Finite Group Databasebeta

← D11×#1497 #14720394

Subgroups — D11×#1497 #14720394

Order 2816.

990 conjugacy classes of subgroups.

The subgroup lattice has 616 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D11×#533C211yesmaximal, characteristic
2D11×#432C211yesmaximal, characteristic
3D11×#431C211yesmaximal, characteristic
4#13067090C211yesmaximal, characteristic, complemented
5#13067089C211yesmaximal, characteristic, complemented
6#13067088C211yesmaximal, characteristic, complemented
7#13067087C214yesmaximal, complemented
8D11×Q8⋊C8C214yesmaximal, complemented
9C11×#1497C211yesmaximal, characteristic, complemented
10C11×#533C2211yescharacteristic
11#10623259C411yescharacteristic
12#10623259C411yescharacteristic
13D11×C4⋊Q8C411yescharacteristic
14D11×C4⋊Q8C411yescharacteristic
15#10623219—21no—
16D11×#125—21no—
17D11×C22⋊Q8—21no—
18D11×C22⋊Q8C412yes—
19#10623153—21no—
20#10623153C412yes—
21#10623109—21no—
22#10623109C2212yes—
23C4×Q8×D11—21no—
24C4×Q8×D11C2212yes—
25D11×#117—21no—
26#10623048—21no—
27C2×C42×D11C2211yescharacteristic
28#10623001C2211yescharacteristic
29C11×#432C2211yescharacteristic
30C11×#431C2211yescharacteristic
31#10622539C2211yescharacteristic
32#10622538C2211yescharacteristic
33#10622448C2212yes—
34#10622446—21no—
35D11×C4⋊C8—21no—
36D11×C4⋊C8C2212yes—
37D11×C22⋊C8—21no—
38D11×C22⋊C8—21no—
39#10622332—21no—
40#10622331—21no—
41#10622318—21no—
42D11×#97—21no—
43#10622298C2212yes—
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
54C11×C4⋊Q8C2×C411yescharacteristic
55C11×C4⋊Q8C2×C411yescharacteristic
56C11×#125—21no—
57C11×C22⋊Q8—21no—
58C11×C22⋊Q8C2×C412yes—
59C4×Q8×C11—21no—
60C4×Q8×C11C2312yes—
61C11×#117—21no—
62C2×C42×C11C2311yescharacteristic
63#66999—21no—
64#66999C2×C412yes—
65Q8×Dic11—21no—
66Q8×Dic11C2×C412yes—
67#66997—21no—
68#66997C2×C412yes—
69#66979—21no—
70#66977—21no—
71#66977C2×C412yes—
72C2×C4×Dic11C2×C411yescharacteristic
73C2×C4×Dic11D411yescharacteristic
74C2×C4×Dic11D411yescharacteristic
75C2×C8×D11—22no—
76C2×C8×D11—22no—
77#66950—21no—
78#66950C2×C412yes—
79#66949—22no—
80#66949—22no—
81#66945—21no—
82#66945—21no—
83C4⋊C4×D11—21no—
84C4⋊C4×D11—21no—
85C4⋊C4×D11—21no—
86C4⋊C4×D11—22no—
87C4⋊C4×D11—22no—
88C4⋊C4×D11C2×C412yes—
89#66943—21no—
90#66943—21no—
91#66942—22no—
92#66942—22no—
93#66941—21no—
94#66941—21no—
95#66941—21no—
96#66941C2×C412yes—
97#66940—21no—
98#66940—22no—
99#66940—22no—
100#66940C2×C412yes—
101C22⋊C4×D11—22no—
102#66931—22no—
103#66931—22no—
104#66930—22no—
105#66925—22no—
106C42×D11—22no—
107C42×D11C2×C411yescharacteristic
108C42×D11C2×C411yescharacteristic
109C42×D11D411yescharacteristic
110C42×D11D411yescharacteristic
111C42×D11D411yescharacteristic
112C42×D11D411yescharacteristic
113C42×D11C2311yescharacteristic
114C42×D11C2311yescharacteristic
115#66923—21no—
116#66922C2×C411yescharacteristic
117#66922C2×C411yescharacteristic
118C4×Dic22—21no—
119C4×Dic22—22no—
120C4×Dic22—22no—
121C4×Dic22C2312yes—
122C11×C4⋊C8—21no—
123C11×C4⋊C8C2312yes—
124C11×C22⋊C8—21no—
125C11×C22⋊C8—21no—
126C11×#97—21no—
127C4×C8×C11C2312yes—
128C22⋊(C11⋊C8)—21no—
129C22⋊(C11⋊C8)—21no—
130(C2×D11)⋊C8—22no—
131(C2×D11)⋊C8—22no—
132#66879—22no—
133Dic11⋊C8—22no—
134Dic11⋊C8—22no—
135C8×Dic11—22no—
136C4⋊(C11⋊C8)—21no—
137C4⋊(C11⋊C8)C2312yes—
138#66867—21no—
139C4×C11⋊C8C2312yes—
140C2×#1497—111nomaximal, Sylow
141C23×D11C22⋊C411yescharacteristic
142C2×Q8×C11—21no—
143C2×Q8×C11C22×C412yes—
144C22×C4×C11C22×C411yescharacteristic
145C22×C4×C11C2×D411yescharacteristic
146C22×C4×C11C2×D411yescharacteristic
147C22×Dic11C22⋊C411yescharacteristic
148C22×Dic11C22⋊C411yescharacteristic
149C22×Dic11C22⋊C411yescharacteristic
150Q8×D11—28no—
151Q8×D11—44no—
152C2×C4×D11—24no—
153C2×C4×D11—24no—
154C2×C4×D11—22no—
155C2×C4×D11—22no—
156C2×C4×D11—42no—
157C2×C4×D11C22⋊C411yescharacteristic
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×D11C2×D411yescharacteristic
166C2×C4×D11C2×D411yescharacteristic
167C2×C4×D11C2×D411yescharacteristic
168C2×C4×D11C2×D411yescharacteristic
169C2×Dic22—22no—
170C2×Dic22—22no—
171C2×Dic22—21no—
172C2×Dic22C22×C412yes—
173C2×C8×C11—22no—
174C2×C8×C11—22no—
175C11×C4⋊C4—21no—
176C11×C4⋊C4—22no—
177C11×C4⋊C4—21no—
178C11×C4⋊C4—21no—
179C11×C4⋊C4—22no—
180C11×C4⋊C4C22×C412yes—
181C11×C22⋊C4—22no—
182C42×C11—22no—
183C42×C11C22×C411yescharacteristic
184C42×C11C2×D411yescharacteristic
185C42×C11C2×D411yescharacteristic
186C42×C11C2411yescharacteristic
187C22⋊Dic11—22no—
188(C2×D11)⋊C4—22no—
189(C2×D11)⋊C4—22no—
190C4⋊Dic11—22no—
191C4⋊Dic11—22no—
192C4⋊Dic11—21no—
193C4⋊Dic11—21no—
194C4⋊Dic11—21no—
195C4⋊Dic11C22×C412yes—
196Dic11⋊C4—22no—
197Dic11⋊C4—22no—
198Dic11⋊C4—22no—
199Dic11⋊C4—22no—
200Dic11⋊C4—22no—
201Dic11⋊C4—22no—
202Dic11⋊C4—22no—
203Dic11⋊C4—22no—
204C4×Dic11—22no—
205C4×Dic11—22no—
206C4×Dic11—22no—
207C4×Dic11C22⋊C411yescharacteristic
208C4×Dic11C22⋊C411yescharacteristic
209C4×Dic11C22⋊C411yescharacteristic
210C4×Dic11C22⋊C411yescharacteristic
211C4×Dic11C22⋊C411yescharacteristic
212C4×Dic11C22⋊C411yescharacteristic
213C4×Dic11C22×C411yescharacteristic
214C4×Dic11C22×C411yescharacteristic
215C4×Dic11C2×D411yescharacteristic
216C4×Dic11C2×D411yescharacteristic
217C4×Dic11C2×D411yescharacteristic
218C4×Dic11C2×D411yescharacteristic
219C2×C11⋊C8—22no—
220C2×C11⋊C8—22no—
221C8×D11—44no—
222C8×D11—44no—
223C2×#533—111no—
224C2×#432—111no—
225C2×#431—111no—
226#1497—111no—
227#1497—111no—
228#1497—114no—
229#1497—111no—
230#1497D1111yescharacteristic, direct product factor
231C2×Q8⋊C8—114no—
232C23×C11C2×C22⋊C411yescharacteristic
233C22×D11—22no—
234C22×D11—22no—
235C22×D11—22no—
236C22×D11C2×C22⋊C411yescharacteristic
237C22×D11C2×C22⋊C411yescharacteristic
238Q8×C11—24no—
239Q8×C11—42no—
240C2×C4×C11—22no—
241C2×C4×C11—22no—
242C2×C4×C11—22no—
243C2×C4×C11—22no—
244C2×C4×C11—41no—
245C2×C4×C11C2×C22⋊C411yescharacteristic
246C2×C4×C11C2×C22⋊C411yescharacteristic
247C2×C4×C11C2×C22⋊C411yescharacteristic
248C2×C4×C11C23×C411yescharacteristic
249C2×C4×C11C22×D411yescharacteristic
250C2×C4×C11C22×D411yescharacteristic
251C2×Dic11—22no—
252C2×Dic11—22no—
253C2×Dic11—22no—
254C2×Dic11—22no—
255C2×Dic11—41no—
256C2×Dic11C2×C22⋊C411yescharacteristic
257C2×Dic11C2×C22⋊C411yescharacteristic
258C2×Dic11C2×C22⋊C411yescharacteristic
259C2×Dic11C2×C22⋊C411yescharacteristic
260C2×Dic11C2×C22⋊C411yescharacteristic
261C2×Dic11C2×C22⋊C411yescharacteristic
262C4×D11—22no—
263C4×D11—22no—
264C4×D11—22no—
265C4×D11—22no—
266C4×D11—22no—
267C4×D11—22no—
268C4×D11—22no—
269C4×D11—22no—
270C4×D11—41no—
271C4×D11—41no—
272C4×D11—44no—
273C4×D11—44no—
274C4×D11#13114yes—
275C4×D11#13714yes—
276Dic22—24no—
277Dic22—44no—
278Dic22—42no—
279Dic22—44no—
280C8×C11—42no—
281C8×C11—42no—
282C11⋊C8—42no—
283C11⋊C8—42no—
284#533—111no—
285#533—111no—
286#533—112no—
287#533—112no—
288#533—111no—
289#533—221no—
290#533—221no—
291#533—221no—
292#533—221no—
293#533C2×D1111yescharacteristic
294C2×C4⋊Q8—111no—
295C2×C4⋊Q8—111no—
296C2×#125—221no—
297C2×C22⋊Q8—112no—
298C2×C22⋊Q8—221no—
299C2×C4×Q8—112no—
300C2×C4×Q8—221no—
301C2×#117—221no—
302C22×C42—111no—
303#432—111no—
304#432—112no—
305#432—221no—
306#432—221no—
307#432C2×D1111yescharacteristic
308#431—111no—
309#431—112no—
310#431—221no—
311#431—221no—
312#431C2×D1111yescharacteristic
313C2×C4⋊C8—112no—
314C2×C4⋊C8—221no—
315C2×C22⋊C8—221no—
316C2×C22⋊C8—221no—
317C2×#97—221no—
318C2×C4×C8—112no—
319Q8⋊C8—114no—
320Q8⋊C8—114no—
321Q8⋊C8—114no—
322Q8⋊C8C2×D1114yescomplemented
323C22×C11—21no—
324C22×C11—21no—
325C22×C11—21no—
326C22×C11C22×C22⋊C411yescharacteristic
327C2×D11—21no—
328C2×D11—21no—
329C2×D11—21no—
330C2×D11—44no—
331C2×D11#40812yes—
332C2×D11#41912yes—
333C2×D11#42112yes—
334C4×C11—21no—
335C4×C11—21no—
336C4×C11—21no—
337C4×C11—21no—
338C4×C11—42no—
339C4×C11—42no—
340C4×C11C2×#13112yes—
341C4×C11C2×#13712yes—
342Dic11—21no—
343Dic11—21no—
344Dic11—21no—
345Dic11—21no—
346Dic11—42no—
347Dic11—42no—
348Dic11#40812yes—
349Dic11#41912yes—
350C22×Q8—112no—
351C22×Q8—221no—
352C23×C4—111no—
353C23×C4—111no—
354C23×C4—111no—
355C22×C8—222no—
356C22×C8—222no—
357C4⋊Q8—112no—
358C4⋊Q8—112no—
359C4⋊Q8—111no—
360C4⋊Q8—111no—
361C4⋊Q8—221no—
362C4⋊Q8—221no—
363C4⋊Q8—221no—
364C4⋊Q8—221no—
365C4⋊Q8C4×D1111yescharacteristic
366C4⋊Q8C4×D1111yescharacteristic
367#125—21no—
368#125—222no—
369#125—222no—
370#125—221no—
371#125—221no—
372#125—221no—
373C22⋊Q8—21no—
374C22⋊Q8—112no—
375C22⋊Q8—112no—
376C22⋊Q8—112no—
377C22⋊Q8—222no—
378C22⋊Q8—222no—
379C22⋊Q8—222no—
380C22⋊Q8—222no—
381C22⋊Q8—221no—
382C22⋊Q8—221no—
383C22⋊Q8—221no—
384C22⋊Q8C4×D1112yes—
385C4×Q8—21no—
386C4×Q8—112no—
387C4×Q8—112no—
388C4×Q8—112no—
389C4×Q8—222no—
390C4×Q8—222no—
391C4×Q8—222no—
392C4×Q8—221no—
393C4×Q8—222no—
394C4×Q8—221no—
395C4×Q8—221no—
396C4×Q8C22×D1112yes—
397#117—21no—
398#117—222no—
399#117—222no—
400#117—221no—
401#117—221no—
402#117—221no—
403C2×C4⋊C4—112no—
404C2×C4⋊C4—221no—
405C2×C4⋊C4—221no—
406C2×C4⋊C4—222no—
407C2×C4⋊C4—222no—
408C2×C4⋊C4—221no—
409C2×C22⋊C4—222no—
410C2×C42—111no—
411C2×C42—111no—
412C2×C42—111no—
413C2×C42—111no—
414C2×C42—111no—
415C2×C42—111no—
416C2×C42—111no—
417C2×C42—111no—
418C2×C42—111no—
419C2×C42—111no—
420C2×C42—111no—
421C2×C42—222no—
422C2×C42C22×D1111yescharacteristic
423C4⋊C8—21no—
424C4⋊C8—112no—
425C4⋊C8—222no—
426C4⋊C8—222no—
427C4⋊C8—221no—
428C4⋊C8C22×D1112yes—
429C22⋊C8—21no—
430C22⋊C8—21no—
431C22⋊C8—222no—
432C22⋊C8—222no—
433C22⋊C8—221no—
434C22⋊C8—221no—
435#97—21no—
436#97—222no—
437#97—221no—
438C4×C8—112no—
439C4×C8—222no—
440C4×C8C22×D1112yes—
441C2×C11—41no—
442C2×C11C2×#40811yescharacteristic
443C2×C11C2×#41911yescharacteristic
444C2×C11C2×#42111yescharacteristic
445D11—41no—
446D11#149714yesdirect product factor
447C24—111no—
448C2×Q8—21no—
449C2×Q8—112no—
450C2×Q8—222no—
451C2×Q8—222no—
452C2×Q8—228no—
453C2×Q8—221no—
454C2×Q8—444no—
455C2×Q8C2×C4×D1112yes—
456C22×C4—111no—
457C22×C4—111no—
458C22×C4—111no—
459C22×C4—111no—
460C22×C4—111no—
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—224no—
472C22×C4—224no—
473C22×C4—222no—
474C22×C4—222no—
475C22×C4—442no—
476C22×C4C2×C4×D1111yescharacteristic
477C22×C4D4×D1111yescharacteristic
478C22×C4D4×D1111yescharacteristic
479C2×C8—22no—
480C2×C8—22no—
481C2×C8—222no—
482C2×C8—222no—
483C2×C8—444no—
484C2×C8—444no—
485C4⋊C4—21no—
486C4⋊C4—21no—
487C4⋊C4—21no—
488C4⋊C4—22no—
489C4⋊C4—22no—
490C4⋊C4—112no—
491C4⋊C4—222no—
492C4⋊C4—222no—
493C4⋊C4—222no—
494C4⋊C4—222no—
495C4⋊C4—222no—
496C4⋊C4—222no—
497C4⋊C4—222no—
498C4⋊C4—222no—
499C4⋊C4—221no—
500C4⋊C4—221no—
501C4⋊C4—222no—
502C4⋊C4—221no—
503C4⋊C4—222no—
504C4⋊C4C2×C4×D1112yes—
505C22⋊C4—22no—
506C22⋊C4—222no—
507C22⋊C4—222no—
508C22⋊C4—222no—
509C42—22no—
510C42—111no—
511C42—111no—
512C42—111no—
513C42—111no—
514C42—111no—
515C42—111no—
516C42—111no—
517C42—111no—
518C42—111no—
519C42—111no—
520C42—111no—
521C42—111no—
522C42—222no—
523C42—222no—
524C42—222no—
525C42C2×C4×D1111yescharacteristic
526C42D4×D1111yescharacteristic
527C42D4×D1111yescharacteristic
528C42C23×D1111yescharacteristic
529C11C2×#149711yescharacteristic, complemented, Sylow
530C23—111no—
531C23—111no—
532C23—222no—
533C23—222no—
534C23—222no—
535C23C22⋊C4×D1111yescharacteristic
536Q8—24no—
537Q8—42no—
538Q8—224no—
539Q8—442no—
540Q8—444no—
541Q8—444no—
542C2×C4—22no—
543C2×C4—22no—
544C2×C4—22no—
545C2×C4—22no—
546C2×C4—41no—
547C2×C4—111no—
548C2×C4—111no—
549C2×C4—114no—
550C2×C4—114no—
551C2×C4—111no—
552C2×C4—111no—
553C2×C4—111no—
554C2×C4—111no—
555C2×C4—222no—
556C2×C4—222no—
557C2×C4—222no—
558C2×C4—222no—
559C2×C4—222no—
560C2×C4—222no—
561C2×C4—222no—
562C2×C4—222no—
563C2×C4—222no—
564C2×C4—222no—
565C2×C4—222no—
566C2×C4—222no—
567C2×C4—441no—
568C2×C4—441no—
569C2×C4—444no—
570C2×C4—444no—
571C2×C4—441no—
572C2×C4C22⋊C4×D1111yescharacteristic
573C2×C4C22⋊C4×D1111yescharacteristic
574C2×C4C22⋊C4×D1111yescharacteristic
575C2×C4C22×C4×D1111yescharacteristic
576C2×C4C2×D4×D1111yescharacteristic
577C2×C4C2×D4×D1111yescharacteristic
578C8—42no—
579C8—42no—
580C8—442no—
581C8—442no—
582C22—21no—
583C22—21no—
584C22—21no—
585C22—112no—
586C22—112no—
587C22—112no—
588C22—221no—
589C22—221no—
590C22—221no—
591C22—444no—
592C22C2×C22⋊C4×D1111yescharacteristic
593C4—21no—
594C4—21no—
595C4—21no—
596C4—21no—
597C4—42no—
598C4—42no—
599C4—112no—
600C4—112no—
601C4—221no—
602C4—221no—
603C4—221no—
604C4—221no—
605C4—442no—
606C4—442no—
607C4D11×#13112yes—
608C4D11×#13712yes—
609C2—41no—
610C2—114no—
611C2—441no—
612C2D11×#40811yescharacteristic
613C2D11×#41911yescharacteristic
614C2D11×#42111yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×#1497C2
socleC22×C11C22×C22⋊C4
prime radicalC23×D11C22⋊C4
cosocleC42×C11C24
hypercenter#1497D11
hypocenterC11C2×#1497
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1497

Complements

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

NH ≅ G/Ntype
4. #13067090C2semidirect
5. #13067089C2semidirect
6. #13067088C2semidirect
7. #13067087C2semidirect
8. D11×Q8⋊C8C2semidirect
9. C11×#1497C2semidirect
45. C11×Q8⋊C8C22semidirect
46. Q8⋊(C11⋊C8)C22semidirect
47. #10622122C22semidirect
48. #10622094C22semidirect
230. #1497D11direct (N × H)
322. Q8⋊C8C2×D11semidirect
446. D11#1497direct (N × H)
529. C11C2×#1497semidirect

Maximal subgroups

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

subgroupindex
D11×#5332
D11×#4322
D11×#4312
#130670902
#130670892
#130670882
#130670872
D11×Q8⋊C82
C11×#14972
C2×#149711