Finite Group Databasebeta

← C11×#24370 #14601563

Subgroups — C11×#24370 #14601563

Order 2816.

1670 conjugacy classes of subgroups.

The subgroup lattice has 628 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C11×AGL(1,ℤ/8)C211yesmaximal, characteristic, complemented
2C2×C11×#460C212yesmaximal, complemented
3C2×C11×#449C211yesmaximal, characteristic, complemented
4C11×#2433C211yesmaximal, characteristic, complemented
5C11×#2341C211yesmaximal, characteristic, complemented
6C11×#2054C212yesmaximal, complemented
7C11×#2011C212yesmaximal, complemented
8C11×#1895C211yesmaximal, characteristic, complemented
9C11×#1880C212yesmaximal, complemented
10C11×#1851C211yesmaximal, characteristic, complemented
11C11×#1786C211yesmaximal, characteristic, complemented
12C22×C11×#41C2211yescharacteristic
13C23×D4×C11C2211yescharacteristic
14C2×C11×AGL(1,ℤ/8)—24no—
15C2×C11×AGL(1,ℤ/8)—28no—
16C22×C11×SD16C2212yes—
17C22×C11×SD16C2211yescharacteristic, complemented
18C22×C11×D8C2212yes—
19C22×C11×D8C2211yescharacteristic, complemented
20C22×C11×M16C2211yescharacteristic
21C2×C11×#127C2212yes—
22C2×C11×#121C2211yescharacteristic
23C2×C11×#120—22no—
24C2×C4×Q8×C11C2212yescomplemented
25C11×#460—28no—
26C11×#449—24no—
27C2×C11×C4⋊C8C2212yescomplemented
28C2×C11×#103C2211yescharacteristic, complemented
29C2×C11×#102C2212yes—
30C2×C11×#102C2212yes—
31C2×C11×#102C2212yescomplemented
32C2×C11×#102C2211yescharacteristic, complemented
33C2×C11×C22⋊C8C2211yescharacteristic
34C11×#392—21no—
35C11×#392—21no—
36C11×#390—22no—
37C11×#390C2212yes—
38C11×#390C2212yescomplemented
39C11×#380—21no—
40C11×#380C2211yescharacteristic
41C4×C11×C22⋊C4—21no—
42C4×C11×C22⋊C4C2211yescharacteristic
43C11×#340C2212yescomplemented
44C11×#336C2212yescomplemented
45C25×C11—21no—
46C2×C11×#41—22no—
47C2×C11×#41—24no—
48C2×C11×#41—42no—
49C2×C11×#41D414yescomplemented
50C22×Q8×C11C2311yescharacteristic
51C22×D4×C11—24no—
52C22×D4×C11—21no—
53C22×D4×C11—21no—
54C22×D4×C11—22no—
55C22×D4×C11—21no—
56C22×D4×C11—22no—
57C22×D4×C11—22no—
58C22×D4×C11—22no—
59C22×D4×C11—42no—
60C22×D4×C11C2311yescharacteristic
61C22×D4×C11C2312yes—
62C22×D4×C11C2311yescharacteristic
63C23×C4×C11—21no—
64C23×C4×C11C2311yescharacteristic
65C11×AGL(1,ℤ/8)—232no—
66C2×C11×SD16—24no—
67C2×C11×SD16—24no—
68C2×C11×SD16—22no—
69C2×C11×SD16—24no—
70C2×C11×SD16D418yescomplemented
71C2×C11×D8—24no—
72C2×C11×D8—24no—
73C2×C11×D8—22no—
74C2×C11×D8—24no—
75C2×C11×D8—42no—
76C2×C11×M16—22no—
77C2×C11×M16—24no—
78C22×C8×C11C2311yescharacteristic
79C22×C8×C11C2311yescharacteristic
80C22×C8×C11C2312yes—
81C11×#127—24no—
82C11×#127—42no—
83C11×#121—22no—
84C11×#121—22no—
85C11×#120—48no—
86C4×Q8×C11—24no—
87C4×Q8×C11—42no—
88C2×C11×C4⋊C4—22no—
89C2×C11×C4⋊C4C2311yescharacteristic
90C2×C11×C4⋊C4C2312yes—
91C2×C11×C22⋊C4—22no—
92C2×C11×C22⋊C4—22no—
93C2×C11×C22⋊C4—22no—
94C2×C11×C22⋊C4—21no—
95C2×C11×C22⋊C4—21no—
96C2×C11×C22⋊C4—22no—
97C2×C11×C22⋊C4D412yes—
98C2×C42×C11—22no—
99C2×C42×C11C2312yes—
100C11×C4⋊C8—24no—
101C11×#103—22no—
102C11×#102—24no—
103C11×#102—22no—
104C11×#102—24no—
105C11×#102—42no—
106C11×C22⋊C8—22no—
107C11×#95—21no—
108C11×#95D411yescharacteristic
109C11×#95D411yescharacteristic
110#24370C1111yesmaximal, characteristic, direct product factor, Sylow
111C24×C11—21no—
112C24×C11—22no—
113C24×C11—21no—
114C24×C11—44no—
115C24×C11—44no—
116C24×C11—42no—
117C24×C11—81no—
118C24×C11—81no—
119C24×C11C2×D411yescharacteristic
120C11×#41—28no—
121C11×#41—44no—
122C11×#41—48no—
123C2×Q8×C11—21no—
124C2×Q8×C11—22no—
125C2×Q8×C11C2×D412yes—
126C2×Q8×C11C2×D414yes—
127C2×D4×C11—28no—
128C2×D4×C11—24no—
129C2×D4×C11—22no—
130C2×D4×C11—22no—
131C2×D4×C11—22no—
132C2×D4×C11—22no—
133C2×D4×C11—21no—
134C2×D4×C11—22no—
135C2×D4×C11—21no—
136C2×D4×C11—21no—
137C2×D4×C11—22no—
138C2×D4×C11—22no—
139C2×D4×C11—22no—
140C2×D4×C11—22no—
141C2×D4×C11—48no—
142C2×D4×C11—44no—
143C2×D4×C11—44no—
144C2×D4×C11—44no—
145C2×D4×C11—44no—
146C2×D4×C11—44no—
147C2×D4×C11—44no—
148C2×D4×C11—44no—
149C2×D4×C11—42no—
150C2×D4×C11—42no—
151C2×D4×C11—44no—
152C2×D4×C11—82no—
153C2×D4×C11—82no—
154C2×D4×C11C2×D414yes—
155C2×D4×C11C2×D412yes—
156C22×C4×C11—21no—
157C22×C4×C11—22no—
158C22×C4×C11—22no—
159C22×C4×C11—24no—
160C22×C4×C11—22no—
161C22×C4×C11—21no—
162C22×C4×C11—44no—
163C22×C4×C11C2×D412yes—
164C22×C4×C11C2×D411yescharacteristic
165C22×C4×C11C2×D412yes—
166C22×C4×C11C2×D412yes—
167C22×C4×C11#4112yes—
168C22×C4×C11C2411yescharacteristic
169C11×SD16—216no—
170C11×SD16—44no—
171C11×D8—216no—
172C11×D8—44no—
173C11×M16—28no—
174C2×C8×C11—22no—
175C2×C8×C11—22no—
176C2×C8×C11—21no—
177C2×C8×C11—21no—
178C2×C8×C11—22no—
179C2×C8×C11—22no—
180C2×C8×C11C2×D414yes—
181C11×C4⋊C4—22no—
182C11×C4⋊C4—21no—
183C11×C4⋊C4—21no—
184C11×C4⋊C4—22no—
185C11×C4⋊C4—44no—
186C11×C22⋊C4—24no—
187C11×C22⋊C4—44no—
188C11×C22⋊C4—42no—
189C11×C22⋊C4—44no—
190C11×C22⋊C4—44no—
191C11×C22⋊C4—82no—
192C11×C22⋊C4—81no—
193C42×C11—22no—
194C42×C11—22no—
195C42×C11—44no—
196C22×AGL(1,ℤ/8)C2×C1111yescharacteristic, complemented
197C2×#460C2×C1112yescomplemented
198C2×#449C2×C1111yescharacteristic, complemented
199#2433C2×C1111yescharacteristic, complemented
200#2341C2×C1111yescharacteristic, complemented
201#2054C2×C1112yescomplemented
202#2011C2×C1112yescomplemented
203#1895C2×C1111yescharacteristic, complemented
204#1880C2×C1112yescomplemented
205#1851C2×C1111yescharacteristic, complemented
206#1786C2×C1111yescharacteristic, complemented
207C23×C11—22no—
208C23×C11—22no—
209C23×C11—21no—
210C23×C11—21no—
211C23×C11—22no—
212C23×C11—24no—
213C23×C11—48no—
214C23×C11—42no—
215C23×C11—42no—
216C23×C11—42no—
217C23×C11—42no—
218C23×C11—42no—
219C23×C11—42no—
220C23×C11—41no—
221C23×C11—42no—
222C23×C11—42no—
223C23×C11—41no—
224C23×C11—41no—
225C23×C11—42no—
226C23×C11—42no—
227C23×C11—41no—
228C23×C11—41no—
229C23×C11—84no—
230C23×C11—84no—
231C23×C11—88no—
232C23×C11—88no—
233C23×C11#12112yes—
234C23×C11C22×D411yescharacteristic
235Q8×C11—22no—
236Q8×C11—24no—
237Q8×C11#12014yescomplemented
238D4×C11—22no—
239D4×C11—24no—
240D4×C11—22no—
241D4×C11—24no—
242D4×C11—48no—
243D4×C11—48no—
244D4×C11—41no—
245D4×C11—42no—
246D4×C11—41no—
247D4×C11—42no—
248D4×C11—42no—
249D4×C11—42no—
250D4×C11—88no—
251D4×C11—88no—
252D4×C11—84no—
253C2×C4×C11—22no—
254C2×C4×C11—22no—
255C2×C4×C11—24no—
256C2×C4×C11—22no—
257C2×C4×C11—22no—
258C2×C4×C11—22no—
259C2×C4×C11—22no—
260C2×C4×C11—24no—
261C2×C4×C11—22no—
262C2×C4×C11—22no—
263C2×C4×C11—22no—
264C2×C4×C11—48no—
265C2×C4×C11—41no—
266C2×C4×C11—42no—
267C2×C4×C11—42no—
268C2×C4×C11—42no—
269C2×C4×C11—42no—
270C2×C4×C11#12112yes—
271C2×C4×C11AGL(1,ℤ/8)14yescomplemented
272C2×C4×C11C22×D411yescharacteristic
273C2×C4×C11C22×D412yes—
274C2×C4×C11C2×#4111yescharacteristic
275C2×C4×C11H(5,𝔽2)12yes—
276C8×C11—24no—
277C8×C11—41no—
278C8×C11—41no—
279C22×#41C22×C1111yescharacteristic
280C23×D4C22×C1111yescharacteristic
281C2×AGL(1,ℤ/8)—24no—
282C2×AGL(1,ℤ/8)—28no—
283C22×SD16C22×C1112yes—
284C22×SD16C22×C1111yescharacteristic, complemented
285C22×D8C22×C1112yes—
286C22×D8C22×C1111yescharacteristic, complemented
287C22×M16C22×C1111yescharacteristic
288C2×#127C22×C1112yes—
289C2×#121C22×C1111yescharacteristic
290C2×#120—22no—
291C2×C4×Q8C22×C1112yescomplemented
292#460—28no—
293#449—24no—
294C2×C4⋊C8C22×C1112yescomplemented
295C2×#103C22×C1111yescharacteristic, complemented
296C2×#102C22×C1112yes—
297C2×#102C22×C1112yes—
298C2×#102C22×C1111yescharacteristic, complemented
299C2×#102C22×C1112yescomplemented
300C2×C22⋊C8C22×C1111yescharacteristic
301#392—21no—
302#392—21no—
303#390—22no—
304#390C22×C1112yes—
305#390C22×C1112yescomplemented
306#380—21no—
307#380C22×C1111yescharacteristic
308C4×C22⋊C4—21no—
309C4×C22⋊C4C22×C1111yescharacteristic
310#340C22×C1112yescomplemented
311#336C22×C1112yescomplemented
312C22×C11—22no—
313C22×C11—22no—
314C22×C11—22no—
315C22×C11—42no—
316C22×C11—42no—
317C22×C11—42no—
318C22×C11—44no—
319C22×C11—44no—
320C22×C11—44no—
321C22×C11—42no—
322C22×C11—42no—
323C22×C11—816no—
324C22×C11—82no—
325C22×C11—82no—
326C22×C11—82no—
327C22×C11—82no—
328C22×C11—82no—
329C22×C11—82no—
330C22×C11—81no—
331C22×C11—82no—
332C22×C11—82no—
333C22×C11—81no—
334C22×C11—81no—
335C22×C11C2×#12111yescharacteristic
336C22×C11D4212yes—
337C22×C11C2×AGL(1,ℤ/8)12yes—
338C22×C11#57611yescharacteristic
339C22×C11#57711yescharacteristic
340C4×C11—22no—
341C4×C11—24no—
342C4×C11—24no—
343C4×C11—42no—
344C4×C11—82no—
345C4×C11—81no—
346C4×C11C2×#12011yescharacteristic
347C4×C11#53411yescharacteristic
348C4×C11#54612yes—
349C25—21no—
350C2×#41—22no—
351C2×#41—24no—
352C2×#41—42no—
353C2×#41D4×C1114yescomplemented
354C22×Q8C23×C1111yescharacteristic
355C22×D4—24no—
356C22×D4—21no—
357C22×D4—21no—
358C22×D4—22no—
359C22×D4—21no—
360C22×D4—22no—
361C22×D4—22no—
362C22×D4—22no—
363C22×D4—42no—
364C22×D4C23×C1111yescharacteristic
365C22×D4C23×C1112yes—
366C22×D4C23×C1111yescharacteristic
367C23×C4—21no—
368C23×C4C23×C1111yescharacteristic
369AGL(1,ℤ/8)—232no—
370C2×SD16—24no—
371C2×SD16—24no—
372C2×SD16—22no—
373C2×SD16—24no—
374C2×SD16D4×C1118yescomplemented
375C2×D8—24no—
376C2×D8—24no—
377C2×D8—22no—
378C2×D8—24no—
379C2×D8—42no—
380C2×M16—22no—
381C2×M16—24no—
382C22×C8C23×C1111yescharacteristic
383C22×C8C23×C1111yescharacteristic
384C22×C8C23×C1112yes—
385#127—24no—
386#127—42no—
387#121—22no—
388#121—22no—
389#120—48no—
390C4×Q8—24no—
391C4×Q8—42no—
392C2×C4⋊C4—22no—
393C2×C4⋊C4C23×C1112yes—
394C2×C4⋊C4C23×C1111yescharacteristic
395C2×C22⋊C4—22no—
396C2×C22⋊C4—22no—
397C2×C22⋊C4—21no—
398C2×C22⋊C4—22no—
399C2×C22⋊C4—21no—
400C2×C22⋊C4—22no—
401C2×C22⋊C4D4×C1112yes—
402C2×C42—22no—
403C2×C42C23×C1112yes—
404C4⋊C8—24no—
405#103—22no—
406#102—24no—
407#102—22no—
408#102—24no—
409#102—42no—
410C22⋊C8—22no—
411#95—21no—
412#95D4×C1111yescharacteristic
413#95D4×C1111yescharacteristic
414C2×C11—42no—
415C2×C11—82no—
416C2×C11—84no—
417C2×C11—161no—
418C2×C11#241011yescharacteristic
419C2×C11#303811yescharacteristic
420C2×C11#304511yescharacteristic
421C2×C11#326512yes—
422C2×C11#327412yes—
423C24—21no—
424C24—22no—
425C24—21no—
426C24—44no—
427C24—44no—
428C24—42no—
429C24—81no—
430C24—81no—
431C24C2×D4×C1111yescharacteristic
432#41—28no—
433#41—44no—
434#41—48no—
435C2×Q8—21no—
436C2×Q8—22no—
437C2×Q8C2×D4×C1112yes—
438C2×Q8C2×D4×C1114yes—
439C2×D4—28no—
440C2×D4—24no—
441C2×D4—22no—
442C2×D4—22no—
443C2×D4—22no—
444C2×D4—22no—
445C2×D4—21no—
446C2×D4—22no—
447C2×D4—21no—
448C2×D4—21no—
449C2×D4—22no—
450C2×D4—22no—
451C2×D4—22no—
452C2×D4—22no—
453C2×D4—48no—
454C2×D4—44no—
455C2×D4—44no—
456C2×D4—44no—
457C2×D4—44no—
458C2×D4—44no—
459C2×D4—44no—
460C2×D4—44no—
461C2×D4—42no—
462C2×D4—42no—
463C2×D4—44no—
464C2×D4—82no—
465C2×D4—82no—
466C2×D4C2×D4×C1114yes—
467C2×D4C2×D4×C1112yes—
468C22×C4—21no—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—24no—
472C22×C4—22no—
473C22×C4—21no—
474C22×C4—44no—
475C22×C4C2×D4×C1112yes—
476C22×C4C2×D4×C1111yescharacteristic
477C22×C4C2×D4×C1112yes—
478C22×C4C2×D4×C1112yes—
479C22×C4C11×#4112yes—
480C22×C4C24×C1111yescharacteristic
481SD16—216no—
482SD16—44no—
483D8—216no—
484D8—44no—
485M16—28no—
486C2×C8—22no—
487C2×C8—22no—
488C2×C8—21no—
489C2×C8—21no—
490C2×C8—22no—
491C2×C8—22no—
492C2×C8C2×D4×C1114yes—
493C4⋊C4—22no—
494C4⋊C4—21no—
495C4⋊C4—21no—
496C4⋊C4—22no—
497C4⋊C4—44no—
498C22⋊C4—24no—
499C22⋊C4—44no—
500C22⋊C4—42no—
501C22⋊C4—44no—
502C22⋊C4—44no—
503C22⋊C4—82no—
504C22⋊C4—81no—
505C42—22no—
506C42—22no—
507C42—44no—
508C11#2437011yescharacteristic, direct product factor, Sylow
509C23—22no—
510C23—22no—
511C23—21no—
512C23—21no—
513C23—22no—
514C23—24no—
515C23—48no—
516C23—42no—
517C23—42no—
518C23—42no—
519C23—42no—
520C23—42no—
521C23—42no—
522C23—41no—
523C23—42no—
524C23—42no—
525C23—41no—
526C23—41no—
527C23—42no—
528C23—42no—
529C23—41no—
530C23—41no—
531C23—84no—
532C23—84no—
533C23—88no—
534C23—88no—
535C23C11×#12112yes—
536C23C22×D4×C1111yescharacteristic
537Q8—22no—
538Q8—24no—
539Q8C11×#12014yescomplemented
540D4—22no—
541D4—24no—
542D4—22no—
543D4—24no—
544D4—48no—
545D4—48no—
546D4—41no—
547D4—42no—
548D4—41no—
549D4—42no—
550D4—42no—
551D4—42no—
552D4—88no—
553D4—88no—
554D4—84no—
555C2×C4—22no—
556C2×C4—22no—
557C2×C4—24no—
558C2×C4—22no—
559C2×C4—22no—
560C2×C4—22no—
561C2×C4—22no—
562C2×C4—24no—
563C2×C4—22no—
564C2×C4—22no—
565C2×C4—22no—
566C2×C4—48no—
567C2×C4—41no—
568C2×C4—42no—
569C2×C4—42no—
570C2×C4—42no—
571C2×C4—42no—
572C2×C4C11×#12112yes—
573C2×C4C11×AGL(1,ℤ/8)14yescomplemented
574C2×C4C22×D4×C1111yescharacteristic
575C2×C4C22×D4×C1112yes—
576C2×C4C2×C11×#4111yescharacteristic
577C2×C4C11×H(5,𝔽2)12yes—
578C8—24no—
579C8—41no—
580C8—41no—
581C22—22no—
582C22—22no—
583C22—22no—
584C22—42no—
585C22—42no—
586C22—42no—
587C22—44no—
588C22—44no—
589C22—44no—
590C22—42no—
591C22—42no—
592C22—816no—
593C22—82no—
594C22—82no—
595C22—82no—
596C22—82no—
597C22—82no—
598C22—82no—
599C22—81no—
600C22—82no—
601C22—82no—
602C22—81no—
603C22—81no—
604C22C2×C11×#12111yescharacteristic
605C22D42×C1112yes—
606C22C2×C11×AGL(1,ℤ/8)12yes—
607C22C11×#57611yescharacteristic
608C22C11×#57711yescharacteristic
609C4—22no—
610C4—24no—
611C4—24no—
612C4—42no—
613C4—82no—
614C4—81no—
615C4C2×C11×#12011yescharacteristic
616C4C11×#53411yescharacteristic
617C4C11×#54612yes—
618C2—42no—
619C2—84no—
620C2—82no—
621C2—161no—
622C2C11×#241011yescharacteristic
623C2C11×#303811yescharacteristic
624C2C11×#304511yescharacteristic
625C2C11×#326512yes—
626C2C11×#327412yes—
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
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
1. C22×C11×AGL(1,ℤ/8)C2semidirect
2. C2×C11×#460C2semidirect
3. C2×C11×#449C2semidirect
4. C11×#2433C2semidirect
5. C11×#2341C2semidirect
6. C11×#2054C2semidirect
7. C11×#2011C2semidirect
8. C11×#1895C2semidirect
9. C11×#1880C2semidirect
10. C11×#1851C2semidirect
11. C11×#1786C2semidirect
17. C22×C11×SD16C22semidirect
19. C22×C11×D8C22semidirect
24. C2×C4×Q8×C11C22semidirect
27. C2×C11×C4⋊C8C22semidirect
28. C2×C11×#103C22semidirect
31. C2×C11×#102C22semidirect
32. C2×C11×#102C22semidirect
38. C11×#390C22semidirect
43. C11×#340C22semidirect
44. C11×#336C22semidirect
49. C2×C11×#41D4semidirect
70. C2×C11×SD16D4semidirect
110. #24370C11direct (N × H)
196. C22×AGL(1,ℤ/8)C2×C11semidirect
197. C2×#460C2×C11semidirect
198. C2×#449C2×C11semidirect
199. #2433C2×C11semidirect
200. #2341C2×C11semidirect
201. #2054C2×C11semidirect
202. #2011C2×C11semidirect
203. #1895C2×C11semidirect
204. #1880C2×C11semidirect
205. #1851C2×C11semidirect
206. #1786C2×C11semidirect
237. Q8×C11#120semidirect
271. C2×C4×C11AGL(1,ℤ/8)semidirect
284. C22×SD16C22×C11semidirect
286. C22×D8C22×C11semidirect
291. C2×C4×Q8C22×C11semidirect
294. C2×C4⋊C8C22×C11semidirect
295. C2×#103C22×C11semidirect
298. C2×#102C22×C11semidirect
299. C2×#102C22×C11semidirect
305. #390C22×C11semidirect
310. #340C22×C11semidirect
311. #336C22×C11semidirect
353. C2×#41D4×C11semidirect
374. C2×SD16D4×C11semidirect
508. C11#24370direct (N × H)
539. Q8C11×#120semidirect
573. C2×C4C11×AGL(1,ℤ/8)semidirect

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
C2×C11×#4602
C2×C11×#4492
C11×#24332
C11×#23412
C11×#20542
C11×#20112
C11×#18952
C11×#18802
C11×#18512
C11×#17862
#2437011