Finite Group Databasebeta

← #14720978

Subgroups — #14720978

Order 2816.

1102 conjugacy classes of subgroups.

The subgroup lattice has 654 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082665C211yesmaximal, characteristic
2#13077651C211yesmaximal, characteristic, complemented
3#13067139C211yesmaximal, characteristic, complemented
4#13067135C212yesmaximal, complemented
5#13067127C211yesmaximal, characteristic, complemented
6#13067118C212yesmaximal, complemented
7#13067114C211yesmaximal, characteristic, complemented
8#13067105C212yesmaximal, complemented
9#13067100C211yesmaximal, characteristic, complemented
10C2×#10622090C212yesmaximal, complemented
11C11×#2275C211yesmaximal, characteristic, complemented
12C2×C4×D4×C11—21no—
13C2×C4×D4×C11C2211yescharacteristic
14#10623337—21no—
15#10623322C2212yes—
16C2×#66977C2212yes—
17#10623095—22no—
18#10623092—21no—
19#10623086C411yescharacteristic, complemented
20#10623083C412yescomplemented
21#10623082C411yescharacteristic, complemented
22#10623077—21no—
23#10623073C411yescharacteristic, complemented
24#10623072C412yescomplemented
25D4×Dic22C411yescharacteristic, complemented
26#10623042—21no—
27#10623026—22no—
28#10623010C2211yescharacteristic
29#10623001C2211yescharacteristic
30C4×C11×C4⋊C4—21no—
31C4×C11×C4⋊C4C2211yescharacteristic
32C4×C11×C22⋊C4—22no—
33C4×C11×C22⋊C4C2212yes—
34C11×#376C2211yescharacteristic
35C2×C11×#95C2212yes—
36#10622820C2212yes—
37C2×C22⋊(C11⋊C8)C2212yes—
38#10622625—21no—
39#10622624—22no—
40D4×C11⋊C8—21no—
41#10622539C2211yescharacteristic
42#10622538C2211yescharacteristic
43#10622090C2211yescharacteristic
44#10622090C2212yes—
45#10622090C2212yes—
46#10622090C2212yes—
47#10622090C2211yescharacteristic
48#10622090C2212yes—
49#10622090C2212yes—
50#10622089C2211yescharacteristic
51#10622089C2211yescharacteristic
52#10622089C2212yes—
53C22×D4×C11D411yescharacteristic
54C23×C4×C11—22no—
55C23×C4×C11C2312yes—
56C2×#4341—21no—
57C2×#4339C2×C412yescomplemented
58C22×Dic22C2×C412yescomplemented
59C4×D4×C11—28no—
60C4×D4×C11C2×C411yescharacteristic
61C4×D4×C11C2×C412yes—
62C4×D4×C11C2×C411yescharacteristic
63C4×D4×C11D411yescharacteristic
64C4×D4×C11D411yescharacteristic
65C4×D4×C11D412yes—
66C2×C11×C4⋊C4—21no—
67C2×C11×C4⋊C4D411yescharacteristic
68C2×C11×C22⋊C4—22no—
69C2×C11×C22⋊C4D412yes—
70C2×C42×C11—21no—
71C2×C42×C11—21no—
72C2×C42×C11—22no—
73C2×C42×C11C2311yescharacteristic
74#67006—22no—
75C2×C22⋊Dic11—22no—
76#66992—22no—
77#66991—21no—
78#66989—21no—
79#66988—22no—
80D4×Dic11—21no—
81#66983C2×C412yescomplemented
82#66983C2311yescharacteristic
83#66982—21no—
84#66982—22no—
85C4×C22⋊D11—21no—
86C4×C22⋊D11—22no—
87C4×C22⋊D11—22no—
88#66979—21no—
89#66979C2×C412yescomplemented
90C2×C4⋊Dic11C2×C412yescomplemented
91#66977—21no—
92#66977—22no—
93#66977—22no—
94#66977C2×C412yescomplemented
95#66977C2×C412yescomplemented
96#66977C2×C412yescomplemented
97#66977C2312yes—
98#66977C2311yescharacteristic
99C2×Dic11⋊C4—22no—
100C2×#4318—22no—
101C22×C11⋊C8—22no—
102#66950—21no—
103#66949—22no—
104C4⋊C4×D11—21no—
105#66942—22no—
106#66941—21no—
107#66940—21no—
108#66939—22no—
109#66938—22no—
110#66936—22no—
111(C22⋊D11)⋊C4—22no—
112#66932—22no—
113#66932—22no—
114#66931—22no—
115#66930—22no—
116#66929—21no—
117#66928C2×C411yescharacteristic, complemented
118C4×D44C2×C411yescharacteristic, complemented
119#66925—21no—
120#66923—21no—
121#66923C2×C411yescharacteristic, complemented
122#66922C2×C411yescharacteristic, complemented
123#66922C2×C411yescharacteristic, complemented
124C4×Dic22—21no—
125C4×Dic22C2×C412yescomplemented
126C4×Dic22C2×C411yescharacteristic, complemented
127C11×#95—22no—
128C11×#95—21no—
129C11×#95C2311yescharacteristic
130C11×#95C2312yes—
131C11×#95C2311yescharacteristic
132C22⋊(C11⋊C8)—22no—
133C22⋊(C11⋊C8)—22no—
134C22⋊(C11⋊C8)C2311yescharacteristic
135C22⋊(C11⋊C8)C2311yescharacteristic
136C22⋊(C11⋊C8)C2312yes—
137C4⋊(C11⋊C8)—21no—
138C4⋊(C11⋊C8)—21no—
139#66867—21no—
140C4×C11⋊C8—21no—
141#17548—111nomaximal, Sylow
142C24×C11C2×D412yes—
143C2×D4×C11—24no—
144C2×D4×C11C22⋊C412yes—
145C2×D4×C11C22⋊C411yescharacteristic
146C2×D4×C11C22⋊C411yescharacteristic
147C22×C4×C11—21no—
148C22×C4×C11—21no—
149C22×C4×C11—22no—
150C22×C4×C11—28no—
151C22×C4×C11—82no—
152C22×C4×C11—82no—
153C22×C4×C11—82no—
154C22×C4×C11C22×C412yes—
155C22×C4×C11C22×C412yes—
156C22×C4×C11C2×D411yescharacteristic
157C22×C4×C11C2×D411yescharacteristic
158C22×C4×C11C2×D412yes—
159C22×C4×C11C2×D412yes—
160C22×C4×C11C2×D412yes—
161C22×C4×C11C2411yescharacteristic
162C2×C22⋊D11—22no—
163C2×C22⋊D11—22no—
164C2×C22⋊D11—21no—
165C22×Dic11—22no—
166C22×Dic11—22no—
167#4341—44no—
168#4339—82no—
169C2×D44C22×C411yescharacteristic
170C2×C4×D11—21no—
171C2×C4×D11—22no—
172C2×Dic22—21no—
173C2×Dic22—22no—
174C2×Dic22—82no—
175C2×Dic22C22×C412yes—
176C2×Dic22C22×C411yescharacteristic
177C11×C4⋊C4—24no—
178C11×C4⋊C4C22⋊C411yescharacteristic
179C11×C4⋊C4C22⋊C411yescharacteristic
180C11×C4⋊C4C22⋊C412yes—
181C11×C22⋊C4—28no—
182C11×C22⋊C4C22⋊C412yes—
183C11×C22⋊C4C22⋊C412yes—
184C11×C22⋊C4C22⋊C412yes—
185C11×C22⋊C4C22⋊C412yes—
186C42×C11—24no—
187C42×C11—81no—
188C42×C11—82no—
189C42×C11C22×C411yescharacteristic
190C42×C11C22×C411yescharacteristic
191C42×C11C2×D411yescharacteristic
192C42×C11C2×D411yescharacteristic
193C22⋊Dic11—22no—
194C22⋊Dic11—22no—
195C22⋊Dic11—22no—
196C22⋊Dic11—22no—
197C22⋊Dic11—22no—
198C22⋊Dic11—21no—
199(C2×D11)⋊C4—21no—
200(C2×D11)⋊C4—21no—
201(C2×D11)⋊C4—21no—
202(C2×D11)⋊C4—22no—
203(C2×D11)⋊C4—21no—
204C4⋊Dic11—21no—
205C4⋊Dic11—21no—
206C4⋊Dic11—21no—
207C4⋊Dic11—22no—
208C4⋊Dic11C22×C412yes—
209C4⋊Dic11C22×C411yescharacteristic
210C4⋊Dic11C22×C411yescharacteristic
211Dic11⋊C4—22no—
212Dic11⋊C4—21no—
213Dic11⋊C4—21no—
214Dic11⋊C4—21no—
215Dic11⋊C4—22no—
216Dic11⋊C4—22no—
217Dic11⋊C4—22no—
218Dic11⋊C4—22no—
219Dic11⋊C4—21no—
220C4×Dic11—22no—
221C4×Dic11—21no—
222C4×Dic11—22no—
223#4318—82no—
224C2×C11⋊C8—21no—
225C2×C11⋊C8—21no—
226C2×C11⋊C8—22no—
227C2×C11⋊C8—82no—
228#3520—111no—
229#2974—111no—
230#2275D1111yescharacteristic, complemented
231#1509—111no—
232#1508—112no—
233#1506—111no—
234#1504—112no—
235#1503—111no—
236#1501—112no—
237#1500—111no—
238C2×#328—112no—
239C23×C11—22no—
240C23×C11—22no—
241C23×C11—24no—
242C23×C11—42no—
243C23×C11C2×C22⋊C412yes—
244C23×C11C2×C22⋊C412yes—
245C23×C11C22×D411yescharacteristic
246C22×D11—21no—
247D4×C11—24no—
248D4×C11—22no—
249D4×C11#10414yes—
250C2×C4×C11—21no—
251C2×C4×C11—21no—
252C2×C4×C11—22no—
253C2×C4×C11—22no—
254C2×C4×C11—22no—
255C2×C4×C11—24no—
256C2×C4×C11—42no—
257C2×C4×C11—42no—
258C2×C4×C11—42no—
259C2×C4×C11—42no—
260C2×C4×C11—42no—
261C2×C4×C11—41no—
262C2×C4×C11—41no—
263C2×C4×C11—42no—
264C2×C4×C11—41no—
265C2×C4×C11—42no—
266C2×C4×C11—41no—
267C2×C4×C11—41no—
268C2×C4×C11—88no—
269C2×C4×C11C2×C22⋊C411yescharacteristic
270C2×C4×C11C2×C22⋊C412yes—
271C2×C4×C11C2×C22⋊C411yescharacteristic
272C2×C4×C11C2×C22⋊C411yescharacteristic
273C2×C4×C11C2×C22⋊C412yes—
274C2×C4×C11C2×C22⋊C411yescharacteristic
275C2×C4×C11C23×C411yescharacteristic
276C2×C4×C11C22×D411yescharacteristic
277C22⋊D11—41no—
278C22⋊D11—41no—
279C22⋊D11—44no—
280C22⋊D11—82no—
281C2×Dic11—21no—
282C2×Dic11—22no—
283C2×Dic11—22no—
284C2×Dic11—21no—
285C2×Dic11—21no—
286C2×Dic11—44no—
287C2×Dic11—82no—
288D44—41no—
289C4×D11—42no—
290C4×D11—82no—
291Dic22—42no—
292Dic22—41no—
293Dic22—42no—
294Dic22—82no—
295C11⋊C8—41no—
296C11⋊C8—42no—
297C11⋊C8—41no—
298#556—111no—
299#554—221no—
300#552—112no—
301#551—222no—
302D4×Q8—111no—
303#548—112no—
304#547—111no—
305#547—111no—
306#546—221no—
307#542—221no—
308#539—222no—
309#533—111no—
310#529—111no—
311#525—112no—
312C2×C22⋊Q8—112no—
313#520—221no—
314C2×C4×D4—21no—
315C2×C4×D4C2×D1111yescharacteristic
316#436—221no—
317#435—222no—
318C8×D4—221no—
319#432—111no—
320#431—111no—
321#407—112no—
322C2×C22⋊C8—112no—
323C4×C4⋊C4—21no—
324C4×C4⋊C4C2×D1111yescharacteristic
325C4×C22⋊C4—22no—
326C4×C22⋊C4C2×D1112yes—
327#376C2×D1111yescharacteristic
328C2×#95C2×D1112yes—
329#328—111no—
330#328—112no—
331#328—112no—
332#328—112no—
333#328—111no—
334#328—112no—
335#328—112no—
336#327—111no—
337#327—111no—
338#327—112no—
339C22×C11—21no—
340C22×C11—22no—
341C22×C11—22no—
342C22×C11—21no—
343C22×C11—22no—
344C22×C11—22no—
345C22×C11—22no—
346C22×C11—44no—
347C22×C11—44no—
348C22×C11C2×#10414yes—
349C22×C11C22×C22⋊C411yescharacteristic
350C22×C11#57711yescharacteristic
351C22×C11#57811yescharacteristic
352C2×D11—41no—
353C2×D11—41no—
354C2×D11—41no—
355C4×C11—21no—
356C4×C11—21no—
357C4×C11—22no—
358C4×C11—22no—
359C4×C11—21no—
360C4×C11—21no—
361C4×C11—21no—
362C4×C11—42no—
363C4×C11—44no—
364C4×C11—42no—
365C4×C11C2×#10412yes—
366Dic11—41no—
367Dic11—42no—
368Dic11—41no—
369Dic11—42no—
370Dic11—41no—
371C2×#41—112no—
372C2×#41—221no—
373C22×Q8—112no—
374C22×D4C22⋊D1111yescharacteristic
375C23×C4—22no—
376C23×C4C22×D1112yes—
377C2×M16—222no—
378C22×C8—222no—
379C4⋊Q8—111no—
380C4⋊Q8—111no—
381C4⋊Q8—221no—
382#126—222no—
383#126—222no—
384#126—221no—
385#125—111no—
386#125—222no—
387#125—221no—
388#124—111no—
389#124—221no—
390#124—222no—
391#123—222no—
392#123—222no—
393#123—221no—
394#123—222no—
395#123—222no—
396C22⋊Q8—112no—
397C22⋊Q8—112no—
398C22⋊Q8—112no—
399C22⋊Q8—111no—
400C22⋊Q8—112no—
401C22⋊Q8—222no—
402C22⋊Q8—222no—
403C22⋊Q8—221no—
404C22⋊Q8—222no—
405C22⋊Q8—221no—
406C22⋊Q8—222no—
407#121—112no—
408#121—111no—
409#121—222no—
410#121—221no—
411#120—222no—
412C4×Q8—111no—
413C4×Q8—112no—
414C4×Q8—221no—
415C4×Q8—221no—
416C4×D4—28no—
417C4×D4—111no—
418C4×D4—221no—
419C4×D4—222no—
420C4×D4—222no—
421C4×D4—221no—
422C4×D4—222no—
423C4×D4C4×D1111yescharacteristic
424C4×D4C4×D1111yescharacteristic
425C4×D4C4×D1112yes—
426C4×D4D4411yescharacteristic
427C4×D4D4412yes—
428C4×D4D4411yescharacteristic
429#117—112no—
430#117—221no—
431#117—222no—
432#117—221no—
433C2×C4⋊C4—21no—
434C2×C4⋊C4—112no—
435C2×C4⋊C4—222no—
436C2×C4⋊C4—221no—
437C2×C4⋊C4C22⋊D1111yescharacteristic
438C2×C22⋊C4—22no—
439C2×C22⋊C4—222no—
440C2×C22⋊C4C22⋊D1112yes—
441C2×C42—21no—
442C2×C42—21no—
443C2×C42—22no—
444C2×C42C22×D1111yescharacteristic
445C4⋊C8—221no—
446C4⋊C8—221no—
447C22⋊C8—111no—
448C22⋊C8—112no—
449C22⋊C8—111no—
450C22⋊C8—222no—
451C22⋊C8—222no—
452#97—221no—
453C4×C8—221no—
454#95—22no—
455#95—21no—
456#95C22×D1111yescharacteristic
457#95C22×D1112yes—
458#95C22×D1111yescharacteristic
459C2×C11—21no—
460C2×C11—21no—
461C2×C11—24no—
462C2×C11—42no—
463C2×C11#288311yescharacteristic
464C2×C11#289811yescharacteristic
465C2×C11C22×#10411yescharacteristic
466D11—81no—
467C24C2×C22⋊D1112yes—
468#41—444no—
469#41—882no—
470C2×Q8—111no—
471C2×Q8—112no—
472C2×Q8—221no—
473C2×Q8—222no—
474C2×Q8—882no—
475C2×D4—24no—
476C2×D4—111no—
477C2×D4—222no—
478C2×D4—221no—
479C2×D4—222no—
480C2×D4(C2×D11)⋊C412yes—
481C2×D4(C2×D11)⋊C411yescharacteristic
482C2×D4(C2×D11)⋊C411yescharacteristic
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—22no—
486C22×C4—28no—
487C22×C4—82no—
488C22×C4—82no—
489C22×C4—82no—
490C22×C4—222no—
491C22×C4—222no—
492C22×C4—221no—
493C22×C4—222no—
494C22×C4C2×C4×D1112yes—
495C22×C4C2×C4×D1112yes—
496C22×C4C2×D4412yes—
497C22×C4C2×D4412yes—
498C22×C4C2×C22⋊D1111yescharacteristic
499C22×C4C2×C22⋊D1111yescharacteristic
500C22×C4C2×C22⋊D1112yes—
501C22×C4C23×D1111yescharacteristic
502M16—882no—
503C2×C8—221no—
504C2×C8—221no—
505C2×C8—222no—
506C2×C8—882no—
507C4⋊C4—24no—
508C4⋊C4—111no—
509C4⋊C4—112no—
510C4⋊C4—111no—
511C4⋊C4—222no—
512C4⋊C4—222no—
513C4⋊C4—221no—
514C4⋊C4—222no—
515C4⋊C4—221no—
516C4⋊C4—221no—
517C4⋊C4—221no—
518C4⋊C4—222no—
519C4⋊C4—221no—
520C4⋊C4—222no—
521C4⋊C4—221no—
522C4⋊C4—221no—
523C4⋊C4—222no—
524C4⋊C4(C2×D11)⋊C411yescharacteristic
525C4⋊C4(C2×D11)⋊C412yes—
526C4⋊C4(C2×D11)⋊C411yescharacteristic
527C22⋊C4—28no—
528C22⋊C4—222no—
529C22⋊C4—222no—
530C22⋊C4—222no—
531C22⋊C4—222no—
532C22⋊C4—221no—
533C22⋊C4—222no—
534C22⋊C4—221no—
535C22⋊C4—221no—
536C22⋊C4—222no—
537C22⋊C4—221no—
538C22⋊C4—221no—
539C22⋊C4(C2×D11)⋊C412yes—
540C22⋊C4(C2×D11)⋊C412yes—
541C22⋊C4(C2×D11)⋊C412yes—
542C22⋊C4(C2×D11)⋊C412yes—
543C42—24no—
544C42—81no—
545C42—82no—
546C42—222no—
547C42—222no—
548C42—221no—
549C42C2×C4×D1111yescharacteristic
550C42C2×C4×D1111yescharacteristic
551C42C2×D4411yescharacteristic
552C42C2×D4411yescharacteristic
553C11#1754811yescharacteristic, complemented, Sylow
554C23—24no—
555C23—22no—
556C23—22no—
557C23—42no—
558C23—221no—
559C23C2×(C2×D11)⋊C412yes—
560C23C2×(C2×D11)⋊C412yes—
561C23C22×C22⋊D1111yescharacteristic
562Q8—441no—
563Q8—442no—
564Q8—442no—
565Q8—882no—
566D4—24no—
567D4—22no—
568D4—441no—
569D4—444no—
570D4—441no—
571D4—441no—
572D4—882no—
573D4#6686914yes—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—22no—
577C2×C4—22no—
578C2×C4—22no—
579C2×C4—24no—
580C2×C4—42no—
581C2×C4—42no—
582C2×C4—42no—
583C2×C4—41no—
584C2×C4—42no—
585C2×C4—42no—
586C2×C4—41no—
587C2×C4—42no—
588C2×C4—41no—
589C2×C4—42no—
590C2×C4—41no—
591C2×C4—41no—
592C2×C4—88no—
593C2×C4—221no—
594C2×C4—222no—
595C2×C4—221no—
596C2×C4—222no—
597C2×C4—221no—
598C2×C4—444no—
599C2×C4—442no—
600C2×C4—882no—
601C2×C4—882no—
602C2×C4C2×(C2×D11)⋊C411yescharacteristic
603C2×C4C2×(C2×D11)⋊C412yes—
604C2×C4C2×(C2×D11)⋊C411yescharacteristic
605C2×C4C2×(C2×D11)⋊C411yescharacteristic
606C2×C4C2×(C2×D11)⋊C412yes—
607C2×C4C2×(C2×D11)⋊C411yescharacteristic
608C2×C4C22×C4×D1111yescharacteristic
609C2×C4C22×D4411yescharacteristic
610C8—441no—
611C8—442no—
612C8—441no—
613C22—21no—
614C22—22no—
615C22—22no—
616C22—21no—
617C22—22no—
618C22—22no—
619C22—22no—
620C22—44no—
621C22—44no—
622C22—441no—
623C22—441no—
624C22—441no—
625C22C2×#6686914yes—
626C22C22×(C2×D11)⋊C411yescharacteristic
627C22#1062336711yescharacteristic
628C22#1062336911yescharacteristic
629C4—21no—
630C4—21no—
631C4—22no—
632C4—22no—
633C4—21no—
634C4—21no—
635C4—21no—
636C4—42no—
637C4—44no—
638C4—42no—
639C4—442no—
640C4—441no—
641C4—441no—
642C4—441no—
643C4—442no—
644C4C2×#6686912yes—
645C2—21no—
646C2—21no—
647C2—24no—
648C2—42no—
649C2—881no—
650C2#1307707611yescharacteristic
651C2#1307714611yescharacteristic
652C2C22×#6686911yescharacteristic
subgroupG/H
centerC22C22×(C2×D11)⋊C4
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#2275C2
socleC22×C11C22×C22⋊C4
prime radical#13082665C2
cosocleC22×C4×C11C24
hypercenter#2275D11
hypocenterC11#17548
LCSG ▷ C2×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C4×D4 ◁ #2275

Complements

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

NH ≅ G/Ntype
2. #13077651C2semidirect
3. #13067139C2semidirect
4. #13067135C2semidirect
5. #13067127C2semidirect
6. #13067118C2semidirect
7. #13067114C2semidirect
8. #13067105C2semidirect
9. #13067100C2semidirect
10. C2×#10622090C2semidirect
11. C11×#2275C2semidirect
19. #10623086C4semidirect
20. #10623083C4semidirect
21. #10623082C4semidirect
23. #10623073C4semidirect
24. #10623072C4semidirect
25. D4×Dic22C4semidirect
57. C2×#4339C2×C4semidirect
58. C22×Dic22C2×C4semidirect
81. #66983C2×C4semidirect
89. #66979C2×C4semidirect
90. C2×C4⋊Dic11C2×C4semidirect
94. #66977C2×C4semidirect
95. #66977C2×C4semidirect
96. #66977C2×C4semidirect
117. #66928C2×C4semidirect
118. C4×D44C2×C4semidirect
121. #66923C2×C4semidirect
122. #66922C2×C4semidirect
123. #66922C2×C4semidirect
125. C4×Dic22C2×C4semidirect
126. C4×Dic22C2×C4semidirect
230. #2275D11semidirect
553. C11#17548semidirect

Maximal subgroups

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

subgroupindex
#130826652
#130776512
#130671392
#130671352
#130671272
#130671182
#130671142
#130671052
#130671002
C2×#106220902
C11×#22752
#1754811