Finite Group Databasebeta

← #15626363

Subgroups — #15626363

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#13082493C211yesmaximal, characteristic
2#13082440C211yesmaximal, characteristic, complemented
3#13079872C218yesmaximal, complemented
4#13079815C214yesmaximal, complemented
5#13079807C214yesmaximal, complemented
6#13079138C211yesmaximal, characteristic, complemented
7#13078991C211yesmaximal, characteristic, complemented
8C2×#10622680C211yesmaximal, characteristic, complemented
9#13078576C214yesmaximal, complemented
10#13078445C214yesmaximal, complemented
11#13077268C211yesmaximal, characteristic, complemented
12C11×#3166C211yesmaximal, characteristic, complemented
13C11×#533C2211yescharacteristic
14C2×C11×#125C2211yescharacteristic
15#10623256C2214yes—
16#10623229C2214yes—
17#10623221—22no—
18#10623220C2214yescomplemented
19#10623219C2212yescomplemented
20D11×#125C2212yescomplemented
21#10623216—22no—
22#10623161—24no—
23#10623116—22no—
24#10623108—22no—
25#10623056C2212yes—
26#10623052C2212yes—
27#10623042—24no—
28#10623035C2212yes—
29#10623031C2212yes—
30C2×#66927C2211yescharacteristic
31C4×#4339C2211yescharacteristic
32#10623001C2211yescharacteristic
33C11×#501C2214yescomplemented
34C11×#499C2214yescomplemented
35C11×#428C2214yes—
36C4×C11×M16C2211yescharacteristic
37#10622744C2214yes—
38#10622742C2212yes—
39#10622732C2212yes—
40#10622693C2212yescomplemented
41#10622693C2212yescomplemented
42#10622680C2214yes—
43#10622680C2214yes—
44#10622678C2214yescomplemented
45#10622611C2214yes—
46C2×#66873C2214yes—
47C2×#66867C2211yescharacteristic
48#10622504C2218yescomplemented
49#10622503C2218yescomplemented
50#10622498C2218yescomplemented
51#10622495C2218yescomplemented
52#10622484C2218yescomplemented
53#10622483C2218yescomplemented
54#10622479C2218yescomplemented
55#10622476C2218yescomplemented
56#10622326C2212yes—
57#10622326C2212yes—
58#10622318C2214yescomplemented
59#10622307C2214yes—
60#10622303C2214yescomplemented
61C2×#4343—24no—
62C2×#4339C2311yescharacteristic
63C22×D44—22no—
64C22×D44C2312yes—
65C2×C11×M16C2312yes—
66C11×C4⋊Q8C2312yes—
67C11×#125—22no—
68C11×#125C2312yes—
69C11×#125C2312yes—
70C11×#125C2312yes—
71C11×C22⋊Q8—22no—
72C4×Q8×C11—22no—
73C11×#117C2312yes—
74C2×C11×C4⋊C4—22no—
75C2×C11×C4⋊C4C2312yes—
76C2×C42×C11C2311yescharacteristic
77#67000—24no—
78C4×C22⋊D11—24no—
79C4×C22⋊D11D414yes—
80#66979C2312yes—
81#66979C2311yescharacteristic
82#66977—22no—
83#66977—24no—
84C22×C11⋊C8C2312yes—
85#66950—24no—
86#66949—24no—
87#66949—24no—
88#66948—24no—
89#66948—28no—
90#66948C2318yes—
91#66947—28no—
92#66946—22no—
93#66946—24no—
94#66946C2318yes—
95#66945C2314yes—
96C4⋊C4×D11—24no—
97C4⋊C4×D11C2314yes—
98#66943—22no—
99#66943C2314yes—
100#66942—24no—
101#66942—24no—
102#66941—22no—
103#66941—24no—
104#66941C2314yes—
105#66940—22no—
106#66940—24no—
107#66935—24no—
108C22⋊C4×D11—24no—
109#66928—22no—
110#66927—22no—
111#66927—22no—
112#66927C2312yes—
113#66927C2312yes—
114C4×D44—24no—
115C4×D44D412yes—
116#66925C2312yes—
117C42×D11C2312yes—
118#66923C2311yescharacteristic
119#66923C2311yescharacteristic
120#66922C2312yes—
121C4×Dic22—22no—
122C4×Dic22D412yes—
123C11×#107C2318yes—
124C11×#106C2318yes—
125C11×#97C2312yes—
126C4×C8×C11C2312yes—
127#66885C2318yes—
128#66885C2318yes—
129(C2×D11)⋊C8C2318yes—
130Dic11⋊C8C2318yes—
131#66873C2318yes—
132#66873C2318yes—
133#66872C2314yes—
134#66872C2314yes—
135#66871C2314yes—
136#66871C2314yes—
137#66867C2312yes—
138#66867C2312yes—
139#60883—111nomaximal, Sylow
140C23×D11—22no—
141C2×Q8×C11—22no—
142C22×C4×C11—22no—
143C22×C4×C11C2×D412yes—
144C22×C4×C11C2411yescharacteristic
145C2×C22⋊D11C2×D412yes—
146#4343—88no—
147#4339—24no—
148C2×D44—28no—
149C2×D44—22no—
150C2×D44—24no—
151C2×D44—24no—
152C2×D44—28no—
153C2×D44—84no—
154C2×D44C2×D411yescharacteristic
155C2×D44C2414yes—
156C2×C4×D11—28no—
157C2×C4×D11—24no—
158C2×C4×D11C2×D414yes—
159C2×C4×D11C2412yes—
160C2×Dic22—24no—
161C2×Dic22—22no—
162C2×Dic22C2×D411yescharacteristic
163C11×M16—24no—
164C2×C8×C11C2414yes—
165C11×C4⋊C4—22no—
166C11×C4⋊C4—24no—
167C11×C4⋊C4—24no—
168C11×C4⋊C4—22no—
169C11×C4⋊C4—24no—
170C11×C4⋊C4C2414yes—
171C11×C4⋊C4C2414yes—
172C11×C22⋊C4—22no—
173C42×C11—22no—
174C42×C11C2×D412yes—
175C42×C11C2411yescharacteristic
176C42×C11C2411yescharacteristic
177C22⋊Dic11—22no—
178C22⋊Dic11C2×D412yes—
179(C2×D11)⋊C4—28no—
180(C2×D11)⋊C4—28no—
181(C2×D11)⋊C4—24no—
182(C2×D11)⋊C4C2×D414yes—
183C4⋊Dic11—24no—
184C4⋊Dic11—22no—
185C4⋊Dic11C2×D412yes—
186C4⋊Dic11C2412yes—
187C4⋊Dic11C2412yes—
188Dic11⋊C4—24no—
189Dic11⋊C4—24no—
190Dic11⋊C4—24no—
191Dic11⋊C4—22no—
192Dic11⋊C4—22no—
193Dic11⋊C4C2×D414yes—
194C4×Dic11—24no—
195C4×Dic11—22no—
196C4×Dic11C2×D414yes—
197C4×Dic11C2412yes—
198C2×C11⋊C8—24no—
199C2×C11⋊C8C2414yes—
200#3508—111no—
201#3504—111no—
202#3241—118no—
203#3235—114no—
204#3234—114no—
205#3166D1111yescharacteristic, complemented
206#3162—111no—
207#3138—111no—
208C2×#490—111no—
209#3096—114no—
210#3081—114no—
211#2923—111no—
212C23×C11C22×D411yescharacteristic
213C22×D11—24no—
214C22×D11—44no—
215C22×D11—84no—
216C22×D11C22×D412yes—
217Q8×C11—44no—
218C2×C4×C11—24no—
219C2×C4×C11—24no—
220C2×C4×C11—42no—
221C2×C4×C11—82no—
222C2×C4×C11C22×D412yes—
223C2×C4×C11C22×D412yes—
224C2×C4×C11C22×D411yescharacteristic
225C2×C4×C112−1+414yes—
226C2×C4×C11C2511yescharacteristic
227C22⋊D11—24no—
228C2×Dic11—22no—
229C2×Dic11—22no—
230C2×Dic11C22×D412yes—
231C2×Dic11C22×D414yes—
232D44—22no—
233D44—28no—
234D44—48no—
235D44—44no—
236D44—84no—
237D44—88no—
238C4×D11—24no—
239C4×D11—44no—
240C4×D11—88no—
241C4×D11—84no—
242Dic22—22no—
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#533C2×D1111yescharacteristic
260#532—114no—
261C2×#127—111no—
262C2×#125—112no—
263C2×#125C2×D1111yescharacteristic
264#520—112no—
265#518—112no—
266C4×#41—111no—
267#501—112no—
268#501—112no—
269#501—114no—
270#501C2×D1114yescomplemented
271#499C2×D1114yescomplemented
272#490—114no—
273#490—114no—
274#490—112no—
275#490—112no—
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#428C2×D1114yes—
288#427—114no—
289#424—112no—
290#418—114no—
291C2×#102—114no—
292#408—112no—
293C4×M16C2×D1111yescharacteristic
294C2×#97—111no—
295C22×C11—22no—
296C22×C11#53612yes—
297C22×C11C23×D411yescharacteristic
298C2×D11—24no—
299C2×D11—22no—
300C2×D11—48no—
301C2×D11—44no—
302C2×D11—164no—
303C4×C11—22no—
304C4×C11—22no—
305C4×C11—44no—
306C4×C11—44no—
307C4×C11#53612yes—
308C4×C11C2×2−1+412yes—
309Dic11—24no—
310Dic11—22no—
311Dic11—42no—
312Dic11—42no—
313C2×#41—111no—
314C2×#41—224no—
315C22×D4—112no—
316C22×D4—222no—
317C2×M16C22×D1112yes—
318C22×C8—112no—
319C4⋊Q8—114no—
320C4⋊Q8—112no—
321C4⋊Q8—224no—
322C4⋊Q8—222no—
323C4⋊Q8C22×D1112yes—
324#127—112no—
325#127—112no—
326#127—222no—
327#127—222no—
328#125—22no—
329#125—114no—
330#125—111no—
331#125—111no—
332#125—224no—
333#125—224no—
334#125—222no—
335#125C22×D1112yes—
336#125C22×D1112yes—
337#125C22×D1112yes—
338#124—222no—
339#124—224no—
340#123—228no—
341C22⋊Q8—22no—
342C22⋊Q8—224no—
343C22⋊Q8—224no—
344C22⋊Q8—224no—
345C22⋊Q8—224no—
346C22⋊Q8—222no—
347#121—118no—
348#121—228no—
349#121—224no—
350#120—224no—
351C4×Q8—22no—
352C4×Q8—112no—
353C4×Q8—224no—
354C4×Q8—222no—
355C4×Q8—222no—
356C4×D4—114no—
357C4×D4—118no—
358C4×D4—112no—
359C4×D4—224no—
360C4×D4—224no—
361C4×D4—222no—
362C4×D4—224no—
363#117—111no—
364#117—112no—
365#117—112no—
366#117—114no—
367#117C22×D1112yes—
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#107C22×D1118yes—
378#106—114no—
379#106—114no—
380#106C22×D1118yes—
381C4⋊C8—118no—
382#102—118no—
383#102—118no—
384#102—118no—
385#102—118no—
386C22⋊C8—118no—
387#97—112no—
388#97—112no—
389#97C22×D1112yes—
390C4×C8C22×D1112yes—
391C2×C11—22no—
392C2×C11C2×#53611yescharacteristic
393C2×C11#358512yes—
394D11—42no—
395D11—84no—
396C24—222no—
397#41—224no—
398#41—888no—
399C2×Q8—22no—
400C2×Q8—111no—
401C2×Q8—224no—
402C2×Q8—222no—
403C2×D4—112no—
404C2×D4—111no—
405C2×D4—114no—
406C2×D4—228no—
407C2×D4—222no—
408C2×D4—224no—
409C2×D4—224no—
410C2×D4—228no—
411C2×D4—884no—
412C22×C4—22no—
413C22×C4—112no—
414C22×C4—114no—
415C22×C4—228no—
416C22×C4—224no—
417C22×C4D4×D1112yes—
418C22×C4C23×D1111yescharacteristic
419M16—24no—
420C2×C8—114no—
421C2×C8—224no—
422C2×C8C23×D1114yes—
423C4⋊C4—24no—
424C4⋊C4—24no—
425C4⋊C4—22no—
426C4⋊C4—22no—
427C4⋊C4—24no—
428C4⋊C4—112no—
429C4⋊C4—114no—
430C4⋊C4—112no—
431C4⋊C4—112no—
432C4⋊C4—224no—
433C4⋊C4—224no—
434C4⋊C4—224no—
435C4⋊C4—224no—
436C4⋊C4—222no—
437C4⋊C4—222no—
438C4⋊C4—222no—
439C4⋊C4C23×D1114yes—
440C4⋊C4C23×D1114yes—
441C22⋊C4—22no—
442C22⋊C4—112no—
443C22⋊C4—114no—
444C22⋊C4—228no—
445C22⋊C4—228no—
446C22⋊C4—224no—
447C22⋊C4—222no—
448C42—22no—
449C42—114no—
450C42—112no—
451C42—224no—
452C42—222no—
453C42D4×D1112yes—
454C42C23×D1111yescharacteristic
455C42C23×D1111yescharacteristic
456C11#6088311yescharacteristic, complemented, Sylow
457C23—112no—
458C23—224no—
459C23—444no—
460C23—884no—
461C23C2×D4×D1111yescharacteristic
462Q8—44no—
463Q8—222no—
464Q8—882no—
465Q8—884no—
466D4—224no—
467D4—222no—
468D4—228no—
469D4—448no—
470D4—444no—
471D4—884no—
472D4—888no—
473C2×C4—24no—
474C2×C4—24no—
475C2×C4—42no—
476C2×C4—82no—
477C2×C4—112no—
478C2×C4—114no—
479C2×C4—224no—
480C2×C4—222no—
481C2×C4—222no—
482C2×C4—444no—
483C2×C4—888no—
484C2×C4—884no—
485C2×C4C2×D4×D1112yes—
486C2×C4C2×D4×D1112yes—
487C2×C4C2×D4×D1111yescharacteristic
488C2×C4#6704014yes—
489C2×C4C24×D1111yescharacteristic
490C8—24no—
491C8—224no—
492C22—22no—
493C22—224no—
494C22—222no—
495C22—448no—
496C22—444no—
497C22—1764no—
498C22#1062325512yes—
499C22C22×D4×D1111yescharacteristic
500C4—22no—
501C4—22no—
502C4—44no—
503C4—44no—
504C4—224no—
505C4—222no—
506C4—442no—
507C4—442no—
508C4#1062325512yes—
509C4C2×#6704012yes—
510C2—22no—
511C2—442no—
512C2—884no—
513C2C2×#1062325511yescharacteristic
514C2#1308339312yes—
subgroupG/H
centerC22C22×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC11×#3166C2
socleC22×C11C23×D4
prime radical#13082493C2
hypercenter#3166D11
hypocenterC11#60883
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3166

Complements

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

NH ≅ G/Ntype
2. #13082440C2semidirect
3. #13079872C2semidirect
4. #13079815C2semidirect
5. #13079807C2semidirect
6. #13079138C2semidirect
7. #13078991C2semidirect
8. C2×#10622680C2semidirect
9. #13078576C2semidirect
10. #13078445C2semidirect
11. #13077268C2semidirect
12. C11×#3166C2semidirect
18. #10623220C22semidirect
19. #10623219C22semidirect
20. D11×#125C22semidirect
33. C11×#501C22semidirect
34. C11×#499C22semidirect
40. #10622693C22semidirect
41. #10622693C22semidirect
44. #10622678C22semidirect
48. #10622504C22semidirect
49. #10622503C22semidirect
50. #10622498C22semidirect
51. #10622495C22semidirect
52. #10622484C22semidirect
53. #10622483C22semidirect
54. #10622479C22semidirect
55. #10622476C22semidirect
58. #10622318C22semidirect
60. #10622303C22semidirect
205. #3166D11semidirect
270. #501C2×D11semidirect
271. #499C2×D11semidirect
456. C11#60883semidirect

Maximal subgroups

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

subgroupindex
#130824932
#130824402
#130798722
#130798152
#130798072
#130791382
#130789912
C2×#106226802
#130785762
#130784452
#130772682
C11×#31662
#6088311