Finite Group Databasebeta

← #14720513

Subgroups — #14720513

Order 2816.

1036 conjugacy classes of subgroups.

The subgroup lattice has 662 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623088C211yesmaximal, characteristic
2#13077244C211yesmaximal, characteristic, complemented
3D11×#423C211yesmaximal, characteristic, complemented
4#13067078C214yesmaximal, complemented
5#13067046C211yesmaximal, characteristic, complemented
6#13067044C211yesmaximal, characteristic, complemented
7#13067041C211yesmaximal, characteristic, complemented
8#13067026C214yesmaximal, complemented
9C11×#1486C211yesmaximal, characteristic, complemented
10C2×C4×D4×C11C2211yescharacteristic
11C2×#66991C411yescharacteristic
12C2×#66989C411yescharacteristic
13C2×C4×C22⋊D11—21no—
14C2×#66979—21no—
15C2×M16×D11—21no—
16#10623088—21no—
17#10623088—21no—
18#10623088—21no—
19#10623088—21no—
20#10623088C412yes—
21#10623088C412yes—
22#10623088C2212yes—
23#10623088C2212yes—
24C2×#66950C411yescharacteristic
25C2×#66943C411yescharacteristic
26C2×#66936—21no—
27C2×#66932—21no—
28C2×C42×D11C2211yescharacteristic
29C2×C4×Dic22C2211yescharacteristic
30C11×#431C2211yescharacteristic
31C11×#423C2211yescharacteristic
32#10622731—21no—
33#10622538C2211yescharacteristic
34#10622537C2211yescharacteristic
35#10622450—21no—
36#10622450—21no—
37#10622450C2212yescomplemented
38#10622448—21no—
39D11×C4⋊C8—21no—
40D11×C4⋊C8C2212yescomplemented
41#10622339—21no—
42#10622332—21no—
43C4×#4313C2212yescomplemented
44#10622298C2212yescomplemented
45C11×D4⋊C8C2214yescomplemented
46D4⋊(C11⋊C8)C2214yescomplemented
47#10622122C2214yescomplemented
48#10622094C2214yescomplemented
49C22×D4×C11C2×C411yescharacteristic
50C23×C4×C11—21no—
51C22×C22⋊D11—21no—
52C22×C4×D11C2×C411yescharacteristic
53C22×C4×D11D411yescharacteristic
54C22×C4×D11D411yescharacteristic
55C22×Dic22C2×C411yescharacteristic
56C2×C11×M16—21no—
57C4×D4×C11—21no—
58C4×D4×C11—21no—
59C4×D4×C11C2×C412yes—
60C4×D4×C11C2312yes—
61C2×C11×C4⋊C4C2×C411yescharacteristic
62C2×C11×C22⋊C4—21no—
63C2×C42×C11C2311yescharacteristic
64C2×C22⋊Dic11—21no—
65C2×C22⋊Dic11—21no—
66C2×C22⋊Dic11—21no—
67#66991—21no—
68#66991—21no—
69#66991C2×C412yes—
70#66991C2×C412yes—
71#66989—21no—
72#66989—21no—
73#66989C2×C412yes—
74#66989C2×C412yes—
75C4×C22⋊D11—22no—
76C4×C22⋊D11—22no—
77C4×C22⋊D11—22no—
78C4×C22⋊D11—22no—
79C2×(C2×D11)⋊C4—21no—
80#66979—22no—
81#66979—22no—
82#66979—22no—
83#66979—22no—
84C2×C4⋊Dic11—21no—
85C2×C4⋊Dic11—21no—
86C2×C4⋊Dic11C2×C411yescharacteristic
87C2×Dic11⋊C4—21no—
88C2×Dic11⋊C4—21no—
89C2×C4×Dic11—21no—
90C2×C4×Dic11C2×C411yescharacteristic
91C2×C4×Dic11D411yescharacteristic
92C2×C4×Dic11D411yescharacteristic
93C2×#4318—21no—
94M16×D11—44no—
95C2×#4313—22no—
96C2×#4313—22no—
97C2×C8×D11—22no—
98#66950—21no—
99#66950—21no—
100#66950C2×C412yes—
101#66950C2×C412yes—
102#66943—21no—
103#66943—21no—
104#66943C2×C412yes—
105#66943C2×C412yes—
106#66936—22no—
107#66936—22no—
108#66936—22no—
109#66936—22no—
110#66932—22no—
111#66932—22no—
112#66932—22no—
113#66932—22no—
114C42×D11C2×C411yescharacteristic
115C42×D11C2×C411yescharacteristic
116C42×D11D411yescharacteristic
117C42×D11D411yescharacteristic
118C42×D11D411yescharacteristic
119C42×D11D411yescharacteristic
120C42×D11C2311yescharacteristic
121C42×D11C2311yescharacteristic
122C4×Dic22—21no—
123C4×Dic22—21no—
124C4×Dic22C2×C412yes—
125C4×Dic22C2312yes—
126C11×C4⋊C8—21no—
127C11×C4⋊C8—21no—
128C11×C4⋊C8C2312yes—
129C11×C22⋊C8—21no—
130C4×C8×C11C2312yes—
131C22⋊(C11⋊C8)—21no—
132(C2×D11)⋊C8—22no—
133#66879—22no—
134Dic11⋊C8—22no—
135Dic11⋊C8—22no—
136Dic11⋊C8—22no—
137C4⋊(C11⋊C8)—21no—
138C4⋊(C11⋊C8)—21no—
139C4⋊(C11⋊C8)C2312yes—
140C4×C11⋊C8C2312yes—
141#17492—111nomaximal, Sylow
142C24×C11—21no—
143C23×D11C22⋊C411yescharacteristic
144C2×D4×C11—21no—
145C2×D4×C11—42no—
146C2×D4×C11C22×C412yes—
147C22×C4×C11—21no—
148C22×C4×C11—22no—
149C22×C4×C11—22no—
150C22×C4×C11—42no—
151C22×C4×C11—42no—
152C22×C4×C11C22×C411yescharacteristic
153C22×C4×C11C2×D411yescharacteristic
154C22×C4×C11C2×D411yescharacteristic
155C2×C22⋊D11—22no—
156C2×C22⋊D11—22no—
157C2×C22⋊D11—44no—
158C22×Dic11—21no—
159C22×Dic11—21no—
160C22×Dic11C22⋊C411yescharacteristic
161C22×Dic11C22⋊C411yescharacteristic
162C22×Dic11C22⋊C411yescharacteristic
163C2×C4×D11—22no—
164C2×C4×D11—22no—
165C2×C4×D11—42no—
166C2×C4×D11—42no—
167C2×C4×D11C22⋊C411yescharacteristic
168C2×C4×D11C22⋊C411yescharacteristic
169C2×C4×D11C22⋊C411yescharacteristic
170C2×C4×D11C22⋊C411yescharacteristic
171C2×C4×D11C22⋊C411yescharacteristic
172C2×C4×D11C22⋊C411yescharacteristic
173C2×C4×D11C22×C411yescharacteristic
174C2×C4×D11C22×C411yescharacteristic
175C2×C4×D11C2×D411yescharacteristic
176C2×C4×D11C2×D411yescharacteristic
177C2×C4×D11C2×D411yescharacteristic
178C2×C4×D11C2×D411yescharacteristic
179C2×Dic22—21no—
180C2×Dic22—42no—
181C2×Dic22C22×C412yes—
182C11×M16—42no—
183C2×C8×C11—22no—
184C2×C8×C11—22no—
185C11×C4⋊C4—21no—
186C11×C4⋊C4C22×C412yes—
187C11×C22⋊C4—22no—
188C11×C22⋊C4—22no—
189C42×C11C22×C411yescharacteristic
190C42×C11C2×D411yescharacteristic
191C42×C11C2×D411yescharacteristic
192C42×C11C2411yescharacteristic
193C22⋊Dic11—22no—
194C22⋊Dic11—22no—
195C22⋊Dic11—22no—
196C22⋊Dic11—22no—
197C22⋊Dic11—22no—
198C22⋊Dic11—22no—
199(C2×D11)⋊C4—22no—
200(C2×D11)⋊C4—22no—
201C4⋊Dic11—22no—
202C4⋊Dic11—22no—
203C4⋊Dic11—22no—
204C4⋊Dic11—22no—
205C4⋊Dic11—21no—
206C4⋊Dic11C22×C412yes—
207Dic11⋊C4—22no—
208Dic11⋊C4—22no—
209Dic11⋊C4—22no—
210Dic11⋊C4—22no—
211C4×Dic11—22no—
212C4×Dic11—22no—
213C4×Dic11C22⋊C411yescharacteristic
214C4×Dic11C22⋊C411yescharacteristic
215C4×Dic11C22⋊C411yescharacteristic
216C4×Dic11C22⋊C411yescharacteristic
217C4×Dic11C22⋊C411yescharacteristic
218C4×Dic11C22⋊C411yescharacteristic
219C4×Dic11C22×C411yescharacteristic
220C4×Dic11C22×C411yescharacteristic
221C4×Dic11C2×D411yescharacteristic
222C4×Dic11C2×D411yescharacteristic
223C4×Dic11C2×D411yescharacteristic
224C4×Dic11C2×D411yescharacteristic
225#4318—42no—
226C2×C11⋊C8—22no—
227C2×C11⋊C8—22no—
228#4313—44no—
229#4313—44no—
230C8×D11—44no—
231C2×#529—111no—
232#2920—111no—
233C2×#423—111no—
234#1495—114no—
235#1487—111no—
236#1487—111no—
237#1486—111no—
238#1486D1111yescharacteristic, complemented
239#1483—114no—
240C23×C11—22no—
241C23×C11—42no—
242C23×C11—42no—
243C23×C11—42no—
244C23×C11C2×C22⋊C411yescharacteristic
245C22×D11—22no—
246C22×D11—22no—
247C22×D11—41no—
248C22×D11C2×C22⋊C411yescharacteristic
249C22×D11C2×C22⋊C411yescharacteristic
250D4×C11—24no—
251D4×C11—42no—
252C2×C4×C11—22no—
253C2×C4×C11—22no—
254C2×C4×C11—41no—
255C2×C4×C11—42no—
256C2×C4×C11—42no—
257C2×C4×C11—42no—
258C2×C4×C11—44no—
259C2×C4×C11C2×C22⋊C411yescharacteristic
260C2×C4×C11C2×C22⋊C411yescharacteristic
261C2×C4×C11C2×C22⋊C411yescharacteristic
262C2×C4×C11AGL(1,ℤ/8)12yes—
263C2×C4×C11#13712yes—
264C2×C4×C11C23×C411yescharacteristic
265C2×C4×C11C22×D411yescharacteristic
266C2×C4×C11C22×D411yescharacteristic
267C22⋊D11—44no—
268C22⋊D11—44no—
269C2×Dic11—22no—
270C2×Dic11—22no—
271C2×Dic11—22no—
272C2×Dic11—41no—
273C2×Dic11—41no—
274C2×Dic11—42no—
275C2×Dic11—42no—
276C2×Dic11C2×C22⋊C411yescharacteristic
277C2×Dic11C2×C22⋊C411yescharacteristic
278C2×Dic11C2×C22⋊C411yescharacteristic
279C2×Dic11C2×C22⋊C411yescharacteristic
280C2×Dic11C2×C22⋊C411yescharacteristic
281C2×Dic11C2×C22⋊C411yescharacteristic
282C4×D11—22no—
283C4×D11—22no—
284C4×D11—22no—
285C4×D11—22no—
286C4×D11—21no—
287C4×D11—21no—
288C4×D11—21no—
289C4×D11—21no—
290C4×D11—22no—
291C4×D11—22no—
292C4×D11—41no—
293C4×D11—41no—
294C4×D11—41no—
295C4×D11—41no—
296Dic22—24no—
297Dic22—42no—
298C8×C11—42no—
299C8×C11—42no—
300C11⋊C8—42no—
301C11⋊C8—42no—
302C22×M16—221no—
303#529—112no—
304#529—112no—
305#529—112no—
306#529—112no—
307#529—221no—
308#529—221no—
309#529—221no—
310#529—221no—
311C2×#126—221no—
312C2×#125—111no—
313C2×#124—111no—
314C2×#123—221no—
315C2×C22⋊Q8—111no—
316C2×#121—111no—
317C2×C4×Q8—111no—
318C2×C4×D4—221no—
319C2×C4×D4C2×D1111yescharacteristic
320C2×#117—221no—
321C22×C42—111no—
322#432—221no—
323#432—221no—
324#431—111no—
325#431—112no—
326#431C2×D1111yescharacteristic
327#423—111no—
328#423—112no—
329#423—221no—
330#423—221no—
331#423—221no—
332#423C2×D1111yescharacteristic
333C2×C4⋊C8—112no—
334C2×C4⋊C8—221no—
335#407—221no—
336C4×M16—112no—
337Q8⋊C8—114no—
338Q8⋊C8—114no—
339D4⋊C8—114no—
340D4⋊C8C2×D1114yescomplemented
341C22×C11—21no—
342C22×C11—21no—
343C22×C11—42no—
344C22×C11—42no—
345C22×C11—42no—
346C22×C11—84no—
347C22×C11#41712yes—
348C22×C11C22×C22⋊C411yescharacteristic
349C2×D11—21no—
350C2×D11—21no—
351C2×D11—21no—
352C2×D11—21no—
353C2×D11—21no—
354C2×D11—44no—
355C2×D11#42112yes—
356C4×C11—21no—
357C4×C11—21no—
358C4×C11—21no—
359C4×C11—42no—
360C4×C11#41712yes—
361C4×C11#56812yes—
362C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
363C4×C11C2×#13711yescharacteristic
364Dic11—21no—
365Dic11—21no—
366Dic11—21no—
367Dic11—21no—
368Dic11—21no—
369Dic11—21no—
370Dic11—42no—
371Dic11—42no—
372C22×Q8—111no—
373C22×D4—221no—
374C22×D4C4×D1111yescharacteristic
375C23×C4—21no—
376C23×C4—111no—
377C23×C4—111no—
378C23×C4—111no—
379C2×M16—21no—
380C2×M16—222no—
381C2×M16—222no—
382C2×M16—221no—
383C2×M16—444no—
384C22×C8—222no—
385#126—222no—
386#126—222no—
387#126—222no—
388#126—222no—
389#125—112no—
390#125—112no—
391#125—221no—
392#125—221no—
393#124—112no—
394#124—112no—
395#124—221no—
396#124—221no—
397#123—222no—
398#123—222no—
399#123—222no—
400#123—222no—
401C22⋊Q8—112no—
402C22⋊Q8—112no—
403C22⋊Q8—221no—
404C22⋊Q8—221no—
405#121—112no—
406#121—112no—
407#121—221no—
408#121—221no—
409C4×Q8—112no—
410C4×Q8—112no—
411C4×Q8—221no—
412C4×Q8—221no—
413C4×D4—21no—
414C4×D4—21no—
415C4×D4—222no—
416C4×D4—222no—
417C4×D4—222no—
418C4×D4—222no—
419C4×D4C4×D1112yes—
420C4×D4C22×D1112yes—
421#117—222no—
422#117—222no—
423#117—222no—
424#117—222no—
425C2×C4⋊C4—111no—
426C2×C4⋊C4—221no—
427C2×C4⋊C4—221no—
428C2×C4⋊C4—221no—
429C2×C4⋊C4—221no—
430C2×C4⋊C4C4×D1111yescharacteristic
431C2×C22⋊C4—21no—
432C2×C22⋊C4—221no—
433C2×C22⋊C4—221no—
434C2×C22⋊C4—221no—
435C2×C22⋊C4—221no—
436C2×C42—111no—
437C2×C42—111no—
438C2×C42—111no—
439C2×C42—111no—
440C2×C42—111no—
441C2×C42—111no—
442C2×C42—111no—
443C2×C42—111no—
444C2×C42—111no—
445C2×C42—111no—
446C2×C42—111no—
447C2×C42—221no—
448C2×C42C22×D1111yescharacteristic
449C4⋊C8—21no—
450C4⋊C8—21no—
451C4⋊C8—112no—
452C4⋊C8—222no—
453C4⋊C8—222no—
454C4⋊C8—222no—
455C4⋊C8—221no—
456C4⋊C8—221no—
457C4⋊C8C22×D1112yes—
458C22⋊C8—21no—
459C22⋊C8—222no—
460C22⋊C8—221no—
461#97—222no—
462C4×C8—112no—
463C4×C8C22×D1112yes—
464C2×C11—22no—
465C2×C11—82no—
466C2×C11#287911yescharacteristic
467C2×C11C2×#41711yescharacteristic
468C2×C11C2×#42111yescharacteristic
469D11—22no—
470D11—41no—
471C24—21no—
472C24—111no—
473C2×Q8—112no—
474C2×Q8—221no—
475C2×Q8—442no—
476C2×D4—21no—
477C2×D4—42no—
478C2×D4—222no—
479C2×D4—222no—
480C2×D4—444no—
481C2×D4C2×C4×D1112yes—
482C22×C4—21no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—42no—
486C22×C4—42no—
487C22×C4—111no—
488C22×C4—111no—
489C22×C4—111no—
490C22×C4—111no—
491C22×C4—111no—
492C22×C4—111no—
493C22×C4—111no—
494C22×C4—111no—
495C22×C4—111no—
496C22×C4—111no—
497C22×C4—111no—
498C22×C4—111no—
499C22×C4—111no—
500C22×C4—111no—
501C22×C4—111no—
502C22×C4—222no—
503C22×C4—222no—
504C22×C4—221no—
505C22×C4—221no—
506C22×C4—442no—
507C22×C4—442no—
508C22×C4C2×C4×D1111yescharacteristic
509C22×C4D4×D1111yescharacteristic
510C22×C4D4×D1111yescharacteristic
511M16—42no—
512M16—444no—
513M16—444no—
514M16—442no—
515C2×C8—22no—
516C2×C8—22no—
517C2×C8—222no—
518C2×C8—222no—
519C2×C8—444no—
520C4⋊C4—21no—
521C4⋊C4—112no—
522C4⋊C4—222no—
523C4⋊C4—222no—
524C4⋊C4—222no—
525C4⋊C4—222no—
526C4⋊C4—222no—
527C4⋊C4—222no—
528C4⋊C4—221no—
529C4⋊C4—222no—
530C4⋊C4—222no—
531C4⋊C4C2×C4×D1112yes—
532C22⋊C4—22no—
533C22⋊C4—22no—
534C22⋊C4—222no—
535C22⋊C4—222no—
536C22⋊C4—222no—
537C22⋊C4—222no—
538C22⋊C4—222no—
539C22⋊C4—222no—
540C22⋊C4—222no—
541C22⋊C4—222no—
542C42—111no—
543C42—111no—
544C42—111no—
545C42—111no—
546C42—111no—
547C42—111no—
548C42—111no—
549C42—111no—
550C42—111no—
551C42—111no—
552C42—111no—
553C42—111no—
554C42—222no—
555C42—222no—
556C42C2×C4×D1111yescharacteristic
557C42D4×D1111yescharacteristic
558C42D4×D1111yescharacteristic
559C42C23×D1111yescharacteristic
560C11#1749211yescharacteristic, complemented, Sylow
561C23—22no—
562C23—42no—
563C23—42no—
564C23—42no—
565C23—111no—
566C23—111no—
567C23—222no—
568C23—222no—
569C23—441no—
570C23C22⋊C4×D1111yescharacteristic
571Q8—224no—
572Q8—442no—
573D4—24no—
574D4—42no—
575D4—444no—
576D4—444no—
577C2×C4—22no—
578C2×C4—22no—
579C2×C4—41no—
580C2×C4—42no—
581C2×C4—42no—
582C2×C4—42no—
583C2×C4—44no—
584C2×C4—111no—
585C2×C4—111no—
586C2×C4—111no—
587C2×C4—111no—
588C2×C4—111no—
589C2×C4—111no—
590C2×C4—222no—
591C2×C4—222no—
592C2×C4—222no—
593C2×C4—222no—
594C2×C4—222no—
595C2×C4—221no—
596C2×C4—221no—
597C2×C4—221no—
598C2×C4—221no—
599C2×C4—222no—
600C2×C4—222no—
601C2×C4—222no—
602C2×C4—222no—
603C2×C4—441no—
604C2×C4—441no—
605C2×C4—441no—
606C2×C4—441no—
607C2×C4—441no—
608C2×C4—441no—
609C2×C4—442no—
610C2×C4—442no—
611C2×C4C22⋊C4×D1111yescharacteristic
612C2×C4C22⋊C4×D1111yescharacteristic
613C2×C4C22⋊C4×D1111yescharacteristic
614C2×C4#6696412yes—
615C2×C4#6696812yes—
616C2×C4C22×C4×D1111yescharacteristic
617C2×C4C2×D4×D1111yescharacteristic
618C2×C4C2×D4×D1111yescharacteristic
619C8—42no—
620C8—42no—
621C8—442no—
622C8—442no—
623C22—21no—
624C22—21no—
625C22—42no—
626C22—42no—
627C22—42no—
628C22—84no—
629C22—112no—
630C22—221no—
631C22—221no—
632C22—221no—
633C22—221no—
634C22—221no—
635C22—444no—
636C22#1062238412yes—
637C22C2×C22⋊C4×D1111yescharacteristic
638C4—21no—
639C4—21no—
640C4—21no—
641C4—42no—
642C4—221no—
643C4—221no—
644C4—221no—
645C4—221no—
646C4—221no—
647C4—221no—
648C4—442no—
649C4—442no—
650C4#1062238412yes—
651C4#1062327612yes—
652C4C2×#6696411yescharacteristic
653C4C2×#6696811yescharacteristic
654C2—22no—
655C2—82no—
656C2—222no—
657C2—441no—
658C2#1307705911yescharacteristic
659C2C2×#1062238411yescharacteristic
660C2D11×#42111yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×#1486C2
socleC22×C11C22×C22⋊C4
prime radicalC2×#66991C4
cosocleC42×C11C24
hypercenter#1486D11
hypocenterC11#17492
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1486

Complements

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

NH ≅ G/Ntype
2. #13077244C2semidirect
3. D11×#423C2semidirect
4. #13067078C2semidirect
5. #13067046C2semidirect
6. #13067044C2semidirect
7. #13067041C2semidirect
8. #13067026C2semidirect
9. C11×#1486C2semidirect
37. #10622450C22semidirect
40. D11×C4⋊C8C22semidirect
43. C4×#4313C22semidirect
44. #10622298C22semidirect
45. C11×D4⋊C8C22semidirect
46. D4⋊(C11⋊C8)C22semidirect
47. #10622122C22semidirect
48. #10622094C22semidirect
238. #1486D11semidirect
340. D4⋊C8C2×D11semidirect
560. C11#17492semidirect

Maximal subgroups

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

subgroupindex
C2×#106230882
#130772442
D11×#4232
#130670782
#130670462
#130670442
#130670412
#130670262
C11×#14862
#1749211