Finite Group Databasebeta

← C11×#20945 #14598138

Subgroups — C11×#20945 #14598138

Order 2816.

1862 conjugacy classes of subgroups.

The subgroup lattice has 636 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C11×AGL(1,ℤ/8)C211yesmaximal, characteristic
2C11×#3428C211yesmaximal, characteristic, complemented
3C2×C11×#421C211yesmaximal, characteristic, complemented
4C2×C11×#418C211yesmaximal, characteristic, complemented
5C11×#2309C211yesmaximal, characteristic, complemented
6C11×#1883C218yesmaximal, complemented
7C11×#1742C211yesmaximal, characteristic, complemented
8C11×#1733C211yesmaximal, characteristic, complemented
9C22×C11×#41C2211yescharacteristic
10C23×D4×C11C2211yescharacteristic
11C2×C11×AGL(1,ℤ/8)—24no—
12C2×C11×AGL(1,ℤ/8)—22no—
13C2×C11×AGL(1,ℤ/8)C418yescomplemented
14C2×C11×AGL(1,ℤ/8)C2214yes—
15C22×C11×SD16—21no—
16C22×C11×D8—21no—
17C22×C11×M16C2211yescharacteristic
18C22×C11×M16C2211yescharacteristic
19C11×#520—22no—
20C11×#520C2214yescomplemented
21C11×#519—21no—
22C11×#518—21no—
23C11×#518—22no—
24C4×C11×#41—22no—
25C4×C11×#41—22no—
26C2×C11×#117—22no—
27C2×C11×#117C2211yescharacteristic
28C2×C11×#117C2211yescharacteristic
29C2×C11×#117C2211yescharacteristic
30C11×#421—24no—
31C2×C11×#104C2214yescomplemented
32C11×#418—22no—
33C11×#418C2214yescomplemented
34C2×C11×#102—22no—
35C11×#390—22no—
36C11×#390C2214yescomplemented
37C11×#379—22no—
38C11×#343C2214yescomplemented
39C11×#339C2214yescomplemented
40C25×C11—21no—
41C2×C11×#41—21no—
42C2×C11×#41—21no—
43C2×C11×#41—22no—
44C2×C11×#41—22no—
45C2×C11×#41C2×C414yes—
46C2×C11×#41D414yes—
47C2×C11×#41D412yes—
48C2×C11×#41C2312yes—
49C22×Q8×C11D411yescharacteristic
50C22×D4×C11—21no—
51C22×D4×C11—21no—
52C22×D4×C11—21no—
53C22×D4×C11—21no—
54C22×D4×C11—21no—
55C22×D4×C11—22no—
56C22×D4×C11—21no—
57C22×D4×C11—22no—
58C22×D4×C11—22no—
59C22×D4×C11C2×C414yescomplemented
60C22×D4×C11D411yescharacteristic
61C22×D4×C11C2312yes—
62C23×C4×C11—21no—
63C23×C4×C11C2311yescharacteristic
64C11×AGL(1,ℤ/8)—216no—
65C11×AGL(1,ℤ/8)—28no—
66C11×AGL(1,ℤ/8)C2×C4116yescomplemented
67C2×C11×SD16—28no—
68C2×C11×SD16—24no—
69C2×C11×D8—28no—
70C2×C11×D8—24no—
71C2×C11×M16—22no—
72C2×C11×M16—21no—
73C2×C11×M16—21no—
74C2×C11×M16—22no—
75C2×C11×M16—22no—
76C2×C11×M16C2×C414yescomplemented
77C2×C11×M16C2312yes—
78C2×C11×M16C2312yes—
79C22×C8×C11—21no—
80C22×C8×C11—21no—
81C4×Q8×C11—24no—
82C4×Q8×C11—24no—
83C4×D4×C11—28no—
84C4×D4×C11—24no—
85C4×D4×C11—24no—
86C4×D4×C11—28no—
87C11×#117—24no—
88C11×#117—24no—
89C11×#117—21no—
90C11×#117—21no—
91C11×#117—21no—
92C11×#117—21no—
93C11×#117—21no—
94C11×#117—21no—
95C11×#117—24no—
96C11×#117—22no—
97C11×#117—22no—
98C11×#117D412yes—
99C11×#117C2312yes—
100C2×C11×C4⋊C4—24no—
101C2×C11×C4⋊C4—21no—
102C2×C11×C4⋊C4D412yes—
103C2×C11×C4⋊C4C2312yes—
104C2×C11×C22⋊C4—24no—
105C2×C11×C22⋊C4—21no—
106C2×C11×C22⋊C4—21no—
107C2×C11×C22⋊C4—28no—
108C2×C11×C22⋊C4D412yes—
109C2×C42×C11—24no—
110C2×C42×C11—21no—
111C2×C42×C11D412yes—
112C2×C42×C11C2312yes—
113C11×#104—28no—
114C11×#102—28no—
115#20945C1111yesmaximal, characteristic, direct product factor, Sylow
116C24×C11—21no—
117C24×C11—22no—
118C24×C11—24no—
119C24×C11—41no—
120C24×C11—41no—
121C24×C11—42no—
122C24×C11—84no—
123C24×C11C2×D411yescharacteristic
124C11×#41—24no—
125C11×#41—24no—
126C11×#41—24no—
127C11×#41—24no—
128C11×#41—24no—
129C11×#41—22no—
130C11×#41—22no—
131C11×#41C22⋊C418yescomplemented
132C11×#41C22×C414yes—
133C11×#41C2×D414yes—
134C2×Q8×C11—21no—
135C2×Q8×C11—22no—
136C2×Q8×C11C22⋊C414yescomplemented
137C2×Q8×C11C2×D412yes—
138C2×D4×C11—24no—
139C2×D4×C11—22no—
140C2×D4×C11—24no—
141C2×D4×C11—22no—
142C2×D4×C11—24no—
143C2×D4×C11—24no—
144C2×D4×C11—24no—
145C2×D4×C11—24no—
146C2×D4×C11—24no—
147C2×D4×C11—21no—
148C2×D4×C11—22no—
149C2×D4×C11—22no—
150C2×D4×C11—22no—
151C2×D4×C11—22no—
152C2×D4×C11—22no—
153C2×D4×C11—22no—
154C2×D4×C11—41no—
155C2×D4×C11—41no—
156C2×D4×C11—42no—
157C2×D4×C11—42no—
158C2×D4×C11—42no—
159C2×D4×C11—42no—
160C2×D4×C11—42no—
161C2×D4×C11C22⋊C414yescomplemented
162C2×D4×C11C22×C414yes—
163C2×D4×C11C2×D412yes—
164C22×C4×C11—21no—
165C22×C4×C11—24no—
166C22×C4×C11—22no—
167C22×C4×C11—24no—
168C22×C4×C11—22no—
169C22×C4×C11—28no—
170C22×C4×C11—22no—
171C22×C4×C11—22no—
172C22×C4×C11C22×C412yes—
173C22×C4×C11C2×D414yes—
174C22×C4×C11C2×D411yescharacteristic
175C22×C4×C11C2×D411yescharacteristic
176C22×C4×C11C2×D412yes—
177C22×C4×C11C2×D411yescharacteristic
178C22×C4×C11C2×D411yescharacteristic
179C22×C4×C11C2×D411yescharacteristic
180C22×C4×C11#4112yes—
181C22×C4×C11#4112yes—
182C22×C4×C11C2411yescharacteristic
183C11×SD16—216no—
184C11×D8—216no—
185C11×M16—24no—
186C11×M16—22no—
187C11×M16—22no—
188C11×M16—22no—
189C11×M16—42no—
190C11×M16C22×C414yes—
191C2×C8×C11—24no—
192C2×C8×C11—22no—
193C2×C8×C11—22no—
194C2×C8×C11—42no—
195C11×C4⋊C4—28no—
196C11×C4⋊C4—22no—
197C11×C4⋊C4—22no—
198C11×C4⋊C4—22no—
199C11×C4⋊C4—42no—
200C11×C4⋊C4C2×D414yes—
201C11×C22⋊C4—28no—
202C11×C22⋊C4—22no—
203C11×C22⋊C4—22no—
204C11×C22⋊C4—22no—
205C11×C22⋊C4—22no—
206C11×C22⋊C4—42no—
207C11×C22⋊C4—88no—
208C42×C11—28no—
209C42×C11—22no—
210C42×C11—22no—
211C42×C11—22no—
212C42×C11—22no—
213C42×C11—22no—
214C42×C11—22no—
215C22×AGL(1,ℤ/8)C2×C1111yescharacteristic
216#3428C2×C1111yescharacteristic, complemented
217C2×#421C2×C1111yescharacteristic, complemented
218C2×#418C2×C1111yescharacteristic, complemented
219#2309C2×C1111yescharacteristic, complemented
220#1883C2×C1118yescomplemented
221#1742C2×C1111yescharacteristic, complemented
222#1733C2×C1111yescharacteristic, complemented
223C23×C11—22no—
224C23×C11—24no—
225C23×C11—24no—
226C23×C11—42no—
227C23×C11—48no—
228C23×C11—42no—
229C23×C11—42no—
230C23×C11—44no—
231C23×C11—44no—
232C23×C11—82no—
233C23×C11—84no—
234C23×C11—84no—
235C23×C11—88no—
236C23×C11—88no—
237C23×C11C4×D412yes—
238C23×C11#12011yescharacteristic
239C23×C11#12011yescharacteristic
240C23×C11#12112yes—
241C23×C11C22×D411yescharacteristic
242Q8×C11—22no—
243Q8×C11—24no—
244Q8×C11C2×C22⋊C414yes—
245D4×C11—24no—
246D4×C11—24no—
247D4×C11—28no—
248D4×C11—24no—
249D4×C11—24no—
250D4×C11—22no—
251D4×C11—24no—
252D4×C11—42no—
253D4×C11—42no—
254D4×C11—44no—
255D4×C11—44no—
256D4×C11C2×C22⋊C414yes—
257C2×C4×C11—22no—
258C2×C4×C11—24no—
259C2×C4×C11—24no—
260C2×C4×C11—24no—
261C2×C4×C11—28no—
262C2×C4×C11—24no—
263C2×C4×C11—24no—
264C2×C4×C11—44no—
265C2×C4×C11—44no—
266C2×C4×C11—42no—
267C2×C4×C11—82no—
268C2×C4×C11—88no—
269C2×C4×C11C2×C22⋊C412yes—
270C2×C4×C11C2×C22⋊C412yes—
271C2×C4×C11C4×D412yes—
272C2×C4×C11C4×D412yes—
273C2×C4×C11C4×D412yes—
274C2×C4×C11#12011yescharacteristic
275C2×C4×C11#12011yescharacteristic
276C2×C4×C11#12112yes—
277C2×C4×C11#12112yes—
278C2×C4×C11#12112yes—
279C2×C4×C11#12312yes—
280C2×C4×C11#12312yes—
281C2×C4×C11C23×C411yescharacteristic
282C2×C4×C11C22×D411yescharacteristic
283C2×C4×C11C22×D411yescharacteristic
284C2×C4×C11C22×D411yescharacteristic
285C2×C4×C11C2×#4111yescharacteristic
286C2×C4×C11C2×#4111yescharacteristic
287C8×C11—24no—
288C8×C11—42no—
289C22×#41C22×C1111yescharacteristic
290C23×D4C22×C1111yescharacteristic
291C2×AGL(1,ℤ/8)—24no—
292C2×AGL(1,ℤ/8)—22no—
293C2×AGL(1,ℤ/8)C4×C1118yescomplemented
294C2×AGL(1,ℤ/8)C22×C1114yes—
295C22×SD16—21no—
296C22×D8—21no—
297C22×M16C22×C1111yescharacteristic
298C22×M16C22×C1111yescharacteristic
299#520—22no—
300#520C22×C1114yescomplemented
301#519—21no—
302#518—21no—
303#518—22no—
304C4×#41—22no—
305C4×#41—22no—
306C2×#117—22no—
307C2×#117C22×C1111yescharacteristic
308C2×#117C22×C1111yescharacteristic
309C2×#117C22×C1111yescharacteristic
310#421—24no—
311C2×#104C22×C1114yescomplemented
312#418—22no—
313#418C22×C1114yescomplemented
314C2×#102—22no—
315#390—22no—
316#390C22×C1114yescomplemented
317#379—22no—
318#343C22×C1114yescomplemented
319#339C22×C1114yescomplemented
320C22×C11—22no—
321C22×C11—22no—
322C22×C11—22no—
323C22×C11—24no—
324C22×C11—42no—
325C22×C11—42no—
326C22×C11—48no—
327C22×C11—44no—
328C22×C11—44no—
329C22×C11—84no—
330C22×C11—84no—
331C22×C11—88no—
332C22×C11—88no—
333C22×C11—84no—
334C22×C11#38612yes—
335C22×C11#38612yes—
336C22×C11C2×C4×D411yescharacteristic
337C22×C11C2×#12011yescharacteristic
338C22×C11C2×#12111yescharacteristic
339C4×C11—24no—
340C4×C11—44no—
341C4×C11—44no—
342C4×C11—82no—
343C4×C11#38612yes—
344C4×C11#38612yes—
345C4×C11C22×C22⋊C411yescharacteristic
346C4×C11C2×C4×D411yescharacteristic
347C4×C11C2×#12111yescharacteristic
348C4×C11C2×#12311yescharacteristic
349C25—21no—
350C2×#41—21no—
351C2×#41—21no—
352C2×#41—22no—
353C2×#41—22no—
354C2×#41C2×C4×C1114yes—
355C2×#41D4×C1114yes—
356C2×#41D4×C1112yes—
357C2×#41C23×C1112yes—
358C22×Q8D4×C1111yescharacteristic
359C22×D4—21no—
360C22×D4—21no—
361C22×D4—21no—
362C22×D4—22no—
363C22×D4—21no—
364C22×D4—21no—
365C22×D4—21no—
366C22×D4—22no—
367C22×D4—22no—
368C22×D4C2×C4×C1114yescomplemented
369C22×D4D4×C1111yescharacteristic
370C22×D4C23×C1112yes—
371C23×C4—21no—
372C23×C4C23×C1111yescharacteristic
373AGL(1,ℤ/8)—216no—
374AGL(1,ℤ/8)—28no—
375AGL(1,ℤ/8)C2×C4×C11116yescomplemented
376C2×SD16—28no—
377C2×SD16—24no—
378C2×D8—28no—
379C2×D8—24no—
380C2×M16—22no—
381C2×M16—21no—
382C2×M16—21no—
383C2×M16—22no—
384C2×M16—22no—
385C2×M16C2×C4×C1114yescomplemented
386C2×M16C23×C1112yes—
387C2×M16C23×C1112yes—
388C22×C8—21no—
389C22×C8—21no—
390C4×Q8—24no—
391C4×Q8—24no—
392C4×D4—28no—
393C4×D4—24no—
394C4×D4—24no—
395C4×D4—28no—
396#117—24no—
397#117—24no—
398#117—21no—
399#117—21no—
400#117—21no—
401#117—21no—
402#117—21no—
403#117—21no—
404#117—24no—
405#117—22no—
406#117—22no—
407#117D4×C1112yes—
408#117C23×C1112yes—
409C2×C4⋊C4—24no—
410C2×C4⋊C4—21no—
411C2×C4⋊C4D4×C1112yes—
412C2×C4⋊C4C23×C1112yes—
413C2×C22⋊C4—24no—
414C2×C22⋊C4—21no—
415C2×C22⋊C4—21no—
416C2×C22⋊C4—28no—
417C2×C22⋊C4D4×C1112yes—
418C2×C42—24no—
419C2×C42—21no—
420C2×C42D4×C1112yes—
421C2×C42C23×C1112yes—
422#104—28no—
423#102—28no—
424C2×C11—21no—
425C2×C11—21no—
426C2×C11—22no—
427C2×C11—22no—
428C2×C11—44no—
429C2×C11—84no—
430C2×C11C2×#38611yescharacteristic
431C2×C11#302112yes—
432C24—21no—
433C24—22no—
434C24—24no—
435C24—41no—
436C24—41no—
437C24—42no—
438C24—84no—
439C24C2×D4×C1111yescharacteristic
440#41—24no—
441#41—24no—
442#41—24no—
443#41—24no—
444#41—24no—
445#41—22no—
446#41—22no—
447#41C11×C22⋊C418yescomplemented
448#41C22×C4×C1114yes—
449#41C2×D4×C1114yes—
450C2×Q8—21no—
451C2×Q8—22no—
452C2×Q8C11×C22⋊C414yescomplemented
453C2×Q8C2×D4×C1112yes—
454C2×D4—24no—
455C2×D4—22no—
456C2×D4—24no—
457C2×D4—22no—
458C2×D4—24no—
459C2×D4—24no—
460C2×D4—24no—
461C2×D4—24no—
462C2×D4—24no—
463C2×D4—21no—
464C2×D4—22no—
465C2×D4—22no—
466C2×D4—22no—
467C2×D4—22no—
468C2×D4—22no—
469C2×D4—22no—
470C2×D4—41no—
471C2×D4—41no—
472C2×D4—42no—
473C2×D4—42no—
474C2×D4—42no—
475C2×D4—42no—
476C2×D4—42no—
477C2×D4C11×C22⋊C414yescomplemented
478C2×D4C22×C4×C1114yes—
479C2×D4C2×D4×C1112yes—
480C22×C4—21no—
481C22×C4—24no—
482C22×C4—22no—
483C22×C4—24no—
484C22×C4—22no—
485C22×C4—28no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4C22×C4×C1112yes—
489C22×C4C2×D4×C1114yes—
490C22×C4C2×D4×C1111yescharacteristic
491C22×C4C2×D4×C1111yescharacteristic
492C22×C4C2×D4×C1112yes—
493C22×C4C2×D4×C1111yescharacteristic
494C22×C4C2×D4×C1111yescharacteristic
495C22×C4C2×D4×C1111yescharacteristic
496C22×C4C11×#4112yes—
497C22×C4C11×#4112yes—
498C22×C4C24×C1111yescharacteristic
499SD16—216no—
500D8—216no—
501M16—24no—
502M16—22no—
503M16—22no—
504M16—22no—
505M16—42no—
506M16C22×C4×C1114yes—
507C2×C8—24no—
508C2×C8—22no—
509C2×C8—22no—
510C2×C8—42no—
511C4⋊C4—28no—
512C4⋊C4—22no—
513C4⋊C4—22no—
514C4⋊C4—22no—
515C4⋊C4—42no—
516C4⋊C4C2×D4×C1114yes—
517C22⋊C4—28no—
518C22⋊C4—22no—
519C22⋊C4—22no—
520C22⋊C4—22no—
521C22⋊C4—22no—
522C22⋊C4—42no—
523C22⋊C4—88no—
524C42—28no—
525C42—22no—
526C42—22no—
527C42—22no—
528C42—22no—
529C42—22no—
530C42—22no—
531C11#2094511yescharacteristic, direct product factor, Sylow
532C23—22no—
533C23—24no—
534C23—24no—
535C23—42no—
536C23—48no—
537C23—42no—
538C23—42no—
539C23—44no—
540C23—44no—
541C23—82no—
542C23—84no—
543C23—84no—
544C23—88no—
545C23—88no—
546C23C4×D4×C1112yes—
547C23C11×#12011yescharacteristic
548C23C11×#12011yescharacteristic
549C23C11×#12112yes—
550C23C22×D4×C1111yescharacteristic
551Q8—24no—
552Q8—22no—
553Q8C2×C11×C22⋊C414yes—
554D4—24no—
555D4—24no—
556D4—28no—
557D4—24no—
558D4—24no—
559D4—24no—
560D4—22no—
561D4—42no—
562D4—44no—
563D4—44no—
564D4—42no—
565D4C2×C11×C22⋊C414yes—
566C2×C4—22no—
567C2×C4—24no—
568C2×C4—24no—
569C2×C4—24no—
570C2×C4—28no—
571C2×C4—24no—
572C2×C4—24no—
573C2×C4—44no—
574C2×C4—44no—
575C2×C4—42no—
576C2×C4—82no—
577C2×C4—88no—
578C2×C4C2×C11×C22⋊C412yes—
579C2×C4C2×C11×C22⋊C412yes—
580C2×C4C4×D4×C1112yes—
581C2×C4C4×D4×C1112yes—
582C2×C4C4×D4×C1112yes—
583C2×C4C11×#12011yescharacteristic
584C2×C4C11×#12011yescharacteristic
585C2×C4C11×#12112yes—
586C2×C4C11×#12112yes—
587C2×C4C11×#12112yes—
588C2×C4C11×#12312yes—
589C2×C4C11×#12312yes—
590C2×C4C23×C4×C1111yescharacteristic
591C2×C4C22×D4×C1111yescharacteristic
592C2×C4C22×D4×C1111yescharacteristic
593C2×C4C22×D4×C1111yescharacteristic
594C2×C4C2×C11×#4111yescharacteristic
595C2×C4C2×C11×#4111yescharacteristic
596C8—24no—
597C8—42no—
598C22—22no—
599C22—22no—
600C22—22no—
601C22—24no—
602C22—42no—
603C22—42no—
604C22—48no—
605C22—44no—
606C22—44no—
607C22—84no—
608C22—84no—
609C22—88no—
610C22—88no—
611C22—84no—
612C22C11×#38612yes—
613C22C11×#38612yes—
614C22C2×C4×D4×C1111yescharacteristic
615C22C2×C11×#12011yescharacteristic
616C22C2×C11×#12111yescharacteristic
617C4—24no—
618C4—44no—
619C4—44no—
620C4—82no—
621C4C11×#38612yes—
622C4C11×#38612yes—
623C4C22×C11×C22⋊C411yescharacteristic
624C4C2×C4×D4×C1111yescharacteristic
625C4C2×C11×#12111yescharacteristic
626C4C2×C11×#12311yescharacteristic
627C2—21no—
628C2—21no—
629C2—22no—
630C2—22no—
631C2—44no—
632C2—84no—
633C2C2×C11×#38611yescharacteristic
634C2C11×#302112yes—
subgroupG/H
center, socleC22×C11C2×#120
commutatorC2×C4C23×C4×C11
Frattini, cosocleC22×C4C24×C11
prime radicalC22×C11×AGL(1,ℤ/8)C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C23×C4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C11×#3428C2semidirect
3. C2×C11×#421C2semidirect
4. C2×C11×#418C2semidirect
5. C11×#2309C2semidirect
6. C11×#1883C2semidirect
7. C11×#1742C2semidirect
8. C11×#1733C2semidirect
13. C2×C11×AGL(1,ℤ/8)C4semidirect
20. C11×#520C22semidirect
31. C2×C11×#104C22semidirect
33. C11×#418C22semidirect
36. C11×#390C22semidirect
38. C11×#343C22semidirect
39. C11×#339C22semidirect
59. C22×D4×C11C2×C4semidirect
66. C11×AGL(1,ℤ/8)C2×C4semidirect
76. C2×C11×M16C2×C4semidirect
115. #20945C11direct (N × H)
131. C11×#41C22⋊C4semidirect
136. C2×Q8×C11C22⋊C4semidirect
161. C2×D4×C11C22⋊C4semidirect
216. #3428C2×C11semidirect
217. C2×#421C2×C11semidirect
218. C2×#418C2×C11semidirect
219. #2309C2×C11semidirect
220. #1883C2×C11semidirect
221. #1742C2×C11semidirect
222. #1733C2×C11semidirect
293. C2×AGL(1,ℤ/8)C4×C11semidirect
300. #520C22×C11semidirect
311. C2×#104C22×C11semidirect
313. #418C22×C11semidirect
316. #390C22×C11semidirect
318. #343C22×C11semidirect
319. #339C22×C11semidirect
368. C22×D4C2×C4×C11semidirect
375. AGL(1,ℤ/8)C2×C4×C11semidirect
385. C2×M16C2×C4×C11semidirect
447. #41C11×C22⋊C4semidirect
452. C2×Q8C11×C22⋊C4semidirect
477. C2×D4C11×C22⋊C4semidirect
531. C11#20945direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C11×AGL(1,ℤ/8)2
C11×#34282
C2×C11×#4212
C2×C11×#4182
C11×#23092
C11×#18832
C11×#17422
C11×#17332
#2094511