Finite Group Databasebeta

← #14722402

Subgroups — #14722402

Order 2816.

952 conjugacy classes of subgroups.

The subgroup lattice has 658 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D11×#533C211yesmaximal, characteristic
2#13077248C211yesmaximal, characteristic
3C2×#10622448C211yesmaximal, characteristic
4#13067340C212yesmaximal, complemented
5#13067331C212yesmaximal, complemented
6#13067325C212yesmaximal, complemented
7#13067323C212yesmaximal, complemented
8#13067307C211yesmaximal, characteristic, complemented
9#13067306C211yesmaximal, characteristic, complemented
10#13067304C211yesmaximal, characteristic, complemented
11C11×#1550C211yesmaximal, characteristic, complemented
12C11×#533C2211yescharacteristic
13#10623259C2211yescharacteristic
14#10623259C2211yescharacteristic
15D11×C4⋊Q8C2211yescharacteristic
16D11×C4⋊Q8C2211yescharacteristic
17#10623219—21no—
18D11×#125—21no—
19D11×C22⋊Q8—21no—
20D11×C22⋊Q8C412yes—
21#10623153—21no—
22#10623153C412yes—
23#10623109—21no—
24#10623109C412yes—
25C4×Q8×D11—21no—
26C4×Q8×D11C412yes—
27D11×#117—21no—
28#10623048—21no—
29C2×C42×D11C2211yescharacteristic
30#10623001C2211yescharacteristic
31C11×#423C2211yescharacteristic
32C2×C11×C4⋊C8C2211yescharacteristic
33#10622739—21no—
34M16×Dic11—21no—
35C2×(C2×D11)⋊C8—21no—
36C2×#66879—21no—
37#10622537C2211yescharacteristic
38C2×C4⋊(C11⋊C8)C2211yescharacteristic
39#10622448—21no—
40#10622448—21no—
41#10622448—21no—
42#10622448C2212yes—
43#10622448C2212yes—
44#10622448C2212yes—
45#10622446—21no—
46#10622446C2212yes—
47C11×#333C2212yescomplemented
48C11×#332C2212yescomplemented
49#10622185C2212yescomplemented
50#10622184C2212yescomplemented
51#10622124C2212yescomplemented
52#10622120C2212yescomplemented
53#10622119C2212yescomplemented
54#10622119C2212yescomplemented
55C2×Q8×D11—21no—
56C2×Q8×D11C2×C412yes—
57C22×C4×D11C2×C411yescharacteristic
58C22×C4×D11D411yescharacteristic
59C22×C4×D11D411yescharacteristic
60C2×C11×M16—21no—
61C22×C8×C11—21no—
62C11×C4⋊Q8C2311yescharacteristic
63C11×C4⋊Q8C2311yescharacteristic
64C11×#125—21no—
65C11×C22⋊Q8—21no—
66C11×C22⋊Q8C2×C412yes—
67C4×Q8×C11—21no—
68C4×Q8×C11C2×C412yes—
69C11×#117—21no—
70C2×C42×C11C2311yescharacteristic
71#66999—21no—
72#66999C2×C412yes—
73Q8×Dic11—21no—
74Q8×Dic11C2×C412yes—
75#66997—21no—
76#66997C2×C412yes—
77#66979—21no—
78#66977—21no—
79#66977C2×C412yes—
80C2×C4×Dic11C2×C411yescharacteristic
81C2×C4×Dic11D411yescharacteristic
82C2×C4×Dic11D411yescharacteristic
83C2×#4318—21no—
84C22×C11⋊C8—21no—
85#66950—21no—
86#66950C2×C412yes—
87#66949—22no—
88#66949—22no—
89#66945—21no—
90#66945—21no—
91C4⋊C4×D11—22no—
92C4⋊C4×D11—22no—
93C4⋊C4×D11—21no—
94C4⋊C4×D11—21no—
95C4⋊C4×D11—21no—
96C4⋊C4×D11C2×C412yes—
97#66943—21no—
98#66943—21no—
99#66942—22no—
100#66942—22no—
101#66941—21no—
102#66941—21no—
103#66941—21no—
104#66941C2×C412yes—
105#66940—22no—
106#66940—22no—
107#66940—21no—
108#66940C2×C412yes—
109C22⋊C4×D11—22no—
110#66931—22no—
111#66931—22no—
112#66930—22no—
113#66925—22no—
114C42×D11—22no—
115C42×D11C2×C411yescharacteristic
116C42×D11C2×C411yescharacteristic
117C42×D11D411yescharacteristic
118C42×D11D411yescharacteristic
119C42×D11D411yescharacteristic
120C42×D11D411yescharacteristic
121C42×D11C2311yescharacteristic
122C42×D11C2311yescharacteristic
123#66923—21no—
124#66922C2311yescharacteristic
125#66922C2311yescharacteristic
126C4×Dic22—21no—
127C4×Dic22—22no—
128C4×Dic22—22no—
129C4×Dic22C2×C412yes—
130C11×C4⋊C8—21no—
131C11×C4⋊C8—21no—
132C11×C4⋊C8C2312yes—
133C11×C4⋊C8C2312yes—
134(C2×D11)⋊C8—22no—
135(C2×D11)⋊C8—22no—
136(C2×D11)⋊C8—22no—
137(C2×D11)⋊C8—22no—
138#66879—22no—
139#66879—22no—
140#66879—22no—
141C8×Dic11—22no—
142C4⋊(C11⋊C8)—21no—
143C4⋊(C11⋊C8)—21no—
144C4⋊(C11⋊C8)C2312yes—
145C4⋊(C11⋊C8)C2312yes—
146#17748—111nomaximal, Sylow
147C23×D11C22⋊C411yescharacteristic
148C2×Q8×C11—21no—
149C2×Q8×C11C22×C412yes—
150C22×C4×C11C22×C411yescharacteristic
151C22×C4×C11C2×D411yescharacteristic
152C22×C4×C11C2×D411yescharacteristic
153C22×Dic11C22⋊C411yescharacteristic
154C22×Dic11C22⋊C411yescharacteristic
155C22×Dic11C22⋊C411yescharacteristic
156Q8×D11—44no—
157Q8×D11—42no—
158Q8×D11—42no—
159C2×C4×D11—22no—
160C2×C4×D11—22no—
161C2×C4×D11—22no—
162C2×C4×D11—22no—
163C2×C4×D11—41no—
164C2×C4×D11—41no—
165C2×C4×D11—42no—
166C2×C4×D11C22⋊C411yescharacteristic
167C2×C4×D11C22⋊C411yescharacteristic
168C2×C4×D11C22⋊C411yescharacteristic
169C2×C4×D11C22⋊C411yescharacteristic
170C2×C4×D11C22⋊C411yescharacteristic
171C2×C4×D11C22⋊C411yescharacteristic
172C2×C4×D11C22×C411yescharacteristic
173C2×C4×D11C22×C411yescharacteristic
174C2×C4×D11C2×D411yescharacteristic
175C2×C4×D11C2×D411yescharacteristic
176C2×C4×D11C2×D411yescharacteristic
177C2×C4×D11C2×D411yescharacteristic
178C2×Dic22—22no—
179C2×Dic22—22no—
180C2×Dic22—21no—
181C2×Dic22C22×C412yes—
182C11×M16—42no—
183C2×C8×C11—22no—
184C2×C8×C11—22no—
185C2×C8×C11—42no—
186C11×C4⋊C4—22no—
187C11×C4⋊C4—22no—
188C11×C4⋊C4—21no—
189C11×C4⋊C4—21no—
190C11×C4⋊C4—21no—
191C11×C4⋊C4C22×C412yes—
192C11×C22⋊C4—22no—
193C42×C11—22no—
194C42×C11C22×C411yescharacteristic
195C42×C11C2×D411yescharacteristic
196C42×C11C2×D411yescharacteristic
197C42×C11C2411yescharacteristic
198C22⋊Dic11—22no—
199(C2×D11)⋊C4—22no—
200(C2×D11)⋊C4—22no—
201C4⋊Dic11—22no—
202C4⋊Dic11—22no—
203C4⋊Dic11—21no—
204C4⋊Dic11—21no—
205C4⋊Dic11—21no—
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—
215C4×Dic11—22no—
216C4×Dic11—22no—
217C4×Dic11—22no—
218C4×Dic11C22⋊C411yescharacteristic
219C4×Dic11C22⋊C411yescharacteristic
220C4×Dic11C22⋊C411yescharacteristic
221C4×Dic11C22⋊C411yescharacteristic
222C4×Dic11C22⋊C411yescharacteristic
223C4×Dic11C22⋊C411yescharacteristic
224C4×Dic11C22×C411yescharacteristic
225C4×Dic11C22×C411yescharacteristic
226C4×Dic11C2×D411yescharacteristic
227C4×Dic11C2×D411yescharacteristic
228C4×Dic11C2×D411yescharacteristic
229C4×Dic11C2×D411yescharacteristic
230#4318—42no—
231C2×C11⋊C8—22no—
232C2×C11⋊C8—22no—
233C2×C11⋊C8—42no—
234C2×#533—111no—
235#2920—111no—
236C2×#432—111no—
237#1558—112no—
238#1556—112no—
239#1554—112no—
240#1554—112no—
241#1550—111no—
242#1550—111no—
243#1550—111no—
244#1550D1111yescharacteristic, complemented
245C23×C11C2×C22⋊C411yescharacteristic
246C22×D11—22no—
247C22×D11—22no—
248C22×D11—41no—
249C22×D11C2×C22⋊C411yescharacteristic
250C22×D11C2×C22⋊C411yescharacteristic
251Q8×C11—42no—
252Q8×C11—41no—
253Q8×C11—41no—
254C2×C4×C11—21no—
255C2×C4×C11—21no—
256C2×C4×C11—22no—
257C2×C4×C11—22no—
258C2×C4×C11—41no—
259C2×C4×C11C2×C22⋊C411yescharacteristic
260C2×C4×C11C2×C22⋊C411yescharacteristic
261C2×C4×C11C2×C22⋊C411yescharacteristic
262C2×C4×C11#13712yes—
263C2×C4×C11#13712yes—
264C2×C4×C11C23×C411yescharacteristic
265C2×C4×C11C22×D411yescharacteristic
266C2×C4×C11C22×D411yescharacteristic
267C2×Dic11—22no—
268C2×Dic11—22no—
269C2×Dic11—22no—
270C2×Dic11—41no—
271C2×Dic11—41no—
272C2×Dic11C2×C22⋊C411yescharacteristic
273C2×Dic11C2×C22⋊C411yescharacteristic
274C2×Dic11C2×C22⋊C411yescharacteristic
275C2×Dic11C2×C22⋊C411yescharacteristic
276C2×Dic11C2×C22⋊C411yescharacteristic
277C2×Dic11C2×C22⋊C411yescharacteristic
278C4×D11—22no—
279C4×D11—22no—
280C4×D11—21no—
281C4×D11—21no—
282C4×D11—21no—
283C4×D11—21no—
284C4×D11—21no—
285C4×D11—21no—
286C4×D11—21no—
287C4×D11—21no—
288C4×D11—22no—
289C4×D11—22no—
290C4×D11—41no—
291C4×D11—41no—
292C4×D11—41no—
293C4×D11—41no—
294C4×D11—44no—
295C4×D11—44no—
296Dic22—44no—
297Dic22—44no—
298Dic22—41no—
299Dic22—41no—
300Dic22—42no—
301C8×C11—42no—
302C8×C11—42no—
303C11⋊C8—42no—
304C11⋊C8—42no—
305#533—111no—
306#533—111no—
307#533—112no—
308#533—112no—
309#533—111no—
310#533—221no—
311#533—221no—
312#533—221no—
313#533—221no—
314#533C2×D1111yescharacteristic
315C2×C4⋊Q8—111no—
316C2×C4⋊Q8—111no—
317C2×#125—221no—
318C2×C22⋊Q8—112no—
319C2×C22⋊Q8—221no—
320C2×C4×Q8—112no—
321C2×C4×Q8—221no—
322C2×#117—221no—
323C22×C42—111no—
324#432—112no—
325#432—112no—
326#432—112no—
327#432—221no—
328#432—221no—
329#432—221no—
330#431—112no—
331#431—221no—
332#423—111no—
333#423C2×D1111yescharacteristic
334C2×C4⋊C8—111no—
335C2×C4⋊C8C2×D1111yescharacteristic
336#407—221no—
337C2×C22⋊C8—221no—
338C4×M16—221no—
339C2×#97—221no—
340#333—112no—
341#333—112no—
342#333—112no—
343#333C2×D1112yescomplemented
344#332—112no—
345#332—112no—
346#332—112no—
347#332C2×D1112yescomplemented
348C22×C11—21no—
349C22×C11—21no—
350C22×C11#41912yes—
351C22×C11C22×C22⋊C411yescharacteristic
352C2×D11—21no—
353C2×D11—21no—
354C2×D11—21no—
355C2×D11—21no—
356C2×D11—21no—
357C2×D11—44no—
358C2×D11#41312yes—
359C4×C11—21no—
360C4×C11—21no—
361C4×C11—21no—
362C4×C11—42no—
363C4×C11—42no—
364C4×C11#41912yes—
365C4×C11C2×#13711yescharacteristic
366C4×C11C2×#13711yescharacteristic
367C4×C11#57511yescharacteristic
368C4×C11#57511yescharacteristic
369Dic11—21no—
370Dic11—21no—
371Dic11—21no—
372Dic11—21no—
373Dic11—21no—
374Dic11—21no—
375Dic11—42no—
376Dic11—42no—
377C22×Q8—112no—
378C22×Q8—221no—
379C23×C4—111no—
380C23×C4—111no—
381C23×C4—111no—
382C2×M16—21no—
383C2×M16—221no—
384C22×C8—21no—
385C22×C8—221no—
386C4⋊Q8—112no—
387C4⋊Q8—112no—
388C4⋊Q8—111no—
389C4⋊Q8—111no—
390C4⋊Q8—221no—
391C4⋊Q8—221no—
392C4⋊Q8—221no—
393C4⋊Q8—221no—
394C4⋊Q8C22×D1111yescharacteristic
395C4⋊Q8C22×D1111yescharacteristic
396#125—21no—
397#125—222no—
398#125—222no—
399#125—221no—
400#125—221no—
401#125—221no—
402C22⋊Q8—21no—
403C22⋊Q8—112no—
404C22⋊Q8—112no—
405C22⋊Q8—112no—
406C22⋊Q8—222no—
407C22⋊Q8—222no—
408C22⋊Q8—222no—
409C22⋊Q8—222no—
410C22⋊Q8—221no—
411C22⋊Q8—221no—
412C22⋊Q8—221no—
413C22⋊Q8C4×D1112yes—
414C4×Q8—21no—
415C4×Q8—112no—
416C4×Q8—112no—
417C4×Q8—112no—
418C4×Q8—222no—
419C4×Q8—222no—
420C4×Q8—222no—
421C4×Q8—222no—
422C4×Q8—221no—
423C4×Q8—221no—
424C4×Q8—221no—
425C4×Q8C4×D1112yes—
426#117—21no—
427#117—222no—
428#117—222no—
429#117—221no—
430#117—221no—
431#117—221no—
432C2×C4⋊C4—112no—
433C2×C4⋊C4—221no—
434C2×C4⋊C4—221no—
435C2×C4⋊C4—222no—
436C2×C4⋊C4—222no—
437C2×C4⋊C4—221no—
438C2×C22⋊C4—222no—
439C2×C42—111no—
440C2×C42—111no—
441C2×C42—111no—
442C2×C42—111no—
443C2×C42—111no—
444C2×C42—111no—
445C2×C42—111no—
446C2×C42—111no—
447C2×C42—111no—
448C2×C42—111no—
449C2×C42—111no—
450C2×C42—222no—
451C2×C42C22×D1111yescharacteristic
452C4⋊C8—21no—
453C4⋊C8—21no—
454C4⋊C8—112no—
455C4⋊C8—112no—
456C4⋊C8—221no—
457C4⋊C8—221no—
458C4⋊C8C22×D1112yes—
459C4⋊C8C22×D1112yes—
460C22⋊C8—222no—
461C22⋊C8—222no—
462C22⋊C8—222no—
463C22⋊C8—222no—
464#97—222no—
465#97—222no—
466#97—222no—
467C4×C8—222no—
468C2×C11—22no—
469C2×C11C2×#41311yescharacteristic
470C2×C11C2×#41911yescharacteristic
471C2×C11#289611yescharacteristic
472D11—22no—
473D11—41no—
474C24—111no—
475C2×Q8—21no—
476C2×Q8—112no—
477C2×Q8—222no—
478C2×Q8—222no—
479C2×Q8—221no—
480C2×Q8—442no—
481C2×Q8—442no—
482C2×Q8—444no—
483C2×Q8C2×C4×D1112yes—
484C22×C4—111no—
485C22×C4—111no—
486C22×C4—111no—
487C22×C4—111no—
488C22×C4—111no—
489C22×C4—111no—
490C22×C4—111no—
491C22×C4—111no—
492C22×C4—111no—
493C22×C4—111no—
494C22×C4—111no—
495C22×C4—111no—
496C22×C4—111no—
497C22×C4—111no—
498C22×C4—111no—
499C22×C4—222no—
500C22×C4—222no—
501C22×C4—222no—
502C22×C4—222no—
503C22×C4—441no—
504C22×C4—441no—
505C22×C4—442no—
506C22×C4C2×C4×D1111yescharacteristic
507C22×C4D4×D1111yescharacteristic
508C22×C4D4×D1111yescharacteristic
509M16—42no—
510M16—442no—
511C2×C8—22no—
512C2×C8—22no—
513C2×C8—42no—
514C2×C8—222no—
515C2×C8—222no—
516C2×C8—442no—
517C4⋊C4—22no—
518C4⋊C4—22no—
519C4⋊C4—21no—
520C4⋊C4—21no—
521C4⋊C4—21no—
522C4⋊C4—112no—
523C4⋊C4—222no—
524C4⋊C4—222no—
525C4⋊C4—222no—
526C4⋊C4—222no—
527C4⋊C4—222no—
528C4⋊C4—222no—
529C4⋊C4—222no—
530C4⋊C4—222no—
531C4⋊C4—222no—
532C4⋊C4—222no—
533C4⋊C4—221no—
534C4⋊C4—221no—
535C4⋊C4—221no—
536C4⋊C4C2×C4×D1112yes—
537C22⋊C4—22no—
538C22⋊C4—222no—
539C22⋊C4—222no—
540C22⋊C4—222no—
541C42—22no—
542C42—111no—
543C42—111no—
544C42—111no—
545C42—111no—
546C42—111no—
547C42—111no—
548C42—111no—
549C42—111no—
550C42—111no—
551C42—111no—
552C42—111no—
553C42—111no—
554C42—222no—
555C42—222no—
556C42—222no—
557C42C2×C4×D1111yescharacteristic
558C42D4×D1111yescharacteristic
559C42D4×D1111yescharacteristic
560C42C23×D1111yescharacteristic
561C11#1774811yescharacteristic, complemented, Sylow
562C23—111no—
563C23—111no—
564C23—222no—
565C23—222no—
566C23—441no—
567C23C22⋊C4×D1111yescharacteristic
568Q8—42no—
569Q8—41no—
570Q8—41no—
571Q8—442no—
572Q8—444no—
573Q8—444no—
574Q8—441no—
575Q8—441no—
576C2×C4—21no—
577C2×C4—21no—
578C2×C4—22no—
579C2×C4—22no—
580C2×C4—41no—
581C2×C4—111no—
582C2×C4—111no—
583C2×C4—111no—
584C2×C4—111no—
585C2×C4—111no—
586C2×C4—111no—
587C2×C4—222no—
588C2×C4—222no—
589C2×C4—222no—
590C2×C4—221no—
591C2×C4—221no—
592C2×C4—221no—
593C2×C4—221no—
594C2×C4—221no—
595C2×C4—221no—
596C2×C4—221no—
597C2×C4—221no—
598C2×C4—222no—
599C2×C4—222no—
600C2×C4—222no—
601C2×C4—222no—
602C2×C4—441no—
603C2×C4—441no—
604C2×C4—441no—
605C2×C4—441no—
606C2×C4—444no—
607C2×C4—444no—
608C2×C4—441no—
609C2×C4—441no—
610C2×C4C22⋊C4×D1111yescharacteristic
611C2×C4C22⋊C4×D1111yescharacteristic
612C2×C4C22⋊C4×D1111yescharacteristic
613C2×C4#6696812yes—
614C2×C4#6697112yes—
615C2×C4C22×C4×D1111yescharacteristic
616C2×C4C2×D4×D1111yescharacteristic
617C2×C4C2×D4×D1111yescharacteristic
618C8—42no—
619C8—42no—
620C8—442no—
621C8—442no—
622C22—21no—
623C22—21no—
624C22—112no—
625C22—221no—
626C22—221no—
627C22—221no—
628C22—221no—
629C22—221no—
630C22—444no—
631C22#1062241512yes—
632C22C2×C22⋊C4×D1111yescharacteristic
633C4—21no—
634C4—21no—
635C4—21no—
636C4—42no—
637C4—42no—
638C4—221no—
639C4—221no—
640C4—221no—
641C4—221no—
642C4—221no—
643C4—221no—
644C4—442no—
645C4—442no—
646C4#1062241512yes—
647C4C2×#6696811yescharacteristic
648C4C2×#6697111yescharacteristic
649C4#1062330411yescharacteristic
650C4#1062330811yescharacteristic
651C2—22no—
652C2—222no—
653C2—441no—
654C2D11×#41311yescharacteristic
655C2C2×#1062241511yescharacteristic
656C2#1307713211yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×#1550C2
socleC22×C11C22×C22⋊C4
prime radicalC23×D11C22⋊C4
cosocleC42×C11C24
hypercenter#1550D11
hypocenterC11#17748
LCSG ▷ C2×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1550

Complements

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

NH ≅ G/Ntype
4. #13067340C2semidirect
5. #13067331C2semidirect
6. #13067325C2semidirect
7. #13067323C2semidirect
8. #13067307C2semidirect
9. #13067306C2semidirect
10. #13067304C2semidirect
11. C11×#1550C2semidirect
47. C11×#333C22semidirect
48. C11×#332C22semidirect
49. #10622185C22semidirect
50. #10622184C22semidirect
51. #10622124C22semidirect
52. #10622120C22semidirect
53. #10622119C22semidirect
54. #10622119C22semidirect
244. #1550D11semidirect
343. #333C2×D11semidirect
347. #332C2×D11semidirect
561. C11#17748semidirect

Maximal subgroups

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

subgroupindex
D11×#5332
#130772482
C2×#106224482
#130673402
#130673312
#130673252
#130673232
#130673072
#130673062
#130673042
C11×#15502
#1774811