Finite Group Databasebeta

← #14721553

Subgroups — #14721553

Order 2816.

1074 conjugacy classes of subgroups.

The subgroup lattice has 686 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082450C211yesmaximal, characteristic
2#13077642C211yesmaximal, characteristic, complemented
3#13071520C211yesmaximal, characteristic, complemented
4#13067187C211yesmaximal, characteristic, complemented
5#13067156C212yesmaximal, complemented
6#13067151C212yesmaximal, complemented
7#13067138C212yesmaximal, complemented
8#13067117C212yesmaximal, complemented
9C2×#10622105C211yesmaximal, characteristic, complemented
10C2×#10622175C211yesmaximal, characteristic, complemented
11C11×#1519C211yesmaximal, characteristic, complemented
12C2×C11×#121C2211yescharacteristic
13#10623337C412yescomplemented
14#10623335—21no—
15#10623329—21no—
16C2×C4×C22⋊D11C2211yescharacteristic
17C2×#66977C2211yescharacteristic
18#10623149C412yescomplemented
19#10623148—21no—
20#10623137C2212yes—
21#10623133—21no—
22#10623132—22no—
23#10623131C2212yes—
24#10623129C412yescomplemented
25#10623044C412yescomplemented
26#10623026—22no—
27C2×(C22⋊D11)⋊C4—21no—
28C2×C11×C22⋊C8C2211yescharacteristic
29C11×#380C2211yescharacteristic
30C2×C11⋊#95C2211yescharacteristic
31C2×C22⋊(C11⋊C8)C2211yescharacteristic
32#10622724—22no—
33#10622602—21no—
34#10622585—21no—
35#10622559—21no—
36#10622343—22no—
37#10622339C2212yescomplemented
38#10622332C2212yescomplemented
39#10622280C2211yescharacteristic, complemented
40D11×#95C2211yescharacteristic, complemented
41#10622263C2211yescharacteristic, complemented
42#10622262C2211yescharacteristic, complemented
43C11×#327C2212yes—
44C11×#327C2212yes—
45#10622175C2212yes—
46#10622175C2212yes—
47#10622105C2212yescomplemented
48#10622105C2212yescomplemented
49#10622090C2212yescomplemented
50#10622090C2212yescomplemented
51C22×D4×C11—21no—
52C22×D4×C11C2×C411yescharacteristic, complemented
53C23×C4×C11C2311yescharacteristic
54C22×C22⋊D11D411yescharacteristic
55C23×Dic11—21no—
56C2×#4341C2×C412yescomplemented
57C22×C4×D11—21no—
58C22×C4×D11C2311yescharacteristic
59C22×Dic22C2×C411yescharacteristic, complemented
60C22×C8×C11—21no—
61C11×#121—21no—
62C11×#121—21no—
63C11×#121C2×C412yescomplemented
64C11×#121C2312yes—
65C2×C11×C4⋊C4—21no—
66C2×C11×C4⋊C4C2×C411yescharacteristic, complemented
67C2×C11×C22⋊C4—21no—
68C2×C11×C22⋊C4—21no—
69#67006—22no—
70C2×C22⋊Dic11—21no—
71C2×C22⋊Dic11—22no—
72C2×C22⋊Dic11D411yescharacteristic
73#66992—22no—
74#66992—22no—
75#66992—22no—
76#66991C2×C412yescomplemented
77#66990—22no—
78#66989C2×C412yescomplemented
79#66988—22no—
80#66988—22no—
81D4×Dic11—22no—
82D4×Dic11—22no—
83D4×Dic11—22no—
84D4×Dic11—22no—
85D4×Dic11C2×C412yescomplemented
86#66982—22no—
87C4×C22⋊D11C2×C412yes—
88C4×C22⋊D11C2×C412yes—
89C4×C22⋊D11D412yes—
90C4×C22⋊D11D412yes—
91C2×(C2×D11)⋊C4—21no—
92C2×(C2×D11)⋊C4D411yescharacteristic
93#66979—22no—
94C2×C4⋊Dic11C2×C411yescharacteristic, complemented
95#66977—21no—
96#66977—21no—
97#66977C2×C412yescomplemented
98#66977C2312yes—
99C2×Dic11⋊C4—21no—
100C2×Dic11⋊C4—21no—
101C2×Dic11⋊C4—21no—
102C2×Dic11⋊C4—21no—
103C2×Dic11⋊C4D411yescharacteristic
104C2×C4×Dic11—21no—
105C2×C4×Dic11C2311yescharacteristic
106C22×C11⋊C8—21no—
107C2×#4313—22no—
108#66951—22no—
109#66950C2×C412yescomplemented
110#66945C2×C412yescomplemented
111#66943C2×C412yescomplemented
112#66942—22no—
113#66940C2×C412yescomplemented
114#66939—22no—
115#66938—22no—
116#66936—22no—
117(C22⋊D11)⋊C4—22no—
118(C22⋊D11)⋊C4—44no—
119#66932—22no—
120#66932—22no—
121#66931—22no—
122#66930—22no—
123C11×C22⋊C8—21no—
124C11×C22⋊C8C2312yes—
125C11×#95C2311yescharacteristic
126C11×#95C2311yescharacteristic
127C11⋊#95—21no—
128C11⋊#95—21no—
129C11⋊#95—21no—
130C11⋊#95C2311yescharacteristic
131C11⋊#95C2311yescharacteristic
132C22⋊(C11⋊C8)—21no—
133C22⋊(C11⋊C8)C2312yes—
134(C2×D11)⋊C8—22no—
135#66879—22no—
136Dic11⋊C8—22no—
137#17622—111nomaximal, Sylow
138C24×C11—21no—
139C24×C11C2×D411yescharacteristic
140C23×D11C2×D411yescharacteristic
141C2×D4×C11—22no—
142C2×D4×C11—22no—
143C2×D4×C11—21no—
144C2×D4×C11—42no—
145C2×D4×C11—42no—
146C2×D4×C11—81no—
147C2×D4×C11C22×C412yes—
148C22×C4×C11—21no—
149C22×C4×C11—21no—
150C22×C4×C11—21no—
151C22×C4×C11—81no—
152C22×C4×C11C22×C411yescharacteristic
153C22×C4×C11C22×C411yescharacteristic
154C22×C4×C11C2×D411yescharacteristic
155C22×C4×C11C2×D411yescharacteristic
156C22×C4×C11C2×D411yescharacteristic
157C22×C4×C11C2411yescharacteristic
158C2×C22⋊D11—22no—
159C2×C22⋊D11—22no—
160C2×C22⋊D11—22no—
161C2×C22⋊D11—22no—
162C2×C22⋊D11C22⋊C412yes—
163C2×C22⋊D11C22⋊C412yes—
164C22×Dic11—22no—
165C22×Dic11—22no—
166C22×Dic11—21no—
167C22×Dic11—21no—
168C22×Dic11—21no—
169C22×Dic11—21no—
170C22×Dic11—42no—
171C22×Dic11—42no—
172C22×Dic11—81no—
173C22×Dic11C2×D411yescharacteristic
174C22×Dic11C2×D411yescharacteristic
175C22×Dic11C2×D411yescharacteristic
176#4341—82no—
177C2×C4×D11—42no—
178C2×C4×D11—42no—
179C2×C4×D11—81no—
180C2×C4×D11—81no—
181C2×C4×D11C22×C412yes—
182C2×C4×D11C2×D412yes—
183C2×Dic22—21no—
184C2×Dic22—81no—
185C2×Dic22C22×C412yes—
186C2×C8×C11—22no—
187C2×C8×C11—81no—
188C11×C4⋊C4—21no—
189C11×C4⋊C4—81no—
190C11×C4⋊C4C22×C412yes—
191C11×C22⋊C4—22no—
192C11×C22⋊C4—22no—
193C11×C22⋊C4—42no—
194C22⋊Dic11—22no—
195C22⋊Dic11—22no—
196C22⋊Dic11—22no—
197C22⋊Dic11—22no—
198C22⋊Dic11—22no—
199C22⋊Dic11—22no—
200C22⋊Dic11C22⋊C412yes—
201C22⋊Dic11C22⋊C412yes—
202(C2×D11)⋊C4—22no—
203(C2×D11)⋊C4—22no—
204(C2×D11)⋊C4—42no—
205(C2×D11)⋊C4C22⋊C412yes—
206(C2×D11)⋊C4C22⋊C412yes—
207C4⋊Dic11—22no—
208C4⋊Dic11—22no—
209C4⋊Dic11—21no—
210C4⋊Dic11C22×C412yes—
211Dic11⋊C4—22no—
212Dic11⋊C4—22no—
213Dic11⋊C4—22no—
214Dic11⋊C4—22no—
215Dic11⋊C4—42no—
216Dic11⋊C4—42no—
217Dic11⋊C4—81no—
218Dic11⋊C4C22⋊C412yes—
219Dic11⋊C4C22⋊C412yes—
220C4×Dic11—22no—
221C4×Dic11—22no—
222C4×Dic11—42no—
223C4×Dic11C22×C412yes—
224C4×Dic11C2×D412yes—
225C2×C11⋊C8—22no—
226C2×C11⋊C8—81no—
227#4313—82no—
228#3505—111no—
229#2973—111no—
230#2349—111no—
231#1520—111no—
232#1519D1111yescharacteristic, complemented
233#1513—112no—
234#1512—112no—
235#1509—112no—
236#1504—112no—
237C2×#328—111no—
238C2×#327—111no—
239C23×C11—22no—
240C23×C11—41no—
241C23×C11—41no—
242C23×C11—42no—
243C23×C11—81no—
244C23×C11—81no—
245C23×C11C2×C22⋊C411yescharacteristic
246C23×C11C2×C22⋊C411yescharacteristic
247C23×C11AGL(1,ℤ/8)12yes—
248C23×C11#13712yes—
249C23×C11C22×D411yescharacteristic
250C22×D11—21no—
251C22×D11—21no—
252C22×D11—41no—
253C22×D11—41no—
254C22×D11C2×C22⋊C412yes—
255D4×C11—42no—
256D4×C11—42no—
257D4×C11—42no—
258D4×C11—44no—
259D4×C11—81no—
260C2×C4×C11—22no—
261C2×C4×C11—41no—
262C2×C4×C11—41no—
263C2×C4×C11—41no—
264C2×C4×C11—41no—
265C2×C4×C11—41no—
266C2×C4×C11—41no—
267C2×C4×C11—42no—
268C2×C4×C11—41no—
269C2×C4×C11—41no—
270C2×C4×C11—41no—
271C2×C4×C11—41no—
272C2×C4×C11—41no—
273C2×C4×C11—41no—
274C2×C4×C11C2×C22⋊C411yescharacteristic
275C2×C4×C11C2×C22⋊C411yescharacteristic
276C2×C4×C11C23×C411yescharacteristic
277C2×C4×C11C22×D411yescharacteristic
278C22⋊D11—24no—
279C22⋊D11—24no—
280C22⋊D11—82no—
281C22⋊D11—82no—
282C2×Dic11—21no—
283C2×Dic11—21no—
284C2×Dic11—22no—
285C2×Dic11—22no—
286C2×Dic11—22no—
287C2×Dic11—41no—
288C2×Dic11—41no—
289C2×Dic11—41no—
290C2×Dic11—41no—
291C2×Dic11—41no—
292C2×Dic11—41no—
293C2×Dic11—41no—
294C2×Dic11—82no—
295C2×Dic11—82no—
296C2×Dic11—81no—
297C2×Dic11—81no—
298C2×Dic11—84no—
299C2×Dic11C2×C22⋊C412yes—
300C2×Dic11C2×C22⋊C412yes—
301C2×Dic11C2×C22⋊C412yes—
302C4×D11—42no—
303C4×D11—42no—
304C4×D11—84no—
305Dic22—42no—
306Dic22—81no—
307C8×C11—42no—
308C11⋊C8—42no—
309#553—112no—
310#553—222no—
311#552—112no—
312#551—222no—
313#548—112no—
314#546—112no—
315#539—221no—
316#538—221no—
317#534—221no—
318#529—112no—
319#525—112no—
320C2×C22⋊Q8—111no—
321C2×#121C2×D1111yescharacteristic
322#518—221no—
323C2×C4×D4—111no—
324C2×C4×D4—221no—
325#435—222no—
326#435—222no—
327#432—112no—
328#407—112no—
329C2×C22⋊C8—111no—
330C2×C22⋊C8C2×D1111yescharacteristic
331#389—221no—
332#385—221no—
333#385—221no—
334#382—111no—
335#380—111no—
336#380C2×D1111yescharacteristic
337C4×C4⋊C4—111no—
338C2×#95—111no—
339C2×#95—111no—
340#328—112no—
341#328—112no—
342#328—112no—
343#328—112no—
344#327—112no—
345#327—112no—
346#327C2×D1112yes—
347#327C2×D1112yes—
348C22×C11—21no—
349C22×C11—21no—
350C22×C11—21no—
351C22×C11—21no—
352C22×C11—21no—
353C22×C11—21no—
354C22×C11—42no—
355C22×C11—42no—
356C22×C11—42no—
357C22×C11—42no—
358C22×C11—42no—
359C22×C11—162no—
360C22×C11#41712yes—
361C22×C11#41712yes—
362C22×C11C22×C22⋊C411yescharacteristic
363C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
364C22×C11C2×#13711yescharacteristic
365C2×D11—22no—
366C2×D11—22no—
367C2×D11—22no—
368C2×D11—42no—
369C2×D11—42no—
370C4×C11—21no—
371C4×C11—21no—
372C4×C11—21no—
373C4×C11—21no—
374C4×C11—42no—
375C4×C11—81no—
376C4×C11—81no—
377Dic11—22no—
378Dic11—22no—
379Dic11—22no—
380Dic11—42no—
381Dic11—42no—
382Dic11—42no—
383Dic11—81no—
384C2×#41—112no—
385C22×Q8—111no—
386C22×D4—21no—
387C22×D4—111no—
388C22×D4C4×D1111yescharacteristic, complemented
389C23×C4—111no—
390C23×C4—221no—
391C23×C4—221no—
392C23×C4C22×D1111yescharacteristic
393C2×M16—222no—
394C22×C8—21no—
395C22×C8—221no—
396#126—222no—
397#126—222no—
398#126—222no—
399#125—112no—
400#125—222no—
401#124—112no—
402#124—222no—
403#123—222no—
404#123—222no—
405#123—222no—
406#123—222no—
407#123—222no—
408C22⋊Q8—112no—
409C22⋊Q8—112no—
410C22⋊Q8—112no—
411C22⋊Q8—222no—
412C22⋊Q8—221no—
413C22⋊Q8—221no—
414#121—21no—
415#121—21no—
416#121—112no—
417#121—222no—
418#121—222no—
419#121—222no—
420#121C4×D1112yescomplemented
421#121C22×D1112yes—
422#120—222no—
423#120—222no—
424C4×Q8—112no—
425C4×D4—112no—
426C4×D4—112no—
427C4×D4—112no—
428C4×D4—112no—
429C4×D4—112no—
430C4×D4—222no—
431C4×D4—222no—
432C4×D4—222no—
433C4×D4—222no—
434C4×D4—222no—
435C4×D4—444no—
436#117—112no—
437#117—222no—
438#117—222no—
439C2×C4⋊C4—21no—
440C2×C4⋊C4—111no—
441C2×C4⋊C4—111no—
442C2×C4⋊C4—221no—
443C2×C4⋊C4—221no—
444C2×C4⋊C4—221no—
445C2×C4⋊C4—221no—
446C2×C4⋊C4C4×D1111yescharacteristic, complemented
447C2×C22⋊C4—21no—
448C2×C22⋊C4—21no—
449C2×C22⋊C4—111no—
450C2×C22⋊C4—111no—
451C2×C22⋊C4—222no—
452C2×C22⋊C4—221no—
453C2×C22⋊C4—221no—
454C2×C42—111no—
455C2×C42—221no—
456C4⋊C8—222no—
457C22⋊C8—21no—
458C22⋊C8—112no—
459C22⋊C8—222no—
460C22⋊C8—221no—
461C22⋊C8C22×D1112yes—
462#97—222no—
463#95—111no—
464#95—111no—
465#95—221no—
466#95—221no—
467#95—221no—
468#95C22×D1111yescharacteristic
469#95C22×D1111yescharacteristic
470C2×C11—21no—
471C2×C11—21no—
472C2×C11—22no—
473C2×C11—22no—
474C2×C11—82no—
475C2×C11#288311yescharacteristic
476C2×C11C2×#41711yescharacteristic
477C2×C11#290111yescharacteristic
478D11—42no—
479C24—21no—
480C24—111no—
481C24D4×D1111yescharacteristic
482#41—882no—
483C2×Q8—112no—
484C2×Q8—221no—
485C2×Q8—881no—
486C2×D4—22no—
487C2×D4—22no—
488C2×D4—21no—
489C2×D4—42no—
490C2×D4—42no—
491C2×D4—81no—
492C2×D4—112no—
493C2×D4—112no—
494C2×D4—222no—
495C2×D4—222no—
496C2×D4—222no—
497C2×D4—222no—
498C2×D4C2×C4×D1112yes—
499C22×C4—21no—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—81no—
503C22×C4—111no—
504C22×C4—111no—
505C22×C4—111no—
506C22×C4—112no—
507C22×C4—112no—
508C22×C4—222no—
509C22×C4—222no—
510C22×C4—221no—
511C22×C4—221no—
512C22×C4—221no—
513C22×C4—221no—
514C22×C4—442no—
515C22×C4—442no—
516C22×C4—442no—
517C22×C4—442no—
518C22×C4—881no—
519C22×C4—881no—
520C22×C4—881no—
521C22×C4C2×C4×D1111yescharacteristic
522C22×C4C2×C4×D1111yescharacteristic
523C22×C4D4×D1111yescharacteristic
524C22×C4D4×D1111yescharacteristic
525C22×C4D4×D1111yescharacteristic
526C22×C4C23×D1111yescharacteristic
527M16—882no—
528C2×C8—22no—
529C2×C8—81no—
530C2×C8—222no—
531C2×C8—881no—
532C4⋊C4—21no—
533C4⋊C4—81no—
534C4⋊C4—112no—
535C4⋊C4—112no—
536C4⋊C4—112no—
537C4⋊C4—222no—
538C4⋊C4—222no—
539C4⋊C4—222no—
540C4⋊C4—222no—
541C4⋊C4—221no—
542C4⋊C4—222no—
543C4⋊C4—222no—
544C4⋊C4—442no—
545C4⋊C4—442no—
546C4⋊C4—881no—
547C4⋊C4C2×C4×D1112yes—
548C22⋊C4—22no—
549C22⋊C4—22no—
550C22⋊C4—42no—
551C22⋊C4—112no—
552C22⋊C4—112no—
553C22⋊C4—112no—
554C22⋊C4—112no—
555C22⋊C4—222no—
556C22⋊C4—222no—
557C22⋊C4—222no—
558C22⋊C4—222no—
559C22⋊C4—222no—
560C22⋊C4—222no—
561C22⋊C4—222no—
562C22⋊C4—222no—
563C22⋊C4—442no—
564C42—112no—
565C42—112no—
566C42—222no—
567C42—222no—
568C42—442no—
569C11#1762211yescharacteristic, complemented, Sylow
570C23—22no—
571C23—41no—
572C23—41no—
573C23—42no—
574C23—81no—
575C23—81no—
576C23—112no—
577C23—221no—
578C23—221no—
579C23—441no—
580C23—441no—
581C23C22⋊C4×D1111yescharacteristic
582C23C22⋊C4×D1111yescharacteristic
583C23#6696412yes—
584C23#6696812yes—
585C23C2×D4×D1111yescharacteristic
586Q8—442no—
587Q8—881no—
588D4—42no—
589D4—42no—
590D4—42no—
591D4—44no—
592D4—81no—
593D4—224no—
594D4—224no—
595D4—882no—
596D4—882no—
597C2×C4—22no—
598C2×C4—41no—
599C2×C4—41no—
600C2×C4—41no—
601C2×C4—41no—
602C2×C4—41no—
603C2×C4—41no—
604C2×C4—42no—
605C2×C4—41no—
606C2×C4—41no—
607C2×C4—41no—
608C2×C4—41no—
609C2×C4—41no—
610C2×C4—41no—
611C2×C4—112no—
612C2×C4—112no—
613C2×C4—112no—
614C2×C4—221no—
615C2×C4—221no—
616C2×C4—222no—
617C2×C4—222no—
618C2×C4—222no—
619C2×C4—442no—
620C2×C4—442no—
621C2×C4—441no—
622C2×C4—441no—
623C2×C4—441no—
624C2×C4—441no—
625C2×C4—441no—
626C2×C4—441no—
627C2×C4—441no—
628C2×C4—884no—
629C2×C4—882no—
630C2×C4—882no—
631C2×C4—881no—
632C2×C4—881no—
633C2×C4—884no—
634C2×C4C22⋊C4×D1111yescharacteristic
635C2×C4C22⋊C4×D1111yescharacteristic
636C2×C4C22×C4×D1111yescharacteristic
637C2×C4C2×D4×D1111yescharacteristic
638C8—42no—
639C8—442no—
640C22—21no—
641C22—21no—
642C22—21no—
643C22—21no—
644C22—21no—
645C22—21no—
646C22—42no—
647C22—42no—
648C22—42no—
649C22—42no—
650C22—42no—
651C22—162no—
652C22—222no—
653C22—222no—
654C22—222no—
655C22—442no—
656C22—442no—
657C22#1062238412yes—
658C22#1062238412yes—
659C22C2×C22⋊C4×D1111yescharacteristic
660C22C2×#6696411yescharacteristic
661C22C2×#6696811yescharacteristic
662C4—21no—
663C4—21no—
664C4—21no—
665C4—21no—
666C4—42no—
667C4—81no—
668C4—81no—
669C4—222no—
670C4—222no—
671C4—222no—
672C4—442no—
673C4—442no—
674C4—442no—
675C4—881no—
676C2—21no—
677C2—22no—
678C2—21no—
679C2—22no—
680C2—82no—
681C2—442no—
682C2#1307707411yescharacteristic
683C2C2×#1062238411yescharacteristic
684C2#1307716211yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1519C2
socleC22×C11C22×C22⋊C4
prime radical#13082450C2
cosocleC22×C4×C11C24
hypercenter#1519D11
hypocenterC11#17622
LCSG ▷ C2×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1519

Complements

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

NH ≅ G/Ntype
2. #13077642C2semidirect
3. #13071520C2semidirect
4. #13067187C2semidirect
5. #13067156C2semidirect
6. #13067151C2semidirect
7. #13067138C2semidirect
8. #13067117C2semidirect
9. C2×#10622105C2semidirect
10. C2×#10622175C2semidirect
11. C11×#1519C2semidirect
13. #10623337C4semidirect
18. #10623149C4semidirect
24. #10623129C4semidirect
25. #10623044C4semidirect
37. #10622339C22semidirect
38. #10622332C22semidirect
39. #10622280C22semidirect
40. D11×#95C22semidirect
41. #10622263C22semidirect
42. #10622262C22semidirect
47. #10622105C22semidirect
48. #10622105C22semidirect
49. #10622090C22semidirect
50. #10622090C22semidirect
52. C22×D4×C11C2×C4semidirect
56. C2×#4341C2×C4semidirect
59. C22×Dic22C2×C4semidirect
63. C11×#121C2×C4semidirect
66. C2×C11×C4⋊C4C2×C4semidirect
76. #66991C2×C4semidirect
78. #66989C2×C4semidirect
85. D4×Dic11C2×C4semidirect
94. C2×C4⋊Dic11C2×C4semidirect
97. #66977C2×C4semidirect
109. #66950C2×C4semidirect
110. #66945C2×C4semidirect
111. #66943C2×C4semidirect
113. #66940C2×C4semidirect
232. #1519D11semidirect
388. C22×D4C4×D11semidirect
420. #121C4×D11semidirect
446. C2×C4⋊C4C4×D11semidirect
569. C11#17622semidirect

Maximal subgroups

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

subgroupindex
#130824502
#130776422
#130715202
#130671872
#130671562
#130671512
#130671382
#130671172
C2×#106221052
C2×#106221752
C11×#15192
#1762211