Finite Group Databasebeta

← #14720362

Subgroups — #14720362

Order 2816.

920 conjugacy classes of subgroups.

The subgroup lattice has 594 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13077727C211yesmaximal, characteristic, complemented
2#13077583C211yesmaximal, characteristic, complemented
3#13067037C212yesmaximal, complemented
4#13067029C212yesmaximal, complemented
5#13067024C212yesmaximal, complemented
6#13067019C212yesmaximal, complemented
7#13067011C211yesmaximal, characteristic, complemented
8#13067003C211yesmaximal, characteristic, complemented
9#13066998C211yesmaximal, characteristic, complemented
10C2×Q8⋊(C11⋊C8)C211yesmaximal, characteristic, complemented
11C11×#3461C211yesmaximal, characteristic
12C11×#544C411yescharacteristic
13C11×#542—21no—
14C11×#542C412yes—
15C11×#541—21no—
16C11×#541C412yes—
17C11×#539—22no—
18C11×#537C411yescharacteristic
19C11×#536C411yescharacteristic
20C11×#536C411yescharacteristic
21C11×#533—21no—
22C11×#533C2212yes—
23C11×#529—22no—
24C11×#529—21no—
25C11×#529C2212yes—
26C4×C11×#41C2211yescharacteristic
27C4×C11×#41C2211yescharacteristic
28C2×C4×Q8×C11C2211yescharacteristic
29#10622637—21no—
30Q8×C11⋊C8—21no—
31#10622625—21no—
32#10622624—22no—
33D4×C11⋊C8—21no—
34D4×C11⋊C8—22no—
35#10622538C2211yescharacteristic
36#10622538C2212yes—
37#10622538C2211yescharacteristic
38#10622538C2212yes—
39C2×C4⋊(C11⋊C8)C2212yes—
40C2×C4⋊(C11⋊C8)C2211yescharacteristic
41C4×#4318C2212yes—
42C2×C4×C11⋊C8C2211yescharacteristic
43Q8⋊(C11⋊C8)C2212yes—
44Q8⋊(C11⋊C8)C2212yes—
45Q8⋊(C11⋊C8)C2211yescharacteristic
46Q8⋊(C11⋊C8)C2212yes—
47Q8⋊(C11⋊C8)C2212yes—
48Q8⋊(C11⋊C8)C2212yes—
49Q8⋊(C11⋊C8)C2211yescharacteristic
50D4⋊(C11⋊C8)C2211yescharacteristic
51D4⋊(C11⋊C8)C2212yes—
52D4⋊(C11⋊C8)C2211yescharacteristic
53C2×C11×#41C2×C411yescharacteristic
54C2×C11×#41C2×C411yescharacteristic
55C22×Q8×C11C2×C411yescharacteristic
56C11×C4⋊Q8—21no—
57C11×C4⋊Q8—21no—
58C11×C4⋊Q8C2×C412yes—
59C11×C4⋊Q8C2×C412yes—
60C11×#126—22no—
61C11×#126—22no—
62C11×#126—22no—
63C11×#126—22no—
64C11×#125—22no—
65C11×#125—21no—
66C11×#125—22no—
67C11×#125—22no—
68C11×#125C2×C412yes—
69C11×#124—21no—
70C11×#124—22no—
71C11×#124C2×C412yes—
72C11×#123—22no—
73C11×#123—22no—
74C11×#123—22no—
75C11×#123—22no—
76C11×C22⋊Q8—21no—
77C11×C22⋊Q8—22no—
78C11×C22⋊Q8—21no—
79C11×C22⋊Q8—21no—
80C11×C22⋊Q8—22no—
81C11×C22⋊Q8—22no—
82C11×C22⋊Q8C2×C412yes—
83C11×C22⋊Q8C2×C412yes—
84C11×C22⋊Q8C2×C412yes—
85C11×#121—22no—
86C11×#121—21no—
87C11×#121C2×C412yes—
88C4×Q8×C11—21no—
89C4×Q8×C11—21no—
90C4×Q8×C11—22no—
91C4×Q8×C11C2×C412yes—
92C4×Q8×C11C2×C411yescharacteristic
93C4×Q8×C11D411yescharacteristic
94C4×Q8×C11D411yescharacteristic
95C4×Q8×C11C2312yes—
96C4×Q8×C11C2311yescharacteristic
97C4×D4×C11—21no—
98C4×D4×C11—21no—
99C4×D4×C11—22no—
100C4×D4×C11C2×C411yescharacteristic
101C4×D4×C11D411yescharacteristic
102C4×D4×C11D412yes—
103C4×D4×C11D412yes—
104C4×D4×C11D411yescharacteristic
105C4×D4×C11C2311yescharacteristic
106C11×#117—22no—
107C11×#117—21no—
108C11×#117—22no—
109C11×#117C2×C411yescharacteristic
110C11×#117C2×C411yescharacteristic
111C11×#117C2×C412yes—
112C2×C11×C4⋊C4—21no—
113C2×C11×C4⋊C4C2×C411yescharacteristic
114C2×C42×C11—21no—
115C2×C42×C11—21no—
116C2×C42×C11C2311yescharacteristic
117C2×C42×C11C2312yes—
118C2×#4318—22no—
119C22×C11⋊C8—21no—
120C22×C11⋊C8—21no—
121C22×C11⋊C8—22no—
122C22⋊(C11⋊C8)—21no—
123C22⋊(C11⋊C8)—22no—
124C22⋊(C11⋊C8)—21no—
125C22⋊(C11⋊C8)—22no—
126C4⋊(C11⋊C8)—21no—
127C4⋊(C11⋊C8)—22no—
128C4⋊(C11⋊C8)—22no—
129C4⋊(C11⋊C8)—21no—
130C4⋊(C11⋊C8)C2311yescharacteristic
131C4⋊(C11⋊C8)C2312yes—
132C4⋊(C11⋊C8)C2311yescharacteristic
133#66867—22no—
134C4×C11⋊C8—21no—
135C4×C11⋊C8—21no—
136C4×C11⋊C8—22no—
137C4×C11⋊C8C2311yescharacteristic
138C4×C11⋊C8C2311yescharacteristic
139C4×C11⋊C8C2312yes—
140#17469—111nomaximal, Sylow
141C11×#41—24no—
142C11×#41—24no—
143C2×Q8×C11—21no—
144C2×Q8×C11—22no—
145C2×Q8×C11—24no—
146C2×Q8×C11C22⋊C411yescharacteristic
147C2×Q8×C11C22×C412yes—
148C2×Q8×C11C22×C411yescharacteristic
149C2×D4×C11—21no—
150C2×D4×C11—22no—
151C2×D4×C11C22⋊C412yes—
152C2×D4×C11C22⋊C411yescharacteristic
153C2×D4×C11C22×C411yescharacteristic
154C22×C4×C11—21no—
155C22×C4×C11—21no—
156C22×C4×C11—21no—
157C22×C4×C11—21no—
158C22×C4×C11—21no—
159C22×C4×C11C22×C412yes—
160C22×C4×C11C22×C411yescharacteristic
161C22×C4×C11C2×D411yescharacteristic
162C22×C4×C11C2×D412yes—
163C22×C4×C11C2×D411yescharacteristic
164C22×C4×C11C2×D412yes—
165C11×C4⋊C4—22no—
166C11×C4⋊C4—21no—
167C11×C4⋊C4—21no—
168C11×C4⋊C4—22no—
169C11×C4⋊C4—22no—
170C11×C4⋊C4—22no—
171C11×C4⋊C4—22no—
172C11×C4⋊C4—22no—
173C11×C4⋊C4—22no—
174C11×C4⋊C4—22no—
175C11×C4⋊C4—22no—
176C11×C4⋊C4—22no—
177C11×C4⋊C4—21no—
178C11×C4⋊C4C22⋊C412yes—
179C11×C4⋊C4C22⋊C411yescharacteristic
180C11×C4⋊C4C22⋊C411yescharacteristic
181C11×C4⋊C4C22⋊C412yes—
182C11×C4⋊C4C22×C412yes—
183C11×C4⋊C4C22×C411yescharacteristic
184C11×C4⋊C4C22×C411yescharacteristic
185C11×C22⋊C4—22no—
186C11×C22⋊C4—22no—
187C11×C22⋊C4—21no—
188C11×C22⋊C4—22no—
189C11×C22⋊C4—21no—
190C11×C22⋊C4—22no—
191C11×C22⋊C4—22no—
192C11×C22⋊C4—22no—
193C11×C22⋊C4—21no—
194C11×C22⋊C4C22⋊C412yes—
195C11×C22⋊C4C22⋊C412yes—
196C11×C22⋊C4C22⋊C412yes—
197C42×C11—21no—
198C42×C11—21no—
199C42×C11—22no—
200C42×C11—22no—
201C42×C11—21no—
202C42×C11C22×C411yescharacteristic
203C42×C11C22×C412yes—
204C42×C11C2×D411yescharacteristic
205C42×C11C2×D411yescharacteristic
206C42×C11C2×D412yes—
207C42×C11C2×D412yes—
208C42×C11C2411yescharacteristic
209#4318—44no—
210C2×C11⋊C8—21no—
211C2×C11⋊C8—21no—
212C2×C11⋊C8—21no—
213C2×C11⋊C8—21no—
214C2×C11⋊C8—22no—
215C2×C11⋊C8—22no—
216C2×C11⋊C8—42no—
217C2×C11⋊C8—81no—
218C2×C11⋊C8—82no—
219#3461D1111yescharacteristic
220#2988—111no—
221#2965—111no—
222#1485—112no—
223#1483—112no—
224#1482—112no—
225#1481—112no—
226#1479—111no—
227#1477—111no—
228#1476—111no—
229C2×Q8⋊C8—111no—
230C23×C11—21no—
231C23×C11C2×C22⋊C412yes—
232C23×C11C2×C22⋊C411yescharacteristic
233Q8×C11—22no—
234Q8×C11—24no—
235Q8×C11—22no—
236Q8×C11—42no—
237Q8×C11—82no—
238D4×C11—24no—
239D4×C11—22no—
240D4×C11—22no—
241D4×C11—42no—
242D4×C11—82no—
243C2×C4×C11—24no—
244C2×C4×C11—21no—
245C2×C4×C11—22no—
246C2×C4×C11—21no—
247C2×C4×C11—22no—
248C2×C4×C11—21no—
249C2×C4×C11—22no—
250C2×C4×C11—21no—
251C2×C4×C11—21no—
252C2×C4×C11—22no—
253C2×C4×C11—41no—
254C2×C4×C11—42no—
255C2×C4×C11—42no—
256C2×C4×C11—41no—
257C2×C4×C11—41no—
258C2×C4×C11—42no—
259C2×C4×C11—81no—
260C2×C4×C11—81no—
261C2×C4×C11C2×C22⋊C411yescharacteristic
262C2×C4×C11C2×C22⋊C411yescharacteristic
263C2×C4×C11C2×C22⋊C412yes—
264C2×C4×C11C2×C22⋊C412yes—
265C2×C4×C11C2×C22⋊C412yes—
266C2×C4×C11C2×C22⋊C411yescharacteristic
267C2×C4×C11#13114yes—
268C2×C4×C11C23×C411yescharacteristic
269C2×C4×C11C22×D411yescharacteristic
270C2×C4×C11C22×D411yescharacteristic
271C11⋊C8—22no—
272C11⋊C8—41no—
273C11⋊C8—42no—
274C11⋊C8—41no—
275C11⋊C8—42no—
276C11⋊C8—41no—
277#544Dic1111yescharacteristic
278#542—21no—
279#542Dic1112yes—
280#541—21no—
281#541Dic1112yes—
282#539—22no—
283#537Dic1111yescharacteristic
284#536Dic1111yescharacteristic
285#536Dic1111yescharacteristic
286#533—21no—
287#533C2×D1112yes—
288#529—22no—
289#529—21no—
290#529C2×D1112yes—
291C4×#41C2×D1111yescharacteristic
292C4×#41C2×D1111yescharacteristic
293C2×C4×Q8C2×D1111yescharacteristic
294#446—221no—
295C8×Q8—221no—
296#436—221no—
297#435—222no—
298C8×D4—221no—
299C8×D4—222no—
300#431—111no—
301#431—112no—
302#431—111no—
303#431—112no—
304C2×C4⋊C8—111no—
305C2×C4⋊C8—112no—
306C4×M16—112no—
307C2×C4×C8—111no—
308Q8⋊C8—112no—
309Q8⋊C8—112no—
310Q8⋊C8—111no—
311Q8⋊C8—111no—
312Q8⋊C8—112no—
313Q8⋊C8—112no—
314Q8⋊C8—112no—
315D4⋊C8—111no—
316D4⋊C8—111no—
317D4⋊C8—112no—
318C22×C11—21no—
319C22×C11—21no—
320C22×C11—22no—
321C22×C11—22no—
322C22×C11—22no—
323C22×C11—41no—
324C22×C11—41no—
325C22×C11—41no—
326C22×C11#40812yes—
327C22×C11C22×C22⋊C411yescharacteristic
328C4×C11—22no—
329C4×C11—21no—
330C4×C11—22no—
331C4×C11—21no—
332C4×C11—21no—
333C4×C11—22no—
334C4×C11—41no—
335C4×C11—42no—
336C4×C11—41no—
337C4×C11—42no—
338C4×C11—41no—
339C4×C11#40812yes—
340C4×C11C2×#13112yes—
341C4×C11#57711yescharacteristic
342C4×C11#57811yescharacteristic
343C2×#41C2×Dic1111yescharacteristic
344C2×#41C2×Dic1111yescharacteristic
345C22×Q8C2×Dic1111yescharacteristic
346C2×M16—222no—
347C22×C8—221no—
348C22×C8—221no—
349C22×C8—222no—
350C4⋊Q8—21no—
351C4⋊Q8—21no—
352C4⋊Q8C2×Dic1112yes—
353C4⋊Q8C2×Dic1112yes—
354#126—22no—
355#126—22no—
356#126—22no—
357#126—22no—
358#125—22no—
359#125—21no—
360#125—22no—
361#125—22no—
362#125C2×Dic1112yes—
363#124—21no—
364#124—22no—
365#124C2×Dic1112yes—
366#123—22no—
367#123—22no—
368#123—22no—
369#123—22no—
370C22⋊Q8—21no—
371C22⋊Q8—22no—
372C22⋊Q8—21no—
373C22⋊Q8—21no—
374C22⋊Q8—22no—
375C22⋊Q8—22no—
376C22⋊Q8C2×Dic1112yes—
377C22⋊Q8C2×Dic1112yes—
378C22⋊Q8C2×Dic1112yes—
379#121—22no—
380#121—21no—
381#121C2×Dic1112yes—
382C4×Q8—21no—
383C4×Q8—21no—
384C4×Q8—22no—
385C4×Q8C2×Dic1112yes—
386C4×Q8C2×Dic1111yescharacteristic
387C4×Q8C22⋊D1111yescharacteristic
388C4×Q8C22⋊D1111yescharacteristic
389C4×Q8C22×D1112yes—
390C4×Q8C22×D1111yescharacteristic
391C4×D4—21no—
392C4×D4—21no—
393C4×D4—22no—
394C4×D4C2×Dic1111yescharacteristic
395C4×D4C22⋊D1111yescharacteristic
396C4×D4C22⋊D1112yes—
397C4×D4C22⋊D1112yes—
398C4×D4C22⋊D1111yescharacteristic
399C4×D4C22×D1111yescharacteristic
400#117—22no—
401#117—21no—
402#117—22no—
403#117C2×Dic1111yescharacteristic
404#117C2×Dic1111yescharacteristic
405#117C2×Dic1112yes—
406C2×C4⋊C4—21no—
407C2×C4⋊C4C2×Dic1111yescharacteristic
408C2×C42—21no—
409C2×C42—21no—
410C2×C42C22×D1111yescharacteristic
411C2×C42C22×D1112yes—
412C4⋊C8—111no—
413C4⋊C8—112no—
414C4⋊C8—111no—
415C4⋊C8—221no—
416C4⋊C8—222no—
417C4⋊C8—222no—
418C4⋊C8—221no—
419C22⋊C8—221no—
420C22⋊C8—222no—
421C22⋊C8—221no—
422C22⋊C8—222no—
423#97—222no—
424C4×C8—111no—
425C4×C8—111no—
426C4×C8—112no—
427C4×C8—221no—
428C4×C8—221no—
429C4×C8—222no—
430C2×C11—22no—
431C2×C11—42no—
432C2×C11—81no—
433C2×C11C2×#40811yescharacteristic
434C2×C11#289811yescharacteristic
435C2×C11#290111yescharacteristic
436#41—24no—
437#41—24no—
438C2×Q8—21no—
439C2×Q8—22no—
440C2×Q8—24no—
441C2×Q8C22⋊Dic1111yescharacteristic
442C2×Q8C22×Dic1112yes—
443C2×Q8C22×Dic1111yescharacteristic
444C2×D4—21no—
445C2×D4—22no—
446C2×D4C22⋊Dic1112yes—
447C2×D4C22⋊Dic1111yescharacteristic
448C2×D4C22×Dic1111yescharacteristic
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4C22×Dic1112yes—
455C22×C4C22×Dic1111yescharacteristic
456C22×C4C2×C22⋊D1111yescharacteristic
457C22×C4C2×C22⋊D1112yes—
458C22×C4C2×C22⋊D1111yescharacteristic
459C22×C4C2×C22⋊D1112yes—
460M16—444no—
461C2×C8—221no—
462C2×C8—221no—
463C2×C8—222no—
464C2×C8—221no—
465C2×C8—221no—
466C2×C8—222no—
467C2×C8—442no—
468C2×C8—881no—
469C2×C8—882no—
470C4⋊C4—22no—
471C4⋊C4—21no—
472C4⋊C4—21no—
473C4⋊C4—22no—
474C4⋊C4—22no—
475C4⋊C4—22no—
476C4⋊C4—22no—
477C4⋊C4—22no—
478C4⋊C4—22no—
479C4⋊C4—22no—
480C4⋊C4—22no—
481C4⋊C4—22no—
482C4⋊C4—21no—
483C4⋊C4C22⋊Dic1112yes—
484C4⋊C4C22⋊Dic1111yescharacteristic
485C4⋊C4C22⋊Dic1111yescharacteristic
486C4⋊C4C22⋊Dic1112yes—
487C4⋊C4C22×Dic1112yes—
488C4⋊C4C22×Dic1111yescharacteristic
489C4⋊C4C22×Dic1111yescharacteristic
490C22⋊C4—22no—
491C22⋊C4—22no—
492C22⋊C4—21no—
493C22⋊C4—22no—
494C22⋊C4—21no—
495C22⋊C4—22no—
496C22⋊C4—22no—
497C22⋊C4—22no—
498C22⋊C4—21no—
499C22⋊C4C22⋊Dic1112yes—
500C22⋊C4C22⋊Dic1112yes—
501C22⋊C4C22⋊Dic1112yes—
502C42—21no—
503C42—21no—
504C42—22no—
505C42—22no—
506C42—21no—
507C42C22×Dic1111yescharacteristic
508C42C22×Dic1112yes—
509C42C2×C22⋊D1111yescharacteristic
510C42C2×C22⋊D1112yes—
511C42C2×C22⋊D1111yescharacteristic
512C42C2×C22⋊D1112yes—
513C42C23×D1111yescharacteristic
514C11#1746911yescharacteristic, complemented, Sylow
515C23—21no—
516C23C2×C22⋊Dic1112yes—
517C23C2×C22⋊Dic1111yescharacteristic
518Q8—22no—
519Q8—24no—
520Q8—22no—
521Q8—42no—
522Q8—82no—
523D4—24no—
524D4—22no—
525D4—22no—
526D4—42no—
527D4—82no—
528C2×C4—24no—
529C2×C4—21no—
530C2×C4—22no—
531C2×C4—21no—
532C2×C4—22no—
533C2×C4—21no—
534C2×C4—22no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—22no—
538C2×C4—41no—
539C2×C4—42no—
540C2×C4—42no—
541C2×C4—42no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—81no—
545C2×C4—81no—
546C2×C4#6700114yes—
547C2×C4C2×C22⋊Dic1111yescharacteristic
548C2×C4C2×C22⋊Dic1111yescharacteristic
549C2×C4C2×C22⋊Dic1112yes—
550C2×C4C2×C22⋊Dic1112yes—
551C2×C4C2×C22⋊Dic1112yes—
552C2×C4C2×C22⋊Dic1111yescharacteristic
553C2×C4C23×Dic1111yescharacteristic
554C2×C4C22×C22⋊D1111yescharacteristic
555C2×C4C22×C22⋊D1111yescharacteristic
556C8—222no—
557C8—441no—
558C8—442no—
559C8—441no—
560C8—442no—
561C8—441no—
562C22—21no—
563C22—21no—
564C22—22no—
565C22—22no—
566C22—22no—
567C22—41no—
568C22—41no—
569C22—41no—
570C22#1062284712yes—
571C22C22×C22⋊Dic1111yescharacteristic
572C4—22no—
573C4—21no—
574C4—22no—
575C4—21no—
576C4—21no—
577C4—22no—
578C4—41no—
579C4—42no—
580C4—41no—
581C4—42no—
582C4—41no—
583C4#1062284712yes—
584C4C2×#6700112yes—
585C4#1062336811yescharacteristic
586C4#1062336911yescharacteristic
587C2—22no—
588C2—42no—
589C2—81no—
590C2C2×#1062284711yescharacteristic
591C2#1307714911yescharacteristic
592C2#1307716311yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×#3461C2
socleC22×C11C22×C22⋊C4
prime radicalC11×#537C4
cosocleC42×C11C24
hypercenter#3461D11
hypocenterC11#17469
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C4×#41 ◁ #3461

Complements

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

NH ≅ G/Ntype
1. #13077727C2semidirect
2. #13077583C2semidirect
3. #13067037C2semidirect
4. #13067029C2semidirect
5. #13067024C2semidirect
6. #13067019C2semidirect
7. #13067011C2semidirect
8. #13067003C2semidirect
9. #13066998C2semidirect
10. C2×Q8⋊(C11⋊C8)C2semidirect
514. C11#17469semidirect

Maximal subgroups

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

subgroupindex
#130777272
#130775832
#130670372
#130670292
#130670242
#130670192
#130670112
#130670032
#130669982
C2×Q8⋊(C11⋊C8)2
C11×#34612
#1746911