Finite Group Databasebeta

← C11×#24373 #14601566

Subgroups — C11×#24373 #14601566

Order 2816.

1568 conjugacy classes of subgroups.

The subgroup lattice has 598 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C11×AGL(1,ℤ/8)C211yesmaximal, characteristic
2C2×C11×#463C212yesmaximal, complemented
3C2×C11×#452C211yesmaximal, characteristic, complemented
4C11×#2435C211yesmaximal, characteristic, complemented
5C11×#2339C211yesmaximal, characteristic, complemented
6C11×#2055C212yesmaximal, complemented
7C11×#2015C212yesmaximal, complemented
8C11×#1894C211yesmaximal, characteristic, complemented
9C11×#1879C212yesmaximal, 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×Q16C2211yescharacteristic, complemented
17C22×C11×SD16C2212yes—
18C22×C11×SD16C2211yescharacteristic, complemented
19C22×C11×D8C2212yes—
20C22×C11×M16C2211yescharacteristic
21C2×C11×#124C2212yes—
22C2×C11×C22⋊Q8C2211yescharacteristic
23C2×C4×D4×C11C2212yescomplemented
24C11×#463—28no—
25C11×#452—24no—
26C2×C11×C4⋊C8C2212yescomplemented
27C2×C11×#103C2212yescomplemented
28C2×C11×#103C2211yescharacteristic, complemented
29C2×C11×#102C2212yes—
30C2×C11×#102C2212yes—
31C2×C11×#102C2211yescharacteristic, complemented
32C2×C11×C22⋊C8C2211yescharacteristic
33C11×#394—21no—
34C11×#394—21no—
35C11×#391C2212yescomplemented
36C11×#390C2212yes—
37C11×#386—22no—
38C11×#381—21no—
39C11×#380C2211yescharacteristic
40C11×#379—22no—
41C4×C11×C22⋊C4C2211yescharacteristic
42C2×C11×#95—21no—
43C11×#340C2212yescomplemented
44C11×#336C2212yescomplemented
45C25×C11—21no—
46C2×C11×#41—22no—
47C2×C11×#41—24no—
48C2×C11×#41—42no—
49C2×C11×#41D414yes—
50C22×Q8×C11C2311yescharacteristic
51C22×Q8×C11C2311yescharacteristic
52C22×D4×C11—24no—
53C22×D4×C11—21no—
54C22×D4×C11—22no—
55C22×D4×C11—21no—
56C22×D4×C11—22no—
57C22×D4×C11—42no—
58C22×D4×C11C2312yes—
59C22×D4×C11C2311yescharacteristic
60C23×C4×C11—21no—
61C23×C4×C11—22no—
62C23×C4×C11C2311yescharacteristic
63C11×AGL(1,ℤ/8)—232no—
64C2×C11×Q16—22no—
65C2×C11×Q16—42no—
66C2×C11×SD16—24no—
67C2×C11×SD16—24no—
68C2×C11×SD16—22no—
69C2×C11×SD16—24no—
70C2×C11×SD16—24no—
71C2×C11×D8—24no—
72C2×C11×D8—24no—
73C2×C11×D8D418yes—
74C2×C11×M16—22no—
75C2×C11×M16—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—22no—
90C2×C11×C22⋊C4—22no—
91C2×C11×C22⋊C4—22no—
92C2×C11×C22⋊C4—21no—
93C2×C11×C22⋊C4—22no—
94C2×C11×C22⋊C4—22no—
95C2×C11×C22⋊C4D412yes—
96C2×C42×C11C2312yes—
97C11×C4⋊C8—24no—
98C11×#103—22no—
99C11×#103—24no—
100C11×#102—24no—
101C11×#102—22no—
102C11×#102—42no—
103C11×C22⋊C8—22no—
104C11×#95—21no—
105C11×#95—22no—
106C11×#95—22no—
107C11×#95D411yescharacteristic
108C11×#95D411yescharacteristic
109#24373C1111yesmaximal, characteristic, direct product factor, Sylow
110C24×C11—21no—
111C24×C11—22no—
112C24×C11—44no—
113C24×C11—44no—
114C24×C11—42no—
115C24×C11—81no—
116C24×C11—81no—
117C24×C11C2×D411yescharacteristic
118C11×#41—28no—
119C11×#41—44no—
120C11×#41—48no—
121C2×Q8×C11—21no—
122C2×Q8×C11—22no—
123C2×Q8×C11—22no—
124C2×Q8×C11—21no—
125C2×Q8×C11—21no—
126C2×Q8×C11—22no—
127C2×Q8×C11—22no—
128C2×Q8×C11C2×D412yes—
129C2×D4×C11—28no—
130C2×D4×C11—24no—
131C2×D4×C11—22no—
132C2×D4×C11—22no—
133C2×D4×C11—21no—
134C2×D4×C11—22no—
135C2×D4×C11—22no—
136C2×D4×C11—22no—
137C2×D4×C11—22no—
138C2×D4×C11—48no—
139C2×D4×C11—44no—
140C2×D4×C11—44no—
141C2×D4×C11—44no—
142C2×D4×C11—42no—
143C2×D4×C11C2×D414yes—
144C2×D4×C11C2×D412yes—
145C2×D4×C11C2×D414yes—
146C22×C4×C11—22no—
147C22×C4×C11—22no—
148C22×C4×C11—21no—
149C22×C4×C11—24no—
150C22×C4×C11—22no—
151C22×C4×C11—21no—
152C22×C4×C11—21no—
153C22×C4×C11—44no—
154C22×C4×C11—44no—
155C22×C4×C11—44no—
156C22×C4×C11—82no—
157C22×C4×C11C2×D412yes—
158C22×C4×C11C2×D412yes—
159C22×C4×C11C2×D411yescharacteristic
160C22×C4×C11C2×D412yes—
161C22×C4×C11#4112yes—
162C22×C4×C11C2411yescharacteristic
163C11×Q16—44no—
164C11×SD16—216no—
165C11×SD16—44no—
166C11×D8—216no—
167C11×M16—28no—
168C2×C8×C11—22no—
169C2×C8×C11—22no—
170C2×C8×C11—21no—
171C2×C8×C11—21no—
172C2×C8×C11—22no—
173C2×C8×C11—22no—
174C2×C8×C11C2×D414yes—
175C11×C4⋊C4—22no—
176C11×C4⋊C4—21no—
177C11×C4⋊C4—21no—
178C11×C4⋊C4—22no—
179C11×C4⋊C4—42no—
180C11×C22⋊C4—42no—
181C11×C22⋊C4—44no—
182C11×C22⋊C4—44no—
183C11×C22⋊C4—44no—
184C11×C22⋊C4—42no—
185C11×C22⋊C4—82no—
186C11×C22⋊C4—82no—
187C11×C22⋊C4—81no—
188C42×C11—22no—
189C42×C11—22no—
190C22×AGL(1,ℤ/8)C2×C1111yescharacteristic
191C2×#463C2×C1112yescomplemented
192C2×#452C2×C1111yescharacteristic, complemented
193#2435C2×C1111yescharacteristic, complemented
194#2339C2×C1111yescharacteristic, complemented
195#2055C2×C1112yescomplemented
196#2015C2×C1112yescomplemented
197#1894C2×C1111yescharacteristic, complemented
198#1879C2×C1112yescomplemented
199#1851C2×C1111yescharacteristic, complemented
200#1786C2×C1111yescharacteristic, complemented
201C23×C11—22no—
202C23×C11—24no—
203C23×C11—22no—
204C23×C11—22no—
205C23×C11—21no—
206C23×C11—21no—
207C23×C11—24no—
208C23×C11—48no—
209C23×C11—42no—
210C23×C11—41no—
211C23×C11—41no—
212C23×C11—42no—
213C23×C11—42no—
214C23×C11—42no—
215C23×C11—42no—
216C23×C11—42no—
217C23×C11—42no—
218C23×C11—84no—
219C23×C11—84no—
220C23×C11—88no—
221C23×C11—88no—
222C23×C11#12112yes—
223C23×C11C22×D411yescharacteristic
224Q8×C11—22no—
225Q8×C11—22no—
226Q8×C11—42no—
227Q8×C11—41no—
228Q8×C11—41no—
229Q8×C11—42no—
230D4×C11—24no—
231D4×C11—22no—
232D4×C11—24no—
233D4×C11—24no—
234D4×C11—48no—
235D4×C11—48no—
236D4×C11—42no—
237D4×C11—42no—
238D4×C11#12014yes—
239C2×C4×C11—22no—
240C2×C4×C11—22no—
241C2×C4×C11—22no—
242C2×C4×C11—24no—
243C2×C4×C11—22no—
244C2×C4×C11—22no—
245C2×C4×C11—22no—
246C2×C4×C11—22no—
247C2×C4×C11—22no—
248C2×C4×C11—22no—
249C2×C4×C11—22no—
250C2×C4×C11—48no—
251C2×C4×C11—42no—
252C2×C4×C11—41no—
253C2×C4×C11—41no—
254C2×C4×C11—42no—
255C2×C4×C11—42no—
256C2×C4×C11—42no—
257C2×C4×C11—41no—
258C2×C4×C11—42no—
259C2×C4×C11—41no—
260C2×C4×C11—88no—
261C2×C4×C11#12112yes—
262C2×C4×C11C22×D411yescharacteristic
263C2×C4×C11C22×D412yes—
264C2×C4×C11C2×#4111yescharacteristic
265C2×C4×C11H(5,𝔽2)12yes—
266C8×C11—24no—
267C8×C11—41no—
268C8×C11—41no—
269C22×#41C22×C1111yescharacteristic
270C23×D4C22×C1111yescharacteristic
271C2×AGL(1,ℤ/8)—24no—
272C2×AGL(1,ℤ/8)—28no—
273C22×Q16C22×C1111yescharacteristic, complemented
274C22×SD16C22×C1112yes—
275C22×SD16C22×C1111yescharacteristic, complemented
276C22×D8C22×C1112yes—
277C22×M16C22×C1111yescharacteristic
278C2×#124C22×C1112yes—
279C2×C22⋊Q8C22×C1111yescharacteristic
280C2×C4×D4C22×C1112yescomplemented
281#463—28no—
282#452—24no—
283C2×C4⋊C8C22×C1112yescomplemented
284C2×#103C22×C1111yescharacteristic, complemented
285C2×#103C22×C1112yescomplemented
286C2×#102C22×C1112yes—
287C2×#102C22×C1112yes—
288C2×#102C22×C1111yescharacteristic, complemented
289C2×C22⋊C8C22×C1111yescharacteristic
290#394—21no—
291#394—21no—
292#391C22×C1112yescomplemented
293#390C22×C1112yes—
294#386—22no—
295#381—21no—
296#380C22×C1111yescharacteristic
297#379—22no—
298C4×C22⋊C4C22×C1111yescharacteristic
299C2×#95—21no—
300#340C22×C1112yescomplemented
301#336C22×C1112yescomplemented
302C22×C11—22no—
303C22×C11—24no—
304C22×C11—22no—
305C22×C11—22no—
306C22×C11—42no—
307C22×C11—44no—
308C22×C11—44no—
309C22×C11—42no—
310C22×C11—42no—
311C22×C11—42no—
312C22×C11—44no—
313C22×C11—44no—
314C22×C11—44no—
315C22×C11—816no—
316C22×C11—82no—
317C22×C11—82no—
318C22×C11—82no—
319C22×C11—82no—
320C22×C11C2×#12111yescharacteristic
321C22×C11D4212yes—
322C22×C11#57512yes—
323C22×C11#57611yescharacteristic
324C22×C11#57711yescharacteristic
325C4×C11—22no—
326C4×C11—42no—
327C4×C11—42no—
328C4×C11—42no—
329C4×C11—81no—
330C4×C11—82no—
331C4×C11—81no—
332C4×C11C2×#12011yescharacteristic
333C4×C11#53411yescharacteristic
334C4×C11#54612yes—
335C25—21no—
336C2×#41—22no—
337C2×#41—24no—
338C2×#41—42no—
339C2×#41D4×C1114yes—
340C22×Q8C23×C1111yescharacteristic
341C22×Q8C23×C1111yescharacteristic
342C22×D4—24no—
343C22×D4—21no—
344C22×D4—22no—
345C22×D4—21no—
346C22×D4—22no—
347C22×D4—42no—
348C22×D4C23×C1112yes—
349C22×D4C23×C1111yescharacteristic
350C23×C4—21no—
351C23×C4—22no—
352C23×C4C23×C1111yescharacteristic
353AGL(1,ℤ/8)—232no—
354C2×Q16—22no—
355C2×Q16—42no—
356C2×SD16—24no—
357C2×SD16—24no—
358C2×SD16—22no—
359C2×SD16—24no—
360C2×SD16—24no—
361C2×D8—24no—
362C2×D8—24no—
363C2×D8D4×C1118yes—
364C2×M16—22no—
365C2×M16—24no—
366C22×C8C23×C1111yescharacteristic
367C22×C8C23×C1111yescharacteristic
368C22×C8C23×C1112yes—
369#124—24no—
370#124—42no—
371C22⋊Q8—22no—
372C22⋊Q8—22no—
373C4×D4—24no—
374C4×D4—42no—
375C2×C4⋊C4—21no—
376C2×C4⋊C4C23×C1112yes—
377C2×C4⋊C4C23×C1111yescharacteristic
378C2×C22⋊C4—21no—
379C2×C22⋊C4—22no—
380C2×C22⋊C4—22no—
381C2×C22⋊C4—22no—
382C2×C22⋊C4—21no—
383C2×C22⋊C4—22no—
384C2×C22⋊C4—22no—
385C2×C22⋊C4D4×C1112yes—
386C2×C42C23×C1112yes—
387C4⋊C8—24no—
388#103—22no—
389#103—24no—
390#102—24no—
391#102—22no—
392#102—42no—
393C22⋊C8—22no—
394#95—21no—
395#95—22no—
396#95—22no—
397#95D4×C1111yescharacteristic
398#95D4×C1111yescharacteristic
399C2×C11—42no—
400C2×C11—44no—
401C2×C11—84no—
402C2×C11#241011yescharacteristic
403C2×C11#304011yescharacteristic
404C2×C11#304511yescharacteristic
405C2×C11#326712yes—
406C2×C11#327312yes—
407C24—21no—
408C24—22no—
409C24—44no—
410C24—44no—
411C24—42no—
412C24—81no—
413C24—81no—
414C24C2×D4×C1111yescharacteristic
415#41—28no—
416#41—44no—
417#41—48no—
418C2×Q8—21no—
419C2×Q8—22no—
420C2×Q8—22no—
421C2×Q8—21no—
422C2×Q8—21no—
423C2×Q8—22no—
424C2×Q8—22no—
425C2×Q8C2×D4×C1112yes—
426C2×D4—28no—
427C2×D4—24no—
428C2×D4—22no—
429C2×D4—22no—
430C2×D4—21no—
431C2×D4—22no—
432C2×D4—22no—
433C2×D4—22no—
434C2×D4—22no—
435C2×D4—48no—
436C2×D4—44no—
437C2×D4—44no—
438C2×D4—44no—
439C2×D4—42no—
440C2×D4C2×D4×C1114yes—
441C2×D4C2×D4×C1112yes—
442C2×D4C2×D4×C1114yes—
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—21no—
446C22×C4—24no—
447C22×C4—22no—
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—44no—
451C22×C4—44no—
452C22×C4—44no—
453C22×C4—82no—
454C22×C4C2×D4×C1112yes—
455C22×C4C2×D4×C1112yes—
456C22×C4C2×D4×C1111yescharacteristic
457C22×C4C2×D4×C1112yes—
458C22×C4C11×#4112yes—
459C22×C4C24×C1111yescharacteristic
460Q16—44no—
461SD16—216no—
462SD16—44no—
463D8—216no—
464M16—28no—
465C2×C8—22no—
466C2×C8—22no—
467C2×C8—21no—
468C2×C8—21no—
469C2×C8—22no—
470C2×C8—22no—
471C2×C8C2×D4×C1114yes—
472C4⋊C4—22no—
473C4⋊C4—21no—
474C4⋊C4—21no—
475C4⋊C4—22no—
476C4⋊C4—42no—
477C22⋊C4—42no—
478C22⋊C4—44no—
479C22⋊C4—44no—
480C22⋊C4—44no—
481C22⋊C4—42no—
482C22⋊C4—82no—
483C22⋊C4—82no—
484C22⋊C4—81no—
485C42—22no—
486C42—22no—
487C11#2437311yescharacteristic, direct product factor, Sylow
488C23—22no—
489C23—24no—
490C23—22no—
491C23—22no—
492C23—21no—
493C23—21no—
494C23—24no—
495C23—48no—
496C23—42no—
497C23—41no—
498C23—41no—
499C23—42no—
500C23—42no—
501C23—42no—
502C23—42no—
503C23—42no—
504C23—42no—
505C23—84no—
506C23—84no—
507C23—88no—
508C23—88no—
509C23C11×#12112yes—
510C23C22×D4×C1111yescharacteristic
511Q8—22no—
512Q8—22no—
513Q8—42no—
514Q8—41no—
515Q8—41no—
516Q8—42no—
517D4—24no—
518D4—22no—
519D4—24no—
520D4—24no—
521D4—48no—
522D4—48no—
523D4—42no—
524D4—42no—
525D4C11×#12014yes—
526C2×C4—22no—
527C2×C4—22no—
528C2×C4—22no—
529C2×C4—24no—
530C2×C4—22no—
531C2×C4—22no—
532C2×C4—22no—
533C2×C4—22no—
534C2×C4—22no—
535C2×C4—22no—
536C2×C4—22no—
537C2×C4—48no—
538C2×C4—42no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—42no—
542C2×C4—42no—
543C2×C4—42no—
544C2×C4—41no—
545C2×C4—42no—
546C2×C4—41no—
547C2×C4—88no—
548C2×C4C11×#12112yes—
549C2×C4C22×D4×C1111yescharacteristic
550C2×C4C22×D4×C1112yes—
551C2×C4C2×C11×#4111yescharacteristic
552C2×C4C11×H(5,𝔽2)12yes—
553C8—24no—
554C8—41no—
555C8—41no—
556C22—22no—
557C22—24no—
558C22—22no—
559C22—22no—
560C22—42no—
561C22—44no—
562C22—44no—
563C22—42no—
564C22—42no—
565C22—42no—
566C22—44no—
567C22—44no—
568C22—44no—
569C22—816no—
570C22—82no—
571C22—82no—
572C22—82no—
573C22—82no—
574C22C2×C11×#12111yescharacteristic
575C22D42×C1112yes—
576C22C11×#57512yes—
577C22C11×#57611yescharacteristic
578C22C11×#57711yescharacteristic
579C4—22no—
580C4—42no—
581C4—42no—
582C4—42no—
583C4—81no—
584C4—82no—
585C4—81no—
586C4C2×C11×#12011yescharacteristic
587C4C11×#53411yescharacteristic
588C4C11×#54612yes—
589C2—42no—
590C2—44no—
591C2—84no—
592C2C11×#241011yescharacteristic
593C2C11×#304011yescharacteristic
594C2C11×#304511yescharacteristic
595C2C11×#326712yes—
596C2C11×#327312yes—
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC22×C11×AGL(1,ℤ/8)C2
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×#452C2semidirect
4. C11×#2435C2semidirect
5. C11×#2339C2semidirect
6. C11×#2055C2semidirect
7. C11×#2015C2semidirect
8. C11×#1894C2semidirect
9. C11×#1879C2semidirect
10. C11×#1851C2semidirect
11. C11×#1786C2semidirect
16. C22×C11×Q16C22semidirect
18. C22×C11×SD16C22semidirect
23. C2×C4×D4×C11C22semidirect
26. C2×C11×C4⋊C8C22semidirect
27. C2×C11×#103C22semidirect
28. C2×C11×#103C22semidirect
31. C2×C11×#102C22semidirect
35. C11×#391C22semidirect
43. C11×#340C22semidirect
44. C11×#336C22semidirect
109. #24373C11direct (N × H)
191. C2×#463C2×C11semidirect
192. C2×#452C2×C11semidirect
193. #2435C2×C11semidirect
194. #2339C2×C11semidirect
195. #2055C2×C11semidirect
196. #2015C2×C11semidirect
197. #1894C2×C11semidirect
198. #1879C2×C11semidirect
199. #1851C2×C11semidirect
200. #1786C2×C11semidirect
273. C22×Q16C22×C11semidirect
275. C22×SD16C22×C11semidirect
280. C2×C4×D4C22×C11semidirect
283. C2×C4⋊C8C22×C11semidirect
284. C2×#103C22×C11semidirect
285. C2×#103C22×C11semidirect
288. C2×#102C22×C11semidirect
292. #391C22×C11semidirect
300. #340C22×C11semidirect
301. #336C22×C11semidirect
487. C11#24373direct (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
C2×C11×#4632
C2×C11×#4522
C11×#24352
C11×#23392
C11×#20552
C11×#20152
C11×#18942
C11×#18792
C11×#18512
C11×#17862
#2437311