Finite Group Databasebeta

← #14720681

Subgroups — #14720681

Order 2816.

1004 conjugacy classes of subgroups.

The subgroup lattice has 642 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13077583C211yesmaximal, characteristic, complemented
2#13077184C211yesmaximal, characteristic, complemented
3#13067081C212yesmaximal, complemented
4#13067071C211yesmaximal, characteristic, complemented
5#13067055C212yesmaximal, complemented
6#13067041C211yesmaximal, characteristic, complemented
7#13067029C212yesmaximal, complemented
8#13067019C211yesmaximal, characteristic, complemented
9#13067003C212yesmaximal, complemented
10C2×D4⋊(C11⋊C8)C211yesmaximal, characteristic, complemented
11C11×#3475C211yesmaximal, characteristic
12C11×#556C411yescharacteristic
13C11×#555C411yescharacteristic
14C11×#554C411yescharacteristic
15C11×#553—21no—
16C11×#552—21no—
17C11×#552C412yes—
18C11×#551—22no—
19C11×#547C411yescharacteristic
20C11×#546C412yes—
21C11×#533C2211yescharacteristic
22C11×#529—22no—
23C11×#529C2212yes—
24C11×#525—21no—
25C4×C11×#41C2212yes—
26C4×C11×#41C2211yescharacteristic
27C2×C4×D4×C11C2211yescharacteristic
28C2×C11×#117—21no—
29C2×#67001—21no—
30#10622637—21no—
31#10622625—21no—
32#10622624—22no—
33#10622612—22no—
34#10622612—21no—
35#10622538C2211yescharacteristic
36#10622538C2212yescomplemented
37#10622537C2211yescharacteristic
38#10622537C2212yescomplemented
39C2×C4⋊(C11⋊C8)C2211yescharacteristic
40C2×C4⋊(C11⋊C8)C2212yescomplemented
41C4×#4318C2212yescomplemented
42C2×C4×C11⋊C8C2211yescharacteristic
43Q8⋊(C11⋊C8)C2212yescomplemented
44Q8⋊(C11⋊C8)C2212yescomplemented
45Q8⋊(C11⋊C8)C2212yescomplemented
46Q8⋊(C11⋊C8)C2212yescomplemented
47D4⋊(C11⋊C8)C2211yescharacteristic
48D4⋊(C11⋊C8)C2212yes—
49D4⋊(C11⋊C8)C2212yes—
50D4⋊(C11⋊C8)C2211yescharacteristic
51D4⋊(C11⋊C8)C2211yescharacteristic
52D4⋊(C11⋊C8)C2211yescharacteristic
53C2×C11×#41C2×C412yes—
54C2×C11×#41D411yescharacteristic
55C22×D4×C11C2×C411yescharacteristic
56C23×C4×C11—21no—
57C11×C4⋊Q8C2×C411yescharacteristic
58C11×C4⋊Q8C2×C411yescharacteristic
59C11×#126—22no—
60C11×#126—22no—
61C11×#126—22no—
62C11×#125—22no—
63C11×#125—21no—
64C11×#125C2×C412yes—
65C11×#124—22no—
66C11×#124C2×C412yes—
67C11×#123—22no—
68C11×#123—22no—
69C11×#123—22no—
70C11×#123—22no—
71C11×C22⋊Q8—21no—
72C11×C22⋊Q8—21no—
73C11×C22⋊Q8—21no—
74C11×C22⋊Q8—22no—
75C11×C22⋊Q8C2×C412yes—
76C11×C22⋊Q8C2×C412yes—
77C11×#121—21no—
78C11×#121—21no—
79C11×#121—22no—
80C11×#121C2×C412yes—
81C11×#120—22no—
82C4×Q8×C11—21no—
83C4×Q8×C11C2×C412yes—
84C4×Q8×C11C2×C411yescharacteristic
85C4×Q8×C11D411yescharacteristic
86C4×Q8×C11C2312yes—
87C4×D4×C11—22no—
88C4×D4×C11—22no—
89C4×D4×C11—22no—
90C4×D4×C11—21no—
91C4×D4×C11—21no—
92C4×D4×C11C2×C411yescharacteristic
93C4×D4×C11C2×C411yescharacteristic
94C4×D4×C11C2×C412yes—
95C4×D4×C11C2×C412yes—
96C4×D4×C11C2×C411yescharacteristic
97C4×D4×C11D412yes—
98C4×D4×C11D411yescharacteristic
99C4×D4×C11C2311yescharacteristic
100C4×D4×C11C2311yescharacteristic
101C11×#117—21no—
102C11×#117—21no—
103C11×#117—21no—
104C11×#117—22no—
105C11×#117—22no—
106C11×#117—22no—
107C11×#117C2×C412yes—
108C11×#117D411yescharacteristic
109C11×#117D412yes—
110C2×C11×C4⋊C4—21no—
111C2×C11×C4⋊C4—21no—
112C2×C11×C4⋊C4C2×C411yescharacteristic
113C2×C11×C22⋊C4—21no—
114C2×C11×C22⋊C4—22no—
115C2×C42×C11—22no—
116C2×C42×C11C2311yescharacteristic
117C2×C42×C11C2312yes—
118#67001—44no—
119C2×#4318—22no—
120C2×#4318—21no—
121C2×#4318—22no—
122C22×C11⋊C8—21no—
123C22×C11⋊C8—21no—
124C22×C11⋊C8—22no—
125C22⋊(C11⋊C8)—21no—
126C22⋊(C11⋊C8)—22no—
127C4⋊(C11⋊C8)—21no—
128C4⋊(C11⋊C8)—22no—
129C4⋊(C11⋊C8)—21no—
130C4⋊(C11⋊C8)—22no—
131C4⋊(C11⋊C8)—21no—
132C4⋊(C11⋊C8)—22no—
133C4⋊(C11⋊C8)C2311yescharacteristic
134C4⋊(C11⋊C8)C2311yescharacteristic
135C4⋊(C11⋊C8)C2312yes—
136#66867—22no—
137C4×C11⋊C8—21no—
138C4×C11⋊C8C2311yescharacteristic
139C4×C11⋊C8C2311yescharacteristic
140C4×C11⋊C8C2312yes—
141#17512—111nomaximal, Sylow
142C24×C11—21no—
143C11×#41—22no—
144C11×#41—22no—
145C11×#41—24no—
146C11×#41—42no—
147C2×Q8×C11—21no—
148C2×Q8×C11C22⋊C411yescharacteristic
149C2×Q8×C11C22×C412yes—
150C2×D4×C11—22no—
151C2×D4×C11—22no—
152C2×D4×C11—22no—
153C2×D4×C11—21no—
154C2×D4×C11—41no—
155C2×D4×C11C22⋊C412yes—
156C2×D4×C11C22⋊C411yescharacteristic
157C2×D4×C11C22×C411yescharacteristic
158C2×D4×C11C22×C411yescharacteristic
159C22×C4×C11—21no—
160C22×C4×C11—22no—
161C22×C4×C11—21no—
162C22×C4×C11—21no—
163C22×C4×C11—21no—
164C22×C4×C11—21no—
165C22×C4×C11—22no—
166C22×C4×C11—42no—
167C22×C4×C11—42no—
168C22×C4×C11C22×C411yescharacteristic
169C22×C4×C11C22×C412yes—
170C22×C4×C11C2×D412yes—
171C22×C4×C11C2×D411yescharacteristic
172C22×C4×C11C2×D412yes—
173C22×C4×C11C2×D411yescharacteristic
174C11×C4⋊C4—21no—
175C11×C4⋊C4—21no—
176C11×C4⋊C4—22no—
177C11×C4⋊C4—22no—
178C11×C4⋊C4—21no—
179C11×C4⋊C4—22no—
180C11×C4⋊C4—22no—
181C11×C4⋊C4—22no—
182C11×C4⋊C4—21no—
183C11×C4⋊C4—22no—
184C11×C4⋊C4C22⋊C411yescharacteristic
185C11×C4⋊C4C22⋊C411yescharacteristic
186C11×C4⋊C4C22⋊C412yes—
187C11×C4⋊C4C22⋊C412yes—
188C11×C4⋊C4C22×C411yescharacteristic
189C11×C4⋊C4C22×C411yescharacteristic
190C11×C4⋊C4C22×C412yes—
191C11×C22⋊C4—22no—
192C11×C22⋊C4—22no—
193C11×C22⋊C4—22no—
194C11×C22⋊C4—22no—
195C11×C22⋊C4—22no—
196C11×C22⋊C4—21no—
197C11×C22⋊C4—21no—
198C11×C22⋊C4—22no—
199C11×C22⋊C4—22no—
200C11×C22⋊C4—21no—
201C11×C22⋊C4—21no—
202C11×C22⋊C4C22⋊C412yes—
203C11×C22⋊C4C22⋊C412yes—
204C11×C22⋊C4C22⋊C412yes—
205C42×C11—22no—
206C42×C11—22no—
207C42×C11—22no—
208C42×C11C22×C411yescharacteristic
209C42×C11C22×C412yes—
210C42×C11C2×D411yescharacteristic
211C42×C11C2×D412yes—
212C42×C11C2×D412yes—
213C42×C11C2×D411yescharacteristic
214C42×C11C2411yescharacteristic
215#4318—44no—
216#4318—44no—
217#4318—42no—
218C2×C11⋊C8—21no—
219C2×C11⋊C8—21no—
220C2×C11⋊C8—22no—
221C2×C11⋊C8—21no—
222C2×C11⋊C8—21no—
223C2×C11⋊C8—22no—
224C2×C11⋊C8—44no—
225C2×C11⋊C8—42no—
226C2×C11⋊C8—42no—
227#3475D1111yescharacteristic
228#2965—111no—
229#2906—111no—
230#1495—112no—
231#1493—111no—
232#1489—112no—
233#1486—111no—
234#1483—112no—
235#1481—111no—
236#1477—112no—
237C2×D4⋊C8—111no—
238C23×C11—21no—
239C23×C11—21no—
240C23×C11—42no—
241C23×C11—42no—
242C23×C11—81no—
243C23×C11C2×C22⋊C412yes—
244C23×C11C2×C22⋊C411yescharacteristic
245Q8×C11—22no—
246Q8×C11—22no—
247Q8×C11—22no—
248Q8×C11—81no—
249D4×C11—24no—
250D4×C11—21no—
251D4×C11—21no—
252D4×C11—21no—
253D4×C11—22no—
254D4×C11—42no—
255D4×C11—44no—
256D4×C11—82no—
257D4×C11#13112yescomplemented
258C2×C4×C11—21no—
259C2×C4×C11—22no—
260C2×C4×C11—21no—
261C2×C4×C11—22no—
262C2×C4×C11—22no—
263C2×C4×C11—22no—
264C2×C4×C11—21no—
265C2×C4×C11—22no—
266C2×C4×C11—22no—
267C2×C4×C11—21no—
268C2×C4×C11—41no—
269C2×C4×C11—42no—
270C2×C4×C11—44no—
271C2×C4×C11—42no—
272C2×C4×C11—41no—
273C2×C4×C11—41no—
274C2×C4×C11—41no—
275C2×C4×C11—41no—
276C2×C4×C11—42no—
277C2×C4×C11—42no—
278C2×C4×C11—82no—
279C2×C4×C11C2×C22⋊C412yes—
280C2×C4×C11C2×C22⋊C412yes—
281C2×C4×C11C2×C22⋊C411yescharacteristic
282C2×C4×C11C2×C22⋊C412yes—
283C2×C4×C11C2×C22⋊C411yescharacteristic
284C2×C4×C11C2×C22⋊C411yescharacteristic
285C2×C4×C11AGL(1,ℤ/8)12yes—
286C2×C4×C11#13712yes—
287C2×C4×C11C23×C411yescharacteristic
288C2×C4×C11C22×D411yescharacteristic
289C2×C4×C11C22×D411yescharacteristic
290C11⋊C8—22no—
291C11⋊C8—41no—
292C11⋊C8—42no—
293C11⋊C8—41no—
294C11⋊C8—42no—
295C11⋊C8—41no—
296C2×#131—221no—
297#556Dic1111yescharacteristic
298#555Dic1111yescharacteristic
299#554Dic1111yescharacteristic
300#553—21no—
301#552—21no—
302#552Dic1112yes—
303#551—22no—
304#547Dic1111yescharacteristic
305#546Dic1112yes—
306#533C2×D1111yescharacteristic
307#529—22no—
308#529C2×D1112yes—
309#525—21no—
310C4×#41C2×D1112yes—
311C4×#41C2×D1111yescharacteristic
312C2×C4×D4C2×D1111yescharacteristic
313C2×#117—21no—
314#446—221no—
315#436—221no—
316#435—222no—
317#431—111no—
318#431—112no—
319#424—221no—
320#424—222no—
321#423—111no—
322#423—112no—
323C2×C4⋊C8—111no—
324C2×C4⋊C8—112no—
325C4×M16—112no—
326C2×C4×C8—111no—
327Q8⋊C8—112no—
328Q8⋊C8—112no—
329Q8⋊C8—112no—
330Q8⋊C8—112no—
331D4⋊C8—111no—
332D4⋊C8—111no—
333D4⋊C8—111no—
334D4⋊C8—111no—
335D4⋊C8—112no—
336D4⋊C8—112no—
337C22×C11—21no—
338C22×C11—21no—
339C22×C11—22no—
340C22×C11—22no—
341C22×C11—22no—
342C22×C11—22no—
343C22×C11—41no—
344C22×C11—41no—
345C22×C11—41no—
346C22×C11—41no—
347C22×C11—41no—
348C22×C11—84no—
349C22×C11#41712yes—
350C22×C11C22×C22⋊C411yescharacteristic
351C4×C11—22no—
352C4×C11—21no—
353C4×C11—22no—
354C4×C11—21no—
355C4×C11—22no—
356C4×C11—21no—
357C4×C11—42no—
358C4×C11—41no—
359C4×C11—41no—
360C4×C11—42no—
361C4×C11#41712yes—
362C4×C11C2×#13111yescharacteristic
363C4×C11#56811yescharacteristic
364C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
365C4×C11C2×#13711yescharacteristic
366C2×#41C2×Dic1112yes—
367C2×#41C22⋊D1111yescharacteristic
368C22×D4C2×Dic1111yescharacteristic
369C23×C4—21no—
370#131—444no—
371C2×M16—222no—
372C2×M16—221no—
373C2×M16—222no—
374C22×C8—222no—
375C22×C8—221no—
376C22×C8—221no—
377C4⋊Q8C2×Dic1111yescharacteristic
378C4⋊Q8C2×Dic1111yescharacteristic
379#126—22no—
380#126—22no—
381#126—22no—
382#125—22no—
383#125—21no—
384#125C2×Dic1112yes—
385#124—22no—
386#124C2×Dic1112yes—
387#123—22no—
388#123—22no—
389#123—22no—
390#123—22no—
391C22⋊Q8—21no—
392C22⋊Q8—21no—
393C22⋊Q8—21no—
394C22⋊Q8—22no—
395C22⋊Q8C2×Dic1112yes—
396C22⋊Q8C2×Dic1112yes—
397#121—21no—
398#121—21no—
399#121—22no—
400#121C2×Dic1112yes—
401#120—22no—
402C4×Q8—21no—
403C4×Q8C2×Dic1112yes—
404C4×Q8C2×Dic1111yescharacteristic
405C4×Q8C22⋊D1111yescharacteristic
406C4×Q8C22×D1112yes—
407C4×D4—22no—
408C4×D4—22no—
409C4×D4—22no—
410C4×D4—21no—
411C4×D4—21no—
412C4×D4C2×Dic1111yescharacteristic
413C4×D4C2×Dic1111yescharacteristic
414C4×D4C2×Dic1112yes—
415C4×D4C2×Dic1112yes—
416C4×D4C2×Dic1111yescharacteristic
417C4×D4C22⋊D1112yes—
418C4×D4C22⋊D1111yescharacteristic
419C4×D4C22×D1111yescharacteristic
420C4×D4C22×D1111yescharacteristic
421#117—21no—
422#117—21no—
423#117—21no—
424#117—22no—
425#117—22no—
426#117—22no—
427#117C2×Dic1112yes—
428#117C22⋊D1111yescharacteristic
429#117C22⋊D1112yes—
430C2×C4⋊C4—21no—
431C2×C4⋊C4—21no—
432C2×C4⋊C4C2×Dic1111yescharacteristic
433C2×C22⋊C4—21no—
434C2×C22⋊C4—22no—
435C2×C42—22no—
436C2×C42C22×D1111yescharacteristic
437C2×C42C22×D1112yes—
438C4⋊C8—111no—
439C4⋊C8—111no—
440C4⋊C8—112no—
441C4⋊C8—222no—
442C4⋊C8—221no—
443C4⋊C8—222no—
444C4⋊C8—221no—
445C4⋊C8—222no—
446C4⋊C8—221no—
447C22⋊C8—221no—
448C22⋊C8—222no—
449#97—222no—
450C4×C8—111no—
451C4×C8—111no—
452C4×C8—112no—
453C4×C8—221no—
454C2×C11—22no—
455C2×C11—42no—
456C2×C11—42no—
457C2×C11—81no—
458C2×C11#288011yescharacteristic
459C2×C11C2×#41711yescharacteristic
460C2×C11#290111yescharacteristic
461C24—21no—
462#41—22no—
463#41—22no—
464#41—24no—
465#41—42no—
466C2×Q8—21no—
467C2×Q8C22⋊Dic1111yescharacteristic
468C2×Q8C22×Dic1112yes—
469C2×D4—22no—
470C2×D4—22no—
471C2×D4—22no—
472C2×D4—21no—
473C2×D4—41no—
474C2×D4C22⋊Dic1112yes—
475C2×D4C22⋊Dic1111yescharacteristic
476C2×D4C22×Dic1111yescharacteristic
477C2×D4C22×Dic1111yescharacteristic
478C22×C4—21no—
479C22×C4—22no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—22no—
485C22×C4—42no—
486C22×C4—42no—
487C22×C4C22×Dic1111yescharacteristic
488C22×C4C22×Dic1112yes—
489C22×C4C2×C22⋊D1112yes—
490C22×C4C2×C22⋊D1111yescharacteristic
491C22×C4C2×C22⋊D1112yes—
492C22×C4C2×C22⋊D1111yescharacteristic
493M16—444no—
494M16—444no—
495M16—442no—
496C2×C8—221no—
497C2×C8—221no—
498C2×C8—222no—
499C2×C8—221no—
500C2×C8—222no—
501C2×C8—221no—
502C2×C8—442no—
503C2×C8—444no—
504C2×C8—442no—
505C4⋊C4—21no—
506C4⋊C4—21no—
507C4⋊C4—22no—
508C4⋊C4—22no—
509C4⋊C4—21no—
510C4⋊C4—22no—
511C4⋊C4—22no—
512C4⋊C4—22no—
513C4⋊C4—21no—
514C4⋊C4—22no—
515C4⋊C4C22⋊Dic1111yescharacteristic
516C4⋊C4C22⋊Dic1111yescharacteristic
517C4⋊C4C22⋊Dic1112yes—
518C4⋊C4C22⋊Dic1112yes—
519C4⋊C4C22×Dic1111yescharacteristic
520C4⋊C4C22×Dic1111yescharacteristic
521C4⋊C4C22×Dic1112yes—
522C22⋊C4—22no—
523C22⋊C4—22no—
524C22⋊C4—22no—
525C22⋊C4—22no—
526C22⋊C4—22no—
527C22⋊C4—21no—
528C22⋊C4—21no—
529C22⋊C4—22no—
530C22⋊C4—22no—
531C22⋊C4—21no—
532C22⋊C4—21no—
533C22⋊C4C22⋊Dic1112yes—
534C22⋊C4C22⋊Dic1112yes—
535C22⋊C4C22⋊Dic1112yes—
536C42—22no—
537C42—22no—
538C42—22no—
539C42C22×Dic1111yescharacteristic
540C42C22×Dic1112yes—
541C42C2×C22⋊D1111yescharacteristic
542C42C2×C22⋊D1112yes—
543C42C2×C22⋊D1112yes—
544C42C2×C22⋊D1111yescharacteristic
545C42C23×D1111yescharacteristic
546C11#1751211yescharacteristic, complemented, Sylow
547C23—21no—
548C23—21no—
549C23—42no—
550C23—42no—
551C23—81no—
552C23C2×C22⋊Dic1112yes—
553C23C2×C22⋊Dic1111yescharacteristic
554Q8—22no—
555Q8—22no—
556Q8—22no—
557Q8—81no—
558D4—24no—
559D4—21no—
560D4—21no—
561D4—21no—
562D4—22no—
563D4—42no—
564D4—44no—
565D4—82no—
566D4#6700112yescomplemented
567C2×C4—21no—
568C2×C4—22no—
569C2×C4—21no—
570C2×C4—22no—
571C2×C4—22no—
572C2×C4—22no—
573C2×C4—21no—
574C2×C4—22no—
575C2×C4—22no—
576C2×C4—21no—
577C2×C4—41no—
578C2×C4—42no—
579C2×C4—44no—
580C2×C4—42no—
581C2×C4—41no—
582C2×C4—41no—
583C2×C4—41no—
584C2×C4—41no—
585C2×C4—42no—
586C2×C4—42no—
587C2×C4—82no—
588C2×C4#6700212yes—
589C2×C4#6700412yes—
590C2×C4C2×C22⋊Dic1112yes—
591C2×C4C2×C22⋊Dic1112yes—
592C2×C4C2×C22⋊Dic1111yescharacteristic
593C2×C4C2×C22⋊Dic1112yes—
594C2×C4C2×C22⋊Dic1111yescharacteristic
595C2×C4C2×C22⋊Dic1111yescharacteristic
596C2×C4C23×Dic1111yescharacteristic
597C2×C4C22×C22⋊D1111yescharacteristic
598C2×C4C22×C22⋊D1111yescharacteristic
599C8—222no—
600C8—441no—
601C8—442no—
602C8—441no—
603C8—442no—
604C8—441no—
605C22—21no—
606C22—21no—
607C22—22no—
608C22—22no—
609C22—22no—
610C22—22no—
611C22—41no—
612C22—41no—
613C22—41no—
614C22—41no—
615C22—41no—
616C22—84no—
617C22#1062284512yes—
618C22C22×C22⋊Dic1111yescharacteristic
619C4—22no—
620C4—21no—
621C4—22no—
622C4—21no—
623C4—22no—
624C4—21no—
625C4—42no—
626C4—41no—
627C4—41no—
628C4—42no—
629C4#1062284512yes—
630C4C2×#6700111yescharacteristic
631C4#1062335011yescharacteristic
632C4C2×#6700211yescharacteristic
633C4C2×#6700411yescharacteristic
634C2—22no—
635C2—42no—
636C2—42no—
637C2—81no—
638C2#1307706511yescharacteristic
639C2C2×#1062284511yescharacteristic
640C2#1307716311yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
Fitting, prime radicalC11×#3475C2
socleC22×C11C22×C22⋊C4
cosocleC42×C11C24
hypercenter#3475D11
hypocenterC11#17512
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C4×#41 ◁ #3475

Complements

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

NH ≅ G/Ntype
1. #13077583C2semidirect
2. #13077184C2semidirect
3. #13067081C2semidirect
4. #13067071C2semidirect
5. #13067055C2semidirect
6. #13067041C2semidirect
7. #13067029C2semidirect
8. #13067019C2semidirect
9. #13067003C2semidirect
10. C2×D4⋊(C11⋊C8)C2semidirect
36. #10622538C22semidirect
38. #10622537C22semidirect
40. C2×C4⋊(C11⋊C8)C22semidirect
41. C4×#4318C22semidirect
43. Q8⋊(C11⋊C8)C22semidirect
44. Q8⋊(C11⋊C8)C22semidirect
45. Q8⋊(C11⋊C8)C22semidirect
46. Q8⋊(C11⋊C8)C22semidirect
257. D4×C11#131semidirect
546. C11#17512semidirect
566. D4#67001semidirect

Maximal subgroups

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

subgroupindex
#130775832
#130771842
#130670812
#130670712
#130670552
#130670412
#130670292
#130670192
#130670032
C2×D4⋊(C11⋊C8)2
C11×#34752
#1751211