Finite Group Databasebeta

← #14785792

Subgroups — #14785792

Order 2816.

1474 conjugacy classes of subgroups.

The subgroup lattice has 538 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13077842C212yesmaximal, complemented
2C2×#10622601C211yesmaximal, characteristic, complemented
3#13069769C212yesmaximal, complemented
4#13069658C212yesmaximal, complemented
5#13069060C212yesmaximal, complemented
6#13068992C214yesmaximal, complemented
7#13068696C211yesmaximal, characteristic, complemented
8C11×#3492C211yesmaximal, characteristic, complemented
9C23×D44C2211yescharacteristic
10C11×#554—22no—
11C11×#553—22no—
12C11×#552—22no—
13C11×#547—22no—
14C11×#544C2211yescharacteristic, complemented
15C11×#539—22no—
16C11×#537C2211yescharacteristic, complemented
17C11×#525—22no—
18C11×#525C2212yes—
19C11×#520C2212yescomplemented
20C22×C11×C4⋊C4C2211yescharacteristic
21C2×#67002C2214yes—
22C22×(C2×D11)⋊C4—22no—
23C22×C4×Dic11C2211yescharacteristic
24C2×#66901C2214yescomplemented
25#10622820C2212yes—
26#10622659—22no—
27#10622659—22no—
28#10622649—22no—
29#10622649—22no—
30#10622614C2214yes—
31#10622601—22no—
32#10622601C2212yes—
33#10622601C2212yes—
34#10622170C2214yescomplemented
35#10622168C2212yescomplemented
36#10622168C2212yescomplemented
37C24×D11—21no—
38C2×C11×#41—22no—
39C2×C11×#41C2312yes—
40C23×C4×C11D412yes—
41C23×C4×C11C2311yescharacteristic
42C23×Dic11—21no—
43C22×D44—21no—
44C22×D44—24no—
45C22×D44—22no—
46C22×D44—22no—
47C22×D44—42no—
48C22×D44C2312yes—
49C11×C4⋊Q8—22no—
50C11×#126—24no—
51C11×#125—24no—
52C11×#125—22no—
53C11×#123—24no—
54C11×#123—24no—
55C11×#123—22no—
56C11×C22⋊Q8—22no—
57C11×C22⋊Q8—24no—
58C11×C22⋊Q8—22no—
59C11×C22⋊Q8—22no—
60C11×C22⋊Q8D412yes—
61C11×C22⋊Q8D412yes—
62C11×#121—22no—
63C11×#121—22no—
64C11×#121—22no—
65C11×#121D412yes—
66C11×#121D412yes—
67C11×#120—22no—
68C4×Q8×C11—22no—
69C4×D4×C11—24no—
70C4×D4×C11—22no—
71C4×D4×C11—24no—
72C4×D4×C11—22no—
73C4×D4×C11—22no—
74C11×#117—22no—
75C11×#117—22no—
76C11×#117C2312yes—
77C2×C11×C4⋊C4—22no—
78C2×C11×C4⋊C4—22no—
79C2×C11×C4⋊C4—22no—
80C2×C11×C4⋊C4D412yes—
81C2×C11×C4⋊C4C2311yescharacteristic
82C2×C11×C4⋊C4C2311yescharacteristic
83#67002—28no—
84#67002—44no—
85C2×#4325—24no—
86C2×#4323—24no—
87C2×(C2×D11)⋊C4—24no—
88C2×(C2×D11)⋊C4—24no—
89C2×(C2×D11)⋊C4—48no—
90C2×C4×Dic11—21no—
91C2×C4×Dic11—42no—
92C2×C4×Dic11C2312yes—
93C2×#4318C2314yes—
94#66901—44no—
95C22⋊(C11⋊C8)—22no—
96C22⋊(C11⋊C8)—22no—
97#66873—24no—
98#66873—24no—
99#23948—111nomaximal, Sylow
100C24×C11C2×D411yescharacteristic
101C23×D11—24no—
102C23×D11—22no—
103C23×D11—44no—
104C23×D11—42no—
105C23×D11—44no—
106C23×D11—41no—
107C23×D11—41no—
108C11×#41—24no—
109C11×#41—24no—
110C11×#41—84no—
111C2×Q8×C11—22no—
112C2×Q8×C11C2×D412yes—
113C2×D4×C11—22no—
114C2×D4×C11—22no—
115C2×D4×C11—22no—
116C2×D4×C11—22no—
117C2×D4×C11C2×D412yes—
118C22×C4×C11—22no—
119C22×C4×C11—22no—
120C22×C4×C11—22no—
121C22×C4×C11—24no—
122C22×C4×C11—22no—
123C22×C4×C11—22no—
124C22×C4×C11—44no—
125C22×C4×C11C2×D411yescharacteristic
126C22×C4×C11C2×D412yes—
127C22×C4×C11C2×D412yes—
128C22×C4×C11C2×D412yes—
129C22×C4×C11C2×D412yes—
130C22×C4×C11C2411yescharacteristic
131C22×Dic11—24no—
132C22×Dic11—22no—
133C22×Dic11—42no—
134C22×Dic11—42no—
135C2×D44—24no—
136C2×D44—24no—
137C2×D44—22no—
138C2×D44—24no—
139C2×D44—48no—
140C2×D44—48no—
141C2×D44—42no—
142C2×D44—42no—
143C2×D44#4114yescomplemented
144C11×C4⋊C4—24no—
145C11×C4⋊C4—22no—
146C11×C4⋊C4—22no—
147C11×C4⋊C4—24no—
148C11×C4⋊C4—24no—
149C11×C4⋊C4—22no—
150C11×C4⋊C4—22no—
151C11×C4⋊C4—22no—
152C11×C4⋊C4—22no—
153C11×C4⋊C4C2×D412yes—
154C11×C4⋊C4C2×D412yes—
155C11×C22⋊C4—24no—
156C11×C22⋊C4—24no—
157C11×C22⋊C4—22no—
158C11×C22⋊C4—22no—
159C11×C22⋊C4—22no—
160C11×C22⋊C4—22no—
161C11×C22⋊C4—22no—
162C42×C11—24no—
163C42×C11—22no—
164#4325—48no—
165#4323—48no—
166(C2×D11)⋊C4—48no—
167(C2×D11)⋊C4—48no—
168C4×Dic11—24no—
169C4×Dic11—42no—
170#4318—24no—
171#4318—24no—
172C2×C11⋊C8—24no—
173#3492D1111yescharacteristic, complemented
174#3003—112no—
175C2×#390—111no—
176#2027—112no—
177#2006—112no—
178#1896—112no—
179#1883—114no—
180#1821—111no—
181C23×C11—21no—
182C23×C11—21no—
183C23×C11—22no—
184C23×C11—22no—
185C23×C11—22no—
186C23×C11#12011yescharacteristic
187C23×C11#12011yescharacteristic
188C23×C11C22×D411yescharacteristic
189C22×D11—24no—
190C22×D11—44no—
191C22×D11—44no—
192C22×D11—44no—
193C22×D11—416no—
194C22×D11—44no—
195C22×D11—42no—
196C22×D11—42no—
197C22×D11—88no—
198C22×D11—82no—
199C22×D11—82no—
200C22×D11—82no—
201C22×D11—82no—
202Q8×C11—24no—
203Q8×C11—82no—
204D4×C11—24no—
205D4×C11—42no—
206D4×C11—42no—
207D4×C11—44no—
208D4×C11—44no—
209D4×C11—82no—
210C2×C4×C11—21no—
211C2×C4×C11—21no—
212C2×C4×C11—24no—
213C2×C4×C11—24no—
214C2×C4×C11—22no—
215C2×C4×C11—22no—
216C2×C4×C11—22no—
217C2×C4×C11—22no—
218C2×C4×C11—22no—
219C2×C4×C11—44no—
220C2×C4×C11—44no—
221C2×C4×C11—42no—
222C2×C4×C11—42no—
223C2×C4×C11—82no—
224C2×C4×C11—84no—
225C2×C4×C11#12012yes—
226C2×C4×C11C22×D412yes—
227C2×C4×C11C2×#4112yes—
228C2×C4×C11H(5,𝔽2)12yes—
229C2×Dic11—24no—
230C2×Dic11—48no—
231C2×Dic11—42no—
232C2×Dic11—42no—
233D44—28no—
234D44—48no—
235D44—44no—
236C11⋊C8—44no—
237C23×D4—111no—
238C2×AGL(1,ℤ/8)—114no—
239#554—22no—
240#553—22no—
241#552—22no—
242#547—22no—
243#544C2×D1111yescharacteristic, complemented
244#539—22no—
245#537C2×D1111yescharacteristic, complemented
246#525—22no—
247#525C2×D1112yes—
248#520C2×D1112yescomplemented
249C22×C4⋊C4C2×D1111yescharacteristic
250C22×C22⋊C4—222no—
251C22×C42—111no—
252#450—222no—
253#450—222no—
254#447—222no—
255#447—222no—
256C2×#104—114no—
257#418—114no—
258#407—112no—
259#390—112no—
260#390—112no—
261#390—222no—
262#343—112no—
263#343—112no—
264#339—114no—
265C22×C11—24no—
266C22×C11—24no—
267C22×C11—21no—
268C22×C11—21no—
269C22×C11—21no—
270C22×C11—21no—
271C22×C11—21no—
272C22×C11—21no—
273C22×C11—42no—
274C22×C11—42no—
275C22×C11—42no—
276C22×C11#45312yes—
277C22×C11#45412yes—
278C22×C11C2×#12011yescharacteristic
279C22×C11#52511yescharacteristic
280C22×C11#53511yescharacteristic
281C2×D11—48no—
282C2×D11—44no—
283C2×D11—84no—
284C2×D11—88no—
285C2×D11—88no—
286C2×D11—82no—
287C2×D11—82no—
288C4×C11—22no—
289C4×C11—42no—
290C4×C11—42no—
291C4×C11—42no—
292C4×C11—42no—
293C4×C11—42no—
294C4×C11#54614yes—
295Dic11—44no—
296C25—221no—
297C2×#41—22no—
298C2×#41C22×D1112yes—
299C22×D4—112no—
300C22×D4—224no—
301C22×D4—221no—
302C22×D4—222no—
303C22×D4—222no—
304C22×D4—442no—
305C23×C4—221no—
306C23×C4C22⋊D1112yes—
307C23×C4C22×D1111yescharacteristic
308AGL(1,ℤ/8)—228no—
309AGL(1,ℤ/8)—444no—
310C2×SD16—224no—
311C2×D8—224no—
312C2×M16—114no—
313C4⋊Q8—22no—
314#126—24no—
315#125—24no—
316#125—22no—
317#123—24no—
318#123—24no—
319#123—22no—
320C22⋊Q8—22no—
321C22⋊Q8—24no—
322C22⋊Q8—22no—
323C22⋊Q8—22no—
324C22⋊Q8C22⋊D1112yes—
325C22⋊Q8C22⋊D1112yes—
326#121—22no—
327#121—22no—
328#121—22no—
329#121C22⋊D1112yes—
330#121C22⋊D1112yes—
331#120—22no—
332C4×Q8—22no—
333C4×D4—24no—
334C4×D4—22no—
335C4×D4—24no—
336C4×D4—22no—
337C4×D4—22no—
338#117—22no—
339#117—22no—
340#117C22×D1112yes—
341C2×C4⋊C4—22no—
342C2×C4⋊C4—22no—
343C2×C4⋊C4—22no—
344C2×C4⋊C4C22⋊D1112yes—
345C2×C4⋊C4C22×D1111yescharacteristic
346C2×C4⋊C4C22×D1111yescharacteristic
347C2×C22⋊C4—224no—
348C2×C22⋊C4—224no—
349C2×C22⋊C4—448no—
350C2×C42—112no—
351C2×C42—221no—
352C2×C42—442no—
353#104—444no—
354#102—224no—
355#102—224no—
356C22⋊C8—222no—
357C22⋊C8—222no—
358C2×C11—21no—
359C2×C11—21no—
360C2×C11—22no—
361C2×C11—22no—
362C2×C11—82no—
363C2×C11#240411yescharacteristic
364C2×C11C2×#45311yescharacteristic
365C2×C11C2×#45411yescharacteristic
366D11—84no—
367C24—224no—
368C24—222no—
369C24—444no—
370C24—442no—
371C24—444no—
372C24—441no—
373C24—441no—
374C24C2×C22⋊D1111yescharacteristic
375#41—24no—
376#41—24no—
377#41—84no—
378C2×Q8—22no—
379C2×Q8C2×C22⋊D1112yes—
380C2×D4—22no—
381C2×D4—22no—
382C2×D4—22no—
383C2×D4—22no—
384C2×D4—114no—
385C2×D4—224no—
386C2×D4—222no—
387C2×D4—224no—
388C2×D4—224no—
389C2×D4—448no—
390C2×D4—448no—
391C2×D4—442no—
392C2×D4—442no—
393C2×D4C2×C22⋊D1112yes—
394C22×C4—22no—
395C22×C4—22no—
396C22×C4—22no—
397C22×C4—24no—
398C22×C4—22no—
399C22×C4—22no—
400C22×C4—44no—
401C22×C4—224no—
402C22×C4—222no—
403C22×C4—442no—
404C22×C4—442no—
405C22×C4C2×C22⋊D1111yescharacteristic
406C22×C4C2×C22⋊D1112yes—
407C22×C4C2×C22⋊D1112yes—
408C22×C4C2×C22⋊D1112yes—
409C22×C4C2×C22⋊D1112yes—
410C22×C4C23×D1111yescharacteristic
411SD16—448no—
412D8—448no—
413M16—224no—
414M16—224no—
415C2×C8—224no—
416C4⋊C4—24no—
417C4⋊C4—22no—
418C4⋊C4—22no—
419C4⋊C4—24no—
420C4⋊C4—24no—
421C4⋊C4—22no—
422C4⋊C4—22no—
423C4⋊C4—22no—
424C4⋊C4—22no—
425C4⋊C4C2×C22⋊D1112yes—
426C4⋊C4C2×C22⋊D1112yes—
427C22⋊C4—24no—
428C22⋊C4—24no—
429C22⋊C4—22no—
430C22⋊C4—22no—
431C22⋊C4—22no—
432C22⋊C4—22no—
433C22⋊C4—22no—
434C22⋊C4—448no—
435C22⋊C4—448no—
436C42—24no—
437C42—22no—
438C42—224no—
439C42—442no—
440C11#2394811yescharacteristic, complemented, Sylow
441C23—21no—
442C23—21no—
443C23—22no—
444C23—22no—
445C23—22no—
446C23—224no—
447C23—444no—
448C23—444no—
449C23—444no—
450C23—4416no—
451C23—444no—
452C23—442no—
453C23—442no—
454C23—888no—
455C23—882no—
456C23—882no—
457C23—882no—
458C23—882no—
459C23#6700611yescharacteristic
460C23#6700611yescharacteristic
461C23C22×C22⋊D1111yescharacteristic
462Q8—24no—
463Q8—82no—
464D4—24no—
465D4—42no—
466D4—42no—
467D4—44no—
468D4—44no—
469D4—82no—
470D4—228no—
471D4—448no—
472D4—444no—
473C2×C4—21no—
474C2×C4—21no—
475C2×C4—24no—
476C2×C4—24no—
477C2×C4—22no—
478C2×C4—22no—
479C2×C4—22no—
480C2×C4—22no—
481C2×C4—22no—
482C2×C4—44no—
483C2×C4—44no—
484C2×C4—42no—
485C2×C4—42no—
486C2×C4—82no—
487C2×C4—84no—
488C2×C4—224no—
489C2×C4—448no—
490C2×C4—442no—
491C2×C4—442no—
492C2×C4#6700612yes—
493C2×C4#41×D1112yes—
494C2×C4#6704212yes—
495C2×C4C22×C22⋊D1112yes—
496C8—444no—
497C22—24no—
498C22—24no—
499C22—21no—
500C22—21no—
501C22—21no—
502C22—21no—
503C22—21no—
504C22—21no—
505C22—42no—
506C22—42no—
507C22—42no—
508C22—448no—
509C22—444no—
510C22—884no—
511C22—888no—
512C22—888no—
513C22—882no—
514C22—882no—
515C22#1062285412yes—
516C22#1062285812yes—
517C22#1062335911yescharacteristic
518C22#1062336111yescharacteristic
519C22C2×#6700611yescharacteristic
520C4—22no—
521C4—42no—
522C4—42no—
523C4—42no—
524C4—42no—
525C4—42no—
526C4—444no—
527C4#1062336014yes—
528C2—21no—
529C2—21no—
530C2—22no—
531C2—22no—
532C2—82no—
533C2—884no—
534C2#1307193111yescharacteristic
535C2C2×#1062285411yescharacteristic
536C2C2×#1062285811yescharacteristic
subgroupG/H
centerC22C2×#67006
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#3492C2
socleC22×C11C2×#120
hypercenter#3492D11
hypocenterC11#23948
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #3492

Complements

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

NH ≅ G/Ntype
1. #13077842C2semidirect
2. C2×#10622601C2semidirect
3. #13069769C2semidirect
4. #13069658C2semidirect
5. #13069060C2semidirect
6. #13068992C2semidirect
7. #13068696C2semidirect
8. C11×#3492C2semidirect
14. C11×#544C22semidirect
16. C11×#537C22semidirect
19. C11×#520C22semidirect
24. C2×#66901C22semidirect
34. #10622170C22semidirect
35. #10622168C22semidirect
36. #10622168C22semidirect
143. C2×D44#41semidirect
173. #3492D11semidirect
243. #544C2×D11semidirect
245. #537C2×D11semidirect
248. #520C2×D11semidirect
440. C11#23948semidirect

Maximal subgroups

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

subgroupindex
#130778422
C2×#106226012
#130697692
#130696582
#130690602
#130689922
#130686962
C11×#34922
#2394811