Finite Group Databasebeta

← #15626362

Subgroups — #15626362

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#13082492C211yesmaximal, characteristic
2#13079869C218yesmaximal, complemented
3#13079814C214yesmaximal, complemented
4#13079806C214yesmaximal, complemented
5#13079165C211yesmaximal, characteristic, complemented
6#13079138C211yesmaximal, characteristic, complemented
7#13078992C211yesmaximal, characteristic, complemented
8C2×#10622680C211yesmaximal, characteristic, complemented
9#13078574C214yesmaximal, complemented
10#13078441C214yesmaximal, complemented
11#13077267C211yesmaximal, characteristic, complemented
12C11×#3504C211yesmaximal, characteristic, complemented
13C11×#557—22no—
14C11×#554—24no—
15C11×#554—22no—
16C11×#544C2212yes—
17C11×#544C2214yescomplemented
18C11×#533C2211yescharacteristic
19C11×#533C2212yescomplemented
20C2×C11×#125C2211yescharacteristic
21C2×C11×#125C2212yescomplemented
22C11×#520C2212yes—
23C4×C11×#41C2211yescharacteristic
24#10623361C2212yes—
25#10623116—22no—
26#10623084—22no—
27#10623081—24no—
28#10623066C2214yes—
29#10623052C2212yes—
30#10623008C2214yes—
31C2×#66927C2211yescharacteristic
32#10623001C2211yescharacteristic
33#10622847C2212yes—
34#10622701C2214yes—
35#10622700C2218yescomplemented
36#10622697C2218yescomplemented
37#10622693C2214yescomplemented
38#10622680C2212yes—
39#10622680C2214yes—
40#10622680C2214yes—
41#10622680C2212yes—
42#10622679C2218yescomplemented
43#10622679C2218yescomplemented
44#10622678C2212yescomplemented
45#10622678C2214yescomplemented
46#10622678C2212yescomplemented
47#10622677C2214yescomplemented
48#10622616C2218yescomplemented
49#10622616C2218yescomplemented
50#10622614C2214yes—
51#10622613C2214yescomplemented
52#10622612C2212yes—
53#10622611C2214yes—
54#10622581C2218yescomplemented
55#10622580C2218yescomplemented
56C2×#66873C2214yes—
57#10622577C2214yes—
58#10622539C2214yescomplemented
59C4×#4318C2211yescharacteristic
60C2×#66867C2211yescharacteristic
61C2×C11×#41C2311yescharacteristic
62C2×#4339—24no—
63C22×D44—22no—
64C22×D44C2312yes—
65C11×C4⋊Q8—22no—
66C11×C4⋊Q8—24no—
67C11×C4⋊Q8C2312yes—
68C11×C4⋊Q8C2314yes—
69C11×#125—22no—
70C11×#125—24no—
71C11×#125—22no—
72C11×#125—24no—
73C11×#125C2312yes—
74C11×#125C2312yes—
75C11×#125C2311yescharacteristic
76C11×#125C2314yes—
77C11×#125C2311yescharacteristic
78C11×C22⋊Q8—22no—
79C11×C22⋊Q8—24no—
80C11×C22⋊Q8—24no—
81C11×C22⋊Q8—24no—
82C11×C22⋊Q8—24no—
83C4×Q8×C11—22no—
84C4×Q8×C11—22no—
85C4×Q8×C11—24no—
86C4×Q8×C11D412yes—
87C4×D4×C11—24no—
88C4×D4×C11—22no—
89C4×D4×C11D414yes—
90C4×D4×C11D412yes—
91C11×#117C2312yes—
92C11×#117C2314yes—
93C11×#117C2311yescharacteristic
94C11×#117C2312yes—
95C2×C11×C4⋊C4—22no—
96C2×C11×C4⋊C4—24no—
97C2×C11×C4⋊C4C2312yes—
98C2×C11×C4⋊C4C2314yes—
99C2×C42×C11C2311yescharacteristic
100C2×C42×C11C2312yes—
101#67000—22no—
102#66993—22no—
103#66990—24no—
104#66983—24no—
105#66983C2318yes—
106#66979C2312yes—
107#66977—22no—
108C2×#4318C2312yes—
109C22×C11⋊C8C2312yes—
110#66947—28no—
111#66946—24no—
112#66937—28no—
113C22⋊C4×D11—24no—
114#66928—24no—
115#66927—22no—
116#66927C2312yes—
117#66927C2312yes—
118C4×D44—24no—
119C4×D44C2318yes—
120#66923C2312yes—
121#66922C2312yes—
122C4×Dic22—22no—
123C22⋊(C11⋊C8)C2318yes—
124#66873C2318yes—
125#66873C2318yes—
126#66873C2318yes—
127#66873C2318yes—
128#66872C2318yes—
129#66872C2314yes—
130#66872C2314yes—
131#66871C2318yes—
132#66871C2314yes—
133#66871C2314yes—
134C4⋊(C11⋊C8)C2318yes—
135#66867C2312yes—
136#66867C2312yes—
137#66867C2312yes—
138C4×C11⋊C8C2312yes—
139#60883—111nomaximal, Sylow
140C23×D11—22no—
141C11×#41—24no—
142C2×Q8×C11—22no—
143C2×Q8×C11—24no—
144C2×Q8×C11C2×D411yescharacteristic
145C2×D4×C11C2×D412yes—
146C2×D4×C11C2×D411yescharacteristic
147C22×C4×C11—24no—
148C22×C4×C11—22no—
149C22×C4×C11C2×D412yes—
150C22×C4×C11C2×D414yes—
151C22×C4×C11C2412yes—
152C22×C4×C11C2411yescharacteristic
153C2×C22⋊D11—28no—
154#4339—88no—
155C2×D44—24no—
156C2×D44—22no—
157C2×D44—24no—
158C2×D44—28no—
159C2×D44—84no—
160C2×D44C2414yes—
161C2×C4×D11—28no—
162C2×Dic22—22no—
163C11×C4⋊C4—24no—
164C11×C4⋊C4—22no—
165C11×C4⋊C4—24no—
166C11×C4⋊C4—24no—
167C11×C4⋊C4—24no—
168C11×C4⋊C4—24no—
169C11×C4⋊C4—22no—
170C11×C4⋊C4—22no—
171C11×C4⋊C4—22no—
172C11×C4⋊C4—24no—
173C11×C4⋊C4C2×D412yes—
174C11×C4⋊C4C2×D414yes—
175C11×C4⋊C4C2414yes—
176C11×C4⋊C4C2412yes—
177C11×C4⋊C4C2412yes—
178C11×C22⋊C4—24no—
179C11×C22⋊C4—22no—
180C11×C22⋊C4C2×D412yes—
181C11×C22⋊C4C2×D414yes—
182C42×C11—24no—
183C42×C11—22no—
184C42×C11C2×D412yes—
185C42×C11C2×D414yes—
186C42×C11C2411yescharacteristic
187C42×C11C2411yescharacteristic
188C42×C11C2412yes—
189C22⋊Dic11—22no—
190(C2×D11)⋊C4—28no—
191(C2×D11)⋊C4—28no—
192C4⋊Dic11—22no—
193C4⋊Dic11C2414yes—
194Dic11⋊C4—24no—
195C4×Dic11—22no—
196#4318—24no—
197C2×C11⋊C8—24no—
198C2×C11⋊C8C2414yes—
199C2×C11⋊C8C2414yes—
200#3508—111no—
201#3504D1111yescharacteristic, complemented
202#3241—118no—
203#3235—114no—
204#3234—114no—
205#3166—111no—
206#3162—111no—
207#3138—111no—
208C2×#490—111no—
209#3096—114no—
210#3081—114no—
211#2923—111no—
212C23×C11C22×D412yes—
213C23×C11C22×D411yescharacteristic
214C22×D11—24no—
215C22×D11—44no—
216C22×D11—84no—
217Q8×C11—22no—
218Q8×C11—84no—
219Q8×C11—82no—
220D4×C11—24no—
221D4×C11—22no—
222C2×C4×C11—24no—
223C2×C4×C11—22no—
224C2×C4×C11—24no—
225C2×C4×C11—22no—
226C2×C4×C11—42no—
227C2×C4×C11—44no—
228C2×C4×C11—82no—
229C2×C4×C11—84no—
230C2×C4×C11C22×D412yes—
231C2×C4×C11C22×D412yes—
232C2×C4×C11C22×D412yes—
233C2×C4×C11C22×D414yes—
234C2×C4×C11C22×D411yescharacteristic
235C2×C4×C112−1+414yes—
236C2×C4×C11C2511yescharacteristic
237C22⋊D11—88no—
238C2×Dic11—24no—
239D44—28no—
240D44—48no—
241D44—44no—
242D44—84no—
243C4×D11—88no—
244Dic22—44no—
245C11⋊C8—24no—
246C11⋊C8—24no—
247#559—222no—
248#557—22no—
249#554—24no—
250#554—22no—
251#550—222no—
252#546—224no—
253#544C2×D1112yes—
254#544C2×D1114yescomplemented
255#540—114no—
256#535—112no—
257#533—111no—
258#533C2×D1111yescharacteristic
259#533C2×D1112yescomplemented
260#532—114no—
261C2×#127—111no—
262C2×#125C2×D1111yescharacteristic
263C2×#125C2×D1112yescomplemented
264#520C2×D1112yes—
265#518—112no—
266C4×#41C2×D1111yescharacteristic
267#501—114no—
268#501—112no—
269#501—112no—
270#501—114no—
271#499—114no—
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#428—114no—
288#427—114no—
289#424—112no—
290#418—114no—
291C2×#102—114no—
292#408—112no—
293C4×M16—111no—
294C2×#97—111no—
295C22×C11—22no—
296C22×C11—24no—
297C22×C11—22no—
298C22×C11#53612yes—
299C22×C11C23×D411yescharacteristic
300C2×D11—48no—
301C2×D11—44no—
302C2×D11—164no—
303C4×C11—22no—
304C4×C11—24no—
305C4×C11—22no—
306C4×C11—22no—
307C4×C11—44no—
308C4×C11—42no—
309C4×C11—42no—
310C4×C11#53612yes—
311C4×C11C2×2−1+412yes—
312Dic11—44no—
313C2×#41—224no—
314C2×#41C22×D1111yescharacteristic
315C22×D4—112no—
316C22×D4—222no—
317C2×M16—112no—
318C22×C8—112no—
319C4⋊Q8—22no—
320C4⋊Q8—24no—
321C4⋊Q8—112no—
322C4⋊Q8C22×D1112yes—
323C4⋊Q8C22×D1114yes—
324#127—112no—
325#127—112no—
326#127—222no—
327#127—222no—
328#125—22no—
329#125—24no—
330#125—22no—
331#125—24no—
332#125—112no—
333#125C22×D1112yes—
334#125C22×D1112yes—
335#125C22×D1111yescharacteristic
336#125C22×D1114yes—
337#125C22×D1111yescharacteristic
338#124—222no—
339#124—224no—
340#123—228no—
341C22⋊Q8—22no—
342C22⋊Q8—24no—
343C22⋊Q8—24no—
344C22⋊Q8—24no—
345C22⋊Q8—24no—
346C22⋊Q8—222no—
347#121—118no—
348#121—224no—
349#121—228no—
350#120—224no—
351C4×Q8—22no—
352C4×Q8—22no—
353C4×Q8—24no—
354C4×Q8—222no—
355C4×Q8C22⋊D1112yes—
356C4×D4—24no—
357C4×D4—22no—
358C4×D4—118no—
359C4×D4—224no—
360C4×D4—224no—
361C4×D4C22⋊D1114yes—
362C4×D4C22⋊D1112yes—
363#117—112no—
364#117C22×D1112yes—
365#117C22×D1114yes—
366#117C22×D1111yescharacteristic
367#117C22×D1112yes—
368C2×C4⋊C4—22no—
369C2×C4⋊C4—24no—
370C2×C4⋊C4C22×D1112yes—
371C2×C4⋊C4C22×D1114yes—
372C2×C22⋊C4—224no—
373C2×C42C22×D1111yescharacteristic
374C2×C42C22×D1112yes—
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#102—118no—
385#102—118no—
386C22⋊C8—118no—
387#97—112no—
388#97—112no—
389#97—112no—
390C4×C8—112no—
391C2×C11—22no—
392C2×C11—42no—
393C2×C11C2×#53611yescharacteristic
394C2×C11#358512yes—
395D11—84no—
396C24—222no—
397#41—24no—
398#41—888no—
399C2×Q8—24no—
400C2×Q8—22no—
401C2×Q8—222no—
402C2×Q8C2×C22⋊D1111yescharacteristic
403C2×D4—114no—
404C2×D4—228no—
405C2×D4—228no—
406C2×D4—222no—
407C2×D4—224no—
408C2×D4—224no—
409C2×D4—884no—
410C2×D4C2×C22⋊D1112yes—
411C2×D4C2×C22⋊D1111yescharacteristic
412C22×C4—24no—
413C22×C4—22no—
414C22×C4—228no—
415C22×C4C2×C22⋊D1114yes—
416C22×C4C2×C22⋊D1112yes—
417C22×C4C23×D1112yes—
418C22×C4C23×D1111yescharacteristic
419M16—224no—
420C2×C8—114no—
421C2×C8—114no—
422C2×C8—224no—
423C4⋊C4—24no—
424C4⋊C4—22no—
425C4⋊C4—24no—
426C4⋊C4—24no—
427C4⋊C4—24no—
428C4⋊C4—24no—
429C4⋊C4—22no—
430C4⋊C4—22no—
431C4⋊C4—24no—
432C4⋊C4—22no—
433C4⋊C4—114no—
434C4⋊C4—222no—
435C4⋊C4—224no—
436C4⋊C4C2×C22⋊D1112yes—
437C4⋊C4C2×C22⋊D1114yes—
438C4⋊C4C23×D1114yes—
439C4⋊C4C23×D1112yes—
440C4⋊C4C23×D1112yes—
441C22⋊C4—24no—
442C22⋊C4—22no—
443C22⋊C4—222no—
444C22⋊C4—228no—
445C22⋊C4—228no—
446C22⋊C4C2×C22⋊D1112yes—
447C22⋊C4C2×C22⋊D1114yes—
448C42—24no—
449C42—22no—
450C42—222no—
451C42C2×C22⋊D1114yes—
452C42C2×C22⋊D1112yes—
453C42C23×D1111yescharacteristic
454C42C23×D1111yescharacteristic
455C42C23×D1112yes—
456C11#6088311yescharacteristic, complemented, Sylow
457C23—224no—
458C23—444no—
459C23—884no—
460C23C22×C22⋊D1112yes—
461C23C22×C22⋊D1111yescharacteristic
462Q8—22no—
463Q8—84no—
464Q8—82no—
465Q8—444no—
466D4—24no—
467D4—22no—
468D4—228no—
469D4—448no—
470D4—444no—
471D4—884no—
472D4—888no—
473C2×C4—24no—
474C2×C4—22no—
475C2×C4—24no—
476C2×C4—22no—
477C2×C4—42no—
478C2×C4—44no—
479C2×C4—82no—
480C2×C4—84no—
481C2×C4—224no—
482C2×C4—888no—
483C2×C4#6704014yes—
484C2×C4C22×C22⋊D1112yes—
485C2×C4C22×C22⋊D1112yes—
486C2×C4C22×C22⋊D1114yes—
487C2×C4C22×C22⋊D1112yes—
488C2×C4C22×C22⋊D1111yescharacteristic
489C2×C4C24×D1111yescharacteristic
490C8—224no—
491C8—224no—
492C22—22no—
493C22—24no—
494C22—22no—
495C22—448no—
496C22—444no—
497C22—1764no—
498C22#1062334712yes—
499C22C23×C22⋊D1111yescharacteristic
500C4—22no—
501C4—24no—
502C4—22no—
503C4—22no—
504C4—44no—
505C4—42no—
506C4—42no—
507C4—444no—
508C4#1062334712yes—
509C4C2×#6704012yes—
510C2—22no—
511C2—42no—
512C2—884no—
513C2C2×#1062334711yescharacteristic
514C2#1308339512yes—
subgroupG/H
centerC22C23×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC11×#3504C2
socleC22×C11C23×D4
prime radical#13082492C2
hypercenter#3504D11
hypocenterC11#60883
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C4×#41 ◁ #3504

Complements

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

NH ≅ G/Ntype
2. #13079869C2semidirect
3. #13079814C2semidirect
4. #13079806C2semidirect
5. #13079165C2semidirect
6. #13079138C2semidirect
7. #13078992C2semidirect
8. C2×#10622680C2semidirect
9. #13078574C2semidirect
10. #13078441C2semidirect
11. #13077267C2semidirect
12. C11×#3504C2semidirect
17. C11×#544C22semidirect
19. C11×#533C22semidirect
21. C2×C11×#125C22semidirect
35. #10622700C22semidirect
36. #10622697C22semidirect
37. #10622693C22semidirect
42. #10622679C22semidirect
43. #10622679C22semidirect
44. #10622678C22semidirect
45. #10622678C22semidirect
46. #10622678C22semidirect
47. #10622677C22semidirect
48. #10622616C22semidirect
49. #10622616C22semidirect
51. #10622613C22semidirect
54. #10622581C22semidirect
55. #10622580C22semidirect
58. #10622539C22semidirect
201. #3504D11semidirect
254. #544C2×D11semidirect
259. #533C2×D11semidirect
263. C2×#125C2×D11semidirect
456. C11#60883semidirect

Maximal subgroups

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

subgroupindex
#130824922
#130798692
#130798142
#130798062
#130791652
#130791382
#130789922
C2×#106226802
#130785742
#130784412
#130772672
C11×#35042
#6088311