Finite Group Databasebeta

← #14720483

Subgroups — #14720483

Order 2816.

1012 conjugacy classes of subgroups.

The subgroup lattice has 656 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623111C211yesmaximal, characteristic
2#13077248C211yesmaximal, characteristic, complemented
3D11×#431C211yesmaximal, characteristic, complemented
4#13067075C214yesmaximal, complemented
5#13067045C211yesmaximal, characteristic, complemented
6#13067042C211yesmaximal, characteristic, complemented
7#13067040C211yesmaximal, characteristic, complemented
8#13067023C214yesmaximal, complemented
9C11×#1487C211yesmaximal, characteristic, complemented
10C2×C4×Q8×C11C2211yescharacteristic
11C2×#67000C411yescharacteristic
12C2×#66999C411yescharacteristic
13#10623111—21no—
14#10623111—21no—
15#10623111—21no—
16#10623111—21no—
17#10623111C412yes—
18#10623111C412yes—
19#10623111C2212yes—
20#10623111C2212yes—
21C2×#66951—21no—
22C2×#66948C411yescharacteristic
23C2×#66947—21no—
24C2×#66943C411yescharacteristic
25C2×C4×D44—21no—
26C2×C4×D44C2211yescharacteristic
27C2×#66925—21no—
28C2×C42×D11C2211yescharacteristic
29C11×#431C2211yescharacteristic
30C11×#423C2211yescharacteristic
31#10622739—21no—
32M16×Dic11—21no—
33#10622538C2211yescharacteristic
34#10622537C2211yescharacteristic
35#10622448—21no—
36#10622448C2212yescomplemented
37#10622446—21no—
38#10622446—21no—
39#10622446C2212yescomplemented
40D11×C4⋊C8—21no—
41D11×C22⋊C8—21no—
42#10622331—21no—
43#10622298C2212yescomplemented
44C4×C8×D11C2212yescomplemented
45C11×Q8⋊C8C2214yescomplemented
46Q8⋊(C11⋊C8)C2214yescomplemented
47#10622121C2214yescomplemented
48#10622097C2214yescomplemented
49C22×Q8×C11C2×C411yescharacteristic
50C22×D44—21no—
51C22×D44C2×C411yescharacteristic
52C22×C4×D11—21no—
53C22×C4×D11C2×C411yescharacteristic
54C22×C4×D11D411yescharacteristic
55C22×C4×D11D411yescharacteristic
56C2×C11×M16—21no—
57C4×Q8×C11—21no—
58C4×Q8×C11—21no—
59C4×Q8×C11C2×C412yes—
60C4×Q8×C11C2312yes—
61C2×C11×C4⋊C4—21no—
62C2×C11×C4⋊C4C2×C411yescharacteristic
63C2×C42×C11—21no—
64C2×C42×C11C2311yescharacteristic
65#67000—21no—
66#67000—21no—
67#67000C2×C412yes—
68#67000C2×C412yes—
69#66999—21no—
70#66999—21no—
71#66999C2×C412yes—
72#66999C2×C412yes—
73C2×(C2×D11)⋊C4—21no—
74C2×(C2×D11)⋊C4—21no—
75C2×(C2×D11)⋊C4—21no—
76C2×(C2×D11)⋊C4—21no—
77C2×(C2×D11)⋊C4—21no—
78C2×C4⋊Dic11—21no—
79C2×C4⋊Dic11C2×C411yescharacteristic
80C2×Dic11⋊C4—21no—
81C2×Dic11⋊C4—21no—
82C2×C4×Dic11C2×C411yescharacteristic
83C2×C4×Dic11D411yescharacteristic
84C2×C4×Dic11D411yescharacteristic
85C2×#4318—21no—
86C2×C8×D11—22no—
87#66951—22no—
88#66951—22no—
89#66951—22no—
90#66951—22no—
91#66948—21no—
92#66948—21no—
93#66948C2×C412yes—
94#66948C2×C412yes—
95#66947—22no—
96#66947—22no—
97#66947—22no—
98#66947—22no—
99#66943—21no—
100#66943—21no—
101#66943C2×C412yes—
102#66943C2×C412yes—
103C4×D44—22no—
104C4×D44—22no—
105C4×D44—22no—
106C4×D44—22no—
107C4×D44—21no—
108C4×D44—21no—
109C4×D44C2×C412yes—
110C4×D44C2312yes—
111#66925—22no—
112#66925—22no—
113#66925—22no—
114#66925—22no—
115C42×D11C2×C411yescharacteristic
116C42×D11C2×C411yescharacteristic
117C42×D11D411yescharacteristic
118C42×D11D411yescharacteristic
119C42×D11D411yescharacteristic
120C42×D11D411yescharacteristic
121C42×D11C2311yescharacteristic
122C42×D11C2311yescharacteristic
123C11×C4⋊C8—21no—
124C11×C4⋊C8—21no—
125C11×C4⋊C8C2312yes—
126C11×C22⋊C8—21no—
127C4×C8×C11C2312yes—
128C22⋊(C11⋊C8)—21no—
129(C2×D11)⋊C8—22no—
130(C2×D11)⋊C8—22no—
131(C2×D11)⋊C8—22no—
132#66879—22no—
133Dic11⋊C8—22no—
134C8×Dic11—22no—
135C8×Dic11—22no—
136C4⋊(C11⋊C8)—21no—
137C4⋊(C11⋊C8)—21no—
138C4⋊(C11⋊C8)C2312yes—
139C4×C11⋊C8C2312yes—
140#17487—111nomaximal, Sylow
141C23×D11—21no—
142C23×D11C22⋊C411yescharacteristic
143C2×Q8×C11—21no—
144C2×Q8×C11—42no—
145C2×Q8×C11C22×C412yes—
146C22×C4×C11—21no—
147C22×C4×C11—21no—
148C22×C4×C11C22×C411yescharacteristic
149C22×C4×C11C2×D411yescharacteristic
150C22×C4×C11C2×D411yescharacteristic
151C22×Dic11—21no—
152C22×Dic11C22⋊C411yescharacteristic
153C22×Dic11C22⋊C411yescharacteristic
154C22×Dic11C22⋊C411yescharacteristic
155C2×D44—22no—
156C2×D44—22no—
157C2×D44—21no—
158C2×D44—42no—
159C2×D44—44no—
160C2×D44C22×C412yes—
161C2×C4×D11—22no—
162C2×C4×D11—22no—
163C2×C4×D11—22no—
164C2×C4×D11—22no—
165C2×C4×D11—42no—
166C2×C4×D11—42no—
167C2×C4×D11—42no—
168C2×C4×D11—42no—
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×D11C22×C411yescharacteristic
176C2×C4×D11C22×C411yescharacteristic
177C2×C4×D11C2×D411yescharacteristic
178C2×C4×D11C2×D411yescharacteristic
179C2×C4×D11C2×D411yescharacteristic
180C2×C4×D11C2×D411yescharacteristic
181C11×M16—42no—
182C2×C8×C11—22no—
183C2×C8×C11—22no—
184C11×C4⋊C4—21no—
185C11×C4⋊C4—22no—
186C11×C4⋊C4—22no—
187C11×C4⋊C4C22×C412yes—
188C42×C11—22no—
189C42×C11—22no—
190C42×C11C22×C411yescharacteristic
191C42×C11C2×D411yescharacteristic
192C42×C11C2×D411yescharacteristic
193C42×C11C2411yescharacteristic
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—
200(C2×D11)⋊C4—22no—
201(C2×D11)⋊C4—22no—
202(C2×D11)⋊C4—22no—
203(C2×D11)⋊C4—22no—
204C4⋊Dic11—22no—
205C4⋊Dic11—22no—
206C4⋊Dic11—21no—
207C4⋊Dic11C22×C412yes—
208Dic11⋊C4—22no—
209Dic11⋊C4—22no—
210Dic11⋊C4—22no—
211Dic11⋊C4—22no—
212C4×Dic11C22⋊C411yescharacteristic
213C4×Dic11C22⋊C411yescharacteristic
214C4×Dic11C22⋊C411yescharacteristic
215C4×Dic11C22⋊C411yescharacteristic
216C4×Dic11C22⋊C411yescharacteristic
217C4×Dic11C22⋊C411yescharacteristic
218C4×Dic11C22×C411yescharacteristic
219C4×Dic11C22×C411yescharacteristic
220C4×Dic11C2×D411yescharacteristic
221C4×Dic11C2×D411yescharacteristic
222C4×Dic11C2×D411yescharacteristic
223C4×Dic11C2×D411yescharacteristic
224#4318—42no—
225C2×C11⋊C8—22no—
226C2×C11⋊C8—22no—
227C8×D11—44no—
228C2×#529—111no—
229#2920—111no—
230C2×#431—111no—
231#1494—114no—
232#1487—111no—
233#1487D1111yescharacteristic, complemented
234#1486—111no—
235#1486—111no—
236#1482—114no—
237C23×C11C2×C22⋊C411yescharacteristic
238C22×D11—22no—
239C22×D11—22no—
240C22×D11—22no—
241C22×D11—41no—
242C22×D11—42no—
243C22×D11—42no—
244C22×D11—42no—
245C22×D11C2×C22⋊C411yescharacteristic
246C22×D11C2×C22⋊C411yescharacteristic
247Q8×C11—24no—
248Q8×C11—42no—
249C2×C4×C11—22no—
250C2×C4×C11—22no—
251C2×C4×C11—22no—
252C2×C4×C11—41no—
253C2×C4×C11—42no—
254C2×C4×C11—42no—
255C2×C4×C11C2×C22⋊C411yescharacteristic
256C2×C4×C11C2×C22⋊C411yescharacteristic
257C2×C4×C11C2×C22⋊C411yescharacteristic
258C2×C4×C11#13512yes—
259C2×C4×C11#13512yes—
260C2×C4×C11C23×C411yescharacteristic
261C2×C4×C11C22×D411yescharacteristic
262C2×C4×C11C22×D411yescharacteristic
263C2×Dic11—22no—
264C2×Dic11—22no—
265C2×Dic11—41no—
266C2×Dic11—41no—
267C2×Dic11—42no—
268C2×Dic11C2×C22⋊C411yescharacteristic
269C2×Dic11C2×C22⋊C411yescharacteristic
270C2×Dic11C2×C22⋊C411yescharacteristic
271C2×Dic11C2×C22⋊C411yescharacteristic
272C2×Dic11C2×C22⋊C411yescharacteristic
273C2×Dic11C2×C22⋊C411yescharacteristic
274D44—24no—
275D44—42no—
276D44—44no—
277D44—44no—
278C4×D11—22no—
279C4×D11—22no—
280C4×D11—22no—
281C4×D11—22no—
282C4×D11—21no—
283C4×D11—21no—
284C4×D11—21no—
285C4×D11—21no—
286C4×D11—22no—
287C4×D11—22no—
288C4×D11—41no—
289C4×D11—41no—
290C4×D11—41no—
291C4×D11—41no—
292C4×D11—42no—
293C4×D11—42no—
294C4×D11—44no—
295C8×C11—42no—
296C8×C11—42no—
297C11⋊C8—42no—
298C11⋊C8—42no—
299#529—112no—
300#529—112no—
301#529—112no—
302#529—112no—
303#529—221no—
304#529—221no—
305#529—221no—
306#529—221no—
307C2×#126—221no—
308C2×#125—111no—
309C2×#124—111no—
310C2×#123—221no—
311C2×C22⋊Q8—111no—
312C2×#121—111no—
313C2×C4×Q8C2×D1111yescharacteristic
314C2×C4×D4—111no—
315C2×C4×D4—221no—
316C2×#117—221no—
317C22×C42—111no—
318#432—112no—
319#432—221no—
320#431—111no—
321#431—112no—
322#431—112no—
323#431—221no—
324#431—221no—
325#431—221no—
326#431C2×D1111yescharacteristic
327#423—111no—
328#423C2×D1111yescharacteristic
329C2×C4⋊C8—221no—
330#407—221no—
331C2×C22⋊C8—221no—
332C4×M16—221no—
333C2×C4×C8—112no—
334Q8⋊C8—114no—
335Q8⋊C8C2×D1114yescomplemented
336D4⋊C8—114no—
337D4⋊C8—114no—
338C22×C11—21no—
339C22×C11—21no—
340C22×C11#41612yes—
341C22×C11C22×C22⋊C411yescharacteristic
342C2×D11—21no—
343C2×D11—21no—
344C2×D11—21no—
345C2×D11—21no—
346C2×D11—21no—
347C2×D11—44no—
348C2×D11—42no—
349C2×D11—42no—
350C2×D11—42no—
351C2×D11—84no—
352C2×D11#42112yes—
353C4×C11—21no—
354C4×C11—21no—
355C4×C11—21no—
356C4×C11—42no—
357C4×C11—42no—
358C4×C11#41612yes—
359C4×C11#56812yes—
360C4×C11C2×#13511yescharacteristic
361C4×C11C2×#13511yescharacteristic
362Dic11—21no—
363Dic11—21no—
364Dic11—21no—
365Dic11—21no—
366Dic11—21no—
367Dic11—21no—
368Dic11—42no—
369C22×Q8C4×D1111yescharacteristic
370C22×D4—111no—
371C22×D4—221no—
372C23×C4—111no—
373C23×C4—111no—
374C23×C4—111no—
375C23×C4—221no—
376C2×M16—21no—
377C2×M16—221no—
378C22×C8—222no—
379#126—222no—
380#126—222no—
381#126—222no—
382#126—222no—
383#125—112no—
384#125—112no—
385#125—221no—
386#125—221no—
387#124—112no—
388#124—112no—
389#124—221no—
390#124—221no—
391#123—222no—
392#123—222no—
393#123—222no—
394#123—222no—
395C22⋊Q8—112no—
396C22⋊Q8—112no—
397C22⋊Q8—221no—
398C22⋊Q8—221no—
399#121—112no—
400#121—112no—
401#121—221no—
402#121—221no—
403C4×Q8—21no—
404C4×Q8—21no—
405C4×Q8C4×D1112yes—
406C4×Q8C22×D1112yes—
407C4×D4—112no—
408C4×D4—112no—
409C4×D4—222no—
410C4×D4—222no—
411C4×D4—222no—
412C4×D4—222no—
413C4×D4—221no—
414C4×D4—221no—
415#117—222no—
416#117—222no—
417#117—222no—
418#117—222no—
419C2×C4⋊C4—21no—
420C2×C4⋊C4—111no—
421C2×C4⋊C4—221no—
422C2×C4⋊C4—221no—
423C2×C4⋊C4—221no—
424C2×C4⋊C4C4×D1111yescharacteristic
425C2×C22⋊C4—221no—
426C2×C22⋊C4—221no—
427C2×C22⋊C4—221no—
428C2×C22⋊C4—221no—
429C2×C22⋊C4—221no—
430C2×C42—21no—
431C2×C42—111no—
432C2×C42—111no—
433C2×C42—111no—
434C2×C42—111no—
435C2×C42—111no—
436C2×C42—111no—
437C2×C42—111no—
438C2×C42—111no—
439C2×C42—111no—
440C2×C42—111no—
441C2×C42—111no—
442C2×C42C22×D1111yescharacteristic
443C4⋊C8—21no—
444C4⋊C8—21no—
445C4⋊C8—112no—
446C4⋊C8—222no—
447C4⋊C8—221no—
448C4⋊C8—221no—
449C4⋊C8C22×D1112yes—
450C22⋊C8—21no—
451C22⋊C8—222no—
452C22⋊C8—222no—
453C22⋊C8—222no—
454C22⋊C8—221no—
455#97—222no—
456C4×C8—112no—
457C4×C8—222no—
458C4×C8—222no—
459C4×C8C22×D1112yes—
460C2×C11—22no—
461C2×C11#287911yescharacteristic
462C2×C11C2×#41611yescharacteristic
463C2×C11C2×#42111yescharacteristic
464D11—22no—
465D11—41no—
466D11—82no—
467C24—111no—
468C24—221no—
469C2×Q8—21no—
470C2×Q8—42no—
471C2×Q8C2×C4×D1112yes—
472C2×D4—112no—
473C2×D4—222no—
474C2×D4—222no—
475C2×D4—221no—
476C2×D4—442no—
477C2×D4—444no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—111no—
481C22×C4—111no—
482C22×C4—111no—
483C22×C4—111no—
484C22×C4—111no—
485C22×C4—111no—
486C22×C4—111no—
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—222no—
496C22×C4—222no—
497C22×C4—221no—
498C22×C4—222no—
499C22×C4—222no—
500C22×C4—442no—
501C22×C4—442no—
502C22×C4—442no—
503C22×C4—442no—
504C22×C4C2×C4×D1111yescharacteristic
505C22×C4D4×D1111yescharacteristic
506C22×C4D4×D1111yescharacteristic
507M16—42no—
508M16—442no—
509C2×C8—22no—
510C2×C8—22no—
511C2×C8—222no—
512C2×C8—222no—
513C2×C8—444no—
514C4⋊C4—22no—
515C4⋊C4—21no—
516C4⋊C4—22no—
517C4⋊C4—112no—
518C4⋊C4—222no—
519C4⋊C4—222no—
520C4⋊C4—222no—
521C4⋊C4—222no—
522C4⋊C4—222no—
523C4⋊C4—222no—
524C4⋊C4—221no—
525C4⋊C4C2×C4×D1112yes—
526C22⋊C4—222no—
527C22⋊C4—222no—
528C22⋊C4—222no—
529C22⋊C4—222no—
530C22⋊C4—222no—
531C22⋊C4—222no—
532C22⋊C4—222no—
533C22⋊C4—222no—
534C22⋊C4—222no—
535C22⋊C4—222no—
536C42—22no—
537C42—22no—
538C42—111no—
539C42—111no—
540C42—111no—
541C42—111no—
542C42—111no—
543C42—111no—
544C42—111no—
545C42—111no—
546C42—111no—
547C42—111no—
548C42—111no—
549C42—111no—
550C42C2×C4×D1111yescharacteristic
551C42D4×D1111yescharacteristic
552C42D4×D1111yescharacteristic
553C42C23×D1111yescharacteristic
554C11#1748711yescharacteristic, complemented, Sylow
555C23—111no—
556C23—111no—
557C23—222no—
558C23—222no—
559C23—222no—
560C23—441no—
561C23—442no—
562C23—442no—
563C23—442no—
564C23C22⋊C4×D1111yescharacteristic
565Q8—24no—
566Q8—42no—
567D4—224no—
568D4—442no—
569D4—444no—
570D4—444no—
571C2×C4—22no—
572C2×C4—22no—
573C2×C4—22no—
574C2×C4—41no—
575C2×C4—42no—
576C2×C4—42no—
577C2×C4—111no—
578C2×C4—111no—
579C2×C4—111no—
580C2×C4—111no—
581C2×C4—111no—
582C2×C4—111no—
583C2×C4—222no—
584C2×C4—222no—
585C2×C4—222no—
586C2×C4—222no—
587C2×C4—222no—
588C2×C4—221no—
589C2×C4—221no—
590C2×C4—221no—
591C2×C4—221no—
592C2×C4—222no—
593C2×C4—222no—
594C2×C4—222no—
595C2×C4—441no—
596C2×C4—441no—
597C2×C4—441no—
598C2×C4—441no—
599C2×C4—441no—
600C2×C4—441no—
601C2×C4—442no—
602C2×C4—442no—
603C2×C4—442no—
604C2×C4—444no—
605C2×C4C22⋊C4×D1111yescharacteristic
606C2×C4C22⋊C4×D1111yescharacteristic
607C2×C4C22⋊C4×D1111yescharacteristic
608C2×C4#6696912yes—
609C2×C4#6697212yes—
610C2×C4C22×C4×D1111yescharacteristic
611C2×C4C2×D4×D1111yescharacteristic
612C2×C4C2×D4×D1111yescharacteristic
613C8—42no—
614C8—42no—
615C8—442no—
616C8—442no—
617C22—21no—
618C22—21no—
619C22—112no—
620C22—221no—
621C22—221no—
622C22—221no—
623C22—221no—
624C22—221no—
625C22—444no—
626C22—442no—
627C22—442no—
628C22—442no—
629C22—884no—
630C22#1062241712yes—
631C22C2×C22⋊C4×D1111yescharacteristic
632C4—21no—
633C4—21no—
634C4—21no—
635C4—42no—
636C4—42no—
637C4—221no—
638C4—221no—
639C4—221no—
640C4—221no—
641C4—221no—
642C4—221no—
643C4—442no—
644C4#1062241712yes—
645C4#1062327612yes—
646C4C2×#6696911yescharacteristic
647C4C2×#6697211yescharacteristic
648C2—22no—
649C2—222no—
650C2—441no—
651C2—882no—
652C2#1307705911yescharacteristic
653C2C2×#1062241711yescharacteristic
654C2D11×#42111yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×#1487C2
socleC22×C11C22×C22⋊C4
prime radicalC2×#66948C4
cosocleC42×C11C24
hypercenter#1487D11
hypocenterC11#17487
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1487

Complements

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

NH ≅ G/Ntype
2. #13077248C2semidirect
3. D11×#431C2semidirect
4. #13067075C2semidirect
5. #13067045C2semidirect
6. #13067042C2semidirect
7. #13067040C2semidirect
8. #13067023C2semidirect
9. C11×#1487C2semidirect
36. #10622448C22semidirect
39. #10622446C22semidirect
43. #10622298C22semidirect
44. C4×C8×D11C22semidirect
45. C11×Q8⋊C8C22semidirect
46. Q8⋊(C11⋊C8)C22semidirect
47. #10622121C22semidirect
48. #10622097C22semidirect
233. #1487D11semidirect
335. Q8⋊C8C2×D11semidirect
554. C11#17487semidirect

Maximal subgroups

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

subgroupindex
C2×#106231112
#130772482
D11×#4312
#130670752
#130670452
#130670422
#130670402
#130670232
C11×#14872
#1748711