Finite Group Databasebeta

← #14720747

Subgroups — #14720747

Order 2816.

1096 conjugacy classes of subgroups.

The subgroup lattice has 652 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082226C211yesmaximal, characteristic
2#13077741C211yesmaximal, characteristic, complemented
3#13067077C212yesmaximal, complemented
4#13067068C211yesmaximal, characteristic, complemented
5#13067060C212yesmaximal, complemented
6#13067056C211yesmaximal, characteristic, complemented
7#13067034C211yesmaximal, characteristic, complemented
8#13067030C212yesmaximal, complemented
9#13066999C211yesmaximal, characteristic, complemented
10C2×#10622097C212yesmaximal, complemented
11C4×C11×#131C211yesmaximal, characteristic, complemented
12C2×C11×#131—21no—
13C4×C11×#41C2211yescharacteristic
14#10623360—21no—
15#10623116C411yescharacteristic
16#10623111—21no—
17#10623110C411yescharacteristic
18#10623096C412yes—
19#10623081C412yes—
20D4×D44C411yescharacteristic
21#10623078—22no—
22C4×D4×D11—21no—
23#10623074C411yescharacteristic
24#10623061—21no—
25#10623058—22no—
26#10623010C2212yes—
27#10623008C2211yescharacteristic
28C4×#4339C2211yescharacteristic
29C2×C4×D44C2212yes—
30C11×#405—22no—
31C11×#405—21no—
32C4×C11×M16C2212yescomplemented
33C4×C11×M16C2211yescharacteristic, complemented
34C2×C4×C8×C11C2211yescharacteristic, complemented
35C2×C4×C8×C11C2212yescomplemented
36#10622637—21no—
37#10622624—22no—
38D4×C11⋊C8—21no—
39#10622539C2212yescomplemented
40#10622538C2211yescharacteristic, complemented
41#10622537C2211yescharacteristic, complemented
42C2×C4⋊(C11⋊C8)C2212yescomplemented
43#10622097C2212yes—
44#10622097C2211yescharacteristic
45#10622097C2211yescharacteristic
46#10622097C2212yescomplemented
47#10622097C2212yescomplemented
48#10622097C2212yescomplemented
49#10622097C2212yescomplemented
50#10622094C2211yescharacteristic, complemented
51#10622094C2212yescomplemented
52#10622094C2211yescharacteristic, complemented
53C2×C11×#41D411yescharacteristic
54C2×D4×D11—21no—
55C2×#4339—21no—
56C2×#4339C2×C411yescharacteristic
57C22×D44C2×C412yes—
58C22×C4×D11—22no—
59C11×#131—28no—
60C2×C11×M16—22no—
61C2×C11×M16—21no—
62C22×C8×C11—22no—
63C22×C8×C11—21no—
64C4×Q8×C11C2×C411yescharacteristic
65C4×Q8×C11D411yescharacteristic
66C4×D4×C11C2×C411yescharacteristic
67C4×D4×C11C2×C412yes—
68C4×D4×C11D411yescharacteristic
69C4×D4×C11D412yes—
70C11×#117D412yes—
71C11×#117D411yescharacteristic
72C2×C42×C11C2312yes—
73C2×C42×C11C2311yescharacteristic
74#67000—21no—
75#66999—21no—
76#66992—22no—
77#66990—22no—
78D4×Dic11—21no—
79#66983—21no—
80#66983C2×C412yes—
81#66983C2×C412yes—
82#66982—22no—
83C4×C22⋊D11—21no—
84C4×C22⋊D11—21no—
85C4×C22⋊D11—22no—
86C2×(C2×D11)⋊C4—22no—
87#66979C2×C411yescharacteristic
88C2×C4⋊Dic11C2×C412yes—
89#66977C2×C412yes—
90C2×#4318—21no—
91C22×C11⋊C8—22no—
92#66951—22no—
93#66949—22no—
94#66948—21no—
95#66947—22no—
96#66947—22no—
97#66946—21no—
98C4⋊C4×D11—21no—
99#66943—21no—
100#66937—22no—
101#66936—22no—
102#66935—22no—
103(C22⋊D11)⋊C4—22no—
104C22⋊C4×D11—22no—
105#66931—22no—
106#66929—22no—
107#66928—21no—
108#66928C2×C412yes—
109#66927C2×C411yescharacteristic
110C4×D44—22no—
111C4×D44—22no—
112C4×D44—21no—
113C4×D44C2×C412yes—
114C4×D44C2×C412yes—
115C4×D44C2×C411yescharacteristic
116C4×D44C2311yescharacteristic
117C4×D44C2312yes—
118#66925—21no—
119#66925—22no—
120C42×D11—21no—
121#66923C2×C412yes—
122#66922C2×C411yescharacteristic
123C4×Dic22C2×C411yescharacteristic
124C4×Dic22C2311yescharacteristic
125C11×#97—21no—
126C11×#97—22no—
127C4×C8×C11—21no—
128C4×C8×C11—22no—
129C4×C8×C11C2311yescharacteristic
130C4×C8×C11C2311yescharacteristic
131C4×C8×C11C2312yes—
132C22⋊(C11⋊C8)—21no—
133C22⋊(C11⋊C8)—22no—
134C4⋊(C11⋊C8)—22no—
135C4⋊(C11⋊C8)—21no—
136C4⋊(C11⋊C8)C2311yescharacteristic
137C4⋊(C11⋊C8)C2312yes—
138C4⋊(C11⋊C8)C2311yescharacteristic
139#66867—22no—
140C4×C11⋊C8—21no—
141#17517—111nomaximal, Sylow
142C23×D11—22no—
143C11×#41—24no—
144C2×Q8×C11C22⋊C411yescharacteristic
145C2×D4×C11C22⋊C412yes—
146C2×D4×C11C22⋊C411yescharacteristic
147C22×C4×C11C22×C412yes—
148C22×C4×C11C22×C411yescharacteristic
149C22×C4×C11C2×D412yes—
150C22×C4×C11C2×D411yescharacteristic
151C22×C4×C11C2×D412yes—
152C22×C4×C11C2×D411yescharacteristic
153C2×C22⋊D11—22no—
154C2×C22⋊D11—21no—
155C2×C22⋊D11—22no—
156C22×Dic11—22no—
157D4×D11—44no—
158#4339—22no—
159#4339—41no—
160#4339—81no—
161#4339—81no—
162C2×D44—24no—
163C2×D44—22no—
164C2×D44—21no—
165C2×D44—21no—
166C2×D44—42no—
167C2×D44C22×C412yes—
168C2×D44C22×C411yescharacteristic
169C2×C4×D11—21no—
170C2×C4×D11—21no—
171C2×C4×D11—22no—
172C2×C4×D11—22no—
173C2×C4×D11—21no—
174C2×C4×D11—22no—
175C2×C4×D11—82no—
176C2×C4×D11—82no—
177C2×Dic22—21no—
178C2×Dic22C22×C411yescharacteristic
179C11×M16—28no—
180C11×M16—24no—
181C2×C8×C11—28no—
182C2×C8×C11—24no—
183C2×C8×C11—21no—
184C2×C8×C11—21no—
185C2×C8×C11—22no—
186C11×C4⋊C4C22⋊C411yescharacteristic
187C11×C4⋊C4C22⋊C411yescharacteristic
188C11×C4⋊C4C22⋊C412yes—
189C11×C4⋊C4C22⋊C412yes—
190C11×C22⋊C4C22⋊C412yes—
191C11×C22⋊C4C22⋊C412yes—
192C11×C22⋊C4C22⋊C412yes—
193C42×C11C22×C411yescharacteristic
194C42×C11C22×C412yes—
195C42×C11C2×D411yescharacteristic
196C42×C11C2×D412yes—
197C42×C11C2×D411yescharacteristic
198C42×C11C2×D412yes—
199C42×C11C2411yescharacteristic
200C22⋊Dic11—22no—
201C22⋊Dic11—21no—
202(C2×D11)⋊C4—21no—
203(C2×D11)⋊C4—22no—
204(C2×D11)⋊C4—22no—
205(C2×D11)⋊C4—22no—
206(C2×D11)⋊C4—22no—
207(C2×D11)⋊C4—22no—
208(C2×D11)⋊C4—22no—
209(C2×D11)⋊C4—21no—
210(C2×D11)⋊C4—22no—
211C4⋊Dic11—21no—
212C4⋊Dic11—22no—
213C4⋊Dic11C22×C411yescharacteristic
214C4⋊Dic11C22×C411yescharacteristic
215C4⋊Dic11C22×C412yes—
216Dic11⋊C4—21no—
217Dic11⋊C4—22no—
218Dic11⋊C4—22no—
219Dic11⋊C4—22no—
220Dic11⋊C4—21no—
221C4×Dic11—21no—
222C4×Dic11—21no—
223C4×Dic11—21no—
224#4318—81no—
225C2×C11⋊C8—21no—
226C2×C11⋊C8—21no—
227C2×C11⋊C8—22no—
228C2×C11⋊C8—82no—
229#3481—111no—
230#2990—111no—
231C4×#131D1111yescharacteristic, complemented
232#1494—112no—
233#1492—111no—
234#1490—112no—
235#1489—111no—
236#1484—111no—
237#1483—112no—
238#1476—111no—
239C2×D4⋊C8—112no—
240C23×C11C2×C22⋊C411yescharacteristic
241C23×C11C2×C22⋊C412yes—
242C22×D11—21no—
243C22×D11—22no—
244C22×D11—44no—
245C22×D11—44no—
246C22×D11—82no—
247Q8×C11—22no—
248D4×C11—24no—
249D4×C11#10414yes—
250C2×C4×C11—24no—
251C2×C4×C11—22no—
252C2×C4×C11—21no—
253C2×C4×C11—22no—
254C2×C4×C11—21no—
255C2×C4×C11—22no—
256C2×C4×C11—21no—
257C2×C4×C11—22no—
258C2×C4×C11—21no—
259C2×C4×C11—22no—
260C2×C4×C11C2×C22⋊C411yescharacteristic
261C2×C4×C11C2×C22⋊C412yes—
262C2×C4×C11C2×C22⋊C412yes—
263C2×C4×C11C2×C22⋊C411yescharacteristic
264C2×C4×C11C2×C22⋊C412yes—
265C2×C4×C11C2×C22⋊C411yescharacteristic
266C2×C4×C11C23×C411yescharacteristic
267C2×C4×C11C22×D411yescharacteristic
268C2×C4×C11C22×D411yescharacteristic
269C22⋊D11—42no—
270C22⋊D11—44no—
271C22⋊D11—82no—
272C2×Dic11—21no—
273C2×Dic11—21no—
274C2×Dic11—21no—
275C2×Dic11—22no—
276C2×Dic11—82no—
277D44—22no—
278D44—21no—
279D44—22no—
280D44—44no—
281D44—42no—
282D44—81no—
283D44#13112yescomplemented
284C4×D11—42no—
285C4×D11—41no—
286C4×D11—42no—
287C4×D11—41no—
288C4×D11—42no—
289C4×D11—42no—
290C4×D11—82no—
291C4×D11—82no—
292Dic22—21no—
293Dic22—21no—
294Dic22—81no—
295C8×C11—22no—
296C8×C11—24no—
297C8×C11—22no—
298C11⋊C8—41no—
299C11⋊C8—42no—
300C11⋊C8—41no—
301C2×#131—21no—
302#559—111no—
303#554—111no—
304#554—111no—
305#553—112no—
306#553—221no—
307#551—222no—
308#546—112no—
309#546—221no—
310D42—111no—
311#532—111no—
312#529—112no—
313#529—221no—
314#525—222no—
315C4×#41—111no—
316C4×#41C2×D1111yescharacteristic
317C2×C4×D4—112no—
318C2×C4×D4—221no—
319#446—221no—
320#435—222no—
321C8×D4—221no—
322#432—112no—
323#431—111no—
324#423—111no—
325C2×C4⋊C8—112no—
326#405—22no—
327#405—21no—
328C4×M16C2×D1112yescomplemented
329C4×M16C2×D1111yescharacteristic, complemented
330C2×C4×C8C2×D1112yescomplemented
331C2×C4×C8C2×D1111yescharacteristic, complemented
332Q8⋊C8—111no—
333Q8⋊C8—111no—
334Q8⋊C8—112no—
335D4⋊C8—111no—
336D4⋊C8—112no—
337D4⋊C8—111no—
338D4⋊C8—112no—
339D4⋊C8—112no—
340D4⋊C8—112no—
341D4⋊C8—112no—
342C22×C11—22no—
343C22×C11—22no—
344C22×C11—21no—
345C22×C11—21no—
346C22×C11—21no—
347C22×C11C2×#10414yes—
348C22×C11C22×C22⋊C411yescharacteristic
349C2×D11—22no—
350C2×D11—41no—
351C2×D11—41no—
352C2×D11—42no—
353C2×D11—42no—
354C2×D11—42no—
355C2×D11—88no—
356C4×C11—21no—
357C4×C11—22no—
358C4×C11—21no—
359C4×C11—22no—
360C4×C11—21no—
361C4×C11—22no—
362C4×C11C2×#10412yes—
363C4×C11C2×#13111yescharacteristic
364C4×C11#56811yescharacteristic
365C4×C11#57611yescharacteristic
366C4×C11#57711yescharacteristic
367Dic11—41no—
368Dic11—42no—
369Dic11—41no—
370Dic11—41no—
371C2×#41—111no—
372C2×#41—221no—
373C2×#41C22⋊D1111yescharacteristic
374C22×D4—112no—
375C22×D4—221no—
376C23×C4—222no—
377#131—28no—
378C2×M16—22no—
379C2×M16—21no—
380C2×M16—221no—
381C22×C8—22no—
382C22×C8—21no—
383C22×C8—222no—
384C4⋊Q8—111no—
385#127—111no—
386#126—222no—
387#126—222no—
388#125—112no—
389#125—221no—
390#124—112no—
391#124—221no—
392#124—221no—
393#123—222no—
394#123—222no—
395#123—222no—
396#123—222no—
397C22⋊Q8—112no—
398C22⋊Q8—221no—
399C22⋊Q8—222no—
400C22⋊Q8—222no—
401#121—112no—
402#121—112no—
403#121—222no—
404#121—221no—
405#121—221no—
406#121—222no—
407#120—222no—
408#120—222no—
409C4×Q8—111no—
410C4×Q8—111no—
411C4×Q8C4×D1111yescharacteristic
412C4×Q8D4411yescharacteristic
413C4×D4—112no—
414C4×D4—112no—
415C4×D4—111no—
416C4×D4—111no—
417C4×D4—112no—
418C4×D4—221no—
419C4×D4—222no—
420C4×D4—221no—
421C4×D4—221no—
422C4×D4—221no—
423C4×D4—222no—
424C4×D4—222no—
425C4×D4—221no—
426C4×D4—222no—
427C4×D4C4×D1111yescharacteristic
428C4×D4C4×D1112yes—
429C4×D4D4411yescharacteristic
430C4×D4D4412yes—
431#117—111no—
432#117—222no—
433#117—221no—
434#117C22⋊D1112yes—
435#117C22⋊D1111yescharacteristic
436C2×C4⋊C4—112no—
437C2×C4⋊C4—221no—
438C2×C22⋊C4—222no—
439C2×C22⋊C4—222no—
440C2×C42—221no—
441C2×C42C22×D1112yes—
442C2×C42C22×D1111yescharacteristic
443C4⋊C8—111no—
444C4⋊C8—112no—
445C4⋊C8—111no—
446C4⋊C8—222no—
447C4⋊C8—221no—
448C22⋊C8—221no—
449C22⋊C8—222no—
450#97—21no—
451#97—22no—
452#97—222no—
453C4×C8—21no—
454C4×C8—22no—
455C4×C8—221no—
456C4×C8C22×D1111yescharacteristic
457C4×C8C22×D1112yes—
458C4×C8C22×D1111yescharacteristic
459C2×C11—24no—
460C2×C11—41no—
461C2×C11#288011yescharacteristic
462C2×C11#289711yescharacteristic
463C2×C11C22×#10411yescharacteristic
464D11—42no—
465D11—82no—
466C24—222no—
467#41—24no—
468#41—222no—
469#41—441no—
470#41—881no—
471#41—881no—
472C2×Q8—111no—
473C2×Q8—221no—
474C2×Q8(C2×D11)⋊C411yescharacteristic
475C2×D4—111no—
476C2×D4—112no—
477C2×D4—224no—
478C2×D4—221no—
479C2×D4—222no—
480C2×D4—222no—
481C2×D4—222no—
482C2×D4—221no—
483C2×D4—221no—
484C2×D4—442no—
485C2×D4—444no—
486C2×D4(C2×D11)⋊C412yes—
487C2×D4(C2×D11)⋊C411yescharacteristic
488C22×C4—222no—
489C22×C4—221no—
490C22×C4—221no—
491C22×C4—221no—
492C22×C4—222no—
493C22×C4—222no—
494C22×C4—222no—
495C22×C4—882no—
496C22×C4—882no—
497C22×C4C2×C4×D1112yes—
498C22×C4C2×C4×D1111yescharacteristic
499C22×C4C2×D4412yes—
500C22×C4C2×D4411yescharacteristic
501C22×C4C2×C22⋊D1112yes—
502C22×C4C2×C22⋊D1111yescharacteristic
503M16—28no—
504M16—24no—
505M16—881no—
506C2×C8—28no—
507C2×C8—24no—
508C2×C8—21no—
509C2×C8—21no—
510C2×C8—22no—
511C2×C8—221no—
512C2×C8—221no—
513C2×C8—222no—
514C2×C8—882no—
515C4⋊C4—111no—
516C4⋊C4—112no—
517C4⋊C4—111no—
518C4⋊C4—222no—
519C4⋊C4—221no—
520C4⋊C4—222no—
521C4⋊C4—221no—
522C4⋊C4—222no—
523C4⋊C4—222no—
524C4⋊C4—221no—
525C4⋊C4(C2×D11)⋊C411yescharacteristic
526C4⋊C4(C2×D11)⋊C411yescharacteristic
527C4⋊C4(C2×D11)⋊C412yes—
528C4⋊C4(C2×D11)⋊C412yes—
529C22⋊C4—222no—
530C22⋊C4—221no—
531C22⋊C4—222no—
532C22⋊C4—222no—
533C22⋊C4—222no—
534C22⋊C4—222no—
535C22⋊C4—221no—
536C22⋊C4—222no—
537C22⋊C4—222no—
538C22⋊C4—221no—
539C22⋊C4—222no—
540C22⋊C4(C2×D11)⋊C412yes—
541C22⋊C4(C2×D11)⋊C412yes—
542C22⋊C4(C2×D11)⋊C412yes—
543C42—221no—
544C42—221no—
545C42—221no—
546C42C2×C4×D1112yes—
547C42C2×C4×D1111yescharacteristic
548C42C2×D4411yescharacteristic
549C42C2×D4412yes—
550C42C2×C22⋊D1111yescharacteristic
551C42C2×C22⋊D1112yes—
552C42C23×D1111yescharacteristic
553C11#1751711yescharacteristic, complemented, Sylow
554C23—221no—
555C23—222no—
556C23—444no—
557C23—444no—
558C23—882no—
559C23C2×(C2×D11)⋊C411yescharacteristic
560C23C2×(C2×D11)⋊C412yes—
561Q8—22no—
562Q8—221no—
563Q8—221no—
564Q8—881no—
565D4—24no—
566D4—112no—
567D4—222no—
568D4—221no—
569D4—222no—
570D4—444no—
571D4—442no—
572D4—444no—
573D4—442no—
574D4—881no—
575D4—882no—
576D4#6686914yes—
577C2×C4—24no—
578C2×C4—22no—
579C2×C4—21no—
580C2×C4—22no—
581C2×C4—21no—
582C2×C4—22no—
583C2×C4—21no—
584C2×C4—22no—
585C2×C4—21no—
586C2×C4—22no—
587C2×C4—221no—
588C2×C4—221no—
589C2×C4—221no—
590C2×C4—222no—
591C2×C4—442no—
592C2×C4—441no—
593C2×C4—442no—
594C2×C4—441no—
595C2×C4—442no—
596C2×C4—442no—
597C2×C4—882no—
598C2×C4—882no—
599C2×C4—882no—
600C2×C4C2×(C2×D11)⋊C411yescharacteristic
601C2×C4C2×(C2×D11)⋊C412yes—
602C2×C4C2×(C2×D11)⋊C412yes—
603C2×C4C2×(C2×D11)⋊C411yescharacteristic
604C2×C4C2×(C2×D11)⋊C412yes—
605C2×C4C2×(C2×D11)⋊C411yescharacteristic
606C2×C4C22×C4×D1111yescharacteristic
607C2×C4C22×D4411yescharacteristic
608C2×C4C22×C22⋊D1111yescharacteristic
609C8—22no—
610C8—24no—
611C8—22no—
612C8—441no—
613C8—441no—
614C8—442no—
615C22—22no—
616C22—22no—
617C22—21no—
618C22—21no—
619C22—21no—
620C22—222no—
621C22—441no—
622C22—441no—
623C22—442no—
624C22—442no—
625C22—442no—
626C22—888no—
627C22C2×#6686914yes—
628C22C22×(C2×D11)⋊C411yescharacteristic
629C4—21no—
630C4—22no—
631C4—22no—
632C4—21no—
633C4—21no—
634C4—22no—
635C4—441no—
636C4—441no—
637C4—442no—
638C4—441no—
639C4C2×#6686912yes—
640C4D11×#13111yescharacteristic
641C4#1062328111yescharacteristic
642C4#1062328211yescharacteristic
643C4#1062328311yescharacteristic
644C2—24no—
645C2—41no—
646C2—442no—
647C2—882no—
648C2#1307706311yescharacteristic
649C2#1307714311yescharacteristic
650C2C22×#6686911yescharacteristic
subgroupG/H
centerC2×C4C22×D44
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC4×C11×#131C2
socleC22×C11C22×C22⋊C4
prime radical#13082226C2
cosocleC42×C11C24
hypercenterC4×#131D11
hypocenterC11#17517
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C4×#41 ◁ C4×#131

Complements

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

NH ≅ G/Ntype
2. #13077741C2semidirect
3. #13067077C2semidirect
4. #13067068C2semidirect
5. #13067060C2semidirect
6. #13067056C2semidirect
7. #13067034C2semidirect
8. #13067030C2semidirect
9. #13066999C2semidirect
10. C2×#10622097C2semidirect
11. C4×C11×#131C2semidirect
32. C4×C11×M16C22semidirect
33. C4×C11×M16C22semidirect
34. C2×C4×C8×C11C22semidirect
35. C2×C4×C8×C11C22semidirect
39. #10622539C22semidirect
40. #10622538C22semidirect
41. #10622537C22semidirect
42. C2×C4⋊(C11⋊C8)C22semidirect
46. #10622097C22semidirect
47. #10622097C22semidirect
48. #10622097C22semidirect
49. #10622097C22semidirect
50. #10622094C22semidirect
51. #10622094C22semidirect
52. #10622094C22semidirect
231. C4×#131D11semidirect
283. D44#131semidirect
328. C4×M16C2×D11semidirect
329. C4×M16C2×D11semidirect
330. C2×C4×C8C2×D11semidirect
331. C2×C4×C8C2×D11semidirect
553. C11#17517semidirect

Maximal subgroups

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

subgroupindex
#130822262
#130777412
#130670772
#130670682
#130670602
#130670562
#130670342
#130670302
#130669992
C2×#106220972
C4×C11×#1312
#1751711