Finite Group Databasebeta

← #14758257

Subgroups — #14758257

Order 2816.

1154 conjugacy classes of subgroups.

The subgroup lattice has 670 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D11×#533C211yesmaximal, characteristic
2C4×M16×D11C211yesmaximal, characteristic
3#13071020C211yesmaximal, characteristic
4#13069561C211yesmaximal, characteristic, complemented
5#13069560C211yesmaximal, characteristic, complemented
6#13069559C211yesmaximal, characteristic, complemented
7#13069558C214yesmaximal, complemented
8#13068324C214yesmaximal
9C11×#1986C211yesmaximal, characteristic, complemented
10C11×#533C2211yescharacteristic
11C2×M16×D11C2212yes—
12#10623259C411yescharacteristic, complemented
13#10623259C411yescharacteristic, complemented
14D11×C4⋊Q8C411yescharacteristic, complemented
15D11×C4⋊Q8C411yescharacteristic, complemented
16#10623219C412yescomplemented
17D11×#125C412yescomplemented
18D11×C22⋊Q8—21no—
19D11×C22⋊Q8—21no—
20#10623153—21no—
21#10623153—21no—
22#10623109—21no—
23#10623109—21no—
24C4×Q8×D11—21no—
25C4×Q8×D11—21no—
26D11×#117C2212yes—
27#10623048C2212yes—
28C2×#66925C2212yes—
29C2×C42×D11C2211yescharacteristic
30#10623001C2211yescharacteristic
31C4×C11×M16C2211yescharacteristic
32C4×C11×C4⋊C4C2211yescharacteristic
33M16×Dic11C2212yes—
34#10622600—21no—
35#10622589—21no—
36C4×C4⋊Dic11C2211yescharacteristic
37C4×Dic11⋊C4C2212yes—
38C4×#4318C2211yescharacteristic
39#10622320—21no—
40D11×#97—21no—
41C4×#4313—21no—
42C4×C8×D11—21no—
43#10622280—21no—
44#10622263—21no—
45C11×#339C2214yes—
46#10622193C2214yes—
47#10622170C2214yes—
48#10622161C2214yes—
49C2×Q8×D11—21no—
50C2×Q8×D11—21no—
51C22×C4×D11D411yescharacteristic
52C22×C4×D11D411yescharacteristic
53C22×C4×D11C2311yescharacteristic
54C2×C11×M16C2312yes—
55C11×C4⋊Q8C2×C411yescharacteristic
56C11×C4⋊Q8C2×C411yescharacteristic
57C11×#125C2×C412yes—
58C11×C22⋊Q8—21no—
59C11×C22⋊Q8—21no—
60C4×Q8×C11—21no—
61C4×Q8×C11—21no—
62C11×#117C2312yes—
63C2×C11×C4⋊C4—21no—
64C2×C42×C11C2312yes—
65C2×C42×C11C2311yescharacteristic
66#66999—21no—
67#66999—21no—
68Q8×Dic11—21no—
69Q8×Dic11—21no—
70#66997—21no—
71#66997—21no—
72C2×(C2×D11)⋊C4—22no—
73#66979C2312yes—
74C2×C4⋊Dic11—21no—
75#66977—21no—
76#66977—21no—
77C2×Dic11⋊C4—22no—
78C2×Dic11⋊C4—22no—
79C2×C4×Dic11D411yescharacteristic
80C2×C4×Dic11D411yescharacteristic
81C2×C4×Dic11C2312yes—
82C2×C4×Dic11C2311yescharacteristic
83C2×#4318C2312yes—
84M16×D11—24no—
85M16×D11Q818yescomplemented
86C2×#4313—22no—
87C2×C8×D11—22no—
88#66950—21no—
89#66950—21no—
90#66949—22no—
91#66949—22no—
92#66945C2×C412yes—
93#66945C2×C412yes—
94C4⋊C4×D11—21no—
95C4⋊C4×D11—21no—
96C4⋊C4×D11—22no—
97C4⋊C4×D11—22no—
98C4⋊C4×D11C2×C412yes—
99C4⋊C4×D11C2×C412yes—
100#66943C2×C412yes—
101#66943C2×C412yes—
102#66942—22no—
103#66942—22no—
104#66941—21no—
105#66941—21no—
106#66941C2×C412yes—
107#66941C2×C412yes—
108#66940—21no—
109#66940—21no—
110#66940—22no—
111#66940—22no—
112C22⋊C4×D11—22no—
113#66931—22no—
114#66931—22no—
115#66930—22no—
116#66925—22no—
117#66925—28no—
118C42×D11—22no—
119C42×D11C2×C411yescharacteristic
120C42×D11C2×C411yescharacteristic
121C42×D11C2×C411yescharacteristic
122C42×D11C2×C411yescharacteristic
123C42×D11D411yescharacteristic
124C42×D11D411yescharacteristic
125C42×D11D411yescharacteristic
126C42×D11D411yescharacteristic
127#66923C2×C412yes—
128#66922C2×C411yescharacteristic
129#66922C2×C411yescharacteristic
130C4×Dic22—21no—
131C4×Dic22—21no—
132C4×Dic22—22no—
133C4×Dic22—22no—
134C11×#97—21no—
135C4×C8×C11—21no—
136C11×#95—21no—
137C11⋊#95—21no—
138C11⋊#95—22no—
139#66879—22no—
140C8×Dic11—22no—
141#66867—21no—
142C4×C11⋊C8—21no—
143#21306—111nomaximal, Sylow
144C23×D11C2×D411yescharacteristic
145C2×Q8×C11—21no—
146C2×Q8×C11—21no—
147C22×C4×C11—22no—
148C22×C4×C11C2×D411yescharacteristic
149C22×C4×C11C2×D411yescharacteristic
150C22×C4×C11C2411yescharacteristic
151C22×Dic11—22no—
152C22×Dic11C2×D411yescharacteristic
153C22×Dic11C2×D411yescharacteristic
154C22×Dic11C2×D411yescharacteristic
155Q8×D11—44no—
156Q8×D11—44no—
157C2×C4×D11—22no—
158C2×C4×D11—22no—
159C2×C4×D11—42no—
160C2×C4×D11—42no—
161C2×C4×D11C22⋊C411yescharacteristic
162C2×C4×D11C22⋊C411yescharacteristic
163C2×C4×D11C22⋊C411yescharacteristic
164C2×C4×D11C22⋊C411yescharacteristic
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×D11C2×D411yescharacteristic
172C2×C4×D11C2×D411yescharacteristic
173C2×C4×D11C2×Q814yes—
174C2×C4×D11#4114yes—
175C2×Dic22—22no—
176C2×Dic22—22no—
177C2×Dic22—21no—
178C2×Dic22—21no—
179C11×M16—22no—
180C11×M16C2×Q814yescomplemented
181C2×C8×C11—22no—
182C11×C4⋊C4—21no—
183C11×C4⋊C4—21no—
184C11×C4⋊C4—22no—
185C11×C4⋊C4—22no—
186C11×C4⋊C4—42no—
187C11×C4⋊C4C22×C412yes—
188C11×C4⋊C4C22×C412yes—
189C11×C22⋊C4—22no—
190C42×C11—22no—
191C42×C11—24no—
192C42×C11C22×C411yescharacteristic
193C42×C11C22×C411yescharacteristic
194C42×C11C2×D411yescharacteristic
195C42×C11C2×D411yescharacteristic
196C22⋊Dic11—22no—
197(C2×D11)⋊C4—22no—
198(C2×D11)⋊C4—22no—
199(C2×D11)⋊C4—44no—
200C4⋊Dic11—22no—
201C4⋊Dic11—22no—
202C4⋊Dic11—21no—
203C4⋊Dic11—21no—
204C4⋊Dic11—42no—
205C4⋊Dic11C22×C412yes—
206C4⋊Dic11C22×C412yes—
207Dic11⋊C4—22no—
208Dic11⋊C4—22no—
209Dic11⋊C4—22no—
210Dic11⋊C4—22no—
211Dic11⋊C4—22no—
212Dic11⋊C4—22no—
213Dic11⋊C4—22no—
214Dic11⋊C4—22no—
215Dic11⋊C4—44no—
216Dic11⋊C4—44no—
217C4×Dic11—22no—
218C4×Dic11—22no—
219C4×Dic11—22no—
220C4×Dic11—24no—
221C4×Dic11C22⋊C411yescharacteristic
222C4×Dic11C22⋊C411yescharacteristic
223C4×Dic11C22⋊C411yescharacteristic
224C4×Dic11C22⋊C411yescharacteristic
225C4×Dic11C22⋊C411yescharacteristic
226C4×Dic11C22⋊C411yescharacteristic
227C4×Dic11C22⋊C411yescharacteristic
228C4×Dic11C22⋊C411yescharacteristic
229C4×Dic11C22×C411yescharacteristic
230C4×Dic11C22×C411yescharacteristic
231C4×Dic11C2×D411yescharacteristic
232C4×Dic11C2×D411yescharacteristic
233#4318—22no—
234#4318C2×Q814yescomplemented
235C2×C11⋊C8—22no—
236#4313—28no—
237C8×D11—28no—
238C2×#533—111no—
239C2×C4×M16—111no—
240#2285—111no—
241#1986—111no—
242#1986—111no—
243#1986—114no—
244#1986—111no—
245#1986D1111yescharacteristic, complemented
246#1733—114no—
247C23×C11C22×D411yescharacteristic
248C22×D11—41no—
249C22×D11—41no—
250C22×D11C2×C22⋊C411yescharacteristic
251C22×D11C2×C22⋊C411yescharacteristic
252C22×D11#12412yes—
253C22×D11C4⋊Q812yes—
254Q8×C11—42no—
255Q8×C11—42no—
256C2×C4×C11—22no—
257C2×C4×C11—22no—
258C2×C4×C11—22no—
259C2×C4×C11—41no—
260C2×C4×C11—42no—
261C2×C4×C11—42no—
262C2×C4×C11—42no—
263C2×C4×C11C2×C22⋊C411yescharacteristic
264C2×C4×C11C2×C22⋊C411yescharacteristic
265C2×C4×C11C2×C22⋊C411yescharacteristic
266C2×C4×C11C2×C22⋊C411yescharacteristic
267C2×C4×C11C23×C411yescharacteristic
268C2×C4×C11C22×D411yescharacteristic
269C2×C4×C11C22×Q812yes—
270C2×C4×C11C2×#4112yes—
271C2×Dic11—22no—
272C2×Dic11—22no—
273C2×Dic11—22no—
274C2×Dic11—41no—
275C2×Dic11—42no—
276C2×Dic11—42no—
277C2×Dic11—42no—
278C2×Dic11C2×C22⋊C411yescharacteristic
279C2×Dic11C2×C22⋊C411yescharacteristic
280C2×Dic11C2×C22⋊C411yescharacteristic
281C2×Dic11C2×C22⋊C411yescharacteristic
282C2×Dic11C2×C22⋊C411yescharacteristic
283C2×Dic11C2×C22⋊C411yescharacteristic
284C2×Dic11#12412yes—
285C2×Dic11C4⋊Q812yes—
286C4×D11—22no—
287C4×D11—22no—
288C4×D11—22no—
289C4×D11—22no—
290C4×D11—41no—
291C4×D11—41no—
292C4×D11—41no—
293C4×D11—41no—
294C4×D11—44no—
295C4×D11—44no—
296C4×D11C4×Q814yes—
297C4×D11C4×Q814yes—
298C4×D11C22⋊Q814yes—
299C4×D11C22⋊Q814yes—
300Dic22—44no—
301Dic22—42no—
302Dic22—42no—
303Dic22—44no—
304C8×C11—24no—
305C11⋊C8—24no—
306C22×M16—112no—
307#533—111no—
308#533—111no—
309#533—112no—
310#533—112no—
311#533—111no—
312#533—221no—
313#533—221no—
314#533—221no—
315#533—221no—
316#533C2×D1111yescharacteristic
317C2×C4⋊Q8—111no—
318C2×C4⋊Q8—111no—
319C2×#125—112no—
320C2×C22⋊Q8—221no—
321C2×C22⋊Q8—221no—
322C2×C4×Q8—221no—
323C2×C4×Q8—221no—
324C2×#117—112no—
325C2×#117—112no—
326C22×C42—111no—
327C4×M16—112no—
328C4×M16—111no—
329C4×M16—221no—
330C4×M16—221no—
331C4×M16C2×D1111yescharacteristic
332C2×#97—221no—
333C2×C4×C8—221no—
334#384—221no—
335#382—221no—
336#380—221no—
337#380—221no—
338C4×C4⋊C4—112no—
339C4×C4⋊C4—111no—
340C4×C4⋊C4C2×D1111yescharacteristic
341#339—114no—
342#339—114no—
343#339—114no—
344#339C2×D1114yes—
345C22×C11—21no—
346C22×C11—21no—
347C22×C11C22×C22⋊C411yescharacteristic
348C22×C11C2×#12411yescharacteristic
349C22×C11C2×C4⋊Q811yescharacteristic
350C2×D11—21no—
351C2×D11—21no—
352C2×D11—21no—
353C2×D11—21no—
354C2×D11—42no—
355C2×D11—42no—
356C2×D11#39112yes—
357C2×D11#39112yes—
358C4×C11—21no—
359C4×C11—21no—
360C4×C11—21no—
361C4×C11—42no—
362C4×C11—42no—
363C4×C11—82no—
364C4×C11#42112yes—
365C4×C11C2×C4×Q812yes—
366C4×C11C2×C22⋊Q812yes—
367Dic11—21no—
368Dic11—21no—
369Dic11—21no—
370Dic11—42no—
371Dic11—42no—
372Dic11—82no—
373Dic11#39112yes—
374Dic11#39112yes—
375Dic11#42112yes—
376C22×Q8—221no—
377C22×Q8—221no—
378C23×C4—111no—
379C23×C4—111no—
380C23×C4—111no—
381C2×M16—112no—
382C2×M16—118no—
383C2×M16—222no—
384C2×M16—224no—
385C2×M16C22×D1112yes—
386C22×C8—222no—
387C4⋊Q8—112no—
388C4⋊Q8—112no—
389C4⋊Q8—111no—
390C4⋊Q8—111no—
391C4⋊Q8—221no—
392C4⋊Q8—221no—
393C4⋊Q8—221no—
394C4⋊Q8—221no—
395C4⋊Q8C4×D1111yescharacteristic
396C4⋊Q8C4×D1111yescharacteristic
397#125—112no—
398#125—112no—
399#125—112no—
400#125—222no—
401#125—222no—
402#125C4×D1112yes—
403C22⋊Q8—21no—
404C22⋊Q8—21no—
405C22⋊Q8—222no—
406C22⋊Q8—222no—
407C22⋊Q8—222no—
408C22⋊Q8—222no—
409C22⋊Q8—221no—
410C22⋊Q8—221no—
411C22⋊Q8—221no—
412C22⋊Q8—221no—
413C22⋊Q8—221no—
414C22⋊Q8—221no—
415C4×Q8—21no—
416C4×Q8—21no—
417C4×Q8—222no—
418C4×Q8—222no—
419C4×Q8—222no—
420C4×Q8—222no—
421C4×Q8—221no—
422C4×Q8—221no—
423C4×Q8—221no—
424C4×Q8—221no—
425C4×Q8—221no—
426C4×Q8—221no—
427#117—112no—
428#117—112no—
429#117—112no—
430#117—222no—
431#117—228no—
432#117—222no—
433#117C22×D1112yes—
434C2×C4⋊C4—21no—
435C2×C4⋊C4—112no—
436C2×C4⋊C4—112no—
437C2×C4⋊C4—222no—
438C2×C4⋊C4—222no—
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×C22⋊C4—222no—
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—111no—
457C2×C42—112no—
458C2×C42—222no—
459C2×C42C22×D1112yes—
460C2×C42C22×D1111yescharacteristic
461#97—21no—
462#97—222no—
463#97—221no—
464C4×C8—21no—
465C4×C8—222no—
466C4×C8—221no—
467#95—21no—
468#95—222no—
469#95—221no—
470C2×C11—21no—
471C2×C11—21no—
472C2×C11C2×#39111yescharacteristic
473C2×C11C2×#42111yescharacteristic
474C2×C11C2×#42111yescharacteristic
475D11—22no—
476D11—22no—
477C24—111no—
478C2×Q8—21no—
479C2×Q8—21no—
480C2×Q8—222no—
481C2×Q8—222no—
482C2×Q8—221no—
483C2×Q8—221no—
484C2×Q8—444no—
485C2×Q8—444no—
486C22×C4—22no—
487C22×C4—111no—
488C22×C4—111no—
489C22×C4—111no—
490C22×C4—111no—
491C22×C4—111no—
492C22×C4—114no—
493C22×C4—114no—
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—222no—
505C22×C4—222no—
506C22×C4—222no—
507C22×C4—442no—
508C22×C4—442no—
509C22×C4D4×D1111yescharacteristic
510C22×C4D4×D1111yescharacteristic
511C22×C4C23×D1111yescharacteristic
512M16—22no—
513M16—114no—
514M16—228no—
515M16—222no—
516M16Q8×D1114yescomplemented
517C2×C8—22no—
518C2×C8—228no—
519C2×C8—222no—
520C4⋊C4—22no—
521C4⋊C4—22no—
522C4⋊C4—21no—
523C4⋊C4—21no—
524C4⋊C4—42no—
525C4⋊C4—112no—
526C4⋊C4—112no—
527C4⋊C4—222no—
528C4⋊C4—222no—
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—221no—
538C4⋊C4—221no—
539C4⋊C4—442no—
540C4⋊C4—444no—
541C4⋊C4—444no—
542C4⋊C4C2×C4×D1112yes—
543C4⋊C4C2×C4×D1112yes—
544C22⋊C4—22no—
545C22⋊C4—222no—
546C22⋊C4—222no—
547C22⋊C4—222no—
548C22⋊C4—444no—
549C42—22no—
550C42—24no—
551C42—111no—
552C42—111no—
553C42—111no—
554C42—111no—
555C42—111no—
556C42—111no—
557C42—111no—
558C42—111no—
559C42—111no—
560C42—111no—
561C42—111no—
562C42—111no—
563C42—222no—
564C42—222no—
565C42—222no—
566C42—224no—
567C42C2×C4×D1111yescharacteristic
568C42C2×C4×D1111yescharacteristic
569C42D4×D1111yescharacteristic
570C42D4×D1111yescharacteristic
571C11#2130611yescharacteristic, complemented, Sylow
572C23—111no—
573C23—111no—
574C23—112no—
575C23—112no—
576C23—441no—
577C23—441no—
578C23C2×D4×D1111yescharacteristic
579Q8—42no—
580Q8—42no—
581Q8—442no—
582Q8—444no—
583Q8—444no—
584Q8—442no—
585C2×C4—22no—
586C2×C4—22no—
587C2×C4—22no—
588C2×C4—41no—
589C2×C4—42no—
590C2×C4—42no—
591C2×C4—42no—
592C2×C4—112no—
593C2×C4—111no—
594C2×C4—111no—
595C2×C4—111no—
596C2×C4—112no—
597C2×C4—114no—
598C2×C4—114no—
599C2×C4—114no—
600C2×C4—114no—
601C2×C4—111no—
602C2×C4—111no—
603C2×C4—111no—
604C2×C4—222no—
605C2×C4—222no—
606C2×C4—222no—
607C2×C4—222no—
608C2×C4—222no—
609C2×C4—222no—
610C2×C4—222no—
611C2×C4—441no—
612C2×C4—441no—
613C2×C4—441no—
614C2×C4—441no—
615C2×C4—444no—
616C2×C4—444no—
617C2×C4—441no—
618C2×C4—442no—
619C2×C4—442no—
620C2×C4—442no—
621C2×C4C22⋊C4×D1111yescharacteristic
622C2×C4C22⋊C4×D1111yescharacteristic
623C2×C4C22⋊C4×D1111yescharacteristic
624C2×C4C22⋊C4×D1111yescharacteristic
625C2×C4C22×C4×D1111yescharacteristic
626C2×C4C2×D4×D1111yescharacteristic
627C2×C4C2×Q8×D1112yes—
628C2×C4#41×D1112yes—
629C8—24no—
630C8—224no—
631C22—21no—
632C22—21no—
633C22—112no—
634C22—112no—
635C22—221no—
636C22—221no—
637C22—221no—
638C22—221no—
639C22—442no—
640C22—442no—
641C22C2×C22⋊C4×D1111yescharacteristic
642C22D11×#12411yescharacteristic
643C22D11×C4⋊Q811yescharacteristic
644C4—21no—
645C4—21no—
646C4—21no—
647C4—42no—
648C4—42no—
649C4—82no—
650C4—112no—
651C4—112no—
652C4—112no—
653C4—221no—
654C4—221no—
655C4—221no—
656C4—442no—
657C4—442no—
658C4—882no—
659C4#1062243412yes—
660C4C4×Q8×D1112yes—
661C4D11×C22⋊Q812yes—
662C2—21no—
663C2—21no—
664C2—222no—
665C2—222no—
666C2D11×#39111yescharacteristic
667C2D11×#42111yescharacteristic
668C2C2×#1062243411yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1986C2
socleC22×C11C22×C22⋊C4
prime radicalC23×D11C2×D4
cosocleC22×C4×C11C24
hypercenter#1986D11
hypocenterC11#21306
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1986

Complements

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

NH ≅ G/Ntype
4. #13069561C2semidirect
5. #13069560C2semidirect
6. #13069559C2semidirect
7. #13069558C2semidirect
9. C11×#1986C2semidirect
12. #10623259C4semidirect
13. #10623259C4semidirect
14. D11×C4⋊Q8C4semidirect
15. D11×C4⋊Q8C4semidirect
16. #10623219C4semidirect
17. D11×#125C4semidirect
85. M16×D11Q8semidirect
180. C11×M16C2×Q8semidirect
234. #4318C2×Q8semidirect
245. #1986D11semidirect
516. M16Q8×D11semidirect
571. C11#21306semidirect

Maximal subgroups

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

subgroupindex
D11×#5332
C4×M16×D112
#130710202
#130695612
#130695602
#130695592
#130695582
#130683242
C11×#19862
#2130611