Finite Group Databasebeta

← C11×#23917 #14601110

Subgroups — C11×#23917 #14601110

Order 2816.

1682 conjugacy classes of subgroups.

The subgroup lattice has 626 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3486C211yesmaximal, characteristic, complemented
2C2×C11×#536C211yesmaximal, characteristic, complemented
3C2×C11×#456C211yesmaximal, characteristic, complemented
4C2×C11×#454C211yesmaximal, characteristic, complemented
5C11×#3005C212yesmaximal, complemented
6C11×#2005C212yesmaximal, complemented
7C11×#2003C212yesmaximal, complemented
8C11×#1897C212yesmaximal, complemented
9C11×#1888C211yesmaximal, characteristic, complemented
10C11×#1886C211yesmaximal, characteristic, complemented
11C11×#1784C211yesmaximal, characteristic, complemented
12C2×C11×2−1+4C2211yescharacteristic
13C22×C11×#41C2211yescharacteristic
14C23×Q8×C11C2211yescharacteristic
15C2×C11×#137C2212yes—
16C2×C11×AGL(1,ℤ/8)C2212yes—
17D4×Q8×C11—24no—
18C11×#548—24no—
19C11×#536—22no—
20C11×#536—24no—
21C11×#536—24no—
22C11×#536C2212yes—
23C2×C11×C4⋊Q8C2211yescharacteristic
24C2×C11×C4⋊Q8C2211yescharacteristic
25C2×C11×#124C2211yescharacteristic
26C2×C11×#124C2211yescharacteristic
27C11×#525—22no—
28C11×#525C2212yes—
29C2×C11×#123—22no—
30C2×C11×C22⋊Q8—22no—
31C11×#519C2211yescharacteristic
32C2×C11×#117C2211yescharacteristic
33C11×#456—24no—
34C11×#454—24no—
35C11×#452—24no—
36C11×#449—24no—
37C2×C11×#104C2212yes—
38C2×C11×#104C2212yes—
39C11×#419C2212yes—
40C11×#418C2212yes—
41C2×C11×#101C2211yescharacteristic
42C2×C11×#101C2211yescharacteristic
43C2×C11×#101C2212yes—
44C11×#407C2212yes—
45C11×#339C2212yes—
46C11×#339C2212yes—
47C11×2−1+4—22no—
48C11×2−1+4—22no—
49C11×2−1+4—42no—
50C2×C11×#41—22no—
51C2×C11×#41—22no—
52C2×C11×#41—22no—
53C2×C11×#41—22no—
54C2×C11×#41—24no—
55C2×C11×#41—42no—
56C2×C11×#41C2312yes—
57C22×Q8×C11—22no—
58C22×Q8×C11—22no—
59C22×Q8×C11—22no—
60C22×Q8×C11—24no—
61C22×Q8×C11—42no—
62C22×Q8×C11D412yes—
63C22×Q8×C11C2311yescharacteristic
64C22×Q8×C11C2311yescharacteristic
65C22×Q8×C11C2311yescharacteristic
66C22×D4×C11—21no—
67C22×D4×C11C2311yescharacteristic
68C23×C4×C11—21no—
69C23×C4×C11D412yes—
70C23×C4×C11C2311yescharacteristic
71C11×#137—24no—
72C11×#137—42no—
73C11×AGL(1,ℤ/8)—24no—
74C11×AGL(1,ℤ/8)—42no—
75C2×C11×Q16—22no—
76C2×C11×SD16—22no—
77C2×C11×SD16—22no—
78C2×C11×D8—22no—
79C2×C11×M16C2312yes—
80C2×C11×M16C2312yes—
81C11×C4⋊Q8—24no—
82C11×C4⋊Q8—22no—
83C11×C4⋊Q8—22no—
84C11×C4⋊Q8—22no—
85C11×C4⋊Q8—22no—
86C11×C4⋊Q8D414yescomplemented
87C11×#124—24no—
88C11×#124—22no—
89C11×#124—22no—
90C11×#124—22no—
91C11×#124—22no—
92C11×#124D414yescomplemented
93C11×#123—216no—
94C11×#123—24no—
95C11×#123—22no—
96C11×C22⋊Q8—216no—
97C11×C22⋊Q8—24no—
98C11×C22⋊Q8—28no—
99C11×C22⋊Q8—24no—
100C11×C22⋊Q8D414yes—
101C11×#121—24no—
102C11×#121D414yes—
103C11×#120—22no—
104C4×Q8×C11—24no—
105C4×D4×C11—28no—
106C4×D4×C11—24no—
107C11×#117—22no—
108C11×#117—22no—
109C11×#117—22no—
110C11×#117C2312yes—
111C2×C11×C4⋊C4—21no—
112C2×C11×C4⋊C4—22no—
113C2×C11×C4⋊C4—22no—
114C2×C11×C22⋊C4—21no—
115C2×C11×C22⋊C4—22no—
116C2×C11×C22⋊C4—22no—
117C2×C42×C11C2311yescharacteristic
118C2×C42×C11C2311yescharacteristic
119C11×#104—24no—
120C11×#104—24no—
121C11×#103—24no—
122C11×#102—24no—
123C11×#101—22no—
124C11×#101—22no—
125C11×#101—42no—
126C11×C22⋊C8—24no—
127#23917C1111yesmaximal, characteristic, direct product factor, Sylow
128C24×C11—21no—
129C24×C11C2×D411yescharacteristic
130C11×#41—22no—
131C11×#41—22no—
132C11×#41—22no—
133C11×#41—22no—
134C11×#41—48no—
135C11×#41—48no—
136C11×#41—44no—
137C11×#41—44no—
138C11×#41—44no—
139C11×#41—44no—
140C2×Q8×C11—22no—
141C2×Q8×C11—24no—
142C2×Q8×C11—24no—
143C2×Q8×C11—22no—
144C2×Q8×C11—22no—
145C2×Q8×C11—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—42no—
153C2×Q8×C11—48no—
154C2×Q8×C11—48no—
155C2×Q8×C11—44no—
156C2×Q8×C11—44no—
157C2×Q8×C11C2×D412yes—
158C2×Q8×C11C2×D412yes—
159C2×Q8×C11C2×D412yes—
160C2×Q8×C11C2×D412yes—
161C2×D4×C11—22no—
162C2×D4×C11—24no—
163C2×D4×C11—24no—
164C2×D4×C11—22no—
165C2×D4×C11—22no—
166C2×D4×C11—21no—
167C2×D4×C11—22no—
168C2×D4×C11—42no—
169C2×D4×C11—42no—
170C2×D4×C11C2×D412yes—
171C2×D4×C11C2×D412yes—
172C22×C4×C11—21no—
173C22×C4×C11—21no—
174C22×C4×C11—22no—
175C22×C4×C11—24no—
176C22×C4×C11—24no—
177C22×C4×C11—24no—
178C22×C4×C11—21no—
179C22×C4×C11—21no—
180C22×C4×C11—21no—
181C22×C4×C11—24no—
182C22×C4×C11—22no—
183C22×C4×C11—42no—
184C22×C4×C11—42no—
185C22×C4×C11—42no—
186C22×C4×C11C2×D412yes—
187C22×C4×C11C2×D412yes—
188C22×C4×C11C2×D411yescharacteristic
189C22×C4×C11C2×D414yes—
190C22×C4×C11C2411yescharacteristic
191C11×Q16—44no—
192C11×SD16—44no—
193C11×SD16—44no—
194C11×D8—44no—
195C11×M16—22no—
196C11×M16—22no—
197C11×M16—22no—
198C11×M16—22no—
199C2×C8×C11—22no—
200C2×C8×C11—22no—
201C11×C4⋊C4—24no—
202C11×C4⋊C4—28no—
203C11×C4⋊C4—24no—
204C11×C4⋊C4—28no—
205C11×C4⋊C4—28no—
206C11×C4⋊C4—24no—
207C11×C4⋊C4C2×D414yes—
208C11×C22⋊C4—24no—
209C11×C22⋊C4—28no—
210C11×C22⋊C4—28no—
211C11×C22⋊C4—24no—
212C11×C22⋊C4—22no—
213C11×C22⋊C4—28no—
214C11×C22⋊C4—24no—
215C42×C11—24no—
216C42×C11—21no—
217C42×C11—21no—
218C42×C11—22no—
219C42×C11C2×D412yes—
220C42×C11C2×D412yes—
221#3486C2×C1111yescharacteristic, complemented
222C2×#536C2×C1111yescharacteristic, complemented
223C2×#456C2×C1111yescharacteristic, complemented
224C2×#454C2×C1111yescharacteristic, complemented
225#3005C2×C1112yescomplemented
226#2005C2×C1112yescomplemented
227#2003C2×C1112yescomplemented
228#1897C2×C1112yescomplemented
229#1888C2×C1111yescharacteristic, complemented
230#1886C2×C1111yescharacteristic, complemented
231#1784C2×C1111yescharacteristic, complemented
232C23×C11—21no—
233C23×C11—21no—
234C23×C11—22no—
235C23×C11—22no—
236C23×C11—42no—
237C23×C11—44no—
238C23×C11—41no—
239C23×C11—41no—
240C23×C11#12012yes—
241C23×C11C22×D411yescharacteristic
242Q8×C11—24no—
243Q8×C11—24no—
244Q8×C11—22no—
245Q8×C11—24no—
246Q8×C11—22no—
247Q8×C11—48no—
248Q8×C11—44no—
249Q8×C11—42no—
250Q8×C11—42no—
251Q8×C11—42no—
252D4×C11—22no—
253D4×C11—24no—
254D4×C11—22no—
255D4×C11—44no—
256D4×C11—48no—
257D4×C11—48no—
258D4×C11—42no—
259D4×C11—42no—
260D4×C11—42no—
261C2×C4×C11—21no—
262C2×C4×C11—22no—
263C2×C4×C11—21no—
264C2×C4×C11—22no—
265C2×C4×C11—24no—
266C2×C4×C11—24no—
267C2×C4×C11—22no—
268C2×C4×C11—22no—
269C2×C4×C11—22no—
270C2×C4×C11—22no—
271C2×C4×C11—24no—
272C2×C4×C11—22no—
273C2×C4×C11—22no—
274C2×C4×C11—22no—
275C2×C4×C11—48no—
276C2×C4×C11—48no—
277C2×C4×C11—48no—
278C2×C4×C11—42no—
279C2×C4×C11—42no—
280C2×C4×C11—41no—
281C2×C4×C11—41no—
282C2×C4×C11—42no—
283C2×C4×C11—42no—
284C2×C4×C11#12014yes—
285C2×C4×C11#12012yes—
286C2×C4×C11C22×D411yescharacteristic
287C2×C4×C11C22×D411yescharacteristic
288C2×C4×C11C22×D412yes—
289C2×C4×C11H(5,𝔽2)12yes—
290C8×C11—42no—
291C8×C11—42no—
292C2×2−1+4C22×C1111yescharacteristic
293C22×#41C22×C1111yescharacteristic
294C23×Q8C22×C1111yescharacteristic
295C2×#137C22×C1112yes—
296C2×AGL(1,ℤ/8)C22×C1112yes—
297D4×Q8—24no—
298#548—24no—
299#536—22no—
300#536—24no—
301#536—24no—
302#536C22×C1112yes—
303C2×C4⋊Q8C22×C1111yescharacteristic
304C2×C4⋊Q8C22×C1111yescharacteristic
305C2×#124C22×C1111yescharacteristic
306C2×#124C22×C1111yescharacteristic
307#525—22no—
308#525C22×C1112yes—
309C2×#123—22no—
310C2×C22⋊Q8—22no—
311#519C22×C1111yescharacteristic
312C2×#117C22×C1111yescharacteristic
313#456—24no—
314#454—24no—
315#452—24no—
316#449—24no—
317C2×#104C22×C1112yes—
318C2×#104C22×C1112yes—
319#419C22×C1112yes—
320#418C22×C1112yes—
321C2×#101C22×C1111yescharacteristic
322C2×#101C22×C1111yescharacteristic
323C2×#101C22×C1112yes—
324#407C22×C1112yes—
325#339C22×C1112yes—
326#339C22×C1112yes—
327C22×C11—22no—
328C22×C11—22no—
329C22×C11—22no—
330C22×C11—22no—
331C22×C11—42no—
332C22×C11—42no—
333C22×C11—44no—
334C22×C11—42no—
335C22×C11—42no—
336C22×C11—44no—
337C22×C11—82no—
338C22×C11—82no—
339C22×C11C2×#12011yescharacteristic
340C22×C11C2×#12011yescharacteristic
341C22×C11#53411yescharacteristic
342C4×C11—22no—
343C4×C11—24no—
344C4×C11—42no—
345C4×C11—42no—
346C4×C11—42no—
347C4×C11—42no—
348C4×C11—42no—
349C4×C11—44no—
350C4×C11D4212yes—
351C4×C11D4212yes—
3522−1+4—22no—
3532−1+4—22no—
3542−1+4—42no—
355C2×#41—22no—
356C2×#41—22no—
357C2×#41—22no—
358C2×#41—22no—
359C2×#41—24no—
360C2×#41—42no—
361C2×#41C23×C1112yes—
362C22×Q8—22no—
363C22×Q8—22no—
364C22×Q8—22no—
365C22×Q8—24no—
366C22×Q8—42no—
367C22×Q8D4×C1112yes—
368C22×Q8C23×C1111yescharacteristic
369C22×Q8C23×C1111yescharacteristic
370C22×Q8C23×C1111yescharacteristic
371C22×D4—21no—
372C22×D4C23×C1111yescharacteristic
373C23×C4—21no—
374C23×C4D4×C1112yes—
375C23×C4C23×C1111yescharacteristic
376#137—24no—
377#137—42no—
378AGL(1,ℤ/8)—24no—
379AGL(1,ℤ/8)—42no—
380C2×Q16—22no—
381C2×SD16—22no—
382C2×SD16—22no—
383C2×D8—22no—
384C2×M16C23×C1112yes—
385C2×M16C23×C1112yes—
386C4⋊Q8—24no—
387C4⋊Q8—22no—
388C4⋊Q8—22no—
389C4⋊Q8—22no—
390C4⋊Q8—22no—
391C4⋊Q8D4×C1114yescomplemented
392#124—24no—
393#124—22no—
394#124—22no—
395#124—22no—
396#124—22no—
397#124D4×C1114yescomplemented
398#123—216no—
399#123—24no—
400#123—22no—
401C22⋊Q8—216no—
402C22⋊Q8—24no—
403C22⋊Q8—28no—
404C22⋊Q8—24no—
405C22⋊Q8D4×C1114yes—
406#121—24no—
407#121D4×C1114yes—
408#120—22no—
409C4×Q8—24no—
410C4×D4—28no—
411C4×D4—24no—
412#117—22no—
413#117—22no—
414#117—22no—
415#117C23×C1112yes—
416C2×C4⋊C4—21no—
417C2×C4⋊C4—22no—
418C2×C4⋊C4—22no—
419C2×C22⋊C4—21no—
420C2×C22⋊C4—22no—
421C2×C22⋊C4—22no—
422C2×C42C23×C1111yescharacteristic
423C2×C42C23×C1111yescharacteristic
424#104—24no—
425#104—24no—
426#103—24no—
427#102—24no—
428#101—22no—
429#101—22no—
430#101—42no—
431C22⋊C8—24no—
432C2×C11—21no—
433C2×C11—21no—
434C2×C11—42no—
435C2×C11—82no—
436C2×C11—82no—
437C2×C11#240311yescharacteristic
438C2×C11#302012yes—
439C24—21no—
440C24C2×D4×C1111yescharacteristic
441#41—22no—
442#41—22no—
443#41—22no—
444#41—22no—
445#41—48no—
446#41—48no—
447#41—44no—
448#41—44no—
449#41—44no—
450#41—44no—
451C2×Q8—22no—
452C2×Q8—24no—
453C2×Q8—24no—
454C2×Q8—22no—
455C2×Q8—22no—
456C2×Q8—21no—
457C2×Q8—21no—
458C2×Q8—21no—
459C2×Q8—22no—
460C2×Q8—22no—
461C2×Q8—22no—
462C2×Q8—22no—
463C2×Q8—42no—
464C2×Q8—48no—
465C2×Q8—48no—
466C2×Q8—44no—
467C2×Q8—44no—
468C2×Q8C2×D4×C1112yes—
469C2×Q8C2×D4×C1112yes—
470C2×Q8C2×D4×C1112yes—
471C2×Q8C2×D4×C1112yes—
472C2×D4—22no—
473C2×D4—24no—
474C2×D4—24no—
475C2×D4—22no—
476C2×D4—22no—
477C2×D4—21no—
478C2×D4—22no—
479C2×D4—42no—
480C2×D4—42no—
481C2×D4C2×D4×C1112yes—
482C2×D4C2×D4×C1112yes—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—22no—
486C22×C4—24no—
487C22×C4—24no—
488C22×C4—24no—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—21no—
492C22×C4—24no—
493C22×C4—22no—
494C22×C4—42no—
495C22×C4—42no—
496C22×C4—42no—
497C22×C4C2×D4×C1112yes—
498C22×C4C2×D4×C1112yes—
499C22×C4C2×D4×C1111yescharacteristic
500C22×C4C2×D4×C1114yes—
501C22×C4C24×C1111yescharacteristic
502Q16—44no—
503SD16—44no—
504SD16—44no—
505D8—44no—
506M16—22no—
507M16—22no—
508M16—22no—
509M16—22no—
510C2×C8—22no—
511C2×C8—22no—
512C4⋊C4—24no—
513C4⋊C4—28no—
514C4⋊C4—24no—
515C4⋊C4—28no—
516C4⋊C4—28no—
517C4⋊C4—24no—
518C4⋊C4C2×D4×C1114yes—
519C22⋊C4—24no—
520C22⋊C4—28no—
521C22⋊C4—28no—
522C22⋊C4—24no—
523C22⋊C4—22no—
524C22⋊C4—28no—
525C22⋊C4—24no—
526C42—24no—
527C42—21no—
528C42—21no—
529C42—22no—
530C42C2×D4×C1112yes—
531C42C2×D4×C1112yes—
532C11#2391711yescharacteristic, direct product factor, Sylow
533C23—21no—
534C23—21no—
535C23—22no—
536C23—22no—
537C23—42no—
538C23—44no—
539C23—41no—
540C23—41no—
541C23C11×#12012yes—
542C23C22×D4×C1111yescharacteristic
543Q8—24no—
544Q8—24no—
545Q8—22no—
546Q8—24no—
547Q8—22no—
548Q8—48no—
549Q8—44no—
550Q8—42no—
551Q8—42no—
552Q8—42no—
553D4—22no—
554D4—24no—
555D4—22no—
556D4—44no—
557D4—48no—
558D4—48no—
559D4—42no—
560D4—42no—
561D4—42no—
562C2×C4—22no—
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—22no—
566C2×C4—24no—
567C2×C4—24no—
568C2×C4—24no—
569C2×C4—22no—
570C2×C4—22no—
571C2×C4—22no—
572C2×C4—22no—
573C2×C4—22no—
574C2×C4—22no—
575C2×C4—22no—
576C2×C4—48no—
577C2×C4—48no—
578C2×C4—48no—
579C2×C4—42no—
580C2×C4—42no—
581C2×C4—41no—
582C2×C4—41no—
583C2×C4—42no—
584C2×C4—42no—
585C2×C4C11×#12014yes—
586C2×C4C11×#12012yes—
587C2×C4C22×D4×C1111yescharacteristic
588C2×C4C22×D4×C1111yescharacteristic
589C2×C4C22×D4×C1112yes—
590C2×C4C11×H(5,𝔽2)12yes—
591C8—42no—
592C8—42no—
593C22—22no—
594C22—22no—
595C22—22no—
596C22—22no—
597C22—42no—
598C22—42no—
599C22—44no—
600C22—42no—
601C22—42no—
602C22—44no—
603C22—82no—
604C22—82no—
605C22C2×C11×#12011yescharacteristic
606C22C2×C11×#12011yescharacteristic
607C22C11×#53411yescharacteristic
608C4—22no—
609C4—24no—
610C4—42no—
611C4—42no—
612C4—42no—
613C4—42no—
614C4—42no—
615C4—44no—
616C4D42×C1112yes—
617C4D42×C1112yes—
618C2—21no—
619C2—21no—
620C2—42no—
621C2—82no—
622C2—82no—
623C2C11×#240311yescharacteristic
624C2C11×#302012yes—
subgroupG/H
center, socleC22×C11C2×#120
commutator, Frattini, cosocleC22×C4C24×C11
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C23×C4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C11×#3486C2semidirect
2. C2×C11×#536C2semidirect
3. C2×C11×#456C2semidirect
4. C2×C11×#454C2semidirect
5. C11×#3005C2semidirect
6. C11×#2005C2semidirect
7. C11×#2003C2semidirect
8. C11×#1897C2semidirect
9. C11×#1888C2semidirect
10. C11×#1886C2semidirect
11. C11×#1784C2semidirect
86. C11×C4⋊Q8D4semidirect
92. C11×#124D4semidirect
127. #23917C11direct (N × H)
221. #3486C2×C11semidirect
222. C2×#536C2×C11semidirect
223. C2×#456C2×C11semidirect
224. C2×#454C2×C11semidirect
225. #3005C2×C11semidirect
226. #2005C2×C11semidirect
227. #2003C2×C11semidirect
228. #1897C2×C11semidirect
229. #1888C2×C11semidirect
230. #1886C2×C11semidirect
231. #1784C2×C11semidirect
391. C4⋊Q8D4×C11semidirect
397. #124D4×C11semidirect
532. C11#23917direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#34862
C2×C11×#5362
C2×C11×#4562
C2×C11×#4542
C11×#30052
C11×#20052
C11×#20032
C11×#18972
C11×#18882
C11×#18862
C11×#17842
#2391711