Finite Group Databasebeta

← #14764011

Subgroups — #14764011

Order 2816.

1218 conjugacy classes of subgroups.

The subgroup lattice has 542 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622739C211yesmaximal, characteristic
2C2×#10622339C211yesmaximal, characteristic
3C4×C22⋊C4×D11C211yesmaximal, characteristic
4#13068801C211yesmaximal, characteristic, complemented
5#13068800C212yesmaximal, complemented
6#13068799C211yesmaximal, characteristic, complemented
7#13068798C211yesmaximal, characteristic, complemented
8#13068797C212yesmaximal, complemented
9#13068595C212yesmaximal, complemented
10#13068593C212yesmaximal, complemented
11C11×#1851C211yesmaximal, characteristic, complemented
12C23×C4×D11C2211yescharacteristic
13C22×C11×M16C2211yescharacteristic
14C22×#4318C2211yescharacteristic
15C22×#4313C2211yescharacteristic
16C22×#4313C2211yescharacteristic
17C2×C22⋊C4×D11C412yes—
18C2×C42×D11C2212yes—
19C2×C11×C4⋊C8C2212yescomplemented
20C2×C11×C22⋊C8C2211yescharacteristic
21C4×C11×C22⋊C4C2211yescharacteristic
22C4×C22⋊Dic11C2211yescharacteristic
23C2×C22⋊(C11⋊C8)C2211yescharacteristic
24#10622739—24no—
25C2×(C2×D11)⋊C8C2212yes—
26C2×(C2×D11)⋊C8C2211yescharacteristic
27C2×(C2×D11)⋊C8C2212yes—
28C2×(C2×D11)⋊C8C2211yescharacteristic
29C2×Dic11⋊C8C2212yescomplemented
30C2×Dic11⋊C8C2212yescomplemented
31C22⋊C4×Dic11C412yes—
32C4×(C2×D11)⋊C4C2212yes—
33C2×C4⋊(C11⋊C8)C2212yescomplemented
34#10622339—24no—
35#10622279C411yescharacteristic
36#10622279C411yescharacteristic
37D11×#95C411yescharacteristic
38D11×#95C411yescharacteristic
39C11×#336C2212yescomplemented
40#10622188C2212yescomplemented
41#10622188C2212yescomplemented
42#10622162C2212yescomplemented
43C24×D11C2×C411yescharacteristic
44C23×C4×C11C2311yescharacteristic
45C23×Dic11C2×C411yescharacteristic
46C22×C4×D11—42no—
47C22×C4×D11—42no—
48C22×C4×D11C2×C412yes—
49C22×C4×D11C2×C411yescharacteristic
50C22×C4×D11C2×C411yescharacteristic
51C22×C4×D11C2×C412yes—
52C22×C4×D11D414yes—
53C22×C4×D11Q814yes—
54C22×C4×D11C2311yescharacteristic
55C22×C4×D11C2311yescharacteristic
56C2×C11×M16—22no—
57C2×C11×M16—42no—
58C22×C8×C11C2312yes—
59C22×C8×C11C2311yescharacteristic
60C22×C8×C11C2311yescharacteristic
61C2×C11×C22⋊C4C2×C412yes—
62C2×C42×C11C2312yes—
63C2×C22⋊Dic11C2×C412yes—
64C2×(C2×D11)⋊C4C2×C412yes—
65C2×(C2×D11)⋊C4C2×C412yes—
66C2×C4×Dic11C2×C412yes—
67C2×C4×Dic11C2×C412yes—
68C2×C4×Dic11C2312yes—
69C2×#4318—22no—
70C2×#4318—42no—
71C22×C11⋊C8C2312yes—
72C22×C11⋊C8C2311yescharacteristic
73C22×C11⋊C8C2311yescharacteristic
74C2×#4313—22no—
75C2×#4313—22no—
76C2×#4313—42no—
77C2×#4313—42no—
78C22⋊C4×D11—28no—
79C42×D11—42no—
80C42×D11—42no—
81C11×C4⋊C8—42no—
82C11×C22⋊C8—22no—
83C11×#95C2×C411yescharacteristic
84C11×#95C2×C411yescharacteristic
85C11⋊#95C2×C411yescharacteristic
86C11⋊#95C2×C411yescharacteristic
87C11⋊#95C2×C412yes—
88C11⋊#95C2×C412yes—
89C22⋊(C11⋊C8)—22no—
90(C2×D11)⋊C8—24no—
91(C2×D11)⋊C8—24no—
92(C2×D11)⋊C8—22no—
93(C2×D11)⋊C8—22no—
94Dic11⋊C8—42no—
95Dic11⋊C8—42no—
96C4⋊(C11⋊C8)—42no—
97#21934—111nomaximal, Sylow
98C24×C11C22×C411yescharacteristic
99C23×D11—24no—
100C23×D11—42no—
101C23×D11—41no—
102C23×D11—41no—
103C23×D11C4⋊C414yes—
104C23×D11C22×C411yescharacteristic
105C23×D11C22×C411yescharacteristic
106C22×C4×C11—22no—
107C22×C4×C11—22no—
108C22×C4×C11C22×C412yes—
109C22×C4×C11C22×C411yescharacteristic
110C22×C4×C11C22×C412yes—
111C22×C4×C11C2×D412yes—
112C22×C4×C11C2×Q812yes—
113C22×C4×C11C2411yescharacteristic
114C22×Dic11—42no—
115C22×Dic11C4⋊C414yes—
116C22×Dic11C22×C412yes—
117C22×Dic11C22×C411yescharacteristic
118C22×Dic11C22×C411yescharacteristic
119C22×Dic11C22×C412yes—
120C2×C4×D11—24no—
121C2×C4×D11—22no—
122C2×C4×D11—22no—
123C2×C4×D11—22no—
124C2×C4×D11—22no—
125C2×C4×D11—42no—
126C2×C4×D11—42no—
127C2×C4×D11—42no—
128C2×C4×D11—42no—
129C2×C4×D11—42no—
130C2×C4×D11—42no—
131C2×C4×D11—44no—
132C2×C4×D11—44no—
133C2×C4×D11—48no—
134C2×C4×D11C4⋊C414yes—
135C2×C4×D11C4⋊C414yes—
136C2×C4×D11M1618yescomplemented
137C2×C4×D11C2×D412yes—
138C2×C4×D11C2×D412yes—
139C2×C4×D11C2×Q812yes—
140C2×C4×D11C2×Q812yes—
141C11×M16—44no—
142C2×C8×C11—22no—
143C2×C8×C11—21no—
144C2×C8×C11—21no—
145C2×C8×C11—22no—
146C2×C8×C11—22no—
147C2×C8×C11—22no—
148C2×C8×C11—22no—
149C11×C22⋊C4—24no—
150C42×C11—22no—
151C42×C11—22no—
152C22⋊Dic11—24no—
153(C2×D11)⋊C4—24no—
154(C2×D11)⋊C4—24no—
155C4×Dic11—22no—
156C4×Dic11—22no—
157C4×Dic11—42no—
158C4×Dic11—42no—
159#4318—44no—
160C2×C11⋊C8—22no—
161C2×C11⋊C8—21no—
162C2×C11⋊C8—21no—
163C2×C11⋊C8—22no—
164C2×C11⋊C8—22no—
165C2×C11⋊C8—22no—
166C2×C11⋊C8—22no—
167#4313—44no—
168#4313—44no—
169C2×#407—111no—
170C2×#407—111no—
171C2×C4×C22⋊C4—111no—
172#1851—112no—
173#1851—111no—
174#1851—111no—
175#1851—112no—
176#1851—111no—
177#1851D1111yescharacteristic, complemented
178#1797—112no—
179#1797—112no—
180C23×C11—22no—
181C23×C11—22no—
182C23×C11—21no—
183C23×C11—21no—
184C23×C11C2×C4⋊C412yes—
185C23×C11C23×C411yescharacteristic
186C22×D11—22no—
187C22×D11—21no—
188C22×D11—21no—
189C22×D11—22no—
190C22×D11—22no—
191C22×D11—21no—
192C22×D11—21no—
193C22×D11—28no—
194C22×D11—44no—
195C22×D11—44no—
196C22×D11—48no—
197C22×D11—48no—
198C22×D11C2×C4⋊C412yes—
199C22×D11C2×C4⋊C412yes—
200C22×D11C2×M1614yes—
201C2×C4×C11—22no—
202C2×C4×C11—22no—
203C2×C4×C11—22no—
204C2×C4×C11—22no—
205C2×C4×C11—22no—
206C2×C4×C11—24no—
207C2×C4×C11—22no—
208C2×C4×C11—22no—
209C2×C4×C11—22no—
210C2×C4×C11C2×C4⋊C412yes—
211C2×C4×C11C2×M1614yes—
212C2×C4×C11C22×D411yescharacteristic
213C2×C4×C11C22×Q811yescharacteristic
214C2×C4×C11H(5,𝔽2)12yes—
215C2×C4×C11H(5,𝔽2)12yes—
216C2×Dic11—22no—
217C2×Dic11—22no—
218C2×Dic11—22no—
219C2×Dic11—22no—
220C2×Dic11—22no—
221C2×Dic11—22no—
222C2×Dic11—22no—
223C2×Dic11—44no—
224C2×Dic11C2×C4⋊C412yes—
225C2×Dic11C2×C4⋊C412yes—
226C2×Dic11C2×M1614yes—
227C4×D11—22no—
228C4×D11—22no—
229C4×D11—22no—
230C4×D11—22no—
231C4×D11—24no—
232C4×D11—24no—
233C4×D11—44no—
234C4×D11—44no—
235C4×D11—48no—
236C4×D11—48no—
237C8×C11—41no—
238C8×C11—41no—
239C8×C11—42no—
240C11⋊C8—41no—
241C11⋊C8—41no—
242C11⋊C8—42no—
243C24×C4—111no—
244C22×M16—111no—
245C22×M16—111no—
246C22×M16—111no—
247C22×M16C2×D1111yescharacteristic
248C22×C22⋊C4—112no—
249C22×C42—112no—
250C2×C4⋊C8—112no—
251C2×C4⋊C8—112no—
252C2×C4⋊C8—112no—
253C2×C4⋊C8C2×D1112yescomplemented
254#407—224no—
255#407—224no—
256C2×C22⋊C8—111no—
257C2×C22⋊C8—111no—
258C2×C22⋊C8—111no—
259C2×C22⋊C8—112no—
260C2×C22⋊C8—112no—
261C2×C22⋊C8C2×D1111yescharacteristic
262C4×C22⋊C4—111no—
263C4×C22⋊C4—112no—
264C4×C22⋊C4—112no—
265C4×C22⋊C4—111no—
266C4×C22⋊C4—111no—
267C4×C22⋊C4C2×D1111yescharacteristic
268C2×#95—111no—
269C2×#95—111no—
270#336—112no—
271#336—112no—
272#336—112no—
273#336C2×D1112yescomplemented
274C22×C11—22no—
275C22×C11—22no—
276C22×C11—22no—
277C22×C11—42no—
278C22×C11—42no—
279C22×C11C22×C4⋊C411yescharacteristic
280C22×C11#51812yes—
281C22×C11C22×M1612yes—
282C22×C11#56811yescharacteristic
283C22×C11#56811yescharacteristic
284C2×D11—22no—
285C2×D11—22no—
286C2×D11—24no—
287C2×D11—24no—
288C2×D11—22no—
289C2×D11—22no—
290C2×D11—22no—
291C2×D11—416no—
292C2×D11—42no—
293C2×D11—42no—
294C2×D11#42314yes—
295C4×C11—22no—
296C4×C11—24no—
297C4×C11—42no—
298C4×C11#53411yescharacteristic
299C4×C11#53411yescharacteristic
300C4×C11#54312yes—
301Dic11—22no—
302Dic11—22no—
303Dic11—24no—
304Dic11—42no—
305C25—111no—
306C23×C4—111no—
307C23×C4—111no—
308C23×C4—111no—
309C23×C4—112no—
310C23×C4—111no—
311C23×C4—111no—
312C23×C4—114no—
313C23×C4—114no—
314C23×C4—112no—
315C23×C4—442no—
316C23×C4—442no—
317C23×C4C22×D1111yescharacteristic
318C2×M16—22no—
319C2×M16—42no—
320C2×M16—222no—
321C2×M16—222no—
322C2×M16—222no—
323C2×M16—442no—
324C2×M16—442no—
325C2×M16—442no—
326C22×C8—111no—
327C22×C8—112no—
328C22×C8—111no—
329C22×C8C22×D1111yescharacteristic
330C22×C8C22×D1111yescharacteristic
331C22×C8C22×D1112yes—
332C2×C22⋊C4—112no—
333C2×C22⋊C4—112no—
334C2×C22⋊C4—112no—
335C2×C22⋊C4—228no—
336C2×C22⋊C4C4×D1112yes—
337C2×C42—112no—
338C2×C42—112no—
339C2×C42—112no—
340C2×C42—442no—
341C2×C42—442no—
342C2×C42C22×D1112yes—
343C4⋊C8—42no—
344C4⋊C8—442no—
345C4⋊C8—442no—
346C4⋊C8—442no—
347C22⋊C8—22no—
348C22⋊C8—222no—
349C22⋊C8—222no—
350C22⋊C8—224no—
351C22⋊C8—224no—
352C22⋊C8—222no—
353#95—112no—
354#95—112no—
355#95—111no—
356#95—111no—
357#95C4×D1111yescharacteristic
358#95C4×D1111yescharacteristic
359C2×C11—42no—
360C2×C11#231511yescharacteristic
361C2×C11C2×#42311yescharacteristic
362C2×C11#290511yescharacteristic
363C2×C11#297312yes—
364C2×C11#297512yes—
365D11—24no—
366D11—42no—
367C24—111no—
368C24—111no—
369C24—114no—
370C24—224no—
371C24—442no—
372C24—441no—
373C24—441no—
374C24C2×C4×D1111yescharacteristic
375C22×C4—22no—
376C22×C4—22no—
377C22×C4—111no—
378C22×C4—112no—
379C22×C4—111no—
380C22×C4—114no—
381C22×C4—112no—
382C22×C4—112no—
383C22×C4—112no—
384C22×C4—112no—
385C22×C4—114no—
386C22×C4—114no—
387C22×C4—118no—
388C22×C4—112no—
389C22×C4—224no—
390C22×C4—222no—
391C22×C4—222no—
392C22×C4—222no—
393C22×C4—222no—
394C22×C4—444no—
395C22×C4—448no—
396C22×C4—444no—
397C22×C4—442no—
398C22×C4—442no—
399C22×C4—442no—
400C22×C4—442no—
401C22×C4—442no—
402C22×C4—442no—
403C22×C4—442no—
404C22×C4C2×C4×D1112yes—
405C22×C4C2×C4×D1111yescharacteristic
406C22×C4C2×C4×D1112yes—
407C22×C4D4×D1112yes—
408C22×C4Q8×D1112yes—
409C22×C4C23×D1111yescharacteristic
410M16—44no—
411M16—444no—
412M16—444no—
413M16—444no—
414C2×C8—21no—
415C2×C8—21no—
416C2×C8—22no—
417C2×C8—22no—
418C2×C8—22no—
419C2×C8—22no—
420C2×C8—22no—
421C2×C8—221no—
422C2×C8—222no—
423C2×C8—221no—
424C2×C8—222no—
425C2×C8—222no—
426C2×C8—222no—
427C2×C8—222no—
428C22⋊C4—24no—
429C22⋊C4—224no—
430C22⋊C4—224no—
431C22⋊C4—224no—
432C42—22no—
433C42—22no—
434C42—222no—
435C42—222no—
436C42—442no—
437C42—442no—
438C11#2193411yescharacteristic, complemented, Sylow
439C23—22no—
440C23—21no—
441C23—21no—
442C23—22no—
443C23—114no—
444C23—112no—
445C23—112no—
446C23—228no—
447C23—221no—
448C23—221no—
449C23—222no—
450C23—222no—
451C23—221no—
452C23—221no—
453C23—222no—
454C23—444no—
455C23—444no—
456C23—448no—
457C23—448no—
458C23C4⋊C4×D1112yes—
459C23C22×C4×D1111yescharacteristic
460C2×C4—22no—
461C2×C4—22no—
462C2×C4—22no—
463C2×C4—22no—
464C2×C4—24no—
465C2×C4—22no—
466C2×C4—22no—
467C2×C4—22no—
468C2×C4—22no—
469C2×C4—114no—
470C2×C4—112no—
471C2×C4—112no—
472C2×C4—222no—
473C2×C4—222no—
474C2×C4—222no—
475C2×C4—222no—
476C2×C4—222no—
477C2×C4—222no—
478C2×C4—224no—
479C2×C4—224no—
480C2×C4—222no—
481C2×C4—222no—
482C2×C4—222no—
483C2×C4—222no—
484C2×C4—222no—
485C2×C4—444no—
486C2×C4—444no—
487C2×C4—448no—
488C2×C4—448no—
489C2×C4—444no—
490C2×C4C4⋊C4×D1112yes—
491C2×C4M16×D1114yes—
492C2×C4C2×D4×D1111yescharacteristic
493C2×C4#6703712yes—
494C2×C4C2×Q8×D1111yescharacteristic
495C2×C4#6704212yes—
496C8—42no—
497C8—41no—
498C8—41no—
499C8—441no—
500C8—441no—
501C8—442no—
502C22—22no—
503C22—22no—
504C22—22no—
505C22—42no—
506C22—42no—
507C22—114no—
508C22—222no—
509C22—224no—
510C22—224no—
511C22—222no—
512C22—222no—
513C22—222no—
514C22—222no—
515C22—4416no—
516C22—442no—
517C22—442no—
518C22C2×C4⋊C4×D1111yescharacteristic
519C22#1062307612yes—
520C22C2×M16×D1112yes—
521C22#1062328111yescharacteristic
522C22#1062328111yescharacteristic
523C4—22no—
524C4—24no—
525C4—42no—
526C4—222no—
527C4—222no—
528C4—224no—
529C4—442no—
530C4#1062312011yescharacteristic
531C4#1062316512yes—
532C4#1062318411yescharacteristic
533C2—42no—
534C2—224no—
535C2—442no—
536C2#1307122711yescharacteristic
537C2D11×#42311yescharacteristic
538C2#1307717711yescharacteristic
539C2#1307764112yes—
540C2#1307765412yes—
subgroupG/H
center, FrattiniC22×C4C23×D11
commutator, socleC23×C11C23×C4
FittingC11×#1851C2
prime radicalC24×D11C2×C4
cosocleC22×C4×C11C24
hypercenter#1851D11
hypocenterC11#21934
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ #1851

Complements

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

NH ≅ G/Ntype
4. #13068801C2semidirect
5. #13068800C2semidirect
6. #13068799C2semidirect
7. #13068798C2semidirect
8. #13068797C2semidirect
9. #13068595C2semidirect
10. #13068593C2semidirect
11. C11×#1851C2semidirect
19. C2×C11×C4⋊C8C22semidirect
29. C2×Dic11⋊C8C22semidirect
30. C2×Dic11⋊C8C22semidirect
33. C2×C4⋊(C11⋊C8)C22semidirect
39. C11×#336C22semidirect
40. #10622188C22semidirect
41. #10622188C22semidirect
42. #10622162C22semidirect
136. C2×C4×D11M16semidirect
177. #1851D11semidirect
253. C2×C4⋊C8C2×D11semidirect
273. #336C2×D11semidirect
438. C11#21934semidirect

Maximal subgroups

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

subgroupindex
C2×#106227392
C2×#106223392
C4×C22⋊C4×D112
#130688012
#130688002
#130687992
#130687982
#130687972
#130685952
#130685932
C11×#18512
#2193411