Finite Group Databasebeta

← #15618343

Subgroups — #15618343

Order 2816.

1878 conjugacy classes of subgroups.

The subgroup lattice has 512 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082005C211yesmaximal, characteristic
2#13077615C218yesmaximal, complemented
3#13077604C218yesmaximal, complemented
4#13077553C211yesmaximal, characteristic, complemented
5#13077550C211yesmaximal, characteristic, complemented
6#13077334C211yesmaximal, characteristic, complemented
7#13077317C212yesmaximal, complemented
8#13077313C212yesmaximal, complemented
9#13077256C212yesmaximal, complemented
10#13077253C211yesmaximal, characteristic, complemented
11#13077042C212yesmaximal, complemented
12C2×#10622302C211yesmaximal, characteristic, complemented
13C11×#2931C211yesmaximal, characteristic, complemented
14C2×C11×#131C2212yes—
15C11×#532C2211yescharacteristic
16#10623359C2212yes—
17#41×Dic11C2212yes—
18C2×#67001C2212yes—
19C22×#4313C2211yescharacteristic
20C22×C8×D11C2211yescharacteristic
21#10623262C412yes—
22#10623250C412yes—
23#10623213C414yes—
24#10623148C414yes—
25#10623133C414yes—
26#10623069C2218yes—
27C2×#66925C2211yescharacteristic
28#10623001C2211yescharacteristic
29C11×#436C2214yescomplemented
30C8×D4×C11C2214yescomplemented
31C11×#423C2211yescharacteristic
32C11×#408C2212yes—
33C2×C4×C8×C11C2211yescharacteristic
34#10622847C2212yes—
35#10622741C2218yes—
36#10622739C2212yes—
37#10622735C2212yes—
38#10622735C2214yescomplemented
39#10622732C2212yes—
40M16×Dic11C2212yes—
41M16×Dic11C2214yescomplemented
42#10622724C2218yes—
43#10622715C2212yes—
44#10622714C2212yes—
45#10622714C2214yescomplemented
46C2×#66879C2211yescharacteristic
47C2×#66879C2214yescomplemented
48C2×C8×Dic11C2211yescharacteristic
49#10622624C2218yescomplemented
50#10622537C2211yescharacteristic
51C2×#66867C2211yescharacteristic
52#10622453C2218yes—
53#10622441C2218yescomplemented
54#10622341C2218yes—
55(C22⋊D11)⋊C8C2218yes—
56#10622333C2218yescomplemented
57#10622331C2218yescomplemented
58#10622302C2214yes—
59#10622302C2214yes—
60#10622292C2214yescomplemented
61C8×Dic22C2214yescomplemented
62C2×C11×#41C2312yes—
63C22×C4×D11C2311yescharacteristic
64C11×#131—28no—
65C2×C11×M16C2312yes—
66C2×C11×M16C2314yes—
67C22×C8×C11C2314yes—
68C22×C8×C11C2311yescharacteristic
69C22×C8×C11C2311yescharacteristic
70C11×C4⋊Q8C2×C411yescharacteristic
71C11×#127C2×C411yescharacteristic
72C11×#124C2×C412yes—
73C11×#121C2×C414yes—
74C4×D4×C11C2314yes—
75C2×C42×C11C2311yescharacteristic
76#67001—28no—
77#66999C2×C414yes—
78Q8×Dic11C2×C414yes—
79#66992C2×C418yes—
80#66991C2×C414yes—
81#66990C2×C414yes—
82#66988C2×C418yes—
83#66988C2×C414yes—
84D4×Dic11C2×C414yes—
85D4×Dic11C2×C418yes—
86C4×C22⋊D11C2318yes—
87C2×(C2×D11)⋊C4C2×C412yes—
88#66979C2312yes—
89#66979C2314yes—
90#66977C2×C414yes—
91C2×Dic11⋊C4C2×C412yes—
92C2×C4×Dic11C2311yescharacteristic
93C2×C4×Dic11C2314yes—
94C2×#4318C2312yes—
95C2×#4318C2314yes—
96C22×C11⋊C8C2311yescharacteristic
97C22×C11⋊C8C2314yes—
98C22×C11⋊C8C2311yescharacteristic
99C2×#4313—24no—
100C2×#4313C2312yes—
101C2×#4313C2312yes—
102C2×C8×D11—24no—
103C2×C8×D11C2314yes—
104#66951C2×C418yes—
105#66942C2×C418yes—
106#66939C2×C418yes—
107#66938C2×C418yes—
108#66932C2×C418yes—
109#66931C2×C418yes—
110#66925C2×C412yes—
111#66925C2×C412yes—
112#66925C2314yes—
113#66923C2×C412yes—
114#66922C2×C412yes—
115C4×Dic22C2314yes—
116C11×C4⋊C8C2314yes—
117C11×C22⋊C8C2318yes—
118C4×C8×C11C2312yes—
119C4×C8×C11C2312yes—
120C22⋊(C11⋊C8)C2318yes—
121(C2×D11)⋊C8C2318yes—
122#66879C2314yes—
123#66879C2314yes—
124#66879C2312yes—
125#66879C2314yes—
126#66879C2312yes—
127Dic11⋊C8C2318yes—
128Dic11⋊C8C2318yes—
129C8×Dic11C2314yes—
130C8×Dic11C2314yes—
131C8×Dic11C2314yes—
132C8×Dic11C2314yes—
133C4⋊(C11⋊C8)C2314yes—
134#66867C2314yes—
135#60209—111nomaximal, Sylow
136C23×D11C22×C411yescharacteristic
137C11×#41—24no—
138C11×#41—24no—
139C2×Q8×C11C22×C412yes—
140C2×D4×C11C22×C414yes—
141C2×D4×C11C22×C412yes—
142C2×D4×C11C22×C414yes—
143C22×C4×C11C22×C412yes—
144C22×C4×C11C2414yes—
145C22×C4×C11C2411yescharacteristic
146C2×C22⋊D11C22×C418yes—
147C22×Dic11C22×C411yescharacteristic
148C22×Dic11C22×C418yes—
149C22×Dic11C22×C412yes—
150C2×C4×D11—22no—
151C2×C4×D11—22no—
152C2×C4×D11C22×C412yes—
153C2×C4×D11C2412yes—
154C2×Dic22C22×C414yes—
155C11×M16—28no—
156C11×M16—24no—
157C2×C8×C11—28no—
158C2×C8×C11—22no—
159C2×C8×C11#4114yes—
160C2×C8×C11C2412yes—
161C2×C8×C11C2414yes—
162C2×C8×C11C2411yescharacteristic
163C2×C8×C11C2411yescharacteristic
164C11×C4⋊C4C22×C414yes—
165C11×C22⋊C4C22×C418yes—
166C42×C11C22×C411yescharacteristic
167C42×C11C22×C411yescharacteristic
168C42×C11C2412yes—
169C22⋊Dic11C22×C418yes—
170C22⋊Dic11C22×C418yes—
171C22⋊Dic11C22×C414yes—
172(C2×D11)⋊C4C22×C414yes—
173(C2×D11)⋊C4C22×C414yes—
174(C2×D11)⋊C4C22×C418yes—
175C4⋊Dic11C22×C414yes—
176C4⋊Dic11C22×C414yes—
177C4⋊Dic11C22×C418yes—
178Dic11⋊C4C22×C418yes—
179Dic11⋊C4C22×C414yes—
180Dic11⋊C4C22×C414yes—
181Dic11⋊C4C22×C418yes—
182C4×Dic11C22×C412yes—
183C4×Dic11C22×C418yes—
184C4×Dic11C2412yes—
185C4×Dic11C2414yes—
186#4318—28no—
187#4318—24no—
188C2×C11⋊C8—28no—
189C2×C11⋊C8—22no—
190C2×C11⋊C8#4114yes—
191C2×C11⋊C8C2412yes—
192C2×C11⋊C8C2414yes—
193C2×C11⋊C8C2412yes—
194#4313—24no—
195#4313—24no—
196C8×D11—28no—
197#3455—111no—
198#2969—118no—
199#2968—118no—
200#2961—111no—
201#2960—111no—
202#2932—111no—
203#2931D1111yescharacteristic, complemented
204#2930—112no—
205#2929—112no—
206#2922—112no—
207#2921—111no—
208#2875—112no—
209C2×#405—111no—
210C23×C11C23×C414yes—
211C23×C11C23×C411yescharacteristic
212C22×D11—22no—
213C22×D11—42no—
214C22×D11C23×C412yes—
215Q8×C11—24no—
216D4×C11—28no—
217D4×C11—24no—
218D4×C11—44no—
219C2×C4×C11—24no—
220C2×C4×C11—24no—
221C2×C4×C11—42no—
222C2×C4×C11C23×C414yes—
223C2×C4×C11C23×C412yes—
224C2×C4×C11C23×C412yes—
225C2×C4×C11C23×C411yescharacteristic
226C2×C4×C11C2×#4112yes—
227C2×C4×C11C2×#4112yes—
228C2×C4×C11C2511yescharacteristic
229C22⋊D11—48no—
230C2×Dic11—22no—
231C2×Dic11—48no—
232C2×Dic11—42no—
233C2×Dic11C23×C414yes—
234C2×Dic11C23×C418yes—
235C2×Dic11C23×C412yes—
236C4×D11—24no—
237C4×D11—22no—
238C4×D11—22no—
239Dic22—44no—
240C8×C11—22no—
241C8×C11—24no—
242C8×C11C2×#4112yes—
243C8×C11C2×#4112yes—
244C11⋊C8—22no—
245C11⋊C8—24no—
246C11⋊C8C2×#4114yes—
247C2×#131—112no—
248C2×#131C2×D1112yes—
249C22×M16—111no—
250C23×C8—111no—
251#542—114no—
252#541—112no—
253#540—112no—
254#539—114no—
255#538—114no—
256#533—111no—
257#532C2×D1111yescharacteristic
258#529—118no—
259#525—112no—
260C4×#41—112no—
261C2×#117—111no—
262#446—118no—
263#446—114no—
264C8×Q8—114no—
265#436—118no—
266#436C2×D1114yescomplemented
267#435—118no—
268#435—118no—
269#435—118no—
270C8×D4—118no—
271C8×D4C2×D1114yescomplemented
272#433—118no—
273#433—118no—
274#431—118no—
275#424—112no—
276#424—112no—
277#423—111no—
278#423C2×D1111yescharacteristic
279#408—112no—
280#408C2×D1112yes—
281#407—112no—
282#405—112no—
283#405—114no—
284#405—112no—
285#405—114no—
286#405—114no—
287#405—114no—
288C4×M16—112no—
289C4×M16—114no—
290C2×#97—111no—
291C2×#97—114no—
292C2×#97—111no—
293C2×C4×C8—111no—
294C2×C4×C8C2×D1111yescharacteristic
295C22×C11—22no—
296C22×C11—24no—
297C22×C11—28no—
298C22×C11C4×#4112yes—
299C22×C11C24×C411yescharacteristic
300C2×D11—22no—
301C2×D11—24no—
302C2×D11—44no—
303C4×C11—24no—
304C4×C11—22no—
305C4×C11—22no—
306C4×C11C4×#4112yes—
307C4×C11C22×#4111yescharacteristic
308C4×C11C22×#4111yescharacteristic
309Dic11—22no—
310Dic11—28no—
311Dic11—24no—
312C2×#41C22×D1112yes—
313C23×C4—111no—
314#131—28no—
315#131—228no—
316C2×M16—112no—
317C2×M16—114no—
318C2×M16—112no—
319C2×M16—112no—
320C2×M16—224no—
321C2×M16C22×D1112yes—
322C2×M16C22×D1114yes—
323C22×C8—111no—
324C22×C8—111no—
325C22×C8—114no—
326C22×C8—114no—
327C22×C8—224no—
328C22×C8C22×D1111yescharacteristic
329C22×C8C22×D1114yes—
330C22×C8C22×D1111yescharacteristic
331C4⋊Q8—112no—
332C4⋊Q8C4×D1111yescharacteristic
333#127C4×D1111yescharacteristic
334#126—118no—
335#126—118no—
336#125—118no—
337#125—112no—
338#124—118no—
339#124C4×D1112yes—
340#123—114no—
341#123—118no—
342#123—118no—
343C22⋊Q8—114no—
344C22⋊Q8—114no—
345C22⋊Q8—118no—
346#121—114no—
347#121—118no—
348#121C4×D1114yes—
349#120—114no—
350C4×Q8—114no—
351C4×Q8—114no—
352C4×D4—118no—
353C4×D4—114no—
354C4×D4—118no—
355C4×D4C22×D1114yes—
356#117—112no—
357#117—114no—
358#117—112no—
359#117—112no—
360#117—114no—
361C2×C4⋊C4—112no—
362C2×C22⋊C4—112no—
363C2×C42—111no—
364C2×C42—114no—
365C2×C42C22×D1111yescharacteristic
366C4⋊C8—118no—
367C4⋊C8—118no—
368C4⋊C8—114no—
369C4⋊C8C22×D1114yes—
370C22⋊C8—118no—
371C22⋊C8—118no—
372C22⋊C8C22×D1118yes—
373#97—112no—
374#97—112no—
375#97—114no—
376#97—114no—
377#97—114no—
378#97—114no—
379C4×C8—114no—
380C4×C8—114no—
381C4×C8—114no—
382C4×C8—114no—
383C4×C8C22×D1112yes—
384C4×C8C22×D1112yes—
385C2×C11—22no—
386C2×C11—44no—
387C2×C11C2×C4×#4111yescharacteristic
388C2×C11#357312yes—
389D11—42no—
390C24—111no—
391#41—24no—
392#41—24no—
393C2×Q8—114no—
394C2×Q8C2×C4×D1112yes—
395C2×D4—118no—
396C2×D4C2×C4×D1114yes—
397C2×D4C2×C4×D1112yes—
398C2×D4C2×C4×D1114yes—
399C22×C4—111no—
400C22×C4—112no—
401C22×C4—118no—
402C22×C4—112no—
403C22×C4—112no—
404C22×C4—222no—
405C22×C4—222no—
406C22×C4C2×C4×D1112yes—
407C22×C4C23×D1114yes—
408C22×C4C23×D1111yescharacteristic
409M16—24no—
410M16—28no—
411M16—228no—
412M16—224no—
413M16—224no—
414M16—224no—
415C2×C8—22no—
416C2×C8—28no—
417C2×C8—114no—
418C2×C8—112no—
419C2×C8—112no—
420C2×C8—114no—
421C2×C8—228no—
422C2×C8—228no—
423C2×C8—222no—
424C2×C8#434114yes—
425C2×C8C23×D1112yes—
426C2×C8C23×D1114yes—
427C2×C8C23×D1111yescharacteristic
428C2×C8C23×D1111yescharacteristic
429C4⋊C4—114no—
430C4⋊C4—114no—
431C4⋊C4—114no—
432C4⋊C4—118no—
433C4⋊C4—118no—
434C4⋊C4—118no—
435C4⋊C4—114no—
436C4⋊C4C2×C4×D1114yes—
437C22⋊C4—114no—
438C22⋊C4—118no—
439C22⋊C4—118no—
440C22⋊C4—114no—
441C22⋊C4—114no—
442C22⋊C4—118no—
443C22⋊C4C2×C4×D1118yes—
444C42—112no—
445C42—118no—
446C42—112no—
447C42—114no—
448C42C2×C4×D1111yescharacteristic
449C42C2×C4×D1111yescharacteristic
450C42C23×D1112yes—
451C11#6020911yescharacteristic, complemented, Sylow
452C23—112no—
453C23—222no—
454C23—442no—
455C23C22×C4×D1114yes—
456C23C22×C4×D1111yescharacteristic
457Q8—24no—
458Q8—444no—
459D4—28no—
460D4—24no—
461D4—44no—
462D4—448no—
463C2×C4—24no—
464C2×C4—24no—
465C2×C4—42no—
466C2×C4—114no—
467C2×C4—118no—
468C2×C4—112no—
469C2×C4—222no—
470C2×C4—224no—
471C2×C4—222no—
472C2×C4—222no—
473C2×C4—442no—
474C2×C4—448no—
475C2×C4C22×C4×D1114yes—
476C2×C4C22×C4×D1112yes—
477C2×C4C22×C4×D1112yes—
478C2×C4C22×C4×D1111yescharacteristic
479C2×C4C2×#434112yes—
480C2×C4#41×D1112yes—
481C2×C4C24×D1111yescharacteristic
482C8—24no—
483C8—22no—
484C8—114no—
485C8—222no—
486C8—224no—
487C8C2×#434112yes—
488C8C2×#434112yes—
489C22—22no—
490C22—28no—
491C22—24no—
492C22—224no—
493C22—222no—
494C22—444no—
495C22C4×#434112yes—
496C22C23×C4×D1111yescharacteristic
497C4—22no—
498C4—22no—
499C4—24no—
500C4—224no—
501C4—228no—
502C4—222no—
503C4C4×#434112yes—
504C4C22×#434111yescharacteristic
505C4C2×#41×D1111yescharacteristic
506C2—22no—
507C2—44no—
508C2—442no—
509C2C2×C4×#434111yescharacteristic
510C2#1308332712yes—
subgroupG/H
center, FrattiniC2×C4C24×D11
commutator, socleC22×C11C24×C4
FittingC11×#2931C2
prime radical#13082005C2
cosocleC2×C4×C11C25
hypercenter#2931D11
hypocenterC11#60209
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ #2931

Complements

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

NH ≅ G/Ntype
2. #13077615C2semidirect
3. #13077604C2semidirect
4. #13077553C2semidirect
5. #13077550C2semidirect
6. #13077334C2semidirect
7. #13077317C2semidirect
8. #13077313C2semidirect
9. #13077256C2semidirect
10. #13077253C2semidirect
11. #13077042C2semidirect
12. C2×#10622302C2semidirect
13. C11×#2931C2semidirect
29. C11×#436C22semidirect
30. C8×D4×C11C22semidirect
38. #10622735C22semidirect
41. M16×Dic11C22semidirect
45. #10622714C22semidirect
47. C2×#66879C22semidirect
49. #10622624C22semidirect
53. #10622441C22semidirect
56. #10622333C22semidirect
57. #10622331C22semidirect
60. #10622292C22semidirect
61. C8×Dic22C22semidirect
203. #2931D11semidirect
266. #436C2×D11semidirect
271. C8×D4C2×D11semidirect
451. C11#60209semidirect

Maximal subgroups

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

subgroupindex
#130820052
#130776152
#130776042
#130775532
#130775502
#130773342
#130773172
#130773132
#130772562
#130772532
#130770422
C2×#106223022
C11×#29312
#6020911