Finite Group Databasebeta

← C11×#24355 #14601548

Subgroups — C11×#24355 #14601548

Order 2816.

1742 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
1C23×C11×D8C211yesmaximal, characteristic
2C2×C11×#463C212yesmaximal, complemented
3C2×C11×#450C211yesmaximal, characteristic, complemented
4C11×#2435C211yesmaximal, characteristic, complemented
5D4×C11×C22⋊C4C211yesmaximal, characteristic, complemented
6C11×#2054C212yesmaximal, complemented
7C11×#2012C212yesmaximal, complemented
8C11×#1892C211yesmaximal, characteristic, complemented
9C11×#1879C212yesmaximal, complemented
10C11×#1850C211yesmaximal, characteristic, complemented
11C11×#1786C211yesmaximal, characteristic, complemented
12C23×D4×C11C2211yescharacteristic
13C23×D4×C11C2211yescharacteristic
14C22×C11×SD16C2211yescharacteristic, complemented
15C22×C11×SD16C2211yescharacteristic, complemented
16C22×C11×D8—24no—
17C22×C11×D8—28no—
18C22×C11×D8C2212yes—
19C22×C11×D8C2212yes—
20C23×C8×C11C2211yescharacteristic
21C2×C11×#124C2212yescomplemented
22C2×C11×C22⋊Q8C2211yescharacteristic
23C2×C4×D4×C11C2212yescomplemented
24C22×C11×C22⋊C4—21no—
25C11×#463—28no—
26C11×#450—24no—
27C2×C11×C4⋊C8C2212yescomplemented
28C2×C11×#103C2212yescomplemented
29C2×C11×#102C2211yescharacteristic, complemented
30C2×C11×#102C2211yescharacteristic, complemented
31C2×C11×#102C2212yescomplemented
32C2×C11×#102C2212yescomplemented
33C2×C11×C22⋊C8C2211yescharacteristic
34C11×#394—22no—
35C11×#390C2212yescomplemented
36C11×#390C2212yescomplemented
37C11×#386—22no—
38C11×#380C2211yescharacteristic
39C11×#379—21no—
40C11×#379—21no—
41C11×#379—21no—
42C4×C11×C22⋊C4C2211yescharacteristic
43C11×#340C2212yescomplemented
44C11×#336C2212yescomplemented
45C25×C11—21no—
46C25×C11—21no—
47C22×Q8×C11C2311yescharacteristic
48C22×D4×C11—24no—
49C22×D4×C11—24no—
50C22×D4×C11—22no—
51C22×D4×C11—21no—
52C22×D4×C11—21no—
53C22×D4×C11—22no—
54C22×D4×C11—22no—
55C22×D4×C11—42no—
56C22×D4×C11—42no—
57C22×D4×C11D414yes—
58C22×D4×C11C2312yes—
59C22×D4×C11C2311yescharacteristic
60C22×D4×C11C2311yescharacteristic
61C23×C4×C11—22no—
62C23×C4×C11C2311yescharacteristic
63C2×C11×SD16—22no—
64C2×C11×SD16—22no—
65C2×C11×SD16—24no—
66C2×C11×SD16—42no—
67C2×C11×D8—232no—
68C2×C11×D8—24no—
69C2×C11×D8—24no—
70C2×C11×D8—24no—
71C2×C11×D8—24no—
72C2×C11×D8—24no—
73C2×C11×D8D418yes—
74C22×C8×C11—22no—
75C22×C8×C11—24no—
76C22×C8×C11C2311yescharacteristic
77C22×C8×C11C2311yescharacteristic
78C22×C8×C11C2312yes—
79C11×#124—24no—
80C11×#124—42no—
81C11×C22⋊Q8—22no—
82C11×C22⋊Q8—22no—
83C4×D4×C11—24no—
84C4×D4×C11—42no—
85C2×C11×C4⋊C4—21no—
86C2×C11×C4⋊C4C2311yescharacteristic
87C2×C11×C4⋊C4C2312yes—
88C2×C11×C22⋊C4—21no—
89C2×C11×C22⋊C4—21no—
90C2×C11×C22⋊C4—22no—
91C2×C11×C22⋊C4—22no—
92C2×C11×C22⋊C4—22no—
93C2×C11×C22⋊C4—22no—
94C2×C11×C22⋊C4—22no—
95C2×C11×C22⋊C4—22no—
96C2×C11×C22⋊C4—22no—
97C2×C11×C22⋊C4—44no—
98C2×C11×C22⋊C4D411yescharacteristic
99C2×C11×C22⋊C4D411yescharacteristic
100C2×C42×C11C2312yes—
101C11×C4⋊C8—24no—
102C11×#103—24no—
103C11×#102—22no—
104C11×#102—22no—
105C11×#102—24no—
106C11×#102—42no—
107C11×C22⋊C8—22no—
108C11×#95—21no—
109C11×#95D412yes—
110#24355C1111yesmaximal, characteristic, direct product factor, Sylow
111C24×C11—21no—
112C24×C11—21no—
113C24×C11—22no—
114C24×C11—24no—
115C24×C11—44no—
116C24×C11—44no—
117C24×C11—42no—
118C24×C11—42no—
119C24×C11—42no—
120C24×C11—42no—
121C24×C11—42no—
122C24×C11—82no—
123C24×C11—82no—
124C24×C11C2×D411yescharacteristic
125C2×Q8×C11—22no—
126C2×Q8×C11—21no—
127C2×Q8×C11—21no—
128C2×Q8×C11—22no—
129C2×D4×C11—28no—
130C2×D4×C11—28no—
131C2×D4×C11—24no—
132C2×D4×C11—22no—
133C2×D4×C11—22no—
134C2×D4×C11—22no—
135C2×D4×C11—21no—
136C2×D4×C11—22no—
137C2×D4×C11—21no—
138C2×D4×C11—22no—
139C2×D4×C11—22no—
140C2×D4×C11—22no—
141C2×D4×C11—22no—
142C2×D4×C11—44no—
143C2×D4×C11—48no—
144C2×D4×C11—48no—
145C2×D4×C11—44no—
146C2×D4×C11—44no—
147C2×D4×C11—44no—
148C2×D4×C11—42no—
149C2×D4×C11C2×D414yes—
150C2×D4×C11C2×D412yes—
151C2×D4×C11C2×D412yes—
152C2×D4×C11C2×D414yes—
153C22×C4×C11—22no—
154C22×C4×C11—22no—
155C22×C4×C11—22no—
156C22×C4×C11—21no—
157C22×C4×C11—21no—
158C22×C4×C11—44no—
159C22×C4×C11—44no—
160C22×C4×C11—82no—
161C22×C4×C11C2×D412yes—
162C22×C4×C11C2×D412yes—
163C22×C4×C11C2×D411yescharacteristic
164C22×C4×C11C2×D412yes—
165C22×C4×C11#4112yes—
166C22×C4×C11C2411yescharacteristic
167C11×SD16—44no—
168C11×SD16—44no—
169C11×D8—216no—
170C11×D8—216no—
171C2×C8×C11—28no—
172C2×C8×C11—22no—
173C2×C8×C11—22no—
174C2×C8×C11—21no—
175C2×C8×C11—21no—
176C2×C8×C11—22no—
177C2×C8×C11—22no—
178C2×C8×C11C2×D414yes—
179C11×C4⋊C4—21no—
180C11×C4⋊C4—22no—
181C11×C4⋊C4—21no—
182C11×C4⋊C4—22no—
183C11×C4⋊C4—42no—
184C11×C22⋊C4—22no—
185C11×C22⋊C4—22no—
186C11×C22⋊C4—44no—
187C11×C22⋊C4—44no—
188C11×C22⋊C4—44no—
189C11×C22⋊C4—44no—
190C11×C22⋊C4—42no—
191C11×C22⋊C4—42no—
192C11×C22⋊C4—82no—
193C11×C22⋊C4—82no—
194C11×C22⋊C4—82no—
195C42×C11—22no—
196C42×C11—22no—
197C23×D8C2×C1111yescharacteristic
198C2×#463C2×C1112yescomplemented
199C2×#450C2×C1111yescharacteristic, complemented
200#2435C2×C1111yescharacteristic, complemented
201D4×C22⋊C4C2×C1111yescharacteristic, complemented
202#2054C2×C1112yescomplemented
203#2012C2×C1112yescomplemented
204#1892C2×C1111yescharacteristic, complemented
205#1879C2×C1112yescomplemented
206#1850C2×C1111yescharacteristic, complemented
207#1786C2×C1111yescharacteristic, complemented
208C23×C11—22no—
209C23×C11—22no—
210C23×C11—22no—
211C23×C11—24no—
212C23×C11—22no—
213C23×C11—24no—
214C23×C11—48no—
215C23×C11—48no—
216C23×C11—41no—
217C23×C11—41no—
218C23×C11—42no—
219C23×C11—42no—
220C23×C11—42no—
221C23×C11—42no—
222C23×C11—42no—
223C23×C11—41no—
224C23×C11—41no—
225C23×C11—42no—
226C23×C11—42no—
227C23×C11—42no—
228C23×C11—42no—
229C23×C11—48no—
230C23×C11—84no—
231C23×C11—88no—
232C23×C11—88no—
233C23×C11—88no—
234C23×C11—88no—
235C23×C11—84no—
236C23×C11—84no—
237C23×C11#12112yes—
238C23×C11#13512yes—
239C23×C11AGL(1,ℤ/8)12yes—
240C23×C11C22×D411yescharacteristic
241Q8×C11—41no—
242Q8×C11—41no—
243Q8×C11—42no—
244D4×C11—22no—
245D4×C11—24no—
246D4×C11—22no—
247D4×C11—22no—
248D4×C11—24no—
249D4×C11—24no—
250D4×C11—48no—
251D4×C11—48no—
252D4×C11—42no—
253D4×C11—42no—
254D4×C11—42no—
255D4×C11#12014yes—
256C2×C4×C11—22no—
257C2×C4×C11—22no—
258C2×C4×C11—22no—
259C2×C4×C11—24no—
260C2×C4×C11—22no—
261C2×C4×C11—22no—
262C2×C4×C11—22no—
263C2×C4×C11—22no—
264C2×C4×C11—22no—
265C2×C4×C11—22no—
266C2×C4×C11—41no—
267C2×C4×C11—41no—
268C2×C4×C11—42no—
269C2×C4×C11—42no—
270C2×C4×C11—42no—
271C2×C4×C11—42no—
272C2×C4×C11—42no—
273C2×C4×C11—88no—
274C2×C4×C11#12112yes—
275C2×C4×C11C22×D411yescharacteristic
276C2×C4×C11C22×D412yes—
277C2×C4×C11C2×#4111yescharacteristic
278C2×C4×C11H(5,𝔽2)12yes—
279C8×C11—24no—
280C8×C11—41no—
281C8×C11—41no—
282C23×D4C22×C1111yescharacteristic
283C23×D4C22×C1111yescharacteristic
284C22×SD16C22×C1111yescharacteristic, complemented
285C22×SD16C22×C1111yescharacteristic, complemented
286C22×D8—24no—
287C22×D8—28no—
288C22×D8C22×C1112yes—
289C22×D8C22×C1112yes—
290C23×C8C22×C1111yescharacteristic
291C2×#124C22×C1112yescomplemented
292C2×C22⋊Q8C22×C1111yescharacteristic
293C2×C4×D4C22×C1112yescomplemented
294C22×C22⋊C4—21no—
295#463—28no—
296#450—24no—
297C2×C4⋊C8C22×C1112yescomplemented
298C2×#103C22×C1112yescomplemented
299C2×#102C22×C1111yescharacteristic, complemented
300C2×#102C22×C1112yescomplemented
301C2×#102C22×C1111yescharacteristic, complemented
302C2×#102C22×C1112yescomplemented
303C2×C22⋊C8C22×C1111yescharacteristic
304#394—22no—
305#390C22×C1112yescomplemented
306#390C22×C1112yescomplemented
307#386—22no—
308#380C22×C1111yescharacteristic
309#379—21no—
310#379—21no—
311#379—21no—
312C4×C22⋊C4C22×C1111yescharacteristic
313#340C22×C1112yescomplemented
314#336C22×C1112yescomplemented
315C22×C11—22no—
316C22×C11—24no—
317C22×C11—24no—
318C22×C11—22no—
319C22×C11—24no—
320C22×C11—44no—
321C22×C11—44no—
322C22×C11—42no—
323C22×C11—42no—
324C22×C11—42no—
325C22×C11—44no—
326C22×C11—44no—
327C22×C11—44no—
328C22×C11—42no—
329C22×C11—42no—
330C22×C11—816no—
331C22×C11—816no—
332C22×C11—82no—
333C22×C11—82no—
334C22×C11—82no—
335C22×C11—82no—
336C22×C11—82no—
337C22×C11—82no—
338C22×C11#46314yescomplemented
339C22×C11C2×#12111yescharacteristic
340C22×C11D4212yes—
341C22×C11C2×#13511yescharacteristic
342C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
343C22×C11#57612yes—
344C4×C11—22no—
345C4×C11—42no—
346C4×C11—42no—
347C4×C11—81no—
348C4×C11—82no—
349C4×C11—81no—
350C4×C11C2×#12011yescharacteristic
351C4×C11#53411yescharacteristic
352C4×C11#54612yes—
353C25—21no—
354C25—21no—
355C22×Q8C23×C1111yescharacteristic
356C22×D4—24no—
357C22×D4—24no—
358C22×D4—22no—
359C22×D4—21no—
360C22×D4—21no—
361C22×D4—22no—
362C22×D4—22no—
363C22×D4—42no—
364C22×D4—42no—
365C22×D4D4×C1114yes—
366C22×D4C23×C1112yes—
367C22×D4C23×C1111yescharacteristic
368C22×D4C23×C1111yescharacteristic
369C23×C4—22no—
370C23×C4C23×C1111yescharacteristic
371C2×SD16—22no—
372C2×SD16—22no—
373C2×SD16—24no—
374C2×SD16—42no—
375C2×D8—232no—
376C2×D8—24no—
377C2×D8—24no—
378C2×D8—24no—
379C2×D8—24no—
380C2×D8—24no—
381C2×D8D4×C1118yes—
382C22×C8—22no—
383C22×C8—24no—
384C22×C8C23×C1111yescharacteristic
385C22×C8C23×C1111yescharacteristic
386C22×C8C23×C1112yes—
387#124—24no—
388#124—42no—
389C22⋊Q8—22no—
390C22⋊Q8—22no—
391C4×D4—24no—
392C4×D4—42no—
393C2×C4⋊C4—21no—
394C2×C4⋊C4C23×C1112yes—
395C2×C4⋊C4C23×C1111yescharacteristic
396C2×C22⋊C4—21no—
397C2×C22⋊C4—21no—
398C2×C22⋊C4—22no—
399C2×C22⋊C4—22no—
400C2×C22⋊C4—22no—
401C2×C22⋊C4—22no—
402C2×C22⋊C4—22no—
403C2×C22⋊C4—22no—
404C2×C22⋊C4—22no—
405C2×C22⋊C4—44no—
406C2×C22⋊C4D4×C1111yescharacteristic
407C2×C22⋊C4D4×C1111yescharacteristic
408C2×C42C23×C1112yes—
409C4⋊C8—24no—
410#103—24no—
411#102—22no—
412#102—22no—
413#102—24no—
414#102—42no—
415C22⋊C8—22no—
416#95—21no—
417#95D4×C1112yes—
418C2×C11—24no—
419C2×C11—44no—
420C2×C11—84no—
421C2×C11—82no—
422C2×C11#241011yescharacteristic
423C2×C11C2×#46311yescharacteristic
424C2×C11#304111yescharacteristic
425C2×C11#326412yes—
426C2×C11#328012yes—
427C24—21no—
428C24—21no—
429C24—22no—
430C24—24no—
431C24—44no—
432C24—44no—
433C24—42no—
434C24—42no—
435C24—42no—
436C24—42no—
437C24—42no—
438C24—82no—
439C24—82no—
440C24C2×D4×C1111yescharacteristic
441C2×Q8—22no—
442C2×Q8—21no—
443C2×Q8—21no—
444C2×Q8—22no—
445C2×D4—28no—
446C2×D4—28no—
447C2×D4—24no—
448C2×D4—22no—
449C2×D4—22no—
450C2×D4—22no—
451C2×D4—21no—
452C2×D4—22no—
453C2×D4—21no—
454C2×D4—22no—
455C2×D4—22no—
456C2×D4—22no—
457C2×D4—22no—
458C2×D4—44no—
459C2×D4—48no—
460C2×D4—48no—
461C2×D4—44no—
462C2×D4—44no—
463C2×D4—44no—
464C2×D4—42no—
465C2×D4C2×D4×C1114yes—
466C2×D4C2×D4×C1112yes—
467C2×D4C2×D4×C1112yes—
468C2×D4C2×D4×C1114yes—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—44no—
475C22×C4—44no—
476C22×C4—82no—
477C22×C4C2×D4×C1112yes—
478C22×C4C2×D4×C1112yes—
479C22×C4C2×D4×C1111yescharacteristic
480C22×C4C2×D4×C1112yes—
481C22×C4C11×#4112yes—
482C22×C4C24×C1111yescharacteristic
483SD16—44no—
484SD16—44no—
485D8—216no—
486D8—216no—
487C2×C8—28no—
488C2×C8—22no—
489C2×C8—22no—
490C2×C8—21no—
491C2×C8—21no—
492C2×C8—22no—
493C2×C8—22no—
494C2×C8C2×D4×C1114yes—
495C4⋊C4—21no—
496C4⋊C4—22no—
497C4⋊C4—21no—
498C4⋊C4—22no—
499C4⋊C4—42no—
500C22⋊C4—22no—
501C22⋊C4—22no—
502C22⋊C4—44no—
503C22⋊C4—44no—
504C22⋊C4—44no—
505C22⋊C4—44no—
506C22⋊C4—42no—
507C22⋊C4—42no—
508C22⋊C4—82no—
509C22⋊C4—82no—
510C22⋊C4—82no—
511C42—22no—
512C42—22no—
513C11#2435511yescharacteristic, direct product factor, Sylow
514C23—22no—
515C23—22no—
516C23—22no—
517C23—24no—
518C23—22no—
519C23—24no—
520C23—48no—
521C23—48no—
522C23—41no—
523C23—41no—
524C23—42no—
525C23—42no—
526C23—42no—
527C23—42no—
528C23—42no—
529C23—41no—
530C23—41no—
531C23—42no—
532C23—42no—
533C23—42no—
534C23—42no—
535C23—48no—
536C23—84no—
537C23—88no—
538C23—88no—
539C23—88no—
540C23—88no—
541C23—84no—
542C23—84no—
543C23C11×#12112yes—
544C23C11×#13512yes—
545C23C11×AGL(1,ℤ/8)12yes—
546C23C22×D4×C1111yescharacteristic
547Q8—41no—
548Q8—41no—
549Q8—42no—
550D4—22no—
551D4—24no—
552D4—22no—
553D4—22no—
554D4—24no—
555D4—24no—
556D4—48no—
557D4—48no—
558D4—42no—
559D4—42no—
560D4—42no—
561D4C11×#12014yes—
562C2×C4—22no—
563C2×C4—22no—
564C2×C4—22no—
565C2×C4—24no—
566C2×C4—22no—
567C2×C4—22no—
568C2×C4—22no—
569C2×C4—22no—
570C2×C4—22no—
571C2×C4—22no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—42no—
575C2×C4—42no—
576C2×C4—42no—
577C2×C4—42no—
578C2×C4—42no—
579C2×C4—88no—
580C2×C4C11×#12112yes—
581C2×C4C22×D4×C1111yescharacteristic
582C2×C4C22×D4×C1112yes—
583C2×C4C2×C11×#4111yescharacteristic
584C2×C4C11×H(5,𝔽2)12yes—
585C8—24no—
586C8—41no—
587C8—41no—
588C22—22no—
589C22—24no—
590C22—24no—
591C22—22no—
592C22—24no—
593C22—44no—
594C22—44no—
595C22—42no—
596C22—42no—
597C22—42no—
598C22—44no—
599C22—44no—
600C22—44no—
601C22—42no—
602C22—42no—
603C22—816no—
604C22—816no—
605C22—82no—
606C22—82no—
607C22—82no—
608C22—82no—
609C22—82no—
610C22—82no—
611C22C11×#46314yescomplemented
612C22C2×C11×#12111yescharacteristic
613C22D42×C1112yes—
614C22C2×C11×#13511yescharacteristic
615C22C2×C11×AGL(1,ℤ/8)11yescharacteristic
616C22C11×#57612yes—
617C4—22no—
618C4—42no—
619C4—42no—
620C4—81no—
621C4—82no—
622C4—81no—
623C4C2×C11×#12011yescharacteristic
624C4C11×#53411yescharacteristic
625C4C11×#54612yes—
626C2—24no—
627C2—44no—
628C2—84no—
629C2—82no—
630C2C11×#241011yescharacteristic
631C2C2×C11×#46311yescharacteristic
632C2C11×#304111yescharacteristic
633C2C11×#326412yes—
634C2C11×#328012yes—
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC23×C11×D8C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C4×C11×C22⋊C4 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C11×#463C2semidirect
3. C2×C11×#450C2semidirect
4. C11×#2435C2semidirect
5. D4×C11×C22⋊C4C2semidirect
6. C11×#2054C2semidirect
7. C11×#2012C2semidirect
8. C11×#1892C2semidirect
9. C11×#1879C2semidirect
10. C11×#1850C2semidirect
11. C11×#1786C2semidirect
14. C22×C11×SD16C22semidirect
15. C22×C11×SD16C22semidirect
21. C2×C11×#124C22semidirect
23. C2×C4×D4×C11C22semidirect
27. C2×C11×C4⋊C8C22semidirect
28. C2×C11×#103C22semidirect
29. C2×C11×#102C22semidirect
30. C2×C11×#102C22semidirect
31. C2×C11×#102C22semidirect
32. C2×C11×#102C22semidirect
35. C11×#390C22semidirect
36. C11×#390C22semidirect
43. C11×#340C22semidirect
44. C11×#336C22semidirect
110. #24355C11direct (N × H)
198. C2×#463C2×C11semidirect
199. C2×#450C2×C11semidirect
200. #2435C2×C11semidirect
201. D4×C22⋊C4C2×C11semidirect
202. #2054C2×C11semidirect
203. #2012C2×C11semidirect
204. #1892C2×C11semidirect
205. #1879C2×C11semidirect
206. #1850C2×C11semidirect
207. #1786C2×C11semidirect
284. C22×SD16C22×C11semidirect
285. C22×SD16C22×C11semidirect
291. C2×#124C22×C11semidirect
293. C2×C4×D4C22×C11semidirect
297. C2×C4⋊C8C22×C11semidirect
298. C2×#103C22×C11semidirect
299. C2×#102C22×C11semidirect
300. C2×#102C22×C11semidirect
301. C2×#102C22×C11semidirect
302. C2×#102C22×C11semidirect
305. #390C22×C11semidirect
306. #390C22×C11semidirect
313. #340C22×C11semidirect
314. #336C22×C11semidirect
338. C22×C11#463semidirect
513. C11#24355direct (N × H)
611. C22C11×#463semidirect

Maximal subgroups

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

subgroupindex
C23×C11×D82
C2×C11×#4632
C2×C11×#4502
C11×#24352
D4×C11×C22⋊C42
C11×#20542
C11×#20122
C11×#18922
C11×#18792
C11×#18502
C11×#17862
#2435511