Finite Group Databasebeta

← #14721626

Subgroups — #14721626

Order 2816.

1066 conjugacy classes of subgroups.

The subgroup lattice has 510 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082468C211yesmaximal, characteristic
2#13077657C211yesmaximal, characteristic, complemented
3#13067179C211yesmaximal, characteristic, complemented
4#13067175C211yesmaximal, characteristic, complemented
5#13067157C214yesmaximal, complemented
6#13067118C214yesmaximal, complemented
7#13067114C211yesmaximal, characteristic, complemented
8#13067110C211yesmaximal, characteristic, complemented
9C11×#2349C211yesmaximal, characteristic, complemented
10C2×C4×D4×C11—21no—
11C2×C4×D4×C11C2211yescharacteristic
12#10623336—21no—
13#10623322C2214yes—
14#10623094C412yescomplemented
15#10623090—22no—
16#10623089—22no—
17#10623084C412yescomplemented
18#10623082C412yescomplemented
19#10623073C412yescomplemented
20#10623035—21no—
21#10623025—22no—
22#10623008C2211yescharacteristic
23#10623001C2211yescharacteristic
24C11×#389—21no—
25C11×#385—22no—
26C11×#382C2211yescharacteristic
27C11×#380C2212yes—
28C4×C11×C4⋊C4C2211yescharacteristic
29C2×C11×#95C2212yes—
30#10622820C2214yes—
31#10622625—22no—
32#10622625—22no—
33#10622538C2211yescharacteristic
34#10622538C2211yescharacteristic
35#10622090C2212yes—
36#10622090C2212yes—
37#10622090C2214yes—
38#10622089C2212yes—
39#10622089C2212yes—
40#10622089C2214yes—
41C22×D4×C11D411yescharacteristic
42C23×C4×C11—22no—
43C23×C4×C11C2312yes—
44C2×#4339—21no—
45C2×#4339C2×C414yescomplemented
46C4×D4×C11—44no—
47C4×D4×C11C2×C412yes—
48C4×D4×C11C2×C412yes—
49C4×D4×C11D412yes—
50C4×D4×C11D412yes—
51C2×C11×C4⋊C4—21no—
52C2×C11×C4⋊C4—21no—
53C2×C11×C4⋊C4—22no—
54C2×C11×C4⋊C4D411yescharacteristic
55C2×C11×C22⋊C4—22no—
56C2×C11×C22⋊C4D412yes—
57C2×C42×C11—21no—
58C2×C42×C11C2311yescharacteristic
59#67006—24no—
60#66993—22no—
61#66991—22no—
62#66991—22no—
63#66989—22no—
64#66983—21no—
65#66983C2×C414yescomplemented
66#66983C2312yes—
67#66982—24no—
68C4×C22⋊D11—24no—
69C4×C22⋊D11—24no—
70#66979—21no—
71#66979C2×C414yescomplemented
72#66977—21no—
73#66977C2×C414yescomplemented
74#66977C2312yes—
75C2×#4318—24no—
76#66946—22no—
77#66945—22no—
78C4⋊C4×D11—22no—
79#66940—22no—
80#66938—24no—
81#66937—24no—
82#66936—24no—
83#66932—24no—
84#66928—21no—
85#66927C2×C411yescharacteristic, complemented
86C4×D44—21no—
87C4×D44C2×C412yescomplemented
88#66923—21no—
89#66922C2×C411yescharacteristic, complemented
90#66922C2×C411yescharacteristic, complemented
91#66922C2×C411yescharacteristic, complemented
92C4×Dic22—21no—
93C4×Dic22C2×C412yescomplemented
94C11×#95—22no—
95C11×#95—21no—
96C11×#95C2311yescharacteristic
97C11×#95C2312yes—
98C11×#95C2311yescharacteristic
99C22⋊(C11⋊C8)—24no—
100C22⋊(C11⋊C8)C2312yes—
101C22⋊(C11⋊C8)C2312yes—
102C4⋊(C11⋊C8)—21no—
103C4⋊(C11⋊C8)—21no—
104C4×C11⋊C8—21no—
105C4×C11⋊C8—21no—
106#17630—111nomaximal, Sylow
107C24×C11C2×D412yes—
108C2×D4×C11—22no—
109C2×D4×C11—22no—
110C2×D4×C11C22⋊C412yes—
111C2×D4×C11C22⋊C412yes—
112C22×C4×C11—21no—
113C22×C4×C11—22no—
114C22×C4×C11—21no—
115C22×C4×C11—44no—
116C22×C4×C11—44no—
117C22×C4×C11—82no—
118C22×C4×C11—82no—
119C22×C4×C11C22×C414yes—
120C22×C4×C11C2×D411yescharacteristic
121C22×C4×C11C2×D412yes—
122C22×C4×C11C2×D414yes—
123C22×C4×C11C2×D411yescharacteristic
124C22×C4×C11C2411yescharacteristic
125C2×C22⋊D11—24no—
126C2×C22⋊D11—24no—
127C2×C22⋊D11—22no—
128#4339—42no—
129#4339—42no—
130#4339—84no—
131C2×D44—21no—
132C2×D44—21no—
133C2×D44C22×C412yes—
134C2×C4×D11—22no—
135C2×C4×D11—24no—
136C2×Dic22—21no—
137C2×Dic22—21no—
138C2×Dic22C22×C412yes—
139C11×C4⋊C4—42no—
140C11×C4⋊C4—42no—
141C11×C4⋊C4—82no—
142C11×C4⋊C4C22⋊C412yes—
143C11×C4⋊C4C22⋊C412yes—
144C11×C22⋊C4—44no—
145C11×C22⋊C4C22⋊C414yes—
146C11×C22⋊C4C22⋊C414yes—
147C42×C11—42no—
148C42×C11C22×C411yescharacteristic
149C42×C11C22×C411yescharacteristic
150C42×C11C2×D411yescharacteristic
151C42×C11C2×D411yescharacteristic
152C22⋊Dic11—24no—
153C22⋊Dic11—24no—
154C22⋊Dic11—22no—
155(C2×D11)⋊C4—22no—
156(C2×D11)⋊C4—24no—
157(C2×D11)⋊C4—22no—
158C4⋊Dic11—21no—
159C4⋊Dic11—21no—
160C4⋊Dic11—21no—
161C4⋊Dic11—21no—
162C4⋊Dic11C22×C412yes—
163C4⋊Dic11C22×C412yes—
164Dic11⋊C4—22no—
165Dic11⋊C4—24no—
166Dic11⋊C4—22no—
167C4×Dic11—22no—
168C4×Dic11—24no—
169#4318—84no—
170C2×C11⋊C8—22no—
171C2×C11⋊C8—22no—
172#3506—111no—
173#2975—111no—
174#2349D1111yescharacteristic, complemented
175#1518—111no—
176#1517—111no—
177#1513—114no—
178#1504—114no—
179#1503—111no—
180#1502—111no—
181C23×C11—22no—
182C23×C11—22no—
183C23×C11—42no—
184C23×C11—42no—
185C23×C11C2×C22⋊C414yes—
186C23×C11C22×D411yescharacteristic
187C22×D11—22no—
188D4×C11—24no—
189D4×C11—24no—
190C2×C4×C11—22no—
191C2×C4×C11—44no—
192C2×C4×C11—41no—
193C2×C4×C11—42no—
194C2×C4×C11—44no—
195C2×C4×C11—41no—
196C2×C4×C11—41no—
197C2×C4×C11—41no—
198C2×C4×C11—41no—
199C2×C4×C11—41no—
200C2×C4×C11—42no—
201C2×C4×C11—42no—
202C2×C4×C11—41no—
203C2×C4×C11—42no—
204C2×C4×C11—88no—
205C2×C4×C11C2×C22⋊C414yes—
206C2×C4×C11C2×C22⋊C411yescharacteristic
207C2×C4×C11C2×C22⋊C411yescharacteristic
208C2×C4×C11C2×C22⋊C411yescharacteristic
209C2×C4×C11C2×C22⋊C411yescharacteristic
210C2×C4×C11AGL(1,ℤ/8)12yes—
211C2×C4×C11#13712yes—
212C2×C4×C11C23×C411yescharacteristic
213C2×C4×C11C22×D411yescharacteristic
214C22⋊D11—42no—
215C22⋊D11—42no—
216C22⋊D11—84no—
217C22⋊D11—84no—
218C2×Dic11—22no—
219C2×Dic11—22no—
220C2×Dic11—22no—
221D44—42no—
222D44—42no—
223D44—81no—
224C4×D11—44no—
225C4×D11—84no—
226Dic22—42no—
227Dic22—42no—
228Dic22—81no—
229C11⋊C8—42no—
230C11⋊C8—42no—
231#559—222no—
232#556—112no—
233#555—112no—
234#553—222no—
235#550—112no—
236#547—112no—
237#538—222no—
238#535—221no—
239#533—111no—
240#532—111no—
241#525—114no—
242#520—221no—
243C2×C4×D4—21no—
244C2×C4×D4C2×D1111yescharacteristic
245#436—222no—
246#436—222no—
247#431—111no—
248#431—111no—
249#407—114no—
250#389—21no—
251#385—22no—
252#382C2×D1111yescharacteristic
253#380C2×D1112yes—
254C4×C4⋊C4C2×D1111yescharacteristic
255C2×#95C2×D1112yes—
256#328—112no—
257#328—112no—
258#328—114no—
259#327—112no—
260#327—112no—
261#327—114no—
262C22×C11—21no—
263C22×C11—21no—
264C22×C11—24no—
265C22×C11—24no—
266C22×C11—24no—
267C22×C11—44no—
268C22×C11—44no—
269C22×C11C22×C22⋊C411yescharacteristic
270C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
271C22×C11C2×#13711yescharacteristic
272C2×D11—42no—
273C2×D11—42no—
274C2×D11—42no—
275C4×C11—21no—
276C4×C11—21no—
277C4×C11—24no—
278C4×C11—21no—
279C4×C11—21no—
280C4×C11—42no—
281C4×C11—81no—
282C4×C11—82no—
283C4×C11#41712yes—
284C4×C11#41712yes—
285Dic11—42no—
286Dic11—42no—
287Dic11—42no—
288C2×#41—114no—
289C2×#41—221no—
290C22×D4C22⋊D1111yescharacteristic
291C23×C4—22no—
292C23×C4C22×D1112yes—
293C2×M16—224no—
294C4⋊Q8—111no—
295C4⋊Q8—111no—
296C4⋊Q8—111no—
297#127—111no—
298#127—222no—
299#126—224no—
300#125—221no—
301#124—222no—
302#124—224no—
303#124—221no—
304#123—224no—
305#123—224no—
306C22⋊Q8—114no—
307C22⋊Q8—112no—
308C22⋊Q8—221no—
309#121—114no—
310#121—112no—
311#121—222no—
312#121—222no—
313#121—221no—
314#121—224no—
315#120—224no—
316C4×Q8—112no—
317C4×Q8—222no—
318C4×Q8—221no—
319C4×D4—44no—
320C4×D4—112no—
321C4×D4—224no—
322C4×D4—224no—
323C4×D4—222no—
324C4×D4—221no—
325C4×D4C4×D1112yes—
326C4×D4C4×D1112yes—
327C4×D4D4412yes—
328C4×D4D4412yes—
329#117—114no—
330#117—221no—
331#117—222no—
332C2×C4⋊C4—21no—
333C2×C4⋊C4—21no—
334C2×C4⋊C4—22no—
335C2×C4⋊C4—222no—
336C2×C4⋊C4C22⋊D1111yescharacteristic
337C2×C22⋊C4—22no—
338C2×C22⋊C4C22⋊D1112yes—
339C2×C42—21no—
340C2×C42C22×D1111yescharacteristic
341C4⋊C8—221no—
342C4⋊C8—221no—
343C22⋊C8—112no—
344C22⋊C8—112no—
345C22⋊C8—224no—
346C4×C8—221no—
347C4×C8—221no—
348#95—22no—
349#95—21no—
350#95C22×D1111yescharacteristic
351#95C22×D1112yes—
352#95C22×D1111yescharacteristic
353C2×C11—21no—
354C2×C11—21no—
355C2×C11—44no—
356C2×C11#288311yescharacteristic
357C2×C11C2×#41711yescharacteristic
358C2×C11#290111yescharacteristic
359D11—82no—
360C24C2×C22⋊D1112yes—
361#41—442no—
362#41—442no—
363#41—884no—
364C2×Q8—112no—
365C2×Q8—221no—
366C2×Q8—221no—
367C2×D4—22no—
368C2×D4—22no—
369C2×D4—112no—
370C2×D4—222no—
371C2×D4—224no—
372C2×D4—224no—
373C2×D4—221no—
374C2×D4—221no—
375C2×D4(C2×D11)⋊C412yes—
376C2×D4(C2×D11)⋊C412yes—
377C22×C4—21no—
378C22×C4—22no—
379C22×C4—21no—
380C22×C4—44no—
381C22×C4—44no—
382C22×C4—82no—
383C22×C4—82no—
384C22×C4—222no—
385C22×C4—224no—
386C22×C4C2×C4×D1114yes—
387C22×C4C2×D4414yes—
388C22×C4C2×C22⋊D1111yescharacteristic
389C22×C4C2×C22⋊D1112yes—
390C22×C4C2×C22⋊D1111yescharacteristic
391C22×C4C23×D1111yescharacteristic
392M16—884no—
393C2×C8—222no—
394C2×C8—222no—
395C4⋊C4—42no—
396C4⋊C4—42no—
397C4⋊C4—82no—
398C4⋊C4—112no—
399C4⋊C4—112no—
400C4⋊C4—221no—
401C4⋊C4—224no—
402C4⋊C4—221no—
403C4⋊C4—221no—
404C4⋊C4—222no—
405C4⋊C4—221no—
406C4⋊C4—222no—
407C4⋊C4(C2×D11)⋊C412yes—
408C4⋊C4(C2×D11)⋊C412yes—
409C22⋊C4—44no—
410C22⋊C4—224no—
411C22⋊C4—224no—
412C22⋊C4—222no—
413C22⋊C4—224no—
414C22⋊C4—222no—
415C22⋊C4—222no—
416C22⋊C4(C2×D11)⋊C414yes—
417C22⋊C4(C2×D11)⋊C414yes—
418C42—42no—
419C42—224no—
420C42—222no—
421C42C2×C4×D1111yescharacteristic
422C42C2×C4×D1111yescharacteristic
423C42C2×D4411yescharacteristic
424C42C2×D4411yescharacteristic
425C11#1763011yescharacteristic, complemented, Sylow
426C23—22no—
427C23—22no—
428C23—42no—
429C23—42no—
430C23—222no—
431C23C2×(C2×D11)⋊C414yes—
432C23C22×C22⋊D1111yescharacteristic
433Q8—442no—
434Q8—442no—
435Q8—881no—
436D4—24no—
437D4—24no—
438D4—442no—
439D4—442no—
440D4—442no—
441D4—442no—
442D4—881no—
443D4—884no—
444D4—884no—
445C2×C4—22no—
446C2×C4—41no—
447C2×C4—42no—
448C2×C4—44no—
449C2×C4—41no—
450C2×C4—44no—
451C2×C4—41no—
452C2×C4—41no—
453C2×C4—41no—
454C2×C4—41no—
455C2×C4—42no—
456C2×C4—42no—
457C2×C4—41no—
458C2×C4—42no—
459C2×C4—88no—
460C2×C4—222no—
461C2×C4—222no—
462C2×C4—222no—
463C2×C4—444no—
464C2×C4—884no—
465C2×C4C2×(C2×D11)⋊C414yes—
466C2×C4C2×(C2×D11)⋊C411yescharacteristic
467C2×C4C2×(C2×D11)⋊C411yescharacteristic
468C2×C4C2×(C2×D11)⋊C411yescharacteristic
469C2×C4C2×(C2×D11)⋊C411yescharacteristic
470C2×C4#6698512yes—
471C2×C4#6699512yes—
472C2×C4C22×C4×D1111yescharacteristic
473C2×C4C22×D4411yescharacteristic
474C8—442no—
475C8—442no—
476C22—21no—
477C22—21no—
478C22—24no—
479C22—24no—
480C22—24no—
481C22—44no—
482C22—44no—
483C22—442no—
484C22—442no—
485C22—442no—
486C22C22×(C2×D11)⋊C411yescharacteristic
487C22C2×#6698511yescharacteristic
488C22C2×#6699511yescharacteristic
489C4—21no—
490C4—21no—
491C4—24no—
492C4—21no—
493C4—21no—
494C4—42no—
495C4—82no—
496C4—81no—
497C4—442no—
498C4—442no—
499C4—442no—
500C4#1062257912yes—
501C4#1062257912yes—
502C2—21no—
503C2—21no—
504C2—44no—
505C2—882no—
506C2#1307707611yescharacteristic
507C2C2×#1062257911yescharacteristic
508C2#1307716411yescharacteristic
subgroupG/H
centerC22C22×(C2×D11)⋊C4
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#2349C2
socleC22×C11C22×C22⋊C4
prime radical#13082468C2
cosocleC22×C4×C11C24
hypercenter#2349D11
hypocenterC11#17630
LCSG ▷ C2×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C4×D4 ◁ #2349

Complements

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

NH ≅ G/Ntype
2. #13077657C2semidirect
3. #13067179C2semidirect
4. #13067175C2semidirect
5. #13067157C2semidirect
6. #13067118C2semidirect
7. #13067114C2semidirect
8. #13067110C2semidirect
9. C11×#2349C2semidirect
14. #10623094C4semidirect
17. #10623084C4semidirect
18. #10623082C4semidirect
19. #10623073C4semidirect
45. C2×#4339C2×C4semidirect
65. #66983C2×C4semidirect
71. #66979C2×C4semidirect
73. #66977C2×C4semidirect
85. #66927C2×C4semidirect
87. C4×D44C2×C4semidirect
89. #66922C2×C4semidirect
90. #66922C2×C4semidirect
91. #66922C2×C4semidirect
93. C4×Dic22C2×C4semidirect
174. #2349D11semidirect
425. C11#17630semidirect

Maximal subgroups

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

subgroupindex
#130824682
#130776572
#130671792
#130671752
#130671572
#130671182
#130671142
#130671102
C11×#23492
#1763011