Finite Group Databasebeta

← #14722408

Subgroups — #14722408

Order 2816.

996 conjugacy classes of subgroups.

The subgroup lattice has 652 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D11×#533C211yesmaximal, characteristic
2#13077246C211yesmaximal, characteristic
3D11×#423C211yesmaximal, characteristic
4#13067347C211yesmaximal, characteristic, complemented
5#13067346C211yesmaximal, characteristic, complemented
6#13067344C211yesmaximal, characteristic, complemented
7#13067305C212yesmaximal, complemented
8#13067303C212yesmaximal, complemented
9#13067295C212yesmaximal, complemented
10#13067286C212yesmaximal, complemented
11C11×#1559C211yesmaximal, 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×#432C2211yescharacteristic
33C11×#423C2211yescharacteristic
34#10622731—21no—
35#10622539C2211yescharacteristic
36#10622537C2211yescharacteristic
37#10622450—21no—
38#10622450C2212yes—
39#10622450C2212yes—
40#10622446C2212yes—
41D11×C4⋊C8—21no—
42D11×C4⋊C8C2212yes—
43#10622339—21no—
44#10622331—21no—
45#10622320—21no—
46#10622318—21no—
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—
61C11×C4⋊Q8C2311yescharacteristic
62C11×C4⋊Q8C2311yescharacteristic
63C11×#125—21no—
64C11×C22⋊Q8—21no—
65C11×C22⋊Q8C2×C412yes—
66C4×Q8×C11—21no—
67C4×Q8×C11C2×C412yes—
68C11×#117—21no—
69C2×C42×C11C2311yescharacteristic
70#66999—21no—
71#66999C2×C412yes—
72Q8×Dic11—21no—
73Q8×Dic11C2×C412yes—
74#66997—21no—
75#66997C2×C412yes—
76#66979—21no—
77#66977—21no—
78#66977C2×C412yes—
79C2×C4×Dic11C2×C411yescharacteristic
80C2×C4×Dic11D411yescharacteristic
81C2×C4×Dic11D411yescharacteristic
82C2×#4318—21no—
83M16×D11—44no—
84C2×#4313—22no—
85C2×#4313—22no—
86C2×C8×D11—22no—
87#66950—21no—
88#66950C2×C412yes—
89#66949—22no—
90#66949—22no—
91#66945—21no—
92#66945—21no—
93C4⋊C4×D11—22no—
94C4⋊C4×D11—22no—
95C4⋊C4×D11—21no—
96C4⋊C4×D11—21no—
97C4⋊C4×D11—21no—
98C4⋊C4×D11C2×C412yes—
99#66943—21no—
100#66943—21no—
101#66942—22no—
102#66942—22no—
103#66941—21no—
104#66941—21no—
105#66941—21no—
106#66941C2×C412yes—
107#66940—22no—
108#66940—22no—
109#66940—21no—
110#66940C2×C412yes—
111C22⋊C4×D11—22no—
112#66931—22no—
113#66931—22no—
114#66930—22no—
115#66925—22no—
116C42×D11—22no—
117C42×D11C2×C411yescharacteristic
118C42×D11C2×C411yescharacteristic
119C42×D11D411yescharacteristic
120C42×D11D411yescharacteristic
121C42×D11D411yescharacteristic
122C42×D11D411yescharacteristic
123C42×D11C2311yescharacteristic
124C42×D11C2311yescharacteristic
125#66923—21no—
126#66922C2311yescharacteristic
127#66922C2311yescharacteristic
128C4×Dic22—21no—
129C4×Dic22—22no—
130C4×Dic22—22no—
131C4×Dic22C2×C412yes—
132C11×C4⋊C8—21no—
133C11×C4⋊C8C2312yes—
134C11×C4⋊C8C2312yes—
135C11×C22⋊C8—21no—
136C11×#97—21no—
137C22⋊(C11⋊C8)—21no—
138(C2×D11)⋊C8—22no—
139Dic11⋊C8—22no—
140Dic11⋊C8—22no—
141Dic11⋊C8—22no—
142C8×Dic11—22no—
143C4⋊(C11⋊C8)—21no—
144C4⋊(C11⋊C8)C2312yes—
145C4⋊(C11⋊C8)C2312yes—
146#66867—21no—
147#17749—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—24no—
163C2×C4×D11—22no—
164C2×C4×D11—22no—
165C2×C4×D11—42no—
166C2×C4×D11C22⋊C411yescharacteristic
167C2×C4×D11C22⋊C411yescharacteristic
168C2×C4×D11C22⋊C411yescharacteristic
169C2×C4×D11C22⋊C411yescharacteristic
170C2×C4×D11C22⋊C411yescharacteristic
171C2×C4×D11C22⋊C411yescharacteristic
172C2×C4×D11C22×C411yescharacteristic
173C2×C4×D11C22×C411yescharacteristic
174C2×C4×D11C2×D411yescharacteristic
175C2×C4×D11C2×D411yescharacteristic
176C2×C4×D11C2×D411yescharacteristic
177C2×C4×D11C2×D411yescharacteristic
178C2×Dic22—22no—
179C2×Dic22—22no—
180C2×Dic22—21no—
181C2×Dic22C22×C412yes—
182C11×M16—42no—
183C2×C8×C11—22no—
184C2×C8×C11—22no—
185C11×C4⋊C4—22no—
186C11×C4⋊C4—22no—
187C11×C4⋊C4—21no—
188C11×C4⋊C4—21no—
189C11×C4⋊C4—21no—
190C11×C4⋊C4C22×C412yes—
191C11×C22⋊C4—22no—
192C42×C11—22no—
193C42×C11C22×C411yescharacteristic
194C42×C11C2×D411yescharacteristic
195C42×C11C2×D411yescharacteristic
196C42×C11C2411yescharacteristic
197C22⋊Dic11—22no—
198(C2×D11)⋊C4—22no—
199(C2×D11)⋊C4—22no—
200C4⋊Dic11—22no—
201C4⋊Dic11—22no—
202C4⋊Dic11—21no—
203C4⋊Dic11—21no—
204C4⋊Dic11—21no—
205C4⋊Dic11C22×C412yes—
206Dic11⋊C4—22no—
207Dic11⋊C4—22no—
208Dic11⋊C4—22no—
209Dic11⋊C4—22no—
210Dic11⋊C4—22no—
211Dic11⋊C4—22no—
212Dic11⋊C4—22no—
213Dic11⋊C4—22no—
214C4×Dic11—22no—
215C4×Dic11—22no—
216C4×Dic11—22no—
217C4×Dic11C22⋊C411yescharacteristic
218C4×Dic11C22⋊C411yescharacteristic
219C4×Dic11C22⋊C411yescharacteristic
220C4×Dic11C22⋊C411yescharacteristic
221C4×Dic11C22⋊C411yescharacteristic
222C4×Dic11C22⋊C411yescharacteristic
223C4×Dic11C22×C411yescharacteristic
224C4×Dic11C22×C411yescharacteristic
225C4×Dic11C2×D411yescharacteristic
226C4×Dic11C2×D411yescharacteristic
227C4×Dic11C2×D411yescharacteristic
228C4×Dic11C2×D411yescharacteristic
229#4318—42no—
230C2×C11⋊C8—22no—
231C2×C11⋊C8—22no—
232#4313—44no—
233#4313—44no—
234C8×D11—44no—
235C2×#533—111no—
236#2920—111no—
237C2×#423—111no—
238#1559—111no—
239#1559—111no—
240#1559—111no—
241#1559D1111yescharacteristic, complemented
242#1550—112no—
243#1550—112no—
244#1548—112no—
245#1546—112no—
246C23×C11C2×C22⋊C411yescharacteristic
247C22×D11—22no—
248C22×D11—22no—
249C22×D11—41no—
250C22×D11C2×C22⋊C411yescharacteristic
251C22×D11C2×C22⋊C411yescharacteristic
252Q8×C11—42no—
253Q8×C11—41no—
254Q8×C11—41no—
255C2×C4×C11—21no—
256C2×C4×C11—22no—
257C2×C4×C11—21no—
258C2×C4×C11—22no—
259C2×C4×C11—22no—
260C2×C4×C11—41no—
261C2×C4×C11C2×C22⋊C411yescharacteristic
262C2×C4×C11C2×C22⋊C411yescharacteristic
263C2×C4×C11C2×C22⋊C411yescharacteristic
264C2×C4×C11C23×C411yescharacteristic
265C2×C4×C11C22×D411yescharacteristic
266C2×C4×C11C22×D411yescharacteristic
267C2×Dic11—22no—
268C2×Dic11—22no—
269C2×Dic11—22no—
270C2×Dic11—22no—
271C2×Dic11—22no—
272C2×Dic11C2×C22⋊C411yescharacteristic
273C2×Dic11C2×C22⋊C411yescharacteristic
274C2×Dic11C2×C22⋊C411yescharacteristic
275C2×Dic11C2×C22⋊C411yescharacteristic
276C2×Dic11C2×C22⋊C411yescharacteristic
277C2×Dic11C2×C22⋊C411yescharacteristic
278C4×D11—22no—
279C4×D11—22no—
280C4×D11—21no—
281C4×D11—22no—
282C4×D11—21no—
283C4×D11—22no—
284C4×D11—22no—
285C4×D11—22no—
286C4×D11—22no—
287C4×D11—41no—
288C4×D11—41no—
289C4×D11—44no—
290C4×D11—44no—
291C4×D11AGL(1,ℤ/8)12yes—
292C4×D11#13712yes—
293C4×D11#13714yes—
294Dic22—41no—
295Dic22—41no—
296Dic22—44no—
297Dic22—44no—
298Dic22—42no—
299C8×C11—42no—
300C8×C11—42no—
301C11⋊C8—42no—
302C11⋊C8—42no—
303C22×M16—221no—
304#533—111no—
305#533—111no—
306#533—112no—
307#533—112no—
308#533—111no—
309#533—221no—
310#533—221no—
311#533—221no—
312#533—221no—
313#533C2×D1111yescharacteristic
314C2×C4⋊Q8—111no—
315C2×C4⋊Q8—111no—
316C2×#125—221no—
317C2×C22⋊Q8—112no—
318C2×C22⋊Q8—221no—
319C2×C4×Q8—112no—
320C2×C4×Q8—221no—
321C2×#117—221no—
322C22×C42—111no—
323#432—111no—
324#432—221no—
325#432C2×D1111yescharacteristic
326#431—112no—
327#431—221no—
328#423—111no—
329#423—112no—
330#423—112no—
331#423—221no—
332#423—221no—
333#423C2×D1111yescharacteristic
334C2×C4⋊C8—112no—
335C2×C4⋊C8—221no—
336#407—221no—
337C4×M16—221no—
338#333—112no—
339#333—112no—
340#333—112no—
341#333C2×D1112yescomplemented
342#332—112no—
343#332—112no—
344#332—112no—
345#332C2×D1112yescomplemented
346C22×C11—21no—
347C22×C11—21no—
348C22×C11—21no—
349C22×C11C22×C22⋊C411yescharacteristic
350C2×D11—21no—
351C2×D11—21no—
352C2×D11—21no—
353C2×D11—21no—
354C2×D11—44no—
355C2×D11#41712yes—
356C2×D11#41912yes—
357C4×C11—21no—
358C4×C11—21no—
359C4×C11—21no—
360C4×C11—21no—
361C4×C11—42no—
362C4×C11—42no—
363C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
364C4×C11C2×#13712yes—
365C4×C11C2×#13711yescharacteristic
366Dic11—21no—
367Dic11—21no—
368Dic11—21no—
369Dic11—42no—
370Dic11—42no—
371Dic11#41312yes—
372Dic11#41712yes—
373Dic11#41912yes—
374C22×Q8—112no—
375C22×Q8—221no—
376C23×C4—111no—
377C23×C4—111no—
378C23×C4—111no—
379C2×M16—21no—
380C2×M16—222no—
381C2×M16—222no—
382C2×M16—221no—
383C2×M16—444no—
384C22×C8—222no—
385C4⋊Q8—112no—
386C4⋊Q8—112no—
387C4⋊Q8—111no—
388C4⋊Q8—111no—
389C4⋊Q8—221no—
390C4⋊Q8—221no—
391C4⋊Q8—221no—
392C4⋊Q8—221no—
393C4⋊Q8C22×D1111yescharacteristic
394C4⋊Q8C22×D1111yescharacteristic
395#125—21no—
396#125—222no—
397#125—222no—
398#125—221no—
399#125—221no—
400#125—221no—
401C22⋊Q8—21no—
402C22⋊Q8—112no—
403C22⋊Q8—112no—
404C22⋊Q8—112no—
405C22⋊Q8—222no—
406C22⋊Q8—222no—
407C22⋊Q8—222no—
408C22⋊Q8—222no—
409C22⋊Q8—221no—
410C22⋊Q8—221no—
411C22⋊Q8—221no—
412C22⋊Q8C4×D1112yes—
413C4×Q8—21no—
414C4×Q8—112no—
415C4×Q8—112no—
416C4×Q8—112no—
417C4×Q8—222no—
418C4×Q8—222no—
419C4×Q8—222no—
420C4×Q8—222no—
421C4×Q8—221no—
422C4×Q8—221no—
423C4×Q8—221no—
424C4×Q8C4×D1112yes—
425#117—21no—
426#117—222no—
427#117—222no—
428#117—221no—
429#117—221no—
430#117—221no—
431C2×C4⋊C4—112no—
432C2×C4⋊C4—221no—
433C2×C4⋊C4—221no—
434C2×C4⋊C4—222no—
435C2×C4⋊C4—222no—
436C2×C4⋊C4—221no—
437C2×C22⋊C4—222no—
438C2×C42—111no—
439C2×C42—111no—
440C2×C42—111no—
441C2×C42—111no—
442C2×C42—111no—
443C2×C42—111no—
444C2×C42—111no—
445C2×C42—111no—
446C2×C42—111no—
447C2×C42—111no—
448C2×C42—111no—
449C2×C42—222no—
450C2×C42C22×D1111yescharacteristic
451C4⋊C8—21no—
452C4⋊C8—112no—
453C4⋊C8—112no—
454C4⋊C8—222no—
455C4⋊C8—222no—
456C4⋊C8—222no—
457C4⋊C8—221no—
458C4⋊C8C22×D1112yes—
459C4⋊C8C22×D1112yes—
460C22⋊C8—21no—
461C22⋊C8—222no—
462C22⋊C8—221no—
463#97—21no—
464#97—221no—
465C4×C8—222no—
466C2×C11—41no—
467C2×C11C2×#41311yescharacteristic
468C2×C11C2×#41911yescharacteristic
469C2×C11C2×#41711yescharacteristic
470D11—22no—
471D11—22no—
472C24—111no—
473C2×Q8—21no—
474C2×Q8—112no—
475C2×Q8—222no—
476C2×Q8—222no—
477C2×Q8—221no—
478C2×Q8—442no—
479C2×Q8—442no—
480C2×Q8—444no—
481C2×Q8C2×C4×D1112yes—
482C22×C4—111no—
483C22×C4—111no—
484C22×C4—111no—
485C22×C4—111no—
486C22×C4—111no—
487C22×C4—111no—
488C22×C4—111no—
489C22×C4—111no—
490C22×C4—111no—
491C22×C4—111no—
492C22×C4—111no—
493C22×C4—111no—
494C22×C4—111no—
495C22×C4—111no—
496C22×C4—111no—
497C22×C4—222no—
498C22×C4—224no—
499C22×C4—222no—
500C22×C4—222no—
501C22×C4—222no—
502C22×C4—442no—
503C22×C4C2×C4×D1111yescharacteristic
504C22×C4D4×D1111yescharacteristic
505C22×C4D4×D1111yescharacteristic
506M16—42no—
507M16—444no—
508M16—444no—
509M16—442no—
510C2×C8—22no—
511C2×C8—22no—
512C2×C8—222no—
513C2×C8—222no—
514C2×C8—444no—
515C4⋊C4—22no—
516C4⋊C4—22no—
517C4⋊C4—21no—
518C4⋊C4—21no—
519C4⋊C4—21no—
520C4⋊C4—112no—
521C4⋊C4—222no—
522C4⋊C4—222no—
523C4⋊C4—222no—
524C4⋊C4—222no—
525C4⋊C4—222no—
526C4⋊C4—222no—
527C4⋊C4—222no—
528C4⋊C4—222no—
529C4⋊C4—222no—
530C4⋊C4—222no—
531C4⋊C4—221no—
532C4⋊C4—221no—
533C4⋊C4—221no—
534C4⋊C4C2×C4×D1112yes—
535C22⋊C4—22no—
536C22⋊C4—222no—
537C22⋊C4—222no—
538C22⋊C4—222no—
539C42—22no—
540C42—111no—
541C42—111no—
542C42—111no—
543C42—111no—
544C42—111no—
545C42—111no—
546C42—111no—
547C42—111no—
548C42—111no—
549C42—111no—
550C42—111no—
551C42—111no—
552C42—222no—
553C42—222no—
554C42—222no—
555C42C2×C4×D1111yescharacteristic
556C42D4×D1111yescharacteristic
557C42D4×D1111yescharacteristic
558C42C23×D1111yescharacteristic
559C11#1774911yescharacteristic, complemented, Sylow
560C23—111no—
561C23—111no—
562C23—222no—
563C23—222no—
564C23—441no—
565C23C22⋊C4×D1111yescharacteristic
566Q8—42no—
567Q8—41no—
568Q8—41no—
569Q8—442no—
570Q8—444no—
571Q8—444no—
572Q8—441no—
573Q8—441no—
574C2×C4—21no—
575C2×C4—22no—
576C2×C4—21no—
577C2×C4—22no—
578C2×C4—22no—
579C2×C4—41no—
580C2×C4—111no—
581C2×C4—111no—
582C2×C4—111no—
583C2×C4—112no—
584C2×C4—114no—
585C2×C4—112no—
586C2×C4—111no—
587C2×C4—111no—
588C2×C4—111no—
589C2×C4—222no—
590C2×C4—222no—
591C2×C4—222no—
592C2×C4—222no—
593C2×C4—222no—
594C2×C4—222no—
595C2×C4—222no—
596C2×C4—222no—
597C2×C4—222no—
598C2×C4—221no—
599C2×C4—222no—
600C2×C4—221no—
601C2×C4—222no—
602C2×C4—222no—
603C2×C4—441no—
604C2×C4—441no—
605C2×C4—444no—
606C2×C4—444no—
607C2×C4C22⋊C4×D1111yescharacteristic
608C2×C4C22⋊C4×D1111yescharacteristic
609C2×C4C22⋊C4×D1111yescharacteristic
610C2×C4C22×C4×D1111yescharacteristic
611C2×C4C2×D4×D1111yescharacteristic
612C2×C4C2×D4×D1111yescharacteristic
613C8—42no—
614C8—42no—
615C8—442no—
616C8—442no—
617C22—21no—
618C22—21no—
619C22—21no—
620C22—112no—
621C22—112no—
622C22—221no—
623C22—221no—
624C22—221no—
625C22—221no—
626C22—444no—
627C22C2×C22⋊C4×D1111yescharacteristic
628C4—21no—
629C4—21no—
630C4—21no—
631C4—21no—
632C4—42no—
633C4—42no—
634C4—112no—
635C4—112no—
636C4—112no—
637C4—221no—
638C4—221no—
639C4—221no—
640C4—442no—
641C4—442no—
642C4D11×AGL(1,ℤ/8)11yescharacteristic
643C4D11×#13712yes—
644C4D11×#13711yescharacteristic
645C2—41no—
646C2—222no—
647C2—222no—
648C2D11×#41311yescharacteristic
649C2D11×#41911yescharacteristic
650C2D11×#41711yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×#1559C2
socleC22×C11C22×C22⋊C4
prime radicalC23×D11C22⋊C4
cosocleC42×C11C24
hypercenter#1559D11
hypocenterC11#17749
LCSG ▷ C2×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1559

Complements

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

NH ≅ G/Ntype
4. #13067347C2semidirect
5. #13067346C2semidirect
6. #13067344C2semidirect
7. #13067305C2semidirect
8. #13067303C2semidirect
9. #13067295C2semidirect
10. #13067286C2semidirect
11. C11×#1559C2semidirect
47. C11×#333C22semidirect
48. C11×#332C22semidirect
49. #10622185C22semidirect
50. #10622184C22semidirect
51. #10622124C22semidirect
52. #10622120C22semidirect
53. #10622119C22semidirect
54. #10622119C22semidirect
241. #1559D11semidirect
341. #333C2×D11semidirect
345. #332C2×D11semidirect
559. C11#17749semidirect

Maximal subgroups

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

subgroupindex
D11×#5332
#130772462
D11×#4232
#130673472
#130673462
#130673442
#130673052
#130673032
#130672952
#130672862
C11×#15592
#1774911