Finite Group Databasebeta

← #15626355

Subgroups — #15626355

Order 2816.

1742 conjugacy classes of subgroups.

The subgroup lattice has 516 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082490C211yesmaximal, characteristic
2#13082440C211yesmaximal, characteristic, complemented
3#13079864C218yesmaximal, complemented
4#13079809C214yesmaximal, complemented
5#13079801C214yesmaximal, complemented
6#13079165C211yesmaximal, characteristic, complemented
7#13079140C211yesmaximal, characteristic, complemented
8#13078990C211yesmaximal, characteristic, complemented
9#13078570C214yesmaximal, complemented
10#13078443C214yesmaximal, complemented
11#13077265C211yesmaximal, characteristic, complemented
12C2×C11×#490C211yesmaximal, characteristic, complemented
13C2×C11×#127C2211yescharacteristic
14C2×C11×#125C2211yescharacteristic
15#10623337—24no—
16#10623336C2212yes—
17#10623329C2212yes—
18#10623250C2214yes—
19#10623249—22no—
20#10623247C2214yes—
21#10623244—22no—
22#10623221—22no—
23#10623220C2214yescomplemented
24#10623219C2212yescomplemented
25D11×#125C2212yescomplemented
26#10623216—22no—
27#10623042—24no—
28#10623035C2212yes—
29#10623031C2212yes—
30C4×#4339C2211yescharacteristic
31#10623001C2211yescharacteristic
32#10623001C2211yescharacteristic
33C11×#490C2214yes—
34C11×#490C2214yes—
35C2×C11×#102C2214yes—
36C2×C11×#97C2211yescharacteristic
37#10622828C2214yes—
38#10622723C2212yes—
39#10622719C2214yes—
40#10622715C2212yes—
41#10622684C2212yes—
42#10622684C2212yes—
43#10622683C2214yes—
44#10622678C2214yescomplemented
45#10622677C2214yescomplemented
46#10622577C2214yes—
47C4×#4318C2211yescharacteristic
48#10622397C2218yescomplemented
49#10622392C2218yescomplemented
50#10622390C2218yescomplemented
51#10622387C2218yescomplemented
52#10622379C2218yescomplemented
53#10622376C2218yescomplemented
54#10622374C2218yescomplemented
55#10622372C2218yescomplemented
56#10622322C2214yescomplemented
57#10622318C2214yescomplemented
58#10622315C2212yescomplemented
59#10622315C2214yescomplemented
60#10622315C2212yescomplemented
61C22×D4×C11—22no—
62C22×D4×C11C2312yes—
63C2×#4341—24no—
64C2×#4339C2311yescharacteristic
65C22×C8×C11C2312yes—
66C11×#127—22no—
67C11×#127C2312yes—
68C11×#127C2312yes—
69C11×#125—22no—
70C11×#125C2312yes—
71C11×#125C2312yes—
72C2×C11×C4⋊C4—22no—
73C2×C11×C4⋊C4C2312yes—
74C2×C42×C11C2311yescharacteristic
75#67006—24no—
76C2×C22⋊Dic11—24no—
77#66993—22no—
78#66992—28no—
79#66991—24no—
80#66991C2318yes—
81#66989—22no—
82#66989—24no—
83#66988—28no—
84D4×Dic11—24no—
85D4×Dic11—24no—
86D4×Dic11C2318yes—
87C4×C22⋊D11—24no—
88C4×C22⋊D11D414yes—
89#66979C2312yes—
90#66979C2312yes—
91#66979C2311yescharacteristic
92#66977—22no—
93#66977—22no—
94#66977—24no—
95C2×#4318C2312yes—
96#66950—24no—
97#66949—24no—
98#66949—24no—
99#66946—22no—
100#66945C2314yes—
101C4⋊C4×D11—24no—
102C4⋊C4×D11C2314yes—
103#66943—22no—
104#66943C2314yes—
105#66942—24no—
106#66942—24no—
107#66941—22no—
108#66941—24no—
109#66941C2314yes—
110#66940—22no—
111#66940—24no—
112C4×D44D412yes—
113#66925C2312yes—
114C42×D11C2312yes—
115#66923C2312yes—
116#66923C2311yescharacteristic
117#66923C2311yescharacteristic
118#66922C2312yes—
119#66922C2312yes—
120C4×Dic22—22no—
121C4×Dic22—22no—
122C4×Dic22D412yes—
123C11×#102C2318yes—
124C11×#102C2318yes—
125C11×#97C2312yes—
126C11×#97C2312yes—
127#66896C2318yes—
128#66896C2318yes—
129(C2×D11)⋊C8C2318yes—
130#66882C2314yes—
131#66882C2314yes—
132#66881C2314yes—
133#66881C2314yes—
134Dic11⋊C8C2318yes—
135#66872C2318yes—
136#66871C2318yes—
137#66867C2312yes—
138C4×C11⋊C8C2312yes—
139#60883—111nomaximal, Sylow
140C24×C11—22no—
141C2×D4×C11—22no—
142C2×D4×C11—24no—
143C2×D4×C11—24no—
144C2×D4×C11—28no—
145C2×D4×C11—84no—
146C2×D4×C11C2414yes—
147C22×C4×C11—22no—
148C22×C4×C11C2×D412yes—
149C22×C4×C11C2411yescharacteristic
150C2×C22⋊D11—28no—
151C2×C22⋊D11C2×D412yes—
152C22×Dic11—28no—
153#4341—88no—
154#4339—24no—
155C2×D44C2×D411yescharacteristic
156C2×C4×D11—24no—
157C2×C4×D11C2×D414yes—
158C2×C4×D11C2412yes—
159C2×Dic22—24no—
160C2×Dic22—22no—
161C2×Dic22—22no—
162C2×Dic22C2×D411yescharacteristic
163C2×C8×C11—24no—
164C2×C8×C11C2414yes—
165C11×C4⋊C4—22no—
166C11×C4⋊C4—24no—
167C11×C4⋊C4—24no—
168C11×C4⋊C4C2414yes—
169C42×C11C2×D412yes—
170C42×C11C2411yescharacteristic
171C42×C11C2411yescharacteristic
172C22⋊Dic11—28no—
173C22⋊Dic11—28no—
174C22⋊Dic11—22no—
175C22⋊Dic11—22no—
176C22⋊Dic11C2×D412yes—
177(C2×D11)⋊C4—24no—
178(C2×D11)⋊C4C2×D414yes—
179C4⋊Dic11—24no—
180C4⋊Dic11—22no—
181C4⋊Dic11—22no—
182C4⋊Dic11C2×D412yes—
183C4⋊Dic11C2414yes—
184C4⋊Dic11C2412yes—
185C4⋊Dic11C2412yes—
186Dic11⋊C4—24no—
187Dic11⋊C4—24no—
188Dic11⋊C4—24no—
189Dic11⋊C4—22no—
190Dic11⋊C4—22no—
191Dic11⋊C4—24no—
192Dic11⋊C4C2×D414yes—
193C4×Dic11—24no—
194C4×Dic11—22no—
195C4×Dic11—22no—
196C4×Dic11C2×D414yes—
197C4×Dic11C2412yes—
198#4318—24no—
199C2×C11⋊C8C2414yes—
200#3508—111no—
201#3504—111no—
202#3241—118no—
203#3235—114no—
204#3234—114no—
205#3166—111no—
206#3162—111no—
207#3138—111no—
208C2×#490D1111yescharacteristic, complemented
209#3096—114no—
210#3081—114no—
211#2923—111no—
212C23×C11—24no—
213C23×C11—44no—
214C23×C11—84no—
215C23×C11C22×D411yescharacteristic
216C22×D11C22×D412yes—
217D4×C11—28no—
218D4×C11—48no—
219D4×C11—44no—
220D4×C11—84no—
221C2×C4×C11—24no—
222C2×C4×C11—42no—
223C2×C4×C11—82no—
224C2×C4×C11C22×D412yes—
225C2×C4×C11C22×D412yes—
226C2×C4×C11C22×D411yescharacteristic
227C2×C4×C112−1+414yes—
228C2×C4×C11C2511yescharacteristic
229C22⋊D11—24no—
230C22⋊D11—88no—
231C2×Dic11—22no—
232C2×Dic11—22no—
233C2×Dic11—24no—
234C2×Dic11—88no—
235C2×Dic11C22×D412yes—
236C2×Dic11C22×D414yes—
237D44—22no—
238C4×D11—24no—
239C4×D11—44no—
240C4×D11—84no—
241Dic22—22no—
242Dic22—44no—
243Dic22—84no—
244Dic22—82no—
245C8×C11—24no—
246C11⋊C8—24no—
247#559—222no—
248#557—222no—
249#554—224no—
250#554—222no—
251#550—222no—
252#546—224no—
253#544—114no—
254#544—112no—
255#540—114no—
256#535—112no—
257#533—112no—
258#533—111no—
259#533—111no—
260#532—114no—
261C2×#127C2×D1111yescharacteristic
262C2×#125—112no—
263C2×#125C2×D1111yescharacteristic
264#520—112no—
265#518—112no—
266C4×#41—111no—
267#501—114no—
268#501—112no—
269#501—112no—
270#501—114no—
271#499—114no—
272#490—112no—
273#490—112no—
274#490C2×D1114yes—
275#490C2×D1114yes—
276#486—114no—
277#482—118no—
278#482—118no—
279#481—118no—
280#480—118no—
281#478—118no—
282#478—118no—
283#476—118no—
284#474—118no—
285#433—114no—
286#432—114no—
287#428—114no—
288#427—114no—
289#424—112no—
290#418—114no—
291C2×#102C2×D1114yes—
292#408—112no—
293C4×M16—111no—
294C2×#97C2×D1111yescharacteristic
295C22×C11—22no—
296C22×C11—48no—
297C22×C11—44no—
298C22×C11—164no—
299C22×C11#53612yes—
300C22×C11C23×D411yescharacteristic
301C2×D11—24no—
302C2×D11—22no—
303C4×C11—22no—
304C4×C11—22no—
305C4×C11—44no—
306C4×C11#53612yes—
307C4×C11C2×2−1+412yes—
308Dic11—24no—
309Dic11—22no—
310Dic11—44no—
311Dic11—42no—
312Dic11—42no—
313C2×#41—111no—
314C2×#41—224no—
315C22×D4—22no—
316C22×D4C22×D1112yes—
317C2×M16—112no—
318C22×C8C22×D1112yes—
319C4⋊Q8—114no—
320C4⋊Q8—112no—
321C4⋊Q8—112no—
322C4⋊Q8—224no—
323C4⋊Q8—222no—
324#127—22no—
325#127—222no—
326#127C22×D1112yes—
327#127C22×D1112yes—
328#125—22no—
329#125—114no—
330#125—111no—
331#125—111no—
332#125—112no—
333#125—224no—
334#125—224no—
335#125—222no—
336#125C22×D1112yes—
337#125C22×D1112yes—
338#124—224no—
339#124—222no—
340#123—228no—
341C22⋊Q8—224no—
342C22⋊Q8—224no—
343C22⋊Q8—224no—
344C22⋊Q8—224no—
345C22⋊Q8—222no—
346C22⋊Q8—222no—
347#121—118no—
348#121—228no—
349#121—224no—
350#120—224no—
351C4×Q8—112no—
352C4×Q8—224no—
353C4×Q8—222no—
354C4×Q8—222no—
355C4×Q8—222no—
356C4×D4—114no—
357C4×D4—118no—
358C4×D4—112no—
359C4×D4—224no—
360C4×D4—222no—
361C4×D4—224no—
362C4×D4—224no—
363#117—111no—
364#117—112no—
365#117—112no—
366#117—112no—
367#117—114no—
368C2×C4⋊C4—22no—
369C2×C4⋊C4—114no—
370C2×C4⋊C4—224no—
371C2×C4⋊C4C22×D1112yes—
372C2×C22⋊C4—224no—
373C2×C42—112no—
374C2×C42C22×D1111yescharacteristic
375#107—114no—
376#107—114no—
377#107—118no—
378#106—114no—
379#106—114no—
380#106—118no—
381C4⋊C8—118no—
382#102—118no—
383#102—118no—
384#102C22×D1118yes—
385#102C22×D1118yes—
386C22⋊C8—118no—
387#97—112no—
388#97C22×D1112yes—
389#97C22×D1112yes—
390C4×C8—112no—
391C2×C11—22no—
392C2×C11—84no—
393C2×C11C2×#53611yescharacteristic
394C2×C11#358512yes—
395D11—42no—
396C24—22no—
397#41—224no—
398#41—888no—
399C2×Q8—111no—
400C2×Q8—224no—
401C2×Q8—222no—
402C2×Q8—222no—
403C2×D4—22no—
404C2×D4—24no—
405C2×D4—24no—
406C2×D4—28no—
407C2×D4—84no—
408C2×D4—112no—
409C2×D4—111no—
410C2×D4—228no—
411C2×D4C23×D1114yes—
412C22×C4—22no—
413C22×C4—112no—
414C22×C4—114no—
415C22×C4—224no—
416C22×C4—228no—
417C22×C4D4×D1112yes—
418C22×C4C23×D1111yescharacteristic
419M16—224no—
420C2×C8—24no—
421C2×C8—114no—
422C2×C8C23×D1114yes—
423C4⋊C4—24no—
424C4⋊C4—24no—
425C4⋊C4—22no—
426C4⋊C4—112no—
427C4⋊C4—114no—
428C4⋊C4—112no—
429C4⋊C4—112no—
430C4⋊C4—114no—
431C4⋊C4—224no—
432C4⋊C4—224no—
433C4⋊C4—224no—
434C4⋊C4—224no—
435C4⋊C4—222no—
436C4⋊C4—222no—
437C4⋊C4—222no—
438C4⋊C4—224no—
439C4⋊C4—222no—
440C4⋊C4C23×D1114yes—
441C22⋊C4—112no—
442C22⋊C4—114no—
443C22⋊C4—224no—
444C22⋊C4—228no—
445C22⋊C4—228no—
446C22⋊C4—222no—
447C22⋊C4—222no—
448C42—114no—
449C42—112no—
450C42—224no—
451C42—222no—
452C42—222no—
453C42D4×D1112yes—
454C42C23×D1111yescharacteristic
455C42C23×D1111yescharacteristic
456C11#6088311yescharacteristic, complemented, Sylow
457C23—24no—
458C23—44no—
459C23—84no—
460C23—112no—
461C23C2×D4×D1111yescharacteristic
462Q8—222no—
463Q8—444no—
464Q8—882no—
465Q8—884no—
466D4—28no—
467D4—48no—
468D4—44no—
469D4—84no—
470D4—224no—
471D4—222no—
472D4—888no—
473C2×C4—24no—
474C2×C4—42no—
475C2×C4—82no—
476C2×C4—112no—
477C2×C4—114no—
478C2×C4—224no—
479C2×C4—222no—
480C2×C4—224no—
481C2×C4—222no—
482C2×C4—444no—
483C2×C4—884no—
484C2×C4—888no—
485C2×C4C2×D4×D1112yes—
486C2×C4C2×D4×D1112yes—
487C2×C4C2×D4×D1111yescharacteristic
488C2×C4#6704314yes—
489C2×C4C24×D1111yescharacteristic
490C8—24no—
491C8—224no—
492C22—22no—
493C22—48no—
494C22—44no—
495C22—164no—
496C22—224no—
497C22—222no—
498C22#1062320612yes—
499C22C22×D4×D1111yescharacteristic
500C4—22no—
501C4—22no—
502C4—44no—
503C4—224no—
504C4—222no—
505C4—444no—
506C4—442no—
507C4—442no—
508C4#1062320612yes—
509C4C2×#6704312yes—
510C2—22no—
511C2—84no—
512C2—442no—
513C2C2×#1062320611yescharacteristic
514C2#1308339212yes—
subgroupG/H
centerC22C22×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#490C2
socleC22×C11C23×D4
prime radical#13082490C2
hypercenterC2×#490D11
hypocenterC11#60883
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#490

Complements

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

NH ≅ G/Ntype
2. #13082440C2semidirect
3. #13079864C2semidirect
4. #13079809C2semidirect
5. #13079801C2semidirect
6. #13079165C2semidirect
7. #13079140C2semidirect
8. #13078990C2semidirect
9. #13078570C2semidirect
10. #13078443C2semidirect
11. #13077265C2semidirect
12. C2×C11×#490C2semidirect
23. #10623220C22semidirect
24. #10623219C22semidirect
25. D11×#125C22semidirect
44. #10622678C22semidirect
45. #10622677C22semidirect
48. #10622397C22semidirect
49. #10622392C22semidirect
50. #10622390C22semidirect
51. #10622387C22semidirect
52. #10622379C22semidirect
53. #10622376C22semidirect
54. #10622374C22semidirect
55. #10622372C22semidirect
56. #10622322C22semidirect
57. #10622318C22semidirect
58. #10622315C22semidirect
59. #10622315C22semidirect
60. #10622315C22semidirect
208. C2×#490D11semidirect
456. C11#60883semidirect

Maximal subgroups

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

subgroupindex
#130824902
#130824402
#130798642
#130798092
#130798012
#130791652
#130791402
#130789902
#130785702
#130784432
#130772652
C2×C11×#4902
#6088311