Finite Group Databasebeta

← #14720448

Subgroups — #14720448

Order 2816.

984 conjugacy classes of subgroups.

The subgroup lattice has 628 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082032C211yesmaximal, characteristic
2#41×C11⋊C8C211yesmaximal, characteristic, complemented
3#13067084C212yesmaximal, complemented
4#13067079C212yesmaximal, complemented
5#13067074C212yesmaximal, complemented
6#13067066C212yesmaximal, complemented
7#13067006C211yesmaximal, characteristic, complemented
8#13067001C211yesmaximal, characteristic, complemented
9#13066996C211yesmaximal, characteristic, complemented
10C2×#10622121C211yesmaximal, characteristic, complemented
11C11×#2989C211yesmaximal, characteristic, complemented
12C4×C11×#41C2211yescharacteristic
13#10623364C411yescharacteristic
14#10623361C411yescharacteristic
15#10623113—21no—
16#10623111—21no—
17#10623093—21no—
18#10623091—22no—
19#10623079—21no—
20#10623078—22no—
21#10623066C412yes—
22#10623065C412yes—
23#10623056C411yescharacteristic
24#10623050C411yescharacteristic
25#10623010C2212yes—
26#10623008C2212yes—
27C4×#4339C2211yescharacteristic
28C2×C4×D44C2211yescharacteristic
29C11×#446—21no—
30C11×#436—21no—
31C11×#435—22no—
32C11×#432C2212yescomplemented
33C11×#431C2211yescharacteristic
34C11×#423C2212yescomplemented
35C2×C11×C4⋊C8C2211yescharacteristic
36Q8×C11⋊C8—21no—
37D4×C11⋊C8—21no—
38D4×C11⋊C8—22no—
39#10622538C2211yescharacteristic
40#10622538C2212yescomplemented
41C2×C4×C11⋊C8C2211yescharacteristic
42C2×C4×C11⋊C8C2212yescomplemented
43#10622122C2211yescharacteristic, complemented
44#10622122C2212yescomplemented
45#10622122C2211yescharacteristic, complemented
46#10622121C2212yes—
47#10622121C2212yes—
48#10622121C2212yes—
49#10622121C2212yes—
50#10622121C2211yescharacteristic, complemented
51#10622121C2212yescomplemented
52#10622121C2211yescharacteristic, complemented
53C2×C11×#41C2×C411yescharacteristic
54C2×#4339—22no—
55C2×#4339C2×C411yescharacteristic
56C22×D44C2×C411yescharacteristic
57C22×C4×D11—21no—
58C2×C11×M16—22no—
59C22×C8×C11—21no—
60C4×Q8×C11D411yescharacteristic
61C4×Q8×C11D411yescharacteristic
62C4×D4×C11D412yes—
63C4×D4×C11D411yescharacteristic
64C4×D4×C11D412yes—
65C4×D4×C11D411yescharacteristic
66C11×#117C2×C411yescharacteristic
67C11×#117C2×C412yes—
68C2×C42×C11C2311yescharacteristic
69C2×C42×C11C2312yes—
70#67000—21no—
71#66999—21no—
72#66993—21no—
73#66992—22no—
74#66991—21no—
75#66990—22no—
76#66983—22no—
77#66983C2×C412yes—
78#66983C2×C412yes—
79#66983C2×C412yes—
80#66982—22no—
81C4×C22⋊D11—21no—
82C4×C22⋊D11—21no—
83C4×C22⋊D11—22no—
84C2×(C2×D11)⋊C4—21no—
85#66979C2×C411yescharacteristic
86C2×C4⋊Dic11C2×C411yescharacteristic
87#66977C2×C412yes—
88C22×C11⋊C8—21no—
89C22×C11⋊C8—22no—
90#66951—22no—
91#66949—22no—
92#66948—21no—
93#66948—21no—
94#66947—22no—
95#66947—22no—
96#66943—21no—
97#66941—21no—
98#66938—22no—
99#66937—22no—
100#66937—22no—
101#66936—22no—
102#66935—22no—
103#66931—22no—
104#66929—22no—
105#66928—22no—
106#66928C2×C412yes—
107#66927C2×C412yes—
108C4×D44—21no—
109C4×D44—21no—
110C4×D44—22no—
111C4×D44C2×C412yes—
112C4×D44C2×C411yescharacteristic
113C4×D44C2312yes—
114C4×D44C2311yescharacteristic
115#66925—21no—
116#66925—22no—
117C42×D11—21no—
118#66923C2×C412yes—
119#66922C2×C412yes—
120C4×Dic22C2×C411yescharacteristic
121C4×Dic22C2311yescharacteristic
122C11×C4⋊C8—21no—
123C11×C4⋊C8—22no—
124C11×C4⋊C8C2312yes—
125C11×C4⋊C8C2311yescharacteristic
126C11×C4⋊C8C2311yescharacteristic
127C11×C22⋊C8—21no—
128C11×C22⋊C8—22no—
129C11×#97—22no—
130C4×C8×C11—21no—
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#17483—111nomaximal, Sylow
141C23×D11—21no—
142C11×#41—24no—
143C2×Q8×C11C22⋊C411yescharacteristic
144C2×D4×C11C22⋊C412yes—
145C2×D4×C11C22⋊C411yescharacteristic
146C22×C4×C11C22×C412yes—
147C22×C4×C11C22×C411yescharacteristic
148C22×C4×C11C2×D411yescharacteristic
149C22×C4×C11C2×D412yes—
150C22×C4×C11C2×D411yescharacteristic
151C22×C4×C11C2×D412yes—
152C2×C22⋊D11—21no—
153C2×C22⋊D11—22no—
154C2×C22⋊D11—22no—
155C2×C22⋊D11—22no—
156C22×Dic11—21no—
157#4339—24no—
158#4339—82no—
159#4339—82no—
160C2×D44—21no—
161C2×D44—22no—
162C2×D44—22no—
163C2×D44—24no—
164C2×D44C22×C411yescharacteristic
165C2×D44C22×C412yes—
166C2×C4×D11—21no—
167C2×C4×D11—21no—
168C2×C4×D11—22no—
169C2×C4×D11—21no—
170C2×C4×D11—22no—
171C2×C4×D11—81no—
172C2×C4×D11—81no—
173C2×Dic22—22no—
174C2×Dic22C22×C411yescharacteristic
175C11×M16—82no—
176C2×C8×C11—21no—
177C2×C8×C11—21no—
178C2×C8×C11—22no—
179C2×C8×C11—81no—
180C11×C4⋊C4C22⋊C411yescharacteristic
181C11×C4⋊C4C22⋊C411yescharacteristic
182C11×C4⋊C4C22⋊C412yes—
183C11×C4⋊C4C22⋊C412yes—
184C11×C22⋊C4C22⋊C412yes—
185C11×C22⋊C4C22⋊C412yes—
186C11×C22⋊C4C22⋊C412yes—
187C42×C11C22×C411yescharacteristic
188C42×C11C22×C412yes—
189C42×C11C2×D411yescharacteristic
190C42×C11C2×D412yes—
191C42×C11C2×D411yescharacteristic
192C42×C11C2×D412yes—
193C42×C11C2411yescharacteristic
194C22⋊Dic11—21no—
195C22⋊Dic11—22no—
196(C2×D11)⋊C4—21no—
197(C2×D11)⋊C4—22no—
198(C2×D11)⋊C4—22no—
199(C2×D11)⋊C4—22no—
200(C2×D11)⋊C4—22no—
201(C2×D11)⋊C4—22no—
202(C2×D11)⋊C4—22no—
203(C2×D11)⋊C4—21no—
204(C2×D11)⋊C4—22no—
205C4⋊Dic11—22no—
206C4⋊Dic11—21no—
207C4⋊Dic11C22×C411yescharacteristic
208C4⋊Dic11C22×C411yescharacteristic
209C4⋊Dic11C22×C412yes—
210Dic11⋊C4—21no—
211Dic11⋊C4—22no—
212Dic11⋊C4—22no—
213Dic11⋊C4—22no—
214Dic11⋊C4—21no—
215C4×Dic11—21no—
216C4×Dic11—21no—
217C4×Dic11—21no—
218C2×C11⋊C8—21no—
219C2×C11⋊C8—21no—
220C2×C11⋊C8—22no—
221C2×C11⋊C8—42no—
222C2×C11⋊C8—44no—
223#3460—111no—
224#2989D1111yescharacteristic, complemented
225C8×#41—111no—
226#1496—112no—
227#1495—112no—
228#1494—112no—
229#1492—112no—
230#1478—111no—
231#1477—111no—
232#1476—111no—
233C2×D4⋊C8—111no—
234C23×C11C2×C22⋊C412yes—
235C23×C11C2×C22⋊C411yescharacteristic
236C22×D11—22no—
237C22×D11—21no—
238C22×D11—42no—
239C22×D11—81no—
240C22×D11—81no—
241Q8×C11—22no—
242D4×C11—24no—
243D4×C11—22no—
244C2×C4×C11—24no—
245C2×C4×C11—21no—
246C2×C4×C11—22no—
247C2×C4×C11—21no—
248C2×C4×C11—22no—
249C2×C4×C11—41no—
250C2×C4×C11—42no—
251C2×C4×C11C2×C22⋊C411yescharacteristic
252C2×C4×C11C2×C22⋊C412yes—
253C2×C4×C11C2×C22⋊C412yes—
254C2×C4×C11C2×C22⋊C412yes—
255C2×C4×C11C2×C22⋊C411yescharacteristic
256C2×C4×C11C2×C22⋊C411yescharacteristic
257C2×C4×C11#13114yes—
258C2×C4×C11C23×C411yescharacteristic
259C2×C4×C11C22×D411yescharacteristic
260C2×C4×C11C22×D411yescharacteristic
261C22⋊D11—42no—
262C22⋊D11—82no—
263C22⋊D11—82no—
264C22⋊D11—82no—
265C2×Dic11—21no—
266C2×Dic11—21no—
267C2×Dic11—21no—
268C2×Dic11—22no—
269C2×Dic11—81no—
270D44—24no—
271D44—22no—
272D44—42no—
273D44—82no—
274D44—82no—
275C4×D11—42no—
276C4×D11—41no—
277C4×D11—42no—
278C4×D11—41no—
279C4×D11—42no—
280C4×D11—81no—
281C4×D11—82no—
282Dic22—22no—
283Dic22—82no—
284C8×C11—42no—
285C8×C11—41no—
286C8×C11—41no—
287C11⋊C8—22no—
288C11⋊C8—41no—
289C11⋊C8—42no—
290#544—111no—
291#542—112no—
292#542—221no—
293#540—112no—
294#540—221no—
295#538—222no—
296#537—111no—
297#535—111no—
298#535—111no—
299#532—112no—
300#532—221no—
301#529—112no—
302#529—221no—
303#525—222no—
304C4×#41—111no—
305C4×#41C2×D1111yescharacteristic
306C2×C4×D4—111no—
307#446—21no—
308C8×Q8—221no—
309#436—21no—
310#435—22no—
311C8×D4—222no—
312C8×D4—221no—
313#432C2×D1112yescomplemented
314#431—111no—
315#431—112no—
316#431C2×D1111yescharacteristic
317#423C2×D1112yescomplemented
318C2×C4⋊C8C2×D1111yescharacteristic
319C2×C4×C8—111no—
320C2×C4×C8—112no—
321Q8⋊C8—111no—
322Q8⋊C8—111no—
323Q8⋊C8—112no—
324D4⋊C8—112no—
325D4⋊C8—112no—
326D4⋊C8—112no—
327D4⋊C8—112no—
328D4⋊C8—111no—
329D4⋊C8—111no—
330D4⋊C8—112no—
331C22×C11—21no—
332C22×C11—21no—
333C22×C11—22no—
334C22×C11—22no—
335C22×C11—22no—
336C22×C11#40812yes—
337C22×C11C22×C22⋊C411yescharacteristic
338C2×D11—42no—
339C2×D11—41no—
340C2×D11—42no—
341C2×D11—41no—
342C2×D11—42no—
343C2×D11—41no—
344C2×D11—84no—
345C4×C11—22no—
346C4×C11—22no—
347C4×C11—21no—
348C4×C11—21no—
349C4×C11—21no—
350C4×C11—22no—
351C4×C11#40812yes—
352C4×C11C2×#13112yes—
353C4×C11#57611yescharacteristic
354C4×C11#57711yescharacteristic
355Dic11—41no—
356Dic11—41no—
357Dic11—42no—
358Dic11—41no—
359C2×#41—111no—
360C2×#41—222no—
361C2×#41C4×D1111yescharacteristic
362C22×D4—111no—
363C23×C4—221no—
364C2×M16—22no—
365C22×C8—21no—
366C22×C8—221no—
367C22×C8—222no—
368C4⋊Q8—112no—
369C4⋊Q8—221no—
370#127—112no—
371#127—221no—
372#126—222no—
373#126—222no—
374#125—112no—
375#125—221no—
376#124—112no—
377#124—221no—
378#124—222no—
379#124—222no—
380#123—222no—
381#123—222no—
382#123—222no—
383#123—222no—
384C22⋊Q8—112no—
385C22⋊Q8—221no—
386C22⋊Q8—222no—
387C22⋊Q8—222no—
388#121—112no—
389#121—112no—
390#121—112no—
391#121—222no—
392#121—221no—
393#121—222no—
394#121—221no—
395#121—221no—
396#121—222no—
397#121—222no—
398#120—222no—
399#120—222no—
400C4×Q8—111no—
401C4×Q8—111no—
402C4×Q8D4411yescharacteristic
403C4×Q8C22⋊D1111yescharacteristic
404C4×D4—112no—
405C4×D4—111no—
406C4×D4—112no—
407C4×D4—111no—
408C4×D4—221no—
409C4×D4—221no—
410C4×D4—222no—
411C4×D4—221no—
412C4×D4—221no—
413C4×D4—222no—
414C4×D4D4412yes—
415C4×D4D4411yescharacteristic
416C4×D4C22⋊D1112yes—
417C4×D4C22⋊D1111yescharacteristic
418#117—111no—
419#117—221no—
420#117—222no—
421#117C4×D1111yescharacteristic
422#117C4×D1112yes—
423C2×C4⋊C4—111no—
424C2×C22⋊C4—221no—
425C2×C42—221no—
426C2×C42C22×D1111yescharacteristic
427C2×C42C22×D1112yes—
428C4⋊C8—21no—
429C4⋊C8—22no—
430C4⋊C8—221no—
431C4⋊C8—222no—
432C4⋊C8C22×D1112yes—
433C4⋊C8C22×D1111yescharacteristic
434C4⋊C8C22×D1111yescharacteristic
435C22⋊C8—21no—
436C22⋊C8—22no—
437C22⋊C8—221no—
438C22⋊C8—222no—
439#97—22no—
440C4×C8—21no—
441C4×C8—111no—
442C4×C8—111no—
443C4×C8—112no—
444C4×C8—221no—
445C4×C8—222no—
446C2×C11—22no—
447C2×C11—42no—
448C2×C11C2×#40811yescharacteristic
449C2×C11#289711yescharacteristic
450C2×C11#290111yescharacteristic
451D11—81no—
452D11—82no—
453C24—221no—
454#41—24no—
455#41—224no—
456#41—882no—
457#41—882no—
458C2×Q8—111no—
459C2×Q8—222no—
460C2×Q8(C2×D11)⋊C411yescharacteristic
461C2×D4—112no—
462C2×D4—111no—
463C2×D4—221no—
464C2×D4—222no—
465C2×D4—222no—
466C2×D4—222no—
467C2×D4—224no—
468C2×D4—221no—
469C2×D4—222no—
470C2×D4—222no—
471C2×D4(C2×D11)⋊C412yes—
472C2×D4(C2×D11)⋊C411yescharacteristic
473C22×C4—221no—
474C22×C4—221no—
475C22×C4—221no—
476C22×C4—222no—
477C22×C4—221no—
478C22×C4—222no—
479C22×C4—881no—
480C22×C4—881no—
481C22×C4C2×C4×D1112yes—
482C22×C4C2×C4×D1111yescharacteristic
483C22×C4C2×D4411yescharacteristic
484C22×C4C2×D4412yes—
485C22×C4C2×C22⋊D1111yescharacteristic
486C22×C4C2×C22⋊D1112yes—
487M16—82no—
488C2×C8—21no—
489C2×C8—21no—
490C2×C8—22no—
491C2×C8—81no—
492C2×C8—221no—
493C2×C8—221no—
494C2×C8—222no—
495C2×C8—442no—
496C2×C8—444no—
497C4⋊C4—112no—
498C4⋊C4—111no—
499C4⋊C4—111no—
500C4⋊C4—221no—
501C4⋊C4—221no—
502C4⋊C4—222no—
503C4⋊C4—222no—
504C4⋊C4—222no—
505C4⋊C4—222no—
506C4⋊C4—221no—
507C4⋊C4(C2×D11)⋊C411yescharacteristic
508C4⋊C4(C2×D11)⋊C412yes—
509C4⋊C4(C2×D11)⋊C411yescharacteristic
510C4⋊C4(C2×D11)⋊C412yes—
511C22⋊C4—221no—
512C22⋊C4—222no—
513C22⋊C4—222no—
514C22⋊C4—221no—
515C22⋊C4—222no—
516C22⋊C4—222no—
517C22⋊C4—222no—
518C22⋊C4—222no—
519C22⋊C4—222no—
520C22⋊C4—222no—
521C22⋊C4—221no—
522C22⋊C4(C2×D11)⋊C412yes—
523C22⋊C4(C2×D11)⋊C412yes—
524C22⋊C4(C2×D11)⋊C412yes—
525C42—221no—
526C42—221no—
527C42—221no—
528C42C2×C4×D1111yescharacteristic
529C42C2×C4×D1112yes—
530C42C2×D4411yescharacteristic
531C42C2×D4412yes—
532C42C2×C22⋊D1111yescharacteristic
533C42C2×C22⋊D1112yes—
534C42C23×D1111yescharacteristic
535C11#1748311yescharacteristic, complemented, Sylow
536C23—222no—
537C23—221no—
538C23—442no—
539C23—881no—
540C23—881no—
541C23C2×(C2×D11)⋊C412yes—
542C23C2×(C2×D11)⋊C411yescharacteristic
543Q8—22no—
544Q8—222no—
545Q8—882no—
546D4—24no—
547D4—22no—
548D4—224no—
549D4—222no—
550D4—442no—
551D4—442no—
552D4—882no—
553D4—882no—
554D4—882no—
555D4—882no—
556D4—882no—
557C2×C4—24no—
558C2×C4—21no—
559C2×C4—22no—
560C2×C4—21no—
561C2×C4—22no—
562C2×C4—41no—
563C2×C4—42no—
564C2×C4—221no—
565C2×C4—221no—
566C2×C4—221no—
567C2×C4—222no—
568C2×C4—442no—
569C2×C4—442no—
570C2×C4—441no—
571C2×C4—442no—
572C2×C4—441no—
573C2×C4—882no—
574C2×C4—881no—
575C2×C4—881no—
576C2×C4#6696014yes—
577C2×C4C2×(C2×D11)⋊C411yescharacteristic
578C2×C4C2×(C2×D11)⋊C411yescharacteristic
579C2×C4C2×(C2×D11)⋊C412yes—
580C2×C4C2×(C2×D11)⋊C412yes—
581C2×C4C2×(C2×D11)⋊C412yes—
582C2×C4C2×(C2×D11)⋊C411yescharacteristic
583C2×C4C22×C4×D1111yescharacteristic
584C2×C4C22×D4411yescharacteristic
585C2×C4C22×C22⋊D1111yescharacteristic
586C8—42no—
587C8—41no—
588C8—41no—
589C8—222no—
590C8—441no—
591C8—442no—
592C22—21no—
593C22—21no—
594C22—22no—
595C22—22no—
596C22—22no—
597C22—441no—
598C22—442no—
599C22—442no—
600C22—441no—
601C22—441no—
602C22—442no—
603C22—884no—
604C22#1062274212yes—
605C22C22×(C2×D11)⋊C411yescharacteristic
606C4—22no—
607C4—21no—
608C4—22no—
609C4—21no—
610C4—21no—
611C4—22no—
612C4—441no—
613C4—442no—
614C4—441no—
615C4—441no—
616C4#1062274212yes—
617C4C2×#6696012yes—
618C4#1062336611yescharacteristic
619C4#1062336811yescharacteristic
620C2—22no—
621C2—42no—
622C2—882no—
623C2—881no—
624C2C2×#1062274211yescharacteristic
625C2#1307713911yescharacteristic
626C2#1307716111yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×#2989C2
socleC22×C11C22×C22⋊C4
prime radical#13082032C2
cosocleC42×C11C24
hypercenter#2989D11
hypocenterC11#17483
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C4×#41 ◁ #2989

Complements

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

NH ≅ G/Ntype
2. #41×C11⋊C8C2semidirect
3. #13067084C2semidirect
4. #13067079C2semidirect
5. #13067074C2semidirect
6. #13067066C2semidirect
7. #13067006C2semidirect
8. #13067001C2semidirect
9. #13066996C2semidirect
10. C2×#10622121C2semidirect
11. C11×#2989C2semidirect
32. C11×#432C22semidirect
34. C11×#423C22semidirect
40. #10622538C22semidirect
42. C2×C4×C11⋊C8C22semidirect
43. #10622122C22semidirect
44. #10622122C22semidirect
45. #10622122C22semidirect
50. #10622121C22semidirect
51. #10622121C22semidirect
52. #10622121C22semidirect
224. #2989D11semidirect
313. #432C2×D11semidirect
317. #423C2×D11semidirect
535. C11#17483semidirect

Maximal subgroups

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

subgroupindex
#130820322
#41×C11⋊C82
#130670842
#130670792
#130670742
#130670662
#130670062
#130670012
#130669962
C2×#106221212
C11×#29892
#1748311