Finite Group Databasebeta

← #14759272

Subgroups — #14759272

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×#4318C211yesmaximal, characteristic, complemented
2C2×#10622341C212yesmaximal, complemented
3C2×(C22⋊D11)⋊C8C211yesmaximal, characteristic, complemented
4C4×#67006C211yesmaximal, characteristic
5#13068911C212yesmaximal, complemented
6#13068906C211yesmaximal, characteristic, complemented
7#13068798C212yesmaximal, complemented
8#13068793C211yesmaximal, characteristic, complemented
9#13068402C212yesmaximal, complemented
10#13068395C211yesmaximal, characteristic, complemented
11C11×#1779C211yesmaximal, characteristic, complemented
12C24×C4×C11C2211yescharacteristic
13C2×#67006C411yescharacteristic
14C2×C4×C22⋊D11C2211yescharacteristic
15C2×C4×C22⋊D11C2212yes—
16C22×#4318—28no—
17C22×#4318—24no—
18C22×#4318C2212yes—
19C22×#4318C2212yes—
20C23×C11⋊C8C2211yescharacteristic
21C23×C11⋊C8C2211yescharacteristic
22C22×C8×D11C2211yescharacteristic, complemented
23C2×C11×C22⋊C8C2211yescharacteristic
24C2×C11×C22⋊C8C2212yes—
25C2×C11×C22⋊C8C2211yescharacteristic
26C2×C11×C22⋊C8C2212yes—
27#10622860C411yescharacteristic
28#10622826C411yescharacteristic
29#10622826C412yes—
30#10622823C412yes—
31#10622823C411yescharacteristic
32C4×C22⋊Dic11C2211yescharacteristic
33C4×C22⋊Dic11C2212yes—
34C2×(C2×D11)⋊C8C2211yescharacteristic, complemented
35C2×(C2×D11)⋊C8C2212yescomplemented
36C2×#66879C2212yescomplemented
37C2×Dic11⋊C8C2211yescharacteristic, complemented
38C2×Dic11⋊C8C2212yescomplemented
39C2×C8×Dic11C2211yescharacteristic, complemented
40#10622341—28no—
41(C22⋊D11)⋊C8—24no—
42#10622188C2212yescomplemented
43#10622188C2212yescomplemented
44#10622188C2212yescomplemented
45C25×C11C2×C411yescharacteristic
46C23×C4×C11—24no—
47C23×C4×C11—22no—
48C23×C4×C11—24no—
49C23×C4×C11—22no—
50C23×C4×C11C2×C412yes—
51C23×C4×C11C2×C411yescharacteristic
52C23×C4×C11C2311yescharacteristic
53C23×C4×C11C2312yes—
54C22×C22⋊D11C2×C412yes—
55C22×C22⋊D11C2×C411yescharacteristic
56C22×C4×D11C2311yescharacteristic
57C22×C8×C11C2311yescharacteristic
58C22×C8×C11C2312yes—
59C22×C8×C11C2311yescharacteristic
60#67006—24no—
61C2×C22⋊Dic11C2×C412yes—
62C2×C22⋊Dic11C2×C411yescharacteristic
63C2×C22⋊Dic11C2×C412yes—
64C2×C22⋊Dic11C2×C411yescharacteristic
65C2×C22⋊Dic11C2×C411yescharacteristic
66C2×C22⋊Dic11C2×C412yes—
67C4×C22⋊D11—22no—
68C4×C22⋊D11—24no—
69C4×C22⋊D11—22no—
70C4×C22⋊D11—24no—
71C2×(C2×D11)⋊C4C2×C411yescharacteristic
72C2×(C2×D11)⋊C4C2×C412yes—
73C2×Dic11⋊C4C2×C412yes—
74C2×Dic11⋊C4C2×C411yescharacteristic
75C2×C4×Dic11C2311yescharacteristic
76C2×C4×Dic11C2312yes—
77C2×#4318—232no—
78C2×#4318—24no—
79C2×#4318—24no—
80C2×#4318—24no—
81C2×#4318—24no—
82C2×#4318—24no—
83C2×#4318D418yescomplemented
84C22×C11⋊C8—22no—
85C22×C11⋊C8—24no—
86C22×C11⋊C8—24no—
87C22×C11⋊C8D414yescomplemented
88C22×C11⋊C8C2312yes—
89C22×C11⋊C8C2311yescharacteristic
90C22×C11⋊C8C2311yescharacteristic
91C2×C8×D11—22no—
92C2×C8×D11—24no—
93C11×C22⋊C8—22no—
94C11×C22⋊C8—24no—
95C11×C22⋊C8—22no—
96C11×C22⋊C8—24no—
97C11⋊#95C2×C412yes—
98C11⋊#95C2×C412yes—
99C11⋊#95C2×C412yes—
100(C2×D11)⋊C8—22no—
101(C2×D11)⋊C8—24no—
102#66879—24no—
103Dic11⋊C8—22no—
104Dic11⋊C8—24no—
105C8×Dic11—22no—
106#21439—111nomaximal, Sylow
107C24×C11—24no—
108C24×C11—22no—
109C24×C11—22no—
110C24×C11—22no—
111C24×C11—42no—
112C24×C11C22×C412yes—
113C24×C11C22×C411yescharacteristic
114C23×D11C22×C411yescharacteristic
115C22×C4×C11—28no—
116C22×C4×C11—28no—
117C22×C4×C11—216no—
118C22×C4×C11—24no—
119C22×C4×C11—22no—
120C22×C4×C11—24no—
121C22×C4×C11—24no—
122C22×C4×C11—24no—
123C22×C4×C11—22no—
124C22×C4×C11—22no—
125C22×C4×C11—22no—
126C22×C4×C11—22no—
127C22×C4×C11—22no—
128C22×C4×C11—22no—
129C22×C4×C11C22×C411yescharacteristic
130C22×C4×C11C22×C412yes—
131C22×C4×C11C2×D412yes—
132C22×C4×C11C2×D414yes—
133C22×C4×C11#4114yes—
134C22×C4×C11#4112yes—
135C22×C4×C11C2411yescharacteristic
136C2×C22⋊D11—22no—
137C2×C22⋊D11—24no—
138C2×C22⋊D11—22no—
139C2×C22⋊D11—24no—
140C2×C22⋊D11—42no—
141C2×C22⋊D11M1614yescomplemented
142C22×Dic11C22×C412yes—
143C22×Dic11C22×C412yes—
144C22×Dic11C22×C411yescharacteristic
145C22×Dic11C22×C411yescharacteristic
146C22×Dic11C22×C411yescharacteristic
147C2×C4×D11—21no—
148C2×C4×D11—22no—
149C2×C4×D11—21no—
150C2×C4×D11—22no—
151C2×C8×C11—21no—
152C2×C8×C11—21no—
153C2×C8×C11—22no—
154C2×C8×C11—22no—
155C2×C8×C11—22no—
156C2×C8×C11—22no—
157C2×C8×C11—22no—
158C22⋊Dic11—24no—
159C22⋊Dic11—24no—
160C22⋊Dic11—22no—
161C22⋊Dic11—22no—
162C22⋊Dic11—22no—
163C22⋊Dic11—42no—
164(C2×D11)⋊C4—22no—
165(C2×D11)⋊C4—24no—
166Dic11⋊C4—22no—
167Dic11⋊C4—24no—
168C4×Dic11—21no—
169C4×Dic11—22no—
170C4×Dic11—21no—
171C4×Dic11—22no—
172#4318—216no—
173#4318—216no—
174C2×C11⋊C8—28no—
175C2×C11⋊C8—28no—
176C2×C11⋊C8—22no—
177C2×C11⋊C8—22no—
178C2×C11⋊C8—22no—
179C2×C11⋊C8C2×D414yes—
180C2×C11⋊C8C2×D412yes—
181C2×C11⋊C8C2×D412yes—
182C2×C11⋊C8C2×D414yes—
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#1850—111no—
192#1779D1111yescharacteristic, complemented
193#1753—112no—
194#1752—111no—
195C23×C11—22no—
196C23×C11—22no—
197C23×C11—28no—
198C23×C11—22no—
199C23×C11—22no—
200C23×C11—22no—
201C23×C11—22no—
202C23×C11—22no—
203C23×C11—22no—
204C23×C11—48no—
205C23×C11—48no—
206C23×C11—44no—
207C23×C11—44no—
208C23×C11C4×D414yes—
209C23×C11C4×D412yes—
210C23×C11C2×M1612yes—
211C23×C11#13112yes—
212C23×C11C23×C411yescharacteristic
213C22×D11—21no—
214C22×D11—22no—
215C22×D11—21no—
216C22×D11—22no—
217C22×D11C2×M1612yescomplemented
218C2×C4×C11—28no—
219C2×C4×C11—216no—
220C2×C4×C11—22no—
221C2×C4×C11—22no—
222C2×C4×C11—22no—
223C2×C4×C11—22no—
224C2×C4×C11—24no—
225C2×C4×C11—22no—
226C2×C4×C11—24no—
227C2×C4×C11—24no—
228C2×C4×C11—24no—
229C2×C4×C11—24no—
230C2×C4×C11C4×D412yes—
231C2×C4×C11C4×D414yes—
232C2×C4×C11C22×D411yescharacteristic
233C2×C4×C11C22×D412yes—
234C2×C4×C11C2×#4111yescharacteristic
235C2×C4×C11C2×#4112yes—
236C22⋊D11—28no—
237C22⋊D11—48no—
238C2×Dic11—21no—
239C2×Dic11—21no—
240C2×Dic11—22no—
241C2×Dic11—21no—
242C2×Dic11—22no—
243C2×Dic11—21no—
244C2×Dic11—22no—
245C2×Dic11—22no—
246C2×Dic11—22no—
247C2×Dic11—22no—
248C2×Dic11—22no—
249C2×Dic11—22no—
250C2×Dic11C2×M1612yescomplemented
251C4×D11—41no—
252C4×D11—41no—
253C4×D11—42no—
254C8×C11—41no—
255C8×C11—41no—
256C8×C11—42no—
257C11⋊C8—24no—
258C11⋊C8—22no—
259C11⋊C8#12014yescomplemented
260C24×C4C2×D1111yescharacteristic
261C22×M16—112no—
262C22×M16—112no—
263C22×M16—224no—
264C22×M16—228no—
265C23×C8—111no—
266C23×C8—111no—
267C23×C8—111no—
268C2×#120—111no—
269C2×C4×D4—111no—
270C2×C4×D4—112no—
271#435—228no—
272C8×D4—224no—
273C2×C4⋊C8—112no—
274C2×C4⋊C8—111no—
275C2×C22⋊C8—112no—
276C2×C22⋊C8—111no—
277C2×C22⋊C8C2×D1111yescharacteristic
278C2×C22⋊C8C2×D1112yes—
279C2×C22⋊C8C2×D1111yescharacteristic
280C2×C22⋊C8C2×D1112yes—
281C2×#97—112no—
282C2×C4×C8—111no—
283#386—111no—
284#386—112no—
285#385—112no—
286#385—111no—
287#379—111no—
288C4×C22⋊C4—111no—
289C4×C22⋊C4—112no—
290#336—112no—
291#336—112no—
292#336—112no—
293C22×C11—22no—
294C22×C11—24no—
295C22×C11—24no—
296C22×C11—22no—
297C22×C11—24no—
298C22×C11—24no—
299C22×C11—24no—
300C22×C11—416no—
301C22×C11—42no—
302C22×C11—42no—
303C22×C11—42no—
304C22×C11—42no—
305C22×C11#43514yescomplemented
306C22×C11C2×C4×D411yescharacteristic
307C22×C11C2×C4×D412yes—
308C22×C11C22×M1611yescharacteristic
309C22×C11C2×#13111yescharacteristic
310C22×C11#56812yes—
311C2×D11—22no—
312C2×D11—24no—
313C2×D11—41no—
314C2×D11—42no—
315C2×D11—41no—
316C4×C11—22no—
317C4×C11—24no—
318C4×C11C2×#12011yescharacteristic
319C4×C11#52511yescharacteristic
320C4×C11#52512yes—
321Dic11—22no—
322Dic11—41no—
323Dic11—42no—
324Dic11—42no—
325Dic11—41no—
326C25C4×D1111yescharacteristic
327C22×D4—111no—
328C22×D4—112no—
329C23×C4—24no—
330C23×C4—22no—
331C23×C4—24no—
332C23×C4—22no—
333C23×C4—111no—
334C23×C4C4×D1112yes—
335C23×C4C4×D1111yescharacteristic
336C23×C4C22×D1111yescharacteristic
337C23×C4C22×D1112yes—
338C2×M16—118no—
339C2×M16—224no—
340C2×M16—224no—
341C2×M16—224no—
342C2×M16—224no—
343C2×M16—2232no—
344C2×M16—224no—
345C22×C8—111no—
346C22×C8—114no—
347C22×C8—111no—
348C22×C8—112no—
349C22×C8—222no—
350C22×C8—224no—
351C22×C8—224no—
352C22×C8—224no—
353C22×C8—222no—
354C22×C8C22×D1111yescharacteristic
355C22×C8C22×D1111yescharacteristic
356C22×C8C22×D1112yes—
357#120—224no—
358C4×D4—222no—
359C4×D4—224no—
360C4×D4—222no—
361C4×D4—224no—
362C2×C4⋊C4—111no—
363C2×C4⋊C4—112no—
364C2×C22⋊C4—112no—
365C2×C22⋊C4—111no—
366C2×C22⋊C4—112no—
367C2×C22⋊C4—111no—
368C2×C22⋊C4—111no—
369C2×C22⋊C4—111no—
370C2×C22⋊C4—112no—
371C2×C22⋊C4—112no—
372C2×C42—111no—
373C2×C42—112no—
374C4⋊C8—222no—
375C4⋊C8—224no—
376C22⋊C8—22no—
377C22⋊C8—24no—
378C22⋊C8—22no—
379C22⋊C8—24no—
380C22⋊C8—222no—
381C22⋊C8—224no—
382#97—224no—
383C4×C8—222no—
384#95—112no—
385#95—112no—
386#95—112no—
387C2×C11—24no—
388C2×C11—44no—
389C2×C11C4×#12011yescharacteristic
390C2×C11C2×#43511yescharacteristic
391C2×C11#293011yescharacteristic
392C2×C11#293312yes—
393C2×C11D4×M1612yes—
394D11—42no—
395C24—24no—
396C24—22no—
397C24—22no—
398C24—22no—
399C24—42no—
400C24—111no—
401C24C2×C4×D1112yes—
402C24C2×C4×D1111yescharacteristic
403C2×D4—114no—
404C2×D4—222no—
405C2×D4—222no—
406C2×D4—224no—
407C2×D4—224no—
408C2×D4—442no—
409C22×C4—28no—
410C22×C4—28no—
411C22×C4—216no—
412C22×C4—24no—
413C22×C4—22no—
414C22×C4—24no—
415C22×C4—24no—
416C22×C4—24no—
417C22×C4—22no—
418C22×C4—22no—
419C22×C4—22no—
420C22×C4—22no—
421C22×C4—22no—
422C22×C4—22no—
423C22×C4—111no—
424C22×C4—112no—
425C22×C4—111no—
426C22×C4—112no—
427C22×C4—111no—
428C22×C4—221no—
429C22×C4—222no—
430C22×C4—221no—
431C22×C4—222no—
432C22×C4C2×C4×D1111yescharacteristic
433C22×C4C2×C4×D1112yes—
434C22×C4D4×D1112yes—
435C22×C4D4×D1114yes—
436C22×C4#434114yes—
437C22×C4#434112yes—
438C22×C4C23×D1111yescharacteristic
439M16—2216no—
440M16—2216no—
441C2×C8—21no—
442C2×C8—22no—
443C2×C8—21no—
444C2×C8—22no—
445C2×C8—22no—
446C2×C8—22no—
447C2×C8—22no—
448C2×C8—112no—
449C2×C8—114no—
450C2×C8—112no—
451C2×C8—114no—
452C2×C8—228no—
453C2×C8—228no—
454C2×C8—222no—
455C2×C8—222no—
456C2×C8—222no—
457C2×C8—444no—
458C4⋊C4—222no—
459C4⋊C4—224no—
460C22⋊C4—224no—
461C22⋊C4—224no—
462C22⋊C4—222no—
463C22⋊C4—222no—
464C22⋊C4—222no—
465C22⋊C4—222no—
466C22⋊C4—224no—
467C22⋊C4—442no—
468C42—221no—
469C42—222no—
470C42—221no—
471C42—222no—
472C11#2143911yescharacteristic, complemented, Sylow
473C23—22no—
474C23—22no—
475C23—28no—
476C23—22no—
477C23—22no—
478C23—22no—
479C23—22no—
480C23—22no—
481C23—22no—
482C23—48no—
483C23—48no—
484C23—44no—
485C23—44no—
486C23—112no—
487C23—221no—
488C23—221no—
489C23—222no—
490C23—222no—
491C23(C22⋊D11)⋊C414yes—
492C23(C22⋊D11)⋊C412yes—
493C23#6695412yes—
494C23M16×D1112yes—
495C23C22×C4×D1111yescharacteristic
496D4—228no—
497D4—448no—
498C2×C4—28no—
499C2×C4—216no—
500C2×C4—22no—
501C2×C4—22no—
502C2×C4—22no—
503C2×C4—22no—
504C2×C4—24no—
505C2×C4—24no—
506C2×C4—24no—
507C2×C4—24no—
508C2×C4—22no—
509C2×C4—24no—
510C2×C4—112no—
511C2×C4—221no—
512C2×C4—221no—
513C2×C4—222no—
514C2×C4—221no—
515C2×C4—222no—
516C2×C4—222no—
517C2×C4—221no—
518C2×C4—222no—
519C2×C4—222no—
520C2×C4—222no—
521C2×C4—222no—
522C2×C4—222no—
523C2×C4—441no—
524C2×C4—442no—
525C2×C4—441no—
526C2×C4(C22⋊D11)⋊C412yes—
527C2×C4(C22⋊D11)⋊C414yes—
528C2×C4C2×D4×D1111yescharacteristic
529C2×C4C2×D4×D1112yes—
530C2×C4C2×#434111yescharacteristic
531C2×C4C2×#434112yes—
532C8—41no—
533C8—42no—
534C8—41no—
535C8—114no—
536C8—222no—
537C8—224no—
538C22—22no—
539C22—22no—
540C22—24no—
541C22—24no—
542C22—24no—
543C22—24no—
544C22—24no—
545C22—416no—
546C22—42no—
547C22—42no—
548C22—42no—
549C22—42no—
550C22—222no—
551C22—224no—
552C22—441no—
553C22—441no—
554C22—442no—
555C22#1062234114yescomplemented
556C22C2×(C22⋊D11)⋊C411yescharacteristic
557C22C2×(C22⋊D11)⋊C412yes—
558C22C2×#6695411yescharacteristic
559C22C2×M16×D1111yescharacteristic
560C22#1062327612yes—
561C4—22no—
562C4—24no—
563C4—222no—
564C4—441no—
565C4—441no—
566C4—442no—
567C4—442no—
568C4#1062311711yescharacteristic
569C4#1062311712yes—
570C4D11×#12011yescharacteristic
571C2—24no—
572C2—44no—
573C2—442no—
574C2#1307111511yescharacteristic
575C2C2×#1062234111yescharacteristic
576C2#1307731511yescharacteristic
577C2#1307733712yes—
578C2#1307734812yes—
subgroupG/H
center, FrattiniC22×C4C23×D11
commutator, socleC23×C11C23×C4
FittingC11×#1779C2
prime radicalC2×#67006C4
cosocleC22×C4×C11C24
hypercenter#1779D11
hypocenterC11#21439
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ #1779

Complements

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

NH ≅ G/Ntype
1. C23×#4318C2semidirect
2. C2×#10622341C2semidirect
3. C2×(C22⋊D11)⋊C8C2semidirect
5. #13068911C2semidirect
6. #13068906C2semidirect
7. #13068798C2semidirect
8. #13068793C2semidirect
9. #13068402C2semidirect
10. #13068395C2semidirect
11. C11×#1779C2semidirect
22. C22×C8×D11C22semidirect
34. C2×(C2×D11)⋊C8C22semidirect
35. C2×(C2×D11)⋊C8C22semidirect
36. C2×#66879C22semidirect
37. C2×Dic11⋊C8C22semidirect
38. C2×Dic11⋊C8C22semidirect
39. C2×C8×Dic11C22semidirect
42. #10622188C22semidirect
43. #10622188C22semidirect
44. #10622188C22semidirect
83. C2×#4318D4semidirect
87. C22×C11⋊C8D4semidirect
141. C2×C22⋊D11M16semidirect
192. #1779D11semidirect
217. C22×D11C2×M16semidirect
250. C2×Dic11C2×M16semidirect
259. C11⋊C8#120semidirect
305. C22×C11#435semidirect
472. C11#21439semidirect
555. C22#10622341semidirect

Maximal subgroups

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

subgroupindex
C23×#43182
C2×#106223412
C2×(C22⋊D11)⋊C82
C4×#670062
#130689112
#130689062
#130687982
#130687932
#130684022
#130683952
C11×#17792
#2143911