Finite Group Databasebeta

← #14721396

Subgroups — #14721396

Order 2816.

930 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#13077274C211yesmaximal, characteristic, complemented
2#13071501C211yesmaximal, characteristic, complemented
3#13067188C211yesmaximal, characteristic, complemented
4#13067180C212yesmaximal, complemented
5#13067159C211yesmaximal, characteristic
6#13067154C212yesmaximal, complemented
7#13067136C211yesmaximal, characteristic, complemented
8#13067128C212yesmaximal, complemented
9#13067107C211yesmaximal, characteristic
10#13067102C212yesmaximal, complemented
11C11×#3495C211yesmaximal, characteristic
12C11×#556—21no—
13C11×#554—21no—
14C11×#552—22no—
15C11×#552—21no—
16C11×#552—21no—
17C11×#551—22no—
18C11×#544C411yescharacteristic, complemented
19C11×#542C412yescomplemented
20C11×#541C412yescomplemented
21C11×#536C411yescharacteristic, complemented
22C11×#533C2212yes—
23C11×#529C2212yes—
24C11×#525C2211yescharacteristic
25C2×C11×C22⋊Q8C2211yescharacteristic
26C11×#520C411yescharacteristic, complemented
27C11×#519C411yescharacteristic, complemented
28C2×C11×#117C2211yescharacteristic
29#10622825C2211yescharacteristic
30C4×C22⋊Dic11C2211yescharacteristic
31#10622820C2211yescharacteristic
32C2×C22⋊(C11⋊C8)C2211yescharacteristic
33#10622613—22no—
34#10622612—21no—
35#10622610—21no—
36#10622598—21no—
37C4⋊C4×Dic11—21no—
38#10622564—22no—
39#10622549C2212yes—
40#10622545C2212yes—
41#10622539C2212yes—
42#10622538C2212yes—
43#10622176C2212yes—
44#10622176C2212yes—
45#10622176C2211yescharacteristic
46#10622176C2211yescharacteristic
47#10622176C2212yes—
48#10622176C2212yes—
49#10622176C2212yes—
50#10622175C2211yescharacteristic
51#10622175C2212yes—
52#10622175C2211yescharacteristic
53C2×C11×#41C2×C411yescharacteristic
54C22×Q8×C11C2×C411yescharacteristic
55C23×C4×C11C2311yescharacteristic
56C11×C4⋊Q8—21no—
57C11×C4⋊Q8C2×C412yes—
58C11×C4⋊Q8C2×C412yes—
59C11×#126—22no—
60C11×#126—22no—
61C11×#126—22no—
62C11×#126—22no—
63C11×#125—22no—
64C11×#125—22no—
65C11×#125—21no—
66C11×#125—22no—
67C11×#125C2×C412yes—
68C11×#124—22no—
69C11×#124C2×C412yes—
70C11×#123—21no—
71C11×#123—22no—
72C11×#123—22no—
73C11×#123—22no—
74C11×C22⋊Q8—21no—
75C11×C22⋊Q8—21no—
76C11×C22⋊Q8—22no—
77C11×C22⋊Q8—21no—
78C11×C22⋊Q8—21no—
79C11×C22⋊Q8—22no—
80C11×C22⋊Q8—22no—
81C11×C22⋊Q8C2×C412yes—
82C11×C22⋊Q8C2×C411yescharacteristic
83C11×C22⋊Q8C2312yes—
84C11×C22⋊Q8C2311yescharacteristic
85C11×#121C2×C411yescharacteristic
86C11×#121C2311yescharacteristic
87C11×#120—21no—
88C4×Q8×C11—21no—
89C4×Q8×C11—21no—
90C4×Q8×C11—22no—
91C4×Q8×C11C2×C412yes—
92C4×Q8×C11C2×C412yes—
93C4×Q8×C11C2×C412yes—
94C4×D4×C11—21no—
95C4×D4×C11—21no—
96C4×D4×C11—22no—
97C4×D4×C11—22no—
98C4×D4×C11C2×C412yes—
99C11×#117—22no—
100C11×#117—21no—
101C11×#117—22no—
102C11×#117—22no—
103C11×#117C2×C411yescharacteristic
104C11×#117C2×C411yescharacteristic
105C11×#117C2×C411yescharacteristic
106C11×#117C2×C412yes—
107C11×#117D411yescharacteristic
108C11×#117D411yescharacteristic
109C11×#117D412yes—
110C2×C11×C4⋊C4—21no—
111C2×C11×C4⋊C4—21no—
112C2×C11×C4⋊C4C2×C411yescharacteristic
113C2×C11×C4⋊C4D411yescharacteristic
114C2×C11×C4⋊C4D411yescharacteristic
115C2×C11×C22⋊C4—21no—
116C2×C11×C22⋊C4D412yes—
117C2×C42×C11C2312yes—
118C2×C22⋊Dic11—21no—
119C2×C22⋊Dic11—21no—
120C2×C4⋊Dic11—21no—
121C2×C4⋊Dic11—22no—
122C2×C4×Dic11—22no—
123C2×C4×Dic11—21no—
124C2×#4318—21no—
125C22×C11⋊C8—21no—
126C11⋊#95—22no—
127C11⋊#95—22no—
128C11⋊#95C2311yescharacteristic
129C11⋊#95C2312yes—
130C11⋊#95C2311yescharacteristic
131C22⋊(C11⋊C8)—21no—
132C22⋊(C11⋊C8)—21no—
133C22⋊(C11⋊C8)C2311yescharacteristic
134C22⋊(C11⋊C8)C2312yes—
135C22⋊(C11⋊C8)C2311yescharacteristic
136C4⋊(C11⋊C8)—22no—
137C4⋊(C11⋊C8)—22no—
138#66867—22no—
139C4×C11⋊C8—22no—
140#17605—111nomaximal, Sylow
141C24×C11C2×D411yescharacteristic
142C11×#41—42no—
143C2×Q8×C11—21no—
144C2×Q8×C11—22no—
145C2×Q8×C11—42no—
146C2×Q8×C11C22×C412yes—
147C2×Q8×C11C22×C411yescharacteristic
148C2×D4×C11—21no—
149C2×D4×C11—21no—
150C2×D4×C11—21no—
151C2×D4×C11C22×C411yescharacteristic
152C22×C4×C11—21no—
153C22×C4×C11—21no—
154C22×C4×C11—21no—
155C22×C4×C11—22no—
156C22×C4×C11—42no—
157C22×C4×C11C22×C411yescharacteristic
158C22×C4×C11C22×C411yescharacteristic
159C22×C4×C11C2×D412yes—
160C22×C4×C11C2×D411yescharacteristic
161C22×C4×C11C2×D411yescharacteristic
162C22×C4×C11C2×D412yes—
163C22×C4×C11C2×D411yescharacteristic
164C22×C4×C11C2411yescharacteristic
165C22×Dic11—21no—
166C22×Dic11—22no—
167C22×Dic11—21no—
168C11×C4⋊C4—21no—
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⋊C4—22no—
179C11×C4⋊C4—22no—
180C11×C4⋊C4—21no—
181C11×C4⋊C4C22⋊C411yescharacteristic
182C11×C4⋊C4C22⋊C411yescharacteristic
183C11×C4⋊C4C22⋊C412yes—
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×C22⋊C4—22no—
191C11×C22⋊C4—21no—
192C11×C22⋊C4—21no—
193C11×C22⋊C4—22no—
194C11×C22⋊C4—21no—
195C11×C22⋊C4—22no—
196C11×C22⋊C4—22no—
197C11×C22⋊C4—21no—
198C11×C22⋊C4—22no—
199C11×C22⋊C4—21no—
200C11×C22⋊C4C22⋊C412yes—
201C11×C22⋊C4C22⋊C412yes—
202C11×C22⋊C4C22⋊C412yes—
203C11×C22⋊C4C22⋊C412yes—
204C42×C11—22no—
205C42×C11—22no—
206C42×C11—22no—
207C42×C11—21no—
208C42×C11C22×C412yes—
209C42×C11C22×C412yes—
210C42×C11C2×D412yes—
211C42×C11C2×D412yes—
212C22⋊Dic11—42no—
213C22⋊Dic11—81no—
214C4⋊Dic11—42no—
215C4⋊Dic11—82no—
216C4×Dic11—42no—
217C4×Dic11—44no—
218#4318—42no—
219C2×C11⋊C8—21no—
220C2×C11⋊C8—22no—
221C2×C11⋊C8—21no—
222C2×C11⋊C8—42no—
223#3495D1111yescharacteristic
224#2924—111no—
225#2346—111no—
226#1520—111no—
227#1518—112no—
228#1513—111no—
229#1512—112no—
230#1508—111no—
231#1506—112no—
232#1501—111no—
233#1500—112no—
234C23×C11—21no—
235C23×C11—21no—
236C23×C11—21no—
237C23×C11—41no—
238C23×C11—41no—
239C23×C11C2×C22⋊C411yescharacteristic
240C23×C11C2×C22⋊C411yescharacteristic
241C23×C11C22×D411yescharacteristic
242Q8×C11—42no—
243Q8×C11—41no—
244Q8×C11—42no—
245Q8×C11—82no—
246D4×C11—41no—
247D4×C11—42no—
248D4×C11—41no—
249D4×C11—41no—
250D4×C11—81no—
251C2×C4×C11—22no—
252C2×C4×C11—22no—
253C2×C4×C11—22no—
254C2×C4×C11—22no—
255C2×C4×C11—22no—
256C2×C4×C11—21no—
257C2×C4×C11—21no—
258C2×C4×C11—22no—
259C2×C4×C11—21no—
260C2×C4×C11—22no—
261C2×C4×C11—42no—
262C2×C4×C11—41no—
263C2×C4×C11—41no—
264C2×C4×C11—41no—
265C2×C4×C11—42no—
266C2×C4×C11—42no—
267C2×C4×C11—82no—
268C2×C4×C11—81no—
269C2×C4×C11C2×C22⋊C412yes—
270C2×C4×C11C2×C22⋊C412yes—
271C2×C4×C11C2×C22⋊C412yes—
272C2×C4×C11C2×C22⋊C412yes—
273C2×C4×C11C2×C22⋊C411yescharacteristic
274C2×C4×C11C2×C22⋊C411yescharacteristic
275C2×C4×C11C23×C411yescharacteristic
276C2×C4×C11C22×D411yescharacteristic
277C2×Dic11—22no—
278C2×Dic11—41no—
279C2×Dic11—41no—
280C2×Dic11—41no—
281C2×Dic11—42no—
282C2×Dic11—42no—
283C2×Dic11—41no—
284C2×Dic11—41no—
285C2×Dic11—42no—
286C11⋊C8—41no—
287C11⋊C8—41no—
288C11⋊C8—42no—
289#556—21no—
290#554—21no—
291#552—22no—
292#552—21no—
293#552—21no—
294#551—22no—
295#544Dic1111yescharacteristic, complemented
296#542Dic1112yescomplemented
297#541Dic1112yescomplemented
298#536Dic1111yescharacteristic, complemented
299#533C2×D1112yes—
300#529C2×D1112yes—
301#525C2×D1111yescharacteristic
302C2×C22⋊Q8C2×D1111yescharacteristic
303#520Dic1111yescharacteristic, complemented
304#519Dic1111yescharacteristic, complemented
305C2×#117C2×D1111yescharacteristic
306#433—222no—
307#432—112no—
308#431—112no—
309#424—221no—
310#407—111no—
311C2×C22⋊C8—111no—
312#405—221no—
313#389—221no—
314#388—222no—
315#382—112no—
316#380—111no—
317C4×C4⋊C4—221no—
318C4×C22⋊C4—111no—
319#376—112no—
320#328—112no—
321#328—112no—
322#328—111no—
323#328—111no—
324#328—112no—
325#328—112no—
326#328—112no—
327#327—111no—
328#327—112no—
329#327—111no—
330C22×C11—21no—
331C22×C11—21no—
332C22×C11—21no—
333C22×C11—21no—
334C22×C11—21no—
335C22×C11—21no—
336C22×C11—21no—
337C22×C11—21no—
338C22×C11—41no—
339C22×C11—41no—
340C22×C11—41no—
341C22×C11—81no—
342C22×C11—81no—
343C22×C11C22×C22⋊C411yescharacteristic
344C22×C11#57711yescharacteristic
345C22×C11#57811yescharacteristic
346C4×C11—21no—
347C4×C11—21no—
348C4×C11—21no—
349C4×C11—22no—
350C4×C11—22no—
351C4×C11—22no—
352C4×C11—22no—
353C4×C11—41no—
354C4×C11—42no—
355C4×C11—41no—
356C4×C11—42no—
357C4×C11—41no—
358C4×C11#41012yes—
359Dic11—42no—
360Dic11—82no—
361Dic11—81no—
362C2×#41C2×Dic1111yescharacteristic
363C22×Q8C2×Dic1111yescharacteristic
364C23×C4C22×D1111yescharacteristic
365C2×M16—221no—
366C22×C8—221no—
367C4⋊Q8—21no—
368C4⋊Q8C2×Dic1112yes—
369C4⋊Q8C2×Dic1112yes—
370#126—22no—
371#126—22no—
372#126—22no—
373#126—22no—
374#125—22no—
375#125—22no—
376#125—21no—
377#125—22no—
378#125C2×Dic1112yes—
379#124—22no—
380#124C2×Dic1112yes—
381#123—21no—
382#123—22no—
383#123—22no—
384#123—22no—
385C22⋊Q8—21no—
386C22⋊Q8—21no—
387C22⋊Q8—22no—
388C22⋊Q8—21no—
389C22⋊Q8—21no—
390C22⋊Q8—22no—
391C22⋊Q8—22no—
392C22⋊Q8C2×Dic1112yes—
393C22⋊Q8C2×Dic1111yescharacteristic
394C22⋊Q8C22×D1112yes—
395C22⋊Q8C22×D1111yescharacteristic
396#121C2×Dic1111yescharacteristic
397#121C22×D1111yescharacteristic
398#120—21no—
399C4×Q8—21no—
400C4×Q8—21no—
401C4×Q8—22no—
402C4×Q8C2×Dic1112yes—
403C4×Q8C2×Dic1112yes—
404C4×Q8C2×Dic1112yes—
405C4×D4—21no—
406C4×D4—21no—
407C4×D4—22no—
408C4×D4—22no—
409C4×D4C2×Dic1112yes—
410#117—22no—
411#117—21no—
412#117—22no—
413#117—22no—
414#117C2×Dic1111yescharacteristic
415#117C2×Dic1111yescharacteristic
416#117C2×Dic1111yescharacteristic
417#117C2×Dic1112yes—
418#117C22⋊D1111yescharacteristic
419#117C22⋊D1112yes—
420#117C22⋊D1111yescharacteristic
421C2×C4⋊C4—21no—
422C2×C4⋊C4—21no—
423C2×C4⋊C4—221no—
424C2×C4⋊C4—222no—
425C2×C4⋊C4C2×Dic1111yescharacteristic
426C2×C4⋊C4C22⋊D1111yescharacteristic
427C2×C4⋊C4C22⋊D1111yescharacteristic
428C2×C22⋊C4—21no—
429C2×C22⋊C4—221no—
430C2×C22⋊C4—221no—
431C2×C22⋊C4C22⋊D1112yes—
432C2×C42—222no—
433C2×C42—221no—
434C2×C42C22×D1112yes—
435C4⋊C8—222no—
436C4⋊C8—222no—
437C22⋊C8—111no—
438C22⋊C8—111no—
439C22⋊C8—112no—
440C22⋊C8—221no—
441C22⋊C8—221no—
442#97—222no—
443C4×C8—222no—
444#95—111no—
445#95—112no—
446#95—111no—
447#95—222no—
448#95—222no—
449C2×C11—21no—
450C2×C11—21no—
451C2×C11—41no—
452C2×C11—41no—
453C2×C11—81no—
454C2×C11C2×#41011yescharacteristic
455C2×C11#289811yescharacteristic
456C2×C11#290111yescharacteristic
457C24C2×C22⋊D1111yescharacteristic
458#41—42no—
459C2×Q8—21no—
460C2×Q8—22no—
461C2×Q8—42no—
462C2×Q8C22×Dic1112yes—
463C2×Q8C22×Dic1111yescharacteristic
464C2×D4—21no—
465C2×D4—21no—
466C2×D4—21no—
467C2×D4C22×Dic1111yescharacteristic
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—22no—
472C22×C4—42no—
473C22×C4—221no—
474C22×C4—221no—
475C22×C4—222no—
476C22×C4C22×Dic1111yescharacteristic
477C22×C4C22×Dic1111yescharacteristic
478C22×C4C2×C22⋊D1112yes—
479C22×C4C2×C22⋊D1111yescharacteristic
480C22×C4C2×C22⋊D1111yescharacteristic
481C22×C4C2×C22⋊D1112yes—
482C22×C4C2×C22⋊D1111yescharacteristic
483C22×C4C23×D1111yescharacteristic
484M16—442no—
485C2×C8—221no—
486C2×C8—222no—
487C2×C8—221no—
488C2×C8—442no—
489C4⋊C4—21no—
490C4⋊C4—22no—
491C4⋊C4—22no—
492C4⋊C4—22no—
493C4⋊C4—22no—
494C4⋊C4—22no—
495C4⋊C4—22no—
496C4⋊C4—22no—
497C4⋊C4—22no—
498C4⋊C4—21no—
499C4⋊C4—22no—
500C4⋊C4—22no—
501C4⋊C4—21no—
502C4⋊C4—442no—
503C4⋊C4—882no—
504C4⋊C4C22⋊Dic1111yescharacteristic
505C4⋊C4C22⋊Dic1111yescharacteristic
506C4⋊C4C22⋊Dic1112yes—
507C4⋊C4C22⋊Dic1111yescharacteristic
508C4⋊C4C22⋊Dic1111yescharacteristic
509C4⋊C4C22⋊Dic1112yes—
510C4⋊C4C22×Dic1112yes—
511C4⋊C4C22×Dic1111yescharacteristic
512C4⋊C4C22×Dic1111yescharacteristic
513C22⋊C4—22no—
514C22⋊C4—21no—
515C22⋊C4—21no—
516C22⋊C4—22no—
517C22⋊C4—21no—
518C22⋊C4—22no—
519C22⋊C4—22no—
520C22⋊C4—21no—
521C22⋊C4—22no—
522C22⋊C4—21no—
523C22⋊C4—442no—
524C22⋊C4—881no—
525C22⋊C4C22⋊Dic1112yes—
526C22⋊C4C22⋊Dic1112yes—
527C22⋊C4C22⋊Dic1112yes—
528C22⋊C4C22⋊Dic1112yes—
529C42—22no—
530C42—22no—
531C42—22no—
532C42—21no—
533C42—442no—
534C42—444no—
535C42C22×Dic1112yes—
536C42C22×Dic1112yes—
537C42C2×C22⋊D1112yes—
538C42C2×C22⋊D1112yes—
539C11#1760511yescharacteristic, complemented, Sylow
540C23—21no—
541C23—21no—
542C23—21no—
543C23—41no—
544C23—41no—
545C23C2×C22⋊Dic1111yescharacteristic
546C23C2×C22⋊Dic1111yescharacteristic
547C23C22×C22⋊D1111yescharacteristic
548Q8—42no—
549Q8—41no—
550Q8—42no—
551Q8—82no—
552D4—41no—
553D4—42no—
554D4—41no—
555D4—41no—
556D4—81no—
557C2×C4—22no—
558C2×C4—22no—
559C2×C4—22no—
560C2×C4—22no—
561C2×C4—22no—
562C2×C4—21no—
563C2×C4—21no—
564C2×C4—22no—
565C2×C4—21no—
566C2×C4—22no—
567C2×C4—42no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—42no—
572C2×C4—42no—
573C2×C4—82no—
574C2×C4—81no—
575C2×C4—222no—
576C2×C4—441no—
577C2×C4—441no—
578C2×C4—441no—
579C2×C4—442no—
580C2×C4—441no—
581C2×C4—442no—
582C2×C4—442no—
583C2×C4—441no—
584C2×C4C2×C22⋊Dic1112yes—
585C2×C4C2×C22⋊Dic1112yes—
586C2×C4C2×C22⋊Dic1112yes—
587C2×C4C2×C22⋊Dic1112yes—
588C2×C4C2×C22⋊Dic1111yescharacteristic
589C2×C4C2×C22⋊Dic1111yescharacteristic
590C2×C4C23×Dic1111yescharacteristic
591C2×C4C22×C22⋊D1111yescharacteristic
592C8—441no—
593C8—441no—
594C8—442no—
595C22—21no—
596C22—21no—
597C22—21no—
598C22—21no—
599C22—21no—
600C22—21no—
601C22—21no—
602C22—21no—
603C22—41no—
604C22—41no—
605C22—41no—
606C22—81no—
607C22—81no—
608C22#1062336811yescharacteristic
609C22#1062336911yescharacteristic
610C22C22×C22⋊Dic1111yescharacteristic
611C4—21no—
612C4—21no—
613C4—21no—
614C4—22no—
615C4—22no—
616C4—22no—
617C4—22no—
618C4—41no—
619C4—42no—
620C4—41no—
621C4—42no—
622C4—41no—
623C4—442no—
624C4—881no—
625C4—882no—
626C4#1062285312yes—
627C2—21no—
628C2—21no—
629C2—41no—
630C2—41no—
631C2—81no—
632C2C2×#1062285311yescharacteristic
633C2#1307714911yescharacteristic
634C2#1307716311yescharacteristic
subgroupG/H
centerC22C22×C22⋊Dic11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#3495C2
socleC22×C11C22×C22⋊C4
prime radicalC11×#525C22
cosocleC22×C4×C11C24
hypercenter#3495D11
hypocenterC11#17605
LCSG ▷ C2×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×#117 ◁ #3495

Complements

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

NH ≅ G/Ntype
1. #13077274C2semidirect
2. #13071501C2semidirect
3. #13067188C2semidirect
4. #13067180C2semidirect
6. #13067154C2semidirect
7. #13067136C2semidirect
8. #13067128C2semidirect
10. #13067102C2semidirect
18. C11×#544C4semidirect
19. C11×#542C4semidirect
20. C11×#541C4semidirect
21. C11×#536C4semidirect
26. C11×#520C4semidirect
27. C11×#519C4semidirect
295. #544Dic11semidirect
296. #542Dic11semidirect
297. #541Dic11semidirect
298. #536Dic11semidirect
303. #520Dic11semidirect
304. #519Dic11semidirect
539. C11#17605semidirect

Maximal subgroups

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

subgroupindex
#130772742
#130715012
#130671882
#130671802
#130671592
#130671542
#130671362
#130671282
#130671072
#130671022
C11×#34952
#1760511