Finite Group Databasebeta

← #14721399

Subgroups — #14721399

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#13082368C211yesmaximal, characteristic
2#13071501C211yesmaximal, characteristic, complemented
3#13067189C211yesmaximal, characteristic, complemented
4#13067181C212yesmaximal, complemented
5#13067160C211yesmaximal, characteristic
6#13067155C212yesmaximal, complemented
7#13067137C211yesmaximal, characteristic, complemented
8#13067129C212yesmaximal, complemented
9#13067108C211yesmaximal, characteristic
10#13067103C212yesmaximal, complemented
11C11×#2924C211yesmaximal, characteristic, complemented
12C2×C11×#117C2211yescharacteristic
13#10623322C2211yescharacteristic
14C2×#66977C2211yescharacteristic
15#10623065C412yescomplemented
16#10623064—21no—
17#10623062—22no—
18#10623060—21no—
19#10623057C411yescharacteristic, complemented
20#10623054C411yescharacteristic, complemented
21#10623050C411yescharacteristic, complemented
22#10623049C412yescomplemented
23#10623047C411yescharacteristic, complemented
24#10623044—21no—
25#10623042—21no—
26#10623026—22no—
27#10623010C2212yes—
28#10623001C2212yes—
29C11×#433—22no—
30C11×#432C2212yes—
31C11×#431C2212yes—
32C11×#424—21no—
33C11×#407C2211yescharacteristic
34C2×C11×C22⋊C8C2211yescharacteristic
35C11×#405—21no—
36#10622825C2211yescharacteristic
37C4×C22⋊Dic11C2211yescharacteristic
38#10622598—21no—
39C4⋊C4×Dic11—21no—
40#10622564—22no—
41#10622549C2212yes—
42#10622545C2212yes—
43#10622108C2211yescharacteristic
44#10622108C2212yes—
45#10622108C2211yescharacteristic
46#10622105C2212yes—
47#10622105C2212yes—
48#10622105C2211yescharacteristic
49#10622105C2211yescharacteristic
50#10622105C2212yes—
51#10622105C2212yes—
52#10622105C2212yes—
53C23×C4×C11C2311yescharacteristic
54C2×#4339C2×C411yescharacteristic
55C22×Dic22C2×C411yescharacteristic
56C2×C11×M16—21no—
57C22×C8×C11—21no—
58C11×#117C2×C411yescharacteristic
59C11×#117C2×C412yes—
60C11×#117C2×C411yescharacteristic
61C11×#117D411yescharacteristic
62C11×#117D412yes—
63C11×#117D411yescharacteristic
64C2×C11×C4⋊C4D411yescharacteristic
65C2×C11×C4⋊C4D411yescharacteristic
66C2×C11×C22⋊C4D412yes—
67C2×C42×C11C2312yes—
68#67006—21no—
69C2×C22⋊Dic11—21no—
70C2×C22⋊Dic11—21no—
71C2×C22⋊Dic11—21no—
72#66983C2×C411yescharacteristic
73#66983C2311yescharacteristic
74#66982—22no—
75#66982—21no—
76C4×C22⋊D11—22no—
77C4×C22⋊D11—21no—
78C4×C22⋊D11—21no—
79#66979—22no—
80#66979C2×C411yescharacteristic
81C2×C4⋊Dic11—21no—
82C2×C4⋊Dic11—22no—
83C2×C4⋊Dic11C2×C411yescharacteristic
84#66977—22no—
85#66977—21no—
86#66977—21no—
87#66977C2×C411yescharacteristic
88#66977C2×C412yes—
89#66977C2311yescharacteristic
90#66977C2312yes—
91C2×Dic11⋊C4—21no—
92C2×C4×Dic11—22no—
93C2×C4×Dic11—21no—
94#66951—22no—
95#66950—21no—
96#66950—21no—
97#66949—22no—
98#66945—21no—
99C4⋊C4×D11—21no—
100#66943—21no—
101#66942—22no—
102#66942—22no—
103#66941—21no—
104#66940—21no—
105#66940—21no—
106#66939—22no—
107#66938—22no—
108#66936—22no—
109(C22⋊D11)⋊C4—22no—
110#66932—22no—
111#66932—22no—
112#66931—22no—
113#66930—22no—
114#66929—22no—
115#66928C2×C412yes—
116C4×D44C2×C412yes—
117#66925—22no—
118#66923—22no—
119#66923C2×C412yes—
120#66922C2×C412yes—
121#66922C2×C412yes—
122C4×Dic22—22no—
123C4×Dic22C2×C412yes—
124C4×Dic22C2×C412yes—
125C4×Dic22C2×C412yes—
126C11×C4⋊C8—22no—
127C11×C4⋊C8—22no—
128C11×C22⋊C8—21no—
129C11×C22⋊C8—21no—
130C11×C22⋊C8C2311yescharacteristic
131C11×C22⋊C8C2311yescharacteristic
132C11×C22⋊C8C2312yes—
133C11×#97—22no—
134C4×C8×C11—22no—
135C11⋊#95—22no—
136C11⋊#95—22no—
137C11⋊#95C2311yescharacteristic
138C11⋊#95C2312yes—
139C11⋊#95C2311yescharacteristic
140#17605—111nomaximal, Sylow
141C24×C11C2×D411yescharacteristic
142C22×C4×C11—42no—
143C22×C4×C11C22×C411yescharacteristic
144C22×C4×C11C22×C411yescharacteristic
145C22×C4×C11C2×D412yes—
146C22×C4×C11C2×D411yescharacteristic
147C22×C4×C11C2×D411yescharacteristic
148C22×C4×C11C2×D412yes—
149C22×C4×C11C2×D411yescharacteristic
150C22×C4×C11C2411yescharacteristic
151C2×C22⋊D11—21no—
152C2×C22⋊D11—21no—
153C2×C22⋊D11—21no—
154C22×Dic11—21no—
155C22×Dic11—21no—
156C22×Dic11—21no—
157C22×Dic11—22no—
158C22×Dic11—21no—
159#4339—42no—
160C2×D44C22×C411yescharacteristic
161C2×C4×D11—21no—
162C2×C4×D11—22no—
163C2×Dic22—21no—
164C2×Dic22—22no—
165C2×Dic22—42no—
166C2×Dic22C22×C411yescharacteristic
167C2×Dic22C22×C412yes—
168C11×M16—42no—
169C2×C8×C11—21no—
170C2×C8×C11—22no—
171C2×C8×C11—21no—
172C2×C8×C11—42no—
173C11×C4⋊C4C22⋊C411yescharacteristic
174C11×C4⋊C4C22⋊C411yescharacteristic
175C11×C4⋊C4C22⋊C411yescharacteristic
176C11×C4⋊C4C22⋊C412yes—
177C11×C4⋊C4C22⋊C412yes—
178C11×C4⋊C4C22⋊C411yescharacteristic
179C11×C22⋊C4C22⋊C412yes—
180C11×C22⋊C4C22⋊C412yes—
181C11×C22⋊C4C22⋊C412yes—
182C11×C22⋊C4C22⋊C412yes—
183C42×C11C22×C412yes—
184C42×C11C22×C412yes—
185C42×C11C2×D412yes—
186C42×C11C2×D412yes—
187C22⋊Dic11—21no—
188C22⋊Dic11—21no—
189C22⋊Dic11—22no—
190C22⋊Dic11—21no—
191C22⋊Dic11—22no—
192C22⋊Dic11—42no—
193C22⋊Dic11—81no—
194(C2×D11)⋊C4—22no—
195(C2×D11)⋊C4—22no—
196(C2×D11)⋊C4—22no—
197(C2×D11)⋊C4—21no—
198(C2×D11)⋊C4—21no—
199C4⋊Dic11—22no—
200C4⋊Dic11—22no—
201C4⋊Dic11—22no—
202C4⋊Dic11—21no—
203C4⋊Dic11—42no—
204C4⋊Dic11—82no—
205C4⋊Dic11C22×C411yescharacteristic
206C4⋊Dic11C22×C411yescharacteristic
207C4⋊Dic11C22×C412yes—
208Dic11⋊C4—22no—
209Dic11⋊C4—22no—
210Dic11⋊C4—22no—
211Dic11⋊C4—22no—
212Dic11⋊C4—22no—
213Dic11⋊C4—21no—
214Dic11⋊C4—22no—
215Dic11⋊C4—21no—
216Dic11⋊C4—22no—
217C4×Dic11—22no—
218C4×Dic11—22no—
219C4×Dic11—22no—
220C4×Dic11—21no—
221C4×Dic11—42no—
222C4×Dic11—44no—
223#3495—111no—
224#2924D1111yescharacteristic, complemented
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—41no—
237C23×C11—41no—
238C23×C11C2×C22⋊C411yescharacteristic
239C23×C11C2×C22⋊C411yescharacteristic
240C23×C11C22×D411yescharacteristic
241C22×D11—21no—
242C2×C4×C11—22no—
243C2×C4×C11—22no—
244C2×C4×C11—22no—
245C2×C4×C11—22no—
246C2×C4×C11—22no—
247C2×C4×C11—42no—
248C2×C4×C11—41no—
249C2×C4×C11—41no—
250C2×C4×C11—41no—
251C2×C4×C11C2×C22⋊C412yes—
252C2×C4×C11C2×C22⋊C412yes—
253C2×C4×C11C2×C22⋊C411yescharacteristic
254C2×C4×C11C2×C22⋊C412yes—
255C2×C4×C11C2×C22⋊C412yes—
256C2×C4×C11C2×C22⋊C411yescharacteristic
257C2×C4×C11C23×C411yescharacteristic
258C2×C4×C11C22×D411yescharacteristic
259C22⋊D11—42no—
260C22⋊D11—41no—
261C22⋊D11—41no—
262C22⋊D11—81no—
263C2×Dic11—22no—
264C2×Dic11—21no—
265C2×Dic11—21no—
266C2×Dic11—21no—
267C2×Dic11—22no—
268C2×Dic11—22no—
269C2×Dic11—41no—
270C2×Dic11—42no—
271C2×Dic11—41no—
272C2×Dic11—41no—
273C2×Dic11—42no—
274C2×Dic11—42no—
275C2×Dic11—41no—
276C2×Dic11—41no—
277C2×Dic11—42no—
278C2×Dic11—81no—
279D44—41no—
280C4×D11—42no—
281C4×D11—82no—
282Dic22—42no—
283Dic22—42no—
284Dic22—41no—
285Dic22—82no—
286C8×C11—41no—
287C8×C11—41no—
288C8×C11—42no—
289#556—221no—
290#554—221no—
291#552—221no—
292#552—222no—
293#552—221no—
294#551—222no—
295#544—111no—
296#542—112no—
297#541—112no—
298#536—111no—
299#533—112no—
300#529—112no—
301#525—111no—
302C2×C22⋊Q8—111no—
303#520—111no—
304#519—111no—
305C2×#117C2×D1111yescharacteristic
306#433—22no—
307#432C2×D1112yes—
308#431C2×D1112yes—
309#424—21no—
310#407C2×D1111yescharacteristic
311C2×C22⋊C8C2×D1111yescharacteristic
312#405—21no—
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—81no—
339C22×C11—81no—
340C22×C11C22×C22⋊C411yescharacteristic
341C22×C11#57711yescharacteristic
342C22×C11#57811yescharacteristic
343C2×D11—41no—
344C2×D11—41no—
345C2×D11—41no—
346C4×C11—21no—
347C4×C11—21no—
348C4×C11—21no—
349C4×C11—22no—
350C4×C11—22no—
351C4×C11—22no—
352C4×C11—22no—
353C4×C11#41012yes—
354Dic11—42no—
355Dic11—42no—
356Dic11—41no—
357Dic11—41no—
358Dic11—41no—
359Dic11—42no—
360Dic11—82no—
361Dic11—81no—
362C2×#41—111no—
363C22×Q8—111no—
364C23×C4C22×D1111yescharacteristic
365C2×M16—21no—
366C22×C8—21no—
367C4⋊Q8—112no—
368C4⋊Q8—112no—
369C4⋊Q8—221no—
370#126—222no—
371#126—222no—
372#126—222no—
373#126—222no—
374#125—112no—
375#125—222no—
376#125—222no—
377#125—221no—
378#125—222no—
379#124—112no—
380#124—222no—
381#123—222no—
382#123—221no—
383#123—222no—
384#123—222no—
385C22⋊Q8—112no—
386C22⋊Q8—111no—
387C22⋊Q8—112no—
388C22⋊Q8—111no—
389C22⋊Q8—221no—
390C22⋊Q8—222no—
391C22⋊Q8—221no—
392C22⋊Q8—221no—
393C22⋊Q8—221no—
394C22⋊Q8—222no—
395C22⋊Q8—222no—
396#121—111no—
397#121—111no—
398#120—221no—
399C4×Q8—112no—
400C4×Q8—112no—
401C4×Q8—112no—
402C4×Q8—221no—
403C4×Q8—221no—
404C4×Q8—222no—
405C4×D4—112no—
406C4×D4—221no—
407C4×D4—222no—
408C4×D4—221no—
409C4×D4—222no—
410#117—111no—
411#117—222no—
412#117—221no—
413#117—222no—
414#117—222no—
415#117C4×D1111yescharacteristic
416#117C4×D1111yescharacteristic
417#117C4×D1112yes—
418#117C22⋊D1111yescharacteristic
419#117C22⋊D1112yes—
420#117C22⋊D1111yescharacteristic
421C2×C4⋊C4—111no—
422C2×C4⋊C4—221no—
423C2×C4⋊C4—221no—
424C2×C4⋊C4—221no—
425C2×C4⋊C4—222no—
426C2×C4⋊C4D4411yescharacteristic
427C2×C4⋊C4D4411yescharacteristic
428C2×C22⋊C4—221no—
429C2×C22⋊C4—221no—
430C2×C22⋊C4—221no—
431C2×C22⋊C4D4412yes—
432C2×C42—222no—
433C2×C42—221no—
434C2×C42C22×D1112yes—
435C4⋊C8—22no—
436C4⋊C8—22no—
437C22⋊C8—21no—
438C22⋊C8—21no—
439C22⋊C8C22×D1111yescharacteristic
440C22⋊C8C22×D1111yescharacteristic
441C22⋊C8C22×D1112yes—
442#97—22no—
443C4×C8—22no—
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×C11C2×#41011yescharacteristic
454C2×C11#289811yescharacteristic
455C2×C11#290111yescharacteristic
456D11—81no—
457C24C2×D4411yescharacteristic
458#41—442no—
459C2×Q8—112no—
460C2×Q8—111no—
461C2×Q8—221no—
462C2×Q8—222no—
463C2×Q8—442no—
464C2×D4—111no—
465C2×D4—221no—
466C2×D4—221no—
467C2×D4—221no—
468C22×C4—42no—
469C22×C4—221no—
470C22×C4—221no—
471C22×C4—221no—
472C22×C4—221no—
473C22×C4—222no—
474C22×C4—221no—
475C22×C4—222no—
476C22×C4C2×C4×D1111yescharacteristic
477C22×C4C2×C4×D1111yescharacteristic
478C22×C4C2×D4412yes—
479C22×C4C2×D4411yescharacteristic
480C22×C4C2×D4412yes—
481C22×C4C2×C22⋊D1111yescharacteristic
482C22×C4C2×C22⋊D1111yescharacteristic
483C22×C4C23×D1111yescharacteristic
484M16—42no—
485C2×C8—21no—
486C2×C8—22no—
487C2×C8—21no—
488C2×C8—42no—
489C4⋊C4—112no—
490C4⋊C4—111no—
491C4⋊C4—111no—
492C4⋊C4—221no—
493C4⋊C4—222no—
494C4⋊C4—222no—
495C4⋊C4—222no—
496C4⋊C4—222no—
497C4⋊C4—222no—
498C4⋊C4—222no—
499C4⋊C4—222no—
500C4⋊C4—221no—
501C4⋊C4—222no—
502C4⋊C4—222no—
503C4⋊C4—222no—
504C4⋊C4—221no—
505C4⋊C4—442no—
506C4⋊C4—882no—
507C4⋊C4(C2×D11)⋊C411yescharacteristic
508C4⋊C4(C2×D11)⋊C411yescharacteristic
509C4⋊C4(C2×D11)⋊C412yes—
510C4⋊C4(C2×D11)⋊C411yescharacteristic
511C4⋊C4(C2×D11)⋊C411yescharacteristic
512C4⋊C4(C2×D11)⋊C412yes—
513C22⋊C4—222no—
514C22⋊C4—221no—
515C22⋊C4—221no—
516C22⋊C4—222no—
517C22⋊C4—221no—
518C22⋊C4—222no—
519C22⋊C4—222no—
520C22⋊C4—221no—
521C22⋊C4—222no—
522C22⋊C4—221no—
523C22⋊C4—442no—
524C22⋊C4—881no—
525C22⋊C4(C2×D11)⋊C412yes—
526C22⋊C4(C2×D11)⋊C412yes—
527C22⋊C4(C2×D11)⋊C412yes—
528C22⋊C4(C2×D11)⋊C412yes—
529C42—221no—
530C42—222no—
531C42—222no—
532C42—222no—
533C42—442no—
534C42—444no—
535C42C2×C4×D1112yes—
536C42C2×C4×D1112yes—
537C42C2×C22⋊D1112yes—
538C42C2×C22⋊D1112yes—
539C11#1760511yescharacteristic, complemented, Sylow
540C23—21no—
541C23—21no—
542C23—41no—
543C23—41no—
544C23—221no—
545C23C2×(C2×D11)⋊C411yescharacteristic
546C23C2×(C2×D11)⋊C411yescharacteristic
547C23C22×D4411yescharacteristic
548Q8—442no—
549Q8—441no—
550Q8—442no—
551Q8—882no—
552D4—441no—
553D4—442no—
554D4—441no—
555D4—441no—
556D4—881no—
557C2×C4—22no—
558C2×C4—22no—
559C2×C4—22no—
560C2×C4—22no—
561C2×C4—22no—
562C2×C4—42no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—41no—
566C2×C4—222no—
567C2×C4—221no—
568C2×C4—221no—
569C2×C4—222no—
570C2×C4—221no—
571C2×C4—222no—
572C2×C4—441no—
573C2×C4—442no—
574C2×C4—441no—
575C2×C4—442no—
576C2×C4—441no—
577C2×C4—442no—
578C2×C4—441no—
579C2×C4—442no—
580C2×C4—442no—
581C2×C4—441no—
582C2×C4—882no—
583C2×C4—881no—
584C2×C4C2×(C2×D11)⋊C412yes—
585C2×C4C2×(C2×D11)⋊C412yes—
586C2×C4C2×(C2×D11)⋊C412yes—
587C2×C4C2×(C2×D11)⋊C412yes—
588C2×C4C2×(C2×D11)⋊C411yescharacteristic
589C2×C4C2×(C2×D11)⋊C411yescharacteristic
590C2×C4C22×C4×D1111yescharacteristic
591C2×C4C22×C22⋊D1111yescharacteristic
592C8—41no—
593C8—41no—
594C8—42no—
595C22—21no—
596C22—21no—
597C22—21no—
598C22—21no—
599C22—21no—
600C22—21no—
601C22—21no—
602C22—21no—
603C22—81no—
604C22—81no—
605C22—441no—
606C22—441no—
607C22—441no—
608C22#1062328211yescharacteristic
609C22#1062328411yescharacteristic
610C22C22×(C2×D11)⋊C411yescharacteristic
611C4—21no—
612C4—21no—
613C4—21no—
614C4—22no—
615C4—22no—
616C4—22no—
617C4—22no—
618C4—442no—
619C4—441no—
620C4—442no—
621C4—441no—
622C4—442no—
623C4—441no—
624C4—881no—
625C4—882no—
626C4#1062261912yes—
627C2—21no—
628C2—21no—
629C2—41no—
630C2—41no—
631C2—881no—
632C2C2×#1062261911yescharacteristic
633C2#1307715011yescharacteristic
634C2#1307716111yescharacteristic
subgroupG/H
centerC22C22×(C2×D11)⋊C4
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#2924C2
socleC22×C11C22×C22⋊C4
prime radical#10623322C22
cosocleC22×C4×C11C24
hypercenter#2924D11
hypocenterC11#17605
LCSG ▷ C2×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×#117 ◁ #2924

Complements

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

NH ≅ G/Ntype
2. #13071501C2semidirect
3. #13067189C2semidirect
4. #13067181C2semidirect
6. #13067155C2semidirect
7. #13067137C2semidirect
8. #13067129C2semidirect
10. #13067103C2semidirect
11. C11×#2924C2semidirect
15. #10623065C4semidirect
19. #10623057C4semidirect
20. #10623054C4semidirect
21. #10623050C4semidirect
22. #10623049C4semidirect
23. #10623047C4semidirect
224. #2924D11semidirect
539. C11#17605semidirect

Maximal subgroups

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

subgroupindex
#130823682
#130715012
#130671892
#130671812
#130671602
#130671552
#130671372
#130671292
#130671082
#130671032
C11×#29242
#1760511