Finite Group Databasebeta

← #14759276

Subgroups — #14759276

Order 2816.

1598 conjugacy classes of subgroups.

The subgroup lattice has 580 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×#4313C211yesmaximal, characteristic, complemented
2C2×#10622449C212yesmaximal, complemented
3C2×(C22⋊D11)⋊C8C211yesmaximal, characteristic, complemented
4C4×#66935C211yesmaximal, characteristic
5#13068912C212yesmaximal, complemented
6#13068908C211yesmaximal, characteristic, complemented
7#13068797C212yesmaximal, complemented
8#13068525C211yesmaximal, characteristic, complemented
9#13068398C212yesmaximal, complemented
10#13068394C211yesmaximal, characteristic, complemented
11C11×#1850C211yesmaximal, characteristic, complemented
12C23×C4×D11C2211yescharacteristic
13C23×C8×C11C2211yescharacteristic
14C2×C4×C22⋊D11C2211yescharacteristic
15C23×C11⋊C8C2211yescharacteristic
16C22×#4313—24no—
17C22×#4313—28no—
18C22×#4313C2212yes—
19C22×#4313C2212yes—
20C22×C8×D11C2211yescharacteristic, complemented
21C2×#66935C411yescharacteristic
22C2×C4×D44C2212yes—
23C2×C11×C4⋊C8C2212yescomplemented
24C2×C11×C22⋊C8C2211yescharacteristic
25C4×C11×C22⋊C4C2211yescharacteristic
26C2×C22⋊(C11⋊C8)C2211yescharacteristic
27C2×(C2×D11)⋊C8C2212yes—
28C2×(C2×D11)⋊C8C2212yes—
29C2×(C2×D11)⋊C8C2211yescharacteristic, complemented
30C2×(C2×D11)⋊C8C2212yescomplemented
31C2×Dic11⋊C8C2211yescharacteristic, complemented
32C2×C8×Dic11C2211yescharacteristic, complemented
33#10622571C411yescharacteristic
34#10622568C411yescharacteristic
35#10622563C411yescharacteristic
36C4×(C2×D11)⋊C4C2212yes—
37C2×#66867C2212yescomplemented
38#10622449—28no—
39(C22⋊D11)⋊C8—24no—
40#10622281C412yes—
41#10622278C412yes—
42C11×#336C2212yescomplemented
43#10622188C2212yescomplemented
44#10622162C2212yescomplemented
45C24×D11C2×C411yescharacteristic
46C23×C4×C11C2311yescharacteristic
47C22×C22⋊D11C2×C411yescharacteristic
48C23×Dic11C2×C411yescharacteristic
49C22×D44C2×C412yes—
50C22×C4×D11—22no—
51C22×C4×D11—22no—
52C22×C4×D11—24no—
53C22×C4×D11—24no—
54C22×C4×D11C2×C412yes—
55C22×C4×D11C2311yescharacteristic
56C22×C4×D11C2312yes—
57C22×C8×C11—22no—
58C22×C8×C11—24no—
59C22×C8×C11C2311yescharacteristic
60C22×C8×C11C2311yescharacteristic
61C22×C8×C11C2312yes—
62C2×C11×C22⋊C4C2×C411yescharacteristic
63C2×C11×C22⋊C4C2×C411yescharacteristic
64C2×C42×C11C2312yes—
65C2×C22⋊Dic11C2×C411yescharacteristic
66C4×C22⋊D11—22no—
67C4×C22⋊D11—22no—
68C2×(C2×D11)⋊C4C2×C412yes—
69C2×(C2×D11)⋊C4C2×C412yes—
70C2×(C2×D11)⋊C4C2×C412yes—
71C2×(C2×D11)⋊C4C2×C411yescharacteristic
72C2×(C2×D11)⋊C4C2×C412yes—
73C2×C4⋊Dic11C2×C412yes—
74C2×Dic11⋊C4C2×C411yescharacteristic
75C2×C4×Dic11C2311yescharacteristic
76C22×C11⋊C8—24no—
77C22×C11⋊C8D414yescomplemented
78C22×C11⋊C8C2312yes—
79C22×C11⋊C8C2311yescharacteristic
80C22×C11⋊C8C2311yescharacteristic
81C2×#4313—232no—
82C2×#4313—24no—
83C2×#4313—24no—
84C2×#4313—24no—
85C2×#4313—24no—
86C2×#4313—24no—
87C2×#4313D418yescomplemented
88C2×C8×D11—22no—
89C2×C8×D11—24no—
90#66935—24no—
91C4×D44—24no—
92C4×D44—24no—
93C11×C4⋊C8—24no—
94C11×C22⋊C8—22no—
95C11×#95C2×C412yes—
96C11⋊#95C2×C412yes—
97C11⋊#95C2×C412yes—
98C22⋊(C11⋊C8)—22no—
99(C2×D11)⋊C8—24no—
100(C2×D11)⋊C8—24no—
101(C2×D11)⋊C8—24no—
102(C2×D11)⋊C8—22no—
103Dic11⋊C8—22no—
104C8×Dic11—22no—
105#66867—24no—
106#21439—111nomaximal, Sylow
107C24×C11C22×C411yescharacteristic
108C23×D11—22no—
109C23×D11—24no—
110C23×D11—22no—
111C23×D11—22no—
112C23×D11—42no—
113C23×D11C22×C412yes—
114C23×D11C22×C411yescharacteristic
115C22×C4×C11—22no—
116C22×C4×C11—22no—
117C22×C4×C11C22×C412yes—
118C22×C4×C11C22×C412yes—
119C22×C4×C11C22×C411yescharacteristic
120C22×C4×C11C2×D412yes—
121C22×C4×C11#4112yes—
122C22×C4×C11C2411yescharacteristic
123C2×C22⋊D11—22no—
124C2×C22⋊D11—22no—
125C2×C22⋊D11M1614yescomplemented
126C22×Dic11—24no—
127C22×Dic11—22no—
128C22×Dic11C22×C411yescharacteristic
129C22×Dic11C22×C411yescharacteristic
130C22×Dic11C22×C412yes—
131C22×Dic11C22×C411yescharacteristic
132C2×D44—24no—
133C2×D44—24no—
134C2×D44—42no—
135C2×C4×D11—28no—
136C2×C4×D11—28no—
137C2×C4×D11—216no—
138C2×C4×D11—24no—
139C2×C4×D11—24no—
140C2×C4×D11—24no—
141C2×C4×D11—22no—
142C2×C4×D11—22no—
143C2×C4×D11—22no—
144C2×C4×D11—21no—
145C2×C4×D11—22no—
146C2×C4×D11—22no—
147C2×C4×D11—22no—
148C2×C4×D11—21no—
149C2×C4×D11C2×D414yes—
150C2×C4×D11#4114yes—
151C2×C8×C11—28no—
152C2×C8×C11—22no—
153C2×C8×C11—22no—
154C2×C8×C11—21no—
155C2×C8×C11—21no—
156C2×C8×C11—22no—
157C2×C8×C11—22no—
158C2×C8×C11C2×D414yes—
159C11×C22⋊C4—22no—
160C11×C22⋊C4—22no—
161C42×C11—22no—
162C42×C11—22no—
163C22⋊Dic11—22no—
164(C2×D11)⋊C4—24no—
165(C2×D11)⋊C4—24no—
166(C2×D11)⋊C4—24no—
167(C2×D11)⋊C4—22no—
168(C2×D11)⋊C4—42no—
169C4⋊Dic11—24no—
170Dic11⋊C4—22no—
171C4×Dic11—21no—
172C4×Dic11—21no—
173C2×C11⋊C8—28no—
174C2×C11⋊C8—22no—
175C2×C11⋊C8—22no—
176C2×C11⋊C8—22no—
177C2×C11⋊C8—22no—
178C2×C11⋊C8C2×D412yes—
179C2×C11⋊C8C2×D414yes—
180C2×C11⋊C8C2×D412yes—
181#4313—216no—
182#4313—216no—
183C8×D11—44no—
184C23×M16—111no—
185C2×#435—112no—
186C2×C8×D4—111no—
187C4×#120—111no—
188#1870—112no—
189#1869—111no—
190#1851—112no—
191#1850D1111yescharacteristic, complemented
192#1779—111no—
193#1753—112no—
194#1752—111no—
195C23×C11—22no—
196C23×C11—22no—
197C23×C11C4×D412yes—
198C23×C11C2×M1612yes—
199C23×C11#13112yes—
200C23×C11C23×C411yescharacteristic
201C22×D11—28no—
202C22×D11—22no—
203C22×D11—21no—
204C22×D11—22no—
205C22×D11—22no—
206C22×D11—22no—
207C22×D11—21no—
208C22×D11—22no—
209C22×D11—22no—
210C22×D11—22no—
211C22×D11—22no—
212C22×D11—48no—
213C22×D11—48no—
214C22×D11—44no—
215C22×D11—44no—
216C22×D11C4×D414yes—
217C22×D11C2×M1612yescomplemented
218C2×C4×C11—22no—
219C2×C4×C11—22no—
220C2×C4×C11—22no—
221C2×C4×C11—24no—
222C2×C4×C11—22no—
223C2×C4×C11—22no—
224C2×C4×C11—22no—
225C2×C4×C11—22no—
226C2×C4×C11—22no—
227C2×C4×C11—22no—
228C2×C4×C11C4×D412yes—
229C2×C4×C11C22×D412yes—
230C2×C4×C11C22×D411yescharacteristic
231C2×C4×C11C2×#4111yescharacteristic
232C2×C4×C11C2×#4112yes—
233C22⋊D11—28no—
234C2×Dic11—28no—
235C2×Dic11—21no—
236C2×Dic11—22no—
237C2×Dic11—22no—
238C2×Dic11—21no—
239C2×Dic11—21no—
240C2×Dic11—21no—
241C2×Dic11—22no—
242C2×Dic11—22no—
243C2×Dic11C4×D414yes—
244C2×Dic11C2×M1612yescomplemented
245D44—48no—
246C4×D11—216no—
247C4×D11—24no—
248C4×D11—24no—
249C4×D11—24no—
250C4×D11—24no—
251C4×D11—41no—
252C4×D11—42no—
253C4×D11—41no—
254C8×C11—24no—
255C8×C11—41no—
256C8×C11—41no—
257C11⋊C8—22no—
258C11⋊C8—42no—
259C11⋊C8#12014yescomplemented
260C24×C4—111no—
261C22×M16—112no—
262C22×M16—112no—
263C22×M16—224no—
264C22×M16—228no—
265C23×C8—111no—
266C23×C8—111no—
267C23×C8C2×D1111yescharacteristic
268C2×#120—111no—
269C2×C4×D4—111no—
270C2×C4×D4—112no—
271#435—228no—
272C8×D4—224no—
273C2×C4⋊C8—111no—
274C2×C4⋊C8C2×D1112yescomplemented
275C2×C22⋊C8—111no—
276C2×C22⋊C8—112no—
277C2×C22⋊C8—112no—
278C2×C22⋊C8—112no—
279C2×C22⋊C8—111no—
280C2×C22⋊C8C2×D1111yescharacteristic
281C2×#97—112no—
282C2×C4×C8—111no—
283#386—111no—
284#386—112no—
285#385—111no—
286#385—112no—
287#379—111no—
288C4×C22⋊C4—112no—
289C4×C22⋊C4C2×D1111yescharacteristic
290#336—112no—
291#336—112no—
292#336C2×D1112yescomplemented
293C22×C11—22no—
294C22×C11—24no—
295C22×C11—24no—
296C22×C11—22no—
297C22×C11#43514yescomplemented
298C22×C11C2×C4×D411yescharacteristic
299C22×C11C2×C4×D412yes—
300C22×C11C22×M1611yescharacteristic
301C22×C11C2×#13111yescharacteristic
302C22×C11#56812yes—
303C2×D11—22no—
304C2×D11—24no—
305C2×D11—24no—
306C2×D11—24no—
307C2×D11—24no—
308C2×D11—416no—
309C2×D11—42no—
310C2×D11—41no—
311C2×D11—42no—
312C2×D11—42no—
313C2×D11—42no—
314C2×D11—42no—
315C2×D11—41no—
316C4×C11—22no—
317C4×C11—42no—
318C4×C11—42no—
319C4×C11C2×#12011yescharacteristic
320C4×C11#52512yes—
321C4×C11#52511yescharacteristic
322Dic11—22no—
323Dic11—24no—
324Dic11—41no—
325Dic11—41no—
326C25—111no—
327C22×D4—111no—
328C22×D4—112no—
329C23×C4—112no—
330C23×C4—111no—
331C23×C4—112no—
332C23×C4—111no—
333C23×C4—224no—
334C23×C4—224no—
335C23×C4—222no—
336C23×C4—222no—
337C23×C4C22×D1111yescharacteristic
338C2×M16—118no—
339C2×M16—224no—
340C2×M16—224no—
341C2×M16—224no—
342C2×M16—224no—
343C2×M16—2232no—
344C2×M16—224no—
345C22×C8—22no—
346C22×C8—24no—
347C22×C8—111no—
348C22×C8—114no—
349C22×C8—111no—
350C22×C8—112no—
351C22×C8—222no—
352C22×C8—224no—
353C22×C8—224no—
354C22×C8C22×D1111yescharacteristic
355C22×C8C22×D1111yescharacteristic
356C22×C8C22×D1112yes—
357#120—224no—
358C4×D4—224no—
359C4×D4—224no—
360C4×D4—222no—
361C4×D4—222no—
362C2×C4⋊C4—111no—
363C2×C4⋊C4—112no—
364C2×C22⋊C4—111no—
365C2×C22⋊C4—112no—
366C2×C22⋊C4—112no—
367C2×C22⋊C4—111no—
368C2×C22⋊C4—112no—
369C2×C22⋊C4—112no—
370C2×C22⋊C4C4×D1111yescharacteristic
371C2×C22⋊C4C4×D1111yescharacteristic
372C2×C42—111no—
373C2×C42C22×D1112yes—
374C4⋊C8—24no—
375C4⋊C8—222no—
376C22⋊C8—22no—
377C22⋊C8—222no—
378C22⋊C8—224no—
379C22⋊C8—224no—
380C22⋊C8—222no—
381C22⋊C8—224no—
382#97—224no—
383C4×C8—222no—
384#95—112no—
385#95—112no—
386#95C4×D1112yes—
387C2×C11—24no—
388C2×C11C4×#12011yescharacteristic
389C2×C11C2×#43511yescharacteristic
390C2×C11#293011yescharacteristic
391C2×C11#293312yes—
392C2×C11D4×M1612yes—
393D11—42no—
394D11—44no—
395C24—112no—
396C24—111no—
397C24—224no—
398C24—222no—
399C24—222no—
400C24—222no—
401C24—442no—
402C24C2×C4×D1111yescharacteristic
403C2×D4—114no—
404C2×D4—224no—
405C2×D4—224no—
406C2×D4—222no—
407C2×D4—222no—
408C2×D4—442no—
409C22×C4—22no—
410C22×C4—22no—
411C22×C4—111no—
412C22×C4—112no—
413C22×C4—114no—
414C22×C4—114no—
415C22×C4—111no—
416C22×C4—111no—
417C22×C4—224no—
418C22×C4—224no—
419C22×C4—228no—
420C22×C4—2216no—
421C22×C4—228no—
422C22×C4—224no—
423C22×C4—222no—
424C22×C4—224no—
425C22×C4—222no—
426C22×C4—222no—
427C22×C4—222no—
428C22×C4—222no—
429C22×C4—221no—
430C22×C4—222no—
431C22×C4—221no—
432C22×C4—222no—
433C22×C4C2×C4×D1112yes—
434C22×C4C2×C4×D1112yes—
435C22×C4C2×C4×D1111yescharacteristic
436C22×C4D4×D1112yes—
437C22×C4#434312yes—
438C22×C4C23×D1111yescharacteristic
439M16—2216no—
440M16—2216no—
441C2×C8—28no—
442C2×C8—22no—
443C2×C8—22no—
444C2×C8—21no—
445C2×C8—21no—
446C2×C8—22no—
447C2×C8—22no—
448C2×C8—112no—
449C2×C8—114no—
450C2×C8—112no—
451C2×C8—228no—
452C2×C8—222no—
453C2×C8—222no—
454C2×C8—222no—
455C2×C8—222no—
456C2×C8—444no—
457C2×C8D4×D1114yes—
458C4⋊C4—224no—
459C4⋊C4—222no—
460C22⋊C4—22no—
461C22⋊C4—22no—
462C22⋊C4—224no—
463C22⋊C4—224no—
464C22⋊C4—224no—
465C22⋊C4—222no—
466C22⋊C4—222no—
467C22⋊C4—442no—
468C42—22no—
469C42—22no—
470C42—221no—
471C42—221no—
472C11#2143911yescharacteristic, complemented, Sylow
473C23—22no—
474C23—22no—
475C23—112no—
476C23—114no—
477C23—228no—
478C23—221no—
479C23—222no—
480C23—222no—
481C23—222no—
482C23—222no—
483C23—222no—
484C23—221no—
485C23—222no—
486C23—222no—
487C23—222no—
488C23—448no—
489C23—448no—
490C23—444no—
491C23—444no—
492C23#6694612yes—
493C23#6695412yes—
494C23M16×D1112yes—
495C23C22×C4×D1111yescharacteristic
496D4—228no—
497D4—448no—
498C2×C4—22no—
499C2×C4—22no—
500C2×C4—24no—
501C2×C4—22no—
502C2×C4—22no—
503C2×C4—22no—
504C2×C4—22no—
505C2×C4—22no—
506C2×C4—22no—
507C2×C4—22no—
508C2×C4—112no—
509C2×C4—114no—
510C2×C4—2216no—
511C2×C4—228no—
512C2×C4—221no—
513C2×C4—221no—
514C2×C4—222no—
515C2×C4—222no—
516C2×C4—224no—
517C2×C4—224no—
518C2×C4—224no—
519C2×C4—224no—
520C2×C4—222no—
521C2×C4—221no—
522C2×C4—221no—
523C2×C4—222no—
524C2×C4—441no—
525C2×C4—442no—
526C2×C4—441no—
527C2×C4#6694612yes—
528C2×C4C2×D4×D1112yes—
529C2×C4C2×D4×D1111yescharacteristic
530C2×C4C2×#434311yescharacteristic
531C2×C4#41×D1112yes—
532C8—24no—
533C8—41no—
534C8—41no—
535C8—114no—
536C8—222no—
537C8—442no—
538C22—22no—
539C22—22no—
540C22—24no—
541C22—24no—
542C22—224no—
543C22—222no—
544C22—224no—
545C22—224no—
546C22—224no—
547C22—4416no—
548C22—441no—
549C22—442no—
550C22—442no—
551C22—441no—
552C22—442no—
553C22—442no—
554C22—442no—
555C22#1062244914yescomplemented
556C22C2×#6694611yescharacteristic
557C22C4×D4×D1112yes—
558C22C2×#6695411yescharacteristic
559C22C2×M16×D1111yescharacteristic
560C22#1062328112yes—
561C4—22no—
562C4—42no—
563C4—42no—
564C4—224no—
565C4—222no—
566C4—441no—
567C4—441no—
568C4D11×#12011yescharacteristic
569C4#1062315812yes—
570C4#1062318711yescharacteristic
571C2—24no—
572C2—444no—
573C2—442no—
574C2#1307111711yescharacteristic
575C2C2×#1062244911yescharacteristic
576C2#1307731811yescharacteristic
577C2#1307733612yes—
578C2#1307734912yes—
subgroupG/H
center, FrattiniC22×C4C23×D11
commutator, socleC23×C11C23×C4
FittingC11×#1850C2
prime radicalC2×#66935C4
cosocleC22×C4×C11C24
hypercenter#1850D11
hypocenterC11#21439
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ #1850

Complements

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

NH ≅ G/Ntype
1. C23×#4313C2semidirect
2. C2×#10622449C2semidirect
3. C2×(C22⋊D11)⋊C8C2semidirect
5. #13068912C2semidirect
6. #13068908C2semidirect
7. #13068797C2semidirect
8. #13068525C2semidirect
9. #13068398C2semidirect
10. #13068394C2semidirect
11. C11×#1850C2semidirect
20. C22×C8×D11C22semidirect
23. C2×C11×C4⋊C8C22semidirect
29. C2×(C2×D11)⋊C8C22semidirect
30. C2×(C2×D11)⋊C8C22semidirect
31. C2×Dic11⋊C8C22semidirect
32. C2×C8×Dic11C22semidirect
37. C2×#66867C22semidirect
42. C11×#336C22semidirect
43. #10622188C22semidirect
44. #10622162C22semidirect
77. C22×C11⋊C8D4semidirect
87. C2×#4313D4semidirect
125. C2×C22⋊D11M16semidirect
191. #1850D11semidirect
217. C22×D11C2×M16semidirect
244. C2×Dic11C2×M16semidirect
259. C11⋊C8#120semidirect
274. C2×C4⋊C8C2×D11semidirect
292. #336C2×D11semidirect
297. C22×C11#435semidirect
472. C11#21439semidirect
555. C22#10622449semidirect

Maximal subgroups

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

subgroupindex
C23×#43132
C2×#106224492
C2×(C22⋊D11)⋊C82
C4×#669352
#130689122
#130689082
#130687972
#130685252
#130683982
#130683942
C11×#18502
#2143911