Finite Group Databasebeta

← #14722175

Subgroups — #14722175

Order 2816.

972 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
3D11×#431C211yesmaximal, characteristic
4#13067315C212yesmaximal, complemented
5#13067313C212yesmaximal, complemented
6#13067299C212yesmaximal, complemented
7#13067286C212yesmaximal, complemented
8#13067281C211yesmaximal, characteristic, complemented
9#13067280C211yesmaximal, characteristic, complemented
10#13067280C211yesmaximal, characteristic, complemented
11C11×#1544C211yesmaximal, characteristic, complemented
12C11×#533C2211yescharacteristic
13#10623259C2211yescharacteristic
14#10623259C2211yescharacteristic
15D11×C4⋊Q8C2211yescharacteristic
16D11×C4⋊Q8C2211yescharacteristic
17#10623219C412yes—
18D11×#125C412yes—
19D11×C22⋊Q8—21no—
20D11×C22⋊Q8—21no—
21#10623153—21no—
22#10623153—21no—
23#10623109—21no—
24#10623109—21no—
25C4×Q8×D11—21no—
26C4×Q8×D11—21no—
27D11×#117C412yes—
28#10623048C412yes—
29C2×C42×D11C2211yescharacteristic
30#10623001C2211yescharacteristic
31C11×#431C2211yescharacteristic
32C11×#431C2211yescharacteristic
33#10622538C2211yescharacteristic
34#10622538C2211yescharacteristic
35#10622450C2212yes—
36#10622448C2212yes—
37#10622446C2212yes—
38D11×C4⋊C8C2212yes—
39#10622339—21no—
40D11×C22⋊C8—21no—
41#10622332—21no—
42#10622331—21no—
43C4×#4313—21no—
44#10622298—21no—
45#10622298—21no—
46C4×C8×D11—21no—
47C11×#332C2212yescomplemented
48C11×#332C2212yescomplemented
49#10622185C2212yescomplemented
50#10622185C2212yescomplemented
51#10622124C2212yescomplemented
52#10622124C2212yescomplemented
53#10622120C2212yescomplemented
54#10622120C2212yescomplemented
55C2×Q8×D11—21no—
56C2×Q8×D11—21no—
57C22×C4×D11C2×C411yescharacteristic
58C22×C4×D11D411yescharacteristic
59C22×C4×D11D411yescharacteristic
60C11×C4⋊Q8C2311yescharacteristic
61C11×C4⋊Q8C2311yescharacteristic
62C11×#125C2×C412yes—
63C11×C22⋊Q8—21no—
64C11×C22⋊Q8—21no—
65C4×Q8×C11—21no—
66C4×Q8×C11—21no—
67C11×#117C2×C412yes—
68C2×C42×C11C2311yescharacteristic
69#66999—21no—
70#66999—21no—
71Q8×Dic11—21no—
72Q8×Dic11—21no—
73#66997—21no—
74#66997—21no—
75#66979C2×C412yes—
76#66977—21no—
77#66977—21no—
78C2×C4×Dic11C2×C411yescharacteristic
79C2×C4×Dic11D411yescharacteristic
80C2×C4×Dic11D411yescharacteristic
81C2×#4313—22no—
82C2×C8×D11—22no—
83#66950—21no—
84#66950—21no—
85#66949—22no—
86#66949—22no—
87#66945C2×C412yes—
88#66945C2×C412yes—
89C4⋊C4×D11—22no—
90C4⋊C4×D11—22no—
91C4⋊C4×D11—21no—
92C4⋊C4×D11—21no—
93C4⋊C4×D11C2×C412yes—
94C4⋊C4×D11C2×C412yes—
95#66943C2×C412yes—
96#66943C2×C412yes—
97#66942—22no—
98#66942—22no—
99#66941—21no—
100#66941—21no—
101#66941C2×C412yes—
102#66941C2×C412yes—
103#66940—22no—
104#66940—22no—
105#66940—21no—
106#66940—21no—
107C22⋊C4×D11—22no—
108#66931—22no—
109#66931—22no—
110#66930—22no—
111#66925—22no—
112C42×D11—22no—
113C42×D11C2×C411yescharacteristic
114C42×D11C2×C411yescharacteristic
115C42×D11D411yescharacteristic
116C42×D11D411yescharacteristic
117C42×D11D411yescharacteristic
118C42×D11D411yescharacteristic
119C42×D11C2311yescharacteristic
120C42×D11C2311yescharacteristic
121#66923C2×C412yes—
122#66922C2311yescharacteristic
123#66922C2311yescharacteristic
124C4×Dic22—21no—
125C4×Dic22—21no—
126C4×Dic22—22no—
127C4×Dic22—22no—
128C11×C4⋊C8C2312yes—
129C11×C4⋊C8C2312yes—
130C11×C22⋊C8—21no—
131C11×C22⋊C8—21no—
132C4×C8×C11—21no—
133C4×C8×C11—21no—
134C22⋊(C11⋊C8)—21no—
135C22⋊(C11⋊C8)—21no—
136(C2×D11)⋊C8—22no—
137(C2×D11)⋊C8—22no—
138#66879—22no—
139Dic11⋊C8—22no—
140Dic11⋊C8—22no—
141C8×Dic11—22no—
142C4⋊(C11⋊C8)C2312yes—
143C4⋊(C11⋊C8)C2312yes—
144C4×C11⋊C8—21no—
145C4×C11⋊C8—21no—
146#17715—111nomaximal, Sylow
147C23×D11C22⋊C411yescharacteristic
148C2×Q8×C11—21no—
149C2×Q8×C11—21no—
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—44no—
158C2×C4×D11—24no—
159C2×C4×D11—24no—
160C2×C4×D11—22no—
161C2×C4×D11—22no—
162C2×C4×D11—42no—
163C2×C4×D11C22⋊C411yescharacteristic
164C2×C4×D11C22⋊C411yescharacteristic
165C2×C4×D11C22⋊C411yescharacteristic
166C2×C4×D11C22⋊C411yescharacteristic
167C2×C4×D11C22⋊C411yescharacteristic
168C2×C4×D11C22⋊C411yescharacteristic
169C2×C4×D11C22×C411yescharacteristic
170C2×C4×D11C22×C411yescharacteristic
171C2×C4×D11C2×D411yescharacteristic
172C2×C4×D11C2×D411yescharacteristic
173C2×C4×D11C2×D411yescharacteristic
174C2×C4×D11C2×D411yescharacteristic
175C2×Dic22—22no—
176C2×Dic22—22no—
177C2×Dic22—21no—
178C2×Dic22—21no—
179C2×C8×C11—22no—
180C2×C8×C11—22no—
181C11×C4⋊C4—22no—
182C11×C4⋊C4—22no—
183C11×C4⋊C4—21no—
184C11×C4⋊C4—21no—
185C11×C4⋊C4C22×C412yes—
186C11×C4⋊C4C22×C412yes—
187C11×C22⋊C4—22no—
188C42×C11—22no—
189C42×C11C22×C411yescharacteristic
190C42×C11C2×D411yescharacteristic
191C42×C11C2×D411yescharacteristic
192C42×C11C2411yescharacteristic
193C22⋊Dic11—22no—
194(C2×D11)⋊C4—22no—
195(C2×D11)⋊C4—22no—
196C4⋊Dic11—22no—
197C4⋊Dic11—22no—
198C4⋊Dic11—21no—
199C4⋊Dic11—21no—
200C4⋊Dic11C22×C412yes—
201C4⋊Dic11C22×C412yes—
202Dic11⋊C4—22no—
203Dic11⋊C4—22no—
204Dic11⋊C4—22no—
205Dic11⋊C4—22no—
206Dic11⋊C4—22no—
207Dic11⋊C4—22no—
208Dic11⋊C4—22no—
209Dic11⋊C4—22no—
210C4×Dic11—22no—
211C4×Dic11—22no—
212C4×Dic11—22no—
213C4×Dic11C22⋊C411yescharacteristic
214C4×Dic11C22⋊C411yescharacteristic
215C4×Dic11C22⋊C411yescharacteristic
216C4×Dic11C22⋊C411yescharacteristic
217C4×Dic11C22⋊C411yescharacteristic
218C4×Dic11C22⋊C411yescharacteristic
219C4×Dic11C22×C411yescharacteristic
220C4×Dic11C22×C411yescharacteristic
221C4×Dic11C2×D411yescharacteristic
222C4×Dic11C2×D411yescharacteristic
223C4×Dic11C2×D411yescharacteristic
224C4×Dic11C2×D411yescharacteristic
225C2×C11⋊C8—22no—
226C2×C11⋊C8—22no—
227#4313—44no—
228C8×D11—44no—
229C2×#533—111no—
230#2920—111no—
231C2×#431—111no—
232#1552—112no—
233#1552—112no—
234#1549—112no—
235#1546—112no—
236#1544—111no—
237#1544—111no—
238#1544—111no—
239#1544D1111yescharacteristic, complemented
240C23×C11C2×C22⋊C411yescharacteristic
241C22×D11—22no—
242C22×D11—22no—
243C22×D11—41no—
244C22×D11C2×C22⋊C411yescharacteristic
245C22×D11C2×C22⋊C411yescharacteristic
246Q8×C11—42no—
247Q8×C11—42no—
248C2×C4×C11—22no—
249C2×C4×C11—22no—
250C2×C4×C11—22no—
251C2×C4×C11—22no—
252C2×C4×C11—22no—
253C2×C4×C11C2×C22⋊C411yescharacteristic
254C2×C4×C11C2×C22⋊C411yescharacteristic
255C2×C4×C11C2×C22⋊C411yescharacteristic
256C2×C4×C11C23×C411yescharacteristic
257C2×C4×C11C22×D411yescharacteristic
258C2×C4×C11C22×D411yescharacteristic
259C2×Dic11—22no—
260C2×Dic11—22no—
261C2×Dic11—22no—
262C2×Dic11—22no—
263C2×Dic11—41no—
264C2×Dic11C2×C22⋊C411yescharacteristic
265C2×Dic11C2×C22⋊C411yescharacteristic
266C2×Dic11C2×C22⋊C411yescharacteristic
267C2×Dic11C2×C22⋊C411yescharacteristic
268C2×Dic11C2×C22⋊C411yescharacteristic
269C2×Dic11C2×C22⋊C411yescharacteristic
270C4×D11—22no—
271C4×D11—22no—
272C4×D11—22no—
273C4×D11—22no—
274C4×D11—22no—
275C4×D11—22no—
276C4×D11—22no—
277C4×D11—22no—
278C4×D11—41no—
279C4×D11—41no—
280C4×D11—44no—
281C4×D11—44no—
282C4×D11#10114yes—
283C4×D11#13514yes—
284Dic22—44no—
285Dic22—42no—
286Dic22—42no—
287Dic22—44no—
288C8×C11—42no—
289C8×C11—42no—
290C11⋊C8—42no—
291C11⋊C8—42no—
292#533—111no—
293#533—111no—
294#533—112no—
295#533—112no—
296#533—111no—
297#533—221no—
298#533—221no—
299#533—221no—
300#533—221no—
301#533C2×D1111yescharacteristic
302C2×C4⋊Q8—111no—
303C2×C4⋊Q8—111no—
304C2×#125—112no—
305C2×C22⋊Q8—221no—
306C2×C22⋊Q8—221no—
307C2×C4×Q8—221no—
308C2×C4×Q8—221no—
309C2×#117—112no—
310C22×C42—111no—
311#432—112no—
312#432—221no—
313#431—111no—
314#431—111no—
315#431—112no—
316#431—221no—
317#431—221no—
318#431—221no—
319#431C2×D1111yescharacteristic
320#431C2×D1111yescharacteristic
321#423—112no—
322C2×C4⋊C8—112no—
323#407—221no—
324C2×C22⋊C8—221no—
325C4×M16—221no—
326C2×C4×C8—221no—
327#332—112no—
328#332—112no—
329#332—112no—
330#332—112no—
331#332—112no—
332#332—112no—
333#332C2×D1112yescomplemented
334#332C2×D1112yescomplemented
335C22×C11—21no—
336C22×C11—21no—
337C22×C11—21no—
338C22×C11C22×C22⋊C411yescharacteristic
339C2×D11—21no—
340C2×D11—21no—
341C2×D11—21no—
342C2×D11—21no—
343C2×D11—44no—
344C2×D11C2×#10112yes—
345C2×D11#41612yes—
346C4×C11—21no—
347C4×C11—21no—
348C4×C11—21no—
349C4×C11—42no—
350C4×C11—42no—
351C4×C11C2×#10112yes—
352C4×C11C2×#13512yes—
353C4×C11#57512yes—
354Dic11—21no—
355Dic11—21no—
356Dic11—21no—
357Dic11—21no—
358Dic11—42no—
359Dic11—42no—
360Dic11C2×#10112yes—
361Dic11#41612yes—
362C22×Q8—221no—
363C22×Q8—221no—
364C23×C4—111no—
365C23×C4—111no—
366C23×C4—111no—
367C2×M16—222no—
368C22×C8—222no—
369C4⋊Q8—112no—
370C4⋊Q8—112no—
371C4⋊Q8—111no—
372C4⋊Q8—111no—
373C4⋊Q8—221no—
374C4⋊Q8—221no—
375C4⋊Q8—221no—
376C4⋊Q8—221no—
377C4⋊Q8C22×D1111yescharacteristic
378C4⋊Q8C22×D1111yescharacteristic
379#125—112no—
380#125—112no—
381#125—112no—
382#125—222no—
383#125—222no—
384#125C4×D1112yes—
385C22⋊Q8—21no—
386C22⋊Q8—21no—
387C22⋊Q8—222no—
388C22⋊Q8—222no—
389C22⋊Q8—222no—
390C22⋊Q8—222no—
391C22⋊Q8—221no—
392C22⋊Q8—221no—
393C22⋊Q8—221no—
394C22⋊Q8—221no—
395C22⋊Q8—221no—
396C22⋊Q8—221no—
397C4×Q8—21no—
398C4×Q8—21no—
399C4×Q8—222no—
400C4×Q8—222no—
401C4×Q8—222no—
402C4×Q8—222no—
403C4×Q8—221no—
404C4×Q8—221no—
405C4×Q8—221no—
406C4×Q8—221no—
407C4×Q8—221no—
408C4×Q8—221no—
409#117—112no—
410#117—112no—
411#117—112no—
412#117—222no—
413#117—222no—
414#117C4×D1112yes—
415C2×C4⋊C4—112no—
416C2×C4⋊C4—112no—
417C2×C4⋊C4—222no—
418C2×C4⋊C4—222no—
419C2×C4⋊C4—221no—
420C2×C4⋊C4—221no—
421C2×C22⋊C4—222no—
422C2×C42—111no—
423C2×C42—111no—
424C2×C42—111no—
425C2×C42—111no—
426C2×C42—111no—
427C2×C42—111no—
428C2×C42—111no—
429C2×C42—111no—
430C2×C42—111no—
431C2×C42—111no—
432C2×C42—111no—
433C2×C42—222no—
434C2×C42C22×D1111yescharacteristic
435C4⋊C8—112no—
436C4⋊C8—112no—
437C4⋊C8—222no—
438C4⋊C8—222no—
439C4⋊C8C22×D1112yes—
440C4⋊C8C22×D1112yes—
441C22⋊C8—21no—
442C22⋊C8—21no—
443C22⋊C8—222no—
444C22⋊C8—222no—
445C22⋊C8—221no—
446C22⋊C8—221no—
447#97—222no—
448C4×C8—21no—
449C4×C8—21no—
450C4×C8—222no—
451C4×C8—221no—
452C4×C8—221no—
453C2×C11—41no—
454C2×C11C22×#10111yescharacteristic
455C2×C11C2×#41611yescharacteristic
456C2×C11#289611yescharacteristic
457D11—22no—
458D11—22no—
459C24—111no—
460C2×Q8—21no—
461C2×Q8—21no—
462C2×Q8—222no—
463C2×Q8—222no—
464C2×Q8—221no—
465C2×Q8—221no—
466C2×Q8—444no—
467C2×Q8—444no—
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—111no—
478C22×C4—111no—
479C22×C4—111no—
480C22×C4—111no—
481C22×C4—111no—
482C22×C4—111no—
483C22×C4—224no—
484C22×C4—224no—
485C22×C4—222no—
486C22×C4—222no—
487C22×C4—442no—
488C22×C4C2×C4×D1111yescharacteristic
489C22×C4D4×D1111yescharacteristic
490C22×C4D4×D1111yescharacteristic
491M16—444no—
492C2×C8—22no—
493C2×C8—22no—
494C2×C8—222no—
495C2×C8—222no—
496C2×C8—444no—
497C4⋊C4—22no—
498C4⋊C4—22no—
499C4⋊C4—21no—
500C4⋊C4—21no—
501C4⋊C4—112no—
502C4⋊C4—112no—
503C4⋊C4—222no—
504C4⋊C4—222no—
505C4⋊C4—222no—
506C4⋊C4—222no—
507C4⋊C4—222no—
508C4⋊C4—222no—
509C4⋊C4—222no—
510C4⋊C4—222no—
511C4⋊C4—222no—
512C4⋊C4—222no—
513C4⋊C4—221no—
514C4⋊C4—221no—
515C4⋊C4C2×C4×D1112yes—
516C4⋊C4C2×C4×D1112yes—
517C22⋊C4—22no—
518C22⋊C4—222no—
519C22⋊C4—222no—
520C22⋊C4—222no—
521C42—22no—
522C42—111no—
523C42—111no—
524C42—111no—
525C42—111no—
526C42—111no—
527C42—111no—
528C42—111no—
529C42—111no—
530C42—111no—
531C42—111no—
532C42—111no—
533C42—111no—
534C42—222no—
535C42—222no—
536C42—222no—
537C42C2×C4×D1111yescharacteristic
538C42D4×D1111yescharacteristic
539C42D4×D1111yescharacteristic
540C42C23×D1111yescharacteristic
541C11#1771511yescharacteristic, complemented, Sylow
542C23—111no—
543C23—111no—
544C23—222no—
545C23—222no—
546C23—441no—
547C23C22⋊C4×D1111yescharacteristic
548Q8—42no—
549Q8—42no—
550Q8—444no—
551Q8—444no—
552Q8—442no—
553Q8—442no—
554C2×C4—22no—
555C2×C4—22no—
556C2×C4—22no—
557C2×C4—22no—
558C2×C4—22no—
559C2×C4—111no—
560C2×C4—111no—
561C2×C4—114no—
562C2×C4—114no—
563C2×C4—111no—
564C2×C4—111no—
565C2×C4—111no—
566C2×C4—111no—
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—222no—
579C2×C4—441no—
580C2×C4—441no—
581C2×C4—444no—
582C2×C4—444no—
583C2×C4—441no—
584C2×C4C22⋊C4×D1111yescharacteristic
585C2×C4C22⋊C4×D1111yescharacteristic
586C2×C4C22⋊C4×D1111yescharacteristic
587C2×C4C22×C4×D1111yescharacteristic
588C2×C4C2×D4×D1111yescharacteristic
589C2×C4C2×D4×D1111yescharacteristic
590C8—42no—
591C8—42no—
592C8—442no—
593C8—442no—
594C22—21no—
595C22—21no—
596C22—21no—
597C22—112no—
598C22—112no—
599C22—221no—
600C22—221no—
601C22—221no—
602C22—221no—
603C22—444no—
604C22C2×C22⋊C4×D1111yescharacteristic
605C4—21no—
606C4—21no—
607C4—21no—
608C4—42no—
609C4—42no—
610C4—112no—
611C4—112no—
612C4—221no—
613C4—221no—
614C4—221no—
615C4—221no—
616C4—442no—
617C4—442no—
618C4D11×#10112yes—
619C4D11×#13512yes—
620C4#1062329912yes—
621C2—41no—
622C2—222no—
623C2—222no—
624C2C2×D11×#10111yescharacteristic
625C2D11×#41611yescharacteristic
626C2#1307713111yescharacteristic
subgroupG/H
centerC2×C4C22⋊C4×D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×#1544C2
socleC22×C11C22×C22⋊C4
prime radicalC23×D11C22⋊C4
cosocleC42×C11C24
hypercenter#1544D11
hypocenterC11#17715
LCSG ▷ C2×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1544

Complements

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

NH ≅ G/Ntype
4. #13067315C2semidirect
5. #13067313C2semidirect
6. #13067299C2semidirect
7. #13067286C2semidirect
8. #13067281C2semidirect
9. #13067280C2semidirect
10. #13067280C2semidirect
11. C11×#1544C2semidirect
47. C11×#332C22semidirect
48. C11×#332C22semidirect
49. #10622185C22semidirect
50. #10622185C22semidirect
51. #10622124C22semidirect
52. #10622124C22semidirect
53. #10622120C22semidirect
54. #10622120C22semidirect
239. #1544D11semidirect
333. #332C2×D11semidirect
334. #332C2×D11semidirect
541. C11#17715semidirect

Maximal subgroups

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

subgroupindex
D11×#5332
#130772442
D11×#4312
#130673152
#130673132
#130672992
#130672862
#130672812
#130672802
C11×#15442
#1771511