Finite Group Databasebeta

← C11×#24753 #14601946

Subgroups — C11×#24753 #14601946

Order 2816.

1132 conjugacy classes of subgroups.

The subgroup lattice has 604 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#465C212yesmaximal, complemented
2C2×C11×#460C211yesmaximal, characteristic, complemented
3C22×C11×C4⋊C8C211yesmaximal, characteristic, complemented
4C11×#2856C211yesmaximal, characteristic
5C4×C11×C22⋊Q8C211yesmaximal, characteristic, complemented
6C11×#2065C212yesmaximal, complemented
7C11×#2055C212yesmaximal, complemented
8C11×#1982C211yesmaximal, characteristic, complemented
9C11×#1948C211yesmaximal, characteristic, complemented
10C11×#1893C212yesmaximal, complemented
11C11×#1803C211yesmaximal, characteristic, complemented
12C22×C11×SD16C2212yes—
13C23×C8×C11C2212yes—
14C2×C11×#127C2211yescharacteristic
15C2×C11×C22⋊Q8C2211yescharacteristic
16C2×C11×#121—21no—
17C2×C11×#121—21no—
18C2×C11×#121C2212yes—
19C2×C4×Q8×C11C2211yescharacteristic
20C22×C42×C11C2211yescharacteristic
21C11×#465—28no—
22C11×#460—24no—
23C2×C11×#106C2212yes—
24C2×C11×C4⋊C8—24no—
25C2×C11×C4⋊C8C2211yescharacteristic
26C2×C11×C4⋊C8C2212yes—
27C2×C11×C4⋊C8C2211yescharacteristic
28C2×C11×#103C2212yes—
29C2×C11×#102C2212yes—
30C2×C11×#102C2212yes—
31C2×C11×#102C2212yes—
32C11×#391C2211yescharacteristic
33C11×#390—21no—
34C11×#390—21no—
35C11×#390C2212yes—
36C11×#389C2211yescharacteristic
37C11×#387—21no—
38C11×#385—21no—
39C11×#384C2211yescharacteristic
40C11×#380C2211yescharacteristic
41C4×C11×C4⋊C4—21no—
42C4×C11×C4⋊C4C2211yescharacteristic
43C4×C11×C22⋊C4—21no—
44C11×#340C2212yes—
45C11×#340C2212yes—
46C22×Q8×C11C2311yescharacteristic
47C22×D4×C11—22no—
48C22×D4×C11—21no—
49C22×D4×C11—21no—
50C22×D4×C11C2312yes—
51C23×C4×C11D411yescharacteristic
52C23×C4×C11D411yescharacteristic
53C23×C4×C11C2311yescharacteristic
54C2×C11×SD16—24no—
55C2×C11×SD16—24no—
56C2×C11×SD16—42no—
57C22×C8×C11—24no—
58C22×C8×C11—24no—
59C22×C8×C11—42no—
60C22×C8×C11C2312yes—
61C22×C8×C11C2312yes—
62C11×#127—22no—
63C11×#127—22no—
64C11×C22⋊Q8—22no—
65C11×C22⋊Q8D414yescomplemented
66C11×#121—24no—
67C11×#121—24no—
68C11×#121—44no—
69C11×#121—44no—
70C4×Q8×C11—22no—
71C4×Q8×C11—22no—
72C2×C11×C4⋊C4—21no—
73C2×C11×C4⋊C4—21no—
74C2×C11×C4⋊C4—21no—
75C2×C11×C4⋊C4—21no—
76C2×C11×C4⋊C4—21no—
77C2×C11×C4⋊C4C2311yescharacteristic
78C2×C11×C4⋊C4C2311yescharacteristic
79C2×C11×C4⋊C4C2312yes—
80C2×C11×C4⋊C4C2311yescharacteristic
81C2×C11×C22⋊C4—21no—
82C2×C11×C22⋊C4—21no—
83C2×C11×C22⋊C4—22no—
84C2×C11×C22⋊C4—22no—
85C2×C11×C22⋊C4—22no—
86C2×C42×C11—22no—
87C2×C42×C11—22no—
88C2×C42×C11—21no—
89C2×C42×C11—21no—
90C2×C42×C11D411yescharacteristic
91C2×C42×C11D411yescharacteristic
92C2×C42×C11C2311yescharacteristic
93C2×C42×C11C2311yescharacteristic
94C11×#106—24no—
95C11×C4⋊C8—24no—
96C11×C4⋊C8—22no—
97C11×C4⋊C8D414yescomplemented
98C11×#103—24no—
99C11×#102—24no—
100C11×#102—24no—
101C11×#102—42no—
102C11×#95—21no—
103C11×#95—21no—
104C11×#95—21no—
105C11×#95—21no—
106C11×#95—21no—
107#24753C1111yesmaximal, characteristic, direct product factor, Sylow
108C24×C11—22no—
109C24×C11C2×D411yescharacteristic
110C2×Q8×C11—21no—
111C2×Q8×C11—21no—
112C2×Q8×C11—21no—
113C2×Q8×C11—21no—
114C2×Q8×C11—21no—
115C2×Q8×C11C2×D412yes—
116C2×D4×C11—22no—
117C2×D4×C11—22no—
118C2×D4×C11—22no—
119C2×D4×C11—22no—
120C2×D4×C11—22no—
121C2×D4×C11—22no—
122C2×D4×C11—42no—
123C2×D4×C11—42no—
124C2×D4×C11—44no—
125C2×D4×C11—44no—
126C2×D4×C11—44no—
127C2×D4×C11—42no—
128C2×D4×C11—42no—
129C2×D4×C11—42no—
130C2×D4×C11—42no—
131C22×C4×C11—22no—
132C22×C4×C11—22no—
133C22×C4×C11—21no—
134C22×C4×C11—21no—
135C22×C4×C11—21no—
136C22×C4×C11—21no—
137C22×C4×C11—22no—
138C22×C4×C11—21no—
139C22×C4×C11—21no—
140C22×C4×C11—22no—
141C22×C4×C11—21no—
142C22×C4×C11—21no—
143C22×C4×C11—22no—
144C22×C4×C11—41no—
145C22×C4×C11SD1614yescomplemented
146C22×C4×C11C2×D411yescharacteristic
147C22×C4×C11C2×D411yescharacteristic
148C22×C4×C11C2×D411yescharacteristic
149C22×C4×C11C2×D412yes—
150C22×C4×C11C2×D411yescharacteristic
151C22×C4×C11C2×D411yescharacteristic
152C22×C4×C11#4112yes—
153C22×C4×C11C2411yescharacteristic
154C11×SD16—48no—
155C2×C8×C11—22no—
156C2×C8×C11—22no—
157C2×C8×C11—22no—
158C2×C8×C11—22no—
159C2×C8×C11—22no—
160C2×C8×C11—48no—
161C2×C8×C11C2×D414yes—
162C11×C4⋊C4—24no—
163C11×C4⋊C4—21no—
164C11×C4⋊C4—21no—
165C11×C4⋊C4—22no—
166C11×C4⋊C4—21no—
167C11×C4⋊C4—22no—
168C11×C4⋊C4—21no—
169C11×C4⋊C4—21no—
170C11×C4⋊C4—42no—
171C11×C4⋊C4—42no—
172C11×C4⋊C4—42no—
173C11×C4⋊C4—42no—
174C11×C4⋊C4C2×D412yes—
175C11×C22⋊C4—24no—
176C11×C22⋊C4—44no—
177C11×C22⋊C4—42no—
178C11×C22⋊C4—44no—
179C11×C22⋊C4—44no—
180C42×C11—22no—
181C42×C11—22no—
182C42×C11—21no—
183C42×C11—21no—
184C42×C11—42no—
185C42×C11—42no—
186C42×C11C2×D412yes—
187C42×C11#4112yes—
188C2×#465C2×C1112yescomplemented
189C2×#460C2×C1111yescharacteristic, complemented
190C22×C4⋊C8C2×C1111yescharacteristic, complemented
191#2856C2×C1111yescharacteristic
192C4×C22⋊Q8C2×C1111yescharacteristic, complemented
193#2065C2×C1112yescomplemented
194#2055C2×C1112yescomplemented
195#1982C2×C1111yescharacteristic, complemented
196#1948C2×C1111yescharacteristic, complemented
197#1893C2×C1112yescomplemented
198#1803C2×C1111yescharacteristic, complemented
199C23×C11—21no—
200C23×C11—21no—
201C23×C11—21no—
202C23×C11—21no—
203C23×C11—42no—
204C23×C11—42no—
205C23×C11—42no—
206C23×C11—42no—
207C23×C11—42no—
208C23×C11—42no—
209C23×C11—42no—
210C23×C11#12112yes—
211C23×C11C2×SD1612yes—
212C23×C11AGL(1,ℤ/8)12yes—
213C23×C11C22×D411yescharacteristic
214Q8×C11—22no—
215Q8×C11—22no—
216Q8×C11—41no—
217Q8×C11—41no—
218D4×C11—42no—
219D4×C11—42no—
220D4×C11—42no—
221D4×C11—42no—
222D4×C11—84no—
223D4×C11—88no—
224D4×C11—84no—
225C2×C4×C11—21no—
226C2×C4×C11—21no—
227C2×C4×C11—21no—
228C2×C4×C11—21no—
229C2×C4×C11—21no—
230C2×C4×C11—21no—
231C2×C4×C11—22no—
232C2×C4×C11—22no—
233C2×C4×C11—22no—
234C2×C4×C11—22no—
235C2×C4×C11—28no—
236C2×C4×C11—21no—
237C2×C4×C11—22no—
238C2×C4×C11—22no—
239C2×C4×C11—21no—
240C2×C4×C11—21no—
241C2×C4×C11—44no—
242C2×C4×C11—41no—
243C2×C4×C11—41no—
244C2×C4×C11—41no—
245C2×C4×C11—41no—
246C2×C4×C11—41no—
247C2×C4×C11—42no—
248C2×C4×C11—41no—
249C2×C4×C11—42no—
250C2×C4×C11—41no—
251C2×C4×C11—42no—
252C2×C4×C11—41no—
253C2×C4×C11—41no—
254C2×C4×C11—41no—
255C2×C4×C11#12112yes—
256C2×C4×C11#12112yes—
257C2×C4×C11#12112yes—
258C2×C4×C11C2×SD1612yes—
259C2×C4×C11C2×SD1612yes—
260C2×C4×C11#13512yes—
261C2×C4×C11C22×D411yescharacteristic
262C2×C4×C11C22×D411yescharacteristic
263C2×C4×C11C2×#4111yescharacteristic
264C2×C4×C11C2×#4111yescharacteristic
265C2×C4×C11H(5,𝔽2)11yescharacteristic
266C2×C4×C112−1+411yescharacteristic
267C8×C11—24no—
268C8×C11—42no—
269C22×SD16C22×C1112yes—
270C23×C8C22×C1112yes—
271C2×#127C22×C1111yescharacteristic
272C2×C22⋊Q8C22×C1111yescharacteristic
273C2×#121—21no—
274C2×#121—21no—
275C2×#121C22×C1112yes—
276C2×C4×Q8C22×C1111yescharacteristic
277C22×C42C22×C1111yescharacteristic
278#465—28no—
279#460—24no—
280C2×#106C22×C1112yes—
281C2×C4⋊C8—24no—
282C2×C4⋊C8C22×C1112yes—
283C2×C4⋊C8C22×C1111yescharacteristic
284C2×C4⋊C8C22×C1111yescharacteristic
285C2×#103C22×C1112yes—
286C2×#102C22×C1112yes—
287C2×#102C22×C1112yes—
288C2×#102C22×C1112yes—
289#391C22×C1111yescharacteristic
290#390—21no—
291#390—21no—
292#390C22×C1112yes—
293#389C22×C1111yescharacteristic
294#387—21no—
295#385—21no—
296#384C22×C1111yescharacteristic
297#380C22×C1111yescharacteristic
298C4×C4⋊C4—21no—
299C4×C4⋊C4C22×C1111yescharacteristic
300C4×C22⋊C4—21no—
301#340C22×C1112yes—
302#340C22×C1112yes—
303C22×C11—22no—
304C22×C11—22no—
305C22×C11—22no—
306C22×C11—22no—
307C22×C11—22no—
308C22×C11—22no—
309C22×C11—82no—
310C22×C11—82no—
311C22×C11—82no—
312C22×C11—82no—
313C22×C11—82no—
314C22×C11—82no—
315C22×C11—82no—
316C22×C11#46014yescomplemented
317C22×C11C2×#12111yescharacteristic
318C22×C11C2×#12111yescharacteristic
319C22×C11#53711yescharacteristic
320C22×C11C22×SD1611yescharacteristic
321C22×C11C2×#13511yescharacteristic
322C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
323C22×C11#57511yescharacteristic
324C4×C11—22no—
325C4×C11—22no—
326C4×C11—22no—
327C4×C11—42no—
328C4×C11—42no—
329C4×C11—41no—
330C4×C11—81no—
331C4×C11—82no—
332C4×C11—81no—
333C4×C11#46514yescomplemented
334C4×C11D4211yescharacteristic
335C4×C11#54711yescharacteristic
336C4×C11#54811yescharacteristic
337C4×C11#55311yescharacteristic
338C22×Q8C23×C1111yescharacteristic
339C22×D4—22no—
340C22×D4—21no—
341C22×D4—21no—
342C22×D4C23×C1112yes—
343C23×C4D4×C1111yescharacteristic
344C23×C4D4×C1111yescharacteristic
345C23×C4C23×C1111yescharacteristic
346C2×SD16—24no—
347C2×SD16—24no—
348C2×SD16—42no—
349C22×C8—24no—
350C22×C8—24no—
351C22×C8—42no—
352C22×C8C23×C1112yes—
353C22×C8C23×C1112yes—
354#127—22no—
355#127—22no—
356C22⋊Q8—22no—
357C22⋊Q8D4×C1114yescomplemented
358#121—24no—
359#121—24no—
360#121—44no—
361#121—44no—
362C4×Q8—22no—
363C4×Q8—22no—
364C2×C4⋊C4—21no—
365C2×C4⋊C4—21no—
366C2×C4⋊C4—21no—
367C2×C4⋊C4—21no—
368C2×C4⋊C4—21no—
369C2×C4⋊C4C23×C1111yescharacteristic
370C2×C4⋊C4C23×C1112yes—
371C2×C4⋊C4C23×C1111yescharacteristic
372C2×C4⋊C4C23×C1111yescharacteristic
373C2×C22⋊C4—21no—
374C2×C22⋊C4—21no—
375C2×C22⋊C4—22no—
376C2×C22⋊C4—22no—
377C2×C22⋊C4—22no—
378C2×C42—22no—
379C2×C42—22no—
380C2×C42—21no—
381C2×C42—21no—
382C2×C42D4×C1111yescharacteristic
383C2×C42D4×C1111yescharacteristic
384C2×C42C23×C1111yescharacteristic
385C2×C42C23×C1111yescharacteristic
386#106—24no—
387C4⋊C8—24no—
388C4⋊C8—22no—
389C4⋊C8D4×C1114yescomplemented
390#103—24no—
391#102—24no—
392#102—24no—
393#102—42no—
394#95—21no—
395#95—21no—
396#95—21no—
397#95—21no—
398#95—21no—
399C2×C11—24no—
400C2×C11—162no—
401C2×C11#241611yescharacteristic
402C2×C11C2×#46011yescharacteristic
403C2×C11#303511yescharacteristic
404C2×C11C2×#46511yescharacteristic
405C2×C11#305511yescharacteristic
406C2×C11#324611yescharacteristic
407C2×C11#324711yescharacteristic
408C24—22no—
409C24C2×D4×C1111yescharacteristic
410C2×Q8—21no—
411C2×Q8—21no—
412C2×Q8—21no—
413C2×Q8—21no—
414C2×Q8—21no—
415C2×Q8C2×D4×C1112yes—
416C2×D4—22no—
417C2×D4—22no—
418C2×D4—22no—
419C2×D4—22no—
420C2×D4—22no—
421C2×D4—22no—
422C2×D4—42no—
423C2×D4—42no—
424C2×D4—44no—
425C2×D4—44no—
426C2×D4—44no—
427C2×D4—42no—
428C2×D4—42no—
429C2×D4—42no—
430C2×D4—42no—
431C22×C4—22no—
432C22×C4—22no—
433C22×C4—21no—
434C22×C4—21no—
435C22×C4—21no—
436C22×C4—21no—
437C22×C4—22no—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—22no—
441C22×C4—21no—
442C22×C4—21no—
443C22×C4—22no—
444C22×C4—41no—
445C22×C4C11×SD1614yescomplemented
446C22×C4C2×D4×C1111yescharacteristic
447C22×C4C2×D4×C1111yescharacteristic
448C22×C4C2×D4×C1111yescharacteristic
449C22×C4C2×D4×C1112yes—
450C22×C4C2×D4×C1111yescharacteristic
451C22×C4C2×D4×C1111yescharacteristic
452C22×C4C11×#4112yes—
453C22×C4C24×C1111yescharacteristic
454SD16—48no—
455C2×C8—22no—
456C2×C8—22no—
457C2×C8—22no—
458C2×C8—22no—
459C2×C8—22no—
460C2×C8—48no—
461C2×C8C2×D4×C1114yes—
462C4⋊C4—24no—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—22no—
466C4⋊C4—21no—
467C4⋊C4—22no—
468C4⋊C4—21no—
469C4⋊C4—21no—
470C4⋊C4—42no—
471C4⋊C4—42no—
472C4⋊C4—42no—
473C4⋊C4—42no—
474C4⋊C4C2×D4×C1112yes—
475C22⋊C4—24no—
476C22⋊C4—44no—
477C22⋊C4—42no—
478C22⋊C4—44no—
479C22⋊C4—44no—
480C42—22no—
481C42—22no—
482C42—21no—
483C42—21no—
484C42—42no—
485C42—42no—
486C42C2×D4×C1112yes—
487C42C11×#4112yes—
488C11#2475311yescharacteristic, direct product factor, Sylow
489C23—21no—
490C23—21no—
491C23—21no—
492C23—21no—
493C23—42no—
494C23—42no—
495C23—42no—
496C23—42no—
497C23—42no—
498C23—42no—
499C23—42no—
500C23C11×#12112yes—
501C23C2×C11×SD1612yes—
502C23C11×AGL(1,ℤ/8)12yes—
503C23C22×D4×C1111yescharacteristic
504Q8—22no—
505Q8—22no—
506Q8—41no—
507Q8—41no—
508D4—42no—
509D4—42no—
510D4—42no—
511D4—42no—
512D4—84no—
513D4—88no—
514D4—84no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—22no—
522C2×C4—22no—
523C2×C4—22no—
524C2×C4—22no—
525C2×C4—28no—
526C2×C4—21no—
527C2×C4—22no—
528C2×C4—22no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—44no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—42no—
538C2×C4—41no—
539C2×C4—42no—
540C2×C4—41no—
541C2×C4—42no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4C11×#12112yes—
546C2×C4C11×#12112yes—
547C2×C4C11×#12112yes—
548C2×C4C2×C11×SD1612yes—
549C2×C4C2×C11×SD1612yes—
550C2×C4C11×#13512yes—
551C2×C4C22×D4×C1111yescharacteristic
552C2×C4C22×D4×C1111yescharacteristic
553C2×C4C2×C11×#4111yescharacteristic
554C2×C4C2×C11×#4111yescharacteristic
555C2×C4C11×H(5,𝔽2)11yescharacteristic
556C2×C4C11×2−1+411yescharacteristic
557C8—24no—
558C8—42no—
559C22—22no—
560C22—22no—
561C22—22no—
562C22—22no—
563C22—22no—
564C22—22no—
565C22—82no—
566C22—82no—
567C22—82no—
568C22—82no—
569C22—82no—
570C22—82no—
571C22—82no—
572C22C11×#46014yescomplemented
573C22C2×C11×#12111yescharacteristic
574C22C2×C11×#12111yescharacteristic
575C22C11×#53711yescharacteristic
576C22C22×C11×SD1611yescharacteristic
577C22C2×C11×#13511yescharacteristic
578C22C2×C11×AGL(1,ℤ/8)11yescharacteristic
579C22C11×#57511yescharacteristic
580C4—22no—
581C4—22no—
582C4—22no—
583C4—42no—
584C4—42no—
585C4—41no—
586C4—81no—
587C4—82no—
588C4—81no—
589C4C11×#46514yescomplemented
590C4D42×C1111yescharacteristic
591C4C11×#54711yescharacteristic
592C4C11×#54811yescharacteristic
593C4C11×#55311yescharacteristic
594C2—24no—
595C2—162no—
596C2C11×#241611yescharacteristic
597C2C2×C11×#46011yescharacteristic
598C2C11×#303511yescharacteristic
599C2C2×C11×#46511yescharacteristic
600C2C11×#305511yescharacteristic
601C2C11×#324611yescharacteristic
602C2C11×#324711yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC11×#2856C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C22×C42×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C11×#465C2semidirect
2. C2×C11×#460C2semidirect
3. C22×C11×C4⋊C8C2semidirect
5. C4×C11×C22⋊Q8C2semidirect
6. C11×#2065C2semidirect
7. C11×#2055C2semidirect
8. C11×#1982C2semidirect
9. C11×#1948C2semidirect
10. C11×#1893C2semidirect
11. C11×#1803C2semidirect
65. C11×C22⋊Q8D4semidirect
97. C11×C4⋊C8D4semidirect
107. #24753C11direct (N × H)
145. C22×C4×C11SD16semidirect
188. C2×#465C2×C11semidirect
189. C2×#460C2×C11semidirect
190. C22×C4⋊C8C2×C11semidirect
192. C4×C22⋊Q8C2×C11semidirect
193. #2065C2×C11semidirect
194. #2055C2×C11semidirect
195. #1982C2×C11semidirect
196. #1948C2×C11semidirect
197. #1893C2×C11semidirect
198. #1803C2×C11semidirect
316. C22×C11#460semidirect
333. C4×C11#465semidirect
357. C22⋊Q8D4×C11semidirect
389. C4⋊C8D4×C11semidirect
445. C22×C4C11×SD16semidirect
488. C11#24753direct (N × H)
572. C22C11×#460semidirect
589. C4C11×#465semidirect

Maximal subgroups

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

subgroupindex
C2×C11×#4652
C2×C11×#4602
C22×C11×C4⋊C82
C11×#28562
C4×C11×C22⋊Q82
C11×#20652
C11×#20552
C11×#19822
C11×#19482
C11×#18932
C11×#18032
#2475311