Finite Group Databasebeta

← #14720656

Subgroups — #14720656

Order 2816.

970 conjugacy classes of subgroups.

The subgroup lattice has 622 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082209C211yesmaximal, characteristic
2#41×C11⋊C8C211yesmaximal, characteristic, complemented
3#13067074C212yesmaximal, complemented
4#13067066C211yesmaximal, characteristic, complemented
5#13067048C212yesmaximal, complemented
6#13067044C211yesmaximal, characteristic, complemented
7#13067022C212yesmaximal, complemented
8#13067014C211yesmaximal, characteristic, complemented
9#13066996C212yesmaximal, complemented
10C2×#10622122C211yesmaximal, characteristic, complemented
11C11×#2925C211yesmaximal, characteristic, complemented
12C4×C11×#41C2211yescharacteristic
13#10623363—21no—
14#10623116C411yescharacteristic
15#10623099—21no—
16#10623098C411yescharacteristic
17#10623096C412yes—
18#10623090—21no—
19#10623084C411yescharacteristic
20#10623083C412yes—
21#10623073C411yescharacteristic
22#10623071—22no—
23#10623059—22no—
24#10623053—21no—
25#10623010C2212yes—
26#10623008C2211yescharacteristic
27C4×#4339C2212yes—
28C2×C4×Dic22C2211yescharacteristic
29C11×#433—22no—
30C11×#432C2212yes—
31C11×#431C2212yes—
32C11×#423C2211yescharacteristic
33C2×C11×C4⋊C8C2211yescharacteristic
34C11×#408—21no—
35C11×#405—21no—
36Q8×C11⋊C8—21no—
37D4×C11⋊C8—22no—
38D4×C11⋊C8—21no—
39#10622538C2211yescharacteristic
40#10622538C2212yes—
41C2×C4×C11⋊C8C2211yescharacteristic
42C2×C4×C11⋊C8C2212yes—
43#10622122C2211yescharacteristic
44#10622122C2212yes—
45#10622122C2212yes—
46#10622122C2211yescharacteristic
47#10622122C2211yescharacteristic
48#10622122C2211yescharacteristic
49#10622121C2212yes—
50#10622121C2212yes—
51#10622121C2212yes—
52#10622121C2212yes—
53C2×C11×#41D411yescharacteristic
54C2×#4339—21no—
55C2×#4339C2×C412yes—
56C22×Dic22C2×C411yescharacteristic
57C2×C11×M16—21no—
58C22×C8×C11—21no—
59C4×Q8×C11C2×C411yescharacteristic
60C4×Q8×C11D411yescharacteristic
61C4×D4×C11C2×C411yescharacteristic
62C4×D4×C11C2×C412yes—
63C4×D4×C11D412yes—
64C4×D4×C11D411yescharacteristic
65C11×#117D411yescharacteristic
66C11×#117D412yes—
67C2×C42×C11C2311yescharacteristic
68C2×C42×C11C2312yes—
69#67000—21no—
70#66997—21no—
71#66993—21no—
72#66992—22no—
73#66992—22no—
74#66989—21no—
75#66983—21no—
76#66983C2×C412yes—
77#66983C2×C412yes—
78#66982—22no—
79C4×C22⋊D11—22no—
80C4×C22⋊D11—22no—
81C4×C22⋊D11—22no—
82#66979C2×C412yes—
83C2×C4⋊Dic11C2×C411yescharacteristic
84#66977C2×C412yes—
85C2×Dic11⋊C4—21no—
86C2×C4×Dic11—21no—
87C22×C11⋊C8—21no—
88C22×C11⋊C8—22no—
89#66951—22no—
90#66949—22no—
91#66947—22no—
92#66946—21no—
93#66946—21no—
94#66942—22no—
95#66940—21no—
96#66940—21no—
97#66938—22no—
98#66937—22no—
99#66936—22no—
100(C22⋊D11)⋊C4—22no—
101(C22⋊D11)⋊C4—22no—
102#66932—22no—
103#66929—22no—
104#66928—21no—
105#66928C2×C412yes—
106#66927C2×C411yescharacteristic
107C4×D44—21no—
108C4×D44C2×C412yes—
109C4×D44C2312yes—
110#66925—22no—
111#66925—22no—
112C42×D11—22no—
113#66923C2×C412yes—
114#66922C2×C411yescharacteristic
115C4×Dic22—21no—
116C4×Dic22—21no—
117C4×Dic22C2×C411yescharacteristic
118C4×Dic22C2×C411yescharacteristic
119C4×Dic22C2×C412yes—
120C4×Dic22C2311yescharacteristic
121C4×Dic22C2311yescharacteristic
122C11×C4⋊C8—21no—
123C11×C4⋊C8—21no—
124C11×C4⋊C8C2311yescharacteristic
125C11×C4⋊C8C2311yescharacteristic
126C11×C4⋊C8C2312yes—
127C11×C22⋊C8—22no—
128C11×C22⋊C8—22no—
129C11×#97—22no—
130C4×C8×C11—22no—
131C22⋊(C11⋊C8)—21no—
132C22⋊(C11⋊C8)—22no—
133C4⋊(C11⋊C8)—21no—
134C4⋊(C11⋊C8)—22no—
135C4×C11⋊C8—21no—
136C4×C11⋊C8—22no—
137C4×C11⋊C8C2311yescharacteristic
138C4×C11⋊C8C2311yescharacteristic
139C4×C11⋊C8C2312yes—
140#17510—111nomaximal, Sylow
141C11×#41—22no—
142C11×#41—22no—
143C2×Q8×C11C22⋊C411yescharacteristic
144C2×D4×C11C22⋊C411yescharacteristic
145C2×D4×C11C22⋊C412yes—
146C22×C4×C11C22×C412yes—
147C22×C4×C11C22×C411yescharacteristic
148C22×C4×C11C2×D412yes—
149C22×C4×C11C2×D411yescharacteristic
150C22×C4×C11C2×D412yes—
151C22×C4×C11C2×D411yescharacteristic
152C2×C22⋊D11—22no—
153C2×C22⋊D11—22no—
154C2×C22⋊D11—22no—
155C22×Dic11—21no—
156C22×Dic11—21no—
157#4339—24no—
158#4339—42no—
159#4339—42no—
160#4339—42no—
161C2×D44—21no—
162C2×D44—21no—
163C2×D44C22×C412yes—
164C2×C4×D11—22no—
165C2×C4×D11—22no—
166C2×C4×D11—22no—
167C2×Dic22—22no—
168C2×Dic22—21no—
169C2×Dic22—21no—
170C2×Dic22—41no—
171C2×Dic22C22×C411yescharacteristic
172C2×Dic22C22×C411yescharacteristic
173C11×M16—42no—
174C2×C8×C11—21no—
175C2×C8×C11—22no—
176C2×C8×C11—21no—
177C2×C8×C11—42no—
178C11×C4⋊C4C22⋊C411yescharacteristic
179C11×C4⋊C4C22⋊C411yescharacteristic
180C11×C4⋊C4C22⋊C412yes—
181C11×C4⋊C4C22⋊C412yes—
182C11×C22⋊C4C22⋊C412yes—
183C11×C22⋊C4C22⋊C412yes—
184C11×C22⋊C4C22⋊C412yes—
185C42×C11C22×C411yescharacteristic
186C42×C11C22×C412yes—
187C42×C11C2×D411yescharacteristic
188C42×C11C2×D412yes—
189C42×C11C2×D412yes—
190C42×C11C2×D411yescharacteristic
191C42×C11C2411yescharacteristic
192C22⋊Dic11—22no—
193C22⋊Dic11—22no—
194(C2×D11)⋊C4—22no—
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—
200C4⋊Dic11—21no—
201C4⋊Dic11—21no—
202C4⋊Dic11C22×C411yescharacteristic
203C4⋊Dic11C22×C411yescharacteristic
204C4⋊Dic11C22×C412yes—
205Dic11⋊C4—21no—
206Dic11⋊C4—21no—
207Dic11⋊C4—22no—
208Dic11⋊C4—22no—
209Dic11⋊C4—22no—
210Dic11⋊C4—22no—
211Dic11⋊C4—21no—
212Dic11⋊C4—21no—
213C4×Dic11—21no—
214C4×Dic11—21no—
215C4×Dic11—22no—
216C4×Dic11—22no—
217C4×Dic11—21no—
218C4×Dic11—21no—
219C2×C11⋊C8—21no—
220C2×C11⋊C8—21no—
221C2×C11⋊C8—22no—
222C2×C11⋊C8—44no—
223C2×C11⋊C8—42no—
224#3480—111no—
225C8×#41—111no—
226#2925D1111yescharacteristic, complemented
227#1494—112no—
228#1492—111no—
229#1488—112no—
230#1487—111no—
231#1482—112no—
232#1480—111no—
233#1476—112no—
234C2×Q8⋊C8—111no—
235C23×C11C2×C22⋊C412yes—
236C23×C11C2×C22⋊C411yescharacteristic
237C22×D11—22no—
238Q8×C11—22no—
239D4×C11—24no—
240D4×C11—22no—
241C2×C4×C11—21no—
242C2×C4×C11—22no—
243C2×C4×C11—21no—
244C2×C4×C11—22no—
245C2×C4×C11—22no—
246C2×C4×C11—22no—
247C2×C4×C11—42no—
248C2×C4×C11—41no—
249C2×C4×C11C2×C22⋊C412yes—
250C2×C4×C11C2×C22⋊C412yes—
251C2×C4×C11C2×C22⋊C411yescharacteristic
252C2×C4×C11C2×C22⋊C412yes—
253C2×C4×C11C2×C22⋊C411yescharacteristic
254C2×C4×C11C2×C22⋊C411yescharacteristic
255C2×C4×C11#13512yes—
256C2×C4×C11#13512yes—
257C2×C4×C11C23×C411yescharacteristic
258C2×C4×C11C22×D411yescharacteristic
259C2×C4×C11C22×D411yescharacteristic
260C22⋊D11—44no—
261C22⋊D11—44no—
262C22⋊D11—82no—
263C2×Dic11—21no—
264C2×Dic11—21no—
265C2×Dic11—21no—
266C2×Dic11—22no—
267C2×Dic11—21no—
268C2×Dic11—42no—
269C2×Dic11—81no—
270D44—22no—
271D44—22no—
272D44—42no—
273D44—81no—
274C4×D11—44no—
275C4×D11—42no—
276C4×D11—42no—
277C4×D11—82no—
278Dic22—21no—
279Dic22—21no—
280Dic22—21no—
281Dic22—42no—
282Dic22—42no—
283Dic22#13112yes—
284C8×C11—41no—
285C8×C11—41no—
286C8×C11—42no—
287C11⋊C8—22no—
288C11⋊C8—41no—
289C11⋊C8—42no—
290#559—111no—
291#559—221no—
292#557—111no—
293#556—111no—
294#556—221no—
295#553—112no—
296#553—222no—
297#550—111no—
298#548—112no—
299#532—111no—
300#532—221no—
301#529—112no—
302#529—222no—
303C4×#41—112no—
304C4×#41—221no—
305C4×#41C2×D1111yescharacteristic
306C2×C4×Q8—111no—
307C8×Q8—221no—
308C8×D4—222no—
309C8×D4—221no—
310#433—22no—
311#432C2×D1112yes—
312#431—111no—
313#431—112no—
314#431C2×D1112yes—
315#423C2×D1111yescharacteristic
316C2×C4⋊C8C2×D1111yescharacteristic
317#408—21no—
318#405—21no—
319C2×C4×C8—111no—
320C2×C4×C8—112no—
321Q8⋊C8—111no—
322Q8⋊C8—111no—
323Q8⋊C8—111no—
324Q8⋊C8—111no—
325Q8⋊C8—112no—
326Q8⋊C8—112no—
327D4⋊C8—112no—
328D4⋊C8—112no—
329D4⋊C8—112no—
330D4⋊C8—112no—
331C22×C11—21no—
332C22×C11—21no—
333C22×C11—22no—
334C22×C11—22no—
335C22×C11—22no—
336C22×C11#41612yes—
337C22×C11C22×C22⋊C411yescharacteristic
338C2×D11—42no—
339C2×D11—42no—
340C2×D11—42no—
341C4×C11—21no—
342C4×C11—22no—
343C4×C11—22no—
344C4×C11—21no—
345C4×C11—22no—
346C4×C11—21no—
347C4×C11#41612yes—
348C4×C11C2×#13111yescharacteristic
349C4×C11#56811yescharacteristic
350C4×C11C2×#13511yescharacteristic
351C4×C11C2×#13511yescharacteristic
352Dic11—22no—
353Dic11—41no—
354Dic11—42no—
355Dic11—41no—
356Dic11—41no—
357C2×#41—112no—
358C2×#41—221no—
359C2×#41C22⋊D1111yescharacteristic
360C22×Q8—111no—
361C2×M16—21no—
362C22×C8—21no—
363C22×C8—221no—
364C22×C8—222no—
365C4⋊Q8—111no—
366C4⋊Q8—221no—
367#127—111no—
368#127—221no—
369#126—222no—
370#126—222no—
371#126—222no—
372#125—112no—
373#125—222no—
374#124—112no—
375#124—221no—
376#124—221no—
377#124—222no—
378#124—221no—
379#123—222no—
380#123—222no—
381#123—222no—
382C22⋊Q8—112no—
383C22⋊Q8—222no—
384#121—112no—
385#121—112no—
386#121—222no—
387#121—222no—
388#121—221no—
389#121—222no—
390C4×Q8—111no—
391C4×Q8—111no—
392C4×Q8—112no—
393C4×Q8—111no—
394C4×Q8—111no—
395C4×Q8—221no—
396C4×Q8—221no—
397C4×Q8—221no—
398C4×Q8—221no—
399C4×Q8C4×D1111yescharacteristic
400C4×Q8D4411yescharacteristic
401C4×D4—112no—
402C4×D4—112no—
403C4×D4—222no—
404C4×D4—222no—
405C4×D4—222no—
406C4×D4—221no—
407C4×D4—221no—
408C4×D4—222no—
409C4×D4—222no—
410C4×D4—221no—
411C4×D4C4×D1112yes—
412C4×D4C4×D1111yescharacteristic
413C4×D4D4412yes—
414C4×D4D4411yescharacteristic
415#117—112no—
416#117—222no—
417#117—222no—
418#117C22⋊D1111yescharacteristic
419#117C22⋊D1112yes—
420C2×C4⋊C4—111no—
421C2×C4⋊C4—221no—
422C2×C42—221no—
423C2×C42—222no—
424C2×C42C22×D1111yescharacteristic
425C2×C42C22×D1112yes—
426C4⋊C8—21no—
427C4⋊C8—21no—
428C4⋊C8—222no—
429C4⋊C8—221no—
430C4⋊C8C22×D1111yescharacteristic
431C4⋊C8C22×D1111yescharacteristic
432C4⋊C8C22×D1112yes—
433C22⋊C8—22no—
434C22⋊C8—22no—
435C22⋊C8—221no—
436C22⋊C8—222no—
437#97—22no—
438C4×C8—22no—
439C4×C8—111no—
440C4×C8—112no—
441C4×C8—111no—
442C4×C8—222no—
443C4×C8—221no—
444C2×C11—22no—
445C2×C11—42no—
446C2×C11#288011yescharacteristic
447C2×C11C2×#41611yescharacteristic
448C2×C11#290111yescharacteristic
449D11—82no—
450#41—22no—
451#41—22no—
452#41—224no—
453#41—442no—
454#41—442no—
455#41—442no—
456C2×Q8—111no—
457C2×Q8—111no—
458C2×Q8—222no—
459C2×Q8—221no—
460C2×Q8—221no—
461C2×Q8—441no—
462C2×Q8(C2×D11)⋊C411yescharacteristic
463C2×D4—112no—
464C2×D4—222no—
465C2×D4—222no—
466C2×D4—222no—
467C2×D4—221no—
468C2×D4—221no—
469C2×D4(C2×D11)⋊C412yes—
470C2×D4(C2×D11)⋊C411yescharacteristic
471C22×C4—221no—
472C22×C4—221no—
473C22×C4—222no—
474C22×C4—222no—
475C22×C4—222no—
476C22×C4C2×C4×D1111yescharacteristic
477C22×C4C2×C4×D1112yes—
478C22×C4C2×D4411yescharacteristic
479C22×C4C2×D4412yes—
480C22×C4C2×C22⋊D1112yes—
481C22×C4C2×C22⋊D1111yescharacteristic
482M16—42no—
483C2×C8—21no—
484C2×C8—22no—
485C2×C8—21no—
486C2×C8—42no—
487C2×C8—221no—
488C2×C8—222no—
489C2×C8—221no—
490C2×C8—444no—
491C2×C8—442no—
492C4⋊C4—111no—
493C4⋊C4—111no—
494C4⋊C4—112no—
495C4⋊C4—221no—
496C4⋊C4—221no—
497C4⋊C4—221no—
498C4⋊C4—222no—
499C4⋊C4—222no—
500C4⋊C4—222no—
501C4⋊C4—222no—
502C4⋊C4—221no—
503C4⋊C4—221no—
504C4⋊C4—221no—
505C4⋊C4(C2×D11)⋊C411yescharacteristic
506C4⋊C4(C2×D11)⋊C411yescharacteristic
507C4⋊C4(C2×D11)⋊C412yes—
508C4⋊C4(C2×D11)⋊C412yes—
509C22⋊C4—222no—
510C22⋊C4—222no—
511C22⋊C4—222no—
512C22⋊C4—222no—
513C22⋊C4—222no—
514C22⋊C4—222no—
515C22⋊C4—222no—
516C22⋊C4—222no—
517C22⋊C4(C2×D11)⋊C412yes—
518C22⋊C4(C2×D11)⋊C412yes—
519C22⋊C4(C2×D11)⋊C412yes—
520C42—222no—
521C42—222no—
522C42—221no—
523C42—221no—
524C42—221no—
525C42—221no—
526C42C2×C4×D1112yes—
527C42C2×C4×D1111yescharacteristic
528C42C2×D4412yes—
529C42C2×D4411yescharacteristic
530C42C2×C22⋊D1112yes—
531C42C2×C22⋊D1111yescharacteristic
532C42C23×D1111yescharacteristic
533C11#1751011yescharacteristic, complemented, Sylow
534C23—222no—
535C23C2×(C2×D11)⋊C412yes—
536C23C2×(C2×D11)⋊C411yescharacteristic
537Q8—22no—
538Q8—112no—
539Q8—221no—
540Q8—221no—
541Q8—221no—
542Q8—442no—
543Q8—442no—
544D4—24no—
545D4—22no—
546D4—222no—
547D4—222no—
548D4—444no—
549D4—444no—
550D4—442no—
551D4—881no—
552D4—882no—
553C2×C4—21no—
554C2×C4—22no—
555C2×C4—21no—
556C2×C4—22no—
557C2×C4—22no—
558C2×C4—22no—
559C2×C4—42no—
560C2×C4—41no—
561C2×C4—221no—
562C2×C4—221no—
563C2×C4—221no—
564C2×C4—222no—
565C2×C4—221no—
566C2×C4—444no—
567C2×C4—442no—
568C2×C4—442no—
569C2×C4—442no—
570C2×C4—882no—
571C2×C4—881no—
572C2×C4C2×(C2×D11)⋊C412yes—
573C2×C4C2×(C2×D11)⋊C412yes—
574C2×C4C2×(C2×D11)⋊C412yes—
575C2×C4C2×(C2×D11)⋊C411yescharacteristic
576C2×C4C2×(C2×D11)⋊C411yescharacteristic
577C2×C4C2×(C2×D11)⋊C411yescharacteristic
578C2×C4#6700312yes—
579C2×C4#6700312yes—
580C2×C4C22×C4×D1111yescharacteristic
581C2×C4C22×D4411yescharacteristic
582C2×C4C22×C22⋊D1111yescharacteristic
583C8—41no—
584C8—41no—
585C8—42no—
586C8—222no—
587C8—442no—
588C8—441no—
589C22—21no—
590C22—21no—
591C22—22no—
592C22—22no—
593C22—22no—
594C22—442no—
595C22—442no—
596C22—442no—
597C22#1062261512yes—
598C22C22×(C2×D11)⋊C411yescharacteristic
599C4—22no—
600C4—21no—
601C4—22no—
602C4—21no—
603C4—22no—
604C4—21no—
605C4—222no—
606C4—441no—
607C4—442no—
608C4—441no—
609C4—441no—
610C4#1062261512yes—
611C4D11×#13111yescharacteristic
612C4#1062328111yescharacteristic
613C4C2×#6700311yescharacteristic
614C4C2×#6700311yescharacteristic
615C2—22no—
616C2—42no—
617C2—882no—
618C2#1307706311yescharacteristic
619C2C2×#1062261511yescharacteristic
620C2#1307716111yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×#2925C2
socleC22×C11C22×C22⋊C4
prime radical#13082209C2
cosocleC42×C11C24
hypercenter#2925D11
hypocenterC11#17510
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C4×#41 ◁ #2925

Complements

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

NH ≅ G/Ntype
2. #41×C11⋊C8C2semidirect
3. #13067074C2semidirect
4. #13067066C2semidirect
5. #13067048C2semidirect
6. #13067044C2semidirect
7. #13067022C2semidirect
8. #13067014C2semidirect
9. #13066996C2semidirect
10. C2×#10622122C2semidirect
11. C11×#2925C2semidirect
226. #2925D11semidirect
533. C11#17510semidirect

Maximal subgroups

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

subgroupindex
#130822092
#41×C11⋊C82
#130670742
#130670662
#130670482
#130670442
#130670222
#130670142
#130669962
C2×#106221222
C11×#29252
#1751011