Finite Group Databasebeta

← C11×#24758 #14601951

Subgroups — C11×#24758 #14601951

Order 2816.

1184 conjugacy classes of subgroups.

The subgroup lattice has 644 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#469C212yesmaximal, complemented
2C2×C11×#459C211yesmaximal, characteristic, complemented
3C2×C11×#423C211yesmaximal, characteristic, complemented
4C11×#2856C211yesmaximal, characteristic, complemented
5C4×C11×#121C211yesmaximal, characteristic, complemented
6C11×#2065C212yesmaximal, complemented
7C11×#2054C212yesmaximal, complemented
8C11×#1982C211yesmaximal, characteristic, complemented
9C11×#1948C211yesmaximal, characteristic, complemented
10C11×#1895C212yesmaximal, complemented
11C11×#1802C211yesmaximal, characteristic, complemented
12C22×C11×D8C2212yes—
13C22×C11×M16C2212yes—
14C2×C11×#127C2211yescharacteristic
15C2×C11×#121—21no—
16C2×C11×#121—21no—
17C2×C11×#121C2212yes—
18C2×C11×#121C2211yescharacteristic
19C2×C4×D4×C11—21no—
20C2×C4×D4×C11C2211yescharacteristic
21C22×C42×C11C2211yescharacteristic
22C11×#469—28no—
23C11×#459—24no—
24C2×C11×#106C2212yes—
25C11×#423—24no—
26C2×C11×C4⋊C8C2211yescharacteristic
27C2×C11×C4⋊C8C2212yes—
28C2×C11×C4⋊C8C2211yescharacteristic
29C2×C11×#102C2212yes—
30C2×C11×#102C2212yes—
31C2×C11×#102C2212yes—
32C2×C11×#102C2212yes—
33C11×#390—21no—
34C11×#390—21no—
35C11×#390C2211yescharacteristic
36C11×#390C2212yes—
37C11×#389C2211yescharacteristic
38C11×#388—21no—
39C11×#386—21no—
40C11×#384C2211yescharacteristic
41C11×#380C2211yescharacteristic
42C4×C11×C4⋊C4C2211yescharacteristic
43C4×C11×C22⋊C4—21no—
44C11×#340C2212yes—
45C11×#340C2212yes—
46C22×D4×C11—21no—
47C22×D4×C11—22no—
48C22×D4×C11—21no—
49C22×D4×C11—21no—
50C22×D4×C11C2312yes—
51C22×D4×C11C2311yescharacteristic
52C23×C4×C11—21no—
53C23×C4×C11D411yescharacteristic
54C23×C4×C11D411yescharacteristic
55C23×C4×C11C2311yescharacteristic
56C2×C11×D8—24no—
57C2×C11×D8—24no—
58C2×C11×D8—42no—
59C2×C11×M16—24no—
60C2×C11×M16—24no—
61C2×C11×M16—42no—
62C22×C8×C11C2312yes—
63C22×C8×C11C2312yes—
64C11×#127—22no—
65C11×#127—22no—
66C11×#121—22no—
67C11×#121—24no—
68C11×#121—24no—
69C11×#121—44no—
70C11×#121—44no—
71C11×#121D414yescomplemented
72C4×D4×C11—22no—
73C4×D4×C11—22no—
74C4×D4×C11—44no—
75C2×C11×C4⋊C4—21no—
76C2×C11×C4⋊C4—21no—
77C2×C11×C4⋊C4—21no—
78C2×C11×C4⋊C4C2311yescharacteristic
79C2×C11×C4⋊C4C2311yescharacteristic
80C2×C11×C4⋊C4C2312yes—
81C2×C11×C4⋊C4C2311yescharacteristic
82C2×C11×C22⋊C4—21no—
83C2×C11×C22⋊C4—21no—
84C2×C11×C22⋊C4—21no—
85C2×C11×C22⋊C4—21no—
86C2×C11×C22⋊C4—21no—
87C2×C11×C22⋊C4—22no—
88C2×C11×C22⋊C4—22no—
89C2×C11×C22⋊C4—22no—
90C2×C42×C11—22no—
91C2×C42×C11—22no—
92C2×C42×C11—21no—
93C2×C42×C11D411yescharacteristic
94C2×C42×C11D411yescharacteristic
95C2×C42×C11C2311yescharacteristic
96C2×C42×C11C2311yescharacteristic
97C11×#106—24no—
98C11×C4⋊C8—24no—
99C11×C4⋊C8—22no—
100C11×C4⋊C8D414yescomplemented
101C11×#102—24no—
102C11×#102—24no—
103C11×#102—24no—
104C11×#102—42no—
105C11×#95—21no—
106C11×#95—21no—
107C11×#95—21no—
108#24758C1111yesmaximal, characteristic, direct product factor, Sylow
109C24×C11—21no—
110C24×C11—22no—
111C24×C11C2×D411yescharacteristic
112C2×D4×C11—24no—
113C2×D4×C11—21no—
114C2×D4×C11—22no—
115C2×D4×C11—22no—
116C2×D4×C11—21no—
117C2×D4×C11—21no—
118C2×D4×C11—22no—
119C2×D4×C11—22no—
120C2×D4×C11—21no—
121C2×D4×C11—22no—
122C2×D4×C11—21no—
123C2×D4×C11—22no—
124C2×D4×C11—42no—
125C2×D4×C11—42no—
126C2×D4×C11—42no—
127C2×D4×C11—42no—
128C2×D4×C11—44no—
129C2×D4×C11—44no—
130C2×D4×C11—44no—
131C2×D4×C11—42no—
132C2×D4×C11—42no—
133C2×D4×C11—42no—
134C2×D4×C11—42no—
135C2×D4×C11C2×D412yes—
136C22×C4×C11—21no—
137C22×C4×C11—21no—
138C22×C4×C11—21no—
139C22×C4×C11—21no—
140C22×C4×C11—21no—
141C22×C4×C11—22no—
142C22×C4×C11—22no—
143C22×C4×C11—22no—
144C22×C4×C11—22no—
145C22×C4×C11—22no—
146C22×C4×C11—21no—
147C22×C4×C11—21no—
148C22×C4×C11—22no—
149C22×C4×C11—41no—
150C22×C4×C11—42no—
151C22×C4×C11—42no—
152C22×C4×C11—42no—
153C22×C4×C11C2×D411yescharacteristic
154C22×C4×C11C2×D411yescharacteristic
155C22×C4×C11C2×D411yescharacteristic
156C22×C4×C11C2×D412yes—
157C22×C4×C11C2×D411yescharacteristic
158C22×C4×C11C2×D411yescharacteristic
159C22×C4×C11#4112yes—
160C22×C4×C11C2411yescharacteristic
161C11×D8—48no—
162C11×M16—48no—
163C2×C8×C11—22no—
164C2×C8×C11—22no—
165C2×C8×C11—22no—
166C2×C8×C11—22no—
167C2×C8×C11—22no—
168C2×C8×C11C2×D414yes—
169C11×C4⋊C4—21no—
170C11×C4⋊C4—21no—
171C11×C4⋊C4—22no—
172C11×C4⋊C4—21no—
173C11×C4⋊C4—22no—
174C11×C4⋊C4—21no—
175C11×C4⋊C4—21no—
176C11×C4⋊C4—42no—
177C11×C4⋊C4—42no—
178C11×C4⋊C4—42no—
179C11×C4⋊C4C2×D412yes—
180C11×C22⋊C4—24no—
181C11×C22⋊C4—42no—
182C11×C22⋊C4—44no—
183C11×C22⋊C4—42no—
184C11×C22⋊C4—42no—
185C11×C22⋊C4—44no—
186C11×C22⋊C4—42no—
187C11×C22⋊C4—44no—
188C42×C11—22no—
189C42×C11—22no—
190C42×C11—21no—
191C42×C11—21no—
192C42×C11—42no—
193C42×C11C2×D412yes—
194C42×C11#4112yes—
195C2×#469C2×C1112yescomplemented
196C2×#459C2×C1111yescharacteristic, complemented
197C2×#423C2×C1111yescharacteristic, complemented
198#2856C2×C1111yescharacteristic, complemented
199C4×#121C2×C1111yescharacteristic, complemented
200#2065C2×C1112yescomplemented
201#2054C2×C1112yescomplemented
202#1982C2×C1111yescharacteristic, complemented
203#1948C2×C1111yescharacteristic, complemented
204#1895C2×C1112yescomplemented
205#1802C2×C1111yescharacteristic, complemented
206C23×C11—21no—
207C23×C11—21no—
208C23×C11—21no—
209C23×C11—21no—
210C23×C11—21no—
211C23×C11—21no—
212C23×C11—22no—
213C23×C11—41no—
214C23×C11—41no—
215C23×C11—41no—
216C23×C11—41no—
217C23×C11—41no—
218C23×C11—41no—
219C23×C11—42no—
220C23×C11—42no—
221C23×C11—42no—
222C23×C11—42no—
223C23×C11—42no—
224C23×C11—42no—
225C23×C11—42no—
226C23×C11#12112yes—
227C23×C11C22×D411yescharacteristic
228D4×C11—22no—
229D4×C11—22no—
230D4×C11—48no—
231D4×C11—42no—
232D4×C11—42no—
233D4×C11—41no—
234D4×C11—42no—
235D4×C11—41no—
236D4×C11—42no—
237D4×C11—84no—
238D4×C11—88no—
239D4×C11—84no—
240C2×C4×C11—21no—
241C2×C4×C11—21no—
242C2×C4×C11—21no—
243C2×C4×C11—21no—
244C2×C4×C11—21no—
245C2×C4×C11—21no—
246C2×C4×C11—22no—
247C2×C4×C11—22no—
248C2×C4×C11—22no—
249C2×C4×C11—22no—
250C2×C4×C11—21no—
251C2×C4×C11—22no—
252C2×C4×C11—21no—
253C2×C4×C11—21no—
254C2×C4×C11—44no—
255C2×C4×C11—41no—
256C2×C4×C11—41no—
257C2×C4×C11—44no—
258C2×C4×C11—41no—
259C2×C4×C11—42no—
260C2×C4×C11—41no—
261C2×C4×C11—41no—
262C2×C4×C11—41no—
263C2×C4×C11—42no—
264C2×C4×C11—42no—
265C2×C4×C11—41no—
266C2×C4×C11—41no—
267C2×C4×C11—84no—
268C2×C4×C11#12112yes—
269C2×C4×C11#12112yes—
270C2×C4×C11#12112yes—
271C2×C4×C11AGL(1,ℤ/8)12yes—
272C2×C4×C11AGL(1,ℤ/8)12yes—
273C2×C4×C11AGL(1,ℤ/8)12yes—
274C2×C4×C11C22×D411yescharacteristic
275C2×C4×C11C22×D411yescharacteristic
276C2×C4×C11C2×#4111yescharacteristic
277C2×C4×C11C2×#4111yescharacteristic
278C2×C4×C11H(5,𝔽2)11yescharacteristic
279C2×C4×C112−1+411yescharacteristic
280C8×C11—24no—
281C8×C11—42no—
282C22×D8C22×C1112yes—
283C22×M16C22×C1112yes—
284C2×#127C22×C1111yescharacteristic
285C2×#121—21no—
286C2×#121—21no—
287C2×#121C22×C1112yes—
288C2×#121C22×C1111yescharacteristic
289C2×C4×D4—21no—
290C2×C4×D4C22×C1111yescharacteristic
291C22×C42C22×C1111yescharacteristic
292#469—28no—
293#459—24no—
294C2×#106C22×C1112yes—
295#423—24no—
296C2×C4⋊C8C22×C1112yes—
297C2×C4⋊C8C22×C1111yescharacteristic
298C2×C4⋊C8C22×C1111yescharacteristic
299C2×#102C22×C1112yes—
300C2×#102C22×C1112yes—
301C2×#102C22×C1112yes—
302C2×#102C22×C1112yes—
303#390—21no—
304#390—21no—
305#390C22×C1111yescharacteristic
306#390C22×C1112yes—
307#389C22×C1111yescharacteristic
308#388—21no—
309#386—21no—
310#384C22×C1111yescharacteristic
311#380C22×C1111yescharacteristic
312C4×C4⋊C4C22×C1111yescharacteristic
313C4×C22⋊C4—21no—
314#340C22×C1112yes—
315#340C22×C1112yes—
316C22×C11—22no—
317C22×C11—22no—
318C22×C11—22no—
319C22×C11—41no—
320C22×C11—41no—
321C22×C11—41no—
322C22×C11—41no—
323C22×C11—42no—
324C22×C11—42no—
325C22×C11—42no—
326C22×C11—81no—
327C22×C11—81no—
328C22×C11—81no—
329C22×C11—81no—
330C22×C11—82no—
331C22×C11—82no—
332C22×C11—82no—
333C22×C11—82no—
334C22×C11—82no—
335C22×C11—82no—
336C22×C11—82no—
337C22×C11C2×#12111yescharacteristic
338C22×C11C2×#12111yescharacteristic
339C22×C11#53711yescharacteristic
340C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
341C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
342C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
343C22×C11#57511yescharacteristic
344C4×C11—22no—
345C4×C11—22no—
346C4×C11—22no—
347C4×C11—42no—
348C4×C11—41no—
349C4×C11—81no—
350C4×C11—82no—
351C4×C11—81no—
352C4×C11#46914yescomplemented
353C4×C11D4211yescharacteristic
354C4×C11#54711yescharacteristic
355C4×C11#54811yescharacteristic
356C4×C11#55311yescharacteristic
357C22×D4—21no—
358C22×D4—22no—
359C22×D4—21no—
360C22×D4—21no—
361C22×D4C23×C1112yes—
362C22×D4C23×C1111yescharacteristic
363C23×C4—21no—
364C23×C4D4×C1111yescharacteristic
365C23×C4D4×C1111yescharacteristic
366C23×C4C23×C1111yescharacteristic
367C2×D8—24no—
368C2×D8—24no—
369C2×D8—42no—
370C2×M16—24no—
371C2×M16—24no—
372C2×M16—42no—
373C22×C8C23×C1112yes—
374C22×C8C23×C1112yes—
375#127—22no—
376#127—22no—
377#121—22no—
378#121—24no—
379#121—24no—
380#121—44no—
381#121—44no—
382#121D4×C1114yescomplemented
383C4×D4—22no—
384C4×D4—22no—
385C4×D4—44no—
386C2×C4⋊C4—21no—
387C2×C4⋊C4—21no—
388C2×C4⋊C4—21no—
389C2×C4⋊C4C23×C1111yescharacteristic
390C2×C4⋊C4C23×C1112yes—
391C2×C4⋊C4C23×C1111yescharacteristic
392C2×C4⋊C4C23×C1111yescharacteristic
393C2×C22⋊C4—21no—
394C2×C22⋊C4—21no—
395C2×C22⋊C4—21no—
396C2×C22⋊C4—21no—
397C2×C22⋊C4—22no—
398C2×C22⋊C4—22no—
399C2×C22⋊C4—22no—
400C2×C22⋊C4—21no—
401C2×C42—22no—
402C2×C42—22no—
403C2×C42—21no—
404C2×C42D4×C1111yescharacteristic
405C2×C42D4×C1111yescharacteristic
406C2×C42C23×C1111yescharacteristic
407C2×C42C23×C1111yescharacteristic
408#106—24no—
409C4⋊C8—24no—
410C4⋊C8—22no—
411C4⋊C8D4×C1114yescomplemented
412#102—24no—
413#102—24no—
414#102—24no—
415#102—42no—
416#95—21no—
417#95—21no—
418#95—21no—
419C2×C11—42no—
420C2×C11—82no—
421C2×C11—162no—
422C2×C11#241611yescharacteristic
423C2×C11#303611yescharacteristic
424C2×C11#303811yescharacteristic
425C2×C11C2×#46911yescharacteristic
426C2×C11#305511yescharacteristic
427C2×C11#325111yescharacteristic
428C2×C11#325311yescharacteristic
429C24—21no—
430C24—22no—
431C24C2×D4×C1111yescharacteristic
432C2×D4—24no—
433C2×D4—21no—
434C2×D4—22no—
435C2×D4—22no—
436C2×D4—21no—
437C2×D4—21no—
438C2×D4—22no—
439C2×D4—22no—
440C2×D4—21no—
441C2×D4—22no—
442C2×D4—21no—
443C2×D4—22no—
444C2×D4—42no—
445C2×D4—42no—
446C2×D4—42no—
447C2×D4—42no—
448C2×D4—44no—
449C2×D4—44no—
450C2×D4—44no—
451C2×D4—42no—
452C2×D4—42no—
453C2×D4—42no—
454C2×D4—42no—
455C2×D4C2×D4×C1112yes—
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—22no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—22no—
465C22×C4—22no—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—22no—
469C22×C4—41no—
470C22×C4—42no—
471C22×C4—42no—
472C22×C4—42no—
473C22×C4C2×D4×C1111yescharacteristic
474C22×C4C2×D4×C1111yescharacteristic
475C22×C4C2×D4×C1111yescharacteristic
476C22×C4C2×D4×C1112yes—
477C22×C4C2×D4×C1111yescharacteristic
478C22×C4C2×D4×C1111yescharacteristic
479C22×C4C11×#4112yes—
480C22×C4C24×C1111yescharacteristic
481D8—48no—
482M16—48no—
483C2×C8—22no—
484C2×C8—22no—
485C2×C8—22no—
486C2×C8—22no—
487C2×C8—22no—
488C2×C8C2×D4×C1114yes—
489C4⋊C4—21no—
490C4⋊C4—21no—
491C4⋊C4—22no—
492C4⋊C4—21no—
493C4⋊C4—22no—
494C4⋊C4—21no—
495C4⋊C4—21no—
496C4⋊C4—42no—
497C4⋊C4—42no—
498C4⋊C4—42no—
499C4⋊C4C2×D4×C1112yes—
500C22⋊C4—24no—
501C22⋊C4—42no—
502C22⋊C4—44no—
503C22⋊C4—42no—
504C22⋊C4—42no—
505C22⋊C4—44no—
506C22⋊C4—44no—
507C22⋊C4—42no—
508C42—22no—
509C42—22no—
510C42—21no—
511C42—21no—
512C42—42no—
513C42C2×D4×C1112yes—
514C42C11×#4112yes—
515C11#2475811yescharacteristic, direct product factor, Sylow
516C23—21no—
517C23—21no—
518C23—21no—
519C23—21no—
520C23—21no—
521C23—21no—
522C23—22no—
523C23—41no—
524C23—41no—
525C23—41no—
526C23—41no—
527C23—41no—
528C23—41no—
529C23—42no—
530C23—42no—
531C23—42no—
532C23—42no—
533C23—42no—
534C23—42no—
535C23—42no—
536C23C11×#12112yes—
537C23C22×D4×C1111yescharacteristic
538D4—22no—
539D4—22no—
540D4—48no—
541D4—42no—
542D4—42no—
543D4—41no—
544D4—42no—
545D4—41no—
546D4—42no—
547D4—84no—
548D4—88no—
549D4—84no—
550C2×C4—21no—
551C2×C4—21no—
552C2×C4—21no—
553C2×C4—21no—
554C2×C4—21no—
555C2×C4—21no—
556C2×C4—22no—
557C2×C4—22no—
558C2×C4—22no—
559C2×C4—22no—
560C2×C4—21no—
561C2×C4—22no—
562C2×C4—21no—
563C2×C4—21no—
564C2×C4—44no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—44no—
568C2×C4—41no—
569C2×C4—42no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—42no—
574C2×C4—42no—
575C2×C4—41no—
576C2×C4—41no—
577C2×C4—84no—
578C2×C4C11×#12112yes—
579C2×C4C11×#12112yes—
580C2×C4C11×#12112yes—
581C2×C4C11×AGL(1,ℤ/8)12yes—
582C2×C4C11×AGL(1,ℤ/8)12yes—
583C2×C4C11×AGL(1,ℤ/8)12yes—
584C2×C4C22×D4×C1111yescharacteristic
585C2×C4C22×D4×C1111yescharacteristic
586C2×C4C2×C11×#4111yescharacteristic
587C2×C4C2×C11×#4111yescharacteristic
588C2×C4C11×H(5,𝔽2)11yescharacteristic
589C2×C4C11×2−1+411yescharacteristic
590C8—24no—
591C8—42no—
592C22—22no—
593C22—22no—
594C22—22no—
595C22—41no—
596C22—41no—
597C22—41no—
598C22—41no—
599C22—42no—
600C22—42no—
601C22—42no—
602C22—81no—
603C22—81no—
604C22—81no—
605C22—81no—
606C22—82no—
607C22—82no—
608C22—82no—
609C22—82no—
610C22—82no—
611C22—82no—
612C22—82no—
613C22C2×C11×#12111yescharacteristic
614C22C2×C11×#12111yescharacteristic
615C22C11×#53711yescharacteristic
616C22C2×C11×AGL(1,ℤ/8)11yescharacteristic
617C22C2×C11×AGL(1,ℤ/8)11yescharacteristic
618C22C2×C11×AGL(1,ℤ/8)11yescharacteristic
619C22C11×#57511yescharacteristic
620C4—22no—
621C4—22no—
622C4—22no—
623C4—42no—
624C4—41no—
625C4—81no—
626C4—82no—
627C4—81no—
628C4C11×#46914yescomplemented
629C4D42×C1111yescharacteristic
630C4C11×#54711yescharacteristic
631C4C11×#54811yescharacteristic
632C4C11×#55311yescharacteristic
633C2—42no—
634C2—82no—
635C2—162no—
636C2C11×#241611yescharacteristic
637C2C11×#303611yescharacteristic
638C2C11×#303811yescharacteristic
639C2C2×C11×#46911yescharacteristic
640C2C11×#305511yescharacteristic
641C2C11×#325111yescharacteristic
642C2C11×#325311yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
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×#469C2semidirect
2. C2×C11×#459C2semidirect
3. C2×C11×#423C2semidirect
4. C11×#2856C2semidirect
5. C4×C11×#121C2semidirect
6. C11×#2065C2semidirect
7. C11×#2054C2semidirect
8. C11×#1982C2semidirect
9. C11×#1948C2semidirect
10. C11×#1895C2semidirect
11. C11×#1802C2semidirect
71. C11×#121D4semidirect
100. C11×C4⋊C8D4semidirect
108. #24758C11direct (N × H)
195. C2×#469C2×C11semidirect
196. C2×#459C2×C11semidirect
197. C2×#423C2×C11semidirect
198. #2856C2×C11semidirect
199. C4×#121C2×C11semidirect
200. #2065C2×C11semidirect
201. #2054C2×C11semidirect
202. #1982C2×C11semidirect
203. #1948C2×C11semidirect
204. #1895C2×C11semidirect
205. #1802C2×C11semidirect
352. C4×C11#469semidirect
382. #121D4×C11semidirect
411. C4⋊C8D4×C11semidirect
515. C11#24758direct (N × H)
628. C4C11×#469semidirect

Maximal subgroups

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

subgroupindex
C2×C11×#4692
C2×C11×#4592
C2×C11×#4232
C11×#28562
C4×C11×#1212
C11×#20652
C11×#20542
C11×#19822
C11×#19482
C11×#18952
C11×#18022
#2475811