Finite Group Databasebeta

← #15618306

Subgroups — #15618306

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#13082006C211yesmaximal, characteristic
2#13077597C218yesmaximal, complemented
3#13077587C218yesmaximal, complemented
4#13077556C211yesmaximal, characteristic, complemented
5#13077550C211yesmaximal, characteristic, complemented
6#13077335C211yesmaximal, characteristic, complemented
7#13077329C211yesmaximal, characteristic, complemented
8#13077319C212yesmaximal, complemented
9#13077310C212yesmaximal, complemented
10#13077265C212yesmaximal, complemented
11#13077254C211yesmaximal, characteristic, complemented
12C4×#66954C212yesmaximal, complemented
13C2×C11×#405C211yesmaximal, characteristic, complemented
14C22×C11×M16C2211yescharacteristic
15C23×C8×C11C2211yescharacteristic
16C2×C11×#117C2211yescharacteristic
17#10623322C2212yes—
18C2×#66954C2212yes—
19C2×#66954C2212yes—
20#10623066C412yes—
21#10623065C414yes—
22#10623059C2218yes—
23#10623049C412yes—
24#10623046C414yes—
25#10623025C414yes—
26#10623008C2211yescharacteristic
27C4×#4339C2212yes—
28#10623001C2211yescharacteristic
29C11×#405C2214yes—
30C11×#405C2214yes—
31C2×C11×#97C2211yescharacteristic
32C2×C11×#97C2211yescharacteristic
33C2×C4×C8×C11C2211yescharacteristic
34C2×C4×C8×C11C2211yescharacteristic
35#10622820C2212yes—
36#10622741C2218yes—
37#10622740C2218yes—
38#10622724C2218yes—
39#10622723C2212yes—
40#10622723C2212yes—
41C8×C22⋊D11C2218yes—
42#10622715C2212yes—
43#10622715C2212yes—
44#10622714C2212yes—
45#10622714C2212yes—
46#10622613C2218yes—
47#10622537C2211yescharacteristic
48#10622537C2211yescharacteristic
49C4×#4318C2212yes—
50#10622322C2218yescomplemented
51#10622319C2218yescomplemented
52#10622318C2218yescomplemented
53#10622314C2218yescomplemented
54#10622302C2214yescomplemented
55#10622302C2214yescomplemented
56#10622301C2214yescomplemented
57C4×#4313C2214yescomplemented
58C8×D44C2214yescomplemented
59C4×C8×D11C2214yescomplemented
60#10622292C2214yescomplemented
61C8×Dic22C2214yescomplemented
62C23×C4×C11C2311yescharacteristic
63C2×#4339C2312yes—
64C2×C11×M16—24no—
65C2×C11×M16C2314yes—
66C22×C8×C11—24no—
67C22×C8×C11C2312yes—
68C22×C8×C11C2311yescharacteristic
69C22×C8×C11C2311yescharacteristic
70C22×C8×C11C2312yes—
71C22×C8×C11C2311yescharacteristic
72C22×C8×C11C2311yescharacteristic
73C11×#117C2×C412yes—
74C11×#117C2×C412yes—
75C11×#117C2314yes—
76C2×C11×C4⋊C4C2×C412yes—
77C2×C11×C22⋊C4C2×C412yes—
78C2×C42×C11C2311yescharacteristic
79C2×C42×C11C2311yescharacteristic
80#67006C2×C414yes—
81#66983C2×C414yes—
82#66983C2×C414yes—
83#66982C2×C414yes—
84C4×C22⋊D11C2×C418yes—
85C4×C22⋊D11C2318yes—
86#66979C2312yes—
87#66977C2×C414yes—
88#66977C2×C414yes—
89C2×#4318C2312yes—
90C2×#4318C2312yes—
91#66954—28no—
92#66954—28no—
93C2×#4313C2314yes—
94C2×#4313C2314yes—
95C2×C8×D11C2314yes—
96C2×C8×D11C2314yes—
97#66951C2×C418yes—
98#66949C2×C418yes—
99#66947C2×C418yes—
100#66942C2×C418yes—
101#66938C2×C418yes—
102#66937C2×C418yes—
103#66936C2×C418yes—
104#66932C2×C418yes—
105#66928C2×C412yes—
106#66927C2×C411yescharacteristic
107C4×D44C2×C414yes—
108C4×D44C2314yes—
109#66925C2314yes—
110C42×D11C2314yes—
111#66923C2×C412yes—
112#66922C2×C412yes—
113#66922C2×C411yescharacteristic
114C4×Dic22C2×C414yes—
115C4×Dic22C2314yes—
116C11×#97C2314yes—
117C11×#97C2314yes—
118C4×C8×C11C2312yes—
119C4×C8×C11C2312yes—
120C4×C8×C11C2312yes—
121C4×C8×C11C2312yes—
122C22⋊(C11⋊C8)C2318yes—
123(C2×D11)⋊C8C2318yes—
124(C2×D11)⋊C8C2318yes—
125#66879C2314yes—
126#66879C2314yes—
127Dic11⋊C8C2318yes—
128Dic11⋊C8C2318yes—
129C8×Dic11C2314yes—
130C8×Dic11C2314yes—
131C4⋊(C11⋊C8)C2314yes—
132C4⋊(C11⋊C8)C2314yes—
133#66867C2314yes—
134C4×C11⋊C8C2314yes—
135#60206—111nomaximal, Sylow
136C24×C11C22×C411yescharacteristic
137C22×C4×C11—22no—
138C22×C4×C11—22no—
139C22×C4×C11C22×C412yes—
140C22×C4×C11C22×C411yescharacteristic
141C22×C4×C11C22×C412yes—
142C22×C4×C11C22×C412yes—
143C22×C4×C11C2412yes—
144C22×C4×C11C2411yescharacteristic
145C2×C22⋊D11C22×C414yes—
146C2×C22⋊D11C22×C418yes—
147#4339—24no—
148#4339—24no—
149C2×D44C22×C412yes—
150C2×D44C22×C414yes—
151C2×C4×D11C22×C418yes—
152C2×C4×D11C2414yes—
153C2×Dic22C22×C412yes—
154C2×Dic22C22×C414yes—
155C11×M16—28no—
156C2×C8×C11—24no—
157C2×C8×C11—24no—
158C2×C8×C11—22no—
159C2×C8×C11—22no—
160C2×C8×C11#4114yes—
161C2×C8×C11#4114yes—
162C2×C8×C11C2412yes—
163C2×C8×C11C2412yes—
164C2×C8×C11C2412yes—
165C2×C8×C11C2411yescharacteristic
166C2×C8×C11C2411yescharacteristic
167C11×C4⋊C4C22×C414yes—
168C11×C4⋊C4C22×C414yes—
169C11×C22⋊C4C22×C414yes—
170C11×C22⋊C4C22×C414yes—
171C42×C11C22×C412yes—
172C42×C11C22×C411yescharacteristic
173C42×C11C22×C411yescharacteristic
174C42×C11C2412yes—
175C42×C11C2412yes—
176C22⋊Dic11C22×C418yes—
177C22⋊Dic11C22×C414yes—
178(C2×D11)⋊C4C22×C418yes—
179(C2×D11)⋊C4C22×C418yes—
180(C2×D11)⋊C4C22×C418yes—
181C4⋊Dic11C22×C414yes—
182C4⋊Dic11C22×C414yes—
183C4⋊Dic11C22×C414yes—
184Dic11⋊C4C22×C418yes—
185Dic11⋊C4C22×C418yes—
186Dic11⋊C4C22×C418yes—
187C4×Dic11C22×C418yes—
188C4×Dic11C2414yes—
189#4318—24no—
190#4318—24no—
191C2×C11⋊C8C2414yes—
192C2×C11⋊C8C2414yes—
193#4313—28no—
194#4313—28no—
195C8×D11—28no—
196C8×D11—28no—
197#3455—111no—
198#2967—118no—
199#2966—118no—
200#2961—111no—
201#2960—111no—
202#2932—111no—
203#2931—111no—
204#2930—112no—
205#2929—112no—
206#2923—112no—
207#2921—111no—
208C4×#131—112no—
209C2×#405D1111yescharacteristic, complemented
210C23×C11—22no—
211C23×C11—42no—
212C23×C11C23×C412yes—
213C23×C11C23×C411yescharacteristic
214C22×D11C23×C414yes—
215C2×C4×C11—22no—
216C2×C4×C11—24no—
217C2×C4×C11—22no—
218C2×C4×C11—22no—
219C2×C4×C11—42no—
220C2×C4×C11—42no—
221C2×C4×C11C23×C414yes—
222C2×C4×C11C23×C412yes—
223C2×C4×C11C23×C412yes—
224C2×C4×C11C23×C412yes—
225C2×C4×C11C23×C411yescharacteristic
226C2×C4×C11C2×#4112yes—
227C2×C4×C11C2×#4112yes—
228C2×C4×C11C2511yescharacteristic
229C22⋊D11—28no—
230C22⋊D11—48no—
231C2×Dic11C23×C414yes—
232C2×Dic11C23×C418yes—
233D44—24no—
234D44—44no—
235C4×D11—24no—
236C4×D11—24no—
237C4×D11—48no—
238Dic22—24no—
239Dic22—44no—
240C8×C11—22no—
241C8×C11—22no—
242C8×C11C2×#4112yes—
243C8×C11C2×#4114yes—
244C8×C11C2×#4112yes—
245C11⋊C8—24no—
246C11⋊C8—24no—
247C2×#131—112no—
248C2×#131—112no—
249C22×M16C2×D1111yescharacteristic
250C23×C8C2×D1111yescharacteristic
251#542—114no—
252#541—112no—
253#540—112no—
254#539—114no—
255#538—114no—
256#533—111no—
257#532—111no—
258#529—118no—
259#525—112no—
260C4×#41—112no—
261C2×#117C2×D1111yescharacteristic
262#446—118no—
263#446—114no—
264C8×Q8—114no—
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#432—118no—
275#424—112no—
276#424—112no—
277#423—111no—
278#423—111no—
279#408—112no—
280#408—112no—
281#407—112no—
282#405—112no—
283#405—112no—
284#405—114no—
285#405—114no—
286#405C2×D1114yes—
287#405C2×D1114yes—
288C4×M16—112no—
289C4×M16—114no—
290C2×#97C2×D1111yescharacteristic
291C2×#97C2×D1111yescharacteristic
292C2×C4×C8—114no—
293C2×C4×C8C2×D1111yescharacteristic
294C2×C4×C8C2×D1111yescharacteristic
295C22×C11—22no—
296C22×C11—22no—
297C22×C11—24no—
298C22×C11—44no—
299C22×C11C4×#4112yes—
300C22×C11C24×C411yescharacteristic
301C2×D11—24no—
302C2×D11—28no—
303C4×C11—22no—
304C4×C11—22no—
305C4×C11—24no—
306C4×C11—22no—
307C4×C11C4×#4112yes—
308C4×C11C22×#4111yescharacteristic
309C4×C11C22×#4111yescharacteristic
310Dic11—24no—
311Dic11—28no—
312C2×#41—112no—
313C23×C4C22×D1111yescharacteristic
314#131—228no—
315#131—228no—
316C2×M16—24no—
317C2×M16—112no—
318C2×M16—112no—
319C2×M16—114no—
320C2×M16—114no—
321C2×M16C22×D1114yes—
322C22×C8—24no—
323C22×C8—114no—
324C22×C8—114no—
325C22×C8C22×D1111yescharacteristic
326C22×C8C22×D1112yes—
327C22×C8C22×D1111yescharacteristic
328C22×C8C22×D1112yes—
329C22×C8C22×D1111yescharacteristic
330C22×C8C22×D1111yescharacteristic
331C4⋊Q8—111no—
332C4⋊Q8—112no—
333#127—111no—
334#126—118no—
335#126—118no—
336#125—118no—
337#125—112no—
338#124—118no—
339#124—112no—
340#123—114no—
341#123—118no—
342#123—118no—
343C22⋊Q8—114no—
344C22⋊Q8—114no—
345C22⋊Q8—118no—
346#121—114no—
347#121—114no—
348#121—118no—
349#120—114no—
350C4×Q8—114no—
351C4×Q8—114no—
352C4×D4—118no—
353C4×D4—118no—
354C4×D4—114no—
355C4×D4—114no—
356#117—112no—
357#117—114no—
358#117C4×D1112yes—
359#117C4×D1112yes—
360#117C22×D1114yes—
361C2×C4⋊C4C4×D1112yes—
362C2×C22⋊C4C4×D1112yes—
363C2×C42—114no—
364C2×C42C22×D1111yescharacteristic
365C2×C42C22×D1111yescharacteristic
366C4⋊C8—118no—
367C4⋊C8—118no—
368C4⋊C8—114no—
369C4⋊C8—114no—
370C22⋊C8—118no—
371C22⋊C8—118no—
372C22⋊C8—118no—
373#97—114no—
374#97—114no—
375#97—114no—
376#97C22×D1114yes—
377#97C22×D1114yes—
378C4×C8—114no—
379C4×C8—114no—
380C4×C8—114no—
381C4×C8C22×D1112yes—
382C4×C8C22×D1112yes—
383C4×C8C22×D1112yes—
384C4×C8C22×D1112yes—
385C2×C11—22no—
386C2×C11—42no—
387C2×C11C2×C4×#4111yescharacteristic
388C2×C11#357312yes—
389D11—44no—
390C24C2×C4×D1111yescharacteristic
391#41—224no—
392#41—224no—
393C2×Q8—112no—
394C2×Q8—114no—
395C2×D4—114no—
396C2×D4—118no—
397C2×D4—112no—
398C2×D4—114no—
399C22×C4—22no—
400C22×C4—22no—
401C22×C4—114no—
402C22×C4—118no—
403C22×C4C2×C4×D1111yescharacteristic
404C22×C4C2×C4×D1112yes—
405C22×C4C2×C4×D1112yes—
406C22×C4C2×C4×D1112yes—
407C22×C4C23×D1112yes—
408C22×C4C23×D1111yescharacteristic
409M16—28no—
410M16—224no—
411M16—224no—
412M16—228no—
413M16—228no—
414C2×C8—22no—
415C2×C8—22no—
416C2×C8—24no—
417C2×C8—24no—
418C2×C8—114no—
419C2×C8—114no—
420C2×C8—228no—
421C2×C8—228no—
422C2×C8#433914yes—
423C2×C8#433914yes—
424C2×C8C23×D1112yes—
425C2×C8C23×D1112yes—
426C2×C8C23×D1112yes—
427C2×C8C23×D1111yescharacteristic
428C2×C8C23×D1111yescharacteristic
429C4⋊C4—114no—
430C4⋊C4—118no—
431C4⋊C4—114no—
432C4⋊C4—118no—
433C4⋊C4—118no—
434C4⋊C4—114no—
435C4⋊C4C2×C4×D1114yes—
436C4⋊C4C2×C4×D1114yes—
437C22⋊C4—114no—
438C22⋊C4—118no—
439C22⋊C4—118no—
440C22⋊C4—118no—
441C22⋊C4—118no—
442C22⋊C4C2×C4×D1114yes—
443C22⋊C4C2×C4×D1114yes—
444C42—118no—
445C42—114no—
446C42C2×C4×D1112yes—
447C42C2×C4×D1111yescharacteristic
448C42C2×C4×D1111yescharacteristic
449C42C23×D1112yes—
450C42C23×D1112yes—
451C11#6020611yescharacteristic, complemented, Sylow
452C23—22no—
453C23—42no—
454C23—114no—
455C23C22×C4×D1112yes—
456C23C22×C4×D1111yescharacteristic
457Q8—224no—
458Q8—444no—
459D4—228no—
460D4—224no—
461D4—444no—
462D4—448no—
463C2×C4—22no—
464C2×C4—24no—
465C2×C4—22no—
466C2×C4—22no—
467C2×C4—42no—
468C2×C4—42no—
469C2×C4—118no—
470C2×C4—114no—
471C2×C4—224no—
472C2×C4—224no—
473C2×C4—448no—
474C2×C4C22×C4×D1114yes—
475C2×C4C22×C4×D1112yes—
476C2×C4C22×C4×D1112yes—
477C2×C4C22×C4×D1112yes—
478C2×C4C22×C4×D1111yescharacteristic
479C2×C4C2×#433912yes—
480C2×C4C2×#433912yes—
481C2×C4C24×D1111yescharacteristic
482C8—22no—
483C8—22no—
484C8—224no—
485C8—224no—
486C8C2×#433912yes—
487C8C2×#433912yes—
488C8C2×#433914yes—
489C22—22no—
490C22—24no—
491C22—22no—
492C22—44no—
493C22—228no—
494C22—224no—
495C22C4×#433912yes—
496C22C23×C4×D1111yescharacteristic
497C4—24no—
498C4—22no—
499C4—22no—
500C4—22no—
501C4—228no—
502C4—224no—
503C4C4×#433912yes—
504C4C22×#433911yescharacteristic
505C4C22×#433911yescharacteristic
506C2—22no—
507C2—42no—
508C2—444no—
509C2C2×C4×#433911yescharacteristic
510C2#1308332712yes—
subgroupG/H
centerC2×C8C23×D11
commutator, socleC22×C11C24×C4
FrattiniC2×C4C24×D11
FittingC2×C11×#405C2
prime radical#13082006C2
cosocleC2×C4×C11C25
hypercenterC2×#405D11
hypocenterC11#60206
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C2×C8 ◁ C2×#405

Complements

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

NH ≅ G/Ntype
2. #13077597C2semidirect
3. #13077587C2semidirect
4. #13077556C2semidirect
5. #13077550C2semidirect
6. #13077335C2semidirect
7. #13077329C2semidirect
8. #13077319C2semidirect
9. #13077310C2semidirect
10. #13077265C2semidirect
11. #13077254C2semidirect
12. C4×#66954C2semidirect
13. C2×C11×#405C2semidirect
50. #10622322C22semidirect
51. #10622319C22semidirect
52. #10622318C22semidirect
53. #10622314C22semidirect
54. #10622302C22semidirect
55. #10622302C22semidirect
56. #10622301C22semidirect
57. C4×#4313C22semidirect
58. C8×D44C22semidirect
59. C4×C8×D11C22semidirect
60. #10622292C22semidirect
61. C8×Dic22C22semidirect
209. C2×#405D11semidirect
451. C11#60206semidirect

Maximal subgroups

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

subgroupindex
#130820062
#130775972
#130775872
#130775562
#130775502
#130773352
#130773292
#130773192
#130773102
#130772652
#130772542
C4×#669542
C2×C11×#4052
#6020611