Finite Group Databasebeta

← D11×#1485 #14720293

Subgroups — D11×#1485 #14720293

Order 2816.

1074 conjugacy classes of subgroups.

The subgroup lattice has 624 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D11×#533C211yesmaximal, characteristic
2D11×#431C211yesmaximal, characteristic
3C4×M16×D11C211yesmaximal, characteristic
4#13067038C211yesmaximal, characteristic, complemented
5#13067037C211yesmaximal, characteristic, complemented
6#13067036C211yesmaximal, characteristic, complemented
7#13067035C214yesmaximal, complemented
8D11×Q8⋊C8C214yesmaximal, complemented
9C11×#1485C211yesmaximal, characteristic, complemented
10C11×#533C2211yescharacteristic
11C2×M16×D11—21no—
12#10623259C411yescharacteristic
13#10623259C411yescharacteristic
14D11×C4⋊Q8C411yescharacteristic
15D11×C4⋊Q8C411yescharacteristic
16#10623219—21no—
17D11×#125—21no—
18D11×C22⋊Q8—21no—
19D11×C22⋊Q8C412yes—
20#10623153—21no—
21#10623153C412yes—
22#10623109—21no—
23#10623109C2212yes—
24C4×Q8×D11—21no—
25C4×Q8×D11C2212yes—
26D11×#117—21no—
27#10623048—21no—
28C2×C42×D11C2211yescharacteristic
29#10623001C2211yescharacteristic
30C11×#431C2211yescharacteristic
31C4×C11×M16C2211yescharacteristic
32M16×Dic11—21no—
33#10622538C2211yescharacteristic
34C4×#4318C2211yescharacteristic
35#10622446C2212yes—
36D11×C4⋊C8C2212yes—
37D11×C22⋊C8—21no—
38#10622331—21no—
39#10622320—21no—
40D11×#97—21no—
41C4×#4313C2212yes—
42#10622298—21no—
43C4×C8×D11—21no—
44C4×C8×D11C2212yes—
45C11×Q8⋊C8C2214yescomplemented
46Q8⋊(C11⋊C8)C2214yescomplemented
47#10622122C2214yescomplemented
48#10622094C2214yescomplemented
49C2×Q8×D11—21no—
50C2×Q8×D11C2×C412yes—
51C22×C4×D11C2×C411yescharacteristic
52C22×C4×D11D411yescharacteristic
53C22×C4×D11D411yescharacteristic
54C2×C11×M16—21no—
55C11×C4⋊Q8C2×C411yescharacteristic
56C11×C4⋊Q8C2×C411yescharacteristic
57C11×#125—21no—
58C11×C22⋊Q8—21no—
59C11×C22⋊Q8C2×C412yes—
60C4×Q8×C11—21no—
61C4×Q8×C11C2312yes—
62C11×#117—21no—
63C2×C42×C11C2311yescharacteristic
64#66999—21no—
65#66999C2×C412yes—
66Q8×Dic11—21no—
67Q8×Dic11C2×C412yes—
68#66997—21no—
69#66997C2×C412yes—
70#66979—21no—
71#66977—21no—
72#66977C2×C412yes—
73C2×C4×Dic11C2×C411yescharacteristic
74C2×C4×Dic11D411yescharacteristic
75C2×C4×Dic11D411yescharacteristic
76C2×#4318—21no—
77M16×D11—28no—
78C2×#4313—22no—
79C2×C8×D11—22no—
80C2×C8×D11—22no—
81#66950—21no—
82#66950C2×C412yes—
83#66949—22no—
84#66949—22no—
85#66945—21no—
86#66945—21no—
87C4⋊C4×D11—21no—
88C4⋊C4×D11—21no—
89C4⋊C4×D11—21no—
90C4⋊C4×D11—22no—
91C4⋊C4×D11—22no—
92C4⋊C4×D11C2×C412yes—
93#66943—21no—
94#66943—21no—
95#66942—22no—
96#66942—22no—
97#66941—21no—
98#66941—21no—
99#66941—21no—
100#66941C2×C412yes—
101#66940—21no—
102#66940—22no—
103#66940—22no—
104#66940C2×C412yes—
105C22⋊C4×D11—22no—
106#66931—22no—
107#66931—22no—
108#66930—22no—
109#66925—22no—
110C42×D11—22no—
111C42×D11C2×C411yescharacteristic
112C42×D11C2×C411yescharacteristic
113C42×D11D411yescharacteristic
114C42×D11D411yescharacteristic
115C42×D11D411yescharacteristic
116C42×D11D411yescharacteristic
117C42×D11C2311yescharacteristic
118C42×D11C2311yescharacteristic
119#66923—21no—
120#66922C2×C411yescharacteristic
121#66922C2×C411yescharacteristic
122C4×Dic22—21no—
123C4×Dic22—22no—
124C4×Dic22—22no—
125C4×Dic22C2312yes—
126C11×C4⋊C8C2312yes—
127C11×C22⋊C8—21no—
128C11×#97—21no—
129C4×C8×C11—21no—
130C4×C8×C11C2312yes—
131C22⋊(C11⋊C8)—21no—
132(C2×D11)⋊C8—22no—
133#66879—22no—
134Dic11⋊C8—22no—
135C8×Dic11—22no—
136C8×Dic11—22no—
137C4⋊(C11⋊C8)C2312yes—
138#66867—21no—
139C4×C11⋊C8—21no—
140C4×C11⋊C8C2312yes—
141C2×#1485—111nomaximal, Sylow
142C23×D11C22⋊C411yescharacteristic
143C2×Q8×C11—21no—
144C2×Q8×C11C22×C412yes—
145C22×C4×C11C22×C411yescharacteristic
146C22×C4×C11C2×D411yescharacteristic
147C22×C4×C11C2×D411yescharacteristic
148C22×Dic11C22⋊C411yescharacteristic
149C22×Dic11C22⋊C411yescharacteristic
150C22×Dic11C22⋊C411yescharacteristic
151Q8×D11—28no—
152Q8×D11—44no—
153C2×C4×D11—24no—
154C2×C4×D11—24no—
155C2×C4×D11—24no—
156C2×C4×D11—22no—
157C2×C4×D11—22no—
158C2×C4×D11C22⋊C411yescharacteristic
159C2×C4×D11C22⋊C411yescharacteristic
160C2×C4×D11C22⋊C411yescharacteristic
161C2×C4×D11C22⋊C411yescharacteristic
162C2×C4×D11C22⋊C411yescharacteristic
163C2×C4×D11C22⋊C411yescharacteristic
164C2×C4×D11C22×C411yescharacteristic
165C2×C4×D11C22×C411yescharacteristic
166C2×C4×D11C2×D411yescharacteristic
167C2×C4×D11C2×D411yescharacteristic
168C2×C4×D11C2×D411yescharacteristic
169C2×C4×D11C2×D411yescharacteristic
170C2×Dic22—22no—
171C2×Dic22—22no—
172C2×Dic22—21no—
173C2×Dic22C22×C412yes—
174C11×M16—24no—
175C2×C8×C11—22no—
176C2×C8×C11—22no—
177C11×C4⋊C4—21no—
178C11×C4⋊C4—22no—
179C11×C4⋊C4—21no—
180C11×C4⋊C4—21no—
181C11×C4⋊C4—22no—
182C11×C4⋊C4C22×C412yes—
183C11×C22⋊C4—22no—
184C42×C11—22no—
185C42×C11C22×C411yescharacteristic
186C42×C11C2×D411yescharacteristic
187C42×C11C2×D411yescharacteristic
188C42×C11C2411yescharacteristic
189C22⋊Dic11—22no—
190(C2×D11)⋊C4—22no—
191(C2×D11)⋊C4—22no—
192C4⋊Dic11—22no—
193C4⋊Dic11—22no—
194C4⋊Dic11—21no—
195C4⋊Dic11—21no—
196C4⋊Dic11—21no—
197C4⋊Dic11C22×C412yes—
198Dic11⋊C4—22no—
199Dic11⋊C4—22no—
200Dic11⋊C4—22no—
201Dic11⋊C4—22no—
202Dic11⋊C4—22no—
203Dic11⋊C4—22no—
204Dic11⋊C4—22no—
205Dic11⋊C4—22no—
206C4×Dic11—22no—
207C4×Dic11—22no—
208C4×Dic11—22no—
209C4×Dic11C22⋊C411yescharacteristic
210C4×Dic11C22⋊C411yescharacteristic
211C4×Dic11C22⋊C411yescharacteristic
212C4×Dic11C22⋊C411yescharacteristic
213C4×Dic11C22⋊C411yescharacteristic
214C4×Dic11C22⋊C411yescharacteristic
215C4×Dic11C22×C411yescharacteristic
216C4×Dic11C22×C411yescharacteristic
217C4×Dic11C2×D411yescharacteristic
218C4×Dic11C2×D411yescharacteristic
219C4×Dic11C2×D411yescharacteristic
220C4×Dic11C2×D411yescharacteristic
221#4318—24no—
222C2×C11⋊C8—22no—
223C2×C11⋊C8—22no—
224#4313—28no—
225C8×D11—28no—
226C8×D11—44no—
227C2×#533—111no—
228C2×#431—111no—
229C2×C4×M16—111no—
230#1485—111no—
231#1485—111no—
232#1485—114no—
233#1485—111no—
234#1485D1111yescharacteristic, direct product factor
235C2×Q8⋊C8—114no—
236C23×C11C2×C22⋊C411yescharacteristic
237C22×D11—22no—
238C22×D11—22no—
239C22×D11—22no—
240C22×D11C2×C22⋊C411yescharacteristic
241C22×D11C2×C22⋊C411yescharacteristic
242Q8×C11—24no—
243Q8×C11—42no—
244C2×C4×C11—22no—
245C2×C4×C11—22no—
246C2×C4×C11—22no—
247C2×C4×C11—22no—
248C2×C4×C11—22no—
249C2×C4×C11C2×C22⋊C411yescharacteristic
250C2×C4×C11C2×C22⋊C411yescharacteristic
251C2×C4×C11C2×C22⋊C411yescharacteristic
252C2×C4×C11C23×C411yescharacteristic
253C2×C4×C11C22×D411yescharacteristic
254C2×C4×C11C22×D411yescharacteristic
255C2×Dic11—22no—
256C2×Dic11—22no—
257C2×Dic11—22no—
258C2×Dic11—22no—
259C2×Dic11—22no—
260C2×Dic11C2×C22⋊C411yescharacteristic
261C2×Dic11C2×C22⋊C411yescharacteristic
262C2×Dic11C2×C22⋊C411yescharacteristic
263C2×Dic11C2×C22⋊C411yescharacteristic
264C2×Dic11C2×C22⋊C411yescharacteristic
265C2×Dic11C2×C22⋊C411yescharacteristic
266C4×D11—22no—
267C4×D11—22no—
268C4×D11—22no—
269C4×D11—22no—
270C4×D11—22no—
271C4×D11—22no—
272C4×D11—22no—
273C4×D11—22no—
274C4×D11—22no—
275C4×D11—44no—
276C4×D11—44no—
277C4×D11#10414yes—
278C4×D11#13114yes—
279C4×D11#13714yes—
280Dic22—24no—
281Dic22—42no—
282Dic22—44no—
283Dic22—44no—
284C8×C11—24no—
285C8×C11—42no—
286C11⋊C8—24no—
287C11⋊C8—42no—
288C22×M16—221no—
289#533—111no—
290#533—111no—
291#533—112no—
292#533—112no—
293#533—111no—
294#533—221no—
295#533—221no—
296#533—221no—
297#533—221no—
298#533C2×D1111yescharacteristic
299C2×C4⋊Q8—111no—
300C2×C4⋊Q8—111no—
301C2×#125—221no—
302C2×C22⋊Q8—112no—
303C2×C22⋊Q8—221no—
304C2×C4×Q8—112no—
305C2×C4×Q8—221no—
306C2×#117—221no—
307C22×C42—111no—
308#431—111no—
309#431—112no—
310#431—221no—
311#431—221no—
312#431C2×D1111yescharacteristic
313C2×C4⋊C8—112no—
314C2×C22⋊C8—221no—
315C4×M16—111no—
316C4×M16—112no—
317C4×M16—221no—
318C4×M16—221no—
319C4×M16C2×D1111yescharacteristic
320C2×#97—221no—
321C2×C4×C8—112no—
322C2×C4×C8—221no—
323Q8⋊C8—114no—
324Q8⋊C8—114no—
325Q8⋊C8—114no—
326Q8⋊C8C2×D1114yescomplemented
327C22×C11—21no—
328C22×C11—21no—
329C22×C11—21no—
330C22×C11C22×C22⋊C411yescharacteristic
331C2×D11—21no—
332C2×D11—21no—
333C2×D11—21no—
334C2×D11—44no—
335C2×D11#40812yes—
336C2×D11#41912yes—
337C2×D11C2×#10412yes—
338C4×C11—21no—
339C4×C11—21no—
340C4×C11—21no—
341C4×C11—42no—
342C4×C11—42no—
343C4×C11C2×#10412yes—
344C4×C11C2×#13112yes—
345C4×C11C2×#13712yes—
346Dic11—21no—
347Dic11—21no—
348Dic11—21no—
349Dic11—42no—
350Dic11—42no—
351Dic11#40812yes—
352Dic11#41912yes—
353Dic11C2×#10412yes—
354C22×Q8—112no—
355C22×Q8—221no—
356C23×C4—111no—
357C23×C4—111no—
358C23×C4—111no—
359C2×M16—21no—
360C2×M16—222no—
361C2×M16—228no—
362C2×M16—221no—
363C22×C8—222no—
364C22×C8—222no—
365C4⋊Q8—112no—
366C4⋊Q8—112no—
367C4⋊Q8—111no—
368C4⋊Q8—111no—
369C4⋊Q8—221no—
370C4⋊Q8—221no—
371C4⋊Q8—221no—
372C4⋊Q8—221no—
373C4⋊Q8C4×D1111yescharacteristic
374C4⋊Q8C4×D1111yescharacteristic
375#125—21no—
376#125—222no—
377#125—222no—
378#125—221no—
379#125—221no—
380#125—221no—
381C22⋊Q8—21no—
382C22⋊Q8—112no—
383C22⋊Q8—112no—
384C22⋊Q8—112no—
385C22⋊Q8—222no—
386C22⋊Q8—222no—
387C22⋊Q8—222no—
388C22⋊Q8—222no—
389C22⋊Q8—221no—
390C22⋊Q8—221no—
391C22⋊Q8—221no—
392C22⋊Q8C4×D1112yes—
393C4×Q8—21no—
394C4×Q8—112no—
395C4×Q8—112no—
396C4×Q8—112no—
397C4×Q8—222no—
398C4×Q8—222no—
399C4×Q8—222no—
400C4×Q8—221no—
401C4×Q8—222no—
402C4×Q8—221no—
403C4×Q8—221no—
404C4×Q8C22×D1112yes—
405#117—21no—
406#117—222no—
407#117—222no—
408#117—221no—
409#117—221no—
410#117—221no—
411C2×C4⋊C4—112no—
412C2×C4⋊C4—221no—
413C2×C4⋊C4—221no—
414C2×C4⋊C4—222no—
415C2×C4⋊C4—222no—
416C2×C4⋊C4—221no—
417C2×C22⋊C4—222no—
418C2×C42—111no—
419C2×C42—111no—
420C2×C42—111no—
421C2×C42—111no—
422C2×C42—111no—
423C2×C42—111no—
424C2×C42—111no—
425C2×C42—111no—
426C2×C42—111no—
427C2×C42—111no—
428C2×C42—111no—
429C2×C42—222no—
430C2×C42C22×D1111yescharacteristic
431C4⋊C8—112no—
432C4⋊C8—222no—
433C4⋊C8C22×D1112yes—
434C22⋊C8—21no—
435C22⋊C8—222no—
436C22⋊C8—221no—
437#97—21no—
438#97—222no—
439#97—221no—
440C4×C8—21no—
441C4×C8—112no—
442C4×C8—222no—
443C4×C8—222no—
444C4×C8—221no—
445C4×C8C22×D1112yes—
446C2×C11—41no—
447C2×C11C2×#40811yescharacteristic
448C2×C11C2×#41911yescharacteristic
449C2×C11C22×#10411yescharacteristic
450D11—41no—
451D11#148514yesdirect product factor
452C24—111no—
453C2×Q8—21no—
454C2×Q8—112no—
455C2×Q8—222no—
456C2×Q8—222no—
457C2×Q8—228no—
458C2×Q8—221no—
459C2×Q8—444no—
460C2×Q8C2×C4×D1112yes—
461C22×C4—111no—
462C22×C4—111no—
463C22×C4—111no—
464C22×C4—111no—
465C22×C4—111no—
466C22×C4—111no—
467C22×C4—111no—
468C22×C4—111no—
469C22×C4—111no—
470C22×C4—111no—
471C22×C4—111no—
472C22×C4—111no—
473C22×C4—111no—
474C22×C4—111no—
475C22×C4—111no—
476C22×C4—224no—
477C22×C4—224no—
478C22×C4—224no—
479C22×C4—222no—
480C22×C4—222no—
481C22×C4C2×C4×D1111yescharacteristic
482C22×C4D4×D1111yescharacteristic
483C22×C4D4×D1111yescharacteristic
484M16—24no—
485M16—228no—
486M16—224no—
487C2×C8—22no—
488C2×C8—22no—
489C2×C8—228no—
490C2×C8—222no—
491C2×C8—222no—
492C2×C8—444no—
493C4⋊C4—21no—
494C4⋊C4—21no—
495C4⋊C4—21no—
496C4⋊C4—22no—
497C4⋊C4—22no—
498C4⋊C4—112no—
499C4⋊C4—222no—
500C4⋊C4—222no—
501C4⋊C4—222no—
502C4⋊C4—222no—
503C4⋊C4—222no—
504C4⋊C4—222no—
505C4⋊C4—222no—
506C4⋊C4—222no—
507C4⋊C4—221no—
508C4⋊C4—221no—
509C4⋊C4—222no—
510C4⋊C4—221no—
511C4⋊C4—222no—
512C4⋊C4C2×C4×D1112yes—
513C22⋊C4—22no—
514C22⋊C4—222no—
515C22⋊C4—222no—
516C22⋊C4—222no—
517C42—22no—
518C42—111no—
519C42—111no—
520C42—111no—
521C42—111no—
522C42—111no—
523C42—111no—
524C42—111no—
525C42—111no—
526C42—111no—
527C42—111no—
528C42—111no—
529C42—111no—
530C42—222no—
531C42—222no—
532C42—222no—
533C42C2×C4×D1111yescharacteristic
534C42D4×D1111yescharacteristic
535C42D4×D1111yescharacteristic
536C42C23×D1111yescharacteristic
537C11C2×#148511yescharacteristic, complemented, Sylow
538C23—111no—
539C23—111no—
540C23—222no—
541C23—222no—
542C23—222no—
543C23C22⋊C4×D1111yescharacteristic
544Q8—24no—
545Q8—42no—
546Q8—224no—
547Q8—444no—
548Q8—444no—
549Q8—442no—
550C2×C4—22no—
551C2×C4—22no—
552C2×C4—22no—
553C2×C4—22no—
554C2×C4—22no—
555C2×C4—111no—
556C2×C4—111no—
557C2×C4—111no—
558C2×C4—114no—
559C2×C4—114no—
560C2×C4—114no—
561C2×C4—111no—
562C2×C4—111no—
563C2×C4—111no—
564C2×C4—222no—
565C2×C4—222no—
566C2×C4—222no—
567C2×C4—222no—
568C2×C4—222no—
569C2×C4—222no—
570C2×C4—222no—
571C2×C4—222no—
572C2×C4—222no—
573C2×C4—222no—
574C2×C4—222no—
575C2×C4—222no—
576C2×C4—222no—
577C2×C4—222no—
578C2×C4—444no—
579C2×C4—444no—
580C2×C4C22⋊C4×D1111yescharacteristic
581C2×C4C22⋊C4×D1111yescharacteristic
582C2×C4C22⋊C4×D1111yescharacteristic
583C2×C4C22×C4×D1111yescharacteristic
584C2×C4C2×D4×D1111yescharacteristic
585C2×C4C2×D4×D1111yescharacteristic
586C8—24no—
587C8—42no—
588C8—224no—
589C8—442no—
590C22—21no—
591C22—21no—
592C22—21no—
593C22—112no—
594C22—112no—
595C22—112no—
596C22—221no—
597C22—221no—
598C22—221no—
599C22—444no—
600C22C2×C22⋊C4×D1111yescharacteristic
601C4—21no—
602C4—21no—
603C4—21no—
604C4—42no—
605C4—42no—
606C4—112no—
607C4—112no—
608C4—112no—
609C4—221no—
610C4—221no—
611C4—221no—
612C4—442no—
613C4—442no—
614C4D11×#10412yes—
615C4D11×#13112yes—
616C4D11×#13712yes—
617C2—41no—
618C2—114no—
619C2—441no—
620C2D11×#40811yescharacteristic
621C2D11×#41911yescharacteristic
622C2C2×D11×#10411yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×#1485C2
socleC22×C11C22×C22⋊C4
prime radicalC23×D11C22⋊C4
cosocleC42×C11C24
hypercenter#1485D11
hypocenterC11C2×#1485
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1485

Complements

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

NH ≅ G/Ntype
4. #13067038C2semidirect
5. #13067037C2semidirect
6. #13067036C2semidirect
7. #13067035C2semidirect
8. D11×Q8⋊C8C2semidirect
9. C11×#1485C2semidirect
45. C11×Q8⋊C8C22semidirect
46. Q8⋊(C11⋊C8)C22semidirect
47. #10622122C22semidirect
48. #10622094C22semidirect
234. #1485D11direct (N × H)
326. Q8⋊C8C2×D11semidirect
451. D11#1485direct (N × H)
537. C11C2×#1485semidirect

Maximal subgroups

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

subgroupindex
D11×#5332
D11×#4312
C4×M16×D112
#130670382
#130670372
#130670362
#130670352
D11×Q8⋊C82
C11×#14852
C2×#148511