Finite Group Databasebeta

← #14720795

Subgroups — #14720795

Order 2816.

1008 conjugacy classes of subgroups.

The subgroup lattice has 646 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13077748C211yesmaximal, characteristic, complemented
2#13077260C211yesmaximal, characteristic, complemented
3#13067081C212yesmaximal, complemented
4#13067067C211yesmaximal, characteristic, complemented
5#13067055C211yesmaximal, characteristic, complemented
6#13067041C212yesmaximal, complemented
7#13067033C211yesmaximal, characteristic, complemented
8#13067024C212yesmaximal, complemented
9#13067007C212yesmaximal, complemented
10#13066998C211yesmaximal, characteristic, complemented
11C11×#3481C211yesmaximal, characteristic
12C11×#559C411yescharacteristic
13C11×#554C411yescharacteristic
14C11×#554C411yescharacteristic
15C11×#553—21no—
16C11×#553C412yes—
17C11×#551—22no—
18C11×#546—21no—
19C11×#546C412yes—
20D42×C11C411yescharacteristic
21C11×#532C2211yescharacteristic
22C11×#529—21no—
23C11×#529C2212yes—
24C11×#525—22no—
25C4×C11×#41C2211yescharacteristic
26C4×C11×#41C2211yescharacteristic
27C2×C4×D4×C11—21no—
28C2×C4×D4×C11C2212yes—
29#10622847—21no—
30Q8×C11⋊C8—21no—
31#10622625—21no—
32#10622625—22no—
33#10622613—22no—
34#10622612—21no—
35#10622538C2212yescomplemented
36#10622538C2211yescharacteristic, complemented
37#10622538C2212yescomplemented
38#10622538C2212yescomplemented
39#10622537C2212yescomplemented
40#10622537C2211yescharacteristic, complemented
41C4×#4318C2211yescharacteristic, complemented
42C2×C4×C11⋊C8C2211yescharacteristic, complemented
43Q8⋊(C11⋊C8)C2211yescharacteristic, complemented
44Q8⋊(C11⋊C8)C2212yescomplemented
45Q8⋊(C11⋊C8)C2211yescharacteristic, complemented
46D4⋊(C11⋊C8)C2211yescharacteristic
47D4⋊(C11⋊C8)C2212yes—
48D4⋊(C11⋊C8)C2211yescharacteristic
49D4⋊(C11⋊C8)C2212yescomplemented
50D4⋊(C11⋊C8)C2212yescomplemented
51D4⋊(C11⋊C8)C2212yescomplemented
52D4⋊(C11⋊C8)C2212yescomplemented
53C2×C11×#41—21no—
54C2×C11×#41C2×C411yescharacteristic
55C2×C11×#41D411yescharacteristic
56C22×D4×C11—21no—
57C22×D4×C11C2×C412yes—
58C23×C4×C11—22no—
59C11×C4⋊Q8C2×C411yescharacteristic
60C11×#127C2×C411yescharacteristic
61C11×#126—22no—
62C11×#126—22no—
63C11×#125—21no—
64C11×#125C2×C412yes—
65C11×#124—21no—
66C11×#124—21no—
67C11×#124C2×C412yes—
68C11×#123—22no—
69C11×#123—22no—
70C11×#123—22no—
71C11×#123—22no—
72C11×C22⋊Q8—21no—
73C11×C22⋊Q8—22no—
74C11×C22⋊Q8—22no—
75C11×C22⋊Q8C2×C412yes—
76C11×#121—22no—
77C11×#121—21no—
78C11×#121—21no—
79C11×#121—22no—
80C11×#121C2×C412yes—
81C11×#121C2×C412yes—
82C11×#120—22no—
83C11×#120—22no—
84C4×Q8×C11C2×C411yescharacteristic
85C4×Q8×C11C2×C411yescharacteristic
86C4×Q8×C11D411yescharacteristic
87C4×Q8×C11C2311yescharacteristic
88C4×D4×C11—21no—
89C4×D4×C11—22no—
90C4×D4×C11—21no—
91C4×D4×C11—21no—
92C4×D4×C11—21no—
93C4×D4×C11—22no—
94C4×D4×C11—21no—
95C4×D4×C11—22no—
96C4×D4×C11—22no—
97C4×D4×C11C2×C412yes—
98C4×D4×C11C2×C412yes—
99C4×D4×C11C2×C411yescharacteristic
100C4×D4×C11C2×C411yescharacteristic
101C4×D4×C11C2×C412yes—
102C4×D4×C11D411yescharacteristic
103C4×D4×C11D412yes—
104C4×D4×C11C2311yescharacteristic
105C4×D4×C11C2312yes—
106C11×#117—21no—
107C11×#117—22no—
108C11×#117C2×C411yescharacteristic
109C11×#117D411yescharacteristic
110C11×#117D412yes—
111C2×C11×C4⋊C4—21no—
112C2×C11×C4⋊C4C2×C412yes—
113C2×C11×C22⋊C4—22no—
114C2×C11×C22⋊C4—22no—
115C2×C42×C11—21no—
116C2×C42×C11C2311yescharacteristic
117C2×C42×C11C2312yes—
118C2×#4318—21no—
119C2×#4318—22no—
120C2×#4318—21no—
121C22×C11⋊C8—21no—
122C22⋊(C11⋊C8)—22no—
123C22⋊(C11⋊C8)—22no—
124C22⋊(C11⋊C8)—22no—
125C22⋊(C11⋊C8)—21no—
126C4⋊(C11⋊C8)—21no—
127C4⋊(C11⋊C8)—22no—
128C4⋊(C11⋊C8)—22no—
129C4⋊(C11⋊C8)—22no—
130C4⋊(C11⋊C8)C2311yescharacteristic
131C4⋊(C11⋊C8)C2312yes—
132C4⋊(C11⋊C8)C2311yescharacteristic
133#66867—21no—
134C4×C11⋊C8—21no—
135C4×C11⋊C8—21no—
136C4×C11⋊C8—22no—
137C4×C11⋊C8C2311yescharacteristic
138C4×C11⋊C8C2311yescharacteristic
139C4×C11⋊C8C2312yes—
140#17522—111nomaximal, Sylow
141C24×C11—22no—
142C11×#41—22no—
143C11×#41—41no—
144C11×#41—42no—
145C11×#41—81no—
146C11×#41—81no—
147C2×Q8×C11—21no—
148C2×Q8×C11C22⋊C411yescharacteristic
149C2×Q8×C11C22×C411yescharacteristic
150C2×D4×C11—24no—
151C2×D4×C11—21no—
152C2×D4×C11—22no—
153C2×D4×C11—22no—
154C2×D4×C11—22no—
155C2×D4×C11—21no—
156C2×D4×C11—21no—
157C2×D4×C11—42no—
158C2×D4×C11—44no—
159C2×D4×C11C22⋊C411yescharacteristic
160C2×D4×C11C22⋊C412yes—
161C2×D4×C11C22×C412yes—
162C2×D4×C11C22×C411yescharacteristic
163C22×C4×C11—22no—
164C22×C4×C11—21no—
165C22×C4×C11—21no—
166C22×C4×C11—21no—
167C22×C4×C11—22no—
168C22×C4×C11—22no—
169C22×C4×C11—22no—
170C22×C4×C11—82no—
171C22×C4×C11—82no—
172C22×C4×C11C22×C412yes—
173C22×C4×C11C22×C411yescharacteristic
174C22×C4×C11C2×D412yes—
175C22×C4×C11C2×D411yescharacteristic
176C22×C4×C11C2×D411yescharacteristic
177C22×C4×C11C2×D412yes—
178C11×C4⋊C4—21no—
179C11×C4⋊C4—22no—
180C11×C4⋊C4—22no—
181C11×C4⋊C4—21no—
182C11×C4⋊C4—22no—
183C11×C4⋊C4—22no—
184C11×C4⋊C4—21no—
185C11×C4⋊C4C22⋊C411yescharacteristic
186C11×C4⋊C4C22⋊C411yescharacteristic
187C11×C4⋊C4C22⋊C412yes—
188C11×C4⋊C4C22⋊C412yes—
189C11×C4⋊C4C22×C411yescharacteristic
190C11×C4⋊C4C22×C412yes—
191C11×C4⋊C4C22×C411yescharacteristic
192C11×C22⋊C4—22no—
193C11×C22⋊C4—21no—
194C11×C22⋊C4—22no—
195C11×C22⋊C4—22no—
196C11×C22⋊C4—22no—
197C11×C22⋊C4—22no—
198C11×C22⋊C4—21no—
199C11×C22⋊C4—22no—
200C11×C22⋊C4—22no—
201C11×C22⋊C4—21no—
202C11×C22⋊C4—22no—
203C11×C22⋊C4C22⋊C412yes—
204C11×C22⋊C4C22⋊C412yes—
205C11×C22⋊C4C22⋊C412yes—
206C42×C11—21no—
207C42×C11—21no—
208C42×C11—21no—
209C42×C11C22×C412yes—
210C42×C11C22×C411yescharacteristic
211C42×C11C2×D411yescharacteristic
212C42×C11C2×D411yescharacteristic
213C42×C11C2×D412yes—
214C42×C11C2×D412yes—
215C42×C11C2411yescharacteristic
216#4318—42no—
217#4318—82no—
218#4318—81no—
219C2×C11⋊C8—21no—
220C2×C11⋊C8—21no—
221C2×C11⋊C8—21no—
222C2×C11⋊C8—21no—
223C2×C11⋊C8—22no—
224C2×C11⋊C8—22no—
225C2×C11⋊C8—42no—
226#3481D1111yescharacteristic
227#2991—111no—
228#2922—111no—
229#1495—112no—
230#1492—111no—
231#1489—111no—
232#1486—112no—
233#1484—111no—
234#1482—112no—
235#1478—112no—
236#1476—111no—
237C23×C11—21no—
238C23×C11—22no—
239C23×C11—44no—
240C23×C11—44no—
241C23×C11—82no—
242C23×C11C2×C22⋊C412yes—
243C23×C11C2×C22⋊C411yescharacteristic
244Q8×C11—22no—
245Q8×C11—21no—
246Q8×C11—21no—
247Q8×C11—81no—
248D4×C11—22no—
249D4×C11—21no—
250D4×C11—22no—
251D4×C11—22no—
252D4×C11—42no—
253D4×C11—44no—
254D4×C11—42no—
255D4×C11—44no—
256D4×C11—42no—
257D4×C11—81no—
258D4×C11—82no—
259D4×C11#13112yes—
260C2×C4×C11—22no—
261C2×C4×C11—21no—
262C2×C4×C11—22no—
263C2×C4×C11—21no—
264C2×C4×C11—22no—
265C2×C4×C11—21no—
266C2×C4×C11—22no—
267C2×C4×C11—21no—
268C2×C4×C11—22no—
269C2×C4×C11—21no—
270C2×C4×C11—21no—
271C2×C4×C11—21no—
272C2×C4×C11—22no—
273C2×C4×C11—42no—
274C2×C4×C11—42no—
275C2×C4×C11—41no—
276C2×C4×C11—42no—
277C2×C4×C11—41no—
278C2×C4×C11—42no—
279C2×C4×C11—42no—
280C2×C4×C11—82no—
281C2×C4×C11—82no—
282C2×C4×C11—82no—
283C2×C4×C11C2×C22⋊C411yescharacteristic
284C2×C4×C11C2×C22⋊C412yes—
285C2×C4×C11C2×C22⋊C412yes—
286C2×C4×C11C2×C22⋊C411yescharacteristic
287C2×C4×C11C2×C22⋊C412yes—
288C2×C4×C11C2×C22⋊C411yescharacteristic
289C2×C4×C11C23×C411yescharacteristic
290C2×C4×C11C22×D411yescharacteristic
291C2×C4×C11C22×D411yescharacteristic
292C11⋊C8—41no—
293C11⋊C8—41no—
294C11⋊C8—42no—
295C11⋊C8—41no—
296C11⋊C8—42no—
297C11⋊C8—41no—
298#559Dic1111yescharacteristic
299#554Dic1111yescharacteristic
300#554Dic1111yescharacteristic
301#553—21no—
302#553Dic1112yes—
303#551—22no—
304#546—21no—
305#546Dic1112yes—
306D42Dic1111yescharacteristic
307#532C2×D1111yescharacteristic
308#529—21no—
309#529C2×D1112yes—
310#525—22no—
311C4×#41C2×D1111yescharacteristic
312C4×#41C2×D1111yescharacteristic
313C2×C4×D4—21no—
314C2×C4×D4C2×D1112yes—
315C8×Q8—221no—
316#436—221no—
317#436—222no—
318#433—222no—
319#431—112no—
320#431—112no—
321#431—111no—
322#431—112no—
323#424—221no—
324#423—112no—
325#423—111no—
326#408—221no—
327C4×M16—111no—
328C2×C4×C8—111no—
329Q8⋊C8—111no—
330Q8⋊C8—111no—
331Q8⋊C8—112no—
332D4⋊C8—111no—
333D4⋊C8—111no—
334D4⋊C8—112no—
335D4⋊C8—112no—
336D4⋊C8—112no—
337D4⋊C8—112no—
338D4⋊C8—112no—
339C22×C11—21no—
340C22×C11—22no—
341C22×C11—22no—
342C22×C11—22no—
343C22×C11—21no—
344C22×C11—21no—
345C22×C11—22no—
346C22×C11—41no—
347C22×C11—41no—
348C22×C11—42no—
349C22×C11—42no—
350C22×C11—42no—
351C22×C11—88no—
352C22×C11C22×C22⋊C411yescharacteristic
353C4×C11—21no—
354C4×C11—22no—
355C4×C11—22no—
356C4×C11—21no—
357C4×C11—21no—
358C4×C11—22no—
359C4×C11—41no—
360C4×C11—41no—
361C4×C11—42no—
362C4×C11—41no—
363C4×C11#42112yes—
364C4×C11C2×#13111yescharacteristic
365C4×C11#56811yescharacteristic
366C4×C11#57611yescharacteristic
367C4×C11#57711yescharacteristic
368C2×#41—21no—
369C2×#41C2×Dic1111yescharacteristic
370C2×#41C22⋊D1111yescharacteristic
371C22×D4—21no—
372C22×D4C2×Dic1112yes—
373C23×C4—22no—
374C2×M16—221no—
375C2×M16—222no—
376C2×M16—221no—
377C22×C8—221no—
378C4⋊Q8C2×Dic1111yescharacteristic
379#127C2×Dic1111yescharacteristic
380#126—22no—
381#126—22no—
382#125—21no—
383#125C2×Dic1112yes—
384#124—21no—
385#124—21no—
386#124C2×Dic1112yes—
387#123—22no—
388#123—22no—
389#123—22no—
390#123—22no—
391C22⋊Q8—21no—
392C22⋊Q8—22no—
393C22⋊Q8—22no—
394C22⋊Q8C2×Dic1112yes—
395#121—22no—
396#121—21no—
397#121—21no—
398#121—22no—
399#121C2×Dic1112yes—
400#121C2×Dic1112yes—
401#120—22no—
402#120—22no—
403C4×Q8C2×Dic1111yescharacteristic
404C4×Q8C2×Dic1111yescharacteristic
405C4×Q8C22⋊D1111yescharacteristic
406C4×Q8C22×D1111yescharacteristic
407C4×D4—21no—
408C4×D4—22no—
409C4×D4—21no—
410C4×D4—21no—
411C4×D4—21no—
412C4×D4—22no—
413C4×D4—21no—
414C4×D4—22no—
415C4×D4—22no—
416C4×D4C2×Dic1112yes—
417C4×D4C2×Dic1112yes—
418C4×D4C2×Dic1111yescharacteristic
419C4×D4C2×Dic1111yescharacteristic
420C4×D4C2×Dic1112yes—
421C4×D4C22⋊D1111yescharacteristic
422C4×D4C22⋊D1112yes—
423C4×D4C22×D1111yescharacteristic
424C4×D4C22×D1112yes—
425#117—21no—
426#117—22no—
427#117C2×Dic1111yescharacteristic
428#117C22⋊D1112yes—
429#117C22⋊D1111yescharacteristic
430C2×C4⋊C4—21no—
431C2×C4⋊C4C2×Dic1112yes—
432C2×C22⋊C4—22no—
433C2×C22⋊C4—22no—
434C2×C42—21no—
435C2×C42C22×D1112yes—
436C2×C42C22×D1111yescharacteristic
437C4⋊C8—111no—
438C4⋊C8—112no—
439C4⋊C8—111no—
440C4⋊C8—221no—
441C4⋊C8—222no—
442C4⋊C8—222no—
443C4⋊C8—222no—
444C22⋊C8—222no—
445C22⋊C8—222no—
446C22⋊C8—222no—
447C22⋊C8—221no—
448#97—221no—
449C4×C8—111no—
450C4×C8—111no—
451C4×C8—112no—
452C4×C8—221no—
453C4×C8—221no—
454C4×C8—222no—
455C2×C11—41no—
456C2×C11—42no—
457C2×C11—42no—
458C2×C11—82no—
459C2×C11#288011yescharacteristic
460C2×C11#289711yescharacteristic
461C2×C11C2×#42111yescharacteristic
462C24—22no—
463#41—22no—
464#41—41no—
465#41—42no—
466#41—81no—
467#41—81no—
468C2×Q8—21no—
469C2×Q8C22⋊Dic1111yescharacteristic
470C2×Q8C22×Dic1111yescharacteristic
471C2×D4—24no—
472C2×D4—21no—
473C2×D4—22no—
474C2×D4—22no—
475C2×D4—22no—
476C2×D4—21no—
477C2×D4—21no—
478C2×D4—42no—
479C2×D4—44no—
480C2×D4C22⋊Dic1111yescharacteristic
481C2×D4C22⋊Dic1112yes—
482C2×D4C22×Dic1112yes—
483C2×D4C22×Dic1111yescharacteristic
484C22×C4—22no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—21no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—82no—
492C22×C4—82no—
493C22×C4C22×Dic1112yes—
494C22×C4C22×Dic1111yescharacteristic
495C22×C4C2×C22⋊D1111yescharacteristic
496C22×C4C2×C22⋊D1112yes—
497C22×C4C2×C22⋊D1111yescharacteristic
498C22×C4C2×C22⋊D1112yes—
499M16—442no—
500M16—882no—
501M16—881no—
502C2×C8—221no—
503C2×C8—221no—
504C2×C8—222no—
505C2×C8—221no—
506C2×C8—221no—
507C2×C8—222no—
508C2×C8—442no—
509C4⋊C4—21no—
510C4⋊C4—22no—
511C4⋊C4—22no—
512C4⋊C4—21no—
513C4⋊C4—22no—
514C4⋊C4—22no—
515C4⋊C4—21no—
516C4⋊C4C22⋊Dic1111yescharacteristic
517C4⋊C4C22⋊Dic1111yescharacteristic
518C4⋊C4C22⋊Dic1112yes—
519C4⋊C4C22⋊Dic1112yes—
520C4⋊C4C22×Dic1111yescharacteristic
521C4⋊C4C22×Dic1112yes—
522C4⋊C4C22×Dic1111yescharacteristic
523C22⋊C4—22no—
524C22⋊C4—21no—
525C22⋊C4—22no—
526C22⋊C4—22no—
527C22⋊C4—22no—
528C22⋊C4—22no—
529C22⋊C4—21no—
530C22⋊C4—22no—
531C22⋊C4—22no—
532C22⋊C4—21no—
533C22⋊C4—22no—
534C22⋊C4C22⋊Dic1112yes—
535C22⋊C4C22⋊Dic1112yes—
536C22⋊C4C22⋊Dic1112yes—
537C42—21no—
538C42—21no—
539C42—21no—
540C42C22×Dic1112yes—
541C42C22×Dic1111yescharacteristic
542C42C2×C22⋊D1111yescharacteristic
543C42C2×C22⋊D1112yes—
544C42C2×C22⋊D1111yescharacteristic
545C42C2×C22⋊D1112yes—
546C42C23×D1111yescharacteristic
547C11#1752211yescharacteristic, complemented, Sylow
548C23—21no—
549C23—22no—
550C23—44no—
551C23—44no—
552C23—82no—
553C23C2×C22⋊Dic1112yes—
554C23C2×C22⋊Dic1111yescharacteristic
555Q8—22no—
556Q8—21no—
557Q8—21no—
558Q8—81no—
559D4—22no—
560D4—21no—
561D4—22no—
562D4—22no—
563D4—42no—
564D4—44no—
565D4—42no—
566D4—44no—
567D4—42no—
568D4—81no—
569D4—82no—
570D4#6700112yes—
571C2×C4—22no—
572C2×C4—21no—
573C2×C4—22no—
574C2×C4—21no—
575C2×C4—22no—
576C2×C4—22no—
577C2×C4—21no—
578C2×C4—22no—
579C2×C4—21no—
580C2×C4—21no—
581C2×C4—21no—
582C2×C4—21no—
583C2×C4—22no—
584C2×C4—42no—
585C2×C4—42no—
586C2×C4—42no—
587C2×C4—41no—
588C2×C4—42no—
589C2×C4—41no—
590C2×C4—42no—
591C2×C4—82no—
592C2×C4—82no—
593C2×C4—82no—
594C2×C4C2×C22⋊Dic1111yescharacteristic
595C2×C4C2×C22⋊Dic1112yes—
596C2×C4C2×C22⋊Dic1112yes—
597C2×C4C2×C22⋊Dic1111yescharacteristic
598C2×C4C2×C22⋊Dic1112yes—
599C2×C4C2×C22⋊Dic1111yescharacteristic
600C2×C4C23×Dic1111yescharacteristic
601C2×C4C22×C22⋊D1111yescharacteristic
602C2×C4C22×C22⋊D1111yescharacteristic
603C8—441no—
604C8—441no—
605C8—442no—
606C8—441no—
607C8—442no—
608C8—441no—
609C22—21no—
610C22—22no—
611C22—22no—
612C22—22no—
613C22—21no—
614C22—21no—
615C22—22no—
616C22—41no—
617C22—41no—
618C22—42no—
619C22—42no—
620C22—42no—
621C22—88no—
622C22C22×C22⋊Dic1111yescharacteristic
623C4—21no—
624C4—22no—
625C4—22no—
626C4—21no—
627C4—21no—
628C4—22no—
629C4—41no—
630C4—41no—
631C4—42no—
632C4—41no—
633C4#1062284912yes—
634C4C2×#6700111yescharacteristic
635C4#1062335011yescharacteristic
636C4#1062336611yescharacteristic
637C4#1062336711yescharacteristic
638C2—42no—
639C2—41no—
640C2—42no—
641C2—82no—
642C2#1307706511yescharacteristic
643C2#1307714211yescharacteristic
644C2C2×#1062284911yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
Fitting, prime radicalC11×#3481C2
socleC22×C11C22×C22⋊C4
cosocleC42×C11C24
hypercenter#3481D11
hypocenterC11#17522
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C4×#41 ◁ #3481

Complements

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

NH ≅ G/Ntype
1. #13077748C2semidirect
2. #13077260C2semidirect
3. #13067081C2semidirect
4. #13067067C2semidirect
5. #13067055C2semidirect
6. #13067041C2semidirect
7. #13067033C2semidirect
8. #13067024C2semidirect
9. #13067007C2semidirect
10. #13066998C2semidirect
35. #10622538C22semidirect
36. #10622538C22semidirect
37. #10622538C22semidirect
38. #10622538C22semidirect
39. #10622537C22semidirect
40. #10622537C22semidirect
41. C4×#4318C22semidirect
42. C2×C4×C11⋊C8C22semidirect
43. Q8⋊(C11⋊C8)C22semidirect
44. Q8⋊(C11⋊C8)C22semidirect
45. Q8⋊(C11⋊C8)C22semidirect
49. D4⋊(C11⋊C8)C22semidirect
50. D4⋊(C11⋊C8)C22semidirect
51. D4⋊(C11⋊C8)C22semidirect
52. D4⋊(C11⋊C8)C22semidirect
547. C11#17522semidirect

Maximal subgroups

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

subgroupindex
#130777482
#130772602
#130670812
#130670672
#130670552
#130670412
#130670332
#130670242
#130670072
#130669982
C11×#34812
#1752211