Finite Group Databasebeta

← #14722129

Subgroups — #14722129

Order 2816.

1018 conjugacy classes of subgroups.

The subgroup lattice has 664 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D11×#533C211yesmaximal, characteristic
2C2×#10622446C211yesmaximal, characteristic
3D11×#423C211yesmaximal, characteristic
4#13067307C211yesmaximal, characteristic, complemented
5#13067306C211yesmaximal, characteristic, complemented
6#13067304C211yesmaximal, characteristic, complemented
7#13067299C212yesmaximal, complemented
8#13067295C212yesmaximal, complemented
9#13067272C212yesmaximal, complemented
10#13067270C212yesmaximal, complemented
11C11×#1550C211yesmaximal, characteristic, complemented
12C11×#533C2211yescharacteristic
13C2×M16×D11—21no—
14#10623259C2211yescharacteristic
15#10623259C2211yescharacteristic
16D11×C4⋊Q8C2211yescharacteristic
17D11×C4⋊Q8C2211yescharacteristic
18#10623219—21no—
19D11×#125—21no—
20D11×C22⋊Q8—21no—
21D11×C22⋊Q8C412yes—
22#10623153—21no—
23#10623153C412yes—
24#10623109—21no—
25#10623109C412yes—
26C4×Q8×D11—21no—
27C4×Q8×D11C412yes—
28D11×#117—21no—
29#10623048—21no—
30C2×C42×D11C2211yescharacteristic
31#10623001C2211yescharacteristic
32C11×#423C2211yescharacteristic
33C2×C11×C4⋊C8C2211yescharacteristic
34#10622731—21no—
35C2×(C2×D11)⋊C8—21no—
36C2×C8×Dic11—21no—
37#10622537C2211yescharacteristic
38C2×C4⋊(C11⋊C8)C2211yescharacteristic
39#10622450—21no—
40#10622450C2212yes—
41#10622446—21no—
42#10622446—21no—
43#10622446C2212yes—
44#10622446C2212yes—
45D11×C4⋊C8—21no—
46D11×C4⋊C8C2212yes—
47C11×#333C2212yescomplemented
48C11×#332C2212yescomplemented
49#10622185C2212yescomplemented
50#10622184C2212yescomplemented
51#10622124C2212yescomplemented
52#10622120C2212yescomplemented
53#10622119C2212yescomplemented
54#10622119C2212yescomplemented
55C2×Q8×D11—21no—
56C2×Q8×D11C2×C412yes—
57C22×C4×D11C2×C411yescharacteristic
58C22×C4×D11D411yescharacteristic
59C22×C4×D11D411yescharacteristic
60C2×C11×M16—21no—
61C22×C8×C11—21no—
62C11×C4⋊Q8C2311yescharacteristic
63C11×C4⋊Q8C2311yescharacteristic
64C11×#125—21no—
65C11×C22⋊Q8—21no—
66C11×C22⋊Q8C2×C412yes—
67C4×Q8×C11—21no—
68C4×Q8×C11C2×C412yes—
69C11×#117—21no—
70C2×C42×C11C2311yescharacteristic
71#66999—21no—
72#66999C2×C412yes—
73Q8×Dic11—21no—
74Q8×Dic11C2×C412yes—
75#66997—21no—
76#66997C2×C412yes—
77#66979—21no—
78#66977—21no—
79#66977C2×C412yes—
80C2×C4×Dic11C2×C411yescharacteristic
81C2×C4×Dic11D411yescharacteristic
82C2×C4×Dic11D411yescharacteristic
83C2×#4318—21no—
84C22×C11⋊C8—21no—
85M16×D11—44no—
86C2×#4313—22no—
87C2×C8×D11—22no—
88#66950—21no—
89#66950C2×C412yes—
90#66949—22no—
91#66949—22no—
92#66945—21no—
93#66945—21no—
94C4⋊C4×D11—22no—
95C4⋊C4×D11—22no—
96C4⋊C4×D11—21no—
97C4⋊C4×D11—21no—
98C4⋊C4×D11—21no—
99C4⋊C4×D11C2×C412yes—
100#66943—21no—
101#66943—21no—
102#66942—22no—
103#66942—22no—
104#66941—21no—
105#66941—21no—
106#66941—21no—
107#66941C2×C412yes—
108#66940—22no—
109#66940—22no—
110#66940—21no—
111#66940C2×C412yes—
112C22⋊C4×D11—22no—
113#66931—22no—
114#66931—22no—
115#66930—22no—
116#66925—22no—
117C42×D11—22no—
118C42×D11C2×C411yescharacteristic
119C42×D11C2×C411yescharacteristic
120C42×D11D411yescharacteristic
121C42×D11D411yescharacteristic
122C42×D11D411yescharacteristic
123C42×D11D411yescharacteristic
124C42×D11C2311yescharacteristic
125C42×D11C2311yescharacteristic
126#66923—21no—
127#66922C2311yescharacteristic
128#66922C2311yescharacteristic
129C4×Dic22—21no—
130C4×Dic22—22no—
131C4×Dic22—22no—
132C4×Dic22C2×C412yes—
133C11×C4⋊C8—21no—
134C11×C4⋊C8—21no—
135C11×C4⋊C8C2312yes—
136C11×C4⋊C8C2312yes—
137(C2×D11)⋊C8—22no—
138(C2×D11)⋊C8—22no—
139Dic11⋊C8—22no—
140Dic11⋊C8—22no—
141C8×Dic11—22no—
142C8×Dic11—22no—
143C4⋊(C11⋊C8)—21no—
144C4⋊(C11⋊C8)—21no—
145C4⋊(C11⋊C8)C2312yes—
146C4⋊(C11⋊C8)C2312yes—
147#17708—111nomaximal, Sylow
148C23×D11C22⋊C411yescharacteristic
149C2×Q8×C11—21no—
150C2×Q8×C11C22×C412yes—
151C22×C4×C11C22×C411yescharacteristic
152C22×C4×C11C2×D411yescharacteristic
153C22×C4×C11C2×D411yescharacteristic
154C22×Dic11C22⋊C411yescharacteristic
155C22×Dic11C22⋊C411yescharacteristic
156C22×Dic11C22⋊C411yescharacteristic
157Q8×D11—42no—
158Q8×D11—42no—
159Q8×D11—44no—
160C2×C4×D11—22no—
161C2×C4×D11—22no—
162C2×C4×D11—41no—
163C2×C4×D11—41no—
164C2×C4×D11—42no—
165C2×C4×D11C22⋊C411yescharacteristic
166C2×C4×D11C22⋊C411yescharacteristic
167C2×C4×D11C22⋊C411yescharacteristic
168C2×C4×D11C22⋊C411yescharacteristic
169C2×C4×D11C22⋊C411yescharacteristic
170C2×C4×D11C22⋊C411yescharacteristic
171C2×C4×D11SD1614yes—
172C2×C4×D11Q1614yes—
173C2×C4×D11C22×C411yescharacteristic
174C2×C4×D11C22×C411yescharacteristic
175C2×C4×D11C2×D411yescharacteristic
176C2×C4×D11C2×D411yescharacteristic
177C2×C4×D11C2×D411yescharacteristic
178C2×C4×D11C2×D411yescharacteristic
179C2×Dic22—22no—
180C2×Dic22—22no—
181C2×Dic22—21no—
182C2×Dic22C22×C412yes—
183C11×M16—42no—
184C2×C8×C11—22no—
185C2×C8×C11—22no—
186C2×C8×C11—42no—
187C11×C4⋊C4—22no—
188C11×C4⋊C4—22no—
189C11×C4⋊C4—21no—
190C11×C4⋊C4—21no—
191C11×C4⋊C4—21no—
192C11×C4⋊C4C22×C412yes—
193C11×C22⋊C4—22no—
194C42×C11—22no—
195C42×C11C22×C411yescharacteristic
196C42×C11C2×D411yescharacteristic
197C42×C11C2×D411yescharacteristic
198C42×C11C2411yescharacteristic
199C22⋊Dic11—22no—
200(C2×D11)⋊C4—22no—
201(C2×D11)⋊C4—22no—
202C4⋊Dic11—22no—
203C4⋊Dic11—22no—
204C4⋊Dic11—21no—
205C4⋊Dic11—21no—
206C4⋊Dic11—21no—
207C4⋊Dic11C22×C412yes—
208Dic11⋊C4—22no—
209Dic11⋊C4—22no—
210Dic11⋊C4—22no—
211Dic11⋊C4—22no—
212Dic11⋊C4—22no—
213Dic11⋊C4—22no—
214Dic11⋊C4—22no—
215Dic11⋊C4—22no—
216C4×Dic11—22no—
217C4×Dic11—22no—
218C4×Dic11—22no—
219C4×Dic11C22⋊C411yescharacteristic
220C4×Dic11C22⋊C411yescharacteristic
221C4×Dic11C22⋊C411yescharacteristic
222C4×Dic11C22⋊C411yescharacteristic
223C4×Dic11C22⋊C411yescharacteristic
224C4×Dic11C22⋊C411yescharacteristic
225C4×Dic11C22×C411yescharacteristic
226C4×Dic11C22×C411yescharacteristic
227C4×Dic11C2×D411yescharacteristic
228C4×Dic11C2×D411yescharacteristic
229C4×Dic11C2×D411yescharacteristic
230C4×Dic11C2×D411yescharacteristic
231#4318—42no—
232C2×C11⋊C8—22no—
233C2×C11⋊C8—22no—
234C2×C11⋊C8—42no—
235#4313—44no—
236C8×D11—44no—
237C2×#533—111no—
238C2×#431—111no—
239C2×#423—111no—
240#1550—111no—
241#1550—111no—
242#1550—111no—
243#1550D1111yescharacteristic, complemented
244#1549—112no—
245#1548—112no—
246#1542—112no—
247#1542—112no—
248C23×C11C2×C22⋊C411yescharacteristic
249C22×D11—41no—
250C22×D11—41no—
251C22×D11#10314yes—
252C22×D11C2×C22⋊C411yescharacteristic
253C22×D11C2×C22⋊C411yescharacteristic
254Q8×C11—42no—
255Q8×C11—41no—
256Q8×C11—41no—
257C2×C4×C11—21no—
258C2×C4×C11—21no—
259C2×C4×C11—22no—
260C2×C4×C11—22no—
261C2×C4×C11—41no—
262C2×C4×C11C2×C22⋊C411yescharacteristic
263C2×C4×C11C2×C22⋊C411yescharacteristic
264C2×C4×C11C2×C22⋊C411yescharacteristic
265C2×C4×C11C2×SD1612yes—
266C2×C4×C11C2×Q1612yes—
267C2×C4×C11C23×C411yescharacteristic
268C2×C4×C11C22×D411yescharacteristic
269C2×C4×C11C22×D411yescharacteristic
270C2×Dic11—22no—
271C2×Dic11—22no—
272C2×Dic11—22no—
273C2×Dic11—41no—
274C2×Dic11#10314yes—
275C2×Dic11C2×C22⋊C411yescharacteristic
276C2×Dic11C2×C22⋊C411yescharacteristic
277C2×Dic11C2×C22⋊C411yescharacteristic
278C2×Dic11C2×C22⋊C411yescharacteristic
279C2×Dic11C2×C22⋊C411yescharacteristic
280C2×Dic11C2×C22⋊C411yescharacteristic
281C4×D11—21no—
282C4×D11—21no—
283C4×D11—21no—
284C4×D11—21no—
285C4×D11—22no—
286C4×D11—22no—
287C4×D11—41no—
288C4×D11—41no—
289C4×D11—41no—
290C4×D11—41no—
291C4×D11—44no—
292C4×D11—44no—
293C4×D11#10314yes—
294C4×D11#10314yes—
295C4×D11C2×SD1612yes—
296C4×D11C2×SD1612yes—
297C4×D11C2×Q1612yes—
298C4×D11C2×Q1612yes—
299Dic22—44no—
300Dic22—41no—
301Dic22—41no—
302Dic22—44no—
303Dic22—42no—
304C8×C11—42no—
305C8×C11—42no—
306C11⋊C8—42no—
307C11⋊C8—42no—
308C22×M16—221no—
309#533—111no—
310#533—111no—
311#533—112no—
312#533—112no—
313#533—111no—
314#533—221no—
315#533—221no—
316#533—221no—
317#533—221no—
318#533C2×D1111yescharacteristic
319C2×C4⋊Q8—111no—
320C2×C4⋊Q8—111no—
321C2×#125—221no—
322C2×C22⋊Q8—112no—
323C2×C22⋊Q8—221no—
324C2×C4×Q8—112no—
325C2×C4×Q8—221no—
326C2×#117—221no—
327C22×C42—111no—
328#431—112no—
329#431—112no—
330#431—221no—
331#431—221no—
332#423—111no—
333#423—112no—
334#423—221no—
335#423—221no—
336#423C2×D1111yescharacteristic
337C2×C4⋊C8—111no—
338C2×C4⋊C8—112no—
339C2×C4⋊C8—221no—
340C2×C4⋊C8C2×D1111yescharacteristic
341C2×C22⋊C8—221no—
342C2×C4×C8—221no—
343#333—112no—
344#333—112no—
345#333—112no—
346#333C2×D1112yescomplemented
347#332—112no—
348#332—112no—
349#332—112no—
350#332C2×D1112yescomplemented
351C22×C11—21no—
352C22×C11—21no—
353C22×C11C2×#10312yes—
354C22×C11C22×C22⋊C411yescharacteristic
355C2×D11—21no—
356C2×D11—21no—
357C2×D11—21no—
358C2×D11—21no—
359C2×D11—44no—
360C2×D11C2×#10312yes—
361C2×D11C2×#10312yes—
362C4×C11—21no—
363C4×C11—21no—
364C4×C11—21no—
365C4×C11—42no—
366C4×C11—42no—
367C4×C11C2×#10312yes—
368C4×C11C22×SD1611yescharacteristic
369C4×C11C22×Q1611yescharacteristic
370C4×C11#57511yescharacteristic
371C4×C11#57511yescharacteristic
372Dic11—21no—
373Dic11—21no—
374Dic11—21no—
375Dic11—42no—
376Dic11—42no—
377Dic11#41312yes—
378Dic11C2×#10312yes—
379Dic11C2×#10312yes—
380C22×Q8—112no—
381C22×Q8—221no—
382C23×C4—111no—
383C23×C4—111no—
384C23×C4—111no—
385C2×M16—21no—
386C2×M16—222no—
387C2×M16—221no—
388C2×M16—444no—
389C22×C8—21no—
390C22×C8—222no—
391C22×C8—221no—
392C4⋊Q8—112no—
393C4⋊Q8—112no—
394C4⋊Q8—111no—
395C4⋊Q8—111no—
396C4⋊Q8—221no—
397C4⋊Q8—221no—
398C4⋊Q8—221no—
399C4⋊Q8—221no—
400C4⋊Q8C22×D1111yescharacteristic
401C4⋊Q8C22×D1111yescharacteristic
402#125—21no—
403#125—222no—
404#125—222no—
405#125—221no—
406#125—221no—
407#125—221no—
408C22⋊Q8—21no—
409C22⋊Q8—112no—
410C22⋊Q8—112no—
411C22⋊Q8—112no—
412C22⋊Q8—222no—
413C22⋊Q8—222no—
414C22⋊Q8—222no—
415C22⋊Q8—222no—
416C22⋊Q8—221no—
417C22⋊Q8—221no—
418C22⋊Q8—221no—
419C22⋊Q8C4×D1112yes—
420C4×Q8—21no—
421C4×Q8—112no—
422C4×Q8—112no—
423C4×Q8—112no—
424C4×Q8—222no—
425C4×Q8—222no—
426C4×Q8—222no—
427C4×Q8—222no—
428C4×Q8—221no—
429C4×Q8—221no—
430C4×Q8—221no—
431C4×Q8C4×D1112yes—
432#117—21no—
433#117—222no—
434#117—222no—
435#117—221no—
436#117—221no—
437#117—221no—
438C2×C4⋊C4—112no—
439C2×C4⋊C4—221no—
440C2×C4⋊C4—221no—
441C2×C4⋊C4—222no—
442C2×C4⋊C4—222no—
443C2×C4⋊C4—221no—
444C2×C22⋊C4—222no—
445C2×C42—111no—
446C2×C42—111no—
447C2×C42—111no—
448C2×C42—111no—
449C2×C42—111no—
450C2×C42—111no—
451C2×C42—111no—
452C2×C42—111no—
453C2×C42—111no—
454C2×C42—111no—
455C2×C42—111no—
456C2×C42—222no—
457C2×C42C22×D1111yescharacteristic
458C4⋊C8—21no—
459C4⋊C8—21no—
460C4⋊C8—112no—
461C4⋊C8—112no—
462C4⋊C8—222no—
463C4⋊C8—222no—
464C4⋊C8—221no—
465C4⋊C8—221no—
466C4⋊C8C22×D1112yes—
467C4⋊C8C22×D1112yes—
468C22⋊C8—222no—
469C22⋊C8—222no—
470C4×C8—222no—
471C4×C8—222no—
472C2×C11—22no—
473C2×C11C2×#41311yescharacteristic
474C2×C11C22×#10311yescharacteristic
475C2×C11#289611yescharacteristic
476D11—22no—
477D11—22no—
478C24—111no—
479C2×Q8—21no—
480C2×Q8—112no—
481C2×Q8—222no—
482C2×Q8—222no—
483C2×Q8—221no—
484C2×Q8—444no—
485C2×Q8—442no—
486C2×Q8—442no—
487C2×Q8C2×C4×D1112yes—
488C22×C4—111no—
489C22×C4—111no—
490C22×C4—111no—
491C22×C4—114no—
492C22×C4—114no—
493C22×C4—111no—
494C22×C4—111no—
495C22×C4—111no—
496C22×C4—111no—
497C22×C4—111no—
498C22×C4—111no—
499C22×C4—111no—
500C22×C4—111no—
501C22×C4—111no—
502C22×C4—111no—
503C22×C4—111no—
504C22×C4—111no—
505C22×C4—222no—
506C22×C4—222no—
507C22×C4—441no—
508C22×C4—441no—
509C22×C4—442no—
510C22×C4C2×C4×D1111yescharacteristic
511C22×C4D4×D1111yescharacteristic
512C22×C4D4×D1111yescharacteristic
513M16—42no—
514M16—444no—
515M16—442no—
516C2×C8—22no—
517C2×C8—22no—
518C2×C8—42no—
519C2×C8—222no—
520C2×C8—222no—
521C2×C8—444no—
522C2×C8—442no—
523C4⋊C4—22no—
524C4⋊C4—22no—
525C4⋊C4—21no—
526C4⋊C4—21no—
527C4⋊C4—21no—
528C4⋊C4—112no—
529C4⋊C4—222no—
530C4⋊C4—222no—
531C4⋊C4—222no—
532C4⋊C4—222no—
533C4⋊C4—222no—
534C4⋊C4—222no—
535C4⋊C4—222no—
536C4⋊C4—222no—
537C4⋊C4—222no—
538C4⋊C4—222no—
539C4⋊C4—221no—
540C4⋊C4—221no—
541C4⋊C4—221no—
542C4⋊C4C2×C4×D1112yes—
543C22⋊C4—22no—
544C22⋊C4—222no—
545C22⋊C4—222no—
546C22⋊C4—222no—
547C42—22no—
548C42—111no—
549C42—111no—
550C42—111no—
551C42—111no—
552C42—111no—
553C42—111no—
554C42—111no—
555C42—111no—
556C42—111no—
557C42—111no—
558C42—111no—
559C42—111no—
560C42—222no—
561C42—222no—
562C42—222no—
563C42C2×C4×D1111yescharacteristic
564C42D4×D1111yescharacteristic
565C42D4×D1111yescharacteristic
566C42C23×D1111yescharacteristic
567C11#1770811yescharacteristic, complemented, Sylow
568C23—111no—
569C23—111no—
570C23—114no—
571C23—441no—
572C23—441no—
573C23C22⋊C4×D1111yescharacteristic
574Q8—42no—
575Q8—41no—
576Q8—41no—
577Q8—442no—
578Q8—444no—
579Q8—444no—
580Q8—441no—
581Q8—441no—
582C2×C4—21no—
583C2×C4—21no—
584C2×C4—22no—
585C2×C4—22no—
586C2×C4—41no—
587C2×C4—111no—
588C2×C4—111no—
589C2×C4—111no—
590C2×C4—114no—
591C2×C4—112no—
592C2×C4—112no—
593C2×C4—112no—
594C2×C4—112no—
595C2×C4—114no—
596C2×C4—114no—
597C2×C4—111no—
598C2×C4—111no—
599C2×C4—111no—
600C2×C4—222no—
601C2×C4—222no—
602C2×C4—222no—
603C2×C4—221no—
604C2×C4—221no—
605C2×C4—221no—
606C2×C4—221no—
607C2×C4—222no—
608C2×C4—222no—
609C2×C4—441no—
610C2×C4—441no—
611C2×C4—441no—
612C2×C4—441no—
613C2×C4—444no—
614C2×C4—444no—
615C2×C4—441no—
616C2×C4C22⋊C4×D1111yescharacteristic
617C2×C4C22⋊C4×D1111yescharacteristic
618C2×C4C22⋊C4×D1111yescharacteristic
619C2×C4SD16×D1112yes—
620C2×C4Q16×D1112yes—
621C2×C4C22×C4×D1111yescharacteristic
622C2×C4C2×D4×D1111yescharacteristic
623C2×C4C2×D4×D1111yescharacteristic
624C8—42no—
625C8—42no—
626C8—442no—
627C8—442no—
628C22—21no—
629C22—21no—
630C22—112no—
631C22—112no—
632C22—221no—
633C22—221no—
634C22—221no—
635C22—221no—
636C22—444no—
637C22D11×#10312yes—
638C22C2×C22⋊C4×D1111yescharacteristic
639C4—21no—
640C4—21no—
641C4—21no—
642C4—42no—
643C4—42no—
644C4—112no—
645C4—112no—
646C4—112no—
647C4—221no—
648C4—221no—
649C4—221no—
650C4—442no—
651C4—442no—
652C4D11×#10312yes—
653C4C2×SD16×D1111yescharacteristic
654C4C2×Q16×D1111yescharacteristic
655C4#1062330411yescharacteristic
656C4#1062330811yescharacteristic
657C2—22no—
658C2—222no—
659C2—222no—
660C2D11×#41311yescharacteristic
661C2C2×D11×#10311yescharacteristic
662C2#1307713211yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×#1550C2
socleC22×C11C22×C22⋊C4
prime radicalC23×D11C22⋊C4
cosocleC42×C11C24
hypercenter#1550D11
hypocenterC11#17708
LCSG ▷ C2×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1550

Complements

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

NH ≅ G/Ntype
4. #13067307C2semidirect
5. #13067306C2semidirect
6. #13067304C2semidirect
7. #13067299C2semidirect
8. #13067295C2semidirect
9. #13067272C2semidirect
10. #13067270C2semidirect
11. C11×#1550C2semidirect
47. C11×#333C22semidirect
48. C11×#332C22semidirect
49. #10622185C22semidirect
50. #10622184C22semidirect
51. #10622124C22semidirect
52. #10622120C22semidirect
53. #10622119C22semidirect
54. #10622119C22semidirect
243. #1550D11semidirect
346. #333C2×D11semidirect
350. #332C2×D11semidirect
567. C11#17708semidirect

Maximal subgroups

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

subgroupindex
D11×#5332
C2×#106224462
D11×#4232
#130673072
#130673062
#130673042
#130672992
#130672952
#130672722
#130672702
C11×#15502
#1770811