Finite Group Databasebeta

← #14720480

Subgroups — #14720480

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×#10623088C211yesmaximal, characteristic
2#13077248C211yesmaximal, characteristic, complemented
3D11×#431C211yesmaximal, characteristic, complemented
4#13067073C214yesmaximal, complemented
5#13067046C211yesmaximal, characteristic, complemented
6#13067044C211yesmaximal, characteristic, complemented
7#13067041C211yesmaximal, characteristic, complemented
8#13067021C214yesmaximal, complemented
9C11×#1486C211yesmaximal, characteristic, complemented
10C2×C4×D4×C11C2211yescharacteristic
11C2×#66991C411yescharacteristic
12C2×#66989C411yescharacteristic
13C2×C4×C22⋊D11—21no—
14C2×#66979—21no—
15#10623088—21no—
16#10623088—21no—
17#10623088—21no—
18#10623088—21no—
19#10623088C412yes—
20#10623088C412yes—
21#10623088C2212yes—
22#10623088C2212yes—
23C2×#66950C411yescharacteristic
24C2×#66943C411yescharacteristic
25C2×#66936—21no—
26C2×#66932—21no—
27C2×C42×D11C2211yescharacteristic
28C2×C4×Dic22C2211yescharacteristic
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×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—
94C2×C8×D11—22no—
95#66950—21no—
96#66950—21no—
97#66950C2×C412yes—
98#66950C2×C412yes—
99#66943—21no—
100#66943—21no—
101#66943C2×C412yes—
102#66943C2×C412yes—
103#66936—22no—
104#66936—22no—
105#66936—22no—
106#66936—22no—
107#66932—22no—
108#66932—22no—
109#66932—22no—
110#66932—22no—
111C42×D11C2×C411yescharacteristic
112C42×D11C2×C411yescharacteristic
113C42×D11D411yescharacteristic
114C42×D11D411yescharacteristic
115C42×D11D411yescharacteristic
116C42×D11D411yescharacteristic
117C42×D11C2311yescharacteristic
118C42×D11C2311yescharacteristic
119C4×Dic22—21no—
120C4×Dic22—21no—
121C4×Dic22C2×C412yes—
122C4×Dic22C2312yes—
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
141C24×C11—21no—
142C23×D11C22⋊C411yescharacteristic
143C2×D4×C11—21no—
144C2×D4×C11—42no—
145C2×D4×C11C22×C412yes—
146C22×C4×C11—21no—
147C22×C4×C11—22no—
148C22×C4×C11—22no—
149C22×C4×C11—42no—
150C22×C4×C11—42no—
151C22×C4×C11C22×C411yescharacteristic
152C22×C4×C11C2×D411yescharacteristic
153C22×C4×C11C2×D411yescharacteristic
154C2×C22⋊D11—22no—
155C2×C22⋊D11—22no—
156C2×C22⋊D11—44no—
157C22×Dic11—21no—
158C22×Dic11—21no—
159C22×Dic11C22⋊C411yescharacteristic
160C22×Dic11C22⋊C411yescharacteristic
161C22×Dic11C22⋊C411yescharacteristic
162C2×C4×D11—22no—
163C2×C4×D11—22no—
164C2×C4×D11—42no—
165C2×C4×D11—42no—
166C2×C4×D11C22⋊C411yescharacteristic
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×D11C2×D411yescharacteristic
175C2×C4×D11C2×D411yescharacteristic
176C2×C4×D11C2×D411yescharacteristic
177C2×C4×D11C2×D411yescharacteristic
178C2×Dic22—21no—
179C2×Dic22—42no—
180C2×Dic22C22×C412yes—
181C11×M16—42no—
182C2×C8×C11—22no—
183C2×C8×C11—22no—
184C11×C4⋊C4—21no—
185C11×C4⋊C4C22×C412yes—
186C11×C22⋊C4—22no—
187C11×C22⋊C4—22no—
188C42×C11C22×C411yescharacteristic
189C42×C11C2×D411yescharacteristic
190C42×C11C2×D411yescharacteristic
191C42×C11C2411yescharacteristic
192C22⋊Dic11—22no—
193C22⋊Dic11—22no—
194C22⋊Dic11—22no—
195C22⋊Dic11—22no—
196C22⋊Dic11—22no—
197C22⋊Dic11—22no—
198(C2×D11)⋊C4—22no—
199(C2×D11)⋊C4—22no—
200C4⋊Dic11—22no—
201C4⋊Dic11—22no—
202C4⋊Dic11—22no—
203C4⋊Dic11—22no—
204C4⋊Dic11—21no—
205C4⋊Dic11C22×C412yes—
206Dic11⋊C4—22no—
207Dic11⋊C4—22no—
208Dic11⋊C4—22no—
209Dic11⋊C4—22no—
210C4×Dic11—22no—
211C4×Dic11—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#1487—111no—
234#1486—111no—
235#1486D1111yescharacteristic, complemented
236#1482—114no—
237C23×C11—22no—
238C23×C11—42no—
239C23×C11—42no—
240C23×C11—42no—
241C23×C11C2×C22⋊C411yescharacteristic
242C22×D11—22no—
243C22×D11—22no—
244C22×D11—41no—
245C22×D11C2×C22⋊C411yescharacteristic
246C22×D11C2×C22⋊C411yescharacteristic
247D4×C11—24no—
248D4×C11—42no—
249C2×C4×C11—22no—
250C2×C4×C11—22no—
251C2×C4×C11—41no—
252C2×C4×C11—42no—
253C2×C4×C11—42no—
254C2×C4×C11—42no—
255C2×C4×C11—44no—
256C2×C4×C11C2×C22⋊C411yescharacteristic
257C2×C4×C11C2×C22⋊C411yescharacteristic
258C2×C4×C11C2×C22⋊C411yescharacteristic
259C2×C4×C11#13512yes—
260C2×C4×C11#13512yes—
261C2×C4×C11C23×C411yescharacteristic
262C2×C4×C11C22×D411yescharacteristic
263C2×C4×C11C22×D411yescharacteristic
264C22⋊D11—44no—
265C22⋊D11—44no—
266C2×Dic11—22no—
267C2×Dic11—22no—
268C2×Dic11—22no—
269C2×Dic11—41no—
270C2×Dic11—41no—
271C2×Dic11—42no—
272C2×Dic11—42no—
273C2×Dic11C2×C22⋊C411yescharacteristic
274C2×Dic11C2×C22⋊C411yescharacteristic
275C2×Dic11C2×C22⋊C411yescharacteristic
276C2×Dic11C2×C22⋊C411yescharacteristic
277C2×Dic11C2×C22⋊C411yescharacteristic
278C2×Dic11C2×C22⋊C411yescharacteristic
279C4×D11—22no—
280C4×D11—22no—
281C4×D11—22no—
282C4×D11—22no—
283C4×D11—21no—
284C4×D11—21no—
285C4×D11—21no—
286C4×D11—21no—
287C4×D11—22no—
288C4×D11—22no—
289C4×D11—41no—
290C4×D11—41no—
291C4×D11—41no—
292C4×D11—41no—
293Dic22—24no—
294Dic22—42no—
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×Q8—111no—
314C2×C4×D4—221no—
315C2×C4×D4C2×D1111yescharacteristic
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⋊C8—114no—
336D4⋊C8—114no—
337D4⋊C8C2×D1114yescomplemented
338C22×C11—21no—
339C22×C11—21no—
340C22×C11—42no—
341C22×C11—42no—
342C22×C11—42no—
343C22×C11—84no—
344C22×C11#41612yes—
345C22×C11C22×C22⋊C411yescharacteristic
346C2×D11—21no—
347C2×D11—21no—
348C2×D11—21no—
349C2×D11—21no—
350C2×D11—21no—
351C2×D11—44no—
352C2×D11#42112yes—
353C4×C11—21no—
354C4×C11—21no—
355C4×C11—21no—
356C4×C11—42no—
357C4×C11#41612yes—
358C4×C11#56812yes—
359C4×C11C2×#13511yescharacteristic
360C4×C11C2×#13511yescharacteristic
361Dic11—21no—
362Dic11—21no—
363Dic11—21no—
364Dic11—21no—
365Dic11—21no—
366Dic11—21no—
367Dic11—42no—
368Dic11—42no—
369C22×Q8—111no—
370C22×D4—221no—
371C22×D4C4×D1111yescharacteristic
372C23×C4—21no—
373C23×C4—111no—
374C23×C4—111no—
375C23×C4—111no—
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—112no—
404C4×Q8—112no—
405C4×Q8—221no—
406C4×Q8—221no—
407C4×D4—21no—
408C4×D4—21no—
409C4×D4—222no—
410C4×D4—222no—
411C4×D4—222no—
412C4×D4—222no—
413C4×D4C4×D1112yes—
414C4×D4C22×D1112yes—
415#117—222no—
416#117—222no—
417#117—222no—
418#117—222no—
419C2×C4⋊C4—111no—
420C2×C4⋊C4—221no—
421C2×C4⋊C4—221no—
422C2×C4⋊C4—221no—
423C2×C4⋊C4—221no—
424C2×C4⋊C4C4×D1111yescharacteristic
425C2×C22⋊C4—21no—
426C2×C22⋊C4—221no—
427C2×C22⋊C4—221no—
428C2×C22⋊C4—221no—
429C2×C22⋊C4—221no—
430C2×C42—111no—
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—221no—
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—82no—
462C2×C11#287911yescharacteristic
463C2×C11C2×#41611yescharacteristic
464C2×C11C2×#42111yescharacteristic
465D11—22no—
466D11—41no—
467C24—21no—
468C24—111no—
469C2×Q8—112no—
470C2×Q8—221no—
471C2×Q8—442no—
472C2×D4—21no—
473C2×D4—42no—
474C2×D4—222no—
475C2×D4—222no—
476C2×D4—444no—
477C2×D4C2×C4×D1112yes—
478C22×C4—21no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—42no—
482C22×C4—42no—
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—111no—
496C22×C4—111no—
497C22×C4—111no—
498C22×C4—222no—
499C22×C4—222no—
500C22×C4—221no—
501C22×C4—221no—
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—21no—
515C4⋊C4—112no—
516C4⋊C4—222no—
517C4⋊C4—222no—
518C4⋊C4—222no—
519C4⋊C4—222no—
520C4⋊C4—222no—
521C4⋊C4—222no—
522C4⋊C4—221no—
523C4⋊C4—222no—
524C4⋊C4—222no—
525C4⋊C4C2×C4×D1112yes—
526C22⋊C4—22no—
527C22⋊C4—22no—
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—111no—
537C42—111no—
538C42—111no—
539C42—111no—
540C42—111no—
541C42—111no—
542C42—111no—
543C42—111no—
544C42—111no—
545C42—111no—
546C42—111no—
547C42—111no—
548C42—222no—
549C42—222no—
550C42C2×C4×D1111yescharacteristic
551C42D4×D1111yescharacteristic
552C42D4×D1111yescharacteristic
553C42C23×D1111yescharacteristic
554C11#1748711yescharacteristic, complemented, Sylow
555C23—22no—
556C23—42no—
557C23—42no—
558C23—42no—
559C23—111no—
560C23—111no—
561C23—222no—
562C23—222no—
563C23—441no—
564C23C22⋊C4×D1111yescharacteristic
565Q8—224no—
566Q8—442no—
567D4—24no—
568D4—42no—
569D4—444no—
570D4—444no—
571C2×C4—22no—
572C2×C4—22no—
573C2×C4—41no—
574C2×C4—42no—
575C2×C4—42no—
576C2×C4—42no—
577C2×C4—44no—
578C2×C4—111no—
579C2×C4—111no—
580C2×C4—111no—
581C2×C4—111no—
582C2×C4—111no—
583C2×C4—111no—
584C2×C4—222no—
585C2×C4—222no—
586C2×C4—222no—
587C2×C4—222no—
588C2×C4—222no—
589C2×C4—221no—
590C2×C4—221no—
591C2×C4—221no—
592C2×C4—221no—
593C2×C4—222no—
594C2×C4—222no—
595C2×C4—222no—
596C2×C4—222no—
597C2×C4—441no—
598C2×C4—441no—
599C2×C4—441no—
600C2×C4—441no—
601C2×C4—441no—
602C2×C4—441no—
603C2×C4—442no—
604C2×C4—442no—
605C2×C4C22⋊C4×D1111yescharacteristic
606C2×C4C22⋊C4×D1111yescharacteristic
607C2×C4C22⋊C4×D1111yescharacteristic
608C2×C4#6696512yes—
609C2×C4#6696912yes—
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—42no—
620C22—42no—
621C22—42no—
622C22—84no—
623C22—112no—
624C22—221no—
625C22—221no—
626C22—221no—
627C22—221no—
628C22—221no—
629C22—444no—
630C22#1062238512yes—
631C22C2×C22⋊C4×D1111yescharacteristic
632C4—21no—
633C4—21no—
634C4—21no—
635C4—42no—
636C4—221no—
637C4—221no—
638C4—221no—
639C4—221no—
640C4—221no—
641C4—221no—
642C4—442no—
643C4—442no—
644C4#1062238512yes—
645C4#1062327612yes—
646C4C2×#6696511yescharacteristic
647C4C2×#6696911yescharacteristic
648C2—22no—
649C2—82no—
650C2—222no—
651C2—441no—
652C2#1307705911yescharacteristic
653C2C2×#1062238511yescharacteristic
654C2D11×#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#17487
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. #13077248C2semidirect
3. D11×#431C2semidirect
4. #13067073C2semidirect
5. #13067046C2semidirect
6. #13067044C2semidirect
7. #13067041C2semidirect
8. #13067021C2semidirect
9. C11×#1486C2semidirect
36. #10622448C22semidirect
39. #10622446C22semidirect
43. #10622298C22semidirect
44. C4×C8×D11C22semidirect
45. C11×D4⋊C8C22semidirect
46. D4⋊(C11⋊C8)C22semidirect
47. #10622122C22semidirect
48. #10622094C22semidirect
235. #1486D11semidirect
337. D4⋊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×#106230882
#130772482
D11×#4312
#130670732
#130670462
#130670442
#130670412
#130670212
C11×#14862
#1748711