Finite Group Databasebeta

← C11×#24320 #14601513

Subgroups — C11×#24320 #14601513

Order 2816.

1092 conjugacy classes of subgroups.

The subgroup lattice has 632 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3503C211yesmaximal, characteristic, complemented
2C11×#3077C211yesmaximal, characteristic, complemented
3C4×C11×AGL(1,ℤ/8)C211yesmaximal, characteristic
4C11×#2542C211yesmaximal, characteristic, complemented
5C11×#2060C212yesmaximal, complemented
6C11×#2027C212yesmaximal, complemented
7C11×#1997C211yesmaximal, characteristic, complemented
8C11×#1986C211yesmaximal, characteristic, complemented
9C11×#1883C212yesmaximal
10C11×#1859C212yesmaximal, complemented
11C11×#1806C211yesmaximal, characteristic, complemented
12C2×C11×AGL(1,ℤ/8)C2211yescharacteristic
13Q82×C11—21no—
14C11×#557—21no—
15C11×#554—21no—
16C11×#554—22no—
17D4×Q8×C11—22no—
18D4×Q8×C11—21no—
19C11×#544—22no—
20C11×#544C2212yes—
21C11×#533—21no—
22C11×#533C2211yescharacteristic
23C2×C11×C4⋊Q8—21no—
24C2×C11×C4⋊Q8C2211yescharacteristic
25C2×C11×C22⋊Q8—22no—
26C11×#520C2212yes—
27C4×C11×#41C2211yescharacteristic
28C2×C4×D4×C11C2211yescharacteristic
29C11×#478—22no—
30C11×#476—21no—
31C11×#474—21no—
32C11×#442—21no—
33C11×#440—21no—
34C4×C11×SD16—21no—
35C4×C11×D8—21no—
36C11×#428C2211yescharacteristic
37C11×#428C2212yes—
38C11×#423C2211yescharacteristic
39C2×C11×#104C2212yes—
40C11×#418C2212yes—
41C11×#418C2211yescharacteristic
42C11×#417C2211yescharacteristic
43C4×C11×M16C2211yescharacteristic
44C11×#399—22no—
45C11×#390C2212yes—
46C11×#384C2212yes—
47C4×C11×C4⋊C4C2211yescharacteristic
48C11×#343C2212yes—
49C11×#343C2212yes—
50C11×#339C2212yes—
51C11×#339C2212yes—
52C11×#339C2212yes—
53C2×C11×#41C2311yescharacteristic
54C22×Q8×C11—22no—
55C22×Q8×C11D412yes—
56C22×D4×C11C2311yescharacteristic
57C23×C4×C11—21no—
58C11×AGL(1,ℤ/8)—22no—
59C11×AGL(1,ℤ/8)Q814yescomplemented
60C2×C11×SD16—21no—
61C2×C11×D8—21no—
62C2×C11×M16C2311yescharacteristic
63C2×C11×M16C2312yes—
64C2×C11×M16C2311yescharacteristic
65C11×C4⋊Q8—22no—
66C11×C4⋊Q8—22no—
67C11×C4⋊Q8—24no—
68C11×C4⋊Q8—22no—
69C11×C4⋊Q8—22no—
70C11×C4⋊Q8—21no—
71C11×C4⋊Q8—21no—
72C11×C4⋊Q8—21no—
73C11×C4⋊Q8—21no—
74C11×C4⋊Q8D411yescharacteristic
75C11×C4⋊Q8D411yescharacteristic
76C11×#125—24no—
77C11×#125—22no—
78C11×#125—22no—
79C11×#125D412yes—
80C11×C22⋊Q8—22no—
81C11×C22⋊Q8—22no—
82C11×C22⋊Q8—24no—
83C11×C22⋊Q8—24no—
84C11×C22⋊Q8—21no—
85C11×C22⋊Q8—21no—
86C11×C22⋊Q8—24no—
87C11×C22⋊Q8—48no—
88C4×Q8×C11—22no—
89C4×Q8×C11—22no—
90C4×Q8×C11—22no—
91C4×Q8×C11—21no—
92C4×Q8×C11—21no—
93C4×Q8×C11D411yescharacteristic
94C4×Q8×C11D411yescharacteristic
95C4×D4×C11—22no—
96C4×D4×C11—21no—
97C4×D4×C11—21no—
98C4×D4×C11—24no—
99C4×D4×C11—21no—
100C4×D4×C11—21no—
101C4×D4×C11—21no—
102C4×D4×C11—21no—
103C4×D4×C11D411yescharacteristic
104C4×D4×C11D411yescharacteristic
105C11×#117—22no—
106C11×#117—21no—
107C11×#117C2311yescharacteristic
108C11×#117C2312yes—
109C2×C11×C4⋊C4—22no—
110C2×C11×C4⋊C4—21no—
111C2×C11×C4⋊C4—22no—
112C2×C11×C4⋊C4—24no—
113C2×C11×C4⋊C4D412yes—
114C2×C11×C4⋊C4C2311yescharacteristic
115C2×C11×C4⋊C4C2312yes—
116C2×C11×C22⋊C4—21no—
117C2×C11×C22⋊C4—24no—
118C2×C42×C11—21no—
119C2×C42×C11C2312yes—
120C2×C42×C11C2311yescharacteristic
121C11×#107—21no—
122C11×#107—22no—
123C11×#106—21no—
124C11×#106—22no—
125C11×C4⋊C8—21no—
126C11×C4⋊C8—21no—
127C11×#104—24no—
128C11×#103—21no—
129C11×#102—21no—
130C11×#102—21no—
131C11×#102—21no—
132C11×#102—22no—
133C11×#102—22no—
134C11×#97—21no—
135C4×C8×C11—21no—
136C11×#95—21no—
137#24320C1111yesmaximal, characteristic, direct product factor, Sylow
138C24×C11—21no—
139C11×#41—21no—
140C11×#41—21no—
141C11×#41C2×Q812yes—
142C11×#41#4112yes—
143C2×Q8×C11—24no—
144C2×Q8×C11—21no—
145C2×Q8×C11—22no—
146C2×Q8×C11—21no—
147C2×Q8×C11—22no—
148C2×Q8×C11—44no—
149C2×Q8×C11—84no—
150C2×Q8×C11C2×D411yescharacteristic
151C2×D4×C11—21no—
152C2×D4×C11—21no—
153C2×D4×C11—21no—
154C2×D4×C11—21no—
155C2×D4×C11—21no—
156C2×D4×C11—21no—
157C2×D4×C11C2×D411yescharacteristic
158C2×D4×C11C2×Q812yescomplemented
159C22×C4×C11—21no—
160C22×C4×C11—22no—
161C22×C4×C11—24no—
162C22×C4×C11—21no—
163C22×C4×C11—21no—
164C22×C4×C11—21no—
165C22×C4×C11—44no—
166C22×C4×C11—41no—
167C22×C4×C11—41no—
168C22×C4×C11C2×D411yescharacteristic
169C22×C4×C11C2×D414yes—
170C22×C4×C11C2×D411yescharacteristic
171C22×C4×C11C2411yescharacteristic
172C11×SD16—24no—
173C11×D8—24no—
174C11×M16—21no—
175C11×M16—22no—
176C11×M16—21no—
177C11×M16—22no—
178C11×M16—21no—
179C11×M16C2×Q812yescomplemented
180C2×C8×C11—21no—
181C2×C8×C11—21no—
182C2×C8×C11—22no—
183C11×C4⋊C4—24no—
184C11×C4⋊C4—24no—
185C11×C4⋊C4—24no—
186C11×C4⋊C4—24no—
187C11×C4⋊C4—24no—
188C11×C4⋊C4—21no—
189C11×C4⋊C4—22no—
190C11×C4⋊C4—22no—
191C11×C4⋊C4—21no—
192C11×C4⋊C4—21no—
193C11×C4⋊C4—21no—
194C11×C4⋊C4—22no—
195C11×C4⋊C4—22no—
196C11×C4⋊C4—22no—
197C11×C4⋊C4—22no—
198C11×C4⋊C4—21no—
199C11×C4⋊C4—21no—
200C11×C4⋊C4—48no—
201C11×C4⋊C4C2×D412yes—
202C11×C4⋊C4C2×D411yescharacteristic
203C11×C4⋊C4C2×D412yes—
204C11×C4⋊C4C2×D411yescharacteristic
205C11×C22⋊C4—24no—
206C11×C22⋊C4—22no—
207C11×C22⋊C4—21no—
208C11×C22⋊C4—21no—
209C11×C22⋊C4—21no—
210C11×C22⋊C4—48no—
211C11×C22⋊C4—41no—
212C11×C22⋊C4—41no—
213C42×C11—24no—
214C42×C11—21no—
215C42×C11—21no—
216C42×C11—21no—
217C42×C11—22no—
218C42×C11—22no—
219C42×C11—22no—
220C42×C11C2×D411yescharacteristic
221C42×C11C2×D411yescharacteristic
222C42×C11C2×D411yescharacteristic
223C42×C11C2×D411yescharacteristic
224#3503C2×C1111yescharacteristic, complemented
225#3077C2×C1111yescharacteristic, complemented
226C4×AGL(1,ℤ/8)C2×C1111yescharacteristic
227#2542C2×C1111yescharacteristic, complemented
228#2060C2×C1112yescomplemented
229#2027C2×C1112yescomplemented
230#1997C2×C1111yescharacteristic, complemented
231#1986C2×C1111yescharacteristic, complemented
232#1883C2×C1112yes—
233#1859C2×C1112yescomplemented
234#1806C2×C1111yescharacteristic, complemented
235C23×C11—21no—
236C23×C11—22no—
237C23×C11—42no—
238C23×C11—42no—
239C23×C11—41no—
240C23×C11—41no—
241C23×C11C22×D411yescharacteristic
242Q8×C11—21no—
243Q8×C11—42no—
244Q8×C11—44no—
245Q8×C11—42no—
246Q8×C11—82no—
247Q8×C11—84no—
248Q8×C11C22⋊Q812yescomplemented
249D4×C11—22no—
250D4×C11—22no—
251D4×C11—22no—
252D4×C11—21no—
253D4×C11—22no—
254D4×C11—41no—
255D4×C11—41no—
256D4×C11C22⋊Q812yescomplemented
257C2×C4×C11—21no—
258C2×C4×C11—22no—
259C2×C4×C11—22no—
260C2×C4×C11—22no—
261C2×C4×C11—24no—
262C2×C4×C11—22no—
263C2×C4×C11—21no—
264C2×C4×C11—21no—
265C2×C4×C11—24no—
266C2×C4×C11—22no—
267C2×C4×C11—41no—
268C2×C4×C11—42no—
269C2×C4×C11—42no—
270C2×C4×C11—42no—
271C2×C4×C11—42no—
272C2×C4×C11—44no—
273C2×C4×C11—42no—
274C2×C4×C11—41no—
275C2×C4×C11—82no—
276C2×C4×C11—84no—
277C2×C4×C11—82no—
278C2×C4×C11#12011yescharacteristic
279C2×C4×C11#12011yescharacteristic
280C2×C4×C11#12011yescharacteristic
281C2×C4×C11#12011yescharacteristic
282C2×C4×C11C22×D411yescharacteristic
283C2×C4×C11C22×D411yescharacteristic
284C2×C4×C11C22×Q811yescharacteristic
285C2×C4×C11C2×#4111yescharacteristic
286C2×C4×C112−1+411yescharacteristic
287C2×C4×C112−1+411yescharacteristic
288C8×C11—22no—
289C8×C11—41no—
290C8×C11—42no—
291C2×AGL(1,ℤ/8)C22×C1111yescharacteristic
292Q82—21no—
293#557—21no—
294#554—21no—
295#554—22no—
296D4×Q8—22no—
297D4×Q8—21no—
298#544—22no—
299#544C22×C1112yes—
300#533—21no—
301#533C22×C1111yescharacteristic
302C2×C4⋊Q8—21no—
303C2×C4⋊Q8C22×C1111yescharacteristic
304C2×C22⋊Q8—22no—
305#520C22×C1112yes—
306C4×#41C22×C1111yescharacteristic
307C2×C4×D4C22×C1111yescharacteristic
308#478—22no—
309#476—21no—
310#474—21no—
311#442—21no—
312#440—21no—
313C4×SD16—21no—
314C4×D8—21no—
315#428C22×C1112yes—
316#428C22×C1111yescharacteristic
317#423C22×C1111yescharacteristic
318C2×#104C22×C1112yes—
319#418C22×C1112yes—
320#418C22×C1111yescharacteristic
321#417C22×C1111yescharacteristic
322C4×M16C22×C1111yescharacteristic
323#399—22no—
324#390C22×C1112yes—
325#384C22×C1112yes—
326C4×C4⋊C4C22×C1111yescharacteristic
327#343C22×C1112yes—
328#343C22×C1112yes—
329#339C22×C1112yes—
330#339C22×C1112yes—
331#339C22×C1112yes—
332C22×C11—21no—
333C22×C11—21no—
334C22×C11—22no—
335C22×C11—44no—
336C22×C11—41no—
337C22×C11—41no—
338C22×C11—42no—
339C22×C11—82no—
340C22×C11—81no—
341C22×C11—81no—
342C22×C11C2×#12011yescharacteristic
343C22×C11#54811yescharacteristic
344C22×C11D4×Q811yescharacteristic
345C4×C11—22no—
346C4×C11—21no—
347C4×C11—21no—
348C4×C11—21no—
349C4×C11—44no—
350C4×C11—41no—
351C4×C11—44no—
352C4×C11—42no—
353C4×C11—41no—
354C4×C11—42no—
355C4×C11—81no—
356C4×C11#45312yes—
357C4×C11C2×C22⋊Q811yescharacteristic
358C4×C11#53611yescharacteristic
359C4×C11#54811yescharacteristic
360C4×C11D4×Q811yescharacteristic
361C2×#41C23×C1111yescharacteristic
362C22×Q8—22no—
363C22×Q8D4×C1112yes—
364C22×D4C23×C1111yescharacteristic
365C23×C4—21no—
366AGL(1,ℤ/8)—22no—
367AGL(1,ℤ/8)Q8×C1114yescomplemented
368C2×SD16—21no—
369C2×D8—21no—
370C2×M16C23×C1111yescharacteristic
371C2×M16C23×C1112yes—
372C2×M16C23×C1111yescharacteristic
373C4⋊Q8—22no—
374C4⋊Q8—22no—
375C4⋊Q8—24no—
376C4⋊Q8—22no—
377C4⋊Q8—22no—
378C4⋊Q8—21no—
379C4⋊Q8—21no—
380C4⋊Q8—21no—
381C4⋊Q8—21no—
382C4⋊Q8D4×C1111yescharacteristic
383C4⋊Q8D4×C1111yescharacteristic
384#125—24no—
385#125—22no—
386#125—22no—
387#125D4×C1112yes—
388C22⋊Q8—22no—
389C22⋊Q8—22no—
390C22⋊Q8—24no—
391C22⋊Q8—24no—
392C22⋊Q8—21no—
393C22⋊Q8—21no—
394C22⋊Q8—24no—
395C22⋊Q8—48no—
396C4×Q8—22no—
397C4×Q8—22no—
398C4×Q8—22no—
399C4×Q8—21no—
400C4×Q8—21no—
401C4×Q8D4×C1111yescharacteristic
402C4×Q8D4×C1111yescharacteristic
403C4×D4—22no—
404C4×D4—21no—
405C4×D4—21no—
406C4×D4—24no—
407C4×D4—21no—
408C4×D4—21no—
409C4×D4—21no—
410C4×D4—21no—
411C4×D4D4×C1111yescharacteristic
412C4×D4D4×C1111yescharacteristic
413#117—22no—
414#117—21no—
415#117C23×C1111yescharacteristic
416#117C23×C1112yes—
417C2×C4⋊C4—22no—
418C2×C4⋊C4—21no—
419C2×C4⋊C4—22no—
420C2×C4⋊C4—24no—
421C2×C4⋊C4D4×C1112yes—
422C2×C4⋊C4C23×C1111yescharacteristic
423C2×C4⋊C4C23×C1112yes—
424C2×C22⋊C4—21no—
425C2×C22⋊C4—24no—
426C2×C42—21no—
427C2×C42C23×C1112yes—
428C2×C42C23×C1111yescharacteristic
429#107—21no—
430#107—22no—
431#106—21no—
432#106—22no—
433C4⋊C8—21no—
434C4⋊C8—21no—
435#104—24no—
436#103—21no—
437#102—21no—
438#102—21no—
439#102—21no—
440#102—22no—
441#102—22no—
442#97—21no—
443C4×C8—21no—
444#95—21no—
445C2×C11—21no—
446C2×C11—21no—
447C2×C11—42no—
448C2×C11—82no—
449C2×C11#240911yescharacteristic
450C2×C11C2×#45311yescharacteristic
451C2×C11#302011yescharacteristic
452C24—21no—
453#41—21no—
454#41—21no—
455#41C2×Q8×C1112yes—
456#41C11×#4112yes—
457C2×Q8—24no—
458C2×Q8—21no—
459C2×Q8—22no—
460C2×Q8—21no—
461C2×Q8—22no—
462C2×Q8—44no—
463C2×Q8—84no—
464C2×Q8C2×D4×C1111yescharacteristic
465C2×D4—21no—
466C2×D4—21no—
467C2×D4—21no—
468C2×D4—21no—
469C2×D4—21no—
470C2×D4—21no—
471C2×D4C2×D4×C1111yescharacteristic
472C2×D4C2×Q8×C1112yescomplemented
473C22×C4—21no—
474C22×C4—22no—
475C22×C4—24no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—44no—
480C22×C4—41no—
481C22×C4—41no—
482C22×C4C2×D4×C1111yescharacteristic
483C22×C4C2×D4×C1114yes—
484C22×C4C2×D4×C1111yescharacteristic
485C22×C4C24×C1111yescharacteristic
486SD16—24no—
487D8—24no—
488M16—21no—
489M16—22no—
490M16—21no—
491M16—21no—
492M16—22no—
493M16C2×Q8×C1112yescomplemented
494C2×C8—21no—
495C2×C8—21no—
496C2×C8—22no—
497C4⋊C4—24no—
498C4⋊C4—24no—
499C4⋊C4—24no—
500C4⋊C4—24no—
501C4⋊C4—24no—
502C4⋊C4—21no—
503C4⋊C4—22no—
504C4⋊C4—22no—
505C4⋊C4—21no—
506C4⋊C4—21no—
507C4⋊C4—21no—
508C4⋊C4—22no—
509C4⋊C4—22no—
510C4⋊C4—22no—
511C4⋊C4—22no—
512C4⋊C4—21no—
513C4⋊C4—21no—
514C4⋊C4—48no—
515C4⋊C4C2×D4×C1112yes—
516C4⋊C4C2×D4×C1111yescharacteristic
517C4⋊C4C2×D4×C1112yes—
518C4⋊C4C2×D4×C1111yescharacteristic
519C22⋊C4—24no—
520C22⋊C4—22no—
521C22⋊C4—21no—
522C22⋊C4—21no—
523C22⋊C4—21no—
524C22⋊C4—48no—
525C22⋊C4—41no—
526C22⋊C4—41no—
527C42—24no—
528C42—21no—
529C42—21no—
530C42—21no—
531C42—22no—
532C42—22no—
533C42—22no—
534C42C2×D4×C1111yescharacteristic
535C42C2×D4×C1111yescharacteristic
536C42C2×D4×C1111yescharacteristic
537C42C2×D4×C1111yescharacteristic
538C11#2432011yescharacteristic, direct product factor, Sylow
539C23—21no—
540C23—22no—
541C23—42no—
542C23—42no—
543C23—41no—
544C23—41no—
545C23C22×D4×C1111yescharacteristic
546Q8—21no—
547Q8—42no—
548Q8—44no—
549Q8—42no—
550Q8—82no—
551Q8—84no—
552Q8C11×C22⋊Q812yescomplemented
553D4—22no—
554D4—22no—
555D4—22no—
556D4—21no—
557D4—22no—
558D4—41no—
559D4—41no—
560D4C11×C22⋊Q812yescomplemented
561C2×C4—21no—
562C2×C4—22no—
563C2×C4—22no—
564C2×C4—22no—
565C2×C4—24no—
566C2×C4—22no—
567C2×C4—21no—
568C2×C4—21no—
569C2×C4—24no—
570C2×C4—22no—
571C2×C4—41no—
572C2×C4—42no—
573C2×C4—42no—
574C2×C4—42no—
575C2×C4—42no—
576C2×C4—44no—
577C2×C4—42no—
578C2×C4—41no—
579C2×C4—82no—
580C2×C4—84no—
581C2×C4—82no—
582C2×C4C11×#12011yescharacteristic
583C2×C4C11×#12011yescharacteristic
584C2×C4C11×#12011yescharacteristic
585C2×C4C11×#12011yescharacteristic
586C2×C4C22×D4×C1111yescharacteristic
587C2×C4C22×D4×C1111yescharacteristic
588C2×C4C22×Q8×C1111yescharacteristic
589C2×C4C2×C11×#4111yescharacteristic
590C2×C4C11×2−1+411yescharacteristic
591C2×C4C11×2−1+411yescharacteristic
592C8—22no—
593C8—41no—
594C8—42no—
595C22—21no—
596C22—21no—
597C22—22no—
598C22—44no—
599C22—41no—
600C22—41no—
601C22—42no—
602C22—82no—
603C22—81no—
604C22—81no—
605C22C2×C11×#12011yescharacteristic
606C22C11×#54811yescharacteristic
607C22D4×Q8×C1111yescharacteristic
608C4—22no—
609C4—21no—
610C4—21no—
611C4—21no—
612C4—44no—
613C4—41no—
614C4—44no—
615C4—42no—
616C4—41no—
617C4—42no—
618C4—81no—
619C4C11×#45312yes—
620C4C2×C11×C22⋊Q811yescharacteristic
621C4C11×#53611yescharacteristic
622C4C11×#54811yescharacteristic
623C4D4×Q8×C1111yescharacteristic
624C2—21no—
625C2—21no—
626C2—42no—
627C2—82no—
628C2C11×#240911yescharacteristic
629C2C2×C11×#45311yescharacteristic
630C2C11×#302011yescharacteristic
subgroupG/H
center, socleC22×C11C2×#120
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC2×C11×AGL(1,ℤ/8)C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C2×C42×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C11×#3503C2semidirect
2. C11×#3077C2semidirect
4. C11×#2542C2semidirect
5. C11×#2060C2semidirect
6. C11×#2027C2semidirect
7. C11×#1997C2semidirect
8. C11×#1986C2semidirect
10. C11×#1859C2semidirect
11. C11×#1806C2semidirect
59. C11×AGL(1,ℤ/8)Q8semidirect
137. #24320C11direct (N × H)
158. C2×D4×C11C2×Q8semidirect
179. C11×M16C2×Q8semidirect
224. #3503C2×C11semidirect
225. #3077C2×C11semidirect
227. #2542C2×C11semidirect
228. #2060C2×C11semidirect
229. #2027C2×C11semidirect
230. #1997C2×C11semidirect
231. #1986C2×C11semidirect
233. #1859C2×C11semidirect
234. #1806C2×C11semidirect
248. Q8×C11C22⋊Q8semidirect
256. D4×C11C22⋊Q8semidirect
367. AGL(1,ℤ/8)Q8×C11semidirect
472. C2×D4C2×Q8×C11semidirect
493. M16C2×Q8×C11semidirect
538. C11#24320direct (N × H)
552. Q8C11×C22⋊Q8semidirect
560. D4C11×C22⋊Q8semidirect

Maximal subgroups

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

subgroupindex
C11×#35032
C11×#30772
C4×C11×AGL(1,ℤ/8)2
C11×#25422
C11×#20602
C11×#20272
C11×#19972
C11×#19862
C11×#18832
C11×#18592
C11×#18062
#2432011