Finite Group Databasebeta

← C11×#23908 #14601101

Subgroups — C11×#23908 #14601101

Order 2816.

1814 conjugacy classes of subgroups.

The subgroup lattice has 648 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3485C211yesmaximal, characteristic, complemented
2C2×C11×#532C211yesmaximal, characteristic, complemented
3C2×C11×#455C211yesmaximal, characteristic, complemented
4C2×C11×#453C211yesmaximal, characteristic, complemented
5C11×#3005C212yesmaximal, complemented
6C11×#2005C212yesmaximal, complemented
7C11×#2003C212yesmaximal, complemented
8C11×#1896C212yesmaximal, complemented
9C11×#1887C211yesmaximal, characteristic, complemented
10C11×#1885C211yesmaximal, characteristic, complemented
11C11×#1785C211yesmaximal, characteristic, complemented
12C2×C11×H(5,𝔽2)C2211yescharacteristic
13C22×C11×#41C2211yescharacteristic
14C22×C11×#41C2211yescharacteristic, complemented
15C2×C11×#137C2212yes—
16C2×C11×AGL(1,ℤ/8)C2212yes—
17C11×#547—24no—
18C11×#546—24no—
19C11×#536C2212yes—
20C11×#534—22no—
21C11×#532—24no—
22C11×#532—24no—
23C2×C11×C4⋊Q8C2211yescharacteristic, complemented
24C2×C11×#127C2211yescharacteristic
25C2×C11×#124C2211yescharacteristic
26C2×C11×#124C2211yescharacteristic, complemented
27C11×#525C2212yes—
28C2×C11×#123—22no—
29C2×C11×#121—22no—
30C11×#518C2211yescharacteristic
31C2×C4×D4×C11—22no—
32C22×C42×C11C2211yescharacteristic, complemented
33C11×#455—24no—
34C11×#453—24no—
35C11×#452—24no—
36C11×#449—24no—
37C2×C11×#104C2212yes—
38C2×C11×#104C2212yes—
39C11×#419C2212yescomplemented
40C11×#418C2212yescomplemented
41C2×C11×#101C2212yescomplemented
42C2×C11×#100C2211yescharacteristic
43C2×C11×#100C2211yescharacteristic
44C11×#407C2212yescomplemented
45C11×#339C2212yescomplemented
46C11×#339C2212yescomplemented
47C11×H(5,𝔽2)—22no—
48C11×H(5,𝔽2)—22no—
49C11×H(5,𝔽2)—42no—
50C2×C11×#41—22no—
51C2×C11×#41—22no—
52C2×C11×#41—22no—
53C2×C11×#41—22no—
54C2×C11×#41—22no—
55C2×C11×#41—24no—
56C2×C11×#41—24no—
57C2×C11×#41—42no—
58C2×C11×#41—42no—
59C2×C11×#41C2312yes—
60C22×Q8×C11C2311yescharacteristic
61C22×Q8×C11C2311yescharacteristic
62C22×D4×C11—22no—
63C22×D4×C11—21no—
64C22×D4×C11—22no—
65C22×D4×C11—22no—
66C22×D4×C11D412yes—
67C22×D4×C11C2311yescharacteristic
68C22×D4×C11C2311yescharacteristic
69C23×C4×C11—21no—
70C23×C4×C11—21no—
71C23×C4×C11D412yes—
72C23×C4×C11C2311yescharacteristic
73C11×#137—24no—
74C11×#137—42no—
75C11×AGL(1,ℤ/8)—24no—
76C11×AGL(1,ℤ/8)—42no—
77C2×C11×Q16—22no—
78C2×C11×SD16—22no—
79C2×C11×SD16—22no—
80C2×C11×D8—22no—
81C2×C11×M16C2312yes—
82C2×C11×M16C2312yes—
83C11×C4⋊Q8—22no—
84C11×C4⋊Q8—22no—
85C11×C4⋊Q8—22no—
86C11×#127—22no—
87C11×#127D414yescomplemented
88C11×#124—22no—
89C11×#124—22no—
90C11×#124—22no—
91C11×#124—22no—
92C11×#124D414yescomplemented
93C11×#123—28no—
94C11×#123—24no—
95C11×#123—22no—
96C11×#123—24no—
97C11×C22⋊Q8—24no—
98C11×C22⋊Q8D414yescomplemented
99C11×#121—216no—
100C11×#121—28no—
101C11×#121D414yescomplemented
102C11×#120—24no—
103C11×#120—22no—
104C4×D4×C11—216no—
105C4×D4×C11—24no—
106C4×D4×C11—24no—
107C11×#117C2312yes—
108C2×C11×C4⋊C4—24no—
109C2×C11×C4⋊C4—22no—
110C2×C11×C22⋊C4—24no—
111C2×C11×C22⋊C4—22no—
112C2×C11×C22⋊C4—22no—
113C2×C11×C22⋊C4—22no—
114C2×C42×C11—21no—
115C2×C42×C11—22no—
116C2×C42×C11—22no—
117C2×C42×C11C2311yescharacteristic
118C2×C42×C11C2311yescharacteristic
119C11×#104—24no—
120C11×#104—24no—
121C11×#103—24no—
122C11×#102—24no—
123C11×#101—42no—
124C11×#100—22no—
125C11×#100—22no—
126C11×C22⋊C8—24no—
127#23908C1111yesmaximal, characteristic, direct product factor, Sylow
128C24×C11—22no—
129C24×C11—21no—
130C24×C11C2×D412yes—
131C24×C11C2×D411yescharacteristic
132C11×#41—22no—
133C11×#41—22no—
134C11×#41—22no—
135C11×#41—22no—
136C11×#41—48no—
137C11×#41—48no—
138C11×#41—48no—
139C11×#41—48no—
140C11×#41—44no—
141C11×#41—44no—
142C2×Q8×C11—22no—
143C2×Q8×C11—21no—
144C2×Q8×C11—21no—
145C2×Q8×C11—21no—
146C2×Q8×C11—22no—
147C2×Q8×C11—22no—
148C2×Q8×C11—22no—
149C2×Q8×C11C2×D412yes—
150C2×Q8×C11C2×D412yes—
151C2×D4×C11—24no—
152C2×D4×C11—24no—
153C2×D4×C11—28no—
154C2×D4×C11—24no—
155C2×D4×C11—24no—
156C2×D4×C11—22no—
157C2×D4×C11—24no—
158C2×D4×C11—22no—
159C2×D4×C11—22no—
160C2×D4×C11—21no—
161C2×D4×C11—22no—
162C2×D4×C11—22no—
163C2×D4×C11—42no—
164C2×D4×C11—48no—
165C2×D4×C11—44no—
166C2×D4×C11—44no—
167C2×D4×C11—42no—
168C2×D4×C11—44no—
169C2×D4×C11—42no—
170C2×D4×C11—44no—
171C2×D4×C11C2×D412yes—
172C2×D4×C11C2×D412yes—
173C2×D4×C11C2×D412yes—
174C2×D4×C11C2×D412yes—
175C22×C4×C11—21no—
176C22×C4×C11—21no—
177C22×C4×C11—21no—
178C22×C4×C11—22no—
179C22×C4×C11—24no—
180C22×C4×C11—22no—
181C22×C4×C11—24no—
182C22×C4×C11—24no—
183C22×C4×C11—21no—
184C22×C4×C11—21no—
185C22×C4×C11—24no—
186C22×C4×C11—24no—
187C22×C4×C11—22no—
188C22×C4×C11—42no—
189C22×C4×C11—44no—
190C22×C4×C11—42no—
191C22×C4×C11—42no—
192C22×C4×C11C2×D412yes—
193C22×C4×C11C2×D411yescharacteristic
194C22×C4×C11C2×D414yes—
195C22×C4×C11C2411yescharacteristic
196C11×Q16—44no—
197C11×SD16—44no—
198C11×SD16—44no—
199C11×D8—44no—
200C11×M16—22no—
201C11×M16—22no—
202C11×M16—22no—
203C11×M16—22no—
204C2×C8×C11—22no—
205C2×C8×C11—22no—
206C11×C4⋊C4—28no—
207C11×C4⋊C4—28no—
208C11×C4⋊C4—24no—
209C11×C4⋊C4C2×D414yes—
210C11×C22⋊C4—24no—
211C11×C22⋊C4—28no—
212C11×C22⋊C4—28no—
213C11×C22⋊C4—28no—
214C11×C22⋊C4—24no—
215C11×C22⋊C4—22no—
216C11×C22⋊C4—24no—
217C42×C11—24no—
218C42×C11—21no—
219C42×C11—21no—
220C42×C11—22no—
221C42×C11C2×D412yes—
222C42×C11C2×D412yes—
223#3485C2×C1111yescharacteristic, complemented
224C2×#532C2×C1111yescharacteristic, complemented
225C2×#455C2×C1111yescharacteristic, complemented
226C2×#453C2×C1111yescharacteristic, complemented
227#3005C2×C1112yescomplemented
228#2005C2×C1112yescomplemented
229#2003C2×C1112yescomplemented
230#1896C2×C1112yescomplemented
231#1887C2×C1111yescharacteristic, complemented
232#1885C2×C1111yescharacteristic, complemented
233#1785C2×C1111yescharacteristic, complemented
234C23×C11—21no—
235C23×C11—22no—
236C23×C11—21no—
237C23×C11—22no—
238C23×C11—22no—
239C23×C11—22no—
240C23×C11—42no—
241C23×C11—44no—
242C23×C11—44no—
243C23×C11—44no—
244C23×C11—41no—
245C23×C11—41no—
246C23×C11—84no—
247C23×C11#12012yes—
248C23×C11#12014yes—
249C23×C11C22×D411yescharacteristic
250Q8×C11—22no—
251Q8×C11—24no—
252Q8×C11—22no—
253Q8×C11—42no—
254Q8×C11—42no—
255Q8×C11—42no—
256D4×C11—24no—
257D4×C11—24no—
258D4×C11—22no—
259D4×C11—24no—
260D4×C11—22no—
261D4×C11—416no—
262D4×C11—48no—
263D4×C11—48no—
264D4×C11—48no—
265D4×C11—42no—
266D4×C11—42no—
267D4×C11—42no—
268D4×C11—84no—
269C2×C4×C11—24no—
270C2×C4×C11—21no—
271C2×C4×C11—22no—
272C2×C4×C11—21no—
273C2×C4×C11—24no—
274C2×C4×C11—24no—
275C2×C4×C11—22no—
276C2×C4×C11—22no—
277C2×C4×C11—22no—
278C2×C4×C11—24no—
279C2×C4×C11—22no—
280C2×C4×C11—22no—
281C2×C4×C11—22no—
282C2×C4×C11—48no—
283C2×C4×C11—48no—
284C2×C4×C11—48no—
285C2×C4×C11—42no—
286C2×C4×C11—44no—
287C2×C4×C11—41no—
288C2×C4×C11—41no—
289C2×C4×C11—42no—
290C2×C4×C11—42no—
291C2×C4×C11—84no—
292C2×C4×C11#12012yes—
293C2×C4×C11C22×D411yescharacteristic
294C2×C4×C11C22×D411yescharacteristic
295C2×C4×C11C22×D412yes—
296C2×C4×C11H(5,𝔽2)12yes—
297C8×C11—42no—
298C8×C11—42no—
299C2×H(5,𝔽2)C22×C1111yescharacteristic
300C22×#41C22×C1111yescharacteristic
301C22×#41C22×C1111yescharacteristic, complemented
302C2×#137C22×C1112yes—
303C2×AGL(1,ℤ/8)C22×C1112yes—
304#547—24no—
305#546—24no—
306#536C22×C1112yes—
307#534—22no—
308#532—24no—
309#532—24no—
310C2×C4⋊Q8C22×C1111yescharacteristic, complemented
311C2×#127C22×C1111yescharacteristic
312C2×#124C22×C1111yescharacteristic
313C2×#124C22×C1111yescharacteristic, complemented
314#525C22×C1112yes—
315C2×#123—22no—
316C2×#121—22no—
317#518C22×C1111yescharacteristic
318C2×C4×D4—22no—
319C22×C42C22×C1111yescharacteristic, complemented
320#455—24no—
321#453—24no—
322#452—24no—
323#449—24no—
324C2×#104C22×C1112yes—
325C2×#104C22×C1112yes—
326#419C22×C1112yescomplemented
327#418C22×C1112yescomplemented
328C2×#101C22×C1112yescomplemented
329C2×#100C22×C1111yescharacteristic
330C2×#100C22×C1111yescharacteristic
331#407C22×C1112yescomplemented
332#339C22×C1112yescomplemented
333#339C22×C1112yescomplemented
334C22×C11—22no—
335C22×C11—22no—
336C22×C11—24no—
337C22×C11—24no—
338C22×C11—44no—
339C22×C11—42no—
340C22×C11—42no—
341C22×C11—44no—
342C22×C11—44no—
343C22×C11—42no—
344C22×C11—42no—
345C22×C11—44no—
346C22×C11—82no—
347C22×C11—82no—
348C22×C11—82no—
349C22×C11—164no—
350C22×C11C2×#12011yescharacteristic
351C22×C11C2×#12011yescharacteristic
352C22×C11#53411yescharacteristic
353C4×C11—24no—
354C4×C11—22no—
355C4×C11—42no—
356C4×C11—42no—
357C4×C11—42no—
358C4×C11—42no—
359C4×C11—44no—
360C4×C11D4212yes—
361C4×C11D4212yes—
362H(5,𝔽2)—22no—
363H(5,𝔽2)—22no—
364H(5,𝔽2)—42no—
365C2×#41—22no—
366C2×#41—22no—
367C2×#41—22no—
368C2×#41—22no—
369C2×#41—22no—
370C2×#41—24no—
371C2×#41—24no—
372C2×#41—42no—
373C2×#41—42no—
374C2×#41C23×C1112yes—
375C22×Q8C23×C1111yescharacteristic
376C22×Q8C23×C1111yescharacteristic
377C22×D4—22no—
378C22×D4—21no—
379C22×D4—22no—
380C22×D4—22no—
381C22×D4D4×C1112yes—
382C22×D4C23×C1111yescharacteristic
383C22×D4C23×C1111yescharacteristic
384C23×C4—21no—
385C23×C4—21no—
386C23×C4D4×C1112yes—
387C23×C4C23×C1111yescharacteristic
388#137—24no—
389#137—42no—
390AGL(1,ℤ/8)—24no—
391AGL(1,ℤ/8)—42no—
392C2×Q16—22no—
393C2×SD16—22no—
394C2×SD16—22no—
395C2×D8—22no—
396C2×M16C23×C1112yes—
397C2×M16C23×C1112yes—
398C4⋊Q8—22no—
399C4⋊Q8—22no—
400C4⋊Q8—22no—
401#127—22no—
402#127D4×C1114yescomplemented
403#124—22no—
404#124—22no—
405#124—22no—
406#124—22no—
407#124D4×C1114yescomplemented
408#123—28no—
409#123—24no—
410#123—22no—
411#123—24no—
412C22⋊Q8—24no—
413C22⋊Q8D4×C1114yescomplemented
414#121—216no—
415#121—28no—
416#121D4×C1114yescomplemented
417#120—24no—
418#120—22no—
419C4×D4—216no—
420C4×D4—24no—
421C4×D4—24no—
422#117C23×C1112yes—
423C2×C4⋊C4—24no—
424C2×C4⋊C4—22no—
425C2×C22⋊C4—24no—
426C2×C22⋊C4—22no—
427C2×C22⋊C4—22no—
428C2×C22⋊C4—22no—
429C2×C42—21no—
430C2×C42—22no—
431C2×C42—22no—
432C2×C42C23×C1111yescharacteristic
433C2×C42C23×C1111yescharacteristic
434#104—24no—
435#104—24no—
436#103—24no—
437#102—24no—
438#101—42no—
439#100—22no—
440#100—22no—
441C22⋊C8—24no—
442C2×C11—21no—
443C2×C11—21no—
444C2×C11—42no—
445C2×C11—44no—
446C2×C11—82no—
447C2×C11—82no—
448C2×C11#240311yescharacteristic
449C2×C11#301812yes—
450C24—22no—
451C24—21no—
452C24C2×D4×C1112yes—
453C24C2×D4×C1111yescharacteristic
454#41—22no—
455#41—22no—
456#41—22no—
457#41—22no—
458#41—48no—
459#41—48no—
460#41—48no—
461#41—48no—
462#41—44no—
463#41—44no—
464C2×Q8—22no—
465C2×Q8—21no—
466C2×Q8—21no—
467C2×Q8—21no—
468C2×Q8—22no—
469C2×Q8—22no—
470C2×Q8—22no—
471C2×Q8C2×D4×C1112yes—
472C2×Q8C2×D4×C1112yes—
473C2×D4—24no—
474C2×D4—24no—
475C2×D4—28no—
476C2×D4—24no—
477C2×D4—24no—
478C2×D4—22no—
479C2×D4—24no—
480C2×D4—22no—
481C2×D4—22no—
482C2×D4—21no—
483C2×D4—22no—
484C2×D4—22no—
485C2×D4—42no—
486C2×D4—48no—
487C2×D4—44no—
488C2×D4—44no—
489C2×D4—42no—
490C2×D4—44no—
491C2×D4—42no—
492C2×D4—44no—
493C2×D4C2×D4×C1112yes—
494C2×D4C2×D4×C1112yes—
495C2×D4C2×D4×C1112yes—
496C2×D4C2×D4×C1112yes—
497C22×C4—21no—
498C22×C4—21no—
499C22×C4—21no—
500C22×C4—22no—
501C22×C4—24no—
502C22×C4—22no—
503C22×C4—24no—
504C22×C4—24no—
505C22×C4—21no—
506C22×C4—21no—
507C22×C4—24no—
508C22×C4—24no—
509C22×C4—22no—
510C22×C4—42no—
511C22×C4—42no—
512C22×C4—44no—
513C22×C4—42no—
514C22×C4C2×D4×C1112yes—
515C22×C4C2×D4×C1111yescharacteristic
516C22×C4C2×D4×C1114yes—
517C22×C4C24×C1111yescharacteristic
518Q16—44no—
519SD16—44no—
520SD16—44no—
521D8—44no—
522M16—22no—
523M16—22no—
524M16—22no—
525M16—22no—
526C2×C8—22no—
527C2×C8—22no—
528C4⋊C4—28no—
529C4⋊C4—28no—
530C4⋊C4—24no—
531C4⋊C4C2×D4×C1114yes—
532C22⋊C4—24no—
533C22⋊C4—28no—
534C22⋊C4—28no—
535C22⋊C4—28no—
536C22⋊C4—24no—
537C22⋊C4—22no—
538C22⋊C4—24no—
539C42—24no—
540C42—21no—
541C42—21no—
542C42—22no—
543C42C2×D4×C1112yes—
544C42C2×D4×C1112yes—
545C11#2390811yescharacteristic, direct product factor, Sylow
546C23—22no—
547C23—21no—
548C23—21no—
549C23—22no—
550C23—22no—
551C23—22no—
552C23—42no—
553C23—44no—
554C23—44no—
555C23—44no—
556C23—41no—
557C23—41no—
558C23—84no—
559C23C11×#12012yes—
560C23C11×#12014yes—
561C23C22×D4×C1111yescharacteristic
562Q8—22no—
563Q8—24no—
564Q8—22no—
565Q8—42no—
566Q8—42no—
567Q8—42no—
568D4—24no—
569D4—24no—
570D4—22no—
571D4—24no—
572D4—22no—
573D4—416no—
574D4—48no—
575D4—48no—
576D4—48no—
577D4—42no—
578D4—42no—
579D4—42no—
580D4—84no—
581C2×C4—24no—
582C2×C4—21no—
583C2×C4—22no—
584C2×C4—21no—
585C2×C4—24no—
586C2×C4—24no—
587C2×C4—22no—
588C2×C4—24no—
589C2×C4—22no—
590C2×C4—22no—
591C2×C4—22no—
592C2×C4—22no—
593C2×C4—22no—
594C2×C4—48no—
595C2×C4—48no—
596C2×C4—48no—
597C2×C4—42no—
598C2×C4—44no—
599C2×C4—41no—
600C2×C4—41no—
601C2×C4—42no—
602C2×C4—42no—
603C2×C4—84no—
604C2×C4C11×#12012yes—
605C2×C4C22×D4×C1111yescharacteristic
606C2×C4C22×D4×C1111yescharacteristic
607C2×C4C22×D4×C1112yes—
608C2×C4C11×H(5,𝔽2)12yes—
609C8—42no—
610C8—42no—
611C22—22no—
612C22—22no—
613C22—24no—
614C22—24no—
615C22—44no—
616C22—42no—
617C22—42no—
618C22—44no—
619C22—44no—
620C22—42no—
621C22—42no—
622C22—44no—
623C22—82no—
624C22—82no—
625C22—82no—
626C22—164no—
627C22C2×C11×#12011yescharacteristic
628C22C2×C11×#12011yescharacteristic
629C22C11×#53411yescharacteristic
630C4—24no—
631C4—22no—
632C4—42no—
633C4—42no—
634C4—42no—
635C4—42no—
636C4—44no—
637C4D42×C1112yes—
638C4D42×C1112yes—
639C2—21no—
640C2—21no—
641C2—42no—
642C2—44no—
643C2—82no—
644C2—82no—
645C2C11×#240311yescharacteristic
646C2C11×#301812yes—
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×#3485C2semidirect
2. C2×C11×#532C2semidirect
3. C2×C11×#455C2semidirect
4. C2×C11×#453C2semidirect
5. C11×#3005C2semidirect
6. C11×#2005C2semidirect
7. C11×#2003C2semidirect
8. C11×#1896C2semidirect
9. C11×#1887C2semidirect
10. C11×#1885C2semidirect
11. C11×#1785C2semidirect
14. C22×C11×#41C22semidirect
23. C2×C11×C4⋊Q8C22semidirect
26. C2×C11×#124C22semidirect
32. C22×C42×C11C22semidirect
39. C11×#419C22semidirect
40. C11×#418C22semidirect
41. C2×C11×#101C22semidirect
44. C11×#407C22semidirect
45. C11×#339C22semidirect
46. C11×#339C22semidirect
87. C11×#127D4semidirect
92. C11×#124D4semidirect
98. C11×C22⋊Q8D4semidirect
101. C11×#121D4semidirect
127. #23908C11direct (N × H)
223. #3485C2×C11semidirect
224. C2×#532C2×C11semidirect
225. C2×#455C2×C11semidirect
226. C2×#453C2×C11semidirect
227. #3005C2×C11semidirect
228. #2005C2×C11semidirect
229. #2003C2×C11semidirect
230. #1896C2×C11semidirect
231. #1887C2×C11semidirect
232. #1885C2×C11semidirect
233. #1785C2×C11semidirect
301. C22×#41C22×C11semidirect
310. C2×C4⋊Q8C22×C11semidirect
313. C2×#124C22×C11semidirect
319. C22×C42C22×C11semidirect
326. #419C22×C11semidirect
327. #418C22×C11semidirect
328. C2×#101C22×C11semidirect
331. #407C22×C11semidirect
332. #339C22×C11semidirect
333. #339C22×C11semidirect
402. #127D4×C11semidirect
407. #124D4×C11semidirect
413. C22⋊Q8D4×C11semidirect
416. #121D4×C11semidirect
545. C11#23908direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#34852
C2×C11×#5322
C2×C11×#4552
C2×C11×#4532
C11×#30052
C11×#20052
C11×#20032
C11×#18962
C11×#18872
C11×#18852
C11×#17852
#2390811