Finite Group Databasebeta

← #14720641

Subgroups — #14720641

Order 2816.

980 conjugacy classes of subgroups.

The subgroup lattice has 636 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#41×C11⋊C8C211yesmaximal, characteristic, complemented
2#13077282C211yesmaximal, characteristic, complemented
3#13067076C212yesmaximal, complemented
4#13067071C211yesmaximal, characteristic, complemented
5#13067050C212yesmaximal, complemented
6#13067041C211yesmaximal, characteristic, complemented
7#13067024C212yesmaximal, complemented
8#13067019C211yesmaximal, characteristic, complemented
9#13066998C212yesmaximal, 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—
29#10622847—21no—
30Q8×C11⋊C8—21no—
31D4×C11⋊C8—21no—
32D4×C11⋊C8—22no—
33#10622613—22no—
34#10622610—21no—
35#10622539C2212yescomplemented
36#10622538C2211yescharacteristic
37#10622538C2212yescomplemented
38#10622538C2212yescomplemented
39#10622537C2211yescharacteristic
40C2×C4⋊(C11⋊C8)C2211yescharacteristic
41C2×C4×C11⋊C8C2211yescharacteristic
42C2×C4×C11⋊C8C2212yescomplemented
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—
118C2×#4318—21no—
119C22×C11⋊C8—21no—
120C22×C11⋊C8—22no—
121C22×C11⋊C8—21no—
122C22⋊(C11⋊C8)—21no—
123C22⋊(C11⋊C8)—22no—
124C22⋊(C11⋊C8)—22no—
125C22⋊(C11⋊C8)—22no—
126C4⋊(C11⋊C8)—21no—
127C4⋊(C11⋊C8)—21no—
128C4⋊(C11⋊C8)—21no—
129C4⋊(C11⋊C8)—22no—
130C4⋊(C11⋊C8)C2311yescharacteristic
131C4⋊(C11⋊C8)C2311yescharacteristic
132C4⋊(C11⋊C8)C2312yes—
133#66867—22no—
134C4×C11⋊C8—21no—
135C4×C11⋊C8—22no—
136C4×C11⋊C8—22no—
137C4×C11⋊C8C2311yescharacteristic
138C4×C11⋊C8C2311yescharacteristic
139C4×C11⋊C8C2312yes—
140#17508—111nomaximal, Sylow
141C24×C11—21no—
142C11×#41—22no—
143C11×#41—22no—
144C11×#41—24no—
145C11×#41—42no—
146C2×Q8×C11—21no—
147C2×Q8×C11C22⋊C411yescharacteristic
148C2×Q8×C11C22×C412yes—
149C2×D4×C11—22no—
150C2×D4×C11—22no—
151C2×D4×C11—22no—
152C2×D4×C11—21no—
153C2×D4×C11—41no—
154C2×D4×C11C22⋊C412yes—
155C2×D4×C11C22⋊C411yescharacteristic
156C2×D4×C11C22×C411yescharacteristic
157C2×D4×C11C22×C411yescharacteristic
158C22×C4×C11—21no—
159C22×C4×C11—22no—
160C22×C4×C11—21no—
161C22×C4×C11—21no—
162C22×C4×C11—21no—
163C22×C4×C11—21no—
164C22×C4×C11—22no—
165C22×C4×C11—42no—
166C22×C4×C11—42no—
167C22×C4×C11C22×C411yescharacteristic
168C22×C4×C11C22×C412yes—
169C22×C4×C11C2×D412yes—
170C22×C4×C11C2×D411yescharacteristic
171C22×C4×C11C2×D412yes—
172C22×C4×C11C2×D411yescharacteristic
173C11×C4⋊C4—21no—
174C11×C4⋊C4—21no—
175C11×C4⋊C4—22no—
176C11×C4⋊C4—22no—
177C11×C4⋊C4—21no—
178C11×C4⋊C4—22no—
179C11×C4⋊C4—22no—
180C11×C4⋊C4—22no—
181C11×C4⋊C4—21no—
182C11×C4⋊C4—22no—
183C11×C4⋊C4C22⋊C411yescharacteristic
184C11×C4⋊C4C22⋊C411yescharacteristic
185C11×C4⋊C4C22⋊C412yes—
186C11×C4⋊C4C22⋊C412yes—
187C11×C4⋊C4C22×C411yescharacteristic
188C11×C4⋊C4C22×C411yescharacteristic
189C11×C4⋊C4C22×C412yes—
190C11×C22⋊C4—22no—
191C11×C22⋊C4—22no—
192C11×C22⋊C4—22no—
193C11×C22⋊C4—22no—
194C11×C22⋊C4—22no—
195C11×C22⋊C4—21no—
196C11×C22⋊C4—21no—
197C11×C22⋊C4—22no—
198C11×C22⋊C4—22no—
199C11×C22⋊C4—21no—
200C11×C22⋊C4—21no—
201C11×C22⋊C4C22⋊C412yes—
202C11×C22⋊C4C22⋊C412yes—
203C11×C22⋊C4C22⋊C412yes—
204C42×C11—22no—
205C42×C11—22no—
206C42×C11—22no—
207C42×C11C22×C411yescharacteristic
208C42×C11C22×C412yes—
209C42×C11C2×D412yes—
210C42×C11C2×D412yes—
211C42×C11C2×D411yescharacteristic
212C42×C11C2×D411yescharacteristic
213C42×C11C2411yescharacteristic
214#4318—42no—
215C2×C11⋊C8—21no—
216C2×C11⋊C8—21no—
217C2×C11⋊C8—21no—
218C2×C11⋊C8—22no—
219C2×C11⋊C8—22no—
220C2×C11⋊C8—21no—
221C2×C11⋊C8—42no—
222C2×C11⋊C8—44no—
223C2×C11⋊C8—42no—
224#3475D1111yescharacteristic
225C8×#41—111no—
226#2925—111no—
227#1494—112no—
228#1493—111no—
229#1488—112no—
230#1486—111no—
231#1482—112no—
232#1481—111no—
233#1476—112no—
234C2×D4⋊C8—111no—
235C23×C11—21no—
236C23×C11—21no—
237C23×C11—42no—
238C23×C11—42no—
239C23×C11—81no—
240C23×C11C2×C22⋊C412yes—
241C23×C11C2×C22⋊C411yescharacteristic
242Q8×C11—22no—
243Q8×C11—22no—
244Q8×C11—22no—
245Q8×C11—81no—
246D4×C11—24no—
247D4×C11—21no—
248D4×C11—21no—
249D4×C11—21no—
250D4×C11—22no—
251D4×C11—42no—
252D4×C11—44no—
253D4×C11—82no—
254D4×C11#13112yes—
255C2×C4×C11—21no—
256C2×C4×C11—22no—
257C2×C4×C11—21no—
258C2×C4×C11—22no—
259C2×C4×C11—22no—
260C2×C4×C11—22no—
261C2×C4×C11—21no—
262C2×C4×C11—22no—
263C2×C4×C11—22no—
264C2×C4×C11—21no—
265C2×C4×C11—42no—
266C2×C4×C11—41no—
267C2×C4×C11—44no—
268C2×C4×C11—42no—
269C2×C4×C11—41no—
270C2×C4×C11—41no—
271C2×C4×C11—41no—
272C2×C4×C11—41no—
273C2×C4×C11—42no—
274C2×C4×C11—42no—
275C2×C4×C11—82no—
276C2×C4×C11C2×C22⋊C412yes—
277C2×C4×C11C2×C22⋊C412yes—
278C2×C4×C11C2×C22⋊C411yescharacteristic
279C2×C4×C11C2×C22⋊C412yes—
280C2×C4×C11C2×C22⋊C411yescharacteristic
281C2×C4×C11C2×C22⋊C411yescharacteristic
282C2×C4×C11#13512yes—
283C2×C4×C11#13512yes—
284C2×C4×C11C23×C411yescharacteristic
285C2×C4×C11C22×D411yescharacteristic
286C2×C4×C11C22×D411yescharacteristic
287C11⋊C8—22no—
288C11⋊C8—41no—
289C11⋊C8—42no—
290C11⋊C8—41no—
291C11⋊C8—41no—
292C11⋊C8—42no—
293#556Dic1111yescharacteristic
294#555Dic1111yescharacteristic
295#554Dic1111yescharacteristic
296#553—21no—
297#552—21no—
298#552Dic1112yes—
299#551—22no—
300#547Dic1111yescharacteristic
301#546Dic1112yes—
302#533C2×D1111yescharacteristic
303#529—22no—
304#529C2×D1112yes—
305#525—21no—
306C4×#41C2×D1112yes—
307C4×#41C2×D1111yescharacteristic
308C2×C4×D4C2×D1111yescharacteristic
309C2×#117—21no—
310C8×Q8—221no—
311C8×D4—222no—
312C8×D4—221no—
313#433—222no—
314#432—112no—
315#431—111no—
316#431—112no—
317#431—112no—
318#423—111no—
319C2×C4⋊C8—111no—
320#408—221no—
321#405—221no—
322C2×C4×C8—111no—
323C2×C4×C8—112no—
324Q8⋊C8—112no—
325Q8⋊C8—112no—
326Q8⋊C8—112no—
327Q8⋊C8—112no—
328D4⋊C8—111no—
329D4⋊C8—111no—
330D4⋊C8—111no—
331D4⋊C8—111no—
332D4⋊C8—112no—
333D4⋊C8—112no—
334C22×C11—21no—
335C22×C11—21no—
336C22×C11—22no—
337C22×C11—22no—
338C22×C11—22no—
339C22×C11—22no—
340C22×C11—41no—
341C22×C11—41no—
342C22×C11—41no—
343C22×C11—41no—
344C22×C11—41no—
345C22×C11—84no—
346C22×C11#41612yes—
347C22×C11C22×C22⋊C411yescharacteristic
348C4×C11—22no—
349C4×C11—21no—
350C4×C11—22no—
351C4×C11—21no—
352C4×C11—22no—
353C4×C11—21no—
354C4×C11—42no—
355C4×C11—41no—
356C4×C11—41no—
357C4×C11—42no—
358C4×C11#41612yes—
359C4×C11C2×#13111yescharacteristic
360C4×C11#56811yescharacteristic
361C4×C11C2×#13511yescharacteristic
362C4×C11C2×#13511yescharacteristic
363C2×#41C2×Dic1112yes—
364C2×#41C22⋊D1111yescharacteristic
365C22×D4C2×Dic1111yescharacteristic
366C23×C4—21no—
367C2×M16—221no—
368C22×C8—221no—
369C22×C8—222no—
370C22×C8—221no—
371C4⋊Q8C2×Dic1111yescharacteristic
372C4⋊Q8C2×Dic1111yescharacteristic
373#126—22no—
374#126—22no—
375#126—22no—
376#125—22no—
377#125—21no—
378#125C2×Dic1112yes—
379#124—22no—
380#124C2×Dic1112yes—
381#123—22no—
382#123—22no—
383#123—22no—
384#123—22no—
385C22⋊Q8—21no—
386C22⋊Q8—21no—
387C22⋊Q8—21no—
388C22⋊Q8—22no—
389C22⋊Q8C2×Dic1112yes—
390C22⋊Q8C2×Dic1112yes—
391#121—21no—
392#121—21no—
393#121—22no—
394#121C2×Dic1112yes—
395#120—22no—
396C4×Q8—21no—
397C4×Q8C2×Dic1112yes—
398C4×Q8C2×Dic1111yescharacteristic
399C4×Q8C22⋊D1111yescharacteristic
400C4×Q8C22×D1112yes—
401C4×D4—22no—
402C4×D4—22no—
403C4×D4—22no—
404C4×D4—21no—
405C4×D4—21no—
406C4×D4C2×Dic1111yescharacteristic
407C4×D4C2×Dic1111yescharacteristic
408C4×D4C2×Dic1112yes—
409C4×D4C2×Dic1112yes—
410C4×D4C2×Dic1111yescharacteristic
411C4×D4C22⋊D1112yes—
412C4×D4C22⋊D1111yescharacteristic
413C4×D4C22×D1111yescharacteristic
414C4×D4C22×D1111yescharacteristic
415#117—21no—
416#117—21no—
417#117—21no—
418#117—22no—
419#117—22no—
420#117—22no—
421#117C2×Dic1112yes—
422#117C22⋊D1111yescharacteristic
423#117C22⋊D1112yes—
424C2×C4⋊C4—21no—
425C2×C4⋊C4—21no—
426C2×C4⋊C4C2×Dic1111yescharacteristic
427C2×C22⋊C4—21no—
428C2×C22⋊C4—22no—
429C2×C42—22no—
430C2×C42C22×D1111yescharacteristic
431C2×C42C22×D1112yes—
432C4⋊C8—111no—
433C4⋊C8—111no—
434C4⋊C8—112no—
435C4⋊C8—221no—
436C4⋊C8—221no—
437C4⋊C8—222no—
438C4⋊C8—221no—
439C22⋊C8—222no—
440C22⋊C8—222no—
441C22⋊C8—221no—
442C22⋊C8—222no—
443#97—222no—
444C4×C8—111no—
445C4×C8—111no—
446C4×C8—112no—
447C4×C8—222no—
448C4×C8—221no—
449C4×C8—222no—
450C2×C11—22no—
451C2×C11—42no—
452C2×C11—42no—
453C2×C11—81no—
454C2×C11#288011yescharacteristic
455C2×C11C2×#41611yescharacteristic
456C2×C11#290111yescharacteristic
457C24—21no—
458#41—22no—
459#41—22no—
460#41—24no—
461#41—42no—
462C2×Q8—21no—
463C2×Q8C22⋊Dic1111yescharacteristic
464C2×Q8C22×Dic1112yes—
465C2×D4—22no—
466C2×D4—22no—
467C2×D4—22no—
468C2×D4—21no—
469C2×D4—41no—
470C2×D4C22⋊Dic1112yes—
471C2×D4C22⋊Dic1111yescharacteristic
472C2×D4C22×Dic1111yescharacteristic
473C2×D4C22×Dic1111yescharacteristic
474C22×C4—21no—
475C22×C4—22no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—22no—
481C22×C4—42no—
482C22×C4—42no—
483C22×C4C22×Dic1111yescharacteristic
484C22×C4C22×Dic1112yes—
485C22×C4C2×C22⋊D1112yes—
486C22×C4C2×C22⋊D1111yescharacteristic
487C22×C4C2×C22⋊D1112yes—
488C22×C4C2×C22⋊D1111yescharacteristic
489M16—442no—
490C2×C8—221no—
491C2×C8—221no—
492C2×C8—222no—
493C2×C8—221no—
494C2×C8—222no—
495C2×C8—221no—
496C2×C8—444no—
497C2×C8—442no—
498C2×C8—442no—
499C4⋊C4—21no—
500C4⋊C4—21no—
501C4⋊C4—22no—
502C4⋊C4—22no—
503C4⋊C4—21no—
504C4⋊C4—22no—
505C4⋊C4—22no—
506C4⋊C4—22no—
507C4⋊C4—21no—
508C4⋊C4—22no—
509C4⋊C4C22⋊Dic1111yescharacteristic
510C4⋊C4C22⋊Dic1111yescharacteristic
511C4⋊C4C22⋊Dic1112yes—
512C4⋊C4C22⋊Dic1112yes—
513C4⋊C4C22×Dic1111yescharacteristic
514C4⋊C4C22×Dic1111yescharacteristic
515C4⋊C4C22×Dic1112yes—
516C22⋊C4—22no—
517C22⋊C4—22no—
518C22⋊C4—22no—
519C22⋊C4—22no—
520C22⋊C4—22no—
521C22⋊C4—21no—
522C22⋊C4—21no—
523C22⋊C4—22no—
524C22⋊C4—22no—
525C22⋊C4—21no—
526C22⋊C4—21no—
527C22⋊C4C22⋊Dic1112yes—
528C22⋊C4C22⋊Dic1112yes—
529C22⋊C4C22⋊Dic1112yes—
530C42—22no—
531C42—22no—
532C42—22no—
533C42C22×Dic1111yescharacteristic
534C42C22×Dic1112yes—
535C42C2×C22⋊D1112yes—
536C42C2×C22⋊D1111yescharacteristic
537C42C2×C22⋊D1112yes—
538C42C2×C22⋊D1111yescharacteristic
539C42C23×D1111yescharacteristic
540C11#1750811yescharacteristic, complemented, Sylow
541C23—21no—
542C23—21no—
543C23—42no—
544C23—42no—
545C23—81no—
546C23C2×C22⋊Dic1112yes—
547C23C2×C22⋊Dic1111yescharacteristic
548Q8—22no—
549Q8—22no—
550Q8—22no—
551Q8—81no—
552D4—24no—
553D4—21no—
554D4—21no—
555D4—21no—
556D4—22no—
557D4—42no—
558D4—44no—
559D4—82no—
560D4#6700112yes—
561C2×C4—21no—
562C2×C4—22no—
563C2×C4—21no—
564C2×C4—22no—
565C2×C4—22no—
566C2×C4—22no—
567C2×C4—21no—
568C2×C4—22no—
569C2×C4—22no—
570C2×C4—21no—
571C2×C4—42no—
572C2×C4—41no—
573C2×C4—44no—
574C2×C4—42no—
575C2×C4—41no—
576C2×C4—41no—
577C2×C4—41no—
578C2×C4—41no—
579C2×C4—42no—
580C2×C4—42no—
581C2×C4—82no—
582C2×C4#6700312yes—
583C2×C4#6700312yes—
584C2×C4C2×C22⋊Dic1112yes—
585C2×C4C2×C22⋊Dic1112yes—
586C2×C4C2×C22⋊Dic1111yescharacteristic
587C2×C4C2×C22⋊Dic1112yes—
588C2×C4C2×C22⋊Dic1111yescharacteristic
589C2×C4C2×C22⋊Dic1111yescharacteristic
590C2×C4C23×Dic1111yescharacteristic
591C2×C4C22×C22⋊D1111yescharacteristic
592C2×C4C22×C22⋊D1111yescharacteristic
593C8—222no—
594C8—441no—
595C8—442no—
596C8—441no—
597C8—441no—
598C8—442no—
599C22—21no—
600C22—21no—
601C22—22no—
602C22—22no—
603C22—22no—
604C22—22no—
605C22—41no—
606C22—41no—
607C22—41no—
608C22—41no—
609C22—41no—
610C22—84no—
611C22#1062284612yes—
612C22C22×C22⋊Dic1111yescharacteristic
613C4—22no—
614C4—21no—
615C4—22no—
616C4—21no—
617C4—22no—
618C4—21no—
619C4—42no—
620C4—41no—
621C4—41no—
622C4—42no—
623C4#1062284612yes—
624C4C2×#6700111yescharacteristic
625C4#1062335011yescharacteristic
626C4C2×#6700311yescharacteristic
627C4C2×#6700311yescharacteristic
628C2—22no—
629C2—42no—
630C2—42no—
631C2—81no—
632C2#1307706511yescharacteristic
633C2C2×#1062284611yescharacteristic
634C2#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#17508
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. #41×C11⋊C8C2semidirect
2. #13077282C2semidirect
3. #13067076C2semidirect
4. #13067071C2semidirect
5. #13067050C2semidirect
6. #13067041C2semidirect
7. #13067024C2semidirect
8. #13067019C2semidirect
9. #13066998C2semidirect
10. C2×D4⋊(C11⋊C8)C2semidirect
35. #10622539C22semidirect
37. #10622538C22semidirect
38. #10622538C22semidirect
42. C2×C4×C11⋊C8C22semidirect
43. Q8⋊(C11⋊C8)C22semidirect
44. Q8⋊(C11⋊C8)C22semidirect
45. Q8⋊(C11⋊C8)C22semidirect
46. Q8⋊(C11⋊C8)C22semidirect
540. C11#17508semidirect

Maximal subgroups

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

subgroupindex
#41×C11⋊C82
#130772822
#130670762
#130670712
#130670502
#130670412
#130670242
#130670192
#130669982
C2×D4⋊(C11⋊C8)2
C11×#34752
#1750811