Finite Group Databasebeta

← C11×#24048 #14601241

Subgroups — C11×#24048 #14601241

Order 2816.

1492 conjugacy classes of subgroups.

The subgroup lattice has 652 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#546C211yesmaximal, characteristic
2C2×C11×#481C211yesmaximal, characteristic, complemented
3C2×C11×#417C211yesmaximal, characteristic, complemented
4C11×#2486C211yesmaximal, characteristic, complemented
5C11×#2042C212yesmaximal, complemented
6C11×#2035C212yesmaximal, complemented
7C11×#1895C211yesmaximal, characteristic, complemented
8C11×#1870C211yesmaximal, characteristic, complemented
9C11×#1864C212yesmaximal, complemented
10C11×#1788C211yesmaximal, characteristic, complemented
11C11×#1786C212yesmaximal, complemented
12C22×C11×#41C2211yescharacteristic
13C23×D4×C11C2211yescharacteristic
14C22×C11×M16C2211yescharacteristic, complemented
15C11×#546—24no—
16C11×#546—24no—
17C2×C11×#124C2211yescharacteristic
18C2×C11×#123—21no—
19C2×C11×#123—21no—
20C2×C11×C22⋊Q8C2211yescharacteristic
21C2×C11×#121—21no—
22C2×C11×#121C2211yescharacteristic
23C2×C11×#120—21no—
24C2×C4×D4×C11C2211yescharacteristic
25C2×C4×D4×C11C2211yescharacteristic
26C22×C11×C4⋊C4C2211yescharacteristic, complemented
27C22×C11×C22⋊C4—21no—
28C11×#481—24no—
29C2×C11×#106C2212yescomplemented
30C11×#417—24no—
31C2×C11×#103C2212yescomplemented
32C2×C11×#103C2212yescomplemented
33C2×C11×#102C2212yes—
34C2×C11×#102C2212yes—
35C2×C11×#102C2212yes—
36C2×C11×#102C2212yes—
37C2×C11×C22⋊C8C2212yes—
38C2×C11×C22⋊C8C2211yescharacteristic, complemented
39C11×#398—21no—
40C11×#397—21no—
41C11×#389C2212yescomplemented
42C11×#381—21no—
43C11×#380C2212yes—
44C11×#380C2211yescharacteristic, complemented
45C11×#340C2212yescomplemented
46C11×#336C2212yescomplemented
47C25×C11—21no—
48C2×C11×#41—22no—
49C2×C11×#41—24no—
50C2×C11×#41—42no—
51C2×C11×#41D414yes—
52C22×Q8×C11C2311yescharacteristic
53C22×D4×C11—21no—
54C22×D4×C11—21no—
55C22×D4×C11—22no—
56C22×D4×C11—22no—
57C22×D4×C11—24no—
58C22×D4×C11—21no—
59C22×D4×C11—42no—
60C22×D4×C11D411yescharacteristic
61C22×D4×C11C2311yescharacteristic
62C22×D4×C11C2311yescharacteristic
63C23×C4×C11—21no—
64C23×C4×C11—21no—
65C23×C4×C11—21no—
66C23×C4×C11C2311yescharacteristic
67C23×C4×C11C2311yescharacteristic
68C2×C11×M16—22no—
69C2×C11×M16—42no—
70C22×C8×C11C2312yes—
71C22×C8×C11C2312yes—
72C11×#124—22no—
73C11×#124—22no—
74C11×#123—28no—
75C11×#123—44no—
76C11×C22⋊Q8—22no—
77C11×C22⋊Q8—22no—
78C11×#121—28no—
79C11×#121—22no—
80C11×#121D414yes—
81C11×#120—28no—
82C4×D4×C11—22no—
83C4×D4×C11—22no—
84C4×D4×C11—22no—
85C4×D4×C11—22no—
86C2×C11×C4⋊C4—21no—
87C2×C11×C4⋊C4—22no—
88C2×C11×C4⋊C4—22no—
89C2×C11×C4⋊C4—21no—
90C2×C11×C4⋊C4—22no—
91C2×C11×C4⋊C4D411yescharacteristic
92C2×C11×C4⋊C4C2312yes—
93C2×C11×C4⋊C4C2312yes—
94C2×C11×C4⋊C4C2311yescharacteristic
95C2×C11×C22⋊C4—28no—
96C2×C11×C22⋊C4—21no—
97C2×C11×C22⋊C4—21no—
98C2×C11×C22⋊C4—21no—
99C2×C11×C22⋊C4—21no—
100C2×C11×C22⋊C4—21no—
101C2×C11×C22⋊C4—22no—
102C2×C11×C22⋊C4—21no—
103C2×C11×C22⋊C4D411yescharacteristic
104C2×C11×C22⋊C4D411yescharacteristic
105C2×C42×C11C2311yescharacteristic
106C11×#106—24no—
107C11×#103—24no—
108C11×#103—42no—
109C11×#102—24no—
110C11×#102—24no—
111C11×#102—24no—
112C11×#102—42no—
113C11×C22⋊C8—22no—
114C11×C22⋊C8—42no—
115C11×#95—22no—
116C11×#95—21no—
117C11×#95—22no—
118#24048C1111yesmaximal, characteristic, direct product factor, Sylow
119C24×C11—21no—
120C24×C11—24no—
121C24×C11—21no—
122C24×C11—44no—
123C24×C11—42no—
124C24×C11—42no—
125C24×C11—82no—
126C24×C11C2×D411yescharacteristic
127C24×C11C2×D411yescharacteristic
128C11×#41—28no—
129C11×#41—44no—
130C11×#41—48no—
131C2×Q8×C11—21no—
132C2×Q8×C11—22no—
133C2×Q8×C11—22no—
134C2×Q8×C11C2×D412yes—
135C2×D4×C11—24no—
136C2×D4×C11—22no—
137C2×D4×C11—24no—
138C2×D4×C11—22no—
139C2×D4×C11—24no—
140C2×D4×C11—21no—
141C2×D4×C11—21no—
142C2×D4×C11—22no—
143C2×D4×C11—22no—
144C2×D4×C11—22no—
145C2×D4×C11—41no—
146C2×D4×C11—44no—
147C2×D4×C11—48no—
148C2×D4×C11—44no—
149C2×D4×C11—44no—
150C2×D4×C11—44no—
151C2×D4×C11—82no—
152C2×D4×C11C2×D412yes—
153C2×D4×C11C2×D412yes—
154C2×D4×C11#4114yes—
155C22×C4×C11—22no—
156C22×C4×C11—22no—
157C22×C4×C11—21no—
158C22×C4×C11—21no—
159C22×C4×C11—24no—
160C22×C4×C11—24no—
161C22×C4×C11—21no—
162C22×C4×C11—21no—
163C22×C4×C11—22no—
164C22×C4×C11—22no—
165C22×C4×C11—22no—
166C22×C4×C11—22no—
167C22×C4×C11—44no—
168C22×C4×C11—42no—
169C22×C4×C11—42no—
170C22×C4×C11—42no—
171C22×C4×C11—82no—
172C22×C4×C11C2×D411yescharacteristic
173C22×C4×C11C2×D411yescharacteristic
174C22×C4×C11C2×D411yescharacteristic
175C22×C4×C11C2×D411yescharacteristic
176C22×C4×C11C2×D412yes—
177C22×C4×C11C2×D412yes—
178C22×C4×C11C2411yescharacteristic
179C11×M16—44no—
180C2×C8×C11—22no—
181C2×C8×C11—22no—
182C2×C8×C11—22no—
183C2×C8×C11—22no—
184C2×C8×C11—22no—
185C2×C8×C11—22no—
186C11×C4⋊C4—24no—
187C11×C4⋊C4—22no—
188C11×C4⋊C4—21no—
189C11×C4⋊C4—22no—
190C11×C4⋊C4—22no—
191C11×C4⋊C4—22no—
192C11×C4⋊C4—22no—
193C11×C4⋊C4—44no—
194C11×C4⋊C4—42no—
195C11×C4⋊C4C2×D412yes—
196C11×C22⋊C4—24no—
197C11×C22⋊C4—24no—
198C11×C22⋊C4—24no—
199C11×C22⋊C4—24no—
200C11×C22⋊C4—22no—
201C11×C22⋊C4—22no—
202C11×C22⋊C4—24no—
203C11×C22⋊C4—42no—
204C11×C22⋊C4—44no—
205C42×C11—21no—
206C42×C11—21no—
207C2×#546C2×C1111yescharacteristic
208C2×#481C2×C1111yescharacteristic, complemented
209C2×#417C2×C1111yescharacteristic, complemented
210#2486C2×C1111yescharacteristic, complemented
211#2042C2×C1112yescomplemented
212#2035C2×C1112yescomplemented
213#1895C2×C1111yescharacteristic, complemented
214#1870C2×C1111yescharacteristic, complemented
215#1864C2×C1112yescomplemented
216#1788C2×C1111yescharacteristic, complemented
217#1786C2×C1112yescomplemented
218C23×C11—21no—
219C23×C11—22no—
220C23×C11—22no—
221C23×C11—22no—
222C23×C11—24no—
223C23×C11—21no—
224C23×C11—21no—
225C23×C11—21no—
226C23×C11—22no—
227C23×C11—22no—
228C23×C11—22no—
229C23×C11—48no—
230C23×C11—48no—
231C23×C11—41no—
232C23×C11—41no—
233C23×C11—42no—
234C23×C11—42no—
235C23×C11—41no—
236C23×C11—41no—
237C23×C11—42no—
238C23×C11—88no—
239C23×C11—84no—
240C23×C11—88no—
241C23×C11#12012yes—
242C23×C11AGL(1,ℤ/8)12yes—
243C23×C11C22×D411yescharacteristic
244Q8×C11—22no—
245Q8×C11—22no—
246Q8×C11—42no—
247D4×C11—22no—
248D4×C11—24no—
249D4×C11—24no—
250D4×C11—44no—
251D4×C11—48no—
252D4×C11—48no—
253D4×C11—41no—
254D4×C11—41no—
255D4×C11—84no—
256D4×C11#12314yescomplemented
257C2×C4×C11—22no—
258C2×C4×C11—22no—
259C2×C4×C11—22no—
260C2×C4×C11—24no—
261C2×C4×C11—21no—
262C2×C4×C11—21no—
263C2×C4×C11—22no—
264C2×C4×C11—22no—
265C2×C4×C11—21no—
266C2×C4×C11—22no—
267C2×C4×C11—21no—
268C2×C4×C11—21no—
269C2×C4×C11—22no—
270C2×C4×C11—48no—
271C2×C4×C11—42no—
272C2×C4×C11—42no—
273C2×C4×C11—41no—
274C2×C4×C11—41no—
275C2×C4×C11—42no—
276C2×C4×C11—42no—
277C2×C4×C11—42no—
278C2×C4×C11—42no—
279C2×C4×C11—42no—
280C2×C4×C11—42no—
281C2×C4×C11—42no—
282C2×C4×C11—84no—
283C2×C4×C11—84no—
284C2×C4×C11#12012yes—
285C2×C4×C11C22×D411yescharacteristic
286C2×C4×C11C22×D411yescharacteristic
287C2×C4×C11C2×#4112yes—
288C2×C4×C11H(5,𝔽2)12yes—
289C8×C11—42no—
290C8×C11—42no—
291C22×#41C22×C1111yescharacteristic
292C23×D4C22×C1111yescharacteristic
293C22×M16C22×C1111yescharacteristic, complemented
294#546—24no—
295#546—24no—
296C2×#124C22×C1111yescharacteristic
297C2×#123—21no—
298C2×#123—21no—
299C2×C22⋊Q8C22×C1111yescharacteristic
300C2×#121—21no—
301C2×#121C22×C1111yescharacteristic
302C2×#120—21no—
303C2×C4×D4C22×C1111yescharacteristic
304C2×C4×D4C22×C1111yescharacteristic
305C22×C4⋊C4C22×C1111yescharacteristic, complemented
306C22×C22⋊C4—21no—
307#481—24no—
308C2×#106C22×C1112yescomplemented
309#417—24no—
310C2×#103C22×C1112yescomplemented
311C2×#103C22×C1112yescomplemented
312C2×#102C22×C1112yes—
313C2×#102C22×C1112yes—
314C2×#102C22×C1112yes—
315C2×#102C22×C1112yes—
316C2×C22⋊C8C22×C1112yes—
317C2×C22⋊C8C22×C1111yescharacteristic, complemented
318#398—21no—
319#397—21no—
320#389C22×C1112yescomplemented
321#381—21no—
322#380C22×C1112yes—
323#380C22×C1111yescharacteristic, complemented
324#340C22×C1112yescomplemented
325#336C22×C1112yescomplemented
326C22×C11—22no—
327C22×C11—24no—
328C22×C11—22no—
329C22×C11—22no—
330C22×C11—22no—
331C22×C11—24no—
332C22×C11—41no—
333C22×C11—42no—
334C22×C11—42no—
335C22×C11—41no—
336C22×C11—42no—
337C22×C11—44no—
338C22×C11—42no—
339C22×C11—42no—
340C22×C11—44no—
341C22×C11—42no—
342C22×C11—42no—
343C22×C11—42no—
344C22×C11—816no—
345C22×C11—82no—
346C22×C11—82no—
347C22×C11C2×#12011yescharacteristic
348C22×C11#54612yes—
349C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
350C22×C11#57511yescharacteristic
351C22×C11#57712yes—
352C4×C11—22no—
353C4×C11—41no—
354C4×C11—42no—
355C4×C11—41no—
356C4×C11—41no—
357C4×C11—42no—
358C4×C11—82no—
359C4×C11—82no—
360C4×C11C2×#12311yescharacteristic
361C4×C11#53411yescharacteristic
362C4×C11#54612yes—
363C25—21no—
364C2×#41—22no—
365C2×#41—24no—
366C2×#41—42no—
367C2×#41D4×C1114yes—
368C22×Q8C23×C1111yescharacteristic
369C22×D4—21no—
370C22×D4—21no—
371C22×D4—22no—
372C22×D4—22no—
373C22×D4—24no—
374C22×D4—21no—
375C22×D4—42no—
376C22×D4D4×C1111yescharacteristic
377C22×D4C23×C1111yescharacteristic
378C22×D4C23×C1111yescharacteristic
379C23×C4—21no—
380C23×C4—21no—
381C23×C4—21no—
382C23×C4C23×C1111yescharacteristic
383C23×C4C23×C1111yescharacteristic
384C2×M16—22no—
385C2×M16—42no—
386C22×C8C23×C1112yes—
387C22×C8C23×C1112yes—
388#124—22no—
389#124—22no—
390#123—28no—
391#123—44no—
392C22⋊Q8—22no—
393C22⋊Q8—22no—
394#121—28no—
395#121—22no—
396#121D4×C1114yes—
397#120—28no—
398C4×D4—22no—
399C4×D4—22no—
400C4×D4—22no—
401C4×D4—22no—
402C2×C4⋊C4—21no—
403C2×C4⋊C4—22no—
404C2×C4⋊C4—22no—
405C2×C4⋊C4—21no—
406C2×C4⋊C4—22no—
407C2×C4⋊C4D4×C1111yescharacteristic
408C2×C4⋊C4C23×C1112yes—
409C2×C4⋊C4C23×C1112yes—
410C2×C4⋊C4C23×C1111yescharacteristic
411C2×C22⋊C4—28no—
412C2×C22⋊C4—21no—
413C2×C22⋊C4—21no—
414C2×C22⋊C4—21no—
415C2×C22⋊C4—21no—
416C2×C22⋊C4—21no—
417C2×C22⋊C4—22no—
418C2×C22⋊C4—21no—
419C2×C22⋊C4D4×C1111yescharacteristic
420C2×C22⋊C4D4×C1111yescharacteristic
421C2×C42C23×C1111yescharacteristic
422#106—24no—
423#103—24no—
424#103—42no—
425#102—24no—
426#102—24no—
427#102—24no—
428#102—42no—
429C22⋊C8—22no—
430C22⋊C8—42no—
431#95—22no—
432#95—21no—
433#95—22no—
434C2×C11—42no—
435C2×C11—42no—
436C2×C11—44no—
437C2×C11—82no—
438C2×C11#240511yescharacteristic
439C2×C11#300611yescharacteristic
440C2×C11#300911yescharacteristic
441C2×C11#330612yes—
442C2×C11#332312yes—
443C24—21no—
444C24—24no—
445C24—21no—
446C24—44no—
447C24—42no—
448C24—42no—
449C24—82no—
450C24C2×D4×C1111yescharacteristic
451C24C2×D4×C1111yescharacteristic
452#41—28no—
453#41—44no—
454#41—48no—
455C2×Q8—21no—
456C2×Q8—22no—
457C2×Q8—22no—
458C2×Q8C2×D4×C1112yes—
459C2×D4—24no—
460C2×D4—22no—
461C2×D4—24no—
462C2×D4—22no—
463C2×D4—24no—
464C2×D4—21no—
465C2×D4—21no—
466C2×D4—22no—
467C2×D4—22no—
468C2×D4—22no—
469C2×D4—41no—
470C2×D4—44no—
471C2×D4—48no—
472C2×D4—44no—
473C2×D4—44no—
474C2×D4—44no—
475C2×D4—82no—
476C2×D4C2×D4×C1112yes—
477C2×D4C2×D4×C1112yes—
478C2×D4C11×#4114yes—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—24no—
484C22×C4—24no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—44no—
492C22×C4—42no—
493C22×C4—42no—
494C22×C4—42no—
495C22×C4—82no—
496C22×C4C2×D4×C1111yescharacteristic
497C22×C4C2×D4×C1111yescharacteristic
498C22×C4C2×D4×C1111yescharacteristic
499C22×C4C2×D4×C1111yescharacteristic
500C22×C4C2×D4×C1112yes—
501C22×C4C2×D4×C1112yes—
502C22×C4C24×C1111yescharacteristic
503M16—44no—
504C2×C8—22no—
505C2×C8—22no—
506C2×C8—22no—
507C2×C8—22no—
508C2×C8—22no—
509C2×C8—22no—
510C4⋊C4—24no—
511C4⋊C4—22no—
512C4⋊C4—21no—
513C4⋊C4—22no—
514C4⋊C4—22no—
515C4⋊C4—22no—
516C4⋊C4—22no—
517C4⋊C4—44no—
518C4⋊C4—42no—
519C4⋊C4C2×D4×C1112yes—
520C22⋊C4—24no—
521C22⋊C4—24no—
522C22⋊C4—24no—
523C22⋊C4—24no—
524C22⋊C4—22no—
525C22⋊C4—22no—
526C22⋊C4—24no—
527C22⋊C4—42no—
528C22⋊C4—44no—
529C42—21no—
530C42—21no—
531C11#2404811yescharacteristic, direct product factor, Sylow
532C23—21no—
533C23—22no—
534C23—22no—
535C23—22no—
536C23—24no—
537C23—21no—
538C23—21no—
539C23—21no—
540C23—22no—
541C23—22no—
542C23—22no—
543C23—48no—
544C23—48no—
545C23—41no—
546C23—41no—
547C23—42no—
548C23—42no—
549C23—41no—
550C23—41no—
551C23—42no—
552C23—88no—
553C23—84no—
554C23—88no—
555C23C11×#12012yes—
556C23C11×AGL(1,ℤ/8)12yes—
557C23C22×D4×C1111yescharacteristic
558Q8—22no—
559Q8—22no—
560Q8—42no—
561D4—22no—
562D4—24no—
563D4—24no—
564D4—44no—
565D4—48no—
566D4—48no—
567D4—41no—
568D4—41no—
569D4—84no—
570D4C11×#12314yescomplemented
571C2×C4—22no—
572C2×C4—22no—
573C2×C4—22no—
574C2×C4—24no—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—22no—
578C2×C4—22no—
579C2×C4—21no—
580C2×C4—22no—
581C2×C4—21no—
582C2×C4—21no—
583C2×C4—22no—
584C2×C4—48no—
585C2×C4—42no—
586C2×C4—42no—
587C2×C4—41no—
588C2×C4—41no—
589C2×C4—42no—
590C2×C4—42no—
591C2×C4—42no—
592C2×C4—42no—
593C2×C4—42no—
594C2×C4—42no—
595C2×C4—42no—
596C2×C4—84no—
597C2×C4—84no—
598C2×C4C11×#12012yes—
599C2×C4C22×D4×C1111yescharacteristic
600C2×C4C22×D4×C1111yescharacteristic
601C2×C4C2×C11×#4112yes—
602C2×C4C11×H(5,𝔽2)12yes—
603C8—42no—
604C8—42no—
605C22—22no—
606C22—24no—
607C22—22no—
608C22—22no—
609C22—22no—
610C22—24no—
611C22—41no—
612C22—42no—
613C22—42no—
614C22—41no—
615C22—42no—
616C22—44no—
617C22—42no—
618C22—42no—
619C22—44no—
620C22—42no—
621C22—42no—
622C22—42no—
623C22—816no—
624C22—82no—
625C22—82no—
626C22C2×C11×#12011yescharacteristic
627C22C11×#54612yes—
628C22C2×C11×AGL(1,ℤ/8)11yescharacteristic
629C22C11×#57511yescharacteristic
630C22C11×#57712yes—
631C4—22no—
632C4—41no—
633C4—42no—
634C4—41no—
635C4—41no—
636C4—42no—
637C4—82no—
638C4—82no—
639C4C2×C11×#12311yescharacteristic
640C4C11×#53411yescharacteristic
641C4C11×#54612yes—
642C2—42no—
643C2—42no—
644C2—44no—
645C2—82no—
646C2C11×#240511yescharacteristic
647C2C11×#300611yescharacteristic
648C2C11×#300911yescharacteristic
649C2C11×#330612yes—
650C2C11×#332312yes—
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC2×C11×#546C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C2×C4×D4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C11×#481C2semidirect
3. C2×C11×#417C2semidirect
4. C11×#2486C2semidirect
5. C11×#2042C2semidirect
6. C11×#2035C2semidirect
7. C11×#1895C2semidirect
8. C11×#1870C2semidirect
9. C11×#1864C2semidirect
10. C11×#1788C2semidirect
11. C11×#1786C2semidirect
14. C22×C11×M16C22semidirect
26. C22×C11×C4⋊C4C22semidirect
29. C2×C11×#106C22semidirect
31. C2×C11×#103C22semidirect
32. C2×C11×#103C22semidirect
38. C2×C11×C22⋊C8C22semidirect
41. C11×#389C22semidirect
44. C11×#380C22semidirect
45. C11×#340C22semidirect
46. C11×#336C22semidirect
118. #24048C11direct (N × H)
208. C2×#481C2×C11semidirect
209. C2×#417C2×C11semidirect
210. #2486C2×C11semidirect
211. #2042C2×C11semidirect
212. #2035C2×C11semidirect
213. #1895C2×C11semidirect
214. #1870C2×C11semidirect
215. #1864C2×C11semidirect
216. #1788C2×C11semidirect
217. #1786C2×C11semidirect
256. D4×C11#123semidirect
293. C22×M16C22×C11semidirect
305. C22×C4⋊C4C22×C11semidirect
308. C2×#106C22×C11semidirect
310. C2×#103C22×C11semidirect
311. C2×#103C22×C11semidirect
317. C2×C22⋊C8C22×C11semidirect
320. #389C22×C11semidirect
323. #380C22×C11semidirect
324. #340C22×C11semidirect
325. #336C22×C11semidirect
531. C11#24048direct (N × H)
570. D4C11×#123semidirect

Maximal subgroups

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

subgroupindex
C2×C11×#5462
C2×C11×#4812
C2×C11×#4172
C11×#24862
C11×#20422
C11×#20352
C11×#18952
C11×#18702
C11×#18642
C11×#17882
C11×#17862
#2404811