Finite Group Databasebeta

← #14721949

Subgroups — #14721949

Order 2816.

940 conjugacy classes of subgroups.

The subgroup lattice has 610 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082577C211yesmaximal, characteristic
2#13077267C211yesmaximal, characteristic, complemented
3#13067245C212yesmaximal, complemented
4#13067239C212yesmaximal, complemented
5#13067228C211yesmaximal, characteristic, complemented
6#13067224C211yesmaximal, characteristic, complemented
7#13067221C212yesmaximal, complemented
8#13067213C212yesmaximal, complemented
9#13067207C211yesmaximal, characteristic, complemented
10#13067205C211yesmaximal, characteristic, complemented
11C11×#2971C211yesmaximal, characteristic, complemented
12C4×C11×#41C2211yescharacteristic
13#10623360—21no—
14#10623116C411yescharacteristic
15#10623115C411yescharacteristic
16#10623113—21no—
17#10623091—22no—
18#10623083C412yes—
19#10623081C412yes—
20D4×D44C411yescharacteristic
21#10623076—21no—
22D4×Dic22C411yescharacteristic
23#10623063—21no—
24#10623058—22no—
25#10623010C2211yescharacteristic
26#10623010C2212yes—
27#10623008C2211yescharacteristic
28C2×#66928C2212yes—
29C8×Q8×C11—21no—
30C11×#436—21no—
31C11×#436—22no—
32C11×#432C2211yescharacteristic, complemented
33C11×#432C2212yescomplemented
34C4×C11×M16C2211yescharacteristic, complemented
35C4×C11×M16C2212yescomplemented
36#10622847—21no—
37#10622613—22no—
38#10622612—21no—
39#10622539C2212yescomplemented
40#10622539C2212yescomplemented
41C4×#4318C2211yescharacteristic, complemented
42C2×#66867C2211yescharacteristic, complemented
43#10622103C2211yescharacteristic, complemented
44#10622103C2211yescharacteristic, complemented
45#10622103C2212yescomplemented
46#10622102C2211yescharacteristic
47#10622102C2211yescharacteristic
48#10622102C2212yes—
49#10622102C2212yescomplemented
50#10622102C2212yescomplemented
51#10622102C2212yescomplemented
52#10622102C2212yescomplemented
53C2×C11×#41D411yescharacteristic
54C2×D4×D11—21no—
55C2×#4339C2×C412yes—
56C22×D44C2×C412yes—
57C22×Dic22C2×C412yes—
58C2×C11×M16—22no—
59C2×C11×M16—21no—
60C4×Q8×C11C2×C411yescharacteristic
61C4×Q8×C11D411yescharacteristic
62C4×D4×C11C2×C411yescharacteristic
63C4×D4×C11C2×C412yes—
64C4×D4×C11D411yescharacteristic
65C4×D4×C11D412yes—
66C11×#117D412yes—
67C11×#117D411yescharacteristic
68C2×C42×C11C2312yes—
69C2×C42×C11C2311yescharacteristic
70#67000—21no—
71#66999—21no—
72#66992—22no—
73#66990—22no—
74D4×Dic11—21no—
75#66983—21no—
76#66983—21no—
77#66983C2×C412yes—
78#66983C2×C411yescharacteristic
79#66982—22no—
80#66982—21no—
81C4×C22⋊D11—21no—
82C4×C22⋊D11—22no—
83C2×(C2×D11)⋊C4—22no—
84C2×(C2×D11)⋊C4—22no—
85#66977C2×C412yes—
86#66977C2×C411yescharacteristic
87C2×#4318—21no—
88C22×C11⋊C8—21no—
89#66951—22no—
90#66949—22no—
91#66948—21no—
92#66947—22no—
93#66947—22no—
94#66946—21no—
95#66945—21no—
96#66941—21no—
97#66938—22no—
98#66937—22no—
99#66935—22no—
100(C22⋊D11)⋊C4—22no—
101C22⋊C4×D11—22no—
102#66931—22no—
103#66929—21no—
104#66929—22no—
105#66928—22no—
106#66928—22no—
107#66928C2×C412yes—
108#66928C2×C412yes—
109#66928C2311yescharacteristic
110#66928C2312yes—
111#66927C2×C411yescharacteristic
112C4×D44—21no—
113C4×D44—21no—
114C4×D44C2×C411yescharacteristic
115C4×D44C2×C412yes—
116#66925—22no—
117#66925—21no—
118#66923C2311yescharacteristic
119#66922C2×C411yescharacteristic
120C4×Dic22C2×C411yescharacteristic
121C4×Dic22C2×C412yes—
122C11×C4⋊C8—21no—
123C11×C4⋊C8—22no—
124C11×C22⋊C8—22no—
125C11×C22⋊C8—21no—
126C11×#97C2311yescharacteristic
127C11×#97C2311yescharacteristic
128C11×#97C2312yes—
129C4×C8×C11—21no—
130C4×C8×C11—22no—
131C22⋊(C11⋊C8)—22no—
132C22⋊(C11⋊C8)—22no—
133C4⋊(C11⋊C8)—22no—
134C4⋊(C11⋊C8)—22no—
135#66867—21no—
136#66867C2311yescharacteristic
137#66867C2311yescharacteristic
138#66867C2312yes—
139C4×C11⋊C8—21no—
140#17681—111nomaximal, Sylow
141C23×D11—22no—
142C11×#41—42no—
143C2×Q8×C11C22⋊C411yescharacteristic
144C2×D4×C11C22⋊C411yescharacteristic
145C2×D4×C11C22⋊C412yes—
146C22×C4×C11C22×C412yes—
147C22×C4×C11C22×C411yescharacteristic
148C22×C4×C11C2×D411yescharacteristic
149C22×C4×C11C2×D412yes—
150C22×C4×C11C2×D412yes—
151C22×C4×C11C2×D411yescharacteristic
152C2×C22⋊D11—22no—
153C2×C22⋊D11—21no—
154C2×C22⋊D11—22no—
155C22×Dic11—22no—
156D4×D11—44no—
157#4339—82no—
158C2×D44—21no—
159C2×D44—21no—
160C2×D44—22no—
161C2×D44—82no—
162C2×D44C22×C412yes—
163C2×D44C22×C411yescharacteristic
164C2×C4×D11—21no—
165C2×C4×D11—22no—
166C2×C4×D11—22no—
167C2×Dic22—22no—
168C2×Dic22—82no—
169C2×Dic22C22×C412yes—
170C2×Dic22C22×C411yescharacteristic
171C11×M16—44no—
172C11×M16—42no—
173C2×C8×C11—21no—
174C2×C8×C11—21no—
175C2×C8×C11—22no—
176C11×C4⋊C4C22⋊C411yescharacteristic
177C11×C4⋊C4C22⋊C411yescharacteristic
178C11×C4⋊C4C22⋊C412yes—
179C11×C4⋊C4C22⋊C412yes—
180C11×C22⋊C4C22⋊C412yes—
181C11×C22⋊C4C22⋊C412yes—
182C11×C22⋊C4C22⋊C412yes—
183C42×C11C22×C411yescharacteristic
184C42×C11C22×C412yes—
185C42×C11C2×D411yescharacteristic
186C42×C11C2×D412yes—
187C42×C11C2×D411yescharacteristic
188C42×C11C2×D412yes—
189C42×C11C2411yescharacteristic
190C22⋊Dic11—22no—
191C22⋊Dic11—21no—
192(C2×D11)⋊C4—21no—
193(C2×D11)⋊C4—22no—
194(C2×D11)⋊C4—21no—
195(C2×D11)⋊C4—22no—
196(C2×D11)⋊C4—22no—
197(C2×D11)⋊C4—22no—
198(C2×D11)⋊C4—22no—
199(C2×D11)⋊C4—22no—
200(C2×D11)⋊C4—22no—
201(C2×D11)⋊C4—21no—
202(C2×D11)⋊C4—22no—
203(C2×D11)⋊C4—21no—
204C4⋊Dic11—21no—
205C4⋊Dic11—21no—
206C4⋊Dic11C22×C411yescharacteristic
207C4⋊Dic11C22×C411yescharacteristic
208Dic11⋊C4—21no—
209Dic11⋊C4—22no—
210Dic11⋊C4—22no—
211Dic11⋊C4—21no—
212Dic11⋊C4—21no—
213Dic11⋊C4—21no—
214C4×Dic11—22no—
215C4×Dic11—21no—
216#4318—42no—
217C2×C11⋊C8—22no—
218C2×C11⋊C8—21no—
219C2×C11⋊C8—21no—
220C2×C11⋊C8—42no—
221#3514—111no—
222#2971D1111yescharacteristic, complemented
223#2923—111no—
224#1535—112no—
225#1533—112no—
226#1530—111no—
227#1529—111no—
228#1529—112no—
229#1527—112no—
230#1525—111no—
231#1524—111no—
232C23×C11C2×C22⋊C412yes—
233C23×C11C2×C22⋊C411yescharacteristic
234C22×D11—21no—
235C22×D11—22no—
236C22×D11—44no—
237C22×D11—82no—
238C22×D11—82no—
239Q8×C11—22no—
240D4×C11—22no—
241D4×C11—42no—
242C2×C4×C11—22no—
243C2×C4×C11—42no—
244C2×C4×C11—41no—
245C2×C4×C11—42no—
246C2×C4×C11—41no—
247C2×C4×C11—42no—
248C2×C4×C11C2×C22⋊C412yes—
249C2×C4×C11C2×C22⋊C411yescharacteristic
250C2×C4×C11C2×C22⋊C412yes—
251C2×C4×C11C2×C22⋊C412yes—
252C2×C4×C11C2×C22⋊C411yescharacteristic
253C2×C4×C11C2×C22⋊C411yescharacteristic
254C2×C4×C11C23×C411yescharacteristic
255C2×C4×C11C22×D411yescharacteristic
256C2×C4×C11C22×D411yescharacteristic
257C22⋊D11—44no—
258C22⋊D11—82no—
259C22⋊D11—81no—
260C2×Dic11—21no—
261C2×Dic11—21no—
262C2×Dic11—22no—
263C2×Dic11—21no—
264C2×Dic11—82no—
265D44—41no—
266D44—42no—
267D44—42no—
268D44—81no—
269D44—82no—
270C4×D11—42no—
271C4×D11—82no—
272C4×D11—82no—
273Dic22—41no—
274Dic22—42no—
275Dic22—82no—
276C8×C11—22no—
277C8×C11—41no—
278C8×C11—42no—
279C11⋊C8—41no—
280C11⋊C8—41no—
281C11⋊C8—42no—
282#559—111no—
283#556—111no—
284#555—221no—
285#551—222no—
286D4×Q8—111no—
287#548—112no—
288#546—112no—
289#546—221no—
290D42—111no—
291#542—221no—
292#538—222no—
293#532—111no—
294#529—111no—
295#529—112no—
296C2×#124—112no—
297#518—221no—
298C4×#41C2×D1111yescharacteristic
299C8×Q8—21no—
300#436—21no—
301#436—22no—
302#433—222no—
303#432—112no—
304#432—112no—
305#432C2×D1111yescharacteristic, complemented
306#432C2×D1112yescomplemented
307#424—221no—
308#408—221no—
309C4×M16—111no—
310C4×M16C2×D1111yescharacteristic, complemented
311C4×M16C2×D1112yescomplemented
312C2×#97—111no—
313#330—111no—
314#330—111no—
315#330—112no—
316#329—111no—
317#329—111no—
318#329—112no—
319#329—112no—
320#329—112no—
321#329—112no—
322#329—112no—
323C22×C11—22no—
324C22×C11—21no—
325C22×C11—21no—
326C22×C11—22no—
327C22×C11—22no—
328C22×C11—21no—
329C22×C11C22×C22⋊C411yescharacteristic
330C2×D11—41no—
331C2×D11—42no—
332C2×D11—41no—
333C2×D11—42no—
334C2×D11—41no—
335C2×D11—42no—
336C2×D11—164no—
337C4×C11—21no—
338C4×C11—22no—
339C4×C11—21no—
340C4×C11—21no—
341C4×C11—22no—
342C4×C11—21no—
343C4×C11—22no—
344C4×C11—21no—
345C4×C11#42112yes—
346Dic11—41no—
347Dic11—42no—
348Dic11—41no—
349Dic11—41no—
350C2×#41—112no—
351C2×#41D4411yescharacteristic
352C22×Q8—112no—
353C22×D4—112no—
354C22×D4—221no—
355C2×M16—22no—
356C2×M16—21no—
357C2×M16—221no—
358C22×C8—221no—
359C4⋊Q8—111no—
360C4⋊Q8—221no—
361#127—111no—
362#126—222no—
363#126—221no—
364#126—222no—
365#125—111no—
366#124—112no—
367#124—112no—
368#124—111no—
369#124—112no—
370#124—221no—
371#124—222no—
372#124—222no—
373#124—222no—
374#123—222no—
375#123—221no—
376#123—222no—
377#123—222no—
378C22⋊Q8—112no—
379C22⋊Q8—111no—
380C22⋊Q8—221no—
381C22⋊Q8—222no—
382C22⋊Q8—222no—
383#121—112no—
384#121—111no—
385#121—222no—
386#121—221no—
387#121—221no—
388#121—221no—
389#121—222no—
390#120—222no—
391#120—222no—
392C4×Q8—112no—
393C4×Q8—111no—
394C4×Q8C4×D1111yescharacteristic
395C4×Q8C22⋊D1111yescharacteristic
396C4×D4—111no—
397C4×D4—112no—
398C4×D4—221no—
399C4×D4—221no—
400C4×D4—222no—
401C4×D4—221no—
402C4×D4—222no—
403C4×D4—221no—
404C4×D4—221no—
405C4×D4C4×D1111yescharacteristic
406C4×D4C4×D1112yes—
407C4×D4C22⋊D1111yescharacteristic
408C4×D4C22⋊D1112yes—
409#117—221no—
410#117—222no—
411#117—221no—
412#117D4412yes—
413#117D4411yescharacteristic
414C2×C22⋊C4—222no—
415C2×C22⋊C4—222no—
416C2×C22⋊C4—222no—
417C2×C42C22×D1112yes—
418C2×C42C22×D1111yescharacteristic
419C4⋊C8—21no—
420C4⋊C8—22no—
421C4⋊C8—222no—
422C4⋊C8—222no—
423C22⋊C8—22no—
424C22⋊C8—21no—
425C22⋊C8—222no—
426C22⋊C8—222no—
427#97—111no—
428#97—111no—
429#97—112no—
430#97—221no—
431#97C22×D1111yescharacteristic
432#97C22×D1111yescharacteristic
433#97C22×D1112yes—
434C4×C8—21no—
435C4×C8—22no—
436C4×C8—221no—
437C2×C11—42no—
438C2×C11—41no—
439C2×C11#288811yescharacteristic
440C2×C11C2×#42111yescharacteristic
441C2×C11#290111yescharacteristic
442D11—82no—
443D11—81no—
444C24—222no—
445#41—42no—
446#41—882no—
447C2×Q8—111no—
448C2×Q8—112no—
449C2×Q8—222no—
450C2×Q8—882no—
451C2×Q8(C2×D11)⋊C411yescharacteristic
452C2×D4—111no—
453C2×D4—112no—
454C2×D4—222no—
455C2×D4—221no—
456C2×D4—222no—
457C2×D4—221no—
458C2×D4—221no—
459C2×D4—222no—
460C2×D4—444no—
461C2×D4—882no—
462C2×D4(C2×D11)⋊C411yescharacteristic
463C2×D4(C2×D11)⋊C412yes—
464C22×C4—222no—
465C22×C4—221no—
466C22×C4—222no—
467C22×C4—222no—
468C22×C4C2×C4×D1112yes—
469C22×C4C2×C4×D1111yescharacteristic
470C22×C4C2×D4411yescharacteristic
471C22×C4C2×D4412yes—
472C22×C4C2×C22⋊D1112yes—
473C22×C4C2×C22⋊D1111yescharacteristic
474M16—44no—
475M16—42no—
476M16—442no—
477C2×C8—21no—
478C2×C8—21no—
479C2×C8—22no—
480C2×C8—222no—
481C2×C8—221no—
482C2×C8—221no—
483C2×C8—442no—
484C4⋊C4—111no—
485C4⋊C4—111no—
486C4⋊C4—221no—
487C4⋊C4—221no—
488C4⋊C4—222no—
489C4⋊C4—221no—
490C4⋊C4—222no—
491C4⋊C4—221no—
492C4⋊C4—221no—
493C4⋊C4—221no—
494C4⋊C4(C2×D11)⋊C411yescharacteristic
495C4⋊C4(C2×D11)⋊C411yescharacteristic
496C4⋊C4(C2×D11)⋊C412yes—
497C4⋊C4(C2×D11)⋊C412yes—
498C22⋊C4—222no—
499C22⋊C4—221no—
500C22⋊C4—221no—
501C22⋊C4—222no—
502C22⋊C4—222no—
503C22⋊C4—222no—
504C22⋊C4—222no—
505C22⋊C4—222no—
506C22⋊C4—221no—
507C22⋊C4—222no—
508C22⋊C4—221no—
509C22⋊C4—222no—
510C22⋊C4—221no—
511C22⋊C4—222no—
512C22⋊C4(C2×D11)⋊C412yes—
513C22⋊C4(C2×D11)⋊C412yes—
514C22⋊C4(C2×D11)⋊C412yes—
515C42—222no—
516C42—221no—
517C42C2×C4×D1112yes—
518C42C2×C4×D1111yescharacteristic
519C42C2×D4411yescharacteristic
520C42C2×D4412yes—
521C42C2×C22⋊D1111yescharacteristic
522C42C2×C22⋊D1112yes—
523C42C23×D1111yescharacteristic
524C11#1768111yescharacteristic, complemented, Sylow
525C23—221no—
526C23—222no—
527C23—444no—
528C23—882no—
529C23—882no—
530C23C2×(C2×D11)⋊C412yes—
531C23C2×(C2×D11)⋊C411yescharacteristic
532Q8—22no—
533Q8—441no—
534Q8—442no—
535Q8—882no—
536D4—22no—
537D4—42no—
538D4—441no—
539D4—442no—
540D4—444no—
541D4—442no—
542D4—882no—
543D4—881no—
544D4—882no—
545D4—881no—
546C2×C4—22no—
547C2×C4—42no—
548C2×C4—41no—
549C2×C4—42no—
550C2×C4—41no—
551C2×C4—42no—
552C2×C4—221no—
553C2×C4—221no—
554C2×C4—221no—
555C2×C4—222no—
556C2×C4—442no—
557C2×C4—882no—
558C2×C4—882no—
559C2×C4—882no—
560C2×C4C2×(C2×D11)⋊C412yes—
561C2×C4C2×(C2×D11)⋊C411yescharacteristic
562C2×C4C2×(C2×D11)⋊C412yes—
563C2×C4C2×(C2×D11)⋊C411yescharacteristic
564C2×C4C2×(C2×D11)⋊C412yes—
565C2×C4C2×(C2×D11)⋊C411yescharacteristic
566C2×C4C22×C4×D1111yescharacteristic
567C2×C4C22×D4411yescharacteristic
568C2×C4C22×C22⋊D1111yescharacteristic
569C8—22no—
570C8—41no—
571C8—42no—
572C8—441no—
573C8—441no—
574C8—442no—
575C22—22no—
576C22—21no—
577C22—21no—
578C22—22no—
579C22—21no—
580C22—22no—
581C22—442no—
582C22—441no—
583C22—441no—
584C22—442no—
585C22—442no—
586C22—441no—
587C22—1764no—
588C22C22×(C2×D11)⋊C411yescharacteristic
589C4—21no—
590C4—21no—
591C4—22no—
592C4—21no—
593C4—22no—
594C4—21no—
595C4—22no—
596C4—21no—
597C4—442no—
598C4—441no—
599C4—441no—
600C4—441no—
601C4#1062275212yes—
602C2—42no—
603C2—41no—
604C2—881no—
605C2—882no—
606C2#1307709411yescharacteristic
607C2C2×#1062275211yescharacteristic
608C2#1307716411yescharacteristic
subgroupG/H
centerC22C22×(C2×D11)⋊C4
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×#2971C2
socleC22×C11C22×C22⋊C4
prime radical#13082577C2
cosocleC42×C11C24
hypercenter#2971D11
hypocenterC11#17681
LCSG ▷ C2×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C4×#41 ◁ #2971

Complements

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

NH ≅ G/Ntype
2. #13077267C2semidirect
3. #13067245C2semidirect
4. #13067239C2semidirect
5. #13067228C2semidirect
6. #13067224C2semidirect
7. #13067221C2semidirect
8. #13067213C2semidirect
9. #13067207C2semidirect
10. #13067205C2semidirect
11. C11×#2971C2semidirect
32. C11×#432C22semidirect
33. C11×#432C22semidirect
34. C4×C11×M16C22semidirect
35. C4×C11×M16C22semidirect
39. #10622539C22semidirect
40. #10622539C22semidirect
41. C4×#4318C22semidirect
42. C2×#66867C22semidirect
43. #10622103C22semidirect
44. #10622103C22semidirect
45. #10622103C22semidirect
49. #10622102C22semidirect
50. #10622102C22semidirect
51. #10622102C22semidirect
52. #10622102C22semidirect
222. #2971D11semidirect
305. #432C2×D11semidirect
306. #432C2×D11semidirect
310. C4×M16C2×D11semidirect
311. C4×M16C2×D11semidirect
524. C11#17681semidirect

Maximal subgroups

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

subgroupindex
#130825772
#130772672
#130672452
#130672392
#130672282
#130672242
#130672212
#130672132
#130672072
#130672052
C11×#29712
#1768111