Finite Group Databasebeta

← #15618339

Subgroups — #15618339

Order 2816.

1878 conjugacy classes of subgroups.

The subgroup lattice has 512 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082008C211yesmaximal, characteristic
2#13077619C218yesmaximal, complemented
3#13077609C218yesmaximal, complemented
4#13077557C211yesmaximal, characteristic, complemented
5#13077333C211yesmaximal, characteristic, complemented
6#13077329C211yesmaximal, characteristic, complemented
7#13077321C212yesmaximal, complemented
8#13077309C212yesmaximal, complemented
9#13077259C212yesmaximal, complemented
10#13077253C211yesmaximal, characteristic, complemented
11#13077043C212yesmaximal, complemented
12C2×#10622302C211yesmaximal, characteristic, complemented
13C11×#2960C211yesmaximal, characteristic, complemented
14C11×#533C2211yescharacteristic
15C2×#66960C2212yes—
16C2×#66954C2212yes—
17C22×#4313C2211yescharacteristic
18C22×C8×D11C2211yescharacteristic
19#10623264C414yes—
20#10623229C412yes—
21#10623228C412yes—
22#10623176C414yes—
23#10623175C414yes—
24#10623111C2218yes—
25#10623055C2212yes—
26#10623053C2212yes—
27#10623008C2211yescharacteristic
28C2×#66925C2211yescharacteristic
29C11×#446C2214yescomplemented
30C8×Q8×C11C2214yescomplemented
31C11×#424C2212yes—
32C11×#423C2211yescharacteristic
33C11×#405C2212yes—
34C2×C4×C8×C11C2211yescharacteristic
35#10622742C2212yes—
36#10622739C2212yes—
37M16×Dic11C2212yes—
38#10622723C2212yes—
39C2×#66879C2211yescharacteristic
40C2×C8×Dic11C2211yescharacteristic
41#10622637C2218yescomplemented
42#10622612C2212yes—
43#10622610C2212yes—
44#10622537C2211yescharacteristic
45C2×#66867C2211yescharacteristic
46#10622453C2218yes—
47#10622453C2218yescomplemented
48#10622449C2218yes—
49#10622449C2218yescomplemented
50#10622447C2218yes—
51#10622446C2218yescomplemented
52#10622321C2214yescomplemented
53#10622319C2218yes—
54D11×#97C2214yescomplemented
55#10622302C2214yes—
56#10622302C2214yes—
57#10622302C2214yescomplemented
58#10622301C2218yes—
59#10622301C2214yescomplemented
60C4×#4313C2214yescomplemented
61C8×D44C2214yescomplemented
62C2×#4339C2312yes—
63C22×C4×D11C2311yescharacteristic
64C2×C11×M16C2312yes—
65C22×C8×C11C2311yescharacteristic
66C22×C8×C11C2311yescharacteristic
67C11×C4⋊Q8C2×C412yes—
68C11×#125C2×C412yes—
69C11×C22⋊Q8C2×C414yes—
70C4×Q8×C11C2314yes—
71C11×#117C2312yes—
72C2×C42×C11C2311yescharacteristic
73#67000C2×C418yes—
74#66999C2×C418yes—
75#66983C2×C414yes—
76C2×(C2×D11)⋊C4C2×C412yes—
77C2×Dic11⋊C4C2×C412yes—
78C2×C4×Dic11C2311yescharacteristic
79C2×#4318C2312yes—
80C22×C11⋊C8C2311yescharacteristic
81C22×C11⋊C8C2311yescharacteristic
82#66960—28no—
83#66954—28no—
84C2×#4313—24no—
85C2×#4313C2312yes—
86C2×#4313C2312yes—
87C2×#4313C2314yes—
88C2×#4313C2314yes—
89C2×C8×D11—24no—
90C2×C8×D11C2314yes—
91C2×C8×D11C2314yes—
92C2×C8×D11C2314yes—
93#66951C2×C418yes—
94#66951C2×C418yes—
95#66950C2×C414yes—
96#66948C2×C414yes—
97#66948C2×C418yes—
98#66947C2×C418yes—
99#66947C2×C418yes—
100#66946C2×C414yes—
101#66943C2×C418yes—
102#66940C2×C414yes—
103#66939C2×C414yes—
104#66935C2×C414yes—
105(C22⋊D11)⋊C4C2×C418yes—
106#66928C2×C412yes—
107#66927C2×C411yescharacteristic
108C4×D44C2314yes—
109C4×D44C2318yes—
110#66925C2×C412yes—
111#66925C2×C412yes—
112#66925C2314yes—
113#66925C2314yes—
114C42×D11C2314yes—
115#66922C2×C411yescharacteristic
116C11×C4⋊C8C2314yes—
117C11×C4⋊C8C2318yes—
118C11×#97C2314yes—
119C4×C8×C11C2312yes—
120C4×C8×C11C2314yes—
121C4×C8×C11C2312yes—
122(C2×D11)⋊C8C2318yes—
123(C2×D11)⋊C8C2318yes—
124(C2×D11)⋊C8C2318yes—
125#66879C2314yes—
126#66879C2312yes—
127#66879C2312yes—
128C8×Dic11C2314yes—
129C8×Dic11C2314yes—
130C4⋊(C11⋊C8)C2314yes—
131C4⋊(C11⋊C8)C2318yes—
132#66867C2314yes—
133#66867C2314yes—
134C4×C11⋊C8C2314yes—
135#60209—111nomaximal, Sylow
136C23×D11C22×C411yescharacteristic
137C2×Q8×C11C22×C414yes—
138C22×C4×C11C22×C412yes—
139C22×C4×C11C2411yescharacteristic
140C2×C22⋊D11C22×C414yes—
141C22×Dic11C22×C411yescharacteristic
142C22×Dic11C22×C412yes—
143#4339—24no—
144#4339—24no—
145C2×D44C22×C412yes—
146C2×D44C22×C414yes—
147C2×D44C22×C418yes—
148C2×C4×D11—22no—
149C2×C4×D11—22no—
150C2×C4×D11C22×C412yes—
151C2×C4×D11C22×C418yes—
152C2×C4×D11C2414yes—
153C2×C4×D11C2412yes—
154C2×Dic22C22×C412yes—
155C11×M16—24no—
156C2×C8×C11—22no—
157C2×C8×C11#4114yes—
158C2×C8×C11C2412yes—
159C2×C8×C11C2414yes—
160C2×C8×C11C2411yescharacteristic
161C2×C8×C11C2411yescharacteristic
162C11×C4⋊C4C22×C414yes—
163C11×C4⋊C4C22×C418yes—
164C11×C4⋊C4C22×C414yes—
165C11×C22⋊C4C22×C414yes—
166C42×C11C22×C411yescharacteristic
167C42×C11C22×C411yescharacteristic
168C42×C11C2414yes—
169C42×C11C2412yes—
170(C2×D11)⋊C4C22×C414yes—
171(C2×D11)⋊C4C22×C414yes—
172(C2×D11)⋊C4C22×C418yes—
173(C2×D11)⋊C4C22×C418yes—
174(C2×D11)⋊C4C22×C418yes—
175(C2×D11)⋊C4C22×C418yes—
176C4⋊Dic11C22×C414yes—
177C4⋊Dic11C22×C418yes—
178Dic11⋊C4C22×C414yes—
179Dic11⋊C4C22×C414yes—
180Dic11⋊C4C22×C418yes—
181C4×Dic11C22×C418yes—
182C4×Dic11C22×C412yes—
183C4×Dic11C2412yes—
184#4318—24no—
185C2×C11⋊C8—22no—
186C2×C11⋊C8#4114yes—
187C2×C11⋊C8C2414yes—
188C2×C11⋊C8C2412yes—
189C2×C11⋊C8C2412yes—
190#4313—24no—
191#4313—24no—
192#4313—28no—
193#4313—28no—
194C8×D11—28no—
195C8×D11—28no—
196C8×D11—28no—
197#3455—111no—
198#2969—118no—
199#2968—118no—
200#2961—111no—
201#2960D1111yescharacteristic, complemented
202#2932—111no—
203#2931—111no—
204#2930—112no—
205#2929—112no—
206#2922—112no—
207#2921—111no—
208#2875—112no—
209C2×#405—111no—
210C23×C11C23×C411yescharacteristic
211C22×D11—22no—
212C22×D11—42no—
213C22×D11C23×C412yes—
214C22×D11C23×C414yes—
215Q8×C11—44no—
216C2×C4×C11—42no—
217C2×C4×C11C23×C418yes—
218C2×C4×C11C23×C412yes—
219C2×C4×C11C23×C412yes—
220C2×C4×C11C23×C411yescharacteristic
221C2×C4×C11C2×#4112yes—
222C2×C4×C11C2×#4112yes—
223C2×C4×C11C2511yescharacteristic
224C22⋊D11—28no—
225C2×Dic11—22no—
226C2×Dic11—42no—
227C2×Dic11C23×C414yes—
228C2×Dic11C23×C414yes—
229C2×Dic11C23×C412yes—
230D44—24no—
231D44—44no—
232D44—48no—
233C4×D11—24no—
234C4×D11—22no—
235C4×D11—24no—
236C4×D11—24no—
237C4×D11—22no—
238C4×D11—48no—
239Dic22—24no—
240C8×C11—22no—
241C8×C11—24no—
242C8×C11C2×#4112yes—
243C8×C11C2×#4112yes—
244C11⋊C8—24no—
245C11⋊C8—22no—
246C11⋊C8C2×#4114yes—
247C2×#131—112no—
248C2×#131—112no—
249C22×M16—111no—
250C23×C8—111no—
251#542—114no—
252#541—112no—
253#540—112no—
254#539—114no—
255#538—114no—
256#533C2×D1111yescharacteristic
257#532—111no—
258#529—118no—
259#525—112no—
260C4×#41—112no—
261C2×#117—111no—
262#446—118no—
263#446C2×D1114yescomplemented
264C8×Q8C2×D1114yescomplemented
265#436—118no—
266#436—114no—
267#435—118no—
268#435—118no—
269#435—118no—
270C8×D4—118no—
271C8×D4—114no—
272#433—118no—
273#433—118no—
274#431—118no—
275#424—112no—
276#424C2×D1112yes—
277#423—111no—
278#423C2×D1111yescharacteristic
279#408—112no—
280#408—112no—
281#407—112no—
282#405—112no—
283#405—114no—
284#405—114no—
285#405—114no—
286#405—114no—
287#405C2×D1112yes—
288C4×M16—112no—
289C4×M16—114no—
290C2×#97—111no—
291C2×#97—111no—
292C2×#97—114no—
293C2×C4×C8—111no—
294C2×C4×C8C2×D1111yescharacteristic
295C22×C11—22no—
296C22×C11C4×#4112yes—
297C22×C11C24×C411yescharacteristic
298C2×D11—22no—
299C2×D11—24no—
300C2×D11—24no—
301C2×D11—28no—
302C2×D11—44no—
303C4×C11—22no—
304C4×C11—22no—
305C4×C11—28no—
306C4×C11C4×#4112yes—
307C4×C11C22×#4111yescharacteristic
308C4×C11C22×#4111yescharacteristic
309Dic11—24no—
310Dic11—22no—
311Dic11—24no—
312C2×#41—112no—
313C23×C4—111no—
314#131—228no—
315#131—228no—
316C2×M16—112no—
317C2×M16—112no—
318C2×M16—112no—
319C2×M16—114no—
320C2×M16—114no—
321C2×M16—224no—
322C2×M16C22×D1112yes—
323C22×C8—111no—
324C22×C8—111no—
325C22×C8—114no—
326C22×C8—114no—
327C22×C8—114no—
328C22×C8—224no—
329C22×C8C22×D1111yescharacteristic
330C22×C8C22×D1111yescharacteristic
331C4⋊Q8—111no—
332C4⋊Q8C4×D1112yes—
333#127—111no—
334#126—118no—
335#126—118no—
336#125—118no—
337#125C4×D1112yes—
338#124—118no—
339#124—112no—
340#123—118no—
341#123—118no—
342#123—114no—
343C22⋊Q8—118no—
344C22⋊Q8—114no—
345C22⋊Q8C4×D1114yes—
346#121—114no—
347#121—114no—
348#121—118no—
349#120—114no—
350C4×Q8—114no—
351C4×Q8C22×D1114yes—
352C4×D4—114no—
353C4×D4—118no—
354C4×D4—118no—
355C4×D4—114no—
356#117—112no—
357#117—112no—
358#117—114no—
359#117—114no—
360#117C22×D1112yes—
361C2×C4⋊C4—112no—
362C2×C22⋊C4—112no—
363C2×C42—111no—
364C2×C42—114no—
365C2×C42C22×D1111yescharacteristic
366C4⋊C8—114no—
367C4⋊C8—118no—
368C4⋊C8C22×D1114yes—
369C4⋊C8C22×D1118yes—
370C22⋊C8—118no—
371C22⋊C8—118no—
372C22⋊C8—118no—
373#97—112no—
374#97—112no—
375#97—114no—
376#97—114no—
377#97—114no—
378#97C22×D1114yes—
379C4×C8—114no—
380C4×C8—114no—
381C4×C8—114no—
382C4×C8C22×D1112yes—
383C4×C8C22×D1112yes—
384C4×C8C22×D1114yes—
385C2×C11—22no—
386C2×C11C2×C4×#4111yescharacteristic
387C2×C11#357312yes—
388D11—44no—
389D11—42no—
390C24—111no—
391#41—224no—
392#41—224no—
393C2×Q8—112no—
394C2×Q8C2×C4×D1114yes—
395C2×D4—114no—
396C2×D4—112no—
397C2×D4—118no—
398C2×D4—114no—
399C22×C4—111no—
400C22×C4—112no—
401C22×C4—112no—
402C22×C4—114no—
403C22×C4—112no—
404C22×C4—118no—
405C22×C4—222no—
406C22×C4—222no—
407C22×C4C2×C4×D1112yes—
408C22×C4C23×D1111yescharacteristic
409M16—24no—
410M16—228no—
411M16—224no—
412M16—224no—
413M16—224no—
414M16—228no—
415C2×C8—22no—
416C2×C8—114no—
417C2×C8—112no—
418C2×C8—112no—
419C2×C8—114no—
420C2×C8—228no—
421C2×C8—228no—
422C2×C8—222no—
423C2×C8—228no—
424C2×C8#434314yes—
425C2×C8C23×D1112yes—
426C2×C8C23×D1114yes—
427C2×C8C23×D1111yescharacteristic
428C2×C8C23×D1111yescharacteristic
429C4⋊C4—114no—
430C4⋊C4—114no—
431C4⋊C4—118no—
432C4⋊C4—114no—
433C4⋊C4—118no—
434C4⋊C4C2×C4×D1114yes—
435C4⋊C4C2×C4×D1118yes—
436C4⋊C4C2×C4×D1114yes—
437C22⋊C4—114no—
438C22⋊C4—114no—
439C22⋊C4—118no—
440C22⋊C4—118no—
441C22⋊C4—118no—
442C22⋊C4—118no—
443C22⋊C4C2×C4×D1114yes—
444C42—112no—
445C42—118no—
446C42—112no—
447C42C2×C4×D1111yescharacteristic
448C42C2×C4×D1111yescharacteristic
449C42C23×D1114yes—
450C42C23×D1112yes—
451C11#6020911yescharacteristic, complemented, Sylow
452C23—112no—
453C23—114no—
454C23—222no—
455C23—442no—
456C23C22×C4×D1111yescharacteristic
457Q8—44no—
458Q8—224no—
459D4—228no—
460D4—224no—
461D4—444no—
462D4—448no—
463C2×C4—42no—
464C2×C4—114no—
465C2×C4—114no—
466C2×C4—112no—
467C2×C4—222no—
468C2×C4—224no—
469C2×C4—224no—
470C2×C4—222no—
471C2×C4—222no—
472C2×C4—224no—
473C2×C4—448no—
474C2×C4—442no—
475C2×C4C22×C4×D1118yes—
476C2×C4C22×C4×D1112yes—
477C2×C4C22×C4×D1112yes—
478C2×C4C22×C4×D1111yescharacteristic
479C2×C4C2×#434312yes—
480C2×C4#41×D1112yes—
481C2×C4C24×D1111yescharacteristic
482C8—22no—
483C8—24no—
484C8—114no—
485C8—222no—
486C8—224no—
487C8C2×#434312yes—
488C8C2×#434312yes—
489C22—22no—
490C22—228no—
491C22—224no—
492C22—222no—
493C22—224no—
494C22—444no—
495C22C4×#434312yes—
496C22C23×C4×D1111yescharacteristic
497C4—22no—
498C4—22no—
499C4—28no—
500C4—224no—
501C4—222no—
502C4—224no—
503C4C4×#434312yes—
504C4C22×#434311yescharacteristic
505C4C2×#41×D1111yescharacteristic
506C2—22no—
507C2—442no—
508C2—444no—
509C2C2×C4×#434311yescharacteristic
510C2#1308332712yes—
subgroupG/H
center, FrattiniC2×C4C24×D11
commutator, socleC22×C11C24×C4
FittingC11×#2960C2
prime radical#13082008C2
cosocleC2×C4×C11C25
hypercenter#2960D11
hypocenterC11#60209
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ #2960

Complements

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

NH ≅ G/Ntype
2. #13077619C2semidirect
3. #13077609C2semidirect
4. #13077557C2semidirect
5. #13077333C2semidirect
6. #13077329C2semidirect
7. #13077321C2semidirect
8. #13077309C2semidirect
9. #13077259C2semidirect
10. #13077253C2semidirect
11. #13077043C2semidirect
12. C2×#10622302C2semidirect
13. C11×#2960C2semidirect
29. C11×#446C22semidirect
30. C8×Q8×C11C22semidirect
41. #10622637C22semidirect
47. #10622453C22semidirect
49. #10622449C22semidirect
51. #10622446C22semidirect
52. #10622321C22semidirect
54. D11×#97C22semidirect
57. #10622302C22semidirect
59. #10622301C22semidirect
60. C4×#4313C22semidirect
61. C8×D44C22semidirect
201. #2960D11semidirect
263. #446C2×D11semidirect
264. C8×Q8C2×D11semidirect
451. C11#60209semidirect

Maximal subgroups

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

subgroupindex
#130820082
#130776192
#130776092
#130775572
#130773332
#130773292
#130773212
#130773092
#130772592
#130772532
#130770432
C2×#106223022
C11×#29602
#6020911