—112no—
362C2×C22⋊C4—224no—
363C2×C42—112no—
364C2×C42C22×D1111yescharacteristic
365C4⋊C8—21no—
366C4⋊C8—21no—
367C4⋊C8—111no—
368C4⋊C8—111no—
369C4⋊C8—111no—
370C4⋊C8—111no—
371C4⋊C8—222no—
372C4⋊C8—221no—
373C4⋊C8C22×D1112yes—
374C4⋊C8C22×D1112yes—
375C22⋊C8—222no—
376C22⋊C8—222no—
377C22⋊C8—222no—
378C22⋊C8—221no—
379#97—222no—
380C4×C8—222no—
381C4×C8—222no—
382C4×C8—221no—
383C2×C11—22no—
384C2×C11#288811yescharacteristic
385C2×C11C2×#41611yescharacteristic
386C2×C11#289711yescharacteristic
387D11—42no—
388D11—84no—
389C24—222no—
390#41—222no—
391#41—222no—
392#41—882no—
393#41—882no—
394#41—884no—
395C2×Q8—21no—
396C2×Q8—111no—
397C2×Q8C2×C4×D1112yes—
398C2×D4—112no—
399C2×D4—111no—
400C2×D4—114no—
401C2×D4—224no—
402C2×D4—224no—
403C2×D4—222no—
404C2×D4—222no—
405C2×D4—222no—
406C2×D4—222no—
407C2×D4—222no—
408C2×D4—442no—
409C2×D4—442no—
410C2×D4—881no—
411C2×D4—881no—
412C2×D4—882no—
413C22×C4—112no—
414C22×C4—112no—
415C22×C4—112no—
416C22×C4—224no—
417C22×C4—224no—
418C22×C4C2×C4×D1111yescharacteristic
419C22×C4D4×D1111yescharacteristic
420C22×C4D4×D1111yescharacteristic
421M16—42no—
422C2×C8—22no—
423C2×C8—22no—
424C2×C8—81no—
425C2×C8—221no—
426C2×C8—221no—
427C2×C8—221no—
428C2×C8—221no—
429C2×C8—442no—
430C2×C8—882no—
431C4⋊C4—22no—
432C4⋊C4—22no—
433C4⋊C4—21no—
434C4⋊C4—21no—
435C4⋊C4—21no—
436C4⋊C4—111no—
437C4⋊C4—111no—
438C4⋊C4—112no—
439C4⋊C4—112no—
440C4⋊C4C2×C4×D1112yes—
441C22⋊C4—22no—
442C22⋊C4—112no—
443C22⋊C4—112no—
444C22⋊C4—112no—
445C22⋊C4—224no—
446C22⋊C4—224no—
447C22⋊C4—224no—
448C22⋊C4—224no—
449C42—22no—
450C42—112no—
451C42—112no—
452C42—112no—
453C42C2×C4×D1111yescharacteristic
454C42D4×D1111yescharacteristic
455C42D4×D1111yescharacteristic
456C42C23×D1111yescharacteristic
457C11#1772411yescharacteristic, complemented, Sylow
458C23—112no—
459C23—224no—
460C23—444no—
461C23—882no—
462C23—882no—
463C23C22⋊C4×D1111yescharacteristic
464Q8—42no—
465Q8—41no—
466Q8—41no—
467Q8—222no—
468D4—224no—
469D4—222no—
470D4—444no—
471D4—442no—
472D4—442no—
473D4—442no—
474D4—442no—
475D4—444no—
476D4—882no—
477D4—882no—
478D4—884no—
479D4—884no—
480C2×C4—21no—
481C2×C4—21no—
482C2×C4—22no—
483C2×C4—22no—
484C2×C4—41no—
485C2×C4—112no—
486C2×C4—112no—
487C2×C4—112no—
488C2×C4—222no—
489C2×C4—222no—
490C2×C4—222no—
491C2×C4—222no—
492C2×C4—442no—
493C2×C4—884no—
494C2×C4—884no—
495C2×C4C22⋊C4×D1111yescharacteristic
496C2×C4C22⋊C4×D1111yescharacteristic
497C2×C4C22⋊C4×D1111yescharacteristic
498C2×C4#6696912yes—
499C2×C4#6697212yes—
500C2×C4C22×C4×D1111yescharacteristic
501C2×C4C2×D4×D1111yescharacteristic
502C2×C4C2×D4×D1111yescharacteristic
503C8—42no—
504C8—42no—
505C8—441no—
506C8—441no—
507C8—441no—
508C8—441no—
509C22—21no—
510C22—21no—
511C22—222no—
512C22—222no—
513C22—222no—
514C22—444no—
515C22—444no—
516C22—444no—
517C22—1764no—
518C22#1062241712yes—
519C22C2×C22⋊C4×D1111yescharacteristic
520C4—21no—
521C4—21no—
522C4—21no—
523C4—42no—
524C4—42no—
525C4—222no—
526C4—222no—
527C4—222no—
528C4#1062241712yes—
529C4C2×#6696911yescharacteristic
530C4C2×#6697211yescharacteristic
531C4#1062330511yescharacteristic
532C4#1062330911yescharacteristic
533C2—22no—
534C2—442no—
535C2—884no—
536C2#1307709311yescharacteristic
537C2C2×#1062241711yescharacteristic
538C2#1307714011yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×#1550C2
socleC22×C11C22×C22⋊C4
prime radical#13082493C2
cosocleC42×C11C24
hypercenter#1550D11
hypocenterC11#17724
LCSG ▷ C2×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1550

Complements

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

NH ≅ G/Ntype
2. #13077725C2semidirect
3. #13077284C2semidirect
4. #13067320C2semidirect
5. #13067310C2semidirect
6. #13067285C2semidirect
7. #13067277C2semidirect
8. #13067273C2semidirect
9. #13067264C2semidirect
10. C2×#10622123C2semidirect
11. C11×#1550C2semidirect
34. #10622448C22semidirect
36. #10622446C22semidirect
37. #10622446C22semidirect
38. D11×C4⋊C8C22semidirect
40. C11×#333C22semidirect
41. C11×#332C22semidirect
42. #10622185C22semidirect
43. #10622185C22semidirect
44. #10622184C22semidirect
45. #10622184C22semidirect
194. #1550D11semidirect
281. #333C2×D11semidirect
284. #332C2×D11semidirect
457. C11#17724semidirect

Maximal subgroups

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

subgroupindex
#130824932
#130777252
#130772842
#130673202
#130673102
#130672852
#130672772
#130672732
#130672642
C2×#106221232
C11×#15502
#1772411