Finite Group Databasebeta

← #14720317

Subgroups — #14720317

Order 2816.

988 conjugacy classes of subgroups.

The subgroup lattice has 628 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D11×#533C211yesmaximal, characteristic
2#13077244C211yesmaximal, characteristic
3C2×#10622446C211yesmaximal, characteristic
4#13067035C214yesmaximal, complemented
5#13067020C211yesmaximal, characteristic, complemented
6#13067019C211yesmaximal, characteristic, complemented
7#13067018C211yesmaximal, characteristic, complemented
8#13067009C214yesmaximal, complemented
9C11×#1481C211yesmaximal, 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×#431C2211yescharacteristic
30C2×C11×C4⋊C8C2211yescharacteristic
31C2×(C2×D11)⋊C8—21no—
32C2×C8×Dic11—21no—
33#10622538C2211yescharacteristic
34C2×C4⋊(C11⋊C8)C2211yescharacteristic
35#10622450—21no—
36#10622448—21no—
37#10622446—21no—
38#10622446—21no—
39#10622446C2212yes—
40#10622446C2212yes—
41#10622339—21no—
42#10622332—21no—
43C4×#4313C2212yes—
44#10622298C2212yes—
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
54C22×C8×C11—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
76C22×C11⋊C8—21no—
77C2×#4313—22no—
78#66950—21no—
79#66950C2×C412yes—
80#66949—22no—
81#66949—22no—
82#66945—21no—
83#66945—21no—
84C4⋊C4×D11—21no—
85C4⋊C4×D11—21no—
86C4⋊C4×D11—21no—
87C4⋊C4×D11—22no—
88C4⋊C4×D11—22no—
89C4⋊C4×D11C2×C412yes—
90#66943—21no—
91#66943—21no—
92#66942—22no—
93#66942—22no—
94#66941—21no—
95#66941—21no—
96#66941—21no—
97#66941C2×C412yes—
98#66940—21no—
99#66940—22no—
100#66940—22no—
101#66940C2×C412yes—
102C22⋊C4×D11—22no—
103#66931—22no—
104#66931—22no—
105#66930—22no—
106#66925—22no—
107C42×D11—22no—
108C42×D11C2×C411yescharacteristic
109C42×D11C2×C411yescharacteristic
110C42×D11D411yescharacteristic
111C42×D11D411yescharacteristic
112C42×D11D411yescharacteristic
113C42×D11D411yescharacteristic
114C42×D11C2311yescharacteristic
115C42×D11C2311yescharacteristic
116#66923—21no—
117#66922C2×C411yescharacteristic
118#66922C2×C411yescharacteristic
119C4×Dic22—21no—
120C4×Dic22—22no—
121C4×Dic22—22no—
122C4×Dic22C2312yes—
123C11×C4⋊C8—21no—
124C11×C4⋊C8—21no—
125C11×C4⋊C8C2312yes—
126C11×C22⋊C8—21no—
127C4×C8×C11C2312yes—
128C22⋊(C11⋊C8)—21no—
129(C2×D11)⋊C8—22no—
130(C2×D11)⋊C8—22no—
131(C2×D11)⋊C8—22no—
132#66879—22no—
133Dic11⋊C8—22no—
134C8×Dic11—22no—
135C8×Dic11—22no—
136C4⋊(C11⋊C8)—21no—
137C4⋊(C11⋊C8)—21no—
138C4⋊(C11⋊C8)C2312yes—
139C4×C11⋊C8C2312yes—
140#17464—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—22no—
154C2×C4×D11—22no—
155C2×C4×D11—22no—
156C2×C4×D11—22no—
157C2×C4×D11—42no—
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—
174C2×C8×C11—22no—
175C2×C8×C11—22no—
176C2×C8×C11—42no—
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
221C2×C11⋊C8—22no—
222C2×C11⋊C8—22no—
223C2×C11⋊C8—42no—
224#4313—44no—
225C2×#533—111no—
226#2920—111no—
227C2×#431—111no—
228#1485—114no—
229#1481—111no—
230#1481—111no—
231#1481—111no—
232#1481D1111yescharacteristic, complemented
233#1479—114no—
234C23×C11C2×C22⋊C411yescharacteristic
235C22×D11—22no—
236C22×D11—22no—
237C22×D11—41no—
238C22×D11C2×C22⋊C411yescharacteristic
239C22×D11C2×C22⋊C411yescharacteristic
240Q8×C11—24no—
241Q8×C11—42no—
242C2×C4×C11—22no—
243C2×C4×C11—22no—
244C2×C4×C11—22no—
245C2×C4×C11—41no—
246C2×C4×C11C2×C22⋊C411yescharacteristic
247C2×C4×C11C2×C22⋊C411yescharacteristic
248C2×C4×C11C2×C22⋊C411yescharacteristic
249C2×C4×C11#13712yes—
250C2×C4×C11#13712yes—
251C2×C4×C11C23×C411yescharacteristic
252C2×C4×C11C22×D411yescharacteristic
253C2×C4×C11C22×D411yescharacteristic
254C2×Dic11—22no—
255C2×Dic11—22no—
256C2×Dic11—22no—
257C2×Dic11—22no—
258C2×Dic11—22no—
259C2×Dic11C2×C22⋊C411yescharacteristic
260C2×Dic11C2×C22⋊C411yescharacteristic
261C2×Dic11C2×C22⋊C411yescharacteristic
262C2×Dic11C2×C22⋊C411yescharacteristic
263C2×Dic11C2×C22⋊C411yescharacteristic
264C2×Dic11C2×C22⋊C411yescharacteristic
265C4×D11—22no—
266C4×D11—22no—
267C4×D11—21no—
268C4×D11—21no—
269C4×D11—21no—
270C4×D11—21no—
271C4×D11—22no—
272C4×D11—22no—
273C4×D11—22no—
274C4×D11—22no—
275C4×D11—22no—
276C4×D11—41no—
277C4×D11—41no—
278C4×D11—44no—
279C4×D11—44no—
280C4×D11#13114yes—
281Dic22—24no—
282Dic22—42no—
283Dic22—44no—
284Dic22—44no—
285C8×C11—42no—
286C8×C11—42no—
287C11⋊C8—42no—
288C11⋊C8—42no—
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#432—221no—
309#432—221no—
310#431—111no—
311#431—112no—
312#431—112no—
313#431—112no—
314#431—221no—
315#431—221no—
316#431C2×D1111yescharacteristic
317#423—221no—
318C2×C4⋊C8—111no—
319C2×C4⋊C8C2×D1111yescharacteristic
320#407—221no—
321C2×C22⋊C8—221no—
322C4×M16—112no—
323C2×C4×C8—221no—
324Q8⋊C8—114no—
325Q8⋊C8—114no—
326Q8⋊C8—114no—
327Q8⋊C8C2×D1114yescomplemented
328C22×C11—21no—
329C22×C11—21no—
330C22×C11#41912yes—
331C22×C11C22×C22⋊C411yescharacteristic
332C2×D11—21no—
333C2×D11—21no—
334C2×D11—21no—
335C2×D11—21no—
336C2×D11—21no—
337C2×D11—44no—
338C2×D11#40812yes—
339C4×C11—21no—
340C4×C11—21no—
341C4×C11—21no—
342C4×C11—42no—
343C4×C11—42no—
344C4×C11#41912yes—
345C4×C11C2×#13112yes—
346C4×C11C2×#13711yescharacteristic
347C4×C11C2×#13711yescharacteristic
348Dic11—21no—
349Dic11—21no—
350Dic11—21no—
351Dic11—21no—
352Dic11—42no—
353Dic11—42no—
354Dic11#40812yes—
355Dic11#42112yes—
356C22×Q8—112no—
357C22×Q8—221no—
358C23×C4—111no—
359C23×C4—111no—
360C23×C4—111no—
361C2×M16—222no—
362C22×C8—21no—
363C22×C8—221no—
364C4⋊Q8—112no—
365C4⋊Q8—112no—
366C4⋊Q8—111no—
367C4⋊Q8—111no—
368C4⋊Q8—221no—
369C4⋊Q8—221no—
370C4⋊Q8—221no—
371C4⋊Q8—221no—
372C4⋊Q8C4×D1111yescharacteristic
373C4⋊Q8C4×D1111yescharacteristic
374#125—21no—
375#125—222no—
376#125—222no—
377#125—221no—
378#125—221no—
379#125—221no—
380C22⋊Q8—21no—
381C22⋊Q8—112no—
382C22⋊Q8—112no—
383C22⋊Q8—112no—
384C22⋊Q8—222no—
385C22⋊Q8—222no—
386C22⋊Q8—222no—
387C22⋊Q8—222no—
388C22⋊Q8—221no—
389C22⋊Q8—221no—
390C22⋊Q8—221no—
391C22⋊Q8C4×D1112yes—
392C4×Q8—21no—
393C4×Q8—112no—
394C4×Q8—112no—
395C4×Q8—112no—
396C4×Q8—222no—
397C4×Q8—222no—
398C4×Q8—222no—
399C4×Q8—221no—
400C4×Q8—222no—
401C4×Q8—221no—
402C4×Q8—221no—
403C4×Q8C22×D1112yes—
404#117—21no—
405#117—222no—
406#117—222no—
407#117—221no—
408#117—221no—
409#117—221no—
410C2×C4⋊C4—112no—
411C2×C4⋊C4—221no—
412C2×C4⋊C4—221no—
413C2×C4⋊C4—222no—
414C2×C4⋊C4—222no—
415C2×C4⋊C4—221no—
416C2×C22⋊C4—222no—
417C2×C42—111no—
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—222no—
429C2×C42C22×D1111yescharacteristic
430C4⋊C8—21no—
431C4⋊C8—21no—
432C4⋊C8—112no—
433C4⋊C8—222no—
434C4⋊C8—221no—
435C4⋊C8—221no—
436C4⋊C8C22×D1112yes—
437C22⋊C8—21no—
438C22⋊C8—222no—
439C22⋊C8—222no—
440C22⋊C8—222no—
441C22⋊C8—221no—
442#97—222no—
443C4×C8—112no—
444C4×C8—222no—
445C4×C8—222no—
446C4×C8C22×D1112yes—
447C2×C11—22no—
448C2×C11C2×#40811yescharacteristic
449C2×C11C2×#41911yescharacteristic
450C2×C11C2×#42111yescharacteristic
451D11—22no—
452D11—41no—
453C24—111no—
454C2×Q8—21no—
455C2×Q8—112no—
456C2×Q8—222no—
457C2×Q8—222no—
458C2×Q8—228no—
459C2×Q8—221no—
460C2×Q8—444no—
461C2×Q8C2×C4×D1112yes—
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—111no—
477C22×C4—224no—
478C22×C4—222no—
479C22×C4—222no—
480C22×C4—222no—
481C22×C4—222no—
482C22×C4—442no—
483C22×C4C2×C4×D1111yescharacteristic
484C22×C4D4×D1111yescharacteristic
485C22×C4D4×D1111yescharacteristic
486M16—444no—
487C2×C8—22no—
488C2×C8—22no—
489C2×C8—42no—
490C2×C8—222no—
491C2×C8—222no—
492C2×C8—442no—
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
537C11#1746411yescharacteristic, complemented, Sylow
538C23—111no—
539C23—111no—
540C23—222no—
541C23—222no—
542C23—441no—
543C23C22⋊C4×D1111yescharacteristic
544Q8—24no—
545Q8—42no—
546Q8—224no—
547Q8—442no—
548Q8—444no—
549Q8—444no—
550C2×C4—22no—
551C2×C4—22no—
552C2×C4—22no—
553C2×C4—41no—
554C2×C4—111no—
555C2×C4—111no—
556C2×C4—114no—
557C2×C4—111no—
558C2×C4—111no—
559C2×C4—111no—
560C2×C4—111no—
561C2×C4—222no—
562C2×C4—222no—
563C2×C4—222no—
564C2×C4—222no—
565C2×C4—222no—
566C2×C4—222no—
567C2×C4—222no—
568C2×C4—222no—
569C2×C4—221no—
570C2×C4—221no—
571C2×C4—221no—
572C2×C4—221no—
573C2×C4—222no—
574C2×C4—222no—
575C2×C4—222no—
576C2×C4—222no—
577C2×C4—441no—
578C2×C4—441no—
579C2×C4—444no—
580C2×C4—444no—
581C2×C4C22⋊C4×D1111yescharacteristic
582C2×C4C22⋊C4×D1111yescharacteristic
583C2×C4C22⋊C4×D1111yescharacteristic
584C2×C4#6696812yes—
585C2×C4#6697112yes—
586C2×C4C22×C4×D1111yescharacteristic
587C2×C4C2×D4×D1111yescharacteristic
588C2×C4C2×D4×D1111yescharacteristic
589C8—42no—
590C8—42no—
591C8—442no—
592C8—442no—
593C22—21no—
594C22—21no—
595C22—112no—
596C22—221no—
597C22—221no—
598C22—221no—
599C22—221no—
600C22—221no—
601C22—444no—
602C22#1062241512yes—
603C22C2×C22⋊C4×D1111yescharacteristic
604C4—21no—
605C4—21no—
606C4—21no—
607C4—42no—
608C4—42no—
609C4—112no—
610C4—112no—
611C4—221no—
612C4—221no—
613C4—221no—
614C4—221no—
615C4—442no—
616C4—442no—
617C4#1062241512yes—
618C4D11×#13112yes—
619C4C2×#6696811yescharacteristic
620C4C2×#6697111yescharacteristic
621C2—22no—
622C2—222no—
623C2—441no—
624C2D11×#40811yescharacteristic
625C2C2×#1062241511yescharacteristic
626C2D11×#42111yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×#1481C2
socleC22×C11C22×C22⋊C4
prime radicalC23×D11C22⋊C4
cosocleC42×C11C24
hypercenter#1481D11
hypocenterC11#17464
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1481

Complements

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

NH ≅ G/Ntype
4. #13067035C2semidirect
5. #13067020C2semidirect
6. #13067019C2semidirect
7. #13067018C2semidirect
8. #13067009C2semidirect
9. C11×#1481C2semidirect
45. C11×Q8⋊C8C22semidirect
46. Q8⋊(C11⋊C8)C22semidirect
47. #10622122C22semidirect
48. #10622094C22semidirect
232. #1481D11semidirect
327. Q8⋊C8C2×D11semidirect
537. C11#17464semidirect

Maximal subgroups

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

subgroupindex
D11×#5332
#130772442
C2×#106224462
#130670352
#130670202
#130670192
#130670182
#130670092
C11×#14812
#1746411