Finite Group Databasebeta

← #15622248

Subgroups — #15622248

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
2#13078868C214yesmaximal, complemented
3#13078859C214yesmaximal, complemented
4#13078800C218yesmaximal, complemented
5#13078547C212yesmaximal, complemented
6#13078413C212yesmaximal, complemented
7#13078080C212yesmaximal, complemented
8#13077843C212yesmaximal, complemented
9C4×#66985C214yesmaximal, complemented
10#13077254C211yesmaximal, characteristic, complemented
11C2×C11×#518C211yesmaximal, characteristic, complemented
12C23×D4×C11C2211yescharacteristic
13C11×#518—24no—
14C11×#518C2214yes—
15C11×#518C2214yes—
16C2×C4×D4×C11—22no—
17C2×C4×D4×C11C2212yes—
18C2×C4×D4×C11C2212yes—
19C2×C11×#117C2211yescharacteristic
20C2×C11×#117C2211yescharacteristic
21C22×C11×C22⋊C4—22no—
22C2×#66985C2214yes—
23#10623322C2212yes—
24#10623066C2212yescomplemented
25#10623065C2214yescomplemented
26#10623059—24no—
27#10623049C2212yescomplemented
28#10623046—22no—
29#10623025—22no—
30#10623008C2211yescharacteristic, complemented
31C4×#4339C2212yescomplemented
32#10623001C2211yescharacteristic, complemented
33#10622831C2218yes—
34#10622830C2218yes—
35#10622828C2214yes—
36#10622820C2212yes—
37#10622632C2214yescomplemented
38#10622631C2218yescomplemented
39C4×#4324C2218yescomplemented
40#10622629C2218yescomplemented
41#10622628C2214yescomplemented
42#10622627C2218yescomplemented
43C4×#4323C2218yescomplemented
44#10622622C2218yescomplemented
45#10622621C2214yescomplemented
46#10622620C2214yescomplemented
47#10622616C2218yescomplemented
48#10622613C2214yescomplemented
49#10622613C2214yescomplemented
50#10622609C2218yescomplemented
51#10622579C2214yescomplemented
52#10622577C2214yescomplemented
53#10622537C2212yescomplemented
54C4×#4318C2212yescomplemented
55C25×C11—21no—
56C22×D4×C11—28no—
57C22×D4×C11—21no—
58C22×D4×C11—22no—
59C22×D4×C11C2314yes—
60C22×D4×C11C2312yes—
61C23×C4×C11—22no—
62C23×C4×C11—22no—
63C23×C4×C11C2311yescharacteristic
64C2×#4339C2312yes—
65C4×D4×C11—28no—
66C4×D4×C11—28no—
67C4×D4×C11—22no—
68C4×D4×C11—22no—
69C4×D4×C11—24no—
70C4×D4×C11C2314yes—
71C4×D4×C11C2314yes—
72C4×D4×C11C2318yes—
73C11×#117—22no—
74C11×#117D414yes—
75C11×#117C2314yes—
76C11×#117C2312yes—
77C11×#117C2312yes—
78C2×C11×C4⋊C4D412yes—
79C2×C11×C4⋊C4C2312yes—
80C2×C11×C22⋊C4—21no—
81C2×C11×C22⋊C4—22no—
82C2×C11×C22⋊C4—22no—
83C2×C11×C22⋊C4—28no—
84C2×C11×C22⋊C4—28no—
85C2×C11×C22⋊C4D412yes—
86C2×C42×C11—21no—
87C2×C42×C11C2311yescharacteristic
88C2×C42×C11C2311yescharacteristic
89#67006—22no—
90C2×#4324C2318yes—
91#66985—216no—
92C2×#4323C2318yes—
93#66983—22no—
94#66983C2314yes—
95#66982—22no—
96C4×C22⋊D11—24no—
97C4×C22⋊D11—24no—
98#66979C2312yes—
99#66977—22no—
100#66977C2314yes—
101C2×#4318C2314yes—
102#66951—24no—
103#66949—24no—
104#66947—24no—
105#66942—24no—
106#66938—24no—
107#66937—24no—
108#66936—24no—
109#66932—24no—
110#66928C2312yescomplemented
111#66927C2311yescharacteristic, complemented
112C4×D44—22no—
113C4×D44C2314yescomplemented
114#66925—22no—
115C42×D11—22no—
116#66923C2312yescomplemented
117#66922C2311yescharacteristic, complemented
118#66922C2312yescomplemented
119C4×Dic22—22no—
120C4×Dic22C2314yescomplemented
121#66896C2318yes—
122#66896C2318yes—
123C22⋊(C11⋊C8)C2318yes—
124#66874C2318yescomplemented
125#66873C2318yescomplemented
126#66872C2318yescomplemented
127#66871C2318yescomplemented
128C4⋊(C11⋊C8)C2314yescomplemented
129C4⋊(C11⋊C8)C2314yescomplemented
130#66867C2314yescomplemented
131C4×C11⋊C8C2314yescomplemented
132#60564—111nomaximal, Sylow
133C24×C11—28no—
134C24×C11—22no—
135C24×C11—24no—
136C24×C11—84no—
137C24×C11C2×D411yescharacteristic
138C2×D4×C11—28no—
139C2×D4×C11—216no—
140C2×D4×C11—216no—
141C2×D4×C11—24no—
142C2×D4×C11—22no—
143C2×D4×C11—24no—
144C2×D4×C11#4118yes—
145C2×D4×C11C2414yes—
146C22×C4×C11—24no—
147C22×C4×C11—22no—
148C22×C4×C11—28no—
149C22×C4×C11—24no—
150C22×C4×C11—24no—
151C22×C4×C11—84no—
152C22×C4×C11—84no—
153C22×C4×C11C2×D412yes—
154C22×C4×C11C2×D411yescharacteristic
155C22×C4×C11C2×D412yes—
156C22×C4×C11C2×D412yes—
157C22×C4×C11C2412yes—
158C22×C4×C11C2411yescharacteristic
159C2×C22⋊D11—22no—
160C2×C22⋊D11—24no—
161#4339—28no—
162C2×D44—22no—
163C2×D44C2412yes—
164C2×C4×D11—22no—
165C2×C4×D11—24no—
166C2×Dic22—22no—
167C2×Dic22C2412yes—
168C11×C4⋊C4—22no—
169C11×C4⋊C4C2×D414yes—
170C11×C4⋊C4C2×D414yes—
171C11×C4⋊C4C2414yes—
172C11×C22⋊C4—24no—
173C11×C22⋊C4—28no—
174C11×C22⋊C4—24no—
175C11×C22⋊C4—24no—
176C11×C22⋊C4C2×D414yes—
177C11×C22⋊C4C2×D414yes—
178C42×C11—24no—
179C42×C11C2×D412yes—
180C42×C11C2×D412yes—
181C42×C11C2412yes—
182C42×C11C2411yescharacteristic
183C42×C11C2411yescharacteristic
184C22⋊Dic11—24no—
185C22⋊Dic11—22no—
186#4324—216no—
187#4323—216no—
188(C2×D11)⋊C4—24no—
189(C2×D11)⋊C4—24no—
190(C2×D11)⋊C4—24no—
191C4⋊Dic11—22no—
192C4⋊Dic11—22no—
193C4⋊Dic11C2414yes—
194Dic11⋊C4—24no—
195Dic11⋊C4—24no—
196Dic11⋊C4—24no—
197C4×Dic11—22no—
198C4×Dic11—24no—
199#4318—28no—
200C2×C11⋊C8C2418yes—
201#3455—111no—
202C2×#518D1111yescharacteristic, complemented
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#2921—111no—
212C23×C11—216no—
213C23×C11—22no—
214C23×C11—28no—
215C23×C11—24no—
216C23×C11—42no—
217C23×C11—44no—
218C23×C11—44no—
219C23×C11—88no—
220C23×C11—816no—
221C23×C11C22×D412yes—
222C23×C11C22×D411yescharacteristic
223C22×D11—22no—
224D4×C11—216no—
225D4×C11—28no—
226D4×C11—24no—
227D4×C11C2×#4118yes—
228C2×C4×C11—22no—
229C2×C4×C11—24no—
230C2×C4×C11—24no—
231C2×C4×C11—24no—
232C2×C4×C11—42no—
233C2×C4×C11—42no—
234C2×C4×C11—44no—
235C2×C4×C11—84no—
236C2×C4×C11—88no—
237C2×C4×C11—84no—
238C2×C4×C11C22×D414yes—
239C2×C4×C11C22×D412yes—
240C2×C4×C11C22×D412yes—
241C2×C4×C11C22×D412yes—
242C2×C4×C11C22×D411yescharacteristic
243C2×C4×C11C2×#4114yes—
244C2×C4×C11C2511yescharacteristic
245C22⋊D11—44no—
246C22⋊D11—84no—
247C2×Dic11—22no—
248C2×Dic11—24no—
249D44—24no—
250D44—82no—
251C4×D11—44no—
252C4×D11—84no—
253Dic22—24no—
254Dic22—82no—
255C11⋊C8—28no—
256C23×D4C2×D1111yescharacteristic
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—24no—
268#518C2×D1114yes—
269#518C2×D1114yes—
270C4×#41—112no—
271C2×C4×D4—22no—
272C2×C4×D4C2×D1112yes—
273C2×C4×D4C2×D1112yes—
274C2×#117C2×D1111yescharacteristic
275C2×#117C2×D1111yescharacteristic
276C22×C22⋊C4—22no—
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#433—114no—
292#433—114no—
293#428—114no—
294#423—112no—
295#418—114no—
296#417—114no—
297#407—112no—
298C4×M16—112no—
299C22×C11—22no—
300C22×C11—24no—
301C22×C11—22no—
302C22×C11—28no—
303C22×C11—416no—
304C22×C11—44no—
305C22×C11—44no—
306C22×C11—44no—
307C22×C11—816no—
308C22×C11#52512yes—
309C22×C11C23×D411yescharacteristic
310C2×D11—44no—
311C2×D11—42no—
312C4×C11—22no—
313C4×C11—24no—
314C4×C11—22no—
315C4×C11—22no—
316C4×C11—44no—
317C4×C11#52512yes—
318C4×C11C22×#4112yes—
319Dic11—44no—
320Dic11—42no—
321C25—21no—
322C2×#41—112no—
323C22×D4—28no—
324C22×D4—21no—
325C22×D4—22no—
326C22×D4C22×D1114yes—
327C22×D4C22×D1112yes—
328C23×C4—22no—
329C23×C4—22no—
330C23×C4C22×D1111yescharacteristic
331AGL(1,ℤ/8)—2216no—
332C2×SD16—118no—
333C2×D8—118no—
334C2×M16—114no—
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—28no—
357C4×D4—28no—
358C4×D4—24no—
359C4×D4—22no—
360C4×D4—22no—
361C4×D4—114no—
362C4×D4—224no—
363C4×D4—224no—
364C4×D4—222no—
365C4×D4C22×D1118yes—
366C4×D4C22×D1114yes—
367C4×D4C22×D1114yes—
368#117—22no—
369#117—112no—
370#117—222no—
371#117C22⋊D1114yes—
372#117C22×D1114yes—
373#117C22×D1112yes—
374#117C22×D1112yes—
375C2×C4⋊C4C22⋊D1112yes—
376C2×C4⋊C4C22×D1112yes—
377C2×C22⋊C4—21no—
378C2×C22⋊C4—22no—
379C2×C22⋊C4—22no—
380C2×C22⋊C4—28no—
381C2×C22⋊C4—28no—
382C2×C22⋊C4C22⋊D1112yes—
383C2×C42—21no—
384C2×C42—222no—
385C2×C42C22×D1111yescharacteristic
386C2×C42C22×D1111yescharacteristic
387#107—118no—
388#106—118no—
389C4⋊C8—114no—
390C4⋊C8—114no—
391#103—118no—
392#102—118no—
393#102—118no—
394#102—118no—
395C22⋊C8—118no—
396#97—114no—
397C4×C8—114no—
398C2×C11—22no—
399C2×C11—42no—
400C2×C11—48no—
401C2×C11C2×#52511yescharacteristic
402C2×C11#358512yes—
403D11—82no—
404C24—28no—
405C24—22no—
406C24—24no—
407C24—84no—
408C24C2×C22⋊D1111yescharacteristic
409#41—228no—
410C2×Q8—112no—
411C2×Q8—222no—
412C2×D4—28no—
413C2×D4—216no—
414C2×D4—216no—
415C2×D4—24no—
416C2×D4—24no—
417C2×D4—22no—
418C2×D4—112no—
419C2×D4—222no—
420C2×D4—224no—
421C2×D4—222no—
422C2×D4#433918yes—
423C2×D4C23×D1114yes—
424C22×C4—24no—
425C22×C4—22no—
426C22×C4—28no—
427C22×C4—24no—
428C22×C4—24no—
429C22×C4—84no—
430C22×C4—84no—
431C22×C4—222no—
432C22×C4—224no—
433C22×C4C2×C22⋊D1111yescharacteristic
434C22×C4C2×C22⋊D1112yes—
435C22×C4C2×C22⋊D1112yes—
436C22×C4C2×C22⋊D1112yes—
437C22×C4C23×D1112yes—
438C22×C4C23×D1111yescharacteristic
439SD16—2216no—
440D8—2216no—
441M16—228no—
442C2×C8—118no—
443C4⋊C4—22no—
444C4⋊C4—114no—
445C4⋊C4—224no—
446C4⋊C4—222no—
447C4⋊C4—224no—
448C4⋊C4—224no—
449C4⋊C4—222no—
450C4⋊C4C2×C22⋊D1114yes—
451C4⋊C4C2×C22⋊D1114yes—
452C4⋊C4C23×D1114yes—
453C22⋊C4—24no—
454C22⋊C4—28no—
455C22⋊C4—24no—
456C22⋊C4—24no—
457C22⋊C4—222no—
458C22⋊C4—224no—
459C22⋊C4—224no—
460C22⋊C4—224no—
461C22⋊C4—224no—
462C22⋊C4C2×C22⋊D1114yes—
463C22⋊C4C2×C22⋊D1114yes—
464C42—24no—
465C42—222no—
466C42—224no—
467C42C2×C22⋊D1112yes—
468C42C2×C22⋊D1112yes—
469C42C23×D1112yes—
470C42C23×D1111yescharacteristic
471C42C23×D1111yescharacteristic
472C11#6056411yescharacteristic, complemented, Sylow
473C23—216no—
474C23—22no—
475C23—28no—
476C23—24no—
477C23—42no—
478C23—44no—
479C23—44no—
480C23—88no—
481C23—816no—
482C23—222no—
483C23C22×C22⋊D1112yes—
484C23C22×C22⋊D1111yescharacteristic
485Q8—224no—
486Q8—882no—
487D4—216no—
488D4—28no—
489D4—24no—
490D4—224no—
491D4—444no—
492D4—882no—
493D4—884no—
494D4C2×#433918yes—
495C2×C4—22no—
496C2×C4—24no—
497C2×C4—24no—
498C2×C4—24no—
499C2×C4—42no—
500C2×C4—42no—
501C2×C4—44no—
502C2×C4—88no—
503C2×C4—84no—
504C2×C4—84no—
505C2×C4—224no—
506C2×C4—222no—
507C2×C4—444no—
508C2×C4—884no—
509C2×C4C2×#433914yes—
510C2×C4C22×C22⋊D1112yes—
511C2×C4C22×C22⋊D1114yes—
512C2×C4C22×C22⋊D1112yes—
513C2×C4C22×C22⋊D1112yes—
514C2×C4C22×C22⋊D1111yescharacteristic
515C2×C4C24×D1111yescharacteristic
516C8—228no—
517C22—22no—
518C22—22no—
519C22—28no—
520C22—24no—
521C22—44no—
522C22—416no—
523C22—44no—
524C22—44no—
525C22—816no—
526C22—442no—
527C22—444no—
528C22#1062332212yes—
529C22C23×C22⋊D1111yescharacteristic
530C4—22no—
531C4—24no—
532C4—22no—
533C4—22no—
534C4—44no—
535C4—442no—
536C4—444no—
537C4#1062332212yes—
538C4C22×#433912yes—
539C2—22no—
540C2—42no—
541C2—48no—
542C2—882no—
543C2C2×#1062332211yescharacteristic
544C2#1308339612yes—
subgroupG/H
centerC22C23×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#518C2
socleC22×C11C23×D4
hypercenterC2×#518D11
hypocenterC11#60564
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×#117 ◁ C2×#518

Complements

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

NH ≅ G/Ntype
1. #13082006C2semidirect
2. #13078868C2semidirect
3. #13078859C2semidirect
4. #13078800C2semidirect
5. #13078547C2semidirect
6. #13078413C2semidirect
7. #13078080C2semidirect
8. #13077843C2semidirect
9. C4×#66985C2semidirect
10. #13077254C2semidirect
11. C2×C11×#518C2semidirect
24. #10623066C22semidirect
25. #10623065C22semidirect
27. #10623049C22semidirect
30. #10623008C22semidirect
31. C4×#4339C22semidirect
32. #10623001C22semidirect
37. #10622632C22semidirect
38. #10622631C22semidirect
39. C4×#4324C22semidirect
40. #10622629C22semidirect
41. #10622628C22semidirect
42. #10622627C22semidirect
43. C4×#4323C22semidirect
44. #10622622C22semidirect
45. #10622621C22semidirect
46. #10622620C22semidirect
47. #10622616C22semidirect
48. #10622613C22semidirect
49. #10622613C22semidirect
50. #10622609C22semidirect
51. #10622579C22semidirect
52. #10622577C22semidirect
53. #10622537C22semidirect
54. C4×#4318C22semidirect
110. #66928C23semidirect
111. #66927C23semidirect
113. C4×D44C23semidirect
116. #66923C23semidirect
117. #66922C23semidirect
118. #66922C23semidirect
120. C4×Dic22C23semidirect
124. #66874C23semidirect
125. #66873C23semidirect
126. #66872C23semidirect
127. #66871C23semidirect
128. C4⋊(C11⋊C8)C23semidirect
129. C4⋊(C11⋊C8)C23semidirect
130. #66867C23semidirect
131. C4×C11⋊C8C23semidirect
202. C2×#518D11semidirect
472. C11#60564semidirect

Maximal subgroups

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

subgroupindex
#130820062
#130788682
#130788592
#130788002
#130785472
#130784132
#130780802
#130778432
C4×#669852
#130772542
C2×C11×#5182
#6056411