Finite Group Databasebeta

← #15622250

Subgroups — #15622250

Order 2816.

2218 conjugacy classes of subgroups.

The subgroup lattice has 546 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082006C211yesmaximal, characteristic, complemented
2C2×#10623052C211yesmaximal, characteristic, complemented
3#13078869C214yesmaximal, complemented
4#13078860C214yesmaximal, complemented
5#13078802C218yesmaximal, complemented
6#13078549C212yesmaximal, complemented
7#13078415C212yesmaximal, complemented
8#13078082C212yesmaximal, complemented
9#13077846C212yesmaximal, complemented
10C4×#66961C214yesmaximal, complemented
11C11×#2921C211yesmaximal, characteristic, complemented
12C23×D44C2211yescharacteristic
13C2×C11×#117C2211yescharacteristic
14#10623322C2212yes—
15C2×#66979C2211yescharacteristic
16C2×#66961C2214yes—
17#10623066C2212yescomplemented
18#10623065C2214yescomplemented
19#10623059—24no—
20#10623052—24no—
21#10623052C2214yes—
22#10623052C2214yes—
23#10623049C2212yescomplemented
24#10623046—22no—
25C2×#66946—22no—
26#10623025—22no—
27C2×C22⋊C4×D11—22no—
28#10623008C2211yescharacteristic, complemented
29C4×#4339C2212yescomplemented
30C2×C4×D44C2212yes—
31C2×C4×D44C2212yes—
32#10623001C2211yescharacteristic, complemented
33C11×#433C2214yescomplemented
34C11×#433C2214yescomplemented
35C11×#423C2212yescomplemented
36C11×#407C2212yes—
37C4×C11×M16C2212yescomplemented
38#10622746C2214yescomplemented
39#10622744C2214yes—
40#10622734C2214yescomplemented
41#10622460C2218yescomplemented
42#10622459C2214yescomplemented
43#10622457C2218yescomplemented
44#10622456C2214yescomplemented
45#10622455C2214yescomplemented
46#10622454C2214yescomplemented
47#10622350C2218yescomplemented
48#10622345C2218yes—
49#10622344C2218yes—
50#10622336C2218yescomplemented
51#10622324C2218yescomplemented
52#10622323C2218yescomplemented
53C4×D88C2218yescomplemented
54C4×#4314C2218yescomplemented
55C24×D11—21no—
56C23×C4×C11C2311yescharacteristic
57C2×#4339C2312yes—
58C22×D44—21no—
59C22×D44—22no—
60C22×D44—28no—
61C22×D44C2314yes—
62C22×D44C2312yes—
63C22×C4×D11—22no—
64C22×C4×D11—22no—
65C2×C11×M16C2314yes—
66C11×#117D414yes—
67C11×#117C2312yes—
68C11×#117C2312yes—
69C2×C11×C4⋊C4D412yes—
70C2×C11×C22⋊C4D412yes—
71C2×C42×C11C2311yescharacteristic
72C2×C42×C11C2311yescharacteristic
73#67006—22no—
74C2×C22⋊Dic11—21no—
75#66983—22no—
76#66983C2314yes—
77#66982—22no—
78C4×C22⋊D11—24no—
79C4×C22⋊D11—24no—
80C2×(C2×D11)⋊C4—22no—
81C2×(C2×D11)⋊C4—22no—
82#66979—22no—
83#66979C2312yes—
84#66979C2314yes—
85C2×C4⋊Dic11C2312yes—
86#66977—22no—
87#66977C2314yes—
88C2×C4×Dic11—21no—
89#66961—216no—
90C2×D88C2318yes—
91C2×#4314C2318yes—
92#66951—24no—
93#66949—24no—
94#66947—24no—
95#66946—28no—
96#66946—28no—
97#66942—24no—
98#66938—24no—
99#66937—24no—
100#66936—24no—
101C22⋊C4×D11—28no—
102C22⋊C4×D11—28no—
103#66932—24no—
104#66928C2312yescomplemented
105#66927C2311yescharacteristic, complemented
106C4×D44—22no—
107C4×D44—22no—
108C4×D44—24no—
109C4×D44—22no—
110C4×D44C2318yes—
111C4×D44C2314yes—
112C4×D44C2314yes—
113C4×D44C2314yescomplemented
114#66925—22no—
115C42×D11—22no—
116#66923C2312yescomplemented
117#66922C2311yescharacteristic, complemented
118#66922C2312yescomplemented
119C4×Dic22—22no—
120C4×Dic22C2314yescomplemented
121C11×C4⋊C8C2314yescomplemented
122C11×C4⋊C8C2314yescomplemented
123C11×C22⋊C8C2318yes—
124C11×#97C2314yescomplemented
125C4×C8×C11C2314yescomplemented
126#66885C2318yes—
127#66885C2318yes—
128#66885C2318yescomplemented
129#66882C2318yescomplemented
130#66881C2318yescomplemented
131#66880C2318yescomplemented
132#60564—111nomaximal, Sylow
133C24×C11C2×D411yescharacteristic
134C23×D11—22no—
135C23×D11—28no—
136C23×D11—24no—
137C23×D11—84no—
138C22×C4×C11—24no—
139C22×C4×C11C2×D411yescharacteristic
140C22×C4×C11C2×D412yes—
141C22×C4×C11C2×D412yes—
142C22×C4×C11C2×D412yes—
143C22×C4×C11C2412yes—
144C22×C4×C11C2411yescharacteristic
145C2×C22⋊D11—22no—
146C2×C22⋊D11—24no—
147C22×Dic11—22no—
148#4339—28no—
149C2×D44—28no—
150C2×D44—216no—
151C2×D44—216no—
152C2×D44—22no—
153C2×D44—24no—
154C2×D44—22no—
155C2×D44—24no—
156C2×D44#4118yes—
157C2×D44C2412yes—
158C2×D44C2414yes—
159C2×C4×D11—22no—
160C2×C4×D11—24no—
161C2×C4×D11—28no—
162C2×C4×D11—24no—
163C2×C4×D11—24no—
164C2×C4×D11—84no—
165C2×C4×D11—84no—
166C2×Dic22—22no—
167C2×Dic22C2412yes—
168C11×M16—28no—
169C2×C8×C11C2418yes—
170C11×C4⋊C4C2×D414yes—
171C11×C4⋊C4C2×D414yes—
172C11×C22⋊C4C2×D414yes—
173C11×C22⋊C4C2×D414yes—
174C42×C11C2×D412yes—
175C42×C11C2×D412yes—
176C42×C11C2412yes—
177C42×C11C2411yescharacteristic
178C42×C11C2411yescharacteristic
179C22⋊Dic11—24no—
180C22⋊Dic11—24no—
181C22⋊Dic11—22no—
182(C2×D11)⋊C4—24no—
183(C2×D11)⋊C4—28no—
184(C2×D11)⋊C4—24no—
185(C2×D11)⋊C4—24no—
186(C2×D11)⋊C4—24no—
187(C2×D11)⋊C4—24no—
188C4⋊Dic11—22no—
189C4⋊Dic11—22no—
190C4⋊Dic11—22no—
191C4⋊Dic11C2414yes—
192C4⋊Dic11C2414yes—
193Dic11⋊C4—24no—
194Dic11⋊C4—24no—
195Dic11⋊C4—24no—
196C4×Dic11—22no—
197C4×Dic11—24no—
198C4×Dic11—24no—
199D88—216no—
200#4314—216no—
201#3455—111no—
202C2×#518—111no—
203#3123—114no—
204#3122—114no—
205#3118—118no—
206#3093—112no—
207#3077—112no—
208#3036—112no—
209#3003—112no—
210C4×AGL(1,ℤ/8)—114no—
211#2921D1111yescharacteristic, complemented
212C23×C11—22no—
213C23×C11—42no—
214C23×C11C22×D412yes—
215C23×C11C22×D411yescharacteristic
216C22×D11—28no—
217C22×D11—24no—
218C22×D11—216no—
219C22×D11—22no—
220C22×D11—44no—
221C22×D11—44no—
222C22×D11—88no—
223C22×D11—816no—
224C2×C4×C11—22no—
225C2×C4×C11—24no—
226C2×C4×C11—24no—
227C2×C4×C11—42no—
228C2×C4×C11—42no—
229C2×C4×C11C22×D412yes—
230C2×C4×C11C22×D414yes—
231C2×C4×C11C22×D412yes—
232C2×C4×C11C22×D412yes—
233C2×C4×C11C22×D411yescharacteristic
234C2×C4×C11C2×#4114yes—
235C2×C4×C11C2511yescharacteristic
236C22⋊D11—44no—
237C22⋊D11—84no—
238C2×Dic11—22no—
239C2×Dic11—24no—
240C2×Dic11—24no—
241C2×Dic11—44no—
242D44—216no—
243D44—28no—
244D44—24no—
245D44—24no—
246D44—82no—
247D44C2×#4118yes—
248C4×D11—44no—
249C4×D11—84no—
250C4×D11—84no—
251C4×D11—88no—
252C4×D11—84no—
253Dic22—24no—
254Dic22—82no—
255C8×C11—28no—
256C23×D4—111no—
257C2×AGL(1,ℤ/8)—114no—
258#542—114no—
259#541—112no—
260#540—112no—
261#539—222no—
262#538—222no—
263#533—111no—
264#532—111no—
265#529—224no—
266#525—112no—
267#518—114no—
268#518—114no—
269#518—224no—
270C4×#41—112no—
271C2×C4×D4—112no—
272C2×C4×D4—112no—
273C2×C4×D4—222no—
274C2×#117—111no—
275C2×#117C2×D1111yescharacteristic
276C22×C22⋊C4—222no—
277#485—118no—
278#482—118no—
279#478—118no—
280#476—114no—
281#474—114no—
282#463—118no—
283#461—114no—
284#459—114no—
285#450—118no—
286#447—118no—
287#442—118no—
288#440—118no—
289C4×SD16—118no—
290C4×D8—118no—
291#433C2×D1114yescomplemented
292#433C2×D1114yescomplemented
293#428—114no—
294#423C2×D1112yescomplemented
295#418—114no—
296#417—114no—
297#407C2×D1112yes—
298C4×M16C2×D1112yescomplemented
299C22×C11—22no—
300C22×C11—24no—
301C22×C11—22no—
302C22×C11—44no—
303C22×C11#52512yes—
304C22×C11C23×D411yescharacteristic
305C2×D11—28no—
306C2×D11—416no—
307C2×D11—44no—
308C2×D11—44no—
309C2×D11—44no—
310C2×D11—42no—
311C2×D11—816no—
312C4×C11—22no—
313C4×C11—24no—
314C4×C11—22no—
315C4×C11—22no—
316C4×C11#52512yes—
317C4×C11C22×#4112yes—
318Dic11—44no—
319Dic11—44no—
320Dic11—42no—
321C25—221no—
322C2×#41—112no—
323C22×D4—112no—
324C22×D4—114no—
325C22×D4—228no—
326C22×D4—221no—
327C22×D4—222no—
328C23×C4—222no—
329C23×C4—222no—
330C23×C4C22×D1111yescharacteristic
331AGL(1,ℤ/8)—2216no—
332C2×SD16—118no—
333C2×D8—118no—
334C2×M16C22×D1114yes—
335C4⋊Q8—112no—
336C4⋊Q8—111no—
337#127—111no—
338#126—224no—
339#126—224no—
340#125—112no—
341#125—224no—
342#124—112no—
343#124—224no—
344#123—222no—
345#123—224no—
346#123—224no—
347C22⋊Q8—114no—
348C22⋊Q8—222no—
349C22⋊Q8—224no—
350#121—114no—
351#121—222no—
352#121—224no—
353#120—222no—
354C4×Q8—114no—
355C4×Q8—222no—
356C4×D4—118no—
357C4×D4—114no—
358C4×D4—114no—
359C4×D4—114no—
360C4×D4—224no—
361C4×D4—224no—
362C4×D4—228no—
363C4×D4—228no—
364C4×D4—224no—
365C4×D4—222no—
366C4×D4—222no—
367C4×D4—222no—
368#117—114no—
369#117—112no—
370#117—222no—
371#117—222no—
372#117D4414yes—
373#117C22×D1112yes—
374#117C22×D1112yes—
375C2×C4⋊C4—112no—
376C2×C4⋊C4D4412yes—
377C2×C22⋊C4—221no—
378C2×C22⋊C4—222no—
379C2×C22⋊C4—222no—
380C2×C22⋊C4—228no—
381C2×C22⋊C4—228no—
382C2×C22⋊C4D4412yes—
383C2×C42—221no—
384C2×C42—222no—
385C2×C42C22×D1111yescharacteristic
386C2×C42C22×D1111yescharacteristic
387#107—118no—
388#106—118no—
389C4⋊C8C22×D1114yescomplemented
390C4⋊C8C22×D1114yescomplemented
391#103—118no—
392#102—118no—
393#102—118no—
394#102—118no—
395C22⋊C8C22×D1118yes—
396#97C22×D1114yescomplemented
397C4×C8C22×D1114yescomplemented
398C2×C11—22no—
399C2×C11—42no—
400C2×C11C2×#52511yescharacteristic
401C2×C11#358512yes—
402D11—48no—
403D11—82no—
404C24—228no—
405C24—222no—
406C24—224no—
407C24—884no—
408C24C2×D4411yescharacteristic
409#41—228no—
410C2×Q8—112no—
411C2×Q8—222no—
412C2×D4—118no—
413C2×D4—114no—
414C2×D4—112no—
415C2×D4—2216no—
416C2×D4—228no—
417C2×D4—2216no—
418C2×D4—222no—
419C2×D4—224no—
420C2×D4—224no—
421C2×D4—222no—
422C2×D4—222no—
423C2×D4—224no—
424C22×C4—24no—
425C22×C4—222no—
426C22×C4—222no—
427C22×C4—224no—
428C22×C4—228no—
429C22×C4—224no—
430C22×C4—224no—
431C22×C4—884no—
432C22×C4—884no—
433C22×C4C2×D4411yescharacteristic
434C22×C4C2×D4412yes—
435C22×C4C2×D4412yes—
436C22×C4C2×D4412yes—
437C22×C4C23×D1112yes—
438C22×C4C23×D1111yescharacteristic
439SD16—2216no—
440D8—2216no—
441M16—28no—
442C2×C8C23×D1118yes—
443C4⋊C4—114no—
444C4⋊C4—114no—
445C4⋊C4—222no—
446C4⋊C4—224no—
447C4⋊C4—222no—
448C4⋊C4—224no—
449C4⋊C4—224no—
450C4⋊C4—222no—
451C4⋊C4C2×D4414yes—
452C4⋊C4C2×D4414yes—
453C22⋊C4—224no—
454C22⋊C4—222no—
455C22⋊C4—224no—
456C22⋊C4—228no—
457C22⋊C4—224no—
458C22⋊C4—224no—
459C22⋊C4—224no—
460C22⋊C4—224no—
461C22⋊C4—224no—
462C22⋊C4C2×D4414yes—
463C22⋊C4C2×D4414yes—
464C42—224no—
465C42—222no—
466C42—224no—
467C42C2×D4412yes—
468C42C2×D4412yes—
469C42C23×D1112yes—
470C42C23×D1111yescharacteristic
471C42C23×D1111yescharacteristic
472C11#6056411yescharacteristic, complemented, Sylow
473C23—22no—
474C23—42no—
475C23—2216no—
476C23—228no—
477C23—224no—
478C23—222no—
479C23—444no—
480C23—444no—
481C23—888no—
482C23—8816no—
483C23C22×D4412yes—
484C23C22×D4411yescharacteristic
485Q8—224no—
486Q8—882no—
487D4—118no—
488D4—2216no—
489D4—228no—
490D4—224no—
491D4—224no—
492D4—444no—
493D4—882no—
494D4—884no—
495C2×C4—22no—
496C2×C4—24no—
497C2×C4—24no—
498C2×C4—42no—
499C2×C4—42no—
500C2×C4—224no—
501C2×C4—224no—
502C2×C4—222no—
503C2×C4—444no—
504C2×C4—444no—
505C2×C4—888no—
506C2×C4—884no—
507C2×C4—884no—
508C2×C4—884no—
509C2×C4C22×D4412yes—
510C2×C4C22×D4414yes—
511C2×C4C22×D4412yes—
512C2×C4C22×D4412yes—
513C2×C4C22×D4411yescharacteristic
514C2×C4#41×D1114yes—
515C2×C4C24×D1111yescharacteristic
516C8—28no—
517C22—22no—
518C22—22no—
519C22—24no—
520C22—44no—
521C22—228no—
522C22—4416no—
523C22—444no—
524C22—444no—
525C22—442no—
526C22—444no—
527C22—8816no—
528C22#1062305512yes—
529C22C23×D4411yescharacteristic
530C4—22no—
531C4—24no—
532C4—22no—
533C4—22no—
534C4—442no—
535C4—444no—
536C4—444no—
537C4#1062305512yes—
538C4C2×#41×D1112yes—
539C2—22no—
540C2—42no—
541C2—448no—
542C2—882no—
543C2C2×#1062305511yescharacteristic
544C2#1308339712yes—
subgroupG/H
centerC22C23×D44
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC11×#2921C2
socleC22×C11C23×D4
hypercenter#2921D11
hypocenterC11#60564
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×#117 ◁ #2921

Complements

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

NH ≅ G/Ntype
1. #13082006C2semidirect
2. C2×#10623052C2semidirect
3. #13078869C2semidirect
4. #13078860C2semidirect
5. #13078802C2semidirect
6. #13078549C2semidirect
7. #13078415C2semidirect
8. #13078082C2semidirect
9. #13077846C2semidirect
10. C4×#66961C2semidirect
11. C11×#2921C2semidirect
17. #10623066C22semidirect
18. #10623065C22semidirect
23. #10623049C22semidirect
28. #10623008C22semidirect
29. C4×#4339C22semidirect
32. #10623001C22semidirect
33. C11×#433C22semidirect
34. C11×#433C22semidirect
35. C11×#423C22semidirect
37. C4×C11×M16C22semidirect
38. #10622746C22semidirect
40. #10622734C22semidirect
41. #10622460C22semidirect
42. #10622459C22semidirect
43. #10622457C22semidirect
44. #10622456C22semidirect
45. #10622455C22semidirect
46. #10622454C22semidirect
47. #10622350C22semidirect
50. #10622336C22semidirect
51. #10622324C22semidirect
52. #10622323C22semidirect
53. C4×D88C22semidirect
54. C4×#4314C22semidirect
104. #66928C23semidirect
105. #66927C23semidirect
113. C4×D44C23semidirect
116. #66923C23semidirect
117. #66922C23semidirect
118. #66922C23semidirect
120. C4×Dic22C23semidirect
121. C11×C4⋊C8C23semidirect
122. C11×C4⋊C8C23semidirect
124. C11×#97C23semidirect
125. C4×C8×C11C23semidirect
128. #66885C23semidirect
129. #66882C23semidirect
130. #66881C23semidirect
131. #66880C23semidirect
211. #2921D11semidirect
291. #433C2×D11semidirect
292. #433C2×D11semidirect
294. #423C2×D11semidirect
298. C4×M16C2×D11semidirect
389. C4⋊C8C22×D11semidirect
390. C4⋊C8C22×D11semidirect
396. #97C22×D11semidirect
397. C4×C8C22×D11semidirect
472. C11#60564semidirect

Maximal subgroups

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

subgroupindex
#130820062
C2×#106230522
#130788692
#130788602
#130788022
#130785492
#130784152
#130780822
#130778462
C4×#669612
C11×#29212
#6056411