Finite Group Databasebeta

← #15625208

Subgroups — #15625208

Order 2816.

2262 conjugacy classes of subgroups.

The subgroup lattice has 586 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13081912C211yesmaximal, characteristic, complemented
2#13079619C214yesmaximal, complemented
3#13079603C214yesmaximal, complemented
4#13079581C218yesmaximal, complemented
5#13079080C212yesmaximal, complemented
6#13079002C212yesmaximal, complemented
7#13078106C214yesmaximal, complemented
8#13077850C212yesmaximal, complemented
9#13077843C212yesmaximal, complemented
10#13077249C211yesmaximal, characteristic, complemented
11C22×C11×#124C211yesmaximal, characteristic, complemented
12C23×Q8×C11C2211yescharacteristic
13C23×D4×C11C2211yescharacteristic
14C2×C11×#124—22no—
15C2×C11×#124—22no—
16C2×C11×#124—22no—
17C2×C11×#124C2214yes—
18C2×C11×#124C2212yes—
19C2×C11×#124C2214yes—
20C2×C11×#124C2212yes—
21C22×C11×C22⋊C4—22no—
22C22×C42×C11C2211yescharacteristic
23C2×#66995C2214yescomplemented
24C2×#66985C2214yes—
25#10623322—22no—
26#10623322C2212yes—
27#10623010—22no—
28#10623010—22no—
29#10623010C2214yescomplemented
30#10623008C2211yescharacteristic, complemented
31#10623008C2212yescomplemented
32C4×#4339—22no—
33C4×#4339C2212yescomplemented
34#10623001C2211yescharacteristic, complemented
35#10623001C2212yescomplemented
36#10622841C2218yescomplemented
37#10622840C2218yescomplemented
38#10622838C2214yescomplemented
39#10622831C2218yes—
40#10622830C2218yes—
41#10622828C2214yes—
42#10622820C2212yes—
43#10622673C2214yescomplemented
44#10622672C2218yescomplemented
45#10622671C2214yescomplemented
46#10622670C22116yescomplemented
47#10622669C2218yescomplemented
48#10622668C2218yescomplemented
49#10622667C22116yescomplemented
50#10622539C2214yescomplemented
51#10622538C2214yescomplemented
52#10622537C2212yescomplemented
53C4×#4318C2212yescomplemented
54C25×C11—21no—
55C22×Q8×C11—22no—
56C22×Q8×C11—21no—
57C22×Q8×C11—44no—
58C22×Q8×C11C2312yes—
59C22×Q8×C11C2314yes—
60C22×D4×C11—22no—
61C22×D4×C11—21no—
62C22×D4×C11—44no—
63C22×D4×C11C2312yes—
64C22×D4×C11C2314yes—
65C23×C4×C11—21no—
66C23×C4×C11D412yes—
67C23×C4×C11C2311yescharacteristic
68C2×#4339—22no—
69C2×#4339C2312yes—
70C11×#124—24no—
71C11×#124—24no—
72C11×#124—24no—
73C11×#124—22no—
74C11×#124—24no—
75C11×#124—22no—
76C11×#124—24no—
77C11×#124C2318yes—
78C11×#124C2314yes—
79C11×#124C2314yes—
80C2×C11×C22⋊C4—24no—
81C2×C11×C22⋊C4—24no—
82C2×C11×C22⋊C4—24no—
83C2×C11×C22⋊C4—24no—
84C2×C11×C22⋊C4—24no—
85C2×C11×C22⋊C4—24no—
86C2×C42×C11D412yes—
87C2×C42×C11D412yes—
88C2×C42×C11D412yes—
89C2×C42×C11C2311yescharacteristic
90C2×C42×C11C2312yes—
91C2×C42×C11C2311yescharacteristic
92C2×C42×C11C2312yes—
93#67006—22no—
94C2×#4326C2318yescomplemented
95#66995—48no—
96C2×#4325C2318yescomplemented
97C2×#4324C2318yes—
98#66985—48no—
99C2×#4323C2318yes—
100#66983—22no—
101#66983—22no—
102#66983C2314yes—
103#66982—22no—
104#66982—24no—
105C4×C22⋊D11—24no—
106C4×C22⋊D11—24no—
107C4×C22⋊D11—24no—
108#66979—22no—
109#66979C2312yes—
110#66977—22no—
111#66977—22no—
112#66977C2314yes—
113C2×#4318C2314yes—
114#66929—24no—
115#66928—22no—
116#66928C2312yescomplemented
117#66927C2311yescharacteristic, complemented
118C4×D44—22no—
119C4×D44—22no—
120C4×D44C2314yescomplemented
121#66925—24no—
122#66925—22no—
123C42×D11—22no—
124#66923—22no—
125#66923C2312yescomplemented
126#66922C2311yescharacteristic, complemented
127#66922C2312yescomplemented
128C4×Dic22—22no—
129C4×Dic22—22no—
130C4×Dic22C2314yescomplemented
131#66899C23116yescomplemented
132#66896C23116yes—
133C22⋊(C11⋊C8)C2318yes—
134C4⋊(C11⋊C8)C2318yescomplemented
135#66867C2314yescomplemented
136C4×C11⋊C8C2314yescomplemented
137#60799—111nomaximal, Sylow
138C24×C11—24no—
139C24×C11—22no—
140C24×C11—44no—
141C24×C11—48no—
142C24×C11C2×D411yescharacteristic
143C2×Q8×C11—24no—
144C2×Q8×C11—22no—
145C2×Q8×C11—28no—
146C2×Q8×C11—48no—
147C2×Q8×C11—44no—
148C2×Q8×C11—48no—
149C2×Q8×C11C2414yes—
150C2×D4×C11—24no—
151C2×D4×C11—22no—
152C2×D4×C11—28no—
153C2×D4×C11—48no—
154C2×D4×C11—44no—
155C2×D4×C11—48no—
156C2×D4×C11C2414yes—
157C22×C4×C11—24no—
158C22×C4×C11—24no—
159C22×C4×C11—22no—
160C22×C4×C11—44no—
161C22×C4×C11—44no—
162C22×C4×C11C2×D412yes—
163C22×C4×C11C2×D412yes—
164C22×C4×C11C2×D411yescharacteristic
165C22×C4×C11C2×D412yes—
166C22×C4×C11C2×D412yes—
167C22×C4×C11C2×D412yes—
168C22×C4×C11C2×D412yes—
169C22×C4×C11C2×D412yes—
170C22×C4×C11C2412yes—
171C22×C4×C11C2411yescharacteristic
172C2×C22⋊D11—22no—
173C2×C22⋊D11—24no—
174#4339—28no—
175#4339—48no—
176C2×D44—22no—
177C2×D44C2412yes—
178C2×C4×D11—22no—
179C2×C4×D11—24no—
180C2×Dic22—22no—
181C2×Dic22C2412yes—
182C11×C22⋊C4—28no—
183C11×C22⋊C4—28no—
184C11×C22⋊C4—28no—
185C11×C22⋊C4—28no—
186C42×C11C2×D412yes—
187C42×C11C2×D412yes—
188C42×C11C2×D412yes—
189C42×C11C2×D411yescharacteristic
190C42×C11C2×D412yes—
191C42×C11C2×D411yescharacteristic
192C42×C11C2×D412yes—
193C42×C11C2411yescharacteristic
194C42×C11C2411yescharacteristic
195C42×C11C2412yes—
196C22⋊Dic11—22no—
197C22⋊Dic11—24no—
198#4326—48no—
199#4325—48no—
200#4324—48no—
201#4323—48no—
202(C2×D11)⋊C4—24no—
203(C2×D11)⋊C4—24no—
204(C2×D11)⋊C4—24no—
205C4⋊Dic11—22no—
206C4⋊Dic11—22no—
207C4⋊Dic11C2414yes—
208Dic11⋊C4—24no—
209Dic11⋊C4—24no—
210Dic11⋊C4—24no—
211C4×Dic11—22no—
212C4×Dic11—24no—
213#4318—28no—
214C2×C11⋊C8C2418yes—
215#3444—111no—
216C22×#124D1111yescharacteristic, complemented
217#3215—114no—
218#3213—114no—
219#3211—118no—
220#3153—112no—
221#3140—112no—
222#3040—114no—
223#3004—112no—
224#3003—112no—
225#2920—111no—
226C23×C11—22no—
227C23×C11—24no—
228C23×C11—24no—
229C23×C11—48no—
230C23×C11—48no—
231C23×C11—48no—
232C23×C11—44no—
233C23×C11—48no—
234C23×C11—816no—
235C23×C11C22×D411yescharacteristic
236C23×C11C22×D412yes—
237C22×D11—22no—
238Q8×C11—28no—
239Q8×C11—48no—
240Q8×C11—44no—
241D4×C11—28no—
242D4×C11—48no—
243D4×C11—44no—
244C2×C4×C11—22no—
245C2×C4×C11—24no—
246C2×C4×C11—24no—
247C2×C4×C11—24no—
248C2×C4×C11—24no—
249C2×C4×C11—24no—
250C2×C4×C11—42no—
251C2×C4×C11—42no—
252C2×C4×C11—42no—
253C2×C4×C11—42no—
254C2×C4×C11—48no—
255C2×C4×C11—44no—
256C2×C4×C11C22×D412yes—
257C2×C4×C11C22×D412yes—
258C2×C4×C11C22×D412yes—
259C2×C4×C11C22×D412yes—
260C2×C4×C11C22×D412yes—
261C2×C4×C11C22×D411yescharacteristic
262C2×C4×C11H(5,𝔽2)14yes—
263C2×C4×C11C2511yescharacteristic
264C22⋊D11—44no—
265C22⋊D11—48no—
266C2×Dic11—22no—
267C2×Dic11—24no—
268D44—24no—
269D44—44no—
270C4×D11—48no—
271C4×D11—44no—
272Dic22—24no—
273Dic22—44no—
274C11⋊C8—28no—
275C23×Q8C2×D1111yescharacteristic
276C23×D4C2×D1111yescharacteristic
277C2×#137—114no—
278C2×AGL(1,ℤ/8)—114no—
279#533—111no—
280#533—112no—
281#532—112no—
282#532—111no—
283#529—114no—
284#529—222no—
285#529—222no—
286C2×#124—22no—
287C2×#124—22no—
288C2×#124—22no—
289C2×#124C2×D1112yes—
290C2×#124C2×D1114yes—
291C2×#124C2×D1114yes—
292C2×#124C2×D1112yes—
293#525—112no—
294#525—222no—
295C4×#41—112no—
296C4×#41—222no—
297C22×C22⋊C4—22no—
298C22×C42C2×D1111yescharacteristic
299#497—114no—
300#496—114no—
301#495—118no—
302#489—118no—
303#488—118no—
304#464—1116no—
305#463—1116no—
306#451—118no—
307#450—118no—
308#448—118no—
309#447—118no—
310#432—114no—
311#431—114no—
312#423—112no—
313#419—114no—
314#418—114no—
315#407—112no—
316C4×M16—112no—
317C22×C11—28no—
318C22×C11—22no—
319C22×C11—22no—
320C22×C11—22no—
321C22×C11—44no—
322C22×C11—48no—
323C22×C11—88no—
324C22×C11—816no—
325C22×C11#53512yes—
326C22×C11#57514yes—
327C22×C11C23×D411yescharacteristic
328C2×D11—42no—
329C2×D11—44no—
330C4×C11—22no—
331C4×C11—22no—
332C4×C11—22no—
333C4×C11—22no—
334C4×C11—22no—
335C4×C11—44no—
336C4×C11#53512yes—
337C4×C11C2×H(5,𝔽2)12yes—
338Dic11—42no—
339Dic11—44no—
340C25—21no—
341C2×#41—112no—
342C2×#41—222no—
343C22×Q8—22no—
344C22×Q8—21no—
345C22×Q8—44no—
346C22×Q8C22×D1112yes—
347C22×Q8C22×D1114yes—
348C22×D4—22no—
349C22×D4—21no—
350C22×D4—44no—
351C22×D4C22×D1112yes—
352C22×D4C22×D1114yes—
353C23×C4—21no—
354C23×C4C22⋊D1112yes—
355C23×C4C22×D1111yescharacteristic
356#137—448no—
357AGL(1,ℤ/8)—448no—
358C2×Q16—118no—
359C2×SD16—118no—
360C2×SD16—118no—
361C2×D8—118no—
362C2×M16—114no—
363C4⋊Q8—112no—
364C4⋊Q8—111no—
365#127—111no—
366#126—224no—
367#125—112no—
368#125—222no—
369#124—22no—
370#124—24no—
371#124—22no—
372#124—24no—
373#124—24no—
374#124—24no—
375#124—24no—
376#124—112no—
377#124—222no—
378#124C22×D1118yes—
379#124C22×D1114yes—
380#124C22×D1114yes—
381#123—222no—
382#123—224no—
383C22⋊Q8—114no—
384C22⋊Q8—222no—
385C22⋊Q8—222no—
386#121—114no—
387#121—222no—
388#121—222no—
389#120—222no—
390C4×Q8—114no—
391C4×Q8—222no—
392C4×Q8—222no—
393C4×D4—114no—
394C4×D4—224no—
395C4×D4—224no—
396C4×D4—224no—
397C4×D4—222no—
398C4×D4—222no—
399#117—112no—
400#117—222no—
401#117—222no—
402#117—224no—
403C2×C22⋊C4—24no—
404C2×C22⋊C4—24no—
405C2×C22⋊C4—24no—
406C2×C22⋊C4—24no—
407C2×C22⋊C4—24no—
408C2×C22⋊C4—24no—
409C2×C42—222no—
410C2×C42C22⋊D1112yes—
411C2×C42C22⋊D1112yes—
412C2×C42C22⋊D1112yes—
413C2×C42C22×D1111yescharacteristic
414C2×C42C22×D1112yes—
415C2×C42C22×D1111yescharacteristic
416C2×C42C22×D1112yes—
417C4⋊C8—118no—
418#103—1116no—
419#102—1116no—
420C22⋊C8—118no—
421#97—114no—
422C4×C8—114no—
423C2×C11—22no—
424C2×C11—24no—
425C2×C11—84no—
426C2×C11C2×#53511yescharacteristic
427C2×C11C2×#57512yes—
428D11—82no—
429C24—24no—
430C24—22no—
431C24—44no—
432C24—48no—
433C24C2×C22⋊D1111yescharacteristic
434#41—228no—
435#41—448no—
436C2×Q8—24no—
437C2×Q8—22no—
438C2×Q8—28no—
439C2×Q8—48no—
440C2×Q8—44no—
441C2×Q8—48no—
442C2×Q8—112no—
443C2×Q8—222no—
444C2×Q8C23×D1114yes—
445C2×D4—28no—
446C2×D4—24no—
447C2×D4—22no—
448C2×D4—48no—
449C2×D4—44no—
450C2×D4—48no—
451C2×D4—112no—
452C2×D4—224no—
453C2×D4—222no—
454C2×D4—222no—
455C2×D4C23×D1114yes—
456C22×C4—24no—
457C22×C4—24no—
458C22×C4—22no—
459C22×C4—44no—
460C22×C4—44no—
461C22×C4—224no—
462C22×C4—222no—
463C22×C4C2×C22⋊D1112yes—
464C22×C4C2×C22⋊D1112yes—
465C22×C4C2×C22⋊D1112yes—
466C22×C4C2×C22⋊D1111yescharacteristic
467C22×C4C2×C22⋊D1112yes—
468C22×C4C2×C22⋊D1112yes—
469C22×C4C2×C22⋊D1112yes—
470C22×C4C2×C22⋊D1112yes—
471C22×C4C23×D1112yes—
472C22×C4C23×D1111yescharacteristic
473Q16—448no—
474SD16—448no—
475SD16—448no—
476D8—448no—
477M16—228no—
478C2×C8—118no—
479C4⋊C4—114no—
480C4⋊C4—224no—
481C4⋊C4—222no—
482C4⋊C4—222no—
483C4⋊C4—224no—
484C4⋊C4—224no—
485C22⋊C4—28no—
486C22⋊C4—28no—
487C22⋊C4—28no—
488C22⋊C4—28no—
489C22⋊C4—222no—
490C22⋊C4—224no—
491C22⋊C4—224no—
492C22⋊C4—224no—
493C22⋊C4—224no—
494C42—222no—
495C42—224no—
496C42C2×C22⋊D1111yescharacteristic
497C42C2×C22⋊D1112yes—
498C42C2×C22⋊D1111yescharacteristic
499C42C2×C22⋊D1112yes—
500C42C2×C22⋊D1112yes—
501C42C2×C22⋊D1112yes—
502C42C2×C22⋊D1112yes—
503C42C23×D1111yescharacteristic
504C42C23×D1111yescharacteristic
505C42C23×D1112yes—
506C11#6079911yescharacteristic, complemented, Sylow
507C23—22no—
508C23—24no—
509C23—24no—
510C23—48no—
511C23—48no—
512C23—48no—
513C23—44no—
514C23—48no—
515C23—816no—
516C23—222no—
517C23C22×C22⋊D1111yescharacteristic
518C23C22×C22⋊D1112yes—
519Q8—28no—
520Q8—48no—
521Q8—44no—
522Q8—224no—
523Q8—444no—
524D4—28no—
525D4—48no—
526D4—44no—
527D4—224no—
528D4—444no—
529D4—444no—
530D4—448no—
531C2×C4—22no—
532C2×C4—24no—
533C2×C4—24no—
534C2×C4—24no—
535C2×C4—24no—
536C2×C4—24no—
537C2×C4—42no—
538C2×C4—42no—
539C2×C4—42no—
540C2×C4—42no—
541C2×C4—48no—
542C2×C4—44no—
543C2×C4—224no—
544C2×C4—222no—
545C2×C4—448no—
546C2×C4—444no—
547C2×C4#6703714yes—
548C2×C4C22×C22⋊D1112yes—
549C2×C4C22×C22⋊D1112yes—
550C2×C4C22×C22⋊D1112yes—
551C2×C4C22×C22⋊D1112yes—
552C2×C4C22×C22⋊D1112yes—
553C2×C4C22×C22⋊D1111yescharacteristic
554C2×C4C24×D1111yescharacteristic
555C8—228no—
556C22—28no—
557C22—22no—
558C22—22no—
559C22—22no—
560C22—44no—
561C22—48no—
562C22—88no—
563C22—816no—
564C22—442no—
565C22—444no—
566C22#1062333612yes—
567C22#1062335314yes—
568C22C23×C22⋊D1111yescharacteristic
569C4—22no—
570C4—22no—
571C4—22no—
572C4—22no—
573C4—22no—
574C4—44no—
575C4—442no—
576C4—444no—
577C4#1062333612yes—
578C4C2×#6703712yes—
579C2—22no—
580C2—24no—
581C2—84no—
582C2—882no—
583C2C2×#1062333611yescharacteristic
584C2C2×#1062335312yes—
subgroupG/H
centerC22C23×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC22×C11×#124C2
socleC22×C11C23×D4
hypercenterC22×#124D11
hypocenterC11#60799
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C42 ◁ C22×#124

Complements

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

NH ≅ G/Ntype
1. #13081912C2semidirect
2. #13079619C2semidirect
3. #13079603C2semidirect
4. #13079581C2semidirect
5. #13079080C2semidirect
6. #13079002C2semidirect
7. #13078106C2semidirect
8. #13077850C2semidirect
9. #13077843C2semidirect
10. #13077249C2semidirect
11. C22×C11×#124C2semidirect
23. C2×#66995C22semidirect
29. #10623010C22semidirect
30. #10623008C22semidirect
31. #10623008C22semidirect
33. C4×#4339C22semidirect
34. #10623001C22semidirect
35. #10623001C22semidirect
36. #10622841C22semidirect
37. #10622840C22semidirect
38. #10622838C22semidirect
43. #10622673C22semidirect
44. #10622672C22semidirect
45. #10622671C22semidirect
46. #10622670C22semidirect
47. #10622669C22semidirect
48. #10622668C22semidirect
49. #10622667C22semidirect
50. #10622539C22semidirect
51. #10622538C22semidirect
52. #10622537C22semidirect
53. C4×#4318C22semidirect
94. C2×#4326C23semidirect
96. C2×#4325C23semidirect
116. #66928C23semidirect
117. #66927C23semidirect
120. C4×D44C23semidirect
125. #66923C23semidirect
126. #66922C23semidirect
127. #66922C23semidirect
130. C4×Dic22C23semidirect
131. #66899C23semidirect
134. C4⋊(C11⋊C8)C23semidirect
135. #66867C23semidirect
136. C4×C11⋊C8C23semidirect
216. C22×#124D11semidirect
506. C11#60799semidirect

Maximal subgroups

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

subgroupindex
#130819122
#130796192
#130796032
#130795812
#130790802
#130790022
#130781062
#130778502
#130778432
#130772492
C22×C11×#1242
#6079911