Finite Group Databasebeta

← C11×#23976 #14601169

Subgroups — C11×#23976 #14601169

Order 2816.

1482 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
1C2×C11×#555C211yesmaximal, characteristic, complemented
2C2×C11×#447C211yesmaximal, characteristic, complemented
3C2×C11×#418C211yesmaximal, characteristic, complemented
4C11×#2408C211yesmaximal, characteristic, complemented
5C11×#2023C212yesmaximal, complemented
6C11×#1999C212yesmaximal, complemented
7C11×#1895C211yesmaximal, characteristic, complemented
8C11×#1879C212yesmaximal, complemented
9C11×#1875C212yesmaximal, complemented
10C11×#1870C211yesmaximal, characteristic, complemented
11C11×#1825C211yesmaximal, characteristic, complemented
12C23×D4×C11C2211yescharacteristic
13C22×C11×D8C2212yes—
14C22×C11×M16C2211yescharacteristic
15C11×#555—24no—
16C11×#555—24no—
17C2×C11×C4⋊Q8C2211yescharacteristic, complemented
18C2×C11×#124—21no—
19C2×C11×#124—21no—
20C2×C11×#121—21no—
21C2×C11×#121C2212yes—
22C2×C11×#121C2211yescharacteristic
23C2×C11×#121C2211yescharacteristic, complemented
24C2×C11×#120—21no—
25C2×C4×D4×C11C2211yescharacteristic
26C2×C4×D4×C11C2211yescharacteristic, complemented
27C2×C11×#117—21no—
28C2×C11×#117C2211yescharacteristic
29C2×C11×#117C2211yescharacteristic, complemented
30C11×#447—24no—
31C11×#418—24no—
32C2×C11×#102C2212yes—
33C2×C11×#102C2212yes—
34C2×C11×#102C2212yes—
35C2×C11×#102C2212yescomplemented
36C2×C11×C22⋊C8C2211yescharacteristic
37C2×C11×C22⋊C8C2212yescomplemented
38C11×#394—21no—
39C11×#392—21no—
40C11×#390C2212yes—
41C11×#380C2211yescharacteristic
42C11×#379—21no—
43C11×#340C2212yescomplemented
44C11×#340C2212yescomplemented
45C11×#340C2212yescomplemented
46C11×#336C2212yescomplemented
47C25×C11—21no—
48C22×Q8×C11—21no—
49C22×D4×C11—24no—
50C22×D4×C11—21no—
51C22×D4×C11—21no—
52C22×D4×C11—22no—
53C22×D4×C11—22no—
54C22×D4×C11—22no—
55C22×D4×C11—21no—
56C22×D4×C11—42no—
57C22×D4×C11D411yescharacteristic
58C22×D4×C11C2311yescharacteristic
59C22×D4×C11C2312yes—
60C23×C4×C11—21no—
61C23×C4×C11C2311yescharacteristic
62C23×C4×C11C2311yescharacteristic
63C2×C11×D8—24no—
64C2×C11×D8—24no—
65C2×C11×D8—42no—
66C2×C11×M16—22no—
67C2×C11×M16—42no—
68C22×C8×C11C2312yes—
69C22×C8×C11C2312yes—
70C11×C4⋊Q8—22no—
71C11×C4⋊Q8—22no—
72C11×#124—28no—
73C11×#124—28no—
74C11×#121—28no—
75C11×#121—22no—
76C11×#121—22no—
77C11×#121—22no—
78C11×#121—24no—
79C11×#121—42no—
80C11×#121D414yescomplemented
81C11×#120—44no—
82C4×D4×C11—22no—
83C4×D4×C11—22no—
84C4×D4×C11—22no—
85C4×D4×C11—22no—
86C11×#117—28no—
87C11×#117—22no—
88C11×#117—22no—
89C11×#117—22no—
90C11×#117D414yescomplemented
91C2×C11×C4⋊C4—21no—
92C2×C11×C4⋊C4D411yescharacteristic
93C2×C11×C4⋊C4C2312yes—
94C2×C11×C4⋊C4C2311yescharacteristic
95C2×C11×C4⋊C4C2311yescharacteristic
96C2×C11×C4⋊C4C2311yescharacteristic
97C2×C11×C22⋊C4—21no—
98C2×C11×C22⋊C4—21no—
99C2×C11×C22⋊C4—21no—
100C2×C11×C22⋊C4—21no—
101C2×C11×C22⋊C4—21no—
102C2×C11×C22⋊C4—21no—
103C2×C11×C22⋊C4—22no—
104C2×C11×C22⋊C4—22no—
105C2×C11×C22⋊C4—22no—
106C2×C11×C22⋊C4D411yescharacteristic
107C2×C11×C22⋊C4D411yescharacteristic
108C2×C42×C11—21no—
109C2×C42×C11—21no—
110C2×C42×C11C2311yescharacteristic
111C11×#102—24no—
112C11×#102—24no—
113C11×#102—24no—
114C11×#102—42no—
115C11×C22⋊C8—22no—
116C11×C22⋊C8—42no—
117C11×#95—21no—
118#23976C1111yesmaximal, characteristic, direct product factor, Sylow
119C24×C11—21no—
120C24×C11—22no—
121C24×C11—44no—
122C24×C11—42no—
123C24×C11—42no—
124C24×C11—42no—
125C24×C11—82no—
126C24×C11C2×D411yescharacteristic
127C24×C11C2×D411yescharacteristic
128C2×Q8×C11—24no—
129C2×Q8×C11—82no—
130C2×D4×C11—28no—
131C2×D4×C11—22no—
132C2×D4×C11—24no—
133C2×D4×C11—24no—
134C2×D4×C11—22no—
135C2×D4×C11—22no—
136C2×D4×C11—22no—
137C2×D4×C11—21no—
138C2×D4×C11—22no—
139C2×D4×C11—22no—
140C2×D4×C11—22no—
141C2×D4×C11—22no—
142C2×D4×C11—22no—
143C2×D4×C11—48no—
144C2×D4×C11—41no—
145C2×D4×C11—44no—
146C2×D4×C11—44no—
147C2×D4×C11—44no—
148C2×D4×C11—44no—
149C2×D4×C11—42no—
150C2×D4×C11—82no—
151C2×D4×C11—82no—
152C2×D4×C11—82no—
153C2×D4×C11C2×D412yes—
154C2×D4×C11#4114yes—
155C22×C4×C11—22no—
156C22×C4×C11—22no—
157C22×C4×C11—24no—
158C22×C4×C11—21no—
159C22×C4×C11—21no—
160C22×C4×C11—21no—
161C22×C4×C11—21no—
162C22×C4×C11—21no—
163C22×C4×C11—22no—
164C22×C4×C11—22no—
165C22×C4×C11—22no—
166C22×C4×C11—42no—
167C22×C4×C11—42no—
168C22×C4×C11C2×D411yescharacteristic
169C22×C4×C11C2×D411yescharacteristic
170C22×C4×C11C2×D411yescharacteristic
171C22×C4×C11C2×D412yes—
172C22×C4×C11C2×D412yes—
173C22×C4×C11C2×D411yescharacteristic
174C22×C4×C11C2411yescharacteristic
175C11×D8—48no—
176C11×M16—44no—
177C2×C8×C11—22no—
178C2×C8×C11—22no—
179C2×C8×C11—22no—
180C2×C8×C11—22no—
181C2×C8×C11—22no—
182C2×C8×C11—22no—
183C11×C4⋊C4—24no—
184C11×C4⋊C4—22no—
185C11×C4⋊C4—21no—
186C11×C4⋊C4—21no—
187C11×C4⋊C4—21no—
188C11×C4⋊C4—22no—
189C11×C4⋊C4—22no—
190C11×C4⋊C4C2×D412yes—
191C11×C4⋊C4C2×D412yes—
192C11×C4⋊C4C2×D412yes—
193C11×C22⋊C4—24no—
194C11×C22⋊C4—24no—
195C11×C22⋊C4—24no—
196C11×C22⋊C4—24no—
197C11×C22⋊C4—22no—
198C11×C22⋊C4—24no—
199C11×C22⋊C4—22no—
200C11×C22⋊C4—44no—
201C11×C22⋊C4—42no—
202C11×C22⋊C4—44no—
203C11×C22⋊C4—82no—
204C42×C11—24no—
205C42×C11—24no—
206C42×C11—21no—
207C42×C11—21no—
208C2×#555C2×C1111yescharacteristic, complemented
209C2×#447C2×C1111yescharacteristic, complemented
210C2×#418C2×C1111yescharacteristic, complemented
211#2408C2×C1111yescharacteristic, complemented
212#2023C2×C1112yescomplemented
213#1999C2×C1112yescomplemented
214#1895C2×C1111yescharacteristic, complemented
215#1879C2×C1112yescomplemented
216#1875C2×C1112yescomplemented
217#1870C2×C1111yescharacteristic, complemented
218#1825C2×C1111yescharacteristic, complemented
219C23×C11—22no—
220C23×C11—21no—
221C23×C11—21no—
222C23×C11—22no—
223C23×C11—21no—
224C23×C11—22no—
225C23×C11—24no—
226C23×C11—22no—
227C23×C11—21no—
228C23×C11—21no—
229C23×C11—22no—
230C23×C11—48no—
231C23×C11—42no—
232C23×C11—42no—
233C23×C11—42no—
234C23×C11—42no—
235C23×C11—41no—
236C23×C11—41no—
237C23×C11—42no—
238C23×C11—42no—
239C23×C11—42no—
240C23×C11—42no—
241C23×C11—84no—
242C23×C11—84no—
243C23×C11—88no—
244C23×C11—88no—
245C23×C11#12012yes—
246C23×C11C22×D411yescharacteristic
247Q8×C11—84no—
248D4×C11—24no—
249D4×C11—24no—
250D4×C11—24no—
251D4×C11—44no—
252D4×C11—48no—
253D4×C11—41no—
254D4×C11—41no—
255D4×C11—42no—
256D4×C11—42no—
257D4×C11—84no—
258D4×C11—84no—
259D4×C11—88no—
260C2×C4×C11—21no—
261C2×C4×C11—22no—
262C2×C4×C11—21no—
263C2×C4×C11—22no—
264C2×C4×C11—22no—
265C2×C4×C11—24no—
266C2×C4×C11—21no—
267C2×C4×C11—22no—
268C2×C4×C11—21no—
269C2×C4×C11—22no—
270C2×C4×C11—22no—
271C2×C4×C11—22no—
272C2×C4×C11—22no—
273C2×C4×C11—48no—
274C2×C4×C11—41no—
275C2×C4×C11—41no—
276C2×C4×C11—42no—
277C2×C4×C11—42no—
278C2×C4×C11—41no—
279C2×C4×C11—41no—
280C2×C4×C11—42no—
281C2×C4×C11—42no—
282C2×C4×C11—42no—
283C2×C4×C11—42no—
284C2×C4×C11#12012yes—
285C2×C4×C11AGL(1,ℤ/8)12yes—
286C2×C4×C11C22×D411yescharacteristic
287C2×C4×C11C22×D411yescharacteristic
288C2×C4×C11C2×#4112yes—
289C2×C4×C11H(5,𝔽2)12yes—
290C8×C11—42no—
291C8×C11—42no—
292C23×D4C22×C1111yescharacteristic
293C22×D8C22×C1112yes—
294C22×M16C22×C1111yescharacteristic
295#555—24no—
296#555—24no—
297C2×C4⋊Q8C22×C1111yescharacteristic, complemented
298C2×#124—21no—
299C2×#124—21no—
300C2×#121—21no—
301C2×#121C22×C1112yes—
302C2×#121C22×C1111yescharacteristic
303C2×#121C22×C1111yescharacteristic, complemented
304C2×#120—21no—
305C2×C4×D4C22×C1111yescharacteristic
306C2×C4×D4C22×C1111yescharacteristic, complemented
307C2×#117—21no—
308C2×#117C22×C1111yescharacteristic
309C2×#117C22×C1111yescharacteristic, complemented
310#447—24no—
311#418—24no—
312C2×#102C22×C1112yes—
313C2×#102C22×C1112yes—
314C2×#102C22×C1112yes—
315C2×#102C22×C1112yescomplemented
316C2×C22⋊C8C22×C1111yescharacteristic
317C2×C22⋊C8C22×C1112yescomplemented
318#394—21no—
319#392—21no—
320#390C22×C1112yes—
321#380C22×C1111yescharacteristic
322#379—21no—
323#340C22×C1112yescomplemented
324#340C22×C1112yescomplemented
325#340C22×C1112yescomplemented
326#336C22×C1112yescomplemented
327C22×C11—22no—
328C22×C11—22no—
329C22×C11—22no—
330C22×C11—42no—
331C22×C11—42no—
332C22×C11—41no—
333C22×C11—44no—
334C22×C11—42no—
335C22×C11—42no—
336C22×C11—41no—
337C22×C11—41no—
338C22×C11—42no—
339C22×C11—42no—
340C22×C11—44no—
341C22×C11—42no—
342C22×C11—44no—
343C22×C11—816no—
344C22×C11—82no—
345C22×C11—82no—
346C22×C11—82no—
347C22×C11—82no—
348C22×C11—82no—
349C22×C11—82no—
350C22×C11C2×#12011yescharacteristic
351C22×C11#54612yes—
352C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
353C22×C11#57511yescharacteristic
354C22×C11#57612yes—
355C4×C11—22no—
356C4×C11—22no—
357C4×C11—41no—
358C4×C11—42no—
359C4×C11—41no—
360C4×C11—42no—
361C4×C11—42no—
362C4×C11—82no—
363C4×C11#52511yescharacteristic
364C4×C11#53511yescharacteristic
365C4×C11#54612yes—
366C25—21no—
367C22×Q8—21no—
368C22×D4—24no—
369C22×D4—21no—
370C22×D4—21no—
371C22×D4—22no—
372C22×D4—22no—
373C22×D4—22no—
374C22×D4—21no—
375C22×D4—42no—
376C22×D4D4×C1111yescharacteristic
377C22×D4C23×C1111yescharacteristic
378C22×D4C23×C1112yes—
379C23×C4—21no—
380C23×C4C23×C1111yescharacteristic
381C23×C4C23×C1111yescharacteristic
382C2×D8—24no—
383C2×D8—24no—
384C2×D8—42no—
385C2×M16—22no—
386C2×M16—42no—
387C22×C8C23×C1112yes—
388C22×C8C23×C1112yes—
389C4⋊Q8—22no—
390C4⋊Q8—22no—
391#124—28no—
392#124—28no—
393#121—28no—
394#121—22no—
395#121—22no—
396#121—22no—
397#121—24no—
398#121—42no—
399#121D4×C1114yescomplemented
400#120—44no—
401C4×D4—22no—
402C4×D4—22no—
403C4×D4—22no—
404C4×D4—22no—
405#117—28no—
406#117—22no—
407#117—22no—
408#117—22no—
409#117D4×C1114yescomplemented
410C2×C4⋊C4—21no—
411C2×C4⋊C4D4×C1111yescharacteristic
412C2×C4⋊C4C23×C1112yes—
413C2×C4⋊C4C23×C1111yescharacteristic
414C2×C4⋊C4C23×C1111yescharacteristic
415C2×C4⋊C4C23×C1111yescharacteristic
416C2×C22⋊C4—21no—
417C2×C22⋊C4—21no—
418C2×C22⋊C4—21no—
419C2×C22⋊C4—21no—
420C2×C22⋊C4—21no—
421C2×C22⋊C4—21no—
422C2×C22⋊C4—22no—
423C2×C22⋊C4—22no—
424C2×C22⋊C4—22no—
425C2×C22⋊C4D4×C1111yescharacteristic
426C2×C22⋊C4D4×C1111yescharacteristic
427C2×C42—21no—
428C2×C42—21no—
429C2×C42C23×C1111yescharacteristic
430#102—24no—
431#102—24no—
432#102—24no—
433#102—42no—
434C22⋊C8—22no—
435C22⋊C8—42no—
436#95—21no—
437C2×C11—42no—
438C2×C11—81no—
439C2×C11—82no—
440C2×C11—84no—
441C2×C11#240411yescharacteristic
442C2×C11#300611yescharacteristic
443C2×C11#300811yescharacteristic
444C2×C11#331912yes—
445C2×C11#332512yes—
446C24—21no—
447C24—22no—
448C24—44no—
449C24—42no—
450C24—42no—
451C24—42no—
452C24—82no—
453C24C2×D4×C1111yescharacteristic
454C24C2×D4×C1111yescharacteristic
455C2×Q8—24no—
456C2×Q8—82no—
457C2×D4—28no—
458C2×D4—22no—
459C2×D4—24no—
460C2×D4—24no—
461C2×D4—22no—
462C2×D4—22no—
463C2×D4—22no—
464C2×D4—21no—
465C2×D4—22no—
466C2×D4—22no—
467C2×D4—22no—
468C2×D4—22no—
469C2×D4—22no—
470C2×D4—48no—
471C2×D4—41no—
472C2×D4—44no—
473C2×D4—44no—
474C2×D4—44no—
475C2×D4—44no—
476C2×D4—42no—
477C2×D4—82no—
478C2×D4—82no—
479C2×D4—82no—
480C2×D4C2×D4×C1112yes—
481C2×D4C11×#4114yes—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—24no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—42no—
494C22×C4—42no—
495C22×C4C2×D4×C1111yescharacteristic
496C22×C4C2×D4×C1111yescharacteristic
497C22×C4C2×D4×C1111yescharacteristic
498C22×C4C2×D4×C1112yes—
499C22×C4C2×D4×C1112yes—
500C22×C4C2×D4×C1111yescharacteristic
501C22×C4C24×C1111yescharacteristic
502D8—48no—
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—21no—
514C4⋊C4—21no—
515C4⋊C4—22no—
516C4⋊C4—22no—
517C4⋊C4C2×D4×C1112yes—
518C4⋊C4C2×D4×C1112yes—
519C4⋊C4C2×D4×C1112yes—
520C22⋊C4—24no—
521C22⋊C4—24no—
522C22⋊C4—24no—
523C22⋊C4—24no—
524C22⋊C4—22no—
525C22⋊C4—24no—
526C22⋊C4—22no—
527C22⋊C4—44no—
528C22⋊C4—42no—
529C22⋊C4—44no—
530C22⋊C4—82no—
531C42—24no—
532C42—24no—
533C42—21no—
534C42—21no—
535C11#2397611yescharacteristic, direct product factor, Sylow
536C23—22no—
537C23—21no—
538C23—21no—
539C23—22no—
540C23—21no—
541C23—22no—
542C23—24no—
543C23—22no—
544C23—21no—
545C23—21no—
546C23—22no—
547C23—48no—
548C23—42no—
549C23—42no—
550C23—42no—
551C23—42no—
552C23—41no—
553C23—41no—
554C23—42no—
555C23—42no—
556C23—42no—
557C23—42no—
558C23—84no—
559C23—84no—
560C23—88no—
561C23—88no—
562C23C11×#12012yes—
563C23C22×D4×C1111yescharacteristic
564Q8—84no—
565D4—24no—
566D4—24no—
567D4—24no—
568D4—44no—
569D4—48no—
570D4—41no—
571D4—41no—
572D4—42no—
573D4—42no—
574D4—84no—
575D4—84no—
576D4—88no—
577C2×C4—21no—
578C2×C4—22no—
579C2×C4—21no—
580C2×C4—22no—
581C2×C4—22no—
582C2×C4—24no—
583C2×C4—21no—
584C2×C4—22no—
585C2×C4—21no—
586C2×C4—22no—
587C2×C4—22no—
588C2×C4—22no—
589C2×C4—22no—
590C2×C4—48no—
591C2×C4—41no—
592C2×C4—41no—
593C2×C4—42no—
594C2×C4—42no—
595C2×C4—41no—
596C2×C4—41no—
597C2×C4—42no—
598C2×C4—42no—
599C2×C4—42no—
600C2×C4—42no—
601C2×C4C11×#12012yes—
602C2×C4C11×AGL(1,ℤ/8)12yes—
603C2×C4C22×D4×C1111yescharacteristic
604C2×C4C22×D4×C1111yescharacteristic
605C2×C4C2×C11×#4112yes—
606C2×C4C11×H(5,𝔽2)12yes—
607C8—42no—
608C8—42no—
609C22—22no—
610C22—22no—
611C22—22no—
612C22—42no—
613C22—42no—
614C22—41no—
615C22—44no—
616C22—42no—
617C22—42no—
618C22—41no—
619C22—41no—
620C22—42no—
621C22—42no—
622C22—44no—
623C22—42no—
624C22—44no—
625C22—816no—
626C22—82no—
627C22—82no—
628C22—82no—
629C22—82no—
630C22—82no—
631C22—82no—
632C22C2×C11×#12011yescharacteristic
633C22C11×#54612yes—
634C22C2×C11×AGL(1,ℤ/8)11yescharacteristic
635C22C11×#57511yescharacteristic
636C22C11×#57612yes—
637C4—22no—
638C4—22no—
639C4—41no—
640C4—42no—
641C4—41no—
642C4—42no—
643C4—42no—
644C4—82no—
645C4C11×#52511yescharacteristic
646C4C11×#53511yescharacteristic
647C4C11×#54612yes—
648C2—42no—
649C2—81no—
650C2—84no—
651C2—82no—
652C2C11×#240411yescharacteristic
653C2C11×#300611yescharacteristic
654C2C11×#300811yescharacteristic
655C2C11×#331912yes—
656C2C11×#332512yes—
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
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
1. C2×C11×#555C2semidirect
2. C2×C11×#447C2semidirect
3. C2×C11×#418C2semidirect
4. C11×#2408C2semidirect
5. C11×#2023C2semidirect
6. C11×#1999C2semidirect
7. C11×#1895C2semidirect
8. C11×#1879C2semidirect
9. C11×#1875C2semidirect
10. C11×#1870C2semidirect
11. C11×#1825C2semidirect
17. C2×C11×C4⋊Q8C22semidirect
23. C2×C11×#121C22semidirect
26. C2×C4×D4×C11C22semidirect
29. C2×C11×#117C22semidirect
35. C2×C11×#102C22semidirect
37. C2×C11×C22⋊C8C22semidirect
43. C11×#340C22semidirect
44. C11×#340C22semidirect
45. C11×#340C22semidirect
46. C11×#336C22semidirect
80. C11×#121D4semidirect
90. C11×#117D4semidirect
118. #23976C11direct (N × H)
208. C2×#555C2×C11semidirect
209. C2×#447C2×C11semidirect
210. C2×#418C2×C11semidirect
211. #2408C2×C11semidirect
212. #2023C2×C11semidirect
213. #1999C2×C11semidirect
214. #1895C2×C11semidirect
215. #1879C2×C11semidirect
216. #1875C2×C11semidirect
217. #1870C2×C11semidirect
218. #1825C2×C11semidirect
297. C2×C4⋊Q8C22×C11semidirect
303. C2×#121C22×C11semidirect
306. C2×C4×D4C22×C11semidirect
309. C2×#117C22×C11semidirect
315. C2×#102C22×C11semidirect
317. C2×C22⋊C8C22×C11semidirect
323. #340C22×C11semidirect
324. #340C22×C11semidirect
325. #340C22×C11semidirect
326. #336C22×C11semidirect
399. #121D4×C11semidirect
409. #117D4×C11semidirect
535. C11#23976direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5552
C2×C11×#4472
C2×C11×#4182
C11×#24082
C11×#20232
C11×#19992
C11×#18952
C11×#18792
C11×#18752
C11×#18702
C11×#18252
#2397611