Finite Group Databasebeta

← #14720452

Subgroups — #14720452

Order 2816.

984 conjugacy classes of subgroups.

The subgroup lattice has 628 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13077733C211yesmaximal, characteristic, complemented
2#41×C11⋊C8C211yesmaximal, characteristic, complemented
3#13067085C212yesmaximal, complemented
4#13067081C212yesmaximal, complemented
5#13067076C212yesmaximal, complemented
6#13067067C212yesmaximal, complemented
7#13067007C211yesmaximal, characteristic, complemented
8#13067003C211yesmaximal, characteristic, complemented
9#13066998C211yesmaximal, characteristic, complemented
10C2×D4⋊(C11⋊C8)C211yesmaximal, characteristic, complemented
11C11×#3460C211yesmaximal, characteristic
12C11×#544C411yescharacteristic
13C11×#542—21no—
14C11×#542C412yes—
15C11×#540—21no—
16C11×#540C412yes—
17C11×#538—22no—
18C11×#537C411yescharacteristic
19C11×#535C411yescharacteristic
20C11×#535C411yescharacteristic
21C11×#532—21no—
22C11×#532C2212yes—
23C11×#529—21no—
24C11×#529C2212yes—
25C11×#525—22no—
26C4×C11×#41C2211yescharacteristic
27C4×C11×#41C2211yescharacteristic
28C2×C4×D4×C11C2211yescharacteristic
29#10622637—21no—
30Q8×C11⋊C8—21no—
31#10622625—21no—
32#10622624—22no—
33D4×C11⋊C8—21no—
34D4×C11⋊C8—22no—
35#10622539C2212yescomplemented
36#10622538C2211yescharacteristic
37#10622538C2211yescharacteristic
38#10622538C2212yescomplemented
39#10622537C2212yescomplemented
40C2×C4⋊(C11⋊C8)C2211yescharacteristic
41C2×C4×C11⋊C8C2211yescharacteristic
42C2×C4×C11⋊C8C2212yescomplemented
43Q8⋊(C11⋊C8)C2211yescharacteristic, complemented
44Q8⋊(C11⋊C8)C2212yescomplemented
45Q8⋊(C11⋊C8)C2211yescharacteristic, complemented
46D4⋊(C11⋊C8)C2212yes—
47D4⋊(C11⋊C8)C2212yes—
48D4⋊(C11⋊C8)C2212yes—
49D4⋊(C11⋊C8)C2212yes—
50D4⋊(C11⋊C8)C2211yescharacteristic, complemented
51D4⋊(C11⋊C8)C2212yescomplemented
52D4⋊(C11⋊C8)C2211yescharacteristic, complemented
53C2×C11×#41—22no—
54C2×C11×#41C2×C411yescharacteristic
55C2×C11×#41C2×C411yescharacteristic
56C22×D4×C11C2×C411yescharacteristic
57C23×C4×C11—21no—
58C11×C4⋊Q8—21no—
59C11×C4⋊Q8C2×C412yes—
60C11×#127—21no—
61C11×#127C2×C412yes—
62C11×#126—22no—
63C11×#126—22no—
64C11×#125—21no—
65C11×#125C2×C412yes—
66C11×#124—21no—
67C11×#124—22no—
68C11×#124—22no—
69C11×#124C2×C412yes—
70C11×#123—22no—
71C11×#123—22no—
72C11×#123—22no—
73C11×#123—22no—
74C11×C22⋊Q8—21no—
75C11×C22⋊Q8—22no—
76C11×C22⋊Q8—22no—
77C11×C22⋊Q8C2×C412yes—
78C11×#121—22no—
79C11×#121—21no—
80C11×#121—22no—
81C11×#121—21no—
82C11×#121—21no—
83C11×#121—22no—
84C11×#121—22no—
85C11×#121C2×C412yes—
86C11×#121C2×C412yes—
87C11×#121C2×C412yes—
88C11×#120—22no—
89C11×#120—22no—
90C4×Q8×C11C2×C411yescharacteristic
91C4×Q8×C11D411yescharacteristic
92C4×Q8×C11D411yescharacteristic
93C4×Q8×C11C2311yescharacteristic
94C4×D4×C11—21no—
95C4×D4×C11—21no—
96C4×D4×C11—22no—
97C4×D4×C11—21no—
98C4×D4×C11—21no—
99C4×D4×C11—22no—
100C4×D4×C11C2×C412yes—
101C4×D4×C11C2×C411yescharacteristic
102C4×D4×C11D412yes—
103C4×D4×C11D412yes—
104C4×D4×C11D411yescharacteristic
105C4×D4×C11D411yescharacteristic
106C4×D4×C11C2312yes—
107C4×D4×C11C2311yescharacteristic
108C11×#117—21no—
109C11×#117—22no—
110C11×#117C2×C411yescharacteristic
111C11×#117C2×C411yescharacteristic
112C11×#117C2×C412yes—
113C2×C11×C4⋊C4C2×C411yescharacteristic
114C2×C11×C22⋊C4—21no—
115C2×C42×C11—21no—
116C2×C42×C11C2311yescharacteristic
117C2×C42×C11C2312yes—
118C2×#4318—22no—
119C22×C11⋊C8—21no—
120C22×C11⋊C8—22no—
121C22×C11⋊C8—21no—
122C22⋊(C11⋊C8)—21no—
123C22⋊(C11⋊C8)—21no—
124C22⋊(C11⋊C8)—22no—
125C22⋊(C11⋊C8)—22no—
126C4⋊(C11⋊C8)—21no—
127C4⋊(C11⋊C8)—22no—
128C4⋊(C11⋊C8)—21no—
129C4⋊(C11⋊C8)—22no—
130C4⋊(C11⋊C8)C2312yes—
131C4⋊(C11⋊C8)C2311yescharacteristic
132C4⋊(C11⋊C8)C2311yescharacteristic
133#66867—22no—
134C4×C11⋊C8—21no—
135C4×C11⋊C8—22no—
136C4×C11⋊C8—21no—
137C4×C11⋊C8C2311yescharacteristic
138C4×C11⋊C8C2311yescharacteristic
139C4×C11⋊C8C2312yes—
140#17483—111nomaximal, Sylow
141C24×C11—21no—
142C11×#41—24no—
143C11×#41—24no—
144C11×#41—82no—
145C11×#41—82no—
146C2×Q8×C11—22no—
147C2×Q8×C11C22⋊C411yescharacteristic
148C2×Q8×C11C22×C411yescharacteristic
149C2×D4×C11—21no—
150C2×D4×C11—22no—
151C2×D4×C11—22no—
152C2×D4×C11—22no—
153C2×D4×C11—21no—
154C2×D4×C11—22no—
155C2×D4×C11—22no—
156C2×D4×C11—24no—
157C2×D4×C11C22⋊C412yes—
158C2×D4×C11C22⋊C411yescharacteristic
159C2×D4×C11C22×C412yes—
160C2×D4×C11C22×C411yescharacteristic
161C22×C4×C11—21no—
162C22×C4×C11—21no—
163C22×C4×C11—21no—
164C22×C4×C11—22no—
165C22×C4×C11—21no—
166C22×C4×C11—22no—
167C22×C4×C11—81no—
168C22×C4×C11—81no—
169C22×C4×C11C22×C412yes—
170C22×C4×C11C22×C411yescharacteristic
171C22×C4×C11C2×D411yescharacteristic
172C22×C4×C11C2×D412yes—
173C22×C4×C11C2×D411yescharacteristic
174C22×C4×C11C2×D412yes—
175C11×C4⋊C4—21no—
176C11×C4⋊C4—21no—
177C11×C4⋊C4—22no—
178C11×C4⋊C4—22no—
179C11×C4⋊C4—22no—
180C11×C4⋊C4—22no—
181C11×C4⋊C4—21no—
182C11×C4⋊C4C22⋊C411yescharacteristic
183C11×C4⋊C4C22⋊C411yescharacteristic
184C11×C4⋊C4C22⋊C412yes—
185C11×C4⋊C4C22⋊C412yes—
186C11×C4⋊C4C22×C412yes—
187C11×C4⋊C4C22×C411yescharacteristic
188C11×C4⋊C4C22×C411yescharacteristic
189C11×C22⋊C4—21no—
190C11×C22⋊C4—22no—
191C11×C22⋊C4—22no—
192C11×C22⋊C4—21no—
193C11×C22⋊C4—22no—
194C11×C22⋊C4—22no—
195C11×C22⋊C4—22no—
196C11×C22⋊C4—22no—
197C11×C22⋊C4—22no—
198C11×C22⋊C4—22no—
199C11×C22⋊C4—21no—
200C11×C22⋊C4C22⋊C412yes—
201C11×C22⋊C4C22⋊C412yes—
202C11×C22⋊C4C22⋊C412yes—
203C42×C11—21no—
204C42×C11—21no—
205C42×C11—21no—
206C42×C11C22×C411yescharacteristic
207C42×C11C22×C412yes—
208C42×C11C2×D411yescharacteristic
209C42×C11C2×D411yescharacteristic
210C42×C11C2×D412yes—
211C42×C11C2×D412yes—
212C42×C11C2411yescharacteristic
213#4318—82no—
214C2×C11⋊C8—21no—
215C2×C11⋊C8—21no—
216C2×C11⋊C8—22no—
217C2×C11⋊C8—21no—
218C2×C11⋊C8—21no—
219C2×C11⋊C8—22no—
220C2×C11⋊C8—42no—
221C2×C11⋊C8—44no—
222C2×C11⋊C8—81no—
223#3460D1111yescharacteristic
224#2989—111no—
225C8×#41—111no—
226#1496—112no—
227#1495—112no—
228#1494—112no—
229#1492—112no—
230#1478—111no—
231#1477—111no—
232#1476—111no—
233C2×D4⋊C8—111no—
234C23×C11—22no—
235C23×C11—21no—
236C23×C11—42no—
237C23×C11—81no—
238C23×C11—81no—
239C23×C11C2×C22⋊C412yes—
240C23×C11C2×C22⋊C411yescharacteristic
241Q8×C11—22no—
242Q8×C11—22no—
243Q8×C11—82no—
244D4×C11—24no—
245D4×C11—24no—
246D4×C11—22no—
247D4×C11—22no—
248D4×C11—42no—
249D4×C11—42no—
250D4×C11—82no—
251D4×C11—82no—
252D4×C11—82no—
253D4×C11—82no—
254D4×C11—82no—
255C2×C4×C11—24no—
256C2×C4×C11—21no—
257C2×C4×C11—22no—
258C2×C4×C11—21no—
259C2×C4×C11—22no—
260C2×C4×C11—21no—
261C2×C4×C11—21no—
262C2×C4×C11—21no—
263C2×C4×C11—22no—
264C2×C4×C11—41no—
265C2×C4×C11—42no—
266C2×C4×C11—42no—
267C2×C4×C11—41no—
268C2×C4×C11—42no—
269C2×C4×C11—41no—
270C2×C4×C11—42no—
271C2×C4×C11—81no—
272C2×C4×C11—82no—
273C2×C4×C11—81no—
274C2×C4×C11C2×C22⋊C411yescharacteristic
275C2×C4×C11C2×C22⋊C412yes—
276C2×C4×C11C2×C22⋊C411yescharacteristic
277C2×C4×C11C2×C22⋊C412yes—
278C2×C4×C11C2×C22⋊C412yes—
279C2×C4×C11C2×C22⋊C411yescharacteristic
280C2×C4×C11#13114yes—
281C2×C4×C11C23×C411yescharacteristic
282C2×C4×C11C22×D411yescharacteristic
283C2×C4×C11C22×D411yescharacteristic
284C11⋊C8—22no—
285C11⋊C8—41no—
286C11⋊C8—42no—
287C11⋊C8—42no—
288C11⋊C8—41no—
289C11⋊C8—41no—
290#544Dic1111yescharacteristic
291#542—21no—
292#542Dic1112yes—
293#540—21no—
294#540Dic1112yes—
295#538—22no—
296#537Dic1111yescharacteristic
297#535Dic1111yescharacteristic
298#535Dic1111yescharacteristic
299#532—21no—
300#532C2×D1112yes—
301#529—21no—
302#529C2×D1112yes—
303#525—22no—
304C4×#41C2×D1111yescharacteristic
305C4×#41C2×D1111yescharacteristic
306C2×C4×D4C2×D1111yescharacteristic
307#446—221no—
308C8×Q8—221no—
309#436—221no—
310#435—222no—
311C8×D4—222no—
312C8×D4—221no—
313#432—112no—
314#431—111no—
315#431—112no—
316#431—111no—
317#423—112no—
318C2×C4⋊C8—111no—
319C2×C4×C8—111no—
320C2×C4×C8—112no—
321Q8⋊C8—111no—
322Q8⋊C8—111no—
323Q8⋊C8—112no—
324D4⋊C8—112no—
325D4⋊C8—112no—
326D4⋊C8—111no—
327D4⋊C8—111no—
328D4⋊C8—112no—
329D4⋊C8—112no—
330D4⋊C8—112no—
331C22×C11—21no—
332C22×C11—21no—
333C22×C11—22no—
334C22×C11—22no—
335C22×C11—22no—
336C22×C11—41no—
337C22×C11—42no—
338C22×C11—42no—
339C22×C11—41no—
340C22×C11—41no—
341C22×C11—42no—
342C22×C11—84no—
343C22×C11#40812yes—
344C22×C11C22×C22⋊C411yescharacteristic
345C4×C11—22no—
346C4×C11—21no—
347C4×C11—22no—
348C4×C11—21no—
349C4×C11—21no—
350C4×C11—22no—
351C4×C11—41no—
352C4×C11—42no—
353C4×C11—41no—
354C4×C11—41no—
355C4×C11#40812yes—
356C4×C11C2×#13112yes—
357C4×C11#57611yescharacteristic
358C4×C11#57711yescharacteristic
359C2×#41—22no—
360C2×#41C2×Dic1111yescharacteristic
361C2×#41C2×Dic1111yescharacteristic
362C22×D4C2×Dic1111yescharacteristic
363C23×C4—21no—
364C2×M16—222no—
365C22×C8—221no—
366C22×C8—222no—
367C22×C8—221no—
368C4⋊Q8—21no—
369C4⋊Q8C2×Dic1112yes—
370#127—21no—
371#127C2×Dic1112yes—
372#126—22no—
373#126—22no—
374#125—21no—
375#125C2×Dic1112yes—
376#124—21no—
377#124—22no—
378#124—22no—
379#124C2×Dic1112yes—
380#123—22no—
381#123—22no—
382#123—22no—
383#123—22no—
384C22⋊Q8—21no—
385C22⋊Q8—22no—
386C22⋊Q8—22no—
387C22⋊Q8C2×Dic1112yes—
388#121—22no—
389#121—21no—
390#121—22no—
391#121—21no—
392#121—21no—
393#121—22no—
394#121—22no—
395#121C2×Dic1112yes—
396#121C2×Dic1112yes—
397#121C2×Dic1112yes—
398#120—22no—
399#120—22no—
400C4×Q8C2×Dic1111yescharacteristic
401C4×Q8C22⋊D1111yescharacteristic
402C4×Q8C22⋊D1111yescharacteristic
403C4×Q8C22×D1111yescharacteristic
404C4×D4—21no—
405C4×D4—21no—
406C4×D4—22no—
407C4×D4—21no—
408C4×D4—21no—
409C4×D4—22no—
410C4×D4C2×Dic1112yes—
411C4×D4C2×Dic1111yescharacteristic
412C4×D4C22⋊D1112yes—
413C4×D4C22⋊D1111yescharacteristic
414C4×D4C22⋊D1112yes—
415C4×D4C22⋊D1111yescharacteristic
416C4×D4C22×D1112yes—
417C4×D4C22×D1111yescharacteristic
418#117—21no—
419#117—22no—
420#117C2×Dic1111yescharacteristic
421#117C2×Dic1111yescharacteristic
422#117C2×Dic1112yes—
423C2×C4⋊C4C2×Dic1111yescharacteristic
424C2×C22⋊C4—21no—
425C2×C42—21no—
426C2×C42C22×D1111yescharacteristic
427C2×C42C22×D1112yes—
428C4⋊C8—112no—
429C4⋊C8—111no—
430C4⋊C8—111no—
431C4⋊C8—221no—
432C4⋊C8—222no—
433C4⋊C8—221no—
434C4⋊C8—222no—
435C22⋊C8—221no—
436C22⋊C8—222no—
437C22⋊C8—221no—
438C22⋊C8—222no—
439#97—222no—
440C4×C8—111no—
441C4×C8—111no—
442C4×C8—112no—
443C4×C8—221no—
444C4×C8—222no—
445C4×C8—221no—
446C2×C11—22no—
447C2×C11—42no—
448C2×C11—81no—
449C2×C11—82no—
450C2×C11C2×#40811yescharacteristic
451C2×C11#289711yescharacteristic
452C2×C11#290111yescharacteristic
453C24—21no—
454#41—24no—
455#41—24no—
456#41—82no—
457#41—82no—
458C2×Q8—22no—
459C2×Q8C22⋊Dic1111yescharacteristic
460C2×Q8C22×Dic1111yescharacteristic
461C2×D4—21no—
462C2×D4—22no—
463C2×D4—22no—
464C2×D4—22no—
465C2×D4—24no—
466C2×D4—21no—
467C2×D4—22no—
468C2×D4—22no—
469C2×D4C22⋊Dic1112yes—
470C2×D4C22⋊Dic1111yescharacteristic
471C2×D4C22×Dic1112yes—
472C2×D4C22×Dic1111yescharacteristic
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—22no—
477C22×C4—21no—
478C22×C4—22no—
479C22×C4—81no—
480C22×C4—81no—
481C22×C4C22×Dic1112yes—
482C22×C4C22×Dic1111yescharacteristic
483C22×C4C2×C22⋊D1111yescharacteristic
484C22×C4C2×C22⋊D1112yes—
485C22×C4C2×C22⋊D1111yescharacteristic
486C22×C4C2×C22⋊D1112yes—
487M16—882no—
488C2×C8—221no—
489C2×C8—221no—
490C2×C8—222no—
491C2×C8—221no—
492C2×C8—221no—
493C2×C8—222no—
494C2×C8—442no—
495C2×C8—444no—
496C2×C8—881no—
497C4⋊C4—21no—
498C4⋊C4—21no—
499C4⋊C4—22no—
500C4⋊C4—22no—
501C4⋊C4—22no—
502C4⋊C4—22no—
503C4⋊C4—21no—
504C4⋊C4C22⋊Dic1111yescharacteristic
505C4⋊C4C22⋊Dic1111yescharacteristic
506C4⋊C4C22⋊Dic1112yes—
507C4⋊C4C22⋊Dic1112yes—
508C4⋊C4C22×Dic1112yes—
509C4⋊C4C22×Dic1111yescharacteristic
510C4⋊C4C22×Dic1111yescharacteristic
511C22⋊C4—21no—
512C22⋊C4—22no—
513C22⋊C4—22no—
514C22⋊C4—21no—
515C22⋊C4—22no—
516C22⋊C4—22no—
517C22⋊C4—22no—
518C22⋊C4—22no—
519C22⋊C4—22no—
520C22⋊C4—22no—
521C22⋊C4—21no—
522C22⋊C4C22⋊Dic1112yes—
523C22⋊C4C22⋊Dic1112yes—
524C22⋊C4C22⋊Dic1112yes—
525C42—21no—
526C42—21no—
527C42—21no—
528C42C22×Dic1111yescharacteristic
529C42C22×Dic1112yes—
530C42C2×C22⋊D1111yescharacteristic
531C42C2×C22⋊D1112yes—
532C42C2×C22⋊D1111yescharacteristic
533C42C2×C22⋊D1112yes—
534C42C23×D1111yescharacteristic
535C11#1748311yescharacteristic, complemented, Sylow
536C23—22no—
537C23—21no—
538C23—42no—
539C23—81no—
540C23—81no—
541C23C2×C22⋊Dic1112yes—
542C23C2×C22⋊Dic1111yescharacteristic
543Q8—22no—
544Q8—22no—
545Q8—82no—
546D4—24no—
547D4—24no—
548D4—22no—
549D4—22no—
550D4—42no—
551D4—42no—
552D4—82no—
553D4—82no—
554D4—82no—
555D4—82no—
556D4—82no—
557C2×C4—24no—
558C2×C4—21no—
559C2×C4—22no—
560C2×C4—21no—
561C2×C4—22no—
562C2×C4—21no—
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—22no—
566C2×C4—41no—
567C2×C4—42no—
568C2×C4—42no—
569C2×C4—42no—
570C2×C4—41no—
571C2×C4—42no—
572C2×C4—41no—
573C2×C4—81no—
574C2×C4—82no—
575C2×C4—81no—
576C2×C4#6700114yes—
577C2×C4C2×C22⋊Dic1111yescharacteristic
578C2×C4C2×C22⋊Dic1112yes—
579C2×C4C2×C22⋊Dic1111yescharacteristic
580C2×C4C2×C22⋊Dic1112yes—
581C2×C4C2×C22⋊Dic1112yes—
582C2×C4C2×C22⋊Dic1111yescharacteristic
583C2×C4C23×Dic1111yescharacteristic
584C2×C4C22×C22⋊D1111yescharacteristic
585C2×C4C22×C22⋊D1111yescharacteristic
586C8—222no—
587C8—441no—
588C8—442no—
589C8—442no—
590C8—441no—
591C8—441no—
592C22—21no—
593C22—21no—
594C22—22no—
595C22—22no—
596C22—22no—
597C22—41no—
598C22—42no—
599C22—42no—
600C22—41no—
601C22—41no—
602C22—42no—
603C22—84no—
604C22#1062284712yes—
605C22C22×C22⋊Dic1111yescharacteristic
606C4—22no—
607C4—21no—
608C4—22no—
609C4—21no—
610C4—21no—
611C4—22no—
612C4—41no—
613C4—42no—
614C4—41no—
615C4—41no—
616C4#1062284712yes—
617C4C2×#6700112yes—
618C4#1062336611yescharacteristic
619C4#1062336711yescharacteristic
620C2—22no—
621C2—42no—
622C2—82no—
623C2—81no—
624C2C2×#1062284711yescharacteristic
625C2#1307714211yescharacteristic
626C2#1307716311yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
Fitting, prime radicalC11×#3460C2
socleC22×C11C22×C22⋊C4
cosocleC42×C11C24
hypercenter#3460D11
hypocenterC11#17483
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C4×#41 ◁ #3460

Complements

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

NH ≅ G/Ntype
1. #13077733C2semidirect
2. #41×C11⋊C8C2semidirect
3. #13067085C2semidirect
4. #13067081C2semidirect
5. #13067076C2semidirect
6. #13067067C2semidirect
7. #13067007C2semidirect
8. #13067003C2semidirect
9. #13066998C2semidirect
10. C2×D4⋊(C11⋊C8)C2semidirect
35. #10622539C22semidirect
38. #10622538C22semidirect
39. #10622537C22semidirect
42. C2×C4×C11⋊C8C22semidirect
43. Q8⋊(C11⋊C8)C22semidirect
44. Q8⋊(C11⋊C8)C22semidirect
45. Q8⋊(C11⋊C8)C22semidirect
50. D4⋊(C11⋊C8)C22semidirect
51. D4⋊(C11⋊C8)C22semidirect
52. D4⋊(C11⋊C8)C22semidirect
535. C11#17483semidirect

Maximal subgroups

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

subgroupindex
#130777332
#41×C11⋊C82
#130670852
#130670812
#130670762
#130670672
#130670072
#130670032
#130669982
C2×D4⋊(C11⋊C8)2
C11×#34602
#1748311