Finite Group Databasebeta

← C11×#24145 #14601338

Subgroups — C11×#24145 #14601338

Order 2816.

1038 conjugacy classes of subgroups.

The subgroup lattice has 642 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3509C211yesmaximal, characteristic, complemented
2C11×#3077C211yesmaximal, characteristic, complemented
3C4×C11×AGL(1,ℤ/8)C211yesmaximal, characteristic
4C11×#2547C211yesmaximal, characteristic, complemented
5C11×#2038C212yesmaximal, complemented
6C11×#2003C212yesmaximal
7C11×#1986C211yesmaximal, characteristic, complemented
8C11×#1966C211yesmaximal, characteristic, complemented
9C11×#1888C212yesmaximal, complemented
10C11×#1857C212yesmaximal, complemented
11C11×#1806C211yesmaximal, characteristic, complemented
12C2×C11×AGL(1,ℤ/8)C2211yescharacteristic
13C11×#557—21no—
14C11×#557—21no—
15C11×#556—21no—
16C11×#556—21no—
17C11×#552—22no—
18C11×#552—22no—
19C11×#541—22no—
20C11×#536C2212yes—
21C11×#533—21no—
22C11×#533—21no—
23C11×#533C2211yescharacteristic
24C2×C11×C4⋊Q8C2211yescharacteristic
25C2×C11×#124C2212yes—
26C11×#519C2212yes—
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×#418C2211yescharacteristic
41C11×#418C2212yes—
42C11×#417C2211yescharacteristic
43C2×C11×#101C2212yes—
44C2×C11×#101C2212yes—
45C4×C11×M16C2211yescharacteristic
46C11×#397—22no—
47C11×#391C2212yes—
48C11×#380—22no—
49C4×C11×C4⋊C4C2211yescharacteristic
50C11×#339C2212yes—
51C11×#339C2212yes—
52C11×#339C2212yes—
53C2×C11×#41C2311yescharacteristic
54C22×Q8×C11C2312yes—
55C22×D4×C11C2311yescharacteristic
56C23×C4×C11—21no—
57C11×AGL(1,ℤ/8)—22no—
58C11×AGL(1,ℤ/8)—22no—
59C2×C11×SD16—21no—
60C2×C11×D8—21no—
61C2×C11×M16C2311yescharacteristic
62C2×C11×M16C2312yes—
63C2×C11×M16C2311yescharacteristic
64C11×C4⋊Q8—22no—
65C11×C4⋊Q8—21no—
66C11×C4⋊Q8—21no—
67C11×C4⋊Q8—21no—
68C11×C4⋊Q8—21no—
69C11×C4⋊Q8D411yescharacteristic
70C11×C4⋊Q8D411yescharacteristic
71C11×#126—24no—
72C11×#126—24no—
73C11×#125—22no—
74C11×#125—22no—
75C11×#125—24no—
76C11×#125—24no—
77C11×#125D412yes—
78C11×#124—22no—
79C11×#124—24no—
80C11×#124—42no—
81C11×#123—24no—
82C11×C22⋊Q8—22no—
83C11×C22⋊Q8—22no—
84C11×C22⋊Q8—21no—
85C11×C22⋊Q8—21no—
86C11×C22⋊Q8—22no—
87C11×C22⋊Q8—22no—
88C4×Q8×C11—22no—
89C4×Q8×C11—22no—
90C4×Q8×C11—22no—
91C4×Q8×C11—22no—
92C4×Q8×C11—22no—
93C4×Q8×C11—22no—
94C4×Q8×C11—21no—
95C4×Q8×C11—21no—
96C4×Q8×C11D411yescharacteristic
97C4×Q8×C11D411yescharacteristic
98C4×D4×C11—21no—
99C4×D4×C11—21no—
100C4×D4×C11—21no—
101C4×D4×C11—21no—
102C4×D4×C11—21no—
103C4×D4×C11—21no—
104C4×D4×C11D411yescharacteristic
105C4×D4×C11D411yescharacteristic
106C11×#117—22no—
107C11×#117—22no—
108C11×#117—24no—
109C11×#117—21no—
110C11×#117C2311yescharacteristic
111C11×#117C2312yes—
112C2×C11×C4⋊C4—21no—
113C2×C11×C4⋊C4D412yes—
114C2×C11×C4⋊C4D412yes—
115C2×C11×C4⋊C4C2311yescharacteristic
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—42no—
128C11×#103—21no—
129C11×#102—21no—
130C11×#102—21no—
131C11×#102—21no—
132C11×#102—22no—
133C11×#102—22no—
134C11×#101—24no—
135C11×#101—42no—
136C11×#97—21no—
137C4×C8×C11—21no—
138C11×#95—21no—
139C11×#95—24no—
140#24145C1111yesmaximal, characteristic, direct product factor, Sylow
141C24×C11—21no—
142C11×#41—21no—
143C11×#41—21no—
144C11×#41—21no—
145C11×#41—21no—
146C2×Q8×C11—21no—
147C2×Q8×C11—21no—
148C2×Q8×C11—22no—
149C2×Q8×C11—22no—
150C2×Q8×C11—22no—
151C2×Q8×C11—22no—
152C2×Q8×C11—22no—
153C2×Q8×C11—22no—
154C2×Q8×C11C2×D411yescharacteristic
155C2×D4×C11—21no—
156C2×D4×C11—21no—
157C2×D4×C11—21no—
158C2×D4×C11—21no—
159C2×D4×C11—21no—
160C2×D4×C11—21no—
161C2×D4×C11C2×D411yescharacteristic
162C2×D4×C11#4112yes—
163C22×C4×C11—21no—
164C22×C4×C11—21no—
165C22×C4×C11—21no—
166C22×C4×C11—21no—
167C22×C4×C11—22no—
168C22×C4×C11—44no—
169C22×C4×C11—41no—
170C22×C4×C11—41no—
171C22×C4×C11C2×D414yes—
172C22×C4×C11C2×D411yescharacteristic
173C22×C4×C11C2×D411yescharacteristic
174C22×C4×C11C2411yescharacteristic
175C11×SD16—24no—
176C11×D8—24no—
177C11×M16—21no—
178C11×M16—22no—
179C11×M16—21no—
180C11×M16—22no—
181C11×M16—21no—
182C11×M16#4112yes—
183C2×C8×C11—21no—
184C2×C8×C11—21no—
185C2×C8×C11—22no—
186C11×C4⋊C4—24no—
187C11×C4⋊C4—24no—
188C11×C4⋊C4—24no—
189C11×C4⋊C4—24no—
190C11×C4⋊C4—22no—
191C11×C4⋊C4—22no—
192C11×C4⋊C4—22no—
193C11×C4⋊C4—22no—
194C11×C4⋊C4—21no—
195C11×C4⋊C4—21no—
196C11×C4⋊C4—21no—
197C11×C4⋊C4—21no—
198C11×C4⋊C4—22no—
199C11×C4⋊C4—22no—
200C11×C4⋊C4—21no—
201C11×C4⋊C4—21no—
202C11×C4⋊C4—42no—
203C11×C4⋊C4C2×D411yescharacteristic
204C11×C4⋊C4C2×D412yes—
205C11×C4⋊C4C2×D411yescharacteristic
206C11×C4⋊C4C2×D412yes—
207C11×C22⋊C4—24no—
208C11×C22⋊C4—24no—
209C11×C22⋊C4—21no—
210C11×C22⋊C4—22no—
211C11×C22⋊C4—21no—
212C11×C22⋊C4—21no—
213C11×C22⋊C4—48no—
214C11×C22⋊C4—41no—
215C11×C22⋊C4—41no—
216C42×C11—24no—
217C42×C11—24no—
218C42×C11—21no—
219C42×C11—21no—
220C42×C11—21no—
221C42×C11—22no—
222C42×C11—22no—
223C42×C11—22no—
224C42×C11C2×D411yescharacteristic
225C42×C11C2×D411yescharacteristic
226C42×C11C2×D411yescharacteristic
227C42×C11C2×D411yescharacteristic
228#3509C2×C1111yescharacteristic, complemented
229#3077C2×C1111yescharacteristic, complemented
230C4×AGL(1,ℤ/8)C2×C1111yescharacteristic
231#2547C2×C1111yescharacteristic, complemented
232#2038C2×C1112yescomplemented
233#2003C2×C1112yes—
234#1986C2×C1111yescharacteristic, complemented
235#1966C2×C1111yescharacteristic, complemented
236#1888C2×C1112yescomplemented
237#1857C2×C1112yescomplemented
238#1806C2×C1111yescharacteristic, complemented
239C23×C11—21no—
240C23×C11—22no—
241C23×C11—42no—
242C23×C11—42no—
243C23×C11—41no—
244C23×C11—41no—
245C23×C11C22×D411yescharacteristic
246Q8×C11—21no—
247Q8×C11—21no—
248Q8×C11—42no—
249Q8×C11—42no—
250Q8×C11—42no—
251Q8×C11—42no—
252Q8×C11—42no—
253Q8×C11—42no—
254D4×C11—21no—
255D4×C11—22no—
256D4×C11—21no—
257D4×C11—22no—
258D4×C11—41no—
259D4×C11—41no—
260D4×C11—41no—
261D4×C11—41no—
262C2×C4×C11—22no—
263C2×C4×C11—21no—
264C2×C4×C11—21no—
265C2×C4×C11—22no—
266C2×C4×C11—22no—
267C2×C4×C11—24no—
268C2×C4×C11—21no—
269C2×C4×C11—24no—
270C2×C4×C11—24no—
271C2×C4×C11—41no—
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—41no—
280C2×C4×C11—42no—
281C2×C4×C11—82no—
282C2×C4×C11—82no—
283C2×C4×C11#12011yescharacteristic
284C2×C4×C11#12011yescharacteristic
285C2×C4×C11#12011yescharacteristic
286C2×C4×C11#12011yescharacteristic
287C2×C4×C11C22×D411yescharacteristic
288C2×C4×C11C22×D411yescharacteristic
289C2×C4×C11C2×#4111yescharacteristic
290C2×C4×C11C2×#4111yescharacteristic
291C2×C4×C11H(5,𝔽2)11yescharacteristic
292C2×C4×C112−1+411yescharacteristic
293C8×C11—22no—
294C8×C11—41no—
295C8×C11—42no—
296C2×AGL(1,ℤ/8)C22×C1111yescharacteristic
297#557—21no—
298#557—21no—
299#556—21no—
300#556—21no—
301#552—22no—
302#552—22no—
303#541—22no—
304#536C22×C1112yes—
305#533—21no—
306#533—21no—
307#533C22×C1111yescharacteristic
308C2×C4⋊Q8C22×C1111yescharacteristic
309C2×#124C22×C1112yes—
310#519C22×C1112yes—
311C4×#41C22×C1111yescharacteristic
312C2×C4×D4C22×C1111yescharacteristic
313#478—22no—
314#476—21no—
315#474—21no—
316#442—21no—
317#440—21no—
318C4×SD16—21no—
319C4×D8—21no—
320#428C22×C1112yes—
321#428C22×C1111yescharacteristic
322#423C22×C1111yescharacteristic
323C2×#104C22×C1112yes—
324#418C22×C1112yes—
325#418C22×C1111yescharacteristic
326#417C22×C1111yescharacteristic
327C2×#101C22×C1112yes—
328C2×#101C22×C1112yes—
329C4×M16C22×C1111yescharacteristic
330#397—22no—
331#391C22×C1112yes—
332#380—22no—
333C4×C4⋊C4C22×C1111yescharacteristic
334#339C22×C1112yes—
335#339C22×C1112yes—
336#339C22×C1112yes—
337C22×C11—21no—
338C22×C11—21no—
339C22×C11—44no—
340C22×C11—41no—
341C22×C11—42no—
342C22×C11—41no—
343C22×C11—41no—
344C22×C11—82no—
345C22×C11—81no—
346C22×C11—81no—
347C22×C11C2×#12011yescharacteristic
348C22×C11#54611yescharacteristic
349C22×C11#54711yescharacteristic
350C4×C11—21no—
351C4×C11—21no—
352C4×C11—21no—
353C4×C11—44no—
354C4×C11—41no—
355C4×C11—41no—
356C4×C11—42no—
357C4×C11—41no—
358C4×C11—42no—
359C4×C11—82no—
360C4×C11—81no—
361C4×C11#45412yes—
362C4×C11#52511yescharacteristic
363C4×C11#53711yescharacteristic
364C4×C11#54811yescharacteristic
365C4×C11#55011yescharacteristic
366C2×#41C23×C1111yescharacteristic
367C22×Q8C23×C1112yes—
368C22×D4C23×C1111yescharacteristic
369C23×C4—21no—
370AGL(1,ℤ/8)—22no—
371AGL(1,ℤ/8)—22no—
372C2×SD16—21no—
373C2×D8—21no—
374C2×M16C23×C1111yescharacteristic
375C2×M16C23×C1112yes—
376C2×M16C23×C1111yescharacteristic
377C4⋊Q8—22no—
378C4⋊Q8—21no—
379C4⋊Q8—21no—
380C4⋊Q8—21no—
381C4⋊Q8—21no—
382C4⋊Q8D4×C1111yescharacteristic
383C4⋊Q8D4×C1111yescharacteristic
384#126—24no—
385#126—24no—
386#125—22no—
387#125—22no—
388#125—24no—
389#125—24no—
390#125D4×C1112yes—
391#124—22no—
392#124—24no—
393#124—42no—
394#123—24no—
395C22⋊Q8—22no—
396C22⋊Q8—22no—
397C22⋊Q8—21no—
398C22⋊Q8—21no—
399C22⋊Q8—22no—
400C22⋊Q8—22no—
401C4×Q8—22no—
402C4×Q8—22no—
403C4×Q8—22no—
404C4×Q8—22no—
405C4×Q8—22no—
406C4×Q8—22no—
407C4×Q8—21no—
408C4×Q8—21no—
409C4×Q8D4×C1111yescharacteristic
410C4×Q8D4×C1111yescharacteristic
411C4×D4—21no—
412C4×D4—21no—
413C4×D4—21no—
414C4×D4—21no—
415C4×D4—21no—
416C4×D4—21no—
417C4×D4D4×C1111yescharacteristic
418C4×D4D4×C1111yescharacteristic
419#117—22no—
420#117—22no—
421#117—24no—
422#117—21no—
423#117C23×C1111yescharacteristic
424#117C23×C1112yes—
425C2×C4⋊C4—21no—
426C2×C4⋊C4D4×C1112yes—
427C2×C4⋊C4D4×C1112yes—
428C2×C4⋊C4C23×C1111yescharacteristic
429C2×C22⋊C4—21no—
430C2×C22⋊C4—24no—
431C2×C42—21no—
432C2×C42C23×C1112yes—
433C2×C42C23×C1111yescharacteristic
434#107—21no—
435#107—22no—
436#106—21no—
437#106—22no—
438C4⋊C8—21no—
439C4⋊C8—21no—
440#104—42no—
441#103—21no—
442#102—21no—
443#102—21no—
444#102—21no—
445#102—22no—
446#102—22no—
447#101—24no—
448#101—42no—
449#97—21no—
450C4×C8—21no—
451#95—21no—
452#95—24no—
453C2×C11—21no—
454C2×C11—21no—
455C2×C11—81no—
456C2×C11—82no—
457C2×C11#240711yescharacteristic
458C2×C11C2×#45411yescharacteristic
459C2×C11#302011yescharacteristic
460C24—21no—
461#41—21no—
462#41—21no—
463#41—21no—
464#41—21no—
465C2×Q8—21no—
466C2×Q8—21no—
467C2×Q8—22no—
468C2×Q8—22no—
469C2×Q8—22no—
470C2×Q8—22no—
471C2×Q8—22no—
472C2×Q8—22no—
473C2×Q8C2×D4×C1111yescharacteristic
474C2×D4—21no—
475C2×D4—21no—
476C2×D4—21no—
477C2×D4—21no—
478C2×D4—21no—
479C2×D4—21no—
480C2×D4C2×D4×C1111yescharacteristic
481C2×D4C11×#4112yes—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—22no—
487C22×C4—44no—
488C22×C4—41no—
489C22×C4—41no—
490C22×C4C2×D4×C1114yes—
491C22×C4C2×D4×C1111yescharacteristic
492C22×C4C2×D4×C1111yescharacteristic
493C22×C4C24×C1111yescharacteristic
494SD16—24no—
495D8—24no—
496M16—21no—
497M16—22no—
498M16—21no—
499M16—22no—
500M16—21no—
501M16C11×#4112yes—
502C2×C8—21no—
503C2×C8—21no—
504C2×C8—22no—
505C4⋊C4—24no—
506C4⋊C4—24no—
507C4⋊C4—24no—
508C4⋊C4—24no—
509C4⋊C4—22no—
510C4⋊C4—22no—
511C4⋊C4—22no—
512C4⋊C4—22no—
513C4⋊C4—21no—
514C4⋊C4—21no—
515C4⋊C4—21no—
516C4⋊C4—21no—
517C4⋊C4—22no—
518C4⋊C4—22no—
519C4⋊C4—21no—
520C4⋊C4—21no—
521C4⋊C4—42no—
522C4⋊C4C2×D4×C1111yescharacteristic
523C4⋊C4C2×D4×C1112yes—
524C4⋊C4C2×D4×C1111yescharacteristic
525C4⋊C4C2×D4×C1112yes—
526C22⋊C4—24no—
527C22⋊C4—24no—
528C22⋊C4—21no—
529C22⋊C4—22no—
530C22⋊C4—21no—
531C22⋊C4—21no—
532C22⋊C4—48no—
533C22⋊C4—41no—
534C22⋊C4—41no—
535C42—24no—
536C42—24no—
537C42—21no—
538C42—21no—
539C42—21no—
540C42—22no—
541C42—22no—
542C42—22no—
543C42C2×D4×C1111yescharacteristic
544C42C2×D4×C1111yescharacteristic
545C42C2×D4×C1111yescharacteristic
546C42C2×D4×C1111yescharacteristic
547C11#2414511yescharacteristic, direct product factor, Sylow
548C23—21no—
549C23—22no—
550C23—42no—
551C23—42no—
552C23—41no—
553C23—41no—
554C23C22×D4×C1111yescharacteristic
555Q8—21no—
556Q8—21no—
557Q8—42no—
558Q8—42no—
559Q8—42no—
560Q8—42no—
561Q8—42no—
562Q8—42no—
563D4—21no—
564D4—22no—
565D4—21no—
566D4—22no—
567D4—41no—
568D4—41no—
569D4—41no—
570D4—41no—
571C2×C4—22no—
572C2×C4—21no—
573C2×C4—21no—
574C2×C4—22no—
575C2×C4—22no—
576C2×C4—24no—
577C2×C4—21no—
578C2×C4—24no—
579C2×C4—24no—
580C2×C4—41no—
581C2×C4—42no—
582C2×C4—41no—
583C2×C4—41no—
584C2×C4—42no—
585C2×C4—42no—
586C2×C4—42no—
587C2×C4—42no—
588C2×C4—41no—
589C2×C4—42no—
590C2×C4—82no—
591C2×C4—82no—
592C2×C4C11×#12011yescharacteristic
593C2×C4C11×#12011yescharacteristic
594C2×C4C11×#12011yescharacteristic
595C2×C4C11×#12011yescharacteristic
596C2×C4C22×D4×C1111yescharacteristic
597C2×C4C22×D4×C1111yescharacteristic
598C2×C4C2×C11×#4111yescharacteristic
599C2×C4C2×C11×#4111yescharacteristic
600C2×C4C11×H(5,𝔽2)11yescharacteristic
601C2×C4C11×2−1+411yescharacteristic
602C8—22no—
603C8—41no—
604C8—42no—
605C22—21no—
606C22—21no—
607C22—44no—
608C22—41no—
609C22—42no—
610C22—41no—
611C22—41no—
612C22—82no—
613C22—81no—
614C22—81no—
615C22C2×C11×#12011yescharacteristic
616C22C11×#54611yescharacteristic
617C22C11×#54711yescharacteristic
618C4—21no—
619C4—21no—
620C4—21no—
621C4—44no—
622C4—41no—
623C4—41no—
624C4—42no—
625C4—41no—
626C4—42no—
627C4—82no—
628C4—81no—
629C4C11×#45412yes—
630C4C11×#52511yescharacteristic
631C4C11×#53711yescharacteristic
632C4C11×#54811yescharacteristic
633C4C11×#55011yescharacteristic
634C2—21no—
635C2—21no—
636C2—82no—
637C2—81no—
638C2C11×#240711yescharacteristic
639C2C2×C11×#45411yescharacteristic
640C2C11×#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×#3509C2semidirect
2. C11×#3077C2semidirect
4. C11×#2547C2semidirect
5. C11×#2038C2semidirect
7. C11×#1986C2semidirect
8. C11×#1966C2semidirect
9. C11×#1888C2semidirect
10. C11×#1857C2semidirect
11. C11×#1806C2semidirect
140. #24145C11direct (N × H)
228. #3509C2×C11semidirect
229. #3077C2×C11semidirect
231. #2547C2×C11semidirect
232. #2038C2×C11semidirect
234. #1986C2×C11semidirect
235. #1966C2×C11semidirect
236. #1888C2×C11semidirect
237. #1857C2×C11semidirect
238. #1806C2×C11semidirect
547. C11#24145direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#35092
C11×#30772
C4×C11×AGL(1,ℤ/8)2
C11×#25472
C11×#20382
C11×#20032
C11×#19862
C11×#19662
C11×#18882
C11×#18572
C11×#18062
#2414511