Finite Group Databasebeta

← #14720516

Subgroups — #14720516

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×#10623111C211yesmaximal, characteristic
2#13077244C211yesmaximal, characteristic, complemented
3D11×#423C211yesmaximal, characteristic, complemented
4#13067080C214yesmaximal, complemented
5#13067045C211yesmaximal, characteristic, complemented
6#13067042C211yesmaximal, characteristic, complemented
7#13067040C211yesmaximal, characteristic, complemented
8#13067028C214yesmaximal, complemented
9C11×#1487C211yesmaximal, characteristic, complemented
10C2×C4×Q8×C11C2211yescharacteristic
11C2×#67000C411yescharacteristic
12C2×#66999C411yescharacteristic
13C2×M16×D11—21no—
14#10623111—21no—
15#10623111—21no—
16#10623111—21no—
17#10623111—21no—
18#10623111C412yes—
19#10623111C412yes—
20#10623111C2212yes—
21#10623111C2212yes—
22C2×#66951—21no—
23C2×#66948C411yescharacteristic
24C2×#66947—21no—
25C2×#66943C411yescharacteristic
26C2×C4×D44—21no—
27C2×C4×D44C2211yescharacteristic
28C2×#66925—21no—
29C2×C42×D11C2211yescharacteristic
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×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—
86M16×D11—44no—
87C2×#4313—22no—
88C2×#4313—22no—
89C2×C8×D11—22no—
90#66951—22no—
91#66951—22no—
92#66951—22no—
93#66951—22no—
94#66948—21no—
95#66948—21no—
96#66948C2×C412yes—
97#66948C2×C412yes—
98#66947—22no—
99#66947—22no—
100#66947—22no—
101#66947—22no—
102#66943—21no—
103#66943—21no—
104#66943C2×C412yes—
105#66943C2×C412yes—
106C4×D44—22no—
107C4×D44—22no—
108C4×D44—22no—
109C4×D44—22no—
110C4×D44—21no—
111C4×D44—21no—
112C4×D44C2×C412yes—
113C4×D44C2312yes—
114#66925—22no—
115#66925—22no—
116#66925—22no—
117#66925—22no—
118C42×D11C2×C411yescharacteristic
119C42×D11C2×C411yescharacteristic
120C42×D11D411yescharacteristic
121C42×D11D411yescharacteristic
122C42×D11D411yescharacteristic
123C42×D11D411yescharacteristic
124C42×D11C2311yescharacteristic
125C42×D11C2311yescharacteristic
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
142C23×D11—21no—
143C23×D11C22⋊C411yescharacteristic
144C2×Q8×C11—21no—
145C2×Q8×C11—42no—
146C2×Q8×C11C22×C412yes—
147C22×C4×C11—21no—
148C22×C4×C11—21no—
149C22×C4×C11C22×C411yescharacteristic
150C22×C4×C11C2×D411yescharacteristic
151C22×C4×C11C2×D411yescharacteristic
152C22×Dic11—21no—
153C22×Dic11C22⋊C411yescharacteristic
154C22×Dic11C22⋊C411yescharacteristic
155C22×Dic11C22⋊C411yescharacteristic
156C2×D44—22no—
157C2×D44—22no—
158C2×D44—21no—
159C2×D44—42no—
160C2×D44—44no—
161C2×D44C22×C412yes—
162C2×C4×D11—22no—
163C2×C4×D11—22no—
164C2×C4×D11—22no—
165C2×C4×D11—22no—
166C2×C4×D11—42no—
167C2×C4×D11—42no—
168C2×C4×D11—42no—
169C2×C4×D11—42no—
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×D11C22×C411yescharacteristic
178C2×C4×D11C2×D411yescharacteristic
179C2×C4×D11C2×D411yescharacteristic
180C2×C4×D11C2×D411yescharacteristic
181C2×C4×D11C2×D411yescharacteristic
182C11×M16—42no—
183C2×C8×C11—22no—
184C2×C8×C11—22no—
185C11×C4⋊C4—21no—
186C11×C4⋊C4—22no—
187C11×C4⋊C4—22no—
188C11×C4⋊C4C22×C412yes—
189C42×C11—22no—
190C42×C11—22no—
191C42×C11C22×C411yescharacteristic
192C42×C11C2×D411yescharacteristic
193C42×C11C2×D411yescharacteristic
194C42×C11C2411yescharacteristic
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—
204(C2×D11)⋊C4—22no—
205C4⋊Dic11—22no—
206C4⋊Dic11—22no—
207C4⋊Dic11—21no—
208C4⋊Dic11C22×C412yes—
209Dic11⋊C4—22no—
210Dic11⋊C4—22no—
211Dic11⋊C4—22no—
212Dic11⋊C4—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#1487D1111yescharacteristic, complemented
237#1486—111no—
238#1486—111no—
239#1483—114no—
240C23×C11C2×C22⋊C411yescharacteristic
241C22×D11—22no—
242C22×D11—22no—
243C22×D11—22no—
244C22×D11—41no—
245C22×D11—42no—
246C22×D11—42no—
247C22×D11—42no—
248C22×D11C2×C22⋊C411yescharacteristic
249C22×D11C2×C22⋊C411yescharacteristic
250Q8×C11—24no—
251Q8×C11—42no—
252C2×C4×C11—22no—
253C2×C4×C11—22no—
254C2×C4×C11—22no—
255C2×C4×C11—41no—
256C2×C4×C11—42no—
257C2×C4×C11—42no—
258C2×C4×C11C2×C22⋊C411yescharacteristic
259C2×C4×C11C2×C22⋊C411yescharacteristic
260C2×C4×C11C2×C22⋊C411yescharacteristic
261C2×C4×C11AGL(1,ℤ/8)12yes—
262C2×C4×C11#13712yes—
263C2×C4×C11C23×C411yescharacteristic
264C2×C4×C11C22×D411yescharacteristic
265C2×C4×C11C22×D411yescharacteristic
266C2×Dic11—22no—
267C2×Dic11—22no—
268C2×Dic11—41no—
269C2×Dic11—41no—
270C2×Dic11—42no—
271C2×Dic11C2×C22⋊C411yescharacteristic
272C2×Dic11C2×C22⋊C411yescharacteristic
273C2×Dic11C2×C22⋊C411yescharacteristic
274C2×Dic11C2×C22⋊C411yescharacteristic
275C2×Dic11C2×C22⋊C411yescharacteristic
276C2×Dic11C2×C22⋊C411yescharacteristic
277D44—24no—
278D44—42no—
279D44—44no—
280D44—44no—
281C4×D11—22no—
282C4×D11—22no—
283C4×D11—22no—
284C4×D11—22no—
285C4×D11—21no—
286C4×D11—21no—
287C4×D11—21no—
288C4×D11—21no—
289C4×D11—22no—
290C4×D11—22no—
291C4×D11—41no—
292C4×D11—41no—
293C4×D11—41no—
294C4×D11—41no—
295C4×D11—42no—
296C4×D11—42no—
297C4×D11—44no—
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×Q8C2×D1111yescharacteristic
318C2×C4×D4—111no—
319C2×C4×D4—221no—
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⋊C8C2×D1114yescomplemented
339D4⋊C8—114no—
340D4⋊C8—114no—
341C22×C11—21no—
342C22×C11—21no—
343C22×C11#41712yes—
344C22×C11C22×C22⋊C411yescharacteristic
345C2×D11—21no—
346C2×D11—21no—
347C2×D11—21no—
348C2×D11—21no—
349C2×D11—21no—
350C2×D11—44no—
351C2×D11—42no—
352C2×D11—42no—
353C2×D11—42no—
354C2×D11—84no—
355C2×D11#42112yes—
356C4×C11—21no—
357C4×C11—21no—
358C4×C11—21no—
359C4×C11—42no—
360C4×C11—42no—
361C4×C11#41712yes—
362C4×C11#56812yes—
363C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
364C4×C11C2×#13711yescharacteristic
365Dic11—21no—
366Dic11—21no—
367Dic11—21no—
368Dic11—21no—
369Dic11—21no—
370Dic11—21no—
371Dic11—42no—
372C22×Q8C4×D1111yescharacteristic
373C22×D4—111no—
374C22×D4—221no—
375C23×C4—111no—
376C23×C4—111no—
377C23×C4—111no—
378C23×C4—221no—
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—21no—
410C4×Q8—21no—
411C4×Q8C4×D1112yes—
412C4×Q8C22×D1112yes—
413C4×D4—112no—
414C4×D4—112no—
415C4×D4—222no—
416C4×D4—222no—
417C4×D4—222no—
418C4×D4—222no—
419C4×D4—221no—
420C4×D4—221no—
421#117—222no—
422#117—222no—
423#117—222no—
424#117—222no—
425C2×C4⋊C4—21no—
426C2×C4⋊C4—111no—
427C2×C4⋊C4—221no—
428C2×C4⋊C4—221no—
429C2×C4⋊C4—221no—
430C2×C4⋊C4C4×D1111yescharacteristic
431C2×C22⋊C4—221no—
432C2×C22⋊C4—221no—
433C2×C22⋊C4—221no—
434C2×C22⋊C4—221no—
435C2×C22⋊C4—221no—
436C2×C42—21no—
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—111no—
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#287911yescharacteristic
466C2×C11C2×#41711yescharacteristic
467C2×C11C2×#42111yescharacteristic
468D11—22no—
469D11—41no—
470D11—82no—
471C24—111no—
472C24—221no—
473C2×Q8—21no—
474C2×Q8—42no—
475C2×Q8C2×C4×D1112yes—
476C2×D4—112no—
477C2×D4—222no—
478C2×D4—222no—
479C2×D4—221no—
480C2×D4—442no—
481C2×D4—444no—
482C22×C4—21no—
483C22×C4—21no—
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—111no—
496C22×C4—111no—
497C22×C4—111no—
498C22×C4—111no—
499C22×C4—222no—
500C22×C4—222no—
501C22×C4—221no—
502C22×C4—222no—
503C22×C4—222no—
504C22×C4—442no—
505C22×C4—442no—
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—22no—
521C4⋊C4—21no—
522C4⋊C4—22no—
523C4⋊C4—112no—
524C4⋊C4—222no—
525C4⋊C4—222no—
526C4⋊C4—222no—
527C4⋊C4—222no—
528C4⋊C4—222no—
529C4⋊C4—222no—
530C4⋊C4—221no—
531C4⋊C4C2×C4×D1112yes—
532C22⋊C4—222no—
533C22⋊C4—222no—
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—22no—
543C42—22no—
544C42—111no—
545C42—111no—
546C42—111no—
547C42—111no—
548C42—111no—
549C42—111no—
550C42—111no—
551C42—111no—
552C42—111no—
553C42—111no—
554C42—111no—
555C42—111no—
556C42C2×C4×D1111yescharacteristic
557C42D4×D1111yescharacteristic
558C42D4×D1111yescharacteristic
559C42C23×D1111yescharacteristic
560C11#1749211yescharacteristic, complemented, Sylow
561C23—111no—
562C23—111no—
563C23—222no—
564C23—222no—
565C23—222no—
566C23—441no—
567C23—442no—
568C23—442no—
569C23—442no—
570C23C22⋊C4×D1111yescharacteristic
571Q8—24no—
572Q8—42no—
573D4—224no—
574D4—442no—
575D4—444no—
576D4—444no—
577C2×C4—22no—
578C2×C4—22no—
579C2×C4—22no—
580C2×C4—41no—
581C2×C4—42no—
582C2×C4—42no—
583C2×C4—111no—
584C2×C4—111no—
585C2×C4—111no—
586C2×C4—111no—
587C2×C4—111no—
588C2×C4—111no—
589C2×C4—222no—
590C2×C4—222no—
591C2×C4—222no—
592C2×C4—222no—
593C2×C4—222no—
594C2×C4—221no—
595C2×C4—221no—
596C2×C4—221no—
597C2×C4—221no—
598C2×C4—222no—
599C2×C4—222no—
600C2×C4—222no—
601C2×C4—441no—
602C2×C4—441no—
603C2×C4—441no—
604C2×C4—441no—
605C2×C4—441no—
606C2×C4—441no—
607C2×C4—442no—
608C2×C4—442no—
609C2×C4—442no—
610C2×C4—444no—
611C2×C4C22⋊C4×D1111yescharacteristic
612C2×C4C22⋊C4×D1111yescharacteristic
613C2×C4C22⋊C4×D1111yescharacteristic
614C2×C4#6696712yes—
615C2×C4#6697112yes—
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—112no—
626C22—221no—
627C22—221no—
628C22—221no—
629C22—221no—
630C22—221no—
631C22—444no—
632C22—442no—
633C22—442no—
634C22—442no—
635C22—884no—
636C22#1062241612yes—
637C22C2×C22⋊C4×D1111yescharacteristic
638C4—21no—
639C4—21no—
640C4—21no—
641C4—42no—
642C4—42no—
643C4—221no—
644C4—221no—
645C4—221no—
646C4—221no—
647C4—221no—
648C4—221no—
649C4—442no—
650C4#1062241612yes—
651C4#1062327612yes—
652C4C2×#6696711yescharacteristic
653C4C2×#6697111yescharacteristic
654C2—22no—
655C2—222no—
656C2—441no—
657C2—882no—
658C2#1307705911yescharacteristic
659C2C2×#1062241611yescharacteristic
660C2D11×#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#17492
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. #13077244C2semidirect
3. D11×#423C2semidirect
4. #13067080C2semidirect
5. #13067045C2semidirect
6. #13067042C2semidirect
7. #13067040C2semidirect
8. #13067028C2semidirect
9. C11×#1487C2semidirect
37. #10622450C22semidirect
40. D11×C4⋊C8C22semidirect
43. C4×#4313C22semidirect
44. #10622298C22semidirect
45. C11×Q8⋊C8C22semidirect
46. Q8⋊(C11⋊C8)C22semidirect
47. #10622121C22semidirect
48. #10622097C22semidirect
236. #1487D11semidirect
338. Q8⋊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×#106231112
#130772442
D11×#4232
#130670802
#130670452
#130670422
#130670402
#130670282
C11×#14872
#1749211