Finite Group Databasebeta

← #14720319

Subgroups — #14720319

Order 2816.

988 conjugacy classes of subgroups.

The subgroup lattice has 618 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D11×#533C211yesmaximal, characteristic
2#13077247C211yesmaximal, characteristic
3D11×#431C211yesmaximal, characteristic
4#13067038C211yesmaximal, characteristic, complemented
5#13067037C211yesmaximal, characteristic, complemented
6#13067036C211yesmaximal, characteristic, complemented
7#13067017C214yesmaximal, complemented
8#13067009C214yesmaximal, complemented
9C11×#1485C211yesmaximal, 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
30C4×C11×M16C2211yescharacteristic
31#10622739—21no—
32#10622731—21no—
33#10622538C2211yescharacteristic
34C4×#4318C2211yescharacteristic
35#10622446C2212yes—
36D11×C4⋊C8C2212yes—
37D11×C22⋊C8—21no—
38#10622331—21no—
39#10622318—21no—
40#10622318—21no—
41#10622298—21no—
42#10622298C2212yes—
43#10622298C2212yes—
44C4×C8×D11—21no—
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—
77C2×C8×D11—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⋊C8C2312yes—
124C11×C22⋊C8—21no—
125C11×#97—21no—
126C4×C8×C11—21no—
127C4×C8×C11C2312yes—
128C22⋊(C11⋊C8)—21no—
129(C2×D11)⋊C8—22no—
130(C2×D11)⋊C8—22no—
131(C2×D11)⋊C8—22no—
132Dic11⋊C8—22no—
133Dic11⋊C8—22no—
134Dic11⋊C8—22no—
135C8×Dic11—22no—
136C4⋊(C11⋊C8)C2312yes—
137#66867—21no—
138C4×C11⋊C8—21no—
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—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—
173C11×M16—42no—
174C2×C8×C11—22no—
175C2×C8×C11—22no—
176C11×C4⋊C4—21no—
177C11×C4⋊C4—22no—
178C11×C4⋊C4—21no—
179C11×C4⋊C4—21no—
180C11×C4⋊C4—22no—
181C11×C4⋊C4C22×C412yes—
182C11×C22⋊C4—22no—
183C42×C11—22no—
184C42×C11C22×C411yescharacteristic
185C42×C11C2×D411yescharacteristic
186C42×C11C2×D411yescharacteristic
187C42×C11C2411yescharacteristic
188C22⋊Dic11—22no—
189(C2×D11)⋊C4—22no—
190(C2×D11)⋊C4—22no—
191C4⋊Dic11—22no—
192C4⋊Dic11—22no—
193C4⋊Dic11—21no—
194C4⋊Dic11—21no—
195C4⋊Dic11—21no—
196C4⋊Dic11C22×C412yes—
197Dic11⋊C4—22no—
198Dic11⋊C4—22no—
199Dic11⋊C4—22no—
200Dic11⋊C4—22no—
201Dic11⋊C4—22no—
202Dic11⋊C4—22no—
203Dic11⋊C4—22no—
204Dic11⋊C4—22no—
205C4×Dic11—22no—
206C4×Dic11—22no—
207C4×Dic11—22no—
208C4×Dic11C22⋊C411yescharacteristic
209C4×Dic11C22⋊C411yescharacteristic
210C4×Dic11C22⋊C411yescharacteristic
211C4×Dic11C22⋊C411yescharacteristic
212C4×Dic11C22⋊C411yescharacteristic
213C4×Dic11C22⋊C411yescharacteristic
214C4×Dic11C22×C411yescharacteristic
215C4×Dic11C22×C411yescharacteristic
216C4×Dic11C2×D411yescharacteristic
217C4×Dic11C2×D411yescharacteristic
218C4×Dic11C2×D411yescharacteristic
219C4×Dic11C2×D411yescharacteristic
220#4318—42no—
221C2×C11⋊C8—22no—
222C2×C11⋊C8—22no—
223C8×D11—44no—
224C2×#533—111no—
225#2920—111no—
226C2×#431—111no—
227#1485—111no—
228#1485—111no—
229#1485—111no—
230#1485D1111yescharacteristic, complemented
231#1481—114no—
232#1479—114no—
233C23×C11C2×C22⋊C411yescharacteristic
234C22×D11—22no—
235C22×D11—22no—
236C22×D11—41no—
237C22×D11C2×C22⋊C411yescharacteristic
238C22×D11C2×C22⋊C411yescharacteristic
239Q8×C11—24no—
240Q8×C11—42no—
241C2×C4×C11—22no—
242C2×C4×C11—22no—
243C2×C4×C11—22no—
244C2×C4×C11—22no—
245C2×C4×C11—22no—
246C2×C4×C11C2×C22⋊C411yescharacteristic
247C2×C4×C11C2×C22⋊C411yescharacteristic
248C2×C4×C11C2×C22⋊C411yescharacteristic
249C2×C4×C11C23×C411yescharacteristic
250C2×C4×C11C22×D411yescharacteristic
251C2×C4×C11C22×D411yescharacteristic
252C2×Dic11—22no—
253C2×Dic11—22no—
254C2×Dic11—22no—
255C2×Dic11—22no—
256C2×Dic11—41no—
257C2×Dic11C2×C22⋊C411yescharacteristic
258C2×Dic11C2×C22⋊C411yescharacteristic
259C2×Dic11C2×C22⋊C411yescharacteristic
260C2×Dic11C2×C22⋊C411yescharacteristic
261C2×Dic11C2×C22⋊C411yescharacteristic
262C2×Dic11C2×C22⋊C411yescharacteristic
263C4×D11—22no—
264C4×D11—22no—
265C4×D11—22no—
266C4×D11—22no—
267C4×D11—22no—
268C4×D11—22no—
269C4×D11—22no—
270C4×D11—22no—
271C4×D11—41no—
272C4×D11—41no—
273C4×D11—44no—
274C4×D11—44no—
275C4×D11#13114yes—
276C4×D11#13714yes—
277Dic22—24no—
278Dic22—44no—
279Dic22—42no—
280Dic22—44no—
281C8×C11—42no—
282C8×C11—42no—
283C11⋊C8—42no—
284C11⋊C8—42no—
285#533—111no—
286#533—111no—
287#533—112no—
288#533—112no—
289#533—111no—
290#533—221no—
291#533—221no—
292#533—221no—
293#533—221no—
294#533C2×D1111yescharacteristic
295C2×C4⋊Q8—111no—
296C2×C4⋊Q8—111no—
297C2×#125—221no—
298C2×C22⋊Q8—112no—
299C2×C22⋊Q8—221no—
300C2×C4×Q8—112no—
301C2×C4×Q8—221no—
302C2×#117—221no—
303C22×C42—111no—
304#432—221no—
305#432—221no—
306#431—112no—
307#431—112no—
308#431—111no—
309#431—112no—
310#431—221no—
311#431—221no—
312#431C2×D1111yescharacteristic
313#423—221no—
314C2×C4⋊C8—112no—
315#407—221no—
316C2×C22⋊C8—221no—
317C4×M16—111no—
318C4×M16C2×D1111yescharacteristic
319C2×C4×C8—221no—
320Q8⋊C8—114no—
321Q8⋊C8—114no—
322Q8⋊C8—114no—
323Q8⋊C8C2×D1114yescomplemented
324C22×C11—21no—
325C22×C11—21no—
326C22×C11—21no—
327C22×C11C22×C22⋊C411yescharacteristic
328C2×D11—21no—
329C2×D11—21no—
330C2×D11—21no—
331C2×D11—21no—
332C2×D11—44no—
333C2×D11#40812yes—
334C2×D11#41912yes—
335C4×C11—21no—
336C4×C11—21no—
337C4×C11—21no—
338C4×C11—42no—
339C4×C11—42no—
340C4×C11#42112yes—
341C4×C11C2×#13112yes—
342C4×C11C2×#13712yes—
343Dic11—21no—
344Dic11—21no—
345Dic11—21no—
346Dic11—21no—
347Dic11—42no—
348Dic11—42no—
349Dic11#40812yes—
350Dic11#41912yes—
351C22×Q8—112no—
352C22×Q8—221no—
353C23×C4—111no—
354C23×C4—111no—
355C23×C4—111no—
356C2×M16—21no—
357C2×M16—221no—
358C22×C8—222no—
359C4⋊Q8—112no—
360C4⋊Q8—112no—
361C4⋊Q8—111no—
362C4⋊Q8—111no—
363C4⋊Q8—221no—
364C4⋊Q8—221no—
365C4⋊Q8—221no—
366C4⋊Q8—221no—
367C4⋊Q8C4×D1111yescharacteristic
368C4⋊Q8C4×D1111yescharacteristic
369#125—21no—
370#125—222no—
371#125—222no—
372#125—221no—
373#125—221no—
374#125—221no—
375C22⋊Q8—21no—
376C22⋊Q8—112no—
377C22⋊Q8—112no—
378C22⋊Q8—112no—
379C22⋊Q8—222no—
380C22⋊Q8—222no—
381C22⋊Q8—222no—
382C22⋊Q8—222no—
383C22⋊Q8—221no—
384C22⋊Q8—221no—
385C22⋊Q8—221no—
386C22⋊Q8C4×D1112yes—
387C4×Q8—21no—
388C4×Q8—112no—
389C4×Q8—112no—
390C4×Q8—112no—
391C4×Q8—222no—
392C4×Q8—222no—
393C4×Q8—222no—
394C4×Q8—221no—
395C4×Q8—222no—
396C4×Q8—221no—
397C4×Q8—221no—
398C4×Q8C22×D1112yes—
399#117—21no—
400#117—222no—
401#117—222no—
402#117—221no—
403#117—221no—
404#117—221no—
405C2×C4⋊C4—112no—
406C2×C4⋊C4—221no—
407C2×C4⋊C4—221no—
408C2×C4⋊C4—222no—
409C2×C4⋊C4—222no—
410C2×C4⋊C4—221no—
411C2×C22⋊C4—222no—
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—111no—
422C2×C42—111no—
423C2×C42—222no—
424C2×C42C22×D1111yescharacteristic
425C4⋊C8—112no—
426C4⋊C8—222no—
427C4⋊C8—222no—
428C4⋊C8—222no—
429C4⋊C8C22×D1112yes—
430C22⋊C8—21no—
431C22⋊C8—222no—
432C22⋊C8—222no—
433C22⋊C8—222no—
434C22⋊C8—221no—
435#97—21no—
436#97—221no—
437C4×C8—21no—
438C4×C8—112no—
439C4×C8—222no—
440C4×C8—221no—
441C4×C8C22×D1112yes—
442C2×C11—41no—
443C2×C11C2×#40811yescharacteristic
444C2×C11C2×#41911yescharacteristic
445C2×C11C2×#42111yescharacteristic
446D11—22no—
447D11—22no—
448C24—111no—
449C2×Q8—21no—
450C2×Q8—112no—
451C2×Q8—222no—
452C2×Q8—222no—
453C2×Q8—228no—
454C2×Q8—221no—
455C2×Q8—444no—
456C2×Q8C2×C4×D1112yes—
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—111no—
472C22×C4—224no—
473C22×C4—224no—
474C22×C4—222no—
475C22×C4—222no—
476C22×C4—442no—
477C22×C4C2×C4×D1111yescharacteristic
478C22×C4D4×D1111yescharacteristic
479C22×C4D4×D1111yescharacteristic
480M16—42no—
481M16—442no—
482C2×C8—22no—
483C2×C8—22no—
484C2×C8—222no—
485C2×C8—222no—
486C2×C8—444no—
487C4⋊C4—21no—
488C4⋊C4—21no—
489C4⋊C4—21no—
490C4⋊C4—22no—
491C4⋊C4—22no—
492C4⋊C4—112no—
493C4⋊C4—222no—
494C4⋊C4—222no—
495C4⋊C4—222no—
496C4⋊C4—222no—
497C4⋊C4—222no—
498C4⋊C4—222no—
499C4⋊C4—222no—
500C4⋊C4—222no—
501C4⋊C4—221no—
502C4⋊C4—221no—
503C4⋊C4—222no—
504C4⋊C4—221no—
505C4⋊C4—222no—
506C4⋊C4C2×C4×D1112yes—
507C22⋊C4—22no—
508C22⋊C4—222no—
509C22⋊C4—222no—
510C22⋊C4—222no—
511C42—22no—
512C42—111no—
513C42—111no—
514C42—111no—
515C42—111no—
516C42—111no—
517C42—111no—
518C42—111no—
519C42—111no—
520C42—111no—
521C42—111no—
522C42—111no—
523C42—111no—
524C42—222no—
525C42—222no—
526C42—222no—
527C42C2×C4×D1111yescharacteristic
528C42D4×D1111yescharacteristic
529C42D4×D1111yescharacteristic
530C42C23×D1111yescharacteristic
531C11#1746411yescharacteristic, complemented, Sylow
532C23—111no—
533C23—111no—
534C23—222no—
535C23—222no—
536C23—441no—
537C23C22⋊C4×D1111yescharacteristic
538Q8—24no—
539Q8—42no—
540Q8—224no—
541Q8—444no—
542Q8—444no—
543Q8—442no—
544C2×C4—22no—
545C2×C4—22no—
546C2×C4—22no—
547C2×C4—22no—
548C2×C4—22no—
549C2×C4—111no—
550C2×C4—111no—
551C2×C4—114no—
552C2×C4—114no—
553C2×C4—111no—
554C2×C4—111no—
555C2×C4—111no—
556C2×C4—111no—
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—222no—
568C2×C4—222no—
569C2×C4—441no—
570C2×C4—441no—
571C2×C4—444no—
572C2×C4—444no—
573C2×C4—441no—
574C2×C4C22⋊C4×D1111yescharacteristic
575C2×C4C22⋊C4×D1111yescharacteristic
576C2×C4C22⋊C4×D1111yescharacteristic
577C2×C4C22×C4×D1111yescharacteristic
578C2×C4C2×D4×D1111yescharacteristic
579C2×C4C2×D4×D1111yescharacteristic
580C8—42no—
581C8—42no—
582C8—442no—
583C8—442no—
584C22—21no—
585C22—21no—
586C22—21no—
587C22—112no—
588C22—112no—
589C22—221no—
590C22—221no—
591C22—221no—
592C22—221no—
593C22—444no—
594C22C2×C22⋊C4×D1111yescharacteristic
595C4—21no—
596C4—21no—
597C4—21no—
598C4—42no—
599C4—42no—
600C4—112no—
601C4—112no—
602C4—221no—
603C4—221no—
604C4—221no—
605C4—221no—
606C4—442no—
607C4—442no—
608C4#1062243412yes—
609C4D11×#13112yes—
610C4D11×#13712yes—
611C2—41no—
612C2—222no—
613C2—222no—
614C2D11×#40811yescharacteristic
615C2D11×#41911yescharacteristic
616C2C2×#1062243411yescharacteristic
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
hypocenterC11#17464
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. #13067017C2semidirect
8. #13067009C2semidirect
9. C11×#1485C2semidirect
45. C11×Q8⋊C8C22semidirect
46. Q8⋊(C11⋊C8)C22semidirect
47. #10622122C22semidirect
48. #10622094C22semidirect
230. #1485D11semidirect
323. Q8⋊C8C2×D11semidirect
531. C11#17464semidirect

Maximal subgroups

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

subgroupindex
D11×#5332
#130772472
D11×#4312
#130670382
#130670372
#130670362
#130670172
#130670092
C11×#14852
#1746411